LMFDB - Embedded newform 22.8.c.a.15.1

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			15.1
Root			$-7.43190 + 5.39959i$ of defining polynomial
Character	$\chi$	$=$	22.15
Dual form			22.8.c.a.3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.47214 - 4.70228i) q^{2} +(-19.8857 + 61.2018i) q^{3} +(19.7771 + 60.8676i) q^{4} +(-37.7557 + 27.4311i) q^{5} +(416.491 - 302.598i) q^{6} +(-204.857 - 630.484i) q^{7} +(158.217 - 486.941i) q^{8} +(-1580.90 - 1148.59i) q^{9} +O(q^{10})$	\(q+(-6.47214 - 4.70228i) q^{2} +(-19.8857 + 61.2018i) q^{3} +(19.7771 + 60.8676i) q^{4} +(-37.7557 + 27.4311i) q^{5} +(416.491 - 302.598i) q^{6} +(-204.857 - 630.484i) q^{7} +(158.217 - 486.941i) q^{8} +(-1580.90 - 1148.59i) q^{9} +373.349 q^{10} +(-3878.93 - 2107.38i) q^{11} -4118.49 q^{12} +(-6223.82 - 4521.87i) q^{13} +(-1638.85 + 5043.87i) q^{14} +(-928.036 - 2856.20i) q^{15} +(-3313.73 + 2407.57i) q^{16} +(12653.3 - 9193.17i) q^{17} +(4830.80 + 14867.7i) q^{18} +(8445.74 - 25993.3i) q^{19} +(-2416.36 - 1755.59i) q^{20} +42660.4 q^{21} +(15195.5 + 31879.1i) q^{22} -15120.2 q^{23} +(26655.4 + 19366.3i) q^{24} +(-23468.9 + 72229.9i) q^{25} +(19018.3 + 58532.3i) q^{26} +(-12125.1 + 8809.39i) q^{27} +(34324.6 - 24938.3i) q^{28} +(28560.9 + 87901.5i) q^{29} +(-7424.29 + 22849.6i) q^{30} +(-263357. - 191340. i) q^{31} +32768.0 q^{32} +(206110. - 195491. i) q^{33} -125123. q^{34} +(25029.4 + 18184.9i) q^{35} +(38646.4 - 118941. i) q^{36} +(21604.8 + 66492.6i) q^{37} +(-176890. + 128518. i) q^{38} +(400511. - 290988. i) q^{39} +(7383.75 + 22724.9i) q^{40} +(-86391.8 + 265887. i) q^{41} +(-276104. - 200601. i) q^{42} -861451. q^{43} +(51556.9 - 277779. i) q^{44} +91195.1 q^{45} +(97859.8 + 71099.3i) q^{46} +(-199698. + 614607. i) q^{47} +(-81451.7 - 250683. i) q^{48} +(310717. - 225749. i) q^{49} +(491540. - 357124. i) q^{50} +(311019. + 957218. i) q^{51} +(152146. - 468258. i) q^{52} +(-849513. - 617208. i) q^{53} +119899. q^{54} +(204260. - 26838.1i) q^{55} -339420. q^{56} +(1.42289e6 + 1.03379e6i) q^{57} +(228487. - 703212. i) q^{58} +(571152. + 1.75783e6i) q^{59} +(155496. - 112975. i) q^{60} +(777106. - 564601. i) q^{61} +(804746. + 2.47675e6i) q^{62} +(-400310. + 1.23203e6i) q^{63} +(-212079. - 154084. i) q^{64} +359024. q^{65} +(-2.25323e6 + 296056. i) q^{66} -1.19782e6 q^{67} +(809812. + 588363. i) q^{68} +(300675. - 925382. i) q^{69} +(-76482.9 - 235390. i) q^{70} +(4.05030e6 - 2.94272e6i) q^{71} +(-809421. + 588079. i) q^{72} +(-1.85870e6 - 5.72050e6i) q^{73} +(172838. - 531941. i) q^{74} +(-3.95391e6 - 2.87268e6i) q^{75} +1.74918e6 q^{76} +(-534041. + 2.87731e6i) q^{77} -3.96047e6 q^{78} +(-410136. - 297981. i) q^{79} +(59070.0 - 181799. i) q^{80} +(-1.61866e6 - 4.98171e6i) q^{81} +(1.80941e6 - 1.31462e6i) q^{82} +(-6.60960e6 + 4.80216e6i) q^{83} +(843699. + 2.59664e6i) q^{84} +(-225556. + 694189. i) q^{85} +(5.57543e6 + 4.05079e6i) q^{86} -5.94768e6 q^{87} +(-1.63988e6 + 1.55539e6i) q^{88} +608839. q^{89} +(-590227. - 428825. i) q^{90} +(-1.57597e6 + 4.85035e6i) q^{91} +(-299033. - 920329. i) q^{92} +(1.69474e7 - 1.23130e7i) q^{93} +(4.18252e6 - 3.03878e6i) q^{94} +(394151. + 1.21307e6i) q^{95} +(-651614. + 2.00546e6i) q^{96} +(8.55176e6 + 6.21322e6i) q^{97} -3.07254e6 q^{98} +(3.71169e6 + 7.78686e6i) 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 $\left(\mathbb{Z}/22\mathbb{Z}\right)^\times$.

$n$	$13$
$\chi(n)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−6.47214	−	4.70228i	−0.572061	−	0.415627i
$2$	−6.47214	−	4.70228i	−0.572061	−	0.415627i
$3$	−19.8857	+	61.2018i	−0.425222	+	1.30870i	0.477559	+	0.878599i	$0.341522\pi$
$3$	−19.8857	+	61.2018i	−0.425222	+	1.30870i	−0.902781	+	0.430100i	$0.858478\pi$
$4$	19.7771	+	60.8676i	0.154508	+	0.475528i
$5$	−37.7557	+	27.4311i	−0.135079	+	0.0981405i	−0.653273	−	0.757123i	$-0.726605\pi$
$5$	−37.7557	+	27.4311i	−0.135079	+	0.0981405i	0.518194	+	0.855263i	$0.326605\pi$
$6$	416.491	−	302.598i	0.787184	−	0.571922i
$7$	−204.857	−	630.484i	−0.225739	−	0.694753i	−0.998216	−	0.0597102i	$-0.980982\pi$
$7$	−204.857	−	630.484i	−0.225739	−	0.694753i	0.772477	−	0.635043i	$-0.219018\pi$
$8$	158.217	−	486.941i	0.109254	−	0.336249i
$9$	−1580.90	−	1148.59i	−0.722862	−	0.525190i
$10$	373.349			0.118063
$11$	−3878.93	−	2107.38i	−0.878695	−	0.477384i
$11$	−3878.93	−	2107.38i	−0.878695	−	0.477384i
$12$	−4118.49			−0.688024
$13$	−6223.82	−	4521.87i	−0.785697	−	0.570842i	0.120986	−	0.992654i	$-0.461394\pi$
$13$	−6223.82	−	4521.87i	−0.785697	−	0.570842i	−0.906683	+	0.421812i	$0.861394\pi$
$14$	−1638.85	+	5043.87i	−0.159622	+	0.491265i
$15$	−928.036	−	2856.20i	−0.0709979	−	0.218509i
$16$	−3313.73	+	2407.57i	−0.202254	+	0.146946i
$17$	12653.3	−	9193.17i	0.624645	−	0.453831i	−0.229896	−	0.973215i	$-0.573839\pi$
$17$	12653.3	−	9193.17i	0.624645	−	0.453831i	0.854541	+	0.519384i	$0.173839\pi$
$18$	4830.80	+	14867.7i	0.195238	+	0.600882i
$19$	8445.74	−	25993.3i	0.282488	−	0.869409i	−0.704652	−	0.709553i	$-0.748897\pi$
$19$	8445.74	−	25993.3i	0.282488	−	0.869409i	0.987140	−	0.159856i	$-0.0511030\pi$
$20$	−2416.36	−	1755.59i	−0.0675394	−	0.0490703i
$21$	42660.4			1.00521
$22$	15195.5	+	31879.1i	0.304254	+	0.638302i
$23$	−15120.2			−0.259125			−0.129563	−	0.991571i	$-0.541357\pi$
$23$	−15120.2			−0.259125			−0.129563	+	0.991571i	$0.541357\pi$
$24$	26655.4	+	19366.3i	0.393592	+	0.285961i
$25$	−23468.9	+	72229.9i	−0.300402	+	0.924543i
$26$	19018.3	+	58532.3i	0.212210	+	0.653114i
$27$	−12125.1	+	8809.39i	−0.118553	+	0.0861336i
$28$	34324.6	−	24938.3i	0.295496	−	0.214691i
$29$	28560.9	+	87901.5i	0.217460	+	0.669273i	0.998970	+	0.0453799i	$0.0144498\pi$
$29$	28560.9	+	87901.5i	0.217460	+	0.669273i	−0.781510	+	0.623893i	$0.785550\pi$
$30$	−7424.29	+	22849.6i	−0.0502031	+	0.154509i
$31$	−263357.	−	191340.i	−1.58774	−	1.15356i	−0.907083	−	0.420952i	$-0.861696\pi$
$31$	−263357.	−	191340.i	−1.58774	−	1.15356i	−0.680653	−	0.732606i	$-0.738304\pi$
$32$	32768.0			0.176777
$33$	206110.	−	195491.i	0.998392	−	0.946953i
$34$	−125123.			−0.545960
$35$	25029.4	+	18184.9i	0.0986760	+	0.0716923i
$36$	38646.4	−	118941.i	0.138054	−	0.424888i
$37$	21604.8	+	66492.6i	0.0701203	+	0.215808i	0.979976	−	0.199118i	$-0.0638076\pi$
$37$	21604.8	+	66492.6i	0.0701203	+	0.215808i	−0.909855	+	0.414926i	$0.863808\pi$
$38$	−176890.	+	128518.i	−0.522950	+	0.379946i
$39$	400511.	−	290988.i	1.08116	−	0.785506i
$40$	7383.75	+	22724.9i	0.0182418	+	0.0561424i
$41$	−86391.8	+	265887.i	−0.195762	+	0.602494i	0.804205	+	0.594353i	$0.202592\pi$
$41$	−86391.8	+	265887.i	−0.195762	+	0.602494i	−0.999967	+	0.00814181i	$0.997408\pi$
$42$	−276104.	−	200601.i	−0.575043	−	0.417793i
$43$	−861451.			−1.65231			−0.826154	−	0.563444i	$-0.809476\pi$
$43$	−861451.			−1.65231			−0.826154	+	0.563444i	$0.809476\pi$
$44$	51556.9	−	277779.i	0.0912437	−	0.491604i
$45$	91195.1			0.149186
$46$	97859.8	+	71099.3i	0.148235	+	0.107699i
$47$	−199698.	+	614607.i	−0.280563	+	0.863485i	0.707130	+	0.707083i	$0.249989\pi$
$47$	−199698.	+	614607.i	−0.280563	+	0.863485i	−0.987694	+	0.156402i	$0.950011\pi$
$48$	−81451.7	−	250683.i	−0.106306	−	0.327175i
$49$	310717.	−	225749.i	0.377293	−	0.274119i
$50$	491540.	−	357124.i	0.556114	−	0.404040i
$51$	311019.	+	957218.i	0.328315	+	1.01045i
$52$	152146.	−	468258.i	0.150055	−	0.461821i
$53$	−849513.	−	617208.i	−0.783799	−	0.569463i	0.122318	−	0.992491i	$-0.460967\pi$
$53$	−849513.	−	617208.i	−0.783799	−	0.569463i	−0.906117	+	0.423028i	$0.860967\pi$
$54$	119899.			0.103619
$55$	204260.	−	26838.1i	0.165544	−	0.0217511i
$56$	−339420.			−0.258273
$57$	1.42289e6	+	1.03379e6i	1.01767	+	0.739384i
$58$	228487.	−	703212.i	0.153767	−	0.473247i
$59$	571152.	+	1.75783e6i	0.362051	+	1.11428i	0.951807	+	0.306697i	$0.0992239\pi$
$59$	571152.	+	1.75783e6i	0.362051	+	1.11428i	−0.589756	+	0.807581i	$0.700776\pi$
$60$	155496.	−	112975.i	0.0929375	−	0.0675230i
$61$	777106.	−	564601.i	0.438355	−	0.318484i	−0.346626	−	0.938003i	$-0.612673\pi$
$61$	777106.	−	564601.i	0.438355	−	0.318484i	0.784981	+	0.619520i	$0.212673\pi$
$62$	804746.	+	2.47675e6i	0.428833	+	1.31981i
$63$	−400310.	+	1.23203e6i	−0.201699	+	0.620767i
$64$	−212079.	−	154084.i	−0.101127	−	0.0734732i
$65$	359024.			0.162154
$66$	−2.25323e6	+	296056.i	−0.964721	+	0.126757i
$67$	−1.19782e6			−0.486553			−0.243276	−	0.969957i	$-0.578222\pi$
$67$	−1.19782e6			−0.486553			−0.243276	+	0.969957i	$0.578222\pi$
$68$	809812.	+	588363.i	0.312322	+	0.226915i
$69$	300675.	−	925382.i	0.110186	−	0.339117i
$70$	−76482.9	−	235390.i	−0.0266515	−	0.0820248i
$71$	4.05030e6	−	2.94272e6i	1.34302	−	0.975762i	0.343695	−	0.939081i	$-0.388321\pi$
$71$	4.05030e6	−	2.94272e6i	1.34302	−	0.975762i	0.999327	−	0.0366810i	$-0.0116785\pi$
$72$	−809421.	+	588079.i	−0.255570	+	0.185683i
$73$	−1.85870e6	−	5.72050e6i	−0.559217	−	1.72109i	−0.684539	−	0.728977i	$-0.739996\pi$
$73$	−1.85870e6	−	5.72050e6i	−0.559217	−	1.72109i	0.125322	−	0.992116i	$-0.460004\pi$
$74$	172838.	−	531941.i	0.0495825	−	0.152599i
$75$	−3.95391e6	−	2.87268e6i	−1.08221	−	0.786272i
$76$	1.74918e6			0.457075
$77$	−534041.	+	2.87731e6i	−0.133308	+	0.718240i
$78$	−3.96047e6			−0.944966
$79$	−410136.	−	297981.i	−0.0935907	−	0.0679976i	0.540006	−	0.841661i	$-0.318422\pi$
$79$	−410136.	−	297981.i	−0.0935907	−	0.0679976i	−0.633596	+	0.773664i	$0.718422\pi$
$80$	59070.0	−	181799.i	0.0128989	−	0.0396987i
