LMFDB - Embedded newform 1000.2.o.a.549.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1000,2,Mod(149,1000)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1000.149"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1000, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 5, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1000 = 2^{3} \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1000.o (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [112] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.98504020213$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			549.20
Character	$\chi$	$=$	1000.549
Dual form			1000.2.o.a.949.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.927056 - 1.06797i) q^{2} +(-0.305611 - 0.940574i) q^{3} +(-0.281133 - 1.98014i) q^{4} +(-1.28783 - 0.545581i) q^{6} +3.68114i q^{7} +(-2.37537 - 1.53546i) q^{8} +(1.63577 - 1.18846i) q^{9} +(2.38116 - 3.27739i) q^{11} +(-1.77655 + 0.869580i) q^{12} +(4.97551 - 3.61492i) q^{13} +(3.93136 + 3.41262i) q^{14} +(-3.84193 + 1.11337i) q^{16} +(-3.70129 - 1.20262i) q^{17} +(0.247211 - 2.84872i) q^{18} +(-3.35127 - 1.08889i) q^{19} +(3.46238 - 1.12500i) q^{21} +(-1.29269 - 5.58134i) q^{22} +(-1.50362 + 2.06955i) q^{23} +(-0.718277 + 2.70346i) q^{24} +(0.751941 - 8.66495i) q^{26} +(-4.01804 - 2.91928i) q^{27} +(7.28918 - 1.03489i) q^{28} +(5.85554 - 1.90258i) q^{29} +(1.35546 - 4.17167i) q^{31} +(-2.37264 + 5.13523i) q^{32} +(-3.81033 - 1.23805i) q^{33} +(-4.71567 + 2.83798i) q^{34} +(-2.81318 - 2.90494i) q^{36} +(-2.99215 + 2.17392i) q^{37} +(-4.26972 + 2.56960i) q^{38} +(-4.92068 - 3.57508i) q^{39} +(-3.35481 + 2.43741i) q^{41} +(2.00836 - 4.74067i) q^{42} +1.74279 q^{43} +(-7.15911 - 3.79365i) q^{44} +(0.816288 + 3.52441i) q^{46} +(4.86486 - 1.58069i) q^{47} +(2.22134 + 3.27336i) q^{48} -6.55078 q^{49} +3.84887i q^{51} +(-8.55685 - 8.83595i) q^{52} +(-3.95398 - 12.1691i) q^{53} +(-6.84266 + 1.58483i) q^{54} +(5.65224 - 8.74405i) q^{56} +3.48489i q^{57} +(3.39651 - 8.01736i) q^{58} +(-0.784512 - 1.07979i) q^{59} +(-0.998070 + 1.37373i) q^{61} +(-3.19865 - 5.31497i) q^{62} +(4.37487 + 6.02149i) q^{63} +(3.28472 + 7.29456i) q^{64} +(-4.85460 + 2.92159i) q^{66} +(-4.50052 + 13.8512i) q^{67} +(-1.34081 + 7.66718i) q^{68} +(2.40609 + 0.781786i) q^{69} +(1.24027 + 3.81715i) q^{71} +(-5.71038 + 0.311357i) q^{72} +(5.69843 - 7.84322i) q^{73} +(-0.452199 + 5.21089i) q^{74} +(-1.21401 + 6.94211i) q^{76} +(12.0645 + 8.76538i) q^{77} +(-8.37984 + 1.94085i) q^{78} +(4.76893 + 14.6772i) q^{79} +(0.356584 - 1.09745i) q^{81} +(-0.507007 + 5.84247i) q^{82} +(0.520370 - 1.60153i) q^{83} +(-3.20105 - 6.53974i) q^{84} +(1.61566 - 1.86125i) q^{86} +(-3.57904 - 4.92612i) q^{87} +(-10.6884 + 4.12881i) q^{88} +(6.61157 + 4.80359i) q^{89} +(13.3070 + 18.3156i) q^{91} +(4.52072 + 2.39556i) q^{92} -4.33801 q^{93} +(2.82186 - 6.66092i) q^{94} +(5.55517 + 0.662258i) q^{96} +(6.90528 - 2.24366i) q^{97} +(-6.07294 + 6.99606i) q^{98} -8.19095i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 5 q^{2} - 3 q^{4} + q^{6} - 10 q^{8} - 30 q^{9} + 5 q^{12} - 3 q^{14} - 15 q^{16} + 10 q^{17} + 30 q^{22} + 10 q^{23} - 16 q^{24} - 14 q^{26} - 15 q^{28} - 18 q^{31} + 10 q^{33} + 9 q^{34} + 41 q^{36}+ \cdots - 90 q^{98}+O(q^{100}) $ 112 * q + 5 * q^2 - 3 * q^4 + q^6 - 10 * q^8 - 30 * q^9 + 5 * q^12 - 3 * q^14 - 15 * q^16 + 10 * q^17 + 30 * q^22 + 10 * q^23 - 16 * q^24 - 14 * q^26 - 15 * q^28 - 18 * q^31 + 10 * q^33 + 9 * q^34 + 41 * q^36 - 45 * q^38 - 10 * q^39 - 10 * q^41 - 75 * q^42 - 32 * q^44 + 13 * q^46 + 10 * q^47 + 70 * q^48 - 80 * q^49 + 100 * q^52 + 43 * q^54 + 36 * q^56 + 30 * q^58 - 20 * q^62 - 60 * q^63 - 36 * q^64 + 40 * q^66 + 22 * q^71 + 65 * q^72 + 10 * q^73 + 4 * q^74 - 36 * q^76 + 55 * q^78 + 14 * q^79 - 6 * q^81 + 78 * q^84 - 59 * q^86 + 10 * q^87 - 110 * q^88 + 24 * q^89 - 90 * q^92 + 45 * q^94 + 46 * q^96 + 50 * q^97 - 90 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1000\mathbb{Z}\right)^\times$.

$n$	$377$	$501$	$751$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$	$1$

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 $

$2$	0.927056	−	1.06797i	0.655528	−	0.755171i
$2$	0.927056	−	1.06797i	0.655528	−	0.755171i
$3$	−0.305611	−	0.940574i	−0.176445	−	0.543041i	0.823252	−	0.567676i	$-0.192158\pi$
$3$	−0.305611	−	0.940574i	−0.176445	−	0.543041i	−0.999697	+	0.0246354i	$0.992158\pi$
$4$	−0.281133	−	1.98014i	−0.140567	−	0.990071i
$5$		0			0
$5$		0			0
$6$	−1.28783	−	0.545581i	−0.525753	−	0.222732i
$7$			3.68114i			1.39134i	0.718362	+	0.695670i	$0.244892\pi$
$7$			3.68114i			1.39134i	−0.718362	+	0.695670i	$0.755108\pi$
$8$	−2.37537	−	1.53546i	−0.839818	−	0.542867i
$9$	1.63577	−	1.18846i	0.545256	−	0.396152i
$10$		0			0
$11$	2.38116	−	3.27739i	0.717947	−	0.988169i	−0.281643	−	0.959519i	$-0.590879\pi$
$11$	2.38116	−	3.27739i	0.717947	−	0.988169i	0.999590	−	0.0286497i	$-0.00912074\pi$
$12$	−1.77655	+	0.869580i	−0.512847	+	0.251026i
$13$	4.97551	−	3.61492i	1.37996	−	1.00260i	0.383076	−	0.923717i	$-0.374865\pi$
$13$	4.97551	−	3.61492i	1.37996	−	1.00260i	0.996884	−	0.0788822i	$-0.0251351\pi$
$14$	3.93136	+	3.41262i	1.05070	+	0.912062i
$15$		0			0
$16$	−3.84193	+	1.11337i	−0.960482	+	0.278342i
$17$	−3.70129	−	1.20262i	−0.897694	−	0.291679i	−0.176409	−	0.984317i	$-0.556448\pi$
$17$	−3.70129	−	1.20262i	−0.897694	−	0.291679i	−0.721285	+	0.692638i	$0.756448\pi$
$18$	0.247211	−	2.84872i	0.0582682	−	0.671450i
$19$	−3.35127	−	1.08889i	−0.768833	−	0.249809i	−0.101768	−	0.994808i	$-0.532450\pi$
$19$	−3.35127	−	1.08889i	−0.768833	−	0.249809i	−0.667065	+	0.744999i	$0.732450\pi$
$20$		0			0
$21$	3.46238	−	1.12500i	0.755554	−	0.245494i
$22$	−1.29269	−	5.58134i	−0.275603	−	1.18994i
$23$	−1.50362	+	2.06955i	−0.313526	+	0.431531i	−0.936477	−	0.350730i	$-0.885934\pi$
$23$	−1.50362	+	2.06955i	−0.313526	+	0.431531i	0.622951	+	0.782261i	$0.285934\pi$
$24$	−0.718277	+	2.70346i	−0.146618	+	0.551842i
$25$		0			0
$26$	0.751941	−	8.66495i	0.147468	−	1.69934i
$27$	−4.01804	−	2.91928i	−0.773272	−	0.561815i
$28$	7.28918	−	1.03489i	1.37753	−	0.195576i
$29$	5.85554	−	1.90258i	1.08735	−	0.353300i	0.290126	−	0.956988i	$-0.406303\pi$
$29$	5.85554	−	1.90258i	1.08735	−	0.353300i	0.797220	+	0.603688i	$0.206303\pi$
$30$		0			0
$31$	1.35546	−	4.17167i	0.243448	−	0.749255i	−0.752440	−	0.658660i	$-0.771123\pi$
$31$	1.35546	−	4.17167i	0.243448	−	0.749255i	0.995888	−	0.0905941i	$-0.0288766\pi$
$32$	−2.37264	+	5.13523i	−0.419427	+	0.907789i
$33$	−3.81033	−	1.23805i	−0.663294	−	0.215517i
$34$	−4.71567	+	2.83798i	−0.808731	+	0.486709i
$35$		0			0
$36$	−2.81318	−	2.90494i	−0.468863	−	0.484157i
$37$	−2.99215	+	2.17392i	−0.491906	+	0.357391i	−0.805917	−	0.592029i	$-0.798327\pi$
$37$	−2.99215	+	2.17392i	−0.491906	+	0.357391i	0.314011	+	0.949420i	$0.398327\pi$
$38$	−4.26972	+	2.56960i	−0.692640	+	0.416844i
$39$	−4.92068	−	3.57508i	−0.787939	−	0.572471i
$40$		0			0
$41$	−3.35481	+	2.43741i	−0.523934	+	0.380660i	−0.818084	−	0.575099i	$-0.804963\pi$
$41$	−3.35481	+	2.43741i	−0.523934	+	0.380660i	0.294150	+	0.955759i	$0.404963\pi$
$42$	2.00836	−	4.74067i	0.309897	−	0.731501i
$43$	1.74279			0.265772			0.132886	−	0.991131i	$-0.457576\pi$
$43$	1.74279			0.265772			0.132886	+	0.991131i	$0.457576\pi$
$44$	−7.15911	−	3.79365i	−1.07928	−	0.571915i
$45$		0			0
$46$	0.816288	+	3.52441i	0.120355	+	0.519646i
$47$	4.86486	−	1.58069i	0.709612	−	0.230567i	0.0680985	−	0.997679i	$-0.478307\pi$
$47$	4.86486	−	1.58069i	0.709612	−	0.230567i	0.641514	+	0.767112i	$0.278307\pi$
$48$	2.22134	+	3.27336i	0.320623	+	0.472469i
$49$	−6.55078			−0.935825
$50$		0			0
$51$			3.84887i			0.538950i
$52$	−8.55685	−	8.83595i	−1.18662	−	1.22533i
$53$	−3.95398	−	12.1691i	−0.543121	−	1.67155i	−0.725416	−	0.688310i	$-0.758353\pi$
$53$	−3.95398	−	12.1691i	−0.543121	−	1.67155i	0.182295	−	0.983244i	$-0.441647\pi$
$54$	−6.84266	+	1.58483i	−0.931168	+	0.215667i
$55$		0			0
$56$	5.65224	−	8.74405i	0.755313	−	1.16847i
$57$			3.48489i			0.461585i
$58$	3.39651	−	8.01736i	0.445984	−	1.05273i
$59$	−0.784512	−	1.07979i	−0.102135	−	0.140576i	0.754891	−	0.655851i	$-0.227690\pi$
$59$	−0.784512	−	1.07979i	−0.102135	−	0.140576i	−0.857025	+	0.515274i	$0.827690\pi$
$60$		0			0
$61$	−0.998070	+	1.37373i	−0.127790	+	0.175888i	−0.868118	−	0.496358i	$-0.834670\pi$
$61$	−0.998070	+	1.37373i	−0.127790	+	0.175888i	0.740328	+	0.672246i	$0.234670\pi$
$62$	−3.19865	−	5.31497i	−0.406229	−	0.675002i
$63$	4.37487	+	6.02149i	0.551182	+	0.758637i
$64$	3.28472	+	7.29456i	0.410590	+	0.911820i
