LMFDB - Embedded newform 62.8.d.a.33.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [62,8,Mod(33,62)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(62, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 8, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("62.33"); S:= CuspForms(chi, 8); N := Newforms(S);

Level:	$ N $	$=$	$ 62 = 2 \cdot 31 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	62.d (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,-80] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$19.3678715800$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			33.6
Character	$\chi$	$=$	62.33
Dual form			62.8.d.a.47.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-6.47214 - 4.70228i) q^{2} +(11.4662 - 8.33068i) q^{3} +(19.7771 + 60.8676i) q^{4} +363.071 q^{5} -113.384 q^{6} +(367.182 + 1130.07i) q^{7} +(158.217 - 486.941i) q^{8} +(-613.747 + 1888.92i) q^{9} +(-2349.84 - 1707.26i) q^{10} +(-908.599 - 2796.38i) q^{11} +(733.836 + 533.163i) q^{12} +(-5591.66 + 4062.58i) q^{13} +(2937.45 - 9040.56i) q^{14} +(4163.04 - 3024.62i) q^{15} +(-3313.73 + 2407.57i) q^{16} +(-7305.76 + 22484.8i) q^{17} +(12854.5 - 9339.33i) q^{18} +(-36160.1 - 26271.8i) q^{19} +(7180.48 + 22099.2i) q^{20} +(13624.4 + 9898.72i) q^{21} +(-7268.79 + 22371.0i) q^{22} +(-15900.3 + 48936.1i) q^{23} +(-2242.40 - 6901.41i) q^{24} +53695.3 q^{25} +55293.4 q^{26} +(18277.0 + 56250.9i) q^{27} +(-61522.9 + 44699.0i) q^{28} +(135177. + 98212.2i) q^{29} -41166.4 q^{30} +(165613. + 9219.76i) q^{31} +32768.0 q^{32} +(-33713.9 - 24494.6i) q^{33} +(153014. - 111171. i) q^{34} +(133313. + 410295. i) q^{35} -127112. q^{36} -405875. q^{37} +(110495. + 340070. i) q^{38} +(-30271.0 + 93164.7i) q^{39} +(57443.8 - 176794. i) q^{40} +(113501. + 82463.4i) q^{41} +(-41632.5 - 128132. i) q^{42} +(629693. + 457499. i) q^{43} +(152240. - 110609. i) q^{44} +(-222833. + 685811. i) q^{45} +(333020. - 241953. i) q^{46} +(-498096. + 361888. i) q^{47} +(-17939.2 + 55211.3i) q^{48} +(-475974. + 345816. i) q^{49} +(-347523. - 252490. i) q^{50} +(103544. + 318677. i) q^{51} +(-357866. - 260005. i) q^{52} +(609815. - 1.87682e6i) q^{53} +(146216. - 450007. i) q^{54} +(-329886. - 1.01528e6i) q^{55} +608371. q^{56} -633481. q^{57} +(-413066. - 1.27129e6i) q^{58} +(1.81177e6 - 1.31633e6i) q^{59} +(266434. + 193576. i) q^{60} -727950. q^{61} +(-1.02851e6 - 838430. i) q^{62} -2.35997e6 q^{63} +(-212079. - 154084. i) q^{64} +(-2.03017e6 + 1.47500e6i) q^{65} +(103021. + 317065. i) q^{66} -308660. q^{67} -1.51308e6 q^{68} +(225355. + 693571. i) q^{69} +(1.06650e6 - 3.28236e6i) q^{70} +(-654480. + 2.01428e6i) q^{71} +(822687. + 597717. i) q^{72} +(87373.6 + 268908. i) q^{73} +(2.62688e6 + 1.90854e6i) q^{74} +(615680. - 447318. i) q^{75} +(883963. - 2.72056e6i) q^{76} +(2.82648e6 - 2.05356e6i) q^{77} +(634005. - 460631. i) q^{78} +(804902. - 2.47723e6i) q^{79} +(-1.20312e6 + 874117. i) q^{80} +(-2.83592e6 - 2.06041e6i) q^{81} +(-346829. - 1.06743e6i) q^{82} +(3.89505e6 + 2.82992e6i) q^{83} +(-333060. + 1.02505e6i) q^{84} +(-2.65251e6 + 8.16357e6i) q^{85} +(-1.92417e6 - 5.92199e6i) q^{86} +2.36814e6 q^{87} -1.50543e6 q^{88} +(973736. + 2.99685e6i) q^{89} +(4.66708e6 - 3.39083e6i) q^{90} +(-6.64416e6 - 4.82726e6i) q^{91} -3.29308e6 q^{92} +(1.97576e6 - 1.27395e6i) q^{93} +4.92545e6 q^{94} +(-1.31287e7 - 9.53853e6i) q^{95} +(375724. - 272980. i) q^{96} +(2.43922e6 + 7.50715e6i) q^{97} +4.70669e6 q^{98} +5.83978e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 80 q^{2} + 28 q^{3} - 640 q^{4} + 168 q^{5} - 1936 q^{6} + 1402 q^{7} - 5120 q^{8} - 6164 q^{9} - 1496 q^{10} - 3402 q^{11} + 1792 q^{12} + 6413 q^{13} + 11216 q^{14} + 46465 q^{15} - 40960 q^{16}+ \cdots + 13336614 q^{99}+O(q^{100}) $ 40 * q - 80 * q^2 + 28 * q^3 - 640 * q^4 + 168 * q^5 - 1936 * q^6 + 1402 * q^7 - 5120 * q^8 - 6164 * q^9 - 1496 * q^10 - 3402 * q^11 + 1792 * q^12 + 6413 * q^13 + 11216 * q^14 + 46465 * q^15 - 40960 * q^16 + 17155 * q^17 - 98152 * q^18 + 67290 * q^19 + 6592 * q^20 + 16727 * q^21 - 27216 * q^22 + 2051 * q^23 + 47616 * q^24 + 787196 * q^25 - 214576 * q^26 + 603289 * q^27 - 62592 * q^28 + 95739 * q^29 - 369200 * q^30 + 540003 * q^31 + 1310720 * q^32 + 941656 * q^33 + 290520 * q^34 - 638364 * q^35 + 2359424 * q^36 + 843716 * q^37 - 169080 * q^38 + 827496 * q^39 + 52736 * q^40 + 175557 * q^41 + 1299656 * q^42 + 566562 * q^43 + 441152 * q^44 - 2450173 * q^45 + 484128 * q^46 - 2289258 * q^47 + 380928 * q^48 - 1290090 * q^49 - 2003912 * q^50 + 351796 * q^51 + 410432 * q^52 - 741339 * q^53 + 4826312 * q^54 - 755935 * q^55 - 434176 * q^56 - 8091472 * q^57 - 1476568 * q^58 - 8176986 * q^59 + 2973760 * q^60 - 10479540 * q^61 + 6613544 * q^62 - 10121022 * q^63 - 2621440 * q^64 + 9085330 * q^65 - 1581152 * q^66 + 7646158 * q^67 - 6844160 * q^68 - 5432460 * q^69 - 5106912 * q^70 - 24632815 * q^71 - 6281728 * q^72 - 11099311 * q^73 - 3436312 * q^74 + 11990582 * q^75 - 1352640 * q^76 + 8000688 * q^77 - 10937992 * q^78 + 10390986 * q^79 - 765952 * q^80 - 23584945 * q^81 + 2535096 * q^82 + 36507958 * q^83 + 10397248 * q^84 + 23914083 * q^85 + 5244176 * q^86 + 16619052 * q^87 - 3574784 * q^88 - 17387733 * q^89 - 2091344 * q^90 - 8973442 * q^91 - 8008576 * q^92 - 21404363 * q^93 - 137504 * q^94 - 12445576 * q^95 + 917504 * q^96 - 1428702 * q^97 + 92378560 * q^98 + 13336614 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/62\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−6.47214	−	4.70228i	−0.572061	−	0.415627i
$2$	−6.47214	−	4.70228i	−0.572061	−	0.415627i
$3$	11.4662	−	8.33068i	0.245186	−	0.178138i	−0.458405	−	0.888743i	$-0.651579\pi$
$3$	11.4662	−	8.33068i	0.245186	−	0.178138i	0.703590	+	0.710606i	$0.251579\pi$
$4$	19.7771	+	60.8676i	0.154508	+	0.475528i
$5$	363.071			1.29896			0.649480	−	0.760378i	$-0.274986\pi$
$5$	363.071			1.29896			0.649480	+	0.760378i	$0.274986\pi$
$6$	−113.384			−0.214300
$7$	367.182	+	1130.07i	0.404611	+	1.24527i	0.921219	+	0.389044i	$0.127194\pi$
$7$	367.182	+	1130.07i	0.404611	+	1.24527i	−0.516608	+	0.856222i	$0.672806\pi$
$8$	158.217	−	486.941i	0.109254	−	0.336249i
$9$	−613.747	+	1888.92i	−0.280634	+	0.863703i
$10$	−2349.84	−	1707.26i	−0.743085	−	0.539883i
$11$	−908.599	−	2796.38i	−0.205825	−	0.633464i	−0.999679	−	0.0253550i	$-0.991928\pi$
$11$	−908.599	−	2796.38i	−0.205825	−	0.633464i	0.793854	−	0.608109i	$-0.208072\pi$
$12$	733.836	+	533.163i	0.122593	+	0.0890689i
$13$	−5591.66	+	4062.58i	−0.705894	+	0.512862i	−0.881846	−	0.471537i	$-0.843699\pi$
$13$	−5591.66	+	4062.58i	−0.705894	+	0.512862i	0.175953	+	0.984399i	$0.443699\pi$
$14$	2937.45	−	9040.56i	0.286103	−	0.880536i
$15$	4163.04	−	3024.62i	0.318486	−	0.231394i
$16$	−3313.73	+	2407.57i	−0.202254	+	0.146946i
$17$	−7305.76	+	22484.8i	−0.360657	+	1.10999i	0.592000	+	0.805938i	$0.298339\pi$
$17$	−7305.76	+	22484.8i	−0.360657	+	1.10999i	−0.952656	+	0.304049i	$0.901661\pi$
$18$	12854.5	−	9339.33i	0.519518	−	0.377452i
$19$	−36160.1	−	26271.8i	−1.20946	−	0.878725i	−0.214279	−	0.976772i	$-0.568740\pi$
$19$	−36160.1	−	26271.8i	−1.20946	−	0.878725i	−0.995182	+	0.0980477i	$0.968740\pi$
$20$	7180.48	+	22099.2i	0.200700	+	0.617693i
$21$	13624.4	+	9898.72i	0.321034	+	0.233245i
$22$	−7268.79	+	22371.0i	−0.145540	+	0.447927i
$23$	−15900.3	+	48936.1i	−0.272495	+	0.838652i	0.717377	+	0.696685i	$0.245343\pi$
$23$	−15900.3	+	48936.1i	−0.272495	+	0.838652i	−0.989871	+	0.141967i	$0.954657\pi$
$24$	−2242.40	−	6901.41i	−0.0331112	−	0.101906i
$25$	53695.3			0.687299
$26$	55293.4			0.616974
$27$	18277.0	+	56250.9i	0.178703	+	0.549992i
$28$	−61522.9	+	44699.0i	−0.529643	+	0.384808i
$29$	135177.	+	98212.2i	1.02923	+	0.747777i	0.968154	−	0.250356i	$-0.0805476\pi$
$29$	135177.	+	98212.2i	1.02923	+	0.747777i	0.0610734	+	0.998133i	$0.480548\pi$
$30$	−41166.4			−0.278367
$31$	165613.	+	9219.76i	0.998454	+	0.0555845i
$31$	165613.	+	9219.76i	0.998454	+	0.0555845i
$32$	32768.0			0.176777
$33$	−33713.9	−	24494.6i	−0.163309	−	0.118651i
$34$	153014.	−	111171.i	0.667658	−	0.485082i
$35$	133313.	+	410295.i	0.525574	+	1.61755i
$36$	−127112.			−0.454075
$37$	−405875.			−1.31731			−0.658653	−	0.752447i	$-0.728873\pi$
$37$	−405875.			−1.31731			−0.658653	+	0.752447i	$0.728873\pi$
$38$	110495.	+	340070.i	0.326664	+	1.00537i
$39$	−30271.0	+	93164.7i	−0.0817149	+	0.251493i
$40$	57443.8	−	176794.i	0.141917	−	0.436775i
$41$	113501.	+	82463.4i	0.257192	+	0.186861i	0.708908	−	0.705301i	$-0.249188\pi$
$41$	113501.	+	82463.4i	0.257192	+	0.186861i	−0.451716	+	0.892162i	$0.649188\pi$
$42$	−41632.5	−	128132.i	−0.0867082	−	0.266860i
$43$	629693.	+	457499.i	1.20778	+	0.877506i	0.995028	−	0.0995994i	$-0.0317561\pi$
$43$	629693.	+	457499.i	1.20778	+	0.877506i	0.212756	+	0.977105i	$0.431756\pi$
$44$	152240.	−	110609.i	0.269428	−	0.195751i
$45$	−222833.	+	685811.i	−0.364533	+	1.12192i
$46$	333020.	−	241953.i	0.504450	−	0.366504i
$47$	−498096.	+	361888.i	−0.699795	+	0.508431i	−0.879865	−	0.475223i	$-0.842367\pi$
$47$	−498096.	+	361888.i	−0.699795	+	0.508431i	0.180070	+	0.983654i	$0.442367\pi$
$48$	−17939.2	+	55211.3i	−0.0234131	+	0.0720582i
$49$	−475974.	+	345816.i	−0.577959	+	0.419912i
$50$	−347523.	−	252490.i	−0.393177	−	0.285660i
$51$	103544.	+	318677.i	0.109303	+	0.336399i
$52$	−357866.	−	260005.i	−0.352947	−	0.256431i
$53$	609815.	−	1.87682e6i	0.562642	−	1.73164i	−0.112212	−	0.993684i	$-0.535793\pi$
$53$	609815.	−	1.87682e6i	0.562642	−	1.73164i	0.674854	−	0.737951i	$-0.264207\pi$
$54$	146216.	−	450007.i	0.126362	−	0.388903i
$55$	−329886.	−	1.01528e6i	−0.267359	−	0.822845i
$56$	608371.			0.462925
$57$	−633481.			−0.453076
$58$	−413066.	−	1.27129e6i	−0.277985	−	0.855549i
$59$	1.81177e6	−	1.31633e6i	1.14847	−	0.834416i	0.160197	−	0.987085i	$-0.448787\pi$
