LMFDB - Embedded newform 312.4.m.a.181.51

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [312,4,Mod(181,312)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			181.51
Character	$\chi$	$=$	312.181
Dual form			312.4.m.a.181.52

$q$-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} +(-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} +(-49.2817 - 123.074i) 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} +(-373.327 + 35.1454i) 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} +(-369.223 + 147.845i) 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} - 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}+ \cdots + 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

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	$-0.682463\pi$
$5$	−12.1272			−1.08469			−0.542344	+	0.840157i	$0.682463\pi$
$6$	−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	$-0.570402\pi$
$11$	−16.0069			−0.438751			−0.219375	+	0.975641i	$0.570402\pi$
$12$	−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	$-0.250318\pi$
$19$	117.007			1.41280			0.706401	+	0.707812i	$0.250318\pi$
$20$	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
$26$	−49.2817	−	123.074i	−0.371728	−	0.928342i
$27$			27.0000i			0.192450i
$28$	91.8844	−	142.095i	0.620161	−	0.959049i
$29$			90.0375i			0.576536i	0.957550	+	0.288268i	$0.0930794\pi$
$29$			90.0375i			0.576536i	−0.957550	+	0.288268i	$0.906921\pi$
$30$	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	$-0.452917\pi$
$37$	66.3382			0.294755			0.147378	+	0.989080i	$0.452917\pi$
$38$	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	$-0.863593\pi$
$43$		−	234.339i		−	0.831077i	0.909576	−	0.415538i	$-0.136407\pi$
$44$	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
$52$	−373.327	+	35.1454i	−0.995598	+	0.0937269i
$53$			241.092i			0.624841i	0.949944	+	0.312420i	$0.101140\pi$
$53$			241.092i			0.624841i	−0.949944	+	0.312420i	$0.898860\pi$
$54$	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	$-0.612236\pi$
$59$	−313.006			−0.690677			−0.345339	+	0.938478i	$0.612236\pi$
$60$	158.043	−	244.405i	0.340054	−	0.525877i
$61$			334.114i			0.701293i	0.936508	+	0.350647i	$0.114038\pi$
$61$			334.114i			0.701293i	−0.936508	+	0.350647i	$0.885962\pi$
$62$	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	$-0.407201\pi$
$67$	315.258			0.574848			0.287424	+	0.957803i	$0.407201\pi$
$68$	−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
$78$	−369.223	+	147.845i	−0.535978	+	0.214617i
$79$	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	$-0.316915\pi$
$83$	822.684			1.08797			0.543984	+	0.839096i	$0.316915\pi$
$84$	−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	$-0.927178\pi$
$101$		−	460.391i		−	0.453570i	0.973945	−	0.226785i	$-0.0728215\pi$
$102$	−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	$0.296897\pi$
$104$	−203.573	+	1040.88i	−0.191942	+	0.981406i
$105$	−769.537			−0.715230
$106$	654.019	+	193.037i	0.599282	+	0.176881i
$107$			488.541i			0.441393i	0.975343	+	0.220696i	$0.0708330\pi$
$107$			488.541i			0.441393i	−0.975343	+	0.220696i	$0.929167\pi$
$108$	117.289	−	181.382i	0.104501	−	0.161606i
$109$	−703.953			−0.618591			−0.309296	−	0.950966i	$-0.600093\pi$
$109$	−703.953			−0.618591			−0.309296	+	0.950966i	$0.600093\pi$
$110$	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
$130$	597.648	+	1492.55i	0.403209	+	1.00696i
$131$		−	833.576i		−	0.555953i	−0.960588	−	0.277977i	$-0.910336\pi$
