LMFDB - Embedded newform 570.2.x.b.103.1

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			103.1
Character	$\chi$	$=$	570.103
Dual form			570.2.x.b.487.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.23391 - 0.0982997i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-0.368637 + 0.368637i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.23391 - 0.0982997i) 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} +(2.18323 - 0.483227i) q^{10} +0.0597684 q^{11} +(-0.707107 - 0.707107i) q^{12} +(-0.741029 - 0.198558i) q^{13} +(0.260665 - 0.451486i) q^{14} +(0.483227 + 2.18323i) q^{15} +(0.500000 - 0.866025i) q^{16} +(1.89657 + 7.07811i) 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} +(-0.0577318 + 0.0154692i) q^{22} +(-1.71194 + 6.38904i) q^{23} +(0.866025 + 0.500000i) q^{24} +(4.98067 + 0.439185i) q^{25} +0.767170 q^{26} +(0.707107 + 0.707107i) q^{27} +(-0.134930 + 0.503567i) q^{28} +(-2.71526 - 4.70297i) q^{29} +(-1.03182 - 1.98377i) q^{30} +3.60368i q^{31} +(-0.258819 + 0.965926i) q^{32} +(-0.0154692 - 0.0577318i) q^{33} +(-3.66390 - 6.34606i) q^{34} +(0.859736 - 0.787263i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(6.95071 + 6.95071i) q^{37} +(-1.22704 + 4.18263i) q^{38} +0.767170i q^{39} +(1.64912 - 1.51010i) q^{40} +(10.3170 + 5.95652i) q^{41} +(-0.503567 - 0.134930i) q^{42} +(9.94802 - 2.66556i) q^{43} +(0.0517609 - 0.0298842i) q^{44} +(1.98377 - 1.03182i) q^{45} -6.61442i q^{46} +(-3.81757 - 1.02291i) q^{47} +(-0.965926 - 0.258819i) q^{48} +6.72821i q^{49} +(-4.92463 + 0.864874i) q^{50} +(6.34606 - 3.66390i) q^{51} +(-0.741029 + 0.198558i) q^{52} +(-12.2323 - 3.27763i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(-0.133517 - 0.00587521i) q^{55} -0.521331i q^{56} +(-4.18263 - 1.22704i) q^{57} +(3.83996 + 3.83996i) q^{58} +(-0.464324 + 0.804233i) q^{59} +(1.51010 + 1.64912i) q^{60} +(0.593198 + 1.02745i) q^{61} +(-0.932701 - 3.48089i) q^{62} +(0.134930 - 0.503567i) q^{63} -1.00000i q^{64} +(1.63587 + 0.516403i) q^{65} +(0.0298842 + 0.0517609i) q^{66} +(-3.06227 + 11.4286i) q^{67} +(5.18153 + 5.18153i) q^{68} +6.61442 q^{69} +(-0.626683 + 0.982953i) q^{70} +(7.61386 + 4.39586i) q^{71} +(0.258819 - 0.965926i) q^{72} +(-13.6624 + 3.66083i) 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} +(-0.198558 - 0.741029i) q^{78} +(1.71914 - 2.97764i) q^{79} +(-1.20208 + 1.88547i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-11.5071 - 3.08332i) q^{82} +(8.15176 + 8.15176i) q^{83} +0.521331 q^{84} +(-3.54099 - 15.9983i) 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} +(-1.64912 + 1.51010i) q^{90} +(0.346366 - 0.199975i) q^{91} +(1.71194 + 6.38904i) q^{92} +(3.48089 - 0.932701i) q^{93} +3.95224 q^{94} +(-5.43191 + 8.09286i) q^{95} +1.00000 q^{96} +(-6.51573 + 1.74588i) q^{97} +(-1.74139 - 6.49896i) 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 $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$3$	−0.258819	−	0.965926i	−0.149429	−	0.557678i
$3$	−0.258819	−	0.965926i	−0.149429	−	0.557678i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−2.23391	−	0.0982997i	−0.999033	−	0.0439610i
$5$	−2.23391	−	0.0982997i	−0.999033	−	0.0439610i
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$	−0.368637	+	0.368637i	−0.139332	+	0.139332i	−0.773332	−	0.634001i	$-0.781412\pi$
$7$	−0.368637	+	0.368637i	−0.139332	+	0.139332i	0.634001	+	0.773332i	$0.281412\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−0.866025	+	0.500000i	−0.288675	+	0.166667i
$10$	2.18323	−	0.483227i	0.690398	−	0.152810i
$11$	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
$13$	−0.741029	−	0.198558i	−0.205524	−	0.0550701i	0.154588	−	0.987979i	$-0.450595\pi$
$13$	−0.741029	−	0.198558i	−0.205524	−	0.0550701i	−0.360112	+	0.932909i	$0.617262\pi$
$14$	0.260665	−	0.451486i	0.0696658	−	0.120665i
$15$	0.483227	+	2.18323i	0.124769	+	0.563707i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	1.89657	+	7.07811i	0.459986	+	1.71669i	0.672999	+	0.739643i	$0.265006\pi$
$17$	1.89657	+	7.07811i	0.459986	+	1.71669i	−0.213013	+	0.977049i	$0.568328\pi$
$18$	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
$22$	−0.0577318	+	0.0154692i	−0.0123085	+	0.00329804i
$23$	−1.71194	+	6.38904i	−0.356964	+	1.33221i	0.521032	+	0.853537i	$0.325547\pi$
$23$	−1.71194	+	6.38904i	−0.356964	+	1.33221i	−0.877995	+	0.478669i	$0.841119\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	4.98067	+	0.439185i	0.996135	+	0.0878369i
$26$	0.767170			0.150454
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	−0.134930	+	0.503567i	−0.0254994	+	0.0951652i
$29$	−2.71526	−	4.70297i	−0.504211	−	0.873320i	−0.999988	−	0.00486978i	$-0.998450\pi$
$29$	−2.71526	−	4.70297i	−0.504211	−	0.873320i	0.495777	−	0.868450i	$-0.334883\pi$
$30$	−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	$0.895100\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$	−0.0154692	−	0.0577318i	−0.00269284	−	0.0100498i
$34$	−3.66390	−	6.34606i	−0.628353	−	1.08834i
$35$	0.859736	−	0.787263i	0.145322	−	0.133072i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	6.95071	+	6.95071i	1.14269	+	1.14269i	0.987956	+	0.154734i	$0.0494522\pi$
$37$	6.95071	+	6.95071i	1.14269	+	1.14269i	0.154734	+	0.987956i	$0.450548\pi$
$38$	−1.22704	+	4.18263i	−0.199052	+	0.678512i
$39$			0.767170i			0.122845i
$40$	1.64912	−	1.51010i	0.260749	−	0.238768i
$41$	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	$0.286254\pi$
$42$	−0.503567	−	0.134930i	−0.0777021	−	0.0208202i
$43$	9.94802	−	2.66556i	1.51706	−	0.406494i	0.598286	−	0.801283i	$-0.295849\pi$
$43$	9.94802	−	2.66556i	1.51706	−	0.406494i	0.918772	+	0.394788i	$0.129182\pi$
$44$	0.0517609	−	0.0298842i	0.00780325	−	0.00450521i
$45$	1.98377	−	1.03182i	0.295723	−	0.153815i
$46$		−	6.61442i		−	0.975243i
$47$	−3.81757	−	1.02291i	−0.556850	−	0.149207i	−0.0305911	−	0.999532i	$-0.509739\pi$
$47$	−3.81757	−	1.02291i	−0.556850	−	0.149207i	−0.526259	+	0.850325i	$0.676406\pi$
$48$	−0.965926	−	0.258819i	−0.139419	−	0.0373573i
$49$			6.72821i			0.961173i
$50$	−4.92463	+	0.864874i	−0.696448	+	0.122312i
$51$	6.34606	−	3.66390i	0.888626	−	0.513048i
$52$	−0.741029	+	0.198558i	−0.102762	+	0.0275351i
$53$	−12.2323	−	3.27763i	−1.68023	−	0.450218i	−0.712394	−	0.701780i	$-0.752389\pi$
$53$	−12.2323	−	3.27763i	−1.68023	−	0.450218i	−0.967841	+	0.251563i	$0.919056\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$	−0.133517	−	0.00587521i	−0.0180034	−	0.000792213i
$56$		−	0.521331i		−	0.0696658i
$57$	−4.18263	−	1.22704i	−0.554003	−	0.162525i
$58$	3.83996	+	3.83996i	0.504211	+	0.504211i
$59$	−0.464324	+	0.804233i	−0.0604498	+	0.104702i	−0.894667	−	0.446735i	$-0.852587\pi$
$59$	−0.464324	+	0.804233i	−0.0604498	+	0.104702i	0.834217	+	0.551437i	$0.185920\pi$
$60$	1.51010	+	1.64912i	0.194953	+	0.212900i
$61$	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	$0.809134\pi$
$62$	−0.932701	−	3.48089i	−0.118453	−	0.442073i
$63$	0.134930	−	0.503567i	0.0169996	−	0.0634435i
$64$		−	1.00000i		−	0.125000i
$65$	1.63587	+	0.516403i	0.202905	+	0.0640519i
$66$	0.0298842	+	0.0517609i	0.00367849	+	0.00637133i
$67$	−3.06227	+	11.4286i	−0.374116	+	1.39622i	0.480515	+	0.876986i	$0.340450\pi$
$67$	−3.06227	+	11.4286i	−0.374116	+	1.39622i	−0.854632	+	0.519235i	$0.826217\pi$
$68$	5.18153	+	5.18153i	0.628353	+	0.628353i
$69$	6.61442			0.796283
$70$	−0.626683	+	0.982953i	−0.0749029	+	0.117485i
$71$	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	$0.491967\pi$
$72$	0.258819	−	0.965926i	0.0305021	−	0.113835i
$73$	−13.6624	+	3.66083i	−1.59906	+	0.428467i	−0.944759	−	0.327766i	$-0.893704\pi$
$73$	−13.6624	+	3.66083i	−1.59906	+	0.428467i	−0.654302	+	0.756233i	$0.727038\pi$
$74$	−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
$78$	−0.198558	−	0.741029i	−0.0224823	−	0.0839050i
$79$	1.71914	−	2.97764i	0.193418	−	0.335010i	−0.752963	−	0.658063i	$-0.771376\pi$
