LMFDB - Embedded newform 102.2.i.b.29.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [102,2,Mod(5,102)] 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("102.5"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(102, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 102 = 2 \cdot 3 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	102.i (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,0,0,0,0,0,0,0,16] 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:	$0.814474100617$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			29.1
Character	$\chi$	$=$	102.29
Dual form			102.2.i.b.95.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.923880 + 0.382683i) q^{2} +(-1.72545 + 0.151023i) q^{3} +(0.707107 - 0.707107i) q^{4} +(0.456232 - 2.29363i) q^{5} +(1.53632 - 0.799829i) q^{6} +(3.60046 - 0.716176i) q^{7} +(-0.382683 + 0.923880i) q^{8} +(2.95438 - 0.521165i) q^{9} +(0.456232 + 2.29363i) q^{10} +(1.50047 + 1.00258i) q^{11} +(-1.11329 + 1.32687i) q^{12} +(-3.71785 - 3.71785i) q^{13} +(-3.05232 + 2.03950i) q^{14} +(-0.440817 + 4.02646i) q^{15} -1.00000i q^{16} +(1.77462 - 3.72165i) q^{17} +(-2.53005 + 1.61209i) q^{18} +(-0.132053 - 0.318803i) q^{19} +(-1.29924 - 1.94445i) q^{20} +(-6.10427 + 1.77948i) q^{21} +(-1.76992 - 0.352060i) q^{22} +(-4.39140 + 6.57220i) q^{23} +(0.520776 - 1.65191i) q^{24} +(-0.433207 - 0.179440i) q^{25} +(4.85760 + 2.01208i) q^{26} +(-5.01895 + 1.34543i) q^{27} +(2.03950 - 3.05232i) q^{28} +(4.77934 + 0.950670i) q^{29} +(-1.13360 - 3.88866i) q^{30} +(2.32141 + 3.47424i) q^{31} +(0.382683 + 0.923880i) q^{32} +(-2.74040 - 1.50330i) q^{33} +(-0.215323 + 4.11748i) q^{34} -8.58488i q^{35} +(1.72055 - 2.45758i) q^{36} +(-5.82914 + 3.89490i) q^{37} +(0.244002 + 0.244002i) q^{38} +(6.97645 + 5.85349i) q^{39} +(1.94445 + 1.29924i) q^{40} +(0.0957457 + 0.481346i) q^{41} +(4.95863 - 3.98003i) q^{42} +(-0.126561 + 0.305546i) q^{43} +(1.76992 - 0.352060i) q^{44} +(0.152523 - 7.01405i) q^{45} +(1.54205 - 7.75243i) q^{46} +(0.933888 - 0.933888i) q^{47} +(0.151023 + 1.72545i) q^{48} +(5.98326 - 2.47835i) q^{49} +0.468900 q^{50} +(-2.49998 + 6.68955i) q^{51} -5.25783 q^{52} +(-0.934197 + 0.386957i) q^{53} +(4.12203 - 3.16368i) q^{54} +(2.98412 - 2.98412i) q^{55} +(-0.716176 + 3.60046i) q^{56} +(0.275997 + 0.530138i) q^{57} +(-4.77934 + 0.950670i) q^{58} +(1.33755 - 3.22914i) q^{59} +(2.53543 + 3.15884i) q^{60} +(2.43704 + 12.2518i) q^{61} +(-3.47424 - 2.32141i) q^{62} +(10.2639 - 3.99229i) q^{63} +(-0.707107 - 0.707107i) q^{64} +(-10.2236 + 6.83117i) q^{65} +(3.10709 + 0.340165i) q^{66} -3.75359i q^{67} +(-1.37676 - 3.88646i) q^{68} +(6.58461 - 12.0032i) q^{69} +(3.28529 + 7.93139i) q^{70} +(-6.78001 - 10.1470i) q^{71} +(-0.649100 + 2.92894i) q^{72} +(-1.31077 - 0.260728i) q^{73} +(3.89490 - 5.82914i) q^{74} +(0.774578 + 0.244192i) q^{75} +(-0.318803 - 0.132053i) q^{76} +(6.12041 + 2.53516i) q^{77} +(-8.68543 - 2.73815i) q^{78} +(-7.42101 + 11.1063i) q^{79} +(-2.29363 - 0.456232i) q^{80} +(8.45677 - 3.07944i) q^{81} +(-0.272661 - 0.408066i) q^{82} +(3.70432 + 8.94302i) q^{83} +(-3.05809 + 5.57465i) q^{84} +(-7.72647 - 5.76827i) q^{85} -0.330720i q^{86} +(-8.39011 - 0.918549i) q^{87} +(-1.50047 + 1.00258i) q^{88} +(7.23981 + 7.23981i) q^{89} +(2.54325 + 6.53850i) q^{90} +(-16.0486 - 10.7233i) q^{91} +(1.54205 + 7.75243i) q^{92} +(-4.53018 - 5.64405i) q^{93} +(-0.505416 + 1.22018i) q^{94} +(-0.791465 + 0.157432i) q^{95} +(-0.799829 - 1.53632i) q^{96} +(0.0243524 - 0.122428i) q^{97} +(-4.57939 + 4.57939i) q^{98} +(4.95547 + 2.18002i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 16 q^{11} - 48 q^{15} - 16 q^{17} - 16 q^{18} - 8 q^{24} - 16 q^{25} - 16 q^{29} - 16 q^{31} + 16 q^{33} - 16 q^{37} - 24 q^{38} + 16 q^{39} + 32 q^{41} + 48 q^{42} - 8 q^{43} - 16 q^{45} + 16 q^{46}+ \cdots + 16 q^{99}+O(q^{100}) $ 24 * q + 16 * q^11 - 48 * q^15 - 16 * q^17 - 16 * q^18 - 8 * q^24 - 16 * q^25 - 16 * q^29 - 16 * q^31 + 16 * q^33 - 16 * q^37 - 24 * q^38 + 16 * q^39 + 32 * q^41 + 48 * q^42 - 8 * q^43 - 16 * q^45 + 16 * q^46 - 16 * q^47 + 32 * q^49 + 8 * q^50 + 64 * q^51 + 16 * q^52 + 64 * q^53 + 8 * q^54 + 32 * q^55 + 8 * q^57 + 16 * q^58 - 64 * q^59 + 16 * q^60 + 16 * q^61 + 16 * q^62 + 48 * q^63 - 16 * q^69 - 16 * q^70 + 16 * q^72 - 64 * q^73 + 16 * q^74 - 80 * q^75 - 16 * q^77 - 16 * q^78 - 32 * q^79 - 16 * q^80 + 32 * q^81 - 64 * q^82 + 72 * q^83 - 16 * q^84 - 32 * q^85 - 32 * q^87 - 16 * q^88 - 48 * q^89 - 64 * q^91 + 16 * q^92 + 96 * q^93 - 32 * q^94 + 32 * q^95 - 16 * q^97 - 16 * q^98 + 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/102\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$-1$	$e\left(\frac{13}{16}\right)$

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 $

$2$	−0.923880	+	0.382683i	−0.653281	+	0.270598i
$2$	−0.923880	+	0.382683i	−0.653281	+	0.270598i
$3$	−1.72545	+	0.151023i	−0.996191	+	0.0871929i
$3$	−1.72545	+	0.151023i	−0.996191	+	0.0871929i
$4$	0.707107	−	0.707107i	0.353553	−	0.353553i
$5$	0.456232	−	2.29363i	0.204033	−	1.02574i	−0.733987	−	0.679163i	$-0.762343\pi$
$5$	0.456232	−	2.29363i	0.204033	−	1.02574i	0.938020	−	0.346580i	$-0.112657\pi$
$6$	1.53632	−	0.799829i	0.627199	−	0.326529i
$7$	3.60046	−	0.716176i	1.36085	−	0.270689i	0.539917	−	0.841718i	$-0.318456\pi$
$7$	3.60046	−	0.716176i	1.36085	−	0.270689i	0.820930	+	0.571029i	$0.193456\pi$
$8$	−0.382683	+	0.923880i	−0.135299	+	0.326641i
$9$	2.95438	−	0.521165i	0.984795	−	0.173722i
$10$	0.456232	+	2.29363i	0.144273	+	0.725310i
$11$	1.50047	+	1.00258i	0.452409	+	0.302290i	0.760820	−	0.648963i	$-0.224797\pi$
$11$	1.50047	+	1.00258i	0.452409	+	0.302290i	−0.308411	+	0.951253i	$0.599797\pi$
$12$	−1.11329	+	1.32687i	−0.321380	+	0.383034i
$13$	−3.71785	−	3.71785i	−1.03114	−	1.03114i	−0.999499	−	0.0316456i	$-0.989925\pi$
$13$	−3.71785	−	3.71785i	−1.03114	−	1.03114i	−0.0316456	−	0.999499i	$-0.510075\pi$
$14$	−3.05232	+	2.03950i	−0.815768	+	0.545079i
$15$	−0.440817	+	4.02646i	−0.113818	+	1.03963i
$16$		−	1.00000i		−	0.250000i
$17$	1.77462	−	3.72165i	0.430410	−	0.902634i
$17$	1.77462	−	3.72165i	0.430410	−	0.902634i
$18$	−2.53005	+	1.61209i	−0.596339	+	0.379973i
$19$	−0.132053	−	0.318803i	−0.0302950	−	0.0731385i	0.908008	−	0.418953i	$-0.137603\pi$
$19$	−0.132053	−	0.318803i	−0.0302950	−	0.0731385i	−0.938303	+	0.345814i	$0.887603\pi$
$20$	−1.29924	−	1.94445i	−0.290519	−	0.434792i
$21$	−6.10427	+	1.77948i	−1.33206	+	0.388314i
$22$	−1.76992	−	0.352060i	−0.377349	−	0.0750594i
$23$	−4.39140	+	6.57220i	−0.915670	+	1.37040i	0.0131684	+	0.999913i	$0.495808\pi$
$23$	−4.39140	+	6.57220i	−0.915670	+	1.37040i	−0.928839	+	0.370484i	$0.879192\pi$
$24$	0.520776	−	1.65191i	0.106303	−	0.337194i
$25$	−0.433207	−	0.179440i	−0.0866414	−	0.0358880i
$26$	4.85760	+	2.01208i	0.952654	+	0.394602i
$27$	−5.01895	+	1.34543i	−0.965897	+	0.258927i
$28$	2.03950	−	3.05232i	0.385429	−	0.576835i
$29$	4.77934	+	0.950670i	0.887502	+	0.176535i	0.617731	−	0.786390i	$-0.288052\pi$
$29$	4.77934	+	0.950670i	0.887502	+	0.176535i	0.269771	+	0.962925i	$0.413052\pi$
$30$	−1.13360	−	3.88866i	−0.206966	−	0.709968i
$31$	2.32141	+	3.47424i	0.416938	+	0.623992i	0.979183	−	0.202979i	$-0.0650623\pi$
$31$	2.32141	+	3.47424i	0.416938	+	0.623992i	−0.562245	+	0.826971i	$0.690062\pi$
$32$	0.382683	+	0.923880i	0.0676495	+	0.163320i
$33$	−2.74040	−	1.50330i	−0.477043	−	0.261692i
$34$	−0.215323	+	4.11748i	−0.0369277	+	0.706142i
$35$		−	8.58488i		−	1.45111i
$36$	1.72055	−	2.45758i	0.286758	−	0.409597i
$37$	−5.82914	+	3.89490i	−0.958304	+	0.640318i	−0.933197	−	0.359366i	$-0.882993\pi$
$37$	−5.82914	+	3.89490i	−0.958304	+	0.640318i	−0.0251076	+	0.999685i	$0.507993\pi$
$38$	0.244002	+	0.244002i	0.0395823	+	0.0395823i
$39$	6.97645	+	5.85349i	1.11713	+	0.937309i
$40$	1.94445	+	1.29924i	0.307444	+	0.205428i
$41$	0.0957457	+	0.481346i	0.0149530	+	0.0751737i	0.987541	−	0.157360i	$-0.0502984\pi$
$41$	0.0957457	+	0.481346i	0.0149530	+	0.0751737i	−0.972588	+	0.232534i	$0.925298\pi$
$42$	4.95863	−	3.98003i	0.765134	−	0.614132i
$43$	−0.126561	+	0.305546i	−0.0193004	+	0.0465953i	−0.933236	−	0.359264i	$-0.883028\pi$
$43$	−0.126561	+	0.305546i	−0.0193004	+	0.0465953i	0.913936	+	0.405859i	$0.133028\pi$
$44$	1.76992	−	0.352060i	0.266826	−	0.0530750i
$45$	0.152523	−	7.01405i	0.0227368	−	1.04559i
$46$	1.54205	−	7.75243i	0.227364	−	1.14303i
$47$	0.933888	−	0.933888i	0.136222	−	0.136222i	−0.635708	−	0.771930i	$-0.719292\pi$
$47$	0.933888	−	0.933888i	0.136222	−	0.136222i	0.771930	+	0.635708i	$0.219292\pi$
$48$	0.151023	+	1.72545i	0.0217982	+	0.249048i
$49$	5.98326	−	2.47835i	0.854751	−	0.354049i
$50$	0.468900			0.0663125
$51$	−2.49998	+	6.68955i	−0.350067	+	0.936725i
$52$	−5.25783			−0.729129
$53$	−0.934197	+	0.386957i	−0.128322	+	0.0531526i	−0.445920	−	0.895073i	$-0.647124\pi$
$53$	−0.934197	+	0.386957i	−0.128322	+	0.0531526i	0.317599	+	0.948225i	$0.397124\pi$
$54$	4.12203	−	3.16368i	0.560937	−	0.430522i
$55$	2.98412	−	2.98412i	0.402378	−	0.402378i
$56$	−0.716176	+	3.60046i	−0.0957031	+	0.481132i
$57$	0.275997	+	0.530138i	0.0365567	+	0.0702185i
$58$	−4.77934	+	0.950670i	−0.627558	+	0.124829i
$59$	1.33755	−	3.22914i	0.174135	−	0.420399i	−0.812582	−	0.582846i	$-0.801939\pi$
$59$	1.33755	−	3.22914i	0.174135	−	0.420399i	0.986717	+	0.162448i	$0.0519389\pi$
$60$	2.53543	+	3.15884i	0.327323	+	0.407805i
$61$	2.43704	+	12.2518i	0.312031	+	1.56869i	0.744866	+	0.667214i	$0.232513\pi$
$61$	2.43704	+	12.2518i	0.312031	+	1.56869i	−0.432835	+	0.901473i	$0.642487\pi$
$62$	−3.47424	−	2.32141i	−0.441229	−	0.294820i
