LMFDB - Embedded newform 490.2.l.d.117.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [490,2,Mod(117,490)] 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("490.117"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(490, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([3, 10])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	490.l (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,0,0,0,0,0,0,0,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$3.91266969904$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			117.4
Character	$\chi$	$=$	490.117
Dual form			490.2.l.d.423.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.965926 + 0.258819i) q^{2} +(0.830751 - 3.10041i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.65469 - 1.50399i) q^{5} +3.20978i q^{6} +(-0.707107 + 0.707107i) q^{8} +(-6.32429 - 3.65133i) q^{9} +(-1.20905 + 1.88101i) q^{10} +(-1.22833 - 2.12753i) q^{11} +(-0.830751 - 3.10041i) q^{12} +(-0.884667 - 0.884667i) q^{13} +(-3.28835 - 6.37966i) q^{15} +(0.500000 - 0.866025i) q^{16} +(4.69086 + 1.25691i) q^{17} +(7.05383 + 1.89007i) q^{18} +(-0.522496 + 0.904990i) q^{19} +(0.681009 - 2.12984i) q^{20} +(1.73712 + 1.73712i) q^{22} +(2.13100 + 7.95301i) q^{23} +(1.60489 + 2.77975i) q^{24} +(0.476010 - 4.97729i) q^{25} +(1.08349 + 0.625554i) q^{26} +(-9.76556 + 9.76556i) q^{27} -1.56821i q^{29} +(4.82748 + 5.31119i) q^{30} +(0.594910 - 0.343471i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-7.61663 + 2.04087i) q^{33} -4.85633 q^{34} -7.30266 q^{36} +(-2.63765 + 0.706756i) q^{37} +(0.270464 - 1.00938i) q^{38} +(-3.47777 + 2.00789i) q^{39} +(-0.106560 + 2.23353i) q^{40} -7.63326i q^{41} +(4.56555 - 4.56555i) q^{43} +(-2.12753 - 1.22833i) q^{44} +(-15.9563 + 3.46986i) q^{45} +(-4.11678 - 7.13047i) q^{46} +(2.63166 + 9.82150i) q^{47} +(-2.26965 - 2.26965i) q^{48} +(0.828427 + 4.93089i) q^{50} +(7.79387 - 13.4994i) q^{51} +(-1.20848 - 0.323811i) q^{52} +(-1.72513 - 0.462247i) q^{53} +(6.90529 - 11.9603i) q^{54} +(-5.23229 - 1.67300i) q^{55} +(2.37177 + 2.37177i) q^{57} +(0.405882 + 1.51477i) q^{58} +(3.42620 + 5.93435i) q^{59} +(-6.03763 - 3.88077i) q^{60} +(0.544847 + 0.314567i) q^{61} +(-0.485742 + 0.485742i) q^{62} -1.00000i q^{64} +(-2.79439 - 0.133318i) q^{65} +(6.82889 - 3.94266i) q^{66} +(0.136078 - 0.507848i) q^{67} +(4.69086 - 1.25691i) q^{68} +26.4279 q^{69} -10.9419 q^{71} +(7.05383 - 1.89007i) q^{72} +(2.60957 - 9.73903i) q^{73} +(2.36485 - 1.36535i) q^{74} +(-15.0362 - 5.61071i) q^{75} +1.04499i q^{76} +(2.83958 - 2.83958i) q^{78} +(-7.06156 - 4.07700i) q^{79} +(-0.475150 - 2.18500i) q^{80} +(11.2105 + 19.4171i) q^{81} +(1.97563 + 7.37316i) q^{82} +(6.80896 + 6.80896i) q^{83} +(9.65231 - 4.97522i) q^{85} +(-3.22833 + 5.59163i) q^{86} +(-4.86208 - 1.30279i) q^{87} +(2.37295 + 0.635829i) q^{88} +(3.90949 - 6.77143i) q^{89} +(14.5146 - 7.48143i) q^{90} +(5.82200 + 5.82200i) q^{92} +(-0.570678 - 2.12980i) q^{93} +(-5.08398 - 8.80571i) q^{94} +(0.496528 + 2.28331i) q^{95} +(2.77975 + 1.60489i) q^{96} +(7.49243 - 7.49243i) q^{97} +17.9401i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{11} - 48 q^{15} + 16 q^{16} + 16 q^{18} + 32 q^{22} - 16 q^{23} - 32 q^{25} - 40 q^{30} - 96 q^{36} + 48 q^{37} + 32 q^{43} + 16 q^{46} - 64 q^{50} + 80 q^{51} - 32 q^{53} + 96 q^{57} - 16 q^{58}+ \cdots - 40 q^{95}+O(q^{100}) $ 32 * q + 16 * q^11 - 48 * q^15 + 16 * q^16 + 16 * q^18 + 32 * q^22 - 16 * q^23 - 32 * q^25 - 40 * q^30 - 96 * q^36 + 48 * q^37 + 32 * q^43 + 16 * q^46 - 64 * q^50 + 80 * q^51 - 32 * q^53 + 96 * q^57 - 16 * q^58 - 40 * q^60 - 32 * q^65 - 16 * q^67 + 32 * q^71 + 16 * q^72 + 112 * q^81 + 48 * q^85 - 48 * q^86 + 16 * q^88 + 32 * q^92 - 64 * q^93 - 40 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$3$	0.830751	−	3.10041i	0.479634	−	1.79002i	−0.123459	−	0.992350i	$-0.539399\pi$
$3$	0.830751	−	3.10041i	0.479634	−	1.79002i	0.603094	−	0.797670i	$-0.293935\pi$
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	1.65469	−	1.50399i	0.740001	−	0.672606i
$5$	1.65469	−	1.50399i	0.740001	−	0.672606i
$6$			3.20978i			1.31039i
$7$		0			0
$7$		0			0
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−6.32429	−	3.65133i	−2.10810	−	1.21711i
$10$	−1.20905	+	1.88101i	−0.382334	+	0.594828i
$11$	−1.22833	−	2.12753i	−0.370355	−	0.641473i	0.619265	−	0.785182i	$-0.287431\pi$
$11$	−1.22833	−	2.12753i	−0.370355	−	0.641473i	−0.989620	+	0.143708i	$0.954097\pi$
$12$	−0.830751	−	3.10041i	−0.239817	−	0.895010i
$13$	−0.884667	−	0.884667i	−0.245363	−	0.245363i	0.573702	−	0.819064i	$-0.305507\pi$
$13$	−0.884667	−	0.884667i	−0.245363	−	0.245363i	−0.819064	+	0.573702i	$0.805507\pi$
$14$		0			0
$15$	−3.28835	−	6.37966i	−0.849049	−	1.64722i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	4.69086	+	1.25691i	1.13770	+	0.304846i	0.778026	−	0.628232i	$-0.216221\pi$
$17$	4.69086	+	1.25691i	1.13770	+	0.304846i	0.359674	+	0.933078i	$0.382888\pi$
$18$	7.05383	+	1.89007i	1.66260	+	0.445493i
$19$	−0.522496	+	0.904990i	−0.119869	+	0.207619i	−0.919716	−	0.392585i	$-0.871581\pi$
$19$	−0.522496	+	0.904990i	−0.119869	+	0.207619i	0.799847	+	0.600204i	$0.204914\pi$
$20$	0.681009	−	2.12984i	0.152278	−	0.476247i
$21$		0			0
$22$	1.73712	+	1.73712i	0.370355	+	0.370355i
$23$	2.13100	+	7.95301i	0.444345	+	1.65832i	0.717661	+	0.696392i	$0.245213\pi$
$23$	2.13100	+	7.95301i	0.444345	+	1.65832i	−0.273317	+	0.961924i	$0.588121\pi$
$24$	1.60489	+	2.77975i	0.327596	+	0.567414i
$25$	0.476010	−	4.97729i	0.0952020	−	0.995458i
$26$	1.08349	+	0.625554i	0.212490	+	0.122681i
$27$	−9.76556	+	9.76556i	−1.87938	+	1.87938i
$28$		0			0
$29$		−	1.56821i		−	0.291209i	−0.989343	−	0.145604i	$-0.953487\pi$
$29$		−	1.56821i		−	0.291209i	0.989343	−	0.145604i	$-0.0465126\pi$
$30$	4.82748	+	5.31119i	0.881373	+	0.969686i
$31$	0.594910	−	0.343471i	0.106849	−	0.0616893i	−0.445623	−	0.895221i	$-0.647018\pi$
$31$	0.594910	−	0.343471i	0.106849	−	0.0616893i	0.552472	+	0.833531i	$0.313685\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$	−7.61663	+	2.04087i	−1.32589	+	0.355270i
$34$	−4.85633			−0.832855
$35$		0			0
$36$	−7.30266			−1.21711
$37$	−2.63765	+	0.706756i	−0.433627	+	0.116190i	−0.469028	−	0.883183i	$-0.655396\pi$
$37$	−2.63765	+	0.706756i	−0.433627	+	0.116190i	0.0354013	+	0.999373i	$0.488729\pi$
$38$	0.270464	−	1.00938i	0.0438750	−	0.163744i
$39$	−3.47777	+	2.00789i	−0.556888	+	0.321520i
$40$	−0.106560	+	2.23353i	−0.0168486	+	0.353152i
$41$		−	7.63326i		−	1.19212i	−0.802942	−	0.596058i	$-0.796733\pi$
$41$		−	7.63326i		−	1.19212i	0.802942	−	0.596058i	$-0.203267\pi$
$42$		0			0
$43$	4.56555	−	4.56555i	0.696239	−	0.696239i	−0.267358	−	0.963597i	$-0.586151\pi$
$43$	4.56555	−	4.56555i	0.696239	−	0.696239i	0.963597	+	0.267358i	$0.0861507\pi$
$44$	−2.12753	−	1.22833i	−0.320737	−	0.185177i
$45$	−15.9563	+	3.46986i	−2.37863	+	0.517257i
$46$	−4.11678	−	7.13047i	−0.606986	−	1.05133i
$47$	2.63166	+	9.82150i	0.383867	+	1.43261i	0.839944	+	0.542672i	$0.182587\pi$
$47$	2.63166	+	9.82150i	0.383867	+	1.43261i	−0.456077	+	0.889940i	$0.650746\pi$
$48$	−2.26965	−	2.26965i	−0.327596	−	0.327596i
$49$		0			0
$50$	0.828427	+	4.93089i	0.117157	+	0.697334i
$51$	7.79387	−	13.4994i	1.09136	−	1.89029i
$52$	−1.20848	−	0.323811i	−0.167586	−	0.0449045i
$53$	−1.72513	−	0.462247i	−0.236965	−	0.0634945i	0.138382	−	0.990379i	$-0.455810\pi$
$53$	−1.72513	−	0.462247i	−0.236965	−	0.0634945i	−0.375347	+	0.926884i	$0.622476\pi$
$54$	6.90529	−	11.9603i	0.939692	−	1.62759i
$55$	−5.23229	−	1.67300i	−0.705522	−	0.225588i
$56$		0			0
$57$	2.37177	+	2.37177i	0.314149	+	0.314149i
$58$	0.405882	+	1.51477i	0.0532949	+	0.198899i
$59$	3.42620	+	5.93435i	0.446053	+	0.772587i	0.998125	−	0.0612096i	$-0.0194958\pi$
$59$	3.42620	+	5.93435i	0.446053	+	0.772587i	−0.552072	+	0.833797i	$0.686162\pi$
$60$	−6.03763	−	3.88077i	−0.779454	−	0.501006i
$61$	0.544847	+	0.314567i	0.0697605	+	0.0402762i	0.534475	−	0.845185i	$-0.320510\pi$
$61$	0.544847	+	0.314567i	0.0697605	+	0.0402762i	−0.464714	+	0.885461i	$0.653843\pi$
$62$	−0.485742	+	0.485742i	−0.0616893	+	0.0616893i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−2.79439	−	0.133318i	−0.346601	−	0.0165361i
$66$	6.82889	−	3.94266i	0.840578	−	0.485308i
$67$	0.136078	−	0.507848i	0.0166245	−	0.0620435i	−0.957115	−	0.289707i	$-0.906442\pi$
$67$	0.136078	−	0.507848i	0.0166245	−	0.0620435i	0.973740	+	0.227664i	$0.0731087\pi$
$68$	4.69086	−	1.25691i	0.568850	−	0.152423i
$69$	26.4279			3.18154
$70$		0			0
$71$	−10.9419			−1.29857			−0.649285	−	0.760546i	$-0.724932\pi$