$131$		−	833.576i		−	0.555953i	0.960588	−	0.277977i	$-0.0896637\pi$
$132$	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	$0.270667\pi$
$139$			2463.08i			1.50299i	−0.659739	+	0.751495i	$0.729333\pi$
$140$	−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	$-0.807285\pi$
$149$	−2991.00			−1.64451			−0.822257	+	0.569117i	$0.807285\pi$
$150$	−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
$156$	105.436	+	1119.98i	0.0541132	+	0.574809i
$157$			1097.78i			0.558042i	0.960285	+	0.279021i	$0.0900099\pi$
$157$			1097.78i			0.558042i	−0.960285	+	0.279021i	$0.909990\pi$
$158$	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	$-0.671796\pi$
$163$	−2138.86			−1.02778			−0.513891	+	0.857856i	$0.671796\pi$
$164$	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	$-0.881511\pi$
$173$		−	1655.20i		−	0.727413i	0.931514	−	0.363706i	$-0.118489\pi$
$174$	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	$0.137501\pi$
$179$			2005.28i			0.837326i	−0.908142	+	0.418663i	$0.862499\pi$
$180$	−733.216	−	474.128i	−0.303615	−	0.196330i
$181$			1629.54i			0.669184i	0.942363	+	0.334592i	$0.108599\pi$
$181$			1629.54i			0.669184i	−0.942363	+	0.334592i	$0.891401\pi$
$182$	2603.25	−	1042.40i	1.06025	−	0.424548i
$183$	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	$-0.619315\pi$
$197$	−2024.67			−0.732244			−0.366122	+	0.930567i	$0.619315\pi$
$198$	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
$208$	2660.62	+	1385.64i	0.886927	+	0.461909i
$209$	−1872.92			−0.619868
$210$	−616.149	+	2087.55i	−0.202468	+	0.685974i
$211$		−	2849.73i		−	0.929780i	−0.885368	−	0.464890i	$-0.846094\pi$
$211$		−	2849.73i		−	0.929780i	0.885368	−	0.464890i	$-0.153906\pi$
$212$	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	$-0.696402\pi$
$227$	−3957.76			−1.15720			−0.578602	+	0.815610i	$0.696402\pi$
$228$	−1524.85	+	2358.10i	−0.442919	+	0.684952i
$229$	−1499.02			−0.432569			−0.216284	−	0.976330i	$-0.569394\pi$
$229$	−1499.02			−0.432569			−0.216284	+	0.976330i	$0.569394\pi$
$230$	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	$0.321816\pi$
$234$	443.535	+	1107.67i	0.123909	+	0.309447i
$235$		−	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	$-0.789617\pi$
$251$		−	4882.12i		−	1.22772i	0.789416	−	0.613858i	$-0.210383\pi$
$252$	−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
$260$	4527.40	−	426.215i	1.07991	−	0.101664i
$261$		−	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	$-0.841940\pi$
$269$		−	4203.72i		−	0.952808i	0.879226	−	0.476404i	$-0.158060\pi$
$270$	−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	$0.414292\pi$
$277$			8888.17i			1.92794i	−0.266019	+	0.963968i	$0.585708\pi$
$278$	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	$-0.859106\pi$
$283$		−	4078.29i		−	0.856640i	0.903627	−	0.428320i	$-0.140894\pi$
$284$	2186.38	−	3381.13i	0.456823	−	0.706455i
$285$			4256.89i			0.884760i
$286$	788.846	+	1970.04i	0.163096	+	0.407310i
$287$	−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	$-0.550677\pi$
$293$	−1590.21			−0.317069			−0.158535	+	0.987353i	$0.550677\pi$
$294$	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	$-0.296329\pi$
$307$	6423.44			1.19415			0.597077	+	0.802184i	$0.296329\pi$
$308$	−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	$0.399097\pi$
$312$	3122.63	+	610.719i	0.566615	+	0.110818i
$313$	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	$-0.694624\pi$
