LMFDB - Embedded newform 819.2.ew.a.470.81

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(176,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 0, 11]))

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

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

chi := DirichletCharacter("819.176");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.ew (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$84$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			470.81
Character	$\chi$	$=$	819.470
Dual form			819.2.ew.a.176.81

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.78823 + 1.78823i) q^{2} +(-1.55687 - 0.759044i) q^{3} +4.39555i q^{4} +(0.310355 - 1.15826i) q^{5} +(-1.42670 - 4.14140i) q^{6} +(0.258819 - 0.965926i) q^{7} +(-4.28379 + 4.28379i) q^{8} +(1.84770 + 2.36347i) q^{9} +O(q^{10})$	\(q+(1.78823 + 1.78823i) q^{2} +(-1.55687 - 0.759044i) q^{3} +4.39555i q^{4} +(0.310355 - 1.15826i) q^{5} +(-1.42670 - 4.14140i) q^{6} +(0.258819 - 0.965926i) q^{7} +(-4.28379 + 4.28379i) q^{8} +(1.84770 + 2.36347i) q^{9} +(2.62623 - 1.51625i) q^{10} +(-4.23220 + 4.23220i) q^{11} +(3.33642 - 6.84331i) q^{12} +(3.51785 + 0.790387i) q^{13} +(2.19013 - 1.26447i) q^{14} +(-1.36236 + 1.56769i) q^{15} -6.52974 q^{16} +(-2.05748 + 3.56367i) q^{17} +(-0.922312 + 7.53056i) q^{18} +(1.17739 + 4.39407i) q^{19} +(5.09120 + 1.36418i) q^{20} +(-1.13613 + 1.30737i) q^{21} -15.1363 q^{22} +(-4.09016 + 7.08437i) q^{23} +(9.92091 - 3.41773i) q^{24} +(3.08488 + 1.78105i) q^{25} +(4.87734 + 7.70413i) q^{26} +(-1.08266 - 5.08211i) q^{27} +(4.24577 + 1.13765i) q^{28} -5.35969i q^{29} +(-5.23961 + 0.367190i) q^{30} +(-2.14777 - 0.575493i) q^{31} +(-3.10910 - 3.10910i) q^{32} +(9.80141 - 3.37656i) q^{33} +(-10.0519 + 2.69340i) q^{34} +(-1.03847 - 0.599561i) q^{35} +(-10.3887 + 8.12167i) q^{36} +(1.19641 - 4.46508i) q^{37} +(-5.75217 + 9.96305i) q^{38} +(-4.87691 - 3.90074i) q^{39} +(3.63226 + 6.29126i) q^{40} +(5.16826 - 1.38483i) q^{41} +(-4.36954 + 0.306216i) q^{42} +(0.241739 - 0.139568i) q^{43} +(-18.6028 - 18.6028i) q^{44} +(3.31096 - 1.40661i) q^{45} +(-19.9826 + 5.35433i) q^{46} +(-0.837675 - 3.12625i) q^{47} +(10.1660 + 4.95636i) q^{48} +(-0.866025 - 0.500000i) q^{49} +(2.33154 + 8.70141i) q^{50} +(5.90822 - 3.98645i) q^{51} +(-3.47418 + 15.4629i) q^{52} -4.41316i q^{53} +(7.15195 - 11.0240i) q^{54} +(3.58851 + 6.21548i) q^{55} +(3.02910 + 5.24655i) q^{56} +(1.50225 - 7.73469i) q^{57} +(9.58436 - 9.58436i) q^{58} +(1.72928 - 1.72928i) q^{59} +(-6.89087 - 5.98830i) q^{60} +(2.24315 + 3.88525i) q^{61} +(-2.81160 - 4.86983i) q^{62} +(2.76116 - 1.17303i) q^{63} +1.93989i q^{64} +(2.00726 - 3.82930i) q^{65} +(23.5653 + 11.4891i) q^{66} +(3.44833 + 12.8693i) q^{67} +(-15.6643 - 9.04376i) q^{68} +(11.7452 - 7.92484i) q^{69} +(-0.784871 - 2.92918i) q^{70} +(2.79759 - 0.749612i) q^{71} +(-18.0398 - 2.20944i) q^{72} +(-6.56366 - 6.56366i) q^{73} +(10.1241 - 5.84513i) q^{74} +(-3.45086 - 5.11443i) q^{75} +(-19.3143 + 5.17526i) q^{76} +(2.99261 + 5.18336i) q^{77} +(-1.74562 - 15.6965i) q^{78} +(4.95719 - 8.58611i) q^{79} +(-2.02654 + 7.56315i) q^{80} +(-2.17199 + 8.73398i) q^{81} +(11.7184 + 6.76565i) q^{82} +(7.32070 - 1.96157i) q^{83} +(-5.74660 - 4.99391i) q^{84} +(3.48911 + 3.48911i) q^{85} +(0.681865 + 0.182705i) q^{86} +(-4.06824 + 8.34435i) q^{87} -36.2597i q^{88} +(-12.6016 - 3.37660i) q^{89} +(8.43612 + 3.40543i) q^{90} +(1.67394 - 3.19342i) q^{91} +(-31.1397 - 17.9785i) q^{92} +(2.90698 + 2.52622i) q^{93} +(4.09250 - 7.08841i) q^{94} +5.45489 q^{95} +(2.48053 + 7.20042i) q^{96} +(-13.6990 - 3.67064i) q^{97} +(-0.654538 - 2.44277i) q^{98} +(-17.8225 - 2.18283i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q + 24 q^{6} - 36 q^{8}+O(q^{10}) $ 336 * q + 24 * q^6 - 36 * q^8	$ 336 q + 24 q^{6} - 36 q^{8} + 16 q^{15} - 336 q^{16} + 20 q^{18} + 8 q^{21} + 8 q^{24} + 96 q^{26} + 24 q^{27} - 96 q^{30} - 72 q^{32} - 36 q^{33} - 12 q^{36} - 72 q^{38} - 16 q^{39} - 48 q^{41} - 28 q^{45} + 60 q^{47} - 48 q^{48} + 132 q^{50} - 36 q^{52} - 108 q^{54} + 68 q^{57} - 72 q^{58} - 44 q^{60} - 36 q^{62} - 8 q^{63} - 72 q^{65} - 20 q^{66} - 72 q^{69} + 48 q^{71} - 104 q^{72} + 12 q^{74} + 104 q^{78} - 12 q^{79} + 96 q^{80} - 68 q^{81} - 120 q^{83} - 12 q^{84} + 36 q^{85} + 48 q^{86} - 24 q^{87} - 60 q^{89} - 72 q^{92} - 172 q^{93} - 48 q^{94} - 152 q^{96} + 48 q^{97}+O(q^{100}) $ 336 * q + 24 * q^6 - 36 * q^8 + 16 * q^15 - 336 * q^16 + 20 * q^18 + 8 * q^21 + 8 * q^24 + 96 * q^26 + 24 * q^27 - 96 * q^30 - 72 * q^32 - 36 * q^33 - 12 * q^36 - 72 * q^38 - 16 * q^39 - 48 * q^41 - 28 * q^45 + 60 * q^47 - 48 * q^48 + 132 * q^50 - 36 * q^52 - 108 * q^54 + 68 * q^57 - 72 * q^58 - 44 * q^60 - 36 * q^62 - 8 * q^63 - 72 * q^65 - 20 * q^66 - 72 * q^69 + 48 * q^71 - 104 * q^72 + 12 * q^74 + 104 * q^78 - 12 * q^79 + 96 * q^80 - 68 * q^81 - 120 * q^83 - 12 * q^84 + 36 * q^85 + 48 * q^86 - 24 * q^87 - 60 * q^89 - 72 * q^92 - 172 * q^93 - 48 * q^94 - 152 * q^96 + 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$1$

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 $

$2$	1.78823	+	1.78823i	1.26447	+	1.26447i	0.948903	+	0.315568i	$0.102195\pi$
$2$	1.78823	+	1.78823i	1.26447	+	1.26447i	0.315568	+	0.948903i	$0.397805\pi$
$3$	−1.55687	−	0.759044i	−0.898861	−	0.438234i
$3$	−1.55687	−	0.759044i	−0.898861	−	0.438234i
$4$			4.39555i			2.19777i
$5$	0.310355	−	1.15826i	0.138795	−	0.517991i	−0.861158	−	0.508337i	$-0.830260\pi$
$5$	0.310355	−	1.15826i	0.138795	−	0.517991i	0.999953	−	0.00965369i	$-0.00307291\pi$
$6$	−1.42670	−	4.14140i	−0.582448	−	1.69072i
$7$	0.258819	−	0.965926i	0.0978244	−	0.365086i
$7$	0.258819	−	0.965926i	0.0978244	−	0.365086i
$8$	−4.28379	+	4.28379i	−1.51455	+	1.51455i
$9$	1.84770	+	2.36347i	0.615901	+	0.787824i
$10$	2.62623	−	1.51625i	0.830487	−	0.479482i
$11$	−4.23220	+	4.23220i	−1.27605	+	1.27605i	−0.333198	+	0.942857i	$0.608128\pi$
$11$	−4.23220	+	4.23220i	−1.27605	+	1.27605i	−0.942857	+	0.333198i	$0.891872\pi$
$12$	3.33642	−	6.84331i	0.963140	−	1.97549i
$13$	3.51785	+	0.790387i	0.975677	+	0.219214i
$13$	3.51785	+	0.790387i	0.975677	+	0.219214i
$14$	2.19013	−	1.26447i	0.585336	−	0.337944i
$15$	−1.36236	+	1.56769i	−0.351759	+	0.404777i
$16$	−6.52974			−1.63244
$17$	−2.05748	+	3.56367i	−0.499013	+	0.864316i	−0.999999	−	0.00113935i	$-0.999637\pi$
$17$	−2.05748	+	3.56367i	−0.499013	+	0.864316i	0.500986	+	0.865455i	$0.332971\pi$
$18$	−0.922312	+	7.53056i	−0.217391	+	1.77497i
$19$	1.17739	+	4.39407i	0.270111	+	1.00807i	0.959047	+	0.283246i	$0.0914113\pi$
$19$	1.17739	+	4.39407i	0.270111	+	1.00807i	−0.688936	+	0.724822i	$0.741922\pi$
$20$	5.09120	+	1.36418i	1.13843	+	0.305040i
$21$	−1.13613	+	1.30737i	−0.247924	+	0.285291i
$22$	−15.1363			−3.22707
$23$	−4.09016	+	7.08437i	−0.852857	+	1.47719i	0.0257613	+	0.999668i	$0.491799\pi$
$23$	−4.09016	+	7.08437i	−0.852857	+	1.47719i	−0.878619	+	0.477524i	$0.841534\pi$
$24$	9.92091	−	3.41773i	2.02510	−	0.697641i
$25$	3.08488	+	1.78105i	0.616975	+	0.356211i
$26$	4.87734	+	7.70413i	0.956525	+	1.51090i
$27$	−1.08266	−	5.08211i	−0.208358	−	0.978053i
$28$	4.24577	+	1.13765i	0.802376	+	0.214996i
$29$		−	5.35969i		−	0.995269i	−0.867387	−	0.497634i	$-0.834202\pi$
$29$		−	5.35969i		−	0.995269i	0.867387	−	0.497634i	$-0.165798\pi$
$30$	−5.23961	+	0.367190i	−0.956617	+	0.0670394i
$31$	−2.14777	−	0.575493i	−0.385751	−	0.103362i	0.0607313	−	0.998154i	$-0.480657\pi$
$31$	−2.14777	−	0.575493i	−0.385751	−	0.103362i	−0.446482	+	0.894793i	$0.647323\pi$
$32$	−3.10910	−	3.10910i	−0.549617	−	0.549617i
$33$	9.80141	−	3.37656i	1.70621	−	0.587784i
$34$	−10.0519	+	2.69340i	−1.72389	+	0.461915i
$35$	−1.03847	−	0.599561i	−0.175533	−	0.101344i
$36$	−10.3887	+	8.12167i	−1.73146	+	1.35361i
$37$	1.19641	−	4.46508i	0.196689	−	0.734055i	−0.795134	−	0.606434i	$-0.792599\pi$
$37$	1.19641	−	4.46508i	0.196689	−	0.734055i	0.991823	−	0.127621i	$-0.0407340\pi$
$38$	−5.75217	+	9.96305i	−0.933125	+	1.61622i
$39$	−4.87691	−	3.90074i	−0.780930	−	0.624618i
$40$	3.63226	+	6.29126i	0.574311	+	0.994735i
$41$	5.16826	−	1.38483i	0.807146	−	0.216274i	0.168427	−	0.985714i	$-0.446131\pi$
$41$	5.16826	−	1.38483i	0.807146	−	0.216274i	0.638719	+	0.769440i	$0.279465\pi$
$42$	−4.36954	+	0.306216i	−0.674235	+	0.0472501i
$43$	0.241739	−	0.139568i	0.0368648	−	0.0212839i	−0.481454	−	0.876471i	$-0.659891\pi$
$43$	0.241739	−	0.139568i	0.0368648	−	0.0212839i	0.518319	+	0.855187i	$0.326558\pi$
$44$	−18.6028	−	18.6028i	−2.80448	−	2.80448i
$45$	3.31096	−	1.40661i	0.493569	−	0.209685i
$46$	−19.9826	+	5.35433i	−2.94628	+	0.789453i
$47$	−0.837675	−	3.12625i	−0.122187	−	0.456010i	0.877536	−	0.479510i	$-0.159186\pi$
$47$	−0.837675	−	3.12625i	−0.122187	−	0.456010i	−0.999724	+	0.0235003i	$0.992519\pi$
$48$	10.1660	+	4.95636i	1.46733	+	0.715389i
$49$	−0.866025	−	0.500000i	−0.123718	−	0.0714286i
$50$	2.33154	+	8.70141i	0.329729	+	1.23057i
$51$	5.90822	−	3.98645i	0.827316	−	0.558215i
$52$	−3.47418	+	15.4629i	−0.481782	+	2.14432i
$53$		−	4.41316i		−	0.606194i	−0.952960	−	0.303097i	$-0.901979\pi$
$53$		−	4.41316i		−	0.606194i	0.952960	−	0.303097i	$-0.0980206\pi$
$54$	7.15195	−	11.0240i	0.973257	−	1.50018i
$55$	3.58851	+	6.21548i	0.483874	+	0.838095i
$56$	3.02910	+	5.24655i	0.404780	+	0.701100i
$57$	1.50225	−	7.73469i	0.198978	−	1.02448i
$58$	9.58436	−	9.58436i	1.25849	−	1.25849i
$59$	1.72928	−	1.72928i	0.225133	−	0.225133i	−0.585523	−	0.810656i	$-0.699111\pi$