$79$	1.71914	−	2.97764i	0.193418	−	0.335010i	0.946381	+	0.323053i	$0.104709\pi$
$80$	−1.20208	+	1.88547i	−0.134397	+	0.210802i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	−11.5071	−	3.08332i	−1.27075	−	0.340496i
$83$	8.15176	+	8.15176i	0.894772	+	0.894772i	0.994968	−	0.100196i	$-0.0319470\pi$
$83$	8.15176	+	8.15176i	0.894772	+	0.894772i	−0.100196	+	0.994968i	$0.531947\pi$
$84$	0.521331			0.0568819
$85$	−3.54099	−	15.9983i	−0.384074	−	1.73525i
$86$	−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	0.763182	−	0.646184i	$-0.223636\pi$
$89$	−1.67945	−	2.90889i	−0.178021	−	0.308342i	−0.941203	+	0.337843i	$0.890303\pi$
$90$	−1.64912	+	1.51010i	−0.173832	+	0.159179i
$91$	0.346366	−	0.199975i	0.0363090	−	0.0209630i
$92$	1.71194	+	6.38904i	0.178482	+	0.666103i
$93$	3.48089	−	0.932701i	0.360951	−	0.0967166i
$94$	3.95224			0.407642
$95$	−5.43191	+	8.09286i	−0.557302	+	0.830310i
$96$	1.00000			0.102062
$97$	−6.51573	+	1.74588i	−0.661572	+	0.177268i	−0.573955	−	0.818887i	$-0.694592\pi$
$97$	−6.51573	+	1.74588i	−0.661572	+	0.177268i	−0.0876167	+	0.996154i	$0.527925\pi$
$98$	−1.74139	−	6.49896i	−0.175907	−	0.656494i
$99$	−0.0517609	+	0.0298842i	−0.00520217	+	0.00300347i
$100$	4.53298	−	2.10999i	0.453298	−	0.210999i
$101$	−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	$-0.678655\pi$
$103$	3.19012	−	3.19012i	0.314331	−	0.314331i	0.846585	+	0.532254i	$0.178655\pi$
$104$	0.664389	−	0.383585i	0.0651487	−	0.0376136i
$105$	−0.982953	−	0.626683i	−0.0959264	−	0.0611580i
$106$	12.6638			1.23002
$107$	−3.51617	−	3.51617i	−0.339921	−	0.339921i	0.516416	−	0.856338i	$-0.327266\pi$
$107$	−3.51617	−	3.51617i	−0.339921	−	0.339921i	−0.856338	+	0.516416i	$0.827266\pi$
$108$	0.965926	+	0.258819i	0.0929463	+	0.0249049i
$109$	−2.94564	+	5.10200i	−0.282141	+	0.488683i	−0.971912	−	0.235345i	$-0.924378\pi$
$109$	−2.94564	+	5.10200i	−0.282141	+	0.488683i	0.689771	+	0.724028i	$0.257711\pi$
$110$	0.130488	−	0.0288817i	0.0124415	−	0.00275376i
$111$	4.91490	−	8.51285i	0.466501	−	0.808004i
$112$	0.134930	+	0.503567i	0.0127497	+	0.0475826i
$113$	9.89626	−	9.89626i	0.930962	−	0.930962i	−0.0668043	−	0.997766i	$-0.521280\pi$
$113$	9.89626	−	9.89626i	0.930962	−	0.930962i	0.997766	+	0.0668043i	$0.0212803\pi$
$114$	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
$117$	0.741029	−	0.198558i	0.0685082	−	0.0183567i
$118$	0.240352	−	0.897005i	0.0221262	−	0.0825760i
$119$	−3.30839	−	1.91010i	−0.303280	−	0.175099i
$120$	−1.88547	−	1.20208i	−0.172119	−	0.109735i
$121$	−10.9964			−0.999675
$122$	−0.838908	−	0.838908i	−0.0759512	−	0.0759512i
$123$	3.08332	−	11.5071i	0.278014	−	1.03756i
$124$	1.80184	+	3.12088i	0.161810	+	0.280263i
$125$	−11.0832	−	1.47070i	−0.991310	−	0.131543i
$126$			0.521331i			0.0464438i
$127$	0.616146	−	2.29949i	0.0546741	−	0.204047i	−0.933186	−	0.359395i	$-0.882983\pi$
$127$	0.616146	−	2.29949i	0.0546741	−	0.204047i	0.987860	+	0.155348i	$0.0496499\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$	−5.14947	−	8.91915i	−0.453386	−	0.785287i
$130$	−1.71379	−	0.0754125i	−0.150309	−	0.00661412i
$131$	−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
$133$	0.536277	+	2.20824i	0.0465011	+	0.191479i
$134$		−	11.8317i		−	1.02210i
$135$	−1.51010	−	1.64912i	−0.129969	−	0.141934i
$136$	−6.34606	−	3.66390i	−0.544170	−	0.314177i
$137$	−15.5553	−	4.16802i	−1.32898	−	0.356098i	−0.476644	−	0.879097i	$-0.658147\pi$
$137$	−15.5553	−	4.16802i	−1.32898	−	0.356098i	−0.852334	+	0.522998i	$0.824813\pi$
$138$	−6.38904	+	1.71194i	−0.543871	+	0.145730i
$139$	−1.65646	+	0.956356i	−0.140499	+	0.0811170i	−0.568602	−	0.822613i	$-0.692515\pi$
$139$	−1.65646	+	0.956356i	−0.140499	+	0.0811170i	0.428103	+	0.903730i	$0.359182\pi$
$140$	0.350922	−	1.11166i	0.0296583	−	0.0939522i
$141$			3.95224i			0.332839i
$142$	−8.49215	−	2.27547i	−0.712646	−	0.190953i
$143$	−0.0442901	−	0.0118675i	−0.00370372	−	0.000992410i
$144$			1.00000i			0.0833333i
$145$	5.60334	+	10.7729i	0.465332	+	0.894641i
$146$	12.2494	−	7.07217i	1.01376	−	0.585297i
$147$	6.49896	−	1.74139i	0.536025	−	0.143627i
$148$	9.49485	+	2.54414i	0.780472	+	0.209127i
$149$	−7.58840	−	4.38116i	−0.621666	−	0.358919i	0.155851	−	0.987781i	$-0.450188\pi$
$149$	−7.58840	−	4.38116i	−0.621666	−	0.358919i	−0.777517	+	0.628862i	$0.783521\pi$
$150$	2.10999	+	4.53298i	0.172280	+	0.370116i
$151$		−	20.5601i		−	1.67316i	−0.547844	−	0.836580i	$-0.684551\pi$
$151$		−	20.5601i		−	1.67316i	0.547844	−	0.836580i	$-0.315449\pi$
$152$	1.02867	+	4.23578i	0.0834360	+	0.343567i
$153$	−5.18153	−	5.18153i	−0.418902	−	0.418902i
$154$	0.0155795	−	0.0269846i	0.00125544	−	0.00217448i
$155$	0.354241	−	8.05028i	0.0284533	−	0.646614i
$156$	0.383585	+	0.664389i	0.0307114	+	0.0531937i
$157$	0.176615	+	0.659138i	0.0140954	+	0.0526049i	0.972615	−	0.232421i	$-0.0746646\pi$
$157$	0.176615	+	0.659138i	0.0140954	+	0.0526049i	−0.958520	+	0.285026i	$0.907998\pi$
$158$	−0.889892	+	3.32112i	−0.0707960	+	0.264214i
$159$			12.6638i			1.00430i
$160$	0.673128	−	2.13235i	0.0532154	−	0.168577i
$161$	−1.72415	−	2.98632i	−0.135882	−	0.235355i
$162$	−0.258819	+	0.965926i	−0.0203347	+	0.0758903i
$163$	0.393946	+	0.393946i	0.0308563	+	0.0308563i	0.722367	−	0.691510i	$-0.243054\pi$
$163$	0.393946	+	0.393946i	0.0308563	+	0.0308563i	−0.691510	+	0.722367i	$0.743054\pi$
$164$	11.9130			0.930252
$165$	0.0288817	+	0.130488i	0.00224844	+	0.0101585i
$166$	−9.98383	−	5.76416i	−0.774895	−	0.447386i
$167$	3.27494	−	12.2222i	0.253422	−	0.945784i	−0.715539	−	0.698572i	$-0.753819\pi$
$167$	3.27494	−	12.2222i	0.253422	−	0.945784i	0.968961	−	0.247212i	$-0.0795143\pi$
$168$	−0.503567	+	0.134930i	−0.0388510	+	0.0104101i
$169$	−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
$173$	2.41054	+	8.99628i	0.183270	+	0.683974i	0.994994	+	0.0999328i	$0.0318628\pi$
$173$	2.41054	+	8.99628i	0.183270	+	0.683974i	−0.811724	+	0.584041i	$0.801471\pi$
$174$	2.71526	−	4.70297i	0.205843	−	0.356531i
$175$	−1.99796	+	1.67416i	−0.151031	+	0.126555i
$176$	0.0298842	−	0.0517609i	0.00225261	−	0.00390163i
$177$	0.897005	+	0.240352i	0.0674230	+	0.0180659i
$178$	2.37510	+	2.37510i	0.178021	+	0.178021i
$179$	14.5111			1.08461			0.542306	−	0.840181i	$-0.317551\pi$
$179$	14.5111			1.08461			0.542306	+	0.840181i	$0.317551\pi$
$180$	1.20208	−	1.88547i	0.0895980	−	0.140535i
$181$	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
$185$	−14.8440	−	16.2105i	−1.09135	−	1.19182i
$186$	−3.12088	+	1.80184i	−0.228834	+	0.132117i
$187$	0.113355	+	0.423047i	0.00828934	+	0.0309362i
$188$	−3.81757	+	1.02291i	−0.278425	+	0.0746037i
$189$	−0.521331			−0.0379212
$190$	3.15224	−	9.22298i	0.228687	−	0.669105i
$191$	13.6608			0.988463			0.494231	−	0.869330i	$-0.335450\pi$
$191$	13.6608			0.988463			0.494231	+	0.869330i	$0.335450\pi$
$192$	−0.965926	+	0.258819i	−0.0697097	+	0.0186787i
$193$	3.71928	+	13.8806i	0.267720	+	0.999144i	0.960564	+	0.278057i	$0.0896905\pi$
$193$	3.71928	+	13.8806i	0.267720	+	0.999144i	−0.692845	+	0.721087i	$0.743643\pi$
$194$	5.84184	−	3.37279i	0.419420	−	0.242152i
$195$	0.0754125	−	1.71379i	0.00540040	−	0.122727i
$196$	3.36411	+	5.82680i	0.240293	+	0.416200i
$197$	−3.83115	+	3.83115i	−0.272958	+	0.272958i	−0.830290	−	0.557332i	$-0.811825\pi$
$197$	−3.83115	+	3.83115i	−0.272958	+	0.272958i	0.557332	+	0.830290i	$0.311825\pi$
$198$	0.0422626	−	0.0422626i	0.00300347	−	0.00300347i
$199$	−12.0319	+	6.94663i	−0.852919	+	0.492433i	−0.861635	−	0.507529i	$-0.830559\pi$
$199$	−12.0319	+	6.94663i	−0.852919	+	0.492433i	0.00871546	+	0.999962i	$0.497226\pi$
$200$	−3.83242	+	3.21132i	−0.270993	+	0.227074i
$201$	11.8317			0.834545
$202$	0.342064	+	0.342064i	0.0240675	+	0.0240675i
$203$	2.73463	+	0.732742i	0.191934	+	0.0514284i
$204$	3.66390	−	6.34606i	0.256524	−	0.444313i
$205$	−22.4617	−	14.3205i	−1.56879	−	1.00018i
$206$	−2.25575	+	3.90708i	−0.157166	+	0.272219i
$207$	−1.71194	−	6.38904i	−0.118988	−	0.444069i
$208$	−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	$0.506793\pi$
