LMFDB - Embedded newform 37.8.e.a.11.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,8,Mod(11,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("37.11");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	37.e (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:	$11.5582459429$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.10
Character	$\chi$	$=$	37.11
Dual form			37.8.e.a.27.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.806849 - 0.465835i) q^{2} +(-38.5559 + 66.7808i) q^{3} +(-63.5660 + 110.100i) q^{4} +(-299.174 - 172.728i) q^{5} +71.8427i q^{6} +(-372.891 + 645.866i) q^{7} +237.699i q^{8} +(-1879.62 - 3255.59i) q^{9} +O(q^{10})$	\(q+(0.806849 - 0.465835i) q^{2} +(-38.5559 + 66.7808i) q^{3} +(-63.5660 + 110.100i) q^{4} +(-299.174 - 172.728i) q^{5} +71.8427i q^{6} +(-372.891 + 645.866i) q^{7} +237.699i q^{8} +(-1879.62 - 3255.59i) q^{9} -321.851 q^{10} +7381.59 q^{11} +(-4901.69 - 8489.97i) q^{12} +(10012.0 + 5780.45i) q^{13} +694.822i q^{14} +(23069.8 - 13319.4i) q^{15} +(-8025.72 - 13901.0i) q^{16} +(-24167.5 + 13953.1i) q^{17} +(-3033.13 - 1751.18i) q^{18} +(-42719.4 - 24664.0i) q^{19} +(38034.5 - 21959.3i) q^{20} +(-28754.3 - 49803.9i) q^{21} +(5955.83 - 3438.60i) q^{22} +52927.0i q^{23} +(-15873.7 - 9164.69i) q^{24} +(20607.4 + 35693.1i) q^{25} +10770.9 q^{26} +121238. q^{27} +(-47406.4 - 82110.3i) q^{28} +1227.63i q^{29} +(12409.2 - 21493.4i) q^{30} -231558. i q^{31} +(-39300.3 - 22690.0i) q^{32} +(-284604. + 492948. i) q^{33} +(-12999.7 + 22516.1i) q^{34} +(223118. - 128817. i) q^{35} +477918. q^{36} +(294319. - 91148.2i) q^{37} -45957.5 q^{38} +(-772045. + 445741. i) q^{39} +(41057.2 - 71113.2i) q^{40} +(-121658. + 210719. i) q^{41} +(-46400.8 - 26789.5i) q^{42} -456303. i q^{43} +(-469218. + 812709. i) q^{44} +1.29865e6i q^{45} +(24655.2 + 42704.1i) q^{46} -332881. q^{47} +1.23776e6 q^{48} +(133676. + 231534. i) q^{49} +(33254.2 + 19199.3i) q^{50} -2.15190e6i q^{51} +(-1.27285e6 + 734880. i) q^{52} +(261539. + 452998. i) q^{53} +(97820.4 - 56476.7i) q^{54} +(-2.20838e6 - 1.27501e6i) q^{55} +(-153522. - 88635.7i) q^{56} +(3.29417e6 - 1.90189e6i) q^{57} +(571.873 + 990.513i) q^{58} +(1.06802e6 - 616622. i) q^{59} +3.38664e6i q^{60} +(-549603. - 317313. i) q^{61} +(-107868. - 186832. i) q^{62} +2.80357e6 q^{63} +2.01230e6 q^{64} +(-1.99689e6 - 3.45871e6i) q^{65} +530313. i q^{66} +(-1.49656e6 + 2.59211e6i) q^{67} -3.54777e6i q^{68} +(-3.53451e6 - 2.04065e6i) q^{69} +(120015. - 207873. i) q^{70} +(334730. - 579769. i) q^{71} +(773849. - 446782. i) q^{72} -2.98051e6 q^{73} +(195011. - 210647. i) q^{74} -3.17815e6 q^{75} +(5.43100e6 - 3.13559e6i) q^{76} +(-2.75253e6 + 4.76752e6i) q^{77} +(-415283. + 719291. i) q^{78} +(-2.32327e6 - 1.34134e6i) q^{79} +5.54507e6i q^{80} +(-563704. + 976365. i) q^{81} +226691. i q^{82} +(-3.23210e6 - 5.59817e6i) q^{83} +7.31118e6 q^{84} +9.64037e6 q^{85} +(-212562. - 368168. i) q^{86} +(-81982.1 - 47332.4i) q^{87} +1.75459e6i q^{88} +(1.11390e6 - 643109. i) q^{89} +(604956. + 1.04781e6i) q^{90} +(-7.46679e6 + 4.31095e6i) q^{91} +(-5.82724e6 - 3.36436e6i) q^{92} +(1.54636e7 + 8.92793e6i) q^{93} +(-268585. + 155068. i) q^{94} +(8.52034e6 + 1.47577e7i) q^{95} +(3.03052e6 - 1.74967e6i) q^{96} +1.61988e6i q^{97} +(215713. + 124542. i) q^{98} +(-1.38745e7 - 2.40314e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 18 q^{2} - 42 q^{3} + 1114 q^{4} - 672 q^{5} + 156 q^{7} - 9128 q^{9}+O(q^{10}) $ 40 * q + 18 * q^2 - 42 * q^3 + 1114 * q^4 - 672 * q^5 + 156 * q^7 - 9128 * q^9	\( 40 q + 18 q^{2} - 42 q^{3} + 1114 q^{4} - 672 q^{5} + 156 q^{7} - 9128 q^{9} - 5124 q^{10} + 12468 q^{11} + 6926 q^{12} + 10512 q^{13} + 36402 q^{15} - 31094 q^{16} - 22440 q^{17} - 153504 q^{18} + 49086 q^{19} + 28662 q^{20} + 7736 q^{21} + 132018 q^{22} + 2754 q^{24} + 72328 q^{25} - 680244 q^{26} + 42984 q^{27} + 105488 q^{28} + 382084 q^{30} + 523656 q^{32} + 9228 q^{33} + 276914 q^{34} - 904452 q^{35} - 204828 q^{36} + 1333776 q^{37} + 50208 q^{38} + 122040 q^{39} - 1205236 q^{40} - 871440 q^{41} + 1436094 q^{42} - 994326 q^{44} - 987942 q^{46} - 586932 q^{47} + 3984388 q^{48} - 1766072 q^{49} + 1818708 q^{50} - 2745228 q^{52} + 1661988 q^{53} + 1102554 q^{54} - 2733258 q^{55} - 5943924 q^{56} + 3920592 q^{57} + 5021672 q^{58} + 5296632 q^{59} - 4588524 q^{61} - 8143398 q^{62} - 2503648 q^{63} + 10662964 q^{64} - 1652736 q^{65} + 1940622 q^{67} - 10266552 q^{69} - 5038546 q^{70} + 6420528 q^{71} - 6576036 q^{72} - 3313032 q^{73} + 16192386 q^{74} - 5168536 q^{75} + 10328022 q^{76} - 8599404 q^{77} + 18210222 q^{78} - 15094374 q^{79} + 1733956 q^{81} - 191670 q^{83} + 1175224 q^{84} - 18053592 q^{85} + 18575940 q^{86} - 3762762 q^{87} - 14873004 q^{89} + 37293212 q^{90} - 76496700 q^{91} + 27846618 q^{92} + 26687652 q^{93} + 35421402 q^{94} + 14310774 q^{95} - 30894534 q^{96} - 13793868 q^{98} - 37141758 q^{99}+O(q^{100}) \) 40 * q + 18 * q^2 - 42 * q^3 + 1114 * q^4 - 672 * q^5 + 156 * q^7 - 9128 * q^9 - 5124 * q^10 + 12468 * q^11 + 6926 * q^12 + 10512 * q^13 + 36402 * q^15 - 31094 * q^16 - 22440 * q^17 - 153504 * q^18 + 49086 * q^19 + 28662 * q^20 + 7736 * q^21 + 132018 * q^22 + 2754 * q^24 + 72328 * q^25 - 680244 * q^26 + 42984 * q^27 + 105488 * q^28 + 382084 * q^30 + 523656 * q^32 + 9228 * q^33 + 276914 * q^34 - 904452 * q^35 - 204828 * q^36 + 1333776 * q^37 + 50208 * q^38 + 122040 * q^39 - 1205236 * q^40 - 871440 * q^41 + 1436094 * q^42 - 994326 * q^44 - 987942 * q^46 - 586932 * q^47 + 3984388 * q^48 - 1766072 * q^49 + 1818708 * q^50 - 2745228 * q^52 + 1661988 * q^53 + 1102554 * q^54 - 2733258 * q^55 - 5943924 * q^56 + 3920592 * q^57 + 5021672 * q^58 + 5296632 * q^59 - 4588524 * q^61 - 8143398 * q^62 - 2503648 * q^63 + 10662964 * q^64 - 1652736 * q^65 + 1940622 * q^67 - 10266552 * q^69 - 5038546 * q^70 + 6420528 * q^71 - 6576036 * q^72 - 3313032 * q^73 + 16192386 * q^74 - 5168536 * q^75 + 10328022 * q^76 - 8599404 * q^77 + 18210222 * q^78 - 15094374 * q^79 + 1733956 * q^81 - 191670 * q^83 + 1175224 * q^84 - 18053592 * q^85 + 18575940 * q^86 - 3762762 * q^87 - 14873004 * q^89 + 37293212 * q^90 - 76496700 * q^91 + 27846618 * q^92 + 26687652 * q^93 + 35421402 * q^94 + 14310774 * q^95 - 30894534 * q^96 - 13793868 * q^98 - 37141758 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.806849	−	0.465835i	0.0713161	−	0.0411744i	−0.463918	−	0.885878i	$-0.653557\pi$
$2$	0.806849	−	0.465835i	0.0713161	−	0.0411744i	0.535234	+	0.844704i	$0.320223\pi$
$3$	−38.5559	+	66.7808i	−0.824454	+	1.42800i	0.0778817	+	0.996963i	$0.475184\pi$
$3$	−38.5559	+	66.7808i	−0.824454	+	1.42800i	−0.902336	+	0.431034i	$0.858149\pi$
$4$	−63.5660	+	110.100i	−0.496609	+	0.860153i
$5$	−299.174	−	172.728i	−1.07036	−	0.617970i	−0.142077	−	0.989856i	$-0.545378\pi$
$5$	−299.174	−	172.728i	−1.07036	−	0.617970i	−0.928279	+	0.371885i	$0.878712\pi$
$6$			71.8427i			0.135785i
$7$	−372.891	+	645.866i	−0.410903	+	0.711704i	−0.994989	−	0.0999876i	$-0.968120\pi$
$7$	−372.891	+	645.866i	−0.410903	+	0.711704i	0.584086	+	0.811692i	$0.301453\pi$
$8$			237.699i			0.164139i
$9$	−1879.62	−	3255.59i	−0.859449	−	1.48861i
$10$	−321.851			−0.101778
$11$	7381.59			1.67215			0.836075	−	0.548615i	$-0.184845\pi$
$11$	7381.59			1.67215			0.836075	+	0.548615i	$0.184845\pi$
$12$	−4901.69	−	8489.97i	−0.818863	−	1.41831i
$13$	10012.0	+	5780.45i	1.26392	+	0.729726i	0.973831	−	0.227273i	$-0.0729811\pi$
$13$	10012.0	+	5780.45i	1.26392	+	0.729726i	0.290091	+	0.956999i	$0.406314\pi$
$14$			694.822i			0.0676746i
$15$	23069.8	−	13319.4i	1.76492	−	1.01898i
$16$	−8025.72	−	13901.0i	−0.489851	−	0.848447i
$17$	−24167.5	+	13953.1i	−1.19305	+	0.688810i	−0.958998	−	0.283413i	$-0.908533\pi$
$17$	−24167.5	+	13953.1i	−1.19305	+	0.688810i	−0.234056	+	0.972223i	$0.575200\pi$
$18$	−3033.13	−	1751.18i	−0.122585	−	0.0707745i
$19$	−42719.4	−	24664.0i	−1.42885	−	0.824948i	−0.431822	−	0.901959i	$-0.642129\pi$
$19$	−42719.4	−	24664.0i	−1.42885	−	0.824948i	−0.997030	+	0.0770104i	$0.975463\pi$
$20$	38034.5	−	21959.3i	1.06310	−	0.613780i
$21$	−28754.3	−	49803.9i	−0.677541	−	1.17353i
$22$	5955.83	−	3438.60i	0.119251	−	0.0688497i
$23$			52927.0i			0.907047i	0.891244	+	0.453523i	$0.149833\pi$
$23$			52927.0i			0.907047i	−0.891244	+	0.453523i	$0.850167\pi$
$24$	−15873.7	−	9164.69i	−0.234390	−	0.135325i
$25$	20607.4	+	35693.1i	0.263775	+	0.456871i
$26$	10770.9			0.120184
$27$	121238.			1.18540
$28$	−47406.4	−	82110.3i	−0.408116	−	0.706878i
$29$			1227.63i			0.00934705i	0.999989	+	0.00467353i	$0.00148764\pi$
$29$			1227.63i			0.00934705i	−0.999989	+	0.00467353i	$0.998512\pi$
$30$	12409.2	−	21493.4i	0.0839114	−	0.145339i
$31$		−	231558.i		−	1.39603i	−0.716085	−	0.698014i	$-0.754067\pi$
$31$		−	231558.i		−	1.39603i	0.716085	−	0.698014i	$-0.245933\pi$
$32$	−39300.3	−	22690.0i	−0.212017	−	0.122408i
$33$	−284604.	+	492948.i	−1.37861	+	2.38782i
$34$	−12999.7	+	22516.1i	−0.0567227	+	0.0982465i
$35$	223118.	−	128817.i	0.879624	−	0.507851i
$36$	477918.			1.70724
$37$	294319.	−	91148.2i	0.955241	−	0.295830i
$37$	294319.	−	91148.2i	0.955241	−	0.295830i
$38$	−45957.5			−0.135867
$39$	−772045.	+	445741.i	−2.08409	+	1.20325i
$40$	41057.2	−	71113.2i	0.101433	−	0.175687i
$41$	−121658.	+	210719.i	−0.275676	+	0.477484i	−0.970305	−	0.241883i	$-0.922235\pi$
$41$	−121658.	+	210719.i	−0.275676	+	0.477484i	0.694630	+	0.719368i	$0.255568\pi$
$42$	−46400.8	−	26789.5i	−0.0966391	−	0.0557946i
$43$		−	456303.i		−	0.875214i	−0.899166	−	0.437607i	$-0.855826\pi$
$43$		−	456303.i		−	0.875214i	0.899166	−	0.437607i	$-0.144174\pi$
$44$	−469218.	+	812709.i	−0.830405	+	1.43830i
$45$			1.29865e6i			2.12446i
$46$	24655.2	+	42704.1i	0.0373471	+	0.0646870i
