LMFDB - Embedded newform 645.2.bn.b.491.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [645,2,Mod(26,645)] 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("645.26"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(645, base_ring=CyclotomicField(42)) chi = DirichletCharacter(H, H._module([21, 0, 17])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 645 = 3 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	645.bn (of order $42$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [348,0,0,-56,29] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$5.15035093037$
Analytic rank:	$0$
Dimension:	$348$
Relative dimension:	$29$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			491.14
Character	$\chi$	$=$	645.491
Dual form			645.2.bn.b.356.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0334865 + 0.0161262i) q^{2} +(-0.165184 + 1.72416i) q^{3} +(-1.24612 - 1.56258i) q^{4} +(-0.733052 + 0.680173i) q^{5} +(-0.0333356 + 0.0550721i) q^{6} +(-3.57076 - 2.06158i) q^{7} +(-0.0330705 - 0.144891i) q^{8} +(-2.94543 - 0.569605i) q^{9} +(-0.0355160 + 0.0109552i) q^{10} +(2.21451 + 1.76601i) q^{11} +(2.89998 - 1.89039i) q^{12} +(4.57487 + 1.41116i) q^{13} +(-0.0863266 - 0.126618i) q^{14} +(-1.05164 - 1.37625i) q^{15} +(-0.888240 + 3.89163i) q^{16} +(5.46398 - 5.88877i) q^{17} +(-0.0894464 - 0.0665728i) q^{18} +(4.77784 + 1.87516i) q^{19} +(1.97630 + 0.297879i) q^{20} +(4.14431 - 5.81600i) q^{21} +(0.0456770 + 0.0948492i) q^{22} +(-0.0751105 + 0.498326i) q^{23} +(0.255278 - 0.0330850i) q^{24} +(0.0747301 - 0.997204i) q^{25} +(0.130440 + 0.121030i) q^{26} +(1.46863 - 4.98429i) q^{27} +(1.22820 + 8.14858i) q^{28} +(6.70784 - 4.57333i) q^{29} +(-0.0130219 - 0.0630447i) q^{30} +(-0.491251 - 6.55529i) q^{31} +(-0.277824 + 0.348381i) q^{32} +(-3.41068 + 3.52644i) q^{33} +(0.277933 - 0.109081i) q^{34} +(4.01978 - 0.917489i) q^{35} +(2.78030 + 5.31227i) q^{36} +(-2.76472 + 1.59621i) q^{37} +(0.129754 + 0.139841i) q^{38} +(-3.18876 + 7.65469i) q^{39} +(0.122793 + 0.0837192i) q^{40} +(0.579505 - 1.20335i) q^{41} +(0.232569 - 0.127925i) q^{42} +(-4.00283 + 5.19397i) q^{43} -5.66101i q^{44} +(2.54658 - 1.58585i) q^{45} +(-0.0105513 + 0.0154759i) q^{46} +(-3.38840 + 2.70216i) q^{47} +(-6.56306 - 2.17430i) q^{48} +(5.00021 + 8.66062i) q^{49} +(0.0185836 - 0.0321877i) q^{50} +(9.25059 + 10.3935i) q^{51} +(-3.49578 - 8.90709i) q^{52} +(-3.59808 - 11.6647i) q^{53} +(0.129557 - 0.143223i) q^{54} +(-2.82454 + 0.211670i) q^{55} +(-0.180618 + 0.585549i) q^{56} +(-4.02230 + 7.92799i) q^{57} +(0.298372 - 0.0449724i) q^{58} +(-2.63150 - 0.600622i) q^{59} +(-0.840041 + 3.35824i) q^{60} +(5.83918 + 0.437586i) q^{61} +(0.0892619 - 0.227436i) q^{62} +(9.34313 + 8.10615i) q^{63} +(7.17790 - 3.45669i) q^{64} +(-4.31345 + 2.07725i) q^{65} +(-0.171080 + 0.0630867i) q^{66} +(-0.534035 + 1.36070i) q^{67} +(-16.0105 - 1.19982i) q^{68} +(-0.846784 - 0.211818i) q^{69} +(0.149404 + 0.0341005i) q^{70} +(13.1344 - 1.97969i) q^{71} +(0.0148759 + 0.445604i) q^{72} +(-0.945017 + 3.06367i) q^{73} +(-0.118322 + 0.00886699i) q^{74} +(1.70699 + 0.293568i) q^{75} +(-3.02365 - 9.80245i) q^{76} +(-4.26670 - 10.8714i) q^{77} +(-0.230222 + 0.204906i) q^{78} +(0.672671 - 1.16510i) q^{79} +(-1.99586 - 3.45693i) q^{80} +(8.35110 + 3.35546i) q^{81} +(0.0388111 - 0.0309509i) q^{82} +(6.38194 - 9.36059i) q^{83} +(-14.2523 + 0.771596i) q^{84} +8.03322i q^{85} +(-0.217800 + 0.109377i) q^{86} +(6.77710 + 12.3208i) q^{87} +(0.182645 - 0.379266i) q^{88} +(4.17178 + 2.84427i) q^{89} +(0.110850 - 0.0120377i) q^{90} +(-13.4265 - 14.4704i) q^{91} +(0.872272 - 0.503606i) q^{92} +(11.3835 + 0.235834i) q^{93} +(-0.157041 + 0.0358437i) q^{94} +(-4.77784 + 1.87516i) q^{95} +(-0.554771 - 0.536559i) q^{96} +(-3.25397 + 4.08035i) q^{97} +(0.0277762 + 0.370648i) q^{98} +(-5.51675 - 6.46306i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 348 q - 56 q^{4} + 29 q^{5} - 4 q^{6} - 3 q^{7} - 8 q^{9} - 7 q^{12} + 5 q^{13} - 42 q^{14} - 7 q^{15} - 68 q^{16} - 22 q^{18} - 30 q^{19} + 28 q^{20} + 4 q^{21} - 42 q^{22} + 6 q^{23} + 9 q^{24} + 29 q^{25}+ \cdots - q^{99}+O(q^{100}) $ 348 * q - 56 * q^4 + 29 * q^5 - 4 * q^6 - 3 * q^7 - 8 * q^9 - 7 * q^12 + 5 * q^13 - 42 * q^14 - 7 * q^15 - 68 * q^16 - 22 * q^18 - 30 * q^19 + 28 * q^20 + 4 * q^21 - 42 * q^22 + 6 * q^23 + 9 * q^24 + 29 * q^25 + 182 * q^26 + 6 * q^27 + 18 * q^28 + 2 * q^29 + 2 * q^30 + 72 * q^31 - 23 * q^33 - 84 * q^34 - 21 * q^35 + 56 * q^36 - 39 * q^37 - 4 * q^39 - 84 * q^42 + 6 * q^43 + 4 * q^45 - 94 * q^46 - 28 * q^47 - 72 * q^48 + 175 * q^49 + 103 * q^51 - 56 * q^52 + 94 * q^53 + 22 * q^54 - 90 * q^56 + 74 * q^57 - 40 * q^58 - 7 * q^60 + 30 * q^61 - 104 * q^62 + q^63 - 76 * q^64 - 10 * q^65 - 22 * q^66 + 9 * q^67 + 98 * q^68 - 244 * q^69 - 8 * q^71 + 85 * q^72 - 75 * q^73 - 42 * q^74 - 14 * q^75 + 30 * q^76 - 16 * q^77 + 44 * q^78 + 20 * q^79 - 148 * q^80 - 136 * q^81 - 30 * q^83 - 124 * q^84 + 38 * q^86 + 42 * q^87 + 42 * q^88 - 102 * q^89 - 82 * q^90 - 13 * q^91 + 24 * q^92 - 167 * q^93 - 56 * q^94 + 30 * q^95 - 494 * q^96 - 64 * q^97 - 12 * q^98 - q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/645\mathbb{Z}\right)^\times$.

$n$	$46$	$431$	$517$
$\chi(n)$	$e\left(\frac{29}{42}\right)$	$-1$	$1$

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 $

$2$	0.0334865	+	0.0161262i	0.0236785	+	0.0114030i	0.445686	−	0.895190i	$-0.352960\pi$
$2$	0.0334865	+	0.0161262i	0.0236785	+	0.0114030i	−0.422007	+	0.906593i	$0.638674\pi$
$3$	−0.165184	+	1.72416i	−0.0953689	+	0.995442i
$3$	−0.165184	+	1.72416i	−0.0953689	+	0.995442i
$4$	−1.24612	−	1.56258i	−0.623059	−	0.781291i
$5$	−0.733052	+	0.680173i	−0.327831	+	0.304182i
$5$	−0.733052	+	0.680173i	−0.327831	+	0.304182i
$6$	−0.0333356	+	0.0550721i	−0.0136092	+	0.0224831i
$7$	−3.57076	−	2.06158i	−1.34962	−	0.779203i	−0.361424	−	0.932401i	$-0.617709\pi$
$7$	−3.57076	−	2.06158i	−1.34962	−	0.779203i	−0.988195	+	0.153198i	$0.951043\pi$
$8$	−0.0330705	−	0.144891i	−0.0116922	−	0.0512268i
$9$	−2.94543	−	0.569605i	−0.981810	−	0.189868i
$10$	−0.0355160	+	0.0109552i	−0.0112311	+	0.00346434i
$11$	2.21451	+	1.76601i	0.667700	+	0.532473i	0.897639	−	0.440732i	$-0.145281\pi$
$11$	2.21451	+	1.76601i	0.667700	+	0.532473i	−0.229939	+	0.973205i	$0.573853\pi$
$12$	2.89998	−	1.89039i	0.837151	−	0.545708i
$13$	4.57487	+	1.41116i	1.26884	+	0.391386i	0.854841	−	0.518891i	$-0.173655\pi$
$13$	4.57487	+	1.41116i	1.26884	+	0.391386i	0.414001	+	0.910277i	$0.364131\pi$
$14$	−0.0863266	−	0.126618i	−0.0230718	−	0.0338401i
$15$	−1.05164	−	1.37625i	−0.271531	−	0.355346i
$16$	−0.888240	+	3.89163i	−0.222060	+	0.972908i
$17$	5.46398	−	5.88877i	1.32521	−	1.42824i	0.497074	−	0.867708i	$-0.334408\pi$
$17$	5.46398	−	5.88877i	1.32521	−	1.42824i	0.828136	−	0.560528i	$-0.189402\pi$
$18$	−0.0894464	−	0.0665728i	−0.0210827	−	0.0156913i
$19$	4.77784	+	1.87516i	1.09611	+	0.430192i	0.843365	−	0.537341i	$-0.180571\pi$
$19$	4.77784	+	1.87516i	1.09611	+	0.430192i	0.252746	+	0.967533i	$0.418666\pi$
$20$	1.97630	+	0.297879i	0.441913	+	0.0666077i
$21$	4.14431	−	5.81600i	0.904363	−	1.26916i
$22$	0.0456770	+	0.0948492i	0.00973837	+	0.0202219i
$23$	−0.0751105	+	0.498326i	−0.0156616	+	0.103908i	−0.995296	−	0.0968824i	$-0.969113\pi$
$23$	−0.0751105	+	0.498326i	−0.0156616	+	0.103908i	0.979634	+	0.200790i	$0.0643510\pi$
$24$	0.255278	−	0.0330850i	0.0521084	−	0.00675345i
$25$	0.0747301	−	0.997204i	0.0149460	−	0.199441i
$26$	0.130440	+	0.121030i	0.0255813	+	0.0237360i
$27$	1.46863	−	4.98429i	0.282637	−	0.959227i
$28$	1.22820	+	8.14858i	0.232108	+	1.53994i
$29$	6.70784	−	4.57333i	1.24561	−	0.849246i	0.252638	−	0.967561i	$-0.418702\pi$
$29$	6.70784	−	4.57333i	1.24561	−	0.849246i	0.992976	+	0.118315i	$0.0377493\pi$
$30$	−0.0130219	−	0.0630447i	−0.00237745	−	0.0115103i
$31$	−0.491251	−	6.55529i	−0.0882313	−	1.17736i	−0.849018	−	0.528363i	$-0.822806\pi$
$31$	−0.491251	−	6.55529i	−0.0882313	−	1.17736i	0.760787	−	0.649001i	$-0.224813\pi$
$32$	−0.277824	+	0.348381i	−0.0491129	+	0.0615856i
$33$	−3.41068	+	3.52644i	−0.593724	+	0.613875i
$34$	0.277933	−	0.109081i	0.0476651	−	0.0187072i
$35$	4.01978	−	0.917489i	0.679467	−	0.155084i
$36$	2.78030	+	5.31227i	0.463383	+	0.885379i
$37$	−2.76472	+	1.59621i	−0.454518	+	0.262416i	−0.709736	−	0.704467i	$-0.751186\pi$
$37$	−2.76472	+	1.59621i	−0.454518	+	0.262416i	0.255218	+	0.966883i	$0.417853\pi$
$38$	0.129754	+	0.139841i	0.0210488	+	0.0226852i
$39$	−3.18876	+	7.65469i	−0.510610	+	1.22573i
$40$	0.122793	+	0.0837192i	0.0194154	+	0.0132372i
$41$	0.579505	−	1.20335i	0.0905034	−	0.187932i	−0.850804	−	0.525484i	$-0.823884\pi$
$41$	0.579505	−	1.20335i	0.0905034	−	0.187932i	0.941307	+	0.337551i	$0.109599\pi$
$42$	0.232569	−	0.127925i	0.0358861	−	0.0197393i
$43$	−4.00283	+	5.19397i	−0.610426	+	0.792073i
$43$	−4.00283	+	5.19397i	−0.610426	+	0.792073i
$44$		−	5.66101i		−	0.853430i
$45$	2.54658	−	1.58585i	0.379622	−	0.236405i
$46$	−0.0105513	+	0.0154759i	−0.00155571	+	0.00228180i
$47$	−3.38840	+	2.70216i	−0.494249	+	0.394151i	−0.838649	−	0.544673i	$-0.816654\pi$
$47$	−3.38840	+	2.70216i	−0.494249	+	0.394151i	0.344400	+	0.938823i	$0.388083\pi$
$48$	−6.56306	−	2.17430i	−0.947296	−	0.313833i
$49$	5.00021	+	8.66062i	0.714316	+	1.23723i
$50$	0.0185836	−	0.0321877i	0.00262812	−	0.00455203i
$51$	9.25059	+	10.3935i	1.29534	+	1.45538i
$52$	−3.49578	−	8.90709i	−0.484777	−	1.23519i
$53$	−3.59808	−	11.6647i	−0.494234	−	1.60227i	−0.767986	−	0.640466i	$-0.778741\pi$
$53$	−3.59808	−	11.6647i	−0.494234	−	1.60227i	0.273753	−	0.961800i	$-0.411735\pi$
$54$	0.129557	−	0.143223i	0.0176305	−	0.0194902i
$55$	−2.82454	+	0.211670i	−0.380861	+	0.0285416i
$56$	−0.180618	+	0.585549i	−0.0241361	+	0.0782473i
$57$	−4.02230	+	7.92799i	−0.532766	+	1.05009i
$58$	0.298372	−	0.0449724i	0.0391782	−	0.00590517i
$59$	−2.63150	−	0.600622i	−0.342591	−	0.0781943i	0.0477636	−	0.998859i	$-0.484791\pi$
