LMFDB - Embedded newform 570.2.x.b.217.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(103,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 2]))

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

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

chi := DirichletCharacter("570.103");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.x (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			217.4
Character	$\chi$	$=$	570.217
Dual form			570.2.x.b.373.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.20208 + 1.88547i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-0.368637 - 0.368637i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.20208 + 1.88547i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-0.368637 - 0.368637i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +(1.51010 - 1.64912i) q^{10} +0.0597684 q^{11} +(0.707107 - 0.707107i) q^{12} +(-0.198558 + 0.741029i) q^{13} +(-0.260665 + 0.451486i) q^{14} +(-1.64912 - 1.51010i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-7.07811 + 1.89657i) q^{17} +(-0.707107 - 0.707107i) q^{18} +(-2.26777 + 3.72253i) q^{19} +(-1.98377 - 1.03182i) q^{20} +(0.451486 + 0.260665i) q^{21} +(-0.0154692 - 0.0577318i) q^{22} +(6.38904 + 1.71194i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(-2.10999 + 4.53298i) q^{25} +0.767170 q^{26} +(-0.707107 + 0.707107i) q^{27} +(0.503567 + 0.134930i) q^{28} +(2.71526 + 4.70297i) q^{29} +(-1.03182 + 1.98377i) q^{30} +3.60368i q^{31} +(-0.965926 - 0.258819i) q^{32} +(-0.0577318 + 0.0154692i) q^{33} +(3.66390 + 6.34606i) q^{34} +(0.251921 - 1.13818i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-6.95071 + 6.95071i) q^{37} +(4.18263 + 1.22704i) q^{38} -0.767170i q^{39} +(-0.483227 + 2.18323i) q^{40} +(10.3170 + 5.95652i) q^{41} +(0.134930 - 0.503567i) q^{42} +(-2.66556 - 9.94802i) q^{43} +(-0.0517609 + 0.0298842i) q^{44} +(1.98377 + 1.03182i) q^{45} -6.61442i q^{46} +(1.02291 - 3.81757i) q^{47} +(-0.258819 + 0.965926i) q^{48} -6.72821i q^{49} +(4.92463 + 0.864874i) q^{50} +(6.34606 - 3.66390i) q^{51} +(-0.198558 - 0.741029i) q^{52} +(-3.27763 + 12.2323i) q^{53} +(0.866025 + 0.500000i) q^{54} +(0.0718465 + 0.112691i) q^{55} -0.521331i q^{56} +(1.22704 - 4.18263i) q^{57} +(3.83996 - 3.83996i) q^{58} +(0.464324 - 0.804233i) q^{59} +(2.18323 + 0.483227i) q^{60} +(0.593198 + 1.02745i) q^{61} +(3.48089 - 0.932701i) q^{62} +(-0.503567 - 0.134930i) q^{63} +1.00000i q^{64} +(-1.63587 + 0.516403i) q^{65} +(0.0298842 + 0.0517609i) q^{66} +(-11.4286 - 3.06227i) q^{67} +(5.18153 - 5.18153i) q^{68} -6.61442 q^{69} +(-1.16460 + 0.0512467i) q^{70} +(7.61386 + 4.39586i) q^{71} +(0.965926 + 0.258819i) q^{72} +(3.66083 + 13.6624i) q^{73} +(8.51285 + 4.91490i) q^{74} +(0.864874 - 4.92463i) q^{75} +(0.102683 - 4.35769i) q^{76} +(-0.0220328 - 0.0220328i) q^{77} +(-0.741029 + 0.198558i) q^{78} +(-1.71914 + 2.97764i) q^{79} +(2.23391 - 0.0982997i) q^{80} +(0.500000 - 0.866025i) q^{81} +(3.08332 - 11.5071i) q^{82} +(8.15176 - 8.15176i) q^{83} -0.521331 q^{84} +(-12.0844 - 11.0657i) q^{85} +(-8.91915 + 5.14947i) q^{86} +(-3.83996 - 3.83996i) q^{87} +(0.0422626 + 0.0422626i) q^{88} +(1.67945 + 2.90889i) q^{89} +(0.483227 - 2.18323i) q^{90} +(0.346366 - 0.199975i) q^{91} +(-6.38904 + 1.71194i) q^{92} +(-0.932701 - 3.48089i) q^{93} -3.95224 q^{94} +(-9.74476 + 0.198974i) q^{95} +1.00000 q^{96} +(-1.74588 - 6.51573i) q^{97} +(-6.49896 + 1.74139i) q^{98} +(0.0517609 - 0.0298842i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 20 q^{6} - 8 q^{7}+O(q^{10}) $ 40 * q + 20 * q^6 - 8 * q^7	$ 40 q + 20 q^{6} - 8 q^{7} + 12 q^{10} + 8 q^{11} + 24 q^{13} + 20 q^{16} + 36 q^{21} - 8 q^{23} + 16 q^{25} + 4 q^{28} - 4 q^{35} - 20 q^{36} + 24 q^{38} + 12 q^{41} - 4 q^{42} - 12 q^{43} - 16 q^{47} + 24 q^{52} + 72 q^{53} + 8 q^{55} - 24 q^{57} - 16 q^{58} + 12 q^{60} + 24 q^{61} - 4 q^{63} + 4 q^{66} - 36 q^{67} - 24 q^{70} - 72 q^{71} - 32 q^{73} + 8 q^{76} - 88 q^{77} + 24 q^{78} + 20 q^{81} + 8 q^{82} - 88 q^{83} - 24 q^{85} - 48 q^{86} + 16 q^{87} - 24 q^{91} + 8 q^{92} - 96 q^{95} + 40 q^{96} - 60 q^{97} - 48 q^{98}+O(q^{100}) $ 40 * q + 20 * q^6 - 8 * q^7 + 12 * q^10 + 8 * q^11 + 24 * q^13 + 20 * q^16 + 36 * q^21 - 8 * q^23 + 16 * q^25 + 4 * q^28 - 4 * q^35 - 20 * q^36 + 24 * q^38 + 12 * q^41 - 4 * q^42 - 12 * q^43 - 16 * q^47 + 24 * q^52 + 72 * q^53 + 8 * q^55 - 24 * q^57 - 16 * q^58 + 12 * q^60 + 24 * q^61 - 4 * q^63 + 4 * q^66 - 36 * q^67 - 24 * q^70 - 72 * q^71 - 32 * q^73 + 8 * q^76 - 88 * q^77 + 24 * q^78 + 20 * q^81 + 8 * q^82 - 88 * q^83 - 24 * q^85 - 48 * q^86 + 16 * q^87 - 24 * q^91 + 8 * q^92 - 96 * q^95 + 40 * q^96 - 60 * q^97 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	1.20208	+	1.88547i	0.537588	+	0.843208i
$5$	1.20208	+	1.88547i	0.537588	+	0.843208i
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$	−0.368637	−	0.368637i	−0.139332	−	0.139332i	0.634001	−	0.773332i	$-0.281412\pi$
$7$	−0.368637	−	0.368637i	−0.139332	−	0.139332i	−0.773332	+	0.634001i	$0.781412\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$	1.51010	−	1.64912i	0.477536	−	0.521497i
$11$	0.0597684			0.0180208			0.00901042	−	0.999959i	$-0.497132\pi$
$11$	0.0597684			0.0180208			0.00901042	+	0.999959i	$0.497132\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$	−0.198558	+	0.741029i	−0.0550701	+	0.205524i	−0.987979	−	0.154588i	$-0.950595\pi$
$13$	−0.198558	+	0.741029i	−0.0550701	+	0.205524i	0.932909	+	0.360112i	$0.117262\pi$
$14$	−0.260665	+	0.451486i	−0.0696658	+	0.120665i
$15$	−1.64912	−	1.51010i	−0.425801	−	0.389907i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−7.07811	+	1.89657i	−1.71669	+	0.459986i	−0.977049	−	0.213013i	$-0.931672\pi$
$17$	−7.07811	+	1.89657i	−1.71669	+	0.459986i	−0.739643	+	0.672999i	$0.765006\pi$
$18$	−0.707107	−	0.707107i	−0.166667	−	0.166667i
$19$	−2.26777	+	3.72253i	−0.520262	+	0.854006i
$19$	−2.26777	+	3.72253i	−0.520262	+	0.854006i
$20$	−1.98377	−	1.03182i	−0.443584	−	0.230723i
$21$	0.451486	+	0.260665i	0.0985223	+	0.0568819i
$22$	−0.0154692	−	0.0577318i	−0.00329804	−	0.0123085i
$23$	6.38904	+	1.71194i	1.33221	+	0.356964i	0.853537	−	0.521032i	$-0.174453\pi$
$23$	6.38904	+	1.71194i	1.33221	+	0.356964i	0.478669	+	0.877995i	$0.341119\pi$
$24$	−0.866025	−	0.500000i	−0.176777	−	0.102062i
$25$	−2.10999	+	4.53298i	−0.421998	+	0.906597i
$26$	0.767170			0.150454
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	0.503567	+	0.134930i	0.0951652	+	0.0254994i
$29$	2.71526	+	4.70297i	0.504211	+	0.873320i	0.999988	+	0.00486978i	$0.00155011\pi$
$29$	2.71526	+	4.70297i	0.504211	+	0.873320i	−0.495777	+	0.868450i	$0.665117\pi$
$30$	−1.03182	+	1.98377i	−0.188384	+	0.362185i
$31$			3.60368i			0.647240i	0.946187	+	0.323620i	$0.104900\pi$
$31$			3.60368i			0.647240i	−0.946187	+	0.323620i	$0.895100\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$	−0.0577318	+	0.0154692i	−0.0100498	+	0.00269284i
$34$	3.66390	+	6.34606i	0.628353	+	1.08834i
$35$	0.251921	−	1.13818i	0.0425825	−	0.192388i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−6.95071	+	6.95071i	−1.14269	+	1.14269i	−0.154734	+	0.987956i	$0.549452\pi$
$37$	−6.95071	+	6.95071i	−1.14269	+	1.14269i	−0.987956	+	0.154734i	$0.950548\pi$
$38$	4.18263	+	1.22704i	0.678512	+	0.199052i
$39$		−	0.767170i		−	0.122845i
$40$	−0.483227	+	2.18323i	−0.0764049	+	0.345199i
$41$	10.3170	+	5.95652i	1.61124	+	0.930252i	0.989082	+	0.147364i	$0.0470788\pi$
$41$	10.3170	+	5.95652i	1.61124	+	0.930252i	0.622162	+	0.782888i	$0.286254\pi$
$42$	0.134930	−	0.503567i	0.0208202	−	0.0777021i
$43$	−2.66556	−	9.94802i	−0.406494	−	1.51706i	−0.801283	−	0.598286i	$-0.795849\pi$
$43$	−2.66556	−	9.94802i	−0.406494	−	1.51706i	0.394788	−	0.918772i	$-0.370818\pi$
$44$	−0.0517609	+	0.0298842i	−0.00780325	+	0.00450521i
$45$	1.98377	+	1.03182i	0.295723	+	0.153815i
$46$		−	6.61442i		−	0.975243i
$47$	1.02291	−	3.81757i	0.149207	−	0.556850i	−0.850325	−	0.526259i	$-0.823594\pi$
$47$	1.02291	−	3.81757i	0.149207	−	0.556850i	0.999532	−	0.0305911i	$-0.00973896\pi$
$48$	−0.258819	+	0.965926i	−0.0373573	+	0.139419i
$49$		−	6.72821i		−	0.961173i
$50$	4.92463	+	0.864874i	0.696448	+	0.122312i
$51$	6.34606	−	3.66390i	0.888626	−	0.513048i
$52$	−0.198558	−	0.741029i	−0.0275351	−	0.102762i
$53$	−3.27763	+	12.2323i	−0.450218	+	1.68023i	0.251563	+	0.967841i	$0.419056\pi$
$53$	−3.27763	+	12.2323i	−0.450218	+	1.68023i	−0.701780	+	0.712394i	$0.747611\pi$
$54$	0.866025	+	0.500000i	0.117851	+	0.0680414i
$55$	0.0718465	+	0.112691i	0.00968779	+	0.0151953i
$56$		−	0.521331i		−	0.0696658i
$57$	1.22704	−	4.18263i	0.162525	−	0.554003i
$58$	3.83996	−	3.83996i	0.504211	−	0.504211i
$59$	0.464324	−	0.804233i	0.0604498	−	0.104702i	−0.834217	−	0.551437i	$-0.814080\pi$
$59$	0.464324	−	0.804233i	0.0604498	−	0.104702i	0.894667	+	0.446735i	$0.147413\pi$
$60$	2.18323	+	0.483227i	0.281854	+	0.0623844i
$61$	0.593198	+	1.02745i	0.0759512	+	0.131551i	0.901500	−	0.432780i	$-0.142467\pi$
$61$	0.593198	+	1.02745i	0.0759512	+	0.131551i	−0.825548	+	0.564331i	$0.809134\pi$
$62$	3.48089	−	0.932701i	0.442073	−	0.118453i
$63$	−0.503567	−	0.134930i	−0.0634435	−	0.0169996i
$64$			1.00000i			0.125000i
$65$	−1.63587	+	0.516403i	−0.202905	+	0.0640519i
$66$	0.0298842	+	0.0517609i	0.00367849	+	0.00637133i
$67$	−11.4286	−	3.06227i	−1.39622	−	0.374116i	−0.519235	−	0.854632i	$-0.673783\pi$