$47$	−332881.			−0.467678			−0.233839	−	0.972275i	$-0.575129\pi$
$47$	−332881.			−0.467678			−0.233839	+	0.972275i	$0.575129\pi$
$48$	1.23776e6			1.61544
$49$	133676.	+	231534.i	0.162318	+	0.281143i
$50$	33254.2	+	19199.3i	0.0376228	+	0.0217215i
$51$		−	2.15190e6i		−	2.27157i
$52$	−1.27285e6	+	734880.i	−1.25535	+	0.724777i
$53$	261539.	+	452998.i	0.241307	+	0.417956i	0.961087	−	0.276246i	$-0.0890905\pi$
$53$	261539.	+	452998.i	0.241307	+	0.417956i	−0.719780	+	0.694203i	$0.755757\pi$
$54$	97820.4	−	56476.7i	0.0845379	−	0.0488080i
$55$	−2.20838e6	−	1.27501e6i	−1.78980	−	1.03334i
$56$	−153522.	−	88635.7i	−0.116818	−	0.0674451i
$57$	3.29417e6	−	1.90189e6i	2.35605	−	1.36026i
$58$	571.873	+	990.513i	0.000384859	+	0.000666595i
$59$	1.06802e6	−	616622.i	0.677014	−	0.390874i	−0.121715	−	0.992565i	$-0.538839\pi$
$59$	1.06802e6	−	616622.i	0.677014	−	0.390874i	0.798729	+	0.601691i	$0.205506\pi$
$60$			3.38664e6i			2.02413i
$61$	−549603.	−	317313.i	−0.310023	−	0.178992i	0.336914	−	0.941536i	$-0.390617\pi$
$61$	−549603.	−	317313.i	−0.310023	−	0.178992i	−0.646937	+	0.762543i	$0.723950\pi$
$62$	−107868.	−	186832.i	−0.0574805	−	0.0995592i
$63$	2.80357e6			1.41260
$64$	2.01230e6			0.959542
$65$	−1.99689e6	−	3.45871e6i	−0.901898	−	1.56213i
$66$			530313.i			0.227054i
$67$	−1.49656e6	+	2.59211e6i	−0.607899	+	1.05291i	0.383688	+	0.923463i	$0.374654\pi$
$67$	−1.49656e6	+	2.59211e6i	−0.607899	+	1.05291i	−0.991586	+	0.129448i	$0.958679\pi$
$68$		−	3.54777e6i		−	1.36828i
$69$	−3.53451e6	−	2.04065e6i	−1.29526	−	0.747818i
$70$	120015.	−	207873.i	0.0418209	−	0.0724359i
$71$	334730.	−	579769.i	0.110992	−	0.192243i	−0.805179	−	0.593032i	$-0.797931\pi$
$71$	334730.	−	579769.i	0.110992	−	0.192243i	0.916170	+	0.400789i	$0.131264\pi$
$72$	773849.	−	446782.i	0.244339	−	0.141069i
$73$	−2.98051e6			−0.896727			−0.448363	−	0.893851i	$-0.647993\pi$
$73$	−2.98051e6			−0.896727			−0.448363	+	0.893851i	$0.647993\pi$
$74$	195011.	−	210647.i	0.0559434	−	0.0604289i
$75$	−3.17815e6			−0.869881
$76$	5.43100e6	−	3.13559e6i	1.41916	−	0.819354i
$77$	−2.75253e6	+	4.76752e6i	−0.687091	+	1.19008i
$78$	−415283.	+	719291.i	−0.0990862	+	0.171622i
$79$	−2.32327e6	−	1.34134e6i	−0.530157	−	0.306086i	0.210923	−	0.977503i	$-0.432353\pi$
$79$	−2.32327e6	−	1.34134e6i	−0.530157	−	0.306086i	−0.741080	+	0.671416i	$0.765686\pi$
$80$			5.54507e6i			1.21085i
$81$	−563704.	+	976365.i	−0.117857	+	0.204134i
$82$			226691.i			0.0454031i
$83$	−3.23210e6	−	5.59817e6i	−0.620457	−	1.07466i	−0.989401	−	0.145212i	$-0.953614\pi$
$83$	−3.23210e6	−	5.59817e6i	−0.620457	−	1.07466i	0.368943	−	0.929452i	$-0.379720\pi$
$84$	7.31118e6			1.34589
$85$	9.64037e6			1.70266
$86$	−212562.	−	368168.i	−0.0360364	−	0.0624168i
$87$	−81982.1	−	47332.4i	−0.0133476	−	0.00770622i
$88$			1.75459e6i			0.274465i
$89$	1.11390e6	−	643109.i	0.167487	−	0.0966985i	−0.413914	−	0.910316i	$-0.635838\pi$
$89$	1.11390e6	−	643109.i	0.167487	−	0.0966985i	0.581400	+	0.813618i	$0.302505\pi$
$90$	604956.	+	1.04781e6i	0.0874731	+	0.151508i
$91$	−7.46679e6	+	4.31095e6i	−1.03870	+	0.599692i
$92$	−5.82724e6	−	3.36436e6i	−0.780199	−	0.450448i
$93$	1.54636e7	+	8.92793e6i	1.99352	+	1.15096i
$94$	−268585.	+	155068.i	−0.0333529	+	0.0192563i
$95$	8.52034e6	+	1.47577e7i	1.01959	+	1.76598i
$96$	3.03052e6	−	1.74967e6i	0.349597	−	0.201840i
$97$			1.61988e6i			0.180211i	0.995932	+	0.0901055i	$0.0287204\pi$
$97$			1.61988e6i			0.180211i	−0.995932	+	0.0901055i	$0.971280\pi$
$98$	215713.	+	124542.i	0.0231518	+	0.0133667i
$99$	−1.38745e7	−	2.40314e7i	−1.43713	−	2.48918i
$100$	−5.23972e6			−0.523972
$101$	−1.29530e7			−1.25097			−0.625485	−	0.780236i	$-0.715099\pi$
$101$	−1.29530e7			−1.25097			−0.625485	+	0.780236i	$0.715099\pi$
$102$	−1.00243e6	−	1.73626e6i	−0.0935304	−	0.161999i
$103$			1.50627e6i			0.135823i	0.997691	+	0.0679113i	$0.0216335\pi$
$103$			1.50627e6i			0.135823i	−0.997691	+	0.0679113i	$0.978367\pi$
$104$	−1.37400e6	+	2.37985e6i	−0.119776	+	0.207459i
$105$			1.98667e7i			1.67480i
$106$	422045.	+	243668.i	0.0344182	+	0.0198713i
$107$	−1.49512e6	+	2.58963e6i	−0.117987	+	0.204359i	−0.918970	−	0.394328i	$-0.870977\pi$
$107$	−1.49512e6	+	2.58963e6i	−0.117987	+	0.204359i	0.800983	+	0.598687i	$0.204311\pi$
$108$	−7.70659e6	+	1.33482e7i	−0.588679	+	1.01962i
$109$	−7.02467e6	+	4.05570e6i	−0.519557	+	0.299966i	−0.736753	−	0.676162i	$-0.763642\pi$
$109$	−7.02467e6	+	4.05570e6i	−0.519557	+	0.299966i	0.217196	+	0.976128i	$0.430309\pi$
$110$	−2.37577e6			−0.170188
$111$	−5.26080e6	+	2.31692e7i	−0.365108	+	1.60798i
$112$	1.19709e7			0.805124
$113$	−1.47138e6	+	849501.i	−0.0959290	+	0.0553846i	−0.547197	−	0.837004i	$-0.684305\pi$
$113$	−1.47138e6	+	849501.i	−0.0959290	+	0.0553846i	0.451268	+	0.892388i	$0.350972\pi$
$114$	1.77193e6	−	3.06908e6i	0.112016	−	0.194017i
$115$	9.14197e6	−	1.58344e7i	0.560528	−	0.970863i
$116$	−135162.	−	78035.6i	−0.00803989	−	0.00464183i
$117$		−	4.34601e7i		−	2.50865i
$118$	574488.	−	995042.i	0.0321880	−	0.0557512i
$119$		−	2.08120e7i		−	1.13214i
$120$	3.16600e6	+	5.48367e6i	0.167254	+	0.289692i
$121$	3.50006e7			1.79609
$122$	−591262.			−0.0294796
$123$	−9.38130e6	−	1.62489e7i	−0.454564	−	0.787328i
$124$	2.54944e7	+	1.47192e7i	1.20080	+	0.693280i
$125$			1.27508e7i			0.583921i
$126$	2.26206e6	−	1.30600e6i	0.100741	−	0.0581629i
$127$	−7.77102e6	−	1.34598e7i	−0.336639	−	0.583077i	0.647159	−	0.762355i	$-0.275957\pi$
$127$	−7.77102e6	−	1.34598e7i	−0.336639	−	0.583077i	−0.983798	+	0.179279i	$0.942624\pi$
$128$	6.65406e6	−	3.84173e6i	0.280448	−	0.161917i
$129$	3.04723e7	+	1.75932e7i	1.24980	+	0.721573i
$130$	−3.22238e6	−	1.86044e6i	−0.128640	−	0.0742701i
$131$	−1.52522e7	+	8.80584e6i	−0.592764	+	0.342232i	−0.766190	−	0.642615i	$-0.777850\pi$
$131$	−1.52522e7	+	8.80584e6i	−0.592764	+	0.342232i	0.173426	+	0.984847i	$0.444516\pi$
$132$	−3.61822e7	−	6.26695e7i	−1.36926	−	2.37163i
$133$	3.18594e7	−	1.83940e7i	1.17424	−	0.677947i
$134$			2.78859e6i			0.100119i
$135$	−3.62711e7	−	2.09411e7i	−1.26880	−	0.732541i
$136$	−3.31663e6	−	5.74458e6i	−0.113061	−	0.195827i
$137$	−4.27136e7			−1.41920			−0.709601	−	0.704603i	$-0.751125\pi$
$137$	−4.27136e7			−1.41920			−0.709601	+	0.704603i	$0.751125\pi$
$138$	−3.80242e6			−0.123164
$139$	−1.28104e7	−	2.21883e7i	−0.404587	−	0.700765i	0.589687	−	0.807632i	$-0.299251\pi$
$139$	−1.28104e7	−	2.21883e7i	−0.404587	−	0.700765i	−0.994273	+	0.106867i	$0.965918\pi$
$140$			3.27536e7i			1.00881i
$141$	1.28345e7	−	2.22301e7i	0.385579	−	0.667842i
$142$		−	623715.i		−	0.0182800i
$143$	7.39046e7	+	4.26689e7i	2.11347	+	1.22021i
$144$	−3.01705e7	+	5.22569e7i	−0.842004	+	1.45839i
$145$	212046.	−	367275.i	0.00577620	−	0.0100047i
$146$	−2.40482e6	+	1.38842e6i	−0.0639511	+	0.0369222i
$147$	−2.06160e7			−0.535296
$148$	−8.67333e6	+	3.81984e7i	−0.219922	+	0.968565i
$149$	−4.17254e7			−1.03335			−0.516676	−	0.856181i	$-0.672831\pi$
$149$	−4.17254e7			−1.03335			−0.516676	+	0.856181i	$0.672831\pi$
$150$	−2.56429e6	+	1.48049e6i	−0.0620365	+	0.0358168i
$151$	2.15057e6	−	3.72490e6i	0.0508317	−	0.0880431i	−0.839490	−	0.543375i	$-0.817146\pi$
$151$	2.15057e6	−	3.72490e6i	0.0508317	−	0.0880431i	0.890322	+	0.455332i	$0.150479\pi$
$152$	5.86261e6	−	1.01543e7i	0.135406	−	0.234530i
$153$	9.08512e7	+	5.24529e7i	2.05074	+	1.18399i
$154$			5.12889e6i			0.113162i
$155$	−3.99965e7	+	6.92761e7i	−0.862703	+	1.49425i
$156$		−	1.13336e8i		−	2.39018i
$157$	−2.76864e7	−	4.79543e7i	−0.570977	−	0.988961i	−0.996466	−	0.0839971i	$-0.973231\pi$
$157$	−2.76864e7	−	4.79543e7i	−0.570977	−	0.988961i	0.425489	−	0.904963i	$-0.360102\pi$
$158$	−2.49937e6			−0.0504116
$159$	−4.03354e7			−0.795787
$160$	7.83841e6	+	1.35765e7i	0.151289	+	0.262041i
$161$	−3.41838e7	−	1.97360e7i	−0.645549	−	0.372708i
$162$			1.05037e6i			0.0194107i
$163$	1.38351e6	−	798769.i	0.0250222	−	0.0144466i	−0.487437	−	0.873158i	$-0.662068\pi$
$163$	1.38351e6	−	798769.i	0.0250222	−	0.0144466i	0.512459	+	0.858712i	$0.328735\pi$
$164$	−1.54667e7	−	2.67891e7i	−0.273806	−	0.474246i
$165$	1.70292e8	−	9.83180e7i	2.95121	−	1.70388i
$166$	−5.21564e6	−	3.01125e6i	−0.0884972	−	0.0510939i
$167$	3.27844e7	+	1.89281e7i	0.544702	+	0.314484i	0.746983	−	0.664844i	$-0.231502\pi$
$167$	3.27844e7	+	1.89281e7i	0.544702	+	0.314484i	−0.202280	+	0.979328i	$0.564835\pi$
$168$	1.18383e7	−	6.83486e6i	0.192623	−	0.111211i
$169$	3.54528e7	+	6.14061e7i	0.564999	+	0.978607i
$170$	7.77832e6	−	4.49082e6i	0.121427	−	0.0701058i
$171$			1.85436e8i			2.83600i
$172$	5.02388e7	+	2.90054e7i	0.752817	+	0.434639i
$173$	5.18134e7	+	8.97434e7i	0.760817	+	1.31777i	0.942430	+	0.334404i	$0.108535\pi$
$173$	5.18134e7	+	8.97434e7i	0.760817	+	1.31777i	−0.181612	+	0.983370i	$0.558132\pi$
$174$	−88196.3			−0.00126919
$175$	−3.07373e7			−0.433543
$176$	−5.92425e7	−	1.02611e8i	−0.819104	−	1.41873i
$177$			9.50976e7i			1.28903i
$178$	599165.	−	1.03778e6i	0.00796300	−	0.0137923i
$179$			2.13119e7i			0.277739i	0.990311	+	0.138869i	$0.0443468\pi$
$179$			2.13119e7i			0.277739i	−0.990311	+	0.138869i	$0.955653\pi$
$180$	−1.42981e8	−	8.25499e7i	−1.82736	−	1.05503i
$181$	5.79663e6	−	1.00401e7i	0.0726609	−	0.125852i	−0.827406	−	0.561605i	$-0.810184\pi$
$181$	5.79663e6	−	1.00401e7i	0.0726609	−	0.125852i	0.900067	+	0.435752i	$0.143518\pi$
$182$	−4.01638e6	+	6.95658e6i	−0.0493839	+	0.0855354i
$183$	4.23809e7	−	2.44686e7i	0.511200	−	0.295142i
$184$	−1.25807e7			−0.148882
$185$	−1.03796e8	−	2.35680e7i	−1.20526	−	0.273667i
$186$	1.66358e7			0.189560
$187$	−1.78394e8	+	1.02996e8i	−1.99497	+	1.15179i
$188$	2.11599e7	−	3.66501e7i	0.232253	−	0.402274i
$189$	−4.52084e7	+	7.83032e7i	−0.487083	+	0.843652i
$190$	1.37493e7	+	7.93814e6i	0.145426	+	0.0839617i
