LMFDB - Embedded newform 91.8.q.a.36.33

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			36.33
Character	$\chi$	$=$	91.36
Dual form			91.8.q.a.43.33

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(6.17622 - 3.56584i) q^{2} +(34.2927 + 59.3966i) q^{3} +(-38.5696 + 66.8044i) q^{4} -466.432i q^{5} +(423.598 + 244.564i) q^{6} +(297.047 + 171.500i) q^{7} +1462.99i q^{8} +(-1258.47 + 2179.74i) q^{9} +O(q^{10})$	\(q+(6.17622 - 3.56584i) q^{2} +(34.2927 + 59.3966i) q^{3} +(-38.5696 + 66.8044i) q^{4} -466.432i q^{5} +(423.598 + 244.564i) q^{6} +(297.047 + 171.500i) q^{7} +1462.99i q^{8} +(-1258.47 + 2179.74i) q^{9} +(-1663.22 - 2880.78i) q^{10} +(-5028.66 + 2903.30i) q^{11} -5290.61 q^{12} +(4984.00 + 6156.97i) q^{13} +2446.17 q^{14} +(27704.5 - 15995.2i) q^{15} +(279.874 + 484.757i) q^{16} +(-12360.5 + 21409.0i) q^{17} +17950.1i q^{18} +(-4995.63 - 2884.23i) q^{19} +(31159.7 + 17990.1i) q^{20} +23524.8i q^{21} +(-20705.4 + 35862.8i) q^{22} +(32597.2 + 56460.1i) q^{23} +(-86896.5 + 50169.7i) q^{24} -139434. q^{25} +(52737.0 + 20254.6i) q^{26} -22629.6 q^{27} +(-22913.9 + 13229.4i) q^{28} +(-100172. - 173503. i) q^{29} +(114073. - 197580. i) q^{30} +138683. i q^{31} +(-158717. - 91635.2i) q^{32} +(-344892. - 199123. i) q^{33} +176303. i q^{34} +(79993.1 - 138552. i) q^{35} +(-97077.6 - 168143. i) q^{36} +(-482434. + 278533. i) q^{37} -41138.8 q^{38} +(-194788. + 507172. i) q^{39} +682384. q^{40} +(38228.6 - 22071.3i) q^{41} +(83885.6 + 145294. i) q^{42} +(211141. - 365707. i) q^{43} -447915. i q^{44} +(1.01670e6 + 586993. i) q^{45} +(402655. + 232473. i) q^{46} +1.14628e6i q^{47} +(-19195.3 + 33247.2i) q^{48} +(58824.5 + 101887. i) q^{49} +(-861173. + 497198. i) q^{50} -1.69550e6 q^{51} +(-603543. + 95482.0i) q^{52} +174919. q^{53} +(-139766. + 80693.7i) q^{54} +(1.35419e6 + 2.34553e6i) q^{55} +(-250902. + 434575. i) q^{56} -395632. i q^{57} +(-1.23737e6 - 714395. i) q^{58} +(908340. + 524430. i) q^{59} +2.46771e6i q^{60} +(1.32578e6 - 2.29631e6i) q^{61} +(494522. + 856538. i) q^{62} +(-747651. + 431657. i) q^{63} -1.37867e6 q^{64} +(2.87181e6 - 2.32470e6i) q^{65} -2.84017e6 q^{66} +(306224. - 176798. i) q^{67} +(-953479. - 1.65147e6i) q^{68} +(-2.23569e6 + 3.87233e6i) q^{69} -1.14097e6i q^{70} +(2.46327e6 + 1.42217e6i) q^{71} +(-3.18893e6 - 1.84113e6i) q^{72} -5.65331e6i q^{73} +(-1.98641e6 + 3.44056e6i) q^{74} +(-4.78156e6 - 8.28190e6i) q^{75} +(385359. - 222487. i) q^{76} -1.99166e6 q^{77} +(605439. + 3.82699e6i) q^{78} +7.24670e6 q^{79} +(226106. - 130542. i) q^{80} +(1.97625e6 + 3.42297e6i) q^{81} +(157405. - 272634. i) q^{82} +3.18628e6i q^{83} +(-1.57156e6 - 907340. i) q^{84} +(9.98586e6 + 5.76534e6i) q^{85} -3.01158e6i q^{86} +(6.87034e6 - 1.18998e7i) q^{87} +(-4.24748e6 - 7.35686e6i) q^{88} +(-9.30419e6 + 5.37178e6i) q^{89} +8.37249e6 q^{90} +(424562. + 2.68366e6i) q^{91} -5.02904e6 q^{92} +(-8.23732e6 + 4.75582e6i) q^{93} +(4.08744e6 + 7.07965e6i) q^{94} +(-1.34530e6 + 2.33012e6i) q^{95} -1.25697e7i q^{96} +(1.06466e7 + 6.14680e6i) q^{97} +(726626. + 419518. i) q^{98} -1.46149e7i 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 $

$2$	6.17622	−	3.56584i	0.545906	−	0.315179i	−0.201563	−	0.979475i	$-0.564602\pi$
$2$	6.17622	−	3.56584i	0.545906	−	0.315179i	0.747469	+	0.664297i	$0.231269\pi$
$3$	34.2927	+	59.3966i	0.733292	+	1.27010i	0.955469	+	0.295092i	$0.0953505\pi$
$3$	34.2927	+	59.3966i	0.733292	+	1.27010i	−0.222177	+	0.975006i	$0.571316\pi$
$4$	−38.5696	+	66.8044i	−0.301325	+	0.521910i
$5$		−	466.432i		−	1.66876i	−0.551191	−	0.834379i	$-0.685827\pi$
$5$		−	466.432i		−	1.66876i	0.551191	−	0.834379i	$-0.314173\pi$
$6$	423.598	+	244.564i	0.800616	+	0.462236i
$7$	297.047	+	171.500i	0.327327	+	0.188982i
$7$	297.047	+	171.500i	0.327327	+	0.188982i
$8$			1462.99i			1.01024i
$9$	−1258.47	+	2179.74i	−0.575434	+	0.996681i
$10$	−1663.22	−	2880.78i	−0.525957	−	0.910984i
$11$	−5028.66	+	2903.30i	−1.13914	+	0.657683i	−0.946218	−	0.323531i	$-0.895130\pi$
$11$	−5028.66	+	2903.30i	−1.13914	+	0.657683i	−0.192923	+	0.981214i	$0.561797\pi$
$12$	−5290.61			−0.883836
$13$	4984.00	+	6156.97i	0.629182	+	0.777258i
$13$	4984.00	+	6156.97i	0.629182	+	0.777258i
$14$	2446.17			0.238253
$15$	27704.5	−	15995.2i	2.11949	−	1.22369i
$16$	279.874	+	484.757i	0.0170822	+	0.0295872i
$17$	−12360.5	+	21409.0i	−0.610190	+	1.05688i	0.381018	+	0.924568i	$0.375574\pi$
$17$	−12360.5	+	21409.0i	−0.610190	+	1.05688i	−0.991208	+	0.132313i	$0.957760\pi$
$18$			17950.1i			0.725458i
$19$	−4995.63	−	2884.23i	−0.167091	−	0.0964700i	0.414122	−	0.910221i	$-0.364089\pi$
$19$	−4995.63	−	2884.23i	−0.167091	−	0.0964700i	−0.581213	+	0.813751i	$0.697422\pi$
$20$	31159.7	+	17990.1i	0.870941	+	0.502838i
$21$			23524.8i			0.554317i
$22$	−20705.4	+	35862.8i	−0.414576	+	0.718066i
$23$	32597.2	+	56460.1i	0.558642	+	0.967596i	0.997610	+	0.0690934i	$0.0220106\pi$
$23$	32597.2	+	56460.1i	0.558642	+	0.967596i	−0.438968	+	0.898502i	$0.644656\pi$
$24$	−86896.5	+	50169.7i	−1.28311	+	0.740802i
$25$	−139434.			−1.78475
$26$	52737.0	+	20254.6i	0.588449	+	0.226004i
$27$	−22629.6			−0.221261
$28$	−22913.9	+	13229.4i	−0.197263	+	0.113890i
$29$	−100172.	−	173503.i	−0.762700	−	1.32103i	−0.941454	−	0.337141i	$-0.890540\pi$
$29$	−100172.	−	173503.i	−0.762700	−	1.32103i	0.178754	−	0.983894i	$-0.442793\pi$
$30$	114073.	−	197580.i	0.771360	−	1.33603i
$31$			138683.i			0.836100i	0.908424	+	0.418050i	$0.137286\pi$
$31$			138683.i			0.836100i	−0.908424	+	0.418050i	$0.862714\pi$
$32$	−158717.	−	91635.2i	−0.856245	−	0.494353i
$33$	−344892.	−	199123.i	−1.67065	−	0.964548i
$34$			176303.i			0.769276i
$35$	79993.1	−	138552.i	0.315366	−	0.546229i
$36$	−97077.6	−	168143.i	−0.346785	−	0.600649i
$37$	−482434.	+	278533.i	−1.56578	+	0.904005i	−0.569130	+	0.822247i	$0.692720\pi$
$37$	−482434.	+	278533.i	−1.56578	+	0.904005i	−0.996652	+	0.0817578i	$0.973947\pi$
$38$	−41138.8			−0.121621
$39$	−194788.	+	507172.i	−0.525820	+	1.36908i
$40$	682384.			1.68585
$41$	38228.6	−	22071.3i	0.0866253	−	0.0500131i	−0.456062	−	0.889948i	$-0.650740\pi$
$41$	38228.6	−	22071.3i	0.0866253	−	0.0500131i	0.542687	+	0.839935i	$0.317407\pi$
$42$	83885.6	+	145294.i	0.174709	+	0.302605i
$43$	211141.	−	365707.i	0.404979	−	0.701444i	−0.589340	−	0.807885i	$-0.700612\pi$
$43$	211141.	−	365707.i	0.404979	−	0.701444i	0.994319	+	0.106441i	$0.0339455\pi$
$44$		−	447915.i		−	0.792705i
$45$	1.01670e6	+	586993.i	1.66322	+	0.960260i
$46$	402655.	+	232473.i	0.609931	+	0.352144i
$47$			1.14628e6i			1.61045i	0.592971	+	0.805224i	$0.297955\pi$
$47$			1.14628e6i			1.61045i	−0.592971	+	0.805224i	$0.702045\pi$
$48$	−19195.3	+	33247.2i	−0.0250524	+	0.0433921i
$49$	58824.5	+	101887.i	0.0714286	+	0.123718i
$50$	−861173.	+	497198.i	−0.974306	+	0.562516i
$51$	−1.69550e6			−1.78979
$52$	−603543.	+	95482.0i	−0.595246	+	0.0941694i
$53$	174919.			0.161388			0.0806941	−	0.996739i	$-0.474286\pi$
$53$	174919.			0.161388			0.0806941	+	0.996739i	$0.474286\pi$
$54$	−139766.	+	80693.7i	−0.120788	+	0.0697367i
$55$	1.35419e6	+	2.34553e6i	1.09751	+	1.90095i
$56$	−250902.	+	434575.i	−0.190918	+	0.330679i
$57$		−	395632.i		−	0.282963i
$58$	−1.23737e6	−	714395.i	−0.832724	−	0.480774i
$59$	908340.	+	524430.i	0.575793	+	0.332434i	0.759460	−	0.650554i	$-0.225463\pi$
$59$	908340.	+	524430.i	0.575793	+	0.332434i	−0.183667	+	0.982989i	$0.558797\pi$
$60$			2.46771e6i			1.47491i
$61$	1.32578e6	−	2.29631e6i	0.747852	−	1.29532i	−0.200999	−	0.979591i	$-0.564419\pi$
$61$	1.32578e6	−	2.29631e6i	0.747852	−	1.29532i	0.948851	−	0.315726i	$-0.102248\pi$
$62$	494522.	+	856538.i	0.263521	+	0.456432i
$63$	−747651.	+	431657.i	−0.376710	+	0.217494i
$64$	−1.37867e6			−0.657403
$65$	2.87181e6	−	2.32470e6i	1.29705	−	1.04995i
$66$	−2.84017e6			−1.21602
$67$	306224.	−	176798.i	0.124388	−	0.0718152i	−0.436515	−	0.899697i	$-0.643787\pi$
$67$	306224.	−	176798.i	0.124388	−	0.0718152i	0.560903	+	0.827882i	$0.310454\pi$
$68$	−953479.	−	1.65147e6i	−0.367731	−	0.636929i
$69$	−2.23569e6	+	3.87233e6i	−0.819295	+	1.41906i
$70$		−	1.14097e6i		−	0.397586i
$71$	2.46327e6	+	1.42217e6i	0.816786	+	0.471572i	0.849307	−	0.527899i	$-0.177020\pi$
$71$	2.46327e6	+	1.42217e6i	0.816786	+	0.471572i	−0.0325207	+	0.999471i	$0.510353\pi$
$72$	−3.18893e6	−	1.84113e6i	−1.00689	−	0.581328i
$73$		−	5.65331e6i		−	1.70088i	−0.526075	−	0.850438i	$-0.676337\pi$
$73$		−	5.65331e6i		−	1.70088i	0.526075	−	0.850438i	$-0.323663\pi$
$74$	−1.98641e6	+	3.44056e6i	−0.569846	+	0.987003i
$75$	−4.78156e6	−	8.28190e6i	−1.30874	−	2.26681i
$76$	385359.	−	222487.i	0.100697	−	0.0581376i
$77$	−1.99166e6			−0.497162
$78$	605439.	+	3.82699e6i	0.144457	+	0.913116i
$79$	7.24670e6			1.65366			0.826828	−	0.562455i	$-0.190143\pi$
$79$	7.24670e6			1.65366			0.826828	+	0.562455i	$0.190143\pi$
$80$	226106.	−	130542.i	0.0493739	−	0.0285060i
$81$	1.97625e6	+	3.42297e6i	0.413185	+	0.715658i
$82$	157405.	−	272634.i	0.0315261	−	0.0546049i