$67$	−11.4286	−	3.06227i	−1.39622	−	0.374116i	−0.876986	+	0.480515i	$0.840450\pi$
$68$	5.18153	−	5.18153i	0.628353	−	0.628353i
$69$	−6.61442			−0.796283
$70$	−1.16460	+	0.0512467i	−0.139197	+	0.00612515i
$71$	7.61386	+	4.39586i	0.903599	+	0.521693i	0.878366	−	0.477989i	$-0.158634\pi$
$71$	7.61386	+	4.39586i	0.903599	+	0.521693i	0.0252327	+	0.999682i	$0.491967\pi$
$72$	0.965926	+	0.258819i	0.113835	+	0.0305021i
$73$	3.66083	+	13.6624i	0.428467	+	1.59906i	0.756233	+	0.654302i	$0.227038\pi$
$73$	3.66083	+	13.6624i	0.428467	+	1.59906i	−0.327766	+	0.944759i	$0.606296\pi$
$74$	8.51285	+	4.91490i	0.989599	+	0.571345i
$75$	0.864874	−	4.92463i	0.0998670	−	0.568647i
$76$	0.102683	−	4.35769i	0.0117786	−	0.499861i
$77$	−0.0220328	−	0.0220328i	−0.00251087	−	0.00251087i
$78$	−0.741029	+	0.198558i	−0.0839050	+	0.0224823i
$79$	−1.71914	+	2.97764i	−0.193418	+	0.335010i	−0.946381	−	0.323053i	$-0.895291\pi$
$79$	−1.71914	+	2.97764i	−0.193418	+	0.335010i	0.752963	+	0.658063i	$0.228624\pi$
$80$	2.23391	−	0.0982997i	0.249758	−	0.0109902i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	3.08332	−	11.5071i	0.340496	−	1.27075i
$83$	8.15176	−	8.15176i	0.894772	−	0.894772i	−0.100196	−	0.994968i	$-0.531947\pi$
$83$	8.15176	−	8.15176i	0.894772	−	0.894772i	0.994968	+	0.100196i	$0.0319470\pi$
$84$	−0.521331			−0.0568819
$85$	−12.0844	−	11.0657i	−1.31074	−	1.20025i
$86$	−8.91915	+	5.14947i	−0.961776	+	0.555282i
$87$	−3.83996	−	3.83996i	−0.411687	−	0.411687i
$88$	0.0422626	+	0.0422626i	0.00450521	+	0.00450521i
$89$	1.67945	+	2.90889i	0.178021	+	0.308342i	0.941203	−	0.337843i	$-0.109697\pi$
$89$	1.67945	+	2.90889i	0.178021	+	0.308342i	−0.763182	+	0.646184i	$0.776364\pi$
$90$	0.483227	−	2.18323i	0.0509366	−	0.230133i
$91$	0.346366	−	0.199975i	0.0363090	−	0.0209630i
$92$	−6.38904	+	1.71194i	−0.666103	+	0.178482i
$93$	−0.932701	−	3.48089i	−0.0967166	−	0.360951i
$94$	−3.95224			−0.407642
$95$	−9.74476	+	0.198974i	−0.999792	+	0.0204143i
$96$	1.00000			0.102062
$97$	−1.74588	−	6.51573i	−0.177268	−	0.661572i	−0.996154	−	0.0876167i	$-0.972075\pi$
$97$	−1.74588	−	6.51573i	−0.177268	−	0.661572i	0.818887	−	0.573955i	$-0.194592\pi$
$98$	−6.49896	+	1.74139i	−0.656494	+	0.175907i
$99$	0.0517609	−	0.0298842i	0.00520217	−	0.00300347i
$100$	−0.439185	−	4.98067i	−0.0439185	−	0.498067i
$101$	−0.241876	−	0.418941i	−0.0240675	−	0.0416862i	0.853741	−	0.520698i	$-0.174328\pi$
$101$	−0.241876	−	0.418941i	−0.0240675	−	0.0416862i	−0.877808	+	0.479012i	$0.840995\pi$
$102$	−5.18153	−	5.18153i	−0.513048	−	0.513048i
$103$	−3.19012	−	3.19012i	−0.314331	−	0.314331i	0.532254	−	0.846585i	$-0.321345\pi$
$103$	−3.19012	−	3.19012i	−0.314331	−	0.314331i	−0.846585	+	0.532254i	$0.821345\pi$
$104$	−0.664389	+	0.383585i	−0.0651487	+	0.0376136i
$105$	0.0512467	+	1.16460i	0.00500116	+	0.113654i
$106$	12.6638			1.23002
$107$	3.51617	−	3.51617i	0.339921	−	0.339921i	−0.516416	−	0.856338i	$-0.672734\pi$
$107$	3.51617	−	3.51617i	0.339921	−	0.339921i	0.856338	+	0.516416i	$0.172734\pi$
$108$	0.258819	−	0.965926i	0.0249049	−	0.0929463i
$109$	2.94564	−	5.10200i	0.282141	−	0.488683i	−0.689771	−	0.724028i	$-0.742289\pi$
$109$	2.94564	−	5.10200i	0.282141	−	0.488683i	0.971912	+	0.235345i	$0.0756220\pi$
$110$	0.0902563	−	0.0985651i	0.00860560	−	0.00939782i
$111$	4.91490	−	8.51285i	0.466501	−	0.808004i
$112$	−0.503567	+	0.134930i	−0.0475826	+	0.0127497i
$113$	−9.89626	−	9.89626i	−0.930962	−	0.930962i	0.0668043	−	0.997766i	$-0.478720\pi$
$113$	−9.89626	−	9.89626i	−0.930962	−	0.930962i	−0.997766	+	0.0668043i	$0.978720\pi$
$114$	−4.35769	−	0.102683i	−0.408135	−	0.00961718i
$115$	4.45235	+	14.1042i	0.415184	+	1.31523i
$116$	−4.70297	−	2.71526i	−0.436660	−	0.252106i
$117$	0.198558	+	0.741029i	0.0183567	+	0.0685082i
$118$	−0.897005	−	0.240352i	−0.0825760	−	0.0221262i
$119$	3.30839	+	1.91010i	0.303280	+	0.175099i
$120$	−0.0982997	−	2.23391i	−0.00897349	−	0.203927i
$121$	−10.9964			−0.999675
$122$	0.838908	−	0.838908i	0.0759512	−	0.0759512i
$123$	−11.5071	−	3.08332i	−1.03756	−	0.278014i
$124$	−1.80184	−	3.12088i	−0.161810	−	0.280263i
$125$	−11.0832	+	1.47070i	−0.991310	+	0.131543i
$126$			0.521331i			0.0464438i
$127$	2.29949	+	0.616146i	0.204047	+	0.0546741i	0.359395	−	0.933186i	$-0.382983\pi$
$127$	2.29949	+	0.616146i	0.204047	+	0.0546741i	−0.155348	+	0.987860i	$0.549650\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$	5.14947	+	8.91915i	0.453386	+	0.785287i
$130$	0.922202	+	1.44648i	0.0808825	+	0.126864i
$131$	−1.39756	+	2.42065i	−0.122106	+	0.211493i	−0.920598	−	0.390512i	$-0.872298\pi$
$131$	−1.39756	+	2.42065i	−0.122106	+	0.211493i	0.798492	+	0.602005i	$0.205631\pi$
$132$	0.0422626	−	0.0422626i	0.00367849	−	0.00367849i
$133$	2.20824	−	0.536277i	0.191479	−	0.0465011i
$134$			11.8317i			1.02210i
$135$	−2.18323	−	0.483227i	−0.187902	−	0.0415896i
$136$	−6.34606	−	3.66390i	−0.544170	−	0.314177i
$137$	4.16802	−	15.5553i	0.356098	−	1.32898i	−0.522998	−	0.852334i	$-0.675187\pi$
$137$	4.16802	−	15.5553i	0.356098	−	1.32898i	0.879097	−	0.476644i	$-0.158147\pi$
$138$	1.71194	+	6.38904i	0.145730	+	0.543871i
$139$	1.65646	−	0.956356i	0.140499	−	0.0811170i	−0.428103	−	0.903730i	$-0.640818\pi$
$139$	1.65646	−	0.956356i	0.140499	−	0.0811170i	0.568602	+	0.822613i	$0.307485\pi$
$140$	0.350922	+	1.11166i	0.0296583	+	0.0939522i
$141$			3.95224i			0.332839i
$142$	2.27547	−	8.49215i	0.190953	−	0.712646i
$143$	−0.0118675	+	0.0442901i	−0.000992410	+	0.00370372i
$144$		−	1.00000i		−	0.0833333i
$145$	−5.60334	+	10.7729i	−0.465332	+	0.894641i
$146$	12.2494	−	7.07217i	1.01376	−	0.585297i
$147$	1.74139	+	6.49896i	0.143627	+	0.536025i
$148$	2.54414	−	9.49485i	0.209127	−	0.780472i
$149$	7.58840	+	4.38116i	0.621666	+	0.358919i	0.777517	−	0.628862i	$-0.216479\pi$
$149$	7.58840	+	4.38116i	0.621666	+	0.358919i	−0.155851	+	0.987781i	$0.549812\pi$
$150$	−4.98067	+	0.439185i	−0.406670	+	0.0358593i
$151$		−	20.5601i		−	1.67316i	−0.547844	−	0.836580i	$-0.684551\pi$
$151$		−	20.5601i		−	1.67316i	0.547844	−	0.836580i	$-0.315449\pi$
$152$	−4.23578	+	1.02867i	−0.343567	+	0.0834360i
$153$	−5.18153	+	5.18153i	−0.418902	+	0.418902i
$154$	−0.0155795	+	0.0269846i	−0.00125544	+	0.00217448i
$155$	−6.79463	+	4.33192i	−0.545758	+	0.347948i
$156$	0.383585	+	0.664389i	0.0307114	+	0.0531937i
$157$	−0.659138	+	0.176615i	−0.0526049	+	0.0140954i	−0.285026	−	0.958520i	$-0.592002\pi$
$157$	−0.659138	+	0.176615i	−0.0526049	+	0.0140954i	0.232421	+	0.972615i	$0.425335\pi$
$158$	3.32112	+	0.889892i	0.264214	+	0.0707960i
$159$		−	12.6638i		−	1.00430i
$160$	−0.673128	−	2.13235i	−0.0532154	−	0.168577i
$161$	−1.72415	−	2.98632i	−0.135882	−	0.235355i
$162$	−0.965926	−	0.258819i	−0.0758903	−	0.0203347i
$163$	0.393946	−	0.393946i	0.0308563	−	0.0308563i	−0.691510	−	0.722367i	$-0.743054\pi$
$163$	0.393946	−	0.393946i	0.0308563	−	0.0308563i	0.722367	+	0.691510i	$0.243054\pi$
$164$	−11.9130			−0.930252
$165$	−0.0985651	−	0.0902563i	−0.00767328	−	0.00702645i
$166$	−9.98383	−	5.76416i	−0.774895	−	0.447386i
$167$	12.2222	+	3.27494i	0.945784	+	0.253422i	0.698572	−	0.715539i	$-0.253819\pi$
$167$	12.2222	+	3.27494i	0.945784	+	0.253422i	0.247212	+	0.968961i	$0.420486\pi$
$168$	0.134930	+	0.503567i	0.0104101	+	0.0388510i
$169$	10.7486	+	6.20573i	0.826818	+	0.477363i
$170$	−7.56099	+	14.5367i	−0.579901	+	1.11491i
$171$	−0.102683	+	4.35769i	−0.00785239	+	0.333241i
$172$	7.28245	+	7.28245i	0.555282	+	0.555282i
$173$	8.99628	−	2.41054i	0.683974	−	0.183270i	0.0999328	−	0.994994i	$-0.468137\pi$
$173$	8.99628	−	2.41054i	0.683974	−	0.183270i	0.584041	+	0.811724i	$0.301471\pi$
$174$	−2.71526	+	4.70297i	−0.205843	+	0.356531i
$175$	2.44884	−	0.893203i	0.185115	−	0.0675198i
$176$	0.0298842	−	0.0517609i	0.00225261	−	0.00390163i
$177$	−0.240352	+	0.897005i	−0.0180659	+	0.0674230i
$178$	2.37510	−	2.37510i	0.178021	−	0.178021i
$179$	−14.5111			−1.08461			−0.542306	−	0.840181i	$-0.682449\pi$
$179$	−14.5111			−1.08461			−0.542306	+	0.840181i	$0.682449\pi$
$180$	−2.23391	+	0.0982997i	−0.166506	+	0.00732683i
$181$	1.33044	−	0.768131i	0.0988910	−	0.0570947i	−0.449739	−	0.893160i	$-0.648483\pi$
$181$	1.33044	−	0.768131i	0.0988910	−	0.0570947i	0.548630	+	0.836065i	$0.315150\pi$
$182$	−0.282807	−	0.282807i	−0.0209630	−	0.0209630i
$183$	−0.838908	−	0.838908i	−0.0620139	−	0.0620139i
$184$	3.30721	+	5.72826i	0.243811	+	0.422293i
$185$	−21.4607	−	4.75003i	−1.57782	−	0.349229i
$186$	−3.12088	+	1.80184i	−0.228834	+	0.132117i
$187$	−0.423047	+	0.113355i	−0.0309362	+	0.00828934i
$188$	1.02291	+	3.81757i	0.0746037	+	0.278425i
$189$	0.521331			0.0379212
$190$	2.71432	+	9.36122i	0.196918	+	0.679134i
$191$	13.6608			0.988463			0.494231	−	0.869330i	$-0.335450\pi$
$191$	13.6608			0.988463			0.494231	+	0.869330i	$0.335450\pi$
$192$	−0.258819	−	0.965926i	−0.0186787	−	0.0697097i
$193$	13.8806	−	3.71928i	0.999144	−	0.267720i	0.278057	−	0.960564i	$-0.410309\pi$
$193$	13.8806	−	3.71928i	0.999144	−	0.267720i	0.721087	+	0.692845i	$0.243643\pi$
$194$	−5.84184	+	3.37279i	−0.419420	+	0.242152i
$195$	1.44648	−	0.922202i	0.103584	−	0.0660402i
$196$	3.36411	+	5.82680i	0.240293	+	0.416200i
$197$	−3.83115	−	3.83115i	−0.272958	−	0.272958i	0.557332	−	0.830290i	$-0.311825\pi$
$197$	−3.83115	−	3.83115i	−0.272958	−	0.272958i	−0.830290	+	0.557332i	$0.811825\pi$
$198$	−0.0422626	−	0.0422626i	−0.00300347	−	0.00300347i
$199$	12.0319	−	6.94663i	0.852919	−	0.492433i	−0.00871546	−	0.999962i	$-0.502774\pi$
$199$	12.0319	−	6.94663i	0.852919	−	0.492433i	0.861635	+	0.507529i	$0.169441\pi$
