LMFDB - Embedded newform 819.2.dk.a.43.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(43,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 1]))

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

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

chi := DirichletCharacter("819.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.dk (of order $6$, degree $2$, 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:	$168$
Relative dimension:	$84$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			43.23
Character	$\chi$	$=$	819.43
Dual form			819.2.dk.a.400.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33948 + 0.773348i) q^{2} +(-0.391838 + 1.68715i) q^{3} +(0.196135 - 0.339716i) q^{4} +(0.780582 - 0.450669i) q^{5} +(-0.779893 - 2.56292i) q^{6} +1.00000i q^{7} -2.48667i q^{8} +(-2.69293 - 1.32218i) q^{9} +O(q^{10})$	\(q+(-1.33948 + 0.773348i) q^{2} +(-0.391838 + 1.68715i) q^{3} +(0.196135 - 0.339716i) q^{4} +(0.780582 - 0.450669i) q^{5} +(-0.779893 - 2.56292i) q^{6} +1.00000i q^{7} -2.48667i q^{8} +(-2.69293 - 1.32218i) q^{9} +(-0.697049 + 1.20732i) q^{10} +(3.38580 - 1.95479i) q^{11} +(0.496297 + 0.464022i) q^{12} +(3.57792 - 0.445527i) q^{13} +(-0.773348 - 1.33948i) q^{14} +(0.454484 + 1.49355i) q^{15} +(2.31533 + 4.01027i) q^{16} +(2.34146 + 4.05552i) q^{17} +(4.62962 - 0.311544i) q^{18} +(-0.626877 + 0.361928i) q^{19} -0.353568i q^{20} +(-1.68715 - 0.391838i) q^{21} +(-3.02347 + 5.23681i) q^{22} +3.05551 q^{23} +(4.19538 + 0.974372i) q^{24} +(-2.09379 + 3.62656i) q^{25} +(-4.44800 + 3.36375i) q^{26} +(3.28589 - 4.02528i) q^{27} +(0.339716 + 0.196135i) q^{28} +(4.05438 + 7.02239i) q^{29} +(-1.76380 - 1.64910i) q^{30} +(-0.726802 + 0.419619i) q^{31} +(-1.89564 - 1.09445i) q^{32} +(1.97134 + 6.47831i) q^{33} +(-6.27266 - 3.62152i) q^{34} +(0.450669 + 0.780582i) q^{35} +(-0.977342 + 0.655505i) q^{36} +(-4.71306 - 2.72109i) q^{37} +(0.559792 - 0.969589i) q^{38} +(-0.650295 + 6.21105i) q^{39} +(-1.12067 - 1.94105i) q^{40} -12.4736i q^{41} +(2.56292 - 0.779893i) q^{42} +1.14136 q^{43} -1.53362i q^{44} +(-2.69792 + 0.181552i) q^{45} +(-4.09279 + 2.36297i) q^{46} +(10.6638 + 6.15676i) q^{47} +(-7.67315 + 2.33493i) q^{48} -1.00000 q^{49} -6.47693i q^{50} +(-7.75973 + 2.36127i) q^{51} +(0.550403 - 1.30286i) q^{52} +1.75264 q^{53} +(-1.28844 + 7.93292i) q^{54} +(1.76193 - 3.05176i) q^{55} +2.48667 q^{56} +(-0.364991 - 1.19945i) q^{57} +(-10.8615 - 6.27089i) q^{58} +(-2.96843 - 1.71382i) q^{59} +(0.596522 + 0.138542i) q^{60} -3.28252 q^{61} +(0.649023 - 1.12414i) q^{62} +(1.32218 - 2.69293i) q^{63} -5.87578 q^{64} +(2.59208 - 1.96023i) q^{65} +(-7.65055 - 7.15302i) q^{66} +4.00875i q^{67} +1.83697 q^{68} +(-1.19726 + 5.15509i) q^{69} +(-1.20732 - 0.697049i) q^{70} +(-2.55290 + 1.47392i) q^{71} +(-3.28782 + 6.69642i) q^{72} +2.98109i q^{73} +8.41739 q^{74} +(-5.29811 - 4.95356i) q^{75} +0.283947i q^{76} +(1.95479 + 3.38580i) q^{77} +(-3.93225 - 8.82247i) q^{78} +(-5.91382 + 10.2430i) q^{79} +(3.61462 + 2.08690i) q^{80} +(5.50370 + 7.12104i) q^{81} +(9.64647 + 16.7082i) q^{82} +(-14.2568 - 8.23114i) q^{83} +(-0.464022 + 0.496297i) q^{84} +(3.65540 + 2.11045i) q^{85} +(-1.52883 + 0.882668i) q^{86} +(-13.4365 + 4.08869i) q^{87} +(-4.86093 - 8.41937i) q^{88} +(8.81581 + 5.08981i) q^{89} +(3.47340 - 2.32961i) q^{90} +(0.445527 + 3.57792i) q^{91} +(0.599293 - 1.03801i) q^{92} +(-0.423170 - 1.39064i) q^{93} -19.0453 q^{94} +(-0.326220 + 0.565029i) q^{95} +(2.58927 - 2.76937i) q^{96} +11.7965i q^{97} +(1.33948 - 0.773348i) q^{98} +(-11.7023 + 0.787489i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q + 84 q^{4} - 2 q^{9}+O(q^{10}) $ 168 * q + 84 * q^4 - 2 * q^9	$ 168 q + 84 q^{4} - 2 q^{9} + 12 q^{12} + 8 q^{14} - 84 q^{16} + 12 q^{18} - 6 q^{21} + 40 q^{23} - 84 q^{24} + 84 q^{25} + 4 q^{26} - 24 q^{27} + 34 q^{29} + 44 q^{30} + 36 q^{32} + 18 q^{33} + 16 q^{35} + 4 q^{36} - 12 q^{38} - 6 q^{39} - 30 q^{45} - 30 q^{47} - 2 q^{48} - 168 q^{49} - 38 q^{51} + 18 q^{52} - 48 q^{53} + 114 q^{54} + 48 q^{56} - 54 q^{57} + 48 q^{59} + 24 q^{60} + 6 q^{62} - 12 q^{63} - 132 q^{64} - 16 q^{65} - 54 q^{66} - 156 q^{68} - 28 q^{69} + 24 q^{71} + 36 q^{72} - 84 q^{74} + 30 q^{75} - 16 q^{77} + 116 q^{78} - 6 q^{79} - 2 q^{81} - 6 q^{82} + 18 q^{83} - 24 q^{84} + 90 q^{85} - 24 q^{86} + 52 q^{87} + 24 q^{88} - 36 q^{89} - 44 q^{90} - 6 q^{91} + 8 q^{92} - 66 q^{93} + 120 q^{94} - 48 q^{95} - 24 q^{96} + 6 q^{99}+O(q^{100}) $ 168 * q + 84 * q^4 - 2 * q^9 + 12 * q^12 + 8 * q^14 - 84 * q^16 + 12 * q^18 - 6 * q^21 + 40 * q^23 - 84 * q^24 + 84 * q^25 + 4 * q^26 - 24 * q^27 + 34 * q^29 + 44 * q^30 + 36 * q^32 + 18 * q^33 + 16 * q^35 + 4 * q^36 - 12 * q^38 - 6 * q^39 - 30 * q^45 - 30 * q^47 - 2 * q^48 - 168 * q^49 - 38 * q^51 + 18 * q^52 - 48 * q^53 + 114 * q^54 + 48 * q^56 - 54 * q^57 + 48 * q^59 + 24 * q^60 + 6 * q^62 - 12 * q^63 - 132 * q^64 - 16 * q^65 - 54 * q^66 - 156 * q^68 - 28 * q^69 + 24 * q^71 + 36 * q^72 - 84 * q^74 + 30 * q^75 - 16 * q^77 + 116 * q^78 - 6 * q^79 - 2 * q^81 - 6 * q^82 + 18 * q^83 - 24 * q^84 + 90 * q^85 - 24 * q^86 + 52 * q^87 + 24 * q^88 - 36 * q^89 - 44 * q^90 - 6 * q^91 + 8 * q^92 - 66 * q^93 + 120 * q^94 - 48 * q^95 - 24 * q^96 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$379$	$703$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	−1.33948	+	0.773348i	−0.947154	+	0.546840i	−0.892196	−	0.451649i	$-0.850836\pi$
$2$	−1.33948	+	0.773348i	−0.947154	+	0.546840i	−0.0549585	+	0.998489i	$0.517503\pi$
$3$	−0.391838	+	1.68715i	−0.226228	+	0.974074i
$3$	−0.391838	+	1.68715i	−0.226228	+	0.974074i
$4$	0.196135	−	0.339716i	0.0980676	−	0.169858i
$5$	0.780582	−	0.450669i	0.349087	−	0.201546i	−0.315196	−	0.949027i	$-0.602070\pi$
$5$	0.780582	−	0.450669i	0.349087	−	0.201546i	0.664283	+	0.747481i	$0.268737\pi$
$6$	−0.779893	−	2.56292i	−0.318390	−	1.04631i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$		−	2.48667i		−	0.879171i
$9$	−2.69293	−	1.32218i	−0.897642	−	0.440725i
$10$	−0.697049	+	1.20732i	−0.220426	+	0.381789i
$11$	3.38580	−	1.95479i	1.02086	−	0.589393i	0.106506	−	0.994312i	$-0.466034\pi$
$11$	3.38580	−	1.95479i	1.02086	−	0.589393i	0.914352	+	0.404920i	$0.132700\pi$
$12$	0.496297	+	0.464022i	0.143269	+	0.133952i
$13$	3.57792	−	0.445527i	0.992336	−	0.123567i
$13$	3.57792	−	0.445527i	0.992336	−	0.123567i
$14$	−0.773348	−	1.33948i	−0.206686	−	0.357991i
$15$	0.454484	+	1.49355i	0.117347	+	0.385632i
$16$	2.31533	+	4.01027i	0.578833	+	1.00257i
$17$	2.34146	+	4.05552i	0.567886	+	0.983608i	0.996775	+	0.0802506i	$0.0255721\pi$
$17$	2.34146	+	4.05552i	0.567886	+	0.983608i	−0.428888	+	0.903358i	$0.641095\pi$
$18$	4.62962	−	0.311544i	1.09121	−	0.0734315i
$19$	−0.626877	+	0.361928i	−0.143816	+	0.0830319i	−0.570181	−	0.821519i	$-0.693127\pi$
$19$	−0.626877	+	0.361928i	−0.143816	+	0.0830319i	0.426366	+	0.904551i	$0.359794\pi$
$20$		−	0.353568i		−	0.0790603i
$21$	−1.68715	−	0.391838i	−0.368166	−	0.0855060i
$22$	−3.02347	+	5.23681i	−0.644607	+	1.11649i
$23$	3.05551			0.637118			0.318559	−	0.947903i	$-0.396801\pi$
$23$	3.05551			0.637118			0.318559	+	0.947903i	$0.396801\pi$
$24$	4.19538	+	0.974372i	0.856378	+	0.198893i
$25$	−2.09379	+	3.62656i	−0.418759	+	0.725312i
$26$	−4.44800	+	3.36375i	−0.872324	+	0.659686i
$27$	3.28589	−	4.02528i	0.632371	−	0.774666i
$28$	0.339716	+	0.196135i	0.0642003	+	0.0370661i
$29$	4.05438	+	7.02239i	0.752879	+	1.30402i	0.946422	+	0.322932i	$0.104669\pi$
$29$	4.05438	+	7.02239i	0.752879	+	1.30402i	−0.193543	+	0.981092i	$0.561998\pi$
$30$	−1.76380	−	1.64910i	−0.322025	−	0.301083i
$31$	−0.726802	+	0.419619i	−0.130537	+	0.0753658i	−0.563847	−	0.825879i	$-0.690679\pi$
$31$	−0.726802	+	0.419619i	−0.130537	+	0.0753658i	0.433309	+	0.901245i	$0.357346\pi$
$32$	−1.89564	−	1.09445i	−0.335104	−	0.193473i
$33$	1.97134	+	6.47831i	0.343166	+	1.12773i
$34$	−6.27266	−	3.62152i	−1.07575	−	0.621086i
$35$	0.450669	+	0.780582i	0.0761770	+	0.131943i
$36$	−0.977342	+	0.655505i	−0.162890	+	0.109251i
$37$	−4.71306	−	2.72109i	−0.774823	−	0.447344i	0.0597697	−	0.998212i	$-0.480963\pi$
$37$	−4.71306	−	2.72109i	−0.774823	−	0.447344i	−0.834592	+	0.550868i	$0.814297\pi$
$38$	0.559792	−	0.969589i	0.0908103	−	0.157288i
$39$	−0.650295	+	6.21105i	−0.104131	+	0.994564i
$40$	−1.12067	−	1.94105i	−0.177193	−	0.306907i
$41$		−	12.4736i		−	1.94806i	−0.226430	−	0.974028i	$-0.572705\pi$
$41$		−	12.4736i		−	1.94806i	0.226430	−	0.974028i	$-0.427295\pi$
$42$	2.56292	−	0.779893i	0.395468	−	0.120340i
$43$	1.14136			0.174056			0.0870278	−	0.996206i	$-0.472263\pi$
$43$	1.14136			0.174056			0.0870278	+	0.996206i	$0.472263\pi$
$44$		−	1.53362i		−	0.231201i
$45$	−2.69792	+	0.181552i	−0.402181	+	0.0270642i
$46$	−4.09279	+	2.36297i	−0.603449	+	0.348401i
$47$	10.6638	+	6.15676i	1.55548	+	0.898056i	0.997680	+	0.0680804i	$0.0216874\pi$
$47$	10.6638	+	6.15676i	1.55548	+	0.898056i	0.557799	+	0.829976i	$0.311646\pi$
$48$	−7.67315	+	2.33493i	−1.10752	+	0.337018i
$49$	−1.00000			−0.142857
$50$		−	6.47693i		−	0.915976i
$51$	−7.75973	+	2.36127i	−1.08658	+	0.330644i
$52$	0.550403	−	1.30286i	0.0763272	−	0.180674i
$53$	1.75264			0.240744			0.120372	−	0.992729i	$-0.461591\pi$
$53$	1.75264			0.240744			0.120372	+	0.992729i	$0.461591\pi$