$59$	1.81177e6	−	1.31633e6i	1.14847	−	0.834416i	0.988277	+	0.152669i	$0.0487869\pi$
$60$	266434.	+	193576.i	0.159243	+	0.115697i
$61$	−727950.			−0.410626			−0.205313	−	0.978696i	$-0.565821\pi$
$61$	−727950.			−0.410626			−0.205313	+	0.978696i	$0.565821\pi$
$62$	−1.02851e6	−	838430.i	−0.548075	−	0.446782i
$63$	−2.35997e6			−1.18909
$64$	−212079.	−	154084.i	−0.101127	−	0.0734732i
$65$	−2.03017e6	+	1.47500e6i	−0.916928	+	0.666187i
$66$	103021.	+	317065.i	0.0441083	+	0.135751i
$67$	−308660.			−0.125377			−0.0626885	−	0.998033i	$-0.519967\pi$
$67$	−308660.			−0.125377			−0.0626885	+	0.998033i	$0.519967\pi$
$68$	−1.51308e6			−0.583555
$69$	225355.	+	693571.i	0.0825838	+	0.254167i
$70$	1.06650e6	−	3.28236e6i	0.371637	−	1.14378i
$71$	−654480.	+	2.01428e6i	−0.217016	+	0.667907i	0.781988	+	0.623293i	$0.214206\pi$
$71$	−654480.	+	2.01428e6i	−0.217016	+	0.667907i	−0.999004	+	0.0446138i	$0.985794\pi$
$72$	822687.	+	597717.i	0.259759	+	0.188726i
$73$	87373.6	+	268908.i	0.0262876	+	0.0809048i	0.963340	−	0.268285i	$-0.0864569\pi$
$73$	87373.6	+	268908.i	0.0262876	+	0.0809048i	−0.937052	+	0.349190i	$0.886457\pi$
$74$	2.62688e6	+	1.90854e6i	0.753579	+	0.547508i
$75$	615680.	−	447318.i	0.168516	−	0.122434i
$76$	883963.	−	2.72056e6i	0.230986	−	0.710903i
$77$	2.82648e6	−	2.05356e6i	0.705552	−	0.512613i
$78$	634005.	−	460631.i	0.151273	−	0.109906i
$79$	804902.	−	2.47723e6i	0.183674	−	0.565291i	−0.816249	−	0.577701i	$-0.803950\pi$
$79$	804902.	−	2.47723e6i	0.183674	−	0.565291i	0.999923	+	0.0124095i	$0.00395015\pi$
$80$	−1.20312e6	+	874117.i	−0.262720	+	0.190878i
$81$	−2.83592e6	−	2.06041e6i	−0.592920	−	0.430781i
$82$	−346829.	−	1.06743e6i	−0.0694651	−	0.213792i
$83$	3.89505e6	+	2.82992e6i	0.747722	+	0.543252i	0.895120	−	0.445825i	$-0.147090\pi$
$83$	3.89505e6	+	2.82992e6i	0.747722	+	0.543252i	−0.147398	+	0.989077i	$0.547090\pi$
$84$	−333060.	+	1.02505e6i	−0.0613120	+	0.188699i
$85$	−2.65251e6	+	8.16357e6i	−0.468479	+	1.44183i
$86$	−1.92417e6	−	5.92199e6i	−0.326211	−	1.00397i
$87$	2.36814e6			0.385559
$88$	−1.50543e6			−0.235489
$89$	973736.	+	2.99685e6i	0.146412	+	0.450609i	0.997190	−	0.0749159i	$-0.0238688\pi$
$89$	973736.	+	2.99685e6i	0.146412	+	0.450609i	−0.850778	+	0.525525i	$0.823869\pi$
$90$	4.66708e6	−	3.39083e6i	0.674834	−	0.490295i
$91$	−6.64416e6	−	4.82726e6i	−0.924262	−	0.671515i
$92$	−3.29308e6			−0.440905
$93$	1.97576e6	−	1.27395e6i	0.254708	−	0.164234i
$94$	4.92545e6			0.611643
$95$	−1.31287e7	−	9.53853e6i	−1.57104	−	1.14143i
$96$	375724.	−	272980.i	0.0433431	−	0.0314906i
$97$	2.43922e6	+	7.50715e6i	0.271363	+	0.835168i	0.990159	+	0.139947i	$0.0446934\pi$
$97$	2.43922e6	+	7.50715e6i	0.271363	+	0.835168i	−0.718796	+	0.695221i	$0.755307\pi$
$98$	4.70669e6			0.505155
$99$	5.83978e6			0.604886
$100$	1.06194e6	+	3.26830e6i	0.106194	+	0.326830i
$101$	−4.26515e6	+	1.31268e7i	−0.411917	+	1.26775i	0.503063	+	0.864249i	$0.332206\pi$
$101$	−4.26515e6	+	1.31268e7i	−0.411917	+	1.26775i	−0.914980	+	0.403499i	$0.867794\pi$
$102$	828356.	−	2.54942e6i	0.0772888	−	0.237870i
$103$	1.50512e7	+	1.09353e7i	1.35719	+	0.986054i	0.998618	+	0.0525499i	$0.0167349\pi$
$103$	1.50512e7	+	1.09353e7i	1.35719	+	0.986054i	0.358568	+	0.933504i	$0.383265\pi$
$104$	1.09354e6	+	3.36558e6i	0.0953277	+	0.293388i
$105$	4.94663e6	+	3.59394e6i	0.417010	+	0.302976i
$106$	−1.27721e7	+	9.27950e6i	−1.04158	+	0.756752i
$107$	1.50856e6	−	4.64287e6i	0.119047	−	0.366389i	−0.873722	−	0.486425i	$-0.838301\pi$
$107$	1.50856e6	−	4.64287e6i	0.119047	−	0.366389i	0.992770	+	0.120035i	$0.0383008\pi$
$108$	−3.06239e6	+	2.22496e6i	−0.233926	+	0.169957i
$109$	1.94491e7	−	1.41306e7i	1.43849	−	1.04513i	0.450136	−	0.892960i	$-0.351375\pi$
$109$	1.94491e7	−	1.41306e7i	1.43849	−	1.04513i	0.988355	−	0.152165i	$-0.0486246\pi$
$110$	−2.63909e6	+	8.12227e6i	−0.189051	+	0.581839i
$111$	−4.65384e6	+	3.38121e6i	−0.322984	+	0.234662i
$112$	−3.93746e6	−	2.86073e6i	−0.264822	−	0.192404i
$113$	−1.99621e6	−	6.14371e6i	−0.130146	−	0.400549i	0.864657	−	0.502362i	$-0.167536\pi$
$113$	−1.99621e6	−	6.14371e6i	−0.130146	−	0.400549i	−0.994804	+	0.101813i	$0.967536\pi$
$114$	4.09997e6	+	2.97881e6i	0.259188	+	0.188311i
$115$	−5.77293e6	+	1.77673e7i	−0.353960	+	1.08938i
$116$	−3.30452e6	+	1.01703e7i	−0.196565	+	0.604965i
$117$	−4.24202e6	−	1.30556e7i	−0.244862	−	0.753609i
$118$	−1.79158e7			−1.00380
$119$	−2.80919e7			−1.52816
$120$	−814151.	−	2.50570e6i	−0.0430101	−	0.132372i
$121$	8.77126e6	−	6.37269e6i	0.450104	−	0.327020i
$122$	4.71139e6	+	3.42302e6i	0.234904	+	0.170667i
$123$	1.98840e6			0.0963466
$124$	2.71415e6	+	1.02628e7i	0.127838	+	0.483381i
$125$	−8.86972e6			−0.406186
$126$	1.52740e7	+	1.10972e7i	0.680231	+	0.494217i
$127$	251107.	−	182440.i	0.0108779	−	0.00790327i	−0.582333	−	0.812950i	$-0.697860\pi$
$127$	251107.	−	182440.i	0.0108779	−	0.00790327i	0.593211	+	0.805047i	$0.297860\pi$
$128$	648056.	+	1.99451e6i	0.0273135	+	0.0840623i
$129$	1.10315e7			0.452448
$130$	2.00754e7			0.801425
$131$	759279.	+	2.33682e6i	0.0295088	+	0.0908189i	0.964726	−	0.263255i	$-0.0847961\pi$
$131$	759279.	+	2.33682e6i	0.0295088	+	0.0908189i	−0.935217	+	0.354074i	$0.884796\pi$
$132$	824165.	−	2.53652e6i	0.0311893	−	0.0959907i
$133$	1.64117e7	−	5.05100e7i	0.604884	−	1.86164i
$134$	1.99769e6	+	1.45140e6i	0.0717234	+	0.0521101i
$135$	6.63585e6	+	2.04230e7i	0.232128	+	0.714418i
$136$	9.79288e6	+	7.11495e6i	0.333829	+	0.242541i
$137$	−2.30623e7	+	1.67558e7i	−0.766269	+	0.556727i	−0.900827	−	0.434179i	$-0.857039\pi$
$137$	−2.30623e7	+	1.67558e7i	−0.766269	+	0.556727i	0.134558	+	0.990906i	$0.457039\pi$
$138$	1.80284e6	−	5.54857e6i	0.0583956	−	0.179723i
$139$	3.75086e7	−	2.72516e7i	1.18462	−	0.860676i	0.191934	−	0.981408i	$-0.438524\pi$
$139$	3.75086e7	−	2.72516e7i	1.18462	−	0.860676i	0.992685	+	0.120731i	$0.0385240\pi$
$140$	−2.23371e7	+	1.62289e7i	−0.687986	+	0.499851i
$141$	−2.69650e6	+	8.29896e6i	−0.0810089	+	0.249320i
$142$	1.37076e7	−	9.95916e6i	0.401747	−	0.291886i
$143$	1.64411e7	+	1.19452e7i	0.470170	+	0.341598i
$144$	−2.51391e6	−	7.73701e6i	−0.0701585	−	0.215926i
$145$	4.90790e7	+	3.56580e7i	1.33693	+	0.971334i
$146$	698989.	−	2.15127e6i	0.0185881	−	0.0572083i
$147$	−2.57674e6	+	7.93038e6i	−0.0669051	+	0.205913i
$148$	−8.02703e6	−	2.47047e7i	−0.203535	−	0.626416i
$149$	−4.50123e7			−1.11476			−0.557378	−	0.830259i	$-0.688192\pi$
$149$	−4.50123e7			−1.11476			−0.557378	+	0.830259i	$0.688192\pi$
$150$	−6.08818e6			−0.147288
$151$	−4.72903e6	−	1.45545e7i	−0.111777	−	0.344015i	0.879484	−	0.475928i	$-0.157888\pi$
$151$	−4.72903e6	−	1.45545e7i	−0.111777	−	0.344015i	−0.991261	+	0.131914i	$0.957888\pi$
$152$	−1.85140e7	+	1.34512e7i	−0.427609	+	0.310676i
$153$	−3.79881e7	−	2.76000e7i	−0.857487	−	0.623001i
$154$	−2.79498e7			−0.616675
$155$	6.01292e7	+	3.34742e6i	1.29695	+	0.0722021i
$156$	−6.26938e6			−0.132217
$157$	−5.12228e7	−	3.72156e7i	−1.05637	−	0.767495i	−0.0829539	−	0.996553i	$-0.526435\pi$
$157$	−5.12228e7	−	3.72156e7i	−1.05637	−	0.767495i	−0.973413	+	0.229058i	$0.926435\pi$
$158$	−1.68581e7	+	1.22481e7i	−0.340023	+	0.247041i
$159$	−8.64290e6	−	2.66001e7i	−0.170518	−	0.524800i
$160$	1.18971e7			0.229626
$161$	−6.11395e7			−1.15460
$162$	8.66579e6	+	2.66706e7i	0.160142	+	0.492867i
$163$	2.37646e7	−	7.31399e7i	0.429807	−	1.32281i	−0.468508	−	0.883459i	$-0.655208\pi$
$163$	2.37646e7	−	7.31399e7i	0.429807	−	1.32281i	0.898315	−	0.439351i	$-0.144792\pi$
$164$	−2.77463e6	+	8.53943e6i	−0.0491192	+	0.151173i
$165$	−1.22405e7	−	8.89327e6i	−0.212132	−	0.154123i
$166$	−1.19022e7	−	3.66313e7i	−0.201953	−	0.621547i
$167$	−6.21798e7	−	4.51763e7i	−1.03310	−	0.750590i	−0.0641724	−	0.997939i	$-0.520441\pi$
$167$	−6.21798e7	−	4.51763e7i	−1.03310	−	0.750590i	−0.968927	+	0.247348i	$0.920441\pi$
$168$	6.97570e6	−	5.06815e6i	0.113503	−	0.0824644i
$169$	−4.62823e6	+	1.42442e7i	−0.0737584	+	0.227005i
$170$	5.55548e7	−	4.03629e7i	0.867262	−	0.630103i
$171$	7.18185e7	−	5.21792e7i	1.09837	−	0.798015i
$172$	−1.53934e7	+	4.73759e7i	−0.230666	+	0.709917i
$173$	8.05184e7	−	5.85000e7i	1.18232	−	0.859003i	0.189885	−	0.981806i	$-0.439188\pi$
$173$	8.05184e7	−	5.85000e7i	1.18232	−	0.859003i	0.992431	+	0.122803i	$0.0391884\pi$
$174$	−1.53270e7	−	1.11357e7i	−0.220563	−	0.160249i
$175$	1.97159e7	+	6.06794e7i	0.278089	+	0.855870i
$176$	9.74333e6	+	7.07895e6i	0.134714	+	0.0978756i
$177$	9.80821e6	−	3.01866e7i	0.132948	−	0.409173i
$178$	7.78989e6	−	2.39748e7i	0.103529	−	0.318629i
$179$	−1.35115e7	−	4.15841e7i	−0.176083	−	0.541928i	0.823598	−	0.567174i	$-0.191963\pi$
$179$	−1.35115e7	−	4.15841e7i	−0.176083	−	0.541928i	−0.999681	+	0.0252456i	$0.991963\pi$
$180$	−4.61507e7			−0.589826
$181$	−1.19942e8			−1.50348			−0.751740	−	0.659460i	$-0.770785\pi$
$181$	−1.19942e8			−1.50348			−0.751740	+	0.659460i	$0.770785\pi$
$182$	2.03027e7	+	6.24854e7i	0.249635	+	0.768296i
$183$	−8.34681e6	+	6.06431e6i	−0.100680	+	0.0731481i
$184$	2.13133e7	+	1.54850e7i	0.252225	+	0.183252i
$185$	−1.47361e8			−1.71113
$186$	−1.87778e7	−	1.04537e6i	−0.213969	−	0.0119118i
$187$	6.95141e7			0.777369
$188$	−3.18782e7	−	2.31608e7i	−0.349898	−	0.254215i
$189$	−5.68564e7	+	4.13086e7i	−0.612581	+	0.445066i
$190$	4.01176e7	+	1.23469e8i	0.424324	+	1.30594i
$191$	7.13655e7			0.741090			0.370545	−	0.928814i	$-0.379171\pi$
$191$	7.13655e7			0.741090			0.370545	+	0.928814i	$0.379171\pi$
$192$	−3.71537e6			−0.0378833
$193$	5.23954e7	+	1.61256e8i	0.524617	+	1.61461i	0.765072	+	0.643945i	$0.222703\pi$
$193$	5.23954e7	+	1.61256e8i	0.524617	+	1.61461i	−0.240455	+	0.970660i	$0.577297\pi$
$194$	1.95138e7	−	6.00572e7i	0.191882	−	0.590553i
$195$	−1.09905e7	+	3.38254e7i	−0.106144	+	0.326679i
$196$	−3.04624e7	−	2.21322e7i	−0.288980	−	0.209956i
