LMFDB - Embedded newform 392.3.h.a.293.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [392,3,Mod(293,392)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(392, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("392.293");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	392.h (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:	$10.6812263629$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			293.18
Character	$\chi$	$=$	392.293
Dual form			392.3.h.a.293.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.28255 - 1.53463i) q^{2} +3.89635 q^{3} +(-0.710153 - 3.93646i) q^{4} +8.85969 q^{5} +(4.99725 - 5.97944i) q^{6} +(-6.95179 - 3.95886i) q^{8} +6.18155 q^{9} +O(q^{10})$	\(q+(1.28255 - 1.53463i) q^{2} +3.89635 q^{3} +(-0.710153 - 3.93646i) q^{4} +8.85969 q^{5} +(4.99725 - 5.97944i) q^{6} +(-6.95179 - 3.95886i) q^{8} +6.18155 q^{9} +(11.3630 - 13.5963i) q^{10} +3.64596i q^{11} +(-2.76701 - 15.3378i) q^{12} -7.79378 q^{13} +34.5205 q^{15} +(-14.9914 + 5.59097i) q^{16} +10.4749i q^{17} +(7.92812 - 9.48637i) q^{18} -10.7853 q^{19} +(-6.29174 - 34.8758i) q^{20} +(5.59518 + 4.67610i) q^{22} -12.9111 q^{23} +(-27.0866 - 15.4251i) q^{24} +53.4941 q^{25} +(-9.99588 + 11.9605i) q^{26} -10.9817 q^{27} +17.2327i q^{29} +(44.2741 - 52.9760i) q^{30} +30.2297i q^{31} +(-10.6471 + 30.1768i) q^{32} +14.2059i q^{33} +(16.0750 + 13.4345i) q^{34} +(-4.38985 - 24.3334i) q^{36} +39.5843i q^{37} +(-13.8326 + 16.5514i) q^{38} -30.3673 q^{39} +(-61.5907 - 35.0743i) q^{40} -73.6801i q^{41} -40.8501i q^{43} +(14.3521 - 2.58919i) q^{44} +54.7667 q^{45} +(-16.5590 + 19.8137i) q^{46} -41.8030i q^{47} +(-58.4116 + 21.7844i) q^{48} +(68.6087 - 82.0935i) q^{50} +40.8138i q^{51} +(5.53478 + 30.6799i) q^{52} +6.41173i q^{53} +(-14.0845 + 16.8527i) q^{54} +32.3020i q^{55} -42.0232 q^{57} +(26.4457 + 22.1017i) q^{58} +15.9148 q^{59} +(-24.5148 - 135.888i) q^{60} +12.1570 q^{61} +(46.3912 + 38.7709i) q^{62} +(32.6548 + 55.0424i) q^{64} -69.0505 q^{65} +(21.8008 + 18.2197i) q^{66} -7.79739i q^{67} +(41.2339 - 7.43878i) q^{68} -50.3060 q^{69} -41.3627 q^{71} +(-42.9729 - 24.4719i) q^{72} -89.6091i q^{73} +(60.7472 + 50.7687i) q^{74} +208.432 q^{75} +(7.65920 + 42.4557i) q^{76} +(-38.9475 + 46.6025i) q^{78} +70.7950 q^{79} +(-132.819 + 49.5343i) q^{80} -98.4224 q^{81} +(-113.071 - 94.4981i) q^{82} -60.8673 q^{83} +92.8043i q^{85} +(-62.6896 - 52.3921i) q^{86} +67.1446i q^{87} +(14.4338 - 25.3459i) q^{88} -27.0204i q^{89} +(70.2407 - 84.0463i) q^{90} +(9.16883 + 50.8238i) q^{92} +117.785i q^{93} +(-64.1520 - 53.6143i) q^{94} -95.5542 q^{95} +(-41.4847 + 117.579i) q^{96} +3.26608i q^{97} +22.5377i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 4 q^{2} + 8 q^{4} - 20 q^{8} + 64 q^{9}+O(q^{10}) $ 28 * q + 4 * q^2 + 8 * q^4 - 20 * q^8 + 64 * q^9	$ 28 q + 4 q^{2} + 8 q^{4} - 20 q^{8} + 64 q^{9} + 28 q^{15} - 32 q^{16} + 84 q^{18} - 92 q^{22} - 60 q^{23} + 64 q^{25} - 44 q^{30} - 176 q^{32} + 256 q^{36} + 40 q^{39} + 84 q^{44} - 136 q^{46} + 400 q^{50} + 124 q^{57} + 44 q^{58} + 124 q^{60} - 520 q^{64} + 104 q^{65} - 136 q^{71} - 192 q^{72} + 276 q^{74} - 956 q^{78} + 324 q^{79} + 36 q^{81} - 336 q^{86} - 100 q^{88} + 1020 q^{92} - 580 q^{95}+O(q^{100}) $ 28 * q + 4 * q^2 + 8 * q^4 - 20 * q^8 + 64 * q^9 + 28 * q^15 - 32 * q^16 + 84 * q^18 - 92 * q^22 - 60 * q^23 + 64 * q^25 - 44 * q^30 - 176 * q^32 + 256 * q^36 + 40 * q^39 + 84 * q^44 - 136 * q^46 + 400 * q^50 + 124 * q^57 + 44 * q^58 + 124 * q^60 - 520 * q^64 + 104 * q^65 - 136 * q^71 - 192 * q^72 + 276 * q^74 - 956 * q^78 + 324 * q^79 + 36 * q^81 - 336 * q^86 - 100 * q^88 + 1020 * q^92 - 580 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	1.28255	−	1.53463i	0.641273	−	0.767313i
$2$	1.28255	−	1.53463i	0.641273	−	0.767313i
$3$	3.89635			1.29878			0.649392	−	0.760454i	$-0.275024\pi$
$3$	3.89635			1.29878			0.649392	+	0.760454i	$0.275024\pi$
$4$	−0.710153	−	3.93646i	−0.177538	−	0.984114i
$5$	8.85969			1.77194			0.885969	−	0.463744i	$-0.153494\pi$
$5$	8.85969			1.77194			0.885969	+	0.463744i	$0.153494\pi$
$6$	4.99725	−	5.97944i	0.832875	−	0.996574i
$7$		0			0
$7$		0			0
$8$	−6.95179	−	3.95886i	−0.868974	−	0.494858i
$9$	6.18155			0.686839
$10$	11.3630	−	13.5963i	1.13630	−	1.35963i
$11$			3.64596i			0.331451i	0.986172	+	0.165725i	$0.0529965\pi$
$11$			3.64596i			0.331451i	−0.986172	+	0.165725i	$0.947004\pi$
$12$	−2.76701	−	15.3378i	−0.230584	−	1.27815i
$13$	−7.79378			−0.599522			−0.299761	−	0.954014i	$-0.596907\pi$
$13$	−7.79378			−0.599522			−0.299761	+	0.954014i	$0.596907\pi$
$14$		0			0
$15$	34.5205			2.30136
$16$	−14.9914	+	5.59097i	−0.936960	+	0.349436i
$17$			10.4749i			0.616170i	0.951359	+	0.308085i	$0.0996881\pi$
$17$			10.4749i			0.616170i	−0.951359	+	0.308085i	$0.900312\pi$
$18$	7.92812	−	9.48637i	0.440451	−	0.527021i
$19$	−10.7853			−0.567646			−0.283823	−	0.958877i	$-0.591603\pi$
$19$	−10.7853			−0.567646			−0.283823	+	0.958877i	$0.591603\pi$
$20$	−6.29174	−	34.8758i	−0.314587	−	1.74379i
$21$		0			0
$22$	5.59518	+	4.67610i	0.254326	+	0.212550i
$23$	−12.9111			−0.561351			−0.280675	−	0.959803i	$-0.590558\pi$
$23$	−12.9111			−0.561351			−0.280675	+	0.959803i	$0.590558\pi$
$24$	−27.0866	−	15.4251i	−1.12861	−	0.642714i
$25$	53.4941			2.13977
$26$	−9.99588	+	11.9605i	−0.384457	+	0.460021i
$27$	−10.9817			−0.406728
$28$		0			0
$29$			17.2327i			0.594231i	0.954842	+	0.297115i	$0.0960246\pi$
$29$			17.2327i			0.594231i	−0.954842	+	0.297115i	$0.903975\pi$
$30$	44.2741	−	52.9760i	1.47580	−	1.76587i
$31$			30.2297i			0.975151i	0.873081	+	0.487575i	$0.162119\pi$
$31$			30.2297i			0.975151i	−0.873081	+	0.487575i	$0.837881\pi$
$32$	−10.6471	+	30.1768i	−0.332720	+	0.943026i
$33$			14.2059i			0.430483i
$34$	16.0750	+	13.4345i	0.472795	+	0.395133i
$35$		0			0
$36$	−4.38985	−	24.3334i	−0.121940	−	0.675928i
$37$			39.5843i			1.06985i	0.844900	+	0.534924i	$0.179660\pi$
$37$			39.5843i			1.06985i	−0.844900	+	0.534924i	$0.820340\pi$
$38$	−13.8326	+	16.5514i	−0.364016	+	0.435562i
$39$	−30.3673			−0.778649
$40$	−61.5907	−	35.0743i	−1.53977	−	0.876858i
$41$		−	73.6801i		−	1.79707i	−0.438897	−	0.898537i	$-0.644631\pi$
$41$		−	73.6801i		−	1.79707i	0.438897	−	0.898537i	$-0.355369\pi$
$42$		0			0
$43$		−	40.8501i		−	0.950002i	−0.879985	−	0.475001i	$-0.842448\pi$
$43$		−	40.8501i		−	0.950002i	0.879985	−	0.475001i	$-0.157552\pi$
$44$	14.3521	−	2.58919i	0.326185	−	0.0588452i
$45$	54.7667			1.21704
$46$	−16.5590	+	19.8137i	−0.359979	+	0.430732i
$47$		−	41.8030i		−	0.889426i	−0.895673	−	0.444713i	$-0.853306\pi$
$47$		−	41.8030i		−	0.889426i	0.895673	−	0.444713i	$-0.146694\pi$
$48$	−58.4116	+	21.7844i	−1.21691	+	0.453842i
$49$		0			0
$50$	68.6087	−	82.0935i	1.37217	−	1.64187i
$51$			40.8138i			0.800271i
$52$	5.53478	+	30.6799i	0.106438	+	0.589998i
$53$			6.41173i			0.120976i	0.998169	+	0.0604880i	$0.0192657\pi$
$53$			6.41173i			0.120976i	−0.998169	+	0.0604880i	$0.980734\pi$
$54$	−14.0845	+	16.8527i	−0.260824	+	0.312088i
$55$			32.3020i			0.587310i
$56$		0			0
$57$	−42.0232			−0.737249
$58$	26.4457	+	22.1017i	0.455961	+	0.381064i
$59$	15.9148			0.269743			0.134871	−	0.990863i	$-0.456938\pi$
$59$	15.9148			0.269743			0.134871	+	0.990863i	$0.456938\pi$
$60$	−24.5148	−	135.888i	−0.408581	−	2.26481i
$61$	12.1570			0.199294			0.0996472	−	0.995023i	$-0.468229\pi$
$61$	12.1570			0.199294			0.0996472	+	0.995023i	$0.468229\pi$
$62$	46.3912	+	38.7709i	0.748246	+	0.625338i
$63$		0			0
$64$	32.6548	+	55.0424i	0.510231	+	0.860037i
