LMFDB - Embedded newform 1815.2.c.k.364.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1815,2,Mod(364,1815)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1815, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1815.364");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1815 = 3 \cdot 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1815.c (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:	$14.4928479669$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			364.20
Character	$\chi$	$=$	1815.364
Dual form			1815.2.c.k.364.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.10651i q^{2} -1.00000i q^{3} -2.43738 q^{4} +(-0.823234 + 2.07901i) q^{5} +2.10651 q^{6} -3.31633i q^{7} -0.921348i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+2.10651i q^{2} -1.00000i q^{3} -2.43738 q^{4} +(-0.823234 + 2.07901i) q^{5} +2.10651 q^{6} -3.31633i q^{7} -0.921348i q^{8} -1.00000 q^{9} +(-4.37946 - 1.73415i) q^{10} +2.43738i q^{12} -2.49889i q^{13} +6.98587 q^{14} +(2.07901 + 0.823234i) q^{15} -2.93393 q^{16} +6.81019i q^{17} -2.10651i q^{18} -1.14769 q^{19} +(2.00654 - 5.06734i) q^{20} -3.31633 q^{21} -5.89026i q^{23} -0.921348 q^{24} +(-3.64457 - 3.42303i) q^{25} +5.26393 q^{26} +1.00000i q^{27} +8.08315i q^{28} -1.12257 q^{29} +(-1.73415 + 4.37946i) q^{30} -1.09673 q^{31} -8.02306i q^{32} -14.3457 q^{34} +(6.89468 + 2.73011i) q^{35} +2.43738 q^{36} -11.5389i q^{37} -2.41763i q^{38} -2.49889 q^{39} +(1.91549 + 0.758486i) q^{40} +0.932568 q^{41} -6.98587i q^{42} +0.552188i q^{43} +(0.823234 - 2.07901i) q^{45} +12.4079 q^{46} -2.13427i q^{47} +2.93393i q^{48} -3.99802 q^{49} +(7.21064 - 7.67732i) q^{50} +6.81019 q^{51} +6.09074i q^{52} -11.6356i q^{53} -2.10651 q^{54} -3.05549 q^{56} +1.14769i q^{57} -2.36469i q^{58} -8.39837 q^{59} +(-5.06734 - 2.00654i) q^{60} +8.21313 q^{61} -2.31027i q^{62} +3.31633i q^{63} +11.0328 q^{64} +(5.19521 + 2.05717i) q^{65} -4.15419i q^{67} -16.5990i q^{68} -5.89026 q^{69} +(-5.75101 + 14.5237i) q^{70} +12.5340 q^{71} +0.921348i q^{72} -5.73761i q^{73} +24.3067 q^{74} +(-3.42303 + 3.64457i) q^{75} +2.79736 q^{76} -5.26393i q^{78} -3.86754 q^{79} +(2.41532 - 6.09968i) q^{80} +1.00000 q^{81} +1.96446i q^{82} -6.08055i q^{83} +8.08315 q^{84} +(-14.1585 - 5.60638i) q^{85} -1.16319 q^{86} +1.12257i q^{87} -12.5950 q^{89} +(4.37946 + 1.73415i) q^{90} -8.28712 q^{91} +14.3568i q^{92} +1.09673i q^{93} +4.49586 q^{94} +(0.944820 - 2.38607i) q^{95} -8.02306 q^{96} -2.86873i q^{97} -8.42187i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{4} - 2 q^{5} + 8 q^{6} - 24 q^{9}+O(q^{10}) $ 24 * q - 24 * q^4 - 2 * q^5 + 8 * q^6 - 24 * q^9	$ 24 q - 24 q^{4} - 2 q^{5} + 8 q^{6} - 24 q^{9} + 6 q^{10} - 12 q^{14} + 48 q^{16} - 32 q^{19} - 2 q^{20} + 16 q^{21} - 24 q^{24} + 2 q^{25} + 32 q^{26} + 8 q^{30} - 12 q^{34} - 10 q^{35} + 24 q^{36} - 36 q^{39} - 34 q^{40} + 2 q^{45} + 56 q^{46} - 24 q^{49} - 46 q^{50} + 36 q^{51} - 8 q^{54} + 12 q^{56} - 40 q^{59} - 26 q^{60} + 40 q^{61} + 12 q^{64} - 10 q^{65} - 2 q^{70} + 64 q^{71} + 136 q^{74} + 20 q^{75} + 68 q^{76} - 64 q^{79} + 76 q^{80} + 24 q^{81} - 60 q^{84} - 72 q^{86} + 20 q^{89} - 6 q^{90} + 4 q^{94} - 64 q^{95} + 56 q^{96}+O(q^{100}) $ 24 * q - 24 * q^4 - 2 * q^5 + 8 * q^6 - 24 * q^9 + 6 * q^10 - 12 * q^14 + 48 * q^16 - 32 * q^19 - 2 * q^20 + 16 * q^21 - 24 * q^24 + 2 * q^25 + 32 * q^26 + 8 * q^30 - 12 * q^34 - 10 * q^35 + 24 * q^36 - 36 * q^39 - 34 * q^40 + 2 * q^45 + 56 * q^46 - 24 * q^49 - 46 * q^50 + 36 * q^51 - 8 * q^54 + 12 * q^56 - 40 * q^59 - 26 * q^60 + 40 * q^61 + 12 * q^64 - 10 * q^65 - 2 * q^70 + 64 * q^71 + 136 * q^74 + 20 * q^75 + 68 * q^76 - 64 * q^79 + 76 * q^80 + 24 * q^81 - 60 * q^84 - 72 * q^86 + 20 * q^89 - 6 * q^90 + 4 * q^94 - 64 * q^95 + 56 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1815\mathbb{Z}\right)^\times$.

$n$	$727$	$1211$	$1696$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$			2.10651i			1.48953i	0.667328	+	0.744764i	$0.267438\pi$
$2$			2.10651i			1.48953i	−0.667328	+	0.744764i	$0.732562\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−2.43738			−1.21869
$5$	−0.823234	+	2.07901i	−0.368162	+	0.929762i
$5$	−0.823234	+	2.07901i	−0.368162	+	0.929762i
$6$	2.10651			0.859979
$7$		−	3.31633i		−	1.25345i	−0.779239	−	0.626727i	$-0.784394\pi$
$7$		−	3.31633i		−	1.25345i	0.779239	−	0.626727i	$-0.215606\pi$
$8$		−	0.921348i		−	0.325746i
$9$	−1.00000			−0.333333
$10$	−4.37946	−	1.73415i	−1.38491	−	0.548387i
$11$		0			0
$11$		0			0
$12$			2.43738i			0.703611i
$13$		−	2.49889i		−	0.693066i	−0.938038	−	0.346533i	$-0.887359\pi$
$13$		−	2.49889i		−	0.693066i	0.938038	−	0.346533i	$-0.112641\pi$
$14$	6.98587			1.86705
$15$	2.07901	+	0.823234i	0.536798	+	0.212558i
$16$	−2.93393			−0.733484
$17$			6.81019i			1.65171i	0.563880	+	0.825857i	$0.309308\pi$
$17$			6.81019i			1.65171i	−0.563880	+	0.825857i	$0.690692\pi$
$18$		−	2.10651i		−	0.496509i
$19$	−1.14769			−0.263299			−0.131649	−	0.991296i	$-0.542027\pi$
$19$	−1.14769			−0.263299			−0.131649	+	0.991296i	$0.542027\pi$
$20$	2.00654	−	5.06734i	0.448675	−	1.13309i
$21$	−3.31633			−0.723682
$22$		0			0
$23$		−	5.89026i		−	1.22820i	−0.789226	−	0.614102i	$-0.789518\pi$
$23$		−	5.89026i		−	1.22820i	0.789226	−	0.614102i	$-0.210482\pi$
$24$	−0.921348			−0.188069
$25$	−3.64457	−	3.42303i	−0.728914	−	0.684605i
$26$	5.26393			1.03234
$27$			1.00000i			0.192450i
$28$			8.08315i			1.52757i
$29$	−1.12257			−0.208455			−0.104228	−	0.994553i	$-0.533237\pi$
$29$	−1.12257			−0.208455			−0.104228	+	0.994553i	$0.533237\pi$
$30$	−1.73415	+	4.37946i	−0.316611	+	0.799575i
$31$	−1.09673			−0.196978			−0.0984892	−	0.995138i	$-0.531401\pi$
$31$	−1.09673			−0.196978			−0.0984892	+	0.995138i	$0.531401\pi$
$32$		−	8.02306i		−	1.41829i
$33$		0			0
$34$	−14.3457			−2.46027
$35$	6.89468	+	2.73011i	1.16541	+	0.461473i
$36$	2.43738			0.406230
$37$		−	11.5389i		−	1.89698i	−0.316810	−	0.948489i	$-0.602612\pi$
$37$		−	11.5389i		−	1.89698i	0.316810	−	0.948489i	$-0.397388\pi$
$38$		−	2.41763i		−	0.392191i
$39$	−2.49889			−0.400142
$40$	1.91549	+	0.758486i	0.302866	+	0.119927i
$41$	0.932568			0.145643			0.0728213	−	0.997345i	$-0.476800\pi$
$41$	0.932568			0.145643			0.0728213	+	0.997345i	$0.476800\pi$
$42$		−	6.98587i		−	1.07794i
$43$			0.552188i			0.0842079i	0.999113	+	0.0421040i	$0.0134061\pi$
$43$			0.552188i			0.0842079i	−0.999113	+	0.0421040i	$0.986594\pi$
$44$		0			0
$45$	0.823234	−	2.07901i	0.122721	−	0.309921i
$46$	12.4079			1.82944
$47$		−	2.13427i		−	0.311316i	−0.987811	−	0.155658i	$-0.950250\pi$
$47$		−	2.13427i		−	0.311316i	0.987811	−	0.155658i	$-0.0497497\pi$
$48$			2.93393i			0.423477i
$49$	−3.99802			−0.571146
$50$	7.21064	−	7.67732i	1.01974	−	1.08574i
$51$	6.81019			0.953617
$52$			6.09074i			0.844633i
$53$		−	11.6356i		−	1.59827i	−0.601150	−	0.799136i	$-0.705291\pi$
$53$		−	11.6356i		−	1.59827i	0.601150	−	0.799136i	$-0.294709\pi$
$54$	−2.10651			−0.286660
$55$		0			0
$56$	−3.05549			−0.408307
$57$			1.14769i			0.152016i
$58$		−	2.36469i		−	0.310500i
