LMFDB - Embedded newform 91.8.u.a.30.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,8,Mod(30,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("91.30");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	91.u (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:	$28.4270373191$
Analytic rank:	$0$
Dimension:	$126$
Relative dimension:	$63$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			30.1
Character	$\chi$	$=$	91.30
Dual form			91.8.u.a.88.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-19.4750 + 11.2439i) q^{2} -9.82037 q^{3} +(188.851 - 327.100i) q^{4} +(-268.738 - 155.156i) q^{5} +(191.252 - 110.419i) q^{6} +(-444.698 - 791.067i) q^{7} +5615.28i q^{8} -2090.56 q^{9} +O(q^{10})$	\(q+(-19.4750 + 11.2439i) q^{2} -9.82037 q^{3} +(188.851 - 327.100i) q^{4} +(-268.738 - 155.156i) q^{5} +(191.252 - 110.419i) q^{6} +(-444.698 - 791.067i) q^{7} +5615.28i q^{8} -2090.56 q^{9} +6978.26 q^{10} +6863.74i q^{11} +(-1854.59 + 3212.24i) q^{12} +(821.880 + 7878.64i) q^{13} +(17555.2 + 10405.9i) q^{14} +(2639.11 + 1523.69i) q^{15} +(-38964.8 - 67488.9i) q^{16} +(-11417.0 + 19774.7i) q^{17} +(40713.7 - 23506.1i) q^{18} +19891.2i q^{19} +(-101503. + 58603.0i) q^{20} +(4367.09 + 7768.57i) q^{21} +(-77175.4 - 133672. i) q^{22} +(-14244.2 - 24671.7i) q^{23} -55144.1i q^{24} +(9084.40 + 15734.6i) q^{25} +(-104593. - 144196. i) q^{26} +42007.2 q^{27} +(-342740. - 3933.43i) q^{28} +(-22368.0 + 38742.5i) q^{29} -68529.0 q^{30} +(-21137.5 + 12203.7i) q^{31} +(895220. + 516855. i) q^{32} -67404.5i q^{33} -513485. i q^{34} +(-3231.62 + 281588. i) q^{35} +(-394805. + 683823. i) q^{36} +(82726.0 - 47761.9i) q^{37} +(-223655. - 387382. i) q^{38} +(-8071.16 - 77371.2i) q^{39} +(871245. - 1.50904e6i) q^{40} +(180486. + 104204. i) q^{41} +(-172398. - 102190. i) q^{42} +(-241264. - 417882. i) q^{43} +(2.24513e6 + 1.29623e6i) q^{44} +(561814. + 324363. i) q^{45} +(554813. + 320321. i) q^{46} +(-27053.6 - 15619.4i) q^{47} +(382648. + 662766. i) q^{48} +(-428031. + 703571. i) q^{49} +(-353838. - 204289. i) q^{50} +(112119. - 194195. i) q^{51} +(2.73232e6 + 1.21906e6i) q^{52} +(-112856. - 195473. i) q^{53} +(-818092. + 472326. i) q^{54} +(1.06495e6 - 1.84455e6i) q^{55} +(4.44206e6 - 2.49710e6i) q^{56} -195339. i q^{57} -1.00602e6i q^{58} +(-1.79043e6 - 1.03370e6i) q^{59} +(996799. - 575502. i) q^{60} -2.62516e6 q^{61} +(274436. - 475337. i) q^{62} +(929667. + 1.65377e6i) q^{63} -1.32709e7 q^{64} +(1.00155e6 - 2.24481e6i) q^{65} +(757891. + 1.31270e6i) q^{66} +992293. i q^{67} +(4.31222e6 + 7.46898e6i) q^{68} +(139883. + 242285. i) q^{69} +(-3.10321e6 - 5.52027e6i) q^{70} +(-1.52600e6 + 881035. i) q^{71} -1.17391e7i q^{72} +(1.83669e6 - 1.06041e6i) q^{73} +(-1.07406e6 + 1.86033e6i) q^{74} +(-89212.1 - 154520. i) q^{75} +(6.50642e6 + 3.75648e6i) q^{76} +(5.42968e6 - 3.05229e6i) q^{77} +(1.02714e6 + 1.41606e6i) q^{78} +(-1.42084e6 + 2.46096e6i) q^{79} +2.41825e7i q^{80} +4.15953e6 q^{81} -4.68663e6 q^{82} -5.88124e6i q^{83} +(3.36583e6 + 38627.7i) q^{84} +(6.13635e6 - 3.54282e6i) q^{85} +(9.39726e6 + 5.42551e6i) q^{86} +(219662. - 380466. i) q^{87} -3.85418e7 q^{88} +(-8.62318e6 + 4.97859e6i) q^{89} -1.45885e7 q^{90} +(5.86705e6 - 4.15378e6i) q^{91} -1.07601e7 q^{92} +(207578. - 119845. i) q^{93} +702494. q^{94} +(3.08624e6 - 5.34553e6i) q^{95} +(-8.79139e6 - 5.07571e6i) q^{96} +(1.18236e7 - 6.82634e6i) q^{97} +(425024. - 1.85148e7i) q^{98} -1.43491e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 126 q - 3 q^{2} - 164 q^{3} + 3841 q^{4} - 6 q^{6} + 754 q^{7} + 85710 q^{9}+O(q^{10}) $ 126 * q - 3 * q^2 - 164 * q^3 + 3841 * q^4 - 6 * q^6 + 754 * q^7 + 85710 * q^9	\( 126 q - 3 q^{2} - 164 q^{3} + 3841 q^{4} - 6 q^{6} + 754 q^{7} + 85710 q^{9} + 7486 q^{10} - 18328 q^{12} + 1816 q^{13} - 6668 q^{14} - 11817 q^{15} - 237219 q^{16} - 28969 q^{17} + 75423 q^{18} + 12342 q^{20} - 54000 q^{21} + 51388 q^{22} + 17067 q^{23} + 810665 q^{25} + 144300 q^{26} - 528170 q^{27} + 18464 q^{28} + 191096 q^{29} - 432160 q^{30} - 259995 q^{31} + 49149 q^{32} + 87303 q^{35} + 1965131 q^{36} - 571857 q^{37} - 1061954 q^{38} - 1352875 q^{39} + 345362 q^{40} - 636567 q^{41} - 3473694 q^{42} - 659976 q^{43} + 2519268 q^{44} + 1980717 q^{45} - 4068600 q^{46} - 294840 q^{47} + 4726652 q^{48} + 541120 q^{49} - 2908992 q^{50} - 502094 q^{51} + 7809224 q^{52} - 434723 q^{53} + 2119563 q^{54} + 2152196 q^{55} - 858015 q^{56} + 1376949 q^{59} - 3768141 q^{60} - 4854916 q^{61} - 1713436 q^{62} + 10091940 q^{63} - 40270472 q^{64} - 4876182 q^{65} + 8270835 q^{66} + 531379 q^{68} - 311689 q^{69} + 5298534 q^{70} + 1505877 q^{71} - 13207461 q^{73} + 3730527 q^{74} + 5624951 q^{75} + 25297146 q^{76} + 11107478 q^{77} - 9362803 q^{78} + 5012226 q^{79} + 45989766 q^{81} - 34046788 q^{82} - 35428032 q^{84} + 19854117 q^{85} + 5226210 q^{86} + 17331733 q^{87} + 24348310 q^{88} - 43738596 q^{89} + 90517324 q^{90} + 9582031 q^{91} - 8502078 q^{92} - 30517344 q^{93} - 7710416 q^{94} + 14810909 q^{95} + 41499936 q^{96} - 60232128 q^{97} - 65830509 q^{98}+O(q^{100}) \) 126 * q - 3 * q^2 - 164 * q^3 + 3841 * q^4 - 6 * q^6 + 754 * q^7 + 85710 * q^9 + 7486 * q^10 - 18328 * q^12 + 1816 * q^13 - 6668 * q^14 - 11817 * q^15 - 237219 * q^16 - 28969 * q^17 + 75423 * q^18 + 12342 * q^20 - 54000 * q^21 + 51388 * q^22 + 17067 * q^23 + 810665 * q^25 + 144300 * q^26 - 528170 * q^27 + 18464 * q^28 + 191096 * q^29 - 432160 * q^30 - 259995 * q^31 + 49149 * q^32 + 87303 * q^35 + 1965131 * q^36 - 571857 * q^37 - 1061954 * q^38 - 1352875 * q^39 + 345362 * q^40 - 636567 * q^41 - 3473694 * q^42 - 659976 * q^43 + 2519268 * q^44 + 1980717 * q^45 - 4068600 * q^46 - 294840 * q^47 + 4726652 * q^48 + 541120 * q^49 - 2908992 * q^50 - 502094 * q^51 + 7809224 * q^52 - 434723 * q^53 + 2119563 * q^54 + 2152196 * q^55 - 858015 * q^56 + 1376949 * q^59 - 3768141 * q^60 - 4854916 * q^61 - 1713436 * q^62 + 10091940 * q^63 - 40270472 * q^64 - 4876182 * q^65 + 8270835 * q^66 + 531379 * q^68 - 311689 * q^69 + 5298534 * q^70 + 1505877 * q^71 - 13207461 * q^73 + 3730527 * q^74 + 5624951 * q^75 + 25297146 * q^76 + 11107478 * q^77 - 9362803 * q^78 + 5012226 * q^79 + 45989766 * q^81 - 34046788 * q^82 - 35428032 * q^84 + 19854117 * q^85 + 5226210 * q^86 + 17331733 * q^87 + 24348310 * q^88 - 43738596 * q^89 + 90517324 * q^90 + 9582031 * q^91 - 8502078 * q^92 - 30517344 * q^93 - 7710416 * q^94 + 14810909 * q^95 + 41499936 * q^96 - 60232128 * q^97 - 65830509 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−19.4750	+	11.2439i	−1.72137	+	0.993831i	−0.805233	+	0.592959i	$0.797960\pi$
$2$	−19.4750	+	11.2439i	−1.72137	+	0.993831i	−0.916134	+	0.400873i	$0.868707\pi$
$3$	−9.82037			−0.209992			−0.104996	−	0.994473i	$-0.533483\pi$
$3$	−9.82037			−0.209992			−0.104996	+	0.994473i	$0.533483\pi$
$4$	188.851	−	327.100i	1.47540	−	2.55547i
$5$	−268.738	−	155.156i	−0.961468	−	0.555104i	−0.0648434	−	0.997895i	$-0.520655\pi$
$5$	−268.738	−	155.156i	−0.961468	−	0.555104i	−0.896625	+	0.442792i	$0.853988\pi$
$6$	191.252	−	110.419i	0.361474	−	0.208697i
$7$	−444.698	−	791.067i	−0.490029	−	0.871706i
$7$	−444.698	−	791.067i	−0.490029	−	0.871706i
$8$			5615.28i			3.87754i
$9$	−2090.56			−0.955903
$10$	6978.26			2.20672
$11$			6863.74i			1.55484i	0.628980	+	0.777422i	$0.283473\pi$
$11$			6863.74i			1.55484i	−0.628980	+	0.777422i	$0.716527\pi$
$12$	−1854.59	+	3212.24i	−0.309823	+	0.536629i
$13$	821.880	+	7878.64i	0.103754	+	0.994603i
$13$	821.880	+	7878.64i	0.103754	+	0.994603i
$14$	17555.2	+	10405.9i	1.70985	+	1.01352i
$15$	2639.11	+	1523.69i	0.201901	+	0.116567i
$16$	−38964.8	−	67488.9i	−2.37822	−	4.11920i
$17$	−11417.0	+	19774.7i	−0.563610	+	0.976202i	0.433567	+	0.901121i	$0.357255\pi$
$17$	−11417.0	+	19774.7i	−0.563610	+	0.976202i	−0.997177	+	0.0750807i	$0.976079\pi$
$18$	40713.7	−	23506.1i	1.64546	−	0.950007i
$19$			19891.2i			0.665309i	0.943049	+	0.332654i	$0.107944\pi$
$19$			19891.2i			0.665309i	−0.943049	+	0.332654i	$0.892056\pi$
$20$	−101503.	+	58603.0i	−2.83710	+	1.63800i
$21$	4367.09	+	7768.57i	0.102902	+	0.183052i
$22$	−77175.4	−	133672.i	−1.54525	−	2.67646i
$23$	−14244.2	−	24671.7i	−0.244113	−	0.422816i	0.717769	−	0.696281i	$-0.245163\pi$
$23$	−14244.2	−	24671.7i	−0.244113	−	0.422816i	−0.961882	+	0.273466i	$0.911830\pi$
$24$		−	55144.1i		−	0.814254i
$25$	9084.40	+	15734.6i	0.116280	+	0.201403i
$26$	−104593.	−	144196.i	−1.16707	−	1.60896i
$27$	42007.2			0.410725
$28$	−342740.	−	3933.43i	−2.95061	−	0.0338624i
$29$	−22368.0	+	38742.5i	−0.170308	+	0.294982i	−0.938527	−	0.345205i	$-0.887809\pi$
$29$	−22368.0	+	38742.5i	−0.170308	+	0.294982i	0.768220	+	0.640186i	$0.221143\pi$
$30$	−68529.0			−0.463394
$31$	−21137.5	+	12203.7i	−0.127435	+	0.0735745i	−0.562362	−	0.826891i	$-0.690107\pi$
$31$	−21137.5	+	12203.7i	−0.127435	+	0.0735745i	0.434927	+	0.900465i	$0.356774\pi$
$32$	895220.	+	516855.i	4.82953	+	2.78833i
$33$		−	67404.5i		−	0.326505i
$34$		−	513485.i		−	2.24054i
$35$	−3231.62	+	281588.i	−0.0127404	+	1.11013i
$36$	−394805.	+	683823.i	−1.41034	+	2.44278i
$37$	82726.0	−	47761.9i	0.268495	−	0.155016i	−0.359708	−	0.933065i	$-0.617124\pi$
$37$	82726.0	−	47761.9i	0.268495	−	0.155016i	0.628204	+	0.778049i	$0.283791\pi$
$38$	−223655.	−	387382.i	−0.661205	−	1.14524i
$39$	−8071.16	−	77371.2i	−0.0217876	−	0.208859i
$40$	871245.	−	1.50904e6i	2.15244	−	3.72813i
$41$	180486.	+	104204.i	0.408978	+	0.236123i	0.690350	−	0.723475i	$-0.257456\pi$
$41$	180486.	+	104204.i	0.408978	+	0.236123i	−0.281373	+	0.959599i	$0.590790\pi$
$42$	−172398.	−	102190.i	−0.359055	−	0.212831i
$43$	−241264.	−	417882.i	−0.462757	−	0.801519i	0.536340	−	0.844002i	$-0.319806\pi$
$43$	−241264.	−	417882.i	−0.462757	−	0.801519i	−0.999097	+	0.0424831i	$0.986473\pi$
$44$	2.24513e6	+	1.29623e6i	3.97336	+	2.29402i
$45$	561814.	+	324363.i	0.919070	+	0.530625i
