LMFDB - Embedded newform 765.2.bh.b.739.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [765,2,Mod(19,765)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("765.19"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(765, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 4, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 765 = 3^{2} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	765.bh (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$6.10855575463$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			739.3
Character	$\chi$	$=$	765.739
Dual form			765.2.bh.b.559.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.176012 - 0.176012i) q^{2} -1.93804i q^{4} +(-1.62749 + 1.53338i) q^{5} +(0.547653 + 1.32215i) q^{7} +(-0.693142 + 0.693142i) q^{8} +(0.556352 + 0.0165642i) q^{10} +(-1.03080 - 2.48857i) q^{11} +0.174664 q^{13} +(0.136321 - 0.329108i) q^{14} -3.63208 q^{16} +(-2.27165 - 3.44088i) q^{17} +(-2.69404 + 2.69404i) q^{19} +(2.97176 + 3.15415i) q^{20} +(-0.256585 + 0.619452i) q^{22} +(-2.54807 + 1.05544i) q^{23} +(0.297464 - 4.99114i) q^{25} +(-0.0307430 - 0.0307430i) q^{26} +(2.56238 - 1.06137i) q^{28} +(-5.94408 - 2.46212i) q^{29} +(-0.188417 + 0.454879i) q^{31} +(2.02557 + 2.02557i) q^{32} +(-0.205798 + 1.00547i) q^{34} +(-2.91867 - 1.31203i) q^{35} +(-5.30576 - 2.19772i) q^{37} +0.948365 q^{38} +(0.0652303 - 2.19094i) q^{40} +(-5.54000 + 2.29474i) q^{41} +(-8.00004 + 8.00004i) q^{43} +(-4.82296 + 1.99773i) q^{44} +(0.634261 + 0.262720i) q^{46} -2.65291 q^{47} +(3.50159 - 3.50159i) q^{49} +(-0.930858 + 0.826143i) q^{50} -0.338506i q^{52} +(8.73501 + 8.73501i) q^{53} +(5.49356 + 2.46952i) q^{55} +(-1.29604 - 0.536837i) q^{56} +(0.612867 + 1.47959i) q^{58} +(5.72232 + 5.72232i) q^{59} +(-6.41902 + 2.65884i) q^{61} +(0.113228 - 0.0469005i) q^{62} +6.55110i q^{64} +(-0.284265 + 0.267828i) q^{65} -12.3901i q^{67} +(-6.66855 + 4.40254i) q^{68} +(0.282788 + 0.744653i) q^{70} +(4.67878 - 11.2956i) q^{71} +(-5.99425 + 14.4714i) q^{73} +(0.547052 + 1.32070i) q^{74} +(5.22115 + 5.22115i) q^{76} +(2.72575 - 2.72575i) q^{77} +(-4.94031 - 11.9270i) q^{79} +(5.91118 - 5.56937i) q^{80} +(1.37901 + 0.571204i) q^{82} +(-6.06390 - 6.06390i) q^{83} +(8.97327 + 2.11669i) q^{85} +2.81621 q^{86} +(2.43943 + 1.01044i) q^{88} -11.4907i q^{89} +(0.0956555 + 0.230933i) q^{91} +(2.04549 + 4.93826i) q^{92} +(0.466944 + 0.466944i) q^{94} +(0.253531 - 8.51552i) q^{95} +(-0.879757 + 2.12392i) q^{97} -1.23264 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 16 q^{10} + 24 q^{14} + 8 q^{16} - 24 q^{19} + 8 q^{20} + 16 q^{25} + 16 q^{26} - 24 q^{29} - 24 q^{31} + 8 q^{34} - 8 q^{35} + 16 q^{40} + 48 q^{41} - 72 q^{44} - 16 q^{46} + 48 q^{49} - 16 q^{50}+ \cdots + 88 q^{95}+O(q^{100}) $ 24 * q - 16 * q^10 + 24 * q^14 + 8 * q^16 - 24 * q^19 + 8 * q^20 + 16 * q^25 + 16 * q^26 - 24 * q^29 - 24 * q^31 + 8 * q^34 - 8 * q^35 + 16 * q^40 + 48 * q^41 - 72 * q^44 - 16 * q^46 + 48 * q^49 - 16 * q^50 - 24 * q^56 + 48 * q^59 + 16 * q^61 - 24 * q^65 + 32 * q^70 - 16 * q^71 + 64 * q^74 - 24 * q^76 - 72 * q^79 + 64 * q^80 - 24 * q^85 - 8 * q^91 - 40 * q^94 + 88 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/765\mathbb{Z}\right)^\times$.

$n$	$307$	$496$	$596$
$\chi(n)$	$-1$	$e\left(\frac{5}{8}\right)$	$1$

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 $

$2$	−0.176012	−	0.176012i	−0.124459	−	0.124459i	0.642134	−	0.766593i	$-0.278049\pi$
$2$	−0.176012	−	0.176012i	−0.124459	−	0.124459i	−0.766593	+	0.642134i	$0.778049\pi$
$3$		0			0
$3$		0			0
$4$		−	1.93804i		−	0.969020i
$5$	−1.62749	+	1.53338i	−0.727837	+	0.685750i
$5$	−1.62749	+	1.53338i	−0.727837	+	0.685750i
$6$		0			0
$7$	0.547653	+	1.32215i	0.206993	+	0.499726i	0.992947	−	0.118559i	$-0.0378275\pi$
$7$	0.547653	+	1.32215i	0.206993	+	0.499726i	−0.785954	+	0.618286i	$0.787828\pi$
$8$	−0.693142	+	0.693142i	−0.245063	+	0.245063i
$9$		0			0
$10$	0.556352	+	0.0165642i	0.175934	+	0.00523805i
$11$	−1.03080	−	2.48857i	−0.310798	−	0.750333i	−0.999676	−	0.0254558i	$-0.991896\pi$
$11$	−1.03080	−	2.48857i	−0.310798	−	0.750333i	0.688878	−	0.724878i	$-0.258104\pi$
$12$		0			0
$13$	0.174664			0.0484432			0.0242216	−	0.999707i	$-0.492289\pi$
$13$	0.174664			0.0484432			0.0242216	+	0.999707i	$0.492289\pi$
$14$	0.136321	−	0.329108i	0.0364333	−	0.0879578i
$15$		0			0
$16$	−3.63208			−0.908019
$17$	−2.27165	−	3.44088i	−0.550955	−	0.834535i
$17$	−2.27165	−	3.44088i	−0.550955	−	0.834535i
$18$		0			0
$19$	−2.69404	+	2.69404i	−0.618055	+	0.618055i	−0.945032	−	0.326978i	$-0.893970\pi$
$19$	−2.69404	+	2.69404i	−0.618055	+	0.618055i	0.326978	+	0.945032i	$0.393970\pi$
$20$	2.97176	+	3.15415i	0.664506	+	0.705288i
$21$		0			0
$22$	−0.256585	+	0.619452i	−0.0547042	+	0.132068i
$23$	−2.54807	+	1.05544i	−0.531309	+	0.220075i	−0.632176	−	0.774825i	$-0.717838\pi$
$23$	−2.54807	+	1.05544i	−0.531309	+	0.220075i	0.100867	+	0.994900i	$0.467838\pi$
$24$		0			0
$25$	0.297464	−	4.99114i	0.0594929	−	0.998229i
$26$	−0.0307430	−	0.0307430i	−0.00602920	−	0.00602920i
$27$		0			0
$28$	2.56238	−	1.06137i	0.484245	−	0.200581i
$29$	−5.94408	−	2.46212i	−1.10379	−	0.457204i	−0.244994	−	0.969525i	$-0.578786\pi$
$29$	−5.94408	−	2.46212i	−1.10379	−	0.457204i	−0.858794	+	0.512321i	$0.828786\pi$
$30$		0			0
$31$	−0.188417	+	0.454879i	−0.0338407	+	0.0816987i	−0.939896	−	0.341460i	$-0.889079\pi$
$31$	−0.188417	+	0.454879i	−0.0338407	+	0.0816987i	0.906056	+	0.423159i	$0.139079\pi$
$32$	2.02557	+	2.02557i	0.358074	+	0.358074i
$33$		0			0
$34$	−0.205798	+	1.00547i	−0.0352941	+	0.172437i
$35$	−2.91867	−	1.31203i	−0.493345	−	0.221773i
$36$		0			0
$37$	−5.30576	−	2.19772i	−0.872261	−	0.361302i	−0.0987704	−	0.995110i	$-0.531491\pi$
$37$	−5.30576	−	2.19772i	−0.872261	−	0.361302i	−0.773490	+	0.633808i	$0.781491\pi$
$38$	0.948365			0.153845
$39$		0			0
$40$	0.0652303	−	2.19094i	0.0103138	−	0.346417i
$41$	−5.54000	+	2.29474i	−0.865203	+	0.358379i	−0.770740	−	0.637150i	$-0.780113\pi$
$41$	−5.54000	+	2.29474i	−0.865203	+	0.358379i	−0.0944627	+	0.995528i	$0.530113\pi$
$42$		0			0
$43$	−8.00004	+	8.00004i	−1.22000	+	1.22000i	−0.252363	+	0.967633i	$0.581208\pi$
$43$	−8.00004	+	8.00004i	−1.22000	+	1.22000i	−0.967633	+	0.252363i	$0.918792\pi$
$44$	−4.82296	+	1.99773i	−0.727088	+	0.301170i
$45$		0			0
$46$	0.634261	+	0.262720i	0.0935167	+	0.0387359i
$47$	−2.65291			−0.386967			−0.193483	−	0.981104i	$-0.561979\pi$
$47$	−2.65291			−0.386967			−0.193483	+	0.981104i	$0.561979\pi$
$48$		0			0
$49$	3.50159	−	3.50159i	0.500227	−	0.500227i
$50$	−0.930858	+	0.826143i	−0.131643	+	0.116834i
$51$		0			0
$52$		−	0.338506i		−	0.0469424i
$53$	8.73501	+	8.73501i	1.19985	+	1.19985i	0.974212	+	0.225633i	$0.0724450\pi$
$53$	8.73501	+	8.73501i	1.19985	+	1.19985i	0.225633	+	0.974212i	$0.427555\pi$
$54$		0			0
$55$	5.49356	+	2.46952i	0.740752	+	0.332990i
$56$	−1.29604	−	0.536837i	−0.173191	−	0.0717379i
$57$		0			0
$58$	0.612867	+	1.47959i	0.0804733	+	0.194280i
$59$	5.72232	+	5.72232i	0.744982	+	0.744982i	0.973532	−	0.228550i	$-0.0733984\pi$
$59$	5.72232	+	5.72232i	0.744982	+	0.744982i	−0.228550	+	0.973532i	$0.573398\pi$
$60$		0			0
$61$	−6.41902	+	2.65884i	−0.821871	+	0.340430i	−0.753679	−	0.657242i	$-0.771723\pi$
$61$	−6.41902	+	2.65884i	−0.821871	+	0.340430i	−0.0681914	+	0.997672i	$0.521723\pi$
$62$	0.113228	−	0.0469005i	0.0143799	−	0.00595637i
$63$		0			0
$64$			6.55110i			0.818888i
$65$	−0.284265	+	0.267828i	−0.0352587	+	0.0332199i
$66$		0			0
$67$		−	12.3901i		−	1.51369i	−0.653594	−	0.756845i	$-0.726740\pi$
$67$		−	12.3901i		−	1.51369i	0.653594	−	0.756845i	$-0.273260\pi$
$68$	−6.66855	+	4.40254i	−0.808681	+	0.533886i
$69$		0			0