$191$			1.15450e7i			0.119888i	0.998202	+	0.0599440i	$0.0190922\pi$
$191$			1.15450e7i			0.119888i	−0.998202	+	0.0599440i	$0.980908\pi$
$192$	−7.75862e7	+	1.34383e8i	−0.791098	+	1.37022i
$193$		−	4.61466e7i		−	0.462050i	−0.972948	−	0.231025i	$-0.925792\pi$
$193$		−	4.61466e7i		−	0.462050i	0.972948	−	0.231025i	$-0.0742080\pi$
$194$	754596.	+	1.30700e6i	0.00742007	+	0.0128519i
$195$	3.07968e8			2.97429
$196$	−3.39890e7			−0.322435
$197$	−8.32524e6	−	1.44197e7i	−0.0775827	−	0.134377i	0.824624	−	0.565682i	$-0.191387\pi$
$197$	−8.32524e6	−	1.44197e7i	−0.0775827	−	0.134377i	−0.902207	+	0.431304i	$0.858054\pi$
$198$	−2.23893e7	−	1.29265e7i	−0.204981	−	0.118346i
$199$		−	1.87037e8i		−	1.68245i	−0.540683	−	0.841226i	$-0.681834\pi$
$199$		−	1.87037e8i		−	1.68245i	0.540683	−	0.841226i	$-0.318166\pi$
$200$	−8.48420e6	+	4.89835e6i	−0.0749904	+	0.0432957i
$201$	−1.15402e8	−	1.99882e8i	−1.00237	−	1.73615i
$202$	−1.04512e7	+	6.03398e6i	−0.0892143	+	0.0515079i
$203$	−792885.	−	457773.i	−0.00665234	−	0.00384073i
$204$	2.36923e8	+	1.36788e8i	1.95390	+	1.12808i
$205$	7.27940e7	−	4.20276e7i	0.590142	−	0.340719i
$206$	701672.	+	1.21533e6i	0.00559241	+	0.00968633i
$207$	1.72309e8	−	9.94824e7i	1.35024	−	0.779561i
$208$		−	1.85569e8i		−	1.42983i
$209$	−3.15337e8	−	1.82060e8i	−2.38926	−	1.37944i
$210$	9.25459e6	+	1.60294e7i	0.0689588	+	0.119440i
$211$	1.19222e8			0.873710			0.436855	−	0.899532i	$-0.356092\pi$
$211$	1.19222e8			0.873710			0.436855	+	0.899532i	$0.356092\pi$
$212$	−6.64999e7			−0.479342
$213$	2.58116e7	+	4.47071e7i	0.183015	+	0.316991i
$214$			2.78592e6i			0.0194321i
$215$	−7.88164e7	+	1.36514e8i	−0.540856	+	0.936790i
$216$			2.88180e7i			0.194570i
$217$	1.49556e8	+	8.63459e7i	0.993558	+	0.573631i
$218$	−3.77857e6	+	6.54467e6i	−0.0247019	+	0.0427849i
$219$	1.14916e8	−	1.99041e8i	0.739310	−	1.28052i
$220$	2.80755e8	−	1.62094e8i	1.77766	−	1.02633i
$221$	−3.22621e8			−2.01057
$222$	6.54834e6	+	2.11447e7i	0.0401694	+	0.129708i
$223$	5.14866e7			0.310905			0.155452	−	0.987843i	$-0.450316\pi$
$223$	5.14866e7			0.310905			0.155452	+	0.987843i	$0.450316\pi$
$224$	2.93095e7	−	1.69218e7i	0.174237	−	0.100596i
$225$	7.74680e7	−	1.34179e8i	0.453402	−	0.785316i
$226$	−791454.	+	1.37084e6i	−0.00456085	+	0.00789963i
$227$	1.40111e7	+	8.08932e6i	0.0795028	+	0.0459010i	0.539224	−	0.842162i	$-0.318717\pi$
$227$	1.40111e7	+	8.08932e6i	0.0795028	+	0.0459010i	−0.459722	+	0.888063i	$0.652051\pi$
$228$			4.83582e8i			2.70208i
$229$	−1.12189e8	+	1.94317e8i	−0.617342	+	1.06927i	0.372626	+	0.927981i	$0.378457\pi$
$229$	−1.12189e8	+	1.94317e8i	−0.617342	+	1.06927i	−0.989969	+	0.141287i	$0.954876\pi$
$230$		−	1.70346e7i		−	0.0923175i
$231$	−2.12252e8	−	3.67632e8i	−1.13295	−	1.96233i
$232$	−291806.			−0.00153422
$233$	−1.13637e8			−0.588537			−0.294269	−	0.955723i	$-0.595076\pi$
$233$	−1.13637e8			−0.588537			−0.294269	+	0.955723i	$0.595076\pi$
$234$	−2.02452e7	−	3.50657e7i	−0.103292	−	0.178907i
$235$	9.95893e7	+	5.74979e7i	0.500582	+	0.289011i
$236$			1.56785e8i			0.776447i
$237$	1.79151e8	−	1.03433e8i	0.874180	−	0.504708i
$238$	−9.69493e6	−	1.67921e7i	−0.0466150	−	0.0807395i
$239$	−2.13122e8	+	1.23046e8i	−1.00980	+	0.583009i	−0.911133	−	0.412112i	$-0.864791\pi$
$239$	−2.13122e8	+	1.23046e8i	−1.00980	+	0.583009i	−0.0986675	+	0.995120i	$0.531458\pi$
$240$	−3.70304e8	−	2.13795e8i	−1.72909	−	0.998293i
$241$	893120.	+	515643.i	0.00411008	+	0.00237296i	0.502054	−	0.864836i	$-0.332578\pi$
$241$	893120.	+	515643.i	0.00411008	+	0.00237296i	−0.497944	+	0.867209i	$0.665911\pi$
$242$	2.82402e7	−	1.63045e7i	0.128090	−	0.0739527i
$243$	8.91050e7	+	1.54334e8i	0.398364	+	0.689987i
$244$	6.98721e7	−	4.03407e7i	0.307921	−	0.177778i
$245$		−	9.23583e7i		−	0.401231i
$246$	−1.51386e7	−	8.74027e6i	−0.0648355	−	0.0374328i
$247$	−2.85138e8	−	4.93874e8i	−1.20397	−	2.08534i
$248$	5.50410e7			0.229143
$249$	4.98467e8			2.04615
$250$	5.93978e6	+	1.02880e7i	0.0240426	+	0.0416429i
$251$			1.88602e8i			0.752816i	0.926454	+	0.376408i	$0.122841\pi$
$251$			1.88602e8i			0.752816i	−0.926454	+	0.376408i	$0.877159\pi$
$252$	−1.78212e8	+	3.08671e8i	−0.701510	+	1.21505i
$253$			3.90685e8i			1.51672i
$254$	−1.25401e7	−	7.24002e6i	−0.0480156	−	0.0277218i
$255$	−3.71693e8	+	6.43791e8i	−1.40376	+	2.43139i
$256$	−1.25208e8	+	2.16867e8i	−0.466437	+	0.807893i
$257$	2.23580e8	−	1.29084e8i	0.821611	−	0.474357i	−0.0293606	−	0.999569i	$-0.509347\pi$
$257$	2.23580e8	−	1.29084e8i	0.821611	−	0.474357i	0.850972	+	0.525211i	$0.176014\pi$
$258$	3.27821e7			0.118841
$259$	−5.08795e7	+	2.24079e8i	−0.181967	+	0.801406i
$260$	5.07737e8			1.79156
$261$	3.99666e6	−	2.30747e6i	0.0139141	−	0.00803332i
$262$	−8.20413e6	+	1.42100e7i	−0.0281824	+	0.0488133i
$263$	7.15157e7	−	1.23869e8i	0.242413	−	0.419872i	−0.718988	−	0.695022i	$-0.755394\pi$
$263$	7.15157e7	−	1.23869e8i	0.242413	−	0.419872i	0.961401	+	0.275151i	$0.0887277\pi$
$264$	−1.17173e8	−	6.76499e7i	−0.391935	−	0.226284i
$265$		−	1.80700e8i		−	0.596483i
$266$	1.71371e7	−	2.96824e7i	0.0558281	−	0.0966970i
$267$			9.91826e7i			0.318894i
$268$	−1.90260e8	−	3.29540e8i	−0.603776	−	1.04577i
$269$	1.85866e7			0.0582193			0.0291096	−	0.999576i	$-0.490733\pi$
$269$	1.85866e7			0.0582193			0.0291096	+	0.999576i	$0.490733\pi$
$270$	−3.90204e7			−0.120648
$271$	2.33883e8	+	4.05097e8i	0.713848	+	1.23642i	0.963402	+	0.268060i	$0.0863825\pi$
$271$	2.33883e8	+	4.05097e8i	0.713848	+	1.23642i	−0.249554	+	0.968361i	$0.580284\pi$
$272$	3.87923e8	+	2.23967e8i	1.16884	+	0.674829i
$273$		−	6.64851e8i		−	1.97767i
$274$	−3.44635e7	+	1.98975e7i	−0.101212	+	0.0584348i
$275$	1.52115e8	+	2.63472e8i	0.441071	+	0.763958i
$276$	4.49349e8	−	2.59432e8i	1.28648	−	0.742747i
$277$	9.94247e7	+	5.74029e7i	0.281070	+	0.162276i	0.633908	−	0.773409i	$-0.281450\pi$
$277$	9.94247e7	+	5.74029e7i	0.281070	+	0.162276i	−0.352838	+	0.935685i	$0.614783\pi$
$278$	−2.06722e7	−	1.19351e7i	−0.0577071	−	0.0333172i
$279$	−7.53858e8	+	4.35240e8i	−2.07814	+	1.19981i
$280$	3.06197e7	+	5.30349e7i	0.0833582	+	0.144381i
$281$	4.32408e8	−	2.49651e8i	1.16258	−	0.671215i	0.210657	−	0.977560i	$-0.432440\pi$
$281$	4.32408e8	−	2.49651e8i	1.16258	−	0.671215i	0.951920	+	0.306345i	$0.0991062\pi$
$282$		−	2.39151e7i		−	0.0635039i
$283$	−1.39772e8	−	8.06976e7i	−0.366580	−	0.211645i	0.305383	−	0.952229i	$-0.401215\pi$
$283$	−1.39772e8	−	8.06976e7i	−0.366580	−	0.211645i	−0.671963	+	0.740585i	$0.734549\pi$
$284$	4.25549e7	+	7.37072e7i	0.110239	+	0.190940i
$285$	−1.31404e9			−3.36241
$286$	7.95065e7			0.200966
$287$	−9.07307e7	−	1.57150e8i	−0.226552	−	0.392399i
$288$			1.70594e8i			0.420814i
$289$	1.84209e8	−	3.19059e8i	0.448919	−	0.777551i
$290$		−	395114.i		−	0.000951326i
$291$	−1.08177e8	−	6.24559e7i	−0.257341	−	0.148576i
$292$	1.89459e8	−	3.28152e8i	0.445323	−	0.771322i
$293$	−3.85733e7	+	6.68108e7i	−0.0895880	+	0.155171i	−0.907337	−	0.420404i	$-0.861888\pi$
$293$	−3.85733e7	+	6.68108e7i	−0.0895880	+	0.155171i	0.817749	+	0.575575i	$0.195222\pi$
$294$	−1.66340e7	+	9.60365e6i	−0.0381752	+	0.0220405i
$295$	−4.26031e8			−0.966194
$296$	2.16658e7	+	6.99593e7i	0.0485572	+	0.156792i
$297$	8.94925e8			1.98216
$298$	−3.36661e7	+	1.94371e7i	−0.0736946	+	0.0425476i
$299$	−3.05942e8	+	5.29906e8i	−0.661895	+	1.14644i
$300$	2.02022e8	−	3.49913e8i	0.431991	−	0.748230i
$301$	2.94711e8	+	1.70151e8i	0.622893	+	0.359628i
$302$		−	4.00725e6i		−	0.00837186i
$303$	4.99416e8	−	8.65014e8i	1.03137	−	1.78638i
$304$			7.91787e8i			1.61641i
$305$	1.09618e8	+	1.89864e8i	0.221224	+	0.383171i
$306$	9.77376e7			0.195001
$307$	−9.94657e8			−1.96195			−0.980977	−	0.194122i	$-0.937814\pi$
$307$	−9.94657e8			−1.96195			−0.980977	+	0.194122i	$0.937814\pi$
$308$	−3.49934e8	−	6.06104e8i	−0.682431	−	1.18201i
$309$	−1.00590e8	−	5.80755e7i	−0.193954	−	0.111979i
$310$			7.45271e7i			0.142085i
$311$	−2.79674e8	+	1.61470e8i	−0.527219	+	0.304390i	−0.739883	−	0.672735i	$-0.765119\pi$
$311$	−2.79674e8	+	1.61470e8i	−0.527219	+	0.304390i	0.212664	+	0.977125i	$0.431786\pi$
$312$	−1.05952e8	−	1.83514e8i	−0.197500	−	0.342081i
$313$	7.27190e8	−	4.19843e8i	1.34043	−	0.773895i	0.353556	−	0.935413i	$-0.384972\pi$
$313$	7.27190e8	−	4.19843e8i	1.34043	−	0.773895i	0.986870	+	0.161518i	$0.0516391\pi$
$314$	−4.46776e7	−	2.57946e7i	−0.0814396	−	0.0470192i
$315$	−8.38753e8	−	4.84254e8i	−1.51198	−	0.872945i
$316$	2.95362e8	−	1.70527e8i	0.526562	−	0.304011i
$317$	4.22312e8	+	7.31466e8i	0.744605	+	1.28969i	0.950379	+	0.311094i	$0.100695\pi$
$317$	4.22312e8	+	7.31466e8i	0.744605	+	1.28969i	−0.205774	+	0.978600i	$0.565971\pi$
$318$	−3.25446e7	+	1.87896e7i	−0.0567524	+	0.0327660i
$319$			9.06186e6i			0.0156297i
$320$	−6.02029e8	−	3.47581e8i	−1.02705	−	0.592968i
$321$	−1.15292e8	−	1.99691e8i	−0.194550	−	0.336970i
$322$	−3.67749e7			−0.0613840
$323$	1.37656e9			2.27293
$324$	−7.16649e7	−	1.24127e8i	−0.117057	−	0.202749i
$325$			4.76480e8i			0.769933i
$326$	744188.	−	1.28897e6i	0.00118966	−	0.00206054i
$327$		−	6.25484e8i		−	0.989234i
$328$	−5.00875e7	−	2.89180e7i	−0.0783738	−	0.0452491i
$329$	1.24128e8	−	2.14997e8i	0.192170	−	0.332848i
$330$	9.15999e7	−	1.58656e8i	0.140312	−	0.243028i
$331$	1.21037e8	−	6.98806e7i	0.183451	−	0.105915i	−0.405462	−	0.914112i	$-0.632889\pi$
$331$	1.21037e8	−	6.98806e7i	0.183451	−	0.105915i	0.588913	+	0.808197i	$0.299556\pi$
$332$	8.21807e8			1.23250
$333$	−8.49948e8	−	7.86859e8i	−1.26136	−	1.16773i
$334$	3.52694e7			0.0517947
$335$	8.95460e8	−	5.16994e8i	1.30134	−	0.751327i
$336$	−4.61548e8	+	7.99424e8i	−0.663788	+	1.14971i
$337$	−2.57312e8	+	4.45677e8i	−0.366231	+	0.634331i	−0.988973	−	0.148097i	$-0.952685\pi$
$337$	−2.57312e8	+	4.45677e8i	−0.366231	+	0.634331i	0.622742	+	0.782427i	$0.286019\pi$