$317$	−6479.78			−1.14808			−0.574039	+	0.818828i	$0.694624\pi$
$318$	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	$-0.244664\pi$
$331$	8657.99			1.43772			0.718861	+	0.695154i	$0.244664\pi$
$332$	−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	$0.243546\pi$
$338$	−5386.33	−	3098.69i	−0.866798	−	0.498659i
$339$			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	$-0.962047\pi$
$347$		−	1537.77i		−	0.237901i	0.992900	−	0.118951i	$-0.0379531\pi$
$348$	−1814.57	−	1173.38i	−0.279515	−	0.180746i
$349$	−8471.05			−1.29927			−0.649634	−	0.760247i	$-0.725078\pi$
$349$	−8471.05			−1.29927			−0.649634	+	0.760247i	$0.725078\pi$
$350$	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
$364$	−743.391	−	7896.55i	−0.107045	−	1.13707i
$365$		−	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	$-0.895797\pi$
$373$		−	4632.74i		−	0.643094i	0.946894	−	0.321547i	$-0.104203\pi$
$374$	−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	$-0.317490\pi$
$379$	8005.02			1.08494			0.542468	+	0.840077i	$0.317490\pi$
$380$	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	$0.351303\pi$
$389$			13700.5i			1.78571i	−0.450339	+	0.892857i	$0.648697\pi$
$390$	4477.64	−	1792.94i	0.581369	−	0.232793i
$391$	−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	$-0.628278\pi$
$397$	−6204.37			−0.784354			−0.392177	+	0.919890i	$0.628278\pi$
$398$	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
$416$	5889.17	−	6108.11i	0.694087	−	0.719891i
$417$	7389.23			0.867751
$418$	−1499.60	+	5080.72i	−0.175473	+	0.594512i
$419$			3615.54i			0.421553i	0.977534	+	0.210776i	$0.0675992\pi$
$419$			3615.54i			0.421553i	−0.977534	+	0.210776i	$0.932401\pi$
$420$	5169.63	+	3342.90i	0.600600	+	0.388373i
$421$	−9792.46			−1.13362			−0.566811	−	0.823848i	$-0.691823\pi$
$421$	−9792.46			−1.13362			−0.566811	+	0.823848i	$0.691823\pi$
$422$	−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
$442$	−2257.32	−	5637.37i	−0.242919	−	0.606656i
$443$		−	6678.46i		−	0.716260i	−0.933672	−	0.358130i	$-0.883414\pi$
$443$		−	6678.46i		−	0.716260i	0.933672	−	0.358130i	$-0.116586\pi$
$444$	−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	$-0.281217\pi$
$461$	12560.1			1.26895			0.634473	+	0.772945i	$0.281217\pi$
$462$	−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	$-0.825242\pi$
$467$		−	10533.0i		−	1.04370i	0.853038	−	0.521849i	$-0.174758\pi$
$468$	3359.94	−	316.309i	0.331866	−	0.0312423i
$469$			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	$0.460174\pi$
$491$			21589.6i			1.98437i	−0.124791	+	0.992183i	$0.539826\pi$
$492$	−2262.22	−	1462.85i	−0.207295	−	0.134045i
$493$			4124.13i			0.376757i
$494$	−5766.30	−	14400.6i	−0.525178	−	1.31156i
$495$	−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	$-0.217819\pi$
$499$	17274.5			1.54973			0.774863	+	0.632130i	$0.217819\pi$
$500$	−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	$-0.375425\pi$
$509$	8760.81			0.762900			0.381450	+	0.924389i	$0.375425\pi$
$510$	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
$520$	2468.77	−	12622.9i	0.208197	−	1.06452i
$521$	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	$-0.783287\pi$
$523$		−	15056.8i		−	1.25887i	0.777054	−	0.629434i	$-0.216713\pi$
$524$	−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	$-0.533389\pi$
$541$	−2634.99			−0.209403			−0.104702	+	0.994504i	$0.533389\pi$
$542$	−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
