LMFDB - Embedded newform 560.2.bb.d.29.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(29,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2, 0]))

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

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

chi := DirichletCharacter("560.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.bb (of order $4$, 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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$70$
Relative dimension:	$35$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			29.4
Character	$\chi$	$=$	560.29
Dual form			560.2.bb.d.309.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33379 - 0.470109i) q^{2} +(0.760413 - 0.760413i) q^{3} +(1.55800 + 1.25405i) q^{4} +(0.975010 - 2.01230i) q^{5} +(-1.37171 + 0.656755i) q^{6} +1.00000 q^{7} +(-1.48850 - 2.40507i) q^{8} +1.84355i q^{9} +O(q^{10})$	\(q+(-1.33379 - 0.470109i) q^{2} +(0.760413 - 0.760413i) q^{3} +(1.55800 + 1.25405i) q^{4} +(0.975010 - 2.01230i) q^{5} +(-1.37171 + 0.656755i) q^{6} +1.00000 q^{7} +(-1.48850 - 2.40507i) q^{8} +1.84355i q^{9} +(-2.24646 + 2.22563i) q^{10} +(2.93284 - 2.93284i) q^{11} +(2.13832 - 0.231121i) q^{12} +(0.294783 - 0.294783i) q^{13} +(-1.33379 - 0.470109i) q^{14} +(-0.788769 - 2.27159i) q^{15} +(0.854698 + 3.90762i) q^{16} -2.07192i q^{17} +(0.866667 - 2.45890i) q^{18} +(0.507302 + 0.507302i) q^{19} +(4.04259 - 1.91244i) q^{20} +(0.760413 - 0.760413i) q^{21} +(-5.29054 + 2.53304i) q^{22} +1.56976 q^{23} +(-2.96072 - 0.696975i) q^{24} +(-3.09871 - 3.92403i) q^{25} +(-0.531758 + 0.254598i) q^{26} +(3.68309 + 3.68309i) q^{27} +(1.55800 + 1.25405i) q^{28} +(4.08582 + 4.08582i) q^{29} +(-0.0158409 + 3.40063i) q^{30} -6.78979 q^{31} +(0.697018 - 5.61375i) q^{32} -4.46033i q^{33} +(-0.974030 + 2.76351i) q^{34} +(0.975010 - 2.01230i) q^{35} +(-2.31190 + 2.87223i) q^{36} +(-3.10623 - 3.10623i) q^{37} +(-0.438148 - 0.915122i) q^{38} -0.448313i q^{39} +(-6.29103 + 0.650336i) q^{40} -7.00823i q^{41} +(-1.37171 + 0.656755i) q^{42} +(6.45884 + 6.45884i) q^{43} +(8.24728 - 0.891410i) q^{44} +(3.70977 + 1.79747i) q^{45} +(-2.09374 - 0.737960i) q^{46} +1.80022i q^{47} +(3.62133 + 2.32148i) q^{48} +1.00000 q^{49} +(2.28831 + 6.69056i) q^{50} +(-1.57552 - 1.57552i) q^{51} +(0.828944 - 0.0895967i) q^{52} +(-3.83361 - 3.83361i) q^{53} +(-3.18102 - 6.64393i) q^{54} +(-3.04220 - 8.76129i) q^{55} +(-1.48850 - 2.40507i) q^{56} +0.771518 q^{57} +(-3.52885 - 7.37042i) q^{58} +(0.471185 - 0.471185i) q^{59} +(1.61980 - 4.52828i) q^{60} +(-9.72941 - 9.72941i) q^{61} +(9.05616 + 3.19194i) q^{62} +1.84355i q^{63} +(-3.56875 + 7.15989i) q^{64} +(-0.305776 - 0.880608i) q^{65} +(-2.09684 + 5.94915i) q^{66} +(5.76866 - 5.76866i) q^{67} +(2.59830 - 3.22805i) q^{68} +(1.19367 - 1.19367i) q^{69} +(-2.24646 + 2.22563i) q^{70} -3.67469i q^{71} +(4.43386 - 2.74411i) q^{72} -4.26700 q^{73} +(2.68279 + 5.60332i) q^{74} +(-5.34018 - 0.627580i) q^{75} +(0.154190 + 1.42656i) q^{76} +(2.93284 - 2.93284i) q^{77} +(-0.210756 + 0.597956i) q^{78} +6.95379 q^{79} +(8.69665 + 2.09006i) q^{80} +0.0707067 q^{81} +(-3.29463 + 9.34751i) q^{82} +(-4.94383 + 4.94383i) q^{83} +(2.13832 - 0.231121i) q^{84} +(-4.16933 - 2.02015i) q^{85} +(-5.57838 - 11.6511i) q^{86} +6.21383 q^{87} +(-11.4192 - 2.68816i) q^{88} -11.7925i q^{89} +(-4.10304 - 4.14145i) q^{90} +(0.294783 - 0.294783i) q^{91} +(2.44569 + 1.96857i) q^{92} +(-5.16304 + 5.16304i) q^{93} +(0.846298 - 2.40111i) q^{94} +(1.51547 - 0.526220i) q^{95} +(-3.73874 - 4.79879i) q^{96} +16.6909i q^{97} +(-1.33379 - 0.470109i) q^{98} +(5.40681 + 5.40681i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 70 q + 2 q^{2} + 2 q^{3} + 2 q^{5} + 70 q^{7} + 8 q^{8}+O(q^{10}) $ 70 * q + 2 * q^2 + 2 * q^3 + 2 * q^5 + 70 * q^7 + 8 * q^8	$ 70 q + 2 q^{2} + 2 q^{3} + 2 q^{5} + 70 q^{7} + 8 q^{8} - 18 q^{10} - 2 q^{11} - 4 q^{12} + 6 q^{13} + 2 q^{14} - 6 q^{15} + 4 q^{16} - 18 q^{18} + 14 q^{19} + 12 q^{20} + 2 q^{21} - 12 q^{22} + 20 q^{24} + 6 q^{25} - 36 q^{26} + 8 q^{27} + 2 q^{29} + 8 q^{30} + 16 q^{31} - 8 q^{32} + 4 q^{34} + 2 q^{35} - 40 q^{36} + 10 q^{37} - 12 q^{38} - 24 q^{40} + 2 q^{43} - 24 q^{44} - 24 q^{45} - 16 q^{46} - 44 q^{48} + 70 q^{49} - 10 q^{50} + 8 q^{51} + 28 q^{52} - 30 q^{53} - 32 q^{54} + 6 q^{55} + 8 q^{56} - 76 q^{57} + 56 q^{58} + 2 q^{59} - 8 q^{60} + 30 q^{61} + 48 q^{62} + 12 q^{64} - 10 q^{65} + 80 q^{66} + 6 q^{67} - 36 q^{68} - 16 q^{69} - 18 q^{70} + 4 q^{72} - 36 q^{73} - 32 q^{74} - 2 q^{75} + 44 q^{76} - 2 q^{77} - 84 q^{78} - 40 q^{79} + 12 q^{80} - 82 q^{81} + 24 q^{82} + 10 q^{83} - 4 q^{84} + 32 q^{85} + 32 q^{86} - 4 q^{87} + 32 q^{88} + 18 q^{90} + 6 q^{91} - 92 q^{92} - 56 q^{93} - 20 q^{94} + 6 q^{95} + 16 q^{96} + 2 q^{98} - 34 q^{99}+O(q^{100}) $ 70 * q + 2 * q^2 + 2 * q^3 + 2 * q^5 + 70 * q^7 + 8 * q^8 - 18 * q^10 - 2 * q^11 - 4 * q^12 + 6 * q^13 + 2 * q^14 - 6 * q^15 + 4 * q^16 - 18 * q^18 + 14 * q^19 + 12 * q^20 + 2 * q^21 - 12 * q^22 + 20 * q^24 + 6 * q^25 - 36 * q^26 + 8 * q^27 + 2 * q^29 + 8 * q^30 + 16 * q^31 - 8 * q^32 + 4 * q^34 + 2 * q^35 - 40 * q^36 + 10 * q^37 - 12 * q^38 - 24 * q^40 + 2 * q^43 - 24 * q^44 - 24 * q^45 - 16 * q^46 - 44 * q^48 + 70 * q^49 - 10 * q^50 + 8 * q^51 + 28 * q^52 - 30 * q^53 - 32 * q^54 + 6 * q^55 + 8 * q^56 - 76 * q^57 + 56 * q^58 + 2 * q^59 - 8 * q^60 + 30 * q^61 + 48 * q^62 + 12 * q^64 - 10 * q^65 + 80 * q^66 + 6 * q^67 - 36 * q^68 - 16 * q^69 - 18 * q^70 + 4 * q^72 - 36 * q^73 - 32 * q^74 - 2 * q^75 + 44 * q^76 - 2 * q^77 - 84 * q^78 - 40 * q^79 + 12 * q^80 - 82 * q^81 + 24 * q^82 + 10 * q^83 - 4 * q^84 + 32 * q^85 + 32 * q^86 - 4 * q^87 + 32 * q^88 + 18 * q^90 + 6 * q^91 - 92 * q^92 - 56 * q^93 - 20 * q^94 + 6 * q^95 + 16 * q^96 + 2 * q^98 - 34 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.33379	−	0.470109i	−0.943132	−	0.332417i
$2$	−1.33379	−	0.470109i	−0.943132	−	0.332417i
$3$	0.760413	−	0.760413i	0.439024	−	0.439024i	−0.452659	−	0.891684i	$-0.649525\pi$
$3$	0.760413	−	0.760413i	0.439024	−	0.439024i	0.891684	+	0.452659i	$0.149525\pi$
$4$	1.55800	+	1.25405i	0.778998	+	0.627027i
$5$	0.975010	−	2.01230i	0.436038	−	0.899928i
$5$	0.975010	−	2.01230i	0.436038	−	0.899928i
$6$	−1.37171	+	0.656755i	−0.559998	+	0.268119i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	−1.48850	−	2.40507i	−0.526263	−	0.850322i
$9$			1.84355i			0.614515i
$10$	−2.24646	+	2.22563i	−0.710393	+	0.703805i
$11$	2.93284	−	2.93284i	0.884283	−	0.884283i	−0.109683	−	0.993967i	$-0.534984\pi$
$11$	2.93284	−	2.93284i	0.884283	−	0.884283i	0.993967	+	0.109683i	$0.0349837\pi$
$12$	2.13832	−	0.231121i	0.617279	−	0.0667189i
$13$	0.294783	−	0.294783i	0.0817580	−	0.0817580i	−0.665045	−	0.746803i	$-0.731588\pi$
$13$	0.294783	−	0.294783i	0.0817580	−	0.0817580i	0.746803	+	0.665045i	$0.231588\pi$
$14$	−1.33379	−	0.470109i	−0.356471	−	0.125642i
$15$	−0.788769	−	2.27159i	−0.203659	−	0.586522i
$16$	0.854698	+	3.90762i	0.213675	+	0.976905i
$17$		−	2.07192i		−	0.502515i	−0.967920	−	0.251258i	$-0.919156\pi$
$17$		−	2.07192i		−	0.502515i	0.967920	−	0.251258i	$-0.0808441\pi$
$18$	0.866667	−	2.45890i	0.204275	−	0.579569i
$19$	0.507302	+	0.507302i	0.116383	+	0.116383i	0.762900	−	0.646517i	$-0.223775\pi$
$19$	0.507302	+	0.507302i	0.116383	+	0.116383i	−0.646517	+	0.762900i	$0.723775\pi$
$20$	4.04259	−	1.91244i	0.903952	−	0.427635i
$21$	0.760413	−	0.760413i	0.165936	−	0.165936i
$22$	−5.29054	+	2.53304i	−1.12795	+	0.540045i
$23$	1.56976			0.327319			0.163659	−	0.986517i	$-0.447670\pi$
$23$	1.56976			0.327319			0.163659	+	0.986517i	$0.447670\pi$
$24$	−2.96072	−	0.696975i	−0.604355	−	0.142269i
$25$	−3.09871	−	3.92403i	−0.619742	−	0.784805i
$26$	−0.531758	+	0.254598i	−0.104286	+	0.0499309i
$27$	3.68309	+	3.68309i	0.708812	+	0.708812i
$28$	1.55800	+	1.25405i	0.294433	+	0.236994i
$29$	4.08582	+	4.08582i	0.758718	+	0.758718i	0.976089	−	0.217371i	$-0.0697480\pi$
$29$	4.08582	+	4.08582i	0.758718	+	0.758718i	−0.217371	+	0.976089i	$0.569748\pi$
$30$	−0.0158409	+	3.40063i	−0.00289214	+	0.620868i
$31$	−6.78979			−1.21948			−0.609741	−	0.792601i	$-0.708727\pi$
$31$	−6.78979			−1.21948			−0.609741	+	0.792601i	$0.708727\pi$
$32$	0.697018	−	5.61375i	0.123217	−	0.992380i
$33$		−	4.46033i		−	0.776444i
$34$	−0.974030	+	2.76351i	−0.167045	+	0.473939i
$35$	0.975010	−	2.01230i	0.164807	−	0.340141i
$36$	−2.31190	+	2.87223i	−0.385317	+	0.478706i
$37$	−3.10623	−	3.10623i	−0.510661	−	0.510661i	0.404068	−	0.914729i	$-0.367596\pi$
$37$	−3.10623	−	3.10623i	−0.510661	−	0.510661i	−0.914729	+	0.404068i	$0.867596\pi$
$38$	−0.438148	−	0.915122i	−0.0710769	−	0.148452i
$39$		−	0.448313i		−	0.0717875i
$40$	−6.29103	+	0.650336i	−0.994699	+	0.102827i
$41$		−	7.00823i		−	1.09450i	−0.836969	−	0.547251i	$-0.815674\pi$
$41$		−	7.00823i		−	1.09450i	0.836969	−	0.547251i	$-0.184326\pi$
$42$	−1.37171	+	0.656755i	−0.211659	+	0.101339i
$43$	6.45884	+	6.45884i	0.984964	+	0.984964i	0.999889	−	0.0149248i	$-0.00475090\pi$
$43$	6.45884	+	6.45884i	0.984964	+	0.984964i	−0.0149248	+	0.999889i	$0.504751\pi$
$44$	8.24728	−	0.891410i	1.24332	−	0.134385i
$45$	3.70977	+	1.79747i	0.553020	+	0.267952i
$46$	−2.09374	−	0.737960i	−0.308705	−	0.108806i
$47$			1.80022i			0.262589i	0.991343	+	0.131294i	$0.0419133\pi$
$47$			1.80022i			0.262589i	−0.991343	+	0.131294i	$0.958087\pi$
