LMFDB - Embedded newform 185.2.p.a.103.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [185,2,Mod(82,185)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(185, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([3, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("185.82"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$185 = 5 \cdot 37$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	185.p (of order $12$ , degree $4$ , minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.47723243739$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			103.7
Character	$\chi$	$=$	185.103
Dual form			185.2.p.a.97.7

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.437629 - 0.757996i) q^{2} +(-0.437443 - 1.63256i) q^{3} +(0.616961 - 1.06861i) q^{4} +(1.43086 - 1.71833i) q^{5} +(-1.04604 + 1.04604i) q^{6} +(0.339600 + 1.26740i) q^{7} -2.83052 q^{8} +(0.124179 - 0.0716950i) q^{9} +(-1.92867 - 0.332594i) q^{10} +3.57208i q^{11} +(-2.01445 - 0.539771i) q^{12} +(0.404453 - 0.700532i) q^{13} +(0.812068 - 0.812068i) q^{14} +(-3.43119 - 1.58429i) q^{15} +(0.00479418 + 0.00830376i) q^{16} +(-3.21749 + 1.85762i) q^{17} +(-0.108689 - 0.0627516i) q^{18} +(1.17687 - 0.315342i) q^{19} +(-0.953435 - 2.58917i) q^{20} +(1.92056 - 1.10883i) q^{21} +(2.70763 - 1.56325i) q^{22} +0.939267 q^{23} +(1.23819 + 4.62099i) q^{24} +(-0.905293 - 4.91736i) q^{25} -0.708001 q^{26} +(-3.75672 - 3.75672i) q^{27} +(1.56388 + 0.419040i) q^{28} +(0.522020 - 0.522020i) q^{29} +(0.300703 + 3.29416i) q^{30} +(7.77798 + 7.77798i) q^{31} +(-2.82632 + 4.89533i) q^{32} +(5.83164 - 1.56258i) q^{33} +(2.81613 + 1.62590i) q^{34} +(2.66373 + 1.22993i) q^{35} -0.176932i q^{36} +(6.08262 - 0.0421153i) q^{37} +(-0.754061 - 0.754061i) q^{38} +(-1.32059 - 0.353850i) q^{39} +(-4.05007 + 4.86375i) q^{40} +(0.709147 + 0.409426i) q^{41} +(-1.68098 - 0.970516i) q^{42} -0.435474 q^{43} +(3.81716 + 2.20384i) q^{44} +(0.0544876 - 0.315966i) q^{45} +(-0.411050 - 0.711960i) q^{46} +(-4.99128 + 4.99128i) q^{47} +(0.0114592 - 0.0114592i) q^{48} +(4.57120 - 2.63918i) q^{49} +(-3.33116 + 2.83819i) q^{50} +(4.44014 + 4.44014i) q^{51} +(-0.499063 - 0.864403i) q^{52} +(1.59914 - 5.96808i) q^{53} +(-1.20353 + 4.49163i) q^{54} +(6.13801 + 5.11114i) q^{55} +(-0.961243 - 3.58741i) q^{56} +(-1.02963 - 1.78337i) q^{57} +(-0.624140 - 0.167238i) q^{58} +(1.62301 - 6.05717i) q^{59} +(-3.80990 + 2.68915i) q^{60} +(-13.0747 + 3.50335i) q^{61} +(2.49181 - 9.29955i) q^{62} +(0.133038 + 0.133038i) q^{63} +4.96670 q^{64} +(-0.625029 - 1.69734i) q^{65} +(-3.73653 - 3.73653i) q^{66} +(13.0576 - 3.49878i) q^{67} +4.58432i q^{68} +(-0.410876 - 1.53341i) q^{69} +(-0.233444 - 2.55735i) q^{70} +(-0.416955 + 0.722187i) q^{71} +(-0.351492 + 0.202934i) q^{72} +(2.94717 - 2.94717i) q^{73} +(-2.69385 - 4.59217i) q^{74} +(-7.63188 + 3.62901i) q^{75} +(0.389107 - 1.45217i) q^{76} +(-4.52727 + 1.21308i) q^{77} +(0.309710 + 1.15585i) q^{78} +(-9.16215 + 2.45499i) q^{79} +(0.0211284 + 0.00364353i) q^{80} +(-4.27463 + 7.40388i) q^{81} -0.716707i q^{82} +(-1.75929 + 6.56576i) q^{83} -2.73643i q^{84} +(-1.41177 + 8.18669i) q^{85} +(0.190576 + 0.330088i) q^{86} +(-1.08058 - 0.623875i) q^{87} -10.1108i q^{88} +(-14.3690 - 3.85016i) q^{89} +(-0.263346 + 0.0969746i) q^{90} +(1.02521 + 0.274704i) q^{91} +(0.579491 - 1.00371i) q^{92} +(9.29560 - 16.1004i) q^{93} +(5.96770 + 1.59904i) q^{94} +(1.14207 - 2.47346i) q^{95} +(9.22828 + 2.47271i) q^{96} +1.86386i q^{97} +(-4.00098 - 2.30996i) q^{98} +(0.256101 + 0.443579i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$68 q - 4 q^{2} - 8 q^{3} - 30 q^{4} - 10 q^{5} - 8 q^{6} - 2 q^{7} + 12 q^{8} - 6 q^{10} + 14 q^{12} - 6 q^{13} - 8 q^{15} - 26 q^{16} + 12 q^{17} + 18 q^{18} + 4 q^{19} + 48 q^{20} - 12 q^{21} + 6 q^{22}+ \cdots + 32 q^{99}+O(q^{100})$ 68 * q - 4 * q^2 - 8 * q^3 - 30 * q^4 - 10 * q^5 - 8 * q^6 - 2 * q^7 + 12 * q^8 - 6 * q^10 + 14 * q^12 - 6 * q^13 - 8 * q^15 - 26 * q^16 + 12 * q^17 + 18 * q^18 + 4 * q^19 + 48 * q^20 - 12 * q^21 + 6 * q^22 - 12 * q^23 + 10 * q^25 - 24 * q^26 - 68 * q^27 - 26 * q^28 + 14 * q^29 + 10 * q^30 - 24 * q^31 - 16 * q^32 - 2 * q^33 - 10 * q^35 - 16 * q^37 - 36 * q^38 + 52 * q^39 + 42 * q^40 - 18 * q^41 + 132 * q^42 + 8 * q^43 - 36 * q^44 - 32 * q^45 - 52 * q^46 - 24 * q^47 - 60 * q^48 - 36 * q^49 - 8 * q^50 - 8 * q^51 - 26 * q^52 + 82 * q^53 + 40 * q^54 + 18 * q^55 + 16 * q^56 - 6 * q^57 + 86 * q^58 - 8 * q^59 + 36 * q^60 + 4 * q^61 + 10 * q^62 - 48 * q^63 - 20 * q^64 + 8 * q^65 + 80 * q^66 - 40 * q^67 + 8 * q^69 - 82 * q^70 + 4 * q^71 - 90 * q^72 - 60 * q^73 - 44 * q^74 + 64 * q^75 + 72 * q^76 + 66 * q^77 - 24 * q^78 + 56 * q^79 + 34 * q^80 - 6 * q^81 + 24 * q^83 - 20 * q^85 - 4 * q^86 - 84 * q^87 - 22 * q^89 - 50 * q^90 + 44 * q^91 + 44 * q^92 - 34 * q^93 - 20 * q^94 - 28 * q^95 - 8 * q^96 + 42 * q^98 + 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/185\mathbb{Z}\right)^\times$ .

$n$	$76$	$112$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{3}{4}\right)$

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

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$	−0.437629	−	0.757996i	−0.309451	−	0.535984i	0.668792	−	0.743450i	$-0.266812\pi$
$2$	−0.437629	−	0.757996i	−0.309451	−	0.535984i	−0.978242	+	0.207466i	$0.933478\pi$
$3$	−0.437443	−	1.63256i	−0.252558	−	0.942559i	−0.969433	−	0.245357i	$-0.921095\pi$
$3$	−0.437443	−	1.63256i	−0.252558	−	0.942559i	0.716875	−	0.697202i	$-0.245572\pi$
$4$	0.616961	−	1.06861i	0.308481	−	0.534304i
$5$	1.43086	−	1.71833i	0.639899	−	0.768459i
$5$	1.43086	−	1.71833i	0.639899	−	0.768459i
$6$	−1.04604	+	1.04604i	−0.427042	+	0.427042i
$7$	0.339600	+	1.26740i	0.128357	+	0.479033i	0.999937	−	0.0112192i	$-0.00357124\pi$
$7$	0.339600	+	1.26740i	0.128357	+	0.479033i	−0.871580	+	0.490252i	$0.836905\pi$
$8$	−2.83052			−1.00074
$9$	0.124179	−	0.0716950i	0.0413931	−	0.0238983i
$10$	−1.92867	−	0.332594i	−0.609899	−	0.105176i
$11$			3.57208i			1.07702i	0.842618	+	0.538512i	$0.181013\pi$
$11$			3.57208i			1.07702i	−0.842618	+	0.538512i	$0.818987\pi$
$12$	−2.01445	−	0.539771i	−0.581523	−	0.155819i
$13$	0.404453	−	0.700532i	0.112175	−	0.194293i	−0.804472	−	0.593991i	$-0.797552\pi$
$13$	0.404453	−	0.700532i	0.112175	−	0.194293i	0.916647	+	0.399698i	$0.130885\pi$
$14$	0.812068	−	0.812068i	0.217034	−	0.217034i
$15$	−3.43119	−	1.58429i	−0.885930	−	0.409062i
$16$	0.00479418	+	0.00830376i	0.00119854	+	0.00207594i
$17$	−3.21749	+	1.85762i	−0.780356	+	0.450539i	−0.836556	−	0.547881i	$-0.815435\pi$
$17$	−3.21749	+	1.85762i	−0.780356	+	0.450539i	0.0562005	+	0.998420i	$0.482101\pi$
$18$	−0.108689	−	0.0627516i	−0.0256182	−	0.0147907i
$19$	1.17687	−	0.315342i	0.269993	−	0.0723443i	−0.121283	−	0.992618i	$-0.538701\pi$
$19$	1.17687	−	0.315342i	0.269993	−	0.0723443i	0.391275	+	0.920274i	$0.372034\pi$
$20$	−0.953435	−	2.58917i	−0.213194	−	0.578956i
$21$	1.92056	−	1.10883i	0.419100	−	0.241967i
$22$	2.70763	−	1.56325i	0.577268	−	0.333286i
$23$	0.939267			0.195851			0.0979253	−	0.995194i	$-0.468779\pi$
$23$	0.939267			0.195851			0.0979253	+	0.995194i	$0.468779\pi$
$24$	1.23819	+	4.62099i	0.252745	+	0.943256i
$25$	−0.905293	−	4.91736i	−0.181059	−	0.983472i
$26$	−0.708001			−0.138850
$27$	−3.75672	−	3.75672i	−0.722981	−	0.722981i
$28$	1.56388	+	0.419040i	0.295545	+	0.0791911i
$29$	0.522020	−	0.522020i	0.0969367	−	0.0969367i	−0.656975	−	0.753912i	$-0.728164\pi$
$29$	0.522020	−	0.522020i	0.0969367	−	0.0969367i	0.753912	+	0.656975i	$0.228164\pi$
$30$	0.300703	+	3.29416i	0.0549006	+	0.601429i
$31$	7.77798	+	7.77798i	1.39697	+	1.39697i	0.808580	+	0.588387i	$0.200237\pi$
$31$	7.77798	+	7.77798i	1.39697	+	1.39697i	0.588387	+	0.808580i	$0.299763\pi$
$32$	−2.82632	+	4.89533i	−0.499628	+	0.865381i
$33$	5.83164	−	1.56258i	1.01516	−	0.272011i
$34$	2.81613	+	1.62590i	0.482963	+	0.278839i
$35$	2.66373	+	1.22993i	0.450253	+	0.207896i
$36$		−	0.176932i		−	0.0294887i
$37$	6.08262	−	0.0421153i	0.999976	−	0.00692372i
$37$	6.08262	−	0.0421153i	0.999976	−	0.00692372i
$38$	−0.754061	−	0.754061i	−0.122325	−	0.122325i
$39$	−1.32059	−	0.353850i	−0.211463	−	0.0566614i
$40$	−4.05007	+	4.86375i	−0.640372	+	0.769027i
$41$	0.709147	+	0.409426i	0.110750	+	0.0639416i	0.554352	−	0.832282i	$-0.312966\pi$
$41$	0.709147	+	0.409426i	0.110750	+	0.0639416i	−0.443602	+	0.896224i	$0.646300\pi$
$42$	−1.68098	−	0.970516i	−0.259381	−	0.149754i
$43$	−0.435474			−0.0664092			−0.0332046	−	0.999449i	$-0.510571\pi$
$43$	−0.435474			−0.0664092			−0.0332046	+	0.999449i	$0.510571\pi$
$44$	3.81716	+	2.20384i	0.575459	+	0.332241i
$45$	0.0544876	−	0.315966i	0.00812253	−	0.0471014i
$46$	−0.411050	−	0.711960i	−0.0606061	−	0.104973i
$47$	−4.99128	+	4.99128i	−0.728053	+	0.728053i	−0.970232	−	0.242179i	$-0.922138\pi$
$47$	−4.99128	+	4.99128i	−0.728053	+	0.728053i	0.242179	+	0.970232i	$0.422138\pi$
$48$	0.0114592	−	0.0114592i	0.00165399	−	0.00165399i
$49$	4.57120	−	2.63918i	0.653028	−	0.377026i
$50$	−3.33116	+	2.83819i	−0.471097	+	0.401381i
$51$	4.44014	+	4.44014i	0.621744	+	0.621744i