$59$	−8.39837			−1.09337			−0.546687	−	0.837337i	$-0.684111\pi$
$59$	−8.39837			−1.09337			−0.546687	+	0.837337i	$0.684111\pi$
$60$	−5.06734	−	2.00654i	−0.654191	−	0.259043i
$61$	8.21313			1.05158			0.525792	−	0.850613i	$-0.323769\pi$
$61$	8.21313			1.05158			0.525792	+	0.850613i	$0.323769\pi$
$62$		−	2.31027i		−	0.293405i
$63$			3.31633i			0.417818i
$64$	11.0328			1.37910
$65$	5.19521	+	2.05717i	0.644386	+	0.255160i
$66$		0			0
$67$		−	4.15419i		−	0.507515i	−0.967268	−	0.253757i	$-0.918334\pi$
$67$		−	4.15419i		−	0.507515i	0.967268	−	0.253757i	$-0.0816665\pi$
$68$		−	16.5990i		−	2.01293i
$69$	−5.89026			−0.709104
$70$	−5.75101	+	14.5237i	−0.687377	+	1.73591i
$71$	12.5340			1.48752			0.743759	−	0.668448i	$-0.233041\pi$
$71$	12.5340			1.48752			0.743759	+	0.668448i	$0.233041\pi$
$72$			0.921348i			0.108582i
$73$		−	5.73761i		−	0.671537i	−0.941945	−	0.335768i	$-0.891004\pi$
$73$		−	5.73761i		−	0.671537i	0.941945	−	0.335768i	$-0.108996\pi$
$74$	24.3067			2.82560
$75$	−3.42303	+	3.64457i	−0.395257	+	0.420839i
$76$	2.79736			0.320880
$77$		0			0
$78$		−	5.26393i		−	0.596022i
$79$	−3.86754			−0.435132			−0.217566	−	0.976046i	$-0.569812\pi$
$79$	−3.86754			−0.435132			−0.217566	+	0.976046i	$0.569812\pi$
$80$	2.41532	−	6.09968i	0.270040	−	0.681965i
$81$	1.00000			0.111111
$82$			1.96446i			0.216939i
$83$		−	6.08055i		−	0.667427i	−0.942675	−	0.333714i	$-0.891698\pi$
$83$		−	6.08055i		−	0.667427i	0.942675	−	0.333714i	$-0.108302\pi$
$84$	8.08315			0.881944
$85$	−14.1585	−	5.60638i	−1.53570	−	0.608097i
$86$	−1.16319			−0.125430
$87$			1.12257i			0.120352i
$88$		0			0
$89$	−12.5950			−1.33506			−0.667531	−	0.744582i	$-0.732649\pi$
$89$	−12.5950			−1.33506			−0.667531	+	0.744582i	$0.732649\pi$
$90$	4.37946	+	1.73415i	0.461635	+	0.182796i
$91$	−8.28712			−0.868726
$92$			14.3568i			1.49680i
$93$			1.09673i			0.113726i
$94$	4.49586			0.463713
$95$	0.944820	−	2.38607i	0.0969365	−	0.244805i
$96$	−8.02306			−0.818850
$97$		−	2.86873i		−	0.291275i	−0.989338	−	0.145638i	$-0.953477\pi$
$97$		−	2.86873i		−	0.291275i	0.989338	−	0.145638i	$-0.0465234\pi$
$98$		−	8.42187i		−	0.850737i
$99$		0			0
$100$	8.88321	+	8.34322i	0.888321	+	0.834322i
$101$	−9.87001			−0.982103			−0.491052	−	0.871131i	$-0.663387\pi$
$101$	−9.87001			−0.982103			−0.491052	+	0.871131i	$0.663387\pi$
$102$			14.3457i			1.42044i
$103$		−	7.71953i		−	0.760628i	−0.924857	−	0.380314i	$-0.875816\pi$
$103$		−	7.71953i		−	0.760628i	0.924857	−	0.380314i	$-0.124184\pi$
$104$	−2.30234			−0.225763
$105$	2.73011	−	6.89468i	0.266432	−	0.672852i
$106$	24.5105			2.38067
$107$			15.5114i			1.49954i	0.661697	+	0.749771i	$0.269837\pi$
$107$			15.5114i			1.49954i	−0.661697	+	0.749771i	$0.730163\pi$
$108$		−	2.43738i		−	0.234537i
$109$	6.79834			0.651163			0.325581	−	0.945514i	$-0.394440\pi$
$109$	6.79834			0.651163			0.325581	+	0.945514i	$0.394440\pi$
$110$		0			0
$111$	−11.5389			−1.09522
$112$			9.72988i			0.919388i
$113$			0.301489i			0.0283617i	0.999899	+	0.0141808i	$0.00451405\pi$
$113$			0.301489i			0.0283617i	−0.999899	+	0.0141808i	$0.995486\pi$
$114$	−2.41763			−0.226431
$115$	12.2459	+	4.84907i	1.14194	+	0.452178i
$116$	2.73612			0.254042
$117$			2.49889i			0.231022i
$118$		−	17.6912i		−	1.62861i
$119$	22.5848			2.07035
$120$	0.758486	−	1.91549i	0.0692399	−	0.174860i
$121$		0			0
$122$			17.3010i			1.56636i
$123$		−	0.932568i		−	0.0840868i
$124$	2.67315			0.240056
$125$	10.1168	−	4.75915i	0.904878	−	0.425671i
$126$	−6.98587			−0.622351
$127$			6.70539i			0.595007i	0.954721	+	0.297504i	$0.0961540\pi$
$127$			6.70539i			0.595007i	−0.954721	+	0.297504i	$0.903846\pi$
$128$			7.19453i			0.635913i
$129$	0.552188			0.0486175
$130$	−4.33344	+	10.9438i	−0.380068	+	0.959831i
$131$	8.07729			0.705716			0.352858	−	0.935677i	$-0.385210\pi$
$131$	8.07729			0.705716			0.352858	+	0.935677i	$0.385210\pi$
$132$		0			0
$133$			3.80612i			0.330033i
$134$	8.75084			0.755957
$135$	−2.07901	−	0.823234i	−0.178933	−	0.0708527i
$136$	6.27456			0.538039
$137$		−	6.43781i		−	0.550020i	−0.961441	−	0.275010i	$-0.911319\pi$
$137$		−	6.43781i		−	0.550020i	0.961441	−	0.275010i	$-0.0886811\pi$
$138$		−	12.4079i		−	1.05623i
$139$	6.97567			0.591669			0.295834	−	0.955239i	$-0.404402\pi$
$139$	6.97567			0.591669			0.295834	+	0.955239i	$0.404402\pi$
$140$	−16.8050	−	6.65433i	−1.42028	−	0.562393i
$141$	−2.13427			−0.179738
$142$			26.4031i			2.21570i
$143$		0			0
$144$	2.93393			0.244495
$145$	0.924135	−	2.33383i	0.0767452	−	0.193814i
$146$	12.0863			1.00027
$147$			3.99802i			0.329751i
$148$			28.1246i			2.31183i
$149$	−19.0205			−1.55822			−0.779110	−	0.626887i	$-0.784329\pi$
$149$	−19.0205			−1.55822			−0.779110	+	0.626887i	$0.784329\pi$
$150$	−7.67732	−	7.21064i	−0.626851	−	0.588746i
$151$	−3.90081			−0.317444			−0.158722	−	0.987323i	$-0.550737\pi$
$151$	−3.90081			−0.317444			−0.158722	+	0.987323i	$0.550737\pi$
$152$			1.05742i			0.0857685i
$153$		−	6.81019i		−	0.550571i
$154$		0			0
$155$	0.902865	−	2.28011i	0.0725199	−	0.183143i
$156$	6.09074			0.487649
$157$		−	18.3843i		−	1.46723i	−0.679568	−	0.733613i	$-0.737833\pi$
$157$		−	18.3843i		−	1.46723i	0.679568	−	0.733613i	$-0.262167\pi$
$158$		−	8.14701i		−	0.648141i
$159$	−11.6356			−0.922763
$160$	16.6800	+	6.60486i	1.31867	+	0.522160i
$161$	−19.5340			−1.53950
$162$			2.10651i			0.165503i
$163$			17.5720i			1.37635i	0.725547	+	0.688173i	$0.241587\pi$
$163$			17.5720i			1.37635i	−0.725547	+	0.688173i	$0.758413\pi$
$164$	−2.27302			−0.177493
$165$		0			0
$166$	12.8087			0.994151
$167$			12.0777i			0.934598i	0.884099	+	0.467299i	$0.154773\pi$
$167$			12.0777i			0.934598i	−0.884099	+	0.467299i	$0.845227\pi$
$168$			3.05549i			0.235736i
$169$	6.75557			0.519659
$170$	11.8099	−	29.8249i	0.905778	−	2.28747i
$171$	1.14769			0.0877662
$172$		−	1.34589i		−	0.102623i
$173$		−	24.2436i		−	1.84321i	−0.388133	−	0.921603i	$-0.626880\pi$
$173$		−	24.2436i		−	1.84321i	0.388133	−	0.921603i	$-0.373120\pi$
$174$	−2.36469			−0.179267
$175$	−11.3519	+	12.0866i	−0.858121	+	0.913660i
$176$		0			0
$177$			8.39837i			0.631260i
$178$		−	26.5314i		−	1.98861i
$179$	19.9390			1.49031			0.745155	−	0.666891i	$-0.232375\pi$
$179$	19.9390			1.49031			0.745155	+	0.666891i	$0.232375\pi$
$180$	−2.00654	+	5.06734i	−0.149558	+	0.377697i
$181$	−5.13290			−0.381525			−0.190763	−	0.981636i	$-0.561096\pi$
$181$	−5.13290			−0.381525			−0.190763	+	0.981636i	$0.561096\pi$
$182$		−	17.4569i		−	1.29399i
$183$		−	8.21313i		−	0.607132i
$184$	−5.42698			−0.400082
$185$	23.9894	+	9.49919i	1.76374	+	0.698395i
$186$	−2.31027			−0.169397
$187$		0			0
$188$			5.20204i			0.379397i
$189$	3.31633			0.241227
$190$	5.02627	+	1.99027i	0.364644	+	0.144390i
$191$	−2.81336			−0.203568			−0.101784	−	0.994807i	$-0.532455\pi$
$191$	−2.81336			−0.203568			−0.101784	+	0.994807i	$0.532455\pi$
$192$		−	11.0328i		−	0.796222i
$193$		−	19.3032i		−	1.38948i	−0.719263	−	0.694738i	$-0.755520\pi$
$193$		−	19.3032i		−	1.38948i	0.719263	−	0.694738i	$-0.244480\pi$
$194$	6.04300			0.433862
$195$	2.05717	−	5.19521i	0.147317	−	0.372037i
$196$	9.74470			0.696050
