LMFDB - Embedded newform 961.2.g.i.846.1

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			846.1
Root			$-0.946294 + 1.05097i$ of defining polynomial
Character	$\chi$	$=$	961.846
Dual form			961.2.g.i.844.1

$q$-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} +(-2.23824 - 0.475753i) q^{3} +(1.50000 + 1.08981i) q^{4} +(1.11803 + 1.93649i) q^{5} +(-0.437016 + 0.756934i) q^{6} +(-0.913545 + 0.406737i) q^{7} +(1.19098 - 0.865300i) q^{8} +(2.04275 + 0.909491i) q^{9} +(0.835438 - 0.177578i) q^{10} +(-0.443477 + 4.21940i) q^{11} +(-2.83888 - 3.15290i) q^{12} +(4.59341 - 5.10149i) q^{13} +(0.0399263 + 0.379874i) q^{14} +(-1.58114 - 4.86624i) q^{15} +(0.972136 + 2.99193i) q^{16} +(-0.0564643 - 0.537222i) q^{17} +(0.571506 - 0.634721i) q^{18} +(0.669131 + 0.743145i) q^{19} +(-0.433364 + 4.12319i) q^{20} +(2.23824 - 0.475753i) q^{21} +(1.48044 + 0.659135i) q^{22} +(-5.55369 + 4.03499i) q^{23} +(-3.07738 + 1.37014i) q^{24} +(-1.31105 - 2.27080i) q^{26} +(1.41421 + 1.02749i) q^{27} +(-1.81359 - 0.385489i) q^{28} +(-1.14412 + 3.52125i) q^{29} -1.95440 q^{30} +4.14590 q^{32} +(3.00000 - 9.23305i) q^{33} +(-0.201822 - 0.0428986i) q^{34} +(-1.80902 - 1.31433i) q^{35} +(2.07295 + 3.59045i) q^{36} +(-2.12132 + 3.67423i) q^{37} +(0.348943 - 0.155360i) q^{38} +(-12.7082 + 9.23305i) q^{39} +(3.00721 + 1.33889i) q^{40} +(-7.30885 + 1.55354i) q^{41} +(0.0913612 - 0.869244i) q^{42} +(-0.138062 - 0.153334i) q^{43} +(-5.26357 + 5.84579i) q^{44} +(0.522642 + 4.97261i) q^{45} +(0.810272 + 2.49376i) q^{46} +(1.14590 + 3.52671i) q^{47} +(-0.752457 - 7.15915i) q^{48} +(-4.01478 + 4.45887i) q^{49} +(-0.129204 + 1.22930i) q^{51} +(12.4498 - 2.64628i) q^{52} +(4.79081 + 2.13301i) q^{53} +(0.540182 - 0.392465i) q^{54} +(-8.66665 + 3.85864i) q^{55} +(-0.736068 + 1.27491i) q^{56} +(-1.14412 - 1.98168i) q^{57} +(1.14412 + 0.831254i) q^{58} +(5.81438 + 1.23588i) q^{59} +(2.93159 - 9.02251i) q^{60} +4.44897 q^{61} -2.23607 q^{63} +(-1.45492 + 4.47777i) q^{64} +(15.0146 + 3.19145i) q^{65} +(-3.00000 - 2.17963i) q^{66} +(-3.00000 - 5.19615i) q^{67} +(0.500776 - 0.867369i) q^{68} +(14.3502 - 6.38910i) q^{69} +(-0.690983 + 0.502029i) q^{70} +(6.82614 + 3.03919i) q^{71} +(3.21986 - 0.684403i) q^{72} +(-0.443477 + 4.21940i) q^{73} +(1.08436 + 1.20430i) q^{74} +(0.193806 + 1.84395i) q^{76} +(-1.31105 - 4.03499i) q^{77} +(1.85410 + 5.70634i) q^{78} +(1.16104 + 11.0465i) q^{79} +(-4.70696 + 5.22761i) q^{80} +(-7.16519 - 7.95775i) q^{81} +(-0.298335 + 2.83847i) q^{82} +(-3.09317 + 0.657474i) q^{83} +(3.87585 + 1.72564i) q^{84} +(0.977198 - 0.709976i) q^{85} +(-0.0719978 + 0.0320555i) q^{86} +(4.23607 - 7.33708i) q^{87} +(3.12287 + 5.40897i) q^{88} +(4.74342 + 3.44629i) q^{89} +(1.86810 + 0.397076i) q^{90} +(-2.12132 + 6.52875i) q^{91} -12.7279 q^{92} +1.41641 q^{94} +(-0.690983 + 2.12663i) q^{95} +(-9.27952 - 1.97242i) 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 $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{15}\right)$

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	$0.0568820\pi$
$3$	−2.23824	−	0.475753i	−1.29225	−	0.274676i	−0.490030	−	0.871705i	$-0.663014\pi$
$3$	−2.23824	−	0.475753i	−1.29225	−	0.274676i	−0.802219	+	0.597029i	$0.796348\pi$
$4$	1.50000	+	1.08981i	0.750000	+	0.544907i
$5$	1.11803	+	1.93649i	0.500000	+	0.866025i	1.00000			$0$
$5$	1.11803	+	1.93649i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$6$	−0.437016	+	0.756934i	−0.178411	+	0.309017i
$7$	−0.913545	+	0.406737i	−0.345288	+	0.153732i	−0.572051	−	0.820218i	$-0.693852\pi$
$7$	−0.913545	+	0.406737i	−0.345288	+	0.153732i	0.226764	+	0.973950i	$0.427186\pi$
$8$	1.19098	−	0.865300i	0.421076	−	0.305930i
$9$	2.04275	+	0.909491i	0.680917	+	0.303164i
$10$	0.835438	−	0.177578i	0.264189	−	0.0561550i
$11$	−0.443477	+	4.21940i	−0.133713	+	1.27220i	0.697638	+	0.716450i	$0.254234\pi$
$11$	−0.443477	+	4.21940i	−0.133713	+	1.27220i	−0.831352	+	0.555747i	$0.812432\pi$
$12$	−2.83888	−	3.15290i	−0.819514	−	0.910163i
$13$	4.59341	−	5.10149i	1.27398	−	1.41490i	0.409441	−	0.912337i	$-0.365724\pi$
$13$	4.59341	−	5.10149i	1.27398	−	1.41490i	0.864540	−	0.502563i	$-0.167610\pi$
$14$	0.0399263	+	0.379874i	0.0106708	+	0.101525i
$15$	−1.58114	−	4.86624i	−0.408248	−	1.25646i
$16$	0.972136	+	2.99193i	0.243034	+	0.747982i
$17$	−0.0564643	−	0.537222i	−0.0136946	−	0.130296i	0.985538	−	0.169452i	$-0.0541997\pi$
$17$	−0.0564643	−	0.537222i	−0.0136946	−	0.130296i	−0.999233	+	0.0391562i	$0.987533\pi$
$18$	0.571506	−	0.634721i	0.134705	−	0.149605i
$19$	0.669131	+	0.743145i	0.153509	+	0.170489i	0.814994	−	0.579469i	$-0.196740\pi$
$19$	0.669131	+	0.743145i	0.153509	+	0.170489i	−0.661485	+	0.749958i	$0.730073\pi$
$20$	−0.433364	+	4.12319i	−0.0969032	+	0.921973i
$21$	2.23824	−	0.475753i	0.488424	−	0.103818i
$22$	1.48044	+	0.659135i	0.315631	+	0.140528i
$23$	−5.55369	+	4.03499i	−1.15802	+	0.841354i	−0.989527	−	0.144348i	$-0.953891\pi$
$23$	−5.55369	+	4.03499i	−1.15802	+	0.841354i	−0.168497	+	0.985702i	$0.553891\pi$
$24$	−3.07738	+	1.37014i	−0.628167	+	0.279678i
$25$		0			0
$26$	−1.31105	−	2.27080i	−0.257118	−	0.445341i
$27$	1.41421	+	1.02749i	0.272166	+	0.197740i
$28$	−1.81359	−	0.385489i	−0.342735	−	0.0728507i
$29$	−1.14412	+	3.52125i	−0.212458	+	0.653879i	0.786866	+	0.617124i	$0.211702\pi$
$29$	−1.14412	+	3.52125i	−0.212458	+	0.653879i	−0.999324	+	0.0367555i	$0.988298\pi$
$30$	−1.95440			−0.356822
$31$		0			0
$31$		0			0
$32$	4.14590			0.732898
$33$	3.00000	−	9.23305i	0.522233	−	1.60727i
$34$	−0.201822	−	0.0428986i	−0.0346122	−	0.00735705i
$35$	−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	$-0.946725\pi$
$37$	−2.12132	+	3.67423i	−0.348743	+	0.604040i	0.637284	+	0.770629i	$0.280058\pi$
$38$	0.348943	−	0.155360i	0.0566061	−	0.0252027i
$39$	−12.7082	+	9.23305i	−2.03494	+	1.47847i
$40$	3.00721	+	1.33889i	0.475481	+	0.211698i
$41$	−7.30885	+	1.55354i	−1.14145	+	0.242623i	−0.739577	−	0.673072i	$-0.764974\pi$
$41$	−7.30885	+	1.55354i	−1.14145	+	0.242623i	−0.401874	+	0.915695i	$0.631641\pi$
$42$	0.0913612	−	0.869244i	0.0140973	−	0.134127i
$43$	−0.138062	−	0.153334i	−0.0210543	−	0.0233832i	0.732526	−	0.680739i	$-0.238341\pi$
$43$	−0.138062	−	0.153334i	−0.0210543	−	0.0233832i	−0.753580	+	0.657356i	$0.771675\pi$
$44$	−5.26357	+	5.84579i	−0.793514	+	0.881286i
$45$	0.522642	+	4.97261i	0.0779109	+	0.741273i
$46$	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	$0.812828\pi$
$48$	−0.752457	−	7.15915i	−0.108608	−	1.03333i
$49$	−4.01478	+	4.45887i	−0.573541	+	0.636981i
$50$		0			0
$51$	−0.129204	+	1.22930i	−0.0180922	+	0.172136i
$52$	12.4498	−	2.64628i	1.72647	−	0.366974i
$53$	4.79081	+	2.13301i	0.658068	+	0.292991i	0.708473	−	0.705738i	$-0.249384\pi$
$53$	4.79081	+	2.13301i	0.658068	+	0.292991i	−0.0504047	+	0.998729i	$0.516051\pi$
$54$	0.540182	−	0.392465i	0.0735094	−	0.0534077i
$55$	−8.66665	+	3.85864i	−1.16861	+	0.520299i
$56$	−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
$59$	5.81438	+	1.23588i	0.756967	+	0.160898i	0.570200	−	0.821506i	$-0.306866\pi$
$59$	5.81438	+	1.23588i	0.756967	+	0.160898i	0.186767	+	0.982404i	$0.440199\pi$
$60$	2.93159	−	9.02251i	0.378467	−	1.16480i
$61$	4.44897			0.569632			0.284816	−	0.958582i	$-0.408067\pi$
$61$	4.44897			0.569632			0.284816	+	0.958582i	$0.408067\pi$
$62$		0			0
$63$	−2.23607			−0.281718
$64$	−1.45492	+	4.47777i	−0.181864	+	0.559721i
$65$	15.0146	+	3.19145i	1.86233	+	0.395850i
$66$	−3.00000	−	2.17963i	−0.369274	−	0.268294i
$67$	−3.00000	−	5.19615i	−0.366508	−	0.634811i	0.622509	−	0.782613i	$-0.286114\pi$
$67$	−3.00000	−	5.19615i	−0.366508	−	0.634811i	−0.989017	+	0.147802i	$0.952780\pi$
$68$	0.500776	−	0.867369i	0.0607280	−	0.105184i
$69$	14.3502	−	6.38910i	1.72756	−	0.769158i
$70$	−0.690983	+	0.502029i	−0.0825883	+	0.0600039i
$71$	6.82614	+	3.03919i	0.810113	+	0.360686i	0.769626	−	0.638494i	$-0.220442\pi$