$59$	1.72928	−	1.72928i	0.225133	−	0.225133i	0.810656	+	0.585523i	$0.199111\pi$
$60$	−6.89087	−	5.98830i	−0.889607	−	0.773087i
$61$	2.24315	+	3.88525i	0.287206	+	0.497455i	0.973142	−	0.230207i	$-0.0739403\pi$
$61$	2.24315	+	3.88525i	0.287206	+	0.497455i	−0.685936	+	0.727662i	$0.740607\pi$
$62$	−2.81160	−	4.86983i	−0.357073	−	0.618469i
$63$	2.76116	−	1.17303i	0.347873	−	0.147788i
$64$			1.93989i			0.242486i
$65$	2.00726	−	3.82930i	0.248970	−	0.474966i
$66$	23.5653	+	11.4891i	2.90069	+	1.41421i
$67$	3.44833	+	12.8693i	0.421280	+	1.57224i	0.771915	+	0.635726i	$0.219299\pi$
$67$	3.44833	+	12.8693i	0.421280	+	1.57224i	−0.350635	+	0.936512i	$0.614034\pi$
$68$	−15.6643	−	9.04376i	−1.89957	−	1.09672i
$69$	11.7452	−	7.92484i	1.41396	−	0.954039i
$70$	−0.784871	−	2.92918i	−0.0938100	−	0.350104i
$71$	2.79759	−	0.749612i	0.332013	−	0.0889626i	−0.0889617	−	0.996035i	$-0.528355\pi$
$71$	2.79759	−	0.749612i	0.332013	−	0.0889626i	0.420974	+	0.907072i	$0.361688\pi$
$72$	−18.0398	−	2.20944i	−2.12601	−	0.260385i
$73$	−6.56366	−	6.56366i	−0.768219	−	0.768219i	0.209574	−	0.977793i	$-0.432792\pi$
$73$	−6.56366	−	6.56366i	−0.768219	−	0.768219i	−0.977793	+	0.209574i	$0.932792\pi$
$74$	10.1241	−	5.84513i	1.17690	−	0.679483i
$75$	−3.45086	−	5.11443i	−0.398471	−	0.590564i
$76$	−19.3143	+	5.17526i	−2.21551	+	0.593643i
$77$	2.99261	+	5.18336i	0.341040	+	0.590699i
$78$	−1.74562	−	15.6965i	−0.197653	−	1.77728i
$79$	4.95719	−	8.58611i	0.557728	−	0.966013i	−0.439958	−	0.898018i	$-0.645007\pi$
$79$	4.95719	−	8.58611i	0.557728	−	0.966013i	0.997686	−	0.0679947i	$-0.0216601\pi$
$80$	−2.02654	+	7.56315i	−0.226574	+	0.845586i
$81$	−2.17199	+	8.73398i	−0.241332	+	0.970443i
$82$	11.7184	+	6.76565i	1.29409	+	0.747141i
$83$	7.32070	−	1.96157i	0.803551	−	0.215311i	0.166408	−	0.986057i	$-0.446783\pi$
$83$	7.32070	−	1.96157i	0.803551	−	0.215311i	0.637142	+	0.770746i	$0.280116\pi$
$84$	−5.74660	−	4.99391i	−0.627005	−	0.544880i
$85$	3.48911	+	3.48911i	0.378447	+	0.378447i
$86$	0.681865	+	0.182705i	0.0735274	+	0.0197016i
$87$	−4.06824	+	8.34435i	−0.436161	+	0.894608i
$88$		−	36.2597i		−	3.86530i
$89$	−12.6016	−	3.37660i	−1.33577	−	0.357918i	−0.480907	−	0.876772i	$-0.659692\pi$
$89$	−12.6016	−	3.37660i	−1.33577	−	0.357918i	−0.854863	+	0.518853i	$0.826359\pi$
$90$	8.43612	+	3.40543i	0.889245	+	0.358964i
$91$	1.67394	−	3.19342i	0.175477	−	0.334761i
$92$	−31.1397	−	17.9785i	−3.24653	−	1.87439i
$93$	2.90698	+	2.52622i	0.301440	+	0.261957i
$94$	4.09250	−	7.08841i	0.422109	−	0.731114i
$95$	5.45489			0.559660
$96$	2.48053	+	7.20042i	0.253168	+	0.734890i
$97$	−13.6990	−	3.67064i	−1.39092	−	0.372697i	−0.515847	−	0.856681i	$-0.672523\pi$
$97$	−13.6990	−	3.67064i	−1.39092	−	0.372697i	−0.875077	+	0.483984i	$0.839189\pi$
$98$	−0.654538	−	2.44277i	−0.0661184	−	0.246757i
$99$	−17.8225	−	2.18283i	−1.79123	−	0.219382i
$100$	−7.82871	+	13.5597i	−0.782871	+	1.35597i
$101$	11.8142			1.17555			0.587777	−	0.809023i	$-0.300003\pi$
$101$	11.8142			1.17555			0.587777	+	0.809023i	$0.300003\pi$
$102$	17.6940	+	3.43657i	1.75196	+	0.340271i
$103$	7.49758	−	4.32873i	0.738758	−	0.426522i	−0.0828594	−	0.996561i	$-0.526405\pi$
$103$	7.49758	−	4.32873i	0.738758	−	0.426522i	0.821618	+	0.570039i	$0.193072\pi$
$104$	−18.4556	+	11.6839i	−1.80972	+	1.14570i
$105$	1.16167	+	1.72168i	0.113368	+	0.168019i
$106$	7.89175	−	7.89175i	0.766514	−	0.766514i
$107$	−13.3523	+	7.70898i	−1.29082	+	0.745255i	−0.978800	−	0.204820i	$-0.934339\pi$
$107$	−13.3523	+	7.70898i	−1.29082	+	0.745255i	−0.312020	+	0.950075i	$0.601006\pi$
$108$	22.3387	−	4.75888i	2.14954	−	0.457923i
$109$	4.27348	−	4.27348i	0.409325	−	0.409325i	−0.472178	−	0.881503i	$-0.656532\pi$
$109$	4.27348	−	4.27348i	0.409325	−	0.409325i	0.881503	+	0.472178i	$0.156532\pi$
$110$	−4.69763	+	17.5318i	−0.447902	+	1.67159i
$111$	−5.25186	+	6.04343i	−0.498484	+	0.573617i
$112$	−1.69002	+	6.30724i	−0.159692	+	0.595979i
$113$			10.4615i			0.984135i	0.870557	+	0.492067i	$0.163759\pi$
$113$			10.4615i			0.984135i	−0.870557	+	0.492067i	$0.836241\pi$
$114$	16.5178	−	11.1450i	1.54703	−	1.04383i
$115$	6.93615	+	6.93615i	0.646799	+	0.646799i
$116$	23.5588			2.18738
$117$	4.63189	+	9.77474i	0.428219	+	0.903675i
$118$	6.18471			0.569348
$119$	2.90972	+	2.90972i	0.266734	+	0.266734i
$120$	−0.879620	−	12.5517i	−0.0802980	−	1.14581i
$121$		−	24.8230i		−	2.25663i
$122$	−2.93646	+	10.9590i	−0.265854	+	0.992181i
$123$	−9.09747	−	1.76693i	−0.820291	−	0.159319i
$124$	2.52961	−	9.44062i	0.227165	−	0.847793i
$125$	7.25987	−	7.25987i	0.649343	−	0.649343i
$126$	7.03525	+	2.83994i	0.626750	+	0.253002i
$127$	8.70644	−	5.02666i	0.772571	−	0.446044i	−0.0612197	−	0.998124i	$-0.519499\pi$
$127$	8.70644	−	5.02666i	0.772571	−	0.446044i	0.833791	+	0.552080i	$0.186166\pi$
$128$	−9.68717	+	9.68717i	−0.856233	+	0.856233i
$129$	−0.482295	+	0.0337990i	−0.0424637	+	0.00297584i
$130$	10.4371	−	3.25822i	0.915396	−	0.285765i
$131$	8.87357	−	5.12316i	0.775288	−	0.447613i	−0.0594700	−	0.998230i	$-0.518941\pi$
$131$	8.87357	−	5.12316i	0.775288	−	0.447613i	0.834758	+	0.550618i	$0.185608\pi$
$132$	14.8418	+	43.0826i	1.29182	+	3.74986i
$133$	4.54907			0.394455
$134$	−16.8469	+	29.1797i	−1.45535	+	2.52075i
$135$	−6.22243	−	0.323258i	−0.535541	−	0.0278216i
$136$	−6.45217	−	24.0798i	−0.553269	−	2.06483i
$137$	2.38887	+	0.640096i	0.204095	+	0.0546871i	0.359418	−	0.933177i	$-0.382975\pi$
$137$	2.38887	+	0.640096i	0.204095	+	0.0546871i	−0.155323	+	0.987864i	$0.549642\pi$
$138$	35.1746	+	6.83170i	2.99426	+	0.581553i
$139$	20.0060			1.69689			0.848443	−	0.529286i	$-0.177540\pi$
$139$	20.0060			1.69689			0.848443	+	0.529286i	$0.177540\pi$
$140$	2.63540	−	4.56464i	0.222732	−	0.385783i
$141$	−1.06881	+	5.50300i	−0.0900097	+	0.463436i
$142$	6.34322	+	3.66226i	0.532311	+	0.307330i
$143$	−18.2333	+	11.5432i	−1.52475	+	0.965288i
$144$	−12.0650	−	15.4328i	−1.00542	−	1.28607i
$145$	−6.20792	−	1.66341i	−0.515540	−	0.138139i
$146$		−	23.4747i		−	1.94278i
$147$	0.968769	+	1.43579i	0.0799027	+	0.118422i
$148$	19.6265	+	5.25890i	1.61329	+	0.432279i
$149$	6.76590	+	6.76590i	0.554284	+	0.554284i	0.927674	−	0.373390i	$-0.121805\pi$
$149$	6.76590	+	6.76590i	0.554284	+	0.554284i	−0.373390	+	0.927674i	$0.621805\pi$
$150$	2.97485	−	15.3167i	0.242896	−	1.25061i
$151$	11.7504	−	3.14850i	0.956232	−	0.256222i	0.253227	−	0.967407i	$-0.418508\pi$
$151$	11.7504	−	3.14850i	0.956232	−	0.256222i	0.703005	+	0.711185i	$0.251841\pi$
$152$	−23.8670	−	13.7796i	−1.93587	−	1.11767i
$153$	−12.2242	+	1.72180i	−0.988271	+	0.139199i
$154$	−3.91756	+	14.6205i	−0.315686	+	1.17816i
$155$	−1.33314	+	2.30907i	−0.107081	+	0.185469i
$156$	17.1459	−	21.4367i	1.37277	−	1.71631i
$157$	3.22796	+	5.59100i	0.257620	+	0.446210i	0.965604	−	0.260018i	$-0.0837285\pi$
$157$	3.22796	+	5.59100i	0.257620	+	0.446210i	−0.707984	+	0.706228i	$0.750395\pi$
$158$	24.2186	−	6.48935i	1.92673	−	0.516265i
$159$	−3.34978	+	6.87072i	−0.265655	+	0.544884i
$160$	−4.56608	+	2.63623i	−0.360981	+	0.208412i
$161$	5.78436	+	5.78436i	0.455871	+	0.455871i
$162$	−19.5024	+	11.7344i	−1.53225	+	0.921940i
$163$	−9.91519	+	2.65677i	−0.776618	+	0.208094i	−0.625293	−	0.780390i	$-0.715021\pi$
$163$	−9.91519	+	2.65677i	−0.776618	+	0.208094i	−0.151325	+	0.988484i	$0.548354\pi$
$164$	6.08709	+	22.7173i	0.475322	+	1.77392i
$165$	−0.869025	−	12.4005i	−0.0676535	−	0.965381i
$166$	16.5989	+	9.58335i	1.28832	+	0.743812i
$167$	1.15390	+	4.30642i	0.0892917	+	0.333241i	0.996092	−	0.0883188i	$-0.0281494\pi$
$167$	1.15390	+	4.30642i	0.0892917	+	0.333241i	−0.906801	+	0.421560i	$0.861483\pi$
$168$	−0.733554	−	10.4674i	−0.0565949	−	0.807580i
$169$	11.7506	+	5.56093i	0.903891	+	0.427764i
$170$			12.4787i			0.957070i
$171$	−8.20979	+	10.9016i	−0.627818	+	0.833670i
$172$	0.613478	+	1.06258i	0.0467773	+	0.0810206i
$173$	−6.19465	−	10.7294i	−0.470970	−	0.815745i	0.528478	−	0.848947i	$-0.322763\pi$
$173$	−6.19465	−	10.7294i	−0.470970	−	0.815745i	−0.999449	+	0.0332022i	$0.989429\pi$
$174$	−22.1966	+	7.64667i	−1.68272	+	0.579693i
$175$	2.51879	−	2.51879i	0.190403	−	0.190403i
$176$	27.6351	−	27.6351i	2.08308	−	2.08308i
$177$	−4.00487	+	1.37967i	−0.301024	+	0.103702i
$178$	−16.4965	−	28.5728i	−1.23646	−	2.14162i
$179$	1.38846	+	2.40488i	0.103778	+	0.179749i	0.913238	−	0.407426i	$-0.133573\pi$
$179$	1.38846	+	2.40488i	0.103778	+	0.179749i	−0.809460	+	0.587175i	$0.800240\pi$
$180$	6.18282	+	14.5535i	0.460840	+	1.08475i
$181$			2.98476i			0.221856i	0.993828	+	0.110928i	$0.0353823\pi$
$181$			2.98476i			0.221856i	−0.993828	+	0.110928i	$0.964618\pi$
$182$	8.70397	−	2.71717i	0.645181	−	0.201410i
$183$	−0.543221	−	7.75149i	−0.0401561	−	0.573007i
$184$	−12.8266	−	47.8694i	−0.945586	−	3.52898i
$185$	−4.80042	−	2.77152i	−0.352934	−	0.203767i
$186$	0.680881	+	9.71582i	0.0499246	+	0.712399i
$187$	−6.37446	−	23.7898i	−0.466146	−	1.73968i
$188$	13.7416	−	3.68204i	1.00221	−	0.268540i
$189$	−5.18915	−	0.269579i	−0.377455	−	0.0196090i
$190$	9.75461	+	9.75461i	0.707674	+	0.707674i
$191$	−17.8167	+	10.2865i	−1.28917	+	0.744304i	−0.978507	−	0.206216i	$-0.933885\pi$
$191$	−17.8167	+	10.2865i	−1.28917	+	0.744304i	−0.310665	+	0.950519i	$0.600552\pi$
$192$	1.47246	−	3.02016i	0.106266	−	0.217961i
$193$	20.5421	−	5.50423i	1.47865	−	0.396203i	0.572763	−	0.819721i	$-0.305872\pi$
$193$	20.5421	−	5.50423i	1.47865	−	0.396203i	0.905888	+	0.423518i	$0.139205\pi$
$194$	−17.9331	−	31.0610i	−1.28752	−	2.23005i
