LMFDB - Embedded newform 59.2.c.a.26.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [59,2,Mod(3,59)] 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("59.3"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(59, base_ring=CyclotomicField(58)) chi = DirichletCharacter(H, H._module([50])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	59.c (of order $29$, degree $28$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$0.471117371926$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$4$ over $\Q(\zeta_{29})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			26.1
Character	$\chi$	$=$	59.26
Dual form			59.2.c.a.25.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.19893 + 1.67159i) q^{2} +(1.14121 - 2.15255i) q^{3} +(1.50605 - 5.42431i) q^{4} +(0.330311 - 0.312887i) q^{5} +(1.08873 + 6.64093i) q^{6} +(-0.362135 - 0.426338i) q^{7} +(3.71073 + 9.31322i) q^{8} +(-1.64754 - 2.42994i) q^{9} +(-0.203314 + 1.24016i) q^{10} +(1.66508 - 1.00184i) q^{11} +(-9.95736 - 9.43211i) q^{12} +(-0.146364 + 0.215870i) q^{13} +(1.50897 + 0.332149i) q^{14} +(-0.296551 - 1.06808i) q^{15} +(-14.0801 - 8.47172i) q^{16} +(-3.05473 + 3.59631i) q^{17} +(7.68469 + 2.58927i) q^{18} +(4.22025 + 1.95250i) q^{19} +(-1.19973 - 2.26293i) q^{20} +(-1.33098 + 0.292971i) q^{21} +(-1.98672 + 4.98630i) q^{22} +(-3.34811 + 1.12811i) q^{23} +(24.2819 + 2.64081i) q^{24} +(-0.259488 + 4.78597i) q^{25} +(-0.0390017 - 0.719343i) q^{26} +(0.155460 - 0.0169073i) q^{27} +(-2.85798 + 1.32224i) q^{28} +(-4.87493 - 3.70583i) q^{29} +(2.43748 + 1.85292i) q^{30} +(0.386926 - 0.179011i) q^{31} +(25.1895 - 2.73952i) q^{32} +(-0.256316 - 4.72747i) q^{33} +(0.705614 - 13.0143i) q^{34} +(-0.253012 - 0.0275168i) q^{35} +(-15.6620 + 5.27715i) q^{36} +(-3.25905 + 8.17960i) q^{37} +(-12.5438 + 2.76110i) q^{38} +(0.297639 + 0.561407i) q^{39} +(4.13968 + 1.91522i) q^{40} +(3.15602 + 1.06339i) q^{41} +(2.43701 - 2.86908i) q^{42} +(3.43733 + 2.06817i) q^{43} +(-2.92661 - 10.5407i) q^{44} +(-1.30450 - 0.287142i) q^{45} +(5.47654 - 8.07730i) q^{46} +(1.40614 + 1.33196i) q^{47} +(-34.3041 + 20.6401i) q^{48} +(1.08185 - 6.59900i) q^{49} +(-7.42956 - 10.9578i) q^{50} +(4.25514 + 10.6796i) q^{51} +(0.950515 + 1.11903i) q^{52} +(-1.36486 - 8.32531i) q^{53} +(-0.313583 + 0.297042i) q^{54} +(0.236529 - 0.851900i) q^{55} +(2.62679 - 4.95466i) q^{56} +(9.01903 - 6.85609i) q^{57} +16.9142 q^{58} +(6.86593 + 3.44368i) q^{59} -6.24020 q^{60} +(-0.900340 + 0.684420i) q^{61} +(-0.551592 + 1.04041i) q^{62} +(-0.439344 + 1.58238i) q^{63} +(-26.9511 + 25.5294i) q^{64} +(0.0191975 + 0.117099i) q^{65} +(8.46598 + 9.96693i) q^{66} +(-1.70447 - 4.27791i) q^{67} +(14.9069 + 21.9860i) q^{68} +(-1.39258 + 8.49438i) q^{69} +(0.602354 - 0.362424i) q^{70} +(-1.83446 - 1.73769i) q^{71} +(16.5170 - 24.3608i) q^{72} +(-10.5528 - 2.32285i) q^{73} +(-6.50647 - 23.4342i) q^{74} +(10.0059 + 6.02034i) q^{75} +(16.9469 - 19.9514i) q^{76} +(-1.03011 - 0.347083i) q^{77} +(-1.59293 - 0.736967i) q^{78} +(1.15299 + 2.17477i) q^{79} +(-7.30150 + 1.60718i) q^{80} +(3.40099 - 8.53584i) q^{81} +(-8.71741 + 2.93724i) q^{82} +(-8.28172 - 0.900691i) q^{83} +(-0.415361 + 7.66089i) q^{84} +(0.116227 + 2.14369i) q^{85} +(-11.0156 + 1.19802i) q^{86} +(-13.5403 + 6.26440i) q^{87} +(15.5090 + 11.7897i) q^{88} +(-10.7195 - 8.14876i) q^{89} +(3.34848 - 1.54917i) q^{90} +(0.145037 - 0.0157737i) q^{91} +(1.07679 + 19.8602i) q^{92} +(0.0562335 - 1.03717i) q^{93} +(-5.31849 - 0.578420i) q^{94} +(2.00491 - 0.675531i) q^{95} +(22.8495 - 57.3479i) q^{96} +(2.50354 - 0.551071i) q^{97} +(8.65188 + 16.3192i) q^{98} +(-5.17770 - 2.39546i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 26 q^{2} - 23 q^{3} - 30 q^{4} - 25 q^{5} - 13 q^{6} - 23 q^{7} - 8 q^{8} - 21 q^{9} - 3 q^{10} - 15 q^{11} + 21 q^{12} - 23 q^{13} + 13 q^{14} + 4 q^{15} - 8 q^{16} - 10 q^{17} + 12 q^{18} - 15 q^{19}+ \cdots + 44 q^{99}+O(q^{100}) $ 112 * q - 26 * q^2 - 23 * q^3 - 30 * q^4 - 25 * q^5 - 13 * q^6 - 23 * q^7 - 8 * q^8 - 21 * q^9 - 3 * q^10 - 15 * q^11 + 21 * q^12 - 23 * q^13 + 13 * q^14 + 4 * q^15 - 8 * q^16 - 10 * q^17 + 12 * q^18 - 15 * q^19 + 7 * q^20 - 12 * q^21 - q^22 + 3 * q^23 + 25 * q^24 - 5 * q^25 + 5 * q^26 + 22 * q^27 + 29 * q^28 - 13 * q^29 + 29 * q^30 + 3 * q^31 + 36 * q^32 + 33 * q^33 + 27 * q^34 + 28 * q^35 + 20 * q^36 - 9 * q^37 + 31 * q^38 + 45 * q^39 + 79 * q^40 + 23 * q^41 + 33 * q^42 + 19 * q^43 + 43 * q^44 + 19 * q^45 - 31 * q^46 + 10 * q^47 - 25 * q^48 - 31 * q^49 - 60 * q^50 - 61 * q^51 - 75 * q^52 - 23 * q^53 - 86 * q^54 - 24 * q^55 - 103 * q^56 - 91 * q^57 + 12 * q^58 - 33 * q^59 - 210 * q^60 - 47 * q^61 - 39 * q^62 - 58 * q^63 - 152 * q^64 - 16 * q^65 - 116 * q^66 - 19 * q^67 - 5 * q^68 - 45 * q^69 + 23 * q^70 - 18 * q^71 - 36 * q^72 + 24 * q^73 + 19 * q^74 + 58 * q^75 + 97 * q^76 + 65 * q^77 + 119 * q^78 + 41 * q^79 + 107 * q^80 + 95 * q^81 + 145 * q^82 + 49 * q^83 + 167 * q^84 + 39 * q^85 + 111 * q^86 + 80 * q^87 + 175 * q^88 + 51 * q^89 + 213 * q^90 + 77 * q^91 + 135 * q^92 + 93 * q^93 + 151 * q^94 + 65 * q^95 + 181 * q^96 + 91 * q^97 + 31 * q^98 + 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/59\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{23}{29}\right)$

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 $

$2$	−2.19893	+	1.67159i	−1.55488	+	1.18199i	−0.647205	+	0.762316i	$0.724062\pi$