$197$	−3.91133e6	−	1.20378e7i	−0.0364496	−	0.112180i	0.931176	−	0.364569i	$-0.118784\pi$
$197$	−3.91133e6	−	1.20378e7i	−0.0364496	−	0.112180i	−0.967626	+	0.252389i	$0.918784\pi$
$198$	−3.77959e7	−	2.74603e7i	−0.346032	−	0.251407i
$199$	1.12954e8	−	8.20661e7i	1.01605	−	0.738207i	0.0505845	−	0.998720i	$-0.483892\pi$
$199$	1.12954e8	−	8.20661e7i	1.01605	−	0.738207i	0.965470	+	0.260513i	$0.0838916\pi$
$200$	8.49549e6	−	2.61464e7i	0.0750902	−	0.231104i
$201$	−3.53915e6	+	2.57134e6i	−0.0307406	+	0.0223344i
$202$	8.93304e7	−	6.49023e7i	0.762552	−	0.554027i
$203$	−6.13519e7	+	1.88822e8i	−0.514744	+	1.58422i
$204$	−1.73493e7	+	1.26050e7i	−0.143079	+	0.103953i
$205$	4.12089e7	+	2.99401e7i	0.334082	+	0.242725i
$206$	−4.59922e7	−	1.41550e8i	−0.366563	−	1.12817i
$207$	−8.26775e7	−	6.00687e7i	−0.647875	−	0.470709i
$208$	8.74834e6	−	2.69246e7i	0.0674068	−	0.207457i
$209$	−4.06110e7	+	1.24988e8i	−0.307703	+	0.947013i
$210$	−1.51155e7	−	4.65209e7i	−0.112631	−	0.346641i
$211$	1.33000e8			0.974685			0.487342	−	0.873211i	$-0.337966\pi$
$211$	1.33000e8			0.974685			0.487342	+	0.873211i	$0.337966\pi$
$212$	1.26298e8			0.910375
$213$	9.27594e6	+	2.85484e7i	0.0657702	+	0.202420i
$214$	−3.15957e7	+	2.29556e7i	−0.220384	+	0.160118i
$215$	2.28623e8	+	1.66104e8i	1.56886	+	1.13985i
$216$	3.02826e7			0.204458
$217$	5.03911e7	+	1.90539e8i	0.334768	+	1.26583i
$218$	−1.92324e8			−1.25729
$219$	3.24203e6	+	2.35547e6i	0.0208575	+	0.0151539i
$220$	5.52737e7	−	4.01587e7i	0.349977	−	0.254273i
$221$	−5.04950e7	−	1.55408e8i	−0.314685	−	0.968500i
$222$	4.60197e7			0.282299
$223$	−1.57275e8			−0.949713			−0.474856	−	0.880063i	$-0.657500\pi$
$223$	−1.57275e8			−0.949713			−0.474856	+	0.880063i	$0.657500\pi$
$224$	1.20318e7	+	3.70301e7i	0.0715259	+	0.220134i
$225$	−3.29553e7	+	1.01426e8i	−0.192880	+	0.593623i
$226$	−1.59697e7	+	4.91497e7i	−0.0920274	+	0.283231i
$227$	2.78028e8	+	2.01999e8i	1.57760	+	1.14620i	0.919377	+	0.393378i	$0.128694\pi$
$227$	2.78028e8	+	2.01999e8i	1.57760	+	1.14620i	0.658228	+	0.752819i	$0.271306\pi$
$228$	−1.25284e7	−	3.85585e7i	−0.0700041	−	0.215451i
$229$	−1.32649e8	−	9.63753e7i	−0.729929	−	0.530324i	0.159612	−	0.987180i	$-0.448976\pi$
$229$	−1.32649e8	−	9.63753e7i	−0.729929	−	0.530324i	−0.889541	+	0.456855i	$0.848976\pi$
$230$	1.20910e8	−	8.78461e7i	0.655261	−	0.476075i
$231$	1.53015e7	−	4.70930e7i	0.0816753	−	0.251371i
$232$	6.92109e7	−	5.02846e7i	0.363887	−	0.264379i
$233$	2.15265e7	−	1.56399e7i	0.111488	−	0.0810007i	−0.530644	−	0.847595i	$-0.678050\pi$
$233$	2.15265e7	−	1.56399e7i	0.111488	−	0.0810007i	0.642132	+	0.766594i	$0.278050\pi$
$234$	−3.39361e7	+	1.04445e8i	−0.173144	+	0.532882i
$235$	−1.80844e8	+	1.31391e8i	−0.909006	+	0.660432i
$236$	1.15953e8	+	8.42451e7i	0.574237	+	0.417208i
$237$	−1.14079e7	−	3.51098e7i	−0.0556654	−	0.171321i
$238$	1.81815e8	+	1.32096e8i	0.874199	+	0.635142i
$239$	−4.11854e7	+	1.26755e8i	−0.195142	+	0.600585i	0.804833	+	0.593501i	$0.202255\pi$
$239$	−4.11854e7	+	1.26755e8i	−0.195142	+	0.600585i	−0.999975	+	0.00708342i	$0.997745\pi$
$240$	−6.51321e6	+	2.00456e7i	−0.0304128	+	0.0936008i
$241$	2.96576e7	+	9.12767e7i	0.136482	+	0.420049i	0.995818	−	0.0913632i	$-0.0291224\pi$
$241$	2.96576e7	+	9.12767e7i	0.136482	+	0.420049i	−0.859335	+	0.511413i	$0.829122\pi$
$242$	−8.67350e7			−0.393406
$243$	−1.79033e8			−0.800410
$244$	−1.43967e7	−	4.43086e7i	−0.0634453	−	0.195264i
$245$	−1.72812e8	+	1.25556e8i	−0.750747	+	0.545449i
$246$	−1.28692e7	−	9.35003e6i	−0.0551162	−	0.0400443i
$247$	3.08926e8			1.30441
$248$	3.06922e7	−	7.91849e7i	0.127775	−	0.329657i
$249$	6.82366e7			0.280104
$250$	5.74060e7	+	4.17079e7i	0.232363	+	0.168822i
$251$	−3.75513e7	+	2.72826e7i	−0.149888	+	0.108900i	−0.660202	−	0.751088i	$-0.729529\pi$
$251$	−3.75513e7	+	2.72826e7i	−0.149888	+	0.108900i	0.510314	+	0.859988i	$0.329529\pi$
$252$	−4.66733e7	−	1.43645e8i	−0.183724	−	0.565445i
$253$	1.51291e8			0.587342
$254$	−2.48308e6			−0.00950765
$255$	3.75940e7	+	1.15702e8i	0.141980	+	0.436970i
$256$	5.18444e6	−	1.59561e7i	0.0193136	−	0.0594410i
$257$	3.64555e7	−	1.12198e8i	0.133967	−	0.412307i	−0.861461	−	0.507824i	$-0.830450\pi$
$257$	3.64555e7	−	1.12198e8i	0.133967	−	0.412307i	0.995428	+	0.0955163i	$0.0304502\pi$
$258$	−7.13971e7	−	5.18730e7i	−0.258828	−	0.188050i
$259$	−1.49030e8	−	4.58667e8i	−0.532997	−	1.64040i
$260$	−1.29931e8	−	9.44002e7i	−0.458464	−	0.333094i
$261$	−2.68479e8	+	1.95062e8i	−0.934694	+	0.679095i
$262$	6.07423e6	−	1.86946e7i	0.0208659	−	0.0642186i
$263$	−7.75055e6	+	5.63111e6i	−0.0262717	+	0.0190875i	−0.600844	−	0.799367i	$-0.705169\pi$
$263$	−7.75055e6	+	5.63111e6i	−0.0262717	+	0.0190875i	0.574572	+	0.818454i	$0.305169\pi$
$264$	−1.72615e7	+	1.25412e7i	−0.0577385	+	0.0419495i
$265$	2.21406e8	−	6.81417e8i	0.730851	−	2.24933i
$266$	−3.43731e8	+	2.49735e8i	−1.11978	+	0.813567i
$267$	3.61308e7	+	2.62506e7i	0.116169	+	0.0844014i
$268$	−6.10439e6	−	1.87874e7i	−0.0193718	−	0.0596203i
$269$	−4.13089e8	−	3.00127e8i	−1.29393	−	0.940095i	−0.294053	−	0.955789i	$-0.595004\pi$
$269$	−4.13089e8	−	3.00127e8i	−1.29393	−	0.940095i	−0.999877	+	0.0156939i	$0.995004\pi$
$270$	5.30868e7	−	1.63384e8i	0.164140	−	0.505170i
$271$	3.45486e7	−	1.06330e8i	0.105448	−	0.324536i	−0.884387	−	0.466754i	$-0.845423\pi$
$271$	3.45486e7	−	1.06330e8i	0.105448	−	0.324536i	0.989835	+	0.142218i	$0.0454234\pi$
$272$	−2.99244e7	−	9.20978e7i	−0.0901642	−	0.277497i
$273$	−1.16398e8			−0.346238
$274$	2.28053e8			0.669743
$275$	−4.87875e7	−	1.50152e8i	−0.141463	−	0.435379i
$276$	−3.77591e7	+	2.74336e7i	−0.108104	+	0.0785419i
$277$	1.62512e8	+	1.18072e8i	0.459415	+	0.333784i	0.793302	−	0.608829i	$-0.208360\pi$
$277$	1.62512e8	+	1.18072e8i	0.459415	+	0.333784i	−0.333887	+	0.942613i	$0.608360\pi$
$278$	−3.70905e8			−1.03540
$279$	−1.19060e8	+	3.07171e8i	−0.328209	+	0.846769i
$280$	2.20882e8			0.601322
$281$	−4.39855e7	−	3.19573e7i	−0.118260	−	0.0859208i	0.527083	−	0.849814i	$-0.323286\pi$
$281$	−4.39855e7	−	3.19573e7i	−0.118260	−	0.0859208i	−0.645343	+	0.763893i	$0.723286\pi$
$282$	5.64761e7	−	4.10323e7i	0.149966	−	0.108957i
$283$	−5.10025e7	−	1.56969e8i	−0.133764	−	0.411683i	0.861632	−	0.507534i	$-0.169443\pi$
$283$	−5.10025e7	−	1.56969e8i	−0.133764	−	0.411683i	−0.995396	+	0.0958511i	$0.969443\pi$
$284$	−1.35548e8			−0.351140
$285$	−2.29998e8			−0.588528
$286$	−5.02395e7	−	1.54621e8i	−0.126989	−	0.390830i
$287$	−5.15139e7	+	1.58543e8i	−0.128629	+	0.395878i
$288$	−2.01113e7	+	6.18961e7i	−0.0496096	+	0.152683i
$289$	−1.20222e8	−	8.73462e7i	−0.292982	−	0.212864i
$290$	−1.49972e8	−	4.61566e8i	−0.361091	−	1.11132i
$291$	9.05082e7	+	6.57581e7i	0.215309	+	0.156431i
$292$	−1.46398e7	+	1.06364e7i	−0.0344109	+	0.0250010i
$293$	1.79884e8	−	5.53625e8i	0.417787	−	1.28582i	−0.491948	−	0.870625i	$-0.663715\pi$
$293$	1.79884e8	−	5.53625e8i	0.417787	−	1.28582i	0.909734	−	0.415191i	$-0.136285\pi$
$294$	5.39679e7	−	3.92100e7i	0.123857	−	0.0899872i
$295$	6.57801e8	−	4.77920e8i	1.49182	−	1.08387i
$296$	−6.42162e7	+	1.97637e8i	−0.143921	+	0.442943i
$297$	1.40692e8	−	1.02219e8i	0.311618	−	0.226404i
$298$	2.91326e8	+	2.11661e8i	0.637709	+	0.463322i
$299$	−1.09898e8	−	3.38230e8i	−0.237760	−	0.731751i
$300$	3.94035e7	+	2.86283e7i	0.0842579	+	0.0612170i
$301$	−2.85793e8	+	8.79582e8i	−0.604045	+	1.85906i
$302$	−3.78323e7	+	1.16436e8i	−0.0790384	+	0.243255i
$303$	6.04499e7	+	1.86046e8i	0.124838	+	0.384212i
$304$	1.83076e8			0.373744
$305$	−2.64297e8			−0.533388
$306$	1.16081e8	+	3.57261e8i	0.231599	+	0.712789i
$307$	4.07029e8	−	2.95724e8i	0.802862	−	0.583313i	−0.108890	−	0.994054i	$-0.534730\pi$
$307$	4.07029e8	−	2.95724e8i	0.802862	−	0.583313i	0.911752	+	0.410740i	$0.134730\pi$
$308$	1.80895e8	+	1.31428e8i	0.352776	+	0.256307i
$309$	2.63678e8			0.508416
$310$	−3.73424e8	−	3.04409e8i	−0.711927	−	0.580352i
$311$	2.78069e8			0.524193			0.262096	−	0.965042i	$-0.415586\pi$
$311$	2.78069e8			0.524193			0.262096	+	0.965042i	$0.415586\pi$
$312$	4.05763e7	+	2.94804e7i	0.0756365	+	0.0549531i
$313$	−1.91449e8	+	1.39096e8i	−0.352897	+	0.256395i	−0.750083	−	0.661343i	$-0.769987\pi$
$313$	−1.91449e8	+	1.39096e8i	−0.352897	+	0.256395i	0.397186	+	0.917738i	$0.369987\pi$
$314$	1.56523e8	+	4.81728e8i	0.285315	+	0.878109i
$315$	−8.56834e8			−1.54458
$316$	1.66702e8			0.297191
$317$	2.68148e8	+	8.25274e8i	0.472788	+	1.45509i	0.848917	+	0.528526i	$0.177255\pi$
$317$	2.68148e8	+	8.25274e8i	0.472788	+	1.45509i	−0.376129	+	0.926567i	$0.622745\pi$
$318$	−6.91432e7	+	2.12801e8i	−0.120574	+	0.371090i
$319$	1.51816e8	−	4.67243e8i	0.261849	−	0.805890i
$320$	−7.69996e7	−	5.59435e7i	−0.131360	−	0.0954388i
$321$	−2.13808e7	−	6.58033e7i	−0.0360791	−	0.111040i
$322$	3.95703e8	+	2.87495e8i	0.660501	+	0.479882i
$323$	8.54894e8	−	6.21117e8i	1.41157	−	1.02557i
$324$	6.93263e7	−	2.13365e8i	0.113238	−	0.348510i
$325$	−3.00246e8	+	2.18141e8i	−0.485160	+	0.352490i
$326$	−4.97732e8	+	3.61623e8i	−0.795671	+	0.578089i
$327$	1.05290e8	−	3.24049e8i	0.166521	−	0.512499i
$328$	5.81126e7	−	4.22213e7i	0.0909310	−	0.0660652i
$329$	−5.91851e8	−	4.30005e8i	−0.916277	−	0.665714i
$330$	3.74037e7	+	1.15117e8i	0.0572949	+	0.176336i
$331$	4.48535e8	+	3.25880e8i	0.679828	+	0.493924i	0.873300	−	0.487182i	$-0.161975\pi$
$331$	4.48535e8	+	3.25880e8i	0.679828	+	0.493924i	−0.193473	+	0.981106i	$0.561975\pi$
$332$	−9.52178e7	+	2.93050e8i	−0.142802	+	0.439500i
$333$	2.49105e8	−	7.66665e8i	0.369681	−	1.13776i
$334$	1.90005e8	+	5.84774e8i	0.279030	+	0.858768i
$335$	−1.12065e8			−0.162860
$336$	−6.89796e7			−0.0992049
$337$	1.37947e8	+	4.24559e8i	0.196340	+	0.604273i	0.999958	+	0.00912760i	$0.00290545\pi$
$337$	1.37947e8	+	4.24559e8i	0.196340	+	0.604273i	−0.803618	+	0.595145i	$0.797095\pi$
$338$	9.69349e7	−	7.04274e7i	0.136544	−	0.0992049i