$197$		−	3.57956i		−	0.255033i	−0.991836	−	0.127516i	$-0.959299\pi$
$197$		−	3.57956i		−	0.255033i	0.991836	−	0.127516i	$-0.0407006\pi$
$198$		0			0
$199$	−12.7087			−0.900893			−0.450447	−	0.892803i	$-0.648735\pi$
$199$	−12.7087			−0.900893			−0.450447	+	0.892803i	$0.648735\pi$
$200$	−3.15380	+	3.35792i	−0.223007	+	0.237441i
$201$	−4.15419			−0.293014
$202$		−	20.7913i		−	1.46287i
$203$			3.72279i			0.261289i
$204$	−16.5990			−1.16216
$205$	−0.767722	+	1.93882i	−0.0536200	+	0.135413i
$206$	16.2613			1.13298
$207$			5.89026i			0.409401i
$208$			7.33157i			0.508353i
$209$		0			0
$210$	14.5237	+	5.75101i	1.00223	+	0.396857i
$211$	3.49518			0.240618			0.120309	−	0.992736i	$-0.461611\pi$
$211$	3.49518			0.240618			0.120309	+	0.992736i	$0.461611\pi$
$212$			28.3604i			1.94780i
$213$		−	12.5340i		−	0.858819i
$214$	−32.6749			−2.23361
$215$	−1.14801	−	0.454581i	−0.0782933	−	0.0310021i
$216$	0.921348			0.0626898
$217$			3.63711i			0.246903i
$218$			14.3208i			0.969925i
$219$	−5.73761			−0.387712
$220$		0			0
$221$	17.0179			1.14475
$222$		−	24.3067i		−	1.63136i
$223$			5.20558i			0.348591i	0.984693	+	0.174296i	$0.0557648\pi$
$223$			5.20558i			0.348591i	−0.984693	+	0.174296i	$0.944235\pi$
$224$	−26.6071			−1.77776
$225$	3.64457	+	3.42303i	0.242971	+	0.228202i
$226$	−0.635089			−0.0422455
$227$			9.70244i			0.643973i	0.946744	+	0.321987i	$0.104351\pi$
$227$			9.70244i			0.643973i	−0.946744	+	0.321987i	$0.895649\pi$
$228$		−	2.79736i		−	0.185260i
$229$	−18.5011			−1.22259			−0.611293	−	0.791404i	$-0.709350\pi$
$229$	−18.5011			−1.22259			−0.611293	+	0.791404i	$0.709350\pi$
$230$	−10.2146	+	25.7961i	−0.673531	+	1.70095i
$231$		0			0
$232$			1.03427i			0.0679034i
$233$			14.9543i			0.979692i	0.871809	+	0.489846i	$0.162947\pi$
$233$			14.9543i			0.979692i	−0.871809	+	0.489846i	$0.837053\pi$
$234$	−5.26393			−0.344114
$235$	4.43717	+	1.75701i	0.289449	+	0.114614i
$236$	20.4700			1.33249
$237$			3.86754i			0.251224i
$238$			47.5751i			3.08384i
$239$	−1.50716			−0.0974901			−0.0487451	−	0.998811i	$-0.515522\pi$
$239$	−1.50716			−0.0974901			−0.0487451	+	0.998811i	$0.515522\pi$
$240$	−6.09968	−	2.41532i	−0.393733	−	0.155908i
$241$	7.09571			0.457075			0.228537	−	0.973535i	$-0.426606\pi$
$241$	7.09571			0.457075			0.228537	+	0.973535i	$0.426606\pi$
$242$		0			0
$243$		−	1.00000i		−	0.0641500i
$244$	−20.0185			−1.28156
$245$	3.29131	−	8.31193i	0.210274	−	0.531029i
$246$	1.96446			0.125250
$247$			2.86795i			0.182483i
$248$			1.01047i			0.0641649i
$249$	−6.08055			−0.385339
$250$	10.0252	+	21.3112i	0.634049	+	1.34784i
$251$	−13.6786			−0.863386			−0.431693	−	0.902021i	$-0.642084\pi$
$251$	−13.6786			−0.863386			−0.431693	+	0.902021i	$0.642084\pi$
$252$		−	8.08315i		−	0.509191i
$253$		0			0
$254$	−14.1250			−0.886279
$255$	−5.60638	+	14.1585i	−0.351085	+	0.886637i
$256$	6.91021			0.431888
$257$			8.30411i			0.517996i	0.965878	+	0.258998i	$0.0833924\pi$
$257$			8.30411i			0.517996i	−0.965878	+	0.258998i	$0.916608\pi$
$258$			1.16319i			0.0724171i
$259$	−38.2667			−2.37777
$260$	−12.6627	−	5.01410i	−0.785308	−	0.310962i
$261$	1.12257			0.0694851
$262$			17.0149i			1.05118i
$263$		−	11.1345i		−	0.686582i	−0.939229	−	0.343291i	$-0.888458\pi$
$263$		−	11.1345i		−	0.686582i	0.939229	−	0.343291i	$-0.111542\pi$
$264$		0			0
$265$	24.1905	+	9.57882i	1.48601	+	0.588422i
$266$	−8.01763			−0.491593
$267$			12.5950i			0.770799i
$268$			10.1253i			0.618504i
$269$	−22.7563			−1.38748			−0.693739	−	0.720227i	$-0.744038\pi$
$269$	−22.7563			−1.38748			−0.693739	+	0.720227i	$0.744038\pi$
$270$	1.73415	−	4.37946i	0.105537	−	0.266525i
$271$	−7.79448			−0.473481			−0.236740	−	0.971573i	$-0.576079\pi$
$271$	−7.79448			−0.473481			−0.236740	+	0.971573i	$0.576079\pi$
$272$		−	19.9806i		−	1.21150i
$273$			8.28712i			0.501559i
$274$	13.5613			0.819269
$275$		0			0
$276$	14.3568			0.864179
$277$			9.46719i			0.568828i	0.958702	+	0.284414i	$0.0917991\pi$
$277$			9.46719i			0.568828i	−0.958702	+	0.284414i	$0.908201\pi$
$278$			14.6943i			0.881307i
$279$	1.09673			0.0656595
$280$	2.51539	−	6.35240i	0.150323	−	0.379628i
$281$	−31.3016			−1.86729			−0.933647	−	0.358194i	$-0.883393\pi$
$281$	−31.3016			−1.86729			−0.933647	+	0.358194i	$0.883393\pi$
$282$		−	4.49586i		−	0.267725i
$283$			24.4123i			1.45116i	0.688136	+	0.725581i	$0.258429\pi$
$283$			24.4123i			1.45116i	−0.688136	+	0.725581i	$0.741571\pi$
$284$	−30.5503			−1.81282
$285$	−2.38607	−	0.944820i	−0.141338	−	0.0559663i
$286$		0			0
$287$		−	3.09270i		−	0.182556i
$288$			8.02306i			0.472763i
$289$	−29.3787			−1.72816
$290$	4.91623	+	1.94670i	0.288691	+	0.114314i
$291$	−2.86873			−0.168168
$292$			13.9847i			0.818395i
$293$		−	11.8197i		−	0.690512i	−0.938509	−	0.345256i	$-0.887792\pi$
$293$		−	11.8197i		−	0.690512i	0.938509	−	0.345256i	$-0.112208\pi$
$294$	−8.42187			−0.491173
$295$	6.91383	−	17.4603i	0.402539	−	1.01658i
$296$	−10.6313			−0.617933
$297$		0			0
$298$		−	40.0669i		−	2.32101i
$299$	−14.7191			−0.851227
$300$	8.34322	−	8.88321i	0.481696	−	0.512872i
$301$	1.83124			0.105551
$302$		−	8.21710i		−	0.472841i
$303$			9.87001i			0.567018i
$304$	3.36725			0.193125
$305$	−6.76133	+	17.0752i	−0.387153	+	0.977723i
$306$	14.3457			0.820091
$307$			22.3217i			1.27396i	0.770878	+	0.636982i	$0.219818\pi$
$307$			22.3217i			1.27396i	−0.770878	+	0.636982i	$0.780182\pi$
$308$		0			0
$309$	−7.71953			−0.439149
$310$	4.80308	+	1.90189i	0.272796	+	0.108020i
$311$	−19.4834			−1.10480			−0.552401	−	0.833578i	$-0.686288\pi$
$311$	−19.4834			−1.10480			−0.552401	+	0.833578i	$0.686288\pi$
$312$			2.30234i			0.130345i
$313$			17.3527i			0.980833i	0.871488	+	0.490416i	$0.163155\pi$
$313$			17.3527i			0.980833i	−0.871488	+	0.490416i	$0.836845\pi$
$314$	38.7267			2.18547
$315$	−6.89468	−	2.73011i	−0.388471	−	0.153824i
$316$	9.42667			0.530292
$317$		−	0.830717i		−	0.0466577i	−0.999728	−	0.0233289i	$-0.992574\pi$
$317$		−	0.830717i		−	0.0466577i	0.999728	−	0.0233289i	$-0.00742648\pi$
$318$		−	24.5105i		−	1.37448i
$319$		0			0
$320$	−9.08256	+	22.9373i	−0.507731	+	1.28223i
$321$	15.5114			0.865762
$322$		−	41.1486i		−	2.29312i
$323$		−	7.81600i		−	0.434894i
$324$	−2.43738			−0.135410
$325$	−8.55375	+	9.10736i	−0.474477	+	0.505186i
$326$	−37.0156			−2.05010
$327$		−	6.79834i		−	0.375949i
$328$		−	0.859219i		−	0.0474425i
$329$	−7.07794			−0.390220
$330$		0			0
$331$	−31.5311			−1.73311			−0.866554	−	0.499084i	$-0.833670\pi$
$331$	−31.5311			−1.73311			−0.866554	+	0.499084i	$0.833670\pi$
$332$			14.8206i			0.813387i
$333$			11.5389i			0.632326i
$334$	−25.4417			−1.39211
$335$	8.63660	+	3.41987i	0.471868	+	0.186847i
$336$	9.72988			0.530809
$337$		−	16.2339i		−	0.884319i	−0.896936	−	0.442160i	$-0.854212\pi$
$337$		−	16.2339i		−	0.884319i	0.896936	−	0.442160i	$-0.145788\pi$
$338$			14.2307i			0.774047i
$339$	0.301489			0.0163746
$340$	34.5096	+	13.6649i	1.87154	+	0.741083i
$341$		0			0
$342$			2.41763i			0.130730i
$343$		−	9.95555i		−	0.537549i
$344$	0.508758			0.0274304
$345$	4.84907	−	12.2459i	0.261065	−	0.659298i
