LMFDB - Embedded newform 18.7.d.a.11.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [18,7,Mod(5,18)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(18, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("18.5");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 18 = 2 \cdot 3^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	18.d (of order $6$, degree $2$, 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:	$4.14097350516$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
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} + 370x^{10} + 51793x^{8} + 3491832x^{6} + 117603792x^{4} + 1832032512x^{2} + 10453017600 $ x^12 + 370x^10 + 51793x^8 + 3491832x^6 + 117603792x^4 + 1832032512*x^2 + 10453017600
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.5
Root			$-8.88570i$ of defining polynomial
Character	$\chi$	$=$	18.11
Dual form			18.7.d.a.5.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.89898 + 2.82843i) q^{2} +(-14.9408 - 22.4894i) q^{3} +(16.0000 + 27.7128i) q^{4} +(202.253 - 116.771i) q^{5} +(-9.58533 - 152.434i) q^{6} +(95.5752 - 165.541i) q^{7} +181.019i q^{8} +(-282.543 + 672.020i) q^{9} +O(q^{10})$	\(q+(4.89898 + 2.82843i) q^{2} +(-14.9408 - 22.4894i) q^{3} +(16.0000 + 27.7128i) q^{4} +(202.253 - 116.771i) q^{5} +(-9.58533 - 152.434i) q^{6} +(95.5752 - 165.541i) q^{7} +181.019i q^{8} +(-282.543 + 672.020i) q^{9} +1321.11 q^{10} +(-673.077 - 388.601i) q^{11} +(384.190 - 773.882i) q^{12} +(45.5802 + 78.9472i) q^{13} +(936.442 - 540.655i) q^{14} +(-5647.92 - 2803.88i) q^{15} +(-512.000 + 886.810i) q^{16} +7047.39i q^{17} +(-3284.93 + 2493.06i) q^{18} +2731.10 q^{19} +(6472.09 + 3736.66i) q^{20} +(-5150.89 + 323.897i) q^{21} +(-2198.26 - 3807.50i) q^{22} +(-17228.9 + 9947.14i) q^{23} +(4071.01 - 2704.58i) q^{24} +(19458.3 - 33702.7i) q^{25} +515.681i q^{26} +(19334.7 - 3686.33i) q^{27} +6116.81 q^{28} +(27104.3 + 15648.7i) q^{29} +(-19738.5 - 29710.9i) q^{30} +(6174.50 + 10694.6i) q^{31} +(-5016.55 + 2896.31i) q^{32} +(1316.94 + 20943.1i) q^{33} +(-19933.0 + 34525.0i) q^{34} -44641.5i q^{35} +(-23144.2 + 2922.26i) q^{36} -27972.0 q^{37} +(13379.6 + 7724.70i) q^{38} +(1094.47 - 2204.61i) q^{39} +(21137.7 + 36611.7i) q^{40} +(-37428.2 + 21609.2i) q^{41} +(-26150.2 - 12982.1i) q^{42} +(19256.1 - 33352.5i) q^{43} -24870.5i q^{44} +(21327.2 + 168911. i) q^{45} -112539. q^{46} +(-143771. - 83006.2i) q^{47} +(27593.5 - 1735.13i) q^{48} +(40555.3 + 70243.8i) q^{49} +(190651. - 110073. i) q^{50} +(158491. - 105294. i) q^{51} +(-1458.57 + 2526.31i) q^{52} -54741.5i q^{53} +(105147. + 36627.6i) q^{54} -181509. q^{55} +(29966.1 + 17301.0i) q^{56} +(-40804.8 - 61420.6i) q^{57} +(88522.3 + 153325. i) q^{58} +(-14102.1 + 8141.84i) q^{59} +(-12663.3 - 201382. i) q^{60} +(29443.7 - 50998.0i) q^{61} +69856.5i q^{62} +(84242.8 + 111001. i) q^{63} -32768.0 q^{64} +(18437.4 + 10644.9i) q^{65} +(-52784.4 + 106325. i) q^{66} +(-147998. - 256341. i) q^{67} +(-195303. + 112758. i) q^{68} +(481120. + 238849. i) q^{69} +(126265. - 218698. i) q^{70} +157251. i q^{71} +(-121649. - 51145.7i) q^{72} +80297.0 q^{73} +(-137034. - 79116.8i) q^{74} +(-1.04868e6 + 65942.7i) q^{75} +(43697.5 + 75686.3i) q^{76} +(-128659. + 74281.3i) q^{77} +(11597.3 - 7704.71i) q^{78} +(188424. - 326360. i) q^{79} +239146. i q^{80} +(-371780. - 379749. i) q^{81} -244480. q^{82} +(733992. + 423771. i) q^{83} +(-91390.3 - 137563. i) q^{84} +(822929. + 1.42535e6i) q^{85} +(188670. - 108929. i) q^{86} +(-53032.3 - 843363. i) q^{87} +(70344.3 - 121840. i) q^{88} +1128.91i q^{89} +(-373270. + 887812. i) q^{90} +17425.3 q^{91} +(-551326. - 318308. i) q^{92} +(148261. - 298646. i) q^{93} +(-469554. - 813291. i) q^{94} +(552371. - 318912. i) q^{95} +(140088. + 69545.8i) q^{96} +(675152. - 1.16940e6i) q^{97} +458831. i q^{98} +(451321. - 342525. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 42 q^{3} + 192 q^{4} + 432 q^{5} - 144 q^{6} + 240 q^{7} + 2190 q^{9}+O(q^{10}) $ 12 * q - 42 * q^3 + 192 * q^4 + 432 * q^5 - 144 * q^6 + 240 * q^7 + 2190 * q^9	\( 12 q - 42 q^{3} + 192 q^{4} + 432 q^{5} - 144 q^{6} + 240 q^{7} + 2190 q^{9} + 378 q^{11} + 384 q^{12} + 1680 q^{13} - 4752 q^{14} - 10872 q^{15} - 6144 q^{16} - 2976 q^{18} - 2820 q^{19} + 13824 q^{20} + 24876 q^{21} - 3600 q^{22} - 76248 q^{23} - 6144 q^{24} + 8094 q^{25} + 127008 q^{27} + 15360 q^{28} + 97092 q^{29} + 34272 q^{30} + 21480 q^{31} - 246258 q^{33} - 27360 q^{34} + 38208 q^{36} - 25536 q^{37} + 97632 q^{38} + 42204 q^{39} - 410562 q^{41} - 222144 q^{42} + 71430 q^{43} + 13716 q^{45} - 135072 q^{46} + 347652 q^{47} + 55296 q^{48} - 135954 q^{49} + 311040 q^{50} + 336402 q^{51} - 53760 q^{52} - 173520 q^{54} + 580392 q^{55} - 152064 q^{56} - 522282 q^{57} + 159264 q^{58} + 369738 q^{59} - 170496 q^{60} + 135744 q^{61} - 103800 q^{63} - 393216 q^{64} - 753840 q^{65} + 909216 q^{66} - 289938 q^{67} + 744768 q^{68} + 2059272 q^{69} + 155952 q^{70} - 374784 q^{72} - 977700 q^{73} - 2197152 q^{74} - 2115342 q^{75} - 45120 q^{76} - 159192 q^{77} - 631488 q^{78} - 764796 q^{79} - 1428282 q^{81} + 1073088 q^{82} + 396900 q^{83} + 1441536 q^{84} + 1619568 q^{85} + 3264624 q^{86} + 3072636 q^{87} + 115200 q^{88} - 1987200 q^{90} + 355584 q^{91} - 2439936 q^{92} - 2526576 q^{93} - 736848 q^{94} - 2089260 q^{95} - 49152 q^{96} - 38874 q^{97} + 4398804 q^{99}+O(q^{100}) \) 12 * q - 42 * q^3 + 192 * q^4 + 432 * q^5 - 144 * q^6 + 240 * q^7 + 2190 * q^9 + 378 * q^11 + 384 * q^12 + 1680 * q^13 - 4752 * q^14 - 10872 * q^15 - 6144 * q^16 - 2976 * q^18 - 2820 * q^19 + 13824 * q^20 + 24876 * q^21 - 3600 * q^22 - 76248 * q^23 - 6144 * q^24 + 8094 * q^25 + 127008 * q^27 + 15360 * q^28 + 97092 * q^29 + 34272 * q^30 + 21480 * q^31 - 246258 * q^33 - 27360 * q^34 + 38208 * q^36 - 25536 * q^37 + 97632 * q^38 + 42204 * q^39 - 410562 * q^41 - 222144 * q^42 + 71430 * q^43 + 13716 * q^45 - 135072 * q^46 + 347652 * q^47 + 55296 * q^48 - 135954 * q^49 + 311040 * q^50 + 336402 * q^51 - 53760 * q^52 - 173520 * q^54 + 580392 * q^55 - 152064 * q^56 - 522282 * q^57 + 159264 * q^58 + 369738 * q^59 - 170496 * q^60 + 135744 * q^61 - 103800 * q^63 - 393216 * q^64 - 753840 * q^65 + 909216 * q^66 - 289938 * q^67 + 744768 * q^68 + 2059272 * q^69 + 155952 * q^70 - 374784 * q^72 - 977700 * q^73 - 2197152 * q^74 - 2115342 * q^75 - 45120 * q^76 - 159192 * q^77 - 631488 * q^78 - 764796 * q^79 - 1428282 * q^81 + 1073088 * q^82 + 396900 * q^83 + 1441536 * q^84 + 1619568 * q^85 + 3264624 * q^86 + 3072636 * q^87 + 115200 * q^88 - 1987200 * q^90 + 355584 * q^91 - 2439936 * q^92 - 2526576 * q^93 - 736848 * q^94 - 2089260 * q^95 - 49152 * q^96 - 38874 * q^97 + 4398804 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/18\mathbb{Z}\right)^\times$.

$n$	$11$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	4.89898	+	2.82843i	0.612372	+	0.353553i
$2$	4.89898	+	2.82843i	0.612372	+	0.353553i
$3$	−14.9408	−	22.4894i	−0.553364	−	0.832939i
$3$	−14.9408	−	22.4894i	−0.553364	−	0.832939i
$4$	16.0000	+	27.7128i	0.250000	+	0.433013i
$5$	202.253	−	116.771i	1.61802	−	0.934165i	0.630591	−	0.776116i	$-0.282813\pi$
$5$	202.253	−	116.771i	1.61802	−	0.934165i	0.987431	−	0.158050i	$-0.0505206\pi$
$6$	−9.58533	−	152.434i	−0.0443765	−	0.705713i
$7$	95.5752	−	165.541i	0.278645	−	0.482627i	−0.692403	−	0.721511i	$-0.743448\pi$
$7$	95.5752	−	165.541i	0.278645	−	0.482627i	0.971048	+	0.238884i	$0.0767814\pi$
$8$			181.019i			0.353553i
$9$	−282.543	+	672.020i	−0.387576	+	0.921838i
$10$	1321.11			1.32111
$11$	−673.077	−	388.601i	−0.505693	−	0.291962i	0.225369	−	0.974274i	$-0.427641\pi$
$11$	−673.077	−	388.601i	−0.505693	−	0.291962i	−0.731061	+	0.682312i	$0.760975\pi$
$12$	384.190	−	773.882i	0.222332	−	0.447849i
$13$	45.5802	+	78.9472i	0.0207466	+	0.0359341i	0.876212	−	0.481925i	$-0.160062\pi$
$13$	45.5802	+	78.9472i	0.0207466	+	0.0359341i	−0.855466	+	0.517859i	$0.826729\pi$
$14$	936.442	−	540.655i	0.341269	−	0.197032i
$15$	−5647.92	−	2803.88i	−1.67346	−	0.830780i
$16$	−512.000	+	886.810i	−0.125000	+	0.216506i
$17$			7047.39i			1.43444i	0.696848	+	0.717219i	$0.254585\pi$
$17$			7047.39i			1.43444i	−0.696848	+	0.717219i	$0.745415\pi$
$18$	−3284.93	+	2493.06i	−0.563260	+	0.427479i
$19$	2731.10			0.398177			0.199088	−	0.979982i	$-0.436202\pi$
$19$	2731.10			0.398177			0.199088	+	0.979982i	$0.436202\pi$
$20$	6472.09	+	3736.66i	0.809011	+	0.467083i
$21$	−5150.89	+	323.897i	−0.556191	+	0.0349743i
$22$	−2198.26	−	3807.50i	−0.206448	−	0.357579i
$23$	−17228.9	+	9947.14i	−1.41604	+	0.817550i	−0.995948	−	0.0899317i	$-0.971335\pi$
$23$	−17228.9	+	9947.14i	−1.41604	+	0.817550i	−0.420091	+	0.907482i	$0.638002\pi$
$24$	4071.01	−	2704.58i	0.294489	−	0.195644i
$25$	19458.3	−	33702.7i	1.24533	−	2.15697i
$26$			515.681i			0.0293401i
$27$	19334.7	−	3686.33i	0.982306	−	0.187285i
$28$	6116.81			0.278645
$29$	27104.3	+	15648.7i	1.11133	+	0.641629i	0.939175	−	0.343440i	$-0.111592\pi$
$29$	27104.3	+	15648.7i	1.11133	+	0.641629i	0.172159	+	0.985069i	$0.444926\pi$
$30$	−19738.5	−	29710.9i	−0.731055	−	1.10040i
$31$	6174.50	+	10694.6i	0.207261	+	0.358986i	0.950851	−	0.309650i	$-0.100212\pi$
$31$	6174.50	+	10694.6i	0.207261	+	0.358986i	−0.743590	+	0.668636i	$0.766879\pi$
$32$	−5016.55	+	2896.31i	−0.153093	+	0.0883883i
$33$	1316.94	+	20943.1i	0.0366458	+	0.582773i
$34$	−19933.0	+	34525.0i	−0.507150	+	0.878410i
$35$		−	44641.5i		−	1.04120i
$36$	−23144.2	+	2922.26i	−0.496061	+	0.0626342i
$37$	−27972.0			−0.552228			−0.276114	−	0.961125i	$-0.589047\pi$
$37$	−27972.0			−0.552228			−0.276114	+	0.961125i	$0.589047\pi$
$38$	13379.6	+	7724.70i	0.243833	+	0.140777i
$39$	1094.47	−	2204.61i	0.0184505	−	0.0371653i
$40$	21137.7	+	36611.7i	0.330277	+	0.572057i
$41$	−37428.2	+	21609.2i	−0.543059	+	0.313535i	−0.746318	−	0.665590i	$-0.768180\pi$
$41$	−37428.2	+	21609.2i	−0.543059	+	0.313535i	0.203259	+	0.979125i	$0.434847\pi$
$42$	−26150.2	−	12982.1i	−0.352961	−	0.175226i
