LMFDB - Embedded newform 588.3.g.h.295.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [588,3,Mod(295,588)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(588, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 0])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("588.295"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	588.g (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,4,0,12,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$16.0218395444$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			295.6
Character	$\chi$	$=$	588.295
Dual form			588.3.g.h.295.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.44448 - 1.38328i) q^{2} +1.73205i q^{3} +(0.173067 + 3.99625i) q^{4} -1.50286 q^{5} +(2.39591 - 2.50192i) q^{6} +(5.27795 - 6.01192i) q^{8} -3.00000 q^{9} +(2.17086 + 2.07888i) q^{10} +9.21570i q^{11} +(-6.92172 + 0.299760i) q^{12} -5.97750 q^{13} -2.60304i q^{15} +(-15.9401 + 1.38324i) q^{16} +3.95449 q^{17} +(4.33345 + 4.14984i) q^{18} -3.59885i q^{19} +(-0.260096 - 6.00582i) q^{20} +(12.7479 - 13.3119i) q^{22} +21.6730i q^{23} +(10.4130 + 9.14168i) q^{24} -22.7414 q^{25} +(8.63441 + 8.26857i) q^{26} -5.19615i q^{27} +47.5775 q^{29} +(-3.60073 + 3.76004i) q^{30} -38.5042i q^{31} +(24.9386 + 20.0516i) q^{32} -15.9621 q^{33} +(-5.71220 - 5.47018i) q^{34} +(-0.519200 - 11.9888i) q^{36} -52.4915 q^{37} +(-4.97822 + 5.19847i) q^{38} -10.3533i q^{39} +(-7.93204 + 9.03510i) q^{40} -64.9569 q^{41} +16.8099i q^{43} +(-36.8283 + 1.59493i) q^{44} +4.50859 q^{45} +(29.9798 - 31.3063i) q^{46} -68.2794i q^{47} +(-2.39584 - 27.6091i) q^{48} +(32.8496 + 31.4578i) q^{50} +6.84938i q^{51} +(-1.03451 - 23.8876i) q^{52} -18.1753 q^{53} +(-7.18774 + 7.50576i) q^{54} -13.8499i q^{55} +6.23338 q^{57} +(-68.7249 - 65.8130i) q^{58} -49.0800i q^{59} +(10.4024 - 0.450499i) q^{60} -98.5495 q^{61} +(-53.2622 + 55.6188i) q^{62} +(-8.28647 - 63.4613i) q^{64} +8.98337 q^{65} +(23.0569 + 22.0800i) q^{66} -129.352i q^{67} +(0.684392 + 15.8032i) q^{68} -37.5387 q^{69} +61.8601i q^{71} +(-15.8339 + 18.0358i) q^{72} -95.7877 q^{73} +(75.8232 + 72.6106i) q^{74} -39.3893i q^{75} +(14.3819 - 0.622841i) q^{76} +(-14.3216 + 14.9552i) q^{78} -13.1219i q^{79} +(23.9558 - 2.07882i) q^{80} +9.00000 q^{81} +(93.8292 + 89.8537i) q^{82} +91.0240i q^{83} -5.94306 q^{85} +(23.2528 - 24.2816i) q^{86} +82.4066i q^{87} +(55.4041 + 48.6400i) q^{88} -90.7057 q^{89} +(-6.51258 - 6.23665i) q^{90} +(-86.6108 + 3.75087i) q^{92} +66.6913 q^{93} +(-94.4496 + 98.6285i) q^{94} +5.40857i q^{95} +(-34.7303 + 43.1950i) q^{96} -7.05515 q^{97} -27.6471i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{2} + 12 q^{4} - 20 q^{8} - 72 q^{9} - 60 q^{16} - 12 q^{18} + 168 q^{22} + 120 q^{25} + 64 q^{29} - 236 q^{32} - 36 q^{36} - 192 q^{37} - 360 q^{44} - 72 q^{46} + 532 q^{50} + 432 q^{53} + 240 q^{58}+ \cdots - 96 q^{93}+O(q^{100}) $ 24 * q + 4 * q^2 + 12 * q^4 - 20 * q^8 - 72 * q^9 - 60 * q^16 - 12 * q^18 + 168 * q^22 + 120 * q^25 + 64 * q^29 - 236 * q^32 - 36 * q^36 - 192 * q^37 - 360 * q^44 - 72 * q^46 + 532 * q^50 + 432 * q^53 + 240 * q^58 + 72 * q^60 - 372 * q^64 - 560 * q^65 + 60 * q^72 + 96 * q^74 + 216 * q^78 + 216 * q^81 + 144 * q^85 + 816 * q^86 - 72 * q^88 - 504 * q^92 - 96 * q^93

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	−1.44448	−	1.38328i	−0.722242	−	0.691641i
$2$	−1.44448	−	1.38328i	−0.722242	−	0.691641i
$3$			1.73205i			0.577350i
$3$			1.73205i			0.577350i
$4$	0.173067	+	3.99625i	0.0432667	+	0.999064i
$5$	−1.50286			−0.300573			−0.150286	−	0.988643i	$-0.548020\pi$
$5$	−1.50286			−0.300573			−0.150286	+	0.988643i	$0.548020\pi$
$6$	2.39591	−	2.50192i	0.399319	−	0.416987i
$7$		0			0
$7$		0			0
$8$	5.27795	−	6.01192i	0.659744	−	0.751491i
$9$	−3.00000			−0.333333
$10$	2.17086	+	2.07888i	0.217086	+	0.207888i
$11$			9.21570i			0.837791i	0.908034	+	0.418895i	$0.137583\pi$
$11$			9.21570i			0.837791i	−0.908034	+	0.418895i	$0.862417\pi$
$12$	−6.92172	+	0.299760i	−0.576810	+	0.0249800i
$13$	−5.97750			−0.459808			−0.229904	−	0.973213i	$-0.573841\pi$
$13$	−5.97750			−0.459808			−0.229904	+	0.973213i	$0.573841\pi$
$14$		0			0
$15$		−	2.60304i		−	0.173536i
$16$	−15.9401	+	1.38324i	−0.996256	+	0.0864524i
$17$	3.95449			0.232617			0.116309	−	0.993213i	$-0.462894\pi$
$17$	3.95449			0.232617			0.116309	+	0.993213i	$0.462894\pi$
$18$	4.33345	+	4.14984i	0.240747	+	0.230547i
$19$		−	3.59885i		−	0.189413i	−0.995505	−	0.0947065i	$-0.969809\pi$
$19$		−	3.59885i		−	0.189413i	0.995505	−	0.0947065i	$-0.0301913\pi$
$20$	−0.260096	−	6.00582i	−0.0130048	−	0.300291i
$21$		0			0
$22$	12.7479	−	13.3119i	0.579450	−	0.605088i
$23$			21.6730i			0.942304i	0.882052	+	0.471152i	$0.156162\pi$
$23$			21.6730i			0.942304i	−0.882052	+	0.471152i	$0.843838\pi$
$24$	10.4130	+	9.14168i	0.433873	+	0.380903i
$25$	−22.7414			−0.909656
$26$	8.63441	+	8.26857i	0.332093	+	0.318022i
$27$		−	5.19615i		−	0.192450i
$28$		0			0
$29$	47.5775			1.64060			0.820301	−	0.571931i	$-0.193806\pi$
$29$	47.5775			1.64060			0.820301	+	0.571931i	$0.193806\pi$
$30$	−3.60073	+	3.76004i	−0.120024	+	0.125335i
$31$		−	38.5042i		−	1.24207i	−0.783782	−	0.621036i	$-0.786712\pi$
$31$		−	38.5042i		−	1.24207i	0.783782	−	0.621036i	$-0.213288\pi$
$32$	24.9386	+	20.0516i	0.779332	+	0.626612i
$33$	−15.9621			−0.483699
$34$	−5.71220	−	5.47018i	−0.168006	−	0.160888i
$35$		0			0
$36$	−0.519200	−	11.9888i	−0.0144222	−	0.333021i
$37$	−52.4915			−1.41869			−0.709345	−	0.704861i	$-0.751009\pi$
$37$	−52.4915			−1.41869			−0.709345	+	0.704861i	$0.751009\pi$
$38$	−4.97822	+	5.19847i	−0.131006	+	0.136802i
$39$		−	10.3533i		−	0.265470i
$40$	−7.93204	+	9.03510i	−0.198301	+	0.225877i
$41$	−64.9569			−1.58432			−0.792158	−	0.610316i	$-0.791042\pi$
$41$	−64.9569			−1.58432			−0.792158	+	0.610316i	$0.791042\pi$
$42$		0			0
$43$			16.8099i			0.390928i	0.980711	+	0.195464i	$0.0626212\pi$
$43$			16.8099i			0.390928i	−0.980711	+	0.195464i	$0.937379\pi$
$44$	−36.8283	+	1.59493i	−0.837006	+	0.0362484i
$45$	4.50859			0.100191
$46$	29.9798	−	31.3063i	0.651736	−	0.680571i
$47$		−	68.2794i		−	1.45275i	−0.687297	−	0.726377i	$-0.741203\pi$
$47$		−	68.2794i		−	1.45275i	0.687297	−	0.726377i	$-0.258797\pi$
$48$	−2.39584	−	27.6091i	−0.0499133	−	0.575189i
$49$		0			0
$50$	32.8496	+	31.4578i	0.656992	+	0.629155i
$51$			6.84938i			0.134302i
$52$	−1.03451	−	23.8876i	−0.0198944	−	0.459377i
$53$	−18.1753			−0.342929			−0.171465	−	0.985190i	$-0.554850\pi$
$53$	−18.1753			−0.342929			−0.171465	+	0.985190i	$0.554850\pi$
$54$	−7.18774	+	7.50576i	−0.133106	+	0.138996i
$55$		−	13.8499i		−	0.251817i
$56$		0			0
$57$	6.23338			0.109358
$58$	−68.7249	−	65.8130i	−1.18491	−	1.13471i
$59$		−	49.0800i		−	0.831865i	−0.909395	−	0.415932i	$-0.863455\pi$
$59$		−	49.0800i		−	0.831865i	0.909395	−	0.415932i	$-0.136545\pi$
$60$	10.4024	−	0.450499i	0.173373	−	0.00750832i
$61$	−98.5495			−1.61557			−0.807783	−	0.589480i	$-0.799333\pi$
$61$	−98.5495			−1.61557			−0.807783	+	0.589480i	$0.799333\pi$
$62$	−53.2622	+	55.6188i	−0.859068	+	0.897077i
$63$		0			0
$64$	−8.28647	−	63.4613i	−0.129476	−	0.991583i
$65$	8.98337			0.138206
$66$	23.0569	+	22.0800i	0.349347	+	0.334546i
$67$		−	129.352i		−	1.93062i	−0.261099	−	0.965312i	$-0.584085\pi$
$67$		−	129.352i		−	1.93062i	0.261099	−	0.965312i	$-0.415915\pi$