$59$	−2.63150	−	0.600622i	−0.342591	−	0.0781943i	−0.390355	+	0.920664i	$0.627648\pi$
$60$	−0.840041	+	3.35824i	−0.108449	+	0.433547i
$61$	5.83918	+	0.437586i	0.747630	+	0.0560271i	0.443096	−	0.896474i	$-0.353880\pi$
$61$	5.83918	+	0.437586i	0.747630	+	0.0560271i	0.304534	+	0.952501i	$0.401499\pi$
$62$	0.0892619	−	0.227436i	0.0113363	−	0.0288843i
$63$	9.34313	+	8.10615i	1.17712	+	1.02128i
$64$	7.17790	−	3.45669i	0.897237	−	0.432087i
$65$	−4.31345	+	2.07725i	−0.535018	+	0.257651i
$66$	−0.171080	+	0.0630867i	−0.0210585	+	0.00776544i
$67$	−0.534035	+	1.36070i	−0.0652427	+	0.166236i	−0.959777	−	0.280764i	$-0.909412\pi$
$67$	−0.534035	+	1.36070i	−0.0652427	+	0.166236i	0.894534	+	0.447000i	$0.147507\pi$
$68$	−16.0105	−	1.19982i	−1.94155	−	0.145499i
$69$	−0.846784	−	0.211818i	−0.101941	−	0.0254998i
$70$	0.149404	+	0.0341005i	0.0178572	+	0.00407579i
$71$	13.1344	−	1.97969i	1.55876	−	0.234946i	0.687656	−	0.726037i	$-0.258640\pi$
$71$	13.1344	−	1.97969i	1.55876	−	0.234946i	0.871108	+	0.491091i	$0.163402\pi$
$72$	0.0148759	+	0.445604i	0.00175314	+	0.0525149i
$73$	−0.945017	+	3.06367i	−0.110606	+	0.358575i	−0.993906	−	0.110233i	$-0.964840\pi$
$73$	−0.945017	+	3.06367i	−0.110606	+	0.358575i	0.883300	+	0.468808i	$0.155316\pi$
$74$	−0.118322	+	0.00886699i	−0.0137546	+	0.00103077i
$75$	1.70699	+	0.293568i	0.197106	+	0.0338983i
$76$	−3.02365	−	9.80245i	−0.346837	−	1.12442i
$77$	−4.26670	−	10.8714i	−0.486236	−	1.23891i
$78$	−0.230222	+	0.204906i	−0.0260675	+	0.0232010i
$79$	0.672671	−	1.16510i	0.0756814	−	0.131084i	−0.825701	−	0.564108i	$-0.809220\pi$
$79$	0.672671	−	1.16510i	0.0756814	−	0.131084i	0.901382	+	0.433024i	$0.142553\pi$
$80$	−1.99586	−	3.45693i	−0.223144	−	0.386496i
$81$	8.35110	+	3.35546i	0.927900	+	0.372829i
$82$	0.0388111	−	0.0309509i	0.00428597	−	0.00341795i
$83$	6.38194	−	9.36059i	0.700509	−	1.02746i	−0.296856	−	0.954922i	$-0.595938\pi$
$83$	6.38194	−	9.36059i	0.700509	−	1.02746i	0.997366	−	0.0725364i	$-0.0231093\pi$
$84$	−14.2523	+	0.771596i	−1.55505	+	0.0841880i
$85$			8.03322i			0.871325i
$86$	−0.217800	+	0.109377i	−0.0234860	+	0.0117945i
$87$	6.77710	+	12.3208i	0.726582	+	1.32093i
$88$	0.182645	−	0.379266i	0.0194700	−	0.0404299i
$89$	4.17178	+	2.84427i	0.442208	+	0.301492i	0.763879	−	0.645359i	$-0.223292\pi$
$89$	4.17178	+	2.84427i	0.442208	+	0.301492i	−0.321671	+	0.946851i	$0.604245\pi$
$90$	0.110850	−	0.0120377i	0.0116846	−	0.00126889i
$91$	−13.4265	−	14.4704i	−1.40748	−	1.51691i
$92$	0.872272	−	0.503606i	0.0909406	−	0.0525046i
$93$	11.3835	+	0.235834i	1.18041	+	0.0244549i
$94$	−0.157041	+	0.0358437i	−0.0161976	+	0.00369699i
$95$	−4.77784	+	1.87516i	−0.490196	+	0.192388i
$96$	−0.554771	−	0.536559i	−0.0566210	−	0.0547624i
$97$	−3.25397	+	4.08035i	−0.330391	+	0.414297i	−0.919085	−	0.394059i	$-0.871071\pi$
$97$	−3.25397	+	4.08035i	−0.330391	+	0.414297i	0.588694	+	0.808356i	$0.299642\pi$
$98$	0.0277762	+	0.370648i	0.00280582	+	0.0374411i
$99$	−5.51675	−	6.46306i	−0.554454	−	0.649562i
$100$	−1.65134	+	1.12586i	−0.165134	+	0.112586i
$101$	−0.298269	−	1.97888i	−0.0296788	−	0.196906i	0.969078	−	0.246755i	$-0.0793642\pi$
$101$	−0.298269	−	1.97888i	−0.0296788	−	0.196906i	−0.998757	+	0.0498486i	$0.984126\pi$
$102$	0.142162	+	0.497218i	0.0140761	+	0.0492320i
$103$	−5.92601	−	5.49853i	−0.583907	−	0.541786i	0.331947	−	0.943298i	$-0.392294\pi$
$103$	−5.92601	−	5.49853i	−0.583907	−	0.541786i	−0.915854	+	0.401512i	$0.868485\pi$
$104$	0.0531717	−	0.709527i	0.00521391	−	0.0695748i
$105$	0.917891	+	7.08228i	0.0895770	+	0.691160i
$106$	0.0676204	−	0.448632i	0.00656788	−	0.0435750i
$107$	2.58187	+	5.36130i	0.249599	+	0.518297i	0.987694	−	0.156400i	$-0.0499888\pi$
$107$	2.58187	+	5.36130i	0.249599	+	0.518297i	−0.738095	+	0.674696i	$0.764275\pi$
$108$	−9.61845	+	3.91616i	−0.925535	+	0.376833i
$109$	14.3561	+	2.16384i	1.37507	+	0.207258i	0.794653	−	0.607064i	$-0.207653\pi$
$109$	14.3561	+	2.16384i	1.37507	+	0.207258i	0.580414	+	0.814322i	$0.302891\pi$
$110$	−0.0979975	−	0.0384612i	−0.00934369	−	0.00366713i
$111$	−2.29544	−	5.03049i	−0.217873	−	0.477473i
$112$	11.1946	−	12.0649i	1.05779	−	1.14003i
$113$	−3.17529	+	13.9119i	−0.298707	+	1.30872i	0.573349	+	0.819312i	$0.305644\pi$
$113$	−3.17529	+	13.9119i	−0.298707	+	1.30872i	−0.872055	+	0.489408i	$0.837213\pi$
$114$	−0.262541	+	0.200616i	−0.0245892	+	0.0187894i
$115$	−0.283888	−	0.416387i	−0.0264727	−	0.0388283i
$116$	−15.5050	−	4.78265i	−1.43960	−	0.444058i
$117$	−12.6712	−	6.76235i	−1.17145	−	0.625179i
$118$	−0.0784337	−	0.0625488i	−0.00722041	−	0.00575809i
$119$	−31.6507	+	9.76295i	−2.90141	+	0.894968i
$120$	−0.164628	+	0.197886i	−0.0150284	+	0.0180644i
$121$	−0.662478	−	2.90251i	−0.0602253	−	0.263864i
$122$	0.188477	+	0.108817i	0.0170639	+	0.00985185i
$123$	1.97905	+	1.19793i	0.178445	+	0.108014i
$124$	−9.63103	+	8.93629i	−0.864892	+	0.802502i
$125$	0.623490	+	0.781831i	0.0557666	+	0.0699291i
$126$	0.182147	+	0.422116i	0.0162269	+	0.0376051i
$127$	2.10756	+	1.01495i	0.187016	+	0.0900622i	0.525049	−	0.851072i	$-0.324047\pi$
$127$	2.10756	+	1.01495i	0.187016	+	0.0900622i	−0.338033	+	0.941134i	$0.609761\pi$
$128$	1.18730			0.104943
$129$	−8.29402	−	7.75946i	−0.730248	−	0.683183i
$130$	−0.177941			−0.0156064
$131$	7.45631	+	3.59077i	0.651461	+	0.313727i	0.730266	−	0.683163i	$-0.239396\pi$
$131$	7.45631	+	3.59077i	0.651461	+	0.313727i	−0.0788051	+	0.996890i	$0.525110\pi$
$132$	9.76047	+	0.935108i	0.849540	+	0.0813907i
$133$	−13.1947	−	16.5456i	−1.14413	−	1.43469i
$134$	−0.0398259	+	0.0369530i	−0.00344043	+	0.00319226i
$135$	2.31360	+	4.65266i	0.199123	+	0.400437i
$136$	−1.03393	−	0.596938i	−0.0886585	−	0.0511870i
$137$	−2.81612	−	12.3382i	−0.240598	−	1.05413i	−0.940475	−	0.339864i	$-0.889619\pi$
$137$	−2.81612	−	12.3382i	−0.240598	−	1.05413i	0.699877	−	0.714263i	$-0.253238\pi$
$138$	−0.0249400	−	0.0207485i	−0.00212303	−	0.00176623i
$139$	−3.16514	+	0.976318i	−0.268464	+	0.0828102i	−0.426065	−	0.904693i	$-0.640100\pi$
$139$	−3.16514	+	0.976318i	−0.268464	+	0.0828102i	0.157601	+	0.987503i	$0.449624\pi$
$140$	−6.44277	−	5.13794i	−0.544514	−	0.434235i
$141$	−4.09924	−	6.28849i	−0.345218	−	0.529586i
$142$	0.471749	+	0.145515i	0.0395883	+	0.0122114i
$143$	7.63897	+	11.2043i	0.638803	+	0.936952i
$144$	4.83294	−	10.9566i	0.402745	−	0.913048i
$145$	−1.80654	+	7.91498i	−0.150025	+	0.657303i
$146$	−0.0810507	+	0.0873519i	−0.00670781	+	0.00722930i
$147$	−15.7582	+	7.19055i	−1.29971	+	0.593066i
$148$	5.93939	+	2.33104i	0.488215	+	0.191610i
$149$	10.7985	+	1.62761i	0.884645	+	0.133339i	0.575622	−	0.817716i	$-0.304760\pi$
$149$	10.7985	+	1.62761i	0.884645	+	0.133339i	0.309023	+	0.951055i	$0.399998\pi$
$150$	0.0524270	+	0.0373579i	0.00428064	+	0.00305026i
$151$	4.89419	+	10.1629i	0.398283	+	0.827043i	0.999607	+	0.0280380i	$0.00892593\pi$
$151$	4.89419	+	10.1629i	0.398283	+	0.827043i	−0.601324	+	0.799005i	$0.705360\pi$
$152$	0.113689	−	0.754280i	0.00922143	−	0.0611802i
$153$	−19.4480	+	14.2326i	−1.57228	+	1.15064i
$154$	0.0324376	−	0.432850i	0.00261390	−	0.0348801i
$155$	4.81884	+	4.47123i	0.387059	+	0.359138i
$156$	15.9347	−	4.55596i	1.27579	−	0.364768i
$157$	−1.44731	−	9.60225i	−0.115508	−	0.766343i	−0.969327	−	0.245774i	$-0.920958\pi$
$157$	−1.44731	−	9.60225i	−0.115508	−	0.766343i	0.853820	−	0.520569i	$-0.174280\pi$
$158$	0.0413141	−	0.0281675i	0.00328677	−	0.00224088i
$159$	20.7061	−	4.27683i	1.64210	−	0.339175i
$160$	−0.0332994	−	0.444350i	−0.00263255	−	0.0351289i
$161$	1.29554	−	1.62455i	0.102103	−	0.128033i
$162$	0.225538	+	0.247034i	0.0177199	+	0.0194089i
$163$	5.49803	−	2.15782i	0.430639	−	0.169013i	−0.140114	−	0.990135i	$-0.544747\pi$
$163$	5.49803	−	2.15782i	0.430639	−	0.169013i	0.570753	+	0.821122i	$0.306652\pi$
$164$	−2.60247	+	0.593997i	−0.203219	+	0.0463834i
$165$	0.101616	−	4.90492i	0.00791081	−	0.381847i
$166$	0.364660	−	0.210537i	0.0283031	−	0.0163408i
$167$	3.40486	+	3.66957i	0.263476	+	0.283960i	0.850909	−	0.525313i	$-0.176052\pi$
$167$	3.40486	+	3.66957i	0.263476	+	0.283960i	−0.587433	+	0.809273i	$0.699861\pi$
$168$	−0.979743	−	0.408137i	−0.0755888	−	0.0314884i
$169$	8.19698	+	5.58860i	0.630537	+	0.429893i
$170$	−0.129546	+	0.269004i	−0.00993570	+	0.0206317i
$171$	−13.0047	−	8.24464i	−0.994493	−	0.630484i
$172$	13.1040	−	0.217551i	0.999172	−	0.0165881i
$173$		−	7.47193i		−	0.568080i	−0.958812	−	0.284040i	$-0.908325\pi$
$173$		−	7.47193i		−	0.568080i	0.958812	−	0.284040i	$-0.0916749\pi$
$174$	0.0282532	+	0.521869i	0.00214187	+	0.0395628i
$175$	−2.32266	+	3.40671i	−0.175576	+	0.257523i
$176$	−8.83969	+	7.04942i	−0.666316	+	0.531370i
$177$	1.47025	−	4.43790i	0.110510	−	0.333573i
$178$	0.0938309	+	0.162520i	0.00703292	+	0.0121814i
$179$	8.85643	−	15.3398i	0.661961	−	1.14655i	−0.318139	−	0.948044i	$-0.603058\pi$
$179$	8.85643	−	15.3398i	0.661961	−	1.14655i	0.980100	−	0.198506i	$-0.0636089\pi$
$180$	−5.65136	−	2.00309i	−0.421228	−	0.149301i
$181$	−4.67679	−	11.9163i	−0.347623	−	0.885729i	−0.992589	−	0.121518i	$-0.961224\pi$
$181$	−4.67679	−	11.9163i	−0.347623	−	0.885729i	0.644966	−	0.764211i	$-0.276871\pi$
$182$	−0.216255	−	0.701081i	−0.0160299	−	0.0519676i
$183$	−1.71900	+	9.99537i	−0.127072	+	0.738879i
$184$	0.0746870	−	0.00559701i	0.00550600	−	0.000412617i
$185$	0.940985	−	3.05060i	0.0691826	−	0.224284i
$186$	0.377390	+	0.191470i	0.0276716	+	0.0140393i
$187$	22.4997	−	3.39128i	1.64534	−	0.247995i
$188$	8.44470	+	1.92745i	0.615893	+	0.140574i
$189$	−15.5196	+	14.7700i	−1.12889	+	1.07436i
$190$	−0.190232	−	0.0142559i	−0.0138009	−	0.00103423i
$191$	−2.88318	+	7.34622i	−0.208620	+	0.531554i	−0.996436	−	0.0843565i	$-0.973117\pi$
$191$	−2.88318	+	7.34622i	−0.208620	+	0.531554i	0.787816	+	0.615911i	$0.211212\pi$
$192$	4.77421	+	12.9468i	0.344549	+	0.934355i
$193$	−14.6429	+	7.05165i	−1.05402	+	0.507589i	−0.878924	−	0.476963i	$-0.841738\pi$
$193$	−14.6429	+	7.05165i	−1.05402	+	0.507589i	−0.175095	+	0.984551i	$0.556023\pi$