$71$	6.82614	+	3.03919i	0.810113	+	0.360686i	0.0404868	+	0.999180i	$0.487109\pi$
$72$	3.21986	−	0.684403i	0.379464	−	0.0806577i
$73$	−0.443477	+	4.21940i	−0.0519050	+	0.493843i	0.937429	+	0.348177i	$0.113199\pi$
$73$	−0.443477	+	4.21940i	−0.0519050	+	0.493843i	−0.989334	+	0.145666i	$0.953467\pi$
$74$	1.08436	+	1.20430i	0.126054	+	0.139997i
$75$		0			0
$76$	0.193806	+	1.84395i	0.0222311	+	0.211515i
$77$	−1.31105	−	4.03499i	−0.149408	−	0.459830i
$78$	1.85410	+	5.70634i	0.209936	+	0.646116i
$79$	1.16104	+	11.0465i	0.130627	+	1.24283i	0.841790	+	0.539805i	$0.181502\pi$
$79$	1.16104	+	11.0465i	0.130627	+	1.24283i	−0.711163	+	0.703027i	$0.751831\pi$
$80$	−4.70696	+	5.22761i	−0.526254	+	0.584464i
$81$	−7.16519	−	7.95775i	−0.796132	−	0.884194i
$82$	−0.298335	+	2.83847i	−0.0329456	+	0.313456i
$83$	−3.09317	+	0.657474i	−0.339520	+	0.0721672i	−0.374517	−	0.927220i	$-0.622191\pi$
$83$	−3.09317	+	0.657474i	−0.339520	+	0.0721672i	0.0349966	+	0.999387i	$0.488858\pi$
$84$	3.87585	+	1.72564i	0.422889	+	0.188282i
$85$	0.977198	−	0.709976i	0.105992	−	0.0770077i
$86$	−0.0719978	+	0.0320555i	−0.00776372	+	0.00345663i
$87$	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	0.810086	−	0.586311i	$-0.199420\pi$
$89$	4.74342	+	3.44629i	0.502801	+	0.365306i	−0.307285	+	0.951618i	$0.599420\pi$
$90$	1.86810	+	0.397076i	0.196915	+	0.0418555i
$91$	−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
$96$	−9.27952	−	1.97242i	−0.947087	−	0.201310i
$97$	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	$0.264515\pi$
$102$	0.431318	+	0.192035i	0.0427068	+	0.0190143i
$103$	2.64902	−	0.563067i	0.261016	−	0.0554807i	−0.0755448	−	0.997142i	$-0.524070\pi$
$103$	2.64902	−	0.563067i	0.261016	−	0.0554807i	0.336561	+	0.941662i	$0.390736\pi$
$104$	1.05635	−	10.0505i	0.103583	−	0.985529i
$105$	3.42372	+	3.80243i	0.334121	+	0.371079i
$106$	1.34034	−	1.48860i	0.130185	−	0.144585i
$107$	0.781051	+	7.43120i	0.0755070	+	0.718401i	0.965142	+	0.261728i	$0.0842924\pi$
$107$	0.781051	+	7.43120i	0.0755070	+	0.718401i	−0.889635	+	0.456673i	$0.849041\pi$
$108$	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	$-0.348782\pi$
$110$	0.378774	+	3.60380i	0.0361147	+	0.343609i
$111$	6.49606	−	7.21460i	0.616578	−	0.684780i
$112$	−2.10502	−	2.33786i	−0.198905	−	0.220907i
$113$	1.48807	−	14.1581i	0.139986	−	1.33188i	−0.668653	−	0.743575i	$-0.733129\pi$
$113$	1.48807	−	14.1581i	0.139986	−	1.33188i	0.808639	−	0.588305i	$-0.200205\pi$
$114$	−0.854932	+	0.181721i	−0.0800718	+	0.0170198i
$115$	−14.0229	−	6.24341i	−1.30765	−	0.582201i
$116$	−5.55369	+	4.03499i	−0.515647	+	0.374640i
$117$	14.0229	−	6.24341i	1.29642	−	0.577204i
$118$	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
$121$	−6.84703	−	1.45538i	−0.622458	−	0.132307i
$122$	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
$127$	−9.27952	−	1.97242i	−0.823425	−	0.175024i	−0.223115	−	0.974792i	$-0.571623\pi$
$127$	−9.27952	−	1.97242i	−0.823425	−	0.175024i	−0.600309	+	0.799768i	$0.704956\pi$
$128$	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
$131$	−17.7378	+	7.89736i	−1.54976	+	0.689996i	−0.990310	−	0.138871i	$-0.955653\pi$
$131$	−17.7378	+	7.89736i	−1.54976	+	0.689996i	−0.559446	+	0.828867i	$0.688986\pi$
$132$	14.5623	−	10.5801i	1.26749	−	0.920883i
$133$	−0.913545	−	0.406737i	−0.0792144	−	0.0352685i
$134$	−2.24171	+	0.476491i	−0.193655	+	0.0411626i
$135$	−0.408580	+	3.88738i	−0.0351650	+	0.334572i
$136$	−0.532106	−	0.590964i	−0.0456278	−	0.0506748i
$137$	4.59341	−	5.10149i	0.392441	−	0.435850i	−0.514253	−	0.857638i	$-0.671931\pi$
$137$	4.59341	−	5.10149i	0.392441	−	0.435850i	0.906694	+	0.421788i	$0.138597\pi$
$138$	−0.627171	−	5.96713i	−0.0533883	−	0.507956i
$139$	0.309496	+	0.952532i	0.0262511	+	0.0807927i	0.963324	−	0.268342i	$-0.0864756\pi$
$139$	0.309496	+	0.952532i	0.0262511	+	0.0807927i	−0.937073	+	0.349134i	$0.886476\pi$
$140$	−1.28115	−	3.94298i	−0.108277	−	0.333243i
$141$	−0.886953	−	8.43880i	−0.0746950	−	0.710675i
$142$	1.90977	−	2.12101i	0.160264	−	0.177991i
$143$	19.4882	+	21.6438i	1.62968	+	1.80995i
$144$	−0.735299	+	6.99591i	−0.0612749	+	0.582992i
$145$	−8.09804	+	1.72129i	−0.672505	+	0.142945i
$146$	1.48044	+	0.659135i	0.122522	+	0.0545504i
$147$	11.1074	−	8.06998i	0.916121	−	0.665601i
$148$	−7.18621	+	3.19951i	−0.590703	+	0.262998i
$149$	−6.70820	+	11.6190i	−0.549557	+	0.951861i	0.448747	+	0.893659i	$0.351870\pi$
$149$	−6.70820	+	11.6190i	−0.549557	+	0.951861i	−0.998305	+	0.0582028i	$0.981463\pi$
$150$		0			0
$151$	−2.45517	−	1.78379i	−0.199799	−	0.145162i	0.483387	−	0.875407i	$-0.339406\pi$
$151$	−2.45517	−	1.78379i	−0.199799	−	0.145162i	−0.683186	+	0.730244i	$0.739406\pi$
$152$	1.43997	+	0.306074i	0.116797	+	0.0248259i
$153$	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	$0.160161\pi$
$158$	4.14993	+	0.882095i	0.330151	+	0.0701757i
$159$	−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
$162$	−3.73656	+	1.66362i	−0.293572	+	0.130706i
$163$	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	$0.138359\pi$
$164$	−12.6564	−	5.63497i	−0.988295	−	0.440017i
$165$	21.2338	−	4.51339i	1.65305	−	0.351367i
$166$	−0.126258	+	1.20127i	−0.00979953	+	0.0932363i
$167$	−4.95486	−	5.50293i	−0.383418	−	0.425829i	0.520282	−	0.853994i	$-0.325827\pi$
$167$	−4.95486	−	5.50293i	−0.383418	−	0.425829i	−0.903700	+	0.428165i	$0.859160\pi$
$168$	2.25404	−	2.50336i	0.173903	−	0.193139i
$169$	−3.56699	−	33.9377i	−0.274384	−	2.61059i
$170$	−0.142571	−	0.438789i	−0.0109347	−	0.0336536i
$171$	0.690983	+	2.12663i	0.0528408	+	0.162627i
$172$	−0.0399883	−	0.380463i	−0.00304908	−	0.0290100i
$173$	12.0444	−	13.3766i	0.915715	−	1.01700i	−0.0840739	−	0.996460i	$-0.526793\pi$
$173$	12.0444	−	13.3766i	0.915715	−	1.01700i	0.999789	−	0.0205451i	$-0.00654016\pi$
$174$	−2.16535	−	2.40487i	−0.164155	−	0.182313i
$175$		0			0
$176$	−13.0553	+	2.77498i	−0.984077	+	0.209172i
$177$	−12.4260	−	5.53241i	−0.933996	−	0.415842i
$178$	1.81182	−	1.31637i	0.135802	−	0.0986659i
$179$	15.0099	−	6.68284i	1.12189	−	0.499499i	0.239917	−	0.970793i	$-0.422880\pi$
$179$	15.0099	−	6.68284i	1.12189	−	0.499499i	0.881976	+	0.471295i	$0.156213\pi$
$180$	−4.63525	+	8.02850i	−0.345492	+	0.598409i
$181$	−9.08922	−	15.7430i	−0.675597	−	1.17017i	−0.976294	−	0.216448i	$-0.930553\pi$
$181$	−9.08922	−	15.7430i	−0.675597	−	1.17017i	0.300698	−	0.953720i	$-0.402781\pi$
$182$	2.12132	+	1.54123i	0.157243	+	0.114244i
$183$	−9.95788	−	2.11661i	−0.736107	−	0.156464i
$184$	−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
$189$	−1.70986	−	0.363443i	−0.124374	−	0.0264366i
$190$	0.690983	+	0.502029i	0.0501292	+	0.0364210i
$191$	−7.11803	−	12.3288i	−0.515043	−	0.892080i	−0.999848	−	0.0174580i	$-0.994443\pi$
$191$	−7.11803	−	12.3288i	−0.515043	−	0.892080i	0.484805	−	0.874622i	$-0.338891\pi$
$192$	5.38676	−	9.33015i	0.388756	−	0.673345i
$193$	−6.66139	+	2.96584i	−0.479497	+	0.213486i	−0.632229	−	0.774782i	$-0.717860\pi$
$193$	−6.66139	+	2.96584i	−0.479497	+	0.213486i	0.152732	+	0.988268i	$0.451193\pi$
$194$	2.16312	−	1.57160i	0.155303	−	0.112834i
$195$	−32.0879	−	14.2865i	−2.29786	−	1.02308i
$196$	−10.8815	+	2.31294i	−0.777251	+	0.165210i
$197$	0.774025	−	7.36435i	0.0551470	−	0.524688i	−0.931723	−	0.363170i	$-0.881694\pi$
$197$	0.774025	−	7.36435i	0.0551470	−	0.524688i	0.986870	−	0.161518i	$-0.0516390\pi$
$198$	2.42469	+	2.69290i	0.172315	+	0.191376i
$199$	−9.85698	+	10.9473i	−0.698743	+	0.776032i	−0.983175	−	0.182664i	$-0.941528\pi$
$199$	−9.85698	+	10.9473i	−0.698743	+	0.776032i	0.284433	+	0.958696i	$0.408195\pi$
$200$		0			0
$201$	4.24264	+	13.0575i	0.299253	+	0.921005i
$202$	−0.263932	−	0.812299i	−0.0185702	−	0.0571532i
$203$	−0.387012	−	3.68218i	−0.0271629	−	0.258438i
$204$	−1.53351	+	1.70314i	−0.107367	+	0.119243i
$205$	−11.1800	−	12.4166i	−0.780843	−	0.867214i
$206$	0.108129	−	1.02878i	0.00753368	−	0.0716782i
$207$	−15.0146	+	3.19145i	−1.04359	+	0.221821i
$208$	19.7287	+	8.78379i	1.36794	+	0.609046i
