LMFDB - Embedded newform 483.2.e.a.344.18

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			344.18
Character	$\chi$	$=$	483.344
Dual form			483.2.e.a.344.32

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.800018i q^{2} +(-1.73165 - 0.0370806i) q^{3} +1.35997 q^{4} +1.73737 q^{5} +(-0.0296651 + 1.38535i) q^{6} +1.00000i q^{7} -2.68804i q^{8} +(2.99725 + 0.128422i) q^{9} +O(q^{10})$	\(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} +(-5.93503 + 5.81166i) 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}+O(q^{10}) $ 48 * q - 4 * q^3 - 40 * q^4 + 6 * q^6 + 4 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

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	$-0.372997\pi$
$5$	1.73737			0.776976			0.388488	+	0.921454i	$0.372997\pi$
$6$	−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	$-0.577031\pi$
$11$	−1.58963			−0.479291			−0.239646	+	0.970860i	$0.577031\pi$
$12$	−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	$-0.226448\pi$
$17$	6.24604			1.51489			0.757444	+	0.652900i	$0.226448\pi$
$18$	0.102740	−	2.39785i	0.0242159	−	0.565180i
$19$			6.45008i			1.47975i	0.672745	+	0.739875i	$0.265115\pi$
$19$			6.45008i			1.47975i	−0.672745	+	0.739875i	$0.734885\pi$
$20$	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	$-0.886303\pi$
$37$		−	4.25359i		−	0.699286i	0.936883	−	0.349643i	$-0.113697\pi$
$38$	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	$0.0302403\pi$
$43$			1.24408i			0.189720i	−0.995491	+	0.0948600i	$0.969760\pi$
$44$	−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	$-0.457172\pi$
$53$	1.95315			0.268286			0.134143	+	0.990962i	$0.457172\pi$
$54$	−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	$0.188496\pi$
$61$			8.71889i			1.11634i	−0.829727	+	0.558170i	$0.811504\pi$
$62$		−	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	$-0.793228\pi$
$67$		−	9.90204i		−	1.20973i	0.796329	−	0.604863i	$-0.206772\pi$
$68$	8.49444			1.03010
$69$	−5.93503	+	5.81166i	−0.714493	+	0.699642i
$70$	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	$0.256432\pi$
$79$			12.8212i			1.44250i	−0.692676	+	0.721249i	$0.743568\pi$
$80$	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	$-0.905798\pi$
$83$	−17.4287			−1.91305			−0.956527	+	0.291645i	$0.905798\pi$
$84$	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	$-0.673053\pi$
$89$	−9.75988			−1.03454			−0.517272	+	0.855821i	$0.673053\pi$
$90$	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	$0.179695\pi$
$97$			10.5386i			1.07004i	−0.844840	+	0.535019i	$0.820305\pi$
$98$			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	$-0.641954\pi$
$103$		−	18.3126i		−	1.80439i	0.431325	−	0.902196i	$-0.358046\pi$
$104$		−	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	$-0.699370\pi$
$107$	−12.1271			−1.17237			−0.586184	+	0.810178i	$0.699370\pi$
$108$	−7.05205	−	0.453580i	−0.678583	−	0.0436457i
$109$			3.09320i			0.296275i	0.988967	+	0.148137i	$0.0473278\pi$
$109$			3.09320i			0.296275i	−0.988967	+	0.148137i	$0.952672\pi$
$110$			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	$-0.666359\pi$
$113$	−10.6123			−0.998325			−0.499162	+	0.866508i	$0.666359\pi$
$114$	−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	$-0.261364\pi$
$137$	15.9516			1.36284			0.681418	+	0.731895i	$0.261364\pi$
$138$	4.64944	+	4.74813i	0.395786	+	0.404188i
$139$	−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	$-0.457934\pi$
$149$	3.21691			0.263539			0.131770	+	0.991280i	$0.457934\pi$
$150$	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	$0.215136\pi$
$157$			15.6769i			1.25115i	−0.780163	+	0.625576i	$0.784864\pi$
$158$	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	$0.00959435\pi$
$181$			0.810903i			0.0602739i	−0.999546	+	0.0301370i	$0.990406\pi$
$182$	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	$-0.688109\pi$
$191$	−15.4002			−1.11432			−0.557160	+	0.830405i	$0.688109\pi$
