LMFDB - Embedded newform 91.8.q.a.36.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,8,Mod(36,91)]

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([0, 5]))

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

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

chi := DirichletCharacter("91.36");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	91.q (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:	$100$
Relative dimension:	$50$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			36.15
Character	$\chi$	$=$	91.36
Dual form			91.8.q.a.43.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-10.2159 + 5.89817i) q^{2} +(-41.7035 - 72.2326i) q^{3} +(5.57692 - 9.65951i) q^{4} -264.816i q^{5} +(852.081 + 491.949i) q^{6} +(297.047 + 171.500i) q^{7} -1378.36i q^{8} +(-2384.87 + 4130.71i) q^{9} +O(q^{10})$	\(q+(-10.2159 + 5.89817i) q^{2} +(-41.7035 - 72.2326i) q^{3} +(5.57692 - 9.65951i) q^{4} -264.816i q^{5} +(852.081 + 491.949i) q^{6} +(297.047 + 171.500i) q^{7} -1378.36i q^{8} +(-2384.87 + 4130.71i) q^{9} +(1561.93 + 2705.35i) q^{10} +(1675.66 - 967.442i) q^{11} -930.309 q^{12} +(-7878.51 + 823.193i) q^{13} -4046.15 q^{14} +(-19128.4 + 11043.8i) q^{15} +(8843.64 + 15317.6i) q^{16} +(-18466.2 + 31984.3i) q^{17} -56265.4i q^{18} +(-23318.3 - 13462.8i) q^{19} +(-2558.00 - 1476.86i) q^{20} -28608.6i q^{21} +(-11412.3 + 19766.6i) q^{22} +(-15805.8 - 27376.4i) q^{23} +(-99562.4 + 57482.4i) q^{24} +7997.36 q^{25} +(75631.0 - 54878.5i) q^{26} +215418. q^{27} +(3313.21 - 1912.88i) q^{28} +(110292. + 191032. i) q^{29} +(130276. - 225645. i) q^{30} -113983. i q^{31} +(-27899.5 - 16107.8i) q^{32} +(-139762. - 80691.4i) q^{33} -435666. i q^{34} +(45416.0 - 78662.8i) q^{35} +(26600.4 + 46073.3i) q^{36} +(36267.8 - 20939.2i) q^{37} +317624. q^{38} +(388023. + 534755. i) q^{39} -365012. q^{40} +(-360961. + 208401. i) q^{41} +(168739. + 292264. i) q^{42} +(-143933. + 249300. i) q^{43} -21581.4i q^{44} +(1.09388e6 + 631551. i) q^{45} +(322941. + 186450. i) q^{46} -140685. i q^{47} +(737622. - 1.27760e6i) q^{48} +(58824.5 + 101887. i) q^{49} +(-81700.5 + 47169.8i) q^{50} +3.08041e6 q^{51} +(-35986.2 + 80693.4i) q^{52} +1.29787e6 q^{53} +(-2.20070e6 + 1.27057e6i) q^{54} +(-256194. - 443741. i) q^{55} +(236388. - 409437. i) q^{56} +2.24579e6i q^{57} +(-2.25348e6 - 1.30104e6i) q^{58} +(1.66323e6 + 960264. i) q^{59} +246361. i q^{60} +(729740. - 1.26395e6i) q^{61} +(672293. + 1.16445e6i) q^{62} +(-1.41683e6 + 818009. i) q^{63} -1.88395e6 q^{64} +(217995. + 2.08636e6i) q^{65} +1.90373e6 q^{66} +(1.47849e6 - 853605. i) q^{67} +(205969. + 356748. i) q^{68} +(-1.31831e6 + 2.28338e6i) q^{69} +1.07149e6i q^{70} +(-4.41113e6 - 2.54677e6i) q^{71} +(5.69359e6 + 3.28720e6i) q^{72} -4.81561e6i q^{73} +(-247006. + 427828. i) q^{74} +(-333518. - 577670. i) q^{75} +(-260089. + 150162. i) q^{76} +663665. q^{77} +(-7.11809e6 - 3.17440e6i) q^{78} -1.42550e6 q^{79} +(4.05636e6 - 2.34194e6i) q^{80} +(-3.76798e6 - 6.52633e6i) q^{81} +(2.45837e6 - 4.25802e6i) q^{82} -7.27134e6i q^{83} +(-276345. - 159548. i) q^{84} +(8.46997e6 + 4.89014e6i) q^{85} -3.39578e6i q^{86} +(9.19914e6 - 1.59334e7i) q^{87} +(-1.33348e6 - 2.30966e6i) q^{88} +(-8.38564e6 + 4.84145e6i) q^{89} -1.49000e7 q^{90} +(-2.48146e6 - 1.10664e6i) q^{91} -352590. q^{92} +(-8.23330e6 + 4.75350e6i) q^{93} +(829783. + 1.43723e6i) q^{94} +(-3.56518e6 + 6.17507e6i) q^{95} +2.68700e6i q^{96} +(6.77837e6 + 3.91349e6i) q^{97} +(-1.20189e6 - 693914. i) q^{98} +9.22887e6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q + 3328 q^{4} + 522 q^{6} - 38792 q^{9}+O(q^{10}) $ 100 * q + 3328 * q^4 + 522 * q^6 - 38792 * q^9	\( 100 q + 3328 q^{4} + 522 q^{6} - 38792 q^{9} - 2728 q^{10} - 3954 q^{11} - 54708 q^{12} - 32008 q^{13} + 21952 q^{14} + 46398 q^{15} - 228808 q^{16} + 16832 q^{17} - 203520 q^{20} + 148982 q^{22} + 154164 q^{23} - 436560 q^{24} - 1918852 q^{25} - 624246 q^{26} + 661404 q^{27} - 451396 q^{29} + 313736 q^{30} + 1854432 q^{32} + 315450 q^{33} - 372498 q^{35} + 2704174 q^{36} + 1777146 q^{37} - 338468 q^{38} + 189708 q^{39} - 2875580 q^{40} - 2158998 q^{41} - 296352 q^{42} + 1876346 q^{43} + 7252980 q^{45} + 234336 q^{46} + 1316674 q^{48} + 5882450 q^{49} + 6432894 q^{50} - 3602684 q^{51} - 14093326 q^{52} + 1719628 q^{53} - 14915976 q^{54} - 1225470 q^{55} + 2107392 q^{56} + 18792564 q^{58} + 5131962 q^{59} + 886858 q^{61} + 3663272 q^{62} - 1848084 q^{63} - 38282980 q^{64} - 17072760 q^{65} + 54390948 q^{66} - 15529368 q^{67} + 2633716 q^{68} + 12342620 q^{69} + 20194104 q^{71} + 12742440 q^{72} - 23243862 q^{74} - 12055866 q^{75} - 7828698 q^{76} - 11143384 q^{77} - 32361130 q^{78} + 38408264 q^{79} - 38368944 q^{80} - 55140914 q^{81} + 27439818 q^{82} + 46422306 q^{84} + 16353300 q^{85} - 15866954 q^{87} - 39468942 q^{88} + 11465844 q^{89} - 22072424 q^{90} - 3481450 q^{91} + 67780968 q^{92} - 71319114 q^{93} - 6119236 q^{94} + 60860930 q^{95} + 45060702 q^{97}+O(q^{100}) \) 100 * q + 3328 * q^4 + 522 * q^6 - 38792 * q^9 - 2728 * q^10 - 3954 * q^11 - 54708 * q^12 - 32008 * q^13 + 21952 * q^14 + 46398 * q^15 - 228808 * q^16 + 16832 * q^17 - 203520 * q^20 + 148982 * q^22 + 154164 * q^23 - 436560 * q^24 - 1918852 * q^25 - 624246 * q^26 + 661404 * q^27 - 451396 * q^29 + 313736 * q^30 + 1854432 * q^32 + 315450 * q^33 - 372498 * q^35 + 2704174 * q^36 + 1777146 * q^37 - 338468 * q^38 + 189708 * q^39 - 2875580 * q^40 - 2158998 * q^41 - 296352 * q^42 + 1876346 * q^43 + 7252980 * q^45 + 234336 * q^46 + 1316674 * q^48 + 5882450 * q^49 + 6432894 * q^50 - 3602684 * q^51 - 14093326 * q^52 + 1719628 * q^53 - 14915976 * q^54 - 1225470 * q^55 + 2107392 * q^56 + 18792564 * q^58 + 5131962 * q^59 + 886858 * q^61 + 3663272 * q^62 - 1848084 * q^63 - 38282980 * q^64 - 17072760 * q^65 + 54390948 * q^66 - 15529368 * q^67 + 2633716 * q^68 + 12342620 * q^69 + 20194104 * q^71 + 12742440 * q^72 - 23243862 * q^74 - 12055866 * q^75 - 7828698 * q^76 - 11143384 * q^77 - 32361130 * q^78 + 38408264 * q^79 - 38368944 * q^80 - 55140914 * q^81 + 27439818 * q^82 + 46422306 * q^84 + 16353300 * q^85 - 15866954 * q^87 - 39468942 * q^88 + 11465844 * q^89 - 22072424 * q^90 - 3481450 * q^91 + 67780968 * q^92 - 71319114 * q^93 - 6119236 * q^94 + 60860930 * q^95 + 45060702 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−10.2159	+	5.89817i	−0.902970	+	0.521330i	−0.878163	−	0.478362i	$-0.841231\pi$
$2$	−10.2159	+	5.89817i	−0.902970	+	0.521330i	−0.0248073	+	0.999692i	$0.507897\pi$
$3$	−41.7035	−	72.2326i	−0.891760	−	1.54457i	−0.837763	−	0.546033i	$-0.816137\pi$
$3$	−41.7035	−	72.2326i	−0.891760	−	1.54457i	−0.0539970	−	0.998541i	$-0.517196\pi$
$4$	5.57692	−	9.65951i	0.0435697	−	0.0754649i
$5$		−	264.816i		−	0.947435i	−0.880677	−	0.473718i	$-0.842912\pi$
$5$		−	264.816i		−	0.947435i	0.880677	−	0.473718i	$-0.157088\pi$
$6$	852.081	+	491.949i	1.61047	+	0.929803i
$7$	297.047	+	171.500i	0.327327	+	0.188982i
$7$	297.047	+	171.500i	0.327327	+	0.188982i
$8$		−	1378.36i		−	0.951803i
$9$	−2384.87	+	4130.71i	−1.09047	+	1.88876i
$10$	1561.93	+	2705.35i	0.493926	+	0.855506i
$11$	1675.66	−	967.442i	0.379587	−	0.219155i	−0.298052	−	0.954550i	$-0.596337\pi$
$11$	1675.66	−	967.442i	0.379587	−	0.219155i	0.677638	+	0.735395i	$0.263003\pi$
$12$	−930.309			−0.155415
$13$	−7878.51	+	823.193i	−0.994586	+	0.103920i
$13$	−7878.51	+	823.193i	−0.994586	+	0.103920i
$14$	−4046.15			−0.394088
$15$	−19128.4	+	11043.8i	−1.46338	+	0.844885i
$16$	8843.64	+	15317.6i	0.539773	+	0.934914i
$17$	−18466.2	+	31984.3i	−0.911602	+	1.57894i	−0.0998005	+	0.995007i	$0.531820\pi$
$17$	−18466.2	+	31984.3i	−0.911602	+	1.57894i	−0.811802	+	0.583933i	$0.801513\pi$
$18$		−	56265.4i		−	2.27399i
$19$	−23318.3	−	13462.8i	−0.779937	−	0.450297i	0.0564712	−	0.998404i	$-0.482015\pi$
$19$	−23318.3	−	13462.8i	−0.779937	−	0.450297i	−0.836408	+	0.548108i	$0.815348\pi$
$20$	−2558.00	−	1476.86i	−0.0714981	−	0.0412795i
$21$		−	28608.6i		−	0.674108i
$22$	−11412.3	+	19766.6i	−0.228504	+	0.395780i
$23$	−15805.8	−	27376.4i	−0.270874	−	0.469168i	0.698212	−	0.715891i	$-0.253979\pi$
$23$	−15805.8	−	27376.4i	−0.270874	−	0.469168i	−0.969086	+	0.246723i	$0.920646\pi$
$24$	−99562.4	+	57482.4i	−1.47013	+	0.848780i
$25$	7997.36			0.102366
$26$	75631.0	−	54878.5i	0.843904	−	0.612344i
$27$	215418.			2.10624
$28$	3313.21	−	1912.88i	0.0285231	−	0.0164678i
$29$	110292.	+	191032.i	0.839753	+	1.45449i	0.890101	+	0.455763i	$0.150634\pi$
$29$	110292.	+	191032.i	0.839753	+	1.45449i	−0.0503480	+	0.998732i	$0.516033\pi$
$30$	130276.	−	225645.i	0.880928	−	1.52581i
$31$		−	113983.i		−	0.687187i	−0.939118	−	0.343594i	$-0.888356\pi$
$31$		−	113983.i		−	0.687187i	0.939118	−	0.343594i	$-0.111644\pi$
$32$	−27899.5	−	16107.8i	−0.150512	−	0.0868981i
$33$	−139762.	−	80691.4i	−0.677001	−	0.390867i
$34$		−	435666.i		−	1.90098i
$35$	45416.0	−	78662.8i	0.179048	−	0.310121i
$36$	26600.4	+	46073.3i	0.0950232	+	0.164585i
$37$	36267.8	−	20939.2i	0.117711	−	0.0679602i	−0.439989	−	0.898003i	$-0.645018\pi$
$37$	36267.8	−	20939.2i	0.117711	−	0.0679602i	0.557699	+	0.830043i	$0.311684\pi$
$38$	317624.			0.939012
$39$	388023.	+	534755.i	1.04744	+	1.44354i
$40$	−365012.			−0.901772
$41$	−360961.	+	208401.i	−0.817932	+	0.472233i	−0.849703	−	0.527262i	$-0.823219\pi$
$41$	−360961.	+	208401.i	−0.817932	+	0.472233i	0.0317709	+	0.999495i	$0.489885\pi$
$42$	168739.	+	292264.i	0.351432	+	0.608699i
$43$	−143933.	+	249300.i	−0.276072	+	0.478170i	−0.970405	−	0.241483i	$-0.922366\pi$
$43$	−143933.	+	249300.i	−0.276072	+	0.478170i	0.694333	+	0.719654i	$0.255699\pi$
$44$		−	21581.4i		−	0.0381940i
$45$	1.09388e6	+	631551.i	1.78947	+	1.03315i