$52$	−0.499063	−	0.864403i	−0.0692076	−	0.119871i
$53$	1.59914	−	5.96808i	0.219659	−	0.819778i	−0.764815	−	0.644250i	$-0.777170\pi$
$53$	1.59914	−	5.96808i	0.219659	−	0.819778i	0.984474	−	0.175529i	$-0.0561635\pi$
$54$	−1.20353	+	4.49163i	−0.163779	+	0.611233i
$55$	6.13801	+	5.11114i	0.827649	+	0.689187i
$56$	−0.961243	−	3.58741i	−0.128451	−	0.479387i
$57$	−1.02963	−	1.78337i	−0.136378	−	0.236213i
$58$	−0.624140	−	0.167238i	−0.0819537	−	0.0219594i
$59$	1.62301	−	6.05717i	0.211298	−	0.788576i	−0.776138	−	0.630563i	$-0.782824\pi$
$59$	1.62301	−	6.05717i	0.211298	−	0.788576i	0.987437	−	0.158014i	$-0.0505091\pi$
$60$	−3.80990	+	2.68915i	−0.491856	+	0.347168i
$61$	−13.0747	+	3.50335i	−1.67404	+	0.448557i	−0.966195	−	0.257811i	$-0.916999\pi$
$61$	−13.0747	+	3.50335i	−1.67404	+	0.448557i	−0.707844	+	0.706369i	$0.750332\pi$
$62$	2.49181	−	9.29955i	0.316460	−	1.18104i
$63$	0.133038	+	0.133038i	0.0167612	+	0.0167612i
$64$	4.96670			0.620837
$65$	−0.625029	−	1.69734i	−0.0775254	−	0.210530i
$66$	−3.73653	−	3.73653i	−0.459935	−	0.459935i
$67$	13.0576	−	3.49878i	1.59524	−	0.427444i	0.651642	−	0.758526i	$-0.274080\pi$
$67$	13.0576	−	3.49878i	1.59524	−	0.427444i	0.943602	+	0.331082i	$0.107414\pi$
$68$			4.58432i			0.555930i
$69$	−0.410876	−	1.53341i	−0.0494636	−	0.184601i
$70$	−0.233444	−	2.55735i	−0.0279019	−	0.305662i
$71$	−0.416955	+	0.722187i	−0.0494835	+	0.0857079i	−0.889706	−	0.456534i	$-0.849091\pi$
$71$	−0.416955	+	0.722187i	−0.0494835	+	0.0857079i	0.840223	+	0.542241i	$0.182424\pi$
$72$	−0.351492	+	0.202934i	−0.0414237	+	0.0239160i
$73$	2.94717	−	2.94717i	0.344940	−	0.344940i	−0.513281	−	0.858221i	$-0.671570\pi$
$73$	2.94717	−	2.94717i	0.344940	−	0.344940i	0.858221	+	0.513281i	$0.171570\pi$
$74$	−2.69385	−	4.59217i	−0.313154	−	0.533829i
$75$	−7.63188	+	3.62901i	−0.881253	+	0.419042i
$76$	0.389107	−	1.45217i	0.0446337	−	0.166575i
$77$	−4.52727	+	1.21308i	−0.515930	+	0.138243i
$78$	0.309710	+	1.15585i	0.0350678	+	0.130875i
$79$	−9.16215	+	2.45499i	−1.03082	+	0.276208i	−0.734305	−	0.678820i	$-0.762492\pi$
$79$	−9.16215	+	2.45499i	−1.03082	+	0.276208i	−0.296517	+	0.955028i	$0.595825\pi$
$80$	0.0211284	+	0.00364353i	0.00236222	+	0.000407359i
$81$	−4.27463	+	7.40388i	−0.474959	+	0.822654i
$82$		−	0.716707i		−	0.0791470i
$83$	−1.75929	+	6.56576i	−0.193107	+	0.720686i	0.799641	+	0.600478i	$0.205023\pi$
$83$	−1.75929	+	6.56576i	−0.193107	+	0.720686i	−0.992749	+	0.120208i	$0.961644\pi$
$84$		−	2.73643i		−	0.298569i
$85$	−1.41177	+	8.18669i	−0.153128	+	0.887971i
$86$	0.190576	+	0.330088i	0.0205504	+	0.0355943i
$87$	−1.08058	−	0.623875i	−0.115851	−	0.0668865i
$88$		−	10.1108i		−	1.07782i
$89$	−14.3690	−	3.85016i	−1.52311	−	0.408116i	−0.602347	−	0.798235i	$-0.705767\pi$
$89$	−14.3690	−	3.85016i	−1.52311	−	0.408116i	−0.920765	+	0.390118i	$0.872434\pi$
$90$	−0.263346	+	0.0969746i	−0.0277591	+	0.0102220i
$91$	1.02521	+	0.274704i	0.107471	+	0.0287968i
$92$	0.579491	−	1.00371i	0.0604162	−	0.104644i
$93$	9.29560	−	16.1004i	0.963909	−	1.66954i
$94$	5.96770	+	1.59904i	0.615521	+	0.164928i
$95$	1.14207	−	2.47346i	0.117174	−	0.253771i
$96$	9.22828	+	2.47271i	0.941858	+	0.252370i
$97$			1.86386i			0.189247i	0.995513	+	0.0946233i	$0.0301647\pi$
$97$			1.86386i			0.189247i	−0.995513	+	0.0946233i	$0.969835\pi$
$98$	−4.00098	−	2.30996i	−0.404160	−	0.233342i
$99$	0.256101	+	0.443579i	0.0257391	+	0.0445814i
$100$	−5.81327	−	2.06642i	−0.581327	−	0.206642i
$101$		−	13.2116i		−	1.31460i	−0.753628	−	0.657301i	$-0.771698\pi$
$101$		−	13.2116i		−	1.31460i	0.753628	−	0.657301i	$-0.228302\pi$
$102$	1.42247	−	5.30875i	0.140846	−	0.525644i
$103$			10.3671i			1.02150i	0.859729	+	0.510750i	$0.170632\pi$
$103$			10.3671i			1.02150i	−0.859729	+	0.510750i	$0.829368\pi$
$104$	−1.14481	+	1.98287i	−0.112258	+	0.194436i
$105$	0.842704	−	4.88673i	0.0822395	−	0.476896i
$106$	−5.22361	+	1.39966i	−0.507362	+	0.135947i
$107$	2.72340	+	10.1638i	0.263281	+	0.982576i	0.963294	+	0.268447i	$0.0865105\pi$
$107$	2.72340	+	10.1638i	0.263281	+	0.982576i	−0.700014	+	0.714129i	$0.746823\pi$
$108$	−6.33221	+	1.69671i	−0.609318	+	0.163266i
$109$	0.858601	−	3.20434i	0.0822390	−	0.306920i	−0.912538	−	0.408992i	$-0.865880\pi$
$109$	0.858601	−	3.20434i	0.0822390	−	0.306920i	0.994777	+	0.102072i	$0.0325471\pi$
$110$	1.18806	−	6.88937i	0.113277	−	0.656876i
$111$	−2.72956	−	9.91182i	−0.259078	−	0.940788i
$112$	−0.00889611	+	0.00889611i	−0.000840603	+	0.000840603i
$113$	−1.47855	+	0.853641i	−0.139090	+	0.0803037i	−0.567930	−	0.823077i	$-0.692256\pi$
$113$	−1.47855	+	0.853641i	−0.139090	+	0.0803037i	0.428840	+	0.903380i	$0.358922\pi$
$114$	−0.901191	+	1.56091i	−0.0844042	+	0.146192i
$115$	1.34396	−	1.61397i	0.125325	−	0.150503i
$116$	−0.235769	−	0.879902i	−0.0218906	−	0.0816968i
$117$		−	0.115989i		−	0.0107232i
$118$	−5.30159	+	1.42056i	−0.488051	+	0.130773i
$119$	−3.44701	−	3.44701i	−0.315987	−	0.315987i
$120$	9.71205	+	4.48436i	0.886585	+	0.409365i
$121$	−1.75979			−0.159981
$122$	8.37738	+	8.37738i	0.758452	+	0.758452i
$123$	0.358201	−	1.33683i	0.0322979	−	0.120537i
$124$	13.1103	−	3.51290i	1.17734	−	0.315468i
$125$	−9.74498	−	5.48046i	−0.871617	−	0.490187i
$126$	0.0426209	−	0.159063i	0.00379697	−	0.0141705i
$127$	−3.93969	−	1.05564i	−0.349591	−	0.0936725i	0.0797507	−	0.996815i	$-0.474588\pi$
$127$	−3.93969	−	1.05564i	−0.349591	−	0.0936725i	−0.429341	+	0.903142i	$0.641254\pi$
$128$	3.47907	+	6.02593i	0.307509	+	0.532622i
$129$	0.190495	+	0.710938i	0.0167722	+	0.0625946i
$130$	−1.01305	+	1.21658i	−0.0888502	+	0.106701i
$131$	−4.20118	+	15.6790i	−0.367059	+	1.36988i	0.497549	+	0.867436i	$0.334233\pi$
$131$	−4.20118	+	15.6790i	−0.367059	+	1.36988i	−0.864608	+	0.502447i	$0.832433\pi$
$132$	1.92811	−	7.19580i	0.167820	−	0.626314i
$133$	0.799330	+	1.38448i	0.0693107	+	0.120050i
$134$	−8.36647	−	8.36647i	−0.722753	−	0.722753i
$135$	−11.8306	+	1.07994i	−1.01822	+	0.0929465i
$136$	9.10716	−	5.25802i	0.780933	−	0.450872i
$137$	−8.47195	+	8.47195i	−0.723808	+	0.723808i	−0.969379	−	0.245571i	$-0.921025\pi$
$137$	−8.47195	+	8.47195i	−0.723808	+	0.723808i	0.245571	+	0.969379i	$0.421025\pi$
$138$	−0.982507	+	0.982507i	−0.0836365	+	0.0836365i
$139$	0.105499	+	0.182729i	0.00894828	+	0.0154989i	0.870465	−	0.492231i	$-0.163818\pi$
$139$	0.105499	+	0.182729i	0.00894828	+	0.0154989i	−0.861517	+	0.507729i	$0.830485\pi$
$140$	2.95773	−	2.08767i	0.249974	−	0.176440i
$141$	10.3320	+	5.96516i	0.870108	+	0.502357i
$142$	0.729887			0.0612507
$143$	2.50236	+	1.44474i	0.209258	+	0.120815i
$144$	0.00119068		0.000687437i	9.92229e−5		5.72864e-5i
$145$	−0.150065	−	1.64394i	−0.0124622	−	0.136522i
$146$	−3.52371	−	0.944175i	−0.291624	−	0.0781405i
$147$	−6.30826	−	6.30826i	−0.520297	−	0.520297i
$148$	3.70774	−	6.52592i	0.304774	−	0.536427i
$149$			17.7293i			1.45244i	0.687463	+	0.726219i	$0.258724\pi$
$149$			17.7293i			1.45244i	−0.687463	+	0.726219i	$0.741276\pi$
$150$	6.09071	+	4.19677i	0.497304	+	0.342665i
$151$	−2.98045	−	1.72076i	−0.242546	−	0.140034i	0.373801	−	0.927509i	$-0.378054\pi$
$151$	−2.98045	−	1.72076i	−0.242546	−	0.140034i	−0.616346	+	0.787475i	$0.711388\pi$
$152$	−3.33115	+	0.892580i	−0.270192	+	0.0723978i
$153$	−0.266364	+	0.461356i	−0.0215342	+	0.0372984i
$154$	2.90077	+	2.90077i	0.233751	+	0.233751i
$155$	24.4943	−	2.23593i	1.96743	−	0.179594i
$156$	−1.19288	+	1.19288i	−0.0955067	+	0.0955067i
$157$	14.5939	+	3.91043i	1.16472	+	0.312086i	0.788850	−	0.614585i	$-0.210677\pi$
$157$	14.5939	+	3.91043i	1.16472	+	0.312086i	0.375872	+	0.926672i	$0.377343\pi$
$158$	5.87049	+	5.87049i	0.467032	+	0.467032i
$159$	−10.4428			−0.828166
$160$	4.36772	+	11.8611i	0.345298	+	0.937700i
$161$	0.318975	+	1.19043i	0.0251387	+	0.0938190i
$162$	7.48282			0.587906
$163$	−15.0733	+	8.70258i	−1.18063	+	0.681639i	−0.956161	−	0.292841i	$-0.905399\pi$
$163$	−15.0733	+	8.70258i	−1.18063	+	0.681639i	−0.224472	+	0.974480i	$0.572066\pi$
$164$	0.875032	−	0.505200i	0.0683285	−	0.0394495i
$165$	5.65922	−	12.2565i	0.440570	−	0.954168i
$166$	5.74674	−	1.53983i	0.446033	−	0.119514i
$167$	−11.9751	−	6.91380i	−0.926658	−	0.535006i	−0.0409048	−	0.999163i	$-0.513024\pi$
$167$	−11.9751	−	6.91380i	−0.926658	−	0.535006i	−0.885753	+	0.464157i	$0.846357\pi$
$168$	−5.43617	+	3.13857i	−0.419410	+	0.242146i
$169$	6.17284	+	10.6917i	0.474834	+	0.822436i
$170$	6.82331	−	2.51261i	0.523324	−	0.192709i
$171$	0.123535	−	0.123535i	0.00944693	−	0.00944693i
$172$	−0.268671	+	0.465352i	−0.0204860	+	0.0354827i
$173$	12.8410	+	3.44074i	0.976285	+	0.261595i	0.711479	−	0.702707i	$-0.248026\pi$
$173$	12.8410	+	3.44074i	0.976285	+	0.261595i	0.264806	+	0.964302i	$0.414692\pi$
$174$			1.09210i			0.0827922i
$175$	5.92484	−	2.81731i	0.447876	−	0.212968i
$176$	−0.0296617	+	0.0171252i	−0.00223584	+	0.00129086i
$177$	−10.5987			−0.796645
$178$	3.36989	+	12.5766i	0.252584	+	0.942655i
$179$	−1.96274	+	1.96274i	−0.146702	+	0.146702i	−0.776643	−	0.629941i	$-0.783079\pi$
$179$	−1.96274	+	1.96274i	−0.146702	+	0.146702i	0.629941	+	0.776643i	$0.283079\pi$
$180$	−0.304027	−	0.253165i	−0.0226609	−	0.0188698i