$194$	−0.174765	+	0.0841623i	−0.0125474	+	0.00604250i
$195$	−2.86899	−	7.78019i	−0.205453	−	0.557151i
$196$	7.30208	−	18.6054i	0.521577	−	1.32896i
$197$	2.76207	+	0.206989i	0.196789	+	0.0147473i	0.172760	−	0.984964i	$-0.444731\pi$
$197$	2.76207	+	0.206989i	0.196789	+	0.0147473i	0.0240293	+	0.999711i	$0.492351\pi$
$198$	−0.0805117	−	0.305390i	−0.00572172	−	0.0217031i
$199$	−16.1338	−	3.68243i	−1.14369	−	0.261040i	−0.391624	−	0.920125i	$-0.628087\pi$
$199$	−16.1338	−	3.68243i	−1.14369	−	0.261040i	−0.752069	+	0.659085i	$0.770944\pi$
$200$	−0.146957	+	0.0221503i	−0.0103915	+	0.00156626i
$201$	−2.25784	−	1.14552i	−0.159256	−	0.0807991i
$202$	0.0219240	−	0.0710758i	0.00154257	−	0.00500087i
$203$	−33.3803	+	2.50151i	−2.34284	+	0.175572i
$204$	4.71334	−	27.4063i	0.330000	−	1.91883i
$205$	0.393682	+	1.27628i	0.0274959	+	0.0891396i
$206$	−0.109770	−	0.279691i	−0.00764807	−	0.0194870i
$207$	0.505082	−	1.42500i	0.0351056	−	0.0990443i
$208$	−9.55531	+	16.5503i	−0.662541	+	1.14756i
$209$	7.26901	+	12.5903i	0.502808	+	0.870889i
$210$	−0.0834736	+	0.251963i	−0.00576023	+	0.0173871i
$211$	−21.4418	+	17.0993i	−1.47611	+	1.17716i	−0.532357	+	0.846520i	$0.678694\pi$
$211$	−21.4418	+	17.0993i	−1.47611	+	1.17716i	−0.943757	+	0.330641i	$0.892735\pi$
$212$	−13.7434	+	20.1579i	−0.943900	+	1.38445i
$213$	1.24371	+	22.9727i	0.0852173	+	1.57407i
$214$			0.221167i			0.0151187i
$215$	−0.598517	−	6.53007i	−0.0408185	−	0.445347i
$216$	−0.770748	−	0.0479581i	−0.0524428	−	0.00326314i
$217$	−11.7601	+	24.4201i	−0.798328	+	1.65774i
$218$	0.445841	+	0.303969i	0.0301962	+	0.0205874i
$219$	−5.12614	−	2.13542i	−0.346393	−	0.144299i
$220$	3.85047	+	4.14982i	0.259598	+	0.279781i
$221$	33.3070	−	19.2298i	2.24047	−	1.29354i
$222$	0.00425676	−	0.205470i	0.000285695	−	0.0137902i
$223$	−12.8980	+	2.94388i	−0.863714	+	0.197137i	−0.631356	−	0.775493i	$-0.717501\pi$
$223$	−12.8980	+	2.94388i	−0.863714	+	0.197137i	−0.232358	+	0.972630i	$0.574644\pi$
$224$	1.71026	−	0.671227i	0.114271	−	0.0448482i
$225$	−0.788125	+	2.89463i	−0.0525416	+	0.192975i
$226$	−0.330676	+	0.414654i	−0.0219962	+	0.0275824i
$227$	0.400079	+	5.33868i	0.0265541	+	0.354340i	0.994616	+	0.103629i	$0.0330455\pi$
$227$	0.400079	+	5.33868i	0.0265541	+	0.354340i	−0.968062	+	0.250711i	$0.919335\pi$
$228$	17.4004	−	3.59405i	1.15237	−	0.238022i
$229$	5.87193	−	4.00342i	0.388028	−	0.264553i	−0.353555	−	0.935414i	$-0.615027\pi$
$229$	5.87193	−	4.00342i	0.388028	−	0.264553i	0.741584	+	0.670860i	$0.234075\pi$
$230$	−0.00279165	−	0.0185214i	−0.000184076	−	0.00122126i
$231$	19.4488	−	5.56069i	1.27963	−	0.365866i
$232$	−0.884467	−	0.820665i	−0.0580681	−	0.0538793i
$233$	1.52169	−	20.3056i	0.0996895	−	1.33026i	−0.693132	−	0.720811i	$-0.743770\pi$
$233$	1.52169	−	20.3056i	0.0996895	−	1.33026i	0.792822	−	0.609454i	$-0.208611\pi$
$234$	−0.315261	−	0.430785i	−0.0206093	−	0.0281613i
$235$	0.645939	−	4.28552i	0.0421364	−	0.279557i
$236$	2.34063	+	4.86038i	0.152362	+	0.316383i
$237$	1.89770	+	1.35225i	0.123269	+	0.0878378i
$238$	−1.21731	−	0.183480i	−0.0789065	−	0.0118932i
$239$	6.70797	+	2.63269i	0.433903	+	0.170294i	0.572232	−	0.820092i	$-0.306078\pi$
$239$	6.70797	+	2.63269i	0.433903	+	0.170294i	−0.138329	+	0.990386i	$0.544173\pi$
$240$	6.28996	−	2.87014i	0.406015	−	0.185267i
$241$	−3.89720	+	4.20018i	−0.251041	+	0.270558i	−0.845982	−	0.533212i	$-0.820985\pi$
$241$	−3.89720	+	4.20018i	−0.251041	+	0.270558i	0.594941	+	0.803769i	$0.297175\pi$
$242$	0.0246224	−	0.107878i	0.00158279	−	0.00693466i
$243$	−7.16481	+	13.8443i	−0.459623	+	0.888114i
$244$	−6.59254	−	9.66949i	−0.422044	−	0.619025i
$245$	−9.55613	−	2.94767i	−0.610519	−	0.188320i
$246$	0.0469531	+	0.0720291i	0.00299362	+	0.00459240i
$247$	19.2118	+	15.3209i	1.22242	+	0.974848i
$248$	−0.933558	+	0.287965i	−0.0592810	+	0.0182858i
$249$	15.0849	+	12.5497i	0.955969	+	0.795304i
$250$	0.00827048	+	0.0362353i	0.000523071	+	0.00229172i
$251$	−11.0929	−	6.40448i	−0.700177	−	0.404247i	0.107236	−	0.994234i	$-0.465800\pi$
$251$	−11.0929	−	6.40448i	−0.700177	−	0.404247i	−0.807413	+	0.589986i	$0.799133\pi$
$252$	1.02390	−	24.7006i	0.0644994	−	1.55599i
$253$	−1.04638	+	0.970901i	−0.0657855	+	0.0610400i
$254$	0.0542076	+	0.0679742i	0.00340129	+	0.00426508i
$255$	−13.8505	−	1.32696i	−0.867354	−	0.0830973i
$256$	−14.3160	−	6.89424i	−0.894752	−	0.430890i
$257$	31.0819			1.93884			0.969418	−	0.245416i	$-0.0789246\pi$
$257$	31.0819			1.93884			0.969418	+	0.245416i	$0.0789246\pi$
$258$	−0.152606	−	0.393588i	−0.00950086	−	0.0245037i
$259$	13.1629			0.817902
$260$	8.62095	+	4.15163i	0.534648	+	0.257473i
$261$	−22.3625	+	9.64959i	−1.38420	+	0.597295i
$262$	0.191780	+	0.240484i	0.0118482	+	0.0148572i
$263$	−10.6863	+	9.91544i	−0.658946	+	0.611412i	−0.937074	−	0.349132i	$-0.886477\pi$
$263$	−10.6863	+	9.91544i	−0.658946	+	0.611412i	0.278128	+	0.960544i	$0.410286\pi$
$264$	0.623744	+	0.377557i	0.0383888	+	0.0232370i
$265$	10.5716	+	6.10350i	0.649406	+	0.374935i
$266$	−0.175025	−	0.766836i	−0.0107315	−	0.0470178i
$267$	−5.59308	+	6.72298i	−0.342291	+	0.411439i
$268$	2.79168	−	0.861118i	0.170529	−	0.0526011i
$269$	14.1390	+	11.2755i	0.862070	+	0.687478i	0.951211	−	0.308541i	$-0.0998407\pi$
$269$	14.1390	+	11.2755i	0.862070	+	0.687478i	−0.0891408	+	0.996019i	$0.528412\pi$
$270$	0.00244435	+	0.193111i	0.000148758	+	0.0117524i
$271$	8.27582	+	2.55275i	0.502720	+	0.155069i	0.535735	−	0.844386i	$-0.320035\pi$
$271$	8.27582	+	2.55275i	0.502720	+	0.155069i	−0.0330148	+	0.999455i	$0.510511\pi$
$272$	18.0636	+	26.4944i	1.09527	+	1.60646i
$273$	27.1670	−	20.7592i	1.64422	−	1.25640i
$274$	0.104667	−	0.458578i	0.00632319	−	0.0277037i
$275$	1.92656	−	2.07634i	0.116176	−	0.125208i
$276$	0.724211	+	1.58712i	0.0435924	+	0.0955334i
$277$	−17.8635	−	7.01090i	−1.07331	−	0.421244i	−0.238139	−	0.971231i	$-0.576538\pi$
$277$	−17.8635	−	7.01090i	−1.07331	−	0.421244i	−0.835173	+	0.549987i	$0.814633\pi$
$278$	−0.121734	−	0.0183484i	−0.00730111	−	0.00110047i
$279$	−2.28698	+	19.5880i	−0.136918	+	1.17270i
$280$	−0.265872	−	0.552089i	−0.0158889	−	0.0329936i
$281$	−1.59584	+	10.5877i	−0.0951997	+	0.631608i	0.889446	+	0.457041i	$0.151091\pi$
$281$	−1.59584	+	10.5877i	−0.0951997	+	0.631608i	−0.984645	+	0.174567i	$0.944147\pi$
$282$	−0.0358594	−	0.276685i	−0.00213540	−	0.0164763i
$283$	−1.10016	+	14.6807i	−0.0653979	+	0.872675i	0.863976	+	0.503534i	$0.167967\pi$
$283$	−1.10016	+	14.6807i	−0.0653979	+	0.872675i	−0.929373	+	0.369141i	$0.879652\pi$
$284$	−19.4604	−	18.0566i	−1.15476	−	1.07146i
$285$	−2.44385	−	8.54749i	−0.144761	−	0.506309i
$286$	0.0751188	+	0.498381i	0.00444187	+	0.0294699i
$287$	−4.55008	+	3.10219i	−0.268583	+	0.183117i
$288$	1.01675	−	0.867880i	0.0599126	−	0.0511403i
$289$	−3.55212	−	47.3997i	−0.208948	−	2.78822i
$290$	−0.188133	+	0.235912i	−0.0110476	+	0.0138532i
$291$	−6.49766	−	6.28436i	−0.380900	−	0.368396i
$292$	5.96484	−	2.34103i	0.349066	−	0.136998i
$293$	19.6680	−	4.48908i	1.14901	−	0.262255i	0.394727	−	0.918799i	$-0.370839\pi$
$293$	19.6680	−	4.48908i	1.14901	−	0.262255i	0.754288	+	0.656544i	$0.227982\pi$
$294$	−0.643643	−	0.0133345i	−0.0375380	−	0.000777683i
$295$	2.33755	−	1.34958i	0.136097	−	0.0785758i
$296$	0.322708	+	0.347797i	0.0187570	+	0.0202153i
$297$	12.0546	−	8.44414i	0.699479	−	0.489979i
$298$	0.335355	+	0.228641i	0.0194266	+	0.0132448i
$299$	−1.04684	+	2.17378i	−0.0605403	+	0.125713i
$300$	−1.66839	−	3.03314i	−0.0963244	−	0.175118i
$301$	25.0009	−	10.2943i	1.44103	−	0.593352i
$302$			0.419244i			0.0241248i
$303$	3.46117	−	0.187382i	0.198839	−	0.0107648i
$304$	−11.5413	+	16.9280i	−0.661940	+	0.970887i
$305$	−4.57806	+	3.65088i	−0.262139	+	0.209049i
$306$	−0.880765	+	0.162977i	−0.0503500	+	0.00931679i
$307$	−3.54105	−	6.13327i	−0.202098	−	0.350044i	0.747106	−	0.664705i	$-0.231443\pi$
$307$	−3.54105	−	6.13327i	−0.202098	−	0.350044i	−0.949204	+	0.314661i	$0.898109\pi$
$308$	−11.6706	+	20.2141i	−0.664996	+	1.15181i
$309$	10.4592	−	9.30909i	0.595003	−	0.529576i
$310$	0.0892619	+	0.227436i	0.00506973	+	0.0129175i
$311$	−9.17813	−	29.7548i	−0.520444	−	1.68724i	−0.709027	−	0.705181i	$-0.750866\pi$
$311$	−9.17813	−	29.7548i	−0.520444	−	1.68724i	0.188583	−	0.982057i	$-0.439611\pi$
$312$	1.21455	+	0.208879i	0.0687605	+	0.0118254i
$313$	8.63269	−	0.646931i	0.487948	−	0.0365667i	0.171515	−	0.985181i	$-0.445134\pi$
$313$	8.63269	−	0.646931i	0.487948	−	0.0365667i	0.316433	+	0.948615i	$0.397515\pi$
$314$	0.106383	−	0.344885i	0.00600354	−	0.0194630i
$315$	−12.3626	+	0.412709i	−0.696553	+	0.0232535i
$316$	−2.65879	+	0.400749i	−0.149569	+	0.0225439i
$317$	−30.3923	−	6.93684i	−1.70700	−	0.389612i	−0.745954	−	0.665997i	$-0.768006\pi$
$317$	−30.3923	−	6.93684i	−1.70700	−	0.389612i	−0.961047	+	0.276385i	$0.910863\pi$
$318$	0.762342	+	0.190695i	0.0427500	+	0.0106936i
$319$	22.9311	+	1.71845i	1.28390	+	0.0962147i
$320$	−2.91062	+	7.41615i	−0.162709	+	0.414575i
$321$	−9.67021	+	3.56594i	−0.539738	+	0.199031i
$322$	0.0695810	−	0.0335084i	0.00387760	−	0.00186735i
$323$	37.1484	−	17.8897i	2.06699	−	0.995411i
$324$	−5.16327	−	17.2306i	−0.286848	−	0.957255i
$325$	1.74910	−	4.45662i	0.0970224	−	0.247209i
$326$	0.218907	+	0.0164048i	0.0121241	+	0.000908579i
$327$	−6.10219	+	24.3948i	−0.337452	+	1.34903i
$328$	−0.193520	−	0.0441697i	−0.0106854	−	0.00243886i
$329$	17.6699	−	2.66331i	0.974172	−	0.146833i
$330$	0.0825007	−	0.162610i	0.00454151	−	0.00895137i
$331$	−2.79797	+	9.07079i	−0.153790	+	0.498576i	−0.999378	−	0.0352603i	$-0.988774\pi$
$331$	−2.79797	+	9.07079i	−0.153790	+	0.498576i	0.845588	+	0.533836i	$0.179250\pi$
$332$	−22.5794	+	1.69209i	−1.23920	+	0.0928654i
$333$	9.05251	−	3.12673i	0.496075	−	0.171344i
$334$	0.0548405	+	0.177789i	0.00300074	+	0.00972816i
$335$	−0.534035	−	1.36070i	−0.0291774	−	0.0743429i
$336$	18.9526	+	21.2942i	1.03395	+	1.16169i
$337$	13.6206	−	23.5915i	0.741960	−	1.28511i	−0.209642	−	0.977778i	$-0.567230\pi$