$48$	3.62133	+	2.32148i	0.522694	+	0.335077i
$49$	1.00000			0.142857
$50$	2.28831	+	6.69056i	0.323616	+	0.946188i
$51$	−1.57552	−	1.57552i	−0.220617	−	0.220617i
$52$	0.828944	−	0.0895967i	0.114954	−	0.0124248i
$53$	−3.83361	−	3.83361i	−0.526587	−	0.526587i	0.392966	−	0.919553i	$-0.371449\pi$
$53$	−3.83361	−	3.83361i	−0.526587	−	0.526587i	−0.919553	+	0.392966i	$0.871449\pi$
$54$	−3.18102	−	6.64393i	−0.432882	−	0.904124i
$55$	−3.04220	−	8.76129i	−0.410211	−	1.18137i
$56$	−1.48850	−	2.40507i	−0.198909	−	0.321391i
$57$	0.771518			0.102190
$58$	−3.52885	−	7.37042i	−0.463361	−	0.967783i
$59$	0.471185	−	0.471185i	0.0613431	−	0.0613431i	−0.675770	−	0.737113i	$-0.736189\pi$
$59$	0.471185	−	0.471185i	0.0613431	−	0.0613431i	0.737113	+	0.675770i	$0.236189\pi$
$60$	1.61980	−	4.52828i	0.209115	−	0.584599i
$61$	−9.72941	−	9.72941i	−1.24572	−	1.24572i	−0.957591	−	0.288132i	$-0.906966\pi$
$61$	−9.72941	−	9.72941i	−1.24572	−	1.24572i	−0.288132	−	0.957591i	$-0.593034\pi$
$62$	9.05616	+	3.19194i	1.15013	+	0.405377i
$63$			1.84355i			0.232265i
$64$	−3.56875	+	7.15989i	−0.446094	+	0.894986i
$65$	−0.305776	−	0.880608i	−0.0379268	−	0.109226i
$66$	−2.09684	+	5.94915i	−0.258103	+	0.732289i
$67$	5.76866	−	5.76866i	0.704754	−	0.704754i	−0.260673	−	0.965427i	$-0.583945\pi$
$67$	5.76866	−	5.76866i	0.704754	−	0.704754i	0.965427	+	0.260673i	$0.0839445\pi$
$68$	2.59830	−	3.22805i	0.315091	−	0.391458i
$69$	1.19367	−	1.19367i	0.143701	−	0.143701i
$70$	−2.24646	+	2.22563i	−0.268503	+	0.266013i
$71$		−	3.67469i		−	0.436106i	−0.975937	−	0.218053i	$-0.930030\pi$
$71$		−	3.67469i		−	0.436106i	0.975937	−	0.218053i	$-0.0699705\pi$
$72$	4.43386	−	2.74411i	0.522535	−	0.323397i
$73$	−4.26700			−0.499414			−0.249707	−	0.968321i	$-0.580334\pi$
$73$	−4.26700			−0.499414			−0.249707	+	0.968321i	$0.580334\pi$
$74$	2.68279	+	5.60332i	0.311868	+	0.651373i
$75$	−5.34018	−	0.627580i	−0.616631	−	0.0724667i
$76$	0.154190	+	1.42656i	0.0176868	+	0.163638i
$77$	2.93284	−	2.93284i	0.334228	−	0.334228i
$78$	−0.210756	+	0.597956i	−0.0238634	+	0.0677052i
$79$	6.95379			0.782363			0.391181	−	0.920314i	$-0.372067\pi$
$79$	6.95379			0.782363			0.391181	+	0.920314i	$0.372067\pi$
$80$	8.69665	+	2.09006i	0.972315	+	0.233675i
$81$	0.0707067			0.00785630
$82$	−3.29463	+	9.34751i	−0.363831	+	1.03226i
$83$	−4.94383	+	4.94383i	−0.542656	+	0.542656i	−0.924307	−	0.381651i	$-0.875356\pi$
$83$	−4.94383	+	4.94383i	−0.542656	+	0.542656i	0.381651	+	0.924307i	$0.375356\pi$
$84$	2.13832	−	0.231121i	0.233310	−	0.0252174i
$85$	−4.16933	−	2.02015i	−0.452228	−	0.219116i
$86$	−5.57838	−	11.6511i	−0.601532	−	1.25637i
$87$	6.21383			0.666192
$88$	−11.4192	−	2.68816i	−1.21729	−	0.286559i
$89$		−	11.7925i		−	1.25000i	−0.780625	−	0.625000i	$-0.785099\pi$
$89$		−	11.7925i		−	1.25000i	0.780625	−	0.625000i	$-0.214901\pi$
$90$	−4.10304	−	4.14145i	−0.432499	−	0.436547i
$91$	0.294783	−	0.294783i	0.0309016	−	0.0309016i
$92$	2.44569	+	1.96857i	0.254980	+	0.205238i
$93$	−5.16304	+	5.16304i	−0.535382	+	0.535382i
$94$	0.846298	−	2.40111i	0.0872889	−	0.247656i
$95$	1.51547	−	0.526220i	0.155484	−	0.0539891i
$96$	−3.73874	−	4.79879i	−0.381584	−	0.489774i
$97$			16.6909i			1.69470i	0.531035	+	0.847350i	$0.321803\pi$
$97$			16.6909i			1.69470i	−0.531035	+	0.847350i	$0.678197\pi$
$98$	−1.33379	−	0.470109i	−0.134733	−	0.0474882i
$99$	5.40681	+	5.40681i	0.543405	+	0.543405i
$100$	0.0931624	−	9.99957i	0.00931624	−	0.999957i
$101$	−8.61074	+	8.61074i	−0.856800	+	0.856800i	−0.990960	−	0.134159i	$-0.957167\pi$
$101$	−8.61074	+	8.61074i	−0.856800	+	0.856800i	0.134159	+	0.990960i	$0.457167\pi$
$102$	1.36075	+	2.84207i	0.134734	+	0.281407i
$103$	1.41797			0.139717			0.0698585	−	0.997557i	$-0.477745\pi$
$103$	1.41797			0.139717			0.0698585	+	0.997557i	$0.477745\pi$
$104$	−1.14776	−	0.270190i	−0.112547	−	0.0264944i
$105$	−0.788769	−	2.27159i	−0.0769760	−	0.221684i
$106$	3.31102	+	6.91545i	0.321595	+	0.671688i
$107$	11.1412	+	11.1412i	1.07706	+	1.07706i	0.996771	+	0.0802925i	$0.0255854\pi$
$107$	11.1412	+	11.1412i	1.07706	+	1.07706i	0.0802925	+	0.996771i	$0.474415\pi$
$108$	1.11944	+	10.3570i	0.107719	+	0.996606i
$109$	1.65354	+	1.65354i	0.158380	+	0.158380i	0.781849	−	0.623468i	$-0.214277\pi$
$109$	1.65354	+	1.65354i	0.158380	+	0.158380i	−0.623468	+	0.781849i	$0.714277\pi$
$110$	−0.0610967	+	13.1159i	−0.00582534	+	1.25055i
$111$	−4.72403			−0.448385
$112$	0.854698	+	3.90762i	0.0807614	+	0.369235i
$113$			12.8034i			1.20445i	0.798327	+	0.602224i	$0.205718\pi$
$113$			12.8034i			1.20445i	−0.798327	+	0.602224i	$0.794282\pi$
$114$	−1.02904	−	0.362698i	−0.0963788	−	0.0339697i
$115$	1.53054	−	3.15884i	0.142723	−	0.294563i
$116$	1.24185	+	11.4895i	0.115303	+	1.06678i
$117$	0.543445	+	0.543445i	0.0502415	+	0.0502415i
$118$	−0.849971	+	0.406954i	−0.0782462	+	0.0374632i
$119$		−	2.07192i		−	0.189933i
$120$	−4.28926	+	5.27830i	−0.391554	+	0.481841i
$121$		−	6.20305i		−	0.563913i
$122$	8.40311	+	17.5509i	0.760782	+	1.58898i
$123$	−5.32915	−	5.32915i	−0.480513	−	0.480513i
$124$	−10.5785	−	8.51476i	−0.949974	−	0.764648i
$125$	−10.9176	+	2.40958i	−0.976500	+	0.215519i
$126$	0.866667	−	2.45890i	0.0772088	−	0.219057i
$127$			12.0046i			1.06523i	0.846357	+	0.532616i	$0.178791\pi$
$127$			12.0046i			1.06523i	−0.846357	+	0.532616i	$0.821209\pi$
$128$	8.12589	−	7.87209i	0.718234	−	0.695801i
$129$	9.82277			0.864846
$130$	−0.00614090	+	1.31829i	−0.000538593	+	0.115622i
$131$	14.6663	+	14.6663i	1.28140	+	1.28140i	0.939872	+	0.341526i	$0.110944\pi$
$131$	14.6663	+	14.6663i	1.28140	+	1.28140i	0.341526	+	0.939872i	$0.389056\pi$
$132$	5.59349	−	6.94917i	0.486851	−	0.604848i
$133$	0.507302	+	0.507302i	0.0439887	+	0.0439887i
$134$	−10.4061	+	4.98229i	−0.898949	+	0.430404i
$135$	11.0025	−	3.82044i	0.946948	−	0.328811i
$136$	−4.98313	+	3.08405i	−0.427300	+	0.264455i
$137$	4.67909			0.399762			0.199881	−	0.979820i	$-0.435944\pi$
$137$	4.67909			0.399762			0.199881	+	0.979820i	$0.435944\pi$
$138$	−2.15326	+	1.03095i	−0.183298	+	0.0877603i
$139$	−4.39777	+	4.39777i	−0.373014	+	0.373014i	−0.868574	−	0.495560i	$-0.834963\pi$
$139$	−4.39777	+	4.39777i	−0.373014	+	0.373014i	0.495560	+	0.868574i	$0.334963\pi$
$140$	4.04259	−	1.91244i	0.341662	−	0.161631i
$141$	1.36891	+	1.36891i	0.115283	+	0.115283i
$142$	−1.72750	+	4.90127i	−0.144969	+	0.411305i
$143$		−	1.72910i		−	0.144594i
$144$	−7.20387	+	1.57568i	−0.600323	+	0.131306i
$145$	12.2056	−	4.23819i	1.01362	−	0.351962i
$146$	5.69128	+	2.00595i	0.471014	+	0.166014i
$147$	0.760413	−	0.760413i	0.0627178	−	0.0627178i
$148$	−0.944112	−	8.73487i	−0.0776055	−	0.718002i
$149$	−4.66753	+	4.66753i	−0.382379	+	0.382379i	−0.871959	−	0.489579i	$-0.837150\pi$
$149$	−4.66753	+	4.66753i	−0.382379	+	0.382379i	0.489579	+	0.871959i	$0.337150\pi$
$150$	6.82765	+	3.34753i	0.557475	+	0.273324i
$151$		−	0.829596i		−	0.0675115i	−0.999430	−	0.0337558i	$-0.989253\pi$
$151$		−	0.829596i		−	0.0675115i	0.999430	−	0.0337558i	$-0.0107468\pi$
$152$	0.464980	−	1.97522i	0.0377149	−	0.160211i
$153$	3.81968			0.308803
$154$	−5.29054	+	2.53304i	−0.426324	+	0.204118i
$155$	−6.62011	+	13.6631i	−0.531740	+	1.09745i
$156$	0.562209	−	0.698470i	0.0450127	−	0.0559223i
$157$	−5.27946	+	5.27946i	−0.421347	+	0.421347i	−0.885667	−	0.464321i	$-0.846299\pi$
$157$	−5.27946	+	5.27946i	−0.421347	+	0.421347i	0.464321	+	0.885667i	$0.346299\pi$
$158$	−9.27490	−	3.26904i	−0.737872	−	0.260071i
$159$	−5.83025			−0.462369
$160$	−10.6170	−	6.87607i	−0.839344	−	0.543601i
$161$	1.56976			0.123715
$162$	−0.0943079	−	0.0332398i	−0.00740953	−	0.00261157i
$163$	−13.2969	+	13.2969i	−1.04149	+	1.04149i	−0.0423903	+	0.999101i	$0.513497\pi$
$163$	−13.2969	+	13.2969i	−1.04149	+	1.04149i	−0.999101	+	0.0423903i	$0.986503\pi$
$164$	8.78870	−	10.9188i	0.686282	−	0.852614i
$165$	−8.97553	−	4.34887i	−0.698744	−	0.338559i
$166$	8.91817	−	4.26990i	0.692184	−	0.331408i
$167$	10.3072			0.797595			0.398797	−	0.917039i	$-0.369428\pi$
$167$	10.3072			0.797595			0.398797	+	0.917039i	$0.369428\pi$
$168$	−2.96072	−	0.696975i	−0.228425	−	0.0537728i
$169$			12.8262i			0.986631i
$170$	4.61133	+	4.65449i	0.353673	+	0.356983i
$171$	−0.935235	+	0.935235i	−0.0715192	+	0.0715192i
$172$	1.96311	+	18.1626i	0.149686	+	1.38488i
$173$	17.4895	−	17.4895i	1.32970	−	1.32970i	0.424080	−	0.905625i	$-0.360598\pi$
$173$	17.4895	−	17.4895i	1.32970	−	1.32970i	0.905625	−	0.424080i	$-0.139402\pi$
$174$	−8.28794	−	2.92117i	−0.628307	−	0.221454i
$175$	−3.09871	−	3.92403i	−0.234241	−	0.296629i
$176$	13.9671	+	8.95371i	1.05281	+	0.674912i
$177$		−	0.716591i		−	0.0538623i
$178$	−5.54375	+	15.7287i	−0.415521	+	1.17892i
$179$	14.3668	+	14.3668i	1.07382	+	1.07382i	0.997048	+	0.0767744i	$0.0244621\pi$
$179$	14.3668	+	14.3668i	1.07382	+	1.07382i	0.0767744	+	0.997048i	$0.475538\pi$
$180$	3.52567	+	7.45270i	0.262788	+	0.555492i
$181$	−6.28644	+	6.28644i	−0.467268	+	0.467268i	−0.901028	−	0.433761i	$-0.857186\pi$
$181$	−6.28644	+	6.28644i	−0.467268	+	0.467268i	0.433761	+	0.901028i	$0.357186\pi$
$182$	−0.531758	+	0.254598i	−0.0394166	+	0.0188721i
$183$	−14.7967			−1.09381
$184$	−2.33659	−	3.77540i	−0.172256	−	0.278326i
$185$	−9.27927	+	3.22206i	−0.682226	+	0.236891i
$186$	9.31361	−	4.45922i	0.682907	−	0.326966i
$187$	−6.07661	−	6.07661i	−0.444366	−	0.444366i
$188$	−2.25757	+	2.80473i	−0.164650	+	0.204556i