$65$		0			0
$66$	−4.85460	+	2.92159i	−0.597560	+	0.359623i
$67$	−4.50052	+	13.8512i	−0.549826	+	1.69219i	0.159404	+	0.987213i	$0.449043\pi$
$67$	−4.50052	+	13.8512i	−0.549826	+	1.69219i	−0.709230	+	0.704977i	$0.750957\pi$
$68$	−1.34081	+	7.66718i	−0.162597	+	0.929782i
$69$	2.40609	+	0.781786i	0.289659	+	0.0941160i
$70$		0			0
$71$	1.24027	+	3.81715i	0.147193	+	0.453013i	0.997286	−	0.0736188i	$-0.0234548\pi$
$71$	1.24027	+	3.81715i	0.147193	+	0.453013i	−0.850094	+	0.526631i	$0.823455\pi$
$72$	−5.71038	+	0.311357i	−0.672974	+	0.0366938i
$73$	5.69843	−	7.84322i	0.666951	−	0.917979i	−0.332736	−	0.943020i	$-0.607972\pi$
$73$	5.69843	−	7.84322i	0.666951	−	0.917979i	0.999686	+	0.0250412i	$0.00797169\pi$
$74$	−0.452199	+	5.21089i	−0.0525670	+	0.605753i
$75$		0			0
$76$	−1.21401	+	6.94211i	−0.139256	+	0.796314i
$77$	12.0645	+	8.76538i	1.37488	+	0.998908i
$78$	−8.37984	+	1.94085i	−0.948830	+	0.219758i
$79$	4.76893	+	14.6772i	0.536546	+	1.65132i	0.740284	+	0.672294i	$0.234691\pi$
$79$	4.76893	+	14.6772i	0.536546	+	1.65132i	−0.203738	+	0.979025i	$0.565309\pi$
$80$		0			0
$81$	0.356584	−	1.09745i	0.0396205	−	0.121939i
$82$	−0.507007	+	5.84247i	−0.0559896	+	0.645193i
$83$	0.520370	−	1.60153i	0.0571181	−	0.175791i	−0.918427	−	0.395590i	$-0.870540\pi$
$83$	0.520370	−	1.60153i	0.0571181	−	0.175791i	0.975545	+	0.219799i	$0.0705401\pi$
$84$	−3.20105	−	6.53974i	−0.349263	−	0.713544i
$85$		0			0
$86$	1.61566	−	1.86125i	0.174221	−	0.200703i
$87$	−3.57904	−	4.92612i	−0.383713	−	0.528136i
$88$	−10.6884	+	4.12881i	−1.13939	+	0.440133i
$89$	6.61157	+	4.80359i	0.700825	+	0.509179i	0.880201	−	0.474602i	$-0.157408\pi$
$89$	6.61157	+	4.80359i	0.700825	+	0.509179i	−0.179376	+	0.983781i	$0.557408\pi$
$90$		0			0
$91$	13.3070	+	18.3156i	1.39496	+	1.91999i
$92$	4.52072	+	2.39556i	0.471318	+	0.249754i
$93$	−4.33801			−0.449831
$94$	2.82186	−	6.66092i	0.291053	−	0.687022i
$95$		0			0
$96$	5.55517	+	0.662258i	0.566972	+	0.0675914i
$97$	6.90528	−	2.24366i	0.701125	−	0.227809i	0.0633041	−	0.997994i	$-0.479836\pi$
$97$	6.90528	−	2.24366i	0.701125	−	0.227809i	0.637820	+	0.770185i	$0.279836\pi$
$98$	−6.07294	+	6.99606i	−0.613460	+	0.706708i
$99$		−	8.19095i		−	0.823221i
$100$		0			0
$101$		−	9.04213i		−	0.899726i	−0.893098	−	0.449863i	$-0.851473\pi$
$101$		−	9.04213i		−	0.899726i	0.893098	−	0.449863i	$-0.148527\pi$
$102$	4.11049	+	3.56812i	0.406999	+	0.353297i
$103$	−10.0754	+	3.27371i	−0.992762	+	0.322568i	−0.759970	−	0.649959i	$-0.774786\pi$
$103$	−10.0754	+	3.27371i	−0.992762	+	0.322568i	−0.232792	+	0.972527i	$0.574786\pi$
$104$	−17.3692	+	0.947055i	−1.70319	+	0.0928664i
$105$		0			0
$106$	−16.6618	−	7.05870i	−1.61834	−	0.685601i
$107$	−0.391362			−0.0378344			−0.0189172	−	0.999821i	$-0.506022\pi$
$107$	−0.391362			−0.0378344			−0.0189172	+	0.999821i	$0.506022\pi$
$108$	−4.65098	+	8.77700i	−0.447541	+	0.844567i
$109$	5.07531	+	6.98557i	0.486127	+	0.669096i	0.979668	−	0.200626i	$-0.0642977\pi$
$109$	5.07531	+	6.98557i	0.486127	+	0.669096i	−0.493541	+	0.869723i	$0.664298\pi$
$110$		0			0
$111$	2.95917	+	2.14996i	0.280872	+	0.204066i
$112$	−4.09846	−	14.1427i	−0.387268	−	1.33636i
$113$	1.59983	+	2.20198i	0.150500	+	0.207145i	0.877610	−	0.479376i	$-0.159137\pi$
$113$	1.59983	+	2.20198i	0.150500	+	0.207145i	−0.727110	+	0.686521i	$0.759137\pi$
$114$	3.72177	+	3.23069i	0.348576	+	0.302582i
$115$		0			0
$116$	−5.41357	−	11.0599i	−0.502637	−	1.02689i
$117$	3.84262	−	11.8264i	0.355250	−	1.09335i
$118$	−1.88047	−	0.163187i	−0.173111	−	0.0150225i
$119$	4.42702	−	13.6250i	0.405824	−	1.24900i
$120$		0			0
$121$	−1.67215	−	5.14634i	−0.152013	−	0.467849i
$122$	0.541835	+	2.33943i	0.0490554	+	0.211802i
$123$	3.31784	+	2.41055i	0.299159	+	0.217352i
$124$	−8.64157	−	1.51121i	−0.776036	−	0.135710i
$125$		0			0
$126$	10.4865	+	0.910018i	0.934215	+	0.0810709i
$127$	2.19692	−	3.02379i	0.194945	−	0.268318i	−0.700343	−	0.713806i	$-0.746970\pi$
$127$	2.19692	−	3.02379i	0.194945	−	0.268318i	0.895288	+	0.445488i	$0.146970\pi$
$128$	10.8355	+	3.25447i	0.957733	+	0.287658i
$129$	−0.532615	−	1.63922i	−0.0468941	−	0.144325i
$130$		0			0
$131$	14.6559	+	4.76200i	1.28049	+	0.416058i	0.868754	−	0.495243i	$-0.164921\pi$
$131$	14.6559	+	4.76200i	1.28049	+	0.416058i	0.411740	+	0.911301i	$0.364921\pi$
$132$	−1.38031	+	7.89306i	−0.120140	+	0.687003i
$133$	4.00836	−	12.3365i	0.347569	−	1.06971i
$134$	10.6205	+	17.6473i	0.917467	+	1.52449i
$135$		0			0
$136$	6.94534	+	8.53985i	0.595558	+	0.732286i
$137$	−4.78116	−	6.58071i	−0.408482	−	0.562228i	0.554365	−	0.832274i	$-0.312961\pi$
$137$	−4.78116	−	6.58071i	−0.408482	−	0.562228i	−0.962847	+	0.270046i	$0.912961\pi$
$138$	3.06551	−	1.84488i	0.260953	−	0.157047i
$139$	0.476853	−	0.656333i	0.0404462	−	0.0556694i	−0.788315	−	0.615272i	$-0.789046\pi$
$139$	0.476853	−	0.656333i	0.0404462	−	0.0556694i	0.828761	+	0.559603i	$0.189046\pi$
$140$		0			0
$141$	−2.97351	−	4.09268i	−0.250415	−	0.344666i
$142$	5.22641	+	2.21414i	0.438591	+	0.185807i
$143$		−	24.9144i		−	2.08345i
$144$	−4.96132	+	6.38717i	−0.413443	+	0.532264i
$145$		0			0
$146$	−3.09358	−	13.3569i	−0.256026	−	1.10542i
$147$	2.00199	+	6.16149i	0.165121	+	0.508192i
$148$	5.14587	+	5.31372i	0.422988	+	0.436785i
$149$			2.79356i			0.228857i	0.993431	+	0.114429i	$0.0365037\pi$
$149$			2.79356i			0.228857i	−0.993431	+	0.114429i	$0.963496\pi$
$150$		0			0
$151$	−4.41781			−0.359516			−0.179758	−	0.983711i	$-0.557531\pi$
$151$	−4.41781			−0.359516			−0.179758	+	0.983711i	$0.557531\pi$
$152$	6.28853	+	7.73225i	0.510067	+	0.627169i
$153$	−7.48372	+	2.43161i	−0.605023	+	0.196584i
$154$	20.5457	−	4.75857i	1.65562	−	0.383457i
$155$		0			0
$156$	−5.69580	+	10.7487i	−0.456029	+	0.860586i
$157$	13.1399			1.04867			0.524337	−	0.851511i	$-0.324313\pi$
$157$	13.1399			1.04867			0.524337	+	0.851511i	$0.324313\pi$
$158$	20.0960	+	8.51355i	1.59875	+	0.677302i
$159$	−10.2376	+	7.43803i	−0.811892	+	0.589874i
$160$		0			0
$161$	−7.61831	−	5.53502i	−0.600407	−	0.436221i
$162$	−0.841477	−	1.39822i	−0.0661127	−	0.109855i
$163$	−0.389815	+	0.283217i	−0.0305327	+	0.0221833i	−0.602947	−	0.797781i	$-0.706007\pi$
$163$	−0.389815	+	0.283217i	−0.0305327	+	0.0221833i	0.572414	+	0.819965i	$0.306007\pi$
$164$	5.76957	+	5.95777i	0.450528	+	0.465223i
$165$		0			0
$166$	−1.22798	−	2.04045i	−0.0953100	−	0.158370i
$167$	9.62622	+	3.12775i	0.744899	+	0.242032i	0.656785	−	0.754078i	$-0.271916\pi$
$167$	9.62622	+	3.12775i	0.744899	+	0.242032i	0.0881142	+	0.996110i	$0.471916\pi$
$168$	−9.95182	−	2.64408i	−0.767799	−	0.203995i
$169$	7.67086	−	23.6085i	0.590066	−	1.81604i
$170$		0			0
$171$	−6.77600	+	2.20165i	−0.518173	+	0.168365i
$172$	−0.489955	−	3.45096i	−0.0373587	−	0.263133i
$173$	−1.25123	−	0.909073i	−0.0951293	−	0.0691155i	0.539204	−	0.842175i	$-0.318725\pi$
$173$	−1.25123	−	0.909073i	−0.0951293	−	0.0691155i	−0.634333	+	0.773060i	$0.718725\pi$
$174$	−8.57893	−	0.744477i	−0.650367	−	0.0564386i
$175$		0			0
$176$	−5.49931	+	15.2426i	−0.414526	+	1.14895i
$177$	−0.775865	+	1.06789i	−0.0583176	+	0.0802673i
$178$	11.2594	−	2.60778i	0.843928	−	0.195462i
$179$	2.90435	−	0.943680i	0.217081	−	0.0705340i	−0.198457	−	0.980110i	$-0.563593\pi$
$179$	2.90435	−	0.943680i	0.217081	−	0.0705340i	0.415539	+	0.909576i	$0.363593\pi$
$180$		0			0
$181$	0.859346	+	0.279218i	0.0638747	+	0.0207541i	0.340780	−	0.940143i	$-0.389309\pi$
$181$	0.859346	+	0.279218i	0.0638747	+	0.0207541i	−0.276905	+	0.960897i	$0.589309\pi$
$182$	31.8969	+	2.76800i	2.36435	+	0.205178i
$183$	1.59711	+	0.518934i	0.118062	+	0.0383607i
$184$	6.74936	−	2.60720i	0.497569	−	0.192205i
$185$		0			0
$186$	−4.02158	+	4.63288i	−0.294877	+	0.339699i
$187$	−12.7548	+	9.26692i	−0.932725	+	0.677664i
$188$	−4.49766	−	9.18872i	−0.328025	−	0.670156i
$189$	10.7463	−	14.7910i	0.781676	−	1.07588i
$190$		0			0
$191$	2.13116	−	1.54838i	0.154205	−	0.112037i	−0.508007	−	0.861353i	$-0.669618\pi$
$191$	2.13116	−	1.54838i	0.154205	−	0.112037i	0.662212	+	0.749316i	$0.269618\pi$
$192$	5.85723	−	5.31882i	0.422709	−	0.383853i
$193$			22.0562i			1.58764i	0.608154	+	0.793819i	$0.291910\pi$
$193$			22.0562i			1.58764i	−0.608154	+	0.793819i	$0.708090\pi$
$194$	4.00541	−	9.45465i	0.287572	−	0.678804i
$195$		0			0
$196$	1.84164	+	12.9715i	0.131546	+	0.926534i
$197$	2.80194	+	8.62350i	0.199630	+	0.614399i	0.999891	+	0.0147469i	$0.00469424\pi$
$197$	2.80194	+	8.62350i	0.199630	+	0.614399i	−0.800261	+	0.599652i	$0.795306\pi$
$198$	−8.74771	−	7.59347i	−0.621673	−	0.539645i
$199$	6.18489			0.438435			0.219217	−	0.975676i	$-0.429650\pi$