$46$	554813.	+	320321.i	0.840415	+	0.485214i
$47$	−27053.6	−	15619.4i	−0.0380087	−	0.0219443i	0.480875	−	0.876789i	$-0.340319\pi$
$47$	−27053.6	−	15619.4i	−0.0380087	−	0.0219443i	−0.518884	+	0.854845i	$0.673652\pi$
$48$	382648.	+	662766.i	0.499408	+	0.865000i
$49$	−428031.	+	703571.i	−0.519743	+	0.854322i
$50$	−353838.	−	204289.i	−0.400322	−	0.231126i
$51$	112119.	−	194195.i	0.118354	−	0.204995i
$52$	2.73232e6	+	1.21906e6i	2.69476	+	1.20230i
$53$	−112856.	−	195473.i	−0.104126	−	0.180352i	0.809255	−	0.587458i	$-0.199871\pi$
$53$	−112856.	−	195473.i	−0.104126	−	0.180352i	−0.913381	+	0.407106i	$0.866538\pi$
$54$	−818092.	+	472326.i	−0.707007	+	0.408191i
$55$	1.06495e6	−	1.84455e6i	0.863100	−	1.49493i
$56$	4.44206e6	−	2.49710e6i	3.38008	−	1.90011i
$57$		−	195339.i		−	0.139710i
$58$		−	1.00602e6i		−	0.677028i
$59$	−1.79043e6	−	1.03370e6i	−1.13494	−	0.655260i	−0.189770	−	0.981828i	$-0.560774\pi$
$59$	−1.79043e6	−	1.03370e6i	−1.13494	−	0.655260i	−0.945174	+	0.326568i	$0.894108\pi$
$60$	996799.	−	575502.i	0.595770	−	0.343968i
$61$	−2.62516e6			−1.48081			−0.740407	−	0.672158i	$-0.765367\pi$
$61$	−2.62516e6			−1.48081			−0.740407	+	0.672158i	$0.765367\pi$
$62$	274436.	−	475337.i	0.146241	−	0.253297i
$63$	929667.	+	1.65377e6i	0.468420	+	0.833267i
$64$	−1.32709e7			−6.32808
$65$	1.00155e6	−	2.24481e6i	0.452351	−	1.01387i
$66$	757891.	+	1.31270e6i	0.324491	+	0.562035i
$67$			992293.i			0.403068i	0.979482	+	0.201534i	$0.0645926\pi$
$67$			992293.i			0.403068i	−0.979482	+	0.201534i	$0.935407\pi$
$68$	4.31222e6	+	7.46898e6i	1.66310	+	2.88058i
$69$	139883.	+	242285.i	0.0512618	+	0.0887880i
$70$	−3.10321e6	−	5.52027e6i	−1.08136	−	1.92361i
$71$	−1.52600e6	+	881035.i	−0.505999	+	0.292139i	−0.731188	−	0.682176i	$-0.761034\pi$
$71$	−1.52600e6	+	881035.i	−0.505999	+	0.292139i	0.225188	+	0.974315i	$0.427700\pi$
$72$		−	1.17391e7i		−	3.70655i
$73$	1.83669e6	−	1.06041e6i	0.552592	−	0.319039i	−0.197575	−	0.980288i	$-0.563306\pi$
$73$	1.83669e6	−	1.06041e6i	0.552592	−	0.319039i	0.750167	+	0.661249i	$0.229973\pi$
$74$	−1.07406e6	+	1.86033e6i	−0.308119	+	0.533678i
$75$	−89212.1	−	154520.i	−0.0244180	−	0.0422932i
$76$	6.50642e6	+	3.75648e6i	1.70018	+	0.981598i
$77$	5.42968e6	−	3.05229e6i	1.35537	−	0.761918i
$78$	1.02714e6	+	1.41606e6i	0.245075	+	0.337870i
$79$	−1.42084e6	+	2.46096e6i	−0.324227	+	0.561578i	−0.981356	−	0.192201i	$-0.938438\pi$
$79$	−1.42084e6	+	2.46096e6i	−0.324227	+	0.561578i	0.657129	+	0.753779i	$0.271771\pi$
$80$			2.41825e7i			5.28064i
$81$	4.15953e6			0.869654
$82$	−4.68663e6			−0.938668
$83$		−	5.88124e6i		−	1.12900i	−0.825432	−	0.564502i	$-0.809068\pi$
$83$		−	5.88124e6i		−	1.12900i	0.825432	−	0.564502i	$-0.190932\pi$
$84$	3.36583e6	+	38627.7i	0.619605	+	0.00711085i
$85$	6.13635e6	−	3.54282e6i	1.08379	−	0.625725i
$86$	9.39726e6	+	5.42551e6i	1.59315	+	0.919805i
$87$	219662.	−	380466.i	0.0357633	−	0.0619438i
$88$	−3.85418e7			−6.02897
$89$	−8.62318e6	+	4.97859e6i	−1.29659	+	0.748586i	−0.979813	−	0.199915i	$-0.935933\pi$
$89$	−8.62318e6	+	4.97859e6i	−1.29659	+	0.748586i	−0.316775	+	0.948501i	$0.602600\pi$
$90$	−1.45885e7			−2.10941
$91$	5.86705e6	−	4.15378e6i	0.816159	−	0.577828i
$92$	−1.07601e7			−1.44066
$93$	207578.	−	119845.i	0.0267603	−	0.0154501i
$94$	702494.			0.0872358
$95$	3.08624e6	−	5.34553e6i	0.369315	−	0.639673i
$96$	−8.79139e6	−	5.07571e6i	−1.01416	−	0.585528i
$97$	1.18236e7	−	6.82634e6i	1.31537	−	0.759428i	0.332389	−	0.943142i	$-0.392145\pi$
$97$	1.18236e7	−	6.82634e6i	1.31537	−	0.759428i	0.982980	+	0.183714i	$0.0588120\pi$
$98$	425024.	−	1.85148e7i	0.0456165	−	1.98714i
$99$		−	1.43491e7i		−	1.48628i
$100$	6.86241e6			0.686241
$101$	5.45039e6			0.526384			0.263192	−	0.964743i	$-0.415225\pi$
$101$	5.45039e6			0.526384			0.263192	+	0.964743i	$0.415225\pi$
$102$			5.04261e6i			0.470495i
$103$	3.45466e6	−	5.98364e6i	0.311512	−	0.539555i	−0.667178	−	0.744898i	$-0.732498\pi$
$103$	3.45466e6	−	5.98364e6i	0.311512	−	0.539555i	0.978690	+	0.205344i	$0.0658312\pi$
$104$	−4.42408e7	+	4.61509e6i	−3.85661	+	0.402312i
$105$	31735.7	−	2.76529e6i	0.00267538	−	0.233120i
$106$	4.39575e6	+	2.53789e6i	0.358478	+	0.206968i
$107$	−1.14260e6	−	1.97904e6i	−0.0901678	−	0.156175i	0.817414	−	0.576051i	$-0.195407\pi$
$107$	−1.14260e6	−	1.97904e6i	−0.0901678	−	0.156175i	−0.907582	+	0.419876i	$0.862074\pi$
$108$	7.93312e6	−	1.37406e7i	0.605984	−	1.04959i
$109$	3.32752e6	−	1.92115e6i	0.246110	−	0.142091i	−0.371872	−	0.928284i	$-0.621284\pi$
$109$	3.32752e6	−	1.92115e6i	0.246110	−	0.142091i	0.617982	+	0.786193i	$0.287951\pi$
$110$			4.78970e7i			3.43110i
$111$	−812400.	+	469039.i	−0.0563819	+	0.0325521i
$112$	−3.60607e7	+	6.08359e7i	−2.42533	+	4.09164i
$113$	−4.14960e6	−	7.18731e6i	−0.270540	−	0.468589i	0.698460	−	0.715649i	$-0.253869\pi$
$113$	−4.14960e6	−	7.18731e6i	−0.270540	−	0.468589i	−0.969000	+	0.247060i	$0.920536\pi$
$114$	2.19637e6	+	3.80423e6i	0.138848	+	0.240492i
$115$			8.84030e6i			0.542032i
$116$	8.44846e6	+	1.46332e7i	0.502545	+	0.870433i
$117$	−1.71819e6	−	1.64708e7i	−0.0991792	−	0.950744i
$118$	4.64915e7			2.60487
$119$	2.07202e7	+	237794.i	1.12715	+	0.0129356i
$120$	−8.55595e6	+	1.48193e7i	−0.451995	+	0.782879i
$121$	−2.76238e7			−1.41754
$122$	5.11250e7	−	2.95171e7i	2.54903	−	1.47168i
$123$	−1.77244e6	−	1.02332e6i	−0.0858822	−	0.0495841i
$124$			9.21878e6i			0.434208i
$125$			1.86052e7i			0.852017i
$126$	−3.67002e7	−	2.17542e7i	−1.63445	−	0.968827i
$127$	−1.46026e7	+	2.52925e7i	−0.632584	+	1.09567i	0.354437	+	0.935080i	$0.384672\pi$
$127$	−1.46026e7	+	2.52925e7i	−0.632584	+	1.09567i	−0.987022	+	0.160588i	$0.948661\pi$
$128$	1.43864e8	−	8.30599e7i	6.06341	−	3.50071i
$129$	2.36930e6	+	4.10375e6i	0.0971754	+	0.168313i
$130$	5.73529e6	+	5.49792e7i	0.228957	+	2.19481i
$131$	2.48418e7	−	4.30272e7i	0.965456	−	1.67222i	0.257073	−	0.966392i	$-0.417242\pi$
$131$	2.48418e7	−	4.30272e7i	0.965456	−	1.67222i	0.708384	−	0.705828i	$-0.249425\pi$
$132$	−2.20480e7	−	1.27294e7i	−0.834374	−	0.481726i
$133$	1.57353e7	−	8.84557e6i	0.579954	−	0.326021i
$134$	−1.11573e7	−	1.93249e7i	−0.400581	−	0.693827i
$135$	−1.12890e7	−	6.51768e6i	−0.394898	−	0.227995i
$136$	−1.11041e8	−	6.41094e7i	−3.78526	−	2.18542i
$137$	3.55660e7	+	2.05340e7i	1.18171	+	0.682263i	0.956411	−	0.292025i	$-0.0943291\pi$
$137$	3.55660e7	+	2.05340e7i	1.18171	+	0.682263i	0.225304	+	0.974288i	$0.427662\pi$
$138$	−5.44846e6	−	3.14567e6i	−0.176481	−	0.101891i
$139$	2.19785e6	+	3.80679e6i	0.0694139	+	0.120228i	0.898643	−	0.438680i	$-0.144554\pi$
$139$	2.19785e6	+	3.80679e6i	0.0694139	+	0.120228i	−0.829230	+	0.558908i	$0.811220\pi$
$140$	9.14971e7	+	5.42353e7i	2.81812	+	1.67045i
$141$	265676.	+	153388.i	0.00798153	+	0.00460814i
$142$	1.98126e7	−	3.43164e7i	0.580673	−	1.00576i
$143$	−5.40770e7	+	5.64118e6i	−1.54645	+	0.161322i
$144$	8.14582e7	+	1.41090e8i	2.27335	+	3.93755i
$145$	1.20223e7	−	6.94107e6i	0.327491	−	0.189077i
$146$	−2.38464e7	+	4.13031e7i	−0.634143	+	1.09837i
$147$	4.20342e6	−	6.90933e6i	0.109142	−	0.179401i
$148$		−	3.60796e7i		−	0.914842i
$149$			2.96731e7i			0.734872i	0.930049	+	0.367436i	$0.119764\pi$
$149$			2.96731e7i			0.734872i	−0.930049	+	0.367436i	$0.880236\pi$
$150$	3.47482e6	+	2.00619e6i	0.0840645	+	0.0485347i
$151$	2.50989e7	−	1.44908e7i	0.593246	−	0.342511i	−0.173134	−	0.984898i	$-0.555389\pi$
$151$	2.50989e7	−	1.44908e7i	0.593246	−	0.342511i	0.766380	+	0.642387i	$0.222056\pi$
$152$	−1.11695e8			−2.57976
$153$	2.38678e7	−	4.13403e7i	0.538757	−	0.933155i
$154$	−7.14236e7	+	1.20494e8i	−1.57586	+	2.65855i
$155$	7.57395e6			0.163366
$156$	−2.68324e7	−	1.19716e7i	−0.565878	−	0.252473i
$157$	−3.33683e7	−	5.77955e7i	−0.688153	−	1.19192i	−0.972435	−	0.233175i	$-0.925089\pi$
$157$	−3.33683e7	−	5.77955e7i	−0.688153	−	1.19192i	0.284282	−	0.958741i	$-0.408245\pi$
$158$		−	6.39031e7i		−	1.28891i
$159$	1.10829e6	+	1.91961e6i	0.0218657	+	0.0378725i
$160$	−1.60387e8	−	2.77798e8i	−3.09562	−	5.36178i
$161$	−1.31826e7	+	2.22395e7i	−0.248949	+	0.419987i
$162$	−8.10070e7	+	4.67694e7i	−1.49699	+	0.864290i
$163$		−	1.77925e7i		−	0.321797i	−0.986971	−	0.160898i	$-0.948561\pi$
$163$		−	1.77925e7i		−	0.321797i	0.986971	−	0.160898i	$-0.0514391\pi$
$164$	6.81700e7	−	3.93580e7i	1.20681	−	0.696754i
$165$	−1.04582e7	+	1.81142e7i	−0.181244	+	0.313924i
$166$	6.61282e7	+	1.14537e8i	1.12204	+	1.94343i
$167$	1.35313e7	+	7.81227e6i	0.224818	+	0.129799i	0.608179	−	0.793800i	$-0.291900\pi$
$167$	1.35313e7	+	7.81227e6i	0.224818	+	0.129799i	−0.383361	+	0.923598i	$0.625234\pi$
$168$	−4.36227e7	+	2.45224e7i	−0.709790	+	0.399008i
$169$	−6.13975e7	+	1.29506e7i	−0.978470	+	0.206389i
$170$	−7.96704e7	+	1.37993e8i	−1.24373	+	2.15420i
$171$		−	4.15838e7i		−	0.635971i
$172$	−1.82252e8			−2.73101
$173$	2.40135e6			0.0352609			0.0176304	−	0.999845i	$-0.494388\pi$
$173$	2.40135e6			0.0352609			0.0176304	+	0.999845i	$0.494388\pi$
$174$			9.87945e6i			0.142171i
$175$	8.40735e6	−	1.41835e7i	0.118584	−	0.200056i
$176$	4.63227e8	−	2.67444e8i	6.40471	−	3.69776i
$177$	1.75826e7	+	1.01513e7i	0.238329	+	0.137600i
$178$	1.11958e8	−	1.93917e8i	1.48794	−	2.57718i
$179$	−1.26372e8			−1.64689			−0.823445	−	0.567396i	$-0.807951\pi$
$179$	−1.26372e8			−1.64689			−0.823445	+	0.567396i	$0.807951\pi$
$180$	2.12199e8	−	1.22513e8i	2.71200	−	1.56577i
$181$	1.27697e7			0.160068			0.0800341	−	0.996792i	$-0.474497\pi$
$181$	1.27697e7			0.160068			0.0800341	+	0.996792i	$0.474497\pi$
$182$	−6.75563e7	+	1.46864e8i	−0.830645	+	1.80578i
$183$	2.57800e7			0.310960
$184$	1.38538e8	−	7.99851e7i	1.63949	−	0.946557i
$185$	−2.96422e7			−0.344199
$186$	−2.69506e6	+	4.66798e6i	−0.0307095	+	0.0531905i
$187$	−1.35729e8	−	7.83631e7i	−1.51784	−	0.876326i
$188$	−1.02182e7	+	5.89950e6i	−0.112156	+	0.0647534i
$189$	−1.86805e7	−	3.32305e7i	−0.201267	−	0.358031i
$190$			1.38806e8i			1.46815i
$191$	1.30921e8			1.35954			0.679769	−	0.733426i	$-0.262080\pi$
