LMFDB - Embedded newform 961.2.g.i.448.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [961,2,Mod(235,961)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(961, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([26]))

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

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

chi := DirichletCharacter("961.235");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.g (of order $15$, degree $8$, not 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:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	16.0.26873856000000000000.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2x^{14} + 8x^{10} - 16x^{8} + 32x^{6} - 128x^{2} + 256 $ x^16 - 2x^14 + 8x^10 - 16x^8 + 32x^6 - 128*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			448.1
Root			$-1.38331 - 0.294032i$ of defining polynomial
Character	$\chi$	$=$	961.448
Dual form			961.2.g.i.547.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.118034 - 0.363271i) q^{2} +(-1.53114 + 1.70050i) q^{3} +(1.50000 + 1.08981i) q^{4} +(1.11803 - 1.93649i) q^{5} +(0.437016 + 0.756934i) q^{6} +(0.104528 - 0.994522i) q^{7} +(1.19098 - 0.865300i) q^{8} +(-0.233733 - 2.22382i) q^{9} +(-0.571506 - 0.634721i) q^{10} +(-3.87585 + 1.72564i) q^{11} +(-4.14993 + 0.882095i) q^{12} +(6.71473 + 1.42726i) q^{13} +(-0.348943 - 0.155360i) q^{14} +(1.58114 + 4.86624i) q^{15} +(0.972136 + 2.99193i) q^{16} +(-0.493480 - 0.219712i) q^{17} +(-0.835438 - 0.177578i) q^{18} +(-0.978148 + 0.207912i) q^{19} +(3.78747 - 1.68629i) q^{20} +(1.53114 + 1.70050i) q^{21} +(0.169393 + 1.61167i) q^{22} +(5.55369 - 4.03499i) q^{23} +(-0.352115 + 3.35016i) q^{24} +(1.31105 - 2.27080i) q^{26} +(-1.41421 - 1.02749i) q^{27} +(1.24064 - 1.37787i) q^{28} +(1.14412 - 3.52125i) q^{29} +1.95440 q^{30} +4.14590 q^{32} +(3.00000 - 9.23305i) q^{33} +(-0.138062 + 0.153334i) q^{34} +(-1.80902 - 1.31433i) q^{35} +(2.07295 - 3.59045i) q^{36} +(2.12132 + 3.67423i) q^{37} +(-0.0399263 + 0.379874i) q^{38} +(-12.7082 + 9.23305i) q^{39} +(-0.344086 - 3.27376i) q^{40} +(4.99983 + 5.55288i) q^{41} +(0.798468 - 0.355501i) q^{42} +(-0.201822 + 0.0428986i) q^{43} +(-7.69439 - 1.63549i) q^{44} +(-4.56773 - 2.03368i) q^{45} +(-0.810272 - 2.49376i) q^{46} +(1.14590 + 3.52671i) q^{47} +(-6.57624 - 2.92793i) q^{48} +(5.86889 + 1.24747i) q^{49} +(1.12920 - 0.502754i) q^{51} +(8.51664 + 9.45869i) q^{52} +(0.548167 + 5.21546i) q^{53} +(-0.540182 + 0.392465i) q^{54} +(-0.991644 + 9.43486i) q^{55} +(-0.736068 - 1.27491i) q^{56} +(1.14412 - 1.98168i) q^{57} +(-1.14412 - 0.831254i) q^{58} +(-3.97749 + 4.41745i) q^{59} +(-2.93159 + 9.02251i) q^{60} -4.44897 q^{61} -2.23607 q^{63} +(-1.45492 + 4.47777i) q^{64} +(10.2712 - 11.4073i) q^{65} +(-3.00000 - 2.17963i) q^{66} +(-3.00000 + 5.19615i) q^{67} +(-0.500776 - 0.867369i) q^{68} +(-1.64195 + 15.6222i) q^{69} +(-0.690983 + 0.502029i) q^{70} +(-0.781051 - 7.43120i) q^{71} +(-2.20264 - 2.44628i) q^{72} +(-3.87585 + 1.72564i) q^{73} +(1.58513 - 0.336930i) q^{74} +(-1.69381 - 0.754131i) q^{76} +(1.31105 + 4.03499i) q^{77} +(1.85410 + 5.70634i) q^{78} +(10.1471 + 4.51778i) q^{79} +(6.88072 + 1.46254i) q^{80} +(10.4742 - 2.22636i) q^{81} +(2.60735 - 1.16087i) q^{82} +(-2.11598 - 2.35003i) q^{83} +(0.443477 + 4.21940i) q^{84} +(-0.977198 + 0.709976i) q^{85} +(-0.00823804 + 0.0783797i) q^{86} +(4.23607 + 7.33708i) q^{87} +(-3.12287 + 5.40897i) q^{88} +(-4.74342 - 3.44629i) q^{89} +(-1.27793 + 1.41928i) q^{90} +(2.12132 - 6.52875i) q^{91} +12.7279 q^{92} +1.41641 q^{94} +(-0.690983 + 2.12663i) q^{95} +(-6.34793 + 7.05009i) q^{96} +(5.66312 + 4.11450i) q^{97} +(1.14590 - 1.98475i) q^{98} +(4.74342 + 8.21584i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{2} + 24 q^{4} - 2 q^{7} + 28 q^{8} + 10 q^{9} + 20 q^{10} + 2 q^{14} - 56 q^{16} - 20 q^{18} + 2 q^{19} - 18 q^{28} + 120 q^{32} + 48 q^{33} - 20 q^{35} + 60 q^{36} - 2 q^{38} - 96 q^{39} - 10 q^{40}+ \cdots + 72 q^{98}+O(q^{100}) $ 16 * q - 16 * q^2 + 24 * q^4 - 2 * q^7 + 28 * q^8 + 10 * q^9 + 20 * q^10 + 2 * q^14 - 56 * q^16 - 20 * q^18 + 2 * q^19 - 18 * q^28 + 120 * q^32 + 48 * q^33 - 20 * q^35 + 60 * q^36 - 2 * q^38 - 96 * q^39 - 10 * q^40 - 14 * q^41 - 10 * q^45 + 72 * q^47 - 12 * q^49 + 8 * q^51 + 24 * q^56 + 46 * q^59 - 68 * q^64 - 48 * q^66 - 48 * q^67 + 48 * q^69 - 20 * q^70 + 26 * q^71 - 50 * q^72 - 12 * q^76 - 24 * q^78 + 80 * q^80 + 22 * q^81 + 14 * q^82 + 32 * q^87 - 40 * q^90 - 192 * q^94 - 20 * q^95 + 28 * q^97 + 72 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{11}{15}\right)$

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 $

$2$	0.118034	−	0.363271i	0.0834626	−	0.256872i	−0.900613	−	0.434622i	$-0.856882\pi$
$2$	0.118034	−	0.363271i	0.0834626	−	0.256872i	0.984076	+	0.177750i	$0.0568820\pi$
$3$	−1.53114	+	1.70050i	−0.884001	+	0.981783i	−0.999934	−	0.0114741i	$-0.996348\pi$
$3$	−1.53114	+	1.70050i	−0.884001	+	0.981783i	0.115933	+	0.993257i	$0.463014\pi$
$4$	1.50000	+	1.08981i	0.750000	+	0.544907i
$5$	1.11803	−	1.93649i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$5$	1.11803	−	1.93649i	0.500000	−	0.866025i	1.00000			$0$
$6$	0.437016	+	0.756934i	0.178411	+	0.309017i
$7$	0.104528	−	0.994522i	0.0395080	−	0.375894i	−0.956847	−	0.290592i	$-0.906148\pi$
$7$	0.104528	−	0.994522i	0.0395080	−	0.375894i	0.996355	−	0.0853021i	$-0.0271855\pi$
$8$	1.19098	−	0.865300i	0.421076	−	0.305930i
$9$	−0.233733	−	2.22382i	−0.0779109	−	0.741273i
$10$	−0.571506	−	0.634721i	−0.180726	−	0.200717i
$11$	−3.87585	+	1.72564i	−1.16861	+	0.520299i	−0.896967	−	0.442098i	$-0.854234\pi$
$11$	−3.87585	+	1.72564i	−1.16861	+	0.520299i	−0.271645	+	0.962398i	$0.587568\pi$
$12$	−4.14993	+	0.882095i	−1.19798	+	0.254639i
$13$	6.71473	+	1.42726i	1.86233	+	0.395850i	0.994827	−	0.101582i	$-0.0323904\pi$
$13$	6.71473	+	1.42726i	1.86233	+	0.395850i	0.867503	+	0.497432i	$0.165724\pi$
$14$	−0.348943	−	0.155360i	−0.0932590	−	0.0415216i
$15$	1.58114	+	4.86624i	0.408248	+	1.25646i
$16$	0.972136	+	2.99193i	0.243034	+	0.747982i
$17$	−0.493480	−	0.219712i	−0.119687	−	0.0532879i	0.346020	−	0.938227i	$-0.387533\pi$
$17$	−0.493480	−	0.219712i	−0.119687	−	0.0532879i	−0.465706	+	0.884939i	$0.654200\pi$
$18$	−0.835438	−	0.177578i	−0.196915	−	0.0418555i
$19$	−0.978148	+	0.207912i	−0.224402	+	0.0476982i	−0.318741	−	0.947842i	$-0.603260\pi$
$19$	−0.978148	+	0.207912i	−0.224402	+	0.0476982i	0.0943381	+	0.995540i	$0.469927\pi$
$20$	3.78747	−	1.68629i	0.846903	−	0.377066i
$21$	1.53114	+	1.70050i	0.334121	+	0.371079i
$22$	0.169393	+	1.61167i	0.0361147	+	0.343609i
$23$	5.55369	−	4.03499i	1.15802	−	0.841354i	0.168497	−	0.985702i	$-0.446109\pi$
$23$	5.55369	−	4.03499i	1.15802	−	0.841354i	0.989527	+	0.144348i	$0.0461086\pi$
$24$	−0.352115	+	3.35016i	−0.0718753	+	0.683848i
$25$		0			0
$26$	1.31105	−	2.27080i	0.257118	−	0.445341i
$27$	−1.41421	−	1.02749i	−0.272166	−	0.197740i
$28$	1.24064	−	1.37787i	0.234458	−	0.260392i
$29$	1.14412	−	3.52125i	0.212458	−	0.653879i	−0.786866	−	0.617124i	$-0.788298\pi$
$29$	1.14412	−	3.52125i	0.212458	−	0.653879i	0.999324	−	0.0367555i	$-0.0117023\pi$
$30$	1.95440			0.356822
$31$		0			0
$31$		0			0
$32$	4.14590			0.732898
$33$	3.00000	−	9.23305i	0.522233	−	1.60727i
$34$	−0.138062	+	0.153334i	−0.0236775	+	0.0262965i
$35$	−1.80902	−	1.31433i	−0.305780	−	0.222162i
$36$	2.07295	−	3.59045i	0.345492	−	0.598409i
$37$	2.12132	+	3.67423i	0.348743	+	0.604040i	0.986026	−	0.166589i	$-0.0532753\pi$
$37$	2.12132	+	3.67423i	0.348743	+	0.604040i	−0.637284	+	0.770629i	$0.719942\pi$
$38$	−0.0399263	+	0.379874i	−0.00647690	+	0.0616236i
$39$	−12.7082	+	9.23305i	−2.03494	+	1.47847i
$40$	−0.344086	−	3.27376i	−0.0544048	−	0.517627i
$41$	4.99983	+	5.55288i	0.780843	+	0.867214i	0.993952	−	0.109814i	$-0.0350256\pi$
$41$	4.99983	+	5.55288i	0.780843	+	0.867214i	−0.213109	+	0.977028i	$0.568359\pi$
$42$	0.798468	−	0.355501i	0.123206	−	0.0548550i
$43$	−0.201822	+	0.0428986i	−0.0307776	+	0.00654198i	−0.223275	−	0.974756i	$-0.571675\pi$
$43$	−0.201822	+	0.0428986i	−0.0307776	+	0.00654198i	0.192497	+	0.981298i	$0.438341\pi$
$44$	−7.69439	−	1.63549i	−1.15997	−	0.246560i
$45$	−4.56773	−	2.03368i	−0.680917	−	0.303164i
$46$	−0.810272	−	2.49376i	−0.119468	−	0.367685i
$47$	1.14590	+	3.52671i	0.167146	+	0.514424i	0.999188	−	0.0402894i	$-0.0128280\pi$
$47$	1.14590	+	3.52671i	0.167146	+	0.514424i	−0.832042	+	0.554713i	$0.812828\pi$
$48$	−6.57624	−	2.92793i	−0.949198	−	0.422610i
$49$	5.86889	+	1.24747i	0.838412	+	0.178210i
$50$		0			0
$51$	1.12920	−	0.502754i	0.158120	−	0.0703997i
$52$	8.51664	+	9.45869i	1.18105	+	1.31168i
$53$	0.548167	+	5.21546i	0.0752966	+	0.716399i	0.965424	+	0.260686i	$0.0839489\pi$
$53$	0.548167	+	5.21546i	0.0752966	+	0.716399i	−0.890127	+	0.455713i	$0.849384\pi$
$54$	−0.540182	+	0.392465i	−0.0735094	+	0.0534077i
$55$	−0.991644	+	9.43486i	−0.133713	+	1.27220i
$56$	−0.736068	−	1.27491i	−0.0983612	−	0.170367i
$57$	1.14412	−	1.98168i	0.151543	−	0.262480i
$58$	−1.14412	−	0.831254i	−0.150231	−	0.109149i
$59$	−3.97749	+	4.41745i	−0.517826	+	0.575104i	−0.944171	−	0.329457i	$-0.893134\pi$
$59$	−3.97749	+	4.41745i	−0.517826	+	0.575104i	0.426345	+	0.904561i	$0.359801\pi$
$60$	−2.93159	+	9.02251i	−0.378467	+	1.16480i
$61$	−4.44897			−0.569632			−0.284816	−	0.958582i	$-0.591933\pi$
$61$	−4.44897			−0.569632			−0.284816	+	0.958582i	$0.591933\pi$
$62$		0			0
$63$	−2.23607			−0.281718
$64$	−1.45492	+	4.47777i	−0.181864	+	0.559721i
