LMFDB - Embedded newform 483.2.e.a.344.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(344,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("483.344");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.e (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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			344.17
Character	$\chi$	$=$	483.344
Dual form			483.2.e.a.344.31

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.800018i q^{2} +(-1.73165 - 0.0370806i) q^{3} +1.35997 q^{4} -1.73737 q^{5} +(-0.0296651 + 1.38535i) q^{6} -1.00000i q^{7} -2.68804i q^{8} +(2.99725 + 0.128422i) q^{9} +1.38993i q^{10} +1.58963 q^{11} +(-2.35500 - 0.0504285i) q^{12} +0.447448 q^{13} -0.800018 q^{14} +(3.00853 + 0.0644228i) q^{15} +0.569463 q^{16} -6.24604 q^{17} +(0.102740 - 2.39785i) q^{18} -6.45008i q^{19} -2.36277 q^{20} +(-0.0370806 + 1.73165i) q^{21} -1.27173i q^{22} +(-3.35397 - 3.42796i) q^{23} +(-0.0996740 + 4.65475i) q^{24} -1.98154 q^{25} -0.357966i q^{26} +(-5.18544 - 0.333521i) q^{27} -1.35997i q^{28} -5.04699i q^{29} +(0.0515394 - 2.40687i) q^{30} +4.59689 q^{31} -5.83166i q^{32} +(-2.75269 - 0.0589444i) q^{33} +4.99695i q^{34} +1.73737i q^{35} +(4.07617 + 0.174650i) q^{36} +4.25359i q^{37} -5.16018 q^{38} +(-0.774825 - 0.0165916i) q^{39} +4.67012i q^{40} -10.5884i q^{41} +(1.38535 + 0.0296651i) q^{42} -1.24408i q^{43} +2.16185 q^{44} +(-5.20734 - 0.223116i) q^{45} +(-2.74243 + 2.68324i) q^{46} +1.56297i q^{47} +(-0.986114 - 0.0211160i) q^{48} -1.00000 q^{49} +1.58527i q^{50} +(10.8160 + 0.231607i) q^{51} +0.608516 q^{52} -1.95315 q^{53} +(-0.266823 + 4.14844i) q^{54} -2.76178 q^{55} -2.68804 q^{56} +(-0.239173 + 11.1693i) q^{57} -4.03769 q^{58} +13.0779i q^{59} +(4.09151 + 0.0876131i) q^{60} -8.71889i q^{61} -3.67759i q^{62} +(0.128422 - 2.99725i) q^{63} -3.52650 q^{64} -0.777383 q^{65} +(-0.0471566 + 2.20220i) q^{66} +9.90204i q^{67} -8.49444 q^{68} +(5.68081 + 6.06040i) q^{69} +1.38993 q^{70} +4.83016i q^{71} +(0.345202 - 8.05672i) q^{72} +2.41684 q^{73} +3.40295 q^{74} +(3.43134 + 0.0734767i) q^{75} -8.77192i q^{76} -1.58963i q^{77} +(-0.0132736 + 0.619874i) q^{78} -12.8212i q^{79} -0.989369 q^{80} +(8.96702 + 0.769823i) q^{81} -8.47095 q^{82} +17.4287 q^{83} +(-0.0504285 + 2.35500i) q^{84} +10.8517 q^{85} -0.995284 q^{86} +(-0.187146 + 8.73965i) q^{87} -4.27298i q^{88} +9.75988 q^{89} +(-0.178497 + 4.16596i) q^{90} -0.447448i q^{91} +(-4.56130 - 4.66192i) q^{92} +(-7.96021 - 0.170455i) q^{93} +1.25041 q^{94} +11.2062i q^{95} +(-0.216241 + 10.0984i) q^{96} -10.5386i q^{97} +0.800018i q^{98} +(4.76452 + 0.204143i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{3} - 40 q^{4} + 6 q^{6} + 4 q^{9} + 22 q^{12} - 8 q^{13} + 24 q^{16} - 14 q^{18} - 12 q^{24} + 88 q^{25} - 16 q^{27} - 8 q^{31} - 10 q^{36} + 8 q^{46} - 98 q^{48} - 48 q^{49} + 28 q^{52} - 28 q^{54}+ \cdots - 6 q^{96}+O(q^{100}) $ 48 * q - 4 * q^3 - 40 * q^4 + 6 * q^6 + 4 * q^9 + 22 * q^12 - 8 * q^13 + 24 * q^16 - 14 * q^18 - 12 * q^24 + 88 * q^25 - 16 * q^27 - 8 * q^31 - 10 * q^36 + 8 * q^46 - 98 * q^48 - 48 * q^49 + 28 * q^52 - 28 * q^54 - 92 * q^58 + 92 * q^64 + 8 * q^69 + 8 * q^70 + 60 * q^72 + 40 * q^73 - 80 * q^75 + 114 * q^78 - 28 * q^81 - 20 * q^82 - 40 * q^85 - 28 * q^87 - 76 * q^93 - 12 * q^94 - 6 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$		−	0.800018i		−	0.565698i	−0.959164	−	0.282849i	$-0.908720\pi$
$2$		−	0.800018i		−	0.565698i	0.959164	−	0.282849i	$-0.0912796\pi$
$3$	−1.73165	−	0.0370806i	−0.999771	−	0.0214085i
$3$	−1.73165	−	0.0370806i	−0.999771	−	0.0214085i
$4$	1.35997			0.679986
$5$	−1.73737			−0.776976			−0.388488	−	0.921454i	$-0.627003\pi$
$5$	−1.73737			−0.776976			−0.388488	+	0.921454i	$0.627003\pi$
$6$	−0.0296651	+	1.38535i	−0.0121107	+	0.565569i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$		−	2.68804i		−	0.950365i
$9$	2.99725	+	0.128422i	0.999083	+	0.0428072i
$10$			1.38993i			0.439534i
$11$	1.58963			0.479291			0.239646	−	0.970860i	$-0.422969\pi$
$11$	1.58963			0.479291			0.239646	+	0.970860i	$0.422969\pi$
$12$	−2.35500	−	0.0504285i	−0.679830	−	0.0145575i
$13$	0.447448			0.124100			0.0620498	−	0.998073i	$-0.480236\pi$
$13$	0.447448			0.124100			0.0620498	+	0.998073i	$0.480236\pi$
$14$	−0.800018			−0.213814
$15$	3.00853	+	0.0644228i	0.776798	+	0.0166339i
$16$	0.569463			0.142366
$17$	−6.24604			−1.51489			−0.757444	−	0.652900i	$-0.773552\pi$
$17$	−6.24604			−1.51489			−0.757444	+	0.652900i	$0.773552\pi$
$18$	0.102740	−	2.39785i	0.0242159	−	0.565180i
$19$		−	6.45008i		−	1.47975i	−0.672745	−	0.739875i	$-0.734885\pi$
$19$		−	6.45008i		−	1.47975i	0.672745	−	0.739875i	$-0.265115\pi$
$20$	−2.36277			−0.528332
$21$	−0.0370806	+	1.73165i	−0.00809165	+	0.377878i
$22$		−	1.27173i		−	0.271134i
$23$	−3.35397	−	3.42796i	−0.699351	−	0.714778i
$23$	−3.35397	−	3.42796i	−0.699351	−	0.714778i
$24$	−0.0996740	+	4.65475i	−0.0203459	+	0.950147i
$25$	−1.98154			−0.396308
$26$		−	0.357966i		−	0.0702030i
$27$	−5.18544	−	0.333521i	−0.997938	−	0.0641862i
$28$		−	1.35997i		−	0.257010i
$29$		−	5.04699i		−	0.937203i	−0.883410	−	0.468602i	$-0.844758\pi$
$29$		−	5.04699i		−	0.937203i	0.883410	−	0.468602i	$-0.155242\pi$
$30$	0.0515394	−	2.40687i	0.00940976	−	0.439433i
$31$	4.59689			0.825625			0.412812	−	0.910816i	$-0.364546\pi$
$31$	4.59689			0.825625			0.412812	+	0.910816i	$0.364546\pi$
$32$		−	5.83166i		−	1.03090i
$33$	−2.75269	−	0.0589444i	−0.479181	−	0.0102609i
$34$			4.99695i			0.856969i
$35$			1.73737i			0.293669i
$36$	4.07617	+	0.174650i	0.679362	+	0.0291083i
$37$			4.25359i			0.699286i	0.936883	+	0.349643i	$0.113697\pi$
$37$			4.25359i			0.699286i	−0.936883	+	0.349643i	$0.886303\pi$
$38$	−5.16018			−0.837092
$39$	−0.774825	−	0.0165916i	−0.124071	−	0.00265679i
$40$			4.67012i			0.738411i
$41$		−	10.5884i		−	1.65364i	−0.562468	−	0.826819i	$-0.690148\pi$
$41$		−	10.5884i		−	1.65364i	0.562468	−	0.826819i	$-0.309852\pi$
$42$	1.38535	+	0.0296651i	0.213765	+	0.00457743i
$43$		−	1.24408i		−	0.189720i	−0.995491	−	0.0948600i	$-0.969760\pi$
$43$		−	1.24408i		−	0.189720i	0.995491	−	0.0948600i	$-0.0302403\pi$
$44$	2.16185			0.325911
$45$	−5.20734	−	0.223116i	−0.776264	−	0.0332601i
$46$	−2.74243	+	2.68324i	−0.404349	+	0.395622i
$47$			1.56297i			0.227983i	0.993482	+	0.113992i	$0.0363637\pi$
$47$			1.56297i			0.227983i	−0.993482	+	0.113992i	$0.963636\pi$
$48$	−0.986114	−	0.0211160i	−0.142333	−	0.00304784i
$49$	−1.00000			−0.142857
$50$			1.58527i			0.224191i
$51$	10.8160	+	0.231607i	1.51454	+	0.0324315i
$52$	0.608516			0.0843860
$53$	−1.95315			−0.268286			−0.134143	−	0.990962i	$-0.542828\pi$
$53$	−1.95315			−0.268286			−0.134143	+	0.990962i	$0.542828\pi$
$54$	−0.266823	+	4.14844i	−0.0363100	+	0.564532i
$55$	−2.76178			−0.372398
$56$	−2.68804			−0.359204
$57$	−0.239173	+	11.1693i	−0.0316792	+	1.47941i
$58$	−4.03769			−0.530174
$59$			13.0779i			1.70259i	0.524683	+	0.851297i	$0.324184\pi$
$59$			13.0779i			1.70259i	−0.524683	+	0.851297i	$0.675816\pi$
$60$	4.09151	+	0.0876131i	0.528211	+	0.0113108i
$61$		−	8.71889i		−	1.11634i	−0.829727	−	0.558170i	$-0.811504\pi$
$61$		−	8.71889i		−	1.11634i	0.829727	−	0.558170i	$-0.188496\pi$
$62$		−	3.67759i		−	0.467055i
$63$	0.128422	−	2.99725i	0.0161796	−	0.377618i
$64$	−3.52650			−0.440813
$65$	−0.777383			−0.0964225
$66$	−0.0471566	+	2.20220i	−0.00580457	+	0.271072i
$67$			9.90204i			1.20973i	0.796329	+	0.604863i	$0.206772\pi$
$67$			9.90204i			1.20973i	−0.796329	+	0.604863i	$0.793228\pi$
$68$	−8.49444			−1.03010
