LMFDB - Embedded newform 22.8.c.a.5.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [22,8,Mod(3,22)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(22, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

N = Newforms(chi, 8, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("22.3");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 22 = 2 \cdot 11 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	22.c (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.87247056065$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 718 x^{10} - 5886 x^{9} + 371698 x^{8} + 6317266 x^{7} + 171079947 x^{6} + \cdots + 475277889155161 $ x^12 - 2x^11 + 718x^10 - 5886x^9 + 371698x^8 + 6317266x^7 + 171079947x^6 + 3212289784x^5 + 91377152203x^4 + 810233740626x^3 + 7721283816133x^2 + 66377062242562*x + 475277889155161
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4}\cdot 11^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			5.2
Root			$2.97963 - 9.17036i$ of defining polynomial
Character	$\chi$	$=$	22.5
Dual form			22.8.c.a.9.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.47214 + 7.60845i) q^{2} +(-5.52734 - 4.01585i) q^{3} +(-51.7771 + 37.6183i) q^{4} +(-14.6685 + 45.1450i) q^{5} +(16.8900 - 51.9822i) q^{6} +(-1183.62 + 859.952i) q^{7} +(-414.217 - 300.946i) q^{8} +(-661.396 - 2035.57i) q^{9} +O(q^{10})$	\(q+(2.47214 + 7.60845i) q^{2} +(-5.52734 - 4.01585i) q^{3} +(-51.7771 + 37.6183i) q^{4} +(-14.6685 + 45.1450i) q^{5} +(16.8900 - 51.9822i) q^{6} +(-1183.62 + 859.952i) q^{7} +(-414.217 - 300.946i) q^{8} +(-661.396 - 2035.57i) q^{9} -379.746 q^{10} +(-2018.15 + 3926.10i) q^{11} +437.259 q^{12} +(-3067.30 - 9440.18i) q^{13} +(-9468.98 - 6879.62i) q^{14} +(262.373 - 190.625i) q^{15} +(1265.73 - 3895.53i) q^{16} +(-11583.6 + 35650.7i) q^{17} +(13852.5 - 10064.4i) q^{18} +(15253.1 + 11082.0i) q^{19} +(-938.783 - 2889.28i) q^{20} +9995.72 q^{21} +(-34860.7 - 5649.13i) q^{22} +47361.7 q^{23} +(1080.96 + 3326.86i) q^{24} +(61381.5 + 44596.3i) q^{25} +(64242.4 - 46674.8i) q^{26} +(-9136.08 + 28118.0i) q^{27} +(28934.6 - 89051.7i) q^{28} +(18711.3 - 13594.5i) q^{29} +(2098.98 + 1525.00i) q^{30} +(3460.92 + 10651.6i) q^{31} +32768.0 q^{32} +(26921.6 - 13596.3i) q^{33} -299883. q^{34} +(-21460.6 - 66048.8i) q^{35} +(110820. + 80515.2i) q^{36} +(-224041. + 162775. i) q^{37} +(-46609.4 + 143449. i) q^{38} +(-20956.3 + 64496.9i) q^{39} +(19662.1 - 14285.4i) q^{40} +(-547184. - 397552. i) q^{41} +(24710.8 + 76052.0i) q^{42} -449613. q^{43} +(-43199.2 - 279201. i) q^{44} +101597. q^{45} +(117085. + 360349. i) q^{46} +(636841. + 462692. i) q^{47} +(-22640.0 + 16448.9i) q^{48} +(406956. - 1.25248e6i) q^{49} +(-187565. + 577267. i) q^{50} +(207194. - 150536. i) q^{51} +(513939. + 373398. i) q^{52} +(-164348. - 505812. i) q^{53} -236520. q^{54} +(-147640. - 148699. i) q^{55} +749076. q^{56} +(-39805.4 - 122508. i) q^{57} +(149690. + 108756. i) q^{58} +(1.60110e6 - 1.16327e6i) q^{59} +(-6413.92 + 19740.0i) q^{60} +(-742718. + 2.28585e6i) q^{61} +(-72486.5 + 52664.5i) q^{62} +(2.53333e6 + 1.84057e6i) q^{63} +(81007.0 + 249314. i) q^{64} +471169. q^{65} +(170001. + 171220. i) q^{66} -3.50463e6 q^{67} +(-741351. - 2.28164e6i) q^{68} +(-261784. - 190197. i) q^{69} +(449476. - 326563. i) q^{70} +(-39482.7 + 121515. i) q^{71} +(-338635. + 1.04221e6i) q^{72} +(-686944. + 499094. i) q^{73} +(-1.79233e6 - 1.30220e6i) q^{74} +(-160185. - 492998. i) q^{75} -1.20665e6 q^{76} +(-987532. - 6.38253e6i) q^{77} -542528. q^{78} +(1.72616e6 + 5.31257e6i) q^{79} +(157297. + 114283. i) q^{80} +(-3.62350e6 + 2.63263e6i) q^{81} +(1.67205e6 - 5.14603e6i) q^{82} +(-587929. + 1.80946e6i) q^{83} +(-517550. + 376022. i) q^{84} +(-1.43954e6 - 1.04588e6i) q^{85} +(-1.11151e6 - 3.42086e6i) q^{86} -158017. q^{87} +(2.01749e6 - 1.01890e6i) q^{88} -4.25791e6 q^{89} +(251162. + 772998. i) q^{90} +(1.17486e7 + 8.53588e6i) q^{91} +(-2.45225e6 + 1.78166e6i) q^{92} +(23645.6 - 72773.7i) q^{93} +(-1.94601e6 + 5.98921e6i) q^{94} +(-724038. + 526045. i) q^{95} +(-181120. - 131591. i) q^{96} +(-1.62814e6 - 5.01090e6i) q^{97} +1.05355e7 q^{98} +(9.32663e6 + 1.51137e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 24 q^{2} + 44 q^{3} - 192 q^{4} + 220 q^{5} - 248 q^{6} + 534 q^{7} - 1536 q^{8} - 3745 q^{9}+O(q^{10}) $ 12 * q - 24 * q^2 + 44 * q^3 - 192 * q^4 + 220 * q^5 - 248 * q^6 + 534 * q^7 - 1536 * q^8 - 3745 * q^9	\( 12 q - 24 q^{2} + 44 q^{3} - 192 q^{4} + 220 q^{5} - 248 q^{6} + 534 q^{7} - 1536 q^{8} - 3745 q^{9} - 6080 q^{10} - 12881 q^{11} - 1664 q^{12} - 1834 q^{13} + 4272 q^{14} - 50174 q^{15} - 12288 q^{16} + 49128 q^{17} + 28720 q^{18} - 24453 q^{19} + 14080 q^{20} + 135280 q^{21} - 10648 q^{22} + 1212 q^{23} - 15872 q^{24} + 233893 q^{25} - 2352 q^{26} + 24029 q^{27} + 25216 q^{28} + 410548 q^{29} - 401392 q^{30} - 285894 q^{31} + 393216 q^{32} - 561803 q^{33} - 416016 q^{34} + 40188 q^{35} + 229760 q^{36} - 229440 q^{37} + 559696 q^{38} + 102742 q^{39} + 81920 q^{40} - 838292 q^{41} - 547200 q^{42} - 774698 q^{43} + 30976 q^{44} - 3155228 q^{45} + 438176 q^{46} + 1107540 q^{47} + 180224 q^{48} + 4281299 q^{49} - 625416 q^{50} + 2561801 q^{51} - 18816 q^{52} - 3013626 q^{53} - 2622208 q^{54} - 4505512 q^{55} - 950272 q^{56} + 10084223 q^{57} + 3284384 q^{58} + 2583885 q^{59} + 3746304 q^{60} + 418618 q^{61} + 1193008 q^{62} + 4045264 q^{63} - 786432 q^{64} - 11397748 q^{65} + 1076416 q^{66} - 18354554 q^{67} + 3144192 q^{68} + 11135006 q^{69} + 207744 q^{70} + 22870340 q^{71} - 1917440 q^{72} - 7374584 q^{73} - 1835520 q^{74} - 19671977 q^{75} - 5825152 q^{76} - 2121482 q^{77} - 20124544 q^{78} + 4715278 q^{79} + 655360 q^{80} - 745714 q^{81} + 12958184 q^{82} - 13257515 q^{83} + 48640 q^{84} + 8622056 q^{85} - 6992984 q^{86} + 6788612 q^{87} + 613888 q^{88} - 34864794 q^{89} + 11604816 q^{90} + 31631268 q^{91} - 3544192 q^{92} + 41624776 q^{93} + 6007840 q^{94} + 2925362 q^{95} + 1441792 q^{96} - 28563397 q^{97} - 5044288 q^{98} + 28188523 q^{99}+O(q^{100}) \) 12 * q - 24 * q^2 + 44 * q^3 - 192 * q^4 + 220 * q^5 - 248 * q^6 + 534 * q^7 - 1536 * q^8 - 3745 * q^9 - 6080 * q^10 - 12881 * q^11 - 1664 * q^12 - 1834 * q^13 + 4272 * q^14 - 50174 * q^15 - 12288 * q^16 + 49128 * q^17 + 28720 * q^18 - 24453 * q^19 + 14080 * q^20 + 135280 * q^21 - 10648 * q^22 + 1212 * q^23 - 15872 * q^24 + 233893 * q^25 - 2352 * q^26 + 24029 * q^27 + 25216 * q^28 + 410548 * q^29 - 401392 * q^30 - 285894 * q^31 + 393216 * q^32 - 561803 * q^33 - 416016 * q^34 + 40188 * q^35 + 229760 * q^36 - 229440 * q^37 + 559696 * q^38 + 102742 * q^39 + 81920 * q^40 - 838292 * q^41 - 547200 * q^42 - 774698 * q^43 + 30976 * q^44 - 3155228 * q^45 + 438176 * q^46 + 1107540 * q^47 + 180224 * q^48 + 4281299 * q^49 - 625416 * q^50 + 2561801 * q^51 - 18816 * q^52 - 3013626 * q^53 - 2622208 * q^54 - 4505512 * q^55 - 950272 * q^56 + 10084223 * q^57 + 3284384 * q^58 + 2583885 * q^59 + 3746304 * q^60 + 418618 * q^61 + 1193008 * q^62 + 4045264 * q^63 - 786432 * q^64 - 11397748 * q^65 + 1076416 * q^66 - 18354554 * q^67 + 3144192 * q^68 + 11135006 * q^69 + 207744 * q^70 + 22870340 * q^71 - 1917440 * q^72 - 7374584 * q^73 - 1835520 * q^74 - 19671977 * q^75 - 5825152 * q^76 - 2121482 * q^77 - 20124544 * q^78 + 4715278 * q^79 + 655360 * q^80 - 745714 * q^81 + 12958184 * q^82 - 13257515 * q^83 + 48640 * q^84 + 8622056 * q^85 - 6992984 * q^86 + 6788612 * q^87 + 613888 * q^88 - 34864794 * q^89 + 11604816 * q^90 + 31631268 * q^91 - 3544192 * q^92 + 41624776 * q^93 + 6007840 * q^94 + 2925362 * q^95 + 1441792 * q^96 - 28563397 * q^97 - 5044288 * q^98 + 28188523 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/22\mathbb{Z}\right)^\times$.

$n$	$13$
$\chi(n)$	$e\left(\frac{2}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.47214	+	7.60845i	0.218508	+	0.672499i
$2$	2.47214	+	7.60845i	0.218508	+	0.672499i
$3$	−5.52734	−	4.01585i	−0.118193	−	0.0858722i	0.527118	−	0.849792i	$-0.323272\pi$
$3$	−5.52734	−	4.01585i	−0.118193	−	0.0858722i	−0.645311	+	0.763920i	$0.723272\pi$
$4$	−51.7771	+	37.6183i	−0.404508	+	0.293893i
$5$	−14.6685	+	45.1450i	−0.0524796	+	0.161516i	−0.973861	−	0.227143i	$-0.927061\pi$
$5$	−14.6685	+	45.1450i	−0.0524796	+	0.161516i	0.921382	+	0.388659i	$0.127061\pi$
$6$	16.8900	−	51.9822i	0.0319228	−	0.0982484i
$7$	−1183.62	+	859.952i	−1.30428	+	0.947614i	−0.999988	−	0.00496555i	$-0.998419\pi$
$7$	−1183.62	+	859.952i	−1.30428	+	0.947614i	−0.304291	+	0.952579i	$0.598419\pi$
$8$	−414.217	−	300.946i	−0.286031	−	0.207813i
$9$	−661.396	−	2035.57i	−0.302421	−	0.930758i
$10$	−379.746			−0.120086
$11$	−2018.15	+	3926.10i	−0.457171	+	0.889379i
$11$	−2018.15	+	3926.10i	−0.457171	+	0.889379i
$12$	437.259			0.0730473
$13$	−3067.30	−	9440.18i	−0.387217	−	1.19173i	−0.934859	−	0.355019i	$-0.884474\pi$
$13$	−3067.30	−	9440.18i	−0.387217	−	1.19173i	0.547642	−	0.836713i	$-0.315526\pi$
$14$	−9468.98	−	6879.62i	−0.922264	−	0.670064i
$15$	262.373	−	190.625i	0.0200724	−	0.0145835i
$16$	1265.73	−	3895.53i	0.0772542	−	0.237764i
$17$	−11583.6	+	35650.7i	−0.571838	+	1.75994i	0.0748648	+	0.997194i	$0.476147\pi$
$17$	−11583.6	+	35650.7i	−0.571838	+	1.75994i	−0.646703	+	0.762742i	$0.723853\pi$
$18$	13852.5	−	10064.4i	0.559852	−	0.406756i
$19$	15253.1	+	11082.0i	0.510177	+	0.370665i	0.812891	−	0.582416i	$-0.197893\pi$
$19$	15253.1	+	11082.0i	0.510177	+	0.370665i	−0.302714	+	0.953082i	$0.597893\pi$
$20$	−938.783	−	2889.28i	−0.0262398	−	0.0807578i
$21$	9995.72			0.235530
$22$	−34860.7	−	5649.13i	−0.698001	−	0.113110i
$23$	47361.7			0.811670			0.405835	−	0.913946i	$-0.366981\pi$
$23$	47361.7			0.811670			0.405835	+	0.913946i	$0.366981\pi$
$24$	1080.96	+	3326.86i	0.0159614	+	0.0491242i
$25$	61381.5	+	44596.3i	0.785684	+	0.570833i
$26$	64242.4	−	46674.8i	0.716828	−	0.520806i
$27$	−9136.08	+	28118.0i	−0.0893278	+	0.274923i
$28$	28934.6	−	89051.7i	0.249095	−	0.766636i
$29$	18711.3	−	13594.5i	0.142466	−	0.103507i	−0.514270	−	0.857629i	$-0.671937\pi$
$29$	18711.3	−	13594.5i	0.142466	−	0.103507i	0.656735	+	0.754121i	$0.271937\pi$
$30$	2098.98	+	1525.00i	0.0141933	+	0.0103121i
$31$	3460.92	+	10651.6i	0.0208654	+	0.0642170i	0.960947	−	0.276732i	$-0.0892515\pi$
$31$	3460.92	+	10651.6i	0.0208654	+	0.0642170i	−0.940082	+	0.340949i	$0.889252\pi$
$32$	32768.0			0.176777
$33$	26921.6	−	13596.3i	0.130407	−	0.0658601i