$200$	−4.69729	+	1.71331i	−0.332149	+	0.121150i
$201$	11.8317			0.834545
$202$	−0.342064	+	0.342064i	−0.0240675	+	0.0240675i
$203$	0.732742	−	2.73463i	0.0514284	−	0.191934i
$204$	−3.66390	+	6.34606i	−0.256524	+	0.444313i
$205$	1.17105	+	26.6126i	0.0817896	+	1.85871i
$206$	−2.25575	+	3.90708i	−0.157166	+	0.272219i
$207$	6.38904	−	1.71194i	0.444069	−	0.118988i
$208$	0.542471	+	0.542471i	0.0376136	+	0.0376136i
$209$	−0.135541	+	0.222489i	−0.00937557	+	0.0153899i
$210$	1.11166	−	0.350922i	0.0767117	−	0.0242159i
$211$	12.1120	+	6.99284i	0.833822	+	0.481407i	0.855159	−	0.518365i	$-0.173459\pi$
$211$	12.1120	+	6.99284i	0.833822	+	0.481407i	−0.0213378	+	0.999772i	$0.506793\pi$
$212$	−3.27763	−	12.2323i	−0.225109	−	0.840117i
$213$	−8.49215	−	2.27547i	−0.581873	−	0.155912i
$214$	−4.30642	−	2.48631i	−0.294380	−	0.169961i
$215$	15.5525	−	16.9842i	1.06067	−	1.15831i
$216$	−1.00000			−0.0680414
$217$	1.32845	−	1.32845i	0.0901809	−	0.0901809i
$218$	−5.69054	−	1.52478i	−0.385412	−	0.103271i
$219$	−7.07217	−	12.2494i	−0.477893	−	0.827735i
$220$	−0.118567	−	0.0616704i	−0.00799376	−	0.00415782i
$221$		−	5.62166i		−	0.378154i
$222$	−9.49485	−	2.54414i	−0.637253	−	0.170751i
$223$	0.261333	−	0.0700240i	0.0175002	−	0.00468915i	−0.250058	−	0.968231i	$-0.580450\pi$
$223$	0.261333	−	0.0700240i	0.0175002	−	0.00468915i	0.267559	+	0.963542i	$0.413783\pi$
$224$	0.260665	+	0.451486i	0.0174164	+	0.0301662i
$225$	0.439185	+	4.98067i	0.0292790	+	0.332045i
$226$	−6.99771	+	12.1204i	−0.465481	+	0.806237i
$227$	−13.5426	+	13.5426i	−0.898852	+	0.898852i	−0.995335	−	0.0964831i	$-0.969241\pi$
$227$	−13.5426	+	13.5426i	−0.898852	+	0.898852i	0.0964831	+	0.995335i	$0.469241\pi$
$228$	1.02867	+	4.23578i	0.0681252	+	0.280521i
$229$		−	18.4985i		−	1.22241i	−0.791470	−	0.611207i	$-0.790684\pi$
$229$		−	18.4985i		−	1.22241i	0.791470	−	0.611207i	$-0.209316\pi$
$230$	12.4713	−	7.95108i	0.822332	−	0.524279i
$231$	0.0269846	+	0.0155795i	0.00177545	+	0.00102506i
$232$	−1.40552	+	5.24548i	−0.0922771	+	0.344383i
$233$	−2.36501	−	8.82632i	−0.154937	−	0.578231i	−0.999111	−	0.0421623i	$-0.986575\pi$
$233$	−2.36501	−	8.82632i	−0.154937	−	0.578231i	0.844174	−	0.536069i	$-0.180091\pi$
$234$	0.664389	−	0.383585i	0.0434324	−	0.0250757i
$235$	8.42754	−	2.66036i	0.549752	−	0.173543i
$236$			0.928648i			0.0604498i
$237$	0.889892	−	3.32112i	0.0578047	−	0.215730i
$238$	0.988742	−	3.69003i	0.0640906	−	0.239189i
$239$		−	24.8366i		−	1.60655i	−0.595611	−	0.803273i	$-0.703090\pi$
$239$		−	24.8366i		−	1.60655i	0.595611	−	0.803273i	$-0.296910\pi$
$240$	−2.13235	+	0.673128i	−0.137642	+	0.0434502i
$241$	0.951428	−	0.549307i	0.0612869	−	0.0353840i	−0.469043	−	0.883175i	$-0.655401\pi$
$241$	0.951428	−	0.549307i	0.0612869	−	0.0353840i	0.530330	+	0.847791i	$0.322068\pi$
$242$	2.84608	+	10.6217i	0.182953	+	0.682791i
$243$	−0.258819	+	0.965926i	−0.0166032	+	0.0619642i
$244$	−1.02745	−	0.593198i	−0.0657757	−	0.0379756i
$245$	12.6858	−	8.08787i	0.810469	−	0.516715i
$246$			11.9130i			0.759548i
$247$	−2.30822	−	2.41962i	−0.146868	−	0.153957i
$248$	−2.54819	+	2.54819i	−0.161810	+	0.161810i
$249$	−5.76416	+	9.98383i	−0.365289	+	0.632699i
$250$	4.28912	+	10.3249i	0.271268	+	0.653004i
$251$	10.8592	+	18.8087i	0.685429	+	1.18720i	0.973302	+	0.229529i	$0.0737184\pi$
$251$	10.8592	+	18.8087i	0.685429	+	1.18720i	−0.287873	+	0.957668i	$0.592948\pi$
$252$	0.503567	−	0.134930i	0.0317217	−	0.00849981i
$253$	0.381862	+	0.102320i	0.0240075	+	0.00643279i
$254$		−	2.38061i		−	0.149373i
$255$	14.5367	+	7.56099i	0.910321	+	0.473487i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	2.86951	+	0.768883i	0.178995	+	0.0479616i	0.347203	−	0.937790i	$-0.387131\pi$
$257$	2.86951	+	0.768883i	0.178995	+	0.0479616i	−0.168208	+	0.985752i	$0.553798\pi$
$258$	7.28245	−	7.28245i	0.453386	−	0.453386i
$259$	5.12457			0.318426
$260$	1.15850	−	1.26515i	0.0718474	−	0.0784615i
$261$	4.70297	+	2.71526i	0.291107	+	0.168070i
$262$	2.69989	+	0.723432i	0.166799	+	0.0446938i
$263$	−2.50949	−	9.36555i	−0.154742	−	0.577504i	−0.999127	−	0.0417683i	$-0.986701\pi$
$263$	−2.50949	−	9.36555i	−0.154742	−	0.577504i	0.844386	−	0.535736i	$-0.179966\pi$
$264$	−0.0517609	−	0.0298842i	−0.00318566	−	0.00183924i
$265$	−27.0036	+	8.52436i	−1.65882	+	0.523647i
$266$	−1.08954	−	1.99420i	−0.0668039	−	0.122272i
$267$	−2.37510	−	2.37510i	−0.145354	−	0.145354i
$268$	11.4286	−	3.06227i	0.698111	−	0.187058i
$269$	−11.2534	+	19.4915i	−0.686133	+	1.18842i	0.286947	+	0.957947i	$0.407360\pi$
$269$	−11.2534	+	19.4915i	−0.686133	+	1.18842i	−0.973079	+	0.230470i	$0.925974\pi$
$270$	0.0982997	+	2.23391i	0.00598233	+	0.135951i
$271$	−8.23345	+	14.2607i	−0.500146	+	0.866279i	0.499854	+	0.866110i	$0.333387\pi$
$271$	−8.23345	+	14.2607i	−0.500146	+	0.866279i	−1.00000		0.000168790i	$0.999946\pi$
$272$	−1.89657	+	7.07811i	−0.114997	+	0.429173i
$273$	−0.282807	+	0.282807i	−0.0171162	+	0.0171162i
$274$	−16.1040			−0.972879
$275$	−0.126111	+	0.270929i	−0.00760477	+	0.0163376i
$276$	5.72826	−	3.30721i	0.344800	−	0.199071i
$277$	−8.84018	−	8.84018i	−0.531155	−	0.531155i	0.389761	−	0.920916i	$-0.372558\pi$
$277$	−8.84018	−	8.84018i	−0.531155	−	0.531155i	−0.920916	+	0.389761i	$0.872558\pi$
$278$	−1.35249	−	1.35249i	−0.0811170	−	0.0811170i
$279$	1.80184	+	3.12088i	0.107873	+	0.186842i
$280$	0.982953	−	0.626683i	0.0587427	−	0.0374515i
$281$	−5.18752	+	2.99502i	−0.309461	+	0.178668i	−0.646685	−	0.762757i	$-0.723845\pi$
$281$	−5.18752	+	2.99502i	−0.309461	+	0.178668i	0.337224	+	0.941424i	$0.390512\pi$
$282$	3.81757	−	1.02291i	0.227333	−	0.0609137i
$283$	3.91829	+	14.6233i	0.232918	+	0.869262i	0.979076	+	0.203493i	$0.0652296\pi$
$283$	3.91829	+	14.6233i	0.232918	+	0.869262i	−0.746158	+	0.665769i	$0.768104\pi$
$284$	−8.79173			−0.521693
$285$	9.36122	−	2.71432i	0.554511	−	0.160783i
$286$	0.0458525			0.00271131
$287$	−1.60743	−	5.99901i	−0.0948836	−	0.354111i
$288$	−0.965926	+	0.258819i	−0.0569177	+	0.0152511i
$289$	31.7802	−	18.3483i	1.86942	−	1.07931i
$290$	11.8561	+	2.62418i	0.696213	+	0.154097i
$291$	3.37279	+	5.84184i	0.197716	+	0.342455i
$292$	−10.0016	−	10.0016i	−0.585297	−	0.585297i
$293$	21.6234	+	21.6234i	1.26325	+	1.26325i	0.949506	+	0.313748i	$0.101585\pi$
$293$	21.6234	+	21.6234i	1.26325	+	1.26325i	0.313748	+	0.949506i	$0.398415\pi$
$294$	5.82680	−	3.36411i	0.339826	−	0.196199i
$295$	2.07451	−	0.0912858i	0.120783	−	0.00531487i
$296$	−9.82979			−0.571345
$297$	−0.0422626	+	0.0422626i	−0.00245233	+	0.00245233i
$298$	2.26786	−	8.46376i	0.131373	−	0.490292i
$299$	−2.53719	+	4.39454i	−0.146730	+	0.254143i
$300$	1.71331	+	4.69729i	0.0989182	+	0.271198i
$301$	−2.68458	+	4.64983i	−0.154737	+	0.268012i
$302$	−19.8596	+	5.32136i	−1.14279	+	0.306210i
$303$	0.342064	+	0.342064i	0.0196510	+	0.0196510i
$304$	2.08992	+	3.82521i	0.119865	+	0.219391i
$305$	−1.22415	+	2.35354i	−0.0700947	+	0.134763i
$306$	6.34606	+	3.66390i	0.362780	+	0.209451i
$307$	6.03940	+	22.5393i	0.344687	+	1.28639i	0.892978	+	0.450101i	$0.148612\pi$
$307$	6.03940	+	22.5393i	0.344687	+	1.28639i	−0.548291	+	0.836288i	$0.684721\pi$
$308$	0.0300974	+	0.00806457i	0.00171496	+	0.000459521i
$309$	3.90708	+	2.25575i	0.222266	+	0.128325i
$310$	5.94290	+	5.44192i	0.337534	+	0.309081i
$311$	3.12024			0.176933			0.0884663	−	0.996079i	$-0.471803\pi$
$311$	3.12024			0.176933			0.0884663	+	0.996079i	$0.471803\pi$
$312$	0.542471	−	0.542471i	0.0307114	−	0.0307114i
$313$	14.3519	+	3.84558i	0.811217	+	0.217365i	0.640503	−	0.767956i	$-0.278726\pi$
$313$	14.3519	+	3.84558i	0.811217	+	0.217365i	0.170714	+	0.985321i	$0.445393\pi$
$314$	0.341195	+	0.590967i	0.0192547	+	0.0333502i
$315$	−0.350922	−	1.11166i	−0.0197722	−	0.0626348i
$316$		−	3.43828i		−	0.193418i
$317$	28.3620	+	7.59958i	1.59297	+	0.426835i	0.942910	−	0.333048i	$-0.108077\pi$
$317$	28.3620	+	7.59958i	1.59297	+	0.426835i	0.650060	+	0.759883i	$0.274744\pi$
$318$	−12.2323	+	3.27763i	−0.685953	+	0.183801i
$319$	0.162287	+	0.281089i	0.00908631	+	0.0157380i
$320$	−1.88547	+	1.20208i	−0.105401	+	0.0671985i
$321$	−2.48631	+	4.30642i	−0.138772	+	0.240361i
$322$	−2.43832	+	2.43832i	−0.135882	+	0.135882i
$323$	8.99148	−	30.6494i	0.500299	−	1.70538i
$324$			1.00000i			0.0555556i
$325$	−2.94012	−	2.46363i	−0.163088	−	0.136657i
$326$	−0.482484	−	0.278562i	−0.0267223	−	0.0154281i
$327$	−1.52478	+	5.69054i	−0.0843203	+	0.314687i
$328$	3.08332	+	11.5071i	0.170248	+	0.635374i
$329$	−1.78438	+	1.03021i	−0.0983760	+	0.0567974i
$330$	−0.0616704	+	0.118567i	−0.00339484	+	0.00652688i
$331$		−	3.55232i		−	0.195253i	−0.995223	−	0.0976265i	$-0.968875\pi$
$331$		−	3.55232i		−	0.195253i	0.995223	−	0.0976265i	$-0.0311250\pi$
$332$	−2.98375	+	11.1355i	−0.163755	+	0.611141i
$333$	−2.54414	+	9.49485i	−0.139418	+	0.520315i
$334$		−	12.6534i		−	0.692362i
$335$	−7.96426	−	25.2293i	−0.435134	−	1.37842i
$336$	0.451486	−	0.260665i	0.0246306	−	0.0142205i
$337$	4.64063	+	17.3191i	0.252791	+	0.943430i	0.969306	+	0.245858i	$0.0790697\pi$
$337$	4.64063	+	17.3191i	0.252791	+	0.943430i	−0.716514	+	0.697572i	$0.754264\pi$
$338$	3.21232	−	11.9885i	0.174727	−	0.652091i
$339$	12.1204	+	6.99771i	0.658289	+	0.380064i
$340$	15.9983	+	3.54099i	0.867627	+	0.192037i
$341$			0.215386i			0.0116638i
$342$	4.23578	−	1.02867i	0.229045	−	0.0556240i
$343$	−5.06072	+	5.06072i	−0.273253	+	0.273253i
$344$	5.14947	−	8.91915i	0.277641	−	0.480888i
$345$	−7.95108	−	12.4713i	−0.428072	−	0.671432i