$2$	−2.19893	+	1.67159i	−1.55488	+	1.18199i	−0.907675	+	0.419673i	$0.862145\pi$
$3$	1.14121	−	2.15255i	0.658877	−	1.24277i	−0.298632	−	0.954368i	$-0.596530\pi$
$3$	1.14121	−	2.15255i	0.658877	−	1.24277i	0.957508	−	0.288405i	$-0.0931250\pi$
$4$	1.50605	−	5.42431i	0.753025	−	2.71215i
$5$	0.330311	−	0.312887i	0.147719	−	0.139927i	−0.610272	−	0.792192i	$-0.708940\pi$
$5$	0.330311	−	0.312887i	0.147719	−	0.139927i	0.757991	+	0.652265i	$0.226181\pi$
$6$	1.08873	+	6.64093i	0.444470	+	2.71115i
$7$	−0.362135	−	0.426338i	−0.136874	−	0.161141i	0.689454	−	0.724329i	$-0.257850\pi$
$7$	−0.362135	−	0.426338i	−0.136874	−	0.161141i	−0.826328	+	0.563189i	$0.809574\pi$
$8$	3.71073	+	9.31322i	1.31194	+	3.29272i
$9$	−1.64754	−	2.42994i	−0.549181	−	0.809981i
$10$	−0.203314	+	1.24016i	−0.0642935	+	0.392173i
$11$	1.66508	−	1.00184i	0.502039	−	0.302067i	−0.241915	−	0.970297i	$-0.577776\pi$
$11$	1.66508	−	1.00184i	0.502039	−	0.302067i	0.743954	+	0.668230i	$0.232948\pi$
$12$	−9.95736	−	9.43211i	−2.87444	−	2.72281i
$13$	−0.146364	+	0.215870i	−0.0405940	+	0.0598716i	−0.847444	−	0.530884i	$-0.821860\pi$
$13$	−0.146364	+	0.215870i	−0.0405940	+	0.0598716i	0.806850	+	0.590756i	$0.201170\pi$
$14$	1.50897	+	0.332149i	0.403289	+	0.0887706i
$15$	−0.296551	−	1.06808i	−0.0765690	−	0.275777i
$16$	−14.0801	−	8.47172i	−3.52003	−	2.11793i
$17$	−3.05473	+	3.59631i	−0.740882	+	0.872233i	−0.995495	−	0.0948096i	$-0.969776\pi$
$17$	−3.05473	+	3.59631i	−0.740882	+	0.872233i	0.254614	+	0.967043i	$0.418052\pi$
$18$	7.68469	+	2.58927i	1.81130	+	0.610297i
$19$	4.22025	+	1.95250i	0.968193	+	0.447934i	0.839266	−	0.543721i	$-0.182985\pi$
$19$	4.22025	+	1.95250i	0.968193	+	0.447934i	0.128926	+	0.991654i	$0.458847\pi$
$20$	−1.19973	−	2.26293i	−0.268268	−	0.506007i
$21$	−1.33098	+	0.292971i	−0.290444	+	0.0639316i
$22$	−1.98672	+	4.98630i	−0.423571	+	1.06308i
$23$	−3.34811	+	1.12811i	−0.698130	+	0.235227i	−0.645916	−	0.763408i	$-0.723524\pi$
$23$	−3.34811	+	1.12811i	−0.698130	+	0.235227i	−0.0522141	+	0.998636i	$0.516628\pi$
$24$	24.2819	+	2.64081i	4.95651	+	0.539053i
$25$	−0.259488	+	4.78597i	−0.0518975	+	0.957193i
$26$	−0.0390017	−	0.719343i	−0.00764885	−	0.141075i
$27$	0.155460	−	0.0169073i	0.0299182	−	0.00325380i
$28$	−2.85798	+	1.32224i	−0.540107	+	0.249880i
$29$	−4.87493	−	3.70583i	−0.905252	−	0.688155i	0.0452161	−	0.998977i	$-0.485602\pi$
$29$	−4.87493	−	3.70583i	−0.905252	−	0.688155i	−0.950468	+	0.310823i	$0.899395\pi$
$30$	2.43748	+	1.85292i	0.445021	+	0.338296i
$31$	0.386926	−	0.179011i	0.0694940	−	0.0321514i	−0.384834	−	0.922986i	$-0.625741\pi$
$31$	0.386926	−	0.179011i	0.0694940	−	0.0321514i	0.454328	+	0.890834i	$0.349879\pi$
$32$	25.1895	−	2.73952i	4.45291	−	0.484283i
$33$	−0.256316	−	4.72747i	−0.0446189	−	0.822946i
$34$	0.705614	−	13.0143i	0.121012	−	2.23193i
$35$	−0.253012	−	0.0275168i	−0.0427669	−	0.00465118i
$36$	−15.6620	+	5.27715i	−2.61034	+	0.879525i
$37$	−3.25905	+	8.17960i	−0.535785	+	1.34472i	0.373147	+	0.927772i	$0.378279\pi$
$37$	−3.25905	+	8.17960i	−0.535785	+	1.34472i	−0.908931	+	0.416946i	$0.863100\pi$
$38$	−12.5438	+	2.76110i	−2.03488	+	0.447910i
$39$	0.297639	+	0.561407i	0.0476604	+	0.0898971i
$40$	4.13968	+	1.91522i	0.654540	+	0.302823i
$41$	3.15602	+	1.06339i	0.492887	+	0.166073i	0.554759	−	0.832011i	$-0.312810\pi$
$41$	3.15602	+	1.06339i	0.492887	+	0.166073i	−0.0618719	+	0.998084i	$0.519707\pi$
$42$	2.43701	−	2.86908i	0.376040	−	0.442708i
$43$	3.43733	+	2.06817i	0.524188	+	0.315393i	0.752938	−	0.658092i	$-0.228636\pi$
$43$	3.43733	+	2.06817i	0.524188	+	0.315393i	−0.228750	+	0.973485i	$0.573464\pi$
$44$	−2.92661	−	10.5407i	−0.441204	−	1.58907i
$45$	−1.30450	−	0.287142i	−0.194463	−	0.0428046i
$46$	5.47654	−	8.07730i	0.807472	−	1.19093i
$47$	1.40614	+	1.33196i	0.205106	+	0.194287i	0.783357	−	0.621572i	$-0.213506\pi$
$47$	1.40614	+	1.33196i	0.205106	+	0.194287i	−0.578251	+	0.815859i	$0.696264\pi$
$48$	−34.3041	+	20.6401i	−4.95137	+	2.97914i
$49$	1.08185	−	6.59900i	0.154550	−	0.942715i
$50$	−7.42956	−	10.9578i	−1.05070	−	1.54966i
$51$	4.25514	+	10.6796i	0.595839	+	1.49544i
$52$	0.950515	+	1.11903i	0.131813	+	0.155182i
$53$	−1.36486	−	8.32531i	−0.187479	−	1.14357i	−0.898034	−	0.439927i	$-0.855004\pi$
$53$	−1.36486	−	8.32531i	−0.187479	−	1.14357i	0.710555	−	0.703642i	$-0.248444\pi$
$54$	−0.313583	+	0.297042i	−0.0426733	+	0.0404223i
$55$	0.236529	−	0.851900i	0.0318936	−	0.114870i
$56$	2.62679	−	4.95466i	0.351020	−	0.662094i
$57$	9.01903	−	6.85609i	1.19460	−	0.908111i
$58$	16.9142			2.22095
$59$	6.86593	+	3.44368i	0.893868	+	0.448329i
$59$	6.86593	+	3.44368i	0.893868	+	0.448329i
$60$	−6.24020			−0.805607
$61$	−0.900340	+	0.684420i	−0.115277	+	0.0876310i	−0.661224	−	0.750188i	$-0.729963\pi$
$61$	−0.900340	+	0.684420i	−0.115277	+	0.0876310i	0.545948	+	0.837819i	$0.316170\pi$
$62$	−0.551592	+	1.04041i	−0.0700523	+	0.132133i
$63$	−0.439344	+	1.58238i	−0.0553522	+	0.199361i
$64$	−26.9511	+	25.5294i	−3.36889	+	3.19118i
$65$	0.0191975	+	0.117099i	0.00238116	+	0.0145244i
$66$	8.46598	+	9.96693i	1.04209	+	1.22684i
$67$	−1.70447	−	4.27791i	−0.208235	−	0.522630i	0.787349	−	0.616508i	$-0.211453\pi$
$67$	−1.70447	−	4.27791i	−0.208235	−	0.522630i	−0.995584	+	0.0938778i	$0.970074\pi$
$68$	14.9069	+	21.9860i	1.80773	+	2.66620i
$69$	−1.39258	+	8.49438i	−0.167647	+	1.02260i
$70$	0.602354	−	0.362424i	0.0719951	−	0.0433180i
$71$	−1.83446	−	1.73769i	−0.217710	−	0.206226i	0.571070	−	0.820901i	$-0.306528\pi$