$43$	19256.1	−	33352.5i	0.242193	−	0.419491i	−0.719146	−	0.694860i	$-0.755467\pi$
$43$	19256.1	−	33352.5i	0.242193	−	0.419491i	0.961339	+	0.275369i	$0.0887999\pi$
$44$		−	24870.5i		−	0.291962i
$45$	21327.2	+	168911.i	0.234043	+	1.85361i
$46$	−112539.			−1.15619
$47$	−143771.	−	83006.2i	−1.38477	−	0.799497i	−0.392050	−	0.919944i	$-0.628234\pi$
$47$	−143771.	−	83006.2i	−1.38477	−	0.799497i	−0.992720	+	0.120447i	$0.961567\pi$
$48$	27593.5	−	1735.13i	0.249507	−	0.0156895i
$49$	40555.3	+	70243.8i	0.344714	+	0.597062i
$50$	190651.	−	110073.i	1.52521	−	0.880581i
$51$	158491.	−	105294.i	1.19480	−	0.793767i
$52$	−1458.57	+	2526.31i	−0.0103733	+	0.0179671i
$53$		−	54741.5i		−	0.367696i	−0.982955	−	0.183848i	$-0.941145\pi$
$53$		−	54741.5i		−	0.367696i	0.982955	−	0.183848i	$-0.0588554\pi$
$54$	105147.	+	36627.6i	0.667752	+	0.232609i
$55$	−181509.			−1.09096
$56$	29966.1	+	17301.0i	0.170634	+	0.0985158i
$57$	−40804.8	−	61420.6i	−0.220337	−	0.331657i
$58$	88522.3	+	153325.i	0.453700	+	0.785832i
$59$	−14102.1	+	8141.84i	−0.0686637	+	0.0396430i	−0.533939	−	0.845523i	$-0.679289\pi$
$59$	−14102.1	+	8141.84i	−0.0686637	+	0.0396430i	0.465275	+	0.885166i	$0.345955\pi$
$60$	−12663.3	−	201382.i	−0.0586263	−	0.932324i
$61$	29443.7	−	50998.0i	0.129719	−	0.224680i	−0.793849	−	0.608115i	$-0.791926\pi$
$61$	29443.7	−	50998.0i	0.129719	−	0.224680i	0.923568	+	0.383436i	$0.125259\pi$
$62$			69856.5i			0.293111i
$63$	84242.8	+	111001.i	0.336908	+	0.443920i
$64$	−32768.0			−0.125000
$65$	18437.4	+	10644.9i	0.0671368	+	0.0387614i
$66$	−52784.4	+	106325.i	−0.183600	+	0.369830i
$67$	−147998.	−	256341.i	−0.492076	−	0.852301i	0.507882	−	0.861427i	$-0.330429\pi$
$67$	−147998.	−	256341.i	−0.492076	−	0.852301i	−0.999958	+	0.00912565i	$0.997095\pi$
$68$	−195303.	+	112758.i	−0.621130	+	0.358609i
$69$	481120.	+	238849.i	1.46456	+	0.727071i
$70$	126265.	−	218698.i	0.368120	−	0.637603i
$71$			157251.i			0.439358i	0.975572	+	0.219679i	$0.0705010\pi$
$71$			157251.i			0.439358i	−0.975572	+	0.219679i	$0.929499\pi$
$72$	−121649.	−	51145.7i	−0.325919	−	0.137029i
$73$	80297.0			0.206410			0.103205	−	0.994660i	$-0.467090\pi$
$73$	80297.0			0.206410			0.103205	+	0.994660i	$0.467090\pi$
$74$	−137034.	−	79116.8i	−0.338169	−	0.195242i
$75$	−1.04868e6	+	65942.7i	−2.48575	+	0.156309i
$76$	43697.5	+	75686.3i	0.0995442	+	0.172416i
$77$	−128659.	+	74281.3i	−0.281817	+	0.162707i
$78$	11597.3	−	7704.71i	0.0244385	−	0.0162358i
$79$	188424.	−	326360.i	0.382169	−	0.661936i	−0.609203	−	0.793014i	$-0.708511\pi$
$79$	188424.	−	326360.i	0.382169	−	0.661936i	0.991372	+	0.131078i	$0.0418438\pi$
$80$			239146.i			0.467083i
$81$	−371780.	−	379749.i	−0.699570	−	0.714564i
$82$	−244480.			−0.443406
$83$	733992.	+	423771.i	1.28368	+	0.741134i	0.977519	−	0.210846i	$-0.0676218\pi$
$83$	733992.	+	423771.i	1.28368	+	0.741134i	0.306162	+	0.951980i	$0.400955\pi$
$84$	−91390.3	−	137563.i	−0.154192	−	0.232094i
$85$	822929.	+	1.42535e6i	1.34000	+	2.32095i
$86$	188670.	−	108929.i	0.296625	−	0.171256i
$87$	−53032.3	−	843363.i	−0.0805346	−	1.28073i
$88$	70344.3	−	121840.i	0.103224	−	0.178789i
$89$			1128.91i			0.00160136i	1.00000		0.000800679i	$0.000254864\pi$
$89$			1128.91i			0.00160136i	−1.00000		0.000800679i	$0.999745\pi$
$90$	−373270.	+	887812.i	−0.512030	+	1.21785i
$91$	17425.3			0.0231237
$92$	−551326.	−	318308.i	−0.708019	−	0.408775i
$93$	148261.	−	298646.i	0.184323	−	0.371286i
$94$	−469554.	−	813291.i	−0.565330	−	0.979180i
$95$	552371.	−	318912.i	0.644259	−	0.371963i
$96$	140088.	+	69545.8i	0.158338	+	0.0786063i
$97$	675152.	−	1.16940e6i	0.739753	−	1.28129i	−0.212854	−	0.977084i	$-0.568276\pi$
$97$	675152.	−	1.16940e6i	0.739753	−	1.28129i	0.952607	−	0.304205i	$-0.0983908\pi$
$98$			458831.i			0.487499i
$99$	451321.	−	342525.i	0.465136	−	0.353009i
$100$	1.24533e6			1.24533
$101$	−137557.	−	79418.5i	−0.133511	−	0.0770828i	0.431757	−	0.901990i	$-0.357894\pi$
$101$	−137557.	−	79418.5i	−0.133511	−	0.0770828i	−0.565268	+	0.824907i	$0.691227\pi$
$102$	1.07426e6	−	67551.6i	1.01230	−	0.0636554i
$103$	−248614.	−	430612.i	−0.227517	−	0.394071i	0.729555	−	0.683923i	$-0.239727\pi$
$103$	−248614.	−	430612.i	−0.227517	−	0.394071i	−0.957072	+	0.289851i	$0.906394\pi$
$104$	−14291.0	+	8250.90i	−0.0127046	+	0.00733502i
$105$	−1.00396e6	+	666981.i	−0.867257	+	0.576164i
$106$	154832.	−	268177.i	0.130000	−	0.225167i
$107$			207159.i			0.169103i	0.996419	+	0.0845516i	$0.0269458\pi$
$107$			207159.i			0.169103i	−0.996419	+	0.0845516i	$0.973054\pi$
$108$	411514.	+	476838.i	0.326673	+	0.378530i
$109$	−2.30287e6			−1.77824			−0.889120	−	0.457673i	$-0.848683\pi$
$109$	−2.30287e6			−1.77824			−0.889120	+	0.457673i	$0.848683\pi$
$110$	−889208.	−	513385.i	−0.668075	−	0.385713i
$111$	417925.	+	629073.i	0.305583	+	0.459973i
$112$	97869.0	+	169514.i	0.0696612	+	0.120657i
$113$	−677545.	+	391181.i	−0.469573	+	0.271108i	−0.716061	−	0.698038i	$-0.754057\pi$
$113$	−677545.	+	391181.i	−0.469573	+	0.271108i	0.246488	+	0.969146i	$0.420723\pi$
$114$	−26178.5	−	416312.i	−0.0176697	−	0.280999i
$115$	−2.32307e6	+	4.02367e6i	−1.52745	+	2.64563i
$116$			1.00152e6i			0.641629i
$117$	−65932.5	+	8324.83i	−0.0411663	+	0.00519778i
$118$	−92114.4			−0.0560637
$119$	1.16663e6	+	673556.i	0.692298	+	0.399699i
$120$	507557.	−	1.02238e6i	0.293725	−	0.591657i
$121$	−583759.	−	1.01110e6i	−0.329517	−	0.570739i
$122$	288488.	−	166559.i	0.158873	−	0.0917251i
$123$	1.04518e6	+	518876.i	0.561665	+	0.278836i
$124$	−197584.	+	342226.i	−0.103630	+	0.179493i
$125$		−	5.43954e6i		−	2.78504i
$126$	98745.9	+	782065.i	0.0493637	+	0.390959i
$127$	1.19415e6			0.582970			0.291485	−	0.956575i	$-0.405851\pi$
$127$	1.19415e6			0.582970			0.291485	+	0.956575i	$0.405851\pi$
$128$	−160530.	−	92681.9i	−0.0765466	−	0.0441942i
$129$	−1.03778e6	+	65257.4i	−0.483432	+	0.0303991i
$130$	60216.4	+	104298.i	0.0274085	+	0.0474729i
$131$	−2.17543e6	+	1.25598e6i	−0.967678	+	0.558689i	−0.898528	−	0.438917i	$-0.855362\pi$
$131$	−2.17543e6	+	1.25598e6i	−0.967678	+	0.558689i	−0.0691503	+	0.997606i	$0.522029\pi$
$132$	−559321.	+	371586.i	−0.243186	+	0.161561i
$133$	261025.	−	452108.i	0.110950	−	0.192171i
$134$		−	1.67441e6i		−	0.695901i
$135$	3.48004e6	−	3.00330e6i	1.41444	−	1.22067i
$136$	−1.27571e6			−0.507150
$137$	703636.	+	406244.i	0.273644	+	0.157989i	0.630543	−	0.776155i	$-0.282832\pi$
$137$	703636.	+	406244.i	0.273644	+	0.157989i	−0.356898	+	0.934143i	$0.616166\pi$
$138$	1.68143e6	+	2.53093e6i	0.639795	+	0.963037i
$139$	−350555.	−	607179.i	−0.130530	−	0.226085i	0.793351	−	0.608765i	$-0.208335\pi$
$139$	−350555.	−	607179.i	−0.130530	−	0.226085i	−0.923881	+	0.382679i	$0.875001\pi$
$140$	1.23714e6	−	714264.i	0.450853	−	0.260300i
$141$	281302.	+	4.47350e6i	0.100350	+	1.59584i
$142$	−444773.	+	770370.i	−0.155336	+	0.269051i
$143$		−	70850.1i		−	0.0242288i
$144$	−451292.	−	594636.i	−0.151137	−	0.199142i
$145$	7.30923e6			2.39755
$146$	393373.	+	227114.i	0.126400	+	0.0729769i
$147$	973808.	−	1.96156e6i	0.306564	−	0.617519i
$148$	−447552.	−	775183.i	−0.138057	−	0.239122i
$149$	265134.	−	153075.i	0.0801505	−	0.0462749i	−0.459389	−	0.888235i	$-0.651932\pi$
$149$	265134.	−	153075.i	0.0801505	−	0.0462749i	0.539540	+	0.841960i	$0.318598\pi$
$150$	−5.32395e6	−	2.64305e6i	−1.57747	−	0.783126i
$151$	−923784.	+	1.60004e6i	−0.268312	+	0.464730i	−0.968426	−	0.249301i	$-0.919799\pi$
$151$	−923784.	+	1.60004e6i	−0.268312	+	0.464730i	0.700114	+	0.714031i	$0.253132\pi$
$152$			494381.i			0.140777i
$153$	−4.73599e6	−	1.99119e6i	−1.32232	−	0.555953i
$154$	−840396.			−0.230103
$155$	2.49762e6	+	1.44200e6i	0.670704	+	0.387231i
$156$	78607.3	−	4942.98i	0.0207057	−	0.00130201i
$157$	−1.57533e6	−	2.72854e6i	−0.407072	−	0.705070i	0.587488	−	0.809233i	$-0.300117\pi$
$157$	−1.57533e6	−	2.72854e6i	−0.407072	−	0.705070i	−0.994560	+	0.104163i	$0.966784\pi$
$158$	1.84617e6	−	1.06589e6i	0.468060	−	0.270234i
$159$	−1.23110e6	+	817883.i	−0.306268	+	0.203470i
$160$	−676408.	+	1.17157e6i	−0.165139	+	0.286029i
$161$			3.80280e6i			0.911225i
$162$	−747252.	−	2.91193e6i	−0.175761	−	0.684915i
$163$	−1.29782e6			−0.299676			−0.149838	−	0.988711i	$-0.547875\pi$
$163$	−1.29782e6			−0.299676			−0.149838	+	0.988711i	$0.547875\pi$
$164$	−1.19770e6	−	691493.i	−0.271529	−	0.156768i
$165$	2.71189e6	+	4.08202e6i	0.603700	+	0.908706i
$166$	2.39721e6	+	4.15209e6i	0.524061	+	0.907700i
$167$	−1.41556e6	+	817272.i	−0.303933	+	0.175476i	−0.644208	−	0.764850i	$-0.722813\pi$
$167$	−1.41556e6	+	817272.i	−0.303933	+	0.175476i	0.340275	+	0.940326i	$0.389480\pi$
$168$	−58631.7	−	932410.i	−0.0123653	−	0.196643i
$169$	2.40925e6	−	4.17294e6i	0.499139	−	0.864534i
$170$			9.31038e6i			1.89505i
$171$	−771651.	+	1.83535e6i	−0.154324	+	0.367055i
$172$	1.23239e6			0.242193
$173$	−8.21215e6	−	4.74129e6i	−1.58606	−	0.915710i	−0.993948	−	0.109851i	$-0.964963\pi$
$173$	−8.21215e6	−	4.74129e6i	−1.58606	−	0.915710i	−0.592108	−	0.805859i	$-0.701704\pi$
$174$	2.12559e6	−	4.28162e6i	0.403489	−	0.812756i
$175$	−3.71946e6	−	6.44229e6i	−0.694009	−	1.20206i
$176$	689231.	−	397928.i	0.126423	−	0.0729905i
$177$	393802.	+	195501.i	0.0710162	+	0.0352557i
$178$	−3193.03	+	5530.50i	−0.000566166	+	0.000980628i
$179$			9.23510e6i			1.61021i	0.593133	+	0.805105i	$0.297891\pi$
$179$			9.23510e6i			1.61021i	−0.593133	+	0.805105i	$0.702109\pi$
$180$	−4.33975e6	+	3.29360e6i	−0.744128	+	0.564747i
$181$	4.59474e6			0.774864			0.387432	−	0.921898i	$-0.373362\pi$
$181$	4.59474e6			0.774864			0.387432	+	0.921898i	$0.373362\pi$
$182$	85366.4	+	49286.3i	0.0141603	+	0.00817546i
$183$	−1.58683e6	+	99782.6i	−0.258926	+	0.0162818i
$184$	−1.80062e6	−	3.11877e6i	−0.289048	−	0.500645i
$185$	−5.65742e6	+	3.26631e6i	−0.893517	+	0.515873i
$186$	1.57103e6	−	1.04371e6i	0.244144	−	0.162197i
$187$	2.73863e6	−	4.74344e6i	0.418801	−	0.725385i
$188$		−	5.31240e6i		−	0.799497i
$189$	1.23768e6	−	3.55301e6i	0.183326	−	0.526273i
$190$	3.60808e6			0.526035
$191$	6.79391e6	+	3.92247e6i	0.975034	+	0.562936i	0.900767	−	0.434302i	$-0.143005\pi$