$54$	−1.28844	+	7.93292i	−0.175335	+	1.07953i
$55$	1.76193	−	3.05176i	0.237579	−	0.411499i
$56$	2.48667			0.332295
$57$	−0.364991	−	1.19945i	−0.0483442	−	0.158871i
$58$	−10.8615	−	6.27089i	−1.42618	−	0.823408i
$59$	−2.96843	−	1.71382i	−0.386457	−	0.223121i	0.294167	−	0.955754i	$-0.404958\pi$
$59$	−2.96843	−	1.71382i	−0.386457	−	0.223121i	−0.680624	+	0.732633i	$0.738291\pi$
$60$	0.596522	+	0.138542i	0.0770106	+	0.0178856i
$61$	−3.28252			−0.420284			−0.210142	−	0.977671i	$-0.567393\pi$
$61$	−3.28252			−0.420284			−0.210142	+	0.977671i	$0.567393\pi$
$62$	0.649023	−	1.12414i	0.0824260	−	0.142766i
$63$	1.32218	−	2.69293i	0.166579	−	0.339277i
$64$	−5.87578			−0.734472
$65$	2.59208	−	1.96023i	0.321507	−	0.243137i
$66$	−7.65055	−	7.15302i	−0.941718	−	0.880476i
$67$			4.00875i			0.489747i	0.969555	+	0.244874i	$0.0787465\pi$
$67$			4.00875i			0.489747i	−0.969555	+	0.244874i	$0.921254\pi$
$68$	1.83697			0.222765
$69$	−1.19726	+	5.15509i	−0.144134	+	0.620600i
$70$	−1.20732	−	0.697049i	−0.144303	−	0.0833133i
$71$	−2.55290	+	1.47392i	−0.302974	+	0.174922i	−0.643778	−	0.765212i	$-0.722634\pi$
$71$	−2.55290	+	1.47392i	−0.302974	+	0.174922i	0.340804	+	0.940134i	$0.389301\pi$
$72$	−3.28782	+	6.69642i	−0.387473	+	0.789181i
$73$			2.98109i			0.348911i	0.984665	+	0.174455i	$0.0558165\pi$
$73$			2.98109i			0.348911i	−0.984665	+	0.174455i	$0.944184\pi$
$74$	8.41739			0.978502
$75$	−5.29811	−	4.95356i	−0.611773	−	0.571988i
$76$			0.283947i			0.0325710i
$77$	1.95479	+	3.38580i	0.222769	+	0.385848i
$78$	−3.93225	−	8.82247i	−0.445239	−	0.998948i
$79$	−5.91382	+	10.2430i	−0.665357	+	1.15243i	0.313831	+	0.949479i	$0.398387\pi$
$79$	−5.91382	+	10.2430i	−0.665357	+	1.15243i	−0.979188	+	0.202953i	$0.934946\pi$
$80$	3.61462	+	2.08690i	0.404126	+	0.233322i
$81$	5.50370	+	7.12104i	0.611522	+	0.791227i
$82$	9.64647	+	16.7082i	1.06527	+	1.84511i
$83$	−14.2568	−	8.23114i	−1.56488	−	0.903485i	−0.996751	−	0.0805476i	$-0.974333\pi$
$83$	−14.2568	−	8.23114i	−1.56488	−	0.903485i	−0.568132	−	0.822938i	$-0.692334\pi$
$84$	−0.464022	+	0.496297i	−0.0506290	+	0.0541505i
$85$	3.65540	+	2.11045i	0.396484	+	0.228910i
$86$	−1.52883	+	0.882668i	−0.164857	+	0.0951805i
$87$	−13.4365	+	4.08869i	−1.44054	+	0.438354i
$88$	−4.86093	−	8.41937i	−0.518177	−	0.897508i
$89$	8.81581	+	5.08981i	0.934474	+	0.539519i	0.888224	−	0.459411i	$-0.151939\pi$
$89$	8.81581	+	5.08981i	0.934474	+	0.539519i	0.0462504	+	0.998930i	$0.485273\pi$
$90$	3.47340	−	2.32961i	0.366128	−	0.245563i
$91$	0.445527	+	3.57792i	0.0467039	+	0.375068i
$92$	0.599293	−	1.03801i	0.0624806	−	0.108220i
$93$	−0.423170	−	1.39064i	−0.0438807	−	0.144203i
$94$	−19.0453			−1.96437
$95$	−0.326220	+	0.565029i	−0.0334694	+	0.0579707i
$96$	2.58927	−	2.76937i	0.264267	−	0.282648i
$97$			11.7965i			1.19776i	0.800841	+	0.598878i	$0.204386\pi$
$97$			11.7965i			1.19776i	−0.800841	+	0.598878i	$0.795614\pi$
$98$	1.33948	−	0.773348i	0.135308	−	0.0781200i
$99$	−11.7023	+	0.787489i	−1.17613	+	0.0791457i
$100$	0.821333	+	1.42259i	0.0821333	+	0.142259i
$101$	4.26793	+	7.39228i	0.424675	+	0.735559i	0.996390	−	0.0848932i	$-0.0270549\pi$
$101$	4.26793	+	7.39228i	0.424675	+	0.735559i	−0.571715	+	0.820452i	$0.693722\pi$
$102$	8.56790	−	9.16384i	0.848349	−	0.907356i
$103$	−2.62154	−	4.54064i	−0.258308	−	0.447402i	0.707481	−	0.706732i	$-0.249832\pi$
$103$	−2.62154	−	4.54064i	−0.258308	−	0.447402i	−0.965789	+	0.259330i	$0.916498\pi$
$104$	−1.10788	−	8.89710i	−0.108636	−	0.872433i
$105$	−1.49355	+	0.454484i	−0.145755	+	0.0443531i
$106$	−2.34762	+	1.35540i	−0.228021	+	0.131648i
$107$	5.58198	−	9.66828i	0.539631	−	0.934667i	−0.459293	−	0.888285i	$-0.651897\pi$
$107$	5.58198	−	9.66828i	0.539631	−	0.934667i	0.998924	−	0.0463828i	$-0.0147694\pi$
$108$	−0.722973	−	1.90577i	−0.0695681	−	0.183383i
$109$			2.28489i			0.218852i	0.993995	+	0.109426i	$0.0349013\pi$
$109$			2.28489i			0.218852i	−0.993995	+	0.109426i	$0.965099\pi$
$110$			5.45035i			0.519670i
$111$	6.43763	−	6.88540i	0.611033	−	0.653533i
$112$	−4.01027	+	2.31533i	−0.378935	+	0.218778i
$113$	−2.78089	+	4.81665i	−0.261604	+	0.453112i	−0.966668	−	0.256032i	$-0.917585\pi$
$113$	−2.78089	+	4.81665i	−0.261604	+	0.453112i	0.705064	+	0.709144i	$0.250918\pi$
$114$	1.41649	+	1.32437i	0.132667	+	0.124039i
$115$	2.38508	−	1.37702i	0.222410	−	0.128408i
$116$	3.18082			0.295332
$117$	−10.2241	−	3.53087i	−0.945222	−	0.326429i
$118$	5.30153			0.488045
$119$	−4.05552	+	2.34146i	−0.371769	+	0.214641i
$120$	3.71396	−	1.13015i	0.339036	−	0.103168i
$121$	2.14244	−	3.71081i	0.194767	−	0.337347i
$122$	4.39687	−	2.53853i	0.398074	−	0.229828i
$123$	21.0449	+	4.88764i	1.89755	+	0.440704i
$124$			0.329208i			0.0295638i
$125$			8.28113i			0.740687i
$126$	0.311544	+	4.62962i	0.0277545	+	0.412439i
$127$	9.56512	−	16.5673i	0.848767	−	1.47011i	−0.0335424	−	0.999437i	$-0.510679\pi$
$127$	9.56512	−	16.5673i	0.848767	−	1.47011i	0.882309	−	0.470670i	$-0.155988\pi$
$128$	11.6617	−	6.73291i	1.03076	−	0.595111i
$129$	−0.447228	+	1.92564i	−0.0393762	+	0.169543i
$130$	−1.95609	+	4.63026i	−0.171560	+	0.406101i
$131$	−4.49301	−	7.78213i	−0.392556	−	0.679928i	0.600229	−	0.799828i	$-0.295076\pi$
$131$	−4.49301	−	7.78213i	−0.392556	−	0.679928i	−0.992786	+	0.119900i	$0.961743\pi$
$132$	2.58743	+	0.600929i	0.225207	+	0.0523041i
$133$	−0.361928	−	0.626877i	−0.0313831	−	0.0543572i
$134$	−3.10016	−	5.36964i	−0.267813	−	0.463866i
$135$	0.750840	−	4.62292i	0.0646220	−	0.397877i
$136$	10.0847	−	5.82243i	0.864759	−	0.499269i
$137$			10.1851i			0.870172i	0.900389	+	0.435086i	$0.143282\pi$
$137$			10.1851i			0.870172i	−0.900389	+	0.435086i	$0.856718\pi$
$138$	−2.38297	−	7.83104i	−0.202852	−	0.666622i
$139$	−9.84740	+	17.0562i	−0.835246	+	1.44669i	0.0585844	+	0.998282i	$0.481341\pi$
$139$	−9.84740	+	17.0562i	−0.835246	+	1.44669i	−0.893830	+	0.448406i	$0.851992\pi$
$140$	0.353568			0.0298820
$141$	−14.5659	+	15.5790i	−1.22667	+	1.31199i
$142$	2.27970	−	3.94856i	0.191309	−	0.331356i
$143$	11.2432	−	8.50256i	0.940205	−	0.711020i
$144$	−0.932732	−	13.8606i	−0.0777277	−	1.15505i
$145$	6.32955	+	3.65437i	0.525640	+	0.303479i
$146$	−2.30542	−	3.99311i	−0.190798	−	0.330472i
$147$	0.391838	−	1.68715i	0.0323182	−	0.139153i
$148$	−1.84879	+	1.06740i	−0.151970	+	0.0877399i
$149$	10.9699	+	6.33350i	0.898693	+	0.518861i	0.876776	−	0.480899i	$-0.159690\pi$
$149$	10.9699	+	6.33350i	0.898693	+	0.518861i	0.0219169	+	0.999760i	$0.493023\pi$
$150$	10.9275	+	2.53791i	0.892229	+	0.207219i
$151$	14.0282	+	8.09918i	1.14160	+	0.659102i	0.946826	−	0.321747i	$-0.104270\pi$
$151$	14.0282	+	8.09918i	1.14160	+	0.659102i	0.194772	+	0.980849i	$0.437603\pi$
$152$	0.899995	+	1.55884i	0.0729992	+	0.126438i
$153$	−0.943256	−	14.0170i	−0.0762577	−	1.13321i
$154$	−5.23681	−	3.02347i	−0.421994	−	0.243638i
$155$	−0.378219	+	0.655095i	−0.0303793	+	0.0526185i
$156$	1.98245	+	1.43912i	0.158723	+	0.115222i
$157$	5.71260	+	9.89451i	0.455915	+	0.789668i	0.998740	−	0.0501778i	$-0.0159788\pi$
$157$	5.71260	+	9.89451i	0.455915	+	0.789668i	−0.542825	+	0.839846i	$0.682645\pi$
$158$		−	18.2938i		−	1.45537i
$159$	−0.686750	+	2.95696i	−0.0544629	+	0.234502i
$160$	−1.97293			−0.155974
$161$			3.05551i			0.240808i
$162$	−12.8791	−	5.28221i	−1.01188	−	0.415009i
$163$	15.8741	−	9.16490i	1.24335	−	0.717850i	0.273578	−	0.961850i	$-0.411793\pi$
$163$	15.8741	−	9.16490i	1.24335	−	0.717850i	0.969775	+	0.244000i	$0.0784596\pi$
$164$	−4.23749	−	2.44652i	−0.330893	−	0.191041i
$165$	4.45837	+	4.16843i	0.347083	+	0.324512i
$166$	25.4622			1.97625
$167$		−	19.2144i		−	1.48686i	−0.668815	−	0.743428i	$-0.733198\pi$
$167$		−	19.2144i		−	1.48686i	0.668815	−	0.743428i	$-0.266802\pi$
$168$	−0.974372	+	4.19538i	−0.0751744	+	0.323680i
$169$	12.6030	−	3.18812i	0.969462	−	0.245240i
$170$	−6.52844			−0.500708
$171$	2.16667	−	0.145803i	0.165689	−	0.0111498i
$172$	0.223861	−	0.387738i	0.0170692	−	0.0295647i
$173$	−4.95992			−0.377096			−0.188548	−	0.982064i	$-0.560378\pi$
$173$	−4.95992			−0.377096			−0.188548	+	0.982064i	$0.560378\pi$
$174$	14.8359	−	15.8678i	1.12470	−	1.20293i
$175$	−3.62656	−	2.09379i	−0.274142	−	0.158276i
$176$	15.6785	+	9.05200i	1.18181	+	0.682320i
$177$	4.05461	−	4.33663i	0.304763	−	0.325961i
$178$	−15.7448			−1.18012
$179$	−5.53364	+	9.58454i	−0.413604	+	0.716382i	−0.995281	−	0.0970374i	$-0.969063\pi$
$179$	−5.53364	+	9.58454i	−0.413604	+	0.716382i	0.581677	+	0.813420i	$0.302397\pi$
$180$	−0.467480	+	0.952134i	−0.0348439	+	0.0709679i
$181$	5.71476			0.424775			0.212387	−	0.977186i	$-0.431876\pi$
$181$	5.71476			0.424775			0.212387	+	0.977186i	$0.431876\pi$
$182$	−3.36375	−	4.44800i	−0.249338	−	0.329708i
$183$	1.28622	−	5.53810i	0.0950799	−	0.409388i
$184$		−	7.59804i		−	0.560135i
$185$	−4.90524			−0.360641
$186$	1.64228	+	1.53548i	0.120418	+	0.112587i
$187$	15.8554	+	9.15413i	1.15946	+	0.669416i
$188$	4.18310	−	2.41512i	0.305084	−	0.176140i
$189$	4.02528	+	3.28589i	0.292796	+	0.239014i
$190$		−	1.00913i		−	0.0732097i
$191$	−20.1065			−1.45486			−0.727429	−	0.686183i	$-0.759285\pi$
$191$	−20.1065			−1.45486			−0.727429	+	0.686183i	$0.759285\pi$
$192$	2.30235	−	9.91329i	0.166158	−	0.715430i
$193$		−	7.40979i		−	0.533368i	−0.963784	−	0.266684i	$-0.914072\pi$