$81$	−1.61866e6	−	4.98171e6i	−0.338421	−	1.04155i
$82$	1.80941e6	−	1.31462e6i	0.362401	−	0.263300i
$83$	−6.60960e6	+	4.80216e6i	−1.26883	+	0.921856i	−0.999155	−	0.0410968i	$-0.986915\pi$
$83$	−6.60960e6	+	4.80216e6i	−1.26883	+	0.921856i	−0.269671	+	0.962953i	$0.586915\pi$
$84$	843699.	+	2.59664e6i	0.155314	+	0.478007i
$85$	−225556.	+	694189.i	−0.0398371	+	0.122606i
$86$	5.57543e6	+	4.05079e6i	0.945222	+	0.686744i
$87$	−5.94768e6			−0.968345
$88$	−1.63988e6	+	1.55539e6i	−0.256521	+	0.243304i
$89$	608839.			0.0915456			0.0457728	−	0.998952i	$-0.485425\pi$
$89$	608839.			0.0915456			0.0457728	+	0.998952i	$0.485425\pi$
$90$	−590227.	−	428825.i	−0.0853435	−	0.0620057i
$91$	−1.57597e6	+	4.85035e6i	−0.219232	+	0.674727i
$92$	−299033.	−	920329.i	−0.0400370	−	0.123221i
$93$	1.69474e7	−	1.23130e7i	2.18480	−	1.58735i
$94$	4.18252e6	−	3.03878e6i	0.519387	−	0.377357i
$95$	394151.	+	1.21307e6i	0.0471661	+	0.145162i
$96$	−651614.	+	2.00546e6i	−0.0751694	+	0.231347i
$97$	8.55176e6	+	6.21322e6i	0.951381	+	0.691218i	0.951133	−	0.308782i	$-0.0999212\pi$
$97$	8.55176e6	+	6.21322e6i	0.951381	+	0.691218i	0.000247580		1.00000i	$0.499921\pi$
$98$	−3.07254e6			−0.329766
$99$	3.71169e6	+	7.78686e6i	0.384458	+	0.806565i
$100$	−4.86061e6			−0.486061
$101$	1.33572e7	+	9.70455e6i	1.29000	+	0.937240i	0.999805	−	0.0197276i	$-0.00627991\pi$
$101$	1.33572e7	+	9.70455e6i	1.29000	+	0.937240i	0.290195	+	0.956968i	$0.406280\pi$
$102$	2.48815e6	−	7.65774e6i	0.232154	−	0.714497i
$103$	−5.14609e6	−	1.58380e7i	−0.464031	−	1.42814i	−0.860198	−	0.509961i	$-0.829660\pi$
$103$	−5.14609e6	−	1.58380e7i	−0.464031	−	1.42814i	0.396167	−	0.918179i	$-0.370340\pi$
$104$	−3.18660e6	+	2.31520e6i	−0.277786	+	0.201823i
$105$	−1.61067e6	+	1.17022e6i	−0.135783	+	0.0986521i
$106$	2.59588e6	+	7.98930e6i	0.211697	+	0.651536i
$107$	−3.01459e6	+	9.27795e6i	−0.237895	+	0.732164i	0.758830	+	0.651289i	$0.225772\pi$
$107$	−3.01459e6	+	9.27795e6i	−0.237895	+	0.732164i	−0.996724	+	0.0808752i	$0.974228\pi$
$108$	−776005.	−	563801.i	−0.0592764	−	0.0430668i
$109$	−9.09015e6			−0.672323			−0.336162	−	0.941804i	$-0.609129\pi$
$109$	−9.09015e6			−0.672323			−0.336162	+	0.941804i	$0.609129\pi$
$110$	−1.44820e6	−	786786.i	−0.103742	−	0.0563615i
$111$	−4.49909e6			−0.312244
$112$	2.19677e6	+	1.59605e6i	0.147748	+	0.107345i
$113$	−4.00988e6	+	1.23412e7i	−0.261431	+	0.804602i	0.731063	+	0.682310i	$0.239025\pi$
$113$	−4.00988e6	+	1.23412e7i	−0.261431	+	0.804602i	−0.992494	+	0.122292i	$0.960975\pi$
$114$	−4.34796e6	−	1.33816e7i	−0.274864	−	0.845946i
$115$	570873.	−	414763.i	0.0350023	−	0.0254307i
$116$	−4.78550e6	+	3.47687e6i	−0.284659	+	0.206817i
$117$	4.64546e6	+	1.42972e7i	0.268150	+	0.825281i
$118$	4.56922e6	−	1.40626e7i	0.256009	−	0.787914i
$119$	−8.38826e6	−	6.09443e6i	−0.456307	−	0.331527i
$120$	−1.53763e6			−0.0812303
$121$	1.06051e7	+	1.63488e7i	0.544209	+	0.838949i
$122$	−7.68445e6			−0.383136
$123$	−1.45548e7	−	1.05747e7i	−0.705241	−	0.512388i
$124$	6.43797e6	−	1.98140e7i	0.303231	−	0.933248i
$125$	−2.22193e6	−	6.83841e6i	−0.101753	−	0.313163i
$126$	8.38421e6	−	6.09148e6i	0.373392	−	0.271285i
$127$	−1.02339e6	+	743536.i	−0.0443331	+	0.0322099i	−0.609731	−	0.792608i	$-0.708723\pi$
$127$	−1.02339e6	+	743536.i	−0.0443331	+	0.0322099i	0.565398	+	0.824818i	$0.308723\pi$
$128$	648056.	+	1.99451e6i	0.0273135	+	0.0840623i
$129$	1.71305e7	−	5.27224e7i	0.702598	−	2.16237i
$130$	−2.32366e6	−	1.68823e6i	−0.0927620	−	0.0673955i
$131$	−1.37648e7			−0.534958			−0.267479	−	0.963564i	$-0.586191\pi$
$131$	−1.37648e7			−0.534958			−0.267479	+	0.963564i	$0.586191\pi$
$132$	1.59753e7	+	8.67921e6i	0.604563	+	0.328451i
$133$	−1.81185e7			−0.667793
$134$	7.75245e6	+	5.63249e6i	0.278338	+	0.202224i
$135$	216140.	−	665209.i	0.00756077	−	0.0232697i
$136$	−2.47457e6	−	7.61593e6i	−0.0843554	−	0.259619i
$137$	3.27915e6	−	2.38244e6i	0.108953	−	0.0791590i	−0.531975	−	0.846760i	$-0.678550\pi$
$137$	3.27915e6	−	2.38244e6i	0.108953	−	0.0791590i	0.640928	+	0.767601i	$0.278550\pi$
$138$	−6.29741e6	+	4.57534e6i	−0.203979	+	0.148199i
$139$	1.64965e7	+	5.07711e7i	0.521004	+	1.60349i	0.772085	+	0.635519i	$0.219214\pi$
$139$	1.64965e7	+	5.07711e7i	0.521004	+	1.60349i	−0.251081	+	0.967966i	$0.580786\pi$
$140$	−611864.	+	1.88312e6i	−0.0188454	+	0.0580003i
$141$	−3.36439e7	−	2.44437e7i	−1.01074	−	0.734346i
$142$	−4.00516e7			−1.17384
$143$	1.46125e7	+	3.06560e7i	0.417877	+	0.876675i
$144$	8.00399e6			0.223377
$145$	−3.48957e6	−	2.53532e6i	−0.0950570	−	0.0690630i
$146$	−1.48696e7	+	4.57640e7i	−0.395426	+	1.21700i
$147$	7.63743e6	+	2.35056e7i	0.198306	+	0.610324i
$148$	−3.61997e6	+	2.63006e6i	−0.0917886	+	0.0666883i
$149$	3.54889e7	−	2.57842e7i	0.878902	−	0.638560i	−0.0540588	−	0.998538i	$-0.517216\pi$
$149$	3.54889e7	−	2.57842e7i	0.878902	−	0.638560i	0.932961	+	0.359978i	$0.117216\pi$
$150$	1.20821e7	+	3.71848e7i	0.292295	+	0.899592i
$151$	2.35137e7	−	7.23679e7i	0.555779	−	1.71051i	−0.138097	−	0.990419i	$-0.544098\pi$
$151$	2.35137e7	−	7.23679e7i	0.555779	−	1.71051i	0.693876	−	0.720094i	$-0.255902\pi$
$152$	−1.13209e7	−	8.22515e6i	−0.261475	−	0.189973i
$153$	−3.05628e7			−0.689880
$154$	1.69863e7	−	1.61112e7i	0.374781	−	0.355471i
$155$	1.51919e7			0.327680
$156$	2.56327e7	+	1.86233e7i	0.540578	+	0.392753i
$157$	−1.45880e7	+	4.48974e7i	−0.300849	+	0.925917i	0.680345	+	0.732892i	$0.261830\pi$
$157$	−1.45880e7	+	4.48974e7i	−0.300849	+	0.925917i	−0.981194	+	0.193025i	$0.938170\pi$
$158$	1.25326e6	+	3.85715e6i	0.0252780	+	0.0777976i
$159$	5.46674e7	−	3.97182e7i	1.07854	−	0.783609i
$160$	−1.23718e6	+	898863.i	−0.0238788	+	0.0173490i
$161$	3.09747e6	+	9.53302e6i	0.0584946	+	0.180028i
$162$	−1.29492e7	+	3.98537e7i	−0.239300	+	0.736488i
$163$	−1.56352e7	−	1.13596e7i	−0.282779	−	0.205451i	0.437350	−	0.899291i	$-0.355917\pi$
$163$	−1.56352e7	−	1.13596e7i	−0.282779	−	0.205451i	−0.720128	+	0.693841i	$0.755917\pi$
$164$	−1.78925e7			−0.316750
$165$	−2.41930e6	+	1.30347e7i	−0.0419272	+	0.225896i
$166$	6.53593e7			1.10899
$167$	1.98729e7	+	1.44385e7i	0.330182	+	0.239891i	0.740508	−	0.672048i	$-0.234585\pi$
$167$	1.98729e7	+	1.44385e7i	0.330182	+	0.239891i	−0.410326	+	0.911939i	$0.634585\pi$
$168$	6.74959e6	−	2.07731e7i	0.109823	−	0.338002i
$169$	−1.10174e6	−	3.39080e6i	−0.0175580	−	0.0540380i
$170$	4.72410e6	−	3.43226e6i	0.0737476	−	0.0535808i
$171$	−4.32076e7	+	3.13921e7i	−0.660805	+	0.480103i
$172$	−1.70370e7	−	5.24345e7i	−0.255296	−	0.785720i
$173$	4.96854e6	−	1.52916e7i	0.0729571	−	0.224539i	−0.907928	−	0.419126i	$-0.862337\pi$
$173$	4.96854e6	−	1.52916e7i	0.0729571	−	0.224539i	0.980885	+	0.194587i	$0.0623366\pi$
$174$	3.84942e7	+	2.79677e7i	0.553953	+	0.402470i
$175$	5.03475e7			0.710142
$176$	1.79274e7	−	2.35552e6i	0.247870	−	0.0325681i
$177$	−1.18940e8			−1.61221
$178$	−3.94049e6	−	2.86293e6i	−0.0523697	−	0.0380488i
$179$	2.49535e7	−	7.67991e7i	0.325197	−	1.00085i	−0.646155	−	0.763207i	$-0.723624\pi$
$179$	2.49535e7	−	7.67991e7i	0.325197	−	1.00085i	0.971352	−	0.237647i	$-0.0763761\pi$
$180$	1.80357e6	+	5.55083e6i	0.0230505	+	0.0709421i
$181$	−4.97413e7	+	3.61392e7i	−0.623508	+	0.453005i	−0.854145	−	0.520035i	$-0.825919\pi$
$181$	−4.97413e7	+	3.61392e7i	−0.623508	+	0.453005i	0.230637	+	0.973040i	$0.425919\pi$
$182$	3.30076e7	−	2.39814e7i	0.405849	−	0.294867i
$183$	1.91013e7	+	5.87878e7i	0.230401	+	0.709101i
$184$	−2.39226e6	+	7.36263e6i	−0.0283104	+	0.0871306i
$185$	−2.63967e6	−	1.91783e6i	−0.0306513	−	0.0222695i
$186$	−1.67585e8			−1.90959
$187$	−6.84549e7	+	8.99441e6i	−0.765524	+	0.100584i
$188$	−4.13591e7			−0.453961
$189$	8.03808e6	+	5.84001e6i	0.0866036	+	0.0629212i
$190$	3.15321e6	−	9.70457e6i	0.0333515	−	0.102645i
$191$	−4.40152e7	−	1.35465e8i	−0.457074	−	1.40673i	−0.868683	−	0.495368i	$-0.835033\pi$
$191$	−4.40152e7	−	1.35465e8i	−0.457074	−	1.40673i	0.411610	−	0.911360i	$-0.364967\pi$
$192$	1.36476e7	−	9.91554e6i	0.139156	−	0.101103i
$193$	−3.30071e7	+	2.39811e7i	−0.330489	+	0.240114i	−0.740638	−	0.671904i	$-0.765477\pi$
$193$	−3.30071e7	+	2.39811e7i	−0.330489	+	0.240114i	0.410149	+	0.912019i	$0.365477\pi$
$194$	−2.61318e7	−	8.04255e7i	−0.256959	−	0.790839i
$195$	−7.13944e6	+	2.19729e7i	−0.0689514	+	0.212211i
$196$	1.98859e7	+	1.44479e7i	0.188646	+	0.137060i
$197$	1.24454e8			1.15978			0.579892	−	0.814694i	$-0.303095\pi$
$197$	1.24454e8			1.15978			0.579892	+	0.814694i	$0.303095\pi$
$198$	1.25934e7	−	6.78511e7i	0.115296	−	0.621196i
$199$	2.16245e7			0.194518			0.0972592	−	0.995259i	$-0.468992\pi$
$199$	2.16245e7			0.194518			0.0972592	+	0.995259i	$0.468992\pi$
$200$	3.14585e7	+	2.28560e7i	0.278057	+	0.202020i
$201$	2.38195e7	−	7.33087e7i	0.206893	−	0.636751i
$202$	−4.08159e7	−	1.25618e8i	−0.348417	−	1.07232i
$203$	4.95695e7	−	3.60144e7i	0.415890	−	0.302162i
$204$	−5.21125e7	+	3.78620e7i	−0.429770	+	0.312247i
$205$	−4.03178e6	−	1.24086e7i	−0.0326858	−	0.100596i
$206$	−4.11687e7	+	1.26704e8i	−0.328119	+	1.00985i
$207$	2.39035e7	+	1.73669e7i	0.187312	+	0.136090i
$208$	3.15108e7			0.242794
$209$	−8.75382e7	+	8.30280e7i	−0.663262	+	0.629090i
$210$	1.59272e7			0.118679
$211$	−1.69714e7	−	1.23304e7i	−0.124374	−	0.0903628i	0.523859	−	0.851805i	$-0.324492\pi$
$211$	−1.69714e7	−	1.23304e7i	−0.124374	−	0.0903628i	−0.648233	+	0.761442i	$0.724492\pi$
$212$	2.07671e7	−	6.39144e7i	0.149692	−	0.460706i
$213$	9.95566e7	+	3.06404e8i	0.705897	+	2.17253i