$34$	−299883.			−1.30851
$35$	−21460.6	−	66048.8i	−0.0846064	−	0.260392i
$36$	110820.	+	80515.2i	0.395875	+	0.287620i
$37$	−224041.	+	162775.i	−0.727145	+	0.528302i	−0.888659	−	0.458569i	$-0.848362\pi$
$37$	−224041.	+	162775.i	−0.727145	+	0.528302i	0.161514	+	0.986870i	$0.448362\pi$
$38$	−46609.4	+	143449.i	−0.137794	+	0.424087i
$39$	−20956.3	+	64496.9i	−0.0565703	+	0.174106i
$40$	19662.1	−	14285.4i	0.0485759	−	0.0352924i
$41$	−547184.	−	397552.i	−1.23991	−	0.900847i	−0.242317	−	0.970197i	$-0.577907\pi$
$41$	−547184.	−	397552.i	−1.23991	−	0.900847i	−0.997592	+	0.0693504i	$0.977907\pi$
$42$	24710.8	+	76052.0i	0.0514653	+	0.158394i
$43$	−449613.			−0.862382			−0.431191	−	0.902261i	$-0.641906\pi$
$43$	−449613.			−0.862382			−0.431191	+	0.902261i	$0.641906\pi$
$44$	−43199.2	−	279201.i	−0.0764524	−	0.494120i
$45$	101597.			0.166203
$46$	117085.	+	360349.i	0.177356	+	0.545847i
$47$	636841.	+	462692.i	0.894723	+	0.650054i	0.937105	−	0.349047i	$-0.113495\pi$
$47$	636841.	+	462692.i	0.894723	+	0.650054i	−0.0423824	+	0.999101i	$0.513495\pi$
$48$	−22640.0	+	16448.9i	−0.0295483	+	0.0214681i
$49$	406956.	−	1.25248e6i	0.494153	−	1.52085i
$50$	−187565.	+	577267.i	−0.212206	+	0.653103i
$51$	207194.	−	150536.i	0.218717	−	0.158907i
$52$	513939.	+	373398.i	0.506874	+	0.368265i
$53$	−164348.	−	505812.i	−0.151635	−	0.466684i	0.846169	−	0.532914i	$-0.178903\pi$
$53$	−164348.	−	505812.i	−0.151635	−	0.466684i	−0.997804	+	0.0662296i	$0.978903\pi$
$54$	−236520.			−0.204404
$55$	−147640.	−	148699.i	−0.119656	−	0.120514i
$56$	749076.			0.569991
$57$	−39805.4	−	122508.i	−0.0284695	−	0.0876201i
$58$	149690.	+	108756.i	0.100738	+	0.0731907i
$59$	1.60110e6	−	1.16327e6i	1.01493	−	0.737389i	0.0496919	−	0.998765i	$-0.484176\pi$
$59$	1.60110e6	−	1.16327e6i	1.01493	−	0.737389i	0.965237	+	0.261375i	$0.0841761\pi$
$60$	−6413.92	+	19740.0i	−0.00383349	+	0.0117983i
$61$	−742718.	+	2.28585e6i	−0.418957	+	1.28942i	0.489706	+	0.871887i	$0.337104\pi$
$61$	−742718.	+	2.28585e6i	−0.418957	+	1.28942i	−0.908663	+	0.417530i	$0.862896\pi$
$62$	−72486.5	+	52664.5i	−0.0386266	+	0.0280639i
$63$	2.53333e6	+	1.84057e6i	1.27644	+	0.927388i
$64$	81007.0	+	249314.i	0.0386271	+	0.118882i
$65$	471169.			0.212804
$66$	170001.	+	171220.i	0.0727859	+	0.0733078i
$67$	−3.50463e6			−1.42358			−0.711788	−	0.702394i	$-0.752114\pi$
$67$	−3.50463e6			−1.42358			−0.711788	+	0.702394i	$0.752114\pi$
$68$	−741351.	−	2.28164e6i	−0.285919	−	0.879968i
$69$	−261784.	−	190197.i	−0.0959338	−	0.0697000i
$70$	449476.	−	326563.i	0.156626	−	0.113795i
$71$	−39482.7	+	121515.i	−0.0130919	+	0.0402927i	−0.957389	−	0.288801i	$-0.906743\pi$
$71$	−39482.7	+	121515.i	−0.0130919	+	0.0402927i	0.944297	+	0.329094i	$0.106743\pi$
$72$	−338635.	+	1.04221e6i	−0.106922	+	0.329072i
$73$	−686944.	+	499094.i	−0.206677	+	0.150159i	−0.686309	−	0.727310i	$-0.740770\pi$
$73$	−686944.	+	499094.i	−0.206677	+	0.150159i	0.479632	+	0.877470i	$0.340770\pi$
$74$	−1.79233e6	−	1.30220e6i	−0.514169	−	0.373566i
$75$	−160185.	−	492998.i	−0.0438436	−	0.134937i
$76$	−1.20665e6			−0.315307
$77$	−987532.	−	6.38253e6i	−0.246510	−	1.59322i
$78$	−542528.			−0.129447
$79$	1.72616e6	+	5.31257e6i	0.393900	+	1.21230i	0.929815	+	0.368027i	$0.119967\pi$
$79$	1.72616e6	+	5.31257e6i	0.393900	+	1.21230i	−0.535915	+	0.844272i	$0.680033\pi$
$80$	157297.	+	114283.i	0.0343483	+	0.0249555i
$81$	−3.62350e6	+	2.63263e6i	−0.757583	+	0.550417i
$82$	1.67205e6	−	5.14603e6i	0.334888	−	1.03068i
$83$	−587929.	+	1.80946e6i	−0.112863	+	0.347357i	−0.991495	−	0.130142i	$-0.958457\pi$
$83$	−587929.	+	1.80946e6i	−0.112863	+	0.347357i	0.878632	+	0.477499i	$0.158457\pi$
$84$	−517550.	+	376022.i	−0.0952740	+	0.0692206i
$85$	−1.43954e6	−	1.04588e6i	−0.254247	−	0.184721i
$86$	−1.11151e6	−	3.42086e6i	−0.188437	−	0.579950i
$87$	−158017.			−0.0257268
$88$	2.01749e6	−	1.01890e6i	0.315590	−	0.159383i
$89$	−4.25791e6			−0.640223			−0.320112	−	0.947380i	$-0.603720\pi$
$89$	−4.25791e6			−0.640223			−0.320112	+	0.947380i	$0.603720\pi$
$90$	251162.	+	772998.i	0.0363166	+	0.111771i
$91$	1.17486e7	+	8.53588e6i	1.63434	+	1.18742i
$92$	−2.45225e6	+	1.78166e6i	−0.328328	+	0.238544i
$93$	23645.6	−	72773.7i	0.00304832	−	0.00938175i
$94$	−1.94601e6	+	5.98921e6i	−0.241656	+	0.743742i
$95$	−724038.	+	526045.i	−0.0866421	+	0.0629492i
$96$	−181120.	−	131591.i	−0.0208938	−	0.0151802i
$97$	−1.62814e6	−	5.01090e6i	−0.181130	−	0.557461i	0.818730	−	0.574179i	$-0.194678\pi$
$97$	−1.62814e6	−	5.01090e6i	−0.181130	−	0.557461i	−0.999860	+	0.0167173i	$0.994678\pi$
$98$	1.05355e7			1.13074
$99$	9.32663e6	+	1.51137e6i	0.966054	+	0.156548i
$100$	−4.85579e6			−0.485579
$101$	−3.51247e6	−	1.08103e7i	−0.339225	−	1.04403i	−0.964603	−	0.263705i	$-0.915055\pi$
$101$	−3.51247e6	−	1.08103e7i	−0.339225	−	1.04403i	0.625379	−	0.780322i	$-0.284945\pi$
$102$	1.65755e6	+	1.20428e6i	0.154656	+	0.112364i
$103$	46966.7	−	34123.3i	0.00423506	−	0.00307695i	−0.585666	−	0.810553i	$-0.699167\pi$
$103$	46966.7	−	34123.3i	0.00423506	−	0.00307695i	0.589901	+	0.807476i	$0.299167\pi$
$104$	−1.57046e6	+	4.83337e6i	−0.136902	+	0.421341i
$105$	−146622.	+	451257.i	−0.0123605	+	0.0380418i
$106$	3.44215e6	−	2.50087e6i	0.280711	−	0.203949i
$107$	3.13175e6	+	2.27535e6i	0.247140	+	0.179558i	0.704459	−	0.709745i	$-0.251190\pi$
$107$	3.13175e6	+	2.27535e6i	0.247140	+	0.179558i	−0.457318	+	0.889303i	$0.651190\pi$
$108$	−584709.	−	1.79955e6i	−0.0446639	−	0.137461i
$109$	2.15674e7			1.59516			0.797582	−	0.603210i	$-0.206112\pi$
$109$	2.15674e7			1.59516			0.797582	+	0.603210i	$0.206112\pi$
$110$	766383.	−	1.49092e6i	0.0548999	−	0.106802i
$111$	1.89203e6			0.131310
$112$	1.85182e6	+	5.69931e6i	0.124547	+	0.383318i
$113$	−5.46866e6	−	3.97321e6i	−0.356538	−	0.259040i	0.395068	−	0.918652i	$-0.370721\pi$
$113$	−5.46866e6	−	3.97321e6i	−0.356538	−	0.259040i	−0.751607	+	0.659611i	$0.770721\pi$
$114$	833695.	−	605715.i	0.0527036	−	0.0382914i
$115$	−694724.	+	2.13814e6i	−0.0425961	+	0.131097i
$116$	−457412.	+	1.40777e6i	−0.0272085	+	0.0837391i
$117$	−1.71874e7	+	1.24874e7i	−0.992110	+	0.720810i
$118$	1.28088e7	+	9.30612e6i	0.717663	+	0.521413i
$119$	−1.69473e7	−	5.21584e7i	−0.921904	−	2.83733i
$120$	−166047.			−0.00877197
$121$	−1.13413e7	−	1.58469e7i	−0.581990	−	0.813196i
$122$	−1.92279e7			−0.958676
$123$	1.42796e6	+	4.39481e6i	0.0691909	+	0.212948i
$124$	−579892.	−	421316.i	−0.0273131	−	0.0198441i
$125$	−5.91388e6	+	4.29668e6i	−0.270824	+	0.196765i
$126$	−7.74118e6	+	2.38249e7i	−0.344755	+	1.06105i
$127$	−1.30860e7	+	4.02746e7i	−0.566884	+	1.74469i	0.0954016	+	0.995439i	$0.469586\pi$
$127$	−1.30860e7	+	4.02746e7i	−0.566884	+	1.74469i	−0.662286	+	0.749251i	$0.730414\pi$
$128$	−1.69663e6	+	1.23268e6i	−0.0715077	+	0.0519534i
$129$	2.48517e6	+	1.80558e6i	0.101927	+	0.0740547i
$130$	1.16479e6	+	3.58487e6i	0.0464994	+	0.143110i
$131$	2.48753e7			0.966759			0.483380	−	0.875411i	$-0.339409\pi$
$131$	2.48753e7			0.966759			0.483380	+	0.875411i	$0.339409\pi$
$132$	−882453.	+	1.71672e6i	−0.0333951	+	0.0649667i
$133$	−2.75840e7			−1.01666
$134$	−8.66393e6	−	2.66648e7i	−0.311063	−	0.957353i
$135$	−1.13537e6	−	824896.i	−0.0397164	−	0.0288557i
$136$	1.55271e7	−	1.12811e7i	0.529302	−	0.384560i
$137$	3.12046e6	−	9.60380e6i	0.103681	−	0.319096i	−0.885738	−	0.464186i	$-0.846347\pi$
$137$	3.12046e6	−	9.60380e6i	0.103681	−	0.319096i	0.989419	+	0.145090i	$0.0463471\pi$
$138$	799941.	−	2.46197e6i	0.0259108	−	0.0797453i
$139$	−2.14393e7	+	1.55765e7i	−0.677109	+	0.491948i	−0.872397	−	0.488798i	$-0.837436\pi$
$139$	−2.14393e7	+	1.55765e7i	−0.677109	+	0.491948i	0.195289	+	0.980746i	$0.437436\pi$
$140$	3.59581e6	+	2.61251e6i	0.110751	+	0.0804654i
$141$	−1.66194e6	−	5.11491e6i	−0.0499284	−	0.153664i
$142$	−1.02215e6			−0.0299575
$143$	4.32533e7	+	7.00915e6i	1.23693	+	0.200442i
$144$	−8.76676e6			−0.244664
$145$	339258.	+	1.04413e6i	0.00924150	+	0.0284424i
$146$	−5.49556e6	−	3.99275e6i	−0.146143	−	0.106179i
$147$	−7.27917e6	+	5.28863e6i	−0.189004	+	0.137319i
$148$	5.47686e6	−	1.68560e7i	0.138872	−	0.427405i
$149$	7.51694e6	−	2.31348e7i	0.186161	−	0.572945i	−0.813805	−	0.581138i	$-0.802608\pi$
$149$	7.51694e6	−	2.31348e7i	0.186161	−	0.572945i	0.999966	+	0.00819243i	$0.00260776\pi$
$150$	3.35495e6	−	2.43752e6i	0.0811647	−	0.0589696i
$151$	1.39730e6	+	1.01520e6i	0.0330272	+	0.0239957i	0.604176	−	0.796851i	$-0.293502\pi$
$151$	1.39730e6	+	1.01520e6i	0.0330272	+	0.0239957i	−0.571149	+	0.820846i	$0.693502\pi$
$152$	−2.98300e6	−	9.18073e6i	−0.0688971	−	0.212043i
$153$	8.02307e7			1.81101
$154$	4.61199e7	−	2.32921e7i	1.01757	−	0.513908i
$155$	−531634.			−0.0114670
$156$	−1.34120e6	−	4.12780e6i	−0.0282852	−	0.0870528i
$157$	6.41711e7	+	4.66231e7i	1.32340	+	0.961506i	0.999883	+	0.0152834i	$0.00486503\pi$
$157$	6.41711e7	+	4.66231e7i	1.32340	+	0.961506i	0.323516	+	0.946223i	$0.395135\pi$
$158$	−3.61531e7	+	2.62668e7i	−0.729199	+	0.529794i
$159$	−1.12285e6	+	3.45579e6i	−0.0221530	+	0.0681800i
$160$	−480657.	+	1.47931e6i	−0.00927717	+	0.0285522i
$161$	−5.60584e7	+	4.07288e7i	−1.05864	+	0.769150i
$162$	−2.89880e7	−	2.10610e7i	−0.535692	−	0.389203i
$163$	−1.45309e7	−	4.47216e7i	−0.262807	−	0.808836i	−0.992191	−	0.124732i	$-0.960193\pi$
$163$	−1.45309e7	−	4.47216e7i	−0.262807	−	0.808836i	0.729384	−	0.684105i	$-0.239807\pi$
$164$	4.32868e7			0.766306
$165$	218906.	+	1.41481e6i	0.00379370	+	0.0245191i
$166$	−1.52206e7			−0.258258
$167$	2.17667e7	+	6.69909e7i	0.361646	+	1.11303i	0.952055	+	0.305928i	$0.0989668\pi$
$167$	2.17667e7	+	6.69909e7i	0.361646	+	1.11303i	−0.590408	+	0.807105i	$0.701033\pi$
$168$	−4.14040e6	−	3.00817e6i	−0.0673689	−	0.0489464i
$169$	−2.89440e7	+	2.10290e7i	−0.461270	+	0.335132i
$170$	4.39883e6	−	1.35382e7i	0.0686698	−	0.211344i
$171$	1.24699e7	−	3.83783e7i	0.190711	−	0.586948i
$172$	2.32797e7	−	1.69137e7i	0.348841	−	0.253448i
$173$	7.20935e7	+	5.23790e7i	1.05861	+	0.769123i	0.973830	−	0.227277i	$-0.0729823\pi$
$173$	7.20935e7	+	5.23790e7i	1.05861	+	0.769123i	0.0847769	+	0.996400i	$0.472982\pi$
$174$	−390639.	−	1.20226e6i	−0.00562152	−	0.0173013i
$175$	−1.11003e8			−1.56568
$176$	1.27398e7	+	1.28311e7i	0.176144	+	0.177407i
$177$	−1.35213e7			−0.183279
$178$	−1.05261e7	−	3.23961e7i	−0.139894	−	0.430549i
$179$	−4.59295e7	−	3.33698e7i	−0.598558	−	0.434878i	0.246809	−	0.969064i	$-0.420618\pi$
$179$	−4.59295e7	−	3.33698e7i	−0.598558	−	0.434878i	−0.845367	+	0.534186i	$0.820618\pi$