$346$	51.0694			2.74551
$347$		−	12.4500i		−	0.668350i	−0.942511	−	0.334175i	$-0.891542\pi$
$347$		−	12.4500i		−	0.668350i	0.942511	−	0.334175i	$-0.108458\pi$
$348$		−	2.73612i		−	0.146671i
$349$	32.6297			1.74663			0.873314	−	0.487157i	$-0.161966\pi$
$349$	32.6297			1.74663			0.873314	+	0.487157i	$0.161966\pi$
$350$	−25.4605	−	23.9128i	−1.36092	−	1.27819i
$351$	2.49889			0.133381
$352$		0			0
$353$		−	15.7921i		−	0.840530i	−0.907402	−	0.420265i	$-0.861937\pi$
$353$		−	15.7921i		−	0.840530i	0.907402	−	0.420265i	$-0.138063\pi$
$354$	−17.6912			−0.940279
$355$	−10.3185	+	26.0584i	−0.547647	+	1.38304i
$356$	30.6987			1.62703
$357$		−	22.5848i		−	1.19531i
$358$			42.0017i			2.21986i
$359$	18.1622			0.958563			0.479282	−	0.877661i	$-0.340897\pi$
$359$	18.1622			0.958563			0.479282	+	0.877661i	$0.340897\pi$
$360$	−1.91549	−	0.758486i	−0.100955	−	0.0399757i
$361$	−17.6828			−0.930674
$362$		−	10.8125i		−	0.568292i
$363$		0			0
$364$	20.1989			1.05871
$365$	11.9286	+	4.72340i	0.624369	+	0.247234i
$366$	17.3010			0.904340
$367$			0.472046i			0.0246406i	0.999924	+	0.0123203i	$0.00392177\pi$
$367$			0.472046i			0.0246406i	−0.999924	+	0.0123203i	$0.996078\pi$
$368$			17.2816i			0.900868i
$369$	−0.932568			−0.0485475
$370$	−20.0101	+	50.5340i	−1.04028	+	2.62714i
$371$	−38.5874			−2.00336
$372$		−	2.67315i		−	0.138596i
$373$		−	15.4102i		−	0.797910i	−0.916970	−	0.398955i	$-0.869373\pi$
$373$		−	15.4102i		−	0.797910i	0.916970	−	0.398955i	$-0.130627\pi$
$374$		0			0
$375$	−4.75915	−	10.1168i	−0.245761	−	0.522432i
$376$	−1.96641			−0.101410
$377$			2.80516i			0.144473i
$378$			6.98587i			0.359314i
$379$	19.2746			0.990068			0.495034	−	0.868874i	$-0.335156\pi$
$379$	19.2746			0.990068			0.495034	+	0.868874i	$0.335156\pi$
$380$	−2.30289	+	5.81575i	−0.118136	+	0.298342i
$381$	6.70539			0.343527
$382$		−	5.92637i		−	0.303220i
$383$		−	7.44824i		−	0.380587i	−0.981727	−	0.190294i	$-0.939056\pi$
$383$		−	7.44824i		−	0.380587i	0.981727	−	0.190294i	$-0.0609440\pi$
$384$	7.19453			0.367144
$385$		0			0
$386$	40.6624			2.06966
$387$		−	0.552188i		−	0.0280693i
$388$			6.99218i			0.354974i
$389$	0.713819			0.0361921			0.0180960	−	0.999836i	$-0.494240\pi$
$389$	0.713819			0.0361921			0.0180960	+	0.999836i	$0.494240\pi$
$390$	10.9438	+	4.33344i	0.554159	+	0.219432i
$391$	40.1138			2.02864
$392$			3.68357i			0.186048i
$393$		−	8.07729i		−	0.407446i
$394$	7.54037			0.379878
$395$	3.18389	−	8.04066i	0.160199	−	0.404569i
$396$		0			0
$397$			0.764171i			0.0383526i	0.999816	+	0.0191763i	$0.00610438\pi$
$397$			0.764171i			0.0383526i	−0.999816	+	0.0191763i	$0.993896\pi$
$398$		−	26.7709i		−	1.34191i
$399$	3.80612			0.190544
$400$	10.6929	+	10.0429i	0.534646	+	0.502147i
$401$	−15.7544			−0.786740			−0.393370	−	0.919380i	$-0.628691\pi$
$401$	−15.7544			−0.786740			−0.393370	+	0.919380i	$0.628691\pi$
$402$		−	8.75084i		−	0.436452i
$403$			2.74060i			0.136519i
$404$	24.0570			1.19688
$405$	−0.823234	+	2.07901i	−0.0409068	+	0.103307i
$406$	−7.84210			−0.389197
$407$		0			0
$408$		−	6.27456i		−	0.310637i
$409$	−2.62100			−0.129600			−0.0648001	−	0.997898i	$-0.520641\pi$
$409$	−2.62100			−0.129600			−0.0648001	+	0.997898i	$0.520641\pi$
$410$	−4.08414	−	1.61721i	−0.201701	−	0.0798684i
$411$	−6.43781			−0.317554
$412$			18.8154i			0.926970i
$413$			27.8517i			1.37049i
$414$	−12.4079			−0.609815
$415$	12.6415	+	5.00572i	0.620548	+	0.245721i
$416$	−20.0487			−0.982968
$417$		−	6.97567i		−	0.341600i
$418$		0			0
$419$	18.0078			0.879737			0.439868	−	0.898062i	$-0.355025\pi$
$419$	18.0078			0.879737			0.439868	+	0.898062i	$0.355025\pi$
$420$	−6.65433	+	16.8050i	−0.324698	+	0.819998i
$421$	1.17117			0.0570792			0.0285396	−	0.999593i	$-0.490914\pi$
$421$	1.17117			0.0570792			0.0285396	+	0.999593i	$0.490914\pi$
$422$			7.36264i			0.358408i
$423$			2.13427i			0.103772i
$424$	−10.7204			−0.520630
$425$	23.3115	−	24.8202i	1.13077	−	1.20396i
$426$	26.4031			1.27923
$427$		−	27.2374i		−	1.31811i
$428$		−	37.8072i		−	1.82748i
$429$		0			0
$430$	0.957578	−	2.41828i	0.0461785	−	0.116620i
$431$	−35.0921			−1.69033			−0.845163	−	0.534508i	$-0.820497\pi$
$431$	−35.0921			−1.69033			−0.845163	+	0.534508i	$0.820497\pi$
$432$		−	2.93393i		−	0.141159i
$433$			18.2260i			0.875888i	0.899002	+	0.437944i	$0.144293\pi$
$433$			18.2260i			0.875888i	−0.899002	+	0.437944i	$0.855707\pi$
$434$	−7.66161			−0.367769
$435$	−2.33383	−	0.924135i	−0.111898	−	0.0443089i
$436$	−16.5701			−0.793566
$437$			6.76021i			0.323385i
$438$		−	12.0863i		−	0.577507i
$439$	−19.8155			−0.945743			−0.472871	−	0.881131i	$-0.656782\pi$
$439$	−19.8155			−0.945743			−0.472871	+	0.881131i	$0.656782\pi$
$440$		0			0
$441$	3.99802			0.190382
$442$			35.8483i			1.70513i
$443$		−	16.6884i		−	0.792892i	−0.918058	−	0.396446i	$-0.870243\pi$
$443$		−	16.6884i		−	0.792892i	0.918058	−	0.396446i	$-0.129757\pi$
$444$	28.1246			1.33474
$445$	10.3686	−	26.1850i	0.491519	−	1.24129i
$446$	−10.9656			−0.519236
$447$			19.0205i			0.899639i
$448$		−	36.5883i		−	1.72863i
$449$	13.1971			0.622808			0.311404	−	0.950278i	$-0.399201\pi$
$449$	13.1971			0.622808			0.311404	+	0.950278i	$0.399201\pi$
$450$	−7.21064	+	7.67732i	−0.339913	+	0.361912i
$451$		0			0
$452$		−	0.734843i		−	0.0345641i
$453$			3.90081i			0.183276i
$454$	−20.4383			−0.959216
$455$	6.82224	−	17.2290i	0.319832	−	0.807708i
$456$	1.05742			0.0495184
$457$		−	21.2673i		−	0.994840i	−0.867510	−	0.497420i	$-0.834281\pi$
$457$		−	21.2673i		−	0.994840i	0.867510	−	0.497420i	$-0.165719\pi$
$458$		−	38.9727i		−	1.82107i
$459$	−6.81019			−0.317872
$460$	−29.8480	−	11.8190i	−1.39167	−	0.551065i
$461$	20.0772			0.935086			0.467543	−	0.883970i	$-0.345139\pi$
$461$	20.0772			0.935086			0.467543	+	0.883970i	$0.345139\pi$
$462$		0			0
$463$			0.962526i			0.0447324i	0.999750	+	0.0223662i	$0.00711997\pi$
$463$			0.962526i			0.0447324i	−0.999750	+	0.0223662i	$0.992880\pi$
$464$	3.29353			0.152898
$465$	−2.28011	−	0.902865i	−0.105738	−	0.0418694i
$466$	−31.5015			−1.45928
$467$		−	14.9130i		−	0.690092i	−0.938586	−	0.345046i	$-0.887863\pi$
$467$		−	14.9130i		−	0.690092i	0.938586	−	0.345046i	$-0.112137\pi$
$468$		−	6.09074i		−	0.281544i
$469$	−13.7766			−0.636146
$470$	−3.70115	+	9.34695i	−0.170721	+	0.431143i
$471$	−18.3843			−0.847103
$472$			7.73783i			0.356162i
$473$		0			0
$474$	−8.14701			−0.374204
$475$	4.18285	+	3.92858i	0.191922	+	0.180256i
$476$	−55.0478			−2.52311
$477$			11.6356i			0.532757i
$478$		−	3.17485i		−	0.145214i
$479$	−0.475527			−0.0217274			−0.0108637	−	0.999941i	$-0.503458\pi$
$479$	−0.475527			−0.0217274			−0.0108637	+	0.999941i	$0.503458\pi$
$480$	6.60486	−	16.6800i	0.301469	−	0.761335i
$481$	−28.8343			−1.31473
$482$			14.9472i			0.680825i
$483$			19.5340i			0.888829i
$484$		0			0
$485$	5.96412	+	2.36164i	0.270817	+	0.107236i
$486$	2.10651			0.0955532
$487$		−	35.3529i		−	1.60199i	−0.598668	−	0.800997i	$-0.704303\pi$
$487$		−	35.3529i		−	1.60199i	0.598668	−	0.800997i	$-0.295697\pi$
$488$		−	7.56716i		−	0.342549i
$489$	17.5720			0.794634
$490$	17.5091	+	6.93317i	0.790983	+	0.313209i