$71$	−1.83446	−	1.73769i	−0.217710	−	0.206226i	−0.788780	+	0.614675i	$0.789287\pi$
$72$	16.5170	−	24.3608i	1.94655	−	2.87094i
$73$	−10.5528	−	2.32285i	−1.23511	−	0.271869i	−0.451021	−	0.892513i	$-0.648940\pi$
$73$	−10.5528	−	2.32285i	−1.23511	−	0.271869i	−0.784092	+	0.620644i	$0.786871\pi$
$74$	−6.50647	−	23.4342i	−0.756361	−	2.72417i
$75$	10.0059	+	6.02034i	1.15538	+	0.695170i
$76$	16.9469	−	19.9514i	1.94394	−	2.28858i
$77$	−1.03011	−	0.347083i	−0.117391	−	0.0395538i
$78$	−1.59293	−	0.736967i	−0.180364	−	0.0834451i
$79$	1.15299	+	2.17477i	0.129721	+	0.244680i	0.939861	−	0.341556i	$-0.110954\pi$
$79$	1.15299	+	2.17477i	0.129721	+	0.244680i	−0.810140	+	0.586236i	$0.800609\pi$
$80$	−7.30150	+	1.60718i	−0.816333	+	0.179688i
$81$	3.40099	−	8.53584i	0.377888	−	0.948427i
$82$	−8.71741	+	2.93724i	−0.962677	+	0.324364i
$83$	−8.28172	−	0.900691i	−0.909037	−	0.0988637i	−0.358361	−	0.933583i	$-0.616664\pi$
$83$	−8.28172	−	0.900691i	−0.909037	−	0.0988637i	−0.550676	+	0.834719i	$0.685630\pi$
$84$	−0.415361	+	7.66089i	−0.0453196	+	0.835871i
$85$	0.116227	+	2.14369i	0.0126066	+	0.232515i
$86$	−11.0156	+	1.19802i	−1.18784	+	0.129185i
$87$	−13.5403	+	6.26440i	−1.45167	+	0.671614i
$88$	15.5090	+	11.7897i	1.65327	+	1.25678i
$89$	−10.7195	−	8.14876i	−1.13627	−	0.863766i	−0.144207	−	0.989548i	$-0.546063\pi$
$89$	−10.7195	−	8.14876i	−1.13627	−	0.863766i	−0.992058	+	0.125781i	$0.959856\pi$
$90$	3.34848	−	1.54917i	0.352961	−	0.163297i
$91$	0.145037	−	0.0157737i	0.0152040	−	0.00165353i
$92$	1.07679	+	19.8602i	0.112263	+	2.07057i
$93$	0.0562335	−	1.03717i	0.00583114	−	0.107549i
$94$	−5.31849	−	0.578420i	−0.548560	−	0.0596595i
$95$	2.00491	−	0.675531i	0.205699	−	0.0693081i
$96$	22.8495	−	57.3479i	2.33207	−	5.85305i
$97$	2.50354	−	0.551071i	0.254196	−	0.0559528i	−0.0860442	−	0.996291i	$-0.527423\pi$
$97$	2.50354	−	0.551071i	0.254196	−	0.0559528i	0.340240	+	0.940339i	$0.389492\pi$
$98$	8.65188	+	16.3192i	0.873971	+	1.64848i
$99$	−5.17770	−	2.39546i	−0.520379	−	0.240753i
$100$	25.5697	+	8.61545i	2.55697	+	0.861545i
$101$	−8.69776	+	10.2398i	−0.865460	+	1.01890i	0.134150	+	0.990961i	$0.457170\pi$
$101$	−8.69776	+	10.2398i	−0.865460	+	1.01890i	−0.999610	+	0.0279367i	$0.991106\pi$
$102$	−27.2086	−	16.3709i	−2.69405	−	1.62096i
$103$	−2.91301	−	10.4917i	−0.287028	−	1.03378i	−0.956689	−	0.291113i	$-0.905974\pi$
$103$	−2.91301	−	10.4917i	−0.287028	−	1.03378i	0.669661	−	0.742667i	$-0.266439\pi$
$104$	−2.55356	−	0.562081i	−0.250397	−	0.0551166i
$105$	−0.347971	+	0.513219i	−0.0339585	+	0.0500850i
$106$	16.9177	+	16.0253i	1.64319	+	1.55651i
$107$	12.5150	−	7.53003i	1.20987	−	0.727955i	0.239811	−	0.970820i	$-0.422915\pi$
$107$	12.5150	−	7.53003i	1.20987	−	0.727955i	0.970060	+	0.242864i	$0.0780870\pi$
$108$	0.142420	−	0.868724i	0.0137044	−	0.0835930i
$109$	4.90864	+	7.23970i	0.470163	+	0.693438i	0.986650	−	0.162857i	$-0.0520709\pi$
$109$	4.90864	+	7.23970i	0.470163	+	0.693438i	−0.516487	+	0.856295i	$0.672761\pi$
$110$	0.903912	+	2.26865i	0.0861847	+	0.216307i
$111$	13.8877	+	16.3499i	1.31816	+	1.55186i
$112$	1.48708	+	9.07079i	0.140516	+	0.857109i
$113$	7.28399	−	6.89976i	0.685220	−	0.649075i	−0.263695	−	0.964606i	$-0.584941\pi$
$113$	7.28399	−	6.89976i	0.685220	−	0.649075i	0.948915	+	0.315531i	$0.102183\pi$
$114$	−8.37170	+	30.1522i	−0.784082	+	2.82401i
$115$	−0.752947	+	1.42021i	−0.0702127	+	0.132435i
$116$	−27.4434	+	20.8619i	−2.54806	+	1.93698i
$117$	0.765692			0.0707883
$118$	−20.8541	+	3.90456i	−1.91978	+	0.359444i
$119$	2.63947			0.241960
$120$	8.84683	−	6.72519i	0.807602	−	0.613923i
$121$	−3.38370	+	6.38234i	−0.307609	+	0.580213i
$122$	0.835719	−	3.00999i	0.0756625	−	0.272512i
$123$	5.89066	−	5.57993i	0.531143	−	0.503125i
$124$	−0.388281	−	2.36841i	−0.0348686	−	0.212689i
$125$	2.88448	+	3.39587i	0.257996	+	0.303736i
$126$	−1.67899	−	4.21394i	−0.149576	−	0.375407i
$127$	−9.87131	−	14.5591i	−0.875937	−	1.29191i	−0.955473	−	0.295078i	$-0.904654\pi$
$127$	−9.87131	−	14.5591i	−0.875937	−	1.29191i	0.0795362	−	0.996832i	$-0.474656\pi$
$128$	8.39056	−	51.1801i	0.741627	−	4.52373i
$129$	8.37454	−	5.03880i	0.737338	−	0.443641i
$130$	−0.237956	−	0.225404i	−0.0208701	−	0.0197692i
$131$	−0.103723	+	0.152980i	−0.00906230	+	0.0133659i	−0.832193	−	0.554486i	$-0.812915\pi$
$131$	−0.103723	+	0.152980i	−0.00906230	+	0.0133659i	0.823131	+	0.567852i	$0.192225\pi$
$132$	−26.0292	−	5.72947i	−2.26556	−	0.498686i
$133$	−0.695876	−	2.50632i	−0.0603401	−	0.217325i
$134$	10.8989	+	6.55766i	0.941523	+	0.566495i
$135$	0.0460599	−	0.0542259i	0.00396421	−	0.00466703i
$136$	−44.8285	−	15.1045i	−3.84401	−	1.29520i
$137$	11.0931	+	5.13221i	0.947748	+	0.438475i	0.831982	−	0.554802i	$-0.187206\pi$
$137$	11.0931	+	5.13221i	0.947748	+	0.438475i	0.115765	+	0.993277i	$0.463068\pi$
$138$	−11.1369	−	21.0064i	−0.948035	−	1.78818i
$139$	−19.0817	+	4.20020i	−1.61849	+	0.356257i	−0.929589	−	0.368598i	$-0.879838\pi$
$139$	−19.0817	+	4.20020i	−1.61849	+	0.356257i	−0.688902	+	0.724855i	$0.741907\pi$
$140$	−0.530309	+	1.33097i	−0.0448193	+	0.112488i
$141$	4.47181	−	1.50673i	0.376594	−	0.126889i
$142$	6.93856	+	0.754614i	0.582271	+	0.0633258i
$143$	−0.0274385	+	0.506074i	−0.00229452	+	0.0423200i
$144$	2.61178	+	48.1714i	0.217648	+	4.01428i
$145$	−2.76975	+	0.301228i	−0.230015	+	0.0250156i
$146$	27.0878	−	12.5321i	2.24180	−	1.03717i
$147$	−12.9700	−	9.85957i	−1.06975	−	0.813204i
$148$	39.4604	+	29.9970i	3.24362	+	2.46574i