$180$	−5.26041e6	+	3.82191e6i	−0.0672304	+	0.0488458i
$181$	3.43254e6	−	1.05643e7i	0.0430270	−	0.132423i	−0.927235	−	0.374479i	$-0.877822\pi$
$181$	3.43254e6	−	1.05643e7i	0.0430270	−	0.132423i	0.970262	+	0.242055i	$0.0778216\pi$
$182$	−3.59006e7	+	1.10491e8i	−0.441420	+	1.35855i
$183$	1.32849e7	−	9.65203e6i	0.160243	−	0.116423i
$184$	−1.96180e7	−	1.42533e7i	−0.232163	−	0.168676i
$185$	−4.06214e6	−	1.25020e7i	−0.0471687	−	0.145170i
$186$	612150.			0.00697530
$187$	−1.16591e8	−	1.17427e8i	−1.30382	−	1.31317i
$188$	−5.03794e7			−0.552969
$189$	−1.33664e7	−	4.11377e7i	−0.144012	−	0.443224i
$190$	−5.79231e6	−	4.20836e6i	−0.0612652	−	0.0445118i
$191$	7.50466e7	−	5.45246e7i	0.779317	−	0.566207i	−0.125457	−	0.992099i	$-0.540040\pi$
$191$	7.50466e7	−	5.45246e7i	0.779317	−	0.566207i	0.904774	+	0.425892i	$0.140040\pi$
$192$	553453.	−	1.70335e6i	0.00564321	−	0.0173680i
$193$	−1.41090e7	+	4.34230e7i	−0.141269	+	0.434780i	−0.996512	−	0.0834459i	$-0.973407\pi$
$193$	−1.41090e7	+	4.34230e7i	−0.141269	+	0.434780i	0.855244	+	0.518226i	$0.173407\pi$
$194$	3.41002e7	−	2.47752e7i	0.335313	−	0.243619i
$195$	−2.60431e6	−	1.89214e6i	−0.0251520	−	0.0182740i
$196$	2.60452e7	+	8.01589e7i	0.247077	+	0.760424i
$197$	−5.63196e6			−0.0524841			−0.0262420	−	0.999656i	$-0.508354\pi$
$197$	−5.63196e6			−0.0524841			−0.0262420	+	0.999656i	$0.508354\pi$
$198$	1.15575e7	+	7.46975e7i	0.105812	+	0.683877i
$199$	−2.24614e6			−0.0202047			−0.0101023	−	0.999949i	$-0.503216\pi$
$199$	−2.24614e6			−0.0202047			−0.0101023	+	0.999949i	$0.503216\pi$
$200$	−1.20042e7	−	3.69451e7i	−0.106103	−	0.326551i
$201$	1.93713e7	+	1.40741e7i	0.168257	+	0.122246i
$202$	7.35661e7	−	5.34489e7i	0.627983	−	0.456256i
$203$	−1.04564e7	+	3.21816e7i	−0.0877298	+	0.270005i
$204$	−5.06504e6	+	1.55886e7i	−0.0417712	+	0.128559i
$205$	2.59739e7	−	1.88711e7i	0.210571	−	0.152989i
$206$	375733.	+	272986.i	0.00299464	+	0.00217573i
$207$	−3.13248e7	−	9.64079e7i	−0.245467	−	0.755468i
$208$	−4.06569e7			−0.313265
$209$	−7.42922e7	+	3.75201e7i	−0.562900	+	0.284283i
$210$	−3.79583e6			−0.0282839
$211$	1.07924e7	+	3.32156e7i	0.0790915	+	0.243418i	0.982782	−	0.184767i	$-0.0591530\pi$
$211$	1.07924e7	+	3.32156e7i	0.0790915	+	0.243418i	−0.903691	+	0.428185i	$0.859153\pi$
$212$	2.75372e7	+	2.00070e7i	0.198493	+	0.144213i
$213$	706221.	−	513100.i	0.00500740	−	0.00363809i
$214$	−9.56977e6	+	2.94527e7i	−0.0667503	+	0.205436i
$215$	6.59515e6	−	2.02978e7i	0.0452574	−	0.139288i
$216$	1.22463e7	−	8.89747e6i	0.0826832	−	0.0600728i
$217$	−1.32563e7	−	9.63128e6i	−0.0880671	−	0.0639845i
$218$	5.33176e7	+	1.64095e8i	0.348556	+	1.07275i
$219$	5.80126e6			0.0373223
$220$	1.32382e7	+	2.14523e6i	0.0838203	+	0.0135830i
$221$	3.72079e8			2.31880
$222$	4.67736e6	+	1.43954e7i	0.0286923	+	0.0883057i
$223$	9.96682e7	+	7.24132e7i	0.601852	+	0.437271i	0.846536	−	0.532332i	$-0.178684\pi$
$223$	9.96682e7	+	7.24132e7i	0.601852	+	0.437271i	−0.244684	+	0.969603i	$0.578684\pi$
$224$	−3.87850e7	+	2.81789e7i	−0.230566	+	0.167516i
$225$	5.01813e7	−	1.54442e8i	0.293699	−	0.903913i
$226$	1.67107e7	−	5.14304e7i	0.0962977	−	0.296374i
$227$	−4.64499e7	+	3.37478e7i	−0.263569	+	0.191494i	−0.711719	−	0.702464i	$-0.752083\pi$
$227$	−4.64499e7	+	3.37478e7i	−0.263569	+	0.191494i	0.448150	+	0.893958i	$0.352083\pi$
$228$	6.66956e6	+	4.84572e6i	0.0372671	+	0.0270761i
$229$	5.93884e6	+	1.82779e7i	0.0326797	+	0.100578i	0.966066	−	0.258296i	$-0.0831609\pi$
$229$	5.93884e6	+	1.82779e7i	0.0326797	+	0.100578i	−0.933386	+	0.358874i	$0.883161\pi$
$230$	−1.79854e7			−0.0974704
$231$	−2.01728e7	+	3.92442e7i	−0.107678	+	0.209476i
$232$	−1.18417e7			−0.0622597
$233$	7.58453e7	+	2.33428e8i	0.392810	+	1.20895i	0.930654	+	0.365901i	$0.119239\pi$
$233$	7.58453e7	+	2.33428e8i	0.392810	+	1.20895i	−0.537844	+	0.843045i	$0.680761\pi$
$234$	−1.37499e8	−	9.98991e7i	−0.701528	−	0.509690i
$235$	−3.02297e7	+	2.19632e7i	−0.151948	+	0.110397i
$236$	−3.91401e7	+	1.20461e8i	−0.193834	+	0.596560i
$237$	1.17934e7	−	3.62964e7i	0.0575466	−	0.177110i
$238$	3.54948e8	−	2.57885e8i	1.70666	−	1.23996i
$239$	−2.61675e8	−	1.90118e8i	−1.23985	−	0.900805i	−0.242263	−	0.970210i	$-0.577890\pi$
$239$	−2.61675e8	−	1.90118e8i	−1.23985	−	0.900805i	−0.997589	+	0.0694053i	$0.977890\pi$
$240$	−410491.	−	1.26336e6i	−0.00191675	−	0.00589914i
$241$	−3.05972e8			−1.40806			−0.704031	−	0.710169i	$-0.748619\pi$
$241$	−3.05972e8			−1.40806			−0.704031	+	0.710169i	$0.748619\pi$
$242$	9.25330e7	−	1.25466e8i	0.419704	−	0.569077i
$243$	9.52592e7			0.425878
$244$	−4.75339e7	−	1.46294e8i	−0.209478	−	0.644708i
$245$	5.05739e7	+	3.67441e7i	0.219708	+	0.159627i
$246$	−2.99076e7	+	2.17292e7i	−0.128088	+	0.0930615i
$247$	5.78305e7	−	1.77984e8i	0.244184	−	0.751522i
$248$	1.77199e6	−	5.45363e6i	0.00737702	−	0.0227041i
$249$	1.05162e7	−	7.64047e6i	0.0431679	−	0.0313633i
$250$	−4.73110e7	−	3.43735e7i	−0.191502	−	0.139134i
$251$	1.45825e8	+	4.48803e8i	0.582068	+	1.79142i	0.610737	+	0.791834i	$0.290873\pi$
$251$	1.45825e8	+	4.48803e8i	0.582068	+	1.79142i	−0.0286685	+	0.999589i	$0.509127\pi$
$252$	−2.00408e8			−0.788883
$253$	−9.55829e7	+	1.85947e8i	−0.371072	+	0.721882i
$254$	−3.38778e8			−1.29717
$255$	3.75669e6	+	1.15619e7i	0.0141878	+	0.0436656i
$256$	−1.35731e7	−	9.86140e6i	−0.0505636	−	0.0367366i
$257$	−8.83848e7	+	6.42153e7i	−0.324797	+	0.235979i	−0.738220	−	0.674561i	$-0.764333\pi$
$257$	−8.83848e7	+	6.42153e7i	−0.324797	+	0.235979i	0.413423	+	0.910539i	$0.364333\pi$
$258$	−7.59399e6	+	2.33719e7i	−0.0275297	+	0.0847276i
$259$	1.25201e8	−	3.85329e8i	0.447774	−	1.37811i
$260$	−2.43958e7	+	1.77246e7i	−0.0860811	+	0.0625416i
$261$	−4.00481e7	−	2.90966e7i	−0.139425	−	0.101298i
$262$	6.14951e7	+	1.89262e8i	0.211245	+	0.650144i
$263$	−3.01654e8			−1.02250			−0.511251	−	0.859432i	$-0.670818\pi$
$263$	−3.01654e8			−1.02250			−0.511251	+	0.859432i	$0.670818\pi$
$264$	−1.52431e7	−	2.47013e6i	−0.0509871	−	0.00826240i
$265$	2.52456e7			0.0833345
$266$	−6.81913e7	−	2.09871e8i	−0.222148	−	0.683703i
$267$	2.35349e7	+	1.70991e7i	0.0756699	+	0.0549774i
$268$	1.81460e8	−	1.31838e8i	0.575848	−	0.418378i
$269$	−3.30152e7	+	1.01610e8i	−0.103414	+	0.318277i	−0.989355	−	0.145522i	$-0.953514\pi$
$269$	−3.30152e7	+	1.01610e8i	−0.103414	+	0.318277i	0.885941	+	0.463799i	$0.153514\pi$
$270$	3.46939e6	−	1.06777e7i	0.0107270	−	0.0330144i
$271$	−3.33136e8	+	2.42038e8i	−1.01679	+	0.738738i	−0.965621	−	0.259952i	$-0.916293\pi$
$271$	−3.33136e8	+	2.42038e8i	−1.01679	+	0.738738i	−0.0511639	+	0.998690i	$0.516293\pi$
$272$	1.24217e8	+	9.02486e7i	0.374273	+	0.271925i
$273$	−3.06599e7	−	9.43614e7i	−0.0912013	−	0.280689i
$274$	8.07843e7			0.237247
$275$	−2.98967e8	+	1.50988e8i	−0.866878	+	0.437803i
$276$	2.07093e7			0.0592903
$277$	1.49850e8	+	4.61190e8i	0.423621	+	1.30377i	0.904309	+	0.426878i	$0.140387\pi$
$277$	1.49850e8	+	4.61190e8i	0.423621	+	1.30377i	−0.480688	+	0.876891i	$0.659613\pi$
$278$	−1.71514e8	−	1.24612e8i	−0.478788	−	0.347860i
$279$	1.93931e7	−	1.40899e7i	0.0534603	−	0.0388412i
$280$	−1.09878e7	+	3.38170e7i	−0.0299129	+	0.0920623i
$281$	1.56561e8	−	4.81845e8i	0.420931	−	1.29549i	−0.485905	−	0.874012i	$-0.661510\pi$
$281$	1.56561e8	−	4.81845e8i	0.420931	−	1.29549i	0.906837	−	0.421482i	$-0.138490\pi$
$282$	3.48080e7	−	2.52895e7i	0.0924289	−	0.0671535i
$283$	4.32991e8	+	3.14587e8i	1.13560	+	0.825064i	0.986501	−	0.163757i	$-0.0523614\pi$
$283$	4.32991e8	+	3.14587e8i	1.13560	+	0.825064i	0.149103	+	0.988822i	$0.452361\pi$
$284$	−2.52689e6	−	7.77698e6i	−0.00654595	−	0.0201464i
$285$	6.11452e6			0.0156461
$286$	5.35993e7	+	3.46418e8i	0.135481	+	0.875629i
$287$	9.89536e8			2.47084
$288$	−2.16726e7	−	6.67014e7i	−0.0534611	−	0.164536i
$289$	−8.04821e8	−	5.84737e8i	−1.96136	−	1.42501i
$290$	−7.10552e6	+	5.16246e6i	−0.0171081	+	0.0124298i
$291$	−1.11237e7	+	3.42353e7i	−0.0264621	+	0.0814421i
$292$	1.67929e7	−	5.16833e7i	0.0394717	−	0.121482i
$293$	1.83620e8	−	1.33407e8i	0.426464	−	0.309844i	−0.353769	−	0.935333i	$-0.615100\pi$
$293$	1.83620e8	−	1.33407e8i	0.426464	−	0.309844i	0.780233	+	0.625488i	$0.215100\pi$
$294$	−5.82333e7	−	4.23090e7i	−0.133646	−	0.0970995i
$295$	2.90299e7	+	8.93448e7i	0.0658368	+	0.202625i
$296$	1.41788e8			0.317774
$297$	−9.19560e7	−	9.26154e7i	−0.203672	−	0.205133i
$298$	1.94603e8			0.425983
$299$	−1.45272e8	−	4.47103e8i	−0.314293	−	0.967293i
$300$	2.68396e7	+	1.95001e7i	0.0573921	+	0.0416978i
$301$	5.32173e8	−	3.86646e8i	1.12479	−	0.817205i
$302$	−4.26978e6	+	1.31410e7i	−0.00892034	+	0.0274540i
$303$	−2.39978e7	+	7.38576e7i	−0.0495589	+	0.152527i
$304$	6.24768e7	−	4.53920e7i	0.127544	−	0.0926663i
$305$	−9.23001e7	−	6.70599e7i	−0.186274	−	0.135336i
$306$	1.98341e8	+	6.10432e8i	0.395720	+	1.21790i
$307$	6.37337e8			1.25714			0.628572	−	0.777751i	$-0.283640\pi$
$307$	6.37337e8			1.25714			0.628572	+	0.777751i	$0.283640\pi$
$308$	2.91231e8	+	2.93320e8i	0.567951	+	0.572023i
$309$	−396635.			−0.000764779
$310$	−1.31427e6	−	4.04491e6i	−0.00250564	−	0.00771157i
$311$	1.97174e8	+	1.43255e8i	0.371696	+	0.270053i	0.757914	−	0.652355i	$-0.226219\pi$
$311$	1.97174e8	+	1.43255e8i	0.371696	+	0.270053i	−0.386218	+	0.922408i	$0.626219\pi$
$312$	2.80905e7	−	2.04090e7i	0.0523623	−	0.0380434i
$313$	−1.46434e8	+	4.50678e8i	−0.269921	+	0.830732i	0.720598	+	0.693353i	$0.243868\pi$
$313$	−1.46434e8	+	4.50678e8i	−0.269921	+	0.830732i	−0.990519	+	0.137378i	$0.956132\pi$
$314$	−1.96090e8	+	6.03502e8i	−0.357438	+	1.10008i
$315$	−1.20253e8	+	8.73688e7i	−0.216775	+	0.157496i
$316$	−2.89225e8	−	2.10134e8i	−0.515622	−	0.374621i
$317$	−1.45501e8	−	4.47807e8i	−0.256543	−	0.789558i	−0.993522	−	0.113642i	$-0.963748\pi$
$317$	−1.45501e8	−	4.47807e8i	−0.256543	−	0.789558i	0.736979	−	0.675916i	$-0.236252\pi$
$318$	−2.90691e7			−0.0506916
$319$	1.56114e7	+	1.00898e8i	0.0269261	+	0.174026i
$320$	−1.24435e7			−0.0212284
$321$	−8.17279e6	−	2.51533e7i	−0.0137912	−	0.0424450i
$322$	−4.48467e8	−	3.25830e8i	−0.748574	−	0.543871i
$323$	−5.71769e8	+	4.15414e8i	−0.944086	+	0.685919i
$324$	8.85794e7	−	2.72619e8i	0.144686	−	0.445296i
$325$	2.32721e8	−	7.16243e8i	0.376049	−	1.15736i
$326$	3.04340e8	−	2.21116e8i	0.486516	−	0.353474i
$327$	−1.19210e8	−	8.66115e7i	−0.188537	−	0.136980i
$328$	1.07011e8	+	3.29346e8i	0.167444	+	0.515340i
$329$	−1.15167e9			−1.78297
$330$	−1.02234e7	+	5.16314e6i	−0.0156601	+	0.00790888i
$331$	−4.78046e8			−0.724555			−0.362278	−	0.932070i	$-0.618001\pi$