$70$	0.282788	+	0.744653i	0.0337996	+	0.0890031i
$71$	4.67878	−	11.2956i	0.555269	−	1.34054i	−0.358205	−	0.933643i	$-0.616611\pi$
$71$	4.67878	−	11.2956i	0.555269	−	1.34054i	0.913474	−	0.406896i	$-0.133389\pi$
$72$		0			0
$73$	−5.99425	+	14.4714i	−0.701574	+	1.69375i	0.0184781	+	0.999829i	$0.494118\pi$
$73$	−5.99425	+	14.4714i	−0.701574	+	1.69375i	−0.720052	+	0.693920i	$0.755882\pi$
$74$	0.547052	+	1.32070i	0.0635935	+	0.153528i
$75$		0			0
$76$	5.22115	+	5.22115i	0.598907	+	0.598907i
$77$	2.72575	−	2.72575i	0.310628	−	0.310628i
$78$		0			0
$79$	−4.94031	−	11.9270i	−0.555828	−	1.34189i	−0.913042	−	0.407865i	$-0.866273\pi$
$79$	−4.94031	−	11.9270i	−0.555828	−	1.34189i	0.357214	−	0.934022i	$-0.383727\pi$
$80$	5.91118	−	5.56937i	0.660890	−	0.622674i
$81$		0			0
$82$	1.37901	+	0.571204i	0.152286	+	0.0630789i
$83$	−6.06390	−	6.06390i	−0.665600	−	0.665600i	0.291094	−	0.956694i	$-0.405981\pi$
$83$	−6.06390	−	6.06390i	−0.665600	−	0.665600i	−0.956694	+	0.291094i	$0.905981\pi$
$84$		0			0
$85$	8.97327	+	2.11669i	0.973288	+	0.229588i
$86$	2.81621			0.303679
$87$		0			0
$88$	2.43943	+	1.01044i	0.260044	+	0.107714i
$89$		−	11.4907i		−	1.21801i	−0.793165	−	0.609006i	$-0.791568\pi$
$89$		−	11.4907i		−	1.21801i	0.793165	−	0.609006i	$-0.208432\pi$
$90$		0			0
$91$	0.0956555	+	0.230933i	0.0100274	+	0.0242083i
$92$	2.04549	+	4.93826i	0.213257	+	0.514849i
$93$		0			0
$94$	0.466944	+	0.466944i	0.0481616	+	0.0481616i
$95$	0.253531	−	8.51552i	0.0260117	−	0.873674i
$96$		0			0
$97$	−0.879757	+	2.12392i	−0.0893258	+	0.215651i	−0.962229	−	0.272242i	$-0.912235\pi$
$97$	−0.879757	+	2.12392i	−0.0893258	+	0.215651i	0.872903	+	0.487894i	$0.162235\pi$
$98$	−1.23264			−0.124516
$99$		0			0
$100$	−9.67303	−	0.576498i	−0.967303	−	0.0576498i
$101$	0.890917			0.0886495			0.0443248	−	0.999017i	$-0.485886\pi$
$101$	0.890917			0.0886495			0.0443248	+	0.999017i	$0.485886\pi$
$102$		0			0
$103$			0.367137i			0.0361751i	0.999836	+	0.0180875i	$0.00575776\pi$
$103$			0.367137i			0.0361751i	−0.999836	+	0.0180875i	$0.994242\pi$
$104$	−0.121067	+	0.121067i	−0.0118716	+	0.0118716i
$105$		0			0
$106$		−	3.07493i		−	0.298664i
$107$	−2.54389	+	6.14149i	−0.245927	+	0.593720i	−0.997851	−	0.0655301i	$-0.979126\pi$
$107$	−2.54389	+	6.14149i	−0.245927	+	0.593720i	0.751924	+	0.659250i	$0.229126\pi$
$108$		0			0
$109$	8.16665	−	3.38274i	0.782223	−	0.324007i	0.0444107	−	0.999013i	$-0.485859\pi$
$109$	8.16665	−	3.38274i	0.782223	−	0.324007i	0.737812	+	0.675006i	$0.235859\pi$
$110$	−0.532267	−	1.40160i	−0.0507497	−	0.133637i
$111$		0			0
$112$	−1.98912	−	4.80216i	−0.187954	−	0.453761i
$113$	−5.27825	+	2.18632i	−0.496536	+	0.205672i	−0.616875	−	0.787061i	$-0.711602\pi$
$113$	−5.27825	+	2.18632i	−0.496536	+	0.205672i	0.120339	+	0.992733i	$0.461602\pi$
$114$		0			0
$115$	2.52856	−	5.62490i	0.235789	−	0.524524i
$116$	−4.77168	+	11.5199i	−0.443040	+	1.06959i
$117$		0			0
$118$		−	2.01439i		−	0.185440i
$119$	3.30529	−	4.88787i	0.302995	−	0.448070i
$120$		0			0
$121$	2.64772	−	2.64772i	0.240702	−	0.240702i
$122$	1.59781	+	0.661835i	0.144659	+	0.0599197i
$123$		0			0
$124$	0.881574	+	0.365160i	0.0791676	+	0.0327923i
$125$	7.16922	+	8.57918i	0.641235	+	0.767345i
$126$		0			0
$127$	11.5590	−	11.5590i	1.02569	−	1.02569i	0.0260300	−	0.999661i	$-0.491713\pi$
$127$	11.5590	−	11.5590i	1.02569	−	1.02569i	0.999661	−	0.0260300i	$-0.00828653\pi$
$128$	5.20422	−	5.20422i	0.459992	−	0.459992i
$129$		0			0
$130$	0.0971749	+	0.00289317i	0.00852280	+	0.000253748i
$131$	8.90518	+	3.68865i	0.778049	+	0.322279i	0.736128	−	0.676842i	$-0.236652\pi$
$131$	8.90518	+	3.68865i	0.778049	+	0.322279i	0.0419214	+	0.999121i	$0.486652\pi$
$132$		0			0
$133$	−5.03733	−	2.08653i	−0.436791	−	0.180925i
$134$	−2.18080	+	2.18080i	−0.188393	+	0.188393i
$135$		0			0
$136$	3.95959	+	0.810442i	0.339532	+	0.0694949i
$137$		−	6.60524i		−	0.564324i	−0.959367	−	0.282162i	$-0.908948\pi$
$137$		−	6.60524i		−	0.564324i	0.959367	−	0.282162i	$-0.0910515\pi$
$138$		0			0
$139$	−1.75923	+	4.24715i	−0.149216	+	0.360239i	−0.980759	−	0.195221i	$-0.937458\pi$
$139$	−1.75923	+	4.24715i	−0.149216	+	0.360239i	0.831544	+	0.555459i	$0.187458\pi$
$140$	−2.54277	+	5.65650i	−0.214903	+	0.478061i
$141$		0			0
$142$	−2.81168	+	1.16464i	−0.235951	+	0.0977340i
$143$	−0.180044	−	0.434665i	−0.0150561	−	0.0363485i
$144$		0			0
$145$	13.4493	−	5.10748i	1.11691	−	0.424153i
$146$	3.60220	−	1.49208i	0.298120	−	0.123485i
$147$		0			0
$148$	−4.25926	+	10.2828i	−0.350109	+	0.845238i
$149$		−	11.6404i		−	0.953619i	−0.879007	−	0.476810i	$-0.841793\pi$
$149$		−	11.6404i		−	0.953619i	0.879007	−	0.476810i	$-0.158207\pi$
$150$		0			0
$151$	0.0974235	−	0.0974235i	0.00792821	−	0.00792821i	−0.703132	−	0.711060i	$-0.748216\pi$
$151$	0.0974235	−	0.0974235i	0.00792821	−	0.00792821i	0.711060	+	0.703132i	$0.248216\pi$
$152$		−	3.73470i		−	0.302924i
$153$		0			0
$154$	−0.959530			−0.0773211
$155$	−0.390857	−	1.02923i	−0.0313944	−	0.0826696i
$156$		0			0
$157$	9.66489			0.771343			0.385671	−	0.922636i	$-0.373970\pi$
$157$	9.66489			0.771343			0.385671	+	0.922636i	$0.373970\pi$
$158$	−1.22973	+	2.96884i	−0.0978323	+	0.236188i
$159$		0			0
$160$	−6.40259	−	0.190623i	−0.506169	−	0.0150701i
$161$	−2.79092	−	2.79092i	−0.219955	−	0.219955i
$162$		0			0
$163$	−4.75100	−	11.4699i	−0.372127	−	0.898394i	−0.993390	−	0.114792i	$-0.963380\pi$
$163$	−4.75100	−	11.4699i	−0.372127	−	0.898394i	0.621263	−	0.783602i	$-0.286620\pi$
$164$	4.44730	+	10.7367i	0.347276	+	0.838399i
$165$		0			0
$166$			2.13464i			0.165680i
$167$	3.86872	+	1.60248i	0.299371	+	0.124003i	0.527313	−	0.849671i	$-0.323200\pi$
$167$	3.86872	+	1.60248i	0.299371	+	0.124003i	−0.227942	+	0.973675i	$0.573200\pi$
$168$		0			0
$169$	−12.9695			−0.997653
$170$	−1.20684	−	1.95197i	−0.0925603	−	0.149709i
$171$		0			0
$172$	15.5044	+	15.5044i	1.18220	+	1.18220i
$173$	−2.73000	−	1.13080i	−0.207558	−	0.0859733i	0.276483	−	0.961019i	$-0.410831\pi$
$173$	−2.73000	−	1.13080i	−0.207558	−	0.0859733i	−0.484040	+	0.875046i	$0.660831\pi$
$174$		0			0
$175$	6.76196	−	2.34012i	0.511156	−	0.176897i
$176$	3.74395	+	9.03869i	0.282211	+	0.681317i
$177$		0			0
$178$	−2.02250	+	2.02250i	−0.151593	+	0.151593i
$179$	16.4589	+	16.4589i	1.23019	+	1.23019i	0.963889	+	0.266304i	$0.0858027\pi$
$179$	16.4589	+	16.4589i	1.23019	+	1.23019i	0.266304	+	0.963889i	$0.414197\pi$
$180$		0			0
$181$	4.37037	+	10.5510i	0.324847	+	0.784250i	0.998959	+	0.0456205i	$0.0145265\pi$
$181$	4.37037	+	10.5510i	0.324847	+	0.784250i	−0.674112	+	0.738629i	$0.735474\pi$
$182$	0.0238104	−	0.0574834i	0.00176495	−	0.00426096i
$183$		0			0
$184$	1.03460	−	2.49775i	0.0762717	−	0.184136i
$185$	12.0050	−	4.55900i	0.882627	−	0.335184i
$186$		0			0
$187$	−6.22126	+	9.20002i	−0.454944	+	0.672772i
$188$			5.14145i			0.374978i
$189$		0			0
$190$	−1.54346	+	1.45421i	−0.111974	+	0.105499i
$191$			3.08201i			0.223007i	0.993764	+	0.111503i	$0.0355666\pi$
$191$			3.08201i			0.223007i	−0.993764	+	0.111503i	$0.964433\pi$
$192$		0			0
$193$	−14.7688	+	6.11743i	−1.06308	+	0.440343i	−0.844544	−	0.535486i	$-0.820128\pi$
$193$	−14.7688	+	6.11743i	−1.06308	+	0.440343i	−0.218537	+	0.975829i	$0.570128\pi$
$194$	0.528683	−	0.218988i	0.0379572	−	0.0157224i
$195$		0			0
$196$	−6.78621	−	6.78621i	−0.484729	−	0.484729i
$197$	−4.08460	−	9.86109i	−0.291015	−	0.702573i	0.708981	−	0.705228i	$-0.249155\pi$
$197$	−4.08460	−	9.86109i	−0.291015	−	0.702573i	−0.999996	+	0.00265412i	$0.999155\pi$
$198$		0			0
$199$	14.6337	+	6.06147i	1.03735	+	0.429686i	0.835362	−	0.549701i	$-0.185258\pi$
$199$	14.6337	+	6.06147i	1.03735	+	0.429686i	0.201993	+	0.979387i	$0.435258\pi$
$200$	3.25339	+	3.66576i	0.230049	+	0.259208i
$201$		0			0