$149$	−4.77405	+	2.20871i	−0.391106	+	0.180945i	−0.605579	−	0.795785i	$-0.707059\pi$
$149$	−4.77405	+	2.20871i	−0.391106	+	0.180945i	0.214474	+	0.976730i	$0.431196\pi$
$150$	−32.0658	+	3.48737i	−2.61816	+	0.284742i
$151$	−0.295991	−	5.45922i	−0.0240874	−	0.444265i	−0.985556	−	0.169350i	$-0.945833\pi$
$151$	−0.295991	−	5.45922i	−0.0240874	−	0.444265i	0.961469	−	0.274915i	$-0.0886497\pi$
$152$	−2.52383	+	46.5493i	−0.204710	+	3.77565i
$153$	13.7716	+	1.49775i	1.11337	+	0.121086i
$154$	2.84531	−	0.958697i	0.229282	−	0.0772540i
$155$	0.0717957	−	0.180194i	0.00576677	−	0.0144735i
$156$	3.49351	−	0.768979i	0.279704	−	0.0615676i
$157$	−3.99154	−	7.52885i	−0.318560	−	0.600867i	0.671583	−	0.740929i	$-0.265615\pi$
$157$	−3.99154	−	7.52885i	−0.318560	−	0.600867i	−0.990143	+	0.140062i	$0.955270\pi$
$158$	−6.17065	−	2.85485i	−0.490910	−	0.227119i
$159$	−19.4782	−	6.56297i	−1.54472	−	0.520478i
$160$	7.46319	−	8.78635i	0.590017	−	0.694622i
$161$	1.69342	+	1.01890i	0.133461	+	0.0803005i
$162$	6.78984	+	24.4548i	0.533460	+	1.92135i
$163$	4.77394	+	1.05082i	0.373924	+	0.0823069i	0.397957	−	0.917404i	$-0.369719\pi$
$163$	4.77394	+	1.05082i	0.373924	+	0.0823069i	−0.0240324	+	0.999711i	$0.507651\pi$
$164$	10.5213	−	15.5177i	0.821572	−	1.21173i
$165$	−1.56383	−	1.48134i	−0.121744	−	0.115322i
$166$	19.7165	−	11.8630i	1.53030	−	0.920750i
$167$	2.13245	−	13.0074i	0.165014	−	1.00654i	−0.766343	−	0.642432i	$-0.777926\pi$
$167$	2.13245	−	13.0074i	0.165014	−	1.00654i	0.931357	−	0.364108i	$-0.118626\pi$
$168$	−7.66742	−	11.3086i	−0.591554	−	0.872477i
$169$	4.78662	+	12.0135i	0.368201	+	0.924116i
$170$	−3.83893	−	4.51954i	−0.294432	−	0.346633i
$171$	−2.20859	−	13.4718i	−0.168895	−	1.03021i
$172$	16.3952	−	15.5303i	1.25012	−	1.18418i
$173$	−3.68273	+	13.2640i	−0.279993	+	1.00844i	0.681094	+	0.732196i	$0.261505\pi$
$173$	−3.68273	+	13.2640i	−0.279993	+	1.00844i	−0.961087	+	0.276247i	$0.910909\pi$
$174$	19.3027	−	36.4087i	1.46333	−	2.76014i
$175$	2.13441	−	1.62253i	0.161346	−	0.122652i
$176$	−31.9318			−2.40695
$177$	15.2482	−	10.8493i	1.14612	−	0.815482i
$178$	37.1928			2.78772
$179$	−3.76889	+	2.86504i	−0.281700	+	0.214143i	−0.736477	−	0.676462i	$-0.763512\pi$
$179$	−3.76889	+	2.86504i	−0.281700	+	0.214143i	0.454777	+	0.890605i	$0.349719\pi$
$180$	−3.52218	+	6.64354i	−0.262528	+	0.495181i
$181$	−5.11465	+	18.4213i	−0.380169	+	1.36925i	0.487942	+	0.872876i	$0.337748\pi$
$181$	−5.11465	+	18.4213i	−0.380169	+	1.36925i	−0.868111	+	0.496370i	$0.834666\pi$
$182$	−0.292559	+	0.277127i	−0.0216859	+	0.0205420i
$183$	0.445772	+	2.71909i	0.0329524	+	0.201001i
$184$	−22.9303	−	26.9956i	−1.69044	−	1.99014i
$185$	1.48279	+	3.72153i	0.109017	+	0.273612i
$186$	1.61006	+	2.37466i	0.118055	+	0.174118i
$187$	−1.48343	+	9.04849i	−0.108479	+	0.661691i
$188$	9.34268	−	5.62131i	0.681385	−	0.409976i
$189$	−0.0635055	−	0.0601556i	−0.00461935	−	0.00437568i
$190$	−3.27944	+	4.83682i	−0.237916	+	0.350900i
$191$	18.1216	+	3.98886i	1.31123	+	0.288624i	0.814947	−	0.579536i	$-0.196766\pi$
$191$	18.1216	+	3.98886i	1.31123	+	0.288624i	0.496285	+	0.868160i	$0.334697\pi$
$192$	24.1965	+	87.1479i	1.74623	+	6.28936i
$193$	2.66195	+	1.60164i	0.191611	+	0.115289i	0.608127	−	0.793840i	$-0.291921\pi$
$193$	2.66195	+	1.60164i	0.191611	+	0.115289i	−0.416516	+	0.909129i	$0.636749\pi$
$194$	−4.58396	+	5.39665i	−0.329109	+	0.387457i
$195$	0.273971	+	0.0923114i	0.0196194	+	0.00661056i
$196$	−34.1657	−	15.8067i	−2.44041	−	1.12905i
$197$	3.01537	+	5.68760i	0.214837	+	0.405225i	0.967384	−	0.253313i	$-0.0815202\pi$
$197$	3.01537	+	5.68760i	0.214837	+	0.405225i	−0.752548	+	0.658538i	$0.771175\pi$
$198$	15.3896	−	3.38751i	1.09369	−	0.240740i
$199$	4.71187	−	11.8259i	0.334016	−	0.838316i	−0.662030	−	0.749477i	$-0.730305\pi$
$199$	4.71187	−	11.8259i	0.334016	−	0.838316i	0.996046	−	0.0888392i	$-0.0283157\pi$
$200$	−45.5356	+	15.3427i	−3.21986	+	1.08490i
$201$	−11.1536	−	1.21302i	−0.786712	−	0.0855600i
$202$	2.00910	−	37.0557i	0.141360	−	2.60723i
$203$	0.185447	+	3.42037i	0.0130158	+	0.240063i
$204$	64.3378	−	6.99716i	4.50455	−	0.489899i
$205$	1.37519	−	0.636229i	0.0960471	−	0.0444361i
$206$	23.9433	+	18.2012i	1.66821	+	1.26814i
$207$	8.25740	+	6.27711i	0.573929	+	0.436290i
$208$	3.88961	−	1.79952i	0.269696	−	0.124775i
$209$	8.98314	−	0.976975i	0.621377	−	0.0675788i
$210$	−0.0927242	−	1.71020i	−0.00639858	−	0.118015i
$211$	1.38963	−	25.6302i	0.0956662	−	1.76446i	−0.419864	−	0.907587i	$-0.637922\pi$
$211$	1.38963	−	25.6302i	0.0956662	−	1.76446i	0.515530	−	0.856872i	$-0.327595\pi$
$212$	−47.2146	−	5.13489i	−3.24271	−	0.352666i
$213$	−5.83397	+	1.96569i	−0.399737	+	0.134687i
$214$	−14.9326	+	37.4779i	−1.02077	+	2.56194i
$215$	1.78249	−	0.392356i	0.121565	−	0.0267584i
$216$	0.734329	+	1.38509i	0.0499648	+	0.0942435i
$217$	−0.216439	−	0.100135i	−0.0146928	−	0.00679762i
$218$	−22.8956	−	7.71441i	−1.55068	−	0.522486i
$219$	−17.0430	+	20.0646i	−1.15166	+	1.35584i
$220$	−4.26474	−	2.56601i	−0.287529	−	0.173000i
$221$	−0.329234	−	1.18579i	−0.0221467	−	0.0797652i
$222$	−57.8684	−	12.7378i	−3.88387	−	0.854905i
$223$	−11.8028	+	17.4078i	−0.790372	+	1.16571i	0.192478	+	0.981301i	$0.438348\pi$
$223$	−11.8028	+	17.4078i	−0.790372	+	1.16571i	−0.982849	+	0.184410i	$0.940963\pi$
$224$	−10.2899	−	9.74715i	−0.687526	−	0.651259i
$225$	12.0571	−	7.25454i	0.803809	−	0.483636i
$226$	−4.48346	+	27.3479i	−0.298236	+	1.81916i