$46$	322941.	+	186450.i	0.489183	+	0.282430i
$47$		−	140685.i		−	0.197654i	−0.995105	−	0.0988268i	$-0.968491\pi$
$47$		−	140685.i		−	0.197654i	0.995105	−	0.0988268i	$-0.0315090\pi$
$48$	737622.	−	1.27760e6i	0.962697	−	1.66744i
$49$	58824.5	+	101887.i	0.0714286	+	0.123718i
$50$	−81700.5	+	47169.8i	−0.0924336	+	0.0533665i
$51$	3.08041e6			3.25172
$52$	−35986.2	+	80693.4i	−0.0354915	+	0.0795841i
$53$	1.29787e6			1.19747			0.598735	−	0.800947i	$-0.295670\pi$
$53$	1.29787e6			1.19747			0.598735	+	0.800947i	$0.295670\pi$
$54$	−2.20070e6	+	1.27057e6i	−1.90187	+	1.09805i
$55$	−256194.	−	443741.i	−0.207635	−	0.359634i
$56$	236388.	−	409437.i	0.179874	−	0.311551i
$57$			2.24579e6i			1.60623i
$58$	−2.25348e6	−	1.30104e6i	−1.51654	−	0.875577i
$59$	1.66323e6	+	960264.i	1.05431	+	0.608707i	0.923853	−	0.382747i	$-0.125022\pi$
$59$	1.66323e6	+	960264.i	1.05431	+	0.608707i	0.130458	+	0.991454i	$0.458355\pi$
$60$			246361.i			0.147246i
$61$	729740.	−	1.26395e6i	0.411636	−	0.712975i	−0.583432	−	0.812162i	$-0.698291\pi$
$61$	729740.	−	1.26395e6i	0.411636	−	0.712975i	0.995069	+	0.0991864i	$0.0316240\pi$
$62$	672293.	+	1.16445e6i	0.358251	+	0.620509i
$63$	−1.41683e6	+	818009.i	−0.713882	+	0.412160i
$64$	−1.88395e6			−0.898336
$65$	217995.	+	2.08636e6i	0.0984577	+	0.942306i
$66$	1.90373e6			0.815082
$67$	1.47849e6	−	853605.i	0.600559	−	0.346733i	−0.168703	−	0.985667i	$-0.553958\pi$
$67$	1.47849e6	−	853605.i	0.600559	−	0.346733i	0.769261	+	0.638934i	$0.220624\pi$
$68$	205969.	+	356748.i	0.0794364	+	0.137588i
$69$	−1.31831e6	+	2.28338e6i	−0.483110	+	0.836771i
$70$			1.07149e6i			0.373373i
$71$	−4.41113e6	−	2.54677e6i	−1.46267	−	0.844472i	−0.463535	−	0.886079i	$-0.653419\pi$
$71$	−4.41113e6	−	2.54677e6i	−1.46267	−	0.844472i	−0.999134	+	0.0416066i	$0.986752\pi$
$72$	5.69359e6	+	3.28720e6i	1.79772	+	1.03792i
$73$		−	4.81561e6i		−	1.44884i	−0.689357	−	0.724422i	$-0.742107\pi$
$73$		−	4.81561e6i		−	1.44884i	0.689357	−	0.724422i	$-0.257893\pi$
$74$	−247006.	+	427828.i	−0.0708594	+	0.122732i
$75$	−333518.	−	577670.i	−0.0912861	−	0.158112i
$76$	−260089.	+	150162.i	−0.0679632	+	0.0392386i
$77$	663665.			0.165665
$78$	−7.11809e6	−	3.17440e6i	−1.69837	−	0.757408i
$79$	−1.42550e6			−0.325292			−0.162646	−	0.986684i	$-0.552003\pi$
$79$	−1.42550e6			−0.325292			−0.162646	+	0.986684i	$0.552003\pi$
$80$	4.05636e6	−	2.34194e6i	0.885771	−	0.511400i
$81$	−3.76798e6	−	6.52633e6i	−0.787791	−	1.36449i
$82$	2.45837e6	−	4.25802e6i	0.492379	−	0.852825i
$83$		−	7.27134e6i		−	1.39586i	−0.716167	−	0.697929i	$-0.754105\pi$
$83$		−	7.27134e6i		−	1.39586i	0.716167	−	0.697929i	$-0.245895\pi$
$84$	−276345.	−	159548.i	−0.0508715	−	0.0293707i
$85$	8.46997e6	+	4.89014e6i	1.49594	+	0.863684i
$86$		−	3.39578e6i		−	0.575698i
$87$	9.19914e6	−	1.59334e7i	1.49772	−	2.59412i
$88$	−1.33348e6	−	2.30966e6i	−0.208592	−	0.361292i
$89$	−8.38564e6	+	4.84145e6i	−1.26087	+	0.727965i	−0.973243	−	0.229776i	$-0.926200\pi$
$89$	−8.38564e6	+	4.84145e6i	−1.26087	+	0.727965i	−0.287629	+	0.957742i	$0.592867\pi$
$90$	−1.49000e7			−2.15445
$91$	−2.48146e6	−	1.10664e6i	−0.345194	−	0.153943i
$92$	−352590.			−0.0472077
$93$	−8.23330e6	+	4.75350e6i	−1.06141	+	0.612806i
$94$	829783.	+	1.43723e6i	0.103043	+	0.178475i
$95$	−3.56518e6	+	6.17507e6i	−0.426627	+	0.738940i
$96$			2.68700e6i			0.309969i
$97$	6.77837e6	+	3.91349e6i	0.754091	+	0.435375i	0.827170	−	0.561951i	$-0.189949\pi$
$97$	6.77837e6	+	3.91349e6i	0.754091	+	0.435375i	−0.0730789	+	0.997326i	$0.523282\pi$
$98$	−1.20189e6	−	693914.i	−0.128996	−	0.0744757i
$99$			9.22887e6i			0.955929i
$100$	44600.6	−	77250.6i	0.00446006	−	0.00772506i
$101$	6.96549e6	+	1.20646e7i	0.672708	+	1.16516i	0.977133	+	0.212628i	$0.0682023\pi$
$101$	6.96549e6	+	1.20646e7i	0.672708	+	1.16516i	−0.304425	+	0.952536i	$0.598464\pi$
$102$	−3.14693e7	+	1.81688e7i	−2.93621	+	1.69522i
$103$	1.58016e7			1.42485			0.712427	−	0.701746i	$-0.247596\pi$
$103$	1.58016e7			1.42485			0.712427	+	0.701746i	$0.247596\pi$
$104$	1.13466e6	+	1.08594e7i	0.0989116	+	0.946650i
$105$	−7.57602e6			−0.638673
$106$	−1.32589e7	+	7.65505e6i	−1.08128	+	0.624277i
$107$	−7.67607e6	−	1.32953e7i	−0.605753	−	1.04919i	−0.991932	−	0.126771i	$-0.959539\pi$
$107$	−7.67607e6	−	1.32953e7i	−0.605753	−	1.04919i	0.386179	−	0.922424i	$-0.373795\pi$
$108$	1.20137e6	−	2.08083e6i	0.0917684	−	0.158947i
$109$		−	3.57681e6i		−	0.264547i	−0.991213	−	0.132274i	$-0.957772\pi$
$109$		−	3.57681e6i		−	0.264547i	0.991213	−	0.132274i	$-0.0422277\pi$
$110$	5.23453e6	+	3.02216e6i	0.374976	+	0.216492i
$111$	−3.02499e6	−	1.74648e6i	−0.209939	−	0.121208i
$112$			6.06674e6i			0.408030i
$113$	−1.68747e6	+	2.92278e6i	−0.110017	+	0.190555i	−0.915777	−	0.401687i	$-0.868424\pi$
$113$	−1.68747e6	+	2.92278e6i	−0.110017	+	0.190555i	0.805760	+	0.592243i	$0.201757\pi$
$114$	−1.32461e7	−	2.29428e7i	−0.837374	−	1.45037i
$115$	−7.24971e6	+	4.18562e6i	−0.444507	+	0.256636i
$116$	2.46036e6			0.146351
$117$	1.53888e7	−	3.45070e7i	0.888289	−	1.99185i
$118$	−2.26552e7			−1.26935
$119$	−1.09706e7	+	6.33389e6i	−0.596784	+	0.344553i
$120$	1.52223e7	+	2.63657e7i	0.804164	+	1.39285i
$121$	−7.87170e6	+	1.36342e7i	−0.403943	+	0.699649i
$122$			1.72165e7i			0.858394i
$123$	3.01067e7	+	1.73821e7i	1.45880	+	0.842238i
$124$	−1.10102e6	−	635675.i	−0.0518585	−	0.0299405i
$125$		−	2.28066e7i		−	1.04442i
$126$	9.64952e6	−	1.67135e7i	0.429743	−	0.744336i
$127$	9.40391e6	+	1.62880e7i	0.407376	+	0.705596i	0.994595	−	0.103832i	$-0.0331105\pi$
$127$	9.40391e6	+	1.62880e7i	0.407376	+	0.705596i	−0.587219	+	0.809428i	$0.699777\pi$
$128$	2.28174e7	−	1.31736e7i	0.961682	−	0.555227i
$129$	2.40101e7			0.984760
$130$	−1.45327e7	−	2.00283e7i	−0.580156	−	0.799545i
$131$	9.74305e6			0.378657			0.189328	−	0.981914i	$-0.439369\pi$
$131$	9.74305e6			0.378657			0.189328	+	0.981914i	$0.439369\pi$
$132$	−1.55888e6	+	900019.i	−0.0589934	+	0.0340599i
$133$	−4.61775e6	−	7.99818e6i	−0.170196	−	0.294788i
$134$	−1.00694e7	+	1.74407e7i	−0.361524	+	0.626179i
$135$		−	5.70461e7i		−	1.99553i
$136$	4.40858e7	+	2.54530e7i	1.50284	+	0.867666i
$137$	1.55398e7	+	8.97189e6i	0.516324	+	0.298100i	0.735429	−	0.677601i	$-0.236980\pi$
$137$	1.55398e7	+	8.97189e6i	0.516324	+	0.298100i	−0.219105	+	0.975701i	$0.570314\pi$
$138$		−	3.11025e7i		−	1.00744i
$139$	5.38063e6	−	9.31952e6i	0.169934	−	0.294335i	−0.768462	−	0.639895i	$-0.778978\pi$
$139$	5.38063e6	−	9.31952e6i	0.169934	−	0.294335i	0.938397	+	0.345560i	$0.112311\pi$
$140$	−506563.	−	877392.i	−0.0156022	−	0.0270238i
$141$	−1.01620e7	+	5.86705e6i	−0.305291	+	0.176260i
$142$	6.00852e7			1.76099
$143$	−1.24053e7	+	9.00139e6i	−0.354757	+	0.257415i
$144$	−8.43636e7			−2.35443
$145$	5.05883e7	−	2.92072e7i	1.37804	−	0.795612i
$146$	2.84033e7	+	4.91960e7i	0.755325	+	1.30826i
$147$	4.90638e6	−	8.49809e6i	0.127394	−	0.220653i
$148$		−	467106.i		−	0.0118440i
$149$	5.06877e6	+	2.92646e6i	0.125531	+	0.0724753i	0.561451	−	0.827510i	$-0.310243\pi$
$149$	5.06877e6	+	2.92646e6i	0.125531	+	0.0724753i	−0.435920	+	0.899986i	$0.643577\pi$
$150$	6.81440e6	+	3.93429e6i	0.164857	+	0.0951804i
$151$			6.93044e7i			1.63810i	0.573719	+	0.819052i	$0.305500\pi$
$151$			6.93044e7i			1.63810i	−0.573719	+	0.819052i	$0.694500\pi$
$152$	−1.85566e7	+	3.21410e7i	−0.428594	+	0.742346i
$153$	−8.80786e7	−	1.52557e8i	−1.98816	−	3.44359i
$154$	−6.77996e6	+	3.91441e6i	−0.149591	+	0.0863662i
$155$	−3.01846e7			−0.651065
$156$	7.32944e6	−	765824.i	0.154573	−	0.0161508i
$157$	−1.14858e7			−0.236871			−0.118435	−	0.992962i	$-0.537788\pi$
$157$	−1.14858e7			−0.236871			−0.118435	+	0.992962i	$0.537788\pi$
$158$	1.45629e7	−	8.40787e6i	0.293729	−	0.169585i
$159$	−5.41256e7	−	9.37483e7i	−1.06786	−	1.84958i
$160$	−4.26560e6	+	7.38823e6i	−0.0823304	+	0.142600i
$161$		−	1.08428e7i		−	0.204762i
$162$	7.69869e7	+	4.44484e7i	1.42270	+	0.821398i
$163$	4.02032e7	+	2.32113e7i	0.727117	+	0.419801i	0.817366	−	0.576118i	$-0.195433\pi$
$163$	4.02032e7	+	2.32113e7i	0.727117	+	0.419801i	−0.0902497	+	0.995919i	$0.528767\pi$
$164$			4.64895e6i			0.0823002i
$165$	−2.13684e7	+	3.70112e7i	−0.370321	+	0.641415i
$166$	4.28876e7	+	7.42835e7i	0.727702	+	1.26042i
$167$	6.07629e6	−	3.50815e6i	0.100956	−	0.0582868i	−0.448672	−	0.893696i	$-0.648103\pi$
$167$	6.07629e6	−	3.50815e6i	0.100956	−	0.0582868i	0.549628	+	0.835410i	$0.314770\pi$
$168$	−3.94329e7			−0.641618
$169$	6.13932e7	−	1.29711e7i	0.978401	−	0.206715i
$170$	−1.15372e8			−1.80106
$171$	1.11222e8	−	6.42141e7i	1.70100	−	0.982073i
$172$	1.60541e6	+	2.78065e6i	0.0240567	+	0.0416675i
$173$	−4.17870e7	+	7.23773e7i	−0.613593	+	1.06277i	0.377037	+	0.926198i	$0.376943\pi$
$173$	−4.17870e7	+	7.23773e7i	−0.613593	+	1.06277i	−0.990630	+	0.136576i	$0.956390\pi$
$174$			2.17033e8i			3.12322i
$175$	2.37559e6	+	1.37155e6i	0.0335072	+	0.0193454i
$176$	2.96378e7	+	1.71114e7i	0.409781	+	0.236587i
$177$		−	1.60185e8i		−	2.17128i
$178$	5.71115e7	−	9.89200e7i	0.759020	−	1.31466i
$179$	6.56026e7	+	1.13627e8i	0.854940	+	1.48080i	0.876701	+	0.481036i	$0.159739\pi$
$179$	6.56026e7	+	1.13627e8i	0.854940	+	1.48080i	−0.0217608	+	0.999763i	$0.506927\pi$
$180$	1.22009e7	−	7.04422e6i	0.155934	−	0.0900283i
$181$	−6.67932e7			−0.837253			−0.418627	−	0.908158i	$-0.637488\pi$
$181$	−6.67932e7			−0.837253			−0.418627	+	0.908158i	$0.637488\pi$
$182$	3.18776e7	−	3.33076e6i	0.391955	−	0.0409538i
$183$	−1.21731e8			−1.46832
$184$	−3.77345e7	+	2.17860e7i	−0.446556	+	0.257819i
$185$	−5.54505e6	−	9.60431e6i	−0.0643879	−	0.111523i
$186$	5.60739e7	−	9.71229e7i	0.638948	−	1.10669i
$187$			7.14597e7i			0.799127i
$188$	−1.35895e6	−	784588.i	−0.0149159	−	0.00861170i
$189$	6.39892e7	+	3.69442e7i	0.689430	+	0.398043i
$190$		−	8.41121e7i		−	0.889654i