$69$	5.68081	+	6.06040i	0.683889	+	0.729586i
$70$	1.38993			0.166128
$71$			4.83016i			0.573235i	0.958045	+	0.286617i	$0.0925308\pi$
$71$			4.83016i			0.573235i	−0.958045	+	0.286617i	$0.907469\pi$
$72$	0.345202	−	8.05672i	0.0406824	−	0.949494i
$73$	2.41684			0.282870			0.141435	−	0.989948i	$-0.454828\pi$
$73$	2.41684			0.282870			0.141435	+	0.989948i	$0.454828\pi$
$74$	3.40295			0.395585
$75$	3.43134	+	0.0734767i	0.396217	+	0.00848436i
$76$		−	8.77192i		−	1.00621i
$77$		−	1.58963i		−	0.181155i
$78$	−0.0132736	+	0.619874i	−0.00150294	+	0.0701869i
$79$		−	12.8212i		−	1.44250i	−0.692676	−	0.721249i	$-0.743568\pi$
$79$		−	12.8212i		−	1.44250i	0.692676	−	0.721249i	$-0.256432\pi$
$80$	−0.989369			−0.110615
$81$	8.96702	+	0.769823i	0.996335	+	0.0855359i
$82$	−8.47095			−0.935460
$83$	17.4287			1.91305			0.956527	−	0.291645i	$-0.0942025\pi$
$83$	17.4287			1.91305			0.956527	+	0.291645i	$0.0942025\pi$
$84$	−0.0504285	+	2.35500i	−0.00550220	+	0.256951i
$85$	10.8517			1.17703
$86$	−0.995284			−0.107324
$87$	−0.187146	+	8.73965i	−0.0200641	+	0.936989i
$88$		−	4.27298i		−	0.455502i
$89$	9.75988			1.03454			0.517272	−	0.855821i	$-0.326947\pi$
$89$	9.75988			1.03454			0.517272	+	0.855821i	$0.326947\pi$
$90$	−0.178497	+	4.16596i	−0.0188152	+	0.439131i
$91$		−	0.447448i		−	0.0469053i
$92$	−4.56130	−	4.66192i	−0.475549	−	0.486039i
$93$	−7.96021	−	0.170455i	−0.825436	−	0.0176754i
$94$	1.25041			0.128970
$95$			11.2062i			1.14973i
$96$	−0.216241	+	10.0984i	−0.0220700	+	1.03066i
$97$		−	10.5386i		−	1.07004i	−0.844840	−	0.535019i	$-0.820305\pi$
$97$		−	10.5386i		−	1.07004i	0.844840	−	0.535019i	$-0.179695\pi$
$98$			0.800018i			0.0808140i
$99$	4.76452	+	0.204143i	0.478852	+	0.0205171i
$100$	−2.69484			−0.269484
$101$			11.4907i			1.14337i	0.820474	+	0.571684i	$0.193710\pi$
$101$			11.4907i			1.14337i	−0.820474	+	0.571684i	$0.806290\pi$
$102$	0.185290	−	8.65298i	0.0183464	−	0.856773i
$103$			18.3126i			1.80439i	0.431325	+	0.902196i	$0.358046\pi$
$103$			18.3126i			1.80439i	−0.431325	+	0.902196i	$0.641954\pi$
$104$		−	1.20276i		−	0.117940i
$105$	0.0644228	−	3.00853i	0.00628702	−	0.293602i
$106$			1.56256i			0.151769i
$107$	12.1271			1.17237			0.586184	−	0.810178i	$-0.300630\pi$
$107$	12.1271			1.17237			0.586184	+	0.810178i	$0.300630\pi$
$108$	−7.05205	−	0.453580i	−0.678583	−	0.0436457i
$109$		−	3.09320i		−	0.296275i	−0.988967	−	0.148137i	$-0.952672\pi$
$109$		−	3.09320i		−	0.296275i	0.988967	−	0.148137i	$-0.0473278\pi$
$110$			2.20947i			0.210665i
$111$	0.157726	−	7.36575i	0.0149707	−	0.699126i
$112$		−	0.569463i		−	0.0538092i
$113$	10.6123			0.998325			0.499162	−	0.866508i	$-0.333641\pi$
$113$	10.6123			0.998325			0.499162	+	0.866508i	$0.333641\pi$
$114$	8.93564	+	0.191343i	0.836900	+	0.0179209i
$115$	5.82709	+	5.95563i	0.543379	+	0.555365i
$116$		−	6.86377i		−	0.637285i
$117$	1.34111	+	0.0574619i	0.123986	+	0.00531236i
$118$	10.4625			0.963155
$119$			6.24604i			0.572574i
$120$	0.173171	−	8.08703i	0.0158083	−	0.738241i
$121$	−8.47308			−0.770280
$122$	−6.97527			−0.631511
$123$	−0.392626	+	18.3355i	−0.0354019	+	1.65326i
$124$	6.25163			0.561413
$125$	12.1295			1.08490
$126$	−2.39785	−	0.102740i	−0.213618	−	0.00915277i
$127$	1.03652			0.0919767			0.0459883	−	0.998942i	$-0.485356\pi$
$127$	1.03652			0.0919767			0.0459883	+	0.998942i	$0.485356\pi$
$128$		−	8.84205i		−	0.781534i
$129$	−0.0461311	+	2.15431i	−0.00406162	+	0.189676i
$130$			0.621920i			0.0545460i
$131$		−	0.318166i		−	0.0277983i	−0.999903	−	0.0138991i	$-0.995576\pi$
$131$		−	0.318166i		−	0.0277983i	0.999903	−	0.0138991i	$-0.00442438\pi$
$132$	−3.74358	−	0.0801627i	−0.325836	−	0.00697727i
$133$	−6.45008			−0.559293
$134$	7.92181			0.684340
$135$	9.00903	+	0.579451i	0.775374	+	0.0498712i
$136$			16.7896i			1.43970i
$137$	−15.9516			−1.36284			−0.681418	−	0.731895i	$-0.738636\pi$
$137$	−15.9516			−1.36284			−0.681418	+	0.731895i	$0.738636\pi$
$138$	4.84843	−	4.54475i	0.412726	−	0.386875i
$139$	−4.18495			−0.354963			−0.177481	−	0.984124i	$-0.556795\pi$
$139$	−4.18495			−0.354963			−0.177481	+	0.984124i	$0.556795\pi$
$140$			2.36277i			0.199691i
$141$	0.0579560	−	2.70653i	0.00488077	−	0.227931i
$142$	3.86422			0.324278
$143$	0.711276			0.0594799
$144$	1.70682	+	0.0731314i	0.142235	+	0.00609428i
$145$			8.76850i			0.728185i
$146$		−	1.93352i		−	0.160019i
$147$	1.73165	+	0.0370806i	0.142824	+	0.00305836i
$148$			5.78476i			0.475505i
$149$	−3.21691			−0.263539			−0.131770	−	0.991280i	$-0.542066\pi$
$149$	−3.21691			−0.263539			−0.131770	+	0.991280i	$0.542066\pi$
$150$	0.0587827	−	2.74514i	0.00479959	−	0.224140i
$151$	−0.0680818			−0.00554042			−0.00277021	−	0.999996i	$-0.500882\pi$
$151$	−0.0680818			−0.00554042			−0.00277021	+	0.999996i	$0.500882\pi$
$152$	−17.3381			−1.40630
$153$	−18.7210	−	0.802126i	−1.51350	−	0.0648481i
$154$	−1.27173			−0.102479
$155$	−7.98650			−0.641491
$156$	−1.05374	−	0.0225641i	−0.0843666	−	0.00180658i
$157$		−	15.6769i		−	1.25115i	−0.780163	−	0.625576i	$-0.784864\pi$
$157$		−	15.6769i		−	1.25115i	0.780163	−	0.625576i	$-0.215136\pi$
$158$	−10.2572			−0.816019
$159$	3.38218	+	0.0724241i	0.268225	+	0.00574360i
$160$			10.1318i			0.800985i
$161$	−3.42796	+	3.35397i	−0.270161	+	0.264330i
$162$	0.615872	−	7.17377i	0.0483875	−	0.563625i
$163$	19.1168			1.49735			0.748673	−	0.662940i	$-0.230691\pi$
$163$	19.1168			1.49735			0.748673	+	0.662940i	$0.230691\pi$
$164$		−	14.4000i		−	1.12445i
$165$	4.78244	+	0.102408i	0.372312	+	0.00797248i
$166$		−	13.9433i		−	1.08221i
$167$		−	14.6050i		−	1.13017i	−0.825034	−	0.565083i	$-0.808844\pi$
$167$		−	14.6050i		−	1.13017i	0.825034	−	0.565083i	$-0.191156\pi$
$168$	4.65475	+	0.0996740i	0.359122	+	0.00769002i
$169$	−12.7998			−0.984599
$170$		−	8.68155i		−	0.665845i
$171$	0.828329	−	19.3325i	0.0633439	−	1.47839i
$172$		−	1.69191i		−	0.129007i
$173$			10.8876i			0.827769i	0.910329	+	0.413884i	$0.135828\pi$
$173$			10.8876i			0.827769i	−0.910329	+	0.413884i	$0.864172\pi$
$174$	6.99188	+	0.149720i	0.530053	+	0.0113502i
$175$			1.98154i			0.149790i
$176$	0.905236			0.0682347
$177$	0.484936	−	22.6464i	0.0364500	−	1.70220i
$178$		−	7.80808i		−	0.585240i
$179$			8.94817i			0.668817i	0.942428	+	0.334409i	$0.108537\pi$
$179$			8.94817i			0.668817i	−0.942428	+	0.334409i	$0.891463\pi$
$180$	−7.08183	−	0.303431i	−0.527848	−	0.0226164i
$181$		−	0.810903i		−	0.0602739i	−0.999546	−	0.0301370i	$-0.990406\pi$
$181$		−	0.810903i		−	0.0602739i	0.999546	−	0.0301370i	$-0.00959435\pi$
$182$	−0.357966			−0.0265342
$183$	−0.323302	+	15.0981i	−0.0238992	+	1.11608i
$184$	−9.21447	+	9.01560i	−0.679300	+	0.664639i
$185$		−	7.39007i		−	0.543329i
$186$	−0.136367	+	6.36831i	−0.00999893	+	0.466948i
$187$	−9.92889			−0.726073
$188$			2.12560i			0.155025i
$189$	−0.333521	+	5.18544i	−0.0242601	+	0.377185i
$190$	8.96515			0.650400
$191$	15.4002			1.11432			0.557160	−	0.830405i	$-0.311891\pi$
$191$	15.4002			1.11432			0.557160	+	0.830405i	$0.311891\pi$
$192$	6.10668	+	0.130765i	0.440712	+	0.00943714i
$193$	−11.9449			−0.859815			−0.429908	−	0.902873i	$-0.641454\pi$
$193$	−11.9449			−0.859815			−0.429908	+	0.902873i	$0.641454\pi$
$194$	−8.43111			−0.605318
$195$	1.34616	+	0.0288258i	0.0964004	+	0.00206426i
$196$	−1.35997			−0.0971408
$197$			3.47782i			0.247784i	0.992296	+	0.123892i	$0.0395377\pi$
$197$			3.47782i			0.247784i	−0.992296	+	0.123892i	$0.960462\pi$
$198$	0.163318	−	3.81170i	0.0116065	−	0.270886i
$199$			1.99160i			0.141180i	0.997505	+	0.0705902i	$0.0224883\pi$
$199$			1.99160i			0.141180i	−0.997505	+	0.0705902i	$0.977512\pi$