$191$	1.30921e8			1.35954			0.679769	+	0.733426i	$0.262080\pi$
$192$	1.30326e8			1.32885
$193$			7.35136e6i			0.0736066i	0.999323	+	0.0368033i	$0.0117175\pi$
$193$			7.35136e6i			0.0736066i	−0.999323	+	0.0368033i	$0.988282\pi$
$194$	−1.53510e8	+	2.65887e8i	−1.50949	+	2.61451i
$195$	−9.83558e6	+	2.20449e7i	−0.0949903	+	0.212906i
$196$	1.49304e8	+	2.72880e8i	1.41637	+	2.58866i
$197$	7.51586e7	+	4.33929e7i	0.700402	+	0.404377i	0.807497	−	0.589872i	$-0.200822\pi$
$197$	7.51586e7	+	4.33929e7i	0.700402	+	0.404377i	−0.107095	+	0.994249i	$0.534155\pi$
$198$	1.61340e8	+	2.79449e8i	1.47711	+	2.55843i
$199$	−2.56181e7	+	4.43718e7i	−0.230441	+	0.399136i	−0.957938	−	0.286975i	$-0.907350\pi$
$199$	−2.56181e7	+	4.43718e7i	−0.230441	+	0.399136i	0.727497	+	0.686111i	$0.240684\pi$
$200$	−8.83544e7	+	5.10114e7i	−0.780950	+	0.450882i
$201$		−	9.74468e6i		−	0.0846411i
$202$	−1.06147e8	+	6.12837e7i	−0.906100	+	0.523137i
$203$	4.05949e7	+	465885.i	0.340593	+	0.00390879i
$204$	−4.23475e7	−	7.33481e7i	−0.349239	−	0.604900i
$205$	−3.23357e7	−	5.60070e7i	−0.262146	−	0.454050i
$206$			1.55376e8i			1.23836i
$207$	2.97784e7	+	5.15776e7i	0.233348	+	0.404171i
$208$	4.99697e8	−	3.62457e8i	3.85022	−	2.79277i
$209$	−1.36528e8			−1.03445
$210$	3.04747e7	+	5.42111e7i	0.227076	+	0.403943i
$211$	1.96752e6	−	3.40784e6i	0.0144188	−	0.0249741i	−0.858726	−	0.512435i	$-0.828744\pi$
$211$	1.96752e6	−	3.40784e6i	0.0144188	−	0.0249741i	0.873145	+	0.487461i	$0.162077\pi$
$212$	−8.52522e7			−0.614511
$213$	1.49859e7	−	8.65209e6i	0.106256	−	0.0613469i
$214$	4.45044e7	+	2.56946e7i	0.310424	+	0.179223i
$215$			1.49735e8i			1.02751i
$216$			2.35882e8i			1.59260i
$217$	1.90538e7	+	1.12942e7i	0.126582	+	0.0750321i
$218$	−4.32024e7	+	7.48288e7i	−0.282430	+	0.489183i
$219$	−1.80369e7	+	1.04136e7i	−0.116040	+	0.0669958i
$220$	−4.02236e8	−	6.96693e8i	−2.54684	−	4.41125i
$221$	−1.65182e8	−	7.36977e7i	−1.02941	−	0.459283i
$222$	1.05477e7	−	1.82691e7i	0.0647026	−	0.112068i
$223$	−1.21643e8	−	7.02306e7i	−0.734547	−	0.424091i	0.0855362	−	0.996335i	$-0.472740\pi$
$223$	−1.21643e8	−	7.02306e7i	−0.734547	−	0.424091i	−0.820083	+	0.572244i	$0.806073\pi$
$224$	1.07652e7	−	9.38023e8i	0.0639959	−	5.57629i
$225$	−1.89915e7	−	3.28942e7i	−0.111153	−	0.192522i
$226$	1.61627e8	+	9.33155e7i	0.931397	+	0.537742i
$227$	1.38969e8	+	8.02337e7i	0.788546	+	0.455267i	0.839450	−	0.543436i	$-0.182877\pi$
$227$	1.38969e8	+	8.02337e7i	0.788546	+	0.455267i	−0.0509044	+	0.998704i	$0.516210\pi$
$228$	−6.38954e7	−	3.68900e7i	−0.357024	−	0.206128i
$229$	2.72415e8	+	1.57279e8i	1.49902	+	0.865459i	0.999999	−	0.00113086i	$-0.000359965\pi$
$229$	2.72415e8	+	1.57279e8i	1.49902	+	0.865459i	0.499020	+	0.866590i	$0.333693\pi$
$230$	−9.93997e7	−	1.72165e8i	−0.538688	−	0.933035i
$231$	−5.33215e7	+	2.99746e7i	−0.284617	+	0.159997i
$232$	−2.17550e8	−	1.25603e8i	−1.14380	−	0.660375i
$233$	3.48485e7	−	6.03594e7i	0.180484	−	0.312607i	−0.761562	−	0.648093i	$-0.775567\pi$
$233$	3.48485e7	−	6.03594e7i	0.180484	−	0.312607i	0.942045	+	0.335485i	$0.108900\pi$
$234$	2.18658e8	+	3.01450e8i	1.11560	+	1.53801i
$235$	4.84690e6	+	8.39507e6i	0.0243628	+	0.0421975i
$236$	−6.76249e8	+	3.90433e8i	−3.34900	+	1.93354i
$237$	1.39531e7	−	2.41675e7i	0.0680852	−	0.117927i
$238$	−4.06201e8	+	2.28346e8i	−1.95309	+	1.09793i
$239$			3.57328e8i			1.69307i	0.532336	+	0.846533i	$0.321314\pi$
$239$			3.57328e8i			1.69307i	−0.532336	+	0.846533i	$0.678686\pi$
$240$		−	2.37481e8i		−	1.10889i
$241$	−4.22455e7	−	2.43904e7i	−0.194411	−	0.112243i	0.399635	−	0.916674i	$-0.369137\pi$
$241$	−4.22455e7	−	2.43904e7i	−0.194411	−	0.112243i	−0.594046	+	0.804431i	$0.702470\pi$
$242$	5.37975e8	−	3.10600e8i	2.44010	−	1.40879i
$243$	−1.32718e8			−0.593345
$244$	−4.95765e8	+	8.58690e8i	−2.18480	+	3.78418i
$245$	2.24192e8	−	1.22665e8i	0.973954	−	0.532892i
$246$	4.60244e7			0.197113
$247$	−1.56716e8	+	1.63482e7i	−0.661718	+	0.0690288i
$248$	−6.85275e7	−	1.18693e8i	−0.285288	−	0.494134i
$249$			5.77559e7i			0.237082i
$250$	−2.09195e8	−	3.62336e8i	−0.846761	−	1.46663i
$251$	−8.04913e7	−	1.39415e8i	−0.321285	−	0.556482i	0.659468	−	0.751732i	$-0.270781\pi$
$251$	−8.04913e7	−	1.39415e8i	−0.321285	−	0.556482i	−0.980753	+	0.195250i	$0.937448\pi$
$252$	7.16519e8	+	8.22307e6i	2.82050	+	0.0323692i
$253$	1.69340e8	−	9.77685e7i	0.657412	−	0.379557i
$254$		−	6.56763e8i		−	2.51473i
$255$	−6.02612e7	+	3.47918e7i	−0.227587	+	0.131397i
$256$	−1.01850e9	+	1.76409e9i	−3.79420	+	6.57175i
$257$	−2.02977e8	−	3.51567e8i	−0.745902	−	1.29194i	−0.949772	−	0.312942i	$-0.898686\pi$
$257$	−2.02977e8	−	3.51567e8i	−0.745902	−	1.29194i	0.203871	−	0.978998i	$-0.434648\pi$
$258$	−9.22845e7	−	5.32805e7i	−0.334549	−	0.193152i
$259$	−7.45709e7	−	4.42022e7i	−0.266698	−	0.158087i
$260$	−5.45135e8	−	7.51544e8i	−1.92352	−	2.65184i
$261$	4.67617e7	−	8.09936e7i	0.162798	−	0.281974i
$262$			1.11727e9i			3.83800i
$263$	−1.65949e8			−0.562508			−0.281254	−	0.959633i	$-0.590750\pi$
$263$	−1.65949e8			−0.562508			−0.281254	+	0.959633i	$0.590750\pi$
$264$	3.78495e8			1.26604
$265$			7.00413e7i			0.231203i
$266$	−2.06986e8	+	3.49194e8i	−0.674304	+	1.13758i
$267$	8.46827e7	−	4.88916e7i	0.272274	−	0.157197i
$268$	3.24579e8	+	1.87396e8i	1.03003	+	0.594687i
$269$	9.86989e7	−	1.70952e8i	0.309157	−	0.535476i	−0.669021	−	0.743243i	$-0.733286\pi$
$269$	9.86989e7	−	1.70952e8i	0.309157	−	0.535476i	0.978178	+	0.207767i	$0.0666197\pi$
$270$	2.93137e8			0.906353
$271$	4.56892e8	−	2.63787e8i	1.39451	−	0.805120i	0.400698	−	0.916210i	$-0.368768\pi$
$271$	4.56892e8	−	2.63787e8i	1.39451	−	0.805120i	0.993810	+	0.111091i	$0.0354344\pi$
$272$	1.77944e9			5.36156
$273$	−5.76165e7	+	4.07916e7i	−0.171387	+	0.121339i
$274$	−9.23532e8			−2.71222
$275$	−1.07999e8	+	6.23530e7i	−0.313151	+	0.180798i
$276$	1.05669e8			0.302527
$277$	2.36332e8	−	4.09338e8i	0.668102	−	1.15719i	−0.310332	−	0.950628i	$-0.600440\pi$
$277$	2.36332e8	−	4.09338e8i	0.668102	−	1.15719i	0.978434	−	0.206558i	$-0.0662263\pi$
$278$	−8.56065e7	−	4.94250e7i	−0.238974	−	0.137972i
$279$	4.41892e7	−	2.55127e7i	0.121815	−	0.0703301i
$280$	−1.58119e9	−	1.81464e7i	−4.30459	−	0.0494013i
$281$		−	7.52023e7i		−	0.202190i	−0.994877	−	0.101095i	$-0.967765\pi$
$281$		−	7.52023e7i		−	0.202190i	0.994877	−	0.101095i	$-0.0322346\pi$
$282$	−6.89874e6			−0.0183188
$283$	3.56179e8			0.934149			0.467074	−	0.884218i	$-0.345308\pi$
$283$	3.56179e8			0.934149			0.467074	+	0.884218i	$0.345308\pi$
$284$			6.65539e8i			1.72409i
$285$	−3.03080e7	+	5.24951e7i	−0.0775534	+	0.134326i
$286$	9.89723e8	−	7.17900e8i	2.50168	−	1.81461i
$287$	2.17037e6	−	1.89115e8i	0.00541935	−	0.472216i
$288$	−1.87151e9	−	1.08052e9i	−4.61656	−	2.66537i
$289$	−5.55244e7	−	9.61711e7i	−0.135314	−	0.234370i
$290$	−1.56090e8	+	2.70355e8i	−0.375821	+	0.650941i
$291$	−1.16112e8	+	6.70372e7i	−0.276217	+	0.159474i
$292$		−	8.01041e8i		−	1.88285i
$293$	−1.66404e8	+	9.60733e7i	−0.386480	+	0.223134i	−0.680634	−	0.732624i	$-0.738295\pi$
$293$	−1.66404e8	+	9.60733e7i	−0.386480	+	0.223134i	0.294154	+	0.955758i	$0.404962\pi$
$294$	−4.17389e6	+	1.81822e8i	−0.00957912	+	0.417284i
$295$	3.20771e8	+	5.55592e8i	0.727475	+	1.26002i
$296$	2.68196e8	+	4.64530e8i	0.601080	+	1.04110i
$297$			2.88327e8i			0.638612i
$298$	−3.33642e8	−	5.77885e8i	−0.730338	−	1.26498i
$299$	1.82672e8	−	1.32502e8i	0.395206	−	0.286664i
$300$	−6.73914e7			−0.144105
$301$	−2.23283e8	+	3.76687e8i	−0.471925	+	0.796156i
$302$	−3.25868e8	+	5.64420e8i	−0.680796	+	1.17917i
$303$	−5.35248e7			−0.110537
$304$	1.34244e9	−	7.75056e8i	2.74054	−	1.58225i
$305$	7.05481e8	+	4.07309e8i	1.42376	+	0.822006i
$306$			1.07347e9i			2.14174i
$307$		−	6.06371e8i		−	1.19606i	−0.801473	−	0.598031i	$-0.795950\pi$
$307$		−	6.06371e8i		−	1.19606i	0.801473	−	0.598031i	$-0.204050\pi$
$308$	2.69981e7	−	2.35248e9i	0.0526508	−	4.58774i
$309$	−3.39260e7	+	5.87616e7i	−0.0654151	+	0.113302i
$310$	−1.47503e8	+	8.51609e7i	−0.281213	+	0.162358i
$311$	4.26125e8	+	7.38070e8i	0.803296	+	1.39135i	0.917436	+	0.397885i	$0.130256\pi$
$311$	4.26125e8	+	7.38070e8i	0.803296	+	1.39135i	−0.114140	+	0.993465i	$0.536411\pi$
$312$	4.34461e8	−	4.53218e7i	0.809859	−	0.0844824i
$313$	−2.20963e8	+	3.82720e8i	−0.407301	+	0.705466i	−0.994586	−	0.103914i	$-0.966863\pi$
$313$	−2.20963e8	+	3.82720e8i	−0.407301	+	0.705466i	0.587285	+	0.809380i	$0.300197\pi$
$314$	1.29970e9	+	7.50380e8i	2.36913	+	1.36782i
$315$	6.75590e6	−	5.88676e8i	0.0121786	−	1.06118i
$316$	5.36654e8	+	9.29512e8i	0.956731	+	1.65711i
$317$	−9.51660e8	−	5.49441e8i	−1.67793	−	0.968754i	−0.962977	−	0.269584i	$-0.913114\pi$
$317$	−9.51660e8	−	5.49441e8i	−1.67793	−	0.968754i	−0.714955	−	0.699170i	$-0.753553\pi$
$318$	−4.31679e7	−	2.49230e7i	−0.0752777	−	0.0434616i
$319$	−2.65919e8	−	1.53528e8i	−0.458650	−	0.264802i
$320$	3.56641e9	+	2.05907e9i	6.08424	+	3.51274i
$321$	1.12208e7	+	1.94349e7i	0.0189345	+	0.0327956i
$322$	6.67171e6	−	5.81340e8i	0.0111363	−	0.970364i
$323$	−3.93343e8	−	2.27097e8i	−0.649476	−	0.374975i
$324$	7.85533e8	−	1.36058e9i	1.28309	−	2.22238i
$325$	−1.16501e8	+	8.45047e7i	−0.188252	+	0.136549i
$326$	2.00058e8	+	3.46510e8i	0.319812	+	0.553930i
$327$	−3.26775e7	+	1.88664e7i	−0.0516811	+	0.0298381i
$328$	−5.85132e8	+	1.01348e9i	−0.915578	+	1.58583i
$329$	−325324.	+	2.83471e7i	−0.000503652	+	0.0438858i
$330$		−	4.70366e8i		−	0.720505i
$331$		−	8.98114e7i		−	0.136124i	−0.997681	−	0.0680618i	$-0.978318\pi$
$331$		−	8.98114e7i		−	0.136124i	0.997681	−	0.0680618i	$-0.0216815\pi$
$332$	−1.92376e9	−	1.11068e9i	−2.88514	−	1.66573i
$333$	−1.72944e8	+	9.98491e7i	−0.256655	+	0.148180i
$334$	−3.51362e8			−0.515992
$335$	1.53960e8	−	2.66667e8i	0.223744	−	0.387537i
$336$	3.54130e8	−	5.97431e8i	0.509301	−	0.859212i
$337$	3.57960e8			0.509483			0.254741	−	0.967009i	$-0.418010\pi$
$337$	3.57960e8			0.509483			0.254741	+	0.967009i	$0.418010\pi$