$214$	6.31383e7	−	4.58727e7i	0.440398	−	0.319968i
$215$	3.25247e7	−	2.36306e7i	0.223192	−	0.162158i
$216$	2.37126e6	+	7.29799e6i	0.0160100	+	0.0492737i
$217$	−6.66863e7	+	2.05239e8i	−0.443024	+	1.36349i
$218$	5.88327e7	+	4.27444e7i	0.384610	+	0.279436i
$219$	3.87067e8			2.49018
$220$	5.67323e6	+	1.19020e7i	0.0359212	+	0.0753600i
$221$	−1.20322e8			−0.749848
$222$	2.91188e7	+	2.11560e7i	0.178623	+	0.129777i
$223$	−1.01635e8	+	3.12800e8i	−0.613727	+	1.88886i	−0.194778	+	0.980847i	$0.562399\pi$
$223$	−1.01635e8	+	3.12800e8i	−0.613727	+	1.88886i	−0.418949	+	0.908010i	$0.637601\pi$
$224$	−6.71274e6	−	2.06597e7i	−0.0399054	−	0.122816i
$225$	1.20065e8	−	8.72321e7i	0.702711	−	0.510549i
$226$	8.39841e7	−	6.10180e7i	0.483969	−	0.351624i
$227$	−6.76118e7	−	2.08088e8i	−0.383647	−	1.18074i	−0.937457	−	0.348101i	$-0.886827\pi$
$227$	−6.76118e7	−	2.08088e8i	−0.383647	−	1.18074i	0.553810	−	0.832643i	$-0.313173\pi$
$228$	−3.47837e7	+	1.07053e8i	−0.194358	+	0.598174i
$229$	8.58949e7	+	6.24063e7i	0.472654	+	0.343403i	0.798475	−	0.602029i	$-0.205641\pi$
$229$	8.58949e7	+	6.24063e7i	0.472654	+	0.343403i	−0.325821	+	0.945431i	$0.605641\pi$
$230$	−5.64510e6			−0.0305931
$231$	−1.65477e8	−	8.99016e7i	−0.883275	−	0.479872i
$232$	4.73216e7			0.248801
$233$	−2.42929e8	−	1.76498e8i	−1.25815	−	0.914102i	−0.259488	−	0.965746i	$-0.583554\pi$
$233$	−2.42929e8	−	1.76498e8i	−1.25815	−	0.914102i	−0.998666	+	0.0516439i	$0.983554\pi$
$234$	3.71637e7	−	1.14378e8i	0.189611	−	0.583562i
$235$	−9.31962e6	−	2.86828e7i	−0.0468447	−	0.144173i
$236$	−9.56989e7	+	6.95294e7i	−0.473931	+	0.344331i
$237$	2.63928e7	−	1.91755e7i	0.128785	−	0.0935680i
$238$	2.56322e7	+	7.88879e7i	0.123244	+	0.379307i
$239$	2.35874e7	−	7.25947e7i	0.111760	−	0.343963i	−0.879497	−	0.475904i	$-0.842121\pi$
$239$	2.35874e7	−	7.25947e7i	0.111760	−	0.343963i	0.991258	+	0.131941i	$0.0421209\pi$
$240$	9.95177e6	+	7.23038e6i	0.0464687	+	0.0337615i
$241$	5.09450e7			0.234445			0.117223	−	0.993106i	$-0.462601\pi$
$241$	5.09450e7			0.234445			0.117223	+	0.993106i	$0.462601\pi$
$242$	8.23879e6	−	1.55680e8i	0.0373689	−	0.706119i
$243$	3.04300e8			1.36044
$244$	4.97348e7	+	3.61344e7i	0.219177	+	0.159242i
$245$	−5.53878e6	+	1.70466e7i	−0.0240621	+	0.0740555i
$246$	4.44755e7	+	1.36881e8i	0.190479	+	0.586235i
$247$	−1.70103e8	+	1.23587e8i	−0.718245	+	0.521836i
$248$	−1.34839e8	+	9.79660e7i	−0.561349	+	0.407844i
$249$	−1.62464e8	−	5.00014e8i	−0.666899	−	2.05250i
$250$	−1.77755e7	+	5.47073e7i	−0.0719500	+	0.221439i
$251$	−2.92702e8	−	2.12661e8i	−1.16834	−	0.848846i	−0.177528	−	0.984116i	$-0.556810\pi$
$251$	−2.92702e8	−	2.12661e8i	−1.16834	−	0.848846i	−0.990809	+	0.135270i	$0.956810\pi$
$252$	−8.29076e7			−0.326357
$253$	5.86502e7	+	3.18639e7i	0.227692	+	0.123702i
$254$	1.01198e7			0.0387485
$255$	−3.80003e7	−	2.76088e7i	−0.143515	−	0.104270i
$256$	5.18444e6	−	1.59561e7i	0.0193136	−	0.0594410i
$257$	3.46749e7	+	1.06718e8i	0.127423	+	0.392169i	0.994335	−	0.106294i	$-0.0338983\pi$
$257$	3.46749e7	+	1.06718e8i	0.127423	+	0.392169i	−0.866912	+	0.498462i	$0.833898\pi$
$258$	−3.58787e8	+	2.60674e8i	−1.30067	+	0.944993i
$259$	3.74966e7	−	2.72429e7i	0.134104	−	0.0974326i
$260$	7.10046e6	+	2.18530e7i	0.0250541	+	0.0771087i
$261$	5.58109e7	−	1.71768e8i	0.194302	−	0.598000i
$262$	8.90874e7	+	6.47258e7i	0.306029	+	0.222343i
$263$	4.50529e7			0.152713			0.0763567	−	0.997081i	$-0.475671\pi$
$263$	4.50529e7			0.152713			0.0763567	+	0.997081i	$0.475671\pi$
$264$	−6.25826e7	−	1.31294e8i	−0.209334	−	0.439167i
$265$	4.90047e7			0.161762
$266$	1.17266e8	+	8.51984e7i	0.382019	+	0.277553i
$267$	−1.21072e7	+	3.72620e7i	−0.0389272	+	0.119806i
$268$	−2.36894e7	−	7.29084e7i	−0.0751765	−	0.231369i
$269$	−1.10615e8	+	8.03668e7i	−0.346484	+	0.251735i	−0.747392	−	0.664383i	$-0.768694\pi$
$269$	−1.10615e8	+	8.03668e7i	−0.346484	+	0.251735i	0.400909	+	0.916118i	$0.368694\pi$
$270$	−4.52689e6	+	3.28898e6i	−0.0139967	+	0.0101692i
$271$	2.13371e7	+	6.56688e7i	0.0651243	+	0.200432i	0.978324	−	0.207081i	$-0.0663963\pi$
$271$	2.13371e7	+	6.56688e7i	0.0651243	+	0.200432i	−0.913200	+	0.407513i	$0.866396\pi$
$272$	−1.97965e7	+	6.09274e7i	−0.0596483	+	0.183578i
$273$	−2.65511e8	−	1.92905e8i	−0.789792	−	0.573818i
$274$	−3.24260e7			−0.0952284
$275$	2.43250e8	−	2.30717e8i	0.705324	−	0.668984i
$276$	6.22723e7			0.178284
$277$	−1.36711e8	−	9.93265e7i	−0.386478	−	0.280793i	0.377533	−	0.925996i	$-0.376773\pi$
$277$	−1.36711e8	−	9.93265e7i	−0.386478	−	0.280793i	−0.764011	+	0.645203i	$0.776773\pi$
$278$	1.31972e8	−	4.06169e8i	0.368405	−	1.13384i
$279$	1.96569e8	+	6.04978e8i	0.541877	+	1.66773i
$280$	1.28150e7	−	9.31067e6i	0.0348872	−	0.0253471i
$281$	3.99435e8	−	2.90207e8i	1.07393	−	0.780253i	0.0973118	−	0.995254i	$-0.468976\pi$
$281$	3.99435e8	−	2.90207e8i	1.07393	−	0.780253i	0.976614	+	0.215001i	$0.0689756\pi$
$282$	1.02807e8	+	3.16406e8i	0.272992	+	0.840182i
$283$	2.85481e7	−	8.78619e7i	0.0748728	−	0.230435i	−0.906615	−	0.421958i	$-0.861343\pi$
$283$	2.85481e7	−	8.78619e7i	0.0748728	−	0.230435i	0.981488	+	0.191523i	$0.0613428\pi$
$284$	2.59219e8	+	1.88334e8i	0.671511	+	0.487881i
$285$	−8.20801e7			−0.210030
$286$	4.95789e7	−	2.67122e8i	0.125319	−	0.675193i
$287$	1.85335e8			0.462776
$288$	−5.18029e7	−	3.76370e7i	−0.127785	−	0.0928414i
$289$	−5.12096e7	+	1.57607e8i	−0.124798	+	0.384090i
$290$	1.06632e7	+	3.28179e7i	0.0256740	+	0.0790165i
$291$	−5.50317e8	+	3.99829e8i	−1.30915	+	0.951150i
$292$	3.11434e8	−	2.26270e8i	0.732024	−	0.531847i
$293$	−4.95767e6	−	1.52581e7i	−0.0115144	−	0.0354377i	0.945134	−	0.326682i	$-0.105931\pi$
$293$	−4.95767e6	−	1.52581e7i	−0.0115144	−	0.0354377i	−0.956649	+	0.291245i	$0.905931\pi$
$294$	6.10995e7	−	1.88045e8i	0.140224	−	0.431565i
$295$	−6.97834e7	−	5.07006e7i	−0.158261	−	0.114984i
$296$	3.57962e7			0.0802262
$297$	6.55971e7	−	8.61893e6i	0.145290	−	0.0190900i
$298$	−3.50933e8			−0.768188
$299$	9.41052e7	+	6.83714e7i	0.203594	+	0.147920i
$300$	9.66565e7	−	2.97478e8i	0.206684	−	0.636108i
$301$	1.76474e8	+	5.43131e8i	0.372991	+	1.14795i
$302$	−4.92478e8	+	3.57806e8i	−1.02888	+	0.747522i
$303$	−8.59553e8	+	6.24501e8i	−1.77510	+	1.28969i
$304$	3.45937e7	+	1.06469e8i	0.0706220	+	0.217352i
$305$	−1.38526e7	+	4.26338e7i	−0.0279563	+	0.0860408i
$306$	1.97807e8	+	1.43715e8i	0.394654	+	0.286733i
$307$	4.87741e8			0.962066			0.481033	−	0.876703i	$-0.340262\pi$
$307$	4.87741e8			0.962066			0.481033	+	0.876703i	$0.340262\pi$
$308$	−1.85697e8	+	2.43991e7i	−0.362141	+	0.0475824i
$309$	1.07165e9			2.06632
$310$	−9.83239e7	−	7.14365e7i	−0.187453	−	0.136193i
$311$	−2.22745e8	+	6.85539e8i	−0.419901	+	1.29232i	0.487892	+	0.872904i	$0.337766\pi$
$311$	−2.22745e8	+	6.85539e8i	−0.419901	+	1.29232i	−0.907793	+	0.419418i	$0.862234\pi$
$312$	−7.83266e7	−	2.41065e8i	−0.146005	−	0.449358i
$313$	−1.89881e8	+	1.37956e8i	−0.350006	+	0.254295i	−0.748872	−	0.662715i	$-0.769404\pi$
$313$	−1.89881e8	+	1.37956e8i	−0.350006	+	0.254295i	0.398865	+	0.917010i	$0.369404\pi$
$314$	3.05536e8	−	2.21985e8i	0.556940	−	0.404641i
$315$	−1.86819e7	−	5.74970e7i	−0.0336771	−	0.103647i
$316$	1.00261e7	−	3.08572e7i	0.0178742	−	0.0550112i
$317$	5.35521e8	+	3.89079e8i	0.944212	+	0.686010i	0.949431	−	0.313976i	$-0.101661\pi$
$317$	5.35521e8	+	3.89079e8i	0.944212	+	0.686010i	−0.00521915	+	0.999986i	$0.501661\pi$
$318$	−5.40581e8			−0.942683
$319$	7.44555e7	−	4.01153e8i	0.128419	−	0.691898i
$320$	1.22339e7			0.0208708
$321$	−5.07880e8	−	3.68996e8i	−0.857025	−	0.622665i
$322$	2.47797e7	−	7.62642e7i	0.0413620	−	0.127299i
$323$	−1.32094e8	−	4.06545e8i	−0.218110	−	0.671273i
$324$	2.71212e8	−	1.97047e8i	0.442998	−	0.321857i
$325$	4.72681e8	−	3.43423e8i	0.763794	−	0.554929i
$326$	4.77769e7	+	1.47042e8i	0.0763759	+	0.235061i
$327$	1.80764e8	−	5.56333e8i	0.285887	−	0.879869i
$328$	1.15802e8	+	8.41354e7i	0.181200	+	0.131650i
$329$	4.28409e8			0.663243
$330$	7.69511e7	−	7.29864e7i	0.117873	−	0.111800i
$331$	−1.40023e8			−0.212227			−0.106113	−	0.994354i	$-0.533841\pi$
$331$	−1.40023e8			−0.212227			−0.106113	+	0.994354i	$0.533841\pi$
$332$	−4.23015e8	−	3.07338e8i	−0.634413	−	0.460928i
$333$	4.22179e7	−	1.29933e8i	0.0626530	−	0.192826i
$334$	−6.07261e7	−	1.86896e8i	−0.0891790	−	0.274465i
$335$	4.52245e7	−	3.28575e7i	0.0657230	−	0.0477505i
$336$	−1.41365e8	+	1.02708e8i	−0.203308	+	0.147712i
$337$	−3.45614e8	−	1.06369e9i	−0.491911	−	1.51395i	−0.821716	−	0.569897i	$-0.806983\pi$
$337$	−3.45614e8	−	1.06369e9i	−0.491911	−	1.51395i	0.329806	−	0.944049i	$-0.393017\pi$
$338$	−8.81391e6	+	2.71264e7i	−0.0124154	+	0.0382106i
$339$	−6.75562e8	−	4.90824e8i	−0.941816	−	0.684269i
$340$	−4.67145e7			−0.0644578
$341$	6.18318e8	+	1.29719e9i	0.844446	+	1.77158i
$342$	4.27260e8			0.577565
$343$	−6.47667e8	−	4.70558e8i	−0.866608	−	0.629627i
$344$	−1.36296e8	+	4.19476e8i	−0.180521	+	0.555588i
$345$	1.40321e7	+	4.31863e7i	0.0183973	+	0.0566212i
$346$	−1.04062e8	+	7.56058e7i	−0.135060	+	0.0981271i
$347$	−8.82931e8	+	6.41487e8i	−1.13442	+	0.824204i	−0.986332	−	0.164771i	$-0.947312\pi$
$347$	−8.82931e8	+	6.41487e8i	−1.13442	+	0.824204i	−0.148087	+	0.988974i	$0.547312\pi$
$348$	−1.17628e8	−	3.62021e8i	−0.149618	−	0.460476i
$349$	−8.93081e7	+	2.74862e8i	−0.112461	+	0.346119i	−0.991409	−	0.130798i	$-0.958246\pi$
$349$	−8.93081e7	+	2.74862e8i	−0.112461	+	0.346119i	0.878948	+	0.476918i	$0.158246\pi$
$350$	−3.25856e8	−	2.36748e8i	−0.406245	−	0.295154i