$331$	−4.78046e8			−0.724555			−0.362278	+	0.932070i	$0.618001\pi$
$332$	−3.76275e7	−	1.15805e8i	−0.0564315	−	0.173678i
$333$	4.79519e8	+	3.48391e8i	0.711625	+	0.517026i
$334$	−4.55887e8	+	3.31221e8i	−0.669490	+	0.486413i
$335$	5.14076e7	−	1.58216e8i	0.0747087	−	0.229930i
$336$	1.26519e7	−	3.89386e7i	0.0181957	−	0.0560007i
$337$	−7.00229e8	+	5.08746e8i	−0.996634	+	0.724097i	−0.961364	−	0.275281i	$-0.911229\pi$
$337$	−7.00229e8	+	5.08746e8i	−0.996634	+	0.724097i	−0.0352701	+	0.999378i	$0.511229\pi$
$338$	−2.31552e8	−	1.68232e8i	−0.326167	−	0.236974i
$339$	1.42713e7	+	4.39226e7i	0.0198960	+	0.0612335i
$340$	1.13879e8			0.157133
$341$	−4.88040e7	−	7.90863e6i	−0.0666523	−	0.0108009i
$342$	3.22827e8			0.436394
$343$	2.23066e8	+	6.86527e8i	0.298472	+	0.918604i
$344$	1.86237e8	+	1.35309e8i	0.246668	+	0.179215i
$345$	1.24264e7	−	9.02833e6i	0.0162922	−	0.0118370i
$346$	−2.20298e8	+	6.78008e8i	−0.285920	+	0.879971i
$347$	3.92924e8	−	1.20929e9i	0.504841	−	1.55374i	−0.296195	−	0.955127i	$-0.595718\pi$
$347$	3.92924e8	−	1.20929e9i	0.504841	−	1.55374i	0.801037	−	0.598615i	$-0.204282\pi$
$348$	8.18166e6	−	5.94432e6i	0.0104067	−	0.00756093i
$349$	−3.54474e8	−	2.57540e8i	−0.446370	−	0.324307i	0.341791	−	0.939776i	$-0.388966\pi$
$349$	−3.54474e8	−	2.57540e8i	−0.446370	−	0.324307i	−0.788161	+	0.615469i	$0.788966\pi$
$350$	−2.74415e8	−	8.44563e8i	−0.342113	−	1.05292i
$351$	2.93462e8			0.362223
$352$	−6.61307e7	+	1.28650e8i	−0.0808171	+	0.157221i
$353$	−1.68086e8			−0.203385			−0.101693	−	0.994816i	$-0.532426\pi$
$353$	−1.68086e8			−0.203385			−0.101693	+	0.994816i	$0.532426\pi$
$354$	−3.34265e7	−	1.02876e8i	−0.0400479	−	0.123255i
$355$	−4.90665e6	−	3.56489e6i	−0.00582084	−	0.00422909i
$356$	2.20462e8	−	1.60175e8i	0.258976	−	0.188157i
$357$	−1.15787e8	+	3.56355e8i	−0.134685	+	0.414518i
$358$	1.40348e8	−	4.31947e8i	0.161665	−	0.497554i
$359$	6.41764e8	−	4.66269e8i	0.732057	−	0.531871i	−0.158156	−	0.987414i	$-0.550555\pi$
$359$	6.41764e8	−	4.66269e8i	0.732057	−	0.531871i	0.890214	+	0.455543i	$0.150555\pi$
$360$	−4.20833e7	−	3.05753e7i	−0.0475391	−	0.0345392i
$361$	−1.66376e8	−	5.12051e8i	−0.186129	−	0.572847i
$362$	8.88636e7			0.0984563
$363$	−951310.	+	1.33136e8i	−0.00104388	+	0.146091i
$364$	−9.29415e8			−1.01008
$365$	−1.24552e7	−	3.83330e7i	−0.0134068	−	0.0412618i
$366$	1.06279e8	+	7.72162e7i	0.113309	+	0.0823237i
$367$	−4.64930e8	+	3.37791e8i	−0.490971	+	0.356711i	−0.805558	−	0.592517i	$-0.798134\pi$
$367$	−4.64930e8	+	3.37791e8i	−0.490971	+	0.356711i	0.314587	+	0.949229i	$0.398134\pi$
$368$	5.99473e7	−	1.84499e8i	0.0627050	−	0.192986i
$369$	−4.47339e8	+	1.37677e9i	−0.463495	+	1.42649i
$370$	8.50786e7	−	6.18132e7i	0.0873201	−	0.0634417i
$371$	6.29500e8	+	4.57359e8i	0.640011	+	0.464995i
$372$	1.51332e6	+	4.65752e6i	0.00152416	+	0.00469088i
$373$	1.70120e9			1.69736			0.848680	−	0.528906i	$-0.177398\pi$
$373$	1.70120e9			1.69736			0.848680	+	0.528906i	$0.177398\pi$
$374$	6.05208e8	−	1.17737e9i	0.598211	−	1.16376i
$375$	4.99428e7			0.0489062
$376$	−1.24545e8	−	3.83309e8i	−0.120828	−	0.371871i
$377$	−1.85728e8	−	1.34939e8i	−0.178518	−	0.129701i
$378$	2.79950e8	−	2.03396e8i	0.266600	−	0.193696i
$379$	−1.48731e8	+	4.57746e8i	−0.140334	+	0.431904i	−0.996382	−	0.0849934i	$-0.972913\pi$
$379$	−1.48731e8	+	4.57746e8i	−0.140334	+	0.431904i	0.856047	+	0.516897i	$0.172913\pi$
$380$	1.76997e7	−	5.44741e7i	0.0165472	−	0.0509269i
$381$	2.34068e8	−	1.70060e8i	0.216822	−	0.157531i
$382$	6.00373e8	+	4.36197e8i	0.551061	+	0.400369i
$383$	1.39120e8	+	4.28168e8i	0.126530	+	0.389421i	0.994177	−	0.107761i	$-0.0343682\pi$
$383$	1.39120e8	+	4.28168e8i	0.126530	+	0.389421i	−0.867646	+	0.497182i	$0.834368\pi$
$384$	1.43281e7			0.0129131
$385$	3.02625e8	+	4.90400e7i	0.270266	+	0.0437963i
$386$	−3.65262e8			−0.323257
$387$	2.97372e8	+	9.15218e8i	0.260803	+	0.802668i
$388$	2.72802e8	+	1.98202e8i	0.237102	+	0.172265i
$389$	4.67526e8	−	3.39677e8i	0.402700	−	0.292579i	−0.367940	−	0.929850i	$-0.619937\pi$
$389$	4.67526e8	−	3.39677e8i	0.402700	−	0.292579i	0.770640	+	0.637271i	$0.219937\pi$
$390$	7.95807e6	−	2.44924e7i	0.00679331	−	0.0209077i
$391$	−5.48619e8	+	1.68848e9i	−0.464144	+	1.42849i
$392$	−5.45498e8	+	3.96328e8i	−0.457396	+	0.332317i
$393$	−1.37494e8	−	9.98953e7i	−0.114264	−	0.0830178i
$394$	−1.39230e7	−	4.28505e7i	−0.0114682	−	0.0352955i
$395$	−2.65156e8			−0.216477
$396$	−5.39761e8	+	2.72597e8i	−0.436785	+	0.220591i
$397$	1.05907e9			0.849489			0.424744	−	0.905313i	$-0.360364\pi$
$397$	1.05907e9			0.849489			0.424744	+	0.905313i	$0.360364\pi$
$398$	−5.55277e6	−	1.70897e7i	−0.00441488	−	0.0135876i
$399$	1.52466e8	+	1.10773e8i	0.120162	+	0.0873029i
$400$	2.51419e8	−	1.82666e8i	0.196421	−	0.142708i
$401$	6.54670e8	−	2.01487e9i	0.507011	−	1.56042i	−0.290353	−	0.956920i	$-0.593773\pi$
$401$	6.54670e8	−	2.01487e9i	0.507011	−	1.56042i	0.797364	−	0.603499i	$-0.206227\pi$
$402$	−5.91934e7	+	1.82179e8i	−0.0454446	+	0.139864i
$403$	8.99375e7	−	6.53434e7i	0.0684500	−	0.0497318i
$404$	5.88529e8	+	4.27591e8i	0.444051	+	0.322622i
$405$	−6.56985e7	−	2.02199e8i	−0.0491432	−	0.151247i
$406$	−2.70702e8			−0.200747
$407$	−1.86924e8	−	1.20811e9i	−0.137431	−	0.888232i
$408$	−1.31126e8			−0.0955828
$409$	−3.80502e8	−	1.17106e9i	−0.274995	−	0.846348i	−0.989221	−	0.146433i	$-0.953221\pi$
$409$	−3.80502e8	−	1.17106e9i	−0.274995	−	0.846348i	0.714225	−	0.699916i	$-0.246779\pi$
$410$	2.07791e8	+	1.50969e8i	0.148896	+	0.108179i
$411$	−5.58153e7	+	4.05522e7i	−0.0396558	+	0.0288116i
$412$	−1.14814e6	+	3.53361e6i	−0.000808825	+	0.00248931i
$413$	−8.94743e8	+	2.75374e9i	−0.624990	+	1.92352i
$414$	6.56075e8	−	4.76667e8i	0.454415	−	0.330152i
$415$	−7.30640e7	−	5.30841e7i	−0.0501805	−	0.0364583i
$416$	−1.00509e8	−	3.09336e8i	−0.0684509	−	0.210670i
$417$	1.81055e8			0.122274
$418$	−4.69130e8	−	4.72494e8i	−0.314178	−	0.316431i
$419$	−1.24557e9			−0.827218			−0.413609	−	0.910455i	$-0.635732\pi$
$419$	−1.24557e9			−0.827218			−0.413609	+	0.910455i	$0.635732\pi$
$420$	−9.38382e6	−	2.88804e7i	−0.00618027	−	0.0190209i
$421$	1.55200e9	+	1.12759e9i	1.01369	+	0.736486i	0.964979	−	0.262327i	$-0.0844899\pi$
$421$	1.55200e9	+	1.12759e9i	1.01369	+	0.736486i	0.0487070	+	0.998813i	$0.484490\pi$
$422$	−2.26039e8	+	1.64227e8i	−0.146416	+	0.106378i
$423$	5.20637e8	−	1.60235e9i	0.334459	−	1.02936i
$424$	−8.41462e7	+	2.58976e8i	−0.0536110	+	0.164998i
$425$	−2.30091e9	+	1.67171e9i	−1.45391	+	1.05633i
$426$	5.64977e6	+	4.10480e6i	0.00354076	+	0.00257252i
$427$	−1.08662e9	−	3.34429e9i	−0.675433	−	2.07877i
$428$	−2.47747e8			−0.152741
$429$	−2.10928e8	−	2.12441e8i	−0.128983	−	0.129908i
$430$	1.70739e8			0.103560
$431$	−7.37006e8	−	2.26827e9i	−0.443405	−	1.36466i	−0.884223	−	0.467064i	$-0.845312\pi$
$431$	−7.37006e8	−	2.26827e9i	−0.443405	−	1.36466i	0.440818	−	0.897596i	$-0.354688\pi$
$432$	9.79705e7	+	7.11797e7i	0.0584658	+	0.0424779i
$433$	4.89456e8	−	3.55610e8i	0.289738	−	0.210507i	−0.433416	−	0.901194i	$-0.642692\pi$
$433$	4.89456e8	−	3.55610e8i	0.289738	−	0.210507i	0.723154	+	0.690687i	$0.242692\pi$
$434$	4.05077e7	−	1.24670e8i	0.0237861	−	0.0732061i
$435$	2.31787e6	−	7.13367e6i	0.00135013	−	0.00415528i
$436$	−1.11670e9	+	8.11329e8i	−0.645258	+	0.468807i
$437$	7.22413e8	+	5.24864e8i	0.414096	+	0.300858i
$438$	1.43415e7	+	4.41386e7i	0.00815522	+	0.0250992i
$439$	−1.04090e9			−0.587198			−0.293599	−	0.955929i	$-0.594853\pi$
$439$	−1.04090e9			−0.587198			−0.293599	+	0.955929i	$0.594853\pi$
$440$	1.64047e7	+	1.06025e8i	0.00918088	+	0.0593370i
$441$	−2.81867e9			−1.56498
$442$	9.19831e8	+	2.83095e9i	0.506676	+	1.55939i
$443$	−6.31376e7	−	4.58721e7i	−0.0345044	−	0.0250689i	0.570399	−	0.821367i	$-0.306788\pi$
$443$	−6.31376e7	−	4.58721e7i	−0.0345044	−	0.0250689i	−0.604904	+	0.796299i	$0.706788\pi$
$444$	−9.79638e7	+	7.11749e7i	−0.0531160	+	0.0385910i
$445$	6.24571e7	−	1.92223e8i	0.0335987	−	0.103406i
$446$	−3.04559e8	+	9.37336e8i	−0.162555	+	0.500291i
$447$	−1.34454e8	+	9.76868e7i	−0.0712030	+	0.0517320i
$448$	−3.10280e8	−	2.25431e8i	−0.163035	−	0.118452i
$449$	6.54418e8	+	2.01409e9i	0.341187	+	1.05007i	0.963593	+	0.267372i	$0.0861554\pi$
$449$	6.54418e8	+	2.01409e9i	0.341187	+	1.05007i	−0.622406	+	0.782695i	$0.713845\pi$
$450$	1.29912e9			0.672056
$451$	2.66513e9	−	1.34598e9i	1.36804	−	0.690908i
$452$	4.32617e8			0.220353
$453$	−3.64648e6	−	1.12227e7i	−0.00184302	−	0.00567224i
$454$	−3.71599e8	−	2.69983e8i	−0.186372	−	0.135407i
$455$	−5.57687e8	+	4.05183e8i	−0.277556	+	0.201656i
$456$	−2.03804e7	+	6.27243e7i	−0.0100655	+	0.0309784i
$457$	2.67657e7	−	8.23763e7i	0.0131181	−	0.0403734i	−0.944283	−	0.329134i	$-0.893243\pi$
$457$	2.67657e7	−	8.23763e7i	0.0131181	−	0.0403734i	0.957401	+	0.288761i	$0.0932432\pi$
$458$	−1.24385e8	+	9.03708e7i	−0.0604976	+	0.0439541i
$459$	−8.96597e8	−	6.51416e8i	−0.432766	−	0.314423i
$460$	−4.44624e7	−	1.36841e8i	−0.0212981	−	0.0655487i
$461$	1.82421e9			0.867206			0.433603	−	0.901104i	$-0.357242\pi$
$461$	1.82421e9			0.867206			0.433603	+	0.901104i	$0.357242\pi$
$462$	−3.48458e8	−	5.64671e7i	−0.164400	−	0.0266409i
$463$	−3.39712e9			−1.59066			−0.795331	−	0.606175i	$-0.792703\pi$
$463$	−3.39712e9			−1.59066			−0.795331	+	0.606175i	$0.792703\pi$
$464$	−2.92744e7	−	9.00972e7i	−0.0136042	−	0.0418696i
$465$	2.93852e6	+	2.13496e6i	0.00135532	+	0.000984701i
$466$	−1.58852e9	+	1.15413e9i	−0.727182	+	0.528328i
$467$	−1.05586e9	+	3.24960e9i	−0.479730	+	1.47646i	0.359740	+	0.933053i	$0.382865\pi$
$467$	−1.05586e9	+	3.24960e9i	−0.479730	+	1.47646i	−0.839470	+	0.543406i	$0.817135\pi$
$468$	4.20160e8	−	1.29312e9i	0.189476	−	0.583148i
$469$	4.14816e9	−	3.01382e9i	1.85674	−	1.34900i
$470$	−2.41838e8	−	1.75705e8i	−0.107444	−	0.0780625i
$471$	−1.67465e8	−	5.15403e8i	−0.0738499	−	0.227287i
$472$	−1.01328e9			−0.443540
$473$	9.07386e8	−	1.76523e9i	0.394256	−	0.766984i
$474$	3.05314e8			0.131681
$475$	4.42042e8	+	1.36047e9i	0.189250	+	0.582452i
$476$	2.83959e9	+	2.06308e9i	1.20679	+	0.876782i
$477$	−9.20914e8	+	6.69083e8i	−0.388512	+	0.282271i
$478$	7.99608e8	−	2.46094e9i	0.334873	−	1.03063i
$479$	3.64833e7	−	1.12284e8i	0.0151677	−	0.0466814i	−0.943186	−	0.332265i	$-0.892187\pi$
$479$	3.64833e7	−	1.12284e8i	0.0151677	−	0.0466814i	0.958354	+	0.285583i	$0.0921873\pi$
$480$	8.59744e6	−	6.24640e6i	0.00354834	−	0.00257802i
$481$	2.22383e9	+	1.61570e9i	0.911157	+	0.661994i