$212$	−12.2323	+	3.27763i	−0.840117	+	0.225109i
$213$	2.27547	−	8.49215i	0.155912	−	0.581873i
$214$	4.30642	+	2.48631i	0.294380	+	0.169961i
$215$	−22.4850	+	4.97673i	−1.53346	+	0.339410i
$216$	−1.00000			−0.0680414
$217$	−1.32845	−	1.32845i	−0.0901809	−	0.0901809i
$218$	1.52478	−	5.69054i	0.103271	−	0.385412i
$219$	7.07217	+	12.2494i	0.477893	+	0.827735i
$220$	−0.118567	+	0.0616704i	−0.00799376	+	0.00415782i
$221$		−	5.62166i		−	0.378154i
$222$	−2.54414	+	9.49485i	−0.170751	+	0.637253i
$223$	0.0700240	+	0.261333i	0.00468915	+	0.0175002i	0.968231	−	0.250058i	$-0.0804498\pi$
$223$	0.0700240	+	0.261333i	0.00468915	+	0.0175002i	−0.963542	+	0.267559i	$0.913783\pi$
$224$	−0.260665	−	0.451486i	−0.0174164	−	0.0301662i
$225$	−4.53298	+	2.10999i	−0.302199	+	0.140666i
$226$	−6.99771	+	12.1204i	−0.465481	+	0.806237i
$227$	13.5426	+	13.5426i	0.898852	+	0.898852i	0.995335	−	0.0964831i	$-0.0307594\pi$
$227$	13.5426	+	13.5426i	0.898852	+	0.898852i	−0.0964831	+	0.995335i	$0.530759\pi$
$228$	−4.23578	+	1.02867i	−0.280521	+	0.0681252i
$229$			18.4985i			1.22241i	0.791470	+	0.611207i	$0.209316\pi$
$229$			18.4985i			1.22241i	−0.791470	+	0.611207i	$0.790684\pi$
$230$	−0.650195	+	14.7760i	−0.0428726	+	0.974300i
$231$	0.0269846	+	0.0155795i	0.00177545	+	0.00102506i
$232$	5.24548	+	1.40552i	0.344383	+	0.0922771i
$233$	8.82632	−	2.36501i	0.578231	−	0.154937i	0.0421623	−	0.999111i	$-0.486575\pi$
$233$	8.82632	−	2.36501i	0.578231	−	0.154937i	0.536069	+	0.844174i	$0.319909\pi$
$234$	−0.664389	+	0.383585i	−0.0434324	+	0.0250757i
$235$	8.42754	+	2.66036i	0.549752	+	0.173543i
$236$			0.928648i			0.0604498i
$237$	−3.32112	−	0.889892i	−0.215730	−	0.0578047i
$238$	3.69003	+	0.988742i	0.239189	+	0.0640906i
$239$			24.8366i			1.60655i	0.595611	+	0.803273i	$0.296910\pi$
$239$			24.8366i			1.60655i	−0.595611	+	0.803273i	$0.703090\pi$
$240$	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	$0.322068\pi$
$242$	10.6217	−	2.84608i	0.682791	−	0.182953i
$243$	−0.965926	−	0.258819i	−0.0619642	−	0.0166032i
$244$	1.02745	+	0.593198i	0.0657757	+	0.0379756i
$245$	0.661381	−	15.0302i	0.0422541	−	0.960244i
$246$			11.9130i			0.759548i
$247$	−2.41962	+	2.30822i	−0.153957	+	0.146868i
$248$	−2.54819	−	2.54819i	−0.161810	−	0.161810i
$249$	5.76416	−	9.98383i	0.365289	−	0.632699i
$250$	11.0862	−	1.44796i	0.701152	−	0.0915768i
$251$	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	$0.592948\pi$
$252$	−0.134930	−	0.503567i	−0.00849981	−	0.0317217i
$253$	−0.102320	+	0.381862i	−0.00643279	+	0.0240075i
$254$			2.38061i			0.149373i
$255$	−14.5367	+	7.56099i	−0.910321	+	0.473487i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	0.768883	−	2.86951i	0.0479616	−	0.178995i	−0.937790	−	0.347203i	$-0.887131\pi$
$257$	0.768883	−	2.86951i	0.0479616	−	0.178995i	0.985752	+	0.168208i	$0.0537981\pi$
$258$	7.28245	+	7.28245i	0.453386	+	0.453386i
$259$	−5.12457			−0.318426
$260$	1.67491	−	0.370717i	0.103873	−	0.0229909i
$261$	4.70297	+	2.71526i	0.291107	+	0.168070i
$262$	0.723432	−	2.69989i	0.0446938	−	0.166799i
$263$	9.36555	−	2.50949i	0.577504	−	0.154742i	0.0417683	−	0.999127i	$-0.486701\pi$
$263$	9.36555	−	2.50949i	0.577504	−	0.154742i	0.535736	+	0.844386i	$0.320034\pi$
$264$	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
$268$	3.06227	+	11.4286i	0.187058	+	0.698111i
$269$	11.2534	−	19.4915i	0.686133	−	1.18842i	−0.286947	−	0.957947i	$-0.592640\pi$
$269$	11.2534	−	19.4915i	0.686133	−	1.18842i	0.973079	−	0.230470i	$-0.0740264\pi$
$270$	1.88547	+	1.20208i	0.114746	+	0.0731565i
$271$	−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	$0.999946\pi$
$272$	7.07811	+	1.89657i	0.429173	+	0.114997i
$273$	−0.282807	−	0.282807i	−0.0171162	−	0.0171162i
$274$	16.1040			0.972879
$275$	0.297687	+	0.0262493i	0.0179512	+	0.00158289i
$276$	5.72826	−	3.30721i	0.344800	−	0.199071i
$277$	−8.84018	+	8.84018i	−0.531155	+	0.531155i	−0.920916	−	0.389761i	$-0.872558\pi$
$277$	−8.84018	+	8.84018i	−0.531155	+	0.531155i	0.389761	+	0.920916i	$0.372558\pi$
$278$	1.35249	−	1.35249i	0.0811170	−	0.0811170i
$279$	−1.80184	−	3.12088i	−0.107873	−	0.186842i
$280$	−0.0512467	+	1.16460i	−0.00306257	+	0.0695984i
$281$	−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	$0.390512\pi$
$282$	−1.02291	−	3.81757i	−0.0609137	−	0.227333i
$283$	−14.6233	+	3.91829i	−0.869262	+	0.232918i	−0.665769	−	0.746158i	$-0.731896\pi$
$283$	−14.6233	+	3.91829i	−0.869262	+	0.232918i	−0.203493	+	0.979076i	$0.565230\pi$
$284$	8.79173			0.521693
$285$	9.22298	+	3.15224i	0.546322	+	0.186722i
$286$	0.0458525			0.00271131
$287$	−5.99901	+	1.60743i	−0.354111	+	0.0948836i
$288$	−0.258819	−	0.965926i	−0.0152511	−	0.0569177i
$289$	−31.7802	+	18.3483i	−1.86942	+	1.07931i
$290$	−8.20064	−	8.95558i	−0.481558	−	0.525890i
$291$	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	−0.313748	+	0.949506i	$0.601585\pi$
$293$	−21.6234	+	21.6234i	−1.26325	+	1.26325i	−0.949506	+	0.313748i	$0.898415\pi$
$294$	−5.82680	+	3.36411i	−0.339826	+	0.196199i
$295$	1.11631	−	1.75094i	0.0649942	−	0.101944i
$296$	−9.82979			−0.571345
$297$	0.0422626	+	0.0422626i	0.00245233	+	0.00245233i
$298$	8.46376	+	2.26786i	0.490292	+	0.131373i
$299$	2.53719	−	4.39454i	0.146730	−	0.254143i
$300$	−3.21132	−	3.83242i	−0.185406	−	0.221265i
$301$	−2.68458	+	4.64983i	−0.154737	+	0.268012i
$302$	5.32136	+	19.8596i	0.306210	+	1.14279i
$303$	−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
$307$	22.5393	−	6.03940i	1.28639	−	0.344687i	0.450101	−	0.892978i	$-0.351388\pi$
$307$	22.5393	−	6.03940i	1.28639	−	0.344687i	0.836288	+	0.548291i	$0.184721\pi$
$308$	−0.00806457	+	0.0300974i	−0.000459521	+	0.00171496i
$309$	−3.90708	−	2.25575i	−0.222266	−	0.128325i
$310$	1.74140	+	7.86766i	0.0989047	+	0.446853i
$311$	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
$313$	−3.84558	+	14.3519i	−0.217365	+	0.811217i	0.767956	+	0.640503i	$0.221274\pi$
$313$	−3.84558	+	14.3519i	−0.217365	+	0.811217i	−0.985321	+	0.170714i	$0.945393\pi$
$314$	−0.341195	−	0.590967i	−0.0192547	−	0.0333502i
$315$	−0.350922	+	1.11166i	−0.0197722	+	0.0626348i
$316$		−	3.43828i		−	0.193418i
$317$	7.59958	−	28.3620i	0.426835	−	1.59297i	−0.333048	−	0.942910i	$-0.608077\pi$
$317$	7.59958	−	28.3620i	0.426835	−	1.59297i	0.759883	−	0.650060i	$-0.225256\pi$
$318$	−3.27763	−	12.2323i	−0.183801	−	0.685953i
$319$	−0.162287	−	0.281089i	−0.00908631	−	0.0157380i
$320$	−0.0982997	+	2.23391i	−0.00549512	+	0.124879i
$321$	−2.48631	+	4.30642i	−0.138772	+	0.240361i
$322$	2.43832	+	2.43832i	0.135882	+	0.135882i
$323$	30.6494	+	8.99148i	1.70538	+	0.500299i
$324$		−	1.00000i		−	0.0555556i
$325$	−3.60362	−	1.31440i	−0.199893	−	0.0729099i
$326$	−0.482484	−	0.278562i	−0.0267223	−	0.0154281i
$327$	5.69054	+	1.52478i	0.314687	+	0.0843203i
$328$	−11.5071	+	3.08332i	−0.635374	+	0.170248i
$329$	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	$-0.0311250\pi$
$332$	11.1355	+	2.98375i	0.611141	+	0.163755i
$333$	−9.49485	−	2.54414i	−0.520315	−	0.139418i
$334$			12.6534i			0.692362i
$335$	7.96426	−	25.2293i	0.435134	−	1.37842i
$336$	0.451486	−	0.260665i	0.0246306	−	0.0142205i
$337$	17.3191	−	4.64063i	0.943430	−	0.252791i	0.245858	−	0.969306i	$-0.420930\pi$
$337$	17.3191	−	4.64063i	0.943430	−	0.252791i	0.697572	+	0.716514i	$0.254264\pi$
$338$	11.9885	+	3.21232i	0.652091	+	0.174727i
$339$	−12.1204	−	6.99771i	−0.658289	−	0.380064i
$340$	−11.0657	−	12.0844i	−0.600123	−	0.655369i
$341$			0.215386i			0.0116638i
$342$	−1.02867	−	4.23578i	−0.0556240	−	0.229045i
$343$	−5.06072	−	5.06072i	−0.273253	−	0.273253i
$344$	−5.14947	+	8.91915i	−0.277641	+	0.480888i
$345$	−14.7760	−	0.650195i	−0.795513	−	0.0350053i
$346$	−4.65681	−	8.06584i	−0.250352	−	0.433622i
$347$	−7.83215	−	29.2300i	−0.420452	−	1.56915i	−0.773659	−	0.633602i	$-0.781576\pi$
$347$	−7.83215	−	29.2300i	−0.420452	−	1.56915i	0.353207	−	0.935545i	$-0.385091\pi$
$348$	−1.40552	+	5.24548i	−0.0753439	+	0.281187i