$209$	−3.43237	+	2.49376i	−0.237422	+	0.172497i
$210$	1.78543	−	0.794924i	0.123206	−	0.0548550i
$211$	2.50000	−	4.33013i	0.172107	−	0.298098i	−0.767049	−	0.641588i	$-0.778276\pi$
$211$	2.50000	−	4.33013i	0.172107	−	0.298098i	0.939156	+	0.343490i	$0.111609\pi$
$212$	4.86163	+	8.42060i	0.333898	+	0.578329i
$213$	−13.8326	−	10.0500i	−0.947797	−	0.688615i
$214$	2.79173	+	0.593401i	0.190839	+	0.0405641i
$215$	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
$220$	−17.2052	−	3.65707i	−1.15997	−	0.246560i
$221$	−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	−0.226900	−	0.973918i	$-0.572859\pi$
$223$	10.9010	−	18.8812i	0.729988	−	1.26438i	0.956888	−	0.290458i	$-0.0938077\pi$
$224$	−3.78747	+	1.68629i	−0.253061	+	0.112670i
$225$		0			0
$226$	−4.96758	−	2.21171i	−0.330439	−	0.147121i
$227$	−15.3649	+	3.26592i	−1.01981	+	0.216767i	−0.687330	−	0.726345i	$-0.741218\pi$
$227$	−15.3649	+	3.26592i	−1.01981	+	0.216767i	−0.332477	+	0.943112i	$0.607884\pi$
$228$	0.443477	−	4.21940i	0.0293700	−	0.279437i
$229$	2.83888	+	3.15290i	0.187599	+	0.208349i	0.829606	−	0.558349i	$-0.188565\pi$
$229$	2.83888	+	3.15290i	0.187599	+	0.208349i	−0.642008	+	0.766698i	$0.721898\pi$
$230$	−3.92324	+	4.35720i	−0.258691	+	0.287305i
$231$	1.01478	+	9.65502i	0.0667679	+	0.635254i
$232$	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	$0.947385\pi$
$234$	−0.612870	−	5.83107i	−0.0400645	−	0.381189i
$235$	−5.54829	+	6.16201i	−0.361931	+	0.401965i
$236$	7.37468	+	8.19041i	0.480051	+	0.533150i
$237$	2.65674	−	25.2772i	0.172574	−	1.64193i
$238$	0.201822	−	0.0428986i	0.0130822	−	0.00278070i
$239$	−14.9379	−	6.65078i	−0.966253	−	0.430203i	−0.137922	−	0.990443i	$-0.544042\pi$
$239$	−14.9379	−	6.65078i	−0.966253	−	0.430203i	−0.828331	+	0.560240i	$0.810709\pi$
$240$	13.0224	−	9.46130i	0.840590	−	0.610725i
$241$	13.4575	−	5.99165i	0.866871	−	0.385956i	0.0753935	−	0.997154i	$-0.475979\pi$
$241$	13.4575	−	5.99165i	0.866871	−	0.385956i	0.791478	+	0.611198i	$0.209312\pi$
$242$	−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
$245$	−13.1232	−	2.78943i	−0.838412	−	0.178210i
$246$	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
$251$	23.2374	+	4.93925i	1.46673	+	0.311763i	0.870944	−	0.491382i	$-0.163508\pi$
$251$	23.2374	+	4.93925i	1.46673	+	0.311763i	0.595784	+	0.803144i	$0.296841\pi$
$252$	−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
$255$	−2.52498	+	1.12419i	−0.158120	+	0.0703997i
$256$	−4.50000	+	3.26944i	−0.281250	+	0.204340i
$257$	21.8742	+	9.73901i	1.36447	+	0.607503i	0.952736	−	0.303799i	$-0.0982553\pi$
$257$	21.8742	+	9.73901i	1.36447	+	0.607503i	0.411738	+	0.911302i	$0.364922\pi$
$258$	0.176399	−	0.0374948i	0.0109821	−	0.00233432i
$259$	0.443477	−	4.21940i	0.0275563	−	0.262181i
$260$	19.0438	+	21.1503i	1.18105	+	1.31168i
$261$	−5.53970	+	6.15246i	−0.342899	+	0.380828i
$262$	0.775226	+	7.37578i	0.0478936	+	0.455677i
$263$	0.834626	+	2.56872i	0.0514653	+	0.158394i	0.973486	−	0.228747i	$-0.0734628\pi$
$263$	0.834626	+	2.56872i	0.0514653	+	0.158394i	−0.922021	+	0.387141i	$0.873463\pi$
$264$	−4.41641	−	13.5923i	−0.271811	−	0.836549i
$265$	1.22574	+	11.6621i	0.0752966	+	0.716399i
$266$	−0.255585	+	0.283856i	−0.0156709	+	0.0174043i
$267$	−8.97733	−	9.97033i	−0.549404	−	0.610175i
$268$	1.16284	−	11.0637i	0.0710317	−	0.675821i
$269$	−14.4862	+	3.07914i	−0.883240	+	0.187738i	−0.627135	−	0.778911i	$-0.715773\pi$
$269$	−14.4862	+	3.07914i	−0.883240	+	0.187738i	−0.256105	+	0.966649i	$0.582439\pi$
$270$	1.36395	+	0.607268i	0.0830071	+	0.0369572i
$271$	22.7155	−	16.5038i	1.37987	−	1.00253i	0.382978	−	0.923757i	$-0.374899\pi$
$271$	22.7155	−	16.5038i	1.37987	−	1.00253i	0.996892	−	0.0787769i	$-0.0251015\pi$
$272$	1.55244	−	0.691190i	0.0941304	−	0.0419096i
$273$	7.85410	−	13.6037i	0.475352	−	0.823334i
$274$	−1.31105	−	2.27080i	−0.0792033	−	0.137184i
$275$		0			0
$276$	28.4882	+	6.05535i	1.71479	+	0.364489i
$277$	6.05446	−	18.6337i	0.363778	−	1.11959i	−0.586966	−	0.809612i	$-0.699678\pi$
$277$	6.05446	−	18.6337i	0.363778	−	1.11959i	0.950743	−	0.309980i	$-0.100322\pi$
$278$	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	$0.715030\pi$
$282$	−3.17026	−	0.673860i	−0.188786	−	0.0401278i
$283$	−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
$286$	10.1628	−	4.52479i	0.600941	−	0.267556i
$287$	6.04508	−	4.39201i	0.356830	−	0.259252i
$288$	8.46903	+	3.77066i	0.499043	+	0.222188i
$289$	16.3431	−	3.47383i	0.961358	−	0.204343i
$290$	−0.330548	+	3.14495i	−0.0194104	+	0.184678i
$291$	−10.7179	−	11.9035i	−0.628297	−	0.697795i
$292$	−5.26357	+	5.84579i	−0.308027	+	0.342099i
$293$	1.64195	+	15.6222i	0.0959240	+	0.912656i	0.931613	+	0.363453i	$0.118402\pi$
$293$	1.64195	+	15.6222i	0.0959240	+	0.912656i	−0.835689	+	0.549203i	$0.814931\pi$
$294$	−1.62054	−	4.98752i	−0.0945121	−	0.290878i
$295$	4.10739	+	12.6412i	0.239142	+	0.736002i
$296$	0.652858	+	6.21153i	0.0379466	+	0.361038i
$297$	−4.96255	+	5.51147i	−0.287956	+	0.319808i
$298$	3.42903	+	3.80833i	0.198639	+	0.220611i
$299$	−4.92586	+	46.8665i	−0.284870	+	2.71036i
$300$		0			0
$301$	0.188493	+	0.0839224i	0.0108645	+	0.00483720i
$302$	−0.937792	+	0.681346i	−0.0539639	+	0.0392070i
$303$	−4.67431	+	2.08114i	−0.268532	+	0.119558i
$304$	−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
$307$	15.7723	+	3.35250i	0.900170	+	0.191337i	0.634679	−	0.772776i	$-0.281133\pi$
$307$	15.7723	+	3.35250i	0.900170	+	0.191337i	0.265491	+	0.964113i	$0.414466\pi$
$308$	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
$313$	20.5478	+	4.36757i	1.16143	+	0.246870i	0.748021	−	0.663675i	$-0.231004\pi$
$313$	20.5478	+	4.36757i	1.16143	+	0.246870i	0.413410	+	0.910545i	$0.364337\pi$
$314$	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
$317$	19.8823	−	8.85219i	1.11670	−	0.497188i	0.236427	−	0.971649i	$-0.424024\pi$
$317$	19.8823	−	8.85219i	1.11670	−	0.497188i	0.880277	+	0.474461i	$0.157357\pi$
$318$	−3.70820	+	2.69417i	−0.207946	+	0.151081i
$319$	−14.3502	−	6.38910i	−0.803455	−	0.357721i
$320$	−10.2978	+	2.18887i	−0.575665	+	0.122361i
$321$	1.78724	−	17.0044i	0.0997538	−	0.949094i
$322$	−1.75452	−	1.94860i	−0.0977758	−	0.108591i
$323$	0.361452	−	0.401433i	0.0201117	−	0.0223363i
$324$	−2.07532	−	19.7453i	−0.115295	−	1.09696i
$325$		0			0
$326$	−1.46556	−	4.51052i	−0.0811698	−	0.249815i
$327$	3.51801	+	33.4716i	0.194546	+	1.85098i
$328$	−7.36044	+	8.17459i	−0.406412	+	0.451366i
$329$	−2.48127	−	2.75573i	−0.136797	−	0.151928i
$330$	0.866729	−	8.24637i	0.0477118	−	0.453948i
$331$	25.0719	−	5.32921i	1.37808	−	0.292920i	0.541470	−	0.840720i	$-0.317868\pi$
$331$	25.0719	−	5.32921i	1.37808	−	0.292920i	0.836609	+	0.547800i	$0.184535\pi$
$332$	−5.35629	−	2.38477i	−0.293964	−	0.130881i
$333$	−7.67501	+	5.57622i	−0.420588	+	0.305575i
$334$	−2.58390	+	1.15042i	−0.141385	+	0.0629485i
$335$	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	0.709437	−	0.704769i	$-0.248949\pi$
$337$	4.74342	+	3.44629i	0.258390	+	0.187732i	−0.451047	+	0.892500i	$0.648949\pi$
$338$	−12.7496	−	2.71001i	−0.693487	−	0.147405i
$339$	−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
$344$	−0.297110	−	0.0631526i	−0.0160191	−	0.00340496i
$345$	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	0.277132	+	0.960832i	$0.410616\pi$
$347$	−12.9192	+	22.3767i	−0.693539	+	1.20124i	−0.970671	+	0.240413i	$0.922717\pi$
$348$	14.3502	−	6.38910i	0.769249	−	0.342492i
$349$	−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
$351$	11.7378	−	2.49494i	0.626516	−	0.133170i
$352$	−1.83861	+	17.4932i	−0.0979982	+	0.932391i
$353$	10.6326	+	11.8087i	0.565917	+	0.628515i	0.956388	−	0.292101i	$-0.0943543\pi$
$353$	10.6326	+	11.8087i	0.565917	+	0.628515i	−0.390470	+	0.920616i	$0.627688\pi$
$354$	−3.47646	+	3.86100i	−0.184772	+	0.205210i
$355$	1.74648	+	16.6167i	0.0926937	+	0.881922i
$356$	3.35931	+	10.3389i	0.178043	+	0.547960i
$357$	−0.381966	−	1.17557i	−0.0202158	−	0.0622178i
