LMFDB - Embedded newform 312.4.m.a.181.33

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [312,4,Mod(181,312)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(312, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("312.181");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 312 = 2^{3} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	312.m (of order $2$, degree $1$, 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:	$18.4085959218$
Analytic rank:	$0$
Dimension:	$84$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			181.33
Character	$\chi$	$=$	312.181
Dual form			312.4.m.a.181.34

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.800675 - 2.71273i) q^{2} +3.00000i q^{3} +(-6.71784 + 4.34403i) q^{4} +12.1272 q^{5} +(8.13820 - 2.40203i) q^{6} +21.1519i q^{7} +(17.1630 + 14.7455i) q^{8} -9.00000 q^{9} +O(q^{10})$	\(q+(-0.800675 - 2.71273i) q^{2} +3.00000i q^{3} +(-6.71784 + 4.34403i) q^{4} +12.1272 q^{5} +(8.13820 - 2.40203i) q^{6} +21.1519i q^{7} +(17.1630 + 14.7455i) q^{8} -9.00000 q^{9} +(-9.70993 - 32.8978i) q^{10} +16.0069 q^{11} +(-13.0321 - 20.1535i) q^{12} +(-36.8012 + 29.0288i) q^{13} +(57.3793 - 16.9358i) q^{14} +36.3815i q^{15} +(26.2587 - 58.3651i) q^{16} +45.8045 q^{17} +(7.20608 + 24.4146i) q^{18} -117.007 q^{19} +(-81.4684 + 52.6809i) q^{20} -63.4556 q^{21} +(-12.8163 - 43.4224i) q^{22} -97.3972 q^{23} +(-44.2366 + 51.4890i) q^{24} +22.0685 q^{25} +(108.213 + 76.5891i) q^{26} -27.0000i q^{27} +(-91.8844 - 142.095i) q^{28} -90.0375i q^{29} +(98.6934 - 29.1298i) q^{30} +151.350i q^{31} +(-179.354 - 24.5015i) q^{32} +48.0206i q^{33} +(-36.6745 - 124.255i) q^{34} +256.512i q^{35} +(60.4606 - 39.0963i) q^{36} -66.3382 q^{37} +(93.6845 + 317.409i) q^{38} +(-87.0865 - 110.404i) q^{39} +(208.139 + 178.822i) q^{40} +112.250i q^{41} +(50.8073 + 172.138i) q^{42} +234.339i q^{43} +(-107.532 + 69.5345i) q^{44} -109.145 q^{45} +(77.9835 + 264.213i) q^{46} +580.433i q^{47} +(175.095 + 78.7762i) q^{48} -104.401 q^{49} +(-17.6697 - 59.8660i) q^{50} +137.414i q^{51} +(121.122 - 354.877i) q^{52} -241.092i q^{53} +(-73.2438 + 21.6182i) q^{54} +194.118 q^{55} +(-311.896 + 363.029i) q^{56} -351.021i q^{57} +(-244.248 + 72.0908i) q^{58} +313.006 q^{59} +(-158.043 - 244.405i) q^{60} -334.114i q^{61} +(410.572 - 121.182i) q^{62} -190.367i q^{63} +(77.1380 + 506.156i) q^{64} +(-446.295 + 352.038i) q^{65} +(130.267 - 38.4489i) q^{66} -315.258 q^{67} +(-307.707 + 198.976i) q^{68} -292.192i q^{69} +(695.849 - 205.383i) q^{70} +503.306i q^{71} +(-154.467 - 132.710i) q^{72} +757.602i q^{73} +(53.1154 + 179.958i) q^{74} +66.2055i q^{75} +(786.034 - 508.282i) q^{76} +338.575i q^{77} +(-229.767 + 324.640i) q^{78} +1134.30 q^{79} +(318.444 - 707.804i) q^{80} +81.0000 q^{81} +(304.503 - 89.8754i) q^{82} -822.684 q^{83} +(426.284 - 275.653i) q^{84} +555.480 q^{85} +(635.698 - 187.629i) q^{86} +270.113 q^{87} +(274.726 + 236.030i) q^{88} -803.525i q^{89} +(87.3894 + 296.080i) q^{90} +(-614.014 - 778.413i) q^{91} +(654.299 - 423.097i) q^{92} -454.049 q^{93} +(1574.56 - 464.738i) q^{94} -1418.96 q^{95} +(73.5044 - 538.061i) q^{96} +750.474i q^{97} +(83.5911 + 283.211i) q^{98} -144.062 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 756 q^{9}+O(q^{10}) $ 84 * q - 756 * q^9	$ 84 q - 756 q^{9} - 36 q^{10} + 12 q^{12} - 208 q^{14} - 148 q^{16} - 104 q^{17} + 620 q^{22} + 2188 q^{25} + 444 q^{26} - 204 q^{30} - 40 q^{38} - 1924 q^{40} + 192 q^{42} + 624 q^{48} - 3396 q^{49} - 1292 q^{52} - 1616 q^{55} + 608 q^{56} - 2120 q^{62} - 2856 q^{64} + 696 q^{65} - 396 q^{66} - 2536 q^{68} - 3936 q^{74} - 156 q^{78} + 3160 q^{79} + 6804 q^{81} + 4276 q^{82} - 2088 q^{87} + 1780 q^{88} + 324 q^{90} + 4792 q^{92} - 860 q^{94} + 2480 q^{95}+O(q^{100}) $ 84 * q - 756 * q^9 - 36 * q^10 + 12 * q^12 - 208 * q^14 - 148 * q^16 - 104 * q^17 + 620 * q^22 + 2188 * q^25 + 444 * q^26 - 204 * q^30 - 40 * q^38 - 1924 * q^40 + 192 * q^42 + 624 * q^48 - 3396 * q^49 - 1292 * q^52 - 1616 * q^55 + 608 * q^56 - 2120 * q^62 - 2856 * q^64 + 696 * q^65 - 396 * q^66 - 2536 * q^68 - 3936 * q^74 - 156 * q^78 + 3160 * q^79 + 6804 * q^81 + 4276 * q^82 - 2088 * q^87 + 1780 * q^88 + 324 * q^90 + 4792 * q^92 - 860 * q^94 + 2480 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/312\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$157$	$209$
$\chi(n)$	$1$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.800675	−	2.71273i	−0.283081	−	0.959096i
$2$	−0.800675	−	2.71273i	−0.283081	−	0.959096i
$3$			3.00000i			0.577350i
$3$			3.00000i			0.577350i
$4$	−6.71784	+	4.34403i	−0.839730	+	0.543004i
$5$	12.1272			1.08469			0.542344	−	0.840157i	$-0.317537\pi$
$5$	12.1272			1.08469			0.542344	+	0.840157i	$0.317537\pi$
$6$	8.13820	−	2.40203i	0.553734	−	0.163437i
$7$			21.1519i			1.14209i	0.820918	+	0.571046i	$0.193462\pi$
$7$			21.1519i			1.14209i	−0.820918	+	0.571046i	$0.806538\pi$
$8$	17.1630	+	14.7455i	0.758505	+	0.651667i
$9$	−9.00000			−0.333333
$10$	−9.70993	−	32.8978i	−0.307055	−	1.04032i
$11$	16.0069			0.438751			0.219375	−	0.975641i	$-0.429598\pi$
$11$	16.0069			0.438751			0.219375	+	0.975641i	$0.429598\pi$
$12$	−13.0321	−	20.1535i	−0.313504	−	0.484818i
$13$	−36.8012	+	29.0288i	−0.785139	+	0.619319i
$13$	−36.8012	+	29.0288i	−0.785139	+	0.619319i
$14$	57.3793	−	16.9358i	1.09538	−	0.323305i
$15$			36.3815i			0.626245i
$16$	26.2587	−	58.3651i	0.410293	−	0.911954i
$17$	45.8045			0.653484			0.326742	−	0.945114i	$-0.394049\pi$
$17$	45.8045			0.653484			0.326742	+	0.945114i	$0.394049\pi$
$18$	7.20608	+	24.4146i	0.0943605	+	0.319699i
$19$	−117.007			−1.41280			−0.706401	−	0.707812i	$-0.749682\pi$
$19$	−117.007			−1.41280			−0.706401	+	0.707812i	$0.749682\pi$
$20$	−81.4684	+	52.6809i	−0.910845	+	0.588990i
$21$	−63.4556			−0.659387
$22$	−12.8163	−	43.4224i	−0.124202	−	0.420804i
$23$	−97.3972			−0.882988			−0.441494	−	0.897264i	$-0.645551\pi$
$23$	−97.3972			−0.882988			−0.441494	+	0.897264i	$0.645551\pi$
$24$	−44.2366	+	51.4890i	−0.376240	+	0.437923i
$25$	22.0685			0.176548
$26$	108.213	+	76.5891i	0.816245	+	0.577706i
$27$		−	27.0000i		−	0.192450i
$28$	−91.8844	−	142.095i	−0.620161	−	0.959049i
$29$		−	90.0375i		−	0.576536i	−0.957550	−	0.288268i	$-0.906921\pi$
$29$		−	90.0375i		−	0.576536i	0.957550	−	0.288268i	$-0.0930794\pi$
$30$	98.6934	−	29.1298i	0.600629	−	0.177278i
$31$			151.350i			0.876878i	0.898761	+	0.438439i	$0.144469\pi$
$31$			151.350i			0.876878i	−0.898761	+	0.438439i	$0.855531\pi$