$349$			1.76685i			0.0945771i	0.998881	+	0.0472886i	$0.0150580\pi$
$349$			1.76685i			0.0945771i	−0.998881	+	0.0472886i	$0.984942\pi$
$350$	1.49658	−	2.13422i	0.0799953	−	0.114079i
$351$	−0.383585	−	0.664389i	−0.0204742	−	0.0354624i
$352$	−0.0154692	+	0.0577318i	−0.000824511	+	0.00307712i
$353$	−12.1665	−	12.1665i	−0.647555	−	0.647555i	0.304846	−	0.952402i	$-0.401395\pi$
$353$	−12.1665	−	12.1665i	−0.647555	−	0.647555i	−0.952402	+	0.304846i	$0.901395\pi$
$354$	−0.928648			−0.0493571
$355$	−16.5765	−	10.5684i	−0.879791	−	0.560912i
$356$	−2.90889	−	1.67945i	−0.154171	−	0.0890106i
$357$	−0.988742	+	3.69003i	−0.0523298	+	0.195297i
$358$	−14.0167	+	3.75575i	−0.740803	+	0.198498i
$359$	6.74241	+	3.89273i	0.355851	+	0.205450i	0.667259	−	0.744826i	$-0.267467\pi$
$359$	6.74241	+	3.89273i	0.355851	+	0.205450i	−0.311408	+	0.950276i	$0.600801\pi$
$360$	−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
$363$	2.84608	+	10.6217i	0.149381	+	0.557496i
$364$	0.199975	−	0.346366i	0.0104815	−	0.0181545i
$365$	30.8804	−	6.83493i	1.61635	−	0.357757i
$366$	−0.593198	+	1.02745i	−0.0310069	+	0.0537056i
$367$	34.8065	+	9.32638i	1.81688	+	0.486833i	0.996396	−	0.0848290i	$-0.0270344\pi$
$367$	34.8065	+	9.32638i	1.81688	+	0.486833i	0.820489	+	0.571662i	$0.193701\pi$
$368$	4.67710	+	4.67710i	0.243811	+	0.243811i
$369$	−11.9130			−0.620168
$370$	18.5338	+	11.8162i	0.963525	+	0.614297i
$371$	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	$-0.786390\pi$
$373$	−3.11567	+	3.11567i	−0.161323	+	0.161323i	0.621830	+	0.783153i	$0.286390\pi$
$374$	−0.218985	−	0.379293i	−0.0113235	−	0.0196128i
$375$	1.44796	+	11.0862i	0.0747722	+	0.572488i
$376$	3.42274	−	1.97612i	0.176514	−	0.101911i
$377$	1.07827	+	4.02418i	0.0555340	+	0.207256i
$378$	0.503567	−	0.134930i	0.0259007	−	0.00694007i
$379$	23.5260			1.20845			0.604225	−	0.796814i	$-0.293483\pi$
$379$	23.5260			1.20845			0.604225	+	0.796814i	$0.293483\pi$
$380$	−0.657745	+	9.72458i	−0.0337416	+	0.498860i
$381$	−2.38061			−0.121962
$382$	−13.1953	+	3.53568i	−0.675133	+	0.180901i
$383$	−4.11117	−	15.3431i	−0.210071	−	0.783996i	−0.987844	−	0.155450i	$-0.950317\pi$
$383$	−4.11117	−	15.3431i	−0.210071	−	0.783996i	0.777773	−	0.628546i	$-0.216349\pi$
$384$	0.866025	−	0.500000i	0.0441942	−	0.0255155i
$385$	0.0513850	−	0.0470534i	0.00261882	−	0.00239806i
$386$	−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	−0.0905839	−	0.995889i	$-0.528873\pi$
$389$	14.3306	−	8.27376i	0.726589	−	0.419496i	0.817173	+	0.576392i	$0.195540\pi$
$390$	0.370717	+	1.67491i	0.0187720	+	0.0848123i
$391$	−48.4691			−2.45119
$392$	−4.75757	−	4.75757i	−0.240293	−	0.240293i
$393$	2.69989	+	0.723432i	0.136191	+	0.0364923i
$394$	2.70903	−	4.69218i	0.136479	−	0.236389i
$395$	−4.13309	+	6.48277i	−0.207959	+	0.326183i
$396$	−0.0298842	+	0.0517609i	−0.00150174	+	0.00260108i
$397$	−3.24940	−	12.1269i	−0.163083	−	0.608633i	−0.998277	−	0.0586781i	$-0.981311\pi$
$397$	−3.24940	−	12.1269i	−0.163083	−	0.608633i	0.835194	−	0.549955i	$-0.185355\pi$
$398$	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	$0.660709\pi$
$402$	−11.4286	+	3.06227i	−0.570005	+	0.152732i
$403$	0.715540	−	2.67043i	0.0356436	−	0.133024i
$404$	−0.418941	−	0.241876i	−0.0208431	−	0.0120338i
$405$	−1.20208	+	1.88547i	−0.0597320	+	0.0936897i
$406$	−2.83110			−0.140505
$407$	0.415433	+	0.415433i	0.0205922	+	0.0205922i
$408$	−1.89657	+	7.07811i	−0.0938943	+	0.350418i
$409$	14.3811	+	24.9088i	0.711100	+	1.23166i	0.964445	+	0.264285i	$0.0851359\pi$
$409$	14.3811	+	24.9088i	0.711100	+	1.23166i	−0.253345	+	0.967376i	$0.581531\pi$
$410$	25.4027	+	8.01900i	1.25455	+	0.396030i
$411$			16.1040i			0.794352i
$412$	1.16766	−	4.35778i	0.0575266	−	0.214692i
$413$	−0.125303	−	0.467636i	−0.00616575	−	0.0230109i
$414$	3.30721	+	5.72826i	0.162540	+	0.281528i
$415$	−17.4090	−	19.0116i	−0.854572	−	0.933242i
$416$	0.383585	−	0.664389i	0.0188068	−	0.0325743i
$417$	1.35249	+	1.35249i	0.0662318	+	0.0662318i
$418$	−0.0733380	+	0.249989i	−0.00358708	+	0.0122274i
$419$		−	13.6352i		−	0.666125i	−0.942905	−	0.333062i	$-0.891918\pi$
$419$		−	13.6352i		−	0.666125i	0.942905	−	0.333062i	$-0.108082\pi$
$420$	−1.16460	−	0.0512467i	−0.0568269	−	0.00250058i
$421$	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	$0.666220\pi$
$422$	−13.5091	−	3.61976i	−0.657614	−	0.176207i
$423$	3.81757	−	1.02291i	0.185617	−	0.0497358i
$424$	10.9672	−	6.33190i	0.532613	−	0.307504i
$425$	6.33762	+	36.0867i	0.307420	+	1.75046i
$426$			8.79173i			0.425960i
$427$	−0.597430	−	0.160081i	−0.0289116	−	0.00774685i
$428$	−4.80318	−	1.28701i	−0.232171	−	0.0622099i
$429$			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	$0.493656\pi$
$432$	0.965926	−	0.258819i	0.0464731	−	0.0124524i
$433$	11.4481	+	3.06751i	0.550161	+	0.147415i	0.523182	−	0.852221i	$-0.324745\pi$
$433$	11.4481	+	3.06751i	0.550161	+	0.147415i	0.0269787	+	0.999636i	$0.491411\pi$
$434$	1.62701	+	0.939355i	0.0780990	+	0.0450905i
$435$	8.95558	−	8.20064i	0.429387	−	0.393191i
$436$			5.89128i			0.282141i
$437$	19.9011	+	20.8616i	0.951998	+	0.997946i
$438$	−10.0016	−	10.0016i	−0.477893	−	0.477893i
$439$	−11.6735	+	20.2190i	−0.557143	+	0.965001i	0.440590	+	0.897709i	$0.354769\pi$
$439$	−11.6735	+	20.2190i	−0.557143	+	0.965001i	−0.997733	+	0.0672922i	$0.978564\pi$
$440$	0.0985651	−	0.0902563i	0.00469891	−	0.00430280i
$441$	−3.36411	−	5.82680i	−0.160196	−	0.277467i
$442$	1.45499	+	5.43011i	0.0692070	+	0.258284i
$443$	9.01050	−	33.6277i	0.428102	−	1.59770i	−0.328953	−	0.944346i	$-0.606696\pi$
$443$	9.01050	−	33.6277i	0.428102	−	1.59770i	0.757054	−	0.653352i	$-0.226638\pi$
$444$		−	9.82979i		−	0.466501i
$445$	3.46579	+	6.66328i	0.164294	+	0.315870i
$446$	−0.135276	−	0.234305i	−0.00640550	−	0.0110947i
$447$	−2.26786	+	8.46376i	−0.107266	+	0.400322i
$448$	0.368637	+	0.368637i	0.0174164	+	0.0174164i
$449$	11.5230			0.543804			0.271902	−	0.962325i	$-0.412347\pi$
$449$	11.5230			0.543804			0.271902	+	0.962325i	$0.412347\pi$
$450$	3.83242	−	3.21132i	0.180662	−	0.151383i
$451$	0.616630	+	0.356012i	0.0290360	+	0.0167639i
$452$	3.62228	−	13.5185i	0.170378	−	0.635859i
$453$	−19.8596	+	5.32136i	−0.933084	+	0.250019i
$454$	−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	0.186562	−	0.982443i	$-0.440265\pi$
$457$	24.9905	−	24.9905i	1.16901	−	1.16901i	0.982443	−	0.186562i	$-0.0597346\pi$
$458$	−4.78776	−	17.8682i	−0.223717	−	0.834925i
$459$	−3.66390	+	6.34606i	−0.171016	+	0.296209i
$460$	−3.19627	−	14.4408i	−0.149027	−	0.673306i
$461$	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	$0.0564572\pi$
$462$	−0.0300974	−	0.00806457i	−0.00140026	−	0.000375198i
$463$	0.920210	+	0.920210i	0.0427658	+	0.0427658i	0.728166	−	0.685400i	$-0.240373\pi$
$463$	0.920210	+	0.920210i	0.0427658	+	0.0427658i	−0.685400	+	0.728166i	$0.740373\pi$
$464$	−5.43052			−0.252106
$465$	−7.86766	+	1.74140i	−0.364854	+	0.0807553i
$466$	−7.91346	+	4.56884i	−0.366584	+	0.211647i
$467$	−12.1803	+	12.1803i	−0.563638	+	0.563638i	−0.930339	−	0.366701i	$-0.880487\pi$
$467$	−12.1803	+	12.1803i	−0.563638	+	0.563638i	0.366701	+	0.930339i	$0.380487\pi$
$468$	0.542471	−	0.542471i	0.0250757	−	0.0250757i
$469$	−3.08412	−	5.34185i	−0.142411	−	0.246664i
$470$	−8.82893	−	0.388504i	−0.407248	−	0.0179203i
$471$	0.590967	−	0.341195i	0.0272303	−	0.0157214i
$472$	−0.240352	−	0.897005i	−0.0110631	−	0.0412880i
$473$	0.594577	−	0.159316i	0.0273387	−	0.00732537i
$474$	3.43828			0.157925
$475$	12.9299	−	17.5447i	0.593265	−	0.805007i
$476$	−3.82021			−0.175099
$477$	12.2323	−	3.27763i	0.560078	−	0.150073i
$478$	−6.42819	−	23.9903i	−0.294018	−	1.09729i
$479$	−25.3540	+	14.6381i	−1.15845	+	0.668833i	−0.950933	−	0.309397i	$-0.899873\pi$
$479$	−25.3540	+	14.6381i	−1.15845	+	0.668833i	−0.207520	+	0.978231i	$0.566539\pi$
$480$	−2.23391	−	0.0982997i	−0.101963	−	0.00448675i
$481$	−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
$485$	14.7272	−	3.25965i	0.668725	−	0.148013i