$71$	−10.9419			−1.29857			−0.649285	+	0.760546i	$0.724932\pi$
$72$	7.05383	−	1.89007i	0.831302	−	0.222747i
$73$	2.60957	−	9.73903i	0.305427	−	1.13987i	−0.627151	−	0.778898i	$-0.715779\pi$
$73$	2.60957	−	9.73903i	0.305427	−	1.13987i	0.932578	−	0.360970i	$-0.117554\pi$
$74$	2.36485	−	1.36535i	0.274908	−	0.158718i
$75$	−15.0362	−	5.61071i	−1.73623	−	0.647869i
$76$			1.04499i			0.119869i
$77$		0			0
$78$	2.83958	−	2.83958i	0.321520	−	0.321520i
$79$	−7.06156	−	4.07700i	−0.794488	−	0.458698i	0.0470521	−	0.998892i	$-0.485017\pi$
$79$	−7.06156	−	4.07700i	−0.794488	−	0.458698i	−0.841540	+	0.540195i	$0.818351\pi$
$80$	−0.475150	−	2.18500i	−0.0531234	−	0.244291i
$81$	11.2105	+	19.4171i	1.24561	+	2.15745i
$82$	1.97563	+	7.37316i	0.218172	+	0.814230i
$83$	6.80896	+	6.80896i	0.747381	+	0.747381i	0.973987	−	0.226606i	$-0.0727629\pi$
$83$	6.80896	+	6.80896i	0.747381	+	0.747381i	−0.226606	+	0.973987i	$0.572763\pi$
$84$		0			0
$85$	9.65231	−	4.97522i	1.04694	−	0.539638i
$86$	−3.22833	+	5.59163i	−0.348120	+	0.602961i
$87$	−4.86208	−	1.30279i	−0.521269	−	0.139674i
$88$	2.37295	+	0.635829i	0.252957	+	0.0677796i
$89$	3.90949	−	6.77143i	0.414405	−	0.717770i	−0.580961	−	0.813931i	$-0.697323\pi$
$89$	3.90949	−	6.77143i	0.414405	−	0.717770i	0.995366	+	0.0961615i	$0.0306565\pi$
$90$	14.5146	−	7.48143i	1.52997	−	0.788612i
$91$		0			0
$92$	5.82200	+	5.82200i	0.606986	+	0.606986i
$93$	−0.570678	−	2.12980i	−0.0591766	−	0.220850i
$94$	−5.08398	−	8.80571i	−0.524373	−	0.908240i
$95$	0.496528	+	2.28331i	0.0509427	+	0.234263i
$96$	2.77975	+	1.60489i	0.283707	+	0.163798i
$97$	7.49243	−	7.49243i	0.760741	−	0.760741i	−0.215715	−	0.976456i	$-0.569208\pi$
$97$	7.49243	−	7.49243i	0.760741	−	0.760741i	0.976456	+	0.215715i	$0.0692083\pi$
$98$		0			0
$99$			17.9401i			1.80305i
$100$	−2.07641	−	4.54846i	−0.207641	−	0.454846i
$101$	−0.346727	+	0.200183i	−0.0345006	+	0.0199189i	−0.517151	−	0.855894i	$-0.673007\pi$
$101$	−0.346727	+	0.200183i	−0.0345006	+	0.0199189i	0.482651	+	0.875813i	$0.339674\pi$
$102$	−4.03441	+	15.0566i	−0.399466	+	1.49083i
$103$	0.549691	−	0.147289i	0.0541627	−	0.0145128i	−0.231636	−	0.972803i	$-0.574408\pi$
$103$	0.549691	−	0.147289i	0.0541627	−	0.0145128i	0.285799	+	0.958290i	$0.407741\pi$
$104$	1.25111			0.122681
$105$		0			0
$106$	1.78598			0.173470
$107$	4.53554	−	1.21529i	0.438467	−	0.117487i	−0.0328310	−	0.999461i	$-0.510452\pi$
$107$	4.53554	−	1.21529i	0.438467	−	0.117487i	0.471298	+	0.881974i	$0.343786\pi$
$108$	−3.57444	+	13.3400i	−0.343951	+	1.28364i
$109$	5.71712	−	3.30078i	0.547601	−	0.316158i	−0.200553	−	0.979683i	$-0.564274\pi$
$109$	5.71712	−	3.30078i	0.547601	−	0.316158i	0.748154	+	0.663525i	$0.230940\pi$
$110$	5.48701	+	0.261782i	0.523166	+	0.0249599i
$111$			8.76492i			0.831930i
$112$		0			0
$113$	−12.9309	+	12.9309i	−1.21644	+	1.21644i	−0.247565	+	0.968871i	$0.579630\pi$
$113$	−12.9309	+	12.9309i	−1.21644	+	1.21644i	−0.968871	+	0.247565i	$0.920370\pi$
$114$	−2.90481	−	1.67710i	−0.272061	−	0.157074i
$115$	15.4874	+	9.95476i	1.44421	+	0.928286i
$116$	−0.784103	−	1.35811i	−0.0728021	−	0.126097i
$117$	2.36468	+	8.82511i	0.218615	+	0.815882i
$118$	−4.84538	−	4.84538i	−0.446053	−	0.446053i
$119$		0			0
$120$	6.83632	+	2.18589i	0.624067	+	0.199543i
$121$	2.48242	−	4.29968i	0.225675	−	0.390880i
$122$	−0.607698	−	0.162832i	−0.0550183	−	0.0147421i
$123$	−23.6662	−	6.34134i	−2.13391	−	0.571779i
$124$	0.343471	−	0.594910i	0.0308446	−	0.0534245i
$125$	−6.69816	−	8.95180i	−0.599102	−	0.800673i
$126$		0			0
$127$	−2.41155	−	2.41155i	−0.213991	−	0.213991i	0.591970	−	0.805960i	$-0.298351\pi$
$127$	−2.41155	−	2.41155i	−0.213991	−	0.213991i	−0.805960	+	0.591970i	$0.798351\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$	−10.3622	−	17.9479i	−0.912342	−	1.58022i
$130$	2.73367	−	0.594465i	0.239759	−	0.0521380i
$131$	11.7298	+	6.77221i	1.02484	+	0.591691i	0.915502	−	0.402314i	$-0.131794\pi$
$131$	11.7298	+	6.77221i	1.02484	+	0.591691i	0.109337	+	0.994005i	$0.465127\pi$
$132$	−5.57576	+	5.57576i	−0.485308	+	0.485308i
$133$		0			0
$134$			0.525763i			0.0454190i
$135$	−1.47166	+	30.8463i	−0.126660	+	2.65483i
$136$	−4.20571	+	2.42817i	−0.360637	+	0.208214i
$137$	−2.13979	+	7.98579i	−0.182814	+	0.682272i	0.812273	+	0.583277i	$0.198230\pi$
$137$	−2.13979	+	7.98579i	−0.182814	+	0.682272i	−0.995088	+	0.0989957i	$0.968437\pi$
$138$	−25.5274	+	6.84004i	−2.17303	+	0.582263i
$139$	−1.44739			−0.122766			−0.0613832	−	0.998114i	$-0.519551\pi$
$139$	−1.44739			−0.122766			−0.0613832	+	0.998114i	$0.519551\pi$
$140$		0			0
$141$	32.6369			2.74852
$142$	10.5691	−	2.83198i	0.886939	−	0.237655i
$143$	−0.795492	+	2.96882i	−0.0665224	+	0.248265i
$144$	−6.32429	+	3.65133i	−0.527024	+	0.304278i
$145$	−2.35857	−	2.59490i	−0.195869	−	0.215495i
$146$			10.0826i			0.834441i
$147$		0			0
$148$	−1.93089	+	1.93089i	−0.158718	+	0.158718i
$149$	18.3274	+	10.5813i	1.50144	+	0.866856i	0.999999	+	0.00166336i	$0.000529463\pi$
$149$	18.3274	+	10.5813i	1.50144	+	0.866856i	0.501440	+	0.865193i	$0.332804\pi$
$150$	15.9760	+	1.52789i	1.30443	+	0.124751i
$151$	3.35419	+	5.80963i	0.272960	+	0.472781i	0.969618	−	0.244622i	$-0.0786640\pi$
$151$	3.35419	+	5.80963i	0.272960	+	0.472781i	−0.696658	+	0.717403i	$0.745331\pi$
$152$	−0.270464	−	1.00938i	−0.0219375	−	0.0818719i
$153$	−25.0770	−	25.0770i	−2.02735	−	2.02735i
$154$		0			0
$155$	0.467814	−	1.46308i	0.0375757	−	0.117517i
$156$	−2.00789	+	3.47777i	−0.160760	+	0.278444i
$157$	17.3474	+	4.64823i	1.38447	+	0.370969i	0.872744	−	0.488178i	$-0.162338\pi$
$157$	17.3474	+	4.64823i	1.38447	+	0.370969i	0.511730	+	0.859146i	$0.329005\pi$
$158$	7.87615	+	2.11041i	0.626593	+	0.167895i
$159$	−2.86630	+	4.96459i	−0.227313	+	0.393717i
$160$	1.02448	+	1.98757i	0.0809923	+	0.157131i
$161$		0			0
$162$	−15.8540	−	15.8540i	−1.24561	−	1.24561i
$163$	0.771907	+	2.88080i	0.0604604	+	0.225641i	0.989545	−	0.144227i	$-0.0460695\pi$
$163$	0.771907	+	2.88080i	0.0604604	+	0.225641i	−0.929084	+	0.369868i	$0.879403\pi$
$164$	−3.81663	−	6.61060i	−0.298029	−	0.516201i
$165$	−9.53372	+	14.8324i	−0.742199	+	1.15470i
$166$	−8.33924	−	4.81466i	−0.647251	−	0.373690i
$167$	6.41955	−	6.41955i	0.496760	−	0.496760i	−0.413668	−	0.910428i	$-0.635753\pi$
$167$	6.41955	−	6.41955i	0.496760	−	0.496760i	0.910428	+	0.413668i	$0.135753\pi$
$168$		0			0
$169$		−	11.4347i		−	0.879594i
$170$	−8.03574	+	7.30389i	−0.616313	+	0.560183i
$171$	6.60883	−	3.81561i	0.505390	−	0.291787i
$172$	1.67111	−	6.23665i	0.127421	−	0.475540i
$173$	21.2267	−	5.68769i	1.61384	−	0.432427i	0.664655	−	0.747150i	$-0.268578\pi$
$173$	21.2267	−	5.68769i	1.61384	−	0.432427i	0.949183	+	0.314723i	$0.101912\pi$
$174$	5.03359			0.381596
$175$		0			0
$176$	−2.45666			−0.185177
$177$	21.2452	−	5.69264i	1.59689	−	0.427885i
$178$	−2.02370	+	7.55255i	−0.151683	+	0.566087i
$179$	11.6386	−	6.71954i	0.869908	−	0.502242i	0.00259060	−	0.999997i	$-0.499175\pi$
$179$	11.6386	−	6.71954i	0.869908	−	0.502242i	0.867318	+	0.497755i	$0.165842\pi$
$180$	−12.0837	+	10.9832i	−0.900663	+	0.818636i
$181$			13.1067i			0.974210i	0.873343	+	0.487105i	$0.161947\pi$
$181$			13.1067i			0.974210i	−0.873343	+	0.487105i	$0.838053\pi$
$182$		0			0
$183$	1.42792	−	1.42792i	0.105555	−	0.105555i
$184$	−7.13047	−	4.11678i	−0.525665	−	0.303493i
$185$	−3.30154	+	5.13647i	−0.242734	+	0.377641i
$186$	1.10247	+	1.90953i	0.0808367	+	0.140013i
$187$	−3.08780	−	11.5238i	−0.225802	−	0.842706i
$188$	7.18984	+	7.18984i	0.524373	+	0.524373i
$189$		0			0
$190$	−1.07057	−	2.07700i	−0.0776675	−	0.150681i
$191$	−2.90542	+	5.03234i	−0.210229	+	0.364127i	−0.951786	−	0.306762i	$-0.900754\pi$
$191$	−2.90542	+	5.03234i	−0.210229	+	0.364127i	0.741557	+	0.670890i	$0.234088\pi$
$192$	−3.10041	−	0.830751i	−0.223753	−	0.0599543i
$193$	−21.0589	−	5.64271i	−1.51585	−	0.406171i	−0.597478	−	0.801885i	$-0.703830\pi$
$193$	−21.0589	−	5.64271i	−1.51585	−	0.406171i	−0.918374	+	0.395714i	$0.870497\pi$
$194$	−5.29795	+	9.17632i	−0.380371	+	0.658821i
$195$	−2.73478	+	8.55298i	−0.195842	+	0.612491i
$196$		0			0
$197$	1.95310	+	1.95310i	0.139152	+	0.139152i	0.773252	−	0.634099i	$-0.218629\pi$
$197$	1.95310	+	1.95310i	0.139152	+	0.139152i	−0.634099	+	0.773252i	$0.718629\pi$
$198$	−4.64325	−	17.3288i	−0.329981	−	1.23151i
$199$	−3.35205	−	5.80592i	−0.237620	−	0.411570i	0.722411	−	0.691464i	$-0.243034\pi$
$199$	−3.35205	−	5.80592i	−0.237620	−	0.411570i	−0.960031	+	0.279894i	$0.909701\pi$
$200$	3.18289	+	3.85607i	0.225064	+	0.272665i
$201$	−1.46149	−	0.843791i	−0.103085	−	0.0595164i
$202$	0.283101	−	0.283101i	0.0199189	−	0.0199189i