$63$	10.2639	−	3.99229i	1.29313	−	0.502982i
$64$	−0.707107	−	0.707107i	−0.0883883	−	0.0883883i
$65$	−10.2236	+	6.83117i	−1.26808	+	0.847303i
$66$	3.10709	+	0.340165i	0.382457	+	0.0418714i
$67$		−	3.75359i		−	0.458574i	−0.973359	−	0.229287i	$-0.926361\pi$
$67$		−	3.75359i		−	0.458574i	0.973359	−	0.229287i	$-0.0736394\pi$
$68$	−1.37676	−	3.88646i	−0.166956	−	0.471302i
$69$	6.58461	−	12.0032i	0.792694	−	1.44502i
$70$	3.28529	+	7.93139i	0.392667	+	0.947983i
$71$	−6.78001	−	10.1470i	−0.804639	−	1.20423i	−0.975731	−	0.218973i	$-0.929729\pi$
$71$	−6.78001	−	10.1470i	−0.804639	−	1.20423i	0.171092	−	0.985255i	$-0.445271\pi$
$72$	−0.649100	+	2.92894i	−0.0764972	+	0.345178i
$73$	−1.31077	−	0.260728i	−0.153414	−	0.0305159i	0.117786	−	0.993039i	$-0.462420\pi$
$73$	−1.31077	−	0.260728i	−0.153414	−	0.0305159i	−0.271200	+	0.962523i	$0.587420\pi$
$74$	3.89490	−	5.82914i	0.452773	−	0.677623i
$75$	0.774578	+	0.244192i	0.0894406	+	0.0281968i
$76$	−0.318803	−	0.132053i	−0.0365693	−	0.0151475i
$77$	6.12041	+	2.53516i	0.697485	+	0.288908i
$78$	−8.68543	−	2.73815i	−0.983432	−	0.310035i
$79$	−7.42101	+	11.1063i	−0.834929	+	1.24956i	0.131162	+	0.991361i	$0.458129\pi$
$79$	−7.42101	+	11.1063i	−0.834929	+	1.24956i	−0.966092	+	0.258199i	$0.916871\pi$
$80$	−2.29363	−	0.456232i	−0.256436	−	0.0510083i
$81$	8.45677	−	3.07944i	0.939642	−	0.342160i
$82$	−0.272661	−	0.408066i	−0.0301103	−	0.0450633i
$83$	3.70432	+	8.94302i	0.406602	+	0.981624i	0.986025	+	0.166597i	$0.0532780\pi$
$83$	3.70432	+	8.94302i	0.406602	+	0.981624i	−0.579423	+	0.815027i	$0.696722\pi$
$84$	−3.05809	+	5.57465i	−0.333665	+	0.608245i
$85$	−7.72647	−	5.76827i	−0.838053	−	0.625657i
$86$		−	0.330720i		−	0.0356625i
$87$	−8.39011	−	0.918549i	−0.899514	−	0.0984788i
$88$	−1.50047	+	1.00258i	−0.159951	+	0.106876i
$89$	7.23981	+	7.23981i	0.767418	+	0.767418i	0.977651	−	0.210233i	$-0.0674222\pi$
$89$	7.23981	+	7.23981i	0.767418	+	0.767418i	−0.210233	+	0.977651i	$0.567422\pi$
$90$	2.54325	+	6.53850i	0.268082	+	0.689219i
$91$	−16.0486	−	10.7233i	−1.68235	−	1.12411i
$92$	1.54205	+	7.75243i	0.160770	+	0.808247i
$93$	−4.53018	−	5.64405i	−0.469758	−	0.585261i
$94$	−0.505416	+	1.22018i	−0.0521297	+	0.125852i
$95$	−0.791465	+	0.157432i	−0.0812026	+	0.0161522i
$96$	−0.799829	−	1.53632i	−0.0816322	−	0.156800i
$97$	0.0243524	−	0.122428i	0.00247262	−	0.0124307i	−0.979529	−	0.201302i	$-0.935483\pi$
$97$	0.0243524	−	0.122428i	0.00247262	−	0.0124307i	0.982002	+	0.188871i	$0.0604828\pi$
$98$	−4.57939	+	4.57939i	−0.462588	+	0.462588i
$99$	4.95547	+	2.18002i	0.498044	+	0.219100i
$100$	−0.433207	+	0.179440i	−0.0433207	+	0.0179440i
$101$	−18.7037			−1.86108			−0.930542	−	0.366186i	$-0.880663\pi$
$101$	−18.7037			−1.86108			−0.930542	+	0.366186i	$0.880663\pi$
$102$	−0.250302	−	7.13704i	−0.0247836	−	0.706672i
$103$	−10.5331			−1.03786			−0.518931	−	0.854816i	$-0.673670\pi$
$103$	−10.5331			−1.03786			−0.518931	+	0.854816i	$0.673670\pi$
$104$	4.85760	−	2.01208i	0.476327	−	0.197301i
$105$	1.29651	+	14.8128i	0.126526	+	1.44558i
$106$	0.715003	−	0.715003i	0.0694472	−	0.0694472i
$107$	−1.30537	+	6.56256i	−0.126195	+	0.634427i	0.864973	+	0.501818i	$0.167335\pi$
$107$	−1.30537	+	6.56256i	−0.126195	+	0.634427i	−0.991168	+	0.132609i	$0.957665\pi$
$108$	−2.59757	+	4.50029i	−0.249952	+	0.433041i
$109$	12.0299	−	2.39289i	1.15225	−	0.229197i	0.418243	−	0.908335i	$-0.362646\pi$
$109$	12.0299	−	2.39289i	1.15225	−	0.229197i	0.734011	+	0.679138i	$0.237646\pi$
$110$	−1.61499	+	3.89894i	−0.153983	+	0.371749i
$111$	9.46969	−	7.60081i	0.898823	−	0.721437i
$112$	−0.716176	−	3.60046i	−0.0676723	−	0.340212i
$113$	15.5871	+	10.4150i	1.46631	+	0.979756i	0.995219	+	0.0976715i	$0.0311394\pi$
$113$	15.5871	+	10.4150i	1.46631	+	0.979756i	0.471090	+	0.882085i	$0.343861\pi$
$114$	−0.457863	−	0.384164i	−0.0428828	−	0.0359802i
$115$	13.0707	+	13.0707i	1.21885	+	1.21885i
$116$	4.05173	−	2.70728i	0.376194	−	0.251365i
$117$	−12.9216	−	9.04633i	−1.19460	−	0.836334i
$118$			3.49520i			0.321759i
$119$	3.72410	−	14.6706i	0.341388	−	1.34485i
$120$	−3.55127	−	1.94812i	−0.324185	−	0.177838i
$121$	−2.96328	−	7.15399i	−0.269389	−	0.650363i
$122$	−6.94011	−	10.3866i	−0.628328	−	0.940359i
$123$	−0.237899	−	0.816081i	−0.0214506	−	0.0735836i
$124$	4.09814	+	0.815172i	0.368024	+	0.0732046i
$125$	5.88698	−	8.81049i	0.526548	−	0.788034i
$126$	−7.95482	+	7.61622i	−0.708672	+	0.678507i
$127$	5.89440	+	2.44154i	0.523044	+	0.216652i	0.628553	−	0.777767i	$-0.283647\pi$
$127$	5.89440	+	2.44154i	0.523044	+	0.216652i	−0.105510	+	0.994418i	$0.533647\pi$
$128$	0.923880	+	0.382683i	0.0816602	+	0.0338248i
$129$	0.172231	−	0.546319i	0.0151641	−	0.0481007i
$130$	6.83117	−	10.2236i	0.599134	−	0.896667i
$131$	1.59970	+	0.318199i	0.139766	+	0.0278012i	0.264478	−	0.964392i	$-0.414801\pi$
$131$	1.59970	+	0.318199i	0.139766	+	0.0278012i	−0.124711	+	0.992193i	$0.539801\pi$
$132$	−3.00075	+	0.874762i	−0.261182	+	0.0761382i
$133$	−0.703770	−	1.05327i	−0.0610246	−	0.0913298i
$134$	1.43644	+	3.46786i	0.124089	+	0.299578i
$135$	0.796108	+	12.1254i	0.0685180	+	1.04359i
$136$	2.75924	+	3.06375i	0.236603	+	0.262715i
$137$		−	4.37844i		−	0.374076i	−0.982353	−	0.187038i	$-0.940111\pi$
$137$		−	4.37844i		−	0.374076i	0.982353	−	0.187038i	$-0.0598887\pi$
$138$	−1.48995	+	13.6094i	−0.126833	+	1.15851i
$139$	13.5587	−	9.05965i	1.15004	−	0.768430i	0.173723	−	0.984794i	$-0.444420\pi$
$139$	13.5587	−	9.05965i	1.15004	−	0.768430i	0.976313	+	0.216365i	$0.0694201\pi$
$140$	−6.07043	−	6.07043i	−0.513045	−	0.513045i
$141$	−1.47034	+	1.75242i	−0.123825	+	0.147580i
$142$	10.1470	+	6.78001i	0.851518	+	0.568966i
$143$	−1.85107	−	9.30596i	−0.154794	−	0.778203i
$144$	−0.521165	−	2.95438i	−0.0434304	−	0.246199i
$145$	4.36098	−	10.5283i	0.362159	−	0.874330i
$146$	1.31077	−	0.260728i	0.108480	−	0.0215780i
$147$	−9.94955	+	5.17988i	−0.820625	+	0.427229i
$148$	−1.36771	+	6.87594i	−0.112425	+	0.565198i
$149$	−4.06236	+	4.06236i	−0.332802	+	0.332802i	−0.853649	−	0.520848i	$-0.825616\pi$
$149$	−4.06236	+	4.06236i	−0.332802	+	0.332802i	0.520848	+	0.853649i	$0.325616\pi$
$150$	−0.809065	+	0.0708145i	−0.0660599	+	0.00578198i
$151$	0.770097	−	0.318985i	0.0626696	−	0.0259586i	−0.351128	−	0.936327i	$-0.614202\pi$
$151$	0.770097	−	0.318985i	0.0626696	−	0.0259586i	0.413798	+	0.910369i	$0.364202\pi$
$152$	0.345070			0.0279889
$153$	3.30333	−	11.9201i	0.267058	−	0.963680i
$154$	−6.62468			−0.533832
$155$	9.02773	−	3.73941i	0.725125	−	0.300357i
$156$	9.07214	−	0.794051i	0.726353	−	0.0635749i
$157$	10.0240	−	10.0240i	0.800000	−	0.800000i	−0.183096	−	0.983095i	$-0.558612\pi$
$157$	10.0240	−	10.0240i	0.800000	−	0.800000i	0.983095	+	0.183096i	$0.0586118\pi$
$158$	2.60591	−	13.1008i	0.207315	−	1.04224i
$159$	1.55347	−	0.808761i	0.123199	−	0.0641389i
$160$	2.29363	−	0.456232i	0.181328	−	0.0360683i
$161$	−11.1042	+	26.8080i	−0.875135	+	2.11276i
$162$	−6.63459	+	6.08130i	−0.521262	+	0.477792i
$163$	−0.393905	−	1.98029i	−0.0308530	−	0.155108i	0.962288	−	0.272034i	$-0.0876962\pi$
$163$	−0.393905	−	1.98029i	−0.0308530	−	0.155108i	−0.993141	+	0.116925i	$0.962696\pi$
$164$	0.408066	+	0.272661i	0.0318646	+	0.0212912i
$165$	−4.69829	+	5.59963i	−0.365761	+	0.435930i
$166$	−6.84469	−	6.84469i	−0.531251	−	0.531251i
$167$	−4.54797	+	3.03885i	−0.351932	+	0.235154i	−0.718952	−	0.695059i	$-0.755378\pi$
$167$	−4.54797	+	3.03885i	−0.351932	+	0.235154i	0.367020	+	0.930213i	$0.380378\pi$
$168$	0.691978	−	6.32059i	0.0533873	−	0.487644i
$169$			14.6447i			1.12652i
$170$	9.34575	+	2.37240i	0.716786	+	0.181955i
$171$	−0.556284	−	0.873047i	−0.0425401	−	0.0667635i
$172$	0.126561	+	0.305546i	0.00965020	+	0.0232976i
$173$	−2.00231	−	2.99667i	−0.152233	−	0.227833i	0.747513	−	0.664248i	$-0.231248\pi$
$173$	−2.00231	−	2.99667i	−0.152233	−	0.227833i	−0.899746	+	0.436415i	$0.856248\pi$
$174$	8.10296	−	2.36213i	0.614284	−	0.179072i
$175$	−1.68826	−	0.335815i	−0.127620	−	0.0253852i
$176$	1.00258	−	1.50047i	0.0755724	−	0.113102i
$177$	−1.82022	+	5.77374i	−0.136816	+	0.433981i
$178$	−9.45927	−	3.91816i	−0.709002	−	0.293678i
$179$	−22.8233	−	9.45371i	−1.70589	−	0.706603i	−0.705893	−	0.708319i	$-0.749454\pi$
$179$	−22.8233	−	9.45371i	−1.70589	−	0.706603i	−0.999999	+	0.00171566i	$0.999454\pi$
$180$	−4.85183	−	5.06753i	−0.361634	−	0.377711i
$181$	−5.27191	+	7.88997i	−0.391858	+	0.586457i	−0.973977	−	0.226647i	$-0.927224\pi$
$181$	−5.27191	+	7.88997i	−0.391858	+	0.586457i	0.582119	+	0.813104i	$0.302224\pi$
$182$	18.9306	+	3.76553i	1.40323	+	0.279120i
$183$	−6.05531	−	20.7719i	−0.447621	−	1.53551i
$184$	−4.39140	−	6.57220i	−0.323738	−	0.484509i
$185$	6.27404	+	15.1469i	0.461277	+	1.11362i
$186$	6.34523	+	3.48080i	0.465255	+	0.255225i
$187$	6.39403	−	3.80502i	0.467578	−	0.278251i
$188$		−	1.32072i		−	0.0963232i
$189$	−17.1070	+	8.43860i	−1.24435	+	0.613818i
$190$	0.670971	−	0.448329i	0.0486774	−	0.0325252i
$191$	−2.86511	−	2.86511i	−0.207312	−	0.207312i	0.595812	−	0.803124i	$-0.296830\pi$
$191$	−2.86511	−	2.86511i	−0.207312	−	0.207312i	−0.803124	+	0.595812i	$0.796830\pi$
$192$	1.32687	+	1.11329i	0.0957586	+	0.0803449i
$193$	11.7039	+	7.82032i	0.842468	+	0.562919i	0.900232	−	0.435411i	$-0.143397\pi$
$193$	11.7039	+	7.82032i	0.842468	+	0.562919i	−0.0577638	+	0.998330i	$0.518397\pi$
$194$	0.0243524	+	0.122428i	0.00174840	+	0.00878982i
$195$	16.6086	−	13.3309i	1.18937	−	0.954643i
$196$	2.47835	−	5.98326i	0.177025	−	0.427375i
$197$	5.28647	−	1.05155i	0.376646	−	0.0749195i	−0.00313733	−	0.999995i	$-0.500999\pi$
$197$	5.28647	−	1.05155i	0.376646	−	0.0749195i	0.379783	+	0.925076i	$0.375999\pi$