$195$	−6.03165	+	4.43813i	−0.431936	+	0.317821i
$196$	2.19777	−	3.80666i	0.156984	−	0.271904i
$197$	4.54397	−	16.9583i	0.323745	−	1.20823i	−0.591823	−	0.806068i	$-0.701592\pi$
$197$	4.54397	−	16.9583i	0.323745	−	1.20823i	0.915568	−	0.402164i	$-0.131742\pi$
$198$	−27.9674	−	35.7742i	−1.98755	−	2.54236i
$199$	−22.4318	−	12.9510i	−1.59015	−	0.918071i	−0.993281	−	0.115730i	$-0.963079\pi$
$199$	−22.4318	−	12.9510i	−1.59015	−	0.918071i	−0.596866	−	0.802341i	$-0.703587\pi$
$200$	−20.8446	+	5.58530i	−1.47394	+	0.394941i
$201$	4.39979	−	22.6533i	0.310337	−	1.59784i
$202$	21.1265	+	21.1265i	1.48645	+	1.48645i
$203$	−5.17706	−	1.38719i	−0.363358	−	0.0973616i
$204$	17.5226	+	25.9699i	1.22683	+	1.81825i
$205$		−	6.41599i		−	0.448112i
$206$	21.1482	+	5.66664i	1.47346	+	0.394813i
$207$	−24.3011	+	3.42283i	−1.68904	+	0.237903i
$208$	−22.9707	−	5.16102i	−1.59273	−	0.357852i
$209$	−23.5795	−	13.6136i	−1.63103	−	0.941674i
$210$	−1.00143	+	5.15611i	−0.0691054	+	0.355805i
$211$	−11.2584	+	19.5001i	−0.775061	+	1.34244i	0.159699	+	0.987166i	$0.448948\pi$
$211$	−11.2584	+	19.5001i	−0.775061	+	1.34244i	−0.934760	+	0.355279i	$0.884386\pi$
$212$	19.3982			1.33228
$213$	−4.92448	−	0.956445i	−0.337420	−	0.0655345i
$214$	−37.6625	−	10.0916i	−2.57456	−	0.689851i
$215$	−0.0866314	−	0.323313i	−0.00590821	−	0.0220498i
$216$	26.4086	+	17.1328i	1.79688	+	1.16574i
$217$	−1.11177	+	1.92564i	−0.0754717	+	0.130721i
$218$	15.2840			1.03516
$219$	5.23668	+	15.2009i	0.353862	+	1.02718i
$220$	−27.3204	+	15.7735i	−1.84194	+	1.06345i
$221$	−10.0546	+	10.9102i	−0.676345	+	0.733902i
$222$	−20.1986	+	1.41551i	−1.35564	+	0.0950028i
$223$	8.35908	−	8.35908i	0.559765	−	0.559765i	−0.369475	−	0.929241i	$-0.620463\pi$
$223$	8.35908	−	8.35908i	0.559765	−	0.559765i	0.929241	+	0.369475i	$0.120463\pi$
$224$	−3.80786	+	2.19847i	−0.254423	+	0.146891i
$225$	1.49047	+	10.5819i	0.0993644	+	0.705458i
$226$	−18.7076	+	18.7076i	−1.24441	+	1.24441i
$227$	−6.05992	+	22.6159i	−0.402211	+	1.50107i	0.406931	+	0.913459i	$0.366599\pi$
$227$	−6.05992	+	22.6159i	−0.402211	+	1.50107i	−0.809142	+	0.587613i	$0.800068\pi$
$228$	33.9982	+	6.60322i	2.25159	+	0.437309i
$229$	2.93339	−	10.9475i	0.193844	−	0.723434i	−0.798720	−	0.601703i	$-0.794489\pi$
$229$	2.93339	−	10.9475i	0.193844	−	0.723434i	0.992563	−	0.121731i	$-0.0388444\pi$
$230$			24.8069i			1.63572i
$231$	−0.724718	−	10.3414i	−0.0476829	−	0.680411i
$232$	22.9598	+	22.9598i	1.50738	+	1.50738i
$233$	−3.95463			−0.259077			−0.129538	−	0.991574i	$-0.541350\pi$
$233$	−3.95463			−0.259077			−0.129538	+	0.991574i	$0.541350\pi$
$234$	−9.19661	+	25.7624i	−0.601201	+	1.68414i
$235$	−3.88099			−0.253168
$236$	7.60113	+	7.60113i	0.494791	+	0.494791i
$237$	−14.2350	+	9.60475i	−0.924660	+	0.623896i
$238$			10.4065i			0.674554i
$239$	2.54052	−	9.48134i	0.164332	−	0.613297i	−0.833792	−	0.552079i	$-0.813835\pi$
$239$	2.54052	−	9.48134i	0.164332	−	0.613297i	0.998124	−	0.0612182i	$-0.0194986\pi$
$240$	8.89583	−	10.2366i	0.574224	−	0.660772i
$241$	−1.85885	+	6.93732i	−0.119739	+	0.446872i	−0.999598	−	0.0283635i	$-0.990970\pi$
$241$	−1.85885	+	6.93732i	−0.119739	+	0.446872i	0.879859	+	0.475235i	$0.157637\pi$
$242$	44.3892	−	44.3892i	2.85345	−	2.85345i
$243$	10.0110	−	11.9491i	0.642205	−	0.766533i
$244$	−17.0778	+	9.85987i	−1.09329	+	0.631214i
$245$	−0.847907	+	0.847907i	−0.0541708	+	0.0541708i
$246$	−13.1087	−	19.4281i	−0.835780	−	1.23869i
$247$	0.668860	+	16.3883i	0.0425585	+	1.04276i
$248$	11.6659	−	6.73531i	0.740785	−	0.427693i
$249$	−12.8863	−	2.50281i	−0.816637	−	0.158609i
$250$	25.9647			1.64215
$251$	10.1697	−	17.6145i	0.641909	−	1.11182i	−0.343098	−	0.939300i	$-0.611476\pi$
$251$	10.1697	−	17.6145i	0.641909	−	1.11182i	0.985006	−	0.172519i	$-0.0551905\pi$
$252$	5.15612	+	12.1368i	0.324805	+	0.764547i
$253$	−12.6721	−	47.2928i	−0.796686	−	2.97327i
$254$	24.5580	+	6.58029i	1.54090	+	0.412884i
$255$	−2.78371	−	8.08049i	−0.174323	−	0.506020i
$256$	−30.7661			−1.92288
$257$	−4.23379	+	7.33313i	−0.264096	+	0.457428i	−0.967326	−	0.253534i	$-0.918407\pi$
$257$	−4.23379	+	7.33313i	−0.264096	+	0.457428i	0.703230	+	0.710962i	$0.251740\pi$
$258$	−0.922896	−	0.802015i	−0.0574570	−	0.0499313i
$259$	−4.00328	−	2.31130i	−0.248752	−	0.143617i
$260$	16.8319	+	8.82301i	1.04387	+	0.547180i
$261$	12.6675	−	9.90311i	0.784096	−	0.612987i
$262$	25.0294	+	6.70661i	1.54632	+	0.414336i
$263$		−	23.5517i		−	1.45226i	−0.687556	−	0.726131i	$-0.741317\pi$
$263$		−	23.5517i		−	1.45226i	0.687556	−	0.726131i	$-0.258683\pi$
$264$	−27.5227	+	56.4517i	−1.69391	+	3.47436i
$265$	−5.11159	−	1.36965i	−0.314003	−	0.0841368i
$266$	8.13480	+	8.13480i	0.498776	+	0.498776i
$267$	17.0561	+	14.8221i	1.04382	+	0.907099i
$268$	−56.5677	+	15.1573i	−3.45542	+	0.925878i
$269$	13.5577	+	7.82756i	0.826630	+	0.477255i	0.852697	−	0.522405i	$-0.174965\pi$
$269$	13.5577	+	7.82756i	0.826630	+	0.477255i	−0.0260677	+	0.999660i	$0.508299\pi$
$270$	−10.5491	−	11.7052i	−0.641997	−	0.712356i
$271$	3.39300	−	12.6628i	0.206110	−	0.769213i	−0.782998	−	0.622024i	$-0.786311\pi$
$271$	3.39300	−	12.6628i	0.206110	−	0.769213i	0.989108	−	0.147189i	$-0.0470226\pi$
$272$	13.4348	−	23.2698i	0.814606	−	1.41094i
$273$	−5.03006	+	3.70115i	−0.304433	+	0.224004i
$274$	3.12721	+	5.41649i	0.188922	+	0.327222i
$275$	−20.5936	+	5.51803i	−1.24184	+	0.332750i
$276$	34.8340	+	51.6266i	2.09676	+	3.10756i
$277$	−11.5741	+	6.68230i	−0.695419	+	0.401501i	−0.805639	−	0.592407i	$-0.798178\pi$
$277$	−11.5741	+	6.68230i	−0.695419	+	0.401501i	0.110220	+	0.993907i	$0.464845\pi$
$278$	35.7754	+	35.7754i	2.14566	+	2.14566i
$279$	−2.60828	−	6.13953i	−0.156154	−	0.367564i
$280$	7.01699	−	1.88020i	0.419345	−	0.112363i
$281$	7.34453	+	27.4102i	0.438138	+	1.63515i	0.733443	+	0.679750i	$0.237912\pi$
$281$	7.34453	+	27.4102i	0.438138	+	1.63515i	−0.295305	+	0.955403i	$0.595421\pi$
$282$	−11.7519	+	7.92936i	−0.699816	+	0.472187i
$283$	18.2112	+	10.5143i	1.08255	+	0.625008i	0.931582	−	0.363532i	$-0.118429\pi$
$283$	18.2112	+	10.5143i	1.08255	+	0.625008i	0.150963	+	0.988539i	$0.451762\pi$
$284$	3.29495	+	12.2969i	0.195520	+	0.729689i
$285$	−8.49257	−	4.14050i	−0.503056	−	0.245262i
$286$	−53.2473	−	11.9635i	−3.14858	−	0.707418i
$287$		−	5.35057i		−	0.315834i
$288$	1.60357	−	13.0930i	0.0944915	−	0.771511i
$289$	0.0335260	+	0.0580687i	0.00197212	+	0.00341581i
$290$	−8.12665	−	14.0758i	−0.477213	−	0.826557i
$291$	18.5414	+	16.1129i	1.08692	+	0.944553i
$292$	28.8509	−	28.8509i	1.68837	−	1.68837i
$293$	2.54565	−	2.54565i	0.148719	−	0.148719i	−0.628827	−	0.777545i	$-0.716465\pi$
$293$	2.54565	−	2.54565i	0.148719	−	0.148719i	0.777545	+	0.628827i	$0.216465\pi$
$294$	−0.835138	+	4.29991i	−0.0487063	+	0.250776i
$295$	−1.46627	−	2.53965i	−0.0853694	−	0.147864i
$296$	14.0023	+	24.2527i	0.813867	+	1.40966i
$297$	26.0905	+	16.9265i	1.51392	+	0.982173i
$298$			24.1980i			1.40175i
$299$	−19.9880	+	21.6889i	−1.15593	+	1.25430i
$300$	22.4807	−	15.1684i	1.29793	−	0.875749i
$301$	−0.0722457	−	0.269625i	−0.00416418	−	0.0155409i
$302$	26.6427	+	15.3821i	1.53311	+	0.885143i
$303$	−18.3932	−	8.96748i	−1.05666	−	0.515168i
$304$	−7.68803	−	28.6921i	−0.440939	−	1.64561i
$305$	5.19631	−	1.39235i	0.297540	−	0.0797256i
$306$	−24.9387	−	18.7808i	−1.42565	−	1.07363i
$307$	−15.2249	−	15.2249i	−0.868931	−	0.868931i	0.123423	−	0.992354i	$-0.460613\pi$
$307$	−15.2249	−	15.2249i	−0.868931	−	0.868931i	−0.992354	+	0.123423i	$0.960613\pi$
$308$	−22.7837	+	13.1542i	−1.29822	+	0.749529i
$309$	−14.9585	+	1.04828i	−0.850958	+	0.0596348i
$310$	−6.51313	+	1.74519i	−0.369921	+	0.0991200i
$311$	−12.9132	−	22.3663i	−0.732241	−	1.26828i	−0.955923	−	0.293616i	$-0.905141\pi$
$311$	−12.9132	−	22.3663i	−0.732241	−	1.26828i	0.223682	−	0.974662i	$-0.428192\pi$
$312$	37.6016	−	4.18172i	2.12877	−	0.236743i
$313$	−7.03784	+	12.1899i	−0.397802	+	0.689014i	−0.993455	−	0.114228i	$-0.963560\pi$
$313$	−7.03784	+	12.1899i	−0.397802	+	0.689014i	0.595652	+	0.803243i	$0.296894\pi$
$314$	−4.22565	+	15.7703i	−0.238467	+	0.889972i
$315$	−0.501740	−	3.56220i	−0.0282698	−	0.200707i
$316$	37.7407	+	21.7896i	2.12308	+	1.22576i
$317$	−6.46033	+	1.73104i	−0.362848	+	0.0972249i	−0.435637	−	0.900122i	$-0.643477\pi$
$317$	−6.46033	+	1.73104i	−0.362848	+	0.0972249i	0.0727885	+	0.997347i	$0.476810\pi$
$318$	−18.2766	+	6.29626i	−1.02490	+	0.353077i
$319$	22.6832	+	22.6832i	1.27002	+	1.27002i
$320$	2.24690	+	0.602055i	0.125605	+	0.0336559i
$321$	26.6394	−	1.86687i	1.48686	−	0.104199i
$322$			20.6876i			1.15287i
$323$	−18.0814	−	4.84491i	−1.00608	−	0.269578i
$324$	−38.3906	−	9.54707i	−2.13281	−	0.530393i
$325$	9.44442	+	8.70373i	0.523882	+	0.482796i
$326$	−22.4816	−	12.9797i	−1.24514	−	0.718882i
$327$	−9.89703	+	3.40950i	−0.547307	+	0.188546i
$328$	−16.2074	+	28.0721i	−0.894905	+	1.55002i
$329$	−3.23653			−0.178436
$330$	20.6210	−	23.7291i	1.13515	−	1.30624i
$331$	−2.62403	−	0.703107i	−0.144230	−	0.0386463i	0.185982	−	0.982553i	$-0.440453\pi$
$331$	−2.62403	−	0.703107i	−0.144230	−	0.0386463i	−0.330212	+	0.943907i	$0.607120\pi$
$332$	8.62219	+	32.1785i	0.473204	+	1.76602i
$333$	12.7637	−	5.42245i	0.699447	−	0.297149i
$334$	−5.63744	+	9.76433i	−0.308467	+	0.534280i
$335$	15.9763			0.872877
$336$	7.41863	−	8.53677i	0.404719	−	0.465719i
$337$	−2.85465	+	1.64813i	−0.155503	+	0.0897795i	−0.575732	−	0.817638i	$-0.695283\pi$
$337$	−2.85465	+	1.64813i	−0.155503	+	0.0897795i	0.420229	+	0.907418i	$0.361950\pi$
