LMFDB - Embedded newform 392.3.h.a.293.19

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			293.19
Character	$\chi$	$=$	392.293
Dual form			392.3.h.a.293.17

$q$-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	$-0.724976\pi$
$3$	−3.89635			−1.29878			−0.649392	+	0.760454i	$0.724976\pi$
$4$	−0.710153	+	3.93646i	−0.177538	+	0.984114i
$5$	−8.85969			−1.77194			−0.885969	−	0.463744i	$-0.846506\pi$
$5$	−8.85969			−1.77194			−0.885969	+	0.463744i	$0.846506\pi$
$6$	−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	$-0.947004\pi$
$11$		−	3.64596i		−	0.331451i	0.986172	−	0.165725i	$-0.0529965\pi$
$12$	2.76701	−	15.3378i	0.230584	−	1.27815i
$13$	7.79378			0.599522			0.299761	−	0.954014i	$-0.403093\pi$
$13$	7.79378			0.599522			0.299761	+	0.954014i	$0.403093\pi$
$14$		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	$-0.408397\pi$
$19$	10.7853			0.567646			0.283823	+	0.958877i	$0.408397\pi$
$20$	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	$-0.903975\pi$
$29$		−	17.2327i		−	0.594231i	0.954842	−	0.297115i	$-0.0960246\pi$
$30$	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	$-0.820340\pi$
$37$		−	39.5843i		−	1.06985i	0.844900	−	0.534924i	$-0.179660\pi$
$38$	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	$0.157552\pi$
$43$			40.8501i			0.950002i	−0.879985	+	0.475001i	$0.842448\pi$
$44$	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	$-0.980734\pi$
$53$		−	6.41173i		−	0.120976i	0.998169	−	0.0604880i	$-0.0192657\pi$
$54$	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	$-0.543062\pi$
$59$	−15.9148			−0.269743			−0.134871	+	0.990863i	$0.543062\pi$
$60$	−24.5148	+	135.888i	−0.408581	+	2.26481i
$61$	−12.1570			−0.199294			−0.0996472	−	0.995023i	$-0.531771\pi$
$61$	−12.1570			−0.199294			−0.0996472	+	0.995023i	$0.531771\pi$
$62$	−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	$0.0185328\pi$
$67$			7.79739i			0.116379i	−0.998306	+	0.0581895i	$0.981467\pi$
$68$	−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	$-0.380498\pi$
$83$	60.8673			0.733341			0.366671	+	0.930351i	$0.380498\pi$
$84$		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	$-0.738782\pi$
$101$	−137.714			−1.36351			−0.681754	+	0.731582i	$0.738782\pi$
$102$	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	$0.144774\pi$
$107$			94.0107i			0.878605i	−0.898339	+	0.439302i	$0.855226\pi$
$108$	−7.79866	+	43.2288i	−0.0722098	+	0.400267i
$109$		−	195.949i		−	1.79770i	−0.438258	−	0.898849i	$-0.644405\pi$
$109$		−	195.949i		−	1.79770i	0.438258	−	0.898849i	$-0.355595\pi$
$110$	−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	$-0.386175\pi$
$131$	91.7051			0.700039			0.350020	+	0.936742i	$0.386175\pi$
$132$	−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	$-0.454646\pi$
$139$	39.4768			0.284006			0.142003	+	0.989866i	$0.454646\pi$
$140$		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	$-0.896967\pi$
$149$		−	94.7831i		−	0.636128i	0.948069	−	0.318064i	$-0.103033\pi$
$150$	−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	$-0.525898\pi$
$157$	−25.5194			−0.162544			−0.0812720	+	0.996692i	$0.525898\pi$
$158$	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	$-0.799417\pi$
$163$		−	192.101i		−	1.17853i	0.807939	−	0.589267i	$-0.200583\pi$
$164$	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	$-0.564755\pi$
$173$	−69.9037			−0.404068			−0.202034	+	0.979379i	$0.564755\pi$
$174$	−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	$-0.766948\pi$
$179$		−	239.313i		−	1.33695i	0.743736	−	0.668473i	$-0.233052\pi$
$180$	38.8927	−	215.587i	0.216071	−	1.19770i
$181$	−36.2834			−0.200461			−0.100230	−	0.994964i	$-0.531958\pi$
$181$	−36.2834			−0.200461			−0.100230	+	0.994964i	$0.531958\pi$
$182$		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	$-0.987470\pi$
$197$		−	15.5053i		−	0.0787071i	0.999225	−	0.0393536i	$-0.0125299\pi$
$198$	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	$0.341051\pi$
$211$			370.470i			1.75578i	−0.478859	+	0.877892i	$0.658949\pi$
$212$	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	$-0.273365\pi$
$227$	296.618			1.30669			0.653344	+	0.757061i	$0.273365\pi$
$228$	29.8429	−	165.423i	0.130890	−	0.725537i
$229$	178.193			0.778135			0.389067	−	0.921209i	$-0.372797\pi$
$229$	178.193			0.778135			0.389067	+	0.921209i	$0.372797\pi$
$230$	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	$-0.583313\pi$
$251$	−129.896			−0.517513			−0.258756	+	0.965943i	$0.583313\pi$
$252$		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	$-0.729141\pi$