$198$	−5.41252	−	0.117697i	−0.384651	−	0.00836438i
$199$	−0.981818	+	4.93593i	−0.0695992	+	0.349899i	−0.999855	−	0.0170120i	$-0.994585\pi$
$199$	−0.981818	+	4.93593i	−0.0695992	+	0.349899i	0.930256	+	0.366911i	$0.119585\pi$
$200$	0.331562	−	0.331562i	0.0234450	−	0.0234450i
$201$	0.566877	+	6.47665i	0.0399844	+	0.456827i
$202$	17.2799	−	7.15758i	1.21581	−	0.503606i
$203$	17.8887			1.25554
$204$	2.96248	+	6.49798i	0.207415	+	0.454950i
$205$	1.14771			0.0801598
$206$	9.73136	−	4.03086i	0.678016	−	0.280843i
$207$	−9.54869	+	21.7054i	−0.663680	+	1.50863i
$208$	−3.71785	+	3.71785i	−0.257786	+	0.257786i
$209$	0.121485	−	0.610748i	0.00840332	−	0.0422464i
$210$	−6.86644	−	13.1891i	−0.473829	−	0.910135i
$211$	−11.5836	+	2.30413i	−0.797451	+	0.158623i	−0.576967	−	0.816768i	$-0.695764\pi$
$211$	−11.5836	+	2.30413i	−0.797451	+	0.158623i	−0.220484	+	0.975391i	$0.570764\pi$
$212$	−0.386957	+	0.934197i	−0.0265763	+	0.0641609i
$213$	13.2310	+	16.4843i	0.906575	+	1.12948i
$214$	−1.30537	−	6.56256i	−0.0892336	−	0.448608i
$215$	0.643069	+	0.429685i	0.0438569	+	0.0293043i
$216$	0.677657	−	5.15177i	0.0461087	−	0.350534i
$217$	10.8463	+	10.8463i	0.736296	+	0.736296i
$218$	−10.1984	+	6.81438i	−0.690725	+	0.461528i
$219$	2.30105	+	0.251919i	0.155491	+	0.0170231i
$220$		−	4.22018i		−	0.284524i
$221$	−20.4343	+	7.23876i	−1.37456	+	0.486931i
$222$	−5.84015	+	10.6461i	−0.391965	+	0.714521i
$223$	−8.18687	−	19.7649i	−0.548233	−	1.32355i	−0.918791	−	0.394743i	$-0.870834\pi$
$223$	−8.18687	−	19.7649i	−0.548233	−	1.32355i	0.370558	−	0.928809i	$-0.379166\pi$
$224$	2.03950	+	3.05232i	0.136270	+	0.203942i
$225$	−1.37338	−	0.304363i	−0.0915585	−	0.0202909i
$226$	−18.3862	−	3.65725i	−1.22303	−	0.243276i
$227$	−6.74383	+	10.0928i	−0.447603	+	0.669886i	−0.984824	−	0.173556i	$-0.944474\pi$
$227$	−6.74383	+	10.0928i	−0.447603	+	0.669886i	0.537221	+	0.843442i	$0.319474\pi$
$228$	0.570024	+	0.179704i	0.0377507	+	0.0119012i
$229$	−15.2528	−	6.31793i	−1.00794	−	0.417501i	−0.183235	−	0.983069i	$-0.558657\pi$
$229$	−15.2528	−	6.31793i	−1.00794	−	0.417501i	−0.824701	+	0.565568i	$0.808657\pi$
$230$	−17.0777	−	7.07382i	−1.12607	−	0.466434i
$231$	−10.9433	−	3.44998i	−0.720020	−	0.226992i
$232$	−2.70728	+	4.05173i	−0.177742	+	0.266009i
$233$	−12.3625	−	2.45905i	−0.809894	−	0.161098i	−0.227262	−	0.973834i	$-0.572977\pi$
$233$	−12.3625	−	2.45905i	−0.809894	−	0.161098i	−0.582633	+	0.812736i	$0.697977\pi$
$234$	15.3998	+	3.41286i	1.00672	+	0.223105i
$235$	−1.71593	−	2.56807i	−0.111935	−	0.167522i
$236$	−1.33755	−	3.22914i	−0.0870674	−	0.210199i
$237$	11.1273	−	20.2842i	0.722797	−	1.31760i
$238$	2.17358	+	14.9790i	0.140892	+	0.970947i
$239$			9.36338i			0.605667i	0.953044	+	0.302833i	$0.0979326\pi$
$239$			9.36338i			0.605667i	−0.953044	+	0.302833i	$0.902067\pi$
$240$	4.02646	+	0.440817i	0.259907	+	0.0284546i
$241$	−5.72656	+	3.82636i	−0.368880	+	0.246478i	−0.726169	−	0.687516i	$-0.758701\pi$
$241$	−5.72656	+	3.82636i	−0.368880	+	0.246478i	0.357289	+	0.933994i	$0.383701\pi$
$242$	5.47543	+	5.47543i	0.351974	+	0.351974i
$243$	−14.1267	+	6.59060i	−0.906229	+	0.422787i
$244$	10.3866	+	6.94011i	0.664934	+	0.444295i
$245$	−2.95466	−	14.8541i	−0.188766	−	0.948993i
$246$	0.532091	+	0.662921i	0.0339249	+	0.0422663i
$247$	−0.694310	+	1.67621i	−0.0441779	+	0.106655i
$248$	−4.09814	+	0.815172i	−0.260232	+	0.0517634i
$249$	−7.74224	−	14.8713i	−0.490644	−	0.942433i
$250$	−2.06723	+	10.3927i	−0.130743	+	0.657291i
$251$	0.314369	−	0.314369i	0.0198428	−	0.0198428i	−0.697116	−	0.716959i	$-0.745534\pi$
$251$	0.314369	−	0.314369i	0.0198428	−	0.0198428i	0.716959	+	0.697116i	$0.245534\pi$
$252$	4.43469	−	10.0807i	0.279360	−	0.635021i
$253$	−13.1783	+	5.45864i	−0.828514	+	0.343182i
$254$	−6.38005			−0.400320
$255$	14.2028	+	8.78602i	0.889414	+	0.550202i
$256$	−1.00000			−0.0625000
$257$	10.7234	−	4.44179i	0.668909	−	0.277071i	−0.0222728	−	0.999752i	$-0.507090\pi$
$257$	10.7234	−	4.44179i	0.668909	−	0.277071i	0.691182	+	0.722681i	$0.257090\pi$
$258$	0.0499462	+	0.570643i	0.00310952	+	0.0355267i
$259$	−18.1981	+	18.1981i	−1.13078	+	1.13078i
$260$	−2.39879	+	12.0595i	−0.148767	+	0.747900i
$261$	14.6155	+	0.317819i	0.904675	+	0.0196725i
$262$	−1.59970	+	0.318199i	−0.0988295	+	0.0196584i
$263$	5.41366	−	13.0697i	0.333821	−	0.805914i	−0.664461	−	0.747323i	$-0.731339\pi$
$263$	5.41366	−	13.0697i	0.333821	−	0.805914i	0.998282	−	0.0585916i	$-0.0186610\pi$
$264$	2.43758	−	1.95651i	0.150023	−	0.120415i
$265$	0.461327	+	2.31925i	0.0283391	+	0.142470i
$266$	1.05327	+	0.703770i	0.0645799	+	0.0431509i
$267$	−13.5853	−	11.3986i	−0.831409	−	0.697582i
$268$	−2.65419	−	2.65419i	−0.162130	−	0.162130i
$269$	14.4774	−	9.67346i	0.882700	−	0.589801i	−0.0294919	−	0.999565i	$-0.509389\pi$
$269$	14.4774	−	9.67346i	0.882700	−	0.589801i	0.912192	+	0.409764i	$0.134389\pi$
$270$	−5.37572	−	10.8978i	−0.327156	−	0.663219i
$271$		−	10.6619i		−	0.647667i	−0.946114	−	0.323833i	$-0.895028\pi$
$271$		−	10.6619i		−	0.647667i	0.946114	−	0.323833i	$-0.104972\pi$
$272$	−3.72165	−	1.77462i	−0.225658	−	0.107602i
$273$	29.3106	+	16.0789i	1.77396	+	0.973140i
$274$	1.67556	+	4.04515i	0.101224	+	0.244377i
$275$	−0.470111	−	0.703570i	−0.0283487	−	0.0424269i
$276$	−3.83154	−	13.1436i	−0.230631	−	0.791151i
$277$	13.9210	+	2.76905i	0.836431	+	0.166376i	0.594680	−	0.803962i	$-0.297279\pi$
$277$	13.9210	+	2.76905i	0.836431	+	0.166376i	0.241750	+	0.970339i	$0.422279\pi$
$278$	−9.05965	+	13.5587i	−0.543362	+	0.813198i
$279$	8.66900	+	9.05440i	0.518999	+	0.542073i
$280$	7.93139	+	3.28529i	0.473991	+	0.196334i
$281$	−5.25486	−	2.17664i	−0.313479	−	0.129847i	0.220397	−	0.975410i	$-0.429265\pi$
$281$	−5.25486	−	2.17664i	−0.313479	−	0.129847i	−0.533875	+	0.845563i	$0.679265\pi$
$282$	0.687798	−	2.18170i	0.0409578	−	0.129918i
$283$	1.60773	−	2.40614i	0.0955696	−	0.143030i	−0.780604	−	0.625026i	$-0.785088\pi$
$283$	1.60773	−	2.40614i	0.0955696	−	0.143030i	0.876173	+	0.481996i	$0.160088\pi$
$284$	−11.9692	−	2.38082i	−0.710242	−	0.141276i
$285$	1.34186	−	0.391171i	0.0794849	−	0.0231710i
$286$	5.27140	+	7.88921i	0.311705	+	0.466499i
$287$	0.689458	+	1.66450i	0.0406974	+	0.0982522i
$288$	1.61209	+	2.53005i	0.0949932	+	0.149085i
$289$	−10.7014	−	13.2091i	−0.629495	−	0.777004i
$290$			11.3958i			0.669183i
$291$	−0.0235296	+	0.214922i	−0.00137933	+	0.0125989i
$292$	−1.11122	+	0.742492i	−0.0650291	+	0.0434510i
$293$	−5.88739	−	5.88739i	−0.343945	−	0.343945i	0.513903	−	0.857848i	$-0.328199\pi$
$293$	−5.88739	−	5.88739i	−0.343945	−	0.343945i	−0.857848	+	0.513903i	$0.828199\pi$
$294$	7.20993	−	8.59311i	0.420492	−	0.501160i
$295$	−6.79623	−	4.54110i	−0.395692	−	0.264393i
$296$	−1.36771	−	6.87594i	−0.0794964	−	0.399656i
$297$	−8.87968	−	3.01313i	−0.515251	−	0.174840i
$298$	2.19853	−	5.30773i	0.127358	−	0.307469i
$299$	40.7610	−	8.10786i	2.35727	−	0.468890i
$300$	0.720379	−	0.375040i	0.0415911	−	0.0216529i
$301$	−0.236854	+	1.19075i	−0.0136520	+	0.0686334i
$302$	−0.589407	+	0.589407i	−0.0339165	+	0.0339165i
$303$	32.2723	−	2.82467i	1.85400	−	0.162273i
$304$	−0.318803	+	0.132053i	−0.0182846	+	0.00757374i
$305$	29.2131			1.67274
$306$	1.50974	+	12.2768i	0.0863060	+	0.701820i
$307$	26.5958			1.51790			0.758951	−	0.651148i	$-0.225712\pi$
$307$	26.5958			1.51790			0.758951	+	0.651148i	$0.225712\pi$
$308$	6.12041	−	2.53516i	0.348743	−	0.144454i
$309$	18.1745	−	1.59074i	1.03391	−	0.0904942i
$310$	−6.90953	+	6.90953i	−0.392435	+	0.392435i
$311$	4.98751	−	25.0739i	0.282816	−	1.42181i	−0.534279	−	0.845308i	$-0.679417\pi$
$311$	4.98751	−	25.0739i	0.282816	−	1.42181i	0.817095	−	0.576503i	$-0.195583\pi$
$312$	−8.07769	+	4.20536i	−0.457309	+	0.238082i
$313$	−5.59092	+	1.11210i	−0.316017	+	0.0628598i	−0.350551	−	0.936544i	$-0.614006\pi$
$313$	−5.59092	+	1.11210i	−0.316017	+	0.0628598i	0.0345332	+	0.999404i	$0.489006\pi$
$314$	−5.42493	+	13.0969i	−0.306147	+	0.739103i
$315$	−4.47414	−	25.3630i	−0.252089	−	1.42905i
$316$	2.60591	+	13.1008i	0.146594	+	0.736978i
$317$	0.698815	+	0.466933i	0.0392494	+	0.0262256i	0.575040	−	0.818125i	$-0.304986\pi$
$317$	0.698815	+	0.466933i	0.0392494	+	0.0262256i	−0.535791	+	0.844351i	$0.679986\pi$
$318$	−1.12572	+	1.34169i	−0.0631274	+	0.0752381i
$319$	6.21813	+	6.21813i	0.348149	+	0.348149i
$320$	−1.94445	+	1.29924i	−0.108698	+	0.0726297i
$321$	1.26127	−	11.5205i	0.0703972	−	0.643014i
$322$		−	29.0167i		−	1.61704i
$323$	−1.42082	−	0.0743017i	−0.0790565	−	0.00413426i
$324$	3.80235	−	8.15734i	0.211241	−	0.453185i
$325$	0.943466	+	2.27773i	0.0523341	+	0.126346i
$326$	1.12175	+	1.67881i	0.0621277	+	0.0929807i
$327$	−20.3956	+	5.94561i	−1.12788	+	0.328793i
$328$	−0.481346	−	0.0957457i	−0.0265779	−	0.00528667i
$329$	2.69360	−	4.03125i	0.148503	−	0.222250i
$330$	2.19777	−	6.97134i	0.120983	−	0.383759i
$331$	23.2840	+	9.64455i	1.27980	+	0.530112i	0.915931	−	0.401336i	$-0.131454\pi$
$331$	23.2840	+	9.64455i	1.27980	+	0.530112i	0.363873	+	0.931448i	$0.381454\pi$
$332$	8.94302	+	3.70432i	0.490812	+	0.203301i
$333$	−15.1916	+	14.5450i	−0.832496	+	0.797060i
$334$	3.03885	−	4.54797i	0.166279	−	0.248854i
$335$	−8.60936	−	1.71251i	−0.470379	−	0.0935643i
$336$	1.77948	+	6.10427i	0.0970786	+	0.333015i
$337$	−11.0677	−	16.5640i	−0.602896	−	0.902297i	0.396984	−	0.917826i	$-0.370057\pi$
$337$	−11.0677	−	16.5640i	−0.602896	−	0.902297i	−0.999879	+	0.0155284i	$0.995057\pi$
$338$	−5.60430	−	13.5300i	−0.304834	−	0.735934i
$339$	−28.4677	−	15.6165i	−1.54615	−	0.848173i
$340$	−9.54222	+	1.38465i	−0.517500	+	0.0750933i
$341$			7.54040i			0.408335i