$491$	30.1328			1.35987			0.679937	−	0.733271i	$-0.262007\pi$
$491$	30.1328			1.35987			0.679937	+	0.733271i	$0.262007\pi$
$492$			2.27302i			0.102476i
$493$		−	7.64488i		−	0.344308i
$494$	−6.04137			−0.271814
$495$		0			0
$496$	3.21773			0.144480
$497$		−	41.5670i		−	1.86453i
$498$		−	12.8087i		−	0.573973i
$499$	36.4797			1.63306			0.816528	−	0.577305i	$-0.195896\pi$
$499$	36.4797			1.63306			0.816528	+	0.577305i	$0.195896\pi$
$500$	−24.6586	+	11.5999i	−1.10277	+	0.518761i
$501$	12.0777			0.539590
$502$		−	28.8141i		−	1.28604i
$503$			15.4251i			0.687772i	0.939011	+	0.343886i	$0.111743\pi$
$503$			15.4251i			0.687772i	−0.939011	+	0.343886i	$0.888257\pi$
$504$	3.05549			0.136102
$505$	8.12534	−	20.5199i	0.361573	−	0.913122i
$506$		0			0
$507$		−	6.75557i		−	0.300025i
$508$		−	16.3436i		−	0.725130i
$509$	−12.6374			−0.560142			−0.280071	−	0.959979i	$-0.590358\pi$
$509$	−12.6374			−0.560142			−0.280071	+	0.959979i	$0.590358\pi$
$510$	−29.8249	−	11.8099i	−1.32067	−	0.522951i
$511$	−19.0278			−0.841740
$512$			28.9455i			1.27922i
$513$		−	1.14769i		−	0.0506719i
$514$	−17.4927			−0.771570
$515$	16.0490	+	6.35498i	0.707203	+	0.280034i
$516$	−1.34589			−0.0592497
$517$		0			0
$518$		−	80.6091i		−	3.54176i
$519$	−24.2436			−1.06418
$520$	1.89537	−	4.78660i	0.0831174	−	0.209906i
$521$	−9.18439			−0.402376			−0.201188	−	0.979553i	$-0.564480\pi$
$521$	−9.18439			−0.402376			−0.201188	+	0.979553i	$0.564480\pi$
$522$			2.36469i			0.103500i
$523$			33.5841i			1.46853i	0.678863	+	0.734265i	$0.262473\pi$
$523$			33.5841i			1.46853i	−0.678863	+	0.734265i	$0.737527\pi$
$524$	−19.6874			−0.860050
$525$	12.0866	+	11.3519i	0.527502	+	0.495436i
$526$	23.4549			1.02268
$527$		−	7.46893i		−	0.325352i
$528$		0			0
$529$	−11.6952			−0.508486
$530$	−20.1779	+	50.9576i	−0.876471	+	2.21346i
$531$	8.39837			0.364458
$532$		−	9.27697i		−	0.402208i
$533$		−	2.33038i		−	0.100940i
$534$	−26.5314			−1.14813
$535$	−32.2484	−	12.7695i	−1.39422	−	0.552074i
$536$	−3.82745			−0.165321
$537$		−	19.9390i		−	0.860431i
$538$		−	47.9364i		−	2.06669i
$539$		0			0
$540$	5.06734	+	2.00654i	0.218064	+	0.0863476i
$541$	−44.6024			−1.91761			−0.958803	−	0.284072i	$-0.908315\pi$
$541$	−44.6024			−1.91761			−0.958803	+	0.284072i	$0.908315\pi$
$542$		−	16.4191i		−	0.705262i
$543$			5.13290i			0.220274i
$544$	54.6385			2.34261
$545$	−5.59663	+	14.1338i	−0.239733	+	0.605426i
$546$	−17.4569			−0.747086
$547$		−	19.2310i		−	0.822256i	−0.911578	−	0.411128i	$-0.865135\pi$
$547$		−	19.2310i		−	0.822256i	0.911578	−	0.411128i	$-0.134865\pi$
$548$			15.6914i			0.670304i
$549$	−8.21313			−0.350528
$550$		0			0
$551$	1.28836			0.0548860
$552$			5.42698i			0.230988i
$553$			12.8260i			0.545418i
$554$	−19.9427			−0.847285
$555$	9.49919	−	23.9894i	0.403218	−	1.01829i
$556$	−17.0024			−0.721061
$557$			33.3669i			1.41380i	0.707314	+	0.706900i	$0.249907\pi$
$557$			33.3669i			1.41380i	−0.707314	+	0.706900i	$0.750093\pi$
$558$			2.31027i			0.0978016i
$559$	1.37986			0.0583617
$560$	−20.2285	−	8.00997i	−0.854811	−	0.338483i
$561$		0			0
$562$		−	65.9370i		−	2.78139i
$563$		−	2.09215i		−	0.0881735i	−0.999028	−	0.0440868i	$-0.985962\pi$
$563$		−	2.09215i		−	0.0881735i	0.999028	−	0.0440868i	$-0.0140378\pi$
$564$	5.20204			0.219045
$565$	−0.626798	−	0.248196i	−0.0263696	−	0.0104417i
$566$	−51.4248			−2.16155
$567$		−	3.31633i		−	0.139273i
$568$		−	11.5482i		−	0.484553i
$569$	−9.31615			−0.390553			−0.195277	−	0.980748i	$-0.562561\pi$
$569$	−9.31615			−0.390553			−0.195277	+	0.980748i	$0.562561\pi$
$570$	1.99027	−	5.02627i	0.0833633	−	0.210527i
$571$	−2.32989			−0.0975029			−0.0487514	−	0.998811i	$-0.515524\pi$
$571$	−2.32989			−0.0975029			−0.0487514	+	0.998811i	$0.515524\pi$
$572$		0			0
$573$			2.81336i			0.117530i
$574$	6.51480			0.271922
$575$	−20.1625	+	21.4675i	−0.840835	+	0.895255i
$576$	−11.0328			−0.459699
$577$			29.4627i			1.22655i	0.789869	+	0.613275i	$0.210148\pi$
$577$			29.4627i			1.22655i	−0.789869	+	0.613275i	$0.789852\pi$
$578$		−	61.8864i		−	2.57414i
$579$	−19.3032			−0.802214
$580$	−2.25247	+	5.68842i	−0.0935287	+	0.236199i
$581$	−20.1651			−0.836589
$582$		−	6.04300i		−	0.250491i
$583$		0			0
$584$	−5.28634			−0.218750
$585$	−5.19521	−	2.05717i	−0.214795	−	0.0850534i
$586$	24.8982			1.02854
$587$			41.5167i			1.71358i	0.515667	+	0.856789i	$0.327544\pi$
$587$			41.5167i			1.71358i	−0.515667	+	0.856789i	$0.672456\pi$
$588$		−	9.74470i		−	0.401865i
$589$	1.25871			0.0518642
$590$	36.7803	+	14.5640i	1.51422	+	0.599592i
$591$	−3.57956			−0.147243
$592$			33.8543i			1.39140i
$593$			9.36964i			0.384765i	0.981320	+	0.192383i	$0.0616214\pi$
$593$			9.36964i			0.384765i	−0.981320	+	0.192383i	$0.938379\pi$
$594$		0			0
$595$	−18.5926	+	46.9541i	−0.762222	+	1.92493i
$596$	46.3602			1.89899
$597$			12.7087i			0.520131i
$598$		−	31.0059i		−	1.26793i
$599$	−1.31702			−0.0538122			−0.0269061	−	0.999638i	$-0.508566\pi$
$599$	−1.31702			−0.0538122			−0.0269061	+	0.999638i	$0.508566\pi$
$600$	3.35792	+	3.15380i	0.137086	+	0.128753i
$601$	−15.6267			−0.637425			−0.318713	−	0.947851i	$-0.603250\pi$
$601$	−15.6267			−0.637425			−0.318713	+	0.947851i	$0.603250\pi$
$602$			3.85752i			0.157221i
$603$			4.15419i			0.169172i
$604$	9.50777			0.386866
$605$		0			0
$606$	−20.7913			−0.844588
$607$			24.2123i			0.982746i	0.870949	+	0.491373i	$0.163505\pi$
$607$			24.2123i			0.982746i	−0.870949	+	0.491373i	$0.836495\pi$
$608$			9.20800i			0.373434i
$609$	3.72279			0.150855
$610$	−35.9691	−	14.2428i	−1.45634	−	0.576675i
$611$	−5.33330			−0.215762
$612$			16.5990i			0.670976i
$613$		−	4.08630i		−	0.165044i	−0.996589	−	0.0825221i	$-0.973702\pi$
$613$		−	4.08630i		−	0.165044i	0.996589	−	0.0825221i	$-0.0262975\pi$
$614$	−47.0208			−1.89760
$615$	1.93882	+	0.767722i	0.0781807	+	0.0309575i
$616$		0			0
$617$		−	16.9835i		−	0.683731i	−0.939749	−	0.341866i	$-0.888941\pi$
$617$		−	16.9835i		−	0.683731i	0.939749	−	0.341866i	$-0.111059\pi$
$618$		−	16.2613i		−	0.654124i
$619$	32.1306			1.29144			0.645720	−	0.763575i	$-0.276558\pi$
$619$	32.1306			1.29144			0.645720	+	0.763575i	$0.276558\pi$
$620$	−2.20063	+	5.55750i	−0.0883793	+	0.223195i
$621$	5.89026			0.236368
$622$		−	41.0420i		−	1.64563i
$623$			41.7690i			1.67344i
$624$	7.33157			0.293498
$625$	1.56579	+	24.9509i	0.0626314	+	0.998037i
$626$	−36.5536			−1.46098
$627$		0			0
$628$			44.8095i			1.78809i
$629$	78.5819			3.13326
$630$	5.75101	−	14.5237i	0.229126	−	0.578638i
$631$	−6.31566			−0.251422			−0.125711	−	0.992067i	$-0.540121\pi$
$631$	−6.31566			−0.251422			−0.125711	+	0.992067i	$0.540121\pi$
$632$			3.56335i			0.141742i
$633$		−	3.49518i		−	0.138921i
$634$	1.74991			0.0694980
$635$	−13.9406	−	5.52011i	−0.553215	−	0.219059i
$636$	28.3604			1.12456
$637$			9.99059i			0.395842i
$638$		0			0
$639$	−12.5340			−0.495839
$640$	−14.9575	−	5.92278i	−0.591247	−	0.234119i
$641$	14.6862			0.580072			0.290036	−	0.957016i	$-0.406333\pi$
$641$	14.6862			0.580072			0.290036	+	0.957016i	$0.406333\pi$
$642$			32.6749i			1.28958i