$199$	6.18489			0.438435			0.219217	+	0.975676i	$0.429650\pi$
$200$		0			0
$201$	14.4035			1.01594
$202$	−9.65675	−	8.38256i	−0.679447	−	0.589795i
$203$	7.00366	+	21.5550i	0.491561	+	1.51287i
$204$	7.62132	−	1.08205i	0.533599	−	0.0757584i
$205$		0			0
$206$	−5.84426	+	13.7952i	−0.407189	+	0.961157i
$207$			5.17229i			0.359499i
$208$	−15.0908	+	19.4279i	−1.04636	+	1.34708i
$209$	−11.5486	+	8.39056i	−0.798835	+	0.580387i
$210$		0			0
$211$	−11.9734	+	16.4800i	−0.824283	+	1.13453i	0.164677	+	0.986348i	$0.447342\pi$
$211$	−11.9734	+	16.4800i	−0.824283	+	1.13453i	−0.988960	+	0.148181i	$0.952658\pi$
$212$	−22.9850	+	11.2506i	−1.57861	+	0.772693i
$213$	3.21128	−	2.33313i	0.220033	−	0.159863i
$214$	−0.362814	+	0.417964i	−0.0248015	+	0.0285714i
$215$		0			0
$216$	5.06188	+	13.1039i	0.344417	+	0.891607i
$217$	15.3565	+	4.98963i	1.04247	+	0.338718i
$218$	12.1655	+	1.05572i	0.823952	+	0.0715022i
$219$	−9.11863	−	2.96282i	−0.616180	−	0.200209i
$220$		0			0
$221$	−22.7632	+	7.39621i	−1.53122	+	0.497523i
$222$	5.03942	−	1.16718i	0.338224	−	0.0783359i
$223$	6.21151	−	8.54941i	0.415953	−	0.572511i	−0.548705	−	0.836016i	$-0.684879\pi$
$223$	6.21151	−	8.54941i	0.415953	−	0.572511i	0.964658	+	0.263506i	$0.0848788\pi$
$224$	−18.9035	−	8.73400i	−1.26304	−	0.583565i
$225$		0			0
$226$	3.83479	+	0.332782i	0.255086	+	0.0221363i
$227$	−7.62995	−	5.54348i	−0.506418	−	0.367934i	0.305045	−	0.952338i	$-0.401328\pi$
$227$	−7.62995	−	5.54348i	−0.506418	−	0.367934i	−0.811463	+	0.584404i	$0.801328\pi$
$228$	6.90058	−	0.979719i	0.457002	−	0.0648835i
$229$	9.67686	−	3.14420i	0.639465	−	0.207775i	0.0287017	−	0.999588i	$-0.490863\pi$
$229$	9.67686	−	3.14420i	0.639465	−	0.207775i	0.610763	+	0.791813i	$0.290863\pi$
$230$		0			0
$231$	4.55744	−	14.0264i	0.299858	−	0.922867i
$232$	−16.8304	−	4.47163i	−1.10497	−	0.293577i
$233$	−4.61735	−	1.50027i	−0.302493	−	0.0982858i	0.153838	−	0.988096i	$-0.450837\pi$
$233$	−4.61735	−	1.50027i	−0.302493	−	0.0982858i	−0.456331	+	0.889810i	$0.650837\pi$
$234$	−9.06791	−	15.0675i	−0.592788	−	0.984994i
$235$		0			0
$236$	−1.91758	+	1.85701i	−0.124824	+	0.120881i
$237$	12.3476	−	8.97106i	0.802063	−	0.582733i
$238$	−10.4470	−	17.3590i	−0.677178	−	1.12522i
$239$	7.15100	+	5.19551i	0.462560	+	0.336069i	0.794535	−	0.607219i	$-0.207715\pi$
$239$	7.15100	+	5.19551i	0.462560	+	0.336069i	−0.331975	+	0.943288i	$0.607715\pi$
$240$		0			0
$241$	2.81129	−	2.04252i	0.181091	−	0.131571i	−0.493547	−	0.869719i	$-0.664300\pi$
$241$	2.81129	−	2.04252i	0.181091	−	0.131571i	0.674638	+	0.738149i	$0.264300\pi$
$242$	−7.04633	−	2.98514i	−0.452955	−	0.191892i
$243$	−16.0409			−1.02903
$244$	3.00076	+	1.59012i	0.192104	+	0.101797i
$245$		0			0
$246$	5.65022	−	1.30865i	0.360245	−	0.0834362i
$247$	−20.6105	+	6.69677i	−1.31142	+	0.426105i
$248$	−9.62515	+	7.82799i	−0.611198	+	0.497078i
$249$	−1.66539			−0.105540
$250$		0			0
$251$		−	10.6028i		−	0.669245i	−0.942352	−	0.334622i	$-0.891391\pi$
$251$		−	10.6028i		−	0.669245i	0.942352	−	0.334622i	$-0.108609\pi$
$252$	10.6935	−	10.3557i	0.673626	−	0.652348i
$253$	3.20237	+	9.85587i	0.201331	+	0.619633i
$254$	−1.19267	−	5.14947i	−0.0748346	−	0.323107i
$255$		0			0
$256$	13.5208	−	8.55496i	0.845052	−	0.534685i
$257$			7.56452i			0.471862i	0.971770	+	0.235931i	$0.0758139\pi$
$257$			7.56452i			0.471862i	−0.971770	+	0.235931i	$0.924186\pi$
$258$	−2.24441	−	0.950830i	−0.139731	−	0.0591961i
$259$	−8.00252	−	11.0145i	−0.497252	−	0.684409i
$260$		0			0
$261$	7.31718	−	10.0712i	0.452922	−	0.623393i
$262$	18.6726	−	11.2375i	1.15359	−	0.694255i
$263$	17.5706	+	24.1838i	1.08345	+	1.49124i	0.855668	+	0.517526i	$0.173147\pi$
$263$	17.5706	+	24.1838i	1.08345	+	1.49124i	0.227780	+	0.973713i	$0.426853\pi$
$264$	7.14996	+	8.79145i	0.440049	+	0.541076i
$265$		0			0
$266$	−9.45904	−	15.7174i	−0.579971	−	0.963697i
$267$	2.49756	−	7.68670i	0.152848	−	0.470419i
$268$	28.6926	+	5.01764i	1.75268	+	0.306501i
$269$	21.8536	+	7.10065i	1.33244	+	0.432934i	0.886748	−	0.462254i	$-0.152959\pi$
$269$	21.8536	+	7.10065i	1.33244	+	0.432934i	0.445688	+	0.895188i	$0.352959\pi$
$270$		0			0
$271$	7.44078	+	22.9004i	0.451995	+	1.39110i	0.874627	+	0.484796i	$0.161106\pi$
$271$	7.44078	+	22.9004i	0.451995	+	1.39110i	−0.422632	+	0.906301i	$0.638894\pi$
$272$	15.5590	+	0.499490i	0.943406	+	0.0302860i
$273$	13.1604	−	18.1137i	0.796502	−	1.09629i
$274$	−11.4604	−	0.994531i	−0.692350	−	0.0600818i
$275$		0			0
$276$	0.871616	−	4.98419i	0.0524651	−	0.300013i
$277$	−2.35420	−	1.71043i	−0.141450	−	0.102770i	0.514810	−	0.857304i	$-0.327863\pi$
$277$	−2.35420	−	1.71043i	−0.141450	−	0.102770i	−0.656260	+	0.754535i	$0.727863\pi$
$278$	−0.258875	−	1.11772i	−0.0155263	−	0.0670366i
$279$	−2.74063	−	8.43480i	−0.164077	−	0.504978i
$280$		0			0
$281$	−7.31490	+	22.5130i	−0.436371	+	1.34301i	0.455305	+	0.890335i	$0.349530\pi$
$281$	−7.31490	+	22.5130i	−0.436371	+	1.34301i	−0.891676	+	0.452675i	$0.850470\pi$
$282$	−7.12748	−	0.618521i	−0.424436	−	0.0368324i
$283$	−8.95835	+	27.5710i	−0.532518	+	1.63892i	0.216432	+	0.976298i	$0.430558\pi$
$283$	−8.95835	+	27.5710i	−0.532518	+	1.63892i	−0.748951	+	0.662626i	$0.769442\pi$
$284$	7.20982	−	3.52904i	0.427824	−	0.209410i
$285$		0			0
$286$	−26.6079	−	23.0970i	−1.57336	−	1.36576i
$287$	−8.97245	−	12.3495i	−0.529627	−	0.728969i
$288$	2.22191	+	11.2198i	0.130927	+	0.661134i
$289$	−1.50005	−	1.08985i	−0.0882381	−	0.0641087i
$290$		0			0
$291$	−4.22066	−	5.80924i	−0.247419	−	0.340544i
$292$	−17.1327	−	9.07871i	−1.00262	−	0.531292i
$293$	13.8184			0.807281			0.403640	−	0.914918i	$-0.367745\pi$
$293$	13.8184			0.807281			0.403640	+	0.914918i	$0.367745\pi$
$294$	8.43627	+	3.57398i	0.492013	+	0.208439i
$295$		0			0
$296$	10.4454	−	0.569535i	0.607128	−	0.0331036i
$297$	−19.1352	+	6.21740i	−1.11034	+	0.360770i
$298$	2.98345	+	2.58979i	0.172826	+	0.150022i
$299$			15.7325i			0.909837i
$300$		0			0
$301$			6.41543i			0.369779i
$302$	−4.09556	+	4.71810i	−0.235673	+	0.271496i
$303$	−8.50480	+	2.76338i	−0.488588	+	0.158752i
$304$	14.0877	+	0.452254i	0.807983	+	0.0259386i
$305$		0			0
$306$	−4.34094	+	10.2466i	−0.248155	+	0.585762i
$307$	7.71657			0.440408			0.220204	−	0.975454i	$-0.429328\pi$
$307$	7.71657			0.440408			0.220204	+	0.975454i	$0.429328\pi$
$308$	13.9650	−	26.3537i	0.795728	−	1.50164i
$309$	6.15833	+	8.47621i	0.350335	+	0.482195i
$310$		0			0
$311$	−8.02122	−	5.82776i	−0.454842	−	0.330462i	0.336663	−	0.941625i	$-0.390702\pi$
$311$	−8.02122	−	5.82776i	−0.454842	−	0.330462i	−0.791504	+	0.611163i	$0.790702\pi$
$312$	6.19901	+	16.0476i	0.350950	+	0.908518i
$313$	1.13921	+	1.56798i	0.0643917	+	0.0886276i	0.839998	−	0.542589i	$-0.182556\pi$
$313$	1.13921	+	1.56798i	0.0643917	+	0.0886276i	−0.775607	+	0.631217i	$0.782556\pi$
$314$	12.1814	−	14.0330i	0.687435	−	0.791929i
$315$		0			0
$316$	27.7223	−	13.5694i	1.55950	−	0.763339i
$317$	−0.587317	+	1.80758i	−0.0329870	+	0.101524i	−0.966194	−	0.257815i	$-0.916998\pi$
$317$	−0.587317	+	1.80758i	−0.0329870	+	0.101524i	0.933207	+	0.359338i	$0.116998\pi$
$318$	−1.54719	+	17.8289i	−0.0867619	+	0.999796i
$319$	7.70749	−	23.7212i	0.431537	−	1.32813i
$320$		0			0
$321$	0.119604	+	0.368105i	0.00667567	+	0.0205456i
$322$	−12.9739	+	3.00487i	−0.723005	+	0.167455i
$323$	11.0945	+	8.06061i	0.617313	+	0.448504i
$324$	−2.27336	−	0.397557i	−0.126298	−	0.0220865i
$325$		0			0
$326$	−0.0589121	+	0.678870i	−0.00326284	+	0.0375991i
$327$	5.01938	−	6.90858i	0.277572	−	0.382045i
$328$	11.7115	−	0.638565i	0.646657	−	0.0352589i
$329$	5.81873	+	17.9082i	0.320797	+	0.987311i
$330$		0			0
$331$	−28.5960	−	9.29140i	−1.57178	−	0.510702i	−0.611856	−	0.790969i	$-0.709577\pi$
$331$	−28.5960	−	9.29140i	−1.57178	−	0.510702i	−0.959922	+	0.280267i	$0.909577\pi$
$332$	−3.31756	−	0.580162i	−0.182075	−	0.0318406i
$333$	−2.31085	+	7.11208i	−0.126634	+	0.389739i
$334$	12.2644	−	7.38094i	0.671078	−	0.403867i
$335$		0			0
$336$	−12.0497	+	8.17706i	−0.657365	+	0.446095i
$337$	−2.92944	−	4.03203i	−0.159577	−	0.219639i	0.721740	−	0.692164i	$-0.243342\pi$
$337$	−2.92944	−	4.03203i	−0.159577	−	0.219639i	−0.881317	+	0.472525i	$0.843342\pi$
$338$	−18.1019	−	30.0786i	−0.984613	−	1.63606i
$339$	1.58220	−	2.17771i	0.0859333	−	0.118277i
$340$		0			0
$341$	−10.4446	−	14.3758i	−0.565608	−	0.778492i
$342$	−3.93042	+	9.27764i	−0.212533	+	0.501677i
$343$			1.65365i			0.0892886i
$344$	−4.13975	−	2.67598i	−0.223200	−	0.144279i
$345$		0			0
$346$	−2.13083	+	0.493520i	−0.114554	+	0.0265318i
$347$	−6.67727	−	20.5505i	−0.358455	−	1.10321i	−0.953979	−	0.299873i	$-0.903056\pi$