$339$	−7.40702e7	−	5.38152e7i	−0.103263	−	0.0750250i
$340$	−5.49356e8			−0.758015
$341$	−1.24694e8	−	4.71494e8i	−0.170296	−	0.643925i
$342$	−7.10180e8			−0.960013
$343$	2.26102e8	+	1.64273e8i	0.302535	+	0.219805i
$344$	3.22403e8	−	2.34239e8i	0.427016	−	0.310245i
$345$	8.18197e7	+	2.51815e8i	0.107273	+	0.330153i
$346$	−7.96209e8			−1.03338
$347$	7.81754e7			0.100442			0.0502212	−	0.998738i	$-0.484007\pi$
$347$	7.81754e7			0.100442			0.0502212	+	0.998738i	$0.484007\pi$
$348$	4.68350e7	+	1.44143e8i	0.0595721	+	0.183344i
$349$	−2.95804e7	+	9.10390e7i	−0.0372490	+	0.114641i	−0.967952	−	0.251135i	$-0.919196\pi$
$349$	−2.95804e7	+	9.10390e7i	−0.0372490	+	0.114641i	0.930703	+	0.365776i	$0.119196\pi$
$350$	1.57727e8	−	4.85435e8i	0.196639	−	0.605192i
$351$	−3.30723e8	−	2.40284e8i	−0.408215	−	0.296586i
$352$	−2.97730e7	−	9.16318e7i	−0.0363850	−	0.111982i
$353$	−1.23297e8	−	8.95803e7i	−0.149190	−	0.108393i	0.510686	−	0.859767i	$-0.329391\pi$
$353$	−1.23297e8	−	8.95803e7i	−0.149190	−	0.108393i	−0.659876	+	0.751374i	$0.729391\pi$
$354$	−2.05426e8	+	1.49251e8i	−0.246118	+	0.178815i
$355$	−2.37622e8	+	7.31327e8i	−0.281896	+	0.867585i
$356$	−1.63154e8	+	1.18538e8i	−0.191656	+	0.139246i
$357$	−3.22108e8	+	2.34025e8i	−0.374682	+	0.272222i
$358$	−1.08092e8	+	3.32673e8i	−0.124510	+	0.383201i
$359$	−3.72613e8	+	2.70719e8i	−0.425038	+	0.308808i	−0.779662	−	0.626201i	$-0.784609\pi$
$359$	−3.72613e8	+	2.70719e8i	−0.425038	+	0.308808i	0.354624	+	0.935009i	$0.384609\pi$
$360$	2.98693e8	+	2.17013e8i	0.337417	+	0.245148i
$361$	3.41121e8	+	1.04986e9i	0.381621	+	1.17451i
$362$	7.76283e8	+	5.64003e8i	0.860083	+	0.624887i
$363$	4.74841e7	−	1.46141e8i	0.0521045	−	0.160361i
$364$	1.62422e8	−	4.99883e8i	0.176518	−	0.543267i
$365$	3.17228e7	+	9.76327e7i	0.0341465	+	0.105092i
$366$	8.25378e7			0.0879973
$367$	9.64965e8			1.01901			0.509507	−	0.860466i	$-0.329828\pi$
$367$	9.64965e8			1.01901			0.509507	+	0.860466i	$0.329828\pi$
$368$	−6.51276e7	−	2.00442e8i	−0.0681236	−	0.209663i
$369$	−2.25428e8	+	1.63783e8i	−0.233569	+	0.169698i
$370$	9.53743e8	+	6.92935e8i	0.978870	+	0.711191i
$371$	2.34485e9			2.38400
$372$	1.16617e8	+	9.50645e7i	0.117452	+	0.0957454i
$373$	−8.85883e8			−0.883884			−0.441942	−	0.897044i	$-0.645710\pi$
$373$	−8.85883e8			−0.883884			−0.441942	+	0.897044i	$0.645710\pi$
$374$	−4.49905e8	−	3.26875e8i	−0.444703	−	0.323096i
$375$	−1.01702e8	+	7.38908e7i	−0.0995909	+	0.0723570i
$376$	9.74110e7	+	2.99800e8i	0.0945041	+	0.290854i
$377$	−1.15486e9			−1.11003
$378$	5.62227e8			0.535415
$379$	1.58086e7	+	4.86539e7i	0.0149161	+	0.0459072i	0.958238	−	0.285973i	$-0.0923169\pi$
$379$	1.58086e7	+	4.86539e7i	0.0149161	+	0.0459072i	−0.943321	+	0.331881i	$0.892317\pi$
$380$	3.20941e8	−	9.87755e8i	0.300042	−	0.923436i
$381$	1.35939e6	−	4.18378e6i	0.00125924	−	0.00387553i
$382$	−4.61887e8	−	3.35580e8i	−0.423949	−	0.308017i
$383$	5.58289e8	+	1.71824e9i	0.507765	+	1.56274i	0.796071	+	0.605203i	$0.206908\pi$
$383$	5.58289e8	+	1.71824e9i	0.507765	+	1.56274i	−0.288306	+	0.957538i	$0.593092\pi$
$384$	2.40464e7	+	1.74707e7i	0.0216715	+	0.0157453i
$385$	1.02621e9	−	7.45587e8i	0.916484	−	0.665865i
$386$	4.19163e8	−	1.29005e9i	0.370960	−	1.14170i
$387$	−1.25065e9	+	9.08650e8i	−1.09685	+	0.796908i
$388$	−4.08702e8	+	2.96939e8i	−0.355218	+	0.258081i
$389$	9.09537e6	−	2.79927e7i	0.00783424	−	0.0241113i	−0.947063	−	0.321048i	$-0.895965\pi$
$389$	9.09537e6	−	2.79927e7i	0.00783424	−	0.0241113i	0.954897	+	0.296937i	$0.0959650\pi$
$390$	2.30189e8	−	1.67242e8i	0.196498	−	0.142764i
$391$	−9.84155e8	−	7.15030e8i	−0.832616	−	0.604931i
$392$	9.30847e7	+	2.86485e8i	0.0780508	+	0.240216i
$393$	2.81734e7	+	2.04691e7i	0.0234134	+	0.0170108i
$394$	−3.12906e7	+	9.63026e7i	−0.0257737	+	0.0793234i
$395$	2.92236e8	−	8.99411e8i	0.238586	−	0.734291i
$396$	1.15494e8	+	3.55454e8i	0.0934600	+	0.287640i
$397$	5.62375e7			0.0451086			0.0225543	−	0.999746i	$-0.492820\pi$
$397$	5.62375e7			0.0451086			0.0225543	+	0.999746i	$0.492820\pi$
$398$	−1.11695e9			−0.888065
$399$	−2.32603e8	−	7.15877e8i	−0.183320	−	0.564200i
$400$	−1.77932e8	+	1.29275e8i	−0.139009	+	0.100996i
$401$	−1.41293e9	−	1.02655e9i	−1.09425	−	0.795016i	−0.114135	−	0.993465i	$-0.536410\pi$
$401$	−1.41293e9	−	1.02655e9i	−1.09425	−	0.795016i	−0.980111	+	0.198449i	$0.936410\pi$
$402$	3.49971e7			0.0268683
$403$	−9.63507e8	+	6.21262e8i	−0.733309	+	0.472832i
$404$	−8.83348e8			−0.666495
$405$	−1.02964e9	−	7.48076e8i	−0.770180	−	0.559568i
$406$	1.28497e9	−	9.33586e8i	0.952910	−	0.692330i
$407$	3.68778e8	+	1.13498e9i	0.271134	+	0.834465i
$408$	1.71559e8			0.125056
$409$	−5.25311e8			−0.379652			−0.189826	−	0.981818i	$-0.560792\pi$
$409$	−5.25311e8			−0.379652			−0.189826	+	0.981818i	$0.560792\pi$
$410$	−1.25923e8	−	3.87552e8i	−0.0902324	−	0.277707i
$411$	−1.24850e8	+	3.84249e8i	−0.0887040	+	0.273003i
$412$	−3.67938e8	+	1.13240e9i	−0.259200	+	0.797734i
$413$	2.15279e9	+	1.56410e9i	1.50376	+	1.09254i
$414$	2.52640e8	+	7.77546e8i	0.174985	+	0.538548i
$415$	1.41418e9	+	1.02746e9i	0.971262	+	0.705663i
$416$	−1.83228e8	+	1.33123e8i	−0.124786	+	0.0906620i
$417$	2.03057e8	−	6.24944e8i	0.137133	−	0.422051i
$418$	8.50569e8	−	6.17974e8i	0.569629	−	0.413860i
$419$	−5.37969e7	+	3.90857e7i	−0.0357280	+	0.0259579i	−0.605506	−	0.795841i	$-0.707029\pi$
$419$	−5.37969e7	+	3.90857e7i	−0.0357280	+	0.0259579i	0.569778	+	0.821799i	$0.307029\pi$
$420$	−1.20924e8	+	3.72167e8i	−0.0796419	+	0.245112i
$421$	2.43635e9	−	1.77011e9i	1.59130	−	1.15615i	0.689240	−	0.724533i	$-0.257945\pi$
$421$	2.43635e9	−	1.77011e9i	1.59130	−	1.15615i	0.902059	−	0.431613i	$-0.142055\pi$
$422$	−8.60796e8	−	6.25405e8i	−0.557579	−	0.405105i
$423$	−3.77872e8	−	1.16297e9i	−0.242747	−	0.747098i
$424$	−8.17416e8	−	5.93888e8i	−0.520790	−	0.378376i
$425$	−3.92285e8	+	1.20733e9i	−0.247879	+	0.762894i
$426$	7.42075e7	−	2.28387e8i	0.0465066	−	0.143133i
$427$	−2.67290e8	−	8.22634e8i	−0.166144	−	0.511339i
$428$	3.12435e8			0.192622
$429$	2.88028e8			0.176130
$430$	−6.98609e8	−	2.15010e9i	−0.423736	−	1.30412i
$431$	−1.00085e9	+	7.27159e8i	−0.602140	+	0.437480i	−0.846638	−	0.532169i	$-0.821377\pi$
$431$	−1.00085e9	+	7.27159e8i	−0.602140	+	0.437480i	0.244498	+	0.969650i	$0.421377\pi$
$432$	−1.95993e8	−	1.42397e8i	−0.116963	−	0.0849784i
$433$	−1.22160e9			−0.723141			−0.361570	−	0.932345i	$-0.617759\pi$
$433$	−1.22160e9			−0.723141			−0.361570	+	0.932345i	$0.617759\pi$
$434$	5.69832e8	−	1.47015e9i	0.334605	−	0.863272i
$435$	8.59804e8			0.500826
$436$	1.24474e9	+	9.04359e8i	0.719246	+	0.522563i
$437$	1.86060e9	−	1.35180e9i	1.06652	−	0.774869i
$438$	−9.90677e6	−	3.04899e7i	−0.00563343	−	0.0173379i
$439$	3.40228e8			0.191931			0.0959653	−	0.995385i	$-0.469406\pi$
$439$	3.40228e8			0.191931			0.0959653	+	0.995385i	$0.469406\pi$
$440$	−5.46577e8			−0.305891
$441$	−3.61090e8	−	1.11132e9i	−0.200484	−	0.617027i
$442$	−4.03960e8	+	1.24326e9i	−0.222516	+	0.684833i
$443$	−6.70489e8	+	2.06355e9i	−0.366419	+	1.12772i	0.582668	+	0.812710i	$0.302009\pi$
$443$	−6.70489e8	+	2.06355e9i	−0.366419	+	1.12772i	−0.949087	+	0.315013i	$0.897991\pi$
$444$	−2.97846e8	−	2.16398e8i	−0.161492	−	0.117331i
$445$	3.53535e8	+	1.08807e9i	0.190183	+	0.585324i
$446$	1.01790e9	+	7.39551e8i	0.543294	+	0.394726i
$447$	−5.16120e8	+	3.74983e8i	−0.273322	+	0.198580i
$448$	9.62545e7	−	2.96241e8i	0.0505764	−	0.155658i
$449$	−6.61972e8	+	4.80951e8i	−0.345126	+	0.250749i	−0.746821	−	0.665025i	$-0.768421\pi$
$449$	−6.61972e8	+	4.80951e8i	−0.345126	+	0.250749i	0.401695	+	0.915773i	$0.368421\pi$
$450$	6.90225e8	−	5.01478e8i	0.357065	−	0.259423i
$451$	1.27472e8	−	3.92319e8i	0.0654331	−	0.201382i
$452$	3.34474e8	−	2.43009e8i	0.170364	−	0.123777i
$453$	−1.75473e8	−	1.27488e8i	−0.0886881	−	0.0644357i
$454$	−8.49578e8	−	2.61473e9i	−0.426096	−	1.31139i
$455$	−2.41230e9	−	1.75264e9i	−1.20058	−	0.872272i
$456$	−1.00227e8	+	3.08468e8i	−0.0495004	+	0.152347i
$457$	5.01933e8	−	1.54479e9i	0.246002	−	0.757118i	−0.749468	−	0.662041i	$-0.769690\pi$
$457$	5.01933e8	−	1.54479e9i	0.246002	−	0.757118i	0.995470	−	0.0950766i	$-0.0303096\pi$
$458$	4.05340e8	+	1.24751e9i	0.197147	+	0.606756i
$459$	−1.39832e9			−0.674935
$460$	−1.19562e9			−0.572719
$461$	9.95602e8	+	3.06415e9i	0.473296	+	1.45665i	0.848243	+	0.529608i	$0.177661\pi$
$461$	9.95602e8	+	3.06415e9i	0.473296	+	1.45665i	−0.374947	+	0.927046i	$0.622339\pi$
$462$	−3.20478e8	+	2.32841e8i	−0.151200	+	0.109853i
$463$	−1.46130e9	−	1.06170e9i	−0.684238	−	0.497128i	0.190523	−	0.981683i	$-0.438982\pi$
$463$	−1.46130e9	−	1.06170e9i	−0.684238	−	0.497128i	−0.874761	+	0.484555i	$0.838982\pi$
$464$	−6.84395e8			−0.318049
$465$	7.17339e8	−	4.62534e8i	0.330856	−	0.213333i
$466$	−2.12866e8			−0.0974440
$467$	−2.69729e9	−	1.95969e9i	−1.22551	−	0.890387i	−0.228967	−	0.973434i	$-0.573535\pi$
$467$	−2.69729e9	−	1.95969e9i	−1.22551	−	0.890387i	−0.996546	+	0.0830470i	$0.973535\pi$
$468$	7.10768e8	−	5.16403e8i	0.320529	−	0.232878i
$469$	−1.13334e8	−	3.48807e8i	−0.0507290	−	0.156128i
$470$	1.78829e9			0.794501
$471$	−8.97362e8			−0.395726
$472$	−3.54322e8	−	1.09049e9i	−0.155096	−	0.477337i
$473$	7.07202e8	−	2.17654e9i	0.307276	−	0.945700i
$474$	−9.12630e7	+	2.80879e8i	−0.0393614	+	0.121142i
$475$	−1.94163e9	−	1.41067e9i	−0.831262	−	0.603947i
$476$	−5.55577e8	−	1.70989e9i	−0.236113	−	0.726681i
$477$	3.17088e9	+	2.30378e9i	1.33772	+	0.971912i
$478$	8.62597e8	−	6.26714e8i	0.361252	−	0.262465i
$479$	3.62880e8	−	1.11683e9i	0.150865	−	0.464315i	−0.846853	−	0.531826i	$-0.821506\pi$
$479$	3.62880e8	−	1.11683e9i	0.150865	−	0.464315i	0.997718	+	0.0675115i	$0.0215059\pi$
$480$	1.36414e8	−	9.91109e7i	0.0563010	−	0.0409051i
$481$	2.26952e9	−	1.64890e9i	0.929877	−	0.675595i
$482$	2.37261e8	−	7.30214e8i	0.0965076	−	0.297020i
$483$	−7.01037e8	+	5.09333e8i	−0.283091	+	0.205678i