$65$	10.2712	−	11.4073i	1.27398	−	1.41490i
$66$	−3.00000	−	2.17963i	−0.369274	−	0.268294i
$67$	−3.00000	+	5.19615i	−0.366508	+	0.634811i	−0.989017	−	0.147802i	$-0.952780\pi$
$67$	−3.00000	+	5.19615i	−0.366508	+	0.634811i	0.622509	+	0.782613i	$0.286114\pi$
$68$	−0.500776	−	0.867369i	−0.0607280	−	0.105184i
$69$	−1.64195	+	15.6222i	−0.197668	+	1.88069i
$70$	−0.690983	+	0.502029i	−0.0825883	+	0.0600039i
$71$	−0.781051	−	7.43120i	−0.0926937	−	0.881922i	−0.937766	−	0.347269i	$-0.887109\pi$
$71$	−0.781051	−	7.43120i	−0.0926937	−	0.881922i	0.845072	−	0.534653i	$-0.179558\pi$
$72$	−2.20264	−	2.44628i	−0.259584	−	0.288297i
$73$	−3.87585	+	1.72564i	−0.453633	+	0.201971i	−0.620818	−	0.783955i	$-0.713199\pi$
$73$	−3.87585	+	1.72564i	−0.453633	+	0.201971i	0.167184	+	0.985926i	$0.446533\pi$
$74$	1.58513	−	0.336930i	0.184268	−	0.0391673i
$75$		0			0
$76$	−1.69381	−	0.754131i	−0.194293	−	0.0865048i
$77$	1.31105	+	4.03499i	0.149408	+	0.459830i
$78$	1.85410	+	5.70634i	0.209936	+	0.646116i
$79$	10.1471	+	4.51778i	1.14164	+	0.508290i	0.888380	−	0.459109i	$-0.151831\pi$
$79$	10.1471	+	4.51778i	1.14164	+	0.508290i	0.253257	+	0.967399i	$0.418498\pi$
$80$	6.88072	+	1.46254i	0.769288	+	0.163517i
$81$	10.4742	−	2.22636i	1.16380	−	0.247373i
$82$	2.60735	−	1.16087i	0.287934	−	0.128196i
$83$	−2.11598	−	2.35003i	−0.232259	−	0.257949i	0.615738	−	0.787951i	$-0.288858\pi$
$83$	−2.11598	−	2.35003i	−0.232259	−	0.257949i	−0.847997	+	0.530002i	$0.822191\pi$
$84$	0.443477	+	4.21940i	0.0483873	+	0.460374i
$85$	−0.977198	+	0.709976i	−0.105992	+	0.0770077i
$86$	−0.00823804	+	0.0783797i	−0.000888330	+	0.00845190i
$87$	4.23607	+	7.33708i	0.454154	+	0.786618i
$88$	−3.12287	+	5.40897i	−0.332899	+	0.576598i
$89$	−4.74342	−	3.44629i	−0.502801	−	0.365306i	0.307285	−	0.951618i	$-0.400580\pi$
$89$	−4.74342	−	3.44629i	−0.502801	−	0.365306i	−0.810086	+	0.586311i	$0.800580\pi$
$90$	−1.27793	+	1.41928i	−0.134705	+	0.149605i
$91$	2.12132	−	6.52875i	0.222375	−	0.684399i
$92$	12.7279			1.32698
$93$		0			0
$94$	1.41641			0.146091
$95$	−0.690983	+	2.12663i	−0.0708934	+	0.218187i
$96$	−6.34793	+	7.05009i	−0.647883	+	0.719547i
$97$	5.66312	+	4.11450i	0.575003	+	0.417764i	0.836919	−	0.547327i	$-0.184354\pi$
$97$	5.66312	+	4.11450i	0.575003	+	0.417764i	−0.261916	+	0.965091i	$0.584354\pi$
$98$	1.14590	−	1.98475i	0.115753	−	0.200490i
$99$	4.74342	+	8.21584i	0.476731	+	0.825723i
$100$		0			0
$101$	1.80902	−	1.31433i	0.180004	−	0.130781i	−0.494135	−	0.869385i	$-0.664515\pi$
$101$	1.80902	−	1.31433i	0.180004	−	0.130781i	0.674139	+	0.738605i	$0.264515\pi$
$102$	−0.0493516	−	0.469550i	−0.00488654	−	0.0464923i
$103$	−1.81214	−	2.01259i	−0.178556	−	0.198306i	0.647223	−	0.762301i	$-0.275930\pi$
$103$	−1.81214	−	2.01259i	−0.178556	−	0.198306i	−0.825778	+	0.563995i	$0.809264\pi$
$104$	9.23213	−	4.11041i	0.905285	−	0.403059i
$105$	5.00486	−	1.06382i	0.488424	−	0.103818i
$106$	1.95933	+	0.416469i	0.190307	+	0.0404510i
$107$	−6.82614	−	3.03919i	−0.659907	−	0.293810i	0.0493267	−	0.998783i	$-0.484292\pi$
$107$	−6.82614	−	3.03919i	−0.659907	−	0.293810i	−0.709234	+	0.704973i	$0.750959\pi$
$108$	−1.00155	−	3.08246i	−0.0963743	−	0.296610i
$109$	−4.54508	−	13.9883i	−0.435340	−	1.33984i	−0.892738	−	0.450577i	$-0.851218\pi$
$109$	−4.54508	−	13.9883i	−0.435340	−	1.33984i	0.457397	−	0.889262i	$-0.348782\pi$
$110$	3.31037	+	1.47387i	0.315631	+	0.140528i
$111$	−9.49606	−	2.01845i	−0.901326	−	0.191583i
$112$	3.07715	−	0.654069i	0.290764	−	0.0618037i
$113$	−13.0053	+	5.79033i	−1.22344	+	0.544708i	−0.913807	−	0.406149i	$-0.866871\pi$
$113$	−13.0053	+	5.79033i	−1.22344	+	0.544708i	−0.309628	+	0.950858i	$0.600205\pi$
$114$	−0.584842	−	0.649532i	−0.0547754	−	0.0608343i
$115$	−1.60451	−	15.2659i	−0.149622	−	1.42356i
$116$	5.55369	−	4.03499i	0.515647	−	0.374640i
$117$	1.60451	−	15.2659i	0.148337	−	1.41134i
$118$	1.13525	+	1.96632i	0.104509	+	0.181014i
$119$	−0.270091	+	0.467811i	−0.0247592	+	0.0428842i
$120$	6.09387	+	4.42746i	0.556292	+	0.404170i
$121$	4.68391	−	5.20201i	0.425810	−	0.472910i
$122$	−0.525130	+	1.61618i	−0.0475430	+	0.146322i
$123$	−17.0981			−1.54168
$124$		0			0
$125$	11.1803			1.00000
$126$	−0.263932	+	0.812299i	−0.0235129	+	0.0723654i
$127$	−6.34793	+	7.05009i	−0.563288	+	0.625594i	−0.955752	−	0.294173i	$-0.904956\pi$
$127$	−6.34793	+	7.05009i	−0.563288	+	0.625594i	0.392465	+	0.919767i	$0.371623\pi$
$128$	8.16312	+	5.93085i	0.721525	+	0.524218i
$129$	0.236068	−	0.408882i	0.0207846	−	0.0360000i
$130$	−2.93159	−	5.07767i	−0.257118	−	0.445341i
$131$	2.02957	−	19.3100i	0.177324	−	1.68713i	−0.438097	−	0.898928i	$-0.644347\pi$
$131$	2.02957	−	19.3100i	0.177324	−	1.68713i	0.615421	−	0.788199i	$-0.288986\pi$
$132$	14.5623	−	10.5801i	1.26749	−	0.920883i
$133$	0.104528	+	0.994522i	0.00906377	+	0.0862360i
$134$	1.53351	+	1.70314i	0.132475	+	0.147129i
$135$	−3.57086	+	1.58985i	−0.307330	+	0.136832i
$136$	−0.777843	+	0.165336i	−0.0666995	+	0.0141774i
$137$	6.71473	+	1.42726i	0.573678	+	0.121939i	0.485610	−	0.874176i	$-0.338597\pi$
$137$	6.71473	+	1.42726i	0.573678	+	0.121939i	0.0880677	+	0.996114i	$0.471931\pi$
$138$	5.48127	+	2.44042i	0.466597	+	0.207742i
$139$	−0.309496	−	0.952532i	−0.0262511	−	0.0807927i	0.937073	−	0.349134i	$-0.113524\pi$
$139$	−0.309496	−	0.952532i	−0.0262511	−	0.0807927i	−0.963324	+	0.268342i	$0.913524\pi$
$140$	−1.28115	−	3.94298i	−0.108277	−	0.333243i
$141$	−7.75169	−	3.45127i	−0.652810	−	0.290650i
$142$	−2.79173	−	0.593401i	−0.234277	−	0.0497971i
$143$	−28.4882	+	6.05535i	−2.38230	+	0.506374i
$144$	6.42628	−	2.86117i	0.535524	−	0.238430i
$145$	−5.53970	−	6.15246i	−0.460047	−	0.510934i
$146$	0.169393	+	1.61167i	0.0140191	+	0.133383i
$147$	−11.1074	+	8.06998i	−0.916121	+	0.665601i
$148$	−0.822251	+	7.82320i	−0.0675886	+	0.643063i
$149$	−6.70820	−	11.6190i	−0.549557	−	0.951861i	−0.998305	−	0.0582028i	$-0.981463\pi$
$149$	−6.70820	−	11.6190i	−0.549557	−	0.951861i	0.448747	−	0.893659i	$-0.351870\pi$
$150$		0			0
$151$	2.45517	+	1.78379i	0.199799	+	0.145162i	0.683186	−	0.730244i	$-0.260594\pi$
$151$	2.45517	+	1.78379i	0.199799	+	0.145162i	−0.483387	+	0.875407i	$0.660594\pi$
$152$	−0.985051	+	1.09401i	−0.0798982	+	0.0887359i
$153$	−0.373256	+	1.14876i	−0.0301760	+	0.0928721i
$154$	1.62054			0.130587
$155$		0			0
$156$	−29.1246			−2.33184
$157$	−1.45492	+	4.47777i	−0.116115	+	0.357365i	−0.992178	−	0.124832i	$-0.960161\pi$
$157$	−1.45492	+	4.47777i	−0.116115	+	0.357365i	0.876063	+	0.482197i	$0.160161\pi$
$158$	2.83888	−	3.15290i	0.225849	−	0.250831i
$159$	−9.70820	−	7.05342i	−0.769911	−	0.559373i
$160$	4.63525	−	8.02850i	0.366449	−	0.634708i
$161$	−3.43237	−	5.94504i	−0.270509	−	0.468535i
$162$	0.427539	−	4.06776i	0.0335907	−	0.319594i
$163$	10.0451	−	7.29818i	0.786792	−	0.571638i	−0.120218	−	0.992748i	$-0.538359\pi$
$163$	10.0451	−	7.29818i	0.786792	−	0.571638i	0.907010	+	0.421110i	$0.138359\pi$
$164$	1.44815	+	13.7782i	0.113081	+	1.07590i
$165$	−14.5256	−	16.1323i	−1.13082	−	1.25590i
$166$	−1.10346	+	0.491290i	−0.0856448	+	0.0381315i
$167$	−7.24310	+	1.53957i	−0.560488	+	0.119135i	−0.479440	−	0.877575i	$-0.659160\pi$
$167$	−7.24310	+	1.53957i	−0.560488	+	0.119135i	−0.0810483	+	0.996710i	$0.525827\pi$
$168$	3.29500	+	0.700373i	0.254214	+	0.0540350i
$169$	31.1744	+	13.8797i	2.39803	+	1.06767i
$170$	0.142571	+	0.438789i	0.0109347	+	0.0336536i
$171$	0.690983	+	2.12663i	0.0528408	+	0.162627i
$172$	−0.349485	−	0.155601i	−0.0266480	−	0.0118644i
$173$	−17.6067	−	3.74241i	−1.33861	−	0.284530i	−0.517687	−	0.855570i	$-0.673207\pi$
$173$	−17.6067	−	3.74241i	−1.33861	−	0.284530i	−0.820922	+	0.571040i	$0.806540\pi$
$174$	3.16535	−	0.672816i	0.239965	−	0.0510061i
$175$		0			0
$176$	−8.93083	−	9.91869i	−0.673187	−	0.747649i
$177$	−1.42179	−	13.5274i	−0.106868	−	1.01678i
$178$	−1.81182	+	1.31637i	−0.135802	+	0.0986659i
$179$	1.71744	−	16.3404i	0.128368	−	1.22134i	−0.720773	−	0.693171i	$-0.756213\pi$
$179$	1.71744	−	16.3404i	0.128368	−	1.22134i	0.849141	−	0.528166i	$-0.177120\pi$
$180$	−4.63525	−	8.02850i	−0.345492	−	0.598409i
$181$	9.08922	−	15.7430i	0.675597	−	1.17017i	−0.300698	−	0.953720i	$-0.597219\pi$
$181$	9.08922	−	15.7430i	0.675597	−	1.17017i	0.976294	−	0.216448i	$-0.0694472\pi$
$182$	−2.12132	−	1.54123i	−0.157243	−	0.114244i
$183$	6.81198	−	7.56547i	0.503556	−	0.559255i
$184$	3.12287	−	9.61121i	0.230221	−	0.708548i
$185$	9.48683			0.697486
$186$		0			0
$187$	2.29180			0.167593
$188$	−2.12461	+	6.53888i	−0.154953	+	0.476897i
$189$	−1.16968	+	1.29906i	−0.0850819	+	0.0944931i
$190$	0.690983	+	0.502029i	0.0501292	+	0.0364210i
$191$	−7.11803	+	12.3288i	−0.515043	+	0.892080i	0.484805	+	0.874622i	$0.338891\pi$
$191$	−7.11803	+	12.3288i	−0.515043	+	0.892080i	−0.999848	+	0.0174580i	$0.994443\pi$
$192$	−5.38676	−	9.33015i	−0.388756	−	0.673345i
$193$	0.762200	−	7.25185i	0.0548644	−	0.522000i	−0.932231	−	0.361864i	$-0.882140\pi$
$193$	0.762200	−	7.25185i	0.0548644	−	0.522000i	0.987095	−	0.160135i	$-0.0511930\pi$
$194$	2.16312	−	1.57160i	0.155303	−	0.112834i
$195$	3.67152	+	34.9322i	0.262923	+	2.50155i
$196$	7.44382	+	8.26720i	0.531701	+	0.590514i
$197$	6.76473	−	3.01185i	0.481967	−	0.214586i	−0.151347	−	0.988481i	$-0.548361\pi$
$197$	6.76473	−	3.01185i	0.481967	−	0.214586i	0.633314	+	0.773895i	$0.281694\pi$
$198$	3.54446	−	0.753399i	0.251894	−	0.0535417i
$199$	−14.4091	−	3.06275i	−1.02144	−	0.217113i	−0.333396	−	0.942787i	$-0.608195\pi$
$199$	−14.4091	−	3.06275i	−1.02144	−	0.217113i	−0.688039	+	0.725674i	$0.741528\pi$