$192$	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	$-0.977512\pi$
$199$		−	1.99160i		−	0.141180i	0.997505	−	0.0705902i	$-0.0224883\pi$
$200$			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
$207$	10.4929	−	9.84372i	0.729308	−	0.684186i
$208$	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	$-0.415216\pi$
$227$	7.93156			0.526436			0.263218	+	0.964736i	$0.415216\pi$
$228$	0.325268	−	15.1899i	0.0215414	−	1.00598i
$229$		−	21.0010i		−	1.38779i	−0.720078	−	0.693893i	$-0.755894\pi$
$229$		−	21.0010i		−	1.38779i	0.720078	−	0.693893i	$-0.244106\pi$
$230$	−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	$-0.895650\pi$
$241$		−	9.99712i		−	0.643971i	0.946745	−	0.321986i	$-0.104350\pi$
$242$			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	$-0.671789\pi$
$251$	−16.2825			−1.02774			−0.513870	+	0.857868i	$0.671789\pi$
$252$	−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	$-0.761246\pi$
$263$	−23.7305			−1.46329			−0.731644	+	0.681687i	$0.761246\pi$
$264$	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
$276$	−8.07147	+	7.90370i	−0.485845	+	0.475747i
$277$	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	$-0.214466\pi$
$281$	26.1999			1.56295			0.781477	+	0.623933i	$0.214466\pi$
$282$	−2.16527	−	0.0463658i	−0.128940	−	0.00276104i
$283$		−	6.12280i		−	0.363962i	−0.983302	−	0.181981i	$-0.941749\pi$
$283$		−	6.12280i		−	0.363962i	0.983302	−	0.181981i	$-0.0582510\pi$
$284$			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	$-0.635326\pi$
$293$	−14.1199			−0.824895			−0.412447	+	0.910981i	$0.635326\pi$
$294$	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	$0.112508\pi$
$313$			12.2477i			0.692281i	−0.938183	+	0.346141i	$0.887492\pi$
$314$	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	$0.108993\pi$
$337$			12.3274i			0.671517i	−0.941948	+	0.335759i	$0.891007\pi$
$338$			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
$345$	−10.3113	+	10.0970i	−0.555144	+	0.543605i
$346$	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	$-0.392252\pi$
$359$	12.5838			0.664149			0.332074	+	0.943253i	$0.392252\pi$
$360$	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	$-0.943526\pi$
$367$		−	6.76209i		−	0.352978i	0.984303	−	0.176489i	$-0.0564740\pi$
$368$	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	$-0.973992\pi$
$373$		−	3.15247i		−	0.163229i	0.996664	−	0.0816143i	$-0.0260076\pi$
$374$			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	$-0.898421\pi$
$379$		−	12.2153i		−	0.627460i	0.949512	−	0.313730i	$-0.101579\pi$
$380$			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	$-0.448129\pi$
$383$	6.35005			0.324473			0.162236	+	0.986752i	$0.448129\pi$
$384$	−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	$-0.483895\pi$
$389$	1.99498			0.101150			0.0505748	+	0.998720i	$0.483895\pi$
$390$	−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	$-0.559974\pi$
$401$	−7.50144			−0.374604			−0.187302	+	0.982302i	$0.559974\pi$
$402$	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
$414$	−7.87515	−	8.39452i	−0.387043	−	0.412568i
$415$	−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	$-0.492851\pi$
$419$	0.919388			0.0449150			0.0224575	+	0.999748i	$0.492851\pi$
$420$	0.0876131	−	4.09151i	0.00427508	−	0.199645i
$421$		−	28.2530i		−	1.37697i	−0.725253	−	0.688483i	$-0.758277\pi$
$421$		−	28.2530i		−	1.37697i	0.725253	−	0.688483i	$-0.241723\pi$
$422$			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	$-0.637865\pi$
$431$	−17.4264			−0.839400			−0.419700	+	0.907663i	$0.637865\pi$
$432$	−2.95292	−	0.189928i	−0.142072	−	0.00913793i
$433$			32.6994i			1.57143i	0.618586	+	0.785717i	$0.287706\pi$
$433$			32.6994i			1.57143i	−0.618586	+	0.785717i	$0.712294\pi$
$434$	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	$0.276323\pi$
$457$			32.6264i			1.52620i	−0.646282	+	0.763098i	$0.723677\pi$
$458$	−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	$-0.700830\pi$