$83$			3.18628e6i			0.611660i	0.952086	+	0.305830i	$0.0989340\pi$
$83$			3.18628e6i			0.611660i	−0.952086	+	0.305830i	$0.901066\pi$
$84$	−1.57156e6	−	907340.i	−0.289303	−	0.167029i
$85$	9.98586e6	+	5.76534e6i	1.76368	+	1.01826i
$86$		−	3.01158e6i		−	0.510563i
$87$	6.87034e6	−	1.18998e7i	1.11856	−	1.93741i
$88$	−4.24748e6	−	7.35686e6i	−0.664419	−	1.15081i
$89$	−9.30419e6	+	5.37178e6i	−1.39899	+	0.807706i	−0.994287	−	0.106743i	$-0.965958\pi$
$89$	−9.30419e6	+	5.37178e6i	−1.39899	+	0.807706i	−0.404701	+	0.914449i	$0.632624\pi$
$90$	8.37249e6			1.21061
$91$	424562.	+	2.68366e6i	0.0590604	+	0.373322i
$92$	−5.02904e6			−0.673330
$93$	−8.23732e6	+	4.75582e6i	−1.06193	+	0.613105i
$94$	4.08744e6	+	7.07965e6i	0.507579	+	0.879152i
$95$	−1.34530e6	+	2.33012e6i	−0.160985	+	0.278834i
$96$		−	1.25697e7i		−	1.45002i
$97$	1.06466e7	+	6.14680e6i	1.18443	+	0.683830i	0.957035	−	0.289973i	$-0.0936462\pi$
$97$	1.06466e7	+	6.14680e6i	1.18443	+	0.683830i	0.227394	+	0.973803i	$0.426980\pi$
$98$	726626.	+	419518.i	0.0779865	+	0.0450255i
$99$		−	1.46149e7i		−	1.51381i
$100$	5.37790e6	−	9.31479e6i	0.537790	−	0.931479i
$101$	−1.70877e6	−	2.95967e6i	−0.165028	−	0.285837i	0.771637	−	0.636063i	$-0.219438\pi$
$101$	−1.70877e6	−	2.95967e6i	−0.165028	−	0.285837i	−0.936665	+	0.350226i	$0.886105\pi$
$102$	−1.04718e7	+	6.04588e6i	−0.977057	+	0.564104i
$103$	9.26377e6			0.835328			0.417664	−	0.908601i	$-0.362849\pi$
$103$	9.26377e6			0.835328			0.417664	+	0.908601i	$0.362849\pi$
$104$	−9.00756e6	+	7.29153e6i	−0.785218	+	0.635627i
$105$	1.09727e7			0.925020
$106$	1.08034e6	−	623734.i	0.0881027	−	0.0508661i
$107$	−3.15501e6	−	5.46463e6i	−0.248976	−	0.431239i	0.714266	−	0.699874i	$-0.246761\pi$
$107$	−3.15501e6	−	5.46463e6i	−0.248976	−	0.431239i	−0.963242	+	0.268636i	$0.913427\pi$
$108$	872815.	−	1.51176e6i	0.0666713	−	0.115478i
$109$		−	5.65006e6i		−	0.417889i	−0.977928	−	0.208944i	$-0.932997\pi$
$109$		−	5.65006e6i		−	0.417889i	0.977928	−	0.208944i	$-0.0670028\pi$
$110$	1.67275e7	+	9.65765e6i	1.19828	+	0.691826i
$111$	−3.30879e7	−	1.91033e7i	−2.29635	−	1.32580i
$112$			191994.i			0.0129129i
$113$	−825605.	+	1.42999e6i	−0.0538267	+	0.0932306i	−0.891683	−	0.452660i	$-0.850475\pi$
$113$	−825605.	+	1.42999e6i	−0.0538267	+	0.0932306i	0.837857	+	0.545890i	$0.183809\pi$
$114$	−1.41076e6	−	2.44351e6i	−0.0891838	−	0.154471i
$115$	2.63348e7	−	1.52044e7i	1.61468	−	0.932238i
$116$	1.54544e7			0.919281
$117$	−1.96928e7	+	3.11545e6i	−1.13673	+	0.179834i
$118$	7.48014e6			0.419105
$119$	−7.34330e6	+	4.23966e6i	−0.399463	+	0.230630i
$120$	2.34008e7	+	4.05313e7i	1.23622	+	2.14120i
$121$	7.11466e6	−	1.23230e7i	0.365095	−	0.632363i
$122$		−	1.89100e7i		−	0.942828i
$123$	2.62192e6	+	1.51377e6i	0.127043	+	0.0733484i
$124$	−9.26466e6	−	5.34895e6i	−0.436369	−	0.251938i
$125$			2.85964e7i			1.30956i
$126$	−3.07844e6	+	5.33201e6i	−0.137099	+	0.237462i
$127$	1.03668e7	+	1.79558e7i	0.449088	+	0.777842i	0.998327	−	0.0578227i	$-0.0184158\pi$
$127$	1.03668e7	+	1.79558e7i	0.449088	+	0.777842i	−0.549239	+	0.835665i	$0.685082\pi$
$128$	1.18008e7	−	6.81317e6i	0.497365	−	0.287154i
$129$	2.89623e7			1.18787
$130$	9.44739e6	−	2.45982e7i	0.377147	−	0.981979i
$131$	1.46333e7			0.568712			0.284356	−	0.958719i	$-0.408220\pi$
$131$	1.46333e7			0.568712			0.284356	+	0.958719i	$0.408220\pi$
$132$	2.66047e7	−	1.53602e7i	1.00681	−	0.581284i
$133$	−989291.	−	1.71350e6i	−0.0364622	−	0.0631545i
$134$	1.26087e6	−	2.18389e6i	0.0452692	−	0.0784086i
$135$			1.05552e7i			0.369231i
$136$	−3.13211e7	−	1.80833e7i	−1.06771	−	0.616440i
$137$	−7.24458e6	−	4.18266e6i	−0.240708	−	0.138973i	0.374794	−	0.927108i	$-0.377713\pi$
$137$	−7.24458e6	−	4.18266e6i	−0.240708	−	0.138973i	−0.615502	+	0.788135i	$0.711047\pi$
$138$			3.18885e7i			1.03290i
$139$	2.23089e7	−	3.86401e7i	0.704572	−	1.22036i	−0.262273	−	0.964994i	$-0.584472\pi$
$139$	2.23089e7	−	3.86401e7i	0.704572	−	1.22036i	0.966846	−	0.255362i	$-0.0821945\pi$
$140$	6.17060e6	+	1.06878e7i	0.190055	+	0.329185i
$141$	−6.80849e7	+	3.93088e7i	−2.04543	+	1.18093i
$142$	2.02850e7			0.594518
$143$	−4.29383e7	−	1.64912e7i	−1.22792	−	0.471603i
$144$	−1.40886e6			−0.0393187
$145$	−8.09274e7	+	4.67235e7i	−2.20449	+	1.27276i
$146$	−2.01588e7	−	3.49161e7i	−0.536080	−	0.928518i
$147$	−4.03450e6	+	6.98796e6i	−0.104756	+	0.181443i
$148$		−	4.29716e7i		−	1.08960i
$149$	9.06744e6	+	5.23509e6i	0.224560	+	0.129650i	0.608060	−	0.793891i	$-0.291948\pi$
$149$	9.06744e6	+	5.23509e6i	0.224560	+	0.129650i	−0.383500	+	0.923541i	$0.625281\pi$
$150$	−5.90638e7	−	3.41005e7i	−1.42890	−	0.824977i
$151$			1.87332e7i			0.442784i	0.975185	+	0.221392i	$0.0710601\pi$
$151$			1.87332e7i			0.442784i	−0.975185	+	0.221392i	$0.928940\pi$
$152$	4.21959e6	−	7.30855e6i	0.0974581	−	0.168802i
$153$	−3.11108e7	−	5.38855e7i	−0.702249	−	1.21633i
$154$	−1.23009e7	+	7.10194e6i	−0.271403	+	0.156695i
$155$	6.46863e7			1.39525
$156$	−2.63684e7	−	3.25741e7i	−0.556094	−	0.686968i
$157$	2.22478e7			0.458815			0.229408	−	0.973330i	$-0.426321\pi$
$157$	2.22478e7			0.458815			0.229408	+	0.973330i	$0.426321\pi$
$158$	4.47572e7	−	2.58406e7i	0.902740	−	0.521197i
$159$	5.99844e6	+	1.03896e7i	0.118345	+	0.204979i
$160$	−4.27416e7	+	7.40306e7i	−0.824956	+	1.42887i
$161$			2.23617e7i			0.422293i
$162$	2.44115e7	+	1.40940e7i	0.451120	+	0.260454i
$163$	9.05609e6	+	5.22854e6i	0.163789	+	0.0945635i	0.579654	−	0.814863i	$-0.303188\pi$
$163$	9.05609e6	+	5.22854e6i	0.163789	+	0.0945635i	−0.415865	+	0.909426i	$0.636521\pi$
$164$			3.40512e6i			0.0602807i
$165$	−9.28776e7	+	1.60869e8i	−1.60960	+	2.78790i
$166$	1.13618e7	+	1.96791e7i	0.192782	+	0.333909i
$167$	−9.32694e7	+	5.38491e7i	−1.54964	+	0.894687i	−0.551474	+	0.834192i	$0.685934\pi$
$167$	−9.32694e7	+	5.38491e7i	−1.54964	+	0.894687i	−0.998169	+	0.0604946i	$0.980732\pi$
$168$	−3.44164e7			−0.559994
$169$	−1.30679e7	+	6.13727e7i	−0.208259	+	0.978074i
$170$	8.22331e7			1.28374
$171$	1.25738e7	−	7.25946e6i	0.192300	−	0.111024i
$172$	1.62872e7	+	2.82103e7i	0.244060	+	0.422725i
$173$	4.15761e7	−	7.20120e7i	0.610496	−	1.05741i	−0.380661	−	0.924715i	$-0.624304\pi$
$173$	4.15761e7	−	7.20120e7i	0.610496	−	1.05741i	0.991157	−	0.132695i	$-0.0423632\pi$
$174$		−	9.79941e7i		−	1.41019i
$175$	−4.14183e7	−	2.39129e7i	−0.584197	−	0.337286i
$176$	−2.81478e6	−	1.62512e6i	−0.0389180	−	0.0224693i
$177$			7.19364e7i			0.975085i
$178$	−3.83098e7	+	6.63546e7i	−0.509143	+	0.881862i
$179$	2.66885e7	+	4.62259e7i	0.347808	+	0.602421i	0.985860	−	0.167573i	$-0.0535929\pi$
$179$	2.66885e7	+	4.62259e7i	0.347808	+	0.602421i	−0.638052	+	0.769993i	$0.720260\pi$
$180$	−7.84274e7	+	4.52801e7i	−1.00234	+	0.578700i
$181$	−3.97539e7			−0.498316			−0.249158	−	0.968463i	$-0.580154\pi$
$181$	−3.97539e7			−0.498316			−0.249158	+	0.968463i	$0.580154\pi$
$182$	1.21917e7	+	1.50610e7i	0.149904	+	0.185184i
$183$	1.81857e8			2.19357
$184$	−8.26003e7	+	4.76893e7i	−0.977506	+	0.564363i
$185$	1.29917e8	+	2.25022e8i	1.50857	+	2.61291i
$186$	−3.39170e7	+	5.87459e7i	−0.386476	+	0.669395i
$187$		−	1.43545e8i		−	1.60525i
$188$	−7.65763e7	−	4.42113e7i	−0.840508	−	0.485267i
$189$	−6.72206e6	−	3.88098e6i	−0.0724246	−	0.0418144i
$190$			1.91885e7i			0.202956i
$191$	−3.81281e7	+	6.60398e7i	−0.395939	+	0.685786i	−0.993221	−	0.116245i	$-0.962914\pi$
$191$	−3.81281e7	+	6.60398e7i	−0.395939	+	0.685786i	0.597282	+	0.802032i	$0.296247\pi$
$192$	−4.72784e7	−	8.18886e7i	−0.482068	−	0.834967i
$193$	1.33027e8	−	7.68034e7i	1.33196	−	0.769007i	0.346359	−	0.938102i	$-0.387418\pi$
$193$	1.33027e8	−	7.68034e7i	1.33196	−	0.769007i	0.985600	+	0.169095i	$0.0540846\pi$
$194$	8.76741e7			0.862115
$195$	2.36561e8	+	9.08555e7i	2.28466	+	0.877466i
$196$	−9.07534e6			−0.0860928
$197$	−2.69567e7	+	1.55635e7i	−0.251209	+	0.145036i	−0.620318	−	0.784351i	$-0.712996\pi$
$197$	−2.69567e7	+	1.55635e7i	−0.251209	+	0.145036i	0.369109	+	0.929386i	$0.379663\pi$
$198$	−5.21144e7	−	9.02647e7i	−0.477122	−	0.826399i
$199$	8.67691e6	−	1.50289e7i	0.0780512	−	0.135189i	−0.824358	−	0.566069i	$-0.808464\pi$
$199$	8.67691e6	−	1.50289e7i	0.0780512	−	0.135189i	0.902409	+	0.430880i	$0.141797\pi$
$200$		−	2.03990e8i		−	1.80303i
$201$	2.10024e7	+	1.21258e7i	0.182425	+	0.105323i
$202$	−2.11074e7	−	1.21864e7i	−0.180180	−	0.104027i
$203$		−	6.87180e7i		−	0.576547i
$204$	6.53947e7	−	1.13267e8i	0.539308	−	0.934109i
$205$	−1.02947e7	−	1.78310e7i	−0.0834598	−	0.144557i
$206$	5.72150e7	−	3.30331e7i	0.456011	−	0.263278i
$207$	−1.64091e8			−1.28585
$208$	−1.58974e6	+	4.13921e6i	−0.0122491	+	0.0318930i
$209$	3.34951e7			0.253787
$210$	6.77698e7	−	3.91269e7i	0.504974	−	0.291547i
$211$	−6.51524e7	−	1.12847e8i	−0.477465	−	0.826994i	0.522201	−	0.852822i	$-0.325111\pi$
$211$	−6.51524e7	−	1.12847e8i	−0.477465	−	0.826994i	−0.999666	+	0.0258282i	$0.991778\pi$
$212$	−6.74655e6	+	1.16854e7i	−0.0486303	+	0.0842301i
$213$			1.95080e8i			1.38320i
$214$	−3.89720e7	−	2.25005e7i	−0.271834	−	0.156944i