$32$	−179.354	−	24.5015i	−0.990797	−	0.135353i
$33$			48.0206i			0.253313i
$34$	−36.6745	−	124.255i	−0.184989	−	0.626754i
$35$			256.512i			1.23881i
$36$	60.4606	−	39.0963i	0.279910	−	0.181001i
$37$	−66.3382			−0.294755			−0.147378	−	0.989080i	$-0.547083\pi$
$37$	−66.3382			−0.294755			−0.147378	+	0.989080i	$0.547083\pi$
$38$	93.6845	+	317.409i	0.399938	+	1.35501i
$39$	−87.0865	−	110.404i	−0.357564	−	0.453300i
$40$	208.139	+	178.822i	0.822741	+	0.706855i
$41$			112.250i			0.427572i	0.976881	+	0.213786i	$0.0685795\pi$
$41$			112.250i			0.427572i	−0.976881	+	0.213786i	$0.931421\pi$
$42$	50.8073	+	172.138i	0.186660	+	0.632416i
$43$			234.339i			0.831077i	0.909576	+	0.415538i	$0.136407\pi$
$43$			234.339i			0.831077i	−0.909576	+	0.415538i	$0.863593\pi$
$44$	−107.532	+	69.5345i	−0.368432	+	0.238243i
$45$	−109.145			−0.361563
$46$	77.9835	+	264.213i	0.249957	+	0.846870i
$47$			580.433i			1.80138i	0.434461	+	0.900690i	$0.356939\pi$
$47$			580.433i			1.80138i	−0.434461	+	0.900690i	$0.643061\pi$
$48$	175.095	+	78.7762i	0.526517	+	0.236882i
$49$	−104.401			−0.304375
$50$	−17.6697	−	59.8660i	−0.0499775	−	0.169327i
$51$			137.414i			0.377289i
$52$	121.122	−	354.877i	0.323012	−	0.946395i
$53$		−	241.092i		−	0.624841i	−0.949944	−	0.312420i	$-0.898860\pi$
$53$		−	241.092i		−	0.624841i	0.949944	−	0.312420i	$-0.101140\pi$
$54$	−73.2438	+	21.6182i	−0.184578	+	0.0544790i
$55$	194.118			0.475908
$56$	−311.896	+	363.029i	−0.744264	+	0.866283i
$57$		−	351.021i		−	0.815681i
$58$	−244.248	+	72.0908i	−0.552954	+	0.163207i
$59$	313.006			0.690677			0.345339	−	0.938478i	$-0.387764\pi$
$59$	313.006			0.690677			0.345339	+	0.938478i	$0.387764\pi$
$60$	−158.043	−	244.405i	−0.340054	−	0.525877i
$61$		−	334.114i		−	0.701293i	−0.936508	−	0.350647i	$-0.885962\pi$
$61$		−	334.114i		−	0.701293i	0.936508	−	0.350647i	$-0.114038\pi$
$62$	410.572	−	121.182i	0.841011	−	0.248228i
$63$		−	190.367i		−	0.380698i
$64$	77.1380	+	506.156i	0.150660	+	0.988586i
$65$	−446.295	+	352.038i	−0.851631	+	0.671768i
$66$	130.267	−	38.4489i	0.242951	−	0.0717081i
$67$	−315.258			−0.574848			−0.287424	−	0.957803i	$-0.592799\pi$
$67$	−315.258			−0.574848			−0.287424	+	0.957803i	$0.592799\pi$
$68$	−307.707	+	198.976i	−0.548750	+	0.354845i
$69$		−	292.192i		−	0.509793i
$70$	695.849	−	205.383i	1.18814	−	0.350685i
$71$			503.306i			0.841288i	0.907226	+	0.420644i	$0.138196\pi$
$71$			503.306i			0.841288i	−0.907226	+	0.420644i	$0.861804\pi$
$72$	−154.467	−	132.710i	−0.252835	−	0.217222i
$73$			757.602i			1.21467i	0.794447	+	0.607333i	$0.207761\pi$
$73$			757.602i			1.21467i	−0.794447	+	0.607333i	$0.792239\pi$
$74$	53.1154	+	179.958i	0.0834397	+	0.282698i
$75$			66.2055i			0.101930i
$76$	786.034	−	508.282i	1.18637	−	0.767157i
$77$			338.575i			0.501094i
$78$	−229.767	+	324.640i	−0.333539	+	0.471259i
$79$	1134.30			1.61543			0.807717	−	0.589571i	$-0.200703\pi$
$79$	1134.30			1.61543			0.807717	+	0.589571i	$0.200703\pi$
$80$	318.444	−	707.804i	0.445039	−	0.989186i
$81$	81.0000			0.111111
$82$	304.503	−	89.8754i	0.410082	−	0.121038i
$83$	−822.684			−1.08797			−0.543984	−	0.839096i	$-0.683085\pi$
$83$	−822.684			−1.08797			−0.543984	+	0.839096i	$0.683085\pi$
$84$	426.284	−	275.653i	0.553707	−	0.358050i
$85$	555.480			0.708826
$86$	635.698	−	187.629i	0.797082	−	0.235262i
$87$	270.113			0.332863
$88$	274.726	+	236.030i	0.332795	+	0.285919i
$89$		−	803.525i		−	0.957005i	−0.878086	−	0.478503i	$-0.841180\pi$
$89$		−	803.525i		−	0.957005i	0.878086	−	0.478503i	$-0.158820\pi$
$90$	87.3894	+	296.080i	0.102352	+	0.346773i
$91$	−614.014	−	778.413i	−0.707320	−	0.896702i
$92$	654.299	−	423.097i	0.741471	−	0.479466i
$93$	−454.049			−0.506266
$94$	1574.56	−	464.738i	1.72770	−	0.509937i
$95$	−1418.96			−1.53245
$96$	73.5044	−	538.061i	0.0781459	−	0.572037i
$97$			750.474i			0.785557i	0.919633	+	0.392779i	$0.128486\pi$
$97$			750.474i			0.785557i	−0.919633	+	0.392779i	$0.871514\pi$
$98$	83.5911	+	283.211i	0.0861630	+	0.291925i
$99$	−144.062			−0.146250
$100$	−148.253	+	95.8664i	−0.148253	+	0.0958664i
$101$			460.391i			0.453570i	0.973945	+	0.226785i	$0.0728215\pi$
$101$			460.391i			0.453570i	−0.973945	+	0.226785i	$0.927178\pi$
$102$	372.766	−	110.024i	0.361857	−	0.106804i
$103$	1245.30			1.19129			0.595645	−	0.803248i	$-0.296897\pi$
$103$	1245.30			1.19129			0.595645	+	0.803248i	$0.296897\pi$
$104$	−1059.66	−	44.4310i	−0.999122	−	0.0418925i
$105$	−769.537			−0.715230
$106$	−654.019	+	193.037i	−0.599282	+	0.176881i
$107$		−	488.541i		−	0.441393i	−0.975343	−	0.220696i	$-0.929167\pi$
$107$		−	488.541i		−	0.441393i	0.975343	−	0.220696i	$-0.0708330\pi$
$108$	117.289	+	181.382i	0.104501	+	0.161606i
$109$	703.953			0.618591			0.309296	−	0.950966i	$-0.399907\pi$
$109$	703.953			0.618591			0.309296	+	0.950966i	$0.399907\pi$
$110$	−155.426	−	526.591i	−0.134721	−	0.456441i
$111$		−	199.015i		−	0.170177i
$112$	1234.53	+	555.421i	1.04154	+	0.468592i
$113$	−2263.50			−1.88435			−0.942177	−	0.335115i	$-0.891225\pi$
$113$	−2263.50			−1.88435			−0.942177	+	0.335115i	$0.891225\pi$
$114$	−952.226	+	281.054i	−0.782317	+	0.230904i
$115$	−1181.15			−0.957766
$116$	391.126	+	604.858i	0.313062	+	0.484135i
$117$	331.211	−	261.260i	0.261713	−	0.206440i
$118$	−250.616	−	849.102i	−0.195518	−	0.662426i
$119$			968.851i			0.746339i
$120$	−536.466	+	624.417i	−0.408103	+	0.475010i
$121$	−1074.78			−0.807498
$122$	−906.361	+	267.516i	−0.672607	+	0.198523i
$123$	−336.749			−0.246859
$124$	−657.469	−	1016.74i	−0.476149	−	0.736341i
$125$	−1248.27			−0.893188
$126$	−516.414	+	152.422i	−0.365125	+	0.107768i
$127$	−1539.77			−1.07585			−0.537923	−	0.842994i	$-0.680791\pi$
$127$	−1539.77			−1.07585			−0.537923	+	0.842994i	$0.680791\pi$
$128$	1311.30	−	614.521i	0.905499	−	0.424348i
$129$	−703.016			−0.479822
$130$	1312.32	+	928.810i	0.885371	+	0.626631i
$131$			833.576i			0.555953i	0.960588	+	0.277977i	$0.0896637\pi$
$131$			833.576i			0.555953i	−0.960588	+	0.277977i	$0.910336\pi$
$132$	−208.603	−	322.595i	−0.137550	−	0.212714i
$133$		−	2474.91i		−	1.61355i
$134$	252.419	+	855.210i	0.162729	+	0.551335i
$135$		−	327.434i		−	0.208748i
$136$	786.144	+	675.413i	0.495671	+	0.425854i
$137$		−	1012.44i		−	0.631379i	−0.948863	−	0.315689i	$-0.897764\pi$
$137$		−	1012.44i		−	0.631379i	0.948863	−	0.315689i	$-0.102236\pi$
$138$	−792.638	+	233.950i	−0.488940	+	0.144313i
$139$		−	2463.08i		−	1.50299i	−0.659739	−	0.751495i	$-0.729333\pi$
$139$		−	2463.08i		−	1.50299i	0.659739	−	0.751495i	$-0.270667\pi$
$140$	−1114.30	−	1723.21i	−0.672681	−	1.04027i