$202$	−0.156812	−	0.156812i	−0.0110333	−	0.0110333i
$203$		−	9.20737i		−	0.646230i
$204$		0			0
$205$	5.49759	−	12.2296i	0.383968	−	0.854154i
$206$	0.0646205	−	0.0646205i	0.00450232	−	0.00450232i
$207$		0			0
$208$	−0.634394			−0.0439873
$209$	9.48133	+	3.92729i	0.655837	+	0.271657i
$210$		0			0
$211$	−4.54512	+	1.88265i	−0.312899	+	0.129607i	−0.533606	−	0.845733i	$-0.679164\pi$
$211$	−4.54512	+	1.88265i	−0.312899	+	0.129607i	0.220707	+	0.975340i	$0.429164\pi$
$212$	16.9288	−	16.9288i	1.16267	−	1.16267i
$213$		0			0
$214$	1.52873	−	0.633221i	0.104502	−	0.0432861i
$215$	0.752870	−	25.2872i	0.0513453	−	1.72457i
$216$		0			0
$217$	−0.704606			−0.0478318
$218$	−2.03283	−	0.842025i	−0.137681	−	0.0570292i
$219$		0			0
$220$	4.78603	−	10.6467i	0.322674	−	0.717803i
$221$	−0.396776	−	0.600998i	−0.0266900	−	0.0404275i
$222$		0			0
$223$	7.10210	+	7.10210i	0.475592	+	0.475592i	0.903719	−	0.428127i	$-0.140826\pi$
$223$	7.10210	+	7.10210i	0.475592	+	0.475592i	−0.428127	+	0.903719i	$0.640826\pi$
$224$	−1.56880	+	3.78743i	−0.104820	+	0.253058i
$225$		0			0
$226$	1.31385	+	0.544216i	0.0873963	+	0.0362007i
$227$	4.13654	−	1.71341i	0.274552	−	0.113723i	−0.241160	−	0.970485i	$-0.577528\pi$
$227$	4.13654	−	1.71341i	0.274552	−	0.113723i	0.515711	+	0.856762i	$0.327528\pi$
$228$		0			0
$229$	−0.847088	−	0.847088i	−0.0559771	−	0.0559771i	0.678564	−	0.734541i	$-0.262603\pi$
$229$	−0.847088	−	0.847088i	−0.0559771	−	0.0559771i	−0.734541	+	0.678564i	$0.762603\pi$
$230$	−1.43511	+	0.544992i	−0.0946280	+	0.0359357i
$231$		0			0
$232$	5.82669	−	2.41349i	0.382541	−	0.158454i
$233$	−9.74096	+	23.5168i	−0.638152	+	1.54063i	0.190987	+	0.981592i	$0.438831\pi$
$233$	−9.74096	+	23.5168i	−0.638152	+	1.54063i	−0.829139	+	0.559042i	$0.811169\pi$
$234$		0			0
$235$	4.31759	−	4.06793i	0.281649	−	0.265363i
$236$	11.0901	−	11.0901i	0.721903	−	0.721903i
$237$		0			0
$238$	−1.44209	+	0.278553i	−0.0934770	+	0.0180559i
$239$	−6.21407			−0.401955			−0.200977	−	0.979596i	$-0.564412\pi$
$239$	−6.21407			−0.401955			−0.200977	+	0.979596i	$0.564412\pi$
$240$		0			0
$241$	10.2576	−	24.7640i	0.660750	−	1.59519i	−0.135880	−	0.990725i	$-0.543386\pi$
$241$	10.2576	−	24.7640i	0.660750	−	1.59519i	0.796631	−	0.604467i	$-0.206614\pi$
$242$	−0.932062			−0.0599152
$243$		0			0
$244$	5.15294	+	12.4403i	0.329883	+	0.796409i
$245$	−0.329528	+	11.0681i	−0.0210528	+	0.707114i
$246$		0			0
$247$	−0.470552	+	0.470552i	−0.0299405	+	0.0299405i
$248$	−0.184696	−	0.445895i	−0.0117282	−	0.0283144i
$249$		0			0
$250$	0.248169	−	2.77191i	0.0156956	−	0.175311i
$251$			10.6052i			0.669394i	0.942326	+	0.334697i	$0.108634\pi$
$251$			10.6052i			0.669394i	−0.942326	+	0.334697i	$0.891366\pi$
$252$		0			0
$253$	5.25310	+	5.25310i	0.330260	+	0.330260i
$254$	−4.06903			−0.255313
$255$		0			0
$256$	11.2702			0.704387
$257$	1.08911	+	1.08911i	0.0679369	+	0.0679369i	0.740259	−	0.672322i	$-0.234703\pi$
$257$	1.08911	+	1.08911i	0.0679369	+	0.0679369i	−0.672322	+	0.740259i	$0.734703\pi$
$258$		0			0
$259$		−	8.21860i		−	0.510679i
$260$	0.519061	+	0.550917i	0.0321908	+	0.0341664i
$261$		0			0
$262$	−0.918172	−	2.21666i	−0.0567249	−	0.136946i
$263$	−0.301535	+	0.301535i	−0.0185935	+	0.0185935i	−0.716342	−	0.697749i	$-0.754185\pi$
$263$	−0.301535	+	0.301535i	−0.0185935	+	0.0185935i	0.697749	+	0.716342i	$0.254185\pi$
$264$		0			0
$265$	−27.6103	−	0.822036i	−1.69609	−	0.0504973i
$266$	0.519375	+	1.25388i	0.0318449	+	0.0768805i
$267$		0			0
$268$	−24.0125			−1.46680
$269$	6.54570	−	15.8027i	0.399098	−	0.963508i	−0.588782	−	0.808292i	$-0.700392\pi$
$269$	6.54570	−	15.8027i	0.399098	−	0.963508i	0.987880	−	0.155217i	$-0.0496075\pi$
$270$		0			0
$271$	16.0704			0.976208			0.488104	−	0.872785i	$-0.337689\pi$
$271$	16.0704			0.976208			0.488104	+	0.872785i	$0.337689\pi$
$272$	8.25079	+	12.4975i	0.500278	+	0.757774i
$273$		0			0
$274$	−1.16260	+	1.16260i	−0.0702353	+	0.0702353i
$275$	−12.7275	+	4.40461i	−0.767495	+	0.265608i
$276$		0			0
$277$	−6.41483	+	15.4868i	−0.385430	+	0.930510i	0.605465	+	0.795872i	$0.292987\pi$
$277$	−6.41483	+	15.4868i	−0.385430	+	0.930510i	−0.990895	+	0.134638i	$0.957013\pi$
$278$	1.05719	−	0.437904i	0.0634063	−	0.0262637i
$279$		0			0
$280$	2.93247	−	1.11363i	0.175249	−	0.0665521i
$281$	−5.54254	−	5.54254i	−0.330640	−	0.330640i	0.522189	−	0.852830i	$-0.325115\pi$
$281$	−5.54254	−	5.54254i	−0.330640	−	0.330640i	−0.852830	+	0.522189i	$0.825115\pi$
$282$		0			0
$283$	−6.07963	+	2.51826i	−0.361396	+	0.149695i	−0.555991	−	0.831189i	$-0.687661\pi$
$283$	−6.07963	+	2.51826i	−0.361396	+	0.149695i	0.194594	+	0.980884i	$0.437661\pi$
$284$	−21.8913	−	9.06767i	−1.29901	−	0.538067i
$285$		0			0
$286$	−0.0448163	+	0.108196i	−0.00265004	+	0.00639777i
$287$	−6.06800	−	6.06800i	−0.358183	−	0.358183i
$288$		0			0
$289$	−6.67925	+	15.6329i	−0.392897	+	0.919582i
$290$	−3.26622	−	1.46826i	−0.191799	−	0.0862194i
$291$		0			0
$292$	28.0461	+	11.6171i	1.64128	+	0.679839i
$293$	3.15115			0.184092			0.0920461	−	0.995755i	$-0.470659\pi$
$293$	3.15115			0.184092			0.0920461	+	0.995755i	$0.470659\pi$
$294$		0			0
$295$	−18.0875	−	0.538517i	−1.05310	−	0.0313537i
$296$	5.20097	−	2.15431i	0.302300	−	0.125217i
$297$		0			0
$298$	−2.04885	+	2.04885i	−0.118687	+	0.118687i
$299$	−0.445057	+	0.184348i	−0.0257383	+	0.0106611i
$300$		0			0
$301$	−14.9585	−	6.19602i	−0.862195	−	0.357133i
$302$	−0.0342954			−0.00197348
$303$		0			0
$304$	9.78495	−	9.78495i	0.561205	−	0.561205i
$305$	6.36987	−	14.1701i	0.364738	−	0.811376i
$306$		0			0
$307$		−	14.9905i		−	0.855551i	−0.903885	−	0.427775i	$-0.859297\pi$
$307$		−	14.9905i		−	0.855551i	0.903885	−	0.427775i	$-0.140703\pi$
$308$	−5.28261	−	5.28261i	−0.301005	−	0.301005i
$309$		0			0
$310$	−0.112361	+	0.249952i	−0.00638167	+	0.0141963i
$311$	−9.26536	−	3.83784i	−0.525390	−	0.217624i	0.104193	−	0.994557i	$-0.466774\pi$
$311$	−9.26536	−	3.83784i	−0.525390	−	0.217624i	−0.629583	+	0.776933i	$0.716774\pi$
$312$		0			0
$313$	1.35503	+	3.27134i	0.0765910	+	0.184907i	0.957537	−	0.288309i	$-0.0930930\pi$
$313$	1.35503	+	3.27134i	0.0765910	+	0.184907i	−0.880946	+	0.473216i	$0.843093\pi$
$314$	−1.70114	−	1.70114i	−0.0960007	−	0.0960007i
$315$		0			0
$316$	−23.1149	+	9.57451i	−1.30032	+	0.538608i
$317$	−11.2813	+	4.67288i	−0.633623	+	0.262455i	−0.676292	−	0.736634i	$-0.736414\pi$
$317$	−11.2813	+	4.67288i	−0.633623	+	0.262455i	0.0426686	+	0.999089i	$0.486414\pi$
$318$		0			0
$319$			17.3302i			0.970307i
$320$	−10.0454	−	10.6619i	−0.561553	−	0.596017i
$321$		0			0
$322$			0.982469i			0.0547508i
$323$	15.3897	+	3.14995i	0.856308	+	0.175268i
$324$		0			0
$325$	0.0519564	−	0.871775i	0.00288203	−	0.0483574i
$326$	−1.18261	+	2.85508i	−0.0654988	+	0.158128i
$327$		0			0
$328$	2.24942	−	5.43059i	0.124204	−	0.299854i
$329$	−1.45288	−	3.50755i	−0.0800996	−	0.193378i
$330$		0			0
$331$	−13.0768	−	13.0768i	−0.718764	−	0.718764i	0.249588	−	0.968352i	$-0.419705\pi$
$331$	−13.0768	−	13.0768i	−0.718764	−	0.718764i	−0.968352	+	0.249588i	$0.919705\pi$
$332$	−11.7521	+	11.7521i	−0.644979	+	0.644979i
$333$		0			0
$334$	−0.398886	−	0.962996i	−0.0218261	−	0.0526928i
$335$	18.9988	+	20.1648i	1.03801	+	1.10172i
$336$		0			0
$337$	−17.0378	−	7.05727i	−0.928106	−	0.384434i	−0.133146	−	0.991096i	$-0.542508\pi$
$337$	−17.0378	−	7.05727i	−0.928106	−	0.384434i	−0.794960	+	0.606662i	$0.792508\pi$
$338$	2.28279	+	2.28279i	0.124167	+	0.124167i
$339$		0			0
$340$	4.10224	−	17.3906i	0.222475	−	0.943135i
$341$	1.32622			0.0718189
$342$		0			0
$343$	15.8023	+	6.54555i	0.853247	+	0.353426i
$344$		−	11.0903i		−	0.597951i
$345$		0			0
$346$	0.281477	+	0.679547i	0.0151323	+	0.0365327i
$347$	1.94225	+	4.68901i	0.104265	+	0.251719i	0.967399	−	0.253256i	$-0.0815016\pi$