$342$	0.848039	+	0.593709i	0.0458567	+	0.0321041i
$343$	−1.59872	+	1.06823i	−0.0863226	+	0.0576789i
$344$	−0.233855	−	0.233855i	−0.0126086	−	0.0126086i
$345$	−24.5269	−	20.5789i	−1.32048	−	1.10793i
$346$	2.99667	+	2.00231i	0.161102	+	0.107645i
$347$	4.54586	+	22.8536i	0.244035	+	1.22685i	0.887297	+	0.461199i	$0.152581\pi$
$347$	4.54586	+	22.8536i	0.244035	+	1.22685i	−0.643262	+	0.765646i	$0.722419\pi$
$348$	−6.58221	+	5.28319i	−0.352844	+	0.283209i
$349$	−11.9994	+	28.9692i	−0.642316	+	1.55069i	0.181232	+	0.983440i	$0.441992\pi$
$349$	−11.9994	+	28.9692i	−0.642316	+	1.55069i	−0.823548	+	0.567247i	$0.808008\pi$
$350$	1.68826	−	0.335815i	0.0902411	−	0.0179501i
$351$	23.6618	+	13.6576i	1.26297	+	0.728988i
$352$	−0.352060	+	1.76992i	−0.0187649	+	0.0943373i
$353$	−5.45842	+	5.45842i	−0.290522	+	0.290522i	−0.837287	−	0.546764i	$-0.815859\pi$
$353$	−5.45842	+	5.45842i	−0.290522	+	0.290522i	0.546764	+	0.837287i	$0.315859\pi$
$354$	−0.527854	−	6.03081i	−0.0280551	−	0.320534i
$355$	−26.3668	+	10.9215i	−1.39940	+	0.579651i
$356$	10.2386			0.542647
$357$	−4.21018	+	25.8759i	−0.222826	+	1.36950i
$358$	24.7037			1.30563
$359$	−21.7105	+	8.99280i	−1.14584	+	0.474622i	−0.873136	−	0.487476i	$-0.837917\pi$
$359$	−21.7105	+	8.99280i	−1.14584	+	0.474622i	−0.272703	+	0.962098i	$0.587917\pi$
$360$	6.42177	+	2.82507i	0.338457	+	0.148894i
$361$	13.3508	−	13.3508i	0.702675	−	0.702675i
$362$	1.85125	−	9.30685i	0.0972995	−	0.489157i
$363$	6.19342	+	11.8964i	0.325070	+	0.624397i
$364$	−18.9306	+	3.76553i	−0.992233	+	0.197367i
$365$	−1.19603	+	2.88747i	−0.0626031	+	0.151137i
$366$	13.5435	+	16.8735i	0.707928	+	0.881992i
$367$	−3.26662	−	16.4224i	−0.170516	−	0.857243i	−0.967428	−	0.253147i	$-0.918534\pi$
$367$	−3.26662	−	16.4224i	−0.170516	−	0.857243i	0.796912	−	0.604096i	$-0.206466\pi$
$368$	6.57220	+	4.39140i	0.342599	+	0.228918i
$369$	0.533731	+	1.37218i	0.0277849	+	0.0714330i
$370$	−11.5929	−	11.5929i	−0.602687	−	0.602687i
$371$	−3.08641	+	2.06227i	−0.160238	+	0.107068i
$372$	−7.19427	−	0.787629i	−0.373006	−	0.0408367i
$373$			9.84556i			0.509784i	0.966970	+	0.254892i	$0.0820399\pi$
$373$			9.84556i			0.509784i	−0.966970	+	0.254892i	$0.917960\pi$
$374$	−4.45120	+	5.96227i	−0.230166	+	0.308302i
$375$	−8.82713	+	16.0912i	−0.455831	+	0.830944i
$376$	0.505416	+	1.22018i	0.0260649	+	0.0629261i
$377$	−14.2344	−	21.3033i	−0.733109	−	1.09718i
$378$	12.5755	−	14.3428i	0.646812	−	0.737714i
$379$	−11.3082	−	2.24933i	−0.580862	−	0.115541i	−0.104090	−	0.994568i	$-0.533193\pi$
$379$	−11.3082	−	2.24933i	−0.580862	−	0.115541i	−0.476771	+	0.879027i	$0.658193\pi$
$380$	−0.448329	+	0.670971i	−0.0229988	+	0.0344201i
$381$	−10.5392	−	3.32258i	−0.539942	−	0.170221i
$382$	3.74345	+	1.55059i	0.191532	+	0.0793350i
$383$	−15.9431	−	6.60383i	−0.814652	−	0.337440i	−0.0638438	−	0.997960i	$-0.520336\pi$
$383$	−15.9431	−	6.60383i	−0.814652	−	0.337440i	−0.750809	+	0.660520i	$0.770336\pi$
$384$	−1.65191	−	0.520776i	−0.0842985	−	0.0265757i
$385$	8.60704	−	12.8813i	0.438656	−	0.656494i
$386$	−13.8057	−	2.74613i	−0.702693	−	0.139774i
$387$	−0.214671	+	0.968659i	−0.0109123	+	0.0492397i
$388$	−0.0693499	−	0.103789i	−0.00352071	−	0.00526911i
$389$	−6.74915	−	16.2939i	−0.342195	−	0.826133i	−0.997493	−	0.0707622i	$-0.977457\pi$
$389$	−6.74915	−	16.2939i	−0.342195	−	0.826133i	0.655298	−	0.755371i	$-0.272543\pi$
$390$	−10.2429	+	18.6720i	−0.518669	+	0.945492i
$391$	16.6664	+	28.0065i	0.842854	+	1.41635i
$392$			6.47623i			0.327099i
$393$	−2.80826	−	0.307448i	−0.141658	−	0.0155087i
$394$	−4.48166	+	2.99455i	−0.225783	+	0.150863i
$395$	22.0881	+	22.0881i	1.11138	+	1.11138i
$396$	5.04556	−	1.96254i	0.253549	−	0.0986215i
$397$	−10.8458	−	7.24691i	−0.544333	−	0.363712i	0.252797	−	0.967519i	$-0.418650\pi$
$397$	−10.8458	−	7.24691i	−0.544333	−	0.363712i	−0.797130	+	0.603807i	$0.793650\pi$
$398$	−0.981818	−	4.93593i	−0.0492141	−	0.247416i
$399$	1.37339	+	1.71108i	0.0687555	+	0.0856610i
$400$	−0.179440	+	0.433207i	−0.00897201	+	0.0216604i
$401$	32.4206	−	6.44886i	1.61901	−	0.322041i	0.699356	−	0.714773i	$-0.253470\pi$
$401$	32.4206	−	6.44886i	1.61901	−	0.322041i	0.919653	+	0.392732i	$0.128470\pi$
$402$	−3.00223	−	5.76671i	−0.149738	−	0.287617i
$403$	4.28603	−	21.5473i	0.213502	−	1.07335i
$404$	−13.2255	+	13.2255i	−0.657992	+	0.657992i
$405$	−3.20486	−	20.8017i	−0.159251	−	1.03364i
$406$	−16.5270	+	6.84570i	−0.820221	+	0.339747i
$407$	−12.6514			−0.627107
$408$	−5.22364	−	4.86966i	−0.258609	−	0.241084i
$409$	−17.5585			−0.868213			−0.434107	−	0.900862i	$-0.642936\pi$
$409$	−17.5585			−0.868213			−0.434107	+	0.900862i	$0.642936\pi$
$410$	−1.06035	+	0.439211i	−0.0523669	+	0.0216911i
$411$	0.661244	+	7.55480i	0.0326167	+	0.372651i
$412$	−7.44806	+	7.44806i	−0.366939	+	0.366939i
$413$	2.50318	−	12.5843i	0.123173	−	0.619234i
$414$	0.515525	−	23.7073i	0.0253367	−	1.16515i
$415$	22.2020	−	4.41626i	1.08986	−	0.216786i
$416$	2.01208	−	4.85760i	0.0986505	−	0.238163i
$417$	−22.0267	+	17.6797i	−1.07865	+	0.865778i
$418$	0.121485	+	0.610748i	0.00594205	+	0.0298727i
$419$	−5.94108	−	3.96970i	−0.290241	−	0.193933i	0.401923	−	0.915674i	$-0.368342\pi$
$419$	−5.94108	−	3.96970i	−0.290241	−	0.193933i	−0.692163	+	0.721741i	$0.743342\pi$
$420$	11.3910	+	9.55747i	0.555825	+	0.466357i
$421$	−13.8800	−	13.8800i	−0.676469	−	0.676469i	0.282730	−	0.959199i	$-0.408760\pi$
$421$	−13.8800	−	13.8800i	−0.676469	−	0.676469i	−0.959199	+	0.282730i	$0.908760\pi$
$422$	9.82014	−	6.56161i	0.478037	−	0.319414i
$423$	2.27235	−	3.24577i	0.110486	−	0.157815i
$424$		−	1.01117i		−	0.0491066i
$425$	−1.43659	+	1.29381i	−0.0696851	+	0.0627589i
$426$	−18.5321	−	10.1662i	−0.897884	−	0.492553i
$427$	17.5490	+	42.3669i	0.849253	+	2.05028i
$428$	3.71739	+	5.56347i	0.179687	+	0.268921i
$429$	4.59935	+	15.7775i	0.222059	+	0.761742i
$430$	−0.758551	−	0.150885i	−0.0365806	−	0.00727633i
$431$	−4.00837	+	5.99895i	−0.193077	+	0.288959i	−0.915359	−	0.402639i	$-0.868093\pi$
$431$	−4.00837	+	5.99895i	−0.193077	+	0.288959i	0.722282	+	0.691598i	$0.243093\pi$
$432$	1.34543	+	5.01895i	0.0647318	+	0.241474i
$433$	−6.20307	−	2.56940i	−0.298101	−	0.123477i	0.228620	−	0.973516i	$-0.426579\pi$
$433$	−6.20307	−	2.56940i	−0.298101	−	0.123477i	−0.526721	+	0.850038i	$0.676579\pi$
$434$	−14.1714	−	5.86999i	−0.680249	−	0.281768i
$435$	−5.93465	+	18.8248i	−0.284545	+	0.902578i
$436$	6.81438	−	10.1984i	0.326350	−	0.488417i
$437$	2.67513	+	0.532117i	0.127969	+	0.0254546i
$438$	−2.22230	+	0.647831i	−0.106185	+	0.0309545i
$439$	−11.1298	−	16.6570i	−0.531198	−	0.794994i	0.464701	−	0.885468i	$-0.346162\pi$
$439$	−11.1298	−	16.6570i	−0.531198	−	0.794994i	−0.995899	+	0.0904740i	$0.971162\pi$
$440$	1.61499	+	3.89894i	0.0769917	+	0.185874i
$441$	16.3852	−	10.4403i	0.780248	−	0.497155i
$442$	16.1087	−	14.5076i	0.766212	−	0.690057i
$443$			35.3871i			1.68129i	0.541584	+	0.840647i	$0.317825\pi$
$443$			35.3871i			1.68129i	−0.541584	+	0.840647i	$0.682175\pi$
$444$	1.32150	−	12.0707i	0.0627155	−	0.572848i
$445$	19.9085	−	13.3024i	0.943753	−	0.630596i
$446$	15.1274	+	15.1274i	0.716301	+	0.716301i
$447$	6.39591	−	7.62293i	0.302516	−	0.360552i
$448$	−3.05232	−	2.03950i	−0.144209	−	0.0963572i
$449$	−2.27455	−	11.4349i	−0.107343	−	0.539649i	−0.996611	−	0.0822620i	$-0.973786\pi$
$449$	−2.27455	−	11.4349i	−0.107343	−	0.539649i	0.889268	−	0.457387i	$-0.151214\pi$
$450$	1.38531	−	0.244374i	0.0653042	−	0.0115199i
$451$	−0.338925	+	0.818239i	−0.0159594	+	0.0385293i
$452$	18.3862	−	3.65725i	0.864815	−	0.172022i
$453$	−1.28059	+	0.666695i	−0.0601675	+	0.0313241i
$454$	2.36812	−	11.9053i	0.111141	−	0.558745i
$455$	−31.9173	+	31.9173i	−1.49630	+	1.49630i
$456$	−0.595403	+	0.0521134i	−0.0278823	+	0.00244043i
$457$	21.0582	−	8.72260i	0.985062	−	0.408026i	0.168764	−	0.985657i	$-0.446023\pi$
$457$	21.0582	−	8.72260i	0.985062	−	0.408026i	0.816298	+	0.577631i	$0.196023\pi$
$458$	16.5096			0.771441
$459$	−3.89954	+	21.0664i	−0.182015	+	0.983296i
$460$	18.4848			0.861857
$461$	16.5066	−	6.83726i	0.768789	−	0.318443i	0.0364074	−	0.999337i	$-0.488409\pi$
$461$	16.5066	−	6.83726i	0.768789	−	0.318443i	0.732382	+	0.680894i	$0.238409\pi$
$462$	11.4306	−	1.00048i	0.531799	−	0.0465464i
$463$	6.85592	−	6.85592i	0.318622	−	0.318622i	−0.529616	−	0.848238i	$-0.677664\pi$
$463$	6.85592	−	6.85592i	0.318622	−	0.318622i	0.848238	+	0.529616i	$0.177664\pi$
$464$	0.950670	−	4.77934i	0.0441338	−	0.221875i
$465$	−15.0122	+	7.81557i	−0.696174	+	0.362438i
$466$	12.3625	−	2.45905i	0.572682	−	0.113913i
$467$	−3.99013	+	9.63302i	−0.184641	+	0.445763i	−0.988913	−	0.148499i	$-0.952556\pi$
$467$	−3.99013	+	9.63302i	−0.184641	+	0.445763i	0.804271	+	0.594262i	$0.202556\pi$
$468$	−15.5336	+	2.74020i	−0.718043	+	0.126666i
$469$	−2.68823	−	13.5147i	−0.124131	−	0.624049i
$470$	2.56807	+	1.71593i	0.118456	+	0.0791498i
$471$	−15.7820	+	18.8097i	−0.727198	+	0.866707i
$472$	2.47148	+	2.47148i	0.113759	+	0.113759i
$473$	−0.496236	+	0.331574i	−0.0228169	+	0.0152458i
$474$	−2.51787	+	22.9984i	−0.115649	+	1.05635i
$475$			0.161803i			0.00742405i
$476$	−7.74035	−	13.0070i	−0.354778	−	0.596176i
$477$	−2.55831	+	1.63009i	−0.117137	+	0.0746367i
$478$	−3.58321	−	8.65064i	−0.163892	−	0.395671i
$479$	10.8975	+	16.3093i	0.497921	+	0.745191i	0.992273	−	0.124070i	$-0.0395949\pi$
$479$	10.8975	+	16.3093i	0.497921	+	0.745191i	−0.494353	+	0.869261i	$0.664595\pi$
$480$	−3.88866	+	1.13360i	−0.177492	+	0.0517414i
$481$	36.1525	+	7.19118i	1.64841	+	0.327889i
$482$	3.82636	−	5.72656i	0.174286	−	0.260838i
$483$	15.1112	−	47.9329i	0.687584	−	2.18102i
$484$	−7.15399	−	2.96328i	−0.325181	−	0.134694i