$200$		0			0
$201$	−4.24264	−	13.0575i	−0.299253	−	0.921005i
$202$	−0.263932	−	0.812299i	−0.0185702	−	0.0571532i
$203$	−3.38236	−	1.50593i	−0.237395	−	0.105695i
$204$	2.24171	+	0.476491i	0.156951	+	0.0333611i
$205$	16.3431	−	3.47383i	1.14145	−	0.242623i
$206$	−0.945010	+	0.420745i	−0.0658419	+	0.0293147i
$207$	−10.2712	−	11.4073i	−0.713895	−	0.792861i
$208$	2.25737	+	21.4775i	0.156521	+	1.48919i
$209$	3.43237	−	2.49376i	0.237422	−	0.172497i
$210$	0.204290	−	1.94369i	0.0140973	−	0.134127i
$211$	2.50000	+	4.33013i	0.172107	+	0.298098i	0.939156	−	0.343490i	$-0.111609\pi$
$211$	2.50000	+	4.33013i	0.172107	+	0.298098i	−0.767049	+	0.641588i	$0.778276\pi$
$212$	−4.86163	+	8.42060i	−0.333898	+	0.578329i
$213$	13.8326	+	10.0500i	0.947797	+	0.688615i
$214$	−1.90977	+	2.12101i	−0.130549	+	0.144989i
$215$	−0.142571	+	0.438789i	−0.00972328	+	0.0299252i
$216$	−2.57339			−0.175097
$217$		0			0
$218$	−5.61803			−0.380501
$219$	3.00000	−	9.23305i	0.202721	−	0.623912i
$220$	−11.7697	+	13.0716i	−0.793514	+	0.881286i
$221$	−3.00000	−	2.17963i	−0.201802	−	0.146618i
$222$	−1.85410	+	3.21140i	−0.124439	+	0.215535i
$223$	−10.9010	−	18.8812i	−0.729988	−	1.26438i	−0.956888	−	0.290458i	$-0.906192\pi$
$223$	−10.9010	−	18.8812i	−0.729988	−	1.26438i	0.226900	−	0.973918i	$-0.427141\pi$
$224$	0.433364	−	4.12319i	0.0289554	−	0.275492i
$225$		0			0
$226$	0.568394	+	5.40791i	0.0378090	+	0.359729i
$227$	10.5108	+	11.6735i	0.697629	+	0.774795i	0.982997	−	0.183623i	$-0.0587824\pi$
$227$	10.5108	+	11.6735i	0.697629	+	0.774795i	−0.285368	+	0.958418i	$0.592116\pi$
$228$	3.87585	−	1.72564i	0.256684	−	0.114283i
$229$	4.14993	−	0.882095i	0.274235	−	0.0582905i	−0.0687412	−	0.997635i	$-0.521898\pi$
$229$	4.14993	−	0.882095i	0.274235	−	0.0582905i	0.342976	+	0.939344i	$0.388565\pi$
$230$	−5.73506	−	1.21902i	−0.378159	−	0.0803801i
$231$	−8.86889	−	3.94868i	−0.583530	−	0.259804i
$232$	−1.68430	−	5.18376i	−0.110580	−	0.340330i
$233$	−1.39919	−	4.30625i	−0.0916638	−	0.282112i	0.894706	−	0.446655i	$-0.147385\pi$
$233$	−1.39919	−	4.30625i	−0.0916638	−	0.282112i	−0.986370	+	0.164543i	$0.947385\pi$
$234$	−5.35629	−	2.38477i	−0.350151	−	0.155897i
$235$	8.11060	+	1.72396i	0.529077	+	0.112459i
$236$	−10.7804	+	2.29145i	−0.701747	+	0.149161i
$237$	−23.2190	+	10.3378i	−1.50824	+	0.671511i
$238$	0.138062	+	0.153334i	0.00894925	+	0.00993915i
$239$	−1.70920	−	16.2620i	−0.110559	−	1.05190i	−0.899347	−	0.437235i	$-0.855958\pi$
$239$	−1.70920	−	16.2620i	−0.110559	−	1.05190i	0.788788	−	0.614666i	$-0.210709\pi$
$240$	−13.0224	+	9.46130i	−0.840590	+	0.610725i
$241$	1.53981	−	14.6503i	0.0991880	−	0.943711i	−0.825864	−	0.563870i	$-0.809312\pi$
$241$	1.53981	−	14.6503i	0.0991880	−	0.943711i	0.925052	−	0.379841i	$-0.124021\pi$
$242$	−1.33688	−	2.31555i	−0.0859380	−	0.148849i
$243$	−9.62940	+	16.6786i	−0.617727	+	1.06993i
$244$	−6.67346	−	4.84855i	−0.427224	−	0.310397i
$245$	8.97733	−	9.97033i	0.573541	−	0.636981i
$246$	−2.01815	+	6.21124i	−0.128673	+	0.396014i
$247$	−6.86474			−0.436793
$248$		0			0
$249$	7.23607			0.458567
$250$	1.31966	−	4.06150i	0.0834626	−	0.256872i
$251$	15.8962	−	17.6545i	1.00336	−	1.11434i	0.00992315	−	0.999951i	$-0.496841\pi$
$251$	15.8962	−	17.6545i	1.00336	−	1.11434i	0.993436	−	0.114392i	$-0.0364920\pi$
$252$	−3.35410	−	2.43690i	−0.211289	−	0.153510i
$253$	−14.5623	+	25.2227i	−0.915524	+	1.58573i
$254$	1.81182	+	3.13817i	0.113684	+	0.196906i
$255$	0.288910	−	2.74879i	0.0180922	−	0.172136i
$256$	−4.50000	+	3.26944i	−0.281250	+	0.204340i
$257$	−2.50286	−	23.8131i	−0.156124	−	1.48542i	−0.739466	−	0.673194i	$-0.764922\pi$
$257$	−2.50286	−	23.8131i	−0.156124	−	1.48542i	0.583342	−	0.812227i	$-0.301745\pi$
$258$	−0.120671	−	0.134019i	−0.00751264	−	0.00834364i
$259$	3.87585	−	1.72564i	0.240833	−	0.107226i
$260$	27.8386	−	5.91727i	1.72647	−	0.366974i
$261$	−8.09804	−	1.72129i	−0.501256	−	0.106545i
$262$	−6.77523	−	3.01652i	−0.418575	−	0.186362i
$263$	−0.834626	−	2.56872i	−0.0514653	−	0.158394i	0.922021	−	0.387141i	$-0.126537\pi$
$263$	−0.834626	−	2.56872i	−0.0514653	−	0.158394i	−0.973486	+	0.228747i	$0.926537\pi$
$264$	−4.41641	−	13.5923i	−0.271811	−	0.836549i
$265$	10.7126	+	4.76954i	0.658068	+	0.292991i
$266$	0.373619	+	0.0794152i	0.0229081	+	0.00486926i
$267$	13.1232	−	2.78943i	0.803128	−	0.170710i
$268$	−10.1628	+	4.52479i	−0.620794	+	0.276395i
$269$	−9.90972	−	11.0059i	−0.604206	−	0.671039i	0.360989	−	0.932570i	$-0.382439\pi$
$269$	−9.90972	−	11.0059i	−0.604206	−	0.671039i	−0.965195	+	0.261531i	$0.915773\pi$
$270$	0.156064	+	1.48485i	0.00949773	+	0.0903649i
$271$	−22.7155	+	16.5038i	−1.37987	+	1.00253i	−0.382978	+	0.923757i	$0.625101\pi$
$271$	−22.7155	+	16.5038i	−1.37987	+	1.00253i	−0.996892	+	0.0787769i	$0.974899\pi$
$272$	0.177631	−	1.69005i	0.0107705	−	0.102474i
$273$	7.85410	+	13.6037i	0.475352	+	0.823334i
$274$	1.31105	−	2.27080i	0.0792033	−	0.137184i
$275$		0			0
$276$	−19.4882	+	21.6438i	−1.17305	+	1.30280i
$277$	−6.05446	+	18.6337i	−0.363778	+	1.11959i	0.586966	+	0.809612i	$0.300322\pi$
$277$	−6.05446	+	18.6337i	−0.363778	+	1.11959i	−0.950743	+	0.309980i	$0.899678\pi$
$278$	−0.382559			−0.0229443
$279$		0			0
$280$	−3.29180			−0.196722
$281$	−9.69098	+	29.8258i	−0.578116	+	1.77926i	0.0472008	+	0.998885i	$0.484970\pi$
$281$	−9.69098	+	29.8258i	−0.578116	+	1.77926i	−0.625316	+	0.780371i	$0.715030\pi$
$282$	−2.16871	+	2.40860i	−0.129145	+	0.143430i
$283$	−19.4164	−	14.1068i	−1.15419	−	0.838565i	−0.165154	−	0.986268i	$-0.552812\pi$
$283$	−19.4164	−	14.1068i	−1.15419	−	0.838565i	−0.989032	+	0.147703i	$0.952812\pi$
$284$	6.92705	−	11.9980i	0.411045	−	0.711951i
$285$	−2.55834	−	4.43117i	−0.151543	−	0.262480i
$286$	−1.16284	+	11.0637i	−0.0687601	+	0.654209i
$287$	6.04508	−	4.39201i	0.356830	−	0.259252i
$288$	−0.969032	−	9.21973i	−0.0571008	−	0.543278i
$289$	−11.1800	−	12.4166i	−0.657645	−	0.730389i
$290$	−2.88888	+	1.28621i	−0.169641	+	0.0755291i
$291$	−15.6677	+	3.33027i	−0.918456	+	0.195224i
$292$	−7.69439	−	1.63549i	−0.450280	−	0.0957100i
$293$	−14.3502	−	6.38910i	−0.838345	−	0.373255i	−0.0577797	−	0.998329i	$-0.518402\pi$
$293$	−14.3502	−	6.38910i	−0.838345	−	0.373255i	−0.780565	+	0.625074i	$0.785069\pi$
$294$	1.62054	+	4.98752i	0.0945121	+	0.290878i
$295$	4.10739	+	12.6412i	0.239142	+	0.736002i
$296$	5.70577	+	2.54037i	0.331641	+	0.147656i
$297$	7.25434	+	1.54196i	0.420940	+	0.0894735i
$298$	−5.01263	+	1.06547i	−0.290374	+	0.0617208i
$299$	43.0505	−	19.1673i	2.48967	−	1.10847i
$300$		0			0
$301$	0.0215675	+	0.205201i	0.00124313	+	0.0118276i
$302$	0.937792	−	0.681346i	0.0539639	−	0.0392070i
$303$	−0.534838	+	5.08864i	−0.0307256	+	0.292335i
$304$	−1.57295	−	2.72443i	−0.0902148	−	0.156257i
$305$	−4.97410	+	8.61540i	−0.284816	+	0.493316i
$306$	0.373256	+	0.271187i	0.0213376	+	0.0155027i
$307$	−10.7895	+	11.9829i	−0.615788	+	0.683901i	−0.967692	−	0.252134i	$-0.918867\pi$
$307$	−10.7895	+	11.9829i	−0.615788	+	0.683901i	0.351905	+	0.936036i	$0.385534\pi$
$308$	−2.43082	+	7.48128i	−0.138509	+	0.426286i
$309$	6.19704			0.352537
$310$		0			0
$311$	16.5279			0.937209			0.468605	−	0.883408i	$-0.344757\pi$
$311$	16.5279			0.937209			0.468605	+	0.883408i	$0.344757\pi$
$312$	−7.14590	+	21.9928i	−0.404557	+	1.24510i
$313$	14.0563	−	15.6111i	0.794511	−	0.882394i	−0.200749	−	0.979643i	$-0.564337\pi$
$313$	14.0563	−	15.6111i	0.794511	−	0.882394i	0.995260	+	0.0972485i	$0.0310042\pi$
$314$	1.45492	+	1.05706i	0.0821056	+	0.0596532i
$315$	−2.50000	+	4.33013i	−0.140859	+	0.243975i
$316$	10.2971	+	17.8351i	0.579257	+	1.00330i
$317$	−2.27495	+	21.6447i	−0.127774	+	1.21569i	0.723259	+	0.690576i	$0.242643\pi$
$317$	−2.27495	+	21.6447i	−0.127774	+	1.21569i	−0.851033	+	0.525112i	$0.824024\pi$
$318$	−3.70820	+	2.69417i	−0.207946	+	0.151081i
$319$	1.64195	+	15.6222i	0.0919318	+	0.874673i
$320$	7.04452	+	7.82373i	0.393800	+	0.437360i
$321$	15.6199	−	6.95442i	0.871816	−	0.388158i
$322$	−2.56480	+	0.545164i	−0.142931	+	0.0303808i
$323$	0.528377	+	0.112310i	0.0293997	+	0.00624910i
$324$	18.1376	+	8.07539i	1.00765	+	0.448633i
$325$		0			0
$326$	−1.46556	−	4.51052i	−0.0811698	−	0.249815i
$327$	30.7463	+	13.6891i	1.70027	+	0.757010i
$328$	10.7596	+	2.28703i	0.594101	+	0.126280i
$329$	3.62717	−	0.770979i	0.199972	−	0.0425054i
$330$	−7.57493	+	3.37258i	−0.416986	+	0.185654i
$331$	17.1512	+	19.0483i	0.942715	+	1.04699i	0.998820	+	0.0485666i	$0.0154653\pi$
$331$	17.1512	+	19.0483i	0.942715	+	1.04699i	−0.0561045	+	0.998425i	$0.517868\pi$
$332$	−0.612870	−	5.83107i	−0.0336356	−	0.320021i
$333$	7.67501	−	5.57622i	0.420588	−	0.305575i
$334$	−0.295651	+	2.81293i	−0.0161773	+	0.153917i
$335$	6.70820	+	11.6190i	0.366508	+	0.634811i
$336$	−3.59929	+	6.23416i	−0.196358	+	0.340101i
$337$	−4.74342	−	3.44629i	−0.258390	−	0.187732i	0.451047	−	0.892500i	$-0.351051\pi$
$337$	−4.74342	−	3.44629i	−0.258390	−	0.187732i	−0.709437	+	0.704769i	$0.751051\pi$
$338$	8.72174	−	9.68648i	0.474400	−	0.526875i
$339$	10.0664	−	30.9813i	0.546733	−	1.68267i
$340$	−2.23954			−0.121456
$341$		0			0
$342$	0.854102			0.0461845
$343$	4.01722	−	12.3637i	0.216910	−	0.667579i
$344$	−0.203247	+	0.225728i	−0.0109583	+	0.0121704i
$345$	28.4164	+	20.6457i	1.52989	+	1.11153i
$346$	−3.43769	+	5.95426i	−0.184812	+	0.320103i
$347$	12.9192	+	22.3767i	0.693539	+	1.20124i	0.970671	+	0.240413i	$0.0772829\pi$
$347$	12.9192	+	22.3767i	0.693539	+	1.20124i	−0.277132	+	0.960832i	$0.589384\pi$
$348$	−1.64195	+	15.6222i	−0.0880180	+	0.837435i