$191$	−3.38749e7	+	5.86731e7i	−0.351772	+	0.609287i	−0.986560	−	0.163399i	$-0.947754\pi$
$191$	−3.38749e7	+	5.86731e7i	−0.351772	+	0.609287i	0.634788	+	0.772686i	$0.281087\pi$
$192$	7.85672e7	+	1.36082e8i	0.801100	+	1.38755i
$193$	1.59181e8	−	9.19034e7i	1.59383	−	0.920198i	0.601188	−	0.799108i	$-0.294694\pi$
$193$	1.59181e8	−	9.19034e7i	1.59383	−	0.920198i	0.992642	−	0.121090i	$-0.0386389\pi$
$194$	−9.23298e7			−0.907896
$195$	1.41612e8	−	1.02755e8i	1.36766	−	0.992386i
$196$	1.31224e6			0.0124485
$197$	−4.71594e6	+	2.72275e6i	−0.0439477	+	0.0253732i	−0.521813	−	0.853060i	$-0.674744\pi$
$197$	−4.71594e6	+	2.72275e6i	−0.0439477	+	0.0253732i	0.477865	+	0.878433i	$0.341411\pi$
$198$	−5.44335e7	−	9.42816e7i	−0.498354	−	0.863175i
$199$	1.50641e6	−	2.60918e6i	0.0135506	−	0.0234703i	−0.859171	−	0.511689i	$-0.829020\pi$
$199$	1.50641e6	−	2.60918e6i	0.0135506	−	0.0234703i	0.872721	+	0.488219i	$0.162353\pi$
$200$		−	1.10232e7i		−	0.0974324i
$201$	−1.23316e8	−	7.11966e7i	−1.07111	−	0.618405i
$202$	−1.42318e8	−	8.21673e7i	−1.21487	−	0.701406i
$203$			7.56604e7i			0.634794i
$204$	1.71792e7	−	2.97553e7i	0.141677	−	0.245391i
$205$	5.51880e7	+	9.55884e7i	0.447410	+	0.774938i
$206$	−1.61428e8	+	9.32005e7i	−1.28660	+	0.742819i
$207$	1.50778e8			1.18153
$208$	−8.22841e7	−	1.13400e8i	−0.634007	−	0.873759i
$209$	−5.20980e7			−0.394738
$210$	7.73962e7	−	4.46847e7i	0.576703	−	0.332959i
$211$	7.06126e7	+	1.22305e8i	0.517480	+	0.896302i	0.999794	+	0.0203035i	$0.00646326\pi$
$211$	7.06126e7	+	1.22305e8i	0.517480	+	0.896302i	−0.482314	+	0.875999i	$0.660203\pi$
$212$	7.23810e6	−	1.25368e7i	0.0521734	−	0.0903670i
$213$			4.24837e8i			3.01227i
$214$	1.56836e8	+	9.05496e7i	1.09395	+	0.631594i
$215$	6.60187e7	+	3.81159e7i	0.453036	+	0.261560i
$216$		−	2.96923e8i		−	2.00473i
$217$	1.95481e7	−	3.38583e7i	0.129866	−	0.224935i
$218$	2.10966e7	+	3.65405e7i	0.137916	+	0.238878i
$219$	−3.47844e8	+	2.00828e8i	−2.23785	+	1.29202i
$220$	−5.71510e6			−0.0361863
$221$	1.19156e8	−	2.67190e8i	0.742582	−	1.66513i
$222$	4.12041e7			0.252758
$223$	9.32147e7	−	5.38175e7i	0.562882	−	0.324980i	−0.191419	−	0.981508i	$-0.561309\pi$
$223$	9.32147e7	−	5.38175e7i	0.562882	−	0.324980i	0.754301	+	0.656528i	$0.227976\pi$
$224$	−5.52496e6	−	9.56952e6i	−0.0328444	−	0.0568882i
$225$	−1.90726e7	+	3.30347e7i	−0.111628	+	0.193345i
$226$		−	3.98119e7i		−	0.229421i
$227$	−1.78475e8	−	1.03043e8i	−1.01271	−	0.584691i	−0.100730	−	0.994914i	$-0.532118\pi$
$227$	−1.78475e8	−	1.03043e8i	−1.01271	−	0.584691i	−0.911985	+	0.410223i	$0.865451\pi$
$228$	2.16932e7	+	1.25246e7i	0.121214	+	0.0699828i
$229$		−	1.29145e8i		−	0.710646i	−0.934744	−	0.355323i	$-0.884371\pi$
$229$		−	1.29145e8i		−	0.710646i	0.934744	−	0.355323i	$-0.115629\pi$
$230$	4.93751e7	−	8.55201e7i	0.267584	−	0.463469i
$231$	−2.76772e7	−	4.79382e7i	−0.147734	−	0.255882i
$232$	2.63310e8	−	1.52022e8i	1.38439	−	0.799280i
$233$	3.34460e7			0.173220			0.0866102	−	0.996242i	$-0.472397\pi$
$233$	3.34460e7			0.173220			0.0866102	+	0.996242i	$0.472397\pi$
$234$	4.63173e7	+	4.43287e8i	0.236313	+	2.26167i
$235$	−3.72556e7			−0.187264
$236$	1.85514e7	−	1.07106e7i	0.0918721	−	0.0530424i
$237$	5.94485e7	+	1.02968e8i	0.290083	+	0.502438i
$238$	7.47168e7	−	1.29413e8i	0.359252	−	0.622242i
$239$			1.98258e8i			0.939374i	0.882833	+	0.469687i	$0.155633\pi$
$239$			1.98258e8i			0.939374i	−0.882833	+	0.469687i	$0.844367\pi$
$240$	−3.38329e8	−	1.95334e8i	−1.57979	−	0.912093i
$241$	−2.18123e8	−	1.25933e8i	−1.00379	−	0.579537i	−0.0944207	−	0.995532i	$-0.530100\pi$
$241$	−2.18123e8	−	1.25933e8i	−1.00379	−	0.579537i	−0.909367	+	0.415995i	$0.863433\pi$
$242$		−	1.85715e8i		−	0.842349i
$243$	−7.87165e7	+	1.36341e8i	−0.351920	+	0.609543i
$244$	−8.13941e6	−	1.40979e7i	−0.0358697	−	0.0621282i
$245$	2.69813e7	−	1.55777e7i	0.117215	−	0.0676740i
$246$	−4.10091e8			−1.75633
$247$	1.94796e8	+	8.68715e7i	0.822509	+	0.366807i
$248$	−1.57110e8			−0.654067
$249$	−5.25228e8	+	3.03240e8i	−2.15601	+	1.24477i
$250$	1.34517e8	+	2.32991e8i	0.544488	+	0.943080i
$251$	2.10168e8	−	3.64022e8i	0.838898	−	1.45301i	−0.0519179	−	0.998651i	$-0.516533\pi$
$251$	2.10168e8	−	3.64022e8i	0.838898	−	1.45301i	0.890816	−	0.454363i	$-0.150133\pi$
$252$			1.82479e7i			0.0718308i
$253$	−5.29701e7	−	3.05823e7i	−0.205641	−	0.118727i
$254$	−1.92139e8	−	1.10932e8i	−0.735696	−	0.424754i
$255$		−	8.15744e8i		−	3.08080i
$256$	−3.48283e7	+	6.03243e7i	−0.129745	+	0.224726i
$257$	−1.01124e8	−	1.75152e8i	−0.371611	−	0.643649i	0.618203	−	0.786019i	$-0.287861\pi$
$257$	−1.01124e8	−	1.75152e8i	−0.371611	−	0.643649i	−0.989814	+	0.142370i	$0.954528\pi$
$258$	−2.45286e8	+	1.41616e8i	−0.889208	+	0.513385i
$259$	1.43643e7			0.0513731
$260$	2.13689e7	+	9.52972e6i	0.0754008	+	0.0336259i
$261$	−1.05213e9			−3.66291
$262$	−9.95344e7	+	5.74662e7i	−0.341915	+	0.197405i
$263$	7.66138e7	+	1.32699e8i	0.259694	+	0.449803i	0.966160	−	0.257944i	$-0.0830450\pi$
$263$	7.66138e7	+	1.32699e8i	0.259694	+	0.449803i	−0.706466	+	0.707747i	$0.749712\pi$
$264$	−1.11222e8	+	1.92642e8i	−0.372028	+	0.644371i
$265$		−	3.43696e8i		−	1.13453i
$266$	9.43493e7	+	5.44726e7i	0.307364	+	0.177457i
$267$	6.99421e8	+	4.03811e8i	2.24879	+	1.29834i
$268$		−	1.90419e7i		−	0.0604282i
$269$	−3.12791e8	+	5.41769e8i	−0.979762	+	1.69700i	−0.316534	+	0.948581i	$0.602519\pi$
$269$	−3.12791e8	+	5.41769e8i	−0.979762	+	1.69700i	−0.663228	+	0.748417i	$0.730814\pi$
$270$	3.36468e8	+	5.82780e8i	1.04033	+	1.80190i
$271$	2.70993e8	−	1.56458e8i	0.827114	−	0.477534i	−0.0257497	−	0.999668i	$-0.508197\pi$
$271$	2.70993e8	−	1.56458e8i	0.827114	−	0.477534i	0.852863	+	0.522134i	$0.174864\pi$
$272$	−6.53232e8			−1.96823
$273$	2.35504e7	+	2.25393e8i	0.0700534	+	0.670458i
$274$	−2.11671e8			−0.621634
$275$	1.34008e7	−	7.73698e6i	0.0388568	−	0.0224340i
$276$	1.47042e7	+	2.54685e7i	0.0420979	+	0.0729157i
$277$	6.69635e7	−	1.15984e8i	0.189304	−	0.327883i	−0.755715	−	0.654901i	$-0.772710\pi$
$277$	6.69635e7	−	1.15984e8i	0.189304	−	0.327883i	0.945018	+	0.327018i	$0.106044\pi$
$278$			1.26944e8i			0.354367i
$279$	4.70831e8	+	2.71835e8i	1.29793	+	0.749359i
$280$	−1.08425e8	−	6.25995e7i	−0.295174	−	0.170419i
$281$			1.47382e8i			0.396252i	0.980177	+	0.198126i	$0.0634856\pi$
$281$			1.47382e8i			0.396252i	−0.980177	+	0.198126i	$0.936514\pi$
$282$	6.92097e7	−	1.19875e8i	0.183779	−	0.318314i
$283$	1.99419e8	+	3.45403e8i	0.523014	+	0.905886i	0.999641	+	0.0267811i	$0.00852572\pi$
$283$	1.99419e8	+	3.45403e8i	0.523014	+	0.905886i	−0.476628	+	0.879105i	$0.658141\pi$
$284$	−4.92011e7	+	2.84063e7i	−0.127456	+	0.0735868i
$285$	5.94721e8			1.52180
$286$	7.36399e7	−	1.65126e8i	0.186137	−	0.417383i
$287$	−1.42963e8			−0.356975
$288$	1.33073e8	−	7.68297e7i	0.328259	−	0.189520i
$289$	−4.76828e8	−	8.25891e8i	−1.16204	−	2.01271i
$290$	−3.44538e8	+	5.96757e8i	−0.829552	+	1.43683i
$291$		−	6.52825e8i		−	1.55300i
$292$	−4.65165e7	−	2.68563e7i	−0.109337	−	0.0631257i
$293$	3.12980e8	+	1.80699e8i	0.726908	+	0.419680i	0.817290	−	0.576227i	$-0.195475\pi$
$293$	3.12980e8	+	1.80699e8i	0.726908	+	0.419680i	−0.0903820	+	0.995907i	$0.528809\pi$
$294$			1.15755e8i			0.265658i
$295$	2.54293e8	−	4.40449e8i	0.576711	−	0.998892i
$296$	−2.88618e7	−	4.99900e7i	−0.0646847	−	0.112037i
$297$	3.60967e8	−	2.08404e8i	0.799502	−	0.461593i
$298$	−6.90430e7			−0.151134
$299$	1.47062e8	+	2.02674e8i	0.318164	+	0.438479i
$300$	−7.44001e6			−0.0159092
$301$	−8.55099e7	+	4.93692e7i	−0.180731	+	0.104345i
$302$	−4.08770e8	−	7.08010e8i	−0.853993	−	1.47916i
$303$	5.80970e8	−	1.00627e9i	1.19979	−	2.07809i
$304$		−	4.76242e8i		−	0.972232i
$305$	−3.34714e8	−	1.93247e8i	−0.675498	−	0.389999i
$306$	1.79961e9	+	1.03901e9i	3.59049	+	2.07297i
$307$		−	3.29311e8i		−	0.649564i	−0.945789	−	0.324782i	$-0.894709\pi$
$307$		−	3.29311e8i		−	0.649564i	0.945789	−	0.324782i	$-0.105291\pi$
$308$	3.70121e6	−	6.41068e6i	0.00721798	−	0.0125019i
$309$	−6.58981e8	−	1.14139e9i	−1.27063	−	2.20079i
$310$	3.08364e8	−	1.78034e8i	0.587892	−	0.339420i
$311$	7.96740e8			1.50195			0.750975	−	0.660331i	$-0.229584\pi$
$311$	7.96740e8			1.50195			0.750975	+	0.660331i	$0.229584\pi$
$312$	7.37084e8	−	5.34834e8i	1.37397	−	0.996961i
$313$	1.48125e8			0.273038			0.136519	−	0.990637i	$-0.456408\pi$
$313$	1.48125e8			0.273038			0.136519	+	0.990637i	$0.456408\pi$
$314$	1.17338e8	−	6.77452e7i	0.213887	−	0.123488i
$315$	2.16622e8	+	3.75200e8i	0.390495	+	0.676357i
$316$	−7.94992e6	+	1.37697e7i	−0.0141729	+	0.0245481i
$317$			1.08073e9i			1.90551i	0.303740	+	0.952755i	$0.401764\pi$
$317$			1.08073e9i			1.90551i	−0.303740	+	0.952755i	$0.598236\pi$
$318$	1.10589e9	+	6.38485e8i	1.92848	+	1.11341i
$319$	3.69624e8	+	2.13402e8i	0.637518	+	0.368071i
$320$			4.98900e8i			0.851115i
$321$	−6.40238e8	+	1.10892e9i	−1.08037	+	1.87126i
$322$	6.39524e7	+	1.10769e8i	0.106748	+	0.184894i
$323$	8.61199e8	−	4.97213e8i	1.42198	−	0.820983i
$324$	−8.40549e7			−0.137295
$325$	−6.30072e7	+	6.58337e6i	−0.101812	+	0.0106379i
$326$	−5.47618e8			−0.875419
$327$	−2.58362e8	+	1.49166e8i	−0.408613	+	0.235913i
$328$	2.87251e8	+	4.97534e8i	0.449473	+	0.778510i
$329$	2.41274e7	−	4.17899e7i	0.0373530	−	0.0646973i
$330$		−	5.04138e8i		−	0.772237i
$331$	−6.09356e8	−	3.51812e8i	−0.923578	−	0.533228i	−0.0388030	−	0.999247i	$-0.512354\pi$
$331$	−6.09356e8	−	3.51812e8i	−0.923578	−	0.533228i	−0.884775	+	0.466019i	$0.845688\pi$
$332$	−7.02376e7	−	4.05517e7i	−0.105338	−	0.0608171i
$333$			1.99749e8i			0.296435i
$334$	−4.13834e7	+	7.16781e7i	−0.0607733	+	0.105263i
$335$	−2.26048e8	−	3.91527e8i	−0.328507	−	0.568991i
$336$	4.38216e8	−	2.53004e8i	0.630233	−	0.363865i
$337$	2.16822e8			0.308602			0.154301	−	0.988024i	$-0.450687\pi$