$338$	1.05010e9	−	9.42563e8i	1.47919	−	1.32771i
$339$	4.07506e7	+	7.05821e7i	0.0568113	+	0.0984001i
$340$		−	2.67627e9i		−	3.69278i
$341$	−8.37634e7	−	1.45082e8i	−0.114397	−	0.198141i
$342$	4.67564e8	+	8.09845e8i	0.632048	+	1.09474i
$343$	7.46916e8	+	2.57248e7i	0.999407	+	0.0344210i
$344$	2.34652e9	−	1.35477e9i	3.10792	−	1.79436i
$345$		−	8.68150e7i		−	0.113822i
$346$	−4.67663e7	+	2.70005e7i	−0.0606969	+	0.0350434i
$347$	4.95673e8	−	8.58531e8i	0.636857	−	1.10307i	−0.349261	−	0.937025i	$-0.613567\pi$
$347$	4.95673e8	−	8.58531e8i	0.636857	−	1.10307i	0.986118	−	0.166044i	$-0.0530993\pi$
$348$	−8.29670e7	−	1.43703e8i	−0.105530	−	0.182784i
$349$	−5.51906e8	−	3.18643e8i	−0.694986	−	0.401250i	0.110492	−	0.993877i	$-0.464758\pi$
$349$	−5.51906e8	−	3.18643e8i	−0.694986	−	0.401250i	−0.805477	+	0.592627i	$0.798091\pi$
$350$	−4.25496e6	+	3.70756e8i	−0.00530465	+	0.462222i
$351$	3.45249e7	+	3.30960e8i	0.0426145	+	0.408508i
$352$	−3.54756e9	+	6.14456e9i	−4.33542	+	7.50916i
$353$		−	6.52358e8i		−	0.789359i	−0.918819	−	0.394680i	$-0.870856\pi$
$353$		−	6.52358e8i		−	0.789359i	0.918819	−	0.394680i	$-0.129144\pi$
$354$	−4.56564e8			−0.547003
$355$	5.46793e8			0.648669
$356$			3.76086e9i			4.41786i
$357$	−2.03480e8	−	2.33523e6i	−0.236692	−	0.00271638i
$358$	2.46110e9	−	1.42091e9i	2.83490	−	1.63673i
$359$	1.21687e8	+	7.02561e7i	0.138808	+	0.0801408i	0.567796	−	0.823169i	$-0.307796\pi$
$359$	1.21687e8	+	7.02561e7i	0.138808	+	0.0801408i	−0.428988	+	0.903310i	$0.641130\pi$
$360$	−1.82139e9	+	3.15474e9i	−2.05752	+	3.56373i
$361$	4.98212e8			0.557364
$362$	−2.48690e8	+	1.43581e8i	−0.275536	+	0.159081i
$363$	2.71276e8			0.297672
$364$	−2.50701e8	−	2.70356e9i	−0.272459	−	2.93820i
$365$	−6.58117e8			−0.708400
$366$	−5.02066e8	+	2.89868e8i	−0.535276	+	0.309042i
$367$	6.52693e8			0.689252			0.344626	−	0.938740i	$-0.388006\pi$
$367$	6.52693e8			0.689252			0.344626	+	0.938740i	$0.388006\pi$
$368$	−1.11004e9	+	1.92265e9i	−1.16111	+	2.01110i
$369$	−3.77317e8	−	2.17844e8i	−0.390943	−	0.225711i
$370$	5.77284e8	−	3.33295e8i	0.592493	−	0.342076i
$371$	−1.04445e8	+	1.76203e8i	−0.106189	+	0.179145i
$372$		−	9.05318e7i		−	0.0911803i
$373$	9.04669e7			0.0902628			0.0451314	−	0.998981i	$-0.485629\pi$
$373$	9.04669e7			0.0902628			0.0451314	+	0.998981i	$0.485629\pi$
$374$	3.52443e9			3.48368
$375$		−	1.82709e8i		−	0.178917i
$376$	8.77074e7	−	1.51914e8i	0.0850900	−	0.147380i
$377$	−3.23622e8	−	1.44388e8i	−0.311060	−	0.138783i
$378$	7.37445e8	+	4.37124e8i	0.702277	+	0.416277i
$379$	4.88498e8	+	2.82034e8i	0.460920	+	0.266112i	0.712431	−	0.701742i	$-0.247594\pi$
$379$	4.88498e8	+	2.82034e8i	0.460920	+	0.266112i	−0.251511	+	0.967854i	$0.580928\pi$
$380$	−1.16568e9	−	2.01902e9i	−1.08978	−	1.88755i
$381$	1.43403e8	−	2.48382e8i	0.132838	−	0.230082i
$382$	−2.54969e9	+	1.47206e9i	−2.34026	+	1.35115i
$383$			3.70988e8i			0.337415i	0.985666	+	0.168707i	$0.0539592\pi$
$383$			3.70988e8i			0.337415i	−0.985666	+	0.168707i	$0.946041\pi$
$384$	−1.41280e9	+	8.15679e8i	−1.27327	+	0.735123i
$385$	−1.93275e9	−	2.21810e7i	−1.72609	−	0.0198093i
$386$	−8.26580e7	−	1.43168e8i	−0.0731526	−	0.126704i
$387$	5.04377e8	+	8.73607e8i	0.442351	+	0.766175i
$388$		−	5.15666e9i		−	4.48185i
$389$	3.66379e8	+	6.34586e8i	0.315578	+	0.546597i	0.979560	−	0.201151i	$-0.0644683\pi$
$389$	3.66379e8	+	6.34586e8i	0.315578	+	0.546597i	−0.663982	+	0.747748i	$0.731135\pi$
$390$	−5.63226e7	−	5.39916e8i	−0.0480792	−	0.460893i
$391$	6.50501e8			0.550338
$392$	−3.95075e9	−	2.40351e9i	−3.31267	−	2.01533i
$393$	−2.43955e8	+	4.22543e8i	−0.202738	+	0.351153i
$394$	−1.95162e9			−1.60753
$395$	7.63667e8	−	4.40903e8i	0.623468	−	0.359959i
$396$	−4.69359e9	−	2.70984e9i	−3.79815	−	2.19286i
$397$			4.60562e8i			0.369421i	0.982793	+	0.184710i	$0.0591347\pi$
$397$			4.60562e8i			0.369421i	−0.982793	+	0.184710i	$0.940865\pi$
$398$		−	1.15219e9i		−	0.916080i
$399$	−1.54526e8	+	8.68667e7i	−0.121786	+	0.0684618i
$400$	7.07943e8	−	1.22619e9i	0.553080	−	0.957963i
$401$	−6.60892e8	+	3.81566e8i	−0.511830	+	0.295505i	−0.733585	−	0.679597i	$-0.762155\pi$
$401$	−6.60892e8	+	3.81566e8i	−0.511830	+	0.295505i	0.221756	+	0.975102i	$0.428821\pi$
$402$	1.09568e8	+	1.89778e8i	0.0841190	+	0.145698i
$403$	−1.13521e8	−	1.56505e8i	−0.0863993	−	0.119113i
$404$	1.02931e9	−	1.78282e9i	0.776628	−	1.34516i
$405$	−1.11783e9	−	6.45377e8i	−0.836145	−	0.482748i
$406$	−7.95826e8	+	4.47373e8i	−0.590170	+	0.331763i
$407$	3.27826e8	+	5.67810e8i	0.241025	+	0.417468i
$408$	1.09046e9	+	6.29578e8i	0.794876	+	0.458922i
$409$	−1.05163e9	−	6.07159e8i	−0.760031	−	0.438804i	0.0692758	−	0.997598i	$-0.477931\pi$
$409$	−1.05163e9	−	6.07159e8i	−0.760031	−	0.438804i	−0.829307	+	0.558793i	$0.811264\pi$
$410$	1.25948e9	+	7.27159e8i	0.902499	+	0.521058i
$411$	−3.49271e8	−	2.01652e8i	−0.248151	−	0.143270i
$412$	−1.30483e9	−	2.26004e9i	−0.919211	−	1.59212i
$413$	−2.15301e7	+	1.87603e9i	−0.0150391	+	1.31043i
$414$	−1.15987e9	−	6.69651e8i	−0.803356	−	0.463818i
$415$	−9.12511e8	+	1.58051e9i	−0.626714	+	1.08550i
$416$	−3.33636e9	+	7.47791e9i	−2.27220	+	5.09276i
$417$	−2.15837e7	−	3.73841e7i	−0.0145764	−	0.0252470i
$418$	2.65889e9	−	1.53511e9i	1.78067	−	1.02807i
$419$	9.68029e8	−	1.67668e9i	0.642894	−	1.11352i	−0.341890	−	0.939740i	$-0.611067\pi$
$419$	9.68029e8	−	1.67668e9i	0.642894	−	1.11352i	0.984784	−	0.173785i	$-0.0555996\pi$
$420$	−8.98535e8	−	5.32611e8i	−0.591783	−	0.350782i
$421$			1.03885e9i			0.678525i	0.940692	+	0.339263i	$0.110178\pi$
$421$			1.03885e9i			0.678525i	−0.940692	+	0.339263i	$0.889822\pi$
$422$			8.84904e7i			0.0573195i
$423$	5.65572e7	+	3.26533e7i	0.0363326	+	0.0209766i
$424$	1.09763e9	−	6.33719e8i	0.699321	−	0.403753i
$425$	−4.14865e8			−0.262147
$426$	−1.94567e8	+	3.37000e8i	−0.121937	+	0.211201i
$427$	1.16740e9	+	2.07667e9i	0.725642	+	1.29084i
$428$	−8.63128e8			−0.532135
$429$	5.31056e8	−	5.53984e7i	0.324743	−	0.0338764i
$430$	−1.68360e9	−	2.91609e9i	−1.02117	−	1.76873i
$431$			1.56159e9i			0.939499i	0.882800	+	0.469749i	$0.155656\pi$
$431$			1.56159e9i			0.939499i	−0.882800	+	0.469749i	$0.844344\pi$
$432$	−1.63680e9	−	2.83502e9i	−0.976793	−	1.69186i
$433$	4.62461e8	+	8.01006e8i	0.273758	+	0.474164i	0.969821	−	0.243817i	$-0.0783998\pi$
$433$	4.62461e8	+	8.01006e8i	0.273758	+	0.474164i	−0.696063	+	0.717981i	$0.745066\pi$
$434$	−4.98064e8	−	5.71600e6i	−0.292463	−	0.00335643i
$435$	−1.18063e8	+	6.81638e7i	−0.0687705	+	0.0397047i
$436$		−	1.45125e9i		−	0.838568i
$437$	4.90749e8	−	2.83334e8i	0.281303	−	0.162410i
$438$	2.34180e8	−	4.05612e8i	0.133165	−	0.230649i
$439$	9.29586e8	+	1.61009e9i	0.524401	+	0.908290i	0.999596	+	0.0284094i	$0.00904421\pi$
$439$	9.29586e8	+	1.61009e9i	0.524401	+	0.908290i	−0.475195	+	0.879881i	$0.657622\pi$
$440$	1.03577e10	+	5.98001e9i	5.79666	+	3.34670i
$441$	8.94825e8	−	1.47086e9i	0.496824	−	0.816650i
$442$	4.04557e9	−	4.22023e8i	2.22844	−	0.232466i
$443$	−6.45285e8	+	1.11767e9i	−0.352646	+	0.610800i	−0.986712	−	0.162479i	$-0.948051\pi$
$443$	−6.45285e8	+	1.11767e9i	−0.352646	+	0.610800i	0.634067	+	0.773278i	$0.281385\pi$
$444$			3.54315e8i			0.192110i
$445$	3.08984e9			1.66217
$446$	3.15867e9			1.68590
$447$		−	2.91401e8i		−	0.154317i
$448$	5.90156e9	+	1.04982e10i	3.10094	+	5.51623i
$449$	−2.02653e9	+	1.17001e9i	−1.05655	+	0.609999i	−0.924476	−	0.381241i	$-0.875497\pi$
$449$	−2.02653e9	+	1.17001e9i	−1.05655	+	0.609999i	−0.132074	+	0.991240i	$0.542164\pi$
$450$	7.39720e8	+	4.27078e8i	0.382669	+	0.220934i
$451$	−7.15227e8	+	1.23881e9i	−0.367135	+	0.635896i
$452$	−3.13463e9			−1.59662
$453$	−2.46480e8	+	1.42305e8i	−0.124577	+	0.0719247i
$454$	−3.60857e9			−1.80984
$455$	−2.22119e9	+	2.05971e8i	−1.10546	+	0.102510i
$456$	1.09688e9			0.541730
$457$	1.76482e9	−	1.01892e9i	0.864957	−	0.499383i	−0.000712351	−	1.00000i	$-0.500227\pi$
$457$	1.76482e9	−	1.01892e9i	0.864957	−	0.499383i	0.865669	+	0.500617i	$0.166893\pi$
$458$	−7.07373e9			−3.44048
$459$	−4.79594e8	+	8.30682e8i	−0.231489	+	0.400950i
$460$	2.89167e9	+	1.66950e9i	1.38515	+	0.799715i
$461$	−1.21870e9	+	7.03619e8i	−0.579355	+	0.334491i	−0.760877	−	0.648896i	$-0.775231\pi$
$461$	−1.21870e9	+	7.03619e8i	−0.579355	+	0.334491i	0.181522	+	0.983387i	$0.441898\pi$
$462$	7.01405e8	−	1.18330e9i	0.330919	−	0.558274i
$463$			2.81463e9i			1.31792i	0.752179	+	0.658959i	$0.229003\pi$
$463$			2.81463e9i			1.31792i	−0.752179	+	0.658959i	$0.770997\pi$
$464$	3.48626e9			1.62012
$465$	−7.43790e7			−0.0343056
$466$			1.56734e9i			0.717482i
$467$	6.33659e8	−	1.09753e9i	0.287903	−	0.498663i	−0.685406	−	0.728161i	$-0.740375\pi$
$467$	6.33659e8	−	1.09753e9i	0.287903	−	0.498663i	0.973309	+	0.229498i	$0.0737085\pi$
$468$	−5.71208e9	−	2.54851e9i	−2.57593	−	1.14928i
$469$	7.84970e8	−	4.41270e8i	0.351357	−	0.197515i
$470$	−1.88787e8	−	1.08996e8i	−0.0838745	−	0.0484249i
$471$	3.27688e8	+	5.67573e8i	0.144507	+	0.250293i
$472$	5.80453e9	−	1.00537e10i	2.54080	−	4.40079i
$473$	2.86823e9	−	1.65598e9i	1.24624	−	0.719515i
$474$			6.27552e8i			0.270661i
$475$	−3.12981e8	+	1.80700e8i	−0.133996	+	0.0773623i
$476$	3.99083e9	−	6.73269e9i	1.69605	−	2.86131i
$477$	2.35933e8	+	4.08647e8i	0.0995345	+	0.172399i
$478$	−4.01776e9	−	6.95897e9i	−1.68262	−	2.91439i
$479$		−	3.14646e9i		−	1.30812i	−0.756442	−	0.654060i	$-0.773064\pi$
$479$		−	3.14646e9i		−	1.30812i	0.756442	−	0.654060i	$-0.226936\pi$
$480$	1.57506e9	+	2.72808e9i	0.650057	+	1.12593i
$481$	4.44290e8	+	6.12514e8i	0.182037	+	0.250962i
$482$	1.09698e9			0.446203
$483$	1.29458e8	−	2.18401e8i	0.0522773	−	0.0881939i
$484$	−5.21680e9	+	9.03576e9i	−2.09144	+	3.62248i
$485$	−4.23660e9			−1.68625
$486$	2.58469e9	−	1.49227e9i	1.02136	−	0.589685i
$487$	−3.95477e9	−	2.28329e9i	−1.55156	−	0.895796i	−0.998015	−	0.0629793i	$-0.979940\pi$
$487$	−3.95477e9	−	2.28329e9i	−1.55156	−	0.895796i	−0.553549	−	0.832817i	$-0.686727\pi$
$488$		−	1.47410e10i		−	5.74192i