$193$		−	7.40979i		−	0.533368i	0.963784	−	0.266684i	$-0.0859280\pi$
$194$	−9.12282	−	15.8012i	−0.654980	−	1.13446i
$195$	2.29152	+	5.14130i	0.164099	+	0.368176i
$196$	−0.196135	+	0.339716i	−0.0140097	+	0.0242654i
$197$	5.57113	+	3.21650i	0.396927	+	0.229166i	0.685157	−	0.728395i	$-0.259734\pi$
$197$	5.57113	+	3.21650i	0.396927	+	0.229166i	−0.288230	+	0.957561i	$0.593067\pi$
$198$	15.0660	−	10.1048i	1.07069	−	0.718115i
$199$	−5.54448	−	9.60332i	−0.393038	−	0.680761i	0.599811	−	0.800142i	$-0.295243\pi$
$199$	−5.54448	−	9.60332i	−0.393038	−	0.680761i	−0.992849	+	0.119380i	$0.961909\pi$
$200$	9.01805	+	5.20657i	0.637673	+	0.368160i
$201$	−6.76336	−	1.57078i	−0.477050	−	0.110794i
$202$	−11.4336	−	6.60120i	−0.804466	−	0.464459i
$203$	−7.02239	+	4.05438i	−0.492875	+	0.284561i
$204$	−0.719793	+	3.09923i	−0.0503956	+	0.216990i
$205$	−5.62149	−	9.73670i	−0.392622	−	0.680041i
$206$	7.02299	+	4.05472i	0.489315	+	0.282506i
$207$	−8.22826	−	4.03992i	−0.571904	−	0.280794i
$208$	10.0708	+	13.3169i	0.698281	+	0.923360i
$209$	−1.41499	+	2.45083i	−0.0978768	+	0.169528i
$210$	1.64910	−	1.76380i	0.113799	−	0.121714i
$211$	−24.2296			−1.66803			−0.834017	−	0.551739i	$-0.813964\pi$
$211$	−24.2296			−1.66803			−0.834017	+	0.551739i	$0.813964\pi$
$212$	0.343754	−	0.595400i	0.0236091	−	0.0408922i
$213$	−1.48639	−	4.88466i	−0.101846	−	0.334691i
$214$			17.2673i			1.18037i
$215$	0.890925	−	0.514376i	0.0607606	−	0.0350801i
$216$	−10.0095	−	8.17094i	−0.681063	−	0.555962i
$217$	−0.419619	−	0.726802i	−0.0284856	−	0.0493385i
$218$	−1.76701	−	3.06055i	−0.119677	−	0.207287i
$219$	−5.02954	−	1.16811i	−0.339865	−	0.0789333i
$220$	−0.691154	−	1.19711i	−0.0465976	−	0.0807093i
$221$	10.1844	+	13.4671i	0.685076	+	0.905898i
$222$	−3.29825	+	14.2014i	−0.221364	+	0.953134i
$223$	−6.77867	+	3.91367i	−0.453933	+	0.262079i	−0.709490	−	0.704716i	$-0.751075\pi$
$223$	−6.77867	+	3.91367i	−0.453933	+	0.262079i	0.255557	+	0.966794i	$0.417741\pi$
$224$	1.09445	−	1.89564i	0.0731258	−	0.126658i
$225$	10.4334	−	6.99769i	0.695559	−	0.466513i
$226$		−	8.60239i		−	0.572223i
$227$		−	12.5154i		−	0.830677i	−0.909667	−	0.415338i	$-0.863663\pi$
$227$		−	12.5154i		−	0.830677i	0.909667	−	0.415338i	$-0.136337\pi$
$228$	−0.479060	−	0.111261i	−0.0317265	−	0.00736845i
$229$	6.38173	−	3.68449i	0.421717	−	0.243478i	−0.274095	−	0.961703i	$-0.588378\pi$
$229$	6.38173	−	3.68449i	0.421717	−	0.243478i	0.695811	+	0.718224i	$0.255045\pi$
$230$	−2.12984	+	3.68899i	−0.140437	+	0.243245i
$231$	−6.47831	+	1.97134i	−0.426241	+	0.129705i
$232$	17.4624	−	10.0819i	1.14646	−	0.661909i
$233$	23.5417			1.54227			0.771133	−	0.636674i	$-0.219690\pi$
$233$	23.5417			1.54227			0.771133	+	0.636674i	$0.219690\pi$
$234$	16.4256	−	3.17730i	1.07378	−	0.207706i
$235$	11.0987			0.723997
$236$	−1.16443	+	0.672282i	−0.0757977	+	0.0437618i
$237$	−14.9643	−	13.9911i	−0.972033	−	0.908819i
$238$	3.62152	−	6.27266i	0.234748	−	0.406596i
$239$	8.88627	−	5.13049i	0.574805	−	0.331864i	−0.184261	−	0.982877i	$-0.558989\pi$
$239$	8.88627	−	5.13049i	0.574805	−	0.331864i	0.759066	+	0.651013i	$0.225656\pi$
$240$	−4.93725	+	5.28066i	−0.318698	+	0.340865i
$241$			22.8192i			1.46991i	0.678114	+	0.734957i	$0.262798\pi$
$241$			22.8192i			1.46991i	−0.678114	+	0.734957i	$0.737202\pi$
$242$			6.62741i			0.426026i
$243$	−14.1708	+	6.49526i	−0.909057	+	0.416671i
$244$	−0.643818	+	1.11513i	−0.0412162	+	0.0713886i
$245$	−0.780582	+	0.450669i	−0.0498696	+	0.0287922i
$246$	−31.9690	+	9.72811i	−2.03827	+	0.620241i
$247$	−2.08167	+	1.57424i	−0.132453	+	0.100166i
$248$	1.04345	+	1.80732i	0.0662594	+	0.114765i
$249$	19.4735	−	20.8280i	1.23408	−	1.31992i
$250$	−6.40420	−	11.0924i	−0.405037	−	0.701545i
$251$	−9.55247	−	16.5454i	−0.602946	−	1.04433i	−0.992372	−	0.123276i	$-0.960660\pi$
$251$	−9.55247	−	16.5454i	−0.602946	−	1.04433i	0.389426	−	0.921058i	$-0.372673\pi$
$252$	−0.655505	−	0.977342i	−0.0412929	−	0.0615667i
$253$	10.3454	−	5.97289i	0.650407	−	0.375512i
$254$			29.5887i			1.85656i
$255$	−4.99295	+	5.34024i	−0.312671	+	0.334419i
$256$	−4.53800	+	7.86005i	−0.283625	+	0.491253i
$257$	23.8964			1.49062			0.745309	−	0.666719i	$-0.232302\pi$
$257$	23.8964			1.49062			0.745309	+	0.666719i	$0.232302\pi$
$258$	−0.890138	−	2.92522i	−0.0554176	−	0.182116i
$259$	2.72109	−	4.71306i	0.169080	−	0.292855i
$260$	−0.157524	−	1.26504i	−0.00976924	−	0.0784544i
$261$	−1.63331	−	24.2714i	−0.101099	−	1.50236i
$262$	12.0366	+	6.94933i	0.743623	+	0.429331i
$263$	2.61347	+	4.52667i	0.161154	+	0.279126i	0.935283	−	0.353902i	$-0.115145\pi$
$263$	2.61347	+	4.52667i	0.161154	+	0.279126i	−0.774129	+	0.633028i	$0.781812\pi$
$264$	16.1094	−	4.90207i	0.991466	−	0.301701i
$265$	1.36808	−	0.789861i	0.0840405	−	0.0485208i
$266$	0.969589	+	0.559792i	0.0594493	+	0.0343231i
$267$	−12.0416	+	12.8792i	−0.736936	+	0.788193i
$268$	1.36184	+	0.786258i	0.0831875	+	0.0480283i
$269$	−6.14239	−	10.6389i	−0.374508	−	0.648667i	0.615745	−	0.787945i	$-0.288855\pi$
$269$	−6.14239	−	10.6389i	−0.374508	−	0.648667i	−0.990253	+	0.139278i	$0.955522\pi$
$270$	2.56939	+	6.77296i	0.156368	+	0.412189i
$271$	−6.35740	−	3.67045i	−0.386185	−	0.222964i	0.294321	−	0.955707i	$-0.404907\pi$
$271$	−6.35740	−	3.67045i	−0.386185	−	0.222964i	−0.680506	+	0.732743i	$0.738240\pi$
$272$	−10.8425	+	18.7798i	−0.657423	+	1.13869i
$273$	−6.21105	−	0.650295i	−0.375910	−	0.0393577i
$274$	−7.87663	−	13.6427i	−0.475845	−	0.824187i
$275$			16.3717i			0.987253i
$276$	1.51644	+	1.41782i	0.0912790	+	0.0853430i
$277$	6.63356			0.398572			0.199286	−	0.979941i	$-0.436138\pi$
$277$	6.63356			0.398572			0.199286	+	0.979941i	$0.436138\pi$
$278$		−	30.4619i		−	1.82698i
$279$	2.51203	−	0.169044i	0.150391	−	0.0101204i
$280$	1.94105	−	1.12067i	0.116000	−	0.0669726i
$281$	−6.63471	−	3.83055i	−0.395794	−	0.228512i	0.288874	−	0.957367i	$-0.406719\pi$
$281$	−6.63471	−	3.83055i	−0.395794	−	0.228512i	−0.684667	+	0.728856i	$0.740053\pi$
$282$	7.46267	−	32.1322i	0.444395	−	1.91344i
$283$	12.7100			0.755531			0.377766	−	0.925901i	$-0.376693\pi$
$283$	12.7100			0.755531			0.377766	+	0.925901i	$0.376693\pi$
$284$			1.15635i			0.0686167i
$285$	−0.825461	−	0.771780i	−0.0488961	−	0.0457163i
$286$	−8.48460	+	20.0839i	−0.501705	+	1.18759i
$287$	12.4736			0.736296
$288$	3.65776	+	5.45363i	0.215536	+	0.321358i
$289$	−2.46483	+	4.26921i	−0.144990	+	0.251130i
$290$	−11.3044			−0.663817
$291$	−19.9025	−	4.62232i	−1.16670	−	0.270965i
$292$	1.01273	+	0.584697i	0.0592653	+	0.0342168i
$293$	−13.4987	−	7.79345i	−0.788600	−	0.455298i	0.0508694	−	0.998705i	$-0.483801\pi$
$293$	−13.4987	−	7.79345i	−0.788600	−	0.455298i	−0.839469	+	0.543407i	$0.817134\pi$
$294$	0.779893	+	2.56292i	0.0454843	+	0.149473i
$295$	−3.08947			−0.179876
$296$	−6.76645	+	11.7198i	−0.393292	+	0.681201i
$297$	3.25679	−	20.0521i	0.188978	−	1.16354i
$298$	−19.5920			−1.13493
$299$	10.9324	−	1.36131i	0.632235	−	0.0787267i
$300$	−2.72195	+	0.828284i	−0.157152	+	0.0478210i
$301$			1.14136i			0.0657868i
$302$	−25.0539			−1.44169
$303$	−14.1442	+	4.30406i	−0.812563	+	0.247262i
$304$	−2.90286	−	1.67597i	−0.166490	−	0.0961232i
$305$	−2.56228	+	1.47933i	−0.146716	+	0.0847064i
$306$	12.1035	+	18.0460i	0.691912	+	1.03162i
$307$		−	8.96295i		−	0.511542i	−0.966737	−	0.255771i	$-0.917671\pi$
$307$		−	8.96295i		−	0.511542i	0.966737	−	0.255771i	$-0.0823294\pi$
$308$	1.53362			0.0873858
$309$	8.68793	−	2.64372i	0.494239	−	0.150396i
$310$		−	1.16998i		−	0.0664504i
$311$	0.534171	+	0.925211i	0.0302900	+	0.0524639i	0.880773	−	0.473539i	$-0.157024\pi$
$311$	0.534171	+	0.925211i	0.0302900	+	0.0524639i	−0.850483	+	0.526003i	$0.823690\pi$
$312$	15.4448	+	1.61707i	0.874391	+	0.0915485i
$313$	14.1403	−	24.4918i	0.799259	−	1.38436i	−0.120839	−	0.992672i	$-0.538559\pi$
$313$	14.1403	−	24.4918i	0.799259	−	1.38436i	0.920099	−	0.391686i	$-0.128108\pi$
$314$	−15.3038	−	8.83566i	−0.863644	−	0.498625i
$315$	−0.181552	−	2.69792i	−0.0102293	−	0.152010i
$316$	2.31982	+	4.01804i	0.130500	+	0.226032i
$317$	−4.82320	−	2.78468i	−0.270898	−	0.156403i	0.358398	−	0.933569i	$-0.383323\pi$
$317$	−4.82320	−	2.78468i	−0.270898	−	0.156403i	−0.629296	+	0.777166i	$0.716657\pi$
$318$	−1.36687	−	4.49188i	−0.0766504	−	0.251892i
$319$	27.4546	+	15.8509i	1.53716	+	0.887482i
$320$	−4.58653	+	2.64803i	−0.256395	+	0.148030i
$321$	14.1246	+	13.2060i	0.788356	+	0.737088i
$322$	−2.36297	−	4.09279i	−0.131683	−	0.228082i
$323$	−2.93561	−	1.69488i	−0.163342	−	0.0943054i
$324$	3.49860	−	0.473009i	0.194367	−	0.0262783i
$325$	−5.87570	+	13.9084i	−0.325925	+	0.771498i
$326$	−14.1753	+	24.5524i	−0.785098	+	1.35983i
$327$	−3.85494	−	0.895305i	−0.213178	−	0.0495105i
$328$	−31.0178			−1.71267
$329$	−6.15676	+	10.6638i	−0.339433	+	0.587916i
$330$	−9.19554	−	2.13565i	−0.506198	−	0.117564i
$331$			9.82188i			0.539859i	0.962880	+	0.269930i	$0.0870004\pi$
$331$			9.82188i			0.539859i	−0.962880	+	0.269930i	$0.913000\pi$
$332$	−5.59250	+	3.22883i	−0.306928	+	0.177205i
$333$	9.09417	+	13.5592i	0.498357	+	0.743039i
$334$	14.8594	+	25.7373i	0.813073	+	1.40828i
$335$	1.80662	+	3.12916i	0.0987064	+	0.170964i
$336$	−2.33493	−	7.67315i	−0.127381	−	0.418605i
$337$	−3.01616	−	5.22414i	−0.164301	−	0.284577i	0.772106	−	0.635494i	$-0.219203\pi$