$347$	1.94225	+	4.68901i	0.104265	+	0.251719i	−0.863134	+	0.504975i	$0.831502\pi$
$348$		0			0
$349$	−17.2978	−	17.2978i	−0.925928	−	0.925928i	0.0715119	−	0.997440i	$-0.477218\pi$
$349$	−17.2978	−	17.2978i	−0.925928	−	0.925928i	−0.997440	+	0.0715119i	$0.977218\pi$
$350$	−1.60207	−	0.778296i	−0.0856345	−	0.0416017i
$351$		0			0
$352$	2.95282	−	7.12875i	0.157386	−	0.379964i
$353$	−17.5325			−0.933161			−0.466580	−	0.884479i	$-0.654514\pi$
$353$	−17.5325			−0.933161			−0.466580	+	0.884479i	$0.654514\pi$
$354$		0			0
$355$	9.70578	+	25.5579i	0.515130	+	1.35647i
$356$	−22.2695			−1.18028
$357$		0			0
$358$		−	5.79391i		−	0.306218i
$359$	1.42687	−	1.42687i	0.0753076	−	0.0753076i	−0.668450	−	0.743757i	$-0.733042\pi$
$359$	1.42687	−	1.42687i	0.0753076	−	0.0753076i	0.743757	+	0.668450i	$0.233042\pi$
$360$		0			0
$361$			4.48433i			0.236017i
$362$	1.08786	−	2.62634i	0.0571769	−	0.138037i
$363$		0			0
$364$	0.447557	−	0.185384i	0.0234584	−	0.00971677i
$365$	−12.4346	−	32.7436i	−0.650858	−	1.71388i
$366$		0			0
$367$	−12.4008	−	29.9381i	−0.647315	−	1.56276i	−0.816609	−	0.577191i	$-0.804149\pi$
$367$	−12.4008	−	29.9381i	−0.647315	−	1.56276i	0.169294	−	0.985566i	$-0.445851\pi$
$368$	9.25478	−	3.83345i	0.482439	−	0.199833i
$369$		0			0
$370$	−2.91546	−	1.31059i	−0.151568	−	0.0681343i
$371$	−6.76525	+	16.3328i	−0.351234	+	0.847955i
$372$		0			0
$373$			20.6108i			1.06719i	0.845741	+	0.533593i	$0.179159\pi$
$373$			20.6108i			1.06719i	−0.845741	+	0.533593i	$0.820841\pi$
$374$	2.71433	−	0.524297i	0.140355	−	0.0271107i
$375$		0			0
$376$	1.83884	−	1.83884i	0.0948311	−	0.0948311i
$377$	−1.03822	−	0.430044i	−0.0534710	−	0.0221484i
$378$		0			0
$379$	15.3385	+	6.35343i	0.787887	+	0.326354i	0.740094	−	0.672504i	$-0.234781\pi$
$379$	15.3385	+	6.35343i	0.787887	+	0.326354i	0.0477935	+	0.998857i	$0.484781\pi$
$380$	−16.5034	−	0.491353i	−0.846607	−	0.0252059i
$381$		0			0
$382$	0.542471	−	0.542471i	0.0277552	−	0.0277552i
$383$	−16.4274	+	16.4274i	−0.839401	+	0.839401i	−0.988780	−	0.149379i	$-0.952273\pi$
$383$	−16.4274	+	16.4274i	−0.839401	+	0.839401i	0.149379	+	0.988780i	$0.452273\pi$
$384$		0			0
$385$	−0.256516	+	8.61577i	−0.0130732	+	0.439100i
$386$	3.67622	+	1.52274i	0.187115	+	0.0775055i
$387$		0			0
$388$	4.11624	+	1.70500i	0.208971	+	0.0865584i
$389$	−25.9259	+	25.9259i	−1.31450	+	1.31450i	−0.396433	+	0.918064i	$0.629752\pi$
$389$	−25.9259	+	25.9259i	−1.31450	+	1.31450i	−0.918064	+	0.396433i	$0.870248\pi$
$390$		0			0
$391$	9.41996	+	6.36999i	0.476388	+	0.322144i
$392$			4.85419i			0.245174i
$393$		0			0
$394$	−1.01673	+	2.45461i	−0.0512222	+	0.123661i
$395$	26.3289	+	11.8356i	1.32475	+	0.595516i
$396$		0			0
$397$	−9.06522	+	3.75494i	−0.454970	+	0.188455i	−0.598386	−	0.801208i	$-0.704191\pi$
$397$	−9.06522	+	3.75494i	−0.454970	+	0.188455i	0.143416	+	0.989662i	$0.454191\pi$
$398$	−1.50881	−	3.64259i	−0.0756299	−	0.182587i
$399$		0			0
$400$	−1.08041	+	18.1282i	−0.0540207	+	0.906411i
$401$	−19.8539	+	8.22376i	−0.991457	+	0.410675i	−0.818657	−	0.574282i	$-0.805281\pi$
$401$	−19.8539	+	8.22376i	−0.991457	+	0.410675i	−0.172799	+	0.984957i	$0.555281\pi$
$402$		0			0
$403$	−0.0329097	+	0.0794512i	−0.00163935	+	0.00395774i
$404$		−	1.72663i		−	0.0859032i
$405$		0			0
$406$	−1.62061	+	1.62061i	−0.0804293	+	0.0804293i
$407$			15.4692i			0.766779i
$408$		0			0
$409$	−31.2735			−1.54638			−0.773189	−	0.634176i	$-0.781339\pi$
$409$	−31.2735			−1.54638			−0.773189	+	0.634176i	$0.781339\pi$
$410$	−3.12020	+	1.18492i	−0.154096	+	0.0585190i
$411$		0			0
$412$	0.711526			0.0350544
$413$	−4.43193	+	10.6996i	−0.218081	+	0.526494i
$414$		0			0
$415$	19.1673	+	0.570663i	0.940883	+	0.0280128i
$416$	0.353795	+	0.353795i	0.0173462	+	0.0173462i
$417$		0			0
$418$	−0.977576	−	2.36008i	−0.0478148	−	0.115435i
$419$	7.78615	+	18.7974i	0.380378	+	0.918314i	0.991892	+	0.127081i	$0.0405608\pi$
$419$	7.78615	+	18.7974i	0.380378	+	0.918314i	−0.611514	+	0.791234i	$0.709439\pi$
$420$		0			0
$421$			1.80862i			0.0881467i	0.999028	+	0.0440733i	$0.0140335\pi$
$421$			1.80862i			0.0881467i	−0.999028	+	0.0440733i	$0.985966\pi$
$422$	1.13136	+	0.468626i	0.0550740	+	0.0228124i
$423$		0			0
$424$	−12.1092			−0.588075
$425$	−17.8496	+	10.3146i	−0.865835	+	0.500330i
$426$		0			0
$427$	−7.03079	−	7.03079i	−0.340244	−	0.340244i
$428$	11.9024	+	4.93016i	0.575327	+	0.238308i
$429$		0			0
$430$	−4.58335	+	4.31833i	−0.221029	+	0.208248i
$431$	−6.37695	−	15.3953i	−0.307167	−	0.741566i	−0.999795	−	0.0202708i	$-0.993547\pi$
$431$	−6.37695	−	15.3953i	−0.307167	−	0.741566i	0.692628	−	0.721295i	$-0.256453\pi$
$432$		0			0
$433$	11.5388	−	11.5388i	0.554519	−	0.554519i	−0.373222	−	0.927742i	$-0.621747\pi$
$433$	11.5388	−	11.5388i	0.554519	−	0.554519i	0.927742	+	0.373222i	$0.121747\pi$
$434$	0.124019	+	0.124019i	0.00595311	+	0.00595311i
$435$		0			0
$436$	−6.55588	−	15.8273i	−0.313970	−	0.757990i
$437$	4.02118	−	9.70800i	0.192359	−	0.464396i
$438$		0			0
$439$	9.19489	−	22.1984i	0.438848	−	1.05947i	−0.537499	−	0.843264i	$-0.680631\pi$
$439$	9.19489	−	22.1984i	0.438848	−	1.05947i	0.976347	−	0.216209i	$-0.0693692\pi$
$440$	−5.51955	+	2.09609i	−0.263134	+	0.0999271i
$441$		0			0
$442$	−0.0359457	+	0.175620i	−0.00170976	+	0.00835340i
$443$		−	21.2757i		−	1.01084i	−0.862874	−	0.505419i	$-0.831338\pi$
$443$		−	21.2757i		−	1.01084i	0.862874	−	0.505419i	$-0.168662\pi$
$444$		0			0
$445$	17.6197	+	18.7010i	0.835253	+	0.886515i
$446$		−	2.50011i		−	0.118384i
$447$		0			0
$448$	−8.66156	+	3.58773i	−0.409220	+	0.169504i
$449$	−26.9783	+	11.1748i	−1.27318	+	0.527370i	−0.913931	−	0.405870i	$-0.866969\pi$
$449$	−26.9783	+	11.1748i	−1.27318	+	0.527370i	−0.359253	+	0.933240i	$0.616969\pi$
$450$		0			0
$451$	11.4213	+	11.4213i	0.537807	+	0.537807i
$452$	4.23718	+	10.2295i	0.199300	+	0.481153i
$453$		0			0
$454$	−1.02966	−	0.426500i	−0.0483244	−	0.0200166i
$455$	−0.509787	−	0.229165i	−0.0238992	−	0.0107434i
$456$		0			0
$457$	0.734055	+	0.734055i	0.0343376	+	0.0343376i	0.724067	−	0.689729i	$-0.242271\pi$
$457$	0.734055	+	0.734055i	0.0343376	+	0.0343376i	−0.689729	+	0.724067i	$0.742271\pi$
$458$			0.298195i			0.0139337i
$459$		0			0
$460$	−10.9013	−	4.90045i	−0.508274	−	0.228485i
$461$	−0.0496372	+	0.0496372i	−0.00231183	+	0.00231183i	−0.708262	−	0.705950i	$-0.750520\pi$
$461$	−0.0496372	+	0.0496372i	−0.00231183	+	0.00231183i	0.705950	+	0.708262i	$0.250520\pi$
$462$		0			0
$463$	40.0649			1.86197			0.930987	−	0.365051i	$-0.118949\pi$
$463$	40.0649			1.86197			0.930987	+	0.365051i	$0.118949\pi$
$464$	21.5894	+	8.94260i	1.00226	+	0.415150i
$465$		0			0
$466$	5.85376	−	2.42471i	0.271170	−	0.112322i
$467$	−16.0563	+	16.0563i	−0.742997	+	0.742997i	−0.973154	−	0.230156i	$-0.926076\pi$
$467$	−16.0563	+	16.0563i	−0.742997	+	0.742997i	0.230156	+	0.973154i	$0.426076\pi$
$468$		0			0
$469$	16.3816	−	6.78547i	0.756431	−	0.313324i
$470$	−1.47595	−	0.0439433i	−0.0680806	−	0.00202695i
$471$		0			0
$472$	−7.93276			−0.365135
$473$	28.1552	+	11.6622i	1.29458	+	0.536231i
$474$		0			0
$475$	12.6449	+	14.2477i	0.580190	+	0.653730i
$476$	−9.47288	−	6.40578i	−0.434189	−	0.293608i
$477$		0			0
$478$	1.09375	+	1.09375i	0.0500270	+	0.0500270i
$479$	8.90144	−	21.4900i	0.406717	−	0.981902i	−0.579278	−	0.815130i	$-0.696665\pi$
$479$	8.90144	−	21.4900i	0.406717	−	0.981902i	0.985995	−	0.166772i	$-0.0533345\pi$
$480$		0			0
$481$	−0.926726	−	0.383863i	−0.0422551	−	0.0175026i
$482$	−6.16422	+	2.55331i	−0.280773	+	0.116300i
$483$		0			0
$484$	−5.13139	−	5.13139i	−0.233245	−	0.233245i
$485$	−1.82499	−	4.80567i	−0.0828685	−	0.218214i
$486$		0			0
$487$	−15.6248	+	6.47199i	−0.708026	+	0.293274i	−0.707488	−	0.706726i	$-0.750171\pi$