$215$	−1.70577e8	−	9.84828e7i	−1.17054	−	0.675812i
$216$		−	3.31069e7i		−	0.223527i
$217$	−2.37842e7	+	4.11954e7i	−0.158008	+	0.273678i
$218$	−2.01472e7	−	3.48960e7i	−0.131710	−	0.228128i
$219$	3.35788e8	−	1.93867e8i	2.16028	−	1.24724i
$220$	−2.08922e8			−1.32283
$221$	−1.93420e8	+	3.05994e7i	−1.20539	+	0.190696i
$222$	−2.72477e8			−1.67146
$223$	7.03949e7	−	4.06425e7i	0.425084	−	0.245422i	−0.272166	−	0.962250i	$-0.587740\pi$
$223$	7.03949e7	−	4.06425e7i	0.425084	−	0.245422i	0.697250	+	0.716828i	$0.254407\pi$
$224$	−3.14309e7	−	5.44399e7i	−0.186848	−	0.323630i
$225$	1.75474e8	−	3.03930e8i	1.02701	−	1.77883i
$226$			1.17759e7i			0.0678602i
$227$	−1.27099e8	−	7.33808e7i	−0.721195	−	0.416382i	0.0939976	−	0.995572i	$-0.470035\pi$
$227$	−1.27099e8	−	7.33808e7i	−0.721195	−	0.416382i	−0.815192	+	0.579191i	$0.803369\pi$
$228$	2.64300e7	+	1.52593e7i	0.147681	+	0.0852637i
$229$			3.08564e7i			0.169793i	0.996390	+	0.0848967i	$0.0270560\pi$
$229$			3.08564e7i			0.169793i	−0.996390	+	0.0848967i	$0.972944\pi$
$230$	1.08433e8	−	1.87811e8i	0.587643	−	1.01783i
$231$	−6.82994e7	−	1.18298e8i	−0.364565	−	0.631445i
$232$	2.53833e8	−	1.46550e8i	1.33457	−	0.770512i
$233$	1.65573e7			0.0857520			0.0428760	−	0.999080i	$-0.486348\pi$
$233$	1.65573e7			0.0857520			0.0428760	+	0.999080i	$0.486348\pi$
$234$	−1.10518e8	+	8.94632e7i	−0.563868	+	0.456446i
$235$	5.34659e8			2.68745
$236$	−7.00685e7	+	4.04541e7i	−0.347001	+	0.200341i
$237$	2.48509e8	+	4.30429e8i	1.21261	+	2.10031i
$238$	−3.02359e7	+	5.23701e7i	−0.145380	+	0.251805i
$239$		−	2.94891e7i		−	0.139723i	−0.997557	−	0.0698617i	$-0.977744\pi$
$239$		−	2.94891e7i		−	0.139723i	0.997557	−	0.0698617i	$-0.0222558\pi$
$240$	1.55076e7	+	8.95329e6i	0.0724109	+	0.0418065i
$241$	1.71077e8	+	9.87711e7i	0.787283	+	0.454538i	0.839005	−	0.544123i	$-0.183138\pi$
$241$	1.71077e8	+	9.87711e7i	0.787283	+	0.454538i	−0.0517220	+	0.998662i	$0.516471\pi$
$242$		−	1.01479e8i		−	0.460280i
$243$	−1.60287e8	+	2.77626e8i	−0.716601	+	1.24119i
$244$	1.02269e8	+	1.77135e8i	0.450692	+	0.780622i
$245$	4.75234e7	−	2.74376e7i	0.206455	−	0.119197i
$246$	2.15914e7			0.0924715
$247$	−7.14014e6	−	4.51330e7i	−0.0301486	−	0.190570i
$248$	−2.02892e8			−0.844663
$249$	−1.89254e8	+	1.09266e8i	−0.776869	+	0.448526i
$250$	1.01970e8	+	1.76617e8i	0.412746	+	0.714897i
$251$	1.19522e8	−	2.07019e8i	0.477080	−	0.826328i	−0.522575	−	0.852594i	$-0.675028\pi$
$251$	1.19522e8	−	2.07019e8i	0.477080	−	0.826328i	0.999655	+	0.0262660i	$0.00836169\pi$
$252$		−	6.65952e7i		−	0.262145i
$253$	−3.27841e8	−	1.89279e8i	−1.27274	−	0.734819i
$254$	1.28055e8	+	7.39326e7i	0.490319	+	0.283086i
$255$			7.90835e8i			2.98673i
$256$	1.36824e8	−	2.36987e8i	0.509711	−	0.882845i
$257$	1.63055e8	+	2.82420e8i	0.599196	+	1.03784i	0.992940	+	0.118618i	$0.0378463\pi$
$257$	1.63055e8	+	2.82420e8i	0.599196	+	1.03784i	−0.393744	+	0.919220i	$0.628820\pi$
$258$	1.78878e8	−	1.03275e8i	0.648466	−	0.374392i
$259$	−1.91074e8			−0.683364
$260$	4.45359e7	+	2.81512e8i	0.157146	+	0.993322i
$261$	5.04256e8			1.75553
$262$	9.03783e7	−	5.21799e7i	0.310463	−	0.179246i
$263$	−2.06277e8	−	3.57281e8i	−0.699205	−	1.21106i	−0.968742	−	0.248069i	$-0.920204\pi$
$263$	−2.06277e8	−	3.57281e8i	−0.699205	−	1.21106i	0.269537	−	0.962990i	$-0.413129\pi$
$264$	2.91315e8	−	5.04572e8i	0.974427	−	1.68776i
$265$		−	8.15879e7i		−	0.269318i
$266$	−1.22202e7	−	7.05531e6i	−0.0398099	−	0.0229842i
$267$	−6.38131e8	−	3.68425e8i	−2.05173	−	1.18457i
$268$			2.72761e7i			0.0865587i
$269$	−2.31962e7	+	4.01769e7i	−0.0726580	+	0.125847i	−0.900065	−	0.435755i	$-0.856481\pi$
$269$	−2.31962e7	+	4.01769e7i	−0.0726580	+	0.125847i	0.827407	+	0.561602i	$0.189815\pi$
$270$	3.76381e7	+	6.51911e7i	0.116374	+	0.201565i
$271$	−4.05199e8	+	2.33942e8i	−1.23673	+	0.714028i	−0.968425	−	0.249305i	$-0.919798\pi$
$271$	−4.05199e8	+	2.33942e8i	−1.23673	+	0.714028i	−0.268309	+	0.963333i	$0.586465\pi$
$272$	−1.38376e7			−0.0416935
$273$	−1.44841e8	+	1.17248e8i	−0.430847	+	0.348766i
$274$	−5.96588e7			−0.175205
$275$	7.01164e8	−	4.04817e8i	2.03308	−	1.17380i
$276$	−1.72459e8	−	2.98708e8i	−0.493748	−	0.855196i
$277$	−8.68052e6	+	1.50351e7i	−0.0245395	+	0.0425037i	−0.878034	−	0.478598i	$-0.841145\pi$
$277$	−8.68052e6	+	1.50351e7i	−0.0245395	+	0.0425037i	0.853495	+	0.521101i	$0.174479\pi$
$278$		−	3.18199e8i		−	0.888265i
$279$	−3.02294e8	−	1.74529e8i	−0.833325	−	0.481120i
$280$	2.02700e8	+	1.17029e8i	0.551824	+	0.318596i
$281$			3.53454e8i			0.950299i	0.879905	+	0.475150i	$0.157606\pi$
$281$			3.53454e8i			0.950299i	−0.879905	+	0.475150i	$0.842394\pi$
$282$	−2.80338e8	+	4.85560e8i	−0.744407	+	1.28935i
$283$	−2.53799e7	−	4.39593e7i	−0.0665638	−	0.115292i	0.830823	−	0.556537i	$-0.187870\pi$
$283$	−2.53799e7	−	4.39593e7i	−0.0665638	−	0.115292i	−0.897387	+	0.441245i	$0.854537\pi$
$284$	−1.90015e8	+	1.09705e8i	−0.492236	+	0.284192i
$285$	−1.84535e8			−0.472196
$286$	−3.24001e8	+	5.12578e7i	−0.818966	+	0.129562i
$287$	1.51409e7			0.0378064
$288$	3.99482e8	−	2.30641e8i	0.985425	−	0.568935i
$289$	−1.00395e8	−	1.73890e8i	−0.244665	−	0.423772i
$290$	−3.33217e8	+	5.77148e8i	−0.802295	+	1.38962i
$291$			8.43161e8i			2.00579i
$292$	3.77666e8	+	2.18046e8i	0.887704	+	0.512516i
$293$	−2.49960e8	−	1.44315e8i	−0.580542	−	0.335176i	0.180806	−	0.983519i	$-0.442129\pi$
$293$	−2.49960e8	−	1.44315e8i	−0.580542	−	0.335176i	−0.761349	+	0.648342i	$0.775463\pi$
$294$			5.75455e7i			0.132067i
$295$	2.44611e8	−	4.23679e8i	0.554752	−	0.960859i
$296$	−4.07490e8	−	7.05794e8i	−0.913264	−	1.58182i
$297$	1.13797e8	−	6.57005e7i	0.252047	−	0.145520i
$298$	7.46699e7			0.163452
$299$	−1.85158e8	+	4.82097e8i	−0.400584	+	1.04300i
$300$	7.37690e8			1.57743
$301$	1.25437e8	−	7.24213e7i	0.265121	−	0.153068i
$302$	6.67995e7	+	1.15700e8i	0.139556	+	0.241718i
$303$	1.17196e8	−	2.02990e8i	0.242028	−	0.419204i
$304$		−	3.22889e6i		−	0.00659167i
$305$	−1.07107e9	−	6.18384e8i	−2.16157	−	1.24798i
$306$	−3.84294e8	−	2.21872e8i	−0.766723	−	0.442668i
$307$			4.17717e7i			0.0823945i	0.999151	+	0.0411972i	$0.0131172\pi$
$307$			4.17717e7i			0.0823945i	−0.999151	+	0.0411972i	$0.986883\pi$
$308$	7.68175e7	−	1.33052e8i	0.149807	−	0.259474i
$309$	3.17679e8	+	5.50237e8i	0.612540	+	1.06095i
$310$	3.99517e8	−	2.30661e8i	0.761674	−	0.439753i
$311$	5.32188e7			0.100324			0.0501619	−	0.998741i	$-0.484026\pi$
$311$	5.32188e7			0.100324			0.0501619	+	0.998741i	$0.484026\pi$
$312$	−7.41986e8	−	2.84973e8i	−1.38310	−	0.531205i
$313$	−7.43409e8			−1.37032			−0.685161	−	0.728391i	$-0.740268\pi$
$313$	−7.43409e8			−1.37032			−0.685161	+	0.728391i	$0.740268\pi$
$314$	1.37407e8	−	7.93320e7i	0.250470	−	0.144609i
$315$	2.01338e8	+	3.48728e8i	0.362944	+	0.628638i
$316$	−2.79502e8	+	4.84111e8i	−0.498287	+	0.863059i
$317$		−	2.66921e8i		−	0.470626i	−0.971920	−	0.235313i	$-0.924388\pi$
$317$		−	2.66921e8i		−	0.470626i	0.971920	−	0.235313i	$-0.0756116\pi$
$318$	7.40954e7	+	4.27790e7i	0.129210	+	0.0745995i
$319$	1.00746e9	+	5.81658e8i	1.73765	+	1.00323i
$320$			6.43057e8i			1.09705i
$321$	2.16387e8	−	3.74794e8i	0.365144	−	0.632448i
$322$	7.97383e7	+	1.38111e8i	0.133098	+	0.230532i
$323$	1.23497e8	−	7.13012e7i	0.203915	−	0.117730i
$324$	−3.04893e8			−0.498012
$325$	−6.94938e8	−	8.58489e8i	−1.12293	−	1.38721i
$326$	7.45765e7			0.119218
$327$	3.35595e8	−	1.93756e8i	0.530760	−	0.306434i
$328$	3.22900e7	+	5.59279e7i	0.0505254	+	0.0875125i
$329$	−1.96586e8	+	3.40497e8i	−0.304346	+	0.527143i
$330$			1.32475e9i			2.02924i
$331$	2.85611e8	+	1.64898e8i	0.432890	+	0.249929i	0.700577	−	0.713577i	$-0.252926\pi$
$331$	2.85611e8	+	1.64898e8i	0.432890	+	0.249929i	−0.267687	+	0.963506i	$0.586259\pi$
$332$	−2.12857e8	−	1.22893e8i	−0.319231	−	0.184308i
$333$		−	1.40211e9i		−	2.08078i
$334$	−3.84035e8	+	6.65168e8i	−0.563972	+	0.976829i
$335$	−8.24643e7	−	1.42832e8i	−0.119842	−	0.207573i
$336$	−1.14038e7	+	6.58398e6i	−0.0164007	+	0.00946893i
$337$	5.57433e8			0.793393			0.396696	−	0.917950i	$-0.370157\pi$
$337$	5.57433e8			0.793393			0.396696	+	0.917950i	$0.370157\pi$
$338$	1.38135e8	+	4.25649e8i	0.194578	+	0.599575i
$339$	−1.13249e8			−0.157883
$340$	−7.70300e8	+	4.44733e8i	−1.06288	+	0.613654i
$341$	−4.02638e8	−	6.97390e8i	−0.549889	−	0.952436i
$342$	5.17722e7	−	8.96720e7i	0.0699850	−	0.121218i
$343$			4.03536e7i			0.0539949i
$344$	5.35024e8	+	3.08896e8i	0.708629	+	0.409127i
$345$	1.80618e9	+	1.04280e9i	2.36807	+	1.36720i
$346$		−	5.93015e8i		−	0.769661i
$347$	−4.78524e8	+	8.28827e8i	−0.614823	+	1.06491i	0.375592	+	0.926785i	$0.377439\pi$
$347$	−4.78524e8	+	8.28827e8i	−0.614823	+	1.06491i	−0.990415	+	0.138120i	$0.955894\pi$
$348$	5.29972e8	+	9.17938e8i	0.674101	+	1.16758i
$349$	−7.12058e8	+	4.11107e8i	−0.896657	+	0.517685i	−0.876114	−	0.482104i	$-0.839873\pi$
$349$	−7.12058e8	+	4.11107e8i	−0.896657	+	0.517685i	−0.0205428	+	0.999789i	$0.506539\pi$
$350$	−3.41078e8			−0.425222
$351$	−1.12786e8	−	1.39330e8i	−0.139213	−	0.171977i
$352$	1.06418e9			1.30051