$337$	−3.01616	−	5.22414i	−0.164301	−	0.284577i	−0.936407	+	0.350917i	$0.885870\pi$
$338$	−14.4159	+	14.0169i	−0.784124	+	0.762421i
$339$	−7.03673	−	6.57912i	−0.382183	−	0.357329i
$340$	1.43390	−	0.827865i	0.0777644	−	0.0448973i
$341$	−1.64054	+	2.84149i	−0.0888401	+	0.153876i
$342$	−2.78945	+	1.87089i	−0.150836	+	0.101166i
$343$		−	1.00000i		−	0.0539949i
$344$		−	2.83818i		−	0.153025i
$345$	1.38868	+	4.56354i	0.0747640	+	0.245693i
$346$	6.64370	−	3.83574i	0.357168	−	0.206211i
$347$	−9.77882	+	16.9374i	−0.524955	+	0.909248i	0.474623	+	0.880189i	$0.342584\pi$
$347$	−9.77882	+	16.9374i	−0.524955	+	0.909248i	−0.999578	+	0.0290590i	$0.990749\pi$
$348$	−1.24637	+	5.36651i	−0.0668123	+	0.287675i
$349$	−6.43373	+	3.71452i	−0.344390	+	0.198834i	−0.662212	−	0.749317i	$-0.730382\pi$
$349$	−6.43373	+	3.71452i	−0.344390	+	0.198834i	0.317822	+	0.948151i	$0.397049\pi$
$350$	6.47693			0.346206
$351$	9.96329	−	15.8661i	0.531801	−	0.846869i
$352$	−8.55767			−0.456125
$353$	−14.4250	+	8.32828i	−0.767765	+	0.443269i	−0.832077	−	0.554660i	$-0.812848\pi$
$353$	−14.4250	+	8.32828i	−0.767765	+	0.443269i	0.0643117	+	0.997930i	$0.479515\pi$
$354$	−2.07734	+	8.94446i	−0.110409	+	0.475393i
$355$	−1.32850	+	2.30103i	−0.0705095	+	0.122126i
$356$	3.45818	−	1.99658i	0.183283	−	0.105819i
$357$	−2.36127	−	7.75973i	−0.124972	−	0.410688i
$358$		−	17.1177i		−	0.904699i
$359$			31.0665i			1.63962i	0.572632	+	0.819812i	$0.305922\pi$
$359$			31.0665i			1.63962i	−0.572632	+	0.819812i	$0.694078\pi$
$360$	0.451461	+	6.70883i	0.0237941	+	0.353586i
$361$	−9.23802	+	16.0007i	−0.486211	+	0.842143i
$362$	−7.65479	+	4.41950i	−0.402327	+	0.232284i
$363$	5.42120	+	5.06865i	0.284539	+	0.266035i
$364$	1.30286	+	0.550403i	0.0682884	+	0.0288490i
$365$	1.34349	+	2.32699i	0.0703214	+	0.121800i
$366$	2.56002	+	8.41286i	0.133814	+	0.439747i
$367$	−9.72750	−	16.8485i	−0.507771	−	0.879486i	−0.999960	−	0.00899700i	$-0.997136\pi$
$367$	−9.72750	−	16.8485i	−0.507771	−	0.879486i	0.492188	−	0.870489i	$-0.336197\pi$
$368$	7.07452	+	12.2534i	0.368785	+	0.638754i
$369$	−16.4923	+	33.5906i	−0.858557	+	1.74866i
$370$	6.57047	−	3.79346i	0.341582	−	0.197213i
$371$			1.75264i			0.0909925i
$372$	−0.555422	−	0.128996i	−0.0287973	−	0.00668814i
$373$	6.39048	−	11.0686i	0.330887	−	0.573113i	−0.651799	−	0.758392i	$-0.725986\pi$
$373$	6.39048	−	11.0686i	0.330887	−	0.573113i	0.982686	+	0.185279i	$0.0593189\pi$
$374$	−28.3173			−1.46425
$375$	−13.9715	−	3.24486i	−0.721484	−	0.167564i
$376$	15.3098	−	26.5174i	0.789545	−	1.36753i
$377$	17.6349	+	23.3192i	0.908243	+	1.20100i
$378$	−7.93292	−	1.28844i	−0.408025	−	0.0662702i
$379$	28.0927	+	16.2193i	1.44302	+	0.833131i	0.998050	−	0.0624129i	$-0.0198796\pi$
$379$	28.0927	+	16.2193i	1.44302	+	0.833131i	0.444974	+	0.895543i	$0.353213\pi$
$380$	0.127966	+	0.221644i	0.00656453	+	0.0113701i
$381$	24.2034	+	22.6294i	1.23998	+	1.15934i
$382$	26.9323	−	15.5493i	1.37797	−	0.795574i
$383$	−10.5652	−	6.09982i	−0.539857	−	0.311686i	0.205164	−	0.978728i	$-0.434227\pi$
$383$	−10.5652	−	6.09982i	−0.539857	−	0.311686i	−0.745021	+	0.667041i	$0.767560\pi$
$384$	6.78990	+	22.3133i	0.346495	+	1.13867i
$385$	3.05176	+	1.76193i	0.155532	+	0.0897964i
$386$	5.73035	+	9.92525i	0.291667	+	0.505182i
$387$	−3.07359	−	1.50908i	−0.156240	−	0.0767107i
$388$	4.00747	+	2.31371i	0.203448	+	0.117461i
$389$	12.9094	−	22.3597i	0.654532	−	1.13368i	−0.327479	−	0.944858i	$-0.606199\pi$
$389$	12.9094	−	22.3597i	0.654532	−	1.13368i	0.982011	−	0.188824i	$-0.0604676\pi$
$390$	−7.04546	−	5.11452i	−0.356761	−	0.258984i
$391$	7.15434	+	12.3917i	0.361810	+	0.626674i
$392$			2.48667i			0.125596i
$393$	14.8901	−	4.53104i	0.751107	−	0.228561i
$394$	−9.94988			−0.501268
$395$			10.6607i			0.536399i
$396$	−2.02771	+	4.12991i	−0.101896	+	0.207536i
$397$	−30.4600	+	17.5861i	−1.52874	+	0.882620i	−0.529328	+	0.848417i	$0.677556\pi$
$397$	−30.4600	+	17.5861i	−1.52874	+	0.882620i	−0.999415	+	0.0342024i	$0.989111\pi$
$398$	14.8534	+	8.57563i	0.744535	+	0.429857i
$399$	1.19945	−	0.364991i	0.0600476	−	0.0182724i
$400$	−19.3913			−0.969566
$401$		−	28.2071i		−	1.40859i	−0.709906	−	0.704297i	$-0.751263\pi$
$401$		−	28.2071i		−	1.40859i	0.709906	−	0.704297i	$-0.248737\pi$
$402$	10.2741	−	3.12640i	0.512427	−	0.155931i
$403$	−2.41349	+	1.82517i	−0.120224	+	0.0909183i
$404$	3.34837			0.166588
$405$	7.50533	+	3.07821i	0.372943	+	0.152958i
$406$	6.27089	−	10.8615i	0.311219	−	0.539047i
$407$	−21.2767			−1.05464
$408$	5.87170	+	19.2959i	0.290693	+	0.955288i
$409$	5.13981	+	2.96747i	0.254147	+	0.146732i	0.621662	−	0.783286i	$-0.286458\pi$
$409$	5.13981	+	2.96747i	0.254147	+	0.146732i	−0.367514	+	0.930018i	$0.619791\pi$
$410$	15.0597	+	8.69474i	0.743747	+	0.429402i
$411$	−17.1838	−	3.99091i	−0.847613	−	0.196857i
$412$	−2.05670			−0.101326
$413$	1.71382	−	2.96843i	0.0843317	−	0.146067i
$414$	14.1458	−	0.951924i	0.695230	−	0.0467845i
$415$	−14.8381			−0.728374
$416$	−7.27004	−	3.07128i	−0.356443	−	0.150582i
$417$	−24.9177	−	23.2973i	−1.22023	−	1.14087i
$418$		−	4.37712i		−	0.214092i
$419$	−31.4302			−1.53547			−0.767733	−	0.640770i	$-0.778615\pi$
$419$	−31.4302			−1.53547			−0.767733	+	0.640770i	$0.778615\pi$
$420$	−0.138542	+	0.596522i	−0.00676013	+	0.0291073i
$421$	8.67844	+	5.01050i	0.422961	+	0.244197i	0.696343	−	0.717709i	$-0.254809\pi$
$421$	8.67844	+	5.01050i	0.422961	+	0.244197i	−0.273382	+	0.961905i	$0.588142\pi$
$422$	32.4550	−	18.7379i	1.57989	−	0.912147i
$423$	−20.5766	−	30.6792i	−1.00047	−	1.49167i
$424$		−	4.35824i		−	0.211655i
$425$	−19.6101			−0.951230
$426$	5.76853	+	5.39339i	0.279486	+	0.261311i
$427$		−	3.28252i		−	0.158852i
$428$	−2.18965	−	3.79258i	−0.105841	−	0.183321i
$429$	9.93955	+	22.3006i	0.479886	+	1.07668i
$430$	−0.795583	+	1.37799i	−0.0383664	+	0.0664526i
$431$	−19.7735	−	11.4163i	−0.952458	−	0.549902i	−0.0586143	−	0.998281i	$-0.518668\pi$
$431$	−19.7735	−	11.4163i	−0.952458	−	0.549902i	−0.893844	+	0.448379i	$0.852002\pi$
$432$	23.7504	+	3.85747i	1.14269	+	0.185593i
$433$	−1.48063	−	2.56452i	−0.0711543	−	0.123243i	0.828253	−	0.560354i	$-0.189335\pi$
$433$	−1.48063	−	2.56452i	−0.0711543	−	0.123243i	−0.899407	+	0.437111i	$0.856002\pi$
$434$	1.12414	+	0.649023i	0.0539605	+	0.0311541i
$435$	−8.64561	+	9.24696i	−0.414525	+	0.443358i
$436$	0.776212	+	0.448146i	0.0371738	+	0.0214623i
$437$	−1.91543	+	1.10587i	−0.0916274	+	0.0529011i
$438$	7.64032	−	2.32494i	0.365068	−	0.111090i
$439$	−0.0298273	−	0.0516624i	−0.00142358	−	0.00246571i	0.865313	−	0.501232i	$-0.167120\pi$
$439$	−0.0298273	−	0.0516624i	−0.00142358	−	0.00246571i	−0.866736	+	0.498767i	$0.833786\pi$
$440$	−7.58871	−	4.38134i	−0.361778	−	0.208872i
$441$	2.69293	+	1.32218i	0.128235	+	0.0629608i
$442$	−24.0566	−	10.1629i	−1.14425	−	0.483399i
$443$	12.1377	−	21.0231i	0.576680	−	0.998840i	−0.419176	−	0.907905i	$-0.637681\pi$
$443$	12.1377	−	21.0231i	0.576680	−	0.998840i	0.995857	−	0.0909349i	$-0.0289855\pi$
$444$	−1.07644	−	3.53743i	−0.0510854	−	0.167879i
$445$	9.17529			0.434951
$446$	6.05326	−	10.4845i	0.286630	−	0.496458i
$447$	−14.9840	+	16.0262i	−0.708718	+	0.758013i
$448$		−	5.87578i		−	0.277604i
$449$	24.8698	−	14.3586i	1.17368	−	0.677622i	0.219133	−	0.975695i	$-0.429677\pi$
$449$	24.8698	−	14.3586i	1.17368	−	0.677622i	0.954543	+	0.298072i	$0.0963437\pi$
$450$	−8.56364	+	17.4419i	−0.403694	+	0.822219i
$451$	−24.3834	−	42.2333i	−1.14817	−	1.98869i
$452$	1.09086	+	1.88943i	0.0513098	+	0.0888712i
$453$	−19.1613	+	20.4940i	−0.900275	+	0.962894i
$454$	9.67877	+	16.7641i	0.454247	+	0.786779i
$455$	1.96023	+	2.59208i	0.0918970	+	0.121518i
$456$	−2.98264	+	0.907612i	−0.139675	+	0.0425028i
$457$	16.8012	−	9.70016i	0.785925	−	0.453754i	−0.0526007	−	0.998616i	$-0.516751\pi$
$457$	16.8012	−	9.70016i	0.785925	−	0.453754i	0.838526	+	0.544861i	$0.183418\pi$
$458$	−5.69879	+	9.87060i	−0.266287	+	0.461223i
$459$	24.0184	+	3.90099i	1.12108	+	0.182083i
$460$		−	1.08033i		−	0.0503707i
$461$			4.26850i			0.198804i	0.995047	+	0.0994020i	$0.0316930\pi$
$461$			4.26850i			0.198804i	−0.995047	+	0.0994020i	$0.968307\pi$
$462$	7.15302	−	7.65055i	0.332789	−	0.355936i
$463$	24.0866	−	13.9064i	1.11940	−	0.646285i	0.178152	−	0.984003i	$-0.442988\pi$
$463$	24.0866	−	13.9064i	1.11940	−	0.646285i	0.941247	+	0.337718i	$0.109655\pi$
$464$	−18.7745	+	32.5183i	−0.871582	+	1.50962i
$465$	−0.957040	−	0.894802i	−0.0443817	−	0.0414954i
$466$	−31.5336	+	18.2059i	−1.46076	+	0.843373i
$467$	−11.2374			−0.520005			−0.260002	−	0.965608i	$-0.583723\pi$
$467$	−11.2374			−0.520005			−0.260002	+	0.965608i	$0.583723\pi$
$468$	−3.20480	+	2.78078i	−0.148142	+	0.128541i
$469$	−4.00875			−0.185107
$470$	−14.8664	+	8.58313i	−0.685737	+	0.395910i
$471$	−18.9319	+	5.76094i	−0.872336	+	0.265450i
$472$	−4.26171	+	7.38150i	−0.196161	+	0.339761i
$473$	3.86442	−	2.23112i	0.177686	−	0.102587i
$474$	30.8643	+	7.16820i	1.41764	+	0.329246i
$475$		−	3.03121i		−	0.139081i
$476$			1.83697i			0.0841972i
$477$	−4.71973	−	2.31730i	−0.216101	−	0.106102i
$478$	−7.93531	+	13.7444i	−0.362953	+	0.628653i
$479$	1.06591	−	0.615406i	0.0487029	−	0.0281186i	−0.475451	−	0.879742i	$-0.657715\pi$
$479$	1.06591	−	0.615406i	0.0487029	−	0.0281186i	0.524154	+	0.851624i	$0.324382\pi$
$480$	0.773071	−	3.32863i	0.0352857	−	0.151930i