$68$	0.684392	+	15.8032i	0.0100646	+	0.232399i
$69$	−37.5387			−0.544039
$70$		0			0
$71$			61.8601i			0.871269i	0.900124	+	0.435635i	$0.143476\pi$
$71$			61.8601i			0.871269i	−0.900124	+	0.435635i	$0.856524\pi$
$72$	−15.8339	+	18.0358i	−0.219915	+	0.250497i
$73$	−95.7877			−1.31216			−0.656080	−	0.754691i	$-0.727787\pi$
$73$	−95.7877			−1.31216			−0.656080	+	0.754691i	$0.727787\pi$
$74$	75.8232	+	72.6106i	1.02464	+	0.981224i
$75$		−	39.3893i		−	0.525190i
$76$	14.3819	−	0.622841i	0.189236	−	0.00819527i
$77$		0			0
$78$	−14.3216	+	14.9552i	−0.183610	+	0.191734i
$79$		−	13.1219i		−	0.166100i	−0.996545	−	0.0830499i	$-0.973534\pi$
$79$		−	13.1219i		−	0.166100i	0.996545	−	0.0830499i	$-0.0264661\pi$
$80$	23.9558	−	2.07882i	0.299447	−	0.0259852i
$81$	9.00000			0.111111
$82$	93.8292	+	89.8537i	1.14426	+	1.09578i
$83$			91.0240i			1.09667i	0.836257	+	0.548337i	$0.184739\pi$
$83$			91.0240i			1.09667i	−0.836257	+	0.548337i	$0.815261\pi$
$84$		0			0
$85$	−5.94306			−0.0699184
$86$	23.2528	−	24.2816i	0.270381	−	0.282344i
$87$			82.4066i			0.947203i
$88$	55.4041	+	48.6400i	0.629592	+	0.552727i
$89$	−90.7057			−1.01917			−0.509583	−	0.860422i	$-0.670200\pi$
$89$	−90.7057			−1.01917			−0.509583	+	0.860422i	$0.670200\pi$
$90$	−6.51258	−	6.23665i	−0.0723620	−	0.0692961i
$91$		0			0
$92$	−86.6108	+	3.75087i	−0.941422	+	0.0407704i
$93$	66.6913			0.717111
$94$	−94.4496	+	98.6285i	−1.00478	+	1.04924i
$95$			5.40857i			0.0569323i
$96$	−34.7303	+	43.1950i	−0.361774	+	0.449947i
$97$	−7.05515			−0.0727335			−0.0363668	−	0.999339i	$-0.511578\pi$
$97$	−7.05515			−0.0727335			−0.0363668	+	0.999339i	$0.511578\pi$
$98$		0			0
$99$		−	27.6471i		−	0.279264i
$100$	−3.93578	−	90.8804i	−0.0393578	−	0.908804i
$101$	−87.1632			−0.863002			−0.431501	−	0.902112i	$-0.642016\pi$
$101$	−87.1632			−0.863002			−0.431501	+	0.902112i	$0.642016\pi$
$102$	9.47462	−	9.89383i	0.0928885	−	0.0969983i
$103$			89.5467i			0.869386i	0.900579	+	0.434693i	$0.143143\pi$
$103$			89.5467i			0.869386i	−0.900579	+	0.434693i	$0.856857\pi$
$104$	−31.5490	+	35.9363i	−0.303356	+	0.345541i
$105$		0			0
$106$	26.2539	+	25.1415i	0.247678	+	0.237184i
$107$			54.0435i			0.505079i	0.967587	+	0.252540i	$0.0812658\pi$
$107$			54.0435i			0.505079i	−0.967587	+	0.252540i	$0.918734\pi$
$108$	20.7651	−	0.899281i	0.192270	−	0.00832668i
$109$	−74.5665			−0.684097			−0.342048	−	0.939682i	$-0.611121\pi$
$109$	−74.5665			−0.684097			−0.342048	+	0.939682i	$0.611121\pi$
$110$	−19.1584	+	20.0060i	−0.174167	+	0.181873i
$111$		−	90.9180i		−	0.819081i
$112$		0			0
$113$	16.5662			0.146603			0.0733016	−	0.997310i	$-0.476646\pi$
$113$	16.5662			0.146603			0.0733016	+	0.997310i	$0.476646\pi$
$114$	−9.00402	−	8.62252i	−0.0789826	−	0.0756362i
$115$		−	32.5715i		−	0.283231i
$116$	8.23408	+	190.132i	0.0709835	+	1.63907i
$117$	17.9325			0.153269
$118$	−67.8915	+	70.8953i	−0.575352	+	0.600808i
$119$		0			0
$120$	−15.6493	−	13.7387i	−0.130410	−	0.114489i
$121$	36.0709			0.298107
$122$	142.353	+	136.322i	1.16683	+	1.11739i
$123$		−	112.509i		−	0.914705i
$124$	153.873	−	6.66380i	1.24091	−	0.0537404i
$125$	71.7488			0.573990
$126$		0			0
$127$			85.8294i			0.675822i	0.941178	+	0.337911i	$0.109720\pi$
$127$			85.8294i			0.675822i	−0.941178	+	0.337911i	$0.890280\pi$
$128$	−75.8151	+	103.131i	−0.592306	+	0.805713i
$129$	−29.1156			−0.225702
$130$	−12.9763	−	12.4265i	−0.0998179	−	0.0955887i
$131$		−	225.955i		−	1.72485i	−0.506187	−	0.862424i	$-0.668945\pi$
$131$		−	225.955i		−	1.72485i	0.506187	−	0.862424i	$-0.331055\pi$
$132$	−2.76250	−	63.7884i	−0.0209280	−	0.483246i
$133$		0			0
$134$	−178.930	+	186.847i	−1.33530	+	1.39438i
$135$			7.80911i			0.0578452i
$136$	20.8716	−	23.7741i	0.153468	−	0.174810i
$137$	−102.233			−0.746228			−0.373114	−	0.927785i	$-0.621710\pi$
$137$	−102.233			−0.746228			−0.373114	+	0.927785i	$0.621710\pi$
$138$	54.2241	+	51.9266i	0.392928	+	0.376280i
$139$		−	204.882i		−	1.47397i	−0.675909	−	0.736985i	$-0.736249\pi$
$139$		−	204.882i		−	1.47397i	0.675909	−	0.736985i	$-0.263751\pi$
$140$		0			0
$141$	118.263			0.838748
$142$	85.5699	−	89.3559i	0.602605	−	0.629267i
$143$		−	55.0869i		−	0.385223i
$144$	47.8203	−	4.14971i	0.332085	−	0.0288175i
$145$	−71.5025			−0.493120
$146$	138.364	+	132.501i	0.947697	+	0.907544i
$147$		0			0
$148$	−9.08454	−	209.770i	−0.0613820	−	1.41736i
$149$	167.149			1.12180			0.560901	−	0.827883i	$-0.310455\pi$
$149$	167.149			1.12180			0.560901	+	0.827883i	$0.310455\pi$
$150$	−54.4864	+	56.8972i	−0.363243	+	0.379314i
$151$		−	102.488i		−	0.678730i	−0.940655	−	0.339365i	$-0.889788\pi$
$151$		−	102.488i		−	0.678730i	0.940655	−	0.339365i	$-0.110212\pi$
$152$	−21.6360	−	18.9945i	−0.142342	−	0.124964i
$153$	−11.8635			−0.0775391
$154$		0			0
$155$			57.8666i			0.373333i
$156$	41.3746	−	1.79182i	0.265222	−	0.0114860i
$157$	41.4338			0.263910			0.131955	−	0.991256i	$-0.457875\pi$
$157$	41.4338			0.263910			0.131955	+	0.991256i	$0.457875\pi$
$158$	−18.1513	+	18.9544i	−0.114881	+	0.119964i
$159$		−	31.4805i		−	0.197990i
$160$	−37.4793	−	30.1348i	−0.234246	−	0.188342i
$161$		0			0
$162$	−13.0004	−	12.4495i	−0.0802491	−	0.0768490i
$163$			193.889i			1.18950i	0.803909	+	0.594752i	$0.202750\pi$
$163$			193.889i			1.18950i	−0.803909	+	0.594752i	$0.797250\pi$
$164$	−11.2419	−	259.584i	−0.0685481	−	1.58283i
$165$	23.9888			0.145387
$166$	125.912	−	131.483i	0.758505	−	0.792064i
$167$			149.318i			0.894120i	0.894504	+	0.447060i	$0.147529\pi$
$167$			149.318i			0.894120i	−0.894504	+	0.447060i	$0.852471\pi$
$168$		0			0
$169$	−133.269			−0.788577
$170$	8.58466	+	8.22093i	0.0504980	+	0.0483584i
$171$			10.7965i			0.0631376i
$172$	−67.1766	+	2.90923i	−0.390562	+	0.0169141i
$173$	52.1094			0.301210			0.150605	−	0.988594i	$-0.451878\pi$
$173$	52.1094			0.301210			0.150605	+	0.988594i	$0.451878\pi$
$174$	113.992	−	119.035i	0.655124	−	0.684109i
$175$		0			0
$176$	−12.7475	−	146.899i	−0.0724290	−	0.834654i
$177$	85.0091			0.480277
$178$	131.023	+	125.472i	0.736084	+	0.704896i
$179$			16.4589i			0.0919494i	0.998943	+	0.0459747i	$0.0146394\pi$
$179$			16.4589i			0.0919494i	−0.998943	+	0.0459747i	$0.985361\pi$
$180$	0.780287	+	18.0175i	0.00433493	+	0.100097i
$181$	317.896			1.75633			0.878164	−	0.478359i	$-0.158768\pi$
$181$	317.896			1.75633			0.878164	+	0.478359i	$0.158768\pi$
$182$		0			0
$183$		−	170.693i		−	0.932747i
$184$	130.296	+	114.389i	0.708132	+	0.621679i
$185$	78.8876			0.426419
$186$	−96.3345	−	92.2528i	−0.517927	−	0.495983i
$187$			36.4434i			0.194885i
$188$	272.862	−	11.8169i	1.45139	−	0.0628558i
$189$		0			0
$190$	7.48158	−	7.81260i	0.0393767	−	0.0411189i
$191$			15.0206i			0.0786418i	0.999227	+	0.0393209i	$0.0125195\pi$
$191$			15.0206i			0.0786418i	−0.999227	+	0.0393209i	$0.987481\pi$
$192$	109.918	−	14.3526i	0.572490	−	0.0747531i
$193$	−209.347			−1.08470			−0.542349	−	0.840153i	$-0.682465\pi$
$193$	−209.347			−1.08470			−0.542349	+	0.840153i	$0.682465\pi$
$194$	10.1910	+	9.75926i	0.0525312	+	0.0503054i
$195$			15.5597i			0.0797931i
$196$		0			0
$197$	6.06078			0.0307654			0.0153827	−	0.999882i	$-0.495103\pi$
$197$	6.06078			0.0307654			0.0153827	+	0.999882i	$0.495103\pi$
$198$	−38.2437	+	39.9358i	−0.193150	+	0.201696i
$199$		−	128.438i		−	0.645417i	−0.946498	−	0.322708i	$-0.895407\pi$