$181$	3.63974	−	6.30421i	0.270540	−	0.468589i	−0.698460	−	0.715649i	$-0.746131\pi$
$181$	3.63974	−	6.30421i	0.270540	−	0.468589i	0.969000	+	0.247060i	$0.0794645\pi$
$182$	−0.240437	−	0.897322i	−0.0178224	−	0.0665140i
$183$	11.4388	+	19.8127i	0.845584	+	1.46459i
$184$	−2.65861			−0.195995
$185$	8.63099	−	10.5122i	0.634563	−	0.772871i
$186$	−16.2721			−1.19313
$187$	−6.63557	−	11.4931i	−0.485241	−	0.840462i
$188$	2.25430	+	8.41315i	0.164411	+	0.613592i
$189$	3.48550	−	6.03706i	0.253533	−	0.439131i
$190$	−2.37468	+	0.216769i	−0.172277	+	0.0157261i
$191$	13.9344	−	13.9344i	1.00826	−	1.00826i	0.00829322	−	0.999966i	$-0.497360\pi$
$191$	13.9344	−	13.9344i	1.00826	−	1.00826i	0.999966	−	0.00829322i	$-0.00263984\pi$
$192$	−2.17265	−	8.10844i	−0.156797	−	0.585176i
$193$	−13.6789			−0.984629			−0.492314	−	0.870417i	$-0.663849\pi$
$193$	−13.6789			−0.984629			−0.492314	+	0.870417i	$0.663849\pi$
$194$	1.41280	−	0.815681i	0.101433	−	0.0585625i
$195$	−2.49760	+	1.76289i	−0.178857	+	0.126243i
$196$		−	6.51309i		−	0.465221i
$197$	23.5812	+	6.31856i	1.68009	+	0.450179i	0.967803	−	0.251710i	$-0.0809928\pi$
$197$	23.5812	+	6.31856i	1.68009	+	0.450179i	0.712287	+	0.701888i	$0.247660\pi$
$198$	0.224154	−	0.388246i	0.0159299	−	0.0275915i
$199$	−16.5195	+	16.5195i	−1.17104	+	1.17104i	−0.189072	+	0.981963i	$0.560548\pi$
$199$	−16.5195	+	16.5195i	−1.17104	+	1.17104i	−0.981963	+	0.189072i	$0.939452\pi$
$200$	2.56245	+	13.9187i	0.181192	+	0.984199i
$201$	−11.4240	−	19.7869i	−0.805783	−	1.39566i
$202$	−10.0143	+	5.78177i	−0.704606	+	0.406804i
$203$	0.838888	+	0.484332i	0.0588784	+	0.0339935i
$204$	7.48417	−	2.00538i	0.523997	−	0.140405i
$205$	1.71822	−	0.632715i	0.120005	−	0.0441907i
$206$	7.85821	−	4.53694i	0.547508	−	0.316104i
$207$	0.116638	−	0.0673407i	0.00810687	−	0.00468050i
$208$	0.00775607			0.000537786
$209$	1.12643	+	4.20388i	0.0779166	+	0.290789i
$210$	−4.07291	+	1.49981i	−0.281058	+	0.103497i
$211$	−5.42053			−0.373164			−0.186582	−	0.982439i	$-0.559741\pi$
$211$	−5.42053			−0.373164			−0.186582	+	0.982439i	$0.559741\pi$
$212$	−5.39093	−	5.39093i	−0.370250	−	0.370250i
$213$	1.36141	+	0.364788i	0.0932822	+	0.0249949i
$214$	6.51232	−	6.51232i	0.445173	−	0.445173i
$215$	−0.623102	+	0.748287i	−0.0424952	+	0.0510328i
$216$	10.6335	+	10.6335i	0.723515	+	0.723515i
$217$	−7.21644	+	12.4992i	−0.489884	+	0.848503i
$218$	−2.80463	+	0.751497i	−0.189953	+	0.0508978i
$219$	−6.10065	−	3.52221i	−0.412244	−	0.238009i
$220$	9.24873	−	3.40575i	0.623549	−	0.229616i
$221$			3.00527i			0.202157i
$222$	−6.31858	+	6.40669i	−0.424076	+	0.429989i
$223$	−17.8181	−	17.8181i	−1.19319	−	1.19319i	−0.976166	−	0.217024i	$-0.930365\pi$
$223$	−17.8181	−	17.8181i	−1.19319	−	1.19319i	−0.217024	−	0.976166i	$-0.569635\pi$
$224$	−7.16418	−	1.91964i	−0.478677	−	0.128261i
$225$	−0.464969	−	0.545730i	−0.0309979	−	0.0363820i
$226$	1.29411	+	0.747156i	0.0860831	+	0.0497001i
$227$	17.1321	+	9.89125i	1.13710	+	0.656505i	0.945711	−	0.325009i	$-0.105367\pi$
$227$	17.1321	+	9.89125i	1.13710	+	0.656505i	0.191389	+	0.981514i	$0.438701\pi$
$228$	−2.54096			−0.168279
$229$	−16.0692	−	9.27755i	−1.06188	−	0.613078i	−0.135930	−	0.990718i	$-0.543402\pi$
$229$	−16.0692	−	9.27755i	−1.06188	−	0.613078i	−0.925952	+	0.377641i	$0.876735\pi$
$230$	−1.81154	−	0.312395i	−0.119449	−	0.0205987i
$231$	3.96085	+	6.86039i	0.260605	+	0.451381i
$232$	−1.47759	+	1.47759i	−0.0970084	+	0.0970084i
$233$	−11.4795	+	11.4795i	−0.752048	+	0.752048i	−0.974861	−	0.222813i	$-0.928476\pi$
$233$	−11.4795	+	11.4795i	−0.752048	+	0.752048i	0.222813	+	0.974861i	$0.428476\pi$
$234$	−0.0879191	+	0.0507601i	−0.00574745	+	0.00331829i
$235$	1.43484	+	15.7184i	0.0935985	+	1.02536i
$236$	−5.47141	−	5.47141i	−0.356158	−	0.356158i
$237$	8.01584	+	13.8838i	0.520685	+	0.901852i
$238$	−1.10431	+	4.12133i	−0.0715816	+	0.267146i
$239$	5.71526	−	21.3296i	0.369689	−	1.37970i	−0.491262	−	0.871012i	$-0.663464\pi$
$239$	5.71526	−	21.3296i	0.369689	−	1.37970i	0.860951	−	0.508687i	$-0.169869\pi$
$240$	−0.00329417	−	0.0360871i	−0.000212638	−	0.00232942i
$241$	−1.15368	−	4.30557i	−0.0743147	−	0.277346i	0.918762	−	0.394811i	$-0.129190\pi$
$241$	−1.15368	−	4.30557i	−0.0743147	−	0.277346i	−0.993077	+	0.117465i	$0.962523\pi$
$242$	0.770135	+	1.33391i	0.0495062	+	0.0857472i
$243$	−1.43812	−	0.385344i	−0.0922556	−	0.0247198i
$244$	−4.32286	+	16.1331i	−0.276743	+	1.03282i
$245$	2.00575	−	11.6311i	0.128143	−	0.743084i
$246$	−1.17007	+	0.313519i	−0.0746008	+	0.0199892i
$247$	0.255081	−	0.951977i	0.0162304	−	0.0605728i
$248$	−22.0157	−	22.0157i	−1.39800	−	1.39800i
$249$	11.4886			0.728060
$250$	0.110524	+	9.78506i	0.00699014	+	0.618862i
$251$	−14.8172	−	14.8172i	−0.935256	−	0.935256i	0.0627717	−	0.998028i	$-0.480006\pi$
$251$	−14.8172	−	14.8172i	−0.935256	−	0.935256i	−0.998028	+	0.0627717i	$0.980006\pi$
$252$	0.224244	−	0.0600861i	0.0141261	−	0.00378507i
$253$			3.35514i			0.210936i
$254$	0.923954	+	3.44824i	0.0579740	+	0.216362i
$255$	13.9828	−	1.27640i	0.875639	−	0.0799315i
$256$	8.01179	−	13.8768i	0.500737	−	0.867301i
$257$	−0.133407	+	0.0770223i	−0.00832167	+	0.00480452i	−0.504155	−	0.863613i	$-0.668196\pi$
$257$	−0.133407	+	0.0770223i	−0.00832167	+	0.00480452i	0.495833	+	0.868418i	$0.334863\pi$
$258$	0.455522	−	0.455522i	0.0283596	−	0.0283596i
$259$	2.11903	+	7.69482i	0.131670	+	0.478133i
$260$	−2.19941	−	0.379284i	−0.136402	−	0.0235222i
$261$	0.0273979	−	0.102250i	0.00169589	−	0.00632914i
$262$	13.7232	−	3.67712i	0.847822	−	0.227173i
$263$	−2.93631	−	10.9585i	−0.181061	−	0.675727i	−0.995440	−	0.0953938i	$-0.969589\pi$
$263$	−2.93631	−	10.9585i	−0.181061	−	0.675727i	0.814379	−	0.580333i	$-0.197078\pi$
$264$	−16.5066	+	4.42292i	−1.01591	+	0.272212i
$265$	−7.96696	−	11.2873i	−0.489406	−	0.693374i
$266$	0.699620	−	1.21178i	0.0428964	−	0.0742988i
$267$			25.1425i			1.53870i
$268$	4.31723	−	16.1121i	0.263717	−	0.984204i
$269$		−	21.0538i		−	1.28367i	−0.766841	−	0.641837i	$-0.778172\pi$
$269$		−	21.0538i		−	1.28367i	0.766841	−	0.641837i	$-0.221828\pi$
$270$	5.99601	+	8.49493i	0.364905	+	0.516985i
$271$	−13.6148	−	23.5815i	−0.827038	−	1.43247i	−0.900352	−	0.435163i	$-0.856691\pi$
$271$	−13.6148	−	23.5815i	−0.827038	−	1.43247i	0.0733137	−	0.997309i	$-0.476643\pi$
$272$	−0.0308504	−	0.0178115i	−0.00187058	−	0.00107998i
$273$		−	1.79388i		−	0.108571i
$274$	10.1293	+	2.71413i	0.611932	+	0.163967i
$275$	17.5652	−	3.23378i	1.05922	−	0.195004i
$276$	−1.89211	−	0.506989i	−0.113892	−	0.0305172i
$277$	−0.707359	+	1.22518i	−0.0425011	+	0.0736140i	−0.886493	−	0.462741i	$-0.846866\pi$
$277$	−0.707359	+	1.22518i	−0.0425011	+	0.0736140i	0.843992	+	0.536355i	$0.180199\pi$
$278$	0.0923386	−	0.159935i	0.00553810	−	0.00959228i
$279$	1.52351	+	0.408222i	0.0912100	+	0.0244396i
$280$	−7.53974	−	3.48134i	−0.450586	−	0.208050i
$281$	2.14390	+	0.574458i	0.127895	+	0.0342693i	0.322199	−	0.946672i	$-0.395578\pi$
$281$	2.14390	+	0.574458i	0.127895	+	0.0342693i	−0.194304	+	0.980941i	$0.562245\pi$
$282$		−	10.4421i		−	0.621819i
$283$	−17.0296	−	9.83207i	−1.01231	−	0.584456i	−0.100441	−	0.994943i	$-0.532025\pi$
$283$	−17.0296	−	9.83207i	−1.01231	−	0.584456i	−0.911866	+	0.410487i	$0.865359\pi$
$284$	0.514490	+	0.891124i	0.0305294	+	0.0528785i
$285$	−4.53766	−	0.782509i	−0.268788	−	0.0463518i
$286$		−	2.52904i		−	0.149545i
$287$	−0.278082	+	1.03782i	−0.0164146	+	0.0612603i
$288$			0.810532i			0.0477611i
$289$	−1.59851	+	2.76869i	−0.0940298	+	0.162864i
$290$	−1.18043	+	0.833184i	−0.0693170	+	0.0489262i
$291$	3.04287	−	0.815334i	0.178376	−	0.0477957i
$292$	−1.33108	−	4.96766i	−0.0778956	−	0.290710i
$293$	26.3276	−	7.05445i	1.53807	−	0.412125i	0.612430	−	0.790525i	$-0.290192\pi$
$293$	26.3276	−	7.05445i	1.53807	−	0.412125i	0.925642	+	0.378400i	$0.123526\pi$
$294$	−2.02096	+	7.54231i	−0.117865	+	0.439877i
$295$	−8.08590	−	11.4558i	−0.470779	−	0.666983i
$296$	−17.2170	+	0.119208i	−1.00072	+	0.00692884i
$297$	13.4193	−	13.4193i	0.778668	−	0.778668i
$298$	13.4387	−	7.75885i	0.778484	−	0.449458i
$299$	0.379889	−	0.657987i	0.0219695	−	0.0380524i
$300$	−0.830580	+	10.3944i	−0.0479535	+	0.600124i
$301$	−0.147887	−	0.551921i	−0.00852406	−	0.0318122i
$302$			3.01223i			0.173334i
$303$	−21.5687	+	5.77932i	−1.23909	+	0.332013i
$304$	0.00826064	+	0.00826064i	0.000473780	+	0.000473780i
$305$	−12.6881	+	27.4793i	−0.726518	+	1.57346i
$306$	0.466274			0.0266551
$307$	4.27057	+	4.27057i	0.243735	+	0.243735i	0.818393	−	0.574659i	$-0.194865\pi$
$307$	4.27057	+	4.27057i	0.243735	+	0.243735i	−0.574659	+	0.818393i	$0.694865\pi$
$308$	−1.49685	+	5.58630i	−0.0852907	+	0.318309i
$309$	16.9249	−	4.53501i	0.962824	−	0.257988i
$310$	−12.4142	−	17.5881i	−0.705081	−	0.998935i
$311$	−7.35427	+	27.4465i	−0.417023	+	1.55635i	0.363727	+	0.931505i	$0.381504\pi$
$311$	−7.35427	+	27.4465i	−0.417023	+	1.55635i	−0.780750	+	0.624844i	$0.785163\pi$
$312$	3.73794	+	1.00158i	0.211619	+	0.0567032i
$313$	3.19653	+	5.53655i	0.180678	+	0.312944i	0.942112	−	0.335299i	$-0.108837\pi$
$313$	3.19653	+	5.53655i	0.180678	+	0.312944i	−0.761433	+	0.648243i	$0.775504\pi$
$314$	−3.42264	−	12.7735i	−0.193151	−	0.720848i