$486$	1.00000			0.0453609
$487$	6.06361	+	6.06361i	0.274768	+	0.274768i	0.831016	−	0.556248i	$-0.187760\pi$
$487$	6.06361	+	6.06361i	0.274768	+	0.274768i	−0.556248	+	0.831016i	$0.687760\pi$
$488$	−1.14597	−	0.307062i	−0.0518756	−	0.0139000i
$489$	0.278562	−	0.482484i	0.0125970	−	0.0218187i
$490$	3.25126	+	14.6892i	0.146877	+	0.663592i
$491$	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	$0.113904\pi$
$492$	−3.08332	−	11.5071i	−0.139007	−	0.518781i
$493$	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
$497$	−4.42722	+	1.18627i	−0.198588	+	0.0532115i
$498$	−2.98375	+	11.1355i	−0.133705	+	0.498994i
$499$	20.6345	+	11.9133i	0.923726	+	0.533314i	0.884822	−	0.465929i	$-0.154280\pi$
$499$	20.6345	+	11.9133i	0.923726	+	0.533314i	0.0389044	+	0.999243i	$0.487613\pi$
$500$	−10.3337	+	4.26793i	−0.462136	+	0.190868i
$501$	−12.6534			−0.565311
$502$	−15.3573	−	15.3573i	−0.685429	−	0.685429i
$503$	3.93182	−	14.6738i	0.175311	−	0.654271i	−0.821187	−	0.570659i	$-0.806688\pi$
$503$	3.93182	−	14.6738i	0.175311	−	0.654271i	0.996498	−	0.0836118i	$-0.0266456\pi$
$504$	0.260665	+	0.451486i	0.0116110	+	0.0201108i
$505$	0.499145	+	0.959650i	0.0222117	+	0.0427039i
$506$		−	0.395333i		−	0.0175747i
$507$	−3.21232	+	11.9885i	−0.142664	+	0.532430i
$508$	−0.616146	−	2.29949i	−0.0273371	−	0.102023i
$509$	−17.0639	−	29.5555i	−0.756343	−	1.31002i	−0.944704	−	0.327924i	$-0.893651\pi$
$509$	−17.0639	−	29.5555i	−0.756343	−	1.31002i	0.188362	−	0.982100i	$-0.439682\pi$
$510$	12.0844	−	11.0657i	0.535106	−	0.489998i
$511$	3.68694	−	6.38597i	0.163101	−	0.282499i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	4.23578	−	1.02867i	0.187014	−	0.0454168i
$514$			2.97074i			0.131034i
$515$	−7.44001	+	6.81283i	−0.327846	+	0.300209i
$516$	−8.91915	−	5.14947i	−0.392644	−	0.226693i
$517$	−0.228170	−	0.0611379i	−0.0100349	−	0.00268884i
$518$	4.94996	−	1.32634i	0.217489	−	0.0582759i
$519$	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	$0.838492\pi$
$522$	−5.24548	−	1.40552i	−0.229589	−	0.0615181i
$523$	4.97673	+	1.33351i	0.217617	+	0.0583103i	0.365980	−	0.930623i	$-0.380734\pi$
$523$	4.97673	+	1.33351i	0.217617	+	0.0583103i	−0.148363	+	0.988933i	$0.547400\pi$
$524$			2.79513i			0.122106i
$525$	2.13422	+	1.49658i	0.0931451	+	0.0653159i
$526$	−8.39692	+	4.84796i	−0.366123	+	0.211381i
$527$	−25.5072	+	6.83464i	−1.11111	+	0.297722i
$528$	−0.0577318	−	0.0154692i	−0.00251245	−	0.000673210i
$529$	−17.9705	−	10.3753i	−0.781326	−	0.451099i
$530$	−28.2897	−	1.24485i	−1.22883	−	0.0540727i
$531$		−	0.928648i		−	0.0402999i
$532$	1.56855	+	1.64426i	0.0680053	+	0.0712876i
$533$	−6.46248	−	6.46248i	−0.279921	−	0.279921i
$534$	1.67945	−	2.90889i	0.0726768	−	0.125880i
$535$	7.50916	+	8.20044i	0.324649	+	0.354536i
$536$	−5.91586	−	10.2466i	−0.255526	−	0.442584i
$537$	−3.75575	−	14.0167i	−0.162073	−	0.604863i
$538$	−5.82519	+	21.7399i	−0.251142	+	0.937275i
$539$			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	$0.918493\pi$
$542$	4.26194	−	15.9058i	0.183066	−	0.683212i
$543$	−1.08630	−	1.08630i	−0.0466177	−	0.0466177i
$544$	−7.32779			−0.314177
$545$	7.08181	−	11.1078i	0.303351	−	0.475807i
$546$	0.346366	+	0.199975i	0.0148231	+	0.00855812i
$547$	9.30625	−	34.7314i	0.397906	−	1.48501i	−0.418866	−	0.908048i	$-0.637572\pi$
$547$	9.30625	−	34.7314i	0.397906	−	1.48501i	0.816773	−	0.576959i	$-0.195761\pi$
$548$	−15.5553	+	4.16802i	−0.664489	+	0.178049i
$549$	−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
$553$	0.463928	+	1.73140i	0.0197282	+	0.0736267i
$554$	6.25095	−	10.8270i	0.265577	−	0.459993i
$555$	−11.8162	+	18.5338i	−0.501571	+	0.786715i
$556$	−0.956356	+	1.65646i	−0.0405585	+	0.0702494i
$557$	−36.6474	−	9.81965i	−1.55280	−	0.416072i	−0.622425	−	0.782679i	$-0.713853\pi$
$557$	−36.6474	−	9.81965i	−1.55280	−	0.416072i	−0.930376	+	0.366608i	$0.880519\pi$
$558$	2.54819	+	2.54819i	0.107873	+	0.107873i
$559$	−7.90104			−0.334178
$560$	−0.251921	−	1.13818i	−0.0106456	−	0.0480971i
$561$	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	$-0.699455\pi$
$563$	5.30602	−	5.30602i	0.223622	−	0.223622i	0.810022	+	0.586400i	$0.199455\pi$
$564$	1.97612	+	3.42274i	0.0832096	+	0.144123i
$565$	−23.0801	+	21.1345i	−0.970988	+	0.889136i
$566$	13.1108	−	7.56955i	0.551090	−	0.318172i
$567$	0.134930	+	0.503567i	0.00566654	+	0.0211478i
$568$	−8.49215	+	2.27547i	−0.356323	+	0.0954764i
$569$	17.8507			0.748340			0.374170	−	0.927360i	$-0.377928\pi$
$569$	17.8507			0.748340			0.374170	+	0.927360i	$0.377928\pi$
$570$	−9.72458	−	0.657745i	−0.407318	−	0.0275499i
$571$	−8.31596			−0.348012			−0.174006	−	0.984745i	$-0.555671\pi$
$571$	−8.31596			−0.348012			−0.174006	+	0.984745i	$0.555671\pi$
$572$	−0.0442901	+	0.0118675i	−0.00185186	+	0.000496205i
$573$	−3.53568	−	13.1953i	−0.147705	−	0.551243i
$574$	5.37857	−	3.10532i	0.224497	−	0.129613i
$575$	−11.3326	+	31.0699i	−0.472601	+	1.29570i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	4.34779	−	4.34779i	0.181001	−	0.181001i	−0.610791	−	0.791792i	$-0.709148\pi$
$577$	4.34779	−	4.34779i	0.181001	−	0.181001i	0.791792	+	0.610791i	$0.209148\pi$
$578$	25.9484	−	25.9484i	1.07931	−	1.07931i
$579$	12.4450	−	7.18511i	0.517195	−	0.298603i
$580$	10.2391	+	6.52794i	0.425155	+	0.271058i
$581$	−6.01007			−0.249340
$582$	−4.76985	−	4.76985i	−0.197716	−	0.197716i
$583$	−0.731104	−	0.195899i	−0.0302792	−	0.00811330i
$584$	7.07217	−	12.2494i	0.292649	−	0.506882i
$585$	−1.67491	+	0.370717i	−0.0692489	+	0.0153273i
$586$	15.2901	−	26.4832i	0.631627	−	1.09401i
$587$	−2.66800	−	9.95712i	−0.110120	−	0.410974i	0.888755	−	0.458382i	$-0.151571\pi$
$587$	−2.66800	−	9.95712i	−0.110120	−	0.410974i	−0.998876	+	0.0474075i	$0.984904\pi$
$588$	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
$592$	9.49485	−	2.54414i	0.390236	−	0.104563i
$593$	−10.3563	+	38.6503i	−0.425283	+	1.58718i	0.338022	+	0.941138i	$0.390242\pi$
$593$	−10.3563	+	38.6503i	−0.425283	+	1.58718i	−0.763305	+	0.646038i	$0.776425\pi$
$594$	−0.0517609	−	0.0298842i	−0.00212378	−	0.00122616i
$595$	7.20288	+	4.59220i	0.295289	+	0.188262i
$596$	−8.76233			−0.358919
$597$	9.82401	+	9.82401i	0.402070	+	0.402070i
$598$	−1.31335	+	4.90148i	−0.0537067	+	0.200436i
$599$	16.8126	+	29.1204i	0.686946	+	1.18983i	0.972821	+	0.231559i	$0.0743826\pi$
$599$	16.8126	+	29.1204i	0.686946	+	1.18983i	−0.285875	+	0.958267i	$0.592284\pi$
$600$	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	$-0.112009\pi$
$602$	1.38964	−	5.18621i	0.0566375	−	0.211374i
$603$	−3.06227	−	11.4286i	−0.124705	−	0.465407i
$604$	−10.2801	−	17.8056i	−0.418290	−	0.724500i
$605$	24.5650	+	1.08095i	0.998709	+	0.0439467i
$606$	0.241876	−	0.418941i	0.00982552	−	0.0170183i
$607$	−11.6583	−	11.6583i	−0.473194	−	0.473194i	0.429753	−	0.902947i	$-0.358601\pi$
$607$	−11.6583	−	11.6583i	−0.473194	−	0.473194i	−0.902947	+	0.429753i	$0.858601\pi$
$608$	3.00874	+	3.15396i	0.122021	+	0.127910i
$609$		−	2.83110i		−	0.114722i
$610$	1.79158	+	1.95651i	0.0725389	+	0.0792167i
$611$	2.62582	+	1.51602i	0.106229	+	0.0613316i
$612$	−7.07811	−	1.89657i	−0.286115	−	0.0766644i
$613$	−18.3692	+	4.92201i	−0.741925	+	0.198798i	−0.609934	−	0.792452i	$-0.708804\pi$
$613$	−18.3692	+	4.92201i	−0.741925	+	0.198798i	−0.131992	+	0.991251i	$0.542137\pi$
$614$	−20.2082	+	11.6672i	−0.815538	+	0.470851i
$615$	−8.01900	+	25.4027i	−0.323357	+	1.02434i
$616$		−	0.0311591i		−	0.00125544i
$617$	35.4093	+	9.48789i	1.42552	+	0.381968i	0.887440	−	0.460923i	$-0.152482\pi$
$617$	35.4093	+	9.48789i	1.42552	+	0.381968i	0.538084	+	0.842891i	$0.319148\pi$
$618$	4.35778	+	1.16766i	0.175296	+	0.0469703i
$619$		−	33.0155i		−	1.32700i	−0.748174	−	0.663502i	$-0.769069\pi$
$619$		−	33.0155i		−	1.32700i	0.748174	−	0.663502i	$-0.230931\pi$
$620$	−3.71836	−	7.14887i	−0.149333	−	0.287106i
$621$	−5.72826	+	3.30721i	−0.229867	+	0.132714i
$622$	−3.01392	+	0.807578i	−0.120847	+	0.0323809i
$623$	1.69143	+	0.453217i	0.0677657	+	0.0181578i