$189$	3.68309	+	3.68309i	0.267906	+	0.267906i
$190$	−2.26870	−	0.0105681i	−0.164589	−	0.000766691i
$191$	−24.7356			−1.78981			−0.894903	−	0.446261i	$-0.852755\pi$
$191$	−24.7356			−1.78981			−0.894903	+	0.446261i	$0.852755\pi$
$192$	2.73075	+	8.15819i	0.197075	+	0.588767i
$193$		−	10.5455i		−	0.759079i	−0.925175	−	0.379540i	$-0.876082\pi$
$193$		−	10.5455i		−	0.759079i	0.925175	−	0.379540i	$-0.123918\pi$
$194$	7.84652	−	22.2621i	0.563347	−	1.59833i
$195$	−0.902141	−	0.437110i	−0.0646037	−	0.0313021i
$196$	1.55800	+	1.25405i	0.111285	+	0.0895753i
$197$	−17.9427	−	17.9427i	−1.27836	−	1.27836i	−0.941583	−	0.336782i	$-0.890662\pi$
$197$	−17.9427	−	17.9427i	−1.27836	−	1.27836i	−0.336782	−	0.941583i	$-0.609338\pi$
$198$	−4.66977	−	9.75335i	−0.331866	−	0.693140i
$199$			16.6288i			1.17878i	0.807847	+	0.589392i	$0.200633\pi$
$199$			16.6288i			1.17878i	−0.807847	+	0.589392i	$0.799367\pi$
$200$	−4.82514	+	13.2935i	−0.341189	+	0.939995i
$201$		−	8.77312i		−	0.618808i
$202$	15.5329	−	7.43694i	1.09289	−	0.523261i
$203$	4.08582	+	4.08582i	0.286769	+	0.286769i
$204$	−0.478865	−	4.43043i	−0.0335273	−	0.310192i
$205$	−14.1027	−	6.83309i	−0.984973	−	0.477244i
$206$	−1.89128	−	0.666602i	−0.131772	−	0.0464443i
$207$			2.89393i			0.201142i
$208$	1.40385	+	0.899948i	0.0973394	+	0.0624002i
$209$	2.97567			0.205831
$210$	−0.0158409	+	3.40063i	−0.00109313	+	0.234666i
$211$	15.3228	+	15.3228i	1.05486	+	1.05486i	0.998405	+	0.0564580i	$0.0179807\pi$
$211$	15.3228	+	15.3228i	1.05486	+	1.05486i	0.0564580	+	0.998405i	$0.482019\pi$
$212$	−1.16519	−	10.7803i	−0.0800258	−	0.740394i
$213$	−2.79428	−	2.79428i	−0.191461	−	0.191461i
$214$	−9.62248	−	20.0977i	−0.657779	−	1.37385i
$215$	19.2946	−	6.69970i	1.31588	−	0.456916i
$216$	3.37583	−	14.3404i	0.229696	−	0.975739i
$217$	−6.78979			−0.460921
$218$	−1.42813	−	2.98281i	−0.0967252	−	0.202022i
$219$	−3.24468	+	3.24468i	−0.219255	+	0.219255i
$220$	6.24739	−	17.4651i	0.421199	−	1.17750i
$221$	−0.610767	−	0.610767i	−0.0410847	−	0.0410847i
$222$	6.30087	+	2.22081i	0.422887	+	0.149051i
$223$		−	12.8932i		−	0.863391i	−0.902019	−	0.431695i	$-0.857916\pi$
$223$		−	12.8932i		−	0.863391i	0.902019	−	0.431695i	$-0.142084\pi$
$224$	0.697018	−	5.61375i	0.0465715	−	0.375084i
$225$	7.23412	−	5.71261i	0.482275	−	0.380841i
$226$	6.01902	−	17.0771i	0.400379	−	1.13595i
$227$	5.59091	−	5.59091i	0.371082	−	0.371082i	−0.496790	−	0.867871i	$-0.665488\pi$
$227$	5.59091	−	5.59091i	0.371082	−	0.371082i	0.867871	+	0.496790i	$0.165488\pi$
$228$	1.20202	+	0.967525i	0.0796058	+	0.0640759i
$229$	−8.39018	+	8.39018i	−0.554439	+	0.554439i	−0.927719	−	0.373280i	$-0.878233\pi$
$229$	−8.39018	+	8.39018i	−0.554439	+	0.554439i	0.373280	+	0.927719i	$0.378233\pi$
$230$	−3.52641	+	3.49371i	−0.232525	+	0.230369i
$231$		−	4.46033i		−	0.293468i
$232$	3.74496	−	15.9084i	0.245869	−	1.04444i
$233$	7.16196			0.469196			0.234598	−	0.972093i	$-0.424623\pi$
$233$	7.16196			0.469196			0.234598	+	0.972093i	$0.424623\pi$
$234$	−0.469364	−	0.980321i	−0.0306833	−	0.0640856i
$235$	3.62258	+	1.75523i	0.236311	+	0.114498i
$236$	1.32500	−	0.143213i	0.0862499	−	0.00932236i
$237$	5.28775	−	5.28775i	0.343476	−	0.343476i
$238$	−0.974030	+	2.76351i	−0.0631370	+	0.179132i
$239$	−18.8367			−1.21845			−0.609224	−	0.792998i	$-0.708519\pi$
$239$	−18.8367			−1.21845			−0.609224	+	0.792998i	$0.708519\pi$
$240$	8.20235	−	5.02373i	0.529459	−	0.324281i
$241$	11.2711			0.726035			0.363017	−	0.931782i	$-0.381747\pi$
$241$	11.2711			0.726035			0.363017	+	0.931782i	$0.381747\pi$
$242$	−2.91611	+	8.27357i	−0.187454	+	0.531845i
$243$	−10.9955	+	10.9955i	−0.705363	+	0.705363i
$244$	−2.95717	−	27.3596i	−0.189313	−	1.75152i
$245$	0.975010	−	2.01230i	0.0622911	−	0.128561i
$246$	4.60269	+	9.61325i	0.293457	+	0.612918i
$247$	0.299088			0.0190305
$248$	10.1066	+	16.3299i	0.641769	+	1.03695i
$249$			7.51870i			0.476478i
$250$	15.6946	+	1.91859i	0.992611	+	0.121342i
$251$	−0.868041	+	0.868041i	−0.0547902	+	0.0547902i	−0.733971	−	0.679181i	$-0.762335\pi$
$251$	−0.868041	+	0.868041i	−0.0547902	+	0.0547902i	0.679181	+	0.733971i	$0.262335\pi$
$252$	−2.31190	+	2.87223i	−0.145636	+	0.180934i
$253$	4.60386	−	4.60386i	0.289442	−	0.289442i
$254$	5.64345	−	16.0116i	0.354101	−	1.00465i
$255$	−4.70656	+	1.63427i	−0.294736	+	0.102342i
$256$	−14.5390	+	6.67967i	−0.908686	+	0.417480i
$257$		−	16.2365i		−	1.01281i	−0.862297	−	0.506403i	$-0.830975\pi$
$257$		−	16.2365i		−	1.01281i	0.862297	−	0.506403i	$-0.169025\pi$
$258$	−13.1015	−	4.61777i	−0.815665	−	0.287490i
$259$	−3.10623	−	3.10623i	−0.193012	−	0.193012i
$260$	0.627933	−	1.75544i	0.0389427	−	0.108868i
$261$	−7.53240	+	7.53240i	−0.466244	+	0.466244i
$262$	−12.6670	−	26.4565i	−0.782570	−	1.63449i
$263$	−4.32524			−0.266705			−0.133353	−	0.991069i	$-0.542574\pi$
$263$	−4.32524			−0.266705			−0.133353	+	0.991069i	$0.542574\pi$
$264$	−10.7274	+	6.63919i	−0.660227	+	0.408614i
$265$	−11.4522	+	3.97657i	−0.703502	+	0.244279i
$266$	−0.438148	−	0.915122i	−0.0268646	−	0.0561097i
$267$	−8.96715	−	8.96715i	−0.548780	−	0.548780i
$268$	16.2218	−	1.75334i	0.990901	−	0.107102i
$269$	5.42333	+	5.42333i	0.330667	+	0.330667i	0.852840	−	0.522173i	$-0.174878\pi$
$269$	5.42333	+	5.42333i	0.330667	+	0.330667i	−0.522173	+	0.852840i	$0.674878\pi$
$270$	−16.4711	−	0.0767261i	−1.00240	−	0.00466940i
$271$	13.7007			0.832258			0.416129	−	0.909306i	$-0.363386\pi$
$271$	13.7007			0.832258			0.416129	+	0.909306i	$0.363386\pi$
$272$	8.09629	−	1.77087i	0.490910	−	0.107375i
$273$		−	0.448313i		−	0.0271331i
$274$	−6.24093	−	2.19968i	−0.377028	−	0.132888i
$275$	−20.5965	−	2.42051i	−1.24202	−	0.145962i
$276$	3.35666	−	0.362806i	0.202047	−	0.0218383i
$277$	4.13765	+	4.13765i	0.248607	+	0.248607i	0.820399	−	0.571792i	$-0.193751\pi$
$277$	4.13765	+	4.13765i	0.248607	+	0.248607i	−0.571792	+	0.820399i	$0.693751\pi$
$278$	7.93314	−	3.79828i	0.475798	−	0.227805i
$279$		−	12.5173i		−	0.749390i
$280$	−6.29103	+	0.650336i	−0.375961	+	0.0388650i
$281$		−	17.9639i		−	1.07164i	−0.844332	−	0.535820i	$-0.820003\pi$
$281$		−	17.9639i		−	1.07164i	0.844332	−	0.535820i	$-0.179997\pi$
$282$	−1.18230	−	2.46937i	−0.0704050	−	0.147049i
$283$	−21.2046	−	21.2046i	−1.26048	−	1.26048i	−0.950860	−	0.309621i	$-0.899798\pi$
$283$	−21.2046	−	21.2046i	−1.26048	−	1.26048i	−0.309621	−	0.950860i	$-0.600202\pi$
$284$	4.60826	−	5.72515i	0.273450	−	0.339725i
$285$	0.752238	−	1.55253i	0.0445587	−	0.0919638i
$286$	−0.812865	+	2.30626i	−0.0480657	+	0.136372i
$287$		−	7.00823i		−	0.413683i
$288$	10.3492	+	1.28498i	0.609832	+	0.0757184i
$289$	12.7071			0.747478
$290$	−18.2722	−	0.0851157i	−1.07298	−	0.00499817i
$291$	12.6919	+	12.6919i	0.744014	+	0.744014i
$292$	−6.64796	−	5.35105i	−0.389043	−	0.313146i
$293$	17.7392	+	17.7392i	1.03633	+	1.03633i	0.999315	+	0.0370182i	$0.0117859\pi$
$293$	17.7392	+	17.7392i	1.03633	+	1.03633i	0.0370182	+	0.999315i	$0.488214\pi$
$294$	−1.37171	+	0.656755i	−0.0799996	+	0.0383027i
$295$	−0.488756	−	1.40758i	−0.0284565	−	0.0819523i
$296$	−2.84709	+	12.0943i	−0.165484	+	0.702968i
$297$	21.6038			1.25358
$298$	8.41976	−	4.03126i	0.487744	−	0.233525i
$299$	0.462739	−	0.462739i	0.0267609	−	0.0267609i
$300$	−7.53296	−	7.67464i	−0.434915	−	0.443095i
$301$	6.45884	+	6.45884i	0.372281	+	0.372281i
$302$	−0.390000	+	1.10651i	−0.0224420	+	0.0636723i
$303$			13.0954i			0.752313i
$304$	−1.54875	+	2.41593i	−0.0888271	+	0.138563i
$305$	−29.0648	+	10.0922i	−1.66424	+	0.577879i
$306$	−5.09466	−	1.79567i	−0.291242	−	0.102651i
$307$	5.05259	−	5.05259i	0.288366	−	0.288366i	−0.548068	−	0.836434i	$-0.684636\pi$
$307$	5.05259	−	5.05259i	0.288366	−	0.288366i	0.836434	+	0.548068i	$0.184636\pi$
$308$	8.24728	−	0.891410i	0.469932	−	0.0507928i
$309$	1.07824	−	1.07824i	0.0613392	−	0.0613392i
$310$	15.2530	−	15.1115i	0.866311	−	0.858278i
$311$		−	11.4546i		−	0.649532i	−0.945794	−	0.324766i	$-0.894714\pi$
$311$		−	11.4546i		−	0.649532i	0.945794	−	0.324766i	$-0.105286\pi$
$312$	−1.07823	+	0.667313i	−0.0610425	+	0.0377792i
$313$	−2.36136			−0.133472			−0.0667361	−	0.997771i	$-0.521259\pi$
$313$	−2.36136			−0.133472			−0.0667361	+	0.997771i	$0.521259\pi$
$314$	9.52361	−	4.55977i	0.537448	−	0.257323i
$315$	3.70977	+	1.79747i	0.209022	+	0.101276i
$316$	10.8340	+	8.72043i	0.609459	+	0.490562i
$317$	−18.1115	+	18.1115i	−1.01724	+	1.01724i	−0.0173945	+	0.999849i	$0.505537\pi$
$317$	−18.1115	+	18.1115i	−1.01724	+	1.01724i	−0.999849	+	0.0173945i	$0.994463\pi$
$318$	7.77634	+	2.74085i	0.436075	+	0.153699i
$319$	23.9661			1.34184
$320$	10.9283	+	14.1624i	0.610910	+	0.791700i
$321$	16.9439			0.945715
$322$	−2.09374	−	0.737960i	−0.116679	−	0.0411249i
$323$	1.05109	−	1.05109i	0.0584843	−	0.0584843i
$324$	0.110161	+	0.0886700i	0.00612004	+	0.00492611i
$325$	−2.07018	−	0.243289i	−0.114833	−	0.0134952i
$326$	23.9862	−	11.4843i	1.32847	−	0.636055i
$327$	2.51474			0.139066
$328$	−16.8553	+	10.4317i	−0.930678	+	0.575996i
$329$			1.80022i			0.0992491i
$330$	9.92704	+	10.0200i	0.546465	+	0.551580i
$331$	15.6731	−	15.6731i	0.861470	−	0.861470i	−0.130039	−	0.991509i	$-0.541510\pi$
$331$	15.6731	−	15.6731i	0.861470	−	0.861470i	0.991509	+	0.130039i	$0.0415101\pi$
$332$	−13.9023	+	1.50264i	−0.762987	+	0.0824678i
$333$	5.72647	−	5.72647i	0.313809	−	0.313809i
$334$	−13.7476	−	4.84551i	−0.752238	−	0.265134i
$335$	−5.98378	−	17.2328i	−0.326929	−	0.941527i