$199$		−	128.438i		−	0.645417i	0.946498	−	0.322708i	$-0.104593\pi$
$200$	−120.028	+	136.720i	−0.600140	+	0.683598i
$201$	224.044			1.11465
$202$	125.906	+	120.571i	0.623296	+	0.596887i
$203$		0			0
$204$	−27.3719	+	1.18540i	−0.134176	+	0.00581079i
$205$	97.6214			0.476202
$206$	123.868	−	129.349i	0.601302	−	0.627907i
$207$		−	65.0190i		−	0.314101i
$208$	95.2820	−	8.26831i	0.458086	−	0.0397515i
$209$	33.1659			0.158688
$210$		0			0
$211$			75.4230i			0.357455i	0.983899	+	0.178727i	$0.0571980\pi$
$211$			75.4230i			0.357455i	−0.983899	+	0.178727i	$0.942802\pi$
$212$	−3.14553	−	72.6329i	−0.0148374	−	0.342608i
$213$	−107.145			−0.503028
$214$	74.7573	−	78.0649i	0.349333	−	0.364789i
$215$		−	25.2630i		−	0.117502i
$216$	−31.2389	−	27.4250i	−0.144624	−	0.126968i
$217$		0			0
$218$	107.710	+	103.146i	0.494083	+	0.473149i
$219$		−	165.909i		−	0.757576i
$220$	55.3479	−	2.39696i	0.251581	−	0.0108953i
$221$	−23.6380			−0.106959
$222$	−125.765	+	131.330i	−0.566510	+	0.591575i
$223$		−	167.759i		−	0.752282i	−0.926562	−	0.376141i	$-0.877251\pi$
$223$		−	167.759i		−	0.752282i	0.926562	−	0.376141i	$-0.122749\pi$
$224$		0			0
$225$	68.2242			0.303219
$226$	−23.9295	−	22.9156i	−0.105883	−	0.101397i
$227$		−	158.856i		−	0.699808i	−0.936786	−	0.349904i	$-0.886214\pi$
$227$		−	158.856i		−	0.699808i	0.936786	−	0.349904i	$-0.113786\pi$
$228$	1.07879	+	24.9102i	0.00473154	+	0.109255i
$229$	−150.418			−0.656849			−0.328425	−	0.944530i	$-0.606518\pi$
$229$	−150.418			−0.656849			−0.328425	+	0.944530i	$0.606518\pi$
$230$	−45.0556	+	47.0491i	−0.195894	+	0.204561i
$231$		0			0
$232$	251.112	−	286.032i	1.08238	−	1.23290i
$233$	79.0711			0.339361			0.169681	−	0.985499i	$-0.445726\pi$
$233$	79.0711			0.339361			0.169681	+	0.985499i	$0.445726\pi$
$234$	−25.9032	−	24.8057i	−0.110698	−	0.106007i
$235$			102.615i			0.436658i
$236$	196.136	−	8.49412i	0.831086	−	0.0359920i
$237$	22.7278			0.0958978
$238$		0			0
$239$		−	98.8210i		−	0.413477i	−0.978396	−	0.206739i	$-0.933715\pi$
$239$		−	98.8210i		−	0.413477i	0.978396	−	0.206739i	$-0.0662850\pi$
$240$	3.60062	+	41.4926i	0.0150026	+	0.172886i
$241$	432.653			1.79524			0.897621	−	0.440768i	$-0.145294\pi$
$241$	432.653			1.79524			0.897621	+	0.440768i	$0.145294\pi$
$242$	−52.1038	−	49.8962i	−0.215305	−	0.206183i
$243$			15.5885i			0.0641500i
$244$	−17.0556	−	393.829i	−0.0699002	−	1.61405i
$245$		0			0
$246$	−155.631	+	162.517i	−0.632647	+	0.660638i
$247$			21.5121i			0.0870936i
$248$	−231.485	−	203.223i	−0.933406	−	0.819450i
$249$	−157.658			−0.633165
$250$	−103.640	−	99.2488i	−0.414560	−	0.396995i
$251$			311.174i			1.23974i	0.784705	+	0.619869i	$0.212814\pi$
$251$			311.174i			1.23974i	−0.784705	+	0.619869i	$0.787186\pi$
$252$		0			0
$253$	−199.732			−0.789454
$254$	118.726	−	123.979i	0.467426	−	0.488107i
$255$		−	10.2937i		−	0.0403674i
$256$	252.173	−	44.0979i	0.985052	−	0.172257i
$257$	437.145			1.70095			0.850477	−	0.526012i	$-0.176313\pi$
$257$	437.145			1.70095			0.850477	+	0.526012i	$0.176313\pi$
$258$	42.0570	+	40.2750i	0.163012	+	0.156105i
$259$		0			0
$260$	1.55472	+	35.8998i	0.00597970	+	0.138076i
$261$	−142.732			−0.546868
$262$	−312.559	+	326.388i	−1.19297	+	1.24576i
$263$			477.684i			1.81629i	0.418655	+	0.908145i	$0.362502\pi$
$263$			477.684i			1.81629i	−0.418655	+	0.908145i	$0.637498\pi$
$264$	−84.2470	+	95.9627i	−0.319117	+	0.363495i
$265$	27.3149			0.103075
$266$		0			0
$267$		−	157.107i		−	0.588415i
$268$	516.923	−	22.3865i	1.92882	−	0.0835317i
$269$	−102.048			−0.379359			−0.189680	−	0.981846i	$-0.560745\pi$
$269$	−102.048			−0.379359			−0.189680	+	0.981846i	$0.560745\pi$
$270$	10.8022	−	11.2801i	0.0400081	−	0.0417782i
$271$			495.848i			1.82970i	0.403795	+	0.914849i	$0.367691\pi$
$271$			495.848i			1.82970i	−0.403795	+	0.914849i	$0.632309\pi$
$272$	−63.0350	+	5.47000i	−0.231746	+	0.0201103i
$273$		0			0
$274$	147.674	+	141.417i	0.538957	+	0.516122i
$275$		−	209.578i		−	0.762101i
$276$	−6.49671	−	150.014i	−0.0235388	−	0.543530i
$277$	297.781			1.07502			0.537511	−	0.843256i	$-0.319364\pi$
$277$	297.781			1.07502			0.537511	+	0.843256i	$0.319364\pi$
$278$	−283.409	+	295.949i	−1.01946	+	1.06456i
$279$			115.513i			0.414024i
$280$		0			0
$281$	58.1842			0.207061			0.103531	−	0.994626i	$-0.466986\pi$
$281$	58.1842			0.207061			0.103531	+	0.994626i	$0.466986\pi$
$282$	−170.830	−	163.592i	−0.605779	−	0.580112i
$283$			232.119i			0.820209i	0.912038	+	0.410105i	$0.134508\pi$
$283$			232.119i			0.820209i	−0.912038	+	0.410105i	$0.865492\pi$
$284$	−247.209	+	10.7059i	−0.870453	+	0.0376969i
$285$	−9.36792			−0.0328699
$286$	−76.2006	+	79.5721i	−0.266436	+	0.278224i
$287$		0			0
$288$	−74.8158	−	60.1547i	−0.259777	−	0.208871i
$289$	−273.362			−0.945889
$290$	103.284	+	98.9080i	0.356152	+	0.341062i
$291$		−	12.2199i		−	0.0419927i
$292$	−16.5777	−	382.792i	−0.0567729	−	1.31093i
$293$	−260.048			−0.887537			−0.443768	−	0.896142i	$-0.646359\pi$
$293$	−260.048			−0.887537			−0.443768	+	0.896142i	$0.646359\pi$
$294$		0			0
$295$			73.7606i			0.250036i
$296$	−277.048	+	315.575i	−0.935972	+	1.06613i
$297$	47.8862			0.161233
$298$	−241.443	−	231.214i	−0.810213	−	0.775884i
$299$		−	129.550i		−	0.433279i
$300$	157.410	−	6.81697i	0.524698	−	0.0227232i
$301$		0			0
$302$	−141.770	+	148.043i	−0.469437	+	0.490207i
$303$		−	150.971i		−	0.498254i
$304$	4.97806	+	57.3659i	0.0163752	+	0.188704i
$305$	148.106			0.485595
$306$	17.1366	+	16.4105i	0.0560020	+	0.0536292i
$307$		−	126.983i		−	0.413625i	−0.978381	−	0.206812i	$-0.933691\pi$
$307$		−	126.983i		−	0.413625i	0.978381	−	0.206812i	$-0.0663090\pi$
$308$		0			0
$309$	−155.099			−0.501940
$310$	80.0458	−	83.5874i	0.258212	−	0.269637i
$311$			355.612i			1.14345i	0.820447	+	0.571723i	$0.193725\pi$
$311$			355.612i			1.14345i	−0.820447	+	0.571723i	$0.806275\pi$
$312$	−62.2435	−	54.6444i	−0.199498	−	0.175142i
$313$	−374.296			−1.19583			−0.597917	−	0.801558i	$-0.704005\pi$
$313$	−374.296			−1.19583			−0.597917	+	0.801558i	$0.704005\pi$
$314$	−59.8505	−	57.3146i	−0.190607	−	0.182531i
$315$		0			0
$316$	52.4384	−	2.27096i	0.165944	−	0.00718659i
$317$	−32.2241			−0.101653			−0.0508266	−	0.998707i	$-0.516186\pi$
$317$	−32.2241			−0.101653			−0.0508266	+	0.998707i	$0.516186\pi$
$318$	−43.5463	+	45.4730i	−0.136938	+	0.142997i
$319$			438.460i			1.37448i
$320$	12.4534	+	95.3736i	0.0389170	+	0.298043i
$321$	−93.6060			−0.291608
$322$		0			0
$323$		−	14.2316i		−	0.0440607i
$324$	1.55760	+	35.9663i	0.00480741	+	0.111007i
$325$	135.937			0.418267
$326$	268.203	−	280.070i	0.822709	−	0.859109i
$327$		−	129.153i		−	0.394963i
$328$	−342.840	+	390.516i	−1.04524	+	1.19060i
$329$		0			0
$330$	−34.6514	−	33.1832i	−0.105004	−	0.100555i
$331$			388.193i			1.17279i	0.810026	+	0.586394i	$0.199453\pi$
$331$			388.193i			1.17279i	−0.810026	+	0.586394i	$0.800547\pi$
$332$	−363.755	+	15.7532i	−1.09565	+	0.0474495i
$333$	157.475			0.472897
$334$	206.549	−	215.688i	0.618410	−	0.645771i
$335$			194.398i			0.580293i
$336$		0			0
$337$	−544.804			−1.61663			−0.808314	−	0.588752i	$-0.799620\pi$
$337$	−544.804			−1.61663			−0.808314	+	0.588752i	$0.799620\pi$
$338$	192.506	+	184.349i	0.569543	+	0.545412i
$339$			28.6934i			0.0846414i
$340$	−1.02855	−	23.7500i	−0.00302514	−	0.0698529i
$341$	354.843			1.04060