$353$	1.82980e8	−	1.05644e8i	0.221408	−	0.127830i	−0.385194	−	0.922836i	$-0.625866\pi$
$353$	1.82980e8	−	1.05644e8i	0.221408	−	0.127830i	0.606602	+	0.795006i	$0.292532\pi$
$354$	2.56514e8	+	4.44295e8i	0.307326	+	0.532304i
$355$	6.63346e8	−	1.14895e9i	0.786939	−	1.36302i
$356$		−	8.28749e8i		−	0.973527i
$357$	−5.03643e8	−	2.90778e8i	−0.585847	−	0.338239i
$358$	3.29668e8	+	1.90334e8i	0.379740	+	0.219243i
$359$			8.73870e8i			0.996819i	0.866942	+	0.498409i	$0.166082\pi$
$359$			8.73870e8i			0.996819i	−0.866942	+	0.498409i	$0.833918\pi$
$360$	−8.58762e8	+	1.48742e9i	−0.970095	+	1.68025i
$361$	−4.30298e8	−	7.45299e8i	−0.481387	−	0.833787i
$362$	−2.45529e8	+	1.41756e8i	−0.272034	+	0.157059i
$363$	9.75923e8			1.07088
$364$	−1.95656e8	−	7.51451e7i	−0.212637	−	0.0816668i
$365$	−2.63688e9			−2.83835
$366$	1.12319e9	−	6.48475e8i	1.19748	−	0.691368i
$367$	−3.27461e8	−	5.67179e8i	−0.345803	−	0.598948i	0.639696	−	0.768628i	$-0.279060\pi$
$367$	−3.27461e8	−	5.67179e8i	−0.345803	−	0.598948i	−0.985499	+	0.169679i	$0.945727\pi$
$368$	−1.82463e7	+	3.16034e7i	−0.0190856	+	0.0330573i
$369$			1.11105e8i			0.115117i
$370$	1.60479e9	+	9.26525e8i	1.64707	+	0.950935i
$371$	5.19592e7	+	2.99986e7i	0.0528267	+	0.0304995i
$372$		−	7.33719e8i		−	0.738975i
$373$	4.63892e8	−	8.03485e8i	0.462846	−	0.801672i	−0.536256	−	0.844056i	$-0.680162\pi$
$373$	4.63892e8	−	8.03485e8i	0.462846	−	0.801672i	0.999101	+	0.0423834i	$0.0134951\pi$
$374$	−5.11858e8	−	8.86565e8i	−0.505940	−	0.876314i
$375$	−1.69853e9	+	9.80645e8i	−1.66327	+	0.960290i
$376$	−1.67699e9			−1.62694
$377$	5.68995e8	−	1.48150e9i	0.546907	−	1.42399i
$378$	−5.53559e7			−0.0527160
$379$	−7.97340e8	+	4.60344e8i	−0.752326	+	0.434356i	−0.826534	−	0.562887i	$-0.809691\pi$
$379$	−7.97340e8	+	4.60344e8i	−0.752326	+	0.434356i	0.0742076	+	0.997243i	$0.476357\pi$
$380$	−1.03775e8	−	1.79744e8i	−0.0970176	−	0.168039i
$381$	−7.11009e8	+	1.23150e9i	−0.658625	+	1.14077i
$382$			5.43835e8i			0.499166i
$383$	−1.95200e6	−	1.12699e6i	−0.00177535	−	0.00102500i	0.499112	−	0.866537i	$-0.333660\pi$
$383$	−1.95200e6	−	1.12699e6i	−0.00177535	−	0.00102500i	−0.500887	+	0.865512i	$0.666993\pi$
$384$	8.09359e8	+	4.67284e8i	0.729427	+	0.421135i
$385$			9.28974e8i			0.829643i
$386$	5.47738e8	−	9.48710e8i	0.484749	−	0.839610i
$387$	5.31431e8	+	9.20465e8i	0.466078	+	0.807270i
$388$	−8.21268e8	+	4.74159e8i	−0.713795	+	0.412110i
$389$	−1.28329e8			−0.110536			−0.0552679	−	0.998472i	$-0.517601\pi$
$389$	−1.28329e8			−0.110536			−0.0552679	+	0.998472i	$0.517601\pi$
$390$	1.78503e9	−	2.82396e8i	1.52377	−	0.241064i
$391$	−1.61167e9			−1.36351
$392$	−1.49059e8	+	8.60595e7i	−0.124985	+	0.0721602i
$393$	5.01814e8	+	8.69168e8i	0.417032	+	0.722320i
$394$	−1.10994e8	+	1.92247e8i	−0.0914243	+	0.158351i
$395$		−	3.38009e9i		−	2.75955i
$396$	9.76340e8	+	5.63690e8i	0.790074	+	0.456149i
$397$	−1.54508e8	−	8.92051e7i	−0.123932	−	0.0715522i	0.436752	−	0.899582i	$-0.356129\pi$
$397$	−1.54508e8	−	8.92051e7i	−0.123932	−	0.0715522i	−0.560684	+	0.828030i	$0.689462\pi$
$398$		−	1.23762e8i		−	0.0984003i
$399$	6.78509e7	−	1.17521e8i	0.0534749	−	0.0926213i
$400$	−3.90239e7	−	6.75914e7i	−0.0304874	−	0.0528058i
$401$	−3.34082e8	+	1.92882e8i	−0.258731	+	0.149378i	−0.623755	−	0.781620i	$-0.714394\pi$
$401$	−3.34082e8	+	1.92882e8i	−0.258731	+	0.149378i	0.365025	+	0.930998i	$0.381061\pi$
$402$	1.72954e8			0.132782
$403$	−8.53868e8	+	6.91198e8i	−0.649865	+	0.526059i
$404$	2.63626e8			0.198908
$405$	1.59658e9	−	9.21787e8i	1.19426	−	0.689506i
$406$	−2.45038e8	−	4.24418e8i	−0.181715	−	0.314740i
$407$	1.61733e9	−	2.80129e9i	1.18910	−	2.05958i
$408$		−	2.48049e9i		−	1.80812i
$409$	1.36306e9	+	7.86961e8i	0.985105	+	0.568750i	0.903807	−	0.427940i	$-0.140760\pi$
$409$	1.36306e9	+	7.86961e8i	0.985105	+	0.568750i	0.0812972	+	0.996690i	$0.474094\pi$
$410$	−1.27165e8	−	7.34189e7i	−0.0911223	−	0.0526095i
$411$		−	5.73738e8i		−	0.407631i
$412$	−3.57299e8	+	6.18861e8i	−0.251705	+	0.435966i
$413$	1.79880e8	+	3.11561e8i	0.125648	+	0.217629i
$414$	−1.01346e9	+	5.85123e8i	−0.701951	+	0.405271i
$415$	1.48618e9			1.02071
$416$	−2.26850e8	−	1.43392e9i	−0.154494	−	0.976561i
$417$	3.06012e9			2.06663
$418$	2.06873e8	−	1.19438e8i	0.138544	−	0.0799882i
$419$	3.96074e8	+	6.86020e8i	0.263043	+	0.455604i	0.967049	−	0.254590i	$-0.0819405\pi$
$419$	3.96074e8	+	6.86020e8i	0.263043	+	0.455604i	−0.704006	+	0.710194i	$0.748607\pi$
$420$	−4.23212e8	+	7.33025e8i	−0.278731	+	0.482777i
$421$			1.22503e9i			0.800127i	0.916487	+	0.400064i	$0.131012\pi$
$421$			1.22503e9i			0.800127i	−0.916487	+	0.400064i	$0.868988\pi$
$422$	−8.04791e8	−	4.64646e8i	−0.521302	−	0.300974i
$423$	−2.49858e9	−	1.44256e9i	−1.60510	−	0.926706i
$424$			2.55904e8i			0.163041i
$425$	1.72347e9	−	2.98514e9i	1.08904	−	1.88627i
$426$	6.95625e8	+	1.20486e9i	0.435955	+	0.755096i
$427$	7.87634e8	−	4.54741e8i	0.489584	−	0.282661i
$428$	4.86749e8			0.300090
$429$	−4.92946e8	−	3.11592e9i	−0.301439	−	1.90540i
$430$	−1.40470e9			−0.852006
$431$	−8.32689e8	+	4.80753e8i	−0.500971	+	0.289236i	−0.729114	−	0.684392i	$-0.760068\pi$
$431$	−8.32689e8	+	4.80753e8i	−0.500971	+	0.289236i	0.228144	+	0.973627i	$0.426734\pi$
$432$	−6.33346e6	−	1.09699e7i	−0.00377962	−	0.00654649i
$433$	1.24398e8	−	2.15464e8i	0.0736388	−	0.127546i	−0.826855	−	0.562416i	$-0.809872\pi$
$433$	1.24398e8	−	2.15464e8i	0.0736388	−	0.127546i	0.900494	+	0.434869i	$0.143205\pi$
$434$			3.39242e8i			0.199203i
$435$	−5.55043e9	−	3.20454e9i	−3.23307	−	1.86661i
$436$	3.77449e8	+	2.17920e8i	0.218100	+	0.125920i
$437$		−	3.76072e8i		−	0.215569i
$438$	1.38260e9	−	2.39473e9i	0.786206	−	1.36175i
$439$	9.22845e8	+	1.59841e9i	0.520599	+	0.901703i	0.999713	+	0.0239509i	$0.00762455\pi$
$439$	9.22845e8	+	1.59841e9i	0.520599	+	0.901703i	−0.479114	+	0.877752i	$0.659042\pi$
$440$	−3.43147e9	+	1.98116e9i	−1.92042	+	1.10875i
$441$	−2.96116e8			−0.164410
$442$	−1.08549e9	+	8.78692e8i	−0.597926	+	0.484015i
$443$	−7.51445e8			−0.410662			−0.205331	−	0.978693i	$-0.565827\pi$
$443$	−7.51445e8			−0.410662			−0.205331	+	0.978693i	$0.565827\pi$
$444$	2.55237e9	−	1.47361e9i	1.38389	−	0.798992i
$445$	2.50557e9	+	4.33977e9i	1.34787	+	2.33457i
$446$	2.89850e8	−	5.02034e8i	0.154704	−	0.267955i
$447$			7.18100e8i			0.380285i
$448$	−4.09530e8	−	2.36443e8i	−0.215186	−	0.124237i
$449$	2.95515e9	+	1.70616e9i	1.54070	+	0.889523i	0.998795	+	0.0490832i	$0.0156300\pi$
$449$	2.95515e9	+	1.70616e9i	1.54070	+	0.889523i	0.541905	+	0.840440i	$0.317703\pi$
$450$		−	2.50285e9i		−	1.29476i
$451$	−1.28159e8	+	2.21978e8i	−0.0657856	+	0.113944i
$452$	−6.36865e7	−	1.10308e8i	−0.0324386	−	0.0561854i
$453$	−1.11269e9	+	6.42411e8i	−0.562380	+	0.324690i
$454$	−1.04666e9			−0.524939
$455$	1.25175e9	−	1.98029e8i	0.622983	−	0.0985574i
$456$	5.78804e8			0.285861
$457$	1.71869e9	−	9.92284e8i	0.842345	−	0.486328i	−0.0157158	−	0.999876i	$-0.505003\pi$
$457$	1.71869e9	−	9.92284e8i	0.842345	−	0.486328i	0.858061	+	0.513548i	$0.171669\pi$
$458$	1.10029e8	+	1.90576e8i	0.0535153	+	0.0926912i
$459$	2.79714e8	−	4.84479e8i	0.135011	−	0.233846i
$460$			2.34571e9i			1.12362i
$461$	2.08138e9	+	1.20169e9i	0.989460	+	0.571265i	0.905113	−	0.425171i	$-0.139786\pi$
$461$	2.08138e9	+	1.20169e9i	0.989460	+	0.571265i	0.0843473	+	0.996436i	$0.473119\pi$
$462$	−8.43663e8	−	4.87089e8i	−0.398036	−	0.229806i
$463$		−	1.50721e9i		−	0.705733i	−0.935674	−	0.352867i	$-0.885207\pi$
$463$		−	1.50721e9i		−	0.705733i	0.935674	−	0.352867i	$-0.114793\pi$
$464$	5.60712e7	−	9.71181e7i	0.0260571	−	0.0451323i
$465$	2.21827e9	+	3.84215e9i	1.02312	+	1.77210i
$466$	1.02262e8	−	5.90407e7i	0.0468125	−	0.0270272i
$467$	−2.82258e9			−1.28244			−0.641220	−	0.767357i	$-0.721572\pi$
$467$	−2.82258e9			−1.28244			−0.641220	+	0.767357i	$0.721572\pi$
$468$	5.51418e8	−	1.43573e9i	0.248668	−	0.647459i
$469$	1.21284e8			0.0542872
$470$	3.30217e9	−	1.90651e9i	1.46709	−	0.847026i
$471$	7.62935e8	+	1.32144e9i	0.336445	+	0.582741i
$472$	−7.67234e8	+	1.32889e9i	−0.335839	+	0.581690i
$473$			2.45202e9i			1.06539i
$474$	3.06969e9	+	1.77228e9i	1.32394	+	0.764380i
$475$	6.96560e8	+	4.02159e8i	0.298216	+	0.172175i
$476$		−	6.54087e8i		−	0.277978i
$477$	−2.20131e8	+	3.81279e8i	−0.0928683	+	0.160853i
$478$	−1.05154e8	−	1.82131e8i	−0.0440379	−	0.0762758i
$479$	2.46004e8	−	1.42031e8i	0.102275	−	0.0590483i	−0.447990	−	0.894038i	$-0.647860\pi$
$479$	2.46004e8	−	1.42031e8i	0.102275	−	0.0590483i	0.550265	+	0.834990i	$0.314527\pi$
$480$	−5.86289e9			−2.41973
$481$	−4.11937e9	−	1.58212e9i	−1.68781	−	0.648233i
$482$	1.40881e9			0.573043
$483$	−1.32821e9	+	7.66843e8i	−0.536354	+	0.309664i
$484$	5.48819e8	+	9.50582e8i	0.220024	+	0.381093i
$485$	2.86707e9	−	4.96590e9i	1.14115	−	1.97652i
$486$			2.28624e9i			0.903430i
$487$	3.88958e9	+	2.24565e9i	1.52599	+	0.881031i	0.999525	+	0.0308345i	$0.00981649\pi$
$487$	3.88958e9	+	2.24565e9i	1.52599	+	0.881031i	0.526466	+	0.850196i	$0.323517\pi$