$141$	−1741.30			−1.04003
$142$	1365.34	−	402.985i	0.806876	−	0.238153i
$143$	−589.072	+	464.661i	−0.344480	+	0.271727i
$144$	−236.328	+	525.285i	−0.136764	+	0.303985i
$145$		−	1091.90i		−	0.625362i
$146$	2055.17	−	606.593i	1.16498	−	0.343849i
$147$		−	313.202i		−	0.175731i
$148$	445.650	−	288.176i	0.247515	−	0.160053i
$149$	2991.00			1.64451			0.822257	−	0.569117i	$-0.192715\pi$
$149$	2991.00			1.64451			0.822257	+	0.569117i	$0.192715\pi$
$150$	179.598	−	53.0091i	0.0977607	−	0.0288545i
$151$			2307.79i			1.24374i	0.783120	+	0.621871i	$0.213627\pi$
$151$			2307.79i			1.24374i	−0.783120	+	0.621871i	$0.786373\pi$
$152$	−2008.19	−	1725.33i	−1.07162	−	0.920676i
$153$	−412.241			−0.217828
$154$	918.464	−	271.089i	0.480597	−	0.141850i
$155$			1835.45i			0.951140i
$156$	1064.63	+	363.366i	0.546401	+	0.186491i
$157$		−	1097.78i		−	0.558042i	−0.960285	−	0.279021i	$-0.909990\pi$
$157$		−	1097.78i		−	0.558042i	0.960285	−	0.279021i	$-0.0900099\pi$
$158$	−908.210	−	3077.07i	−0.457299	−	1.54936i
$159$	723.277			0.360752
$160$	−2175.05	−	297.134i	−1.07471	−	0.146815i
$161$		−	2060.13i		−	1.00845i
$162$	−64.8547	−	219.731i	−0.0314535	−	0.106566i
$163$	2138.86			1.02778			0.513891	−	0.857856i	$-0.328204\pi$
$163$	2138.86			1.02778			0.513891	+	0.857856i	$0.328204\pi$
$164$	−487.616	−	754.075i	−0.232173	−	0.359045i
$165$			582.355i			0.274765i
$166$	658.703	+	2231.72i	0.307983	+	1.04347i
$167$			2341.22i			1.08484i	0.840106	+	0.542422i	$0.182493\pi$
$167$			2341.22i			1.08484i	−0.840106	+	0.542422i	$0.817507\pi$
$168$	−1089.09	−	935.687i	−0.500149	−	0.429701i
$169$	511.653	−	2136.59i	0.232887	−	0.972504i
$170$	−444.759	−	1506.87i	−0.200656	−	0.679832i
$171$	1053.06			0.470934
$172$	−1017.98	−	1574.25i	−0.451278	−	0.697880i
$173$			1655.20i			0.727413i	0.931514	+	0.363706i	$0.118489\pi$
$173$			1655.20i			0.727413i	−0.931514	+	0.363706i	$0.881511\pi$
$174$	−216.272	−	732.743i	−0.0942274	−	0.319248i
$175$			466.790i			0.201634i
$176$	420.320	−	934.243i	0.180016	−	0.400120i
$177$			939.019i			0.398763i
$178$	−2179.75	+	643.362i	−0.917860	+	0.270910i
$179$		−	2005.28i		−	0.837326i	−0.908142	−	0.418663i	$-0.862499\pi$
$179$		−	2005.28i		−	0.837326i	0.908142	−	0.418663i	$-0.137501\pi$
$180$	733.216	−	474.128i	0.303615	−	0.196330i
$181$		−	1629.54i		−	0.669184i	−0.942363	−	0.334592i	$-0.891401\pi$
$181$		−	1629.54i		−	0.669184i	0.942363	−	0.334592i	$-0.108599\pi$
$182$	−1620.00	+	2288.91i	−0.659794	+	0.932227i
$183$	1002.34			0.404892
$184$	−1671.63	−	1436.17i	−0.669751	−	0.575414i
$185$	−804.496			−0.319717
$186$	363.546	+	1231.71i	0.143314	+	0.485558i
$187$	733.188			0.286717
$188$	−2521.42	−	3899.26i	−0.978158	−	1.51267i
$189$	571.100			0.219796
$190$	1136.13	+	3849.27i	0.433808	+	1.46977i
$191$	4723.88			1.78957			0.894786	−	0.446495i	$-0.147328\pi$
$191$	4723.88			1.78957			0.894786	+	0.446495i	$0.147328\pi$
$192$	−1518.47	+	231.414i	−0.570760	+	0.0869837i
$193$		−	10.6845i		−	0.00398491i	−0.999998	−	0.00199245i	$-0.999366\pi$
$193$		−	10.6845i		−	0.00398491i	0.999998	−	0.00199245i	$-0.000634218\pi$
$194$	2035.83	−	600.886i	0.753425	−	0.222377i
$195$	−1056.11	−	1338.88i	−0.387846	−	0.491689i
$196$	701.348	−	453.521i	0.255593	−	0.165277i
$197$	2024.67			0.732244			0.366122	−	0.930567i	$-0.380685\pi$
$197$	2024.67			0.732244			0.366122	+	0.930567i	$0.380685\pi$
$198$	115.347	+	390.802i	0.0414007	+	0.140268i
$199$	1829.71			0.651782			0.325891	−	0.945407i	$-0.394336\pi$
$199$	1829.71			0.651782			0.325891	+	0.945407i	$0.394336\pi$
$200$	378.762	+	325.412i	0.133913	+	0.115051i
$201$		−	945.773i		−	0.331889i
$202$	1248.92	−	368.623i	0.435017	−	0.128397i
$203$	1904.46			0.658458
$204$	−596.929	−	923.122i	−0.204870	−	0.316821i
$205$			1361.27i			0.463782i
$206$	−997.079	−	3378.16i	−0.337232	−	1.14256i
$207$	876.575			0.294329
$208$	727.918	+	2910.16i	0.242654	+	0.970113i
$209$	−1872.92			−0.619868
$210$	616.149	+	2087.55i	0.202468	+	0.685974i
$211$			2849.73i			0.929780i	0.885368	+	0.464890i	$0.153906\pi$
$211$			2849.73i			0.929780i	−0.885368	+	0.464890i	$0.846094\pi$
$212$	1047.31	+	1619.62i	0.339291	+	0.524698i
$213$	−1509.92			−0.485718
$214$	−1325.28	+	391.162i	−0.423338	+	0.124950i
$215$			2841.87i			0.901459i
$216$	398.130	−	463.401i	0.125413	−	0.145974i
$217$	−3201.33			−1.00148
$218$	−563.637	−	1909.64i	−0.175112	−	0.593288i
$219$	−2272.81			−0.701288
$220$	−1304.06	+	843.257i	−0.399634	+	0.258420i
$221$	−1685.66	+	1329.65i	−0.513076	+	0.404715i
$222$	−539.874	+	159.346i	−0.163216	+	0.0481739i
$223$			1372.76i			0.412228i	0.978528	+	0.206114i	$0.0660817\pi$
$223$			1372.76i			0.412228i	−0.978528	+	0.206114i	$0.933918\pi$
$224$	518.251	−	3793.66i	0.154585	−	1.13158i
$225$	−198.617			−0.0588494
$226$	1812.33	+	6140.27i	0.533426	+	1.80728i
$227$	3957.76			1.15720			0.578602	−	0.815610i	$-0.303598\pi$
$227$	3957.76			1.15720			0.578602	+	0.815610i	$0.303598\pi$
$228$	1524.85	+	2358.10i	0.442919	+	0.684952i
$229$	1499.02			0.432569			0.216284	−	0.976330i	$-0.430606\pi$
$229$	1499.02			0.432569			0.216284	+	0.976330i	$0.430606\pi$
$230$	945.720	+	3204.15i	0.271126	+	0.918590i
$231$	−1015.73			−0.289307
$232$	1327.65	−	1545.32i	0.375710	−	0.437306i
$233$	3777.11			1.06200			0.531001	−	0.847371i	$-0.321816\pi$
$233$	3777.11			1.06200			0.531001	+	0.847371i	$0.321816\pi$
$234$	−973.919	−	689.302i	−0.272082	−	0.192569i
$235$			7039.02i			1.95394i
$236$	−2102.73	+	1359.71i	−0.579982	+	0.375041i
$237$			3402.91i			0.932671i
$238$	2628.23	−	775.734i	0.715811	−	0.211275i
$239$		−	4920.95i		−	1.33184i	−0.746023	−	0.665920i	$-0.768039\pi$
$239$		−	4920.95i		−	1.33184i	0.746023	−	0.665920i	$-0.231961\pi$
$240$	2123.41	+	955.333i	0.571107	+	0.256944i
$241$		−	1467.06i		−	0.392123i	−0.980592	−	0.196061i	$-0.937185\pi$
$241$		−	1467.06i		−	0.392123i	0.980592	−	0.196061i	$-0.0628152\pi$
$242$	860.549	+	2915.59i	0.228588	+	0.774468i
$243$			243.000i			0.0641500i
$244$	1451.40	+	2244.52i	0.380805	+	0.588897i
$245$	−1266.09			−0.330152
$246$	269.626	+	913.509i	0.0698811	+	0.236761i
$247$	4305.99	−	3396.57i	1.10925	−	0.874975i
$248$	−2231.74	+	2597.62i	−0.571433	+	0.665117i
$249$		−	2468.05i		−	0.628138i
$250$	999.458	+	3386.22i	0.252845	+	0.856653i
$251$			4882.12i			1.22772i	0.789416	+	0.613858i	$0.210383\pi$
$251$			4882.12i			1.22772i	−0.789416	+	0.613858i	$0.789617\pi$
$252$	826.959	+	1278.85i	0.206720	+	0.319683i
$253$	−1559.03			−0.387411
$254$	1232.85	+	4176.98i	0.304552	+	1.03184i