$349$	−4.85410	+	3.52671i	−0.259834	+	0.188781i	−0.710074	−	0.704127i	$-0.751338\pi$
$349$	−4.85410	+	3.52671i	−0.259834	+	0.188781i	0.450240	+	0.892908i	$0.351338\pi$
$350$		0			0
$351$	−8.02957	−	8.91774i	−0.428587	−	0.475994i
$352$	−16.0689	+	7.15432i	−0.856473	+	0.381326i
$353$	15.5430	−	3.30376i	0.827268	−	0.175841i	0.225227	−	0.974306i	$-0.427688\pi$
$353$	15.5430	−	3.30376i	0.827268	−	0.175841i	0.602041	+	0.798465i	$0.294354\pi$
$354$	−5.08195	−	1.08020i	−0.270103	−	0.0574121i
$355$	−15.2637	−	6.79584i	−0.810113	−	0.360686i
$356$	−3.35931	−	10.3389i	−0.178043	−	0.547960i
$357$	−0.381966	−	1.17557i	−0.0202158	−	0.0622178i
$358$	−5.73327	−	2.55262i	−0.303013	−	0.134910i
$359$	−9.55057	−	2.03004i	−0.504060	−	0.107141i	−0.0511381	−	0.998692i	$-0.516285\pi$
$359$	−9.55057	−	2.03004i	−0.504060	−	0.107141i	−0.452921	+	0.891550i	$0.649618\pi$
$360$	−7.19983	+	1.53037i	−0.379464	+	0.0806577i
$361$	−16.4438	+	7.32126i	−0.865464	+	0.385329i
$362$	−4.64614	−	5.16006i	−0.244196	−	0.271207i
$363$	1.67431	+	15.9300i	0.0878784	+	0.836107i
$364$	10.2971	−	7.48128i	0.539715	−	0.392126i
$365$	−0.991644	+	9.43486i	−0.0519050	+	0.493843i
$366$	−1.94427	−	3.36758i	−0.101629	−	0.176026i
$367$	−6.15763	+	10.6653i	−0.321426	+	0.556726i	−0.980782	−	0.195105i	$-0.937495\pi$
$367$	−6.15763	+	10.6653i	−0.321426	+	0.556726i	0.659357	+	0.751830i	$0.270829\pi$
$368$	17.4713	+	12.6937i	0.910756	+	0.661703i
$369$	11.1800	−	12.4166i	0.582006	−	0.646383i
$370$	1.11977	−	3.44629i	0.0582140	−	0.179164i
$371$	5.24419			0.272265
$372$		0			0
$373$	−22.7082			−1.17579			−0.587893	−	0.808939i	$-0.700042\pi$
$373$	−22.7082			−1.17579			−0.587893	+	0.808939i	$0.700042\pi$
$374$	0.270510	−	0.832544i	0.0139877	−	0.0430498i
$375$	−17.1186	+	19.0121i	−0.884001	+	0.981783i
$376$	4.41641	+	3.20871i	0.227759	+	0.165476i
$377$	12.7082	−	22.0113i	0.654506	−	1.13364i
$378$	0.333851	+	0.578246i	0.0171714	+	0.0297418i
$379$	2.02957	−	19.3100i	0.104252	−	0.991890i	−0.809914	−	0.586549i	$-0.800486\pi$
$379$	2.02957	−	19.3100i	0.104252	−	0.991890i	0.914166	−	0.405341i	$-0.132847\pi$
$380$	−3.35410	+	2.43690i	−0.172062	+	0.125010i
$381$	−2.26913	−	21.5893i	−0.116251	−	1.10605i
$382$	3.63853	+	4.04099i	0.186163	+	0.206755i
$383$	17.4053	−	7.74934i	0.889369	−	0.395973i	0.0893876	−	0.995997i	$-0.471509\pi$
$383$	17.4053	−	7.74934i	0.889369	−	0.395973i	0.799982	+	0.600024i	$0.204842\pi$
$384$	−22.5842	+	4.80043i	−1.15250	+	0.244971i
$385$	9.27952	+	1.97242i	0.472928	+	0.100524i
$386$	−2.54442	−	1.13285i	−0.129508	−	0.0576606i
$387$	0.142571	+	0.438789i	0.00724730	+	0.0223049i
$388$	4.01064	+	12.3435i	0.203610	+	0.626646i
$389$	−30.8628	−	13.7410i	−1.56480	−	0.696696i	−0.572430	−	0.819954i	$-0.693999\pi$
$389$	−30.8628	−	13.7410i	−1.56480	−	0.696696i	−0.992375	+	0.123258i	$0.960666\pi$
$390$	13.1232	+	2.78943i	0.664520	+	0.141248i
$391$	−3.62717	+	0.770979i	−0.183434	+	0.0389901i
$392$	8.06918	−	3.59263i	0.407555	−	0.181455i
$393$	29.7291	+	33.0176i	1.49964	+	1.66552i
$394$	−0.295651	−	2.81293i	−0.0148947	−	0.141714i
$395$	20.0934	−	14.5987i	1.01101	−	0.734542i
$396$	−1.83861	+	17.4932i	−0.0923936	+	0.879066i
$397$	−0.645898	−	1.11873i	−0.0324167	−	0.0561474i	0.849362	−	0.527811i	$-0.176987\pi$
$397$	−0.645898	−	1.11873i	−0.0324167	−	0.0561474i	−0.881779	+	0.471664i	$0.843654\pi$
$398$	−2.81338	+	4.87291i	−0.141022	+	0.244257i
$399$	−1.85123	−	1.34500i	−0.0926774	−	0.0673341i
$400$		0			0
$401$	1.14412	−	3.52125i	0.0571348	−	0.175843i	−0.918416	−	0.395615i	$-0.870531\pi$
$401$	1.14412	−	3.52125i	0.0571348	−	0.175843i	0.975551	+	0.219772i	$0.0705314\pi$
$402$	−5.24419			−0.261557
$403$		0			0
$404$	4.14590			0.206266
$405$	7.39919	−	22.7724i	0.367669	−	1.13157i
$406$	−0.946294	+	1.05097i	−0.0469638	+	0.0521585i
$407$	−14.5623	−	10.5801i	−0.721827	−	0.524438i
$408$	0.909830	−	1.57587i	0.0450433	−	0.0780173i
$409$	−8.67656	−	15.0282i	−0.429028	−	0.743099i	0.567759	−	0.823195i	$-0.307811\pi$
$409$	−8.67656	−	15.0282i	−0.429028	−	0.743099i	−0.996787	+	0.0800961i	$0.974477\pi$
$410$	0.667097	−	6.34700i	0.0329456	−	0.313456i
$411$	−12.7082	+	9.23305i	−0.626849	+	0.455433i
$412$	−0.524867	−	4.99378i	−0.0258584	−	0.246026i
$413$	3.97749	+	4.41745i	0.195720	+	0.217369i
$414$	−5.35629	+	2.38477i	−0.263247	+	0.117205i
$415$	−6.91655	+	1.47016i	−0.339520	+	0.0721672i
$416$	27.8386	+	5.91727i	1.36490	+	0.290118i
$417$	2.09366	+	0.932157i	0.102527	+	0.0456479i
$418$	−0.500776	−	1.54123i	−0.0244937	−	0.0753840i
$419$	−5.74671	−	17.6866i	−0.280745	−	0.864045i	−0.987642	−	0.156728i	$-0.949905\pi$
$419$	−5.74671	−	17.6866i	−0.280745	−	0.864045i	0.706897	−	0.707317i	$-0.250095\pi$
$420$	8.66665	+	3.85864i	0.422889	+	0.188282i
$421$	0.407308	+	0.0865761i	0.0198510	+	0.00421946i	0.217826	−	0.975988i	$-0.430103\pi$
$421$	0.407308	+	0.0865761i	0.0198510	+	0.00421946i	−0.197975	+	0.980207i	$0.563437\pi$
$422$	1.86810	−	0.397076i	0.0909375	−	0.0193294i
$423$	7.57493	−	3.37258i	0.368306	−	0.163980i
$424$	5.16580	+	5.73720i	0.250873	+	0.278623i
$425$		0			0
$426$	5.28360	−	3.83876i	0.255991	−	0.185988i
$427$	−0.465044	+	4.42460i	−0.0225051	+	0.214121i
$428$	−6.92705	−	11.9980i	−0.334832	−	0.579945i
$429$	33.3221	−	57.7156i	1.60881	−	2.78654i
$430$	0.142571	+	0.103584i	0.00687539	+	0.00499527i
$431$	−0.0745787	+	0.0828281i	−0.00359233	+	0.00398969i	−0.744938	−	0.667133i	$-0.767521\pi$
$431$	−0.0745787	+	0.0828281i	−0.00359233	+	0.00398969i	0.741346	+	0.671123i	$0.234188\pi$
$432$	1.69936	−	5.23008i	0.0817603	−	0.251632i
$433$	−21.5958			−1.03783			−0.518913	−	0.854827i	$-0.673663\pi$
$433$	−21.5958			−1.03783			−0.518913	+	0.854827i	$0.673663\pi$
$434$		0			0
$435$	18.9443			0.908308
$436$	8.42705	−	25.9358i	0.403583	−	1.24210i
$437$	−4.59341	+	5.10149i	−0.219732	+	0.244038i
$438$	−3.00000	−	2.17963i	−0.143346	−	0.104147i
$439$	12.5000	−	21.6506i	0.596592	−	1.03333i	−0.396728	−	0.917936i	$-0.629854\pi$
$439$	12.5000	−	21.6506i	0.596592	−	1.03333i	0.993320	−	0.115392i	$-0.0368124\pi$
$440$	6.98295	+	12.0948i	0.332899	+	0.576598i
$441$	1.40240	−	13.3429i	0.0667808	−	0.635377i
$442$	−1.14590	+	0.832544i	−0.0545048	+	0.0396001i
$443$	−2.50286	−	23.8131i	−0.118914	−	1.13139i	−0.877418	−	0.479726i	$-0.840736\pi$
$443$	−2.50286	−	23.8131i	−0.118914	−	1.13139i	0.758504	−	0.651669i	$-0.225931\pi$
$444$	−12.0444	−	13.3766i	−0.571600	−	0.634826i
$445$	−11.9770	+	5.33251i	−0.567765	+	0.252785i
$446$	−8.14568	+	1.73142i	−0.385709	+	0.0819850i
$447$	30.0292	+	6.38290i	1.42033	+	0.301901i
$448$	4.30116	+	1.91500i	0.203211	+	0.0904752i
$449$	13.0374	+	40.1250i	0.615274	+	1.89362i	0.397421	+	0.917637i	$0.369905\pi$
$449$	13.0374	+	40.1250i	0.615274	+	1.89362i	0.217853	+	0.975982i	$0.430095\pi$
$450$		0			0
$451$	−28.9608	−	12.8942i	−1.36371	−	0.607164i
$452$	−25.8183	−	5.48785i	−1.21439	−	0.258127i
$453$	−6.79252	+	1.44380i	−0.319141	+	0.0678354i
$454$	5.48127	−	2.44042i	0.257249	−	0.114535i
$455$	−10.2712	−	11.4073i	−0.481520	−	0.534782i
$456$	−0.352115	−	3.35016i	−0.0164893	−	0.156885i
$457$	9.15298	−	6.65003i	0.428158	−	0.311075i	−0.352754	−	0.935716i	$-0.614755\pi$
$457$	9.15298	−	6.65003i	0.428158	−	0.311075i	0.780912	+	0.624641i	$0.214755\pi$
$458$	0.169393	−	1.61167i	0.00791522	−	0.0753083i
$459$	0.472136	+	0.817763i	0.0220374	+	0.0381699i
$460$	14.2302	−	24.6475i	0.663489	−	1.14920i
$461$	−31.6378	−	22.9862i	−1.47352	−	1.07058i	−0.979574	−	0.201083i	$-0.935554\pi$
$461$	−31.6378	−	22.9862i	−1.47352	−	1.07058i	−0.493946	−	0.869492i	$-0.664446\pi$
$462$	−2.48127	+	2.75573i	−0.115439	+	0.128208i
$463$	−4.67966	+	14.4025i	−0.217482	+	0.669341i	0.781486	+	0.623923i	$0.214462\pi$
$463$	−4.67966	+	14.4025i	−0.217482	+	0.669341i	−0.998968	+	0.0454182i	$0.985538\pi$
$464$	11.6476			0.540724
$465$		0			0
$466$	−1.72949			−0.0801171
$467$	4.83688	−	14.8864i	0.223824	−	0.688860i	−0.774585	−	0.632470i	$-0.782041\pi$
$467$	4.83688	−	14.8864i	0.223824	−	0.688860i	0.998409	−	0.0563897i	$-0.0179589\pi$
$468$	19.0438	−	21.1503i	0.880300	−	0.977672i
$469$	4.85410	+	3.52671i	0.224142	+	0.162848i
$470$	1.58359	−	2.74286i	0.0730457	−	0.126519i
$471$	−5.38676	−	9.33015i	−0.248209	−	0.429911i
$472$	−0.914705	+	8.70284i	−0.0421027	+	0.400581i
$473$	0.708204	−	0.514540i	0.0325633	−	0.0236586i
$474$	1.01478	+	9.65502i	0.0466106	+	0.443470i
$475$		0			0
$476$	−0.914963	+	0.407368i	−0.0419373	+	0.0186717i
$477$	11.4701	−	2.43805i	0.525181	−	0.111631i
$478$	−6.10926	−	1.29856i	−0.279431	−	0.0593949i
$479$	23.2700	+	10.3605i	1.06323	+	0.473381i	0.862391	−	0.506243i	$-0.168966\pi$
$479$	23.2700	+	10.3605i	1.06323	+	0.473381i	0.200840	+	0.979624i	$0.435633\pi$
$480$	6.55524	+	20.1750i	0.299204	+	0.920857i
$481$	9.00000	+	27.6992i	0.410365	+	1.26297i
$482$	−5.14029	−	2.28861i	−0.234134	−	0.104243i
$483$	15.3649	+	3.26592i	0.699129	+	0.148604i
$484$	12.6951	−	2.69843i	0.577050	−	0.122656i
$485$	14.2992	−	6.36644i	0.649295	−	0.289085i
$486$	4.92227	+	5.46673i	0.223278	+	0.247976i
$487$	1.94330	+	18.4893i	0.0880593	+	0.837828i	0.946019	+	0.324111i	$0.105065\pi$
$487$	1.94330	+	18.4893i	0.0880593	+	0.837828i	−0.857960	+	0.513717i	$0.828268\pi$
$488$	−5.29865	+	3.84969i	−0.239859	+	0.174267i
$489$	−2.96984	+	28.2561i	−0.134301	+	1.27779i
$490$	−2.56231	−	4.43804i	−0.115753	−	0.200490i
$491$	−4.78282	+	8.28409i	−0.215846	+	0.373856i	−0.953534	−	0.301286i	$-0.902584\pi$
$491$	−4.78282	+	8.28409i	−0.215846	+	0.373856i	0.737688	+	0.675142i	$0.235917\pi$