$482$	−7.56404e8	−	2.32797e9i	−0.307673	−	0.946920i
$483$	4.73414e8			0.191173
$484$	1.18335e9	+	3.93865e8i	0.474412	+	0.157902i
$485$	2.50099e8			0.0995443
$486$	2.35494e8	+	7.24775e8i	0.0930577	+	0.286402i
$487$	1.91809e9	+	1.39357e9i	0.752520	+	0.546738i	0.896607	−	0.442827i	$-0.146025\pi$
$487$	1.91809e9	+	1.39357e9i	0.752520	+	0.546738i	−0.144087	+	0.989565i	$0.546025\pi$
$488$	9.95564e8	−	7.23319e8i	0.387793	−	0.281748i
$489$	−9.92777e7	+	3.05545e8i	−0.0383947	+	0.118167i
$490$	−1.54540e8	+	4.75625e8i	−0.0593410	+	0.182633i
$491$	−5.29061e7	+	3.84386e7i	−0.0201707	+	0.0146549i	−0.597825	−	0.801627i	$-0.703968\pi$
$491$	−5.29061e7	+	3.84386e7i	−0.0201707	+	0.0146549i	0.577654	+	0.816282i	$0.303968\pi$
$492$	−2.39261e8	−	1.73833e8i	−0.0905720	−	0.0658044i
$493$	2.67910e8	+	8.24543e8i	0.100699	+	0.309920i
$494$	1.49715e9			0.558754
$495$	−2.05038e8	+	3.98881e8i	−0.0759830	+	0.147817i
$496$	4.58743e7			0.0168804
$497$	−5.77647e7	−	1.77782e8i	−0.0211065	−	0.0649590i
$498$	8.41296e7	+	6.11237e7i	0.0305243	+	0.0221772i
$499$	3.01429e9	−	2.19001e9i	1.08601	−	0.789032i	0.107288	−	0.994228i	$-0.465783\pi$
$499$	3.01429e9	−	2.19001e9i	1.08601	−	0.789032i	0.978721	+	0.205196i	$0.0657833\pi$
$500$	1.44570e8	−	4.44939e8i	0.0517228	−	0.159186i
$501$	1.48713e8	−	4.57693e8i	0.0528346	−	0.162608i
$502$	−3.05420e9	+	2.21901e9i	−1.07754	+	0.782880i
$503$	−6.70340e8	−	4.87030e8i	−0.234859	−	0.170635i	0.464131	−	0.885767i	$-0.346367\pi$
$503$	−6.70340e8	−	4.87030e8i	−0.234859	−	0.170635i	−0.698990	+	0.715132i	$0.746367\pi$
$504$	−4.95435e8	−	1.52479e9i	−0.172377	−	0.530523i
$505$	5.39552e8			0.186429
$506$	−1.65106e9	−	2.67552e8i	−0.566547	−	0.0918083i
$507$	2.44433e8			0.0832974
$508$	−8.37505e8	−	2.57758e9i	−0.283442	−	0.872345i
$509$	4.81459e7	+	3.49800e7i	0.0161825	+	0.0117573i	0.595847	−	0.803098i	$-0.296816\pi$
$509$	4.81459e7	+	3.49800e7i	0.0161825	+	0.0117573i	−0.579665	+	0.814855i	$0.696816\pi$
$510$	−7.86812e7	+	5.71652e7i	−0.0262649	+	0.0190825i
$511$	3.83886e8	−	1.18148e9i	0.127271	−	0.391699i
$512$	4.14756e7	−	1.27649e8i	0.0136568	−	0.0420312i
$513$	−4.50958e8	+	3.27640e8i	−0.147477	+	0.107149i
$514$	−7.07078e8	−	5.13723e8i	−0.229666	−	0.166862i
$515$	851565.	+	2.62085e6i	0.000274721	+	0.000845505i
$516$	−1.96597e8			−0.0629947
$517$	−3.10181e9	+	1.56652e9i	−0.987185	+	0.498562i
$518$	3.24127e9			1.02462
$519$	−1.88139e8	−	5.79033e8i	−0.0590736	−	0.181810i
$520$	−1.95166e8	−	1.41796e8i	−0.0608685	−	0.0442236i
$521$	−1.91534e9	+	1.39157e9i	−0.593353	+	0.431096i	−0.843513	−	0.537108i	$-0.819517\pi$
$521$	−1.91534e9	+	1.39157e9i	−0.593353	+	0.431096i	0.250160	+	0.968204i	$0.419517\pi$
$522$	1.22376e8	−	3.76635e8i	0.0376574	−	0.115897i
$523$	−1.29487e9	+	3.98520e9i	−0.395795	+	1.21813i	0.532546	+	0.846401i	$0.321235\pi$
$523$	−1.29487e9	+	3.98520e9i	−0.395795	+	1.21813i	−0.928341	+	0.371730i	$0.878765\pi$
$524$	−1.28797e9	+	9.35765e8i	−0.391062	+	0.284123i
$525$	6.13553e8	+	4.45772e8i	0.185052	+	0.134448i
$526$	−7.45730e8	−	2.29512e9i	−0.223425	−	0.687631i
$527$	−4.19828e8			−0.124949
$528$	−1.88892e7	−	1.22083e8i	−0.00558464	−	0.0360942i
$529$	−1.16170e9			−0.341191
$530$	6.24105e7	+	1.92080e8i	0.0182093	+	0.0560423i
$531$	−3.42686e9	−	2.48976e9i	−0.993267	−	0.721651i
$532$	1.42822e9	−	1.03766e9i	0.411248	−	0.298789i
$533$	−2.07459e9	+	6.38493e9i	−0.593453	+	1.82646i
$534$	−7.19163e7	+	2.21336e8i	−0.0204377	+	0.0629009i
$535$	−1.48659e8	+	1.08007e8i	−0.0419712	+	0.0304939i
$536$	1.45168e9	+	1.05471e9i	0.407186	+	0.295838i
$537$	1.19860e8	+	3.68892e8i	0.0334014	+	0.102799i
$538$	−8.54715e8			−0.236637
$539$	4.09607e9	+	4.12545e9i	1.12670	+	1.13478i
$540$	8.98174e7			0.0245461
$541$	−1.04761e9	−	3.22421e9i	−0.284452	−	0.875454i	−0.986562	−	0.163385i	$-0.947759\pi$
$541$	−1.04761e9	−	3.22421e9i	−0.284452	−	0.875454i	0.702110	−	0.712068i	$-0.252241\pi$
$542$	−2.66509e9	−	1.93630e9i	−0.718976	−	0.522367i
$543$	−6.13974e7	+	4.46078e7i	−0.0164570	+	0.0119567i
$544$	−3.79572e8	+	1.16820e9i	−0.101088	+	0.311116i
$545$	−3.16362e8	+	9.73661e8i	−0.0837136	+	0.257644i
$546$	6.42149e8	−	4.66548e8i	0.168835	−	0.122666i
$547$	−5.65466e9	−	4.10835e9i	−1.47724	−	1.07328i	−0.978433	−	0.206565i	$-0.933772\pi$
$547$	−5.65466e9	−	4.10835e9i	−1.47724	−	1.07328i	−0.498807	−	0.866713i	$-0.666228\pi$
$548$	1.99710e8	+	6.14643e8i	0.0518403	+	0.159548i
$549$	5.14423e9			1.32684
$550$	−1.88787e9	−	1.90141e9i	−0.483841	−	0.487311i
$551$	4.36060e8			0.111049
$552$	5.11962e7	+	1.57566e8i	0.0129554	+	0.0398727i
$553$	−6.61168e9	−	4.80367e9i	−1.66255	−	1.20791i
$554$	−3.13850e9	+	2.28025e9i	−0.784219	+	0.569768i
$555$	−2.77532e7	+	8.54156e7i	−0.00689109	+	0.0212086i
$556$	5.24101e8	−	1.61302e9i	0.129316	−	0.397994i
$557$	1.87261e9	−	1.36053e9i	0.459149	−	0.333591i	−0.334048	−	0.942556i	$-0.608415\pi$
$557$	1.87261e9	−	1.36053e9i	0.459149	−	0.333591i	0.793197	+	0.608965i	$0.208415\pi$
$558$	1.55144e8	+	1.12719e8i	0.0378021	+	0.0274649i
$559$	1.37910e9	+	4.24443e9i	0.333929	+	1.02773i
$560$	−2.84458e8			−0.0684480
$561$	1.72869e8	+	1.11727e9i	0.0413377	+	0.267170i
$562$	4.05314e9			0.963195
$563$	−8.60369e8	−	2.64794e9i	−0.203191	−	0.625359i	−0.999783	−	0.0208408i	$-0.993366\pi$
$563$	−8.60369e8	−	2.64794e9i	−0.203191	−	0.625359i	0.796591	−	0.604518i	$-0.206634\pi$
$564$	2.78464e8	+	2.02316e8i	0.0653571	+	0.0474847i
$565$	2.59588e8	−	1.88601e8i	0.0605500	−	0.0439922i
$566$	−1.32310e9	+	4.07210e9i	−0.306716	+	0.943975i
$567$	2.02492e9	−	6.23207e9i	0.466517	−	1.43579i
$568$	5.29239e7	−	3.84515e7i	0.0121181	−	0.00880428i
$569$	5.15114e9	+	3.74252e9i	1.17222	+	0.851671i	0.991273	−	0.131821i	$-0.0420825\pi$
$569$	5.15114e9	+	3.74252e9i	1.17222	+	0.851671i	0.180951	+	0.983492i	$0.442083\pi$
$570$	1.51159e7	+	4.65220e7i	0.00341879	+	0.0105220i
$571$	−5.32664e8			−0.119737			−0.0598683	−	0.998206i	$-0.519068\pi$
$571$	−5.32664e8			−0.119737			−0.0598683	+	0.998206i	$0.519068\pi$
$572$	−2.50320e9	+	1.26420e9i	−0.559255	+	0.282443i
$573$	−6.33771e8			−0.140731
$574$	2.44627e9	+	7.52884e9i	0.539899	+	1.66164i
$575$	2.90713e9	+	2.11216e9i	0.637716	+	0.463328i
$576$	4.53917e8	−	3.29790e8i	0.0989687	−	0.0719050i
$577$	2.47923e9	−	7.63028e9i	0.537281	−	1.65358i	−0.201387	−	0.979512i	$-0.564545\pi$
$577$	2.47923e9	−	7.63028e9i	0.537281	−	1.65358i	0.738668	−	0.674069i	$-0.235455\pi$
$578$	2.45932e9	−	7.56899e9i	0.529745	−	1.63039i
$579$	2.52366e8	−	1.83354e8i	0.0540325	−	0.0392569i
$580$	−5.68441e7	−	4.12997e7i	−0.0120973	−	0.00878919i
$581$	−8.60163e8	−	2.64731e9i	−0.181955	−	0.560000i
$582$	−2.87977e8			−0.0605519
$583$	2.31754e9	+	3.75555e8i	0.484382	+	0.0784936i
$584$	4.34744e8			0.0903210
$585$	−3.11629e8	−	9.59096e8i	−0.0643565	−	0.198069i
$586$	1.46896e9	+	1.06726e9i	0.301556	+	0.219093i
$587$	−1.50295e9	+	1.09196e9i	−0.306699	+	0.222830i	−0.730479	−	0.682936i	$-0.760703\pi$
$587$	−1.50295e9	+	1.09196e9i	−0.306699	+	0.222830i	0.423780	+	0.905765i	$0.360703\pi$
$588$	1.77945e8	−	5.47659e8i	0.0360966	−	0.111094i
$589$	−6.52518e7	+	2.00825e8i	−0.0131580	+	0.0404961i
$590$	−6.08010e8	+	4.41745e8i	−0.121879	+	0.0885502i
$591$	3.11298e7	+	2.26171e7i	0.00620325	+	0.00450693i
$592$	3.50519e8	+	1.07879e9i	0.0694362	+	0.213703i
$593$	−5.07200e9			−0.998822			−0.499411	−	0.866365i	$-0.666450\pi$
$593$	−5.07200e9			−0.998822			−0.499411	+	0.866365i	$0.666450\pi$
$594$	4.77332e8	−	9.28600e8i	0.0934476	−	0.181793i
$595$	2.60328e9			0.506654
$596$	4.81084e8	+	1.48062e9i	0.0930806	+	0.286473i
$597$	1.24152e7	+	9.02017e6i	0.00238805	+	0.00173502i
$598$	3.04263e9	−	2.21060e9i	0.581828	−	0.422723i
$599$	−7.83898e8	+	2.41259e9i	−0.149027	+	0.458659i	−0.997507	−	0.0705692i	$-0.977518\pi$
$599$	−7.83898e8	+	2.41259e9i	−0.149027	+	0.458659i	0.848480	+	0.529228i	$0.177518\pi$
$600$	−8.20146e7	+	2.52415e8i	−0.0155011	+	0.0477074i
$601$	2.35872e9	−	1.71371e9i	0.443217	−	0.322016i	−0.343695	−	0.939081i	$-0.611679\pi$
$601$	2.35872e9	−	1.71371e9i	0.443217	−	0.322016i	0.786912	+	0.617065i	$0.211679\pi$
$602$	4.25738e9	+	3.09317e9i	0.795344	+	0.577851i
$603$	2.31795e9	+	7.13391e9i	0.430520	+	1.32500i
$604$	−1.10538e8			−0.0204119
$605$	8.81768e8	−	2.79554e8i	0.161886	−	0.0513242i
$606$	−6.21267e8			−0.113403
$607$	2.62652e9	+	8.08361e9i	0.476673	+	1.46705i	0.843688	+	0.536834i	$0.180380\pi$
$607$	2.62652e9	+	8.08361e9i	0.476673	+	1.46705i	−0.367014	+	0.930215i	$0.619620\pi$
$608$	4.99814e8	+	3.63136e8i	0.0901874	+	0.0655250i
$609$	1.87033e8	−	1.35887e8i	0.0335549	−	0.0243791i
$610$	2.82044e8	−	8.68042e8i	0.0503109	−	0.154841i
$611$	2.41451e9	−	7.43110e9i	0.428238	−	1.31798i
$612$	−4.15411e9	+	3.01814e9i	−0.732569	+	0.532242i
$613$	−8.18128e9	−	5.94405e9i	−1.43453	−	1.04225i	−0.989151	−	0.146905i	$-0.953069\pi$
$613$	−8.18128e9	−	5.94405e9i	−1.43453	−	1.04225i	−0.445379	−	0.895342i	$-0.646931\pi$
$614$	1.57558e9	+	4.84915e9i	0.274696	+	0.845427i
$615$	−2.19350e8			−0.0380254
$616$	−1.51175e9	+	2.94095e9i	−0.260583	+	0.506938i
$617$	4.15575e9			0.712281			0.356141	−	0.934432i	$-0.384092\pi$
$617$	4.15575e9			0.712281			0.356141	+	0.934432i	$0.384092\pi$
$618$	−980535.	−	3.01778e6i	−0.000167110	−	0.000514313i
$619$	−2.22951e8	−	1.61984e8i	−0.0377827	−	0.0274507i	0.568734	−	0.822522i	$-0.307434\pi$
$619$	−2.22951e8	−	1.61984e8i	−0.0377827	−	0.0274507i	−0.606516	+	0.795071i	$0.707434\pi$
$620$	2.75264e7	−	1.99991e7i	0.00463852	−	0.00337008i
$621$	−4.32700e8	+	1.33171e9i	−0.0725048	+	0.223147i
$622$	−6.02509e8	+	1.85433e9i	−0.100392	+	0.308974i
$623$	5.03976e9	−	3.66160e9i	0.835030	−	0.606684i
$624$	2.24724e8	+	1.63272e8i	0.0370257	+	0.0269008i
$625$	1.72447e9	+	5.30736e9i	0.282537	+	0.869558i
$626$	−3.79096e9			−0.617646
$627$	5.61313e8	+	9.09601e7i	0.0909429	+	0.0147372i
$628$	−5.07647e9			−0.817906
$629$	−3.20785e9	−	9.87274e9i	−0.513968	−	1.58183i
$630$	−9.62023e8	−	6.98951e8i	−0.153283	−	0.111366i
$631$	−2.38703e9	+	1.73428e9i	−0.378229	+	0.274799i	−0.760615	−	0.649203i	$-0.775102\pi$
$631$	−2.38703e9	+	1.73428e9i	−0.378229	+	0.274799i	0.382386	+	0.924003i	$0.375102\pi$
$632$	8.83793e8	−	2.72004e9i	0.139265	−	0.428612i
$633$	7.37355e7	−	2.26935e8i	0.0115548	−	0.0355621i
$634$	3.04742e9	−	2.21408e9i	0.474920	−	0.345049i
$635$	−1.62624e9	−	1.18154e9i	−0.252045	−	0.183121i
$636$	−7.18627e7	−	2.21171e8i	−0.0110765	−	0.0340900i
$637$	−1.30719e10			−2.00379
$638$	−7.29084e8	+	3.68212e8i	−0.111149	+	0.0561339i