$546$	−3127.20	−	7809.76i	−0.245113	−	0.612137i
$547$			2007.56i			0.156923i	0.996917	+	0.0784616i	$0.0250008\pi$
$547$			2007.56i			0.156923i	−0.996917	+	0.0784616i	$0.974999\pi$
$548$	−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	$-0.305598\pi$
$557$	15077.3			1.14694			0.573468	+	0.819228i	$0.305598\pi$
$558$	−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	$0.176105\pi$
$563$			14038.8i			1.05091i	−0.850821	+	0.525455i	$0.823895\pi$
$564$	−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	$0.0804152\pi$
$571$			6820.92i			0.499906i	−0.968258	+	0.249953i	$0.919585\pi$
$572$	5975.80	−	562.569i	0.436819	−	0.0411227i
$573$		−	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	$-0.632919\pi$
$587$	−11535.3			−0.811093			−0.405547	+	0.914074i	$0.632919\pi$
$588$	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
$598$	4799.90	+	11987.1i	0.328231	+	0.819714i
$599$	−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	$-0.507455\pi$
$613$	−710.858			−0.0468373			−0.0234187	+	0.999726i	$0.507455\pi$
$614$	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	$-0.717499\pi$
$619$	−19446.3			−1.26270			−0.631351	+	0.775497i	$0.717499\pi$
$620$	−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
$624$	4156.93	−	7981.86i	0.266683	−	0.512068i
$625$	−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	$-0.371391\pi$
$643$	12820.0			0.786268			0.393134	+	0.919481i	$0.371391\pi$
$644$	−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
$650$	−1087.57	−	2716.07i	−0.0656279	−	0.163897i
$651$			9603.99i			0.578203i
$652$	14368.5	+	9291.28i	0.863058	+	0.558090i
$653$		−	23782.4i		−	1.42523i	−0.701553	−	0.712617i	$-0.747510\pi$
$653$		−	23782.4i		−	1.42523i	0.701553	−	0.712617i	$-0.252490\pi$
$654$	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	$0.298785\pi$
$659$			27296.5i			1.61354i	−0.590868	+	0.806768i	$0.701215\pi$
$660$	−2529.77	+	3912.17i	−0.149199	+	0.230729i
$661$	−27338.9			−1.60871			−0.804357	−	0.594147i	$-0.797490\pi$
$661$	−27338.9			−1.60871			−0.804357	+	0.594147i	$0.797490\pi$
$662$	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
$676$	−12718.6	+	12130.6i	−0.723636	+	0.690182i
$677$		−	12731.9i		−	0.722787i	−0.932413	−	0.361393i	$-0.882301\pi$
$677$		−	12731.9i		−	0.722787i	0.932413	−	0.361393i	$-0.117699\pi$
$678$	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	$-0.405687\pi$
$683$	10423.4			0.583955			0.291977	+	0.956425i	$0.405687\pi$
$684$	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	$-0.392762\pi$
$691$	12008.8			0.661124			0.330562	+	0.943784i	$0.392762\pi$
$692$	−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	$-0.910641\pi$
$701$		−	10284.3i		−	0.554114i	0.960853	−	0.277057i	$-0.0893591\pi$
$702$	3323.01	−	1330.61i	0.178659	−	0.0715391i
$703$	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	$-0.648135\pi$
$709$	−16944.0			−0.897524			−0.448762	+	0.893651i	$0.648135\pi$
$710$	−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	$0.435419\pi$
$728$	−22016.4	−	4305.95i	−1.12086	−	0.219216i
$729$	−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	$-0.500151\pi$
$733$	−18.8350			−0.000949093			−0.000474547		1.00000i	$0.500151\pi$
$734$	−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	$-0.610854\pi$
$739$	−13711.5			−0.682525			−0.341262	+	0.939968i	$0.610854\pi$
$740$	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
$754$	11081.3	−	4437.20i	0.535223	−	0.214315i