$337$	2.16822e8			0.308602			0.154301	+	0.988024i	$0.450687\pi$
$338$	−5.50684e8	+	4.94620e8i	−0.775700	+	0.696727i
$339$	2.81493e8			0.392436
$340$	9.44727e7	−	5.45438e7i	0.130356	−	0.0752609i
$341$	−1.10272e8	−	1.90997e8i	−0.150600	−	0.260847i
$342$	−7.57492e8	+	1.31201e9i	−1.02397	+	1.77356i
$343$			4.03536e7i			0.0539949i
$344$	3.43625e8	+	1.98392e8i	0.455124	+	0.262766i
$345$	6.04677e8	+	3.49110e8i	0.792787	+	0.457716i
$346$		−	9.85869e8i		−	1.27954i
$347$	−3.51508e8	+	6.08829e8i	−0.451629	+	0.782244i	−0.998487	−	0.0549808i	$-0.982490\pi$
$347$	−3.51508e8	+	6.08829e8i	−0.451629	+	0.782244i	0.546858	+	0.837225i	$0.315824\pi$
$348$	−1.02606e8	−	1.77718e8i	−0.130510	−	0.226050i
$349$	−1.05984e9	+	6.11899e8i	−1.33460	+	0.770532i	−0.986001	−	0.166740i	$-0.946676\pi$
$349$	−1.05984e9	+	6.11899e8i	−1.33460	+	0.770532i	−0.348599	+	0.937272i	$0.613343\pi$
$350$	−3.23585e7			−0.0403413
$351$	−1.69717e9	+	1.77331e8i	−2.09484	+	0.218881i
$352$	−6.23333e7			−0.0761765
$353$	1.82889e8	−	1.05591e8i	0.221297	−	0.127766i	−0.385254	−	0.922811i	$-0.625886\pi$
$353$	1.82889e8	−	1.05591e8i	0.221297	−	0.127766i	0.606551	+	0.795045i	$0.292553\pi$
$354$	9.44802e8	+	1.63644e9i	1.13196	+	1.96060i
$355$	−6.74426e8	+	1.16814e9i	−0.800083	+	1.38578i
$356$			1.08002e8i			0.126869i
$357$	9.15027e8	+	5.28291e8i	1.06438	+	0.614518i
$358$	−1.34038e9	−	7.73871e8i	−1.54397	−	0.891411i
$359$			1.00332e9i			1.14448i	0.820087	+	0.572239i	$0.193925\pi$
$359$			1.00332e9i			1.14448i	−0.820087	+	0.572239i	$0.806075\pi$
$360$	8.70503e8	−	1.50776e9i	0.983358	−	1.70323i
$361$	−8.44403e7	−	1.46255e8i	−0.0944658	−	0.163620i
$362$	6.82355e8	−	3.93958e8i	0.756015	−	0.436485i
$363$	1.31311e9			1.44088
$364$	−2.45285e7	+	1.77981e7i	−0.0266573	+	0.0193428i
$365$	−1.27525e9			−1.37269
$366$	1.24360e9	−	7.17990e8i	1.32585	−	0.765481i
$367$	8.53972e8	+	1.47912e9i	0.901804	+	1.56197i	0.825151	+	0.564913i	$0.191090\pi$
$367$	8.53972e8	+	1.47912e9i	0.901804	+	1.56197i	0.0766536	+	0.997058i	$0.475576\pi$
$368$	2.79561e8	−	4.84214e8i	0.292421	−	0.506489i
$369$		−	1.98803e9i		−	2.05983i
$370$	1.13296e8	+	6.54113e7i	0.116281	+	0.0671347i
$371$	3.85527e8	+	2.22584e8i	0.391964	+	0.226301i
$372$			1.06040e8i			0.106799i
$373$	5.04346e7	−	8.73553e7i	0.0503208	−	0.0871583i	−0.839768	−	0.542946i	$-0.817309\pi$
$373$	5.04346e7	−	8.73553e7i	0.0503208	−	0.0871583i	0.890089	+	0.455787i	$0.150642\pi$
$374$	−4.21482e8	−	7.30028e8i	−0.416609	−	0.721587i
$375$	−1.64738e9	+	9.51115e8i	−1.61319	+	0.931373i
$376$	−1.93914e8			−0.188127
$377$	−1.02619e9	−	1.41425e9i	−0.986358	−	1.35935i
$378$	−8.71612e8			−0.830046
$379$	3.45232e8	−	1.99320e8i	0.325742	−	0.188067i	−0.328207	−	0.944606i	$-0.606444\pi$
$379$	3.45232e8	−	1.99320e8i	0.325742	−	0.188067i	0.653949	+	0.756539i	$0.273111\pi$
$380$	3.97654e7	+	6.88757e7i	0.0371760	+	0.0643907i
$381$	7.84352e8	−	1.35854e9i	0.726563	−	1.25844i
$382$		−	7.99201e8i		−	0.733557i
$383$	−5.96822e8	−	3.44576e8i	−0.542812	−	0.313393i	0.203406	−	0.979095i	$-0.434799\pi$
$383$	−5.96822e8	−	3.44576e8i	−0.542812	−	0.313393i	−0.746218	+	0.665702i	$0.768132\pi$
$384$	−1.90313e9	−	1.09877e9i	−1.71518	−	0.990260i
$385$		−	1.75749e8i		−	0.156957i
$386$	−1.08412e9	+	1.87776e9i	−0.959453	+	1.66182i
$387$	−6.86524e8	−	1.18909e9i	−0.602098	−	1.04286i
$388$	7.56048e7	−	4.36505e7i	0.0657111	−	0.0379383i
$389$	1.60593e9			1.38326			0.691629	−	0.722253i	$-0.256893\pi$
$389$	1.60593e9			1.38326			0.691629	+	0.722253i	$0.256893\pi$
$390$	−8.40632e8	+	1.88499e9i	−0.717596	+	1.60910i
$391$	1.16749e9			0.987719
$392$	1.40437e8	−	8.10812e7i	0.117755	−	0.0679859i
$393$	−4.06319e8	−	7.03766e8i	−0.337671	−	0.584863i
$394$	3.21185e7	−	5.56309e7i	0.0264556	−	0.0458225i
$395$			3.77497e8i			0.308193i
$396$	8.91464e7	+	5.14687e7i	0.0721391	+	0.0416495i
$397$	5.24176e8	+	3.02633e8i	0.420446	+	0.242744i	0.695268	−	0.718751i	$-0.255286\pi$
$397$	5.24176e8	+	3.02633e8i	0.420446	+	0.242744i	−0.274822	+	0.961495i	$0.588619\pi$
$398$			3.55403e7i			0.0282573i
$399$	−3.85153e8	+	6.67104e8i	−0.303548	+	0.525761i
$400$	7.07258e7	+	1.22501e8i	0.0552545	+	0.0957036i
$401$	−1.07517e9	+	6.20751e8i	−0.832669	+	0.480742i	−0.854766	−	0.519014i	$-0.826299\pi$
$401$	−1.07517e9	+	6.20751e8i	−0.832669	+	0.480742i	0.0220964	+	0.999756i	$0.492966\pi$
$402$	1.67972e9			1.28957
$403$	9.38302e7	+	8.98018e8i	0.0714127	+	0.683466i
$404$	1.55384e8			0.117239
$405$	−1.72828e9	+	9.97822e8i	−1.29277	+	0.746381i
$406$	−4.46258e8	−	7.72942e8i	−0.330937	−	0.573200i
$407$	4.05150e7	−	7.01740e7i	0.0297876	−	0.0515936i
$408$		−	4.24591e9i		−	3.09500i
$409$	9.31350e8	+	5.37715e8i	0.673102	+	0.388616i	0.797251	−	0.603648i	$-0.206287\pi$
$409$	9.31350e8	+	5.37715e8i	0.673102	+	0.388616i	−0.124149	+	0.992264i	$0.539620\pi$
$410$	−1.12759e9	−	6.51017e8i	−0.807996	−	0.466497i
$411$		−	1.49664e9i		−	1.06334i
$412$	8.81242e7	−	1.52636e8i	0.0620804	−	0.107526i
$413$	3.29370e8	+	5.70486e8i	0.230070	+	0.398492i
$414$	−1.54034e9	+	8.89318e8i	−1.06688	+	0.615964i
$415$	−1.92557e9			−1.32248
$416$	2.33066e8	+	1.03938e8i	0.158728	+	0.0707864i
$417$	−8.97564e8			−0.606163
$418$	5.32230e8	−	3.07283e8i	0.356437	−	0.205789i
$419$	1.03879e9	+	1.79924e9i	0.689888	+	1.19492i	0.971874	+	0.235502i	$0.0756734\pi$
$419$	1.03879e9	+	1.79924e9i	0.689888	+	1.19492i	−0.281986	+	0.959418i	$0.590993\pi$
$420$	−4.22509e7	+	7.31807e7i	−0.0278268	+	0.0481974i
$421$		−	1.47331e9i		−	0.962292i	−0.876640	−	0.481146i	$-0.840221\pi$
$421$		−	1.47331e9i		−	0.962292i	0.876640	−	0.481146i	$-0.159779\pi$
$422$	−1.44275e9	−	8.32971e8i	−0.934538	−	0.539556i
$423$	5.81128e8	+	3.35514e8i	0.373319	+	0.215536i
$424$		−	1.78893e9i		−	1.13976i
$425$	−1.47680e8	+	2.55790e8i	−0.0933172	+	0.161630i
$426$	−2.50576e9	−	4.34011e9i	−1.57039	−	2.71999i
$427$	4.33534e8	−	2.50301e8i	0.269479	−	0.155584i
$428$	−1.71235e8			−0.105570
$429$	1.16754e9	+	5.20677e8i	0.713954	+	0.318396i
$430$	−8.99257e8			−0.545437
$431$	−7.37583e8	+	4.25844e8i	−0.443752	+	0.256201i	−0.705188	−	0.709020i	$-0.749137\pi$
$431$	−7.37583e8	+	4.25844e8i	−0.443752	+	0.256201i	0.261436	+	0.965221i	$0.415804\pi$
$432$	1.90508e9	+	3.29969e9i	1.13689	+	1.96916i
$433$	3.39206e7	−	5.87523e7i	0.0200797	−	0.0347790i	−0.855811	−	0.517289i	$-0.826941\pi$
$433$	3.39206e7	−	5.87523e7i	0.0200797	−	0.0347790i	0.875891	+	0.482510i	$0.160275\pi$
$434$			4.61193e8i			0.270812i
$435$	−4.21942e9	−	2.43608e9i	−2.45776	−	1.41899i
$436$	−3.45502e7	−	1.99476e7i	−0.0199640	−	0.0115262i
$437$			8.51161e8i			0.487895i
$438$	2.36904e9	−	4.10329e9i	1.34714	−	2.33331i
$439$	9.81446e8	+	1.69991e9i	0.553657	+	0.958961i	0.998007	+	0.0631080i	$0.0201013\pi$
$439$	9.81446e8	+	1.69991e9i	0.553657	+	0.958961i	−0.444350	+	0.895853i	$0.646565\pi$
$440$	−6.11635e8	+	3.53127e8i	−0.342301	+	0.197627i
$441$	−5.61154e8			−0.311564
$442$	3.58638e8	+	3.43240e9i	0.197550	+	1.89069i
$443$	2.43459e9			1.33049			0.665247	−	0.746623i	$-0.268326\pi$
$443$	2.43459e9			1.33049			0.665247	+	0.746623i	$0.268326\pi$
$444$	−3.37403e7	+	1.94799e7i	−0.0182940	+	0.0105620i
$445$	1.28210e9	+	2.22065e9i	0.689700	+	1.19460i
$446$	−6.34850e8	+	1.09959e9i	−0.338844	+	0.586894i
$447$		−	4.88174e8i		−	0.258522i
$448$	−5.59620e8	−	3.23097e8i	−0.294049	−	0.169769i
$449$	1.83717e9	+	1.06069e9i	0.957826	+	0.553001i	0.895503	−	0.445055i	$-0.146816\pi$
$449$	1.83717e9	+	1.06069e9i	0.957826	+	0.553001i	0.0623225	+	0.998056i	$0.480149\pi$
$450$		−	4.49975e8i		−	0.232779i
$451$	−4.03232e8	+	6.98418e8i	−0.206984	+	0.358507i
$452$	1.88217e7	+	3.26002e7i	0.00958684	+	0.0166049i
$453$	5.00604e9	−	2.89024e9i	2.53017	−	1.46080i
$454$	2.43105e9			1.21927
$455$	−2.93055e8	+	6.57132e8i	−0.145851	+	0.327049i
$456$	3.09550e9			1.52881
$457$	−1.75604e9	+	1.01385e9i	−0.860651	+	0.496897i	−0.864230	−	0.503096i	$-0.832194\pi$
$457$	−1.75604e9	+	1.01385e9i	−0.860651	+	0.496897i	0.00357893	+	0.999994i	$0.498861\pi$
$458$	7.61720e8	+	1.31934e9i	0.370481	+	0.641692i
$459$	−3.97794e9	+	6.88999e9i	−1.92006	+	3.32563i
$460$			9.33715e7i			0.0447262i
$461$	6.16875e8	+	3.56153e8i	0.293254	+	0.169310i	0.639408	−	0.768867i	$-0.279179\pi$
$461$	6.16875e8	+	3.56153e8i	0.293254	+	0.169310i	−0.346155	+	0.938178i	$0.612513\pi$
$462$	5.65496e8	+	3.26489e8i	0.266798	+	0.154036i
$463$		−	2.04421e9i		−	0.957177i	−0.878039	−	0.478589i	$-0.841149\pi$
$463$		−	2.04421e9i		−	0.957177i	0.878039	−	0.478589i	$-0.158851\pi$
$464$	−1.95077e9	+	3.37883e9i	−0.906552	+	1.57019i
$465$	1.25880e9	+	2.18031e9i	0.580594	+	1.00562i
$466$	−3.41683e8	+	1.97271e8i	−0.156413	+	0.0903049i
$467$	−3.30532e9			−1.50177			−0.750887	−	0.660431i	$-0.770374\pi$
$467$	−3.30532e9			−1.50177			−0.750887	+	0.660431i	$0.770374\pi$
$468$	−2.47499e8	−	3.41091e8i	−0.111612	−	0.153819i
$469$	5.85573e8			0.262105
$470$	3.80601e8	−	2.19740e8i	0.169094	−	0.0976263i
$471$	4.78997e8	+	8.29648e8i	0.211232	+	0.365865i
$472$	1.32359e9	−	2.29252e9i	0.579369	−	1.00350i
$473$			5.56989e8i			0.242010i
$474$	−1.21464e9	−	7.01275e8i	−0.523872	−	0.302458i
$475$	−1.86485e8	−	1.07667e8i	−0.0798391	−	0.0460952i
$476$			1.41294e8i			0.0600483i
$477$	−3.09524e9	+	5.36111e9i	−1.30581	+	2.26173i
$478$	−1.16936e9	−	2.02539e9i	−0.489724	−	0.848227i
$479$	4.55307e8	−	2.62872e8i	0.189291	−	0.109287i	−0.402360	−	0.915482i	$-0.631810\pi$
$479$	4.55307e8	−	2.62872e8i	0.189291	−	0.109287i	0.591651	+	0.806194i	$0.298476\pi$
$480$	7.11562e8			0.293676
$481$	−2.68499e8	+	1.94825e8i	−0.110011	+	0.0798248i
$482$	2.97111e9			1.20852
$483$	−7.83200e8	+	4.52181e8i	−0.316270	+	0.182598i
$484$	8.77997e7	+	1.52073e8i	0.0351993	+	0.0609670i
$485$	1.03636e9	−	1.79502e9i	0.412490	−	0.714453i
$486$		−	1.85714e9i		−	0.733866i