$342$	14.9346	−	15.5954i	0.0436686	−	0.0456006i
$343$		0			0
$344$	101.060	+	88.7218i	0.293778	+	0.257912i
$345$	56.4156			0.163523
$346$	−75.2712	−	72.0820i	−0.217547	−	0.208329i
$347$		−	482.711i		−	1.39110i	−0.718479	−	0.695548i	$-0.755161\pi$
$347$		−	482.711i		−	1.39110i	0.718479	−	0.695548i	$-0.244839\pi$
$348$	−329.318	+	14.2618i	−0.946316	+	0.0409823i
$349$	−188.243			−0.539378			−0.269689	−	0.962948i	$-0.586921\pi$
$349$	−188.243			−0.539378			−0.269689	+	0.962948i	$0.586921\pi$
$350$		0			0
$351$			31.0600i			0.0884901i
$352$	−184.789	+	229.827i	−0.524969	+	0.652917i
$353$	−290.445			−0.822789			−0.411395	−	0.911457i	$-0.634958\pi$
$353$	−290.445			−0.822789			−0.411395	+	0.911457i	$0.634958\pi$
$354$	−122.794	−	117.592i	−0.346877	−	0.332179i
$355$		−	92.9673i		−	0.261880i
$356$	−15.6981	−	362.483i	−0.0440959	−	1.01821i
$357$		0			0
$358$	22.7673	−	23.7747i	0.0635959	−	0.0664097i
$359$		−	493.462i		−	1.37455i	−0.726399	−	0.687273i	$-0.758807\pi$
$359$		−	493.462i		−	1.37455i	0.726399	−	0.687273i	$-0.241193\pi$
$360$	23.7961	−	27.1053i	0.0661003	−	0.0752925i
$361$	348.048			0.964123
$362$	−459.195	−	439.739i	−1.26849	−	1.21475i
$363$			62.4766i			0.172112i
$364$		0			0
$365$	143.956			0.394400
$366$	−236.116	+	246.563i	−0.645126	+	0.673669i
$367$			344.402i			0.938424i	0.883085	+	0.469212i	$0.155462\pi$
$367$			344.402i			0.938424i	−0.883085	+	0.469212i	$0.844538\pi$
$368$	−29.9789	−	345.470i	−0.0814644	−	0.938776i
$369$	194.871			0.528105
$370$	−113.952	−	109.124i	−0.307978	−	0.294929i
$371$		0			0
$372$	11.5420	+	266.515i	0.0310270	+	0.716439i
$373$	−500.930			−1.34298			−0.671488	−	0.741015i	$-0.734345\pi$
$373$	−500.930			−1.34298			−0.671488	+	0.741015i	$0.734345\pi$
$374$	50.4115	−	52.6419i	0.134790	−	0.140754i
$375$			124.273i			0.331393i
$376$	−410.491	−	360.375i	−1.09173	−	0.958445i
$377$	−284.395			−0.754362
$378$		0			0
$379$			642.548i			1.69538i	0.530493	+	0.847689i	$0.322007\pi$
$379$			642.548i			1.69538i	−0.530493	+	0.847689i	$0.677993\pi$
$380$	−21.6140	+	0.936044i	−0.0568790	+	0.00246327i
$381$	−148.661			−0.390186
$382$	20.7777	−	21.6970i	0.0543918	−	0.0567984i
$383$			594.877i			1.55320i	0.629992	+	0.776602i	$0.283058\pi$
$383$			594.877i			1.55320i	−0.629992	+	0.776602i	$0.716942\pi$
$384$	−178.629	−	131.316i	−0.465179	−	0.341968i
$385$		0			0
$386$	302.398	+	289.585i	0.783415	+	0.750221i
$387$		−	50.4297i		−	0.130309i
$388$	−1.22101	−	28.1942i	−0.00314694	−	0.0726654i
$389$	655.009			1.68383			0.841914	−	0.539612i	$-0.181429\pi$
$389$	655.009			1.68383			0.841914	+	0.539612i	$0.181429\pi$
$390$	21.5234	−	22.4757i	0.0551881	−	0.0576299i
$391$			85.7057i			0.219196i
$392$		0			0
$393$	391.366			0.995841
$394$	−8.75470	−	8.38376i	−0.0222201	−	0.0212786i
$395$			19.7204i			0.0499251i
$396$	110.485	−	4.78479i	0.279002	−	0.0120828i
$397$	−227.461			−0.572950			−0.286475	−	0.958088i	$-0.592484\pi$
$397$	−227.461			−0.572950			−0.286475	+	0.958088i	$0.592484\pi$
$398$	−177.666	+	185.526i	−0.446396	+	0.466147i
$399$		0			0
$400$	362.500	−	31.4568i	0.906250	−	0.0786419i
$401$	−632.391			−1.57704			−0.788518	−	0.615012i	$-0.789151\pi$
$401$	−632.391			−1.57704			−0.788518	+	0.615012i	$0.789151\pi$
$402$	−323.628	−	309.916i	−0.805044	−	0.770935i
$403$			230.159i			0.571115i
$404$	−15.0851	−	348.326i	−0.0373392	−	0.862194i
$405$	−13.5258			−0.0333970
$406$		0			0
$407$		−	483.746i		−	1.18857i
$408$	41.1780	+	36.1507i	0.100926	+	0.0886047i
$409$	147.048			0.359531			0.179766	−	0.983709i	$-0.442466\pi$
$409$	147.048			0.359531			0.179766	+	0.983709i	$0.442466\pi$
$410$	−141.013	−	135.038i	−0.343933	−	0.329361i
$411$		−	177.073i		−	0.430835i
$412$	−357.851	+	15.4976i	−0.868571	+	0.0376154i
$413$		0			0
$414$	−89.9395	+	93.9188i	−0.217245	+	0.226857i
$415$		−	136.797i		−	0.329630i
$416$	−149.071	−	119.858i	−0.358343	−	0.288121i
$417$	354.866			0.850997
$418$	−47.9076	−	45.8777i	−0.114611	−	0.109755i
$419$		−	706.980i		−	1.68730i	−0.536890	−	0.843652i	$-0.680401\pi$
$419$		−	706.980i		−	1.68730i	0.536890	−	0.843652i	$-0.319599\pi$
$420$		0			0
$421$	103.455			0.245736			0.122868	−	0.992423i	$-0.460791\pi$
$421$	103.455			0.245736			0.122868	+	0.992423i	$0.460791\pi$
$422$	104.331	−	108.947i	0.247230	−	0.258169i
$423$			204.838i			0.484251i
$424$	−95.9281	+	109.268i	−0.226245	+	0.257708i
$425$	−89.9307			−0.211602
$426$	154.769	+	148.211i	0.363308	+	0.347914i
$427$		0			0
$428$	−215.971	+	9.35313i	−0.504606	+	0.0218531i
$429$	95.4133			0.222409
$430$	−34.9458	+	36.4919i	−0.0812693	+	0.0848650i
$431$			163.774i			0.379987i	0.981785	+	0.189993i	$0.0608466\pi$
$431$			163.774i			0.379987i	−0.981785	+	0.189993i	$0.939153\pi$
$432$	7.18751	+	82.8272i	0.0166378	+	0.191730i
$433$	−42.7877			−0.0988170			−0.0494085	−	0.998779i	$-0.515734\pi$
$433$	−42.7877			−0.0988170			−0.0494085	+	0.998779i	$0.515734\pi$
$434$		0			0
$435$		−	123.846i		−	0.284703i
$436$	−12.9050	−	297.987i	−0.0295986	−	0.683456i
$437$	77.9977			0.178485
$438$	−229.499	+	239.653i	−0.523971	+	0.547153i
$439$			788.666i			1.79651i	0.439479	+	0.898253i	$0.355163\pi$
$439$			788.666i			1.79651i	−0.439479	+	0.898253i	$0.644837\pi$
$440$	−83.2648	−	73.0993i	−0.189238	−	0.166135i
$441$		0			0
$442$	34.1447	+	32.6980i	0.0772505	+	0.0739774i
$443$			142.178i			0.320944i	0.987040	+	0.160472i	$0.0513016\pi$
$443$			142.178i			0.320944i	−0.987040	+	0.160472i	$0.948698\pi$
$444$	363.332	−	15.7349i	0.818314	−	0.0354389i
$445$	136.318			0.306333
$446$	−232.058	+	242.325i	−0.520309	+	0.543330i
$447$			289.510i			0.647673i
$448$		0			0
$449$	153.780			0.342495			0.171248	−	0.985228i	$-0.445220\pi$
$449$	153.780			0.342495			0.171248	+	0.985228i	$0.445220\pi$
$450$	−98.5488	−	94.3733i	−0.218997	−	0.209718i
$451$		−	598.624i		−	1.32732i
$452$	2.86705	+	66.2026i	0.00634303	+	0.146466i
$453$	177.515			0.391865
$454$	−219.743	+	229.465i	−0.484015	+	0.505430i
$455$		0			0
$456$	32.8995	−	37.4746i	0.0721480	−	0.0821812i
$457$	−113.717			−0.248833			−0.124417	−	0.992230i	$-0.539706\pi$
$457$	−113.717			−0.248833			−0.124417	+	0.992230i	$0.539706\pi$
$458$	217.277	+	208.071i	0.474404	+	0.454304i
$459$		−	20.5482i		−	0.0447672i
$460$	130.164	−	5.63705i	0.282966	−	0.0122545i
$461$	350.917			0.761209			0.380605	−	0.924738i	$-0.375716\pi$
$461$	350.917			0.761209			0.380605	+	0.924738i	$0.375716\pi$
$462$		0			0
$463$		−	408.534i		−	0.882363i	−0.897418	−	0.441182i	$-0.854559\pi$
$463$		−	408.534i		−	0.882363i	0.897418	−	0.441182i	$-0.145441\pi$
$464$	−758.390	+	65.8110i	−1.63446	+	0.141834i
$465$	−100.228			−0.215544
$466$	−114.217	−	109.378i	−0.245101	−	0.234716i
$467$		−	41.4409i		−	0.0887386i	−0.999015	−	0.0443693i	$-0.985872\pi$
$467$		−	41.4409i		−	0.0887386i	0.999015	−	0.0443693i	$-0.0141278\pi$
$468$	3.10352	+	71.6629i	0.00663146	+	0.153126i
$469$		0			0
$470$	141.945	−	148.225i	0.302010	−	0.315373i
$471$			71.7654i			0.152368i
$472$	−295.065	−	259.042i	−0.625139	−	0.548818i
$473$	−154.915			−0.327516
$474$	−32.8299	−	31.4389i	−0.0692614	−	0.0663268i
$475$			81.8428i			0.172301i
$476$		0			0
$477$	54.5258			0.114310
$478$	−136.697	+	142.745i	−0.285978	+	0.298630i
$479$			439.056i			0.916609i	0.888795	+	0.458305i	$0.151543\pi$
$479$			439.056i			0.916609i	−0.888795	+	0.458305i	$0.848457\pi$