$492$	−25.6471	−	18.6337i	−1.15626	−	0.840073i
$493$	−1.33826	+	1.48629i	−0.0602723	+	0.0669391i
$494$	−0.810272	+	2.49376i	−0.0364559	+	0.112200i
$495$	21.2132			0.953463
$496$		0			0
$497$	−7.47214			−0.335171
$498$	0.854102	−	2.62866i	0.0382732	−	0.117793i
$499$	−12.3018	+	13.6626i	−0.550705	+	0.611620i	−0.952659	−	0.304040i	$-0.901664\pi$
$499$	−12.3018	+	13.6626i	−0.550705	+	0.611620i	0.401954	+	0.915660i	$0.368331\pi$
$500$	16.7705	+	12.1845i	0.750000	+	0.544907i
$501$	8.47214	−	14.6742i	0.378507	−	0.655594i
$502$	−4.53709	−	7.85846i	−0.202500	−	0.350740i
$503$	−0.301935	+	2.87272i	−0.0134626	+	0.128088i	−0.999189	−	0.0402674i	$-0.987179\pi$
$503$	−0.301935	+	2.87272i	−0.0134626	+	0.128088i	0.985726	+	0.168356i	$0.0538457\pi$
$504$	−2.66312	+	1.93487i	−0.118625	+	0.0861859i
$505$	−0.522642	−	4.97261i	−0.0232573	−	0.221278i
$506$	7.44382	+	8.26720i	0.330918	+	0.367522i
$507$	−71.3346	+	31.7602i	−3.16808	+	1.41052i
$508$	−17.2052	+	3.65707i	−0.763356	+	0.162256i
$509$	−4.67831	−	0.994405i	−0.207362	−	0.0440762i	0.103059	−	0.994675i	$-0.467137\pi$
$509$	−4.67831	−	0.994405i	−0.207362	−	0.0440762i	−0.310422	+	0.950599i	$0.600470\pi$
$510$	−0.964456	−	0.429403i	−0.0427068	−	0.0190143i
$511$	1.31105	+	4.03499i	0.0579974	+	0.178497i
$512$	6.89261	+	21.2133i	0.304613	+	0.937503i
$513$	1.59694	+	0.711002i	0.0705064	+	0.0313915i
$514$	−8.94604	−	1.90154i	−0.394593	−	0.0838733i
$515$	−5.92340	+	1.25906i	−0.261016	+	0.0554807i
$516$	0.799707	−	0.356052i	0.0352051	−	0.0156743i
$517$	−10.5271	−	11.6916i	−0.462983	−	0.514195i
$518$	−0.169393	−	1.61167i	−0.00744270	−	0.0708126i
$519$	33.3221	−	24.2099i	1.46268	−	1.06270i
$520$	2.36206	−	22.4735i	0.103583	−	0.985529i
$521$	−6.70820	−	11.6190i	−0.293892	−	0.509035i	0.680835	−	0.732437i	$-0.261617\pi$
$521$	−6.70820	−	11.6190i	−0.293892	−	0.509035i	−0.974726	+	0.223402i	$0.928284\pi$
$522$	−1.58114	+	2.73861i	−0.0692046	+	0.119866i
$523$	23.5258	+	17.0925i	1.02871	+	0.747403i	0.968050	−	0.250756i	$-0.0806791\pi$
$523$	23.5258	+	17.0925i	1.02871	+	0.747403i	0.0606612	+	0.998158i	$0.480679\pi$
$524$	24.0887	−	26.7532i	1.05232	−	1.16872i
$525$		0			0
$526$	−1.03165			−0.0449823
$527$		0			0
$528$	30.5410			1.32913
$529$	7.45492	−	22.9439i	0.324127	−	0.997560i
$530$	2.99709	−	3.32860i	0.130185	−	0.144585i
$531$	10.7533	+	7.81272i	0.466653	+	0.339043i
$532$	−0.927051	+	1.60570i	−0.0401928	+	0.0696159i
$533$	25.6471	+	44.4221i	1.11090	+	1.92414i
$534$	0.535668	−	5.09654i	0.0231806	−	0.220549i
$535$	−13.5172	+	9.82084i	−0.584400	+	0.424592i
$536$	0.923281	+	8.78443i	0.0398797	+	0.379430i
$537$	25.1571	+	27.9398i	1.08561	+	1.20569i
$538$	−5.16779	+	2.30085i	−0.222799	+	0.0991967i
$539$	−24.8996	+	5.29257i	−1.07250	+	0.227967i
$540$	−7.08892	−	1.50680i	−0.305059	−	0.0648422i
$541$	−25.4265	−	11.3206i	−1.09317	−	0.486712i	−0.220683	−	0.975345i	$-0.570829\pi$
$541$	−25.4265	−	11.3206i	−1.09317	−	0.486712i	−0.872489	+	0.488634i	$0.837495\pi$
$542$	3.31415	+	10.1999i	0.142355	+	0.438124i
$543$	12.8541	+	39.5609i	0.551622	+	1.69772i
$544$	−2.04592	−	0.910902i	−0.0877181	−	0.0390546i
$545$	−32.1699	−	6.83791i	−1.37800	−	0.292904i
$546$	5.86889	−	1.24747i	0.251165	−	0.0533868i
$547$	−22.3055	+	9.93105i	−0.953714	+	0.424621i	−0.823785	−	0.566902i	$-0.808142\pi$
$547$	−22.3055	+	9.93105i	−0.953714	+	0.424621i	−0.129929	+	0.991523i	$0.541475\pi$
$548$	8.51664	+	9.45869i	0.363813	+	0.404055i
$549$	1.03987	+	9.89371i	0.0443806	+	0.422253i
$550$		0			0
$551$	−0.387012	+	3.68218i	−0.0164873	+	0.156866i
$552$	11.5623	+	20.0265i	0.492124	+	0.852384i
$553$	5.55369	−	9.61927i	0.236167	−	0.409053i
$554$	6.05446	+	4.39883i	0.257230	+	0.186888i
$555$	−14.5256	+	16.1323i	−0.616578	+	0.684780i
$556$	0.573838	−	1.76609i	0.0243362	−	0.0748990i
$557$	23.2951			0.987046			0.493523	−	0.869733i	$-0.335709\pi$
$557$	23.2951			0.987046			0.493523	+	0.869733i	$0.335709\pi$
$558$		0			0
$559$	−1.41641			−0.0599077
$560$	2.17376	−	6.69015i	0.0918582	−	0.282711i
$561$	−3.50905	+	3.89719i	−0.148152	+	0.164540i
$562$	9.69098	+	7.04091i	0.408789	+	0.297003i
$563$	−7.11803	+	12.3288i	−0.299989	+	0.519597i	−0.976133	−	0.217173i	$-0.930316\pi$
$563$	−7.11803	+	12.3288i	−0.299989	+	0.519597i	0.676144	+	0.736770i	$0.263650\pi$
$564$	−7.86629	−	13.6248i	−0.331230	−	0.573708i
$565$	−3.32744	+	31.6584i	−0.139986	+	1.33188i
$566$	−7.41641	+	5.38834i	−0.311735	+	0.226489i
$567$	−1.11931	−	10.6495i	−0.0470067	−	0.447239i
$568$	−7.36044	−	8.17459i	−0.308837	−	0.342998i
$569$	28.0459	−	12.4868i	1.17574	−	0.523475i	0.276539	−	0.961003i	$-0.410812\pi$
$569$	28.0459	−	12.4868i	1.17574	−	0.523475i	0.899205	+	0.437527i	$0.144146\pi$
$570$	−1.91169	+	0.406342i	−0.0800718	+	0.0170198i
$571$	6.71473	+	1.42726i	0.281003	+	0.0597289i	0.346257	−	0.938140i	$-0.387453\pi$
$571$	6.71473	+	1.42726i	0.281003	+	0.0597289i	−0.0652544	+	0.997869i	$0.520786\pi$
$572$	−49.3315	−	21.9638i	−2.06265	−	0.918352i
$573$	−10.0664	−	30.9813i	−0.420531	−	1.29426i
$574$	−0.881966	−	2.71441i	−0.0368126	−	0.113297i
$575$		0			0
$576$	10.2978	+	2.18887i	0.429075	+	0.0912028i
$577$	29.3444	−	6.23735i	1.22162	−	0.259664i	0.448421	−	0.893822i	$-0.351987\pi$
$577$	29.3444	−	6.23735i	1.22162	−	0.259664i	0.773203	+	0.634158i	$0.218653\pi$
$578$	−5.83022	+	2.59578i	−0.242505	+	0.107970i
$579$	11.1647	+	12.3997i	0.463990	+	0.515313i
$580$	−1.60451	−	15.2659i	−0.0666238	−	0.633883i
$581$	−2.55834	+	1.85874i	−0.106138	+	0.0771135i
$582$	−0.639529	+	6.08471i	−0.0265093	+	0.252219i
$583$	−11.1246	−	19.2684i	−0.460734	−	0.798015i
$584$	−3.12287	+	5.40897i	−0.129225	+	0.223825i
$585$	−27.7684	−	20.1750i	−1.14808	−	0.834132i
$586$	−4.01478	+	4.45887i	−0.165849	+	0.184194i
$587$	−12.7279	+	39.1725i	−0.525338	+	1.61682i	0.238310	+	0.971189i	$0.423407\pi$
$587$	−12.7279	+	39.1725i	−0.525338	+	1.61682i	−0.763647	+	0.645634i	$0.776593\pi$
$588$	−25.4558			−1.04978
$589$		0			0
$590$	5.07701			0.209017
$591$	−5.23607	+	16.1150i	−0.215383	+	0.662881i
$592$	−8.93083	+	9.91869i	−0.367055	+	0.407656i
$593$	13.8992	+	10.0984i	0.570771	+	0.414690i	0.835385	−	0.549665i	$-0.185245\pi$
$593$	13.8992	+	10.0984i	0.570771	+	0.414690i	−0.264614	+	0.964354i	$0.585245\pi$
$594$	1.41641	−	2.45329i	0.0581159	−	0.100660i
$595$	0.603941	+	1.04606i	0.0247592	+	0.0428842i
$596$	2.60019	−	24.7391i	0.106508	−	1.01335i
$597$	27.2705	−	19.8132i	1.11611	−	0.810900i
$598$	−1.88151	−	17.9014i	−0.0769408	−	0.732042i
$599$	16.0218	+	17.7941i	0.654635	+	0.727046i	0.975481	−	0.220086i	$-0.0706337\pi$
$599$	16.0218	+	17.7941i	0.654635	+	0.727046i	−0.320846	+	0.947131i	$0.603967\pi$
$600$		0			0
$601$	8.50168	−	1.80709i	0.346791	−	0.0737126i	−0.0312235	−	0.999512i	$-0.509940\pi$
$601$	8.50168	−	1.80709i	0.346791	−	0.0737126i	0.378014	+	0.925800i	$0.376607\pi$
$602$	0.0770892	+	0.0163858i	0.00314192	+	0.000667836i
$603$	12.2565	+	5.45694i	0.499123	+	0.222224i
$604$	1.73876	+	5.35136i	0.0707492	+	0.217744i
$605$	−4.83688	−	14.8864i	−0.196647	−	0.605218i
$606$	1.78543	+	0.794924i	0.0725281	+	0.0322916i
$607$	24.5756	+	5.22370i	0.997492	+	0.212023i	0.677600	−	0.735431i	$-0.263020\pi$
$607$	24.5756	+	5.22370i	0.997492	+	0.212023i	0.319892	+	0.947454i	$0.396353\pi$
$608$	−4.05530	+	0.861981i	−0.164464	+	0.0349579i
$609$	7.73968	−	3.44593i	0.313628	−	0.139636i
$610$	2.54261	+	2.82386i	0.102947	+	0.114335i
$611$	2.66086	+	25.3164i	0.107647	+	1.02419i
$612$	−1.81182	+	1.31637i	−0.0732386	+	0.0532110i
$613$	−3.90502	+	37.1538i	−0.157722	+	1.50063i	0.573905	+	0.818922i	$0.305428\pi$
$613$	−3.90502	+	37.1538i	−0.157722	+	1.50063i	−0.731627	+	0.681705i	$0.761239\pi$
$614$	3.07953	+	5.33390i	0.124280	+	0.215259i
$615$	−19.1162	+	33.1103i	−0.770841	+	1.33514i
$616$	5.05291	+	3.67116i	0.203588	+	0.147915i
$617$	−31.5325	+	35.0204i	−1.26945	+	1.40987i	−0.399499	+	0.916734i	$0.630816\pi$
$617$	−31.5325	+	35.0204i	−1.26945	+	1.40987i	−0.869953	+	0.493135i	$0.835851\pi$
$618$	0.731461	−	2.25121i	0.0294237	−	0.0905567i
$619$	21.5958			0.868007			0.434003	−	0.900911i	$-0.357101\pi$
$619$	21.5958			0.868007			0.434003	+	0.900911i	$0.357101\pi$
$620$		0			0
$621$	−12.0000			−0.481543
$622$	1.95085	−	6.00410i	0.0782219	−	0.240742i
$623$	−3.92324	+	4.35720i	−0.157181	+	0.174567i
$624$	−39.9787	−	29.0462i	−1.60043	−	1.16278i
$625$	12.5000	−	21.6506i	0.500000	−	0.866025i
$626$	−4.01196	−	6.94891i	−0.160350	−	0.277734i
$627$	−1.01478	+	9.65502i	−0.0405266	+	0.385584i
$628$	−7.06231	+	5.13107i	−0.281817	+	0.204752i
$629$	−0.239558	−	2.27924i	−0.00955180	−	0.0908793i
$630$	1.27793	+	1.41928i	0.0509138	+	0.0565455i
$631$	4.25283	−	1.89348i	0.169303	−	0.0753783i	−0.320335	−	0.947304i	$-0.603796\pi$
$631$	4.25283	−	1.89348i	0.169303	−	0.0753783i	0.489638	+	0.871926i	$0.337129\pi$
$632$	15.9942	−	3.39968i	0.636217	−	0.135232i
$633$	−11.1912	−	2.37877i	−0.444811	−	0.0945474i
$634$	7.59438	+	3.38124i	0.301611	+	0.134286i
$635$	6.55524	+	20.1750i	0.260137	+	0.800619i
$636$	−6.87539	−	21.1603i	−0.272627	−	0.839059i
$637$	37.6275	+	16.7528i	1.49086	+	0.663772i
$638$	5.86889	+	1.24747i	0.232351	+	0.0493878i
$639$	−16.3431	+	3.47383i	−0.646523	+	0.137423i
$640$	20.6117	−	9.17692i	0.814749	−	0.362749i
$641$	5.67776	+	6.30579i	0.224258	+	0.249064i	0.844765	−	0.535137i	$-0.179740\pi$
$641$	5.67776	+	6.30579i	0.224258	+	0.249064i	−0.620507	+	0.784201i	$0.713073\pi$
$642$	−0.682664	−	6.49511i	−0.0269426	−	0.256342i