$338$	5.72102e7	+	3.30303e7i	0.0805870	+	0.0465269i
$339$		−	1.31013e8i		−	0.182648i
$340$	−6.12800e8	+	1.06140e9i	−0.845556	+	1.46455i
$341$		−	1.70927e9i		−	2.33437i
$342$	8.63824e7	+	1.49619e8i	0.116771	+	0.202253i
$343$	−8.13570e8			−1.08859
$344$	1.08463e8			0.143657
$345$	7.04954e8	+	1.22102e9i	0.924259	+	1.60086i
$346$	8.36112e7	+	4.82729e7i	0.108517	+	0.0626523i
$347$		−	3.90428e8i		−	0.501635i	−0.968034	−	0.250818i	$-0.919301\pi$
$347$		−	3.90428e8i		−	0.501635i	0.968034	−	0.250818i	$-0.0806994\pi$
$348$	1.04226e7	−	6.01746e6i	0.0132570	−	0.00765396i
$349$	−5.76012e8	−	9.97682e8i	−0.725342	−	1.25633i	−0.958833	−	0.283970i	$-0.908349\pi$
$349$	−5.76012e8	−	9.97682e8i	−0.725342	−	1.25633i	0.233492	−	0.972359i	$-0.424985\pi$
$350$	−2.48004e7	+	1.43185e7i	−0.0309186	+	0.0178509i
$351$	1.21383e9	+	7.00807e8i	1.49825	+	0.865015i
$352$	−2.90098e8	−	1.67488e8i	−0.354524	−	0.204685i
$353$	2.00733e8	−	1.15893e8i	0.242889	−	0.140232i	−0.373615	−	0.927584i	$-0.621882\pi$
$353$	2.00733e8	−	1.15893e8i	0.242889	−	0.140232i	0.616504	+	0.787352i	$0.288549\pi$
$354$	4.42998e7	+	7.67295e7i	0.0530750	+	0.0919286i
$355$	−2.00285e8	+	1.15634e8i	−0.237601	+	0.137179i
$356$			1.63519e8i			0.192085i
$357$	1.38984e9	+	8.02424e8i	1.61669	+	0.933394i
$358$	9.92783e6	+	1.71955e7i	0.0114357	+	0.0198073i
$359$	−1.61945e9			−1.84730			−0.923652	−	0.383233i	$-0.874811\pi$
$359$	−1.61945e9			−1.84730			−0.923652	+	0.383233i	$0.874811\pi$
$360$	−3.08687e8			−0.348706
$361$	7.69695e8	+	1.33315e9i	0.861080	+	1.49143i
$362$		−	1.08011e7i		−	0.0119671i
$363$	−1.34948e9	+	2.33737e9i	−1.48079	+	2.56480i
$364$		−	1.09612e9i		−	1.19125i
$365$	8.91689e8	+	5.14817e8i	0.959817	+	0.554151i
$366$	2.27967e7	−	3.94850e7i	0.0243045	−	0.0420967i
$367$	−8.13736e7	+	1.40943e8i	−0.0859315	+	0.148838i	−0.905788	−	0.423732i	$-0.860720\pi$
$367$	−8.13736e7	+	1.40943e8i	−0.0859315	+	0.148838i	0.819856	+	0.572569i	$0.194053\pi$
$368$	7.35735e8	−	4.24777e8i	0.769581	−	0.444318i
$369$	9.14684e8			0.947717
$370$	−9.47269e7	+	2.93361e7i	−0.0972226	+	0.0301090i
$371$	−3.90102e8			−0.396615
$372$	−1.96592e9	+	1.13503e9i	−1.98000	+	1.14316i
$373$	8.76060e7	−	1.51738e8i	0.0874083	−	0.151396i	−0.819007	−	0.573784i	$-0.805475\pi$
$373$	8.76060e7	−	1.51738e8i	0.0874083	−	0.151396i	0.906415	+	0.422388i	$0.138808\pi$
$374$	−9.59583e7	+	1.66205e8i	−0.0948488	+	0.164283i
$375$	−8.51511e8	−	4.91620e8i	−0.833837	−	0.481416i
$376$		−	7.91254e7i		−	0.0767642i
$377$	−7.09625e6	+	1.22911e7i	−0.00682079	+	0.0118139i
$378$			8.42386e7i			0.0802213i
$379$	4.30607e8	+	7.45834e8i	0.406298	+	0.703728i	0.994472	−	0.105006i	$-0.0334863\pi$
$379$	4.30607e8	+	7.45834e8i	0.406298	+	0.703728i	−0.588174	+	0.808734i	$0.700153\pi$
$380$	−2.16642e9			−2.02535
$381$	1.19847e9			1.11018
$382$	5.37804e6	+	9.31504e6i	0.00493631	+	0.00854994i
$383$	−1.72679e9	−	9.96960e8i	−1.57052	−	0.906738i	−0.996105	−	0.0881719i	$-0.971898\pi$
$383$	−1.72679e9	−	9.96960e8i	−1.57052	−	0.906738i	−0.574412	−	0.818567i	$-0.694769\pi$
$384$			5.92485e8i			0.533971i
$385$	1.64697e9	−	9.50877e8i	1.47086	−	0.849204i
$386$	−2.14967e7	−	3.72334e7i	−0.0190246	−	0.0329516i
$387$	−1.48554e9	+	8.57675e8i	−1.30285	+	0.752202i
$388$	−1.78348e8	−	1.02969e8i	−0.155009	−	0.0894945i
$389$	1.16645e9	+	6.73450e8i	1.00471	+	0.580071i	0.909639	−	0.415399i	$-0.136358\pi$
$389$	1.16645e9	+	6.73450e8i	1.00471	+	0.580071i	0.0950738	+	0.995470i	$0.469691\pi$
$390$	2.48483e8	−	1.43462e8i	0.212115	−	0.122465i
$391$	−7.38496e8	−	1.27911e9i	−0.624783	−	1.08216i
$392$	−5.50352e7	+	3.17746e7i	−0.0461466	+	0.0266427i
$393$		−	1.35807e9i		−	1.12862i
$394$	−1.34344e7	−	7.75638e6i	−0.0110658	−	0.00638884i
$395$	4.63374e8	+	8.02587e8i	0.378304	+	0.655243i
$396$	3.52780e9			2.85476
$397$	−2.45063e9			−1.96567			−0.982835	−	0.184485i	$-0.940938\pi$
$397$	−2.45063e9			−1.96567			−0.982835	+	0.184485i	$0.940938\pi$
$398$	−8.71285e7	−	1.50911e8i	−0.0692739	−	0.119986i
$399$			2.83679e9i			2.23574i
$400$	3.30779e8	−	5.72925e8i	0.258421	−	0.447598i
$401$			2.20127e9i			1.70478i	0.522909	+	0.852389i	$0.324847\pi$
$401$			2.20127e9i			1.70478i	−0.522909	+	0.852389i	$0.675153\pi$
$402$	−1.86224e8	−	1.07517e8i	−0.142970	−	0.0825438i
$403$	1.33851e9	−	2.31836e9i	1.01872	−	1.76447i
$404$	8.23373e8	−	1.42612e9i	0.621243	−	1.07603i
$405$	3.37291e8	−	1.94735e8i	0.252297	−	0.145664i
$406$	−852985.			−0.000632558
$407$	2.17254e9	−	6.72818e8i	1.59731	−	0.494672i
$408$	5.11503e8			0.372853
$409$	−5.04454e8	+	2.91247e8i	−0.364578	+	0.210489i	−0.671087	−	0.741379i	$-0.734172\pi$
$409$	−5.04454e8	+	2.91247e8i	−0.364578	+	0.210489i	0.306509	+	0.951868i	$0.400839\pi$
$410$	3.91558e7	−	6.78199e7i	0.0280578	−	0.0485975i
$411$	1.64686e9	−	2.85245e9i	1.17007	−	2.02662i
$412$	−1.65839e8	−	9.57474e7i	−0.116828	−	0.0674507i
$413$			9.19731e8i			0.642444i
$414$	9.26847e7	−	1.60535e8i	0.0641958	−	0.111190i
$415$			2.23310e9i			1.53370i
$416$	−2.62317e8	−	4.54346e8i	−0.178649	−	0.309429i
$417$	1.97567e9			1.33425
$418$	−3.39239e8			−0.227190
$419$	−8.89957e8	−	1.54145e9i	−0.591044	−	1.02372i	−0.994092	−	0.108540i	$-0.965383\pi$
$419$	−8.89957e8	−	1.54145e9i	−0.591044	−	1.02372i	0.403048	−	0.915179i	$-0.367951\pi$
$420$	−2.18731e9	−	1.26285e9i	−1.44058	−	0.831721i
$421$			1.06276e9i			0.694140i	0.937839	+	0.347070i	$0.112823\pi$
$421$			1.06276e9i			0.694140i	−0.937839	+	0.347070i	$0.887177\pi$
$422$	9.61941e7	−	5.55377e7i	0.0623096	−	0.0359745i
$423$	6.25689e8	+	1.08372e9i	0.401945	+	0.696190i
$424$	−1.07677e8	+	6.21674e7i	−0.0686030	+	0.0396079i
$425$	−9.96059e8	−	5.75075e8i	−0.629396	−	0.363382i
$426$	4.16522e7	+	2.40479e7i	0.0261038	+	0.0150711i
$427$	4.09884e8	−	2.36647e8i	0.254779	−	0.147097i
$428$	−1.90078e8	−	3.29225e8i	−0.117187	−	0.202973i
$429$	−5.69892e9	+	3.29027e9i	−3.48491	+	2.01202i
$430$			1.46862e8i			0.0890776i
$431$	−7.80646e8	−	4.50706e8i	−0.469660	−	0.271159i	0.246437	−	0.969159i	$-0.420740\pi$
$431$	−7.80646e8	−	4.50706e8i	−0.469660	−	0.271159i	−0.716098	+	0.698000i	$0.754073\pi$
$432$	−9.73019e8	−	1.68532e9i	−0.580668	−	1.00575i
$433$	1.06516e8			0.0630533			0.0315266	−	0.999503i	$-0.489963\pi$
$433$	1.06516e8			0.0630533			0.0315266	+	0.999503i	$0.489963\pi$
$434$	1.60892e8			0.0944756
$435$	1.63513e7	+	2.83212e7i	0.00952443	+	0.0164968i
$436$		−	1.03122e9i		−	0.595865i
$437$	1.30539e9	−	2.26101e9i	0.748267	−	1.29604i
$438$		−	2.14128e8i		−	0.121762i
$439$	−1.00641e9	−	5.81049e8i	−0.567738	−	0.327784i	0.188507	−	0.982072i	$-0.439635\pi$
$439$	−1.00641e9	−	5.81049e8i	−0.567738	−	0.327784i	−0.756245	+	0.654288i	$0.772968\pi$
$440$	3.03067e8	−	5.24928e8i	0.169611	−	0.293775i
$441$	5.02519e8	−	8.70388e8i	0.279008	−	0.483257i
$442$	−2.60306e8	+	1.50288e8i	−0.143386	+	0.0827839i
$443$	1.37419e9			0.750988			0.375494	−	0.926825i	$-0.377473\pi$
$443$	1.37419e9			0.750988			0.375494	+	0.926825i	$0.377473\pi$
$444$	−2.21651e9	−	2.05198e9i	−1.20179	−	1.11259i
$445$	−4.44332e8			−0.239027
$446$	4.15419e7	−	2.39843e7i	0.0221725	−	0.0128013i
$447$	1.60876e9	−	2.78645e9i	0.851951	−	1.47562i
$448$	−7.50371e8	+	1.29968e9i	−0.394278	+	0.682910i
$449$	2.36895e9	+	1.36771e9i	1.23507	+	0.713070i	0.968083	−	0.250629i	$-0.0806374\pi$
$449$	2.36895e9	+	1.36771e9i	1.23507	+	0.713070i	0.266991	+	0.963699i	$0.413971\pi$
$450$		−	1.44349e8i		−	0.0746742i
$451$	−8.98032e8	+	1.55544e9i	−0.460971	+	0.798426i
$452$		−	2.15998e8i		−	0.110018i
$453$	1.65835e8	+	2.87234e8i	0.0838169	+	0.145175i
$454$	1.50732e7			0.00755977
$455$	2.97849e9			1.48237
$456$	4.52077e8	+	7.83020e8i	0.223272	+	0.386719i
$457$	2.12304e8	+	1.22574e8i	0.104052	+	0.0600745i	0.551123	−	0.834424i	$-0.314200\pi$
$457$	2.12304e8	+	1.22574e8i	0.104052	+	0.0600745i	−0.447071	+	0.894499i	$0.647533\pi$
$458$			2.09046e8i			0.101675i
$459$	−2.93001e9	+	1.69164e9i	−1.41424	+	0.816514i
$460$	1.16224e9	+	2.01305e9i	0.556727	+	0.964279i
$461$	−2.98605e9	+	1.72400e9i	−1.41953	+	0.819565i	−0.996257	−	0.0864386i	$-0.972451\pi$
$461$	−2.98605e9	+	1.72400e9i	−1.41953	+	0.819565i	−0.423271	+	0.906003i	$0.639118\pi$
$462$	−3.42511e8	−	1.97749e8i	−0.161595	−	0.0932970i
$463$	2.88549e8	+	1.66594e8i	0.135109	+	0.0780055i	0.566031	−	0.824384i	$-0.308478\pi$
$463$	2.88549e8	+	1.66594e8i	0.135109	+	0.0780055i	−0.430922	+	0.902389i	$0.641812\pi$
$464$	1.70652e7	−	9.85262e6i	0.00793048	−	0.00457866i
$465$	−3.08421e9	−	5.34200e9i	−1.42252	−	2.46387i
$466$	−9.16880e7	+	5.29361e7i	−0.0419722	+	0.0242327i
$467$			3.08591e9i			1.40209i	0.713119	+	0.701043i	$0.247282\pi$
$467$			3.08591e9i			1.40209i	−0.713119	+	0.701043i	$0.752718\pi$
$468$	4.78493e9	+	2.76258e9i	2.15782	+	1.24582i
$469$	−1.11610e9	−	1.93315e9i	−0.499574	−	0.865288i
$470$	1.07138e8			0.0475994
$471$	4.26990e9			1.88298
$472$	1.46570e8	+	2.53867e8i	0.0641577	+	0.111124i
$473$		−	3.36824e9i		−	1.46349i
$474$	9.63654e7	−	1.66910e8i	0.0415621	−	0.0719876i
$475$		−	2.03305e9i		−	0.870403i
$476$	2.29139e9	+	1.32293e9i	0.973809	+	0.562229i
$477$	9.83184e8	−	1.70293e9i	0.414783	−	0.718425i
$478$	−1.14638e8	+	1.98559e8i	−0.0480100	+	0.0831558i
$479$	−9.05501e8	+	5.22792e8i	−0.376457	+	0.217347i	−0.676275	−	0.736649i	$-0.736407\pi$
$479$	−9.05501e8	+	5.22792e8i	−0.376457	+	0.217347i	0.299819	+	0.953996i	$0.403074\pi$
$480$	−1.20887e9			−0.498924
$481$	3.47361e9	+	7.88719e8i	1.42322	+	0.323158i
$482$	960818.			0.000390820
$483$	2.63597e9	−	1.52188e9i	1.06445	−	0.614561i
$484$	−2.22485e9	+	3.85355e9i	−0.891953	+	1.54491i
$485$	2.79798e8	−	4.84625e8i	0.111365	−	0.192890i
$486$	1.43789e8	+	8.30164e7i	0.0568195	+	0.0328048i
$487$		−	2.40114e9i		−	0.942034i	−0.882124	−	0.471017i	$-0.843887\pi$
$487$		−	2.40114e9i		−	0.942034i	0.882124	−	0.471017i	$-0.156113\pi$