$484$	5.61361e8	+	4.07852e8i	0.225052	+	0.163510i
$485$	8.85609e8	+	2.72562e9i	0.352489	+	1.08485i
$486$	1.15873e9	+	8.41866e8i	0.457883	+	0.332672i
$487$	−1.12269e9	+	3.45529e9i	−0.440463	+	1.35561i	0.446920	+	0.894574i	$0.352521\pi$
$487$	−1.12269e9	+	3.45529e9i	−0.440463	+	1.35561i	−0.887383	+	0.461033i	$0.847479\pi$
$488$	−1.15174e8	+	3.54468e8i	−0.0448626	+	0.138073i
$489$	−3.36815e8	−	1.03661e9i	−0.130260	−	0.400899i
$490$	1.70886e9			0.656177
$491$	−3.08439e9			−1.17594			−0.587969	−	0.808884i	$-0.700072\pi$
$491$	−3.08439e9			−1.17594			−0.587969	+	0.808884i	$0.700072\pi$
$492$	3.93248e7	+	1.21029e8i	0.0148864	+	0.0458155i
$493$	−3.19586e9	+	2.32193e9i	−1.20122	+	0.872738i
$494$	−1.99941e9	−	1.45266e9i	−0.746205	−	0.542150i
$495$	2.12025e9			0.785723
$496$	−5.70994e8	+	3.68172e8i	−0.210109	+	0.135477i
$497$	−2.51659e9			−0.919529
$498$	−4.41637e8	−	3.20868e8i	−0.160237	−	0.116419i
$499$	4.31868e9	−	3.13770e9i	1.55596	−	1.13047i	0.616738	−	0.787169i	$-0.288454\pi$
$499$	4.31868e9	−	3.13770e9i	1.55596	−	1.13047i	0.939224	−	0.343304i	$-0.111546\pi$
$500$	−1.75417e8	−	5.39879e8i	−0.0627592	−	0.193153i
$501$	−1.08932e9			−0.387009
$502$	3.71328e8			0.131007
$503$	1.14146e9	+	3.51306e9i	0.399920	+	1.23083i	0.925063	+	0.379814i	$0.124012\pi$
$503$	1.14146e9	+	3.51306e9i	0.399920	+	1.23083i	−0.525143	+	0.851014i	$0.675988\pi$
$504$	−3.73386e8	+	1.14916e9i	−0.129913	+	0.399830i
$505$	−1.54855e9	+	4.76595e9i	−0.535063	+	1.64676i
$506$	−9.79175e8	−	7.11412e8i	−0.335996	−	0.244115i
$507$	6.55959e7	+	2.01883e8i	0.0223537	+	0.0687975i
$508$	1.60708e7	+	1.16762e7i	0.00543896	+	0.00395163i
$509$	−1.64781e9	+	1.19720e9i	−0.553852	+	0.402397i	−0.829204	−	0.558946i	$-0.811206\pi$
$509$	−1.64781e9	+	1.19720e9i	−0.553852	+	0.402397i	0.275352	+	0.961344i	$0.411206\pi$
$510$	3.00752e8	−	9.25618e8i	0.100395	−	0.308984i
$511$	−2.71803e8	+	1.97477e8i	−0.0901117	+	0.0654700i
$512$	−1.08584e8	+	7.88912e7i	−0.0357538	+	0.0259767i
$513$	8.16916e8	−	2.51421e9i	0.267157	−	0.822225i
$514$	−7.63534e8	+	5.54740e8i	−0.248003	+	0.180185i
$515$	5.46463e9	+	3.97029e9i	1.76293	+	1.28084i
$516$	2.18170e8	+	6.71458e8i	0.0699071	+	0.215152i
$517$	1.46455e9	+	1.06406e9i	0.466108	+	0.338647i
$518$	−1.19224e9	+	3.66934e9i	−0.376886	+	1.15993i
$519$	4.35894e8	−	1.34155e9i	0.136866	−	0.421230i
$520$	3.97033e8	+	1.22194e9i	0.123827	+	0.381100i
$521$	3.60355e9			1.11635			0.558173	−	0.829725i	$-0.311503\pi$
$521$	3.60355e9			1.11635			0.558173	+	0.829725i	$0.311503\pi$
$522$	2.65487e9			0.816952
$523$	−1.69465e9	−	5.21560e9i	−0.517994	−	1.59422i	−0.777768	−	0.628551i	$-0.783648\pi$
$523$	−1.69465e9	−	5.21560e9i	−0.517994	−	1.59422i	0.259774	−	0.965669i	$-0.416352\pi$
$524$	−1.27220e8	+	9.24311e7i	−0.0386276	+	0.0280646i
$525$	7.31567e8	+	5.31515e8i	0.220646	+	0.160309i
$526$	7.66417e7			0.0229623
$527$	−1.41723e9	+	3.65642e9i	−0.421797	+	1.08822i
$528$	1.70691e8			0.0504653
$529$	6.12642e8	+	4.45110e8i	0.179933	+	0.130729i
$530$	−4.63719e9	+	3.36911e9i	−1.35297	+	0.982992i
$531$	1.37447e9	+	4.23018e9i	0.398386	+	1.22611i
$532$	3.39900e9			0.978723
$533$	−9.69675e8			−0.277384
$534$	−1.10406e8	−	3.39795e8i	−0.0313761	−	0.0965656i
$535$	5.47713e8	−	1.68569e9i	0.154638	−	0.475926i
$536$	−4.88351e7	+	1.50299e8i	−0.0136979	+	0.0421579i
$537$	−5.01349e8	−	3.64252e8i	−0.139711	−	0.101506i
$538$	1.26229e9	+	3.88492e9i	0.349479	+	1.07558i
$539$	1.39950e9	+	1.01680e9i	0.384958	+	0.279688i
$540$	−1.11186e9	+	8.07817e8i	−0.303860	+	0.220767i
$541$	−1.11104e9	+	3.41944e9i	−0.301676	+	0.928462i	0.679221	+	0.733934i	$0.262318\pi$
$541$	−1.11104e9	+	3.41944e9i	−0.301676	+	0.928462i	−0.980897	+	0.194529i	$0.937682\pi$
$542$	−7.23596e8	+	5.25723e8i	−0.195209	+	0.141827i
$543$	−1.37528e9	+	9.99201e8i	−0.368632	+	0.267827i
$544$	−2.39395e8	+	7.36782e8i	−0.0637557	+	0.196220i
$545$	7.06140e9	−	5.13041e9i	1.86854	−	1.35758i
$546$	7.53341e8	+	5.47334e8i	0.198069	+	0.143906i
$547$	−3.14141e8	−	9.66826e8i	−0.0820670	−	0.252576i	0.901601	−	0.432569i	$-0.142393\pi$
$547$	−3.14141e8	−	9.66826e8i	−0.0820670	−	0.252576i	−0.983668	+	0.179992i	$0.942393\pi$
$548$	−1.47599e9	−	1.07237e9i	−0.383134	−	0.278363i
$549$	4.46777e8	−	1.37504e9i	0.115236	−	0.354659i
$550$	−3.90300e8	+	1.20122e9i	−0.100030	+	0.307860i
$551$	−2.30781e9	−	7.10272e9i	−0.587720	−	1.80881i
$552$	3.73383e8			0.0944860
$553$	3.09499e9			0.778254
$554$	−4.96591e8	−	1.52835e9i	−0.124084	−	0.381890i
$555$	−1.68967e9	+	1.22762e9i	−0.419544	+	0.304816i
$556$	2.40055e9	+	1.74410e9i	0.592310	+	0.430338i
$557$	4.50454e9			1.10448			0.552240	−	0.833685i	$-0.313773\pi$
$557$	4.50454e9			1.10448			0.552240	+	0.833685i	$0.313773\pi$
$558$	2.21497e9	−	1.42820e9i	0.539695	−	0.347991i
$559$	−5.37965e9			−1.30261
$560$	−1.42958e9	−	1.03865e9i	−0.343993	−	0.249925i
$561$	7.97062e8	−	5.79100e8i	0.190600	−	0.138479i
$562$	1.34408e8	+	4.13664e8i	0.0319409	+	0.0983039i
$563$	4.21996e9			0.996618			0.498309	−	0.867000i	$-0.333955\pi$
$563$	4.21996e9			0.996618			0.498309	+	0.867000i	$0.333955\pi$
$564$	−5.58467e8			−0.131075
$565$	−7.24766e8	−	2.23060e9i	−0.169055	−	0.520298i
$566$	−4.08020e8	+	1.25576e9i	−0.0945853	+	0.291104i
$567$	1.28711e9	−	3.96133e9i	0.296535	−	0.912642i
$568$	8.77287e8	+	6.37386e8i	0.200873	+	0.145943i
$569$	−2.35648e9	−	7.25250e9i	−0.536254	−	1.65042i	−0.740923	−	0.671590i	$-0.765612\pi$
$569$	−2.35648e9	−	7.25250e9i	−0.536254	−	1.65042i	0.204668	−	0.978831i	$-0.434388\pi$
$570$	1.48858e9	+	1.08152e9i	0.336674	+	0.244608i
$571$	1.07961e9	−	7.84380e8i	0.242683	−	0.176319i	−0.459795	−	0.888025i	$-0.652077\pi$
$571$	1.07961e9	−	7.84380e8i	0.242683	−	0.176319i	0.702478	+	0.711706i	$0.252077\pi$
$572$	−4.01916e8	+	1.23697e9i	−0.0897944	+	0.276359i
$573$	8.18290e8	−	5.94523e8i	0.181705	−	0.132016i
$574$	1.07892e9	−	7.83881e8i	0.238121	−	0.173005i
$575$	−8.53771e8	+	2.62764e9i	−0.187285	+	0.576405i
$576$	4.21216e8	−	3.06031e8i	0.0918387	−	0.0667247i
$577$	2.76376e9	+	2.00799e9i	0.598943	+	0.435158i	0.845504	−	0.533970i	$-0.179300\pi$
$577$	2.76376e9	+	2.00799e9i	0.598943	+	0.435158i	−0.246560	+	0.969127i	$0.579300\pi$
$578$	3.67365e8	+	1.13063e9i	0.0791316	+	0.243542i
$579$	1.94415e9	+	1.41251e9i	0.416251	+	0.302424i
$580$	−1.19978e9	+	3.69253e9i	−0.255330	+	0.785825i
$581$	−1.76782e9	+	5.44078e9i	−0.373956	+	1.15092i
$582$	−2.76568e8	−	8.51190e8i	−0.0581530	−	0.178977i
$583$	−5.80237e9			−1.21273
$584$	1.44766e8			0.0300762
$585$	−1.54015e9	−	4.74010e9i	−0.318067	−	0.978908i
$586$	−3.76753e9	+	2.73727e9i	−0.773419	+	0.561922i
$587$	3.29100e9	+	2.39105e9i	0.671576	+	0.487928i	0.870552	−	0.492076i	$-0.163762\pi$
$587$	3.29100e9	+	2.39105e9i	0.671576	+	0.487928i	−0.198977	+	0.980004i	$0.563762\pi$
$588$	−5.33664e8			−0.108255
$589$	−5.74635e9	−	4.68434e9i	−1.15875	−	0.944593i
$590$	−6.50469e9			−1.30390
$591$	−1.45131e8	−	1.05444e8i	−0.0289204	−	0.0210119i
$592$	1.34496e9	−	9.77172e8i	0.266431	−	0.193573i
$593$	1.95692e9	+	6.02278e9i	0.385373	+	1.18606i	0.936209	+	0.351443i	$0.114309\pi$
$593$	1.95692e9	+	6.02278e9i	0.385373	+	1.18606i	−0.550836	+	0.834613i	$0.685691\pi$
$594$	−1.39124e9			−0.272365
$595$	−1.01994e10			−1.98501
$596$	−8.90213e8	−	2.73979e9i	−0.172239	−	0.530098i
$597$	6.11490e8	−	1.88197e9i	0.117619	−	0.361995i
$598$	−8.79181e8	+	2.70584e9i	−0.168122	+	0.517426i
$599$	1.28330e9	+	9.32373e8i	0.243969	+	0.177254i	0.703050	−	0.711141i	$-0.251821\pi$
$599$	1.28330e9	+	9.32373e8i	0.243969	+	0.177254i	−0.459081	+	0.888395i	$0.651821\pi$
$600$	−1.20407e8	−	3.70573e8i	−0.0227573	−	0.0700397i
$601$	−4.55058e9	−	3.30619e9i	−0.855080	−	0.621252i	0.0714622	−	0.997443i	$-0.477233\pi$
$601$	−4.55058e9	−	3.30619e9i	−0.855080	−	0.621252i	−0.926542	+	0.376192i	$0.877233\pi$
$602$	5.98574e9	−	4.34889e9i	1.11823	−	0.812439i
$603$	1.89439e8	−	5.83033e8i	0.0351851	−	0.108289i
$604$	7.92369e8	−	5.75690e8i	0.146318	−	0.106306i
$605$	3.18459e9	−	2.31374e9i	0.584668	−	0.424786i
$606$	4.83599e8	−	1.48837e9i	0.0882737	−	0.271679i
$607$	2.69680e9	−	1.95934e9i	0.489428	−	0.355590i	−0.315537	−	0.948913i	$-0.602184\pi$
$607$	2.69680e9	−	1.95934e9i	0.489428	−	0.355590i	0.804964	+	0.593323i	$0.202184\pi$
$608$	−1.18489e9	−	8.60876e8i	−0.213804	−	0.155338i
$609$	8.69540e8	+	2.67617e9i	0.156002	+	0.480123i
$610$	1.71057e9	+	1.24280e9i	0.305131	+	0.221690i
$611$	1.31499e9	−	4.04711e9i	0.233226	−	0.717796i
$612$	9.28650e8	−	2.85809e9i	0.163765	−	0.504018i
$613$	1.37721e9	+	4.23861e9i	0.241484	+	0.743210i	0.996195	+	0.0871529i	$0.0277769\pi$
$613$	1.37721e9	+	4.23861e9i	0.241484	+	0.743210i	−0.754711	+	0.656057i	$0.772223\pi$
$614$	−4.02492e9			−0.701727
$615$	7.21931e8			0.125151
$616$	−5.52766e8	−	1.70124e9i	−0.0952815	−	0.293246i
$617$	1.81779e9	−	1.32070e9i	0.311562	−	0.226363i	−0.421004	−	0.907059i	$-0.638322\pi$
$617$	1.81779e9	−	1.32070e9i	0.311562	−	0.226363i	0.732567	+	0.680695i	$0.238322\pi$
$618$	−1.70656e9	−	1.23989e9i	−0.290845	−	0.211311i
$619$	−7.90011e9			−1.33880			−0.669401	−	0.742902i	$-0.733449\pi$
$619$	−7.90011e9			−1.33880			−0.669401	+	0.742902i	$0.733449\pi$
$620$	9.85430e8	+	3.72612e9i	0.166056	+	0.627893i
$621$	−3.04331e9			−0.509947
$622$	−1.79970e9	−	1.30756e9i	−0.299871	−	0.217869i
$623$	−3.02911e9	+	2.20078e9i	−0.501888	+	0.364643i
$624$	−1.23990e8	−	3.81602e8i	−0.0204287	−	0.0628731i
$625$	−7.41528e9			−1.21492
$626$	1.89315e9			0.308444
$627$	5.75580e8	+	1.77145e9i	0.0932544	+	0.287008i
$628$	1.25218e9	−	3.85383e9i	0.201748	−	0.620917i
$629$	2.96523e9	−	9.12603e9i	0.475095	−	1.46219i
$630$	5.54555e9	+	4.02908e9i	0.883593	+	0.641968i
$631$	−1.82510e9	−	5.61707e9i	−0.289190	−	0.890035i	−0.985111	−	0.171917i	$-0.945004\pi$
$631$	−1.82510e9	−	5.61707e9i	−0.289190	−	0.890035i	0.695922	−	0.718118i	$-0.254996\pi$