$485$	−0.269694	−	0.111711i	−0.0122462	−	0.00507254i
$486$	10.5293	−	11.4950i	0.477617	−	0.521423i
$487$	−8.50156	+	12.7235i	−0.385242	+	0.576556i	−0.972517	−	0.232832i	$-0.925201\pi$
$487$	−8.50156	+	12.7235i	−0.385242	+	0.576556i	0.587275	+	0.809388i	$0.300201\pi$
$488$	−12.2518	−	2.43704i	−0.554615	−	0.110320i
$489$	0.978733	+	3.35741i	0.0442598	+	0.151828i
$490$	8.41417	+	12.5927i	0.380113	+	0.568880i
$491$	−4.44463	−	10.7303i	−0.200583	−	0.484251i	0.791296	−	0.611433i	$-0.209407\pi$
$491$	−4.44463	−	10.7303i	−0.200583	−	0.484251i	−0.991879	+	0.127182i	$0.959407\pi$
$492$	−0.745277	−	0.408837i	−0.0335997	−	0.0184318i
$493$	12.0196	−	16.1000i	0.541336	−	0.725106i
$494$		−	1.81432i		−	0.0816301i
$495$	7.26101	−	10.3714i	0.326358	−	0.466162i
$496$	3.47424	−	2.32141i	0.155998	−	0.104234i
$497$	−31.6782	−	31.6782i	−1.42096	−	1.42096i
$498$	12.8439	+	10.7765i	0.575549	+	0.482907i
$499$	−15.4446	−	10.3198i	−0.691395	−	0.461976i	0.159577	−	0.987185i	$-0.448987\pi$
$499$	−15.4446	−	10.3198i	−0.691395	−	0.461976i	−0.850973	+	0.525210i	$0.823987\pi$
$500$	−2.06723	−	10.3927i	−0.0924495	−	0.464775i
$501$	7.38837	−	5.93025i	0.330088	−	0.264944i
$502$	−0.170135	+	0.410742i	−0.00759350	+	0.0183323i
$503$	−14.6518	+	2.91442i	−0.653291	+	0.129948i	−0.510598	−	0.859819i	$-0.670576\pi$
$503$	−14.6518	+	2.91442i	−0.653291	+	0.129948i	−0.142693	+	0.989767i	$0.545576\pi$
$504$	−0.239425	+	11.0104i	−0.0106648	+	0.490442i
$505$	−8.53321	+	42.8993i	−0.379723	+	1.90900i
$506$	10.0863	−	10.0863i	0.448389	−	0.448389i
$507$	−2.21169	−	25.2688i	−0.0982245	−	1.12223i
$508$	5.89440	−	2.44154i	0.261522	−	0.108326i
$509$	0.355586			0.0157611			0.00788054	−	0.999969i	$-0.497492\pi$
$509$	0.355586			0.0157611			0.00788054	+	0.999969i	$0.497492\pi$
$510$	−16.4839	−	2.68205i	−0.729921	−	0.118763i
$511$	−4.90610			−0.217033
$512$	0.923880	−	0.382683i	0.0408301	−	0.0169124i
$513$	1.09169	+	1.42239i	0.0481994	+	0.0628001i
$514$	−8.20736	+	8.20736i	−0.362011	+	0.362011i
$515$	−4.80556	+	24.1592i	−0.211758	+	1.06458i
$516$	−0.264520	−	0.508092i	−0.0116448	−	0.0223675i
$517$	2.33757	−	0.464971i	0.102806	−	0.0204494i
$518$	9.84876	−	23.7770i	0.432730	−	1.04470i
$519$	3.90746	+	4.86822i	0.171519	+	0.213691i
$520$	−2.39879	−	12.0595i	−0.105194	−	0.528845i
$521$	−31.9817	−	21.3695i	−1.40114	−	0.936213i	−0.999794	−	0.0202879i	$-0.993542\pi$
$521$	−31.9817	−	21.3695i	−1.40114	−	0.936213i	−0.401348	−	0.915926i	$-0.631458\pi$
$522$	−13.6246	+	5.29947i	−0.596331	+	0.231952i
$523$	0.783021	+	0.783021i	0.0342391	+	0.0342391i	0.724019	−	0.689780i	$-0.242293\pi$
$523$	0.783021	+	0.783021i	0.0342391	+	0.0342391i	−0.689780	+	0.724019i	$0.742293\pi$
$524$	1.35616	−	0.906155i	0.0592440	−	0.0395856i
$525$	2.96372	+	0.324469i	0.129348	+	0.0141610i
$526$			14.1466i			0.616820i
$527$	17.0496	−	2.47403i	0.742690	−	0.107770i
$528$	−1.50330	+	2.74040i	−0.0654229	+	0.119261i
$529$	−15.1076	−	36.4731i	−0.656854	−	1.58579i
$530$	−1.31375	−	1.96616i	−0.0570655	−	0.0854046i
$531$	2.26873	−	10.2372i	0.0984547	−	0.444257i
$532$	−1.24241	−	0.247131i	−0.0538654	−	0.0107145i
$533$	1.43360	−	2.14554i	0.0620963	−	0.0929336i
$534$	16.9133	+	5.33204i	0.731909	+	0.230740i
$535$	14.4566	+	5.98810i	0.625011	+	0.258888i
$536$	3.46786	+	1.43644i	0.149789	+	0.0620446i
$537$	40.8082	+	12.8651i	1.76100	+	0.555170i
$538$	−9.67346	+	14.4774i	−0.417052	+	0.624163i
$539$	11.4624	+	2.28002i	0.493722	+	0.0982074i
$540$	9.13692	+	8.01105i	0.393190	+	0.344741i
$541$	19.0553	+	28.5183i	0.819253	+	1.22610i	0.971331	+	0.237731i	$0.0764036\pi$
$541$	19.0553	+	28.5183i	0.819253	+	1.22610i	−0.152078	+	0.988369i	$0.548596\pi$
$542$	4.08015	+	9.85035i	0.175257	+	0.423109i
$543$	7.90487	−	14.4100i	0.339231	−	0.618391i
$544$	4.11748	+	0.215323i	0.176535	+	0.00923192i
$545$		−	28.6838i		−	1.22868i
$546$	−33.2326	−	3.63830i	−1.42222	−	0.155705i
$547$	9.26045	−	6.18764i	0.395948	−	0.264564i	−0.341618	−	0.939839i	$-0.610975\pi$
$547$	9.26045	−	6.18764i	0.395948	−	0.264564i	0.737566	+	0.675275i	$0.235975\pi$
$548$	−3.09603	−	3.09603i	−0.132256	−	0.132256i
$549$	13.5852	+	34.9265i	0.579802	+	1.49063i
$550$	0.703570	+	0.470111i	0.0300003	+	0.0200456i
$551$	−0.328048	−	1.64921i	−0.0139753	−	0.0702587i
$552$	8.56971	+	10.6768i	0.364751	+	0.454436i
$553$	−18.7650	+	45.3027i	−0.797968	+	1.92647i
$554$	−13.9210	+	2.76905i	−0.591446	+	0.117646i
$555$	−13.1131	−	25.1877i	−0.556620	−	1.06916i
$556$	3.18133	−	15.9936i	0.134918	−	0.678280i
$557$	1.08136	−	1.08136i	0.0458189	−	0.0458189i	−0.683826	−	0.729645i	$-0.739685\pi$
$557$	1.08136	−	1.08136i	0.0458189	−	0.0458189i	0.729645	+	0.683826i	$0.239685\pi$
$558$	−11.4741	−	5.04769i	−0.485736	−	0.213686i
$559$	1.60651	−	0.665437i	0.0679480	−	0.0281450i
$560$	−8.58488			−0.362777
$561$	−10.4580	+	7.53104i	−0.441536	+	0.317961i
$562$	5.68782			0.239926
$563$	24.8646	−	10.2993i	1.04792	−	0.434062i	0.208770	−	0.977965i	$-0.433054\pi$
$563$	24.8646	−	10.2993i	1.04792	−	0.434062i	0.839148	+	0.543903i	$0.183054\pi$
$564$	0.199458	+	2.27884i	0.00839870	+	0.0959563i
$565$	30.9994	−	30.9994i	1.30415	−	1.30415i
$566$	−0.564559	+	2.83823i	−0.0237302	+	0.119300i
$567$	28.2429	−	17.1440i	1.18609	−	0.719979i
$568$	11.9692	−	2.38082i	0.502217	−	0.0998971i
$569$	−8.75766	+	21.1429i	−0.367140	+	0.886355i	0.627076	+	0.778958i	$0.284252\pi$
$569$	−8.75766	+	21.1429i	−0.367140	+	0.886355i	−0.994216	+	0.107397i	$0.965748\pi$
$570$	−1.09002	+	0.874903i	−0.0456560	+	0.0366456i
$571$	−7.77780	−	39.1016i	−0.325491	−	1.63635i	−0.703603	−	0.710593i	$-0.748427\pi$
$571$	−7.77780	−	39.1016i	−0.325491	−	1.63635i	0.378112	−	0.925760i	$-0.376573\pi$
$572$	−7.88921	−	5.27140i	−0.329864	−	0.220408i
$573$	5.37632	+	4.51093i	0.224599	+	0.188447i
$574$	−1.27395	−	1.27395i	−0.0531737	−	0.0531737i
$575$	3.08170	−	2.05913i	0.128516	−	0.0858716i
$576$	−2.45758	−	1.72055i	−0.102399	−	0.0716894i
$577$			43.3291i			1.80382i	0.431929	+	0.901908i	$0.357833\pi$
$577$			43.3291i			1.80382i	−0.431929	+	0.901908i	$0.642167\pi$
$578$	14.9417	+	8.10834i	0.621493	+	0.337262i
$579$	−21.3757	−	11.7260i	−0.888342	−	0.487318i
$580$	−4.36098	−	10.5283i	−0.181080	−	0.437165i
$581$	19.7420	+	29.5461i	0.819038	+	1.22578i
$582$	−0.0605084	−	0.207566i	−0.00250815	−	0.00860389i
$583$	−1.78969	−	0.355991i	−0.0741214	−	0.0147437i
$584$	0.742492	−	1.11122i	0.0307245	−	0.0459825i
$585$	−26.6442	+	25.5101i	−1.10160	+	1.05471i
$586$	7.69224	+	3.18623i	0.317764	+	0.131622i
$587$	8.25855	+	3.42080i	0.340867	+	0.141192i	0.546549	−	0.837427i	$-0.315941\pi$
$587$	8.25855	+	3.42080i	0.340867	+	0.141192i	−0.205682	+	0.978619i	$0.565941\pi$
$588$	−3.37267	+	10.6981i	−0.139086	+	0.441183i
$589$	0.801050	−	1.19886i	0.0330067	−	0.0493980i
$590$	8.01670	+	1.59462i	0.330042	+	0.0656495i
$591$	−8.96276	+	2.61277i	−0.368679	+	0.107475i
$592$	3.89490	+	5.82914i	0.160080	+	0.239576i
$593$	0.956755	+	2.30981i	0.0392892	+	0.0948525i	0.942306	−	0.334753i	$-0.108653\pi$
$593$	0.956755	+	2.30981i	0.0392892	+	0.0948525i	−0.903017	+	0.429605i	$0.858653\pi$
$594$	9.35683	−	0.614331i	0.383915	−	0.0252063i
$595$	−31.9500	−	15.2349i	−1.30982	−	0.624571i
$596$			5.74505i			0.235326i
$597$	0.948645	−	8.66500i	0.0388254	−	0.354635i
$598$	−34.5555	+	23.0892i	−1.41308	+	0.944189i
$599$	12.6651	+	12.6651i	0.517483	+	0.517483i	0.916809	−	0.399326i	$-0.130756\pi$
$599$	12.6651	+	12.6651i	0.517483	+	0.517483i	−0.399326	+	0.916809i	$0.630756\pi$
$600$	−0.522022	+	0.622169i	−0.0213115	+	0.0253999i
$601$	−25.6405	−	17.1325i	−1.04590	−	0.698847i	−0.0910219	−	0.995849i	$-0.529013\pi$
$601$	−25.6405	−	17.1325i	−1.04590	−	0.698847i	−0.954877	+	0.297002i	$0.904013\pi$
$602$	−0.236854	−	1.19075i	−0.00965345	−	0.0485312i
$603$	−1.95624	−	11.0895i	−0.0796642	−	0.451601i
$604$	0.318985	−	0.770097i	0.0129793	−	0.0313348i
$605$	−17.7606	+	3.53280i	−0.722070	+	0.143629i
$606$	−28.7348	+	14.9597i	−1.16727	+	0.607698i
$607$	4.85681	−	24.4168i	0.197132	−	0.991049i	−0.747836	−	0.663884i	$-0.768907\pi$
$607$	4.85681	−	24.4168i	0.197132	−	0.991049i	0.944967	−	0.327165i	$-0.106093\pi$
$608$	0.244002	−	0.244002i	0.00989557	−	0.00989557i
$609$	−30.8661	+	2.70160i	−1.25076	+	0.109474i
$610$	−26.9894	+	11.1794i	−1.09277	+	0.452639i
$611$	−6.94410			−0.280928
$612$	−6.09296	−	10.7646i	−0.246293	−	0.435132i
$613$	2.26525			0.0914927			0.0457464	−	0.998953i	$-0.485433\pi$
$613$	2.26525			0.0914927			0.0457464	+	0.998953i	$0.485433\pi$
$614$	−24.5713	+	10.1778i	−0.991617	+	0.410741i
$615$	−1.98033	+	0.173331i	−0.0798545	+	0.00698937i
$616$	−4.68436	+	4.68436i	−0.188738	+	0.188738i
$617$	2.66596	−	13.4027i	0.107327	−	0.539571i	−0.889287	−	0.457350i	$-0.848799\pi$
$617$	2.66596	−	13.4027i	0.107327	−	0.539571i	0.996614	−	0.0822209i	$-0.0262013\pi$
$618$	−16.1823	+	8.42472i	−0.650946	+	0.338892i
$619$	−29.6241	+	5.89259i	−1.19069	+	0.236843i	−0.750383	−	0.661003i	$-0.770131\pi$
$619$	−29.6241	+	5.89259i	−1.19069	+	0.236843i	−0.440308	+	0.897847i	$0.645131\pi$
$620$	3.73941	−	9.02773i	0.150178	−	0.362562i
$621$	13.1978	−	38.8938i	0.529610	−	1.56075i
$622$	4.98751	+	25.0739i	0.199981	+	1.00537i
$623$	31.2516	+	20.8817i	1.25207	+	0.836607i
$624$	5.85349	−	6.97645i	0.234327	−	0.279282i
$625$	−19.1800	−	19.1800i	−0.767200	−	0.767200i
$626$	4.73975	−	3.16700i	0.189439	−	0.126579i
$627$	−0.117381	+	1.07217i	−0.00468773	+	0.0428182i
$628$		−	14.1760i		−	0.565685i
$629$	4.15096	+	28.6060i	0.165510	+	1.14060i
$630$	13.8396	+	21.7202i	0.551382	+	0.865354i
$631$	14.6572	+	35.3856i	0.583493	+	1.40868i	0.889626	+	0.456689i	$0.150965\pi$