$269$	−354.695			−1.31857			−0.659285	+	0.751893i	$0.729141\pi$
$270$	−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	$0.231660\pi$
$277$			368.529i			1.33043i	−0.746653	+	0.665214i	$0.768340\pi$
$278$	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	$-0.387071\pi$
$283$	196.617			0.694761			0.347380	+	0.937724i	$0.387071\pi$
$284$	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	$-0.317693\pi$
$293$	317.573			1.08387			0.541933	+	0.840421i	$0.317693\pi$
$294$		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	$-0.569072\pi$
$307$	−132.193			−0.430596			−0.215298	+	0.976548i	$0.569072\pi$
$308$		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	$-0.909920\pi$
$317$		−	177.033i		−	0.558463i	0.960224	−	0.279231i	$-0.0900796\pi$
$318$	−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	$0.269700\pi$
$331$			496.160i			1.49897i	−0.662019	+	0.749487i	$0.730300\pi$
$332$	−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	$-0.661863\pi$
$347$		−	606.190i		−	1.74694i	0.486874	−	0.873472i	$-0.338137\pi$
$348$	−264.312	−	47.6830i	−0.759517	−	0.137020i
$349$	136.343			0.390669			0.195335	−	0.980737i	$-0.437421\pi$
$349$	136.343			0.390669			0.195335	+	0.980737i	$0.437421\pi$
$350$		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	$-0.839652\pi$
$373$		−	360.104i		−	0.965425i	0.875779	−	0.482713i	$-0.160348\pi$
$374$	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	$-0.995258\pi$
$379$		−	11.2929i		−	0.0297966i	0.999889	−	0.0148983i	$-0.00474246\pi$
$380$	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	$-0.982331\pi$
$389$		−	43.1631i		−	0.110959i	0.998460	−	0.0554796i	$-0.0176688\pi$
$390$	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	$-0.710072\pi$
$397$	−486.790			−1.22617			−0.613086	+	0.790016i	$0.710072\pi$
$398$	−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	$-0.727975\pi$
$419$	−550.169			−1.31305			−0.656527	+	0.754303i	$0.727975\pi$
$420$		0			0
$421$		−	579.599i		−	1.37672i	−0.725369	−	0.688360i	$-0.758331\pi$
$421$		−	579.599i		−	1.37672i	0.725369	−	0.688360i	$-0.241669\pi$
$422$	−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	$-0.853512\pi$
$443$		−	393.501i		−	0.888265i	0.895961	−	0.444133i	$-0.146488\pi$
$444$	−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	$-0.813366\pi$
$461$	−768.006			−1.66596			−0.832978	+	0.553306i	$0.813366\pi$
$462$		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	$-0.490136\pi$
$467$	28.9376			0.0619648			0.0309824	+	0.999520i	$0.490136\pi$
$468$	−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	$-0.975275\pi$
$491$		−	76.2017i		−	0.155197i	0.996985	−	0.0775985i	$-0.0247252\pi$
$492$	−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	$-0.824470\pi$
$499$		−	522.871i		−	1.04784i	0.851768	−	0.523919i	$-0.175530\pi$
$500$	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	$-0.598547\pi$
$509$	−310.157			−0.609346			−0.304673	+	0.952457i	$0.598547\pi$
$510$	−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	$-0.336541\pi$
$523$	513.846			0.982497			0.491249	+	0.871019i	$0.336541\pi$
$524$	−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	$0.0315525\pi$
$541$			107.078i			0.197926i	−0.995091	+	0.0989630i	$0.968447\pi$
$542$	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	$0.0126088\pi$
$547$			43.3240i			0.0792030i	−0.999216	+	0.0396015i	$0.987391\pi$
$548$	−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	$-0.979269\pi$
$557$		−	72.5011i		−	0.130164i	0.997880	−	0.0650818i	$-0.0207308\pi$
$558$	−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	$-0.673877\pi$
$563$	−584.943			−1.03897			−0.519487	+	0.854478i	$0.673877\pi$
$564$	−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	$-0.640816\pi$
$571$		−	1032.06i		−	1.80747i	0.428097	−	0.903733i	$-0.359184\pi$
$572$	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	$-0.526136\pi$
$587$	−96.2876			−0.164033			−0.0820167	+	0.996631i	$0.526136\pi$
$588$		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	$0.0883671\pi$
$613$			335.999i			0.548123i	−0.961712	+	0.274061i	$0.911633\pi$
$614$	−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	$-0.699484\pi$
$619$	−726.053			−1.17294			−0.586472	+	0.809969i	$0.699484\pi$
$620$	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	$-0.213187\pi$
$643$	1008.20			1.56796			0.783979	+	0.620787i	$0.213187\pi$
$644$		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	$0.274070\pi$
$653$			990.608i			1.51701i	−0.651666	+	0.758506i	$0.725930\pi$
$654$	−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	$-0.980127\pi$