$347$	−6.67727	−	20.5505i	−0.358455	−	1.10321i	0.595525	−	0.803337i	$-0.296944\pi$
$348$	−8.74824	+	8.47190i	−0.468955	+	0.454141i
$349$			3.79138i			0.202948i	0.994838	+	0.101474i	$0.0323558\pi$
$349$			3.79138i			0.202948i	−0.994838	+	0.101474i	$0.967644\pi$
$350$		0			0
$351$	−30.5448			−1.63036
$352$	11.1805	+	20.0039i	0.595923	+	1.06621i
$353$	−23.7877	+	7.72909i	−1.26609	+	0.411378i	−0.863661	−	0.504072i	$-0.831834\pi$
$353$	−23.7877	+	7.72909i	−1.26609	+	0.411378i	−0.402430	+	0.915451i	$0.631834\pi$
$354$	0.421204	+	1.81859i	0.0223867	+	0.0966572i
$355$		0			0
$356$	7.65305	−	14.4423i	0.405611	−	0.765440i
$357$	−14.1682			−0.749862
$358$	1.68467	−	3.97661i	0.0890376	−	0.210170i
$359$	−18.7926	+	13.6536i	−0.991834	+	0.720609i	−0.960322	−	0.278894i	$-0.910032\pi$
$359$	−18.7926	+	13.6536i	−0.991834	+	0.720609i	−0.0315118	+	0.999503i	$0.510032\pi$
$360$		0			0
$361$	−5.32603	−	3.86959i	−0.280317	−	0.203662i
$362$	1.09486	−	0.658907i	0.0575446	−	0.0346314i
$363$	−4.32949	+	3.14556i	−0.227239	+	0.165099i
$364$	32.5264	−	31.4989i	1.70484	−	1.65099i
$365$		0			0
$366$	2.03482	−	1.22459i	0.106362	−	0.0640105i
$367$	−3.79273	−	1.23233i	−0.197979	−	0.0643272i	0.208349	−	0.978054i	$-0.433191\pi$
$367$	−3.79273	−	1.23233i	−0.197979	−	0.0643272i	−0.406328	+	0.913727i	$0.633191\pi$
$368$	3.47262	−	9.62515i	0.181023	−	0.501746i
$369$	−2.59094	+	7.97409i	−0.134879	+	0.415114i
$370$		0			0
$371$	44.7961	−	14.5551i	2.32570	−	0.755666i
$372$	1.21956	+	8.58988i	0.0632312	+	0.445365i
$373$	−16.6167	−	12.0728i	−0.860382	−	0.625104i	0.0676065	−	0.997712i	$-0.478464\pi$
$373$	−16.6167	−	12.0728i	−0.860382	−	0.625104i	−0.927989	+	0.372608i	$0.878464\pi$
$374$	−1.92762	+	22.2128i	−0.0996746	+	1.14859i
$375$		0			0
$376$	−13.9829	−	3.71508i	−0.721113	−	0.191591i
$377$	22.2566	−	30.6336i	1.14628	−	1.57771i
$378$	−5.83396	−	25.1888i	−0.300067	−	1.29557i
$379$	−27.2341	+	8.84890i	−1.39892	+	0.454538i	−0.908843	−	0.417139i	$-0.863033\pi$
$379$	−27.2341	+	8.84890i	−1.39892	+	0.454538i	−0.490081	+	0.871677i	$0.663033\pi$
$380$		0			0
$381$	−3.51551	−	1.14226i	−0.180105	−	0.0585196i
$382$	0.322079	−	3.71146i	0.0164790	−	0.189895i
$383$	−11.6284	−	3.77828i	−0.594181	−	0.193061i	−0.00353757	−	0.999994i	$-0.501126\pi$
$383$	−11.6284	−	3.77828i	−0.594181	−	0.193061i	−0.590644	+	0.806933i	$0.701126\pi$
$384$	−0.250379	−	11.1862i	−0.0127771	−	0.570844i
$385$		0			0
$386$	23.5554	+	20.4473i	1.19894	+	1.04074i
$387$	2.85079	−	2.07122i	0.144914	−	0.105286i
$388$	−6.38407	−	13.0427i	−0.324102	−	0.662141i
$389$	−16.6269	+	22.8849i	−0.843015	+	1.16031i	0.142344	+	0.989817i	$0.454536\pi$
$389$	−16.6269	+	22.8849i	−0.843015	+	1.16031i	−0.985359	+	0.170494i	$0.945464\pi$
$390$		0			0
$391$	8.05421	−	5.85173i	0.407319	−	0.295935i
$392$	15.5605	+	10.0585i	0.785923	+	0.508029i
$393$		−	15.2403i		−	0.768772i
$394$	11.8072	+	5.00207i	0.594839	+	0.252000i
$395$		0			0
$396$	−16.2192	+	2.30275i	−0.815048	+	0.115717i
$397$	−2.11608	−	6.51261i	−0.106203	−	0.326859i	0.883808	−	0.467850i	$-0.154971\pi$
$397$	−2.11608	−	6.51261i	−0.106203	−	0.326859i	−0.990011	+	0.140991i	$0.954971\pi$
$398$	5.73374	−	6.60529i	0.287406	−	0.331093i
$399$	−12.8284			−0.642222
$400$		0			0
$401$	34.1131			1.70352			0.851762	−	0.523929i	$-0.175534\pi$
$401$	34.1131			1.70352			0.851762	+	0.523929i	$0.175534\pi$
$402$	13.3528	−	15.3825i	0.665979	−	0.767211i
$403$	−8.33617	−	25.6561i	−0.415254	−	1.27802i
$404$	−17.9047	+	2.54204i	−0.890793	+	0.126471i
$405$		0			0
$406$	29.5130	+	12.5030i	1.46471	+	0.620515i
$407$			14.9829i			0.742675i
$408$	5.90979	−	9.14248i	0.292578	−	0.452620i
$409$	−21.8970	+	15.9091i	−1.08274	+	0.786655i	−0.978158	−	0.207861i	$-0.933350\pi$
$409$	−21.8970	+	15.9091i	−1.08274	+	0.786655i	−0.104580	+	0.994516i	$0.533350\pi$
$410$		0			0
$411$	−4.72847	+	6.50818i	−0.233238	+	0.321025i
$412$	9.31494	+	19.0304i	0.458914	+	0.937563i
$413$	3.97485	−	2.88790i	0.195589	−	0.142104i
$414$	5.52387	+	4.79500i	0.271483	+	0.235662i
$415$		0			0
$416$	6.75837	+	34.1273i	0.331357	+	1.67323i
$417$	−0.763061	−	0.247934i	−0.0373673	−	0.0121414i
$418$	−1.74532	+	20.1121i	−0.0853666	+	0.983717i
$419$	−19.6287	−	6.37775i	−0.958925	−	0.311573i	−0.212588	−	0.977142i	$-0.568189\pi$
$419$	−19.6287	−	6.37775i	−0.958925	−	0.311573i	−0.746337	+	0.665568i	$0.768189\pi$
$420$		0			0
$421$	−8.92197	+	2.89892i	−0.434830	+	0.141285i	−0.518249	−	0.855230i	$-0.673416\pi$
$421$	−8.92197	+	2.89892i	−0.434830	+	0.141285i	0.0834190	+	0.996515i	$0.473416\pi$
$422$	6.50015	+	28.0651i	0.316423	+	1.36619i
$423$	6.07920	−	8.36730i	0.295581	−	0.406832i
$424$	−9.29303	+	34.9772i	−0.451309	+	1.69864i
$425$		0			0
$426$	0.485315	−	5.59250i	0.0235136	−	0.270957i
$427$	−5.05688	−	3.67404i	−0.244719	−	0.177799i
$428$	0.110025	+	0.774952i	0.00531825	+	0.0374587i
$429$	−23.4338	+	7.61412i	−1.13140	+	0.367613i
$430$		0			0
$431$	0.317339	−	0.976670i	0.0152857	−	0.0470446i	−0.943123	−	0.332445i	$-0.892127\pi$
$431$	0.317339	−	0.976670i	0.0152857	−	0.0470446i	0.958408	+	0.285400i	$0.0921265\pi$
$432$	18.6873	+	6.74210i	0.899091	+	0.324379i
$433$	25.6115	+	8.32169i	1.23081	+	0.399915i	0.851008	−	0.525152i	$-0.175992\pi$
$433$	25.6115	+	8.32169i	1.23081	+	0.399915i	0.379803	+	0.925067i	$0.375992\pi$
$434$	19.5651	−	11.7747i	0.939157	−	0.565202i
$435$		0			0
$436$	12.4056	−	12.0137i	0.594120	−	0.575353i
$437$	7.29254	−	5.29834i	0.348850	−	0.253454i
$438$	−11.6177	+	6.99175i	−0.555115	+	0.334079i
$439$	1.22399	+	0.889282i	0.0584179	+	0.0424431i	0.616611	−	0.787268i	$-0.288505\pi$
$439$	1.22399	+	0.889282i	0.0584179	+	0.0424431i	−0.558193	+	0.829711i	$0.688505\pi$
$440$		0			0
$441$	−10.7156	+	7.78531i	−0.510265	+	0.370729i
$442$	−13.2038	+	31.1672i	−0.628041	+	1.48247i
$443$	15.1085			0.717828			0.358914	−	0.933371i	$-0.383147\pi$
$443$	15.1085			0.717828			0.358914	+	0.933371i	$0.383147\pi$
$444$	3.42531	−	6.46401i	0.162558	−	0.306768i
$445$		0			0
$446$	−3.37212	−	14.5595i	−0.159674	−	0.689412i
$447$	2.62755	−	0.853743i	0.124279	−	0.0403807i
$448$	−26.8523	+	12.0915i	−1.26865	+	0.571270i
$449$	32.5044			1.53398			0.766988	−	0.641661i	$-0.221755\pi$
$449$	32.5044			1.53398			0.766988	+	0.641661i	$0.221755\pi$
$450$		0			0
$451$			16.7989i			0.791029i
$452$	3.91047	−	3.78694i	0.183933	−	0.178123i
$453$	1.35013	+	4.15528i	0.0634347	+	0.195232i
$454$	−12.9937	+	3.00946i	−0.609824	+	0.141241i
$455$		0			0
$456$	5.35092	−	8.27789i	0.250580	−	0.387648i
$457$			0.743713i			0.0347894i	0.999849	+	0.0173947i	$0.00553719\pi$
$457$			0.743713i			0.0347894i	−0.999849	+	0.0173947i	$0.994463\pi$
$458$	5.61307	−	13.2495i	0.262282	−	0.619108i
$459$	11.3611	+	15.6373i	0.530293	+	0.729886i
$460$		0			0
$461$	16.2261	−	22.3333i	0.755723	−	1.04016i	−0.241834	−	0.970318i	$-0.577749\pi$
$461$	16.2261	−	22.3333i	0.755723	−	1.04016i	0.997558	−	0.0698465i	$-0.0222509\pi$
$462$	−10.7548	−	17.8705i	−0.500358	−	0.831409i
$463$	10.5034	+	14.4567i	0.488133	+	0.671858i	0.980042	−	0.198789i	$-0.0637008\pi$
$463$	10.5034	+	14.4567i	0.488133	+	0.671858i	−0.491909	+	0.870646i	$0.663701\pi$
$464$	−20.3783	+	13.8289i	−0.946038	+	0.641993i
$465$		0			0
$466$	−5.88279	+	3.54037i	−0.272515	+	0.164005i
$467$	2.08094	−	6.40448i	0.0962945	−	0.296364i	−0.891294	−	0.453425i	$-0.850202\pi$
$467$	2.08094	−	6.40448i	0.0962945	−	0.296364i	0.987589	+	0.157061i	$0.0502020\pi$
$468$	−24.4982	−	4.28415i	−1.13243	−	0.198035i
$469$	−50.9881	−	16.5670i	−2.35441	−	0.764995i
$470$		0			0
$471$	−4.01569	−	12.3590i	−0.185033	−	0.569473i
$472$	0.205530	+	3.76948i	0.00946029	+	0.173504i
$473$	4.14985	−	5.71178i	0.190810	−	0.262628i
$474$	1.86607	−	21.5036i	0.0857116	−	0.987693i
$475$		0			0
$476$	−28.2239	−	4.93570i	−1.29364	−	0.226227i
$477$	−20.9302	−	15.2067i	−0.958329	−	0.696267i
$478$	12.1780	−	2.82055i	0.557011	−	0.129009i
$479$	1.53203	+	4.71509i	0.0700001	+	0.215438i	0.979937	−	0.199309i	$-0.0638699\pi$
$479$	1.53203	+	4.71509i	0.0700001	+	0.215438i	−0.909937	+	0.414748i	$0.863870\pi$
$480$		0			0
$481$	−7.02892	+	21.6328i	−0.320491	+	0.986370i
$482$	0.424866	−	4.89592i	0.0193521	−	0.223003i
$483$	−2.87786	+	8.85715i	−0.130947	+	0.403014i
$484$	−9.72039	+	4.75790i	−0.441836	+	0.216268i
$485$		0			0
$486$	−14.8708	+	17.1313i	−0.674555	+	0.777091i
$487$	22.3423	+	30.7515i	1.01243	+	1.39349i	0.917380	+	0.398012i	$0.130300\pi$
$487$	22.3423	+	30.7515i	1.01243	+	1.39349i	0.0950461	+	0.995473i	$0.469700\pi$
$488$	4.48008	−	1.73060i	0.202804	−	0.0783407i
$489$	0.385518	+	0.280096i	0.0174337	+	0.0126664i