$487$	−1.72009e9	−	9.93095e8i	−0.674839	−	0.389618i	0.123069	−	0.992398i	$-0.460726\pi$
$487$	−1.72009e9	−	9.93095e8i	−0.674839	−	0.389618i	−0.797908	+	0.602780i	$0.794060\pi$
$488$	−1.74217e9	−	1.00584e9i	−0.678612	−	0.391797i
$489$		−	3.87198e9i		−	1.49745i
$490$	−1.83760e8	+	3.18281e8i	−0.0705609	+	0.122215i
$491$	−2.26566e8	−	3.92423e8i	−0.0863792	−	0.149613i	0.819599	−	0.572938i	$-0.194196\pi$
$491$	−2.26566e8	−	3.92423e8i	−0.0863792	−	0.149613i	−0.905978	+	0.423325i	$0.860863\pi$
$492$	3.35805e8	−	1.93877e8i	0.127119	−	0.0733921i
$493$	−8.14669e9			−3.06208
$494$	−2.50241e9	+	2.61466e8i	−0.933928	+	0.0975824i
$495$	2.44396e9			0.905681
$496$	1.74595e9	−	1.00803e9i	0.642461	−	0.370925i
$497$	−8.73542e8	−	1.51302e9i	−0.319180	−	0.552837i
$498$	3.57713e9	−	6.19577e9i	1.29787	−	2.24798i
$499$			3.31421e9i			1.19406i	0.802217	+	0.597032i	$0.203654\pi$
$499$			3.31421e9i			1.19406i	−0.802217	+	0.597032i	$0.796346\pi$
$500$	−2.20301e8	−	1.27191e8i	−0.0788171	−	0.0455051i
$501$	−5.06806e8	−	2.92604e8i	−0.180057	−	0.103956i
$502$			4.95844e9i			1.74937i
$503$	−1.00956e6	+	1.74861e6i	−0.000353708	+	0.000612639i	−0.866202	−	0.499694i	$-0.833446\pi$
$503$	−1.00956e6	+	1.74861e6i	−0.000353708	+	0.000612639i	0.865848	+	0.500306i	$0.166779\pi$
$504$	1.12751e9	+	1.95290e9i	0.392295	+	0.679475i
$505$	3.19490e9	−	1.84457e9i	1.10392	−	0.637347i
$506$	7.21519e8			0.247583
$507$	−3.49725e9	−	3.89365e9i	−1.19179	−	1.32687i
$508$	2.09779e8			0.0709970
$509$	−7.97952e8	+	4.60698e8i	−0.268203	+	0.154847i	−0.628071	−	0.778156i	$-0.716155\pi$
$509$	−7.97952e8	+	4.60698e8i	−0.268203	+	0.154847i	0.359867	+	0.933003i	$0.382822\pi$
$510$	4.81140e9	+	8.33359e9i	1.60611	+	2.78187i
$511$	8.25877e8	−	1.43046e9i	0.273806	−	0.474245i
$512$			2.55076e9i			0.839894i
$513$	−5.02318e9	−	2.90013e9i	−1.64274	−	0.948434i
$514$	2.06615e9	+	1.19289e9i	0.671107	+	0.387464i
$515$		−	4.18452e9i		−	1.34996i
$516$	1.33903e8	−	2.31926e8i	0.0429057	−	0.0743148i
$517$	−1.36104e8	−	2.35740e8i	−0.0433167	−	0.0750266i
$518$	−1.46745e8	+	8.47232e7i	−0.0463884	+	0.0267823i
$519$	6.97067e9			2.18871
$520$	2.87575e9	−	3.00475e8i	0.896889	−	0.0937124i
$521$	3.51331e9			1.08839			0.544195	−	0.838959i	$-0.316835\pi$
$521$	3.51331e9			1.08839			0.544195	+	0.838959i	$0.316835\pi$
$522$	1.07485e10	−	6.20563e9i	3.30750	−	1.90959i
$523$	4.39192e8	+	7.60703e8i	0.134245	+	0.232519i	0.925309	−	0.379214i	$-0.123806\pi$
$523$	4.39192e8	+	7.60703e8i	0.134245	+	0.232519i	−0.791064	+	0.611734i	$0.790472\pi$
$524$	5.43362e7	−	9.41131e7i	0.0164980	−	0.0285753i
$525$		−	2.28793e8i		−	0.0690058i
$526$	−1.56536e9	−	9.03763e8i	−0.468991	−	0.270772i
$527$	3.64568e9	+	2.10483e9i	1.08503	+	0.626441i
$528$		−	2.85442e9i		−	0.843917i
$529$	1.20277e9	−	2.08326e9i	0.353254	−	0.611854i
$530$	2.02718e9	+	3.51118e9i	0.591462	+	1.02444i
$531$	−7.93314e9	+	4.58020e9i	−2.29940	+	1.32756i
$532$	−1.03011e8			−0.0296616
$533$	2.67228e9	−	1.93903e9i	0.764429	−	0.554676i
$534$	−9.52699e9			−2.70746
$535$	−3.52082e9	+	2.03275e9i	−0.994044	+	0.573912i
$536$	−1.17657e9	−	2.03788e9i	−0.330021	−	0.571614i
$537$	5.47172e9	−	9.47730e9i	1.52480	−	2.64104i
$538$		−	7.37958e9i		−	2.04312i
$539$	1.97140e8	+	1.13819e8i	0.0542267	+	0.0313078i
$540$	−5.51038e8	−	3.18142e8i	−0.150592	−	0.0869446i
$541$			5.08900e9i			1.38179i	0.722956	+	0.690894i	$0.242783\pi$
$541$			5.08900e9i			1.38179i	−0.722956	+	0.690894i	$0.757217\pi$
$542$	−1.84563e9	+	3.19673e9i	−0.497906	+	0.862398i
$543$	2.78551e9	+	4.82464e9i	0.746630	+	1.29320i
$544$	1.03039e9	−	5.94897e8i	0.274414	−	0.158433i
$545$	−9.47197e8			−0.250641
$546$	−1.57000e9	−	2.16370e9i	−0.412786	−	0.568882i
$547$	3.97439e9			1.03828			0.519141	−	0.854689i	$-0.326252\pi$
$547$	3.97439e9			1.03828			0.519141	+	0.854689i	$0.326252\pi$
$548$	1.73328e8	−	1.00071e8i	0.0449922	−	0.0259763i
$549$	3.48066e9	+	6.02869e9i	0.897757	+	1.55496i
$550$	−9.12681e7	+	1.58081e8i	−0.0233910	+	0.0405145i
$551$		−	5.93938e9i		−	1.51255i
$552$	3.14732e9	+	1.81711e9i	0.796442	+	0.459826i
$553$	−4.23441e8	−	2.44474e8i	−0.106477	−	0.0614744i
$554$			1.57985e9i			0.394759i
$555$	−4.62496e8	+	8.01067e8i	−0.114837	+	0.198904i
$556$	−6.00147e7	−	1.03948e8i	−0.0148080	−	0.0256482i
$557$	9.61350e8	−	5.55035e8i	0.235716	−	0.136090i	−0.377490	−	0.926013i	$-0.623213\pi$
$557$	9.61350e8	−	5.55035e8i	0.235716	−	0.136090i	0.613206	+	0.789923i	$0.289880\pi$
$558$	−6.41331e9			−1.56265
$559$	9.28759e8	−	2.08260e9i	0.224886	−	0.504271i
$560$	1.60657e9			0.386582
$561$	5.16172e9	−	2.98012e9i	1.23431	−	0.712630i
$562$	−8.69284e8	−	1.50564e9i	−0.206578	−	0.357804i
$563$	−3.95164e9	+	6.84445e9i	−0.933251	+	1.61644i	−0.155527	+	0.987832i	$0.549708\pi$
$563$	−3.95164e9	+	6.84445e9i	−0.933251	+	1.61644i	−0.777724	+	0.628606i	$0.783626\pi$
$564$			1.30880e8i			0.0307183i
$565$	7.73999e8	+	4.46869e8i	0.180539	+	0.104234i
$566$	−4.07450e9	−	2.35241e9i	−0.944531	−	0.545325i
$567$		−	2.58483e9i		−	0.595514i
$568$	−3.51036e9	+	6.08012e9i	−0.803771	+	1.39217i
$569$	−1.95002e9	−	3.37754e9i	−0.443759	−	0.768613i	0.554206	−	0.832380i	$-0.313022\pi$
$569$	−1.95002e9	−	3.37754e9i	−0.443759	−	0.768613i	−0.997965	+	0.0637668i	$0.979689\pi$
$570$	−6.07564e9	+	3.50777e9i	−1.37414	+	0.793358i
$571$	1.07909e9			0.242566			0.121283	−	0.992618i	$-0.461299\pi$
$571$	1.07909e9			0.242566			0.121283	+	0.992618i	$0.461299\pi$
$572$	1.77657e7	+	1.70029e8i	0.00396913	+	0.0379872i
$573$	5.65081e9			1.25479
$574$	1.46050e9	−	8.43222e8i	0.322337	−	0.186102i
$575$	−1.26404e8	−	2.18939e8i	−0.0277284	−	0.0480270i
$576$	4.49296e9	−	7.78203e9i	0.979611	−	1.69674i
$577$			2.82522e7i			0.00612262i	0.999995	+	0.00306131i	$0.000974447\pi$
$577$			2.82522e7i			0.00612262i	−0.999995	+	0.00306131i	$0.999026\pi$
$578$	9.74250e9	+	5.62483e9i	2.09857	+	1.21161i
$579$	−1.32768e10	−	7.66539e9i	−2.84263	−	1.64119i
$580$		−	6.51544e8i		−	0.138658i
$581$	1.24703e9	−	2.15993e9i	0.263792	−	0.456901i
$582$	3.85048e9	+	6.66922e9i	0.809625	+	1.40231i
$583$	2.17478e9	−	1.25561e9i	0.454544	−	0.262431i
$584$	−6.63764e9			−1.37901
$585$	−9.13802e9	−	4.07521e9i	−1.88715	−	0.841597i
$586$	−4.26317e9			−0.875168
$587$	4.10267e8	−	2.36868e8i	0.0837207	−	0.0483362i	−0.457555	−	0.889181i	$-0.651275\pi$
$587$	4.10267e8	−	2.36868e8i	0.0837207	−	0.0483362i	0.541276	+	0.840845i	$0.317941\pi$
$588$	−5.47249e7	−	9.47864e7i	−0.0111011	−	0.0192276i
$589$	−1.53454e9	+	2.65790e9i	−0.309438	+	0.535962i
$590$			5.99947e9i			1.20263i
$591$	3.93342e8	+	2.27096e8i	0.0783817	+	0.0452537i
$592$	6.41479e8	+	3.70358e8i	0.127074	+	0.0733662i
$593$			5.67737e9i			1.11804i	0.829156	+	0.559018i	$0.188822\pi$
$593$			5.67737e9i			1.11804i	−0.829156	+	0.559018i	$0.811178\pi$
$594$	−2.45841e9	+	4.25809e9i	−0.481284	+	0.833609i
$595$	1.67732e9	+	2.90520e9i	0.326442	+	0.565414i
$596$	5.65362e7	−	3.26412e7i	0.0109387	−	0.00631545i
$597$	−2.51290e8			−0.0483354
$598$	−2.69778e9	−	1.20311e9i	−0.515884	−	0.230065i
$599$	−3.48500e9			−0.662534			−0.331267	−	0.943537i	$-0.607476\pi$
$599$	−3.48500e9			−0.662534			−0.331267	+	0.943537i	$0.607476\pi$
$600$	−7.96236e8	+	4.59707e8i	−0.150492	+	0.0868864i
$601$	−4.07309e9	−	7.05480e9i	−0.765356	−	1.32564i	−0.940058	−	0.341015i	$-0.889229\pi$
$601$	−4.07309e9	−	7.05480e9i	−0.765356	−	1.32564i	0.174702	−	0.984621i	$-0.444104\pi$
$602$	5.82376e8	−	1.00870e9i	0.108797	−	0.188441i
$603$			8.14293e9i			1.51241i
$604$	6.69447e8	+	3.86505e8i	0.123619	+	0.0713717i
$605$	3.61055e9	+	2.08455e9i	0.662872	+	0.382710i
$606$			1.37067e10i			2.50194i
$607$	−1.34443e9	+	2.32862e9i	−0.243994	+	0.422609i	−0.961848	−	0.273584i	$-0.911791\pi$
$607$	−1.34443e9	+	2.32862e9i	−0.243994	+	0.422609i	0.717855	+	0.696193i	$0.245124\pi$
$608$	4.33712e8	+	7.51212e8i	0.0782599	+	0.135550i
$609$	5.46515e9	−	3.15530e9i	0.980486	−	0.566084i
$610$	4.55922e9			0.813272
$611$	1.15811e8	+	1.10839e9i	0.0205402	+	0.196583i
$612$	−1.96483e9			−0.346493
$613$	5.23942e9	−	3.02498e9i	0.918695	−	0.530409i	0.0354767	−	0.999371i	$-0.488705\pi$
$613$	5.23942e9	−	3.02498e9i	0.918695	−	0.530409i	0.883219	+	0.468962i	$0.155372\pi$
$614$	1.94233e9	+	3.36422e9i	0.338637	+	0.586537i
$615$	4.60307e9	−	7.97274e9i	0.797966	−	1.38212i
$616$		−	9.14768e8i		−	0.157681i
$617$	−3.24681e9	−	1.87455e9i	−0.556493	−	0.321291i	0.195244	−	0.980755i	$-0.437450\pi$
$617$	−3.24681e9	−	1.87455e9i	−0.556493	−	0.321291i	−0.751737	+	0.659464i	$0.770783\pi$
$618$	1.34642e10	+	7.77357e9i	2.29468	+	1.32483i
$619$			3.25349e9i			0.551357i	0.961250	+	0.275678i	$0.0889025\pi$
$619$			3.25349e9i			0.551357i	−0.961250	+	0.275678i	$0.911098\pi$
$620$	−1.68337e8	+	2.91569e8i	−0.0283667	+	0.0491326i
$621$	−3.40484e9	−	5.89736e9i	−0.570527	−	0.988182i
$622$	−8.13945e9	+	4.69931e9i	−1.35622	+	0.783011i
$623$	−3.32124e9			−0.550290
$624$	−4.75965e9	+	1.06728e10i	−0.784203	+	1.75845i
$625$	−5.41476e9			−0.887155
$626$	−1.51324e9	+	8.73668e8i	−0.246545	+	0.142343i
$627$	2.17267e9	+	3.76317e9i	0.352012	+	0.609702i
$628$	−6.40553e7	+	1.10947e8i	−0.0103204	+	0.0178754i
$629$			1.54667e9i			0.247811i
$630$	−4.42599e9	−	2.55535e9i	−0.705211	−	0.407154i
$631$	−2.28634e9	−	1.32002e9i	−0.362276	−	0.209160i	0.307803	−	0.951450i	$-0.400406\pi$
$631$	−2.28634e9	−	1.32002e9i	−0.362276	−	0.209160i	−0.670078	+	0.742290i	$0.733740\pi$
$632$			1.96485e9i			0.309614i
$633$	5.88959e9	−	1.02011e10i	0.922937	−	1.59857i
$634$	−6.37435e9	−	1.10407e10i	−0.993399	−	1.72062i
$635$	4.31334e9	−	2.49031e9i	0.668506	−	0.385962i
$636$	−1.20742e9			−0.186105
$637$	−5.47322e8	−	7.54294e8i	−0.0838986	−	0.115625i
$638$	−5.03474e9			−0.767546
$639$	2.10399e10	−	1.21474e10i	3.19000	−	1.84175i