$191$	6.79391e6	+	3.92247e6i	0.975034	+	0.562936i	0.0742671	+	0.997238i	$0.476338\pi$
$192$	489581.	+	736931.i	0.0691705	+	0.104117i
$193$	2.71892e6	+	4.70931e6i	0.378203	+	0.655066i	0.990801	−	0.135328i	$-0.0432089\pi$
$193$	2.71892e6	+	4.70931e6i	0.378203	+	0.655066i	−0.612598	+	0.790395i	$0.709876\pi$
$194$	6.61511e6	−	3.81924e6i	0.906008	−	0.523084i
$195$	−36074.7	−	573689.i	−0.00486517	−	0.0773701i
$196$	−1.29777e6	+	2.24780e6i	−0.172357	+	0.298531i
$197$		−	1.01096e7i		−	1.32232i	−0.750246	−	0.661159i	$-0.770065\pi$
$197$		−	1.01096e7i		−	1.32232i	0.750246	−	0.661159i	$-0.229935\pi$
$198$	3.17982e6	−	401493.i	0.409644	−	0.0517229i
$199$	−6.91799e6			−0.877851			−0.438925	−	0.898523i	$-0.644641\pi$
$199$	−6.91799e6			−0.877851			−0.438925	+	0.898523i	$0.644641\pi$
$200$	6.10084e6	+	3.52232e6i	0.762606	+	0.440291i
$201$	−3.55372e6	+	7.15833e6i	−0.437618	+	0.881502i
$202$	−449259.	−	778139.i	−0.0545058	−	0.0944068i
$203$	5.18100e6	−	2.99125e6i	0.619335	−	0.357573i
$204$	5.45385e6	+	2.70754e6i	0.642411	+	0.318922i
$205$	−5.04663e6	+	8.74102e6i	−0.585787	+	1.01461i
$206$		−	2.81275e6i		−	0.321758i
$207$	−1.81676e6	−	1.43887e7i	−0.204826	−	1.62222i
$208$	−93348.3			−0.0103733
$209$	−1.83824e6	−	1.06131e6i	−0.201355	−	0.116252i
$210$	−6.80488e6	+	427904.i	−0.734789	+	0.0462049i
$211$	4.27596e6	+	7.40617e6i	0.455183	+	0.788400i	0.998699	−	0.0509990i	$-0.0162405\pi$
$211$	4.27596e6	+	7.40617e6i	0.455183	+	0.788400i	−0.543516	+	0.839399i	$0.682907\pi$
$212$	1.51704e6	−	875863.i	0.159217	−	0.0919240i
$213$	3.53648e6	−	2.34946e6i	0.365959	−	0.243125i
$214$	−585933.	+	1.01487e6i	−0.0597870	+	0.103554i
$215$		−	8.99417e6i		−	0.904994i
$216$	667297.	+	3.49996e6i	0.0662153	+	0.347297i
$217$	2.36052e6			0.231008
$218$	−1.12817e7	−	6.51351e6i	−1.08895	−	0.628703i
$219$	−1.19970e6	−	1.80583e6i	−0.114220	−	0.171927i
$220$	−2.90414e6	−	5.03012e6i	−0.272741	−	0.472401i
$221$	−556372.	+	321222.i	−0.0515452	+	0.0297597i
$222$	268121.	+	4.26389e6i	0.0245060	+	0.389715i
$223$	2.62933e6	−	4.55413e6i	0.237099	−	0.410668i	−0.722782	−	0.691077i	$-0.757137\pi$
$223$	2.62933e6	−	4.55413e6i	0.237099	−	0.410668i	0.959881	+	0.280409i	$0.0904700\pi$
$224$			1.10726e6i			0.0985158i
$225$	1.71511e7	+	2.25988e7i	1.50572	+	1.98398i
$226$	−4.42570e6			−0.383404
$227$	−7.00311e6	−	4.04325e6i	−0.598706	−	0.345663i	0.169827	−	0.985474i	$-0.445679\pi$
$227$	−7.00311e6	−	4.04325e6i	−0.598706	−	0.345663i	−0.768532	+	0.639811i	$0.779013\pi$
$228$	1.04926e6	−	2.11355e6i	0.0885276	−	0.178323i
$229$	6.10057e6	+	1.05665e7i	0.508001	+	0.879883i	0.999957	+	0.00926306i	$0.00294857\pi$
$229$	6.10057e6	+	1.05665e7i	0.508001	+	0.879883i	−0.491957	+	0.870620i	$0.663718\pi$
$230$	−2.27613e7	+	1.31413e7i	−1.87074	+	1.08007i
$231$	3.59281e6	+	1.78363e6i	0.291473	+	0.144700i
$232$	−2.83272e6	+	4.90641e6i	−0.226850	+	0.392916i
$233$		−	5.57473e6i		−	0.440713i	−0.975419	−	0.220357i	$-0.929278\pi$
$233$		−	5.57473e6i		−	0.440713i	0.975419	−	0.220357i	$-0.0707221\pi$
$234$	−346548.	−	145702.i	−0.0270468	−	0.0113715i
$235$	−3.87708e7			−2.98745
$236$	−451266.	−	260539.i	−0.0343318	−	0.0198215i
$237$	−1.01549e7	+	638556.i	−0.762832	+	0.0479683i
$238$	3.81021e6	+	6.59947e6i	0.282630	+	0.489529i
$239$	1.42628e7	−	8.23463e6i	1.04475	−	0.603185i	0.123573	−	0.992336i	$-0.460565\pi$
$239$	1.42628e7	−	8.23463e6i	1.04475	−	0.603185i	0.921174	+	0.389151i	$0.127231\pi$
$240$	5.37825e6	−	3.57305e6i	0.389052	−	0.258467i
$241$	−2.30270e6	+	3.98840e6i	−0.164508	+	0.284936i	−0.936480	−	0.350720i	$-0.885937\pi$
$241$	−2.30270e6	+	3.98840e6i	−0.164508	+	0.284936i	0.771972	+	0.635656i	$0.219270\pi$
$242$		−	6.60448e6i		−	0.466007i
$243$	−2.98560e6	+	1.40349e7i	−0.208071	+	0.978114i
$244$	1.88440e6			0.129719
$245$	1.64048e7	+	9.47133e6i	1.11551	+	0.644040i
$246$	3.65273e6	+	5.49819e6i	0.245365	+	0.369330i
$247$	124484.	+	215612.i	0.00826080	+	0.0143081i
$248$	−1.93592e6	+	1.11770e6i	−0.126921	+	0.0732777i
$249$	−1.43613e6	−	2.28385e7i	−0.0930240	−	1.47935i
$250$	1.53853e7	−	2.66482e7i	0.984662	−	1.70548i
$251$			1.58119e7i			0.999913i	0.866051	+	0.499956i	$0.166651\pi$
$251$			1.58119e7i			0.999913i	−0.866051	+	0.499956i	$0.833349\pi$
$252$	−1.72826e6	+	4.11062e6i	−0.107996	+	0.256865i
$253$	1.54619e7			0.954774
$254$	5.85010e6	+	3.37756e6i	0.356995	+	0.206111i
$255$	1.97601e7	−	3.98031e7i	1.19170	−	2.40047i
$256$	−524288.	−	908093.i	−0.0312500	−	0.0541266i
$257$	1.62608e7	−	9.38815e6i	0.957946	−	0.553071i	0.0624061	−	0.998051i	$-0.480123\pi$
$257$	1.62608e7	−	9.38815e6i	0.957946	−	0.553071i	0.895540	+	0.444980i	$0.146789\pi$
$258$	−5.26863e6	−	2.61558e6i	−0.306788	−	0.152303i
$259$	−2.67343e6	+	4.63052e6i	−0.153876	+	0.266520i
$260$			681271.i			0.0387614i
$261$	−1.81744e7	+	1.37932e7i	−1.02220	+	0.775790i
$262$	−1.42098e7			−0.790106
$263$	−7.38572e6	−	4.26415e6i	−0.406000	−	0.234404i	0.283070	−	0.959099i	$-0.408647\pi$
$263$	−7.38572e6	−	4.26415e6i	−0.406000	−	0.234404i	−0.689069	+	0.724695i	$0.741981\pi$
$264$	−3.79111e6	+	238392.i	−0.206041	+	0.0129563i
$265$	−6.39220e6	−	1.10716e7i	−0.343489	−	0.594940i
$266$	2.55751e6	−	1.47658e6i	0.135885	−	0.0784534i
$267$	25388.4	−	16866.8i	0.00133383	−	0.000886134i
$268$	4.73595e6	−	8.20290e6i	0.246038	−	0.426150i
$269$			1.62898e7i			0.836871i	0.908247	+	0.418436i	$0.137421\pi$
$269$			1.62898e7i			0.836871i	−0.908247	+	0.418436i	$0.862579\pi$
$270$	2.55433e7	−	4.87005e6i	1.29773	−	0.247424i
$271$	2.43919e7			1.22557			0.612785	−	0.790250i	$-0.290049\pi$
$271$	2.43919e7			1.22557			0.612785	+	0.790250i	$0.290049\pi$
$272$	−6.24970e6	−	3.60826e6i	−0.310565	−	0.179305i
$273$	−260349.	−	391885.i	−0.0127958	−	0.0192606i
$274$	2.29806e6	+	3.98036e6i	0.111715	+	0.193496i
$275$	−2.61938e7	+	1.51230e7i	−1.25951	+	0.727177i
$276$	1.07872e6	+	1.71548e7i	0.0513078	+	0.815939i
$277$	1.65615e7	−	2.86854e7i	0.779223	−	1.34965i	−0.153168	−	0.988200i	$-0.548947\pi$
$277$	1.65615e7	−	2.86854e7i	0.779223	−	1.34965i	0.932390	−	0.361453i	$-0.117719\pi$
$278$		−	3.96608e6i		−	0.184598i
$279$	−8.93151e6	+	1.12772e6i	−0.411256	+	0.0519264i
$280$	8.08098e6			0.368120
$281$	−3.13249e6	−	1.80854e6i	−0.141179	−	0.0815098i	0.427747	−	0.903899i	$-0.359308\pi$
$281$	−3.13249e6	−	1.80854e6i	−0.141179	−	0.0815098i	−0.568926	+	0.822389i	$0.692641\pi$
$282$	−1.12749e7	+	2.27112e7i	−0.502764	+	1.01273i
$283$	1.61928e7	+	2.80467e7i	0.714435	+	1.23744i	0.963177	+	0.268868i	$0.0866494\pi$
$283$	1.61928e7	+	2.80467e7i	0.714435	+	1.23744i	−0.248742	+	0.968570i	$0.580017\pi$
$284$	−4.35787e6	+	2.51602e6i	−0.190248	+	0.109839i
$285$	−1.54250e7	−	7.65767e6i	−0.666333	−	0.330797i
$286$	200394.	−	347093.i	0.00856618	−	0.0148371i
$287$			8.26120e6i			0.349460i
$288$	−528986.	−	4.18956e6i	−0.0221445	−	0.175384i
$289$	−2.55282e7			−1.05761
$290$	3.58078e7	+	2.06736e7i	1.46819	+	0.847662i
$291$	−3.63864e7	+	2.28804e6i	−1.47659	+	0.0928507i
$292$	1.28475e6	+	2.22526e6i	0.0516025	+	0.0893781i
$293$	−1.44996e7	+	8.37133e6i	−0.576437	+	0.332806i	−0.759716	−	0.650255i	$-0.774662\pi$
$293$	−1.44996e7	+	8.37133e6i	−0.576437	+	0.332806i	0.183279	+	0.983061i	$0.441329\pi$
$294$	1.03188e7	−	6.85531e6i	0.406057	−	0.269765i
$295$	−1.90146e6	+	3.29342e6i	−0.0740662	+	0.128286i
$296$		−	5.06348e6i		−	0.195242i
$297$	−1.44463e7	−	5.03231e6i	−0.551425	−	0.192087i
$298$	1.73185e6			0.0654426
$299$	−1.57060e6	−	906785.i	−0.0587559	−	0.0339227i
$300$	−1.86063e7	−	2.80067e7i	−0.689121	−	1.03728i
$301$	−3.68080e6	−	6.37534e6i	−0.134972	−	0.233778i
$302$	−9.05120e6	+	5.22571e6i	−0.328613	+	0.189725i
$303$	269144.	+	4.28015e6i	0.00967511	+	0.153862i
$304$	−1.39832e6	+	2.42196e6i	−0.0497721	+	0.0862078i
$305$		−	1.37527e7i		−	0.484716i
$306$	−1.75696e7	−	2.31502e7i	−0.613192	−	0.807961i
$307$	1.09311e7			0.377790			0.188895	−	0.981997i	$-0.439509\pi$
$307$	1.09311e7			0.377790			0.188895	+	0.981997i	$0.439509\pi$
$308$	−4.11708e6	−	2.37700e6i	−0.140909	−	0.0813536i
$309$	−5.96969e6	+	1.20249e7i	−0.202338	+	0.407573i
$310$	8.15719e6	+	1.41287e7i	0.273814	+	0.474260i
$311$	4.40580e7	−	2.54369e7i	1.46468	−	0.845635i	0.465461	−	0.885068i	$-0.345888\pi$
$311$	4.40580e7	−	2.54369e7i	1.46468	−	0.845635i	0.999222	+	0.0394328i	$0.0125551\pi$
$312$	399077.	+	198120.i	0.0131399	+	0.00652324i
$313$	−1.19934e7	+	2.07732e7i	−0.391120	+	0.677440i	−0.992598	−	0.121450i	$-0.961246\pi$
$313$	−1.19934e7	+	2.07732e7i	−0.391120	+	0.677440i	0.601478	+	0.798890i	$0.294579\pi$
$314$		−	1.78228e7i		−	0.575687i
$315$	3.00000e7	+	1.26131e7i	0.959819	+	0.403544i
$316$	1.20592e7			0.382169
$317$	1.93571e7	+	1.11758e7i	0.607662	+	0.350834i	0.772050	−	0.635562i	$-0.219232\pi$
$317$	1.93571e7	+	1.11758e7i	0.607662	+	0.350834i	−0.164388	+	0.986396i	$0.552565\pi$
$318$	−8.34446e6	+	524715.i	−0.259488	+	0.0163171i
$319$	−1.21622e7	−	2.10655e7i	−0.374662	−	0.648934i
$320$	−6.62742e6	+	3.82634e6i	−0.202253	+	0.116771i
$321$	4.65886e6	−	3.09512e6i	0.140853	−	0.0935756i
$322$	−1.07559e7	+	1.86298e7i	−0.322167	+	0.558009i
$323$			1.92471e7i			0.571160i
$324$	4.57542e6	−	1.63791e7i	0.134523	−	0.481564i
$325$	3.54765e6			0.103345
$326$	−6.35800e6	−	3.67079e6i	−0.183513	−	0.105952i
$327$	3.44069e7	+	5.17902e7i	0.984015	+	1.48117i
$328$	−3.91168e6	−	6.77522e6i	−0.110851	−	0.192000i
$329$	−2.74819e7	+	1.58667e7i	−0.771718	+	0.445551i
$330$	1.73982e6	+	2.76681e7i	0.0484131	+	0.769906i
$331$	2.20105e7	−	3.81233e7i	0.606941	−	1.05125i	−0.384801	−	0.923000i	$-0.625730\pi$
$331$	2.20105e7	−	3.81233e7i	0.606941	−	1.05125i	0.991742	−	0.128252i	$-0.0409368\pi$
$332$			2.71213e7i			0.741134i
$333$	7.90329e6	−	1.87978e7i	0.214030	−	0.509065i
$334$	−9.24638e6			−0.248160
$335$	−5.98661e7	−	3.45637e7i	−1.59238	−	0.919361i
$336$	2.35002e6	−	4.73369e6i	0.0619517	−	0.124791i
$337$	−2.44378e7	−	4.23275e7i	−0.638516	−	1.10594i	−0.985758	−	0.168167i	$-0.946215\pi$
$337$	−2.44378e7	−	4.23275e7i	−0.638516	−	1.10594i	0.347242	−	0.937776i	$-0.387118\pi$
$338$	2.36057e7	−	1.36288e7i	0.611318	−	0.352945i