$481$	−18.0753	−	7.63603i	−0.824161	−	0.348173i
$482$	−17.6472	−	30.5658i	−0.803808	−	1.39224i
$483$	−5.15509	−	1.19726i	−0.234565	−	0.0544774i
$484$	−0.840415	−	1.45564i	−0.0382007	−	0.0661656i
$485$	5.31633	+	9.20816i	0.241402	+	0.418121i
$486$	13.9584	−	19.6592i	0.633165	−	0.891760i
$487$	−23.1059	+	13.3402i	−1.04703	+	0.604502i	−0.921816	−	0.387628i	$-0.873295\pi$
$487$	−23.1059	+	13.3402i	−1.04703	+	0.604502i	−0.125212	+	0.992130i	$0.539961\pi$
$488$			8.16256i			0.369502i
$489$	9.24246	+	30.3730i	0.417959	+	1.37352i
$490$	0.697049	−	1.20732i	0.0314895	−	0.0545413i
$491$	43.8656			1.97963			0.989814	−	0.142369i	$-0.0454718\pi$
$491$	43.8656			1.97963			0.989814	+	0.142369i	$0.0454718\pi$
$492$	5.78805	−	6.19064i	0.260945	−	0.279095i
$493$	−18.9863	+	32.8852i	−0.855099	+	1.48108i
$494$	1.57091	−	3.71851i	0.0706788	−	0.167304i
$495$	−8.77971	+	5.88857i	−0.394619	+	0.264671i
$496$	−3.36557	−	1.94312i	−0.151119	−	0.0872484i
$497$	−1.47392	−	2.55290i	−0.0661143	−	0.114513i
$498$	−9.97704	+	42.9584i	−0.447082	+	1.92501i
$499$	2.83925	−	1.63924i	0.127102	−	0.0733824i	−0.435101	−	0.900382i	$-0.643287\pi$
$499$	2.83925	−	1.63924i	0.127102	−	0.0733824i	0.562203	+	0.826999i	$0.309954\pi$
$500$	2.81323	+	1.62422i	0.125812	+	0.0726374i
$501$	32.4176	+	7.52894i	1.44831	+	0.336368i
$502$	25.5906	+	14.7748i	1.14217	+	0.659430i
$503$	−8.80240	−	15.2462i	−0.392480	−	0.679795i	0.600296	−	0.799778i	$-0.295049\pi$
$503$	−8.80240	−	15.2462i	−0.392480	−	0.679795i	−0.992776	+	0.119983i	$0.961716\pi$
$504$	−6.69642	−	3.28782i	−0.298282	−	0.146451i
$505$	6.66295	+	3.84686i	0.296497	+	0.171183i
$506$	−9.23825	+	16.0011i	−0.410690	+	0.711336i
$507$	0.440486	+	22.5124i	0.0195627	+	0.999809i
$508$	−3.75211	−	6.49885i	−0.166473	−	0.288340i
$509$		−	23.9442i		−	1.06131i	−0.847589	−	0.530654i	$-0.821946\pi$
$509$		−	23.9442i		−	1.06131i	0.847589	−	0.530654i	$-0.178054\pi$
$510$	2.55809	−	11.0144i	0.113274	−	0.487727i
$511$	−2.98109			−0.131876
$512$			12.8938i			0.569833i
$513$	−0.602991	+	3.71261i	−0.0266227	+	0.163916i
$514$	−32.0088	+	18.4803i	−1.41185	+	0.815130i
$515$	−4.09265	−	2.36289i	−0.180344	−	0.104122i
$516$	0.566453	+	0.529616i	0.0249367	+	0.0233150i
$517$	48.1408			2.11723
$518$			8.41739i			0.369839i
$519$	1.94348	−	8.36811i	0.0853095	−	0.367319i
$520$	−4.87444	−	6.44564i	−0.213759	−	0.282660i
$521$	−39.7508			−1.74151			−0.870757	−	0.491714i	$-0.836371\pi$
$521$	−39.7508			−1.74151			−0.870757	+	0.491714i	$0.836371\pi$
$522$	20.9580	+	31.2479i	0.917307	+	1.36768i
$523$	7.12633	−	12.3432i	0.311613	−	0.539729i	−0.667099	−	0.744969i	$-0.732464\pi$
$523$	7.12633	−	12.3432i	0.311613	−	0.539729i	0.978712	+	0.205240i	$0.0657976\pi$
$524$	−3.52495			−0.153988
$525$	4.95356	−	5.29811i	0.216191	−	0.231228i
$526$	−7.00138	−	4.04225i	−0.305275	−	0.176250i
$527$	−3.40355	−	1.96504i	−0.148261	−	0.0855984i
$528$	−21.4155	+	22.9050i	−0.931989	+	0.996814i
$529$	−13.6639			−0.594081
$530$	−1.22168	+	2.11600i	−0.0530662	+	0.0919133i
$531$	5.72778	+	8.53999i	0.248565	+	0.370604i
$532$	−0.283947			−0.0123107
$533$	−5.55734	−	44.6297i	−0.240715	−	1.93313i
$534$	6.16941	−	26.5638i	0.266976	−	1.14953i
$535$		−	10.0625i		−	0.435040i
$536$	9.96845			0.430571
$537$	−14.0022	−	13.0916i	−0.604241	−	0.564946i
$538$	16.4552	+	9.50041i	0.709434	+	0.409592i
$539$	−3.38580	+	1.95479i	−0.145837	+	0.0841989i
$540$	−1.42321	−	1.16179i	−0.0612453	−	0.0499954i
$541$		−	4.38752i		−	0.188634i	−0.995542	−	0.0943172i	$-0.969933\pi$
$541$		−	4.38752i		−	0.188634i	0.995542	−	0.0943172i	$-0.0300668\pi$
$542$	11.3541			0.487702
$543$	−2.23926	+	9.64163i	−0.0960958	+	0.413762i
$544$		−	10.2504i		−	0.439482i
$545$	1.02973	+	1.78354i	0.0441087	+	0.0763985i
$546$	8.82247	−	3.93225i	0.377567	−	0.168285i
$547$	9.19592	−	15.9278i	0.393189	−	0.681024i	−0.599679	−	0.800241i	$-0.704705\pi$
$547$	9.19592	−	15.9278i	0.393189	−	0.681024i	0.992868	+	0.119217i	$0.0380384\pi$
$548$	3.46004	+	1.99766i	0.147806	+	0.0853357i
$549$	8.83960	+	4.34007i	0.377265	+	0.185230i
$550$	−12.6611	−	21.9296i	−0.539869	−	0.935081i
$551$	−5.08319	−	2.93478i	−0.216551	−	0.125026i
$552$	12.8190	+	2.97720i	0.545613	+	0.126718i
$553$	−10.2430	−	5.91382i	−0.435578	−	0.251481i
$554$	−8.88551	+	5.13005i	−0.377509	+	0.217955i
$555$	1.92206	−	8.27586i	0.0815869	−	0.351291i
$556$	3.86284	+	6.69064i	0.163821	+	0.283746i
$557$	21.5329	+	12.4320i	0.912376	+	0.526761i	0.881195	−	0.472753i	$-0.156740\pi$
$557$	21.5329	+	12.4320i	0.912376	+	0.526761i	0.0311814	+	0.999514i	$0.490073\pi$
$558$	−3.23408	+	2.16911i	−0.136910	+	0.0918256i
$559$	4.08369	−	0.508506i	0.172722	−	0.0215075i
$560$	−2.08690	+	3.61462i	−0.0881876	+	0.152745i
$561$	−21.6571	+	23.1635i	−0.914364	+	0.977962i
$562$	11.8494			0.499837
$563$	16.8414	−	29.1701i	0.709780	−	1.22937i	−0.255159	−	0.966899i	$-0.582128\pi$
$563$	16.8414	−	29.1701i	0.709780	−	1.22937i	0.964939	−	0.262475i	$-0.0845388\pi$
$564$	2.43556	+	8.00384i	0.102555	+	0.337022i
$565$			5.01305i			0.210901i
$566$	−17.0248	+	9.82926i	−0.715605	+	0.413155i
$567$	−7.12104	+	5.50370i	−0.299056	+	0.231134i
$568$	3.66515	+	6.34822i	0.153786	+	0.266366i
$569$	1.97801	+	3.42601i	0.0829224	+	0.143626i	0.904504	−	0.426465i	$-0.140241\pi$
$569$	1.97801	+	3.42601i	0.0829224	+	0.143626i	−0.821582	+	0.570091i	$0.806908\pi$
$570$	1.70254	+	0.395414i	0.0713117	+	0.0165621i
$571$	1.03352	+	1.79011i	0.0432516	+	0.0749139i	0.886841	−	0.462075i	$-0.152895\pi$
$571$	1.03352	+	1.79011i	0.0432516	+	0.0749139i	−0.843589	+	0.536989i	$0.819562\pi$
$572$	−0.683267	−	5.48715i	−0.0285688	−	0.229429i
$573$	7.87850	−	33.9227i	0.329129	−	1.41714i
$574$	−16.7082	+	9.64647i	−0.697386	+	0.402636i
$575$	−6.39761	+	11.0810i	−0.266799	+	0.462109i
$576$	15.8230	+	7.76881i	0.659293	+	0.323700i
$577$		−	46.0133i		−	1.91556i	−0.287501	−	0.957780i	$-0.592825\pi$
$577$		−	46.0133i		−	1.91556i	0.287501	−	0.957780i	$-0.407175\pi$
$578$		−	7.62468i		−	0.317145i
$579$	12.5014	+	2.90344i	0.519540	+	0.120663i
$580$	2.48289	−	1.43350i	0.103097	−	0.0595228i
$581$	8.23114	−	14.2568i	0.341485	−	0.591470i
$582$	30.2336	−	9.20003i	1.25322	−	0.381353i
$583$	5.93409	−	3.42605i	0.245765	−	0.141892i
$584$	7.41300			0.306752
$585$	−9.57204	+	1.85157i	−0.395755	+	0.0765531i
$586$	24.1082			0.995901
$587$	−30.1487	+	17.4064i	−1.24437	+	0.718438i	−0.969981	−	0.243180i	$-0.921809\pi$
$587$	−30.1487	+	17.4064i	−1.24437	+	0.718438i	−0.274391	+	0.961618i	$0.588476\pi$
$588$	−0.496297	−	0.464022i	−0.0204670	−	0.0191360i
$589$	0.303744	−	0.526099i	0.0125155	−	0.0216775i
$590$	4.13828	−	2.38924i	0.170370	−	0.0983634i
$591$	−7.60968	+	8.13897i	−0.313020	+	0.334793i
$592$		−	25.2009i		−	1.03575i
$593$		−	12.6099i		−	0.517827i	−0.965901	−	0.258913i	$-0.916636\pi$
$593$		−	12.6099i		−	0.517827i	0.965901	−	0.258913i	$-0.0833644\pi$
$594$	11.1448	+	29.3779i	0.457277	+	1.20539i
$595$	−2.11045	+	3.65540i	−0.0865198	+	0.149857i
$596$	4.30318	−	2.48444i	0.176265	−	0.101767i
$597$	18.3747	−	5.59140i	0.752028	−	0.228841i
$598$	−13.5909	+	10.2780i	−0.555773	+	0.420298i
$599$	−10.6408	−	18.4305i	−0.434773	−	0.753049i	0.562504	−	0.826794i	$-0.309838\pi$
$599$	−10.6408	−	18.4305i	−0.434773	−	0.753049i	−0.997277	+	0.0737456i	$0.976505\pi$
$600$	−12.3179	+	13.1746i	−0.502875	+	0.537852i
$601$	10.3272	+	17.8873i	0.421256	+	0.729637i	0.996063	−	0.0886527i	$-0.0282561\pi$
$601$	10.3272	+	17.8873i	0.421256	+	0.729637i	−0.574807	+	0.818289i	$0.694923\pi$
$602$	−0.882668	−	1.52883i	−0.0359749	−	0.0623103i
$603$	5.30028	−	10.7953i	0.215844	−	0.439618i
$604$	5.50284	−	3.17707i	0.223907	−	0.129273i
$605$		−	3.86213i		−	0.157018i
$606$	15.6173	−	16.7036i	0.634410	−	0.678537i
$607$	−11.6463	+	20.1721i	−0.472711	+	0.818759i	−0.999512	−	0.0312295i	$-0.990058\pi$
$607$	−11.6463	+	20.1721i	−0.472711	+	0.818759i	0.526802	+	0.849988i	$0.323391\pi$
$608$	1.58444			0.0642576
$609$	−4.08869	−	13.4365i	−0.165682	−	0.544472i
$610$	2.28808	−	3.96307i	0.0926417	−	0.160460i
$611$	40.8973	+	17.2774i	1.65453	+	0.698968i
$612$	−4.94682	−	2.42879i	−0.199963	−	0.0981781i
$613$	−39.7637	−	22.9576i	−1.60604	−	0.927249i	−0.990244	−	0.139345i	$-0.955500\pi$
$613$	−39.7637	−	22.9576i	−1.60604	−	0.927249i	−0.615798	−	0.787904i	$-0.711166\pi$
$614$	6.93148	+	12.0057i	0.279732	+	0.484510i
$615$	18.6300	−	5.66906i	0.751232	−	0.228599i
$616$	8.41937	−	4.86093i	0.339226	−	0.195852i
$617$	6.81711	+	3.93586i	0.274446	+	0.158452i	0.630907	−	0.775859i	$-0.282683\pi$
$617$	6.81711	+	3.93586i	0.274446	+	0.158452i	−0.356460	+	0.934311i	$0.616016\pi$
$618$	−9.59278	+	10.2600i	−0.385878	+	0.412718i
$619$	−21.4514	−	12.3850i	−0.862205	−	0.497794i	0.00254506	−	0.999997i	$-0.499190\pi$
$619$	−21.4514	−	12.3850i	−0.862205	−	0.497794i	−0.864750	+	0.502202i	$0.832523\pi$
$620$	0.148364	+	0.256974i	0.00595844	+	0.0103203i
$621$	10.0401	−	12.2993i	0.402895	−	0.493553i
$622$	−1.43102	−	0.826200i	−0.0573787	−	0.0331276i
$623$	−5.08981	+	8.81581i	−0.203919	+	0.353198i
$624$	−26.4136	+	11.7728i	−1.05739	+	0.471288i
$625$	−6.73692	−	11.6687i	−0.269477	−	0.466747i
$626$			43.7416i			1.74827i
$627$	−3.58047	−	3.34762i	−0.142990	−	0.133691i
$628$	4.48176			0.178842
$629$		−	25.4852i		−	1.01616i
$630$	2.32961	+	3.47340i	0.0928140	+	0.138383i