$640$	−3.48859e9	−	6.04242e9i	−0.526042	−	0.911132i
$641$	−2.43710e9	+	4.22117e9i	−0.365485	+	0.633039i	−0.988854	−	0.148889i	$-0.952430\pi$
$641$	−2.43710e9	+	4.22117e9i	−0.365485	+	0.633039i	0.623369	+	0.781928i	$0.285764\pi$
$642$		−	1.51049e10i		−	2.25292i
$643$	2.09412e9	+	1.20904e9i	0.310644	+	0.179351i	0.647215	−	0.762308i	$-0.275934\pi$
$643$	2.09412e9	+	1.20904e9i	0.310644	+	0.179351i	−0.336570	+	0.941658i	$0.609267\pi$
$644$	−1.04736e8	−	6.04692e7i	−0.0154523	−	0.00892141i
$645$		−	6.35827e9i		−	0.932996i
$646$	−5.86530e9	+	1.01590e10i	−0.856006	+	1.48265i
$647$	5.18202e9	+	8.97551e9i	0.752201	+	1.30285i	0.946754	+	0.321958i	$0.104341\pi$
$647$	5.18202e9	+	8.97551e9i	0.752201	+	1.30285i	−0.194553	+	0.980892i	$0.562326\pi$
$648$	−8.99562e9	+	5.19362e9i	−1.29873	+	0.749822i
$649$	3.71600e9			0.533604
$650$	6.04848e8	−	4.38883e8i	0.0863872	−	0.0626833i
$651$	−3.26090e9			−0.463238
$652$	4.48420e8	−	2.58896e8i	0.0633605	−	0.0365812i
$653$	−3.12539e9	−	5.41333e9i	−0.439246	−	0.760796i	0.558386	−	0.829581i	$-0.311421\pi$
$653$	−3.12539e9	−	5.41333e9i	−0.439246	−	0.760796i	−0.997631	+	0.0687856i	$0.978088\pi$
$654$	1.75961e9	−	3.04773e9i	0.245977	−	0.426044i
$655$		−	2.58012e9i		−	0.358753i
$656$	−6.38442e9	−	3.68605e9i	−0.882995	−	0.509797i
$657$	1.98919e10	+	1.14846e10i	2.73651	+	1.57993i
$658$			5.69231e8i			0.0778929i
$659$	1.37175e9	−	2.37593e9i	0.186713	−	0.323396i	−0.757439	−	0.652905i	$-0.773550\pi$
$659$	1.37175e9	−	2.37593e9i	0.186713	−	0.323396i	0.944152	+	0.329509i	$0.106883\pi$
$660$	2.38340e8	+	4.12817e8i	0.0322695	+	0.0558925i
$661$	8.09155e9	−	4.67166e9i	1.08975	−	0.629167i	0.156239	−	0.987719i	$-0.450063\pi$
$661$	8.09155e9	−	4.67166e9i	1.08975	−	0.629167i	0.933510	+	0.358553i	$0.116730\pi$
$662$	8.30020e9			1.11195
$663$	−2.42691e10	+	2.53578e9i	−3.23412	+	0.337920i
$664$	−1.00225e10			−1.32858
$665$	−2.11805e9	+	1.22286e9i	−0.279293	+	0.161250i
$666$	−1.17815e9	−	2.04062e9i	−0.154541	−	0.267672i
$667$	3.48650e9	−	6.03880e9i	0.454935	−	0.787971i
$668$		−	7.82587e7i		−	0.0101582i
$669$	−7.77476e9	−	4.48876e9i	−1.00391	−	0.579609i
$670$	4.61859e9	+	2.66655e9i	0.593264	+	0.342521i
$671$		−	2.82392e9i		−	0.360848i
$672$	−4.60821e8	+	7.98165e8i	−0.0585787	+	0.101461i
$673$	6.85803e9	+	1.18785e10i	0.867255	+	1.50213i	0.864791	+	0.502132i	$0.167451\pi$
$673$	6.85803e9	+	1.18785e10i	0.867255	+	1.50213i	0.00246406	+	0.999997i	$0.499216\pi$
$674$	−2.21504e9	+	1.27886e9i	−0.278659	+	0.160884i
$675$	1.72277e9			0.215608
$676$	2.17091e8	−	6.65367e8i	0.0270289	−	0.0828415i
$677$	−1.51188e10			−1.87265			−0.936325	−	0.351134i	$-0.885796\pi$
$677$	−1.51188e10			−1.87265			−0.936325	+	0.351134i	$0.885796\pi$
$678$	−2.87572e9	+	1.66030e9i	−0.354358	+	0.204589i
$679$	1.34233e9	+	2.32498e9i	0.164556	+	0.285020i
$680$	6.74036e9	−	1.16746e10i	0.822057	−	1.42384i
$681$			1.71890e10i			2.08562i
$682$	2.25307e9	+	1.30081e9i	0.271975	+	0.157025i
$683$	7.99306e9	+	4.61479e9i	0.959932	+	0.554217i	0.896152	−	0.443747i	$-0.146351\pi$
$683$	7.99306e9	+	4.61479e9i	0.959932	+	0.554217i	0.0637799	+	0.997964i	$0.479684\pi$
$684$		−	1.43247e9i		−	0.171154i
$685$	2.37590e9	−	4.11518e9i	0.282430	−	0.489184i
$686$	−2.38013e8	−	4.12250e8i	−0.0281492	−	0.0487558i
$687$	−9.32848e9	+	5.38580e9i	−1.09765	+	0.633726i
$688$	−5.09158e9			−0.596065
$689$	−1.02253e10	+	1.06840e9i	−1.19099	+	0.124441i
$690$	−8.23645e9			−0.954483
$691$	6.45786e9	−	3.72845e9i	0.744587	−	0.429888i	−0.0791476	−	0.996863i	$-0.525220\pi$
$691$	6.45786e9	−	3.72845e9i	0.744587	−	0.429888i	0.823735	+	0.566975i	$0.191887\pi$
$692$	4.66086e8	+	8.07285e8i	0.0534681	+	0.0926095i
$693$	−1.58275e9	+	2.74141e9i	−0.180654	+	0.312901i
$694$		−	8.29302e9i		−	0.941791i
$695$	−2.46796e9	−	1.42488e9i	−0.278863	−	0.161002i
$696$	−2.19619e10	−	1.26797e10i	−2.46909	−	1.42553i
$697$		−	1.53935e10i		−	1.72195i
$698$	7.21817e9	−	1.25022e10i	0.803402	−	1.39153i
$699$	−1.39482e9	−	2.41589e9i	−0.154471	−	0.267552i
$700$	2.64969e7	−	1.52980e7i	0.00291980	−	0.00168575i
$701$	−9.31755e9			−1.02162			−0.510809	−	0.859694i	$-0.670654\pi$
$701$	−9.31755e9			−1.02162			−0.510809	+	0.859694i	$0.670654\pi$
$702$	1.62923e10	−	1.18218e10i	1.77747	−	1.28975i
$703$	−1.12761e9			−0.122409
$704$	−3.15685e9	+	1.82261e9i	−0.340996	+	0.196874i
$705$	1.55369e9	+	2.69107e9i	0.166995	+	0.289243i
$706$	−1.24559e9	+	2.15742e9i	−0.133217	+	0.230738i
$707$			4.77832e9i			0.508519i
$708$	−1.54731e9	−	8.93341e8i	−0.163856	−	0.0946022i
$709$	1.08515e10	+	6.26510e9i	1.14348	+	0.660186i	0.947289	−	0.320380i	$-0.103811\pi$
$709$	1.08515e10	+	6.26510e9i	1.14348	+	0.660186i	0.196187	+	0.980567i	$0.437144\pi$
$710$		−	1.59115e10i		−	1.66843i
$711$	3.39963e9	−	5.88834e9i	0.354722	−	0.614397i
$712$	6.67326e9	+	1.15584e10i	0.692880	+	1.20010i
$713$	−3.12045e9	+	1.80159e9i	−0.322406	+	0.186141i
$714$	−1.24638e10			−1.28147
$715$	2.38371e9	+	3.28512e9i	0.243884	+	0.336109i
$716$	1.46344e9			0.148998
$717$	1.43207e10	−	8.26806e9i	1.45093	−	0.837697i
$718$	−5.91774e9	−	1.02498e10i	−0.596651	−	1.03343i
$719$	−3.84470e9	+	6.65922e9i	−0.385755	+	0.668147i	−0.991874	−	0.127227i	$-0.959392\pi$
$719$	−3.84470e9	+	6.65922e9i	−0.385755	+	0.668147i	0.606119	+	0.795374i	$0.292726\pi$
$720$			2.23408e10i			2.23067i
$721$	4.69381e9	+	2.70997e9i	0.466393	+	0.269272i
$722$	1.72527e9	+	9.96088e8i	0.170600	+	0.0984957i
$723$			2.10075e10i			2.06723i
$724$	−3.72500e8	+	6.45189e8i	−0.0364789	+	0.0631833i
$725$	8.82046e8	+	1.52775e9i	0.0859623	+	0.148891i
$726$	−1.34146e10	+	7.74495e9i	−1.30107	+	0.751174i
$727$	1.05892e10			1.02210			0.511051	−	0.859550i	$-0.329256\pi$
$727$	1.05892e10			1.02210			0.511051	+	0.859550i	$0.329256\pi$
$728$	−1.52534e9	+	3.42034e9i	−0.146524	+	0.328556i
$729$	−3.35012e9			−0.320268
$730$	1.30279e10	−	7.52166e9i	1.23949	−	0.715622i
$731$	−5.31580e9	−	9.20723e9i	−0.503335	−	0.871802i
$732$	−6.78884e8	+	1.17586e9i	−0.0639744	+	0.110807i
$733$		−	1.44346e9i		−	0.135376i	−0.997707	−	0.0676881i	$-0.978438\pi$
$733$		−	1.44346e9i		−	0.135376i	0.997707	−	0.0676881i	$-0.0215623\pi$
$734$	−1.74482e10	−	1.00737e10i	−1.62860	−	0.940275i
$735$	−2.25043e9	−	1.29929e9i	−0.209055	−	0.120698i
$736$			1.01838e9i			0.0941539i
$737$	1.65163e9	−	2.86070e9i	0.151976	−	0.263230i
$738$	1.17258e10	+	2.03096e10i	1.07385	+	1.85996i
$739$	−4.35130e9	+	2.51222e9i	−0.396610	+	0.228983i	−0.685020	−	0.728524i	$-0.740207\pi$
$739$	−4.35130e9	+	2.51222e9i	−0.396610	+	0.228983i	0.288410	+	0.957507i	$0.406873\pi$
$740$	−1.23697e8			−0.0112214
$741$	−1.84872e9	−	1.76935e10i	−0.166920	−	1.59753i
$742$	−5.25136e9			−0.471909
$743$	1.16276e10	−	6.71318e9i	1.03999	−	0.600437i	0.120157	−	0.992755i	$-0.461660\pi$
$743$	1.16276e10	−	6.71318e9i	1.03999	−	0.600437i	0.919830	+	0.392318i	$0.128327\pi$
$744$	6.55203e9	+	1.13484e10i	0.583271	+	1.01025i
$745$	7.74973e8	−	1.34229e9i	0.0686657	−	0.118932i
$746$			1.18989e9i			0.104935i
$747$	3.00358e10	+	1.73412e10i	2.63643	+	1.52214i
$748$	6.90266e8	+	3.98525e8i	0.0603060	+	0.0348177i
$749$		−	5.26578e9i		−	0.457906i
$750$	1.12197e10	−	1.94331e10i	0.971105	−	1.68200i
$751$	−8.16970e9	−	1.41503e10i	−0.703828	−	1.21907i	−0.967113	−	0.254348i	$-0.918139\pi$
$751$	−8.16970e9	−	1.41503e10i	−0.703828	−	1.21907i	0.263285	−	0.964718i	$-0.415194\pi$
$752$	2.15496e9	−	1.24417e9i	0.184789	−	0.106688i
$753$	−3.50590e10			−2.99239
$754$	1.88250e10	+	8.39524e9i	1.59932	+	0.713236i
$755$	1.83529e10			1.55200
$756$	7.13725e8	−	4.12069e8i	0.0600765	−	0.0346852i
$757$	−1.02905e9	−	1.78237e9i	−0.0862189	−	0.149335i	0.819691	−	0.572806i	$-0.194145\pi$
$757$	−1.02905e9	−	1.78237e9i	−0.0862189	−	0.149335i	−0.905910	+	0.423470i	$0.860812\pi$
$758$	−2.35125e9	+	4.07248e9i	−0.196090	+	0.339638i
$759$			5.10156e9i			0.423503i
$760$	8.51145e9	+	4.91409e9i	0.703325	+	0.406065i
$761$	2.09062e10	+	1.20702e10i	1.71961	+	0.992817i	0.919628	+	0.392792i	$0.128491\pi$
$761$	2.09062e10	+	1.20702e10i	1.71961	+	0.992817i	0.799981	+	0.600025i	$0.204843\pi$
$762$			1.85050e10i			1.51512i
$763$	6.13423e8	−	1.06248e9i	0.0499947	−	0.0865934i
$764$	3.77835e8	+	6.54430e8i	0.0306532	+	0.0530929i
$765$	−4.03995e10	+	2.33246e10i	−3.26258	+	1.88365i
$766$	8.12947e9			0.653524
$767$	−1.38942e10	−	6.19629e9i	−1.11186	−	0.495847i
$768$	5.80984e9			0.462807
$769$	1.08900e10	−	6.28733e9i	0.863544	−	0.498567i	−0.00165362	−	0.999999i	$-0.500526\pi$
$769$	1.08900e10	−	6.28733e9i	0.863544	−	0.498567i	0.865197	+	0.501431i	$0.167193\pi$
$770$	1.03660e9	+	1.79544e9i	0.0818264	+	0.141728i
$771$	−8.43445e9	+	1.46089e10i	−0.662776	+	1.14796i
$772$		−	2.05015e9i		−	0.160371i
$773$	−8.07057e9	−	4.65955e9i	−0.628458	−	0.362840i	0.151697	−	0.988427i	$-0.451526\pi$
$773$	−8.07057e9	−	4.65955e9i	−0.628458	−	0.362840i	−0.780155	+	0.625587i	$0.784860\pi$
$774$	1.40270e10	+	8.09847e9i	1.08735	+	0.627783i
$775$		−	9.11565e8i		−	0.0703447i
$776$	5.39419e9	−	9.34302e9i	0.414391	−	0.717746i
$777$	−5.99042e8	−	1.03757e9i	−0.0458125	−	0.0793496i
$778$	−1.64061e10	+	9.47206e9i	−1.24904	+	0.721134i
$779$	1.12227e10			0.850580
$780$	−2.02803e8	−	1.94096e9i	−0.0153018	−	0.146448i
$781$	−9.85540e9			−0.740280
$782$	−1.19270e10	+	6.88604e9i	−0.891880	+	0.514927i
$783$	2.37589e10	+	4.11516e10i	1.76872	+	3.06352i
$784$	−1.04045e9	+	1.80210e9i	−0.0771104	+	0.133559i
$785$			3.04162e9i			0.224420i
$786$	8.30187e9	+	4.79309e9i	0.609813	+	0.352076i
$787$	1.97069e9	+	1.13778e9i	0.144114	+	0.0832045i	0.570323	−	0.821420i	$-0.306818\pi$
$787$	1.97069e9	+	1.13778e9i	0.144114	+	0.0832045i	−0.426209	+	0.904625i	$0.640151\pi$
$788$			6.07382e7i			0.00442202i
$789$	6.39012e9	−	1.10680e10i	0.463169	−	0.802233i