$255$			1666.44i			0.409241i
$256$	−2716.96	−	3065.18i	−0.663320	−	0.748336i
$257$	−1903.23			−0.461946			−0.230973	−	0.972960i	$-0.574191\pi$
$257$	−1903.23			−0.461946			−0.230973	+	0.972960i	$0.574191\pi$
$258$	562.887	+	1907.09i	0.135829	+	0.460196i
$259$		−	1403.18i		−	0.336638i
$260$	1468.87	−	4303.65i	0.350367	−	1.02654i
$261$			810.338i			0.192179i
$262$	2261.27	−	667.423i	0.533212	−	0.157380i
$263$	5914.88			1.38680			0.693398	−	0.720555i	$-0.256113\pi$
$263$	5914.88			1.38680			0.693398	+	0.720555i	$0.256113\pi$
$264$	−708.090	+	824.179i	−0.165076	+	0.192139i
$265$		−	2923.77i		−	0.677757i
$266$	−6713.78	+	1981.60i	−1.54755	+	0.456766i
$267$	2410.57			0.552527
$268$	2117.85	−	1369.49i	0.482717	−	0.312145i
$269$			4203.72i			0.952808i	0.879226	+	0.476404i	$0.158060\pi$
$269$			4203.72i			0.952808i	−0.879226	+	0.476404i	$0.841940\pi$
$270$	−888.241	+	262.168i	−0.200210	+	0.0590928i
$271$		−	2759.47i		−	0.618545i	−0.950974	−	0.309272i	$-0.899915\pi$
$271$		−	2759.47i		−	0.618545i	0.950974	−	0.309272i	$-0.100085\pi$
$272$	1202.77	−	2673.38i	0.268120	−	0.595947i
$273$	2335.24	−	1842.04i	0.517711	−	0.408371i
$274$	−2746.49	+	810.638i	−0.605553	+	0.178732i
$275$	353.248			0.0774606
$276$	1269.29	+	1962.90i	0.276820	+	0.428089i
$277$		−	8888.17i		−	1.92794i	−0.266019	−	0.963968i	$-0.585708\pi$
$277$		−	8888.17i		−	1.92794i	0.266019	−	0.963968i	$-0.414292\pi$
$278$	−6681.67	+	1972.12i	−1.44151	+	0.425468i
$279$		−	1362.15i		−	0.292293i
$280$	−3782.41	+	4402.52i	−0.807294	+	0.939647i
$281$			4050.83i			0.859972i	0.902835	+	0.429986i	$0.141482\pi$
$281$			4050.83i			0.859972i	−0.902835	+	0.429986i	$0.858518\pi$
$282$	1394.22	+	4723.68i	0.294412	+	0.997486i
$283$			4078.29i			0.856640i	0.903627	+	0.428320i	$0.140894\pi$
$283$			4078.29i			0.856640i	−0.903627	+	0.428320i	$0.859106\pi$
$284$	−2186.38	−	3381.13i	−0.456823	−	0.706455i
$285$		−	4256.89i		−	0.884760i
$286$	1732.16	+	1225.95i	0.358128	+	0.253469i
$287$	−2374.29			−0.488326
$288$	1614.18	+	220.513i	0.330266	+	0.0451176i
$289$	−2814.95			−0.572959
$290$	−2962.04	+	874.258i	−0.599782	+	0.177028i
$291$	−2251.42			−0.453542
$292$	−3291.05	−	5089.45i	−0.659569	−	1.01999i
$293$	1590.21			0.317069			0.158535	−	0.987353i	$-0.449323\pi$
$293$	1590.21			0.317069			0.158535	+	0.987353i	$0.449323\pi$
$294$	−849.634	+	250.773i	−0.168543	+	0.0497463i
$295$	3795.88			0.749169
$296$	−1138.56	−	978.193i	−0.223573	−	0.192082i
$297$		−	432.186i		−	0.0844376i
$298$	−2394.82	−	8113.79i	−0.465531	−	1.57725i
$299$	3584.33	−	2827.33i	0.693268	−	0.546851i
$300$	−287.599	−	444.758i	−0.0553485	−	0.0855937i
$301$	−4956.70			−0.949167
$302$	6260.41	−	1847.79i	1.19287	−	0.352080i
$303$	−1381.17			−0.261869
$304$	−3072.45	+	6829.12i	−0.579662	+	1.28841i
$305$		−	4051.86i		−	0.760684i
$306$	330.071	+	1118.30i	0.0616631	+	0.208918i
$307$	−6423.44			−1.19415			−0.597077	−	0.802184i	$-0.703671\pi$
$307$	−6423.44			−1.19415			−0.597077	+	0.802184i	$0.703671\pi$
$308$	−1470.78	−	2274.49i	−0.272096	−	0.420783i
$309$			3735.89i			0.687791i
$310$	4979.08	−	1469.60i	0.912234	−	0.269250i
$311$	3419.21			0.623427			0.311713	−	0.950176i	$-0.399097\pi$
$311$	3419.21			0.623427			0.311713	+	0.950176i	$0.399097\pi$
$312$	133.293	−	3178.99i	0.0241867	−	0.576843i
$313$	8831.43			1.59483			0.797415	−	0.603431i	$-0.206200\pi$
$313$	8831.43			1.59483			0.797415	+	0.603431i	$0.206200\pi$
$314$	−2977.99	+	878.967i	−0.535216	+	0.157971i
$315$		−	2308.61i		−	0.412938i
$316$	−7620.08	+	4927.46i	−1.35653	+	0.877188i
$317$	6479.78			1.14808			0.574039	−	0.818828i	$-0.305376\pi$
$317$	6479.78			1.14808			0.574039	+	0.818828i	$0.305376\pi$
$318$	−579.110	−	1962.06i	−0.102122	−	0.345996i
$319$		−	1441.22i		−	0.252956i
$320$	935.466	+	6138.24i	0.163419	+	1.07231i
$321$	1465.62			0.254838
$322$	−5588.58	+	1649.50i	−0.967204	+	0.285474i
$323$	−5359.45			−0.923243
$324$	−544.145	+	351.867i	−0.0933033	+	0.0603338i
$325$	−812.147	+	640.623i	−0.138615	+	0.109340i
$326$	−1712.53	−	5802.15i	−0.290946	−	0.985741i
$327$			2111.86i			0.357144i
$328$	−1655.18	+	1926.54i	−0.278634	+	0.324315i
$329$	−12277.2			−2.05734
$330$	1579.77	−	466.277i	0.263526	−	0.0777809i
$331$	−8657.99			−1.43772			−0.718861	−	0.695154i	$-0.755336\pi$
$331$	−8657.99			−1.43772			−0.718861	+	0.695154i	$0.755336\pi$
$332$	5526.66	−	3573.77i	0.913599	−	0.590771i
$333$	597.044			0.0982517
$334$	6351.11	−	1874.56i	1.04047	−	0.307099i
$335$	−3823.19			−0.623531
$336$	−1666.26	+	3703.59i	−0.270542	+	0.601331i
$337$	8924.60			1.44259			0.721297	−	0.692626i	$-0.243546\pi$
$337$	8924.60			1.44259			0.721297	+	0.692626i	$0.243546\pi$
$338$	−6205.67	+	322.736i	−0.998650	+	0.0519365i
$339$		−	6790.50i		−	1.08793i
$340$	−3731.62	+	2413.02i	−0.595223	+	0.384896i
$341$			2422.64i			0.384731i
$342$	−843.161	−	2856.68i	−0.133313	−	0.451671i
$343$			5046.81i			0.794468i
$344$	−3455.45	+	4021.96i	−0.541585	+	0.630376i
$345$		−	3543.46i		−	0.552966i
$346$	4490.11	−	1325.28i	0.697659	−	0.205917i
$347$			1537.77i			0.237901i	0.992900	+	0.118951i	$0.0379531\pi$
$347$			1537.77i			0.237901i	−0.992900	+	0.118951i	$0.962047\pi$
$348$	−1814.57	+	1173.38i	−0.279515	+	0.180746i
$349$	8471.05			1.29927			0.649634	−	0.760247i	$-0.274922\pi$
$349$	8471.05			1.29927			0.649634	+	0.760247i	$0.274922\pi$
$350$	1266.28	−	373.747i	0.193387	−	0.0570789i
$351$	783.779	+	993.632i	0.119188	+	0.151100i
$352$	−2870.89	−	392.192i	−0.434713	−	0.0593861i
$353$			6922.13i			1.04370i	0.853036	+	0.521852i	$0.174759\pi$
$353$			6922.13i			1.04370i	−0.853036	+	0.521852i	$0.825241\pi$
$354$	2547.31	−	751.849i	0.382452	−	0.112882i
$355$			6103.68i			0.912535i
$356$	3490.54	+	5397.95i	0.519658	+	0.803626i
$357$	−2906.55			−0.430899
$358$	−5439.78	+	1605.57i	−0.803076	+	0.237031i
$359$			4046.73i			0.594925i	0.954733	+	0.297463i	$0.0961404\pi$
$359$			4046.73i			0.594925i	−0.954733	+	0.297463i	$0.903860\pi$
$360$	−1873.25	−	1609.40i	−0.274247	−	0.235618i
$361$	6831.62			0.996008
$362$	−4420.49	+	1304.73i	−0.641812	+	0.189434i
$363$		−	3224.34i		−	0.466209i
$364$	7506.30	+	2561.96i	1.08087	+	0.368909i
$365$			9187.58i			1.31753i
$366$	−802.549	−	2719.08i	−0.114617	−	0.388330i
$367$	−567.928			−0.0807783			−0.0403891	−	0.999184i	$-0.512860\pi$
$367$	−567.928			−0.0807783			−0.0403891	+	0.999184i	$0.512860\pi$
$368$	−2557.53	+	5684.59i	−0.362283	+	0.805244i
$369$		−	1010.25i		−	0.142524i
$370$	644.140	+	2182.38i	0.0905060	+	0.306640i
$371$	5099.55			0.713626
$372$	3050.23	−	1972.41i	0.425127	−	0.274905i