$337$	13.6206	−	23.5915i	0.741960	−	1.28511i	0.951602	−	0.307333i	$-0.0994367\pi$
$338$	0.184365	+	0.319329i	0.0100281	+	0.0173692i
$339$	−23.4617	−	7.77272i	−1.27427	−	0.422156i
$340$	12.5526	−	10.0103i	0.680759	−	0.542887i
$341$	10.4888	−	15.3843i	0.568003	−	0.833107i
$342$	−0.302526	−	0.485801i	−0.0163587	−	0.0262691i
$343$		−	12.3712i		−	0.667981i
$344$	0.884937	+	0.408208i	0.0477126	+	0.0220091i
$345$	0.764809	−	0.420686i	0.0411759	−	0.0226490i
$346$	0.120494	−	0.250209i	0.00647780	−	0.0134513i
$347$	17.3677	+	11.8411i	0.932347	+	0.635664i	0.931268	−	0.364336i	$-0.118704\pi$
$347$	17.3677	+	11.8411i	0.932347	+	0.635664i	0.00107959	+	0.999999i	$0.499656\pi$
$348$	10.8072	−	25.9430i	0.579327	−	1.39069i
$349$	16.0344	+	17.2809i	0.858299	+	0.925027i	0.997873	−	0.0651849i	$-0.0207637\pi$
$349$	16.0344	+	17.2809i	0.858299	+	0.925027i	−0.139574	+	0.990212i	$0.544573\pi$
$350$	−0.132715	+	0.0766231i	−0.00709392	+	0.00409567i
$351$	13.7524	−	20.7300i	0.734049	−	1.10649i
$352$	−1.23049	+	0.280851i	−0.0655853	+	0.0149694i
$353$	−0.497294	+	0.195173i	−0.0264683	+	0.0103880i	−0.378538	−	0.925586i	$-0.623573\pi$
$353$	−0.497294	+	0.195173i	−0.0264683	+	0.0103880i	0.352070	+	0.935974i	$0.385478\pi$
$354$	0.120800	−	0.124900i	0.00642044	−	0.00663836i
$355$	−8.28165	+	10.3849i	−0.439544	+	0.551171i
$356$	−0.754122	−	10.0631i	−0.0399684	−	0.533341i
$357$	−11.6047	−	56.1834i	−0.614184	−	2.97354i
$358$	0.543944	−	0.370855i	0.0287483	−	0.0196003i
$359$	−3.58600	−	23.7916i	−0.189262	−	1.25567i	−0.858574	−	0.512689i	$-0.828649\pi$
$359$	−3.58600	−	23.7916i	−0.189262	−	1.25567i	0.669312	−	0.742981i	$-0.266589\pi$
$360$	−0.313992	−	0.316533i	−0.0165489	−	0.0166827i
$361$	5.38352	+	4.99518i	0.283343	+	0.262904i
$362$	0.0355553	−	0.474453i	0.00186875	−	0.0249367i
$363$	5.11380	−	0.662768i	0.268405	−	0.0347863i
$364$	−5.88010	+	39.0119i	−0.308201	+	2.04478i
$365$	−1.39108	−	2.88860i	−0.0728123	−	0.151196i
$366$	−0.218751	+	0.306989i	−0.0114343	+	0.0160466i
$367$	−25.2879	−	3.81154i	−1.32002	−	0.198961i	−0.549027	−	0.835805i	$-0.685001\pi$
$367$	−25.2879	−	3.81154i	−1.32002	−	0.198961i	−0.770993	+	0.636844i	$0.780240\pi$
$368$	−1.87258	−	0.734935i	−0.0976152	−	0.0383111i
$369$	−2.39233	+	3.21430i	−0.124540	+	0.167330i
$370$	0.0807049	−	0.0869792i	0.00419565	−	0.00452184i
$371$	−11.1998	+	49.0694i	−0.581464	+	2.54756i
$372$	−13.8167	−	18.0815i	−0.716361	−	0.937483i
$373$	−8.21031	−	12.0423i	−0.425114	−	0.623527i	0.552606	−	0.833443i	$-0.313634\pi$
$373$	−8.21031	−	12.0423i	−0.425114	−	0.623527i	−0.977720	+	0.209915i	$0.932681\pi$
$374$	0.808123	+	0.249273i	0.0417871	+	0.0128896i
$375$	−1.45099	+	0.945848i	−0.0749288	+	0.0488434i
$376$	0.503576	+	0.401588i	0.0259699	+	0.0207103i
$377$	37.1412	−	11.4565i	1.91287	−	0.590042i
$378$	−0.757882	+	0.244323i	−0.0389812	+	0.0125666i
$379$	2.49711	+	10.9406i	0.128268	+	0.561979i	0.997691	+	0.0679111i	$0.0216334\pi$
$379$	2.49711	+	10.9406i	0.128268	+	0.561979i	−0.869423	+	0.494068i	$0.835509\pi$
$380$	8.88385	+	5.12909i	0.455732	+	0.263117i
$381$	−2.09807	+	3.46612i	−0.107487	+	0.177575i
$382$	−0.215015	+	0.199504i	−0.0110011	+	0.0102075i
$383$	−2.71083	−	3.39927i	−0.138517	−	0.173695i	0.707734	−	0.706479i	$-0.249717\pi$
$383$	−2.71083	−	3.39927i	−0.138517	−	0.173695i	−0.846251	+	0.532784i	$0.821146\pi$
$384$	−0.196122	+	2.04709i	−0.0100083	+	0.104465i
$385$	10.5221	+	5.06719i	0.536258	+	0.258248i
$386$	−0.604056			−0.0307456
$387$	14.7486	−	13.0184i	0.749712	−	0.661765i
$388$	10.4307			0.529540
$389$	6.33525	+	3.05089i	0.321210	+	0.154686i	0.587539	−	0.809196i	$-0.300097\pi$
$389$	6.33525	+	3.05089i	0.321210	+	0.154686i	−0.266330	+	0.963882i	$0.585811\pi$
$390$	0.0293929	−	0.306797i	0.00148837	−	0.0155353i
$391$	2.52412	+	3.16515i	0.127650	+	0.160068i
$392$	1.08949	−	1.01090i	0.0550275	−	0.0510580i
$393$	−7.42271	+	12.2627i	−0.374426	+	0.618572i
$394$	0.0891541	+	0.0514731i	0.00449152	+	0.00259318i
$395$	0.299367	+	1.31161i	0.0150628	+	0.0659944i
$396$	−3.22454	+	16.6741i	−0.162039	+	0.837906i
$397$	30.8303	−	9.50990i	1.54733	−	0.477288i	0.600663	−	0.799502i	$-0.294903\pi$
$397$	30.8303	−	9.50990i	1.54733	−	0.477288i	0.946667	+	0.322214i	$0.104427\pi$
$398$	−0.480880	−	0.383489i	−0.0241043	−	0.0192226i
$399$	30.7068	−	20.0167i	1.53726	−	1.00209i
$400$	3.81437	+	1.17658i	0.190719	+	0.0588289i
$401$	5.43745	+	7.97527i	0.271533	+	0.398266i	0.937650	−	0.347582i	$-0.112997\pi$
$401$	5.43745	+	7.97527i	0.271533	+	0.398266i	−0.666117	+	0.745848i	$0.732045\pi$
$402$	−0.0571342	−	0.0747701i	−0.00284960	−	0.00372919i
$403$	7.00316	−	30.6828i	0.348852	−	1.52842i
$404$	−2.72049	+	2.93199i	−0.135349	+	0.145872i
$405$	−8.40408	+	3.22046i	−0.417602	+	0.160026i
$406$	−1.15813	−	0.454533i	−0.0574770	−	0.0225581i
$407$	−8.94144	−	1.34771i	−0.443211	−	0.0668033i
$408$	1.20000	−	1.68405i	0.0594090	−	0.0833728i
$409$	11.9474	+	24.8091i	0.590761	+	1.22673i	0.955327	+	0.295551i	$0.0955033\pi$
$409$	11.9474	+	24.8091i	0.590761	+	1.22673i	−0.364565	+	0.931178i	$0.618782\pi$
$410$	−0.00739865	+	0.0490869i	−0.000365394	+	0.00242423i
$411$	21.7382	−	2.81736i	1.07227	−	0.138970i
$412$	−1.20740	+	16.1117i	−0.0594846	+	0.793766i
$413$	8.15820	+	7.56971i	0.401439	+	0.372481i
$414$	0.0398933	−	0.0395731i	0.00196065	−	0.00194491i
$415$	1.68852	+	11.2026i	0.0828864	+	0.549915i
$416$	−1.76263	+	1.20174i	−0.0864201	+	0.0589203i
$417$	−1.16049	−	5.61847i	−0.0568296	−	0.275138i
$418$	0.0403794	+	0.538826i	0.00197502	+	0.0263549i
$419$	−15.6338	+	19.6042i	−0.763761	+	0.957726i	−0.999902	−	0.0139925i	$-0.995546\pi$
$419$	−15.6338	+	19.6042i	−0.763761	+	0.957726i	0.236141	+	0.971719i	$0.424117\pi$
$420$	9.92285	−	10.2596i	0.484186	−	0.500619i
$421$	−14.4069	+	5.65431i	−0.702151	+	0.275574i	−0.689438	−	0.724345i	$-0.742142\pi$
$421$	−14.4069	+	5.65431i	−0.702151	+	0.275574i	−0.0127137	+	0.999919i	$0.504047\pi$
$422$	−0.993757	+	0.226818i	−0.0483753	+	0.0110413i
$423$	11.5195	−	6.02897i	0.560095	−	0.293139i
$424$	−1.57112	+	0.907086i	−0.0763003	+	0.0440520i
$425$	−5.46398	−	5.88877i	−0.265042	−	0.285647i
$426$	−0.328816	+	0.789332i	−0.0159312	+	0.0382433i
$427$	−19.9482	−	13.6004i	−0.965360	−	0.658171i
$428$	5.16017	−	10.7152i	0.249426	−	0.517939i
$429$	−20.5798	+	11.3200i	−0.993603	+	0.546535i
$430$	0.0852632	−	0.228321i	0.00411176	−	0.0110106i
$431$		−	10.2172i		−	0.492145i	−0.969251	−	0.246072i	$-0.920860\pi$
$431$		−	10.2172i		−	0.492145i	0.969251	−	0.246072i	$-0.0791401\pi$
$432$	18.0925	+	10.1426i	0.870477	+	0.487986i
$433$	−20.0436	+	29.3985i	−0.963232	+	1.41280i	−0.0530513	+	0.998592i	$0.516895\pi$
$433$	−20.0436	+	29.3985i	−0.963232	+	1.41280i	−0.910181	+	0.414211i	$0.864058\pi$
$434$	−0.787609	+	0.628097i	−0.0378064	+	0.0301496i
$435$	−13.3482	−	4.42219i	−0.639999	−	0.212028i
$436$	−14.5082	−	25.1290i	−0.694819	−	1.20346i
$437$	−1.29331	+	2.24008i	−0.0618673	+	0.107157i
$438$	−0.137220	−	0.154173i	−0.00655663	−	0.00736668i
$439$	9.62094	+	24.5137i	0.459182	+	1.16998i	0.953687	+	0.300802i	$0.0972544\pi$
$439$	9.62094	+	24.5137i	0.459182	+	1.16998i	−0.494504	+	0.869175i	$0.664650\pi$
$440$	0.124078	+	0.402252i	0.00591520	+	0.0191766i
$441$	−9.79462	−	28.3574i	−0.466411	−	1.35035i
$442$	1.42544	−	0.106822i	0.0678012	−	0.00508100i
$443$	−11.5337	+	37.3912i	−0.547981	+	1.77651i	0.0783180	+	0.996928i	$0.475045\pi$
$443$	−11.5337	+	37.3912i	−0.547981	+	1.77651i	−0.626299	+	0.779583i	$0.715431\pi$
$444$	−5.00017	+	9.85539i	−0.237297	+	0.467716i
$445$	−4.99273	+	0.752533i	−0.236678	+	0.0356735i
$446$	−0.479382	−	0.109416i	−0.0226994	−	0.00518099i
$447$	−4.58998	+	18.3494i	−0.217099	+	0.867896i
$448$	−32.7568	−	2.45478i	−1.54761	−	0.115978i
$449$	−2.78373	+	7.09284i	−0.131373	+	0.334732i	−0.981391	−	0.192022i	$-0.938496\pi$
$449$	−2.78373	+	7.09284i	−0.131373	+	0.334732i	0.850018	+	0.526753i	$0.176591\pi$
$450$	−0.0730709	+	0.0842213i	−0.00344460	+	0.00397023i
$451$	3.40846	−	1.64143i	0.160498	−	0.0772917i
$452$	25.6953	−	12.3742i	1.20860	−	0.582032i
$453$	−18.3308	+	6.75960i	−0.861258	+	0.317594i
$454$	−0.0726956	+	0.185225i	−0.00341177	+	0.00869305i
$455$	19.6847	+	1.47516i	0.922833	+	0.0691568i
$456$	1.28172	+	0.320613i	0.0600219	+	0.0150141i
$457$	−14.6889	−	3.35265i	−0.687119	−	0.156830i	−0.135313	−	0.990803i	$-0.543204\pi$
$457$	−14.6889	−	3.35265i	−0.687119	−	0.156830i	−0.551806	+	0.833973i	$0.686061\pi$
$458$	0.261190	−	0.0393681i	0.0122046	−	0.00183955i
$459$	−21.3268	−	35.8824i	−0.995449	−	1.67485i
$460$	−0.296881	+	0.962465i	−0.0138422	+	0.0448752i
$461$	−39.3649	+	2.94999i	−1.83341	+	0.137395i	−0.946119	−	0.323819i	$-0.895033\pi$
$461$	−39.3649	+	2.94999i	−1.83341	+	0.137395i	−0.887289	+	0.461214i	$0.847414\pi$
$462$	0.740943	+	0.127427i	0.0344718	+	0.00592846i
$463$	−5.26433	−	17.0665i	−0.244654	−	0.793150i	−0.991722	−	0.128402i	$-0.959015\pi$
$463$	−5.26433	−	17.0665i	−0.244654	−	0.793150i	0.747068	−	0.664748i	$-0.231461\pi$
$464$	11.8395	+	30.1667i	0.549637	+	1.40045i
$465$	−8.50510	+	7.56986i	−0.394414	+	0.351044i
$466$	0.378409	−	0.655424i	0.0175295	−	0.0303619i
$467$	8.13834	+	14.0960i	0.376598	+	0.652286i	0.990565	−	0.137045i	$-0.0437606\pi$
$467$	8.13834	+	14.0960i	0.376598	+	0.652286i	−0.613967	+	0.789332i	$0.710427\pi$
$468$	5.22303	+	28.2264i	0.241435	+	1.30477i
$469$	4.71210	−	3.75777i	0.217584	−	0.173518i
$470$	0.0907396	−	0.133091i	0.00418550	−	0.00613901i
$471$	16.7948	−	0.909246i	0.773866	−	0.0418958i
$472$			0.401143i			0.0184641i
$473$	−18.0369	+	4.43305i	−0.829339	+	0.203832i
$474$	0.0417407	+	0.0758847i	0.00191721	+	0.00348550i
$475$	2.22697	−	4.62435i	0.102180	−	0.212180i
$476$	54.6959	+	37.2911i	2.50698	+	1.70923i
$477$	3.95361	+	36.4069i	0.181024	+	1.66696i
$478$	0.182171	+	0.196334i	0.00833231	+	0.00898010i
$479$	−11.6652	+	6.73493i	−0.532998	+	0.307727i	−0.742236	−	0.670138i	$-0.766235\pi$
$479$	−11.6652	+	6.73493i	−0.532998	+	0.307727i	0.209238	+	0.977865i	$0.432902\pi$