$339$	1.89205e7	+	9.39298e6i	0.485661	+	0.241104i
$340$	−2.63337e7	+	4.56113e7i	−0.670001	+	1.16048i
$341$		−	9.59768e6i		−	0.242049i
$342$	−8.97146e6	+	6.80878e6i	−0.224277	+	0.170212i
$343$	3.79930e7			0.941501
$344$	6.03744e6	+	3.48572e6i	0.148312	+	0.0856282i
$345$	1.25198e8	−	7.87271e6i	3.04889	−	0.191720i
$346$	−2.68208e7	−	4.64549e7i	−0.647505	−	1.12151i
$347$	4.77428e7	−	2.75643e7i	1.14267	−	0.659719i	0.195577	−	0.980688i	$-0.437342\pi$
$347$	4.77428e7	−	2.75643e7i	1.14267	−	0.659719i	0.947089	+	0.320970i	$0.104009\pi$
$348$	2.25235e7	−	1.49635e7i	0.534438	−	0.355055i
$349$	−9.97084e6	+	1.72700e7i	−0.234561	+	0.406271i	−0.959145	−	0.282915i	$-0.908699\pi$
$349$	−9.97084e6	+	1.72700e7i	−0.234561	+	0.406271i	0.724584	+	0.689186i	$0.242032\pi$
$350$		−	4.20808e7i		−	0.981477i
$351$	1.17231e6	+	1.35840e6i	0.0271094	+	0.0314128i
$352$	4.50204e6			0.103224
$353$	−6.52970e7	−	3.76992e7i	−1.48446	−	0.857054i	−0.484617	−	0.874726i	$-0.661041\pi$
$353$	−6.52970e7	−	3.76992e7i	−1.48446	−	0.857054i	−0.999844	+	0.0176724i	$0.994374\pi$
$354$	1.37627e6	+	2.07159e6i	0.0310236	+	0.0466976i
$355$	1.83623e7	+	3.18045e7i	0.410433	+	0.710891i
$356$	−31285.2	+	18062.5i	−0.000693408	+	0.000400340i
$357$	−2.28263e6	−	3.63003e7i	−0.0501685	−	0.797821i
$358$	−2.61208e7	+	4.52425e7i	−0.569295	+	0.986048i
$359$			5.29978e7i			1.14545i	0.819749	+	0.572723i	$0.194113\pi$
$359$			5.29978e7i			1.14545i	−0.819749	+	0.572723i	$0.805887\pi$
$360$	−3.05761e7	+	3.86063e6i	−0.655351	+	0.0827466i
$361$	−3.95870e7			−0.841455
$362$	2.25096e7	+	1.29959e7i	0.474506	+	0.273956i
$363$	−1.40171e7	+	2.82350e7i	−0.293049	+	0.590294i
$364$	278805.	+	482905.i	0.00578092	+	0.0100129i
$365$	1.62403e7	−	9.37633e6i	0.333976	−	0.192821i
$366$	−8.05606e6	−	3.99939e6i	−0.164316	−	0.0815738i
$367$	−2.03953e7	+	3.53257e7i	−0.412602	+	0.714648i	−0.995173	−	0.0981316i	$-0.968713\pi$
$367$	−2.03953e7	+	3.53257e7i	−0.412602	+	0.714648i	0.582571	+	0.812780i	$0.302047\pi$
$368$		−	2.03717e7i		−	0.408775i
$369$	−3.94673e6	−	3.12580e7i	−0.0785521	−	0.622131i
$370$	−3.69541e7			−0.729554
$371$	−9.06196e6	−	5.23192e6i	−0.177460	−	0.102457i
$372$	1.06485e7	−	669598.i	0.206852	−	0.0130072i
$373$	2.14508e7	+	3.71539e7i	0.413349	+	0.715941i	0.995254	−	0.0973156i	$-0.0310256\pi$
$373$	2.14508e7	+	3.71539e7i	0.413349	+	0.715941i	−0.581905	+	0.813257i	$0.697692\pi$
$374$	2.68329e7	−	1.54920e7i	0.512924	−	0.296137i
$375$	−1.22332e8	+	8.12713e7i	−2.31977	+	1.54114i
$376$	1.50257e7	−	2.60253e7i	0.282665	−	0.489590i
$377$			2.85308e6i			0.0532464i
$378$	1.61128e7	−	1.39054e7i	0.298329	−	0.257460i
$379$	−3.56353e6			−0.0654579			−0.0327290	−	0.999464i	$-0.510420\pi$
$379$	−3.56353e6			−0.0654579			−0.0327290	+	0.999464i	$0.510420\pi$
$380$	1.76759e7	+	1.02052e7i	0.322129	+	0.185982i
$381$	−1.78416e7	−	2.68556e7i	−0.322595	−	0.485579i
$382$	2.21888e7	+	3.84322e7i	0.398056	+	0.689453i
$383$	−5.10154e7	+	2.94538e7i	−0.908040	+	0.524257i	−0.879800	−	0.475344i	$-0.842324\pi$
$383$	−5.10154e7	+	2.94538e7i	−0.908040	+	0.524257i	−0.0282400	+	0.999601i	$0.508990\pi$
$384$	314092.	+	4.99496e6i	0.00554707	+	0.0882141i
$385$	−1.73477e7	+	3.00472e7i	−0.303991	+	0.526528i
$386$			3.07611e7i			0.534860i
$387$	1.69729e7	+	2.23640e7i	0.292834	+	0.385847i
$388$	4.32097e7			0.739753
$389$	3.81501e7	+	2.20260e7i	0.648108	+	0.374185i	0.787731	−	0.616020i	$-0.211256\pi$
$389$	3.81501e7	+	2.20260e7i	0.648108	+	0.374185i	−0.139623	+	0.990205i	$0.544589\pi$
$390$	1.44591e6	−	2.91253e6i	0.0243752	−	0.0490994i
$391$	−7.01014e7	−	1.21419e8i	−1.17273	−	2.03122i
$392$	−1.27155e7	+	7.34129e6i	−0.211093	+	0.121875i
$393$	6.07490e7	+	3.01585e7i	1.00083	+	0.496858i
$394$	2.85943e7	−	4.95268e7i	0.467510	−	0.809751i
$395$		−	8.80097e7i		−	1.42804i
$396$	1.67135e7	+	7.02697e6i	0.269141	+	0.113157i
$397$	2.93968e6			0.0469818			0.0234909	−	0.999724i	$-0.492522\pi$
$397$	2.93968e6			0.0469818			0.0234909	+	0.999724i	$0.492522\pi$
$398$	−3.38911e7	−	1.95670e7i	−0.537572	−	0.310367i
$399$	−1.40676e7	+	884594.i	−0.221462	+	0.0139260i
$400$	1.99253e7	+	3.45116e7i	0.311332	+	0.539244i
$401$	−1.38960e7	+	8.02289e6i	−0.215505	+	0.124422i	−0.603867	−	0.797085i	$-0.706374\pi$
$401$	−1.38960e7	+	8.02289e6i	−0.215505	+	0.124422i	0.388362	+	0.921507i	$0.373041\pi$
$402$	−3.76564e7	+	2.50171e7i	−0.579643	+	0.385087i
$403$	−562870.	+	974920.i	−0.00859989	+	0.0148955i
$404$		−	5.08278e6i		−	0.0770828i
$405$	−1.19537e8	−	3.33922e7i	−1.79944	−	0.502666i
$406$	3.38422e7			0.505685
$407$	1.88273e7	+	1.08700e7i	0.279258	+	0.161230i
$408$	1.90602e7	+	2.86900e7i	0.280639	+	0.422425i
$409$	9.04280e6	+	1.56626e7i	0.132170	+	0.228925i	0.924513	−	0.381151i	$-0.124472\pi$
$409$	9.04280e6	+	1.56626e7i	0.132170	+	0.228925i	−0.792343	+	0.610076i	$0.791139\pi$
$410$	−4.94467e7	+	2.85481e7i	−0.717440	+	0.414214i
$411$	−1.37673e6	−	2.18939e7i	−0.0198301	−	0.315354i
$412$	7.95565e6	−	1.37796e7i	0.113759	−	0.197036i
$413$			3.11263e6i			0.0441853i
$414$	3.17971e7	−	7.56284e7i	0.448112	−	1.06582i
$415$	1.97936e8			2.76937
$416$	−457311.	−	264029.i	−0.00635231	−	0.00366751i
$417$	−8.41748e6	+	1.69555e7i	−0.116084	+	0.233831i
$418$	−6.00366e6	−	1.03986e7i	−0.0822029	−	0.142380i
$419$	−6.46244e6	+	3.73109e6i	−0.0878525	+	0.0507217i	−0.543283	−	0.839550i	$-0.682819\pi$
$419$	−6.46244e6	+	3.73109e6i	−0.0878525	+	0.0507217i	0.455430	+	0.890272i	$0.349485\pi$
$420$	−3.45473e7	−	1.71508e7i	−0.466301	−	0.231493i
$421$	1.16773e7	−	2.02257e7i	0.156494	−	0.271055i	−0.777108	−	0.629367i	$-0.783314\pi$
$421$	1.16773e7	−	2.02257e7i	0.156494	−	0.271055i	0.933602	+	0.358312i	$0.116648\pi$
$422$			4.83769e7i			0.643726i
$423$	9.64032e7	−	7.31641e7i	1.27371	−	0.966667i
$424$	9.90926e6			0.130000
$425$	2.37516e8	+	1.37130e8i	3.09405	+	1.78635i
$426$	2.39704e7	−	1.50730e6i	0.310061	−	0.0194972i
$427$	−5.62818e6	−	9.74829e6i	−0.0722910	−	0.125212i
$428$	−5.74095e6	+	3.31454e6i	−0.0732238	+	0.0422758i
$429$	−1.59337e6	+	1.05856e6i	−0.0201811	+	0.0134074i
$430$	2.54394e7	−	4.40623e7i	0.319964	−	0.554193i
$431$		−	7.00387e7i		−	0.874795i	−0.899268	−	0.437397i	$-0.855900\pi$
$431$		−	7.00387e7i		−	0.874795i	0.899268	−	0.437397i	$-0.144100\pi$
$432$	−6.63030e6	+	1.90336e7i	−0.0822398	+	0.236086i
$433$	−8.83901e7			−1.08878			−0.544390	−	0.838832i	$-0.683239\pi$
$433$	−8.83901e7			−1.08878			−0.544390	+	0.838832i	$0.683239\pi$
$434$	1.15641e7	+	6.67655e6i	0.141463	+	0.0816738i
$435$	−1.09206e8	−	1.64380e8i	−1.32672	−	1.99701i
$436$	−3.68460e7	−	6.38191e7i	−0.444560	−	0.770001i
$437$	−4.70539e7	+	2.71666e7i	−0.563834	+	0.325530i
$438$	−769674.	−	1.22400e7i	−0.00915976	−	0.145666i
$439$	−5.11723e7	+	8.86331e7i	−0.604842	+	1.04762i	0.387235	+	0.921981i	$0.373430\pi$
$439$	−5.11723e7	+	8.86331e7i	−0.604842	+	1.04762i	−0.992076	+	0.125635i	$0.959903\pi$
$440$		−	3.28566e7i		−	0.385713i
$441$	−5.86638e7	+	7.40707e6i	−0.683998	+	0.0863636i
$442$	−3.63421e6			−0.0420865
$443$	−1.10522e8	−	6.38100e7i	−1.27127	−	0.733969i	−0.296045	−	0.955174i	$-0.595668\pi$
$443$	−1.10522e8	−	6.38100e7i	−1.27127	−	0.733969i	−0.975227	+	0.221205i	$0.929001\pi$
$444$	−1.07466e7	+	2.16471e7i	−0.122778	+	0.247315i
$445$	131823.	+	228325.i	0.00149593	+	0.00259103i
$446$	2.57620e7	−	1.48737e7i	0.290386	−	0.167654i
$447$	−7.40388e6	−	3.67562e6i	−0.0828966	−	0.0411536i
$448$	−3.13181e6	+	5.42445e6i	−0.0348306	+	0.0603284i
$449$			1.44858e8i			1.60031i	0.599795	+	0.800154i	$0.295249\pi$
$449$			1.44858e8i			1.60031i	−0.599795	+	0.800154i	$0.704751\pi$
$450$	2.01038e7	+	1.59222e8i	0.220618	+	1.74729i
$451$	3.35894e7			0.366161
$452$	−2.16814e7	−	1.25178e7i	−0.234786	−	0.135554i
$453$	4.97860e7	−	3.13064e6i	0.535566	−	0.0336774i
$454$	−2.28721e7	−	3.96156e7i	−0.244421	−	0.423349i
$455$	3.52432e6	−	2.03477e6i	0.0374146	−	0.0216014i
$456$	1.11183e7	−	7.38647e6i	0.117259	−	0.0779009i
$457$	5.09129e7	−	8.81838e7i	0.533433	−	0.923933i	−0.465805	−	0.884888i	$-0.654235\pi$
$457$	5.09129e7	−	8.81838e7i	0.533433	−	0.923933i	0.999237	−	0.0390451i	$-0.0124316\pi$
$458$			6.90201e7i			0.718421i
$459$	2.59790e7	+	1.36259e8i	0.268649	+	1.40906i
$460$	−1.48676e8			−1.52745
$461$	5.98283e7	+	3.45419e7i	0.610666	+	0.352568i	0.773226	−	0.634130i	$-0.218642\pi$
$461$	5.98283e7	+	3.45419e7i	0.610666	+	0.352568i	−0.162560	+	0.986699i	$0.551975\pi$
$462$	1.25562e7	+	1.89000e7i	0.127331	+	0.191662i
$463$	6.74662e7	+	1.16855e8i	0.679741	+	1.17735i	0.975059	+	0.221947i	$0.0712411\pi$
$463$	6.74662e7	+	1.16855e8i	0.679741	+	1.17735i	−0.295318	+	0.955399i	$0.595426\pi$
$464$	−2.77548e7	+	1.60243e7i	−0.277833	+	0.160407i
$465$	−4.88684e6	−	7.77146e7i	−0.0486037	−	0.772936i
$466$	1.57677e7	−	2.73105e7i	0.155816	−	0.269881i
$467$			1.23430e8i			1.21191i	0.795500	+	0.605954i	$0.207208\pi$
$467$			1.23430e8i			1.21191i	−0.795500	+	0.605954i	$0.792792\pi$
$468$	−1.28562e6	−	1.69398e6i	−0.0125423	−	0.0165261i
$469$	−5.65798e7			−0.548458
$470$	−1.89937e8	−	1.09660e8i	−1.82943	−	1.05622i
$471$	−3.78265e7	+	7.61948e7i	−0.362021	+	0.729227i
$472$	−1.47383e6	−	2.55275e6i	−0.0140159	−	0.0242763i
$473$	−2.59216e7	+	1.49659e7i	−0.244951	+	0.141422i
$474$	−5.15545e7	−	2.55940e7i	−0.484096	−	0.240327i
$475$	5.31424e7	−	9.20453e7i	0.495861	−	0.858857i
$476$			4.31076e7i			0.399699i
$477$	3.67873e7	+	1.54668e7i	0.338956	+	0.142510i
$478$	9.31642e7			0.853032
$479$	−6.01036e7	−	3.47008e7i	−0.546882	−	0.315743i	0.200981	−	0.979595i	$-0.435587\pi$
$479$	−6.01036e7	−	3.47008e7i	−0.546882	−	0.315743i	−0.747864	+	0.663852i	$0.768920\pi$
$480$	3.64540e7	−	2.29230e6i	0.329626	−	0.0207275i
$481$	−1.27497e6	−	2.20831e6i	−0.0114568	−	0.0198438i
$482$	−2.25618e7	+	1.30261e7i	−0.201480	+	0.116325i
$483$	8.55225e7	−	5.68170e7i	0.758995	−	0.504239i
$484$	1.86803e7	−	3.23552e7i	0.164758	−	0.285370i
$485$		−	3.15352e8i		−	2.76420i
$486$	−5.43230e7	+	6.03120e7i	−0.473233	+	0.525405i
$487$	−2.01197e8			−1.74195			−0.870973	−	0.491331i	$-0.836511\pi$