$631$	20.2630	−	11.6989i	0.806659	−	0.465725i	−0.0391356	−	0.999234i	$-0.512460\pi$
$631$	20.2630	−	11.6989i	0.806659	−	0.465725i	0.845794	+	0.533509i	$0.179127\pi$
$632$	25.4711	+	14.7057i	1.01318	+	0.584962i
$633$	9.49407	−	40.8789i	0.377355	−	1.62479i
$634$	8.61410			0.342110
$635$		−	17.2428i		−	0.684261i
$636$	0.869830	+	0.813264i	0.0344910	+	0.0322480i
$637$	−3.57792	+	0.445527i	−0.141762	+	0.0176524i
$638$	−49.0332			−1.94124
$639$	8.82355	−	0.593768i	0.349054	−	0.0234891i
$640$	6.06864	−	10.5112i	0.239884	−	0.415491i
$641$	−29.0370			−1.14689			−0.573447	−	0.819243i	$-0.694394\pi$
$641$	−29.0370			−1.14689			−0.573447	+	0.819243i	$0.694394\pi$
$642$	−29.1324	−	6.76597i	−1.14976	−	0.267031i
$643$	−13.4269	−	7.75202i	−0.529505	−	0.305710i	0.211310	−	0.977419i	$-0.432227\pi$
$643$	−13.4269	−	7.75202i	−0.529505	−	0.305710i	−0.740815	+	0.671709i	$0.765560\pi$
$644$	1.03801	+	0.599293i	0.0409031	+	0.0236154i
$645$	0.518729	+	1.70467i	0.0204249	+	0.0671214i
$646$	5.24292			0.206280
$647$	−1.06713	+	1.84832i	−0.0419530	+	0.0726648i	−0.886239	−	0.463227i	$-0.846691\pi$
$647$	−1.06713	+	1.84832i	−0.0419530	+	0.0726648i	0.844286	+	0.535892i	$0.180025\pi$
$648$	17.7077	−	13.6859i	0.695624	−	0.537633i
$649$	−13.4007			−0.526023
$650$	−2.88565	−	23.1739i	−0.113184	−	0.908956i
$651$	1.39064	−	0.423170i	0.0545036	−	0.0165854i
$652$		−	7.19023i		−	0.281591i
$653$	17.3527			0.679062			0.339531	−	0.940595i	$-0.389732\pi$
$653$	17.3527			0.679062			0.339531	+	0.940595i	$0.389732\pi$
$654$	5.85599	−	1.78197i	0.228987	−	0.0696804i
$655$	−7.01434	−	4.04973i	−0.274073	−	0.158236i
$656$	50.0227	−	28.8806i	1.95306	−	1.12760i
$657$	3.94153	−	8.02787i	0.153774	−	0.313197i
$658$		−	19.0453i		−	0.742463i
$659$	25.6603			0.999583			0.499792	−	0.866146i	$-0.333410\pi$
$659$	25.6603			0.999583			0.499792	+	0.866146i	$0.333410\pi$
$660$	2.29053	−	0.697003i	0.0891586	−	0.0271308i
$661$		−	20.7610i		−	0.807509i	−0.914867	−	0.403755i	$-0.867705\pi$
$661$		−	20.7610i		−	0.807509i	0.914867	−	0.403755i	$-0.132295\pi$
$662$	−7.59573	−	13.1562i	−0.295217	−	0.511330i
$663$	−26.7117	+	11.9056i	−1.03740	+	0.462375i
$664$	−20.4681	+	35.4519i	−0.794318	+	1.37580i
$665$	−0.565029	−	0.326220i	−0.0219109	−	0.0126503i
$666$	−22.6674	−	11.1293i	−0.878345	−	0.431251i
$667$	12.3882	+	21.4570i	0.479672	+	0.830817i
$668$	−6.52745	−	3.76862i	−0.252555	−	0.145812i
$669$	−3.94679	−	12.9701i	−0.152592	−	0.501454i
$670$	−4.83987	−	2.79430i	−0.186980	−	0.107953i
$671$	−11.1140	+	6.41666i	−0.429050	+	0.247712i
$672$	2.76937	+	2.58927i	0.106831	+	0.0998834i
$673$	17.9370	+	31.0677i	0.691419	+	1.19757i	0.971373	+	0.237560i	$0.0763476\pi$
$673$	17.9370	+	31.0677i	0.691419	+	1.19757i	−0.279954	+	0.960014i	$0.590319\pi$
$674$	8.08016	+	4.66508i	0.311236	+	0.179692i
$675$	7.71793	+	20.3446i	0.297063	+	0.783064i
$676$	1.38884	−	4.90675i	0.0534169	−	0.188721i
$677$	5.46317	−	9.46248i	0.209967	−	0.363673i	−0.741737	−	0.670691i	$-0.765998\pi$
$677$	5.46317	−	9.46248i	0.209967	−	0.363673i	0.951704	+	0.307018i	$0.0993311\pi$
$678$	14.5135	+	3.37074i	0.557387	+	0.129453i
$679$	−11.7965			−0.452709
$680$	5.24798	−	9.08977i	0.201251	−	0.348577i
$681$	21.1153	+	4.90401i	0.809141	+	0.187922i
$682$		−	5.07483i		−	0.194325i
$683$	25.5689	−	14.7622i	0.978365	−	0.564859i	0.0765890	−	0.997063i	$-0.475597\pi$
$683$	25.5689	−	14.7622i	0.978365	−	0.564859i	0.901776	+	0.432203i	$0.142264\pi$
$684$	0.375428	−	0.764648i	0.0143548	−	0.0292371i
$685$	4.59012	+	7.95031i	0.175379	+	0.303766i
$686$	0.773348	+	1.33948i	0.0295266	+	0.0511415i
$687$	3.71568	+	12.2106i	0.141762	+	0.465865i
$688$	2.64262	+	4.57716i	0.100749	+	0.174503i
$689$	6.27080	−	0.780848i	0.238899	−	0.0297479i
$690$	−5.38931	−	5.03884i	−0.205168	−	0.191825i
$691$	25.0233	−	14.4472i	0.951933	−	0.549599i	0.0582520	−	0.998302i	$-0.481447\pi$
$691$	25.0233	−	14.4472i	0.951933	−	0.549599i	0.893681	+	0.448703i	$0.148114\pi$
$692$	−0.972814	+	1.68496i	−0.0369808	+	0.0640527i
$693$	−0.787489	−	11.7023i	−0.0299142	−	0.444534i
$694$		−	30.2497i		−	1.14826i
$695$			17.7517i			0.673360i
$696$	10.1672	+	33.4120i	0.385388	+	1.26648i
$697$	50.5871	−	29.2065i	1.91612	−	1.10627i
$698$	5.74523	−	9.95103i	0.217460	−	0.376652i
$699$	−9.22452	+	39.7183i	−0.348903	+	1.50228i
$700$	−1.42259	+	0.821333i	−0.0537689	+	0.0310435i
$701$	12.4649			0.470792			0.235396	−	0.971900i	$-0.424361\pi$
$701$	12.4649			0.470792			0.235396	+	0.971900i	$0.424361\pi$
$702$	−1.07561	+	28.9574i	−0.0405962	+	1.09293i
$703$	3.93935			0.148575
$704$	−19.8942	+	11.4859i	−0.749792	+	0.432892i
$705$	−4.34888	+	18.7251i	−0.163788	+	0.705227i
$706$	12.8813	−	22.3111i	0.484795	−	0.839689i
$707$	−7.39228	+	4.26793i	−0.278015	+	0.160512i
$708$	−0.677972	−	2.22798i	−0.0254797	−	0.0837328i
$709$		−	45.3060i		−	1.70150i	−0.525570	−	0.850751i	$-0.676148\pi$
$709$		−	45.3060i		−	1.70150i	0.525570	−	0.850751i	$-0.323852\pi$
$710$		−	4.10957i		−	0.154230i
$711$	29.4686	−	19.7646i	1.10516	−	0.741232i
$712$	12.6567	−	21.9220i	0.474329	−	0.821562i
$713$	−2.22075	+	1.28215i	−0.0831677	+	0.0480169i
$714$	9.16384	+	8.56790i	0.342948	+	0.320646i
$715$	4.94441	−	11.7039i	0.184910	−	0.437702i
$716$	2.17068	+	3.75973i	0.0811222	+	0.140508i
$717$	5.17391	+	17.0028i	0.193223	+	0.634980i
$718$	−24.0252	−	41.6128i	−0.896612	−	1.55298i
$719$	−15.2223	−	26.3658i	−0.567696	−	0.983278i	−0.996793	−	0.0800199i	$-0.974502\pi$
$719$	−15.2223	−	26.3658i	−0.567696	−	0.983278i	0.429097	−	0.903258i	$-0.358832\pi$
$720$	−6.97464	−	10.3990i	−0.259930	−	0.387549i
$721$	4.54064	−	2.62154i	0.169102	−	0.0976311i
$722$		−	28.5768i		−	1.06352i
$723$	−38.4993	−	8.94143i	−1.43181	−	0.332535i
$724$	1.12086	−	1.94139i	0.0416566	−	0.0721514i
$725$	−33.9561			−1.26110
$726$	−11.1814	−	2.59687i	−0.414981	−	0.0963789i
$727$	11.5815	−	20.0598i	0.429535	−	0.743976i	−0.567297	−	0.823513i	$-0.692011\pi$
$727$	11.5815	−	20.0598i	0.429535	−	0.743976i	0.996832	+	0.0795373i	$0.0253443\pi$
$728$	8.89710	−	1.10788i	0.329749	−	0.0410607i
$729$	−5.40579	−	26.4533i	−0.200214	−	0.979752i
$730$	−3.59915	−	2.07797i	−0.133210	−	0.0769091i
$731$	2.67244	+	4.62880i	0.0988438	+	0.171202i
$732$	−1.62911	−	1.52316i	−0.0602136	−	0.0562978i
$733$	18.8576	−	10.8874i	0.696521	−	0.402136i	−0.109530	−	0.993984i	$-0.534934\pi$
$733$	18.8576	−	10.8874i	0.696521	−	0.402136i	0.806050	+	0.591847i	$0.201601\pi$
$734$	26.0596	+	15.0455i	0.961876	+	0.555339i
$735$	−0.454484	−	1.49355i	−0.0167639	−	0.0550903i
$736$	−5.79214	−	3.34409i	−0.213501	−	0.123265i
$737$	7.83629	+	13.5729i	0.288653	+	0.499962i
$738$	−3.88608	−	57.7482i	−0.143049	−	2.12574i
$739$	−30.7649	−	17.7621i	−1.13170	−	0.653389i	−0.187341	−	0.982295i	$-0.559987\pi$
$739$	−30.7649	−	17.7621i	−1.13170	−	0.653389i	−0.944363	+	0.328906i	$0.893320\pi$
$740$	−0.962091	+	1.66639i	−0.0353672	+	0.0612577i
$741$	−1.84030	−	4.12892i	−0.0676049	−	0.151680i
$742$	−1.35540	−	2.34762i	−0.0497583	−	0.0861839i
$743$		−	18.4927i		−	0.678431i	−0.940709	−	0.339216i	$-0.889838\pi$
$743$		−	18.4927i		−	0.678431i	0.940709	−	0.339216i	$-0.110162\pi$
$744$	−3.45807	+	1.05229i	−0.126779	+	0.0385786i
$745$	11.4173			0.418296
$746$			19.7683i			0.723768i
$747$	27.5094	+	41.0158i	1.00652	+	1.50069i
$748$	6.21961	−	3.59089i	0.227411	−	0.131296i
$749$	9.66828	+	5.58198i	0.353271	+	0.203961i
$750$	21.2239	−	6.45840i	0.774987	−	0.235827i
$751$	−6.26614			−0.228655			−0.114327	−	0.993443i	$-0.536471\pi$
$751$	−6.26614			−0.228655			−0.114327	+	0.993443i	$0.536471\pi$
$752$			57.0198i			2.07930i
$753$	31.6575	−	9.63331i	1.15366	−	0.351057i
$754$	−41.6554	−	17.5976i	−1.51700	−	0.640868i
$755$	14.6002			0.531356
$756$	1.90577	−	0.722973i	0.0693122	−	0.0262943i
$757$	−19.9636	+	34.5780i	−0.725590	+	1.25676i	0.233141	+	0.972443i	$0.425100\pi$
$757$	−19.9636	+	34.5780i	−0.725590	+	1.25676i	−0.958731	+	0.284315i	$0.908234\pi$
$758$	−50.1727			−1.82236
$759$	6.02344	+	19.7945i	0.218637	+	0.718496i
$760$	1.40504	+	0.811201i	0.0509662	+	0.0294253i
$761$	−38.2589	−	22.0888i	−1.38688	−	0.800718i	−0.393922	−	0.919144i	$-0.628882\pi$
$761$	−38.2589	−	22.0888i	−1.38688	−	0.800718i	−0.992963	+	0.118426i	$0.962215\pi$
$762$	−49.9204	−	11.5940i	−1.80843	−	0.420005i
$763$	−2.28489			−0.0827184
$764$	−3.94360	+	6.83051i	−0.142674	+	0.247119i
$765$	−7.05334	−	10.5164i	−0.255014	−	0.380220i
$766$	18.8691			0.681770
$767$	−11.3844	−	4.80941i	−0.411065	−	0.173658i
$768$	−11.4829	−	10.7361i	−0.414353	−	0.387407i
$769$			40.4949i			1.46028i	0.683296	+	0.730142i	$0.260546\pi$
$769$			40.4949i			1.46028i	−0.683296	+	0.730142i	$0.739454\pi$
$770$	−5.45035			−0.196417
$771$	−9.36353	+	40.3168i	−0.337219	+	1.45197i
$772$	−2.51722	−	1.45332i	−0.0905969	−	0.0523061i
$773$	8.33485	−	4.81213i	0.299784	−	0.173080i	−0.342562	−	0.939495i	$-0.611295\pi$
$773$	8.33485	−	4.81213i	0.299784	−	0.173080i	0.642346	+	0.766415i	$0.277961\pi$
$774$	5.28406	−	0.355583i	0.189931	−	0.0127812i
$775$		−	3.51438i		−	0.126240i
$776$	29.3341			1.05303
$777$	6.88540	+	6.43763i	0.247012	+	0.230949i
$778$			39.9338i			1.43170i
$779$	4.51456	+	7.81944i	0.161751	+	0.280161i
$780$	2.19603	+	0.229924i	0.0786305	+	0.00823260i
$781$	−5.76241	+	9.98079i	−0.206195	+	0.357141i