$336$	3.62133	+	2.32148i	0.197560	+	0.126647i
$337$			32.2576i			1.75718i	0.477573	+	0.878592i	$0.341517\pi$
$337$			32.2576i			1.75718i	−0.477573	+	0.878592i	$0.658483\pi$
$338$	6.02971	−	17.1075i	0.327973	−	0.930524i
$339$	9.73591	+	9.73591i	0.528782	+	0.528782i
$340$	−3.96243	−	8.37595i	−0.214893	−	0.454250i
$341$	−19.9133	+	19.9133i	−1.07837	+	1.07837i
$342$	1.68707	−	0.807745i	0.0912263	−	0.0436778i
$343$	1.00000			0.0539949
$344$	5.92001	−	25.1479i	0.319186	−	1.35589i
$345$	−1.23818	−	3.56586i	−0.0666615	−	0.191979i
$346$	−31.5494	+	15.1054i	−1.69610	+	0.812071i
$347$	4.86000	+	4.86000i	0.260898	+	0.260898i	0.825419	−	0.564521i	$-0.190939\pi$
$347$	4.86000	+	4.86000i	0.260898	+	0.260898i	−0.564521	+	0.825419i	$0.690939\pi$
$348$	9.68111	+	7.79247i	0.518962	+	0.417720i
$349$	4.58622	+	4.58622i	0.245495	+	0.245495i	0.819119	−	0.573624i	$-0.194463\pi$
$349$	4.58622	+	4.58622i	0.245495	+	0.245495i	−0.573624	+	0.819119i	$0.694463\pi$
$350$	2.28831	+	6.69056i	0.122315	+	0.357626i
$351$	2.17142			0.115902
$352$	−14.4200	−	18.5084i	−0.768586	−	0.986503i
$353$		−	28.0009i		−	1.49034i	−0.666875	−	0.745170i	$-0.732369\pi$
$353$		−	28.0009i		−	1.49034i	0.666875	−	0.745170i	$-0.267631\pi$
$354$	−0.336876	+	0.955782i	−0.0179047	+	0.0507992i
$355$	−7.39458	−	3.58286i	−0.392464	−	0.190158i
$356$	14.7884	−	18.3726i	0.783783	−	0.973747i
$357$	−1.57552	−	1.57552i	−0.0833852	−	0.0833852i
$358$	−12.4083	−	25.9162i	−0.655800	−	1.36971i
$359$			15.5305i			0.819666i	0.912161	+	0.409833i	$0.134413\pi$
$359$			15.5305i			0.819666i	−0.912161	+	0.409833i	$0.865587\pi$
$360$	−1.19892	−	11.5978i	−0.0631889	−	0.611258i
$361$		−	18.4853i		−	0.972910i
$362$	11.3401	−	5.42949i	0.596023	−	0.285367i
$363$	−4.71688	−	4.71688i	−0.247572	−	0.247572i
$364$	0.828944	−	0.0895967i	0.0434484	−	0.00469614i
$365$	−4.16037	+	8.58649i	−0.217764	+	0.449437i
$366$	19.7357	+	6.95607i	1.03160	+	0.363600i
$367$		−	25.8255i		−	1.34808i	−0.738695	−	0.674040i	$-0.764558\pi$
$367$		−	25.8255i		−	1.34808i	0.738695	−	0.674040i	$-0.235442\pi$
$368$	1.34168	+	6.13404i	0.0699397	+	0.319759i
$369$	12.9200			0.672588
$370$	13.8913	+	0.0647088i	0.722176	+	0.00336405i
$371$	−3.83361	−	3.83361i	−0.199031	−	0.199031i
$372$	−14.5187	+	1.56926i	−0.752761	+	0.0813625i
$373$	13.6446	+	13.6446i	0.706490	+	0.706490i	0.965795	−	0.259305i	$-0.0834935\pi$
$373$	13.6446	+	13.6446i	0.706490	+	0.706490i	−0.259305	+	0.965795i	$0.583494\pi$
$374$	5.24826	+	10.9616i	0.271381	+	0.566811i
$375$	−6.46961	+	10.1342i	−0.334089	+	0.523325i
$376$	4.32965	−	2.67962i	0.223285	−	0.138191i
$377$	2.40886			0.124063
$378$	−3.18102	−	6.64393i	−0.163614	−	0.341727i
$379$	−13.7497	+	13.7497i	−0.706274	+	0.706274i	−0.965750	−	0.259475i	$-0.916450\pi$
$379$	−13.7497	+	13.7497i	−0.706274	+	0.706274i	0.259475	+	0.965750i	$0.416450\pi$
$380$	3.02100	+	1.08063i	0.154974	+	0.0554352i
$381$	9.12841	+	9.12841i	0.467663	+	0.467663i
$382$	32.9921	+	11.6284i	1.68802	+	0.594962i
$383$		−	20.9654i		−	1.07128i	−0.844446	−	0.535640i	$-0.820070\pi$
$383$		−	20.9654i		−	1.07128i	0.844446	−	0.535640i	$-0.179930\pi$
$384$	0.192991	−	12.1651i	0.00984851	−	0.620796i
$385$	−3.04220	−	8.76129i	−0.155045	−	0.446517i
$386$	−4.95752	+	14.0654i	−0.252331	+	0.715912i
$387$	−11.9072	+	11.9072i	−0.605275	+	0.605275i
$388$	−20.9312	+	26.0043i	−1.06262	+	1.32017i
$389$	−9.41835	+	9.41835i	−0.477529	+	0.477529i	−0.904341	−	0.426811i	$-0.859637\pi$
$389$	−9.41835	+	9.41835i	−0.477529	+	0.477529i	0.426811	+	0.904341i	$0.359637\pi$
$390$	0.997778	+	1.00712i	0.0505245	+	0.0509974i
$391$		−	3.25243i		−	0.164483i
$392$	−1.48850	−	2.40507i	−0.0751805	−	0.121475i
$393$	22.3048			1.12513
$394$	15.4968	+	32.3668i	0.780717	+	1.63062i
$395$	6.78001	−	13.9931i	0.341140	−	0.704070i
$396$	1.64336	+	15.2042i	0.0825817	+	0.764041i
$397$	−15.3498	+	15.3498i	−0.770385	+	0.770385i	−0.978174	−	0.207789i	$-0.933373\pi$
$397$	−15.3498	+	15.3498i	−0.770385	+	0.770385i	0.207789	+	0.978174i	$0.433373\pi$
$398$	7.81734	−	22.1793i	0.391848	−	1.11175i
$399$	0.771518			0.0386242
$400$	12.6851	−	15.4624i	0.634257	−	0.773122i
$401$	−28.0499			−1.40074			−0.700372	−	0.713778i	$-0.746983\pi$
$401$	−28.0499			−1.40074			−0.700372	+	0.713778i	$0.746983\pi$
$402$	−4.12432	+	11.7015i	−0.205703	+	0.583618i
$403$	−2.00151	+	2.00151i	−0.0997024	+	0.0997024i
$404$	−24.2138	+	2.61716i	−1.20468	+	0.130209i
$405$	0.0689397	−	0.142283i	0.00342564	−	0.00707011i
$406$	−3.52885	−	7.37042i	−0.175134	−	0.365788i
$407$	−18.2201			−0.903138
$408$	−1.44408	+	6.13439i	−0.0714926	+	0.303697i
$409$			23.9892i			1.18619i	0.805133	+	0.593094i	$0.202094\pi$
$409$			23.9892i			1.18619i	−0.805133	+	0.593094i	$0.797906\pi$
$410$	15.5977	+	15.7437i	0.770316	+	0.777526i
$411$	3.55804	−	3.55804i	0.175505	−	0.175505i
$412$	2.20919	+	1.77821i	0.108839	+	0.0876063i
$413$	0.471185	−	0.471185i	0.0231855	−	0.0231855i
$414$	1.36046	−	3.85990i	0.0668631	−	0.189704i
$415$	5.12819	+	14.7688i	0.251733	+	0.724970i
$416$	−1.44937	−	1.86030i	−0.0710611	−	0.0912089i
$417$			6.68824i			0.327525i
$418$	−3.96892	−	1.39889i	−0.194126	−	0.0684218i
$419$	−16.1395	−	16.1395i	−0.788464	−	0.788464i	0.192778	−	0.981242i	$-0.438250\pi$
$419$	−16.1395	−	16.1395i	−0.788464	−	0.788464i	−0.981242	+	0.192778i	$0.938250\pi$
$420$	1.61980	−	4.52828i	0.0790379	−	0.220958i
$421$	−3.03744	+	3.03744i	−0.148036	+	0.148036i	−0.777240	−	0.629204i	$-0.783381\pi$
$421$	−3.03744	+	3.03744i	−0.148036	+	0.148036i	0.629204	+	0.777240i	$0.283381\pi$
$422$	−13.2340	−	27.6407i	−0.644221	−	1.34553i
$423$	−3.31878			−0.161365
$424$	−3.51379	+	14.9264i	−0.170645	+	0.724892i
$425$	−8.13028	+	6.42029i	−0.394377	+	0.311430i
$426$	2.41337	+	5.04060i	0.116928	+	0.244218i
$427$	−9.72941	−	9.72941i	−0.470839	−	0.470839i
$428$	3.38628	+	31.3297i	0.163682	+	1.51438i
$429$	−1.31483	−	1.31483i	−0.0634805	−	0.0634805i
$430$	−28.8845	−	0.134550i	−1.39293	−	0.00648859i
$431$	−11.6832			−0.562760			−0.281380	−	0.959596i	$-0.590792\pi$
$431$	−11.6832			−0.562760			−0.281380	+	0.959596i	$0.590792\pi$
$432$	−11.2442	+	17.5401i	−0.540986	+	0.843897i
$433$			3.60891i			0.173433i	0.996233	+	0.0867165i	$0.0276374\pi$
$433$			3.60891i			0.173433i	−0.996233	+	0.0867165i	$0.972363\pi$
$434$	9.05616	+	3.19194i	0.434709	+	0.153218i
$435$	6.05854	−	12.5041i	0.290485	−	0.599525i
$436$	0.502579	+	4.64983i	0.0240691	+	0.222686i
$437$	0.796345	+	0.796345i	0.0380943	+	0.0380943i
$438$	5.85308	−	2.80237i	0.279671	−	0.133902i
$439$		−	13.5536i		−	0.646880i	−0.946249	−	0.323440i	$-0.895161\pi$
$439$		−	13.5536i		−	0.646880i	0.946249	−	0.323440i	$-0.104839\pi$
$440$	−16.5432	+	20.3579i	−0.788667	+	0.970524i
$441$			1.84355i			0.0877879i
$442$	0.527509	+	1.10176i	0.0250910	+	0.0524055i
$443$	−11.2564	−	11.2564i	−0.534806	−	0.534806i	0.387192	−	0.921999i	$-0.373445\pi$
$443$	−11.2564	−	11.2564i	−0.534806	−	0.534806i	−0.921999	+	0.387192i	$0.873445\pi$
$444$	−7.36002	−	5.92419i	−0.349291	−	0.281150i
$445$	−23.7300	−	11.4978i	−1.12491	−	0.545047i
$446$	−6.06120	+	17.1968i	−0.287006	+	0.814292i
$447$			7.09851i			0.335748i
$448$	−3.56875	+	7.15989i	−0.168608	+	0.338273i
$449$	6.54753			0.308997			0.154498	−	0.987993i	$-0.450624\pi$
$449$	6.54753			0.308997			0.154498	+	0.987993i	$0.450624\pi$
$450$	−12.3344	+	4.21861i	−0.581447	+	0.198867i
$451$	−20.5540	−	20.5540i	−0.967849	−	0.967849i
$452$	−16.0562	+	19.9477i	−0.755221	+	0.938262i
$453$	−0.630835	−	0.630835i	−0.0296392	−	0.0296392i
$454$	−10.0854	+	4.82876i	−0.473333	+	0.226625i
$455$	−0.305776	−	0.880608i	−0.0143350	−	0.0412835i
$456$	−1.14840	−	1.85556i	−0.0537789	−	0.0868944i
$457$	−25.2927			−1.18314			−0.591572	−	0.806252i	$-0.701492\pi$
$457$	−25.2927			−1.18314			−0.591572	+	0.806252i	$0.701492\pi$
$458$	15.1350	−	7.24645i	0.707214	−	0.338604i
$459$	7.63109	−	7.63109i	0.356189	−	0.356189i
$460$	6.34592	−	3.00208i	0.295880	−	0.139973i
$461$	23.6682	+	23.6682i	1.10234	+	1.10234i	0.994128	+	0.108211i	$0.0345124\pi$
$461$	23.6682	+	23.6682i	1.10234	+	1.10234i	0.108211	+	0.994128i	$0.465488\pi$
$462$	−2.09684	+	5.94915i	−0.0975539	+	0.276779i
$463$			25.2801i			1.17487i	0.809272	+	0.587433i	$0.199862\pi$
$463$			25.2801i			1.17487i	−0.809272	+	0.587433i	$0.800138\pi$
$464$	−12.4737	+	19.4580i	−0.579077	+	0.903315i
$465$	5.35558	+	15.4236i	0.248359	+	0.715253i
$466$	−9.55256	−	3.36690i	−0.442514	−	0.155969i
$467$	−5.46958	+	5.46958i	−0.253102	+	0.253102i	−0.822241	−	0.569139i	$-0.807277\pi$
$467$	−5.46958	+	5.46958i	−0.253102	+	0.253102i	0.569139	+	0.822241i	$0.307277\pi$
$468$	0.165176	+	1.52819i	0.00763524	+	0.0706408i
$469$	5.76866	−	5.76866i	0.266372	−	0.266372i
$470$	−4.00661	−	4.04411i	−0.184811	−	0.186541i
$471$			8.02913i			0.369963i
$472$	−1.83459	−	0.431877i	−0.0844440	−	0.0198787i
$473$	37.8854			1.74197
$474$	−9.53857	+	4.56693i	−0.438121	+	0.209766i
$475$	0.418684	−	3.56265i	0.0192105	−	0.163466i
$476$	2.59830	−	3.22805i	0.119093	−	0.147957i
$477$	7.06744	−	7.06744i	0.323596	−	0.323596i
$478$	25.1243	+	8.85532i	1.14916	+	0.405033i
$479$	11.3955			0.520674			0.260337	−	0.965518i	$-0.416166\pi$
$479$	11.3955			0.520674			0.260337	+	0.965518i	$0.416166\pi$
$480$	−13.3019	+	2.84461i	−0.607147	+	0.129838i
$481$	−1.83133			−0.0835012
$482$	−15.0333	−	5.29864i	−0.684747	−	0.241347i