$346$	−4.65681	−	8.06584i	−0.250352	−	0.433622i
$347$	29.2300	−	7.83215i	1.56915	−	0.420452i	0.633602	−	0.773659i	$-0.281576\pi$
$347$	29.2300	−	7.83215i	1.56915	−	0.420452i	0.935545	+	0.353207i	$0.114909\pi$
$348$	5.24548	+	1.40552i	0.281187	+	0.0753439i
$349$		−	1.76685i		−	0.0945771i	−0.998881	−	0.0472886i	$-0.984942\pi$
$349$		−	1.76685i		−	0.0945771i	0.998881	−	0.0472886i	$-0.0150580\pi$
$350$	−1.49658	−	2.13422i	−0.0799953	−	0.114079i
$351$	−0.383585	−	0.664389i	−0.0204742	−	0.0354624i
$352$	−0.0577318	−	0.0154692i	−0.00307712	−	0.000824511i
$353$	−12.1665	+	12.1665i	−0.647555	+	0.647555i	−0.952402	−	0.304846i	$-0.901395\pi$
$353$	−12.1665	+	12.1665i	−0.647555	+	0.647555i	0.304846	+	0.952402i	$0.401395\pi$
$354$	0.928648			0.0493571
$355$	0.864224	+	19.6399i	0.0458682	+	1.04238i
$356$	−2.90889	−	1.67945i	−0.154171	−	0.0890106i
$357$	−3.69003	−	0.988742i	−0.195297	−	0.0523298i
$358$	3.75575	+	14.0167i	0.198498	+	0.740803i
$359$	−6.74241	−	3.89273i	−0.355851	−	0.205450i	0.311408	−	0.950276i	$-0.399199\pi$
$359$	−6.74241	−	3.89273i	−0.355851	−	0.205450i	−0.667259	+	0.744826i	$0.732533\pi$
$360$	0.673128	+	2.13235i	0.0354769	+	0.112384i
$361$	−8.71443	−	16.8837i	−0.458654	−	0.888615i
$362$	−1.08630	−	1.08630i	−0.0570947	−	0.0570947i
$363$	10.6217	−	2.84608i	0.557496	−	0.149381i
$364$	−0.199975	+	0.346366i	−0.0104815	+	0.0181545i
$365$	−21.3594	+	23.3257i	−1.11800	+	1.22092i
$366$	−0.593198	+	1.02745i	−0.0310069	+	0.0537056i
$367$	−9.32638	+	34.8065i	−0.486833	+	1.81688i	0.0848290	+	0.996396i	$0.472966\pi$
$367$	−9.32638	+	34.8065i	−0.486833	+	1.81688i	−0.571662	+	0.820489i	$0.693701\pi$
$368$	4.67710	−	4.67710i	0.243811	−	0.243811i
$369$	11.9130			0.620168
$370$	0.966266	+	21.9588i	0.0502338	+	1.14159i
$371$	5.71753	−	3.30101i	0.296839	−	0.171380i
$372$	2.54819	+	2.54819i	0.132117	+	0.132117i
$373$	3.11567	+	3.11567i	0.161323	+	0.161323i	0.783153	−	0.621830i	$-0.213610\pi$
$373$	3.11567	+	3.11567i	0.161323	+	0.161323i	−0.621830	+	0.783153i	$0.713610\pi$
$374$	0.218985	+	0.379293i	0.0113235	+	0.0196128i
$375$	10.3249	−	4.28912i	0.533175	−	0.221489i
$376$	3.42274	−	1.97612i	0.176514	−	0.101911i
$377$	−4.02418	+	1.07827i	−0.207256	+	0.0555340i
$378$	−0.134930	−	0.503567i	−0.00694007	−	0.0259007i
$379$	−23.5260			−1.20845			−0.604225	−	0.796814i	$-0.706517\pi$
$379$	−23.5260			−1.20845			−0.604225	+	0.796814i	$0.706517\pi$
$380$	8.33973	−	5.04470i	0.427819	−	0.258788i
$381$	−2.38061			−0.121962
$382$	−3.53568	−	13.1953i	−0.180901	−	0.675133i
$383$	−15.3431	+	4.11117i	−0.783996	+	0.210071i	−0.628546	−	0.777773i	$-0.716349\pi$
$383$	−15.3431	+	4.11117i	−0.783996	+	0.210071i	−0.155450	+	0.987844i	$0.549683\pi$
$384$	−0.866025	+	0.500000i	−0.0441942	+	0.0255155i
$385$	0.0150569	−	0.0680274i	0.000767372	−	0.00346700i
$386$	−7.18511	−	12.4450i	−0.365712	−	0.633432i
$387$	−7.28245	−	7.28245i	−0.370188	−	0.370188i
$388$	4.76985	+	4.76985i	0.242152	+	0.242152i
$389$	−14.3306	+	8.27376i	−0.726589	+	0.419496i	−0.817173	−	0.576392i	$-0.804460\pi$
$389$	−14.3306	+	8.27376i	−0.726589	+	0.419496i	0.0905839	+	0.995889i	$0.471127\pi$
$390$	−1.26515	−	1.15850i	−0.0640636	−	0.0586632i
$391$	−48.4691			−2.45119
$392$	4.75757	−	4.75757i	0.240293	−	0.240293i
$393$	0.723432	−	2.69989i	0.0364923	−	0.136191i
$394$	−2.70903	+	4.69218i	−0.136479	+	0.236389i
$395$	−7.68079	+	0.337982i	−0.386462	+	0.0170057i
$396$	−0.0298842	+	0.0517609i	−0.00150174	+	0.00260108i
$397$	12.1269	−	3.24940i	0.608633	−	0.163083i	0.0586781	−	0.998277i	$-0.481311\pi$
$397$	12.1269	−	3.24940i	0.608633	−	0.163083i	0.549955	+	0.835194i	$0.314645\pi$
$398$	−9.82401	−	9.82401i	−0.492433	−	0.492433i
$399$	−1.99420	+	1.08954i	−0.0998349	+	0.0545452i
$400$	2.87068	+	4.09380i	0.143534	+	0.204690i
$401$	0.649182	+	0.374806i	0.0324186	+	0.0187169i	0.516122	−	0.856515i	$-0.327375\pi$
$401$	0.649182	+	0.374806i	0.0324186	+	0.0187169i	−0.483703	+	0.875232i	$0.660709\pi$
$402$	−3.06227	−	11.4286i	−0.152732	−	0.570005i
$403$	−2.67043	−	0.715540i	−0.133024	−	0.0356436i
$404$	0.418941	+	0.241876i	0.0208431	+	0.0120338i
$405$	2.23391	−	0.0982997i	0.111004	−	0.00488455i
$406$	−2.83110			−0.140505
$407$	−0.415433	+	0.415433i	−0.0205922	+	0.0205922i
$408$	7.07811	+	1.89657i	0.350418	+	0.0938943i
$409$	−14.3811	−	24.9088i	−0.711100	−	1.23166i	−0.964445	−	0.264285i	$-0.914864\pi$
$409$	−14.3811	−	24.9088i	−0.711100	−	1.23166i	0.253345	−	0.967376i	$-0.418469\pi$
$410$	25.4027	−	8.01900i	1.25455	−	0.396030i
$411$			16.1040i			0.794352i
$412$	4.35778	+	1.16766i	0.214692	+	0.0575266i
$413$	−0.467636	+	0.125303i	−0.0230109	+	0.00616575i
$414$	−3.30721	−	5.72826i	−0.162540	−	0.281528i
$415$	25.1690	+	5.57080i	1.23550	+	0.273460i
$416$	0.383585	−	0.664389i	0.0188068	−	0.0325743i
$417$	−1.35249	+	1.35249i	−0.0662318	+	0.0662318i
$418$	0.249989	+	0.0733380i	0.0122274	+	0.00358708i
$419$			13.6352i			0.666125i	0.942905	+	0.333062i	$0.108082\pi$
$419$			13.6352i			0.666125i	−0.942905	+	0.333062i	$0.891918\pi$
$420$	−0.626683	−	0.982953i	−0.0305790	−	0.0479632i
$421$	0.0498201	+	0.0287637i	0.00242808	+	0.00140186i	0.501214	−	0.865324i	$-0.332887\pi$
$421$	0.0498201	+	0.0287637i	0.00242808	+	0.00140186i	−0.498785	+	0.866725i	$0.666220\pi$
$422$	3.61976	−	13.5091i	0.176207	−	0.657614i
$423$	−1.02291	−	3.81757i	−0.0497358	−	0.185617i
$424$	−10.9672	+	6.33190i	−0.532613	+	0.307504i
$425$	6.33762	−	36.0867i	0.307420	−	1.75046i
$426$			8.79173i			0.425960i
$427$	0.160081	−	0.597430i	0.00774685	−	0.0289116i
$428$	−1.28701	+	4.80318i	−0.0622099	+	0.232171i
$429$		−	0.0458525i		−	0.00221378i
$430$	−20.4307	−	10.6267i	−0.985257	−	0.512464i
$431$	−17.3549	+	10.0199i	−0.835958	+	0.482640i	−0.855888	−	0.517161i	$-0.826989\pi$
$431$	−17.3549	+	10.0199i	−0.835958	+	0.482640i	0.0199304	+	0.999801i	$0.493656\pi$
$432$	0.258819	+	0.965926i	0.0124524	+	0.0464731i
$433$	3.06751	−	11.4481i	0.147415	−	0.550161i	−0.852221	−	0.523182i	$-0.824745\pi$
$433$	3.06751	−	11.4481i	0.147415	−	0.550161i	0.999636	−	0.0269787i	$-0.00858861\pi$
$434$	−1.62701	−	0.939355i	−0.0780990	−	0.0450905i
$435$	2.62418	−	11.8561i	0.125820	−	0.568455i
$436$			5.89128i			0.282141i
$437$	−20.8616	+	19.9011i	−0.997946	+	0.951998i
$438$	−10.0016	+	10.0016i	−0.477893	+	0.477893i
$439$	11.6735	−	20.2190i	0.557143	−	0.965001i	−0.440590	−	0.897709i	$-0.645231\pi$
$439$	11.6735	−	20.2190i	0.557143	−	0.965001i	0.997733	−	0.0672922i	$-0.0214360\pi$
$440$	−0.0288817	+	0.130488i	−0.00137688	+	0.00622077i
$441$	−3.36411	−	5.82680i	−0.160196	−	0.277467i
$442$	−5.43011	+	1.45499i	−0.258284	+	0.0692070i
$443$	−33.6277	−	9.01050i	−1.59770	−	0.428102i	−0.653352	−	0.757054i	$-0.726638\pi$
$443$	−33.6277	−	9.01050i	−1.59770	−	0.428102i	−0.944346	+	0.328953i	$0.893304\pi$
$444$			9.82979i			0.466501i
$445$	−3.46579	+	6.66328i	−0.164294	+	0.315870i
$446$	−0.135276	−	0.234305i	−0.00640550	−	0.0110947i
$447$	−8.46376	−	2.26786i	−0.400322	−	0.107266i
$448$	0.368637	−	0.368637i	0.0174164	−	0.0174164i
$449$	−11.5230			−0.543804			−0.271902	−	0.962325i	$-0.587653\pi$
$449$	−11.5230			−0.543804			−0.271902	+	0.962325i	$0.587653\pi$
$450$	4.69729	−	1.71331i	0.221432	−	0.0807664i
$451$	0.616630	+	0.356012i	0.0290360	+	0.0167639i
$452$	13.5185	+	3.62228i	0.635859	+	0.170378i
$453$	5.32136	+	19.8596i	0.250019	+	0.933084i
$454$	16.5862	+	9.57604i	0.778428	+	0.449426i
$455$	0.793407	+	0.412677i	0.0371955	+	0.0193466i
$456$	3.82521	−	2.08992i	0.179132	−	0.0978694i
$457$	24.9905	+	24.9905i	1.16901	+	1.16901i	0.982443	+	0.186562i	$0.0597346\pi$
$457$	24.9905	+	24.9905i	1.16901	+	1.16901i	0.186562	+	0.982443i	$0.440265\pi$
$458$	−17.8682	+	4.78776i	−0.834925	+	0.223717i
$459$	3.66390	−	6.34606i	0.171016	−	0.296209i
$460$	−10.9080	−	9.98845i	−0.508586	−	0.465714i
$461$	7.28630	−	12.6202i	0.339357	−	0.587783i	−0.644955	−	0.764221i	$-0.723124\pi$
$461$	7.28630	−	12.6202i	0.339357	−	0.587783i	0.984312	+	0.176437i	$0.0564572\pi$
$462$	0.00806457	−	0.0300974i	0.000375198	−	0.00140026i
$463$	0.920210	−	0.920210i	0.0427658	−	0.0427658i	−0.685400	−	0.728166i	$-0.740373\pi$
$463$	0.920210	−	0.920210i	0.0427658	−	0.0427658i	0.728166	+	0.685400i	$0.240373\pi$
$464$	5.43052			0.252106
$465$	5.44192	−	5.94290i	0.252363	−	0.275595i
$466$	−7.91346	+	4.56884i	−0.366584	+	0.211647i
$467$	−12.1803	−	12.1803i	−0.563638	−	0.563638i	0.366701	−	0.930339i	$-0.380487\pi$
$467$	−12.1803	−	12.1803i	−0.563638	−	0.563638i	−0.930339	+	0.366701i	$0.880487\pi$
$468$	−0.542471	−	0.542471i	−0.0250757	−	0.0250757i
$469$	3.08412	+	5.34185i	0.142411	+	0.246664i
$470$	−4.75092	−	7.45183i	−0.219144	−	0.343727i
$471$	0.590967	−	0.341195i	0.0272303	−	0.0157214i
$472$	0.897005	−	0.240352i	0.0412880	−	0.0110631i
$473$	−0.159316	−	0.594577i	−0.00732537	−	0.0273387i
$474$	−3.43828			−0.157925
$475$	−12.0892	−	18.1343i	−0.554689	−	0.832057i
$476$	−3.82021			−0.175099
$477$	3.27763	+	12.2323i	0.150073	+	0.560078i
$478$	−23.9903	+	6.42819i	−1.09729	+	0.294018i
$479$	25.3540	−	14.6381i	1.15845	−	0.668833i	0.207520	−	0.978231i	$-0.433461\pi$
$479$	25.3540	−	14.6381i	1.15845	−	0.668833i	0.950933	+	0.309397i	$0.100127\pi$
$480$	1.20208	+	1.88547i	0.0548673	+	0.0860595i
$481$	−3.77056	−	6.53080i	−0.171923	−	0.297779i
$482$	−0.776838	−	0.776838i	−0.0353840	−	0.0353840i
$483$	2.43832	+	2.43832i	0.110947	+	0.110947i
$484$	9.52319	−	5.49821i	0.432872	−	0.249919i
$485$	10.1865	−	11.1243i	0.462546	−	0.505127i