$487$	−2.01197e8			−1.74195			−0.870973	+	0.491331i	$0.836511\pi$
$488$	9.23163e6	+	5.32988e6i	0.0794363	+	0.0458626i
$489$	1.93905e7	+	2.91872e7i	0.165830	+	0.249612i
$490$	5.35779e7	+	9.27997e7i	0.455405	+	0.788785i
$491$	1.72658e8	−	9.96841e7i	1.45862	−	0.842135i	0.459676	−	0.888087i	$-0.347965\pi$
$491$	1.72658e8	−	9.96841e7i	1.45862	−	0.842135i	0.998944	+	0.0459519i	$0.0146321\pi$
$492$	2.34342e6	+	3.72670e7i	0.0196768	+	0.312917i
$493$	−1.10282e8	+	1.91015e8i	−0.920377	+	1.59414i
$494$			1.40837e6i			0.0116825i
$495$	5.12840e7	−	1.21978e8i	0.422831	−	1.00569i
$496$	−1.26454e7			−0.103630
$497$	2.60315e7	+	1.50293e7i	0.212046	+	0.122425i
$498$	5.75615e7	−	1.15947e8i	0.466062	−	0.938799i
$499$	4.38674e7	+	7.59805e7i	0.353053	+	0.611506i	0.986783	−	0.162049i	$-0.0518102\pi$
$499$	4.38674e7	+	7.59805e7i	0.353053	+	0.611506i	−0.633730	+	0.773555i	$0.718477\pi$
$500$	1.50745e8	−	8.70326e7i	1.20596	−	0.696261i
$501$	3.95295e7	+	1.96242e7i	0.314346	+	0.156056i
$502$	−4.47227e7	+	7.74620e7i	−0.353523	+	0.612319i
$503$		−	1.53094e8i		−	1.20297i	−0.798885	−	0.601484i	$-0.794576\pi$
$503$		−	1.53094e8i		−	1.20297i	0.798885	−	0.601484i	$-0.205424\pi$
$504$	−2.00933e7	+	1.52496e7i	−0.156949	+	0.119115i
$505$	−3.70950e7			−0.288032
$506$	7.57474e7	+	4.37328e7i	0.584677	+	0.337564i
$507$	−1.29843e8	+	8.16477e6i	−0.996310	+	0.0626499i
$508$	1.91063e7	+	3.30932e7i	0.145743	+	0.252434i
$509$	1.05471e8	−	6.08939e7i	0.799799	−	0.461764i	−0.0436020	−	0.999049i	$-0.513883\pi$
$509$	1.05471e8	−	6.08939e7i	0.799799	−	0.461764i	0.843401	+	0.537285i	$0.180550\pi$
$510$	2.09384e8	−	1.39105e8i	1.57846	−	1.04865i
$511$	7.67440e6	−	1.32924e7i	0.0575151	−	0.0996190i
$512$		−	5.93164e6i		−	0.0441942i
$513$	5.28050e7	−	1.00677e7i	0.391131	−	0.0745726i
$514$	1.06215e8			0.782160
$515$	−1.00566e8	−	5.80617e7i	−0.736255	−	0.425077i
$516$	−1.84129e7	−	2.77156e7i	−0.134021	−	0.201732i
$517$	6.45126e7	+	1.11739e8i	0.466845	+	0.808600i
$518$	−2.61942e7	+	1.51232e7i	−0.188458	+	0.108806i
$519$	1.60679e7	+	2.55525e8i	0.114936	+	1.82781i
$520$	−1.92693e6	+	3.33753e6i	−0.0137042	+	0.0237364i
$521$			1.44805e8i			1.02393i	0.859006	+	0.511965i	$0.171082\pi$
$521$			1.44805e8i			1.02393i	−0.859006	+	0.511965i	$0.828918\pi$
$522$	−1.28049e8	+	1.61678e7i	−0.900253	+	0.113669i
$523$	−2.14387e8			−1.49863			−0.749313	−	0.662216i	$-0.769616\pi$
$523$	−2.14387e8			−1.49863			−0.749313	+	0.662216i	$0.769616\pi$
$524$	−6.96137e7	−	4.01915e7i	−0.483839	−	0.279345i
$525$	−8.93111e7	+	1.79901e8i	−0.617202	+	1.24324i
$526$	−2.41217e7	−	4.17800e7i	−0.165749	−	0.287085i
$527$	−7.53687e7	+	4.35141e7i	−0.514943	+	0.297302i
$528$	−1.92468e7	−	9.55499e6i	−0.130755	−	0.0649125i
$529$	1.23873e8	−	2.14554e8i	0.836777	−	1.44934i
$530$		−	7.23194e7i		−	0.485766i
$531$	−1.48704e6	−	1.17773e7i	−0.00993203	−	0.0786614i
$532$	1.67056e7			0.110950
$533$	−3.41197e6	−	1.96990e6i	−0.0225332	−	0.0130096i
$534$	172084.	−	10821.0i	0.00113010	−	7.10627e-5i
$535$	2.41900e7	+	4.18984e7i	0.157970	+	0.273612i
$536$	4.64026e7	−	2.67906e7i	0.301334	−	0.173975i
$537$	2.07691e8	−	1.37980e8i	1.34121	−	0.891032i
$538$	−4.60745e7	+	7.98033e7i	−0.295879	+	0.512477i
$539$		−	6.30393e7i		−	0.402573i
$540$	1.38911e8	+	4.83890e7i	0.882174	+	0.307302i
$541$	3.66711e7			0.231596			0.115798	−	0.993273i	$-0.463057\pi$
$541$	3.66711e7			0.231596			0.115798	+	0.993273i	$0.463057\pi$
$542$	1.19496e8	+	6.89908e7i	0.750505	+	0.433304i
$543$	−6.86493e7	−	1.03333e8i	−0.428782	−	0.645415i
$544$	−2.04114e7	−	3.53536e7i	−0.126788	−	0.219603i
$545$	−4.65762e8	+	2.68908e8i	−2.87723	+	1.66117i
$546$	−167028.	−	2.65621e6i	−0.00102615	−	0.0163187i
$547$	1.50211e8	−	2.60172e8i	0.917780	−	1.58964i	0.115001	−	0.993365i	$-0.463313\pi$
$547$	1.50211e8	−	2.60172e8i	0.917780	−	1.58964i	0.802779	−	0.596277i	$-0.203354\pi$
$548$			2.59996e7i			0.157989i
$549$	2.59526e7	+	3.41959e7i	0.156842	+	0.206660i
$550$	−1.71097e8			−1.02838
$551$	7.40245e7	+	4.27381e7i	0.442507	+	0.255482i
$552$	−4.32364e7	+	8.70919e7i	−0.257058	+	0.517798i
$553$	−3.60174e7	−	6.23839e7i	−0.212979	−	0.368890i
$554$	1.62269e8	−	9.36863e7i	0.954349	−	0.550994i
$555$	1.57984e8	+	7.84303e7i	0.924131	+	0.458780i
$556$	1.12178e7	−	1.94297e7i	0.0652652	−	0.113043i
$557$		−	2.64642e8i		−	1.53141i	−0.643190	−	0.765707i	$-0.722389\pi$
$557$		−	2.64642e8i		−	1.53141i	0.643190	−	0.765707i	$-0.277611\pi$
$558$	−4.69450e7	−	1.97375e7i	−0.270201	−	0.113603i
$559$	3.51078e6			0.0200987
$560$	3.95885e7	+	2.28564e7i	0.225427	+	0.130150i
$561$	−1.47594e8	+	9.28100e6i	−0.835951	+	0.0525662i
$562$	−1.02307e7	−	1.77200e7i	−0.0576361	−	0.0998287i
$563$	−5.98361e7	+	3.45464e7i	−0.335304	+	0.193588i	−0.658193	−	0.752849i	$-0.728679\pi$
$563$	−5.98361e7	+	3.45464e7i	−0.335304	+	0.193588i	0.322890	+	0.946437i	$0.395346\pi$
$564$	−1.19472e8	+	7.93716e7i	−0.665933	+	0.442413i
$565$	−9.13569e7	+	1.58235e8i	−0.506519	+	0.877317i
$566$			1.83201e8i			1.01036i
$567$	−9.83969e7	+	2.52503e7i	−0.539799	+	0.138522i
$568$	−2.84655e7			−0.155336
$569$	−1.21080e8	−	6.99054e7i	−0.657256	−	0.379467i	0.133975	−	0.990985i	$-0.457226\pi$
$569$	−1.21080e8	−	6.99054e7i	−0.657256	−	0.379467i	−0.791231	+	0.611518i	$0.790559\pi$
$570$	−5.39077e7	−	8.11433e7i	−0.291089	−	0.438155i
$571$	−1.02493e8	−	1.77523e8i	−0.550537	−	0.953557i	−0.998236	−	0.0593731i	$-0.981090\pi$
$571$	−1.02493e8	−	1.77523e8i	−0.550537	−	0.953557i	0.447699	−	0.894184i	$-0.352244\pi$
$572$	1.96346e6	−	1.13360e6i	0.0104914	−	0.00605721i
$573$	−1.32930e7	−	2.11396e8i	−0.0706574	−	1.12365i
$574$	−2.33662e7	+	4.04714e7i	−0.123553	+	0.214000i
$575$			7.74216e8i			4.07248i
$576$	9.25836e6	−	2.20207e7i	0.0484470	−	0.115230i
$577$	1.77665e8			0.924854			0.462427	−	0.886657i	$-0.346979\pi$
$577$	1.77665e8			0.924854			0.462427	+	0.886657i	$0.346979\pi$
$578$	−1.25062e8	−	7.22046e7i	−0.647652	−	0.373922i
$579$	6.52864e7	−	1.31508e8i	0.336347	−	0.677510i
$580$	1.16948e8	+	2.02559e8i	0.599387	+	1.03817i
$581$	1.40303e8	−	8.10039e7i	0.715382	−	0.413026i
$582$	−1.84728e8	−	9.17071e7i	−0.937050	−	0.465194i
$583$	−2.12726e7	+	3.68452e7i	−0.107353	+	0.185941i
$584$			1.45353e7i			0.0729769i
$585$	−1.23629e7	+	9.38270e6i	−0.0617524	+	0.0468662i
$586$	−9.47107e7			−0.470659
$587$	2.92418e8	+	1.68828e8i	1.44574	+	0.834698i	0.998224	−	0.0595787i	$-0.0189757\pi$
$587$	2.92418e8	+	1.68828e8i	1.44574	+	0.834698i	0.447515	+	0.894276i	$0.352309\pi$
$588$	6.99414e7	−	4.39804e6i	0.344035	−	0.0216335i
$589$	1.68632e7	+	2.92078e7i	0.0825264	+	0.142940i
$590$	−1.86304e7	+	1.07563e7i	−0.0907122	+	0.0523727i
$591$	−2.27359e8	+	1.51046e8i	−1.10141	+	0.731723i
$592$	1.43217e7	−	2.48059e7i	0.0690285	−	0.119561i
$593$		−	1.84023e8i		−	0.882488i	−0.897387	−	0.441244i	$-0.854537\pi$
$593$		−	1.84023e8i		−	0.882488i	0.897387	−	0.441244i	$-0.145463\pi$
$594$	−5.65385e7	−	6.55134e7i	−0.269764	−	0.312587i
$595$	3.14606e8			1.49354
$596$	8.48428e6	+	4.89840e6i	0.0400752	+	0.0231375i
$597$	1.03361e8	+	1.55581e8i	0.485771	+	0.731197i
$598$	−5.12955e6	−	8.88464e6i	−0.0239870	−	0.0415467i
$599$	1.41355e8	−	8.16115e7i	0.657705	−	0.379726i	−0.133697	−	0.991022i	$-0.542685\pi$
$599$	1.41355e8	−	8.16115e7i	0.657705	−	0.379726i	0.791402	+	0.611296i	$0.209351\pi$
$600$	−1.19369e7	−	1.89831e8i	−0.0552634	−	0.878845i
$601$	8.57858e7	−	1.48585e8i	0.395177	−	0.684467i	−0.597947	−	0.801536i	$-0.704017\pi$
$601$	8.57858e7	−	1.48585e8i	0.395177	−	0.684467i	0.993124	+	0.117069i	$0.0373498\pi$
$602$		−	4.16435e7i		−	0.190879i
$603$	2.14082e8	−	2.70306e7i	0.976400	−	0.123283i
$604$	−5.91222e7			−0.268312
$605$	−2.36134e8	−	1.36332e8i	−1.06633	−	0.615646i
$606$	−1.07876e7	+	2.17296e7i	−0.0484736	+	0.0976414i
$607$	−9.26524e6	−	1.60479e7i	−0.0414277	−	0.0717549i	0.844568	−	0.535448i	$-0.179857\pi$
$607$	−9.26524e6	−	1.60479e7i	−0.0414277	−	0.0717549i	−0.885996	+	0.463693i	$0.846524\pi$
$608$	−1.37007e7	+	7.91010e6i	−0.0609581	+	0.0351942i
$609$	−1.44680e8	−	7.18256e7i	−0.640555	−	0.318000i
$610$	3.88984e7	−	6.73740e7i	0.171373	−	0.296826i
$611$		−	1.51338e7i		−	0.0663473i
$612$	−2.05943e7	−	1.63107e8i	−0.0898449	−	0.711569i
$613$	3.64689e8			1.58322			0.791609	−	0.611028i	$-0.209244\pi$
$613$	3.64689e8			1.58322			0.791609	+	0.611028i	$0.209244\pi$
$614$	5.35514e7	+	3.09179e7i	0.231348	+	0.133569i
$615$	2.71981e8	−	1.71027e7i	1.16927	−	0.0735256i
$616$	−1.34463e7	−	2.32897e7i	−0.0575257	−	0.0996375i
$617$	−6.50805e7	+	3.75743e7i	−0.277074	+	0.159969i	−0.632098	−	0.774888i	$-0.717806\pi$
$617$	−6.50805e7	+	3.75743e7i	−0.277074	+	0.159969i	0.355024	+	0.934857i	$0.384473\pi$
$618$	−6.32569e7	+	4.20248e7i	−0.268005	+	0.178049i
$619$	1.42862e6	−	2.47445e6i	0.00602345	−	0.0104329i	−0.862998	−	0.505207i	$-0.831416\pi$
$619$	1.42862e6	−	2.47445e6i	0.00602345	−	0.0104329i	0.869021	+	0.494774i	$0.164749\pi$
$620$			9.22881e7i			0.387231i
$621$	−2.96448e8	+	2.55837e8i	−1.23787	+	1.06829i
$622$	2.87786e8			1.19591
$623$	186881.	+	107896.i	0.000772859	+	0.000446210i
$624$	1.39470e6	+	2.09934e6i	0.00574020	+	0.00864032i
$625$	−3.31143e8	−	5.73557e8i	−1.35636	−	2.34929i
$626$	−1.17511e8	+	6.78450e7i	−0.479022	+	0.276564i
$627$	3.59669e6	+	5.71976e7i	0.0145915	+	0.232047i
$628$	5.04104e7	−	8.73134e7i	0.203536	−	0.352535i
$629$		−	1.97130e8i		−	0.792137i
$630$	1.11294e8	+	1.46644e8i	0.445092	+	0.586467i
$631$	−9.87283e7			−0.392965			−0.196482	−	0.980507i	$-0.562952\pi$
$631$	−9.87283e7			−0.392965			−0.196482	+	0.980507i	$0.562952\pi$
$632$	5.90775e7	+	3.41084e7i	0.234030	+	0.135117i
$633$	1.02674e8	−	2.06818e8i	0.404807	−	0.815412i
$634$	6.32200e7	+	1.09500e8i	0.248077	+	0.429682i
$635$	2.41519e8	−	1.39441e8i	0.943259	−	0.544591i
$636$	−4.23634e7	−	2.10311e7i	−0.164672	−	0.0817506i
$637$	−3.69704e6	+	6.40345e6i	−0.0143033	+	0.0247740i
$638$		−	1.37600e8i		−	0.529853i
$639$	−1.05676e8	−	4.44301e7i	−0.405017	−	0.170285i
$640$	−4.32901e7			−0.165139
$641$	4.02095e8	+	2.32150e8i	1.52670	+	0.881442i	0.999497	+	0.0317046i	$0.0100936\pi$