$480$	0.771629	+	0.0159860i	0.0352199	+	0.000729657i
$481$	−14.9008	+	3.40101i	−0.679417	+	0.155072i
$482$	−0.198237	+	0.0778022i	−0.00902944	+	0.00354379i
$483$	2.58698	+	2.50206i	0.117712	+	0.113848i
$484$	−3.70988	+	4.65204i	−0.168631	+	0.211456i
$485$	−0.390014	−	5.20437i	−0.0177096	−	0.236318i
$486$	−0.463181	+	0.348056i	−0.0210103	+	0.0157882i
$487$	−17.2754	+	11.7782i	−0.782825	+	0.533721i	−0.887512	−	0.460784i	$-0.847568\pi$
$487$	−17.2754	+	11.7782i	−0.782825	+	0.533721i	0.104687	+	0.994505i	$0.466616\pi$
$488$	−0.129702	−	0.860517i	−0.00587134	−	0.0389538i
$489$	2.81223	+	9.83590i	0.127173	+	0.444795i
$490$	−0.272466	−	0.252812i	−0.0123088	−	0.0114209i
$491$	−0.330085	+	4.40468i	−0.0148965	+	0.198781i	0.984790	+	0.173748i	$0.0555879\pi$
$491$	−0.330085	+	4.40468i	−0.0148965	+	0.198781i	−0.999687	+	0.0250323i	$0.992031\pi$
$492$	−0.594258	−	4.58519i	−0.0267912	−	0.206716i
$493$	9.72022	−	64.4895i	0.437777	−	2.90446i
$494$	0.396268	+	0.822859i	0.0178289	+	0.0370222i
$495$	8.44006	+	0.985415i	0.379352	+	0.0442911i
$496$	25.9471	+	3.91090i	1.16506	+	0.175605i
$497$	−50.9810	−	20.0086i	−2.28681	−	0.897506i
$498$	0.302762	+	0.663508i	0.0135671	+	0.0297325i
$499$	−14.6643	+	15.8044i	−0.656465	+	0.707501i	−0.970281	−	0.241983i	$-0.922202\pi$
$499$	−14.6643	+	15.8044i	−0.656465	+	0.707501i	0.313815	+	0.949484i	$0.398393\pi$
$500$	0.444734	−	1.94851i	0.0198891	−	0.0871400i
$501$	−6.88934	+	5.26436i	−0.307793	+	0.235194i
$502$	−0.268182	−	0.393350i	−0.0119695	−	0.0175561i
$503$	10.7180	+	3.30608i	0.477894	+	0.147411i	0.524338	−	0.851510i	$-0.324313\pi$
$503$	10.7180	+	3.30608i	0.477894	+	0.147411i	−0.0464444	+	0.998921i	$0.514789\pi$
$504$	0.865529	−	1.62181i	0.0385537	−	0.0722412i
$505$	1.56463	+	1.24775i	0.0696251	+	0.0555241i
$506$	−0.0506966	+	0.0156378i	−0.00225374	+	0.000695187i
$507$	−10.9896	+	13.2097i	−0.488067	+	0.586664i
$508$	−1.04033	−	4.55799i	−0.0461572	−	0.202228i
$509$	−12.6939	−	7.32882i	−0.562647	−	0.324844i	0.191560	−	0.981481i	$-0.438645\pi$
$509$	−12.6939	−	7.32882i	−0.562647	−	0.324844i	−0.754207	+	0.656637i	$0.771979\pi$
$510$	−0.442407	−	0.267792i	−0.0195901	−	0.0118580i
$511$	9.69042	−	8.99139i	0.428679	−	0.397756i
$512$	−1.84875	−	2.31826i	−0.0817040	−	0.102454i
$513$	16.3632	−	21.0602i	0.722454	−	0.929831i
$514$	1.04082	+	0.501234i	0.0459088	+	0.0221085i
$515$	8.08402			0.356224
$516$	−1.78948	+	22.6293i	−0.0787774	+	0.996199i
$517$	−12.2757			−0.539885
$518$	0.440779	+	0.212268i	0.0193667	+	0.00932651i
$519$	12.8828	+	1.23424i	0.565491	+	0.0541772i
$520$	0.443623	+	0.556286i	0.0194542	+	0.0243947i
$521$	−21.5906	+	20.0332i	−0.945902	+	0.877669i	−0.992623	−	0.121239i	$-0.961313\pi$
$521$	−21.5906	+	20.0332i	−0.945902	+	0.877669i	0.0467214	+	0.998908i	$0.485123\pi$
$522$	−0.904451	−	0.0374915i	−0.0395868	−	0.00164096i
$523$	26.2018	+	15.1276i	1.14572	+	0.661484i	0.947841	−	0.318742i	$-0.103260\pi$
$523$	26.2018	+	15.1276i	1.14572	+	0.661484i	0.197882	+	0.980226i	$0.436594\pi$
$524$	−3.68057	−	16.1256i	−0.160786	−	0.704451i
$525$	−5.49004	−	4.56736i	−0.239605	−	0.199336i
$526$	−0.517746	+	0.159703i	−0.0225748	+	0.00696340i
$527$	−41.2868	−	32.9251i	−1.79848	−	1.43424i
$528$	−10.6941	−	16.4054i	−0.465402	−	0.713956i
$529$	21.7355	+	6.70451i	0.945021	+	0.291500i
$530$	0.255578	+	0.374864i	0.0111016	+	0.0162831i
$531$	7.40876	+	3.26800i	0.321513	+	0.141819i
$532$	−9.41177	+	41.2357i	−0.408052	+	1.78779i
$533$	4.34929	−	4.68742i	0.188389	−	0.203035i
$534$	−0.295709	+	0.134933i	−0.0127966	+	0.00583914i
$535$	−5.53925	−	2.17400i	−0.239483	−	0.0939901i
$536$	0.214814	+	0.0323780i	0.00927856	+	0.00139852i
$537$	24.9853	+	17.8038i	1.07819	+	0.768289i
$538$	0.291634	+	0.605585i	0.0125733	+	0.0261086i
$539$	−4.22174	+	28.0094i	−0.181843	+	1.20645i
$540$	4.38715	−	9.41296i	0.188793	−	0.405069i
$541$	1.69236	−	22.5830i	0.0727602	−	0.970917i	−0.834680	−	0.550736i	$-0.814347\pi$
$541$	1.69236	−	22.5830i	0.0727602	−	0.970917i	0.907440	−	0.420182i	$-0.138034\pi$
$542$	0.235962	+	0.218940i	0.0101354	+	0.00940430i
$543$	21.3180	−	6.09514i	0.914844	−	0.261568i
$544$	0.533507	+	3.53959i	0.0228739	+	0.151759i
$545$	−11.9956	+	8.17843i	−0.513833	+	0.350326i
$546$	1.24450	−	0.257050i	0.0532595	−	0.0110007i
$547$	1.08405	+	14.4657i	0.0463507	+	0.618507i	0.971214	+	0.238208i	$0.0765599\pi$
$547$	1.08405	+	14.4657i	0.0463507	+	0.618507i	−0.924864	+	0.380299i	$0.875821\pi$
$548$	−15.7703	+	19.7753i	−0.673674	+	0.844760i
$549$	−16.9496	−	4.61491i	−0.723393	−	0.196959i
$550$	0.0979975	−	0.0384612i	0.00417863	−	0.00163999i
$551$	40.6247	−	9.27233i	1.73067	−	0.395014i
$552$	−0.00268695	+	0.129697i	−0.000114364	+	0.00552025i
$553$	−4.80389	+	2.77353i	−0.204282	+	0.117942i
$554$	−0.485126	−	0.522841i	−0.0206110	−	0.0222134i
$555$	5.10427	+	2.12631i	0.216664	+	0.0902570i
$556$	5.46972	+	3.72919i	0.231968	+	0.158153i
$557$	10.1525	−	21.0820i	0.430177	−	0.893272i	−0.567383	−	0.823454i	$-0.692044\pi$
$557$	10.1525	−	21.0820i	0.430177	−	0.893272i	0.997560	−	0.0698175i	$-0.0222417\pi$
$558$	−0.392463	+	0.619051i	−0.0166143	+	0.0262065i
$559$	−25.6420	+	18.1131i	−1.08454	+	0.766104i
$560$			16.4585i			0.695497i
$561$	2.13051	+	39.3531i	0.0899504	+	1.66149i
$562$	−0.224179	+	0.328809i	−0.00945640	+	0.0138700i
$563$	11.7121	−	9.34005i	0.493604	−	0.393636i	−0.344808	−	0.938673i	$-0.612056\pi$
$563$	11.7121	−	9.34005i	0.493604	−	0.393636i	0.838412	+	0.545037i	$0.183484\pi$
$564$	−4.71815	+	14.2416i	−0.198670	+	0.599680i
$565$	−7.13482	−	12.3579i	−0.300164	−	0.519900i
$566$	−0.273584	+	0.473862i	−0.0114996	+	0.0199179i
$567$	−22.9022	−	29.1980i	−0.961802	−	1.22620i
$568$	−0.721200	−	1.83759i	−0.0302609	−	0.0771034i
$569$	−6.19344	−	20.0787i	−0.259643	−	0.841741i	−0.987718	−	0.156244i	$-0.950061\pi$
$569$	−6.19344	−	20.0787i	−0.259643	−	0.841741i	0.728076	−	0.685497i	$-0.240415\pi$
$570$	0.0560028	−	0.325635i	0.00234570	−	0.0136394i
$571$	0.913386	−	0.0684488i	0.0382240	−	0.00286449i	−0.0556044	−	0.998453i	$-0.517709\pi$
$571$	0.913386	−	0.0684488i	0.0382240	−	0.00286449i	0.0938284	+	0.995588i	$0.470090\pi$
$572$	7.98860	−	25.8984i	0.334020	−	1.08287i
$573$	−12.1898	−	6.18453i	−0.509235	−	0.258362i
$574$	−0.202393	+	0.0305058i	−0.00844771	+	0.00127329i
$575$	0.491319	+	0.112140i	0.0204894	+	0.00467658i
$576$	−23.1109	+	6.09287i	−0.962956	+	0.253870i
$577$	−39.6029	−	2.96783i	−1.64869	−	0.123552i	−0.782295	−	0.622909i	$-0.785951\pi$
$577$	−39.6029	−	2.96783i	−1.64869	−	0.123552i	−0.866397	+	0.499356i	$0.833570\pi$
$578$	0.645431	−	1.64453i	0.0268464	−	0.0684035i
$579$	−9.73937	−	26.4115i	−0.404755	−	1.09762i
$580$	14.6190	−	7.04013i	0.607020	−	0.292325i
$581$	−42.0860	+	20.2675i	−1.74602	+	0.840839i
$582$	−0.116241	−	0.315224i	−0.00481833	−	0.0130665i
$583$	12.6320	−	32.1858i	0.523163	−	1.33300i
$584$	0.475151	+	0.0356076i	0.0196619	+	0.00147345i
$585$	13.8882	−	3.66142i	0.574205	−	0.151381i
$586$	0.731003	+	0.166847i	0.0301975	+	0.00689237i
$587$	−5.01201	+	0.755439i	−0.206868	+	0.0311803i	−0.251659	−	0.967816i	$-0.580976\pi$
$587$	−5.01201	+	0.755439i	−0.206868	+	0.0311803i	0.0447908	+	0.998996i	$0.485738\pi$
$588$	30.8724	+	15.6632i	1.27316	+	0.645941i
$589$	9.94512	−	32.2413i	0.409782	−	1.32848i
$590$	0.100040	−	0.00749696i	0.00411858	−	0.000308645i
$591$	−0.813130	+	4.72805i	−0.0334477	+	0.194486i
$592$	−3.75614	−	12.1771i	−0.154376	−	0.500476i
$593$	8.66848	+	22.0869i	0.355972	+	0.907001i	0.990921	+	0.134447i	$0.0429258\pi$
$593$	8.66848	+	22.0869i	0.355972	+	0.907001i	−0.634949	+	0.772554i	$0.718979\pi$
$594$	0.539838	−	0.0883693i	0.0221498	−	0.00362584i
$595$	16.5611	−	28.6847i	0.678939	−	1.17596i
$596$	−10.9129	−	18.9017i	−0.447009	−	0.774243i
$597$	9.01412	−	27.2089i	0.368923	−	1.11358i
$598$	−0.0701099	+	0.0559108i	−0.00286701	+	0.00228636i
$599$	−9.50905	+	13.9472i	−0.388529	+	0.569868i	−0.969818	−	0.243830i	$-0.921596\pi$
$599$	−9.50905	+	13.9472i	−0.388529	+	0.569868i	0.581289	+	0.813697i	$0.302549\pi$
$600$	−0.0139155	−	0.257036i	−0.000568099	−	0.0104935i
$601$			28.5485i			1.16452i	0.813003	+	0.582259i	$0.197831\pi$
$601$			28.5485i			1.16452i	−0.813003	+	0.582259i	$0.802169\pi$
$602$	1.00320	+	0.0584518i	0.0408874	+	0.00238232i
$603$	2.34802	−	3.70365i	0.0956189	−	0.150824i
$604$	9.78161	−	20.3117i	0.398008	−	0.826472i
$605$	2.45984	+	1.67709i	0.100007	+	0.0681833i
$606$	0.118924	+	0.0495409i	0.00483097	+	0.00201246i
$607$	−21.5375	−	23.2119i	−0.874179	−	0.942141i	0.124567	−	0.992211i	$-0.460246\pi$
$607$	−21.5375	−	23.2119i	−0.874179	−	0.942141i	−0.998746	+	0.0500706i	$0.984055\pi$
$608$	−1.98067	+	1.14354i	−0.0803268	+	0.0463767i
$609$	1.20090	−	57.9661i	0.0486628	−	2.34891i
$610$	−0.212178	+	0.0484282i	−0.00859083	+	0.00196080i
$611$	−19.3147	+	7.58046i	−0.781389	+	0.306673i
$612$	46.4742	+	12.6536i	1.87861	+	0.511492i
$613$	26.5510	−	33.2939i	1.07238	−	1.34473i	0.137209	−	0.990542i	$-0.456187\pi$
$613$	26.5510	−	33.2939i	1.07238	−	1.34473i	0.935175	−	0.354185i	$-0.115242\pi$
$614$	−0.0196706	−	0.262485i	−0.000793839	−	0.0105930i
$615$	−2.26554	+	0.467947i	−0.0913555	+	0.0188694i
$616$	−1.43407	+	0.977730i	−0.0577802	+	0.0393939i
$617$	2.31912	+	15.3864i	0.0933643	+	0.619432i	0.985757	+	0.168173i	$0.0537867\pi$
$617$	2.31912	+	15.3864i	0.0933643	+	0.619432i	−0.892393	+	0.451259i	$0.850975\pi$
$618$	0.500363	−	0.143061i	0.0201275	−	0.00575476i
$619$	−8.80369	−	8.16863i	−0.353850	−	0.328325i	0.483140	−	0.875543i	$-0.339496\pi$
$619$	−8.80369	−	8.16863i	−0.353850	−	0.328325i	−0.836990	+	0.547218i	$0.815687\pi$
$620$	0.981823	−	13.1015i	0.0394310	−	0.526170i
$621$	2.37349	+	1.10623i	0.0952449	+	0.0443913i
$622$	0.172489	−	1.14439i	0.00691619	−	0.0458859i
$623$	−9.03273	−	18.7567i	−0.361889	−	0.751470i
$624$	−26.9569	−	19.2087i	−1.07914	−	0.768962i
$625$	−0.988831	−	0.149042i	−0.0395532	−	0.00596169i
$626$	0.299511	+	0.117549i	0.0119709	+	0.00469822i