$487$	−15.6248	+	6.47199i	−0.708026	+	0.293274i	−0.000538564		1.00000i	$0.500171\pi$
$488$	2.60633	−	6.29224i	0.117983	−	0.284837i
$489$		0			0
$490$	2.00611	−	1.89011i	0.0906270	−	0.0853866i
$491$	14.8915	−	14.8915i	0.672045	−	0.672045i	−0.286142	−	0.958187i	$-0.592373\pi$
$491$	14.8915	−	14.8915i	0.672045	−	0.672045i	0.958187	+	0.286142i	$0.0923729\pi$
$492$		0			0
$493$	5.03100	+	26.0459i	0.226585	+	1.17305i
$494$	0.165646			0.00745275
$495$		0			0
$496$	0.684345	−	1.65216i	0.0307280	−	0.0741840i
$497$	17.4968			0.784840
$498$		0			0
$499$	8.62028	+	20.8112i	0.385897	+	0.931637i	0.990800	+	0.135338i	$0.0432120\pi$
$499$	8.62028	+	20.8112i	0.385897	+	0.931637i	−0.604903	+	0.796299i	$0.706788\pi$
$500$	16.6268	−	13.8942i	0.743572	−	0.621369i
$501$		0			0
$502$	1.86664	−	1.86664i	0.0833122	−	0.0833122i
$503$	−11.1063	−	26.8129i	−0.495204	−	1.19553i	−0.952039	−	0.305977i	$-0.901017\pi$
$503$	−11.1063	−	26.8129i	−0.495204	−	1.19553i	0.456835	−	0.889551i	$-0.348983\pi$
$504$		0			0
$505$	−1.44996	+	1.36612i	−0.0645224	+	0.0607915i
$506$		−	1.84922i		−	0.0822077i
$507$		0			0
$508$	−22.4017	−	22.4017i	−0.993915	−	0.993915i
$509$	4.38401			0.194318			0.0971589	−	0.995269i	$-0.469024\pi$
$509$	4.38401			0.194318			0.0971589	+	0.995269i	$0.469024\pi$
$510$		0			0
$511$	−22.4162			−0.991633
$512$	−12.3921	−	12.3921i	−0.547660	−	0.547660i
$513$		0			0
$514$		−	0.383393i		−	0.0169107i
$515$	−0.562962	−	0.597513i	−0.0248071	−	0.0263295i
$516$		0			0
$517$	2.73462	+	6.60196i	0.120269	+	0.290354i
$518$	−1.44657	+	1.44657i	−0.0635587	+	0.0635587i
$519$		0			0
$520$	0.0113934	−	0.382678i	0.000499634	−	0.0167816i
$521$	1.22242	+	2.95118i	0.0535551	+	0.129294i	0.948393	−	0.317099i	$-0.102709\pi$
$521$	1.22242	+	2.95118i	0.0535551	+	0.129294i	−0.894837	+	0.446392i	$0.852709\pi$
$522$		0			0
$523$	−34.0520			−1.48899			−0.744494	−	0.667629i	$-0.767309\pi$
$523$	−34.0520			−1.48899			−0.744494	+	0.667629i	$0.767309\pi$
$524$	7.14875	−	17.2586i	0.312294	−	0.753945i
$525$		0			0
$526$	0.106148			0.00462825
$527$	1.99320	−	0.385004i	0.0868251	−	0.0167710i
$528$		0			0
$529$	−10.8848	+	10.8848i	−0.473251	+	0.473251i
$530$	4.71505	+	5.00443i	0.204809	+	0.217378i
$531$		0			0
$532$	−4.04377	+	9.76254i	−0.175320	+	0.423260i
$533$	−0.967641	+	0.400810i	−0.0419132	+	0.0173610i
$534$		0			0
$535$	−5.27710	−	13.8960i	−0.228149	−	0.600776i
$536$	8.58809	+	8.58809i	0.370949	+	0.370949i
$537$		0			0
$538$	−3.93359	+	1.62934i	−0.169589	+	0.0702460i
$539$	−12.3234	−	5.10452i	−0.530806	−	0.219867i
$540$		0			0
$541$	−10.3587	+	25.0081i	−0.445355	+	1.07518i	0.528687	+	0.848817i	$0.322685\pi$
$541$	−10.3587	+	25.0081i	−0.445355	+	1.07518i	−0.974042	+	0.226366i	$0.927315\pi$
$542$	−2.82859	−	2.82859i	−0.121498	−	0.121498i
$543$		0			0
$544$	2.36836	−	11.5711i	0.101543	−	0.496108i
$545$	−8.10412	+	18.0280i	−0.347143	+	0.772234i
$546$		0			0
$547$	−12.5020	−	5.17849i	−0.534546	−	0.221416i	0.0990470	−	0.995083i	$-0.468421\pi$
$547$	−12.5020	−	5.17849i	−0.534546	−	0.221416i	−0.633593	+	0.773667i	$0.718421\pi$
$548$	−12.8012			−0.546841
$549$		0			0
$550$	3.01545	+	1.46492i	0.128579	+	0.0624644i
$551$	22.6466	−	9.38053i	0.964778	−	0.399624i
$552$		0			0
$553$	13.0637	−	13.0637i	0.555524	−	0.555524i
$554$	3.85494	−	1.59677i	0.163781	−	0.0678402i
$555$		0			0
$556$	8.23114	+	3.40945i	0.349078	+	0.144593i
$557$	−30.5182			−1.29310			−0.646548	−	0.762873i	$-0.723788\pi$
$557$	−30.5182			−1.29310			−0.646548	+	0.762873i	$0.723788\pi$
$558$		0			0
$559$	−1.39732	+	1.39732i	−0.0591005	+	0.0591005i
$560$	10.6008	+	4.76539i	0.447967	+	0.201375i
$561$		0			0
$562$			1.95111i			0.0823024i
$563$	−5.73355	−	5.73355i	−0.241640	−	0.241640i	0.575888	−	0.817529i	$-0.304656\pi$
$563$	−5.73355	−	5.73355i	−0.241640	−	0.241640i	−0.817529	+	0.575888i	$0.804656\pi$
$564$		0			0
$565$	5.23784	−	11.6518i	0.220358	−	0.490196i
$566$	1.51333	+	0.626842i	0.0636101	+	0.0263481i
$567$		0			0
$568$	4.58638	+	11.0725i	0.192440	+	0.464592i
$569$	2.71124	+	2.71124i	0.113661	+	0.113661i	0.761650	−	0.647989i	$-0.224390\pi$
$569$	2.71124	+	2.71124i	0.113661	+	0.113661i	−0.647989	+	0.761650i	$0.724390\pi$
$570$		0			0
$571$	6.06730	−	2.51316i	0.253909	−	0.105172i	−0.252099	−	0.967701i	$-0.581121\pi$
$571$	6.06730	−	2.51316i	0.253909	−	0.105172i	0.506007	+	0.862529i	$0.331121\pi$
$572$	−0.842398	+	0.348933i	−0.0352224	+	0.0145896i
$573$		0			0
$574$			2.13608i			0.0891583i
$575$	4.50991	+	13.0317i	0.188076	+	0.543461i
$576$		0			0
$577$		−	23.2880i		−	0.969493i	−0.874655	−	0.484746i	$-0.838912\pi$
$577$		−	23.2880i		−	0.969493i	0.874655	−	0.484746i	$-0.161088\pi$
$578$	3.92720	−	1.57595i	0.163350	−	0.0655508i
$579$		0			0
$580$	−9.89850	−	26.0653i	−0.411013	−	1.08230i
$581$	4.69649	−	11.3383i	0.194843	−	0.470393i
$582$		0			0
$583$	12.7337	−	30.7418i	0.527374	−	1.27319i
$584$	−5.87587	−	14.1856i	−0.243145	−	0.587004i
$585$		0			0
$586$	−0.554640	−	0.554640i	−0.0229120	−	0.0229120i
$587$	26.0085	−	26.0085i	1.07348	−	1.07348i	0.0764077	−	0.997077i	$-0.475655\pi$
$587$	26.0085	−	26.0085i	1.07348	−	1.07348i	0.997077	−	0.0764077i	$-0.0243450\pi$
$588$		0			0
$589$	−0.717858	−	1.73306i	−0.0295788	−	0.0714096i
$590$	3.08884	+	3.27841i	0.127165	+	0.134970i
$591$		0			0
$592$	19.2709	+	7.98227i	0.792030	+	0.328069i
$593$	19.1275	+	19.1275i	0.785474	+	0.785474i	0.980749	−	0.195275i	$-0.0625598\pi$
$593$	19.1275	+	19.1275i	0.785474	+	0.785474i	−0.195275	+	0.980749i	$0.562560\pi$
$594$		0			0
$595$	2.11565	+	13.0232i	0.0867332	+	0.533901i
$596$	−22.5596			−0.924076
$597$		0			0
$598$	0.110783	+	0.0458877i	0.00453025	+	0.00187649i
$599$		−	12.2973i		−	0.502456i	−0.967928	−	0.251228i	$-0.919166\pi$
$599$		−	12.2973i		−	0.502456i	0.967928	−	0.251228i	$-0.0808344\pi$
$600$		0			0
$601$	−3.08883	−	7.45710i	−0.125996	−	0.304181i	0.848277	−	0.529553i	$-0.177640\pi$
$601$	−3.08883	−	7.45710i	−0.125996	−	0.304181i	−0.974273	+	0.225372i	$0.927640\pi$
$602$	1.54230	+	3.72345i	0.0628596	+	0.151757i
$603$		0			0
$604$	−0.188811	−	0.188811i	−0.00768260	−	0.00768260i
$605$	−0.249173	+	8.36913i	−0.0101303	+	0.340254i
$606$		0			0
$607$	−9.22388	+	22.2684i	−0.374386	+	0.903847i	0.618610	+	0.785698i	$0.287696\pi$
$607$	−9.22388	+	22.2684i	−0.374386	+	0.903847i	−0.992996	+	0.118149i	$0.962304\pi$
$608$	−10.9139			−0.442619
$609$		0			0
$610$	−3.61527	+	1.37293i	−0.146378	+	0.0555882i
$611$	−0.463369			−0.0187459
$612$		0			0
$613$		−	39.8359i		−	1.60896i	−0.593983	−	0.804478i	$-0.702445\pi$
$613$		−	39.8359i		−	1.60896i	0.593983	−	0.804478i	$-0.297555\pi$
$614$	−2.63850	+	2.63850i	−0.106481	+	0.106481i
$615$		0			0
$616$			3.77867i			0.152247i
$617$	9.87155	−	23.8320i	0.397414	−	0.959442i	−0.590863	−	0.806772i	$-0.701213\pi$
$617$	9.87155	−	23.8320i	0.397414	−	0.959442i	0.988277	−	0.152670i	$-0.0487872\pi$
$618$		0			0
$619$	−3.48155	+	1.44210i	−0.139935	+	0.0579630i	−0.451552	−	0.892245i	$-0.649129\pi$
$619$	−3.48155	+	1.44210i	−0.139935	+	0.0579630i	0.311617	+	0.950208i	$0.399129\pi$
$620$	−1.99468	+	0.757496i	−0.0801085	+	0.0304218i
$621$		0			0
$622$	0.955308	+	2.30632i	0.0383044	+	0.0924749i
$623$	15.1925	−	6.29293i	0.608673	−	0.252121i
$624$		0			0
$625$	−24.8230	−	2.96938i	−0.992921	−	0.118775i
$626$	0.337293	−	0.814297i	0.0134809	−	0.0325459i
$627$		0			0
$628$		−	18.7309i		−	0.747446i
$629$	4.49073	+	23.2489i	0.179057	+	0.926994i
$630$		0			0
$631$	13.6572	−	13.6572i	0.543685	−	0.543685i	−0.380922	−	0.924607i	$-0.624393\pi$
$631$	13.6572	−	13.6572i	0.543685	−	0.543685i	0.924607	+	0.380922i	$0.124393\pi$
$632$	11.6914	+	4.84274i	0.465059	+	0.192634i
$633$		0			0
$634$	2.80813	+	1.16317i	0.111525	+	0.0461952i