$643$		−	16.1510i		−	0.636933i	−0.947934	−	0.318467i	$-0.896832\pi$
$643$		−	16.1510i		−	0.636933i	0.947934	−	0.318467i	$-0.103168\pi$
$644$	47.6119			1.87617
$645$	−0.454581	+	1.14801i	−0.0178991	+	0.0452027i
$646$	16.4645			0.647786
$647$		−	27.7874i		−	1.09243i	−0.837644	−	0.546217i	$-0.816067\pi$
$647$		−	27.7874i		−	1.09243i	0.837644	−	0.546217i	$-0.183933\pi$
$648$		−	0.921348i		−	0.0361940i
$649$		0			0
$650$	−19.1847	−	18.0186i	−0.752488	−	0.706746i
$651$	3.63711			0.142550
$652$		−	42.8297i		−	1.67734i
$653$		−	34.0655i		−	1.33309i	−0.745467	−	0.666543i	$-0.767773\pi$
$653$		−	34.0655i		−	1.33309i	0.745467	−	0.666543i	$-0.232227\pi$
$654$	14.3208			0.559986
$655$	−6.64951	+	16.7928i	−0.259818	+	0.656148i
$656$	−2.73609			−0.106826
$657$			5.73761i			0.223846i
$658$		−	14.9098i		−	0.581243i
$659$	14.4196			0.561709			0.280855	−	0.959750i	$-0.409382\pi$
$659$	14.4196			0.561709			0.280855	+	0.959750i	$0.409382\pi$
$660$		0			0
$661$	26.4275			1.02791			0.513956	−	0.857817i	$-0.328179\pi$
$661$	26.4275			1.02791			0.513956	+	0.857817i	$0.328179\pi$
$662$		−	66.4206i		−	2.58151i
$663$		−	17.0179i		−	0.660920i
$664$	−5.60231			−0.217412
$665$	−7.91297	−	3.13333i	−0.306852	−	0.121505i
$666$	−24.3067			−0.941867
$667$			6.61220i			0.256026i
$668$		−	29.4379i		−	1.13899i
$669$	5.20558			0.201259
$670$	−7.20399	+	18.1931i	−0.278314	+	0.702860i
$671$		0			0
$672$			26.6071i			1.02639i
$673$		−	36.3130i		−	1.39976i	−0.714260	−	0.699881i	$-0.753236\pi$
$673$		−	36.3130i		−	1.39976i	0.714260	−	0.699881i	$-0.246764\pi$
$674$	34.1970			1.31722
$675$	3.42303	−	3.64457i	0.131752	−	0.140280i
$676$	−16.4659			−0.633304
$677$			11.3442i			0.435994i	0.975949	+	0.217997i	$0.0699523\pi$
$677$			11.3442i			0.435994i	−0.975949	+	0.217997i	$0.930048\pi$
$678$			0.635089i			0.0243904i
$679$	−9.51364			−0.365100
$680$	−5.16543	+	13.0449i	−0.198085	+	0.500248i
$681$	9.70244			0.371798
$682$		0			0
$683$			39.4269i			1.50863i	0.656514	+	0.754314i	$0.272030\pi$
$683$			39.4269i			1.50863i	−0.656514	+	0.754314i	$0.727970\pi$
$684$	−2.79736			−0.106960
$685$	13.3843	+	5.29983i	0.511387	+	0.202496i
$686$	20.9715			0.800694
$687$			18.5011i			0.705860i
$688$		−	1.62008i		−	0.0617651i
$689$	−29.0760			−1.10771
$690$	25.7961	+	10.2146i	0.982042	+	0.388863i
$691$	14.7763			0.562118			0.281059	−	0.959691i	$-0.409314\pi$
$691$	14.7763			0.562118			0.281059	+	0.959691i	$0.409314\pi$
$692$			59.0909i			2.24630i
$693$		0			0
$694$	26.2260			0.995526
$695$	−5.74261	+	14.5025i	−0.217830	+	0.550111i
$696$	1.03427			0.0392040
$697$			6.35096i			0.240560i
$698$			68.7348i			2.60165i
$699$	14.9543			0.565625
$700$	27.6688	−	29.4596i	1.04578	−	1.11347i
$701$	7.12932			0.269271			0.134635	−	0.990895i	$-0.457014\pi$
$701$	7.12932			0.269271			0.134635	+	0.990895i	$0.457014\pi$
$702$			5.26393i			0.198674i
$703$			13.2431i			0.499472i
$704$		0			0
$705$	1.75701	−	4.43717i	0.0661727	−	0.167114i
$706$	33.2662			1.25199
$707$			32.7322i			1.23102i
$708$		−	20.4700i		−	0.769311i
$709$	5.35482			0.201104			0.100552	−	0.994932i	$-0.467939\pi$
$709$	5.35482			0.201104			0.100552	+	0.994932i	$0.467939\pi$
$710$	−54.8923	−	21.7359i	−2.06007	−	0.815735i
$711$	3.86754			0.145044
$712$			11.6043i			0.434891i
$713$			6.46002i			0.241930i
$714$	47.5751			1.78045
$715$		0			0
$716$	−48.5989			−1.81623
$717$			1.50716i			0.0562860i
$718$			38.2588i			1.42781i
$719$	40.7829			1.52095			0.760473	−	0.649370i	$-0.224967\pi$
$719$	40.7829			1.52095			0.760473	+	0.649370i	$0.224967\pi$
$720$	−2.41532	+	6.09968i	−0.0900135	+	0.227322i
$721$	−25.6005			−0.953412
$722$		−	37.2490i		−	1.38626i
$723$		−	7.09571i		−	0.263892i
$724$	12.5108			0.464961
$725$	4.09127	+	3.84257i	0.151946	+	0.142710i
$726$		0			0
$727$			28.6101i			1.06109i	0.847656	+	0.530546i	$0.178013\pi$
$727$			28.6101i			1.06109i	−0.847656	+	0.530546i	$0.821987\pi$
$728$			7.63532i			0.282984i
$729$	−1.00000			−0.0370370
$730$	−9.94988	+	25.1276i	−0.368262	+	0.930015i
$731$	−3.76051			−0.139087
$732$			20.0185i			0.739907i
$733$		−	4.39612i		−	0.162374i	−0.996699	−	0.0811871i	$-0.974129\pi$
$733$		−	4.39612i		−	0.162374i	0.996699	−	0.0811871i	$-0.0258711\pi$
$734$	−0.994370			−0.0367029
$735$	−8.31193	−	3.29131i	−0.306590	−	0.121402i
$736$	−47.2579			−1.74195
$737$		0			0
$738$		−	1.96446i		−	0.0723129i
$739$	−10.5172			−0.386882			−0.193441	−	0.981112i	$-0.561965\pi$
$739$	−10.5172			−0.386882			−0.193441	+	0.981112i	$0.561965\pi$
$740$	−58.4714	−	23.1532i	−2.14945	−	0.851127i
$741$	2.86795			0.105357
$742$		−	81.2848i		−	2.98406i
$743$			34.4901i			1.26532i	0.774431	+	0.632659i	$0.218036\pi$
$743$			34.4901i			1.26532i	−0.774431	+	0.632659i	$0.781964\pi$
$744$	1.01047			0.0370456
$745$	15.6583	−	39.5438i	0.573677	−	1.44877i
$746$	32.4617			1.18851
$747$			6.08055i			0.222476i
$748$		0			0
$749$	51.4408			1.87961
$750$	21.3112	−	10.0252i	0.778176	−	0.366068i
$751$	−2.38104			−0.0868854			−0.0434427	−	0.999056i	$-0.513833\pi$
$751$	−2.38104			−0.0868854			−0.0434427	+	0.999056i	$0.513833\pi$
$752$			6.26181i			0.228345i
$753$			13.6786i			0.498476i
$754$	−5.90910			−0.215197
$755$	3.21128	−	8.10983i	0.116871	−	0.295147i
$756$	−8.08315			−0.293981
$757$			8.39549i			0.305139i	0.988293	+	0.152570i	$0.0487548\pi$
$757$			8.39549i			0.305139i	−0.988293	+	0.152570i	$0.951245\pi$
$758$			40.6021i			1.47473i
$759$		0			0
$760$	−2.19840	−	0.870508i	−0.0797442	−	0.0315767i
$761$	−10.4681			−0.379467			−0.189734	−	0.981836i	$-0.560762\pi$
$761$	−10.4681			−0.379467			−0.189734	+	0.981836i	$0.560762\pi$
$762$			14.1250i			0.511693i
$763$		−	22.5455i		−	0.816202i
$764$	6.85724			0.248086
$765$	14.1585	+	5.60638i	0.511900	+	0.202699i
$766$	15.6898			0.566895
$767$			20.9866i			0.757781i
$768$		−	6.91021i		−	0.249351i
$769$	−9.70799			−0.350079			−0.175040	−	0.984561i	$-0.556005\pi$
$769$	−9.70799			−0.350079			−0.175040	+	0.984561i	$0.556005\pi$
$770$		0			0
$771$	8.30411			0.299065
$772$			47.0493i			1.69334i
$773$			31.9598i			1.14952i	0.818324	+	0.574758i	$0.194904\pi$
$773$			31.9598i			1.14952i	−0.818324	+	0.574758i	$0.805096\pi$
$774$	1.16319			0.0418100
$775$	3.99711	+	3.75413i	0.143580	+	0.134852i
$776$	−2.64310			−0.0948817
$777$			38.2667i			1.37281i
$778$			1.50367i			0.0539090i
$779$	−1.07030			−0.0383475
$780$	−5.01410	+	12.6627i	−0.179534	+	0.453398i
$781$		0			0
$782$			84.5001i			3.02172i
$783$		−	1.12257i		−	0.0401172i
$784$	11.7299			0.418926
$785$	38.2211	+	15.1346i	1.36417	+	0.540176i
$786$	17.0149			0.606901
$787$		−	46.4715i		−	1.65653i	−0.560336	−	0.828266i	$-0.689328\pi$
$787$		−	46.4715i		−	1.65653i	0.560336	−	0.828266i	$-0.310672\pi$
$788$			8.72475i			0.310806i
$789$	−11.1345			−0.396398
$790$	16.9377	+	6.70690i	0.602617	+	0.238621i
$791$	0.999835			0.0355500
$792$		0			0
$793$		−	20.5237i		−	0.728817i
$794$	−1.60973			−0.0571273
$795$	9.57882	−	24.1905i	0.339726	−	0.857950i
$796$	30.9759			1.09791
$797$			32.2353i			1.14183i	0.821008	+	0.570917i	$0.193412\pi$
$797$			32.2353i			1.14183i	−0.821008	+	0.570917i	$0.806588\pi$