$315$	0.418960	−	0.0382442i	0.0236057	−	0.00215482i
$316$	−3.02927	+	11.3054i	−0.170410	+	0.635978i
$317$	4.71439	−	17.5943i	0.264786	−	0.988196i	−0.697595	−	0.716493i	$-0.745746\pi$
$317$	4.71439	−	17.5943i	0.264786	−	0.988196i	0.962381	−	0.271703i	$-0.0875870\pi$
$318$	4.57006	+	7.91558i	0.256276	+	0.443884i
$319$	1.86470	+	1.86470i	0.104403	+	0.104403i
$320$	7.10664	−	8.53441i	0.397273	−	0.477088i
$321$	15.4018	−	8.89221i	0.859643	−	0.496315i
$322$	0.762748	−	0.762748i	0.0425063	−	0.0425063i
$323$	−3.20079	+	3.20079i	−0.178096	+	0.178096i
$324$	5.27457	+	9.13582i	0.293032	+	0.507546i
$325$	−3.81092	−	1.35465i	−0.211392	−	0.0751426i
$326$	13.1930	+	7.61701i	0.730695	+	0.421867i
$327$	−5.60687			−0.310061
$328$	−2.00725	−	1.15889i	−0.110832	−	0.0639889i
$329$	−8.02099	−	4.63092i	−0.442212	−	0.255311i
$330$	−11.7670	+	1.07414i	−0.647753	+	0.0591293i
$331$	13.9069	+	3.72633i	0.764390	+	0.204818i	0.619892	−	0.784687i	$-0.287176\pi$
$331$	13.9069	+	3.72633i	0.764390	+	0.204818i	0.144498	+	0.989505i	$0.453843\pi$
$332$	5.93082	+	5.93082i	0.325496	+	0.325496i
$333$	0.752316	−	0.441323i	0.0412267	−	0.0241843i
$334$			12.1027i			0.662232i
$335$	12.6716	−	27.4435i	0.692322	−	1.49940i
$336$	0.0184150	+	0.0106319i	0.00100462	+	0.000580017i
$337$	26.1440	−	7.00527i	1.42416	−	0.381601i	0.537199	−	0.843455i	$-0.319482\pi$
$337$	26.1440	−	7.00527i	1.42416	−	0.381601i	0.886956	+	0.461854i	$0.152816\pi$
$338$	5.40283	−	9.35797i	0.293875	−	0.509006i
$339$	2.04040	+	2.04040i	0.110819	+	0.110819i
$340$	7.87735	+	6.55950i	0.427209	+	0.355739i
$341$	−27.7836	+	27.7836i	−1.50457	+	1.50457i
$342$	−0.147701	−	0.0395764i	−0.00798676	−	0.00214005i
$343$	11.3919	+	11.3919i	0.615105	+	0.615105i
$344$	1.23262			0.0664583
$345$	−3.22280	−	1.48807i	−0.173510	−	0.0801151i
$346$	−3.01154	−	11.2392i	−0.161901	−	0.604224i
$347$	6.35746			0.341287			0.170643	−	0.985333i	$-0.445415\pi$
$347$	6.35746			0.341287			0.170643	+	0.985333i	$0.445415\pi$
$348$	−1.33336	+	0.769814i	−0.0714754	+	0.0412664i
$349$	−26.2401	+	15.1497i	−1.40460	+	0.810945i	−0.994860	−	0.101258i	$-0.967713\pi$
$349$	−26.2401	+	15.1497i	−1.40460	+	0.810945i	−0.409738	+	0.912203i	$0.634380\pi$
$350$	−4.72839	−	3.25807i	−0.252743	−	0.174151i
$351$	−4.15112	+	1.11229i	−0.221570	+	0.0593696i
$352$	−17.4865	−	10.0959i	−0.932036	−	0.538111i
$353$	3.25369	−	1.87852i	0.173176	−	0.0999833i	−0.410906	−	0.911678i	$-0.634788\pi$
$353$	3.25369	−	1.87852i	0.173176	−	0.0999833i	0.584083	+	0.811694i	$0.301454\pi$
$354$	4.63829	+	8.03375i	0.246522	+	0.426989i
$355$	0.644350	+	1.74981i	0.0341986	+	0.0928704i
$356$	−12.9794	+	12.9794i	−0.687909	+	0.687909i
$357$	−4.11958	+	7.13532i	−0.218031	+	0.377641i
$358$	2.34670	+	0.628796i	0.124027	+	0.0332329i
$359$			5.56278i			0.293592i	0.989167	+	0.146796i	$0.0468961\pi$
$359$			5.56278i			0.293592i	−0.989167	+	0.146796i	$0.953104\pi$
$360$	−0.154228	+	0.894347i	−0.00812853	+	0.0471362i
$361$	−15.1689	+	8.75777i	−0.798363	+	0.460935i
$362$	−6.37143			−0.334875
$363$	0.769808	+	2.87296i	0.0404044	+	0.150791i
$364$	0.926065	−	0.926065i	0.0485390	−	0.0485390i
$365$	−0.847219	−	9.28117i	−0.0443455	−	0.485799i
$366$	10.0119	−	17.3412i	0.523333	−	0.906439i
$367$	−3.11863	−	11.6389i	−0.162791	−	0.607546i	−0.998312	−	0.0580859i	$-0.981500\pi$
$367$	−3.11863	−	11.6389i	−0.162791	−	0.607546i	0.835520	−	0.549460i	$-0.185166\pi$
$368$	0.00450301	+	0.00779944i	0.000234736	+	0.000406574i
$369$	0.117415			0.00611239
$370$	−11.7454	−	1.94182i	−0.610612	−	0.100950i
$371$	8.10702			0.420896
$372$	−11.4701	−	19.8667i	−0.594694	−	1.03004i
$373$	−3.90790	−	14.5845i	−0.202343	−	0.755156i	−0.990243	−	0.139352i	$-0.955498\pi$
$373$	−3.90790	−	14.5845i	−0.202343	−	0.755156i	0.787900	−	0.615804i	$-0.211169\pi$
$374$	−5.80784	+	10.0595i	−0.300316	+	0.520163i
$375$	−4.68430	+	18.3067i	−0.241896	+	0.945352i
$376$	14.1279	−	14.1279i	0.728591	−	0.728591i
$377$	−0.154560	−	0.576824i	−0.00796023	−	0.0297080i
$378$	−6.10142			−0.313823
$379$	−2.33795	+	1.34981i	−0.120092	+	0.0693353i	−0.558843	−	0.829274i	$-0.688755\pi$
$379$	−2.33795	+	1.34981i	−0.120092	+	0.0693353i	0.438751	+	0.898609i	$0.355421\pi$
$380$	−1.93854	−	2.74646i	−0.0994451	−	0.140890i
$381$			6.89356i			0.353168i
$382$	−16.6603	−	4.46412i	−0.852417	−	0.228404i
$383$	−4.24438	+	7.35148i	−0.216877	+	0.375643i	−0.953852	−	0.300278i	$-0.902921\pi$
$383$	−4.24438	+	7.35148i	−0.216877	+	0.375643i	0.736974	+	0.675921i	$0.236254\pi$
$384$	8.31579	−	8.31579i	0.424364	−	0.424364i
$385$	−4.39341	+	9.51507i	−0.223909	+	0.484933i
$386$	5.98629	+	10.3685i	0.304694	+	0.527745i
$387$	−0.0540769	+	0.0312213i	−0.00274888	+	0.00158707i
$388$	1.99174	+	1.14993i	0.101115	+	0.0583789i
$389$	0.760378	−	0.203743i	0.0385527	−	0.0103302i	−0.239491	−	0.970899i	$-0.576981\pi$
$389$	0.760378	−	0.203743i	0.0385527	−	0.0103302i	0.278044	+	0.960568i	$0.410314\pi$
$390$	2.42929	+	1.12168i	0.123012	+	0.0567984i
$391$	−3.02208	+	1.74480i	−0.152833	+	0.0882383i
$392$	−12.9388	+	7.47025i	−0.653511	+	0.377305i
$393$	27.4347			1.38390
$394$	−5.53037	−	20.6396i	−0.278616	−	1.03981i
$395$	−8.89125	+	19.2563i	−0.447368	+	0.968890i
$396$	0.632017			0.0317600
$397$	−12.0623	−	12.0623i	−0.605391	−	0.605391i	0.336347	−	0.941738i	$-0.390808\pi$
$397$	−12.0623	−	12.0623i	−0.605391	−	0.605391i	−0.941738	+	0.336347i	$0.890808\pi$
$398$	19.7511	+	5.29229i	0.990034	+	0.265279i
$399$	1.91059	−	1.91059i	0.0956489	−	0.0956489i
$400$	0.0364924	−	0.0310920i	0.00182462	−	0.00155460i
$401$	23.5931	+	23.5931i	1.17818	+	1.17818i	0.980207	+	0.197976i	$0.0634367\pi$
$401$	23.5931	+	23.5931i	1.17818	+	1.17818i	0.197976	+	0.980207i	$0.436563\pi$
$402$	−9.99891	+	17.3186i	−0.498700	+	0.863774i
$403$	8.59455	−	2.30290i	0.428125	−	0.114716i
$404$	−14.1180	−	8.15104i	−0.702397	−	0.405529i
$405$	6.60590	+	17.9391i	0.328250	+	0.891402i
$406$		−	0.847831i		−	0.0420772i
$407$	0.150440	+	21.7276i	0.00745701	+	1.07700i
$408$	−12.5679	−	12.5679i	−0.622204	−	0.622204i
$409$	35.8537	+	9.60697i	1.77285	+	0.475034i	0.989250	−	0.146231i	$-0.0467144\pi$
$409$	35.8537	+	9.60697i	1.77285	+	0.475034i	0.783600	+	0.621265i	$0.213381\pi$
$410$	−1.23154	−	1.02551i	−0.0608213	−	0.0506461i
$411$	17.5370	+	10.1250i	0.865035	+	0.499428i
$412$	11.0784	+	6.39610i	0.545792	+	0.315113i
$413$	8.22805			0.404876
$414$	−0.102088	−	0.0589405i	−0.00501735	−	0.00289677i
$415$	8.76483	+	12.4177i	0.430249	+	0.609561i
$416$	2.28623	+	3.95986i	0.112091	+	0.194148i
$417$	0.252167	−	0.252167i	0.0123487	−	0.0123487i
$418$	2.69357	−	2.69357i	0.131747	−	0.131747i
$419$	3.02327	−	1.74548i	0.147696	−	0.0852725i	−0.424331	−	0.905507i	$-0.639491\pi$
$419$	3.02327	−	1.74548i	0.147696	−	0.0852725i	0.572027	+	0.820235i	$0.306157\pi$
$420$	−4.70208	−	3.91544i	−0.229438	−	0.191054i
$421$	12.7648	+	12.7648i	0.622116	+	0.622116i	0.946072	−	0.323956i	$-0.105013\pi$
$421$	12.7648	+	12.7648i	0.622116	+	0.622116i	−0.323956	+	0.946072i	$0.605013\pi$
$422$	2.37218	+	4.10874i	0.115476	+	0.200010i
$423$	−0.261964	+	0.977663i	−0.0127371	+	0.0475356i
$424$	−4.52640	+	16.8927i	−0.219821	+	0.820384i
$425$	12.0474	+	14.1399i	0.584382	+	0.685885i
$426$	−0.319284	−	1.19158i	−0.0154694	−	0.0577324i
$427$	−8.88030	−	15.3811i	−0.429748	−	0.744345i
$428$	12.5414	+	3.36046i	0.606212	+	0.162434i
$429$	1.26398	−	4.71725i	0.0610256	−	0.227751i
$430$	0.839886	+	0.144836i	0.0405029	+	0.00698463i
$431$	14.9043	−	3.99360i	0.717916	−	0.192365i	0.118675	−	0.992933i	$-0.462135\pi$
$431$	14.9043	−	3.99360i	0.717916	−	0.192365i	0.599242	+	0.800568i	$0.295469\pi$
$432$	0.0131845	−	0.0492053i	0.000634340	−	0.00236739i
$433$	14.4440	+	14.4440i	0.694132	+	0.694132i	0.963138	−	0.269006i	$-0.0866952\pi$
$433$	14.4440	+	14.4440i	0.694132	+	0.694132i	−0.269006	+	0.963138i	$0.586695\pi$
$434$	12.6325			0.606379
$435$	−2.61818	+	0.964119i	−0.125532	+	0.0462260i
$436$	−2.89446	−	2.89446i	−0.138620	−	0.138620i
$437$	1.10540	−	0.296190i	0.0528782	−	0.0141687i
$438$			6.16569i			0.294608i
$439$	−9.30839	−	34.7394i	−0.444265	−	1.65802i	−0.717870	−	0.696178i	$-0.754883\pi$
$439$	−9.30839	−	34.7394i	−0.444265	−	1.65802i	0.273604	−	0.961842i	$-0.411784\pi$
$440$	−17.3737	−	14.4672i	−0.828261	−	0.689696i
$441$	0.378432	−	0.655464i	0.0180206	−	0.0312125i
$442$	2.27799	−	1.31520i	0.108353	−	0.0625575i
$443$	7.82083	−	7.82083i	0.371579	−	0.371579i	−0.496473	−	0.868052i	$-0.665372\pi$
$443$	7.82083	−	7.82083i	0.371579	−	0.371579i	0.868052	+	0.496473i	$0.165372\pi$
$444$	−12.2759	−	3.19838i	−0.582588	−	0.151789i
$445$	−27.1758	+	19.1816i	−1.28826	+	0.909295i
$446$	−5.70834	+	21.3038i	−0.270298	+	1.00876i
$447$	28.9441	−	7.75555i	1.36901	−	0.366825i
$448$	1.68669	+	6.29481i	0.0796886	+	0.297402i
$449$	9.04378	−	2.42327i	0.426802	−	0.114361i	−0.0390224	−	0.999238i	$-0.512424\pi$
$449$	9.04378	−	2.42327i	0.426802	−	0.114361i	0.465825	+	0.884877i	$0.345758\pi$
$450$	−0.210177	+	0.591272i	−0.00990784	+	0.0278728i
$451$	−1.46250	+	2.53313i	−0.0688666	+	0.119281i
$452$			2.10665i			0.0990886i