$358$	−0.656005	−	6.24147i	−0.0346709	−	0.329872i
$359$	6.53335	−	7.25602i	0.344817	−	0.382958i	−0.545645	−	0.838017i	$-0.683715\pi$
$359$	6.53335	−	7.25602i	0.344817	−	0.382958i	0.890461	+	0.455059i	$0.150382\pi$
$360$	4.92526	+	5.47005i	0.259584	+	0.288297i
$361$	1.88151	−	17.9014i	0.0990270	−	0.942179i
$362$	−6.79182	+	1.44364i	−0.356970	+	0.0758763i
$363$	14.6329	+	6.51499i	0.768029	+	0.341948i
$364$	−10.2971	+	7.48128i	−0.539715	+	0.392126i
$365$	−8.66665	+	3.85864i	−0.453633	+	0.201971i
$366$	−1.94427	+	3.36758i	−0.101629	+	0.176026i
$367$	6.15763	+	10.6653i	0.321426	+	0.556726i	0.980782	−	0.195105i	$-0.0625046\pi$
$367$	6.15763	+	10.6653i	0.321426	+	0.556726i	−0.659357	+	0.751830i	$0.729171\pi$
$368$	−17.4713	−	12.6937i	−0.910756	−	0.661703i
$369$	−16.3431	−	3.47383i	−0.850787	−	0.180840i
$370$	−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
$375$	−25.0243	−	5.31908i	−1.29225	−	0.274676i
$376$	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
$379$	−17.7378	+	7.89736i	−0.911128	+	0.405660i	−0.808118	−	0.589020i	$-0.799514\pi$
$379$	−17.7378	+	7.89736i	−0.911128	+	0.405660i	−0.103010	+	0.994680i	$0.532847\pi$
$380$	−3.35410	+	2.43690i	−0.172062	+	0.125010i
$381$	19.8314	+	8.82952i	1.01599	+	0.452350i
$382$	−5.31887	+	1.13056i	−0.272137	+	0.0578445i
$383$	1.99153	−	18.9481i	0.101762	−	0.968203i	−0.817865	−	0.575410i	$-0.804842\pi$
$383$	1.99153	−	18.9481i	0.101762	−	0.968203i	0.919627	−	0.392793i	$-0.128491\pi$
$384$	−15.4494	−	17.1583i	−0.788400	−	0.875606i
$385$	6.34793	−	7.05009i	0.323520	−	0.359306i
$386$	0.291135	+	2.76996i	0.0148184	+	0.140987i
$387$	−0.142571	−	0.438789i	−0.00724730	−	0.0223049i
$388$	4.01064	+	12.3435i	0.203610	+	0.626646i
$389$	−3.53134	−	33.5984i	−0.179046	−	1.70351i	−0.602932	−	0.797793i	$-0.706001\pi$
$389$	−3.53134	−	33.5984i	−0.179046	−	1.70351i	0.423886	−	0.905716i	$-0.360666\pi$
$390$	−8.97733	+	9.97033i	−0.454585	+	0.504867i
$391$	2.48127	+	2.75573i	0.125483	+	0.139363i
$392$	−0.923281	+	8.78443i	−0.0466327	+	0.443681i
$393$	43.4586	−	9.23741i	2.19220	−	0.465966i
$394$	−2.58390	−	1.15042i	−0.130175	−	0.0579576i
$395$	−20.0934	+	14.5987i	−1.01101	+	0.734542i
$396$	−16.0689	+	7.15432i	−0.807491	+	0.359518i
$397$	−0.645898	+	1.11873i	−0.0324167	+	0.0561474i	−0.881779	−	0.471664i	$-0.843654\pi$
$397$	−0.645898	+	1.11873i	−0.0324167	+	0.0561474i	0.849362	+	0.527811i	$0.176987\pi$
$398$	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	−0.975551	−	0.219772i	$-0.929469\pi$
$401$	−1.14412	+	3.52125i	−0.0571348	+	0.175843i	0.918416	+	0.395615i	$0.129469\pi$
$402$	5.24419			0.261557
$403$		0			0
$404$	4.14590			0.206266
$405$	7.39919	−	22.7724i	0.367669	−	1.13157i
$406$	−1.38331	−	0.294032i	−0.0686525	−	0.0145925i
$407$	−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	$-0.692189\pi$
$409$	8.67656	−	15.0282i	0.429028	−	0.743099i	0.996787	+	0.0800961i	$0.0255227\pi$
$410$	−5.83022	+	2.59578i	−0.287934	+	0.128196i
$411$	−12.7082	+	9.23305i	−0.626849	+	0.455433i
$412$	4.58717	+	2.04234i	0.225994	+	0.100619i
$413$	−5.81438	+	1.23588i	−0.286107	+	0.0608139i
$414$	−0.612870	+	5.83107i	−0.0301209	+	0.286581i
$415$	−4.73147	−	5.25483i	−0.232259	−	0.257949i
$416$	19.0438	−	21.1503i	0.933699	−	1.03698i
$417$	−0.239558	−	2.27924i	−0.0117312	−	0.111615i
$418$	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	$-0.250095\pi$
$420$	0.991644	+	9.43486i	0.0483873	+	0.460374i
$421$	−0.278631	+	0.309451i	−0.0135797	+	0.0150817i	−0.749896	−	0.661555i	$-0.769897\pi$
$421$	−0.278631	+	0.309451i	−0.0135797	+	0.0150817i	0.736317	+	0.676637i	$0.236563\pi$
$422$	−1.27793	−	1.41928i	−0.0622085	−	0.0690895i
$423$	−0.866729	+	8.24637i	−0.0421418	+	0.400952i
$424$	7.55146	−	1.60511i	0.366731	−	0.0779511i
$425$		0			0
$426$	−5.28360	+	3.83876i	−0.255991	+	0.185988i
$427$	−4.06434	+	1.80956i	−0.196687	+	0.0875707i
$428$	−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
$431$	0.109021	+	0.0231730i	0.00525134	+	0.00111621i	0.210537	−	0.977586i	$-0.432479\pi$
$431$	0.109021	+	0.0231730i	0.00525134	+	0.00111621i	−0.205285	+	0.978702i	$0.565812\pi$
$432$	−1.69936	+	5.23008i	−0.0817603	+	0.251632i
$433$	21.5958			1.03783			0.518913	−	0.854827i	$-0.326337\pi$
$433$	21.5958			1.03783			0.518913	+	0.854827i	$0.326337\pi$
$434$		0			0
$435$	18.9443			0.908308
$436$	8.42705	−	25.9358i	0.403583	−	1.24210i
$437$	−6.71473	−	1.42726i	−0.321209	−	0.0682751i
$438$	−3.00000	−	2.17963i	−0.143346	−	0.104147i
$439$	12.5000	+	21.6506i	0.596592	+	1.03333i	0.993320	+	0.115392i	$0.0368124\pi$
$439$	12.5000	+	21.6506i	0.596592	+	1.03333i	−0.396728	+	0.917936i	$0.629854\pi$
$440$	−6.98295	+	12.0948i	−0.332899	+	0.576598i
$441$	−12.2565	+	5.45694i	−0.583643	+	0.259855i
$442$	−1.14590	+	0.832544i	−0.0545048	+	0.0396001i
$443$	21.8742	+	9.73901i	1.03927	+	0.462714i	0.854164	−	0.520003i	$-0.174069\pi$
$443$	21.8742	+	9.73901i	1.03927	+	0.462714i	0.185110	+	0.982718i	$0.440736\pi$
$444$	17.6067	−	3.74241i	0.835575	−	0.177607i
$445$	−1.37042	+	13.0387i	−0.0649641	+	0.618092i
$446$	−5.57229	−	6.18866i	−0.263856	−	0.293041i
$447$	20.5423	−	22.8146i	0.971619	−	1.07909i
$448$	−0.492141	−	4.68241i	−0.0232515	−	0.221223i
$449$	−13.0374	−	40.1250i	−0.615274	−	1.89362i	−0.397421	−	0.917637i	$-0.630095\pi$
$449$	−13.0374	−	40.1250i	−0.615274	−	1.89362i	−0.217853	−	0.975982i	$-0.569905\pi$
$450$		0			0
$451$	−3.31372	−	31.5279i	−0.156037	−	1.48459i
$452$	17.6618	−	19.6154i	0.830740	−	0.922631i
$453$	4.64662	+	5.16060i	0.218317	+	0.242466i
$454$	−0.627171	+	5.96713i	−0.0294346	+	0.280051i
$455$	−15.0146	+	3.19145i	−0.703895	+	0.149617i
$456$	−3.07738	−	1.37014i	−0.144111	−	0.0641625i
$457$	−9.15298	+	6.65003i	−0.428158	+	0.311075i	−0.780912	−	0.624641i	$-0.785245\pi$
$457$	−9.15298	+	6.65003i	−0.428158	+	0.311075i	0.352754	+	0.935716i	$0.385245\pi$
$458$	1.48044	−	0.659135i	0.0691765	−	0.0307993i
$459$	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	$0.0644461\pi$
$461$	31.6378	+	22.9862i	1.47352	+	1.07058i	0.493946	+	0.869492i	$0.335554\pi$
$462$	3.62717	+	0.770979i	0.168751	+	0.0358692i
$463$	4.67966	−	14.4025i	0.217482	−	0.669341i	−0.781486	−	0.623923i	$-0.785538\pi$
$463$	4.67966	−	14.4025i	0.217482	−	0.669341i	0.998968	−	0.0454182i	$-0.0144620\pi$
$464$	−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	$-0.0179589\pi$
$468$	27.8386	+	5.91727i	1.28684	+	0.273526i
$469$	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
$472$	7.99423	−	3.55926i	0.367964	−	0.163828i
$473$	0.708204	−	0.514540i	0.0325633	−	0.0236586i
$474$	−8.86889	−	3.94868i	−0.407361	−	0.181369i
$475$		0			0
$476$	−0.104691	+	0.996065i	−0.00479849	+	0.0456546i
$477$	7.84647	+	8.71439i	0.359265	+	0.399005i
$478$	−4.17922	+	4.64149i	−0.191153	+	0.212297i
$479$	−2.66256	−	25.3326i	−0.121656	−	1.15748i	−0.869615	−	0.493731i	$-0.835633\pi$
$479$	−2.66256	−	25.3326i	−0.121656	−	1.15748i	0.747959	−	0.663745i	$-0.231034\pi$
$480$	−6.55524	−	20.1750i	−0.299204	−	0.920857i
$481$	9.00000	+	27.6992i	0.410365	+	1.26297i
$482$	−0.588156	−	5.59593i	−0.0267898	−	0.254887i
$483$	−10.5108	+	11.6735i	−0.478260	+	0.531161i
$484$	−8.68445	−	9.64506i	−0.394748	−	0.438412i
$485$	−1.63613	+	15.5667i	−0.0742928	+	0.706849i
$486$	7.19546	−	1.52944i	0.326393	−	0.0693769i
$487$	16.9838	+	7.56168i	0.769610	+	0.342653i	0.753698	−	0.657221i	$-0.228268\pi$
$487$	16.9838	+	7.56168i	0.769610	+	0.342653i	0.0159123	+	0.999873i	$0.494935\pi$
$488$	5.29865	−	3.84969i	0.239859	−	0.174267i
$489$	−25.9555	+	11.5561i	−1.17375	+	0.522586i
$490$	−2.56231	+	4.43804i	−0.115753	+	0.200490i
$491$	4.78282	+	8.28409i	0.215846	+	0.373856i	0.953534	−	0.301286i	$-0.0974158\pi$
$491$	4.78282	+	8.28409i	0.215846	+	0.373856i	−0.737688	+	0.675142i	$0.764083\pi$
$492$	25.6471	+	18.6337i	1.15626	+	0.840073i
$493$	1.95630	+	0.415823i	0.0881071	+	0.0187277i
$494$	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