$639$	2.73466e8			0.0414620
$640$	−3.07620e7	−	9.46759e7i	−0.00463858	−	0.0142761i
$641$	−8.15829e9	−	5.92735e9i	−1.22348	−	0.888909i	−0.227094	−	0.973873i	$-0.572923\pi$
$641$	−8.15829e9	−	5.92735e9i	−1.22348	−	0.888909i	−0.996384	+	0.0849638i	$0.972923\pi$
$642$	1.71173e8	−	1.24365e8i	0.0255307	−	0.0185491i
$643$	−8.91766e8	+	2.74457e9i	−0.132286	+	0.407133i	−0.995158	−	0.0982889i	$-0.968663\pi$
$643$	−8.91766e8	+	2.74457e9i	−0.132286	+	0.407133i	0.862872	+	0.505422i	$0.168663\pi$
$644$	1.37039e9	−	4.21764e9i	0.202183	−	0.622255i
$645$	−1.17966e8	+	8.57076e7i	−0.0173101	+	0.0125765i
$646$	−4.57415e9	−	3.32331e9i	−0.667570	−	0.485018i
$647$	2.06306e9	+	6.34943e9i	0.299465	+	0.921658i	0.981685	+	0.190511i	$0.0610146\pi$
$647$	2.06306e9	+	6.34943e9i	0.299465	+	0.921658i	−0.682220	+	0.731147i	$0.738985\pi$
$648$	2.29319e9			0.331076
$649$	1.33584e9	+	8.63371e9i	0.191822	+	1.23977i
$650$	6.02482e9			0.860493
$651$	3.45944e7	+	1.06471e8i	0.00491442	+	0.0151250i
$652$	2.43472e9	+	1.76893e9i	0.344019	+	0.249944i
$653$	2.64851e9	−	1.92425e9i	0.372224	−	0.270437i	−0.385908	−	0.922537i	$-0.626112\pi$
$653$	2.64851e9	−	1.92425e9i	0.372224	−	0.270437i	0.758133	+	0.652100i	$0.226112\pi$
$654$	3.64275e8	−	1.12112e9i	0.0509222	−	0.156722i
$655$	−3.64883e8	+	1.12299e9i	−0.0507351	+	0.156147i
$656$	−2.24127e9	+	1.62837e9i	−0.309977	+	0.225212i
$657$	1.47028e9	+	1.06822e9i	0.202266	+	0.146954i
$658$	−2.84709e9	−	8.76245e9i	−0.389593	−	1.19904i
$659$	−8.72958e8			−0.118821			−0.0594107	−	0.998234i	$-0.518922\pi$
$659$	−8.72958e8			−0.118821			−0.0594107	+	0.998234i	$0.518922\pi$
$660$	−6.45571e7	−	6.50200e7i	−0.00874057	−	0.00880325i
$661$	6.48742e9			0.873710			0.436855	−	0.899532i	$-0.356092\pi$
$661$	6.48742e9			0.873710			0.436855	+	0.899532i	$0.356092\pi$
$662$	−1.18179e9	−	3.63719e9i	−0.158321	−	0.487262i
$663$	−2.05661e9	−	1.49421e9i	−0.274065	−	0.199120i
$664$	7.88080e8	−	5.72574e8i	0.104468	−	0.0759002i
$665$	4.04615e8	−	1.24528e9i	0.0533539	−	0.164206i
$666$	−1.46528e9	+	4.50967e9i	−0.192203	+	0.591541i
$667$	8.86196e8	−	6.43859e8i	0.115635	−	0.0840138i
$668$	−3.64709e9	−	2.64977e9i	−0.473401	−	0.343946i
$669$	−2.60100e8	−	8.00504e8i	−0.0335852	−	0.103365i
$670$	1.33087e9			0.170952
$671$	−7.47556e9	−	7.52917e9i	−0.955245	−	0.962095i
$672$	3.27540e8			0.0416363
$673$	1.43850e9	+	4.42725e9i	0.181910	+	0.559862i	0.999881	−	0.0153970i	$-0.00490122\pi$
$673$	1.43850e9	+	4.42725e9i	0.181910	+	0.559862i	−0.817971	+	0.575259i	$0.804901\pi$
$674$	−5.60184e9	−	4.06997e9i	−0.704727	−	0.512014i
$675$	−1.81474e9	+	1.31849e9i	−0.227118	+	0.165011i
$676$	7.07560e8	−	2.17764e9i	0.0880947	−	0.271128i
$677$	−2.06480e9	+	6.35479e9i	−0.255751	+	0.787120i	0.737930	+	0.674877i	$0.235803\pi$
$677$	−2.06480e9	+	6.35479e9i	−0.255751	+	0.787120i	−0.993681	+	0.112243i	$0.964197\pi$
$678$	−2.98902e8	+	2.17165e8i	−0.0368320	+	0.0267600i
$679$	6.23624e9	+	4.53089e9i	0.764502	+	0.555443i
$680$	2.81525e8	+	8.66445e8i	0.0343349	+	0.105672i
$681$	3.92271e8			0.0475961
$682$	−6.04777e7	−	3.90874e8i	−0.00730045	−	0.0471836i
$683$	4.37135e8			0.0524981			0.0262491	−	0.999655i	$-0.491644\pi$
$683$	4.37135e8			0.0524981			0.0262491	+	0.999655i	$0.491644\pi$
$684$	7.98072e8	+	2.45621e9i	0.0953555	+	0.293474i
$685$	3.87791e8	+	2.81746e8i	0.0460978	+	0.0334920i
$686$	−4.67196e9	+	3.39438e9i	−0.552541	+	0.401445i
$687$	4.05752e7	−	1.24878e8i	0.00477432	−	0.0146939i
$688$	−5.69091e8	+	1.75148e9i	−0.0666227	+	0.205043i
$689$	−4.27085e9	+	3.10295e9i	−0.497447	+	0.361416i
$690$	9.94114e7	+	7.22266e7i	0.0115203	+	0.00837000i
$691$	2.46018e9	+	7.57165e9i	0.283657	+	0.873006i	0.986798	+	0.161956i	$0.0517801\pi$
$691$	2.46018e9	+	7.57165e9i	0.283657	+	0.873006i	−0.703141	+	0.711050i	$0.748220\pi$
$692$	−5.70320e9			−0.654255
$693$	−1.23389e10	+	6.23157e9i	−1.40835	+	0.711264i
$694$	1.01722e10			1.15520
$695$	−3.88721e8	−	1.19636e9i	−0.0439229	−	0.135181i
$696$	6.54533e7	+	4.75546e7i	0.00735866	+	0.00534638i
$697$	2.05114e10	−	1.49024e10i	2.29446	−	1.66702i
$698$	1.08317e9	−	3.33367e9i	0.120560	−	0.371047i
$699$	5.18188e8	−	1.59482e9i	0.0573874	−	0.176620i
$700$	5.74743e9	−	4.17575e9i	0.633331	−	0.460142i
$701$	3.66923e8	+	2.66585e8i	0.0402311	+	0.0292296i	0.607719	−	0.794152i	$-0.292085\pi$
$701$	3.66923e8	+	2.66585e8i	0.0402311	+	0.0292296i	−0.567488	+	0.823382i	$0.692085\pi$
$702$	7.25477e8	+	2.23279e9i	0.0791487	+	0.243595i
$703$	−5.22120e9			−0.566796
$704$	−1.14231e9	−	1.85111e8i	−0.123390	−	0.0199953i
$705$	2.55291e8			0.0274393
$706$	−4.15531e8	−	1.27887e9i	−0.0444414	−	0.136776i
$707$	1.34538e10	+	9.77472e9i	1.43178	+	1.04025i
$708$	7.00094e8	−	5.08648e8i	0.0741378	−	0.0538643i
$709$	−3.48123e9	+	1.07141e10i	−0.366835	+	1.12900i	0.581988	+	0.813197i	$0.302275\pi$
$709$	−3.48123e9	+	1.07141e10i	−0.366835	+	1.12900i	−0.948824	+	0.315806i	$0.897725\pi$
$710$	1.49934e7	−	4.61449e7i	0.00157216	−	0.00483860i
$711$	9.67242e9	−	7.02742e9i	1.00923	−	0.733251i
$712$	1.76370e9	+	1.28140e9i	0.183124	+	0.133047i
$713$	1.63915e8	+	5.04479e8i	0.0169358	+	0.0521230i
$714$	−2.99755e9			−0.308193
$715$	−9.50889e8	+	1.84986e9i	−0.0972878	+	0.189263i
$716$	3.63341e9			0.369929
$717$	6.82882e8	+	2.10170e9i	0.0691877	+	0.212938i
$718$	5.13411e9	+	3.73015e9i	0.517643	+	0.376089i
$719$	−1.38821e9	+	1.00859e9i	−0.139285	+	0.101196i	−0.655246	−	0.755416i	$-0.727435\pi$
$719$	−1.38821e9	+	1.00859e9i	−0.139285	+	0.101196i	0.515961	+	0.856612i	$0.327435\pi$
$720$	1.28595e8	−	3.95775e8i	0.0128399	−	0.0395171i
$721$	−2.62464e7	+	8.07782e7i	−0.00260794	+	0.00802640i
$722$	3.48461e9	−	2.53172e9i	0.344568	−	0.250343i
$723$	1.69121e9	+	1.22874e9i	0.166423	+	0.120913i
$724$	2.19683e8	+	6.76114e8i	0.0215135	+	0.0662117i
$725$	1.75479e9			0.171018
$726$	−1.01531e9	+	3.21893e8i	−0.0984740	+	0.0312200i
$727$	−1.21511e10			−1.17286			−0.586430	−	0.810000i	$-0.699467\pi$
$727$	−1.21511e10			−1.17286			−0.586430	+	0.810000i	$0.699467\pi$
$728$	−2.29764e9	−	7.07141e9i	−0.220710	−	0.679276i
$729$	7.39806e9	+	5.37501e9i	0.707248	+	0.513846i
$730$	2.60864e8	−	1.89529e8i	0.0248190	−	0.0180321i
$731$	5.20815e9	−	1.60290e10i	0.493143	−	1.51774i
$732$	−3.24760e8	+	9.99508e8i	−0.0306037	+	0.0941884i
$733$	−2.38797e8	+	1.73496e8i	−0.0223957	+	0.0162714i	−0.598927	−	0.800804i	$-0.704406\pi$
$733$	−2.38797e8	+	1.73496e8i	−0.0223957	+	0.0162714i	0.576531	+	0.817075i	$0.304406\pi$
$734$	−3.71944e9	−	2.70233e9i	−0.347169	−	0.252233i
$735$	−1.31980e8	−	4.06194e8i	−0.0122604	−	0.0377336i
$736$	1.55195e9			0.143484
$737$	7.07286e9	−	1.37595e10i	0.650817	−	1.26610i
$738$	−1.15810e10			−1.06059
$739$	1.88649e9	+	5.80601e9i	0.171949	+	0.529203i	0.999481	−	0.0322146i	$-0.0102560\pi$
$739$	1.88649e9	+	5.80601e9i	0.171949	+	0.529203i	−0.827532	+	0.561418i	$0.810256\pi$
$740$	6.80628e8	+	4.94506e8i	0.0617446	+	0.0448601i
$741$	−1.03441e9	+	7.51540e8i	−0.0933958	+	0.0678560i
$742$	−1.92358e9	+	5.92017e9i	−0.172861	+	0.532011i
$743$	3.44504e9	−	1.06027e10i	0.308129	−	0.948324i	−0.670362	−	0.742035i	$-0.733861\pi$
$743$	3.44504e9	−	1.06027e10i	0.308129	−	0.948324i	0.978491	−	0.206290i	$-0.0661390\pi$
$744$	−3.16954e7	+	2.30280e7i	−0.00282157	+	0.00204999i
$745$	9.34156e8	+	6.78704e8i	0.0827699	+	0.0601359i
$746$	4.20559e9	+	1.29435e10i	0.370887	+	1.14147i
$747$	4.07213e9			0.357437
$748$	1.04541e10	+	1.69408e9i	0.913339	+	0.148005i
$749$	−5.66350e9			−0.492491
$750$	1.23465e8	+	3.79988e8i	0.0106864	+	0.0328893i
$751$	−4.07793e9	−	2.96279e9i	−0.351318	−	0.255247i	0.398104	−	0.917340i	$-0.369668\pi$
$751$	−4.07793e9	−	2.96279e9i	−0.351318	−	0.255247i	−0.749422	+	0.662093i	$0.769668\pi$
$752$	2.60850e9	−	1.89519e9i	0.223681	−	0.162514i
$753$	9.96301e8	−	3.06630e9i	0.0850371	−	0.261717i
$754$	5.67533e8	−	1.74669e9i	0.0482160	−	0.148394i
$755$	−6.63275e7	+	4.81898e7i	−0.00560892	+	0.00407512i
$756$	2.23960e9	+	1.62717e9i	0.188515	+	0.136964i
$757$	−6.10755e9	−	1.87971e10i	−0.511719	−	1.57491i	−0.789173	−	0.614171i	$-0.789491\pi$
$757$	−6.10755e9	−	1.87971e10i	−0.511719	−	1.57491i	0.277454	−	0.960739i	$-0.410509\pi$
$758$	−3.85042e9			−0.321119
$759$	1.27505e9	−	6.43944e8i	0.105848	−	0.0534567i
$760$	4.58220e8			0.0378640
$761$	1.61935e9	+	4.98384e9i	0.133197	+	0.409938i	0.995305	−	0.0967863i	$-0.0308563\pi$
$761$	1.61935e9	+	4.98384e9i	0.133197	+	0.409938i	−0.862108	+	0.506724i	$0.830856\pi$
$762$	1.87254e9	+	1.36048e9i	0.153316	+	0.111391i
$763$	−2.55277e10	+	1.85470e10i	−2.08054	+	1.51160i
$764$	−1.83458e9	+	5.64625e9i	−0.148836	+	0.458071i
$765$	−1.17686e9	+	3.62201e9i	−0.0950410	+	0.292506i
$766$	−2.91377e9	+	2.11698e9i	−0.234237	+	0.170183i
$767$	−1.58925e10	−	1.15466e10i	−1.27177	−	0.923993i
$768$	3.54210e7	+	1.09015e8i	0.00282161	+	0.00868401i
$769$	−5.15358e7			−0.00408664			−0.00204332	−	0.999998i	$-0.500650\pi$
$769$	−5.15358e7			−0.00408664			−0.00204332	+	0.999998i	$0.500650\pi$
$770$	3.75011e8	+	2.42374e9i	0.0296024	+	0.191324i
$771$	7.46412e8			0.0586527
$772$	−9.02976e8	−	2.77907e9i	−0.0706343	−	0.217390i
$773$	−5.74478e9	−	4.17382e9i	−0.447347	−	0.325017i	0.341200	−	0.939991i	$-0.389167\pi$
$773$	−5.74478e9	−	4.17382e9i	−0.447347	−	0.325017i	−0.788548	+	0.614974i	$0.789167\pi$
$774$	−6.22825e9	+	4.52509e9i	−0.482806	+	0.350779i
$775$	−2.62586e8	+	8.08158e8i	−0.0202636	+	0.0623649i
$776$	−8.33608e8	+	2.56558e9i	−0.0640392	+	0.197092i
$777$	−2.23945e9	+	1.62706e9i	−0.171265	+	0.124431i
$778$	3.74021e9	+	2.71742e9i	0.284752	+	0.206885i
$779$	−3.94057e9	−	1.21278e10i	−0.298661	−	0.919183i
$780$	2.06023e8			0.0155448
$781$	−3.97399e8	−	4.00249e8i	−0.0298503	−	0.0300643i
$782$	−1.42030e10			−1.06208
$783$	2.11303e8	+	6.50323e8i	0.0157304	+	0.0484131i
$784$	−4.36398e9	−	3.17062e9i	−0.323428	−	0.234984i
$785$	−3.04609e9	+	2.21311e9i	−0.224750	+	0.163290i
$786$	4.20145e8	−	1.29307e9i	0.0308617	−	0.0949826i
$787$	4.93897e8	−	1.52006e9i	0.0361181	−	0.111160i	−0.931372	−	0.364069i	$-0.881387\pi$
$787$	4.93897e8	−	1.52006e9i	0.0361181	−	0.111160i	0.967490	+	0.252909i	$0.0813873\pi$
$788$	2.91606e8	−	2.11864e8i	0.0212303	−	0.0154247i
$789$	1.66734e9	+	1.21140e9i	0.120853	+	0.0878045i
$790$	−6.55501e8	−	2.01743e9i	−0.0473019	−	0.145580i
$791$	9.88961e9			0.710496
$792$	−3.40841e9	−	3.43285e9i	−0.243788	−	0.245537i
$793$	2.38570e10			1.69887
$794$	2.61816e9	+	8.05788e9i	0.185620	+	0.571280i
$795$	−1.39541e8	−	1.01382e8i	−0.00984955	−	0.00715612i