$467$	−25.4953			−1.17978			−0.589892	+	0.807482i	$0.700830\pi$
$468$	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	$-0.393668\pi$
$479$	14.3517			0.655746			0.327873	+	0.944722i	$0.393668\pi$
$480$	−0.375691	+	17.5447i	−0.0171479	+	0.800802i
$481$		−	1.90326i		−	0.0867812i
$482$	−7.99788			−0.364293
$483$	−5.81166	−	5.93503i	−0.264440	−	0.270053i
$484$	−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	$-0.693417\pi$
$503$	−25.6093			−1.14186			−0.570930	+	0.820999i	$0.693417\pi$
$504$	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	$-0.468315\pi$
$521$	4.53658			0.198751			0.0993755	+	0.995050i	$0.468315\pi$
$522$	−12.1020	−	0.518526i	−0.529688	−	0.0226953i
$523$		−	13.8468i		−	0.605480i	−0.953073	−	0.302740i	$-0.902099\pi$
$523$		−	13.8468i		−	0.605480i	0.953073	−	0.302740i	$-0.0979014\pi$
$524$		−	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
$552$	15.6220	+	15.9536i	0.664915	+	0.679029i
$553$	−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	$-0.694836\pi$
$557$	−27.1213			−1.14917			−0.574584	+	0.818446i	$0.694836\pi$
$558$	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	$-0.566632\pi$
$563$	−9.86141			−0.415609			−0.207804	+	0.978170i	$0.566632\pi$
$564$	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	$-0.353909\pi$
$569$	21.1351			0.886032			0.443016	+	0.896514i	$0.353909\pi$
$570$	−15.5245	−	0.332433i	−0.650251	−	0.0139241i
$571$			46.2771i			1.93664i	0.249716	+	0.968319i	$0.419663\pi$
$571$			46.2771i			1.93664i	−0.249716	+	0.968319i	$0.580337\pi$
$572$	−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	$0.189128\pi$
$613$			27.7208i			1.11963i	−0.828617	+	0.559816i	$0.810872\pi$
$614$			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	$-0.321172\pi$
$617$	26.4648			1.06543			0.532716	+	0.846294i	$0.321172\pi$
$618$	25.3694	+	0.543246i	1.02051	+	0.0218525i
$619$			5.60773i			0.225394i	0.993629	+	0.112697i	$0.0359489\pi$
$619$			5.60773i			0.225394i	−0.993629	+	0.112697i	$0.964051\pi$
$620$	10.8614			0.436204
$621$	−18.5351	+	16.6568i	−0.743788	+	0.668415i
$622$	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	$-0.709028\pi$
$631$		−	39.7908i		−	1.58405i	0.610491	−	0.792023i	$-0.290972\pi$
$632$	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	$-0.426959\pi$
$641$	11.5175			0.454915			0.227458	+	0.973788i	$0.426959\pi$
$642$	0.359751	−	16.8003i	0.0141982	−	0.663054i
$643$		−	9.92359i		−	0.391348i	−0.980669	−	0.195674i	$-0.937311\pi$
$643$		−	9.92359i		−	0.391348i	0.980669	−	0.195674i	$-0.0626895\pi$
$644$	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	$-0.415499\pi$
$659$	13.4701			0.524722			0.262361	+	0.964970i	$0.415499\pi$
$660$	6.50398	+	0.139272i	0.253167	+	0.00542117i
$661$		−	1.07819i		−	0.0419368i	−0.999780	−	0.0209684i	$-0.993325\pi$
$661$		−	1.07819i		−	0.0419368i	0.999780	−	0.0209684i	$-0.00667494\pi$
$662$		−	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	$-0.284210\pi$
$677$	32.6373			1.25435			0.627177	+	0.778877i	$0.284210\pi$
$678$	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
$690$	8.07780	+	8.24926i	0.307516	+	0.314044i
$691$	−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	$-0.629998\pi$
$701$	−21.0298			−0.794286			−0.397143	+	0.917757i	$0.629998\pi$
$702$	−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	$0.0820525\pi$
$709$			13.5761i			0.509860i	−0.966959	+	0.254930i	$0.917948\pi$
$710$	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	$0.133594\pi$
$727$			21.9740i			0.814970i	−0.913212	+	0.407485i	$0.866406\pi$
$728$	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	$0.227356\pi$
$733$			35.4700i			1.31011i	−0.755579	+	0.655057i	$0.772644\pi$
$734$	−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	$-0.216601\pi$
$743$	42.3740			1.55455			0.777275	+	0.629161i	$0.216601\pi$
$744$	−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	$0.0935290\pi$
$751$			15.8737i			0.579240i	−0.957142	+	0.289620i	$0.906471\pi$