$635$	−1.08779	+	36.5364i	−0.0431677	+	1.44990i
$636$		0			0
$637$	0.611602	−	0.611602i	0.0242326	−	0.0242326i
$638$	3.05033	−	3.05033i	0.120764	−	0.120764i
$639$		0			0
$640$	−0.489760	+	16.4499i	−0.0193594	+	0.650239i
$641$	−19.0839	−	7.90483i	−0.753770	−	0.312222i	−0.0274914	−	0.999622i	$-0.508752\pi$
$641$	−19.0839	−	7.90483i	−0.753770	−	0.312222i	−0.726279	+	0.687400i	$0.758752\pi$
$642$		0			0
$643$	26.8106	+	11.1053i	1.05731	+	0.437951i	0.842495	−	0.538704i	$-0.181086\pi$
$643$	26.8106	+	11.1053i	1.05731	+	0.437951i	0.214813	+	0.976655i	$0.431086\pi$
$644$	−5.40890	+	5.40890i	−0.213141	+	0.213141i
$645$		0			0
$646$	−2.15435	−	3.26321i	−0.0847618	−	0.128389i
$647$		−	41.2848i		−	1.62307i	−0.584302	−	0.811536i	$-0.698632\pi$
$647$		−	41.2848i		−	1.62307i	0.584302	−	0.811536i	$-0.301368\pi$
$648$		0			0
$649$	8.34184	−	20.1390i	0.327446	−	0.790524i
$650$	−0.162588	+	0.144298i	−0.00637721	+	0.00565983i
$651$		0			0
$652$	−22.2292	+	9.20763i	−0.870562	+	0.360598i
$653$	−9.39804	−	22.6889i	−0.367774	−	0.887884i	−0.994114	−	0.108335i	$-0.965448\pi$
$653$	−9.39804	−	22.6889i	−0.367774	−	0.887884i	0.626341	−	0.779549i	$-0.284552\pi$
$654$		0			0
$655$	−20.1492	+	7.65182i	−0.787296	+	0.298981i
$656$	20.1217	−	8.33468i	0.785621	−	0.325415i
$657$		0			0
$658$	−0.361647	+	0.873094i	−0.0140985	+	0.0340368i
$659$			17.7024i			0.689588i	0.938678	+	0.344794i	$0.112051\pi$
$659$			17.7024i			0.689588i	−0.938678	+	0.344794i	$0.887949\pi$
$660$		0			0
$661$	10.0305	−	10.0305i	0.390141	−	0.390141i	−0.484597	−	0.874738i	$-0.661034\pi$
$661$	10.0305	−	10.0305i	0.390141	−	0.390141i	0.874738	+	0.484597i	$0.161034\pi$
$662$			4.60333i			0.178914i
$663$		0			0
$664$	8.40629			0.326227
$665$	11.3977	−	4.32835i	0.441982	−	0.167846i
$666$		0			0
$667$	17.7445			0.687072
$668$	3.10566	−	7.49773i	0.120162	−	0.290096i
$669$		0			0
$670$	0.205231	−	6.89325i	0.00792878	−	0.266309i
$671$	13.2335	+	13.2335i	0.510872	+	0.510872i
$672$		0			0
$673$	0.124393	+	0.300312i	0.00479501	+	0.0115762i	0.926259	−	0.376888i	$-0.123006\pi$
$673$	0.124393	+	0.300312i	0.00479501	+	0.0115762i	−0.921464	+	0.388464i	$0.873006\pi$
$674$	1.75668	+	4.24101i	0.0676650	+	0.163358i
$675$		0			0
$676$			25.1354i			0.966746i
$677$	−15.9805	−	6.61933i	−0.614180	−	0.254402i	0.0538347	−	0.998550i	$-0.482856\pi$
$677$	−15.9805	−	6.61933i	−0.614180	−	0.254402i	−0.668014	+	0.744148i	$0.732856\pi$
$678$		0			0
$679$	−3.28995			−0.126257
$680$	−7.68692	+	4.75258i	−0.294780	+	0.182253i
$681$		0			0
$682$	−0.233431	−	0.233431i	−0.00893852	−	0.00893852i
$683$	31.8570	+	13.1956i	1.21898	+	0.504916i	0.897084	−	0.441860i	$-0.145681\pi$
$683$	31.8570	+	13.1956i	1.21898	+	0.504916i	0.321891	+	0.946777i	$0.395681\pi$
$684$		0			0
$685$	10.1284	+	10.7500i	0.386985	+	0.410736i
$686$	−1.62931	−	3.93350i	−0.0622072	−	0.150182i
$687$		0			0
$688$	29.0568	−	29.0568i	1.10778	−	1.10778i
$689$	1.52569	+	1.52569i	0.0581243	+	0.0581243i
$690$		0			0
$691$	16.1221	+	38.9223i	0.613315	+	1.48067i	0.859337	+	0.511409i	$0.170876\pi$
$691$	16.1221	+	38.9223i	0.613315	+	1.48067i	−0.246022	+	0.969264i	$0.579124\pi$
$692$	−2.19154	+	5.29084i	−0.0833098	+	0.201128i
$693$		0			0
$694$	0.483462	−	1.16718i	0.0183520	−	0.0443056i
$695$	−3.64938	−	9.60978i	−0.138429	−	0.364520i
$696$		0			0
$697$	20.4808	+	13.8496i	0.775767	+	0.524591i
$698$			6.08922i			0.230481i
$699$		0			0
$700$	−4.53525	−	13.1049i	−0.171416	−	0.495320i
$701$			29.6266i			1.11898i	0.828836	+	0.559491i	$0.189003\pi$
$701$			29.6266i			1.11898i	−0.828836	+	0.559491i	$0.810997\pi$
$702$		0			0
$703$	20.2146	−	8.37317i	0.762409	−	0.315800i
$704$	16.3029	−	6.75289i	0.614439	−	0.254509i
$705$		0			0
$706$	3.08593	+	3.08593i	0.116140	+	0.116140i
$707$	0.487914	+	1.17793i	0.0183499	+	0.0443005i
$708$		0			0
$709$	15.0352	+	6.22777i	0.564657	+	0.233889i	0.646706	−	0.762740i	$-0.276146\pi$
$709$	15.0352	+	6.22777i	0.564657	+	0.233889i	−0.0820483	+	0.996628i	$0.526146\pi$
$710$	2.79015	−	6.20682i	0.104713	−	0.232938i
$711$		0			0
$712$	7.96469	+	7.96469i	0.298489	+	0.298489i
$713$		−	1.35793i		−	0.0508547i
$714$		0			0
$715$	0.959530	+	0.431337i	0.0358844	+	0.0161311i
$716$	31.8979	−	31.8979i	1.19208	−	1.19208i
$717$		0			0
$718$	−0.502294			−0.0187454
$719$	29.0292	+	12.0243i	1.08261	+	0.448430i	0.851423	−	0.524480i	$-0.175740\pi$
$719$	29.0292	+	12.0243i	1.08261	+	0.448430i	0.231184	+	0.972910i	$0.425740\pi$
$720$		0			0
$721$	−0.485411	+	0.201064i	−0.0180776	+	0.00748800i
$722$	0.789295	−	0.789295i	0.0293745	−	0.0293745i
$723$		0			0
$724$	20.4483	−	8.46994i	0.759953	−	0.314783i
$725$	−14.0569	+	28.9354i	−0.522062	+	1.07463i
$726$		0			0
$727$	−21.6544			−0.803118			−0.401559	−	0.915833i	$-0.631532\pi$
$727$	−21.6544			−0.803118			−0.401559	+	0.915833i	$0.631532\pi$
$728$	−0.226372	−	0.0937664i	−0.00838991	−	0.00347521i
$729$		0			0
$730$	−3.57462	+	7.95190i	−0.132303	+	0.294313i
$731$	45.7004	+	9.35389i	1.69029	+	0.345966i
$732$		0			0
$733$	−22.2422	−	22.2422i	−0.821534	−	0.821534i	0.164794	−	0.986328i	$-0.447304\pi$
$733$	−22.2422	−	22.2422i	−0.821534	−	0.821534i	−0.986328	+	0.164794i	$0.947304\pi$
$734$	−3.08678	+	7.45215i	−0.113935	+	0.275064i
$735$		0			0
$736$	−7.29917	−	3.02342i	−0.269051	−	0.111445i
$737$	−30.8337	+	12.7717i	−1.13577	+	0.470452i
$738$		0			0
$739$	−9.68961	−	9.68961i	−0.356438	−	0.356438i	0.506060	−	0.862498i	$-0.331101\pi$
$739$	−9.68961	−	9.68961i	−0.356438	−	0.356438i	−0.862498	+	0.506060i	$0.831101\pi$
$740$	−8.83552	−	23.2662i	−0.324800	−	0.855283i
$741$		0			0
$742$	4.06552	−	1.68400i	0.149250	−	0.0618214i
$743$	6.20770	−	14.9867i	0.227738	−	0.549809i	−0.768163	−	0.640254i	$-0.778829\pi$
$743$	6.20770	−	14.9867i	0.227738	−	0.549809i	0.995901	+	0.0904453i	$0.0288290\pi$
$744$		0			0
$745$	17.8492	+	18.9447i	0.653945	+	0.694079i
$746$	3.62775	−	3.62775i	0.132821	−	0.132821i
$747$		0			0
$748$	17.8300	+	12.0570i	0.651929	+	0.440849i
$749$	−9.51315			−0.347603
$750$		0			0
$751$	−4.26568	+	10.2983i	−0.155657	+	0.375789i	−0.982400	−	0.186791i	$-0.940191\pi$
$751$	−4.26568	+	10.2983i	−0.155657	+	0.375789i	0.826743	+	0.562580i	$0.190191\pi$
$752$	9.63558			0.351373
$753$		0			0
$754$	0.107046	+	0.258432i	0.00389838	+	0.00941153i
$755$	−0.00916835	+	0.307944i	−0.000333671	+	0.0112072i
$756$		0			0
$757$	−14.0667	+	14.0667i	−0.511262	+	0.511262i	−0.914913	−	0.403651i	$-0.867741\pi$
$757$	−14.0667	+	14.0667i	−0.511262	+	0.511262i	0.403651	+	0.914913i	$0.367741\pi$
$758$	−1.58149	−	3.81804i	−0.0574421	−	0.138678i
$759$		0			0
$760$	5.72673	+	6.07820i	0.207730	+	0.220479i
$761$			45.4255i			1.64667i	0.567553	+	0.823337i	$0.307890\pi$
$761$			45.4255i			1.64667i	−0.567553	+	0.823337i	$0.692110\pi$
$762$		0			0
$763$	8.94498	+	8.94498i	0.323830	+	0.323830i
$764$	5.97306			0.216098
$765$		0			0
$766$	5.78284			0.208942
$767$	0.999485	+	0.999485i	0.0360893	+	0.0360893i
$768$		0			0
$769$		−	5.98158i		−	0.215701i	−0.994167	−	0.107851i	$-0.965603\pi$
$769$		−	5.98158i		−	0.215701i	0.994167	−	0.107851i	$-0.0343968\pi$
$770$	1.56163	−	1.47133i	0.0562771	−	0.0530230i
$771$		0			0
$772$	11.8558	+	28.6225i	0.426701	+	1.03015i
$773$	9.29889	−	9.29889i	0.334458	−	0.334458i	−0.519819	−	0.854277i	$-0.674001\pi$
$773$	9.29889	−	9.29889i	0.334458	−	0.334458i	0.854277	+	0.519819i	$0.174001\pi$
$774$		0			0
$775$	2.21432	+	1.07573i	0.0795407	+	0.0386413i
$776$	−0.862382	−	2.08197i	−0.0309577	−	0.0747385i
$777$		0			0
$778$	9.12654			0.327202
$779$	8.74284	−	21.1071i	0.313245	−	0.756240i
$780$		0			0
$781$	−32.9328			−1.17843
$782$	−0.536831	−	2.77922i	−0.0191970	−	0.0993847i
$783$		0			0
$784$	−12.7180	+	12.7180i	−0.454215	+	0.454215i
$785$	−15.7295	+	14.8200i	−0.561412	+	0.528948i