$373$			4632.74i			0.643094i	0.946894	+	0.321547i	$0.104203\pi$
$373$			4632.74i			0.643094i	−0.946894	+	0.321547i	$0.895797\pi$
$374$	−587.045	−	1988.94i	−0.0811641	−	0.274989i
$375$		−	3744.81i		−	0.515683i
$376$	−8558.80	+	9961.98i	−1.17390	+	1.36636i
$377$	2613.68	+	3313.49i	0.357060	+	0.452661i
$378$	−457.265	−	1549.24i	−0.0622201	−	0.210805i
$379$	−8005.02			−1.08494			−0.542468	−	0.840077i	$-0.682510\pi$
$379$	−8005.02			−1.08494			−0.542468	+	0.840077i	$0.682510\pi$
$380$	9532.37	−	6164.03i	1.28684	−	0.832126i
$381$		−	4619.31i		−	0.621140i
$382$	−3782.30	−	12814.6i	−0.506595	−	1.71637i
$383$		−	9120.11i		−	1.21675i	−0.793649	−	0.608376i	$-0.791821\pi$
$383$		−	9120.11i		−	1.21675i	0.793649	−	0.608376i	$-0.208179\pi$
$384$	1843.56	+	3933.91i	0.244997	+	0.522790i
$385$			4105.96i			0.543530i
$386$	−28.9842	+	8.55481i	−0.00382191	+	0.00112805i
$387$		−	2109.05i		−	0.277026i
$388$	−3260.08	−	5041.56i	−0.426561	−	0.659656i
$389$		−	13700.5i		−	1.78571i	−0.450339	−	0.892857i	$-0.648697\pi$
$389$		−	13700.5i		−	1.78571i	0.450339	−	0.892857i	$-0.351303\pi$
$390$	−2786.43	+	3936.97i	−0.361785	+	0.511169i
$391$	−4461.23			−0.577018
$392$	−1791.83	−	1539.45i	−0.230870	−	0.198351i
$393$	−2500.73			−0.320980
$394$	−1621.11	−	5492.40i	−0.207285	−	0.702292i
$395$	13755.9			1.75224
$396$	967.785	−	625.810i	0.122811	−	0.0794145i
$397$	6204.37			0.784354			0.392177	−	0.919890i	$-0.371722\pi$
$397$	6204.37			0.784354			0.392177	+	0.919890i	$0.371722\pi$
$398$	−1465.00	−	4963.51i	−0.184507	−	0.625122i
$399$	7424.74			0.931584
$400$	579.491	−	1288.03i	0.0724364	−	0.161004i
$401$		−	3377.04i		−	0.420552i	−0.977642	−	0.210276i	$-0.932564\pi$
$401$		−	3377.04i		−	0.420552i	0.977642	−	0.210276i	$-0.0674363\pi$
$402$	−2565.63	+	757.257i	−0.318313	+	0.0939516i
$403$	−4393.51	−	5569.85i	−0.543068	−	0.688472i
$404$	−1999.95	−	3092.83i	−0.246291	−	0.380876i
$405$	982.302			0.120521
$406$	−1524.85	−	5166.29i	−0.186397	−	0.631524i
$407$	−1061.87			−0.129324
$408$	−2026.24	+	2358.43i	−0.245867	+	0.286176i
$409$		−	5434.16i		−	0.656973i	−0.944509	−	0.328486i	$-0.893461\pi$
$409$		−	5434.16i		−	0.656973i	0.944509	−	0.328486i	$-0.106539\pi$
$410$	3692.76	−	1089.94i	0.444811	−	0.131288i
$411$	3037.33			0.364527
$412$	−8365.71	+	5409.62i	−1.00036	+	0.646875i
$413$			6620.66i			0.788817i
$414$	−701.851	−	2377.91i	−0.0833191	−	0.282290i
$415$	−9976.84			−1.18011
$416$	7311.67	−	4304.74i	0.861741	−	0.507349i
$417$	7389.23			0.867751
$418$	1499.60	+	5080.72i	0.175473	+	0.594512i
$419$		−	3615.54i		−	0.421553i	−0.977534	−	0.210776i	$-0.932401\pi$
$419$		−	3615.54i		−	0.421553i	0.977534	−	0.210776i	$-0.0675992\pi$
$420$	5169.63	−	3342.90i	0.600600	−	0.388373i
$421$	9792.46			1.13362			0.566811	−	0.823848i	$-0.308177\pi$
$421$	9792.46			1.13362			0.566811	+	0.823848i	$0.308177\pi$
$422$	7730.56	−	2281.71i	0.891748	−	0.263203i
$423$		−	5223.90i		−	0.600460i
$424$	3555.04	−	4137.87i	0.407188	−	0.473945i
$425$	1010.84			0.115371
$426$	1208.95	+	4096.01i	0.137498	+	0.465850i
$427$	7067.12			0.800942
$428$	2122.24	+	3281.94i	0.239678	+	0.370651i
$429$	−1393.98	−	1767.22i	−0.156881	−	0.198886i
$430$	7709.23	−	2275.41i	0.864586	−	0.255186i
$431$			8176.94i			0.913850i	0.889505	+	0.456925i	$0.151049\pi$
$431$			8176.94i			0.913850i	−0.889505	+	0.456925i	$0.848951\pi$
$432$	−1575.86	−	708.985i	−0.175506	−	0.0789608i
$433$	−14447.6			−1.60348			−0.801740	−	0.597673i	$-0.796092\pi$
$433$	−14447.6			−1.60348			−0.801740	+	0.597673i	$0.796092\pi$
$434$	2563.22	+	8684.35i	0.283499	+	0.960512i
$435$	3275.70			0.361053
$436$	−4729.04	+	3058.00i	−0.519450	+	0.335898i
$437$	11396.1			1.24749
$438$	1819.78	+	6165.52i	0.198521	+	0.672602i
$439$	−14823.9			−1.61163			−0.805816	−	0.592166i	$-0.798273\pi$
$439$	−14823.9			−1.61163			−0.805816	+	0.592166i	$0.798273\pi$
$440$	3331.66	+	2862.38i	0.360978	+	0.310133i
$441$	939.607			0.101458
$442$	4956.66	+	3508.13i	0.533403	+	0.377522i
$443$			6678.46i			0.716260i	0.933672	+	0.358130i	$0.116586\pi$
$443$			6678.46i			0.716260i	−0.933672	+	0.358130i	$0.883414\pi$
$444$	864.527	+	1336.95i	0.0924068	+	0.142903i
$445$		−	9744.49i		−	1.03805i
$446$	3723.93	−	1099.13i	0.395366	−	0.116694i
$447$			8973.01i			0.949460i
$448$	−10706.1	+	1631.61i	−1.12906	+	0.172068i
$449$			13672.9i			1.43712i	0.695467	+	0.718558i	$0.255198\pi$
$449$			13672.9i			1.43712i	−0.695467	+	0.718558i	$0.744802\pi$
$450$	159.027	+	538.794i	0.0166592	+	0.0564422i
$451$			1796.77i			0.187597i
$452$	15205.8	−	9832.72i	1.58235	−	1.02321i
$453$	−6923.36			−0.718075
$454$	−3168.88	−	10736.3i	−0.327583	−	1.10987i
$455$	−7446.25	−	9439.96i	−0.767221	−	0.972642i
$456$	5175.99	−	6024.57i	0.531553	−	0.618698i
$457$		−	8454.03i		−	0.865345i	−0.901551	−	0.432672i	$-0.857571\pi$
$457$		−	8454.03i		−	0.865345i	0.901551	−	0.432672i	$-0.142429\pi$
$458$	−1200.23	−	4066.45i	−0.122452	−	0.414875i
$459$		−	1236.72i		−	0.125763i
$460$	7934.80	−	5130.97i	0.804265	−	0.520071i
$461$	−12560.1			−1.26895			−0.634473	−	0.772945i	$-0.718783\pi$
$461$	−12560.1			−1.26895			−0.634473	+	0.772945i	$0.718783\pi$
$462$	813.266	+	2755.39i	0.0818973	+	0.277473i
$463$		−	14540.8i		−	1.45954i	−0.683690	−	0.729772i	$-0.739626\pi$
$463$		−	14540.8i		−	1.45954i	0.683690	−	0.729772i	$-0.260374\pi$
$464$	−5255.05	−	2364.27i	−0.525774	−	0.236548i
$465$	−5506.34			−0.549141
$466$	−3024.24	−	10246.3i	−0.300633	−	1.01856i
$467$			10533.0i			1.04370i	0.853038	+	0.521849i	$0.174758\pi$
$467$			10533.0i			1.04370i	−0.853038	+	0.521849i	$0.825242\pi$
$468$	−1090.10	+	3193.89i	−0.107671	+	0.315465i
$469$		−	6668.28i		−	0.656530i
$470$	19095.0	−	5635.97i	1.87401	−	0.553123i
$471$	3293.35			0.322186
$472$	5372.13	+	4615.45i	0.523882	+	0.450092i
$473$			3751.03i			0.364635i
$474$	9231.20	−	2724.63i	0.894521	−	0.264022i
$475$	−2582.17			−0.249427
$476$	−4208.72	−	6508.58i	−0.405266	−	0.626723i
$477$			2169.83i			0.208280i
$478$	−13349.2	+	3940.08i	−1.27736	+	0.377019i
$479$			9522.04i			0.908295i	0.890927	+	0.454147i	$0.150056\pi$
$479$			9522.04i			0.908295i	−0.890927	+	0.454147i	$0.849944\pi$
$480$	891.401	−	6525.16i	0.0847639	−	0.620482i
$481$	2441.33	−	1925.72i	0.231424	−	0.182548i
$482$	−3979.74	+	1174.64i	−0.376083	+	0.111003i
$483$	6180.39			0.582231
$484$	7220.20	−	4668.88i	0.678080	−	0.438475i
$485$			9101.13i			0.852085i
$486$	659.194	−	194.564i	0.0615260	−	0.0181597i
$487$		−	15094.0i		−	1.40446i	−0.711950	−	0.702230i	$-0.752188\pi$