$203$		0			0
$204$		−	15.5877i		−	1.09136i
$205$	−11.4804	−	12.6307i	−0.801824	−	0.882166i
$206$	−0.492839	+	0.284541i	−0.0343377	+	0.0198249i
$207$	15.5620	−	58.0781i	1.08163	−	4.03671i
$208$	−1.20848	+	0.323811i	−0.0837929	+	0.0224522i
$209$	2.56719			0.177576
$210$		0			0
$211$	−20.7751			−1.43022			−0.715108	−	0.699014i	$-0.753623\pi$
$211$	−20.7751			−1.43022			−0.715108	+	0.699014i	$0.753623\pi$
$212$	−1.72513	+	0.462247i	−0.118482	+	0.0317472i
$213$	−9.09003	+	33.9244i	−0.622838	+	2.32446i
$214$	−4.06645	+	2.34777i	−0.277977	+	0.160490i
$215$	0.688022	−	14.4211i	0.0469227	−	0.983512i
$216$		−	13.8106i		−	0.939692i
$217$		0			0
$218$	−4.66801	+	4.66801i	−0.316158	+	0.316158i
$219$	−28.0270	−	16.1814i	−1.89389	−	1.09344i
$220$	−5.36780	+	1.16728i	−0.361897	+	0.0786981i
$221$	−3.03790	−	5.26180i	−0.204351	−	0.353947i
$222$	−2.26853	−	8.46626i	−0.152254	−	0.568218i
$223$	5.36473	+	5.36473i	0.359249	+	0.359249i	0.863536	−	0.504287i	$-0.168245\pi$
$223$	5.36473	+	5.36473i	0.359249	+	0.359249i	−0.504287	+	0.863536i	$0.668245\pi$
$224$		0			0
$225$	−21.1842	+	29.7398i	−1.41228	+	1.98265i
$226$	9.14352	−	15.8370i	0.608218	−	1.05346i
$227$	−19.6002	−	5.25185i	−1.30091	−	0.348577i	−0.459115	−	0.888377i	$-0.651833\pi$
$227$	−19.6002	−	5.25185i	−1.30091	−	0.348577i	−0.841793	+	0.539800i	$0.818500\pi$
$228$	3.23990	+	0.868128i	0.214568	+	0.0574932i
$229$	3.57868	−	6.19845i	0.236486	−	0.409605i	−0.723218	−	0.690620i	$-0.757338\pi$
$229$	3.57868	−	6.19845i	0.236486	−	0.409605i	0.959703	+	0.281015i	$0.0906711\pi$
$230$	−17.5362	−	5.60712i	−1.15630	−	0.369723i
$231$		0			0
$232$	1.10889	+	1.10889i	0.0728021	+	0.0728021i
$233$	−1.00998	−	3.76930i	−0.0661661	−	0.246935i	0.924919	−	0.380164i	$-0.124132\pi$
$233$	−1.00998	−	3.76930i	−0.0661661	−	0.246935i	−0.991085	+	0.133228i	$0.957466\pi$
$234$	−4.56821	−	7.91238i	−0.298633	−	0.517248i
$235$	19.1261	+	12.2936i	1.24765	+	0.801943i
$236$	5.93435	+	3.42620i	0.386294	+	0.223027i
$237$	−18.5067	+	18.5067i	−1.20214	+	1.20214i
$238$		0			0
$239$		−	4.13821i		−	0.267679i	−0.991003	−	0.133839i	$-0.957269\pi$
$239$		−	4.13821i		−	0.267679i	0.991003	−	0.133839i	$-0.0427306\pi$
$240$	−7.16912	−	0.342034i	−0.462765	−	0.0220782i
$241$	6.78622	−	3.91802i	0.437139	−	0.252382i	−0.265244	−	0.964181i	$-0.585453\pi$
$241$	6.78622	−	3.91802i	0.437139	−	0.252382i	0.702383	+	0.711799i	$0.252119\pi$
$242$	−1.28499	+	4.79567i	−0.0826026	+	0.308277i
$243$	29.4939	−	7.90287i	1.89203	−	0.506969i
$244$	0.629135			0.0402762
$245$		0			0
$246$	24.5011			1.56213
$247$	1.26285	−	0.338380i	0.0803532	−	0.0215306i
$248$	−0.177794	+	0.663536i	−0.0112899	+	0.0421346i
$249$	26.7671	−	15.4540i	1.69630	−	0.979357i
$250$	8.78682	+	6.91316i	0.555727	+	0.437227i
$251$			12.6769i			0.800158i	0.916481	+	0.400079i	$0.131017\pi$
$251$			12.6769i			0.800158i	−0.916481	+	0.400079i	$0.868983\pi$
$252$		0			0
$253$	14.3027	−	14.3027i	0.899201	−	0.899201i
$254$	2.95354	+	1.70523i	0.185321	+	0.106995i
$255$	−7.40652	−	34.0593i	−0.463814	−	2.13287i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.42876	+	12.7963i	0.213880	+	0.798212i	0.986558	+	0.163413i	$0.0522503\pi$
$257$	3.42876	+	12.7963i	0.213880	+	0.798212i	−0.772677	+	0.634799i	$0.781083\pi$
$258$	14.6544	+	14.6544i	0.912342	+	0.912342i
$259$		0			0
$260$	−2.48667	+	1.28174i	−0.154217	+	0.0794899i
$261$	−5.72604	+	9.91779i	−0.354433	+	0.613896i
$262$	−13.0829	−	3.50555i	−0.808265	−	0.216574i
$263$	26.1727	+	7.01294i	1.61388	+	0.432437i	0.949194	−	0.314691i	$-0.101901\pi$
$263$	26.1727	+	7.01294i	1.61388	+	0.432437i	0.664681	+	0.747127i	$0.268567\pi$
$264$	3.94266	−	6.82889i	0.242654	−	0.420289i
$265$	−3.54977	+	1.82971i	−0.218061	+	0.112398i
$266$		0			0
$267$	−17.7464	−	17.7464i	−1.08606	−	1.08606i
$268$	−0.136078	−	0.507848i	−0.00831226	−	0.0310218i
$269$	1.56915	+	2.71785i	0.0956729	+	0.165710i	0.909889	−	0.414851i	$-0.136166\pi$
$269$	1.56915	+	2.71785i	0.0956729	+	0.165710i	−0.814216	+	0.580562i	$0.802833\pi$
$270$	−6.56211	−	30.1762i	−0.399357	−	1.83646i
$271$	−28.2799	−	16.3274i	−1.71788	−	0.991818i	−0.922770	−	0.385352i	$-0.874080\pi$
$271$	−28.2799	−	16.3274i	−1.71788	−	0.991818i	−0.795109	−	0.606466i	$-0.792587\pi$
$272$	3.43395	−	3.43395i	0.208214	−	0.208214i
$273$		0			0
$274$		−	8.26750i		−	0.499458i
$275$	−11.1740	+	5.10102i	−0.673818	+	0.307603i
$276$	22.8872	−	13.2139i	1.37765	−	0.795386i
$277$	−8.17724	+	30.5179i	−0.491323	+	1.83364i	0.0583973	+	0.998293i	$0.481401\pi$
$277$	−8.17724	+	30.5179i	−0.491323	+	1.83364i	−0.549720	+	0.835349i	$0.685266\pi$
$278$	1.39807	−	0.374613i	0.0838510	−	0.0224678i
$279$	−5.01651			−0.300331
$280$		0			0
$281$	−28.8795			−1.72281			−0.861404	−	0.507920i	$-0.830414\pi$
$281$	−28.8795			−1.72281			−0.861404	+	0.507920i	$0.830414\pi$
$282$	−31.5248	+	8.44705i	−1.87728	+	0.503014i
$283$	1.12024	−	4.18079i	0.0665914	−	0.248522i	−0.924604	−	0.380930i	$-0.875604\pi$
$283$	1.12024	−	4.18079i	0.0665914	−	0.248522i	0.991195	+	0.132407i	$0.0422707\pi$
$284$	−9.47600	+	5.47097i	−0.562297	+	0.324642i
$285$	7.49168	+	0.357423i	0.443769	+	0.0211719i
$286$		−	3.07354i		−	0.181742i
$287$		0			0
$288$	5.16376	−	5.16376i	0.304278	−	0.304278i
$289$	5.70190	+	3.29199i	0.335406	+	0.193647i
$290$	2.94981	+	1.89604i	0.173219	+	0.111339i
$291$	−17.0052	−	29.4539i	−0.996864	−	1.72662i
$292$	−2.60957	−	9.73903i	−0.152713	−	0.569934i
$293$	1.50173	+	1.50173i	0.0877317	+	0.0877317i	0.749611	−	0.661879i	$-0.230241\pi$
$293$	1.50173	+	1.50173i	0.0877317	+	0.0877317i	−0.661879	+	0.749611i	$0.730241\pi$
$294$		0			0
$295$	14.5945	+	4.66655i	0.849727	+	0.271697i
$296$	1.36535	−	2.36485i	0.0793592	−	0.137454i
$297$	32.7718	+	8.78118i	1.90161	+	0.509536i
$298$	−20.4415	−	5.47730i	−1.18415	−	0.317291i
$299$	5.15054	−	8.92099i	0.297863	−	0.515914i
$300$	−15.8271	+	2.65907i	−0.913776	+	0.153521i
$301$		0			0
$302$	−4.74354	−	4.74354i	−0.272960	−	0.272960i
$303$	0.332604	+	1.24130i	0.0191076	+	0.0713106i
$304$	0.522496	+	0.904990i	0.0299672	+	0.0519047i
$305$	1.37466	−	0.298934i	0.0787128	−	0.0171169i
$306$	30.7129	+	17.7321i	1.75574	+	1.01368i
$307$	13.6493	−	13.6493i	0.779006	−	0.779006i	−0.200656	−	0.979662i	$-0.564307\pi$
$307$	13.6493	−	13.6493i	0.779006	−	0.779006i	0.979662	+	0.200656i	$0.0643073\pi$
$308$		0			0
$309$		−	1.82663i		−	0.103913i
$310$	−0.0732007	+	1.53431i	−0.00415752	+	0.0871427i
$311$	−26.3403	+	15.2076i	−1.49362	+	0.862343i	−0.999973	−	0.00731761i	$-0.997671\pi$
$311$	−26.3403	+	15.2076i	−1.49362	+	0.862343i	−0.493649	+	0.869661i	$0.664337\pi$
$312$	1.03936	−	3.87894i	0.0588422	−	0.219602i
$313$	−18.7948	+	5.03606i	−1.06235	+	0.284655i	−0.747345	−	0.664437i	$-0.768672\pi$
$313$	−18.7948	+	5.03606i	−1.06235	+	0.284655i	−0.315001	+	0.949091i	$0.602005\pi$
$314$	−17.9594			−1.01351
$315$		0			0
$316$	−8.15399			−0.458698
$317$	13.3162	−	3.56808i	0.747914	−	0.200403i	0.135322	−	0.990802i	$-0.456793\pi$
$317$	13.3162	−	3.56808i	0.747914	−	0.200403i	0.612593	+	0.790399i	$0.290127\pi$
$318$	1.48371	−	5.53728i	0.0832022	−	0.310515i
$319$	−3.33640	+	1.92627i	−0.186803	+	0.107851i
$320$	−1.50399	−	1.65469i	−0.0840758	−	0.0925001i
$321$		−	15.0716i		−	0.841216i
$322$		0			0
$323$	−3.58845	+	3.58845i	−0.199667	+	0.199667i
$324$	19.4171	+	11.2105i	1.07873	+	0.622803i
$325$	−4.82436	+	3.98214i	−0.267607	+	0.220889i
$326$	−1.49121	−	2.58285i	−0.0825905	−	0.143051i
$327$	−5.48426	−	20.4675i	−0.303280	−	1.13186i
$328$	5.39753	+	5.39753i	0.298029	+	0.298029i
$329$		0			0
$330$	5.36997	−	16.7945i	0.295607	−	0.924506i
$331$	−8.52457	+	14.7650i	−0.468553	+	0.811557i	−0.999354	−	0.0359392i	$-0.988558\pi$
$331$	−8.52457	+	14.7650i	−0.468553	+	0.811557i	0.530801	+	0.847496i	$0.321891\pi$
$332$	9.30122	+	2.49225i	0.510471	+	0.136780i
$333$	19.2619	+	5.16120i	1.05554	+	0.282832i
$334$	−4.53931	+	7.86231i	−0.248380	+	0.430207i
$335$	−0.538634	−	1.04499i	−0.0294287	−	0.0570940i
$336$		0			0
$337$	12.6551	+	12.6551i	0.689365	+	0.689365i	0.962092	−	0.272727i	$-0.0879255\pi$
$337$	12.6551	+	12.6551i	0.689365	+	0.689365i	−0.272727	+	0.962092i	$0.587926\pi$
$338$	2.95953	+	11.0451i	0.160977	+	0.600774i
$339$	29.3487	+	50.8334i	1.59400	+	2.76089i
$340$	5.87154	−	9.13482i	0.318429	−	0.495405i
$341$	−1.46149	−	0.843791i	−0.0791441	−	0.0456938i
$342$	−5.39609	+	5.39609i	−0.291787	+	0.291787i
$343$		0			0
$344$			6.45666i			0.348120i
$345$	43.7300	−	39.7473i	2.35434	−	2.13993i
$346$	−19.0314	+	10.9878i	−1.02313	+	0.590706i
$347$	−8.14551	+	30.3995i	−0.437274	+	1.63193i	0.298291	+	0.954475i	$0.403583\pi$