$782$	−19.1662	−	11.0656i	−0.685381	−	0.395705i
$783$	41.5893	+	6.75481i	1.48628	+	0.241397i
$784$	−2.31533	−	4.01027i	−0.0826904	−	0.143224i
$785$	8.91831	+	5.14899i	0.318308	+	0.183775i
$786$	−16.4409	+	17.5845i	−0.586429	+	0.627218i
$787$	14.4362	+	8.33476i	0.514596	+	0.297102i	0.734721	−	0.678370i	$-0.237313\pi$
$787$	14.4362	+	8.33476i	0.514596	+	0.297102i	−0.220125	+	0.975472i	$0.570646\pi$
$788$	2.18539	−	1.26174i	0.0778513	−	0.0449475i
$789$	−8.66120	+	2.63559i	−0.308347	+	0.0938295i
$790$	−8.24445	−	14.2798i	−0.293324	−	0.508053i
$791$	−4.81665	−	2.78089i	−0.171260	−	0.0988771i
$792$	1.95823	+	29.0998i	0.0695825	+	1.03401i
$793$	−11.7446	+	1.46245i	−0.417063	+	0.0519332i
$794$	27.2003	−	47.1123i	0.965303	−	1.67195i
$795$	0.796546	+	2.61765i	0.0282506	+	0.0928384i
$796$	−4.34987			−0.154177
$797$	12.9090	−	22.3591i	0.457261	−	0.791999i	−0.541554	−	0.840666i	$-0.682164\pi$
$797$	12.9090	−	22.3591i	0.457261	−	0.791999i	0.998815	+	0.0486669i	$0.0154973\pi$
$798$	−1.32437	+	1.41649i	−0.0468823	+	0.0501432i
$799$			57.6632i			2.03998i
$800$	7.93815	−	4.58309i	0.280656	−	0.162037i
$801$	−17.0107	−	25.3625i	−0.601044	−	0.896141i
$802$	21.8139	+	37.7827i	0.770275	+	1.33416i
$803$	5.82743	+	10.0934i	0.205645	+	0.356188i
$804$	−1.86015	+	1.98953i	−0.0656025	+	0.0701655i
$805$	1.37702	+	2.38508i	0.0485337	+	0.0840629i
$806$	1.82132	−	4.31124i	0.0641532	−	0.151857i
$807$	20.3563	−	6.19437i	0.716574	−	0.218052i
$808$	18.3822	−	10.6129i	0.646682	−	0.373362i
$809$	−18.5101	+	32.0604i	−0.650779	+	1.12718i	0.332155	+	0.943225i	$0.392224\pi$
$809$	−18.5101	+	32.0604i	−0.650779	+	1.12718i	−0.982934	+	0.183958i	$0.941109\pi$
$810$	−12.4338	+	1.68104i	−0.436878	+	0.0590656i
$811$			6.60322i			0.231870i	0.993257	+	0.115935i	$0.0369865\pi$
$811$			6.60322i			0.231870i	−0.993257	+	0.115935i	$0.963014\pi$
$812$			3.18082i			0.111625i
$813$	8.68366	−	9.28765i	0.304549	−	0.325732i
$814$	28.4996	−	16.4543i	0.998912	−	0.576722i
$815$	8.26068	−	14.3079i	0.289359	−	0.501184i
$816$	−27.4357	−	25.6515i	−0.960441	−	0.897982i
$817$	−0.715492	+	0.413089i	−0.0250319	+	0.0144522i
$818$	−9.17956			−0.320956
$819$	3.53087	−	10.2241i	0.123378	−	0.357260i
$820$	−4.41029			−0.154014
$821$	−7.68942	+	4.43949i	−0.268363	+	0.154939i	−0.628143	−	0.778098i	$-0.716185\pi$
$821$	−7.68942	+	4.43949i	−0.268363	+	0.154939i	0.359781	+	0.933037i	$0.382852\pi$
$822$	26.1036	−	7.94330i	0.910469	−	0.277054i
$823$	−25.6014	+	44.3429i	−0.892408	+	1.54570i	−0.0554289	+	0.998463i	$0.517653\pi$
$823$	−25.6014	+	44.3429i	−0.892408	+	1.54570i	−0.836980	+	0.547234i	$0.815681\pi$
$824$	−11.2911	+	6.51890i	−0.393343	+	0.227097i
$825$	−27.6215	−	6.41507i	−0.961658	−	0.223344i
$826$			5.30153i			0.184464i
$827$			0.197172i			0.00685633i	0.999994	+	0.00342817i	$0.00109122\pi$
$827$			0.197172i			0.00685633i	−0.999994	+	0.00342817i	$0.998909\pi$
$828$	−2.98628	+	2.00290i	−0.103780	+	0.0696056i
$829$	2.53719	−	4.39454i	0.0881201	−	0.152629i	−0.818596	−	0.574369i	$-0.805247\pi$
$829$	2.53719	−	4.39454i	0.0881201	−	0.152629i	0.906716	+	0.421741i	$0.138581\pi$
$830$	19.8753	−	11.4750i	0.689882	−	0.398304i
$831$	−2.59928	+	11.1918i	−0.0901681	+	0.388239i
$832$	−21.0231	+	2.61782i	−0.728843	+	0.0907565i
$833$	−2.34146	−	4.05552i	−0.0811266	−	0.140515i
$834$	51.3937	+	11.9361i	1.77962	+	0.413314i
$835$	−8.65936	−	14.9984i	−0.299669	−	0.519043i
$836$	0.555058	+	0.961389i	0.0191971	+	0.0332503i
$837$	−0.699108	+	4.30441i	−0.0241647	+	0.148782i
$838$	42.1001	−	24.3065i	1.45432	−	0.839654i
$839$		−	50.6680i		−	1.74925i	−0.484797	−	0.874627i	$-0.661107\pi$
$839$		−	50.6680i		−	1.74925i	0.484797	−	0.874627i	$-0.338893\pi$
$840$	1.13015	+	3.71396i	0.0389939	+	0.128144i
$841$	−18.3759	+	31.8280i	−0.633653	+	1.09752i
$842$	−15.4994			−0.534146
$843$	9.06243	−	9.69277i	0.312127	−	0.333837i
$844$	−4.75227	+	8.23118i	−0.163580	+	0.283329i
$845$	8.40090	−	8.16838i	0.289000	−	0.281001i
$846$	51.2876	+	25.1812i	1.76330	+	0.865748i
$847$	3.71081	+	2.14244i	0.127505	+	0.0736151i
$848$	4.05794	+	7.02856i	0.139350	+	0.241362i
$849$	−4.98026	+	21.4436i	−0.170922	+	0.735944i
$850$	26.2673	−	15.1654i	0.900961	−	0.520170i
$851$	−14.4008	−	8.31431i	−0.493653	−	0.285011i
$852$	−1.95093	−	0.453101i	−0.0668377	−	0.0155230i
$853$	−12.8166	−	7.39967i	−0.438832	−	0.253360i	0.264270	−	0.964449i	$-0.414869\pi$
$853$	−12.8166	−	7.39967i	−0.438832	−	0.253360i	−0.703102	+	0.711089i	$0.748202\pi$
$854$	2.53853	+	4.39687i	0.0868669	+	0.150458i
$855$	1.62555	−	1.09026i	0.0555927	−	0.0372862i
$856$	−24.0418	−	13.8805i	−0.821732	−	0.474427i
$857$	−11.6263	+	20.1373i	−0.397147	+	0.687879i	−0.993373	−	0.114938i	$-0.963333\pi$
$857$	−11.6263	+	20.1373i	−0.397147	+	0.687879i	0.596226	+	0.802817i	$0.296666\pi$
$858$	−30.5599	−	22.1844i	−1.04330	−	0.757363i
$859$	17.1461	+	29.6980i	0.585019	+	1.01328i	0.994873	+	0.101131i	$0.0322461\pi$
$859$	17.1461	+	29.6980i	0.585019	+	1.01328i	−0.409855	+	0.912151i	$0.634421\pi$
$860$		−	0.403548i		−	0.0137609i
$861$	−4.88764	+	21.0449i	−0.166570	+	0.717207i
$862$	35.3150			1.20283
$863$		−	31.4258i		−	1.06975i	−0.844933	−	0.534873i	$-0.820360\pi$
$863$		−	31.4258i		−	1.06975i	0.844933	−	0.534873i	$-0.179640\pi$
$864$	−10.6343	+	4.03424i	−0.361787	+	0.137248i
$865$	−3.87162	+	2.23528i	−0.131639	+	0.0760019i
$866$	3.96653	+	2.29008i	0.134788	+	0.0778200i
$867$	−6.23697	−	5.83136i	−0.211818	−	0.198044i
$868$	−0.329208			−0.0111741
$869$			46.2412i			1.56863i
$870$	4.42949	−	19.0722i	0.150174	−	0.646607i
$871$	1.78601	+	14.3430i	0.0605166	+	0.485994i
$872$	5.68176			0.192409
$873$	15.5971	−	31.7672i	0.527881	−	1.07516i
$874$	1.71045	−	2.96259i	0.0578569	−	0.100211i
$875$	−8.28113			−0.279953
$876$	−1.38329	+	1.47951i	−0.0467372	+	0.0499880i
$877$	9.74593	+	5.62681i	0.329097	+	0.190004i	0.655440	−	0.755247i	$-0.272483\pi$
$877$	9.74593	+	5.62681i	0.329097	+	0.190004i	−0.326343	+	0.945251i	$0.605817\pi$
$878$	0.0799060	+	0.0461338i	0.00269670	+	0.00155694i
$879$	18.4380	−	19.7204i	0.621898	−	0.665154i
$880$	16.3178			0.550074
$881$	1.81278	−	3.13983i	0.0610742	−	0.105784i	−0.833872	−	0.551958i	$-0.813881\pi$
$881$	1.81278	−	3.13983i	0.0610742	−	0.105784i	0.894946	+	0.446175i	$0.147214\pi$
$882$	−4.62962	+	0.311544i	−0.155887	+	0.0104902i
$883$	−8.02801			−0.270164			−0.135082	−	0.990834i	$-0.543130\pi$
$883$	−8.02801			−0.270164			−0.135082	+	0.990834i	$0.543130\pi$
$884$	6.57252	−	0.818418i	0.221058	−	0.0275264i
$885$	1.21057	−	5.21239i	0.0406929	−	0.175213i
$886$			37.5467i			1.26141i
$887$	45.3213			1.52174			0.760869	−	0.648905i	$-0.224773\pi$
$887$	45.3213			1.52174			0.760869	+	0.648905i	$0.224773\pi$
$888$	−17.1217	−	16.0083i	−0.574567	−	0.537202i
$889$	16.5673	+	9.56512i	0.555648	+	0.320804i
$890$	−12.2901	+	7.09570i	−0.411965	+	0.237848i
$891$	32.5546	+	13.3518i	1.09062	+	0.447304i
$892$			3.07043i			0.102806i
$893$	−8.91321			−0.298269
$894$	7.67689	−	33.0546i	0.256754	−	1.10551i
$895$			9.97537i			0.333440i
$896$	6.73291	+	11.6617i	0.224931	+	0.389592i
$897$	−1.98698	+	18.9779i	−0.0663434	+	0.633654i
$898$	−22.2083	+	38.4660i	−0.741102	+	1.28363i
$899$	−5.89345	−	3.40259i	−0.196558	−	0.113483i
$900$	−0.330874	−	4.91688i	−0.0110291	−	0.163896i
$901$	4.10373	+	7.10786i	0.136715	+	0.236797i
$902$	65.3221	+	37.7137i	2.17499	+	1.25573i
$903$	−1.92564	−	0.447228i	−0.0640813	−	0.0148828i
$904$	11.9774	+	6.91516i	0.398363	+	0.229995i
$905$	4.46084	−	2.57547i	0.148283	−	0.0856114i
$906$	9.81708	−	42.2697i	0.326151	−	1.40432i
$907$	−29.1253	−	50.4465i	−0.967090	−	1.67505i	−0.703893	−	0.710306i	$-0.748557\pi$
$907$	−29.1253	−	50.4465i	−0.967090	−	1.67505i	−0.263197	−	0.964742i	$-0.584777\pi$
$908$	−4.25168	−	2.45471i	−0.141097	−	0.0814624i
$909$	−1.71934	−	25.5498i	−0.0570269	−	0.847434i
$910$	−4.63026	−	1.95609i	−0.153492	−	0.0648437i
$911$	−7.74980	+	13.4231i	−0.256762	+	0.444725i	−0.965373	−	0.260875i	$-0.915989\pi$
$911$	−7.74980	+	13.4231i	−0.256762	+	0.444725i	0.708610	+	0.705600i	$0.249322\pi$
$912$	3.96505	−	4.24084i	0.131296	−	0.140428i
$913$	−64.3608			−2.13003
$914$	−15.0032	+	25.9863i	−0.496262	+	0.859551i
$915$	−1.49185	−	4.90260i	−0.0493192	−	0.162075i
$916$		−	2.89063i		−	0.0955092i
$917$	7.78213	−	4.49301i	0.256989	−	0.148372i
$918$	−35.1889	+	13.3493i	−1.16141	+	0.440592i
$919$	−7.59016	−	13.1465i	−0.250376	−	0.433664i	0.713253	−	0.700907i	$-0.247221\pi$
$919$	−7.59016	−	13.1465i	−0.250376	−	0.433664i	−0.963629	+	0.267242i	$0.913888\pi$
$920$	−3.42421	−	5.93090i	−0.112893	−	0.195536i
$921$	15.1218	+	3.51202i	0.498280	+	0.115725i
$922$	−3.30104	−	5.71757i	−0.108714	−	0.188298i
$923$	−8.47740	+	6.41095i	−0.279037	+	0.211019i
$924$	−0.600929	+	2.58743i	−0.0197691	+	0.0851203i
$925$	19.7364	−	11.3948i	0.648927	−	0.374658i
$926$	−21.5090	+	37.2547i	−0.706829	+	1.22426i
$927$	1.05609	+	15.6937i	0.0346865	+	0.515450i
$928$		−	17.7492i		−	0.582646i
$929$			32.3560i			1.06157i	0.847508	+	0.530783i	$0.178102\pi$
$929$			32.3560i			1.06157i	−0.847508	+	0.530783i	$0.821898\pi$
$930$	1.97393	+	0.458443i	0.0647276	+	0.0150329i
$931$	0.626877	−	0.361928i	0.0205451	−	0.0118617i
$932$	4.61735	−	7.99748i	0.151246	−	0.261966i
$933$	−1.77027	+	0.538691i	−0.0579562	+	0.0176360i