$798$			8.01763i			0.283821i
$799$	14.5348			0.514204
$800$	−27.4631	+	29.2406i	−0.970968	+	1.03381i
$801$	12.5950			0.445021
$802$		−	33.1869i		−	1.17187i
$803$		0			0
$804$	10.1253			0.357093
$805$	16.0811	−	40.6115i	0.566784	−	1.43137i
$806$	−5.77310			−0.203349
$807$			22.7563i			0.801061i
$808$			9.09372i			0.319916i
$809$	21.1977			0.745273			0.372637	−	0.927977i	$-0.378454\pi$
$809$	21.1977			0.745273			0.372637	+	0.927977i	$0.378454\pi$
$810$	−4.37946	−	1.73415i	−0.153878	−	0.0609319i
$811$	23.6049			0.828879			0.414440	−	0.910077i	$-0.363978\pi$
$811$	23.6049			0.828879			0.414440	+	0.910077i	$0.363978\pi$
$812$		−	9.07387i		−	0.318430i
$813$			7.79448i			0.273364i
$814$		0			0
$815$	−36.5324	−	14.4659i	−1.27967	−	0.506718i
$816$	−19.9806			−0.699463
$817$		−	0.633743i		−	0.0221718i
$818$		−	5.52117i		−	0.193043i
$819$	8.28712			0.289575
$820$	1.87123	−	4.72564i	0.0653462	−	0.165026i
$821$	44.5174			1.55367			0.776834	−	0.629706i	$-0.216825\pi$
$821$	44.5174			1.55367			0.776834	+	0.629706i	$0.216825\pi$
$822$		−	13.5613i		−	0.473005i
$823$		−	0.136429i		−	0.00475560i	−0.999997	−	0.00237780i	$-0.999243\pi$
$823$		−	0.136429i		−	0.00475560i	0.999997	−	0.00237780i	$-0.000756879\pi$
$824$	−7.11238			−0.247771
$825$		0			0
$826$	−58.6700			−2.04139
$827$			11.7712i			0.409325i	0.978833	+	0.204662i	$0.0656096\pi$
$827$			11.7712i			0.409325i	−0.978833	+	0.204662i	$0.934390\pi$
$828$		−	14.3568i		−	0.498934i
$829$	−11.0290			−0.383052			−0.191526	−	0.981488i	$-0.561344\pi$
$829$	−11.0290			−0.383052			−0.191526	+	0.981488i	$0.561344\pi$
$830$	−10.5446	+	26.6295i	−0.366008	+	0.924324i
$831$	9.46719			0.328413
$832$		−	27.5696i		−	0.955805i
$833$		−	27.2273i		−	0.943369i
$834$	14.6943			0.508823
$835$	−25.1096	−	9.94275i	−0.868953	−	0.344083i
$836$		0			0
$837$		−	1.09673i		−	0.0379085i
$838$			37.9335i			1.31039i
$839$	10.5903			0.365616			0.182808	−	0.983149i	$-0.441481\pi$
$839$	10.5903			0.365616			0.182808	+	0.983149i	$0.441481\pi$
$840$	−6.35240	−	2.51539i	−0.219179	−	0.0867891i
$841$	−27.7398			−0.956546
$842$			2.46708i			0.0850211i
$843$			31.3016i			1.07808i
$844$	−8.51910			−0.293239
$845$	−5.56142	+	14.0449i	−0.191319	+	0.483159i
$846$	−4.49586			−0.154571
$847$		0			0
$848$			34.1381i			1.17231i
$849$	24.4123			0.837829
$850$	52.2840	+	49.1058i	1.79333	+	1.68431i
$851$	−67.9670			−2.32988
$852$			30.5503i			1.04663i
$853$		−	44.5811i		−	1.52643i	−0.646145	−	0.763215i	$-0.723620\pi$
$853$		−	44.5811i		−	1.52643i	0.646145	−	0.763215i	$-0.276380\pi$
$854$	57.3759			1.96336
$855$	−0.944820	+	2.38607i	−0.0323122	+	0.0816017i
$856$	14.2914			0.488470
$857$			24.3105i			0.830430i	0.909723	+	0.415215i	$0.136294\pi$
$857$			24.3105i			0.830430i	−0.909723	+	0.415215i	$0.863706\pi$
$858$		0			0
$859$	35.5045			1.21140			0.605699	−	0.795694i	$-0.292893\pi$
$859$	35.5045			1.21140			0.605699	+	0.795694i	$0.292893\pi$
$860$	2.79813	+	1.10799i	0.0954154	+	0.0377820i
$861$	−3.09270			−0.105399
$862$		−	73.9218i		−	2.51779i
$863$		−	11.6720i		−	0.397319i	−0.980069	−	0.198659i	$-0.936341\pi$
$863$		−	11.6720i		−	0.397319i	0.980069	−	0.198659i	$-0.0636588\pi$
$864$	8.02306			0.272950
$865$	50.4027	+	19.9582i	1.71374	+	0.678598i
$866$	−38.3933			−1.30466
$867$			29.3787i			0.997752i
$868$		−	8.86503i		−	0.300899i
$869$		0			0
$870$	1.94670	−	4.91623i	0.0659992	−	0.166676i
$871$	−10.3808			−0.351741
$872$		−	6.26364i		−	0.212114i
$873$			2.86873i			0.0970917i
$874$	−14.2404			−0.481690
$875$	−15.7829	−	33.5508i	−0.533559	−	1.13422i
$876$	13.9847			0.472501
$877$			26.4819i			0.894230i	0.894476	+	0.447115i	$0.147549\pi$
$877$			26.4819i			0.894230i	−0.894476	+	0.447115i	$0.852451\pi$
$878$		−	41.7416i		−	1.40871i
$879$	−11.8197			−0.398667
$880$		0			0
$881$	10.3488			0.348658			0.174329	−	0.984687i	$-0.444224\pi$
$881$	10.3488			0.348658			0.174329	+	0.984687i	$0.444224\pi$
$882$			8.42187i			0.283579i
$883$			2.71148i			0.0912487i	0.998959	+	0.0456243i	$0.0145277\pi$
$883$			2.71148i			0.0912487i	−0.998959	+	0.0456243i	$0.985472\pi$
$884$	−41.4791			−1.39509
$885$	−17.4603	−	6.91383i	−0.586922	−	0.232406i
$886$	35.1543			1.18103
$887$		−	0.122673i		−	0.00411896i	−0.999998	−	0.00205948i	$-0.999344\pi$
$887$		−	0.122673i		−	0.00411896i	0.999998	−	0.00205948i	$-0.000655553\pi$
$888$			10.6313i			0.356764i
$889$	22.2373			0.745814
$890$	55.1590	+	21.8416i	1.84894	+	0.732131i
$891$		0			0
$892$		−	12.6880i		−	0.424825i
$893$			2.44949i			0.0819690i
$894$	−40.0669			−1.34004
$895$	−16.4145	+	41.4534i	−0.548675	+	1.38563i
$896$	23.8594			0.797087
$897$			14.7191i			0.491456i
$898$			27.7997i			0.927689i
$899$	1.23115			0.0410612
$900$	−8.88321	−	8.34322i	−0.296107	−	0.278107i
$901$	79.2406			2.63989
$902$		0			0
$903$		−	1.83124i		−	0.0609398i
$904$	0.277776			0.00923870
$905$	4.22558	−	10.6713i	0.140463	−	0.354728i
$906$	−8.21710			−0.272995
$907$		−	13.8188i		−	0.458844i	−0.973327	−	0.229422i	$-0.926316\pi$
$907$		−	13.8188i		−	0.458844i	0.973327	−	0.229422i	$-0.0736836\pi$
$908$		−	23.6485i		−	0.784804i
$909$	9.87001			0.327368
$910$	36.2931	+	14.3711i	1.20310	+	0.476398i
$911$	23.2558			0.770501			0.385250	−	0.922812i	$-0.374115\pi$
$911$	23.2558			0.770501			0.385250	+	0.922812i	$0.374115\pi$
$912$		−	3.36725i		−	0.111501i
$913$		0			0
$914$	44.7997			1.48184
$915$	17.0752	+	6.76133i	0.564488	+	0.223523i
$916$	45.0942			1.48995
$917$		−	26.7869i		−	0.884583i
$918$		−	14.3457i		−	0.473480i
$919$	26.4278			0.871772			0.435886	−	0.900002i	$-0.356435\pi$
$919$	26.4278			0.871772			0.435886	+	0.900002i	$0.356435\pi$
$920$	4.46768	−	11.2828i	0.147295	−	0.371981i
$921$	22.3217			0.735524
$922$			42.2927i			1.39284i
$923$		−	31.3212i		−	1.03095i
$924$		0			0
$925$	−39.4978	+	42.0542i	−1.29868	+	1.38273i
$926$	−2.02757			−0.0666301
$927$			7.71953i			0.253543i
$928$			9.00641i			0.295650i
$929$	8.03463			0.263608			0.131804	−	0.991276i	$-0.457923\pi$
$929$	8.03463			0.263608			0.131804	+	0.991276i	$0.457923\pi$
$930$	1.90189	−	4.80308i	0.0623656	−	0.157499i
$931$	4.58850			0.150382
$932$		−	36.4494i		−	1.19394i
$933$			19.4834i			0.637858i
$934$	31.4144			1.02791
$935$		0			0
$936$	2.30234			0.0752545
$937$		−	13.4913i		−	0.440740i	−0.975416	−	0.220370i	$-0.929274\pi$
$937$		−	13.4913i		−	0.440740i	0.975416	−	0.220370i	$-0.0707265\pi$
$938$		−	29.0206i		−	0.947557i
$939$	17.3527			0.566284
$940$	−10.8151	−	4.28249i	−0.352749	−	0.139680i
$941$	31.9040			1.04004			0.520021	−	0.854154i	$-0.325924\pi$
$941$	31.9040			1.04004			0.520021	+	0.854154i	$0.325924\pi$
$942$		−	38.7267i		−	1.26178i
$943$		−	5.49307i		−	0.178879i
$944$	24.6403			0.801973
$945$	−2.73011	+	6.89468i	−0.0888106	+	0.224284i
$946$		0			0
$947$		−	10.2719i		−	0.333793i	−0.985974	−	0.166896i	$-0.946625\pi$
$947$		−	10.2719i		−	0.333793i	0.985974	−	0.166896i	$-0.0533745\pi$
$948$		−	9.42667i		−	0.306164i
$949$	−14.3376			−0.465419
$950$	−8.27559	+	8.81120i	−0.268496	+	0.285873i
$951$	−0.830717			−0.0269379
$952$		−	20.8085i		−	0.674407i