$643$	−19.1162	+	13.8888i	−0.753871	+	0.547719i	−0.897024	−	0.441981i	$-0.854276\pi$
$643$	−19.1162	+	13.8888i	−0.753871	+	0.547719i	0.143153	+	0.989701i	$0.454276\pi$
$644$	1.33043	−	12.6582i	0.0524263	−	0.498803i
$645$	−0.527864	−	0.914287i	−0.0207846	−	0.0360000i
$646$	0.103165	−	0.178688i	0.00405899	−	0.00703038i
$647$	15.4775	+	11.2451i	0.608485	+	0.442090i	0.848880	−	0.528585i	$-0.177277\pi$
$647$	15.4775	+	11.2451i	0.608485	+	0.442090i	−0.240396	+	0.970675i	$0.577277\pi$
$648$	10.5481	−	11.7149i	0.414370	−	0.460204i
$649$	7.79323	−	23.9851i	0.305911	−	0.941497i
$650$		0			0
$651$		0			0
$652$	23.0213			0.901583
$653$	−2.05573	+	6.32688i	−0.0804469	+	0.247590i	−0.983189	−	0.182593i	$-0.941551\pi$
$653$	−2.05573	+	6.32688i	−0.0804469	+	0.247590i	0.902742	+	0.430183i	$0.141551\pi$
$654$	8.60197	−	9.55345i	0.336364	−	0.373570i
$655$	−35.1246	−	25.5195i	−1.37243	−	0.997130i
$656$	−11.7533	+	20.3573i	−0.458889	+	0.794819i
$657$	4.74342	+	8.21584i	0.185058	+	0.320530i
$658$	0.148055	−	1.40865i	0.00577178	−	0.0549148i
$659$	−38.1697	+	27.7319i	−1.48688	+	1.08028i	−0.511623	+	0.859210i	$0.670955\pi$
$659$	−38.1697	+	27.7319i	−1.48688	+	1.08028i	−0.975258	+	0.221072i	$0.929045\pi$
$660$	−4.20719	−	40.0287i	−0.163765	−	1.55812i
$661$	−30.6681	−	34.0604i	−1.19285	−	1.32480i	−0.933313	−	0.359064i	$-0.883096\pi$
$661$	−30.6681	−	34.0604i	−1.19285	−	1.32480i	−0.259540	−	0.965732i	$-0.583571\pi$
$662$	8.94414	−	3.98219i	0.347624	−	0.154772i
$663$	8.29986	−	1.76419i	0.322340	−	0.0685154i
$664$	−4.55357	−	0.967892i	−0.176713	−	0.0375615i
$665$	2.04275	+	0.909491i	0.0792144	+	0.0352685i
$666$	−1.11977	−	3.44629i	−0.0433902	−	0.133541i
$667$	−7.85410	−	24.1724i	−0.304112	−	0.935961i
$668$	−12.5425	−	5.58428i	−0.485284	−	0.216062i
$669$	48.7984	+	10.3724i	1.88665	+	0.401021i
$670$	5.01263	−	1.06547i	0.193655	−	0.0411626i
$671$	17.2435	−	7.67731i	0.665679	−	0.296379i
$672$	6.34793	+	7.05009i	0.244877	+	0.271963i
$673$	−0.779116	−	7.41279i	−0.0300327	−	0.285742i	−0.999222	−	0.0394269i	$-0.987447\pi$
$673$	−0.779116	−	7.41279i	−0.0300327	−	0.285742i	0.969190	−	0.246315i	$-0.0792199\pi$
$674$	−1.81182	+	1.31637i	−0.0697888	+	0.0507046i
$675$		0			0
$676$	31.6353	+	54.7939i	1.21674	+	2.10746i
$677$	−10.6066	+	18.3712i	−0.407645	+	0.706062i	−0.994625	−	0.103540i	$-0.966983\pi$
$677$	−10.6066	+	18.3712i	−0.407645	+	0.706062i	0.586981	+	0.809601i	$0.300317\pi$
$678$	−10.0664	−	7.31368i	−0.386599	−	0.280880i
$679$	4.68391	−	5.20201i	0.179752	−	0.199635i
$680$	−0.549484	+	1.69114i	−0.0210717	+	0.0648522i
$681$	−35.9442			−1.37739
$682$		0			0
$683$	−18.8197			−0.720114			−0.360057	−	0.932930i	$-0.617243\pi$
$683$	−18.8197			−0.720114			−0.360057	+	0.932930i	$0.617243\pi$
$684$	−1.28115	+	3.94298i	−0.0489861	+	0.150764i
$685$	10.2712	−	11.4073i	0.392441	−	0.435850i
$686$	−4.01722	−	2.91868i	−0.153378	−	0.111436i
$687$	−4.85410	+	8.40755i	−0.185196	+	0.320768i
$688$	−0.324548	−	0.562134i	−0.0123733	−	0.0214312i
$689$	−3.76302	+	35.8028i	−0.143360	+	1.36398i
$690$	10.8541	−	7.88597i	0.413209	−	0.300214i
$691$	2.25610	+	21.4654i	0.0858261	+	0.816581i	0.949761	+	0.312977i	$0.101326\pi$
$691$	2.25610	+	21.4654i	0.0858261	+	0.816581i	−0.863935	+	0.503604i	$0.832007\pi$
$692$	−22.3315	−	24.8016i	−0.848915	−	0.942815i
$693$	8.66665	−	3.85864i	0.329219	−	0.146578i
$694$	9.65372	−	2.05196i	0.366450	−	0.0778914i
$695$	−2.19060	−	0.465626i	−0.0830941	−	0.0176622i
$696$	11.3939	+	5.07287i	0.431883	+	0.192287i
$697$	−1.24729	−	3.83876i	−0.0472444	−	0.145403i
$698$	0.708204	+	2.17963i	0.0268059	+	0.0825001i
$699$	9.46512	+	4.21414i	0.358004	+	0.159394i
$700$		0			0
$701$	−27.0482	+	5.74927i	−1.02160	+	0.217147i	−0.688109	−	0.725607i	$-0.741559\pi$
$701$	−27.0482	+	5.74927i	−1.02160	+	0.217147i	−0.333488	+	0.942754i	$0.608226\pi$
$702$	−4.18732	+	1.86431i	−0.158040	+	0.0703640i
$703$	−2.83888	−	3.15290i	−0.107070	−	0.118914i
$704$	−2.08798	−	19.8658i	−0.0786937	−	0.748720i
$705$	−15.3500	+	11.1524i	−0.578115	+	0.420025i
$706$	0.634437	−	6.03627i	0.0238774	−	0.227178i
$707$	−1.11803	−	1.93649i	−0.0420480	−	0.0728293i
$708$	12.6097	−	21.8406i	0.473902	−	0.820822i
$709$	12.7279	+	9.24738i	0.478007	+	0.347293i	0.800554	−	0.599261i	$-0.204539\pi$
$709$	12.7279	+	9.24738i	0.478007	+	0.347293i	−0.322546	+	0.946554i	$0.604539\pi$
$710$	−4.27037	+	4.74273i	−0.160264	+	0.177991i
$711$	7.67501	−	23.6212i	0.287835	−	0.885866i
$712$	−8.63141			−0.323476
$713$		0			0
$714$	−0.472136			−0.0176692
$715$	−20.1246	+	61.9372i	−0.752618	+	2.31632i
$716$	20.3841	−	22.6389i	0.761791	−	0.846054i
$717$	30.2705	+	21.9928i	1.13047	+	0.821337i
$718$	−1.86475	+	3.22983i	−0.0695917	+	0.120536i
$719$	−4.55214	−	7.88453i	−0.169766	−	0.294043i	0.768571	−	0.639764i	$-0.220968\pi$
$719$	−4.55214	−	7.88453i	−0.169766	−	0.294043i	−0.938338	+	0.345720i	$0.887635\pi$
$720$	1.64418	−	15.6433i	0.0612749	−	0.582992i
$721$	−2.19098	+	1.59184i	−0.0815965	+	0.0592833i
$722$	0.718674	+	6.83772i	0.0267463	+	0.254474i
$723$	22.5552	+	25.0501i	0.838837	+	0.931622i
$724$	30.7908	−	13.7089i	1.14433	−	0.509488i
$725$		0			0
$726$	5.98453	+	1.27205i	0.222107	+	0.0472102i
$727$	−3.27377	−	1.45758i	−0.121418	−	0.0540586i	0.345129	−	0.938555i	$-0.387835\pi$
$727$	−3.27377	−	1.45758i	−0.121418	−	0.0540586i	−0.466546	+	0.884497i	$0.654502\pi$
$728$	−3.12287	−	9.61121i	−0.115741	−	0.356215i
$729$	−3.69098	−	11.3597i	−0.136703	−	0.420729i
$730$	3.31037	+	1.47387i	0.122522	+	0.0545504i
$731$	0.109021	+	0.0231730i	0.00403227	+	0.000857086i
$732$	18.4629	−	3.92441i	0.682409	−	0.145051i
$733$	11.3430	−	5.05021i	0.418962	−	0.186534i	−0.186418	−	0.982470i	$-0.559688\pi$
$733$	11.3430	−	5.05021i	0.418962	−	0.186534i	0.605380	+	0.795937i	$0.293021\pi$
$734$	3.14760	+	3.49576i	0.116180	+	0.129031i
$735$	3.20903	+	30.5319i	0.118367	+	1.12618i
$736$	23.0250	−	16.7287i	0.848714	−	0.616627i
$737$	2.66086	−	25.3164i	0.0980140	−	0.932541i
$738$	−3.19098	−	5.52694i	−0.117462	−	0.203450i
$739$	−12.8311	+	22.2241i	−0.471999	+	0.817527i	−0.999487	−	0.0320362i	$-0.989801\pi$
$739$	−12.8311	+	22.2241i	−0.471999	+	0.817527i	0.527488	+	0.849563i	$0.323134\pi$
$740$	14.2302	+	10.3389i	0.523114	+	0.380065i
$741$	10.5108	−	11.6735i	0.386125	−	0.428836i
$742$	0.618993	−	1.90506i	0.0227239	−	0.0699371i
$743$	1.69936			0.0623433			0.0311717	−	0.999514i	$-0.490076\pi$
$743$	1.69936			0.0623433			0.0311717	+	0.999514i	$0.490076\pi$
$744$		0			0
$745$	−30.0000			−1.09911
$746$	−2.68034	+	8.24924i	−0.0981342	+	0.302026i
$747$	−4.73147	+	5.25483i	−0.173115	+	0.192264i
$748$	3.43769	+	2.49763i	0.125695	+	0.0913224i
$749$	−3.73607	+	6.47106i	−0.136513	+	0.236447i
$750$	4.88599	+	8.46278i	0.178411	+	0.309017i
$751$	−3.08788	+	29.3792i	−0.112678	+	1.07206i	0.781363	+	0.624077i	$0.214525\pi$
$751$	−3.08788	+	29.3792i	−0.112678	+	1.07206i	−0.894041	+	0.447985i	$0.852142\pi$
$752$	−9.43769	+	6.85689i	−0.344157	+	0.250045i
$753$	5.68224	+	54.0629i	0.207072	+	1.97016i
$754$	−6.49606	−	7.21460i	−0.236572	−	0.262740i
$755$	6.19925	−	2.76008i	0.225614	−	0.100450i
$756$	−3.17026	+	0.673860i	−0.115301	+	0.0245081i
$757$	−18.7609	−	3.98775i	−0.681875	−	0.144937i	−0.146064	−	0.989275i	$-0.546661\pi$
$757$	−18.7609	−	3.98775i	−0.681875	−	0.144937i	−0.535811	+	0.844338i	$0.679994\pi$
$758$	−6.77523	−	3.01652i	−0.246087	−	0.109565i
$759$	−20.5942	−	63.3825i	−0.747522	−	2.30064i
$760$	1.01722	+	3.13068i	0.0368985	+	0.113562i
$761$	−2.04592	−	0.910902i	−0.0741645	−	0.0330202i	0.369319	−	0.929303i	$-0.379591\pi$
$761$	−2.04592	−	0.910902i	−0.0741645	−	0.0330202i	−0.443484	+	0.896282i	$0.646258\pi$
$762$	−8.11060	−	1.72396i	−0.293816	−	0.0624525i
$763$	−14.3868	+	3.05801i	−0.520837	+	0.110707i
$764$	−24.1131	+	10.7359i	−0.872383	+	0.388410i
$765$	1.80726	+	2.00717i	0.0653416	+	0.0725692i
$766$	−0.760695	−	7.23753i	−0.0274850	−	0.261503i
$767$	−33.0126	+	23.9851i	−1.19202	+	0.866051i
$768$	1.33043	−	12.6582i	0.0480078	−	0.456763i
$769$	−6.93769	−	12.0164i	−0.250180	−	0.433324i	0.713395	−	0.700762i	$-0.247156\pi$
$769$	−6.93769	−	12.0164i	−0.250180	−	0.433324i	−0.963575	+	0.267438i	$0.913823\pi$
$770$	1.81182	−	3.13817i	0.0652936	−	0.113092i
$771$	44.3263	+	32.2050i	1.59637	+	1.15983i
$772$	9.04647	−	10.0471i	0.325589	−	0.361604i
$773$	8.34271	−	25.6762i	0.300066	−	0.923510i	−0.681406	−	0.731906i	$-0.738631\pi$
$773$	8.34271	−	25.6762i	0.300066	−	0.923510i	0.981472	−	0.191604i	$-0.0613689\pi$
$774$	0.176228			0.00633437
$775$		0			0
$776$	10.3050			0.369926
$777$	−3.00000	+	9.23305i	−0.107624	+	0.331234i
$778$	−8.63456	+	9.58965i	−0.309564	+	0.343806i
$779$	−6.04508	−	4.39201i	−0.216588	−	0.157360i
$780$	−32.5623	+	56.3996i	−1.16592	+	2.01943i
$781$	15.8508	+	27.4544i	0.567186	+	0.982395i
$782$	−0.148055	+	1.40865i	−0.00529443	+	0.0503732i
$783$	−5.23607	+	3.80423i	−0.187122	+	0.135952i
$784$	1.97302	+	18.7720i	0.0704648	+	0.670428i
$785$	7.04452	+	7.82373i	0.251430	+	0.279241i
$786$	15.5034	−	6.90255i	0.552987	−	0.246206i
$787$	−8.90532	+	1.89289i	−0.317441	+	0.0674741i	−0.363877	−	0.931447i	$-0.618547\pi$
$787$	−8.90532	+	1.89289i	−0.317441	+	0.0674741i	0.0464360	+	0.998921i	$0.485214\pi$
$788$	13.4295	+	2.85452i	0.478404	+	0.101688i
$789$	5.64602	+	2.51377i	0.201004	+	0.0894926i
$790$	−2.93159	−	9.02251i	−0.104301	−	0.321007i
$791$	4.39919	+	13.5393i	0.156417	+	0.481402i
$792$	12.7585	+	5.68045i	0.453353	+	0.201846i
$793$	−29.8736	−	6.34984i	−1.06084	−	0.225489i
$794$	−0.482640	+	0.102588i	−0.0171282	+	0.00364072i