$490$		0			0
$491$	−9.39398	−	12.9297i	−0.423944	−	0.583509i	0.542606	−	0.839988i	$-0.317438\pi$
$491$	−9.39398	−	12.9297i	−0.423944	−	0.583509i	−0.966550	+	0.256478i	$0.917438\pi$
$492$	3.84048	−	7.24747i	0.173142	−	0.326741i
$493$	−23.9611			−1.07915
$494$	−11.9552	+	28.2198i	−0.537888	+	1.26967i
$495$		0			0
$496$	−0.562969	+	17.5364i	−0.0252780	+	0.787407i
$497$	−14.0515	+	4.56560i	−0.630294	+	0.204795i
$498$	−1.54391	+	1.77860i	−0.0691844	+	0.0797008i
$499$		−	8.08744i		−	0.362044i	−0.983479	−	0.181022i	$-0.942060\pi$
$499$		−	8.08744i		−	0.362044i	0.983479	−	0.181022i	$-0.0579405\pi$
$500$		0			0
$501$		−	10.0100i		−	0.447216i
$502$	−11.3235	−	9.82942i	−0.505394	−	0.438709i
$503$	24.0791	−	7.82378i	1.07364	−	0.348845i	0.281733	−	0.959493i	$-0.409091\pi$
$503$	24.0791	−	7.82378i	1.07364	−	0.348845i	0.791903	+	0.610648i	$0.209091\pi$
$504$	−1.14615	−	21.0207i	−0.0510536	−	0.936336i
$505$		0			0
$506$	13.4946	+	5.71690i	0.599907	+	0.254147i
$507$	−24.5498			−1.09030
$508$	−6.60517	−	3.50012i	−0.293057	−	0.155293i
$509$	−8.31244	−	11.4411i	−0.368442	−	0.507117i	0.584034	−	0.811729i	$-0.301473\pi$
$509$	−8.31244	−	11.4411i	−0.368442	−	0.507117i	−0.952477	+	0.304612i	$0.901473\pi$
$510$		0			0
$511$	28.8720	+	20.9767i	1.27722	+	0.927955i
$512$	3.39810	−	22.3708i	0.150176	−	0.988659i
$513$	10.2867	+	14.1585i	0.454171	+	0.625113i
$514$	8.07870	+	7.01274i	0.356336	+	0.309319i
$515$		0			0
$516$	−3.09615	+	1.51549i	−0.136300	+	0.0667158i
$517$	6.40348	−	19.7079i	0.281625	−	0.866752i
$518$	−19.1820	−	1.66461i	−0.842808	−	0.0731386i
$519$	−0.472660	+	1.45470i	−0.0207475	+	0.0638542i
$520$		0			0
$521$	−12.1780	−	37.4801i	−0.533530	−	1.64204i	−0.746805	−	0.665043i	$-0.768413\pi$
$521$	−12.1780	−	37.4801i	−0.533530	−	1.64204i	0.213275	−	0.976992i	$-0.431587\pi$
$522$	−3.97237	−	17.1511i	−0.173866	−	0.750685i
$523$	−26.6792	−	19.3836i	−1.16660	−	0.847586i	−0.176003	−	0.984390i	$-0.556317\pi$
$523$	−26.6792	−	19.3836i	−1.16660	−	0.847586i	−0.990598	+	0.136804i	$0.956317\pi$
$524$	5.30917	−	30.3596i	0.231932	−	1.32627i
$525$		0			0
$526$	42.1166	+	3.65486i	1.83637	+	0.159360i
$527$	−10.0339	+	13.8105i	−0.437083	+	0.601593i
$528$	16.0174	+	0.514206i	0.697070	+	0.0223779i
$529$	5.08521	+	15.6507i	0.221096	+	0.680464i
$530$		0			0
$531$	−2.56656	−	0.833926i	−0.111379	−	0.0361893i
$532$	−25.5549	−	4.46894i	−1.10794	−	0.193753i
$533$	−7.88085	+	24.2548i	−0.341358	+	1.05059i
$534$	−5.89381	−	9.79333i	−0.255050	−	0.423799i
$535$		0			0
$536$	31.9583	−	25.9912i	1.38039	−	1.12265i
$537$	−1.77520	−	2.44336i	−0.0766057	−	0.105439i
$538$	27.8428	−	16.7563i	1.20039	−	0.722416i
$539$	−15.5985	+	21.4694i	−0.671873	+	0.924754i
$540$		0			0
$541$	1.48837	+	2.04857i	0.0639902	+	0.0880749i	0.839813	−	0.542876i	$-0.182665\pi$
$541$	1.48837	+	2.04857i	0.0639902	+	0.0880749i	−0.775822	+	0.630951i	$0.782665\pi$
$542$	31.3550	+	13.2834i	1.34681	+	0.570570i
$543$		−	0.893611i		−	0.0383485i
$544$	14.9576	−	16.1536i	0.641300	−	0.692579i
$545$		0			0
$546$	−7.14454	−	30.8473i	−0.305758	−	1.32014i
$547$	1.55043	+	4.77172i	0.0662915	+	0.204024i	0.978715	−	0.205222i	$-0.0657917\pi$
$547$	1.55043	+	4.77172i	0.0662915	+	0.204024i	−0.912424	+	0.409246i	$0.865792\pi$
$548$	−11.6866	+	11.3174i	−0.499226	+	0.483457i
$549$			3.43326i			0.146528i
$550$		0			0
$551$	−21.6952			−0.924245
$552$	−4.51494	−	5.55148i	−0.192169	−	0.236287i
$553$	−54.0290	+	17.5551i	−2.29755	+	0.746518i
$554$	−4.00917	+	0.928561i	−0.170333	+	0.0394508i
$555$		0			0
$556$	−1.43369	−	0.759721i	−0.0608021	−	0.0322193i
$557$	−12.1514			−0.514869			−0.257435	−	0.966296i	$-0.582877\pi$
$557$	−12.1514			−0.514869			−0.257435	+	0.966296i	$0.582877\pi$
$558$	−11.5489	−	4.89261i	−0.488902	−	0.207121i
$559$	8.67125	−	6.30003i	0.366755	−	0.266463i
$560$		0			0
$561$	12.6142	+	9.16478i	0.532574	+	0.386937i
$562$	17.2619	+	28.6829i	0.728150	+	1.20991i
$563$	28.4313	−	20.6565i	1.19824	−	0.870569i	0.204126	−	0.978945i	$-0.434565\pi$
$563$	28.4313	−	20.6565i	1.19824	−	0.870569i	0.994110	+	0.108375i	$0.0345648\pi$
$564$	−7.26814	+	7.03856i	−0.306044	+	0.296377i
$565$		0			0
$566$	21.1402	+	35.1271i	0.888587	+	1.47650i
$567$	4.03988	+	1.31264i	0.169659	+	0.0551255i
$568$	2.91500	−	10.9715i	0.122311	−	0.460354i
$569$	11.1973	−	34.4618i	0.469415	−	1.44471i	−0.383928	−	0.923363i	$-0.625429\pi$
$569$	11.1973	−	34.4618i	0.469415	−	1.44471i	0.853344	−	0.521349i	$-0.174571\pi$
$570$		0			0
$571$	−34.0692	+	11.0697i	−1.42575	+	0.463255i	−0.917425	−	0.397910i	$-0.869736\pi$
$571$	−34.0692	+	11.0697i	−1.42575	+	0.463255i	−0.508327	+	0.861164i	$0.669736\pi$
$572$	−49.3340	+	7.00426i	−2.06276	+	0.292863i
$573$	−2.10767	−	1.53131i	−0.0880492	−	0.0639715i
$574$	−21.5069	−	1.86636i	−0.897682	−	0.0779005i
$575$		0			0
$576$	14.0423	+	8.02847i	0.585096	+	0.334520i
$577$	−22.3615	+	30.7780i	−0.930922	+	1.28130i	0.0285774	+	0.999592i	$0.490902\pi$
$577$	−22.3615	+	30.7780i	−0.930922	+	1.28130i	−0.959499	+	0.281712i	$0.909098\pi$
$578$	−2.55456	+	0.591660i	−0.106256	+	0.0246098i
$579$	20.7455	−	6.74061i	0.862152	−	0.280130i
$580$		0			0
$581$	5.89547	+	1.91555i	0.244585	+	0.0794706i
$582$	−10.1169	−	0.877941i	−0.419359	−	0.0363918i
$583$	−49.2979	−	16.0179i	−2.04171	−	0.663392i
$584$	−25.5788	+	9.88079i	−1.05846	+	0.408870i
$585$		0			0
$586$	12.8105	−	14.7577i	0.529195	−	0.609635i
$587$	12.8092	−	9.30640i	0.528690	−	0.384116i	−0.291177	−	0.956669i	$-0.594047\pi$
$587$	12.8092	−	9.30640i	0.528690	−	0.384116i	0.819868	+	0.572553i	$0.194047\pi$
$588$	11.6378	−	5.69643i	0.479935	−	0.234917i
$589$	−9.08500	+	12.5044i	−0.374341	+	0.515236i
$590$		0			0
$591$	7.25474	−	5.27087i	0.298420	−	0.216815i
$592$	9.07525	−	11.6834i	0.372990	−	0.480186i
$593$		−	31.5299i		−	1.29478i	−0.762160	−	0.647389i	$-0.775861\pi$
$593$		−	31.5299i		−	1.29478i	0.762160	−	0.647389i	$-0.224139\pi$
$594$	−11.0994	+	26.1998i	−0.455413	+	1.07499i
$595$		0			0
$596$	5.53165	−	0.785363i	0.226585	−	0.0321697i
$597$	−1.89017	−	5.81735i	−0.0773595	−	0.238088i
$598$	16.8019	+	14.5850i	0.687082	+	0.596423i
$599$	28.8872			1.18030			0.590149	−	0.807294i	$-0.299069\pi$
$599$	28.8872			1.18030			0.590149	+	0.807294i	$0.299069\pi$
$600$		0			0
$601$	−16.6170			−0.677822			−0.338911	−	0.940818i	$-0.610059\pi$
$601$	−16.6170			−0.677822			−0.338911	+	0.940818i	$0.610059\pi$
$602$	6.85151	+	5.94747i	0.279247	+	0.242401i
$603$	9.09970	+	28.0060i	0.370568	+	1.14049i
$604$	1.24199	+	8.74789i	0.0505360	+	0.355947i
$605$		0			0
$606$	−4.93321	+	11.6447i	−0.200398	+	0.473034i
$607$		−	46.4232i		−	1.88426i	−0.335249	−	0.942129i	$-0.608821\pi$
$607$		−	46.4232i		−	1.88426i	0.335249	−	0.942129i	$-0.391179\pi$
$608$	13.5430	−	14.6260i	0.549243	−	0.593162i
$609$	18.1337	−	13.1749i	0.734816	−	0.533875i
$610$		0			0
$611$	18.4911	−	25.4508i	0.748070	−	1.02963i
$612$	6.91885	+	14.1352i	0.279678	+	0.571382i
$613$	−29.1219	+	21.1583i	−1.17622	+	0.854576i	−0.991741	−	0.128259i	$-0.959061\pi$
$613$	−29.1219	+	21.1583i	−1.17622	+	0.854576i	−0.184483	+	0.982836i	$0.559061\pi$
$614$	7.15369	−	8.24109i	0.288700	−	0.332583i
$615$		0			0
$616$	−15.1987	−	39.3456i	−0.612374	−	1.58528i
$617$	−8.45602	−	2.74753i	−0.340427	−	0.110611i	0.133814	−	0.991006i	$-0.457277\pi$
$617$	−8.45602	−	2.74753i	−0.340427	−	0.110611i	−0.474241	+	0.880395i	$0.657277\pi$
$618$	14.7615	+	1.28100i	0.593794	+	0.0515292i
$619$	24.2453	+	7.87779i	0.974503	+	0.316635i	0.752632	−	0.658441i	$-0.228784\pi$
$619$	24.2453	+	7.87779i	0.974503	+	0.316635i	0.221870	+	0.975076i	$0.428784\pi$
$620$		0			0
$621$	12.0832	−	3.92607i	0.484882	−	0.157548i
$622$	−13.6600	+	3.16379i	−0.547717	+	0.126856i
$623$	−17.6827	+	24.3381i	−0.708441	+	0.975085i
$624$	22.8853	+	8.25668i	0.916144	+	0.330532i
$625$		0			0
$626$	2.73067	+	0.236967i	0.109140	+	0.00947109i
$627$	11.4213	+	8.29809i	0.456124	+	0.331394i
$628$	−3.69405	−	26.0188i	−0.147409	−	1.03826i
$629$	13.6892	−	4.44790i	0.545825	−	0.177349i
$630$		0			0
$631$	11.0609	−	34.0420i	0.440328	−	1.35519i	−0.447199	−	0.894435i	$-0.647578\pi$
$631$	11.0609	−	34.0420i	0.440328	−	1.35519i	0.887527	−	0.460756i	$-0.152422\pi$
$632$	11.2084	−	42.1863i	0.445846	−	1.67808i
$633$	19.1599	+	6.22541i	0.761536	+	0.247438i
$634$	1.38597	+	2.30296i	0.0550438	+	0.0914624i
$635$		0			0
$636$	17.6065	+	18.1808i	0.698142	+	0.720914i
$637$	−32.5935	+	23.6806i	−1.29140	+	0.938258i
$638$	−18.1883	−	30.2223i	−0.720083	−	1.19651i
$639$	6.56531	+	4.76997i	0.259720	+	0.188697i
$640$		0			0