$227$	−0.391450	−	0.577346i	−0.0259815	−	0.0383198i	0.814476	−	0.580197i	$-0.197024\pi$
$227$	−0.391450	−	0.577346i	−0.0259815	−	0.0383198i	−0.840458	+	0.541877i	$0.817714\pi$
$228$	−23.6064	−	59.2476i	−1.56337	−	3.92377i
$229$	5.80508	+	6.83426i	0.383610	+	0.451621i	0.919748	−	0.392510i	$-0.128393\pi$
$229$	5.80508	+	6.83426i	0.383610	+	0.451621i	−0.536138	+	0.844131i	$0.680117\pi$
$230$	−0.718320	−	4.38156i	−0.0473646	−	0.288911i
$231$	−1.92268	+	1.82126i	−0.126503	+	0.119830i
$232$	16.4236	−	59.1526i	1.07826	−	3.88356i
$233$	5.33325	−	10.0596i	0.349393	−	0.659025i	−0.645069	−	0.764125i	$-0.723171\pi$
$233$	5.33325	−	10.0596i	0.349393	−	0.659025i	0.994462	+	0.105099i	$0.0335161\pi$
$234$	−1.68371	+	1.27992i	−0.110067	+	0.0836710i
$235$	0.881215			0.0574842
$236$	29.0200	−	32.0566i	1.88904	−	2.08670i
$237$	5.99708			0.389553
$238$	−5.80401	+	4.41209i	−0.376218	+	0.285993i
$239$	−3.17436	+	5.98747i	−0.205332	+	0.387298i	−0.964695	−	0.263370i	$-0.915166\pi$
$239$	−3.17436	+	5.98747i	−0.205332	+	0.387298i	0.759363	+	0.650668i	$0.225511\pi$
$240$	−4.87300	+	17.5510i	−0.314551	+	1.13291i
$241$	−8.73229	+	8.27166i	−0.562496	+	0.532825i	−0.915247	−	0.402893i	$-0.868005\pi$
$241$	−8.73229	+	8.27166i	−0.562496	+	0.532825i	0.352751	+	0.935717i	$0.385246\pi$
$242$	−3.22809	−	19.6905i	−0.207510	−	1.26575i
$243$	−14.1889	−	16.7044i	−0.910215	−	1.07159i
$244$	2.35655	+	5.91449i	0.150863	+	0.378636i
$245$	−1.70739	−	2.51822i	−0.109081	−	0.160883i
$246$	−3.62584	+	22.1166i	−0.231175	+	1.41010i
$247$	−1.03918	+	0.625252i	−0.0661213	+	0.0397839i
$248$	3.10295	+	2.93927i	0.197037	+	0.186644i
$249$	−11.3899	+	16.7989i	−0.721808	+	1.06459i
$250$	−12.0193	−	2.64564i	−0.760166	−	0.167325i
$251$	2.39913	+	8.64089i	0.151432	+	0.545408i	0.999870	+	0.0161139i	$0.00512943\pi$
$251$	2.39913	+	8.64089i	0.151432	+	0.545408i	−0.848438	+	0.529294i	$0.822457\pi$
$252$	7.92161	+	4.76627i	0.499015	+	0.300247i
$253$	−4.44468	+	5.23268i	−0.279434	+	0.328976i
$254$	46.0431	+	15.5137i	2.88900	+	0.973418i
$255$	4.74702	+	2.19621i	0.297270	+	0.137532i
$256$	32.3243	+	60.9700i	2.02027	+	3.81063i
$257$	10.7130	−	2.35810i	0.668255	−	0.147094i	0.132130	−	0.991232i	$-0.457818\pi$
$257$	10.7130	−	2.35810i	0.668255	−	0.147094i	0.536126	+	0.844138i	$0.319887\pi$
$258$	−9.99228	+	25.0787i	−0.622092	+	1.56133i
$259$	4.66749	−	1.57266i	0.290024	−	0.0977203i
$260$	0.664096	+	0.0722248i	0.0411855	+	0.00447919i
$261$	−0.973291	+	17.9513i	−0.0602452	+	1.11116i
$262$	−0.0276391	−	0.509773i	−0.00170755	−	0.0314939i
$263$	−17.2455	+	1.87556i	−1.06340	+	0.115652i	−0.623056	−	0.782177i	$-0.714109\pi$
$263$	−17.2455	+	1.87556i	−1.06340	+	0.115652i	−0.440345	+	0.897829i	$0.645144\pi$
$264$	43.0768	−	19.9295i	2.65119	−	1.22657i
$265$	−3.05571	−	2.32289i	−0.187711	−	0.142694i
$266$	5.71971	+	4.34801i	0.350698	+	0.266594i
$267$	−29.7738	+	13.7748i	−1.82212	+	0.843005i
$268$	−25.7717	+	2.80284i	−1.57426	+	0.171211i
$269$	−1.17735	−	21.7149i	−0.0717843	−	1.32398i	−0.783445	−	0.621461i	$-0.786540\pi$
$269$	−1.17735	−	21.7149i	−0.0717843	−	1.32398i	0.711661	−	0.702523i	$-0.247943\pi$
$270$	−0.0106394	+	0.196232i	−0.000647494	+	0.0119423i
$271$	20.6243	+	2.24302i	1.25283	+	0.136254i	0.710372	−	0.703826i	$-0.248527\pi$
$271$	20.6243	+	2.24302i	1.25283	+	0.136254i	0.542462	+	0.840080i	$0.317492\pi$
$272$	73.4779	−	24.7576i	4.45525	−	1.50115i
$273$	0.131564	−	0.330200i	0.00796259	−	0.0199846i
$274$	−32.9719	+	7.25767i	−1.99191	+	0.438452i
$275$	4.36272	+	8.22897i	0.263082	+	0.496225i
$276$	43.9788	+	20.3468i	2.64721	+	1.22473i
$277$	3.61404	+	1.21771i	0.217147	+	0.0731652i	0.425772	−	0.904830i	$-0.360002\pi$
$277$	3.61404	+	1.21771i	0.217147	+	0.0731652i	−0.208626	+	0.977996i	$0.566899\pi$
$278$	34.9384	−	41.1327i	2.09547	−	2.46697i
$279$	−1.07246	−	0.645280i	−0.0642067	−	0.0386319i
$280$	−0.682590	−	2.45847i	−0.0407926	−	0.146922i
$281$	12.8386	+	2.82598i	0.765885	+	0.168584i	0.580698	−	0.814119i	$-0.302780\pi$
$281$	12.8386	+	2.82598i	0.765885	+	0.168584i	0.185187	+	0.982703i	$0.440711\pi$
$282$	−7.31458	+	10.7882i	−0.435577	+	0.642428i
$283$	−6.42058	−	6.08189i	−0.381664	−	0.361531i	0.472685	−	0.881232i	$-0.343285\pi$
$283$	−6.42058	−	6.08189i	−0.381664	−	0.361531i	−0.854348	+	0.519701i	$0.826044\pi$
$284$	−12.1886	+	7.33362i	−0.723259	+	0.435170i
$285$	0.833902	−	5.08658i	0.0493961	−	0.301303i
$286$	−0.785610	−	1.15869i	−0.0464541	−	0.0685146i
$287$	−0.689541	−	1.73062i	−0.0407023	−	0.102155i
$288$	−48.1576	−	56.6955i	−2.83771	−	3.34081i
$289$	−0.851755	−	5.19548i	−0.0501033	−	0.305616i
$290$	5.58696	−	5.29225i	0.328077	−	0.310771i
$291$	1.67086	−	6.01788i	0.0979473	−	0.352774i
$292$	−28.4929	+	53.7434i	−1.66742	+	3.14509i
$293$	−9.26205	+	7.04083i	−0.541095	+	0.411329i	−0.839703	−	0.543046i	$-0.817271\pi$
$293$	−9.26205	+	7.04083i	−0.541095	+	0.411329i	0.298608	+	0.954376i	$0.403478\pi$
$294$	45.0014			2.62453
$295$	3.34538	−	1.01078i	0.194775	−	0.0588496i
$296$	−88.2719			−5.13070
$297$	0.241914	−	0.183898i	0.0140373	−	0.0106708i
$298$	6.80577	−	12.8370i	0.394248	−	0.743630i
$299$	0.246517	−	0.887872i	0.0142564	−	0.0513470i
$300$	47.7256	−	45.2081i	2.75544	−	2.61009i
$301$	−0.363036	−	2.21442i	−0.0209250	−	0.127637i
$302$	9.77642	+	11.5097i	0.562570	+	0.662308i
$303$	12.1157	+	30.4081i	0.696028	+	1.74690i
$304$	−42.8806	−	63.2442i	−2.45937	−	3.62730i
$305$	−0.0832456	+	0.507776i	−0.00476663	+	0.0290752i