$65$	−69.0505			−1.06232
$66$	21.8008	+	18.2197i	0.330315	+	0.276057i
$67$		−	7.79739i		−	0.116379i	−0.998306	−	0.0581895i	$-0.981467\pi$
$67$		−	7.79739i		−	0.116379i	0.998306	−	0.0581895i	$-0.0185328\pi$
$68$	41.2339	−	7.43878i	0.606381	−	0.109394i
$69$	−50.3060			−0.729073
$70$		0			0
$71$	−41.3627			−0.582574			−0.291287	−	0.956636i	$-0.594083\pi$
$71$	−41.3627			−0.582574			−0.291287	+	0.956636i	$0.594083\pi$
$72$	−42.9729	−	24.4719i	−0.596845	−	0.339888i
$73$		−	89.6091i		−	1.22752i	−0.789492	−	0.613761i	$-0.789656\pi$
$73$		−	89.6091i		−	1.22752i	0.789492	−	0.613761i	$-0.210344\pi$
$74$	60.7472	+	50.7687i	0.820907	+	0.686064i
$75$	208.432			2.77909
$76$	7.65920	+	42.4557i	0.100779	+	0.558628i
$77$		0			0
$78$	−38.9475	+	46.6025i	−0.499326	+	0.597467i
$79$	70.7950			0.896140			0.448070	−	0.893999i	$-0.352112\pi$
$79$	70.7950			0.896140			0.448070	+	0.893999i	$0.352112\pi$
$80$	−132.819	+	49.5343i	−1.66024	+	0.619179i
$81$	−98.4224			−1.21509
$82$	−113.071	−	94.4981i	−1.37892	−	1.15242i
$83$	−60.8673			−0.733341			−0.366671	−	0.930351i	$-0.619502\pi$
$83$	−60.8673			−0.733341			−0.366671	+	0.930351i	$0.619502\pi$
$84$		0			0
$85$			92.8043i			1.09182i
$86$	−62.6896	−	52.3921i	−0.728949	−	0.609211i
$87$			67.1446i			0.771777i
$88$	14.4338	−	25.3459i	0.164021	−	0.288022i
$89$		−	27.0204i		−	0.303600i	−0.988411	−	0.151800i	$-0.951493\pi$
$89$		−	27.0204i		−	0.303600i	0.988411	−	0.151800i	$-0.0485070\pi$
$90$	70.2407	−	84.0463i	0.780453	−	0.933848i
$91$		0			0
$92$	9.16883	+	50.8238i	0.0996612	+	0.552433i
$93$			117.785i			1.26651i
$94$	−64.1520	−	53.6143i	−0.682468	−	0.570365i
$95$	−95.5542			−1.00583
$96$	−41.4847	+	117.579i	−0.432132	+	1.22479i
$97$			3.26608i			0.0336710i	0.999858	+	0.0168355i	$0.00535916\pi$
$97$			3.26608i			0.0336710i	−0.999858	+	0.0168355i	$0.994641\pi$
$98$		0			0
$99$			22.5377i			0.227653i
$100$	−37.9891	−	210.577i	−0.379891	−	2.10577i
$101$	137.714			1.36351			0.681754	−	0.731582i	$-0.261218\pi$
$101$	137.714			1.36351			0.681754	+	0.731582i	$0.261218\pi$
$102$	62.6340	+	52.3456i	0.614059	+	0.513192i
$103$			99.6787i			0.967754i	0.875136	+	0.483877i	$0.160772\pi$
$103$			99.6787i			0.967754i	−0.875136	+	0.483877i	$0.839228\pi$
$104$	54.1807	+	30.8545i	0.520969	+	0.296678i
$105$		0			0
$106$	9.83960	+	8.22333i	0.0928265	+	0.0775786i
$107$		−	94.0107i		−	0.878605i	−0.898339	−	0.439302i	$-0.855226\pi$
$107$		−	94.0107i		−	0.878605i	0.898339	−	0.439302i	$-0.144774\pi$
$108$	7.79866	+	43.2288i	0.0722098	+	0.400267i
$109$			195.949i			1.79770i	0.438258	+	0.898849i	$0.355595\pi$
$109$			195.949i			1.79770i	−0.438258	+	0.898849i	$0.644405\pi$
$110$	49.5716	+	41.4288i	0.450650	+	0.376626i
$111$			154.234i			1.38950i
$112$		0			0
$113$	101.873			0.901527			0.450763	−	0.892643i	$-0.351152\pi$
$113$	101.873			0.901527			0.450763	+	0.892643i	$0.351152\pi$
$114$	−53.8967	+	64.4899i	−0.472778	+	0.565701i
$115$	−114.388			−0.994679
$116$	67.8357	−	12.2379i	0.584791	−	0.105499i
$117$	−48.1777			−0.411775
$118$	20.4115	−	24.4233i	0.172979	−	0.206977i
$119$		0			0
$120$	−239.979	−	136.662i	−1.99983	−	1.13885i
$121$	107.707			0.890141
$122$	15.5919	−	18.6564i	0.127802	−	0.152921i
$123$		−	287.083i		−	2.33401i
$124$	118.998	−	21.4677i	0.959659	−	0.173127i
$125$	252.449			2.01960
$126$		0			0
$127$	−139.079			−1.09511			−0.547554	−	0.836770i	$-0.684441\pi$
$127$	−139.079			−1.09511			−0.547554	+	0.836770i	$0.684441\pi$
$128$	126.351	+	20.4815i	0.987115	+	0.160012i
$129$		−	159.166i		−	1.23385i
$130$	−88.5604	+	105.967i	−0.681234	+	0.815128i
$131$	−91.7051			−0.700039			−0.350020	−	0.936742i	$-0.613825\pi$
$131$	−91.7051			−0.700039			−0.350020	+	0.936742i	$0.613825\pi$
$132$	55.9210	−	10.0884i	0.423644	−	0.0764272i
$133$		0			0
$134$	−11.9661	−	10.0005i	−0.0892991	−	0.0746307i
$135$	−97.2941			−0.720697
$136$	41.4687	−	72.8192i	0.304917	−	0.535435i
$137$	199.581			1.45679			0.728397	−	0.685155i	$-0.240266\pi$
$137$	199.581			1.45679			0.728397	+	0.685155i	$0.240266\pi$
$138$	−64.5198	+	77.2009i	−0.467535	+	0.559427i
$139$	−39.4768			−0.284006			−0.142003	−	0.989866i	$-0.545354\pi$
$139$	−39.4768			−0.284006			−0.142003	+	0.989866i	$0.545354\pi$
$140$		0			0
$141$		−	162.879i		−	1.15517i
$142$	−53.0496	+	63.4763i	−0.373589	+	0.447017i
$143$		−	28.4158i		−	0.198712i
$144$	−92.6699	+	34.5609i	−0.643541	+	0.240006i
$145$			152.676i			1.05294i
$146$	−137.516	−	114.928i	−0.941894	−	0.787177i
$147$		0			0
$148$	155.822	−	28.1110i	1.05285	−	0.189939i
$149$			94.7831i			0.636128i	0.948069	+	0.318064i	$0.103033\pi$
$149$			94.7831i			0.636128i	−0.948069	+	0.318064i	$0.896967\pi$
$150$	267.324	−	319.865i	1.78216	−	2.13243i
$151$	66.5686			0.440852			0.220426	−	0.975404i	$-0.429255\pi$
$151$	66.5686			0.440852			0.220426	+	0.975404i	$0.429255\pi$
$152$	74.9770	+	42.6974i	0.493270	+	0.280904i
$153$			64.7511i			0.423210i
$154$		0			0
$155$			267.826i			1.72791i
$156$	21.5654	+	119.540i	0.138240	+	0.766279i
$157$	25.5194			0.162544			0.0812720	−	0.996692i	$-0.474102\pi$
$157$	25.5194			0.162544			0.0812720	+	0.996692i	$0.474102\pi$
$158$	90.7979	−	108.644i	0.574670	−	0.687620i
$159$			24.9823i			0.157122i
$160$	−94.3296	+	267.357i	−0.589560	+	1.67098i
$161$		0			0
$162$	−126.231	+	151.042i	−0.779205	+	0.932355i
$163$			192.101i			1.17853i	0.807939	+	0.589267i	$0.200583\pi$
$163$			192.101i			1.17853i	−0.807939	+	0.589267i	$0.799417\pi$
$164$	−290.038	+	52.3242i	−1.76853	+	0.319050i
$165$			125.860i			0.762789i
$166$	−78.0651	+	93.4086i	−0.470272	+	0.562702i
$167$		−	184.150i		−	1.10269i	−0.834276	−	0.551346i	$-0.814114\pi$
$167$		−	184.150i		−	1.10269i	0.834276	−	0.551346i	$-0.185886\pi$
$168$		0			0
$169$	−108.257			−0.640574
$170$	142.420	+	119.026i	0.837764	+	0.700151i
$171$	−66.6697			−0.389882
$172$	−160.805	+	29.0098i	−0.934910	+	0.168662i
$173$	69.9037			0.404068			0.202034	−	0.979379i	$-0.435245\pi$
$173$	69.9037			0.404068			0.202034	+	0.979379i	$0.435245\pi$
$174$	103.042	+	86.1160i	0.592195	+	0.494920i
$175$		0			0
$176$	−20.3844	−	54.6578i	−0.115821	−	0.310556i
$177$	62.0098			0.350338
$178$	−41.4663	−	34.6549i	−0.232957	−	0.194691i
$179$			239.313i			1.33695i	0.743736	+	0.668473i	$0.233052\pi$
$179$			239.313i			1.33695i	−0.743736	+	0.668473i	$0.766948\pi$
$180$	−38.8927	−	215.587i	−0.216071	−	1.19770i
$181$	36.2834			0.200461			0.100230	−	0.994964i	$-0.468042\pi$
$181$	36.2834			0.200461			0.100230	+	0.994964i	$0.468042\pi$
$182$		0			0
$183$	47.3678			0.258840
$184$	89.7550	+	51.1131i	0.487799	+	0.277789i
$185$			350.705i			1.89570i
$186$	180.757	+	151.065i	0.971809	+	0.812178i
$187$	−38.1910			−0.204230
$188$	−164.556	+	29.6866i	−0.875296	+	0.157907i
$189$		0			0
$190$	−122.553	+	146.640i	−0.645014	+	0.771789i
$191$	−325.243			−1.70284			−0.851422	−	0.524481i	$-0.824260\pi$
$191$	−325.243			−1.70284			−0.851422	+	0.524481i	$0.824260\pi$
$192$	127.235	+	214.464i	0.662680	+	1.11700i
$193$	199.640			1.03440			0.517201	−	0.855864i	$-0.326974\pi$
$193$	199.640			1.03440			0.517201	+	0.855864i	$0.326974\pi$
$194$	5.01222	+	4.18890i	0.0258362	+	0.0215923i
$195$	−269.045			−1.37972
$196$		0			0
$197$			15.5053i			0.0787071i	0.999225	+	0.0393536i	$0.0125299\pi$
$197$			15.5053i			0.0787071i	−0.999225	+	0.0393536i	$0.987470\pi$
$198$	34.5869	+	28.9056i	0.174681	+	0.145988i
$199$			56.1617i			0.282220i	0.989994	+	0.141110i	$0.0450671\pi$
$199$			56.1617i			0.282220i	−0.989994	+	0.141110i	$0.954933\pi$
$200$	−371.880	−	211.776i	−1.85940	−	1.05888i