$347$	−8.14551	+	30.3995i	−0.437274	+	1.63193i	−0.735565	+	0.677454i	$0.763083\pi$
$348$	−4.86208	+	1.30279i	−0.260635	+	0.0698368i
$349$	−29.3377			−1.57041			−0.785206	−	0.619235i	$-0.787443\pi$
$349$	−29.3377			−1.57041			−0.785206	+	0.619235i	$0.787443\pi$
$350$		0			0
$351$	17.2785			0.922261
$352$	2.37295	−	0.635829i	0.126479	−	0.0338898i
$353$	4.03406	−	15.0553i	0.214712	−	0.801314i	−0.771556	−	0.636161i	$-0.780521\pi$
$353$	4.03406	−	15.0553i	0.214712	−	0.801314i	0.986268	−	0.165153i	$-0.0528119\pi$
$354$	−19.0480	+	10.9973i	−1.01239	+	0.584502i
$355$	−18.1055	+	16.4566i	−0.960942	+	0.873426i
$356$		−	7.81897i		−	0.414405i
$357$		0			0
$358$	−9.50286	+	9.50286i	−0.502242	+	0.502242i
$359$	4.41633	+	2.54977i	0.233085	+	0.134572i	0.611994	−	0.790862i	$-0.290368\pi$
$359$	4.41633	+	2.54977i	0.233085	+	0.134572i	−0.378910	+	0.925434i	$0.623701\pi$
$360$	8.82927	−	13.7364i	0.465343	−	0.723972i
$361$	8.95400	+	15.5088i	0.471263	+	0.816251i
$362$	−3.39225	−	12.6601i	−0.178293	−	0.665398i
$363$	−11.2685	−	11.2685i	−0.591441	−	0.591441i
$364$		0			0
$365$	−10.3294	−	20.0399i	−0.540666	−	1.04893i
$366$	−1.00969	+	1.74884i	−0.0527774	+	0.0914131i
$367$	13.0370	+	3.49325i	0.680526	+	0.182346i	0.582492	−	0.812837i	$-0.302078\pi$
$367$	13.0370	+	3.49325i	0.680526	+	0.182346i	0.0980341	+	0.995183i	$0.468745\pi$
$368$	7.95301	+	2.13100i	0.414579	+	0.111086i
$369$	−27.8716	+	48.2750i	−1.45094	+	2.51309i
$370$	1.85963	−	5.81595i	0.0966774	−	0.302357i
$371$		0			0
$372$	−1.55912	−	1.55912i	−0.0808367	−	0.0808367i
$373$	6.47676	+	24.1716i	0.335354	+	1.25156i	0.903485	+	0.428620i	$0.141000\pi$
$373$	6.47676	+	24.1716i	0.335354	+	1.25156i	−0.568131	+	0.822938i	$0.692333\pi$
$374$	5.96517	+	10.3320i	0.308452	+	0.534254i
$375$	−33.3187	+	13.3303i	−1.72057	+	0.688374i
$376$	−8.80571	−	5.08398i	−0.454120	−	0.262186i
$377$	−1.38734	+	1.38734i	−0.0714517	+	0.0714517i
$378$		0			0
$379$			27.5397i			1.41462i	0.706903	+	0.707311i	$0.250092\pi$
$379$			27.5397i			1.41462i	−0.706903	+	0.707311i	$0.749908\pi$
$380$	1.57166	+	1.72914i	0.0806245	+	0.0887030i
$381$	−9.48019	+	5.47339i	−0.485685	+	0.280410i
$382$	1.50396	−	5.61285i	0.0769492	−	0.287178i
$383$	−23.5667	+	6.31468i	−1.20420	+	0.322665i	−0.804484	−	0.593974i	$-0.797558\pi$
$383$	−23.5667	+	6.31468i	−1.20420	+	0.322665i	−0.399717	+	0.916639i	$0.630892\pi$
$384$	3.20978			0.163798
$385$		0			0
$386$	21.8018			1.10968
$387$	−45.5442	+	12.2035i	−2.31514	+	0.620340i
$388$	2.74242	−	10.2349i	0.139225	−	0.519596i
$389$	18.1725	−	10.4919i	0.921382	−	0.531960i	0.0373065	−	0.999304i	$-0.488122\pi$
$389$	18.1725	−	10.4919i	0.921382	−	0.531960i	0.884076	+	0.467344i	$0.154789\pi$
$390$	0.427922	−	8.96935i	0.0216687	−	0.454181i
$391$			39.9849i			2.02212i
$392$		0			0
$393$	30.7412	−	30.7412i	1.55069	−	1.55069i
$394$	−2.39204	−	1.38105i	−0.120509	−	0.0695761i
$395$	−17.8165	+	3.87437i	−0.896445	+	0.194941i
$396$	8.97007	+	15.5366i	0.450763	+	0.780744i
$397$	6.28677	+	23.4625i	0.315524	+	1.17755i	0.923501	+	0.383597i	$0.125315\pi$
$397$	6.28677	+	23.4625i	0.315524	+	1.17755i	−0.607977	+	0.793955i	$0.708019\pi$
$398$	4.74051	+	4.74051i	0.237620	+	0.237620i
$399$		0			0
$400$	−4.07245	−	2.90088i	−0.203623	−	0.145044i
$401$	−18.6178	+	32.2469i	−0.929727	+	1.61033i	−0.145949	+	0.989292i	$0.546623\pi$
$401$	−18.6178	+	32.2469i	−0.929727	+	1.61033i	−0.783778	+	0.621041i	$0.786710\pi$
$402$	1.63008	+	0.436778i	0.0813010	+	0.0217845i
$403$	−0.830155	−	0.222439i	−0.0413530	−	0.0110805i
$404$	−0.200183	+	0.346727i	−0.00995946	+	0.0172503i
$405$	47.7530	+	15.2688i	2.37287	+	0.758714i
$406$		0			0
$407$	4.74354	+	4.74354i	0.235129	+	0.235129i
$408$	4.03441	+	15.0566i	0.199733	+	0.745413i
$409$	−10.8522	−	18.7965i	−0.536606	−	0.929428i	−0.999084	−	0.0427977i	$-0.986373\pi$
$409$	−10.8522	−	18.7965i	−0.536606	−	0.929428i	0.462478	−	0.886631i	$-0.346960\pi$
$410$	14.3583	+	9.22898i	0.709103	+	0.455787i
$411$	22.9816	+	13.2684i	1.13360	+	0.654483i
$412$	0.402402	−	0.402402i	0.0198249	−	0.0198249i
$413$		0			0
$414$			60.1269i			2.95508i
$415$	21.5074	+	1.02610i	1.05576	+	0.0503694i
$416$	1.08349	−	0.625554i	0.0531226	−	0.0306703i
$417$	−1.20242	+	4.48751i	−0.0588830	+	0.219754i
$418$	−2.47971	+	0.664437i	−0.121287	+	0.0324987i
$419$	−19.6046			−0.957749			−0.478874	−	0.877883i	$-0.658955\pi$
$419$	−19.6046			−0.957749			−0.478874	+	0.877883i	$0.658955\pi$
$420$		0			0
$421$	14.2142			0.692757			0.346378	−	0.938095i	$-0.387411\pi$
$421$	14.2142			0.692757			0.346378	+	0.938095i	$0.387411\pi$
$422$	20.0672	−	5.37699i	0.976856	−	0.261748i
$423$	19.2181	−	71.7231i	0.934418	−	3.48730i
$424$	1.54671	−	0.892992i	0.0751148	−	0.0433675i
$425$	8.48891	−	22.7495i	0.411773	−	1.10351i
$426$		−	35.1212i		−	1.70163i
$427$		0			0
$428$	3.32024	−	3.32024i	0.160490	−	0.160490i
$429$	8.54368	+	4.93269i	0.412493	+	0.238153i
$430$	3.06788	+	14.1078i	0.147946	+	0.680339i
$431$	−6.61065	−	11.4500i	−0.318424	−	0.551526i	0.661736	−	0.749737i	$-0.269820\pi$
$431$	−6.61065	−	11.4500i	−0.318424	−	0.551526i	−0.980159	+	0.198211i	$0.936487\pi$
$432$	3.57444	+	13.3400i	0.171975	+	0.641821i
$433$	7.65911	+	7.65911i	0.368073	+	0.368073i	0.866774	−	0.498701i	$-0.166189\pi$
$433$	7.65911	+	7.65911i	0.368073	+	0.368073i	−0.498701	+	0.866774i	$0.666189\pi$
$434$		0			0
$435$	−10.0046	+	5.15681i	−0.479685	+	0.247250i
$436$	3.30078	−	5.71712i	0.158079	−	0.273801i
$437$	−8.31083	−	2.22688i	−0.397561	−	0.106526i
$438$	31.2601	+	8.37612i	1.49367	+	0.400227i
$439$	13.8841	−	24.0480i	0.662652	−	1.14775i	−0.317264	−	0.948337i	$-0.602764\pi$
$439$	13.8841	−	24.0480i	0.662652	−	1.14775i	0.979916	−	0.199409i	$-0.0639024\pi$
$440$	4.88278	−	2.51680i	0.232777	−	0.119984i
$441$		0			0
$442$	4.29624	+	4.29624i	0.204351	+	0.204351i
$443$	−8.63132	−	32.2125i	−0.410087	−	1.53046i	−0.794478	−	0.607293i	$-0.792255\pi$
$443$	−8.63132	−	32.2125i	−0.410087	−	1.53046i	0.384391	−	0.923170i	$-0.374411\pi$
$444$	4.38246	+	7.59064i	0.207982	+	0.360236i
$445$	−3.71519	−	17.0845i	−0.176117	−	0.809881i
$446$	−6.57042	−	3.79344i	−0.311119	−	0.179624i
$447$	48.0319	−	48.0319i	2.27183	−	2.27183i
$448$		0			0
$449$			18.2049i			0.859144i	0.903033	+	0.429572i	$0.141336\pi$
$449$			18.2049i			0.859144i	−0.903033	+	0.429572i	$0.858664\pi$
$450$	12.7651	−	34.2093i	0.601753	−	1.61264i
$451$	−16.2400	+	9.37615i	−0.764710	+	0.441506i
$452$	−4.73304	+	17.6639i	−0.222623	+	0.830841i
$453$	20.7987	−	5.57300i	0.977208	−	0.261842i
$454$	20.2916			0.952331
$455$		0			0
$456$	−3.35419			−0.157074
$457$	−31.8056	+	8.52227i	−1.48780	+	0.398655i	−0.908994	−	0.416809i	$-0.863148\pi$
$457$	−31.8056	+	8.52227i	−1.48780	+	0.398655i	−0.578807	+	0.815464i	$0.696482\pi$
$458$	−1.85246	+	6.91347i	−0.0865597	+	0.323045i
$459$	−58.0833	+	33.5344i	−2.71110	+	1.56525i
$460$	18.3899	+	0.877369i	0.857432	+	0.0409075i
$461$		−	21.3025i		−	0.992156i	−0.868278	−	0.496078i	$-0.834773\pi$
$461$		−	21.3025i		−	0.992156i	0.868278	−	0.496078i	$-0.165227\pi$
$462$		0			0
$463$	−4.73701	+	4.73701i	−0.220147	+	0.220147i	−0.808560	−	0.588413i	$-0.799753\pi$
$463$	−4.73701	+	4.73701i	−0.220147	+	0.220147i	0.588413	+	0.808560i	$0.299753\pi$
$464$	−1.35811	−	0.784103i	−0.0630485	−	0.0364011i
$465$	−4.14750	−	2.66587i	−0.192336	−	0.123627i
$466$	1.95113	+	3.37946i	0.0903845	+	0.156551i
$467$	−1.32248	−	4.93558i	−0.0611972	−	0.228391i	0.928553	−	0.371200i	$-0.121053\pi$
$467$	−1.32248	−	4.93558i	−0.0611972	−	0.228391i	−0.989750	+	0.142808i	$0.954387\pi$
$468$	6.46043	+	6.46043i	0.298633	+	0.298633i
$469$		0			0
$470$	−21.6562	−	6.92447i	−0.998924	−	0.319402i
$471$	28.8228	−	49.9225i	1.32808	−	2.30031i
$472$	−6.61891	−	1.77353i	−0.304660	−	0.0816334i
$473$	−15.3213	−	4.10533i	−0.704475	−	0.188763i
$474$	13.0862	−	22.6660i	0.601071	−	1.04109i
$475$	4.25568	+	3.03140i	0.195264	+	0.139090i
$476$		0			0
$477$	9.22240	+	9.22240i	0.422265	+	0.422265i
$478$	1.07105	+	3.99721i	0.0489886	+	0.182828i
$479$	13.6094	+	23.5722i	0.621829	+	1.07704i	0.989145	+	0.146943i	$0.0469434\pi$
$479$	13.6094	+	23.5722i	0.621829	+	1.07704i	−0.367316	+	0.930096i	$0.619723\pi$
$480$	7.01337	−	1.52513i	0.320115	−	0.0696122i
$481$	2.95869	+	1.70820i	0.134904	+	0.0778871i
$482$	−5.54092	+	5.54092i	−0.252382	+	0.252382i
$483$		0			0
$484$		−	4.96484i		−	0.225675i
$485$	1.12910	−	23.6662i	0.0512698	−	1.07463i
$486$	−26.4435	+	15.2672i	−1.19950	+	0.692533i
$487$	1.32394	−	4.94101i	0.0599935	−	0.223899i	−0.929420	−	0.369024i	$-0.879692\pi$
$487$	1.32394	−	4.94101i	0.0599935	−	0.223899i	0.989413	+	0.145126i	$0.0463586\pi$