$489$			1.74729e8i			0.0675748i
$490$	−2.98691e9	+	4.90970e9i	−1.14693	+	1.88525i
$491$	−1.13556e9	+	1.96685e9i	−0.432937	+	0.749869i	−0.997125	−	0.0757774i	$-0.975856\pi$
$491$	−1.13556e9	+	1.96685e9i	−0.432937	+	0.749869i	0.564188	+	0.825647i	$0.309189\pi$
$492$	−6.69455e8	+	3.86510e8i	−0.253421	+	0.146313i
$493$	−5.10749e8	−	8.84643e8i	−0.191974	−	0.332509i
$494$	2.86823e9	−	2.08048e9i	1.07046	−	0.776460i
$495$	−2.22635e9	+	3.85615e9i	−0.825040	+	1.42901i
$496$	1.64724e9	+	9.51032e8i	0.606136	+	0.349953i
$497$	1.37557e9	+	8.15372e8i	0.502613	+	0.297926i
$498$	−6.49403e8	−	1.12480e9i	−0.235620	−	0.408105i
$499$	−2.22298e9	−	1.28344e9i	−0.800911	−	0.462406i	0.0428784	−	0.999080i	$-0.486347\pi$
$499$	−2.22298e9	−	1.28344e9i	−0.800911	−	0.462406i	−0.843790	+	0.536674i	$0.819681\pi$
$500$	6.08575e9	+	3.51361e9i	2.17730	+	1.25707i
$501$	−1.32882e8	−	7.67194e7i	−0.0472100	−	0.0272567i
$502$	3.13514e9	+	1.81007e9i	1.10610	+	0.638607i
$503$	1.33450e9	+	2.31142e9i	0.467551	+	0.809823i	0.999313	−	0.0370714i	$-0.0118029\pi$
$503$	1.33450e9	+	2.31142e9i	0.467551	+	0.809823i	−0.531761	+	0.846894i	$0.678470\pi$
$504$	−9.28640e9	+	5.22034e9i	−3.23103	+	1.81632i
$505$	−1.46473e9	−	8.45661e8i	−0.506101	−	0.292198i
$506$	−2.19860e9	+	3.80809e9i	−0.754432	+	1.30671i
$507$	6.02946e8	−	1.27180e8i	0.205471	−	0.0433401i
$508$	5.51546e9	+	9.55305e9i	1.86663	+	3.23310i
$509$	−3.62954e9	+	2.09552e9i	−1.21994	+	0.704334i	−0.964905	−	0.262598i	$-0.915421\pi$
$509$	−3.62954e9	+	2.09552e9i	−1.21994	+	0.704334i	−0.255037	+	0.966931i	$0.582088\pi$
$510$	7.82393e8	−	1.35514e9i	0.261174	−	0.452366i
$511$	−1.65563e9	−	9.81379e8i	−0.548895	−	0.325360i
$512$		−	2.45443e10i		−	8.08175i
$513$			8.35574e8i			0.273259i
$514$	7.90598e9	+	4.56452e9i	2.56794	+	1.48260i
$515$	−1.85680e9	+	1.07202e9i	−0.599018	+	0.345843i
$516$	1.78978e9			0.573491
$517$	1.07208e8	−	1.85689e8i	0.0341200	−	0.0590976i
$518$	1.94928e9	+	2.23707e7i	0.616197	+	0.00707174i
$519$	−2.35821e7			−0.00740451
$520$	1.26053e10	+	5.62398e9i	3.93133	+	1.75401i
$521$	−2.38595e9	−	4.13259e9i	−0.739145	−	1.28024i	−0.952881	−	0.303346i	$-0.901896\pi$
$521$	−2.38595e9	−	4.13259e9i	−0.739145	−	1.28024i	0.213735	−	0.976892i	$-0.431437\pi$
$522$			2.10314e9i			0.647174i
$523$	2.33436e8	+	4.04322e8i	0.0713528	+	0.123587i	0.899494	−	0.436932i	$-0.143935\pi$
$523$	2.33436e8	+	4.04322e8i	0.0713528	+	0.123587i	−0.828142	+	0.560519i	$0.810602\pi$
$524$	−9.38280e9	−	1.62515e10i	−2.84887	−	4.93439i
$525$	−8.25632e7	+	1.39287e8i	−0.0249017	+	0.0420102i
$526$	3.23186e9	−	1.86591e9i	0.968282	−	0.559038i
$527$		−	5.57319e8i		−	0.165869i
$528$	−4.54906e9	+	2.62640e9i	−1.34494	+	0.776501i
$529$	1.29662e9	−	2.24581e9i	0.380818	−	0.659596i
$530$	−7.87539e8	−	1.36406e9i	−0.229777	−	0.397985i
$531$	3.74300e9	+	2.16102e9i	1.08490	+	0.626365i
$532$	7.82407e7	−	6.81751e9i	0.0225290	−	1.96307i
$533$	−6.72645e8	+	1.50763e9i	−0.192416	+	0.431269i
$534$	−1.09947e9	+	1.90433e9i	−0.312455	+	0.541188i
$535$			7.09127e8i			0.200210i
$536$	−5.57200e9			−1.56291
$537$	1.24102e9			0.345834
$538$			4.43905e9i			1.22900i
$539$	−4.82913e9	−	2.93790e9i	−1.32834	−	0.808120i
$540$	−4.26387e9	+	2.46175e9i	−1.16527	+	0.672768i
$541$	1.01780e9	+	5.87628e8i	0.276359	+	0.159556i	0.631774	−	0.775153i	$-0.282327\pi$
$541$	1.01780e9	+	5.87628e8i	0.276359	+	0.159556i	−0.355415	+	0.934709i	$0.615661\pi$
$542$	−5.93199e9	+	1.02745e10i	−1.60031	+	2.77181i
$543$	−1.25403e8			−0.0336131
$544$	−2.04414e10	+	1.18018e10i	−5.44395	+	3.14306i
$545$	−1.19231e9			−0.315502
$546$	6.63427e8	−	1.44225e9i	0.174429	−	0.379199i
$547$	2.04086e9			0.533160			0.266580	−	0.963813i	$-0.414106\pi$
$547$	2.04086e9			0.533160			0.266580	+	0.963813i	$0.414106\pi$
$548$	1.34334e10	−	7.75576e9i	3.48701	−	2.01323i
$549$	5.48805e9			1.41552
$550$	1.40218e9	−	2.42865e9i	0.359365	−	0.622438i
$551$	−7.70635e8	−	4.44926e8i	−0.196254	−	0.113307i
$552$	−1.36050e9	+	7.85483e8i	−0.344279	+	0.198770i
$553$	2.57863e9	+	2.95934e7i	0.648411	+	0.00744144i
$554$			1.06292e10i			2.65592i
$555$	2.91097e8			0.0722791
$556$	1.66027e9			0.409654
$557$		−	3.52837e8i		−	0.0865130i	−0.999064	−	0.0432565i	$-0.986227\pi$
$557$		−	3.52837e8i		−	0.0865130i	0.999064	−	0.0432565i	$-0.0137733\pi$
$558$	−5.73725e8	+	9.93721e8i	−0.139793	+	0.242128i
$559$	3.09405e9	−	2.24428e9i	0.749180	−	0.543421i
$560$	1.91300e10	−	1.07539e10i	4.60316	−	2.58766i
$561$	1.33291e9	+	7.69554e8i	0.318735	+	0.184022i
$562$	8.45569e8	+	1.46457e9i	0.200942	+	0.348043i
$563$	−2.22964e9	+	3.86185e9i	−0.526570	+	0.912046i	0.472951	+	0.881089i	$0.343189\pi$
$563$	−2.22964e9	+	3.86185e9i	−0.526570	+	0.912046i	−0.999521	+	0.0309568i	$0.990145\pi$
$564$	1.00347e8	−	5.79352e7i	0.0235519	−	0.0135977i
$565$			2.57534e9i			0.600711i
$566$	−6.93660e9	+	4.00485e9i	−1.60801	+	0.928386i
$567$	−1.84973e9	−	3.29047e9i	−0.426156	−	0.758083i
$568$	−4.94726e9	−	8.56891e9i	−1.13278	−	1.96203i
$569$	−3.20071e9	−	5.54379e9i	−0.728372	−	1.26158i	−0.957571	−	0.288198i	$-0.906944\pi$
$569$	−3.20071e9	−	5.54379e9i	−0.728372	−	1.26158i	0.229199	−	0.973380i	$-0.426389\pi$
$570$		−	1.36312e9i		−	0.308300i
$571$	−2.50229e9	−	4.33410e9i	−0.562486	−	0.974254i	−0.997279	−	0.0737238i	$-0.976512\pi$
$571$	−2.50229e9	−	4.33410e9i	−0.562486	−	0.974254i	0.434793	−	0.900531i	$-0.356822\pi$
$572$	−8.36729e9	+	1.87539e10i	−1.86938	+	4.18993i
$573$	−1.28569e9			−0.285493
$574$	2.08413e9	+	3.70744e9i	0.459974	+	0.818242i
$575$	2.58800e8	−	4.48255e8i	0.0567710	−	0.0983303i
$576$	2.77437e10			6.04903
$577$	7.65383e9	−	4.41894e9i	1.65868	−	0.957642i	0.685361	−	0.728203i	$-0.259644\pi$
$577$	7.65383e9	−	4.41894e9i	1.65868	−	0.957642i	0.973323	−	0.229438i	$-0.0736890\pi$
$578$	2.16268e9	+	1.24862e9i	0.465849	+	0.268958i
$579$		−	7.21930e7i		−	0.0154568i
$580$		−	5.24332e9i		−	1.11586i
$581$	−4.65245e9	+	2.61537e9i	−0.984160	+	0.553245i
$582$	1.50752e9	−	2.61110e9i	0.316981	−	0.549027i
$583$	1.34167e9	−	7.74616e8i	0.280419	−	0.161900i
$584$	5.95450e9	+	1.03135e10i	1.23709	+	2.14270i
$585$	−2.09380e9	+	4.69292e9i	−0.432404	+	0.969165i
$586$	2.16048e9	−	3.74206e9i	0.443515	−	0.768191i
$587$	4.61420e9	+	2.66401e9i	0.941593	+	0.543629i	0.890459	−	0.455063i	$-0.150383\pi$
$587$	4.61420e9	+	2.66401e9i	0.941593	+	0.543629i	0.0511337	+	0.998692i	$0.483717\pi$
$588$	−1.46622e9	−	2.67978e9i	−0.297426	−	0.543598i
$589$	−2.42747e8	−	4.20450e8i	−0.0489498	−	0.0847835i
$590$	−1.24941e10	−	7.21345e9i	−2.50450	−	1.44597i
$591$	−7.38085e8	−	4.26134e8i	−0.147079	−	0.0849161i
$592$	−6.44680e9	−	3.72206e9i	−1.27708	−	0.737323i
$593$	−1.02004e9	−	5.88917e8i	−0.200874	−	0.115975i	0.396189	−	0.918169i	$-0.370332\pi$
$593$	−1.02004e9	−	5.88917e8i	−0.200874	−	0.115975i	−0.597063	+	0.802194i	$0.703666\pi$
$594$	−3.24192e9	−	5.61517e9i	−0.634673	−	1.09929i
$595$	−5.53143e9	−	3.27878e9i	−1.07653	−	0.638121i
$596$	9.70609e9	+	5.60381e9i	1.87794	+	1.08423i
$597$	2.51579e8	−	4.35747e8i	0.0483909	−	0.0838155i
$598$	−2.06771e9	+	4.63444e9i	−0.395398	+	0.886223i
$599$	9.50769e8	+	1.64678e9i	0.180751	+	0.313070i	0.942137	−	0.335229i	$-0.108814\pi$
$599$	9.50769e8	+	1.64678e9i	0.180751	+	0.313070i	−0.761385	+	0.648300i	$0.775480\pi$
$600$	8.67673e8	−	5.00951e8i	0.163993	−	0.0946817i
$601$	3.23469e9	−	5.60265e9i	0.607816	−	1.05277i	−0.383784	−	0.923423i	$-0.625379\pi$
$601$	3.23469e9	−	5.60265e9i	0.607816	−	1.05277i	0.991600	−	0.129345i	$-0.0412874\pi$
$602$	1.13003e8	−	9.84657e9i	0.0211108	−	1.83949i
$603$		−	2.07445e9i		−	0.385294i
$604$		−	1.09465e10i		−	2.02137i
$605$	7.42358e9	+	4.28601e9i	1.36292	+	0.786881i
$606$	1.04240e9	−	6.01829e8i	0.190274	−	0.109855i
$607$	7.88389e9			1.43080			0.715402	−	0.698713i	$-0.246244\pi$
$607$	7.88389e9			1.43080			0.715402	+	0.698713i	$0.246244\pi$
$608$	−1.02809e10	+	1.78070e10i	−1.85510	+	3.21313i
$609$	−3.98657e8	−	4.57516e6i	−0.0715219	−	0.000820815i
$610$	−1.83190e10			−3.26774
$611$	1.00825e8	−	2.25983e8i	0.0178823	−	0.0400804i
$612$	−9.01495e9	−	1.56144e10i	−1.58977	−	2.75356i
$613$		−	2.29392e9i		−	0.402222i	−0.979568	−	0.201111i	$-0.935545\pi$
$613$		−	2.29392e9i		−	0.402222i	0.979568	−	0.201111i	$-0.0644552\pi$
$614$	6.81798e9	+	1.18091e10i	1.18868	+	2.05886i
$615$	3.17548e8	+	5.50009e8i	0.0550486	+	0.0953470i
$616$	1.71395e10	+	3.04892e10i	2.95437	+	5.25549i
$617$	−7.48201e9	+	4.31974e9i	−1.28239	+	0.740388i	−0.977285	−	0.211931i	$-0.932025\pi$
$617$	−7.48201e9	+	4.31974e9i	−1.28239	+	0.740388i	−0.305105	+	0.952319i	$0.598692\pi$
$618$		−	1.52585e9i		−	0.260046i
$619$	1.79334e9	−	1.03539e9i	0.303910	−	0.175463i	−0.340288	−	0.940321i	$-0.610524\pi$
$619$	1.79334e9	−	1.03539e9i	0.303910	−	0.175463i	0.644198	+	0.764859i	$0.277191\pi$
$620$	1.43035e9	−	2.47744e9i	0.241030	−	0.417477i
$621$	−5.98359e8	−	1.03639e9i	−0.100263	−	0.173661i
$622$	−1.65976e10	−	9.58263e9i	−2.76553	−	1.59668i
$623$	7.77311e9	+	4.60754e9i	1.28791	+	0.763416i
$624$	−4.90721e9	+	3.55946e9i	−0.808515	+	0.586460i
$625$	3.59642e9	−	6.22919e9i	0.589238	−	1.02059i
$626$		−	9.93798e9i		−	1.61915i
$627$	1.34076e9			0.217227
$628$	−2.52066e10			−4.06121
$629$			2.18118e9i			0.349474i
$630$	6.48746e9	+	1.15405e10i	1.03367	+	1.83879i
$631$	2.63799e9	−	1.52304e9i	0.417994	−	0.241329i	−0.276225	−	0.961093i	$-0.589083\pi$
$631$	2.63799e9	−	1.52304e9i	0.417994	−	0.241329i	0.694219	+	0.719764i	$0.255750\pi$
$632$	−1.38190e10	−	7.97839e9i	−2.17754	−	1.25720i
$633$	−1.93217e7	+	3.34662e7i	−0.00302784	+	0.00524437i
$634$	2.47115e10			3.85111
$635$	7.84858e9	−	4.53138e9i	1.21642	−	0.702300i
$636$	8.37207e8			0.129043
$637$	−5.89498e9	−	2.79405e9i	−0.903637	−	0.428299i
$638$	6.90504e9			1.05267
$639$	3.19019e9	−	1.84186e9i	0.483686	−	0.279256i
$640$	−5.15491e10			−7.77304
$641$	3.17787e9	−	5.50424e9i	0.476578	−	0.825457i	−0.523062	−	0.852295i	$-0.675210\pi$