$790$	−2.22654e9	−	3.85648e9i	−0.160670	−	0.278289i
$791$	−1.00251e9	+	5.78801e8i	−0.0720232	+	0.0415826i
$792$	1.27207e10			0.909856
$793$	−4.70879e9	+	1.05587e10i	−0.335315	+	0.751892i
$794$	−7.13993e9			−0.506200
$795$	−2.48261e10	+	1.43333e10i	−1.75236	+	1.01173i
$796$	−1.68023e7	−	2.91024e7i	−0.00118079	−	0.00204518i
$797$	1.39765e10	−	2.42080e10i	0.977900	−	1.69377i	0.307888	−	0.951423i	$-0.400378\pi$
$797$	1.39765e10	−	2.42080e10i	0.977900	−	1.69377i	0.670012	−	0.742350i	$-0.266289\pi$
$798$		−	9.08679e9i		−	0.632995i
$799$	4.49971e9	+	2.59791e9i	0.312083	+	0.180181i
$800$	−2.23122e8	−	1.28820e8i	−0.0154073	−	0.00889543i
$801$		−	4.61848e10i		−	3.17531i
$802$	7.32259e9	−	1.26831e10i	0.501250	−	0.868191i
$803$	−4.65882e9	−	8.06932e9i	−0.317521	−	0.549962i
$804$	−1.37545e9	+	7.94116e8i	−0.0933358	+	0.0538875i
$805$	−2.87134e9			−0.193999
$806$	−6.25523e9	−	8.62067e9i	−0.420795	−	0.579920i
$807$	5.21779e10			3.49485
$808$	1.66293e10	−	9.60093e9i	1.10901	−	0.640285i
$809$	−4.91995e9	−	8.52161e9i	−0.326694	−	0.565850i	0.655160	−	0.755490i	$-0.272601\pi$
$809$	−4.91995e9	−	8.52161e9i	−0.326694	−	0.565850i	−0.981854	+	0.189640i	$0.939268\pi$
$810$	1.17707e10	−	2.03874e10i	0.778221	−	1.34792i
$811$			1.34392e9i			0.0884711i	0.999021	+	0.0442356i	$0.0140852\pi$
$811$			1.34392e9i			0.0884711i	−0.999021	+	0.0442356i	$0.985915\pi$
$812$	7.30843e8	+	4.21952e8i	0.0479047	+	0.0276578i
$813$	−2.26027e10	−	1.30497e10i	−1.47517	−	0.851692i
$814$			9.55857e8i			0.0621166i
$815$	6.14674e9	−	1.06465e10i	0.397734	−	0.688896i
$816$	2.72421e10	+	4.71847e10i	1.75519	+	3.04008i
$817$	6.71257e9	−	3.87550e9i	0.430637	−	0.248628i
$818$	−1.26861e10			−0.810388
$819$	1.04891e10	−	7.61102e9i	0.667185	−	0.484115i
$820$	1.23112e9			0.0779741
$821$	1.16421e10	−	6.72159e9i	0.734229	−	0.423907i	−0.0857383	−	0.996318i	$-0.527325\pi$
$821$	1.16421e10	−	6.72159e9i	0.734229	−	0.423907i	0.819967	+	0.572410i	$0.193992\pi$
$822$	8.82743e9	+	1.52896e10i	0.554348	+	0.960160i
$823$	6.22412e9	−	1.07805e10i	0.389205	−	0.674123i	−0.603138	−	0.797637i	$-0.706083\pi$
$823$	6.22412e9	−	1.07805e10i	0.389205	−	0.674123i	0.992343	+	0.123514i	$0.0394163\pi$
$824$		−	2.17802e10i		−	1.35618i
$825$	−1.11772e9	−	6.45318e8i	−0.0693020	−	0.0400115i
$826$	−6.72966e9	−	3.88537e9i	−0.415492	−	0.239884i
$827$			2.64791e10i			1.62792i	0.580920	+	0.813961i	$0.302693\pi$
$827$			2.64791e10i			1.62792i	−0.580920	+	0.813961i	$0.697307\pi$
$828$	8.40879e8	−	1.45645e9i	0.0514787	−	0.0891637i
$829$	3.38636e9	+	5.86535e9i	0.206439	+	0.357563i	0.950590	−	0.310448i	$-0.100479\pi$
$829$	3.38636e9	+	5.86535e9i	0.206439	+	0.357563i	−0.744151	+	0.668011i	$0.767146\pi$
$830$	1.96715e10	−	1.13573e10i	1.19416	−	0.689451i
$831$	−1.11705e10			−0.675254
$832$	1.48427e10	−	1.55085e9i	0.893472	−	0.0933553i
$833$	−4.34505e9			−0.260458
$834$	9.16946e9	−	5.29399e9i	0.547347	−	0.316011i
$835$	−9.29015e8	−	1.60910e9i	−0.0552230	−	0.0956491i
$836$	−2.90546e8	+	5.03241e8i	−0.0171986	+	0.0297889i
$837$		−	2.45540e10i		−	1.44738i
$838$	−2.12244e10	−	1.22539e10i	−1.24590	−	0.719318i
$839$	−8.53751e9	−	4.92913e9i	−0.499073	−	0.288140i	0.229257	−	0.973366i	$-0.426370\pi$
$839$	−8.53751e9	−	4.92913e9i	−0.499073	−	0.288140i	−0.728331	+	0.685226i	$0.759704\pi$
$840$			1.04425e10i			0.607891i
$841$	−1.57038e10	+	2.71997e10i	−0.910370	+	1.57681i
$842$	8.68984e9	+	1.50512e10i	0.501672	+	0.868921i
$843$	1.06458e10	−	6.14634e9i	0.612041	−	0.353362i
$844$	1.57520e9			0.0901858
$845$	−3.43495e9	−	1.62579e10i	−0.195849	−	0.926972i
$846$	−7.91568e9			−0.449461
$847$	−4.67652e9	+	2.69999e9i	−0.264443	+	0.152676i
$848$	1.14779e10	+	1.98803e10i	0.646362	+	1.11953i
$849$	1.66329e10	−	2.88090e10i	0.932806	−	1.61567i
$850$		−	3.48418e9i		−	0.194596i
$851$	−1.14648e9	−	6.61921e8i	−0.0637695	−	0.0368174i
$852$	4.10372e9	+	2.36928e9i	0.227321	+	0.131244i
$853$			2.47798e10i			1.36702i	0.729940	+	0.683511i	$0.239548\pi$
$853$			2.47798e10i			1.36702i	−0.729940	+	0.683511i	$0.760452\pi$
$854$	−2.95264e9	+	5.11412e9i	−0.162221	+	0.280975i
$855$	−1.70049e10	−	2.94534e10i	−0.930451	−	1.61159i
$856$	−1.83257e10	+	1.05804e10i	−0.998627	+	0.576557i
$857$	5.24506e9			0.284654			0.142327	−	0.989820i	$-0.454541\pi$
$857$	5.24506e9			0.284654			0.142327	+	0.989820i	$0.454541\pi$
$858$	−1.49985e10	+	1.56714e9i	−0.810669	+	0.0847035i
$859$	−1.60370e10			−0.863272			−0.431636	−	0.902048i	$-0.642063\pi$
$859$	−1.60370e10			−0.863272			−0.431636	+	0.902048i	$0.642063\pi$
$860$	7.36362e8	−	4.25139e8i	0.0394772	−	0.0227922i
$861$	5.96206e9	+	1.03266e10i	0.318336	+	0.551374i
$862$	5.02340e9	−	8.70079e9i	0.267130	−	0.462683i
$863$			1.27351e10i			0.674475i	0.941420	+	0.337238i	$0.109493\pi$
$863$			1.27351e10i			0.674475i	−0.941420	+	0.337238i	$0.890507\pi$
$864$	−6.01004e9	−	3.46990e9i	−0.317015	−	0.183029i
$865$	1.91667e10	+	1.10659e10i	1.00691	+	0.581340i
$866$			8.00279e8i			0.0418725i
$867$	−3.97708e10	+	6.88851e10i	−2.07252	+	3.58970i
$868$	−2.18037e8	−	3.77651e8i	−0.0113165	−	0.0196007i
$869$	−2.38866e9	+	1.37909e9i	−0.123477	+	0.0712892i
$870$	5.74737e10			2.95905
$871$	−1.09456e10	+	7.94221e9i	−0.561275	+	0.407266i
$872$	−4.93012e9			−0.251797
$873$	−3.23310e10	+	1.86663e10i	−1.64463	+	0.949529i
$874$	−5.02030e9	−	8.69541e9i	−0.254354	−	0.440555i
$875$	3.91133e9	−	6.77463e9i	0.197377	−	0.341867i
$876$			4.48001e9i			0.225172i
$877$	−1.29289e10	−	7.46451e9i	−0.647237	−	0.373683i	0.140160	−	0.990129i	$-0.455238\pi$
$877$	−1.29289e10	−	7.46451e9i	−0.647237	−	0.373683i	−0.787397	+	0.616446i	$0.788572\pi$
$878$	−2.00528e10	−	1.15775e10i	−0.999870	−	0.577275i
$879$		−	3.01431e10i		−	1.49702i
$880$	4.53138e9	−	7.84858e9i	0.224151	−	0.388241i
$881$	−5.46445e9	−	9.46471e9i	−0.269235	−	0.466328i	0.699430	−	0.714701i	$-0.253437\pi$
$881$	−5.46445e9	−	9.46471e9i	−0.269235	−	0.466328i	−0.968664	+	0.248373i	$0.920104\pi$
$882$	5.73271e9	−	3.30978e9i	0.281333	−	0.162428i
$883$	−1.45946e10			−0.713395			−0.356698	−	0.934220i	$-0.616097\pi$
$883$	−1.45946e10			−0.713395			−0.356698	+	0.934220i	$0.616097\pi$
$884$	−1.91640e9	−	2.64109e9i	−0.0933045	−	0.128588i
$885$	−4.24197e10			−2.05715
$886$	−2.48716e10	+	1.43596e10i	−1.20140	+	0.693626i
$887$	−4.72712e9	−	8.18761e9i	−0.227439	−	0.393935i	0.729610	−	0.683864i	$-0.239702\pi$
$887$	−4.72712e9	−	8.18761e9i	−0.227439	−	0.393935i	−0.957048	+	0.289929i	$0.906368\pi$
$888$	−2.40727e9	+	4.16952e9i	−0.115367	+	0.199821i
$889$			6.45108e9i			0.307947i
$890$	−2.61956e10	−	1.51240e10i	−1.24556	−	0.719123i
$891$	−1.26277e10	−	7.29060e9i	−0.598070	−	0.345296i
$892$		−	1.20054e9i		−	0.0566371i
$893$	−1.89401e9	+	3.28053e9i	−0.0890027	+	0.154157i
$894$	2.87933e9	+	4.98715e9i	0.134775	+	0.233438i
$895$	3.00903e10	−	1.73726e10i	1.40296	−	0.810000i
$896$	9.03712e9			0.419712
$897$	8.50666e9	−	1.90749e10i	0.393537	−	0.882446i
$898$	−2.50245e10			−1.15318
$899$	2.17744e10	−	1.25715e10i	0.999510	−	0.577068i
$900$	2.12733e8	+	3.68464e8i	0.00972716	+	0.0168479i
$901$	−2.39666e10	+	4.15114e10i	−1.09162	+	1.89073i
$902$		−	9.51333e9i		−	0.431628i
$903$	7.13213e9	+	4.11774e9i	0.322338	+	0.186102i
$904$	4.02864e9	+	2.32593e9i	0.181371	+	0.104715i
$905$			1.76879e10i			0.793244i
$906$	−3.40942e10	+	5.90530e10i	−1.52311	+	2.63811i
$907$	−7.59846e9	−	1.31609e10i	−0.338143	−	0.585680i	0.645941	−	0.763387i	$-0.276465\pi$
$907$	−7.59846e9	−	1.31609e10i	−0.338143	−	0.585680i	−0.984083	+	0.177707i	$0.943132\pi$
$908$	−1.99068e9	+	1.14932e9i	−0.0882474	+	0.0509496i
$909$	−6.64470e10			−2.93428
$910$	−8.82040e8	−	8.44171e9i	−0.0388010	−	0.371352i
$911$	1.76283e10			0.772497			0.386249	−	0.922395i	$-0.373771\pi$
$911$	1.76283e10			0.772497			0.386249	+	0.922395i	$0.373771\pi$
$912$	−3.44002e10	+	1.98610e10i	−1.50168	+	0.866998i
$913$	−7.03459e9	−	1.21843e10i	−0.305908	−	0.529849i
$914$	1.19597e10	−	2.07148e10i	0.518095	−	0.897367i
$915$			3.22363e10i			1.39114i
$916$	−1.24748e9	−	7.20231e8i	−0.0536289	−	0.0309626i
$917$	2.89414e9	+	1.67093e9i	0.123944	+	0.0715594i
$918$		−	9.38503e10i		−	4.00393i
$919$	−9.03954e9	+	1.56569e10i	−0.384187	+	0.665431i	−0.991656	−	0.128912i	$-0.958851\pi$
$919$	−9.03954e9	+	1.56569e10i	−0.384187	+	0.665431i	0.607469	+	0.794343i	$0.292185\pi$
$920$	5.76929e9	+	9.99270e9i	0.244267	+	0.423083i
$921$	−2.37870e10	+	1.37334e10i	−1.00330	+	0.579255i
$922$	−8.40260e9			−0.353066
$923$	3.68496e10	+	1.64335e10i	1.54251	+	0.687899i
$924$	−6.17413e8			−0.0257468
$925$	2.90047e8	−	1.67459e8i	0.0120496	−	0.00695683i
$926$	1.20571e10	+	2.08835e10i	0.499005	+	0.864302i
$927$	−3.76846e10	+	6.52717e10i	−1.55376	+	2.69120i
$928$		−	7.10624e9i		−	0.291892i
$929$	3.25194e10	+	1.87751e10i	1.33072	+	0.768293i	0.985410	−	0.170195i	$-0.0544399\pi$
$929$	3.25194e10	+	1.87751e10i	1.33072	+	0.768293i	0.345312	+	0.938488i	$0.387773\pi$
$930$	−2.57197e10	−	1.48493e10i	−1.04852	−	0.605362i
$931$		−	3.16778e9i		−	0.128656i
$932$	1.86526e8	−	3.23072e8i	0.00754716	−	0.0130721i
$933$	−3.32269e10	−	5.75506e10i	−1.33938	−	2.31987i
$934$	3.37669e10	−	1.94953e10i	1.35606	−	0.782919i
$935$	1.89237e10			0.757121
$936$	−4.75630e10	−	2.12113e10i	−1.89585	−	0.845476i
$937$	−1.23587e10			−0.490779			−0.245389	−	0.969425i	$-0.578916\pi$
$937$	−1.23587e10			−0.490779			−0.245389	+	0.969425i	$0.578916\pi$
$938$	−5.98218e9	+	3.45381e9i	−0.236673	+	0.136643i
$939$	−6.17734e9	−	1.06995e10i	−0.243485	−	0.421728i
$940$	−2.07772e8	+	3.59871e8i	−0.00815903	+	0.0141319i
$941$			2.53325e10i			0.991093i	0.868581	+	0.495547i	$0.165032\pi$
$941$			2.53325e10i			0.991093i	−0.868581	+	0.495547i	$0.834968\pi$
$942$	−9.78682e9	−	5.65042e9i	−0.381473	−	0.220243i
$943$	1.14105e10	+	6.58788e9i	0.443114	+	0.255832i