$953$		−	9.83426i		−	0.318563i	−0.987233	−	0.159281i	$-0.949082\pi$
$953$		−	9.83426i		−	0.318563i	0.987233	−	0.159281i	$-0.0509177\pi$
$954$	−24.5105			−0.793557
$955$	2.31606	−	5.84901i	0.0749458	−	0.189270i
$956$	3.67353			0.118810
$957$		0			0
$958$		−	1.00170i		−	0.0323635i
$959$	−21.3499			−0.689424
$960$	22.9373	+	9.08256i	0.740297	+	0.293138i
$961$	−29.7972			−0.961199
$962$		−	60.7397i		−	1.95833i
$963$		−	15.5114i		−	0.499848i
$964$	−17.2949			−0.557033
$965$	40.1316	+	15.8911i	1.29188	+	0.511551i
$966$	−41.1486			−1.32393
$967$		−	3.85001i		−	0.123808i	−0.998082	−	0.0619041i	$-0.980283\pi$
$967$		−	3.85001i		−	0.123808i	0.998082	−	0.0619041i	$-0.0197173\pi$
$968$		0			0
$969$	−7.81600			−0.251086
$970$	−4.97481	+	12.5635i	−0.159731	+	0.403389i
$971$	21.3920			0.686502			0.343251	−	0.939244i	$-0.388472\pi$
$971$	21.3920			0.686502			0.343251	+	0.939244i	$0.388472\pi$
$972$			2.43738i			0.0781790i
$973$		−	23.1336i		−	0.741630i
$974$	74.4713			2.38621
$975$	9.10736	+	8.55375i	0.291669	+	0.273939i
$976$	−24.0968			−0.771320
$977$			16.6681i			0.533258i	0.963799	+	0.266629i	$0.0859099\pi$
$977$			16.6681i			0.533258i	−0.963799	+	0.266629i	$0.914090\pi$
$978$			37.0156i			1.18363i
$979$		0			0
$980$	−8.02217	+	20.2593i	−0.256259	+	0.647161i
$981$	−6.79834			−0.217054
$982$			63.4750i			2.02557i
$983$			51.8570i			1.65398i	0.562216	+	0.826991i	$0.309949\pi$
$983$			51.8570i			1.65398i	−0.562216	+	0.826991i	$0.690051\pi$
$984$	−0.859219			−0.0273909
$985$	7.44194	+	2.94682i	0.237120	+	0.0938933i
$986$	16.1040			0.512856
$987$			7.07794i			0.225293i
$988$		−	6.99029i		−	0.222391i
$989$	3.25253			0.103425
$990$		0			0
$991$	19.8195			0.629588			0.314794	−	0.949160i	$-0.398065\pi$
$991$	19.8195			0.629588			0.314794	+	0.949160i	$0.398065\pi$
$992$			8.79912i			0.279372i
$993$			31.5311i			1.00061i
$994$	87.5613			2.77727
$995$	10.4622	−	26.4215i	0.331674	−	0.837616i
$996$	14.8206			0.469609
$997$		−	51.6594i		−	1.63607i	−0.575168	−	0.818036i	$-0.695063\pi$
$997$		−	51.6594i		−	1.63607i	0.575168	−	0.818036i	$-0.304937\pi$
$998$			76.8449i			2.43248i
$999$	11.5389			0.365074

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1815.2.c.k.364.20		24
5.2	odd	4		9075.2.a.dx.1.3		12
5.3	odd	4		9075.2.a.ea.1.10		12
5.4	even	2	inner	1815.2.c.k.364.5		24
11.7	odd	10		165.2.s.a.49.10	yes	48
11.8	odd	10		165.2.s.a.64.3	yes	48
11.10	odd	2		1815.2.c.j.364.5		24
33.8	even	10		495.2.ba.c.64.10		48
33.29	even	10		495.2.ba.c.379.3		48
55.7	even	20		825.2.n.o.676.5		24
55.8	even	20		825.2.n.p.526.2		24
55.18	even	20		825.2.n.p.676.2		24
55.19	odd	10		165.2.s.a.64.10	yes	48
55.29	odd	10		165.2.s.a.49.3	✓	48
55.32	even	4		9075.2.a.dz.1.10		12
55.43	even	4		9075.2.a.dy.1.3		12
55.52	even	20		825.2.n.o.526.5		24
55.54	odd	2		1815.2.c.j.364.20		24
165.29	even	10		495.2.ba.c.379.10		48
165.74	even	10		495.2.ba.c.64.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.s.a.49.3	✓	48	55.29	odd	10
165.2.s.a.49.10	yes	48	11.7	odd	10
165.2.s.a.64.3	yes	48	11.8	odd	10
165.2.s.a.64.10	yes	48	55.19	odd	10
495.2.ba.c.64.3		48	165.74	even	10
495.2.ba.c.64.10		48	33.8	even	10
495.2.ba.c.379.3		48	33.29	even	10
495.2.ba.c.379.10		48	165.29	even	10
825.2.n.o.526.5		24	55.52	even	20
825.2.n.o.676.5		24	55.7	even	20
825.2.n.p.526.2		24	55.8	even	20
825.2.n.p.676.2		24	55.18	even	20
1815.2.c.j.364.5		24	11.10	odd	2
1815.2.c.j.364.20		24	55.54	odd	2
1815.2.c.k.364.5		24	5.4	even	2	inner
1815.2.c.k.364.20		24	1.1	even	1	trivial
9075.2.a.dx.1.3		12	5.2	odd	4
9075.2.a.dy.1.3		12	55.43	even	4
9075.2.a.dz.1.10		12	55.32	even	4
9075.2.a.ea.1.10		12	5.3	odd	4

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:	\( N \)	\(=\)	\( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1815.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.10651i q^{2} -1.00000i q^{3} -2.43738 q^{4} +(-0.823234 + 2.07901i) q^{5} +2.10651 q^{6} -3.31633i q^{7} -0.921348i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+2.10651i q^{2} -1.00000i q^{3} -2.43738 q^{4} +(-0.823234 + 2.07901i) q^{5} +2.10651 q^{6} -3.31633i q^{7} -0.921348i q^{8} -1.00000 q^{9} +(-4.37946 - 1.73415i) q^{10} +2.43738i q^{12} -2.49889i q^{13} +6.98587 q^{14} +(2.07901 + 0.823234i) q^{15} -2.93393 q^{16} +6.81019i q^{17} -2.10651i q^{18} -1.14769 q^{19} +(2.00654 - 5.06734i) q^{20} -3.31633 q^{21} -5.89026i q^{23} -0.921348 q^{24} +(-3.64457 - 3.42303i) q^{25} +5.26393 q^{26} +1.00000i q^{27} +8.08315i q^{28} -1.12257 q^{29} +(-1.73415 + 4.37946i) q^{30} -1.09673 q^{31} -8.02306i q^{32} -14.3457 q^{34} +(6.89468 + 2.73011i) q^{35} +2.43738 q^{36} -11.5389i q^{37} -2.41763i q^{38} -2.49889 q^{39} +(1.91549 + 0.758486i) q^{40} +0.932568 q^{41} -6.98587i q^{42} +0.552188i q^{43} +(0.823234 - 2.07901i) q^{45} +12.4079 q^{46} -2.13427i q^{47} +2.93393i q^{48} -3.99802 q^{49} +(7.21064 - 7.67732i) q^{50} +6.81019 q^{51} +6.09074i q^{52} -11.6356i q^{53} -2.10651 q^{54} -3.05549 q^{56} +1.14769i q^{57} -2.36469i q^{58} -8.39837 q^{59} +(-5.06734 - 2.00654i) q^{60} +8.21313 q^{61} -2.31027i q^{62} +3.31633i q^{63} +11.0328 q^{64} +(5.19521 + 2.05717i) q^{65} -4.15419i q^{67} -16.5990i q^{68} -5.89026 q^{69} +(-5.75101 + 14.5237i) q^{70} +12.5340 q^{71} +0.921348i q^{72} -5.73761i q^{73} +24.3067 q^{74} +(-3.42303 + 3.64457i) q^{75} +2.79736 q^{76} -5.26393i q^{78} -3.86754 q^{79} +(2.41532 - 6.09968i) q^{80} +1.00000 q^{81} +1.96446i q^{82} -6.08055i q^{83} +8.08315 q^{84} +(-14.1585 - 5.60638i) q^{85} -1.16319 q^{86} +1.12257i q^{87} -12.5950 q^{89} +(4.37946 + 1.73415i) q^{90} -8.28712 q^{91} +14.3568i q^{92} +1.09673i q^{93} +4.49586 q^{94} +(0.944820 - 2.38607i) q^{95} -8.02306 q^{96} -2.86873i q^{97} -8.42187i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{4} - 2 q^{5} + 8 q^{6} - 24 q^{9}+O(q^{10}) \) 24 * q - 24 * q^4 - 2 * q^5 + 8 * q^6 - 24 * q^9	\( 24 q - 24 q^{4} - 2 q^{5} + 8 q^{6} - 24 q^{9} + 6 q^{10} - 12 q^{14} + 48 q^{16} - 32 q^{19} - 2 q^{20} + 16 q^{21} - 24 q^{24} + 2 q^{25} + 32 q^{26} + 8 q^{30} - 12 q^{34} - 10 q^{35} + 24 q^{36} - 36 q^{39} - 34 q^{40} + 2 q^{45} + 56 q^{46} - 24 q^{49} - 46 q^{50} + 36 q^{51} - 8 q^{54} + 12 q^{56} - 40 q^{59} - 26 q^{60} + 40 q^{61} + 12 q^{64} - 10 q^{65} - 2 q^{70} + 64 q^{71} + 136 q^{74} + 20 q^{75} + 68 q^{76} - 64 q^{79} + 76 q^{80} + 24 q^{81} - 60 q^{84} - 72 q^{86} + 20 q^{89} - 6 q^{90} + 4 q^{94} - 64 q^{95} + 56 q^{96}+O(q^{100}) \) 24 * q - 24 * q^4 - 2 * q^5 + 8 * q^6 - 24 * q^9 + 6 * q^10 - 12 * q^14 + 48 * q^16 - 32 * q^19 - 2 * q^20 + 16 * q^21 - 24 * q^24 + 2 * q^25 + 32 * q^26 + 8 * q^30 - 12 * q^34 - 10 * q^35 + 24 * q^36 - 36 * q^39 - 34 * q^40 + 2 * q^45 + 56 * q^46 - 24 * q^49 - 46 * q^50 + 36 * q^51 - 8 * q^54 + 12 * q^56 - 40 * q^59 - 26 * q^60 + 40 * q^61 + 12 * q^64 - 10 * q^65 - 2 * q^70 + 64 * q^71 + 136 * q^74 + 20 * q^75 + 68 * q^76 - 64 * q^79 + 76 * q^80 + 24 * q^81 - 60 * q^84 - 72 * q^86 + 20 * q^89 - 6 * q^90 + 4 * q^94 - 64 * q^95 + 56 * q^96

Introduction

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