$488$	7.54250e7	−	1.30640e8i	0.0293796	−	0.0508870i
$489$			1.23189e8i			0.0476421i
$490$	−4.30237e7	−	7.45193e7i	−0.0165204	−	0.0286142i
$491$	−2.16202e9			−0.824280			−0.412140	−	0.911121i	$-0.635219\pi$
$491$	−2.16202e9			−0.824280			−0.412140	+	0.911121i	$0.635219\pi$
$492$	2.38533e9			0.902963
$493$	−1.71293e7	−	2.96688e7i	−0.00643835	−	0.0111515i
$494$	−4.60128e8	−	2.65655e8i	−0.171725	−	0.0991456i
$495$			9.58609e9i			3.55241i
$496$	−3.21888e9	+	1.85842e9i	−1.18445	+	0.683845i
$497$	2.49636e8	+	4.32382e8i	0.0912135	+	0.157986i
$498$	4.02188e8	−	2.32203e8i	0.145924	−	0.0842491i
$499$	−2.65796e9	−	1.53458e9i	−0.957629	−	0.552887i	−0.0621863	−	0.998065i	$-0.519807\pi$
$499$	−2.65796e9	−	1.53458e9i	−0.957629	−	0.552887i	−0.895442	+	0.445177i	$0.853141\pi$
$500$	−1.40386e9	−	8.10520e8i	−0.502261	−	0.289980i
$501$	−2.52806e9	+	1.45958e9i	−0.898164	+	0.518555i
$502$	8.78575e7	+	1.52174e8i	0.0309967	+	0.0536879i
$503$	1.70152e9	−	9.82371e8i	0.596140	−	0.344182i	−0.171382	−	0.985205i	$-0.554823\pi$
$503$	1.70152e9	−	9.82371e8i	0.596140	−	0.344182i	0.767522	+	0.641023i	$0.221490\pi$
$504$			6.66404e8i			0.231863i
$505$	3.87521e9	+	2.23735e9i	1.33898	+	0.773063i
$506$	1.81995e8	+	3.15224e8i	0.0624499	+	0.108166i
$507$	−5.46767e9			−1.86326
$508$	1.97589e9			0.668713
$509$	−1.15264e8	−	1.99644e8i	−0.0387421	−	0.0671032i	0.846004	−	0.533176i	$-0.179002\pi$
$509$	−1.15264e8	−	1.99644e8i	−0.0387421	−	0.0671032i	−0.884746	+	0.466073i	$0.845668\pi$
$510$			6.92590e8i			0.231196i
$511$	1.11140e9	−	1.92501e9i	0.368467	−	0.638204i
$512$			1.21679e9i			0.400654i
$513$	−5.17919e9	−	2.99021e9i	−1.69376	−	0.977892i
$514$	1.20263e8	−	2.08302e8i	0.0390627	−	0.0676586i
$515$	2.60175e8	−	4.50635e8i	0.0839343	−	0.145378i
$516$	−3.87400e9	+	2.23666e9i	−1.24133	+	0.716680i
$517$	−2.45719e9			−0.782027
$518$	6.33318e7	+	2.04500e8i	0.0200202	+	0.0646455i
$519$	−7.99084e9			−2.50904
$520$	8.22132e8	−	4.74658e8i	0.256407	−	0.148037i
$521$	−2.42900e9	+	4.20715e9i	−0.752481	+	1.30334i	0.194136	+	0.980975i	$0.437810\pi$
$521$	−2.42900e9	+	4.20715e9i	−0.752481	+	1.30334i	−0.946617	+	0.322361i	$0.895524\pi$
$522$	2.14980e6	−	3.72357e6i	0.000661534	−	0.00114581i
$523$	4.88639e9	+	2.82116e9i	1.49359	+	0.862326i	0.999973	−	0.00735228i	$-0.00234033\pi$
$523$	4.88639e9	+	2.82116e9i	1.49359	+	0.862326i	0.493619	+	0.869678i	$0.335674\pi$
$524$		−	2.23901e9i		−	0.679823i
$525$	1.18510e9	−	2.05266e9i	0.357436	−	0.619098i
$526$		−	1.33258e8i		−	0.0399248i
$527$	3.23095e9	+	5.59618e9i	0.961598	+	1.66554i
$528$	9.13660e9			2.70126
$529$	6.03560e8			0.177266
$530$	−8.41764e7	−	1.45798e8i	−0.0245598	−	0.0425388i
$531$	−4.01493e9	−	2.31802e9i	−1.16372	−	0.671873i
$532$			4.67693e9i			1.34670i
$533$	−2.43609e9	+	1.40648e9i	−0.696865	+	0.402335i
$534$	4.62027e7	+	8.00254e7i	0.0131302	+	0.0227423i
$535$	8.94603e8	−	5.16499e8i	0.252576	−	0.145825i
$536$	−6.16141e8	−	3.55729e8i	−0.172824	−	0.0997799i
$537$	−1.42323e9	−	8.21700e8i	−0.396610	−	0.228983i
$538$	1.49966e7	−	8.65828e6i	0.00415197	−	0.00239714i
$539$	9.86741e8	+	1.70909e9i	0.271420	+	0.470114i
$540$	4.61121e9	−	2.66229e9i	1.26019	−	0.727573i
$541$		−	3.76059e9i		−	1.02109i	−0.859850	−	0.510547i	$-0.829443\pi$
$541$		−	3.76059e9i		−	1.02109i	0.859850	−	0.510547i	$-0.170557\pi$
$542$	3.77416e8	+	2.17901e8i	0.101818	+	0.0587845i
$543$	4.46989e8	+	7.74208e8i	0.119811	+	0.207519i
$544$	1.26639e9			0.337264
$545$	2.80213e9			0.741482
$546$	−3.09711e8	−	5.36434e8i	−0.0814295	−	0.141040i
$547$		−	4.94944e9i		−	1.29301i	−0.762911	−	0.646503i	$-0.776231\pi$
$547$		−	4.94944e9i		−	1.29301i	0.762911	−	0.646503i	$-0.223769\pi$
$548$	2.71513e9	−	4.70275e9i	0.704789	−	1.22073i
$549$			2.38571e9i			0.615339i
$550$	2.45468e8	+	1.41721e8i	0.0629109	+	0.0363216i
$551$	3.02783e7	−	5.24436e7i	0.00771084	−	0.0133556i
$552$	4.85059e8	−	8.40147e8i	0.122746	−	0.212603i
$553$	1.73265e9	−	1.00035e9i	0.435686	−	0.251543i
$554$	1.06961e8			0.0267264
$555$	5.57586e9	−	6.02292e9i	1.38448	−	1.49548i
$556$	3.25723e9			0.803686
$557$	−4.17820e9	+	2.41229e9i	−1.02446	+	0.591474i	−0.915394	−	0.402560i	$-0.868120\pi$
$557$	−4.17820e9	+	2.41229e9i	−1.02446	+	0.591474i	−0.109069	+	0.994034i	$0.534787\pi$
$558$	−4.05500e8	+	7.02346e8i	−0.0988032	+	0.171132i
$559$	2.63764e9	−	4.56852e9i	0.638666	−	1.10620i
$560$	−3.58137e9	−	2.06771e9i	−0.861770	−	0.497543i
$561$		−	1.58844e10i		−	3.79841i
$562$	2.32592e8	−	4.02862e8i	0.0552737	−	0.0957368i
$563$			6.12075e9i			1.44552i	0.691098	+	0.722761i	$0.257127\pi$
$563$			6.12075e9i			1.44552i	−0.691098	+	0.722761i	$0.742873\pi$
$564$	1.63168e9	+	2.82615e9i	0.382964	+	0.663313i
$565$	5.86930e8			0.136904
$566$	−1.50367e8			−0.0348574
$567$	−4.20401e8	−	7.28155e8i	−0.0968551	−	0.167758i
$568$	1.37810e8	+	7.95649e7i	0.0315546	+	0.0182181i
$569$		−	1.49490e9i		−	0.340189i	−0.985428	−	0.170094i	$-0.945593\pi$
$569$		−	1.49490e9i		−	0.340189i	0.985428	−	0.170094i	$-0.0544073\pi$
$570$	−1.06023e9	+	6.12125e8i	−0.239794	+	0.138445i
$571$	−2.55150e9	−	4.41933e9i	−0.573547	−	0.993413i	−0.996198	−	0.0871200i	$-0.972234\pi$
$571$	−2.55150e9	−	4.41933e9i	−0.573547	−	0.993413i	0.422651	−	0.906293i	$-0.361100\pi$
$572$	−9.39564e9	+	5.42458e9i	−2.09914	+	1.21194i
$573$	−7.70981e8	−	4.45126e8i	−0.171199	−	0.0988421i
$574$	−1.46412e8	−	8.45310e7i	−0.0323136	−	0.0186562i
$575$	−1.88913e9	+	1.09069e9i	−0.414404	+	0.239256i
$576$	−3.78236e9	−	6.55124e9i	−0.824677	−	1.42838i
$577$	4.17213e9	−	2.40878e9i	0.904155	−	0.522014i	0.0256089	−	0.999672i	$-0.491848\pi$
$577$	4.17213e9	−	2.40878e9i	0.904155	−	0.522014i	0.878546	+	0.477658i	$0.158514\pi$
$578$		−	3.43244e8i		−	0.0739359i
$579$	3.08171e9	+	1.77922e9i	0.659806	+	0.380939i
$580$	2.69579e7	+	4.66924e7i	0.00573703	+	0.00993683i
$581$	4.82089e9			1.01979
$582$	−1.16376e8			−0.0244700
$583$	1.93057e9	+	3.34385e9i	0.403502	+	0.698886i
$584$		−	7.08463e8i		−	0.147188i
$585$	−7.50677e9	+	1.30021e10i	−1.55027	+	2.68515i
$586$			7.18751e7i			0.0147549i
$587$	−2.28285e9	−	1.31801e9i	−0.465848	−	0.268958i	0.248652	−	0.968593i	$-0.420012\pi$
$587$	−2.28285e9	−	1.31801e9i	−0.465848	−	0.268958i	−0.714500	+	0.699635i	$0.753346\pi$
$588$	1.31048e9	−	2.26981e9i	0.265833	−	0.460436i
$589$	−5.71116e9	+	9.89202e9i	−1.15165	+	1.99472i
$590$	−3.43743e8	+	1.98460e8i	−0.0689052	+	0.0397824i
$591$	1.28395e9			0.255854
$592$	−3.62917e9	−	3.35979e9i	−0.718922	−	0.665558i
$593$	−5.06663e9			−0.997764			−0.498882	−	0.866670i	$-0.666256\pi$
$593$	−5.06663e9			−0.997764			−0.498882	+	0.866670i	$0.666256\pi$
$594$	7.22070e8	−	4.16887e8i	0.141360	−	0.0816143i
$595$	−3.59481e9	+	6.22639e9i	−0.699626	+	1.21179i
$596$	2.65232e9	−	4.59394e9i	0.513172	−	0.888841i
$597$	1.24905e10	+	7.21140e9i	2.40254	+	1.38710i
$598$			5.70073e8i			0.109012i
$599$	1.31804e9	−	2.28292e9i	0.250574	−	0.434006i	−0.713110	−	0.701052i	$-0.752714\pi$
$599$	1.31804e9	−	2.28292e9i	0.250574	−	0.434006i	0.963684	+	0.267046i	$0.0860475\pi$
$600$		−	7.55442e8i		−	0.142781i
$601$	−2.80158e9	−	4.85249e9i	−0.526433	−	0.911808i	−0.999526	−	0.0307959i	$-0.990196\pi$
$601$	−2.80158e9	−	4.85249e9i	−0.526433	−	0.911808i	0.473093	−	0.881013i	$-0.343138\pi$
$602$	3.17050e8			0.0592297
$603$	1.12518e10			2.08983
$604$	2.73407e8	+	4.73554e8i	0.0504870	+	0.0874461i
$605$	−1.04713e10	−	6.04559e9i	−1.92245	−	1.10993i
$606$		−	9.30582e8i		−	0.169864i
$607$	6.74401e9	−	3.89366e9i	1.22393	−	0.706638i	0.258179	−	0.966097i	$-0.416877\pi$
$607$	6.74401e9	−	3.89366e9i	1.22393	−	0.706638i	0.965754	+	0.259459i	$0.0835441\pi$
$608$	1.11926e9	+	1.93861e9i	0.201961	+	0.349806i
$609$	6.11408e7	−	3.52997e7i	0.0109691	−	0.00633301i
$610$	1.76890e8	+	1.02128e8i	0.0315536	+	0.0182175i
$611$	−3.33281e9	−	1.92420e9i	−0.591108	−	0.341276i
$612$	−1.15501e10	+	6.66845e9i	−2.03683	+	1.17597i
$613$	−1.61054e9	−	2.78953e9i	−0.282396	−	0.489125i	0.689578	−	0.724211i	$-0.257796\pi$
$613$	−1.61054e9	−	2.78953e9i	−0.282396	−	0.489125i	−0.971974	+	0.235087i	$0.924463\pi$
$614$	−8.02538e8	+	4.63346e8i	−0.139919	+	0.0807822i
$615$			6.48165e9i			1.12363i
$616$	−1.13323e9	−	6.54272e8i	−0.195338	−	0.112778i
$617$	−1.54717e9	−	2.67978e9i	−0.265180	−	0.459305i	0.702431	−	0.711752i	$-0.252098\pi$
$617$	−1.54717e9	−	2.67978e9i	−0.265180	−	0.459305i	−0.967611	+	0.252447i	$0.918765\pi$
$618$	−1.08214e8			−0.0184427
$619$	−1.06946e10			−1.81236			−0.906182	−	0.422887i	$-0.861017\pi$
$619$	−1.06946e10			−1.81236			−0.906182	+	0.422887i	$0.861017\pi$
$620$	−5.08484e9	−	8.80720e9i	−0.856853	−	1.48411i
$621$			6.41674e9i			1.07521i
$622$	−1.50437e8	+	2.60564e8i	−0.0250661	+	0.0434158i
$623$			9.59239e8i			0.158935i
$624$	1.23924e10	+	7.15478e9i	2.04179	+	1.17883i
$625$	3.81238e9	−	6.60324e9i	0.624621	−	1.08187i
$626$	3.91155e8	−	6.77501e8i	0.0637293	−	0.110382i
$627$	2.43162e10	−	1.40390e10i	3.93966	−	2.27457i
$628$	7.03966e9			1.13421
$629$	−5.84116e9	+	6.30949e9i	−0.935883	+	1.01092i
$630$	−9.02330e8			−0.143772
$631$	2.14103e9	−	1.23612e9i	0.339250	−	0.195866i	−0.320690	−	0.947184i	$-0.603915\pi$
$631$	2.14103e9	−	1.23612e9i	0.339250	−	0.195866i	0.659940	+	0.751318i	$0.270582\pi$
$632$	3.18835e8	−	5.52238e8i	0.0502407	−	0.0870194i
$633$	−4.59671e9	+	7.96173e9i	−0.720334	+	1.24766i
$634$	6.81484e8	+	3.93455e8i	0.106205	+	0.0613173i
$635$			5.36909e9i			0.832133i
$636$	2.56396e9	−	4.44091e9i	0.395195	−	0.684498i
$637$			3.09083e9i			0.473791i
$638$	4.22133e6	+	7.31156e6i	0.000643542	+	0.00111465i
$639$	−2.51665e9			−0.381567
$640$	−2.65429e9			−0.400239
$641$	5.95698e9	+	1.03178e10i	0.893353	+	1.54733i	0.835830	+	0.548988i	$0.184987\pi$
$641$	5.95698e9	+	1.03178e10i	0.893353	+	1.54733i	0.0575230	+	0.998344i	$0.481680\pi$