$201$		−	30.3814i		−	0.151151i
$202$	176.625	−	211.340i	0.874380	−	1.04624i
$203$		0			0
$204$	160.662	−	28.9841i	0.787558	−	0.142079i
$205$		−	652.783i		−	3.18431i
$206$	152.969	+	127.842i	0.742570	+	0.620594i
$207$	−79.8104			−0.385558
$208$	116.839	−	43.5748i	0.561728	−	0.209494i
$209$		−	39.3226i		−	0.188147i
$210$		0			0
$211$		−	370.470i		−	1.75578i	−0.478859	−	0.877892i	$-0.658949\pi$
$211$		−	370.470i		−	1.75578i	0.478859	−	0.877892i	$-0.341051\pi$
$212$	25.2395	−	4.55331i	0.119054	−	0.0214779i
$213$	−161.164			−0.756638
$214$	−144.271	−	120.573i	−0.674165	−	0.563425i
$215$		−	361.919i		−	1.68335i
$216$	76.3422	+	43.4749i	0.353436	+	0.201273i
$217$		0			0
$218$	300.709	+	251.314i	1.37940	+	1.15281i
$219$		−	349.149i		−	1.59429i
$220$	127.156	−	22.9394i	0.577980	−	0.104270i
$221$		−	81.6390i		−	0.369407i
$222$	236.692	+	197.813i	1.06618	+	0.891049i
$223$		−	6.78533i		−	0.0304275i	−0.999884	−	0.0152137i	$-0.995157\pi$
$223$		−	6.78533i		−	0.0304275i	0.999884	−	0.0152137i	$-0.00484287\pi$
$224$		0			0
$225$	330.677			1.46968
$226$	130.656	−	156.336i	0.578125	−	0.691753i
$227$	−296.618			−1.30669			−0.653344	−	0.757061i	$-0.726635\pi$
$227$	−296.618			−1.30669			−0.653344	+	0.757061i	$0.726635\pi$
$228$	29.8429	+	165.423i	0.130890	+	0.725537i
$229$	−178.193			−0.778135			−0.389067	−	0.921209i	$-0.627203\pi$
$229$	−178.193			−0.778135			−0.389067	+	0.921209i	$0.627203\pi$
$230$	−146.708	+	175.543i	−0.637860	+	0.763230i
$231$		0			0
$232$	68.2219	−	119.798i	0.294060	−	0.516371i
$233$	117.802			0.505589			0.252795	−	0.967520i	$-0.418650\pi$
$233$	117.802			0.505589			0.252795	+	0.967520i	$0.418650\pi$
$234$	−61.7901	+	73.9347i	−0.264060	+	0.315960i
$235$		−	370.362i		−	1.57601i
$236$	−11.3020	−	62.6480i	−0.0478897	−	0.265458i
$237$	275.842			1.16389
$238$		0			0
$239$	46.3543			0.193951			0.0969755	−	0.995287i	$-0.469083\pi$
$239$	46.3543			0.193951			0.0969755	+	0.995287i	$0.469083\pi$
$240$	−517.509	+	193.003i	−2.15629	+	0.804180i
$241$		−	366.618i		−	1.52124i	−0.649199	−	0.760619i	$-0.724896\pi$
$241$		−	366.618i		−	1.52124i	0.649199	−	0.760619i	$-0.275104\pi$
$242$	138.139	−	165.290i	0.570823	−	0.683016i
$243$	−284.653			−1.17141
$244$	−8.63331	−	47.8553i	−0.0353824	−	0.196128i
$245$		0			0
$246$	−440.566	−	368.198i	−1.79092	−	1.49674i
$247$	84.0581			0.340316
$248$	119.675	−	210.150i	0.482561	−	0.847380i
$249$	−237.160			−0.952452
$250$	323.778	−	387.415i	1.29511	−	1.54966i
$251$	129.896			0.517513			0.258756	−	0.965943i	$-0.416687\pi$
$251$	129.896			0.517513			0.258756	+	0.965943i	$0.416687\pi$
$252$		0			0
$253$		−	47.0732i		−	0.186060i
$254$	−178.375	+	213.434i	−0.702263	+	0.840291i
$255$			361.598i			1.41803i
$256$	193.482	−	167.633i	0.755789	−	0.654815i
$257$			268.345i			1.04415i	0.852901	+	0.522073i	$0.174841\pi$
$257$			268.345i			1.04415i	−0.852901	+	0.522073i	$0.825159\pi$
$258$	−244.261	−	204.138i	−0.946747	−	0.791233i
$259$		0			0
$260$	49.0365	+	271.814i	0.188602	+	1.04544i
$261$			106.525i			0.408141i
$262$	−117.616	+	140.733i	−0.448916	+	0.537149i
$263$	−235.383			−0.894991			−0.447495	−	0.894286i	$-0.647684\pi$
$263$	−235.383			−0.894991			−0.447495	+	0.894286i	$0.647684\pi$
$264$	56.2393	−	98.7566i	0.213028	−	0.374078i
$265$			56.8059i			0.214362i
$266$		0			0
$267$		−	105.281i		−	0.394311i
$268$	−30.6941	+	5.53735i	−0.114530	+	0.0206617i
$269$	354.695			1.31857			0.659285	−	0.751893i	$-0.270859\pi$
$269$	354.695			1.31857			0.659285	+	0.751893i	$0.270859\pi$
$270$	−124.784	+	149.310i	−0.462164	+	0.553000i
$271$		−	421.870i		−	1.55672i	−0.627820	−	0.778358i	$-0.716053\pi$
$271$		−	421.870i		−	1.55672i	0.627820	−	0.778358i	$-0.283947\pi$
$272$	−58.5648	−	157.033i	−0.215312	−	0.577327i
$273$		0			0
$274$	255.972	−	306.282i	0.934203	−	1.11782i
$275$			195.037i			0.709226i
$276$	35.7250	+	198.027i	0.129438	+	0.717491i
$277$		−	368.529i		−	1.33043i	−0.746653	−	0.665214i	$-0.768340\pi$
$277$		−	368.529i		−	1.33043i	0.746653	−	0.665214i	$-0.231660\pi$
$278$	−50.6308	+	60.5821i	−0.182125	+	0.217921i
$279$			186.866i			0.669772i
$280$		0			0
$281$	−35.2868			−0.125576			−0.0627879	−	0.998027i	$-0.519999\pi$
$281$	−35.2868			−0.125576			−0.0627879	+	0.998027i	$0.519999\pi$
$282$	−249.959	−	208.900i	−0.886378	−	0.740780i
$283$	−196.617			−0.694761			−0.347380	−	0.937724i	$-0.612929\pi$
$283$	−196.617			−0.694761			−0.347380	+	0.937724i	$0.612929\pi$
$284$	29.3739	+	162.823i	0.103429	+	0.573319i
$285$	−372.313			−1.30636
$286$	−43.6076	−	36.4445i	−0.152474	−	0.127428i
$287$		0			0
$288$	−65.8153	+	186.540i	−0.228525	+	0.647707i
$289$	179.277			0.620335
$290$	234.301	+	195.814i	0.807935	+	0.675222i
$291$			12.7258i			0.0437313i
$292$	−352.742	+	63.6362i	−1.20802	+	0.217932i
$293$	−317.573			−1.08387			−0.541933	−	0.840421i	$-0.682307\pi$
$293$	−317.573			−1.08387			−0.541933	+	0.840421i	$0.682307\pi$
$294$		0			0
$295$	141.001			0.477968
$296$	156.709	−	275.182i	0.529422	−	0.929669i
$297$		−	40.0386i		−	0.134810i
$298$	145.457	+	121.564i	0.488109	+	0.407932i
$299$	100.626			0.336542
$300$	−148.019	−	820.483i	−0.493396	−	2.73494i
$301$		0			0
$302$	85.3773	−	102.158i	0.282706	−	0.338271i
$303$	536.583			1.77090
$304$	161.686	−	60.3002i	0.531862	−	0.198356i
$305$	107.707			0.353137
$306$	99.3687	+	83.0462i	0.324734	+	0.271393i
$307$	132.193			0.430596			0.215298	−	0.976548i	$-0.430928\pi$
$307$	132.193			0.430596			0.215298	+	0.976548i	$0.430928\pi$
$308$		0			0
$309$			388.383i			1.25690i
$310$	411.012	+	343.499i	1.32585	+	1.10806i
$311$		−	462.404i		−	1.48683i	−0.668831	−	0.743414i	$-0.733205\pi$
$311$		−	462.404i		−	1.48683i	0.668831	−	0.743414i	$-0.266795\pi$
$312$	211.107	+	120.220i	0.676626	+	0.385321i
$313$		−	566.042i		−	1.80844i	−0.427067	−	0.904220i	$-0.640453\pi$
$313$		−	566.042i		−	1.80844i	0.427067	−	0.904220i	$-0.359547\pi$
$314$	32.7298	−	39.1627i	0.104235	−	0.124722i
$315$		0			0
$316$	−50.2753	−	278.682i	−0.159099	−	0.881904i
$317$			177.033i			0.558463i	0.960224	+	0.279231i	$0.0900796\pi$
$317$			177.033i			0.558463i	−0.960224	+	0.279231i	$0.909920\pi$
$318$	38.3386	+	32.0410i	0.120561	+	0.100758i
$319$	−62.8296			−0.196958
$320$	289.311	+	487.659i	0.904098	+	1.52393i
$321$		−	366.299i		−	1.14112i
$322$		0			0
$323$		−	112.975i		−	0.349766i
$324$	69.8950	+	387.435i	0.215725	+	1.19579i
$325$	−416.922			−1.28284
$326$	294.803	+	246.378i	0.904304	+	0.755761i
$327$			763.486i			2.33482i
$328$	−291.689	+	512.208i	−0.889297	+	1.56161i
$329$		0			0
$330$	193.148	+	161.421i	0.585298	+	0.489156i
$331$		−	496.160i		−	1.49897i	−0.662019	−	0.749487i	$-0.730300\pi$
$331$		−	496.160i		−	1.49897i	0.662019	−	0.749487i	$-0.269700\pi$
$332$	43.2251	+	239.601i	0.130196	+	0.721691i
$333$			244.693i			0.734813i
$334$	−282.601	−	236.180i	−0.846111	−	0.707127i
$335$		−	69.0825i		−	0.206216i
$336$		0			0
$337$	−206.191			−0.611843			−0.305922	−	0.952057i	$-0.598965\pi$
$337$	−206.191			−0.611843			−0.305922	+	0.952057i	$0.598965\pi$
$338$	−138.845	+	166.134i	−0.410783	+	0.491521i
$339$	396.931			1.17089
$340$	365.320	−	65.9053i	1.07447	−	0.193839i
$341$	−110.216			−0.323214
$342$	−85.5070	+	102.313i	−0.250020	+	0.299161i
$343$		0			0
$344$	−161.720	+	283.981i	−0.470116	+	0.825527i
$345$	−445.696			−1.29187
$346$	89.6547	−	107.276i	0.259118	−	0.310046i
$347$			606.190i			1.74694i	0.486874	+	0.873472i	$0.338137\pi$
$347$			606.190i			1.74694i	−0.486874	+	0.873472i	$0.661863\pi$
$348$	264.312	−	47.6830i	0.759517	−	0.137020i