$200$			5.32646i			0.376637i
$201$	0.367173	−	17.1469i	0.0258984	−	1.20945i
$202$	9.19277			0.646801
$203$	−5.04699			−0.354230
$204$	14.7094	+	0.314979i	1.02987	+	0.0220529i
$205$			18.3961i			1.28484i
$206$	14.6504			1.02074
$207$	−9.61247	−	10.7052i	−0.668113	−	0.744060i
$208$	0.254805			0.0176676
$209$		−	10.2532i		−	0.709231i
$210$	−2.40687	−	0.0515394i	−0.166090	−	0.00355655i
$211$	−3.96041			−0.272646			−0.136323	−	0.990664i	$-0.543528\pi$
$211$	−3.96041			−0.272646			−0.136323	+	0.990664i	$0.543528\pi$
$212$	−2.65623			−0.182431
$213$	0.179105	−	8.36417i	0.0122721	−	0.573103i
$214$		−	9.70187i		−	0.663206i
$215$			2.16142i			0.147408i
$216$	−0.896518	+	13.9387i	−0.0610003	+	0.948405i
$217$		−	4.59689i		−	0.312057i
$218$	−2.47462			−0.167602
$219$	−4.18514	−	0.0896180i	−0.282805	−	0.00605582i
$220$	−3.75594			−0.253225
$221$	−2.79478			−0.187997
$222$	−5.89273	−	0.126183i	−0.395494	−	0.00846888i
$223$	−16.0123			−1.07226			−0.536131	−	0.844135i	$-0.680115\pi$
$223$	−16.0123			−1.07226			−0.536131	+	0.844135i	$0.680115\pi$
$224$	−5.83166			−0.389644
$225$	−5.93918	−	0.254473i	−0.395945	−	0.0169648i
$226$		−	8.49006i		−	0.564751i
$227$	−7.93156			−0.526436			−0.263218	−	0.964736i	$-0.584784\pi$
$227$	−7.93156			−0.526436			−0.263218	+	0.964736i	$0.584784\pi$
$228$	−0.325268	+	15.1899i	−0.0215414	+	1.00598i
$229$			21.0010i			1.38779i	0.720078	+	0.693893i	$0.244106\pi$
$229$			21.0010i			1.38779i	−0.720078	+	0.693893i	$0.755894\pi$
$230$	4.76461	−	4.66178i	0.314169	−	0.307389i
$231$	−0.0589444	+	2.75269i	−0.00387826	+	0.181114i
$232$	−13.5665			−0.890685
$233$			8.53274i			0.558998i	0.960146	+	0.279499i	$0.0901684\pi$
$233$			8.53274i			0.558998i	−0.960146	+	0.279499i	$0.909832\pi$
$234$	0.0459706	−	1.07291i	0.00300519	−	0.0701386i
$235$		−	2.71546i		−	0.177137i
$236$			17.7855i			1.15774i
$237$	−0.475418	+	22.2019i	−0.0308817	+	1.44217i
$238$	4.99695			0.323904
$239$		−	3.59163i		−	0.232323i	−0.993230	−	0.116161i	$-0.962941\pi$
$239$		−	3.59163i		−	0.232323i	0.993230	−	0.116161i	$-0.0370590\pi$
$240$	1.71325	+	0.0366864i	0.110590	+	0.00236810i
$241$			9.99712i			0.643971i	0.946745	+	0.321986i	$0.104350\pi$
$241$			9.99712i			0.643971i	−0.946745	+	0.321986i	$0.895650\pi$
$242$			6.77862i			0.435746i
$243$	−15.4992	−	1.66557i	−0.994276	−	0.106846i
$244$		−	11.8574i		−	0.759095i
$245$	1.73737			0.110997
$246$	14.6688	+	0.314108i	0.935245	+	0.0200268i
$247$		−	2.88607i		−	0.183636i
$248$		−	12.3566i		−	0.784645i
$249$	−30.1806	−	0.646268i	−1.91261	−	0.0409556i
$250$		−	9.70384i		−	0.613725i
$251$	16.2825			1.02774			0.513870	−	0.857868i	$-0.328211\pi$
$251$	16.2825			1.02774			0.513870	+	0.857868i	$0.328211\pi$
$252$	0.174650	−	4.07617i	0.0110019	−	0.256775i
$253$	−5.33157	−	5.44918i	−0.335193	−	0.342587i
$254$		−	0.829238i		−	0.0520310i
$255$	−18.7914	−	0.402387i	−1.17676	−	0.0251985i
$256$	−14.1268			−0.882925
$257$		−	13.6562i		−	0.851849i	−0.904759	−	0.425925i	$-0.859949\pi$
$257$		−	13.6562i		−	0.851849i	0.904759	−	0.425925i	$-0.140051\pi$
$258$	1.72349	+	0.0369057i	0.107300	+	0.00229765i
$259$	4.25359			0.264305
$260$	−1.05722			−0.0655659
$261$	0.648143	−	15.1271i	0.0401190	−	0.936344i
$262$	−0.254538			−0.0157254
$263$	23.7305			1.46329			0.731644	−	0.681687i	$-0.238754\pi$
$263$	23.7305			1.46329			0.731644	+	0.681687i	$0.238754\pi$
$264$	−0.158445	+	7.39933i	−0.00975160	+	0.455397i
$265$	3.39335			0.208452
$266$			5.16018i			0.316391i
$267$	−16.9007	−	0.361902i	−1.03431	−	0.0221480i
$268$			13.4665i			0.822596i
$269$			6.16232i			0.375723i	0.982196	+	0.187862i	$0.0601556\pi$
$269$			6.16232i			0.375723i	−0.982196	+	0.187862i	$0.939844\pi$
$270$	0.463571	−	7.20739i	0.0282120	−	0.438628i
$271$	15.8139			0.960625			0.480312	−	0.877097i	$-0.340523\pi$
$271$	15.8139			0.960625			0.480312	+	0.877097i	$0.340523\pi$
$272$	−3.55689			−0.215668
$273$	−0.0165916	+	0.774825i	−0.00100417	+	0.0468945i
$274$			12.7616i			0.770954i
$275$	−3.14992			−0.189947
$276$	7.72573	+	8.24197i	0.465034	+	0.496108i
$277$	24.0550			1.44533			0.722663	−	0.691201i	$-0.242918\pi$
$277$	24.0550			1.44533			0.722663	+	0.691201i	$0.242918\pi$
$278$			3.34803i			0.200802i
$279$	13.7780	+	0.590339i	0.824868	+	0.0353427i
$280$	4.67012			0.279093
$281$	−26.1999			−1.56295			−0.781477	−	0.623933i	$-0.785534\pi$
$281$	−26.1999			−1.56295			−0.781477	+	0.623933i	$0.785534\pi$
$282$	−2.16527	−	0.0463658i	−0.128940	−	0.00276104i
$283$			6.12280i			0.363962i	0.983302	+	0.181981i	$0.0582510\pi$
$283$			6.12280i			0.363962i	−0.983302	+	0.181981i	$0.941749\pi$
$284$			6.56888i			0.389791i
$285$	0.415532	−	19.4052i	0.0246140	−	1.14947i
$286$		−	0.569034i		−	0.0336477i
$287$	−10.5884			−0.625016
$288$	0.748910	−	17.4789i	0.0441300	−	1.02996i
$289$	22.0131			1.29489
$290$	7.01496			0.411933
$291$	−0.390779	+	18.2493i	−0.0229079	+	1.06979i
$292$	3.28684			0.192348
$293$	14.1199			0.824895			0.412447	−	0.910981i	$-0.364674\pi$
$293$	14.1199			0.824895			0.412447	+	0.910981i	$0.364674\pi$
$294$	0.0296651	−	1.38535i	0.00173011	−	0.0807955i
$295$		−	22.7211i		−	1.32288i
$296$	11.4338			0.664577
$297$	−8.24292	−	0.530175i	−0.478303	−	0.0307639i
$298$			2.57358i			0.149084i
$299$	−1.50073	−	1.53383i	−0.0867893	−	0.0887037i
$300$	4.66653	+	0.0999262i	0.269422	+	0.00576924i
$301$	−1.24408			−0.0717074
$302$			0.0544667i			0.00313421i
$303$	0.426082	−	19.8979i	0.0244778	−	1.14311i
$304$		−	3.67308i		−	0.210666i
$305$			15.1480i			0.867369i
$306$	−0.641716	+	14.9771i	−0.0366844	+	0.856184i
$307$	−2.65580			−0.151574			−0.0757872	−	0.997124i	$-0.524147\pi$
$307$	−2.65580			−0.151574			−0.0757872	+	0.997124i	$0.524147\pi$
$308$		−	2.16185i		−	0.123183i
$309$	0.679042	−	31.7111i	0.0386293	−	1.80398i
$310$			6.38934i			0.362890i
$311$			6.62662i			0.375761i	0.982192	+	0.187881i	$0.0601618\pi$
$311$			6.62662i			0.375761i	−0.982192	+	0.187881i	$0.939838\pi$
$312$	−0.0445989	+	2.08276i	−0.00252492	+	0.117913i
$313$		−	12.2477i		−	0.692281i	−0.938183	−	0.346141i	$-0.887492\pi$
$313$		−	12.2477i		−	0.692281i	0.938183	−	0.346141i	$-0.112508\pi$
$314$	−12.5418			−0.707774
$315$	−0.223116	+	5.20734i	−0.0125712	+	0.293400i
$316$		−	17.4365i		−	0.980878i
$317$		−	11.4393i		−	0.642496i	−0.946995	−	0.321248i	$-0.895898\pi$
$317$		−	11.4393i		−	0.642496i	0.946995	−	0.321248i	$-0.104102\pi$
$318$	0.0579406	−	2.70581i	0.00324915	−	0.151734i
$319$		−	8.02285i		−	0.449193i
$320$	6.12685			0.342501
$321$	−20.9999	−	0.449679i	−1.17210	−	0.0250986i
$322$	2.68324	+	2.74243i	0.149531	+	0.152829i
$323$			40.2875i			2.24165i
$324$	12.1949	+	1.04694i	0.677493	+	0.0581632i
$325$	−0.886636			−0.0491817
$326$		−	15.2938i		−	0.847046i
$327$	−0.114698	+	5.35635i	−0.00634280	+	0.296207i
$328$	−28.4621			−1.57156
$329$	1.56297			0.0861695
$330$	0.0819285	−	3.82604i	0.00451002	−	0.210616i
$331$	10.4770			0.575868			0.287934	−	0.957650i	$-0.407032\pi$
$331$	10.4770			0.575868			0.287934	+	0.957650i	$0.407032\pi$
$332$	23.7026			1.30085
$333$	−0.546253	+	12.7491i	−0.0299345	+	0.698645i
$334$	−11.6842			−0.639333
$335$		−	17.2035i		−	0.939928i
$336$	−0.0211160	+	0.986114i	−0.00115197	+	0.0537969i
$337$		−	12.3274i		−	0.671517i	−0.941948	−	0.335759i	$-0.891007\pi$
$337$		−	12.3274i		−	0.671517i	0.941948	−	0.335759i	$-0.108993\pi$
$338$			10.2401i			0.556986i
$339$	−18.3769	−	0.393512i	−0.998096	−	0.0213726i
$340$	14.7580			0.800365
$341$	7.30734			0.395715
$342$	−15.4663	−	0.662678i	−0.836324	−	0.0358335i