$642$	−1.86046e8	−	1.07414e8i	−0.0277490	−	0.0160209i
$643$			1.03324e10i			1.53271i	0.642415	+	0.766357i	$0.277933\pi$
$643$			1.03324e10i			1.53271i	−0.642415	+	0.766357i	$0.722067\pi$
$644$	4.34585e9	−	2.50908e9i	0.641171	−	0.370180i
$645$	−6.07767e9	−	1.05268e10i	−0.891822	−	1.54468i
$646$	1.11068e9	−	6.41250e8i	0.162097	−	0.0935865i
$647$	−5.71690e9	−	3.30065e9i	−0.829842	−	0.479110i	0.0239565	−	0.999713i	$-0.492374\pi$
$647$	−5.71690e9	−	3.30065e9i	−0.829842	−	0.479110i	−0.853799	+	0.520603i	$0.825707\pi$
$648$	−2.32081e8	−	1.33992e8i	−0.0335063	−	0.0193449i
$649$	7.88368e9	−	4.55165e9i	1.13207	−	0.653600i
$650$	2.21961e8	+	3.84448e8i	0.0317015	+	0.0549086i
$651$	−1.15325e10	+	6.65829e9i	−1.63829	+	0.945865i
$652$			2.03098e8i			0.0286972i
$653$	9.93265e8	+	5.73462e8i	0.139595	+	0.0805950i	0.568171	−	0.822911i	$-0.307651\pi$
$653$	9.93265e8	+	5.73462e8i	0.139595	+	0.0805950i	−0.428576	+	0.903506i	$0.640985\pi$
$654$	−2.91372e8	−	5.04672e8i	−0.0407311	−	0.0705483i
$655$	6.08406e9			0.845958
$656$	3.90558e9			0.540160
$657$	5.60221e9	+	9.70331e9i	0.770691	+	1.33488i
$658$		−	2.31293e8i		−	0.0316499i
$659$	−1.62734e9	+	2.81863e9i	−0.221502	+	0.383654i	−0.955264	−	0.295753i	$-0.904429\pi$
$659$	−1.62734e9	+	2.81863e9i	−0.221502	+	0.383654i	0.733762	+	0.679407i	$0.237763\pi$
$660$			2.49987e10i			3.38465i
$661$	−8.26078e9	−	4.76936e9i	−1.11254	−	0.642326i	−0.173054	−	0.984912i	$-0.555364\pi$
$661$	−8.26078e9	−	4.76936e9i	−1.11254	−	0.642326i	−0.939486	+	0.342587i	$0.888697\pi$
$662$	6.51056e7	−	1.12766e8i	0.00872198	−	0.0151069i
$663$	1.24389e10	−	2.15449e10i	1.65762	−	2.87109i
$664$	1.33068e9	−	7.68267e8i	0.176394	−	0.101841i
$665$	−1.27086e10			−1.67580
$666$	−1.05233e9	−	2.38942e8i	−0.138036	−	0.0313424i
$667$	−6.49748e7			−0.00847822
$668$	−4.16794e9	+	2.40636e9i	−0.541008	+	0.312351i
$669$	−1.98511e9	+	3.43832e9i	−0.256327	+	0.443971i
$670$	4.81668e8	−	8.34273e8i	0.0618708	−	0.107163i
$671$	−4.05694e9	−	2.34228e9i	−0.518406	−	0.299302i
$672$			2.60974e9i			0.331746i
$673$	−4.59641e9	+	7.96121e9i	−0.581254	+	1.00676i	0.414077	+	0.910242i	$0.364104\pi$
$673$	−4.59641e9	+	7.96121e9i	−0.581254	+	1.00676i	−0.995331	+	0.0965194i	$0.969229\pi$
$674$			4.79459e8i			0.0603173i
$675$	2.49839e9	+	4.32734e9i	0.312678	+	0.541574i
$676$	−9.01438e9			−1.12234
$677$	2.68916e9			0.333086			0.166543	−	0.986034i	$-0.446740\pi$
$677$	2.68916e9			0.333086			0.166543	+	0.986034i	$0.446740\pi$
$678$	−6.10305e7	−	1.05708e8i	−0.00752043	−	0.0130258i
$679$	−1.04622e9	−	6.04038e8i	−0.128257	−	0.0740492i
$680$			2.29150e9i			0.279473i
$681$	−1.08042e9	+	6.23782e8i	−0.131093	+	0.0756865i
$682$	−7.96235e8	−	1.37912e9i	−0.0961161	−	0.166478i
$683$	6.65252e9	−	3.84083e9i	0.798939	−	0.461268i	−0.0441610	−	0.999024i	$-0.514061\pi$
$683$	6.65252e9	−	3.84083e9i	0.798939	−	0.461268i	0.843100	+	0.537757i	$0.180728\pi$
$684$	−2.04164e10	−	1.17874e10i	−2.43940	−	1.40839i
$685$	1.27788e10	+	7.37784e9i	1.51905	+	0.877025i
$686$	−6.56428e8	+	3.78989e8i	−0.0776342	+	0.0448221i
$687$	−8.65110e9	−	1.49841e10i	−1.01794	−	1.76313i
$688$	−6.34305e9	+	3.66216e9i	−0.742572	+	0.428724i
$689$			6.04724e9i			0.704352i
$690$	1.13758e9	+	6.56784e8i	0.131829	+	0.0761116i
$691$	7.85530e9	+	1.36058e10i	0.905711	+	1.56874i	0.819960	+	0.572420i	$0.193995\pi$
$691$	7.85530e9	+	1.36058e10i	0.905711	+	1.56874i	0.0857504	+	0.996317i	$0.472671\pi$
$692$	−1.31743e10			−1.51132
$693$	2.06948e10			2.36208
$694$	−1.81875e8	−	3.15017e8i	−0.0206545	−	0.0357746i
$695$			8.85087e9i			1.00009i
$696$	1.12509e7	−	1.94870e7i	0.00126489	−	0.00219086i
$697$		−	6.79005e9i		−	0.759553i
$698$	−9.29510e8	−	5.36653e8i	−0.103457	−	0.0597310i
$699$	4.38138e9	−	7.58877e9i	0.485222	−	0.840429i
$700$	1.95385e9	−	3.38416e9i	0.215302	−	0.372913i
$701$	1.02837e10	−	5.93728e9i	1.12755	−	0.650990i	0.184230	−	0.982883i	$-0.441021\pi$
$701$	1.02837e10	−	5.93728e9i	1.12755	−	0.650990i	0.943317	+	0.331893i	$0.107687\pi$
$702$	1.30584e9			0.142466
$703$	−1.48212e10	−	3.36531e9i	−1.60894	−	0.365327i
$704$	1.48540e10			1.60450
$705$	−7.67951e9	+	4.43377e9i	−0.825413	+	0.476553i
$706$	1.07974e8	−	1.87017e8i	0.0115479	−	0.0200016i
$707$	4.83007e9	−	8.36593e9i	0.514027	−	0.890321i
$708$	−1.04702e10	−	6.04498e9i	−1.10876	−	0.640145i
$709$			2.03776e9i			0.214729i	0.994220	+	0.107365i	$0.0342412\pi$
$709$			2.03776e9i			0.214729i	−0.994220	+	0.107365i	$0.965759\pi$
$710$	−1.07733e8	+	1.86599e8i	−0.0112965	+	0.0195662i
$711$			1.00848e10i			1.05226i
$712$	1.52866e8	+	2.64772e8i	0.0158720	+	0.0274911i
$713$	1.22557e10			1.26626
$714$	1.49519e9			0.153728
$715$	−1.47402e10	−	2.55308e10i	−1.50811	−	2.61212i
$716$	−2.34643e9	−	1.35471e9i	−0.238898	−	0.137928i
$717$		−	1.89766e10i		−	1.92266i
$718$	−1.30666e9	+	7.54398e8i	−0.131742	+	0.0760616i
$719$	−7.01853e9	−	1.21565e10i	−0.704199	−	1.21971i	−0.966980	−	0.254852i	$-0.917973\pi$
$719$	−7.01853e9	−	1.21565e10i	−0.704199	−	1.21971i	0.262781	−	0.964855i	$-0.415360\pi$
$720$	1.80525e10	−	1.04226e10i	1.80249	−	1.04067i
$721$	−9.72847e8	−	5.61674e8i	−0.0966654	−	0.0558098i
$722$	1.24206e9	+	7.17101e8i	0.122818	+	0.0709088i
$723$	−6.88701e7	+	3.97622e7i	−0.00677714	+	0.00391279i
$724$	7.36938e8	+	1.27641e9i	0.0721682	+	0.124999i
$725$	−4.38179e7	+	2.52983e7i	−0.00427040	+	0.00246552i
$726$			2.51454e9i			0.243882i
$727$	1.31224e10	+	7.57623e9i	1.26661	+	0.731278i	0.974345	−	0.225059i	$-0.0722576\pi$
$727$	1.31224e10	+	7.57623e9i	1.26661	+	0.731278i	0.292265	+	0.956337i	$0.405591\pi$
$728$	−1.02471e9	−	1.77485e9i	−0.0984329	−	0.170491i
$729$	−1.62077e10			−1.54944
$730$	9.59279e8			0.0912672
$731$	6.36685e9	+	1.10277e10i	0.602856	+	1.04418i
$732$			6.22149e9i			0.586280i
$733$	−5.26123e9	+	9.11272e9i	−0.493428	+	0.854642i	−0.999971	−	0.00757250i	$-0.997590\pi$
$733$	−5.26123e9	+	9.11272e9i	−0.493428	+	0.854642i	0.506544	+	0.862214i	$0.330923\pi$
$734$			1.51627e8i			0.0141527i
$735$	6.16776e9	+	3.56096e9i	0.572957	+	0.330797i
$736$	1.20091e9	−	2.08005e9i	0.111030	−	0.192309i
$737$	−1.10470e10	+	1.91339e10i	−1.01650	+	1.76063i
$738$	7.38012e8	−	4.26092e8i	0.0675875	−	0.0390216i
$739$	−1.46076e9			−0.133144			−0.0665722	−	0.997782i	$-0.521206\pi$
$739$	−1.46076e9			−0.133144			−0.0665722	+	0.997782i	$0.521206\pi$
$740$	9.19275e9	−	9.92981e9i	0.833940	−	0.900804i
$741$	4.39751e10			3.97048
$742$	−3.14753e8	+	1.81723e8i	−0.0282850	+	0.0163304i
$743$	9.48428e9	−	1.64273e10i	0.848289	−	1.46928i	−0.0344458	−	0.999407i	$-0.510967\pi$
$743$	9.48428e9	−	1.64273e10i	0.848289	−	1.46928i	0.882734	−	0.469872i	$-0.155700\pi$
$744$	−2.12216e9	+	3.67568e9i	−0.188918	+	0.327215i
$745$	1.24831e10	+	7.20714e9i	1.10605	+	0.638581i
$746$		−	1.63240e8i		−	0.0143959i
$747$	−1.21502e10	+	2.10448e10i	−1.06650	+	1.84724i
$748$		−	2.61882e10i		−	2.28797i
$749$	−1.11504e9	−	1.93130e9i	−0.0969622	−	0.167944i
$750$	−9.16055e8			−0.0792879
$751$	−1.41792e10			−1.22155			−0.610774	−	0.791805i	$-0.709142\pi$
$751$	−1.41792e10			−1.22155			−0.610774	+	0.791805i	$0.709142\pi$
$752$	2.67161e9	+	4.62737e9i	0.229092	+	0.396800i
$753$	−1.25950e10	−	7.27173e9i	−1.07502	−	0.620662i
$754$			1.32227e7i			0.00112337i
$755$	−1.28679e9	+	7.42928e8i	−0.108816	+	0.0628250i
$756$	−5.74743e9	−	9.95485e9i	−0.483780	−	0.837931i
$757$	2.49265e9	−	1.43913e9i	0.208846	−	0.120577i	−0.391929	−	0.919995i	$-0.628192\pi$
$757$	2.49265e9	−	1.43913e9i	0.208846	−	0.120577i	0.600775	+	0.799418i	$0.294859\pi$
$758$	6.94871e8	+	4.01184e8i	0.0579511	+	0.0334581i
$759$	−2.60903e10	−	1.50632e10i	−2.16587	−	1.25046i
$760$	−3.50788e9	+	2.02527e9i	−0.289866	+	0.167354i
$761$	6.04308e9	+	1.04669e10i	0.497064	+	0.860939i	0.999994	−	0.00338737i	$-0.00107824\pi$
$761$	6.04308e9	+	1.04669e10i	0.497064	+	0.860939i	−0.502931	+	0.864327i	$0.667745\pi$
$762$	9.66989e8	−	5.58291e8i	0.0791733	−	0.0457108i
$763$		−	6.04933e9i		−	0.493028i
$764$	−1.27109e9	−	7.33866e8i	−0.103122	−	0.0595375i
$765$	−1.81202e10	−	3.13851e10i	−1.46335	−	2.53459i
$766$	−1.85767e9			−0.149338
$767$	1.42574e10			1.14092
$768$	−9.65504e9	−	1.67230e10i	−0.769112	−	1.33214i
$769$			2.17224e10i			1.72253i	0.508157	+	0.861265i	$0.330327\pi$
$769$			2.17224e10i			1.72253i	−0.508157	+	0.861265i	$0.669673\pi$
$770$	8.85903e8	−	1.53443e9i	0.0699308	−	0.121124i
$771$			1.99078e10i			1.56434i
$772$	5.08072e9	+	2.93335e9i	0.397434	+	0.229458i
$773$	−9.89271e9	+	1.71347e10i	−0.770348	+	1.33428i	0.167024	+	0.985953i	$0.446584\pi$
$773$	−9.89271e9	+	1.71347e10i	−0.770348	+	1.33428i	−0.937372	+	0.348329i	$0.886749\pi$
$774$	−7.99069e8	+	1.38403e9i	−0.0619428	+	0.107288i
$775$	8.26502e9	−	4.77181e9i	0.637805	−	0.368237i
$776$	−3.85043e8			−0.0295797
$777$	−1.30025e10	−	1.20374e10i	−0.994381	−	0.920571i
$778$	1.25486e9			0.0955363
$779$	1.03943e10	−	6.00118e9i	0.787800	−	0.454837i
$780$	−1.95763e10	+	3.39071e10i	−1.47706	+	2.55835i
$781$	2.47084e9	−	4.27962e9i	0.185595	−	0.321460i
$782$	−1.19171e9	−	6.88034e8i	−0.0891142	−	0.0514501i
$783$			1.48835e8i			0.0110800i
$784$	2.14569e9	−	3.71645e9i	0.159023	−	0.275437i
$785$			1.91289e10i			1.41139i
$786$	−6.32635e8	−	1.09576e9i	−0.0464702	−	0.0804887i
$787$	−7.27217e8			−0.0531805			−0.0265903	−	0.999646i	$-0.508465\pi$
$787$	−7.27217e8			−0.0531805			−0.0265903	+	0.999646i	$0.508465\pi$
$788$	2.11681e9			0.154113
$789$	5.51470e9	+	9.55174e9i	0.399717	+	0.692330i
$790$	7.47745e8	+	4.31711e8i	0.0539584	+	0.0311529i
$791$		−	1.26709e9i		−	0.0910308i
$792$	5.71223e9	−	3.29796e9i	0.408571	−	0.235889i
$793$	−3.66843e9	−	6.35390e9i	−0.261230	−	0.452464i
$794$	−1.97729e9	+	1.14159e9i	−0.140184	+	0.0809352i
$795$	1.20673e10	+	6.96706e9i	0.851776	+	0.491773i