$627$	−22.9083	+	10.4532i	−0.914871	+	0.417460i
$628$	−13.2008	+	14.2271i	−0.526769	+	0.567722i
$629$	−5.70666	+	25.0025i	−0.227539	+	0.996915i
$630$	−0.420635	−	0.185542i	−0.0167585	−	0.00739216i
$631$	20.5734	+	30.1757i	0.819015	+	1.20127i	0.976875	+	0.213813i	$0.0685882\pi$
$631$	20.5734	+	30.1757i	0.819015	+	1.20127i	−0.157860	+	0.987462i	$0.550459\pi$
$632$	−0.191058	−	0.0589337i	−0.00759990	−	0.00234426i
$633$	−25.9399	−	39.7935i	−1.03102	−	1.58165i
$634$	−0.905866	−	0.722404i	−0.0359765	−	0.0286903i
$635$	−2.23529	+	0.689497i	−0.0887050	+	0.0273619i
$636$	−32.4851	−	27.0255i	−1.28812	−	1.07163i
$637$	10.6538	+	46.6773i	0.422119	+	1.84942i
$638$	0.740171	+	0.427338i	0.0293036	+	0.0169185i
$639$	−39.8140	−	1.65038i	−1.57502	−	0.0652880i
$640$	−0.870350	+	0.807567i	−0.0344036	+	0.0319219i
$641$	−23.8291	−	29.8808i	−0.941194	−	1.18022i	−0.983462	−	0.181114i	$-0.942030\pi$
$641$	−23.8291	−	29.8808i	−0.941194	−	1.18022i	0.0422682	−	0.999106i	$-0.486542\pi$
$642$	−0.381326	−	0.0365332i	−0.0150498	−	0.00144185i
$643$	8.33018	+	4.01160i	0.328510	+	0.158202i	0.590867	−	0.806769i	$-0.298786\pi$
$643$	8.33018	+	4.01160i	0.328510	+	0.158202i	−0.262357	+	0.964971i	$0.584500\pi$
$644$	−4.15290			−0.163647
$645$	11.3577	+	0.0467248i	0.447210	+	0.00183979i
$646$	1.53246			0.0602940
$647$	8.59849	+	4.14082i	0.338042	+	0.162792i	0.595201	−	0.803577i	$-0.297072\pi$
$647$	8.59849	+	4.14082i	0.338042	+	0.162792i	−0.257160	+	0.966369i	$0.582787\pi$
$648$	0.210002	−	1.32097i	0.00824967	−	0.0518925i
$649$	−4.76677	−	5.97734i	−0.187112	−	0.234631i
$650$	0.130440	−	0.121030i	0.00511626	−	0.00474720i
$651$	−40.1615	−	24.3101i	−1.57405	−	0.952786i
$652$	−10.2230	−	5.90223i	−0.400362	−	0.231149i
$653$	5.59226	+	24.5013i	0.218842	+	0.958810i	0.958335	+	0.285646i	$0.0922081\pi$
$653$	5.59226	+	24.5013i	0.218842	+	0.958810i	−0.739493	+	0.673164i	$0.764935\pi$
$654$	−0.597736	+	0.718489i	−0.0233733	+	0.0280951i
$655$	−7.90820	+	2.43936i	−0.308999	+	0.0953136i
$656$	4.16827	+	3.32409i	0.162744	+	0.129784i
$657$	4.52856	−	8.48553i	0.176676	−	0.331052i
$658$	0.634651	+	0.195764i	0.0247413	+	0.00763167i
$659$	9.33814	+	13.6965i	0.363762	+	0.533541i	0.963868	−	0.266379i	$-0.0858273\pi$
$659$	9.33814	+	13.6965i	0.363762	+	0.533541i	−0.600106	+	0.799920i	$0.704875\pi$
$660$	−7.79097	+	5.95333i	−0.303263	+	0.231733i
$661$	−1.00509	+	4.40358i	−0.0390934	+	0.171279i	−0.990706	−	0.136021i	$-0.956568\pi$
$661$	−1.00509	+	4.40358i	−0.0390934	+	0.171279i	0.951613	+	0.307300i	$0.0994256\pi$
$662$	−0.239972	+	0.258628i	−0.00932677	+	0.0100519i
$663$	27.6534	+	60.6029i	1.07397	+	2.35362i
$664$	−1.56732	−	0.615129i	−0.0608239	−	0.0238716i
$665$	20.9263	+	3.15413i	0.811487	+	0.122312i
$666$	0.353559	+	0.0412796i	0.0137001	+	0.00159955i
$667$	1.77518	+	3.68619i	0.0687351	+	0.142730i
$668$	1.49115	−	9.89310i	0.0576941	−	0.382776i
$669$	−2.94517	−	22.7244i	−0.113867	−	0.878577i
$670$	0.00406000	−	0.0541770i	0.000156852	−	0.00209304i
$671$	12.1581	+	11.2811i	0.469360	+	0.435502i
$672$	0.874792	+	3.05963i	0.0337459	+	0.118028i
$673$	−2.80810	−	18.6305i	−0.108244	−	0.718153i	−0.975453	−	0.220208i	$-0.929326\pi$
$673$	−2.80810	−	18.6305i	−0.108244	−	0.718153i	0.867209	−	0.497945i	$-0.165912\pi$
$674$	0.836547	−	0.570348i	0.0322226	−	0.0219690i
$675$	−4.86060	−	1.83700i	−0.187085	−	0.0707060i
$676$	−1.48175	−	19.7725i	−0.0569902	−	0.760482i
$677$	−22.4910	+	28.2028i	−0.864400	+	1.08392i	0.131305	+	0.991342i	$0.458083\pi$
$677$	−22.4910	+	28.2028i	−0.864400	+	1.08392i	−0.995705	+	0.0925815i	$0.970488\pi$
$678$	−0.660306	−	0.638631i	−0.0253589	−	0.0245265i
$679$	20.0311	−	7.86163i	0.768724	−	0.301702i
$680$	1.16394	−	0.265663i	0.0446352	−	0.0101877i
$681$	−9.27080	−	0.192065i	−0.355258	−	0.00735995i
$682$	0.599325	−	0.346021i	0.0229494	−	0.0132498i
$683$	−16.2228	−	17.4840i	−0.620749	−	0.669008i	0.341908	−	0.939734i	$-0.388927\pi$
$683$	−16.2228	−	17.4840i	−0.620749	−	0.669008i	−0.962657	+	0.270725i	$0.912737\pi$
$684$	3.32243	+	30.5947i	0.127036	+	1.16982i
$685$	10.4565	+	7.12912i	0.399522	+	0.272390i
$686$	0.199501	−	0.414268i	0.00761697	−	0.0158168i
$687$	5.93257	+	10.7854i	0.226342	+	0.411490i
$688$	−16.6576	−	20.1910i	−0.635064	−	0.769776i
$689$		−	58.4419i		−	2.22646i
$690$	0.0323949	−	0.00175380i	0.00123325	−	6.67662e-5i
$691$	−9.97032	+	14.6238i	−0.379289	+	0.556315i	−0.967654	−	0.252281i	$-0.918819\pi$
$691$	−9.97032	+	14.6238i	−0.379289	+	0.556315i	0.588365	+	0.808595i	$0.299772\pi$
$692$	−11.6755	+	9.31091i	−0.443836	+	0.353948i
$693$	6.37488	+	34.4512i	0.242161	+	1.30869i
$694$	0.390631	+	0.676592i	0.0148281	+	0.0256831i
$695$	1.65615	−	2.86854i	0.0628214	−	0.108810i
$696$	1.56105	−	1.38940i	0.0591716	−	0.0526650i
$697$	−3.91987	−	9.98767i	−0.148476	−	0.378310i
$698$	0.258258	+	0.837251i	0.00977520	+	0.0316904i
$699$	34.7587	+	5.97780i	1.31469	+	0.226101i
$700$	8.21757	−	0.615822i	0.310595	−	0.0232759i
$701$	0.699306	−	2.26709i	0.0264124	−	0.0856269i	−0.941407	−	0.337273i	$-0.890496\pi$
$701$	0.699306	−	2.26709i	0.0264124	−	0.0856269i	0.967819	+	0.251646i	$0.0809718\pi$
$702$	0.794817	−	0.472401i	0.0299984	−	0.0178296i
$703$	−16.2026	+	2.44214i	−0.611092	+	0.0921072i
$704$	22.0001	+	5.02138i	0.829159	+	0.189250i
$705$	7.28221	+	1.82160i	0.274264	+	0.0686054i
$706$	−0.0198000	−	0.00148381i	−0.000745184	−	5.58438e-5i
$707$	−3.01458	+	7.68102i	−0.113375	+	0.288874i
$708$	−8.76668	+	3.23276i	−0.329472	+	0.121495i
$709$	−11.1648	+	5.37668i	−0.419302	+	0.201925i	−0.631625	−	0.775274i	$-0.717612\pi$
$709$	−11.1648	+	5.37668i	−0.419302	+	0.201925i	0.212322	+	0.977200i	$0.431897\pi$
$710$	−0.444792	+	0.214201i	−0.0166927	+	0.00803880i
$711$	−2.64495	+	3.04856i	−0.0991935	+	0.114330i
$712$	0.274147	−	0.698516i	0.0102741	−	0.0261780i
$713$	3.30357	+	0.247568i	0.123720	+	0.00927150i
$714$	0.517428	−	2.06852i	0.0193643	−	0.0774126i
$715$	−13.2206	−	3.01752i	−0.494423	−	0.112849i
$716$	−35.0059	+	5.27628i	−1.30823	+	0.197184i
$717$	−5.64721	+	11.1307i	−0.210899	+	0.415684i
$718$	0.263586	−	0.854524i	0.00983694	−	0.0318906i
$719$	18.5204	−	1.38791i	0.690693	−	0.0517603i	0.275241	−	0.961375i	$-0.411242\pi$
$719$	18.5204	−	1.38791i	0.690693	−	0.0517603i	0.415452	+	0.909615i	$0.363623\pi$
$720$	3.90957	+	11.3190i	0.145701	+	0.421833i
$721$	9.82468	+	31.8508i	0.365890	+	1.18619i
$722$	0.0997217	+	0.254087i	0.00371126	+	0.00945613i
$723$	−6.59802	−	7.41319i	−0.245383	−	0.275699i
$724$	−12.7923	+	22.1570i	−0.475423	+	0.823457i
$725$	−4.05926	−	7.03085i	−0.150757	−	0.261119i
$726$	0.181931	+	0.0602726i	0.00675210	+	0.00223693i
$727$	20.8648	−	16.6391i	0.773832	−	0.617110i	−0.154871	−	0.987935i	$-0.549496\pi$
$727$	20.8648	−	16.6391i	0.773832	−	0.617110i	0.928703	+	0.370824i	$0.120925\pi$
$728$	−1.65261	+	2.42393i	−0.0612497	+	0.0898369i
$729$	−22.6863	−	14.6401i	−0.840233	−	0.542226i
$730$		−	0.119162i		−	0.00441038i
$731$	8.71473	+	51.9515i	0.322326	+	1.92150i
$732$	17.7607	−	9.76933i	0.656454	−	0.361085i
$733$	−17.7633	+	36.8858i	−0.656102	+	1.36241i	0.261614	+	0.965173i	$0.415745\pi$
$733$	−17.7633	+	36.8858i	−0.656102	+	1.36241i	−0.917716	+	0.397237i	$0.869969\pi$
$734$	−0.785338	−	0.535434i	−0.0289874	−	0.0197632i
$735$	6.66077	−	15.9893i	0.245686	−	0.589776i
$736$	−0.152739	−	0.164614i	−0.00563005	−	0.00606775i
$737$	−3.58564	+	2.07017i	−0.132079	+	0.0762556i
$738$	−0.131945	+	0.0690565i	−0.00485697	+	0.00254201i
$739$	23.3063	−	5.31950i	0.857335	−	0.195681i	0.228810	−	0.973471i	$-0.426516\pi$
$739$	23.3063	−	5.31950i	0.857335	−	0.195681i	0.628524	+	0.777790i	$0.283659\pi$
$740$	−5.93939	+	2.33104i	−0.218336	+	0.0856907i
$741$	−29.5892	+	30.5935i	−1.08699	+	1.12388i
$742$	−1.16635	+	1.46255i	−0.0428179	+	0.0536920i
$743$	−2.77340	−	37.0085i	−0.101746	−	1.35771i	−0.781333	−	0.624114i	$-0.785460\pi$
$743$	−2.77340	−	37.0085i	−0.101746	−	1.35771i	0.679587	−	0.733595i	$-0.262159\pi$
$744$	−0.342287	−	1.65717i	−0.0125489	−	0.0607547i
$745$	−9.02289	+	6.15170i	−0.330573	+	0.225381i
$746$	−0.0807372	−	0.535656i	−0.00295600	−	0.0196118i
$747$	−24.1294	+	23.9358i	−0.882849	+	0.875764i
$748$	−33.3364	−	30.9317i	−1.21890	−	1.13097i
$749$	1.83352	−	24.4666i	0.0669954	−	0.893991i
$750$	−0.0638415	+	0.00827410i	−0.00233116	+	0.000302128i
$751$	−2.59913	+	17.2441i	−0.0948435	+	0.629246i	0.890021	+	0.455920i	$0.150690\pi$
$751$	−2.59913	+	17.2441i	−0.0948435	+	0.629246i	−0.984864	+	0.173326i	$0.944549\pi$
$752$	−7.50610	−	15.5866i	−0.273719	−	0.568384i
$753$	12.8747	−	18.0680i	0.469180	−	0.658433i
$754$	1.42848	+	0.215309i	0.0520222	+	0.00784108i
$755$	−10.5002	−	4.12103i	−0.382142	−	0.149980i
$756$	42.4186	+	5.84550i	1.54275	+	0.212599i
$757$	8.39436	−	9.04697i	0.305098	−	0.328818i	−0.561828	−	0.827254i	$-0.689902\pi$
$757$	8.39436	−	9.04697i	0.305098	−	0.328818i	0.866926	+	0.498436i	$0.166092\pi$
$758$	−0.0928106	+	0.406630i	−0.00337103	+	0.0147695i
$759$	−1.50114	−	1.96450i	−0.0544879	−	0.0713070i
$760$	0.429700	+	0.630255i	0.0155869	+	0.0228617i
$761$	−5.52811	−	1.70520i	−0.200394	−	0.0618133i	0.192933	−	0.981212i	$-0.438200\pi$
$761$	−5.52811	−	1.70520i	−0.200394	−	0.0618133i	−0.393327	+	0.919399i	$0.628676\pi$
$762$	−0.126152	+	0.0822341i	−0.00457001	+	0.00297903i
$763$	−46.8013	−	37.3228i	−1.69432	−	1.35118i
$764$	15.0719	−	4.64906i	0.545281	−	0.168197i
$765$	4.57577	−	23.6613i	0.165437	−	0.855475i
$766$	−0.0359587	−	0.157545i	−0.00129924	−	0.00569234i
$767$	−11.1912	−	6.46123i	−0.404090	−	0.233302i
$768$	14.2515	−	23.5443i	0.514258	−	0.849581i
$769$	39.7737	−	36.9046i	1.43427	−	1.33081i	0.576179	−	0.817324i	$-0.304543\pi$
$769$	39.7737	−	36.9046i	1.43427	−	1.33081i	0.858096	−	0.513489i	$-0.171647\pi$
$770$	0.270635	+	0.339365i	0.00975299	+	0.0122299i
$771$	−5.13423	+	53.5900i	−0.184905	+	1.93000i
$772$	29.2656	+	14.0936i	1.05329	+	0.507238i
$773$	16.3522			0.588148			0.294074	−	0.955783i	$-0.404989\pi$