$453$	−1.50547	+	5.61850i	−0.0707333	+	0.263980i
$454$		−	17.3148i		−	0.812623i
$455$	1.93896	−	1.36858i	0.0908998	−	0.0641601i
$456$	2.91438	+	5.04786i	0.136478	+	0.236388i
$457$	−31.9224	−	18.4304i	−1.49327	−	0.862138i	−0.493297	−	0.869861i	$-0.664208\pi$
$457$	−31.9224	−	18.4304i	−1.49327	−	0.862138i	−0.999970	+	0.00772278i	$0.997542\pi$
$458$			16.2405i			0.758869i
$459$	19.0658	+	5.10865i	0.889913	+	0.238452i
$460$	−0.895529	−	2.43192i	−0.0417543	−	0.113389i
$461$	−30.8596	−	8.26880i	−1.43727	−	0.385117i	−0.545696	−	0.837983i	$-0.683735\pi$
$461$	−30.8596	−	8.26880i	−1.43727	−	0.385117i	−0.891578	+	0.452867i	$0.850401\pi$
$462$	3.46677	−	6.00461i	0.161289	−	0.279360i
$463$	1.51361	−	2.62165i	0.0703434	−	0.121838i	−0.828708	−	0.559681i	$-0.810924\pi$
$463$	1.51361	−	2.62165i	0.0703434	−	0.121838i	0.899052	+	0.437842i	$0.144257\pi$
$464$	0.00683739	+	0.00183207i	0.000317418	+	8.50518e-5i
$465$	−14.3652	−	39.0103i	−0.666168	−	1.80906i
$466$	13.7252	+	3.67765i	0.635807	+	0.170364i
$467$			23.2547i			1.07610i	0.842914	+	0.538049i	$0.180838\pi$
$467$			23.2547i			1.07610i	−0.842914	+	0.538049i	$0.819162\pi$
$468$	−0.123947	−	0.0715607i	−0.00572944	−	0.00330789i
$469$	8.86874	+	15.3611i	0.409520	+	0.709310i
$470$	11.2866	−	7.96645i	0.520612	−	0.367465i
$471$		−	25.5361i		−	1.17664i
$472$	−4.59397	+	17.1449i	−0.211455	+	0.789159i
$473$		−	1.55555i		−	0.0715243i
$474$	7.01593	−	12.1519i	0.322252	−	0.558157i
$475$	−2.61606	−	5.50162i	−0.120033	−	0.252432i
$476$	−5.81018	+	1.55683i	−0.266309	+	0.0713573i
$477$	−0.229301	−	0.855762i	−0.0104990	−	0.0391827i
$478$	−18.6689	+	5.00233i	−0.853897	+	0.228801i
$479$	6.37422	−	23.7889i	0.291245	−	1.08694i	−0.652908	−	0.757437i	$-0.726451\pi$
$479$	6.37422	−	23.7889i	0.291245	−	1.08694i	0.944154	−	0.329506i	$-0.106882\pi$
$480$	17.4533	−	12.3191i	0.796630	−	0.562288i
$481$	2.43063	−	4.27810i	0.110827	−	0.195065i
$482$	−2.75873	+	2.75873i	−0.125657	+	0.125657i
$483$	1.80391	−	1.04149i	0.0820810	−	0.0473895i
$484$	−1.08572	+	1.88053i	−0.0493510	+	0.0854785i
$485$	3.20273	+	2.66692i	0.145428	+	0.121099i
$486$	0.337275	+	1.25873i	0.0152991	+	0.0570971i
$487$		−	26.6628i		−	1.20821i	−0.796905	−	0.604104i	$-0.793531\pi$
$487$		−	26.6628i		−	1.20821i	0.796905	−	0.604104i	$-0.206469\pi$
$488$	37.0081	−	9.91628i	1.67528	−	0.448889i
$489$	20.8012	+	20.8012i	0.940664	+	0.940664i
$490$	−9.69410	+	3.56975i	−0.437935	+	0.161265i
$491$	32.1874			1.45259			0.726297	−	0.687381i	$-0.241239\pi$
$491$	32.1874			1.45259			0.726297	+	0.687381i	$0.241239\pi$
$492$	−1.20755	−	1.20755i	−0.0544404	−	0.0544404i
$493$	−0.709880	+	2.64931i	−0.0319714	+	0.119319i
$494$	−0.833225	+	0.223262i	−0.0374886	+	0.0100450i
$495$	1.12866	+	0.194634i	0.0507294	+	0.00874816i
$496$	−0.0272974	+	0.101875i	−0.00122569	+	0.00457434i
$497$	−1.05690	−	0.283196i	−0.0474085	−	0.0127031i
$498$	−5.02774	−	8.70831i	−0.225299	−	0.390229i
$499$	3.62194	+	13.5173i	0.162140	+	0.605116i	0.998388	+	0.0567635i	$0.0180781\pi$
$499$	3.62194	+	13.5173i	0.162140	+	0.605116i	−0.836247	+	0.548352i	$0.815255\pi$
$500$	−11.8687	+	7.03234i	−0.530786	+	0.314496i
$501$	−6.04879	+	22.5744i	−0.270240	+	1.00855i
$502$	−4.74695	+	17.7159i	−0.211867	+	0.790698i
$503$	−14.0634	−	24.3585i	−0.627055	−	1.08609i	−0.988140	−	0.153558i	$-0.950927\pi$
$503$	−14.0634	−	24.3585i	−0.627055	−	1.08609i	0.361084	−	0.932533i	$-0.382407\pi$
$504$	−0.376566	−	0.376566i	−0.0167736	−	0.0167736i
$505$	−22.7018	−	18.9039i	−1.01022	−	0.841212i
$506$	2.54318	−	1.46831i	0.113058	−	0.0652742i
$507$	14.7545	−	14.7545i	0.655271	−	0.655271i
$508$	−3.55870	+	3.55870i	−0.157892	+	0.157892i
$509$	−18.1195	−	31.3838i	−0.803131	−	1.39106i	−0.917545	−	0.397631i	$-0.869832\pi$
$509$	−18.1195	−	31.3838i	−0.803131	−	1.39106i	0.114414	−	0.993433i	$-0.463501\pi$
$510$	−7.08680	−	10.0403i	−0.313809	−	0.444594i
$511$	4.73611	+	2.73439i	0.209513	+	0.120962i
$512$	−0.108480			−0.00479416
$513$	−5.60582	−	3.23652i	−0.247503	−	0.142896i
$514$	0.116765	+	0.0674144i	0.00515029	+	0.00297352i
$515$	17.8140	+	14.8338i	0.784981	+	0.653657i
$516$	0.877243	+	0.235057i	0.0386185	+	0.0103478i
$517$	−17.8293	−	17.8293i	−0.784130	−	0.784130i
$518$	4.90530	−	4.97370i	0.215526	−	0.218532i
$519$		−	22.4689i		−	0.986274i
$520$	1.76916	+	4.80436i	0.0775827	+	0.210685i
$521$	−4.34142	−	2.50652i	−0.190201	−	0.109813i	0.401876	−	0.915694i	$-0.368358\pi$
$521$	−4.34142	−	2.50652i	−0.190201	−	0.109813i	−0.592077	+	0.805882i	$0.701692\pi$
$522$	−0.0894955	+	0.0239802i	−0.00391711	+	0.00104959i
$523$	10.7774	−	18.6670i	0.471263	−	0.816251i	−0.528197	−	0.849122i	$-0.677132\pi$
$523$	10.7774	−	18.6670i	0.471263	−	0.816251i	0.999460	+	0.0328708i	$0.0104650\pi$
$524$	14.1628	+	14.1628i	0.618704	+	0.618704i
$525$	−7.19120	−	8.44025i	−0.313850	−	0.368363i
$526$	−7.02145	+	7.02145i	−0.306150	+	0.306150i
$527$	−39.4741	−	10.5771i	−1.71952	−	0.460744i
$528$	0.0409332	+	0.0409332i	0.00178139	+	0.00178139i
$529$	−22.1178			−0.961643
$530$	−5.06916	+	10.9786i	−0.220190	+	0.476879i
$531$	−0.232724	−	0.868537i	−0.0100994	−	0.0376913i
$532$	1.97262			0.0855240
$533$	0.573632	−	0.331187i	0.0248468	−	0.0143453i
$534$	19.0579	−	11.0031i	0.824716	−	0.476150i
$535$	21.3616	+	9.86334i	0.923543	+	0.426429i
$536$	−36.9599	+	9.90337i	−1.59642	+	0.427760i
$537$	4.06287	+	2.34570i	0.175326	+	0.101224i
$538$	−15.9587	+	9.21377i	−0.688029	+	0.397234i
$539$	9.42738	+	16.3287i	0.406066	+	0.703327i
$540$	−6.14499	+	13.3086i	−0.264438	+	0.572709i
$541$	−27.2250	+	27.2250i	−1.17050	+	1.17050i	−0.188405	+	0.982091i	$0.560332\pi$
$541$	−27.2250	+	27.2250i	−1.17050	+	1.17050i	−0.982091	+	0.188405i	$0.939668\pi$
$542$	−11.9164	+	20.6399i	−0.511855	+	0.886558i
$543$	−11.8842	−	3.18436i	−0.509999	−	0.136654i
$544$		−	21.0009i		−	0.900407i
$545$	−4.27757	−	6.06031i	−0.183231	−	0.259595i
$546$	−1.35976	+	0.785055i	−0.0581922	+	0.0335973i
$547$	21.8141			0.932703			0.466352	−	0.884599i	$-0.345568\pi$
$547$	21.8141			0.932703			0.466352	+	0.884599i	$0.345568\pi$
$548$	3.82633	+	14.2801i	0.163453	+	0.610015i
$549$	−1.37243	+	1.37243i	−0.0585739	+	0.0585739i
$550$	−10.1383	−	11.8992i	−0.432297	−	0.507383i
$551$	0.449736	−	0.778965i	0.0191594	−	0.0331850i
$552$	1.16299	+	4.34034i	0.0495002	+	0.184737i
$553$	−6.22292	−	10.7784i	−0.264626	−	0.458345i
$554$	1.23824			0.0526079
$555$	−20.9373	−	9.49213i	−0.888741	−	0.402918i
$556$	0.260355			0.0110415
$557$	−15.7039	−	27.1999i	−0.665395	−	1.15250i	−0.979178	−	0.203003i	$-0.934930\pi$
$557$	−15.7039	−	27.1999i	−0.665395	−	1.15250i	0.313784	−	0.949495i	$-0.398403\pi$
$558$	−0.357300	−	1.33346i	−0.0151257	−	0.0564499i
$559$	−0.176129	+	0.305064i	−0.00744945	+	0.0129028i
$560$	0.00255735	+	0.0280155i	0.000108068	+	0.00118387i
$561$	−15.8606	+	15.8606i	−0.669634	+	0.669634i
$562$	−0.502799	−	1.87647i	−0.0212093	−	0.0791541i
$563$	−28.4281			−1.19810			−0.599052	−	0.800710i	$-0.704456\pi$
$563$	−28.4281			−1.19810			−0.599052	+	0.800710i	$0.704456\pi$
$564$	12.7488	−	7.36055i	0.536823	−	0.309935i
$565$	−0.648760	+	3.76207i	−0.0272935	+	0.158271i
$566$			17.2112i			0.723440i
$567$	−10.8354	−	2.90333i	−0.455043	−	0.121928i
$568$	1.18020	−	2.04416i	0.0495200	−	0.0857712i
$569$	−3.42814	+	3.42814i	−0.143715	+	0.143715i	−0.775304	−	0.631589i	$-0.782403\pi$
$569$	−3.42814	+	3.42814i	−0.143715	+	0.143715i	0.631589	+	0.775304i	$0.282403\pi$
$570$	1.39267	+	3.78198i	0.0583327	+	0.158410i
$571$	4.19237	+	7.26140i	0.175445	+	0.303880i	0.940315	−	0.340305i	$-0.110530\pi$
$571$	4.19237	+	7.26140i	0.175445	+	0.303880i	−0.764870	+	0.644185i	$0.777197\pi$
$572$	3.08772	−	1.78270i	0.129104	−	0.0745383i
$573$	−28.8443	−	16.6533i	−1.20499	−	0.695700i
$574$	0.908357	−	0.243393i	0.0379141	−	0.0101590i
$575$	−0.850311	−	4.61871i	−0.0354604	−	0.192614i
$576$	0.616762	−	0.356087i	0.0256984	−	0.0148370i
$577$	−8.72813	+	5.03919i	−0.363357	+	0.209784i	−0.670552	−	0.741862i	$-0.733943\pi$
$577$	−8.72813	+	5.03919i	−0.363357	+	0.209784i	0.307195	+	0.951646i	$0.400609\pi$
$578$	2.79821			0.116390
$579$	5.98374	+	22.3316i	0.248676	+	0.928071i
$580$	−1.84931	−	0.853886i	−0.0767884	−	0.0354557i
$581$	−8.91892			−0.370019
$582$	−1.94967	−	1.94967i	−0.0808164	−	0.0808164i
$583$	21.3185	+	5.71227i	0.882921	+	0.236578i
$584$	−8.34201	+	8.34201i	−0.345195	+	0.345195i
$585$	−0.199307	−	0.165964i	−0.00824032	−	0.00686175i
$586$	−16.8689	−	16.8689i	−0.696850	−	0.696850i
$587$	−11.0427	+	19.1265i	−0.455781	+	0.789436i	−0.998733	−	0.0503280i	$-0.983973\pi$
$587$	−11.0427	+	19.1265i	−0.455781	+	0.789436i	0.542952	+	0.839764i	$0.317307\pi$
$588$	−10.6330	+	2.84911i	−0.438498	+	0.117495i
$589$	11.6064	+	6.70096i	0.478233	+	0.276108i
$590$	−5.14484	+	11.1425i	−0.211810	+	0.458728i
$591$		−	41.2617i		−	1.69728i
$592$	0.0295109	+	0.0503067i	0.00121289	+	0.00206759i
$593$	−25.5766	−	25.5766i	−1.05031	−	1.05031i	−0.998666	−	0.0516413i	$-0.983555\pi$
$593$	−25.5766	−	25.5766i	−1.05031	−	1.05031i	−0.0516413	−	0.998666i	$-0.516445\pi$
$594$	−16.0445	−	4.29910i	−0.658313	−	0.176394i
$595$	−10.8553	+	0.990908i	−0.445023	+	0.0406233i