$306$	−32.7865	+	19.7270i	−1.87428	+	1.12772i
$307$	6.56327	+	6.21706i	0.374586	+	0.354827i	0.851714	−	0.524007i	$-0.175564\pi$
$307$	6.56327	+	6.21706i	0.374586	+	0.354827i	−0.477128	+	0.878834i	$0.658322\pi$
$308$	−3.43407	+	5.06488i	−0.195675	+	0.288598i
$309$	−25.9083	−	5.70284i	−1.47387	−	0.324423i
$310$	0.143335	+	0.516246i	0.00814088	+	0.0293208i
$311$	3.65309	+	2.19799i	0.207148	+	0.124637i	0.615348	−	0.788256i	$-0.289016\pi$
$311$	3.65309	+	2.19799i	0.207148	+	0.124637i	−0.408200	+	0.912893i	$0.633843\pi$
$312$	−4.12405	+	4.85521i	−0.233478	+	0.274872i
$313$	−9.74534	−	3.28359i	−0.550839	−	0.185599i	0.0300992	−	0.999547i	$-0.490418\pi$
$313$	−9.74534	−	3.28359i	−0.550839	−	0.185599i	−0.580938	+	0.813948i	$0.697314\pi$
$314$	21.3622	+	9.88322i	1.20554	+	0.557743i
$315$	0.349984	+	0.660141i	0.0197194	+	0.0371947i
$316$	13.5331	−	2.97885i	0.761294	−	0.167573i
$317$	9.25431	−	23.2266i	0.519774	−	1.30453i	−0.401586	−	0.915821i	$-0.631541\pi$
$317$	9.25431	−	23.2266i	0.519774	−	1.30453i	0.921359	−	0.388712i	$-0.127080\pi$
$318$	53.8018	−	18.1279i	3.01706	−	1.01656i
$319$	−11.8298	−	1.28657i	−0.662341	−	0.0720339i
$320$	−0.914410	+	16.8653i	−0.0511171	+	0.942799i
$321$	−1.92651	−	35.5325i	−0.107528	−	1.98323i
$322$	−5.42690	+	0.590211i	−0.302429	+	0.0328912i
$323$	−19.9135	+	9.21298i	−1.10802	+	0.512624i
$324$	−41.1789	−	31.3034i	−2.28772	−	1.73908i
$325$	−0.995168	−	0.756507i	−0.0552020	−	0.0419635i
$326$	−12.2541	+	5.66936i	−0.678693	+	0.313997i
$327$	21.1856	−	2.30407i	1.17157	−	0.127415i
$328$	1.80757	+	33.3386i	0.0998062	+	1.84082i
$329$	0.0586556	−	1.08184i	0.00323379	−	0.0596437i
$330$	5.91493	+	0.643287i	0.325606	+	0.0354118i
$331$	3.83599	−	1.29250i	0.210845	−	0.0710420i	−0.211897	−	0.977292i	$-0.567964\pi$
$331$	3.83599	−	1.29250i	0.210845	−	0.0710420i	0.422742	+	0.906250i	$0.361068\pi$
$332$	−17.3583	+	43.5661i	−0.952661	+	2.39100i
$333$	25.2454	−	5.55693i	1.38344	−	0.304518i
$334$	17.0538	+	32.1669i	0.933142	+	1.76009i
$335$	−1.90151	−	0.879731i	−0.103890	−	0.0480649i
$336$	21.2224	+	7.15065i	1.15777	+	0.390100i
$337$	10.4610	−	12.3157i	0.569849	−	0.670878i	−0.399452	−	0.916754i	$-0.630800\pi$
$337$	10.4610	−	12.3157i	0.569849	−	0.670878i	0.969301	+	0.245876i	$0.0790755\pi$
$338$	−30.6070	−	18.4156i	−1.66480	−	1.00168i
$339$	−6.53951	−	23.5532i	−0.355178	−	1.27923i
$340$	11.8030	+	2.59805i	0.640110	+	0.140899i
$341$	0.464921	−	0.685707i	0.0251769	−	0.0371331i
$342$	27.3758	+	25.9317i	1.48031	+	1.40223i
$343$	−6.56034	+	3.94722i	−0.354225	+	0.213130i
$344$	−6.50635	+	39.6870i	−0.350799	+	2.13978i
$345$	2.19780	+	3.24151i	0.118325	+	0.174517i
$346$	−14.0738	−	35.3226i	−0.756613	−	1.89896i
$347$	−2.52185	−	2.96896i	−0.135380	−	0.159382i	0.690294	−	0.723529i	$-0.257481\pi$
$347$	−2.52185	−	2.96896i	−0.135380	−	0.159382i	−0.825675	+	0.564147i	$0.809205\pi$
$348$	13.5877	+	82.8811i	0.728375	+	4.44289i
$349$	4.15856	−	3.93920i	0.222603	−	0.210860i	−0.568268	−	0.822843i	$-0.692386\pi$
$349$	4.15856	−	3.93920i	0.222603	−	0.210860i	0.790871	+	0.611983i	$0.209628\pi$
$350$	−1.98121	+	7.13569i	−0.105900	+	0.381419i
$351$	−0.0191039	+	0.0360337i	−0.00101969	+	0.00192334i
$352$	39.1978	−	29.7974i	2.08925	−	1.58821i
$353$	−8.94551			−0.476121			−0.238061	−	0.971250i	$-0.576512\pi$
$353$	−8.94551			−0.476121			−0.238061	+	0.971250i	$0.576512\pi$
$354$	−15.3942	+	49.3454i	−0.818190	+	2.62268i
$355$	−1.14964			−0.0610167
$356$	−60.3455	+	45.8734i	−3.19830	+	2.43129i
$357$	3.01218	−	5.68158i	0.159422	−	0.300701i
$358$	3.49839	−	12.6001i	0.184895	−	0.665933i
$359$	14.8703	−	14.0859i	0.784826	−	0.743426i	−0.186171	−	0.982517i	$-0.559608\pi$
$359$	14.8703	−	14.0859i	0.784826	−	0.743426i	0.970997	+	0.239091i	$0.0768494\pi$
$360$	−2.16642	−	13.2146i	−0.114180	−	0.696469i
$361$	1.69796	+	1.99899i	0.0893661	+	0.105210i
$362$	−19.5460	−	49.0568i	−1.02732	−	2.57837i
$363$	9.87678	+	14.5672i	0.518397	+	0.764578i
$364$	0.132872	−	0.810480i	0.00696436	−	0.0424807i
$365$	−4.21250	+	2.53458i	−0.220492	+	0.132666i
$366$	−5.52541	−	5.23395i	−0.288818	−	0.273583i
$367$	17.7943	−	26.2447i	0.928857	−	1.36996i	−0.000190189	−	1.00000i	$-0.500061\pi$
$367$	17.7943	−	26.2447i	0.928857	−	1.36996i	0.929047	−	0.369961i	$-0.120629\pi$
$368$	56.6989	+	12.4804i	2.95563	+	0.650584i
$369$	−2.61570	−	9.42091i	−0.136168	−	0.490433i
$370$	−9.48140	−	5.70477i	−0.492915	−	0.296577i
$371$	−3.05513	+	3.59677i	−0.158614	+	0.186735i
$372$	−5.54122	−	1.86705i	−0.287299	−	0.0968022i
$373$	16.4416	+	7.60669i	0.851314	+	0.393860i	0.796501	−	0.604637i	$-0.206682\pi$
$373$	16.4416	+	7.60669i	0.851314	+	0.393860i	0.0548126	+	0.998497i	$0.482544\pi$
$374$	−11.8634	−	22.3767i	−0.613440	−	1.15707i
$375$	10.6016	−	2.33358i	0.547463	−	0.120506i
$376$	−7.18707	+	18.0382i	−0.370645	+	0.930249i
$377$	1.51349	−	0.509954i	0.0779487	−	0.0262640i
$378$	0.240200	+	0.0261233i	0.0123545	+	0.00134364i
$379$	0.733744	−	13.5331i	0.0376899	−	0.695149i	−0.917243	−	0.398328i	$-0.869591\pi$
$379$	0.733744	−	13.5331i	0.0376899	−	0.695149i	0.954933	−	0.296821i	$-0.0959266\pi$
$380$	−0.644798	−	11.8926i	−0.0330775	−	0.610078i
$381$	−42.6043	+	4.63350i	−2.18269	+	0.237381i
$382$	−46.5159	+	21.5205i	−2.37996	+	1.10109i
$383$	22.4018	+	17.0294i	1.14468	+	0.870161i	0.992982	−	0.118266i	$-0.0377336\pi$
$383$	22.4018	+	17.0294i	1.14468	+	0.870161i	0.151695	+	0.988427i	$0.451527\pi$