$351$	1.15299e8			0.142315
$352$	−1.27105e8	−	6.90545e7i	−0.155333	−	0.0843903i
$353$	−1.22512e9			−1.48241			−0.741204	−	0.671279i	$-0.765745\pi$
$353$	−1.22512e9			−1.48241			−0.741204	+	0.671279i	$0.765745\pi$
$354$	7.69795e8	+	5.59289e8i	0.922282	+	0.670077i
$355$	−7.21999e7	+	2.22209e8i	−0.0856520	+	0.263610i
$356$	1.20411e7	+	3.70586e7i	0.0141446	+	0.0435325i
$357$	5.39796e8	−	3.92185e8i	0.627901	−	0.456196i
$358$	−5.22634e8	+	3.79716e8i	−0.602014	+	0.437389i
$359$	5.74309e7	+	1.76754e8i	0.0655112	+	0.201623i	0.978454	−	0.206465i	$-0.0661959\pi$
$359$	5.74309e7	+	1.76754e8i	0.0655112	+	0.201623i	−0.912943	+	0.408087i	$0.866196\pi$
$360$	1.44286e7	−	4.44066e7i	0.0162992	−	0.0501636i
$361$	1.18836e8	+	8.63393e7i	0.132945	+	0.0965902i
$362$	4.91869e8			0.544966
$363$	−1.21146e9	+	3.23945e8i	−1.32934	+	0.355466i
$364$	−3.26397e8			−0.354725
$365$	2.27096e8	+	1.64995e8i	0.244447	+	0.177601i
$366$	1.52810e8	−	4.70302e8i	0.162918	−	0.501410i
$367$	−5.49861e8	−	1.69230e9i	−0.580659	−	1.78709i	−0.616044	−	0.787712i	$-0.711265\pi$
$367$	−5.49861e8	−	1.69230e9i	−0.580659	−	1.78709i	0.0353842	−	0.999374i	$-0.488735\pi$
$368$	5.01042e7	−	3.64029e7i	0.0524091	−	0.0380775i
$369$	4.41972e8	−	3.21111e8i	0.457933	−	0.332708i
$370$	8.06611e6	+	2.48249e7i	0.00827863	+	0.0254790i
$371$	−2.15111e8	+	6.62043e8i	−0.218703	+	0.673097i
$372$	1.08463e9	+	7.88031e8i	1.09240	+	0.793675i
$373$	1.37112e8			0.136802			0.0684011	−	0.997658i	$-0.478210\pi$
$373$	1.37112e8			0.136802			0.0684011	+	0.997658i	$0.478210\pi$
$374$	4.85343e8	+	2.63681e8i	0.479732	+	0.260632i
$375$	4.62707e8			0.453103
$376$	2.67682e8	+	1.94482e8i	0.259693	+	0.188678i
$377$	2.19721e8	−	6.76232e8i	0.211192	−	0.649981i
$378$	−2.45622e7	−	7.55946e7i	−0.0233908	−	0.0719896i
$379$	1.57355e9	−	1.14325e9i	1.48472	−	1.07871i	0.508718	−	0.860933i	$-0.330120\pi$
$379$	1.57355e9	−	1.14325e9i	1.48472	−	1.07871i	0.975999	−	0.217777i	$-0.0698804\pi$
$380$	−6.60416e7	+	4.79820e7i	−0.0617412	+	0.0448576i
$381$	−2.51550e7	−	7.74190e7i	−0.0233016	−	0.0717150i
$382$	−3.52122e8	+	1.08372e9i	−0.323200	+	0.994707i
$383$	1.33359e9	+	9.68910e8i	1.21290	+	0.881227i	0.995491	−	0.0948527i	$-0.0302380\pi$
$383$	1.33359e9	+	9.68910e8i	1.21290	+	0.881227i	0.217413	+	0.976080i	$0.430238\pi$
$384$	−1.34955e8			−0.121627
$385$	−5.87649e7	−	1.23284e8i	−0.0524814	−	0.110102i
$386$	3.26393e8			0.288858
$387$	1.36187e9	+	9.89456e8i	1.19439	+	0.867777i
$388$	−2.09055e8	+	6.43404e8i	−0.181698	+	0.559207i
$389$	1.82011e8	+	5.60171e8i	0.156774	+	0.482500i	0.998336	−	0.0576599i	$-0.0183639\pi$
$389$	1.82011e8	+	5.60171e8i	0.156774	+	0.482500i	−0.841563	+	0.540160i	$0.818364\pi$
$390$	1.49530e8	−	1.08640e8i	0.127645	−	0.0927394i
$391$	−1.91320e8	+	1.39002e8i	−0.161861	+	0.117599i
$392$	−6.07659e7	−	1.87018e8i	−0.0509517	−	0.156813i
$393$	2.73722e8	−	8.42429e8i	0.227476	−	0.700099i
$394$	−8.05483e8	−	5.85217e8i	−0.663467	−	0.482037i
$395$	2.36589e7			0.0193154
$396$	−4.00561e8	+	3.79923e8i	−0.324142	+	0.307442i
$397$	−1.18729e9			−0.952340			−0.476170	−	0.879353i	$-0.657975\pi$
$397$	−1.18729e9			−0.952340			−0.476170	+	0.879353i	$0.657975\pi$
$398$	−1.39957e8	−	1.01685e8i	−0.111277	−	0.0808471i
$399$	3.60299e8	−	1.10889e9i	0.283960	−	0.873940i
$400$	−9.61287e7	−	2.95854e8i	−0.0751006	−	0.231136i
$401$	−3.57933e8	+	2.60054e8i	−0.277202	+	0.201399i	−0.717696	−	0.696356i	$-0.754803\pi$
$401$	−3.57933e8	+	2.60054e8i	−0.277202	+	0.201399i	0.440494	+	0.897756i	$0.354803\pi$
$402$	−4.98881e8	+	3.62458e8i	−0.383006	+	0.278270i
$403$	7.73870e8	+	2.38173e9i	0.588980	+	1.81269i
$404$	−3.26527e8	+	1.00495e9i	−0.246368	+	0.758243i
$405$	1.97767e8	+	1.43686e8i	0.147932	+	0.107479i
$406$	−4.90171e8			−0.363501
$407$	5.63215e7	−	3.03450e8i	0.0414089	−	0.223104i
$408$	5.15317e8			0.375633
$409$	−1.69436e7	−	1.23103e7i	−0.0122454	−	0.00889684i	0.581646	−	0.813442i	$-0.302409\pi$
$409$	−1.69436e7	−	1.23103e7i	−0.0122454	−	0.00889684i	−0.593891	+	0.804545i	$0.702409\pi$
$410$	−3.22543e7	+	9.92685e7i	−0.0231123	+	0.0711325i
$411$	8.06016e7	+	2.48066e8i	0.0572661	+	0.176247i
$412$	8.62248e8	−	6.26460e8i	0.607424	−	0.441319i
$413$	9.91276e8	−	7.20204e8i	0.692420	−	0.503072i
$414$	−7.30426e7	−	2.24802e8i	−0.0505912	−	0.155704i
$415$	1.17822e8	−	3.62617e8i	0.0809201	−	0.249046i
$416$	−2.03942e8	−	1.48173e8i	−0.138893	−	0.100912i
$417$	−3.43533e9			−2.32002
$418$	9.56980e8	−	1.25739e8i	0.640893	−	0.0842082i
$419$	−2.00155e9			−1.32928			−0.664642	−	0.747162i	$-0.731416\pi$
$419$	−2.00155e9			−1.32928			−0.664642	+	0.747162i	$0.731416\pi$
$420$	−1.03083e8	−	7.48943e7i	−0.0678915	−	0.0493260i
$421$	−7.98203e7	+	2.45662e8i	−0.0521346	+	0.160454i	−0.973734	−	0.227689i	$-0.926883\pi$
$421$	−7.98203e7	+	2.45662e8i	−0.0521346	+	0.160454i	0.921599	+	0.388142i	$0.126883\pi$
$422$	5.18599e7	+	1.59608e8i	0.0335922	+	0.103386i
$423$	1.02163e9	−	7.42261e8i	0.656303	−	0.476832i
$424$	−4.34951e8	+	3.16010e8i	−0.277115	+	0.201336i
$425$	3.67062e8	+	1.12970e9i	0.231942	+	0.713843i
$426$	7.96452e8	−	2.45123e9i	0.499144	−	1.53621i
$427$	−5.15167e8	−	3.74291e8i	−0.320221	−	0.232654i
$428$	−6.24346e8			−0.384922
$429$	−2.16678e9	+	2.84697e8i	−1.32499	+	0.174094i
$430$	−3.21622e8			−0.195077
$431$	−6.87037e8	−	4.99162e8i	−0.413342	−	0.300311i	0.361611	−	0.932329i	$-0.382227\pi$
$431$	−6.87037e8	−	4.99162e8i	−0.413342	−	0.300311i	−0.774954	+	0.632018i	$0.782227\pi$
$432$	1.89701e7	−	5.83839e7i	0.0113208	−	0.0348418i
$433$	−5.06723e8	−	1.55953e9i	−0.299960	−	0.923181i	−0.981510	−	0.191410i	$-0.938694\pi$
$433$	−5.06723e8	−	1.55953e9i	−0.299960	−	0.923181i	0.681551	−	0.731771i	$-0.261306\pi$
$434$	1.39670e9	−	1.01476e9i	0.820139	−	0.595866i
$435$	2.24559e8	−	1.63152e8i	0.130803	−	0.0950339i
$436$	−1.79777e8	−	5.53295e8i	−0.103880	−	0.319709i
$437$	−1.27701e8	+	3.93023e8i	−0.0731997	+	0.225286i
$438$	−2.50515e9	−	1.82010e9i	−1.42454	−	1.03499i
$439$	1.73535e9			0.978954			0.489477	−	0.872016i	$-0.337188\pi$
$439$	1.73535e9			0.978954			0.489477	+	0.872016i	$0.337188\pi$
$440$	1.92487e7	−	1.03709e8i	0.0107725	−	0.0580404i
$441$	−7.50506e8			−0.416696
$442$	7.78742e8	+	5.65789e8i	0.428959	+	0.311657i
$443$	1.05749e8	−	3.25463e8i	0.0577916	−	0.177864i	−0.917994	−	0.396595i	$-0.870192\pi$
$443$	1.05749e8	−	3.25463e8i	0.0577916	−	0.177864i	0.975785	+	0.218731i	$0.0701917\pi$
$444$	−8.89790e7	−	2.73849e8i	−0.0482444	−	0.148481i
$445$	−2.29871e7	+	1.67011e7i	−0.0123659	+	0.00898433i
$446$	2.12867e9	−	1.54657e9i	1.13615	−	0.825461i
$447$	8.72318e8	+	2.68472e9i	0.461954	+	1.42175i
$448$	−5.37019e7	+	1.65277e8i	−0.0282174	+	0.0868442i
$449$	−2.05961e9	−	1.49640e9i	−1.07380	−	0.780161i	−0.0972080	−	0.995264i	$-0.530991\pi$
$449$	−2.05961e9	−	1.49640e9i	−1.07380	−	0.780161i	−0.976591	+	0.215103i	$0.930991\pi$
$450$	−1.18726e9			−0.614192
$451$	8.95431e8	−	8.49297e8i	0.459636	−	0.435955i
$452$	−8.30480e8			−0.423004
$453$	3.96146e9	+	2.87817e9i	2.00222	+	1.45470i
$454$	−5.40894e8	+	1.66470e9i	−0.271279	+	0.834912i
$455$	−7.35485e7	−	2.26359e8i	−0.0366045	−	0.112657i
$456$	7.28519e8	−	5.29300e8i	0.359802	−	0.261412i
$457$	−6.12009e8	+	4.44651e8i	−0.299952	+	0.217928i	−0.727573	−	0.686030i	$-0.759352\pi$
$457$	−6.12009e8	+	4.44651e8i	−0.299952	+	0.217928i	0.427621	+	0.903958i	$0.359352\pi$
$458$	−2.62471e8	−	8.07804e8i	−0.127659	−	0.392895i
$459$	−7.24363e7	+	2.22936e8i	−0.0349632	+	0.107606i
$460$	3.65358e7	+	2.65448e7i	0.0175012	+	0.0127153i
$461$	−1.99223e9			−0.947079			−0.473539	−	0.880773i	$-0.657024\pi$
$461$	−1.99223e9			−0.947079			−0.473539	+	0.880773i	$0.657024\pi$
$462$	6.48247e8	+	1.35998e9i	0.305840	+	0.641629i
$463$	1.44558e9			0.676876			0.338438	−	0.940989i	$-0.390101\pi$
$463$	1.44558e9			0.676876			0.338438	+	0.940989i	$0.390101\pi$
$464$	−3.06272e8	−	2.22520e8i	−0.142329	−	0.103408i
$465$	−3.02101e8	+	9.29770e8i	−0.139337	+	0.428835i
$466$	7.42325e8	+	2.28464e9i	0.339816	+	1.04585i
$467$	8.65301e7	−	6.28678e7i	0.0393150	−	0.0285640i	−0.567954	−	0.823060i	$-0.692265\pi$
$467$	8.65301e7	−	6.28678e7i	0.0393150	−	0.0285640i	0.607269	+	0.794496i	$0.292265\pi$
$468$	−7.78366e8	+	5.65516e8i	−0.351013	+	0.255026i
$469$	2.45381e8	+	7.55206e8i	0.109834	+	0.338034i
$470$	−7.45569e7	+	2.29463e8i	−0.0331242	+	0.101946i
$471$	−2.45771e9	−	1.78563e9i	−1.08382	−	0.787441i
$472$	9.46323e8			0.414231
$473$	3.34151e9	+	1.81540e9i	1.45188	+	0.788786i
$474$	−2.60986e8			−0.112562
$475$	1.67928e9	+	1.22007e9i	0.718946	+	0.522345i
$476$	2.05058e8	−	6.31103e8i	0.0871469	−	0.268211i
$477$	6.34077e8	+	1.95149e9i	0.267502	+	0.823287i
$478$	−4.94022e8	+	3.58928e8i	−0.206894	+	0.150317i
$479$	2.36540e9	−	1.71856e9i	0.983400	−	0.714482i	0.0249338	−	0.999689i	$-0.492063\pi$
$479$	2.36540e9	−	1.71856e9i	0.983400	−	0.714482i	0.958466	+	0.285208i	$0.0920625\pi$
$480$	−3.04099e7	−	9.35920e7i	−0.0125508	−	0.0386273i
$481$	1.66207e8	−	5.11532e8i	0.0680991	−	0.209587i
$482$	−3.29723e8	−	2.39558e8i	−0.134117	−	0.0974418i
$483$	−6.45033e8			−0.260476
$484$	−7.85372e8	+	9.68838e8i	−0.314859	+	0.388412i
$485$	−4.93313e8			−0.196348
$486$	−1.96947e9	−	1.43090e9i	−0.778257	−	0.565436i
$487$	3.72249e8	−	1.14567e9i	0.146044	−	0.449476i	−0.851100	−	0.525003i	$-0.824064\pi$
$487$	3.72249e8	−	1.14567e9i	0.146044	−	0.449476i	0.997144	+	0.0755274i	$0.0240640\pi$
$488$	−1.51976e8	−	4.67734e8i	−0.0591978	−	0.182192i