$499$	−17.9830	−	3.82241i	−0.805031	−	0.171115i	−0.213023	−	0.977047i	$-0.568331\pi$
$499$	−17.9830	−	3.82241i	−0.805031	−	0.171115i	−0.592007	+	0.805933i	$0.701664\pi$
$500$	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
$503$	2.63882	−	1.17488i	0.117659	−	0.0523852i	−0.347063	−	0.937842i	$-0.612821\pi$
$503$	2.63882	−	1.17488i	0.117659	−	0.0523852i	0.464722	+	0.885457i	$0.346154\pi$
$504$	−2.66312	+	1.93487i	−0.118625	+	0.0861859i
$505$	4.56773	+	2.03368i	0.203261	+	0.0904977i
$506$	−10.8815	+	2.31294i	−0.483742	+	0.102823i
$507$	−8.16216	+	77.6577i	−0.362494	+	3.44890i
$508$	−11.7697	−	13.0716i	−0.522196	−	0.579958i
$509$	−3.20033	+	3.55433i	−0.141852	+	0.157543i	−0.809884	−	0.586590i	$-0.800470\pi$
$509$	−3.20033	+	3.55433i	−0.141852	+	0.157543i	0.668032	+	0.744132i	$0.267137\pi$
$510$	0.110354	+	1.04994i	0.00488654	+	0.0464923i
$511$	−1.31105	−	4.03499i	−0.0579974	−	0.178497i
$512$	6.89261	+	21.2133i	0.304613	+	0.937503i
$513$	0.182722	+	1.73849i	0.00806739	+	0.0767561i
$514$	6.11980	−	6.79673i	0.269933	−	0.299791i
$515$	4.05207	+	4.50028i	0.178556	+	0.198306i
$516$	−0.0915030	+	0.870593i	−0.00402819	+	0.0383257i
$517$	−15.3888	+	3.27099i	−0.676798	+	0.143858i
$518$	−1.48044	−	0.659135i	−0.0650468	−	0.0289607i
$519$	−33.3221	+	24.2099i	−1.46268	+	1.06270i
$520$	20.6437	−	9.19116i	0.905285	−	0.403059i
$521$	−6.70820	+	11.6190i	−0.293892	+	0.509035i	−0.974726	−	0.223402i	$-0.928284\pi$
$521$	−6.70820	+	11.6190i	−0.293892	+	0.509035i	0.680835	+	0.732437i	$0.261617\pi$
$522$	1.58114	+	2.73861i	0.0692046	+	0.119866i
$523$	−23.5258	−	17.0925i	−1.02871	−	0.747403i	−0.0606612	−	0.998158i	$-0.519321\pi$
$523$	−23.5258	−	17.0925i	−1.02871	−	0.747403i	−0.968050	+	0.250756i	$0.919321\pi$
$524$	−35.2133	−	7.48482i	−1.53830	−	0.326976i
$525$		0			0
$526$	1.03165			0.0449823
$527$		0			0
$528$	30.5410			1.32913
$529$	7.45492	−	22.9439i	0.324127	−	0.997560i
$530$	4.38120	+	0.931252i	0.190307	+	0.0404510i
$531$	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
$534$	−4.68157	+	2.08437i	−0.202591	+	0.0901994i
$535$	−13.5172	+	9.82084i	−0.584400	+	0.424592i
$536$	−8.06918	−	3.59263i	−0.348535	−	0.155178i
$537$	−36.7752	+	7.81680i	−1.58697	+	0.337320i
$538$	−0.591302	+	5.62587i	−0.0254929	+	0.242548i
$539$	−17.0333	−	18.9174i	−0.733675	−	0.814829i
$540$	−4.84939	+	5.38579i	−0.208684	+	0.231768i
$541$	2.90932	+	27.6803i	0.125081	+	1.19007i	0.859414	+	0.511281i	$0.170829\pi$
$541$	2.90932	+	27.6803i	0.125081	+	1.19007i	−0.734332	+	0.678790i	$0.762505\pi$
$542$	−3.31415	−	10.1999i	−0.142355	−	0.438124i
$543$	12.8541	+	39.5609i	0.551622	+	1.69772i
$544$	−0.234095	−	2.22727i	−0.0100368	−	0.0954934i
$545$	22.0067	−	24.4410i	0.942665	−	1.04694i
$546$	−4.01478	−	4.45887i	−0.171817	−	0.190822i
$547$	2.55221	−	24.2827i	0.109125	−	1.03825i	−0.793720	−	0.608284i	$-0.791858\pi$
$547$	2.55221	−	24.2827i	0.109125	−	1.03825i	0.902844	−	0.429968i	$-0.141475\pi$
$548$	12.4498	−	2.64628i	0.531829	−	0.113044i
$549$	9.08814	+	4.04630i	0.387872	+	0.172692i
$550$		0			0
$551$	−3.38236	+	1.50593i	−0.144094	+	0.0641546i
$552$	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
$555$	21.2338	+	4.51339i	0.901326	+	0.191583i
$556$	−0.573838	+	1.76609i	−0.0243362	+	0.0748990i
$557$	−23.2951			−0.987046			−0.493523	−	0.869733i	$-0.664291\pi$
$557$	−23.2951			−0.987046			−0.493523	+	0.869733i	$0.664291\pi$
$558$		0			0
$559$	−1.41641			−0.0599077
$560$	2.17376	−	6.69015i	0.0918582	−	0.282711i
$561$	−5.12959	−	1.09033i	−0.216572	−	0.0460337i
$562$	9.69098	+	7.04091i	0.408789	+	0.297003i
$563$	−7.11803	−	12.3288i	−0.299989	−	0.519597i	0.676144	−	0.736770i	$-0.263650\pi$
$563$	−7.11803	−	12.3288i	−0.299989	−	0.519597i	−0.976133	+	0.217173i	$0.930316\pi$
$564$	7.86629	−	13.6248i	0.331230	−	0.573708i
$565$	29.0807	−	12.9476i	1.22344	−	0.544708i
$566$	−7.41641	+	5.38834i	−0.311735	+	0.226489i
$567$	9.78243	+	4.35542i	0.410823	+	0.182910i
$568$	10.7596	−	2.28703i	0.451464	−	0.0959616i
$569$	3.20903	−	30.5319i	0.134529	−	1.27996i	−0.693983	−	0.719991i	$-0.744146\pi$
$569$	3.20903	−	30.5319i	0.134529	−	1.27996i	0.828512	−	0.559971i	$-0.189188\pi$
$570$	−1.30775	−	1.45240i	−0.0547754	−	0.0608343i
$571$	4.59341	−	5.10149i	0.192228	−	0.213491i	−0.639324	−	0.768937i	$-0.720786\pi$
$571$	4.59341	−	5.10149i	0.192228	−	0.213491i	0.831552	+	0.555446i	$0.187453\pi$
$572$	5.64454	+	53.7042i	0.236010	+	2.24548i
$573$	10.0664	+	30.9813i	0.420531	+	1.29426i
$574$	−0.881966	−	2.71441i	−0.0368126	−	0.113297i
$575$		0			0
$576$	−7.04452	+	7.82373i	−0.293522	+	0.325989i
$577$	−20.0739	−	22.2943i	−0.835688	−	0.928126i	0.162595	−	0.986693i	$-0.448013\pi$
$577$	−20.0739	−	22.2943i	−0.835688	−	0.928126i	−0.998283	+	0.0585671i	$0.981347\pi$
$578$	0.667097	−	6.34700i	0.0277476	−	0.264001i
$579$	16.3208	−	3.46909i	0.678269	−	0.144171i
$580$	−14.0229	−	6.24341i	−0.582271	−	0.259244i
$581$	2.55834	−	1.85874i	0.106138	−	0.0771135i
$582$	−5.58928	+	2.48851i	−0.231683	+	0.103152i
$583$	−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
$586$	5.86889	+	1.24747i	0.242441	+	0.0515325i
$587$	12.7279	−	39.1725i	0.525338	−	1.61682i	−0.238310	−	0.971189i	$-0.576593\pi$
$587$	12.7279	−	39.1725i	0.525338	−	1.61682i	0.763647	−	0.645634i	$-0.223407\pi$
$588$	25.4558			1.04978
$589$		0			0
$590$	5.07701			0.209017
$591$	−5.23607	+	16.1150i	−0.215383	+	0.662881i
$592$	−13.0553	−	2.77498i	−0.536568	−	0.114051i
$593$	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
$596$	−22.7248	+	10.1177i	−0.930844	+	0.414438i
$597$	27.2705	−	19.8132i	1.11611	−	0.810900i
$598$	16.4438	+	7.32126i	0.672438	+	0.299389i
$599$	−23.4210	+	4.97829i	−0.956957	+	0.203408i	−0.659817	−	0.751426i	$-0.729366\pi$
$599$	−23.4210	+	4.97829i	−0.956957	+	0.203408i	−0.297140	+	0.954834i	$0.596033\pi$
$600$		0			0
$601$	5.81582	+	6.45913i	0.237232	+	0.263473i	0.849991	−	0.526797i	$-0.176607\pi$
$601$	5.81582	+	6.45913i	0.237232	+	0.263473i	−0.612759	+	0.790270i	$0.709940\pi$
$602$	0.0527351	−	0.0585683i	0.00214932	−	0.00238707i
$603$	−1.40240	−	13.3429i	−0.0571100	−	0.543365i
$604$	−1.73876	−	5.35136i	−0.0707492	−	0.217744i
$605$	−4.83688	−	14.8864i	−0.196647	−	0.605218i
$606$	0.204290	+	1.94369i	0.00829871	+	0.0789570i
$607$	−16.8116	+	18.6712i	−0.682364	+	0.757842i	−0.980465	−	0.196693i	$-0.936980\pi$
$607$	−16.8116	+	18.6712i	−0.682364	+	0.757842i	0.298102	+	0.954534i	$0.403647\pi$
$608$	2.77415	+	3.08100i	0.112507	+	0.124951i
$609$	−0.885579	+	8.42572i	−0.0358855	+	0.341428i
$610$	3.71684	−	0.790039i	0.150490	−	0.0319877i
$611$	23.2551	+	10.3538i	0.940799	+	0.418871i
$612$	1.81182	−	1.31637i	0.0732386	−	0.0532110i
$613$	−34.1286	+	15.1950i	−1.37844	+	0.613722i	−0.956188	−	0.292755i	$-0.905428\pi$
$613$	−34.1286	+	15.1950i	−1.37844	+	0.613722i	−0.422255	+	0.906477i	$0.638761\pi$
$614$	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
$617$	46.0948	+	9.79776i	1.85571	+	0.394443i	0.993664	−	0.112391i	$-0.0358509\pi$
$617$	46.0948	+	9.79776i	1.85571	+	0.394443i	0.862044	+	0.506834i	$0.169184\pi$
$618$	−0.731461	+	2.25121i	−0.0294237	+	0.0905567i
$619$	−21.5958			−0.868007			−0.434003	−	0.900911i	$-0.642899\pi$
$619$	−21.5958			−0.868007			−0.434003	+	0.900911i	$0.642899\pi$
$620$		0			0
$621$	−12.0000			−0.481543
$622$	1.95085	−	6.00410i	0.0782219	−	0.240742i
$623$	−5.73506	−	1.21902i	−0.229770	−	0.0488392i
$624$	−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
$627$	8.86889	−	3.94868i	0.354189	−	0.157695i
$628$	−7.06231	+	5.13107i	−0.281817	+	0.204752i
$629$	2.09366	+	0.932157i	0.0834797	+	0.0371676i
$630$	−1.86810	+	0.397076i	−0.0744267	+	0.0158199i
$631$	0.486612	−	4.62980i	0.0193717	−	0.184309i	−0.980557	−	0.196233i	$-0.937129\pi$
$631$	0.486612	−	4.62980i	0.0193717	−	0.184309i	0.999929	+	0.0119240i	$0.00379562\pi$
$632$	10.9413	+	12.1516i	0.435223	+	0.483364i
$633$	−7.65568	+	8.50249i	−0.304286	+	0.337944i