$486$	1.00000			0.0453609
$487$	−6.06361	+	6.06361i	−0.274768	+	0.274768i	−0.831016	−	0.556248i	$-0.812240\pi$
$487$	−6.06361	+	6.06361i	−0.274768	+	0.274768i	0.556248	+	0.831016i	$0.312240\pi$
$488$	−0.307062	+	1.14597i	−0.0139000	+	0.0518756i
$489$	−0.278562	+	0.482484i	−0.0125970	+	0.0218187i
$490$	−11.0956	−	10.1603i	−0.501249	−	0.458995i
$491$	3.65615	−	6.33263i	0.165000	−	0.285788i	−0.771656	−	0.636041i	$-0.780571\pi$
$491$	3.65615	−	6.33263i	0.165000	−	0.285788i	0.936655	+	0.350253i	$0.113904\pi$
$492$	11.5071	−	3.08332i	0.518781	−	0.139007i
$493$	−28.1384	−	28.1384i	−1.26729	−	1.26729i
$494$	−1.73977	+	2.85581i	−0.0782757	+	0.128489i
$495$	0.118567	+	0.0616704i	0.00532917	+	0.00277188i
$496$	3.12088	+	1.80184i	0.140132	+	0.0809050i
$497$	−1.18627	−	4.42722i	−0.0532115	−	0.198588i
$498$	11.1355	+	2.98375i	0.498994	+	0.133705i
$499$	−20.6345	−	11.9133i	−0.923726	−	0.533314i	−0.0389044	−	0.999243i	$-0.512387\pi$
$499$	−20.6345	−	11.9133i	−0.923726	−	0.533314i	−0.884822	+	0.465929i	$0.845720\pi$
$500$	8.86297	−	6.81525i	0.396364	−	0.304787i
$501$	−12.6534			−0.565311
$502$	15.3573	−	15.3573i	0.685429	−	0.685429i
$503$	−14.6738	−	3.93182i	−0.654271	−	0.175311i	−0.0836118	−	0.996498i	$-0.526646\pi$
$503$	−14.6738	−	3.93182i	−0.654271	−	0.175311i	−0.570659	+	0.821187i	$0.693312\pi$
$504$	−0.260665	−	0.451486i	−0.0116110	−	0.0201108i
$505$	0.499145	−	0.959650i	0.0222117	−	0.0427039i
$506$		−	0.395333i		−	0.0175747i
$507$	−11.9885	−	3.21232i	−0.532430	−	0.142664i
$508$	−2.29949	+	0.616146i	−0.102023	+	0.0273371i
$509$	17.0639	+	29.5555i	0.756343	+	1.31002i	0.944704	+	0.327924i	$0.106349\pi$
$509$	17.0639	+	29.5555i	0.756343	+	1.31002i	−0.188362	+	0.982100i	$0.560318\pi$
$510$	3.54099	−	15.9983i	0.156798	−	0.708415i
$511$	3.68694	−	6.38597i	0.163101	−	0.282499i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−1.02867	−	4.23578i	−0.0454168	−	0.187014i
$514$		−	2.97074i		−	0.131034i
$515$	2.18008	−	9.84965i	0.0960659	−	0.434027i
$516$	−8.91915	−	5.14947i	−0.392644	−	0.226693i
$517$	0.0611379	−	0.228170i	0.00268884	−	0.0100349i
$518$	−1.32634	−	4.94996i	−0.0582759	−	0.217489i
$519$	−8.06584	+	4.65681i	−0.354051	+	0.204411i
$520$	−1.52189	−	0.791583i	−0.0667392	−	0.0347132i
$521$			22.1818i			0.971801i	0.874014	+	0.485901i	$0.161508\pi$
$521$			22.1818i			0.971801i	−0.874014	+	0.485901i	$0.838492\pi$
$522$	1.40552	−	5.24548i	0.0615181	−	0.229589i
$523$	1.33351	−	4.97673i	0.0583103	−	0.217617i	−0.930623	−	0.365980i	$-0.880734\pi$
$523$	1.33351	−	4.97673i	0.0583103	−	0.217617i	0.988933	+	0.148363i	$0.0474004\pi$
$524$		−	2.79513i		−	0.122106i
$525$	−2.13422	+	1.49658i	−0.0931451	+	0.0653159i
$526$	−8.39692	+	4.84796i	−0.366123	+	0.211381i
$527$	−6.83464	−	25.5072i	−0.297722	−	1.11111i
$528$	−0.0154692	+	0.0577318i	−0.000673210	+	0.00251245i
$529$	17.9705	+	10.3753i	0.781326	+	0.451099i
$530$	15.2229	+	23.8772i	0.661242	+	1.03716i
$531$		−	0.928648i		−	0.0402999i
$532$	−1.64426	+	1.56855i	−0.0712876	+	0.0680053i
$533$	−6.46248	+	6.46248i	−0.279921	+	0.279921i
$534$	−1.67945	+	2.90889i	−0.0726768	+	0.125880i
$535$	10.8564	+	2.40291i	0.469362	+	0.103887i
$536$	−5.91586	−	10.2466i	−0.255526	−	0.442584i
$537$	14.0167	−	3.75575i	0.604863	−	0.162073i
$538$	21.7399	+	5.82519i	0.937275	+	0.251142i
$539$		−	0.402134i		−	0.0173212i
$540$	2.13235	−	0.673128i	0.0917616	−	0.0289668i
$541$	−6.14879	−	10.6500i	−0.264357	−	0.457880i	0.703038	−	0.711152i	$-0.251826\pi$
$541$	−6.14879	−	10.6500i	−0.264357	−	0.457880i	−0.967395	+	0.253272i	$0.918493\pi$
$542$	15.9058	+	4.26194i	0.683212	+	0.183066i
$543$	−1.08630	+	1.08630i	−0.0466177	+	0.0466177i
$544$	7.32779			0.314177
$545$	13.1606	−	0.579111i	0.563737	−	0.0248064i
$546$	0.346366	+	0.199975i	0.0148231	+	0.00855812i
$547$	34.7314	+	9.30625i	1.48501	+	0.397906i	0.908048	−	0.418866i	$-0.137572\pi$
$547$	34.7314	+	9.30625i	1.48501	+	0.397906i	0.576959	+	0.816773i	$0.304239\pi$
$548$	4.16802	+	15.5553i	0.178049	+	0.664489i
$549$	1.02745	+	0.593198i	0.0438504	+	0.0253171i
$550$	0.294337	+	0.0516921i	0.0125506	+	0.00220416i
$551$	−23.6645	−	0.557624i	−1.00814	−	0.0237556i
$552$	−4.67710	−	4.67710i	−0.199071	−	0.199071i
$553$	1.73140	−	0.463928i	0.0736267	−	0.0197282i
$554$	−6.25095	+	10.8270i	−0.265577	+	0.459993i
$555$	21.9588	−	0.966266i	0.932101	−	0.0410157i
$556$	−0.956356	+	1.65646i	−0.0405585	+	0.0702494i
$557$	9.81965	−	36.6474i	0.416072	−	1.55280i	−0.366608	−	0.930376i	$-0.619481\pi$
$557$	9.81965	−	36.6474i	0.416072	−	1.55280i	0.782679	−	0.622425i	$-0.213853\pi$
$558$	2.54819	−	2.54819i	0.107873	−	0.107873i
$559$	7.90104			0.334178
$560$	−0.859736	−	0.787263i	−0.0363305	−	0.0332679i
$561$	0.379293	−	0.218985i	0.0160138	−	0.00924556i
$562$	4.23559	+	4.23559i	0.178668	+	0.178668i
$563$	−5.30602	−	5.30602i	−0.223622	−	0.223622i	0.586400	−	0.810022i	$-0.300545\pi$
$563$	−5.30602	−	5.30602i	−0.223622	−	0.223622i	−0.810022	+	0.586400i	$0.800545\pi$
$564$	−1.97612	−	3.42274i	−0.0832096	−	0.144123i
$565$	6.76297	−	30.5552i	0.284520	−	1.28547i
$566$	13.1108	−	7.56955i	0.551090	−	0.318172i
$567$	−0.503567	+	0.134930i	−0.0211478	+	0.00566654i
$568$	2.27547	+	8.49215i	0.0954764	+	0.356323i
$569$	−17.8507			−0.748340			−0.374170	−	0.927360i	$-0.622072\pi$
$569$	−17.8507			−0.748340			−0.374170	+	0.927360i	$0.622072\pi$
$570$	−5.04470	−	8.33973i	−0.211299	−	0.349313i
$571$	−8.31596			−0.348012			−0.174006	−	0.984745i	$-0.555671\pi$
$571$	−8.31596			−0.348012			−0.174006	+	0.984745i	$0.555671\pi$
$572$	−0.0118675	−	0.0442901i	−0.000496205	−	0.00185186i
$573$	−13.1953	+	3.53568i	−0.551243	+	0.147705i
$574$	−5.37857	+	3.10532i	−0.224497	+	0.129613i
$575$	−21.2410	+	25.3492i	−0.885811	+	1.05714i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	4.34779	+	4.34779i	0.181001	+	0.181001i	0.791792	−	0.610791i	$-0.209148\pi$
$577$	4.34779	+	4.34779i	0.181001	+	0.181001i	−0.610791	+	0.791792i	$0.709148\pi$
$578$	−25.9484	−	25.9484i	−1.07931	−	1.07931i
$579$	−12.4450	+	7.18511i	−0.517195	+	0.298603i
$580$	−0.533819	−	12.1313i	−0.0221656	−	0.503724i
$581$	−6.01007			−0.249340
$582$	4.76985	−	4.76985i	0.197716	−	0.197716i
$583$	−0.195899	+	0.731104i	−0.00811330	+	0.0302792i
$584$	−7.07217	+	12.2494i	−0.292649	+	0.506882i
$585$	−1.15850	+	1.26515i	−0.0478983	+	0.0523077i
$586$	15.2901	−	26.4832i	0.631627	−	1.09401i
$587$	9.95712	−	2.66800i	0.410974	−	0.110120i	−0.0474075	−	0.998876i	$-0.515096\pi$
$587$	9.95712	−	2.66800i	0.410974	−	0.110120i	0.458382	+	0.888755i	$0.348429\pi$
$588$	−4.75757	−	4.75757i	−0.196199	−	0.196199i
$589$	−13.4148	−	8.17232i	−0.552747	−	0.336735i
$590$	−0.625099	−	1.98020i	−0.0257349	−	0.0815235i
$591$	4.69218	+	2.70903i	0.193011	+	0.111435i
$592$	2.54414	+	9.49485i	0.104563	+	0.390236i
$593$	38.6503	+	10.3563i	1.58718	+	0.425283i	0.941138	−	0.338022i	$-0.109758\pi$
$593$	38.6503	+	10.3563i	1.58718	+	0.425283i	0.646038	+	0.763305i	$0.276425\pi$
$594$	0.0517609	+	0.0298842i	0.00212378	+	0.00122616i
$595$	0.375525	+	8.53398i	0.0153950	+	0.349859i
$596$	−8.76233			−0.358919
$597$	−9.82401	+	9.82401i	−0.402070	+	0.402070i
$598$	4.90148	+	1.31335i	0.200436	+	0.0537067i
$599$	−16.8126	−	29.1204i	−0.686946	−	1.18983i	−0.972821	−	0.231559i	$-0.925617\pi$
$599$	−16.8126	−	29.1204i	−0.686946	−	1.18983i	0.285875	−	0.958267i	$-0.407716\pi$
$600$	4.09380	−	2.87068i	0.167129	−	0.117195i
$601$		−	16.8994i		−	0.689341i	−0.938724	−	0.344671i	$-0.887991\pi$
$601$		−	16.8994i		−	0.689341i	0.938724	−	0.344671i	$-0.112009\pi$
$602$	5.18621	+	1.38964i	0.211374	+	0.0566375i
$603$	−11.4286	+	3.06227i	−0.465407	+	0.124705i
$604$	10.2801	+	17.8056i	0.418290	+	0.724500i
$605$	−13.2186	−	20.7334i	−0.537413	−	0.842934i
$606$	0.241876	−	0.418941i	0.00982552	−	0.0170183i
$607$	11.6583	−	11.6583i	0.473194	−	0.473194i	−0.429753	−	0.902947i	$-0.641399\pi$
$607$	11.6583	−	11.6583i	0.473194	−	0.473194i	0.902947	+	0.429753i	$0.141399\pi$
$608$	3.15396	−	3.00874i	0.127910	−	0.122021i
$609$			2.83110i			0.114722i
$610$	2.59017	+	0.573299i	0.104873	+	0.0232122i
$611$	2.62582	+	1.51602i	0.106229	+	0.0613316i
$612$	1.89657	−	7.07811i	0.0766644	−	0.286115i
$613$	4.92201	+	18.3692i	0.198798	+	0.741925i	0.991251	+	0.131992i	$0.0421372\pi$
$613$	4.92201	+	18.3692i	0.198798	+	0.741925i	−0.792452	+	0.609934i	$0.791196\pi$
$614$	20.2082	−	11.6672i	0.815538	−	0.470851i
$615$	−8.01900	−	25.4027i	−0.323357	−	1.02434i
$616$		−	0.0311591i		−	0.00125544i
$617$	−9.48789	+	35.4093i	−0.381968	+	1.42552i	0.460923	+	0.887440i	$0.347518\pi$
$617$	−9.48789	+	35.4093i	−0.381968	+	1.42552i	−0.842891	+	0.538084i	$0.819148\pi$
$618$	1.16766	−	4.35778i	0.0469703	−	0.175296i
$619$			33.0155i			1.32700i	0.748174	+	0.663502i	$0.230931\pi$
$619$			33.0155i			1.32700i	−0.748174	+	0.663502i	$0.769069\pi$
$620$	3.71836	−	7.14887i	0.149333	−	0.287106i
$621$	−5.72826	+	3.30721i	−0.229867	+	0.132714i
$622$	−0.807578	−	3.01392i	−0.0323809	−	0.120847i
$623$	0.453217	−	1.69143i	0.0181578	−	0.0677657i
$624$	−0.664389	−	0.383585i	−0.0265968	−	0.0153557i
$625$	−16.0959	−	19.1291i	−0.643835	−	0.765165i
$626$		−	14.8582i		−	0.593852i
$627$	0.0733380	−	0.249989i	0.00292884	−	0.00998359i
$628$	0.482522	−	0.482522i	0.0192547	−	0.0192547i
$629$	36.0154	−	62.3804i	1.43603	−	2.48727i
$630$	−0.982953	+	0.626683i	−0.0391618	+	0.0249676i
$631$	−7.15089	−	12.3857i	−0.284672	−	0.493067i	0.687857	−	0.725846i	$-0.258551\pi$