$632$	−1.07892e9	−	7.83879e8i	−0.170012	−	0.123521i
$633$	1.52501e9	−	1.10798e9i	0.238979	−	0.173628i
$634$	2.14518e9	−	6.60219e9i	0.334312	−	1.02891i
$635$	9.11695e7	−	6.62386e7i	0.0141300	−	0.0102660i
$636$	1.44815e9	−	1.05215e9i	0.223211	−	0.162172i
$637$	1.25658e9	−	3.86737e9i	0.192621	−	0.592827i
$638$	−3.17969e9	+	2.31018e9i	−0.484743	+	0.352187i
$639$	−3.40313e9	−	2.47252e9i	−0.515971	−	0.374875i
$640$	2.35290e8	+	7.24148e8i	0.0354792	+	0.109194i
$641$	3.85069e9	+	2.79769e9i	0.577478	+	0.419562i	0.837814	−	0.545956i	$-0.183833\pi$
$641$	3.85069e9	+	2.79769e9i	0.577478	+	0.419562i	−0.260336	+	0.965518i	$0.583833\pi$
$642$	−1.71046e8	+	5.26427e8i	−0.0255118	+	0.0785173i
$643$	7.75167e8	−	2.38572e9i	0.114989	−	0.353900i	−0.876956	−	0.480571i	$-0.840429\pi$
$643$	7.75167e8	−	2.38572e9i	0.114989	−	0.353900i	0.991945	+	0.126671i	$0.0404293\pi$
$644$	−1.20916e9	−	3.72141e9i	−0.178395	−	0.549044i
$645$	4.00520e9			0.587712
$646$	−8.45366e9			−1.23376
$647$	9.68022e8	+	2.97927e9i	0.140514	+	0.432458i	0.996407	−	0.0846951i	$-0.0269916\pi$
$647$	9.68022e8	+	2.97927e9i	0.140514	+	0.432458i	−0.855893	+	0.517154i	$0.826992\pi$
$648$	−1.45199e9	+	1.05493e9i	−0.209629	+	0.152304i
$649$	−5.32713e9	−	3.87039e9i	−0.764957	−	0.555774i
$650$	2.96899e9			0.424046
$651$	2.16512e9	+	1.76497e9i	0.307573	+	0.250729i
$652$	4.92184e9			0.695442
$653$	1.07158e10	+	7.78548e9i	1.50601	+	1.09418i	0.967908	+	0.251303i	$0.0808590\pi$
$653$	1.07158e10	+	7.78548e9i	1.50601	+	1.09418i	0.538103	+	0.842879i	$0.319141\pi$
$654$	−2.20522e9	+	1.60219e9i	−0.308269	+	0.223970i
$655$	2.75672e8	+	8.48431e8i	0.0383308	+	0.117970i
$656$	−5.74649e8			−0.0794766
$657$	−5.61571e8			−0.0772549
$658$	1.80854e9	+	5.56610e9i	0.247478	+	0.761658i
$659$	1.96222e9	−	6.03909e9i	0.267085	−	0.822002i	−0.724121	−	0.689673i	$-0.757754\pi$
$659$	1.96222e9	−	6.03909e9i	0.267085	−	0.822002i	0.991206	−	0.132329i	$-0.0422456\pi$
$660$	2.99230e8	−	9.20935e8i	0.0405136	−	0.124688i
$661$	3.05221e9	+	2.21756e9i	0.411064	+	0.298656i	0.774032	−	0.633146i	$-0.218237\pi$
$661$	3.05221e9	+	2.21756e9i	0.411064	+	0.298656i	−0.362968	+	0.931801i	$0.618237\pi$
$662$	−1.37060e9	−	4.21828e9i	−0.183615	−	0.565109i
$663$	−1.87364e9	−	1.36128e9i	−0.249683	−	0.181405i
$664$	1.99427e9	−	1.44892e9i	0.264360	−	0.192069i
$665$	5.95860e9	−	1.83387e10i	0.785721	−	2.41820i
$666$	−5.21731e9	+	3.79060e9i	−0.684364	+	0.497220i
$667$	−6.95548e9	+	5.05345e9i	−0.907584	+	0.659398i
$668$	1.52004e9	−	4.67819e9i	0.197304	−	0.607240i
$669$	−1.80334e9	+	1.31021e9i	−0.232856	+	0.169180i
$670$	7.25302e8	+	5.26962e8i	0.0931659	+	0.0676890i
$671$	6.61414e8	+	2.03562e9i	0.0845172	+	0.260117i
$672$	4.46445e8	+	3.24361e8i	0.0567513	+	0.0412322i
$673$	−1.67995e9	+	5.17034e9i	−0.212443	+	0.653832i	0.786882	+	0.617103i	$0.211694\pi$
$673$	−1.67995e9	+	5.17034e9i	−0.212443	+	0.653832i	−0.999325	+	0.0367291i	$0.988306\pi$
$674$	1.10358e9	−	3.39647e9i	0.138833	−	0.427285i
$675$	9.81390e8	+	3.02041e9i	0.122823	+	0.378009i
$676$	−9.58545e8			−0.119344
$677$	−7.38570e9			−0.914811			−0.457406	−	0.889258i	$-0.651221\pi$
$677$	−7.38570e9			−0.914811			−0.457406	+	0.889258i	$0.651221\pi$
$678$	2.26338e8	+	6.96598e8i	0.0278904	+	0.0858378i
$679$	−7.58796e9	+	5.51298e9i	−0.930210	+	0.675837i
$680$	3.55551e9	+	2.58323e9i	0.433631	+	0.315051i
$681$	4.87071e9			0.590987
$682$	−1.41006e9	+	3.63792e9i	−0.170213	+	0.439144i
$683$	−2.61448e9			−0.313988			−0.156994	−	0.987600i	$-0.550180\pi$
$683$	−2.61448e9			−0.313988			−0.156994	+	0.987600i	$0.550180\pi$
$684$	4.59638e9	+	3.33947e9i	0.549187	+	0.399007i
$685$	−8.37325e9	+	6.08352e9i	−0.995353	+	0.723166i
$686$	−6.90908e8	−	2.12639e9i	−0.0817119	−	0.251484i
$687$	−2.32385e9			−0.273439
$688$	−3.18809e9			−0.373226
$689$	4.21484e9	+	1.29720e10i	0.490924	+	1.51091i
$690$	6.54558e8	−	2.01452e9i	0.0758536	−	0.233453i
$691$	2.04715e9	−	6.30049e9i	0.236036	−	0.726443i	−0.760947	−	0.648814i	$-0.775265\pi$
$691$	2.04715e9	−	6.30049e9i	0.236036	−	0.726443i	0.996982	−	0.0776286i	$-0.0247348\pi$
$692$	5.15318e9	+	3.74400e9i	0.591158	+	0.429501i
$693$	2.14426e9	+	6.59936e9i	0.244744	+	0.753244i
$694$	−5.05962e8	−	3.67603e8i	−0.0574592	−	0.0417465i
$695$	1.36183e10	−	9.89425e9i	1.53877	−	1.11798i
$696$	3.74680e8	−	1.15315e9i	0.0421239	−	0.129644i
$697$	−2.68339e9	+	1.94960e9i	−0.300171	+	0.218087i
$698$	6.19539e8	−	4.50121e8i	0.0689564	−	0.0500998i
$699$	1.16536e8	−	3.58661e8i	0.0129059	−	0.0397204i
$700$	−3.30349e9	+	2.40012e9i	−0.364023	+	0.264479i
$701$	1.41458e10	+	1.02776e10i	1.55101	+	1.12688i	0.942924	+	0.333009i	$0.108064\pi$
$701$	1.41458e10	+	1.02776e10i	1.55101	+	1.12688i	0.608089	+	0.793869i	$0.291936\pi$
$702$	1.01060e9	+	3.11030e9i	0.110255	+	0.339330i
$703$	1.46765e10	+	1.06631e10i	1.59323	+	1.15755i
$704$	−2.38184e8	+	7.33054e8i	−0.0257281	+	0.0791830i
$705$	−9.79018e8	+	3.01311e9i	−0.105227	+	0.323857i
$706$	3.76761e8	+	1.15955e9i	0.0402949	+	0.124015i
$707$	−1.64003e10			−1.74535
$708$	2.03136e9			0.215115
$709$	−3.44310e9	−	1.05968e10i	−0.362817	−	1.11664i	−0.951337	−	0.308153i	$-0.900289\pi$
$709$	−3.44310e9	−	1.05968e10i	−0.362817	−	1.11664i	0.588519	−	0.808483i	$-0.299711\pi$
$710$	4.97683e9	−	3.61588e9i	0.521853	−	0.379149i
$711$	4.18529e9	+	3.04079e9i	0.436698	+	0.317280i
$712$	1.61335e9			0.167513
$713$	−3.08447e9	+	7.95785e9i	−0.318689	+	0.822209i
$714$	3.18518e9			0.327484
$715$	5.96928e9	+	4.33694e9i	0.610732	+	0.443723i
$716$	2.26391e9	−	1.64483e9i	0.230496	−	0.167465i
$717$	5.83720e8	+	1.79651e9i	0.0591408	+	0.182017i
$718$	3.68460e9			0.371496
$719$	−2.34396e9			−0.235179			−0.117590	−	0.993062i	$-0.537517\pi$
$719$	−2.34396e9			−0.235179			−0.117590	+	0.993062i	$0.537517\pi$
$720$	−9.12726e8	−	2.80908e9i	−0.0911332	−	0.280479i
$721$	−6.83114e9	+	2.10241e10i	−0.678766	+	2.08903i
$722$	2.72896e9	−	8.39889e9i	0.269847	−	0.830504i
$723$	1.10046e9	+	7.99529e8i	0.108290	+	0.0786774i
$724$	−2.37211e9	−	7.30061e9i	−0.232300	−	0.714947i
$725$	7.25839e9	+	5.27353e9i	0.707387	+	0.513947i
$726$	−9.94520e8	+	7.22561e8i	−0.0964574	+	0.0700804i
$727$	2.66475e9	−	8.20124e9i	0.257209	−	0.791606i	−0.736178	−	0.676788i	$-0.763371\pi$
$727$	2.66475e9	−	8.20124e9i	0.257209	−	0.791606i	0.993386	−	0.114818i	$-0.0366286\pi$
$728$	−3.40181e9	+	2.47156e9i	−0.326776	+	0.237417i
$729$	4.14932e9	−	3.01466e9i	0.396671	−	0.288198i
$730$	2.53782e8	−	7.81062e8i	0.0241452	−	0.0743114i
$731$	−1.48872e10	+	1.08161e10i	−1.40962	+	1.02415i
$732$	−5.34196e8	−	3.88116e8i	−0.0503398	−	0.0365740i
$733$	−3.01637e9	−	9.28344e9i	−0.282892	−	0.870653i	−0.987022	−	0.160582i	$-0.948663\pi$
$733$	−3.01637e9	−	9.28344e9i	−0.282892	−	0.870653i	0.704130	−	0.710071i	$-0.251337\pi$
$734$	−6.24539e9	−	4.53754e9i	−0.582939	−	0.423530i
$735$	−9.35537e8	+	2.87929e9i	−0.0869071	+	0.267473i
$736$	−5.21021e8	+	1.60354e9i	−0.0481707	+	0.148254i
$737$	2.80448e8	+	8.63130e8i	0.0258057	+	0.0794218i
$738$	2.22915e9			0.204147
$739$	−3.61669e9			−0.329652			−0.164826	−	0.986323i	$-0.552706\pi$
$739$	−3.61669e9			−0.329652			−0.164826	+	0.986323i	$0.552706\pi$
$740$	−2.91438e9	−	8.96953e9i	−0.264384	−	0.813690i
$741$	3.54221e9	−	2.57357e9i	0.319824	−	0.232365i
$742$	−1.51762e10	−	1.10261e10i	−1.36379	−	0.990854i
$743$	5.23894e9			0.468579			0.234290	−	0.972167i	$-0.424724\pi$
$743$	5.23894e9			0.468579			0.234290	+	0.972167i	$0.424724\pi$
$744$	−3.07742e8	−	1.16364e9i	−0.0273956	−	0.103589i
$745$	−1.63427e10			−1.44802
$746$	5.73355e9	+	4.16567e9i	0.505636	+	0.367366i
$747$	−7.73607e9	+	5.62058e9i	−0.679044	+	0.493355i
$748$	1.37479e9	+	4.23116e9i	0.120110	+	0.369661i
$749$	5.80068e9			0.504420
$750$	1.00568e9			0.0870456
$751$	−1.00317e9	−	3.08743e9i	−0.0864237	−	0.265985i	0.898500	−	0.438973i	$-0.144658\pi$
$751$	−1.00317e9	−	3.08743e9i	−0.0864237	−	0.265985i	−0.984924	+	0.172988i	$0.944658\pi$
$752$	7.79288e8	−	2.39840e9i	0.0668245	−	0.205665i
$753$	−2.03288e8	+	6.25656e8i	−0.0173512	+	0.0534015i
$754$	7.47442e9	+	5.43048e9i	0.635006	+	0.461359i
$755$	−1.71697e9	−	5.28430e9i	−0.145194	−	0.446861i
$756$	−3.63881e9	−	2.64375e9i	−0.306290	−	0.222533i
$757$	8.70459e9	−	6.32426e9i	0.729311	−	0.529876i	−0.160034	−	0.987111i	$-0.551160\pi$
$757$	8.70459e9	−	6.32426e9i	0.729311	−	0.529876i	0.889346	+	0.457236i	$0.151160\pi$
$758$	1.26469e8	−	3.89231e8i	0.0105473	−	0.0324613i
$759$	1.73473e9	−	1.26036e9i	0.144008	−	0.104628i
$760$	−6.72188e9	+	4.88373e9i	−0.555447	+	0.403556i
$761$	−3.58810e9	+	1.10430e10i	−0.295133	+	0.908327i	0.688043	+	0.725670i	$0.258470\pi$
$761$	−3.58810e9	+	1.10430e10i	−0.295133	+	0.908327i	−0.983177	+	0.182657i	$0.941530\pi$
$762$	−2.84715e7	+	2.06858e7i	−0.00233114	+	0.00169367i
$763$	2.31099e10	+	1.67904e10i	1.88349	+	1.36843i
$764$	1.41140e9	+	4.34384e9i	0.114505	+	0.352409i
$765$	−1.37924e10	−	1.00207e10i	−1.11384	−	0.809253i
$766$	4.46631e9	−	1.37459e10i	0.359044	−	1.10503i
$767$	−4.78312e9	+	1.47209e10i	−0.382761	+	1.17802i
$768$	−7.34791e7	−	2.26145e8i	−0.00585328	−	0.0180146i
$769$	1.60058e10			1.26921			0.634606	−	0.772836i	$-0.281163\pi$
$769$	1.60058e10			1.26921			0.634606	+	0.772836i	$0.281163\pi$
$770$	−1.01478e10			−0.801037
$771$	−5.16683e8	−	1.59019e9i	−0.0406008	−	0.124956i
$772$	−8.77906e9	+	6.37836e9i	−0.686733	+	0.498940i
$773$	−5.36416e9	−	3.89729e9i	−0.417709	−	0.303483i	0.359006	−	0.933335i	$-0.383116\pi$
$773$	−5.36416e9	−	3.89729e9i	−0.417709	−	0.303483i	−0.776715	+	0.629852i	$0.783116\pi$
$774$	1.23671e10			0.958682
$775$	8.89263e9	+	4.95057e8i	0.686237	+	0.0382032i
$776$	4.04146e9			0.310472
$777$	−5.52981e9	−	4.01765e9i	−0.422899	−	0.307254i
$778$	−1.90496e8	+	1.38403e8i	−0.0145030	+	0.0105370i
$779$	−1.93775e9	−	5.96377e9i	−0.146864	−	0.452001i