$338$	11.0685	+	30.9570i	0.602048	+	1.68384i
$339$	7.94074	−	16.2872i	0.431282	−	0.884600i
$340$	−15.3365	+	15.3365i	−0.831741	+	0.831741i
$341$	11.5254	−	6.65418i	0.624134	−	0.360344i
$342$	−34.1757	+	4.81368i	−1.84801	+	0.260294i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	−0.437679	+	1.63344i	−0.0235981	+	0.0880692i
$345$	−5.53386	−	16.0635i	−0.297933	−	0.864832i
$346$	8.10927	−	30.2642i	0.435957	−	1.62701i
$347$		−	1.20736i		−	0.0648142i	−0.999475	−	0.0324071i	$-0.989683\pi$
$347$		−	1.20736i		−	0.0648142i	0.999475	−	0.0324071i	$-0.0103173\pi$
$348$	−36.6780	−	17.8821i	−1.96615	−	0.958583i
$349$	−8.65790	−	8.65790i	−0.463447	−	0.463447i	0.436337	−	0.899784i	$-0.356276\pi$
$349$	−8.65790	−	8.65790i	−0.463447	−	0.463447i	−0.899784	+	0.436337i	$0.856276\pi$
$350$	9.00836			0.481517
$351$	0.208199	−	18.7338i	0.0111128	−	0.999938i
$352$	26.3167			1.40268
$353$	−1.84902	−	1.84902i	−0.0984134	−	0.0984134i	0.656186	−	0.754599i	$-0.272169\pi$
$353$	−1.84902	−	1.84902i	−0.0984134	−	0.0984134i	−0.754599	+	0.656186i	$0.772169\pi$
$354$	−9.62880	−	4.69447i	−0.511765	−	0.249508i
$355$		−	3.47299i		−	0.184327i
$356$	14.8420	−	55.3910i	0.786624	−	2.93572i
$357$	−2.32146	−	6.73867i	−0.122865	−	0.356648i
$358$	−1.81760	+	6.78337i	−0.0960631	+	0.358512i
$359$	20.5228	−	20.5228i	1.08315	−	1.08315i	0.0869380	−	0.996214i	$-0.472292\pi$
$359$	20.5228	−	20.5228i	1.08315	−	1.08315i	0.996214	−	0.0869380i	$-0.0277082\pi$
$360$	−8.15786	+	20.2091i	−0.429957	+	1.06511i
$361$	−1.46710	+	0.847030i	−0.0772157	+	0.0445805i
$362$	−5.33745	+	5.33745i	−0.280530	+	0.280530i
$363$	−18.8417	+	38.6462i	−0.988934	+	2.02840i
$364$	14.0368	+	7.35789i	0.735729	+	0.385658i
$365$	−9.63952	+	5.56538i	−0.504555	+	0.291305i
$366$	12.8901	−	14.8329i	0.673774	−	0.775326i
$367$	−1.28009			−0.0668200			−0.0334100	−	0.999442i	$-0.510637\pi$
$367$	−1.28009			−0.0668200			−0.0334100	+	0.999442i	$0.510637\pi$
$368$	26.7077	−	46.2591i	1.39223	−	2.41142i
$369$	12.8224	+	9.65627i	0.667508	+	0.502685i
$370$	−3.62814	−	13.5404i	−0.188618	−	0.703932i
$371$	−4.26278	−	1.14221i	−0.221313	−	0.0593005i
$372$	−11.1041	+	12.7778i	−0.575722	+	0.662496i
$373$	28.7643			1.48936			0.744680	−	0.667422i	$-0.232602\pi$
$373$	28.7643			1.48936			0.744680	+	0.667422i	$0.232602\pi$
$374$	31.1427	−	53.9407i	1.61035	−	2.78921i
$375$	−16.8133	+	5.79213i	−0.868233	+	0.299104i
$376$	16.9806	+	9.80376i	0.875709	+	0.505591i
$377$	4.23623	−	18.8546i	0.218177	−	0.971061i
$378$	−8.79734	−	9.76148i	−0.452486	−	0.502076i
$379$	14.9661	+	4.01015i	0.768756	+	0.205988i	0.621822	−	0.783159i	$-0.286393\pi$
$379$	14.9661	+	4.01015i	0.768756	+	0.205988i	0.146934	+	0.989146i	$0.453059\pi$
$380$			23.9772i			1.23001i
$381$	−17.3703	+	1.21730i	−0.889906	+	0.0623643i
$382$	−50.2550	−	13.4658i	−2.57127	−	0.688970i
$383$	3.86892	+	3.86892i	0.197693	+	0.197693i	0.799010	−	0.601317i	$-0.205357\pi$
$383$	3.86892	+	3.86892i	0.197693	+	0.197693i	−0.601317	+	0.799010i	$0.705357\pi$
$384$	22.4347	−	7.72870i	1.14487	−	0.394403i
$385$	6.93246	−	1.85755i	0.353311	−	0.0946694i
$386$	46.5768	+	26.8911i	2.37070	+	1.36872i
$387$	0.776527	+	0.313463i	0.0394731	+	0.0159342i
$388$	16.1345	−	60.2146i	0.819103	−	3.05693i
$389$	−2.17814	+	3.77265i	−0.110436	+	0.191281i	−0.915946	−	0.401301i	$-0.868558\pi$
$389$	−2.17814	+	3.77265i	−0.110436	+	0.191281i	0.805510	+	0.592582i	$0.201891\pi$
$390$	−18.7224	−	2.84960i	−0.948045	−	0.144295i
$391$	−16.8309	−	29.1519i	−0.851174	−	1.47428i
$392$	5.85177	−	1.56798i	0.295559	−	0.0791948i
$393$	−17.7037	+	1.24067i	−0.893035	+	0.0625835i
$394$	38.4511	−	22.1998i	1.93714	−	1.11841i
$395$	−8.40648	−	8.40648i	−0.422976	−	0.422976i
$396$	9.59472	−	78.3397i	0.482153	−	3.93672i
$397$	−30.6456	+	8.21146i	−1.53806	+	0.412122i	−0.925638	−	0.378410i	$-0.876471\pi$
$397$	−30.6456	+	8.21146i	−1.53806	+	0.412122i	−0.612421	+	0.790532i	$0.709804\pi$
$398$	−16.9538	−	63.2726i	−0.849819	−	3.17157i
$399$	−7.08233	−	3.45295i	−0.354560	−	0.172864i
$400$	−20.1434	−	11.6298i	−1.00717	−	0.581491i
$401$	−1.05980	−	3.95524i	−0.0529240	−	0.197515i	0.934402	−	0.356220i	$-0.115935\pi$
$401$	−1.05980	−	3.95524i	−0.0529240	−	0.197515i	−0.987326	+	0.158705i	$0.949268\pi$
$402$	48.3773	−	32.6416i	2.41284	−	1.62801i
$403$	−7.10068	−	3.72207i	−0.353710	−	0.185409i
$404$			51.9297i			2.58360i
$405$	9.44216	+	5.22637i	0.469185	+	0.259700i
$406$	−6.77717	−	11.7384i	−0.336345	−	0.582567i
$407$	13.8336	+	23.9606i	0.685708	+	1.18768i
$408$	−8.23246	+	42.3867i	−0.407567	+	2.09846i
$409$	−9.87548	+	9.87548i	−0.488311	+	0.488311i	−0.907773	−	0.419462i	$-0.862219\pi$
$409$	−9.87548	+	9.87548i	−0.488311	+	0.488311i	0.419462	+	0.907773i	$0.362219\pi$
$410$	11.4733	−	11.4733i	0.566625	−	0.566625i
$411$	−3.23330	−	2.80981i	−0.159487	−	0.138598i
$412$	19.0271	+	32.9560i	0.937399	+	1.62362i
$413$	−1.22279	−	2.11793i	−0.0601693	−	0.104216i
$414$	−49.5768	−	37.3352i	−2.43657	−	1.83492i
$415$		−	9.08807i		−	0.446116i
$416$	−8.47997	−	13.3948i	−0.415765	−	0.656732i
$417$	−31.1468	−	15.1854i	−1.52526	−	0.743634i
$418$	−17.8213	−	66.5099i	−0.871667	−	3.25310i
$419$	26.1470	+	15.0960i	1.27736	+	0.737486i	0.976363	−	0.216137i	$-0.0693459\pi$
$419$	26.1470	+	15.0960i	1.27736	+	0.737486i	0.301001	+	0.953624i	$0.402679\pi$
$420$	−7.56774	+	5.10618i	−0.369268	+	0.249156i
$421$	−0.785295	−	2.93076i	−0.0382729	−	0.142836i	0.944146	−	0.329529i	$-0.106890\pi$
$421$	−0.785295	−	2.93076i	−0.0382729	−	0.142836i	−0.982418	+	0.186692i	$0.940223\pi$
$422$	−55.0034	+	14.7381i	−2.67752	+	0.717441i
$423$	5.84101	−	7.75619i	0.284000	−	0.377119i
$424$	18.9051	+	18.9051i	0.918111	+	0.918111i
$425$	−12.6942	+	7.32898i	−0.615757	+	0.355508i
$426$	−7.09576	−	10.5165i	−0.343791	−	0.509524i
$427$	4.33343	−	1.16114i	0.209710	−	0.0561915i
$428$	−33.8852	−	58.6909i	−1.63790	−	2.83693i
$429$	37.1487	−	4.13135i	1.79356	−	0.199463i
$430$	0.423241	−	0.733076i	0.0204105	−	0.0353520i
$431$	−8.98601	+	33.5363i	−0.432841	+	1.61538i	0.313340	+	0.949641i	$0.398552\pi$
$431$	−8.98601	+	33.5363i	−0.432841	+	1.61538i	−0.746181	+	0.665744i	$0.768114\pi$
$432$	7.06948	+	33.1849i	0.340131	+	1.59661i
$433$	12.8160	+	7.39932i	0.615897	+	0.355588i	0.775270	−	0.631630i	$-0.217614\pi$
$433$	12.8160	+	7.39932i	0.615897	+	0.355588i	−0.159373	+	0.987218i	$0.550947\pi$
$434$	−5.43158	+	1.45539i	−0.260724	+	0.0698609i
$435$	8.40234	+	7.30180i	0.402862	+	0.350095i
$436$	18.7843	+	18.7843i	0.899604	+	0.899604i
$437$	−35.9449	−	9.63140i	−1.71948	−	0.460732i
$438$	−17.8183	+	36.5471i	−0.851394	+	1.74629i
$439$		−	4.45688i		−	0.212715i	−0.994328	−	0.106358i	$-0.966081\pi$
$439$		−	4.45688i		−	0.212715i	0.994328	−	0.106358i	$-0.0339189\pi$
$440$	−41.9983	−	11.2534i	−2.00219	−	0.536485i
$441$	−0.418423	−	2.97068i	−0.0199249	−	0.141461i
$442$	−37.4900	+	1.53009i	−1.78322	+	0.0727791i
$443$	−7.10176	−	4.10020i	−0.337415	−	0.194806i	0.321714	−	0.946837i	$-0.395741\pi$
$443$	−7.10176	−	4.10020i	−0.337415	−	0.194806i	−0.659128	+	0.752031i	$0.729075\pi$
$444$	−26.5642	−	23.0848i	−1.26068	−	1.09556i
$445$	−7.82197	+	13.5480i	−0.370797	+	0.642239i
$446$	29.8959			1.41561
$447$	−5.39802	−	15.6693i	−0.255318	−	0.741130i
$448$	1.87379	+	0.502080i	0.0885281	+	0.0237210i
$449$	−2.96886	−	11.0799i	−0.140109	−	0.522894i	−0.999924	−	0.0122889i	$-0.996088\pi$
$449$	−2.96886	−	11.0799i	−0.140109	−	0.522894i	0.859816	−	0.510605i	$-0.170578\pi$
$450$	−16.2575	+	21.5881i	−0.766388	+	1.01767i
$451$	−16.0122	+	27.7339i	−0.753985	+	1.30594i
$452$	−45.9840			−2.16291
$453$	−20.6837	−	4.01724i	−0.971805	−	0.188746i
$454$	−51.2791	+	29.6060i	−2.40665	+	1.38948i
$455$	−3.17930	−	2.92996i	−0.149048	−	0.137359i
$456$	26.6985	+	39.5692i	1.25027	+	1.85300i
$457$	17.4187	−	17.4187i	0.814814	−	0.814814i	−0.170537	−	0.985351i	$-0.554550\pi$
$457$	17.4187	−	17.4187i	0.814814	−	0.814814i	0.985351	+	0.170537i	$0.0545502\pi$
$458$	24.8223	−	14.3312i	1.15987	−	0.669652i
$459$	20.3385	+	6.59812i	0.949320	+	0.307974i
$460$	−30.4882	+	30.4882i	−1.42152	+	1.42152i
$461$	0.875048	−	3.26572i	0.0407550	−	0.152100i	−0.942550	−	0.334066i	$-0.891579\pi$
$461$	0.875048	−	3.26572i	0.0407550	−	0.152100i	0.983305	+	0.181966i	$0.0582460\pi$
$462$	17.1968	−	19.7887i	0.800067	−	0.920654i
$463$	−1.55462	+	5.80193i	−0.0722494	+	0.269638i	−0.992596	−	0.121466i	$-0.961240\pi$
$463$	−1.55462	+	5.80193i	−0.0722494	+	0.269638i	0.920346	+	0.391105i	$0.127907\pi$
$464$			34.9974i			1.62471i
$465$	3.82822	−	2.58302i	0.177530	−	0.119785i
$466$	−7.07180	−	7.07180i	−0.327595	−	0.327595i
$467$	−12.7151			−0.588386			−0.294193	−	0.955746i	$-0.595051\pi$
$467$	−12.7151			−0.588386			−0.294193	+	0.955746i	$0.595051\pi$
$468$	−42.9653	+	20.3597i	−1.98607	+	0.941127i
$469$	13.3233			0.615213
$470$	−6.94011	−	6.94011i	−0.320123	−	0.320123i
$471$	−0.781713	−	11.1546i	−0.0360194	−	0.513979i
$472$			14.8158i			0.681950i
$473$	−0.432407	+	1.61377i	−0.0198821	+	0.0742010i
$474$	−42.6309	−	8.27989i	−1.95810	−	0.380308i
$475$	−4.19398	+	15.6521i	−0.192433	+	0.718169i
$476$	−12.7898	+	12.7898i	−0.586220	+	0.586220i
$477$	10.4304	−	8.15421i	0.477574	−	0.373355i
$478$	21.4979	−	12.4118i	0.983290	−	0.567703i
$479$	−18.4145	+	18.4145i	−0.841379	+	0.841379i	−0.989038	−	0.147660i	$-0.952826\pi$
$479$	−18.4145	+	18.4145i	−0.841379	+	0.841379i	0.147660	+	0.989038i	$0.452826\pi$
$480$	9.10983	−	0.638413i	0.415805	−	0.0291394i
$481$	7.73795	−	14.7619i	0.352820	−	0.673083i