$489$	1.00615e9	−	7.31008e8i	0.389117	−	0.282710i
$490$	1.16006e8	−	8.42831e7i	0.0445444	−	0.0323634i
$491$	1.22772e8	+	3.77854e8i	0.0468075	+	0.144059i	0.971729	−	0.236100i	$-0.0758693\pi$
$491$	1.22772e8	+	3.77854e8i	0.0468075	+	0.144059i	−0.924921	+	0.380159i	$0.875869\pi$
$492$	3.55804e8	−	1.09505e9i	0.134689	−	0.414531i
$493$	1.16948e9	+	8.49680e8i	0.439572	+	0.319368i
$494$	1.68207e9			0.627769
$495$	−3.53740e8	−	1.92182e8i	−0.131089	−	0.0712189i
$496$	1.33336e9			0.490637
$497$	−2.68506e9	−	1.95081e9i	−0.981087	−	0.712801i
$498$	−1.29971e9	+	4.00011e9i	−0.471569	+	1.45134i
$499$	−6.44844e8	−	1.98463e9i	−0.232329	−	0.715034i	−0.997465	−	0.0711652i	$-0.977328\pi$
$499$	−6.44844e8	−	1.98463e9i	−0.232329	−	0.715034i	0.765136	−	0.643869i	$-0.222672\pi$
$500$	3.72294e8	−	2.70488e8i	0.133196	−	0.0967726i
$501$	−1.27885e9	+	9.29136e8i	−0.454346	+	0.330101i
$502$	8.94418e8	+	2.75274e9i	0.315557	+	0.971184i
$503$	7.35759e8	−	2.26443e9i	0.257779	−	0.793363i	−0.735490	−	0.677535i	$-0.763048\pi$
$503$	7.35759e8	−	2.26443e9i	0.257779	−	0.793363i	0.993269	−	0.115827i	$-0.0369519\pi$
$504$	5.36589e8	+	3.89855e8i	0.186696	+	0.135643i
$505$	−7.70516e8			−0.266233
$506$	−2.29759e8	−	4.82017e8i	−0.0788398	−	0.165400i
$507$	2.29432e8			0.0781855
$508$	−6.54969e7	−	4.75863e7i	−0.0221665	−	0.0161049i
$509$	3.53191e7	−	1.08701e8i	0.0118713	−	0.0365361i	−0.944945	−	0.327228i	$-0.893885\pi$
$509$	3.53191e7	−	1.08701e8i	0.0118713	−	0.0365361i	0.956817	+	0.290692i	$0.0938855\pi$
$510$	1.16119e8	+	3.57376e8i	0.0387620	+	0.119297i
$511$	−3.22592e9	+	2.34377e9i	−1.06950	+	0.777036i
$512$	−1.08584e8	+	7.88912e7i	−0.0357538	+	0.0259767i
$513$	1.26580e8	+	3.89573e8i	0.0413956	+	0.127402i
$514$	2.77399e8	−	8.53746e8i	0.0901019	−	0.277305i
$515$	6.28749e8	+	4.56813e8i	0.202839	+	0.147371i
$516$	3.54788e9			1.13683
$517$	2.06982e9	−	1.96318e9i	0.658743	−	0.624803i
$518$	−3.70787e8			−0.117212
$519$	8.37071e8	+	6.08167e8i	0.262831	+	0.190958i
$520$	5.68037e7	−	1.74824e8i	0.0177160	−	0.0545241i
$521$	−1.01255e9	−	3.11630e9i	−0.313677	−	0.965399i	−0.976295	−	0.216442i	$-0.930555\pi$
$521$	−1.01255e9	−	3.11630e9i	−0.313677	−	0.965399i	0.662618	−	0.748957i	$-0.269445\pi$
$522$	−1.16892e9	+	8.49269e8i	−0.359698	+	0.261336i
$523$	−6.78224e7	+	4.92759e7i	−0.0207309	+	0.0150618i	−0.598102	−	0.801420i	$-0.704078\pi$
$523$	−6.78224e7	+	4.92759e7i	−0.0207309	+	0.0150618i	0.577372	+	0.816482i	$0.304078\pi$
$524$	−2.72227e8	−	8.37829e8i	−0.0826555	−	0.254387i
$525$	−1.00119e9	+	3.08136e9i	−0.301968	+	0.929362i
$526$	−2.91588e8	−	2.11851e8i	−0.0873615	−	0.0634718i
$527$	−5.09135e9			−1.51529
$528$	−2.12337e8	+	1.14403e9i	−0.0627778	+	0.338235i
$529$	−3.17621e9			−0.932854
$530$	−3.17165e8	−	2.30434e8i	−0.0925379	−	0.0672327i
$531$	1.11609e9	−	3.43497e9i	0.323495	−	0.995616i
$532$	−3.58332e8	−	1.10283e9i	−0.103180	−	0.317555i
$533$	1.73999e9	−	1.26418e9i	0.497739	−	0.361629i
$534$	2.53576e8	−	1.84234e8i	0.0720632	−	0.0523570i
$535$	−1.40687e8	−	4.32989e8i	−0.0397205	−	0.122247i
$536$	−1.89515e8	+	5.83268e8i	−0.0531578	+	0.163603i
$537$	4.20402e9	+	3.05440e9i	1.17153	+	0.851170i
$538$	1.09383e9			0.302838
$539$	−1.68099e9	+	2.20868e8i	−0.462385	+	0.0607537i
$540$	4.47643e7			0.0122336
$541$	−1.59805e9	−	1.16105e9i	−0.433910	−	0.315254i	0.349300	−	0.937011i	$-0.386419\pi$
$541$	−1.59805e9	−	1.16105e9i	−0.433910	−	0.315254i	−0.783211	+	0.621756i	$0.786419\pi$
$542$	1.70697e8	−	5.25351e8i	0.0460498	−	0.141727i
$543$	−1.22264e9	−	3.76291e9i	−0.327718	−	1.00861i
$544$	4.14624e8	−	3.01242e8i	0.110423	−	0.0802267i
$545$	3.43205e8	−	2.49353e8i	0.0908167	−	0.0659822i
$546$	8.11329e8	+	2.49701e9i	0.213316	+	0.656518i
$547$	−3.34030e6	+	1.02804e7i	−0.000872628	+	0.00268567i	−0.951492	−	0.307674i	$-0.900449\pi$
$547$	−3.34030e6	+	1.02804e7i	−0.000872628	+	0.00268567i	0.950619	+	0.310360i	$0.100449\pi$
$548$	2.09866e8	+	1.52476e8i	0.0544765	+	0.0395795i
$549$	−1.87702e9			−0.484135
$550$	−2.65925e9	+	3.49403e8i	−0.681536	+	0.0895484i
$551$	2.52607e9			0.643301
$552$	−4.03035e8	−	2.92822e8i	−0.101990	−	0.0740997i
$553$	−1.03853e8	+	3.19627e8i	−0.0261145	+	0.0803722i
$554$	4.17752e8	+	1.28571e9i	0.104384	+	0.321261i
$555$	1.69866e8	−	1.23415e8i	0.0421776	−	0.0306438i
$556$	−2.76406e9	+	2.00821e9i	−0.682003	+	0.495504i
$557$	−2.42689e9	−	7.46921e9i	−0.595056	−	1.83139i	−0.554449	−	0.832217i	$-0.687071\pi$
$557$	−2.42689e9	−	7.46921e9i	−0.595056	−	1.83139i	−0.0406062	−	0.999175i	$-0.512929\pi$
$558$	1.57255e9	−	4.83983e9i	0.383165	−	1.17926i
$559$	5.36152e9	+	3.89537e9i	1.29821	+	0.943208i
$560$	−1.26722e8			−0.0304926
$561$	8.10796e8	−	4.36842e9i	0.193884	−	1.04461i
$562$	−3.94983e9			−0.938645
$563$	−1.19590e9	−	8.68870e8i	−0.282432	−	0.205199i	0.437545	−	0.899196i	$-0.355848\pi$
$563$	−1.19590e9	−	8.68870e8i	−0.282432	−	0.205199i	−0.719978	+	0.693997i	$0.755848\pi$
$564$	8.22453e8	−	2.53125e9i	0.193034	−	0.594098i
$565$	−1.87136e8	−	5.75944e8i	−0.0436503	−	0.134342i
$566$	−5.97919e8	+	4.34413e8i	−0.138607	+	0.100704i
$567$	−2.80929e9	+	2.04107e9i	−0.647227	+	0.470238i
$568$	−7.92104e8	−	2.43784e9i	−0.181369	−	0.558196i
$569$	−1.89632e9	+	5.83627e9i	−0.431537	+	1.32814i	0.465056	+	0.885281i	$0.346034\pi$
$569$	−1.89632e9	+	5.83627e9i	−0.431537	+	1.32814i	−0.896594	+	0.442854i	$0.853966\pi$
$570$	5.31234e8	+	3.85964e8i	0.120150	+	0.0872940i
$571$	9.86349e8			0.221720			0.110860	−	0.993836i	$-0.464640\pi$
$571$	9.86349e8			0.221720			0.110860	+	0.993836i	$0.464640\pi$
$572$	−1.57696e9	+	1.49571e9i	−0.352318	+	0.334166i
$573$	9.16597e9			2.03534
$574$	−1.19951e9	−	8.71498e8i	−0.264736	−	0.192342i
$575$	3.54854e8	−	1.09213e9i	0.0778417	−	0.239572i
$576$	1.58296e8	+	4.87184e8i	0.0345136	+	0.106222i
$577$	−1.43110e9	+	1.03976e9i	−0.310139	+	0.225329i	−0.731956	−	0.681352i	$-0.761392\pi$
$577$	−1.43110e9	+	1.03976e9i	−0.310139	+	0.225329i	0.421817	+	0.906681i	$0.361392\pi$
$578$	1.07255e9	−	7.79252e8i	0.231031	−	0.167854i
$579$	−8.11317e8	−	2.49698e9i	−0.173706	−	0.534613i
$580$	8.53055e7	−	2.62543e8i	0.0181543	−	0.0558731i
$581$	4.38170e9	+	3.18349e9i	0.926886	+	0.673422i
$582$	5.44184e9			1.14423
$583$	1.99452e9	+	4.18435e9i	0.416868	+	0.874558i
$584$	−3.07963e9			−0.639813
$585$	−5.67582e8	−	4.12372e8i	−0.117215	−	0.0851616i
$586$	−3.96614e7	+	1.22065e8i	−0.00814191	+	0.0250582i
$587$	2.11267e9	+	6.50214e9i	0.431121	+	1.32685i	0.897010	+	0.442010i	$0.145735\pi$
$587$	2.11267e9	+	6.50214e9i	0.431121	+	1.32685i	−0.465889	+	0.884843i	$0.654265\pi$
$588$	−1.27968e9	+	9.29745e8i	−0.259587	+	0.188601i
$589$	−7.19780e9	+	5.22950e9i	−1.45143	+	1.05453i
$590$	2.13239e8	+	6.56282e8i	0.0427449	+	0.131555i
$591$	−2.47485e9	+	7.61680e9i	−0.493165	+	1.51781i
$592$	−2.31678e8	−	1.68324e8i	−0.0458943	−	0.0333442i
$593$	3.33993e9			0.657727			0.328863	−	0.944378i	$-0.393334\pi$
$593$	3.33993e9			0.657727			0.328863	+	0.944378i	$0.393334\pi$
$594$	−4.65082e8	−	2.52673e8i	−0.0910494	−	0.0494660i
$595$	4.83881e8			0.0941737
$596$	2.27129e9	+	1.65019e9i	0.439451	+	0.319280i
$597$	−4.30018e8	+	1.32346e9i	−0.0827136	+	0.254566i
$598$	−2.87560e8	−	8.85019e8i	−0.0549888	−	0.169238i
$599$	−6.75239e9	+	4.90590e9i	−1.28370	+	0.932663i	−0.999658	−	0.0261487i	$-0.991676\pi$
$599$	−6.75239e9	+	4.90590e9i	−1.28370	+	0.932663i	−0.284042	+	0.958812i	$0.591676\pi$
$600$	−2.02440e9	+	1.47081e9i	−0.382619	+	0.277989i
$601$	−1.81539e9	−	5.58718e9i	−0.341121	−	1.04986i	−0.963628	−	0.267248i	$-0.913886\pi$
$601$	−1.81539e9	−	5.58718e9i	−0.341121	−	1.04986i	0.622507	−	0.782614i	$-0.286114\pi$
$602$	1.41179e9	−	4.34505e9i	0.263744	−	0.811721i
$603$	1.89363e9	+	1.37581e9i	0.351711	+	0.255533i
$604$	4.86989e9			0.899270
$605$	−8.48867e8	−	3.26349e8i	−0.155846	−	0.0599153i
$606$	8.49972e9			1.55150
$607$	2.78491e9	+	2.02336e9i	0.505419	+	0.367208i	0.811083	−	0.584931i	$-0.198878\pi$
$607$	2.78491e9	+	2.02336e9i	0.505419	+	0.367208i	−0.305664	+	0.952139i	$0.598878\pi$
$608$	2.76750e8	−	8.51749e8i	0.0499373	−	0.153691i
$609$	1.21842e9	+	3.74992e9i	0.218593	+	0.672761i
$610$	2.90132e8	−	2.10793e8i	0.0517536	−	0.0376012i
$611$	4.02205e9	−	2.92219e9i	0.713352	−	0.518280i
$612$	−6.04444e8	−	1.86029e9i	−0.106592	−	0.328057i
$613$	3.00142e9	−	9.23742e9i	0.526278	−	1.61972i	−0.235497	−	0.971875i	$-0.575672\pi$
$613$	3.00142e9	−	9.23742e9i	0.526278	−	1.61972i	0.761775	−	0.647842i	$-0.224328\pi$
$614$	−3.15672e9	−	2.29349e9i	−0.550361	−	0.399860i
$615$	8.39601e8			0.145549
$616$	1.31659e9	+	7.15286e8i	0.226943	+	0.123295i
$617$	1.03976e10			1.78212			0.891058	−	0.453890i	$-0.149964\pi$
$617$	1.03976e10			1.78212			0.891058	+	0.453890i	$0.149964\pi$
$618$	−6.93586e9	−	5.03919e9i	−1.18206	−	0.858819i
$619$	−1.78748e9	+	5.50128e9i	−0.302916	+	0.932281i	0.677530	+	0.735495i	$0.263050\pi$
$619$	−1.78748e9	+	5.50128e9i	−0.302916	+	0.932281i	−0.980447	+	0.196786i	$0.936950\pi$
$620$	3.00451e8	+	9.24693e8i	0.0506294	+	0.155821i
$621$	1.83333e8	−	1.33200e8i	0.0307200	−	0.0223194i
$622$	4.66523e9	−	3.38949e9i	0.777333	−	0.564765i
$623$	−1.24725e8	−	3.83863e8i	−0.0206654	−	0.0636016i
$624$	−6.26613e8	+	1.92852e9i	−0.103241	+	0.317744i
$625$	−4.52872e9	−	3.29030e9i	−0.741985	−	0.539083i
$626$	1.87764e9			0.305917
$627$	−3.34071e9	−	7.00856e9i	−0.541255	−	1.13551i
$628$	−3.02131e9			−0.486783
$629$	8.84650e8	+	6.42736e8i	0.141741	+	0.102981i