$349$	−136.343			−0.390669			−0.195335	−	0.980737i	$-0.562579\pi$
$349$	−136.343			−0.390669			−0.195335	+	0.980737i	$0.562579\pi$
$350$		0			0
$351$	85.5887			0.243842
$352$	−110.023	−	38.8187i	−0.312566	−	0.110280i
$353$			10.0743i			0.0285390i	0.999898	+	0.0142695i	$0.00454228\pi$
$353$			10.0743i			0.0285390i	−0.999898	+	0.0142695i	$0.995458\pi$
$354$	79.5304	−	95.1618i	0.224662	−	0.268819i
$355$	−366.461			−1.03229
$356$	−106.365	+	19.1887i	−0.298777	+	0.0539007i
$357$		0			0
$358$	367.257	+	306.930i	1.02586	+	0.857347i
$359$	395.616			1.10199			0.550997	−	0.834507i	$-0.314248\pi$
$359$	395.616			1.10199			0.550997	+	0.834507i	$0.314248\pi$
$360$	−380.726	−	216.814i	−1.05757	−	0.602260i
$361$	−244.678			−0.677778
$362$	46.5351	−	55.6814i	0.128550	−	0.153816i
$363$	419.664			1.15610
$364$		0			0
$365$		−	793.909i		−	2.17509i
$366$	60.7513	−	72.6918i	0.165987	−	0.198612i
$367$		−	189.932i		−	0.517526i	−0.965941	−	0.258763i	$-0.916685\pi$
$367$		−	189.932i		−	0.517526i	0.965941	−	0.258763i	$-0.0833149\pi$
$368$	193.554	−	72.1854i	0.525963	−	0.196156i
$369$		−	455.457i		−	1.23430i
$370$	538.201	+	449.795i	1.45460	+	1.21566i
$371$		0			0
$372$	463.657	−	83.6457i	1.24639	−	0.224854i
$373$			360.104i			0.965425i	0.875779	+	0.482713i	$0.160348\pi$
$373$			360.104i			0.965425i	−0.875779	+	0.482713i	$0.839652\pi$
$374$	−48.9817	+	58.6089i	−0.130967	+	0.156708i
$375$	983.631			2.62302
$376$	−165.492	+	290.606i	−0.440140	+	0.772888i
$377$		−	134.308i		−	0.356254i
$378$		0			0
$379$			11.2929i			0.0297966i	0.999889	+	0.0148983i	$0.00474246\pi$
$379$			11.2929i			0.0297966i	−0.999889	+	0.0148983i	$0.995258\pi$
$380$	67.8581	+	376.145i	0.178574	+	0.989855i
$381$	−541.900			−1.42231
$382$	−417.139	+	499.127i	−1.09199	+	1.30661i
$383$			434.253i			1.13382i	0.823779	+	0.566910i	$0.191861\pi$
$383$			434.253i			1.13382i	−0.823779	+	0.566910i	$0.808139\pi$
$384$	492.307	+	79.8031i	1.28205	+	0.207820i
$385$		0			0
$386$	256.047	−	306.372i	0.663334	−	0.793710i
$387$		−	252.517i		−	0.652499i
$388$	12.8568	−	2.31942i	0.0331361	−	0.00597789i
$389$			43.1631i			0.110959i	0.998460	+	0.0554796i	$0.0176688\pi$
$389$			43.1631i			0.110959i	−0.998460	+	0.0554796i	$0.982331\pi$
$390$	−345.063	+	412.883i	−0.884776	+	1.05868i
$391$		−	135.242i		−	0.345887i
$392$		0			0
$393$	−357.315			−0.909199
$394$	23.7948	+	19.8863i	0.0603930	+	0.0504727i
$395$	627.222			1.58790
$396$	88.7185	−	16.0052i	0.224037	−	0.0404172i
$397$	486.790			1.22617			0.613086	−	0.790016i	$-0.289928\pi$
$397$	486.790			1.22617			0.613086	+	0.790016i	$0.289928\pi$
$398$	86.1872	+	72.0300i	0.216551	+	0.180980i
$399$		0			0
$400$	−801.950	+	299.084i	−2.00488	+	0.747711i
$401$	−546.914			−1.36388			−0.681938	−	0.731410i	$-0.738862\pi$
$401$	−546.914			−1.36388			−0.681938	+	0.731410i	$0.738862\pi$
$402$	−46.6241	−	38.9655i	−0.115980	−	0.0969291i
$403$		−	235.603i		−	0.584624i
$404$	−97.7983	−	542.106i	−0.242075	−	1.34185i
$405$	−871.992			−2.15307
$406$		0			0
$407$	−144.323			−0.354601
$408$	161.576	−	283.729i	0.396021	−	0.695415i
$409$		−	66.7668i		−	0.163244i	−0.996663	−	0.0816220i	$-0.973990\pi$
$409$		−	66.7668i		−	0.163244i	0.996663	−	0.0816220i	$-0.0260100\pi$
$410$	−1001.78	−	837.224i	−2.44336	−	2.04201i
$411$	777.637			1.89206
$412$	392.381	−	70.7871i	0.952380	−	0.171813i
$413$		0			0
$414$	−102.360	+	122.479i	−0.247248	+	0.295843i
$415$	−539.266			−1.29944
$416$	82.9808	−	235.192i	0.199473	−	0.565364i
$417$	−153.815			−0.368862
$418$	−60.3455	−	50.4331i	−0.144367	−	0.120653i
$419$	550.169			1.31305			0.656527	−	0.754303i	$-0.272025\pi$
$419$	550.169			1.31305			0.656527	+	0.754303i	$0.272025\pi$
$420$		0			0
$421$			579.599i			1.37672i	0.725369	+	0.688360i	$0.241669\pi$
$421$			579.599i			1.37672i	−0.725369	+	0.688360i	$0.758331\pi$
$422$	−568.534	−	475.145i	−1.34724	−	1.12594i
$423$		−	258.408i		−	0.610893i
$424$	25.3832	−	44.5730i	0.0598659	−	0.105125i
$425$			560.345i			1.31846i
$426$	−206.700	+	247.326i	−0.485211	+	0.580578i
$427$		0			0
$428$	−370.069	+	66.7620i	−0.864647	+	0.155986i
$429$		−	110.718i		−	0.258084i
$430$	−555.411	−	464.178i	−1.29165	−	1.07948i
$431$	−431.870			−1.00202			−0.501009	−	0.865442i	$-0.667038\pi$
$431$	−431.870			−1.00202			−0.501009	+	0.865442i	$0.667038\pi$
$432$	164.630	−	61.3982i	0.381088	−	0.142125i
$433$		−	0.143463i		−	0.000331322i	−1.00000		0.000165661i	$-0.999947\pi$
$433$		−	0.143463i		−	0.000331322i	1.00000		0.000165661i	$-5.27316e-5\pi$
$434$		0			0
$435$			594.881i			1.36754i
$436$	771.345	−	139.154i	1.76914	−	0.319160i
$437$	139.249			0.318648
$438$	−535.812	−	447.799i	−1.22332	−	1.02237i
$439$		−	191.349i		−	0.435874i	−0.975963	−	0.217937i	$-0.930067\pi$
$439$		−	191.349i		−	0.435874i	0.975963	−	0.217937i	$-0.0699328\pi$
$440$	127.879	−	224.557i	0.290635	−	0.510357i
$441$		0			0
$442$	−125.285	−	104.706i	−0.283451	−	0.236891i
$443$			393.501i			0.888265i	0.895961	+	0.444133i	$0.146488\pi$
$443$			393.501i			0.888265i	−0.895961	+	0.444133i	$0.853512\pi$
$444$	607.137	−	109.530i	1.36743	−	0.246690i
$445$		−	239.393i		−	0.537961i
$446$	−10.4129	−	8.70250i	−0.0233474	−	0.0195123i
$447$			369.308i			0.826193i
$448$		0			0
$449$	−725.831			−1.61655			−0.808275	−	0.588805i	$-0.799598\pi$
$449$	−725.831			−1.61655			−0.808275	+	0.588805i	$0.799598\pi$
$450$	424.108	−	507.465i	0.942463	−	1.12770i
$451$	268.634			0.595641
$452$	−72.3451	−	401.017i	−0.160056	−	0.887205i
$453$	259.375			0.572571
$454$	−380.427	+	455.198i	−0.837944	+	1.00264i
$455$		0			0
$456$	292.137	+	166.364i	0.640650	+	0.364834i
$457$	−69.3427			−0.151735			−0.0758673	−	0.997118i	$-0.524173\pi$
$457$	−69.3427			−0.151735			−0.0758673	+	0.997118i	$0.524173\pi$
$458$	−228.541	+	273.459i	−0.498997	+	0.597073i
$459$		−	115.032i		−	0.250614i
$460$	81.2331	+	450.283i	0.176594	+	0.978877i
$461$	768.006			1.66596			0.832978	−	0.553306i	$-0.186634\pi$
$461$	768.006			1.66596			0.832978	+	0.553306i	$0.186634\pi$
$462$		0			0
$463$	215.717			0.465911			0.232956	−	0.972487i	$-0.425160\pi$
$463$	215.717			0.465911			0.232956	+	0.972487i	$0.425160\pi$
$464$	−96.3475	−	258.342i	−0.207646	−	0.556770i
$465$			1043.54i			2.24418i
$466$	151.087	−	180.782i	0.324221	−	0.387945i
$467$	−28.9376			−0.0619648			−0.0309824	−	0.999520i	$-0.509864\pi$
$467$	−28.9376			−0.0619648			−0.0309824	+	0.999520i	$0.509864\pi$
$468$	34.2135	+	189.649i	0.0731058	+	0.405233i
$469$		0			0
$470$	−568.367	−	475.006i	−1.20929	−	1.01065i
$471$	99.4325			0.211109
$472$	−110.637	−	63.0047i	−0.234400	−	0.133484i
$473$	148.938			0.314879
$474$	353.780	−	423.315i	0.746372	−	0.893069i
$475$	−576.949			−1.21463
$476$		0			0
$477$			39.6344i			0.0830911i
$478$	59.4515	−	71.1365i	0.124375	−	0.148821i
$479$			802.952i			1.67631i	0.545433	+	0.838154i	$0.316365\pi$
$479$			802.952i			1.67631i	−0.545433	+	0.838154i	$0.683635\pi$
$480$	−367.541	+	1041.72i	−0.765711	+	2.17025i
$481$		−	308.512i		−	0.641396i
$482$	−562.622	−	470.205i	−1.16726	−	0.975528i
$483$		0			0
$484$	−76.4885	−	423.984i	−0.158034	−	0.876000i
$485$			28.9365i			0.0596629i
$486$	−365.081	+	436.836i	−0.751195	+	0.898840i
$487$	19.9239			0.0409116			0.0204558	−	0.999791i	$-0.493488\pi$
$487$	19.9239			0.0409116			0.0204558	+	0.999791i	$0.493488\pi$
$488$	−84.5126	−	48.1278i	−0.173182	−	0.0986224i
$489$			748.493i			1.53066i
$490$		0			0
$491$			76.2017i			0.155197i	0.996985	+	0.0775985i	$0.0247252\pi$
$491$			76.2017i			0.155197i	−0.996985	+	0.0775985i	$0.975275\pi$