$631$	14.6572	+	35.3856i	0.583493	+	1.40868i	−0.306133	+	0.951989i	$0.599035\pi$
$632$	−7.42101	−	11.1063i	−0.295192	−	0.441786i
$633$	19.6391	−	5.72506i	0.780583	−	0.227551i
$634$	−0.824309	−	0.163965i	−0.0327375	−	0.00651189i
$635$	8.28921	−	12.4057i	0.328947	−	0.492305i
$636$	0.526592	−	1.67035i	0.0208807	−	0.0662338i
$637$	−31.4589	−	13.0307i	−1.24645	−	0.516296i
$638$	−8.12438	−	3.36523i	−0.321647	−	0.133231i
$639$	−25.3190	−	26.4446i	−1.00160	−	1.04613i
$640$	1.29924	−	1.94445i	0.0513569	−	0.0768611i
$641$	21.7589	+	4.32811i	0.859424	+	0.170950i	0.605081	−	0.796164i	$-0.293141\pi$
$641$	21.7589	+	4.32811i	0.859424	+	0.170950i	0.254343	+	0.967114i	$0.418141\pi$
$642$	3.24346	+	11.1263i	0.128009	+	0.439118i
$643$	12.5697	+	18.8119i	0.495701	+	0.741869i	0.991994	−	0.126286i	$-0.0403058\pi$
$643$	12.5697	+	18.8119i	0.495701	+	0.741869i	−0.496293	+	0.868155i	$0.665306\pi$
$644$	11.1042	+	26.8080i	0.437567	+	1.05638i
$645$	−1.17448	−	0.644283i	−0.0462450	−	0.0253686i
$646$	1.34110	−	0.475078i	0.0527649	−	0.0186917i
$647$		−	10.0596i		−	0.395485i	−0.980254	−	0.197743i	$-0.936639\pi$
$647$		−	10.0596i		−	0.395485i	0.980254	−	0.197743i	$-0.0633611\pi$
$648$	−0.391232	+	8.99149i	−0.0153690	+	0.353219i
$649$	5.24444	−	3.50422i	0.205862	−	0.137553i
$650$	−1.74330	−	1.74330i	−0.0683778	−	0.0683778i
$651$	−20.3529	−	17.0768i	−0.797692	−	0.669292i
$652$	−1.67881	−	1.12175i	−0.0657473	−	0.0439309i
$653$	4.15479	+	20.8876i	0.162590	+	0.817393i	0.972870	+	0.231351i	$0.0743146\pi$
$653$	4.15479	+	20.8876i	0.162590	+	0.817393i	−0.810281	+	0.586042i	$0.800685\pi$
$654$	16.5678	−	13.2981i	0.647853	−	0.519997i
$655$	1.45966	−	3.52394i	0.0570338	−	0.137692i
$656$	0.481346	−	0.0957457i	0.0187934	−	0.00373824i
$657$	−4.00840	−	0.0871642i	−0.156383	−	0.00340060i
$658$	−0.945866	+	4.75519i	−0.0368737	+	0.185377i
$659$	27.8177	−	27.8177i	1.08362	−	1.08362i	0.0874541	−	0.996169i	$-0.472127\pi$
$659$	27.8177	−	27.8177i	1.08362	−	1.08362i	0.996169	−	0.0874541i	$-0.0278731\pi$
$660$	0.637342	+	7.28172i	0.0248085	+	0.283441i
$661$	−1.87049	+	0.774784i	−0.0727537	+	0.0301356i	−0.418764	−	0.908095i	$-0.637536\pi$
$661$	−1.87049	+	0.774784i	−0.0727537	+	0.0301356i	0.346010	+	0.938231i	$0.387536\pi$
$662$	−25.2024			−0.979520
$663$	34.1653	−	15.5762i	1.32687	−	0.604929i
$664$	−9.67986			−0.375651
$665$	−2.73689	+	1.13366i	−0.106132	+	0.0439613i
$666$	8.46910	−	19.2514i	0.328171	−	0.745977i
$667$	−27.2360	+	27.2360i	−1.05458	+	1.05458i
$668$	−1.06710	+	5.36469i	−0.0412875	+	0.207566i
$669$	17.1110	+	32.8669i	0.661550	+	1.27071i
$670$	8.60936	−	1.71251i	0.332608	−	0.0661599i
$671$	−8.62676	+	20.8268i	−0.333032	+	0.804011i
$672$	−3.98003	−	4.95863i	−0.153533	−	0.191283i
$673$	2.36653	+	11.8974i	0.0912232	+	0.458610i	0.999215	+	0.0396214i	$0.0126152\pi$
$673$	2.36653	+	11.8974i	0.0912232	+	0.458610i	−0.907992	+	0.418988i	$0.862385\pi$
$674$	16.5640	+	11.0677i	0.638020	+	0.426312i
$675$	2.41567	+	0.317753i	0.0929791	+	0.0122303i
$676$	10.3554	+	10.3554i	0.398285	+	0.398285i
$677$	−2.16139	+	1.44419i	−0.0830690	+	0.0555049i	−0.596411	−	0.802679i	$-0.703407\pi$
$677$	−2.16139	+	1.44419i	−0.0830690	+	0.0555049i	0.513342	+	0.858184i	$0.328407\pi$
$678$	32.2769	+	3.53368i	1.23959	+	0.135710i
$679$		−	0.458238i		−	0.0175856i
$680$	8.28598	−	4.93090i	0.317753	−	0.189092i
$681$	10.1119	−	18.4332i	0.387489	−	0.706362i
$682$	−2.88558	−	6.96642i	−0.110495	−	0.266758i
$683$	−0.169562	−	0.253767i	−0.00648810	−	0.00971013i	0.828211	−	0.560416i	$-0.189359\pi$
$683$	−0.169562	−	0.253767i	−0.00648810	−	0.00971013i	−0.834699	+	0.550706i	$0.814359\pi$
$684$	−1.01069	−	0.223985i	−0.0386447	−	0.00856429i
$685$	−10.0425	−	1.99759i	−0.383706	−	0.0763238i
$686$	1.06823	−	1.59872i	0.0407852	−	0.0610393i
$687$	27.2722	+	8.59778i	1.04050	+	0.328026i
$688$	0.305546	+	0.126561i	0.0116488	+	0.00482510i
$689$	4.91184	+	2.03455i	0.187126	+	0.0775103i
$690$	30.5351	+	9.62643i	1.16245	+	0.366472i
$691$	−2.41026	+	3.60721i	−0.0916907	+	0.137225i	−0.874479	−	0.485063i	$-0.838797\pi$
$691$	−2.41026	+	3.60721i	−0.0916907	+	0.137225i	0.782788	+	0.622288i	$0.213797\pi$
$692$	−3.53481	−	0.703118i	−0.134373	−	0.0267285i
$693$	19.4033	+	4.30008i	0.737069	+	0.163347i
$694$	−12.9455	−	19.3743i	−0.491405	−	0.735440i
$695$	−14.5936	−	35.2320i	−0.553566	−	1.33643i
$696$	4.05938	−	7.39994i	0.153871	−	0.280494i
$697$	1.96132	+	0.497876i	0.0742902	+	0.0188584i
$698$		−	31.3561i		−	1.18684i
$699$	21.7023	+	2.37597i	0.820856	+	0.0898674i
$700$	−1.43123	+	0.956320i	−0.0540956	+	0.0361455i
$701$	−8.32463	−	8.32463i	−0.314417	−	0.314417i	0.532201	−	0.846618i	$-0.321365\pi$
$701$	−8.32463	−	8.32463i	−0.314417	−	0.314417i	−0.846618	+	0.532201i	$0.821365\pi$
$702$	−27.0871	−	3.56300i	−1.02234	−	0.134477i
$703$	2.01146	+	1.34402i	0.0758637	+	0.0506905i
$704$	−0.352060	−	1.76992i	−0.0132688	−	0.0667065i
$705$	3.34859	+	4.17193i	0.126115	+	0.157124i
$706$	2.95407	−	7.13177i	0.111178	−	0.268408i
$707$	−67.3418	+	13.3951i	−2.53265	+	0.503775i
$708$	2.79556	+	5.36974i	0.105064	+	0.201807i
$709$	−2.18152	+	10.9672i	−0.0819285	+	0.411883i	0.917956	+	0.396682i	$0.129839\pi$
$709$	−2.18152	+	10.9672i	−0.0819285	+	0.411883i	−0.999884	+	0.0152002i	$0.995161\pi$
$710$	20.1802	−	20.1802i	0.757351	−	0.757351i
$711$	−16.1363	+	36.6799i	−0.605158	+	1.37561i
$712$	−9.45927	+	3.91816i	−0.354501	+	0.146839i
$713$	−33.0276			−1.23689
$714$	−6.01258	−	25.5174i	−0.225015	−	0.954964i
$715$	−22.1890			−0.829820
$716$	−22.8233	+	9.45371i	−0.852946	+	0.353302i
$717$	−1.41408	−	16.1561i	−0.0528099	−	0.603360i
$718$	16.6165	−	16.6165i	0.620123	−	0.620123i
$719$	7.65595	−	38.4891i	0.285519	−	1.43540i	−0.525707	−	0.850666i	$-0.676199\pi$
$719$	7.65595	−	38.4891i	0.285519	−	1.43540i	0.811225	−	0.584734i	$-0.198801\pi$
$720$	−7.01405	−	0.152523i	−0.261398	−	0.00568420i
$721$	−37.9242	+	7.54359i	−1.41237	+	0.280938i
$722$	−7.22542	+	17.4437i	−0.268902	+	0.649187i
$723$	9.30305	−	7.46705i	0.345984	−	0.277703i
$724$	1.85125	+	9.30685i	0.0688011	+	0.345887i
$725$	−1.89986	−	1.26944i	−0.0705589	−	0.0471459i
$726$	−10.2745	−	8.62068i	−0.381323	−	0.319944i
$727$	−0.527489	−	0.527489i	−0.0195635	−	0.0195635i	0.697257	−	0.716821i	$-0.254403\pi$
$727$	−0.527489	−	0.527489i	−0.0195635	−	0.0195635i	−0.716821	+	0.697257i	$0.754403\pi$
$728$	16.0486	−	10.7233i	0.594800	−	0.397433i
$729$	23.3797	−	13.5052i	0.865913	−	0.500194i
$730$		−	3.12538i		−	0.115675i
$731$	0.912537	+	1.01325i	0.0337514	+	0.0374763i
$732$	−18.9697	−	10.4062i	−0.701141	−	0.384625i
$733$	17.9135	+	43.2469i	0.661649	+	1.59736i	0.795220	+	0.606322i	$0.207356\pi$
$733$	17.9135	+	43.2469i	0.661649	+	1.59736i	−0.133571	+	0.991039i	$0.542644\pi$
$734$	9.30255	+	13.9222i	0.343363	+	0.513880i
$735$	7.34144	+	25.1838i	0.270793	+	0.928920i
$736$	−7.75243	−	1.54205i	−0.285758	−	0.0568409i
$737$	3.76328	−	5.63215i	0.138622	−	0.207463i
$738$	−1.01821	−	1.06348i	−0.0374810	−	0.0391473i
$739$	26.7811	+	11.0931i	0.985159	+	0.408066i	0.816334	−	0.577580i	$-0.196003\pi$
$739$	26.7811	+	11.0931i	0.985159	+	0.408066i	0.168825	+	0.985646i	$0.446003\pi$
$740$	15.1469	+	6.27404i	0.556810	+	0.230638i
$741$	0.944854	−	2.99709i	0.0347101	−	0.110101i
$742$	2.06227	−	3.08641i	0.0757084	−	0.113306i
$743$	−48.0065	−	9.54910i	−1.76119	−	0.350322i	−0.794695	−	0.607009i	$-0.792369\pi$
$743$	−48.0065	−	9.54910i	−1.76119	−	0.350322i	−0.966495	+	0.256687i	$0.917369\pi$
$744$	6.94805	−	2.02545i	0.254728	−	0.0742567i
$745$	7.46419	+	11.1709i	0.273467	+	0.409272i
$746$	−3.76773	−	9.09611i	−0.137947	−	0.333032i
$747$	15.6048	+	24.4906i	0.570949	+	0.896063i
$748$	1.83071	−	7.21182i	0.0669372	−	0.263690i
$749$			24.5631i			0.897517i
$750$	1.99739	−	18.2443i	0.0729342	−	0.666187i
$751$	24.2509	−	16.2040i	0.884929	−	0.591291i	−0.0279099	−	0.999610i	$-0.508885\pi$
$751$	24.2509	−	16.2040i	0.884929	−	0.591291i	0.912839	+	0.408320i	$0.133885\pi$
$752$	−0.933888	−	0.933888i	−0.0340554	−	0.0340554i
$753$	−0.494952	+	0.589905i	−0.0180370	+	0.0214973i
$754$	21.3033	+	14.2344i	0.775820	+	0.518387i
$755$	−0.380291	−	1.91185i	−0.0138402	−	0.0695794i
$756$	−6.12946	+	18.0634i	−0.222926	+	0.656961i
$757$	12.8550	−	31.0348i	0.467223	−	1.12798i	−0.498147	−	0.867093i	$-0.665986\pi$
$757$	12.8550	−	31.0348i	0.467223	−	1.12798i	0.965370	−	0.260884i	$-0.0840142\pi$
$758$	11.3082	−	2.24933i	0.410731	−	0.0816995i
$759$	21.9142	−	11.4089i	0.795436	−	0.414115i
$760$	0.157432	−	0.791465i	0.00571066	−	0.0287094i
$761$	3.28842	−	3.28842i	0.119205	−	0.119205i	−0.644988	−	0.764193i	$-0.723138\pi$
$761$	3.28842	−	3.28842i	0.119205	−	0.119205i	0.764193	+	0.644988i	$0.223138\pi$
$762$	11.0085	−	0.963532i	0.398796	−	0.0349051i
$763$	41.5994	−	17.2310i	1.50600	−	0.623805i
$764$	−4.05188			−0.146592
$765$	−25.8332	−	13.0149i	−0.934001	−	0.470556i
$766$	17.2566			0.623508
$767$	−16.9783	+	7.03263i	−0.613050	+	0.253934i
$768$	1.72545	−	0.151023i	0.0622620	−	0.00544956i
$769$	−24.5365	+	24.5365i	−0.884810	+	0.884810i	−0.994019	−	0.109209i	$-0.965168\pi$
$769$	−24.5365	+	24.5365i	−0.884810	+	0.884810i	0.109209	+	0.994019i	$0.465168\pi$
$770$	−3.02239	+	15.1946i	−0.108919	+	0.547575i
$771$	−17.8320	+	9.28359i	−0.642203	+	0.334340i
$772$	13.8057	−	2.74613i	0.496879	−	0.0988354i
$773$	10.9248	−	26.3748i	0.392938	−	0.948637i	−0.596358	−	0.802718i	$-0.703386\pi$
$773$	10.9248	−	26.3748i	0.392938	−	0.948637i	0.989297	−	0.145919i	$-0.0466138\pi$
$774$	−0.172360	−	0.977075i	−0.00619535	−	0.0351202i
$775$	−0.382234	−	1.92162i	−0.0137302	−	0.0690266i