$488$	−0.607698	+	0.162832i	−0.0275092	+	0.00737106i
$489$	9.57290			0.432901
$490$		0			0
$491$	−2.12537			−0.0959165			−0.0479582	−	0.998849i	$-0.515271\pi$
$491$	−2.12537			−0.0959165			−0.0479582	+	0.998849i	$0.515271\pi$
$492$	−23.6662	+	6.34134i	−1.06696	+	0.285890i
$493$	1.97110	−	7.35623i	0.0887737	−	0.331308i
$494$	−1.13224	+	0.653699i	−0.0509419	+	0.0294113i
$495$	26.9818	+	29.6854i	1.21274	+	1.33426i
$496$		−	0.686943i		−	0.0308446i
$497$		0			0
$498$	−21.8553	+	21.8553i	−0.979357	+	0.979357i
$499$	7.24451	+	4.18262i	0.324309	+	0.187240i	0.653311	−	0.757089i	$-0.273379\pi$
$499$	7.24451	+	4.18262i	0.324309	+	0.187240i	−0.329003	+	0.944329i	$0.606713\pi$
$500$	−10.2767	−	4.40340i	−0.459587	−	0.196926i
$501$	−14.5702	−	25.2363i	−0.650947	−	1.12747i
$502$	−3.28102	−	12.2449i	−0.146439	−	0.546518i
$503$	10.4440	+	10.4440i	0.465673	+	0.465673i	0.900510	−	0.434836i	$-0.143194\pi$
$503$	10.4440	+	10.4440i	0.465673	+	0.465673i	−0.434836	+	0.900510i	$0.643194\pi$
$504$		0			0
$505$	−0.272652	+	0.852715i	−0.0121329	+	0.0379453i
$506$	−10.1135	+	17.5171i	−0.449600	+	0.778731i
$507$	−35.4523	−	9.49941i	−1.57449	−	0.421884i
$508$	−3.29424	−	0.882690i	−0.146158	−	0.0391630i
$509$	−1.64902	+	2.85618i	−0.0730914	+	0.126598i	−0.900255	−	0.435364i	$-0.856620\pi$
$509$	−1.64902	+	2.85618i	−0.0730914	+	0.126598i	0.827163	+	0.561962i	$0.189953\pi$
$510$	15.9693	+	30.9818i	0.707134	+	1.37190i
$511$		0			0
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−3.73526	−	13.9402i	−0.164916	−	0.615475i
$514$	−6.62386	−	11.4729i	−0.292166	−	0.506046i
$515$	0.688047	−	1.07045i	0.0303190	−	0.0471696i
$516$	−17.9479	−	10.3622i	−0.790111	−	0.456171i
$517$	17.6630	−	17.6630i	0.776816	−	0.776816i
$518$		0			0
$519$		−	70.5365i		−	3.09621i
$520$	2.07020	−	1.88166i	0.0907842	−	0.0825162i
$521$	23.1368	−	13.3580i	1.01364	−	0.585226i	0.101385	−	0.994847i	$-0.467673\pi$
$521$	23.1368	−	13.3580i	1.01364	−	0.585226i	0.912255	+	0.409622i	$0.134339\pi$
$522$	2.96402	−	11.0619i	0.129731	−	0.484165i
$523$	17.3200	−	4.64087i	0.757349	−	0.202931i	0.140574	−	0.990070i	$-0.455105\pi$
$523$	17.3200	−	4.64087i	0.757349	−	0.202931i	0.616776	+	0.787139i	$0.288439\pi$
$524$	13.5444			0.591691
$525$		0			0
$526$	−27.0959			−1.18144
$527$	3.22235	−	0.863426i	0.140368	−	0.0376114i
$528$	−2.04087	+	7.61663i	−0.0888175	+	0.331471i
$529$	−38.7905	+	22.3957i	−1.68655	+	0.973727i
$530$	2.95525	−	2.68611i	0.128368	−	0.116677i
$531$		−	50.0408i		−	2.17159i
$532$		0			0
$533$	−6.75290	+	6.75290i	−0.292500	+	0.292500i
$534$	21.7348	+	12.5486i	0.940555	+	0.543030i
$535$	5.67712	−	8.83235i	0.245443	−	0.381856i
$536$	0.262882	+	0.455324i	0.0113548	+	0.0196670i
$537$	−11.1645	−	41.6666i	−0.481785	−	1.79805i
$538$	−2.21912	−	2.21912i	−0.0956729	−	0.0956729i
$539$		0			0
$540$	14.1487	+	27.4495i	0.608862	+	1.18124i
$541$	1.69664	−	2.93866i	0.0729441	−	0.126343i	−0.827246	−	0.561839i	$-0.810094\pi$
$541$	1.69664	−	2.93866i	0.0729441	−	0.126343i	0.900190	+	0.435497i	$0.143427\pi$
$542$	31.5421	+	8.45168i	1.35485	+	0.363031i
$543$	40.6359	+	10.8884i	1.74386	+	0.467265i
$544$	−2.42817	+	4.20571i	−0.104107	+	0.180318i
$545$	4.49572	−	14.0603i	0.192576	−	0.602277i
$546$		0			0
$547$	23.9016	+	23.9016i	1.02196	+	1.02196i	0.999753	+	0.0222038i	$0.00706828\pi$
$547$	23.9016	+	23.9016i	1.02196	+	1.02196i	0.0222038	+	0.999753i	$0.492932\pi$
$548$	2.13979	+	7.98579i	0.0914072	+	0.341136i
$549$	−2.29718	−	3.97883i	−0.0980412	−	0.169812i
$550$	9.47303	−	7.81926i	0.403931	−	0.333414i
$551$	1.41921	+	0.819381i	0.0604604	+	0.0349068i
$552$	−18.6873	+	18.6873i	−0.795386	+	0.795386i
$553$		0			0
$554$		−	31.5944i		−	1.34232i
$555$	13.1824	+	14.5032i	0.559561	+	0.615628i
$556$	−1.25348	+	0.723697i	−0.0531594	+	0.0306916i
$557$	3.32361	−	12.4039i	0.140826	−	0.525569i	−0.859080	−	0.511841i	$-0.828964\pi$
$557$	3.32361	−	12.4039i	0.140826	−	0.525569i	0.999906	−	0.0137276i	$-0.00436976\pi$
$558$	4.84558	−	1.29837i	0.205130	−	0.0549643i
$559$	−8.07798			−0.341662
$560$		0			0
$561$	−38.2937			−1.61676
$562$	27.8955	−	7.47457i	1.17670	−	0.315296i
$563$	1.10957	−	4.14097i	0.0467627	−	0.174521i	−0.938595	−	0.345021i	$-0.887872\pi$
$563$	1.10957	−	4.14097i	0.0467627	−	0.174521i	0.985358	+	0.170500i	$0.0545384\pi$
$564$	28.2644	−	16.3184i	1.19014	−	0.687130i
$565$	−1.94867	+	40.8446i	−0.0819812	+	1.71835i
$566$			4.32828i			0.181931i
$567$		0			0
$568$	7.73712	−	7.73712i	0.324642	−	0.324642i
$569$	−15.0238	−	8.67402i	−0.629832	−	0.363634i	0.150855	−	0.988556i	$-0.451797\pi$
$569$	−15.0238	−	8.67402i	−0.629832	−	0.363634i	−0.780687	+	0.624922i	$0.785131\pi$
$570$	−7.32891	+	1.59374i	−0.306974	+	0.0667546i
$571$	12.5023	+	21.6545i	0.523203	+	0.906214i	0.999635	+	0.0270031i	$0.00859640\pi$
$571$	12.5023	+	21.6545i	0.523203	+	0.906214i	−0.476432	+	0.879211i	$0.658070\pi$
$572$	0.795492	+	2.96882i	0.0332612	+	0.124132i
$573$	13.1886	+	13.1886i	0.550962	+	0.550962i
$574$		0			0
$575$	40.5988	−	6.82090i	1.69309	−	0.284451i
$576$	−3.65133	+	6.32429i	−0.152139	+	0.263512i
$577$	−18.9114	−	5.06730i	−0.787294	−	0.210955i	−0.157296	−	0.987552i	$-0.550278\pi$
$577$	−18.9114	−	5.06730i	−0.787294	−	0.210955i	−0.629998	+	0.776597i	$0.716944\pi$
$578$	−6.35964	−	1.70406i	−0.264526	−	0.0708796i
$579$	−34.9894	+	60.6034i	−1.45411	+	2.51859i
$580$	−3.34003	−	1.06796i	−0.138687	−	0.0443447i
$581$		0			0
$582$	24.0490	+	24.0490i	0.996864	+	0.996864i
$583$	1.13558	+	4.23805i	0.0470310	+	0.175522i
$584$	5.04129	+	8.73178i	0.208610	+	0.361323i
$585$	17.1857	+	11.0464i	0.710542	+	0.456711i
$586$	−1.83923	−	1.06188i	−0.0759779	−	0.0438659i
$587$	−14.3179	+	14.3179i	−0.590961	+	0.590961i	−0.937891	−	0.346930i	$-0.887224\pi$
$587$	−14.3179	+	14.3179i	−0.590961	+	0.590961i	0.346930	+	0.937891i	$0.387224\pi$
$588$		0			0
$589$			0.717850i			0.0295785i
$590$	−15.3050	−	0.730193i	−0.630098	−	0.0300616i
$591$	7.67792	−	4.43285i	0.315828	−	0.182343i
$592$	−0.706756	+	2.63765i	−0.0290475	+	0.108407i
$593$	−1.95951	+	0.525050i	−0.0804676	+	0.0215612i	−0.298828	−	0.954307i	$-0.596596\pi$
$593$	−1.95951	+	0.525050i	−0.0804676	+	0.0215612i	0.218361	+	0.975868i	$0.429929\pi$
$594$	−33.9279			−1.39208
$595$		0			0
$596$	21.1626			0.866856
$597$	−20.7854	+	5.56943i	−0.850690	+	0.227942i
$598$	−2.66611	+	9.95007i	−0.109026	+	0.406889i
$599$	4.97354	−	2.87148i	0.203214	−	0.117325i	−0.394940	−	0.918707i	$-0.629235\pi$
$599$	4.97354	−	2.87148i	0.203214	−	0.117325i	0.598154	+	0.801382i	$0.295901\pi$
$600$	14.5996	−	6.66481i	0.596024	−	0.272090i
$601$			4.20038i			0.171337i	0.996324	+	0.0856684i	$0.0273026\pi$
$601$			4.20038i			0.171337i	−0.996324	+	0.0856684i	$0.972697\pi$
$602$		0			0
$603$	−2.71492	+	2.71492i	−0.110560	+	0.110560i
$604$	5.80963	+	3.35419i	0.236390	+	0.136480i
$605$	−2.35904	−	10.8482i	−0.0959088	−	0.441041i
$606$	−0.642542	−	1.11292i	−0.0261015	−	0.0452091i
$607$	7.11838	+	26.5662i	0.288926	+	1.07829i	0.945922	+	0.324393i	$0.105160\pi$
$607$	7.11838	+	26.5662i	0.288926	+	1.07829i	−0.656996	+	0.753894i	$0.728173\pi$
$608$	−0.738921	−	0.738921i	−0.0299672	−	0.0299672i
$609$		0			0
$610$	−1.25045	+	0.644536i	−0.0506293	+	0.0260965i
$611$	6.36061	−	11.0169i	0.257323	−	0.445696i
$612$	−34.2558	−	9.17880i	−1.38471	−	0.371031i
$613$	−40.5212	−	10.8576i	−1.63663	−	0.438535i	−0.680807	−	0.732463i	$-0.738371\pi$
$613$	−40.5212	−	10.8576i	−1.63663	−	0.438535i	−0.955828	+	0.293928i	$0.905037\pi$
$614$	−9.65151	+	16.7169i	−0.389503	+	0.674639i
$615$	−48.6976	+	25.1008i	−1.96368	+	1.01216i
$616$		0			0
$617$	4.72792	+	4.72792i	0.190339	+	0.190339i	0.795843	−	0.605504i	$-0.207028\pi$
$617$	4.72792	+	4.72792i	0.190339	+	0.190339i	−0.605504	+	0.795843i	$0.707028\pi$
$618$	0.472766	+	1.76438i	0.0190174	+	0.0709740i
$619$	9.76333	+	16.9106i	0.392421	+	0.679694i	0.992768	−	0.120046i	$-0.0383042\pi$
$619$	9.76333	+	16.9106i	0.392421	+	0.679694i	−0.600347	+	0.799740i	$0.704971\pi$
$620$	−0.326401	−	1.50097i	−0.0131086	−	0.0602804i
$621$	−98.4760	−	56.8551i	−3.95171	−	2.28152i
$622$	21.5068	−	21.5068i	0.862343	−	0.862343i
$623$		0			0
$624$			4.01578i			0.160760i
$625$	−24.5468	−	4.73848i	−0.981873	−	0.189539i
$626$	16.8510	−	9.72891i	0.673500	−	0.388845i
$627$	2.13269	−	7.95932i	0.0851716	−	0.317865i
$628$	17.3474	−	4.64823i	0.692237	−	0.185484i
$629$	−13.2612			−0.528758
$630$		0			0
$631$	−21.3074			−0.848234			−0.424117	−	0.905607i	$-0.639415\pi$
$631$	−21.3074			−0.848234			−0.424117	+	0.905607i	$0.639415\pi$
$632$	7.87615	−	2.11041i	0.313297	−	0.0839475i