$796$	1.16299e8	−	8.44960e7i	0.00817296	−	0.00593800i
$797$	−1.84664e9	+	5.68339e9i	−0.129205	+	0.397652i	−0.994644	−	0.103363i	$-0.967040\pi$
$797$	−1.84664e9	+	5.68339e9i	−0.129205	+	0.397652i	0.865439	+	0.501015i	$0.167040\pi$
$798$	−4.65894e8	+	1.43388e9i	−0.0324547	+	0.0998853i
$799$	−2.38722e10	+	1.73442e10i	−1.65569	+	1.20293i
$800$	2.01135e9	+	1.46133e9i	0.138891	+	0.100910i
$801$	2.81616e9	+	8.66726e9i	0.193617	+	0.595893i
$802$	1.69485e10			1.16017
$803$	−5.73138e8	−	3.70426e9i	−0.0390621	−	0.252462i
$804$	−1.53243e9			−0.103988
$805$	−1.01641e9	−	3.12818e9i	−0.0686725	−	0.211352i
$806$	7.19500e8	+	5.22747e8i	0.0484014	+	0.0351657i
$807$	5.90538e8	−	4.29051e8i	0.0395540	−	0.0287377i
$808$	−1.79838e9	+	5.53486e9i	−0.119934	+	0.369119i
$809$	−6.85331e9	+	2.10923e10i	−0.455072	+	1.40057i	0.415978	+	0.909375i	$0.363439\pi$
$809$	−6.85331e9	+	2.10923e10i	−0.455072	+	1.40057i	−0.871050	+	0.491194i	$0.836561\pi$
$810$	1.37601e9	−	9.99728e8i	0.0909753	−	0.0660974i
$811$	−7.24652e9	−	5.26490e9i	−0.477042	−	0.346591i	0.323138	−	0.946352i	$-0.395262\pi$
$811$	−7.24652e9	−	5.26490e9i	−0.477042	−	0.346591i	−0.800179	+	0.599761i	$0.795262\pi$
$812$	−6.69211e8	−	2.05962e9i	−0.0438649	−	0.135002i
$813$	2.81334e9			0.183614
$814$	8.72975e9	−	4.40882e9i	0.567305	−	0.286508i
$815$	2.23210e9			0.144432
$816$	−3.24162e8	−	9.97669e8i	−0.0208856	−	0.0642793i
$817$	−6.85800e9	−	4.98263e9i	−0.439967	−	0.319655i
$818$	7.96933e9	−	5.79006e9i	0.509079	−	0.369868i
$819$	9.60486e9	−	2.95607e10i	0.610938	−	1.88027i
$820$	−6.34952e8	+	1.95418e9i	−0.0402154	+	0.123770i
$821$	−1.01093e10	+	7.34482e9i	−0.637557	+	0.463212i	−0.859010	−	0.511959i	$-0.828920\pi$
$821$	−1.01093e10	+	7.34482e9i	−0.637557	+	0.463212i	0.221453	+	0.975171i	$0.428920\pi$
$822$	−4.46522e8	−	3.24417e8i	−0.0280409	−	0.0203729i
$823$	−9.26486e9	−	2.85143e10i	−0.579348	−	1.78305i	−0.620871	−	0.783913i	$-0.713221\pi$
$823$	−9.26486e9	−	2.85143e10i	−0.579348	−	1.78305i	0.0415231	−	0.999138i	$-0.486779\pi$
$824$	−2.97237e7			−0.00185079
$825$	2.25883e9	+	3.66041e8i	0.140054	+	0.0226956i
$826$	−2.31636e10			−1.43013
$827$	−5.04903e9	−	1.55393e10i	−0.310412	−	0.955350i	−0.977602	−	0.210462i	$-0.932503\pi$
$827$	−5.04903e9	−	1.55393e10i	−0.310412	−	0.955350i	0.667190	−	0.744887i	$-0.267497\pi$
$828$	5.24860e9	+	3.81333e9i	0.321320	+	0.233453i
$829$	2.48452e10	−	1.80511e10i	1.51461	−	1.10043i	0.550534	−	0.834813i	$-0.314424\pi$
$829$	2.48452e10	−	1.80511e10i	1.51461	−	1.10043i	0.964078	−	0.265618i	$-0.0855758\pi$
$830$	2.23264e8	−	6.87135e8i	0.0135533	−	0.0417127i
$831$	1.02380e9	−	3.15093e9i	0.0618887	−	0.190474i
$832$	2.10509e9	−	1.52944e9i	0.126718	−	0.0920663i
$833$	3.99379e10	+	2.90166e10i	2.39402	+	1.73936i
$834$	4.47593e8	+	1.37755e9i	0.0267179	+	0.0822292i
$835$	−3.34358e9			−0.198751
$836$	2.43520e9	−	4.73742e9i	0.144149	−	0.280427i
$837$	−3.31121e8			−0.0195186
$838$	−3.07923e9	−	9.47688e9i	−0.180754	−	0.556303i
$839$	2.24618e10	+	1.63195e10i	1.31304	+	0.953980i	0.999991	+	0.00424382i	$0.00135086\pi$
$839$	2.24618e10	+	1.63195e10i	1.31304	+	0.953980i	0.313050	+	0.949737i	$0.398649\pi$
$840$	1.96537e8	−	1.42793e8i	0.0114411	−	0.00831244i
$841$	−5.16520e9	+	1.58969e10i	−0.299434	+	0.921564i
$842$	−4.74248e9	+	1.45959e10i	−0.273787	+	0.842630i
$843$	−2.80038e9	+	2.03460e9i	−0.160998	+	0.116972i
$844$	−1.80831e9	−	1.31382e9i	−0.103532	−	0.0752204i
$845$	−5.24791e8	−	1.61514e9i	−0.0299218	−	0.0920898i
$846$	1.34785e10			0.765325
$847$	2.70514e10	+	9.00374e9i	1.52967	+	0.509133i
$848$	−2.17842e9			−0.122675
$849$	−1.12996e9	−	3.47766e9i	−0.0633703	−	0.195034i
$850$	−1.84073e10	−	1.33737e10i	−1.02807	−	0.746938i
$851$	−1.06109e10	+	7.70931e9i	−0.590202	+	0.428807i
$852$	−1.72642e7	+	5.31336e7i	−0.000956328	+	0.00294327i
$853$	−3.71120e9	+	1.14219e10i	−0.204735	+	0.630110i	0.794989	+	0.606624i	$0.207477\pi$
$853$	−3.71120e9	+	1.14219e10i	−0.204735	+	0.630110i	−0.999724	+	0.0234860i	$0.992523\pi$
$854$	2.27586e10	−	1.65351e10i	1.25038	−	0.908455i
$855$	1.54967e9	+	1.12590e9i	0.0847928	+	0.0616056i
$856$	−6.12465e8	−	1.88497e9i	−0.0333752	−	0.102718i
$857$	3.44911e10			1.87186			0.935932	−	0.352180i	$-0.114560\pi$
$857$	3.44911e10			1.87186			0.935932	+	0.352180i	$0.114560\pi$
$858$	1.09490e9	−	2.13002e9i	0.0591793	−	0.115127i
$859$	−1.56074e10			−0.840145			−0.420073	−	0.907491i	$-0.637995\pi$
$859$	−1.56074e10			−0.840145			−0.420073	+	0.907491i	$0.637995\pi$
$860$	4.22089e8	+	1.29906e9i	0.0226287	+	0.0696440i
$861$	−5.46950e9	−	3.97382e9i	−0.292036	−	0.212177i
$862$	1.54361e10	−	1.12150e10i	0.820845	−	0.596379i
$863$	−3.59575e9	+	1.10666e10i	−0.190437	+	0.586105i	−1.00000		0.000928579i	$-0.999704\pi$
$863$	−3.59575e9	+	1.10666e10i	−0.190437	+	0.586105i	0.809562	+	0.587034i	$0.199704\pi$
$864$	−2.99371e8	+	9.21370e8i	−0.0157911	+	0.0486000i
$865$	−3.42215e9	+	2.48634e9i	−0.179781	+	0.130618i
$866$	3.91564e9	+	2.84488e9i	0.204876	+	0.148851i
$867$	2.10031e9	+	6.46408e9i	0.109450	+	0.336853i
$868$	1.04869e9			0.0544285
$869$	−2.43413e10	−	3.94448e9i	−1.25827	−	0.203902i
$870$	6.00063e7			0.00308944
$871$	1.07498e10	+	3.30843e10i	0.551233	+	1.69652i
$872$	−8.93359e9	−	6.49063e9i	−0.456266	−	0.331497i
$873$	−9.12318e9	+	6.62837e9i	−0.464084	+	0.337176i
$874$	−2.20750e9	+	6.79398e9i	−0.111843	+	0.344219i
$875$	3.30486e9	−	1.01713e10i	0.166773	−	0.513273i
$876$	−3.00372e8	+	2.18233e8i	−0.0150972	+	0.0109687i
$877$	2.55902e9	+	1.85924e9i	0.128108	+	0.0930757i	0.649994	−	0.759939i	$-0.274771\pi$
$877$	2.55902e9	+	1.85924e9i	0.128108	+	0.0930757i	−0.521886	+	0.853015i	$0.674771\pi$
$878$	−2.57326e9	−	7.91967e9i	−0.128308	−	0.394890i
$879$	−1.55067e9			−0.0770121
$880$	−7.66135e8	+	3.86924e8i	−0.0378980	+	0.0191397i
$881$	4.50382e9			0.221904			0.110952	−	0.993826i	$-0.464610\pi$
$881$	4.50382e9			0.221904			0.110952	+	0.993826i	$0.464610\pi$
$882$	−6.96814e9	−	2.14457e10i	−0.341961	−	1.05245i
$883$	1.10324e10	+	8.01552e9i	0.539272	+	0.391804i	0.823815	−	0.566859i	$-0.191842\pi$
$883$	1.10324e10	+	8.01552e9i	0.539272	+	0.391804i	−0.284542	+	0.958663i	$0.591842\pi$
$884$	−1.92652e10	+	1.39970e10i	−0.937973	+	0.681477i
$885$	1.98337e8	−	6.10419e8i	0.00961839	−	0.0296024i
$886$	1.92931e8	−	5.93781e8i	0.00931933	−	0.0286819i
$887$	−1.89643e10	+	1.37784e10i	−0.912440	+	0.662927i	−0.941631	−	0.336647i	$-0.890707\pi$
$887$	−1.89643e10	+	1.37784e10i	−0.912440	+	0.662927i	0.0291905	+	0.999574i	$0.490707\pi$
$888$	−7.83710e8	−	5.69399e8i	−0.0375587	−	0.0272880i
$889$	−1.91453e10	−	5.89233e10i	−0.913917	−	2.81275i
$890$	1.61692e9			0.0768820
$891$	−3.02319e9	−	1.95392e10i	−0.143184	−	0.925413i
$892$	−7.88458e9			−0.371965
$893$	4.58624e9	+	1.41150e10i	0.215514	+	0.663285i
$894$	−1.07563e9	−	7.81495e8i	−0.0503482	−	0.0365801i
$895$	2.18019e9	−	1.58400e9i	0.101652	−	0.0738542i
$896$	9.48130e8	−	2.91805e9i	0.0440342	−	0.135523i
$897$	−9.92526e8	+	3.05468e9i	−0.0459164	+	0.141316i
$898$	−1.37063e10	+	9.95822e9i	−0.631616	+	0.458896i
$899$	2.09562e8	+	1.52256e8i	0.00961952	+	0.00698899i
$900$	3.21160e9	+	9.88429e9i	0.146850	+	0.451957i
$901$	1.99363e10			0.908045
$902$	1.68294e10	+	1.69501e10i	0.763563	+	0.769039i
$903$	−4.49421e9			−0.203117
$904$	1.06949e9	+	3.29154e9i	0.0481489	+	0.148187i
$905$	4.26574e8	+	3.09924e8i	0.0191304	+	0.0138991i
$906$	7.63729e7	−	5.54882e7i	0.00341186	−	0.00247886i
$907$	−1.14160e10	+	3.51348e10i	−0.508028	+	1.56355i	0.287591	+	0.957753i	$0.407146\pi$
$907$	−1.14160e10	+	3.51348e10i	−0.508028	+	1.56355i	−0.795619	+	0.605797i	$0.792854\pi$
$908$	1.13551e9	−	3.49473e9i	0.0503372	−	0.154922i
$909$	−1.96819e10	+	1.42997e10i	−0.869147	+	0.631472i
$910$	−4.46149e9	−	3.24146e9i	−0.196262	−	0.142592i
$911$	−2.37290e9	−	7.30303e9i	−0.103984	−	0.320029i	0.885507	−	0.464626i	$-0.153811\pi$
$911$	−2.37290e9	−	7.30303e9i	−0.103984	−	0.320029i	−0.989491	+	0.144597i	$0.953811\pi$
$912$	−5.27618e8			−0.0230323
$913$	−5.91759e9	−	5.96003e9i	−0.257334	−	0.259179i
$914$	6.92924e8			0.0300175
$915$	2.40871e8	+	7.41326e8i	0.0103947	+	0.0319916i
$916$	−9.95078e8	−	7.22966e8i	−0.0427782	−	0.0310802i
$917$	−2.94430e10	+	2.13916e10i	−1.26092	+	0.916114i
$918$	2.73976e9	−	8.43210e9i	0.116886	−	0.359738i
$919$	1.05985e10	−	3.26187e10i	0.450442	−	1.38632i	−0.425962	−	0.904741i	$-0.640064\pi$
$919$	1.05985e10	−	3.26187e10i	0.450442	−	1.38632i	0.876404	−	0.481577i	$-0.159936\pi$
$920$	9.31232e8	−	6.76579e8i	0.0394276	−	0.0286458i
$921$	−3.52278e9	−	2.55945e9i	−0.148586	−	0.107954i
$922$	4.50970e9	+	1.38794e10i	0.189491	+	0.583195i
$923$	1.26823e9			0.0530875
$924$	−4.31807e8	−	2.79082e9i	−0.0180069	−	0.116380i
$925$	−2.10111e10			−0.872878
$926$	−8.39815e9	−	2.58469e10i	−0.347572	−	1.06972i
$927$	−1.00524e8	−	7.30348e7i	−0.00414467	−	0.00301128i
$928$	6.13130e8	−	4.45465e8i	0.0251846	−	0.0182977i
$929$	1.03815e10	−	3.19510e10i	0.424821	−	1.30746i	−0.478345	−	0.878172i	$-0.658763\pi$
$929$	1.03815e10	−	3.19510e10i	0.424821	−	1.30746i	0.903166	−	0.429291i	$-0.141237\pi$
$930$	−8.97932e6	+	2.76355e7i	−0.000366061	+	0.00112662i
$931$	2.00874e10	−	1.45944e10i	0.815831	−	0.592736i
$932$	−1.27082e10	−	9.23304e9i	−0.514195	−	0.373585i
$933$	−5.14555e8	−	1.58364e9i	−0.0207418	−	0.0638367i
$934$	−2.73347e10			−1.09774
$935$	7.01144e9	−	3.54101e9i	0.280522	−	0.141673i
$936$	1.08773e10			0.433568
$937$	−1.54885e9	−	4.76688e9i	−0.0615066	−	0.189298i	0.915582	−	0.402132i	$-0.131731\pi$
$937$	−1.54885e9	−	4.76688e9i	−0.0615066	−	0.189298i	−0.977088	+	0.212834i	$0.931731\pi$
$938$	3.31853e10	+	2.41105e10i	1.31291	+	0.953887i
$939$	2.61924e9	−	1.90299e9i	0.103240	−	0.0750079i
$940$	7.38990e8	−	2.27438e9i	0.0290196	−	0.0893131i
$941$	−5.62720e9	+	1.73187e10i	−0.220155	+	0.677567i	0.778592	+	0.627530i	$0.215934\pi$
$941$	−5.62720e9	+	1.73187e10i	−0.220155	+	0.677567i	−0.998747	+	0.0500373i	$0.984066\pi$
$942$	3.50742e9	−	2.54829e9i	0.136713	−	0.0993279i
$943$	−2.59156e10	−	1.88288e10i	−1.00640	−	0.731191i
$944$	−2.50497e9	−	7.70950e9i	−0.0969171	−	0.298280i
$945$	2.05322e9			0.0791453
$946$	1.56738e10	+	2.53992e9i	0.601944	+	0.0975443i
$947$	−2.14352e10			−0.820167			−0.410083	−	0.912048i	$-0.634500\pi$
$947$	−2.14352e10			−0.820167			−0.410083	+	0.912048i	$0.634500\pi$
$948$	7.54778e8	+	2.32297e9i	0.0287733	+	0.0885552i
$949$	6.81860e9	+	4.95401e9i	0.258978	+	0.188159i