$641$	−1.61137	+	1.17073i	−0.0636453	+	0.0462410i	−0.619153	−	0.785270i	$-0.712524\pi$
$641$	−1.61137	+	1.17073i	−0.0636453	+	0.0462410i	0.555508	+	0.831511i	$0.312524\pi$
$642$	0.504006	+	0.213519i	0.0198915	+	0.00842694i
$643$	−14.4169			−0.568548			−0.284274	−	0.958743i	$-0.591752\pi$
$643$	−14.4169			−0.568548			−0.284274	+	0.958743i	$0.591752\pi$
$644$	−8.81838	+	16.6414i	−0.347493	+	0.655763i
$645$		0			0
$646$	18.8937	−	4.37597i	0.743363	−	0.172170i
$647$	3.84494	−	1.24930i	0.151160	−	0.0491149i	−0.232460	−	0.972606i	$-0.574677\pi$
$647$	3.84494	−	1.24930i	0.151160	−	0.0491149i	0.383620	+	0.923491i	$0.374677\pi$
$648$	−2.53211	+	2.05933i	−0.0994709	+	0.0808982i
$649$	−5.40693			−0.212240
$650$		0			0
$651$		−	15.9688i		−	0.625868i
$652$	0.670400	+	0.692267i	0.0262549	+	0.0271113i
$653$	10.5252	+	32.3932i	0.411882	+	1.26764i	0.915010	+	0.403431i	$0.132183\pi$
$653$	10.5252	+	32.3932i	0.411882	+	1.26764i	−0.503128	+	0.864212i	$0.667817\pi$
$654$	−2.72493	−	11.7652i	−0.106553	−	0.460056i
$655$		0			0
$656$	10.1752	−	13.0995i	0.397275	−	0.511450i
$657$		−	19.6020i		−	0.764748i
$658$	24.5198	+	10.3877i	0.955880	+	0.404953i
$659$	6.87300	+	9.45988i	0.267734	+	0.368504i	0.921623	−	0.388086i	$-0.126864\pi$
$659$	6.87300	+	9.45988i	0.267734	+	0.368504i	−0.653889	+	0.756591i	$0.726864\pi$
$660$		0			0
$661$	−23.0527	+	31.7294i	−0.896647	+	1.23413i	0.0748777	+	0.997193i	$0.476143\pi$
$661$	−23.0527	+	31.7294i	−0.896647	+	1.23413i	−0.971525	+	0.236937i	$0.923857\pi$
$662$	−36.4331	+	21.9261i	−1.41601	+	0.852182i
$663$	13.9134	+	19.1501i	0.540351	+	0.743729i
$664$	−3.69516	+	3.00522i	−0.143400	+	0.116625i
$665$		0			0
$666$	5.45321	+	9.06122i	0.211308	+	0.351115i
$667$	−4.86700	+	14.9791i	−0.188451	+	0.579993i
$668$	3.48714	−	19.9406i	0.134921	−	0.771525i
$669$	−9.93966	−	3.22959i	−0.384289	−	0.124863i
$670$		0			0
$671$	2.12567	+	6.54212i	0.0820604	+	0.252556i
$672$	−2.43786	+	20.4494i	−0.0940426	+	0.788851i
$673$	19.4849	−	26.8187i	0.751088	−	1.03378i	−0.246816	−	0.969062i	$-0.579384\pi$
$673$	19.4849	−	26.8187i	0.751088	−	1.03378i	0.997903	−	0.0647213i	$-0.0206158\pi$
$674$	−7.02185	−	0.609354i	−0.270472	−	0.0234714i
$675$		0			0
$676$	−48.9047	−	8.55226i	−1.88095	−	0.328933i
$677$	11.1735	+	8.11803i	0.429433	+	0.312001i	0.781422	−	0.624003i	$-0.214495\pi$
$677$	11.1735	+	8.11803i	0.429433	+	0.312001i	−0.351989	+	0.936004i	$0.614495\pi$
$678$	−0.858948	−	3.70861i	−0.0329877	−	0.142428i
$679$	8.25922	+	25.4193i	0.316960	+	0.975502i
$680$		0			0
$681$	−2.88226	+	8.87069i	−0.110448	+	0.339925i
$682$	−25.0357	−	2.17259i	−0.958666	−	0.0831927i
$683$	15.0801	−	46.4117i	0.577023	−	1.77589i	−0.0521629	−	0.998639i	$-0.516611\pi$
$683$	15.0801	−	46.4117i	0.577023	−	1.77589i	0.629186	−	0.777255i	$-0.283389\pi$
$684$	6.26455	+	12.7985i	0.239531	+	0.489362i
$685$		0			0
$686$	1.76605	+	1.53302i	0.0674282	+	0.0585311i
$687$	−5.91471	−	8.14090i	−0.225660	−	0.310595i
$688$	−6.69566	+	1.94036i	−0.255269	+	0.0739756i
$689$	−63.6634	−	46.2542i	−2.42538	−	1.76214i
$690$		0			0
$691$	−18.4219	−	25.3556i	−0.700803	−	0.964573i	−0.999946	−	0.0103648i	$-0.996701\pi$
$691$	−18.4219	−	25.3556i	−0.700803	−	0.964573i	0.299143	−	0.954208i	$-0.403299\pi$
$692$	−1.44833	+	2.73319i	−0.0550573	+	0.103900i
$693$	30.1520			1.14538
$694$	−28.1376	−	11.9203i	−1.06809	−	0.452490i
$695$		0			0
$696$	0.937654	+	17.1968i	0.0355417	+	0.651843i
$697$	15.3484	−	4.98700i	0.581363	−	0.188896i
$698$	4.04909	+	3.51482i	0.153260	+	0.133038i
$699$			4.80146i			0.181608i
$700$		0			0
$701$			10.0510i			0.379622i	0.981821	+	0.189811i	$0.0607875\pi$
$701$			10.0510i			0.379622i	−0.981821	+	0.189811i	$0.939212\pi$
$702$	−28.3167	+	32.6210i	−1.06875	+	1.23120i
$703$	12.3947	−	4.02727i	0.467473	−	0.151891i
$704$	31.7285	+	6.60422i	1.19581	+	0.248906i
$705$		0			0
$706$	−13.7981	+	32.5699i	−0.519298	+	1.22579i
$707$	33.2853			1.25182
$708$	2.33269	+	1.23610i	0.0876678	+	0.0464557i
$709$	−10.3892	−	14.2995i	−0.390175	−	0.537030i	0.568069	−	0.822981i	$-0.307691\pi$
$709$	−10.3892	−	14.2995i	−0.390175	−	0.537030i	−0.958244	+	0.285951i	$0.907691\pi$
$710$		0			0
$711$	25.2441	+	18.3409i	0.946729	+	0.687839i
$712$	−8.32917	−	21.5621i	−0.312149	−	0.808073i
$713$	6.59540	+	9.07779i	0.247000	+	0.339966i
$714$	−13.1347	+	15.1313i	−0.491556	+	0.566274i
$715$		0			0
$716$	−2.68513	−	5.48573i	−0.100348	−	0.205011i
$717$	2.70134	−	8.31386i	0.100883	−	0.310487i
$718$	−2.84009	+	32.7276i	−0.105991	+	1.22138i
$719$	−6.84341	+	21.0618i	−0.255216	+	0.785474i	0.738571	+	0.674176i	$0.235501\pi$
$719$	−6.84341	+	21.0618i	−0.255216	+	0.785474i	−0.993787	+	0.111298i	$0.964499\pi$
$720$		0			0
$721$	−12.0510	−	37.0891i	−0.448801	−	1.38127i
$722$	−9.07014	+	2.10073i	−0.337556	+	0.0781811i
$723$	−2.78031	−	2.02001i	−0.103401	−	0.0751251i
$724$	0.311302	−	1.78013i	0.0115694	−	0.0661578i
$725$		0			0
$726$	−0.654309	+	7.53989i	−0.0242837	+	0.279832i
$727$	6.64344	−	9.14391i	0.246392	−	0.339129i	−0.667852	−	0.744294i	$-0.732786\pi$
$727$	6.64344	−	9.14391i	0.246392	−	0.339129i	0.914243	+	0.405165i	$0.132786\pi$
$728$	−3.48624	−	63.9386i	−0.129209	−	2.36972i
$729$	3.83253	+	11.7953i	0.141946	+	0.436864i
$730$		0			0
$731$	−6.45055	−	2.09591i	−0.238582	−	0.0775201i
$732$	0.578561	−	3.30840i	0.0213842	−	0.122282i
$733$	10.8888	−	33.5122i	0.402186	−	1.23780i	−0.521036	−	0.853535i	$-0.674454\pi$
$733$	10.8888	−	33.5122i	0.402186	−	1.23780i	0.923222	−	0.384267i	$-0.125546\pi$
$734$	−4.83217	+	2.90809i	−0.178359	+	0.107340i
$735$		0			0
$736$	−7.06009	−	12.6317i	−0.260238	−	0.465611i
$737$	34.6792	+	47.7318i	1.27742	+	1.75822i
$738$	6.11417	+	10.1595i	0.225066	+	0.373976i
$739$	11.1878	−	15.3987i	0.411549	−	0.566449i	−0.552046	−	0.833814i	$-0.686153\pi$
$739$	11.1878	−	15.3987i	0.411549	−	0.566449i	0.963595	+	0.267365i	$0.0861528\pi$
$740$		0			0
$741$	12.5976	+	17.3391i	0.462785	+	0.636969i
$742$	25.9840	−	61.3345i	0.953904	−	2.25166i
$743$		−	11.0416i		−	0.405078i	−0.979274	−	0.202539i	$-0.935081\pi$
$743$		−	11.0416i		−	0.405078i	0.979274	−	0.202539i	$-0.0649193\pi$
$744$	10.3044	+	6.66085i	0.377776	+	0.244199i
$745$		0			0
$746$	−28.2981	+	6.55410i	−1.03607	+	0.239963i
$747$	−1.05215	−	3.23818i	−0.0384961	−	0.118479i
$748$	21.9356	+	22.6511i	0.802046	+	0.828207i
$749$		−	1.44066i		−	0.0526404i
$750$		0			0
$751$	−40.7628			−1.48746			−0.743728	−	0.668483i	$-0.766944\pi$
$751$	−40.7628			−1.48746			−0.743728	+	0.668483i	$0.766944\pi$
$752$	−16.9305	+	11.4893i	−0.617393	+	0.418970i
$753$	−9.97275	+	3.24034i	−0.363427	+	0.118085i
$754$	−12.0827	−	52.1686i	−0.440028	−	1.89987i
$755$		0			0
$756$	−32.3094	−	17.1209i	−1.17508	−	0.622681i
$757$	−15.9064			−0.578128			−0.289064	−	0.957310i	$-0.593344\pi$
$757$	−15.9064			−0.578128			−0.289064	+	0.957310i	$0.593344\pi$
$758$	−15.7972	+	37.2888i	−0.573779	+	1.35439i
$759$	8.29150	−	6.02413i	0.300962	−	0.218662i
$760$		0			0
$761$	−28.7709	−	20.9033i	−1.04294	−	0.757743i	−0.0720855	−	0.997398i	$-0.522965\pi$
$761$	−28.7709	−	20.9033i	−1.04294	−	0.757743i	−0.970858	+	0.239656i	$0.922965\pi$
$762$	−4.47897	+	2.69553i	−0.162256	+	0.0976487i
$763$	−25.7148	+	18.6829i	−0.930940	+	0.676368i
$764$	−3.66515	−	3.78470i	−0.132600	−	0.136926i
$765$		0			0
$766$	−14.8152	+	8.91609i	−0.535296	+	0.322151i
$767$	−7.80670	−	2.53655i	−0.281883	−	0.0915895i
$768$	−12.1787	−	10.1029i	−0.439461	−	0.364555i
$769$	−11.6054	+	35.7176i	−0.418500	+	1.28801i	0.490582	+	0.871395i	$0.336784\pi$
$769$	−11.6054	+	35.7176i	−0.418500	+	1.28801i	−0.909082	+	0.416616i	$0.863216\pi$
$770$		0			0
$771$	7.11499	−	2.31180i	0.256240	−	0.0832575i
$772$	43.6744	−	6.20072i	1.57187	−	0.223169i
$773$	32.1938	+	23.3902i	1.15793	+	0.841287i	0.989515	−	0.144429i	$-0.0461347\pi$
$773$	32.1938	+	23.3902i	1.15793	+	0.841287i	0.168416	+	0.985716i	$0.446135\pi$
$774$	0.430836	−	4.96471i	0.0154861	−	0.178453i
$775$		0			0
$776$	−19.8476	−	5.27327i	−0.712488	−	0.189299i
$777$	−7.91432	+	10.8931i	−0.283925	+	0.390789i
$778$	9.02643	+	38.9726i	0.323613	+	1.39724i
$779$	13.8969	−	4.51539i	0.497910	−	0.161781i
$780$		0			0
$781$	15.4636	+	5.02441i	0.553330	+	0.179788i
$782$	1.21722	−	14.0266i	0.0435277	−	0.501589i
$783$	−29.0820	−	9.44930i	−1.03930	−	0.337690i
$784$	25.1676	−	7.29343i	0.898844	−	0.260479i
$785$		0			0
$786$	−16.2763	−	14.1286i	−0.580555	−	0.503952i
$787$	37.0424	−	26.9129i	1.32042	−	0.959341i	0.320492	−	0.947251i	$-0.396152\pi$
$787$	37.0424	−	26.9129i	1.32042	−	0.959341i	0.999927	−	0.0120896i	$-0.00384833\pi$
$788$	16.2880	−	7.97260i	0.580237	−	0.284012i