$641$	4.02095e8	+	2.32150e8i	1.52670	+	0.881442i	0.527206	+	0.849738i	$0.323240\pi$
$642$	3.15780e7	−	1.98568e6i	0.119338	−	0.00750421i
$643$	1.98827e8	+	3.44378e8i	0.747897	+	1.29540i	0.948829	+	0.315790i	$0.102270\pi$
$643$	1.98827e8	+	3.44378e8i	0.747897	+	1.29540i	−0.200932	+	0.979605i	$0.564397\pi$
$644$	−1.05386e8	+	6.08447e7i	−0.394572	+	0.227806i
$645$	−2.02273e8	+	1.34380e8i	−0.753805	+	0.500791i
$646$	−5.44390e7	+	9.42911e7i	−0.201936	+	0.349763i
$647$		−	1.29737e8i		−	0.479017i	−0.970894	−	0.239509i	$-0.923014\pi$
$647$		−	1.29737e8i		−	0.479017i	0.970894	−	0.239509i	$-0.0769863\pi$
$648$	6.87418e7	−	6.72994e7i	0.252637	−	0.247335i
$649$	1.26557e7			0.0462970
$650$	1.73799e7	+	1.00343e7i	0.0632858	+	0.0365381i
$651$	−3.52681e7	−	5.30865e7i	−0.127832	−	0.192416i
$652$	−2.07652e7	−	3.59663e7i	−0.0749191	−	0.129764i
$653$	−3.10514e8	+	1.79275e8i	−1.11517	+	0.643844i	−0.940164	−	0.340723i	$-0.889328\pi$
$653$	−3.10514e8	+	1.79275e8i	−1.11517	+	0.643844i	−0.175007	+	0.984567i	$0.555995\pi$
$654$	2.20738e7	+	3.51036e8i	0.0789122	+	1.25493i
$655$	−2.93324e8	+	5.08052e8i	−1.04382	+	1.80794i
$656$		−	4.42556e7i		−	0.156768i
$657$	−2.26873e7	+	5.39612e7i	−0.0799995	+	0.190277i
$658$	−1.79511e8			−0.630105
$659$	−3.63796e8	−	2.10038e8i	−1.27117	−	0.733908i	−0.295958	−	0.955201i	$-0.595639\pi$
$659$	−3.63796e8	−	2.10038e8i	−1.27117	−	0.733908i	−0.975207	+	0.221293i	$0.928972\pi$
$660$	−6.97339e7	+	1.40467e8i	−0.242556	+	0.488586i
$661$	2.06107e8	+	3.56988e8i	0.713655	+	1.23609i	0.963476	+	0.267794i	$0.0862948\pi$
$661$	2.06107e8	+	3.56988e8i	0.713655	+	1.23609i	−0.249821	+	0.968292i	$0.580372\pi$
$662$	2.15658e8	−	1.24510e8i	0.743347	−	0.429172i
$663$	1.55367e7	+	7.71313e6i	0.0533113	+	0.0264661i
$664$	−7.67107e7	+	1.32867e8i	−0.262030	+	0.453850i
$665$		−	1.21920e8i		−	0.414582i
$666$	9.18861e7	−	6.97359e7i	0.311048	−	0.236066i
$667$	−6.22638e8			−2.09826
$668$	−4.52978e7	−	2.61527e7i	−0.151967	−	0.0877379i
$669$	−1.41704e8	+	8.91060e6i	−0.473264	+	0.0297597i
$670$	−1.95522e8	−	3.38654e8i	−0.650086	−	1.12598i
$671$	−3.96358e7	+	2.28837e7i	−0.131196	+	0.0757459i
$672$	2.49016e7	−	1.65434e7i	0.0820577	−	0.0545151i
$673$	−2.35837e8	+	4.08482e8i	−0.773690	+	1.34007i	0.161838	+	0.986817i	$0.448258\pi$
$673$	−2.35837e8	+	4.08482e8i	−0.773690	+	1.34007i	−0.935528	+	0.353252i	$0.885076\pi$
$674$		−	2.76482e8i		−	0.902999i
$675$	2.51981e8	−	7.23362e8i	0.819325	−	2.35204i
$676$	1.54192e8			0.499139
$677$	6.57025e7	+	3.79334e7i	0.211746	+	0.122252i	0.602123	−	0.798404i	$-0.294322\pi$
$677$	6.57025e7	+	3.79334e7i	0.211746	+	0.122252i	−0.390376	+	0.920655i	$0.627655\pi$
$678$	6.61237e7	+	9.95313e7i	0.212162	+	0.319353i
$679$	−1.29056e8	−	2.23531e8i	−0.412256	−	0.714049i
$680$	−2.58017e8	+	1.48966e8i	−0.820580	+	0.473762i
$681$	1.37023e7	+	2.17905e8i	0.0433862	+	0.689963i
$682$	2.71463e7	−	4.70188e7i	0.0855772	−	0.148224i
$683$			2.50625e8i			0.786616i	0.919407	+	0.393308i	$0.128669\pi$
$683$			2.50625e8i			0.786616i	−0.919407	+	0.393308i	$0.871331\pi$
$684$	−6.32091e7	+	7.98097e6i	−0.197520	+	0.0249395i
$685$	1.89750e8			0.590350
$686$	1.86127e8	+	1.07460e8i	0.576549	+	0.332871i
$687$	1.46486e8	−	2.95070e8i	0.451780	−	0.910029i
$688$	1.97182e7	+	3.41529e7i	0.0605483	+	0.104873i
$689$	4.32169e6	−	2.49513e6i	0.0132128	−	0.00762843i
$690$	6.35612e8	+	3.15546e8i	1.93484	+	0.960540i
$691$	−9.23965e7	+	1.60035e8i	−0.280041	+	0.485045i	−0.971394	−	0.237472i	$-0.923681\pi$
$691$	−9.23965e7	+	1.60035e8i	−0.280041	+	0.485045i	0.691354	+	0.722516i	$0.257015\pi$
$692$		−	3.03442e8i		−	0.915710i
$693$	−1.35668e7	−	1.07449e8i	−0.0407642	−	0.322851i
$694$	3.11855e8			0.932983
$695$	−1.41801e8	−	8.18691e7i	−0.422402	−	0.243874i
$696$	1.52665e8	−	9.59987e6i	0.452806	−	0.0284733i
$697$	−1.52288e8	−	2.63771e8i	−0.449747	−	0.778984i
$698$	−9.76939e7	+	5.64036e7i	−0.287277	+	0.165860i
$699$	−1.25372e8	+	8.32911e7i	−0.367087	+	0.243875i
$700$	1.19023e8	−	2.06153e8i	0.347005	−	0.601030i
$701$		−	1.48993e8i		−	0.432525i	−0.976335	−	0.216262i	$-0.930613\pi$
$701$		−	1.48993e8i		−	0.432525i	0.976335	−	0.216262i	$-0.0693866\pi$
$702$	1.90097e6	+	9.97055e6i	0.00549496	+	0.0288209i
$703$	−7.63942e7			−0.219885
$704$	2.20554e7	+	1.27337e7i	0.0632116	+	0.0364952i
$705$	5.79267e8	+	8.71929e8i	1.65315	+	2.48836i
$706$	−2.13259e8	−	3.69375e8i	−0.606029	−	1.04967i
$707$	−2.62940e7	+	1.51809e7i	−0.0744045	+	0.0429575i
$708$	882947.	+	1.40414e7i	0.00248791	+	0.0395648i
$709$	1.76797e8	−	3.06222e8i	0.496063	−	0.859206i	−0.503927	−	0.863746i	$-0.668112\pi$
$709$	1.76797e8	−	3.06222e8i	0.496063	−	0.859206i	0.999990	+	0.00454038i	$0.00144525\pi$
$710$			2.07746e8i			0.580440i
$711$	1.66083e8	+	2.18836e8i	0.462078	+	0.608848i
$712$	−204354.			−0.000566166
$713$	−2.12760e8	−	1.22837e8i	−0.586978	−	0.338892i
$714$	9.14902e7	−	1.84291e8i	0.251351	−	0.506301i
$715$	−8.27321e6	−	1.43296e7i	−0.0226337	−	0.0392028i
$716$	−2.55930e8	+	1.47762e8i	−0.697241	+	0.402552i
$717$	−3.98290e8	−	1.97729e8i	−1.08054	−	0.536430i
$718$	−1.49900e8	+	2.59635e8i	−0.404976	+	0.701440i
$719$		−	1.15532e8i		−	0.310824i	−0.987850	−	0.155412i	$-0.950330\pi$
$719$		−	1.15532e8i		−	0.310824i	0.987850	−	0.155412i	$-0.0496705\pi$
$720$	−1.60711e8	−	6.75691e7i	−0.430574	−	0.181030i
$721$	−9.50453e7			−0.253586
$722$	−1.93936e8	−	1.11969e8i	−0.515284	−	0.297499i
$723$	1.24101e8	−	7.80369e6i	0.328367	−	0.0206484i
$724$	7.35159e7	+	1.27333e8i	0.193716	+	0.335526i
$725$	1.05481e9	−	6.08993e8i	2.76795	−	1.59808i
$726$	−1.48530e8	+	9.86764e7i	−0.388155	+	0.257872i
$727$	4.29149e7	−	7.43308e7i	0.111688	−	0.193449i	−0.804763	−	0.593596i	$-0.797708\pi$
$727$	4.29149e7	−	7.43308e7i	0.111688	−	0.193449i	0.916451	+	0.400147i	$0.131041\pi$
$728$			3.15432e6i			0.00817546i
$729$	3.60242e8	−	1.42548e8i	0.929849	−	0.367942i
$730$	1.06081e8			0.272690
$731$	2.35048e8	+	1.35705e8i	0.601734	+	0.347411i
$732$	−2.81545e7	−	4.23789e7i	−0.0717818	−	0.108048i
$733$	1.65809e8	+	2.87190e8i	0.421014	+	0.729218i	0.996039	−	0.0889179i	$-0.0283409\pi$
$733$	1.65809e8	+	2.87190e8i	0.421014	+	0.729218i	−0.575025	+	0.818136i	$0.695008\pi$
$734$	−1.99832e8	+	1.15373e8i	−0.505332	+	0.291754i
$735$	−3.20977e7	−	5.10444e8i	−0.0808372	−	1.28554i
$736$	5.76200e7	−	9.98007e7i	0.144524	−	0.250323i
$737$			2.30049e8i			0.574670i
$738$	6.90760e7	−	1.64295e8i	0.171853	−	0.408748i
$739$	−4.32705e7			−0.107216			−0.0536079	−	0.998562i	$-0.517072\pi$
$739$	−4.32705e7			−0.107216			−0.0536079	+	0.998562i	$0.517072\pi$
$740$	−1.81037e8	−	1.04522e8i	−0.446759	−	0.257936i
$741$	2.98909e6	−	6.02099e6i	0.00734657	−	0.0147984i
$742$	−2.95962e7	−	5.12622e7i	−0.0724477	−	0.125483i
$743$	4.91261e8	−	2.83630e8i	1.19770	−	0.691490i	0.237654	−	0.971350i	$-0.423621\pi$
$743$	4.91261e8	−	2.83630e8i	1.19770	−	0.691490i	0.960041	+	0.279860i	$0.0902881\pi$
$744$	5.40607e7	+	2.68382e7i	0.131269	+	0.0651680i
$745$	3.57493e7	−	6.19197e7i	0.0864568	−	0.149748i
$746$			2.42688e8i			0.584564i
$747$	−4.92166e8	+	3.73524e8i	−1.18073	+	0.896100i
$748$	1.75272e8			0.418801
$749$	3.42932e7	+	1.97992e7i	0.0816137	+	0.0471197i
$750$	−8.29171e8	+	5.21398e7i	−1.96544	+	0.123591i
$751$	3.02087e7	+	5.23230e7i	0.0713202	+	0.123530i	0.899480	−	0.436962i	$-0.143945\pi$
$751$	3.02087e7	+	5.23230e7i	0.0713202	+	0.123530i	−0.828160	+	0.560492i	$0.810612\pi$
$752$	1.47221e8	−	8.49983e7i	0.346192	−	0.199874i
$753$	3.55599e8	−	2.36243e8i	0.832867	−	0.553316i
$754$	−8.06973e6	+	1.39772e7i	−0.0188254	+	0.0326066i
$755$			4.31484e8i			1.00259i
$756$	1.18267e8	−	2.25486e7i	0.273714	−	0.0521860i
$757$	2.57979e8			0.594697			0.297349	−	0.954769i	$-0.403898\pi$
$757$	2.57979e8			0.594697			0.297349	+	0.954769i	$0.403898\pi$
$758$	−1.74576e7	−	1.00792e7i	−0.0400846	−	0.0231429i
$759$	−2.31013e8	−	3.47728e8i	−0.528338	−	0.795269i
$760$	5.77292e7	+	9.99899e7i	0.131509	+	0.227780i
$761$	−2.59671e8	+	1.49921e8i	−0.589209	+	0.340180i	−0.764785	−	0.644286i	$-0.777155\pi$
$761$	−2.59671e8	+	1.49921e8i	−0.589209	+	0.340180i	0.175576	+	0.984466i	$0.443821\pi$
$762$	−1.14463e7	−	1.82029e8i	−0.0258702	−	0.411410i
$763$	−2.20098e8	+	3.81220e8i	−0.495498	+	0.858227i
$764$			2.51038e8i			0.562936i
$765$	−1.19038e9	+	1.50301e8i	−2.65889	+	0.335720i
$766$	−3.33231e8			−0.741412
$767$	−1.28555e6	−	742213.i	−0.00284907	−	0.00164491i
$768$	−1.25891e7	+	2.53586e7i	−0.0277915	+	0.0559811i
$769$	2.17509e8	+	3.76737e8i	0.478299	+	0.828438i	0.999690	−	0.0248798i	$-0.00792030\pi$
$769$	2.17509e8	+	3.76737e8i	0.478299	+	0.828438i	−0.521392	+	0.853317i	$0.674587\pi$
$770$	−1.69972e8	+	9.81336e7i	−0.372311	+	0.214954i
$771$	−4.54083e8	−	2.25427e8i	−0.990768	−	0.491862i
$772$	−8.70055e7	+	1.50698e8i	−0.189101	+	0.327533i
$773$			5.68247e8i			1.23027i	0.788423	+	0.615133i	$0.210898\pi$
$773$			5.68247e8i			1.23027i	−0.788423	+	0.615133i	$0.789102\pi$
$774$	1.98949e7	+	1.57567e8i	0.0429061	+	0.339815i
$775$	4.80581e8			1.03243
$776$	2.11684e8	+	1.22216e8i	0.453004	+	0.261542i
$777$	1.44081e8	−	9.06006e6i	0.307144	−	0.0193138i
$778$	1.24598e8	+	2.15810e8i	0.264589	+	0.458281i
$779$	−1.02220e8	+	5.90167e7i	−0.216233	+	0.124842i
$780$	1.53214e7	−	1.01788e7i	0.0322859	−	0.0214492i
$781$	6.11079e7	−	1.05842e8i	0.128276	−	0.222180i
$782$		−	7.93106e8i		−	1.65848i
$783$	5.81741e8	+	2.02647e8i	1.21184	+	0.422139i
$784$	−8.30572e7			−0.172357
$785$	−6.37228e8	−	3.67904e8i	−1.31730	−	0.760545i
$786$	2.12307e8	+	3.19570e8i	0.437216	+	0.658110i
$787$	−4.11256e8	−	7.12316e8i	−0.843700	−	1.46133i	−0.886745	−	0.462258i	$-0.847039\pi$
$787$	−4.11256e8	−	7.12316e8i	−0.843700	−	1.46133i	0.0430452	−	0.999073i	$-0.486294\pi$
$788$	2.80166e8	−	1.61754e8i	0.572580	−	0.330579i
$789$	1.44509e7	+	2.29810e8i	0.0294214	+	0.467884i
$790$	2.48929e8	−	4.31158e8i	0.504887	−	0.874490i
$791$			1.49549e8i			0.302171i
$792$	6.20036e7	+	8.16978e7i	0.124808	+	0.164450i
$793$	5.36820e6			0.0107649
$794$	1.44015e7	+	8.31468e6i	0.0287703	+	0.0166106i
$795$	−1.53489e8	+	3.09175e8i	−0.305474	+	0.615324i