$343$			1.00000i			0.0539949i
$344$	−3.34412			−0.180303
$345$	−9.86967	−	10.5292i	−0.531365	−	0.566871i
$346$	8.71027			0.468267
$347$		−	25.8602i		−	1.38825i	−0.719854	−	0.694125i	$-0.755791\pi$
$347$		−	25.8602i		−	1.38825i	0.719854	−	0.694125i	$-0.244209\pi$
$348$	−0.254513	+	11.8857i	−0.0136433	+	0.637139i
$349$	−8.00268			−0.428374			−0.214187	−	0.976793i	$-0.568710\pi$
$349$	−8.00268			−0.428374			−0.214187	+	0.976793i	$0.568710\pi$
$350$	1.58527			0.0847362
$351$	−2.32021	−	0.149233i	−0.123844	−	0.00796549i
$352$		−	9.27017i		−	0.494102i
$353$		−	29.7862i		−	1.58536i	−0.609637	−	0.792681i	$-0.708685\pi$
$353$		−	29.7862i		−	1.58536i	0.609637	−	0.792681i	$-0.291315\pi$
$354$	−18.1175	−	0.387957i	−0.962934	−	0.0206197i
$355$		−	8.39178i		−	0.445390i
$356$	13.2731			0.703475
$357$	0.231607	−	10.8160i	0.0122579	−	0.572443i
$358$	7.15869			0.378349
$359$	−12.5838			−0.664149			−0.332074	−	0.943253i	$-0.607748\pi$
$359$	−12.5838			−0.664149			−0.332074	+	0.943253i	$0.607748\pi$
$360$	−0.599744	+	13.9975i	−0.0316093	+	0.737734i
$361$	−22.6035			−1.18966
$362$	−0.648737			−0.0340969
$363$	14.6724	+	0.314187i	0.770103	+	0.0164905i
$364$		−	0.608516i		−	0.0318949i
$365$	−4.19895			−0.219783
$366$	12.0788	+	0.258647i	0.631367	+	0.0135197i
$367$			6.76209i			0.352978i	0.984303	+	0.176489i	$0.0564740\pi$
$367$			6.76209i			0.352978i	−0.984303	+	0.176489i	$0.943526\pi$
$368$	−1.90996	−	1.95210i	−0.0995638	−	0.101760i
$369$	1.35978	−	31.7362i	0.0707876	−	1.65212i
$370$	−5.91219			−0.307360
$371$			1.95315i			0.101403i
$372$	−10.8257	−	0.231814i	−0.561284	−	0.0120190i
$373$			3.15247i			0.163229i	0.996664	+	0.0816143i	$0.0260076\pi$
$373$			3.15247i			0.163229i	−0.996664	+	0.0816143i	$0.973992\pi$
$374$			7.94329i			0.410738i
$375$	−21.0041	−	0.449770i	−1.08465	−	0.0232260i
$376$	4.20133			0.216667
$377$		−	2.25827i		−	0.116307i
$378$	4.14844	+	0.266823i	0.213373	+	0.0137239i
$379$			12.2153i			0.627460i	0.949512	+	0.313730i	$0.101579\pi$
$379$			12.2153i			0.627460i	−0.949512	+	0.313730i	$0.898421\pi$
$380$			15.2401i			0.781800i
$381$	−1.79490	−	0.0384349i	−0.0919556	−	0.00196908i
$382$		−	12.3204i		−	0.630368i
$383$	−6.35005			−0.324473			−0.162236	−	0.986752i	$-0.551871\pi$
$383$	−6.35005			−0.324473			−0.162236	+	0.986752i	$0.551871\pi$
$384$	−0.327868	+	15.3114i	−0.0167315	+	0.781355i
$385$			2.76178i			0.140753i
$386$			9.55616i			0.486396i
$387$	0.159766	−	3.72881i	0.00812137	−	0.189546i
$388$		−	14.3323i		−	0.727610i
$389$	−1.99498			−0.101150			−0.0505748	−	0.998720i	$-0.516105\pi$
$389$	−1.99498			−0.101150			−0.0505748	+	0.998720i	$0.516105\pi$
$390$	0.0230612	−	1.07695i	0.00116775	−	0.0545335i
$391$	20.9490	+	21.4112i	1.05944	+	1.08281i
$392$			2.68804i			0.135766i
$393$	−0.0117978	+	0.550953i	−0.000595119	+	0.0277919i
$394$	2.78232			0.140171
$395$			22.2752i			1.12079i
$396$	6.47960	+	0.277628i	0.325612	+	0.0139513i
$397$	37.3364			1.87386			0.936930	−	0.349517i	$-0.113654\pi$
$397$	37.3364			1.87386			0.936930	+	0.349517i	$0.113654\pi$
$398$	1.59331			0.0798655
$399$	11.1693	+	0.239173i	0.559165	+	0.0119736i
$400$	−1.12842			−0.0564208
$401$	7.50144			0.374604			0.187302	−	0.982302i	$-0.440026\pi$
$401$	7.50144			0.374604			0.187302	+	0.982302i	$0.440026\pi$
$402$	−13.7178	−	0.293745i	−0.684183	−	0.0146507i
$403$	2.05687			0.102460
$404$			15.6270i			0.777473i
$405$	−15.5790	−	1.33747i	−0.774128	−	0.0664593i
$406$			4.03769i			0.200387i
$407$			6.76163i			0.335162i
$408$	0.622568	−	29.0738i	0.0308217	−	1.43937i
$409$	−12.2996			−0.608174			−0.304087	−	0.952644i	$-0.598351\pi$
$409$	−12.2996			−0.608174			−0.304087	+	0.952644i	$0.598351\pi$
$410$	14.7172			0.726830
$411$	27.6226	+	0.591494i	1.36252	+	0.0291763i
$412$			24.9046i			1.22696i
$413$	13.0779			0.643520
$414$	−8.56432	+	7.69015i	−0.420913	+	0.377950i
$415$	−30.2802			−1.48640
$416$		−	2.60936i		−	0.127934i
$417$	7.24688	+	0.155180i	0.354881	+	0.00759921i
$418$	−8.20277			−0.401211
$419$	−0.919388			−0.0449150			−0.0224575	−	0.999748i	$-0.507149\pi$
$419$	−0.919388			−0.0449150			−0.0224575	+	0.999748i	$0.507149\pi$
$420$	0.0876131	−	4.09151i	0.00427508	−	0.199645i
$421$			28.2530i			1.37697i	0.725253	+	0.688483i	$0.241723\pi$
$421$			28.2530i			1.37697i	−0.725253	+	0.688483i	$0.758277\pi$
$422$			3.16840i			0.154235i
$423$	−0.200719	+	4.68462i	−0.00975931	+	0.227774i
$424$			5.25015i			0.254970i
$425$	12.3768			0.600363
$426$	−6.69148	−	0.143287i	−0.324203	−	0.00694230i
$427$	−8.71889			−0.421937
$428$	16.4925			0.797193
$429$	−1.23168	−	0.0263745i	−0.0594663	−	0.00127337i
$430$	1.72918			0.0833883
$431$	17.4264			0.839400			0.419700	−	0.907663i	$-0.362135\pi$
$431$	17.4264			0.839400			0.419700	+	0.907663i	$0.362135\pi$
$432$	−2.95292	−	0.189928i	−0.142072	−	0.00913793i
$433$		−	32.6994i		−	1.57143i	−0.618586	−	0.785717i	$-0.712294\pi$
$433$		−	32.6994i		−	1.57143i	0.618586	−	0.785717i	$-0.287706\pi$
$434$	−3.67759			−0.176530
$435$	0.325141	−	15.1840i	0.0155893	−	0.728018i
$436$		−	4.20666i		−	0.201463i
$437$	−22.1106	+	21.6334i	−1.05769	+	1.03486i
$438$	−0.0716960	+	3.34818i	−0.00342577	+	0.159982i
$439$	15.1628			0.723683			0.361842	−	0.932240i	$-0.382148\pi$
$439$	15.1628			0.723683			0.361842	+	0.932240i	$0.382148\pi$
$440$			7.42376i			0.353914i
$441$	−2.99725	−	0.128422i	−0.142726	−	0.00611531i
$442$			2.23587i			0.106350i
$443$			17.7728i			0.844410i	0.906500	+	0.422205i	$0.138744\pi$
$443$			17.7728i			0.844410i	−0.906500	+	0.422205i	$0.861256\pi$
$444$	0.214502	−	10.0172i	0.0101798	−	0.475396i
$445$	−16.9565			−0.803816
$446$			12.8101i			0.606577i
$447$	5.57057	+	0.119285i	0.263479	+	0.00564198i
$448$			3.52650i			0.166612i
$449$		−	8.92986i		−	0.421426i	−0.977548	−	0.210713i	$-0.932421\pi$
$449$		−	8.92986i		−	0.421426i	0.977548	−	0.210713i	$-0.0675786\pi$
$450$	−0.203583	+	4.75145i	−0.00959698	+	0.223985i
$451$		−	16.8317i		−	0.792574i
$452$	14.4325			0.678846
$453$	0.117894	+	0.00252451i	0.00553915	+	0.000118612i
$454$			6.34539i			0.297804i
$455$			0.777383i			0.0364443i
$456$	30.0235	+	0.642905i	1.40598	+	0.0301068i
$457$		−	32.6264i		−	1.52620i	−0.646282	−	0.763098i	$-0.723677\pi$
$457$		−	32.6264i		−	1.52620i	0.646282	−	0.763098i	$-0.276323\pi$
$458$	16.8012			0.785068
$459$	32.3885	+	2.08319i	1.51176	+	0.0972350i
$460$	7.92468	+	8.09949i	0.369490	+	0.377640i
$461$			29.3081i			1.36501i	0.730880	+	0.682506i	$0.239110\pi$
$461$			29.3081i			1.36501i	−0.730880	+	0.682506i	$0.760890\pi$
$462$	2.20220	+	0.0471566i	0.102456	+	0.00219392i
$463$	1.49430			0.0694459			0.0347229	−	0.999397i	$-0.488945\pi$
$463$	1.49430			0.0694459			0.0347229	+	0.999397i	$0.488945\pi$
$464$		−	2.87408i		−	0.133426i
$465$	13.8298	+	0.296144i	0.641344	+	0.0137334i
$466$	6.82634			0.316224
$467$	25.4953			1.17978			0.589892	−	0.807482i	$-0.299170\pi$
$467$	25.4953			1.17978			0.589892	+	0.807482i	$0.299170\pi$
$468$	1.82387	+	0.0781465i	0.0843086	+	0.00361233i
$469$	9.90204			0.457234
$470$	−2.17242			−0.100206
$471$	−0.581308	+	27.1469i	−0.0267853	+	1.25087i
$472$	35.1538			1.61809
$473$		−	1.97762i		−	0.0909311i
$474$	17.7619	+	0.380343i	0.815832	+	0.0174697i
$475$			12.7811i			0.586437i
$476$			8.49444i			0.389342i
$477$	−5.85409	−	0.250827i	−0.268040	−	0.0114846i
$478$	−2.87337			−0.131425
$479$	−14.3517			−0.655746			−0.327873	−	0.944722i	$-0.606332\pi$
$479$	−14.3517			−0.655746			−0.327873	+	0.944722i	$0.606332\pi$
$480$	0.375691	−	17.5447i	0.0171479	−	0.800802i
$481$			1.90326i			0.0867812i