$630$	−1.49455e8	+	4.59976e8i	−0.0238133	+	0.0732898i
$631$	9.52598e8	+	2.93179e9i	0.150941	+	0.464548i	0.997727	−	0.0673853i	$-0.0214657\pi$
$631$	9.52598e8	+	2.93179e9i	0.150941	+	0.464548i	−0.846786	+	0.531933i	$0.821466\pi$
$632$	−2.09989e8	+	1.52566e8i	−0.0330893	+	0.0240408i
$633$	1.09213e9	−	7.93480e8i	0.171144	−	0.124343i
$634$	−1.63641e9	−	5.03634e9i	−0.255023	−	0.784880i
$635$	1.82428e7	−	5.61454e7i	0.00282737	−	0.00870175i
$636$	3.49871e9	+	2.54196e9i	0.539272	+	0.391804i
$637$	−2.95465e9			−0.452917
$638$	−2.36822e9	+	2.24620e9i	−0.361035	+	0.342434i
$639$	−9.78310e9			−1.48328
$640$	−7.91794e7	−	5.75272e7i	−0.0119394	−	0.00867448i
$641$	5.22764e8	−	1.60890e9i	0.0783976	−	0.241283i	−0.904175	−	0.427162i	$-0.859513\pi$
$641$	5.22764e8	−	1.60890e9i	0.0783976	−	0.241283i	0.982573	+	0.185879i	$0.0595133\pi$
$642$	1.55194e9	+	4.77639e9i	0.231475	+	0.712405i
$643$	−1.30195e9	+	9.45925e8i	−0.193133	+	0.140320i	−0.680150	−	0.733073i	$-0.738085\pi$
$643$	−1.30195e9	+	9.45925e8i	−0.193133	+	0.140320i	0.487016	+	0.873393i	$0.338085\pi$
$644$	−5.18993e8	+	3.77071e8i	−0.0765705	+	0.0556317i
$645$	7.99458e8	+	2.46048e9i	0.117310	+	0.361045i
$646$	−1.05675e9	+	3.25236e9i	−0.154227	+	0.474662i
$647$	8.21735e8	+	5.97025e8i	0.119280	+	0.0866618i	0.645826	−	0.763485i	$-0.276513\pi$
$647$	8.21735e8	+	5.97025e8i	0.119280	+	0.0866618i	−0.526546	+	0.850147i	$0.676513\pi$
$648$	−2.68190e9			−0.387195
$649$	1.48894e9	−	8.02212e9i	0.213806	−	1.15195i
$650$	−4.67412e9			−0.667580
$651$	−1.12349e10	−	8.16264e9i	−1.59601	−	1.15957i
$652$	3.82215e8	−	1.17634e9i	0.0540059	−	0.166213i
$653$	−8.61861e8	−	2.65253e9i	−0.121127	−	0.372791i	0.872049	−	0.489419i	$-0.162791\pi$
$653$	−8.61861e8	−	2.65253e9i	−0.121127	−	0.372791i	−0.993176	+	0.116629i	$0.962791\pi$
$654$	−3.78596e9	+	2.75066e9i	−0.529242	+	0.384517i
$655$	5.19698e8	−	3.77583e8i	0.0722615	−	0.0525010i
$656$	−3.53861e8	−	1.08907e9i	−0.0489406	−	0.150624i
$657$	−3.63209e9	+	1.11784e10i	−0.499664	+	1.53781i
$658$	−2.77272e9	−	2.01450e9i	−0.379416	−	0.275662i
$659$	−1.67394e9			−0.227846			−0.113923	−	0.993490i	$-0.536342\pi$
$659$	−1.67394e9			−0.227846			−0.113923	+	0.993490i	$0.536342\pi$
$660$	−8.41241e8	+	1.10532e8i	−0.113898	+	0.0149653i
$661$	7.26540e9			0.978485			0.489243	−	0.872148i	$-0.337273\pi$
$661$	7.26540e9			0.978485			0.489243	+	0.872148i	$0.337273\pi$
$662$	9.06245e8	+	6.58426e8i	0.121407	+	0.0882072i
$663$	2.39269e9	−	7.36394e9i	0.318852	−	0.981325i
$664$	1.29262e9	+	3.97827e9i	0.171349	+	0.527358i
$665$	6.84077e8	−	4.97011e8i	0.0902047	−	0.0655376i
$666$	−8.84223e8	+	6.42425e8i	−0.115985	+	0.0842681i
$667$	−4.31846e8	−	1.32909e9i	−0.0563493	−	0.173425i
$668$	−4.85809e8	+	1.49517e9i	−0.0630591	+	0.194076i
$669$	−1.71228e10	−	1.24405e10i	−2.21098	−	1.60637i
$670$	−4.47205e8			−0.0574440
$671$	−4.20417e9	+	5.52394e8i	−0.537219	+	0.0705862i
$672$	1.39790e9			0.177698
$673$	7.61378e9	+	5.53174e9i	0.962826	+	0.699534i	0.953805	−	0.300426i	$-0.0971287\pi$
$673$	7.61378e9	+	5.53174e9i	0.962826	+	0.699534i	0.00902030	+	0.999959i	$0.497129\pi$
$674$	−2.76491e9	+	8.50952e9i	−0.347833	+	1.07052i
$675$	−3.51739e8	−	1.08254e9i	−0.0440207	−	0.135482i
$676$	1.84601e8	−	1.34120e8i	0.0229837	−	0.0166987i
$677$	6.45850e9	−	4.69237e9i	0.799965	−	0.581209i	−0.110939	−	0.993827i	$-0.535386\pi$
$677$	6.45850e9	−	4.69237e9i	0.799965	−	0.581209i	0.910904	+	0.412619i	$0.135386\pi$
$678$	2.06433e9	+	6.35336e9i	0.254376	+	0.782888i
$679$	2.16545e9	−	6.66456e9i	0.265463	−	0.817010i
$680$	3.02342e8	+	2.19665e8i	0.0368738	+	0.0267904i
$681$	1.40798e10			1.70837
$682$	2.09790e9	−	1.13031e10i	0.253244	−	1.36443i
$683$	−9.00646e9			−1.08164			−0.540819	−	0.841139i	$-0.681886\pi$
$683$	−9.00646e9			−1.08164			−0.540819	+	0.841139i	$0.681886\pi$
$684$	−2.76528e9	−	2.00910e9i	−0.330402	−	0.240051i
$685$	−5.84535e7	+	1.79901e8i	−0.00694854	+	0.0213854i
$686$	1.97909e9	+	6.09103e9i	0.234063	+	0.720371i
$687$	−5.52745e9	+	4.01593e9i	−0.650394	+	0.472539i
$688$	2.85462e9	−	2.07400e9i	0.334186	−	0.242801i
$689$	2.49629e9	+	7.68278e9i	0.290755	+	0.894851i
$690$	1.12257e8	−	3.45490e8i	0.0130089	−	0.0400372i
$691$	6.84117e9	+	4.97040e9i	0.788783	+	0.573084i	0.907602	−	0.419832i	$-0.137911\pi$
$691$	6.84117e9	+	4.97040e9i	0.788783	+	0.573084i	−0.118819	+	0.992916i	$0.537911\pi$
$692$	1.02903e9			0.118047
$693$	4.14912e9	−	3.93535e9i	0.473576	−	0.449177i
$694$	8.73090e9			0.991519
$695$	−2.01555e9	−	1.46438e9i	−0.227744	−	0.165465i
$696$	−9.41022e8	+	2.89617e9i	−0.105796	+	0.325605i
$697$	1.35120e9	+	4.15856e9i	0.151149	+	0.465188i
$698$	1.87049e9	−	1.35899e9i	0.208191	−	0.151260i
$699$	1.56328e10	−	1.13579e10i	1.73128	−	1.25785i
$700$	9.95728e8	+	3.06454e9i	0.109723	+	0.337693i
$701$	−8.70304e8	+	2.67852e9i	−0.0954241	+	0.293685i	−0.987364	−	0.158469i	$-0.949344\pi$
$701$	−8.70304e8	+	2.67852e9i	−0.0954241	+	0.293685i	0.891940	+	0.452154i	$0.149344\pi$
$702$	−7.46232e8	−	5.42170e8i	−0.0814131	−	0.0591501i
$703$	1.91083e9			0.207433
$704$	4.97927e8	+	1.04461e9i	0.0537850	+	0.112837i
$705$	1.94077e9			0.208599
$706$	7.92916e9	+	5.76087e9i	0.848029	+	0.616129i
$707$	3.38226e9	−	1.04095e10i	0.359947	−	1.10780i
$708$	−2.35228e9	−	7.23959e9i	−0.249100	−	0.766650i
$709$	−1.26588e10	+	9.19717e9i	−1.33393	+	0.969154i	−0.334282	+	0.942473i	$0.608494\pi$
$709$	−1.26588e10	+	9.19717e9i	−1.33393	+	0.969154i	−0.999644	+	0.0266803i	$0.991506\pi$
$710$	1.51217e9	−	1.09866e9i	0.158562	−	0.115202i
$711$	3.06125e8	+	9.42156e8i	0.0319415	+	0.0983058i
$712$	9.63285e7	−	2.96469e8i	0.0100017	−	0.0307821i
$713$	3.98200e9	+	2.89309e9i	0.411422	+	0.298916i
$714$	−5.33780e9			−0.548805
$715$	−1.39263e9	−	7.56600e8i	−0.142484	−	0.0774096i
$716$	5.16809e9			0.526180
$717$	3.97387e9	+	2.88719e9i	0.402621	+	0.292522i
$718$	4.59448e8	−	1.41403e9i	0.0463234	−	0.142569i
$719$	4.58017e9	+	1.40963e10i	0.459548	+	1.41434i	0.865712	+	0.500542i	$0.166866\pi$
$719$	4.58017e9	+	1.40963e10i	0.459548	+	1.41434i	−0.406164	+	0.913800i	$0.633134\pi$
$720$	−3.02196e8	+	2.19558e8i	−0.0301735	+	0.0219223i
$721$	−8.93140e9	+	6.48904e9i	−0.887455	+	0.644774i
$722$	−3.63130e8	−	1.11760e9i	−0.0359072	−	0.110511i
$723$	−1.01307e9	+	3.11792e9i	−0.0996914	+	0.306818i
$724$	−3.18344e9	−	2.31291e9i	−0.311754	−	0.226503i
$725$	−7.01941e9			−0.684097
$726$	9.36403e9	+	3.60002e9i	0.908207	+	0.349162i
$727$	−1.44416e10			−1.39394			−0.696972	−	0.717099i	$-0.745470\pi$
$727$	−1.44416e10			−1.39394			−0.696972	+	0.717099i	$0.745470\pi$
$728$	2.11249e9	+	1.53481e9i	0.202925	+	0.147433i
$729$	−2.51121e9	+	7.72872e9i	−0.240070	+	0.738858i
$730$	−6.93945e8	−	2.13574e9i	−0.0660230	−	0.203198i
$731$	−1.09002e10	+	7.91947e9i	−1.03211	+	0.749869i
$732$	−3.20050e9	+	2.32530e9i	−0.301599	+	0.219124i
$733$	−9.27457e8	−	2.85442e9i	−0.0869821	−	0.267703i	0.898099	−	0.439793i	$-0.144948\pi$
$733$	−9.27457e8	−	2.85442e9i	−0.0869821	−	0.267703i	−0.985081	+	0.172090i	$0.944948\pi$
$734$	−4.39889e9	+	1.35384e10i	−0.410588	+	1.26366i
$735$	−9.33142e8	−	6.77967e8i	−0.0866846	−	0.0629800i
$736$	−4.95458e8			−0.0458073
$737$	4.64627e9	+	2.52426e9i	0.427531	+	0.232272i
$738$	−4.37046e9			−0.400249
$739$	9.86637e9	+	7.16833e9i	0.899294	+	0.653375i	0.938285	−	0.345864i	$-0.112414\pi$
$739$	9.86637e9	+	7.16833e9i	0.899294	+	0.653375i	−0.0389906	+	0.999240i	$0.512414\pi$
$740$	6.45289e7	−	1.98600e8i	0.00585387	−	0.0180164i
$741$	−4.18114e9	−	1.28682e10i	−0.377512	−	1.16186i
$742$	4.50534e9	−	3.27332e9i	0.404869	−	0.294154i
$743$	1.62916e9	−	1.18365e9i	0.145714	−	0.105868i	−0.512540	−	0.858664i	$-0.671295\pi$
$743$	1.62916e9	−	1.18365e9i	0.145714	−	0.105868i	0.658254	+	0.752796i	$0.271295\pi$
$744$	−3.31434e9	−	1.02005e10i	−0.295047	−	0.908062i
$745$	−6.32618e8	+	1.94700e9i	−0.0560525	+	0.172512i
$746$	−8.87405e8	−	6.44737e8i	−0.0782593	−	0.0568587i
$747$	1.59648e10			1.40134
$748$	−1.90131e9	−	3.98880e9i	−0.166110	−	0.348487i
$749$	6.46715e9			0.562376
$750$	−2.99471e9	−	2.17578e9i	−0.259203	−	0.188322i
$751$	1.31591e9	−	4.04996e9i	0.113367	−	0.348908i	−0.878236	−	0.478228i	$-0.841279\pi$
$751$	1.31591e9	−	4.04996e9i	0.113367	−	0.348908i	0.991603	+	0.129320i	$0.0412794\pi$
$752$	−8.17962e8	−	2.51743e9i	−0.0701408	−	0.215871i
$753$	1.88358e10	−	1.36850e10i	1.60769	−	1.16805i
$754$	−4.60190e9	+	3.34347e9i	−0.390964	+	0.284052i
$755$	1.09735e9	+	3.37731e9i	0.0927966	+	0.285599i
$756$	−1.96497e8	+	6.04757e8i	−0.0165398	+	0.0509043i
$757$	−8.84068e9	−	6.42313e9i	−0.740713	−	0.538160i	0.152221	−	0.988346i	$-0.451357\pi$
$757$	−8.84068e9	−	6.42313e9i	−0.740713	−	0.538160i	−0.892934	+	0.450187i	$0.851357\pi$
$758$	−1.55601e10			−1.29769
$759$	−3.11643e9	+	2.95586e9i	−0.258708	+	0.245379i
$760$	6.53055e8			0.0539638
$761$	−1.09107e10	−	7.92710e9i	−0.897443	−	0.652030i	0.0403650	−	0.999185i	$-0.487148\pi$
$761$	−1.09107e10	−	7.92710e9i	−0.897443	−	0.652030i	−0.937808	+	0.347155i	$0.887148\pi$
$762$	−2.01240e8	+	6.19352e8i	−0.0164767	+	0.0507102i
$763$	1.86218e9	+	5.73119e9i	0.151770	+	0.467099i
$764$	7.37494e9	−	5.35821e9i	0.598317	−	0.434703i
$765$	1.15392e9	−	8.38372e8i	0.0931882	−	0.0677052i
$766$	−4.07509e9	−	1.25418e10i	−0.327594	−	1.00823i
$767$	4.39391e9	−	1.35231e10i	0.351615	−	1.08216i
$768$	8.73445e8	+	6.34595e8i	0.0695779	+	0.0505513i
$769$	−6.51045e9			−0.516261			−0.258130	−	0.966110i	$-0.583106\pi$