$796$	−1.10688e8	−	1.91717e8i	−0.219463	−	0.380121i
$797$	−4.33986e8	+	2.50562e8i	−0.857236	+	0.494925i	−0.863086	−	0.505058i	$-0.831471\pi$
$797$	−4.33986e8	+	2.50562e8i	−0.857236	+	0.494925i	0.00584980	+	0.999983i	$0.498138\pi$
$798$	−7.14187e7	−	3.54555e7i	−0.140541	−	0.0697709i
$799$	5.84977e8	−	1.01321e9i	1.14683	−	1.98637i
$800$			2.25429e8i			0.440291i
$801$	−758648.	−	318965.i	−0.00147619	−	0.000620648i
$802$	−9.07686e7			−0.175959
$803$	−5.40461e7	−	3.12035e7i	−0.104380	−	0.0602638i
$804$	−2.55237e8	+	1.60498e7i	−0.491106	+	0.0308817i
$805$	4.44055e8	+	7.69126e8i	0.851234	+	1.47438i
$806$	−5.51498e6	+	3.18407e6i	−0.0105327	+	0.00608104i
$807$	3.66347e8	−	2.43383e8i	0.697063	−	0.463095i
$808$	1.43763e7	−	2.49005e7i	0.0272529	−	0.0472034i
$809$			4.25261e8i			0.803174i	0.915821	+	0.401587i	$0.131541\pi$
$809$			4.25261e8i			0.803174i	−0.915821	+	0.401587i	$0.868459\pi$
$810$	−4.91162e8	−	5.01689e8i	−0.924208	−	0.944017i
$811$	3.17254e8			0.594763			0.297381	−	0.954759i	$-0.403887\pi$
$811$	3.17254e8			0.594763			0.297381	+	0.954759i	$0.403887\pi$
$812$	1.65792e8	+	9.57201e7i	0.309667	+	0.178787i
$813$	−3.64436e8	−	5.48559e8i	−0.678187	−	1.02083i
$814$	6.14898e7	+	1.06503e8i	0.114007	+	0.197465i
$815$	−2.62488e8	+	1.51548e8i	−0.484883	+	0.279947i
$816$	1.22281e7	+	1.94462e8i	0.0225056	+	0.357903i
$817$	5.25901e7	−	9.10888e7i	0.0964357	−	0.167032i
$818$			1.02308e8i			0.186917i
$819$	−4.92340e6	+	1.17102e7i	−0.00896218	+	0.0213163i
$820$	−3.22984e8			−0.585787
$821$	2.06773e7	+	1.19380e7i	0.0373649	+	0.0215726i	0.518566	−	0.855038i	$-0.326466\pi$
$821$	2.06773e7	+	1.19380e7i	0.0373649	+	0.0215726i	−0.481201	+	0.876610i	$0.659799\pi$
$822$	5.51809e7	−	1.11152e8i	0.0993512	−	0.200125i
$823$	−5.26330e8	−	9.11631e8i	−0.944189	−	1.63538i	−0.757368	−	0.652988i	$-0.773515\pi$
$823$	−5.26330e8	−	9.11631e8i	−0.944189	−	1.63538i	−0.186821	−	0.982394i	$-0.559818\pi$
$824$	7.79491e7	−	4.50040e7i	0.139325	−	0.0804395i
$825$	7.31465e8	+	3.63132e8i	1.30266	+	0.646700i
$826$	−8.80385e6	+	1.52487e7i	−0.0156218	+	0.0270578i
$827$			1.79106e8i			0.316660i	0.987386	+	0.158330i	$0.0506109\pi$
$827$			1.79106e8i			0.316660i	−0.987386	+	0.158330i	$0.949389\pi$
$828$	3.69683e8	−	2.80566e8i	0.651236	−	0.494248i
$829$	−1.21964e8			−0.214076			−0.107038	−	0.994255i	$-0.534137\pi$
$829$	−1.21964e8			−0.214076			−0.107038	+	0.994255i	$0.534137\pi$
$830$	9.69684e8	+	5.59847e8i	1.69588	+	0.979118i
$831$	−8.92561e8	+	5.61259e7i	−1.55537	+	0.0978048i
$832$	−1.49357e6	−	2.58694e6i	−0.00259332	−	0.00449176i
$833$	−4.95036e8	+	2.85809e8i	−0.856449	+	0.494471i
$834$	−8.91945e7	+	5.92565e7i	−0.153759	+	0.102150i
$835$	−1.90867e8	+	3.30591e8i	−0.327847	+	0.567848i
$836$		−	6.79236e7i		−	0.116252i
$837$	1.58806e8	+	1.84015e8i	0.270826	+	0.313817i
$838$	−4.22125e7			−0.0717313
$839$	4.91209e8	+	2.83600e8i	0.831727	+	0.480198i	0.854444	−	0.519544i	$-0.173898\pi$
$839$	4.91209e8	+	2.83600e8i	0.831727	+	0.480198i	−0.0227168	+	0.999742i	$0.507232\pi$
$840$	−1.20737e8	−	1.81736e8i	−0.203705	−	0.306622i
$841$	1.92351e8	+	3.33162e8i	0.323375	+	0.560102i
$842$	1.14414e8	−	6.60569e7i	0.191665	−	0.110658i
$843$	6.12902e6	+	9.74688e7i	0.0102308	+	0.162698i
$844$	−1.36831e8	+	2.36998e8i	−0.227591	+	0.394200i
$845$		−	1.12532e9i		−	1.86511i
$846$	6.79217e8	−	8.57600e7i	1.12175	−	0.141636i
$847$	−2.23171e8			−0.367272
$848$	4.85453e7	+	2.80276e7i	0.0796085	+	0.0459620i
$849$	3.88819e8	−	7.83208e8i	0.635367	−	1.27983i
$850$	7.75725e8	+	1.34360e9i	1.26314	+	2.18782i
$851$	4.81928e8	−	2.78241e8i	0.781977	−	0.451474i
$852$	1.21694e8	+	6.04143e7i	0.196766	+	0.0976834i
$853$	4.59944e8	−	7.96646e8i	0.741068	−	1.28357i	−0.210942	−	0.977499i	$-0.567653\pi$
$853$	4.59944e8	−	7.96646e8i	0.741068	−	1.28357i	0.952010	−	0.306068i	$-0.0990135\pi$
$854$		−	6.36756e7i		−	0.102235i
$855$	5.82465e7	+	4.61311e8i	0.0931904	+	0.738066i
$856$	−3.74997e7			−0.0597870
$857$	5.10368e8	+	2.94661e8i	0.810851	+	0.468145i	0.847251	−	0.531192i	$-0.178256\pi$
$857$	5.10368e8	+	2.94661e8i	0.810851	+	0.468145i	−0.0364004	+	0.999337i	$0.511589\pi$
$858$	−1.08000e7	+	679122.i	−0.0170986	+	0.00107519i
$859$	5.10737e7	+	8.84623e7i	0.0805783	+	0.139566i	0.903498	−	0.428591i	$-0.140990\pi$
$859$	5.10737e7	+	8.84623e7i	0.0805783	+	0.139566i	−0.822920	+	0.568157i	$0.807657\pi$
$860$	2.49254e8	−	1.43907e8i	0.391874	−	0.226249i
$861$	1.85789e8	−	1.23429e8i	0.291079	−	0.193379i
$862$	1.98099e8	−	3.43118e8i	0.309287	−	0.535700i
$863$		−	8.24326e8i		−	1.28253i	−0.767321	−	0.641264i	$-0.778410\pi$
$863$		−	8.24326e8i		−	1.28253i	0.767321	−	0.641264i	$-0.221590\pi$
$864$	−8.63169e7	+	7.44920e7i	−0.133830	+	0.115496i
$865$	−2.21457e9			−3.42170
$866$	−4.33021e8	−	2.50005e8i	−0.666739	−	0.384942i
$867$	3.81412e8	+	5.74112e8i	0.585244	+	0.880926i
$868$	3.77683e7	+	6.54165e7i	0.0577521	+	0.100030i
$869$	−2.53648e8	+	1.46444e8i	−0.386520	+	0.223158i
$870$	−7.00614e7	−	1.11418e9i	−0.106395	−	1.69198i
$871$	1.34916e7	−	2.33681e7i	0.0204178	−	0.0353646i
$872$		−	4.16865e8i		−	0.628703i
$873$	5.95099e8	+	7.84121e8i	0.894431	+	1.17853i
$874$	−3.07355e8			−0.460368
$875$	−9.00467e8	−	5.19885e8i	−1.34414	−	0.776038i
$876$	3.08493e7	−	6.21404e7i	0.0458916	−	0.0924404i
$877$	−3.55715e8	−	6.16116e8i	−0.527355	−	0.913406i	−0.999492	−	0.0318803i	$-0.989850\pi$
$877$	−3.55715e8	−	6.16116e8i	−0.527355	−	0.913406i	0.472137	−	0.881525i	$-0.343483\pi$
$878$	−5.01384e8	+	2.89474e8i	−0.740777	+	0.427688i
$879$	4.04901e8	+	2.01011e8i	0.596187	+	0.295974i
$880$	9.29325e7	−	1.60964e8i	0.136370	−	0.236200i
$881$		−	1.35023e8i		−	0.197460i	−0.995114	−	0.0987302i	$-0.968522\pi$
$881$		−	1.35023e8i		−	0.197460i	0.995114	−	0.0987302i	$-0.0314781\pi$
$882$	−3.08343e8	−	1.29639e8i	−0.449395	−	0.188943i
$883$	4.91077e8			0.713293			0.356646	−	0.934239i	$-0.383920\pi$
$883$	4.91077e8			0.713293			0.356646	+	0.934239i	$0.383920\pi$
$884$	−1.78039e7	−	1.02791e7i	−0.0257726	−	0.0148798i
$885$	1.02476e8	−	6.44389e6i	0.147840	−	0.00929648i
$886$	−3.60964e8	−	6.25208e8i	−0.518995	−	0.898925i
$887$	−8.12126e8	+	4.68881e8i	−1.16373	+	0.671881i	−0.952195	−	0.305490i	$-0.901180\pi$
$887$	−8.12126e8	+	4.68881e8i	−1.16373	+	0.671881i	−0.211536	+	0.977370i	$0.567847\pi$
$888$	−1.13874e8	+	7.56526e7i	−0.162625	+	0.108040i
$889$	1.14131e8	−	1.97680e8i	0.162442	−	0.281357i
$890$			1.49141e6i			0.00211557i
$891$	1.02666e8	+	4.00074e8i	0.145142	+	0.565598i
$892$	1.68277e8			0.237099
$893$	−3.92652e8	−	2.26698e8i	−0.551383	−	0.318341i
$894$	−2.58752e7	−	3.89481e7i	−0.0362136	−	0.0545097i
$895$	1.07839e9	+	1.86782e9i	1.50420	+	2.60535i
$896$	−3.06853e7	+	1.77162e7i	−0.0426586	+	0.0246290i
$897$	3.07303e6	+	4.88699e7i	0.00425784	+	0.0677117i
$898$	−4.09720e8	+	7.09656e8i	−0.565794	+	0.979984i
$899$			3.86491e8i			0.531938i
$900$	−3.51859e8	+	8.36886e8i	−0.482660	+	1.14799i
$901$	3.85784e8			0.527437
$902$	1.64554e8	+	9.50051e7i	0.224227	+	0.129458i
$903$	−8.83830e7	+	1.78032e8i	−0.120034	+	0.241788i
$904$	−7.08113e7	−	1.22649e8i	−0.0958511	−	0.166019i
$905$	9.29300e8	−	5.36531e8i	1.25375	−	0.723851i
$906$	2.52755e8	+	1.25479e8i	0.339872	+	0.168728i
$907$	−3.58999e8	+	6.21805e8i	−0.481140	+	0.833360i	−0.999766	−	0.0216419i	$-0.993111\pi$
$907$	−3.58999e8	+	6.21805e8i	−0.481140	+	0.833360i	0.518625	+	0.855002i	$0.326444\pi$
$908$		−	2.58768e8i		−	0.345663i
$909$	9.22365e7	−	7.00018e7i	0.122804	−	0.0932004i
$910$	2.30208e7			0.0305489
$911$	−6.57988e8	−	3.79889e8i	−0.870287	−	0.502461i	−0.00284370	−	0.999996i	$-0.500905\pi$
$911$	−6.57988e8	−	3.79889e8i	−0.870287	−	0.502461i	−0.867444	+	0.497535i	$0.834239\pi$
$912$	7.53605e7	−	4.73881e6i	0.0993480	−	0.00624719i
$913$	−3.29355e8	−	5.70460e8i	−0.432765	−	0.749572i
$914$	4.98843e8	−	2.88007e8i	0.653319	−	0.377194i
$915$	−3.09288e8	+	2.05476e8i	−0.403739	+	0.268224i
$916$	−1.95218e8	+	3.38128e8i	−0.254000	+	0.439941i
$917$			4.80163e8i			0.622703i
$918$	−2.58129e8	+	7.41012e8i	−0.333664	+	0.957849i
$919$	−9.15355e8			−1.17935			−0.589676	−	0.807640i	$-0.700744\pi$
$919$	−9.15355e8			−1.17935			−0.589676	+	0.807640i	$0.700744\pi$
$920$	−7.28362e8	−	4.20520e8i	−0.935371	−	0.540037i
$921$	−1.63320e8	−	2.45834e8i	−0.209055	−	0.314676i
$922$	1.95398e8	+	3.38440e8i	0.249303	+	0.431806i
$923$	−1.24145e7	+	7.16754e6i	−0.0157879	+	0.00911517i
$924$	8.05548e6	+	1.28105e8i	0.0102112	+	0.162387i
$925$	−5.44287e8	+	9.42733e8i	−0.687706	+	1.19114i
$926$			7.63293e8i			0.961299i
$927$	3.59624e8	−	4.54072e7i	0.451450	−	0.0570014i
$928$	−1.81294e8			−0.226850
$929$	4.28783e8	+	2.47558e8i	0.534799	+	0.308766i	0.742968	−	0.669327i	$-0.233417\pi$
$929$	4.28783e8	+	2.47558e8i	0.534799	+	0.308766i	−0.208170	+	0.978093i	$0.566751\pi$
$930$	1.95870e8	−	3.94544e8i	0.243511	−	0.490509i
$931$	1.10760e8	+	1.91842e8i	0.137257	+	0.237736i
$932$	1.54491e8	−	8.91957e7i	0.190834	−	0.110178i
$933$	−1.23032e9	−	6.10788e8i	−1.51487	−	0.752048i
$934$	−3.49112e8	+	6.04680e8i	−0.428474	+	0.742139i
$935$		−	1.27916e9i		−	1.56492i
$936$	−1.50696e6	−	1.19350e7i	−0.00183769	−	0.0145545i
$937$	5.39309e8			0.655570			0.327785	−	0.944752i	$-0.393698\pi$
$937$	5.39309e8			0.655570			0.327785	+	0.944752i	$0.393698\pi$
$938$	−2.77184e8	−	1.60032e8i	−0.335860	−	0.193909i
$939$	6.46368e8	−	4.06448e7i	0.780698	−	0.0490918i
$940$	−6.20332e8	−	1.07445e9i	−0.746862	−	1.29360i
$941$	7.63585e8	−	4.40856e8i	0.916408	−	0.529088i	0.0339205	−	0.999425i	$-0.489201\pi$
$941$	7.63585e8	−	4.40856e8i	0.916408	−	0.529088i	0.882487	+	0.470336i	$0.155867\pi$
$942$	−4.00823e8	+	2.66287e8i	−0.479512	+	0.318565i
$943$	4.29898e8	−	7.44606e8i	0.512662	−	0.887956i
$944$		−	1.66745e7i		−	0.0198215i
$945$	−1.64563e8	−	8.63131e8i	−0.195001	−	1.02278i
$946$	−1.69319e8			−0.200001
$947$	7.71869e8	+	4.45639e8i	0.908853	+	0.524727i	0.880062	−	0.474859i	$-0.157501\pi$
$947$	7.71869e8	+	4.45639e8i	0.908853	+	0.524727i	0.0287913	+	0.999585i	$0.490834\pi$
$948$	−1.80174e8	−	2.71203e8i	−0.211479	−	0.318324i