$488$	3.35947e9	+	1.93959e9i	1.30858	+	0.755511i
$489$			7.17202e8i			0.277371i
$490$	1.95676e8	−	3.38921e8i	0.0751367	−	0.130141i
$491$	1.29071e9	+	2.23558e9i	0.492090	+	0.852325i	0.999959	−	0.00910977i	$-0.00289977\pi$
$491$	1.29071e9	+	2.23558e9i	0.492090	+	0.852325i	−0.507869	+	0.861435i	$0.669566\pi$
$492$	−2.02253e8	+	1.16771e8i	−0.0765625	+	0.0442034i
$493$	4.95271e9			1.86157
$494$	−2.05036e8	−	2.53290e8i	−0.0765219	−	0.0945310i
$495$	−6.81685e9			−2.52619
$496$	−6.72276e7	+	3.88139e7i	−0.0247378	+	0.0142824i
$497$	4.87805e8	+	8.44903e8i	0.178237	+	0.308716i
$498$	−7.79250e8	+	1.34970e9i	−0.282731	+	0.489705i
$499$			4.04020e9i			1.45563i	0.685774	+	0.727815i	$0.259464\pi$
$499$			4.04020e9i			1.45563i	−0.685774	+	0.727815i	$0.740536\pi$
$500$	−1.91036e9	−	1.10295e9i	−0.683472	−	0.394603i
$501$	−6.39691e9	−	3.69326e9i	−2.27268	−	1.31213i
$502$		−	1.70479e9i		−	0.601463i
$503$	2.18373e9	−	3.78232e9i	0.765086	−	1.32517i	−0.175115	−	0.984548i	$-0.556030\pi$
$503$	2.18373e9	−	3.78232e9i	0.765086	−	1.32517i	0.940201	−	0.340620i	$-0.110637\pi$
$504$	−6.31508e8	−	1.09380e9i	−0.219721	−	0.380568i
$505$	−1.38049e9	+	7.97024e8i	−0.476993	+	0.275392i
$506$	−2.69975e9			−0.926397
$507$	−4.09347e9	+	1.32844e9i	−1.39496	+	0.452704i
$508$	−1.59937e9			−0.541285
$509$	−3.77235e9	+	2.17797e9i	−1.26794	+	0.732048i	−0.974599	−	0.223959i	$-0.928102\pi$
$509$	−3.77235e9	+	2.17797e9i	−1.26794	+	0.732048i	−0.293345	+	0.956007i	$0.594768\pi$
$510$	2.81999e9	+	4.88437e9i	0.941353	+	1.63047i
$511$	9.69542e8	−	1.67930e9i	0.321435	−	0.556742i
$512$		−	2.07405e8i		−	0.0682928i
$513$	1.13049e8	+	6.52691e7i	0.0369707	+	0.0213450i
$514$	2.01413e9	+	1.16286e9i	0.654209	+	0.377708i
$515$		−	4.32092e9i		−	1.39396i
$516$	−1.11706e9	+	1.93481e9i	−0.357935	+	0.619962i
$517$	−3.32798e9	−	5.76422e9i	−1.05916	−	1.83453i
$518$	−1.18011e9	+	6.81339e8i	−0.373052	+	0.215382i
$519$	5.70303e9			1.79069
$520$	3.40100e9	+	4.20141e9i	1.06071	+	1.31034i
$521$	−2.24622e9			−0.695857			−0.347928	−	0.937521i	$-0.613115\pi$
$521$	−2.24622e9			−0.695857			−0.347928	+	0.937521i	$0.613115\pi$
$522$	3.11439e9	−	1.79810e9i	0.958356	−	0.553307i
$523$	−1.81585e9	−	3.14515e9i	−0.555041	−	0.961359i	−0.997900	−	0.0647677i	$-0.979369\pi$
$523$	−1.81585e9	−	3.14515e9i	−0.555041	−	0.961359i	0.442860	−	0.896591i	$-0.353964\pi$
$524$	−5.64399e8	+	9.77568e8i	−0.171367	+	0.296816i
$525$		−	3.28015e9i		−	0.989318i
$526$	−2.54802e9	−	1.47110e9i	−0.763400	−	0.440749i
$527$	−2.96908e9	−	1.71420e9i	−0.883658	−	0.510180i
$528$		−	2.22918e8i		−	0.0659063i
$529$	−4.22747e8	+	7.32219e8i	−0.124161	+	0.215053i
$530$	−2.90929e8	−	5.03904e8i	−0.0848833	−	0.147022i
$531$	−2.28624e9	+	1.31996e9i	−0.662662	+	0.382588i
$532$	1.52626e8			0.0439479
$533$	3.26423e8	+	1.25369e8i	0.0933762	+	0.0358628i
$534$	−5.25498e9			−1.49340
$535$	−2.54888e9	+	1.47160e9i	−0.719633	+	0.415480i
$536$	2.58654e8	+	4.48001e8i	0.0725507	+	0.125662i
$537$	−1.83044e9	+	3.17042e9i	−0.510089	+	0.883500i
$538$			3.30855e8i			0.0916010i
$539$	−5.91616e8	−	3.41570e8i	−0.162734	−	0.0939548i
$540$	−7.05133e8	−	4.07109e8i	−0.192705	−	0.111258i
$541$			3.20304e9i			0.869704i	0.900502	+	0.434852i	$0.143199\pi$
$541$			3.20304e9i			0.869704i	−0.900502	+	0.434852i	$0.856801\pi$
$542$	−1.66840e9	+	2.88975e9i	−0.450093	+	0.779584i
$543$	−1.36327e9	−	2.36125e9i	−0.365411	−	0.632911i
$544$	3.92364e9	−	2.26532e9i	1.04494	−	0.603299i
$545$	−2.63537e9			−0.697355
$546$	−4.76485e8	+	1.24063e9i	−0.125278	+	0.326187i
$547$	−1.99240e9			−0.520499			−0.260250	−	0.965541i	$-0.583805\pi$
$547$	−1.99240e9			−0.520499			−0.260250	+	0.965541i	$0.583805\pi$
$548$	5.58840e8	−	3.22647e8i	0.145063	−	0.0837520i
$549$	3.33691e9	+	5.77969e9i	0.860679	+	1.49074i
$550$	2.88703e9	−	5.00048e9i	0.739915	−	1.28157i
$551$			1.15568e9i			0.294311i
$552$	−5.66517e9	−	3.27079e9i	−1.43359	−	0.827686i
$553$	2.15261e9	+	1.24281e9i	0.541286	+	0.312512i
$554$			1.23813e8i			0.0309374i
$555$	−8.91038e9	+	1.54332e10i	−2.21244	+	3.83205i
$556$	1.72089e9	+	2.98066e9i	0.424610	+	0.735446i
$557$	3.18600e9	−	1.83944e9i	0.781183	−	0.451016i	−0.0556662	−	0.998449i	$-0.517728\pi$
$557$	3.18600e9	−	1.83944e9i	0.781183	−	0.451016i	0.836849	+	0.547433i	$0.184395\pi$
$558$	−2.48938e9			−0.606556
$559$	3.30397e9	−	5.22696e8i	0.800009	−	0.126563i
$560$	8.95520e7			0.0215485
$561$	8.52609e9	−	4.92254e9i	2.03882	−	1.17712i
$562$	1.26036e9	+	2.18301e9i	0.299514	+	0.518774i
$563$	1.61226e9	−	2.79251e9i	0.380763	−	0.659500i	−0.610409	−	0.792087i	$-0.708995\pi$
$563$	1.61226e9	−	2.79251e9i	0.380763	−	0.659500i	0.991171	+	0.132586i	$0.0423282\pi$
$564$		−	6.06450e9i		−	1.42337i
$565$	6.66993e8	+	3.85089e8i	0.155579	+	0.0898238i
$566$	−3.13504e8	−	1.81002e8i	−0.0726751	−	0.0419590i
$567$			1.35571e9i			0.312339i
$568$	−2.08062e9	+	3.60374e9i	−0.476402	+	0.825152i
$569$	−3.82506e8	−	6.62521e8i	−0.0870454	−	0.150767i	0.819216	−	0.573486i	$-0.194409\pi$
$569$	−3.82506e8	−	6.62521e8i	−0.0870454	−	0.150767i	−0.906261	+	0.422719i	$0.861076\pi$
$570$	−1.13973e9	+	6.58024e8i	−0.257775	+	0.148826i
$571$	4.92581e9			1.10727			0.553633	−	0.832761i	$-0.313241\pi$
$571$	4.92581e9			1.10727			0.553633	+	0.832761i	$0.313241\pi$
$572$	2.75780e9	−	2.23241e9i	0.616136	−	0.498756i
$573$	−5.23005e9			−1.16136
$574$	9.35135e7	−	5.39900e7i	0.0206387	−	0.0119158i
$575$	−4.54515e9	−	7.87244e9i	−0.997037	−	1.72692i
$576$	1.73503e9	−	3.00515e9i	0.378292	−	0.655221i
$577$			4.57539e8i			0.0991546i	0.998770	+	0.0495773i	$0.0157874\pi$
$577$			4.57539e8i			0.0991546i	−0.998770	+	0.0495773i	$0.984213\pi$
$578$	−1.24013e9	−	7.15988e8i	−0.267128	−	0.154226i
$579$	9.12373e9	+	5.26759e9i	1.95343	+	1.12781i
$580$		−	7.20841e9i		−	1.53406i
$581$	−5.46447e8	+	9.46473e8i	−0.115593	+	0.200213i
$582$	3.00658e9	+	5.20755e9i	0.632182	+	1.09497i
$583$	−8.79608e8	+	5.07842e8i	−0.183844	+	0.106142i
$584$	8.27072e9			1.71830
$585$	1.45315e9	+	9.18537e9i	0.300099	+	1.89693i
$586$	−2.05841e9			−0.422562
$587$	−1.25950e9	+	7.27173e8i	−0.257019	+	0.148390i	−0.622974	−	0.782243i	$-0.714076\pi$
$587$	−1.25950e9	+	7.27173e8i	−0.257019	+	0.148390i	0.365955	+	0.930633i	$0.380742\pi$
$588$	−3.11218e8	−	5.39045e8i	−0.0631311	−	0.109346i
$589$	3.99995e8	−	6.92811e8i	0.0806586	−	0.139705i
$590$		−	3.48898e9i		−	0.699384i
$591$	−1.84884e9	−	1.06743e9i	−0.368419	−	0.212707i
$592$	−2.70042e8	−	1.55909e8i	−0.0534939	−	0.0308847i
$593$		−	1.85105e9i		−	0.364524i	−0.983250	−	0.182262i	$-0.941658\pi$
$593$		−	1.85105e9i		−	0.364524i	0.983250	−	0.182262i	$-0.0583419\pi$
$594$	4.68555e8	−	8.11562e8i	0.0917293	−	0.158880i
$595$	1.97751e9	+	3.42515e9i	0.384866	+	0.666608i
$596$	−6.99454e8	+	4.03830e8i	−0.135331	+	0.0781334i
$597$	1.19022e9			0.228937
$598$	5.75506e8	+	3.63778e9i	0.110051	+	0.695637i
$599$	−6.38164e9			−1.21322			−0.606608	−	0.795001i	$-0.707470\pi$
$599$	−6.38164e9			−1.21322			−0.606608	+	0.795001i	$0.707470\pi$
$600$	1.21163e10	−	6.99535e9i	2.29003	−	1.32215i
$601$	2.59993e9	+	4.50321e9i	0.488541	+	0.846178i	0.999913	−	0.0131816i	$-0.00419595\pi$
$601$	2.59993e9	+	4.50321e9i	0.488541	+	0.846178i	−0.511372	+	0.859359i	$0.670863\pi$
$602$	5.16486e8	−	8.94579e8i	0.0964874	−	0.167121i
$603$			8.89984e8i			0.165300i
$604$	−1.25146e9	−	7.22530e8i	−0.231093	−	0.133422i
$605$	−5.74782e9	−	3.31851e9i	−1.05526	−	0.609255i
$606$		−	1.67161e9i		−	0.305128i
$607$	−2.41699e9	+	4.18636e9i	−0.438647	+	0.759759i	−0.997585	−	0.0694503i	$-0.977875\pi$
$607$	−2.41699e9	+	4.18636e9i	−0.438647	+	0.759759i	0.558938	+	0.829209i	$0.311209\pi$
$608$	5.28594e8	+	9.15552e8i	0.0953805	+	0.165204i
$609$	4.08162e9	−	2.35653e9i	0.732272	−	0.422777i
$610$	−8.82023e9			−1.57335
$611$	−7.05758e9	+	5.71304e9i	−1.25173	+	1.01326i
$612$	4.79972e9			0.846420
$613$	3.13278e9	−	1.80871e9i	0.549311	−	0.317145i	−0.199533	−	0.979891i	$-0.563942\pi$
$613$	3.13278e9	−	1.80871e9i	0.549311	−	0.317145i	0.748844	+	0.662746i	$0.230609\pi$
$614$	1.48951e8	+	2.57991e8i	0.0259690	+	0.0449796i
$615$	7.06069e8	−	1.22295e9i	0.122401	−	0.212004i
$616$		−	2.91377e9i		−	0.502254i
$617$	8.94130e9	+	5.16226e9i	1.53251	+	0.884794i	0.999245	+	0.0388436i	$0.0123674\pi$
$617$	8.94130e9	+	5.16226e9i	1.53251	+	0.884794i	0.533262	+	0.845950i	$0.320966\pi$
$618$	3.92411e9	+	2.26559e9i	0.668778	+	0.386119i
$619$		−	3.44142e9i		−	0.583204i	−0.956540	−	0.291602i	$-0.905812\pi$
$619$		−	3.44142e9i		−	0.583204i	0.956540	−	0.291602i	$-0.0941883\pi$
$620$	−2.49492e9	+	4.32133e9i	−0.420423	+	0.728193i
$621$	−7.37664e8	−	1.27767e9i	−0.123606	−	0.214091i
$622$	3.28691e8	−	1.89770e8i	0.0547673	−	0.0316199i
$623$	−3.68504e9			−0.610568
$624$	−3.00371e8	+	4.75194e7i	−0.0494894	+	0.00782934i
$625$	2.44499e9			0.400587
$626$	−4.59146e9	+	2.65088e9i	−0.748067	+	0.431897i
$627$	1.14864e9	+	1.98950e9i	0.186100	+	0.322334i
$628$	−8.58087e8	+	1.48625e9i	−0.138252	+	0.239460i
$629$		−	1.37713e10i		−	2.20646i