$596$	18.9457	+	10.9383i	0.776044	+	0.448049i
$597$	34.1954	+	19.7427i	1.39952	+	0.808016i
$598$	−0.665002			−0.0271939
$599$	−3.93078	−	2.26944i	−0.160607	−	0.0927266i	0.417542	−	0.908658i	$-0.362892\pi$
$599$	−3.93078	−	2.26944i	−0.160607	−	0.0927266i	−0.578149	+	0.815931i	$0.696225\pi$
$600$	21.6022	−	10.2720i	0.881904	−	0.419352i
$601$	−2.17118	−	3.76060i	−0.0885643	−	0.153398i	0.818340	−	0.574734i	$-0.194895\pi$
$601$	−2.17118	−	3.76060i	−0.0885643	−	0.153398i	−0.906904	+	0.421336i	$0.861561\pi$
$602$	−0.353635	+	0.353635i	−0.0144131	+	0.0144131i
$603$	1.37064	−	1.37064i	0.0558169	−	0.0558169i
$604$	−3.67765	+	2.12329i	−0.149641	+	0.0863955i
$605$	−2.51801	+	3.02389i	−0.102372	+	0.122939i
$606$	13.8198	+	13.8198i	0.561391	+	0.561391i
$607$	−3.13653	−	5.43263i	−0.127308	−	0.220504i	0.795325	−	0.606183i	$-0.207300\pi$
$607$	−3.13653	−	5.43263i	−0.127308	−	0.220504i	−0.922633	+	0.385680i	$0.873967\pi$
$608$	−1.78251	+	6.65243i	−0.0722905	+	0.269792i
$609$	0.423736	−	1.58140i	0.0171706	−	0.0640817i
$610$	26.3819	−	2.40824i	1.06817	−	0.0975066i
$611$	1.47782	+	5.51528i	0.0597860	+	0.223125i
$612$	0.328672	+	0.569277i	0.0132858	+	0.0230117i
$613$	31.9210	+	8.55321i	1.28928	+	0.345461i	0.837386	−	0.546612i	$-0.184083\pi$
$613$	31.9210	+	8.55321i	1.28928	+	0.345461i	0.451892	+	0.892073i	$0.350749\pi$
$614$	1.36815	−	5.10601i	0.0552140	−	0.206062i
$615$	−1.78457	−	2.52831i	−0.0719607	−	0.101951i
$616$	12.8145	−	3.43364i	0.516312	−	0.138345i
$617$	2.05064	−	7.65311i	0.0825559	−	0.308103i	−0.912284	−	0.409558i	$-0.865683\pi$
$617$	2.05064	−	7.65311i	0.0825559	−	0.308103i	0.994840	+	0.101455i	$0.0323498\pi$
$618$	−10.8444	−	10.8444i	−0.436224	−	0.436224i
$619$	5.36753			0.215739			0.107870	−	0.994165i	$-0.465597\pi$
$619$	5.36753			0.215739			0.107870	+	0.994165i	$0.465597\pi$
$620$	12.7227	−	27.5543i	0.510956	−	1.10661i
$621$	−3.52856	−	3.52856i	−0.141596	−	0.141596i
$622$	24.0228	−	6.43689i	0.963226	−	0.258096i
$623$		−	19.5188i		−	0.782005i
$624$	−0.00339284	−	0.0126622i	−0.000135822	−	0.000506896i
$625$	−23.3609	+	8.90330i	−0.934436	+	0.356132i
$626$	2.79779	−	4.84591i	0.111822	−	0.193681i
$627$	6.37034	−	3.67792i	0.254407	−	0.146882i
$628$	13.1826	−	13.1826i	0.526043	−	0.526043i
$629$	−19.4925	+	11.4347i	−0.777218	+	0.455931i
$630$	−0.212338	−	0.300833i	−0.00845975	−	0.0119855i
$631$	−1.34489	+	5.01918i	−0.0535391	+	0.199811i	−0.987515	−	0.157526i	$-0.949648\pi$
$631$	−1.34489	+	5.01918i	−0.0535391	+	0.199811i	0.933976	+	0.357336i	$0.116315\pi$
$632$	25.9336	−	6.94889i	1.03158	−	0.276412i
$633$	2.37117	+	8.84934i	0.0942456	+	0.351730i
$634$	−15.3996	+	4.12631i	−0.611596	+	0.163877i
$635$	−7.45106	+	5.25920i	−0.295686	+	0.208705i
$636$	−6.44279	+	11.1592i	−0.255473	+	0.442493i
$637$		−	4.26969i		−	0.169171i
$638$	0.597388	−	2.22948i	0.0236508	−	0.0882661i
$639$			0.119574i			0.00473029i
$640$	15.3326	+	2.64406i	0.606073	+	0.104516i
$641$	−1.24593	−	2.15802i	−0.0492113	−	0.0852365i	0.840370	−	0.542012i	$-0.182337\pi$
$641$	−1.24593	−	2.15802i	−0.0492113	−	0.0852365i	−0.889582	+	0.456776i	$0.849004\pi$
$642$	−13.4805	−	7.78298i	−0.532034	−	0.307170i
$643$		−	9.01780i		−	0.355627i	−0.984064	−	0.177814i	$-0.943098\pi$
$643$		−	9.01780i		−	0.355627i	0.984064	−	0.177814i	$-0.0569024\pi$
$644$	1.46890	+	0.393590i	0.0578827	+	0.0155096i
$645$	1.49420	+	0.689918i	0.0588339	+	0.0271655i
$646$	3.82694	+	1.02543i	0.150569	+	0.0403448i
$647$	10.6944	−	18.5233i	0.420441	−	0.728225i	−0.575542	−	0.817772i	$-0.695209\pi$
$647$	10.6944	−	18.5233i	0.420441	−	0.728225i	0.995983	+	0.0895475i	$0.0285421\pi$
$648$	12.0994	−	20.9568i	0.475310	−	0.823262i
$649$	21.6367	+	5.79754i	0.849316	+	0.227573i
$650$	0.640948	+	3.48150i	0.0251401	+	0.136556i
$651$	23.5625	+	6.31356i	0.923489	+	0.247448i
$652$			21.4766i			0.841090i
$653$	40.0018	+	23.0950i	1.56539	+	0.903779i	0.996695	+	0.0812309i	$0.0258851\pi$
$653$	40.0018	+	23.0950i	1.56539	+	0.903779i	0.568696	+	0.822548i	$0.307448\pi$
$654$	2.45373	+	4.24998i	0.0959484	+	0.166188i
$655$	20.9304	+	29.6535i	0.817818	+	1.15866i
$656$			0.00785144i			0.000306547i
$657$	0.154680	−	0.577275i	0.00603465	−	0.0225216i
$658$			8.10651i			0.316025i
$659$	6.66040	−	11.5362i	0.259452	−	0.449385i	−0.706643	−	0.707570i	$-0.749791\pi$
$659$	6.66040	−	11.5362i	0.259452	−	0.449385i	0.966095	+	0.258186i	$0.0831246\pi$
$660$	−9.60588	−	13.6093i	−0.373909	−	0.529741i
$661$	38.4969	−	10.3152i	1.49736	−	0.401215i	0.585142	−	0.810931i	$-0.301039\pi$
$661$	38.4969	−	10.3152i	1.49736	−	0.401215i	0.912213	+	0.409716i	$0.134372\pi$
$662$	−3.26150	−	12.1721i	−0.126762	−	0.473082i
$663$	4.90629	−	1.31464i	0.190545	−	0.0510563i
$664$	4.97970	−	18.5845i	0.193250	−	0.721219i
$665$	3.52272	+	0.607484i	0.136605	+	0.0235572i
$666$	−0.663756	−	0.377117i	−0.0257200	−	0.0146130i
$667$	0.490316	−	0.490316i	0.0189851	−	0.0189851i
$668$	−14.7763	+	8.53110i	−0.571712	+	0.330078i
$669$	−21.2948	+	36.8836i	−0.823303	+	1.42600i
$670$	−26.3475	+	2.40510i	−1.01789	+	0.0929171i
$671$	−12.5142	−	46.7038i	−0.483107	−	1.80298i
$672$			12.5357i			0.483574i
$673$	−27.5758	+	7.38891i	−1.06297	+	0.284822i	−0.747601	−	0.664148i	$-0.768795\pi$
$673$	−27.5758	+	7.38891i	−1.06297	+	0.284822i	−0.315368	+	0.948970i	$0.602128\pi$
$674$	−16.7513	−	16.7513i	−0.645238	−	0.645238i
$675$	−15.0722	+	21.8741i	−0.580130	+	0.841934i
$676$	15.2336			0.585908
$677$	−3.66831	−	3.66831i	−0.140984	−	0.140984i	0.633092	−	0.774077i	$-0.281785\pi$
$677$	−3.66831	−	3.66831i	−0.140984	−	0.140984i	−0.774077	+	0.633092i	$0.781785\pi$
$678$	0.653677	−	2.43955i	0.0251043	−	0.0936905i
$679$	−2.36227	+	0.632967i	−0.0906554	+	0.0242911i
$680$	3.99605	−	23.1726i	0.153242	−	0.888627i
$681$	8.65372	−	32.2961i	0.331611	−	1.23759i
$682$	33.2188	+	8.90094i	1.27201	+	0.340835i
$683$	−3.17879	−	5.50582i	−0.121633	−	0.210674i	0.798779	−	0.601625i	$-0.205480\pi$
$683$	−3.17879	−	5.50582i	−0.121633	−	0.210674i	−0.920412	+	0.390950i	$0.872146\pi$
$684$	−0.0557941	−	0.208226i	−0.00213334	−	0.00796173i
$685$	2.43542	+	26.6797i	0.0930528	+	1.01938i
$686$	3.64959	−	13.6204i	0.139342	−	0.520031i
$687$	−8.11680	+	30.2923i	−0.309675	+	1.15572i
$688$	−0.00208774	−	0.00361607i	−7.95944e−5	−	0.000137861i
$689$	−3.53405	−	3.53405i	−0.134637	−	0.134637i
$690$	0.282440	+	3.09410i	0.0107523	+	0.117790i
$691$	−18.4410	+	10.6469i	−0.701530	+	0.405029i	−0.807917	−	0.589296i	$-0.799405\pi$
$691$	−18.4410	+	10.6469i	−0.701530	+	0.405029i	0.106387	+	0.994325i	$0.466072\pi$
$692$	11.5992	−	11.5992i	0.440936	−	0.440936i
$693$	−0.475222	+	0.475222i	−0.0180522	+	0.0180522i
$694$	−2.78221	−	4.81893i	−0.105611	−	0.182924i
$695$	0.464942	+	0.0801781i	0.0176363	+	0.00304133i
$696$	3.05861	+	1.76589i	0.115936	+	0.0669359i
$697$	−3.04223			−0.115233
$698$	22.9668	+	13.2599i	0.869307	+	0.501895i
$699$	23.7626	+	13.7194i	0.898785	+	0.518914i
$700$	0.644803	−	8.06951i	0.0243712	−	0.304999i
$701$	−10.6253	−	2.84703i	−0.401310	−	0.107531i	0.0525178	−	0.998620i	$-0.483275\pi$
$701$	−10.6253	−	2.84703i	−0.401310	−	0.107531i	−0.453828	+	0.891089i	$0.649942\pi$
$702$	2.65976	+	2.65976i	0.100386	+	0.100386i
$703$	7.14517	−	1.96767i	0.269485	−	0.0742119i
$704$			17.7415i			0.668657i
$705$	25.0337	−	9.21839i	0.942822	−	0.347185i
$706$	−2.84781	−	1.64419i	−0.107179	−	0.0618798i
$707$	16.7444	−	4.48665i	0.629738	−	0.168738i
$708$	−6.53897	+	11.3258i	−0.245750	+	0.425651i
$709$	23.6203	+	23.6203i	0.887079	+	0.887079i	0.994241	−	0.107163i	$-0.0341766\pi$
$709$	23.6203	+	23.6203i	0.887079	+	0.887079i	−0.107163	+	0.994241i	$0.534177\pi$
$710$	1.04436	−	1.25418i	0.0391943	−	0.0470687i
$711$	−0.961739	+	0.961739i	−0.0360680	+	0.0360680i
$712$	40.6717	+	10.8980i	1.52424	+	0.408418i
$713$	7.30560	+	7.30560i	0.273597	+	0.273597i
$714$	7.21139			0.269880
$715$	6.06306	−	2.23266i	0.226745	−	0.0834967i
$716$	0.886465	+	3.30833i	0.0331287	+	0.123638i
$717$	−37.3220			−1.39382
$718$	4.21657	−	2.43444i	0.157361	−	0.0908523i
$719$	−26.3473	+	15.2116i	−0.982588	+	0.567297i	−0.903050	−	0.429534i	$-0.858678\pi$
$719$	−26.3473	+	15.2116i	−0.982588	+	0.567297i	−0.0795375	+	0.996832i	$0.525344\pi$
$720$	0.00288493	−	0.00106235i	0.000107515	−	3.95913e-5i
$721$	−13.1393	+	3.52066i	−0.489332	+	0.131116i
$722$	13.2767	+	7.66531i	0.494108	+	0.285273i
$723$	−6.52444	+	3.76689i	−0.242647	+	0.140092i
$724$	−4.49116	−	7.77891i	−0.166913	−	0.289101i
$725$	−3.03954	−	2.09438i	−0.112886	−	0.0777834i
$726$	1.84080	−	1.84080i	0.0683186	−	0.0683186i
$727$	−15.2113	+	26.3468i	−0.564157	+	0.977149i	0.432971	+	0.901408i	$0.357465\pi$
$727$	−15.2113	+	26.3468i	−0.564157	+	0.977149i	−0.997128	+	0.0757406i	$0.975868\pi$
$728$	−2.90187	−	0.777554i	−0.107551	−	0.0288181i
$729$			28.1642i			1.04312i
$730$	−6.66432	+	4.70390i	−0.246658	+	0.174099i
$731$	1.40113	−	0.808945i	0.0518228	−	0.0299199i
$732$	28.2293			1.04339
$733$	9.32093	+	34.7862i	0.344276	+	1.28486i	0.893455	+	0.449152i	$0.148274\pi$
$733$	9.32093	+	34.7862i	0.344276	+	1.28486i	−0.549179	+	0.835705i	$0.685059\pi$
$734$	−7.45743	+	7.45743i	−0.275259	+	0.275259i