$482$	−15.7296	+	9.08148i	−0.716463	+	0.413650i
$483$	−4.61492	−	13.3961i	−0.209986	−	0.609543i
$484$	109.110			4.95957
$485$	−8.50312	+	14.7278i	−0.386107	+	0.668757i
$486$	39.2697	−	3.46573i	1.78131	−	0.157209i
$487$	−4.56014	−	17.0187i	−0.206640	−	0.771190i	−0.988943	−	0.148293i	$-0.952622\pi$
$487$	−4.56014	−	17.0187i	−0.206640	−	0.771190i	0.782304	−	0.622897i	$-0.214044\pi$
$488$	−26.2528	−	7.03442i	−1.18841	−	0.318433i
$489$	17.4533	+	3.38982i	0.789265	+	0.153293i
$490$	−3.03251			−0.136995
$491$	−2.06154	+	3.57069i	−0.0930361	+	0.161143i	−0.908787	−	0.417260i	$-0.862991\pi$
$491$	−2.06154	+	3.57069i	−0.0930361	+	0.161143i	0.815751	+	0.578403i	$0.196324\pi$
$492$	7.76664	−	39.9883i	0.350147	−	1.80281i
$493$	19.1001	+	11.0275i	0.860227	+	0.496652i
$494$	−28.1100	+	30.5021i	−1.26473	+	1.37235i
$495$	−8.05960	+	19.9657i	−0.362252	+	0.897391i
$496$	14.0244	+	3.75782i	0.629713	+	0.168731i
$497$		−	2.89628i		−	0.129916i
$498$	−18.5681	−	27.5193i	−0.832057	−	1.23317i
$499$	24.6796	+	6.61288i	1.10481	+	0.296033i	0.764722	−	0.644360i	$-0.222876\pi$
$499$	24.6796	+	6.61288i	1.10481	+	0.296033i	0.340089	+	0.940393i	$0.389543\pi$
$500$	31.9111	+	31.9111i	1.42711	+	1.42711i
$501$	1.47229	−	7.58041i	0.0657769	−	0.338668i
$502$	49.6847	−	13.3130i	2.21754	−	0.594187i
$503$	−0.793437	−	0.458091i	−0.0353776	−	0.0204253i	0.482207	−	0.876057i	$-0.339835\pi$
$503$	−0.793437	−	0.458091i	−0.0353776	−	0.0204253i	−0.517584	+	0.855632i	$0.673169\pi$
$504$	−6.80320	+	16.8533i	−0.303039	+	0.750704i
$505$	3.66659	−	13.6839i	0.163161	−	0.608926i
$506$	61.9099	−	107.231i	2.75223	−	4.76700i
$507$	−14.0732	−	17.5769i	−0.625011	−	0.780616i
$508$	22.0949	+	38.2696i	0.980304	+	1.69794i
$509$	27.7778	−	7.44303i	1.23123	−	0.329906i	0.416170	−	0.909287i	$-0.363372\pi$
$509$	27.7778	−	7.44303i	1.23123	−	0.329906i	0.815057	+	0.579380i	$0.196705\pi$
$510$	9.47187	−	19.4277i	0.419421	−	0.860273i
$511$	−8.03881	+	4.64121i	−0.355616	+	0.205315i
$512$	−35.6425	−	35.6425i	−1.57519	−	1.57519i
$513$	21.0564	−	10.7409i	0.929664	−	0.474222i
$514$	−20.6843	+	5.54235i	−0.912347	+	0.244463i
$515$	−2.68689	−	10.0276i	−0.118398	−	0.441869i
$516$	−0.148565	−	2.11995i	−0.00654022	−	0.0933256i
$517$	16.7761	+	9.68568i	0.737811	+	0.425976i
$518$	−3.02566	−	11.2919i	−0.132940	−	0.496139i
$519$	1.50015	+	21.4064i	0.0658493	+	0.939636i
$520$	7.80522	+	25.0026i	0.342282	+	1.09644i
$521$			24.4393i			1.07070i	0.844629	+	0.535352i	$0.179821\pi$
$521$			24.4393i			1.07070i	−0.844629	+	0.535352i	$0.820179\pi$
$522$	40.3614	+	4.94330i	1.76657	+	0.216362i
$523$	9.61928	+	16.6611i	0.420622	+	0.728539i	0.996000	−	0.0893487i	$-0.0284786\pi$
$523$	9.61928	+	16.6611i	0.420622	+	0.728539i	−0.575378	+	0.817887i	$0.695145\pi$
$524$	22.5191	+	39.0042i	0.983751	+	1.70391i
$525$	−5.83331	+	2.00956i	−0.254586	+	0.0877045i
$526$	42.1160	−	42.1160i	1.83634	−	1.83634i
$527$	6.46987	−	6.46987i	0.281832	−	0.281832i
$528$	−64.0007	+	22.0481i	−2.78527	+	0.959520i
$529$	−21.9588	−	38.0338i	−0.954731	−	1.65364i
$530$	−6.69147	−	11.5900i	−0.290659	−	0.503436i
$531$	7.28230	+	0.891906i	0.316025	+	0.0387054i
$532$			19.9957i			0.866922i
$533$	19.2757	−	0.786707i	0.834924	−	0.0340760i
$534$	3.99494	+	57.0057i	0.172878	+	2.46688i
$535$	4.78505	+	17.8580i	0.206876	+	0.772071i
$536$	−69.9015	−	40.3576i	−3.01928	−	1.74318i
$537$	−0.336242	−	4.79800i	−0.0145099	−	0.207049i
$538$	10.2469	+	38.2419i	0.441774	+	1.64872i
$539$	5.78129	−	1.54909i	0.249018	−	0.0667241i
$540$	1.42089	−	27.3510i	0.0611456	−	1.17700i
$541$	21.1936	+	21.1936i	0.911183	+	0.911183i	0.996365	−	0.0851825i	$-0.0271473\pi$
$541$	21.1936	+	21.1936i	0.911183	+	0.911183i	−0.0851825	+	0.996365i	$0.527147\pi$
$542$	28.7116	−	16.5766i	1.23327	−	0.712027i
$543$	2.26557	−	4.64690i	0.0972249	−	0.199417i
$544$	17.4767	−	4.68288i	0.749309	−	0.200777i
$545$	−3.62351	−	6.27611i	−0.155214	−	0.268839i
$546$	−15.6134	−	2.37641i	−0.668193	−	0.101701i
$547$	−10.2563	+	17.7645i	−0.438528	+	0.759553i	−0.997576	−	0.0695821i	$-0.977833\pi$
$547$	−10.2563	+	17.7645i	−0.438528	+	0.759553i	0.559048	+	0.829135i	$0.311167\pi$
$548$	−2.81357	+	10.5004i	−0.120190	+	0.448554i
$549$	−5.03800	+	12.4804i	−0.215017	+	0.532651i
$550$	−46.6936	−	26.9586i	−1.99102	−	1.14952i
$551$	23.5508	−	6.31042i	1.00330	−	0.268833i
$552$	−16.3657	+	84.2624i	−0.696569	+	3.58645i
$553$	−7.01053	−	7.01053i	−0.298118	−	0.298118i
$554$	−32.6467	−	8.74765i	−1.38702	−	0.371652i
$555$	5.36993	+	7.95864i	0.227941	+	0.337826i
$556$			87.9373i			3.72937i
$557$	28.2243	+	7.56268i	1.19590	+	0.320441i	0.801216	−	0.598375i	$-0.204187\pi$
$557$	28.2243	+	7.56268i	1.19590	+	0.320441i	0.394686	+	0.918816i	$0.370853\pi$
$558$	6.31470	−	15.6431i	0.267322	−	0.662226i
$559$	0.960715	−	0.299913i	0.0406339	−	0.0126850i
$560$	6.78094	+	3.91498i	0.286547	+	0.165438i
$561$	−8.13330	+	41.8762i	−0.343388	+	1.76801i
$562$	−35.8820	+	62.1495i	−1.51359	+	2.62162i
$563$	−30.7537			−1.29611			−0.648056	−	0.761593i	$-0.724418\pi$
$563$	−30.7537			−1.29611			−0.648056	+	0.761593i	$0.724418\pi$
$564$	−24.1887	−	4.69799i	−1.01853	−	0.197821i
$565$	12.1172	+	3.24678i	0.509773	+	0.136593i
$566$	13.7640	+	51.3678i	0.578543	+	2.15915i
$567$	7.87423	+	4.35850i	0.330687	+	0.183040i
$568$	−8.77311	+	15.1955i	−0.368112	+	0.637588i
$569$	17.8266			0.747328			0.373664	−	0.927564i	$-0.378101\pi$
$569$	17.8266			0.747328			0.373664	+	0.927564i	$0.378101\pi$
$570$	−7.78250	−	22.5909i	−0.325973	−	0.946227i
$571$	8.78640	−	5.07283i	0.367699	−	0.212291i	−0.304754	−	0.952431i	$-0.598574\pi$
$571$	8.78640	−	5.07283i	0.367699	−	0.212291i	0.672453	+	0.740140i	$0.265241\pi$
$572$	−50.7385	−	80.1454i	−2.12148	−	3.35105i
$573$	35.5462	−	2.49107i	1.48497	−	0.104066i
$574$	9.56807	−	9.56807i	0.399363	−	0.399363i
$575$	−25.2353	+	14.5696i	−1.05238	+	0.607594i
$576$	−4.58487	+	3.58434i	−0.191036	+	0.149347i
$577$	10.6314	−	10.6314i	0.442591	−	0.442591i	−0.450291	−	0.892882i	$-0.648680\pi$
$577$	10.6314	−	10.6314i	0.442591	−	0.442591i	0.892882	+	0.450291i	$0.148680\pi$
$578$	−0.0438881	+	0.163793i	−0.00182550	+	0.00681288i
$579$	−36.1593	−	7.02296i	−1.50273	−	0.291864i
$580$	7.31159	−	27.2872i	0.303597	−	1.13304i
$581$		−	7.57894i		−	0.314427i
$582$	4.34283	+	61.9699i	0.180016	+	2.56874i
$583$	18.6773	+	18.6773i	0.773537	+	0.773537i
$584$	56.2348			2.32701
$585$	12.7592	−	2.33130i	0.527530	−	0.0963875i
$586$	9.10443			0.376101
$587$	1.50049	+	1.50049i	0.0619318	+	0.0619318i	0.737394	−	0.675463i	$-0.236056\pi$
$587$	1.50049	+	1.50049i	0.0619318	+	0.0619318i	−0.675463	+	0.737394i	$0.736056\pi$
$588$	−6.31107	+	4.25827i	−0.260264	+	0.175608i
$589$		−	10.1150i		−	0.416782i
$590$	1.91946	−	7.16351i	0.0790228	−	0.294917i
$591$	−19.9465	+	22.9529i	−0.820490	+	0.944156i
$592$	−7.81228	+	29.1558i	−0.321083	+	1.19830i
$593$	−15.3491	+	15.3491i	−0.630312	+	0.630312i	−0.948146	−	0.317834i	$-0.897044\pi$
$593$	−15.3491	+	15.3491i	−0.630312	+	0.630312i	0.317834	+	0.948146i	$0.397044\pi$
$594$	16.3874	+	76.9243i	0.672385	+	3.15624i
$595$	4.27327	−	2.46717i	0.175187	−	0.101144i
$596$	−29.7398	+	29.7398i	−1.21819	+	1.21819i
$597$	25.0930	+	37.1898i	1.02699	+	1.52208i
$598$	−74.5280	+	3.04174i	−3.04768	+	0.124386i
$599$	−12.8323	+	7.40874i	−0.524314	+	0.302713i	−0.738698	−	0.674037i	$-0.764559\pi$
$599$	−12.8323	+	7.40874i	−0.524314	+	0.302713i	0.214384	+	0.976749i	$0.431226\pi$
$600$	36.6919	+	7.12640i	1.49794	+	0.290934i
$601$	10.3757			0.423234			0.211617	−	0.977353i	$-0.432127\pi$
$601$	10.3757			0.423234			0.211617	+	0.977353i	$0.432127\pi$
$602$	0.352960	−	0.611344i	0.0143856	−	0.0249165i
$603$	−24.0448	+	31.9287i	−0.979180	+	1.30024i
$604$	13.8394	+	51.6493i	0.563117	+	2.10158i
$605$	−28.7515	−	7.70394i	−1.16891	−	0.313210i
$606$	−16.8553	−	48.9272i	−0.684699	−	1.98753i
$607$	22.7120			0.921853			0.460927	−	0.887438i	$-0.347517\pi$
$607$	22.7120			0.921853			0.460927	+	0.887438i	$0.347517\pi$
$608$	10.0010	−	17.3222i	0.405594	−	0.702509i
$609$	7.00708	+	6.08929i	0.283941	+	0.246751i
$610$	11.7821	+	6.80237i	0.477041	+	0.275420i
$611$	−0.475874	−	11.6598i	−0.0192518	−	0.471703i
$612$	−7.56823	−	53.7322i	−0.305928	−	2.17200i
$613$	8.52091	+	2.28317i	0.344156	+	0.0922164i	0.426757	−	0.904366i	$-0.359656\pi$
$613$	8.52091	+	2.28317i	0.344156	+	0.0922164i	−0.0826008	+	0.996583i	$0.526323\pi$
$614$		−	54.4513i		−	2.19748i
$615$	−4.87002	+	9.98888i	−0.196378	+	0.402790i
$616$	−35.0242	−	9.38470i	−1.41116	−	0.378120i
$617$	−10.1738	−	10.1738i	−0.409582	−	0.409582i	0.472011	−	0.881593i	$-0.343528\pi$
$617$	−10.1738	−	10.1738i	−0.409582	−	0.409582i	−0.881593	+	0.472011i	$0.843528\pi$
$618$	−28.6238	−	24.8746i	−1.15142	−	1.00060i
$619$	−0.708060	+	0.189724i	−0.0284593	+	0.00762565i	−0.273021	−	0.962008i	$-0.588023\pi$
$619$	−0.708060	+	0.189724i	−0.0284593	+	0.00762565i	0.244561	+	0.969634i	$0.421356\pi$
$620$	−10.1496	−	5.85990i	−0.407619	−	0.235339i
$621$	40.4318	+	13.1167i	1.62247	+	0.526355i
$622$	16.9044	−	63.0880i	0.677804	−	2.52960i
$623$	−6.52308	+	11.2983i	−0.261342	+	0.452657i
$624$	31.8450	+	25.4708i	1.27482	+	1.01965i
$625$	2.74957	+	4.76240i	0.109983	+	0.190496i
$626$	−34.3837	+	9.21308i	−1.37425	+	0.368229i
$627$	26.3769	+	39.0925i	1.05339	+	1.56121i
$628$	−24.5755	+	14.1887i	−0.980669	+	0.566190i
$629$	13.4504	+	13.4504i	0.536305	+	0.536305i
$630$	5.47282	−	7.26727i	0.218042	−	0.289535i