$482$	7.99788			0.364293
$483$	6.06040	−	5.68081i	0.275758	−	0.258486i
$484$	−11.5231			−0.523779
$485$			18.3095i			0.831393i
$486$	−1.33249	+	12.3997i	−0.0604428	+	0.562460i
$487$	28.2471			1.28000			0.639998	−	0.768376i	$-0.278935\pi$
$487$	28.2471			1.28000			0.639998	+	0.768376i	$0.278935\pi$
$488$	−23.4367			−1.06093
$489$	−33.1037	−	0.708863i	−1.49700	−	0.0320559i
$490$		−	1.38993i		−	0.0627906i
$491$			25.5440i			1.15278i	0.817174	+	0.576392i	$0.195540\pi$
$491$			25.5440i			1.15278i	−0.817174	+	0.576392i	$0.804460\pi$
$492$	−0.533960	+	24.9358i	−0.0240728	+	1.12419i
$493$			31.5237i			1.41976i
$494$	−2.30891			−0.103883
$495$	−8.27773	−	0.354671i	−0.372056	−	0.0159413i
$496$	2.61776			0.117541
$497$	4.83016			0.216662
$498$	−0.517026	+	24.1450i	−0.0231685	+	1.08196i
$499$	22.4299			1.00410			0.502050	−	0.864839i	$-0.332579\pi$
$499$	22.4299			1.00410			0.502050	+	0.864839i	$0.332579\pi$
$500$	16.4958			0.737715
$501$	−0.541561	+	25.2907i	−0.0241952	+	1.12991i
$502$		−	13.0263i		−	0.581390i
$503$	25.6093			1.14186			0.570930	−	0.820999i	$-0.306583\pi$
$503$	25.6093			1.14186			0.570930	+	0.820999i	$0.306583\pi$
$504$	−8.05672	−	0.345202i	−0.358875	−	0.0153765i
$505$		−	19.9636i		−	0.888369i
$506$	−4.35944	+	4.26535i	−0.193801	+	0.189618i
$507$	22.1648	+	0.474624i	0.984374	+	0.0210788i
$508$	1.40964			0.0625428
$509$		−	15.4895i		−	0.686562i	−0.939233	−	0.343281i	$-0.888462\pi$
$509$		−	15.4895i		−	0.686562i	0.939233	−	0.343281i	$-0.111538\pi$
$510$	−0.321917	+	15.0334i	−0.0142547	+	0.665692i
$511$		−	2.41684i		−	0.106915i
$512$		−	6.38239i		−	0.282065i
$513$	−2.15124	+	33.4465i	−0.0949795	+	1.47670i
$514$	−10.9252			−0.481890
$515$		−	31.8158i		−	1.40197i
$516$	−0.0627370	+	2.92980i	−0.00276184	+	0.128977i
$517$			2.48455i			0.109270i
$518$		−	3.40295i		−	0.149517i
$519$	0.403719	−	18.8535i	0.0177213	−	0.827579i
$520$			2.08963i			0.0916365i
$521$	−4.53658			−0.198751			−0.0993755	−	0.995050i	$-0.531685\pi$
$521$	−4.53658			−0.198751			−0.0993755	+	0.995050i	$0.531685\pi$
$522$	−12.1020	−	0.518526i	−0.529688	−	0.0226953i
$523$			13.8468i			0.605480i	0.953073	+	0.302740i	$0.0979014\pi$
$523$			13.8468i			0.605480i	−0.953073	+	0.302740i	$0.902099\pi$
$524$		−	0.432696i		−	0.0189024i
$525$	0.0734767	−	3.43134i	0.00320679	−	0.149756i
$526$		−	18.9849i		−	0.827779i
$527$	−28.7123			−1.25073
$528$	−1.56756	−	0.0335667i	−0.0682191	−	0.00146080i
$529$	−0.501756	+	22.9945i	−0.0218155	+	0.999762i
$530$		−	2.71474i		−	0.117921i
$531$	−1.67948	+	39.1977i	−0.0728833	+	1.70103i
$532$	−8.77192			−0.380311
$533$		−	4.73778i		−	0.205216i
$534$	−0.289528	+	13.5209i	−0.0125291	+	0.585106i
$535$	−21.0692			−0.910902
$536$	26.6170			1.14968
$537$	0.331803	−	15.4951i	0.0143184	−	0.668664i
$538$	4.92996			0.212546
$539$	−1.58963			−0.0684702
$540$	12.2520	+	0.788036i	0.527243	+	0.0339117i
$541$	−8.14527			−0.350193			−0.175096	−	0.984551i	$-0.556024\pi$
$541$	−8.14527			−0.350193			−0.175096	+	0.984551i	$0.556024\pi$
$542$		−	12.6514i		−	0.543424i
$543$	−0.0300688	+	1.40420i	−0.00129037	+	0.0602601i
$544$			36.4248i			1.56170i
$545$			5.37404i			0.230199i
$546$	0.619874	+	0.0132736i	0.0265281	+	0.000568058i
$547$	−40.0618			−1.71292			−0.856460	−	0.516213i	$-0.827341\pi$
$547$	−40.0618			−1.71292			−0.856460	+	0.516213i	$0.827341\pi$
$548$	−21.6937			−0.926709
$549$	1.11969	−	26.1327i	0.0477874	−	1.11532i
$550$			2.51999i			0.107453i
$551$	−32.5535			−1.38683
$552$	16.2906	−	15.2702i	0.693373	−	0.649944i
$553$	−12.8212			−0.545213
$554$		−	19.2444i		−	0.817618i
$555$	−0.274028	+	12.7970i	−0.0116318	+	0.543204i
$556$	−5.69141			−0.241369
$557$	27.1213			1.14917			0.574584	−	0.818446i	$-0.305164\pi$
$557$	27.1213			1.14917			0.574584	+	0.818446i	$0.305164\pi$
$558$	0.472282	−	11.0227i	0.0199933	−	0.466626i
$559$		−	0.556659i		−	0.0235442i
$560$			0.989369i			0.0418085i
$561$	17.1934	+	0.368169i	0.725906	+	0.0155441i
$562$			20.9604i			0.884161i
$563$	9.86141			0.415609			0.207804	−	0.978170i	$-0.433368\pi$
$563$	9.86141			0.415609			0.207804	+	0.978170i	$0.433368\pi$
$564$	0.0788184	−	3.68080i	0.00331886	−	0.154990i
$565$	−18.4376			−0.775674
$566$	4.89835			0.205893
$567$	0.769823	−	8.96702i	0.0323295	−	0.376579i
$568$	12.9837			0.544782
$569$	−21.1351			−0.886032			−0.443016	−	0.896514i	$-0.646091\pi$
$569$	−21.1351			−0.886032			−0.443016	+	0.896514i	$0.646091\pi$
$570$	−15.5245	−	0.332433i	−0.650251	−	0.0139241i
$571$		−	46.2771i		−	1.93664i	−0.249716	−	0.968319i	$-0.580337\pi$
$571$		−	46.2771i		−	1.93664i	0.249716	−	0.968319i	$-0.419663\pi$
$572$	0.967315			0.0404455
$573$	−26.6678	−	0.571049i	−1.11406	−	0.0238559i
$574$			8.47095i			0.353571i
$575$	6.64603	+	6.79264i	0.277159	+	0.283273i
$576$	−10.5698	−	0.452879i	−0.440409	−	0.0188700i
$577$	−40.9377			−1.70426			−0.852130	−	0.523330i	$-0.824689\pi$
$577$	−40.9377			−1.70426			−0.852130	+	0.523330i	$0.824689\pi$
$578$		−	17.6108i		−	0.732515i
$579$	20.6845	+	0.442925i	0.859618	+	0.0184073i
$580$			11.9249i			0.495155i
$581$		−	17.4287i		−	0.723066i
$582$	14.5998	+	0.312631i	0.605180	+	0.0129590i
$583$	−3.10479			−0.128587
$584$		−	6.49657i		−	0.268830i
$585$	−2.33001	−	0.0998327i	−0.0963341	−	0.00412757i
$586$		−	11.2962i		−	0.466642i
$587$		−	40.8718i		−	1.68696i	−0.537162	−	0.843479i	$-0.680504\pi$
$587$		−	40.8718i		−	1.68696i	0.537162	−	0.843479i	$-0.319496\pi$
$588$	2.35500	+	0.0504285i	0.0971185	+	0.00207964i
$589$		−	29.6503i		−	1.22172i
$590$	−18.1773			−0.748348
$591$	0.128960	−	6.02238i	0.00530469	−	0.247727i
$592$			2.42227i			0.0995545i
$593$			26.1054i			1.07202i	0.844212	+	0.536010i	$0.180069\pi$
$593$			26.1054i			1.07202i	−0.844212	+	0.536010i	$0.819931\pi$
$594$	−0.424150	+	6.59449i	−0.0174031	+	0.270575i
$595$		−	10.8517i		−	0.444876i
$596$	−4.37490			−0.179203
$597$	0.0738496	−	3.44875i	0.00302246	−	0.141148i
$598$	−1.22709	+	1.20061i	−0.0501795	+	0.0490965i
$599$		−	44.0421i		−	1.79951i	−0.436393	−	0.899756i	$-0.643744\pi$
$599$		−	44.0421i		−	1.79951i	0.436393	−	0.899756i	$-0.356256\pi$
$600$	0.197508	−	9.22358i	0.00806324	−	0.376551i
$601$	44.8191			1.82821			0.914104	−	0.405479i	$-0.132895\pi$
$601$	44.8191			1.82821			0.914104	+	0.405479i	$0.132895\pi$
$602$			0.995284i			0.0405647i
$603$	−1.27163	+	29.6789i	−0.0517850	+	1.20862i
$604$	−0.0925893			−0.00376741
$605$	14.7209			0.598489
$606$	−15.9187	−	0.340873i	−0.646653	−	0.0138470i
$607$	−21.1214			−0.857292			−0.428646	−	0.903473i	$-0.641009\pi$
$607$	−21.1214			−0.857292			−0.428646	+	0.903473i	$0.641009\pi$
$608$	−37.6146			−1.52548
$609$	8.73965	+	0.187146i	0.354148	+	0.00758352i
$610$	12.1186			0.490669
$611$			0.699349i			0.0282926i
$612$	−25.4600	−	1.09087i	−1.02916	−	0.0440958i
$613$		−	27.7208i		−	1.11963i	−0.828617	−	0.559816i	$-0.810872\pi$
$613$		−	27.7208i		−	1.11963i	0.828617	−	0.559816i	$-0.189128\pi$
$614$			2.12469i			0.0857454i
$615$	0.682137	−	31.8556i	0.0275064	−	1.28454i
$616$	−4.27298			−0.172163
$617$	−26.4648			−1.06543			−0.532716	−	0.846294i	$-0.678828\pi$
$617$	−26.4648			−1.06543			−0.532716	+	0.846294i	$0.678828\pi$
$618$	−25.3694	−	0.543246i	−1.02051	−	0.0218525i
$619$		−	5.60773i		−	0.225394i	−0.993629	−	0.112697i	$-0.964051\pi$
$619$		−	5.60773i		−	0.225394i	0.993629	−	0.112697i	$-0.0359489\pi$
$620$	−10.8614			−0.436204
$621$	16.2485	+	18.8941i	0.652030	+	0.758193i
$622$	5.30141			0.212567
$623$		−	9.75988i		−	0.391021i
$624$	−0.441234	−	0.00944833i	−0.0176635	−	0.000378236i
$625$	−11.1658			−0.446631