$780$	−2.27623e9			−0.171745
$781$	6.22736e9			0.467762
$782$	3.00731e9	+	9.25555e9i	0.224882	+	0.692115i
$783$	−3.05388e9	+	9.39888e9i	−0.227345	+	0.699697i
$784$	7.44678e8	−	2.29188e9i	0.0551902	−	0.169858i
$785$	−1.85975e10	−	1.35119e10i	−1.37218	−	0.996946i
$786$	−8.60901e7	−	2.64958e8i	−0.00632374	−	0.0194625i
$787$	1.51134e10	+	1.09805e10i	1.10523	+	0.802994i	0.981905	−	0.189372i	$-0.0606454\pi$
$787$	1.51134e10	+	1.09805e10i	1.10523	+	0.802994i	0.123322	+	0.992367i	$0.460645\pi$
$788$	6.55359e8	−	4.76146e8i	0.0477131	−	0.0346656i
$789$	−4.19584e7	+	1.29135e8i	−0.00304123	+	0.00935995i
$790$	−6.12068e9	+	4.44693e9i	−0.441677	+	0.320897i
$791$	6.20985e9	−	4.51172e9i	0.446132	−	0.324134i
$792$	9.23951e8	−	2.84363e9i	0.0660862	−	0.203393i
$793$	4.07045e9	−	2.95735e9i	0.289859	−	0.210595i
$794$	−3.63977e8	−	2.64445e8i	−0.0258049	−	0.0187484i
$795$	−3.13798e9	−	9.65772e9i	−0.221496	−	0.681695i
$796$	7.22908e9	+	5.25223e9i	0.508027	+	0.369104i
$797$	−2.61516e9	+	8.04862e9i	−0.182976	+	0.563141i	−0.999908	−	0.0135929i	$-0.995673\pi$
$797$	−2.61516e9	+	8.04862e9i	−0.182976	+	0.563141i	0.816932	+	0.576734i	$0.195673\pi$
$798$	−1.86082e9	+	5.72702e9i	−0.129627	+	0.398950i
$799$	−4.49802e9	−	1.38435e10i	−0.311966	−	0.960133i
$800$	1.75949e9			0.121499
$801$	−6.25843e9			−0.430281
$802$	4.31753e9	+	1.32880e10i	0.295546	+	0.909596i
$803$	6.72582e8	−	4.88660e8i	0.0458396	−	0.0333044i
$804$	−2.26506e8	−	1.64566e8i	−0.0153703	−	0.0111672i
$805$	−2.21979e10			−1.49978
$806$	9.15730e9	+	5.09792e8i	0.616020	+	0.0342942i
$807$	−7.23682e9			−0.484719
$808$	5.71715e9	+	4.15375e9i	0.381276	+	0.277013i
$809$	1.30313e10	−	9.46782e9i	0.865305	−	0.628681i	−0.0640178	−	0.997949i	$-0.520391\pi$
$809$	1.30313e10	−	9.46782e9i	0.865305	−	0.628681i	0.929323	+	0.369268i	$0.120391\pi$
$810$	3.14629e9	+	9.68330e9i	0.208018	+	0.640215i
$811$	−2.95260e9			−0.194371			−0.0971855	−	0.995266i	$-0.530984\pi$
$811$	−2.95260e9			−0.194371			−0.0971855	+	0.995266i	$0.530984\pi$
$812$	−1.27065e10			−0.832874
$813$	−4.89658e8	−	1.50701e9i	−0.0319577	−	0.0983557i
$814$	2.95022e9	−	9.07985e9i	0.191721	−	0.590056i
$815$	8.62822e9	−	2.65549e10i	0.558303	−	1.71828i
$816$	−1.11036e9	−	8.06721e8i	−0.0715396	−	0.0519766i
$817$	−1.07504e10	−	3.30864e10i	−0.689680	−	2.12262i
$818$	3.39989e9	+	2.47016e9i	0.217184	+	0.157793i
$819$	1.31961e10	−	9.58755e9i	0.839369	−	0.609837i
$820$	−1.00739e9	+	3.10042e9i	−0.0638040	+	0.196368i
$821$	−2.21656e10	+	1.61043e10i	−1.39791	+	1.01564i	−0.402965	+	0.915215i	$0.632021\pi$
$821$	−2.21656e10	+	1.61043e10i	−1.39791	+	1.01564i	−0.994945	+	0.100426i	$0.967979\pi$
$822$	2.61490e9	−	1.89983e9i	0.164211	−	0.119307i
$823$	−4.22869e9	+	1.30146e10i	−0.264428	+	0.813824i	0.727397	+	0.686217i	$0.240730\pi$
$823$	−4.22869e9	+	1.30146e10i	−0.264428	+	0.813824i	−0.991825	+	0.127608i	$0.959270\pi$
$824$	7.70619e9	−	5.59887e9i	0.479838	−	0.348623i
$825$	−1.81028e9	−	1.31524e9i	−0.112242	−	0.0815488i
$826$	−6.57835e9	−	2.02461e10i	−0.406150	−	1.25000i
$827$	1.27789e10	+	9.28438e9i	0.785638	+	0.570800i	0.906666	−	0.421850i	$-0.138619\pi$
$827$	1.27789e10	+	9.28438e9i	0.785638	+	0.570800i	−0.121028	+	0.992649i	$0.538619\pi$
$828$	2.02112e9	−	6.22037e9i	0.123733	−	0.380811i
$829$	3.35263e9	−	1.03183e10i	0.204383	−	0.629026i	−0.795355	−	0.606144i	$-0.792716\pi$
$829$	3.35263e9	−	1.03183e10i	0.204383	−	0.629026i	0.999738	−	0.0228827i	$-0.00728441\pi$
$830$	−4.32135e9	−	1.32997e10i	−0.262329	−	0.807365i
$831$	2.84700e9			0.172101
$832$	1.81185e9			0.109067
$833$	−4.29825e9	−	1.32286e10i	−0.257652	−	0.792972i
$834$	−4.25287e9	+	3.08989e9i	−0.253864	+	0.184443i
$835$	−2.25757e10	−	1.64022e10i	−1.34196	−	0.974988i
$836$	−8.41089e9			−0.497874
$837$	2.50829e9	+	9.48438e9i	0.147856	+	0.559075i
$838$	5.31973e8			0.0312274
$839$	7.29688e9	+	5.30150e9i	0.426551	+	0.309907i	0.780268	−	0.625445i	$-0.215083\pi$
$839$	7.29688e9	+	5.30150e9i	0.426551	+	0.309907i	−0.353718	+	0.935352i	$0.615083\pi$
$840$	2.53267e9	−	1.84009e9i	0.147435	−	0.107118i
$841$	3.29681e9	+	1.01465e10i	0.191121	+	0.588209i
$842$	−2.40919e10			−1.39085
$843$	−7.70572e8			−0.0443013
$844$	2.63036e9	+	8.09541e9i	0.150597	+	0.463490i
$845$	−1.68037e9	+	5.17166e9i	−0.0958093	+	0.294871i
$846$	−3.02298e9	+	9.30377e9i	−0.171648	+	0.528278i
$847$	1.04222e10	+	7.57220e9i	0.589344	+	0.428184i
$848$	2.49780e9	+	7.68744e9i	0.140661	+	0.432909i
$849$	−1.89247e9	−	1.37496e9i	−0.106133	−	0.0771103i
$850$	8.21612e9	−	5.96936e9i	0.458881	−	0.333397i
$851$	6.45353e9	−	1.98619e10i	0.358958	−	1.10476i
$852$	−1.55422e9	+	1.12921e9i	−0.0860943	+	0.0625512i
$853$	−5.42687e9	+	3.94285e9i	−0.299384	+	0.217515i	−0.727328	−	0.686290i	$-0.759238\pi$
$853$	−5.42687e9	+	3.94285e9i	−0.299384	+	0.217515i	0.427944	+	0.903805i	$0.359238\pi$
$854$	−2.13832e9	+	6.58107e9i	−0.117482	+	0.361571i
$855$	2.60752e10	−	1.89447e10i	1.42674	−	1.03659i
$856$	−2.02212e9	−	1.46916e9i	−0.110192	−	0.0800590i
$857$	−4.56360e9	−	1.40453e10i	−0.247671	−	0.762252i	−0.995186	−	0.0980068i	$-0.968753\pi$
$857$	−4.56360e9	−	1.40453e10i	−0.247671	−	0.762252i	0.747515	−	0.664245i	$-0.231247\pi$
$858$	−1.86416e9	−	1.35439e9i	−0.100757	−	0.0732045i
$859$	−6.78802e9	+	2.08914e10i	−0.365399	+	1.12458i	0.584332	+	0.811514i	$0.301356\pi$
$859$	−6.78802e9	+	2.08914e10i	−0.365399	+	1.12458i	−0.949731	+	0.313067i	$0.898644\pi$
$860$	−5.58888e9	+	1.72008e10i	−0.299626	+	0.922155i
$861$	7.30106e8	+	2.24703e9i	0.0389829	+	0.119977i
$862$	9.89693e9			0.526290
$863$	3.37795e10			1.78902			0.894511	−	0.447046i	$-0.147524\pi$
$863$	3.37795e10			1.78902			0.894511	+	0.447046i	$0.147524\pi$
$864$	5.98902e8	+	1.84323e9i	0.0315906	+	0.0972258i
$865$	2.92339e10	−	2.12396e10i	1.53578	−	1.11581i
$866$	7.90639e9	+	5.74433e9i	0.413681	+	0.300557i
$867$	−2.10614e9			−0.109754
$868$	−1.06011e10	+	6.83550e9i	−0.550214	+	0.354773i
$869$	−7.65862e9			−0.395896
$870$	−5.56477e9	−	4.04304e9i	−0.286503	−	0.208157i
$871$	1.72592e9	−	1.25395e9i	0.0885028	−	0.0643011i
$872$	−3.80360e9	−	1.17063e10i	−0.194262	−	0.597876i
$873$	−1.56775e10			−0.797491
$874$	−1.83986e10			−0.932169
$875$	−3.25680e9	−	1.00234e10i	−0.164347	−	0.505809i
$876$	−7.92541e7	+	2.43919e8i	−0.00398343	+	0.0122597i
$877$	−1.14201e10	+	3.51476e10i	−0.571706	+	1.75953i	0.0754251	+	0.997151i	$0.475969\pi$
$877$	−1.14201e10	+	3.51476e10i	−0.571706	+	1.75953i	−0.647131	+	0.762379i	$0.724031\pi$
$878$	−2.20200e9	−	1.59985e9i	−0.109796	−	0.0797715i
$879$	−2.54949e9	−	7.84652e9i	−0.126617	−	0.389687i
$880$	3.53752e9	+	2.57016e9i	0.174988	+	0.127137i
$881$	−8.29115e9	+	6.02387e9i	−0.408506	+	0.296797i	−0.772997	−	0.634410i	$-0.781243\pi$
$881$	−8.29115e9	+	6.02387e9i	−0.408506	+	0.296797i	0.364490	+	0.931207i	$0.381243\pi$
$882$	−2.88872e9	+	8.89056e9i	−0.141764	+	0.436304i
$883$	−1.08571e10	+	7.88813e9i	−0.530702	+	0.385577i	−0.820620	−	0.571474i	$-0.806372\pi$
$883$	−1.08571e10	+	7.88813e9i	−0.530702	+	0.385577i	0.289919	+	0.957051i	$0.406372\pi$
$884$	8.46065e9	−	6.14702e9i	0.411928	−	0.299283i
$885$	3.56107e9	−	1.09599e10i	0.172695	−	0.531500i
$886$	1.40429e10	−	1.02028e10i	0.678327	−	0.492833i
$887$	2.12101e9	+	1.54100e9i	0.102049	+	0.0741432i	0.637640	−	0.770335i	$-0.279911\pi$
$887$	2.12101e9	+	1.54100e9i	0.102049	+	0.0741432i	−0.535590	+	0.844478i	$0.679911\pi$
$888$	9.10136e8	+	2.80111e9i	0.0436175	+	0.134241i
$889$	2.98372e8	+	2.16780e8i	0.0142430	+	0.0103481i
$890$	2.82828e9	−	8.70455e9i	0.134480	−	0.413886i
$891$	−3.18499e9	+	9.80239e9i	−0.150847	+	0.464259i
$892$	−3.11044e9	−	9.57295e9i	−0.146739	−	0.451615i
$893$	2.75187e10			1.29315
$894$	5.10368e9			0.238892
$895$	−4.90563e9	−	1.50980e10i	−0.228725	−	0.703944i
$896$	−2.01598e9	+	1.46470e9i	−0.0936286	+	0.0680251i
$897$	−4.07779e9	−	2.96269e9i	−0.188648	−	0.137061i
$898$	6.54594e9			0.301651
$899$	2.14816e10	+	1.75115e10i	0.986071	+	0.803830i
$900$	−6.82532e9			−0.312086
$901$	3.77447e10	+	2.74231e10i	1.71917	+	1.24905i
$902$	−2.66981e9	+	1.93973e9i	−0.121132	+	0.0880073i
$903$	4.05055e9	+	1.24663e10i	0.183066	+	0.563418i
$904$	−3.30746e9			−0.148903
$905$	−4.35476e10			−1.95296
$906$	5.36196e8	+	1.65024e9i	0.0239538	+	0.0737223i
$907$	6.33074e9	−	1.94840e10i	0.281727	−	0.867068i	−0.705633	−	0.708577i	$-0.749337\pi$
$907$	6.33074e9	−	1.94840e10i	0.281727	−	0.867068i	0.987361	−	0.158490i	$-0.0506627\pi$
$908$	−6.79663e9	+	2.09179e10i	−0.301296	+	0.927293i
$909$	−2.21777e10	−	1.61130e10i	−0.979360	−	0.711547i
$910$	7.37133e9	+	2.26866e10i	0.324265	+	0.997987i
$911$	−2.40521e10	−	1.74749e10i	−1.05400	−	0.765773i	−0.0810275	−	0.996712i	$-0.525820\pi$
$911$	−2.40521e10	−	1.74749e10i	−1.05400	−	0.765773i	−0.972968	+	0.230939i	$0.925820\pi$
$912$	2.09919e9	−	1.52515e9i	0.0916366	−	0.0665779i
$913$	4.37450e9	−	1.34633e10i	0.190231	−	0.585470i
$914$	−1.05126e10	+	7.63787e9i	−0.455407	+	0.330873i
$915$	−3.03048e9	+	2.20177e9i	−0.130779	+	0.0950165i
$916$	3.24272e9	−	9.98007e9i	0.139404	−	0.429041i
$917$	−2.36198e9	+	1.71608e9i	−0.101154	+	0.0734927i
$918$	9.05011e9	+	6.57529e9i	0.386104	+	0.280521i
$919$	−7.78186e9	−	2.39501e10i	−0.330734	−	1.01790i	−0.968785	−	0.247901i	$-0.920259\pi$
$919$	−7.78186e9	−	2.39501e10i	−0.330734	−	1.01790i	0.638051	−	0.769994i	$-0.279741\pi$
$920$	7.73823e9	+	5.62215e9i	0.327630	+	0.238037i
$921$	2.20349e9	−	6.78165e9i	0.0929400	−	0.286040i
$922$	7.96481e9	−	2.45132e10i	0.334670	−	1.03001i
$923$	−4.52355e9	−	1.39221e10i	−0.189354	−	0.582771i
$924$	3.16906e9			0.132153
$925$	−2.17936e10			−0.905383
$926$	4.46535e9	+	1.37429e10i	0.184806	+	0.568775i
$927$	−2.98935e10	+	2.17189e10i	−1.23253	+	0.895485i
$928$	4.42949e9	+	3.21822e9i	0.181943	+	0.132190i
$929$	−3.64976e10			−1.49351			−0.746757	−	0.665097i	$-0.768390\pi$