$631$	−15.0928	+	4.04409i	−0.600833	+	0.160993i	−0.546400	−	0.837525i	$-0.684002\pi$
$631$	−15.0928	+	4.04409i	−0.600833	+	0.160993i	−0.0544336	+	0.998517i	$0.517335\pi$
$632$	15.5455	+	58.0167i	0.618368	+	2.30778i
$633$	32.3294	−	21.8136i	1.28498	−	0.867013i
$634$	−14.6481	−	8.45707i	−0.581749	−	0.335873i
$635$	−3.12011	−	11.6444i	−0.123818	−	0.462094i
$636$	−30.2006	−	14.7241i	−1.19753	−	0.583850i
$637$	−2.65136	−	2.44342i	−0.105051	−	0.0968119i
$638$			81.1258i			3.21180i
$639$	6.94080	+	5.22696i	0.274574	+	0.206775i
$640$	8.21382	+	14.2268i	0.324680	+	0.562362i
$641$	13.4458	+	23.2889i	0.531079	+	0.919856i	0.999342	+	0.0362669i	$0.0115466\pi$
$641$	13.4458	+	23.2889i	0.531079	+	0.919856i	−0.468263	+	0.883589i	$0.655120\pi$
$642$	50.9757	+	44.2989i	2.01185	+	1.74834i
$643$	2.04248	−	2.04248i	0.0805477	−	0.0805477i	−0.665685	−	0.746233i	$-0.731861\pi$
$643$	2.04248	−	2.04248i	0.0805477	−	0.0805477i	0.746233	+	0.665685i	$0.231861\pi$
$644$	−25.4254	+	25.4254i	−1.00190	+	1.00190i
$645$	−0.110535	+	0.569114i	−0.00435230	+	0.0224088i
$646$	−23.6700	−	40.9976i	−0.931283	−	1.61303i
$647$	−17.9475	−	31.0860i	−0.705590	−	1.22212i	−0.966478	−	0.256748i	$-0.917349\pi$
$647$	−17.9475	−	31.0860i	−0.705590	−	1.22212i	0.260889	−	0.965369i	$-0.415984\pi$
$648$	−28.1102	−	46.7189i	−1.10427	−	1.83529i
$649$			14.6373i			0.574564i
$650$	1.32452	+	32.4531i	0.0519519	+	1.27292i
$651$	3.19252	−	2.15409i	0.125125	−	0.0844255i
$652$	−11.6779	−	43.5827i	−0.457344	−	1.70683i
$653$	40.2968	+	23.2654i	1.57694	+	0.910444i	0.995284	+	0.0970065i	$0.0309268\pi$
$653$	40.2968	+	23.2654i	1.57694	+	0.910444i	0.581652	+	0.813438i	$0.302407\pi$
$654$	−23.7952	−	11.6012i	−0.930464	−	0.453643i
$655$	−3.18000	−	11.8679i	−0.124253	−	0.463718i
$656$	−33.7474	+	9.04258i	−1.31761	+	0.353054i
$657$	3.38532	−	27.6407i	0.132074	−	1.07837i
$658$	−5.78766	−	5.78766i	−0.225627	−	0.225627i
$659$	−24.3194	+	14.0408i	−0.947351	+	0.546953i	−0.892257	−	0.451528i	$-0.850879\pi$
$659$	−24.3194	+	14.0408i	−0.947351	+	0.546953i	−0.0550936	+	0.998481i	$0.517546\pi$
$660$	54.5072	−	3.81984i	2.12169	−	0.148687i
$661$	−34.5219	+	9.25011i	−1.34275	+	0.359788i	−0.857452	−	0.514563i	$-0.827954\pi$
$661$	−34.5219	+	9.25011i	−1.34275	+	0.359788i	−0.485294	+	0.874351i	$0.661287\pi$
$662$	−3.43506	−	5.94969i	−0.133507	−	0.231241i
$663$	23.9351	−	9.35397i	0.929562	−	0.363278i
$664$	−22.9574	+	39.7633i	−0.890919	+	1.54312i
$665$	1.41183	−	5.26902i	0.0547484	−	0.204324i
$666$	32.5211	+	13.1279i	1.26017	+	0.508694i
$667$	37.9700	+	21.9220i	1.47020	+	0.848822i
$668$	−18.9291	+	5.07203i	−0.732388	+	0.196243i
$669$	−19.3589	+	6.66911i	−0.748460	+	0.257843i
$670$	28.5693	+	28.5693i	1.10373	+	1.10373i
$671$	−25.9366	−	6.94969i	−1.00127	−	0.268290i
$672$	7.59708	−	0.532400i	0.293064	−	0.0205378i
$673$			9.68332i			0.373265i	0.982430	+	0.186632i	$0.0597573\pi$
$673$			9.68332i			0.373265i	−0.982430	+	0.186632i	$0.940243\pi$
$674$	−8.05202	−	2.15753i	−0.310152	−	0.0831050i
$675$	5.71164	−	17.6060i	0.219841	−	0.677653i
$676$	−24.4433	+	51.6502i	−0.940128	+	1.98655i
$677$	−22.6250	−	13.0625i	−0.869549	−	0.502034i	−0.00235041	−	0.999997i	$-0.500748\pi$
$677$	−22.6250	−	13.0625i	−0.869549	−	0.502034i	−0.867198	+	0.497963i	$0.834081\pi$
$678$	43.3252	−	14.9254i	1.66389	−	0.573208i
$679$	−7.09113	+	12.2822i	−0.272133	+	0.471347i
$680$	−29.8932			−1.14635
$681$	26.6010	−	30.6104i	1.01935	−	1.17299i
$682$	32.5093	+	8.71083i	1.24484	+	0.333555i
$683$	−8.71483	−	32.5242i	−0.333464	−	1.24450i	−0.905525	−	0.424293i	$-0.860523\pi$
$683$	−8.71483	−	32.5242i	−0.333464	−	1.24450i	0.572062	−	0.820211i	$-0.306144\pi$
$684$	−47.9187	−	36.0865i	−1.83222	−	1.37980i
$685$	1.48280	−	2.56828i	0.0566548	−	0.0981290i
$686$	−2.52894			−0.0965555
$687$	−12.8766	+	14.8174i	−0.491272	+	0.565317i
$688$	−1.57849	+	0.911343i	−0.0601795	+	0.0347446i
$689$	3.48810	−	15.5248i	0.132886	−	0.591449i
$690$	18.8295	−	38.6212i	0.716828	−	1.47028i
$691$	5.27462	−	5.27462i	0.200656	−	0.200656i	−0.599625	−	0.800281i	$-0.704684\pi$
$691$	5.27462	−	5.27462i	0.200656	−	0.200656i	0.800281	+	0.599625i	$0.204684\pi$
$692$	47.1618	−	27.2289i	1.79282	−	1.03509i
$693$	−6.72125	+	16.6503i	−0.255319	+	0.632491i
$694$	2.15903	−	2.15903i	0.0819557	−	0.0819557i
$695$	6.20897	−	23.1722i	0.235520	−	0.878972i
$696$	−18.3180	−	53.1730i	−0.694341	−	2.01552i
$697$	−5.69853	+	21.2672i	−0.215847	+	0.805553i
$698$		−	30.9647i		−	1.17203i
$699$	6.15686	+	3.00174i	0.232874	+	0.113536i
$700$	11.0715	+	11.0715i	0.418462	+	0.418462i
$701$	17.3436			0.655058			0.327529	−	0.944841i	$-0.393784\pi$
$701$	17.3436			0.655058			0.327529	+	0.944841i	$0.393784\pi$
$702$	33.8728	−	33.1281i	1.27844	−	1.25034i
$703$	21.0285			0.793105
$704$	−8.20998	−	8.20998i	−0.309425	−	0.309425i
$705$	6.04221	+	2.94584i	0.227563	+	0.110947i
$706$		−	6.61296i		−	0.248882i
$707$	3.05773	−	11.4116i	0.114998	−	0.429178i
$708$	−6.06439	−	17.6036i	−0.227914	−	0.661583i
$709$	6.94295	−	25.9115i	0.260748	−	0.973125i	−0.704054	−	0.710147i	$-0.748629\pi$
$709$	6.94295	−	25.9115i	0.260748	−	0.973125i	0.964802	−	0.262978i	$-0.0847048\pi$
$710$	6.21051	−	6.21051i	0.233076	−	0.233076i
$711$	29.4524	−	4.14840i	1.10455	−	0.155577i
$712$	68.4474	−	39.5181i	2.56518	−	1.48100i
$713$	12.8617	−	12.8617i	0.481675	−	0.481675i
$714$	7.89900	−	16.2016i	0.295613	−	0.606330i
$715$	7.71121	+	24.7014i	0.288383	+	0.923782i
$716$	−10.5708	+	6.10304i	−0.395048	+	0.228081i
$717$	−11.1520	+	12.8329i	−0.416480	+	0.479252i
$718$	73.3990			2.73923
$719$	4.55752	−	7.89385i	0.169967	−	0.294391i	−0.768441	−	0.639920i	$-0.778967\pi$
$719$	4.55752	−	7.89385i	0.169967	−	0.294391i	0.938408	+	0.345529i	$0.112301\pi$
$720$	−21.6197	+	9.18479i	−0.805720	+	0.342297i
$721$	−2.24071	−	8.36246i	−0.0834486	−	0.311434i
$722$	−4.13820	−	1.10883i	−0.154008	−	0.0412663i
$723$	8.15972	−	9.38957i	0.303463	−	0.349202i
$724$	−13.1197			−0.487589
$725$	9.54589	−	16.5340i	0.354525	−	0.614056i
$726$	−102.802	+	35.4149i	−3.81533	+	1.31437i
$727$	−46.4407	−	26.8126i	−1.72239	−	0.994423i	−0.913927	−	0.405878i	$-0.866966\pi$
$727$	−46.4407	−	26.8126i	−1.72239	−	0.994423i	−0.808464	−	0.588546i	$-0.799701\pi$
$728$	6.50912	+	20.8508i	0.241244	+	0.772781i
$729$	−24.6557	+	11.0044i	−0.913174	+	0.407570i
$730$	−27.1899	−	7.28551i	−1.00634	−	0.269649i
$731$			1.14864i			0.0424838i
$732$	34.0720	−	2.38775i	1.25934	−	0.0882539i
$733$	−12.2527	−	3.28310i	−0.452563	−	0.121264i	0.0253353	−	0.999679i	$-0.491935\pi$
$733$	−12.2527	−	3.28310i	−0.452563	−	0.121264i	−0.477898	+	0.878415i	$0.658601\pi$
$734$	−2.28909	−	2.28909i	−0.0844920	−	0.0844920i
$735$	1.96368	−	0.676484i	0.0724315	−	0.0249525i
$736$	34.7427	−	9.30929i	1.28063	−	0.343145i
$737$	−69.0595	−	39.8715i	−2.54384	−	1.46869i
$738$	5.66180	+	40.1971i	0.208414	+	1.47968i
$739$	−5.30036	+	19.7812i	−0.194977	+	0.727664i	0.797296	+	0.603589i	$0.206263\pi$
$739$	−5.30036	+	19.7812i	−0.194977	+	0.727664i	−0.992273	+	0.124075i	$0.960404\pi$
$740$	12.1824	−	21.1005i	0.447833	−	0.775669i
$741$	11.3981	−	26.0221i	0.418719	−	0.955947i
$742$	−5.58031	−	9.66538i	−0.204860	−	0.354827i
$743$	7.11154	−	1.90553i	0.260897	−	0.0699072i	−0.125999	−	0.992030i	$-0.540214\pi$
$743$	7.11154	−	1.90553i	0.260897	−	0.0699072i	0.386897	+	0.922123i	$0.373547\pi$
$744$	−23.2747	+	1.63108i	−0.853292	+	0.0597984i
$745$	9.93652	−	5.73685i	0.364046	−	0.210182i
$746$	51.4373	+	51.4373i	1.88325	+	1.88325i
$747$	18.1626	+	13.6778i	0.664535	+	0.500446i
$748$	104.569	−	28.0192i	3.82343	−	1.02448i
$749$	3.99046	+	14.8926i	0.145808	+	0.544164i
$750$	−40.4237	−	19.7083i	−1.47606	−	0.719647i
$751$	−18.0339	−	10.4119i	−0.658066	−	0.379934i	0.133474	−	0.991052i	$-0.457387\pi$
$751$	−18.0339	−	10.4119i	−0.658066	−	0.379934i	−0.791540	+	0.611118i	$0.790720\pi$
$752$	5.46980	+	20.4136i	0.199463	+	0.744406i
$753$	−29.2032	+	19.7043i	−1.06422	+	0.718063i
$754$	41.2917	−	26.1410i	1.50376	−	0.952000i
$755$		−	14.5872i		−	0.530882i
$756$	1.18495	−	22.8092i	0.0430961	−	0.829562i
$757$	−14.9747	−	25.9370i	−0.544265	−	0.942695i	−0.998653	−	0.0518907i	$-0.983475\pi$
$757$	−14.9747	−	25.9370i	−0.544265	−	0.942695i	0.454388	−	0.890804i	$-0.349858\pi$
$758$	19.5918	+	33.9339i	0.711605	+	1.23254i
$759$	−16.1685	+	83.2475i	−0.586881	+	3.02169i
$760$	−23.3676	+	23.3676i	−0.847633	+	0.847633i
$761$	−11.5945	+	11.5945i	−0.420300	+	0.420300i	−0.885307	−	0.465007i	$-0.846052\pi$
$761$	−11.5945	+	11.5945i	−0.420300	+	0.420300i	0.465007	+	0.885307i	$0.346052\pi$
$762$	−33.2389	−	28.8853i	−1.20412	−	1.04640i
$763$	−3.02181	−	5.23392i	−0.109397	−	0.189481i
$764$	−45.2147	−	78.3142i	−1.63581	−	2.83331i
$765$	−1.79957	+	14.6932i	−0.0650635	+	0.531235i
$766$			13.8371i			0.499953i
$767$	7.45015	−	4.71655i	0.269009	−	0.170305i
$768$	47.8988	+	23.3528i	1.72840	+	0.842672i
$769$	−8.47700	−	31.6366i	−0.305688	−	1.14084i	−0.932351	−	0.361554i	$-0.882246\pi$
$769$	−8.47700	−	31.6366i	−0.305688	−	1.14084i	0.626663	−	0.779291i	$-0.284420\pi$
$770$	15.7186	+	9.07513i	0.566458	+	0.327045i
$771$	12.1576	−	8.20312i	0.437847	−	0.295428i
$772$	24.1941	+	90.2937i	0.870765	+	3.24974i
$773$	13.3784	−	3.58474i	0.481188	−	0.128934i	−0.0100675	−	0.999949i	$-0.503205\pi$
$773$	13.3784	−	3.58474i	0.481188	−	0.128934i	0.491256	+	0.871015i	$0.336538\pi$
$774$	0.828066	+	1.94915i	0.0297642	+	0.0700609i
$775$	−5.60062	−	5.60062i	−0.201180	−	0.201180i
$776$	74.4080	−	42.9595i	2.67109	−	1.54216i