$630$	2.48702e9	+	1.43588e9i	0.396267	+	0.228785i
$631$	9.06643e9	+	5.23451e9i	1.43659	+	0.829417i	0.997611	−	0.0690790i	$-0.0220060\pi$
$631$	9.06643e9	+	5.23451e9i	1.43659	+	0.829417i	0.438981	+	0.898496i	$0.355339\pi$
$632$			1.06018e10i			1.67059i
$633$	4.46850e9	−	7.73967e9i	0.700243	−	1.21286i
$634$	−9.51799e8	−	1.64857e9i	−0.148331	−	0.256918i
$635$	8.37516e9	−	4.83540e9i	1.29803	−	0.749418i
$636$	−9.25429e8			−0.142641
$637$	−3.34133e8	+	8.69986e8i	−0.0512191	+	0.133360i
$638$	8.29640e9			1.26479
$639$	−6.19993e9	+	3.57953e9i	−0.940013	+	0.542717i
$640$	−3.17788e9	−	5.50425e9i	−0.479190	−	0.829981i
$641$	3.13597e9	−	5.43167e9i	0.470294	−	0.814573i	−0.529129	−	0.848541i	$-0.677481\pi$
$641$	3.13597e9	−	5.43167e9i	0.470294	−	0.814573i	0.999423	+	0.0339685i	$0.0108146\pi$
$642$		−	3.08641e9i		−	0.460342i
$643$	−6.14893e9	−	3.55009e9i	−0.912140	−	0.526624i	−0.0310207	−	0.999519i	$-0.509876\pi$
$643$	−6.14893e9	−	3.55009e9i	−0.912140	−	0.526624i	−0.881119	+	0.472895i	$0.843209\pi$
$644$	−1.49386e9	−	8.62481e8i	−0.220399	−	0.127247i
$645$		−	1.35090e10i		−	1.98227i
$646$	5.08497e8	−	8.80743e8i	0.0742121	−	0.128539i
$647$	4.08187e9	+	7.07001e9i	0.592508	+	1.02625i	0.993893	+	0.110345i	$0.0351955\pi$
$647$	4.08187e9	+	7.07001e9i	0.592508	+	1.02625i	−0.401385	+	0.915909i	$0.631471\pi$
$648$	−5.00776e9	+	2.89123e9i	−0.722988	+	0.417417i
$649$	−6.09030e9			−0.874546
$650$	−7.35332e9	−	2.82417e9i	−1.05024	−	0.403362i
$651$	−3.26249e9			−0.463464
$652$	−6.98579e8	+	4.03325e8i	−0.0987072	+	0.0569886i
$653$	1.92993e9	+	3.34274e9i	0.271235	+	0.469793i	0.969178	−	0.246360i	$-0.0792346\pi$
$653$	1.92993e9	+	3.34274e9i	0.271235	+	0.469793i	−0.697943	+	0.716153i	$0.745901\pi$
$654$	1.38180e9	−	2.39336e9i	0.193163	−	0.334569i
$655$		−	6.82543e9i		−	0.949042i
$656$	2.13984e7	+	1.23544e7i	0.00295950	+	0.00170867i
$657$	1.23228e10	+	7.11454e9i	1.69523	+	0.978742i
$658$			2.80398e9i			0.383693i
$659$	1.45481e9	−	2.51980e9i	0.198019	−	0.342979i	−0.749867	−	0.661589i	$-0.769883\pi$
$659$	1.45481e9	−	2.51980e9i	0.198019	−	0.342979i	0.947886	+	0.318609i	$0.103216\pi$
$660$	−7.16449e9	−	1.24093e10i	−0.970022	−	1.68013i
$661$	6.26638e9	−	3.61790e9i	0.843940	−	0.487249i	−0.0146616	−	0.999893i	$-0.504667\pi$
$661$	6.26638e9	−	3.61790e9i	0.843940	−	0.487249i	0.858602	+	0.512644i	$0.171334\pi$
$662$	2.35200e9			0.315089
$663$	−8.45038e9	−	1.04391e10i	−1.12610	−	1.39113i
$664$	−4.66148e9			−0.617925
$665$	−7.99232e8	+	4.61437e8i	−0.105389	+	0.0608466i
$666$	−4.99969e9	−	8.65972e9i	−0.655818	−	1.13591i
$667$	6.53067e9	−	1.13114e10i	0.852152	−	1.47597i
$668$		−	8.30775e9i		−	1.07836i
$669$	4.82806e9	+	2.78748e9i	0.623421	+	0.359932i
$670$	−1.01864e9	−	5.88109e8i	−0.130845	−	0.0755434i
$671$			1.53965e10i			1.96740i
$672$	2.15570e9	−	3.73378e9i	0.274028	−	0.474631i
$673$	−2.82850e9	−	4.89910e9i	−0.357687	−	0.619532i	0.629887	−	0.776687i	$-0.283101\pi$
$673$	−2.82850e9	−	4.89910e9i	−0.357687	−	0.619532i	−0.987574	+	0.157155i	$0.949768\pi$
$674$	3.44283e9	−	1.98772e9i	0.433118	−	0.250061i
$675$	3.15534e9			0.394896
$676$	−3.59594e9	−	3.24011e9i	−0.447713	−	0.403410i
$677$	4.43469e8			0.0549292			0.0274646	−	0.999623i	$-0.491257\pi$
$677$	4.43469e8			0.0549292			0.0274646	+	0.999623i	$0.491257\pi$
$678$	−6.99449e8	+	4.03827e8i	−0.0861891	+	0.0497613i
$679$	2.10835e9	+	3.65178e9i	0.258464	+	0.447672i
$680$	−8.43462e9	+	1.46092e10i	−1.02869	+	1.78174i
$681$		−	1.00657e10i		−	1.22132i
$682$	−4.97357e9	−	2.87149e9i	−0.600375	−	0.346627i
$683$	−9.88516e9	−	5.70720e9i	−1.18716	−	0.685410i	−0.229504	−	0.973308i	$-0.573710\pi$
$683$	−9.88516e9	−	5.70720e9i	−1.18716	−	0.685410i	−0.957661	+	0.287898i	$0.907044\pi$
$684$			1.11998e9i			0.133817i
$685$	−1.95092e9	+	3.37910e9i	−0.231912	+	0.401684i
$686$	1.43895e8	+	2.49233e8i	0.0170181	+	0.0294761i
$687$	−1.83277e9	+	1.05815e9i	−0.215655	+	0.124508i
$688$	2.36372e8			0.0276717
$689$	8.71798e8	+	1.07697e9i	0.101543	+	0.125440i
$690$	1.48738e10			1.72366
$691$	4.67587e9	−	2.69961e9i	0.539124	−	0.311264i	−0.205600	−	0.978636i	$-0.565914\pi$
$691$	4.67587e9	−	2.69961e9i	0.539124	−	0.311264i	0.744724	+	0.667373i	$0.232581\pi$
$692$	3.20715e9	+	5.55494e9i	0.367915	+	0.637247i
$693$	2.50645e9	−	4.34131e9i	0.286084	−	0.495512i
$694$			6.82536e9i			0.775117i
$695$	−1.80230e10	−	1.04056e10i	−2.03648	−	1.17576i
$696$	1.74092e10	+	1.00512e10i	1.95725	+	1.13002i
$697$			1.09125e9i			0.122070i
$698$	−2.93188e9	+	5.07817e9i	−0.326327	+	0.565214i
$699$	5.67794e8	+	9.83449e8i	0.0628812	+	0.108913i
$700$	3.19497e9	−	1.84462e9i	0.352066	−	0.203265i
$701$	1.02069e10			1.11913			0.559566	−	0.828786i	$-0.310968\pi$
$701$	1.02069e10			1.11913			0.559566	+	0.828786i	$0.310968\pi$
$702$	−1.19342e9	−	4.58354e8i	−0.130201	−	0.0500059i
$703$	3.21342e9			0.348838
$704$	6.93287e9	−	4.00270e9i	0.748874	−	0.432363i
$705$	1.83349e10	+	3.17570e10i	1.97068	+	3.41332i
$706$	7.53417e8	−	1.30496e9i	0.0805785	−	0.139566i
$707$		−	1.17221e9i		−	0.124750i
$708$	−4.80567e9	−	2.77456e9i	−0.508906	−	0.293817i
$709$	−4.30763e9	−	2.48701e9i	−0.453917	−	0.262069i	0.255566	−	0.966792i	$-0.417738\pi$
$709$	−4.30763e9	−	2.48701e9i	−0.453917	−	0.262069i	−0.709483	+	0.704723i	$0.751071\pi$
$710$		−	9.46155e9i		−	0.992106i
$711$	−9.11978e9	+	1.57959e10i	−0.951570	+	1.64817i
$712$	−7.85884e9	−	1.36119e10i	−0.815978	−	1.41332i
$713$	−7.83007e9	+	4.52069e9i	−0.809007	+	0.467080i
$714$	−4.14748e9			−0.426423
$715$	−7.69203e9	+	2.00278e10i	−0.786992	+	2.04910i
$716$	−4.11746e9			−0.419212
$717$	1.75156e9	−	1.01126e9i	0.177463	−	0.102458i
$718$	3.11608e9	+	5.39721e9i	0.314176	+	0.544169i
$719$	6.12330e9	−	1.06059e10i	0.614376	−	1.06413i	−0.376118	−	0.926572i	$-0.622741\pi$
$719$	6.12330e9	−	1.06059e10i	0.614376	−	1.06413i	0.990494	−	0.137558i	$-0.0439255\pi$
$720$			6.57137e8i			0.0656133i
$721$	2.75177e9	+	1.58874e9i	0.273425	+	0.157862i
$722$	−5.31523e9	−	3.06875e9i	−0.525584	−	0.303446i
$723$			1.35485e10i			1.33324i
$724$	1.53329e9	−	2.65574e9i	0.150155	−	0.260076i
$725$	1.39674e10	+	2.41922e10i	1.36123	+	2.35772i
$726$	6.02751e9	−	3.47999e9i	0.584602	−	0.337520i
$727$	−8.03843e9			−0.775891			−0.387946	−	0.921682i	$-0.626815\pi$
$727$	−8.03843e9			−0.775891			−0.387946	+	0.921682i	$0.626815\pi$
$728$	−3.92616e9	+	6.21129e8i	−0.377145	+	0.0596653i
$729$	−1.33426e10			−1.27554
$730$	−1.62860e10	+	9.40271e9i	−1.54947	+	0.894588i
$731$	5.21962e9	+	9.04064e9i	0.494229	+	0.856029i
$732$	−7.01416e9	+	1.21489e10i	−0.660978	+	1.14485i
$733$			1.01938e10i			0.956035i	0.878350	+	0.478018i	$0.158645\pi$
$733$			1.01938e10i			0.956035i	−0.878350	+	0.478018i	$0.841355\pi$
$734$	−4.04494e9	−	2.33535e9i	−0.377552	−	0.217979i
$735$	3.25941e9	+	1.88182e9i	0.302784	+	0.174812i
$736$		−	1.19482e10i		−	1.10467i
$737$	−1.02660e9	+	1.77811e9i	−0.0944633	+	0.163615i
$738$	3.96181e8	+	6.86206e8i	0.0362824	+	0.0628430i
$739$	1.47368e10	−	8.50831e9i	1.34322	−	0.775511i	0.355945	−	0.934507i	$-0.384159\pi$
$739$	1.47368e10	−	8.50831e9i	1.34322	−	0.775511i	0.987279	+	0.158996i	$0.0508258\pi$
$740$	−2.00433e10			−1.81827
$741$	2.43589e9	−	1.97183e9i	0.219935	−	0.178035i
$742$	4.27881e8			0.0384512
$743$	3.57783e9	−	2.06566e9i	0.320007	−	0.184756i	−0.331389	−	0.943494i	$-0.607517\pi$
$743$	3.57783e9	−	2.06566e9i	0.320007	−	0.184756i	0.651396	+	0.758738i	$0.274184\pi$
$744$	−6.95770e9	−	1.20511e10i	−0.619385	−	1.07281i
$745$	2.44181e9	−	4.22934e9i	0.216354	−	0.374736i
$746$		−	6.61666e9i		−	0.583516i
$747$	−6.94526e9	−	4.00985e9i	−0.609630	−	0.351970i
$748$	9.58944e9	+	5.53646e9i	0.837795	+	0.483701i
$749$		−	2.16433e9i		−	0.188208i
$750$	−6.99365e9	+	1.21134e10i	−0.605326	+	1.04846i
$751$	−9.44095e9	−	1.63522e10i	−0.813347	−	1.40876i	−0.910509	−	0.413489i	$-0.864310\pi$
$751$	−9.44095e9	−	1.63522e10i	−0.813347	−	1.40876i	0.0971621	−	0.995269i	$-0.469023\pi$
$752$	−5.55665e8	+	3.20813e8i	−0.0476486	+	0.0275099i
$753$	1.63950e10			1.39936
$754$	−1.76854e9	−	1.11790e10i	−0.150250	−	0.949736i
$755$	8.73775e9			0.738900
$756$	5.18534e8	−	2.99376e8i	0.0436466	−	0.0251994i
$757$	5.74341e9	+	9.94788e9i	0.481210	+	0.833479i	0.999767	−	0.0215631i	$-0.00686429\pi$
$757$	5.74341e9	+	9.94788e9i	0.481210	+	0.833479i	−0.518558	+	0.855042i	$0.673531\pi$
$758$	−3.28303e9	+	5.68637e9i	−0.273799	+	0.474234i
$759$		−	2.59635e10i		−	2.15535i
$760$	−3.40894e9	−	1.96815e9i	−0.281690	−	0.162634i
$761$	9.93955e9	+	5.73860e9i	0.817561	+	0.472019i	0.849575	−	0.527468i	$-0.176859\pi$
$761$	9.93955e9	+	5.73860e9i	0.817561	+	0.472019i	−0.0320136	+	0.999487i	$0.510192\pi$
$762$			1.01414e10i			0.830338i
$763$	9.68986e8	−	1.67833e9i	0.0789735	−	0.136786i
$764$	−2.94117e9	−	5.09425e9i	−0.238612	−	0.413289i
$765$	−2.51339e10	+	1.45111e10i	−2.02976	+	1.17188i
$766$	−1.60746e7			−0.00129223
$767$	1.29827e9	+	8.20638e9i	0.103892	+	0.656701i
$768$	1.87683e10			1.49507
$769$	−1.33602e10	+	7.71352e9i	−1.05943	+	0.611660i	−0.925274	−	0.379300i	$-0.876165\pi$