$631$	−7.15089	−	12.3857i	−0.284672	−	0.493067i	−0.972530	+	0.232779i	$0.925218\pi$
$632$	−3.32112	+	0.889892i	−0.132107	+	0.0353980i
$633$	−13.5091	−	3.61976i	−0.536940	−	0.143873i
$634$		−	29.3625i		−	1.16613i
$635$	1.60245	+	5.07628i	0.0635914	+	0.201446i
$636$	6.33190	+	10.9672i	0.251076	+	0.434877i
$637$	4.98580	+	1.33594i	0.197545	+	0.0529319i
$638$	0.229508	−	0.229508i	0.00908631	−	0.00908631i
$639$	8.79173			0.347795
$640$	1.64912	+	1.51010i	0.0651871	+	0.0596920i
$641$	−1.70594	−	0.984925i	−0.0673806	−	0.0389022i	0.465931	−	0.884821i	$-0.345719\pi$
$641$	−1.70594	−	0.984925i	−0.0673806	−	0.0389022i	−0.533312	+	0.845919i	$0.679053\pi$
$642$	4.80318	+	1.28701i	0.189566	+	0.0507942i
$643$	10.5943	+	39.5386i	0.417800	+	1.55925i	0.779160	+	0.626825i	$0.215646\pi$
$643$	10.5943	+	39.5386i	0.417800	+	1.55925i	−0.361360	+	0.932427i	$0.617687\pi$
$644$	2.98632	+	1.72415i	0.117677	+	0.0679410i
$645$	−10.6267	+	20.4307i	−0.418425	+	0.804459i
$646$	−31.9323	−	0.752443i	−1.25636	−	0.0296045i
$647$	−3.97461	−	3.97461i	−0.156258	−	0.156258i	0.624648	−	0.780906i	$-0.285242\pi$
$647$	−3.97461	−	3.97461i	−0.156258	−	0.156258i	−0.780906	+	0.624648i	$0.785242\pi$
$648$	0.965926	−	0.258819i	0.0379452	−	0.0101674i
$649$	0.0277519	−	0.0480677i	0.00108936	−	0.00188682i
$650$	−1.61872	+	3.47757i	−0.0634915	+	0.136401i
$651$	−0.939355	+	1.62701i	−0.0368162	+	0.0637676i
$652$	−0.144194	+	0.538141i	−0.00564709	+	0.0210752i
$653$	−8.26950	+	8.26950i	−0.323611	+	0.323611i	−0.850150	−	0.526540i	$-0.823489\pi$
$653$	−8.26950	+	8.26950i	−0.323611	+	0.323611i	0.526540	+	0.850150i	$0.323489\pi$
$654$	5.89128			0.230367
$655$	−6.24405	+	0.274760i	−0.243975	+	0.0107358i
$656$	10.3170	−	5.95652i	0.402811	−	0.232563i
$657$	10.0016	+	10.0016i	0.390198	+	0.390198i
$658$	1.45694	+	1.45694i	0.0567974	+	0.0567974i
$659$	23.2988	+	40.3547i	0.907593	+	1.57200i	0.817398	+	0.576074i	$0.195416\pi$
$659$	23.2988	+	40.3547i	0.907593	+	1.57200i	0.0901954	+	0.995924i	$0.471251\pi$
$660$	0.130488	+	0.0288817i	0.00507924	+	0.00112422i
$661$	−1.82991	+	1.05650i	−0.0711752	+	0.0410930i	−0.535165	−	0.844747i	$-0.679751\pi$
$661$	−1.82991	+	1.05650i	−0.0711752	+	0.0410930i	0.463990	+	0.885840i	$0.346417\pi$
$662$	−3.43127	+	0.919407i	−0.133360	+	0.0357338i
$663$	1.45499	+	5.43011i	0.0565073	+	0.210888i
$664$	11.5283			0.447386
$665$	3.66563	+	3.51893i	0.142147	+	0.136458i
$666$	9.82979			0.380897
$667$	9.29672	+	34.6958i	0.359970	+	1.34343i
$668$	−12.2222	+	3.27494i	−0.472892	+	0.126711i
$669$	−0.234305	+	0.135276i	−0.00905875	+	0.00523007i
$670$	−22.3083	+	14.2227i	−0.861847	+	0.549471i
$671$	0.0354545	+	0.0614089i	0.00136870	+	0.00237067i
$672$	−0.368637	−	0.368637i	−0.0142205	−	0.0142205i
$673$	7.33893	+	7.33893i	0.282895	+	0.282895i	0.834263	−	0.551367i	$-0.185894\pi$
$673$	7.33893	+	7.33893i	0.282895	+	0.282895i	−0.551367	+	0.834263i	$0.685894\pi$
$674$	15.5279	−	8.96501i	0.598111	−	0.345319i
$675$	−1.71331	−	4.69729i	−0.0659455	−	0.180799i
$676$	−12.4115			−0.477363
$677$	−14.0612	+	14.0612i	−0.540415	+	0.540415i	−0.923650	−	0.383236i	$-0.874810\pi$
$677$	−14.0612	+	14.0612i	−0.540415	+	0.540415i	0.383236	+	0.923650i	$0.374810\pi$
$678$	3.62228	−	13.5185i	0.139113	−	0.519176i
$679$	−1.75834	+	3.04553i	−0.0674789	+	0.116877i
$680$	−0.720320	−	16.3696i	−0.0276230	−	0.627746i
$681$	9.57604	−	16.5862i	0.366955	−	0.635584i
$682$	0.208047	−	0.0557460i	0.00796653	−	0.00213463i
$683$	13.8268	+	13.8268i	0.529067	+	0.529067i	0.920294	−	0.391227i	$-0.127949\pi$
$683$	13.8268	+	13.8268i	0.529067	+	0.529067i	−0.391227	+	0.920294i	$0.627949\pi$
$684$	−2.08992	−	3.82521i	−0.0799100	−	0.146261i
$685$	34.3393	−	10.8401i	1.31204	−	0.414177i
$686$	6.19809	+	3.57847i	0.236644	+	0.136627i
$687$	4.78776	+	17.8682i	0.182665	+	0.681713i
$688$	−9.94802	−	2.66556i	−0.379265	−	0.101624i
$689$	−8.41368	−	4.85764i	−0.320536	−	0.185061i
$690$	−9.98845	+	10.9080i	−0.380254	+	0.415259i
$691$	−2.34466			−0.0891949			−0.0445975	−	0.999005i	$-0.514201\pi$
$691$	−2.34466			−0.0891949			−0.0445975	+	0.999005i	$0.514201\pi$
$692$	−6.58573	+	6.58573i	−0.250352	+	0.250352i
$693$	−0.0300974	−	0.00806457i	−0.00114330	−	0.000306348i
$694$	−15.1306	−	26.2069i	−0.574348	−	0.994800i
$695$	3.79438	+	1.97358i	0.143929	+	0.0748621i
$696$		−	5.43052i		−	0.205843i
$697$	−84.3218	−	22.5940i	−3.19392	−	0.855807i
$698$	−1.70664	+	0.457294i	−0.0645974	+	0.0173088i
$699$	4.56884	+	7.91346i	0.172809	+	0.299315i
$700$	−1.67416	+	1.99796i	−0.0632773	+	0.0755157i
$701$	16.8165	−	29.1270i	0.635150	−	1.10011i	−0.351334	−	0.936250i	$-0.614272\pi$
$701$	16.8165	−	29.1270i	0.635150	−	1.10011i	0.986483	−	0.163861i	$-0.0523950\pi$
$702$	−0.542471	+	0.542471i	−0.0204742	+	0.0204742i
$703$	−10.1116	−	41.6369i	−0.381366	−	1.57036i
$704$			0.0597684i			0.00225261i
$705$	−7.45183	+	4.75092i	−0.280652	+	0.178930i
$706$	14.9008	+	8.60299i	0.560799	+	0.323778i
$707$	−0.0652727	+	0.243601i	−0.00245483	+	0.00916156i
$708$	−0.240352	−	0.897005i	−0.00903297	−	0.0337115i
$709$	−8.19089	+	4.72902i	−0.307616	+	0.177602i	−0.645859	−	0.763457i	$-0.723501\pi$
$709$	−8.19089	+	4.72902i	−0.307616	+	0.177602i	0.338243	+	0.941059i	$0.390167\pi$
$710$	18.7470	−	5.91795i	0.703562	−	0.222097i
$711$			3.43828i			0.128945i
$712$	−0.869346	+	3.24444i	−0.0325801	+	0.121591i
$713$	−6.16928	+	23.0241i	−0.231041	+	0.862258i
$714$			3.82021i			0.142968i
$715$	−0.0977734	+	0.0308646i	−0.00365652	+	0.00115427i
$716$	12.5670	−	7.25556i	0.469651	−	0.271153i
$717$	6.42819	+	23.9903i	0.240065	+	0.895935i
$718$	−2.01503	+	7.52018i	−0.0752001	+	0.280651i
$719$	−18.0103	−	10.3983i	−0.671672	−	0.387790i	0.125038	−	0.992152i	$-0.460095\pi$
$719$	−18.0103	−	10.3983i	−0.671672	−	0.387790i	−0.796710	+	0.604362i	$0.793428\pi$
$720$	1.88547	−	1.20208i	0.0702673	−	0.0447990i
$721$			2.35199i			0.0875926i
$722$	−14.0529	+	12.7873i	−0.522996	+	0.475894i
$723$	−0.776838	+	0.776838i	−0.0288909	+	0.0288909i
$724$	−0.768131	+	1.33044i	−0.0285474	+	0.0494455i
$725$	−27.0477	+	2.38500i	−1.00453	+	0.0885767i
$726$	−5.49821	−	9.52319i	−0.204058	−	0.353439i
$727$	38.1815	−	10.2307i	1.41607	−	0.379436i	0.531985	−	0.846754i	$-0.321446\pi$
$727$	38.1815	−	10.2307i	1.41607	−	0.379436i	0.884089	+	0.467318i	$0.154780\pi$
$728$	0.386321	+	0.103514i	0.0143180	+	0.00383650i
$729$		−	1.00000i		−	0.0370370i
$730$	28.0591	+	14.5945i	1.03851	+	0.540165i
$731$	37.7343	+	65.3577i	1.39565	+	2.41734i
$732$	1.14597	+	0.307062i	0.0423563	+	0.0113493i
$733$	34.9712	−	34.9712i	1.29169	−	1.29169i	0.357950	−	0.933741i	$-0.383476\pi$
$733$	34.9712	−	34.9712i	1.29169	−	1.29169i	0.933741	−	0.357950i	$-0.116524\pi$
$734$	36.0343			1.33005
$735$	−10.1603	+	11.0956i	−0.374768	+	0.409268i
$736$	−5.72826	−	3.30721i	−0.211146	−	0.121905i
$737$	−0.683067	−	0.183027i	−0.0251611	−	0.00674189i
$738$	−3.08332	−	11.5071i	−0.113499	−	0.423583i
$739$	3.82117	+	2.20615i	0.140564	+	0.0811547i	0.568633	−	0.822591i	$-0.307473\pi$
$739$	3.82117	+	2.20615i	0.140564	+	0.0811547i	−0.428069	+	0.903746i	$0.640806\pi$
$740$	20.9605	−	6.61671i	0.770524	−	0.243235i
$741$	2.85581	+	1.73977i	0.104911	+	0.0639119i
$742$	−4.66834	−	4.66834i	−0.171380	−	0.171380i
$743$	−21.9779	+	5.88897i	−0.806293	+	0.216045i	−0.638345	−	0.769750i	$-0.720381\pi$
$743$	−21.9779	+	5.88897i	−0.806293	+	0.216045i	−0.167948	+	0.985796i	$0.553714\pi$
$744$	1.80184	−	3.12088i	0.0660587	−	0.114417i
$745$	0.861334	+	19.5742i	0.0315568	+	0.717144i
$746$	2.20311	−	3.81589i	0.0806615	−	0.139710i
$747$	2.98375	−	11.1355i	0.109170	−	0.407427i
$748$	0.309692	−	0.309692i	0.0113235	−	0.0113235i
$749$	−2.59238			−0.0947235
$750$	−6.81525	−	8.86297i	−0.248858	−	0.323630i
$751$	12.8407	−	7.41360i	0.468565	−	0.270526i	−0.247074	−	0.968997i	$-0.579469\pi$
$751$	12.8407	−	7.41360i	0.468565	−	0.270526i	0.715639	+	0.698471i	$0.246136\pi$
$752$	−2.79465	−	2.79465i	−0.101911	−	0.101911i
$753$	−15.3573	−	15.3573i	−0.559650	−	0.559650i
$754$	2.08307	+	3.60798i	0.0758608	+	0.131395i
$755$	38.7655	−	24.7150i	1.41082	−	0.899471i
$756$	−0.451486	+	0.260665i	−0.0164204	+	0.00948031i
$757$	−23.0438	+	6.17456i	−0.837540	+	0.224418i	−0.652000	−	0.758219i	$-0.726070\pi$
$757$	−23.0438	+	6.17456i	−0.837540	+	0.224418i	−0.185540	+	0.982637i	$0.559403\pi$
$758$	6.08898	+	22.7244i	0.221162	+	0.825386i
$759$	−0.395333			−0.0143497
$760$	−7.03128	−	6.74989i	−0.255051	−	0.244844i
$761$	−15.0394			−0.545177			−0.272589	−	0.962131i	$-0.587880\pi$
$761$	−15.0394			−0.545177			−0.272589	+	0.962131i	$0.587880\pi$
$762$	0.616146	+	2.29949i	0.0223206	+	0.0833017i
$763$	−2.96665	+	0.794912i	−0.107400	+	0.0287778i
$764$	−11.8306	+	6.83041i	−0.428017	+	0.247116i
$765$	−15.9983	−	3.54099i	−0.578418	−	0.128025i
$766$	7.94217	+	13.7562i	0.286962	+	0.497033i
$767$	0.503765	+	0.503765i	0.0181899	+	0.0181899i
$768$	0.707107	+	0.707107i	0.0255155	+	0.0255155i
$769$	21.8997	−	12.6438i	0.789722	−	0.455946i	−0.0501428	−	0.998742i	$-0.515968\pi$
$769$	21.8997	−	12.6438i	0.789722	−	0.455946i	0.839865	+	0.542796i	$0.182634\pi$
$770$	−0.0696065	+	0.00306293i	−0.00250844	+	0.000110380i
$771$	−2.97074			−0.106988
$772$	−10.1613	+	10.1613i	−0.365712	+	0.365712i
$773$	−8.49759	+	31.7135i	−0.305637	+	1.14065i	0.626758	+	0.779214i	$0.284381\pi$
$773$	−8.49759	+	31.7135i	−0.305637	+	1.14065i	−0.932395	+	0.361440i	$0.882285\pi$
$774$	−5.14947	+	8.91915i	−0.185094	+	0.320592i
$775$	−16.3354	−	7.60374i	−0.586786	−	0.273134i