$755$		−	27987.0i		−	1.34907i
$756$	3836.56	+	2480.88i	0.184569	+	0.119350i
$757$		−	29792.5i		−	1.43042i	−0.698911	−	0.715209i	$-0.746332\pi$
$757$		−	29792.5i		−	1.43042i	0.698911	−	0.715209i	$-0.253668\pi$
$758$	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	$-0.359984\pi$
$773$	18303.4			0.851652			0.425826	+	0.904805i	$0.359984\pi$
$774$	5721.28	+	1688.66i	0.265694	+	0.0784208i
$775$			3340.07i			0.154811i
$776$	−11066.1	−	12880.4i	−0.511922	−	0.595849i
$777$	4209.53			0.194358
$778$	37165.8	+	10969.7i	1.71267	+	0.505503i
$779$			13134.0i			0.604074i
$780$	−1278.65	−	13582.2i	−0.0586960	−	0.623488i
$781$		−	8056.36i		−	0.369116i
$782$	−3572.00	+	12102.1i	−0.163343	+	0.553416i
$783$	−2431.01			−0.110954
$784$	−2741.43	−	6093.36i	−0.124883	−	0.277576i
$785$		−	13313.0i		−	0.605302i
$786$	−2002.27	+	6783.80i	−0.0908634	+	0.307850i
$787$	−21435.4			−0.970890			−0.485445	−	0.874267i	$-0.661342\pi$
$787$	−21435.4			−0.970890			−0.485445	+	0.874267i	$0.661342\pi$
$788$	13601.4	+	8795.25i	0.614887	+	0.397612i
$789$		−	17744.6i		−	0.800667i
$790$	−11014.0	+	37316.1i	−0.496027	+	1.68057i
$791$		−	47877.2i		−	2.15211i
$792$	−2472.54	+	2124.27i	−0.110932	+	0.0953064i
$793$	9698.93	+	12295.8i	0.434324	+	0.550613i
$794$	−4967.69	+	16830.8i	−0.222036	+	0.752271i
$795$	−8771.31			−0.391303
$796$	−12291.7	−	7948.32i	−0.547321	−	0.353921i
$797$		−	37587.1i		−	1.67052i	−0.549858	−	0.835258i	$-0.685318\pi$
$797$		−	37587.1i		−	1.67052i	0.549858	−	0.835258i	$-0.314682\pi$
$798$	5944.80	−	20141.3i	0.263714	−	0.893478i
$799$			26586.5i			1.17717i
$800$	3958.06	−	540.711i	0.174923	−	0.0238963i
$801$			7231.72i			0.319002i
$802$	−9161.01	−	2703.91i	−0.403350	−	0.119050i
$803$		−	12126.8i		−	0.532935i
$804$	−4108.47	+	6353.55i	−0.180217	+	0.278697i
$805$			24983.6i			1.09386i
$806$	18627.3	−	7458.78i	0.814043	−	0.325961i
$807$	−12611.2			−0.550104
$808$	6788.71	+	7901.69i	0.295577	+	0.344035i
$809$	−16820.1			−0.730980			−0.365490	−	0.930815i	$-0.619099\pi$
$809$	−16820.1			−0.730980			−0.365490	+	0.930815i	$0.619099\pi$
$810$	−786.504	+	2664.72i	−0.0341172	+	0.115591i
$811$	1522.68			0.0659291			0.0329646	−	0.999457i	$-0.489505\pi$
$811$	1522.68			0.0659291			0.0329646	+	0.999457i	$0.489505\pi$
$812$	12793.9	+	8273.04i	0.552927	+	0.357545i
$813$	−8278.40			−0.357117
$814$	−850.211	+	2880.57i	−0.0366092	+	0.124034i
$815$	25938.3			1.11482
$816$	8020.15	−	3608.30i	0.344070	−	0.154799i
$817$		−	27419.2i		−	1.17415i
$818$	−14741.4	−	4351.00i	−0.630100	−	0.185977i
$819$	−5526.12	−	7005.72i	−0.235773	−	0.298901i
$820$	−5913.41	+	9144.80i	−0.251836	+	0.389451i
$821$	12103.0			0.514490			0.257245	−	0.966346i	$-0.417185\pi$
$821$	12103.0			0.514490			0.257245	+	0.966346i	$0.417185\pi$
$822$	−2431.91	+	8239.46i	−0.103191	+	0.349616i
$823$	30802.3			1.30462			0.652308	−	0.757954i	$-0.273801\pi$
$823$	30802.3			1.30462			0.652308	+	0.757954i	$0.273801\pi$
$824$	−21373.1	+	18362.6i	−0.903599	+	0.776324i
$825$			1059.74i			0.0447219i
$826$	−17960.1	−	5301.00i	−0.756551	−	0.223299i
$827$	1901.88			0.0799697			0.0399848	−	0.999200i	$-0.487269\pi$
$827$	1901.88			0.0799697			0.0399848	+	0.999200i	$0.487269\pi$
$828$	−5888.69	−	3807.87i	−0.247157	−	0.159822i
$829$			27753.6i			1.16275i	0.813635	+	0.581376i	$0.197485\pi$
$829$			27753.6i			1.16275i	−0.813635	+	0.581376i	$0.802515\pi$
$830$	−7988.20	+	27064.5i	−0.334066	+	1.13183i
$831$	26664.5			1.11309