$492$	−1130.09	+	203.873i	−2.29693	+	0.414377i
$493$	−180.510			−0.366147
$494$	107.808	−	128.998i	0.218235	−	0.261129i
$495$			199.677i			0.403387i
$496$	−169.013	−	453.184i	−0.340753	−	0.913677i
$497$		0			0
$498$	−304.169	+	363.953i	−0.610781	+	0.730828i
$499$			522.871i			1.04784i	0.851768	+	0.523919i	$0.175530\pi$
$499$			522.871i			1.04784i	−0.851768	+	0.523919i	$0.824470\pi$
$500$	−179.278	−	993.756i	−0.358556	−	1.98751i
$501$		−	717.512i		−	1.43216i
$502$	166.597	−	199.341i	0.331867	−	0.397094i
$503$		−	132.060i		−	0.262545i	−0.991346	−	0.131273i	$-0.958094\pi$
$503$		−	132.060i		−	0.262545i	0.991346	−	0.131273i	$-0.0419064\pi$
$504$		0			0
$505$	1220.11			2.41605
$506$	−72.2397	−	60.3735i	−0.142766	−	0.119315i
$507$	−421.807			−0.831967
$508$	98.7672	+	547.477i	0.194424	+	1.07771i
$509$	310.157			0.609346			0.304673	−	0.952457i	$-0.401453\pi$
$509$	310.157			0.609346			0.304673	+	0.952457i	$0.401453\pi$
$510$	554.918	+	463.766i	1.08807	+	0.909345i
$511$		0			0
$512$	−9.10394	−	511.919i	−0.0177811	−	0.999842i
$513$	118.440			0.230878
$514$	411.810	+	344.165i	0.801186	+	0.669582i
$515$			883.122i			1.71480i
$516$	−626.551	+	113.032i	−1.21425	+	0.219055i
$517$	152.412			0.294801
$518$		0			0
$519$	272.369			0.524797
$520$	480.025	+	273.362i	0.923124	+	0.525695i
$521$		−	61.0976i		−	0.117270i	−0.998279	−	0.0586349i	$-0.981325\pi$
$521$		−	61.0976i		−	0.117270i	0.998279	−	0.0586349i	$-0.0186748\pi$
$522$	163.476	+	136.623i	0.313172	+	0.261730i
$523$	−513.846			−0.982497			−0.491249	−	0.871019i	$-0.663459\pi$
$523$	−513.846			−0.982497			−0.491249	+	0.871019i	$0.663459\pi$
$524$	65.1247	+	360.993i	0.124284	+	0.688918i
$525$		0			0
$526$	−301.889	+	361.224i	−0.573933	+	0.686738i
$527$	−316.652			−0.600858
$528$	−79.4250	−	212.966i	−0.150426	−	0.403345i
$529$	−362.304			−0.684886
$530$	87.1759	+	72.8562i	0.164483	+	0.137465i
$531$	98.3784			0.185270
$532$		0			0
$533$			574.246i			1.07739i
$534$	−161.567	−	135.028i	−0.302560	−	0.252861i
$535$		−	832.906i		−	1.55683i
$536$	−30.8688	+	54.2058i	−0.0575911	+	0.101130i
$537$			932.449i			1.73640i
$538$	454.913	−	544.325i	0.845563	−	1.01176i
$539$		0			0
$540$	69.0938	+	382.994i	0.127951	+	0.709248i
$541$		−	107.078i		−	0.197926i	−0.995091	−	0.0989630i	$-0.968447\pi$
$541$		−	107.078i		−	0.197926i	0.995091	−	0.0989630i	$-0.0315525\pi$
$542$	−647.413	−	541.068i	−1.19449	−	0.998280i
$543$	141.373			0.260355
$544$	−316.099	−	111.527i	−0.581064	−	0.205012i
$545$			1736.05i			3.18541i
$546$		0			0
$547$		−	43.3240i		−	0.0792030i	−0.999216	−	0.0396015i	$-0.987391\pi$
$547$		−	43.3240i		−	0.0792030i	0.999216	−	0.0396015i	$-0.0126088\pi$
$548$	−141.733	−	785.641i	−0.258637	−	1.43365i
$549$	75.1489			0.136883
$550$	299.309	+	250.144i	0.544199	+	0.454808i
$551$		−	185.859i		−	0.337313i
$552$	349.717	+	199.155i	0.633545	+	0.360788i
$553$		0			0
$554$	−565.553	−	472.655i	−1.02085	−	0.853167i
$555$			1366.47i			2.46211i
$556$	28.0346	+	155.399i	0.0504219	+	0.279494i
$557$			72.5011i			0.130164i	0.997880	+	0.0650818i	$0.0207308\pi$
$557$			72.5011i			0.130164i	−0.997880	+	0.0650818i	$0.979269\pi$
$558$	286.770	+	239.665i	0.513924	+	0.429506i
$559$			318.377i			0.569547i
$560$		0			0
$561$	−148.805			−0.265250
$562$	−45.2569	+	54.1520i	−0.0805283	+	0.0963559i
$563$	584.943			1.03897			0.519487	−	0.854478i	$-0.326123\pi$
$563$	584.943			1.03897			0.519487	+	0.854478i	$0.326123\pi$
$564$	−641.167	+	115.669i	−1.13682	+	0.205087i
$565$	902.559			1.59745
$566$	−252.171	+	301.734i	−0.445531	+	0.533099i
$567$		0			0
$568$	287.545	+	163.749i	0.506241	+	0.288291i
$569$	743.529			1.30673			0.653365	−	0.757043i	$-0.273357\pi$
$569$	743.529			1.30673			0.653365	+	0.757043i	$0.273357\pi$
$570$	−477.508	+	571.361i	−0.837733	+	1.00239i
$571$			1032.06i			1.80747i	0.428097	+	0.903733i	$0.359184\pi$
$571$			1032.06i			1.80747i	−0.428097	+	0.903733i	$0.640816\pi$
$572$	−111.857	+	20.1796i	−0.195555	+	0.0352790i
$573$	−1267.26			−2.21163
$574$		0			0
$575$	−690.666			−1.20116
$576$	201.857	+	340.247i	0.350447	+	0.590707i
$577$			953.094i			1.65181i	0.563810	+	0.825905i	$0.309335\pi$
$577$			953.094i			1.65181i	−0.563810	+	0.825905i	$0.690665\pi$
$578$	229.931	−	275.123i	0.397804	−	0.475991i
$579$	777.866			1.34346
$580$	601.004	−	108.424i	1.03621	−	0.186937i
$581$		0			0
$582$	19.5294	+	16.3214i	0.0335556	+	0.0280437i
$583$	−23.3769			−0.0400976
$584$	−354.750	+	622.944i	−0.607449	+	1.06668i
$585$	−426.839			−0.729640
$586$	−407.302	+	487.356i	−0.695054	+	0.831665i
$587$	96.2876			0.164033			0.0820167	−	0.996631i	$-0.473864\pi$
$587$	96.2876			0.164033			0.0820167	+	0.996631i	$0.473864\pi$
$588$		0			0
$589$		−	326.035i		−	0.553540i
$590$	180.840	−	216.383i	0.306508	−	0.366751i
$591$			60.4141i			0.102224i
$592$	−221.315	−	593.423i	−0.373843	−	1.00240i
$593$			51.0193i			0.0860358i	0.999074	+	0.0430179i	$0.0136973\pi$
$593$			51.0193i			0.0860358i	−0.999074	+	0.0430179i	$0.986303\pi$
$594$	−61.4443	−	51.3514i	−0.103442	−	0.0864501i
$595$		0			0
$596$	373.109	−	67.3105i	0.626023	−	0.112937i
$597$			218.826i			0.366542i
$598$	129.057	−	154.423i	0.215815	−	0.258233i
$599$	902.236			1.50624			0.753119	−	0.657885i	$-0.228549\pi$
$599$	902.236			1.50624			0.753119	+	0.657885i	$0.228549\pi$
$600$	−1448.98	−	825.154i	−2.41496	−	1.37526i
$601$		−	903.595i		−	1.50349i	−0.659456	−	0.751743i	$-0.729213\pi$
$601$		−	903.595i		−	1.50349i	0.659456	−	0.751743i	$-0.270787\pi$
$602$		0			0
$603$		−	48.2000i		−	0.0799337i
$604$	−47.2739	−	262.044i	−0.0782681	−	0.433848i
$605$	954.251			1.57727
$606$	688.192	−	823.454i	1.13563	−	1.35884i
$607$		−	354.410i		−	0.583872i	−0.956438	−	0.291936i	$-0.905701\pi$
$607$		−	354.410i		−	0.583872i	0.956438	−	0.291936i	$-0.0942994\pi$
$608$	114.831	−	325.465i	0.188867	−	0.535305i
$609$		0			0
$610$	138.139	−	165.290i	0.226457	−	0.270967i
$611$			325.804i			0.533230i
$612$	254.890	−	45.9832i	0.416486	−	0.0751359i
$613$		−	335.999i		−	0.548123i	−0.961712	−	0.274061i	$-0.911633\pi$
$613$		−	335.999i		−	0.548123i	0.961712	−	0.274061i	$-0.0883671\pi$
$614$	169.544	−	202.867i	0.276130	−	0.330402i
$615$		−	2543.47i		−	4.13573i
$616$		0			0
$617$	223.359			0.362008			0.181004	−	0.983482i	$-0.442065\pi$
$617$	223.359			0.362008			0.181004	+	0.983482i	$0.442065\pi$
$618$	596.023	+	498.119i	0.964438	+	0.806018i
$619$	726.053			1.17294			0.586472	−	0.809969i	$-0.300516\pi$
$619$	726.053			1.17294			0.586472	+	0.809969i	$0.300516\pi$
$620$	1054.28	−	190.197i	1.70046	−	0.306770i
$621$	141.785			0.228317
$622$	−709.617	−	593.054i	−1.14086	−	0.953463i
$623$		0			0
$624$	455.247	−	169.783i	0.729563	−	0.272088i
$625$	899.270			1.43883
$626$	−868.662	−	725.974i	−1.38764	−	1.15970i
$627$		−	153.215i		−	0.244362i
$628$	−18.1227	−	100.456i	−0.0288578	−	0.159962i
$629$	−414.642			−0.659208
$630$		0			0
$631$	−326.157			−0.516888			−0.258444	−	0.966026i	$-0.583210\pi$
$631$	−326.157			−0.516888			−0.258444	+	0.966026i	$0.583210\pi$
$632$	−492.152	−	280.268i	−0.778722	−	0.443462i
$633$		−	1443.48i		−	2.28038i
$634$	271.679	+	227.052i	0.428516	+	0.358127i
$635$	−1232.19			−1.94046
$636$	98.3419	−	17.7413i	0.154626	−	0.0278951i
$637$		0			0
$638$	−80.5818	+	96.4200i	−0.126304	+	0.151128i
$639$	−255.686			−0.400135
$640$	1119.43	+	181.460i	1.74911	+	0.283531i
$641$	−598.375			−0.933502			−0.466751	−	0.884389i	$-0.654576\pi$
$641$	−598.375			−0.933502			−0.466751	+	0.884389i	$0.654576\pi$
$642$	−562.131	−	469.795i	−0.875594	−	0.731768i