$633$	−17.2589	+	64.4112i	−0.685981	+	2.56012i
$634$	−11.9390	+	6.89299i	−0.474159	+	0.273756i
$635$	−7.61734	−	0.363418i	−0.302285	−	0.0144218i
$636$			5.73261i			0.227313i
$637$		0			0
$638$	2.72416	−	2.72416i	0.107851	−	0.107851i
$639$	69.2000	+	39.9526i	2.73751	+	1.58050i
$640$	1.88101	+	1.20905i	0.0743535	+	0.0477918i
$641$	−10.2340	−	17.7258i	−0.404218	−	0.700125i	0.590012	−	0.807394i	$-0.299123\pi$
$641$	−10.2340	−	17.7258i	−0.404218	−	0.700125i	−0.994230	+	0.107269i	$0.965789\pi$
$642$	3.90082	+	14.5581i	0.153953	+	0.574561i
$643$	−7.63085	−	7.63085i	−0.300931	−	0.300931i	0.540447	−	0.841378i	$-0.318255\pi$
$643$	−7.63085	−	7.63085i	−0.300931	−	0.300931i	−0.841378	+	0.540447i	$0.818255\pi$
$644$		0			0
$645$	−44.1397	−	14.1135i	−1.73800	−	0.555719i
$646$	2.53742	−	4.39493i	0.0998333	−	0.172916i
$647$	−13.7404	−	3.68172i	−0.540189	−	0.144743i	−0.0215999	−	0.999767i	$-0.506876\pi$
$647$	−13.7404	−	3.68172i	−0.540189	−	0.144743i	−0.518589	+	0.855023i	$0.673543\pi$
$648$	−21.6569	−	5.80296i	−0.850765	−	0.227962i
$649$	8.41700	−	14.5787i	0.330396	−	0.572263i
$650$	3.62932	−	5.09508i	0.142354	−	0.199846i
$651$		0			0
$652$	2.10889	+	2.10889i	0.0825905	+	0.0825905i
$653$	−3.38708	−	12.6408i	−0.132547	−	0.494672i	0.867449	−	0.497526i	$-0.165758\pi$
$653$	−3.38708	−	12.6408i	−0.132547	−	0.494672i	−0.999996	+	0.00285443i	$0.999091\pi$
$654$	10.5948	+	18.3507i	0.414288	+	0.717569i
$655$	29.5946	−	6.43563i	1.15636	−	0.251461i
$656$	−6.61060	−	3.81663i	−0.258100	−	0.149014i
$657$	−52.0641	+	52.0641i	−2.03121	+	2.03121i
$658$		0			0
$659$		−	18.9238i		−	0.737165i	−0.929595	−	0.368583i	$-0.879843\pi$
$659$		−	18.9238i		−	0.737165i	0.929595	−	0.368583i	$-0.120157\pi$
$660$	−0.840260	+	17.6121i	−0.0327071	+	0.685549i
$661$	5.11264	−	2.95179i	0.198859	−	0.114811i	−0.397264	−	0.917704i	$-0.630040\pi$
$661$	5.11264	−	2.95179i	0.198859	−	0.114811i	0.596123	+	0.802893i	$0.296707\pi$
$662$	4.41264	−	16.4682i	0.171502	−	0.640055i
$663$	−18.8375	+	5.04748i	−0.731586	+	0.196028i
$664$	−9.62933			−0.373690
$665$		0			0
$666$	−19.9414			−0.772712
$667$	12.4720	−	3.34185i	0.482916	−	0.129397i
$668$	2.34972	−	8.76927i	0.0909134	−	0.339293i
$669$	21.0896	−	12.1761i	0.815371	−	0.470755i
$670$	0.790744	+	0.869976i	0.0305491	+	0.0336101i
$671$		−	1.54557i		−	0.0596660i
$672$		0			0
$673$	−6.81402	+	6.81402i	−0.262661	+	0.262661i	−0.826134	−	0.563473i	$-0.809465\pi$
$673$	−6.81402	+	6.81402i	−0.262661	+	0.262661i	0.563473	+	0.826134i	$0.309465\pi$
$674$	−15.4992	−	8.94847i	−0.597007	−	0.344682i
$675$	43.9575	+	53.2545i	1.69193	+	2.04977i
$676$	−5.71736	−	9.90276i	−0.219899	−	0.380876i
$677$	5.79004	+	21.6087i	0.222529	+	0.830490i	0.983379	+	0.181563i	$0.0581155\pi$
$677$	5.79004	+	21.6087i	0.222529	+	0.830490i	−0.760850	+	0.648928i	$0.775218\pi$
$678$	−41.5053	−	41.5053i	−1.59400	−	1.59400i
$679$		0			0
$680$	−3.30721	+	10.3432i	−0.126826	+	0.396645i
$681$	−32.5657	+	56.4055i	−1.24792	+	2.16146i
$682$	1.63008	+	0.436778i	0.0624190	+	0.0167251i
$683$	−20.9710	−	5.61915i	−0.802431	−	0.215011i	−0.165780	−	0.986163i	$-0.553014\pi$
$683$	−20.9710	−	5.61915i	−0.802431	−	0.215011i	−0.636651	+	0.771152i	$0.719681\pi$
$684$	3.81561	−	6.60883i	0.145894	−	0.252695i
$685$	8.46989	+	16.4323i	0.323618	+	0.627844i
$686$		0			0
$687$	−16.2447	−	16.2447i	−0.619775	−	0.619775i
$688$	−1.67111	−	6.23665i	−0.0637103	−	0.237770i
$689$	1.11723	+	1.93510i	0.0425631	+	0.0737214i
$690$	−31.9526	+	49.7111i	−1.21641	+	1.89247i
$691$	−0.554917	−	0.320381i	−0.0211100	−	0.0121879i	0.489408	−	0.872055i	$-0.337213\pi$
$691$	−0.554917	−	0.320381i	−0.0211100	−	0.0121879i	−0.510518	+	0.859867i	$0.670546\pi$
$692$	15.5390	−	15.5390i	0.590706	−	0.590706i
$693$		0			0
$694$		−	31.4718i		−	1.19466i
$695$	−2.39499	+	2.17687i	−0.0908472	+	0.0825734i
$696$	4.35922	−	2.51680i	0.165236	−	0.0953989i
$697$	9.59434	−	35.8066i	0.363411	−	1.35627i
$698$	28.3380	−	7.59316i	1.07261	−	0.287405i
$699$	−12.5254			−0.473754
$700$		0			0
$701$	38.5834			1.45727			0.728637	−	0.684900i	$-0.240154\pi$
$701$	38.5834			1.45727			0.728637	+	0.684900i	$0.240154\pi$
$702$	−16.6898	+	4.47202i	−0.629916	+	0.168785i
$703$	0.738554	−	2.75632i	0.0278551	−	0.103957i
$704$	−2.12753	+	1.22833i	−0.0801842	+	0.0462944i
$705$	54.0040	−	49.0856i	2.03391	−	1.84867i
$706$			15.5864i			0.586603i
$707$		0			0
$708$	15.5526	−	15.5526i	0.584502	−	0.584502i
$709$	−12.9839	−	7.49625i	−0.487620	−	0.281527i	0.235967	−	0.971761i	$-0.424174\pi$
$709$	−12.9839	−	7.49625i	−0.487620	−	0.281527i	−0.723586	+	0.690234i	$0.757508\pi$
$710$	13.2293	−	20.5819i	0.496488	−	0.772425i
$711$	29.7729	+	51.5682i	1.11657	+	1.93396i
$712$	2.02370	+	7.55255i	0.0758413	+	0.283044i
$713$	3.99938	+	3.99938i	0.149778	+	0.149778i
$714$		0			0
$715$	3.14878	+	6.10889i	0.117758	+	0.228459i
$716$	6.71954	−	11.6386i	0.251121	−	0.434954i
$717$	−12.8301	−	3.43783i	−0.479150	−	0.128388i
$718$	−4.92577	−	1.31986i	−0.183828	−	0.0492566i
$719$	−22.6721	+	39.2693i	−0.845528	+	1.46450i	0.0396339	+	0.999214i	$0.487381\pi$
$719$	−22.6721	+	39.2693i	−0.845528	+	1.46450i	−0.885162	+	0.465283i	$0.845952\pi$
$720$	−4.97318	+	15.5535i	−0.185339	+	0.579646i
$721$		0			0
$722$	−12.6629	−	12.6629i	−0.471263	−	0.471263i
$723$	−6.50981	−	24.2949i	−0.242102	−	0.903538i
$724$	6.55333	+	11.3507i	0.243552	+	0.421845i
$725$	−7.80542	−	0.746482i	−0.289886	−	0.0277236i
$726$	13.8010	+	7.96801i	0.512203	+	0.295721i
$727$	−3.25230	+	3.25230i	−0.120621	+	0.120621i	−0.764841	−	0.644219i	$-0.777182\pi$
$727$	−3.25230	+	3.25230i	−0.120621	+	0.120621i	0.644219	+	0.764841i	$0.277182\pi$
$728$		0			0
$729$		−	30.7457i		−	1.13873i
$730$	15.1641	+	16.6836i	0.561250	+	0.617487i
$731$	27.1548	−	15.6778i	1.00436	−	0.579866i
$732$	0.522654	−	1.95057i	0.0193179	−	0.0720953i
$733$	11.9011	−	3.18888i	0.439576	−	0.117784i	−0.0322421	−	0.999480i	$-0.510265\pi$
$733$	11.9011	−	3.18888i	0.439576	−	0.117784i	0.471818	+	0.881696i	$0.343598\pi$
$734$	−13.4969			−0.498179
$735$		0			0
$736$	−8.23356			−0.303493
$737$	−1.24761	+	0.334296i	−0.0459563	+	0.0123139i
$738$	14.4274	−	53.8437i	0.531079	−	1.98202i
$739$	30.3007	−	17.4941i	1.11463	−	0.643532i	0.174606	−	0.984638i	$-0.444135\pi$
$739$	30.3007	−	17.4941i	1.11463	−	0.643532i	0.940025	+	0.341106i	$0.110801\pi$
$740$	−0.290983	+	6.09908i	−0.0106968	+	0.224207i
$741$		−	4.19646i		−	0.154161i
$742$		0			0
$743$	−11.0169	+	11.0169i	−0.404170	+	0.404170i	−0.879700	−	0.475530i	$-0.842256\pi$
$743$	−11.0169	+	11.0169i	−0.404170	+	0.404170i	0.475530	+	0.879700i	$0.342256\pi$
$744$	1.90953	+	1.10247i	0.0700067	+	0.0404184i
$745$	46.2404	−	10.0554i	1.69412	−	0.368403i
$746$	−12.5121	−	21.6717i	−0.458102	−	0.793456i
$747$	−18.2001	−	67.9237i	−0.665907	−	2.48520i
$748$	−8.43603	−	8.43603i	−0.308452	−	0.308452i
$749$		0			0
$750$	28.7333	−	21.4996i	1.04919	−	0.785054i
$751$	−16.8682	+	29.2166i	−0.615530	+	1.06613i	0.374762	+	0.927121i	$0.377725\pi$
$751$	−16.8682	+	29.2166i	−0.615530	+	1.06613i	−0.990291	+	0.139008i	$0.955609\pi$
$752$	9.82150	+	2.63166i	0.358153	+	0.0959669i
$753$	39.3035	+	10.5313i	1.43230	+	0.383784i
$754$	0.980998	−	1.69914i	0.0357258	−	0.0618790i
$755$	14.2878	+	4.56847i	0.519986	+	0.166263i
$756$		0			0
$757$	−34.1307	−	34.1307i	−1.24050	−	1.24050i	−0.959794	−	0.280706i	$-0.909431\pi$
$757$	−34.1307	−	34.1307i	−1.24050	−	1.24050i	−0.280706	−	0.959794i	$-0.590569\pi$
$758$	−7.12781	−	26.6013i	−0.258894	−	0.966204i
$759$	−32.4621	−	56.2260i	−1.17830	−	2.04088i
$760$	−1.96564	−	1.26344i	−0.0713013	−	0.0458300i
$761$	33.8469	+	19.5415i	1.22695	+	0.708380i	0.966391	−	0.257078i	$-0.0827596\pi$
$761$	33.8469	+	19.5415i	1.22695	+	0.708380i	0.260560	+	0.965458i	$0.416093\pi$
$762$	7.74055	−	7.74055i	0.280410	−	0.280410i
$763$		0			0
$764$			5.81085i			0.210229i
$765$	−79.2102	−	3.77907i	−2.86385	−	0.136632i
$766$	21.1293	−	12.1990i	0.763433	−	0.440768i
$767$	2.21888	−	8.28098i	0.0801192	−	0.299009i
$768$	−3.10041	+	0.830751i	−0.111876	+	0.0299772i
$769$	26.4297			0.953078			0.476539	−	0.879153i	$-0.341891\pi$
$769$	26.4297			0.953078			0.476539	+	0.879153i	$0.341891\pi$
$770$		0			0
$771$	42.5222			1.53140
$772$	−21.0589	+	5.64271i	−0.757926	+	0.203086i
$773$	1.62456	−	6.06294i	0.0584314	−	0.218069i	−0.930536	−	0.366199i	$-0.880659\pi$
$773$	1.62456	−	6.06294i	0.0584314	−	0.218069i	0.988968	+	0.148130i	$0.0473255\pi$
$774$	40.8338	−	23.5754i	1.46774	−	0.847400i
$775$	−1.42637	−	3.12453i	−0.0512368	−	0.112237i
$776$			10.5959i			0.380371i
$777$		0			0
$778$	−14.8378	+	14.8378i	−0.531960	+	0.531960i