$773$	16.3522			0.588148			0.294074	+	0.955783i	$0.404989\pi$
$774$	0.703816	−	0.198103i	0.0252981	−	0.00712066i
$775$	−6.57367			−0.236133
$776$	0.698818	+	0.336533i	0.0250861	+	0.0120808i
$777$	−2.17430	+	22.6949i	−0.0780024	+	0.814174i
$778$	0.162946	+	0.204327i	0.00584188	+	0.00732549i
$779$	5.02527	−	4.66277i	0.180049	−	0.167061i
$780$	−8.58210	+	14.1781i	−0.307288	+	0.507657i
$781$	32.5824	+	18.8114i	1.16589	+	0.673126i
$782$	0.0334820	+	0.146694i	0.00119731	+	0.00524578i
$783$	−12.9435	−	40.1503i	−0.462562	−	1.43486i
$784$	−38.1453	+	11.7663i	−1.36233	+	0.420224i
$785$	7.59214	+	6.05453i	0.270975	+	0.216095i
$786$	−0.446312	+	0.290934i	−0.0159194	+	0.0103773i
$787$	−42.6129	−	13.1443i	−1.51899	−	0.468545i	−0.580617	−	0.814177i	$-0.697188\pi$
$787$	−42.6129	−	13.1443i	−1.51899	−	0.468545i	−0.938370	+	0.345632i	$0.887665\pi$
$788$	−3.11843	−	4.57390i	−0.111089	−	0.162938i
$789$	−15.3306	−	20.0627i	−0.545783	−	0.714252i
$790$	−0.0111266	+	0.0487489i	−0.000395867	+	0.00173441i
$791$	40.0186	−	43.1298i	1.42290	−	1.53352i
$792$	−0.753999	+	1.01307i	−0.0267922	+	0.0359977i
$793$	26.0960	+	10.2419i	0.926696	+	0.363701i
$794$	1.18576	+	0.178724i	0.0420810	+	0.00634269i
$795$	−12.2696	+	17.2188i	−0.435159	+	0.610689i
$796$	14.3505	+	29.7991i	0.508640	+	1.05620i
$797$	−7.63857	+	50.6786i	−0.270572	+	1.79513i	0.279643	+	0.960104i	$0.409784\pi$
$797$	−7.63857	+	50.6786i	−0.270572	+	1.79513i	−0.550215	+	0.835023i	$0.685454\pi$
$798$	1.35106	−	0.175102i	0.0478269	−	0.00619855i
$799$	−2.60176	+	34.7181i	−0.0920436	+	1.22824i
$800$	0.326645	+	0.303082i	0.0115486	+	0.0107156i
$801$	−10.6676	−	10.7539i	−0.376920	−	0.379969i
$802$	0.0534699	+	0.354749i	0.00188809	+	0.0125266i
$803$	−7.50322	+	5.11561i	−0.264783	+	0.180526i
$804$	1.02356	+	4.95553i	0.0360982	+	0.174768i
$805$	0.155280	+	2.07207i	0.00547291	+	0.0730310i
$806$	0.729310	−	0.914526i	0.0256888	−	0.0322128i
$807$	−21.7762	+	22.5153i	−0.766559	+	0.792577i
$808$	−0.276859	+	0.108659i	−0.00973986	+	0.00382261i
$809$	11.3082	−	2.58103i	0.397576	−	0.0907441i	−0.0190582	−	0.999818i	$-0.506067\pi$
$809$	11.3082	−	2.58103i	0.397576	−	0.0907441i	0.416634	+	0.909074i	$0.363210\pi$
$810$	−0.333357	−	0.0276843i	−0.0117130	−	0.000972729i
$811$	17.8638	−	10.3136i	0.627281	−	0.362161i	−0.152417	−	0.988316i	$-0.548706\pi$
$811$	17.8638	−	10.3136i	0.627281	−	0.362161i	0.779698	+	0.626155i	$0.215372\pi$
$812$	45.5047	+	49.0424i	1.59690	+	1.72105i
$813$	−5.76837	+	13.8471i	−0.202306	+	0.485640i
$814$	−0.277684	−	0.189322i	−0.00973282	−	0.00663572i
$815$	−2.56265	+	5.32140i	−0.0897658	+	0.186401i
$816$	−48.6644	+	26.7680i	−1.70359	+	0.937068i
$817$	−28.8644	+	17.3100i	−1.00984	+	0.605600i
$818$			1.02343i			0.0357836i
$819$	31.3045	+	50.2693i	1.09387	+	1.75655i
$820$	1.50373	−	2.20556i	0.0525124	−	0.0770215i
$821$	4.80534	−	3.83213i	0.167708	−	0.133742i	−0.536040	−	0.844193i	$-0.680080\pi$
$821$	4.80534	−	3.83213i	0.167708	−	0.133742i	0.703747	+	0.710451i	$0.251509\pi$
$822$	0.773370	+	0.256213i	0.0269744	+	0.00893644i
$823$	10.8628	+	18.8149i	0.378654	+	0.655847i	0.990867	−	0.134846i	$-0.0430539\pi$
$823$	10.8628	+	18.8149i	0.378654	+	0.655847i	−0.612213	+	0.790693i	$0.709721\pi$
$824$	−0.600713	+	1.04047i	−0.0209268	+	0.0362463i
$825$	3.26170	+	3.66468i	0.113558	+	0.127588i
$826$	0.151119	+	0.385044i	0.00525809	+	0.0133974i
$827$	15.9438	+	51.6884i	0.554419	+	1.79738i	0.601977	+	0.798513i	$0.294380\pi$
$827$	15.9438	+	51.6884i	0.554419	+	1.79738i	−0.0475584	+	0.998868i	$0.515144\pi$
$828$	−2.85607	+	0.986486i	−0.0992553	+	0.0342828i
$829$	−19.9660	+	1.49624i	−0.693447	+	0.0519666i	−0.416791	−	0.909002i	$-0.636845\pi$
$829$	−19.9660	+	1.49624i	−0.693447	+	0.0519666i	−0.276656	+	0.960969i	$0.589226\pi$
$830$	−0.124113	+	0.402366i	−0.00430804	+	0.0139663i
$831$	15.0386	−	29.6414i	0.521685	−	1.02825i
$832$	37.7159	−	5.68476i	1.30756	−	0.197084i
$833$	78.3214	+	17.8763i	2.71368	+	0.619379i
$834$	0.0517440	−	0.206857i	0.00179175	−	0.00716288i
$835$	−4.99188	−	0.374090i	−0.172751	−	0.0129459i
$836$	10.6153	−	27.0474i	0.367139	−	0.935454i
$837$	−33.3949	−	7.17873i	−1.15430	−	0.248133i
$838$	−0.839663	+	0.404360i	−0.0290057	+	0.0139684i
$839$	24.9028	−	11.9926i	0.859740	−	0.414029i	0.0485563	−	0.998820i	$-0.484538\pi$
$839$	24.9028	−	11.9926i	0.859740	−	0.414029i	0.811184	+	0.584792i	$0.198824\pi$
$840$	0.995806	−	0.367209i	0.0343586	−	0.0126699i
$841$	13.4849	−	34.3590i	0.464996	−	1.18479i
$842$	−0.573620	−	0.0429869i	−0.0197683	−	0.00148143i
$843$	−17.9912	−	4.50039i	−0.619650	−	0.155002i
$844$	53.4380	+	12.1969i	1.83941	+	0.419834i
$845$	−9.81003	+	1.47862i	−0.337475	+	0.0508662i
$846$	0.482971	−	0.0161234i	0.0166049	−	0.000554333i
$847$	−3.61819	+	11.7299i	−0.124323	+	0.403044i
$848$	48.5906	−	3.64136i	1.66861	−	0.125045i
$849$	−25.1300	−	4.32186i	−0.862460	−	0.148326i
$850$	−0.0880057	−	0.285308i	−0.00301857	−	0.00978597i
$851$	−0.587775	−	1.49763i	−0.0201487	−	0.0513379i
$852$	34.3470	−	30.5701i	1.17671	−	1.04732i
$853$	2.50074	−	4.33141i	0.0856237	−	0.148305i	−0.820033	−	0.572316i	$-0.806045\pi$
$853$	2.50074	−	4.33141i	0.0856237	−	0.148305i	0.905657	+	0.424011i	$0.139378\pi$
$854$	−0.448670	−	0.777120i	−0.0153532	−	0.0265925i
$855$	15.1409	−	2.80168i	0.517807	−	0.0958154i
$856$	0.691422	−	0.551391i	0.0236323	−	0.0188462i
$857$	10.8658	−	15.9372i	0.371169	−	0.544405i	−0.594528	−	0.804075i	$-0.702661\pi$
$857$	10.8658	−	15.9372i	0.371169	−	0.544405i	0.965698	+	0.259669i	$0.0836135\pi$
$858$	−0.871695	+	0.0471921i	−0.0297592	+	0.00161111i
$859$		−	30.5755i		−	1.04322i	−0.853184	−	0.521611i	$-0.825331\pi$
$859$		−	30.5755i		−	1.04322i	0.853184	−	0.521611i	$-0.174669\pi$
$860$	−9.45795	+	9.07247i	−0.322513	+	0.309369i
$861$	−4.59706	−	8.35748i	−0.156668	−	0.284822i
$862$	0.164765	−	0.342138i	0.00561191	−	0.0116533i
$863$	12.2652	+	8.36229i	0.417513	+	0.284656i	0.753800	−	0.657104i	$-0.228219\pi$
$863$	12.2652	+	8.36229i	0.417513	+	0.284656i	−0.336287	+	0.941760i	$0.609171\pi$
$864$	1.32841	+	1.89640i	0.0451934	+	0.0645167i
$865$	5.08220	+	5.47731i	0.172800	+	0.186234i
$866$	−1.14528	+	0.661225i	−0.0389181	+	0.0224694i
$867$	82.3113	+	1.70526i	2.79544	+	0.0579137i
$868$	52.8129	−	12.0542i	1.79259	−	0.409146i
$869$	3.54722	−	1.39218i	0.120331	−	0.0472265i
$870$	−0.375672	−	0.363340i	−0.0127365	−	0.0123184i
$871$	−4.36331	+	5.47141i	−0.147845	+	0.185392i
$872$	−0.161243	−	2.15163i	−0.00546037	−	0.0728635i
$873$	11.9085	−	10.1649i	0.403043	−	0.344030i
$874$	−0.0794323	+	0.0541560i	−0.00268684	+	0.00183186i
$875$	−0.614525	−	4.07710i	−0.0207747	−	0.137831i
$876$	3.05100	+	10.6710i	0.103084	+	0.360540i
$877$	3.33217	+	3.09180i	0.112519	+	0.104403i	0.734426	−	0.678689i	$-0.237451\pi$
$877$	3.33217	+	3.09180i	0.112519	+	0.104403i	−0.621907	+	0.783091i	$0.713642\pi$
$878$	−0.0731432	+	0.976029i	−0.00246846	+	0.0329394i
$879$	4.49105	+	34.6522i	0.151479	+	1.16879i
$880$	1.68513	−	11.1801i	0.0568057	−	0.376881i
$881$	−14.7152	−	30.5564i	−0.495767	−	1.02947i	−0.987338	−	0.158633i	$-0.949291\pi$
$881$	−14.7152	−	30.5564i	−0.495767	−	1.02947i	0.491570	−	0.870838i	$-0.336423\pi$
$882$	0.129310	−	1.10754i	0.00435410	−	0.0372928i
$883$	−29.6491	−	4.46888i	−0.997770	−	0.150390i	−0.370202	−	0.928951i	$-0.620712\pi$
$883$	−29.6491	−	4.46888i	−0.997770	−	0.150390i	−0.627568	+	0.778562i	$0.715950\pi$
$884$	−71.5526	−	28.0823i	−2.40658	−	0.944511i
$885$	1.94077	+	4.25323i	0.0652382	+	0.142971i
$886$	−0.989202	+	1.06611i	−0.0332329	+	0.0358165i
$887$	6.16216	−	26.9982i	0.206905	−	0.906510i	−0.759707	−	0.650266i	$-0.774658\pi$
$887$	6.16216	−	26.9982i	0.206905	−	0.906510i	0.966612	−	0.256244i	$-0.0824852\pi$
$888$	−0.652962	+	0.498949i	−0.0219120	+	0.0167436i
$889$	−5.43320	−	7.96905i	−0.182224	−	0.267273i
$890$	−0.179324	−	0.0553143i	−0.00601097	−	0.00185414i
$891$	12.5678	+	22.1789i	0.421037	+	0.743019i
$892$	20.6725	+	16.4858i	0.692166	+	0.551984i
$893$	−21.2562	+	6.55668i	−0.711313	+	0.219411i
$894$	−0.449609	+	0.540437i	−0.0150372	+	0.0180749i
$895$	3.94148	+	17.2688i	0.131749	+	0.577231i
$896$	−4.23955	−	2.44771i	−0.141633	−	0.0817721i
$897$	−3.57502	−	2.16399i	−0.119366	−	0.0722534i
$898$	−0.207598	+	0.192623i	−0.00692764	+	0.00642791i
$899$	−33.2747	−	41.7252i	−1.10977	−	1.39161i
$900$	5.50519	−	2.37554i	0.183506	−	0.0791845i
$901$	−88.3504	−	42.5473i	−2.94338	−	1.41746i
$902$	0.140607			0.00468171
$903$	13.6192	+	44.8059i	0.453218	+	1.49105i
$904$	2.12072			0.0705340
$905$	11.5335	+	5.55422i	0.383385	+	0.184628i
$906$	−0.722842	−	0.0692523i	−0.0240148	−	0.00230075i
$907$	19.0238	+	23.8551i	0.631675	+	0.792095i	0.989934	−	0.141527i	$-0.0452011\pi$
$907$	19.0238	+	23.8551i	0.631675	+	0.792095i	−0.358260	+	0.933622i	$0.616630\pi$
$908$	7.84358	−	7.27778i	0.260298	−	0.241522i
$909$	−0.248653	+	5.99855i	−0.00824731	+	0.198959i
$910$	0.635383	+	0.366838i	0.0210627	+	0.0121606i
$911$	−9.96854	−	43.6750i	−0.330273	−	1.44702i	−0.818603	−	0.574360i	$-0.805251\pi$
$911$	−9.96854	−	43.6750i	−0.330273	−	1.44702i	0.488330	−	0.872659i	$-0.337606\pi$
$912$	−27.2801	−	22.6953i	−0.903334	−	0.751515i
$913$	30.6638	−	9.45853i	1.01482	−	0.313032i
$914$	−0.437815	−	0.349145i	−0.0144816	−	0.0115487i
$915$	−5.53846	−	8.49635i	−0.183096	−	0.280881i
$916$	−13.5728	−	4.18665i	−0.448458	−	0.138331i
$917$	−19.2220	−	28.1935i	−0.634767	−	0.931032i
$918$	−0.135510	−	1.54550i	−0.00447250	−	0.0510090i
$919$	5.16731	−	22.6395i	0.170454	−	0.746807i	−0.815358	−	0.578956i	$-0.803460\pi$
$919$	5.16731	−	22.6395i	0.170454	−	0.746807i	0.985812	−	0.167851i	$-0.0536827\pi$
$920$	−0.0509425	+	0.0549029i	−0.00167952	+	0.00181010i
$921$	11.1596	−	5.09220i	0.367723	−	0.167794i
$922$	−1.36577	−	0.536023i	−0.0449791	−	0.0176530i
$923$	62.8818	+	9.47790i	2.06978	+	0.311969i
$924$	−32.9245	−	23.4610i	−1.08314	−	0.771811i
$925$	1.38514	+	2.87628i	0.0455432	+	0.0945715i
$926$	0.0989353	−	0.656393i	0.00325121	−	0.0215704i