$789$	17.3769	−	23.9173i	0.618635	−	0.851478i
$790$		0			0
$791$	−8.10579	+	5.88920i	−0.288209	+	0.209396i
$792$	−12.5769	+	19.4565i	−0.446900	+	0.691357i
$793$			10.4429i			0.370840i
$794$	−8.91701	−	3.77764i	−0.316453	−	0.134064i
$795$		0			0
$796$	−1.73878	−	12.2470i	−0.0616293	−	0.434082i
$797$	1.61885	+	4.98230i	0.0573425	+	0.176482i	0.975625	−	0.219443i	$-0.0704240\pi$
$797$	1.61885	+	4.98230i	0.0573425	+	0.176482i	−0.918283	+	0.395925i	$0.870424\pi$
$798$	−11.8926	+	13.7004i	−0.420994	+	0.484987i
$799$	−19.9072			−0.704266
$800$		0			0
$801$	16.5238			0.583841
$802$	31.6247	−	36.4318i	1.11671	−	1.28645i
$803$	−12.1364	−	37.3519i	−0.428283	−	1.31812i
$804$	−4.04930	−	28.5209i	−0.142808	−	1.00586i
$805$		0			0
$806$	−35.1281	−	14.8818i	−1.23734	−	0.524190i
$807$		−	22.7249i		−	0.799956i
$808$	−13.8838	+	21.4784i	−0.488432	+	0.755606i
$809$	8.37189	−	6.08254i	0.294340	−	0.213851i	−0.430808	−	0.902444i	$-0.641771\pi$
$809$	8.37189	−	6.08254i	0.294340	−	0.213851i	0.725148	+	0.688593i	$0.241771\pi$
$810$		0			0
$811$	7.75245	−	10.6703i	0.272225	−	0.374686i	−0.650914	−	0.759151i	$-0.725614\pi$
$811$	7.75245	−	10.6703i	0.272225	−	0.374686i	0.923139	+	0.384465i	$0.125614\pi$
$812$	40.7131	−	19.9281i	1.42875	−	0.699339i
$813$	19.2655	−	13.9972i	0.675671	−	0.490904i
$814$	16.0013	+	13.8900i	0.560846	+	0.486844i
$815$		0			0
$816$	−4.28521	−	14.7871i	−0.150012	−	0.517652i
$817$	−5.84054	−	1.89771i	−0.204334	−	0.0663923i
$818$	−3.30926	+	38.1341i	−0.115706	+	1.33333i
$819$	43.5345	+	14.1452i	1.52122	+	0.494273i
$820$		0			0
$821$	22.3506	−	7.26213i	0.780040	−	0.253450i	0.108183	−	0.994131i	$-0.465497\pi$
$821$	22.3506	−	7.26213i	0.780040	−	0.253450i	0.671857	+	0.740681i	$0.265497\pi$
$822$	2.56700	+	11.0833i	0.0895345	+	0.386575i
$823$	13.8810	−	19.1055i	0.483861	−	0.665977i	−0.495380	−	0.868676i	$-0.664971\pi$
$823$	13.8810	−	19.1055i	0.483861	−	0.665977i	0.979241	+	0.202699i	$0.0649713\pi$
$824$	28.9595	+	7.69418i	1.00885	+	0.268040i
$825$		0			0
$826$	0.600712	−	6.92227i	0.0209015	−	0.240857i
$827$	−35.9043	−	26.0860i	−1.24852	−	0.907100i	−0.250381	−	0.968147i	$-0.580556\pi$
$827$	−35.9043	−	26.0860i	−1.24852	−	0.907100i	−0.998135	+	0.0610478i	$0.980556\pi$
$828$	10.2419	−	1.45410i	0.355930	−	0.0505336i
$829$	−19.4026	+	6.30430i	−0.673881	+	0.218957i	−0.625915	−	0.779892i	$-0.715274\pi$
$829$	−19.4026	+	6.30430i	−0.673881	+	0.218957i	−0.0479668	+	0.998849i	$0.515274\pi$
$830$		0			0
$831$	−0.889314	+	2.73703i	−0.0308499	+	0.0949464i
$832$	42.7124	+	24.4202i	1.48079	+	0.846617i
$833$	24.2463	+	7.87811i	0.840085	+	0.272960i
$834$	−0.972187	+	0.585081i	−0.0336641	+	0.0202597i
$835$		0			0
$836$	19.8612	+	20.5090i	0.686914	+	0.709320i
$837$	−17.6246	+	12.8050i	−0.609194	+	0.442605i
$838$	−25.0082	+	15.0504i	−0.863893	+	0.519907i
$839$	−36.5182	−	26.5320i	−1.26075	−	0.915988i	−0.261955	−	0.965080i	$-0.584367\pi$
$839$	−36.5182	−	26.5320i	−1.26075	−	0.915988i	−0.998794	+	0.0490920i	$0.984367\pi$
$840$		0			0
$841$	7.20604	−	5.23549i	0.248484	−	0.180534i
$842$	−5.17519	+	12.2159i	−0.178349	+	0.420987i
$843$	23.4106			0.806305
$844$	35.9988	+	19.0760i	1.23913	+	0.656622i
$845$		0			0
$846$	−3.30029	−	14.2494i	−0.113466	−	0.489904i
$847$	18.9444	−	6.15541i	0.650937	−	0.211502i
$848$	28.7396	+	42.3506i	0.986922	+	1.45432i
$849$	28.6703			0.983963
$850$		0			0
$851$		−	9.46116i		−	0.324324i
$852$	−5.52272	−	5.70286i	−0.189205	−	0.195377i
$853$	−0.692652	−	2.13176i	−0.0237160	−	0.0729902i	0.938498	−	0.345285i	$-0.112218\pi$
$853$	−0.692652	−	2.13176i	−0.0237160	−	0.0729902i	−0.962214	+	0.272294i	$0.912218\pi$
$854$	−8.61178	+	1.99457i	−0.294689	+	0.0682528i
$855$		0			0
$856$	0.929627	+	0.600920i	0.0317740	+	0.0205390i
$857$		−	2.14330i		−	0.0732138i	−0.999330	−	0.0366069i	$-0.988345\pi$
$857$		−	2.14330i		−	0.0732138i	0.999330	−	0.0366069i	$-0.0116549\pi$
$858$	−13.5928	+	32.0854i	−0.464051	+	1.09538i
$859$	−5.15215	−	7.09132i	−0.175789	−	0.241953i	0.712026	−	0.702153i	$-0.247778\pi$
$859$	−5.15215	−	7.09132i	−0.175789	−	0.241953i	−0.887815	+	0.460200i	$0.847778\pi$
$860$		0			0
$861$	−8.87356	+	12.2134i	−0.302410	+	0.416232i
$862$	−0.748866	−	1.24434i	−0.0255065	−	0.0423823i
$863$	1.54670	+	2.12885i	0.0526504	+	0.0724670i	0.834530	−	0.550962i	$-0.185739\pi$
$863$	1.54670	+	2.12885i	0.0526504	+	0.0724670i	−0.781880	+	0.623429i	$0.785739\pi$
$864$	24.5245	−	13.7072i	0.834341	−	0.466328i
$865$		0			0
$866$	32.6307	−	19.6378i	1.10884	−	0.667318i
$867$	−0.566652	+	1.74398i	−0.0192445	+	0.0592285i
$868$	5.56296	−	31.8108i	0.188819	−	1.07973i
$869$	59.4586	+	19.3193i	2.01699	+	0.655361i
$870$		0			0
$871$	27.6785	+	85.1858i	0.937851	+	2.88641i
$872$	−1.32966	−	24.3862i	−0.0450278	−	0.825822i
$873$	8.62895	−	11.8767i	0.292046	−	0.401966i
$874$	1.10211	−	12.7001i	0.0372794	−	0.429587i
$875$		0			0
$876$	−3.30326	+	18.8891i	−0.111607	+	0.638205i
$877$	17.1035	+	12.4265i	0.577546	+	0.419611i	0.837838	−	0.545918i	$-0.183819\pi$
$877$	17.1035	+	12.4265i	0.577546	+	0.419611i	−0.260293	+	0.965530i	$0.583819\pi$
$878$	2.08444	−	0.482776i	0.0703464	−	0.0162929i
$879$	−4.22306	−	12.9973i	−0.142440	−	0.438387i
$880$		0			0
$881$	−9.15253	+	28.1686i	−0.308357	+	0.949024i	0.670047	+	0.742319i	$0.266274\pi$
$881$	−9.15253	+	28.1686i	−0.308357	+	0.949024i	−0.978403	+	0.206705i	$0.933726\pi$
$882$	−1.61943	+	18.6613i	−0.0545289	+	0.628360i
$883$	9.33779	−	28.7388i	0.314242	−	0.967137i	−0.661824	−	0.749660i	$-0.730217\pi$
$883$	9.33779	−	28.7388i	0.314242	−	0.967137i	0.976065	−	0.217477i	$-0.0697827\pi$
$884$	21.0450	+	42.9951i	0.707822	+	1.44608i
$885$		0			0
$886$	14.0065	−	16.1355i	0.470556	−	0.542083i
$887$	−0.435322	−	0.599169i	−0.0146167	−	0.0201181i	0.801646	−	0.597799i	$-0.203958\pi$
$887$	−0.435322	−	0.599169i	−0.0146167	−	0.0201181i	−0.816263	+	0.577681i	$0.803958\pi$
$888$	−3.72793	−	9.65064i	−0.125101	−	0.323854i
$889$	11.1310	+	8.08715i	0.373322	+	0.271234i
$890$		0			0
$891$	−2.74769	−	3.78188i	−0.0920512	−	0.126698i
$892$	−18.6753	−	9.89615i	−0.625295	−	0.331347i
$893$	−18.0246			−0.603171
$894$	1.52411	−	3.59762i	0.0509740	−	0.120322i
$895$		0			0
$896$	−11.9802	+	39.8870i	−0.400229	+	1.33253i
$897$	14.7976	−	4.80804i	0.494079	−	0.160536i
$898$	30.1334	−	34.7138i	1.00556	−	1.15841i
$899$		−	27.0063i		−	0.900709i
$900$		0			0
$901$			49.7965i			1.65896i
$902$	17.9408	+	15.5735i	0.597362	+	0.518541i
$903$	6.03419	−	1.96063i	0.200805	−	0.0652456i
$904$	−0.419132	−	7.68698i	−0.0139401	−	0.255665i
$905$		0			0
$906$	5.68937	+	2.41027i	0.189017	+	0.0800759i
$907$	25.0444			0.831586			0.415793	−	0.909459i	$-0.363504\pi$
$907$	25.0444			0.831586			0.415793	+	0.909459i	$0.363504\pi$
$908$	−8.83185	+	16.6668i	−0.293095	+	0.553109i
$909$	−10.7462	−	14.7908i	−0.356428	−	0.490581i
$910$		0			0
$911$	−10.3682	−	7.53297i	−0.343515	−	0.249579i	0.402628	−	0.915364i	$-0.368097\pi$
$911$	−10.3682	−	7.53297i	−0.343515	−	0.249579i	−0.746144	+	0.665785i	$0.768097\pi$
$912$	−3.87997	−	13.3887i	−0.128479	−	0.443344i
$913$	−4.00976	−	5.51897i	−0.132704	−	0.182651i
$914$	0.794266	+	0.689464i	0.0262720	+	0.0228054i
$915$		0			0
$916$	−8.94646	−	18.2776i	−0.295599	−	0.603910i
$917$	−17.5296	+	53.9505i	−0.578878	+	1.78160i
$918$	27.2326	+	2.36324i	0.898810	+	0.0779984i
$919$	−9.20989	+	28.3451i	−0.303806	+	0.935019i	0.676314	+	0.736613i	$0.263576\pi$
$919$	−9.20989	+	28.3451i	−0.303806	+	0.935019i	−0.980120	+	0.198405i	$0.936424\pi$
$920$		0			0
$921$	−2.35827	−	7.25801i	−0.0777076	−	0.239159i
$922$	−8.80885	−	38.0332i	−0.290104	−	1.25256i
$923$	19.9697	+	14.5088i	0.657310	+	0.477564i
$924$	−29.0555	−	5.08111i	−0.955854	−	0.167156i
$925$		0			0
$926$	25.1765	+	2.18481i	0.827352	+	0.0717973i
$927$	−12.5904	+	17.3292i	−0.413524	+	0.569167i
$928$	−4.12288	+	34.5837i	−0.135340	+	1.13526i
$929$	−1.45324	−	4.47263i	−0.0476794	−	0.146742i	0.924382	−	0.381467i	$-0.124581\pi$
$929$	−1.45324	−	4.47263i	−0.0476794	−	0.146742i	−0.972062	+	0.234725i	$0.924581\pi$
$930$		0			0
$931$	21.9534	+	7.13309i	0.719494	+	0.233778i
$932$	−1.67265	+	9.56478i	−0.0547896	+	0.313305i
$933$	−3.03007	+	9.32559i	−0.0991999	+	0.305306i
$934$	−4.91066	−	8.15970i	−0.160682	−	0.266994i
$935$		0			0
$936$	−27.2865	+	22.1917i	−0.891888	+	0.725359i
$937$	−26.5112	−	36.4895i	−0.866083	−	1.19206i	−0.980085	−	0.198581i	$-0.936367\pi$
$937$	−26.5112	−	36.4895i	−0.866083	−	1.19206i	0.114001	−	0.993481i	$-0.463633\pi$
$938$	−64.9620	+	39.0953i	−2.12108	+	1.27651i
$939$	1.12665	−	1.55070i	0.0367668	−	0.0506052i