$626$	−9.79838			−0.391622
$627$	−0.380196	+	17.7550i	−0.0151836	+	0.709068i
$628$		−	21.3201i		−	0.850765i
$629$		−	26.5681i		−	1.05934i
$630$	4.16596	+	0.178497i	0.165976	+	0.00711148i
$631$			39.7908i			1.58405i	0.610491	+	0.792023i	$0.290972\pi$
$631$			39.7908i			1.58405i	−0.610491	+	0.792023i	$0.709028\pi$
$632$	−34.4639			−1.37090
$633$	6.85806	+	0.146854i	0.272584	+	0.00583694i
$634$	−9.15166			−0.363459
$635$	−1.80083			−0.0714636
$636$	4.59967	+	0.0984946i	0.182389	+	0.00390557i
$637$	−0.447448			−0.0177285
$638$	−6.41843			−0.254108
$639$	−0.620297	+	14.4772i	−0.0245386	+	0.572709i
$640$			15.3619i			0.607233i
$641$	−11.5175			−0.454915			−0.227458	−	0.973788i	$-0.573041\pi$
$641$	−11.5175			−0.454915			−0.227458	+	0.973788i	$0.573041\pi$
$642$	−0.359751	+	16.8003i	−0.0141982	+	0.663054i
$643$			9.92359i			0.391348i	0.980669	+	0.195674i	$0.0626895\pi$
$643$			9.92359i			0.391348i	−0.980669	+	0.195674i	$0.937311\pi$
$644$	−4.66192	+	4.56130i	−0.183705	+	0.179741i
$645$	0.0801469	−	3.74284i	0.00315578	−	0.147374i
$646$	32.2307			1.26810
$647$		−	22.6249i		−	0.889478i	−0.895660	−	0.444739i	$-0.853296\pi$
$647$		−	22.6249i		−	0.889478i	0.895660	−	0.444739i	$-0.146704\pi$
$648$	2.06931	−	24.1037i	0.0812903	−	0.946882i
$649$			20.7890i			0.816039i
$650$			0.709325i			0.0278220i
$651$	−0.170455	+	7.96021i	−0.00668067	+	0.311985i
$652$	25.9983			1.01817
$653$			44.7493i			1.75117i	0.483060	+	0.875587i	$0.339525\pi$
$653$			44.7493i			1.75117i	−0.483060	+	0.875587i	$0.660475\pi$
$654$	4.28518	+	0.0917603i	0.167564	+	0.00358811i
$655$			0.552772i			0.0215986i
$656$		−	6.02973i		−	0.235422i
$657$	7.24388	+	0.310375i	0.282611	+	0.0121089i
$658$		−	1.25041i		−	0.0487459i
$659$	−13.4701			−0.524722			−0.262361	−	0.964970i	$-0.584501\pi$
$659$	−13.4701			−0.524722			−0.262361	+	0.964970i	$0.584501\pi$
$660$	6.50398	+	0.139272i	0.253167	+	0.00542117i
$661$			1.07819i			0.0419368i	0.999780	+	0.0209684i	$0.00667494\pi$
$661$			1.07819i			0.0419368i	−0.999780	+	0.0209684i	$0.993325\pi$
$662$		−	8.38179i		−	0.325767i
$663$	4.83959	+	0.103632i	0.187954	+	0.00402474i
$664$		−	46.8491i		−	1.81810i
$665$	11.2062			0.434557
$666$	10.1995	+	0.437012i	0.395222	+	0.0169339i
$667$	−17.3009	+	16.9275i	−0.669892	+	0.655434i
$668$		−	19.8623i		−	0.768497i
$669$	27.7278	+	0.593745i	1.07202	+	0.0229555i
$670$	−13.7631			−0.531716
$671$		−	13.8598i		−	0.535052i
$672$	10.0984	+	0.216241i	0.389555	+	0.00834169i
$673$	23.6511			0.911683			0.455842	−	0.890061i	$-0.349338\pi$
$673$	23.6511			0.911683			0.455842	+	0.890061i	$0.349338\pi$
$674$	−9.86216			−0.379876
$675$	10.2752	+	0.660887i	0.395491	+	0.0254375i
$676$	−17.4073			−0.669513
$677$	−32.6373			−1.25435			−0.627177	−	0.778877i	$-0.715790\pi$
$677$	−32.6373			−1.25435			−0.627177	+	0.778877i	$0.715790\pi$
$678$	−0.314817	+	14.7019i	−0.0120905	+	0.564621i
$679$	−10.5386			−0.404436
$680$		−	29.1698i		−	1.11861i
$681$	13.7347	+	0.294107i	0.526315	+	0.0112702i
$682$		−	5.84601i		−	0.223855i
$683$		−	19.6396i		−	0.751489i	−0.926723	−	0.375745i	$-0.877387\pi$
$683$		−	19.6396i		−	0.751489i	0.926723	−	0.375745i	$-0.122613\pi$
$684$	1.12650	−	26.2916i	0.0430729	−	1.00529i
$685$	27.7138			1.05889
$686$	0.800018			0.0305448
$687$	0.778730	−	36.3665i	0.0297104	−	1.38747i
$688$		−	0.708456i		−	0.0270096i
$689$	−0.873934			−0.0332942
$690$	−8.42352	+	7.89591i	−0.320678	+	0.300592i
$691$	−22.0101			−0.837303			−0.418651	−	0.908147i	$-0.637497\pi$
$691$	−22.0101			−0.837303			−0.418651	+	0.908147i	$0.637497\pi$
$692$			14.8068i			0.562871i
$693$	0.204143	−	4.76452i	0.00775474	−	0.180989i
$694$	−20.6887			−0.785331
$695$	7.27081			0.275797
$696$	23.4925	+	0.503054i	0.890481	+	0.0190682i
$697$			66.1359i			2.50508i
$698$			6.40229i			0.242330i
$699$	0.316399	−	14.7757i	0.0119673	−	0.558870i
$700$			2.69484i			0.101855i
$701$	21.0298			0.794286			0.397143	−	0.917757i	$-0.370002\pi$
$701$	21.0298			0.794286			0.397143	+	0.917757i	$0.370002\pi$
$702$	−0.119389	+	1.85621i	−0.00450606	+	0.0700582i
$703$	27.4360			1.03477
$704$	−5.60583			−0.211278
$705$	−0.100691	+	4.70224i	−0.00379224	+	0.177097i
$706$	−23.8295			−0.896836
$707$	11.4907			0.432152
$708$	0.659498	−	30.7984i	0.0247855	−	1.15747i
$709$		−	13.5761i		−	0.509860i	−0.966959	−	0.254930i	$-0.917948\pi$
$709$		−	13.5761i		−	0.509860i	0.966959	−	0.254930i	$-0.0820525\pi$
$710$	−6.71358			−0.251956
$711$	1.64652	−	38.4284i	0.0617493	−	1.44118i
$712$		−	26.2349i		−	0.983195i
$713$	−15.4178	−	15.7579i	−0.577402	−	0.590139i
$714$	−8.65298	−	0.185290i	−0.323830	−	0.00693430i
$715$	−1.23575			−0.0462144
$716$			12.1692i			0.454786i
$717$	−0.133180	+	6.21945i	−0.00497368	+	0.232270i
$718$			10.0673i			0.375708i
$719$		−	18.3669i		−	0.684970i	−0.939523	−	0.342485i	$-0.888731\pi$
$719$		−	18.3669i		−	0.684970i	0.939523	−	0.342485i	$-0.111269\pi$
$720$	−2.96539	−	0.127056i	−0.110513	−	0.00473511i
$721$	18.3126			0.681996
$722$			18.0832i			0.672988i
$723$	0.370699	−	17.3116i	0.0137865	−	0.643824i
$724$		−	1.10280i		−	0.0409854i
$725$			10.0008i			0.371421i
$726$	0.251355	−	11.7382i	0.00932866	−	0.435646i
$727$		−	21.9740i		−	0.814970i	−0.913212	−	0.407485i	$-0.866406\pi$
$727$		−	21.9740i		−	0.814970i	0.913212	−	0.407485i	$-0.133594\pi$
$728$	−1.20276			−0.0445771
$729$	26.7775	+	3.45891i	0.991760	+	0.128108i
$730$			3.35924i			0.124331i
$731$			7.77056i			0.287404i
$732$	−0.439681	+	20.5330i	−0.0162511	+	0.758921i
$733$		−	35.4700i		−	1.31011i	−0.755579	−	0.655057i	$-0.772644\pi$
$733$		−	35.4700i		−	1.31011i	0.755579	−	0.655057i	$-0.227356\pi$
$734$	5.40979			0.199679
$735$	−3.00853	−	0.0644228i	−0.110971	−	0.00237627i
$736$	−19.9907	+	19.5592i	−0.736865	+	0.720962i
$737$			15.7406i			0.579811i
$738$	−25.3896	−	1.08785i	−0.934602	−	0.0400444i
$739$	−10.3861			−0.382058			−0.191029	−	0.981584i	$-0.561182\pi$
$739$	−10.3861			−0.382058			−0.191029	+	0.981584i	$0.561182\pi$
$740$		−	10.0503i		−	0.369456i
$741$	−0.107017	+	4.99768i	−0.00393138	+	0.183594i
$742$	1.56256			0.0573633
$743$	−42.3740			−1.55455			−0.777275	−	0.629161i	$-0.783399\pi$
$743$	−42.3740			−1.55455			−0.777275	+	0.629161i	$0.783399\pi$
$744$	−0.458190	+	21.3974i	−0.0167981	+	0.784465i
$745$	5.58896			0.204764
$746$	2.52203			0.0923382
$747$	52.2383	+	2.23823i	1.91130	+	0.0818924i
$748$	−13.5030			−0.493719
$749$		−	12.1271i		−	0.443113i
$750$	−0.359824	+	16.8037i	−0.0131389	+	0.613584i
$751$		−	15.8737i		−	0.579240i	−0.957142	−	0.289620i	$-0.906471\pi$
$751$		−	15.8737i		−	0.579240i	0.957142	−	0.289620i	$-0.0935290\pi$
$752$			0.890056i			0.0324570i
$753$	−28.1956	−	0.603763i	−1.02750	−	0.0220024i
$754$	−1.80665			−0.0657945
$755$	0.118283			0.00430477
$756$	−0.453580	+	7.05205i	−0.0164965	+	0.256480i
$757$			45.8695i			1.66716i	0.552402	+	0.833578i	$0.313711\pi$
$757$			45.8695i			1.66716i	−0.552402	+	0.833578i	$0.686289\pi$
$758$	9.77249			0.354953
$759$	9.03038	+	9.63379i	0.327782	+	0.349684i
$760$	30.1226			1.09266
$761$		−	34.1727i		−	1.23876i	−0.785092	−	0.619380i	$-0.787384\pi$
$761$		−	34.1727i		−	1.23876i	0.785092	−	0.619380i	$-0.212616\pi$
$762$	−0.0307486	+	1.43595i	−0.00111391	+	0.0520191i
$763$	−3.09320			−0.111981
$764$	20.9438			0.757721
$765$	32.5252	+	1.39359i	1.17595	+	0.0503854i
$766$			5.08016i			0.183554i
$767$			5.85167i			0.211291i
$768$	24.4627	+	0.523830i	0.882723	+	0.0189021i
$769$			22.2925i			0.803888i	0.915664	+	0.401944i	$0.131665\pi$
$769$			22.2925i			0.803888i	−0.915664	+	0.401944i	$0.868335\pi$