$643$	−1008.20			−1.56796			−0.783979	−	0.620787i	$-0.786813\pi$
$643$	−1008.20			−1.56796			−0.783979	+	0.620787i	$0.786813\pi$
$644$		0			0
$645$		−	1410.16i		−	2.18630i
$646$	−173.374	−	144.895i	−0.268380	−	0.224296i
$647$		−	663.235i		−	1.02509i	−0.858660	−	0.512546i	$-0.828702\pi$
$647$		−	663.235i		−	1.02509i	0.858660	−	0.512546i	$-0.171298\pi$
$648$	684.212	+	389.641i	1.05588	+	0.601298i
$649$			58.0248i			0.0894064i
$650$	−534.721	+	639.819i	−0.822648	+	0.984337i
$651$		0			0
$652$	756.197	−	136.421i	1.15981	−	0.209235i
$653$		−	990.608i		−	1.51701i	−0.651666	−	0.758506i	$-0.725930\pi$
$653$		−	990.608i		−	1.51701i	0.651666	−	0.758506i	$-0.274070\pi$
$654$	1171.67	+	979.206i	1.79154	+	1.49726i
$655$	−812.479			−1.24043
$656$	411.943	+	1104.56i	0.627963	+	1.68379i
$657$		−	553.924i		−	0.843110i
$658$		0			0
$659$			82.2318i			0.124783i	0.998052	+	0.0623914i	$0.0198727\pi$
$659$			82.2318i			0.124783i	−0.998052	+	0.0623914i	$0.980127\pi$
$660$	495.443	−	89.3800i	0.750671	−	0.135424i
$661$	−626.220			−0.947382			−0.473691	−	0.880691i	$-0.657079\pi$
$661$	−626.220			−0.947382			−0.473691	+	0.880691i	$0.657079\pi$
$662$	−761.421	−	636.348i	−1.15018	−	0.961251i
$663$		−	318.094i		−	0.479780i
$664$	423.137	+	240.965i	0.637254	+	0.362900i
$665$		0			0
$666$	375.512	+	313.830i	0.563831	+	0.471216i
$667$		−	222.492i		−	0.333572i
$668$	−724.897	+	130.775i	−1.08518	+	0.195770i
$669$		−	26.4380i		−	0.0395187i
$670$	−106.016	−	88.6015i	−0.158233	−	0.132241i
$671$			44.3237i			0.0660562i
$672$		0			0
$673$	−150.211			−0.223196			−0.111598	−	0.993753i	$-0.535597\pi$
$673$	−150.211			−0.223196			−0.111598	+	0.993753i	$0.535597\pi$
$674$	−264.450	+	316.426i	−0.392359	+	0.469475i
$675$	−587.455			−0.870303
$676$	76.8791	+	426.149i	0.113726	+	0.630398i
$677$	−556.414			−0.821882			−0.410941	−	0.911662i	$-0.634800\pi$
$677$	−556.414			−0.821882			−0.410941	+	0.911662i	$0.634800\pi$
$678$	509.082	−	609.141i	0.750859	−	0.898438i
$679$		0			0
$680$	367.400	−	645.156i	0.540293	−	0.948759i
$681$	−1155.73			−1.69711
$682$	−141.357	+	169.140i	−0.207268	+	0.248006i
$683$		−	791.356i		−	1.15865i	−0.815098	−	0.579323i	$-0.803317\pi$
$683$		−	791.356i		−	1.15865i	0.815098	−	0.579323i	$-0.196683\pi$
$684$	47.3457	+	262.442i	0.0692189	+	0.383688i
$685$	1768.22			2.58135
$686$		0			0
$687$	−694.302			−1.01063
$688$	228.392	+	612.399i	0.331965	+	0.890114i
$689$		−	49.9716i		−	0.0725277i
$690$	−571.625	+	683.977i	−0.828443	+	0.991270i
$691$	976.534			1.41322			0.706609	−	0.707604i	$-0.250224\pi$
$691$	976.534			1.41322			0.706609	+	0.707604i	$0.250224\pi$
$692$	−49.6424	−	275.173i	−0.0717375	−	0.397649i
$693$		0			0
$694$	930.275	+	777.466i	1.34045	+	1.12027i
$695$	−349.752			−0.503241
$696$	265.816	−	466.775i	0.381920	−	0.670654i
$697$	771.790			1.10730
$698$	−174.867	+	209.236i	−0.250525	+	0.299765i
$699$	458.999			0.656651
$700$		0			0
$701$			855.098i			1.21983i	0.792468	+	0.609913i	$0.208796\pi$
$701$			855.098i			1.21983i	−0.792468	+	0.609913i	$0.791204\pi$
$702$	109.771	−	131.347i	0.156369	−	0.187103i
$703$		−	426.928i		−	0.607294i
$704$	−200.682	+	119.058i	−0.285060	+	0.169116i
$705$		−	1443.06i		−	2.04689i
$706$	15.4602	+	12.9207i	0.0218983	+	0.0183013i
$707$		0			0
$708$	−44.0365	−	244.099i	−0.0621984	−	0.344772i
$709$			333.471i			0.470340i	0.971954	+	0.235170i	$0.0755647\pi$
$709$			333.471i			0.470340i	−0.971954	+	0.235170i	$0.924435\pi$
$710$	−470.003	+	562.381i	−0.661976	+	0.792086i
$711$	437.623			0.615504
$712$	−106.970	+	187.840i	−0.150239	+	0.263821i
$713$		−	390.297i		−	0.547401i
$714$		0			0
$715$		−	251.755i		−	0.352105i
$716$	942.047	−	169.949i	1.31571	−	0.237359i
$717$	180.613			0.251900
$718$	507.395	−	607.122i	0.706679	−	0.845574i
$719$		−	39.8230i		−	0.0553866i	−0.999616	−	0.0276933i	$-0.991184\pi$
$719$		−	39.8230i		−	0.0553866i	0.999616	−	0.0276933i	$-0.00881618\pi$
$720$	−821.027	+	306.199i	−1.14032	+	0.425276i
$721$		0			0
$722$	−313.811	+	375.489i	−0.434641	+	0.520068i
$723$		−	1428.47i		−	1.97576i
$724$	−25.7667	−	142.828i	−0.0355894	−	0.197276i
$725$			921.848i			1.27151i
$726$	538.239	−	644.028i	0.741376	−	0.887091i
$727$			489.402i			0.673180i	0.941651	+	0.336590i	$0.109274\pi$
$727$			489.402i			0.673180i	−0.941651	+	0.336590i	$0.890726\pi$
$728$		0			0
$729$	−223.307			−0.306320
$730$	−1218.35	−	1018.22i	−1.66898	−	1.39483i
$731$	427.900			0.585363
$732$	−33.6384	−	186.461i	−0.0459541	−	0.254728i
$733$	178.318			0.243272			0.121636	−	0.992575i	$-0.461186\pi$
$733$	178.318			0.243272			0.121636	+	0.992575i	$0.461186\pi$
$734$	−291.475	−	243.597i	−0.397105	−	0.331876i
$735$		0			0
$736$	137.465	−	389.615i	0.186773	−	0.529368i
$737$	28.4289			0.0385739
$738$	−698.956	−	584.145i	−0.947096	−	0.791524i
$739$		−	882.401i		−	1.19405i	−0.802224	−	0.597024i	$-0.796350\pi$
$739$		−	882.401i		−	1.19405i	0.802224	−	0.597024i	$-0.203650\pi$
$740$	1380.53	−	249.054i	1.86559	−	0.336560i
$741$	327.520			0.441997
$742$		0			0
$743$	1404.00			1.88964			0.944819	−	0.327591i	$-0.106237\pi$
$743$	1404.00			1.88964			0.944819	+	0.327591i	$0.106237\pi$
$744$	466.296	−	818.820i	0.626743	−	1.10056i
$745$			839.749i			1.12718i
$746$	552.624	+	461.849i	0.740783	+	0.619101i
$747$	−376.255			−0.503687
$748$	27.1215	+	150.337i	0.0362586	+	0.200985i
$749$		0			0
$750$	1261.55	−	1509.51i	1.68207	−	2.01268i
$751$	205.680			0.273875			0.136938	−	0.990580i	$-0.456274\pi$
$751$	205.680			0.273875			0.136938	+	0.990580i	$0.456274\pi$
$752$	233.720	+	626.684i	0.310797	+	0.833357i
$753$	506.119			0.672137
$754$	−206.112	−	172.256i	−0.273358	−	0.228456i
$755$	589.777			0.781162
$756$		0			0
$757$			15.0345i			0.0198606i	0.999951	+	0.00993032i	$0.00316097\pi$
$757$			15.0345i			0.0198606i	−0.999951	+	0.00993032i	$0.996839\pi$
$758$	17.3304	+	14.4837i	0.0228633	+	0.0191078i
$759$		−	183.414i		−	0.241652i
$760$	664.273	+	378.286i	0.874043	+	0.497745i
$761$		−	628.491i		−	0.825876i	−0.910759	−	0.412938i	$-0.864503\pi$
$761$		−	628.491i		−	0.825876i	0.910759	−	0.412938i	$-0.135497\pi$
$762$	−695.011	+	831.613i	−0.912088	+	1.09136i
$763$		0			0
$764$	230.973	+	1280.31i	0.302320	+	1.67579i
$765$			573.675i			0.749901i
$766$	666.417	+	556.950i	0.869996	+	0.727089i
$767$	−124.037			−0.161717
$768$	753.874	−	653.156i	0.981607	−	0.850463i
$769$		−	442.918i		−	0.575967i	−0.957635	−	0.287983i	$-0.907015\pi$
$769$		−	442.918i		−	0.575967i	0.957635	−	0.287983i	$-0.0929848\pi$
$770$		0			0
$771$			1045.57i			1.35612i
$772$	−141.775	−	785.872i	−0.183646	−	1.01797i
$773$	−169.198			−0.218885			−0.109442	−	0.993993i	$-0.534907\pi$
$773$	−169.198			−0.218885			−0.109442	+	0.993993i	$0.534907\pi$
$774$	−387.519	−	323.865i	−0.500671	−	0.418430i
$775$			1617.11i			2.08659i
$776$	12.9300	−	22.7051i	0.0166624	−	0.0292592i
$777$		0			0
$778$	66.2392	+	55.3586i	0.0851404	+	0.0711551i
$779$			794.660i			1.02010i
$780$	191.063	+	1059.08i	0.244953	+	1.35780i
$781$		−	150.807i		−	0.193094i
$782$	−207.546	−	173.454i	−0.265404	−	0.221808i
$783$		−	189.244i		−	0.241690i
$784$		0			0
$785$	226.094			0.288018
$786$	−458.273	+	548.345i	−0.583045	+	0.697640i
$787$	−46.4874			−0.0590691			−0.0295346	−	0.999564i	$-0.509403\pi$
$787$	−46.4874			−0.0590691			−0.0295346	+	0.999564i	$0.509403\pi$
$788$	61.0359	−	11.0111i	0.0774568	−	0.0139735i
$789$	−917.133			−1.16240
$790$	804.441	−	962.551i	1.01828	−	1.21842i
$791$		0			0
$792$	89.2236	−	156.677i	0.112656	−	0.197825i
$793$	−94.7487			−0.119481