$641$	3.17787e9	−	5.50424e9i	0.476578	−	0.825457i	0.999640	+	0.0268379i	$0.00854378\pi$
$642$	−4.37050e8	−	2.52331e8i	−0.0651866	−	0.0376355i
$643$	3.14565e9	−	1.81614e9i	0.466629	−	0.269408i	−0.248199	−	0.968709i	$-0.579839\pi$
$643$	3.14565e9	−	1.81614e9i	0.466629	−	0.269408i	0.714827	+	0.699301i	$0.246505\pi$
$644$	4.78501e9	+	8.51200e9i	0.705964	+	1.25583i
$645$		−	1.47045e9i		−	0.215770i
$646$	1.02138e10			1.49065
$647$	9.55853e9			1.38748			0.693739	−	0.720227i	$-0.255962\pi$
$647$	9.55853e9			1.38748			0.693739	+	0.720227i	$0.255962\pi$
$648$			2.33569e10i			3.37212i
$649$	7.09508e9	−	1.22890e10i	1.01883	−	1.76466i
$650$	1.31870e9	−	2.95567e9i	0.188343	−	0.422142i
$651$	−1.87115e8	−	1.10913e8i	−0.0265813	−	0.0157562i
$652$	−5.81995e9	−	3.36015e9i	−0.822342	−	0.474779i
$653$	9.47090e8	+	1.64041e9i	0.133105	+	0.230545i	0.924872	−	0.380278i	$-0.124172\pi$
$653$	9.47090e8	+	1.64041e9i	0.133105	+	0.230545i	−0.791767	+	0.610823i	$0.790839\pi$
$654$	4.24264e8	−	7.34846e8i	0.0593081	−	0.102725i
$655$	−1.33519e10	+	7.70870e9i	−1.85651	+	1.07186i
$656$		−	1.62411e10i		−	2.24621i
$657$	−3.83970e9	+	2.21685e9i	−0.528225	+	0.304971i
$658$	−3.12397e8	−	5.55720e8i	−0.0427481	−	0.0760440i
$659$	3.50255e9	+	6.06660e9i	0.476745	+	0.825746i	0.999645	−	0.0266478i	$-0.00848325\pi$
$659$	3.50255e9	+	6.06660e9i	0.476745	+	0.825746i	−0.522900	+	0.852394i	$0.675150\pi$
$660$	3.95010e9	+	6.84178e9i	0.534816	+	0.926329i
$661$		−	7.51189e8i		−	0.101168i	−0.998720	−	0.0505841i	$-0.983892\pi$
$661$		−	7.51189e8i		−	0.101168i	0.998720	−	0.0505841i	$-0.0161083\pi$
$662$	1.00983e9	+	1.74908e9i	0.135284	+	0.234319i
$663$	1.62214e9	+	7.23738e8i	0.216168	+	0.0964459i
$664$	3.30248e10			4.37776
$665$	−5.60112e9	−	6.42808e7i	−0.738582	−	0.00847628i
$666$	2.24539e9	−	3.88913e9i	0.294532	−	0.510144i
$667$	1.27446e9			0.166297
$668$	5.11079e9	−	2.95072e9i	0.663393	−	0.383010i
$669$	1.19458e9	+	6.89690e8i	0.154249	+	0.0890558i
$670$			6.92447e9i			0.889457i
$671$		−	1.80184e10i		−	2.30244i
$672$	−1.05718e8	+	9.21173e9i	−0.0134386	+	1.17098i
$673$	4.41949e9	−	7.65477e9i	0.558881	−	0.968010i	−0.438710	−	0.898629i	$-0.644564\pi$
$673$	4.41949e9	−	7.65477e9i	0.558881	−	0.968010i	0.997590	−	0.0693807i	$-0.0221023\pi$
$674$	−6.97128e9	+	4.02487e9i	−0.877007	+	0.506340i
$675$	3.81610e8	+	6.60968e8i	0.0477592	+	0.0827213i
$676$	−7.35887e9	+	2.25289e10i	−0.916216	+	2.80496i
$677$	−1.57285e9	+	2.72426e9i	−0.194817	+	0.337433i	−0.946841	−	0.321703i	$-0.895745\pi$
$677$	−1.57285e9	+	2.72426e9i	−0.194817	+	0.337433i	0.752023	+	0.659136i	$0.229078\pi$
$678$	−1.58724e9	−	9.16392e8i	−0.195586	−	0.112922i
$679$	−1.06580e10	−	6.31758e9i	−1.30657	−	0.774473i
$680$	1.98939e10	+	3.44573e10i	2.42627	+	4.20243i
$681$	−1.36473e9	−	7.87925e8i	−0.165589	−	0.0956026i
$682$	3.26259e9	+	1.88366e9i	0.393838	+	0.227382i
$683$	8.64703e9	+	4.99237e9i	1.03847	+	0.599562i	0.919400	−	0.393324i	$-0.128675\pi$
$683$	8.64703e9	+	4.99237e9i	1.03847	+	0.599562i	0.119072	+	0.992886i	$0.462008\pi$
$684$	−1.36021e10	−	7.85315e9i	−1.62521	−	0.938313i
$685$	−6.37196e9	−	1.10366e10i	−0.757454	−	1.31195i
$686$	−1.48355e10	+	7.89728e9i	−1.75456	+	0.933991i
$687$	−2.67522e9	−	1.54454e9i	−0.314783	−	0.181740i
$688$	−1.88016e10	+	3.25653e10i	−2.20108	+	3.81238i
$689$	1.44730e9	−	1.04981e9i	0.168575	−	0.122276i
$690$	9.76141e8	+	1.69073e9i	0.113120	+	0.195930i
$691$	1.29516e9	−	7.47761e8i	0.149331	−	0.0862164i	−0.423473	−	0.905909i	$-0.639189\pi$
$691$	1.29516e9	−	7.47761e8i	0.149331	−	0.0862164i	0.572804	+	0.819693i	$0.305856\pi$
$692$	4.53498e8	−	7.85481e8i	0.0520240	−	0.0901082i
$693$	−1.13511e10	+	6.38100e9i	−1.29560	+	0.728320i
$694$			2.22932e10i			2.53172i
$695$		−	1.36404e9i		−	0.154128i
$696$	2.13642e9	+	1.23346e9i	0.240190	+	0.138674i
$697$	−4.12120e9	+	2.37937e9i	−0.461008	+	0.266163i
$698$	1.43312e10			1.59510
$699$	−3.42225e8	+	5.92751e8i	−0.0379002	+	0.0656451i
$700$	−3.05170e9	−	5.42863e9i	−0.336278	−	0.598200i
$701$	−6.08835e9			−0.667554			−0.333777	−	0.942652i	$-0.608323\pi$
$701$	−6.08835e9			−0.667554			−0.333777	+	0.942652i	$0.608323\pi$
$702$	−4.39366e9	−	6.05726e9i	−0.479343	−	0.660840i
$703$	9.50042e8	+	1.64552e9i	0.103133	+	0.178632i
$704$		−	9.10884e10i		−	9.83917i
$705$	−4.75983e7	−	8.24427e7i	−0.00511599	−	0.00886115i
$706$	7.33507e9	+	1.27047e10i	0.784490	+	1.35878i
$707$	−2.42377e9	−	4.31162e9i	−0.257943	−	0.458852i
$708$	6.64102e9	−	3.83419e9i	0.703264	−	0.406029i
$709$		−	1.12380e10i		−	1.18421i	−0.805862	−	0.592104i	$-0.798297\pi$
$709$		−	1.12380e10i		−	1.18421i	0.805862	−	0.592104i	$-0.201703\pi$
$710$	−1.06488e10	+	6.14809e9i	−1.11660	+	0.644668i
$711$	2.97034e9	−	5.14479e9i	0.309930	−	0.536814i
$712$	−2.79562e10	−	4.84215e10i	−2.90267	−	5.02758i
$713$	6.02174e8	+	3.47665e8i	0.0622169	+	0.0359210i
$714$	3.98905e9	−	2.24244e9i	0.410133	−	0.230556i
$715$	1.54078e10	+	6.87438e9i	1.57641	+	0.703335i
$716$	−2.38655e10	+	4.13363e10i	−2.42983	+	4.20858i
$717$		−	3.50909e9i		−	0.355531i
$718$	−3.15982e9			−0.318586
$719$	1.01307e10			1.01645			0.508227	−	0.861223i	$-0.330301\pi$
$719$	1.01307e10			1.01645			0.508227	+	0.861223i	$0.330301\pi$
$720$		−	5.05550e10i		−	5.04778i
$721$	−6.26974e9	−	7.19542e7i	−0.622983	−	0.00714962i
$722$	−9.70270e9	+	5.60185e9i	−0.959428	+	0.553926i
$723$	4.14866e8	+	2.39523e8i	0.0408248	+	0.0235702i
$724$	2.41157e9	−	4.17697e9i	0.236165	−	0.409050i
$725$	−8.12800e8			−0.0792137
$726$	−5.28311e9	+	3.05021e9i	−0.512403	+	0.295836i
$727$	5.91773e9			0.571196			0.285598	−	0.958350i	$-0.407808\pi$
$727$	5.91773e9			0.571196			0.285598	+	0.958350i	$0.407808\pi$
$728$	2.33246e10	+	3.29451e10i	2.24055	+	3.16469i
$729$	−7.79355e9			−0.745056
$730$	1.28169e10	−	7.39982e9i	1.21942	−	0.704030i
$731$	1.10180e10			1.04326
$732$	4.86859e9	−	8.43265e9i	0.458791	−	0.794648i
$733$	−1.03278e10	−	5.96277e9i	−0.968600	−	0.559222i	−0.0697912	−	0.997562i	$-0.522233\pi$
$733$	−1.03278e10	−	5.96277e9i	−0.968600	−	0.559222i	−0.898809	+	0.438340i	$0.855567\pi$
$734$	−1.27112e10	+	7.33883e9i	−1.18646	+	0.685000i
$735$	−2.20165e9	+	1.20461e9i	−0.204523	+	0.111903i
$736$		−	2.94488e10i		−	2.72267i
$737$	−6.81085e9			−0.626707
$738$	9.79767e9			0.897275
$739$			9.12596e9i			0.831808i	0.909409	+	0.415904i	$0.136535\pi$
$739$			9.12596e9i			0.831808i	−0.909409	+	0.415904i	$0.863465\pi$
$740$	−5.59798e9	+	9.69598e9i	−0.507832	+	0.879591i
$741$	1.53901e9	−	1.60545e8i	0.138956	−	0.0144955i
$742$	5.28596e7	−	4.60593e9i	0.00475018	−	0.413908i
$743$	1.21092e10	+	6.99126e9i	1.08307	+	0.625308i	0.931722	−	0.363173i	$-0.118306\pi$
$743$	1.21092e10	+	6.99126e9i	1.08307	+	0.625308i	0.151344	+	0.988481i	$0.451640\pi$
$744$	6.72965e8	+	1.16561e9i	0.0599083	+	0.103764i
$745$	4.60397e9	−	7.97431e9i	0.407930	−	0.706555i
$746$	−1.76185e9	+	1.01720e9i	−0.155375	+	0.0897060i
$747$			1.22951e10i			1.07922i
$748$	−5.12652e10	+	2.95980e10i	−4.47885	+	2.58587i
$749$	−1.05744e9	+	1.78395e9i	−0.0919541	+	0.155130i
$750$	2.05437e9	+	3.55827e9i	0.177813	+	0.307982i
$751$	3.03495e9	+	5.25669e9i	0.261464	+	0.452869i	0.966631	−	0.256172i	$-0.0824614\pi$
$751$	3.03495e9	+	5.25669e9i	0.261464	+	0.452869i	−0.705167	+	0.709041i	$0.749128\pi$
$752$			2.43443e9i			0.208754i
$753$	7.90454e8	+	1.36911e9i	0.0674674	+	0.116857i
$754$	7.92604e9	−	8.26825e8i	0.673375	−	0.0702447i
$755$	−8.99338e9			−0.760517
$756$	−1.43976e10	−	1.65232e8i	−1.21189	−	0.0139081i
$757$	−6.36128e9	+	1.10181e10i	−0.532978	+	0.923144i	0.466281	+	0.884637i	$0.345594\pi$
$757$	−6.36128e9	+	1.10181e10i	−0.532978	+	0.923144i	−0.999258	+	0.0385076i	$0.987740\pi$
$758$	−1.26847e10			−1.05788
$759$	−1.66298e9	+	9.60123e8i	−0.138052	+	0.0797041i
$760$	3.00166e10	+	1.73301e10i	2.48036	+	1.43204i
$761$		−	3.51790e9i		−	0.289359i	−0.989479	−	0.144680i	$-0.953785\pi$
$761$		−	3.51790e9i		−	0.289359i	0.989479	−	0.144680i	$-0.0462152\pi$
$762$			6.44966e9i			0.528073i
$763$	−2.99950e9	−	1.77796e9i	−0.244463	−	0.144906i
$764$	2.47246e10	−	4.28242e10i	2.00587	−	3.47426i
$765$	−1.28284e10	+	7.40649e9i	−1.03600	+	0.598132i
$766$	−4.17136e9	−	7.22500e9i	−0.335333	−	0.580814i
$767$	6.67266e9	−	1.49557e10i	0.533968	−	1.19680i
$768$	1.00020e10	−	1.73240e10i	0.796753	−	1.38002i
$769$	9.07669e9	+	5.24043e9i	0.719756	+	0.415551i	0.814663	−	0.579935i	$-0.196922\pi$
$769$	9.07669e9	+	5.24043e9i	0.719756	+	0.415551i	−0.0949069	+	0.995486i	$0.530255\pi$
$770$	3.78897e10	−	2.12997e10i	2.99091	−	1.68134i
$771$	1.99331e9	+	3.45252e9i	0.156634	+	0.271297i
$772$	2.40463e9	+	1.38831e9i	0.188100	+	0.108599i
$773$	−1.05852e10	−	6.11134e9i	−0.824269	−	0.475892i	0.0276171	−	0.999619i	$-0.491208\pi$
$773$	−1.05852e10	−	6.11134e9i	−0.824269	−	0.475892i	−0.851887	+	0.523726i	$0.824541\pi$
$774$	−1.96455e10	−	1.13424e10i	−1.52290	−	0.879245i
$775$	−3.84043e8	−	2.21727e8i	−0.0296363	−	0.0171105i
$776$	3.83318e10	+	6.63926e10i	2.94471	+	5.10040i
$777$	7.32314e8	+	4.34082e8i	0.0560046	+	0.0331970i
$778$	−1.42705e10	−	8.23906e9i	−1.08645	−	0.627262i
$779$	−2.07273e9	+	3.59008e9i	−0.157095	+	0.272097i
$780$	5.35343e9	+	7.38043e9i	0.403925	+	0.556866i
$781$	−6.04720e9	−	1.04741e10i	−0.454230	−	0.786750i
$782$	−1.26685e10	+	7.31419e9i	−0.947334	+	0.546943i
$783$	−9.39617e8	+	1.62746e9i	−0.0699495	+	0.121156i
$784$	6.41614e10	+	1.47288e9i	4.75519	+	0.109159i
$785$			2.07092e10i			1.52798i
$786$		−	1.09720e10i		−	0.805951i
$787$	1.55925e9	+	9.00234e8i	0.114026	+	0.0658331i	0.555928	−	0.831230i	$-0.312363\pi$
$787$	1.55925e9	+	9.00234e8i	0.114026	+	0.0658331i	−0.441902	+	0.897063i	$0.645696\pi$
$788$	2.83876e10	−	1.63896e10i	2.06675	−	1.19324i
$789$	1.62968e9			0.118122
$790$	−9.91496e9	+	1.71732e10i	−0.715478	+	1.23924i
$791$	−3.84033e9	+	6.47879e9i	−0.275900	+	0.465454i
$792$	8.05740e10			5.76311
$793$	−2.15756e9	−	2.06827e10i	−0.153641	−	1.47282i
$794$	−5.17852e9	−	8.96946e9i	−0.367142	−	0.635909i