$735$	−19.8659	+	1.81343i	−0.732764	+	0.0668894i
$736$	−2.65467	+	4.59802i	−0.0978524	+	0.169485i
$737$	12.4980	+	46.6430i	0.460368	+	1.71812i
$738$	−0.0513843	−	0.0890002i	−0.00189148	−	0.00327614i
$739$	−22.4663			−0.826435			−0.413217	−	0.910632i	$-0.635595\pi$
$739$	−22.4663			−0.826435			−0.413217	+	0.910632i	$0.635595\pi$
$740$	−5.90842	−	15.7088i	−0.217198	−	0.577466i
$741$	−1.66574			−0.0611926
$742$	−3.54787	−	6.14509i	−0.130246	−	0.225593i
$743$	−9.54195	−	35.6110i	−0.350060	−	1.30644i	−0.886588	−	0.462560i	$-0.846931\pi$
$743$	−9.54195	−	35.6110i	−0.350060	−	1.30644i	0.536528	−	0.843883i	$-0.319736\pi$
$744$	−26.3114	+	45.5726i	−0.964621	+	1.67077i
$745$	30.4647	+	25.3681i	1.11614	+	0.929414i
$746$	−9.34476	+	9.34476i	−0.342136	+	0.342136i
$747$	0.252265	+	0.941464i	0.00922988	+	0.0344464i
$748$	−16.3756			−0.598750
$749$	−11.9568	+	6.90328i	−0.436893	+	0.252240i
$750$	15.9264	−	4.46085i	0.581548	−	0.162887i
$751$		−	12.9393i		−	0.472163i	−0.971733	−	0.236082i	$-0.924137\pi$
$751$		−	12.9393i		−	0.472163i	0.971733	−	0.236082i	$-0.0758632\pi$
$752$	−0.0653754	−	0.0175173i	−0.00238400	−	0.000638790i
$753$	−17.7083	+	30.6718i	−0.645328	+	1.11774i
$754$	−0.369591	+	0.369591i	−0.0134597	+	0.0134597i
$755$	−7.22144	+	2.65922i	−0.262815	+	0.0967789i
$756$	−4.30083	−	7.44926i	−0.156420	−	0.270927i
$757$	−17.1167	+	9.88233i	−0.622117	+	0.359179i	−0.777693	−	0.628645i	$-0.783610\pi$
$757$	−17.1167	+	9.88233i	−0.622117	+	0.359179i	0.155576	+	0.987824i	$0.450277\pi$
$758$	2.04631	+	1.18144i	0.0743253	+	0.0429117i
$759$	5.47747	−	1.46768i	0.198820	−	0.0532735i
$760$	−3.23266	+	7.00116i	−0.117261	+	0.253959i
$761$	9.87321	−	5.70030i	0.357903	−	0.206636i	−0.310257	−	0.950653i	$-0.600415\pi$
$761$	9.87321	−	5.70030i	0.357903	−	0.206636i	0.668161	+	0.744017i	$0.267082\pi$
$762$	5.22529	−	3.01682i	0.189292	−	0.109288i
$763$	4.35277			0.157581
$764$	−6.29344	−	23.4874i	−0.227689	−	0.849745i
$765$	0.411631	+	1.11783i	0.0148826	+	0.0404154i
$766$	7.42985			0.268451
$767$	−3.58681	−	3.58681i	−0.129512	−	0.129512i
$768$	−26.1594	−	7.00940i	−0.943948	−	0.252930i
$769$	13.9769	−	13.9769i	0.504021	−	0.504021i	−0.408664	−	0.912685i	$-0.634005\pi$
$769$	13.9769	−	13.9769i	0.504021	−	0.504021i	0.912685	+	0.408664i	$0.134005\pi$
$770$	9.13507	−	0.833883i	0.329205	−	0.0300510i
$771$	0.184101	+	0.184101i	0.00663025	+	0.00663025i
$772$	−8.43935	+	14.6174i	−0.303739	+	0.526091i
$773$	−4.29500	+	1.15084i	−0.154480	+	0.0413929i	−0.335230	−	0.942136i	$-0.608814\pi$
$773$	−4.29500	+	1.15084i	−0.154480	+	0.0413929i	0.180750	+	0.983529i	$0.442148\pi$
$774$	0.0473313	+	0.0273267i	0.00170129	+	0.000982239i
$775$	31.2058	−	45.2885i	1.12095	−	1.62681i
$776$		−	5.27570i		−	0.189387i
$777$	11.6353	−	6.82550i	0.417414	−	0.244863i
$778$	−0.487200	−	0.487200i	−0.0174670	−	0.0174670i
$779$	0.963683	+	0.258218i	0.0345275	+	0.00925162i
$780$	0.342915	+	3.75659i	0.0122783	+	0.134508i
$781$	−2.57971	−	1.48940i	−0.0923094	−	0.0532949i
$782$	2.64510	+	1.52715i	0.0945886	+	0.0546108i
$783$	−3.92217			−0.140167
$784$	0.0438302	+	0.0253054i	0.00156537	+	0.000903764i
$785$	27.6012	−	19.4819i	0.985130	−	0.695337i
$786$	−12.0062	−	20.7954i	−0.428248	−	0.741748i
$787$	−27.0617	+	27.0617i	−0.964647	+	0.964647i	−0.999396	−	0.0347491i	$-0.988937\pi$
$787$	−27.0617	+	27.0617i	−0.964647	+	0.964647i	0.0347491	+	0.999396i	$0.488937\pi$
$788$	21.3007	−	21.3007i	0.758808	−	0.758808i
$789$	−16.6059	+	9.58740i	−0.591184	+	0.341320i
$790$	18.4873	−	1.68759i	0.657748	−	0.0600416i
$791$	−1.58402	−	1.58402i	−0.0563213	−	0.0563213i
$792$	−0.724897	−	1.25556i	−0.0257581	−	0.0446143i
$793$	−2.83387	+	10.5762i	−0.100634	+	0.375571i
$794$	−3.86437	+	14.4220i	−0.137141	+	0.511818i
$795$	−14.9421	+	17.9441i	−0.529943	+	0.636412i
$796$	7.46098	+	27.8447i	0.264447	+	0.986931i
$797$	−8.14331	−	14.1046i	−0.288451	−	0.499612i	0.684989	−	0.728553i	$-0.259807\pi$
$797$	−8.14331	−	14.1046i	−0.288451	−	0.499612i	−0.973440	+	0.228942i	$0.926474\pi$
$798$	−2.28434	−	0.612088i	−0.0808649	−	0.0216677i
$799$	6.78749	−	25.3313i	0.240124	−	0.896156i
$800$	26.6308	+	9.46634i	0.941540	+	0.334686i
$801$	−2.06037	+	0.552075i	−0.0727996	+	0.0195066i
$802$	7.55844	−	28.2085i	0.266898	−	0.996076i
$803$	10.5275	+	10.5275i	0.371509	+	0.371509i
$804$	−28.1926			−0.994275
$805$	2.50195	+	1.15523i	0.0881823	+	0.0407166i
$806$	−5.50682	−	5.50682i	−0.193969	−	0.193969i
$807$	−34.3716	+	9.20986i	−1.20994	+	0.324202i
$808$			37.3956i			1.31557i
$809$	−5.88309	−	21.9560i	−0.206838	−	0.771931i	−0.988881	−	0.148707i	$-0.952489\pi$
$809$	−5.88309	−	21.9560i	−0.206838	−	0.771931i	0.782043	−	0.623224i	$-0.214178\pi$
$810$	10.7068	−	12.8579i	0.376200	−	0.451782i
$811$	24.4816	−	42.4035i	0.859667	−	1.48899i	−0.0125801	−	0.999921i	$-0.504004\pi$
$811$	24.4816	−	42.4035i	0.859667	−	1.48899i	0.872247	−	0.489066i	$-0.162662\pi$
$812$	1.03512	−	0.597629i	0.0363257	−	0.0209726i
$813$	−32.5425	+	32.5425i	−1.14131	+	1.14131i
$814$	16.4036	−	9.62267i	0.574946	−	0.337275i
$815$	−6.61389	+	38.3530i	−0.231674	+	1.34345i
$816$	−0.0155830	+	0.0581567i	−0.000545516	+	0.00203589i
$817$	−0.512497	+	0.137323i	−0.0179300	+	0.00480433i
$818$	−8.40858	−	31.3812i	−0.293999	−	1.09722i
$819$	0.147005	−	0.0393898i	0.00513676	−	0.00137639i
$820$	0.383948	−	2.22646i	0.0134080	−	0.0777514i
$821$	13.8466	−	23.9829i	0.483248	−	0.837010i	−0.516567	−	0.856247i	$-0.672790\pi$
$821$	13.8466	−	23.9829i	0.483248	−	0.837010i	0.999815	+	0.0192367i	$0.00612361\pi$
$822$		−	17.7239i		−	0.618193i
$823$	8.80315	−	32.8538i	0.306859	−	1.14521i	−0.624475	−	0.781045i	$-0.714687\pi$
$823$	8.80315	−	32.8538i	0.306859	−	1.14521i	0.931334	−	0.364167i	$-0.118646\pi$
$824$		−	29.3442i		−	1.02225i
$825$	−12.9631	−	27.2617i	−0.451319	−	0.949131i
$826$	−3.60083	−	6.23683i	−0.125289	−	0.217007i
$827$	0.426215	+	0.246075i	0.0148209	+	0.00855687i	0.507392	−	0.861715i	$-0.330610\pi$
$827$	0.426215	+	0.246075i	0.0148209	+	0.00855687i	−0.492571	+	0.870272i	$0.663943\pi$
$828$		−	0.166186i		−	0.00577538i
$829$	24.3838	+	6.53363i	0.846886	+	0.226922i	0.656067	−	0.754703i	$-0.272219\pi$
$829$	24.3838	+	6.53363i	0.846886	+	0.226922i	0.190819	+	0.981625i	$0.438886\pi$
$830$	5.57683	−	12.0781i	0.193574	−	0.419235i
$831$	2.30961	+	0.618859i	0.0801196	+	0.0214680i
$832$	2.00879	−	3.47933i	0.0696424	−	0.120624i
$833$	−9.80518	+	16.9831i	−0.339729	+	0.588429i
$834$	−0.301497	−	0.0807858i	−0.0104400	−	0.00279738i
$835$	−29.0148	+	10.6844i	−1.00410	+	0.369749i
$836$	5.18727	+	1.38992i	0.179405	+	0.0480715i
$837$		−	58.4394i		−	2.01996i
$838$	−2.64614	−	1.52775i	−0.0914094	−	0.0527752i
$839$	15.6937	+	27.1823i	0.541807	+	0.938438i	0.998800	+	0.0489677i	$0.0155932\pi$
$839$	15.6937	+	27.1823i	0.541807	+	0.938438i	−0.456993	+	0.889470i	$0.651074\pi$
$840$	−2.38529	+	13.8320i	−0.0823003	+	0.477248i
$841$			28.4550i			0.981207i
$842$	4.08940	−	15.2619i	0.140930	−	0.525958i
$843$		−	3.75135i		−	0.129203i
$844$	−3.34426	+	5.79242i	−0.115114	+	0.199383i
$845$	27.2042	+	4.69130i	0.935854	+	0.161386i
$846$	0.855708	−	0.229286i	0.0294198	−	0.00788302i
$847$	−0.597624	−	2.23036i	−0.0205346	−	0.0766362i
$848$	0.0572240	−	0.0153331i	0.00196508	−	0.000526542i
$849$	−8.60194	+	32.1029i	−0.295218	+	1.10177i
$850$	5.44569	−	15.3199i	0.186786	−	0.525467i
$851$	5.71320	−	0.0395575i	0.195846	−	0.00135602i
$852$	1.22975	−	1.22975i	0.0421306	−	0.0421306i
$853$	−2.52559	+	1.45815i	−0.0864747	+	0.0499262i	−0.542614	−	0.839982i	$-0.682565\pi$
$853$	−2.52559	+	1.45815i	−0.0864747	+	0.0499262i	0.456139	+	0.889908i	$0.349232\pi$
$854$	−7.77256	+	13.4625i	−0.265971	+	0.460676i
$855$	−0.0355124	−	0.389033i	−0.00121450	−	0.0133047i
$856$	−7.70862	−	28.7690i	−0.263475	−	0.983303i
$857$			11.5325i			0.393943i	0.980409	+	0.196971i	$0.0631106\pi$
$857$			11.5325i			0.393943i	−0.980409	+	0.196971i	$0.936889\pi$
$858$	−4.12881	+	1.10631i	−0.140955	+	0.0377688i
$859$	−17.5145	−	17.5145i	−0.597587	−	0.597587i	0.342083	−	0.939670i	$-0.388868\pi$
$859$	−17.5145	−	17.5145i	−0.597587	−	0.597587i	−0.939670	+	0.342083i	$0.888868\pi$
$860$	0.415196	+	1.12752i	0.0141581	+	0.0384480i
$861$	1.81594			0.0618871
$862$	−9.54971	−	9.54971i	−0.325264	−	0.325264i
$863$	−13.2670	+	49.5130i	−0.451613	+	1.68544i	0.246246	+	0.969207i	$0.420803\pi$
$863$	−13.2670	+	49.5130i	−0.451613	+	1.68544i	−0.697859	+	0.716235i	$0.745864\pi$
$864$	29.0081	−	7.77269i	0.986875	−	0.264432i
$865$	24.2860	−	17.1419i	0.825748	−	0.582841i
$866$	4.62736	−	17.2696i	0.157244	−	0.586843i
$867$	5.21932	+	1.39851i	0.177257	+	0.0474959i
$868$	8.90453	+	15.4231i	0.302239	+	0.523494i
$869$	−8.76943	−	32.7280i	−0.297483	−	1.11022i
$870$	1.87659	+	1.56265i	0.0636224	+	0.0529786i
$871$	2.83018	−	10.5624i	0.0958971	−	0.357893i
$872$	−2.43028	+	9.06995i	−0.0822998	+	0.307147i
$873$	0.133630	+	0.231453i	0.00452268	+	0.00783351i
$874$	−0.708264	−	0.708264i	−0.0239574	−	0.0239574i
$875$	3.63655	−	14.2120i	0.122938	−	0.480452i
$876$	−7.52773	+	4.34614i	−0.254338	+	0.146842i