$950$	−9.25825e9	+	6.72651e9i	−0.350345	+	0.254541i
$951$	−9.94090e8	+	3.05950e9i	−0.0374795	+	0.115350i
$952$	−8.67701e9	+	2.67051e10i	−0.325942	+	1.00315i
$953$	1.16393e10	−	8.45645e9i	0.435614	−	0.316492i	−0.348276	−	0.937392i	$-0.613233\pi$
$953$	1.16393e10	−	8.45645e9i	0.435614	−	0.316492i	0.783890	+	0.620900i	$0.213233\pi$
$954$	−7.36731e9	−	5.35267e9i	−0.274720	−	0.199596i
$955$	1.36069e9	+	4.18777e9i	0.0505530	+	0.155586i
$956$	2.07007e10			0.766271
$957$	3.18902e8	−	6.20390e8i	0.0117616	−	0.0228809i
$958$	9.44501e8			0.0347075
$959$	4.56536e9	+	1.40507e10i	0.167151	+	0.514439i
$960$	6.87795e7	+	4.99712e7i	0.00250905	+	0.00182293i
$961$	2.21567e10	−	1.60978e10i	0.805329	−	0.585105i
$962$	−6.79541e9	+	2.09141e10i	−0.246095	+	0.757403i
$963$	2.56030e9	−	7.87979e9i	0.0923844	−	0.284330i
$964$	1.58423e10	−	1.15101e10i	0.569573	−	0.413819i
$965$	−1.75337e9	−	1.27390e9i	−0.0628100	−	0.0456342i
$966$	1.17034e9	+	3.60195e9i	0.0417728	+	0.128564i
$967$	−1.32637e10			−0.471705			−0.235852	−	0.971789i	$-0.575788\pi$
$967$	−1.32637e10			−0.471705			−0.235852	+	0.971789i	$0.575788\pi$
$968$	−7.12908e7	+	9.97718e9i	−0.00252621	+	0.353544i
$969$	4.82860e9			0.170486
$970$	6.18279e8	+	1.90287e9i	0.0217512	+	0.0669434i
$971$	3.10311e10	+	2.25454e10i	1.08775	+	0.790299i	0.979018	−	0.203772i	$-0.0653202\pi$
$971$	3.10311e10	+	2.25454e10i	1.08775	+	0.790299i	0.108734	+	0.994071i	$0.465320\pi$
$972$	−4.93224e9	+	3.58348e9i	−0.172271	+	0.125162i
$973$	1.19809e10	−	3.68735e10i	0.416961	−	1.28327i
$974$	−5.86116e9	+	1.80388e10i	−0.203249	+	0.625535i
$975$	−4.16265e9	+	3.02434e9i	−0.143831	+	0.104500i
$976$	7.96451e9	+	5.78656e9i	0.274211	+	0.199226i
$977$	1.29242e10	+	3.97767e10i	0.443377	+	1.36458i	0.884253	+	0.467007i	$0.154668\pi$
$977$	1.29242e10	+	3.97767e10i	0.443377	+	1.36458i	−0.440876	+	0.897568i	$0.645332\pi$
$978$	−2.57016e9			−0.0878564
$979$	8.59309e9	−	1.67170e10i	0.292691	−	0.569401i
$980$	−4.00082e9			−0.135787
$981$	−1.42646e10	−	4.39019e10i	−0.482412	−	1.48471i
$982$	−4.23249e8	−	3.07509e8i	−0.0142628	−	0.0103626i
$983$	1.32870e10	−	9.65360e9i	0.446160	−	0.324154i	−0.341918	−	0.939730i	$-0.611076\pi$
$983$	1.32870e10	−	9.65360e9i	0.446160	−	0.324154i	0.788078	+	0.615576i	$0.211076\pi$
$984$	7.31117e8	−	2.25015e9i	0.0244627	−	0.0752883i
$985$	8.26123e7	−	2.54255e8i	0.00275434	−	0.00847700i
$986$	−5.61118e9	+	4.07676e9i	−0.186417	+	0.135440i
$987$	6.36569e9	+	4.62494e9i	0.210734	+	0.153107i
$988$	3.70115e9	+	1.13910e10i	0.122092	+	0.375761i
$989$	−2.12944e10			−0.699970
$990$	−3.54175e9	−	5.73936e8i	−0.116010	−	0.0187992i
$991$	2.61079e10			0.852147			0.426073	−	0.904689i	$-0.359897\pi$
$991$	2.61079e10			0.852147			0.426073	+	0.904689i	$0.359897\pi$
$992$	1.13408e8	+	3.49032e8i	0.00368851	+	0.0113521i
$993$	2.64232e9	+	1.91976e9i	0.0856374	+	0.0622192i
$994$	1.20984e9	−	8.79000e8i	0.0390729	−	0.0283881i
$995$	3.29475e7	−	1.01402e8i	0.00106033	−	0.00326337i
$996$	−2.57077e8	+	7.91202e8i	−0.00824434	+	0.0253735i
$997$	6.75196e9	−	4.90558e9i	0.215773	−	0.156768i	−0.474649	−	0.880175i	$-0.657425\pi$
$997$	6.75196e9	−	4.90558e9i	0.215773	−	0.156768i	0.690422	+	0.723407i	$0.257425\pi$
$998$	2.41143e10	+	1.75201e10i	0.767924	+	0.557930i
$999$	−2.53005e9	−	7.78670e9i	−0.0802879	−	0.247101i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.8.c.a.5.2	✓	12
11.3	even	5		242.8.a.q.1.3		6
11.8	odd	10		242.8.a.o.1.3		6
11.9	even	5	inner	22.8.c.a.9.2	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.8.c.a.5.2	✓	12	1.1	even	1	trivial
22.8.c.a.9.2	yes	12	11.9	even	5	inner
242.8.a.o.1.3		6	11.8	odd	10
242.8.a.q.1.3		6	11.3	even	5

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	22.c (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.47214 + 7.60845i) q^{2} +(-5.52734 - 4.01585i) q^{3} +(-51.7771 + 37.6183i) q^{4} +(-14.6685 + 45.1450i) q^{5} +(16.8900 - 51.9822i) q^{6} +(-1183.62 + 859.952i) q^{7} +(-414.217 - 300.946i) q^{8} +(-661.396 - 2035.57i) q^{9} +O(q^{10})\)	\(q+(2.47214 + 7.60845i) q^{2} +(-5.52734 - 4.01585i) q^{3} +(-51.7771 + 37.6183i) q^{4} +(-14.6685 + 45.1450i) q^{5} +(16.8900 - 51.9822i) q^{6} +(-1183.62 + 859.952i) q^{7} +(-414.217 - 300.946i) q^{8} +(-661.396 - 2035.57i) q^{9} -379.746 q^{10} +(-2018.15 + 3926.10i) q^{11} +437.259 q^{12} +(-3067.30 - 9440.18i) q^{13} +(-9468.98 - 6879.62i) q^{14} +(262.373 - 190.625i) q^{15} +(1265.73 - 3895.53i) q^{16} +(-11583.6 + 35650.7i) q^{17} +(13852.5 - 10064.4i) q^{18} +(15253.1 + 11082.0i) q^{19} +(-938.783 - 2889.28i) q^{20} +9995.72 q^{21} +(-34860.7 - 5649.13i) q^{22} +47361.7 q^{23} +(1080.96 + 3326.86i) q^{24} +(61381.5 + 44596.3i) q^{25} +(64242.4 - 46674.8i) q^{26} +(-9136.08 + 28118.0i) q^{27} +(28934.6 - 89051.7i) q^{28} +(18711.3 - 13594.5i) q^{29} +(2098.98 + 1525.00i) q^{30} +(3460.92 + 10651.6i) q^{31} +32768.0 q^{32} +(26921.6 - 13596.3i) q^{33} -299883. q^{34} +(-21460.6 - 66048.8i) q^{35} +(110820. + 80515.2i) q^{36} +(-224041. + 162775. i) q^{37} +(-46609.4 + 143449. i) q^{38} +(-20956.3 + 64496.9i) q^{39} +(19662.1 - 14285.4i) q^{40} +(-547184. - 397552. i) q^{41} +(24710.8 + 76052.0i) q^{42} -449613. q^{43} +(-43199.2 - 279201. i) q^{44} +101597. q^{45} +(117085. + 360349. i) q^{46} +(636841. + 462692. i) q^{47} +(-22640.0 + 16448.9i) q^{48} +(406956. - 1.25248e6i) q^{49} +(-187565. + 577267. i) q^{50} +(207194. - 150536. i) q^{51} +(513939. + 373398. i) q^{52} +(-164348. - 505812. i) q^{53} -236520. q^{54} +(-147640. - 148699. i) q^{55} +749076. q^{56} +(-39805.4 - 122508. i) q^{57} +(149690. + 108756. i) q^{58} +(1.60110e6 - 1.16327e6i) q^{59} +(-6413.92 + 19740.0i) q^{60} +(-742718. + 2.28585e6i) q^{61} +(-72486.5 + 52664.5i) q^{62} +(2.53333e6 + 1.84057e6i) q^{63} +(81007.0 + 249314. i) q^{64} +471169. q^{65} +(170001. + 171220. i) q^{66} -3.50463e6 q^{67} +(-741351. - 2.28164e6i) q^{68} +(-261784. - 190197. i) q^{69} +(449476. - 326563. i) q^{70} +(-39482.7 + 121515. i) q^{71} +(-338635. + 1.04221e6i) q^{72} +(-686944. + 499094. i) q^{73} +(-1.79233e6 - 1.30220e6i) q^{74} +(-160185. - 492998. i) q^{75} -1.20665e6 q^{76} +(-987532. - 6.38253e6i) q^{77} -542528. q^{78} +(1.72616e6 + 5.31257e6i) q^{79} +(157297. + 114283. i) q^{80} +(-3.62350e6 + 2.63263e6i) q^{81} +(1.67205e6 - 5.14603e6i) q^{82} +(-587929. + 1.80946e6i) q^{83} +(-517550. + 376022. i) q^{84} +(-1.43954e6 - 1.04588e6i) q^{85} +(-1.11151e6 - 3.42086e6i) q^{86} -158017. q^{87} +(2.01749e6 - 1.01890e6i) q^{88} -4.25791e6 q^{89} +(251162. + 772998. i) q^{90} +(1.17486e7 + 8.53588e6i) q^{91} +(-2.45225e6 + 1.78166e6i) q^{92} +(23645.6 - 72773.7i) q^{93} +(-1.94601e6 + 5.98921e6i) q^{94} +(-724038. + 526045. i) q^{95} +(-181120. - 131591. i) q^{96} +(-1.62814e6 - 5.01090e6i) q^{97} +1.05355e7 q^{98} +(9.32663e6 + 1.51137e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 24 q^{2} + 44 q^{3} - 192 q^{4} + 220 q^{5} - 248 q^{6} + 534 q^{7} - 1536 q^{8} - 3745 q^{9}+O(q^{10}) \) 12 * q - 24 * q^2 + 44 * q^3 - 192 * q^4 + 220 * q^5 - 248 * q^6 + 534 * q^7 - 1536 * q^8 - 3745 * q^9	\( 12 q - 24 q^{2} + 44 q^{3} - 192 q^{4} + 220 q^{5} - 248 q^{6} + 534 q^{7} - 1536 q^{8} - 3745 q^{9} - 6080 q^{10} - 12881 q^{11} - 1664 q^{12} - 1834 q^{13} + 4272 q^{14} - 50174 q^{15} - 12288 q^{16} + 49128 q^{17} + 28720 q^{18} - 24453 q^{19} + 14080 q^{20} + 135280 q^{21} - 10648 q^{22} + 1212 q^{23} - 15872 q^{24} + 233893 q^{25} - 2352 q^{26} + 24029 q^{27} + 25216 q^{28} + 410548 q^{29} - 401392 q^{30} - 285894 q^{31} + 393216 q^{32} - 561803 q^{33} - 416016 q^{34} + 40188 q^{35} + 229760 q^{36} - 229440 q^{37} + 559696 q^{38} + 102742 q^{39} + 81920 q^{40} - 838292 q^{41} - 547200 q^{42} - 774698 q^{43} + 30976 q^{44} - 3155228 q^{45} + 438176 q^{46} + 1107540 q^{47} + 180224 q^{48} + 4281299 q^{49} - 625416 q^{50} + 2561801 q^{51} - 18816 q^{52} - 3013626 q^{53} - 2622208 q^{54} - 4505512 q^{55} - 950272 q^{56} + 10084223 q^{57} + 3284384 q^{58} + 2583885 q^{59} + 3746304 q^{60} + 418618 q^{61} + 1193008 q^{62} + 4045264 q^{63} - 786432 q^{64} - 11397748 q^{65} + 1076416 q^{66} - 18354554 q^{67} + 3144192 q^{68} + 11135006 q^{69} + 207744 q^{70} + 22870340 q^{71} - 1917440 q^{72} - 7374584 q^{73} - 1835520 q^{74} - 19671977 q^{75} - 5825152 q^{76} - 2121482 q^{77} - 20124544 q^{78} + 4715278 q^{79} + 655360 q^{80} - 745714 q^{81} + 12958184 q^{82} - 13257515 q^{83} + 48640 q^{84} + 8622056 q^{85} - 6992984 q^{86} + 6788612 q^{87} + 613888 q^{88} - 34864794 q^{89} + 11604816 q^{90} + 31631268 q^{91} - 3544192 q^{92} + 41624776 q^{93} + 6007840 q^{94} + 2925362 q^{95} + 1441792 q^{96} - 28563397 q^{97} - 5044288 q^{98} + 28188523 q^{99}+O(q^{100}) \) 12 * q - 24 * q^2 + 44 * q^3 - 192 * q^4 + 220 * q^5 - 248 * q^6 + 534 * q^7 - 1536 * q^8 - 3745 * q^9 - 6080 * q^10 - 12881 * q^11 - 1664 * q^12 - 1834 * q^13 + 4272 * q^14 - 50174 * q^15 - 12288 * q^16 + 49128 * q^17 + 28720 * q^18 - 24453 * q^19 + 14080 * q^20 + 135280 * q^21 - 10648 * q^22 + 1212 * q^23 - 15872 * q^24 + 233893 * q^25 - 2352 * q^26 + 24029 * q^27 + 25216 * q^28 + 410548 * q^29 - 401392 * q^30 - 285894 * q^31 + 393216 * q^32 - 561803 * q^33 - 416016 * q^34 + 40188 * q^35 + 229760 * q^36 - 229440 * q^37 + 559696 * q^38 + 102742 * q^39 + 81920 * q^40 - 838292 * q^41 - 547200 * q^42 - 774698 * q^43 + 30976 * q^44 - 3155228 * q^45 + 438176 * q^46 + 1107540 * q^47 + 180224 * q^48 + 4281299 * q^49 - 625416 * q^50 + 2561801 * q^51 - 18816 * q^52 - 3013626 * q^53 - 2622208 * q^54 - 4505512 * q^55 - 950272 * q^56 + 10084223 * q^57 + 3284384 * q^58 + 2583885 * q^59 + 3746304 * q^60 + 418618 * q^61 + 1193008 * q^62 + 4045264 * q^63 - 786432 * q^64 - 11397748 * q^65 + 1076416 * q^66 - 18354554 * q^67 + 3144192 * q^68 + 11135006 * q^69 + 207744 * q^70 + 22870340 * q^71 - 1917440 * q^72 - 7374584 * q^73 - 1835520 * q^74 - 19671977 * q^75 - 5825152 * q^76 - 2121482 * q^77 - 20124544 * q^78 + 4715278 * q^79 + 655360 * q^80 - 745714 * q^81 + 12958184 * q^82 - 13257515 * q^83 + 48640 * q^84 + 8622056 * q^85 - 6992984 * q^86 + 6788612 * q^87 + 613888 * q^88 - 34864794 * q^89 + 11604816 * q^90 + 31631268 * q^91 - 3544192 * q^92 + 41624776 * q^93 + 6007840 * q^94 + 2925362 * q^95 + 1441792 * q^96 - 28563397 * q^97 - 5044288 * q^98 + 28188523 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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