$752$			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	$-0.686289\pi$
$757$		−	45.8695i		−	1.66716i	0.552402	−	0.833578i	$-0.313711\pi$
$758$	−9.77249			−0.354953
$759$	9.43449	−	9.23839i	0.342450	−	0.335332i
$760$	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	$-0.868335\pi$
$769$		−	22.2925i		−	0.803888i	0.915664	−	0.401944i	$-0.131665\pi$
$770$	−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	$-0.763614\pi$
$773$	−40.9644			−1.47339			−0.736694	+	0.676226i	$0.763614\pi$
$774$	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	$0.0936860\pi$
$787$			16.2762i			0.580184i	−0.956999	+	0.290092i	$0.906314\pi$
$788$			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	$-0.840791\pi$
$797$	−49.5458			−1.75500			−0.877501	+	0.479575i	$0.840791\pi$
$798$	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	$-0.184293\pi$
$827$	48.1417			1.67405			0.837025	+	0.547165i	$0.184293\pi$
$828$	14.2701	−	13.3872i	0.495919	−	0.465236i
$829$	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	$-0.306918\pi$
$839$	33.0244			1.14013			0.570064	+	0.821600i	$0.306918\pi$
$840$	−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	$-0.583178\pi$
$881$	−15.3363			−0.516693			−0.258346	+	0.966052i	$0.583178\pi$
$882$	−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
$897$	−2.65561	+	2.60042i	−0.0886684	+	0.0868254i
$898$	−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	$-0.892527\pi$
$907$		−	19.9526i		−	0.662514i	0.943541	−	0.331257i	$-0.107473\pi$
$908$	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	$-0.492768\pi$
$911$	1.37139			0.0454363			0.0227182	+	0.999742i	$0.492768\pi$
$912$	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	$-0.741148\pi$
$919$		−	44.0475i		−	1.45299i	0.687171	−	0.726496i	$-0.258852\pi$
$920$	−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	$-0.921033\pi$
$937$		−	15.0325i		−	0.491089i	0.969385	−	0.245545i	$-0.0789668\pi$
$938$		−	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	$-0.398007\pi$
$941$	19.3237			0.629933			0.314967	+	0.949103i	$0.398007\pi$
$942$	−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	$-0.481581\pi$
$953$	3.57067			0.115665			0.0578327	+	0.998326i	$0.481581\pi$
$954$	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
$966$	−4.74813	+	4.64944i	−0.152769	+	0.149593i
$967$	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	$-0.464221\pi$
$971$	6.99033			0.224330			0.112165	+	0.993690i	$0.464221\pi$
$972$	−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	$-0.104739\pi$
$977$	59.1602			1.89270			0.946351	+	0.323141i	$0.104739\pi$
$978$	−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	$-0.717696\pi$
$983$	−39.6193			−1.26366			−0.631830	+	0.775107i	$0.717696\pi$
$984$	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.344.18	yes	48
3.2	odd	2	inner	483.2.e.a.344.31	yes	48
23.22	odd	2	inner	483.2.e.a.344.17	✓	48
69.68	even	2	inner	483.2.e.a.344.32	yes	48

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-0.800018i q^{2} +(-1.73165 - 0.0370806i) q^{3} +1.35997 q^{4} +1.73737 q^{5} +(-0.0296651 + 1.38535i) q^{6} +1.00000i q^{7} -2.68804i q^{8} +(2.99725 + 0.128422i) q^{9} +O(q^{10})\)	\(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} +(-5.93503 + 5.81166i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{3} - 40 q^{4} + 6 q^{6} + 4 q^{9}+O(q^{10}) \) 48 * q - 4 * q^3 - 40 * q^4 + 6 * q^6 + 4 * q^9	\( 48 q - 4 q^{3} - 40 q^{4} + 6 q^{6} + 4 q^{9} + 22 q^{12} - 8 q^{13} + 24 q^{16} - 14 q^{18} - 12 q^{24} + 88 q^{25} - 16 q^{27} - 8 q^{31} - 10 q^{36} + 8 q^{46} - 98 q^{48} - 48 q^{49} + 28 q^{52} - 28 q^{54} - 92 q^{58} + 92 q^{64} + 8 q^{69} + 8 q^{70} + 60 q^{72} + 40 q^{73} - 80 q^{75} + 114 q^{78} - 28 q^{81} - 20 q^{82} - 40 q^{85} - 28 q^{87} - 76 q^{93} - 12 q^{94} - 6 q^{96}+O(q^{100}) \) 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

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