$776$	3.37279	−	5.84184i	0.121076	−	0.209710i
$777$	−4.94996	+	1.32634i	−0.177579	+	0.0475821i
$778$	11.7009	+	11.7009i	0.419496	+	0.419496i
$779$	−45.5699	+	24.8973i	−1.63271	+	0.892038i
$780$	−0.791583	+	1.52189i	−0.0283432	+	0.0544923i
$781$	0.455068	+	0.262734i	0.0162836	+	0.00940135i
$782$	12.5447	+	46.8176i	0.448599	+	1.67419i
$783$	−5.24548	−	1.40552i	−0.187458	−	0.0502293i
$784$	−5.82680	−	3.36411i	−0.208100	−	0.120147i
$785$	−1.12534	−	1.03048i	−0.0401652	−	0.0367793i
$786$	−2.79513			−0.0996989
$787$	8.57494	−	8.57494i	0.305664	−	0.305664i	−0.537561	−	0.843225i	$-0.680654\pi$
$787$	8.57494	−	8.57494i	0.305664	−	0.305664i	0.843225	+	0.537561i	$0.180654\pi$
$788$	5.23345	+	1.40230i	0.186434	+	0.0499548i
$789$	4.84796	+	8.39692i	0.172592	+	0.298938i
$790$	2.31440	+	7.33160i	0.0823426	+	0.260846i
$791$			7.29625i			0.259425i
$792$	0.0577318	+	0.0154692i	0.00205141	+	0.000549674i
$793$	−0.879154	+	0.235569i	−0.0312197	+	0.00836528i
$794$	−6.27736	−	10.8727i	−0.222775	−	0.385858i
$795$	23.8772	−	15.2229i	0.846838	−	0.539902i
$796$	−6.94663	+	12.0319i	−0.246217	+	0.426460i
$797$	−14.4964	+	14.4964i	−0.513490	+	0.513490i	−0.915594	−	0.402104i	$-0.868279\pi$
$797$	−14.4964	+	14.4964i	−0.513490	+	0.513490i	0.402104	+	0.915594i	$0.368279\pi$
$798$	1.56855	+	1.64426i	0.0555261	+	0.0582060i
$799$			28.9612i			1.02457i
$800$	3.21132	−	3.83242i	0.113537	−	0.135496i
$801$	2.90889	+	1.67945i	0.102781	+	0.0593404i
$802$	0.194014	−	0.724069i	0.00685086	−	0.0255678i
$803$	0.218802	+	0.816579i	0.00772134	+	0.0288164i
$804$	−10.2466	+	5.91586i	−0.361369	+	0.208636i
$805$	3.55804	−	6.84063i	0.125404	−	0.241101i
$806$			2.76463i			0.0973801i
$807$	5.82519	−	21.7399i	0.205057	−	0.765281i
$808$	0.125204	−	0.467268i	0.00440466	−	0.0164384i
$809$			4.27002i			0.150126i	0.997179	+	0.0750630i	$0.0239158\pi$
$809$			4.27002i			0.150126i	−0.997179	+	0.0750630i	$0.976084\pi$
$810$	−0.673128	−	2.13235i	−0.0236513	−	0.0749230i
$811$	−23.4400	+	13.5331i	−0.823090	+	0.475211i	−0.851481	−	0.524385i	$-0.824295\pi$
$811$	−23.4400	+	13.5331i	−0.823090	+	0.475211i	0.0283906	+	0.999597i	$0.490962\pi$
$812$	0.732742	+	2.73463i	0.0257142	+	0.0959668i
$813$	4.26194	−	15.9058i	0.149473	−	0.557841i
$814$	0.508799	+	0.293755i	0.0178334	+	0.0102961i
$815$	1.21633	+	0.269218i	0.0426062	+	0.00943029i
$816$		−	7.32779i		−	0.256524i
$817$	43.0767	+	12.6372i	1.50706	+	0.442119i
$818$	−20.3380	+	20.3380i	−0.711100	+	0.711100i
$819$	0.199975	−	0.346366i	0.00698768	−	0.0121030i
$820$	−14.3205	−	22.4617i	−0.500092	−	0.784396i
$821$	26.6841	+	46.2182i	0.931280	+	1.61302i	0.781136	+	0.624361i	$0.214640\pi$
$821$	26.6841	+	46.2182i	0.931280	+	1.61302i	0.150144	+	0.988664i	$0.452026\pi$
$822$	15.5553	−	4.16802i	0.542553	−	0.145377i
$823$	−44.3152	−	11.8742i	−1.54473	−	0.413909i	−0.616939	−	0.787011i	$-0.711628\pi$
$823$	−44.3152	−	11.8742i	−1.54473	−	0.413909i	−0.927790	+	0.373102i	$0.878294\pi$
$824$		−	4.51150i		−	0.157166i
$825$	0.0516921	−	0.294337i	0.00179969	−	0.0102475i
$826$	0.242066	+	0.419271i	0.00842257	+	0.0145883i
$827$	34.8156	+	9.32881i	1.21066	+	0.324395i	0.807020	−	0.590524i	$-0.201079\pi$
$827$	34.8156	+	9.32881i	1.21066	+	0.324395i	0.403637	+	0.914919i	$0.367746\pi$
$828$	−4.67710	+	4.67710i	−0.162540	+	0.162540i
$829$	6.08544			0.211356			0.105678	−	0.994400i	$-0.466299\pi$
$829$	6.08544			0.211356			0.105678	+	0.994400i	$0.466299\pi$
$830$	−1.13323	−	25.7532i	−0.0393350	−	0.893907i
$831$	10.8270	+	6.25095i	0.375583	+	0.216843i
$832$	−0.741029	−	0.198558i	−0.0256906	−	0.00688377i
$833$	12.7605	+	47.6230i	0.442127	+	1.65004i
$834$	1.65646	+	0.956356i	0.0573584	+	0.0331159i
$835$	8.51734	+	26.9814i	0.294755	+	0.933729i
$836$	0.00613722	−	0.260452i	0.000212260	−	0.00900792i
$837$	−2.54819	−	2.54819i	−0.0880782	−	0.0880782i
$838$	13.1706	−	3.52906i	0.454972	−	0.121909i
$839$	−4.36061	+	7.55279i	−0.150545	+	0.260751i	−0.931428	−	0.363926i	$-0.881436\pi$
$839$	−4.36061	+	7.55279i	−0.150545	+	0.260751i	0.780883	+	0.624677i	$0.214769\pi$
$840$	−0.787263	+	0.859736i	−0.0271631	+	0.0296637i
$841$	−0.245291	+	0.424857i	−0.00845832	+	0.0146502i
$842$	0.0148892	−	0.0555671i	0.000513115	−	0.00191497i
$843$	4.23559	−	4.23559i	0.145882	−	0.145882i
$844$	−13.9857			−0.481407
$845$	1.22004	+	27.7260i	0.0419707	+	0.953804i
$846$	−3.42274	+	1.97612i	−0.117676	+	0.0679404i
$847$	4.05369	+	4.05369i	0.139286	+	0.139286i
$848$	8.95466	+	8.95466i	0.307504	+	0.307504i
$849$	−7.56955	−	13.1108i	−0.259786	−	0.449963i
$850$	−36.4974	+	3.21825i	−1.25185	+	0.110385i
$851$	−56.3076	+	32.5092i	−1.93020	+	1.11440i
$852$	8.49215	−	2.27547i	0.290936	−	0.0779562i
$853$	−1.24447	−	4.64443i	−0.0426099	−	0.159022i	0.941343	−	0.337452i	$-0.109565\pi$
$853$	−1.24447	−	4.64443i	−0.0426099	−	0.159022i	−0.983953	+	0.178430i	$0.942898\pi$
$854$	−0.618505			−0.0211648
$855$	−8.33973	+	5.04470i	−0.285213	+	0.172525i
$856$	4.97262			0.169961
$857$	−10.5684	−	39.4417i	−0.361009	−	1.34730i	−0.872752	−	0.488164i	$-0.837667\pi$
$857$	−10.5684	−	39.4417i	−0.361009	−	1.34730i	0.511743	−	0.859138i	$-0.329000\pi$
$858$	−0.0442901	+	0.0118675i	−0.00151204	+	0.000405150i
$859$	27.8307	−	16.0681i	0.949572	−	0.548236i	0.0566239	−	0.998396i	$-0.481966\pi$
$859$	27.8307	−	16.0681i	0.949572	−	0.548236i	0.892948	+	0.450160i	$0.148633\pi$
$860$	−4.97673	+	22.4850i	−0.169705	+	0.766731i
$861$	3.10532	+	5.37857i	0.105829	+	0.183301i
$862$	14.1702	+	14.1702i	0.482640	+	0.482640i
$863$	20.6160	+	20.6160i	0.701776	+	0.701776i	0.964792	−	0.263016i	$-0.0847171\pi$
$863$	20.6160	+	20.6160i	0.701776	+	0.701776i	−0.263016	+	0.964792i	$0.584717\pi$
$864$	0.866025	−	0.500000i	0.0294628	−	0.0170103i
$865$	15.3593	+	14.0645i	0.522231	+	0.478208i
$866$	−11.8520			−0.402746
$867$	−25.9484	+	25.9484i	−0.881254	+	0.881254i
$868$	−0.486246	+	1.81469i	−0.0165043	+	0.0615947i
$869$	−0.102750	+	0.177968i	−0.00348556	+	0.00603716i
$870$	−12.1313	+	0.533819i	−0.411289	+	0.0180981i
$871$	4.53847	−	7.86086i	0.153780	−	0.266355i
$872$	5.69054	−	1.52478i	0.192706	−	0.0516354i
$873$	−4.76985	−	4.76985i	−0.161435	−	0.161435i
$874$	24.6224	+	15.0000i	0.832864	+	0.507382i
$875$	4.62782	+	3.54352i	0.156449	+	0.119793i
$876$	12.2494	+	7.07217i	0.413868	+	0.238947i
$877$	−10.5163	−	39.2472i	−0.355109	−	1.32529i	−0.880347	−	0.474330i	$-0.842690\pi$
$877$	−10.5163	−	39.2472i	−0.355109	−	1.32529i	0.525238	−	0.850955i	$-0.323976\pi$
$878$	−22.5514	−	6.04262i	−0.761072	−	0.203929i
$879$	−26.4832	−	15.2901i	−0.893256	−	0.515721i
$880$	0.133517	−	0.00587521i	0.00450085	−	0.000198053i
$881$	17.8541			0.601521			0.300760	−	0.953700i	$-0.402760\pi$
$881$	17.8541			0.601521			0.300760	+	0.953700i	$0.402760\pi$
$882$	−4.75757	+	4.75757i	−0.160196	+	0.160196i
$883$	−54.5008	−	14.6034i	−1.83410	−	0.491445i	−0.835760	−	0.549095i	$-0.814972\pi$
$883$	−54.5008	−	14.6034i	−1.83410	−	0.491445i	−0.998337	+	0.0576506i	$0.981639\pi$
$884$	2.81083	+	4.86850i	0.0945385	+	0.163745i
$885$	−1.98020	+	0.625099i	−0.0665637	+	0.0210125i
$886$			34.8139i			1.16960i
$887$	43.2579	+	11.5909i	1.45246	+	0.389185i	0.896878	−	0.442278i	$-0.145829\pi$
$887$	43.2579	+	11.5909i	1.45246	+	0.389185i	0.555580	+	0.831463i	$0.312496\pi$
$888$	9.49485	−	2.54414i	0.318626	−	0.0853757i
$889$	−0.620542	−	1.07481i	−0.0208123	−	0.0360480i
$890$	7.33324	+	1.62311i	0.245811	+	0.0544068i
$891$	0.0298842	−	0.0517609i	0.00100116	−	0.00173406i
$892$	−0.191309	+	0.191309i	−0.00640550	+	0.00640550i
$893$	11.8913	+	12.4652i	0.397926	+	0.417132i
$894$			8.76233i			0.293056i
$895$	−17.4436	−	27.3603i	−0.583074	−	0.914553i
$896$	−0.451486	−	0.260665i	−0.0150831	−	0.00870822i
$897$	1.31335	−	4.90148i	0.0438514	−	0.163656i
$898$	2.98237	+	11.1304i	0.0995230	+	0.371425i
$899$	−16.9480	+	9.78494i	−0.565248	+	0.326346i
$900$	−2.87068	−	4.09380i	−0.0956894	−	0.136460i
$901$		−	92.7977i		−	3.09154i
$902$	0.184285	−	0.687762i	0.00613602	−	0.0229000i
$903$	1.38964	−	5.18621i	0.0462443	−	0.172586i
$904$		−	13.9954i		−	0.465481i
$905$	3.04759	+	1.58515i	0.101305	+	0.0526922i
$906$	17.8056	−	10.2801i	0.591552	−	0.341532i
$907$	13.5281	+	50.4875i	0.449193	+	1.67641i	0.704622	+	0.709583i	$0.251116\pi$
$907$	13.5281	+	50.4875i	0.449193	+	1.67641i	−0.255429	+	0.966828i	$0.582217\pi$
$908$	4.95692	−	18.4995i	0.164501	−	0.613927i
$909$	−0.418941	−	0.241876i	−0.0138954	−	0.00802250i
$910$	0.193266	−	0.873181i	0.00640672	−	0.0289457i
$911$		−	25.3691i		−	0.840516i	−0.907405	−	0.420258i	$-0.861940\pi$
$911$		−	25.3691i		−	0.840516i	0.907405	−	0.420258i	$-0.138060\pi$
$912$	−3.00874	−	3.15396i	−0.0996295	−	0.104438i
$913$	0.487217	−	0.487217i	0.0161245	−	0.0161245i
$914$	17.6709	−	30.6070i	0.584503	−	1.01239i
$915$	0.573299	−	2.59017i	0.0189527	−	0.0856285i
$916$	9.24925	+	16.0202i	0.305604	+	0.529321i
$917$	1.40753	−	0.377147i	0.0464809	−	0.0124545i
$918$	−7.07811	−	1.89657i	−0.233612	−	0.0625962i
$919$		−	12.1412i		−	0.400502i	−0.979745	−	0.200251i	$-0.935824\pi$
$919$		−	12.1412i		−	0.400502i	0.979745	−	0.200251i	$-0.0641758\pi$
$920$	−6.82491	+	13.1215i	−0.225011	+	0.432602i
$921$	−11.6672	−	20.2082i	−0.384448	−	0.665884i
$922$	−14.0761	−	3.77167i	−0.463570	−	0.124213i
$923$	−4.76926	+	4.76926i	−0.156982	+	0.156982i
$924$	−0.0311591			−0.00102506
$925$	−16.8415	−	46.1734i	−0.553746	−	1.51817i
$926$	−1.12702	−	0.650687i	−0.0370363	−	0.0213829i
$927$	−4.35778	−	1.16766i	−0.143128	−	0.0383511i