$796$	2.05927e10	+	1.18892e10i	1.44717	+	0.835522i
$797$	−6.56061e8	+	3.78777e8i	−0.0459029	+	0.0265020i	−0.522776	−	0.852470i	$-0.675104\pi$
$797$	−6.56061e8	+	3.78777e8i	−0.0459029	+	0.0265020i	0.476873	+	0.878972i	$0.341770\pi$
$798$	1.32148e9	+	2.28886e9i	0.0920553	+	0.159445i
$799$	8.04490e9	−	4.64473e9i	0.557965	−	0.322141i
$800$		−	1.87033e9i		−	0.129153i
$801$	−4.18740e9	−	2.41760e9i	−0.287893	−	0.166215i
$802$	1.02543e9	+	1.77609e9i	0.0701931	+	0.121578i
$803$	−2.20009e10			−1.49946
$804$	2.93426e10			1.99114
$805$	6.81792e9	+	1.18090e10i	0.460645	+	0.797860i
$806$		−	2.49410e9i		−	0.167780i
$807$	−7.16623e8	+	1.24123e9i	−0.0479991	+	0.0831369i
$808$		−	3.07892e9i		−	0.205333i
$809$	1.26627e9	+	7.31082e8i	0.0840828	+	0.0485452i	0.541452	−	0.840732i	$-0.317875\pi$
$809$	1.26627e9	+	7.31082e8i	0.0840828	+	0.0485452i	−0.457369	+	0.889277i	$0.651208\pi$
$810$	1.81429e8	−	3.14244e8i	0.0119952	−	0.0207763i
$811$	9.08840e9	−	1.57416e10i	0.598294	−	1.03628i	−0.394779	−	0.918776i	$-0.629179\pi$
$811$	9.08840e9	−	1.57416e10i	0.598294	−	1.03628i	0.993073	−	0.117499i	$-0.0374878\pi$
$812$	1.00801e8	−	5.81975e7i	0.00660723	−	0.00381468i
$813$	−3.60702e10			−2.35414
$814$	1.43949e9	−	1.55491e9i	0.0935458	−	0.101046i
$815$	−5.51879e8			−0.0357102
$816$	−2.99134e10	+	1.72705e10i	−1.92731	+	1.11273i
$817$	−1.12543e10	+	1.94930e10i	−0.722006	+	1.25055i
$818$	−2.71346e8	+	4.69984e8i	−0.0173335	+	0.0300225i
$819$	2.80694e10	+	1.62059e10i	1.78542	+	1.03081i
$820$			1.06861e10i			0.676817i
$821$	−3.68228e8	+	6.37790e8i	−0.0232229	+	0.0402232i	−0.877403	−	0.479754i	$-0.840726\pi$
$821$	−3.68228e8	+	6.37790e8i	−0.0232229	+	0.0402232i	0.854180	+	0.519977i	$0.174059\pi$
$822$		−	3.06866e9i		−	0.192707i
$823$	−3.21649e9	−	5.57112e9i	−0.201133	−	0.348372i	0.747761	−	0.663968i	$-0.231129\pi$
$823$	−3.21649e9	−	5.57112e9i	−0.201133	−	0.348372i	−0.948894	+	0.315596i	$0.897796\pi$
$824$	−3.58038e8			−0.0222938
$825$	−2.34598e10			−1.45457
$826$	4.28443e8	+	7.42084e8i	0.0264522	+	0.0458166i
$827$	1.13921e10	+	6.57723e9i	0.700381	+	0.404365i	0.807489	−	0.589882i	$-0.200826\pi$
$827$	1.13921e10	+	6.57723e9i	0.700381	+	0.404365i	−0.107108	+	0.994247i	$0.534159\pi$
$828$			2.52948e10i			1.54855i
$829$	4.13919e9	−	2.38976e9i	0.252333	−	0.145685i	−0.368499	−	0.929628i	$-0.620128\pi$
$829$	4.13919e9	−	2.38976e9i	0.252333	−	0.145685i	0.620832	+	0.783944i	$0.286795\pi$
$830$	1.04025e9	+	1.80177e9i	0.0631490	+	0.109377i
$831$	−7.66682e9	+	4.42644e9i	−0.463459	+	0.267578i
$832$	2.01472e10	+	1.16320e10i	1.21279	+	0.700202i
$833$	−6.46123e9	−	3.73039e9i	−0.387309	−	0.223613i
$834$	1.59407e9	−	9.20336e8i	0.0951537	−	0.0549370i
$835$	−6.53881e9	−	1.13256e10i	−0.388684	−	0.673220i
$836$	4.00894e10	−	2.31456e10i	2.37305	−	1.37008i
$837$		−	2.80735e10i		−	1.65485i
$838$	−1.43612e9	−	8.29146e8i	−0.0843019	−	0.0486717i
$839$	−1.50991e10	−	2.61524e10i	−0.882641	−	1.52878i	−0.848394	−	0.529365i	$-0.822430\pi$
$839$	−1.50991e10	−	2.61524e10i	−0.882641	−	1.52878i	−0.0342466	−	0.999413i	$-0.510903\pi$
$840$	−4.72229e9			−0.274900
$841$	1.72484e10			0.999913
$842$	4.95070e8	+	8.57486e8i	0.0285808	+	0.0495034i
$843$			3.85021e10i			2.21354i
$844$	−7.57846e9	+	1.31263e10i	−0.433893	+	0.751524i
$845$		−	2.44948e10i		−	1.39661i
$846$	1.00967e9	+	5.82935e8i	0.0573303	+	0.0330997i
$847$	−1.30514e10	+	2.26057e10i	−0.738016	+	1.27828i
$848$	4.19807e9	−	7.27127e9i	0.236409	−	0.409473i
$849$	1.07781e10	−	6.22274e9i	0.604457	−	0.348983i
$850$	−1.07156e9			−0.0598480
$851$	4.82420e9	+	1.55774e10i	0.268332	+	0.866448i
$852$	−6.56297e9			−0.363548
$853$	−8.05809e9	+	4.65234e9i	−0.444540	+	0.256655i	−0.705521	−	0.708689i	$-0.749287\pi$
$853$	−8.05809e9	+	4.65234e9i	−0.444540	+	0.256655i	0.260982	+	0.965344i	$0.415954\pi$
$854$	2.20476e8	−	3.81876e8i	0.0121132	−	0.0209807i
$855$	3.20299e10	−	5.54775e10i	1.75257	−	3.03554i
$856$	−6.15552e8	−	3.55389e8i	−0.0335433	−	0.0193663i
$857$		−	1.37064e10i		−	0.743861i	−0.928261	−	0.371930i	$-0.878696\pi$
$857$		−	1.37064e10i		−	0.743861i	0.928261	−	0.371930i	$-0.121304\pi$
$858$	−3.06545e9	+	5.30951e9i	−0.165687	+	0.286978i
$859$			1.17767e9i			0.0633941i	0.999498	+	0.0316970i	$0.0100912\pi$
$859$			1.17767e9i			0.0633941i	−0.999498	+	0.0316970i	$0.989909\pi$
$860$	−1.00201e10	−	1.73553e10i	−0.537188	−	0.930438i
$861$	1.39928e10			0.747126
$862$	−8.39819e8			−0.0446591
$863$	1.03158e10	+	1.78675e10i	0.546342	+	0.946292i	0.998521	+	0.0543651i	$0.0173135\pi$
$863$	1.03158e10	+	1.78675e10i	0.546342	+	0.946292i	−0.452179	+	0.891927i	$0.649353\pi$
$864$	−4.76467e9	−	2.75088e9i	−0.251324	−	0.145102i
$865$		−	3.57985e10i		−	1.88065i
$866$	8.59424e7	−	4.96189e7i	0.00449671	−	0.00259618i
$867$	1.42047e10	+	2.46032e10i	0.740227	+	1.28211i
$868$	−1.90133e10	+	1.09773e10i	−0.986821	+	0.569741i
$869$	−1.71494e10	−	9.90121e9i	−0.886502	−	0.511822i
$870$	2.63860e7	+	1.52340e7i	0.00135849	+	0.000784325i
$871$	−2.99671e10	+	1.73015e10i	−1.53667	+	0.887198i
$872$	−9.64034e8	−	1.66976e9i	−0.0492362	−	0.0852796i
$873$	5.27366e9	−	3.04475e9i	0.268264	−	0.154882i
$874$		−	2.43239e9i		−	0.123238i
$875$	−8.23534e9	−	4.75468e9i	−0.415579	−	0.239934i
$876$	1.46095e10	+	2.53044e10i	0.734297	+	1.27184i
$877$	−1.15491e10			−0.578162			−0.289081	−	0.957305i	$-0.593350\pi$
$877$	−1.15491e10			−0.578162			−0.289081	+	0.957305i	$0.593350\pi$
$878$	−1.08269e9			−0.0539851
$879$	−2.97445e9	−	5.15190e9i	−0.147722	−	0.255863i
$880$			4.09314e10i			2.02473i
$881$	−1.48757e10	+	2.57654e10i	−0.732927	+	1.26947i	0.222701	+	0.974887i	$0.428513\pi$
$881$	−1.48757e10	+	2.57654e10i	−0.732927	+	1.26947i	−0.955627	+	0.294579i	$0.904821\pi$
$882$		−	9.36363e8i		−	0.0459520i
$883$	−2.91762e10	−	1.68449e10i	−1.42616	−	0.823391i	−0.429341	−	0.903143i	$-0.641254\pi$
$883$	−2.91762e10	−	1.68449e10i	−1.42616	−	0.823391i	−0.996815	+	0.0797514i	$0.974587\pi$
$884$	2.05077e10	−	3.55204e10i	0.998468	−	1.72940i
$885$	1.64260e10	−	2.84507e10i	0.796583	−	1.37972i
$886$	1.10876e9	−	6.40145e8i	0.0535576	−	0.0309215i
$887$	2.21494e10			1.06569			0.532843	−	0.846214i	$-0.321124\pi$
$887$	2.21494e10			1.06569			0.532843	+	0.846214i	$0.321124\pi$
$888$	−5.50728e9	−	1.25048e9i	−0.263932	−	0.0599285i
$889$	1.15910e10			0.553304
$890$	−3.58509e8	+	2.06985e8i	−0.0170465	+	0.00984179i
$891$	−4.16103e9	+	7.20712e9i	−0.197074	+	0.341342i
$892$	−3.27280e9	+	5.66865e9i	−0.154398	+	0.267426i
$893$	1.42205e10	+	8.21020e9i	0.668243	+	0.385810i
$894$		−	2.99766e9i		−	0.140314i
$895$	3.68116e9	−	6.37596e9i	0.171634	−	0.297280i
$896$			5.73018e9i			0.266128i
$897$	−2.35917e10	−	4.08620e10i	−1.09140	−	1.89037i
$898$	2.54851e9			0.117441
$899$	2.84268e8			0.0130487
$900$	9.84866e9	+	1.70584e10i	0.450327	+	0.779990i
$901$	−1.26415e10	−	7.29855e9i	−0.575785	−	0.332430i
$902$			1.67334e9i			0.0759208i
$903$	−2.27257e10	+	1.31207e10i	−1.02709	+	0.592993i
$904$	−2.01925e8	−	3.49745e8i	−0.00909078	−	0.0157457i
$905$	−3.46840e9	+	2.00248e9i	−0.155546	+	0.0898046i
$906$	2.67607e8	+	1.54503e8i	0.0119550	+	0.00690221i
$907$	1.30728e10	+	7.54757e9i	0.581758	+	0.335878i	0.761832	−	0.647775i	$-0.224300\pi$
$907$	1.30728e10	+	7.54757e9i	0.581758	+	0.335878i	−0.180074	+	0.983653i	$0.557634\pi$
$908$	−1.78126e9	+	1.02841e9i	−0.0789637	+	0.0455897i
$909$	2.43467e10	+	4.21698e10i	1.07515	+	1.86221i
$910$	2.40319e9	−	1.38748e9i	0.105717	−	0.0610356i
$911$			5.90307e9i			0.258680i	0.991600	+	0.129340i	$0.0412859\pi$
$911$			5.90307e9i			0.258680i	−0.991600	+	0.129340i	$0.958714\pi$
$912$	−5.28762e10	−	3.05281e10i	−2.30822	−	1.33265i
$913$	−2.38580e10	−	4.13234e10i	−1.03750	−	1.79700i
$914$	2.28396e8			0.00989411
$915$	−1.69057e10			−0.729555
$916$	−1.42628e10	−	2.47039e10i	−0.613156	−	1.06202i
$917$		−	1.31345e10i		−	0.562497i
$918$	−1.57605e9	+	2.72980e9i	−0.0672389	+	0.116461i
$919$			6.59819e9i			0.280427i	0.990121	+	0.140214i	$0.0447790\pi$
$919$			6.59819e9i			0.280427i	−0.990121	+	0.140214i	$0.955221\pi$
$920$	3.76381e9	+	2.17303e9i	0.159357	+	0.0920045i
$921$	3.83499e10	−	6.64240e10i	1.61754	−	2.80166i
$922$	−1.60620e9	+	2.78201e9i	−0.0674901	+	0.116896i
$923$	6.70265e9	−	3.86978e9i	0.280570	−	0.161987i
$924$	5.39681e10			2.25053
$925$	9.31852e9	+	8.62684e9i	0.387125	+	0.358390i
$926$	3.10420e8			0.0128473
$927$	4.90379e9	−	2.83120e9i	0.202187	−	0.116733i
$928$	2.78550e7	−	4.82462e7i	0.00114416	−	0.00198174i
$929$	5.58784e9	−	9.67842e9i	0.228659	−	0.396049i	−0.728752	−	0.684778i	$-0.759899\pi$
$929$	5.58784e9	−	9.67842e9i	0.228659	−	0.396049i	0.957411	+	0.288729i	$0.0932325\pi$
$930$	−4.97698e9	−	2.87346e9i	−0.202897	−	0.117143i
$931$		−	1.31880e10i		−	0.535616i
$932$	7.22345e9	−	1.25114e10i	0.292273	−	0.506232i
$933$		−	2.49025e10i		−	1.00382i
$934$	1.43753e9	+	2.48987e9i	0.0577300	+	0.0999913i
$935$	7.11612e10			2.84710
$936$	1.03304e10			0.411767
$937$	1.17035e10	+	2.02711e10i	0.464759	+	0.804987i	0.999191	−	0.0402250i	$-0.0128075\pi$
$937$	1.17035e10	+	2.02711e10i	0.464759	+	0.804987i	−0.534431	+	0.845212i	$0.679474\pi$
$938$	−1.80106e9	−	1.03984e9i	−0.0712554	−	0.0411393i
$939$			6.47498e10i			2.55216i
$940$	−1.26610e10	+	7.30982e9i	−0.497187	+	0.287051i
$941$	8.65076e9	+	1.49836e10i	0.338447	+	0.586207i	0.984141	−	0.177389i	$-0.0567651\pi$
$941$	8.65076e9	+	1.49836e10i	0.338447	+	0.586207i	−0.645694	+	0.763596i	$0.723432\pi$
$942$	3.44517e9	−	1.98907e9i	0.134286	−	0.0775303i
$943$	−1.11527e10	−	6.43901e9i	−0.433101	−	0.250051i
$944$	−1.71433e10	−	9.89767e9i	−0.663272	−	0.382940i
$945$	2.70503e10	−	1.56175e10i	1.04270	−	0.602006i
$946$	−1.56904e9	−	2.71766e9i	−0.0602582	−	0.104370i
$947$	−4.31594e10	+	2.49181e10i	−1.65139	+	0.953433i	−0.674894	+	0.737915i	$0.735810\pi$