$777$	4.47822	+	6.63706i	0.160655	+	0.238103i
$778$	−10.6414	+	2.85135i	−0.381512	+	0.102226i
$779$	12.1701	+	21.0792i	0.436038	+	0.755240i
$780$	−19.5080	−	26.5124i	−0.698498	−	0.949297i
$781$	−8.66744	+	15.0124i	−0.310145	+	0.537188i
$782$	22.0329	−	82.2279i	0.787895	−	2.94046i
$783$	−27.2385	+	5.80271i	−0.973425	+	0.207372i
$784$	5.65492	+	3.26487i	0.201961	+	0.116603i
$785$	7.47766	−	2.00363i	0.266889	−	0.0715127i
$786$	−33.8770	−	29.4398i	−1.20835	−	1.05008i
$787$	−20.2560	−	20.2560i	−0.722048	−	0.722048i	0.246974	−	0.969022i	$-0.420564\pi$
$787$	−20.2560	−	20.2560i	−0.722048	−	0.722048i	−0.969022	+	0.246974i	$0.920564\pi$
$788$	74.5412	+	19.9732i	2.65542	+	0.711517i
$789$	−17.8768	+	36.6670i	−0.636431	+	1.30538i
$790$		−	30.0655i		−	1.06968i
$791$	10.1050	+	2.70763i	0.359294	+	0.0962724i
$792$	85.6987	−	66.9972i	3.04517	−	2.38064i
$793$	4.82022	+	15.4407i	0.171171	+	0.548315i
$794$	−69.4854	−	40.1174i	−2.46595	−	1.42371i
$795$	6.91848	+	6.01229i	0.245373	+	0.213234i
$796$	56.9267	−	98.5999i	2.01771	−	3.49478i
$797$	−11.9917			−0.424767			−0.212383	−	0.977186i	$-0.568123\pi$
$797$	−11.9917			−0.424767			−0.212383	+	0.977186i	$0.568123\pi$
$798$	−6.49017	−	18.8395i	−0.229749	−	0.666912i
$799$	12.8644	+	3.44700i	0.455110	+	0.121946i
$800$	−4.05372	−	15.1287i	−0.143321	−	0.534879i
$801$	−15.3036	−	36.0225i	−0.540725	−	1.27279i
$802$	5.17771	−	8.96806i	0.182831	−	0.316673i
$803$	55.5574			1.96058
$804$	99.5738	+	19.3395i	3.51170	+	0.682051i
$805$	8.49502	−	4.90460i	0.299410	−	0.172864i
$806$	−6.04173	−	19.3536i	−0.212811	−	0.681701i
$807$	−15.1662	−	22.4774i	−0.533875	−	0.791243i
$808$	−50.6095	+	50.6095i	−1.78043	+	1.78043i
$809$	−15.7274	+	9.08019i	−0.552944	+	0.319243i	−0.750309	−	0.661088i	$-0.770095\pi$
$809$	−15.7274	+	9.08019i	−0.552944	+	0.319243i	0.197364	+	0.980330i	$0.436762\pi$
$810$	7.53881	+	26.2307i	0.264887	+	0.921654i
$811$	−33.8270	+	33.8270i	−1.18783	+	1.18783i	−0.210160	+	0.977667i	$0.567398\pi$
$811$	−33.8270	+	33.8270i	−1.18783	+	1.18783i	−0.977667	+	0.210160i	$0.932602\pi$
$812$	6.09745	−	22.7560i	0.213979	−	0.798579i
$813$	−14.8941	+	17.1390i	−0.522360	+	0.601091i
$814$	−18.1093	+	67.5848i	−0.634730	+	2.36884i
$815$			12.3089i			0.431163i
$816$	−38.5791	+	26.0305i	−1.35054	+	0.911249i
$817$	0.897892	+	0.897892i	0.0314133	+	0.0314133i
$818$	−35.3193			−1.23491
$819$	10.6405	−	1.94417i	0.371809	−	0.0679350i
$820$	28.2018			0.984849
$821$	39.3194	+	39.3194i	1.37226	+	1.37226i	0.857091	+	0.515165i	$0.172269\pi$
$821$	39.3194	+	39.3194i	1.37226	+	1.37226i	0.515165	+	0.857091i	$0.327731\pi$
$822$	−0.757314	−	10.8065i	−0.0264144	−	0.376919i
$823$		−	44.7594i		−	1.56022i	−0.625645	−	0.780108i	$-0.715164\pi$
$823$		−	44.7594i		−	1.56022i	0.625645	−	0.780108i	$-0.284836\pi$
$824$	−13.5747	+	50.6615i	−0.472897	+	1.76488i
$825$	36.2500	+	7.04056i	1.26206	+	0.245121i
$826$	1.60072	−	5.97397i	0.0556962	−	0.207861i
$827$	21.0886	−	21.0886i	0.733322	−	0.733322i	−0.237954	−	0.971276i	$-0.576477\pi$
$827$	21.0886	−	21.0886i	0.733322	−	0.733322i	0.971276	+	0.237954i	$0.0764768\pi$
$828$	−15.0452	−	106.817i	−0.522857	−	3.71213i
$829$	−19.4808	+	11.2473i	−0.676597	+	0.390634i	−0.798572	−	0.601900i	$-0.794411\pi$
$829$	−19.4808	+	11.2473i	−0.676597	+	0.390634i	0.121974	+	0.992533i	$0.461077\pi$
$830$	16.2516	−	16.2516i	0.564101	−	0.564101i
$831$	23.0915	−	1.61825i	0.801037	−	0.0561363i
$832$	−1.53326	+	6.82424i	−0.0531563	+	0.236588i
$833$	3.56367	−	2.05748i	0.123474	−	0.0712876i
$834$	−28.5426	−	82.8528i	−0.988349	−	2.86896i
$835$	5.34609			0.185009
$836$	59.8393	−	103.645i	2.06959	−	3.58463i
$837$	−0.599418	+	11.5383i	−0.0207189	+	0.398821i
$838$	19.7618	+	73.7520i	0.682659	+	2.54772i
$839$	36.6713	+	9.82605i	1.26603	+	0.339233i	0.828510	−	0.559974i	$-0.189189\pi$
$839$	36.6713	+	9.82605i	1.26603	+	0.339233i	0.437524	+	0.899207i	$0.355855\pi$
$840$	−12.3517	−	2.39898i	−0.426174	−	0.0827726i
$841$	0.273764			0.00944014
$842$	3.83659	−	6.64517i	0.132218	−	0.229008i
$843$	9.37103	−	48.2490i	0.322756	−	1.66178i
$844$	−85.7138	−	49.4869i	−2.95039	−	1.70341i
$845$	10.0879	−	11.8844i	0.347033	−	0.408835i
$846$	24.3150	−	3.42479i	0.835966	−	0.117747i
$847$	−23.9771	−	6.42465i	−0.823864	−	0.220754i
$848$			28.8168i			0.989572i
$849$	−20.3718	−	30.1925i	−0.699157	−	1.03620i
$850$	−35.8060	−	9.59419i	−1.22814	−	0.329078i
$851$	26.7387	+	26.7387i	0.916592	+	0.916592i
$852$	4.20410	−	21.6458i	0.144030	−	0.741572i
$853$	46.9399	−	12.5775i	1.60719	−	0.430646i	0.659987	−	0.751277i	$-0.270562\pi$
$853$	46.9399	−	12.5775i	1.60719	−	0.430646i	0.947204	+	0.320631i	$0.103895\pi$
$854$	9.82557	+	5.67280i	0.336224	+	0.194119i
$855$	10.0790	+	12.8925i	0.344695	+	0.440913i
$856$	24.1750	−	90.2224i	0.826285	−	3.08374i
$857$	4.55415	−	7.88802i	0.155567	−	0.269450i	−0.777698	−	0.628638i	$-0.783613\pi$
$857$	4.55415	−	7.88802i	0.155567	−	0.269450i	0.933265	+	0.359188i	$0.116946\pi$
$858$	73.8183	+	59.0427i	2.52012	+	2.01569i
$859$	25.6050	+	44.3492i	0.873632	+	1.51317i	0.858213	+	0.513293i	$0.171575\pi$
$859$	25.6050	+	44.3492i	0.873632	+	1.51317i	0.0154186	+	0.999881i	$0.495092\pi$
$860$	1.42114	−	0.380793i	0.0484604	−	0.0129849i
$861$	−4.06132	+	8.33016i	−0.138410	+	0.283891i
$862$	−76.0397	+	43.9015i	−2.58992	+	1.49529i
$863$	−27.7741	−	27.7741i	−0.945442	−	0.945442i	0.0531448	−	0.998587i	$-0.483076\pi$
$863$	−27.7741	−	27.7741i	−0.945442	−	0.945442i	−0.998587	+	0.0531448i	$0.983076\pi$
$864$	−12.4347	+	19.1669i	−0.423037	+	0.652071i
$865$	−14.3501	+	3.84509i	−0.487917	+	0.130737i
$866$	9.68627	+	36.1497i	0.329153	+	1.22842i
$867$	−0.00811895	−	0.115853i	−0.000275734	−	0.00393459i
$868$	−8.46423	−	4.88683i	−0.287295	−	0.165870i
$869$	15.3583	+	57.3179i	0.520994	+	1.94438i
$870$	1.96802	+	28.0827i	0.0667222	+	0.952091i
$871$	1.95896	+	47.9979i	0.0663767	+	1.62635i
$872$			36.6134i			1.23989i
$873$	−16.6363	−	39.1595i	−0.563052	−	1.32535i
$874$	−47.0546	−	81.5009i	−1.59165	−	2.75681i
$875$	−5.13350	−	8.89149i	−0.173544	−	0.300587i
$876$	−66.8163	+	23.0181i	−2.25751	+	0.777708i
$877$	17.6809	−	17.6809i	0.597042	−	0.597042i	−0.342482	−	0.939524i	$-0.611268\pi$
$877$	17.6809	−	17.6809i	0.597042	−	0.597042i	0.939524	+	0.342482i	$0.111268\pi$
$878$	7.96994	−	7.96994i	0.268972	−	0.268972i
$879$	−5.89552	+	2.03099i	−0.198851	+	0.0685037i
$880$	−23.4320	−	40.5855i	−0.789893	−	1.36814i
$881$	−9.02103	−	15.6249i	−0.303926	−	0.526416i	0.673095	−	0.739556i	$-0.264964\pi$
$881$	−9.02103	−	15.6249i	−0.303926	−	0.526416i	−0.977022	+	0.213140i	$0.931631\pi$
$882$	4.56402	−	6.06050i	0.153679	−	0.204068i
$883$			45.2391i			1.52242i	0.648507	+	0.761209i	$0.275394\pi$
$883$			45.2391i			1.52242i	−0.648507	+	0.761209i	$0.724606\pi$
$884$	−47.9565	−	44.1955i	−1.61295	−	1.48645i
$885$	0.355085	+	5.06688i	0.0119360	+	0.170321i
$886$	−5.36748	−	20.0317i	−0.180324	−	0.672978i
$887$	−21.7897	−	12.5803i	−0.731627	−	0.422405i	0.0873902	−	0.996174i	$-0.472147\pi$
$887$	−21.7897	−	12.5803i	−0.731627	−	0.422405i	−0.819017	+	0.573769i	$0.805481\pi$
$888$	−3.39092	−	48.3867i	−0.113792	−	1.62375i
$889$	−2.60199	−	9.71077i	−0.0872680	−	0.325689i
$890$	−38.2145	+	10.2396i	−1.28095	+	0.343231i
$891$	−27.7717	−	46.1562i	−0.930386	−	1.54629i
$892$	36.7427	+	36.7427i	1.23024	+	1.23024i
$893$	12.7507	−	7.36160i	0.426685	−	0.246347i
$894$	18.3674	−	37.6732i	0.614296	−	1.25998i
$895$	3.21640	−	0.861832i	0.107512	−	0.0288079i
$896$	6.84987	+	11.8643i	0.228838	+	0.396359i
$897$	47.5816	−	18.5952i	1.58870	−	0.620874i
$898$	14.5045	−	25.1225i	0.484020	−	0.838348i
$899$	−3.08446	+	11.5114i	−0.102873	+	0.383926i
$900$	−46.5131	+	6.55142i	−1.55044	+	0.218381i
$901$	15.7270	+	9.08000i	0.523943	+	0.302499i
$902$	−78.2283	+	20.9612i	−2.60472	+	0.697932i
$903$	−0.0921798	+	0.474609i	−0.00306755	+	0.0157940i
$904$	−44.8149	−	44.8149i	−1.49052	−	1.49052i
$905$	3.45714	+	0.926338i	0.114919	+	0.0307925i
$906$	−29.8035	−	44.1710i	−0.990154	−	1.46748i
$907$		−	29.1208i		−	0.966939i	−0.875361	−	0.483470i	$-0.839376\pi$
$907$		−	29.1208i		−	0.966939i	0.875361	−	0.483470i	$-0.160624\pi$
$908$	−99.4094	−	26.6367i	−3.29902	−	0.883969i
$909$	21.8291	+	27.9224i	0.724025	+	0.926129i
$910$	−0.445876	−	10.9248i	−0.0147807	−	0.362153i
$911$	38.8274	+	22.4170i	1.28641	+	0.742708i	0.978012	−	0.208550i	$-0.0668742\pi$
$911$	38.8274	+	22.4170i	1.28641	+	0.742708i	0.308397	+	0.951258i	$0.400208\pi$
$912$	−9.80931	+	50.5055i	−0.324819	+	1.67240i
$913$	−22.6808	+	39.2844i	−0.750626	+	1.30012i
$914$	62.2975			2.06062
$915$	−9.14685	−	1.77652i	−0.302386	−	0.0587301i
$916$	48.1204	+	12.8938i	1.58994	+	0.426024i
$917$	−2.65194	−	9.89718i	−0.0875749	−	0.326834i
$918$	24.5710	+	48.1689i	0.810963	+	1.58981i
$919$	−12.6794	+	21.9614i	−0.418255	+	0.724439i	−0.995764	−	0.0919454i	$-0.970691\pi$
$919$	−12.6794	+	21.9614i	−0.418255	+	0.724439i	0.577509	+	0.816384i	$0.304025\pi$
$920$	−59.4261			−1.95922
$921$	12.1469	+	35.2596i	0.400253	+	1.16184i
$922$	7.40466	−	4.27508i	0.243859	−	0.140792i
$923$	10.4340	−	0.425846i	0.343439	−	0.0140169i
$924$	45.4559	−	3.18553i	1.49539	−	0.104796i
$925$	11.6433	−	11.6433i	0.382831	−	0.382831i
$926$	−13.1552	+	7.59517i	−0.432307	+	0.249593i
$927$	24.0841	+	9.72210i	0.791026	+	0.319316i
$928$	−16.6638	+	16.6638i	−0.547017	+	0.547017i
$929$	−0.257272	+	0.960151i	−0.00844081	+	0.0315015i	−0.970018	−	0.243034i	$-0.921857\pi$