$769$	−1.33602e10	+	7.71352e9i	−1.05943	+	0.611660i	−0.134153	+	0.990961i	$0.542831\pi$
$770$	3.31257e9	+	5.73755e9i	0.261486	+	0.452907i
$771$	−1.11832e10	+	1.93699e10i	−0.878771	+	1.52208i
$772$			1.18491e10i			0.926883i
$773$	−6.38041e9	−	3.68373e9i	−0.496845	−	0.286853i	0.230565	−	0.973057i	$-0.425943\pi$
$773$	−6.38041e9	−	3.68373e9i	−0.496845	−	0.286853i	−0.727410	+	0.686204i	$0.759276\pi$
$774$	6.56446e9	+	3.78999e9i	0.508869	+	0.293795i
$775$		−	1.93371e10i		−	1.49223i
$776$	−8.99269e9	+	1.55758e10i	−0.690834	+	1.19656i
$777$	−6.55243e9	−	1.13491e10i	−0.501105	−	0.867939i
$778$	−7.92591e8	+	4.57602e8i	−0.0603421	+	0.0348385i
$779$	−2.54635e8			−0.0192991
$780$	−1.51936e10	+	1.22991e10i	−1.14638	+	0.927986i
$781$	−1.65159e10			−1.24058
$782$	−9.95405e9	+	5.74698e9i	−0.744348	+	0.429750i
$783$	2.26686e9	+	3.92631e9i	0.168756	+	0.292293i
$784$	−3.29269e7	+	5.70311e7i	−0.00244031	+	0.00422674i
$785$		−	1.03771e10i		−	0.765651i
$786$	6.19863e9	+	3.57878e9i	0.455320	+	0.262879i
$787$	2.82316e9	+	1.62995e9i	0.206454	+	0.119196i	0.599662	−	0.800253i	$-0.295302\pi$
$787$	2.82316e9	+	1.62995e9i	0.206454	+	0.119196i	−0.393208	+	0.919449i	$0.628635\pi$
$788$		−	2.40110e9i		−	0.174811i
$789$	1.41475e10	−	2.45043e10i	1.02544	−	1.77612i
$790$	−1.20529e10	−	2.08762e10i	−0.869752	−	1.50645i
$791$	−4.90487e8	+	2.83183e8i	−0.0352379	+	0.0203446i
$792$	2.13814e10			1.52932
$793$	2.07460e10	−	3.28206e9i	1.47733	−	0.233717i
$794$	−1.27237e9			−0.0902070
$795$	4.84605e9	−	2.79787e9i	0.342060	−	0.197489i
$796$	6.69329e8	+	1.15931e9i	0.0470375	+	0.0814713i
$797$	−8.75048e9	+	1.51563e10i	−0.612249	+	1.06045i	0.378612	+	0.925556i	$0.376402\pi$
$797$	−8.75048e9	+	1.51563e10i	−0.612249	+	1.06045i	−0.990861	+	0.134890i	$0.956932\pi$
$798$		−	9.67781e8i		−	0.0674167i
$799$	−2.45407e10	−	1.41686e10i	−1.70205	−	0.982679i
$800$	2.21305e10	+	1.27770e10i	1.52818	+	0.882298i
$801$		−	2.70410e10i		−	1.85913i
$802$	−1.37558e9	+	2.38257e9i	−0.0941617	+	0.163093i
$803$	1.64132e10	+	2.84285e10i	1.11864	+	1.93754i
$804$	−1.62011e9	+	9.35371e8i	−0.109938	+	0.0634728i
$805$	1.04302e10			0.704705
$806$	−2.80897e9	+	7.31375e9i	−0.188962	+	0.492002i
$807$	−3.18183e9			−0.213118
$808$	4.32996e9	−	2.49990e9i	0.288765	−	0.166718i
$809$	2.86061e9	+	4.95472e9i	0.189950	+	0.329002i	0.945233	−	0.326396i	$-0.105834\pi$
$809$	2.86061e9	+	4.95472e9i	0.189950	+	0.329002i	−0.755284	+	0.655398i	$0.772501\pi$
$810$	6.57389e9	−	1.13863e10i	0.434635	−	0.752811i
$811$			1.06839e10i			0.703329i	0.936126	+	0.351665i	$0.114384\pi$
$811$			1.06839e10i			0.703329i	−0.936126	+	0.351665i	$0.885616\pi$
$812$	4.59067e9	+	2.65042e9i	0.300905	+	0.173728i
$813$	−2.77907e10	−	1.60450e10i	−1.81377	−	1.04718i
$814$		−	2.30685e10i		−	1.49911i
$815$	2.43876e9	−	4.22405e9i	0.157804	−	0.273324i
$816$	−4.74527e8	−	8.21905e8i	−0.0305735	−	0.0529549i
$817$	−2.10956e9	+	1.21796e9i	−0.135337	+	0.0781367i
$818$	1.12247e10			0.717032
$819$	−6.38399e9	−	2.45189e9i	−0.406068	−	0.155958i
$820$	1.58826e9			0.100594
$821$	1.35908e10	−	7.84665e9i	0.857125	−	0.494861i	−0.00592372	−	0.999982i	$-0.501886\pi$
$821$	1.35908e10	−	7.84665e9i	0.857125	−	0.494861i	0.863048	+	0.505121i	$0.168552\pi$
$822$	−2.04586e9	−	3.54353e9i	−0.128477	−	0.222528i
$823$	−6.49177e9	+	1.12441e10i	−0.405942	+	0.703112i	−0.994431	−	0.105394i	$-0.966390\pi$
$823$	−6.49177e9	+	1.12441e10i	−0.405942	+	0.703112i	0.588489	+	0.808505i	$0.299723\pi$
$824$			1.35528e10i			0.843884i
$825$	4.80896e10	+	2.77645e10i	2.98169	+	1.72148i
$826$	2.22195e9	+	1.28284e9i	0.137184	+	0.0792034i
$827$		−	1.38216e10i		−	0.849743i	−0.905254	−	0.424871i	$-0.860319\pi$
$827$		−	1.38216e10i		−	0.849743i	0.905254	−	0.424871i	$-0.139681\pi$
$828$	6.32892e9	−	1.09620e10i	0.387457	−	0.671095i
$829$	−4.40196e9	−	7.62442e9i	−0.268352	−	0.464800i	0.700084	−	0.714060i	$-0.253146\pi$
$829$	−4.40196e9	−	7.62442e9i	−0.268352	−	0.464800i	−0.968436	+	0.249261i	$0.919812\pi$
$830$	9.17898e9	−	5.29949e9i	0.557213	−	0.321707i
$831$	−1.19071e9			−0.0719786
$832$	−6.87131e9	−	8.48845e9i	−0.413626	−	0.510971i
$833$	−2.90840e9			−0.174340
$834$	1.89000e10	−	1.09119e10i	1.12818	−	0.651358i
$835$	2.51169e10	+	4.35038e10i	1.49302	+	2.58598i
$836$	−1.29189e9	+	2.23762e9i	−0.0764723	+	0.132454i
$837$		−	3.13835e9i		−	0.184996i
$838$	4.89248e9	+	2.82467e9i	0.287194	+	0.165811i
$839$	−2.75130e10	−	1.58846e10i	−1.60831	−	0.928560i	−0.989748	−	0.142826i	$-0.954381\pi$
$839$	−2.75130e10	−	1.58846e10i	−1.60831	−	0.928560i	−0.618565	−	0.785734i	$-0.712285\pi$
$840$			1.60529e10i			0.934494i
$841$	−1.14440e10	+	1.98215e10i	−0.663422	+	1.14908i
$842$	4.36826e9	+	7.56605e9i	0.252183	+	0.436794i
$843$	−2.09940e10	+	1.21209e10i	−1.20697	+	0.696847i
$844$	1.00516e10			0.575488
$845$	2.86262e10	+	6.09531e9i	1.63217	+	0.347534i
$846$	−2.05757e10			−1.16831
$847$	4.22677e9	−	2.44033e9i	0.239011	−	0.137993i
$848$	4.89554e7	+	8.47932e7i	0.00275686	+	0.00477502i
$849$	1.74069e9	−	3.01496e9i	0.0976213	−	0.169085i
$850$		−	2.45825e10i		−	1.37297i
$851$	−3.14520e10	−	1.81588e10i	−1.74942	−	1.01003i
$852$	−1.30322e10	−	7.52416e9i	−0.721905	−	0.416792i
$853$			2.04338e10i			1.12727i	0.826024	+	0.563634i	$0.190597\pi$
$853$			2.04338e10i			1.12727i	−0.826024	+	0.563634i	$0.809403\pi$
$854$	3.24307e9	−	5.61716e9i	0.178178	−	0.308613i
$855$	−3.38604e9	−	5.86480e9i	−0.185273	−	0.320902i
$856$	7.99468e9	−	4.61573e9i	0.435655	−	0.251526i
$857$	−7.10700e9			−0.385703			−0.192852	−	0.981228i	$-0.561774\pi$
$857$	−7.10700e9			−0.385703			−0.192852	+	0.981228i	$0.561774\pi$
$858$	−1.41554e10	−	1.74868e10i	−0.765098	−	0.945161i
$859$	−1.39160e10			−0.749096			−0.374548	−	0.927208i	$-0.622202\pi$
$859$	−1.39160e10			−0.749096			−0.374548	+	0.927208i	$0.622202\pi$
$860$	1.31582e10	−	7.59688e9i	0.705426	−	0.407278i
$861$	5.19222e8	+	8.99318e8i	0.0277231	+	0.0480178i
$862$	−3.42858e9	+	5.93847e9i	−0.182322	+	0.315791i
$863$			1.31256e10i			0.695152i	0.937652	+	0.347576i	$0.112995\pi$
$863$			1.31256e10i			0.695152i	−0.937652	+	0.347576i	$0.887005\pi$
$864$	3.59170e9	+	2.07367e9i	0.189453	+	0.109381i
$865$	−3.35887e10	−	1.93924e10i	−1.76456	−	1.01877i
$866$		−	1.77434e9i		−	0.0928375i
$867$	6.88565e9	−	1.19263e10i	0.358821	−	0.621497i
$868$	−1.83469e9	−	3.17778e9i	−0.0952234	−	0.164932i
$869$	−3.64411e10	+	2.10393e10i	−1.88375	+	1.08758i
$870$	−4.57076e10			−2.35326
$871$	2.61476e9	+	1.00425e9i	0.134081	+	0.0514963i
$872$	8.26597e9			0.422169
$873$	−2.67969e10	+	1.54712e10i	−1.36312	+	0.786998i
$874$	−1.34101e9	−	2.32270e9i	−0.0679427	−	0.117680i
$875$	−4.90427e9	+	8.49445e9i	−0.247484	+	0.428654i
$876$			2.99095e10i			1.50330i
$877$	−2.64318e10	−	1.52604e10i	−1.32321	−	0.763955i	−0.338970	−	0.940797i	$-0.610079\pi$
$877$	−2.64318e10	−	1.52604e10i	−1.32321	−	0.763955i	−0.984239	+	0.176842i	$0.943412\pi$
$878$	1.13994e10	+	6.58144e9i	0.568396	+	0.328163i
$879$		−	1.97957e10i		−	0.983128i
$880$	−7.58006e8	+	1.31290e9i	−0.0374959	+	0.0649447i
$881$	−1.91642e10	−	3.31934e10i	−0.944225	−	1.63545i	−0.757295	−	0.653072i	$-0.773480\pi$
$881$	−1.91642e10	−	3.31934e10i	−0.944225	−	1.63545i	−0.186930	−	0.982373i	$-0.559854\pi$
$882$	−1.82888e9	+	1.05590e9i	−0.0897522	+	0.0518185i
$883$	2.73726e10			1.33799			0.668995	−	0.743267i	$-0.266725\pi$
$883$	2.73726e10			1.33799			0.668995	+	0.743267i	$0.266725\pi$
$884$	5.41593e9	−	1.41015e10i	0.263688	−	0.686566i
$885$	3.35535e10			1.62718
$886$	−4.64109e9	+	2.67953e9i	−0.224183	+	0.129432i
$887$	7.65490e9	+	1.32587e10i	0.368304	+	0.637922i	0.989301	−	0.145892i	$-0.0466052\pi$
$887$	7.65490e9	+	1.32587e10i	0.368304	+	0.637922i	−0.620996	+	0.783813i	$0.713272\pi$
$888$	2.79479e10	−	4.84071e10i	1.33938	−	2.31987i
$889$			7.11161e9i			0.339478i
$890$	3.09499e10	+	1.78689e10i	1.47161	+	0.849637i
$891$	−1.98758e10	−	1.14753e10i	−0.941353	−	0.543490i
$892$			6.27026e9i			0.295807i
$893$	3.30612e9	−	5.72637e9i	0.155360	−	0.269091i
$894$	2.56063e9	+	4.43514e9i	0.119858	+	0.207600i
$895$	2.15612e10	−	1.24484e10i	1.00529	−	0.580407i
$896$	4.67384e9			0.217068
$897$	−3.49845e10	+	5.53464e9i	−1.61846	+	0.256045i
$898$	2.43356e10			1.12144
$899$	2.40620e10	−	1.38922e10i	1.10452	−	0.637693i
$900$	1.35359e10	+	2.34449e10i	0.618925	+	1.07201i
$901$	−2.16209e9	+	3.74485e9i	−0.0984775	+	0.170568i
$902$			1.82798e9i			0.0829369i
$903$	8.60316e9	+	4.96704e9i	0.388822	+	0.224487i
$904$	−2.09206e9	−	1.20785e9i	−0.0941855	−	0.0543780i
$905$			1.85425e10i			0.831569i
$906$	−4.58147e9	+	7.93534e9i	−0.204671	+	0.354500i
$907$	1.01289e9	+	1.75437e9i	0.0450750	+	0.0780722i	0.887683	−	0.460456i	$-0.152314\pi$
$907$	1.01289e9	+	1.75437e9i	0.0450750	+	0.0780722i	−0.842608	+	0.538528i	$0.818981\pi$
$908$	9.80432e9	−	5.66053e9i	0.434627	−	0.250932i
$909$	8.60176e9			0.379851
$910$	7.02492e9	−	5.68660e9i	0.309027	−	0.250154i
$911$	2.94868e10			1.29215			0.646075	−	0.763274i	$-0.276409\pi$