$483$	1.19367	−	1.19367i	0.0543138	−	0.0543138i
$484$	7.77895	−	9.66432i	0.353589	−	0.439287i
$485$	33.5870	+	16.2737i	1.52511	+	0.738953i
$486$	19.8348	−	9.49662i	0.899725	−	0.430776i
$487$	−16.9163			−0.766549			−0.383275	−	0.923634i	$-0.625204\pi$
$487$	−16.9163			−0.766549			−0.383275	+	0.923634i	$0.625204\pi$
$488$	−8.91773	+	37.8821i	−0.403687	+	1.71484i
$489$			20.2222i			0.914480i
$490$	−2.24646	+	2.22563i	−0.101485	+	0.100544i
$491$	7.78488	−	7.78488i	0.351327	−	0.351327i	−0.509276	−	0.860603i	$-0.670087\pi$
$491$	7.78488	−	7.78488i	0.351327	−	0.351327i	0.860603	+	0.509276i	$0.170087\pi$
$492$	−1.61975	−	14.9858i	−0.0730239	−	0.675613i
$493$	8.46552	−	8.46552i	0.381268	−	0.381268i
$494$	−0.398921	−	0.140604i	−0.0179483	−	0.00632607i
$495$	16.1518	−	5.60844i	0.725971	−	0.252081i
$496$	−5.80322	−	26.5319i	−0.260572	−	1.19132i
$497$		−	3.67469i		−	0.164832i
$498$	3.53461	−	10.0284i	0.158390	−	0.449382i
$499$	13.9297	+	13.9297i	0.623580	+	0.623580i	0.946445	−	0.322865i	$-0.104646\pi$
$499$	13.9297	+	13.9297i	0.623580	+	0.623580i	−0.322865	+	0.946445i	$0.604646\pi$
$500$	−20.0313	−	9.93715i	−0.895827	−	0.444403i
$501$	7.83772	−	7.83772i	0.350164	−	0.350164i
$502$	1.56586	−	0.749711i	0.0698877	−	0.0334612i
$503$	−4.45314			−0.198556			−0.0992778	−	0.995060i	$-0.531653\pi$
$503$	−4.45314			−0.198556			−0.0992778	+	0.995060i	$0.531653\pi$
$504$	4.43386	−	2.74411i	0.197500	−	0.122232i
$505$	8.93184	+	25.7230i	0.397462	+	1.14466i
$506$	−8.30490	+	3.97627i	−0.369198	+	0.176767i
$507$	9.75321	+	9.75321i	0.433155	+	0.433155i
$508$	−15.0544	+	18.7030i	−0.667929	+	0.829813i
$509$	−25.3444	−	25.3444i	−1.12337	−	1.12337i	−0.991231	−	0.132142i	$-0.957815\pi$
$509$	−25.3444	−	25.3444i	−1.12337	−	1.12337i	−0.132142	−	0.991231i	$-0.542185\pi$
$510$	7.04585	+	0.0328211i	0.311996	+	0.00145334i
$511$	−4.26700			−0.188761
$512$	22.5321	−	2.07438i	0.995789	−	0.0916756i
$513$			3.73688i			0.164987i
$514$	−7.63293	+	21.6561i	−0.336674	+	0.955211i
$515$	1.38254	−	2.85339i	0.0609219	−	0.125735i
$516$	15.3038	+	12.3183i	0.673713	+	0.542282i
$517$	5.27974	+	5.27974i	0.232203	+	0.232203i
$518$	2.68279	+	5.60332i	0.117875	+	0.246196i
$519$		−	26.5985i		−	1.16755i
$520$	−1.66278	+	2.04620i	−0.0729177	+	0.0897316i
$521$		−	19.2564i		−	0.843640i	−0.906680	−	0.421820i	$-0.861391\pi$
$521$		−	19.2564i		−	0.843640i	0.906680	−	0.421820i	$-0.138609\pi$
$522$	13.5877	−	6.50560i	0.594717	−	0.284742i
$523$	−2.53041	−	2.53041i	−0.110647	−	0.110647i	0.649616	−	0.760263i	$-0.274930\pi$
$523$	−2.53041	−	2.53041i	−0.110647	−	0.110647i	−0.760263	+	0.649616i	$0.774930\pi$
$524$	4.45769	+	41.2423i	0.194735	+	1.80168i
$525$	−5.34018	−	0.627580i	−0.233065	−	0.0273898i
$526$	5.76896	+	2.03333i	0.251539	+	0.0886575i
$527$			14.0679i			0.612808i
$528$	17.4293	−	3.81224i	0.758512	−	0.165906i
$529$	−20.5358			−0.892863
$530$	17.1442	+	0.0798616i	0.744698	+	0.00346897i
$531$	0.868651	+	0.868651i	0.0376963	+	0.0376963i
$532$	0.154190	+	1.42656i	0.00668499	+	0.0618492i
$533$	−2.06591	−	2.06591i	−0.0894843	−	0.0894843i
$534$	7.74476	+	16.1758i	0.335149	+	0.699997i
$535$	33.2823	−	11.5567i	1.43892	−	0.499640i
$536$	−22.4607	−	5.28741i	−0.970154	−	0.228381i
$537$	21.8494			0.942869
$538$	−4.68403	−	9.78315i	−0.201943	−	0.421782i
$539$	2.93284	−	2.93284i	0.126326	−	0.126326i
$540$	21.9330	+	7.84555i	0.943844	+	0.337619i
$541$	8.02545	+	8.02545i	0.345041	+	0.345041i	0.858259	−	0.513217i	$-0.171547\pi$
$541$	8.02545	+	8.02545i	0.345041	+	0.345041i	−0.513217	+	0.858259i	$0.671547\pi$
$542$	−18.2739	−	6.44082i	−0.784930	−	0.276657i
$543$			9.56058i			0.410284i
$544$	−11.6313	−	1.44417i	−0.498686	−	0.0619182i
$545$	4.93963	−	1.71520i	0.211590	−	0.0734711i
$546$	−0.210756	+	0.597956i	−0.00901952	+	0.0255901i
$547$	28.8566	−	28.8566i	1.23382	−	1.23382i	0.271334	−	0.962485i	$-0.412535\pi$
$547$	28.8566	−	28.8566i	1.23382	−	1.23382i	0.962485	−	0.271334i	$-0.0874647\pi$
$548$	7.29000	+	5.86783i	0.311413	+	0.250661i
$549$	17.9366	−	17.9366i	0.765515	−	0.765515i
$550$	26.3336	+	12.9111i	1.12287	+	0.550530i
$551$			4.14550i			0.176604i
$552$	−4.64763	−	1.09409i	−0.197816	−	0.0465674i
$553$	6.95379			0.295705
$554$	−3.57361	−	7.46390i	−0.151828	−	0.317111i
$555$	−4.60598	+	9.50617i	−0.195513	+	0.403515i
$556$	−12.3668	+	1.33667i	−0.524467	+	0.0566872i
$557$	32.3190	−	32.3190i	1.36940	−	1.36940i	0.508107	−	0.861294i	$-0.330345\pi$
$557$	32.3190	−	32.3190i	1.36940	−	1.36940i	0.861294	−	0.508107i	$-0.169655\pi$
$558$	−5.88448	+	16.6954i	−0.249110	+	0.706774i
$559$	3.80791			0.161057
$560$	8.69665	+	2.09006i	0.367500	+	0.0883210i
$561$	−9.24146			−0.390175
$562$	−8.44501	+	23.9601i	−0.356231	+	1.01070i
$563$	−0.0473856	+	0.0473856i	−0.00199707	+	0.00199707i	−0.708105	−	0.706108i	$-0.750449\pi$
$563$	−0.0473856	+	0.0473856i	−0.00199707	+	0.00199707i	0.706108	+	0.708105i	$0.250449\pi$
$564$	0.416068	+	3.84943i	0.0175196	+	0.162090i
$565$	25.7644	+	12.4835i	1.08392	+	0.525184i
$566$	18.3140	+	38.2509i	0.769795	+	1.60781i
$567$	0.0707067			0.00296940
$568$	−8.83790	+	5.46977i	−0.370830	+	0.229506i
$569$		−	21.6225i		−	0.906463i	−0.891393	−	0.453231i	$-0.850271\pi$
$569$		−	21.6225i		−	0.906463i	0.891393	−	0.453231i	$-0.149729\pi$
$570$	−1.73318	+	1.71711i	−0.0725951	+	0.0719219i
$571$	6.78010	−	6.78010i	0.283738	−	0.283738i	−0.550860	−	0.834598i	$-0.685700\pi$
$571$	6.78010	−	6.78010i	0.283738	−	0.283738i	0.834598	+	0.550860i	$0.185700\pi$
$572$	2.16838	−	2.69393i	0.0906646	−	0.112639i
$573$	−18.8093	+	18.8093i	−0.785769	+	0.785769i
$574$	−3.29463	+	9.34751i	−0.137515	+	0.390158i
$575$	−4.86425	−	6.15980i	−0.202853	−	0.256881i
$576$	−13.1996	−	6.57915i	−0.549983	−	0.274131i
$577$			3.88320i			0.161660i	0.996728	+	0.0808298i	$0.0257570\pi$
$577$			3.88320i			0.161660i	−0.996728	+	0.0808298i	$0.974243\pi$
$578$	−16.9487	−	5.97374i	−0.704971	−	0.248475i
$579$	−8.01891	−	8.01891i	−0.333254	−	0.333254i
$580$	24.3312	+	8.70343i	1.01030	+	0.361390i
$581$	−4.94383	+	4.94383i	−0.205105	+	0.205105i
$582$	−10.9618	−	22.8950i	−0.454381	−	0.949027i
$583$	−22.4867			−0.931304
$584$	6.35142	+	10.2624i	0.262824	+	0.424663i
$585$	1.62344	−	0.563711i	0.0671210	−	0.0233066i
$586$	−15.3210	−	31.9997i	−0.632904	−	1.32189i
$587$	−8.26705	−	8.26705i	−0.341218	−	0.341218i	0.515607	−	0.856825i	$-0.327566\pi$
$587$	−8.26705	−	8.26705i	−0.341218	−	0.341218i	−0.856825	+	0.515607i	$0.827566\pi$
$588$	2.13832	−	0.231121i	0.0881827	−	0.00953127i
$589$	−3.44447	−	3.44447i	−0.141927	−	0.141927i
$590$	−0.00981572	+	2.10718i	−0.000404107	+	0.0867513i
$591$	−27.2877			−1.12247
$592$	9.48307	−	14.7928i	0.389752	−	0.607982i
$593$		−	12.3057i		−	0.505333i	−0.967553	−	0.252666i	$-0.918693\pi$
$593$		−	12.3057i		−	0.505333i	0.967553	−	0.252666i	$-0.0813075\pi$
$594$	−28.8150	−	10.1561i	−1.18229	−	0.416712i
$595$	−4.16933	−	2.02015i	−0.170926	−	0.0828179i
$596$	−13.1253	+	1.41866i	−0.537635	+	0.0581105i
$597$	12.6447	+	12.6447i	0.517515	+	0.517515i
$598$	−0.834736	+	0.399660i	−0.0341349	+	0.0163433i
$599$			23.8688i			0.975251i	0.873053	+	0.487625i	$0.162137\pi$
$599$			23.8688i			0.975251i	−0.873053	+	0.487625i	$0.837863\pi$
$600$	6.43947	+	13.7777i	0.262890	+	0.562471i
$601$		−	23.0907i		−	0.941889i	−0.882163	−	0.470944i	$-0.843913\pi$
$601$		−	23.0907i		−	0.941889i	0.882163	−	0.470944i	$-0.156087\pi$
$602$	−5.57838	−	11.6511i	−0.227358	−	0.474863i
$603$	10.6348	+	10.6348i	0.433082	+	0.433082i
$604$	1.04036	−	1.29251i	0.0423315	−	0.0525913i
$605$	−12.4824	−	6.04803i	−0.507482	−	0.245887i
$606$	6.15628	−	17.4666i	0.250082	−	0.709531i
$607$		−	12.7350i		−	0.516898i	−0.966025	−	0.258449i	$-0.916789\pi$
$607$		−	12.7350i		−	0.516898i	0.966025	−	0.258449i	$-0.0832114\pi$
$608$	3.20147	−	2.49427i	0.129837	−	0.101156i
$609$	6.21383			0.251797
$610$	43.5108	+	0.202683i	1.76170	+	0.00820638i
$611$	0.530673	+	0.530673i	0.0214687	+	0.0214687i
$612$	5.95105	+	4.79009i	0.240557	+	0.193628i
$613$	11.6503	+	11.6503i	0.470552	+	0.470552i	0.902093	−	0.431541i	$-0.142030\pi$
$613$	11.6503	+	11.6503i	0.470552	+	0.470552i	−0.431541	+	0.902093i	$0.642030\pi$
$614$	−9.11436	+	4.36383i	−0.367826	+	0.176110i
$615$	−15.9198	+	5.52788i	−0.641949	+	0.222906i
$616$	−11.4192	−	2.68816i	−0.460093	−	0.108309i
$617$	−21.8561			−0.879894			−0.439947	−	0.898024i	$-0.645003\pi$
$617$	−21.8561			−0.879894			−0.439947	+	0.898024i	$0.645003\pi$
$618$	−1.94504	+	0.931260i	−0.0782412	+	0.0374608i
$619$	7.08809	−	7.08809i	0.284894	−	0.284894i	−0.550163	−	0.835057i	$-0.685434\pi$
$619$	7.08809	−	7.08809i	0.284894	−	0.284894i	0.835057	+	0.550163i	$0.185434\pi$
$620$	−27.4484	+	12.9851i	−1.10235	+	0.521493i
$621$	5.78159	+	5.78159i	0.232007	+	0.232007i
$622$	−5.38492	+	15.2781i	−0.215916	+	0.612595i
$623$		−	11.7925i		−	0.472455i
$624$	1.75184	−	0.383173i	0.0701296	−	0.0153392i
$625$	−5.79597	+	24.3189i	−0.231839	+	0.972754i
$626$	3.14956	+	1.11010i	0.125882	+	0.0443684i
$627$	2.26274	−	2.26274i	0.0903650	−	0.0903650i
$628$	−14.8461	+	1.60465i	−0.592424	+	0.0640324i
$629$	−6.43587	+	6.43587i	−0.256615	+	0.256615i
$630$	−4.10304	−	4.14145i	−0.163469	−	0.164999i
$631$		−	44.1640i		−	1.75814i	−0.476690	−	0.879071i	$-0.658164\pi$
$631$		−	44.1640i		−	1.75814i	0.476690	−	0.879071i	$-0.341836\pi$
$632$	−10.3507	−	16.7244i	−0.411729	−	0.665260i
$633$	23.3033			0.926221