$487$		−	15094.0i		−	1.40446i	0.711950	−	0.702230i	$-0.247812\pi$
$488$	4926.69	−	5734.40i	0.457010	−	0.531934i
$489$			6416.58i			0.593390i
$490$	1013.72	+	3434.56i	0.0934600	+	0.316648i
$491$		−	21589.6i		−	1.98437i	−0.124791	−	0.992183i	$-0.539826\pi$
$491$		−	21589.6i		−	1.98437i	0.124791	−	0.992183i	$-0.460174\pi$
$492$	2262.22	−	1462.85i	0.207295	−	0.134045i
$493$		−	4124.13i		−	0.376757i
$494$	−12661.7	−	8961.45i	−1.15319	−	0.816184i
$495$	−1747.07			−0.158636
$496$	8833.54	+	3974.25i	0.799673	+	0.359777i
$497$	−10645.9			−0.960829
$498$	−6695.17	+	1976.11i	−0.602445	+	0.177814i
$499$	−17274.5			−1.54973			−0.774863	−	0.632130i	$-0.782181\pi$
$499$	−17274.5			−1.54973			−0.774863	+	0.632130i	$0.782181\pi$
$500$	8385.67	−	5422.52i	0.750037	−	0.485005i
$501$	−7023.66			−0.626335
$502$	13243.9	−	3908.99i	1.17750	−	0.347544i
$503$	−5755.02			−0.510146			−0.255073	−	0.966922i	$-0.582100\pi$
$503$	−5755.02			−0.510146			−0.255073	+	0.966922i	$0.582100\pi$
$504$	2807.06	−	3267.27i	0.248088	−	0.288761i
$505$			5583.24i			0.491982i
$506$	1248.27	+	4229.22i	0.109669	+	0.371565i
$507$	6409.77	+	1534.96i	0.561475	+	0.134458i
$508$	10343.9	−	6688.81i	0.903420	−	0.584189i
$509$	−8760.81			−0.762900			−0.381450	−	0.924389i	$-0.624575\pi$
$509$	−8760.81			−0.762900			−0.381450	+	0.924389i	$0.624575\pi$
$510$	4520.60	−	1334.28i	0.392501	−	0.115849i
$511$	−16024.7			−1.38726
$512$	−6139.62	+	9824.60i	−0.529952	+	0.848028i
$513$			3159.19i			0.271894i
$514$	1523.87	+	5162.95i	0.130768	+	0.443050i
$515$	15101.9			1.29218
$516$	4722.75	−	3053.93i	0.402921	−	0.260546i
$517$			9290.93i			0.790357i
$518$	−3806.44	+	1123.49i	−0.322868	+	0.0952958i
$519$	−4965.60			−0.419972
$520$	−12850.7	−	538.823i	−1.08374	−	0.0454403i
$521$	16422.2			1.38094			0.690468	−	0.723363i	$-0.257405\pi$
$521$	16422.2			1.38094			0.690468	+	0.723363i	$0.257405\pi$
$522$	2198.23	−	648.817i	0.184318	−	0.0544022i
$523$			15056.8i			1.25887i	0.777054	+	0.629434i	$0.216713\pi$
$523$			15056.8i			1.25887i	−0.777054	+	0.629434i	$0.783287\pi$
$524$	−3621.08	−	5599.83i	−0.301885	−	0.466850i
$525$	−1400.37			−0.116414
$526$	−4735.90	−	16045.5i	−0.392576	−	1.33007i
$527$			6932.51i			0.573026i
$528$	2802.73	+	1260.96i	0.231010	+	0.103932i
$529$	−2680.79			−0.220333
$530$	−7931.41	+	2340.99i	−0.650034	+	0.191861i
$531$	−2817.06			−0.230226
$532$	10751.1	+	16626.1i	0.876165	+	1.35495i
$533$	−3258.47	−	4130.92i	−0.264803	−	0.335703i
$534$	−1930.09	−	6539.24i	−0.156410	−	0.529926i
$535$		−	5924.62i		−	0.478773i
$536$	−5410.77	−	4648.64i	−0.436026	−	0.374610i
$537$	6015.83			0.483430
$538$	11403.6	−	3365.81i	0.913835	−	0.269722i
$539$	−1671.13			−0.133545
$540$	1422.38	+	2199.65i	0.113351	+	0.175292i
$541$	2634.99			0.209403			0.104702	−	0.994504i	$-0.466611\pi$
$541$	2634.99			0.209403			0.104702	+	0.994504i	$0.466611\pi$
$542$	−7485.69	+	2209.43i	−0.593244	+	0.175098i
$543$	4888.61			0.386354
$544$	−8215.20	−	1122.28i	−0.647470	−	0.0884508i
$545$	8536.96			0.670978
$546$	−6866.73	−	4860.00i	−0.538222	−	0.380932i
$547$		−	2007.56i		−	0.156923i	−0.996917	−	0.0784616i	$-0.974999\pi$
$547$		−	2007.56i		−	0.156923i	0.996917	−	0.0784616i	$-0.0250008\pi$
$548$	4398.09	+	6801.43i	0.342841	+	0.530187i
$549$			3007.02i			0.233764i
$550$	−282.837	−	958.268i	−0.0219276	−	0.0742921i
$551$			10535.0i			0.814531i
$552$	4308.52	−	5014.89i	0.332215	−	0.386681i
$553$			23992.6i			1.84497i
$554$	−24111.2	+	7116.53i	−1.84907	+	0.545763i
$555$		−	2413.49i		−	0.184589i
$556$	10699.7	+	16546.6i	0.816130	+	1.26211i
$557$	−15077.3			−1.14694			−0.573468	−	0.819228i	$-0.694402\pi$
$557$	−15077.3			−1.14694			−0.573468	+	0.819228i	$0.694402\pi$
$558$	−3695.14	+	1090.64i	−0.280337	+	0.0827427i
$559$	−6802.58	−	8623.94i	−0.514702	−	0.652511i
$560$	14971.4	+	6735.69i	1.12974	+	0.508276i
$561$			2199.56i			0.165536i
$562$	10988.8	−	3243.40i	0.824796	−	0.243442i
$563$		−	14038.8i		−	1.05091i	−0.850821	−	0.525455i	$-0.823895\pi$
$563$		−	14038.8i		−	1.05091i	0.850821	−	0.525455i	$-0.176105\pi$
$564$	11697.8	−	7564.27i	0.873342	−	0.564740i
$565$	−27449.9			−2.04394
$566$	11063.3	−	3265.39i	0.821600	−	0.242499i
$567$			1713.30i			0.126899i
$568$	−7421.52	+	8638.25i	−0.548240	+	0.638121i
$569$	5607.45			0.413140			0.206570	−	0.978432i	$-0.433770\pi$
$569$	5607.45			0.413140			0.206570	+	0.978432i	$0.433770\pi$
$570$	−11547.8	+	3408.39i	−0.848569	+	0.250459i
$571$		−	6820.92i		−	0.499906i	−0.968258	−	0.249953i	$-0.919585\pi$
$571$		−	6820.92i		−	0.499906i	0.968258	−	0.249953i	$-0.0804152\pi$
$572$	1938.79	−	5680.47i	0.141722	−	0.415231i
$573$			14171.7i			1.03321i
$574$	1901.03	+	6440.80i	0.138236	+	0.468352i
$575$	−2149.41			−0.155890
$576$	−694.242	−	4555.40i	−0.0502200	−	0.329529i
$577$			23328.9i			1.68318i	0.540117	+	0.841590i	$0.318380\pi$
$577$			23328.9i			1.68318i	−0.540117	+	0.841590i	$0.681620\pi$
$578$	2253.86	+	7636.19i	0.162194	+	0.549522i
$579$	32.0535			0.00230069
$580$	4743.26	+	7335.22i	0.339574	+	0.525135i
$581$		−	17401.3i		−	1.24256i
$582$	1802.66	+	6107.50i	0.128389	+	0.434990i
$583$		−	3859.14i		−	0.274149i
$584$	−11171.3	+	13002.7i	−0.791558	+	0.921330i
$585$	4016.65	−	3168.34i	0.283877	−	0.223923i
$586$	−1273.24	−	4313.82i	−0.0897564	−	0.304100i
$587$	11535.3			0.811093			0.405547	−	0.914074i	$-0.367081\pi$
$587$	11535.3			0.811093			0.405547	+	0.914074i	$0.367081\pi$
$588$	1360.56	+	2104.04i	0.0954228	+	0.147567i
$589$		−	17709.0i		−	1.23886i
$590$	−3039.27	−	10297.2i	−0.212076	−	0.718525i
$591$			6074.02i			0.422761i
$592$	−1741.96	+	3871.83i	−0.120936	+	0.268803i
$593$			17605.5i			1.21917i	0.792720	+	0.609586i	$0.208664\pi$
$593$			17605.5i			1.21917i	−0.792720	+	0.609586i	$0.791336\pi$
$594$	−1172.40	+	346.040i	−0.0809837	+	0.0239027i
$595$			11749.4i			0.809545i
$596$	−20093.1	+	12993.0i	−1.38095	+	0.892978i
$597$			5489.13i			0.376307i
$598$	−10539.7	−	7459.56i	−0.720734	−	0.510107i
$599$	−23660.0			−1.61389			−0.806945	−	0.590627i	$-0.798881\pi$
$599$	−23660.0			−1.61389			−0.806945	+	0.590627i	$0.798881\pi$
$600$	−976.237	+	1136.29i	−0.0664245	+	0.0773145i
$601$	−408.208			−0.0277057			−0.0138529	−	0.999904i	$-0.504410\pi$
$601$	−408.208			−0.0277057			−0.0138529	+	0.999904i	$0.504410\pi$
$602$	3968.70	+	13446.2i	0.268691	+	0.910342i
$603$	2837.32			0.191616
$604$	−10025.1	−	15503.3i	−0.675357	−	1.04441i
$605$	−13034.0			−0.875883
$606$	1105.87	+	3746.75i	0.0741302	+	0.251157i
$607$	19900.9			1.33073			0.665363	−	0.746520i	$-0.268277\pi$