$911$	2.94868e10			1.29215			0.646075	+	0.763274i	$0.276409\pi$
$912$	1.91785e8	−	1.10727e8i	0.00837207	−	0.00483362i
$913$	−9.25070e9	−	1.60227e10i	−0.402279	−	0.696767i
$914$	7.07665e9	−	1.22571e10i	0.306561	−	0.530978i
$915$		−	8.48241e10i		−	3.66054i
$916$	−2.06134e9	−	1.19012e9i	−0.0886169	−	0.0511630i
$917$	4.34677e9	+	2.50961e9i	0.186155	+	0.107476i
$918$		−	3.98966e9i		−	0.170211i
$919$	−1.21155e10	+	2.09846e10i	−0.514915	+	0.891859i	0.484935	+	0.874550i	$0.338843\pi$
$919$	−1.21155e10	+	2.09846e10i	−0.514915	+	0.891859i	−0.999850	+	0.0173090i	$0.994490\pi$
$920$	2.22438e10	+	3.85274e10i	0.941786	+	1.63122i
$921$	−2.48110e9	+	1.43246e9i	−0.104649	+	0.0604192i
$922$	1.71401e10			0.720203
$923$	3.52070e9	+	2.22544e10i	0.147375	+	0.931558i
$924$	1.05371e10			0.439409
$925$	6.72675e10	−	3.88369e10i	2.79453	−	1.61342i
$926$	−5.37447e9	−	9.30886e9i	−0.222432	−	0.385264i
$927$	−1.16582e10	+	2.01926e10i	−0.480676	+	0.832556i
$928$			3.67171e10i			1.50817i
$929$	2.61450e10	+	1.50948e10i	1.06988	+	0.617693i	0.928147	−	0.372213i	$-0.121401\pi$
$929$	2.61450e10	+	1.50948e10i	1.06988	+	0.617693i	0.141728	+	0.989906i	$0.454734\pi$
$930$	2.74010e10	+	1.58200e10i	1.11706	+	0.644934i
$931$		−	6.78654e8i		−	0.0275629i
$932$	−6.38608e8	+	1.10610e9i	−0.0258392	+	0.0447548i
$933$	1.82502e9	+	3.16102e9i	0.0735666	+	0.127421i
$934$	−1.74329e10	+	1.00649e10i	−0.700092	+	0.404198i
$935$	−6.69539e10			−2.67877
$936$	−4.55787e9	−	2.88104e10i	−0.181675	−	1.14837i
$937$	−4.24869e10			−1.68720			−0.843600	−	0.536972i	$-0.819568\pi$
$937$	−4.24869e10			−1.68720			−0.843600	+	0.536972i	$0.819568\pi$
$938$	7.49074e8	−	4.32478e8i	0.0296357	−	0.0171102i
$939$	−2.54935e10	−	4.41560e10i	−1.00485	−	1.74045i
$940$	−2.06216e10	+	3.57176e10i	−0.809794	+	1.40260i
$941$			4.54783e10i			1.77926i	0.456678	+	0.889632i	$0.349039\pi$
$941$			4.54783e10i			1.77926i	−0.456678	+	0.889632i	$0.650961\pi$
$942$	9.42411e9	+	5.44101e9i	0.367335	+	0.212081i
$943$	2.49229e9	+	1.43893e9i	0.0967850	+	0.0558788i
$944$			5.87098e8i			0.0227148i
$945$	−1.81021e9	+	3.13538e9i	−0.0697780	+	0.120859i
$946$	8.74350e9	+	1.51442e10i	0.335789	+	0.581603i
$947$	−2.86944e10	+	1.65667e10i	−1.09792	+	0.633886i	−0.935675	−	0.352864i	$-0.885208\pi$
$947$	−2.86944e10	+	1.65667e10i	−1.09792	+	0.633886i	−0.162248	+	0.986750i	$0.551875\pi$
$948$	−3.83395e10			−1.46156
$949$	3.48072e10	−	2.81761e10i	1.32202	−	1.07016i
$950$	5.73614e9			0.217064
$951$	1.58542e10	−	9.15345e9i	0.597742	−	0.345106i
$952$	−6.20256e9	−	1.07432e10i	−0.232992	−	0.403555i
$953$	2.21423e10	−	3.83517e10i	0.828702	−	1.43535i	−0.0703549	−	0.997522i	$-0.522413\pi$
$953$	2.21423e10	−	3.83517e10i	0.828702	−	1.43535i	0.899057	−	0.437832i	$-0.144253\pi$
$954$			3.13981e9i			0.117080i
$955$	3.08031e10	+	1.77842e10i	1.14441	+	0.660726i
$956$	1.97001e9	+	1.13738e9i	0.0729230	+	0.0421021i
$957$			7.97865e10i			2.94264i
$958$	1.01292e9	−	1.75442e9i	0.0372216	−	0.0644696i
$959$	−1.43465e9	−	2.48489e9i	−0.0525268	−	0.0909792i
$960$	−3.81955e10	+	2.20522e10i	−1.39336	+	0.804455i
$961$	8.27957e9			0.300937
$962$	−3.10837e10	+	4.91752e9i	−1.12569	+	0.178087i
$963$	1.58820e10			0.573076
$964$	−1.31967e10	+	7.61912e9i	−0.474456	+	0.273927i
$965$	−3.58236e10	−	6.20483e10i	−1.28329	−	2.22272i
$966$	−5.46888e9	+	9.47237e9i	−0.195199	+	0.338095i
$967$		−	2.91783e10i		−	1.03769i	−0.854869	−	0.518844i	$-0.826362\pi$
$967$		−	2.91783e10i		−	1.03769i	0.854869	−	0.518844i	$-0.173638\pi$
$968$	1.80283e10	+	1.04087e10i	0.638839	+	0.368834i
$969$	8.47010e9	+	4.89021e9i	0.299058	+	0.172661i
$970$		−	4.08940e10i		−	1.43866i
$971$	−8.90070e9	+	1.54165e10i	−0.312002	+	0.540403i	−0.978796	−	0.204839i	$-0.934333\pi$
$971$	−8.90070e9	+	1.54165e10i	−0.312002	+	0.540403i	0.666794	+	0.745242i	$0.267666\pi$
$972$	−1.23644e10	−	2.14158e10i	−0.431859	−	0.748002i
$973$	1.32535e10	−	7.65194e9i	0.461251	−	0.266303i
$974$	3.20306e10			1.11073
$975$	2.71601e10	−	7.07169e10i	0.938458	−	2.44347i
$976$	1.48420e9			0.0510997
$977$	3.63983e10	−	2.10146e10i	1.24868	−	0.720924i	0.277832	−	0.960630i	$-0.410384\pi$
$977$	3.63983e10	−	2.10146e10i	1.24868	−	0.720924i	0.970846	+	0.239706i	$0.0770509\pi$
$978$	2.55743e9	+	4.42960e9i	0.0874213	+	0.151418i
$979$	3.11917e10	−	5.40257e10i	1.06243	−	1.84018i
$980$			4.23303e9i			0.143668i
$981$	1.23157e10	+	7.11046e9i	0.416502	+	0.240467i
$982$	1.59434e10	+	9.20495e9i	0.537269	+	0.310193i
$983$		−	2.61155e10i		−	0.876923i	−0.898750	−	0.438462i	$-0.855523\pi$
$983$		−	2.61155e10i		−	0.876923i	0.898750	−	0.438462i	$-0.144477\pi$
$984$	−2.21462e9	+	3.83583e9i	−0.0740997	+	0.128344i
$985$	7.25930e9	+	1.25735e10i	0.242029	+	0.419207i
$986$	3.05890e10	−	1.76606e10i	1.01624	−	0.586727i
$987$	−2.69659e10			−0.892698
$988$	3.29047e9	+	1.26377e9i	0.108545	+	0.0416886i
$989$	2.75304e10			0.904953
$990$	−4.21024e10	+	2.43078e10i	−1.37906	+	0.796201i
$991$	−1.87248e10	−	3.24324e10i	−0.611167	−	1.05857i	−0.991044	−	0.133536i	$-0.957367\pi$
$991$	−1.87248e10	−	3.24324e10i	−0.611167	−	1.05857i	0.379877	−	0.925037i	$-0.375966\pi$
$992$	1.27083e10	−	2.20114e10i	0.413329	−	0.715906i
$993$			2.26191e10i			0.733084i
$994$	6.02558e9	+	3.47887e9i	0.194602	+	0.112353i
$995$	−7.00994e9	−	4.04719e9i	−0.225597	−	0.130249i
$996$		−	1.68574e10i		−	0.540607i
$997$	1.43733e10	−	2.48954e10i	0.459330	−	0.795583i	−0.539596	−	0.841924i	$-0.681423\pi$
$997$	1.43733e10	−	2.48954e10i	0.459330	−	0.795583i	0.998926	+	0.0463415i	$0.0147562\pi$
$998$	1.44067e10	+	2.49531e10i	0.458784	+	0.794636i
$999$	1.09173e10	−	6.30311e9i	0.346446	−	0.200021i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.q.a.36.33	✓	100
13.4	even	6	inner	91.8.q.a.43.33	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.q.a.36.33	✓	100	1.1	even	1	trivial
91.8.q.a.43.33	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)

\(f(q)\)	\(=\)	\(q+(6.17622 - 3.56584i) q^{2} +(34.2927 + 59.3966i) q^{3} +(-38.5696 + 66.8044i) q^{4} -466.432i q^{5} +(423.598 + 244.564i) q^{6} +(297.047 + 171.500i) q^{7} +1462.99i q^{8} +(-1258.47 + 2179.74i) q^{9} +O(q^{10})\)	\(q+(6.17622 - 3.56584i) q^{2} +(34.2927 + 59.3966i) q^{3} +(-38.5696 + 66.8044i) q^{4} -466.432i q^{5} +(423.598 + 244.564i) q^{6} +(297.047 + 171.500i) q^{7} +1462.99i q^{8} +(-1258.47 + 2179.74i) q^{9} +(-1663.22 - 2880.78i) q^{10} +(-5028.66 + 2903.30i) q^{11} -5290.61 q^{12} +(4984.00 + 6156.97i) q^{13} +2446.17 q^{14} +(27704.5 - 15995.2i) q^{15} +(279.874 + 484.757i) q^{16} +(-12360.5 + 21409.0i) q^{17} +17950.1i q^{18} +(-4995.63 - 2884.23i) q^{19} +(31159.7 + 17990.1i) q^{20} +23524.8i q^{21} +(-20705.4 + 35862.8i) q^{22} +(32597.2 + 56460.1i) q^{23} +(-86896.5 + 50169.7i) q^{24} -139434. q^{25} +(52737.0 + 20254.6i) q^{26} -22629.6 q^{27} +(-22913.9 + 13229.4i) q^{28} +(-100172. - 173503. i) q^{29} +(114073. - 197580. i) q^{30} +138683. i q^{31} +(-158717. - 91635.2i) q^{32} +(-344892. - 199123. i) q^{33} +176303. i q^{34} +(79993.1 - 138552. i) q^{35} +(-97077.6 - 168143. i) q^{36} +(-482434. + 278533. i) q^{37} -41138.8 q^{38} +(-194788. + 507172. i) q^{39} +682384. q^{40} +(38228.6 - 22071.3i) q^{41} +(83885.6 + 145294. i) q^{42} +(211141. - 365707. i) q^{43} -447915. i q^{44} +(1.01670e6 + 586993. i) q^{45} +(402655. + 232473. i) q^{46} +1.14628e6i q^{47} +(-19195.3 + 33247.2i) q^{48} +(58824.5 + 101887. i) q^{49} +(-861173. + 497198. i) q^{50} -1.69550e6 q^{51} +(-603543. + 95482.0i) q^{52} +174919. q^{53} +(-139766. + 80693.7i) q^{54} +(1.35419e6 + 2.34553e6i) q^{55} +(-250902. + 434575. i) q^{56} -395632. i q^{57} +(-1.23737e6 - 714395. i) q^{58} +(908340. + 524430. i) q^{59} +2.46771e6i q^{60} +(1.32578e6 - 2.29631e6i) q^{61} +(494522. + 856538. i) q^{62} +(-747651. + 431657. i) q^{63} -1.37867e6 q^{64} +(2.87181e6 - 2.32470e6i) q^{65} -2.84017e6 q^{66} +(306224. - 176798. i) q^{67} +(-953479. - 1.65147e6i) q^{68} +(-2.23569e6 + 3.87233e6i) q^{69} -1.14097e6i q^{70} +(2.46327e6 + 1.42217e6i) q^{71} +(-3.18893e6 - 1.84113e6i) q^{72} -5.65331e6i q^{73} +(-1.98641e6 + 3.44056e6i) q^{74} +(-4.78156e6 - 8.28190e6i) q^{75} +(385359. - 222487. i) q^{76} -1.99166e6 q^{77} +(605439. + 3.82699e6i) q^{78} +7.24670e6 q^{79} +(226106. - 130542. i) q^{80} +(1.97625e6 + 3.42297e6i) q^{81} +(157405. - 272634. i) q^{82} +3.18628e6i q^{83} +(-1.57156e6 - 907340. i) q^{84} +(9.98586e6 + 5.76534e6i) q^{85} -3.01158e6i q^{86} +(6.87034e6 - 1.18998e7i) q^{87} +(-4.24748e6 - 7.35686e6i) q^{88} +(-9.30419e6 + 5.37178e6i) q^{89} +8.37249e6 q^{90} +(424562. + 2.68366e6i) q^{91} -5.02904e6 q^{92} +(-8.23732e6 + 4.75582e6i) q^{93} +(4.08744e6 + 7.07965e6i) q^{94} +(-1.34530e6 + 2.33012e6i) q^{95} -1.25697e7i q^{96} +(1.06466e7 + 6.14680e6i) q^{97} +(726626. + 419518. i) q^{98} -1.46149e7i 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

Fields

Representations

Groups

Database

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