$770$	2.20947			0.0796238
$771$	−0.506380	+	23.6478i	−0.0182368	+	0.851654i
$772$	−16.2448			−0.584662
$773$	40.9644			1.47339			0.736694	−	0.676226i	$-0.236386\pi$
$773$	40.9644			1.47339			0.736694	+	0.676226i	$0.236386\pi$
$774$	−2.98311	−	0.127816i	−0.107226	−	0.00459425i
$775$	−9.10892			−0.327202
$776$	−28.3283			−1.01693
$777$	−7.36575	−	0.157726i	−0.264245	−	0.00565838i
$778$			1.59602i			0.0572202i
$779$	−68.2963			−2.44697
$780$	1.83074	+	0.0392023i	0.0655509	+	0.00140367i
$781$			7.67816i			0.274746i
$782$	17.1293	−	16.7596i	0.612543	−	0.599323i
$783$	−1.68328	+	26.1709i	−0.0601556	+	0.935271i
$784$	−0.569463			−0.0203380
$785$			27.2366i			0.972115i
$786$	0.440773	+	0.00943844i	0.0157218	+	0.000336658i
$787$		−	16.2762i		−	0.580184i	−0.956999	−	0.290092i	$-0.906314\pi$
$787$		−	16.2762i		−	0.580184i	0.956999	−	0.290092i	$-0.0936860\pi$
$788$			4.72973i			0.168490i
$789$	−41.0931	−	0.879942i	−1.46295	−	0.0313268i
$790$	17.8206			0.634027
$791$		−	10.6123i		−	0.377331i
$792$	0.548743	−	12.8072i	0.0194987	−	0.455084i
$793$		−	3.90125i		−	0.138537i
$794$		−	29.8698i		−	1.06004i
$795$	−5.87611	−	0.125827i	−0.208404	−	0.00446264i
$796$			2.70851i			0.0960007i
$797$	49.5458			1.75500			0.877501	−	0.479575i	$-0.159209\pi$
$797$	49.5458			1.75500			0.877501	+	0.479575i	$0.159209\pi$
$798$	0.191343	−	8.93564i	0.00677345	−	0.316318i
$799$		−	9.76240i		−	0.345369i
$800$			11.5557i			0.408555i
$801$	29.2528	+	1.25338i	1.03360	+	0.0442859i
$802$		−	6.00129i		−	0.211913i
$803$	3.84189			0.135577
$804$	0.499345	−	23.3193i	0.0176105	−	0.822408i
$805$	5.95563	−	5.82709i	0.209908	−	0.205378i
$806$		−	1.64553i		−	0.0579613i
$807$	0.228502	−	10.6710i	0.00804366	−	0.375637i
$808$	30.8874			1.08662
$809$			31.6824i			1.11389i	0.830548	+	0.556947i	$0.188027\pi$
$809$			31.6824i			1.11389i	−0.830548	+	0.556947i	$0.811973\pi$
$810$	−1.07000	+	12.4635i	−0.0375959	+	0.437923i
$811$	−38.0713			−1.33686			−0.668431	−	0.743774i	$-0.733034\pi$
$811$	−38.0713			−1.33686			−0.668431	+	0.743774i	$0.733034\pi$
$812$	−6.86377			−0.240871
$813$	−27.3842	−	0.586388i	−0.960405	−	0.0205655i
$814$	5.40943			0.189600
$815$	−33.2130			−1.16340
$816$	6.15931	+	0.131892i	0.215619	+	0.00461713i
$817$	−8.02439			−0.280738
$818$			9.83987i			0.344043i
$819$	0.0574619	−	1.34111i	0.00200788	−	0.0468623i
$820$			25.0181i			0.873670i
$821$		−	30.0819i		−	1.04986i	−0.851144	−	0.524932i	$-0.824091\pi$
$821$		−	30.0819i		−	1.04986i	0.851144	−	0.524932i	$-0.175909\pi$
$822$	0.473206	−	22.0986i	0.0165050	−	0.770777i
$823$	41.1787			1.43540			0.717700	−	0.696352i	$-0.245195\pi$
$823$	41.1787			1.43540			0.717700	+	0.696352i	$0.245195\pi$
$824$	49.2249			1.71483
$825$	5.45456	+	0.116801i	0.189904	+	0.00406648i
$826$		−	10.4625i		−	0.364038i
$827$	−48.1417			−1.67405			−0.837025	−	0.547165i	$-0.815707\pi$
$827$	−48.1417			−1.67405			−0.837025	+	0.547165i	$0.815707\pi$
$828$	−13.0727	−	14.5587i	−0.454307	−	0.505950i
$829$	16.8742			0.586065			0.293032	−	0.956103i	$-0.405336\pi$
$829$	16.8742			0.586065			0.293032	+	0.956103i	$0.405336\pi$
$830$			24.2247i			0.840852i
$831$	−41.6549	−	0.891974i	−1.44499	−	0.0309422i
$832$	−1.57793			−0.0547047
$833$	6.24604			0.216413
$834$	0.124147	−	5.79763i	0.00429886	−	0.200756i
$835$			25.3742i			0.878112i
$836$		−	13.9441i		−	0.482267i
$837$	−23.8369	−	1.53316i	−0.823922	−	0.0529938i
$838$			0.735527i			0.0254084i
$839$	−33.0244			−1.14013			−0.570064	−	0.821600i	$-0.693082\pi$
$839$	−33.0244			−1.14013			−0.570064	+	0.821600i	$0.693082\pi$
$840$	−8.08703	−	0.173171i	−0.279029	−	0.00597496i
$841$	3.52785			0.121650
$842$	22.6029			0.778947
$843$	45.3692	+	0.971508i	1.56260	+	0.0334605i
$844$	−5.38605			−0.185395
$845$	22.2380			0.765010
$846$	3.74778	+	0.160579i	0.128851	+	0.00552082i
$847$			8.47308i			0.291138i
$848$	−1.11225			−0.0381948
$849$	0.227037	−	10.6026i	0.00779189	−	0.363879i
$850$		−	9.90166i		−	0.339624i
$851$	14.5811	−	14.2664i	0.499834	−	0.489047i
$852$	0.243578	−	11.3750i	0.00834484	−	0.389702i
$853$	−39.6890			−1.35892			−0.679462	−	0.733710i	$-0.737787\pi$
$853$	−39.6890			−1.35892			−0.679462	+	0.733710i	$0.737787\pi$
$854$			6.97527i			0.238689i
$855$	−1.43911	+	33.5877i	−0.0492167	+	1.14868i
$856$		−	32.5980i		−	1.11418i
$857$		−	6.38424i		−	0.218081i	−0.994037	−	0.109041i	$-0.965222\pi$
$857$		−	6.38424i		−	0.218081i	0.994037	−	0.109041i	$-0.0347779\pi$
$858$	−0.0211001	+	0.985369i	−0.000720346	+	0.0336400i
$859$	26.0799			0.889834			0.444917	−	0.895572i	$-0.353233\pi$
$859$	26.0799			0.889834			0.444917	+	0.895572i	$0.353233\pi$
$860$			2.93947i			0.100235i
$861$	18.3355	+	0.392626i	0.624873	+	0.0133807i
$862$		−	13.9414i		−	0.474847i
$863$			43.9186i			1.49501i	0.664259	+	0.747503i	$0.268747\pi$
$863$			43.9186i			1.49501i	−0.664259	+	0.747503i	$0.731253\pi$
$864$	−1.94498	+	30.2397i	−0.0661696	+	1.02878i
$865$		−	18.9158i		−	0.643156i
$866$	−26.1601			−0.888957
$867$	−38.1190	−	0.816257i	−1.29459	−	0.0277216i
$868$		−	6.25163i		−	0.212194i
$869$		−	20.3810i		−	0.691377i
$870$	−12.1475	−	0.260119i	−0.411838	−	0.00881886i
$871$			4.43064i			0.150127i
$872$	−8.31464			−0.281569
$873$	1.35339	−	31.5870i	0.0458053	−	1.06906i
$874$	17.3071	+	17.6889i	0.585421	+	0.598335i
$875$		−	12.1295i		−	0.410053i
$876$	−5.69166	−	0.121878i	−0.192304	−	0.00411787i
$877$	−46.2340			−1.56121			−0.780606	−	0.625024i	$-0.785089\pi$
$877$	−46.2340			−1.56121			−0.780606	+	0.625024i	$0.785089\pi$
$878$		−	12.1306i		−	0.409386i
$879$	−24.4508	−	0.523575i	−0.824706	−	0.0176598i
$880$	−1.57273			−0.0530167
$881$	15.3363			0.516693			0.258346	−	0.966052i	$-0.416822\pi$
$881$	15.3363			0.516693			0.258346	+	0.966052i	$0.416822\pi$
$882$	−0.102740	+	2.39785i	−0.00345942	+	0.0807400i
$883$	31.8019			1.07022			0.535110	−	0.844783i	$-0.320270\pi$
$883$	31.8019			1.07022			0.535110	+	0.844783i	$0.320270\pi$
$884$	−3.80082			−0.127835
$885$	−0.842513	+	39.3451i	−0.0283208	+	1.32257i
$886$	14.2185			0.477681
$887$			38.9351i			1.30731i	0.756792	+	0.653656i	$0.226766\pi$
$887$			38.9351i			1.30731i	−0.756792	+	0.653656i	$0.773234\pi$
$888$	−19.7994	−	0.423973i	−0.664425	−	0.0142276i
$889$		−	1.03652i		−	0.0347639i
$890$			13.5655i			0.454718i
$891$	14.2542	+	1.22373i	0.477535	+	0.0409966i
$892$	−21.7763			−0.729123
$893$	10.0813			0.337358
$894$	0.0954300	−	4.45656i	0.00319166	−	0.149050i
$895$		−	15.5463i		−	0.519655i
$896$	−8.84205			−0.295392
$897$	2.54186	+	2.71171i	0.0848704	+	0.0905414i
$898$	−7.14405			−0.238400
$899$		−	23.2005i		−	0.773778i
$900$	−8.07711	−	0.346075i	−0.269237	−	0.0115358i
$901$	12.1995			0.406423
$902$	−13.4657			−0.448358
$903$	2.15431	+	0.0461311i	0.0716910	+	0.00153515i
$904$		−	28.5264i		−	0.948773i
$905$			1.40884i			0.0468314i
$906$	0.00201966	−	0.0943174i	6.70986e−5	−	0.00313349i
$907$			19.9526i			0.662514i	0.943541	+	0.331257i	$0.107473\pi$
$907$			19.9526i			0.662514i	−0.943541	+	0.331257i	$0.892527\pi$
$908$	−10.7867			−0.357969
$909$	−1.47565	+	34.4405i	−0.0489443	+	1.14232i
$910$	0.621920			0.0206165
$911$	−1.37139			−0.0454363			−0.0227182	−	0.999742i	$-0.507232\pi$
$911$	−1.37139			−0.0454363			−0.0227182	+	0.999742i	$0.507232\pi$
$912$	−0.136200	+	6.36051i	−0.00451004	+	0.210618i
$913$	27.7052			0.916910
$914$	−26.1017			−0.863367
$915$	0.561695	−	26.2310i	0.0185691	−	0.867170i
$916$			28.5608i			0.943674i
$917$	−0.318166			−0.0105068
$918$	1.66659	−	25.9114i	0.0550056	−	0.855202i
$919$			44.0475i			1.45299i	0.687171	+	0.726496i	$0.258852\pi$