$928$	−1.40552	−	5.24548i	−0.0461385	−	0.172191i
$929$	15.4017	+	8.89215i	0.505312	+	0.291742i	0.730905	−	0.682480i	$-0.239098\pi$
$929$	15.4017	+	8.89215i	0.505312	+	0.291742i	−0.225592	+	0.974222i	$0.572432\pi$
$930$	−7.14887	−	3.71836i	−0.234421	−	0.121930i
$931$	25.0460	+	15.2580i	0.820848	+	0.500062i
$932$	6.46131	+	6.46131i	0.211647	+	0.211647i
$933$	−3.01392	+	0.807578i	−0.0986714	+	0.0264389i
$934$	−8.61278	+	14.9178i	−0.281819	+	0.488125i
$935$	−0.722265	−	0.661380i	−0.0236206	−	0.0216294i
$936$	−0.383585	+	0.664389i	−0.0125379	+	0.0217162i
$937$	−4.16352	+	15.5385i	−0.136016	+	0.507620i	0.863975	+	0.503534i	$0.167967\pi$
$937$	−4.16352	+	15.5385i	−0.136016	+	0.507620i	−0.999992	+	0.00408557i	$0.998700\pi$
$938$	4.36160	−	4.36160i	0.142411	−	0.142411i
$939$	−14.8582			−0.484878
$940$	−5.96828	+	6.51771i	−0.194664	+	0.212584i
$941$	33.5166	−	19.3508i	1.09261	−	0.630818i	0.158339	−	0.987385i	$-0.449386\pi$
$941$	33.5166	−	19.3508i	1.09261	−	0.630818i	0.934270	+	0.356567i	$0.116053\pi$
$942$	−0.482522	−	0.482522i	−0.0157214	−	0.0157214i
$943$	55.7185	+	55.7185i	1.81444	+	1.81444i
$944$	−0.464324	−	0.804233i	−0.0151125	−	0.0261755i
$945$	0.626683	+	0.982953i	0.0203860	+	0.0319755i
$946$	−0.533083	+	0.307776i	−0.0173320	+	0.0100066i
$947$	−49.7172	+	13.3217i	−1.61559	+	0.432897i	−0.949703	−	0.313153i	$-0.898615\pi$
$947$	−49.7172	+	13.3217i	−1.61559	+	0.432897i	−0.665890	+	0.746050i	$0.731948\pi$
$948$	0.889892	+	3.32112i	0.0289023	+	0.107865i
$949$	−10.8511			−0.352242
$950$	−14.3875	+	16.3707i	−0.466791	+	0.531137i
$951$	−29.3625			−0.952145
$952$	0.988742	+	3.69003i	0.0320453	+	0.119595i
$953$	2.27064	−	0.608415i	0.0735531	−	0.0197085i	−0.221855	−	0.975080i	$-0.571211\pi$
$953$	2.27064	−	0.608415i	0.0735531	−	0.0197085i	0.295408	+	0.955371i	$0.404544\pi$
$954$	10.9672	−	6.33190i	0.355075	−	0.205003i
$955$	16.4214	+	25.7571i	0.531386	+	0.833479i
$956$	12.4183	+	21.5091i	0.401637	+	0.695655i
$957$	−0.229508	−	0.229508i	−0.00741894	−	0.00741894i
$958$	−20.7014	−	20.7014i	−0.668833	−	0.668833i
$959$	−7.27073	+	4.19776i	−0.234784	+	0.135553i
$960$	1.51010	−	1.64912i	0.0487383	−	0.0532251i
$961$	18.0135			0.581080
$962$	−5.33238	+	5.33238i	−0.171923	+	0.171923i
$963$	1.28701	−	4.80318i	0.0414733	−	0.154780i
$964$	−0.549307	+	0.951428i	−0.0176920	+	0.0306434i
$965$	23.6982	+	21.7005i	0.762871	+	0.698563i
$966$	1.72415	−	2.98632i	0.0554736	−	0.0960831i
$967$	−0.705996	+	0.189171i	−0.0227033	+	0.00608333i	−0.270153	−	0.962817i	$-0.587074\pi$
$967$	−0.705996	+	0.189171i	−0.0227033	+	0.00608333i	0.247450	+	0.968901i	$0.420408\pi$
$968$	−7.77565	−	7.77565i	−0.249919	−	0.249919i
$969$	−0.752443	+	31.9323i	−0.0241719	+	1.02581i
$970$	−13.3817	−	6.96025i	−0.429660	−	0.223480i
$971$	−18.9634	−	10.9485i	−0.608564	−	0.351355i	0.163839	−	0.986487i	$-0.447612\pi$
$971$	−18.9634	−	10.9485i	−0.608564	−	0.351355i	−0.772403	+	0.635132i	$0.780946\pi$
$972$	−0.258819	−	0.965926i	−0.00830162	−	0.0309821i
$973$	−0.963178	−	0.258083i	−0.0308781	−	0.00827375i
$974$	7.42637	+	4.28762i	0.237956	+	0.137384i
$975$	3.47757	+	1.61872i	0.111371	+	0.0518406i
$976$	1.18640			0.0379756
$977$	39.4296	−	39.4296i	1.26147	−	1.26147i	0.311082	−	0.950383i	$-0.399309\pi$
$977$	39.4296	−	39.4296i	1.26147	−	1.26147i	0.950383	−	0.311082i	$-0.100691\pi$
$978$	0.538141	+	0.144194i	0.0172078	+	0.00461083i
$979$	0.100378	+	0.173860i	0.00320809	+	0.00555658i
$980$	−6.94233	+	13.3472i	−0.221764	+	0.426361i
$981$		−	5.89128i		−	0.188094i
$982$	−7.06314	−	1.89256i	−0.225394	−	0.0603941i
$983$	46.3747	−	12.4261i	1.47912	−	0.396330i	0.573075	−	0.819503i	$-0.305750\pi$
$983$	46.3747	−	12.4261i	1.47912	−	0.396330i	0.906049	+	0.423173i	$0.139084\pi$
$984$	−5.95652	−	10.3170i	−0.189887	−	0.328894i
$985$	2.61816	−	11.8289i	0.0834214	−	0.376899i
$986$	−19.8969	+	34.4624i	−0.633646	+	1.09751i
$987$	1.45694	−	1.45694i	0.0463749	−	0.0463749i
$988$	3.20879	+	0.941346i	0.102085	+	0.0299482i
$989$		−	68.1215i		−	2.16614i
$990$	0.0288817	−	0.130488i	0.000917921	−	0.00414718i
$991$	29.3868	+	16.9665i	0.933504	+	0.538959i	0.887918	−	0.460002i	$-0.152151\pi$
$991$	29.3868	+	16.9665i	0.933504	+	0.538959i	0.0455858	+	0.998960i	$0.485485\pi$
$992$	0.932701	−	3.48089i	0.0296133	−	0.110518i
$993$	0.919407	+	3.43127i	0.0291765	+	0.108888i
$994$	−3.96934	+	2.29170i	−0.125900	+	0.0726883i
$995$	27.5610	+	14.3354i	0.873743	+	0.454462i
$996$		−	11.5283i		−	0.365289i
$997$	3.50340	−	13.0749i	0.110954	−	0.414085i	−0.887999	−	0.459846i	$-0.847905\pi$
$997$	3.50340	−	13.0749i	0.110954	−	0.414085i	0.998952	+	0.0457610i	$0.0145713\pi$
$998$	−6.16679	+	23.0148i	−0.195206	+	0.728520i
$999$		−	9.82979i		−	0.311001i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.x.b.217.4	yes	40
5.3	odd	4	inner	570.2.x.b.103.1	✓	40
19.12	odd	6	inner	570.2.x.b.487.1	yes	40
95.88	even	12	inner	570.2.x.b.373.4	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.x.b.103.1	✓	40	5.3	odd	4	inner
570.2.x.b.217.4	yes	40	1.1	even	1	trivial
570.2.x.b.373.4	yes	40	95.88	even	12	inner
570.2.x.b.487.1	yes	40	19.12	odd	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.20208 + 1.88547i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-0.368637 - 0.368637i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.20208 + 1.88547i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-0.368637 - 0.368637i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +(1.51010 - 1.64912i) q^{10} +0.0597684 q^{11} +(0.707107 - 0.707107i) q^{12} +(-0.198558 + 0.741029i) q^{13} +(-0.260665 + 0.451486i) q^{14} +(-1.64912 - 1.51010i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-7.07811 + 1.89657i) q^{17} +(-0.707107 - 0.707107i) q^{18} +(-2.26777 + 3.72253i) q^{19} +(-1.98377 - 1.03182i) q^{20} +(0.451486 + 0.260665i) q^{21} +(-0.0154692 - 0.0577318i) q^{22} +(6.38904 + 1.71194i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(-2.10999 + 4.53298i) q^{25} +0.767170 q^{26} +(-0.707107 + 0.707107i) q^{27} +(0.503567 + 0.134930i) q^{28} +(2.71526 + 4.70297i) q^{29} +(-1.03182 + 1.98377i) q^{30} +3.60368i q^{31} +(-0.965926 - 0.258819i) q^{32} +(-0.0577318 + 0.0154692i) q^{33} +(3.66390 + 6.34606i) q^{34} +(0.251921 - 1.13818i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-6.95071 + 6.95071i) q^{37} +(4.18263 + 1.22704i) q^{38} -0.767170i q^{39} +(-0.483227 + 2.18323i) q^{40} +(10.3170 + 5.95652i) q^{41} +(0.134930 - 0.503567i) q^{42} +(-2.66556 - 9.94802i) q^{43} +(-0.0517609 + 0.0298842i) q^{44} +(1.98377 + 1.03182i) q^{45} -6.61442i q^{46} +(1.02291 - 3.81757i) q^{47} +(-0.258819 + 0.965926i) q^{48} -6.72821i q^{49} +(4.92463 + 0.864874i) q^{50} +(6.34606 - 3.66390i) q^{51} +(-0.198558 - 0.741029i) q^{52} +(-3.27763 + 12.2323i) q^{53} +(0.866025 + 0.500000i) q^{54} +(0.0718465 + 0.112691i) q^{55} -0.521331i q^{56} +(1.22704 - 4.18263i) q^{57} +(3.83996 - 3.83996i) q^{58} +(0.464324 - 0.804233i) q^{59} +(2.18323 + 0.483227i) q^{60} +(0.593198 + 1.02745i) q^{61} +(3.48089 - 0.932701i) q^{62} +(-0.503567 - 0.134930i) q^{63} +1.00000i q^{64} +(-1.63587 + 0.516403i) q^{65} +(0.0298842 + 0.0517609i) q^{66} +(-11.4286 - 3.06227i) q^{67} +(5.18153 - 5.18153i) q^{68} -6.61442 q^{69} +(-1.16460 + 0.0512467i) q^{70} +(7.61386 + 4.39586i) q^{71} +(0.965926 + 0.258819i) q^{72} +(3.66083 + 13.6624i) q^{73} +(8.51285 + 4.91490i) q^{74} +(0.864874 - 4.92463i) q^{75} +(0.102683 - 4.35769i) q^{76} +(-0.0220328 - 0.0220328i) q^{77} +(-0.741029 + 0.198558i) q^{78} +(-1.71914 + 2.97764i) q^{79} +(2.23391 - 0.0982997i) q^{80} +(0.500000 - 0.866025i) q^{81} +(3.08332 - 11.5071i) q^{82} +(8.15176 - 8.15176i) q^{83} -0.521331 q^{84} +(-12.0844 - 11.0657i) q^{85} +(-8.91915 + 5.14947i) q^{86} +(-3.83996 - 3.83996i) q^{87} +(0.0422626 + 0.0422626i) q^{88} +(1.67945 + 2.90889i) q^{89} +(0.483227 - 2.18323i) q^{90} +(0.346366 - 0.199975i) q^{91} +(-6.38904 + 1.71194i) q^{92} +(-0.932701 - 3.48089i) q^{93} -3.95224 q^{94} +(-9.74476 + 0.198974i) q^{95} +1.00000 q^{96} +(-1.74588 - 6.51573i) q^{97} +(-6.49896 + 1.74139i) q^{98} +(0.0517609 - 0.0298842i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 20 q^{6} - 8 q^{7}+O(q^{10}) \) 40 * q + 20 * q^6 - 8 * q^7	\( 40 q + 20 q^{6} - 8 q^{7} + 12 q^{10} + 8 q^{11} + 24 q^{13} + 20 q^{16} + 36 q^{21} - 8 q^{23} + 16 q^{25} + 4 q^{28} - 4 q^{35} - 20 q^{36} + 24 q^{38} + 12 q^{41} - 4 q^{42} - 12 q^{43} - 16 q^{47} + 24 q^{52} + 72 q^{53} + 8 q^{55} - 24 q^{57} - 16 q^{58} + 12 q^{60} + 24 q^{61} - 4 q^{63} + 4 q^{66} - 36 q^{67} - 24 q^{70} - 72 q^{71} - 32 q^{73} + 8 q^{76} - 88 q^{77} + 24 q^{78} + 20 q^{81} + 8 q^{82} - 88 q^{83} - 24 q^{85} - 48 q^{86} + 16 q^{87} - 24 q^{91} + 8 q^{92} - 96 q^{95} + 40 q^{96} - 60 q^{97} - 48 q^{98}+O(q^{100}) \) 40 * q + 20 * q^6 - 8 * q^7 + 12 * q^10 + 8 * q^11 + 24 * q^13 + 20 * q^16 + 36 * q^21 - 8 * q^23 + 16 * q^25 + 4 * q^28 - 4 * q^35 - 20 * q^36 + 24 * q^38 + 12 * q^41 - 4 * q^42 - 12 * q^43 - 16 * q^47 + 24 * q^52 + 72 * q^53 + 8 * q^55 - 24 * q^57 - 16 * q^58 + 12 * q^60 + 24 * q^61 - 4 * q^63 + 4 * q^66 - 36 * q^67 - 24 * q^70 - 72 * q^71 - 32 * q^73 + 8 * q^76 - 88 * q^77 + 24 * q^78 + 20 * q^81 + 8 * q^82 - 88 * q^83 - 24 * q^85 - 48 * q^86 + 16 * q^87 - 24 * q^91 + 8 * q^92 - 96 * q^95 + 40 * q^96 - 60 * q^97 - 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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