$795$	−24.5130	+	10.9139i	−0.869386	+	0.387076i
$796$	−18.2758	−	20.2974i	−0.647770	−	0.719422i
$797$	0.548167	+	5.21546i	0.0194171	+	0.184741i	0.999931	−	0.0117060i	$-0.00372623\pi$
$797$	0.548167	+	5.21546i	0.0194171	+	0.184741i	−0.980514	+	0.196447i	$0.937060\pi$
$798$	−0.707107	+	0.513743i	−0.0250313	+	0.0181863i
$799$	0.209381	−	1.99213i	0.00740738	−	0.0704765i
$800$		0			0
$801$	−6.55524	+	11.3540i	−0.231618	+	0.401174i
$802$	−1.14412	−	0.831254i	−0.0404004	−	0.0293526i
$803$	12.0444	−	13.3766i	0.425036	−	0.472050i
$804$	7.86629	−	24.2099i	0.277423	−	0.853819i
$805$	−15.3500			−0.541017
$806$		0			0
$807$	33.8885			1.19293
$808$	1.01722	−	3.13068i	0.0357857	−	0.110137i
$809$	14.7591	−	16.3916i	0.518902	−	0.576300i	−0.425555	−	0.904932i	$-0.639921\pi$
$809$	14.7591	−	16.3916i	0.518902	−	0.576300i	0.944458	+	0.328633i	$0.106588\pi$
$810$	−7.39919	−	5.37582i	−0.259981	−	0.188887i
$811$	21.7082	−	37.5997i	0.762278	−	1.32030i	−0.179396	−	0.983777i	$-0.557414\pi$
$811$	21.7082	−	37.5997i	0.762278	−	1.32030i	0.941674	−	0.336527i	$-0.109252\pi$
$812$	−3.43237	−	5.94504i	−0.120453	−	0.208630i
$813$	6.71587	−	63.8973i	0.235536	−	2.24097i
$814$	−5.56231	+	4.04125i	−0.194959	+	0.141646i
$815$	−2.90212	−	27.6118i	−0.101657	−	0.967201i
$816$	2.60194	+	2.88975i	0.0910862	+	0.101162i
$817$	0.188493	−	0.0839224i	0.00659453	−	0.00293607i
$818$	−6.48346	+	1.37810i	−0.226689	+	0.0481842i
$819$	−15.0146	−	3.19145i	−0.524652	−	0.111518i
$820$	28.3005	+	12.6002i	0.988295	+	0.440017i
$821$	−4.43392	−	13.6462i	−0.154745	−	0.476256i	0.843390	−	0.537302i	$-0.180556\pi$
$821$	−4.43392	−	13.6462i	−0.154745	−	0.476256i	−0.998135	+	0.0610460i	$0.980556\pi$
$822$	1.85410	+	5.70634i	0.0646692	+	0.199031i
$823$	−13.6460	−	6.07557i	−0.475668	−	0.211781i	0.154877	−	0.987934i	$-0.450502\pi$
$823$	−13.6460	−	6.07557i	−0.475668	−	0.211781i	−0.630545	+	0.776153i	$0.717169\pi$
$824$	−3.89972	−	0.828912i	−0.135853	−	0.0288765i
$825$		0			0
$826$	2.07421	−	0.923500i	0.0721711	−	0.0321327i
$827$	−32.1538	−	35.7105i	−1.11810	−	1.24177i	−0.967416	−	0.253192i	$-0.918520\pi$
$827$	−32.1538	−	35.7105i	−1.11810	−	1.24177i	−0.150682	−	0.988582i	$-0.548147\pi$
$828$	−2.97493	−	28.3046i	−0.103386	−	0.983652i
$829$	−4.71906	+	3.42860i	−0.163900	+	0.119080i	−0.666712	−	0.745316i	$-0.732299\pi$
$829$	−4.71906	+	3.42860i	−0.163900	+	0.119080i	0.502812	+	0.864396i	$0.332299\pi$
$830$	−0.282322	+	2.68611i	−0.00979953	+	0.0932363i
$831$	−22.4164	−	38.8264i	−0.777617	−	1.34687i
$832$	−16.1603	+	27.9904i	−0.560257	+	0.970394i
$833$	−2.62210	−	1.90506i	−0.0908502	−	0.0660066i
$834$	0.585749	−	0.650540i	0.0202828	−	0.0225264i
$835$	−5.11667	+	15.7475i	−0.177070	+	0.544965i
$836$	7.86629			0.272061
$837$		0			0
$838$	−7.10333			−0.245380
$839$	2.29180	−	7.05342i	0.0791216	−	0.243511i	−0.903670	−	0.428230i	$-0.859137\pi$
$839$	2.29180	−	7.05342i	0.0791216	−	0.243511i	0.982791	+	0.184719i	$0.0591374\pi$
$840$	5.04018	−	5.59769i	0.173903	−	0.193139i
$841$	12.3713	+	8.98829i	0.426597	+	0.309941i
$842$	0.0795268	−	0.137745i	0.00274068	−	0.00474699i
$843$	−35.8805	−	62.1468i	−1.23579	−	2.14045i
$844$	−0.969032	+	9.21973i	−0.0333555	+	0.317356i
$845$	61.7320	−	44.8509i	2.12365	−	1.54292i
$846$	−0.331061	−	3.14983i	−0.0113821	−	0.108294i
$847$	−4.68391	−	5.20201i	−0.160941	−	0.178743i
$848$	−15.0714	+	6.71022i	−0.517554	+	0.230430i
$849$	53.7178	−	11.4181i	1.84359	−	0.391867i
$850$		0			0
$851$	26.6067	+	11.8460i	0.912064	+	0.406077i
$852$	9.79633	+	30.1500i	0.335617	+	1.03292i
$853$	−14.1246	−	43.4711i	−0.483617	−	1.48842i	−0.833973	−	0.551805i	$-0.813939\pi$
$853$	−14.1246	−	43.4711i	−0.483617	−	1.48842i	0.350356	−	0.936617i	$-0.386061\pi$
$854$	1.55244	+	0.691190i	0.0531234	+	0.0236520i
$855$	4.89074	+	1.03956i	0.167260	+	0.0355521i
$856$	−10.7596	+	2.28703i	−0.367756	+	0.0781690i
$857$	−5.48127	+	2.44042i	−0.187237	+	0.0833632i	−0.498214	−	0.867054i	$-0.666010\pi$
$857$	−5.48127	+	2.44042i	−0.187237	+	0.0833632i	0.310977	+	0.950417i	$0.399344\pi$
$858$	−17.0333	−	18.9174i	−0.581507	−	0.645829i
$859$	−0.381921	−	3.63374i	−0.0130310	−	0.123981i	0.986073	−	0.166316i	$-0.0531872\pi$
$859$	−0.381921	−	3.63374i	−0.0130310	−	0.123981i	−0.999103	+	0.0423345i	$0.986520\pi$
$860$	−0.692055	+	0.502807i	−0.0235989	+	0.0171456i
$861$	−1.78724	+	17.0044i	−0.0609088	+	0.579509i
$862$	0.0212862	+	0.0368688i	0.000725012	+	0.00125576i
$863$	17.6626	−	30.5926i	0.601243	−	1.04138i	−0.391391	−	0.920225i	$-0.628006\pi$
$863$	17.6626	−	30.5926i	0.601243	−	1.04138i	0.992633	−	0.121158i	$-0.0386608\pi$
$864$	−5.86319	−	4.25985i	−0.199470	−	0.144923i
$865$	−26.9320	+	29.9110i	−0.915715	+	1.01700i
$866$	−2.54903	+	7.84512i	−0.0866197	+	0.266588i
$867$	38.2325			1.29844
$868$		0			0
$869$	−47.1246			−1.59859
$870$	2.23607	−	6.88191i	0.0758098	−	0.233319i
$871$	−27.5604	+	30.6090i	−0.933850	+	1.03715i
$872$	−17.5172	−	12.7270i	−0.593208	−	0.430991i
$873$	7.82624	−	13.5554i	0.264878	−	0.458782i
$874$	1.31105	+	2.27080i	0.0443469	+	0.0768110i
$875$	1.16866	−	11.1191i	0.0395080	−	0.375894i
$876$	14.5623	−	10.5801i	0.492015	−	0.357470i
$877$	1.59843	+	15.2080i	0.0539751	+	0.513539i	0.987791	+	0.155785i	$0.0497906\pi$
$877$	1.59843	+	15.2080i	0.0539751	+	0.513539i	−0.933816	+	0.357754i	$0.883543\pi$
$878$	−6.38963	−	7.09640i	−0.215640	−	0.239492i
$879$	32.8367	−	14.6198i	1.10755	−	0.493115i
$880$	−29.1924	+	6.20504i	−0.984077	+	0.209172i
$881$	−48.5882	−	10.3277i	−1.63698	−	0.347951i	−0.704648	−	0.709557i	$-0.748895\pi$
$881$	−48.5882	−	10.3277i	−1.63698	−	0.347951i	−0.932331	+	0.361607i	$0.882228\pi$
$882$	−4.68157	−	2.08437i	−0.157637	−	0.0701843i
$883$	10.4884	+	32.2799i	0.352962	+	1.08631i	0.957182	+	0.289488i	$0.0934851\pi$
$883$	10.4884	+	32.2799i	0.352962	+	1.08631i	−0.604219	+	0.796818i	$0.706515\pi$
$884$	−2.12461	−	6.53888i	−0.0714584	−	0.219926i
$885$	−27.7854	−	12.3709i	−0.933996	−	0.415842i
$886$	−8.94604	−	1.90154i	−0.300548	−	0.0638835i
$887$	18.9376	−	4.02531i	0.635862	−	0.135157i	0.121309	−	0.992615i	$-0.461291\pi$
$887$	18.9376	−	4.02531i	0.635862	−	0.135157i	0.514554	+	0.857458i	$0.327958\pi$
$888$	−13.0562	+	5.81300i	−0.438138	+	0.195071i
$889$	6.34793	+	7.05009i	0.212903	+	0.236452i
$890$	0.523453	+	4.98033i	0.0175462	+	0.166941i
$891$	−36.7545	+	26.7037i	−1.23132	+	0.894608i
$892$	4.22539	−	40.2019i	0.141476	−	1.34606i
$893$	−1.85410	−	3.21140i	−0.0620452	−	0.107465i
$894$	5.86319	−	10.1553i	0.196094	−	0.339645i
$895$	−29.7228	−	21.5949i	−0.993525	−	0.721838i
$896$	6.75164	−	7.49846i	0.225557	−	0.250506i
$897$	−33.3221	+	102.555i	−1.11259	+	3.42421i
$898$	16.1151			0.537769
$899$		0			0
$900$		0			0
$901$	0.875388	−	2.69417i	0.0291634	−	0.0897557i
$902$	−8.10246	+	8.99869i	−0.269782	+	0.299624i
$903$	−0.381966	−	0.277515i	−0.0127110	−	0.00923511i
$904$	−10.4787	+	18.1497i	−0.348517	+	0.603649i
$905$	−20.3241	−	35.2024i	−0.675597	−	1.17017i
$906$	−0.277259	+	2.63795i	−0.00921132	+	0.0876399i
$907$	44.9336	−	32.6462i	1.49200	−	1.08400i	0.518560	−	0.855041i	$-0.326468\pi$
$907$	44.9336	−	32.6462i	1.49200	−	1.08400i	0.973436	−	0.228958i	$-0.0735318\pi$
$908$	3.04435	+	28.9651i	0.101030	+	0.961239i
$909$	−3.34565	−	3.71572i	−0.110968	−	0.123243i
$910$	−5.35629	+	2.38477i	−0.177559	+	0.0790544i
$911$	13.8807	−	2.95044i	0.459889	−	0.0977525i	0.0278596	−	0.999612i	$-0.491131\pi$
$911$	13.8807	−	2.95044i	0.459889	−	0.0977525i	0.432030	+	0.901859i	$0.357798\pi$
$912$	7.04128	+	1.49667i	0.233160	+	0.0495597i
$913$	12.2565	+	5.45694i	0.405631	+	0.180599i
$914$	−1.33540	−	4.10995i	−0.0441712	−	0.135945i
$915$	−7.03444	−	21.6498i	−0.232551	−	0.715720i
$916$	7.18621	+	3.19951i	0.237439	+	0.105715i
$917$	−18.9921	−	4.03690i	−0.627175	−	0.133310i
$918$	0.352798	−	0.0749895i	0.0116441	−	0.00247502i
$919$	22.4193	−	9.98173i	0.739546	−	0.329267i	−0.00215526	−	0.999998i	$-0.500686\pi$
$919$	22.4193	−	9.98173i	0.739546	−	0.329267i	0.741701	+	0.670731i	$0.234019\pi$
$920$	−15.1206	−	16.7931i	−0.498510	−	0.553651i
$921$	−3.85679	−	36.6949i	−0.127086	−	1.20914i
$922$	−12.0846	+	8.77996i	−0.397984	+	0.289153i
$923$	5.36171	−	51.0133i	0.176483	−	1.67912i
$924$	−9.00000	−	15.5885i	−0.296078	−	0.512823i
$925$		0			0
$926$	4.67966	+	3.39997i	0.153783	+	0.111730i
$927$	−4.05207	+	4.50028i	−0.133088	+	0.147809i
$928$	4.74342	−	14.5987i	0.155710	−	0.479227i
$929$	−23.2951			−0.764288			−0.382144	−	0.924103i	$-0.624814\pi$
$929$	−23.2951			−0.764288			−0.382144	+	0.924103i	$0.624814\pi$
$930$		0			0
$931$	−6.00000			−0.196642
$932$	2.59424	−	7.98424i	0.0849770	−	0.261532i
$933$	−25.3064	+	28.1056i	−0.828494	+	0.920136i
$934$	−4.83688	−	3.51420i	−0.158268	−	0.114988i
$935$	2.56231	−	4.43804i	0.0837964	−	0.145140i
$936$	−11.2987	−	19.5698i	−0.369308	−	0.639660i
$937$	5.87964	−	55.9411i	0.192080	−	1.82752i	−0.296542	−	0.955020i	$-0.595833\pi$
$937$	5.87964	−	55.9411i	0.192080	−	1.82752i	0.488622	−	0.872496i	$-0.337500\pi$
$938$	1.85410	−	1.34708i	0.0605386	−	0.0439838i
$939$	5.02457	+	47.8056i	0.163971	+	1.56008i
$940$	10.2871	+	11.4250i	0.335528	+	0.372642i
$941$	−46.4381	+	20.6756i	−1.51384	+	0.674005i	−0.984657	−	0.174502i	$-0.944168\pi$
$941$	−46.4381	+	20.6756i	−1.51384	+	0.674005i	−0.529183	+	0.848507i	$0.677502\pi$
$942$	−4.02520	+	0.855582i	−0.131148	+	0.0278764i
$943$	50.1733	+	10.6647i	1.63387	+	0.347290i
$944$	−17.0834	−	7.60601i	−0.556016	−	0.247554i
$945$	1.20788	+	3.71748i	0.0392924	+	0.120930i