$832$	−11854.3	−	20866.4i	−0.493961	−	0.869484i
$833$	−4782.03			−0.198905
$834$	5916.37	−	20045.0i	0.245644	−	0.832257i
$835$		−	28392.4i		−	1.17672i
$836$	12581.9	+	8136.01i	0.520521	+	0.336591i
$837$	−4086.45			−0.168755
$838$	9807.99	+	2894.87i	0.404310	+	0.119334i
$839$			3004.84i			0.123646i	0.998087	+	0.0618228i	$0.0196914\pi$
$839$			3004.84i			0.123646i	−0.998087	+	0.0618228i	$0.980309\pi$
$840$	13207.6	−	11347.2i	0.542505	−	0.466092i
$841$	16282.2			0.667606
$842$	−7840.58	+	26564.3i	−0.320907	+	1.08725i
$843$	12152.5			0.496505
$844$	−12379.3	+	19144.0i	−0.504875	+	0.780764i
$845$	−6204.91	+	25910.8i	−0.252610	+	1.05486i
$846$	−14171.0	−	4182.65i	−0.575899	−	0.169979i
$847$		−	22733.6i		−	0.922237i
$848$	−14071.4	+	6330.77i	−0.569826	+	0.256368i
$849$	−12234.9			−0.494582
$850$	809.353	−	2742.13i	0.0326595	−	0.110652i
$851$	−6461.16			−0.260265
$852$	−10143.4	−	6559.14i	−0.407872	−	0.263747i
$853$	−16104.2			−0.646422			−0.323211	−	0.946327i	$-0.604762\pi$
$853$	−16104.2			−0.646422			−0.323211	+	0.946327i	$0.604762\pi$
$854$	−5658.47	+	19171.2i	−0.226732	+	0.768180i
$855$	12770.7			0.510816
$856$	−7203.80	−	8384.83i	−0.287641	−	0.334799i
$857$	12084.0			0.481659			0.240829	−	0.970567i	$-0.422581\pi$
$857$	12084.0			0.481659			0.240829	+	0.970567i	$0.422581\pi$
$858$	5910.11	−	2366.54i	0.235161	−	0.0941635i
$859$		−	33789.7i		−	1.34213i	−0.741398	−	0.671066i	$-0.765837\pi$
$859$		−	33789.7i		−	1.34213i	0.741398	−	0.671066i	$-0.234163\pi$
$860$	12345.2	−	19091.2i	0.489496	−	0.756982i
$861$			7122.86i			0.281935i
$862$	22181.9	+	6547.07i	0.876470	+	0.258694i
$863$		−	19465.7i		−	0.767808i	−0.923373	−	0.383904i	$-0.874579\pi$
$863$		−	19465.7i		−	0.767808i	0.923373	−	0.383904i	$-0.125421\pi$
$864$	661.539	+	4842.54i	0.0260486	+	0.190679i
$865$			20072.9i			0.789016i
$866$	−11567.8	+	39192.4i	−0.453915	+	1.53789i
$867$			8444.84i			0.330798i
$868$	21506.0	+	13906.7i	0.840970	+	0.543806i
$869$	−18156.7			−0.708772
$870$	−2622.77	+	8886.11i	−0.102207	+	0.346284i
$871$	11601.9	−	9151.56i	0.451336	−	0.356015i
$872$	12081.9	−	10380.2i	0.469205	−	0.403116i
$873$		−	6754.26i		−	0.261852i
$874$	−9124.61	+	30914.7i	−0.353140	+	1.19646i
$875$			26403.2i			1.02010i
$876$	−15268.3	−	9873.15i	−0.588892	−	0.380802i
$877$	−25080.8			−0.965701			−0.482850	−	0.875703i	$-0.660399\pi$
$877$	−25080.8			−0.965701			−0.482850	+	0.875703i	$0.660399\pi$
$878$	−11869.1	+	40213.3i	−0.456223	+	1.54571i
$879$			4770.64i			0.183060i
$880$	5097.30	+	11329.7i	0.195261	+	0.434006i
$881$	−44550.8			−1.70369			−0.851847	−	0.523791i	$-0.824517\pi$
$881$	−44550.8			−1.70369			−0.851847	+	0.523791i	$0.824517\pi$
$882$	752.320	−	2548.90i	0.0287210	−	0.0973084i
$883$			33955.9i			1.29412i	0.762439	+	0.647060i	$0.224002\pi$
$883$			33955.9i			1.29412i	−0.762439	+	0.647060i	$0.775998\pi$
$884$	−17100.1	+	1609.82i	−0.650607	+	0.0612490i
$885$		−	11387.7i		−	0.432533i
$886$	−18116.9	−	5347.28i	−0.686962	−	0.202760i
$887$	−11017.1			−0.417045			−0.208522	−	0.978018i	$-0.566865\pi$
$887$	−11017.1			−0.417045			−0.208522	+	0.978018i	$0.566865\pi$
$888$	2934.58	+	3415.69i	0.110899	+	0.129080i
$889$		−	32569.0i		−	1.22872i
$890$	26434.2	+	7802.17i	0.995591	+	0.293853i
$891$	−1296.56			−0.0487501
$892$	5963.31	−	9221.97i	0.223841	−	0.346160i
$893$			67914.7i			2.54499i
$894$	24341.4	+	7184.46i	0.910623	+	0.268775i
$895$		−	24318.3i		−	0.908238i
$896$	12998.3	−	27736.5i	0.484644	−	1.03416i