$634$	32.6713	−	15.6426i	1.29754	−	0.621246i
$635$	24.1568	+	11.7046i	0.958632	+	0.464481i
$636$	−9.08351	−	7.31145i	−0.360185	−	0.289918i
$637$	0.294783	−	0.294783i	0.0116797	−	0.0116797i
$638$	−31.9658	−	11.2667i	−1.26554	−	0.446052i
$639$	6.77446			0.267993
$640$	−7.91820	−	24.0271i	−0.312994	−	0.949755i
$641$	−38.4510			−1.51872			−0.759362	−	0.650669i	$-0.774489\pi$
$641$	−38.4510			−1.51872			−0.759362	+	0.650669i	$0.774489\pi$
$642$	−22.5996	−	7.96547i	−0.891934	−	0.314372i
$643$	−29.0296	+	29.0296i	−1.14482	+	1.14482i	−0.157259	+	0.987557i	$0.550266\pi$
$643$	−29.0296	+	29.0296i	−1.14482	+	1.14482i	−0.987557	+	0.157259i	$0.949734\pi$
$644$	2.44569	+	1.96857i	0.0963735	+	0.0775725i
$645$	9.57729	−	19.7664i	0.377106	−	0.778300i
$646$	−1.89606	+	0.907809i	−0.0745996	+	0.0357173i
$647$	−45.1710			−1.77586			−0.887928	−	0.459983i	$-0.847856\pi$
$647$	−45.1710			−1.77586			−0.887928	+	0.459983i	$0.847856\pi$
$648$	−0.105247	−	0.170055i	−0.00413448	−	0.00668038i
$649$		−	2.76382i		−	0.108489i
$650$	2.64682	+	1.29771i	0.103817	+	0.0509003i
$651$	−5.16304	+	5.16304i	−0.202356	+	0.202356i
$652$	−37.3915	+	4.04147i	−1.46436	+	0.158276i
$653$	32.8231	−	32.8231i	1.28447	−	1.28447i	0.346366	−	0.938099i	$-0.387415\pi$
$653$	32.8231	−	32.8231i	1.28447	−	1.28447i	0.938099	−	0.346366i	$-0.112585\pi$
$654$	−3.35414	−	1.18220i	−0.131157	−	0.0462278i
$655$	43.8127	−	15.2132i	1.71190	−	0.594429i
$656$	27.3855	−	5.98992i	1.06922	−	0.233867i
$657$		−	7.86640i		−	0.306898i
$658$	0.846298	−	2.40111i	0.0329921	−	0.0936051i
$659$	−31.1951	−	31.1951i	−1.21519	−	1.21519i	−0.969297	−	0.245892i	$-0.920919\pi$
$659$	−31.1951	−	31.1951i	−1.21519	−	1.21519i	−0.245892	−	0.969297i	$-0.579081\pi$
$660$	−8.53012	−	18.0313i	−0.332034	−	0.701868i
$661$	26.3662	−	26.3662i	1.02553	−	1.02553i	0.0258598	−	0.999666i	$-0.491768\pi$
$661$	26.3662	−	26.3662i	1.02553	−	1.02553i	0.999666	−	0.0258598i	$-0.00823235\pi$
$662$	−28.2727	+	13.5366i	−1.09885	+	0.526113i
$663$	−0.928871			−0.0360743
$664$	19.2491	+	4.53139i	0.747012	+	0.175852i
$665$	1.51547	−	0.526220i	0.0587674	−	0.0204059i
$666$	−10.3300	+	4.94585i	−0.400279	+	0.191648i
$667$	6.41378	+	6.41378i	0.248343	+	0.248343i
$668$	16.0586	+	12.9258i	0.621325	+	0.500113i
$669$	−9.80413	−	9.80413i	−0.379050	−	0.379050i
$670$	−0.120172	+	25.7979i	−0.00464267	+	0.996662i
$671$	−57.0695			−2.20314
$672$	−3.73874	−	4.79879i	−0.144225	−	0.185117i
$673$			33.3860i			1.28694i	0.765473	+	0.643468i	$0.222505\pi$
$673$			33.3860i			1.28694i	−0.765473	+	0.643468i	$0.777495\pi$
$674$	15.1646	−	43.0249i	0.584118	−	1.65726i
$675$	3.03971	−	25.8654i	0.116999	−	0.995560i
$676$	−16.0848	+	19.9832i	−0.618644	+	0.768583i
$677$	−11.3156	−	11.3156i	−0.434895	−	0.434895i	0.455395	−	0.890290i	$-0.349498\pi$
$677$	−11.3156	−	11.3156i	−0.434895	−	0.434895i	−0.890290	+	0.455395i	$0.849498\pi$
$678$	−8.40872	−	17.5626i	−0.322935	−	0.674487i
$679$			16.6909i			0.640536i
$680$	1.34745	+	13.0345i	0.0516722	+	0.499852i
$681$		−	8.50279i		−	0.325828i
$682$	35.9216	−	17.1988i	1.37551	−	0.658575i
$683$	11.2502	+	11.2502i	0.430478	+	0.430478i	0.888791	−	0.458313i	$-0.151546\pi$
$683$	11.2502	+	11.2502i	0.430478	+	0.430478i	−0.458313	+	0.888791i	$0.651546\pi$
$684$	−2.62993	+	0.284257i	−0.100558	+	0.0108688i
$685$	4.56216	−	9.41574i	0.174311	−	0.359757i
$686$	−1.33379	−	0.470109i	−0.0509244	−	0.0179488i
$687$			12.7600i			0.486824i
$688$	−19.7183	+	30.7590i	−0.751754	+	1.17268i
$689$	−2.26017			−0.0861054
$690$	−0.0248665	+	5.33819i	−0.000946650	+	0.203221i
$691$	20.7890	+	20.7890i	0.790850	+	0.790850i	0.981632	−	0.190782i	$-0.0611024\pi$
$691$	20.7890	+	20.7890i	0.790850	+	0.790850i	−0.190782	+	0.981632i	$0.561102\pi$
$692$	49.1814	−	5.31580i	1.86960	−	0.202076i
$693$	5.40681	+	5.40681i	0.205388	+	0.205388i
$694$	−4.19749	−	8.76695i	−0.159335	−	0.332789i
$695$	4.56177	+	13.1375i	0.173038	+	0.498334i
$696$	−9.24926	−	14.9447i	−0.350592	−	0.566477i
$697$	−14.5205			−0.550004
$698$	−3.96104	−	8.27309i	−0.149927	−	0.313141i
$699$	5.44605	−	5.44605i	0.205988	−	0.205988i
$700$	0.0931624	−	9.99957i	0.00352121	−	0.377948i
$701$	3.18148	+	3.18148i	0.120163	+	0.120163i	0.764631	−	0.644468i	$-0.222921\pi$
$701$	3.18148	+	3.18148i	0.120163	+	0.120163i	−0.644468	+	0.764631i	$0.722921\pi$
$702$	−2.89623	−	1.02081i	−0.109311	−	0.0385278i
$703$		−	3.15159i		−	0.118865i
$704$	10.5322	+	31.4653i	0.396948	+	1.18589i
$705$	4.08935	−	1.41996i	0.154014	−	0.0534786i
$706$	−13.1635	+	37.3474i	−0.495414	+	1.40559i
$707$	−8.61074	+	8.61074i	−0.323840	+	0.323840i
$708$	0.898643	−	1.11644i	0.0337731	−	0.0419586i
$709$	19.3264	−	19.3264i	0.725820	−	0.725820i	−0.243964	−	0.969784i	$-0.578448\pi$
$709$	19.3264	−	19.3264i	0.725820	−	0.725820i	0.969784	+	0.243964i	$0.0784480\pi$
$710$	8.17849	+	8.25504i	0.306933	+	0.309806i
$711$			12.8196i			0.480774i
$712$	−28.3618	+	17.5531i	−1.06290	+	0.657829i
$713$	−10.6584			−0.399159
$714$	1.36075	+	2.84207i	0.0509246	+	0.106362i
$715$	−3.47947	−	1.68589i	−0.130125	−	0.0630486i
$716$	4.36666	+	40.4001i	0.163190	+	1.50982i
$717$	−14.3237	+	14.3237i	−0.534929	+	0.534929i
$718$	7.30100	−	20.7144i	0.272471	−	0.773054i
$719$	18.2760			0.681580			0.340790	−	0.940140i	$-0.389306\pi$
$719$	18.2760			0.681580			0.340790	+	0.940140i	$0.389306\pi$
$720$	−3.85311	+	16.0327i	−0.143597	+	0.597502i
$721$	1.41797			0.0528081
$722$	−8.69010	+	24.6555i	−0.323412	+	0.917583i
$723$	8.57068	−	8.57068i	0.318747	−	0.318747i
$724$	−17.6778	+	1.91071i	−0.656990	+	0.0710110i
$725$	3.37209	−	28.6937i	0.125236	−	1.06566i
$726$	4.07388	+	8.50877i	0.151196	+	0.315790i
$727$	32.6621			1.21137			0.605684	−	0.795705i	$-0.292899\pi$
$727$	32.6621			1.21137			0.605684	+	0.795705i	$0.292899\pi$
$728$	−1.14776	−	0.270190i	−0.0425387	−	0.0100139i
$729$			16.9344i			0.627199i
$730$	9.58564	−	9.49675i	0.354780	−	0.351491i
$731$	13.3822	−	13.3822i	0.494959	−	0.494959i
$732$	−23.0532	−	18.5559i	−0.852072	−	0.685846i
$733$	−2.22940	+	2.22940i	−0.0823447	+	0.0823447i	−0.747079	−	0.664735i	$-0.768545\pi$
$733$	−2.22940	+	2.22940i	−0.0823447	+	0.0823447i	0.664735	+	0.747079i	$0.268545\pi$
$734$	−12.1408	+	34.4458i	−0.448125	+	1.27142i
$735$	−0.788769	−	2.27159i	−0.0290942	−	0.0837888i
$736$	1.09415	−	8.81226i	0.0403310	−	0.324824i
$737$		−	33.8371i		−	1.24640i
$738$	−17.2326	−	6.07380i	−0.634339	−	0.223580i
$739$	25.9898	+	25.9898i	0.956050	+	0.956050i	0.999074	−	0.0430240i	$-0.0136992\pi$
$739$	25.9898	+	25.9898i	0.956050	+	0.956050i	−0.0430240	+	0.999074i	$0.513699\pi$
$740$	−18.4977	−	6.61674i	−0.679989	−	0.243236i
$741$	0.227430	−	0.227430i	0.00835486	−	0.00835486i
$742$	3.31102	+	6.91545i	0.121551	+	0.253874i
$743$	−26.3096			−0.965205			−0.482603	−	0.875839i	$-0.660308\pi$
$743$	−26.3096			−0.965205			−0.482603	+	0.875839i	$0.660308\pi$
$744$	20.1027	+	4.73231i	0.736999	+	0.173495i
$745$	4.84159	+	13.9434i	0.177382	+	0.510846i
$746$	−11.7846	−	24.6135i	−0.431464	−	0.901164i
$747$	−9.11417	−	9.11417i	−0.333470	−	0.333470i
$748$	−1.84693	−	17.0877i	−0.0675306	−	0.624789i
$749$	11.1412	+	11.1412i	0.407092	+	0.407092i
$750$	13.3933	−	10.4754i	0.489053	−	0.382508i
$751$	41.3008			1.50709			0.753544	−	0.657398i	$-0.228343\pi$
$751$	41.3008			1.50709			0.753544	+	0.657398i	$0.228343\pi$
$752$	−7.03456	+	1.53864i	−0.256524	+	0.0561085i
$753$			1.32014i			0.0481085i
$754$	−3.21292	−	1.13243i	−0.117008	−	0.0412406i
$755$	−1.66940	−	0.808864i	−0.0607555	−	0.0294376i
$756$	1.11944	+	10.3570i	0.0407138	+	0.376682i
$757$	−25.6365	−	25.6365i	−0.931774	−	0.931774i	0.0660430	−	0.997817i	$-0.478963\pi$
$757$	−25.6365	−	25.6365i	−0.931774	−	0.931774i	−0.997817	+	0.0660430i	$0.978963\pi$
$758$	24.8031	−	11.8754i	0.900888	−	0.431333i
$759$		−	7.00167i		−	0.254144i
$760$	−3.52137	−	2.86154i	−0.127734	−	0.103799i
$761$			17.9005i			0.648894i	0.945904	+	0.324447i	$0.105178\pi$
$761$			17.9005i			0.648894i	−0.945904	+	0.324447i	$0.894822\pi$
$762$	−7.88404	−	16.4667i	−0.285609	−	0.596527i
$763$	1.65354	+	1.65354i	0.0598621	+	0.0598621i
$764$	−38.5380	−	31.0198i	−1.39425	−	1.12226i
$765$	3.72423	−	7.68636i	0.134650	−	0.277901i
$766$	−9.85600	+	27.9634i	−0.356112	+	1.01036i
$767$		−	0.277795i		−	0.0100306i
$768$	−5.97632	+	16.1349i	−0.215652	+	0.582219i
$769$	−5.23682			−0.188844			−0.0944222	−	0.995532i	$-0.530100\pi$
$769$	−5.23682			−0.188844			−0.0944222	+	0.995532i	$0.530100\pi$
$770$	−0.0610967	+	13.1159i	−0.00220177	+	0.472664i
$771$	−12.3465	−	12.3465i	−0.444647	−	0.444647i
$772$	13.2246	−	16.4298i	0.475963	−	0.591321i
$773$	−26.7274	−	26.7274i	−0.961316	−	0.961316i	0.0379629	−	0.999279i	$-0.487913\pi$
$773$	−26.7274	−	26.7274i	−0.961316	−	0.961316i	−0.999279	+	0.0379629i	$0.987913\pi$
$774$	21.4793	−	10.2840i	0.772058	−	0.369651i
$775$	21.0396	+	26.6433i	0.755765	+	0.957056i
$776$	40.1427	−	24.8443i	1.44104	−	0.891858i
$777$	−4.72403			−0.169474
$778$	16.9898	−	8.13446i	0.609112	−	0.291634i
$779$	3.55529	−	3.55529i	0.127382	−	0.127382i
$780$	−0.857372	−	1.81235i	−0.0306989	−	0.0648925i
$781$	−10.7773	−	10.7773i	−0.385641	−	0.385641i
$782$	−1.52900	+	4.33806i	−0.0546768	+	0.155129i
$783$			30.0969i			1.07558i
$784$	0.854698	+	3.90762i	0.0305249	+	0.139558i
$785$	5.47634	+	15.7714i	0.195459	+	0.562905i
$786$	−29.7500	−	10.4857i	−1.06115	−	0.374013i