$776$	0.103789	+	0.0693499i	0.00372582	+	0.00248952i
$777$	28.6517	−	34.1484i	1.02788	−	1.22507i
$778$	12.4708	+	12.4708i	0.447100	+	0.447100i
$779$	0.140811	−	0.0940872i	0.00504509	−	0.00337102i
$780$	2.31774	−	21.1704i	0.0829884	−	0.758023i
$781$		−	22.0228i		−	0.788037i
$782$	−26.1153	−	19.4966i	−0.933882	−	0.697199i
$783$	−25.2663	+	1.65888i	−0.902945	+	0.0592837i
$784$	−2.47835	−	5.98326i	−0.0885123	−	0.213688i
$785$	−18.4180	−	27.5646i	−0.657368	−	0.983821i
$786$	2.71215	−	0.790628i	0.0967391	−	0.0282008i
$787$	0.262354	+	0.0521855i	0.00935191	+	0.00186021i	0.199764	−	0.979844i	$-0.435982\pi$
$787$	0.262354	+	0.0521855i	0.00935191	+	0.00186021i	−0.190412	+	0.981704i	$0.560982\pi$
$788$	2.99455	−	4.48166i	0.106676	−	0.159652i
$789$	−7.36720	+	23.3688i	−0.262279	+	0.831952i
$790$	−28.8596	−	11.9540i	−1.02678	−	0.425305i
$791$	63.5796	+	26.3355i	2.26063	+	0.936384i
$792$	−3.91045	+	3.74400i	−0.138952	+	0.133037i
$793$	36.4899	−	54.6110i	1.29579	−	1.93929i
$794$	12.7935	+	2.54478i	0.454023	+	0.0903107i
$795$	−1.14626	−	3.93208i	−0.0406535	−	0.139457i
$796$	2.79598	+	4.18448i	0.0991009	+	0.148315i
$797$	18.3741	+	44.3590i	0.650844	+	1.57128i	0.811555	+	0.584276i	$0.198621\pi$
$797$	18.3741	+	44.3590i	0.650844	+	1.57128i	−0.160711	+	0.987002i	$0.551379\pi$
$798$	−1.92365	−	1.05526i	−0.0680964	−	0.0373557i
$799$	−1.81831	−	5.13291i	−0.0643271	−	0.181589i
$800$		−	0.468900i		−	0.0165781i
$801$	25.1623	+	17.6160i	0.889067	+	0.622432i
$802$	−27.4849	+	18.3648i	−0.970525	+	0.648484i
$803$	−1.70537	−	1.70537i	−0.0601812	−	0.0601812i
$804$	4.98052	+	4.17884i	0.175649	+	0.147376i
$805$	56.4215	+	37.6996i	1.98860	+	1.32874i
$806$	4.28603	+	21.5473i	0.150969	+	0.758973i
$807$	−23.5191	+	18.8775i	−0.827911	+	0.664520i
$808$	7.15758	−	17.2799i	0.251803	−	0.607906i
$809$	−23.2138	+	4.61751i	−0.816153	+	0.162343i	−0.585478	−	0.810688i	$-0.699093\pi$
$809$	−23.2138	+	4.61751i	−0.816153	+	0.162343i	−0.230675	+	0.973031i	$0.574093\pi$
$810$	10.9214	+	17.9918i	0.383738	+	0.632167i
$811$	3.52270	−	17.7098i	0.123699	−	0.621876i	−0.868343	−	0.495965i	$-0.834815\pi$
$811$	3.52270	−	17.7098i	0.123699	−	0.621876i	0.992041	−	0.125911i	$-0.0401855\pi$
$812$	12.6492	−	12.6492i	0.443900	−	0.443900i
$813$	1.61019	+	18.3967i	0.0564720	+	0.645200i
$814$	11.6884	−	4.84148i	0.409677	−	0.169694i
$815$	−4.72177			−0.165397
$816$	6.68955	+	2.49998i	0.234181	+	0.0875168i
$817$	0.114122			0.00399262
$818$	16.2220	−	6.71936i	0.567188	−	0.234937i
$819$	−53.0023	−	23.3169i	−1.85205	−	0.814757i
$820$	0.811556	−	0.811556i	0.0283408	−	0.0283408i
$821$	−9.79413	+	49.2384i	−0.341817	+	1.71843i	0.302048	+	0.953293i	$0.402330\pi$
$821$	−9.79413	+	49.2384i	−0.341817	+	1.71843i	−0.643865	+	0.765139i	$0.722670\pi$
$822$	−3.50201	−	6.72668i	−0.122146	−	0.234620i
$823$	−34.3585	+	6.83434i	−1.19766	+	0.238230i	−0.753337	−	0.657635i	$-0.771557\pi$
$823$	−34.3585	+	6.83434i	−1.19766	+	0.238230i	−0.444326	+	0.895865i	$0.646557\pi$
$824$	4.03086	−	9.73136i	0.140422	−	0.339008i
$825$	0.917409	+	1.14298i	0.0319401	+	0.0397935i
$826$	2.50318	+	12.5843i	0.0870967	+	0.437865i
$827$	8.55992	+	5.71955i	0.297658	+	0.198888i	0.695427	−	0.718597i	$-0.255215\pi$
$827$	8.55992	+	5.71955i	0.297658	+	0.198888i	−0.397769	+	0.917486i	$0.630215\pi$
$828$	8.59612	+	22.1000i	0.298736	+	0.768028i
$829$	3.32888	+	3.32888i	0.115617	+	0.115617i	0.762548	−	0.646931i	$-0.223948\pi$
$829$	3.32888	+	3.32888i	0.115617	+	0.115617i	−0.646931	+	0.762548i	$0.723948\pi$
$830$	−18.8220	+	12.5764i	−0.653321	+	0.436535i
$831$	−24.4382	−	2.67549i	−0.847752	−	0.0928119i
$832$			5.25783i			0.182282i
$833$	1.39448	−	26.6657i	0.0483160	−	0.923913i
$834$	13.5843	−	24.7632i	0.470387	−	0.857478i
$835$	4.89509	+	11.8178i	0.169402	+	0.408972i
$836$	−0.345961	−	0.517768i	−0.0119653	−	0.0179074i
$837$	−16.3254	−	14.3137i	−0.564288	−	0.494755i
$838$	7.00798	+	1.39397i	0.242087	+	0.0481540i
$839$	−1.70563	+	2.55266i	−0.0588849	+	0.0881275i	−0.859744	−	0.510726i	$-0.829377\pi$
$839$	−1.70563	+	2.55266i	−0.0588849	+	0.0881275i	0.800859	+	0.598853i	$0.204377\pi$
$840$	−14.1814	−	4.47080i	−0.489305	−	0.154257i
$841$	−4.85417	−	2.01066i	−0.167385	−	0.0693332i
$842$	18.1351	+	7.51179i	0.624976	+	0.258874i
$843$	9.39575	+	2.96208i	0.323607	+	0.102020i
$844$	−6.56161	+	9.82014i	−0.225860	+	0.338023i
$845$	33.5897	+	6.68140i	1.15552	+	0.229847i
$846$	−0.857277	+	3.86830i	−0.0294738	+	0.132995i
$847$	−15.7927	−	23.6354i	−0.542643	−	0.812123i
$848$	0.386957	+	0.934197i	0.0132882	+	0.0320804i
$849$	−2.41068	+	4.39448i	−0.0827344	+	0.150818i
$850$	0.832121	−	1.74508i	0.0285415	−	0.0598559i
$851$		−	55.4143i		−	1.89958i
$852$	21.0119	+	2.30038i	0.719855	+	0.0788097i
$853$	−10.4436	+	6.97819i	−0.357582	+	0.238929i	−0.721365	−	0.692555i	$-0.756485\pi$
$853$	−10.4436	+	6.97819i	−0.357582	+	0.238929i	0.363783	+	0.931484i	$0.381485\pi$
$854$	−32.4262	−	32.4262i	−1.10960	−	1.10960i
$855$	−2.25624	+	0.877599i	−0.0771619	+	0.0300132i
$856$	−5.56347	−	3.71739i	−0.190156	−	0.127058i
$857$	3.57612	+	17.9784i	0.122158	+	0.614130i	0.992557	+	0.121783i	$0.0388611\pi$
$857$	3.57612	+	17.9784i	0.122158	+	0.614130i	−0.870399	+	0.492348i	$0.836139\pi$
$858$	−10.2870	−	12.8164i	−0.351193	−	0.437544i
$859$	20.4836	−	49.4517i	0.698890	−	1.68727i	−0.0271626	−	0.999631i	$-0.508647\pi$
$859$	20.4836	−	49.4517i	0.698890	−	1.68727i	0.726053	−	0.687639i	$-0.241353\pi$
$860$	0.758551	−	0.150885i	0.0258664	−	0.00514514i
$861$	−1.44100	−	2.76789i	−0.0491093	−	0.0943295i
$862$	1.40755	−	7.07625i	0.0479415	−	0.241018i
$863$	20.8499	−	20.8499i	0.709738	−	0.709738i	−0.256742	−	0.966480i	$-0.582649\pi$
$863$	20.8499	−	20.8499i	0.709738	−	0.709738i	0.966480	+	0.256742i	$0.0826491\pi$
$864$	−3.16368	−	4.12203i	−0.107631	−	0.140234i
$865$	−7.78678	+	3.22539i	−0.264759	+	0.109667i
$866$	6.71416			0.228156
$867$	20.4597	+	21.1755i	0.694847	+	0.719158i
$868$	15.3390			0.520640
$869$	−22.2700	+	9.22454i	−0.755458	+	0.312921i
$870$	−1.72102	−	19.6629i	−0.0583481	−	0.666635i
$871$	−13.9553	+	13.9553i	−0.472856	+	0.472856i
$872$	−2.39289	+	12.0299i	−0.0810335	+	0.407383i
$873$	0.00814127	−	0.374391i	0.000275540	−	0.0126712i
$874$	−2.67513	+	0.532117i	−0.0904878	+	0.0179991i
$875$	14.8860	−	35.9379i	0.503238	−	1.21492i
$876$	1.80522	−	1.44895i	0.0609928	−	0.0489556i
$877$	−2.81857	−	14.1699i	−0.0951763	−	0.478483i	−0.998747	−	0.0500444i	$-0.984064\pi$
$877$	−2.81857	−	14.1699i	−0.0951763	−	0.478483i	0.903571	−	0.428439i	$-0.140936\pi$
$878$	16.6570	+	11.1298i	0.562145	+	0.375614i
$879$	11.0475	+	9.26929i	0.372624	+	0.312645i
$880$	−2.98412	−	2.98412i	−0.100595	−	0.100595i
$881$	−14.2928	+	9.55013i	−0.481536	+	0.321752i	−0.772536	−	0.634971i	$-0.781012\pi$
$881$	−14.2928	+	9.55013i	−0.481536	+	0.321752i	0.291000	+	0.956723i	$0.406012\pi$
$882$	−11.1426	+	15.9159i	−0.375193	+	0.535916i
$883$			25.8266i			0.869134i	0.900640	+	0.434567i	$0.143099\pi$
$883$			25.8266i			0.869134i	−0.900640	+	0.434567i	$0.856901\pi$
$884$	−9.33067	+	19.5678i	−0.313824	+	0.658137i
$885$	12.4124	+	6.80907i	0.417238	+	0.228884i
$886$	−13.5421	−	32.6934i	−0.454955	−	1.09836i
$887$	−15.6338	−	23.3976i	−0.524931	−	0.785614i	0.470368	−	0.882471i	$-0.344121\pi$
$887$	−15.6338	−	23.3976i	−0.524931	−	0.785614i	−0.995298	+	0.0968562i	$0.969121\pi$
$888$	3.39834	+	11.6576i	0.114041	+	0.391202i
$889$	22.9711	+	4.56924i	0.770427	+	0.153248i
$890$	−13.3024	+	19.9085i	−0.445899	+	0.667334i
$891$	15.7765	+	3.85799i	0.528534	+	0.129248i
$892$	−19.7649	−	8.18687i	−0.661776	−	0.274117i
$893$	−0.421049	−	0.174404i	−0.0140899	−	0.00583621i
$894$	−2.99188	+	9.49027i	−0.100064	+	0.317402i
$895$	−32.0960	+	48.0351i	−1.07285	+	1.60564i
$896$	3.60046	+	0.716176i	0.120283	+	0.0239258i
$897$	−69.1067	+	20.1456i	−2.30741	+	0.672641i
$898$	6.47738	+	9.69408i	0.216153	+	0.323496i
$899$	7.79197	+	18.8115i	0.259877	+	0.627398i
$900$	−1.18634	+	0.755908i	−0.0395447	+	0.0251969i
$901$	−0.217728	+	4.16346i	−0.00725357	+	0.138705i
$902$		−	0.885655i		−	0.0294891i
$903$	0.228851	−	2.09035i	0.00761570	−	0.0695624i
$904$	−15.5871	+	10.4150i	−0.518419	+	0.346396i
$905$	15.6915	+	15.6915i	0.521602	+	0.521602i
$906$	0.927980	−	1.10601i	0.0308301	−	0.0367447i
$907$	6.03574	+	4.03295i	0.200413	+	0.133912i	0.651727	−	0.758453i	$-0.274045\pi$
$907$	6.03574	+	4.03295i	0.200413	+	0.133912i	−0.451314	+	0.892365i	$0.649045\pi$
$908$	2.36812	+	11.9053i	0.0785887	+	0.395092i
$909$	−55.2578	+	9.74769i	−1.83279	+	0.323311i
$910$	17.2735	−	41.7019i	0.572611	−	1.38240i
$911$	19.1584	−	3.81084i	0.634746	−	0.126259i	0.132779	−	0.991146i	$-0.457610\pi$
$911$	19.1584	−	3.81084i	0.634746	−	0.126259i	0.501967	+	0.864887i	$0.332610\pi$
$912$	0.530138	−	0.275997i	0.0175546	−	0.00913919i
$913$	−3.40789	+	17.1326i	−0.112785	+	0.567007i
$914$	−16.1173	+	16.1173i	−0.533112	+	0.533112i
$915$	−50.4058	+	4.41183i	−1.66637	+	0.145851i
$916$	−15.2528	+	6.31793i	−0.503968	+	0.208750i
$917$	5.98753			0.197726
$918$	−4.45906	−	20.9551i	−0.147171	−	0.691622i
$919$	−24.8220			−0.818804			−0.409402	−	0.912354i	$-0.634263\pi$
$919$	−24.8220			−0.818804			−0.409402	+	0.912354i	$0.634263\pi$
$920$	−17.0777	+	7.07382i	−0.563035	+	0.233217i
$921$	−45.8898	+	4.01657i	−1.51212	+	0.132350i
$922$	−12.6336	+	12.6336i	−0.416066	+	0.416066i
$923$	−12.5180	+	62.9320i	−0.412034	+	2.07143i
$924$	−10.1776	+	5.29862i	−0.334819	+	0.174312i
$925$	3.22413	−	0.641318i	0.106009	−	0.0210864i
$926$	−3.71040	+	8.95769i	−0.121931	+	0.294368i
$927$	−31.1190	+	5.48951i	−1.02208	+	0.180299i
$928$	0.950670	+	4.77934i	0.0312073	+	0.156890i