$659$		−	82.2318i		−	0.124783i	0.998052	−	0.0623914i	$-0.0198727\pi$
$660$	495.443	+	89.3800i	0.750671	+	0.135424i
$661$	626.220			0.947382			0.473691	−	0.880691i	$-0.342921\pi$
$661$	626.220			0.947382			0.473691	+	0.880691i	$0.342921\pi$
$662$	−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	$-0.365200\pi$
$677$	556.414			0.821882			0.410941	+	0.911662i	$0.365200\pi$
$678$	−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	$0.196683\pi$
$683$			791.356i			1.15865i	−0.815098	+	0.579323i	$0.803317\pi$
$684$	−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	$-0.749776\pi$
$691$	−976.534			−1.41322			−0.706609	+	0.707604i	$0.749776\pi$
$692$	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	$-0.791204\pi$
$701$		−	855.098i		−	1.21983i	0.792468	−	0.609913i	$-0.208796\pi$
$702$	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	$-0.924435\pi$
$709$		−	333.471i		−	0.470340i	0.971954	−	0.235170i	$-0.0755647\pi$
$710$	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	$-0.538814\pi$
$733$	−178.318			−0.243272			−0.121636	+	0.992575i	$0.538814\pi$
$734$	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	$0.203650\pi$
$739$			882.401i			1.19405i	−0.802224	+	0.597024i	$0.796350\pi$
$740$	−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	$-0.996839\pi$
$757$		−	15.0345i		−	0.0198606i	0.999951	−	0.00993032i	$-0.00316097\pi$
$758$	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	$-0.465093\pi$
$773$	169.198			0.218885			0.109442	+	0.993993i	$0.465093\pi$
$774$	−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	$-0.490597\pi$
$787$	46.4874			0.0590691			0.0295346	+	0.999564i	$0.490597\pi$
$788$	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	$-0.177752\pi$
$797$	1351.86			1.69618			0.848092	+	0.529850i	$0.177752\pi$
$798$		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	$-0.360342\pi$
$811$	689.037			0.849614			0.424807	+	0.905284i	$0.360342\pi$
$812$		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	$-0.995669\pi$
$821$		−	22.3423i		−	0.0272135i	0.999907	−	0.0136067i	$-0.00433129\pi$
$822$	−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	$-0.909012\pi$
$827$		−	466.377i		−	0.563938i	0.959424	−	0.281969i	$-0.0909875\pi$
$828$	56.6776	−	314.170i	0.0684513	−	0.379433i
$829$	1500.70			1.81025			0.905126	−	0.425142i	$-0.139776\pi$
$829$	1500.70			1.81025			0.905126	+	0.425142i	$0.139776\pi$
$830$	−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	$-0.319000\pi$
$853$	918.640			1.07695			0.538476	+	0.842641i	$0.319000\pi$
$854$		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	$-0.204019\pi$
$859$	1377.03			1.60306			0.801532	+	0.597952i	$0.204019\pi$
$860$	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	$-0.869337\pi$
$877$		−	699.948i		−	0.798116i	0.916926	−	0.399058i	$-0.130663\pi$
$878$	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	$0.340297\pi$
$883$			1548.35i			1.75351i	−0.480935	+	0.876756i	$0.659703\pi$
$884$	−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	$-0.869347\pi$
$907$		−	723.838i		−	0.798057i	0.916939	−	0.399029i	$-0.130653\pi$
$908$	−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	$-0.455783\pi$
$941$	260.591			0.276930			0.138465	+	0.990367i	$0.455783\pi$
$942$	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	$0.173730\pi$
$947$			983.163i			1.03819i	−0.854717	+	0.519093i	$0.826270\pi$
$948$	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	$-0.740244\pi$
$971$	−1330.47			−1.37021			−0.685105	+	0.728445i	$0.740244\pi$
$972$	−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	$-0.780452\pi$
$997$	−1538.21			−1.54283			−0.771417	+	0.636330i	$0.780452\pi$
$998$	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.293.19		28
4.3	odd	2		1568.3.h.a.881.26		28
7.2	even	3		56.3.j.a.45.10	yes	28
7.3	odd	6		56.3.j.a.5.1	✓	28
7.4	even	3		392.3.j.e.117.1		28
7.5	odd	6		392.3.j.e.325.10		28
7.6	odd	2	inner	392.3.h.a.293.20		28
8.3	odd	2		1568.3.h.a.881.3		28
8.5	even	2	inner	392.3.h.a.293.18		28
28.3	even	6		224.3.n.a.145.13		28
28.23	odd	6		224.3.n.a.17.2		28
28.27	even	2		1568.3.h.a.881.4		28
56.3	even	6		224.3.n.a.145.2		28
56.5	odd	6		392.3.j.e.325.1		28
56.13	odd	2	inner	392.3.h.a.293.17		28
56.27	even	2		1568.3.h.a.881.25		28
56.37	even	6		56.3.j.a.45.1	yes	28
56.45	odd	6		56.3.j.a.5.10	yes	28
56.51	odd	6		224.3.n.a.17.13		28
56.53	even	6		392.3.j.e.117.10		28

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

Fields

Representations

Groups

Database

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