$794$	624.331	−	747.041i	0.786310	−	0.940857i
$795$			221.336i			0.278410i
$796$	221.078	−	39.8834i	0.277736	−	0.0501048i
$797$	−1351.86			−1.69618			−0.848092	−	0.529850i	$-0.822248\pi$
$797$	−1351.86			−1.69618			−0.848092	+	0.529850i	$0.822248\pi$
$798$		0			0
$799$	437.882			0.548038
$800$	−569.555	+	1614.28i	−0.711944	+	2.01785i
$801$		−	167.028i		−	0.208525i
$802$	−701.442	+	839.308i	−0.874616	+	1.04652i
$803$	326.711			0.406863
$804$	−119.595	+	21.5754i	−0.148750	+	0.0268351i
$805$		0			0
$806$	−361.563	−	302.172i	−0.448590	−	0.374903i
$807$	1382.02			1.71254
$808$	−957.361	−	545.192i	−1.18485	−	0.674743i
$809$	−1403.13			−1.73440			−0.867198	−	0.497963i	$-0.834081\pi$
$809$	−1403.13			−1.73440			−0.867198	+	0.497963i	$0.834081\pi$
$810$	−1118.37	+	1338.18i	−1.38070	+	1.65208i
$811$	−689.037			−0.849614			−0.424807	−	0.905284i	$-0.639658\pi$
$811$	−689.037			−0.849614			−0.424807	+	0.905284i	$0.639658\pi$
$812$		0			0
$813$		−	1643.75i		−	2.02184i
$814$	−185.101	+	221.481i	−0.227396	+	0.272090i
$815$			1701.95i			2.08829i
$816$	−228.189	−	611.855i	−0.279644	−	0.749823i
$817$			440.579i			0.539265i
$818$	−102.462	−	85.6314i	−0.125259	−	0.104684i
$819$		0			0
$820$	−2569.65	+	463.576i	−3.13372	+	0.565336i
$821$			22.3423i			0.0272135i	0.999907	+	0.0136067i	$0.00433129\pi$
$821$			22.3423i			0.0272135i	−0.999907	+	0.0136067i	$0.995669\pi$
$822$	997.355	−	1193.38i	1.21333	−	1.45180i
$823$	1024.22			1.24450			0.622249	−	0.782819i	$-0.286219\pi$
$823$	1024.22			1.24450			0.622249	+	0.782819i	$0.286219\pi$
$824$	394.614	−	692.945i	0.478901	−	0.840953i
$825$			759.934i			0.921132i
$826$		0			0
$827$			466.377i			0.563938i	0.959424	+	0.281969i	$0.0909875\pi$
$827$			466.377i			0.563938i	−0.959424	+	0.281969i	$0.909012\pi$
$828$	56.6776	+	314.170i	0.0684513	+	0.379433i
$829$	−1500.70			−1.81025			−0.905126	−	0.425142i	$-0.860224\pi$
$829$	−1500.70			−1.81025			−0.905126	+	0.425142i	$0.860224\pi$
$830$	−691.633	+	827.571i	−0.833293	+	0.997074i
$831$		−	1435.92i		−	1.72794i
$832$	−254.504	−	428.988i	−0.305895	−	0.515611i
$833$		0			0
$834$	−197.275	+	236.049i	−0.236541	+	0.283033i
$835$		−	1631.51i		−	1.95390i
$836$	−154.792	+	27.9251i	−0.185158	+	0.0334032i
$837$		−	331.972i		−	0.396621i
$838$	705.617	−	844.304i	0.842025	−	1.00752i
$839$			1068.18i			1.27316i	0.771212	+	0.636579i	$0.219651\pi$
$839$			1068.18i			1.27316i	−0.771212	+	0.636579i	$0.780349\pi$
$840$		0			0
$841$	544.034			0.646890
$842$	889.468	+	743.362i	1.05637	+	0.882853i
$843$	−137.490			−0.163096
$844$	−1458.34	+	263.091i	−1.72789	+	0.311719i
$845$	−959.123			−1.13506
$846$	−396.559	−	331.420i	−0.468746	−	0.391749i
$847$		0			0
$848$	−35.8478	−	96.1206i	−0.0422734	−	0.113350i
$849$	−766.090			−0.902344
$850$	859.920	+	718.668i	1.01167	+	0.845492i
$851$		−	511.076i		−	0.600559i
$852$	114.451	+	634.414i	0.134332	+	0.744617i
$853$	−918.640			−1.07695			−0.538476	−	0.842641i	$-0.681000\pi$
$853$	−918.640			−1.07695			−0.538476	+	0.842641i	$0.681000\pi$
$854$		0			0
$855$	−590.673			−0.690846
$856$	−372.176	+	653.543i	−0.434785	+	0.763485i
$857$			505.952i			0.590375i	0.955439	+	0.295188i	$0.0953822\pi$
$857$			505.952i			0.590375i	−0.955439	+	0.295188i	$0.904618\pi$
$858$	−169.910	−	142.001i	−0.198031	−	0.165502i
$859$	−1377.03			−1.60306			−0.801532	−	0.597952i	$-0.795981\pi$
$859$	−1377.03			−1.60306			−0.801532	+	0.597952i	$0.795981\pi$
$860$	−1424.68	+	257.018i	−1.65660	+	0.298858i
$861$		0			0
$862$	−553.893	+	662.758i	−0.642567	+	0.768861i
$863$	917.635			1.06331			0.531654	−	0.846962i	$-0.321571\pi$
$863$	917.635			1.06331			0.531654	+	0.846962i	$0.321571\pi$
$864$	116.922	−	331.392i	0.135327	−	0.383555i
$865$	619.325			0.715983
$866$	−0.220161	−	0.183997i	−0.000254228	−	0.000212468i
$867$	698.525			0.805681
$868$		0			0
$869$			258.116i			0.297026i
$870$	912.919	+	762.961i	1.04933	+	0.876967i
$871$			60.7712i			0.0697717i
$872$	775.736	−	1362.20i	0.889605	−	1.56215i
$873$			20.1895i			0.0231265i
$874$	178.594	−	213.696i	0.204341	−	0.244503i
$875$		0			0
$876$	−1374.41	+	247.949i	−1.56896	+	0.283047i
$877$			699.948i			0.798116i	0.916926	+	0.399058i	$0.130663\pi$
$877$			699.948i			0.798116i	−0.916926	+	0.399058i	$0.869337\pi$
$878$	−293.649	−	245.414i	−0.334452	−	0.279514i
$879$	−1237.38			−1.40771
$880$	−180.600	−	484.252i	−0.205227	−	0.550286i
$881$			6.37652i			0.00723783i	0.999993	+	0.00361891i	$0.00115194\pi$
$881$			6.37652i			0.00723783i	−0.999993	+	0.00361891i	$0.998848\pi$
$882$		0			0
$883$		−	1548.35i		−	1.75351i	−0.480935	−	0.876756i	$-0.659703\pi$
$883$		−	1548.35i		−	1.75351i	0.480935	−	0.876756i	$-0.340297\pi$
$884$	−321.368	+	57.9762i	−0.363539	+	0.0655839i
$885$	549.388			0.620777
$886$	603.878	+	504.684i	0.681577	+	0.569620i
$887$			732.369i			0.825670i	0.910806	+	0.412835i	$0.135461\pi$
$887$			732.369i			0.825670i	−0.910806	+	0.412835i	$0.864539\pi$
$888$	610.593	−	1072.21i	0.687605	−	1.20744i
$889$		0			0
$890$	−367.378	−	307.032i	−0.412785	−	0.344980i
$891$		−	358.844i		−	0.402743i
$892$	−26.7102	+	4.81863i	−0.0299441	+	0.00540205i
$893$			450.857i			0.504879i
$894$	566.750	+	473.655i	0.633949	+	0.529815i
$895$			2120.24i			2.36899i
$896$		0			0
$897$	392.074			0.437095
$898$	−930.911	+	1113.88i	−1.03665	+	1.24040i
$899$	−520.938			−0.579464
$900$	−234.831	−	1301.69i	−0.260924	−	1.44633i
$901$	−67.1621			−0.0745418
$902$	344.536	−	412.253i	0.381969	−	0.457043i
$903$		0			0
$904$	−708.197	−	403.299i	−0.783403	−	0.446128i
$905$	321.459			0.355204
$906$	332.660	−	398.043i	0.367174	−	0.439341i
$907$			723.838i			0.798057i	0.916939	+	0.399029i	$0.130653\pi$
$907$			723.838i			0.798057i	−0.916939	+	0.399029i	$0.869347\pi$
$908$	210.644	+	1167.62i	0.231987	+	1.28593i
$909$	851.288			0.936511
$910$		0			0
$911$	1600.04			1.75636			0.878179	−	0.478332i	$-0.158758\pi$
$911$	1600.04			1.75636			0.878179	+	0.478332i	$0.158758\pi$
$912$	629.985	−	234.951i	0.690773	−	0.257621i
$913$		−	221.920i		−	0.243066i
$914$	−88.9352	+	106.415i	−0.0973033	+	0.116428i
$915$	419.664			0.458649
$916$	126.544	+	701.448i	0.138149	+	0.765773i
$917$		0			0
$918$	−176.531	−	147.533i	−0.192299	−	0.160712i
$919$	−524.085			−0.570277			−0.285139	−	0.958486i	$-0.592040\pi$
$919$	−524.085			−0.570277			−0.285139	+	0.958486i	$0.592040\pi$
$920$	795.202	+	452.847i	0.864350	+	0.492225i
$921$	515.070			0.559251
$922$	985.003	−	1178.60i	1.06833	−	1.27831i
$923$	322.372			0.349266
$924$		0			0
$925$			2117.53i			2.28922i
$926$	276.667	−	331.045i	0.298776	−	0.357500i
$927$			616.169i			0.664691i
$928$	−520.028	−	183.477i	−0.560375	−	0.197713i
$929$			637.154i			0.685849i	0.939363	+	0.342924i	$0.111417\pi$
$929$			637.154i			0.685849i	−0.939363	+	0.342924i	$0.888583\pi$
$930$	1601.45	+	1338.39i	1.72199	+	1.43913i
$931$		0			0
$932$	−83.6577	−	463.723i	−0.0897615	−	0.497557i
$933$		−	1801.69i		−	1.93107i
$934$	−37.1138	+	44.4084i	−0.0397364	+	0.0475464i
$935$	−338.360			−0.361883
$936$	334.921	+	190.729i	0.357822	+	0.203770i
$937$			383.587i			0.409378i	0.978827	+	0.204689i	$0.0656182\pi$
$937$			383.587i			0.409378i	−0.978827	+	0.204689i	$0.934382\pi$
$938$		0			0
$939$		−	2205.50i		−	2.34877i
$940$	−1457.91	+	263.014i	−1.55097	+	0.279802i
$941$	−260.591			−0.276930			−0.138465	−	0.990367i	$-0.544217\pi$
$941$	−260.591			−0.276930			−0.138465	+	0.990367i	$0.544217\pi$
$942$	127.527	−	152.592i	0.135379	−	0.161987i
$943$			951.288i			1.00879i
$944$	−238.585	+	88.9794i	−0.252738	+	0.0942579i