$927$	14.3226	+	19.5710i	0.470417	+	0.642796i
$928$	−0.270342	+	3.60746i	−0.00887441	+	0.118421i
$929$	13.8403	+	12.8420i	0.454087	+	0.421331i	0.873770	−	0.486340i	$-0.161668\pi$
$929$	13.8403	+	12.8420i	0.454087	+	0.421331i	−0.419683	+	0.907671i	$0.637859\pi$
$930$	−0.406879	+	0.116333i	−0.0133421	+	0.00381470i
$931$	7.65012	+	50.7552i	0.250723	+	1.66344i
$932$	−33.6254	+	22.9254i	−1.10144	+	0.750947i
$933$	52.8180	−	10.9095i	1.72918	−	0.357162i
$934$	0.0452086	+	0.603267i	0.00147927	+	0.0197395i
$935$	−14.1868	+	17.7896i	−0.463957	+	0.581784i
$936$	−0.560764	+	2.05957i	−0.0183291	+	0.0673193i
$937$	−43.6575	+	17.1343i	−1.42623	+	0.559753i	−0.947940	−	0.318450i	$-0.896838\pi$
$937$	−43.6575	+	17.1343i	−1.42623	+	0.559753i	−0.478288	+	0.878203i	$0.658742\pi$
$938$	0.218390	−	0.0498461i	0.00713069	−	0.00162753i
$939$	−0.310571	+	14.9910i	−0.0101351	+	0.489212i
$940$	−7.50140	+	4.33094i	−0.244669	+	0.141260i
$941$	25.1172	+	27.0699i	0.818797	+	0.882453i	0.994791	−	0.101938i	$-0.0325045\pi$
$941$	25.1172	+	27.0699i	0.818797	+	0.882453i	−0.175994	+	0.984391i	$0.556314\pi$
$942$	0.577063	+	0.240390i	0.0188017	+	0.00783234i
$943$	0.556135	+	0.379167i	0.0181103	+	0.0123474i
$944$	4.67480	−	9.70732i	0.152152	−	0.315946i
$945$	1.33052	−	21.3832i	0.0432819	−	0.695595i
$946$	−0.675482	−	0.142420i	−0.0219618	−	0.00463048i
$947$		−	52.9457i		−	1.72050i	−0.509870	−	0.860251i	$-0.670307\pi$
$947$		−	52.9457i		−	1.72050i	0.509870	−	0.860251i	$-0.329693\pi$
$948$	−0.251764	−	4.65037i	−0.00817690	−	0.151037i
$949$	−8.64666	+	12.6823i	−0.280682	+	0.411686i
$950$	0.149147	−	0.118941i	0.00483896	−	0.00385894i
$951$	16.9805	−	51.2552i	0.550631	−	1.66206i
$952$	2.46127	+	4.26304i	0.0797702	+	0.138166i
$953$	−2.00558	+	3.47376i	−0.0649670	+	0.112526i	−0.896679	−	0.442681i	$-0.854028\pi$
$953$	−2.00558	+	3.47376i	−0.0649670	+	0.112526i	0.831712	+	0.555207i	$0.187361\pi$
$954$	−0.454714	+	1.28290i	−0.0147219	+	0.0415353i
$955$	−2.88318	−	7.34622i	−0.0932975	−	0.237718i
$956$	−4.24514	−	13.7624i	−0.137298	−	0.445108i
$957$	−6.75073	+	39.2530i	−0.218220	+	1.26887i
$958$	−0.499237	+	0.0374126i	−0.0161296	+	0.00120875i
$959$	−15.3806	+	49.8625i	−0.496664	+	1.61015i
$960$	−12.3058	−	6.24340i	−0.397168	−	0.201505i
$961$	−12.0767	+	1.82027i	−0.389572	+	0.0587185i
$962$	−0.553820	−	0.126406i	−0.0178559	−	0.00407549i
$963$	−4.55088	−	17.2620i	−0.146650	−	0.556260i
$964$	11.4195	+	0.855774i	0.367798	+	0.0275626i
$965$	5.93767	−	15.1289i	0.191140	−	0.487017i
$966$	0.0462801	+	0.125504i	0.00148904	+	0.00403801i
$967$	1.45385	−	0.700139i	0.0467528	−	0.0225150i	−0.410361	−	0.911923i	$-0.634597\pi$
$967$	1.45385	−	0.700139i	0.0467528	−	0.0225150i	0.457114	+	0.889408i	$0.348883\pi$
$968$	−0.398639	+	0.191975i	−0.0128127	+	0.00617029i
$969$	24.7084	+	67.0048i	0.793747	+	2.15250i
$970$	0.0708668	−	0.180566i	0.00227539	−	0.00579761i
$971$	19.0279	+	1.42594i	0.610634	+	0.0457607i	0.376458	−	0.926434i	$-0.377142\pi$
$971$	19.0279	+	1.42594i	0.610634	+	0.0457607i	0.234176	+	0.972194i	$0.424761\pi$
$972$	30.5611	−	6.05607i	0.980248	−	0.194248i
$973$	13.3147	+	3.03900i	0.426850	+	0.0974258i
$974$	−0.768432	+	0.115822i	−0.0246221	+	0.00371119i
$975$	7.39499	+	3.75188i	0.236829	+	0.120156i
$976$	−6.88952	+	22.3353i	−0.220528	+	0.714934i
$977$	−11.2941	+	0.846377i	−0.361331	+	0.0270780i	−0.254159	−	0.967162i	$-0.581799\pi$
$977$	−11.2941	+	0.846377i	−0.361331	+	0.0270780i	−0.107172	+	0.994240i	$0.534180\pi$
$978$	−0.0644444	+	0.374720i	−0.00206070	+	0.0119822i
$979$	4.21543	+	13.6661i	0.134726	+	0.436770i
$980$	7.30208	+	18.6054i	0.233256	+	0.594327i
$981$	−41.0524	−	14.5507i	−1.31070	−	0.464570i
$982$	−0.0820844	+	0.142174i	−0.00261942	+	0.00453696i
$983$	−11.4765	−	19.8778i	−0.366043	−	0.634005i	0.622900	−	0.782301i	$-0.285954\pi$
$983$	−11.4765	−	19.8778i	−0.366043	−	0.634005i	−0.988943	+	0.148297i	$0.952621\pi$
$984$	0.108122	−	0.326363i	0.00344680	−	0.0104041i
$985$	−2.16553	+	1.72695i	−0.0689995	+	0.0550252i
$986$	1.36547	−	2.00277i	0.0434854	−	0.0637813i
$987$	1.67318	+	30.9056i	0.0532578	+	0.983735i
$988$		−	49.1118i		−	1.56245i
$989$	−2.28764	−	2.38483i	−0.0727426	−	0.0758333i
$990$	0.266737	+	0.169105i	0.00847745	+	0.00537449i
$991$	−3.65670	+	7.59321i	−0.116159	+	0.241206i	−0.950940	−	0.309376i	$-0.899880\pi$
$991$	−3.65670	+	7.59321i	−0.116159	+	0.241206i	0.834781	+	0.550582i	$0.185594\pi$
$992$	2.42022	+	1.65008i	0.0768420	+	0.0523900i
$993$	−15.1773	−	6.32248i	−0.481637	−	0.200638i
$994$	−1.38451	−	1.49215i	−0.0439140	−	0.0473280i
$995$	14.3316	−	8.27434i	0.454342	−	0.262314i
$996$	0.812319	−	39.2098i	0.0257393	−	1.24241i
$997$	18.2414	−	4.16347i	0.577710	−	0.131858i	0.0763250	−	0.997083i	$-0.475681\pi$
$997$	18.2414	−	4.16347i	0.577710	−	0.131858i	0.501385	+	0.865225i	$0.332824\pi$
$998$	−0.745922	+	0.292753i	−0.0236117	+	0.00926692i
$999$	3.89565	+	16.1244i	0.123253	+	0.510154i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	645.2.bn.b.491.14	yes	348
3.2	odd	2		645.2.bn.a.491.16	yes	348
43.12	odd	42		645.2.bn.a.356.16	✓	348
129.98	even	42	inner	645.2.bn.b.356.14	yes	348

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
645.2.bn.a.356.16	✓	348	43.12	odd	42
645.2.bn.a.491.16	yes	348	3.2	odd	2
645.2.bn.b.356.14	yes	348	129.98	even	42	inner
645.2.bn.b.491.14	yes	348	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 645 = 3 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	645.bn (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0334865 + 0.0161262i) q^{2} +(-0.165184 + 1.72416i) q^{3} +(-1.24612 - 1.56258i) q^{4} +(-0.733052 + 0.680173i) q^{5} +(-0.0333356 + 0.0550721i) q^{6} +(-3.57076 - 2.06158i) q^{7} +(-0.0330705 - 0.144891i) q^{8} +(-2.94543 - 0.569605i) q^{9} +(-0.0355160 + 0.0109552i) q^{10} +(2.21451 + 1.76601i) q^{11} +(2.89998 - 1.89039i) q^{12} +(4.57487 + 1.41116i) q^{13} +(-0.0863266 - 0.126618i) q^{14} +(-1.05164 - 1.37625i) q^{15} +(-0.888240 + 3.89163i) q^{16} +(5.46398 - 5.88877i) q^{17} +(-0.0894464 - 0.0665728i) q^{18} +(4.77784 + 1.87516i) q^{19} +(1.97630 + 0.297879i) q^{20} +(4.14431 - 5.81600i) q^{21} +(0.0456770 + 0.0948492i) q^{22} +(-0.0751105 + 0.498326i) q^{23} +(0.255278 - 0.0330850i) q^{24} +(0.0747301 - 0.997204i) q^{25} +(0.130440 + 0.121030i) q^{26} +(1.46863 - 4.98429i) q^{27} +(1.22820 + 8.14858i) q^{28} +(6.70784 - 4.57333i) q^{29} +(-0.0130219 - 0.0630447i) q^{30} +(-0.491251 - 6.55529i) q^{31} +(-0.277824 + 0.348381i) q^{32} +(-3.41068 + 3.52644i) q^{33} +(0.277933 - 0.109081i) q^{34} +(4.01978 - 0.917489i) q^{35} +(2.78030 + 5.31227i) q^{36} +(-2.76472 + 1.59621i) q^{37} +(0.129754 + 0.139841i) q^{38} +(-3.18876 + 7.65469i) q^{39} +(0.122793 + 0.0837192i) q^{40} +(0.579505 - 1.20335i) q^{41} +(0.232569 - 0.127925i) q^{42} +(-4.00283 + 5.19397i) q^{43} -5.66101i q^{44} +(2.54658 - 1.58585i) q^{45} +(-0.0105513 + 0.0154759i) q^{46} +(-3.38840 + 2.70216i) q^{47} +(-6.56306 - 2.17430i) q^{48} +(5.00021 + 8.66062i) q^{49} +(0.0185836 - 0.0321877i) q^{50} +(9.25059 + 10.3935i) q^{51} +(-3.49578 - 8.90709i) q^{52} +(-3.59808 - 11.6647i) q^{53} +(0.129557 - 0.143223i) q^{54} +(-2.82454 + 0.211670i) q^{55} +(-0.180618 + 0.585549i) q^{56} +(-4.02230 + 7.92799i) q^{57} +(0.298372 - 0.0449724i) q^{58} +(-2.63150 - 0.600622i) q^{59} +(-0.840041 + 3.35824i) q^{60} +(5.83918 + 0.437586i) q^{61} +(0.0892619 - 0.227436i) q^{62} +(9.34313 + 8.10615i) q^{63} +(7.17790 - 3.45669i) q^{64} +(-4.31345 + 2.07725i) q^{65} +(-0.171080 + 0.0630867i) q^{66} +(-0.534035 + 1.36070i) q^{67} +(-16.0105 - 1.19982i) q^{68} +(-0.846784 - 0.211818i) q^{69} +(0.149404 + 0.0341005i) q^{70} +(13.1344 - 1.97969i) q^{71} +(0.0148759 + 0.445604i) q^{72} +(-0.945017 + 3.06367i) q^{73} +(-0.118322 + 0.00886699i) q^{74} +(1.70699 + 0.293568i) q^{75} +(-3.02365 - 9.80245i) q^{76} +(-4.26670 - 10.8714i) q^{77} +(-0.230222 + 0.204906i) q^{78} +(0.672671 - 1.16510i) q^{79} +(-1.99586 - 3.45693i) q^{80} +(8.35110 + 3.35546i) q^{81} +(0.0388111 - 0.0309509i) q^{82} +(6.38194 - 9.36059i) q^{83} +(-14.2523 + 0.771596i) q^{84} +8.03322i q^{85} +(-0.217800 + 0.109377i) q^{86} +(6.77710 + 12.3208i) q^{87} +(0.182645 - 0.379266i) q^{88} +(4.17178 + 2.84427i) q^{89} +(0.110850 - 0.0120377i) q^{90} +(-13.4265 - 14.4704i) q^{91} +(0.872272 - 0.503606i) q^{92} +(11.3835 + 0.235834i) q^{93} +(-0.157041 + 0.0358437i) q^{94} +(-4.77784 + 1.87516i) q^{95} +(-0.554771 - 0.536559i) q^{96} +(-3.25397 + 4.08035i) q^{97} +(0.0277762 + 0.370648i) q^{98} +(-5.51675 - 6.46306i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 348 q - 56 q^{4} + 29 q^{5} - 4 q^{6} - 3 q^{7} - 8 q^{9} - 7 q^{12} + 5 q^{13} - 42 q^{14} - 7 q^{15} - 68 q^{16} - 22 q^{18} - 30 q^{19} + 28 q^{20} + 4 q^{21} - 42 q^{22} + 6 q^{23} + 9 q^{24} + 29 q^{25}+ \cdots - q^{99}+O(q^{100}) \) 348 * q - 56 * q^4 + 29 * q^5 - 4 * q^6 - 3 * q^7 - 8 * q^9 - 7 * q^12 + 5 * q^13 - 42 * q^14 - 7 * q^15 - 68 * q^16 - 22 * q^18 - 30 * q^19 + 28 * q^20 + 4 * q^21 - 42 * q^22 + 6 * q^23 + 9 * q^24 + 29 * q^25 + 182 * q^26 + 6 * q^27 + 18 * q^28 + 2 * q^29 + 2 * q^30 + 72 * q^31 - 23 * q^33 - 84 * q^34 - 21 * q^35 + 56 * q^36 - 39 * q^37 - 4 * q^39 - 84 * q^42 + 6 * q^43 + 4 * q^45 - 94 * q^46 - 28 * q^47 - 72 * q^48 + 175 * q^49 + 103 * q^51 - 56 * q^52 + 94 * q^53 + 22 * q^54 - 90 * q^56 + 74 * q^57 - 40 * q^58 - 7 * q^60 + 30 * q^61 - 104 * q^62 + q^63 - 76 * q^64 - 10 * q^65 - 22 * q^66 + 9 * q^67 + 98 * q^68 - 244 * q^69 - 8 * q^71 + 85 * q^72 - 75 * q^73 - 42 * q^74 - 14 * q^75 + 30 * q^76 - 16 * q^77 + 44 * q^78 + 20 * q^79 - 148 * q^80 - 136 * q^81 - 30 * q^83 - 124 * q^84 + 38 * q^86 + 42 * q^87 + 42 * q^88 - 102 * q^89 - 82 * q^90 - 13 * q^91 + 24 * q^92 - 167 * q^93 - 56 * q^94 + 30 * q^95 - 494 * q^96 - 64 * q^97 - 12 * q^98 - q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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