$480$	52.1949	−	64.9161i	0.108739	−	0.135242i
$481$	313.768			0.652325
$482$	−624.961	−	598.481i	−1.29660	−	1.24166i
$483$		0			0
$484$	6.24267	+	144.148i	0.0128981	+	0.297827i
$485$	10.6029			0.0218617
$486$	21.5632	−	22.5173i	0.0443688	−	0.0463318i
$487$			501.637i			1.03005i	0.857174	+	0.515027i	$0.172218\pi$
$487$			501.637i			1.03005i	−0.857174	+	0.515027i	$0.827782\pi$
$488$	−520.139	+	592.472i	−1.06586	+	1.21408i
$489$	−335.826			−0.686760
$490$		0			0
$491$		−	581.000i		−	1.18330i	−0.806195	−	0.591650i	$-0.798477\pi$
$491$		−	581.000i		−	1.18330i	0.806195	−	0.591650i	$-0.201523\pi$
$492$	449.613	−	19.4715i	0.913848	−	0.0395763i
$493$	188.145			0.381633
$494$	29.7573	−	31.0739i	0.0602375	−	0.0629026i
$495$			41.5498i			0.0839390i
$496$	53.2605	+	613.761i	0.107380	+	1.23742i
$497$		0			0
$498$	227.735	+	218.086i	0.457299	+	0.437923i
$499$		−	410.045i		−	0.821734i	−0.911695	−	0.410867i	$-0.865226\pi$
$499$		−	410.045i		−	0.821734i	0.911695	−	0.410867i	$-0.134774\pi$
$500$	12.4173	+	286.726i	0.0248347	+	0.573453i
$501$	−258.626			−0.516220
$502$	430.442	−	449.486i	0.857453	−	0.895391i
$503$		−	220.402i		−	0.438175i	−0.975705	−	0.219087i	$-0.929692\pi$
$503$		−	220.402i		−	0.438175i	0.975705	−	0.219087i	$-0.0703080\pi$
$504$		0			0
$505$	130.994			0.259395
$506$	288.509	+	276.285i	0.570176	+	0.546018i
$507$		−	230.829i		−	0.455285i
$508$	−342.996	+	14.8542i	−0.675189	+	0.0292406i
$509$	−130.336			−0.256063			−0.128031	−	0.991770i	$-0.540866\pi$
$509$	−130.336			−0.256063			−0.128031	+	0.991770i	$0.540866\pi$
$510$	−14.2391	+	14.8691i	−0.0279197	+	0.0291550i
$511$		0			0
$512$	−425.260	−	285.128i	−0.830586	−	0.556890i
$513$	−18.7002			−0.0364525
$514$	−631.449	−	604.695i	−1.22850	−	1.17645i
$515$		−	134.576i		−	0.261314i
$516$	−5.03894	−	116.353i	−0.00976539	−	0.225491i
$517$	629.243			1.21710
$518$		0			0
$519$			90.2562i			0.173904i
$520$	47.4138	−	54.0073i	0.0911804	−	0.103860i
$521$	788.071			1.51261			0.756306	−	0.654218i	$-0.227002\pi$
$521$	788.071			1.51261			0.756306	+	0.654218i	$0.227002\pi$
$522$	206.175	+	197.439i	0.394971	+	0.378236i
$523$			377.791i			0.722354i	0.932497	+	0.361177i	$0.117625\pi$
$523$			377.791i			0.722354i	−0.932497	+	0.361177i	$0.882375\pi$
$524$	902.974	−	39.1053i	1.72323	−	0.0746285i
$525$		0			0
$526$	660.772	−	690.007i	1.25622	−	1.31180i
$527$		−	152.265i		−	0.288928i
$528$	254.437	−	22.0793i	0.481888	−	0.0418169i
$529$	59.2815			0.112063
$530$	−39.4560	−	37.7842i	−0.0744452	−	0.0712910i
$531$			147.240i			0.277288i
$532$		0			0
$533$	388.280			0.728481
$534$	−217.323	+	226.938i	−0.406972	+	0.424978i
$535$		−	81.2199i		−	0.151813i
$536$	−777.653	−	682.713i	−1.45085	−	1.27372i
$537$	−28.5077			−0.0530870
$538$	147.406	+	141.161i	0.273989	+	0.262380i
$539$		0			0
$540$	−31.2072	+	1.35150i	−0.0577911	+	0.00250277i
$541$	−403.833			−0.746456			−0.373228	−	0.927740i	$-0.621749\pi$
$541$	−403.833			−0.746456			−0.373228	+	0.927740i	$0.621749\pi$
$542$	685.898	−	716.245i	1.26549	−	1.32149i
$543$			550.611i			1.01402i
$544$	98.6196	+	79.2938i	0.181286	+	0.145761i
$545$	112.063			0.205621
$546$		0			0
$547$			63.3919i			0.115890i	0.998320	+	0.0579451i	$0.0184548\pi$
$547$			63.3919i			0.115890i	−0.998320	+	0.0579451i	$0.981545\pi$
$548$	−17.6932	−	408.550i	−0.0322868	−	0.745530i
$549$	295.649			0.538522
$550$	−289.905	+	302.732i	−0.527100	+	0.550422i
$551$		−	171.224i		−	0.310751i
$552$	−198.128	+	225.680i	−0.358927	+	0.408840i
$553$		0			0
$554$	−430.140	−	411.915i	−0.776427	−	0.743529i
$555$			136.637i			0.246193i
$556$	818.760	−	35.4582i	1.47259	−	0.0637738i
$557$	159.295			0.285988			0.142994	−	0.989724i	$-0.454327\pi$
$557$	159.295			0.285988			0.142994	+	0.989724i	$0.454327\pi$
$558$	159.787	−	166.856i	0.286356	−	0.299026i
$559$		−	100.481i		−	0.179752i
$560$		0			0
$561$	−63.1219			−0.112517
$562$	−84.0461	−	80.4851i	−0.149548	−	0.143212i
$563$			300.463i			0.533681i	0.963741	+	0.266841i	$0.0859797\pi$
$563$			300.463i			0.533681i	−0.963741	+	0.266841i	$0.914020\pi$
$564$	20.4675	+	472.611i	0.0362898	+	0.837962i
$565$	−24.8967			−0.0440649
$566$	321.086	−	335.293i	0.567290	−	0.592390i
$567$		0			0
$568$	371.898	+	326.495i	0.654751	+	0.574815i
$569$	177.946			0.312735			0.156367	−	0.987699i	$-0.450022\pi$
$569$	177.946			0.312735			0.156367	+	0.987699i	$0.450022\pi$
$570$	13.5318	+	12.9585i	0.0237400	+	0.0227342i
$571$		−	768.726i		−	1.34628i	−0.739515	−	0.673140i	$-0.764945\pi$
$571$		−	768.726i		−	1.34628i	0.739515	−	0.673140i	$-0.235055\pi$
$572$	220.141	−	9.53371i	0.384862	−	0.0166673i
$573$	−26.0164			−0.0454039
$574$		0			0
$575$		−	492.874i		−	0.857173i
$576$	24.8594	+	190.384i	0.0431587	+	0.330528i
$577$	−870.034			−1.50786			−0.753929	−	0.656956i	$-0.771844\pi$
$577$	−870.034			−1.50786			−0.753929	+	0.656956i	$0.771844\pi$
$578$	394.867	+	378.136i	0.683161	+	0.654215i
$579$		−	362.599i		−	0.626251i
$580$	−12.3747	−	285.742i	−0.0213357	−	0.492659i
$581$		0			0
$582$	−16.9035	+	17.6514i	−0.0290439	+	0.0303289i
$583$		−	167.498i		−	0.287303i
$584$	−505.563	+	575.869i	−0.865690	+	0.986076i
$585$	−26.9501			−0.0460686
$586$	375.635	+	359.720i	0.641016	+	0.613856i
$587$		−	270.224i		−	0.460347i	−0.973150	−	0.230173i	$-0.926071\pi$
$587$		−	270.224i		−	0.460347i	0.973150	−	0.230173i	$-0.0739294\pi$
$588$		0			0
$589$	−138.571			−0.235265
$590$	102.032	−	106.546i	0.172935	−	0.180586i
$591$			10.4976i			0.0177624i
$592$	836.720	−	72.6083i	1.41338	−	0.122649i
$593$	−498.133			−0.840022			−0.420011	−	0.907519i	$-0.637974\pi$
$593$	−498.133			−0.840022			−0.420011	+	0.907519i	$0.637974\pi$
$594$	−69.1708	−	66.2400i	−0.116449	−	0.111515i
$595$		0			0
$596$	28.9279	+	667.968i	0.0485367	+	1.12075i
$597$	222.461			0.372631
$598$	−179.205	+	187.133i	−0.299673	+	0.312932i
$599$		−	306.148i		−	0.511099i	−0.966796	−	0.255550i	$-0.917744\pi$
$599$		−	306.148i		−	0.511099i	0.966796	−	0.255550i	$-0.0822564\pi$
$600$	−236.805	−	207.895i	−0.394675	−	0.346491i
$601$	61.2555			0.101923			0.0509613	−	0.998701i	$-0.483771\pi$
$601$	61.2555			0.101923			0.0509613	+	0.998701i	$0.483771\pi$
$602$		0			0
$603$			388.055i			0.643541i
$604$	409.569	−	17.7373i	0.678095	−	0.0293664i
$605$	−54.2096			−0.0896027
$606$	−208.835	+	218.075i	−0.344613	+	0.359860i
$607$		−	675.583i		−	1.11299i	−0.830852	−	0.556494i	$-0.812146\pi$
$607$		−	675.583i		−	1.11299i	0.830852	−	0.556494i	$-0.187854\pi$
$608$	72.1625	−	89.7502i	0.118688	−	0.147616i
$609$		0			0
$610$	−213.937	−	204.873i	−0.350717	−	0.335857i
$611$			408.141i			0.667988i
$612$	−2.05317	−	47.4095i	−0.00335486	−	0.0774665i
$613$	−975.309			−1.59104			−0.795521	−	0.605926i	$-0.792803\pi$
$613$	−975.309			−1.59104			−0.795521	+	0.605926i	$0.792803\pi$
$614$	−175.653	+	183.425i	−0.286080	+	0.298737i
$615$			169.085i			0.274935i
$616$		0			0
$617$	−1017.11			−1.64847			−0.824237	−	0.566245i	$-0.808396\pi$
$617$	−1017.11			−1.64847			−0.824237	+	0.566245i	$0.808396\pi$
$618$	224.039	+	214.546i	0.362522	+	0.347162i
$619$		−	1034.26i		−	1.67085i	−0.549601	−	0.835427i	$-0.685220\pi$
$619$		−	1034.26i		−	1.67085i	0.549601	−	0.835427i	$-0.314780\pi$
$620$	−231.250	+	10.0148i	−0.372983	+	0.0161529i
$621$	112.616			0.181346
$622$	491.911	−	513.676i	0.790854	−	0.825845i
$623$		0			0