$634$	−0.868954	−	8.26754i	−0.0345106	−	0.328346i
$635$	−6.55524	−	20.1750i	−0.260137	−	0.800619i
$636$	−6.87539	−	21.1603i	−0.272627	−	0.839059i
$637$	4.30536	+	40.9628i	0.170585	+	1.62300i
$638$	−4.01478	+	4.45887i	−0.158947	+	0.176528i
$639$	11.1800	+	12.4166i	0.442273	+	0.491194i
$640$	−2.35840	+	22.4387i	−0.0932241	+	0.886968i
$641$	8.29986	−	1.76419i	0.327825	−	0.0696813i	−0.0410594	−	0.999157i	$-0.513073\pi$
$641$	8.29986	−	1.76419i	0.327825	−	0.0696813i	0.368884	+	0.929475i	$0.379740\pi$
$642$	−5.96626	−	2.65635i	−0.235470	−	0.104838i
$643$	19.1162	−	13.8888i	0.753871	−	0.547719i	−0.143153	−	0.989701i	$-0.545724\pi$
$643$	19.1162	−	13.8888i	0.753871	−	0.547719i	0.897024	+	0.441981i	$0.145724\pi$
$644$	11.6275	−	5.17691i	0.458189	−	0.203999i
$645$	−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	0.240396	−	0.970675i	$-0.422723\pi$
$647$	−15.4775	−	11.2451i	−0.608485	−	0.442090i	−0.848880	+	0.528585i	$0.822723\pi$
$648$	−15.4195	−	3.27751i	−0.605733	−	0.128753i
$649$	−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	$0.141551\pi$
$654$	12.5745	+	2.67280i	0.491703	+	0.104515i
$655$	−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
$658$	−1.29395	+	0.576105i	−0.0504435	+	0.0224589i
$659$	−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	$0.929045\pi$
$660$	36.7695	+	16.3708i	1.43125	+	0.637234i
$661$	44.8313	−	9.52918i	1.74373	−	0.370642i	0.777615	−	0.628740i	$-0.216429\pi$
$661$	44.8313	−	9.52918i	1.74373	−	0.370642i	0.966119	+	0.258098i	$0.0830959\pi$
$662$	1.02339	−	9.73695i	0.0397753	−	0.378437i
$663$	5.67776	+	6.30579i	0.220506	+	0.244897i
$664$	−3.11501	+	3.45956i	−0.120886	+	0.134257i
$665$	−0.233733	−	2.22382i	−0.00906377	−	0.0862360i
$666$	1.11977	+	3.44629i	0.0433902	+	0.133541i
$667$	−7.85410	−	24.1724i	−0.304112	−	0.935961i
$668$	−1.43512	−	13.6543i	−0.0555265	−	0.528299i
$669$	−33.3820	+	37.0744i	−1.29062	+	1.43338i
$670$	−3.42903	−	3.80833i	−0.132475	−	0.147129i
$671$	−1.97302	+	18.7720i	−0.0761674	+	0.724685i
$672$	9.27952	−	1.97242i	0.357965	−	0.0760879i
$673$	−6.80923	−	3.03166i	−0.262476	−	0.116862i	0.271280	−	0.962501i	$-0.412553\pi$
$673$	−6.80923	−	3.03166i	−0.262476	−	0.116862i	−0.533756	+	0.845639i	$0.679220\pi$
$674$	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	$-0.0330168\pi$
$677$	10.6066	+	18.3712i	0.407645	+	0.706062i	−0.586981	+	0.809601i	$0.699683\pi$
$678$	10.0664	+	7.31368i	0.386599	+	0.280880i
$679$	−6.84703	−	1.45538i	−0.262765	−	0.0558524i
$680$	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
$685$	15.0146	+	3.19145i	0.573678	+	0.121939i
$686$	−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
$689$	32.8876	−	14.6425i	1.25292	−	0.557836i
$690$	10.8541	−	7.88597i	0.413209	−	0.300214i
$691$	−19.7176	−	8.77884i	−0.750093	−	0.333963i	−0.00416636	−	0.999991i	$-0.501326\pi$
$691$	−19.7176	−	8.77884i	−0.750093	−	0.333963i	−0.745926	+	0.666029i	$0.767993\pi$
$692$	32.6445	−	6.93881i	1.24096	−	0.263774i
$693$	0.991644	−	9.43486i	0.0376694	−	0.358401i
$694$	6.60391	+	7.33439i	0.250681	+	0.278410i
$695$	−1.49854	+	1.66430i	−0.0568430	+	0.0631305i
$696$	−1.30369	−	12.4038i	−0.0494164	−	0.470165i
$697$	1.24729	+	3.83876i	0.0472444	+	0.145403i
$698$	0.708204	+	2.17963i	0.0268059	+	0.0825001i
$699$	1.08301	+	10.3041i	0.0409630	+	0.389737i
$700$		0			0
$701$	18.5031	+	20.5498i	0.698853	+	0.776155i	0.983193	−	0.182568i	$-0.0584411\pi$
$701$	18.5031	+	20.5498i	0.698853	+	0.776155i	−0.284340	+	0.958724i	$0.591774\pi$
$702$	0.479116	−	4.55848i	0.0180831	−	0.172049i
$703$	−4.14993	+	0.882095i	−0.156518	+	0.0332688i
$704$	−18.2483	−	8.12465i	−0.687758	−	0.306209i
$705$	15.3500	−	11.1524i	0.578115	−	0.420025i
$706$	5.54478	−	2.46869i	0.208681	−	0.0929105i
$707$	−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	0.322546	−	0.946554i	$-0.395461\pi$
$709$	−12.7279	−	9.24738i	−0.478007	−	0.347293i	−0.800554	+	0.599261i	$0.795461\pi$
$710$	6.24250	+	1.32689i	0.234277	+	0.0497971i
$711$	−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
$716$	29.7979	+	6.33374i	1.11360	+	0.236703i
$717$	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	$-0.779032\pi$
$719$	4.55214	−	7.88453i	0.169766	−	0.294043i	0.938338	+	0.345720i	$0.112365\pi$
$720$	−14.3696	+	6.39776i	−0.535524	+	0.238430i
$721$	−2.19098	+	1.59184i	−0.0815965	+	0.0592833i
$722$	−6.28098	−	2.79647i	−0.233754	−	0.104074i
$723$	−32.9716	+	7.00833i	−1.22623	+	0.260643i
$724$	3.52310	−	33.5201i	0.130935	−	1.24576i
$725$		0			0
$726$	4.09389	−	4.54673i	0.151939	−	0.168745i
$727$	0.374587	+	3.56396i	0.0138927	+	0.132180i	0.999270	−	0.0382074i	$-0.0121648\pi$
$727$	0.374587	+	3.56396i	0.0138927	+	0.132180i	−0.985377	+	0.170387i	$0.945498\pi$
$728$	3.12287	+	9.61121i	0.115741	+	0.356215i
$729$	−3.69098	−	11.3597i	−0.136703	−	0.420729i
$730$	0.378774	+	3.60380i	0.0140191	+	0.133383i
$731$	−0.0745787	+	0.0828281i	−0.00275839	+	0.00306351i
$732$	−12.6301	−	14.0271i	−0.466822	−	0.518458i
$733$	−1.29787	+	12.3484i	−0.0479378	+	0.456098i	0.944053	+	0.329792i	$0.106979\pi$
$733$	−1.29787	+	12.3484i	−0.0479378	+	0.456098i	−0.991991	+	0.126306i	$0.959688\pi$
$734$	4.60122	−	0.978019i	0.169834	−	0.0360993i
$735$	28.0459	+	12.4868i	1.03449	+	0.460584i
$736$	−23.0250	+	16.7287i	−0.848714	+	0.616627i
$737$	23.2551	−	10.3538i	0.856612	−	0.381388i
$738$	−3.19098	+	5.52694i	−0.117462	+	0.203450i
$739$	12.8311	+	22.2241i	0.471999	+	0.817527i	0.999487	−	0.0320362i	$-0.0101992\pi$
$739$	12.8311	+	22.2241i	0.471999	+	0.817527i	−0.527488	+	0.849563i	$0.676866\pi$
$740$	−14.2302	−	10.3389i	−0.523114	−	0.380065i
$741$	−15.3649	−	3.26592i	−0.564445	−	0.119977i
$742$	−0.618993	+	1.90506i	−0.0227239	+	0.0699371i
$743$	−1.69936			−0.0623433			−0.0311717	−	0.999514i	$-0.509924\pi$
$743$	−1.69936			−0.0623433			−0.0311717	+	0.999514i	$0.509924\pi$
$744$		0			0
$745$	−30.0000			−1.09911
$746$	−2.68034	+	8.24924i	−0.0981342	+	0.302026i
$747$	−6.91655	−	1.47016i	−0.253063	−	0.0537903i
$748$	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
$751$	26.9871	−	12.0154i	0.984772	−	0.438449i	0.149785	−	0.988719i	$-0.452142\pi$
$751$	26.9871	−	12.0154i	0.984772	−	0.438449i	0.834987	+	0.550270i	$0.185475\pi$
$752$	−9.43769	+	6.85689i	−0.344157	+	0.250045i
$753$	−49.6610	−	22.1105i	−1.80975	−	0.805751i
$754$	9.49606	−	2.01845i	0.345826	−	0.0735076i
$755$	0.709322	−	6.74875i	0.0258149	−	0.245612i
$756$	−2.16871	−	2.40860i	−0.0788753	−	0.0875999i
$757$	−12.8339	+	14.2535i	−0.466457	+	0.518053i	−0.929770	−	0.368142i	$-0.879994\pi$
$757$	−12.8339	+	14.2535i	−0.466457	+	0.518053i	0.463313	+	0.886195i	$0.346661\pi$
$758$	0.775226	+	7.37578i	0.0281575	+	0.267900i
$759$	20.5942	+	63.3825i	0.747522	+	2.30064i
$760$	1.01722	+	3.13068i	0.0368985	+	0.113562i
$761$	−0.234095	−	2.22727i	−0.00848595	−	0.0807384i	0.989459	−	0.144812i	$-0.0462576\pi$
$761$	−0.234095	−	2.22727i	−0.00848595	−	0.0807384i	−0.997945	+	0.0640731i	$0.979591\pi$
$762$	5.54829	−	6.16201i	0.200994	−	0.223226i
$763$	9.84171	+	10.9303i	0.356294	+	0.395704i
$764$	2.75904	−	26.2505i	0.0998186	−	0.949711i
$765$	2.64189	−	0.561550i	0.0955176	−	0.0203029i
$766$	−6.64823	−	2.95998i	−0.240210	−	0.106949i
$767$	33.0126	−	23.9851i	1.19202	−	0.866051i
$768$	11.6275	−	5.17691i	0.419573	−	0.186806i
$769$	−6.93769	+	12.0164i	−0.250180	+	0.433324i	−0.963575	−	0.267438i	$-0.913823\pi$
$769$	−6.93769	+	12.0164i	−0.250180	+	0.433324i	0.713395	+	0.700762i	$0.247156\pi$
$770$	−1.81182	−	3.13817i	−0.0652936	−	0.113092i
$771$	−44.3263	−	32.2050i	−1.59637	−	1.15983i
$772$	−13.2243	−	2.81091i	−0.475953	−	0.101167i
$773$	−8.34271	+	25.6762i	−0.300066	+	0.923510i	0.681406	+	0.731906i	$0.261369\pi$
$773$	−8.34271	+	25.6762i	−0.300066	+	0.923510i	−0.981472	+	0.191604i	$0.938631\pi$
$774$	−0.176228			−0.00633437
$775$		0			0
$776$	10.3050			0.369926
$777$	−3.00000	+	9.23305i	−0.107624	+	0.331234i