$949$	3.65995e6	+	6.33922e6i	0.00428230	+	0.00741716i
$950$	5.20687e8	−	3.00619e8i	0.607304	−	0.350627i
$951$	−3.78740e7	−	6.02305e8i	−0.0440352	−	0.700285i
$952$	−1.21927e8	+	2.11183e8i	−0.141315	+	0.244764i
$953$			2.13491e8i			0.246661i	0.992366	+	0.123331i	$0.0393576\pi$
$953$			2.13491e8i			0.246661i	−0.992366	+	0.123331i	$0.960642\pi$
$954$	1.36474e8	+	1.79822e8i	0.157182	+	0.207108i
$955$	1.83212e9			2.10350
$956$	4.56410e8	+	2.63508e8i	0.522374	+	0.301592i
$957$	−2.92037e8	+	5.88257e8i	−0.333198	+	0.671168i
$958$	−1.96298e8	−	3.39997e8i	−0.223264	−	0.386704i
$959$	1.34500e8	−	7.76537e7i	0.152499	−	0.0880454i
$960$	1.85071e8	+	9.18776e7i	0.209182	+	0.103848i
$961$	3.67503e8	−	6.36534e8i	0.414086	−	0.717218i
$962$		−	1.44246e7i		−	0.0162024i
$963$	−1.39215e8	−	5.85312e7i	−0.155886	−	0.0655403i
$964$	−1.47373e8			−0.164508
$965$	1.09982e9	+	6.34981e8i	1.22388	+	0.706608i
$966$	5.79675e8	−	3.64511e7i	0.643063	−	0.0404370i
$967$	6.06482e8	+	1.05046e9i	0.670716	+	1.16171i	0.977701	+	0.210000i	$0.0673463\pi$
$967$	6.06482e8	+	1.05046e9i	0.670716	+	1.16171i	−0.306986	+	0.951714i	$0.599320\pi$
$968$	1.83029e8	−	1.05672e8i	0.201787	−	0.116502i
$969$	4.32855e8	−	2.87568e8i	0.475742	−	0.316060i
$970$	8.91950e8	−	1.54490e9i	0.977294	−	1.69272i
$971$		−	4.38734e8i		−	0.479230i	−0.970868	−	0.239615i	$-0.922979\pi$
$971$		−	4.38734e8i		−	0.479230i	0.970868	−	0.239615i	$-0.0770212\pi$
$972$	−4.36715e8	+	1.41818e8i	−0.475553	+	0.154431i
$973$	−1.34017e8			−0.145486
$974$	−9.85660e8	−	5.69071e8i	−1.06672	−	0.615871i
$975$	−5.30048e7	−	7.97844e7i	−0.0571876	−	0.0860803i
$976$	3.01504e7	+	5.22220e7i	0.0324297	+	0.0561699i
$977$	−1.03164e9	+	5.95616e8i	−1.10623	+	0.638679i	−0.937849	−	0.347044i	$-0.887186\pi$
$977$	−1.03164e9	+	5.95616e8i	−1.10623	+	0.638679i	−0.168376	+	0.985723i	$0.553852\pi$
$978$	1.24401e7	+	1.97832e8i	0.0132986	+	0.211485i
$979$	438695.	−	759842.i	0.000467535	−	0.000809795i
$980$			6.06165e8i			0.644040i
$981$	6.50660e8	−	1.54758e9i	0.689203	−	1.63925i
$982$	1.12780e9			1.19096
$983$	4.17380e8	+	2.40974e8i	0.439411	+	0.253694i	0.703348	−	0.710846i	$-0.251688\pi$
$983$	4.17380e8	+	2.40974e8i	0.439411	+	0.253694i	−0.263937	+	0.964540i	$0.585021\pi$
$984$	−9.39267e7	+	1.89199e8i	−0.0985834	+	0.198579i
$985$	−1.18051e9	−	2.04470e9i	−1.23526	−	2.13954i
$986$	−1.08054e9	+	6.23852e8i	−1.12723	+	0.650805i
$987$	7.67433e8	+	3.80988e8i	0.798158	+	0.396242i
$988$	−3.98348e6	+	6.89960e6i	−0.00413040	+	0.00715407i
$989$			7.66170e8i			0.792021i
$990$	5.96244e8	−	4.52512e8i	0.614495	−	0.466364i
$991$	−8.26440e8			−0.849162			−0.424581	−	0.905390i	$-0.639579\pi$
$991$	−8.26440e8			−0.849162			−0.424581	+	0.905390i	$0.639579\pi$
$992$	−6.19495e7	−	3.57665e7i	−0.0634604	−	0.0366389i
$993$	−1.18622e9	+	7.45920e7i	−1.21149	+	0.0761807i
$994$	8.50185e7	+	1.47256e8i	0.0865674	+	0.149939i
$995$	−1.39918e9	+	8.07818e8i	−1.42038	+	0.820058i
$996$	6.09941e8	−	4.05215e8i	0.617319	−	0.410117i
$997$	−6.50181e8	+	1.12615e9i	−0.656068	+	1.13634i	0.325557	+	0.945522i	$0.394448\pi$
$997$	−6.50181e8	+	1.12615e9i	−0.656068	+	1.13634i	−0.981625	+	0.190820i	$0.938885\pi$
$998$			4.96303e8i			0.499292i
$999$	−5.40831e8	+	1.03114e8i	−0.542457	+	0.103424i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	18.7.d.a.11.5	yes	12
3.2	odd	2		54.7.d.a.35.1		12
4.3	odd	2		144.7.q.c.65.4		12
9.2	odd	6		162.7.b.c.161.7		12
9.4	even	3		54.7.d.a.17.1		12
9.5	odd	6	inner	18.7.d.a.5.5	✓	12
9.7	even	3		162.7.b.c.161.6		12
12.11	even	2		432.7.q.b.305.1		12
36.23	even	6		144.7.q.c.113.4		12
36.31	odd	6		432.7.q.b.17.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.7.d.a.5.5	✓	12	9.5	odd	6	inner
18.7.d.a.11.5	yes	12	1.1	even	1	trivial
54.7.d.a.17.1		12	9.4	even	3
54.7.d.a.35.1		12	3.2	odd	2
144.7.q.c.65.4		12	4.3	odd	2
144.7.q.c.113.4		12	36.23	even	6
162.7.b.c.161.6		12	9.7	even	3
162.7.b.c.161.7		12	9.2	odd	6
432.7.q.b.17.1		12	36.31	odd	6
432.7.q.b.305.1		12	12.11	even	2

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:	\( N \)	\(=\)	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	18.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.89898 + 2.82843i) q^{2} +(-14.9408 - 22.4894i) q^{3} +(16.0000 + 27.7128i) q^{4} +(202.253 - 116.771i) q^{5} +(-9.58533 - 152.434i) q^{6} +(95.5752 - 165.541i) q^{7} +181.019i q^{8} +(-282.543 + 672.020i) q^{9} +O(q^{10})\)	\(q+(4.89898 + 2.82843i) q^{2} +(-14.9408 - 22.4894i) q^{3} +(16.0000 + 27.7128i) q^{4} +(202.253 - 116.771i) q^{5} +(-9.58533 - 152.434i) q^{6} +(95.5752 - 165.541i) q^{7} +181.019i q^{8} +(-282.543 + 672.020i) q^{9} +1321.11 q^{10} +(-673.077 - 388.601i) q^{11} +(384.190 - 773.882i) q^{12} +(45.5802 + 78.9472i) q^{13} +(936.442 - 540.655i) q^{14} +(-5647.92 - 2803.88i) q^{15} +(-512.000 + 886.810i) q^{16} +7047.39i q^{17} +(-3284.93 + 2493.06i) q^{18} +2731.10 q^{19} +(6472.09 + 3736.66i) q^{20} +(-5150.89 + 323.897i) q^{21} +(-2198.26 - 3807.50i) q^{22} +(-17228.9 + 9947.14i) q^{23} +(4071.01 - 2704.58i) q^{24} +(19458.3 - 33702.7i) q^{25} +515.681i q^{26} +(19334.7 - 3686.33i) q^{27} +6116.81 q^{28} +(27104.3 + 15648.7i) q^{29} +(-19738.5 - 29710.9i) q^{30} +(6174.50 + 10694.6i) q^{31} +(-5016.55 + 2896.31i) q^{32} +(1316.94 + 20943.1i) q^{33} +(-19933.0 + 34525.0i) q^{34} -44641.5i q^{35} +(-23144.2 + 2922.26i) q^{36} -27972.0 q^{37} +(13379.6 + 7724.70i) q^{38} +(1094.47 - 2204.61i) q^{39} +(21137.7 + 36611.7i) q^{40} +(-37428.2 + 21609.2i) q^{41} +(-26150.2 - 12982.1i) q^{42} +(19256.1 - 33352.5i) q^{43} -24870.5i q^{44} +(21327.2 + 168911. i) q^{45} -112539. q^{46} +(-143771. - 83006.2i) q^{47} +(27593.5 - 1735.13i) q^{48} +(40555.3 + 70243.8i) q^{49} +(190651. - 110073. i) q^{50} +(158491. - 105294. i) q^{51} +(-1458.57 + 2526.31i) q^{52} -54741.5i q^{53} +(105147. + 36627.6i) q^{54} -181509. q^{55} +(29966.1 + 17301.0i) q^{56} +(-40804.8 - 61420.6i) q^{57} +(88522.3 + 153325. i) q^{58} +(-14102.1 + 8141.84i) q^{59} +(-12663.3 - 201382. i) q^{60} +(29443.7 - 50998.0i) q^{61} +69856.5i q^{62} +(84242.8 + 111001. i) q^{63} -32768.0 q^{64} +(18437.4 + 10644.9i) q^{65} +(-52784.4 + 106325. i) q^{66} +(-147998. - 256341. i) q^{67} +(-195303. + 112758. i) q^{68} +(481120. + 238849. i) q^{69} +(126265. - 218698. i) q^{70} +157251. i q^{71} +(-121649. - 51145.7i) q^{72} +80297.0 q^{73} +(-137034. - 79116.8i) q^{74} +(-1.04868e6 + 65942.7i) q^{75} +(43697.5 + 75686.3i) q^{76} +(-128659. + 74281.3i) q^{77} +(11597.3 - 7704.71i) q^{78} +(188424. - 326360. i) q^{79} +239146. i q^{80} +(-371780. - 379749. i) q^{81} -244480. q^{82} +(733992. + 423771. i) q^{83} +(-91390.3 - 137563. i) q^{84} +(822929. + 1.42535e6i) q^{85} +(188670. - 108929. i) q^{86} +(-53032.3 - 843363. i) q^{87} +(70344.3 - 121840. i) q^{88} +1128.91i q^{89} +(-373270. + 887812. i) q^{90} +17425.3 q^{91} +(-551326. - 318308. i) q^{92} +(148261. - 298646. i) q^{93} +(-469554. - 813291. i) q^{94} +(552371. - 318912. i) q^{95} +(140088. + 69545.8i) q^{96} +(675152. - 1.16940e6i) q^{97} +458831. i q^{98} +(451321. - 342525. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 42 q^{3} + 192 q^{4} + 432 q^{5} - 144 q^{6} + 240 q^{7} + 2190 q^{9}+O(q^{10}) \) 12 * q - 42 * q^3 + 192 * q^4 + 432 * q^5 - 144 * q^6 + 240 * q^7 + 2190 * q^9	\( 12 q - 42 q^{3} + 192 q^{4} + 432 q^{5} - 144 q^{6} + 240 q^{7} + 2190 q^{9} + 378 q^{11} + 384 q^{12} + 1680 q^{13} - 4752 q^{14} - 10872 q^{15} - 6144 q^{16} - 2976 q^{18} - 2820 q^{19} + 13824 q^{20} + 24876 q^{21} - 3600 q^{22} - 76248 q^{23} - 6144 q^{24} + 8094 q^{25} + 127008 q^{27} + 15360 q^{28} + 97092 q^{29} + 34272 q^{30} + 21480 q^{31} - 246258 q^{33} - 27360 q^{34} + 38208 q^{36} - 25536 q^{37} + 97632 q^{38} + 42204 q^{39} - 410562 q^{41} - 222144 q^{42} + 71430 q^{43} + 13716 q^{45} - 135072 q^{46} + 347652 q^{47} + 55296 q^{48} - 135954 q^{49} + 311040 q^{50} + 336402 q^{51} - 53760 q^{52} - 173520 q^{54} + 580392 q^{55} - 152064 q^{56} - 522282 q^{57} + 159264 q^{58} + 369738 q^{59} - 170496 q^{60} + 135744 q^{61} - 103800 q^{63} - 393216 q^{64} - 753840 q^{65} + 909216 q^{66} - 289938 q^{67} + 744768 q^{68} + 2059272 q^{69} + 155952 q^{70} - 374784 q^{72} - 977700 q^{73} - 2197152 q^{74} - 2115342 q^{75} - 45120 q^{76} - 159192 q^{77} - 631488 q^{78} - 764796 q^{79} - 1428282 q^{81} + 1073088 q^{82} + 396900 q^{83} + 1441536 q^{84} + 1619568 q^{85} + 3264624 q^{86} + 3072636 q^{87} + 115200 q^{88} - 1987200 q^{90} + 355584 q^{91} - 2439936 q^{92} - 2526576 q^{93} - 736848 q^{94} - 2089260 q^{95} - 49152 q^{96} - 38874 q^{97} + 4398804 q^{99}+O(q^{100}) \) 12 * q - 42 * q^3 + 192 * q^4 + 432 * q^5 - 144 * q^6 + 240 * q^7 + 2190 * q^9 + 378 * q^11 + 384 * q^12 + 1680 * q^13 - 4752 * q^14 - 10872 * q^15 - 6144 * q^16 - 2976 * q^18 - 2820 * q^19 + 13824 * q^20 + 24876 * q^21 - 3600 * q^22 - 76248 * q^23 - 6144 * q^24 + 8094 * q^25 + 127008 * q^27 + 15360 * q^28 + 97092 * q^29 + 34272 * q^30 + 21480 * q^31 - 246258 * q^33 - 27360 * q^34 + 38208 * q^36 - 25536 * q^37 + 97632 * q^38 + 42204 * q^39 - 410562 * q^41 - 222144 * q^42 + 71430 * q^43 + 13716 * q^45 - 135072 * q^46 + 347652 * q^47 + 55296 * q^48 - 135954 * q^49 + 311040 * q^50 + 336402 * q^51 - 53760 * q^52 - 173520 * q^54 + 580392 * q^55 - 152064 * q^56 - 522282 * q^57 + 159264 * q^58 + 369738 * q^59 - 170496 * q^60 + 135744 * q^61 - 103800 * q^63 - 393216 * q^64 - 753840 * q^65 + 909216 * q^66 - 289938 * q^67 + 744768 * q^68 + 2059272 * q^69 + 155952 * q^70 - 374784 * q^72 - 977700 * q^73 - 2197152 * q^74 - 2115342 * q^75 - 45120 * q^76 - 159192 * q^77 - 631488 * q^78 - 764796 * q^79 - 1428282 * q^81 + 1073088 * q^82 + 396900 * q^83 + 1441536 * q^84 + 1619568 * q^85 + 3264624 * q^86 + 3072636 * q^87 + 115200 * q^88 - 1987200 * q^90 + 355584 * q^91 - 2439936 * q^92 - 2526576 * q^93 - 736848 * q^94 - 2089260 * q^95 - 49152 * q^96 - 38874 * q^97 + 4398804 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more