$769$	−6.51045e9			−0.516261			−0.258130	+	0.966110i	$0.583106\pi$
$770$	−1.99384e8	+	1.07424e9i	−0.0157388	+	0.0847978i
$771$	−7.22088e9			−0.567414
$772$	−2.11246e9	−	1.53479e9i	−0.165245	−	0.120057i
$773$	−3.23352e9	+	9.95177e9i	−0.251796	+	0.774947i	0.742649	+	0.669681i	$0.233569\pi$
$773$	−3.23352e9	+	9.95177e9i	−0.251796	+	0.774947i	−0.994444	+	0.105266i	$0.966431\pi$
$774$	−4.16150e9	−	1.28078e10i	−0.322594	−	0.992843i
$775$	2.00012e10	−	1.45317e10i	1.54347	−	1.12140i
$776$	4.37850e9	−	3.18117e9i	0.336364	−	0.244383i
$777$	9.21669e8	+	2.83661e9i	0.0704858	+	0.216933i
$778$	1.45608e9	−	4.48137e9i	0.110856	−	0.341179i
$779$	6.18163e9	+	4.49122e9i	0.468513	+	0.340395i
$780$	−1.47864e9			−0.111566
$781$	−2.19123e10	+	2.87909e9i	−1.64592	+	0.216261i
$782$	1.89188e9			0.141472
$783$	−1.12066e9	−	8.14209e8i	−0.0834273	−	0.0606135i
$784$	−4.86127e8	+	1.49614e9i	−0.0360283	+	0.110884i
$785$	−6.80803e8	−	2.09530e9i	−0.0502317	−	0.154597i
$786$	−5.73290e9	+	4.16520e9i	−0.421110	+	0.305954i
$787$	−8.23701e9	+	5.98454e9i	−0.602362	+	0.437642i	−0.846717	−	0.532044i	$-0.821424\pi$
$787$	−8.23701e9	+	5.98454e9i	−0.602362	+	0.437642i	0.244354	+	0.969686i	$0.421424\pi$
$788$	2.46134e9	+	7.57521e9i	0.179196	+	0.551510i
$789$	−8.95906e8	+	2.75732e9i	−0.0649371	+	0.199856i
$790$	−1.53124e8	−	1.11251e8i	−0.0110496	−	0.00802802i
$791$	8.60235e9			0.618015
$792$	4.37899e9	−	5.75364e8i	0.313210	−	0.0411533i
$793$	−7.38962e9			−0.526218
$794$	7.68433e9	+	5.58300e9i	0.544797	+	0.395818i
$795$	−9.74491e8	+	2.99917e9i	−0.0687848	+	0.211698i
$796$	4.27670e8	+	1.31623e9i	0.0300548	+	0.0924990i
$797$	5.32005e9	−	3.86525e9i	0.372230	−	0.270441i	−0.385905	−	0.922539i	$-0.626111\pi$
$797$	5.32005e9	−	3.86525e9i	0.372230	−	0.270441i	0.758135	+	0.652097i	$0.226111\pi$
$798$	−7.54620e9	+	5.48263e9i	−0.525676	+	0.381926i
$799$	3.12334e9	+	9.61267e9i	0.216624	+	0.666700i
$800$	−7.69030e8	+	2.36683e9i	−0.0531041	+	0.163438i
$801$	−9.62513e8	−	6.99307e8i	−0.0661748	−	0.0480788i
$802$	3.53944e9			0.242284
$803$	−4.84546e9	+	2.61065e10i	−0.330241	+	1.77928i
$804$	4.93321e9			0.334760
$805$	−3.78448e8	−	2.74959e8i	−0.0255694	−	0.0185773i
$806$	6.19096e9	−	1.90538e10i	0.416472	−	1.28177i
$807$	−2.71893e9	−	8.36801e9i	−0.182113	−	0.560486i
$808$	6.83887e9	−	4.96873e9i	0.456084	−	0.331364i
$809$	−1.94536e10	+	1.41339e10i	−1.29176	+	0.938515i	−0.999839	−	0.0179287i	$-0.994293\pi$
$809$	−1.94536e10	+	1.41339e10i	−1.29176	+	0.938515i	−0.291916	+	0.956444i	$0.594293\pi$
$810$	−6.04323e8	−	1.85992e9i	−0.0399550	−	0.122969i
$811$	6.43379e9	−	1.98012e10i	0.423539	−	1.30352i	−0.480846	−	0.876805i	$-0.659671\pi$
$811$	6.43379e9	−	1.98012e10i	0.423539	−	1.30352i	0.904386	−	0.426716i	$-0.140329\pi$
$812$	3.17245e9	+	2.30492e9i	0.207945	+	0.151081i
$813$	−4.44335e9			−0.289997
$814$	−1.79143e9	+	1.69913e9i	−0.116416	+	0.110418i
$815$	9.01925e8			0.0583605
$816$	−3.33520e9	−	2.42317e9i	−0.214885	−	0.156123i
$817$	−7.27559e9	+	2.23920e10i	−0.466757	+	1.43653i
$818$	5.17751e7	+	1.59347e8i	0.00330738	+	0.0101791i
$819$	8.06253e9	−	5.85777e9i	0.512835	−	0.372596i
$820$	6.75542e8	−	4.90810e8i	0.0427862	−	0.0310860i
$821$	−5.74381e9	−	1.76776e10i	−0.362242	−	1.11487i	−0.951690	−	0.307060i	$-0.900655\pi$
$821$	−5.74381e9	−	1.76776e10i	−0.362242	−	1.11487i	0.589448	−	0.807806i	$-0.299345\pi$
$822$	6.44813e8	−	1.98453e9i	0.0404932	−	0.124625i
$823$	1.49261e10	+	1.08444e10i	0.933354	+	0.678121i	0.946812	−	0.321788i	$-0.104284\pi$
$823$	1.49261e10	+	1.08444e10i	0.933354	+	0.678121i	−0.0134580	+	0.999909i	$0.504284\pi$
$824$	−8.52638e9			−0.530908
$825$	9.28312e9	+	1.94753e10i	0.575580	+	1.20752i
$826$	−9.80228e9			−0.605197
$827$	−1.64272e10	−	1.19351e10i	−1.00994	−	0.733764i	−0.0457433	−	0.998953i	$-0.514566\pi$
$827$	−1.64272e10	−	1.19351e10i	−1.00994	−	0.733764i	−0.964196	+	0.265189i	$0.914566\pi$
$828$	−5.84340e8	+	1.79841e9i	−0.0357734	+	0.110099i
$829$	−4.00110e9	−	1.23141e10i	−0.243915	−	0.750692i	−0.995813	−	0.0914133i	$-0.970862\pi$
$829$	−4.00110e9	−	1.23141e10i	−0.243915	−	0.750692i	0.751898	−	0.659279i	$-0.229138\pi$
$830$	−2.46769e9	+	1.79288e9i	−0.149802	+	0.108837i
$831$	8.79755e9	−	6.39180e9i	0.531812	−	0.386384i
$832$	6.23192e8	+	1.91799e9i	0.0375137	+	0.115455i
$833$	1.85625e9	−	5.71295e9i	0.111270	−	0.342454i
$834$	2.22339e10	+	1.61539e10i	1.32720	+	0.964264i
$835$	−1.14638e9			−0.0681436
$836$	−6.78497e9	−	3.68619e9i	−0.401630	−	0.218200i
$837$	4.87881e9			0.287591
$838$	1.29543e10	+	9.41186e9i	0.760432	+	0.552486i
$839$	8.96664e9	−	2.75965e10i	0.524159	−	1.61319i	−0.241815	−	0.970322i	$-0.577743\pi$
$839$	8.96664e9	−	2.75965e10i	0.524159	−	1.61319i	0.765974	−	0.642872i	$-0.222257\pi$
$840$	3.14994e8	+	9.69452e8i	0.0183369	+	0.0564350i
$841$	7.04450e9	−	5.11813e9i	0.408380	−	0.296705i
$842$	1.67178e9	−	1.21462e9i	0.0965131	−	0.0701209i
$843$	9.81813e9	+	3.02171e10i	0.564459	+	1.73723i
$844$	4.14879e8	−	1.27687e9i	0.0237533	−	0.0731050i
$845$	1.34610e8	+	9.78002e7i	0.00767504	+	0.00557624i
$846$	−1.01025e10			−0.573629
$847$	8.13510e9	−	1.00355e10i	0.460014	−	0.567475i
$848$	4.30103e9			0.242207
$849$	4.80961e9	+	3.49439e9i	0.269732	+	0.195972i
$850$	2.93650e9	−	9.03762e9i	0.164007	−	0.504763i
$851$	−3.26668e8	−	1.00538e9i	−0.0181699	−	0.0559213i
$852$	−1.66811e10	+	1.21195e10i	−0.924031	+	0.671348i
$853$	−1.47323e10	+	1.07036e10i	−0.812732	+	0.590485i	−0.914621	−	0.404311i	$-0.867511\pi$
$853$	−1.47323e10	+	1.07036e10i	−0.812732	+	0.590485i	0.101889	+	0.994796i	$0.467511\pi$
$854$	1.57421e9	+	4.84492e9i	0.0864888	+	0.266185i
$855$	7.70210e8	−	2.37046e9i	0.0421432	−	0.129704i
$856$	4.04085e9	+	2.93585e9i	0.220199	+	0.159984i
$857$	6.60403e8			0.0358407			0.0179203	−	0.999839i	$-0.494295\pi$
$857$	6.60403e8			0.0358407			0.0179203	+	0.999839i	$0.494295\pi$
$858$	1.53624e10	+	8.34621e9i	0.830336	+	0.451111i
$859$	−7.93116e9			−0.426934			−0.213467	−	0.976950i	$-0.568476\pi$
$859$	−7.93116e9			−0.426934			−0.213467	+	0.976950i	$0.568476\pi$
$860$	2.08158e9	+	1.51236e9i	0.111596	+	0.0810792i
$861$	−3.68551e9	+	1.13428e10i	−0.196783	+	0.605635i
$862$	2.09940e9	+	6.46129e9i	0.111640	+	0.343592i
$863$	1.28258e10	−	9.31847e9i	0.679275	−	0.493522i	−0.193842	−	0.981033i	$-0.562095\pi$
$863$	1.28258e10	−	9.31847e9i	0.679275	−	0.493522i	0.873117	+	0.487510i	$0.162095\pi$
$864$	−3.97315e8	+	2.88666e8i	−0.0209574	+	0.0152264i
$865$	2.31875e8	+	7.13638e8i	0.0121814	+	0.0374905i
$866$	−4.05378e9	+	1.24763e10i	−0.212104	+	0.652787i
$867$	−8.62750e9	−	6.26825e9i	−0.449592	−	0.326647i
$868$	−1.38113e10			−0.716828
$869$	9.62931e8	+	2.02016e9i	0.0497767	+	0.104428i
$870$	−2.22056e9			−0.114326
$871$	7.45501e9	+	5.41638e9i	0.382283	+	0.277745i
$872$	−1.43821e9	+	4.42636e9i	−0.0734540	+	0.226068i
$873$	−6.38303e9	−	1.96449e10i	−0.324696	−	0.999312i
$874$	2.67461e9	−	1.94321e9i	0.135509	−	0.0984534i
$875$	−3.85633e9	+	2.80178e9i	−0.194601	+	0.141386i
$876$	7.65505e9	+	2.35598e10i	0.384755	+	1.18415i
$877$	5.00630e9	−	1.54078e10i	0.250622	−	0.771334i	−0.744039	−	0.668136i	$-0.767092\pi$
$877$	5.00630e9	−	1.54078e10i	0.250622	−	0.771334i	0.994661	−	0.103198i	$-0.0329076\pi$
$878$	−1.12315e10	−	8.16013e9i	−0.560022	−	0.406880i
$879$	1.03241e9			0.0512734
$880$	−6.12247e8	+	5.80703e8i	−0.0302857	+	0.0287253i
$881$	3.01828e10			1.48711			0.743555	−	0.668675i	$-0.233138\pi$
$881$	3.01828e10			1.48711			0.743555	+	0.668675i	$0.233138\pi$
$882$	4.85738e9	+	3.52909e9i	0.238376	+	0.173190i
$883$	−9.24712e7	+	2.84597e8i	−0.00452006	+	0.0139113i	−0.953291	−	0.302053i	$-0.902328\pi$
$883$	−9.24712e7	+	2.84597e8i	−0.00452006	+	0.0139113i	0.948771	+	0.315964i	$0.102328\pi$
$884$	−2.37962e9	−	7.32373e9i	−0.115858	−	0.356574i
$885$	4.49066e9	−	3.26265e9i	0.217775	−	0.158223i
$886$	−2.21484e9	+	1.60918e9i	−0.106986	+	0.0777295i
$887$	−4.53943e8	−	1.39709e9i	−0.0218408	−	0.0672191i	0.939542	−	0.342434i	$-0.111251\pi$
$887$	−4.53943e8	−	1.39709e9i	−0.0218408	−	0.0672191i	−0.961383	+	0.275214i	$0.911251\pi$
$888$	−7.11832e8	+	2.19079e9i	−0.0341140	+	0.104992i
$889$	6.78435e8	+	4.92912e8i	0.0323856	+	0.0235295i
$890$	2.27309e8			0.0108082
$891$	−4.21968e9	+	2.27348e10i	−0.199851	+	1.07676i
$892$	−2.10494e10			−0.993031
$893$	1.42891e10	+	1.03816e10i	0.671465	+	0.487848i
$894$	6.97855e9	−	2.14778e10i	0.326651	−	1.00533i
$895$	1.16455e9	+	3.58411e9i	0.0542971	+	0.167109i
$896$	1.12475e9	−	8.17177e8i	0.0522369	−	0.0379523i
$897$	−6.05580e9	+	4.39980e9i	−0.280155	+	0.203544i
$898$	6.29361e9	+	1.93697e10i	0.290023	+	0.892600i
$899$	9.29734e9	−	2.86143e10i	0.426776	−	1.31348i
$900$	7.68414e9	+	5.58285e9i	0.351355	+	0.255275i
$901$	−1.64233e10			−0.748036
$902$	−9.78899e9	+	1.28619e9i	−0.444135	+	0.0583557i
$903$	−3.67499e10			−1.66092
$904$	5.37498e9	+	3.90515e9i	0.241984	+	0.175812i
$905$	8.86680e8	−	2.72892e9i	0.0397646	−	0.122383i
$906$	−1.21051e10	−	3.72558e10i	−0.540780	−	1.66435i
$907$	−9.25427e9	+	6.72362e9i	−0.411829	+	0.299211i	−0.774342	−	0.632768i	$-0.781919\pi$
$907$	−9.25427e9	+	6.72362e9i	−0.411829	+	0.299211i	0.362513	+	0.931979i	$0.381919\pi$
$908$	1.13286e10	−	8.23074e9i	0.502201	−	0.364870i
$909$	−9.96979e9	−	3.06839e10i	−0.440263	−	1.35499i
$910$	−5.88388e8	+	1.81087e9i	−0.0258833	+	0.0796605i
$911$	−3.11857e10	−	2.26578e10i	−1.36660	−	0.992893i	−0.997994	−	0.0633079i	$-0.979835\pi$