$934$	15.0523	−	8.69042i	0.492525	−	0.284359i
$935$	16.5019			0.539671
$936$	−8.78010	+	25.4241i	−0.286987	+	0.831011i
$937$	−33.4172			−1.09169			−0.545846	−	0.837885i	$-0.683792\pi$
$937$	−33.4172			−1.09169			−0.545846	+	0.837885i	$0.683792\pi$
$938$	5.36964	−	3.10016i	0.175325	−	0.101224i
$939$	35.7805	+	33.4536i	1.16765	+	1.09172i
$940$	2.17684	−	3.77039i	0.0710006	−	0.122977i
$941$	15.1428	−	8.74273i	0.493643	−	0.285005i	−0.232442	−	0.972610i	$-0.574671\pi$
$941$	15.1428	−	8.74273i	0.493643	−	0.285005i	0.726084	+	0.687606i	$0.241338\pi$
$942$	20.9037	−	22.3576i	0.681078	−	0.728450i
$943$		−	38.1133i		−	1.24114i
$944$		−	15.8723i		−	0.516599i
$945$	4.62292	+	0.750840i	0.150384	+	0.0244248i
$946$	−3.45087	+	5.97708i	−0.112197	+	0.194332i
$947$	6.23951	−	3.60239i	0.202757	−	0.117062i	−0.395184	−	0.918602i	$-0.629319\pi$
$947$	6.23951	−	3.60239i	0.202757	−	0.117062i	0.597941	+	0.801540i	$0.295986\pi$
$948$	−7.68802	+	2.33945i	−0.249695	+	0.0759818i
$949$	1.32816	+	10.6661i	0.0431138	+	0.346237i
$950$	2.34418	+	4.06024i	0.0760552	+	0.131732i
$951$	6.58807	−	7.04631i	0.213633	−	0.228492i
$952$	5.82243	+	10.0847i	0.188706	+	0.326848i
$953$	−12.1933	−	21.1195i	−0.394981	−	0.684127i	0.598118	−	0.801408i	$-0.295915\pi$
$953$	−12.1933	−	21.1195i	−0.394981	−	0.684127i	−0.993099	+	0.117281i	$0.962582\pi$
$954$	8.11405	−	0.546024i	0.262702	−	0.0176782i
$955$	−15.6948	+	9.06140i	−0.507872	+	0.293220i
$956$		−	4.02508i		−	0.130180i
$957$	−37.5006	+	40.1090i	−1.21222	+	1.29654i
$958$	−0.951846	+	1.64865i	−0.0307528	+	0.0532653i
$959$	−10.1851			−0.328894
$960$	−2.67044	−	8.77574i	−0.0861882	−	0.283236i
$961$	−15.1478	+	26.2368i	−0.488640	+	0.846349i
$962$	30.1168	−	3.75018i	0.971003	−	0.120911i
$963$	−27.8150	+	18.6556i	−0.896327	+	0.601168i
$964$	7.75205	+	4.47565i	0.249677	+	0.144151i
$965$	−3.33937	−	5.78395i	−0.107498	−	0.186192i
$966$	7.83104	−	2.38297i	0.251959	−	0.0766708i
$967$	−17.4411	+	10.0696i	−0.560868	+	0.323817i	−0.753494	−	0.657455i	$-0.771633\pi$
$967$	−17.4411	+	10.0696i	−0.560868	+	0.323817i	0.192626	+	0.981272i	$0.438300\pi$
$968$	−9.22757	−	5.32754i	−0.296585	−	0.171234i
$969$	4.00979	−	4.28869i	0.128813	−	0.137773i
$970$	−14.2422	−	8.22275i	−0.457290	−	0.264017i
$971$	−9.75648	−	16.8987i	−0.313100	−	0.542306i	0.665932	−	0.746013i	$-0.268034\pi$
$971$	−9.75648	−	16.8987i	−0.313100	−	0.542306i	−0.979032	+	0.203707i	$0.934701\pi$
$972$	−0.572850	+	6.08800i	−0.0183742	+	0.195273i
$973$	−17.0562	−	9.84740i	−0.546797	−	0.315693i
$974$	20.6332	−	35.7378i	0.661132	−	1.14511i
$975$	−21.1631	−	15.3630i	−0.677763	−	0.492009i
$976$	−7.60013	−	13.1638i	−0.243274	−	0.421364i
$977$			37.8476i			1.21085i	0.795902	+	0.605425i	$0.206997\pi$
$977$			37.8476i			1.21085i	−0.795902	+	0.605425i	$0.793003\pi$
$978$	−35.8690	−	33.5364i	−1.14696	−	1.07238i
$979$	39.7981			1.27195
$980$			0.353568i			0.0112943i
$981$	3.02102	−	6.15303i	0.0964538	−	0.196451i
$982$	−58.7570	+	33.9234i	−1.87501	+	1.08254i
$983$	−11.5993	−	6.69688i	−0.369962	−	0.213597i	0.303480	−	0.952838i	$-0.401851\pi$
$983$	−11.5993	−	6.69688i	−0.369962	−	0.213597i	−0.673442	+	0.739240i	$0.735185\pi$
$984$	12.1540	−	52.3316i	0.387454	−	1.66827i
$985$	5.79831			0.184749
$986$		−	58.7320i		−	1.87041i
$987$	−15.5790	−	14.5659i	−0.495885	−	0.463636i
$988$	0.126506	+	1.01594i	0.00402469	+	0.0323213i
$989$	3.48743			0.110894
$990$	7.20632	−	14.6774i	0.229032	−	0.466478i
$991$	−13.4347	+	23.2696i	−0.426768	+	0.739183i	−0.996584	−	0.0825890i	$-0.973681\pi$
$991$	−13.4347	+	23.2696i	−0.426768	+	0.739183i	0.569816	+	0.821772i	$0.307014\pi$
$992$	1.83700			0.0583249
$993$	−16.5709	−	3.84858i	−0.525863	−	0.122131i
$994$	3.94856	+	2.27970i	0.125241	+	0.0723078i
$995$	−8.65585	−	4.99746i	−0.274409	−	0.158430i
$996$	−3.25616	−	10.7005i	−0.103175	−	0.339060i
$997$	−11.8929			−0.376651			−0.188325	−	0.982107i	$-0.560306\pi$
$997$	−11.8929			−0.376651			−0.188325	+	0.982107i	$0.560306\pi$
$998$	−2.53541	+	4.39145i	−0.0802569	+	0.139009i
$999$	−26.4398	+	10.0302i	−0.836517	+	0.317341i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.dk.a.43.23	yes	168
9.4	even	3		819.2.bh.a.589.23	✓	168
13.10	even	6		819.2.bh.a.673.62	yes	168
117.49	even	6	inner	819.2.dk.a.400.23	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.bh.a.589.23	✓	168	9.4	even	3
819.2.bh.a.673.62	yes	168	13.10	even	6
819.2.dk.a.43.23	yes	168	1.1	even	1	trivial
819.2.dk.a.400.23	yes	168	117.49	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.dk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33948 + 0.773348i) q^{2} +(-0.391838 + 1.68715i) q^{3} +(0.196135 - 0.339716i) q^{4} +(0.780582 - 0.450669i) q^{5} +(-0.779893 - 2.56292i) q^{6} +1.00000i q^{7} -2.48667i q^{8} +(-2.69293 - 1.32218i) q^{9} +O(q^{10})\)	\(q+(-1.33948 + 0.773348i) q^{2} +(-0.391838 + 1.68715i) q^{3} +(0.196135 - 0.339716i) q^{4} +(0.780582 - 0.450669i) q^{5} +(-0.779893 - 2.56292i) q^{6} +1.00000i q^{7} -2.48667i q^{8} +(-2.69293 - 1.32218i) q^{9} +(-0.697049 + 1.20732i) q^{10} +(3.38580 - 1.95479i) q^{11} +(0.496297 + 0.464022i) q^{12} +(3.57792 - 0.445527i) q^{13} +(-0.773348 - 1.33948i) q^{14} +(0.454484 + 1.49355i) q^{15} +(2.31533 + 4.01027i) q^{16} +(2.34146 + 4.05552i) q^{17} +(4.62962 - 0.311544i) q^{18} +(-0.626877 + 0.361928i) q^{19} -0.353568i q^{20} +(-1.68715 - 0.391838i) q^{21} +(-3.02347 + 5.23681i) q^{22} +3.05551 q^{23} +(4.19538 + 0.974372i) q^{24} +(-2.09379 + 3.62656i) q^{25} +(-4.44800 + 3.36375i) q^{26} +(3.28589 - 4.02528i) q^{27} +(0.339716 + 0.196135i) q^{28} +(4.05438 + 7.02239i) q^{29} +(-1.76380 - 1.64910i) q^{30} +(-0.726802 + 0.419619i) q^{31} +(-1.89564 - 1.09445i) q^{32} +(1.97134 + 6.47831i) q^{33} +(-6.27266 - 3.62152i) q^{34} +(0.450669 + 0.780582i) q^{35} +(-0.977342 + 0.655505i) q^{36} +(-4.71306 - 2.72109i) q^{37} +(0.559792 - 0.969589i) q^{38} +(-0.650295 + 6.21105i) q^{39} +(-1.12067 - 1.94105i) q^{40} -12.4736i q^{41} +(2.56292 - 0.779893i) q^{42} +1.14136 q^{43} -1.53362i q^{44} +(-2.69792 + 0.181552i) q^{45} +(-4.09279 + 2.36297i) q^{46} +(10.6638 + 6.15676i) q^{47} +(-7.67315 + 2.33493i) q^{48} -1.00000 q^{49} -6.47693i q^{50} +(-7.75973 + 2.36127i) q^{51} +(0.550403 - 1.30286i) q^{52} +1.75264 q^{53} +(-1.28844 + 7.93292i) q^{54} +(1.76193 - 3.05176i) q^{55} +2.48667 q^{56} +(-0.364991 - 1.19945i) q^{57} +(-10.8615 - 6.27089i) q^{58} +(-2.96843 - 1.71382i) q^{59} +(0.596522 + 0.138542i) q^{60} -3.28252 q^{61} +(0.649023 - 1.12414i) q^{62} +(1.32218 - 2.69293i) q^{63} -5.87578 q^{64} +(2.59208 - 1.96023i) q^{65} +(-7.65055 - 7.15302i) q^{66} +4.00875i q^{67} +1.83697 q^{68} +(-1.19726 + 5.15509i) q^{69} +(-1.20732 - 0.697049i) q^{70} +(-2.55290 + 1.47392i) q^{71} +(-3.28782 + 6.69642i) q^{72} +2.98109i q^{73} +8.41739 q^{74} +(-5.29811 - 4.95356i) q^{75} +0.283947i q^{76} +(1.95479 + 3.38580i) q^{77} +(-3.93225 - 8.82247i) q^{78} +(-5.91382 + 10.2430i) q^{79} +(3.61462 + 2.08690i) q^{80} +(5.50370 + 7.12104i) q^{81} +(9.64647 + 16.7082i) q^{82} +(-14.2568 - 8.23114i) q^{83} +(-0.464022 + 0.496297i) q^{84} +(3.65540 + 2.11045i) q^{85} +(-1.52883 + 0.882668i) q^{86} +(-13.4365 + 4.08869i) q^{87} +(-4.86093 - 8.41937i) q^{88} +(8.81581 + 5.08981i) q^{89} +(3.47340 - 2.32961i) q^{90} +(0.445527 + 3.57792i) q^{91} +(0.599293 - 1.03801i) q^{92} +(-0.423170 - 1.39064i) q^{93} -19.0453 q^{94} +(-0.326220 + 0.565029i) q^{95} +(2.58927 - 2.76937i) q^{96} +11.7965i q^{97} +(1.33948 - 0.773348i) q^{98} +(-11.7023 + 0.787489i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q + 84 q^{4} - 2 q^{9}+O(q^{10}) \) 168 * q + 84 * q^4 - 2 * q^9	\( 168 q + 84 q^{4} - 2 q^{9} + 12 q^{12} + 8 q^{14} - 84 q^{16} + 12 q^{18} - 6 q^{21} + 40 q^{23} - 84 q^{24} + 84 q^{25} + 4 q^{26} - 24 q^{27} + 34 q^{29} + 44 q^{30} + 36 q^{32} + 18 q^{33} + 16 q^{35} + 4 q^{36} - 12 q^{38} - 6 q^{39} - 30 q^{45} - 30 q^{47} - 2 q^{48} - 168 q^{49} - 38 q^{51} + 18 q^{52} - 48 q^{53} + 114 q^{54} + 48 q^{56} - 54 q^{57} + 48 q^{59} + 24 q^{60} + 6 q^{62} - 12 q^{63} - 132 q^{64} - 16 q^{65} - 54 q^{66} - 156 q^{68} - 28 q^{69} + 24 q^{71} + 36 q^{72} - 84 q^{74} + 30 q^{75} - 16 q^{77} + 116 q^{78} - 6 q^{79} - 2 q^{81} - 6 q^{82} + 18 q^{83} - 24 q^{84} + 90 q^{85} - 24 q^{86} + 52 q^{87} + 24 q^{88} - 36 q^{89} - 44 q^{90} - 6 q^{91} + 8 q^{92} - 66 q^{93} + 120 q^{94} - 48 q^{95} - 24 q^{96} + 6 q^{99}+O(q^{100}) \) 168 * q + 84 * q^4 - 2 * q^9 + 12 * q^12 + 8 * q^14 - 84 * q^16 + 12 * q^18 - 6 * q^21 + 40 * q^23 - 84 * q^24 + 84 * q^25 + 4 * q^26 - 24 * q^27 + 34 * q^29 + 44 * q^30 + 36 * q^32 + 18 * q^33 + 16 * q^35 + 4 * q^36 - 12 * q^38 - 6 * q^39 - 30 * q^45 - 30 * q^47 - 2 * q^48 - 168 * q^49 - 38 * q^51 + 18 * q^52 - 48 * q^53 + 114 * q^54 + 48 * q^56 - 54 * q^57 + 48 * q^59 + 24 * q^60 + 6 * q^62 - 12 * q^63 - 132 * q^64 - 16 * q^65 - 54 * q^66 - 156 * q^68 - 28 * q^69 + 24 * q^71 + 36 * q^72 - 84 * q^74 + 30 * q^75 - 16 * q^77 + 116 * q^78 - 6 * q^79 - 2 * q^81 - 6 * q^82 + 18 * q^83 - 24 * q^84 + 90 * q^85 - 24 * q^86 + 52 * q^87 + 24 * q^88 - 36 * q^89 - 44 * q^90 - 6 * q^91 + 8 * q^92 - 66 * q^93 + 120 * q^94 - 48 * q^95 - 24 * q^96 + 6 * q^99

Introduction

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