$787$	12.6025	−	12.6025i	0.449232	−	0.449232i	−0.445867	−	0.895099i	$-0.647105\pi$
$787$	12.6025	−	12.6025i	0.449232	−	0.449232i	0.895099	+	0.445867i	$0.147105\pi$
$788$	−5.45353	−	50.4558i	−0.194274	−	1.79741i
$789$	−3.28896	+	3.28896i	−0.117090	+	0.117090i
$790$	−15.6214	+	15.4766i	−0.555785	+	0.550631i
$791$			12.8034i			0.455238i
$792$	4.95575	−	21.0518i	0.176095	−	0.748044i
$793$	−5.73612			−0.203696
$794$	27.6895	−	13.2574i	0.982664	−	0.470486i
$795$	−5.68455	+	11.7322i	−0.201610	+	0.416099i
$796$	−20.8534	+	25.9076i	−0.739129	+	0.918270i
$797$	−10.1060	+	10.1060i	−0.357972	+	0.357972i	−0.863065	−	0.505093i	$-0.831458\pi$
$797$	−10.1060	+	10.1060i	−0.357972	+	0.357972i	0.505093	+	0.863065i	$0.331458\pi$
$798$	−1.02904	−	0.362698i	−0.0364278	−	0.0128394i
$799$	3.72991			0.131955
$800$	−24.1884	+	14.6603i	−0.855187	+	0.518319i
$801$	21.7400			0.768144
$802$	37.4127	+	13.1865i	1.32109	+	0.465632i
$803$	−12.5144	+	12.5144i	−0.441624	+	0.441624i
$804$	11.0020	−	13.6685i	0.388009	−	0.482050i
$805$	1.53054	−	3.15884i	0.0539443	−	0.111334i
$806$	3.61053	−	1.72867i	0.127175	−	0.0608898i
$807$	8.24794			0.290341
$808$	33.5265	+	7.89239i	1.17946	+	0.277653i
$809$		−	22.8518i		−	0.803425i	−0.915766	−	0.401713i	$-0.868415\pi$
$809$		−	22.8518i		−	0.803425i	0.915766	−	0.401713i	$-0.131585\pi$
$810$	−0.158840	+	0.157367i	−0.00558106	+	0.00552931i
$811$	−23.8895	+	23.8895i	−0.838872	+	0.838872i	−0.988711	−	0.149838i	$-0.952125\pi$
$811$	−23.8895	+	23.8895i	−0.838872	+	0.838872i	0.149838	+	0.988711i	$0.452125\pi$
$812$	1.24185	+	11.4895i	0.0435804	+	0.403204i
$813$	10.4182	−	10.4182i	0.365382	−	0.365382i
$814$	24.3018	+	8.56544i	0.851778	+	0.300218i
$815$	13.7927	+	39.7219i	0.483138	+	1.39140i
$816$	4.80993	−	7.50311i	0.168381	−	0.262662i
$817$			6.55317i			0.229266i
$818$	11.2775	−	31.9965i	0.394309	−	1.11873i
$819$	0.543445	+	0.543445i	0.0189895	+	0.0189895i
$820$	−13.4028	−	28.3314i	−0.468047	−	0.989377i
$821$	−30.4385	+	30.4385i	−1.06231	+	1.06231i	−0.0643860	+	0.997925i	$0.520509\pi$
$821$	−30.4385	+	30.4385i	−1.06231	+	1.06231i	−0.997925	+	0.0643860i	$0.979491\pi$
$822$	−6.41835	+	3.07301i	−0.223866	+	0.107184i
$823$	−25.7139			−0.896330			−0.448165	−	0.893951i	$-0.647922\pi$
$823$	−25.7139			−0.896330			−0.448165	+	0.893951i	$0.647922\pi$
$824$	−2.11065	−	3.41033i	−0.0735279	−	0.118804i
$825$	−17.5025	+	13.8213i	−0.609357	+	0.481195i
$826$	−0.849971	+	0.406954i	−0.0295743	+	0.0141597i
$827$	−16.2307	−	16.2307i	−0.564398	−	0.564398i	0.366155	−	0.930554i	$-0.380674\pi$
$827$	−16.2307	−	16.2307i	−0.564398	−	0.564398i	−0.930554	+	0.366155i	$0.880674\pi$
$828$	−3.62915	+	4.50873i	−0.126122	+	0.156689i
$829$	0.410075	+	0.410075i	0.0142425	+	0.0142425i	0.714192	−	0.699950i	$-0.246794\pi$
$829$	0.410075	+	0.410075i	0.0142425	+	0.0142425i	−0.699950	+	0.714192i	$0.746794\pi$
$830$	0.102990	−	22.1092i	0.00357482	−	0.767423i
$831$	6.29264			0.218289
$832$	1.05861	+	3.16262i	0.0367006	+	0.109644i
$833$		−	2.07192i		−	0.0717879i
$834$	3.14420	−	8.92072i	0.108875	−	0.308899i
$835$	10.0496	−	20.7412i	0.347781	−	0.717778i
$836$	4.63608	+	3.73165i	0.160342	+	0.129062i
$837$	−25.0074	−	25.0074i	−0.864383	−	0.864383i
$838$	13.9394	+	29.1140i	0.481527	+	1.00573i
$839$		−	0.954812i		−	0.0329638i	−0.999864	−	0.0164819i	$-0.994753\pi$
$839$		−	0.954812i		−	0.0329638i	0.999864	−	0.0164819i	$-0.00524659\pi$
$840$	−4.28926	+	5.27830i	−0.147993	+	0.182119i
$841$			4.38792i			0.151307i
$842$	5.47923	−	2.62338i	0.188827	−	0.0904076i
$843$	−13.6600	−	13.6600i	−0.470476	−	0.470476i
$844$	4.65723	+	43.0884i	0.160308	+	1.48316i
$845$	25.8102	+	12.5057i	0.887898	+	0.430208i
$846$	4.42656	+	1.56019i	0.152188	+	0.0536404i
$847$		−	6.20305i		−	0.213139i
$848$	11.7037	−	18.2569i	0.401907	−	0.626944i
$849$	−32.2485			−1.10676
$850$	13.8623	−	4.74121i	0.475474	−	0.162622i
$851$	−4.87605	−	4.87605i	−0.167149	−	0.167149i
$852$	−0.849298	−	7.85766i	−0.0290965	−	0.269199i
$853$	26.7515	+	26.7515i	0.915955	+	0.915955i	0.996732	−	0.0807769i	$-0.0257401\pi$
$853$	26.7515	+	26.7515i	0.915955	+	0.915955i	−0.0807769	+	0.996732i	$0.525740\pi$
$854$	8.40311	+	17.5509i	0.287549	+	0.600578i
$855$	0.970111	+	2.79384i	0.0331771	+	0.0955472i
$856$	10.2118	−	43.3792i	0.349031	−	1.48267i
$857$	27.7470			0.947819			0.473909	−	0.880574i	$-0.342842\pi$
$857$	27.7470			0.947819			0.473909	+	0.880574i	$0.342842\pi$
$858$	1.13559	+	2.37182i	0.0387685	+	0.0809726i
$859$	−32.1482	+	32.1482i	−1.09688	+	1.09688i	−0.102111	+	0.994773i	$0.532560\pi$
$859$	−32.1482	+	32.1482i	−1.09688	+	1.09688i	−0.994773	+	0.102111i	$0.967440\pi$
$860$	38.4626	+	13.7583i	1.31156	+	0.469155i
$861$	−5.32915	−	5.32915i	−0.181617	−	0.181617i
$862$	15.5829	+	5.49238i	0.530757	+	0.187071i
$863$		−	23.9973i		−	0.816876i	−0.912786	−	0.408438i	$-0.866074\pi$
$863$		−	23.9973i		−	0.816876i	0.912786	−	0.408438i	$-0.133926\pi$
$864$	23.2431	−	18.1088i	0.790748	−	0.616073i
$865$	−18.1417	−	52.2467i	−0.616838	−	1.77644i
$866$	1.69658	−	4.81353i	0.0576521	−	0.163570i
$867$	9.66266	−	9.66266i	0.328161	−	0.328161i
$868$	−10.5785	−	8.51476i	−0.359056	−	0.289010i
$869$	20.3943	−	20.3943i	0.691830	−	0.691830i
$870$	−13.9591	+	13.8297i	−0.473258	+	0.468869i
$871$		−	3.40100i		−	0.115239i
$872$	1.51559	−	6.43816i	0.0513244	−	0.218024i
$873$	−30.7703			−1.04142
$874$	−0.687789	−	1.43653i	−0.0232648	−	0.0485912i
$875$	−10.9176	+	2.40958i	−0.369082	+	0.0814585i
$876$	−9.12420	+	0.986193i	−0.308278	+	0.0333204i
$877$	−2.34838	+	2.34838i	−0.0792990	+	0.0792990i	−0.745644	−	0.666345i	$-0.767858\pi$
$877$	−2.34838	+	2.34838i	−0.0792990	+	0.0792990i	0.666345	+	0.745644i	$0.267858\pi$
$878$	−6.37168	+	18.0777i	−0.215034	+	0.610093i
$879$	26.9782			0.909951
$880$	31.6356	−	19.3760i	1.06644	−	0.653166i
$881$	32.4131			1.09203			0.546013	−	0.837777i	$-0.316145\pi$
$881$	32.4131			1.09203			0.546013	+	0.837777i	$0.316145\pi$
$882$	0.866667	−	2.45890i	0.0291822	−	0.0827956i
$883$	39.1941	−	39.1941i	1.31899	−	1.31899i	0.404407	−	0.914579i	$-0.367478\pi$
$883$	39.1941	−	39.1941i	1.31899	−	1.31899i	0.914579	−	0.404407i	$-0.132522\pi$
$884$	−0.185638	−	1.71751i	−0.00624367	−	0.0577660i
$885$	−1.44200	−	0.698683i	−0.0484722	−	0.0234860i
$886$	9.72193	+	20.3054i	0.326614	+	0.682172i
$887$	4.26391			0.143168			0.0715841	−	0.997435i	$-0.477195\pi$
$887$	4.26391			0.143168			0.0715841	+	0.997435i	$0.477195\pi$
$888$	7.03171	+	11.3616i	0.235969	+	0.381272i
$889$			12.0046i			0.402620i
$890$	26.2457	+	26.4913i	0.879756	+	0.887991i
$891$	0.207371	−	0.207371i	0.00694719	−	0.00694719i
$892$	16.1687	−	20.0875i	0.541369	−	0.672579i
$893$	−0.913254	+	0.913254i	−0.0305609	+	0.0305609i
$894$	3.33707	−	9.46792i	0.111608	−	0.316655i
$895$	42.9180	−	14.9025i	1.43459	−	0.498137i
$896$	8.12589	−	7.87209i	0.271467	−	0.262988i
$897$		−	0.703746i		−	0.0234974i
$898$	−8.73303	−	3.07805i	−0.291425	−	0.102716i
$899$	−27.7419	−	27.7419i	−0.925243	−	0.925243i
$900$	18.4347	+	0.171749i	0.614488	+	0.00572497i
$901$	−7.94295	+	7.94295i	−0.264618	+	0.264618i
$902$	17.7521	+	37.0773i	0.591080	+	1.23454i
$903$	9.82277			0.326881
$904$	30.7932	−	19.0579i	1.02417	−	0.633857i
$905$	6.52087	+	18.7796i	0.216761	+	0.624254i
$906$	0.544841	+	1.13796i	0.0181011	+	0.0378063i
$907$	−11.5277	−	11.5277i	−0.382770	−	0.382770i	0.489329	−	0.872099i	$-0.337242\pi$
$907$	−11.5277	−	11.5277i	−0.382770	−	0.382770i	−0.872099	+	0.489329i	$0.837242\pi$
$908$	15.7219	−	1.69931i	0.521750	−	0.0563935i
$909$	−15.8743	−	15.8743i	−0.526517	−	0.526517i
$910$	−0.00614090	+	1.31829i	−0.000203569	+	0.0437010i
$911$	−47.3485			−1.56873			−0.784363	−	0.620302i	$-0.787010\pi$
$911$	−47.3485			−1.56873			−0.784363	+	0.620302i	$0.787010\pi$
$912$	0.659415	+	3.01480i	0.0218354	+	0.0998300i
$913$			28.9989i			0.959723i
$914$	33.7352	+	11.8903i	1.11586	+	0.393297i
$915$	−14.4270	+	29.7755i	−0.476940	+	0.984347i
$916$	−23.5936	+	2.55012i	−0.779554	+	0.0842585i
$917$	14.6663	+	14.6663i	0.484323	+	0.484323i
$918$	−13.7657	+	6.59083i	−0.454336	+	0.217530i
$919$			13.2023i			0.435503i	0.976004	+	0.217752i	$0.0698722\pi$
$919$			13.2023i			0.435503i	−0.976004	+	0.217752i	$0.930128\pi$
$920$	−9.87544	+	1.02087i	−0.325583	+	0.0336572i
$921$		−	7.68411i		−	0.253200i
$922$	−20.4418	−	42.6951i	−0.673215	−	1.40609i
$923$	−1.08324	−	1.08324i	−0.0356551	−	0.0356551i
$924$	5.59349	−	6.94917i	0.184012	−	0.228611i
$925$	−2.56362	+	21.8142i	−0.0842912	+	0.717247i
$926$	11.8844	−	33.7184i	0.390546	−	1.10806i
$927$			2.61410i			0.0858582i
$928$	25.7847	−	20.0889i	0.846424	−	0.659450i
$929$	−27.7495			−0.910431			−0.455216	−	0.890381i	$-0.650438\pi$
$929$	−27.7495			−0.910431			−0.455216	+	0.890381i	$0.650438\pi$
$930$	0.107556	−	23.0896i	0.00352691	−	0.757137i
$931$	0.507302	+	0.507302i	0.0166262	+	0.0166262i
$932$	11.1583	+	8.98148i	0.365502	+	0.294198i
$933$	−8.71024	−	8.71024i	−0.285161	−	0.285161i
$934$	9.86657	−	4.72398i	0.322844	−	0.154573i
$935$	−18.1527	+	6.30322i	−0.593658	+	0.206137i
$936$	0.498108	−	2.11594i	0.0162812	−	0.0691617i
$937$	−54.3990			−1.77714			−0.888570	−	0.458742i	$-0.848300\pi$
$937$	−54.3990			−1.77714			−0.888570	+	0.458742i	$0.848300\pi$
$938$	−10.4061	+	4.98229i	−0.339771	+	0.162677i
$939$	−1.79561	+	1.79561i	−0.0585975	+	0.0585975i
$940$	3.44281	+	7.27754i	0.112292	+	0.237367i