$624$	0.664389	+	0.383585i	0.0265968	+	0.0153557i
$625$	24.6142	+	4.37487i	0.984569	+	0.174995i
$626$		−	14.8582i		−	0.593852i
$627$	−0.249989	−	0.0733380i	−0.00998359	−	0.00292884i
$628$	0.482522	+	0.482522i	0.0192547	+	0.0192547i
$629$	−36.0154	+	62.3804i	−1.43603	+	2.48727i
$630$	0.0512467	−	1.16460i	0.00204172	−	0.0463989i
$631$	−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	$0.925218\pi$
$632$	0.889892	+	3.32112i	0.0353980	+	0.132107i
$633$	3.61976	−	13.5091i	0.143873	−	0.536940i
$634$			29.3625i			1.16613i
$635$	−1.60245	+	5.07628i	−0.0635914	+	0.201446i
$636$	6.33190	+	10.9672i	0.251076	+	0.434877i
$637$	1.33594	−	4.98580i	0.0529319	−	0.197545i
$638$	0.229508	+	0.229508i	0.00908631	+	0.00908631i
$639$	−8.79173			−0.347795
$640$	−0.483227	−	2.18323i	−0.0191012	−	0.0862997i
$641$	−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	$0.679053\pi$
$642$	1.28701	−	4.80318i	0.0507942	−	0.189566i
$643$	−39.5386	+	10.5943i	−1.55925	+	0.417800i	−0.932427	−	0.361360i	$-0.882313\pi$
$643$	−39.5386	+	10.5943i	−1.55925	+	0.417800i	−0.626825	+	0.779160i	$0.715646\pi$
$644$	−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	−0.780906	−	0.624648i	$-0.785242\pi$
$647$	−3.97461	+	3.97461i	−0.156258	+	0.156258i	0.624648	+	0.780906i	$0.285242\pi$
$648$	0.258819	+	0.965926i	0.0101674	+	0.0379452i
$649$	−0.0277519	+	0.0480677i	−0.00108936	+	0.00188682i
$650$	3.82102	+	0.336929i	0.149873	+	0.0132154i
$651$	−0.939355	+	1.62701i	−0.0368162	+	0.0637676i
$652$	0.538141	+	0.144194i	0.0210752	+	0.00564709i
$653$	−8.26950	−	8.26950i	−0.323611	−	0.323611i	0.526540	−	0.850150i	$-0.323489\pi$
$653$	−8.26950	−	8.26950i	−0.323611	−	0.323611i	−0.850150	+	0.526540i	$0.823489\pi$
$654$	−5.89128			−0.230367
$655$	3.35998	−	5.27013i	0.131285	−	0.205921i
$656$	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	$-0.804584\pi$
$659$	−23.2988	−	40.3547i	−0.907593	−	1.57200i	−0.0901954	−	0.995924i	$-0.528749\pi$
$660$	0.0902563	+	0.0985651i	0.00351322	+	0.00383664i
$661$	−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	$0.346417\pi$
$662$	0.919407	+	3.43127i	0.0357338	+	0.133360i
$663$	−5.43011	+	1.45499i	−0.210888	+	0.0565073i
$664$	−11.5283			−0.447386
$665$	−0.980922	−	4.98572i	−0.0380385	−	0.193338i
$666$	9.82979			0.380897
$667$	34.6958	−	9.29672i	1.34343	−	0.359970i
$668$	−3.27494	−	12.2222i	−0.126711	−	0.472892i
$669$	0.234305	−	0.135276i	0.00905875	−	0.00523007i
$670$	−1.16305	+	26.4310i	−0.0449327	+	1.02112i
$671$	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	$-0.814106\pi$
$673$	−7.33893	+	7.33893i	−0.282895	+	0.282895i	0.551367	+	0.834263i	$0.314106\pi$
$674$	−15.5279	+	8.96501i	−0.598111	+	0.345319i
$675$	3.21132	+	3.83242i	0.123604	+	0.147510i
$676$	−12.4115			−0.477363
$677$	14.0612	+	14.0612i	0.540415	+	0.540415i	0.923650	−	0.383236i	$-0.125190\pi$
$677$	14.0612	+	14.0612i	0.540415	+	0.540415i	−0.383236	+	0.923650i	$0.625190\pi$
$678$	13.5185	+	3.62228i	0.519176	+	0.139113i
$679$	1.75834	−	3.04553i	0.0674789	−	0.116877i
$680$	13.8163	+	8.80862i	0.529832	+	0.337795i
$681$	9.57604	−	16.5862i	0.366955	−	0.635584i
$682$	−0.0557460	−	0.208047i	−0.00213463	−	0.00796653i
$683$	−13.8268	+	13.8268i	−0.529067	+	0.529067i	−0.920294	−	0.391227i	$-0.872051\pi$
$683$	−13.8268	+	13.8268i	−0.529067	+	0.529067i	0.391227	+	0.920294i	$0.372051\pi$
$684$	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
$687$	17.8682	−	4.78776i	0.681713	−	0.182665i
$688$	2.66556	−	9.94802i	0.101624	−	0.379265i
$689$	8.41368	+	4.85764i	0.320536	+	0.185061i
$690$	14.4408	−	3.19627i	0.549752	−	0.121680i
$691$	−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
$693$	0.00806457	−	0.0300974i	0.000306348	−	0.00114330i
$694$	15.1306	+	26.2069i	0.574348	+	0.994800i
$695$	3.79438	−	1.97358i	0.143929	−	0.0748621i
$696$		−	5.43052i		−	0.205843i
$697$	−22.5940	+	84.3218i	−0.855807	+	3.19392i
$698$	−0.457294	−	1.70664i	−0.0173088	−	0.0645974i
$699$	−4.56884	−	7.91346i	−0.172809	−	0.299315i
$700$	−0.893203	+	2.44884i	−0.0337599	+	0.0925576i
$701$	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
$703$	41.6369	−	10.1116i	1.57036	−	0.381366i
$704$		−	0.0597684i		−	0.00225261i
$705$	0.388504	−	8.82893i	0.0146319	−	0.332517i
$706$	14.9008	+	8.60299i	0.560799	+	0.323778i
$707$	0.243601	+	0.0652727i	0.00916156	+	0.00245483i
$708$	0.897005	−	0.240352i	0.0337115	−	0.00903297i
$709$	8.19089	−	4.72902i	0.307616	−	0.177602i	−0.338243	−	0.941059i	$-0.609833\pi$
$709$	8.19089	−	4.72902i	0.307616	−	0.177602i	0.645859	+	0.763457i	$0.276499\pi$
$710$	18.7470	+	5.91795i	0.703562	+	0.222097i
$711$			3.43828i			0.128945i
$712$	3.24444	+	0.869346i	0.121591	+	0.0325801i
$713$	−23.0241	−	6.16928i	−0.862258	−	0.231041i
$714$		−	3.82021i		−	0.142968i
$715$	0.0977734	+	0.0308646i	0.00365652	+	0.00115427i
$716$	12.5670	−	7.25556i	0.469651	−	0.271153i
$717$	23.9903	−	6.42819i	0.895935	−	0.240065i
$718$	−7.52018	−	2.01503i	−0.280651	−	0.0752001i
$719$	18.0103	+	10.3983i	0.671672	+	0.387790i	0.796710	−	0.604362i	$-0.206572\pi$
$719$	18.0103	+	10.3983i	0.671672	+	0.387790i	−0.125038	+	0.992152i	$0.539905\pi$
$720$	0.0982997	−	2.23391i	0.00366341	−	0.0832528i
$721$			2.35199i			0.0875926i
$722$	12.7873	+	14.0529i	0.475894	+	0.522996i
$723$	−0.776838	−	0.776838i	−0.0288909	−	0.0288909i
$724$	0.768131	−	1.33044i	0.0285474	−	0.0494455i
$725$	−11.4584	−	24.6165i	−0.425553	−	0.914233i
$726$	−5.49821	−	9.52319i	−0.204058	−	0.353439i
$727$	−10.2307	−	38.1815i	−0.379436	−	1.41607i	−0.846754	−	0.531985i	$-0.821446\pi$
$727$	−10.2307	−	38.1815i	−0.379436	−	1.41607i	0.467318	−	0.884089i	$-0.345220\pi$
$728$	−0.103514	+	0.386321i	−0.00383650	+	0.0143180i
$729$			1.00000i			0.0370370i
$730$	−28.0591	+	14.5945i	−1.03851	+	0.540165i
$731$	37.7343	+	65.3577i	1.39565	+	2.41734i
$732$	0.307062	−	1.14597i	0.0113493	−	0.0423563i
$733$	34.9712	+	34.9712i	1.29169	+	1.29169i	0.933741	+	0.357950i	$0.116524\pi$
$733$	34.9712	+	34.9712i	1.29169	+	1.29169i	0.357950	+	0.933741i	$0.383476\pi$
$734$	−36.0343			−1.33005
$735$	−14.6892	+	3.25126i	−0.541821	+	0.119924i
$736$	−5.72826	−	3.30721i	−0.211146	−	0.121905i
$737$	−0.183027	+	0.683067i	−0.00674189	+	0.0251611i
$738$	11.5071	−	3.08332i	0.423583	−	0.113499i
$739$	−3.82117	−	2.20615i	−0.140564	−	0.0811547i	0.428069	−	0.903746i	$-0.359194\pi$
$739$	−3.82117	−	2.20615i	−0.140564	−	0.0811547i	−0.568633	+	0.822591i	$0.692527\pi$
$740$	−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
$743$	−5.88897	−	21.9779i	−0.216045	−	0.806293i	−0.985796	−	0.167948i	$-0.946286\pi$
$743$	−5.88897	−	21.9779i	−0.216045	−	0.806293i	0.769750	−	0.638345i	$-0.220381\pi$
$744$	−1.80184	+	3.12088i	−0.0660587	+	0.114417i
$745$	16.5211	+	10.5330i	0.605286	+	0.385901i
$746$	2.20311	−	3.81589i	0.0806615	−	0.139710i
$747$	−11.1355	−	2.98375i	−0.407427	−	0.109170i
$748$	0.309692	+	0.309692i	0.0113235	+	0.0113235i
$749$	2.59238			0.0947235
$750$	−4.26793	−	10.3337i	−0.155843	−	0.377332i
$751$	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
$755$	−2.02106	+	45.9294i	−0.0735537	+	1.67154i
$756$	−0.451486	+	0.260665i	−0.0164204	+	0.00948031i
$757$	6.17456	+	23.0438i	0.224418	+	0.837540i	0.982637	+	0.185540i	$0.0594033\pi$
$757$	6.17456	+	23.0438i	0.224418	+	0.837540i	−0.758219	+	0.652000i	$0.773930\pi$
$758$	−22.7244	+	6.08898i	−0.825386	+	0.221162i
$759$	0.395333			0.0143497
$760$	−1.88157	−	9.56346i	−0.0682518	−	0.346903i
$761$	−15.0394			−0.545177			−0.272589	−	0.962131i	$-0.587880\pi$
$761$	−15.0394			−0.545177			−0.272589	+	0.962131i	$0.587880\pi$
$762$	2.29949	−	0.616146i	0.0833017	−	0.0223206i
$763$	−0.794912	−	2.96665i	−0.0287778	−	0.107400i
$764$	11.8306	−	6.83041i	0.428017	−	0.247116i
$765$	11.0657	+	12.0844i	0.400082	+	0.436913i
$766$	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	−0.839865	−	0.542796i	$-0.817366\pi$
$769$	−21.8997	+	12.6438i	−0.789722	+	0.455946i	0.0501428	+	0.998742i	$0.484032\pi$