$877$	7.33508	−	7.33508i	0.247688	−	0.247688i	−0.572333	−	0.820021i	$-0.693962\pi$
$877$	7.33508	−	7.33508i	0.247688	−	0.247688i	0.820021	+	0.572333i	$0.193962\pi$
$878$	−22.2587	+	22.2587i	−0.751194	+	0.751194i
$879$	−23.0336	−	39.8954i	−0.776905	−	1.34564i
$880$	−0.0130150	+	0.0754723i	−0.000438736	+	0.00254417i
$881$	−8.93312	−	5.15754i	−0.300965	−	0.173762i	0.341912	−	0.939732i	$-0.388926\pi$
$881$	−8.93312	−	5.15754i	−0.300965	−	0.173762i	−0.642876	+	0.765970i	$0.722259\pi$
$882$	−0.662452			−0.0223059
$883$	−38.9309	−	22.4768i	−1.31013	−	0.756404i	−0.328013	−	0.944673i	$-0.606379\pi$
$883$	−38.9309	−	22.4768i	−1.31013	−	0.756404i	−0.982118	+	0.188269i	$0.939712\pi$
$884$	3.21146	+	1.85414i	0.108013	+	0.0623614i
$885$	−15.1652	+	18.2120i	−0.509772	+	0.612189i
$886$	−9.35078	−	2.50553i	−0.314145	−	0.0841750i
$887$	6.65382	+	6.65382i	0.223413	+	0.223413i	0.809934	−	0.586521i	$-0.199503\pi$
$887$	6.65382	+	6.65382i	0.223413	+	0.223413i	−0.586521	+	0.809934i	$0.699503\pi$
$888$	7.72606	+	28.0556i	0.259269	+	0.941483i
$889$		−	5.35166i		−	0.179489i
$890$	26.4325	+	12.2047i	0.886020	+	0.409104i
$891$	−26.4473	−	15.2694i	−0.886018	−	0.511543i
$892$	−30.0337	+	8.04751i	−1.00560	+	0.269450i
$893$	−4.30013	+	7.44804i	−0.143898	+	0.249239i
$894$	−18.5455	−	18.5455i	−0.620253	−	0.620253i
$895$	0.564226	+	6.18102i	0.0188600	+	0.206609i
$896$	−6.45579	+	6.45579i	−0.215673	+	0.215673i
$897$	−1.24038	−	0.332360i	−0.0414152	−	0.0110972i
$898$	−5.79465	−	5.79465i	−0.193370	−	0.193370i
$899$	8.12053			0.270835
$900$	−0.870039	+	0.160175i	−0.0290013	+	0.00533918i
$901$	5.94119	+	22.1728i	0.197930	+	0.738684i
$902$	2.56014			0.0852433
$903$	−0.836353	+	0.482869i	−0.0278321	+	0.0160689i
$904$	4.18506	−	2.41624i	0.139193	−	0.0803631i
$905$	−5.62475	−	15.2747i	−0.186973	−	0.507748i
$906$	4.91764	−	1.31768i	0.163378	−	0.0437769i
$907$	−2.62685	−	1.51661i	−0.0872230	−	0.0503582i	0.455754	−	0.890106i	$-0.349370\pi$
$907$	−2.62685	−	1.51661i	−0.0872230	−	0.0503582i	−0.542977	+	0.839747i	$0.682703\pi$
$908$	21.1397	−	12.2050i	0.701547	−	0.405038i
$909$	−0.947204	−	1.64061i	−0.0314168	−	0.0544155i
$910$	−1.88592	−	0.870792i	−0.0625178	−	0.0288665i
$911$	−13.3661	+	13.3661i	−0.442839	+	0.442839i	−0.892965	−	0.450126i	$-0.851379\pi$
$911$	−13.3661	+	13.3661i	−0.442839	+	0.442839i	0.450126	+	0.892965i	$0.351379\pi$
$912$	0.00987244	−	0.0170996i	0.000326909	−	0.000566223i
$913$	−23.4535	−	6.28434i	−0.776196	−	0.207981i
$914$			32.2627i			1.06716i
$915$	50.4120	+	8.69343i	1.66657	+	0.287396i
$916$	−19.8281	+	11.4478i	−0.655140	+	0.378245i
$917$	−21.2984			−0.703334
$918$	−4.47139	−	16.6875i	−0.147578	−	0.550768i
$919$	14.2230	−	14.2230i	0.469172	−	0.469172i	−0.432474	−	0.901646i	$-0.642359\pi$
$919$	14.2230	−	14.2230i	0.469172	−	0.469172i	0.901646	+	0.432474i	$0.142359\pi$
$920$	−3.80409	+	4.56836i	−0.125417	+	0.150614i
$921$	5.10384	−	8.84010i	0.168177	−	0.291291i
$922$	7.23734	+	27.0101i	0.238349	+	0.889531i
$923$	0.337277	+	0.584181i	0.0111016	+	0.0192286i
$924$	9.77476			0.321566
$925$	−5.71365	−	29.8723i	−0.187864	−	0.982195i
$926$	−2.64960			−0.0870712
$927$	0.743268	+	1.28738i	0.0244121	+	0.0422831i
$928$	1.08007	+	4.03086i	0.0354549	+	0.132319i
$929$	17.1505	−	29.7055i	0.562689	−	0.974607i	−0.434571	−	0.900638i	$-0.643100\pi$
$929$	17.1505	−	29.7055i	0.562689	−	0.974607i	0.997261	−	0.0739691i	$-0.0235666\pi$
$930$	−23.2831	+	27.9608i	−0.763481	+	0.916870i
$931$	4.54746	−	4.54746i	0.149037	−	0.149037i
$932$	5.18469	+	19.3495i	0.169830	+	0.633815i
$933$	48.0252			1.57227
$934$	17.6269	−	10.1769i	0.576771	−	0.332999i
$935$	−29.2435	−	5.04298i	−0.956366	−	0.164923i
$936$			0.328309i			0.0107311i
$937$	55.1192	+	14.7691i	1.80066	+	0.482487i	0.994082	−	0.108634i	$-0.0346478\pi$
$937$	55.1192	+	14.7691i	1.80066	+	0.482487i	0.806583	+	0.591121i	$0.201314\pi$
$938$	7.76244	−	13.4449i	0.253453	−	0.438993i
$939$	7.64045	−	7.64045i	0.249337	−	0.249337i
$940$	17.6821	+	8.16440i	0.576727	+	0.266293i
$941$	−9.54525	−	16.5329i	−0.311166	−	0.538956i	0.667449	−	0.744656i	$-0.267386\pi$
$941$	−9.54525	−	16.5329i	−0.311166	−	0.538956i	−0.978615	+	0.205700i	$0.934053\pi$
$942$	−19.3562	+	11.1753i	−0.630660	+	0.364112i
$943$	0.666078	+	0.384560i	0.0216905	+	0.0125230i
$944$	0.0580783	−	0.0155620i	0.00189029	−	0.000506501i
$945$	−5.38639	−	14.6274i	−0.175219	−	0.475829i
$946$	−1.17910	+	0.680755i	−0.0383359	+	0.0221332i
$947$	12.4292	−	7.17600i	0.403895	−	0.233189i	−0.284268	−	0.958745i	$-0.591751\pi$
$947$	12.4292	−	7.17600i	0.403895	−	0.233189i	0.688163	+	0.725556i	$0.258417\pi$
$948$	19.7819			0.642485
$949$	−0.872597	−	3.25658i	−0.0283257	−	0.105713i
$950$	−3.02534	+	4.39063i	−0.0981551	+	0.142451i
$951$	−30.7861			−0.998307
$952$	9.75682	+	9.75682i	0.316220	+	0.316220i
$953$	1.50572	+	0.403456i	0.0487750	+	0.0130692i	0.283124	−	0.959083i	$-0.408629\pi$
$953$	1.50572	+	0.403456i	0.0487750	+	0.0130692i	−0.234349	+	0.972153i	$0.575296\pi$
$954$	−0.548316	+	0.548316i	−0.0177524	+	0.0177524i
$955$	−4.00571	−	43.8820i	−0.129622	−	1.41999i
$956$	−19.2669	−	19.2669i	−0.623137	−	0.623137i
$957$	2.22854	−	3.85994i	0.0720383	−	0.124774i
$958$	−20.8214	+	5.57909i	−0.672710	+	0.180252i
$959$	−13.6145	−	7.86031i	−0.439634	−	0.253823i
$960$	−17.0417	−	7.86870i	−0.550018	−	0.253961i
$961$			89.9939i			2.90303i
$962$	−4.30650	+	0.0298177i	−0.138847	+	0.000961361i
$963$	1.06689	+	1.06689i	0.0343799	+	0.0343799i
$964$	−5.31275	−	1.42355i	−0.171112	−	0.0458493i
$965$	−19.5726	+	23.5048i	−0.630063	+	0.756647i
$966$	−1.57889	−	0.911573i	−0.0508000	−	0.0293294i
$967$	−4.86278	−	2.80753i	−0.156377	−	0.0902841i	0.419770	−	0.907631i	$-0.362111\pi$
$967$	−4.86278	−	2.80753i	−0.156377	−	0.0902841i	−0.576146	+	0.817347i	$0.695444\pi$
$968$	4.98112			0.160099
$969$	6.62564	+	3.82531i	0.212846	+	0.122887i
$970$	0.619911	−	3.59478i	0.0199041	−	0.115421i
$971$	−8.92123	−	15.4520i	−0.286296	−	0.495879i	0.686627	−	0.727010i	$-0.259091\pi$
$971$	−8.92123	−	15.4520i	−0.286296	−	0.495879i	−0.972923	+	0.231131i	$0.925757\pi$
$972$	−1.29905	+	1.29905i	−0.0416670	+	0.0416670i
$973$	−0.195764	+	0.195764i	−0.00627591	+	0.00627591i
$974$	−20.2103	+	11.6684i	−0.647580	+	0.373881i
$975$	−0.544491	+	6.81414i	−0.0174377	+	0.218227i
$976$	−0.0917732	−	0.0917732i	−0.00293759	−	0.00293759i
$977$	−25.7028	−	44.5186i	−0.822306	−	1.42428i	−0.903961	−	0.427615i	$-0.859354\pi$
$977$	−25.7028	−	44.5186i	−0.822306	−	1.42428i	0.0816553	−	0.996661i	$-0.473979\pi$
$978$	6.66402	−	24.8705i	0.213092	−	0.795269i
$979$	13.7531	−	51.3273i	0.439551	−	1.64043i
$980$	−11.1916	−	9.31931i	−0.357503	−	0.297694i
$981$	−0.123115	−	0.459470i	−0.00393075	−	0.0146698i
$982$	−14.0861	−	24.3979i	−0.449506	−	0.778568i
$983$	−1.73964	−	0.466136i	−0.0554861	−	0.0148674i	0.230969	−	0.972961i	$-0.425810\pi$
$983$	−1.73964	−	0.466136i	−0.0554861	−	0.0148674i	−0.286455	+	0.958094i	$0.592477\pi$
$984$	−1.01390	+	3.78391i	−0.0323218	+	0.120627i
$985$	44.5987	−	31.4792i	1.42103	−	1.00301i
$986$	2.31883	−	0.621329i	0.0738466	−	0.0197871i
$987$	−4.05153	+	15.1205i	−0.128962	+	0.481292i
$988$	−0.859915	−	0.859915i	−0.0273575	−	0.0273575i
$989$	−0.409027			−0.0130063
$990$	−0.346401	−	0.940695i	−0.0110094	−	0.0298973i
$991$	5.30288	+	5.30288i	0.168452	+	0.168452i	0.786298	−	0.617847i	$-0.211995\pi$
$991$	5.30288	+	5.30288i	0.168452	+	0.168452i	−0.617847	+	0.786298i	$0.711995\pi$
$992$	−60.0589	+	16.0927i	−1.90687	+	0.510945i
$993$		−	24.3339i		−	0.772211i
$994$	0.247869	+	0.925061i	0.00786194	+	0.0293411i
$995$	4.74884	+	52.0229i	0.150548	+	1.64924i
$996$	7.08802	−	12.2768i	0.224592	−	0.389006i
$997$	18.9046	−	10.9146i	0.598716	−	0.345669i	−0.169820	−	0.985475i	$-0.554319\pi$
$997$	18.9046	−	10.9146i	0.598716	−	0.345669i	0.768536	+	0.639806i	$0.220985\pi$
$998$	8.66097	−	8.66097i	0.274158	−	0.274158i
$999$	−23.0089	−	22.6925i	−0.727969	−	0.717958i

Display

a_p

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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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	185.2.p.a.103.7	yes	68
5.2	odd	4		185.2.u.a.177.11	yes	68
5.3	odd	4		925.2.y.b.732.7		68
5.4	even	2		925.2.t.b.843.11		68
37.23	odd	12		185.2.u.a.23.11	yes	68
185.23	even	12		925.2.t.b.282.11		68
185.97	even	12	inner	185.2.p.a.97.7	✓	68
185.134	odd	12		925.2.y.b.393.7		68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.p.a.97.7	✓	68	185.97	even	12	inner
185.2.p.a.103.7	yes	68	1.1	even	1	trivial
185.2.u.a.23.11	yes	68	37.23	odd	12
185.2.u.a.177.11	yes	68	5.2	odd	4
925.2.t.b.282.11		68	185.23	even	12
925.2.t.b.843.11		68	5.4	even	2
925.2.y.b.393.7		68	185.134	odd	12
925.2.y.b.732.7		68	5.3	odd	4

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
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Abelian varieties over $\F_{q}$
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Newspace parameters

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	185.2.p.a.103.7

Level	$185$
Weight	$2$
Character	185.103
Analytic conductor	$1.477$
Analytic rank	$0$
Dimension	$68$
Inner twists	$2$