$795$		−	6.87831e8i		−	0.0485509i
$796$	9.67602e9	+	1.67594e10i	0.679987	+	1.17777i
$797$	−7.80317e9	−	1.35155e10i	−0.545968	−	0.945644i	−0.998545	−	0.0539190i	$-0.982829\pi$
$797$	−7.80317e9	−	1.35155e10i	−0.545968	−	0.945644i	0.452577	−	0.891725i	$-0.350505\pi$
$798$	2.03268e9	−	3.42921e9i	0.141599	−	0.238882i
$799$	6.17740e8	−	3.56652e8i	0.0428442	−	0.0247361i
$800$			1.87813e10i			1.29691i
$801$	1.80273e10	−	1.04080e10i	1.23941	−	0.715576i
$802$	8.58060e9	−	1.48620e10i	0.587364	−	1.01734i
$803$	7.27839e9	+	1.26065e10i	0.496056	+	0.859195i
$804$	−3.18749e9	−	1.84030e9i	−0.216298	−	0.124880i
$805$	6.99327e9	−	3.93126e9i	0.472492	−	0.265611i
$806$	3.97056e9	+	1.77151e9i	0.267104	+	0.119171i
$807$	−9.69259e8	+	1.67881e9i	−0.0649206	+	0.112446i
$808$			3.06054e10i			2.04107i
$809$	−2.43795e10			−1.61884			−0.809422	−	0.587228i	$-0.800219\pi$
$809$	−2.43795e10			−1.61884			−0.809422	+	0.587228i	$0.800219\pi$
$810$	2.90263e10			1.91908
$811$			2.37511e10i			1.56355i	0.623562	+	0.781774i	$0.285685\pi$
$811$			2.37511e10i			1.56355i	−0.623562	+	0.781774i	$0.714315\pi$
$812$	7.81880e9	−	1.31906e10i	0.512500	−	0.864608i
$813$	−4.48685e9	+	2.59048e9i	−0.292836	+	0.169069i
$814$	−1.27688e10	−	7.37209e9i	−0.829785	−	0.479077i
$815$	−2.76062e9	+	4.78154e9i	−0.178630	+	0.309397i
$816$	−1.74747e10			−1.12589
$817$	8.31217e9	−	4.79903e9i	0.533258	−	0.307877i
$818$	2.73074e10			1.74439
$819$	−1.22654e10	+	8.68372e9i	−0.780169	+	0.552347i
$820$	−2.44265e10			−1.54708
$821$	−2.38520e10	+	1.37709e10i	−1.50426	+	0.868486i	−0.504273	+	0.863544i	$0.668240\pi$
$821$	−2.38520e10	+	1.37709e10i	−1.50426	+	0.868486i	−0.999988	+	0.00494156i	$0.998427\pi$
$822$	9.06942e9			0.569545
$823$	4.09050e9	−	7.08495e9i	0.255786	−	0.443034i	−0.709323	−	0.704884i	$-0.750999\pi$
$823$	4.09050e9	−	7.08495e9i	0.255786	−	0.443034i	0.965109	+	0.261850i	$0.0843325\pi$
$824$	3.35998e10	+	1.93989e10i	2.09215	+	1.20790i
$825$	1.06059e9	−	6.12329e8i	0.0657592	−	0.0379661i
$826$	−2.06747e10	−	3.67779e10i	−1.27646	−	2.27068i
$827$			1.30887e10i			0.804685i	0.915489	+	0.402343i	$0.131804\pi$
$827$			1.30887e10i			0.804685i	−0.915489	+	0.402343i	$0.868196\pi$
$828$	2.24947e10			1.37713
$829$	−7.05184e9			−0.429894			−0.214947	−	0.976626i	$-0.568958\pi$
$829$	−7.05184e9			−0.429894			−0.214947	+	0.976626i	$0.568958\pi$
$830$		−	4.10408e10i		−	2.49139i
$831$	−2.32086e9	+	4.01985e9i	−0.140296	+	0.243000i
$832$	−1.09071e10	−	1.04557e11i	−0.656566	−	6.29393i
$833$	−9.02613e9	−	1.64968e10i	−0.541058	−	0.988880i
$834$	8.40687e8	+	4.85371e8i	0.0501826	+	0.0289730i
$835$	−2.42425e9	−	4.19892e9i	−0.144103	−	0.249594i
$836$	−2.57835e10	+	4.46584e10i	−1.52623	+	2.64351i
$837$	−8.87928e8	+	5.12645e8i	−0.0523406	+	0.0302189i
$838$			4.35378e10i			2.55571i
$839$	−3.99013e8	+	2.30370e8i	−0.0233249	+	0.0134667i	−0.511617	−	0.859214i	$-0.670953\pi$
$839$	−3.99013e8	+	2.30370e8i	−0.0233249	+	0.0134667i	0.488292	+	0.872680i	$0.337620\pi$
$840$	1.55279e10	+	1.78205e8i	0.903931	+	0.0103739i
$841$	7.62428e9	+	1.32056e10i	0.441991	+	0.765550i
$842$	−1.16808e10	−	2.02317e10i	−0.674340	−	1.16799i
$843$			7.38514e8i			0.0424583i
$844$	−7.43137e8	−	1.28715e9i	−0.0425471	−	0.0736938i
$845$	1.85092e10	+	6.04589e9i	1.05533	+	0.344716i
$846$	−1.46861e9			−0.0833890
$847$	1.22842e10	+	2.18523e10i	0.694635	+	1.23568i
$848$	−8.79482e9	+	1.52331e10i	−0.495269	+	0.857832i
$849$	−3.49781e9			−0.196164
$850$	8.07951e9	−	4.66471e9i	0.451252	−	0.260530i
$851$	−2.35673e9	−	1.36066e9i	−0.131086	−	0.0756826i
$852$		−	6.53584e9i		−	0.362045i
$853$		−	1.05872e10i		−	0.584061i	−0.956409	−	0.292031i	$-0.905669\pi$
$853$		−	1.05872e10i		−	0.584061i	0.956409	−	0.292031i	$-0.0943309\pi$
$854$	−4.60851e10	−	2.73172e10i	−2.53197	−	1.50084i
$855$	−6.45198e9	+	1.11752e10i	−0.353030	+	0.611466i
$856$	1.11129e10	−	6.41602e9i	0.605576	−	0.349629i
$857$	8.12907e9	+	1.40800e10i	0.441172	+	0.764133i	0.997777	−	0.0666450i	$-0.0212295\pi$
$857$	8.12907e9	+	1.40800e10i	0.441172	+	0.764133i	−0.556605	+	0.830778i	$0.687896\pi$
$858$	−9.71944e9	+	7.05004e9i	−0.525334	+	0.381053i
$859$	1.66302e9	−	2.88044e9i	0.0895205	−	0.155054i	−0.817788	−	0.575520i	$-0.804800\pi$
$859$	1.66302e9	−	2.88044e9i	0.0895205	−	0.155054i	0.907309	+	0.420465i	$0.138133\pi$
$860$	4.89782e10	+	2.82776e10i	2.62578	+	1.51599i
$861$	−2.13138e7	+	1.85718e9i	−0.00113802	+	0.0991616i
$862$	−1.75584e10	−	3.04120e10i	−0.933703	−	1.61722i
$863$	6.03631e9	+	3.48507e9i	0.319694	+	0.184575i	0.651256	−	0.758858i	$-0.274242\pi$
$863$	6.03631e9	+	3.48507e9i	0.319694	+	0.184575i	−0.331562	+	0.943433i	$0.607576\pi$
$864$	3.76057e10	+	2.17117e10i	1.98361	+	1.14524i
$865$	−6.45334e8	−	3.72584e8i	−0.0339022	−	0.0195735i
$866$	−1.80129e10	−	1.03998e10i	−0.942477	−	0.544140i
$867$	5.45270e8	+	9.44435e8i	0.0284148	+	0.0492159i
$868$	7.29268e9	−	4.09957e9i	0.378502	−	0.212774i
$869$	−1.68914e10	−	9.75226e9i	−0.873166	−	0.504122i
$870$	1.53286e9	−	2.65499e9i	0.0789195	−	0.136693i
$871$	−7.81792e9	+	8.15546e8i	−0.400892	+	0.0418201i
$872$	1.07878e10	+	1.86850e10i	0.550965	+	0.954300i
$873$	−2.47179e10	+	1.42709e10i	−1.25737	+	0.725940i
$874$	−6.37157e9	+	1.10359e10i	−0.322817	+	0.559136i
$875$	1.47179e10	−	8.27367e9i	0.742708	−	0.417513i
$876$			7.86651e9i			0.395383i
$877$			3.40737e10i			1.70577i	0.522097	+	0.852886i	$0.325150\pi$
$877$			3.40737e10i			1.70577i	−0.522097	+	0.852886i	$0.674850\pi$
$878$	−3.62075e10	−	2.09044e10i	−1.80537	−	1.04233i
$879$	1.63415e9	−	9.43475e8i	0.0811577	−	0.0468564i
$880$	−1.65982e11			−8.21056
$881$	9.55853e9	−	1.65559e10i	0.470951	−	0.815711i	−0.528497	−	0.848935i	$-0.677244\pi$
$881$	9.55853e9	−	1.65559e10i	0.470951	−	0.815711i	0.999448	+	0.0332245i	$0.0105776\pi$
$882$	−8.88538e8	+	3.87064e10i	−0.0436050	+	1.89951i
$883$	−1.76909e10			−0.864742			−0.432371	−	0.901696i	$-0.642323\pi$
$883$	−1.76909e10			−0.864742			−0.432371	+	0.901696i	$0.642323\pi$
$884$	−5.53013e10	+	4.01130e10i	−2.69248	+	1.95300i
$885$	−3.15009e9	−	5.45611e9i	−0.152764	−	0.264595i
$886$		−	2.90221e10i		−	1.40188i
$887$	−1.29794e10	−	2.24811e10i	−0.624487	−	1.08164i	−0.988640	−	0.150304i	$-0.951975\pi$
$887$	−1.29794e10	−	2.24811e10i	−0.624487	−	1.08164i	0.364153	−	0.931339i	$-0.381359\pi$
$888$	−2.63379e9	−	4.56185e9i	−0.126222	−	0.218623i
$889$	2.65018e10	+	3.04146e8i	1.26508	+	0.0145187i
$890$	−6.01747e10	+	3.47419e10i	−2.86121	+	1.65192i
$891$			2.85499e10i			1.35218i
$892$	−4.59449e10	+	2.65263e10i	−2.16750	+	1.25141i
$893$	3.10689e8	−	5.38129e8i	0.0145998	−	0.0252875i
$894$	3.27649e9	+	5.67505e9i	0.153365	+	0.265637i
$895$	3.39610e10	+	1.96074e10i	1.58343	+	0.914195i
$896$	−1.29682e11	−	7.68695e10i	−6.02284	−	3.57007i
$897$	−1.79391e9	+	1.30122e9i	−0.0829902	+	0.0601973i
$898$	2.63111e10	−	4.55722e10i	1.21247	−	2.10006i
$899$		−	1.09189e9i		−	0.0501212i
$900$	−1.43463e10			−0.655980
$901$	5.15389e9			0.234746
$902$		−	3.21678e10i		−	1.45948i
$903$	2.19272e9	−	3.69921e9i	0.0991005	−	0.167187i
$904$	4.03588e10	−	2.33011e10i	1.81697	−	1.04903i
$905$	−3.43171e9	−	1.98130e9i	−0.153900	−	0.0888545i
$906$	3.20014e9	−	5.54281e9i	0.142962	−	0.247617i
$907$	7.83245e9			0.348556			0.174278	−	0.984697i	$-0.444241\pi$
$907$	7.83245e9			0.348556			0.174278	+	0.984697i	$0.444241\pi$
$908$	5.24890e10	−	3.03045e10i	2.32684	−	1.34340i
$909$	−1.13944e10			−0.503172
$910$	4.09418e10	−	2.89861e10i	1.80103	−	1.27510i
$911$	−1.19394e10			−0.523201			−0.261601	−	0.965176i	$-0.584250\pi$
$911$	−1.19394e10			−0.523201			−0.261601	+	0.965176i	$0.584250\pi$
$912$	−1.31832e10	+	7.61133e9i	−0.575492	+	0.332260i
$913$	4.03673e10			1.75542
$914$	−2.29133e10	+	3.96870e10i	−0.992605	+	1.71924i
$915$	−6.92808e9	−	3.99993e9i	−0.298978	−	0.172615i
$916$	1.02892e11	−	5.94048e10i	4.42331	−	2.55380i
$917$	−4.50844e10	−	5.17408e8i	−1.93079	−	0.0221585i
$918$		−	2.15701e10i		−	0.920243i
$919$	2.24180e10			0.952782			0.476391	−	0.879234i	$-0.341945\pi$
$919$	2.24180e10			0.952782			0.476391	+	0.879234i	$0.341945\pi$
$920$	−4.96408e10			−2.10175
$921$			5.95478e9i			0.251164i
$922$	1.58229e10	−	2.74060e10i	0.664855	−	1.15156i
$923$	−8.19555e9	−	1.12987e10i	−0.343062	−	0.472958i
$924$	−2.65131e8	+	2.31022e10i	−0.0110563	+	0.963389i
$925$	1.50303e9	+	8.67777e8i	0.0624414	+	0.0360505i
$926$	−3.16475e10	−	5.48151e10i	−1.30979	−	2.26862i
$927$	−7.22217e9	+	1.25092e10i	−0.297775	+	0.515762i
$928$	−4.00486e10	+	2.31220e10i	−1.64501	+	0.949748i
$929$			2.32166e10i			0.950044i	0.879974	+	0.475022i	$0.157560\pi$
$929$			2.32166e10i			0.950044i	−0.879974	+	0.475022i	$0.842440\pi$
$930$	1.44853e9	−	8.36311e8i	0.0590525	−	0.0340940i
$931$	−1.39949e10	−	8.51405e9i	−0.568388	−	0.345790i
$932$	−1.31624e10	−	2.27979e10i	−0.532573	−	0.922443i
$933$	−4.18470e9	−	7.24812e9i	−0.168686	−	0.292173i
$934$			2.84992e10i			1.14451i
$935$	2.43170e10	+	4.21183e10i	0.972904	+	1.68512i
$936$	9.24880e10	−	9.64812e9i	3.68655	−	0.384571i
$937$	−2.96630e10			−1.17795			−0.588975	−	0.808151i	$-0.700468\pi$
$937$	−2.96630e10			−1.17795			−0.588975	+	0.808151i	$0.700468\pi$
$938$	−1.03257e10	+	1.74199e10i	−0.408517	+	0.689185i
$939$	2.16994e9	−	3.75845e9i	0.0855300	−	0.148142i
$940$	3.66137e9			0.143779
$941$	3.82009e10	−	2.20553e10i	1.49455	−	0.862878i	0.494568	−	0.869139i	$-0.335326\pi$
$941$	3.82009e10	−	2.20553e10i	1.49455	−	0.862878i	0.999980	+	0.00626148i	$0.00199310\pi$
$942$	−1.27635e10	−	7.36901e9i	−0.497498	−	0.287231i
$943$		−	5.93718e9i		−	0.230563i
$944$			1.61112e11i			6.23341i
$945$	−1.35751e8	+	1.18287e10i	−0.00523278	+	0.455959i
$946$	−3.72393e10	+	6.45004e10i	−1.43015	+	2.47710i
$947$	6.53148e9	−	3.77095e9i	0.249912	−	0.144287i	−0.369812	−	0.929107i	$-0.620578\pi$
$947$	6.53148e9	−	3.77095e9i	0.249912	−	0.144287i	0.619724	+	0.784820i	$0.287245\pi$
$948$	−5.27014e9	−	9.12815e9i	−0.200906	−	0.347979i