$384$	−100.592	−	76.4682i	−5.13333	−	3.90225i
$385$	−0.448852	+	0.207661i	−0.0228756	+	0.0105834i
$386$	−8.53072	+	0.927771i	−0.434202	+	0.0472223i
$387$	−0.637604	−	11.7599i	−0.0324112	−	0.597790i
$388$	0.781283	−	14.4099i	0.0396636	−	0.731553i
$389$	28.5137	+	3.10105i	1.44570	+	0.157230i	0.797077	−	0.603878i	$-0.206379\pi$
$389$	28.5137	+	3.10105i	1.44570	+	0.157230i	0.648626	+	0.761108i	$0.275344\pi$
$390$	−0.756749	+	0.254978i	−0.0383195	+	0.0129113i
$391$	6.17056	−	15.4869i	0.312059	−	0.783208i
$392$	65.4724	−	14.4116i	3.30686	−	0.727894i
$393$	0.210927	+	0.397850i	0.0106398	+	0.0200689i
$394$	−16.1379	−	7.46619i	−0.813016	−	0.376141i
$395$	1.06130	+	0.357594i	0.0533998	+	0.0179925i
$396$	−20.7916	+	24.4778i	−1.04482	+	1.23005i
$397$	15.5055	+	9.32933i	0.778197	+	0.468226i	0.848432	−	0.529305i	$-0.177547\pi$
$397$	15.5055	+	9.32933i	0.778197	+	0.468226i	−0.0702345	+	0.997531i	$0.522375\pi$
$398$	9.40692	+	33.8807i	0.471526	+	1.69828i
$399$	−6.18911	−	1.36233i	−0.309843	−	0.0682016i
$400$	44.1990	−	65.1887i	2.20995	−	3.25943i
$401$	−14.0940	−	13.3505i	−0.703821	−	0.666694i	0.249596	−	0.968350i	$-0.419702\pi$
$401$	−14.0940	−	13.3505i	−0.703821	−	0.666694i	−0.953417	+	0.301656i	$0.902461\pi$
$402$	26.5536	−	15.9768i	1.32437	−	0.796849i
$403$	−0.0179888	+	0.109727i	−0.000896084	+	0.00546587i
$404$	42.4445	+	62.6010i	2.11169	+	3.11451i
$405$	−1.54737	−	3.88361i	−0.0768894	−	0.192978i
$406$	−6.12523	−	7.21118i	−0.303990	−	0.357885i
$407$	2.76811	+	16.8847i	0.137210	+	0.836944i
$408$	−83.6717	+	79.2581i	−4.14237	+	3.92386i
$409$	2.52893	−	9.10840i	0.125048	−	0.450381i	−0.874342	−	0.485310i	$-0.838707\pi$
$409$	2.52893	−	9.10840i	0.125048	−	0.450381i	0.999390	+	0.0349289i	$0.0111205\pi$
$410$	−1.96043	+	3.69776i	−0.0968188	+	0.182620i
$411$	23.7069	−	18.0215i	1.16937	−	0.888935i
$412$	−61.2975			−3.01991
$413$	−1.01822	−	4.17428i	−0.0501033	−	0.205403i
$414$	−28.6502			−1.40808
$415$	−3.01735	+	2.29373i	−0.148116	+	0.112595i
$416$	−3.09544	+	5.83862i	−0.151767	+	0.286262i
$417$	−12.7351	+	45.8676i	−0.623639	+	2.24615i
$418$	−18.1202	+	17.1644i	−0.886289	+	0.839537i
$419$	2.41565	+	14.7348i	0.118012	+	0.719842i	0.977855	+	0.209283i	$0.0671130\pi$
$419$	2.41565	+	14.7348i	0.118012	+	0.719842i	−0.859843	+	0.510559i	$0.829439\pi$
$420$	2.25979	+	2.66043i	0.110267	+	0.129816i
$421$	14.2104	+	35.6655i	0.692575	+	1.73823i	0.674366	+	0.738397i	$0.264417\pi$
$421$	14.2104	+	35.6655i	0.692575	+	1.73823i	0.0182089	+	0.999834i	$0.494204\pi$
$422$	39.7874	+	58.6821i	1.93682	+	2.85660i
$423$	0.919925	−	5.61129i	0.0447283	−	0.272830i
$424$	72.4708	−	43.6042i	3.51949	−	2.11761i
$425$	−16.4192	−	15.5530i	−0.796446	−	0.754434i
$426$	9.54268	−	14.0744i	0.462344	−	0.681907i
$427$	0.617838	+	0.135996i	0.0298993	+	0.00658133i
$428$	−21.9969	−	79.2258i	−1.06326	−	3.82952i
$429$	1.05803	+	0.636598i	0.0510824	+	0.0307352i
$430$	−3.26372	+	3.84235i	−0.157391	+	0.185294i
$431$	−20.7188	−	6.98099i	−0.997991	−	0.336262i	−0.227545	−	0.973768i	$-0.573070\pi$
$431$	−20.7188	−	6.98099i	−0.997991	−	0.336262i	−0.770446	+	0.637505i	$0.779966\pi$
$432$	−2.33212	−	1.07896i	−0.112204	−	0.0519113i
$433$	−6.69581	−	12.6296i	−0.321780	−	0.606942i	0.668868	−	0.743381i	$-0.266779\pi$
$433$	−6.69581	−	12.6296i	−0.321780	−	0.606942i	−0.990648	+	0.136439i	$0.956434\pi$
$434$	0.643318	−	0.141605i	0.0308803	−	0.00679726i
$435$	−2.51245	+	6.30577i	−0.120463	+	0.302339i
$436$	46.6630	−	15.7226i	2.23475	−	0.752976i
$437$	−16.3325	−	1.77627i	−0.781291	−	0.0849705i
$438$	3.93677	−	72.6095i	0.188106	−	3.46942i
$439$	−1.01404	−	18.7028i	−0.0483974	−	0.892637i	−0.917434	−	0.397889i	$-0.869743\pi$
$439$	−1.01404	−	18.7028i	−0.0483974	−	0.892637i	0.869036	−	0.494748i	$-0.164740\pi$
$440$	8.81163	−	0.958322i	0.420078	−	0.0456862i
$441$	−17.8176	+	8.24329i	−0.848457	+	0.392538i
$442$	2.70612	+	2.05714i	0.128717	+	0.0978481i
$443$	14.2390	+	10.8242i	0.676517	+	0.514275i	0.886087	−	0.463519i	$-0.153413\pi$
$443$	14.2390	+	10.8242i	0.676517	+	0.514275i	−0.209570	+	0.977794i	$0.567206\pi$
$444$	109.602	−	50.7075i	5.20150	−	2.40647i
$445$	−6.09041	+	0.662372i	−0.288713	+	0.0313994i
$446$	−3.14509	−	58.0079i	−0.148925	−	2.74675i
$447$	−0.693832	+	12.7970i	−0.0328171	+	0.605276i
$448$	20.6441	+	2.24518i	0.975341	+	0.106075i
$449$	−17.6640	+	5.95170i	−0.833616	+	0.280878i	−0.703567	−	0.710629i	$-0.748410\pi$
$449$	−17.6640	+	5.95170i	−0.833616	+	0.280878i	−0.130050	+	0.991507i	$0.541514\pi$
$450$	−14.3863	+	36.1068i	−0.678175	+	1.70209i
$451$	6.32035	−	1.39122i	0.297614	−	0.0655098i
$452$	−26.4564	−	49.9020i	−1.24440	−	2.34719i
$453$	−12.0890	−	5.59298i	−0.567992	−	0.262781i
$454$	1.82586	+	0.615202i	0.0856917	+	0.0288729i
$455$	0.0429719	−	0.0505904i	0.00201455	−	0.00237171i
$456$	97.3194	+	58.5551i	4.55740	+	2.74210i
$457$	9.32995	+	33.6034i	0.436437	+	1.57190i	0.775631	+	0.631187i	$0.217432\pi$
$457$	9.32995	+	33.6034i	0.436437	+	1.57190i	−0.339194	+	0.940716i	$0.610154\pi$
$458$	−24.1890	−	5.32441i	−1.13028	−	0.248793i
$459$	−0.414084	+	0.610728i	−0.0193278	+	0.0285064i
$460$	6.56967	+	6.22312i	0.306312	+	0.290154i
$461$	−28.8377	+	17.3511i	−1.34310	+	0.808119i	−0.991758	−	0.128126i	$-0.959104\pi$
$461$	−28.8377	+	17.3511i	−1.34310	+	0.808119i	−0.351347	+	0.936245i	$0.614276\pi$
$462$	1.18345	−	7.21874i	0.0550592	−	0.335846i
$463$	−12.5141	−	18.4569i	−0.581578	−	0.857764i	0.417116	−	0.908853i	$-0.363041\pi$