$929$	−3.64976e10			−1.49351			−0.746757	+	0.665097i	$0.768390\pi$
$930$	−6.81768e9	−	3.79544e8i	−0.277937	−	0.0154729i
$931$	2.62965e10			1.06801
$932$	1.37770e9	+	1.00096e9i	0.0557440	+	0.0405004i
$933$	3.18839e9	−	2.31650e9i	0.128525	−	0.0933785i
$934$	8.24217e9	+	2.53668e10i	0.331000	+	1.01871i
$935$	2.52385e10			1.00977
$936$	−7.02846e9			−0.280153
$937$	−1.39726e10	−	4.30032e10i	−0.554867	−	1.70770i	−0.696295	−	0.717755i	$-0.745170\pi$
$937$	−1.39726e10	−	4.30032e10i	−0.554867	−	1.70770i	0.141429	−	0.989948i	$-0.454830\pi$
$938$	−9.06674e8	+	2.79046e9i	−0.0358708	+	0.110399i
$939$	−1.03643e9	+	3.18980e9i	−0.0408517	+	0.125729i
$940$	−1.15740e10	−	8.40902e9i	−0.454503	−	0.330216i
$941$	9.16703e9	+	2.82132e10i	0.358645	+	1.10380i	0.953866	+	0.300234i	$0.0970647\pi$
$941$	9.16703e9	+	2.82132e10i	0.358645	+	1.10380i	−0.595220	+	0.803562i	$0.702935\pi$
$942$	5.80785e9	+	4.21965e9i	0.226379	+	0.164474i
$943$	−5.84014e9	+	4.24311e9i	−0.226794	+	0.164776i
$944$	−2.83458e9	+	8.72393e9i	−0.109670	+	0.337528i
$945$	−2.06429e10	+	1.49979e10i	−0.795718	+	0.578123i
$946$	−1.48118e10	+	1.07614e10i	−0.568839	+	0.413286i
$947$	6.57162e9	−	2.02254e10i	0.251448	−	0.773876i	−0.743061	−	0.669223i	$-0.766627\pi$
$947$	6.57162e9	−	2.02254e10i	0.251448	−	0.773876i	0.994509	−	0.104653i	$-0.0333731\pi$
$948$	1.91144e9	−	1.38874e9i	0.0728670	−	0.0529410i
$949$	−1.58103e9	−	1.14868e9i	−0.0600492	−	0.0436283i
$950$	5.93308e9	+	1.82601e10i	0.224516	+	0.690990i
$951$	9.94973e9	+	7.22890e9i	0.375128	+	0.272546i
$952$	−4.44461e9	+	1.36791e10i	−0.166957	+	0.513841i
$953$	1.04659e9	−	3.22108e9i	0.0391699	−	0.120553i	−0.929560	−	0.368672i	$-0.879813\pi$
$953$	1.04659e9	−	3.22108e9i	0.0391699	−	0.120553i	0.968729	+	0.248119i	$0.0798125\pi$
$954$	−9.68936e9	−	2.98208e10i	−0.361306	−	1.11199i
$955$	2.59107e10			0.962648
$956$	−8.52983e9			−0.315746
$957$	−2.15169e9	−	6.62223e9i	−0.0793577	−	0.244238i
$958$	−7.60025e9	+	5.52191e9i	−0.279286	+	0.202913i
$959$	−2.74032e10	−	1.99096e10i	−1.00331	−	0.728950i
$960$	−1.34894e9			−0.0492089
$961$	2.73426e10	+	3.05382e9i	0.993821	+	0.110997i
$962$	−2.24422e10			−0.812742
$963$	7.84412e9	+	5.69909e9i	0.283043	+	0.205643i
$964$	−4.96926e9	+	3.61038e9i	−0.178658	+	0.129802i
$965$	1.90232e10	+	5.85475e10i	0.681457	+	2.09731i
$966$	6.93224e9			0.247431
$967$	5.03111e10			1.78925			0.894625	−	0.446818i	$-0.147443\pi$
$967$	5.03111e10			1.78925			0.894625	+	0.446818i	$0.147443\pi$
$968$	−1.71537e9	−	5.27935e9i	−0.0607845	−	0.187075i
$969$	4.62806e9	−	1.42437e10i	0.163405	−	0.502909i
$970$	7.08487e9	−	2.18050e10i	0.249248	−	0.767105i
$971$	2.16662e10	+	1.57414e10i	0.759477	+	0.551792i	0.898750	−	0.438462i	$-0.144477\pi$
$971$	2.16662e10	+	1.57414e10i	0.759477	+	0.551792i	−0.139273	+	0.990254i	$0.544477\pi$
$972$	−3.54076e9	−	1.08973e10i	−0.123670	−	0.380617i
$973$	4.45687e10	+	3.23810e10i	1.55108	+	1.12693i
$974$	2.35140e10	−	1.70839e10i	0.815399	−	0.592422i
$975$	−1.62541e9	+	5.00250e9i	−0.0561626	+	0.172851i
$976$	2.41223e9	−	1.75259e9i	0.0830509	−	0.0603400i
$977$	1.10721e10	−	8.04432e9i	0.379837	−	0.275968i	−0.381441	−	0.924393i	$-0.624572\pi$
$977$	1.10721e10	−	8.04432e9i	0.379837	−	0.275968i	0.761278	+	0.648425i	$0.224572\pi$
$978$	−2.69452e9	+	8.29289e9i	−0.0921077	+	0.283478i
$979$	7.49560e9	−	5.44587e9i	0.255310	−	0.185493i
$980$	−1.10600e10	−	8.03555e9i	−0.375373	−	0.272725i
$981$	1.47547e10	+	4.54104e10i	0.498988	+	1.53573i
$982$	1.99626e10	+	1.45037e10i	0.672709	+	0.488751i
$983$	−9.88615e9	+	3.04264e10i	−0.331963	+	1.02168i	0.636235	+	0.771495i	$0.280491\pi$
$983$	−9.88615e9	+	3.04264e10i	−0.331963	+	1.02168i	−0.968199	+	0.250183i	$0.919509\pi$
$984$	3.14599e8	−	9.68235e8i	0.0105263	−	0.0323965i
$985$	−1.42009e9	−	4.37058e9i	−0.0473466	−	0.145718i
$986$	3.16024e10			1.04991
$987$	−1.03685e10			−0.343247
$988$	6.10966e9	+	1.88036e10i	0.201543	+	0.620286i
$989$	−3.24005e10	+	2.35403e10i	−1.06504	+	0.773794i
$990$	−1.37226e10	−	9.97003e9i	−0.449482	−	0.326568i
$991$	−4.17715e10			−1.36340			−0.681698	−	0.731634i	$-0.738758\pi$
$991$	−4.17715e10			−1.36340			−0.681698	+	0.731634i	$0.738758\pi$
$992$	5.42680e9	+	3.02113e8i	0.176503	+	0.00982604i
$993$	7.85780e9			0.254670
$994$	1.62877e10	+	1.18337e10i	0.526027	+	0.382181i
$995$	4.10104e10	−	2.97958e10i	1.31982	−	0.958902i
$996$	1.34952e9	+	4.15340e9i	0.0432785	+	0.133197i
$997$	4.87584e10			1.55818			0.779089	−	0.626914i	$-0.215682\pi$
$997$	4.87584e10			1.55818			0.779089	+	0.626914i	$0.215682\pi$
$998$	−4.27054e10			−1.35996
$999$	−7.41819e9	−	2.28308e10i	−0.235407	−	0.724507i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.8.d.a.33.6	✓	40
31.16	even	5	inner	62.8.d.a.47.6	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.8.d.a.33.6	✓	40	1.1	even	1	trivial
62.8.d.a.47.6	yes	40	31.16	even	5	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	62.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-6.47214 - 4.70228i) q^{2} +(11.4662 - 8.33068i) q^{3} +(19.7771 + 60.8676i) q^{4} +363.071 q^{5} -113.384 q^{6} +(367.182 + 1130.07i) q^{7} +(158.217 - 486.941i) q^{8} +(-613.747 + 1888.92i) q^{9} +(-2349.84 - 1707.26i) q^{10} +(-908.599 - 2796.38i) q^{11} +(733.836 + 533.163i) q^{12} +(-5591.66 + 4062.58i) q^{13} +(2937.45 - 9040.56i) q^{14} +(4163.04 - 3024.62i) q^{15} +(-3313.73 + 2407.57i) q^{16} +(-7305.76 + 22484.8i) q^{17} +(12854.5 - 9339.33i) q^{18} +(-36160.1 - 26271.8i) q^{19} +(7180.48 + 22099.2i) q^{20} +(13624.4 + 9898.72i) q^{21} +(-7268.79 + 22371.0i) q^{22} +(-15900.3 + 48936.1i) q^{23} +(-2242.40 - 6901.41i) q^{24} +53695.3 q^{25} +55293.4 q^{26} +(18277.0 + 56250.9i) q^{27} +(-61522.9 + 44699.0i) q^{28} +(135177. + 98212.2i) q^{29} -41166.4 q^{30} +(165613. + 9219.76i) q^{31} +32768.0 q^{32} +(-33713.9 - 24494.6i) q^{33} +(153014. - 111171. i) q^{34} +(133313. + 410295. i) q^{35} -127112. q^{36} -405875. q^{37} +(110495. + 340070. i) q^{38} +(-30271.0 + 93164.7i) q^{39} +(57443.8 - 176794. i) q^{40} +(113501. + 82463.4i) q^{41} +(-41632.5 - 128132. i) q^{42} +(629693. + 457499. i) q^{43} +(152240. - 110609. i) q^{44} +(-222833. + 685811. i) q^{45} +(333020. - 241953. i) q^{46} +(-498096. + 361888. i) q^{47} +(-17939.2 + 55211.3i) q^{48} +(-475974. + 345816. i) q^{49} +(-347523. - 252490. i) q^{50} +(103544. + 318677. i) q^{51} +(-357866. - 260005. i) q^{52} +(609815. - 1.87682e6i) q^{53} +(146216. - 450007. i) q^{54} +(-329886. - 1.01528e6i) q^{55} +608371. q^{56} -633481. q^{57} +(-413066. - 1.27129e6i) q^{58} +(1.81177e6 - 1.31633e6i) q^{59} +(266434. + 193576. i) q^{60} -727950. q^{61} +(-1.02851e6 - 838430. i) q^{62} -2.35997e6 q^{63} +(-212079. - 154084. i) q^{64} +(-2.03017e6 + 1.47500e6i) q^{65} +(103021. + 317065. i) q^{66} -308660. q^{67} -1.51308e6 q^{68} +(225355. + 693571. i) q^{69} +(1.06650e6 - 3.28236e6i) q^{70} +(-654480. + 2.01428e6i) q^{71} +(822687. + 597717. i) q^{72} +(87373.6 + 268908. i) q^{73} +(2.62688e6 + 1.90854e6i) q^{74} +(615680. - 447318. i) q^{75} +(883963. - 2.72056e6i) q^{76} +(2.82648e6 - 2.05356e6i) q^{77} +(634005. - 460631. i) q^{78} +(804902. - 2.47723e6i) q^{79} +(-1.20312e6 + 874117. i) q^{80} +(-2.83592e6 - 2.06041e6i) q^{81} +(-346829. - 1.06743e6i) q^{82} +(3.89505e6 + 2.82992e6i) q^{83} +(-333060. + 1.02505e6i) q^{84} +(-2.65251e6 + 8.16357e6i) q^{85} +(-1.92417e6 - 5.92199e6i) q^{86} +2.36814e6 q^{87} -1.50543e6 q^{88} +(973736. + 2.99685e6i) q^{89} +(4.66708e6 - 3.39083e6i) q^{90} +(-6.64416e6 - 4.82726e6i) q^{91} -3.29308e6 q^{92} +(1.97576e6 - 1.27395e6i) q^{93} +4.92545e6 q^{94} +(-1.31287e7 - 9.53853e6i) q^{95} +(375724. - 272980. i) q^{96} +(2.43922e6 + 7.50715e6i) q^{97} +4.70669e6 q^{98} +5.83978e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 80 q^{2} + 28 q^{3} - 640 q^{4} + 168 q^{5} - 1936 q^{6} + 1402 q^{7} - 5120 q^{8} - 6164 q^{9} - 1496 q^{10} - 3402 q^{11} + 1792 q^{12} + 6413 q^{13} + 11216 q^{14} + 46465 q^{15} - 40960 q^{16}+ \cdots + 13336614 q^{99}+O(q^{100}) \) 40 * q - 80 * q^2 + 28 * q^3 - 640 * q^4 + 168 * q^5 - 1936 * q^6 + 1402 * q^7 - 5120 * q^8 - 6164 * q^9 - 1496 * q^10 - 3402 * q^11 + 1792 * q^12 + 6413 * q^13 + 11216 * q^14 + 46465 * q^15 - 40960 * q^16 + 17155 * q^17 - 98152 * q^18 + 67290 * q^19 + 6592 * q^20 + 16727 * q^21 - 27216 * q^22 + 2051 * q^23 + 47616 * q^24 + 787196 * q^25 - 214576 * q^26 + 603289 * q^27 - 62592 * q^28 + 95739 * q^29 - 369200 * q^30 + 540003 * q^31 + 1310720 * q^32 + 941656 * q^33 + 290520 * q^34 - 638364 * q^35 + 2359424 * q^36 + 843716 * q^37 - 169080 * q^38 + 827496 * q^39 + 52736 * q^40 + 175557 * q^41 + 1299656 * q^42 + 566562 * q^43 + 441152 * q^44 - 2450173 * q^45 + 484128 * q^46 - 2289258 * q^47 + 380928 * q^48 - 1290090 * q^49 - 2003912 * q^50 + 351796 * q^51 + 410432 * q^52 - 741339 * q^53 + 4826312 * q^54 - 755935 * q^55 - 434176 * q^56 - 8091472 * q^57 - 1476568 * q^58 - 8176986 * q^59 + 2973760 * q^60 - 10479540 * q^61 + 6613544 * q^62 - 10121022 * q^63 - 2621440 * q^64 + 9085330 * q^65 - 1581152 * q^66 + 7646158 * q^67 - 6844160 * q^68 - 5432460 * q^69 - 5106912 * q^70 - 24632815 * q^71 - 6281728 * q^72 - 11099311 * q^73 - 3436312 * q^74 + 11990582 * q^75 - 1352640 * q^76 + 8000688 * q^77 - 10937992 * q^78 + 10390986 * q^79 - 765952 * q^80 - 23584945 * q^81 + 2535096 * q^82 + 36507958 * q^83 + 10397248 * q^84 + 23914083 * q^85 + 5244176 * q^86 + 16619052 * q^87 - 3574784 * q^88 - 17387733 * q^89 - 2091344 * q^90 - 8973442 * q^91 - 8008576 * q^92 - 21404363 * q^93 - 137504 * q^94 - 12445576 * q^95 + 917504 * q^96 - 1428702 * q^97 + 92378560 * q^98 + 13336614 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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