$607$	19900.9			1.33073			0.665363	+	0.746520i	$0.268277\pi$
$608$	20985.6	+	2866.84i	1.39980	+	0.191226i
$609$			5713.38i			0.380161i
$610$	−10991.6	+	3244.22i	−0.729569	+	0.215336i
$611$	−16849.3	−	21360.6i	−1.11563	−	1.41433i
$612$	2769.37	−	1790.79i	0.182917	−	0.118282i
$613$	710.858			0.0468373			0.0234187	−	0.999726i	$-0.492545\pi$
$613$	710.858			0.0468373			0.0234187	+	0.999726i	$0.492545\pi$
$614$	5143.09	+	17425.1i	0.338043	+	1.14531i
$615$	−4083.81			−0.267765
$616$	−4992.47	+	5810.97i	−0.326546	+	0.380082i
$617$		−	16609.5i		−	1.08375i	−0.840459	−	0.541875i	$-0.817714\pi$
$617$		−	16609.5i		−	1.08375i	0.840459	−	0.541875i	$-0.182286\pi$
$618$	10134.5	−	2991.24i	0.659658	−	0.194701i
$619$	19446.3			1.26270			0.631351	−	0.775497i	$-0.282501\pi$
$619$	19446.3			1.26270			0.631351	+	0.775497i	$0.282501\pi$
$620$	−7973.24	−	12330.2i	−0.516473	−	0.798700i
$621$			2629.72i			0.169931i
$622$	−2737.68	−	9275.41i	−0.176481	−	0.597926i
$623$	16996.0			1.09299
$624$	−8730.49	+	2183.75i	−0.560095	+	0.140096i
$625$	−17896.5			−1.14538
$626$	−7071.10	−	23957.3i	−0.451467	−	1.52960i
$627$		−	5618.75i		−	0.357881i
$628$	4768.81	+	7374.73i	0.303019	+	0.468605i
$629$	−3038.59			−0.192618
$630$	−6262.64	+	1848.45i	−0.396047	+	0.116895i
$631$			25295.7i			1.59589i	0.602733	+	0.797943i	$0.294078\pi$
$631$			25295.7i			1.59589i	−0.602733	+	0.797943i	$0.705922\pi$
$632$	19468.1	+	16725.9i	1.22531	+	1.05272i
$633$	−8549.20			−0.536809
$634$	−5188.20	−	17577.9i	−0.325000	−	1.10112i
$635$	−18673.1			−1.16696
$636$	−4858.86	+	3141.94i	−0.302934	+	0.195890i
$637$	3842.07	−	3030.63i	0.238977	−	0.188506i
$638$	−3909.65	+	1153.95i	−0.242609	+	0.0716070i
$639$		−	4529.76i		−	0.280429i
$640$	15902.4	−	7452.41i	0.982184	−	0.460285i
$641$	25718.1			1.58471			0.792357	−	0.610057i	$-0.208854\pi$
$641$	25718.1			1.58471			0.792357	+	0.610057i	$0.208854\pi$
$642$	−1173.49	−	3975.84i	−0.0721399	−	0.244414i
$643$	−12820.0			−0.786268			−0.393134	−	0.919481i	$-0.628609\pi$
$643$	−12820.0			−0.786268			−0.393134	+	0.919481i	$0.628609\pi$
$644$	8949.28	+	13839.6i	0.547595	+	0.846829i
$645$	−8525.60			−0.520458
$646$	4291.18	+	14538.7i	0.261353	+	0.885479i
$647$	−5429.39			−0.329910			−0.164955	−	0.986301i	$-0.552748\pi$
$647$	−5429.39			−0.329910			−0.164955	+	0.986301i	$0.552748\pi$
$648$	1390.20	+	1194.39i	0.0842783	+	0.0724074i
$649$	5010.25			0.303035
$650$	2388.11	+	1690.21i	0.144106	+	0.101993i
$651$		−	9603.99i		−	0.578203i
$652$	−14368.5	+	9291.28i	−0.863058	+	0.558090i
$653$			23782.4i			1.42523i	0.701553	+	0.712617i	$0.252490\pi$
$653$			23782.4i			1.42523i	−0.701553	+	0.712617i	$0.747510\pi$
$654$	5728.91	−	1690.91i	0.342535	−	0.101101i
$655$			10108.9i			0.603036i
$656$	6551.45	+	2947.53i	0.389926	+	0.175429i
$657$		−	6818.42i		−	0.404889i
$658$	9830.08	+	33304.9i	0.582396	+	1.97319i
$659$		−	27296.5i		−	1.61354i	−0.590868	−	0.806768i	$-0.701215\pi$
$659$		−	27296.5i		−	1.61354i	0.590868	−	0.806768i	$-0.298785\pi$
$660$	−2529.77	−	3912.17i	−0.149199	−	0.230729i
$661$	27338.9			1.60871			0.804357	−	0.594147i	$-0.202510\pi$
$661$	27338.9			1.60871			0.804357	+	0.594147i	$0.202510\pi$
$662$	6932.24	+	23486.8i	0.406992	+	1.37891i
$663$	−3988.96	−	5056.98i	−0.233662	−	0.296225i
$664$	−14119.7	−	12130.9i	−0.825229	−	0.708993i
$665$		−	30013.7i		−	1.75020i
$666$	−478.038	−	1619.62i	−0.0278132	−	0.0942328i
$667$			8769.40i			0.509074i
$668$	−10170.3	−	15727.9i	−0.589076	−	0.910977i
$669$	−4118.28			−0.238000
$670$	3061.13	+	10371.3i	0.176510	+	0.598026i
$671$		−	5348.12i		−	0.307693i
$672$	11381.0	+	1554.75i	0.653319	+	0.0892499i
$673$	26689.5			1.52868			0.764342	−	0.644811i	$-0.223064\pi$
$673$	26689.5			1.52868			0.764342	+	0.644811i	$0.223064\pi$
$674$	−7145.70	−	24210.1i	−0.408371	−	1.38359i
$675$		−	595.850i		−	0.0339767i
$676$	5844.22	+	16575.9i	0.332511	+	0.943099i
$677$			12731.9i			0.722787i	0.932413	+	0.361393i	$0.117699\pi$
$677$			12731.9i			0.722787i	−0.932413	+	0.361393i	$0.882301\pi$
$678$	−18420.8	+	5436.98i	−1.04343	+	0.307973i
$679$	−15873.9			−0.897179
$680$	9533.71	+	8190.85i	0.537648	+	0.461919i
$681$			11873.3i			0.668112i
$682$	6571.97	−	1939.75i	0.368994	−	0.108910i
$683$	−10423.4			−0.583955			−0.291977	−	0.956425i	$-0.594313\pi$
$683$	−10423.4			−0.583955			−0.291977	+	0.956425i	$0.594313\pi$
$684$	−7074.30	+	4574.54i	−0.395457	+	0.255719i
$685$		−	12278.1i		−	0.684849i
$686$	13690.7	−	4040.86i	0.761971	−	0.224899i
$687$			4497.07i			0.249744i
$688$	13677.2	+	6153.43i	0.757904	+	0.340985i
$689$	6998.63	+	8872.48i	0.386976	+	0.490587i
$690$	−9612.46	+	2837.16i	−0.530348	+	0.156535i
$691$	−12008.8			−0.661124			−0.330562	−	0.943784i	$-0.607238\pi$
$691$	−12008.8			−0.661124			−0.330562	+	0.943784i	$0.607238\pi$
$692$	−7190.24	−	11119.4i	−0.394988	−	0.610830i
$693$		−	3047.18i		−	0.167031i
$694$	4171.56	−	1231.25i	0.228170	−	0.0673455i
$695$		−	29870.2i		−	1.63027i
$696$	4635.95	+	3982.96i	0.252479	+	0.216916i
$697$			5141.54i			0.279411i
$698$	−6782.56	−	22979.7i	−0.367799	−	1.24612i
$699$			11331.3i			0.613147i
$700$	−2027.75	−	3135.82i	−0.109488	−	0.169318i
$701$			10284.3i			0.554114i	0.960853	+	0.277057i	$0.0893591\pi$
$701$			10284.3i			0.554114i	−0.960853	+	0.277057i	$0.910641\pi$
$702$	2067.91	−	2921.76i	0.111180	−	0.157086i
$703$	7762.03			0.416430
$704$	1234.74	+	8101.98i	0.0661022	+	0.433743i
$705$	−21117.1			−1.12811
$706$	18777.9	−	5542.38i	1.00101	−	0.295453i
$707$	−9738.12			−0.518019
$708$	−4079.13	−	6308.18i	−0.216530	−	0.334853i
$709$	16944.0			0.897524			0.448762	−	0.893651i	$-0.351865\pi$
$709$	16944.0			0.897524			0.448762	+	0.893651i	$0.351865\pi$
$710$	16557.7	−	4887.07i	0.875209	−	0.258322i
$711$	−10208.7			−0.538478
$712$	11848.4	−	13790.9i	0.623649	−	0.725893i
$713$		−	14741.0i		−	0.774273i
$714$	2327.20	+	7884.70i	0.121980	+	0.413274i
$715$	−7143.78	+	5635.03i	−0.373654	+	0.294739i
$716$	8710.99	+	13471.1i	0.454672	+	0.703128i
$717$	14762.9			0.768939
$718$	10977.7	−	3240.12i	0.570590	−	0.168412i
$719$	14267.6			0.740041			0.370021	−	0.929023i	$-0.379351\pi$
$719$	14267.6			0.740041			0.370021	+	0.929023i	$0.379351\pi$
$720$	−2866.00	+	6370.23i	−0.148346	+	0.329729i
$721$			26340.3i			1.36056i
$722$	−5469.91	−	18532.4i	−0.281951	−	0.955267i
$723$	4401.18			0.226392
$724$	7078.76	+	10947.0i	0.363370	+	0.561934i
$725$		−	1986.99i		−	0.101786i
$726$	−8746.77	+	2581.65i	−0.447139	+	0.131975i
$727$	7899.54			0.402996			0.201498	−	0.979489i	$-0.435419\pi$