$624$	14.3211	+	165.033i	0.0229505	+	0.264476i
$625$	460.706			0.737130
$626$	540.664	+	517.756i	0.863681	+	0.827087i
$627$			57.4450i			0.0916188i
$628$	7.17081	+	165.580i	0.0114185	+	0.263662i
$629$	−207.577			−0.330012
$630$		0			0
$631$			557.700i			0.883835i	0.897056	+	0.441917i	$0.145702\pi$
$631$			557.700i			0.883835i	−0.897056	+	0.441917i	$0.854298\pi$
$632$	−78.8878	−	69.2567i	−0.124822	−	0.109583i
$633$	−130.636			−0.206377
$634$	46.5472	+	44.5750i	0.0734182	+	0.0703075i
$635$		−	128.990i		−	0.203134i
$636$	125.804	−	5.44822i	0.197805	−	0.00856639i
$637$		0			0
$638$	606.513	−	633.348i	0.950648	−	0.992709i
$639$		−	185.580i		−	0.290423i
$640$	113.940	−	154.992i	0.178031	−	0.242175i
$641$	−399.002			−0.622468			−0.311234	−	0.950333i	$-0.600742\pi$
$641$	−399.002			−0.622468			−0.311234	+	0.950333i	$0.600742\pi$
$642$	135.212	+	129.483i	0.210611	+	0.201688i
$643$			646.867i			1.00601i	0.864282	+	0.503007i	$0.167773\pi$
$643$			646.867i			1.00601i	−0.864282	+	0.503007i	$0.832227\pi$
$644$		0			0
$645$	43.7567			0.0678399
$646$	−19.6863	+	20.5573i	−0.0304742	+	0.0318225i
$647$			246.758i			0.381388i	0.981650	+	0.190694i	$0.0610738\pi$
$647$			246.758i			0.381388i	−0.981650	+	0.190694i	$0.938926\pi$
$648$	47.5016	−	54.1073i	0.0733049	−	0.0834990i
$649$	452.307			0.696929
$650$	−196.359	−	188.039i	−0.302090	−	0.289291i
$651$		0			0
$652$	−774.830	+	33.5558i	−1.18839	+	0.0514659i
$653$	837.563			1.28264			0.641319	−	0.767274i	$-0.278387\pi$
$653$	837.563			1.28264			0.641319	+	0.767274i	$0.278387\pi$
$654$	−178.655	+	186.559i	−0.273173	+	0.285259i
$655$			339.580i			0.518442i
$656$	1035.42	−	89.8509i	1.57838	−	0.136968i
$657$	287.363			0.437387
$658$		0			0
$659$			984.401i			1.49378i	0.664948	+	0.746890i	$0.268454\pi$
$659$			984.401i			1.49378i	−0.664948	+	0.746890i	$0.731546\pi$
$660$	4.15166	+	95.8653i	0.00629040	+	0.145250i
$661$	38.8758			0.0588136			0.0294068	−	0.999568i	$-0.490638\pi$
$661$	38.8758			0.0588136			0.0294068	+	0.999568i	$0.490638\pi$
$662$	536.980	−	560.739i	0.811148	−	0.847037i
$663$		−	40.9422i		−	0.0617530i
$664$	547.229	+	480.420i	0.824141	+	0.723524i
$665$		0			0
$666$	−227.470	−	217.832i	−0.341546	−	0.327075i
$667$			1031.15i			1.54595i
$668$	−596.713	+	25.8420i	−0.893283	+	0.0386856i
$669$	290.567			0.434330
$670$	268.907	−	280.805i	0.401354	−	0.419112i
$671$		−	908.203i		−	1.35351i
$672$		0			0
$673$	−138.096			−0.205195			−0.102598	−	0.994723i	$-0.532715\pi$
$673$	−138.096			−0.205195			−0.102598	+	0.994723i	$0.532715\pi$
$674$	786.960	+	753.616i	1.16760	+	1.11813i
$675$			118.168i			0.175063i
$676$	−23.0645	−	532.579i	−0.0341191	−	0.787838i
$677$	656.741			0.970075			0.485037	−	0.874493i	$-0.338806\pi$
$677$	656.741			0.970075			0.485037	+	0.874493i	$0.338806\pi$
$678$	39.6911	−	41.4472i	0.0585414	−	0.0611315i
$679$		0			0
$680$	−31.3672	+	35.7292i	−0.0461282	+	0.0525430i
$681$	275.147			0.404034
$682$	−512.566	−	490.848i	−0.751563	−	0.719719i
$683$		−	989.363i		−	1.44855i	−0.689509	−	0.724277i	$-0.742174\pi$
$683$		−	989.363i		−	1.44855i	0.689509	−	0.724277i	$-0.257826\pi$
$684$	−43.1457	+	1.86852i	−0.0630785	+	0.00273176i
$685$	153.643			0.224296
$686$		0			0
$687$		−	260.532i		−	0.379232i
$688$	−23.2521	−	267.951i	−0.0337966	−	0.389464i
$689$	108.643			0.157682
$690$	−81.4914	−	78.0386i	−0.118103	−	0.113099i
$691$		−	1122.12i		−	1.62391i	−0.583720	−	0.811955i	$-0.698403\pi$
$691$		−	1122.12i		−	1.62391i	0.583720	−	0.811955i	$-0.301597\pi$
$692$	9.01841	+	208.242i	0.0130324	+	0.300928i
$693$		0			0
$694$	−667.724	+	697.268i	−0.962139	+	1.00471i
$695$			307.909i			0.443035i
$696$	495.422	+	434.938i	0.711814	+	0.624911i
$697$	−256.872			−0.368539
$698$	271.914	+	260.393i	0.389561	+	0.373056i
$699$			136.955i			0.195930i
$700$		0			0
$701$	414.598			0.591438			0.295719	−	0.955275i	$-0.404441\pi$
$701$	414.598			0.591438			0.295719	+	0.955275i	$0.404441\pi$
$702$	42.9647	−	44.8657i	0.0612033	−	0.0639113i
$703$			188.909i			0.268718i
$704$	584.840	−	76.3656i	0.830739	−	0.108474i
$705$	−177.734			−0.252105
$706$	419.543	+	401.767i	0.594253	+	0.569074i
$707$		0			0
$708$	14.7123	+	339.718i	0.0207800	+	0.479828i
$709$	379.857			0.535764			0.267882	−	0.963452i	$-0.413676\pi$
$709$	379.857			0.535764			0.267882	+	0.963452i	$0.413676\pi$
$710$	−128.600	+	134.290i	−0.181127	+	0.189140i
$711$			39.3657i			0.0553666i
$712$	−478.740	+	545.316i	−0.672388	+	0.765893i
$713$	834.502			1.17041
$714$		0			0
$715$			82.7880i			0.115787i
$716$	−65.7741	+	2.84850i	−0.0918633	+	0.00397835i
$717$	171.163			0.238721
$718$	−682.597	+	712.798i	−0.950692	+	0.992755i
$719$			319.573i			0.444469i	0.974993	+	0.222234i	$0.0713350\pi$
$719$			319.573i			0.444469i	−0.974993	+	0.222234i	$0.928665\pi$
$720$	−71.8673	+	6.23645i	−0.0998158	+	0.00866174i
$721$		0			0
$722$	−502.750	−	481.449i	−0.696330	−	0.666826i
$723$			749.378i			1.03648i
$724$	55.0172	+	1270.39i	0.0759905	+	1.75468i
$725$	−1081.98			−1.49238
$726$	86.4227	−	90.2465i	0.119040	−	0.124306i
$727$			1082.72i			1.48929i	0.667458	+	0.744647i	$0.267382\pi$
$727$			1082.72i			1.48929i	−0.667458	+	0.744647i	$0.732618\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$	−207.942	−	199.131i	−0.284852	−	0.272783i
$731$			66.4746i			0.0909366i
$732$	682.132	−	29.5412i	0.931874	−	0.0403569i
$733$	−367.661			−0.501584			−0.250792	−	0.968041i	$-0.580691\pi$
$733$	−367.661			−0.501584			−0.250792	+	0.968041i	$0.580691\pi$
$734$	476.404	−	497.483i	0.649052	−	0.677769i
$735$		0			0
$736$	−434.577	+	540.494i	−0.590459	+	0.734367i
$737$	1192.07			1.61746
$738$	−281.488	−	269.561i	−0.381420	−	0.365259i
$739$		−	928.708i		−	1.25671i	−0.777927	−	0.628354i	$-0.783729\pi$
$739$		−	928.708i		−	1.25671i	0.777927	−	0.628354i	$-0.216271\pi$
$740$	13.6528	+	315.255i	0.0184498	+	0.426020i
$741$	−37.2601			−0.0502835
$742$		0			0
$743$		−	103.027i		−	0.138663i	−0.997594	−	0.0693315i	$-0.977913\pi$
$743$		−	103.027i		−	0.138663i	0.997594	−	0.0693315i	$-0.0220866\pi$
$744$	351.993	−	400.943i	0.473109	−	0.538902i
$745$	−251.201			−0.337183
$746$	723.586	+	692.927i	0.969954	+	0.928857i
$747$		−	273.072i		−	0.365558i
$748$	−145.637	+	6.30715i	−0.194702	+	0.00843201i
$749$		0			0
$750$	171.904	−	179.510i	0.229205	−	0.239346i
$751$		−	788.472i		−	1.04990i	−0.851134	−	0.524948i	$-0.824085\pi$
$751$		−	788.472i		−	1.04990i	0.851134	−	0.524948i	$-0.175915\pi$
$752$	94.4467	+	1088.38i	0.125594	+	1.44731i
$753$	−538.970			−0.715763
$754$	410.803	+	393.398i	0.544832	+	0.521748i
$755$			154.026i			0.204008i
$756$		0			0
$757$	−876.519			−1.15788			−0.578942	−	0.815369i	$-0.696534\pi$
$757$	−876.519			−1.15788			−0.578942	+	0.815369i	$0.696534\pi$
$758$	888.825	−	928.151i	1.17259	−	1.22447i
$759$		−	345.946i		−	0.455791i
$760$	32.5159	+	28.5462i	0.0427841	+	0.0375608i
$761$	−392.509			−0.515781			−0.257890	−	0.966174i	$-0.583027\pi$
$761$	−392.509			−0.515781			−0.257890	+	0.966174i	$0.583027\pi$
$762$	214.738	+	205.640i	0.281809	+	0.269868i
$763$		0			0
$764$	−60.0261	+	2.59956i	−0.0785681	+	0.00340257i
$765$	17.8292			0.0233061
$766$	822.882	−	859.290i	1.07426	−	1.12179i
$767$			293.376i			0.382498i
$768$	76.3798	+	436.777i	0.0994528	+	0.568720i
$769$	−496.681			−0.645879			−0.322939	−	0.946420i	$-0.604671\pi$