$949$	9.86414e9	+	1.35991e10i	0.374651	+	0.516508i
$950$	4.06354e9	−	7.03826e9i	0.153770	−	0.266338i
$951$	9.34565e9	+	5.39571e9i	0.352353	+	0.203431i
$952$	−1.33528e9	+	1.16350e11i	−0.0501584	+	4.37056i
$953$	−1.83337e10	−	3.17550e10i	−0.686161	−	1.18846i	−0.973071	−	0.230507i	$-0.925961\pi$
$953$	−1.83337e10	−	3.17550e10i	−0.686161	−	1.18846i	0.286910	−	0.957958i	$-0.407372\pi$
$954$	−9.18959e9	−	5.30561e9i	−0.342671	−	0.197841i
$955$	−3.51834e10	−	2.03132e10i	−1.30715	−	0.754685i
$956$	1.16882e11	+	6.74818e10i	4.32658	+	2.49795i
$957$	2.61142e9	+	1.50770e9i	0.0963130	+	0.0556063i
$958$	3.53785e10	+	6.12774e10i	1.30005	+	2.25176i
$959$	4.27686e8	−	3.72665e10i	0.0156589	−	1.36444i
$960$	−3.50235e10	−	2.02208e10i	−1.27764	−	0.737648i
$961$	−1.34584e10	+	2.33107e10i	−0.489174	+	0.847274i
$962$	−1.55396e10	−	6.93318e9i	−0.562766	−	0.251085i
$963$	2.38868e9	+	4.13731e9i	0.0861917	+	0.149288i
$964$	−1.59562e10	+	9.21233e9i	−0.573668	+	0.331207i
$965$	1.14061e9	−	1.97559e9i	0.0408593	−	0.0707704i
$966$	−6.55186e7	+	5.70897e9i	−0.00233854	+	0.203769i
$967$			4.98815e10i			1.77397i	0.461795	+	0.886987i	$0.347206\pi$
$967$			4.98815e10i			1.77397i	−0.461795	+	0.886987i	$0.652794\pi$
$968$		−	1.55115e11i		−	5.49656i
$969$	3.86278e9	+	2.23017e9i	0.136385	+	0.0787419i
$970$	8.25079e10	−	4.76360e10i	2.90265	−	1.67584i
$971$	3.47524e10			1.21820			0.609098	−	0.793095i	$-0.291532\pi$
$971$	3.47524e10			1.21820			0.609098	+	0.793095i	$0.291532\pi$
$972$	−2.50640e10	+	4.34121e10i	−0.875423	+	1.51628i
$973$	2.03405e9	−	3.43152e9i	0.0707891	−	0.119424i
$974$	1.02692e11			3.56108
$975$	1.14409e9	−	8.29867e8i	0.0395314	−	0.0286743i
$976$	1.02289e11	+	1.77169e11i	3.52170	+	6.09977i
$977$			2.86048e10i			0.981313i	0.871353	+	0.490656i	$0.163243\pi$
$977$			2.86048e10i			0.981313i	−0.871353	+	0.490656i	$0.836757\pi$
$978$	−1.96464e9	−	3.40286e9i	−0.0671579	−	0.116321i
$979$	−3.41718e10	−	5.91873e10i	−1.16393	−	2.01599i
$980$	2.21521e9	−	9.64987e10i	0.0751837	−	3.27514i
$981$	−6.95639e9	+	4.01627e9i	−0.235257	+	0.135826i
$982$		−	5.10726e10i		−	1.72107i
$983$	1.63291e9	−	9.42761e8i	0.0548308	−	0.0316566i	−0.472334	−	0.881420i	$-0.656588\pi$
$983$	1.63291e9	−	9.42761e8i	0.0548308	−	0.0316566i	0.527165	+	0.849763i	$0.323255\pi$
$984$	5.74621e9	−	9.95273e9i	0.192264	−	0.333012i
$985$	−1.34653e10	−	2.33227e10i	−0.448942	−	0.777591i
$986$	1.98937e10	+	1.14856e10i	0.660917	+	0.381580i
$987$	3.19480e6	−	2.78379e8i	0.000105763	−	0.00921567i
$988$	−2.42485e10	+	5.43491e10i	−0.799899	+	1.79285i
$989$	−6.87323e9	+	1.19048e10i	−0.225930	+	0.391322i
$990$		−	1.00132e11i		−	3.27980i
$991$	−7.95253e9			−0.259566			−0.129783	−	0.991542i	$-0.541428\pi$
$991$	−7.95253e9			−0.259566			−0.129783	+	0.991542i	$0.541428\pi$
$992$	−2.52303e10			−0.820600
$993$			8.81980e8i			0.0285849i
$994$	−3.59572e10	−	4.12660e8i	−1.16127	−	0.0133272i
$995$	1.37691e10	−	7.94960e9i	0.443124	−	0.255838i
$996$	1.88920e10	+	1.09073e10i	0.605856	+	0.349791i
$997$	1.11746e10	−	1.93549e10i	0.357106	−	0.618526i	−0.630370	−	0.776295i	$-0.717097\pi$
$997$	1.11746e10	−	1.93549e10i	0.357106	−	0.618526i	0.987476	+	0.157769i	$0.0504302\pi$
$998$	5.77236e10			1.83822
$999$	3.47509e9	−	2.00634e9i	0.110277	−	0.0636687i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.u.a.30.1	yes	126
7.4	even	3		91.8.k.a.4.1	✓	126
13.10	even	6		91.8.k.a.23.63	yes	126
91.88	even	6	inner	91.8.u.a.88.1	yes	126

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.k.a.4.1	✓	126	7.4	even	3
91.8.k.a.23.63	yes	126	13.10	even	6
91.8.u.a.30.1	yes	126	1.1	even	1	trivial
91.8.u.a.88.1	yes	126	91.88	even	6	inner

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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	91.u (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-19.4750 + 11.2439i) q^{2} -9.82037 q^{3} +(188.851 - 327.100i) q^{4} +(-268.738 - 155.156i) q^{5} +(191.252 - 110.419i) q^{6} +(-444.698 - 791.067i) q^{7} +5615.28i q^{8} -2090.56 q^{9} +O(q^{10})\)	\(q+(-19.4750 + 11.2439i) q^{2} -9.82037 q^{3} +(188.851 - 327.100i) q^{4} +(-268.738 - 155.156i) q^{5} +(191.252 - 110.419i) q^{6} +(-444.698 - 791.067i) q^{7} +5615.28i q^{8} -2090.56 q^{9} +6978.26 q^{10} +6863.74i q^{11} +(-1854.59 + 3212.24i) q^{12} +(821.880 + 7878.64i) q^{13} +(17555.2 + 10405.9i) q^{14} +(2639.11 + 1523.69i) q^{15} +(-38964.8 - 67488.9i) q^{16} +(-11417.0 + 19774.7i) q^{17} +(40713.7 - 23506.1i) q^{18} +19891.2i q^{19} +(-101503. + 58603.0i) q^{20} +(4367.09 + 7768.57i) q^{21} +(-77175.4 - 133672. i) q^{22} +(-14244.2 - 24671.7i) q^{23} -55144.1i q^{24} +(9084.40 + 15734.6i) q^{25} +(-104593. - 144196. i) q^{26} +42007.2 q^{27} +(-342740. - 3933.43i) q^{28} +(-22368.0 + 38742.5i) q^{29} -68529.0 q^{30} +(-21137.5 + 12203.7i) q^{31} +(895220. + 516855. i) q^{32} -67404.5i q^{33} -513485. i q^{34} +(-3231.62 + 281588. i) q^{35} +(-394805. + 683823. i) q^{36} +(82726.0 - 47761.9i) q^{37} +(-223655. - 387382. i) q^{38} +(-8071.16 - 77371.2i) q^{39} +(871245. - 1.50904e6i) q^{40} +(180486. + 104204. i) q^{41} +(-172398. - 102190. i) q^{42} +(-241264. - 417882. i) q^{43} +(2.24513e6 + 1.29623e6i) q^{44} +(561814. + 324363. i) q^{45} +(554813. + 320321. i) q^{46} +(-27053.6 - 15619.4i) q^{47} +(382648. + 662766. i) q^{48} +(-428031. + 703571. i) q^{49} +(-353838. - 204289. i) q^{50} +(112119. - 194195. i) q^{51} +(2.73232e6 + 1.21906e6i) q^{52} +(-112856. - 195473. i) q^{53} +(-818092. + 472326. i) q^{54} +(1.06495e6 - 1.84455e6i) q^{55} +(4.44206e6 - 2.49710e6i) q^{56} -195339. i q^{57} -1.00602e6i q^{58} +(-1.79043e6 - 1.03370e6i) q^{59} +(996799. - 575502. i) q^{60} -2.62516e6 q^{61} +(274436. - 475337. i) q^{62} +(929667. + 1.65377e6i) q^{63} -1.32709e7 q^{64} +(1.00155e6 - 2.24481e6i) q^{65} +(757891. + 1.31270e6i) q^{66} +992293. i q^{67} +(4.31222e6 + 7.46898e6i) q^{68} +(139883. + 242285. i) q^{69} +(-3.10321e6 - 5.52027e6i) q^{70} +(-1.52600e6 + 881035. i) q^{71} -1.17391e7i q^{72} +(1.83669e6 - 1.06041e6i) q^{73} +(-1.07406e6 + 1.86033e6i) q^{74} +(-89212.1 - 154520. i) q^{75} +(6.50642e6 + 3.75648e6i) q^{76} +(5.42968e6 - 3.05229e6i) q^{77} +(1.02714e6 + 1.41606e6i) q^{78} +(-1.42084e6 + 2.46096e6i) q^{79} +2.41825e7i q^{80} +4.15953e6 q^{81} -4.68663e6 q^{82} -5.88124e6i q^{83} +(3.36583e6 + 38627.7i) q^{84} +(6.13635e6 - 3.54282e6i) q^{85} +(9.39726e6 + 5.42551e6i) q^{86} +(219662. - 380466. i) q^{87} -3.85418e7 q^{88} +(-8.62318e6 + 4.97859e6i) q^{89} -1.45885e7 q^{90} +(5.86705e6 - 4.15378e6i) q^{91} -1.07601e7 q^{92} +(207578. - 119845. i) q^{93} +702494. q^{94} +(3.08624e6 - 5.34553e6i) q^{95} +(-8.79139e6 - 5.07571e6i) q^{96} +(1.18236e7 - 6.82634e6i) q^{97} +(425024. - 1.85148e7i) q^{98} -1.43491e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 126 q - 3 q^{2} - 164 q^{3} + 3841 q^{4} - 6 q^{6} + 754 q^{7} + 85710 q^{9}+O(q^{10}) \) 126 * q - 3 * q^2 - 164 * q^3 + 3841 * q^4 - 6 * q^6 + 754 * q^7 + 85710 * q^9	\( 126 q - 3 q^{2} - 164 q^{3} + 3841 q^{4} - 6 q^{6} + 754 q^{7} + 85710 q^{9} + 7486 q^{10} - 18328 q^{12} + 1816 q^{13} - 6668 q^{14} - 11817 q^{15} - 237219 q^{16} - 28969 q^{17} + 75423 q^{18} + 12342 q^{20} - 54000 q^{21} + 51388 q^{22} + 17067 q^{23} + 810665 q^{25} + 144300 q^{26} - 528170 q^{27} + 18464 q^{28} + 191096 q^{29} - 432160 q^{30} - 259995 q^{31} + 49149 q^{32} + 87303 q^{35} + 1965131 q^{36} - 571857 q^{37} - 1061954 q^{38} - 1352875 q^{39} + 345362 q^{40} - 636567 q^{41} - 3473694 q^{42} - 659976 q^{43} + 2519268 q^{44} + 1980717 q^{45} - 4068600 q^{46} - 294840 q^{47} + 4726652 q^{48} + 541120 q^{49} - 2908992 q^{50} - 502094 q^{51} + 7809224 q^{52} - 434723 q^{53} + 2119563 q^{54} + 2152196 q^{55} - 858015 q^{56} + 1376949 q^{59} - 3768141 q^{60} - 4854916 q^{61} - 1713436 q^{62} + 10091940 q^{63} - 40270472 q^{64} - 4876182 q^{65} + 8270835 q^{66} + 531379 q^{68} - 311689 q^{69} + 5298534 q^{70} + 1505877 q^{71} - 13207461 q^{73} + 3730527 q^{74} + 5624951 q^{75} + 25297146 q^{76} + 11107478 q^{77} - 9362803 q^{78} + 5012226 q^{79} + 45989766 q^{81} - 34046788 q^{82} - 35428032 q^{84} + 19854117 q^{85} + 5226210 q^{86} + 17331733 q^{87} + 24348310 q^{88} - 43738596 q^{89} + 90517324 q^{90} + 9582031 q^{91} - 8502078 q^{92} - 30517344 q^{93} - 7710416 q^{94} + 14810909 q^{95} + 41499936 q^{96} - 60232128 q^{97} - 65830509 q^{98}+O(q^{100}) \) 126 * q - 3 * q^2 - 164 * q^3 + 3841 * q^4 - 6 * q^6 + 754 * q^7 + 85710 * q^9 + 7486 * q^10 - 18328 * q^12 + 1816 * q^13 - 6668 * q^14 - 11817 * q^15 - 237219 * q^16 - 28969 * q^17 + 75423 * q^18 + 12342 * q^20 - 54000 * q^21 + 51388 * q^22 + 17067 * q^23 + 810665 * q^25 + 144300 * q^26 - 528170 * q^27 + 18464 * q^28 + 191096 * q^29 - 432160 * q^30 - 259995 * q^31 + 49149 * q^32 + 87303 * q^35 + 1965131 * q^36 - 571857 * q^37 - 1061954 * q^38 - 1352875 * q^39 + 345362 * q^40 - 636567 * q^41 - 3473694 * q^42 - 659976 * q^43 + 2519268 * q^44 + 1980717 * q^45 - 4068600 * q^46 - 294840 * q^47 + 4726652 * q^48 + 541120 * q^49 - 2908992 * q^50 - 502094 * q^51 + 7809224 * q^52 - 434723 * q^53 + 2119563 * q^54 + 2152196 * q^55 - 858015 * q^56 + 1376949 * q^59 - 3768141 * q^60 - 4854916 * q^61 - 1713436 * q^62 + 10091940 * q^63 - 40270472 * q^64 - 4876182 * q^65 + 8270835 * q^66 + 531379 * q^68 - 311689 * q^69 + 5298534 * q^70 + 1505877 * q^71 - 13207461 * q^73 + 3730527 * q^74 + 5624951 * q^75 + 25297146 * q^76 + 11107478 * q^77 - 9362803 * q^78 + 5012226 * q^79 + 45989766 * q^81 - 34046788 * q^82 - 35428032 * q^84 + 19854117 * q^85 + 5226210 * q^86 + 17331733 * q^87 + 24348310 * q^88 - 43738596 * q^89 + 90517324 * q^90 + 9582031 * q^91 - 8502078 * q^92 - 30517344 * q^93 - 7710416 * q^94 + 14810909 * q^95 + 41499936 * q^96 - 60232128 * q^97 - 65830509 * q^98

Introduction

L-functions

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