$919$			44.0475i			1.45299i	−0.687171	+	0.726496i	$0.741148\pi$
$920$	16.0090	−	15.6634i	0.527800	−	0.516408i
$921$	4.59892	+	0.0984786i	0.151540	+	0.00324498i
$922$	23.4470			0.772185
$923$			2.16124i			0.0711382i
$924$	−0.0801627	+	3.74358i	−0.00263716	+	0.123155i
$925$		−	8.42867i		−	0.277133i
$926$		−	1.19546i		−	0.0392854i
$927$	−2.35173	+	54.8874i	−0.0772410	+	1.80274i
$928$	−29.4323			−0.966164
$929$		−	13.5330i		−	0.444005i	−0.975046	−	0.222002i	$-0.928741\pi$
$929$		−	13.5330i		−	0.444005i	0.975046	−	0.222002i	$-0.0712592\pi$
$930$	0.236921	−	11.0641i	0.00776893	−	0.362807i
$931$			6.45008i			0.211393i
$932$			11.6043i			0.380111i
$933$	0.245719	−	11.4750i	0.00804448	−	0.375675i
$934$		−	20.3967i		−	0.667402i
$935$	17.2502			0.564141
$936$	0.154460	−	3.60496i	0.00504868	−	0.117832i
$937$			15.0325i			0.491089i	0.969385	+	0.245545i	$0.0789668\pi$
$937$			15.0325i			0.491089i	−0.969385	+	0.245545i	$0.921033\pi$
$938$		−	7.92181i		−	0.258656i
$939$	−0.454152	+	21.2088i	−0.0148207	+	0.692123i
$940$		−	3.69295i		−	0.120451i
$941$	−19.3237			−0.629933			−0.314967	−	0.949103i	$-0.601993\pi$
$941$	−19.3237			−0.629933			−0.314967	+	0.949103i	$0.601993\pi$
$942$	21.7180	+	0.465057i	0.707612	+	0.0151524i
$943$	−36.2967	+	35.5133i	−1.18198	+	1.15647i
$944$			7.44737i			0.242391i
$945$	0.579451	−	9.00903i	0.0188495	−	0.293064i
$946$	−1.58213			−0.0514396
$947$		−	42.8111i		−	1.39117i	−0.718442	−	0.695586i	$-0.755145\pi$
$947$		−	42.8111i		−	1.39117i	0.718442	−	0.695586i	$-0.244855\pi$
$948$	−0.646555	+	30.1939i	−0.0209991	+	0.980653i
$949$	1.08141			0.0351041
$950$	10.2251			0.331746
$951$	−0.424177	+	19.8089i	−0.0137549	+	0.642349i
$952$	16.7896			0.544154
$953$	−3.57067			−0.115665			−0.0578327	−	0.998326i	$-0.518419\pi$
$953$	−3.57067			−0.115665			−0.0578327	+	0.998326i	$0.518419\pi$
$954$	−0.200666	+	4.68337i	−0.00649680	+	0.151630i
$955$	−26.7559			−0.865799
$956$		−	4.88451i		−	0.157976i
$957$	−0.297492	+	13.8928i	−0.00961655	+	0.449090i
$958$			11.4816i			0.370954i
$959$			15.9516i			0.515104i
$960$	−10.6096	−	0.227187i	−0.342423	−	0.00733243i
$961$	−9.86865			−0.318343
$962$	1.52264			0.0490920
$963$	36.3479	+	1.55738i	1.17129	+	0.0501858i
$964$			13.5958i			0.437891i
$965$	20.7528			0.668056
$966$	−4.54475	−	4.84843i	−0.146225	−	0.155996i
$967$	18.0987			0.582015			0.291008	−	0.956721i	$-0.406009\pi$
$967$	18.0987			0.582015			0.291008	+	0.956721i	$0.406009\pi$
$968$			22.7760i			0.732047i
$969$	1.49388	−	69.7640i	0.0479905	−	2.24114i
$970$	14.6480			0.470318
$971$	−6.99033			−0.224330			−0.112165	−	0.993690i	$-0.535779\pi$
$971$	−6.99033			−0.224330			−0.112165	+	0.993690i	$0.535779\pi$
$972$	−21.0785	−	2.26513i	−0.676093	−	0.0726539i
$973$			4.18495i			0.134163i
$974$		−	22.5982i		−	0.724092i
$975$	1.53535	+	0.0328770i	0.0491705	+	0.00105291i
$976$		−	4.96509i		−	0.158929i
$977$	−59.1602			−1.89270			−0.946351	−	0.323141i	$-0.895261\pi$
$977$	−59.1602			−1.89270			−0.946351	+	0.323141i	$0.895261\pi$
$978$	−0.567104	+	26.4836i	−0.0181340	+	0.846852i
$979$	15.5146			0.495848
$980$	2.36277			0.0754761
$981$	0.397234	−	9.27110i	0.0126827	−	0.296003i
$982$	20.4356			0.652128
$983$	39.6193			1.26366			0.631830	−	0.775107i	$-0.282304\pi$
$983$	39.6193			1.26366			0.631830	+	0.775107i	$0.282304\pi$
$984$	49.2866	+	1.05539i	1.57120	+	0.0336447i
$985$		−	6.04226i		−	0.192522i
$986$	25.2196			0.803155
$987$	−2.70653	−	0.0579560i	−0.0861497	−	0.00184476i
$988$		−	3.92498i		−	0.124870i
$989$	−4.26464	+	4.17260i	−0.135608	+	0.132681i
$990$	−0.283744	+	6.62234i	−0.00901796	+	0.210472i
$991$	13.1506			0.417743			0.208872	−	0.977943i	$-0.433021\pi$
$991$	13.1506			0.417743			0.208872	+	0.977943i	$0.433021\pi$
$992$		−	26.8075i		−	0.851138i
$993$	−18.1425	−	0.388493i	−0.575736	−	0.0123285i
$994$		−	3.86422i		−	0.122565i
$995$		−	3.46014i		−	0.109694i
$996$	−41.0447	−	0.878906i	−1.30055	−	0.0278492i
$997$	2.70829			0.0857723			0.0428862	−	0.999080i	$-0.486345\pi$
$997$	2.70829			0.0857723			0.0428862	+	0.999080i	$0.486345\pi$
$998$		−	17.9443i		−	0.568017i
$999$	1.41866	−	22.0567i	0.0448845	−	0.697844i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.e.a.344.17	✓	48
3.2	odd	2	inner	483.2.e.a.344.32	yes	48
23.22	odd	2	inner	483.2.e.a.344.18	yes	48
69.68	even	2	inner	483.2.e.a.344.31	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.e.a.344.17	✓	48	1.1	even	1	trivial
483.2.e.a.344.18	yes	48	23.22	odd	2	inner
483.2.e.a.344.31	yes	48	69.68	even	2	inner
483.2.e.a.344.32	yes	48	3.2	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.800018i q^{2} +(-1.73165 - 0.0370806i) q^{3} +1.35997 q^{4} -1.73737 q^{5} +(-0.0296651 + 1.38535i) q^{6} -1.00000i q^{7} -2.68804i q^{8} +(2.99725 + 0.128422i) q^{9} +1.38993i q^{10} +1.58963 q^{11} +(-2.35500 - 0.0504285i) q^{12} +0.447448 q^{13} -0.800018 q^{14} +(3.00853 + 0.0644228i) q^{15} +0.569463 q^{16} -6.24604 q^{17} +(0.102740 - 2.39785i) q^{18} -6.45008i q^{19} -2.36277 q^{20} +(-0.0370806 + 1.73165i) q^{21} -1.27173i q^{22} +(-3.35397 - 3.42796i) q^{23} +(-0.0996740 + 4.65475i) q^{24} -1.98154 q^{25} -0.357966i q^{26} +(-5.18544 - 0.333521i) q^{27} -1.35997i q^{28} -5.04699i q^{29} +(0.0515394 - 2.40687i) q^{30} +4.59689 q^{31} -5.83166i q^{32} +(-2.75269 - 0.0589444i) q^{33} +4.99695i q^{34} +1.73737i q^{35} +(4.07617 + 0.174650i) q^{36} +4.25359i q^{37} -5.16018 q^{38} +(-0.774825 - 0.0165916i) q^{39} +4.67012i q^{40} -10.5884i q^{41} +(1.38535 + 0.0296651i) q^{42} -1.24408i q^{43} +2.16185 q^{44} +(-5.20734 - 0.223116i) q^{45} +(-2.74243 + 2.68324i) q^{46} +1.56297i q^{47} +(-0.986114 - 0.0211160i) q^{48} -1.00000 q^{49} +1.58527i q^{50} +(10.8160 + 0.231607i) q^{51} +0.608516 q^{52} -1.95315 q^{53} +(-0.266823 + 4.14844i) q^{54} -2.76178 q^{55} -2.68804 q^{56} +(-0.239173 + 11.1693i) q^{57} -4.03769 q^{58} +13.0779i q^{59} +(4.09151 + 0.0876131i) q^{60} -8.71889i q^{61} -3.67759i q^{62} +(0.128422 - 2.99725i) q^{63} -3.52650 q^{64} -0.777383 q^{65} +(-0.0471566 + 2.20220i) q^{66} +9.90204i q^{67} -8.49444 q^{68} +(5.68081 + 6.06040i) q^{69} +1.38993 q^{70} +4.83016i q^{71} +(0.345202 - 8.05672i) q^{72} +2.41684 q^{73} +3.40295 q^{74} +(3.43134 + 0.0734767i) q^{75} -8.77192i q^{76} -1.58963i q^{77} +(-0.0132736 + 0.619874i) q^{78} -12.8212i q^{79} -0.989369 q^{80} +(8.96702 + 0.769823i) q^{81} -8.47095 q^{82} +17.4287 q^{83} +(-0.0504285 + 2.35500i) q^{84} +10.8517 q^{85} -0.995284 q^{86} +(-0.187146 + 8.73965i) q^{87} -4.27298i q^{88} +9.75988 q^{89} +(-0.178497 + 4.16596i) q^{90} -0.447448i q^{91} +(-4.56130 - 4.66192i) q^{92} +(-7.96021 - 0.170455i) q^{93} +1.25041 q^{94} +11.2062i q^{95} +(-0.216241 + 10.0984i) q^{96} -10.5386i q^{97} +0.800018i q^{98} +(4.76452 + 0.204143i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{3} - 40 q^{4} + 6 q^{6} + 4 q^{9} + 22 q^{12} - 8 q^{13} + 24 q^{16} - 14 q^{18} - 12 q^{24} + 88 q^{25} - 16 q^{27} - 8 q^{31} - 10 q^{36} + 8 q^{46} - 98 q^{48} - 48 q^{49} + 28 q^{52} - 28 q^{54}+ \cdots - 6 q^{96}+O(q^{100}) \) 48 * q - 4 * q^3 - 40 * q^4 + 6 * q^6 + 4 * q^9 + 22 * q^12 - 8 * q^13 + 24 * q^16 - 14 * q^18 - 12 * q^24 + 88 * q^25 - 16 * q^27 - 8 * q^31 - 10 * q^36 + 8 * q^46 - 98 * q^48 - 48 * q^49 + 28 * q^52 - 28 * q^54 - 92 * q^58 + 92 * q^64 + 8 * q^69 + 8 * q^70 + 60 * q^72 + 40 * q^73 - 80 * q^75 + 114 * q^78 - 28 * q^81 - 20 * q^82 - 40 * q^85 - 28 * q^87 - 76 * q^93 - 12 * q^94 - 6 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more