$778$	−12.6222	−	2.68292i	−0.452526	−	0.0961875i
$779$	−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
$782$	1.29395	−	0.576105i	0.0462717	−	0.0206015i
$783$	−5.23607	+	3.80423i	−0.187122	+	0.135952i
$784$	−17.2435	−	7.67731i	−0.615840	−	0.274190i
$785$	−10.2978	+	2.18887i	−0.367544	+	0.0781240i
$786$	1.77391	−	16.8776i	0.0632732	−	0.602004i
$787$	−6.09195	−	6.76579i	−0.217155	−	0.241175i	0.624719	−	0.780850i	$-0.285214\pi$
$787$	−6.09195	−	6.76579i	−0.217155	−	0.241175i	−0.841873	+	0.539675i	$0.818547\pi$
$788$	9.18681	−	10.2030i	0.327267	−	0.363466i
$789$	−0.646021	−	6.14648i	−0.0229990	−	0.218821i
$790$	2.93159	+	9.02251i	0.104301	+	0.321007i
$791$	4.39919	+	13.5393i	0.156417	+	0.481402i
$792$	1.45983	+	13.8894i	0.0518730	+	0.493538i
$793$	20.4359	−	22.6964i	0.725701	−	0.805973i
$794$	0.330164	+	0.366684i	0.0117171	+	0.0130131i
$795$	2.80479	−	26.6858i	0.0994758	−	0.946449i
$796$	−26.7160	+	5.67866i	−0.946923	+	0.201275i
$797$	4.79081	+	2.13301i	0.169699	+	0.0755549i	0.489828	−	0.871819i	$-0.337060\pi$
$797$	4.79081	+	2.13301i	0.169699	+	0.0755549i	−0.320129	+	0.947374i	$0.603726\pi$
$798$	0.707107	−	0.513743i	0.0250313	−	0.0181863i
$799$	1.82993	−	0.814735i	0.0647381	−	0.0288233i
$800$		0			0
$801$	6.55524	+	11.3540i	0.231618	+	0.401174i
$802$	1.14412	+	0.831254i	0.0404004	+	0.0293526i
$803$	−17.6067	−	3.74241i	−0.621325	−	0.132067i
$804$	−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
$809$	21.5751	+	4.58594i	0.758541	+	0.161233i	0.570917	−	0.821008i	$-0.306588\pi$
$809$	21.5751	+	4.58594i	0.758541	+	0.161233i	0.187624	+	0.982241i	$0.439921\pi$
$810$	−7.39919	−	5.37582i	−0.259981	−	0.188887i
$811$	21.7082	+	37.5997i	0.762278	+	1.32030i	0.941674	+	0.336527i	$0.109252\pi$
$811$	21.7082	+	37.5997i	0.762278	+	1.32030i	−0.179396	+	0.983777i	$0.557414\pi$
$812$	3.43237	−	5.94504i	0.120453	−	0.208630i
$813$	−58.6946	+	26.1325i	−2.05851	+	0.916507i
$814$	−5.56231	+	4.04125i	−0.194959	+	0.141646i
$815$	25.3636	+	11.2926i	0.888449	+	0.395563i
$816$	−3.80357	+	0.808474i	−0.133152	+	0.0283022i
$817$	0.0215675	−	0.205201i	0.000754550	−	0.00717906i
$818$	−4.43520	−	4.92579i	−0.155073	−	0.172226i
$819$	−10.2712	+	11.4073i	−0.358904	+	0.398603i
$820$	−3.23816	−	30.8090i	−0.113081	−	1.07590i
$821$	4.43392	+	13.6462i	0.154745	+	0.476256i	0.998135	−	0.0610460i	$-0.0194436\pi$
$821$	4.43392	+	13.6462i	0.154745	+	0.476256i	−0.843390	+	0.537302i	$0.819444\pi$
$822$	1.85410	+	5.70634i	0.0646692	+	0.199031i
$823$	−1.56138	−	14.8555i	−0.0544262	−	0.517831i	−0.987440	−	0.157992i	$-0.949498\pi$
$823$	−1.56138	−	14.8555i	−0.0544262	−	0.517831i	0.933014	−	0.359840i	$-0.117169\pi$
$824$	2.66772	−	2.96280i	0.0929344	−	0.103214i
$825$		0			0
$826$	−0.237333	+	2.25807i	−0.00825787	+	0.0785684i
$827$	−47.0031	+	9.99081i	−1.63446	+	0.347415i	−0.931479	−	0.363796i	$-0.881480\pi$
$827$	−47.0031	+	9.99081i	−1.63446	+	0.347415i	−0.702979	+	0.711211i	$0.748147\pi$
$828$	−26.0000	−	11.5759i	−0.903561	−	0.402291i
$829$	4.71906	−	3.42860i	0.163900	−	0.119080i	−0.502812	−	0.864396i	$-0.667701\pi$
$829$	4.71906	−	3.42860i	0.163900	−	0.119080i	0.666712	+	0.745316i	$0.267701\pi$
$830$	−2.46740	+	1.09856i	−0.0856448	+	0.0381315i
$831$	−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
$834$	−0.856259	−	0.182003i	−0.0296498	−	0.00630226i
$835$	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	$0.0591374\pi$
$840$	7.36784	+	1.56608i	0.254214	+	0.0540350i
$841$	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
$844$	8.46903	−	3.77066i	0.291516	−	0.129791i
$845$	61.7320	−	44.8509i	2.12365	−	1.54292i
$846$	2.89337	+	1.28821i	0.0994760	+	0.0442896i
$847$	6.84703	−	1.45538i	0.235267	−	0.0500075i
$848$	−1.72448	+	16.4073i	−0.0592188	+	0.563430i
$849$	36.7472	+	40.8119i	1.26116	+	1.40066i
$850$		0			0
$851$	−3.04435	−	28.9651i	−0.104359	−	0.992910i
$852$	−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	$-0.386061\pi$
$854$	0.177631	+	1.69005i	0.00607841	+	0.0578322i
$855$	−3.34565	+	3.71572i	−0.114419	+	0.127075i
$856$	7.36044	+	8.17459i	0.251575	+	0.279402i
$857$	0.627171	−	5.96713i	0.0214237	−	0.203833i	−0.978574	−	0.205895i	$-0.933990\pi$
$857$	0.627171	−	5.96713i	0.0214237	−	0.203833i	0.999998	+	0.00206149i	$0.000656192\pi$
$858$	−24.8996	+	5.29257i	−0.850057	+	0.180685i
$859$	−3.33787	−	1.48611i	−0.113887	−	0.0507056i	0.349002	−	0.937122i	$-0.386520\pi$
$859$	−3.33787	−	1.48611i	−0.113887	−	0.0507056i	−0.462889	+	0.886416i	$0.653187\pi$
$860$	0.692055	−	0.502807i	0.0235989	−	0.0171456i
$861$	−15.6199	+	6.95442i	−0.532324	+	0.237006i
$862$	0.0212862	−	0.0368688i	0.000725012	−	0.00125576i
$863$	−17.6626	−	30.5926i	−0.601243	−	1.04138i	−0.992633	−	0.121158i	$-0.961339\pi$
$863$	−17.6626	−	30.5926i	−0.601243	−	1.04138i	0.391391	−	0.920225i	$-0.371994\pi$
$864$	5.86319	+	4.25985i	0.199470	+	0.144923i
$865$	39.3697	+	8.36828i	1.33861	+	0.284530i
$866$	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
$871$	−40.2884	−	8.56355i	−1.36512	−	0.290165i
$872$	−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
$875$	−10.2137	+	4.54745i	−0.345288	+	0.153732i
$876$	14.5623	−	10.5801i	0.492015	−	0.357470i
$877$	−13.9698	−	6.21973i	−0.471725	−	0.210025i	0.157084	−	0.987585i	$-0.449791\pi$
$877$	−13.9698	−	6.21973i	−0.471725	−	0.210025i	−0.628809	+	0.777560i	$0.716457\pi$
$878$	9.34048	−	1.98538i	0.315226	−	0.0670033i
$879$	3.75719	−	35.7473i	0.126727	−	1.20573i
$880$	−19.9699	−	22.1789i	−0.673187	−	0.747649i
$881$	−33.2382	+	36.9148i	−1.11982	+	1.24369i	−0.153005	+	0.988225i	$0.548895\pi$
$881$	−33.2382	+	36.9148i	−1.11982	+	1.24369i	−0.966819	+	0.255464i	$0.917772\pi$
$882$	0.535668	+	5.09654i	0.0180369	+	0.171609i
$883$	−10.4884	−	32.2799i	−0.352962	−	1.08631i	−0.957182	−	0.289488i	$-0.906515\pi$
$883$	−10.4884	−	32.2799i	−0.352962	−	1.08631i	0.604219	−	0.796818i	$-0.293485\pi$
$884$	−2.12461	−	6.53888i	−0.0714584	−	0.219926i
$885$	−3.17922	−	30.2483i	−0.106868	−	1.01678i
$886$	6.11980	−	6.79673i	0.205599	−	0.228341i
$887$	−12.9548	−	14.3878i	−0.434980	−	0.483095i	0.485304	−	0.874346i	$-0.338709\pi$
$887$	−12.9548	−	14.3878i	−0.434980	−	0.483095i	−0.920284	+	0.391251i	$0.872042\pi$
$888$	1.49390	−	14.2135i	0.0501320	−	0.476974i
$889$	9.27952	−	1.97242i	0.311225	−	0.0661530i
$890$	4.57481	+	2.03684i	0.153348	+	0.0682750i
$891$	36.7545	−	26.7037i	1.23132	−	0.894608i
$892$	36.9285	−	16.4416i	1.23646	−	0.550507i
$893$	−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
$896$	−9.86968	−	2.09786i	−0.329723	−	0.0700847i
$897$	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
$902$	−11.8443	−	2.51759i	−0.394373	−	0.0838265i
$903$	−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
$906$	2.42316	−	1.07886i	0.0805040	−	0.0358427i
$907$	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	$-0.0735318\pi$
$908$	−26.6067	−	11.8460i	−0.882973	−	0.393125i
$909$	4.89074	−	1.03956i	0.162216	−	0.0344800i
$910$	−0.612870	+	5.83107i	−0.0203164	+	0.193298i
$911$	9.49553	+	10.5459i	0.314601	+	0.349400i	0.879619	−	0.475679i	$-0.157798\pi$
$911$	9.49553	+	10.5459i	0.314601	+	0.349400i	−0.565018	+	0.825078i	$0.691131\pi$
$912$	4.81680	−	5.34959i	0.159500	−	0.177143i
$913$	−1.40240	−	13.3429i	−0.0464125	−	0.441586i
$914$	1.33540	+	4.10995i	0.0441712	+	0.135945i
$915$	−7.03444	−	21.6498i	−0.232551	−	0.715720i
$916$	0.822251	+	7.82320i	0.0271679	+	0.258486i
$917$	12.9921	−	14.4292i	0.429037	−	0.476494i
$918$	−0.241342	−	0.268037i	−0.00796547	−	0.00884655i
$919$	−2.56524	+	24.4066i	−0.0846193	+	0.805099i	0.867101	+	0.498132i	$0.165981\pi$
$919$	−2.56524	+	24.4066i	−0.0846193	+	0.805099i	−0.951720	+	0.306967i	$0.900686\pi$
$920$	−22.1035	+	4.69825i	−0.728731	+	0.154897i
$921$	−33.7072	−	15.0074i	−1.11069	−	0.494510i
$922$	12.0846	−	8.77996i	0.397984	−	0.289153i
$923$	46.8596	−	20.8632i	1.54240	−	0.686722i
$924$	−9.00000	+	15.5885i	−0.296078	+	0.512823i
$925$		0			0