$944$			3.39689e10i			1.31425i
$945$	9.78341e9	−	1.69454e10i	0.377120	−	0.653190i
$946$	−3.28522e9	−	5.69016e9i	−0.126167	−	0.218527i
$947$	7.32216e9	−	4.22745e9i	0.280165	−	0.161754i	−0.353333	−	0.935498i	$-0.614952\pi$
$947$	7.32216e9	−	4.22745e9i	0.280165	−	0.161754i	0.633498	+	0.773744i	$0.281618\pi$
$948$	1.32616e9			0.0505552
$949$	3.96418e9	+	3.79398e10i	0.150564	+	1.44100i
$950$	2.54016e9			0.0961231
$951$	7.80642e10	−	4.50704e10i	2.94320	−	1.69926i
$952$	8.73037e9	+	1.51214e10i	0.327947	+	0.568020i
$953$	−5.91023e9	+	1.02368e10i	−0.221197	+	0.383125i	−0.955172	−	0.296052i	$-0.904330\pi$
$953$	−5.91023e9	+	1.02368e10i	−0.221197	+	0.383125i	0.733975	+	0.679177i	$0.237663\pi$
$954$		−	7.30250e10i		−	2.72303i
$955$	1.55376e10	+	8.97063e9i	0.577260	+	0.333281i
$956$	1.91508e9	+	1.10567e9i	0.0708898	+	0.0409282i
$957$		−	3.55985e10i		−	1.31293i
$958$	−3.10093e9	+	5.37096e9i	−0.113949	+	0.197366i
$959$	3.07736e9	+	5.33014e9i	0.112671	+	0.195152i
$960$	3.60368e10	−	2.08059e10i	1.31461	−	0.758991i
$961$	1.45204e10			0.527774
$962$	1.59386e9	−	3.57398e9i	0.0577214	−	0.129431i
$963$	7.32255e10			2.64223
$964$	−2.43291e9	+	1.40464e9i	−0.0874694	+	0.0505005i
$965$	−2.43375e10	−	4.21538e10i	−0.871828	−	1.51005i
$966$	5.33408e9	−	9.23890e9i	0.190388	−	0.329762i
$967$		−	1.65172e10i		−	0.587413i	−0.955896	−	0.293706i	$-0.905111\pi$
$967$		−	1.65172e10i		−	0.587413i	0.955896	−	0.293706i	$-0.0948888\pi$
$968$	1.87928e10	+	1.08500e10i	0.665928	+	0.384474i
$969$	−7.18300e10	−	4.14711e10i	−2.53614	−	1.46424i
$970$			2.44504e10i			0.860173i
$971$	−2.63795e10	+	4.56907e10i	−0.924697	+	1.60162i	−0.132650	+	0.991163i	$0.542349\pi$
$971$	−2.63795e10	+	4.56907e10i	−0.924697	+	1.60162i	−0.792047	+	0.610460i	$0.790985\pi$
$972$	8.77992e8	+	1.52073e9i	0.0306661	+	0.0531152i
$973$	3.19660e9	−	1.84556e9i	0.111248	−	0.0642292i
$974$	2.34298e10			0.812479
$975$	3.10316e9	+	4.27663e9i	0.107223	+	0.147770i
$976$	2.58142e10			0.888761
$977$	1.77145e9	−	1.02275e9i	0.0607711	−	0.0350862i	−0.469307	−	0.883035i	$-0.655496\pi$
$977$	1.77145e9	−	1.02275e9i	0.0607711	−	0.0350862i	0.530078	+	0.847949i	$0.322163\pi$
$978$	2.28376e10	+	3.95559e10i	0.780664	+	1.35215i
$979$	−9.36765e9	+	1.62252e10i	−0.319074	+	0.552652i
$980$		−	3.47502e8i		−	0.0117941i
$981$	1.47748e10	+	8.53021e9i	0.499665	+	0.288482i
$982$	4.62916e9	+	2.67265e9i	0.155996	+	0.0900641i
$983$		−	2.19323e10i		−	0.736457i	−0.929735	−	0.368228i	$-0.879964\pi$
$983$		−	2.19323e10i		−	0.736457i	0.929735	−	0.368228i	$-0.120036\pi$
$984$	2.39588e10	−	4.14978e10i	0.801644	−	1.38849i
$985$	7.21028e8	+	1.24886e9i	0.0240395	+	0.0416376i
$986$	8.32261e10	−	4.80506e10i	2.76497	−	1.59636i
$987$	−4.02479e9			−0.133240
$988$	1.92550e9	−	1.39716e9i	0.0635175	−	0.0460889i
$989$	9.09991e9			0.299123
$990$	−2.49673e10	+	1.44149e10i	−0.817802	+	0.472158i
$991$	1.13618e9	+	1.96792e9i	0.0370842	+	0.0642317i	0.883972	−	0.467540i	$-0.154860\pi$
$991$	1.13618e9	+	1.96792e9i	0.0370842	+	0.0642317i	−0.846888	+	0.531772i	$0.821526\pi$
$992$	−1.83602e9	+	3.18007e9i	−0.0597153	+	0.103430i
$993$			5.86872e10i			1.90205i
$994$	1.78481e10	+	1.03046e10i	0.576421	+	0.332797i
$995$	−6.90953e8	−	3.98922e8i	−0.0222366	−	0.0128383i
$996$			6.76459e9i			0.216937i
$997$	−1.12530e10	+	1.94907e10i	−0.359612	+	0.622867i	−0.987896	−	0.155118i	$-0.950424\pi$
$997$	−1.12530e10	+	1.94907e10i	−0.359612	+	0.622867i	0.628284	+	0.777984i	$0.283758\pi$
$998$	−1.95478e10	−	3.38577e10i	−0.622502	−	1.07820i
$999$	7.81273e9	−	4.51068e9i	0.247927	−	0.143141i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.q.a.36.15	✓	100
13.4	even	6	inner	91.8.q.a.43.15	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.q.a.36.15	✓	100	1.1	even	1	trivial
91.8.q.a.43.15	yes	100	13.4	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.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-10.2159 + 5.89817i) q^{2} +(-41.7035 - 72.2326i) q^{3} +(5.57692 - 9.65951i) q^{4} -264.816i q^{5} +(852.081 + 491.949i) q^{6} +(297.047 + 171.500i) q^{7} -1378.36i q^{8} +(-2384.87 + 4130.71i) q^{9} +O(q^{10})\)	\(q+(-10.2159 + 5.89817i) q^{2} +(-41.7035 - 72.2326i) q^{3} +(5.57692 - 9.65951i) q^{4} -264.816i q^{5} +(852.081 + 491.949i) q^{6} +(297.047 + 171.500i) q^{7} -1378.36i q^{8} +(-2384.87 + 4130.71i) q^{9} +(1561.93 + 2705.35i) q^{10} +(1675.66 - 967.442i) q^{11} -930.309 q^{12} +(-7878.51 + 823.193i) q^{13} -4046.15 q^{14} +(-19128.4 + 11043.8i) q^{15} +(8843.64 + 15317.6i) q^{16} +(-18466.2 + 31984.3i) q^{17} -56265.4i q^{18} +(-23318.3 - 13462.8i) q^{19} +(-2558.00 - 1476.86i) q^{20} -28608.6i q^{21} +(-11412.3 + 19766.6i) q^{22} +(-15805.8 - 27376.4i) q^{23} +(-99562.4 + 57482.4i) q^{24} +7997.36 q^{25} +(75631.0 - 54878.5i) q^{26} +215418. q^{27} +(3313.21 - 1912.88i) q^{28} +(110292. + 191032. i) q^{29} +(130276. - 225645. i) q^{30} -113983. i q^{31} +(-27899.5 - 16107.8i) q^{32} +(-139762. - 80691.4i) q^{33} -435666. i q^{34} +(45416.0 - 78662.8i) q^{35} +(26600.4 + 46073.3i) q^{36} +(36267.8 - 20939.2i) q^{37} +317624. q^{38} +(388023. + 534755. i) q^{39} -365012. q^{40} +(-360961. + 208401. i) q^{41} +(168739. + 292264. i) q^{42} +(-143933. + 249300. i) q^{43} -21581.4i q^{44} +(1.09388e6 + 631551. i) q^{45} +(322941. + 186450. i) q^{46} -140685. i q^{47} +(737622. - 1.27760e6i) q^{48} +(58824.5 + 101887. i) q^{49} +(-81700.5 + 47169.8i) q^{50} +3.08041e6 q^{51} +(-35986.2 + 80693.4i) q^{52} +1.29787e6 q^{53} +(-2.20070e6 + 1.27057e6i) q^{54} +(-256194. - 443741. i) q^{55} +(236388. - 409437. i) q^{56} +2.24579e6i q^{57} +(-2.25348e6 - 1.30104e6i) q^{58} +(1.66323e6 + 960264. i) q^{59} +246361. i q^{60} +(729740. - 1.26395e6i) q^{61} +(672293. + 1.16445e6i) q^{62} +(-1.41683e6 + 818009. i) q^{63} -1.88395e6 q^{64} +(217995. + 2.08636e6i) q^{65} +1.90373e6 q^{66} +(1.47849e6 - 853605. i) q^{67} +(205969. + 356748. i) q^{68} +(-1.31831e6 + 2.28338e6i) q^{69} +1.07149e6i q^{70} +(-4.41113e6 - 2.54677e6i) q^{71} +(5.69359e6 + 3.28720e6i) q^{72} -4.81561e6i q^{73} +(-247006. + 427828. i) q^{74} +(-333518. - 577670. i) q^{75} +(-260089. + 150162. i) q^{76} +663665. q^{77} +(-7.11809e6 - 3.17440e6i) q^{78} -1.42550e6 q^{79} +(4.05636e6 - 2.34194e6i) q^{80} +(-3.76798e6 - 6.52633e6i) q^{81} +(2.45837e6 - 4.25802e6i) q^{82} -7.27134e6i q^{83} +(-276345. - 159548. i) q^{84} +(8.46997e6 + 4.89014e6i) q^{85} -3.39578e6i q^{86} +(9.19914e6 - 1.59334e7i) q^{87} +(-1.33348e6 - 2.30966e6i) q^{88} +(-8.38564e6 + 4.84145e6i) q^{89} -1.49000e7 q^{90} +(-2.48146e6 - 1.10664e6i) q^{91} -352590. q^{92} +(-8.23330e6 + 4.75350e6i) q^{93} +(829783. + 1.43723e6i) q^{94} +(-3.56518e6 + 6.17507e6i) q^{95} +2.68700e6i q^{96} +(6.77837e6 + 3.91349e6i) q^{97} +(-1.20189e6 - 693914. i) q^{98} +9.22887e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q + 3328 q^{4} + 522 q^{6} - 38792 q^{9}+O(q^{10}) \) 100 * q + 3328 * q^4 + 522 * q^6 - 38792 * q^9	\( 100 q + 3328 q^{4} + 522 q^{6} - 38792 q^{9} - 2728 q^{10} - 3954 q^{11} - 54708 q^{12} - 32008 q^{13} + 21952 q^{14} + 46398 q^{15} - 228808 q^{16} + 16832 q^{17} - 203520 q^{20} + 148982 q^{22} + 154164 q^{23} - 436560 q^{24} - 1918852 q^{25} - 624246 q^{26} + 661404 q^{27} - 451396 q^{29} + 313736 q^{30} + 1854432 q^{32} + 315450 q^{33} - 372498 q^{35} + 2704174 q^{36} + 1777146 q^{37} - 338468 q^{38} + 189708 q^{39} - 2875580 q^{40} - 2158998 q^{41} - 296352 q^{42} + 1876346 q^{43} + 7252980 q^{45} + 234336 q^{46} + 1316674 q^{48} + 5882450 q^{49} + 6432894 q^{50} - 3602684 q^{51} - 14093326 q^{52} + 1719628 q^{53} - 14915976 q^{54} - 1225470 q^{55} + 2107392 q^{56} + 18792564 q^{58} + 5131962 q^{59} + 886858 q^{61} + 3663272 q^{62} - 1848084 q^{63} - 38282980 q^{64} - 17072760 q^{65} + 54390948 q^{66} - 15529368 q^{67} + 2633716 q^{68} + 12342620 q^{69} + 20194104 q^{71} + 12742440 q^{72} - 23243862 q^{74} - 12055866 q^{75} - 7828698 q^{76} - 11143384 q^{77} - 32361130 q^{78} + 38408264 q^{79} - 38368944 q^{80} - 55140914 q^{81} + 27439818 q^{82} + 46422306 q^{84} + 16353300 q^{85} - 15866954 q^{87} - 39468942 q^{88} + 11465844 q^{89} - 22072424 q^{90} - 3481450 q^{91} + 67780968 q^{92} - 71319114 q^{93} - 6119236 q^{94} + 60860930 q^{95} + 45060702 q^{97}+O(q^{100}) \) 100 * q + 3328 * q^4 + 522 * q^6 - 38792 * q^9 - 2728 * q^10 - 3954 * q^11 - 54708 * q^12 - 32008 * q^13 + 21952 * q^14 + 46398 * q^15 - 228808 * q^16 + 16832 * q^17 - 203520 * q^20 + 148982 * q^22 + 154164 * q^23 - 436560 * q^24 - 1918852 * q^25 - 624246 * q^26 + 661404 * q^27 - 451396 * q^29 + 313736 * q^30 + 1854432 * q^32 + 315450 * q^33 - 372498 * q^35 + 2704174 * q^36 + 1777146 * q^37 - 338468 * q^38 + 189708 * q^39 - 2875580 * q^40 - 2158998 * q^41 - 296352 * q^42 + 1876346 * q^43 + 7252980 * q^45 + 234336 * q^46 + 1316674 * q^48 + 5882450 * q^49 + 6432894 * q^50 - 3602684 * q^51 - 14093326 * q^52 + 1719628 * q^53 - 14915976 * q^54 - 1225470 * q^55 + 2107392 * q^56 + 18792564 * q^58 + 5131962 * q^59 + 886858 * q^61 + 3663272 * q^62 - 1848084 * q^63 - 38282980 * q^64 - 17072760 * q^65 + 54390948 * q^66 - 15529368 * q^67 + 2633716 * q^68 + 12342620 * q^69 + 20194104 * q^71 + 12742440 * q^72 - 23243862 * q^74 - 12055866 * q^75 - 7828698 * q^76 - 11143384 * q^77 - 32361130 * q^78 + 38408264 * q^79 - 38368944 * q^80 - 55140914 * q^81 + 27439818 * q^82 + 46422306 * q^84 + 16353300 * q^85 - 15866954 * q^87 - 39468942 * q^88 + 11465844 * q^89 - 22072424 * q^90 - 3481450 * q^91 + 67780968 * q^92 - 71319114 * q^93 - 6119236 * q^94 + 60860930 * q^95 + 45060702 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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