$911$	−3.11857e10	−	2.26578e10i	−1.36660	−	0.992893i	−0.368607	−	0.929586i	$-0.620165\pi$
$912$	−7.20399e9			−0.314479
$913$	3.57582e10	−	4.69833e9i	1.55499	−	0.204313i
$914$	6.05188e9			0.262167
$915$	−2.33380e9	−	1.69560e9i	−0.100714	−	0.0731729i
$916$	−2.09977e9	+	6.46243e9i	−0.0902688	+	0.277819i
$917$	2.81980e9	+	8.67846e9i	0.120761	+	0.371664i
$918$	1.51713e9	−	1.10226e9i	0.0647250	−	0.0470255i
$919$	2.83975e10	−	2.06320e10i	1.20691	−	0.876873i	0.211965	−	0.977277i	$-0.432014\pi$
$919$	2.83975e10	−	2.06320e10i	1.20691	−	0.876873i	0.994947	+	0.100404i	$0.0320136\pi$
$920$	−1.11644e8	−	3.43604e8i	−0.00472690	−	0.0145479i
$921$	−9.69905e9	+	2.98506e10i	−0.409092	+	1.25905i
$922$	1.28940e10	+	9.36803e9i	0.541787	+	0.393631i
$923$	−3.85149e10			−1.61221
$924$	2.19944e9	−	1.18502e10i	0.0917193	−	0.494166i
$925$	−5.30980e9			−0.220588
$926$	−9.35600e9	−	6.79754e9i	−0.387215	−	0.281328i
$927$	−1.00560e10	+	3.09491e10i	−0.414615	+	1.27605i
$928$	9.35884e8	+	2.88036e9i	0.0384418	+	0.118312i
$929$	1.59975e10	−	1.16229e10i	0.654631	−	0.475617i	−0.210214	−	0.977655i	$-0.567416\pi$
$929$	1.59975e10	−	1.16229e10i	0.654631	−	0.475617i	0.864846	+	0.502038i	$0.167416\pi$
$930$	6.32728e9	−	4.59704e9i	0.257945	−	0.187408i
$931$	−3.24373e9	−	9.98318e9i	−0.131741	−	0.405457i
$932$	5.93860e9	−	1.82771e10i	0.240286	−	0.739524i
$933$	−3.75268e10	−	2.72648e10i	−1.51271	−	1.09905i
$934$	−8.55657e8			−0.0343626
$935$	2.33783e9	−	2.21738e9i	0.0935347	−	0.0887156i
$936$	7.69690e9			0.306797
$937$	−2.11428e10	−	1.53612e10i	−0.839604	−	0.610008i	0.0826562	−	0.996578i	$-0.473660\pi$
$937$	−2.11428e10	−	1.53612e10i	−0.839604	−	0.610008i	−0.922260	+	0.386570i	$0.873660\pi$
$938$	1.96305e9	−	6.04165e9i	0.0776643	−	0.239026i
$939$	−4.66728e9	−	1.43644e10i	−0.183965	−	0.566185i
$940$	1.56154e9	−	1.13453e9i	0.0613205	−	0.0445520i
$941$	3.58041e9	−	2.60132e9i	0.140078	−	0.101772i	−0.515540	−	0.856866i	$-0.672409\pi$
$941$	3.58041e9	−	2.60132e9i	0.140078	−	0.101772i	0.655617	+	0.755093i	$0.272409\pi$
$942$	7.51008e9	+	2.31137e10i	0.292730	+	0.900929i
$943$	1.30626e9	−	4.02025e9i	0.0507269	−	0.156121i
$944$	−6.12473e9	−	4.44988e9i	−0.236966	−	0.172166i
$945$	−4.63681e8			−0.0178734
$946$	−1.30902e10	−	2.74623e10i	−0.502721	−	1.05467i
$947$	1.37318e10			0.525413			0.262707	−	0.964876i	$-0.415385\pi$
$947$	1.37318e10			0.525413			0.262707	+	0.964876i	$0.415385\pi$
$948$	1.68914e9	+	1.22723e9i	0.0643926	+	0.0467840i
$949$	−1.42991e10	+	4.40082e10i	−0.543098	+	1.67148i
$950$	−5.13143e9	−	1.57929e10i	−0.194181	−	0.597626i
$951$	−3.44615e10	+	2.50378e10i	−1.29928	+	0.943982i
$952$	−4.29479e9	+	3.12035e9i	−0.161329	+	0.117212i
$953$	7.51281e9	+	2.31221e10i	0.281176	+	0.865369i	0.987519	+	0.157500i	$0.0503434\pi$
$953$	7.51281e9	+	2.31221e10i	0.281176	+	0.865369i	−0.706343	+	0.707869i	$0.749657\pi$
$954$	5.07261e9	−	1.56119e10i	0.189153	−	0.582152i
$955$	5.37778e9	+	3.90719e9i	0.199798	+	0.145162i
$956$	4.88515e9			0.180832
$957$	2.30707e10	+	1.25340e10i	0.850880	+	0.462272i
$958$	−2.33903e10			−0.859523
$959$	−2.17385e9	−	1.57939e9i	−0.0795909	−	0.0578262i
$960$	−2.43279e8	+	7.48736e8i	−0.00887474	+	0.0273136i
$961$	2.42439e10	+	7.46152e10i	0.881193	+	2.71203i
$962$	−3.48108e9	+	2.52915e9i	−0.126067	+	0.0915930i
$963$	1.54223e10	−	1.12050e10i	0.556491	−	0.404314i
$964$	1.00754e9	+	3.10090e9i	0.0362238	+	0.111485i
$965$	5.88379e8	−	1.81085e9i	0.0210771	−	0.0648688i
$966$	4.17474e9	+	3.03313e9i	0.149008	+	0.108261i
$967$	3.87137e10			1.37680			0.688402	−	0.725329i	$-0.258312\pi$
$967$	3.87137e10			1.37680			0.688402	+	0.725329i	$0.258312\pi$
$968$	9.63878e9	−	2.57741e9i	0.341553	−	0.0913314i
$969$	2.75080e10			0.971240
$970$	3.19279e9	+	2.31970e9i	0.112323	+	0.0816075i
$971$	−2.63837e9	+	8.12007e9i	−0.0924844	+	0.284638i	−0.986590	−	0.163219i	$-0.947812\pi$
$971$	−2.63837e9	+	8.12007e9i	−0.0924844	+	0.284638i	0.894106	+	0.447856i	$0.147812\pi$
$972$	6.01817e9	+	1.85220e10i	0.210200	+	0.646929i
$973$	2.86309e10	−	2.08016e10i	0.996416	−	0.723938i
$974$	−7.79649e9	+	5.66448e9i	−0.270360	+	0.196428i
$975$	1.16185e10	+	3.57581e10i	0.401453	+	1.23554i
$976$	−1.21581e9	+	3.74187e9i	−0.0418592	+	0.128829i
$977$	−7.59772e9	−	5.52007e9i	−0.260647	−	0.189371i	0.449785	−	0.893137i	$-0.351500\pi$
$977$	−7.59772e9	−	5.52007e9i	−0.260647	−	0.189371i	−0.710432	+	0.703766i	$0.751500\pi$
$978$	−9.94932e9			−0.340101
$979$	−2.36165e9	−	1.28305e9i	−0.0804406	−	0.0437024i
$980$	−1.14713e9			−0.0389333
$981$	1.43706e10	+	1.04409e10i	0.485997	+	0.353098i
$982$	9.82179e8	−	3.02284e9i	0.0330979	−	0.101865i
$983$	−4.22154e9	−	1.29926e10i	−0.141753	−	0.436272i	0.854826	−	0.518915i	$-0.173664\pi$
$983$	−4.22154e9	−	1.29926e10i	−0.141753	−	0.436272i	−0.996579	+	0.0826430i	$0.973664\pi$
$984$	−7.45205e9	+	5.41423e9i	−0.249341	+	0.181156i
$985$	−4.69884e9	+	3.41391e9i	−0.156662	+	0.113822i
$986$	−3.57362e9	−	1.09985e10i	−0.118724	−	0.365396i
$987$	−8.51920e9	+	2.62194e10i	−0.282026	+	0.867986i
$988$	−1.08866e10	−	7.90958e9i	−0.359123	−	0.260918i
$989$	1.30253e10			0.428155
$990$	1.38576e9	+	2.90722e9i	0.0453904	+	0.0952257i
$991$	−5.18430e8			−0.0169213			−0.00846063	−	0.999964i	$-0.502693\pi$
$991$	−5.18430e8			−0.0169213			−0.00846063	+	0.999964i	$0.502693\pi$
$992$	−8.62967e9	−	6.26982e9i	−0.280675	−	0.203922i
$993$	2.78444e9	−	8.56964e9i	0.0902435	−	0.277741i
$994$	8.20483e9	+	2.52519e10i	0.264982	+	0.815532i
$995$	−8.16449e8	+	5.93185e8i	−0.0262753	+	0.0190901i
$996$	2.72216e10	−	1.97776e10i	0.872982	−	0.634259i
$997$	−1.52878e10	−	4.70511e10i	−0.488555	−	1.50362i	−0.826766	−	0.562546i	$-0.809822\pi$
$997$	−1.52878e10	−	4.70511e10i	−0.488555	−	1.50362i	0.338211	−	0.941070i	$-0.390178\pi$
$998$	−5.15875e9	+	1.58770e10i	−0.164281	+	0.505605i
$999$	−8.47719e8	−	6.15904e8i	−0.0269013	−	0.0195449i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.8.c.a.15.1	yes	12
11.3	even	5	inner	22.8.c.a.3.1	✓	12
11.5	even	5		242.8.a.q.1.1		6
11.6	odd	10		242.8.a.o.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.8.c.a.3.1	✓	12	11.3	even	5	inner
22.8.c.a.15.1	yes	12	1.1	even	1	trivial
242.8.a.o.1.1		6	11.6	odd	10
242.8.a.q.1.1		6	11.5	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)

\(f(q)\)	\(=\)	\(q+(-6.47214 - 4.70228i) q^{2} +(-19.8857 + 61.2018i) q^{3} +(19.7771 + 60.8676i) q^{4} +(-37.7557 + 27.4311i) q^{5} +(416.491 - 302.598i) q^{6} +(-204.857 - 630.484i) q^{7} +(158.217 - 486.941i) q^{8} +(-1580.90 - 1148.59i) q^{9} +O(q^{10})\)	\(q+(-6.47214 - 4.70228i) q^{2} +(-19.8857 + 61.2018i) q^{3} +(19.7771 + 60.8676i) q^{4} +(-37.7557 + 27.4311i) q^{5} +(416.491 - 302.598i) q^{6} +(-204.857 - 630.484i) q^{7} +(158.217 - 486.941i) q^{8} +(-1580.90 - 1148.59i) q^{9} +373.349 q^{10} +(-3878.93 - 2107.38i) q^{11} -4118.49 q^{12} +(-6223.82 - 4521.87i) q^{13} +(-1638.85 + 5043.87i) q^{14} +(-928.036 - 2856.20i) q^{15} +(-3313.73 + 2407.57i) q^{16} +(12653.3 - 9193.17i) q^{17} +(4830.80 + 14867.7i) q^{18} +(8445.74 - 25993.3i) q^{19} +(-2416.36 - 1755.59i) q^{20} +42660.4 q^{21} +(15195.5 + 31879.1i) q^{22} -15120.2 q^{23} +(26655.4 + 19366.3i) q^{24} +(-23468.9 + 72229.9i) q^{25} +(19018.3 + 58532.3i) q^{26} +(-12125.1 + 8809.39i) q^{27} +(34324.6 - 24938.3i) q^{28} +(28560.9 + 87901.5i) q^{29} +(-7424.29 + 22849.6i) q^{30} +(-263357. - 191340. i) q^{31} +32768.0 q^{32} +(206110. - 195491. i) q^{33} -125123. q^{34} +(25029.4 + 18184.9i) q^{35} +(38646.4 - 118941. i) q^{36} +(21604.8 + 66492.6i) q^{37} +(-176890. + 128518. i) q^{38} +(400511. - 290988. i) q^{39} +(7383.75 + 22724.9i) q^{40} +(-86391.8 + 265887. i) q^{41} +(-276104. - 200601. i) q^{42} -861451. q^{43} +(51556.9 - 277779. i) q^{44} +91195.1 q^{45} +(97859.8 + 71099.3i) q^{46} +(-199698. + 614607. i) q^{47} +(-81451.7 - 250683. i) q^{48} +(310717. - 225749. i) q^{49} +(491540. - 357124. i) q^{50} +(311019. + 957218. i) q^{51} +(152146. - 468258. i) q^{52} +(-849513. - 617208. i) q^{53} +119899. q^{54} +(204260. - 26838.1i) q^{55} -339420. q^{56} +(1.42289e6 + 1.03379e6i) q^{57} +(228487. - 703212. i) q^{58} +(571152. + 1.75783e6i) q^{59} +(155496. - 112975. i) q^{60} +(777106. - 564601. i) q^{61} +(804746. + 2.47675e6i) q^{62} +(-400310. + 1.23203e6i) q^{63} +(-212079. - 154084. i) q^{64} +359024. q^{65} +(-2.25323e6 + 296056. i) q^{66} -1.19782e6 q^{67} +(809812. + 588363. i) q^{68} +(300675. - 925382. i) q^{69} +(-76482.9 - 235390. i) q^{70} +(4.05030e6 - 2.94272e6i) q^{71} +(-809421. + 588079. i) q^{72} +(-1.85870e6 - 5.72050e6i) q^{73} +(172838. - 531941. i) q^{74} +(-3.95391e6 - 2.87268e6i) q^{75} +1.74918e6 q^{76} +(-534041. + 2.87731e6i) q^{77} -3.96047e6 q^{78} +(-410136. - 297981. i) q^{79} +(59070.0 - 181799. i) q^{80} +(-1.61866e6 - 4.98171e6i) q^{81} +(1.80941e6 - 1.31462e6i) q^{82} +(-6.60960e6 + 4.80216e6i) q^{83} +(843699. + 2.59664e6i) q^{84} +(-225556. + 694189. i) q^{85} +(5.57543e6 + 4.05079e6i) q^{86} -5.94768e6 q^{87} +(-1.63988e6 + 1.55539e6i) q^{88} +608839. q^{89} +(-590227. - 428825. i) q^{90} +(-1.57597e6 + 4.85035e6i) q^{91} +(-299033. - 920329. i) q^{92} +(1.69474e7 - 1.23130e7i) q^{93} +(4.18252e6 - 3.03878e6i) q^{94} +(394151. + 1.21307e6i) q^{95} +(-651614. + 2.00546e6i) q^{96} +(8.55176e6 + 6.21322e6i) q^{97} -3.07254e6 q^{98} +(3.71169e6 + 7.78686e6i) 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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