$770$	−0.0374558	+	0.0587495i	−0.00134981	+	0.00211719i
$771$	−2.97074			−0.106988
$772$	10.1613	+	10.1613i	0.365712	+	0.365712i
$773$	−31.7135	−	8.49759i	−1.14065	−	0.305637i	−0.361440	−	0.932395i	$-0.617715\pi$
$773$	−31.7135	−	8.49759i	−1.14065	−	0.305637i	−0.779214	+	0.626758i	$0.784381\pi$
$774$	5.14947	−	8.91915i	0.185094	−	0.320592i
$775$	−1.58268	+	17.9488i	−0.0568516	+	0.644738i
$776$	3.37279	−	5.84184i	0.121076	−	0.209710i
$777$	1.32634	+	4.94996i	0.0475821	+	0.177579i
$778$	−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
$782$	46.8176	−	12.5447i	1.67419	−	0.448599i
$783$	1.40552	−	5.24548i	0.0502293	−	0.187458i
$784$	5.82680	+	3.36411i	0.208100	+	0.120147i
$785$	−0.329749	−	1.48981i	−0.0117693	−	0.0531737i
$786$	−2.79513			−0.0996989
$787$	−8.57494	−	8.57494i	−0.305664	−	0.305664i	0.537561	−	0.843225i	$-0.319346\pi$
$787$	−8.57494	−	8.57494i	−0.305664	−	0.305664i	−0.843225	+	0.537561i	$0.819346\pi$
$788$	−1.40230	+	5.23345i	−0.0499548	+	0.186434i
$789$	−4.84796	−	8.39692i	−0.172592	−	0.298938i
$790$	2.31440	−	7.33160i	0.0823426	−	0.260846i
$791$			7.29625i			0.259425i
$792$	0.0154692	−	0.0577318i	0.000549674	−	0.00205141i
$793$	−0.235569	−	0.879154i	−0.00836528	−	0.0312197i
$794$	6.27736	+	10.8727i	0.222775	+	0.385858i
$795$	1.24485	−	28.2897i	0.0441502	−	1.00333i
$796$	−6.94663	+	12.0319i	−0.246217	+	0.426460i
$797$	14.4964	+	14.4964i	0.513490	+	0.513490i	0.915594	−	0.402104i	$-0.131721\pi$
$797$	14.4964	+	14.4964i	0.513490	+	0.513490i	−0.402104	+	0.915594i	$0.631721\pi$
$798$	−1.64426	+	1.56855i	−0.0582060	+	0.0555261i
$799$		−	28.9612i		−	1.02457i
$800$	−1.71331	+	4.69729i	−0.0605748	+	0.166074i
$801$	2.90889	+	1.67945i	0.102781	+	0.0593404i
$802$	−0.724069	−	0.194014i	−0.0255678	−	0.00685086i
$803$	−0.816579	+	0.218802i	−0.0288164	+	0.00772134i
$804$	10.2466	−	5.91586i	0.361369	−	0.208636i
$805$	3.55804	+	6.84063i	0.125404	+	0.241101i
$806$			2.76463i			0.0973801i
$807$	−21.7399	−	5.82519i	−0.765281	−	0.205057i
$808$	0.467268	+	0.125204i	0.0164384	+	0.00440466i
$809$		−	4.27002i		−	0.150126i	−0.997179	−	0.0750630i	$-0.976084\pi$
$809$		−	4.27002i		−	0.150126i	0.997179	−	0.0750630i	$-0.0239158\pi$
$810$	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	$0.490962\pi$
$812$	2.73463	−	0.732742i	0.0959668	−	0.0257142i
$813$	15.9058	+	4.26194i	0.557841	+	0.149473i
$814$	−0.508799	−	0.293755i	−0.0178334	−	0.0102961i
$815$	−0.841315	−	0.918764i	−0.0294700	−	0.0321829i
$816$		−	7.32779i		−	0.256524i
$817$	12.6372	−	43.0767i	0.442119	−	1.50706i
$818$	−20.3380	−	20.3380i	−0.711100	−	0.711100i
$819$	−0.199975	+	0.346366i	−0.00698768	+	0.0121030i
$820$	−26.6126	−	1.17105i	−0.929353	−	0.0408948i
$821$	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	$0.452026\pi$
$822$	−4.16802	−	15.5553i	−0.145377	−	0.542553i
$823$	11.8742	−	44.3152i	0.413909	−	1.54473i	−0.373102	−	0.927790i	$-0.621706\pi$
$823$	11.8742	−	44.3152i	0.413909	−	1.54473i	0.787011	−	0.616939i	$-0.211628\pi$
$824$			4.51150i			0.157166i
$825$	−0.0516921	−	0.294337i	−0.00179969	−	0.0102475i
$826$	0.242066	+	0.419271i	0.00842257	+	0.0145883i
$827$	9.32881	−	34.8156i	0.324395	−	1.21066i	−0.590524	−	0.807020i	$-0.701079\pi$
$827$	9.32881	−	34.8156i	0.324395	−	1.21066i	0.914919	−	0.403637i	$-0.132254\pi$
$828$	−4.67710	−	4.67710i	−0.162540	−	0.162540i
$829$	−6.08544			−0.211356			−0.105678	−	0.994400i	$-0.533701\pi$
$829$	−6.08544			−0.211356			−0.105678	+	0.994400i	$0.533701\pi$
$830$	21.7363	+	13.8580i	0.754478	+	0.481019i
$831$	10.8270	+	6.25095i	0.375583	+	0.216843i
$832$	−0.198558	+	0.741029i	−0.00688377	+	0.0256906i
$833$	−47.6230	+	12.7605i	−1.65004	+	0.442127i
$834$	−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
$838$	3.52906	+	13.1706i	0.121909	+	0.454972i
$839$	4.36061	−	7.55279i	0.150545	−	0.260751i	−0.780883	−	0.624677i	$-0.785231\pi$
$839$	4.36061	−	7.55279i	0.150545	−	0.260751i	0.931428	+	0.363926i	$0.118564\pi$
$840$	1.13818	−	0.251921i	0.0392711	−	0.00869211i
$841$	−0.245291	+	0.424857i	−0.00845832	+	0.0146502i
$842$	−0.0555671	−	0.0148892i	−0.00191497	−	0.000513115i
$843$	4.23559	+	4.23559i	0.145882	+	0.145882i
$844$	13.9857			0.481407
$845$	23.4014	+	14.9196i	0.805033	+	0.513250i
$846$	−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
$850$	−15.4616	−	33.2168i	−0.530328	−	1.13933i
$851$	−56.3076	+	32.5092i	−1.93020	+	1.11440i
$852$	−2.27547	−	8.49215i	−0.0779562	−	0.290936i
$853$	4.64443	−	1.24447i	0.159022	−	0.0426099i	−0.178430	−	0.983953i	$-0.557102\pi$
$853$	4.64443	−	1.24447i	0.159022	−	0.0426099i	0.337452	+	0.941343i	$0.390435\pi$
$854$	0.618505			0.0211648
$855$	0.657745	−	9.72458i	0.0224944	−	0.332573i
$856$	4.97262			0.169961
$857$	−39.4417	+	10.5684i	−1.34730	+	0.361009i	−0.859138	−	0.511743i	$-0.829000\pi$
$857$	−39.4417	+	10.5684i	−1.34730	+	0.361009i	−0.488164	+	0.872752i	$0.662333\pi$
$858$	−0.0118675	−	0.0442901i	−0.000405150	−	0.00151204i
$859$	−27.8307	+	16.0681i	−0.949572	+	0.548236i	−0.892948	−	0.450160i	$-0.851367\pi$
$859$	−27.8307	+	16.0681i	−0.949572	+	0.548236i	−0.0566239	+	0.998396i	$0.518034\pi$
$860$	−16.9842	+	15.5525i	−0.579156	+	0.530334i
$861$	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	$-0.915283\pi$
$863$	−20.6160	+	20.6160i	−0.701776	+	0.701776i	0.263016	+	0.964792i	$0.415283\pi$
$864$	−0.866025	+	0.500000i	−0.0294628	+	0.0170103i
$865$	−4.50060	−	20.3338i	−0.153025	−	0.691370i
$866$	−11.8520			−0.402746
$867$	25.9484	+	25.9484i	0.881254	+	0.881254i
$868$	−1.81469	−	0.486246i	−0.0615947	−	0.0165043i
$869$	0.102750	−	0.177968i	0.00348556	−	0.00603716i
$870$	−6.52794	+	10.2391i	−0.221318	+	0.347138i
$871$	4.53847	−	7.86086i	0.153780	−	0.266355i
$872$	−1.52478	−	5.69054i	−0.0516354	−	0.192706i
$873$	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
$877$	−39.2472	+	10.5163i	−1.32529	+	0.355109i	−0.850955	−	0.525238i	$-0.823976\pi$
$877$	−39.2472	+	10.5163i	−1.32529	+	0.355109i	−0.474330	+	0.880347i	$0.657310\pi$
$878$	6.04262	−	22.5514i	0.203929	−	0.761072i
$879$	26.4832	+	15.2901i	0.893256	+	0.515721i
$880$	−0.0718465	+	0.112691i	−0.00242195	+	0.00379883i
$881$	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
$883$	14.6034	−	54.5008i	0.491445	−	1.83410i	−0.0576506	−	0.998337i	$-0.518361\pi$
$883$	14.6034	−	54.5008i	0.491445	−	1.83410i	0.549095	−	0.835760i	$-0.314972\pi$
$884$	−2.81083	−	4.86850i	−0.0945385	−	0.163745i
$885$	−1.98020	−	0.625099i	−0.0665637	−	0.0210125i
$886$			34.8139i			1.16960i
$887$	11.5909	−	43.2579i	0.389185	−	1.45246i	−0.442278	−	0.896878i	$-0.645829\pi$
$887$	11.5909	−	43.2579i	0.389185	−	1.45246i	0.831463	−	0.555580i	$-0.187504\pi$
$888$	2.54414	+	9.49485i	0.0853757	+	0.318626i
$889$	0.620542	+	1.07481i	0.0208123	+	0.0360480i
$890$	−5.07228	−	5.53922i	−0.170023	−	0.185675i
$891$	0.0298842	−	0.0517609i	0.00100116	−	0.00173406i
$892$	0.191309	+	0.191309i	0.00640550	+	0.00640550i
$893$	−12.4652	+	11.8913i	−0.417132	+	0.397926i
$894$		−	8.76233i		−	0.293056i
$895$	−32.4165	−	1.42644i	−1.08356	−	0.0476806i
$896$	−0.451486	−	0.260665i	−0.0150831	−	0.00870822i
$897$	−4.90148	−	1.31335i	−0.163656	−	0.0438514i
$898$	−11.1304	+	2.98237i	−0.371425	+	0.0995230i
$899$	16.9480	−	9.78494i	0.565248	−	0.326346i
$900$	−2.87068	+	4.09380i	−0.0956894	+	0.136460i
$901$		−	92.7977i		−	3.09154i
$902$	−0.687762	−	0.184285i	−0.0229000	−	0.00613602i
$903$	5.18621	+	1.38964i	0.172586	+	0.0462443i
$904$			13.9954i			0.465481i
$905$	−3.04759	+	1.58515i	−0.101305	+	0.0526922i
$906$	17.8056	−	10.2801i	0.591552	−	0.341532i
$907$	50.4875	−	13.5281i	1.67641	−	0.449193i	0.709583	−	0.704622i	$-0.248884\pi$
$907$	50.4875	−	13.5281i	1.67641	−	0.449193i	0.966828	+	0.255429i	$0.0822168\pi$
$908$	18.4995	+	4.95692i	0.613927	+	0.164501i
$909$	0.418941	+	0.241876i	0.0138954	+	0.00802250i
$910$	0.659564	−	0.603964i	0.0218643	−	0.0200212i
$911$		−	25.3691i		−	0.840516i	−0.907405	−	0.420258i	$-0.861940\pi$