$897$	8481.98	+	10753.0i	0.315725	+	0.400259i
$898$	37091.0	+	10947.6i	1.37833	+	0.406821i
$899$	−13627.2			−0.505552
$900$	1334.27	+	862.797i	0.0494176	+	0.0319555i
$901$			11043.1i			0.408324i
$902$	−4874.15	−	1438.63i	−0.179924	−	0.0531053i
$903$		−	14870.1i		−	0.548002i
$904$	38848.5	−	33376.5i	1.42929	−	1.22797i
$905$		−	19761.7i		−	0.725856i
$906$	5543.36	−	18781.2i	0.203274	−	0.688703i
$907$			8138.50i			0.297943i	0.988841	+	0.148972i	$0.0475963\pi$
$907$			8138.50i			0.297943i	−0.988841	+	0.148972i	$0.952404\pi$
$908$	26587.6	+	17192.6i	0.971739	+	0.628367i
$909$			4143.52i			0.151190i
$910$	−31570.1	+	12641.4i	−1.15004	+	0.460502i
$911$	−6633.32			−0.241242			−0.120621	−	0.992699i	$-0.538489\pi$
$911$	−6633.32			−0.241242			−0.120621	+	0.992699i	$0.538489\pi$
$912$	20487.3	−	9217.36i	0.743864	−	0.334668i
$913$	−13168.6			−0.477346
$914$	−22933.5	−	6768.93i	−0.829949	−	0.244963i
$915$	−12155.6			−0.439181
$916$	10070.2	+	6511.81i	0.363241	+	0.234887i
$917$	17631.7			0.634950
$918$	3354.90	+	990.213i	0.120619	+	0.0356012i
$919$	21612.6			0.775770			0.387885	−	0.921708i	$-0.373206\pi$
$919$	21612.6			0.775770			0.387885	+	0.921708i	$0.373206\pi$
$920$	−20272.1	+	17416.7i	−0.726470	+	0.624145i
$921$		−	19270.3i		−	0.689445i
$922$	10056.6	−	34072.3i	0.359215	−	1.21704i
$923$	14610.4	+	18522.3i	0.521026	+	0.660528i
$924$	6823.48	+	4412.35i	0.242939	+	0.157095i
$925$	1463.99			0.0520385
$926$	−39445.4	−	11642.5i	−1.39984	−	0.413170i
$927$	−11207.7			−0.397096
$928$	2206.05	+	16148.5i	0.0780357	+	0.571231i
$929$			1942.93i			0.0686172i	0.999411	+	0.0343086i	$0.0109229\pi$
$929$			1942.93i			0.0686172i	−0.999411	+	0.0343086i	$0.989077\pi$
$930$	−4408.79	+	14937.2i	−0.155451	+	0.526679i
$931$	−12215.6			−0.430022
$932$	−25374.0	−	16407.9i	−0.891795	−	0.576672i
$933$		−	10257.6i		−	0.359936i
$934$	−28573.1	−	8433.47i	−1.00101	−	0.295451i
$935$	8891.50			0.310998
$936$	1832.16	−	9367.88i	0.0639807	−	0.327135i
$937$	−54173.2			−1.88875			−0.944376	−	0.328868i	$-0.893333\pi$
$937$	−54173.2			−1.88875			−0.944376	+	0.328868i	$0.893333\pi$
$938$	18089.3	+	5339.13i	0.629675	+	0.185851i
$939$		−	26494.3i		−	0.920776i
$940$	−30577.7	+	47287.0i	−1.06100	+	1.64078i
$941$	−16100.0			−0.557753			−0.278876	−	0.960327i	$-0.589962\pi$
$941$	−16100.0			−0.557753			−0.278876	+	0.960327i	$0.589962\pi$
$942$	2636.90	−	8933.98i	0.0912048	−	0.309007i
$943$		−	10932.8i		−	0.377540i
$944$	−8219.15	−	18268.6i	−0.283380	−	0.629866i
$945$	6925.83			0.238410
$946$	10175.5	+	3003.36i	0.349720	+	0.103222i
$947$	20297.4			0.696492			0.348246	−	0.937403i	$-0.386777\pi$
$947$	20297.4			0.696492			0.348246	+	0.937403i	$0.386777\pi$
$948$	−14782.4	+	22860.2i	−0.506444	+	0.783192i
$949$	21992.3	+	27880.6i	0.752266	+	0.953682i
$950$	2067.48	−	7004.73i	0.0706083	−	0.239225i
$951$			19439.3i			0.662843i
$952$	−14286.2	−	16628.4i	−0.486365	−	0.566102i
$953$	15564.2			0.529040			0.264520	−	0.964380i	$-0.414787\pi$
$953$	15564.2			0.529040			0.264520	+	0.964380i	$0.414787\pi$
$954$	−5886.17	−	1737.33i	−0.199761	−	0.0589603i
$955$	−57287.4			−1.94113
$956$	−21376.8	+	33058.2i	−0.723195	+	1.11839i
$957$	−4323.66			−0.146044
$958$	25830.8	+	7624.06i	0.871142	+	0.257121i
$959$	21415.0			0.721093
$960$	18414.7	+	2806.40i	0.619097	+	0.0943501i
$961$	6884.23			0.231084
$962$	−3269.26	−	8164.54i	−0.109569	−	0.273633i
$963$		−	4396.87i		−	0.147131i
$964$	−6372.96	+	9855.47i	−0.212924	+	0.329277i