$929$	−14.3770	−	9.60640i	−0.471694	−	0.315176i	0.296905	−	0.954907i	$-0.404046\pi$
$929$	−14.3770	−	9.60640i	−0.471694	−	0.315176i	−0.768599	+	0.639731i	$0.779046\pi$
$930$	10.8786	−	12.9656i	0.356723	−	0.425158i
$931$	−1.58021	−	1.58021i	−0.0517893	−	0.0517893i
$932$	−10.4804	+	7.00279i	−0.343298	+	0.229384i
$933$	−4.81900	+	44.0171i	−0.157767	+	1.44106i
$934$		−	10.4267i		−	0.341172i
$935$	−5.81017	−	16.4015i	−0.190013	−	0.536388i
$936$	13.3026	−	8.47608i	0.434809	−	0.277049i
$937$	−19.4834	−	47.0371i	−0.636495	−	1.53664i	−0.831318	−	0.555797i	$-0.812413\pi$
$937$	−19.4834	−	47.0371i	−0.636495	−	1.53664i	0.194823	−	0.980838i	$-0.437587\pi$
$938$	7.65544	+	11.4572i	0.249959	+	0.374090i
$939$	9.47892	−	2.76324i	0.309333	−	0.0901749i
$940$	−3.02924	−	0.602553i	−0.0988029	−	0.0196531i
$941$	20.7947	−	31.1215i	0.677889	−	1.01453i	−0.319859	−	0.947465i	$-0.603636\pi$
$941$	20.7947	−	31.1215i	0.677889	−	1.01453i	0.997748	−	0.0670681i	$-0.0213645\pi$
$942$	7.38254	−	23.4175i	0.240536	−	0.762982i
$943$	−3.58396	−	1.48453i	−0.116710	−	0.0483428i
$944$	−3.22914	−	1.33755i	−0.105100	−	0.0435337i
$945$	11.5503	+	43.0871i	0.375732	+	1.40162i
$946$	0.331574	−	0.496236i	0.0107804	−	0.0161340i
$947$	22.2705	+	4.42987i	0.723692	+	0.143951i	0.543174	−	0.839620i	$-0.317222\pi$
$947$	22.2705	+	4.42987i	0.723692	+	0.143951i	0.180519	+	0.983572i	$0.442222\pi$
$948$	−6.47490	−	22.2113i	−0.210295	−	0.721389i
$949$	3.90389	+	5.84259i	0.126726	+	0.189658i
$950$	−0.0619195	−	0.149487i	−0.00200893	−	0.00485000i
$951$	−1.27629	−	0.700135i	−0.0413866	−	0.0227034i
$952$	12.1287	+	9.05483i	0.393094	+	0.293469i
$953$			6.16085i			0.199570i	0.995009	+	0.0997848i	$0.0318154\pi$
$953$			6.16085i			0.199570i	−0.995009	+	0.0997848i	$0.968185\pi$
$954$	1.73976	−	2.48503i	0.0563268	−	0.0804558i
$955$	−7.87868	+	5.26436i	−0.254948	+	0.170351i
$956$	6.62091	+	6.62091i	0.214136	+	0.214136i
$957$	−11.6682	−	9.79002i	−0.377179	−	0.316467i
$958$	−16.3093	−	10.8975i	−0.526930	−	0.352083i
$959$	−3.13574	−	15.7644i	−0.101258	−	0.509059i
$960$	3.15884	−	2.53543i	0.101951	−	0.0818307i
$961$	5.18180	−	12.5100i	0.167155	−	0.403548i
$962$	−36.1525	+	7.19118i	−1.16560	+	0.231853i
$963$	−0.436400	+	20.0686i	−0.0140628	+	0.646703i
$964$	−1.34364	+	6.75494i	−0.0432757	+	0.217562i
$965$	23.2767	−	23.2767i	0.749302	−	0.749302i
$966$	4.38218	+	50.0670i	0.140994	+	1.61088i
$967$	44.0772	−	18.2574i	1.41743	−	0.587118i	0.463215	−	0.886246i	$-0.346696\pi$
$967$	44.0772	−	18.2574i	1.41743	−	0.587118i	0.954213	+	0.299128i	$0.0966957\pi$
$968$	7.74342			0.248883
$969$	2.46278	−	0.0863717i	0.0791159	−	0.00277466i
$970$	0.291915			0.00937283
$971$	3.94435	−	1.63380i	0.126580	−	0.0524312i	−0.318494	−	0.947925i	$-0.603177\pi$
$971$	3.94435	−	1.63380i	0.126580	−	0.0524312i	0.445074	+	0.895494i	$0.353177\pi$
$972$	−5.32883	+	14.6494i	−0.170922	+	0.469878i
$973$	42.3294	−	42.3294i	1.35702	−	1.35702i
$974$	2.98535	−	15.0084i	0.0956568	−	0.480899i
$975$	−1.97190	−	3.78763i	−0.0631512	−	0.121301i
$976$	12.2518	−	2.43704i	0.392172	−	0.0780078i
$977$	23.3656	−	56.4095i	0.747531	−	1.80470i	0.175476	−	0.984484i	$-0.443854\pi$
$977$	23.3656	−	56.4095i	0.747531	−	1.80470i	0.572055	−	0.820215i	$-0.306146\pi$
$978$	−2.18906	−	2.72730i	−0.0699984	−	0.0872095i
$979$	3.60461	+	18.1216i	0.115204	+	0.579169i
$980$	−12.5927	−	8.41417i	−0.402259	−	0.268781i
$981$	34.2938	−	13.3391i	1.09492	−	0.425884i
$982$	8.21260	+	8.21260i	0.262075	+	0.262075i
$983$	−1.70648	+	1.14023i	−0.0544282	+	0.0363678i	−0.582487	−	0.812840i	$-0.697920\pi$
$983$	−1.70648	+	1.14023i	−0.0544282	+	0.0363678i	0.528058	+	0.849208i	$0.322920\pi$
$984$	0.845001	+	0.0925107i	0.0269376	+	0.00294913i
$985$		−	12.6050i		−	0.401628i
$986$	−4.94347	+	19.4741i	−0.157432	+	0.620183i
$987$	−4.03887	+	7.36254i	−0.128559	+	0.234352i
$988$	0.694310	+	1.67621i	0.0220890	+	0.0533274i
$989$	−1.45233	−	2.17356i	−0.0461813	−	0.0691152i
$990$	−2.73932	+	12.3606i	−0.0870613	+	0.392847i
$991$	1.55623	+	0.309553i	0.0494351	+	0.00983326i	0.219746	−	0.975557i	$-0.429477\pi$
$991$	1.55623	+	0.309553i	0.0494351	+	0.00983326i	−0.170311	+	0.985390i	$0.554477\pi$
$992$	−2.32141	+	3.47424i	−0.0737049	+	0.110307i
$993$	−41.6320	−	13.1248i	−1.32115	−	0.416503i
$994$	41.3896	+	17.1441i	1.31280	+	0.543779i
$995$	10.8733	+	4.50386i	0.344706	+	0.142782i
$996$	−15.9902	−	5.04104i	−0.506669	−	0.159731i
$997$	−8.01959	+	12.0022i	−0.253983	+	0.380112i	−0.936448	−	0.350806i	$-0.885908\pi$
$997$	−8.01959	+	12.0022i	−0.253983	+	0.380112i	0.682465	+	0.730918i	$0.260908\pi$
$998$	18.2182	+	3.62382i	0.576686	+	0.114710i
$999$	24.0158	−	27.3910i	0.759827	−	0.866613i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	102.2.i.b.29.1	yes	24
3.2	odd	2		102.2.i.a.29.2	✓	24
4.3	odd	2		816.2.cj.a.641.3		24
12.11	even	2		816.2.cj.b.641.2		24
17.10	odd	16		102.2.i.a.95.2	yes	24
51.44	even	16	inner	102.2.i.b.95.1	yes	24
68.27	even	16		816.2.cj.b.401.2		24
204.95	odd	16		816.2.cj.a.401.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
102.2.i.a.29.2	✓	24	3.2	odd	2
102.2.i.a.95.2	yes	24	17.10	odd	16
102.2.i.b.29.1	yes	24	1.1	even	1	trivial
102.2.i.b.95.1	yes	24	51.44	even	16	inner
816.2.cj.a.401.3		24	204.95	odd	16
816.2.cj.a.641.3		24	4.3	odd	2
816.2.cj.b.401.2		24	68.27	even	16
816.2.cj.b.641.2		24	12.11	even	2

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:	\( N \)	\(=\)	\( 102 = 2 \cdot 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	102.i (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.923880 + 0.382683i) q^{2} +(-1.72545 + 0.151023i) q^{3} +(0.707107 - 0.707107i) q^{4} +(0.456232 - 2.29363i) q^{5} +(1.53632 - 0.799829i) q^{6} +(3.60046 - 0.716176i) q^{7} +(-0.382683 + 0.923880i) q^{8} +(2.95438 - 0.521165i) q^{9} +(0.456232 + 2.29363i) q^{10} +(1.50047 + 1.00258i) q^{11} +(-1.11329 + 1.32687i) q^{12} +(-3.71785 - 3.71785i) q^{13} +(-3.05232 + 2.03950i) q^{14} +(-0.440817 + 4.02646i) q^{15} -1.00000i q^{16} +(1.77462 - 3.72165i) q^{17} +(-2.53005 + 1.61209i) q^{18} +(-0.132053 - 0.318803i) q^{19} +(-1.29924 - 1.94445i) q^{20} +(-6.10427 + 1.77948i) q^{21} +(-1.76992 - 0.352060i) q^{22} +(-4.39140 + 6.57220i) q^{23} +(0.520776 - 1.65191i) q^{24} +(-0.433207 - 0.179440i) q^{25} +(4.85760 + 2.01208i) q^{26} +(-5.01895 + 1.34543i) q^{27} +(2.03950 - 3.05232i) q^{28} +(4.77934 + 0.950670i) q^{29} +(-1.13360 - 3.88866i) q^{30} +(2.32141 + 3.47424i) q^{31} +(0.382683 + 0.923880i) q^{32} +(-2.74040 - 1.50330i) q^{33} +(-0.215323 + 4.11748i) q^{34} -8.58488i q^{35} +(1.72055 - 2.45758i) q^{36} +(-5.82914 + 3.89490i) q^{37} +(0.244002 + 0.244002i) q^{38} +(6.97645 + 5.85349i) q^{39} +(1.94445 + 1.29924i) q^{40} +(0.0957457 + 0.481346i) q^{41} +(4.95863 - 3.98003i) q^{42} +(-0.126561 + 0.305546i) q^{43} +(1.76992 - 0.352060i) q^{44} +(0.152523 - 7.01405i) q^{45} +(1.54205 - 7.75243i) q^{46} +(0.933888 - 0.933888i) q^{47} +(0.151023 + 1.72545i) q^{48} +(5.98326 - 2.47835i) q^{49} +0.468900 q^{50} +(-2.49998 + 6.68955i) q^{51} -5.25783 q^{52} +(-0.934197 + 0.386957i) q^{53} +(4.12203 - 3.16368i) q^{54} +(2.98412 - 2.98412i) q^{55} +(-0.716176 + 3.60046i) q^{56} +(0.275997 + 0.530138i) q^{57} +(-4.77934 + 0.950670i) q^{58} +(1.33755 - 3.22914i) q^{59} +(2.53543 + 3.15884i) q^{60} +(2.43704 + 12.2518i) q^{61} +(-3.47424 - 2.32141i) q^{62} +(10.2639 - 3.99229i) q^{63} +(-0.707107 - 0.707107i) q^{64} +(-10.2236 + 6.83117i) q^{65} +(3.10709 + 0.340165i) q^{66} -3.75359i q^{67} +(-1.37676 - 3.88646i) q^{68} +(6.58461 - 12.0032i) q^{69} +(3.28529 + 7.93139i) q^{70} +(-6.78001 - 10.1470i) q^{71} +(-0.649100 + 2.92894i) q^{72} +(-1.31077 - 0.260728i) q^{73} +(3.89490 - 5.82914i) q^{74} +(0.774578 + 0.244192i) q^{75} +(-0.318803 - 0.132053i) q^{76} +(6.12041 + 2.53516i) q^{77} +(-8.68543 - 2.73815i) q^{78} +(-7.42101 + 11.1063i) q^{79} +(-2.29363 - 0.456232i) q^{80} +(8.45677 - 3.07944i) q^{81} +(-0.272661 - 0.408066i) q^{82} +(3.70432 + 8.94302i) q^{83} +(-3.05809 + 5.57465i) q^{84} +(-7.72647 - 5.76827i) q^{85} -0.330720i q^{86} +(-8.39011 - 0.918549i) q^{87} +(-1.50047 + 1.00258i) q^{88} +(7.23981 + 7.23981i) q^{89} +(2.54325 + 6.53850i) q^{90} +(-16.0486 - 10.7233i) q^{91} +(1.54205 + 7.75243i) q^{92} +(-4.53018 - 5.64405i) q^{93} +(-0.505416 + 1.22018i) q^{94} +(-0.791465 + 0.157432i) q^{95} +(-0.799829 - 1.53632i) q^{96} +(0.0243524 - 0.122428i) q^{97} +(-4.57939 + 4.57939i) q^{98} +(4.95547 + 2.18002i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 16 q^{11} - 48 q^{15} - 16 q^{17} - 16 q^{18} - 8 q^{24} - 16 q^{25} - 16 q^{29} - 16 q^{31} + 16 q^{33} - 16 q^{37} - 24 q^{38} + 16 q^{39} + 32 q^{41} + 48 q^{42} - 8 q^{43} - 16 q^{45} + 16 q^{46}+ \cdots + 16 q^{99}+O(q^{100}) \) 24 * q + 16 * q^11 - 48 * q^15 - 16 * q^17 - 16 * q^18 - 8 * q^24 - 16 * q^25 - 16 * q^29 - 16 * q^31 + 16 * q^33 - 16 * q^37 - 24 * q^38 + 16 * q^39 + 32 * q^41 + 48 * q^42 - 8 * q^43 - 16 * q^45 + 16 * q^46 - 16 * q^47 + 32 * q^49 + 8 * q^50 + 64 * q^51 + 16 * q^52 + 64 * q^53 + 8 * q^54 + 32 * q^55 + 8 * q^57 + 16 * q^58 - 64 * q^59 + 16 * q^60 + 16 * q^61 + 16 * q^62 + 48 * q^63 - 16 * q^69 - 16 * q^70 + 16 * q^72 - 64 * q^73 + 16 * q^74 - 80 * q^75 - 16 * q^77 - 16 * q^78 - 32 * q^79 - 16 * q^80 + 32 * q^81 - 64 * q^82 + 72 * q^83 - 16 * q^84 - 32 * q^85 - 32 * q^87 - 16 * q^88 - 48 * q^89 - 64 * q^91 + 16 * q^92 + 96 * q^93 - 32 * q^94 + 32 * q^95 - 16 * q^97 - 16 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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