$926$	−4.67966	−	3.39997i	−0.153783	−	0.111730i
$927$	5.92340	+	1.25906i	0.194550	+	0.0413528i
$928$	−4.74342	+	14.5987i	−0.155710	+	0.479227i
$929$	23.2951			0.764288			0.382144	−	0.924103i	$-0.375186\pi$
$929$	23.2951			0.764288			0.382144	+	0.924103i	$0.375186\pi$
$930$		0			0
$931$	−6.00000			−0.196642
$932$	2.59424	−	7.98424i	0.0849770	−	0.261532i
$933$	−36.9934	−	7.86318i	−1.21111	−	0.257429i
$934$	−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
$937$	−51.3862	+	22.8786i	−1.67871	+	0.747412i	−0.678800	+	0.734323i	$0.737500\pi$
$937$	−51.3862	+	22.8786i	−1.67871	+	0.747412i	−0.999914	+	0.0130891i	$0.995833\pi$
$938$	1.85410	−	1.34708i	0.0605386	−	0.0439838i
$939$	−43.9131	−	19.5514i	−1.43305	−	0.638035i
$940$	−15.0379	+	3.19640i	−0.490482	+	0.104255i
$941$	−5.31348	+	50.5544i	−0.173215	+	1.64803i	0.470237	+	0.882540i	$0.344168\pi$
$941$	−5.31348	+	50.5544i	−0.173215	+	1.64803i	−0.643452	+	0.765487i	$0.722498\pi$
$942$	−2.75355	−	3.05813i	−0.0897156	−	0.0996393i
$943$	34.3226	−	38.1191i	1.11770	−	1.24133i
$944$	1.95469	+	18.5976i	0.0636197	+	0.605301i
$945$	−1.20788	−	3.71748i	−0.0392924	−	0.120930i
$946$	−0.103326	−	0.318003i	−0.00335940	−	0.0103392i
$947$	−0.234095	−	2.22727i	−0.00760708	−	0.0723765i	0.990060	−	0.140647i	$-0.0449184\pi$
$947$	−0.234095	−	2.22727i	−0.00760708	−	0.0723765i	−0.997667	+	0.0682710i	$0.978252\pi$
$948$	31.5325	−	35.0204i	1.02413	−	1.13741i
$949$	19.4882	+	21.6438i	0.632613	+	0.702588i
$950$		0			0
$951$	−48.7129	+	10.3543i	−1.57963	+	0.335760i
$952$	0.726470	+	0.323445i	0.0235450	+	0.0104829i
$953$	−43.2460	+	31.4200i	−1.40087	+	1.01780i	−0.406303	+	0.913738i	$0.633182\pi$
$953$	−43.2460	+	31.4200i	−1.40087	+	1.01780i	−0.994571	+	0.104057i	$0.966818\pi$
$954$	4.09184	−	1.82180i	0.132478	−	0.0589831i
$955$	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
$958$	−9.51688	−	2.02287i	−0.307476	−	0.0653561i
$959$	−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
$964$	26.7160	+	5.67866i	0.860464	+	0.182897i
$965$	−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	$-0.766806\pi$
$967$	6.45207	−	11.1753i	0.207485	−	0.359374i	0.950922	+	0.309432i	$0.100139\pi$
$968$	−9.41404	+	4.19140i	−0.302579	+	0.134717i
$969$	−1.00000	+	0.726543i	−0.0321246	+	0.0233399i
$970$	5.46183	+	2.43176i	0.175369	+	0.0780792i
$971$	−17.7157	+	3.76558i	−0.568523	+	0.120843i	−0.483200	−	0.875510i	$-0.660526\pi$
$971$	−17.7157	+	3.76558i	−0.568523	+	0.120843i	−0.0853232	+	0.996353i	$0.527192\pi$
$972$	−3.73248	+	35.5122i	−0.119719	+	1.13905i
$973$	−0.670169	−	0.744298i	−0.0214846	−	0.0238611i
$974$	4.75161	−	5.27720i	0.152251	−	0.169092i
$975$		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	$0.662148\pi$
$978$	1.13438	+	10.7929i	0.0362734	+	0.345119i
$979$	−16.6449	+	18.4860i	−0.531973	+	0.590816i
$980$	−16.6449	−	18.4860i	−0.531701	−	0.590514i
$981$	3.43779	−	32.7084i	0.109760	−	1.04430i
$982$	3.57391	−	0.759658i	0.114048	−	0.0242416i
$983$	−2.74489	−	1.22210i	−0.0875484	−	0.0389790i	0.362495	−	0.931986i	$-0.381925\pi$
$983$	−2.74489	−	1.22210i	−0.0875484	−	0.0389790i	−0.450044	+	0.893007i	$0.648592\pi$
$984$	20.3635	−	14.7950i	0.649165	−	0.471646i
$985$	15.1264	−	6.73470i	0.481967	−	0.214586i
$986$	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
$989$	1.38546	+	0.294488i	0.0440549	+	0.00936417i
$990$	−2.50388	+	7.70615i	−0.0795785	+	0.244917i
$991$	−4.44897			−0.141326			−0.0706631	−	0.997500i	$-0.522512\pi$
$991$	−4.44897			−0.141326			−0.0706631	+	0.997500i	$0.522512\pi$
$992$		0			0
$993$	−58.6525			−1.86128
$994$	−0.881966	+	2.71441i	−0.0279743	+	0.0860959i
$995$	−32.2198	−	6.84852i	−1.02144	−	0.217113i
$996$	10.8541	+	7.88597i	0.343925	+	0.249876i
$997$	−24.3328	−	42.1457i	−0.770628	−	1.33477i	−0.937219	−	0.348741i	$-0.886609\pi$
$997$	−24.3328	−	42.1457i	−0.770628	−	1.33477i	0.166591	−	0.986026i	$-0.446724\pi$
$998$	−3.51118	+	6.08154i	−0.111144	+	0.192508i
$999$	−6.77523	+	3.01652i	−0.214359	+	0.0954386i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
961.2.a.h.1.1	✓	4	31.21	odd	30
961.2.a.h.1.2	yes	4	31.10	even	15
961.2.c.h.439.1		8	31.2	even	5
961.2.c.h.439.2		8	31.29	odd	10
961.2.c.h.521.1		8	31.19	even	15
961.2.c.h.521.2		8	31.12	odd	30
961.2.d.h.531.1		8	31.11	odd	30
961.2.d.h.531.2		8	31.20	even	15
961.2.d.h.628.1		8	31.26	odd	6
961.2.d.h.628.2		8	31.5	even	3
961.2.d.j.374.1		8	31.18	even	15
961.2.d.j.374.2		8	31.13	odd	30
961.2.d.j.388.1		8	31.9	even	15
961.2.d.j.388.2		8	31.22	odd	30
961.2.g.i.448.1		16	31.6	odd	6	inner
961.2.g.i.448.2		16	31.25	even	3	inner
961.2.g.i.547.1		16	31.27	odd	10	inner
961.2.g.i.547.2		16	31.4	even	5	inner
961.2.g.i.844.1		16	31.7	even	15	inner
961.2.g.i.844.2		16	31.24	odd	30	inner
961.2.g.i.846.1		16	1.1	even	1	trivial
961.2.g.i.846.2		16	31.30	odd	2	inner
961.2.g.p.235.1		16	31.23	odd	10
961.2.g.p.235.2		16	31.8	even	5
961.2.g.p.338.1		16	31.14	even	15
961.2.g.p.338.2		16	31.17	odd	30
961.2.g.p.732.1		16	31.3	odd	30
961.2.g.p.732.2		16	31.28	even	15
961.2.g.p.816.1		16	31.16	even	5
961.2.g.p.816.2		16	31.15	odd	10
8649.2.a.r.1.3		4	93.41	odd	30
8649.2.a.r.1.4		4	93.83	even	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} +(-2.23824 - 0.475753i) q^{3} +(1.50000 + 1.08981i) q^{4} +(1.11803 + 1.93649i) q^{5} +(-0.437016 + 0.756934i) q^{6} +(-0.913545 + 0.406737i) q^{7} +(1.19098 - 0.865300i) q^{8} +(2.04275 + 0.909491i) q^{9} +(0.835438 - 0.177578i) q^{10} +(-0.443477 + 4.21940i) q^{11} +(-2.83888 - 3.15290i) q^{12} +(4.59341 - 5.10149i) q^{13} +(0.0399263 + 0.379874i) q^{14} +(-1.58114 - 4.86624i) q^{15} +(0.972136 + 2.99193i) q^{16} +(-0.0564643 - 0.537222i) q^{17} +(0.571506 - 0.634721i) q^{18} +(0.669131 + 0.743145i) q^{19} +(-0.433364 + 4.12319i) q^{20} +(2.23824 - 0.475753i) q^{21} +(1.48044 + 0.659135i) q^{22} +(-5.55369 + 4.03499i) q^{23} +(-3.07738 + 1.37014i) q^{24} +(-1.31105 - 2.27080i) q^{26} +(1.41421 + 1.02749i) q^{27} +(-1.81359 - 0.385489i) q^{28} +(-1.14412 + 3.52125i) q^{29} -1.95440 q^{30} +4.14590 q^{32} +(3.00000 - 9.23305i) q^{33} +(-0.201822 - 0.0428986i) q^{34} +(-1.80902 - 1.31433i) q^{35} +(2.07295 + 3.59045i) q^{36} +(-2.12132 + 3.67423i) q^{37} +(0.348943 - 0.155360i) q^{38} +(-12.7082 + 9.23305i) q^{39} +(3.00721 + 1.33889i) q^{40} +(-7.30885 + 1.55354i) q^{41} +(0.0913612 - 0.869244i) q^{42} +(-0.138062 - 0.153334i) q^{43} +(-5.26357 + 5.84579i) q^{44} +(0.522642 + 4.97261i) q^{45} +(0.810272 + 2.49376i) q^{46} +(1.14590 + 3.52671i) q^{47} +(-0.752457 - 7.15915i) q^{48} +(-4.01478 + 4.45887i) q^{49} +(-0.129204 + 1.22930i) q^{51} +(12.4498 - 2.64628i) q^{52} +(4.79081 + 2.13301i) q^{53} +(0.540182 - 0.392465i) q^{54} +(-8.66665 + 3.85864i) q^{55} +(-0.736068 + 1.27491i) q^{56} +(-1.14412 - 1.98168i) q^{57} +(1.14412 + 0.831254i) q^{58} +(5.81438 + 1.23588i) q^{59} +(2.93159 - 9.02251i) q^{60} +4.44897 q^{61} -2.23607 q^{63} +(-1.45492 + 4.47777i) q^{64} +(15.0146 + 3.19145i) q^{65} +(-3.00000 - 2.17963i) q^{66} +(-3.00000 - 5.19615i) q^{67} +(0.500776 - 0.867369i) q^{68} +(14.3502 - 6.38910i) q^{69} +(-0.690983 + 0.502029i) q^{70} +(6.82614 + 3.03919i) q^{71} +(3.21986 - 0.684403i) q^{72} +(-0.443477 + 4.21940i) q^{73} +(1.08436 + 1.20430i) q^{74} +(0.193806 + 1.84395i) q^{76} +(-1.31105 - 4.03499i) q^{77} +(1.85410 + 5.70634i) q^{78} +(1.16104 + 11.0465i) q^{79} +(-4.70696 + 5.22761i) q^{80} +(-7.16519 - 7.95775i) q^{81} +(-0.298335 + 2.83847i) q^{82} +(-3.09317 + 0.657474i) q^{83} +(3.87585 + 1.72564i) q^{84} +(0.977198 - 0.709976i) q^{85} +(-0.0719978 + 0.0320555i) q^{86} +(4.23607 - 7.33708i) q^{87} +(3.12287 + 5.40897i) q^{88} +(4.74342 + 3.44629i) q^{89} +(1.86810 + 0.397076i) q^{90} +(-2.12132 + 6.52875i) q^{91} -12.7279 q^{92} +1.41641 q^{94} +(-0.690983 + 2.12663i) q^{95} +(-9.27952 - 1.97242i) 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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