$786$		0			0
$787$	−9.83375	+	23.7408i	−0.350535	+	0.846267i	0.646019	+	0.763322i	$0.276433\pi$
$787$	−9.83375	+	23.7408i	−0.350535	+	0.846267i	−0.996554	+	0.0829458i	$0.973567\pi$
$788$	−19.1112	+	7.91611i	−0.680808	+	0.282000i
$789$		0			0
$790$	−2.55099	−	6.71742i	−0.0907601	−	0.238995i
$791$	−5.78130	−	5.78130i	−0.205560	−	0.205560i
$792$		0			0
$793$	−1.12117	+	0.464405i	−0.0398140	+	0.0164915i
$794$	2.25650	+	0.934673i	0.0800802	+	0.0331703i
$795$		0			0
$796$	11.7474	−	28.3607i	0.416375	−	1.00522i
$797$	35.6691	+	35.6691i	1.26347	+	1.26347i	0.949402	+	0.314064i	$0.101691\pi$
$797$	35.6691	+	35.6691i	1.26347	+	1.26347i	0.314064	+	0.949402i	$0.398309\pi$
$798$		0			0
$799$	6.02647	+	9.12834i	0.213201	+	0.322937i
$800$	10.7125	−	9.50739i	0.378743	−	0.336137i
$801$		0			0
$802$	4.94200	+	2.04704i	0.174508	+	0.0722836i
$803$	42.1920			1.48892
$804$		0			0
$805$	8.82174	+	0.262648i	0.310926	+	0.00925713i
$806$	0.0197769	−	0.00819184i	0.000696610	−	0.000288545i
$807$		0			0
$808$	−0.617532	+	0.617532i	−0.0217247	+	0.0217247i
$809$	8.50125	−	3.52133i	0.298888	−	0.123803i	−0.228200	−	0.973614i	$-0.573284\pi$
$809$	8.50125	−	3.52133i	0.298888	−	0.123803i	0.527088	+	0.849811i	$0.323284\pi$
$810$		0			0
$811$	9.89831	+	4.10002i	0.347577	+	0.143971i	0.549640	−	0.835401i	$-0.314765\pi$
$811$	9.89831	+	4.10002i	0.347577	+	0.143971i	−0.202064	+	0.979372i	$0.564765\pi$
$812$	−17.8442			−0.626210
$813$		0			0
$814$	2.72276	−	2.72276i	0.0954327	−	0.0954327i
$815$	25.3200	+	11.3821i	0.886922	+	0.398698i
$816$		0			0
$817$		−	43.1048i		−	1.50805i
$818$	5.50452	+	5.50452i	0.192461	+	0.192461i
$819$		0			0
$820$	−23.7015	−	10.6545i	−0.827692	−	0.372073i
$821$	−26.0334	−	10.7834i	−0.908572	−	0.376343i	−0.121062	−	0.992645i	$-0.538630\pi$
$821$	−26.0334	−	10.7834i	−0.908572	−	0.376343i	−0.787510	+	0.616302i	$0.788630\pi$
$822$		0			0
$823$	−13.5250	−	32.6522i	−0.471452	−	1.13819i	−0.963522	−	0.267630i	$-0.913760\pi$
$823$	−13.5250	−	32.6522i	−0.471452	−	1.13819i	0.492070	−	0.870556i	$-0.336240\pi$
$824$	−0.254478	−	0.254478i	−0.00886516	−	0.00886516i
$825$		0			0
$826$	2.66333	−	1.10319i	0.0926692	−	0.0383848i
$827$	−36.2562	+	15.0178i	−1.26075	+	0.522221i	−0.910140	−	0.414300i	$-0.864026\pi$
$827$	−36.2562	+	15.0178i	−1.26075	+	0.522221i	−0.350612	+	0.936521i	$0.614026\pi$
$828$		0			0
$829$			17.4130i			0.604779i	0.953184	+	0.302389i	$0.0977843\pi$
$829$			17.4130i			0.604779i	−0.953184	+	0.302389i	$0.902216\pi$
$830$	−3.27322	−	3.47411i	−0.113615	−	0.120588i
$831$		0			0
$832$			1.14424i			0.0396695i
$833$	−20.0029	−	4.09416i	−0.693059	−	0.141854i
$834$		0			0
$835$	−8.75353	+	3.32422i	−0.302928	+	0.115039i
$836$	7.61125	−	18.3752i	0.263241	−	0.635519i
$837$		0			0
$838$	1.93812	−	4.67903i	0.0669511	−	0.161634i
$839$	10.2960	+	24.8566i	0.355456	+	0.858147i	0.995927	+	0.0901643i	$0.0287392\pi$
$839$	10.2960	+	24.8566i	0.355456	+	0.858147i	−0.640471	+	0.767982i	$0.721261\pi$
$840$		0			0
$841$	8.76397	+	8.76397i	0.302206	+	0.302206i
$842$	0.318338	−	0.318338i	0.0109707	−	0.0109707i
$843$		0			0
$844$	3.64865	+	8.80862i	0.125592	+	0.303205i
$845$	21.1078	−	19.8872i	0.726129	−	0.684141i
$846$		0			0
$847$	4.95073	+	2.05066i	0.170109	+	0.0704615i
$848$	−31.7262	−	31.7262i	−1.08948	−	1.08948i
$849$		0			0
$850$	4.95724	+	1.32626i	0.170032	+	0.0454904i
$851$	15.8390			0.542954
$852$		0			0
$853$	15.1019	+	6.25540i	0.517078	+	0.214181i	0.625933	−	0.779877i	$-0.284718\pi$
$853$	15.1019	+	6.25540i	0.517078	+	0.214181i	−0.108855	+	0.994058i	$0.534718\pi$
$854$			2.47501i			0.0846930i
$855$		0			0
$856$	−2.49365	−	6.02020i	−0.0852311	−	0.205766i
$857$	1.47991	+	3.57282i	0.0505527	+	0.122045i	0.947138	−	0.320825i	$-0.103960\pi$
$857$	1.47991	+	3.57282i	0.0505527	+	0.122045i	−0.896586	+	0.442870i	$0.853960\pi$
$858$		0			0
$859$	27.6000	+	27.6000i	0.941701	+	0.941701i	0.998392	−	0.0566905i	$-0.0180548\pi$
$859$	27.6000	+	27.6000i	0.941701	+	0.941701i	−0.0566905	+	0.998392i	$0.518055\pi$
$860$	−49.0075	−	1.45909i	−1.67114	−	0.0497546i
$861$		0			0
$862$	−1.58734	+	3.83218i	−0.0540650	+	0.130524i
$863$	22.1279			0.753243			0.376621	−	0.926367i	$-0.377086\pi$
$863$	22.1279			0.753243			0.376621	+	0.926367i	$0.377086\pi$
$864$		0			0
$865$	6.17700	−	2.34576i	0.210024	−	0.0797583i
$866$	−4.06193			−0.138030
$867$		0			0
$868$			1.36556i			0.0463500i
$869$	−24.5886	+	24.5886i	−0.834112	+	0.834112i
$870$		0			0
$871$		−	2.16411i		−	0.0733280i
$872$	−3.31593	+	8.00536i	−0.112292	+	0.271096i
$873$		0			0
$874$	−2.41650	+	1.00095i	−0.0817393	+	0.0338575i
$875$	−7.41673	+	14.1772i	−0.250731	+	0.479277i
$876$		0			0
$877$	−7.55317	−	18.2350i	−0.255052	−	0.615751i	0.743546	−	0.668685i	$-0.233143\pi$
$877$	−7.55317	−	18.2350i	−0.255052	−	0.615751i	−0.998598	+	0.0529342i	$0.983143\pi$
$878$	−5.52560	+	2.28878i	−0.186480	+	0.0772425i
$879$		0			0
$880$	−19.9530	−	8.96949i	−0.672617	−	0.302362i
$881$	−4.37489	+	10.5619i	−0.147394	+	0.355840i	−0.980283	−	0.197600i	$-0.936685\pi$
$881$	−4.37489	+	10.5619i	−0.147394	+	0.355840i	0.832889	+	0.553440i	$0.186685\pi$
$882$		0			0
$883$		−	13.2658i		−	0.446431i	−0.974769	−	0.223216i	$-0.928345\pi$
$883$		−	13.2658i		−	0.446431i	0.974769	−	0.223216i	$-0.0716554\pi$
$884$	−1.16476	+	0.768967i	−0.0391751	+	0.0258631i
$885$		0			0
$886$	−3.74477	+	3.74477i	−0.125808	+	0.125808i
$887$	28.2772	+	11.7128i	0.949455	+	0.393277i	0.803026	−	0.595944i	$-0.203222\pi$
$887$	28.2772	+	11.7128i	0.949455	+	0.393277i	0.146429	+	0.989221i	$0.453222\pi$
$888$		0			0
$889$	21.6130	+	8.95239i	0.724876	+	0.300254i
$890$	0.190334	−	6.39288i	0.00638001	−	0.214290i
$891$		0			0
$892$	13.7642	−	13.7642i	0.460858	−	0.460858i
$893$	7.14704	−	7.14704i	0.239167	−	0.239167i
$894$		0			0
$895$	−52.0245	−	1.54891i	−1.73899	−	0.0517745i
$896$	9.73087	+	4.03066i	0.325086	+	0.134655i
$897$		0			0
$898$	6.71539	+	2.78161i	0.224096	+	0.0928234i
$899$	2.23993	−	2.23993i	0.0747059	−	0.0747059i
$900$		0			0
$901$	10.2132	−	49.8989i	0.340252	−	1.66237i
$902$		−	4.02056i		−	0.133870i
$903$		0			0
$904$	2.14315	−	5.17401i	0.0712799	−	0.172085i
$905$	−23.2915	−	10.4702i	−0.774235	−	0.348042i
$906$		0			0
$907$	−0.707707	+	0.293142i	−0.0234990	+	0.00973362i	−0.394402	−	0.918938i	$-0.629048\pi$
$907$	−0.707707	+	0.293142i	−0.0234990	+	0.00973362i	0.370903	+	0.928672i	$0.379048\pi$
$908$	−3.32066	−	8.01678i	−0.110200	−	0.266046i
$909$		0			0
$910$	0.0493929	+	0.130064i	0.00163736	+	0.00431159i
$911$	−7.79323	+	3.22806i	−0.258201	+	0.106951i	−0.508029	−	0.861340i	$-0.669626\pi$
$911$	−7.79323	+	3.22806i	−0.258201	+	0.106951i	0.249828	+	0.968290i	$0.419626\pi$
$912$		0			0
$913$	−8.83979	+	21.3412i	−0.292555	+	0.706289i
$914$		−	0.258405i		−	0.00854727i
$915$		0			0
$916$	−1.64169	+	1.64169i	−0.0542430	+	0.0542430i
$917$			13.7941i			0.455522i
$918$		0			0
$919$	−13.0143			−0.429302			−0.214651	−	0.976691i	$-0.568861\pi$
$919$	−13.0143			−0.429302			−0.214651	+	0.976691i	$0.568861\pi$
$920$	2.14620	+	5.65150i	0.0707581	+	0.186324i
$921$		0			0
$922$	0.0174735			0.000575458
$923$	0.817217	−	1.97294i	0.0268990	−	0.0649400i
$924$		0			0
$925$	−12.5474	+	25.8280i	−0.412556	+	0.849221i
$926$	−7.05190	−	7.05190i	−0.231740	−	0.231740i
$927$		0			0
$928$	−7.05297	−	17.0274i	−0.231525	−	0.558951i
$929$	−9.89198	−	23.8814i	−0.324545	−	0.783522i	−0.998979	−	0.0451859i	$-0.985612\pi$
$929$	−9.89198	−	23.8814i	−0.324545	−	0.783522i	0.674433	−	0.738336i	$-0.264388\pi$
$930$		0			0
$931$			18.8668i			0.618335i
$932$	45.5764	+	18.8784i	1.49291	+	0.618382i
$933$		0			0
$934$	5.65220			0.184946
$935$	−3.98211	−	24.5125i	−0.130229	−	0.801646i
$936$		0			0