$911$		−	25.3691i		−	0.840516i	0.907405	−	0.420258i	$-0.138060\pi$
$912$	−3.15396	+	3.00874i	−0.104438	+	0.0996295i
$913$	0.487217	+	0.487217i	0.0161245	+	0.0161245i
$914$	−17.6709	+	30.6070i	−0.584503	+	1.01239i
$915$	−1.95651	+	1.79158i	−0.0646801	+	0.0592278i
$916$	9.24925	+	16.0202i	0.305604	+	0.529321i
$917$	−0.377147	−	1.40753i	−0.0124545	−	0.0464809i
$918$	1.89657	−	7.07811i	0.0625962	−	0.233612i
$919$			12.1412i			0.400502i	0.979745	+	0.200251i	$0.0641758\pi$
$919$			12.1412i			0.400502i	−0.979745	+	0.200251i	$0.935824\pi$
$920$	6.82491	+	13.1215i	0.225011	+	0.432602i
$921$	−11.6672	−	20.2082i	−0.384448	−	0.665884i
$922$	−3.77167	+	14.0761i	−0.124213	+	0.463570i
$923$	−4.76926	−	4.76926i	−0.156982	−	0.156982i
$924$	0.0311591			0.00102506
$925$	31.5666	+	37.6719i	1.03790	+	1.23864i
$926$	−1.12702	−	0.650687i	−0.0370363	−	0.0213829i
$927$	−1.16766	+	4.35778i	−0.0383511	+	0.143128i
$928$	5.24548	−	1.40552i	0.172191	−	0.0461385i
$929$	−15.4017	−	8.89215i	−0.505312	−	0.291742i	0.225592	−	0.974222i	$-0.427568\pi$
$929$	−15.4017	−	8.89215i	−0.505312	−	0.291742i	−0.730905	+	0.682480i	$0.760902\pi$
$930$	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
$933$	−0.807578	−	3.01392i	−0.0264389	−	0.0986714i
$934$	8.61278	−	14.9178i	0.281819	−	0.488125i
$935$	−0.211639	−	0.956190i	−0.00692134	−	0.0312707i
$936$	−0.383585	+	0.664389i	−0.0125379	+	0.0217162i
$937$	15.5385	+	4.16352i	0.507620	+	0.136016i	0.503534	−	0.863975i	$-0.332033\pi$
$937$	15.5385	+	4.16352i	0.507620	+	0.136016i	0.00408557	+	0.999992i	$0.498700\pi$
$938$	4.36160	+	4.36160i	0.142411	+	0.142411i
$939$	14.8582			0.484878
$940$	8.62864	−	1.90983i	0.281435	−	0.0622918i
$941$	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
$945$	1.16460	+	0.0512467i	0.0378846	+	0.00166705i
$946$	−0.533083	+	0.307776i	−0.0173320	+	0.0100066i
$947$	13.3217	+	49.7172i	0.432897	+	1.61559i	0.746050	+	0.665890i	$0.231948\pi$
$947$	13.3217	+	49.7172i	0.432897	+	1.61559i	−0.313153	+	0.949703i	$0.601385\pi$
$948$	−3.32112	+	0.889892i	−0.107865	+	0.0289023i
$949$	10.8511			0.352242
$950$	−7.94842	+	20.2934i	−0.257881	+	0.658405i
$951$	−29.3625			−0.952145
$952$	3.69003	−	0.988742i	0.119595	−	0.0320453i
$953$	0.608415	+	2.27064i	0.0197085	+	0.0735531i	0.975080	−	0.221855i	$-0.0712111\pi$
$953$	0.608415	+	2.27064i	0.0197085	+	0.0735531i	−0.955371	+	0.295408i	$0.904544\pi$
$954$	−10.9672	+	6.33190i	−0.355075	+	0.205003i
$955$	−30.5170	−	1.34285i	−0.987507	−	0.0434538i
$956$	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
$960$	2.18323	−	0.483227i	0.0704634	−	0.0155961i
$961$	18.0135			0.581080
$962$	5.33238	+	5.33238i	0.171923	+	0.171923i
$963$	4.80318	+	1.28701i	0.154780	+	0.0414733i
$964$	0.549307	−	0.951428i	0.0176920	−	0.0306434i
$965$	−6.94408	−	31.3735i	−0.223538	−	1.00995i
$966$	1.72415	−	2.98632i	0.0554736	−	0.0960831i
$967$	0.189171	+	0.705996i	0.00608333	+	0.0227033i	0.968901	−	0.247450i	$-0.0795924\pi$
$967$	0.189171	+	0.705996i	0.00608333	+	0.0227033i	−0.962817	+	0.270153i	$0.912926\pi$
$968$	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	$0.780946\pi$
$972$	−0.965926	+	0.258819i	−0.0309821	+	0.00830162i
$973$	0.258083	−	0.963178i	0.00827375	−	0.0308781i
$974$	−7.42637	−	4.28762i	−0.237956	−	0.137384i
$975$	−0.336929	+	3.82102i	−0.0107904	+	0.122371i
$976$	1.18640			0.0379756
$977$	−39.4296	−	39.4296i	−1.26147	−	1.26147i	−0.950383	−	0.311082i	$-0.899309\pi$
$977$	−39.4296	−	39.4296i	−1.26147	−	1.26147i	−0.311082	−	0.950383i	$-0.600691\pi$
$978$	−0.144194	+	0.538141i	−0.00461083	+	0.0172078i
$979$	−0.100378	−	0.173860i	−0.00320809	−	0.00555658i
$980$	−6.94233	−	13.3472i	−0.221764	−	0.426361i
$981$		−	5.89128i		−	0.188094i
$982$	−1.89256	+	7.06314i	−0.0603941	+	0.225394i
$983$	12.4261	+	46.3747i	0.396330	+	1.47912i	0.819503	+	0.573075i	$0.194250\pi$
$983$	12.4261	+	46.3747i	0.396330	+	1.47912i	−0.423173	+	0.906049i	$0.639084\pi$
$984$	5.95652	+	10.3170i	0.189887	+	0.328894i
$985$	8.93503	−	8.18183i	0.284694	−	0.260695i
$986$	−19.8969	+	34.4624i	−0.633646	+	1.09751i
$987$	−1.45694	−	1.45694i	−0.0463749	−	0.0463749i
$988$	−0.941346	+	3.20879i	−0.0299482	+	0.102085i
$989$			68.1215i			2.16614i
$990$	−0.0985651	+	0.0902563i	−0.00313261	+	0.00286853i
$991$	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	$0.485485\pi$
$992$	−3.48089	−	0.932701i	−0.110518	−	0.0296133i
$993$	−3.43127	+	0.919407i	−0.108888	+	0.0291765i
$994$	3.96934	−	2.29170i	0.125900	−	0.0726883i
$995$	27.5610	−	14.3354i	0.873743	−	0.454462i
$996$		−	11.5283i		−	0.365289i
$997$	−13.0749	−	3.50340i	−0.414085	−	0.110954i	0.0457610	−	0.998952i	$-0.485429\pi$
$997$	−13.0749	−	3.50340i	−0.414085	−	0.110954i	−0.459846	+	0.887999i	$0.652095\pi$
$998$	−23.0148	−	6.16679i	−0.728520	−	0.195206i
$999$			9.82979i			0.311001i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.x.b.103.1	✓	40	1.1	even	1	trivial
570.2.x.b.217.4	yes	40	5.2	odd	4	inner
570.2.x.b.373.4	yes	40	19.12	odd	6	inner
570.2.x.b.487.1	yes	40	95.12	even	12	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)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.23391 - 0.0982997i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-0.368637 + 0.368637i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.965926 + 0.258819i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.23391 - 0.0982997i) 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} +(2.18323 - 0.483227i) q^{10} +0.0597684 q^{11} +(-0.707107 - 0.707107i) q^{12} +(-0.741029 - 0.198558i) q^{13} +(0.260665 - 0.451486i) q^{14} +(0.483227 + 2.18323i) q^{15} +(0.500000 - 0.866025i) q^{16} +(1.89657 + 7.07811i) 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} +(-0.0577318 + 0.0154692i) q^{22} +(-1.71194 + 6.38904i) q^{23} +(0.866025 + 0.500000i) q^{24} +(4.98067 + 0.439185i) q^{25} +0.767170 q^{26} +(0.707107 + 0.707107i) q^{27} +(-0.134930 + 0.503567i) q^{28} +(-2.71526 - 4.70297i) q^{29} +(-1.03182 - 1.98377i) q^{30} +3.60368i q^{31} +(-0.258819 + 0.965926i) q^{32} +(-0.0154692 - 0.0577318i) q^{33} +(-3.66390 - 6.34606i) q^{34} +(0.859736 - 0.787263i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(6.95071 + 6.95071i) q^{37} +(-1.22704 + 4.18263i) q^{38} +0.767170i q^{39} +(1.64912 - 1.51010i) q^{40} +(10.3170 + 5.95652i) q^{41} +(-0.503567 - 0.134930i) q^{42} +(9.94802 - 2.66556i) q^{43} +(0.0517609 - 0.0298842i) q^{44} +(1.98377 - 1.03182i) q^{45} -6.61442i q^{46} +(-3.81757 - 1.02291i) q^{47} +(-0.965926 - 0.258819i) q^{48} +6.72821i q^{49} +(-4.92463 + 0.864874i) q^{50} +(6.34606 - 3.66390i) q^{51} +(-0.741029 + 0.198558i) q^{52} +(-12.2323 - 3.27763i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(-0.133517 - 0.00587521i) q^{55} -0.521331i q^{56} +(-4.18263 - 1.22704i) q^{57} +(3.83996 + 3.83996i) q^{58} +(-0.464324 + 0.804233i) q^{59} +(1.51010 + 1.64912i) q^{60} +(0.593198 + 1.02745i) q^{61} +(-0.932701 - 3.48089i) q^{62} +(0.134930 - 0.503567i) q^{63} -1.00000i q^{64} +(1.63587 + 0.516403i) q^{65} +(0.0298842 + 0.0517609i) q^{66} +(-3.06227 + 11.4286i) q^{67} +(5.18153 + 5.18153i) q^{68} +6.61442 q^{69} +(-0.626683 + 0.982953i) q^{70} +(7.61386 + 4.39586i) q^{71} +(0.258819 - 0.965926i) q^{72} +(-13.6624 + 3.66083i) 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} +(-0.198558 - 0.741029i) q^{78} +(1.71914 - 2.97764i) q^{79} +(-1.20208 + 1.88547i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-11.5071 - 3.08332i) q^{82} +(8.15176 + 8.15176i) q^{83} +0.521331 q^{84} +(-3.54099 - 15.9983i) 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} +(-1.64912 + 1.51010i) q^{90} +(0.346366 - 0.199975i) q^{91} +(1.71194 + 6.38904i) q^{92} +(3.48089 - 0.932701i) q^{93} +3.95224 q^{94} +(-5.43191 + 8.09286i) q^{95} +1.00000 q^{96} +(-6.51573 + 1.74588i) q^{97} +(-1.74139 - 6.49896i) 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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