$965$			129.573i			0.00432238i
$966$	−4948.49	+	16765.8i	−0.164819	+	0.558415i
$967$			48814.5i			1.62334i	0.584116	+	0.811670i	$0.301441\pi$
$967$			48814.5i			1.62334i	−0.584116	+	0.811670i	$0.698559\pi$
$968$	18446.5	−	15848.2i	0.612491	−	0.526220i
$969$		−	16078.3i		−	0.533035i
$970$	−24688.9	−	7287.05i	−0.817231	−	0.241209i
$971$			661.961i			0.0218778i	0.999940	+	0.0109389i	$0.00348203\pi$
$971$			661.961i			0.0218778i	−0.999940	+	0.0109389i	$0.996518\pi$
$972$	−1055.60	+	1632.43i	−0.0348337	+	0.0538687i
$973$	−52098.7			−1.71655
$974$	−40945.9	−	12085.4i	−1.34701	−	0.397577i
$975$	−1921.87	−	2436.44i	−0.0631273	−	0.0800293i
$976$	−19500.6	+	8773.40i	−0.639547	+	0.287735i
$977$			3254.29i			0.106565i	0.998579	+	0.0532825i	$0.0169684\pi$
$977$			3254.29i			0.106565i	−0.998579	+	0.0532825i	$0.983032\pi$
$978$	17406.5	+	5137.59i	0.569118	+	0.167978i
$979$			12861.9i			0.419887i
$980$	−8505.37	−	5499.93i	−0.277239	−	0.179274i
$981$	6335.57			0.206197
$982$	58566.7	+	17286.2i	1.90320	+	0.561737i
$983$			9245.76i			0.299994i	0.988686	+	0.149997i	$0.0479264\pi$
$983$			9245.76i			0.299994i	−0.988686	+	0.149997i	$0.952074\pi$
$984$	−5779.62	+	4965.54i	−0.187244	+	0.160870i
$985$	24553.6			0.794256
$986$	11187.7	+	3302.09i	0.361346	+	0.106653i
$987$			36831.7i			1.18781i
$988$	−43681.8	+	4112.26i	−1.40658	+	0.132417i
$989$			22823.9i			0.733831i
$990$	−1398.83	+	4739.32i	−0.0449069	+	0.152147i
$991$	−36969.4			−1.18504			−0.592518	−	0.805557i	$-0.701866\pi$
$991$	−36969.4			−1.18504			−0.592518	+	0.805557i	$0.701866\pi$
$992$	3708.29	+	27145.1i	0.118688	+	0.868809i
$993$		−	25974.0i		−	0.830069i
$994$	−8523.87	+	28879.4i	−0.271993	+	0.921527i
$995$	−22189.2			−0.706980
$996$	−10721.3	+	16580.0i	−0.341082	+	0.527466i
$997$			17296.3i			0.549428i	0.961526	+	0.274714i	$0.0885833\pi$
$997$			17296.3i			0.549428i	−0.961526	+	0.274714i	$0.911417\pi$
$998$	13831.3	−	46861.1i	0.438698	−	1.48634i
$999$			1791.13i			0.0567256i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	312.4.m.a.181.51	yes	84
4.3	odd	2		1248.4.m.a.337.63		84
8.3	odd	2		1248.4.m.a.337.62		84
8.5	even	2	inner	312.4.m.a.181.33	✓	84
13.12	even	2	inner	312.4.m.a.181.34	yes	84
52.51	odd	2		1248.4.m.a.337.64		84
104.51	odd	2		1248.4.m.a.337.61		84
104.77	even	2	inner	312.4.m.a.181.52	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.4.m.a.181.33	✓	84	8.5	even	2	inner
312.4.m.a.181.34	yes	84	13.12	even	2	inner
312.4.m.a.181.51	yes	84	1.1	even	1	trivial
312.4.m.a.181.52	yes	84	104.77	even	2	inner
1248.4.m.a.337.61		84	104.51	odd	2
1248.4.m.a.337.62		84	8.3	odd	2
1248.4.m.a.337.63		84	4.3	odd	2
1248.4.m.a.337.64		84	52.51	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 312 = 2^{3} \cdot 3 \cdot 13 \)
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} +(-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} +(-49.2817 - 123.074i) 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} +(-373.327 + 35.1454i) 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} +(-369.223 + 147.845i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 756 q^{9} - 36 q^{10} + 12 q^{12} - 208 q^{14} - 148 q^{16} - 104 q^{17} + 620 q^{22} + 2188 q^{25} + 444 q^{26} - 204 q^{30} - 40 q^{38} - 1924 q^{40} + 192 q^{42} + 624 q^{48} - 3396 q^{49} - 1292 q^{52}+ \cdots + 2480 q^{95}+O(q^{100}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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