$769$	−496.681			−0.645879			−0.322939	+	0.946420i	$0.604671\pi$
$770$		0			0
$771$			757.158i			0.982046i
$772$	−36.2310	−	836.603i	−0.0469313	−	1.08368i
$773$	−1193.35			−1.54379			−0.771894	−	0.635751i	$-0.780691\pi$
$773$	−1193.35			−1.54379			−0.771894	+	0.635751i	$0.780691\pi$
$774$	−69.7584	+	72.8449i	−0.0901272	+	0.0941148i
$775$			875.640i			1.12986i
$776$	−37.2367	+	42.4150i	−0.0479855	+	0.0546585i
$777$		0			0
$778$	−946.150	−	906.062i	−1.21613	−	1.16460i
$779$			233.770i			0.300090i
$780$	−62.1803	+	2.69286i	−0.0797184	+	0.00345238i
$781$	−570.084			−0.729941
$782$	118.555	−	123.801i	0.151605	−	0.158313i
$783$		−	247.220i		−	0.315734i
$784$		0			0
$785$	−62.2693			−0.0793240
$786$	−565.321	−	541.369i	−0.719238	−	0.688764i
$787$		−	188.057i		−	0.238955i	−0.992837	−	0.119477i	$-0.961878\pi$
$787$		−	188.057i		−	0.238955i	0.992837	−	0.119477i	$-0.0381219\pi$
$788$	1.04892	+	24.2204i	0.00133112	+	0.0307366i
$789$	−827.374			−1.04864
$790$	27.2789	−	28.4858i	0.0345302	−	0.0360580i
$791$		0			0
$792$	−166.212	−	145.920i	−0.209864	−	0.184242i
$793$	589.080			0.742850
$794$	328.564	+	314.643i	0.413809	+	0.396276i
$795$			47.3108i			0.0595105i
$796$	513.270	−	22.2283i	0.644812	−	0.0279250i
$797$	−1473.12			−1.84833			−0.924165	−	0.381994i	$-0.875238\pi$
$797$	−1473.12			−1.84833			−0.924165	+	0.381994i	$0.875238\pi$
$798$		0			0
$799$		−	270.011i		−	0.337936i
$800$	−567.139	−	456.001i	−0.708924	−	0.570001i
$801$	272.117			0.339722
$802$	913.479	+	874.775i	1.13900	+	1.09074i
$803$		−	882.751i		−	1.09932i
$804$	38.7746	+	895.337i	0.0482271	+	1.11360i
$805$		0			0
$806$	318.375	−	332.461i	0.395006	−	0.412483i
$807$		−	176.752i		−	0.219023i
$808$	−460.043	+	524.019i	−0.569360	+	0.648538i
$809$	449.624			0.555778			0.277889	−	0.960613i	$-0.410365\pi$
$809$	449.624			0.555778			0.277889	+	0.960613i	$0.410365\pi$
$810$	19.5378	+	18.7099i	0.0241207	+	0.0230987i
$811$		−	745.766i		−	0.919563i	−0.888032	−	0.459782i	$-0.847928\pi$
$811$		−	745.766i		−	0.919563i	0.888032	−	0.459782i	$-0.152072\pi$
$812$		0			0
$813$	−858.835			−1.05638
$814$	−669.157	+	698.764i	−0.822060	+	0.858432i
$815$		−	291.389i		−	0.357532i
$816$	−9.47433	−	109.180i	−0.0116107	−	0.133799i
$817$	60.4962			0.0740468
$818$	−212.409	−	203.409i	−0.259669	−	0.248666i
$819$		0			0
$820$	16.8950	+	390.120i	0.0206037	+	0.475756i
$821$	−614.108			−0.748000			−0.374000	−	0.927429i	$-0.622014\pi$
$821$	−614.108			−0.748000			−0.374000	+	0.927429i	$0.622014\pi$
$822$	−244.942	+	255.779i	−0.297983	+	0.311167i
$823$			723.683i			0.879323i	0.898163	+	0.439662i	$0.144902\pi$
$823$			723.683i			0.879323i	−0.898163	+	0.439662i	$0.855098\pi$
$824$	538.348	+	472.623i	0.653335	+	0.573572i
$825$	363.000			0.440000
$826$		0			0
$827$			417.540i			0.504885i	0.967612	+	0.252443i	$0.0812339\pi$
$827$			417.540i			0.504885i	−0.967612	+	0.252443i	$0.918766\pi$
$828$	259.832	−	11.2526i	0.313807	−	0.0135901i
$829$	432.322			0.521498			0.260749	−	0.965407i	$-0.416030\pi$
$829$	432.322			0.521498			0.260749	+	0.965407i	$0.416030\pi$
$830$	−189.228	+	197.601i	−0.227986	+	0.238073i
$831$			515.772i			0.620665i
$832$	49.5324	+	379.340i	0.0595341	+	0.455938i
$833$		0			0
$834$	−512.598	−	490.879i	−0.614626	−	0.588584i
$835$		−	224.405i		−	0.268748i
$836$	5.73991	+	132.539i	0.00686592	+	0.158540i
$837$	−200.074			−0.239037
$838$	−977.953	+	1021.22i	−1.16701	+	1.21864i
$839$			794.458i			0.946911i	0.880818	+	0.473455i	$0.156993\pi$
$839$			794.458i			0.946911i	−0.880818	+	0.473455i	$0.843007\pi$
$840$		0			0
$841$	1422.62			1.69158
$842$	−149.439	−	143.107i	−0.177481	−	0.169961i
$843$			100.778i			0.119547i
$844$	−301.409	+	13.0532i	−0.357120	+	0.0154659i
$845$	200.286			0.237025
$846$	283.349	−	295.886i	0.334928	−	0.349747i
$847$		0			0
$848$	289.715	−	25.1407i	0.341645	−	0.0296470i
$849$	−402.042			−0.473548
$850$	129.903	+	124.399i	0.152828	+	0.146352i
$851$		−	1137.65i		−	1.33684i
$852$	−18.5432	−	428.178i	−0.0217643	−	0.502557i
$853$	−276.585			−0.324250			−0.162125	−	0.986770i	$-0.551835\pi$
$853$	−276.585			−0.324250			−0.162125	+	0.986770i	$0.551835\pi$
$854$		0			0
$855$		−	16.2257i		−	0.0189774i
$856$	324.905	+	285.239i	0.379562	+	0.333223i
$857$	−1105.61			−1.29009			−0.645046	−	0.764144i	$-0.723162\pi$
$857$	−1105.61			−1.29009			−0.645046	+	0.764144i	$0.723162\pi$
$858$	−137.823	−	131.983i	−0.160633	−	0.153827i
$859$		−	1437.66i		−	1.67364i	−0.547476	−	0.836821i	$-0.684411\pi$
$859$		−	1437.66i		−	1.67364i	0.547476	−	0.836821i	$-0.315589\pi$
$860$	100.957	−	4.37218i	0.117392	−	0.00508393i
$861$		0			0
$862$	226.546	−	236.569i	0.262814	−	0.274442i
$863$		−	1230.38i		−	1.42570i	−0.701318	−	0.712848i	$-0.747405\pi$
$863$		−	1230.38i		−	1.42570i	0.701318	−	0.712848i	$-0.252595\pi$
$864$	104.191	−	129.585i	0.120591	−	0.149982i
$865$	−78.3133			−0.0905356
$866$	61.8062	+	59.1875i	0.0713698	+	0.0683458i
$867$		−	473.477i		−	0.546109i
$868$		0			0
$869$	120.927			0.139157
$870$	−171.314	+	178.893i	−0.196912	+	0.205625i
$871$			773.201i			0.887717i
$872$	−393.558	+	448.288i	−0.451329	+	0.514092i
$873$	21.1655			0.0242445
$874$	−112.666	−	107.893i	−0.128909	−	0.123447i
$875$		0			0
$876$	663.015	−	28.7134i	0.756867	−	0.0327778i
$877$	1074.90			1.22566			0.612830	−	0.790215i	$-0.290031\pi$
$877$	1074.90			1.22566			0.612830	+	0.790215i	$0.290031\pi$
$878$	1090.95	−	1139.22i	1.24254	−	1.29751i
$879$		−	450.417i		−	0.512419i
$880$	19.1577	+	220.769i	0.0217702	+	0.250874i
$881$	866.262			0.983271			0.491636	−	0.870801i	$-0.336399\pi$
$881$	866.262			0.983271			0.491636	+	0.870801i	$0.336399\pi$
$882$		0			0
$883$			271.473i			0.307443i	0.988114	+	0.153722i	$0.0491259\pi$
$883$			271.473i			0.307443i	−0.988114	+	0.153722i	$0.950874\pi$
$884$	−4.09095	−	94.4635i	−0.00462778	−	0.106859i
$885$	−127.757			−0.144358
$886$	196.672	−	205.374i	0.221978	−	0.231799i
$887$			1276.55i			1.43918i	0.694401	+	0.719588i	$0.255670\pi$
$887$			1276.55i			1.43918i	−0.694401	+	0.719588i	$0.744330\pi$
$888$	−546.592	−	479.861i	−0.615532	−	0.540384i
$889$		0			0
$890$	−196.910	−	188.567i	−0.221247	−	0.211873i
$891$			82.9413i			0.0930879i
$892$	670.407	−	29.0335i	0.751578	−	0.0325488i
$893$	−245.727			−0.275170
$894$	400.474	−	418.192i	0.447957	−	0.467777i
$895$		−	24.7355i		−	0.0276375i
$896$		0			0
$897$	224.388			0.250154
$898$	−222.133	−	212.721i	−0.247364	−	0.236884i
$899$		−	1831.94i		−	2.03775i
$900$	11.8073	+	272.641i	0.0131193	+	0.302935i
$901$	−71.8739			−0.0797713
$902$	−828.065	+	864.702i	−0.918032	+	0.958650i
$903$		0			0
$904$	87.4353	−	99.5945i	0.0967205	−	0.110171i
$905$	−477.753			−0.527904
$906$	−256.417	−	245.553i	−0.283021	−	0.271030i
$907$		−	1381.29i		−	1.52292i	−0.648212	−	0.761460i	$-0.724483\pi$
$907$		−	1381.29i		−	1.52292i	0.648212	−	0.761460i	$-0.275517\pi$
$908$	634.830	−	27.4928i	0.699152	−	0.0302784i
$909$	261.490			0.287667
$910$		0			0
$911$			866.867i			0.951556i	0.879565	+	0.475778i	$0.157833\pi$
$911$			866.867i			0.951556i	−0.879565	+	0.475778i	$0.842167\pi$
$912$	−99.3607	+	8.62225i	−0.108948	+	0.00945422i
$913$	−838.850			−0.918784
$914$	164.262	+	157.302i	0.179718	+	0.172103i
$915$			256.528i			0.280358i
$916$	−26.0324	−	601.111i	−0.0284197	−	0.656234i
$917$		0			0
$918$	−28.4239	+	29.6815i	−0.0309628	+	0.0323328i