$945$		0			0
$946$	191.019	−	228.564i	0.201923	−	0.241610i
$947$		−	983.163i		−	1.03819i	−0.854717	−	0.519093i	$-0.826270\pi$
$947$		−	983.163i		−	1.03819i	0.854717	−	0.519093i	$-0.173730\pi$
$948$	−195.890	−	1085.84i	−0.206635	−	1.14540i
$949$			698.394i			0.735926i
$950$	−739.963	+	885.401i	−0.778909	+	0.932001i
$951$			689.781i			0.725322i
$952$		0			0
$953$	−1137.60			−1.19370			−0.596851	−	0.802352i	$-0.703582\pi$
$953$	−1137.60			−1.19370			−0.596851	+	0.802352i	$0.703582\pi$
$954$	60.8240	+	50.8330i	0.0637569	+	0.0532840i
$955$	−2881.56			−3.01734
$956$	−32.9187	−	182.472i	−0.0344337	−	0.190870i
$957$	−244.806			−0.255806
$958$	1232.23	+	1029.82i	1.28625	+	1.07497i
$959$		0			0
$960$	1127.26	+	1900.09i	1.17423	+	1.97926i
$961$	47.1670			0.0490812
$962$	−473.450	−	395.680i	−0.492152	−	0.411310i
$963$		−	581.132i		−	0.603460i
$964$	−1443.18	+	260.355i	−1.49707	+	0.270078i
$965$	1768.75			1.83290
$966$		0			0
$967$	−1296.35			−1.34059			−0.670297	−	0.742093i	$-0.733833\pi$
$967$	−1296.35			−1.34059			−0.670297	+	0.742093i	$0.733833\pi$
$968$	−748.757	−	426.397i	−0.773509	−	0.440493i
$969$		−	440.188i		−	0.454271i
$970$	44.4067	+	37.1124i	0.0457801	+	0.0382602i
$971$	1330.47			1.37021			0.685105	−	0.728445i	$-0.259756\pi$
$971$	1330.47			1.37021			0.685105	+	0.728445i	$0.259756\pi$
$972$	202.147	+	1120.52i	0.207971	+	1.15280i
$973$		0			0
$974$	25.5534	−	30.5758i	0.0262355	−	0.0313920i
$975$	−1624.47			−1.66613
$976$	−182.249	+	67.9693i	−0.186731	+	0.0696406i
$977$	1386.16			1.41879			0.709397	−	0.704809i	$-0.248967\pi$
$977$	1386.16			1.41879			0.709397	+	0.704809i	$0.248967\pi$
$978$	1148.66	+	959.976i	1.17449	+	0.981570i
$979$	98.5153			0.100629
$980$		0			0
$981$			1211.27i			1.23473i
$982$	116.941	+	97.7322i	0.119085	+	0.0995236i
$983$			694.161i			0.706166i	0.935592	+	0.353083i	$0.114867\pi$
$983$			694.161i			0.706166i	−0.935592	+	0.353083i	$0.885133\pi$
$984$	−1136.52	+	1995.74i	−1.15500	+	2.02820i
$985$			137.372i			0.139464i
$986$	−231.513	+	277.016i	−0.234800	+	0.280949i
$987$		0			0
$988$	−59.6941	−	330.891i	−0.0604192	−	0.334910i
$989$			527.418i			0.533284i
$990$	306.429	+	256.095i	0.309524	+	0.258681i
$991$	−934.514			−0.943001			−0.471500	−	0.881866i	$-0.656287\pi$
$991$	−934.514			−0.943001			−0.471500	+	0.881866i	$0.656287\pi$
$992$	−912.235	−	321.857i	−0.919592	−	0.324453i
$993$		−	1933.22i		−	1.94684i
$994$		0			0
$995$			497.576i			0.500076i
$996$	168.420	+	933.572i	0.169097	+	0.937321i
$997$	1538.21			1.54283			0.771417	−	0.636330i	$-0.219548\pi$
$997$	1538.21			1.54283			0.771417	+	0.636330i	$0.219548\pi$
$998$	802.411	+	670.606i	0.804019	+	0.671950i
$999$		−	434.702i		−	0.435137i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.3.h.a.293.18		28
4.3	odd	2		1568.3.h.a.881.3		28
7.2	even	3		56.3.j.a.45.1	yes	28
7.3	odd	6		56.3.j.a.5.10	yes	28
7.4	even	3		392.3.j.e.117.10		28
7.5	odd	6		392.3.j.e.325.1		28
7.6	odd	2	inner	392.3.h.a.293.17		28
8.3	odd	2		1568.3.h.a.881.26		28
8.5	even	2	inner	392.3.h.a.293.19		28
28.3	even	6		224.3.n.a.145.2		28
28.23	odd	6		224.3.n.a.17.13		28
28.27	even	2		1568.3.h.a.881.25		28
56.3	even	6		224.3.n.a.145.13		28
56.5	odd	6		392.3.j.e.325.10		28
56.13	odd	2	inner	392.3.h.a.293.20		28
56.27	even	2		1568.3.h.a.881.4		28
56.37	even	6		56.3.j.a.45.10	yes	28
56.45	odd	6		56.3.j.a.5.1	✓	28
56.51	odd	6		224.3.n.a.17.2		28
56.53	even	6		392.3.j.e.117.1		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.j.a.5.1	✓	28	56.45	odd	6
56.3.j.a.5.10	yes	28	7.3	odd	6
56.3.j.a.45.1	yes	28	7.2	even	3
56.3.j.a.45.10	yes	28	56.37	even	6
224.3.n.a.17.2		28	56.51	odd	6
224.3.n.a.17.13		28	28.23	odd	6
224.3.n.a.145.2		28	28.3	even	6
224.3.n.a.145.13		28	56.3	even	6
392.3.h.a.293.17		28	7.6	odd	2	inner
392.3.h.a.293.18		28	1.1	even	1	trivial
392.3.h.a.293.19		28	8.5	even	2	inner
392.3.h.a.293.20		28	56.13	odd	2	inner
392.3.j.e.117.1		28	56.53	even	6
392.3.j.e.117.10		28	7.4	even	3
392.3.j.e.325.1		28	7.5	odd	6
392.3.j.e.325.10		28	56.5	odd	6
1568.3.h.a.881.3		28	4.3	odd	2
1568.3.h.a.881.4		28	56.27	even	2
1568.3.h.a.881.25		28	28.27	even	2
1568.3.h.a.881.26		28	8.3	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	392.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.28255 - 1.53463i) q^{2} +3.89635 q^{3} +(-0.710153 - 3.93646i) q^{4} +8.85969 q^{5} +(4.99725 - 5.97944i) q^{6} +(-6.95179 - 3.95886i) q^{8} +6.18155 q^{9} +O(q^{10})\)	\(q+(1.28255 - 1.53463i) q^{2} +3.89635 q^{3} +(-0.710153 - 3.93646i) q^{4} +8.85969 q^{5} +(4.99725 - 5.97944i) q^{6} +(-6.95179 - 3.95886i) q^{8} +6.18155 q^{9} +(11.3630 - 13.5963i) q^{10} +3.64596i q^{11} +(-2.76701 - 15.3378i) q^{12} -7.79378 q^{13} +34.5205 q^{15} +(-14.9914 + 5.59097i) q^{16} +10.4749i q^{17} +(7.92812 - 9.48637i) q^{18} -10.7853 q^{19} +(-6.29174 - 34.8758i) q^{20} +(5.59518 + 4.67610i) q^{22} -12.9111 q^{23} +(-27.0866 - 15.4251i) q^{24} +53.4941 q^{25} +(-9.99588 + 11.9605i) q^{26} -10.9817 q^{27} +17.2327i q^{29} +(44.2741 - 52.9760i) q^{30} +30.2297i q^{31} +(-10.6471 + 30.1768i) q^{32} +14.2059i q^{33} +(16.0750 + 13.4345i) q^{34} +(-4.38985 - 24.3334i) q^{36} +39.5843i q^{37} +(-13.8326 + 16.5514i) q^{38} -30.3673 q^{39} +(-61.5907 - 35.0743i) q^{40} -73.6801i q^{41} -40.8501i q^{43} +(14.3521 - 2.58919i) q^{44} +54.7667 q^{45} +(-16.5590 + 19.8137i) q^{46} -41.8030i q^{47} +(-58.4116 + 21.7844i) q^{48} +(68.6087 - 82.0935i) q^{50} +40.8138i q^{51} +(5.53478 + 30.6799i) q^{52} +6.41173i q^{53} +(-14.0845 + 16.8527i) q^{54} +32.3020i q^{55} -42.0232 q^{57} +(26.4457 + 22.1017i) q^{58} +15.9148 q^{59} +(-24.5148 - 135.888i) q^{60} +12.1570 q^{61} +(46.3912 + 38.7709i) q^{62} +(32.6548 + 55.0424i) q^{64} -69.0505 q^{65} +(21.8008 + 18.2197i) q^{66} -7.79739i q^{67} +(41.2339 - 7.43878i) q^{68} -50.3060 q^{69} -41.3627 q^{71} +(-42.9729 - 24.4719i) q^{72} -89.6091i q^{73} +(60.7472 + 50.7687i) q^{74} +208.432 q^{75} +(7.65920 + 42.4557i) q^{76} +(-38.9475 + 46.6025i) q^{78} +70.7950 q^{79} +(-132.819 + 49.5343i) q^{80} -98.4224 q^{81} +(-113.071 - 94.4981i) q^{82} -60.8673 q^{83} +92.8043i q^{85} +(-62.6896 - 52.3921i) q^{86} +67.1446i q^{87} +(14.4338 - 25.3459i) q^{88} -27.0204i q^{89} +(70.2407 - 84.0463i) q^{90} +(9.16883 + 50.8238i) q^{92} +117.785i q^{93} +(-64.1520 - 53.6143i) q^{94} -95.5542 q^{95} +(-41.4847 + 117.579i) q^{96} +3.26608i q^{97} +22.5377i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{2} + 8 q^{4} - 20 q^{8} + 64 q^{9}+O(q^{10}) \) 28 * q + 4 * q^2 + 8 * q^4 - 20 * q^8 + 64 * q^9	\( 28 q + 4 q^{2} + 8 q^{4} - 20 q^{8} + 64 q^{9} + 28 q^{15} - 32 q^{16} + 84 q^{18} - 92 q^{22} - 60 q^{23} + 64 q^{25} - 44 q^{30} - 176 q^{32} + 256 q^{36} + 40 q^{39} + 84 q^{44} - 136 q^{46} + 400 q^{50} + 124 q^{57} + 44 q^{58} + 124 q^{60} - 520 q^{64} + 104 q^{65} - 136 q^{71} - 192 q^{72} + 276 q^{74} - 956 q^{78} + 324 q^{79} + 36 q^{81} - 336 q^{86} - 100 q^{88} + 1020 q^{92} - 580 q^{95}+O(q^{100}) \) 28 * q + 4 * q^2 + 8 * q^4 - 20 * q^8 + 64 * q^9 + 28 * q^15 - 32 * q^16 + 84 * q^18 - 92 * q^22 - 60 * q^23 + 64 * q^25 - 44 * q^30 - 176 * q^32 + 256 * q^36 + 40 * q^39 + 84 * q^44 - 136 * q^46 + 400 * q^50 + 124 * q^57 + 44 * q^58 + 124 * q^60 - 520 * q^64 + 104 * q^65 - 136 * q^71 - 192 * q^72 + 276 * q^74 - 956 * q^78 + 324 * q^79 + 36 * q^81 - 336 * q^86 - 100 * q^88 + 1020 * q^92 - 580 * q^95

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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