$779$	6.90802	+	3.98835i	0.247506	+	0.142897i
$780$	1.90810	+	8.77448i	0.0683209	+	0.314177i
$781$	13.4403	+	23.2793i	0.480931	+	0.832998i
$782$	−10.3489	−	38.6225i	−0.370074	−	1.38114i
$783$	15.3144	+	15.3144i	0.547292	+	0.547292i
$784$		0			0
$785$	35.6955	−	18.3990i	1.27403	−	0.656689i
$786$	−21.7373	+	37.6501i	−0.775343	+	1.34293i
$787$	17.9432	+	4.80787i	0.639607	+	0.171382i	0.564025	−	0.825758i	$-0.309252\pi$
$787$	17.9432	+	4.80787i	0.639607	+	0.171382i	0.0755813	+	0.997140i	$0.475919\pi$
$788$	2.66798	+	0.714882i	0.0950428	+	0.0254666i
$789$	43.4859	−	75.3199i	1.54814	−	2.68146i
$790$	16.2066	−	8.35360i	0.576607	−	0.297208i
$791$		0			0
$792$	−12.6856	−	12.6856i	−0.450763	−	0.450763i
$793$	−0.203721	−	0.760296i	−0.00723433	−	0.0269989i
$794$	−12.1451	−	21.0359i	−0.431014	−	0.746538i
$795$	2.72385	+	12.5258i	0.0966050	+	0.444243i
$796$	−5.80592	−	3.35205i	−0.205785	−	0.118810i
$797$	−20.2150	+	20.2150i	−0.716053	+	0.716053i	−0.967795	−	0.251741i	$-0.918997\pi$
$797$	−20.2150	+	20.2150i	−0.716053	+	0.716053i	0.251741	+	0.967795i	$0.418997\pi$
$798$		0			0
$799$			49.3790i			1.74690i
$800$	4.68449	+	1.74801i	0.165622	+	0.0618014i
$801$	−49.4495	+	28.5497i	−1.74721	+	1.00875i
$802$	9.63726	−	35.9667i	0.340304	−	1.27003i
$803$	−23.9255	+	6.41081i	−0.844311	+	0.226232i
$804$	−1.68758			−0.0595164
$805$		0			0
$806$	0.859440			0.0302725
$807$	9.73002	−	2.60715i	0.342513	−	0.0917760i
$808$	0.103622	−	0.386723i	0.00364542	−	0.0136049i
$809$	−0.500492	+	0.288959i	−0.0175963	+	0.0101593i	−0.508772	−	0.860901i	$-0.669901\pi$
$809$	−0.500492	+	0.288959i	−0.0175963	+	0.0101593i	0.491176	+	0.871060i	$0.336567\pi$
$810$	−50.0777	−	2.38917i	−1.75955	−	0.0839470i
$811$			3.39036i			0.119052i	0.998227	+	0.0595258i	$0.0189589\pi$
$811$			3.39036i			0.119052i	−0.998227	+	0.0595258i	$0.981041\pi$
$812$		0			0
$813$	−74.1150	+	74.1150i	−2.59933	+	2.59933i
$814$	−5.80963	−	3.35419i	−0.203627	−	0.117564i
$815$	5.60997	+	3.60589i	0.196509	+	0.126309i
$816$	−7.79387	−	13.4994i	−0.272840	−	0.472573i
$817$	1.74629	+	6.51725i	0.0610950	+	0.228010i
$818$	15.3473	+	15.3473i	0.536606	+	0.536606i
$819$		0			0
$820$	−16.2576	−	5.19832i	−0.567741	−	0.181533i
$821$	9.62000	−	16.6623i	0.335740	−	0.581520i	−0.647886	−	0.761737i	$-0.724347\pi$
$821$	9.62000	−	16.6623i	0.335740	−	0.581520i	0.983627	+	0.180217i	$0.0576802\pi$
$822$	−25.6326	−	6.86824i	−0.894040	−	0.239557i
$823$	7.70585	+	2.06478i	0.268609	+	0.0719736i	0.390610	−	0.920556i	$-0.372264\pi$
$823$	7.70585	+	2.06478i	0.268609	+	0.0719736i	−0.122000	+	0.992530i	$0.538931\pi$
$824$	−0.284541	+	0.492839i	−0.00991245	+	0.0171689i
$825$	6.53241	+	38.8817i	0.227429	+	1.35369i
$826$		0			0
$827$	8.62349	+	8.62349i	0.299868	+	0.299868i	0.840962	−	0.541094i	$-0.181990\pi$
$827$	8.62349	+	8.62349i	0.299868	+	0.299868i	−0.541094	+	0.840962i	$0.681990\pi$
$828$	−15.5620	−	58.0781i	−0.540816	−	2.01835i
$829$	−14.1674	−	24.5387i	−0.492055	−	0.852263i	0.507904	−	0.861414i	$-0.330421\pi$
$829$	−14.1674	−	24.5387i	−0.492055	−	0.852263i	−0.999958	+	0.00915046i	$0.997087\pi$
$830$	−21.0401	+	4.57538i	−0.730313	+	0.158814i
$831$	87.8246	+	50.7055i	3.04660	+	1.75896i
$832$	−0.884667	+	0.884667i	−0.0306703	+	0.0306703i
$833$		0			0
$834$		−	4.64581i		−	0.160871i
$835$	0.967419	−	20.2773i	0.0334789	−	0.701726i
$836$	2.22325	−	1.28359i	0.0768927	−	0.0443940i
$837$	−2.45544	+	9.16382i	−0.0848723	+	0.316748i
$838$	18.9366	−	5.07405i	0.654155	−	0.175280i
$839$	3.84212			0.132645			0.0663223	−	0.997798i	$-0.478873\pi$
$839$	3.84212			0.132645			0.0663223	+	0.997798i	$0.478873\pi$
$840$		0			0
$841$	26.5407			0.915198
$842$	−13.7298	+	3.67890i	−0.473162	+	0.126783i
$843$	−23.9917	+	89.5383i	−0.826318	+	3.08386i
$844$	−17.9918	+	10.3875i	−0.619302	+	0.357554i
$845$	−17.1977	−	18.9209i	−0.591621	−	0.650900i
$846$			74.2532i			2.55288i
$847$		0			0
$848$	−1.26288	+	1.26288i	−0.0433675	+	0.0433675i
$849$	−12.0315	−	6.94640i	−0.412921	−	0.238400i
$850$	−2.31166	+	24.1714i	−0.0792894	+	0.829072i
$851$	−11.2417	−	19.4711i	−0.385359	−	0.667462i
$852$	9.09003	+	33.9244i	0.311419	+	1.16223i
$853$	−31.3166	−	31.3166i	−1.07226	−	1.07226i	−0.997177	−	0.0750839i	$-0.976078\pi$
$853$	−31.3166	−	31.3166i	−1.07226	−	1.07226i	−0.0750839	−	0.997177i	$-0.523922\pi$
$854$		0			0
$855$	5.19693	−	16.2533i	0.177731	−	0.555851i
$856$	−2.34777	+	4.06645i	−0.0802450	+	0.138988i
$857$	−30.5751	−	8.19258i	−1.04443	−	0.279853i	−0.304479	−	0.952519i	$-0.598482\pi$
$857$	−30.5751	−	8.19258i	−1.04443	−	0.279853i	−0.739946	+	0.672666i	$0.765149\pi$
$858$	−9.52923	−	2.55335i	−0.325323	−	0.0871700i
$859$	21.0251	−	36.4165i	0.717367	−	1.24252i	−0.244672	−	0.969606i	$-0.578680\pi$
$859$	21.0251	−	36.4165i	0.717367	−	1.24252i	0.962039	−	0.272911i	$-0.0879863\pi$
$860$	−6.61472	−	12.8331i	−0.225560	−	0.437604i
$861$		0			0
$862$	9.34887	+	9.34887i	0.318424	+	0.318424i
$863$	−12.4187	−	46.3472i	−0.422737	−	1.57768i	−0.768815	−	0.639471i	$-0.779153\pi$
$863$	−12.4187	−	46.3472i	−0.422737	−	1.57768i	0.346078	−	0.938206i	$-0.387513\pi$
$864$	−6.90529	−	11.9603i	−0.234923	−	0.406898i
$865$	26.5695	−	41.3362i	0.903389	−	1.40547i
$866$	−9.38046	−	5.41581i	−0.318761	−	0.184037i
$867$	14.9434	−	14.9434i	0.507504	−	0.507504i
$868$		0			0
$869$			20.0316i			0.679524i
$870$	8.32904	−	7.57049i	0.282381	−	0.256663i
$871$	−0.569660	+	0.328893i	−0.0193022	+	0.0111441i
$872$	−1.70861	+	6.37662i	−0.0578609	+	0.215940i
$873$	−74.7417	+	20.0270i	−2.52962	+	0.677810i
$874$	8.60400			0.291035
$875$		0			0
$876$	−32.3628			−1.09344
$877$	17.6842	−	4.73846i	0.597152	−	0.160006i	0.0524319	−	0.998625i	$-0.483303\pi$
$877$	17.6842	−	4.73846i	0.597152	−	0.160006i	0.544720	+	0.838618i	$0.316636\pi$
$878$	−7.18694	+	26.8220i	−0.242547	+	0.905199i
$879$	5.90352	−	3.40840i	0.199121	−	0.114962i
$880$	−4.06501	+	3.69479i	−0.137031	+	0.124551i
$881$		−	34.4306i		−	1.16000i	−0.814618	−	0.579998i	$-0.803053\pi$
$881$		−	34.4306i		−	1.16000i	0.814618	−	0.579998i	$-0.196947\pi$
$882$		0			0
$883$	7.78975	−	7.78975i	0.262146	−	0.262146i	−0.563779	−	0.825925i	$-0.690653\pi$
$883$	7.78975	−	7.78975i	0.262146	−	0.262146i	0.825925	+	0.563779i	$0.190653\pi$
$884$	−5.26180	−	3.03790i	−0.176973	−	0.102176i
$885$	26.5926	−	41.3722i	0.893901	−	1.39071i
$886$	16.6744	+	28.8810i	0.560189	+	0.970275i
$887$	7.45543	+	27.8241i	0.250329	+	0.934240i	0.970630	+	0.240578i	$0.0773371\pi$
$887$	7.45543	+	27.8241i	0.250329	+	0.934240i	−0.720301	+	0.693662i	$0.755996\pi$
$888$	−6.19774	−	6.19774i	−0.207982	−	0.207982i
$889$		0			0
$890$	8.01038	+	15.5408i	0.268508	+	0.520928i
$891$	27.5402	−	47.7011i	0.922633	−	1.59805i
$892$	7.32836	+	1.96363i	0.245372	+	0.0657471i
$893$	−10.2634	−	2.75007i	−0.343451	−	0.0920274i
$894$	−33.9637	+	58.8268i	−1.13592	+	1.96746i
$895$	9.15213	−	28.6231i	0.305922	−	0.956765i
$896$		0			0
$897$	−23.3799	−	23.3799i	−0.780632	−	0.780632i
$898$	−4.71178	−	17.5846i	−0.157234	−	0.586806i
$899$	−0.538634	−	0.932941i	−0.0179644	−	0.0311153i
$900$	−3.47614	+	36.3475i	−0.115871	+	1.21158i
$901$	−7.51133	−	4.33667i	−0.250239	−	0.144475i
$902$	13.2599	−	13.2599i	0.441506	−	0.441506i
$903$		0			0
$904$		−	18.2870i		−	0.608218i
$905$	19.7123	+	21.6875i	0.655260	+	0.720916i
$906$	−18.6476	+	10.7662i	−0.619525	+	0.357683i
$907$	−4.74142	+	17.6952i	−0.157436	+	0.587560i	0.841448	+	0.540338i	$0.181704\pi$
$907$	−4.74142	+	17.6952i	−0.157436	+	0.587560i	−0.998884	+	0.0472221i	$0.984963\pi$
$908$	−19.6002	+	5.25185i	−0.650454	+	0.174289i
$909$	2.92373			0.0969741
$910$		0			0
$911$	8.52576			0.282471			0.141236	−	0.989976i	$-0.454893\pi$
$911$	8.52576			0.282471			0.141236	+	0.989976i	$0.454893\pi$
$912$	3.23990	−	0.868128i	0.107284	−	0.0287466i
$913$	6.12261	−	22.8499i	0.202629	−	0.756221i
$914$	28.5161	−	16.4638i	0.943228	−	0.544573i
$915$	0.215186	−	4.51034i	0.00711382	−	0.149107i
$916$		−	7.15735i		−	0.236486i
$917$		0			0
$918$	47.4248	−	47.4248i	1.56525	−	1.56525i
$919$	28.3612	+	16.3743i	0.935549	+	0.540140i	0.888562	−	0.458756i	$-0.151705\pi$
$919$	28.3612	+	16.3743i	0.935549	+	0.540140i	0.0469869	+	0.998896i	$0.485038\pi$
$920$	−17.9903	+	3.91218i	−0.593124	+	0.128981i
$921$	−30.9792	−	53.6575i	−1.02080	−	1.76807i
$922$	5.51349	+	20.5766i	0.181577	+	0.677655i
$923$	9.67998	+	9.67998i	0.318620	+	0.318620i
$924$		0			0
$925$	2.26218	+	13.4648i	0.0743801	+	0.442719i
$926$	3.34957	−	5.80162i	0.110074	−	0.190653i
$927$	−4.01421	−	1.07560i	−0.131844	−	0.0353275i
$928$	1.51477	+	0.405882i	0.0497248	+	0.0133237i