$919$			894.310i			0.973134i	0.873643	+	0.486567i	$0.161751\pi$
$919$			894.310i			0.973134i	−0.873643	+	0.486567i	$0.838249\pi$
$920$	−195.818	−	171.911i	−0.212845	−	0.186860i
$921$	219.941			0.238806
$922$	−506.895	−	485.417i	−0.549777	−	0.526483i
$923$		−	369.769i		−	0.400617i
$924$		0			0
$925$	1193.73			1.29052
$926$	−565.118	+	590.121i	−0.610278	+	0.637280i
$927$		−	268.640i		−	0.289795i
$928$	1186.52	+	954.003i	1.27857	+	1.02802i
$929$	−1320.64			−1.42157			−0.710785	−	0.703409i	$-0.751660\pi$
$929$	−1320.64			−1.42157			−0.710785	+	0.703409i	$0.751660\pi$
$930$	144.778	+	138.643i	0.155675	+	0.149079i
$931$		0			0
$932$	13.6846	+	315.988i	0.0146830	+	0.339043i
$933$	−615.938			−0.660169
$934$	−57.3245	+	59.8608i	−0.0613752	+	0.0640908i
$935$		−	54.7695i		−	0.0585770i
$936$	94.6469	−	107.809i	0.101119	−	0.115180i
$937$	−450.769			−0.481076			−0.240538	−	0.970640i	$-0.577324\pi$
$937$	−450.769			−0.481076			−0.240538	+	0.970640i	$0.577324\pi$
$938$		0			0
$939$		−	648.299i		−	0.690415i
$940$	−410.074	+	17.7592i	−0.436249	+	0.0188927i
$941$	1060.66			1.12716			0.563581	−	0.826061i	$-0.309423\pi$
$941$	1060.66			1.12716			0.563581	+	0.826061i	$0.309423\pi$
$942$	99.2718	−	103.664i	0.105384	−	0.110047i
$943$		−	1407.81i		−	1.49291i
$944$	67.8893	+	782.340i	0.0719167	+	0.828750i
$945$		0			0
$946$	223.772	+	214.291i	0.236546	+	0.226523i
$947$			1697.01i			1.79198i	0.444073	+	0.895990i	$0.353533\pi$
$947$			1697.01i			1.79198i	−0.444073	+	0.895990i	$0.646467\pi$
$948$	3.93342	+	90.8260i	0.00414918	+	0.0958080i
$949$	572.572			0.603342
$950$	113.212	−	118.221i	0.119170	−	0.124443i
$951$		−	55.8137i		−	0.0586895i
$952$		0			0
$953$	292.816			0.307257			0.153628	−	0.988129i	$-0.450904\pi$
$953$	292.816			0.307257			0.153628	+	0.988129i	$0.450904\pi$
$954$	−78.7616	−	75.4244i	−0.0825593	−	0.0790613i
$955$		−	22.5739i		−	0.0236376i
$956$	394.914	−	17.1026i	0.413090	−	0.0178898i
$957$	−759.435			−0.793558
$958$	607.338	−	634.209i	0.633964	−	0.662013i
$959$		0			0
$960$	−165.192	+	21.5700i	−0.172075	+	0.0224687i
$961$	−521.577			−0.542744
$962$	−453.233	−	434.030i	−0.471137	−	0.451175i
$963$		−	162.130i		−	0.168360i
$964$	74.8779	+	1728.99i	0.0776742	+	1.79356i
$965$	314.620			0.326031
$966$		0			0
$967$		−	1740.04i		−	1.79942i	−0.436486	−	0.899711i	$-0.643777\pi$
$967$		−	1740.04i		−	1.79942i	0.436486	−	0.899711i	$-0.356223\pi$
$968$	190.380	−	216.856i	0.196674	−	0.224024i
$969$	24.6499			0.0254385
$970$	−15.3158	−	14.6668i	−0.0157894	−	0.0151204i
$971$		−	809.699i		−	0.833881i	−0.908934	−	0.416941i	$-0.863102\pi$
$971$		−	809.699i		−	0.833881i	0.908934	−	0.416941i	$-0.136898\pi$
$972$	−62.2954	+	2.69784i	−0.0640900	+	0.00277556i
$973$		0			0
$974$	693.904	−	724.606i	0.712427	−	0.743949i
$975$			235.449i			0.241487i
$976$	1570.89	−	136.317i	1.60952	−	0.139669i
$977$	−431.197			−0.441348			−0.220674	−	0.975348i	$-0.570826\pi$
$977$	−431.197			−0.441348			−0.220674	+	0.975348i	$0.570826\pi$
$978$	485.095	+	464.542i	0.496007	+	0.474991i
$979$		−	835.917i		−	0.853847i
$980$		0			0
$981$	223.700			0.228032
$982$	−803.686	+	839.245i	−0.818418	+	0.854629i
$983$			91.8393i			0.0934275i	0.998908	+	0.0467138i	$0.0148749\pi$
$983$			91.8393i			0.0934275i	−0.998908	+	0.0467138i	$0.985125\pi$
$984$	−676.394	−	593.815i	−0.687392	−	0.603471i
$985$	−9.10853			−0.00924723
$986$	−271.772	−	260.257i	−0.275631	−	0.263953i
$987$		0			0
$988$	−85.9679	+	3.72303i	−0.0870120	+	0.00376825i
$989$	−364.321			−0.368373
$990$	57.4751	−	60.0180i	0.0580556	−	0.0606243i
$991$			297.377i			0.300077i	0.988680	+	0.150039i	$0.0479398\pi$
$991$			297.377i			0.300077i	−0.988680	+	0.150039i	$0.952060\pi$
$992$	772.070	−	960.243i	0.778297	−	0.967986i
$993$	−672.370			−0.677110
$994$		0			0
$995$			193.025i			0.193995i
$996$	−27.2854	−	630.042i	−0.0273950	−	0.632573i
$997$	−685.012			−0.687073			−0.343537	−	0.939139i	$-0.611625\pi$
$997$	−685.012			−0.687073			−0.343537	+	0.939139i	$0.611625\pi$
$998$	−567.208	+	592.303i	−0.568344	+	0.593490i
$999$			272.754i			0.273027i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.3.g.h.295.6	yes	24
4.3	odd	2	inner	588.3.g.h.295.7	yes	24
7.6	odd	2	inner	588.3.g.h.295.5	✓	24
28.27	even	2	inner	588.3.g.h.295.8	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.3.g.h.295.5	✓	24	7.6	odd	2	inner
588.3.g.h.295.6	yes	24	1.1	even	1	trivial
588.3.g.h.295.7	yes	24	4.3	odd	2	inner
588.3.g.h.295.8	yes	24	28.27	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	588.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.44448 - 1.38328i) q^{2} +1.73205i q^{3} +(0.173067 + 3.99625i) q^{4} -1.50286 q^{5} +(2.39591 - 2.50192i) q^{6} +(5.27795 - 6.01192i) q^{8} -3.00000 q^{9} +(2.17086 + 2.07888i) q^{10} +9.21570i q^{11} +(-6.92172 + 0.299760i) q^{12} -5.97750 q^{13} -2.60304i q^{15} +(-15.9401 + 1.38324i) q^{16} +3.95449 q^{17} +(4.33345 + 4.14984i) q^{18} -3.59885i q^{19} +(-0.260096 - 6.00582i) q^{20} +(12.7479 - 13.3119i) q^{22} +21.6730i q^{23} +(10.4130 + 9.14168i) q^{24} -22.7414 q^{25} +(8.63441 + 8.26857i) q^{26} -5.19615i q^{27} +47.5775 q^{29} +(-3.60073 + 3.76004i) q^{30} -38.5042i q^{31} +(24.9386 + 20.0516i) q^{32} -15.9621 q^{33} +(-5.71220 - 5.47018i) q^{34} +(-0.519200 - 11.9888i) q^{36} -52.4915 q^{37} +(-4.97822 + 5.19847i) q^{38} -10.3533i q^{39} +(-7.93204 + 9.03510i) q^{40} -64.9569 q^{41} +16.8099i q^{43} +(-36.8283 + 1.59493i) q^{44} +4.50859 q^{45} +(29.9798 - 31.3063i) q^{46} -68.2794i q^{47} +(-2.39584 - 27.6091i) q^{48} +(32.8496 + 31.4578i) q^{50} +6.84938i q^{51} +(-1.03451 - 23.8876i) q^{52} -18.1753 q^{53} +(-7.18774 + 7.50576i) q^{54} -13.8499i q^{55} +6.23338 q^{57} +(-68.7249 - 65.8130i) q^{58} -49.0800i q^{59} +(10.4024 - 0.450499i) q^{60} -98.5495 q^{61} +(-53.2622 + 55.6188i) q^{62} +(-8.28647 - 63.4613i) q^{64} +8.98337 q^{65} +(23.0569 + 22.0800i) q^{66} -129.352i q^{67} +(0.684392 + 15.8032i) q^{68} -37.5387 q^{69} +61.8601i q^{71} +(-15.8339 + 18.0358i) q^{72} -95.7877 q^{73} +(75.8232 + 72.6106i) q^{74} -39.3893i q^{75} +(14.3819 - 0.622841i) q^{76} +(-14.3216 + 14.9552i) q^{78} -13.1219i q^{79} +(23.9558 - 2.07882i) q^{80} +9.00000 q^{81} +(93.8292 + 89.8537i) q^{82} +91.0240i q^{83} -5.94306 q^{85} +(23.2528 - 24.2816i) q^{86} +82.4066i q^{87} +(55.4041 + 48.6400i) q^{88} -90.7057 q^{89} +(-6.51258 - 6.23665i) q^{90} +(-86.6108 + 3.75087i) q^{92} +66.6913 q^{93} +(-94.4496 + 98.6285i) q^{94} +5.40857i q^{95} +(-34.7303 + 43.1950i) q^{96} -7.05515 q^{97} -27.6471i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} + 12 q^{4} - 20 q^{8} - 72 q^{9} - 60 q^{16} - 12 q^{18} + 168 q^{22} + 120 q^{25} + 64 q^{29} - 236 q^{32} - 36 q^{36} - 192 q^{37} - 360 q^{44} - 72 q^{46} + 532 q^{50} + 432 q^{53} + 240 q^{58}+ \cdots - 96 q^{93}+O(q^{100}) \) 24 * q + 4 * q^2 + 12 * q^4 - 20 * q^8 - 72 * q^9 - 60 * q^16 - 12 * q^18 + 168 * q^22 + 120 * q^25 + 64 * q^29 - 236 * q^32 - 36 * q^36 - 192 * q^37 - 360 * q^44 - 72 * q^46 + 532 * q^50 + 432 * q^53 + 240 * q^58 + 72 * q^60 - 372 * q^64 - 560 * q^65 + 60 * q^72 + 96 * q^74 + 216 * q^78 + 216 * q^81 + 144 * q^85 + 816 * q^86 - 72 * q^88 - 504 * q^92 - 96 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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