$727$	7899.54			0.402996			0.201498	+	0.979489i	$0.435419\pi$
$728$	939.798	−	22413.9i	0.0478451	−	1.14109i
$729$	−729.000			−0.0370370
$730$	24923.4	−	7356.26i	1.26364	−	0.372969i
$731$			10733.8i			0.543095i
$732$	−6733.57	+	4354.20i	−0.340000	+	0.219858i
$733$	18.8350			0.000949093			0.000474547	−	1.00000i	$-0.499849\pi$
$733$	18.8350			0.000949093			0.000474547		1.00000i	$0.499849\pi$
$734$	454.726	+	1540.64i	0.0228668	+	0.0774741i
$735$		−	3798.26i		−	0.190614i
$736$	17468.5	+	2386.37i	0.874862	+	0.119515i
$737$	−5046.29			−0.252215
$738$	−2740.53	+	808.879i	−0.136694	+	0.0403459i
$739$	13711.5			0.682525			0.341262	−	0.939968i	$-0.389146\pi$
$739$	13711.5			0.682525			0.341262	+	0.939968i	$0.389146\pi$
$740$	5404.47	−	3494.76i	0.268476	−	0.173608i
$741$	10189.7	+	12918.0i	0.505167	+	0.640423i
$742$	−4083.08	−	13833.7i	−0.202014	−	0.684436i
$743$			11169.5i			0.551506i	0.961229	+	0.275753i	$0.0889271\pi$
$743$			11169.5i			0.551506i	−0.961229	+	0.275753i	$0.911073\pi$
$744$	−7792.86	−	6695.21i	−0.384005	−	0.329917i
$745$	36272.4			1.78378
$746$	12567.4	−	3709.32i	0.616789	−	0.182048i
$747$	7404.16			0.362656
$748$	−4925.44	+	3184.99i	−0.240764	+	0.155688i
$749$	10333.5			0.504111
$750$	−10158.7	+	2998.37i	−0.494589	+	0.145980i
$751$	−31229.1			−1.51740			−0.758698	−	0.651443i	$-0.774164\pi$
$751$	−31229.1			−1.51740			−0.758698	+	0.651443i	$0.774164\pi$
$752$	33877.0	+	15241.4i	1.64278	+	0.739093i
$753$	−14646.4			−0.708822
$754$	6895.89	−	9743.26i	0.333068	−	0.470595i
$755$			27987.0i			1.34907i
$756$	−3836.56	+	2480.88i	−0.184569	+	0.119350i
$757$			29792.5i			1.43042i	0.698911	+	0.715209i	$0.253668\pi$
$757$			29792.5i			1.43042i	−0.698911	+	0.715209i	$0.746332\pi$
$758$	6409.42	+	21715.5i	0.307125	+	1.04056i
$759$		−	4677.08i		−	0.223672i
$760$	−24353.7	−	20923.4i	−1.16237	−	0.998646i
$761$		−	3531.27i		−	0.168211i	−0.996457	−	0.0841054i	$-0.973197\pi$
$761$		−	3531.27i		−	0.168211i	0.996457	−	0.0841054i	$-0.0268033\pi$
$762$	−12530.9	+	3698.56i	−0.595733	+	0.175833i
$763$			14889.9i			0.706488i
$764$	−31734.3	+	20520.7i	−1.50276	+	0.971746i
$765$	−4999.32			−0.236275
$766$	−24740.4	+	7302.25i	−1.16698	+	0.344440i
$767$	−11519.0	+	9086.21i	−0.542278	+	0.427750i
$768$	9195.55	−	8150.88i	0.432052	−	0.382968i
$769$		−	10014.1i		−	0.469596i	−0.972044	−	0.234798i	$-0.924557\pi$
$769$		−	10014.1i		−	0.469596i	0.972044	−	0.234798i	$-0.0754428\pi$
$770$	11138.4	−	3287.54i	0.521298	−	0.153863i
$771$		−	5709.68i		−	0.266705i
$772$	46.4138	+	71.7767i	0.00216382	+	0.00334624i
$773$	−18303.4			−0.851652			−0.425826	−	0.904805i	$-0.640016\pi$
$773$	−18303.4			−0.851652			−0.425826

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:	\( N \)	\(=\)	\( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	312.m (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.800675 - 2.71273i) q^{2} +3.00000i q^{3} +(-6.71784 + 4.34403i) q^{4} +12.1272 q^{5} +(8.13820 - 2.40203i) q^{6} +21.1519i q^{7} +(17.1630 + 14.7455i) q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q+(-0.800675 - 2.71273i) q^{2} +3.00000i q^{3} +(-6.71784 + 4.34403i) q^{4} +12.1272 q^{5} +(8.13820 - 2.40203i) q^{6} +21.1519i q^{7} +(17.1630 + 14.7455i) q^{8} -9.00000 q^{9} +(-9.70993 - 32.8978i) q^{10} +16.0069 q^{11} +(-13.0321 - 20.1535i) q^{12} +(-36.8012 + 29.0288i) q^{13} +(57.3793 - 16.9358i) q^{14} +36.3815i q^{15} +(26.2587 - 58.3651i) q^{16} +45.8045 q^{17} +(7.20608 + 24.4146i) q^{18} -117.007 q^{19} +(-81.4684 + 52.6809i) q^{20} -63.4556 q^{21} +(-12.8163 - 43.4224i) q^{22} -97.3972 q^{23} +(-44.2366 + 51.4890i) q^{24} +22.0685 q^{25} +(108.213 + 76.5891i) q^{26} -27.0000i q^{27} +(-91.8844 - 142.095i) q^{28} -90.0375i q^{29} +(98.6934 - 29.1298i) q^{30} +151.350i q^{31} +(-179.354 - 24.5015i) q^{32} +48.0206i q^{33} +(-36.6745 - 124.255i) q^{34} +256.512i q^{35} +(60.4606 - 39.0963i) q^{36} -66.3382 q^{37} +(93.6845 + 317.409i) q^{38} +(-87.0865 - 110.404i) q^{39} +(208.139 + 178.822i) q^{40} +112.250i q^{41} +(50.8073 + 172.138i) q^{42} +234.339i q^{43} +(-107.532 + 69.5345i) q^{44} -109.145 q^{45} +(77.9835 + 264.213i) q^{46} +580.433i q^{47} +(175.095 + 78.7762i) q^{48} -104.401 q^{49} +(-17.6697 - 59.8660i) q^{50} +137.414i q^{51} +(121.122 - 354.877i) q^{52} -241.092i q^{53} +(-73.2438 + 21.6182i) q^{54} +194.118 q^{55} +(-311.896 + 363.029i) q^{56} -351.021i q^{57} +(-244.248 + 72.0908i) q^{58} +313.006 q^{59} +(-158.043 - 244.405i) q^{60} -334.114i q^{61} +(410.572 - 121.182i) q^{62} -190.367i q^{63} +(77.1380 + 506.156i) q^{64} +(-446.295 + 352.038i) q^{65} +(130.267 - 38.4489i) q^{66} -315.258 q^{67} +(-307.707 + 198.976i) q^{68} -292.192i q^{69} +(695.849 - 205.383i) q^{70} +503.306i q^{71} +(-154.467 - 132.710i) q^{72} +757.602i q^{73} +(53.1154 + 179.958i) q^{74} +66.2055i q^{75} +(786.034 - 508.282i) q^{76} +338.575i q^{77} +(-229.767 + 324.640i) q^{78} +1134.30 q^{79} +(318.444 - 707.804i) q^{80} +81.0000 q^{81} +(304.503 - 89.8754i) q^{82} -822.684 q^{83} +(426.284 - 275.653i) q^{84} +555.480 q^{85} +(635.698 - 187.629i) q^{86} +270.113 q^{87} +(274.726 + 236.030i) q^{88} -803.525i q^{89} +(87.3894 + 296.080i) q^{90} +(-614.014 - 778.413i) q^{91} +(654.299 - 423.097i) q^{92} -454.049 q^{93} +(1574.56 - 464.738i) q^{94} -1418.96 q^{95} +(73.5044 - 538.061i) q^{96} +750.474i q^{97} +(83.5911 + 283.211i) q^{98} -144.062 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 756 q^{9}+O(q^{10}) \) 84 * q - 756 * q^9	\( 84 q - 756 q^{9} - 36 q^{10} + 12 q^{12} - 208 q^{14} - 148 q^{16} - 104 q^{17} + 620 q^{22} + 2188 q^{25} + 444 q^{26} - 204 q^{30} - 40 q^{38} - 1924 q^{40} + 192 q^{42} + 624 q^{48} - 3396 q^{49} - 1292 q^{52} - 1616 q^{55} + 608 q^{56} - 2120 q^{62} - 2856 q^{64} + 696 q^{65} - 396 q^{66} - 2536 q^{68} - 3936 q^{74} - 156 q^{78} + 3160 q^{79} + 6804 q^{81} + 4276 q^{82} - 2088 q^{87} + 1780 q^{88} + 324 q^{90} + 4792 q^{92} - 860 q^{94} + 2480 q^{95}+O(q^{100}) \) 84 * q - 756 * q^9 - 36 * q^10 + 12 * q^12 - 208 * q^14 - 148 * q^16 - 104 * q^17 + 620 * q^22 + 2188 * q^25 + 444 * q^26 - 204 * q^30 - 40 * q^38 - 1924 * q^40 + 192 * q^42 + 624 * q^48 - 3396 * q^49 - 1292 * q^52 - 1616 * q^55 + 608 * q^56 - 2120 * q^62 - 2856 * q^64 + 696 * q^65 - 396 * q^66 - 2536 * q^68 - 3936 * q^74 - 156 * q^78 + 3160 * q^79 + 6804 * q^81 + 4276 * q^82 - 2088 * q^87 + 1780 * q^88 + 324 * q^90 + 4792 * q^92 - 860 * q^94 + 2480 * q^95

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