$929$	−0.315361	+	0.546221i	−0.0103467	+	0.0179209i	−0.871152	−	0.491013i	$-0.836627\pi$
$929$	−0.315361	+	0.546221i	−0.0103467	+	0.0179209i	0.860806	+	0.508934i	$0.169960\pi$
$930$	4.69616	+	1.50158i	0.153993	+	0.0492387i
$931$		0			0
$932$	−2.75932	−	2.75932i	−0.0903845	−	0.0903845i
$933$	25.2675	+	94.2994i	0.827219	+	3.08722i
$934$	2.55484	+	4.42512i	0.0835970	+	0.144794i
$935$	−22.4411	−	14.4244i	−0.733903	−	0.471727i
$936$	−7.91238	−	4.56821i	−0.258624	−	0.149317i
$937$	−0.810245	+	0.810245i	−0.0264696	+	0.0264696i	−0.720218	−	0.693748i	$-0.755958\pi$
$937$	−0.810245	+	0.810245i	−0.0264696	+	0.0264696i	0.693748	+	0.720218i	$0.255958\pi$
$938$		0			0
$939$			62.4553i			2.03815i
$940$	22.7104	+	1.08350i	0.740732	+	0.0353399i
$941$	28.4240	−	16.4106i	0.926597	−	0.534971i	0.0408632	−	0.999165i	$-0.486989\pi$
$941$	28.4240	−	16.4106i	0.926597	−	0.534971i	0.885734	+	0.464194i	$0.153656\pi$
$942$	−14.9198	+	55.6813i	−0.486112	+	1.81420i
$943$	60.7074	−	16.2665i	1.97690	−	0.529710i
$944$	6.85240			0.223027
$945$		0			0
$946$	15.8618			0.515711
$947$	−13.7289	+	3.67864i	−0.446129	+	0.119540i	−0.474887	−	0.880047i	$-0.657511\pi$
$947$	−13.7289	+	3.67864i	−0.446129	+	0.119540i	0.0287587	+	0.999586i	$0.490845\pi$
$948$	−6.77394	+	25.2807i	−0.220007	+	0.821079i
$949$	−10.9244	+	6.30721i	−0.354621	+	0.204741i
$950$	−4.89526	−	1.82665i	−0.158823	−	0.0592645i
$951$		−	44.2499i		−	1.43490i
$952$		0			0
$953$	23.7218	−	23.7218i	0.768424	−	0.768424i	−0.209405	−	0.977829i	$-0.567153\pi$
$953$	23.7218	−	23.7218i	0.768424	−	0.768424i	0.977829	+	0.209405i	$0.0671528\pi$
$954$	−11.2951	−	6.52122i	−0.365692	−	0.211132i
$955$	2.76103	+	12.6967i	0.0893447	+	0.410856i
$956$	−2.06911	−	3.58380i	−0.0669197	−	0.115908i
$957$	3.20051	+	11.9444i	0.103458	+	0.386109i
$958$	−19.2466	−	19.2466i	−0.621829	−	0.621829i
$959$		0			0
$960$	−6.37966	+	3.28835i	−0.205903	+	0.106131i
$961$	−15.2641	+	26.4381i	−0.492389	+	0.852843i
$962$	−3.29999	−	0.884229i	−0.106396	−	0.0285087i
$963$	−33.1215	−	8.87488i	−1.06733	−	0.285989i
$964$	3.91802	−	6.78622i	0.126191	−	0.218569i
$965$	−43.3326	+	22.3355i	−1.39492	+	0.719004i
$966$		0			0
$967$	−16.9594	−	16.9594i	−0.545378	−	0.545378i	0.379723	−	0.925100i	$-0.376019\pi$
$967$	−16.9594	−	16.9594i	−0.545378	−	0.545378i	−0.925100	+	0.379723i	$0.876019\pi$
$968$	1.28499	+	4.79567i	0.0413013	+	0.154139i
$969$	8.14454	+	14.1067i	0.261640	+	0.453174i
$970$	5.03464	+	23.1521i	0.161653	+	0.743368i
$971$	−44.8299	−	25.8826i	−1.43866	−	0.830611i	−0.440903	−	0.897555i	$-0.645342\pi$
$971$	−44.8299	−	25.8826i	−1.43866	−	0.830611i	−0.997757	+	0.0669437i	$0.978675\pi$
$972$	21.5910	−	21.5910i	0.692533	−	0.692533i
$973$		0			0
$974$			5.11531i			0.163905i
$975$	8.33840	+	18.2656i	0.267042	+	0.584968i
$976$	0.544847	−	0.314567i	0.0174401	−	0.0100691i
$977$	5.42231	−	20.2363i	0.173475	−	0.647418i	−0.823331	−	0.567561i	$-0.807887\pi$
$977$	5.42231	−	20.2363i	0.173475	−	0.647418i	0.996806	−	0.0798566i	$-0.0254462\pi$
$978$	−9.24671	+	2.47765i	−0.295677	+	0.0792265i
$979$	−19.2085			−0.613907
$980$		0			0
$981$	−48.2090			−1.53920
$982$	2.05295	−	0.550086i	0.0655122	−	0.0175539i
$983$	−2.85572	+	10.6577i	−0.0910834	+	0.339928i	−0.996397	−	0.0848169i	$-0.972969\pi$
$983$	−2.85572	+	10.6577i	−0.0910834	+	0.339928i	0.905313	+	0.424745i	$0.139636\pi$
$984$	21.2185	−	12.2505i	0.676422	−	0.390533i
$985$	6.16921	+	0.294329i	0.196567	+	0.00937810i
$986$			7.61573i			0.242534i
$987$		0			0
$988$	0.924470	−	0.924470i	0.0294113	−	0.0294113i
$989$	46.0390	+	26.5806i	1.46395	+	0.845215i
$990$	−33.7456	−	21.6905i	−1.07251	−	0.689369i
$991$	18.4820	+	32.0118i	0.587101	+	1.01689i	0.994610	+	0.103687i	$0.0330640\pi$
$991$	18.4820	+	32.0118i	0.587101	+	1.01689i	−0.407509	+	0.913201i	$0.633603\pi$
$992$	0.177794	+	0.663536i	0.00564496	+	0.0210673i
$993$	38.6957	+	38.6957i	1.22797	+	1.22797i
$994$		0			0
$995$	−14.2787	−	4.56555i	−0.452664	−	0.144738i
$996$	15.4540	−	26.7671i	0.489679	−	0.848148i
$997$	42.4016	+	11.3615i	1.34287	+	0.359821i	0.857499	−	0.514486i	$-0.172017\pi$
$997$	42.4016	+	11.3615i	1.34287	+	0.359821i	0.485372	+	0.874308i	$0.338684\pi$
$998$	−8.08020	−	2.16508i	−0.255774	−	0.0685345i
$999$	18.8563	−	32.6600i	0.596586	−	1.03332i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.2.l.d.117.4		32
5.3	odd	4	inner	490.2.l.d.313.8		32
7.2	even	3		490.2.g.b.97.8	yes	16
7.3	odd	6	inner	490.2.l.d.227.8		32
7.4	even	3	inner	490.2.l.d.227.5		32
7.5	odd	6		490.2.g.b.97.5	✓	16
7.6	odd	2	inner	490.2.l.d.117.1		32
35.3	even	12	inner	490.2.l.d.423.4		32
35.13	even	4	inner	490.2.l.d.313.5		32
35.18	odd	12	inner	490.2.l.d.423.1		32
35.23	odd	12		490.2.g.b.293.5	yes	16
35.33	even	12		490.2.g.b.293.8	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
490.2.g.b.97.5	✓	16	7.5	odd	6
490.2.g.b.97.8	yes	16	7.2	even	3
490.2.g.b.293.5	yes	16	35.23	odd	12
490.2.g.b.293.8	yes	16	35.33	even	12
490.2.l.d.117.1		32	7.6	odd	2	inner
490.2.l.d.117.4		32	1.1	even	1	trivial
490.2.l.d.227.5		32	7.4	even	3	inner
490.2.l.d.227.8		32	7.3	odd	6	inner
490.2.l.d.313.5		32	35.13	even	4	inner
490.2.l.d.313.8		32	5.3	odd	4	inner
490.2.l.d.423.1		32	35.18	odd	12	inner
490.2.l.d.423.4		32	35.3	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	490.l (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(0.830751 - 3.10041i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.65469 - 1.50399i) q^{5} +3.20978i q^{6} +(-0.707107 + 0.707107i) q^{8} +(-6.32429 - 3.65133i) q^{9} +(-1.20905 + 1.88101i) q^{10} +(-1.22833 - 2.12753i) q^{11} +(-0.830751 - 3.10041i) q^{12} +(-0.884667 - 0.884667i) q^{13} +(-3.28835 - 6.37966i) q^{15} +(0.500000 - 0.866025i) q^{16} +(4.69086 + 1.25691i) q^{17} +(7.05383 + 1.89007i) q^{18} +(-0.522496 + 0.904990i) q^{19} +(0.681009 - 2.12984i) q^{20} +(1.73712 + 1.73712i) q^{22} +(2.13100 + 7.95301i) q^{23} +(1.60489 + 2.77975i) q^{24} +(0.476010 - 4.97729i) q^{25} +(1.08349 + 0.625554i) q^{26} +(-9.76556 + 9.76556i) q^{27} -1.56821i q^{29} +(4.82748 + 5.31119i) q^{30} +(0.594910 - 0.343471i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-7.61663 + 2.04087i) q^{33} -4.85633 q^{34} -7.30266 q^{36} +(-2.63765 + 0.706756i) q^{37} +(0.270464 - 1.00938i) q^{38} +(-3.47777 + 2.00789i) q^{39} +(-0.106560 + 2.23353i) q^{40} -7.63326i q^{41} +(4.56555 - 4.56555i) q^{43} +(-2.12753 - 1.22833i) q^{44} +(-15.9563 + 3.46986i) q^{45} +(-4.11678 - 7.13047i) q^{46} +(2.63166 + 9.82150i) q^{47} +(-2.26965 - 2.26965i) q^{48} +(0.828427 + 4.93089i) q^{50} +(7.79387 - 13.4994i) q^{51} +(-1.20848 - 0.323811i) q^{52} +(-1.72513 - 0.462247i) q^{53} +(6.90529 - 11.9603i) q^{54} +(-5.23229 - 1.67300i) q^{55} +(2.37177 + 2.37177i) q^{57} +(0.405882 + 1.51477i) q^{58} +(3.42620 + 5.93435i) q^{59} +(-6.03763 - 3.88077i) q^{60} +(0.544847 + 0.314567i) q^{61} +(-0.485742 + 0.485742i) q^{62} -1.00000i q^{64} +(-2.79439 - 0.133318i) q^{65} +(6.82889 - 3.94266i) q^{66} +(0.136078 - 0.507848i) q^{67} +(4.69086 - 1.25691i) q^{68} +26.4279 q^{69} -10.9419 q^{71} +(7.05383 - 1.89007i) q^{72} +(2.60957 - 9.73903i) q^{73} +(2.36485 - 1.36535i) q^{74} +(-15.0362 - 5.61071i) q^{75} +1.04499i q^{76} +(2.83958 - 2.83958i) q^{78} +(-7.06156 - 4.07700i) q^{79} +(-0.475150 - 2.18500i) q^{80} +(11.2105 + 19.4171i) q^{81} +(1.97563 + 7.37316i) q^{82} +(6.80896 + 6.80896i) q^{83} +(9.65231 - 4.97522i) q^{85} +(-3.22833 + 5.59163i) q^{86} +(-4.86208 - 1.30279i) q^{87} +(2.37295 + 0.635829i) q^{88} +(3.90949 - 6.77143i) q^{89} +(14.5146 - 7.48143i) q^{90} +(5.82200 + 5.82200i) q^{92} +(-0.570678 - 2.12980i) q^{93} +(-5.08398 - 8.80571i) q^{94} +(0.496528 + 2.28331i) q^{95} +(2.77975 + 1.60489i) q^{96} +(7.49243 - 7.49243i) q^{97} +17.9401i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{11} - 48 q^{15} + 16 q^{16} + 16 q^{18} + 32 q^{22} - 16 q^{23} - 32 q^{25} - 40 q^{30} - 96 q^{36} + 48 q^{37} + 32 q^{43} + 16 q^{46} - 64 q^{50} + 80 q^{51} - 32 q^{53} + 96 q^{57} - 16 q^{58}+ \cdots - 40 q^{95}+O(q^{100}) \) 32 * q + 16 * q^11 - 48 * q^15 + 16 * q^16 + 16 * q^18 + 32 * q^22 - 16 * q^23 - 32 * q^25 - 40 * q^30 - 96 * q^36 + 48 * q^37 + 32 * q^43 + 16 * q^46 - 64 * q^50 + 80 * q^51 - 32 * q^53 + 96 * q^57 - 16 * q^58 - 40 * q^60 - 32 * q^65 - 16 * q^67 + 32 * q^71 + 16 * q^72 + 112 * q^81 + 48 * q^85 - 48 * q^86 + 16 * q^88 + 32 * q^92 - 64 * q^93 - 40 * q^95

Introduction

L-functions

Modular forms

Varieties

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Database

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