$946$	−0.103326	−	0.318003i	−0.00335940	−	0.0103392i
$947$	−2.04592	−	0.910902i	−0.0664834	−	0.0296003i	0.373226	−	0.927741i	$-0.378252\pi$
$947$	−2.04592	−	0.910902i	−0.0664834	−	0.0296003i	−0.439709	+	0.898140i	$0.644918\pi$
$948$	−46.0948	−	9.79776i	−1.49709	−	0.318216i
$949$	−28.4882	+	6.05535i	−0.924765	+	0.196565i
$950$		0			0
$951$	−33.3235	−	37.0095i	−1.08059	−	1.20012i
$952$	0.0831232	+	0.790864i	0.00269404	+	0.0256321i
$953$	43.2460	−	31.4200i	1.40087	−	1.01780i	0.406303	−	0.913738i	$-0.366818\pi$
$953$	43.2460	−	31.4200i	1.40087	−	1.01780i	0.994571	−	0.104057i	$-0.0331824\pi$
$954$	0.468191	−	4.45454i	0.0151582	−	0.144221i
$955$	15.9164	+	27.5680i	0.515043	+	0.892080i
$956$	15.1587	−	26.2557i	0.490269	−	0.849170i
$957$	−29.0795	−	21.1275i	−0.940006	−	0.682955i
$958$	6.51030	−	7.23042i	0.210338	−	0.233604i
$959$	2.12132	−	6.52875i	0.0685010	−	0.210824i
$960$	−24.0903			−0.777512
$961$		0			0
$962$	11.1246			0.358672
$963$	−5.16312	+	15.8904i	−0.166379	+	0.512062i
$964$	18.2758	−	20.2974i	0.588625	−	0.653735i
$965$	−13.1910	−	9.58381i	−0.424633	−	0.308514i
$966$	3.00000	−	5.19615i	0.0965234	−	0.167183i
$967$	−6.45207	−	11.1753i	−0.207485	−	0.359374i	0.743437	−	0.668806i	$-0.233194\pi$
$967$	−6.45207	−	11.1753i	−0.207485	−	0.359374i	−0.950922	+	0.309432i	$0.899861\pi$
$968$	1.07716	−	10.2485i	0.0346213	−	0.329399i
$969$	−1.00000	+	0.726543i	−0.0321246	+	0.0233399i
$970$	−0.624946	−	5.94596i	−0.0200658	−	0.190913i
$971$	12.1189	+	13.4594i	0.388915	+	0.431934i	0.905529	−	0.424285i	$-0.139474\pi$
$971$	12.1189	+	13.4594i	0.388915	+	0.431934i	−0.516614	+	0.856218i	$0.672808\pi$
$972$	−32.6207	+	14.5237i	−1.04631	+	0.465847i
$973$	−0.979665	+	0.208234i	−0.0314066	+	0.00667568i
$974$	6.94599	+	1.47642i	0.222564	+	0.0473074i
$975$		0			0
$976$	−4.32501	−	13.3110i	−0.138440	−	0.426075i
$977$	13.1287	+	40.4059i	0.420024	+	1.29270i	0.907680	+	0.419664i	$0.137852\pi$
$977$	13.1287	+	40.4059i	0.420024	+	1.29270i	−0.487656	+	0.873036i	$0.662148\pi$
$978$	9.91410	+	4.41404i	0.317018	+	0.141146i
$979$	24.3318	+	5.17188i	0.777648	+	0.165294i
$980$	24.3318	−	5.17188i	0.777251	−	0.165210i
$981$	−30.0452	+	13.3770i	−0.959269	+	0.427094i
$982$	2.44484	+	2.71527i	0.0780179	+	0.0866476i
$983$	−0.314072	−	2.98820i	−0.0100173	−	0.0953086i	0.988371	−	0.152063i	$-0.0485916\pi$
$983$	−0.314072	−	2.98820i	−0.0100173	−	0.0953086i	−0.998388	+	0.0567541i	$0.981925\pi$
$984$	−20.3635	+	14.7950i	−0.649165	+	0.471646i
$985$	1.73077	−	16.4672i	0.0551470	−	0.524688i
$986$	0.381966	+	0.661585i	0.0121643	+	0.0210691i
$987$	−4.24264	+	7.34847i	−0.135045	+	0.233904i
$988$	−10.2971	−	7.48128i	−0.327595	−	0.238011i
$989$	−0.947762	+	1.05260i	−0.0301371	+	0.0334706i
$990$	2.50388	−	7.70615i	0.0795785	−	0.244917i
$991$	4.44897			0.141326			0.0706631	−	0.997500i	$-0.477488\pi$
$991$	4.44897			0.141326			0.0706631	+	0.997500i	$0.477488\pi$
$992$		0			0
$993$	−58.6525			−1.86128
$994$	−0.881966	+	2.71441i	−0.0279743	+	0.0860959i
$995$	−22.0409	+	24.4789i	−0.698743	+	0.776032i
$996$	10.8541	+	7.88597i	0.343925	+	0.249876i
$997$	−24.3328	+	42.1457i	−0.770628	+	1.33477i	0.166591	+	0.986026i	$0.446724\pi$
$997$	−24.3328	+	42.1457i	−0.770628	+	1.33477i	−0.937219	+	0.348741i	$0.886609\pi$
$998$	3.51118	+	6.08154i	0.111144	+	0.192508i
$999$	0.775226	−	7.37578i	0.0245271	−	0.233359i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.g.i.448.1		16
31.2	even	5		961.2.c.h.521.2		8
31.3	odd	30		961.2.d.j.374.1		8
31.4	even	5	inner	961.2.g.i.844.2		16
31.5	even	3	inner	961.2.g.i.846.2		16
31.6	odd	6		961.2.d.h.628.2		8
31.7	even	15		961.2.d.h.531.1		8
31.8	even	5		961.2.g.p.338.2		16
31.9	even	15		961.2.g.p.235.1		16
31.10	even	15		961.2.c.h.439.2		8
31.11	odd	30	inner	961.2.g.i.547.2		16
31.12	odd	30		961.2.a.h.1.2	yes	4
31.13	odd	30		961.2.g.p.816.1		16
31.14	even	15		961.2.d.j.388.2		8
31.15	odd	10		961.2.g.p.732.2		16
31.16	even	5		961.2.g.p.732.1		16
31.17	odd	30		961.2.d.j.388.1		8
31.18	even	15		961.2.g.p.816.2		16
31.19	even	15		961.2.a.h.1.1	✓	4
31.20	even	15	inner	961.2.g.i.547.1		16
31.21	odd	30		961.2.c.h.439.1		8
31.22	odd	30		961.2.g.p.235.2		16
31.23	odd	10		961.2.g.p.338.1		16
31.24	odd	30		961.2.d.h.531.2		8
31.25	even	3		961.2.d.h.628.1		8
31.26	odd	6	inner	961.2.g.i.846.1		16
31.27	odd	10	inner	961.2.g.i.844.1		16
31.28	even	15		961.2.d.j.374.2		8
31.29	odd	10		961.2.c.h.521.1		8
31.30	odd	2	inner	961.2.g.i.448.2		16
93.50	odd	30		8649.2.a.r.1.4		4
93.74	even	30		8649.2.a.r.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
961.2.a.h.1.1	✓	4	31.19	even	15
961.2.a.h.1.2	yes	4	31.12	odd	30
961.2.c.h.439.1		8	31.21	odd	30
961.2.c.h.439.2		8	31.10	even	15
961.2.c.h.521.1		8	31.29	odd	10
961.2.c.h.521.2		8	31.2	even	5
961.2.d.h.531.1		8	31.7	even	15
961.2.d.h.531.2		8	31.24	odd	30
961.2.d.h.628.1		8	31.25	even	3
961.2.d.h.628.2		8	31.6	odd	6
961.2.d.j.374.1		8	31.3	odd	30
961.2.d.j.374.2		8	31.28	even	15
961.2.d.j.388.1		8	31.17	odd	30
961.2.d.j.388.2		8	31.14	even	15
961.2.g.i.448.1		16	1.1	even	1	trivial
961.2.g.i.448.2		16	31.30	odd	2	inner
961.2.g.i.547.1		16	31.20	even	15	inner
961.2.g.i.547.2		16	31.11	odd	30	inner
961.2.g.i.844.1		16	31.27	odd	10	inner
961.2.g.i.844.2		16	31.4	even	5	inner
961.2.g.i.846.1		16	31.26	odd	6	inner
961.2.g.i.846.2		16	31.5	even	3	inner
961.2.g.p.235.1		16	31.9	even	15
961.2.g.p.235.2		16	31.22	odd	30
961.2.g.p.338.1		16	31.23	odd	10
961.2.g.p.338.2		16	31.8	even	5
961.2.g.p.732.1		16	31.16	even	5
961.2.g.p.732.2		16	31.15	odd	10
961.2.g.p.816.1		16	31.13	odd	30
961.2.g.p.816.2		16	31.18	even	15
8649.2.a.r.1.3		4	93.74	even	30
8649.2.a.r.1.4		4	93.50	odd	30

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:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.g (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.118034 - 0.363271i) q^{2} +(-1.53114 + 1.70050i) q^{3} +(1.50000 + 1.08981i) q^{4} +(1.11803 - 1.93649i) q^{5} +(0.437016 + 0.756934i) q^{6} +(0.104528 - 0.994522i) q^{7} +(1.19098 - 0.865300i) q^{8} +(-0.233733 - 2.22382i) q^{9} +(-0.571506 - 0.634721i) q^{10} +(-3.87585 + 1.72564i) q^{11} +(-4.14993 + 0.882095i) q^{12} +(6.71473 + 1.42726i) q^{13} +(-0.348943 - 0.155360i) q^{14} +(1.58114 + 4.86624i) q^{15} +(0.972136 + 2.99193i) q^{16} +(-0.493480 - 0.219712i) q^{17} +(-0.835438 - 0.177578i) q^{18} +(-0.978148 + 0.207912i) q^{19} +(3.78747 - 1.68629i) q^{20} +(1.53114 + 1.70050i) q^{21} +(0.169393 + 1.61167i) q^{22} +(5.55369 - 4.03499i) q^{23} +(-0.352115 + 3.35016i) q^{24} +(1.31105 - 2.27080i) q^{26} +(-1.41421 - 1.02749i) q^{27} +(1.24064 - 1.37787i) q^{28} +(1.14412 - 3.52125i) q^{29} +1.95440 q^{30} +4.14590 q^{32} +(3.00000 - 9.23305i) q^{33} +(-0.138062 + 0.153334i) q^{34} +(-1.80902 - 1.31433i) q^{35} +(2.07295 - 3.59045i) q^{36} +(2.12132 + 3.67423i) q^{37} +(-0.0399263 + 0.379874i) q^{38} +(-12.7082 + 9.23305i) q^{39} +(-0.344086 - 3.27376i) q^{40} +(4.99983 + 5.55288i) q^{41} +(0.798468 - 0.355501i) q^{42} +(-0.201822 + 0.0428986i) q^{43} +(-7.69439 - 1.63549i) q^{44} +(-4.56773 - 2.03368i) q^{45} +(-0.810272 - 2.49376i) q^{46} +(1.14590 + 3.52671i) q^{47} +(-6.57624 - 2.92793i) q^{48} +(5.86889 + 1.24747i) q^{49} +(1.12920 - 0.502754i) q^{51} +(8.51664 + 9.45869i) q^{52} +(0.548167 + 5.21546i) q^{53} +(-0.540182 + 0.392465i) q^{54} +(-0.991644 + 9.43486i) q^{55} +(-0.736068 - 1.27491i) q^{56} +(1.14412 - 1.98168i) q^{57} +(-1.14412 - 0.831254i) q^{58} +(-3.97749 + 4.41745i) q^{59} +(-2.93159 + 9.02251i) q^{60} -4.44897 q^{61} -2.23607 q^{63} +(-1.45492 + 4.47777i) q^{64} +(10.2712 - 11.4073i) q^{65} +(-3.00000 - 2.17963i) q^{66} +(-3.00000 + 5.19615i) q^{67} +(-0.500776 - 0.867369i) q^{68} +(-1.64195 + 15.6222i) q^{69} +(-0.690983 + 0.502029i) q^{70} +(-0.781051 - 7.43120i) q^{71} +(-2.20264 - 2.44628i) q^{72} +(-3.87585 + 1.72564i) q^{73} +(1.58513 - 0.336930i) q^{74} +(-1.69381 - 0.754131i) q^{76} +(1.31105 + 4.03499i) q^{77} +(1.85410 + 5.70634i) q^{78} +(10.1471 + 4.51778i) q^{79} +(6.88072 + 1.46254i) q^{80} +(10.4742 - 2.22636i) q^{81} +(2.60735 - 1.16087i) q^{82} +(-2.11598 - 2.35003i) q^{83} +(0.443477 + 4.21940i) q^{84} +(-0.977198 + 0.709976i) q^{85} +(-0.00823804 + 0.0783797i) q^{86} +(4.23607 + 7.33708i) q^{87} +(-3.12287 + 5.40897i) q^{88} +(-4.74342 - 3.44629i) q^{89} +(-1.27793 + 1.41928i) q^{90} +(2.12132 - 6.52875i) q^{91} +12.7279 q^{92} +1.41641 q^{94} +(-0.690983 + 2.12663i) q^{95} +(-6.34793 + 7.05009i) q^{96} +(5.66312 + 4.11450i) q^{97} +(1.14590 - 1.98475i) q^{98} +(4.74342 + 8.21584i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{2} + 24 q^{4} - 2 q^{7} + 28 q^{8} + 10 q^{9} + 20 q^{10} + 2 q^{14} - 56 q^{16} - 20 q^{18} + 2 q^{19} - 18 q^{28} + 120 q^{32} + 48 q^{33} - 20 q^{35} + 60 q^{36} - 2 q^{38} - 96 q^{39} - 10 q^{40}+ \cdots + 72 q^{98}+O(q^{100}) \) 16 * q - 16 * q^2 + 24 * q^4 - 2 * q^7 + 28 * q^8 + 10 * q^9 + 20 * q^10 + 2 * q^14 - 56 * q^16 - 20 * q^18 + 2 * q^19 - 18 * q^28 + 120 * q^32 + 48 * q^33 - 20 * q^35 + 60 * q^36 - 2 * q^38 - 96 * q^39 - 10 * q^40 - 14 * q^41 - 10 * q^45 + 72 * q^47 - 12 * q^49 + 8 * q^51 + 24 * q^56 + 46 * q^59 - 68 * q^64 - 48 * q^66 - 48 * q^67 + 48 * q^69 - 20 * q^70 + 26 * q^71 - 50 * q^72 - 12 * q^76 - 24 * q^78 + 80 * q^80 + 22 * q^81 + 14 * q^82 + 32 * q^87 - 40 * q^90 - 192 * q^94 - 20 * q^95 + 28 * q^97 + 72 * q^98

Introduction

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