$947$	−4.31594e10	+	2.49181e10i	−1.65139	+	0.953433i	−0.976500	+	0.215517i	$0.930856\pi$
$948$			2.62993e10i			1.00257i
$949$	−2.98409e10	−	1.72287e10i	−1.13339	−	0.654365i
$950$	−9.47065e8	−	1.64036e9i	−0.0358383	−	0.0620737i
$951$	−6.51305e10			−2.45557
$952$	4.94697e9			0.185828
$953$	1.44022e10	+	2.49454e10i	0.539020	+	0.933610i	0.998957	+	0.0456586i	$0.0145387\pi$
$953$	1.44022e10	+	2.49454e10i	0.539020	+	0.933610i	−0.459937	+	0.887952i	$0.652128\pi$
$954$		−	1.83201e9i		−	0.0683136i
$955$	1.99414e9	−	3.45395e9i	0.0740872	−	0.128323i
$956$		−	3.12862e10i		−	1.15811i
$957$	−6.05158e8	−	3.49388e8i	−0.0223191	−	0.0128860i
$958$	−4.87069e8	+	8.43628e8i	−0.0178983	+	0.0310007i
$959$	1.59275e10	−	2.75873e10i	0.583154	−	1.01005i
$960$	4.64235e10	−	2.68026e10i	1.69351	−	0.977750i
$961$	−2.61065e10			−0.948892
$962$	3.17009e9	−	9.81751e8i	0.114805	−	0.0355540i
$963$	1.12410e10			0.405615
$964$	−1.13544e8	+	6.55547e7i	−0.00408221	+	0.00235686i
$965$	−7.97081e9	+	1.38058e10i	−0.285533	+	0.494558i
$966$	1.41789e9	−	2.45585e9i	0.0506083	−	0.0876562i
$967$	1.47400e10	+	8.51014e9i	0.524209	+	0.302652i	0.738655	−	0.674083i	$-0.235461\pi$
$967$	1.47400e10	+	8.51014e9i	0.524209	+	0.302652i	−0.214446	+	0.976736i	$0.568795\pi$
$968$			8.31961e9i			0.294808i
$969$	−5.30745e10	+	9.19278e10i	−1.87393	+	3.24574i
$970$		−	5.21359e8i		−	0.0183415i
$971$	8.14600e9	+	1.41093e10i	0.285547	+	0.494581i	0.972742	−	0.231892i	$-0.0744916\pi$
$971$	8.14600e9	+	1.41093e10i	0.285547	+	0.494581i	−0.687195	+	0.726473i	$0.741158\pi$
$972$	−2.26562e10			−0.791325
$973$	1.91076e10			0.664983
$974$	−1.11854e9	−	1.93736e9i	−0.0387876	−	0.0671822i
$975$	−3.18197e10	−	1.83711e10i	−1.09946	−	0.634774i
$976$			1.01867e10i			0.350718i
$977$	1.13286e10	−	6.54058e9i	0.388639	−	0.224381i	−0.292931	−	0.956133i	$-0.594631\pi$
$977$	1.13286e10	−	6.54058e9i	0.388639	−	0.224381i	0.681570	+	0.731753i	$0.261297\pi$
$978$	5.73857e7	+	9.93950e7i	0.00196163	+	0.00339765i
$979$	8.22233e9	−	4.74716e9i	0.280063	−	0.161694i
$980$	1.01686e10	+	5.87085e9i	0.345120	+	0.199255i
$981$	2.64074e10	+	1.52463e10i	0.893066	+	0.515612i
$982$	−1.74443e9	+	1.00714e9i	−0.0587844	+	0.0339392i
$983$	−1.66895e10	−	2.89070e10i	−0.560409	−	0.970657i	−0.997461	−	0.0712207i	$-0.977311\pi$
$983$	−1.66895e10	−	2.89070e10i	−0.560409	−	0.970657i	0.437051	−	0.899437i	$-0.356023\pi$
$984$	3.86234e9	−	2.22992e9i	0.129231	−	0.0746117i
$985$			5.75201e9i			0.191775i
$986$	−2.76415e7	−	1.59588e7i	−0.000918316	−	0.000530190i
$987$	9.57177e9	+	1.65788e10i	0.316871	+	0.548836i
$988$	7.25004e10			2.39161
$989$	2.41508e10			0.793860
$990$	4.46553e9	+	7.73453e9i	0.146268	+	0.253344i
$991$		−	1.23237e10i		−	0.402237i	−0.979567	−	0.201119i	$-0.935542\pi$
$991$		−	1.23237e10i		−	0.402237i	0.979567	−	0.201119i	$-0.0644577\pi$
$992$	−5.25406e9	+	9.10030e9i	−0.170885	+	0.295982i
$993$			1.07772e10i			0.349289i
$994$	4.02837e8	+	2.32578e8i	0.0130100	+	0.00751132i
$995$	−3.23066e10	+	5.59567e10i	−1.03971	+	1.80082i
$996$	−3.16855e10	+	5.48809e10i	−1.01614	+	1.76001i
$997$	−5.06899e10	+	2.92658e10i	−1.61990	+	0.935250i	−0.632957	+	0.774187i	$0.718159\pi$
$997$	−5.06899e10	+	2.92658e10i	−1.61990	+	0.935250i	−0.986944	+	0.161063i	$0.948508\pi$
$998$	−2.85944e9			−0.0910591
$999$	3.56826e10	−	1.10506e10i	1.13234	−	0.350676i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.8.e.a.11.10	✓	40
37.27	even	6	inner	37.8.e.a.27.10	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.8.e.a.11.10	✓	40	1.1	even	1	trivial
37.8.e.a.27.10	yes	40	37.27	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:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	37.e (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.806849 - 0.465835i) q^{2} +(-38.5559 + 66.7808i) q^{3} +(-63.5660 + 110.100i) q^{4} +(-299.174 - 172.728i) q^{5} +71.8427i q^{6} +(-372.891 + 645.866i) q^{7} +237.699i q^{8} +(-1879.62 - 3255.59i) q^{9} +O(q^{10})\)	\(q+(0.806849 - 0.465835i) q^{2} +(-38.5559 + 66.7808i) q^{3} +(-63.5660 + 110.100i) q^{4} +(-299.174 - 172.728i) q^{5} +71.8427i q^{6} +(-372.891 + 645.866i) q^{7} +237.699i q^{8} +(-1879.62 - 3255.59i) q^{9} -321.851 q^{10} +7381.59 q^{11} +(-4901.69 - 8489.97i) q^{12} +(10012.0 + 5780.45i) q^{13} +694.822i q^{14} +(23069.8 - 13319.4i) q^{15} +(-8025.72 - 13901.0i) q^{16} +(-24167.5 + 13953.1i) q^{17} +(-3033.13 - 1751.18i) q^{18} +(-42719.4 - 24664.0i) q^{19} +(38034.5 - 21959.3i) q^{20} +(-28754.3 - 49803.9i) q^{21} +(5955.83 - 3438.60i) q^{22} +52927.0i q^{23} +(-15873.7 - 9164.69i) q^{24} +(20607.4 + 35693.1i) q^{25} +10770.9 q^{26} +121238. q^{27} +(-47406.4 - 82110.3i) q^{28} +1227.63i q^{29} +(12409.2 - 21493.4i) q^{30} -231558. i q^{31} +(-39300.3 - 22690.0i) q^{32} +(-284604. + 492948. i) q^{33} +(-12999.7 + 22516.1i) q^{34} +(223118. - 128817. i) q^{35} +477918. q^{36} +(294319. - 91148.2i) q^{37} -45957.5 q^{38} +(-772045. + 445741. i) q^{39} +(41057.2 - 71113.2i) q^{40} +(-121658. + 210719. i) q^{41} +(-46400.8 - 26789.5i) q^{42} -456303. i q^{43} +(-469218. + 812709. i) q^{44} +1.29865e6i q^{45} +(24655.2 + 42704.1i) q^{46} -332881. q^{47} +1.23776e6 q^{48} +(133676. + 231534. i) q^{49} +(33254.2 + 19199.3i) q^{50} -2.15190e6i q^{51} +(-1.27285e6 + 734880. i) q^{52} +(261539. + 452998. i) q^{53} +(97820.4 - 56476.7i) q^{54} +(-2.20838e6 - 1.27501e6i) q^{55} +(-153522. - 88635.7i) q^{56} +(3.29417e6 - 1.90189e6i) q^{57} +(571.873 + 990.513i) q^{58} +(1.06802e6 - 616622. i) q^{59} +3.38664e6i q^{60} +(-549603. - 317313. i) q^{61} +(-107868. - 186832. i) q^{62} +2.80357e6 q^{63} +2.01230e6 q^{64} +(-1.99689e6 - 3.45871e6i) q^{65} +530313. i q^{66} +(-1.49656e6 + 2.59211e6i) q^{67} -3.54777e6i q^{68} +(-3.53451e6 - 2.04065e6i) q^{69} +(120015. - 207873. i) q^{70} +(334730. - 579769. i) q^{71} +(773849. - 446782. i) q^{72} -2.98051e6 q^{73} +(195011. - 210647. i) q^{74} -3.17815e6 q^{75} +(5.43100e6 - 3.13559e6i) q^{76} +(-2.75253e6 + 4.76752e6i) q^{77} +(-415283. + 719291. i) q^{78} +(-2.32327e6 - 1.34134e6i) q^{79} +5.54507e6i q^{80} +(-563704. + 976365. i) q^{81} +226691. i q^{82} +(-3.23210e6 - 5.59817e6i) q^{83} +7.31118e6 q^{84} +9.64037e6 q^{85} +(-212562. - 368168. i) q^{86} +(-81982.1 - 47332.4i) q^{87} +1.75459e6i q^{88} +(1.11390e6 - 643109. i) q^{89} +(604956. + 1.04781e6i) q^{90} +(-7.46679e6 + 4.31095e6i) q^{91} +(-5.82724e6 - 3.36436e6i) q^{92} +(1.54636e7 + 8.92793e6i) q^{93} +(-268585. + 155068. i) q^{94} +(8.52034e6 + 1.47577e7i) q^{95} +(3.03052e6 - 1.74967e6i) q^{96} +1.61988e6i q^{97} +(215713. + 124542. i) q^{98} +(-1.38745e7 - 2.40314e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 18 q^{2} - 42 q^{3} + 1114 q^{4} - 672 q^{5} + 156 q^{7} - 9128 q^{9}+O(q^{10}) \) 40 * q + 18 * q^2 - 42 * q^3 + 1114 * q^4 - 672 * q^5 + 156 * q^7 - 9128 * q^9	\( 40 q + 18 q^{2} - 42 q^{3} + 1114 q^{4} - 672 q^{5} + 156 q^{7} - 9128 q^{9} - 5124 q^{10} + 12468 q^{11} + 6926 q^{12} + 10512 q^{13} + 36402 q^{15} - 31094 q^{16} - 22440 q^{17} - 153504 q^{18} + 49086 q^{19} + 28662 q^{20} + 7736 q^{21} + 132018 q^{22} + 2754 q^{24} + 72328 q^{25} - 680244 q^{26} + 42984 q^{27} + 105488 q^{28} + 382084 q^{30} + 523656 q^{32} + 9228 q^{33} + 276914 q^{34} - 904452 q^{35} - 204828 q^{36} + 1333776 q^{37} + 50208 q^{38} + 122040 q^{39} - 1205236 q^{40} - 871440 q^{41} + 1436094 q^{42} - 994326 q^{44} - 987942 q^{46} - 586932 q^{47} + 3984388 q^{48} - 1766072 q^{49} + 1818708 q^{50} - 2745228 q^{52} + 1661988 q^{53} + 1102554 q^{54} - 2733258 q^{55} - 5943924 q^{56} + 3920592 q^{57} + 5021672 q^{58} + 5296632 q^{59} - 4588524 q^{61} - 8143398 q^{62} - 2503648 q^{63} + 10662964 q^{64} - 1652736 q^{65} + 1940622 q^{67} - 10266552 q^{69} - 5038546 q^{70} + 6420528 q^{71} - 6576036 q^{72} - 3313032 q^{73} + 16192386 q^{74} - 5168536 q^{75} + 10328022 q^{76} - 8599404 q^{77} + 18210222 q^{78} - 15094374 q^{79} + 1733956 q^{81} - 191670 q^{83} + 1175224 q^{84} - 18053592 q^{85} + 18575940 q^{86} - 3762762 q^{87} - 14873004 q^{89} + 37293212 q^{90} - 76496700 q^{91} + 27846618 q^{92} + 26687652 q^{93} + 35421402 q^{94} + 14310774 q^{95} - 30894534 q^{96} - 13793868 q^{98} - 37141758 q^{99}+O(q^{100}) \) 40 * q + 18 * q^2 - 42 * q^3 + 1114 * q^4 - 672 * q^5 + 156 * q^7 - 9128 * q^9 - 5124 * q^10 + 12468 * q^11 + 6926 * q^12 + 10512 * q^13 + 36402 * q^15 - 31094 * q^16 - 22440 * q^17 - 153504 * q^18 + 49086 * q^19 + 28662 * q^20 + 7736 * q^21 + 132018 * q^22 + 2754 * q^24 + 72328 * q^25 - 680244 * q^26 + 42984 * q^27 + 105488 * q^28 + 382084 * q^30 + 523656 * q^32 + 9228 * q^33 + 276914 * q^34 - 904452 * q^35 - 204828 * q^36 + 1333776 * q^37 + 50208 * q^38 + 122040 * q^39 - 1205236 * q^40 - 871440 * q^41 + 1436094 * q^42 - 994326 * q^44 - 987942 * q^46 - 586932 * q^47 + 3984388 * q^48 - 1766072 * q^49 + 1818708 * q^50 - 2745228 * q^52 + 1661988 * q^53 + 1102554 * q^54 - 2733258 * q^55 - 5943924 * q^56 + 3920592 * q^57 + 5021672 * q^58 + 5296632 * q^59 - 4588524 * q^61 - 8143398 * q^62 - 2503648 * q^63 + 10662964 * q^64 - 1652736 * q^65 + 1940622 * q^67 - 10266552 * q^69 - 5038546 * q^70 + 6420528 * q^71 - 6576036 * q^72 - 3313032 * q^73 + 16192386 * q^74 - 5168536 * q^75 + 10328022 * q^76 - 8599404 * q^77 + 18210222 * q^78 - 15094374 * q^79 + 1733956 * q^81 - 191670 * q^83 + 1175224 * q^84 - 18053592 * q^85 + 18575940 * q^86 - 3762762 * q^87 - 14873004 * q^89 + 37293212 * q^90 - 76496700 * q^91 + 27846618 * q^92 + 26687652 * q^93 + 35421402 * q^94 + 14310774 * q^95 - 30894534 * q^96 - 13793868 * q^98 - 37141758 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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