$937$	0.615699	+	0.615699i	0.0201140	+	0.0201140i	0.717092	−	0.696978i	$-0.245473\pi$
$937$	0.615699	+	0.615699i	0.0201140	+	0.0201140i	−0.696978	+	0.717092i	$0.745473\pi$
$938$	−4.07768	−	1.68903i	−0.133141	−	0.0551488i
$939$		0			0
$940$	−7.88381	−	8.36767i	−0.257142	−	0.272923i
$941$	−20.4139	−	49.2834i	−0.665473	−	1.60659i	−0.789100	−	0.614265i	$-0.789453\pi$
$941$	−20.4139	−	49.2834i	−0.665473	−	1.60659i	0.123627	−	0.992329i	$-0.460547\pi$
$942$		0			0
$943$	11.6943	−	11.6943i	0.380820	−	0.380820i
$944$	−20.7839	−	20.7839i	−0.676458	−	0.676458i
$945$		0			0
$946$	−2.90295	−	7.00834i	−0.0943830	−	0.227861i
$947$	−5.21997	+	12.6021i	−0.169626	+	0.409514i	−0.985717	−	0.168409i	$-0.946137\pi$
$947$	−5.21997	+	12.6021i	−0.169626	+	0.409514i	0.816091	+	0.577924i	$0.196137\pi$
$948$		0			0
$949$	−1.04698	+	2.52764i	−0.0339865	+	0.0820506i
$950$	0.282105	−	4.73343i	0.00915269	−	0.153573i
$951$		0			0
$952$	1.09695	+	5.67902i	0.0355525	+	0.184058i
$953$		−	10.3660i		−	0.335788i	−0.985805	−	0.167894i	$-0.946303\pi$
$953$		−	10.3660i		−	0.335788i	0.985805	−	0.167894i	$-0.0536967\pi$
$954$		0			0
$955$	−4.72591	−	5.01595i	−0.152927	−	0.162312i
$956$			12.0431i			0.389502i
$957$		0			0
$958$	−5.34925	+	2.21573i	−0.172827	+	0.0715871i
$959$	8.73313	−	3.61738i	0.282007	−	0.116811i
$960$		0			0
$961$	21.7489	+	21.7489i	0.701577	+	0.701577i
$962$	0.0955505	+	0.230679i	0.00308067	+	0.00743740i
$963$		0			0
$964$	−47.9937	−	19.8796i	−1.54577	−	0.640280i
$965$	14.6557	−	32.6023i	0.471784	−	1.04951i
$966$		0			0
$967$	−10.1327	−	10.1327i	−0.325847	−	0.325847i	0.525158	−	0.851005i	$-0.324006\pi$
$967$	−10.1327	−	10.1327i	−0.325847	−	0.325847i	−0.851005	+	0.525158i	$0.824006\pi$
$968$			3.67050i			0.117974i
$969$		0			0
$970$	−0.524635	+	1.16708i	−0.0168450	+	0.0374725i
$971$	−21.0309	+	21.0309i	−0.674913	+	0.674913i	−0.958845	−	0.283931i	$-0.908361\pi$
$971$	−21.0309	+	21.0309i	−0.674913	+	0.674913i	0.283931	+	0.958845i	$0.408361\pi$
$972$		0			0
$973$	−6.57882			−0.210907
$974$	3.88929	+	1.61100i	0.124621	+	0.0516197i
$975$		0			0
$976$	23.3144	−	9.65712i	0.746274	−	0.309117i
$977$	26.2437	−	26.2437i	0.839611	−	0.839611i	−0.149196	−	0.988808i	$-0.547669\pi$
$977$	26.2437	−	26.2437i	0.839611	−	0.839611i	0.988808	+	0.149196i	$0.0476686\pi$
$978$		0			0
$979$	−28.5955	+	11.8446i	−0.913916	+	0.378556i
$980$	21.4504	+	0.638638i	0.685207	+	0.0204006i
$981$		0			0
$982$	−5.24217			−0.167284
$983$	−42.9257	−	17.7804i	−1.36912	−	0.567107i	−0.427568	−	0.903983i	$-0.640629\pi$
$983$	−42.9257	−	17.7804i	−1.36912	−	0.567107i	−0.941549	+	0.336877i	$0.890629\pi$
$984$		0			0
$985$	21.7685	+	9.78559i	0.693602	+	0.311795i
$986$	3.69887	−	5.46991i	0.117796	−	0.174197i
$987$		0			0
$988$	0.911949	+	0.911949i	0.0290130	+	0.0290130i
$989$	11.9411	−	28.8283i	0.379703	−	0.916685i
$990$		0			0
$991$	−40.9290	−	16.9534i	−1.30015	−	0.538541i	−0.378158	−	0.925741i	$-0.623442\pi$
$991$	−40.9290	−	16.9534i	−1.30015	−	0.538541i	−0.921996	+	0.387200i	$0.873442\pi$
$992$	−1.30304	+	0.539738i	−0.0413717	+	0.0171367i
$993$		0			0
$994$	−3.07965	−	3.07965i	−0.0976806	−	0.0976806i
$995$	−33.1108	+	12.5741i	−1.04968	+	0.398625i
$996$		0			0
$997$	22.7561	−	9.42589i	0.720693	−	0.298521i	0.00797178	−	0.999968i	$-0.497462\pi$
$997$	22.7561	−	9.42589i	0.720693	−	0.298521i	0.712721	+	0.701447i	$0.247462\pi$
$998$	2.14575	−	5.18029i	0.0679224	−	0.163979i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	765.2.bh.b.739.3		24
3.2	odd	2		85.2.m.a.59.4	yes	24
5.4	even	2	inner	765.2.bh.b.739.4		24
15.2	even	4		425.2.m.e.76.3		24
15.8	even	4		425.2.m.e.76.4		24
15.14	odd	2		85.2.m.a.59.3	yes	24
17.15	even	8	inner	765.2.bh.b.559.4		24
51.32	odd	8		85.2.m.a.49.3	✓	24
51.41	even	16		1445.2.b.i.579.12		24
51.44	even	16		1445.2.b.i.579.11		24
85.49	even	8	inner	765.2.bh.b.559.3		24
255.32	even	8		425.2.m.e.151.3		24
255.44	even	16		1445.2.b.i.579.14		24
255.83	even	8		425.2.m.e.151.4		24
255.92	odd	16		7225.2.a.by.1.14		24
255.134	odd	8		85.2.m.a.49.4	yes	24
255.143	odd	16		7225.2.a.by.1.11		24
255.194	even	16		1445.2.b.i.579.13		24
255.197	odd	16		7225.2.a.by.1.13		24
255.248	odd	16		7225.2.a.by.1.12		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.m.a.49.3	✓	24	51.32	odd	8
85.2.m.a.49.4	yes	24	255.134	odd	8
85.2.m.a.59.3	yes	24	15.14	odd	2
85.2.m.a.59.4	yes	24	3.2	odd	2
425.2.m.e.76.3		24	15.2	even	4
425.2.m.e.76.4		24	15.8	even	4
425.2.m.e.151.3		24	255.32	even	8
425.2.m.e.151.4		24	255.83	even	8
765.2.bh.b.559.3		24	85.49	even	8	inner
765.2.bh.b.559.4		24	17.15	even	8	inner
765.2.bh.b.739.3		24	1.1	even	1	trivial
765.2.bh.b.739.4		24	5.4	even	2	inner
1445.2.b.i.579.11		24	51.44	even	16
1445.2.b.i.579.12		24	51.41	even	16
1445.2.b.i.579.13		24	255.194	even	16
1445.2.b.i.579.14		24	255.44	even	16
7225.2.a.by.1.11		24	255.143	odd	16
7225.2.a.by.1.12		24	255.248	odd	16
7225.2.a.by.1.13		24	255.197	odd	16
7225.2.a.by.1.14		24	255.92	odd	16

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 765 = 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	765.bh (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.176012 - 0.176012i) q^{2} -1.93804i q^{4} +(-1.62749 + 1.53338i) q^{5} +(0.547653 + 1.32215i) q^{7} +(-0.693142 + 0.693142i) q^{8} +(0.556352 + 0.0165642i) q^{10} +(-1.03080 - 2.48857i) q^{11} +0.174664 q^{13} +(0.136321 - 0.329108i) q^{14} -3.63208 q^{16} +(-2.27165 - 3.44088i) q^{17} +(-2.69404 + 2.69404i) q^{19} +(2.97176 + 3.15415i) q^{20} +(-0.256585 + 0.619452i) q^{22} +(-2.54807 + 1.05544i) q^{23} +(0.297464 - 4.99114i) q^{25} +(-0.0307430 - 0.0307430i) q^{26} +(2.56238 - 1.06137i) q^{28} +(-5.94408 - 2.46212i) q^{29} +(-0.188417 + 0.454879i) q^{31} +(2.02557 + 2.02557i) q^{32} +(-0.205798 + 1.00547i) q^{34} +(-2.91867 - 1.31203i) q^{35} +(-5.30576 - 2.19772i) q^{37} +0.948365 q^{38} +(0.0652303 - 2.19094i) q^{40} +(-5.54000 + 2.29474i) q^{41} +(-8.00004 + 8.00004i) q^{43} +(-4.82296 + 1.99773i) q^{44} +(0.634261 + 0.262720i) q^{46} -2.65291 q^{47} +(3.50159 - 3.50159i) q^{49} +(-0.930858 + 0.826143i) q^{50} -0.338506i q^{52} +(8.73501 + 8.73501i) q^{53} +(5.49356 + 2.46952i) q^{55} +(-1.29604 - 0.536837i) q^{56} +(0.612867 + 1.47959i) q^{58} +(5.72232 + 5.72232i) q^{59} +(-6.41902 + 2.65884i) q^{61} +(0.113228 - 0.0469005i) q^{62} +6.55110i q^{64} +(-0.284265 + 0.267828i) q^{65} -12.3901i q^{67} +(-6.66855 + 4.40254i) q^{68} +(0.282788 + 0.744653i) q^{70} +(4.67878 - 11.2956i) q^{71} +(-5.99425 + 14.4714i) q^{73} +(0.547052 + 1.32070i) q^{74} +(5.22115 + 5.22115i) q^{76} +(2.72575 - 2.72575i) q^{77} +(-4.94031 - 11.9270i) q^{79} +(5.91118 - 5.56937i) q^{80} +(1.37901 + 0.571204i) q^{82} +(-6.06390 - 6.06390i) q^{83} +(8.97327 + 2.11669i) q^{85} +2.81621 q^{86} +(2.43943 + 1.01044i) q^{88} -11.4907i q^{89} +(0.0956555 + 0.230933i) q^{91} +(2.04549 + 4.93826i) q^{92} +(0.466944 + 0.466944i) q^{94} +(0.253531 - 8.51552i) q^{95} +(-0.879757 + 2.12392i) q^{97} -1.23264 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 16 q^{10} + 24 q^{14} + 8 q^{16} - 24 q^{19} + 8 q^{20} + 16 q^{25} + 16 q^{26} - 24 q^{29} - 24 q^{31} + 8 q^{34} - 8 q^{35} + 16 q^{40} + 48 q^{41} - 72 q^{44} - 16 q^{46} + 48 q^{49} - 16 q^{50}+ \cdots + 88 q^{95}+O(q^{100}) \) 24 * q - 16 * q^10 + 24 * q^14 + 8 * q^16 - 24 * q^19 + 8 * q^20 + 16 * q^25 + 16 * q^26 - 24 * q^29 - 24 * q^31 + 8 * q^34 - 8 * q^35 + 16 * q^40 + 48 * q^41 - 72 * q^44 - 16 * q^46 + 48 * q^49 - 16 * q^50 - 24 * q^56 + 48 * q^59 + 16 * q^61 - 24 * q^65 + 32 * q^70 - 16 * q^71 + 64 * q^74 - 24 * q^76 - 72 * q^79 + 64 * q^80 - 24 * q^85 - 8 * q^91 - 40 * q^94 + 88 * q^95

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