$941$	26.1290	+	26.1290i	0.851782	+	0.851782i	0.990353	−	0.138571i	$-0.0442509\pi$
$941$	26.1290	+	26.1290i	0.851782	+	0.851782i	−0.138571	+	0.990353i	$0.544251\pi$
$942$	3.77457	−	10.7092i	0.122982	−	0.348924i
$943$		−	11.0013i		−	0.358251i
$944$	2.24393	+	1.43849i	0.0730338	+	0.0468189i
$945$	11.0025	−	3.82044i	0.357913	−	0.124279i
$946$	−50.5312	−	17.8103i	−1.64291	−	0.579062i
$947$	−18.7011	+	18.7011i	−0.607703	+	0.607703i	−0.942345	−	0.334642i	$-0.891385\pi$
$947$	−18.7011	+	18.7011i	−0.607703	+	0.607703i	0.334642	+	0.942345i	$0.391385\pi$
$948$	14.8694	−	1.60717i	0.482936	−	0.0521984i
$949$	−1.25784	+	1.25784i	−0.0408311	+	0.0408311i
$950$	−2.23327	+	4.55500i	−0.0724569	+	0.147784i
$951$			27.5444i			0.893189i
$952$	−4.98313	+	3.08405i	−0.161504	+	0.0999548i
$953$	56.3747			1.82616			0.913079	−	0.407784i	$-0.133698\pi$
$953$	56.3747			1.82616			0.913079	+	0.407784i	$0.133698\pi$
$954$	−12.7489	+	6.10402i	−0.412762	+	0.197625i
$955$	−24.1175	+	49.7755i	−0.780423	+	1.61070i
$956$	−29.3476	−	23.6223i	−0.949168	−	0.764000i
$957$	18.2241	−	18.2241i	0.589102	−	0.589102i
$958$	−15.1992	−	5.35713i	−0.491064	−	0.173081i
$959$	4.67909			0.151096
$960$	19.0793	+	2.45923i	0.615780	+	0.0793712i
$961$	15.1012			0.487136
$962$	2.44260	+	0.860922i	0.0787527	+	0.0277572i
$963$	−20.5394	+	20.5394i	−0.661872	+	0.661872i
$964$	17.5603	+	14.1346i	0.565580	+	0.455243i
$965$	−21.2207	−	10.2819i	−0.683117	−	0.330987i
$966$	−2.15326	+	1.03095i	−0.0692800	+	0.0331703i
$967$	22.8740			0.735577			0.367788	−	0.929909i	$-0.380115\pi$
$967$	22.8740			0.735577			0.367788	+	0.929909i	$0.380115\pi$
$968$	−14.9188	+	9.23322i	−0.479508	+	0.296767i
$969$		−	1.59853i		−	0.0513521i
$970$	−37.1476	−	37.4953i	−1.19274	−	1.20390i
$971$	15.5512	−	15.5512i	0.499062	−	0.499062i	−0.412084	−	0.911146i	$-0.635199\pi$
$971$	15.5512	−	15.5512i	0.499062	−	0.499062i	0.911146	+	0.412084i	$0.135199\pi$
$972$	−30.9199	+	3.34199i	−0.991757	+	0.107194i
$973$	−4.39777	+	4.39777i	−0.140986	+	0.140986i
$974$	22.5628	+	7.95249i	0.722958	+	0.254814i
$975$	−1.75919	+	1.38919i	−0.0563393	+	0.0444898i
$976$	29.7031	−	46.3345i	0.950773	−	1.48313i
$977$			15.9701i			0.510930i	0.966818	+	0.255465i	$0.0822285\pi$
$977$			15.9701i			0.510930i	−0.966818	+	0.255465i	$0.917771\pi$
$978$	9.50665	−	26.9722i	0.303989	−	0.862476i
$979$	−34.5854	−	34.5854i	−1.10535	−	1.10535i
$980$	4.04259	−	1.91244i	0.129136	−	0.0610907i
$981$	−3.04837	+	3.04837i	−0.0973270	+	0.0973270i
$982$	−14.0431	+	6.72366i	−0.448134	+	0.214560i
$983$	−35.3003			−1.12590			−0.562952	−	0.826490i	$-0.690334\pi$
$983$	−35.3003			−1.12590			−0.562952	+	0.826490i	$0.690334\pi$
$984$	−4.88456	+	20.7494i	−0.155714	+	0.661467i
$985$	−53.6004	+	18.6118i	−1.70785	+	0.593022i
$986$	−15.2709	+	7.31151i	−0.486326	+	0.232846i
$987$	1.36891	+	1.36891i	0.0435728	+	0.0435728i
$988$	0.465978	+	0.375072i	0.0148247	+	0.0119326i
$989$	10.1389	+	10.1389i	0.322397	+	0.322397i
$990$	−24.1797	−	0.112635i	−0.768483	−	0.00357976i
$991$	−12.4824			−0.396516			−0.198258	−	0.980150i	$-0.563528\pi$
$991$	−12.4824			−0.396516			−0.198258	+	0.980150i	$0.563528\pi$
$992$	−4.73260	+	38.1162i	−0.150260	+	1.21019i
$993$		−	23.8360i		−	0.756413i
$994$	−1.72750	+	4.90127i	−0.0547931	+	0.155459i
$995$	33.4621	+	16.2132i	1.06082	+	0.513994i
$996$	−9.42886	+	11.7141i	−0.298765	+	0.371176i
$997$	3.91335	+	3.91335i	0.123937	+	0.123937i	0.766355	−	0.642418i	$-0.222069\pi$
$997$	3.91335	+	3.91335i	0.123937	+	0.123937i	−0.642418	+	0.766355i	$0.722069\pi$
$998$	−12.0308	−	25.1278i	−0.380830	−	0.795407i
$999$		−	22.8811i		−	0.723925i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.bb.d.29.4	yes	70
5.4	even	2		560.2.bb.c.29.32	✓	70
16.5	even	4		560.2.bb.c.309.32	yes	70
80.69	even	4	inner	560.2.bb.d.309.4	yes	70

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bb.c.29.32	✓	70	5.4	even	2
560.2.bb.c.309.32	yes	70	16.5	even	4
560.2.bb.d.29.4	yes	70	1.1	even	1	trivial
560.2.bb.d.309.4	yes	70	80.69	even	4	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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.bb (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33379 - 0.470109i) q^{2} +(0.760413 - 0.760413i) q^{3} +(1.55800 + 1.25405i) q^{4} +(0.975010 - 2.01230i) q^{5} +(-1.37171 + 0.656755i) q^{6} +1.00000 q^{7} +(-1.48850 - 2.40507i) q^{8} +1.84355i q^{9} +O(q^{10})\)	\(q+(-1.33379 - 0.470109i) q^{2} +(0.760413 - 0.760413i) q^{3} +(1.55800 + 1.25405i) q^{4} +(0.975010 - 2.01230i) q^{5} +(-1.37171 + 0.656755i) q^{6} +1.00000 q^{7} +(-1.48850 - 2.40507i) q^{8} +1.84355i q^{9} +(-2.24646 + 2.22563i) q^{10} +(2.93284 - 2.93284i) q^{11} +(2.13832 - 0.231121i) q^{12} +(0.294783 - 0.294783i) q^{13} +(-1.33379 - 0.470109i) q^{14} +(-0.788769 - 2.27159i) q^{15} +(0.854698 + 3.90762i) q^{16} -2.07192i q^{17} +(0.866667 - 2.45890i) q^{18} +(0.507302 + 0.507302i) q^{19} +(4.04259 - 1.91244i) q^{20} +(0.760413 - 0.760413i) q^{21} +(-5.29054 + 2.53304i) q^{22} +1.56976 q^{23} +(-2.96072 - 0.696975i) q^{24} +(-3.09871 - 3.92403i) q^{25} +(-0.531758 + 0.254598i) q^{26} +(3.68309 + 3.68309i) q^{27} +(1.55800 + 1.25405i) q^{28} +(4.08582 + 4.08582i) q^{29} +(-0.0158409 + 3.40063i) q^{30} -6.78979 q^{31} +(0.697018 - 5.61375i) q^{32} -4.46033i q^{33} +(-0.974030 + 2.76351i) q^{34} +(0.975010 - 2.01230i) q^{35} +(-2.31190 + 2.87223i) q^{36} +(-3.10623 - 3.10623i) q^{37} +(-0.438148 - 0.915122i) q^{38} -0.448313i q^{39} +(-6.29103 + 0.650336i) q^{40} -7.00823i q^{41} +(-1.37171 + 0.656755i) q^{42} +(6.45884 + 6.45884i) q^{43} +(8.24728 - 0.891410i) q^{44} +(3.70977 + 1.79747i) q^{45} +(-2.09374 - 0.737960i) q^{46} +1.80022i q^{47} +(3.62133 + 2.32148i) q^{48} +1.00000 q^{49} +(2.28831 + 6.69056i) q^{50} +(-1.57552 - 1.57552i) q^{51} +(0.828944 - 0.0895967i) q^{52} +(-3.83361 - 3.83361i) q^{53} +(-3.18102 - 6.64393i) q^{54} +(-3.04220 - 8.76129i) q^{55} +(-1.48850 - 2.40507i) q^{56} +0.771518 q^{57} +(-3.52885 - 7.37042i) q^{58} +(0.471185 - 0.471185i) q^{59} +(1.61980 - 4.52828i) q^{60} +(-9.72941 - 9.72941i) q^{61} +(9.05616 + 3.19194i) q^{62} +1.84355i q^{63} +(-3.56875 + 7.15989i) q^{64} +(-0.305776 - 0.880608i) q^{65} +(-2.09684 + 5.94915i) q^{66} +(5.76866 - 5.76866i) q^{67} +(2.59830 - 3.22805i) q^{68} +(1.19367 - 1.19367i) q^{69} +(-2.24646 + 2.22563i) q^{70} -3.67469i q^{71} +(4.43386 - 2.74411i) q^{72} -4.26700 q^{73} +(2.68279 + 5.60332i) q^{74} +(-5.34018 - 0.627580i) q^{75} +(0.154190 + 1.42656i) q^{76} +(2.93284 - 2.93284i) q^{77} +(-0.210756 + 0.597956i) q^{78} +6.95379 q^{79} +(8.69665 + 2.09006i) q^{80} +0.0707067 q^{81} +(-3.29463 + 9.34751i) q^{82} +(-4.94383 + 4.94383i) q^{83} +(2.13832 - 0.231121i) q^{84} +(-4.16933 - 2.02015i) q^{85} +(-5.57838 - 11.6511i) q^{86} +6.21383 q^{87} +(-11.4192 - 2.68816i) q^{88} -11.7925i q^{89} +(-4.10304 - 4.14145i) q^{90} +(0.294783 - 0.294783i) q^{91} +(2.44569 + 1.96857i) q^{92} +(-5.16304 + 5.16304i) q^{93} +(0.846298 - 2.40111i) q^{94} +(1.51547 - 0.526220i) q^{95} +(-3.73874 - 4.79879i) q^{96} +16.6909i q^{97} +(-1.33379 - 0.470109i) q^{98} +(5.40681 + 5.40681i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 70 q + 2 q^{2} + 2 q^{3} + 2 q^{5} + 70 q^{7} + 8 q^{8}+O(q^{10}) \) 70 * q + 2 * q^2 + 2 * q^3 + 2 * q^5 + 70 * q^7 + 8 * q^8	\( 70 q + 2 q^{2} + 2 q^{3} + 2 q^{5} + 70 q^{7} + 8 q^{8} - 18 q^{10} - 2 q^{11} - 4 q^{12} + 6 q^{13} + 2 q^{14} - 6 q^{15} + 4 q^{16} - 18 q^{18} + 14 q^{19} + 12 q^{20} + 2 q^{21} - 12 q^{22} + 20 q^{24} + 6 q^{25} - 36 q^{26} + 8 q^{27} + 2 q^{29} + 8 q^{30} + 16 q^{31} - 8 q^{32} + 4 q^{34} + 2 q^{35} - 40 q^{36} + 10 q^{37} - 12 q^{38} - 24 q^{40} + 2 q^{43} - 24 q^{44} - 24 q^{45} - 16 q^{46} - 44 q^{48} + 70 q^{49} - 10 q^{50} + 8 q^{51} + 28 q^{52} - 30 q^{53} - 32 q^{54} + 6 q^{55} + 8 q^{56} - 76 q^{57} + 56 q^{58} + 2 q^{59} - 8 q^{60} + 30 q^{61} + 48 q^{62} + 12 q^{64} - 10 q^{65} + 80 q^{66} + 6 q^{67} - 36 q^{68} - 16 q^{69} - 18 q^{70} + 4 q^{72} - 36 q^{73} - 32 q^{74} - 2 q^{75} + 44 q^{76} - 2 q^{77} - 84 q^{78} - 40 q^{79} + 12 q^{80} - 82 q^{81} + 24 q^{82} + 10 q^{83} - 4 q^{84} + 32 q^{85} + 32 q^{86} - 4 q^{87} + 32 q^{88} + 18 q^{90} + 6 q^{91} - 92 q^{92} - 56 q^{93} - 20 q^{94} + 6 q^{95} + 16 q^{96} + 2 q^{98} - 34 q^{99}+O(q^{100}) \) 70 * q + 2 * q^2 + 2 * q^3 + 2 * q^5 + 70 * q^7 + 8 * q^8 - 18 * q^10 - 2 * q^11 - 4 * q^12 + 6 * q^13 + 2 * q^14 - 6 * q^15 + 4 * q^16 - 18 * q^18 + 14 * q^19 + 12 * q^20 + 2 * q^21 - 12 * q^22 + 20 * q^24 + 6 * q^25 - 36 * q^26 + 8 * q^27 + 2 * q^29 + 8 * q^30 + 16 * q^31 - 8 * q^32 + 4 * q^34 + 2 * q^35 - 40 * q^36 + 10 * q^37 - 12 * q^38 - 24 * q^40 + 2 * q^43 - 24 * q^44 - 24 * q^45 - 16 * q^46 - 44 * q^48 + 70 * q^49 - 10 * q^50 + 8 * q^51 + 28 * q^52 - 30 * q^53 - 32 * q^54 + 6 * q^55 + 8 * q^56 - 76 * q^57 + 56 * q^58 + 2 * q^59 - 8 * q^60 + 30 * q^61 + 48 * q^62 + 12 * q^64 - 10 * q^65 + 80 * q^66 + 6 * q^67 - 36 * q^68 - 16 * q^69 - 18 * q^70 + 4 * q^72 - 36 * q^73 - 32 * q^74 - 2 * q^75 + 44 * q^76 - 2 * q^77 - 84 * q^78 - 40 * q^79 + 12 * q^80 - 82 * q^81 + 24 * q^82 + 10 * q^83 - 4 * q^84 + 32 * q^85 + 32 * q^86 - 4 * q^87 + 32 * q^88 + 18 * q^90 + 6 * q^91 - 92 * q^92 - 56 * q^93 - 20 * q^94 + 6 * q^95 + 16 * q^96 + 2 * q^98 - 34 * q^99

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