$940$		0			0
$941$	19.7024	+	27.1181i	0.642281	+	0.884024i	0.998735	−	0.0502890i	$-0.0160142\pi$
$941$	19.7024	+	27.1181i	0.642281	+	0.884024i	−0.356454	+	0.934313i	$0.616014\pi$
$942$	−16.9219	−	7.16885i	−0.551344	−	0.233574i
$943$		−	10.6079i		−	0.345441i
$944$	4.21624	+	3.27502i	0.137227	+	0.106593i
$945$		0			0
$946$	−2.25288	−	9.72707i	−0.0732475	−	0.316254i
$947$	13.5036	+	41.5598i	0.438808	+	1.35051i	0.889133	+	0.457648i	$0.151308\pi$
$947$	13.5036	+	41.5598i	0.438808	+	1.35051i	−0.450325	+	0.892865i	$0.648692\pi$
$948$	−21.2353	−	21.9280i	−0.689691	−	0.712187i
$949$		−	59.6234i		−	1.93546i
$950$		0			0
$951$	1.87965			0.0609518
$952$	−31.4364	+	25.5667i	−1.01886	+	0.828623i
$953$	18.8268	−	6.11721i	0.609861	−	0.198156i	0.0122276	−	0.999925i	$-0.496108\pi$
$953$	18.8268	−	6.11721i	0.609861	−	0.198156i	0.597634	+	0.801769i	$0.296108\pi$
$954$	−35.6439	+	8.25546i	−1.15401	+	0.267280i
$955$		0			0
$956$	8.27746	−	15.6206i	0.267712	−	0.505207i
$957$	−24.6671			−0.797373
$958$	6.45587	+	2.73499i	0.208580	+	0.0883636i
$959$	24.2245	−	17.6001i	0.782249	−	0.568338i
$960$		0			0
$961$	9.51394	+	6.91228i	0.306901	+	0.222977i
$962$	16.5870	+	27.5615i	0.534787	+	0.888619i
$963$	−0.640177	+	0.465116i	−0.0206294	+	0.0149882i
$964$	−4.83484	−	4.99254i	−0.155720	−	0.160799i
$965$		0			0
$966$	6.79126	+	11.2846i	0.218505	+	0.363075i
$967$	−26.8836	−	8.73502i	−0.864519	−	0.280899i	−0.157004	−	0.987598i	$-0.550184\pi$
$967$	−26.8836	−	8.73502i	−0.864519	−	0.280899i	−0.707515	+	0.706699i	$0.750184\pi$
$968$	−3.93004	+	14.7920i	−0.126316	+	0.475432i
$969$	4.19101	−	12.8986i	0.134635	−	0.414363i
$970$		0			0
$971$	−43.8882	+	14.2601i	−1.40844	+	0.457629i	−0.911910	−	0.410391i	$-0.865392\pi$
$971$	−43.8882	+	14.2601i	−1.40844	+	0.457629i	−0.496528	+	0.868021i	$0.665392\pi$
$972$	4.50964	+	31.7633i	0.144647	+	1.01881i
$973$	2.41605	+	1.75536i	0.0774550	+	0.0562744i
$974$	53.5544	+	4.64743i	1.71599	+	0.148913i
$975$		0			0
$976$	2.30505	−	6.38898i	0.0737829	−	0.204506i
$977$	2.24013	−	3.08328i	0.0716682	−	0.0986428i	−0.771678	−	0.636013i	$-0.780582\pi$
$977$	2.24013	−	3.08328i	0.0716682	−	0.0986428i	0.843346	+	0.537371i	$0.180582\pi$
$978$	0.656532	−	0.152059i	0.0209936	−	0.00486231i
$979$	31.4864	−	10.2306i	1.00631	−	0.326970i
$980$		0			0
$981$	16.6041	+	5.39499i	0.530127	+	0.172249i
$982$	−22.5173	−	1.95404i	−0.718557	−	0.0623561i
$983$	−20.2704	−	6.58625i	−0.646525	−	0.210069i	−0.0326438	−	0.999467i	$-0.510393\pi$
$983$	−20.2704	−	6.58625i	−0.646525	−	0.210069i	−0.613881	+	0.789398i	$0.710393\pi$
$984$	−4.17977	−	10.8203i	−0.133246	−	0.344940i
$985$		0			0
$986$	−22.2133	+	25.5898i	−0.707416	+	0.814947i
$987$	15.0657	−	10.9459i	0.479548	−	0.348412i
$988$	19.0549	+	38.9291i	0.606216	+	1.23850i
$989$	−2.62048	+	3.60678i	−0.0833265	+	0.114689i
$990$		0			0
$991$	18.4326	−	13.3921i	0.585532	−	0.425414i	−0.255182	−	0.966893i	$-0.582135\pi$
$991$	18.4326	−	13.3921i	0.585532	−	0.425414i	0.840714	+	0.541479i	$0.182135\pi$
$992$	18.2065	+	16.8585i	0.578057	+	0.535257i
$993$			29.7362i			0.943651i
$994$	−8.15056	+	19.2392i	−0.258520	+	0.610229i
$995$		0			0
$996$	0.468198	+	3.29772i	0.0148354	+	0.104492i
$997$	5.01908	+	15.4471i	0.158956	+	0.489216i	0.998540	−	0.0540134i	$-0.0172014\pi$
$997$	5.01908	+	15.4471i	0.158956	+	0.489216i	−0.839584	+	0.543229i	$0.817201\pi$
$998$	−8.63717	−	7.49751i	−0.273405	−	0.237330i
$999$	18.3689			0.581165

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1000.2.o.a.549.20		112
5.2	odd	4		1000.2.t.b.701.45		224
5.3	odd	4		1000.2.t.b.701.12		224
5.4	even	2		200.2.o.a.109.9	✓	112
8.5	even	2	inner	1000.2.o.a.549.19		112
20.19	odd	2		800.2.be.a.209.11		112
25.2	odd	20		1000.2.t.b.301.47		224
25.11	even	5		200.2.o.a.189.10	yes	112
25.14	even	10	inner	1000.2.o.a.949.19		112
25.23	odd	20		1000.2.t.b.301.10		224
40.13	odd	4		1000.2.t.b.701.10		224
40.19	odd	2		800.2.be.a.209.18		112
40.29	even	2		200.2.o.a.109.10	yes	112
40.37	odd	4		1000.2.t.b.701.47		224
100.11	odd	10		800.2.be.a.689.18		112
200.11	odd	10		800.2.be.a.689.11		112
200.61	even	10		200.2.o.a.189.9	yes	112
200.77	odd	20		1000.2.t.b.301.45		224
200.173	odd	20		1000.2.t.b.301.12		224
200.189	even	10	inner	1000.2.o.a.949.20		112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.109.9	✓	112	5.4	even	2
200.2.o.a.109.10	yes	112	40.29	even	2
200.2.o.a.189.9	yes	112	200.61	even	10
200.2.o.a.189.10	yes	112	25.11	even	5
800.2.be.a.209.11		112	20.19	odd	2
800.2.be.a.209.18		112	40.19	odd	2
800.2.be.a.689.11		112	200.11	odd	10
800.2.be.a.689.18		112	100.11	odd	10
1000.2.o.a.549.19		112	8.5	even	2	inner
1000.2.o.a.549.20		112	1.1	even	1	trivial
1000.2.o.a.949.19		112	25.14	even	10	inner
1000.2.o.a.949.20		112	200.189	even	10	inner
1000.2.t.b.301.10		224	25.23	odd	20
1000.2.t.b.301.12		224	200.173	odd	20
1000.2.t.b.301.45		224	200.77	odd	20
1000.2.t.b.301.47		224	25.2	odd	20
1000.2.t.b.701.10		224	40.13	odd	4
1000.2.t.b.701.12		224	5.3	odd	4
1000.2.t.b.701.45		224	5.2	odd	4
1000.2.t.b.701.47		224	40.37	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1000 = 2^{3} \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1000.o (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.927056 - 1.06797i) q^{2} +(-0.305611 - 0.940574i) q^{3} +(-0.281133 - 1.98014i) q^{4} +(-1.28783 - 0.545581i) q^{6} +3.68114i q^{7} +(-2.37537 - 1.53546i) q^{8} +(1.63577 - 1.18846i) q^{9} +(2.38116 - 3.27739i) q^{11} +(-1.77655 + 0.869580i) q^{12} +(4.97551 - 3.61492i) q^{13} +(3.93136 + 3.41262i) q^{14} +(-3.84193 + 1.11337i) q^{16} +(-3.70129 - 1.20262i) q^{17} +(0.247211 - 2.84872i) q^{18} +(-3.35127 - 1.08889i) q^{19} +(3.46238 - 1.12500i) q^{21} +(-1.29269 - 5.58134i) q^{22} +(-1.50362 + 2.06955i) q^{23} +(-0.718277 + 2.70346i) q^{24} +(0.751941 - 8.66495i) q^{26} +(-4.01804 - 2.91928i) q^{27} +(7.28918 - 1.03489i) q^{28} +(5.85554 - 1.90258i) q^{29} +(1.35546 - 4.17167i) q^{31} +(-2.37264 + 5.13523i) q^{32} +(-3.81033 - 1.23805i) q^{33} +(-4.71567 + 2.83798i) q^{34} +(-2.81318 - 2.90494i) q^{36} +(-2.99215 + 2.17392i) q^{37} +(-4.26972 + 2.56960i) q^{38} +(-4.92068 - 3.57508i) q^{39} +(-3.35481 + 2.43741i) q^{41} +(2.00836 - 4.74067i) q^{42} +1.74279 q^{43} +(-7.15911 - 3.79365i) q^{44} +(0.816288 + 3.52441i) q^{46} +(4.86486 - 1.58069i) q^{47} +(2.22134 + 3.27336i) q^{48} -6.55078 q^{49} +3.84887i q^{51} +(-8.55685 - 8.83595i) q^{52} +(-3.95398 - 12.1691i) q^{53} +(-6.84266 + 1.58483i) q^{54} +(5.65224 - 8.74405i) q^{56} +3.48489i q^{57} +(3.39651 - 8.01736i) q^{58} +(-0.784512 - 1.07979i) q^{59} +(-0.998070 + 1.37373i) q^{61} +(-3.19865 - 5.31497i) q^{62} +(4.37487 + 6.02149i) q^{63} +(3.28472 + 7.29456i) q^{64} +(-4.85460 + 2.92159i) q^{66} +(-4.50052 + 13.8512i) q^{67} +(-1.34081 + 7.66718i) q^{68} +(2.40609 + 0.781786i) q^{69} +(1.24027 + 3.81715i) q^{71} +(-5.71038 + 0.311357i) q^{72} +(5.69843 - 7.84322i) q^{73} +(-0.452199 + 5.21089i) q^{74} +(-1.21401 + 6.94211i) q^{76} +(12.0645 + 8.76538i) q^{77} +(-8.37984 + 1.94085i) q^{78} +(4.76893 + 14.6772i) q^{79} +(0.356584 - 1.09745i) q^{81} +(-0.507007 + 5.84247i) q^{82} +(0.520370 - 1.60153i) q^{83} +(-3.20105 - 6.53974i) q^{84} +(1.61566 - 1.86125i) q^{86} +(-3.57904 - 4.92612i) q^{87} +(-10.6884 + 4.12881i) q^{88} +(6.61157 + 4.80359i) q^{89} +(13.3070 + 18.3156i) q^{91} +(4.52072 + 2.39556i) q^{92} -4.33801 q^{93} +(2.82186 - 6.66092i) q^{94} +(5.55517 + 0.662258i) q^{96} +(6.90528 - 2.24366i) q^{97} +(-6.07294 + 6.99606i) q^{98} -8.19095i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 5 q^{2} - 3 q^{4} + q^{6} - 10 q^{8} - 30 q^{9} + 5 q^{12} - 3 q^{14} - 15 q^{16} + 10 q^{17} + 30 q^{22} + 10 q^{23} - 16 q^{24} - 14 q^{26} - 15 q^{28} - 18 q^{31} + 10 q^{33} + 9 q^{34} + 41 q^{36}+ \cdots - 90 q^{98}+O(q^{100}) \) 112 * q + 5 * q^2 - 3 * q^4 + q^6 - 10 * q^8 - 30 * q^9 + 5 * q^12 - 3 * q^14 - 15 * q^16 + 10 * q^17 + 30 * q^22 + 10 * q^23 - 16 * q^24 - 14 * q^26 - 15 * q^28 - 18 * q^31 + 10 * q^33 + 9 * q^34 + 41 * q^36 - 45 * q^38 - 10 * q^39 - 10 * q^41 - 75 * q^42 - 32 * q^44 + 13 * q^46 + 10 * q^47 + 70 * q^48 - 80 * q^49 + 100 * q^52 + 43 * q^54 + 36 * q^56 + 30 * q^58 - 20 * q^62 - 60 * q^63 - 36 * q^64 + 40 * q^66 + 22 * q^71 + 65 * q^72 + 10 * q^73 + 4 * q^74 - 36 * q^76 + 55 * q^78 + 14 * q^79 - 6 * q^81 + 78 * q^84 - 59 * q^86 + 10 * q^87 - 110 * q^88 + 24 * q^89 - 90 * q^92 + 45 * q^94 + 46 * q^96 + 50 * q^97 - 90 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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