$929$	−0.257272	+	0.960151i	−0.00844081	+	0.0315015i	0.961577	+	0.274535i	$0.0885241\pi$
$930$	11.4648	+	2.22672i	0.375945	+	0.0730170i
$931$	1.17739	−	4.39407i	0.0385873	−	0.144010i
$932$		−	17.3828i		−	0.569392i
$933$	3.12718	+	44.6232i	0.102379	+	1.46090i
$934$	−22.7376	−	22.7376i	−0.743997	−	0.743997i
$935$	−29.5332			−0.965838
$936$	−61.7151	−	22.0309i	−2.01722	−	0.720103i
$937$	7.86018			0.256781			0.128390	−	0.991724i	$-0.459019\pi$
$937$	7.86018			0.256781			0.128390	+	0.991724i	$0.459019\pi$
$938$	23.8252	+	23.8252i	0.777919	+	0.777919i
$939$	20.2097	−	13.6361i	0.659519	−	0.444997i
$940$		−	17.0591i		−	0.556406i
$941$	11.1395	−	41.5730i	0.363136	−	1.35524i	−0.506795	−	0.862067i	$-0.669170\pi$
$941$	11.1395	−	41.5730i	0.363136	−	1.35524i	0.869930	−	0.493174i	$-0.164164\pi$
$942$	18.5492	−	21.3450i	0.604366	−	0.695457i
$943$	−11.3284	+	42.2780i	−0.368902	+	1.37676i
$944$	−11.2917	+	11.2917i	−0.367515	+	0.367515i
$945$	−1.92273	+	5.92674i	−0.0625463	+	0.192797i
$946$	−3.65903	+	2.11254i	−0.118965	+	0.0686847i
$947$	12.5664	−	12.5664i	0.408353	−	0.408353i	−0.472811	−	0.881164i	$-0.656761\pi$
$947$	12.5664	−	12.5664i	0.408353	−	0.408353i	0.881164	+	0.472811i	$0.156761\pi$
$948$	−42.2181	−	62.5704i	−1.37118	−	2.03219i
$949$	−17.9022	−	28.2778i	−0.581129	−	0.917938i
$950$	−35.4895	+	20.4898i	−1.15143	+	0.664778i
$951$	11.3719	+	2.20867i	0.368758	+	0.0716210i
$952$	−24.9293			−0.807963
$953$	−22.6208	+	39.1803i	−0.732759	+	1.26918i	0.222941	+	0.974832i	$0.428434\pi$
$953$	−22.6208	+	39.1803i	−0.732759	+	1.26918i	−0.955700	+	0.294343i	$0.904899\pi$
$954$	33.2335	+	4.07031i	1.07598	+	0.131781i
$955$	6.38493	+	23.8289i	0.206612	+	0.771085i
$956$	41.6757	+	11.1670i	1.34789	+	0.361165i
$957$	−18.0973	−	52.5325i	−0.585003	−	1.69813i
$958$	−65.8587			−2.12780
$959$	1.23657	−	2.14180i	0.0399309	−	0.0691624i
$960$	−3.04115	−	2.64282i	−0.0981526	−	0.0852966i
$961$	−22.5651	−	13.0279i	−0.727905	−	0.420256i
$962$	40.2349	−	12.5604i	1.29722	−	0.404963i
$963$	−42.8911	−	17.3140i	−1.38215	−	0.557935i
$964$	−30.4933	−	8.17066i	−0.982123	−	0.263159i
$965$		−	25.5014i		−	0.820919i
$966$	15.7028	−	32.2079i	0.505228	−	1.03627i
$967$	−4.81479	−	1.29012i	−0.154833	−	0.0414874i	0.180570	−	0.983562i	$-0.442206\pi$
$967$	−4.81479	−	1.29012i	−0.154833	−	0.0414874i	−0.335403	+	0.942075i	$0.608872\pi$
$968$	106.336	+	106.336i	3.41778	+	3.41778i
$969$	24.4730	+	21.2675i	0.786186	+	0.683211i
$970$	−41.5424	+	11.1312i	−1.33384	+	0.357403i
$971$	5.60360	+	3.23524i	0.179828	+	0.103824i	0.587212	−	0.809433i	$-0.300226\pi$
$971$	5.60360	+	3.23524i	0.179828	+	0.103824i	−0.407384	+	0.913257i	$0.633559\pi$
$972$	52.5227	+	44.0038i	1.68467	+	1.41142i
$973$	5.17793	−	19.3243i	0.165997	−	0.619509i
$974$	22.2788	−	38.5879i	0.713857	−	1.23644i
$975$	−8.09723	−	20.7193i	−0.259319	−	0.663550i
$976$	−14.6472	−	25.3697i	−0.468845	−	0.812063i
$977$	−20.4412	+	5.47720i	−0.653971	+	0.175231i	−0.570524	−	0.821281i	$-0.693260\pi$
$977$	−20.4412	+	5.47720i	−0.653971	+	0.175231i	−0.0834474	+	0.996512i	$0.526593\pi$
$978$	25.1488	+	37.2723i	0.804168	+	1.19184i
$979$	67.6230	−	39.0421i	2.16124	−	1.24779i
$980$	−3.72702	−	3.72702i	−0.119055	−	0.119055i
$981$	17.9964	+	2.20412i	0.574580	+	0.0703722i
$982$	−10.0717	+	2.69872i	−0.321402	+	0.0861195i
$983$	−1.90595	−	7.11311i	−0.0607904	−	0.226873i	0.928847	−	0.370464i	$-0.120801\pi$
$983$	−1.90595	−	7.11311i	−0.0607904	−	0.226873i	−0.989637	+	0.143592i	$0.954135\pi$
$984$	46.5408	−	31.4025i	1.48367	−	1.00107i
$985$	−18.2320	−	10.5262i	−0.580918	−	0.335393i
$986$	14.4358	+	53.8751i	0.459729	+	1.71573i
$987$	5.03886	+	2.45667i	0.160389	+	0.0781966i
$988$	−72.0354	+	2.94001i	−2.29175	+	0.0935340i
$989$			2.28342i			0.0726086i
$990$	−50.1157	+	21.2908i	−1.59278	+	0.676668i
$991$	−17.5366	−	30.3742i	−0.557068	−	0.964870i	−0.997739	−	0.0672012i	$-0.978593\pi$
$991$	−17.5366	−	30.3742i	−0.557068	−	0.964870i	0.440672	−	0.897668i	$-0.354740\pi$
$992$	4.88837	+	8.46690i	0.155206	+	0.268824i
$993$	3.55159	+	3.08640i	0.112706	+	0.0979441i
$994$	5.17922	−	5.17922i	0.164275	−	0.164275i
$995$	−21.9625	+	21.9625i	−0.696257	+	0.696257i
$996$	11.0012	−	56.6424i	0.348587	−	1.79478i
$997$	4.18983	+	7.25699i	0.132693	+	0.229831i	0.924714	−	0.380663i	$-0.124304\pi$
$997$	4.18983	+	7.25699i	0.132693	+	0.229831i	−0.792021	+	0.610494i	$0.790971\pi$
$998$	32.3075	+	55.9583i	1.02268	+	1.77133i
$999$	−23.9873	−	1.24615i	−0.758926	−	0.0394265i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.ew.a.470.81	yes	336
9.5	odd	6		819.2.fy.a.743.81	yes	336
13.7	odd	12		819.2.fy.a.722.81	yes	336
117.59	even	12	inner	819.2.ew.a.176.81	✓	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.ew.a.176.81	✓	336	117.59	even	12	inner
819.2.ew.a.470.81	yes	336	1.1	even	1	trivial
819.2.fy.a.722.81	yes	336	13.7	odd	12
819.2.fy.a.743.81	yes	336	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.ew (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.78823 + 1.78823i) q^{2} +(-1.55687 - 0.759044i) q^{3} +4.39555i q^{4} +(0.310355 - 1.15826i) q^{5} +(-1.42670 - 4.14140i) q^{6} +(0.258819 - 0.965926i) q^{7} +(-4.28379 + 4.28379i) q^{8} +(1.84770 + 2.36347i) q^{9} +O(q^{10})\)	\(q+(1.78823 + 1.78823i) q^{2} +(-1.55687 - 0.759044i) q^{3} +4.39555i q^{4} +(0.310355 - 1.15826i) q^{5} +(-1.42670 - 4.14140i) q^{6} +(0.258819 - 0.965926i) q^{7} +(-4.28379 + 4.28379i) q^{8} +(1.84770 + 2.36347i) q^{9} +(2.62623 - 1.51625i) q^{10} +(-4.23220 + 4.23220i) q^{11} +(3.33642 - 6.84331i) q^{12} +(3.51785 + 0.790387i) q^{13} +(2.19013 - 1.26447i) q^{14} +(-1.36236 + 1.56769i) q^{15} -6.52974 q^{16} +(-2.05748 + 3.56367i) q^{17} +(-0.922312 + 7.53056i) q^{18} +(1.17739 + 4.39407i) q^{19} +(5.09120 + 1.36418i) q^{20} +(-1.13613 + 1.30737i) q^{21} -15.1363 q^{22} +(-4.09016 + 7.08437i) q^{23} +(9.92091 - 3.41773i) q^{24} +(3.08488 + 1.78105i) q^{25} +(4.87734 + 7.70413i) q^{26} +(-1.08266 - 5.08211i) q^{27} +(4.24577 + 1.13765i) q^{28} -5.35969i q^{29} +(-5.23961 + 0.367190i) q^{30} +(-2.14777 - 0.575493i) q^{31} +(-3.10910 - 3.10910i) q^{32} +(9.80141 - 3.37656i) q^{33} +(-10.0519 + 2.69340i) q^{34} +(-1.03847 - 0.599561i) q^{35} +(-10.3887 + 8.12167i) q^{36} +(1.19641 - 4.46508i) q^{37} +(-5.75217 + 9.96305i) q^{38} +(-4.87691 - 3.90074i) q^{39} +(3.63226 + 6.29126i) q^{40} +(5.16826 - 1.38483i) q^{41} +(-4.36954 + 0.306216i) q^{42} +(0.241739 - 0.139568i) q^{43} +(-18.6028 - 18.6028i) q^{44} +(3.31096 - 1.40661i) q^{45} +(-19.9826 + 5.35433i) q^{46} +(-0.837675 - 3.12625i) q^{47} +(10.1660 + 4.95636i) q^{48} +(-0.866025 - 0.500000i) q^{49} +(2.33154 + 8.70141i) q^{50} +(5.90822 - 3.98645i) q^{51} +(-3.47418 + 15.4629i) q^{52} -4.41316i q^{53} +(7.15195 - 11.0240i) q^{54} +(3.58851 + 6.21548i) q^{55} +(3.02910 + 5.24655i) q^{56} +(1.50225 - 7.73469i) q^{57} +(9.58436 - 9.58436i) q^{58} +(1.72928 - 1.72928i) q^{59} +(-6.89087 - 5.98830i) q^{60} +(2.24315 + 3.88525i) q^{61} +(-2.81160 - 4.86983i) q^{62} +(2.76116 - 1.17303i) q^{63} +1.93989i q^{64} +(2.00726 - 3.82930i) q^{65} +(23.5653 + 11.4891i) q^{66} +(3.44833 + 12.8693i) q^{67} +(-15.6643 - 9.04376i) q^{68} +(11.7452 - 7.92484i) q^{69} +(-0.784871 - 2.92918i) q^{70} +(2.79759 - 0.749612i) q^{71} +(-18.0398 - 2.20944i) q^{72} +(-6.56366 - 6.56366i) q^{73} +(10.1241 - 5.84513i) q^{74} +(-3.45086 - 5.11443i) q^{75} +(-19.3143 + 5.17526i) q^{76} +(2.99261 + 5.18336i) q^{77} +(-1.74562 - 15.6965i) q^{78} +(4.95719 - 8.58611i) q^{79} +(-2.02654 + 7.56315i) q^{80} +(-2.17199 + 8.73398i) q^{81} +(11.7184 + 6.76565i) q^{82} +(7.32070 - 1.96157i) q^{83} +(-5.74660 - 4.99391i) q^{84} +(3.48911 + 3.48911i) q^{85} +(0.681865 + 0.182705i) q^{86} +(-4.06824 + 8.34435i) q^{87} -36.2597i q^{88} +(-12.6016 - 3.37660i) q^{89} +(8.43612 + 3.40543i) q^{90} +(1.67394 - 3.19342i) q^{91} +(-31.1397 - 17.9785i) q^{92} +(2.90698 + 2.52622i) q^{93} +(4.09250 - 7.08841i) q^{94} +5.45489 q^{95} +(2.48053 + 7.20042i) q^{96} +(-13.6990 - 3.67064i) q^{97} +(-0.654538 - 2.44277i) q^{98} +(-17.8225 - 2.18283i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q + 24 q^{6} - 36 q^{8}+O(q^{10}) \) 336 * q + 24 * q^6 - 36 * q^8	\( 336 q + 24 q^{6} - 36 q^{8} + 16 q^{15} - 336 q^{16} + 20 q^{18} + 8 q^{21} + 8 q^{24} + 96 q^{26} + 24 q^{27} - 96 q^{30} - 72 q^{32} - 36 q^{33} - 12 q^{36} - 72 q^{38} - 16 q^{39} - 48 q^{41} - 28 q^{45} + 60 q^{47} - 48 q^{48} + 132 q^{50} - 36 q^{52} - 108 q^{54} + 68 q^{57} - 72 q^{58} - 44 q^{60} - 36 q^{62} - 8 q^{63} - 72 q^{65} - 20 q^{66} - 72 q^{69} + 48 q^{71} - 104 q^{72} + 12 q^{74} + 104 q^{78} - 12 q^{79} + 96 q^{80} - 68 q^{81} - 120 q^{83} - 12 q^{84} + 36 q^{85} + 48 q^{86} - 24 q^{87} - 60 q^{89} - 72 q^{92} - 172 q^{93} - 48 q^{94} - 152 q^{96} + 48 q^{97}+O(q^{100}) \) 336 * q + 24 * q^6 - 36 * q^8 + 16 * q^15 - 336 * q^16 + 20 * q^18 + 8 * q^21 + 8 * q^24 + 96 * q^26 + 24 * q^27 - 96 * q^30 - 72 * q^32 - 36 * q^33 - 12 * q^36 - 72 * q^38 - 16 * q^39 - 48 * q^41 - 28 * q^45 + 60 * q^47 - 48 * q^48 + 132 * q^50 - 36 * q^52 - 108 * q^54 + 68 * q^57 - 72 * q^58 - 44 * q^60 - 36 * q^62 - 8 * q^63 - 72 * q^65 - 20 * q^66 - 72 * q^69 + 48 * q^71 - 104 * q^72 + 12 * q^74 + 104 * q^78 - 12 * q^79 + 96 * q^80 - 68 * q^81 - 120 * q^83 - 12 * q^84 + 36 * q^85 + 48 * q^86 - 24 * q^87 - 60 * q^89 - 72 * q^92 - 172 * q^93 - 48 * q^94 - 152 * q^96 + 48 * q^97

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