$463$	−12.5141	−	18.4569i	−0.581578	−	0.857764i	−0.998694	+	0.0510897i	$0.983731\pi$
$464$	37.2448	+	93.4775i	1.72905	+	4.33958i
$465$	−0.305941	−	0.360182i	−0.0141877	−	0.0167030i
$466$	5.08799	+	31.0353i	0.235696	+	1.43768i
$467$	−11.3029	+	10.7067i	−0.523038	+	0.495448i	−0.903051	−	0.429533i	$-0.858678\pi$
$467$	−11.3029	+	10.7067i	−0.523038	+	0.495448i	0.380013	+	0.924981i	$0.375919\pi$
$468$	1.15317	−	4.15335i	0.0533054	−	0.191989i
$469$	−1.20658	+	2.27586i	−0.0557149	+	0.105089i
$470$	−1.93773	+	1.47303i	−0.0893810	+	0.0679457i
$471$	−20.7614			−0.956634
$472$	−6.59418	+	76.7225i	−0.303522	+	3.53144i
$473$	7.79540			0.358433
$474$	−13.1872	+	10.0246i	−0.605707	+	0.460447i
$475$	−10.4397	+	19.6913i	−0.479006	+	0.903501i
$476$	3.97517	−	14.3173i	0.182202	−	0.656231i
$477$	−17.9813	+	17.0328i	−0.823309	+	0.779880i
$478$	−3.02837	−	18.4723i	−0.138515	−	0.844902i
$479$	−6.25544	−	7.36447i	−0.285818	−	0.336491i	0.600451	−	0.799662i	$-0.294988\pi$
$479$	−6.25544	−	7.36447i	−0.285818	−	0.336491i	−0.886269	+	0.463170i	$0.846712\pi$
$480$	−10.3960	−	26.0919i	−0.474509	−	1.19093i
$481$	−1.28873	−	1.90073i	−0.0587608	−	0.0866657i
$482$	5.37492	−	32.7856i	0.244821	−	1.49334i
$483$	4.12578	−	2.48240i	0.187729	−	0.112953i
$484$	29.5237	+	27.9664i	1.34199	+	1.27120i
$485$	0.654524	−	0.965350i	0.0297204	−	0.0438343i
$486$	59.1232	+	13.0140i	2.68188	+	0.590327i
$487$	4.15232	+	14.9553i	0.188159	+	0.677689i	0.996085	+	0.0884041i	$0.0281767\pi$
$487$	4.15232	+	14.9553i	0.188159	+	0.677689i	−0.807925	+	0.589285i	$0.799410\pi$
$488$	−9.71507	−	5.84536i	−0.439781	−	0.264607i
$489$	7.71001	−	9.07693i	0.348659	−	0.410473i
$490$	7.96386	+	2.68334i	0.359771	+	0.121221i
$491$	18.9172	+	8.75202i	0.853721	+	0.394973i	0.797408	−	0.603440i	$-0.206204\pi$
$491$	18.9172	+	8.75202i	0.853721	+	0.394973i	0.0563121	+	0.998413i	$0.482066\pi$
$492$	−21.3956	−	40.3564i	−0.964589	−	1.81941i
$493$	28.2189	−	6.21145i	1.27092	−	0.279750i
$494$	1.23992	−	3.11196i	0.0557866	−	0.140014i
$495$	−2.45976	+	0.828789i	−0.110558	+	0.0372513i
$496$	−6.96450	−	0.757435i	−0.312715	−	0.0340098i
$497$	−0.0765227	+	1.41138i	−0.00343251	+	0.0633090i
$498$	−3.03509	−	55.9789i	−0.136006	−	2.50848i
$499$	−4.27293	+	0.464710i	−0.191283	+	0.0208033i	−0.203259	−	0.979125i	$-0.565153\pi$
$499$	−4.27293	+	0.464710i	−0.191283	+	0.0208033i	0.0119761	+	0.999928i	$0.496188\pi$
$500$	22.7644	−	10.5320i	1.01806	−	0.471003i
$501$	−25.5654	−	19.4343i	−1.14218	−	0.868260i
$502$	−19.7195	−	14.9904i	−0.880125	−	0.669053i
$503$	−38.1484	+	17.6493i	−1.70095	+	0.786944i	−0.703893	+	0.710306i	$0.748556\pi$
$503$	−38.1484	+	17.6493i	−1.70095	+	0.786944i	−0.997059	+	0.0766376i	$0.975582\pi$
$504$	−16.3673	+	1.78005i	−0.729057	+	0.0792897i
$505$	0.330935	+	6.10373i	0.0147264	+	0.271612i
$506$	1.02668	−	18.9360i	0.0456414	−	0.841806i
$507$	31.3222	+	3.40649i	1.39107	+	0.151288i
$508$	−93.8396	+	31.6183i	−4.16346	+	1.40283i
$509$	1.99509	−	5.00731i	0.0884310	−	0.221945i	−0.878109	−	0.478460i	$-0.841195\pi$
$509$	1.99509	−	5.00731i	0.0884310	−	0.221945i	0.966540	+	0.256515i	$0.0825744\pi$
$510$	−14.1095	+	3.10574i	−0.624781	+	0.137525i
$511$	2.83122	+	5.34025i	0.125246	+	0.236239i
$512$	−78.8556	−	36.4825i	−3.48496	−	1.61231i
$513$	0.689091	+	0.232182i	0.0304241	+	0.0102511i
$514$	−19.6153	+	23.0929i	−0.865193	+	1.01858i
$515$	−4.24492	−	2.55408i	−0.187054	−	0.112546i
$516$	−14.7195	−	53.0148i	−0.647989	−	2.33385i
$517$	3.67574	+	0.809092i	0.161659	+	0.0355838i
$518$	−7.63466	+	11.2603i	−0.335448	+	0.494748i
$519$	24.3486	+	23.0642i	1.06879	+	1.01241i
$520$	−1.01934	+	0.613314i	−0.0447009	+	0.0268956i
$521$	−1.21887	+	7.43479i	−0.0533997	+	0.325724i	0.946595	+	0.322426i	$0.104498\pi$
$521$	−1.21887	+	7.43479i	−0.0533997	+	0.325724i	−0.999995	+	0.00329846i	$0.998950\pi$
$522$	−27.8669	−	41.1006i	−1.21970	−	1.79893i
$523$	−3.55951	−	8.93369i	−0.155646	−	0.390643i	0.830388	−	0.557186i	$-0.188119\pi$
$523$	−3.55951	−	8.93369i	−0.155646	−	0.390643i	−0.986034	+	0.166543i	$0.946740\pi$
$524$	0.673596	+	0.793019i	0.0294262	+	0.0346432i
$525$	−1.05678	−	6.44606i	−0.0461216	−	0.281329i
$526$	34.7865	−	32.9515i	1.51676	−	1.43675i
$527$	−0.538177	+	1.93834i	−0.0234434	+	0.0844353i
$528$	−36.4408	+	68.7347i	−1.58588	+	2.99129i
$529$	−8.37291	+	6.36492i	−0.364039	+	0.276736i
$530$	10.6022			0.460530
$531$	−2.94396	−	22.3574i	−0.127757	−	0.970230i
$532$	−14.6431			−0.634858
$533$	−0.691479	+	0.525649i	−0.0299513	+	0.0227684i
$534$	42.4447	−	80.0593i	1.83676	−	3.46450i
$535$	1.77779	−	6.40303i	0.0768607	−	0.276827i
$536$	33.5163	−	31.7483i	1.44768	−	1.37132i
$537$	1.86604	+	11.3823i	0.0805255	+	0.491184i
$538$	38.8873	+	45.7817i	1.67655	+	1.97379i
$539$	−4.80980	−	12.0717i	−0.207173	−	0.519964i
$540$	−0.224769	−	0.331510i	−0.00967254	−	0.0142659i
$541$	3.90020	−	23.7902i	0.167683	−	1.02282i	−0.760129	−	0.649772i	$-0.774864\pi$
$541$	3.90020	−	23.7902i	0.167683	−	1.02282i	0.927812	−	0.373048i	$-0.121687\pi$
$542$	−49.1007	+	29.5429i	−2.10906	+	1.26898i
$543$	33.8159	+	32.0321i	1.45118	+	1.37463i
$544$	−67.0950	+	98.9577i	−2.87667	+	4.24277i
$545$	3.88659	+	0.855502i	0.166483	+	0.0366457i
$546$	0.262658	+	0.946007i	0.0112407	+	0.0404854i
$547$	10.5455	+	6.34501i	0.450892	+	0.271293i	0.722835	−	0.691020i	$-0.242839\pi$
$547$	10.5455	+	6.34501i	0.450892	+	0.271293i	−0.271943	+	0.962313i	$0.587666\pi$
$548$	44.5455	−	52.4430i	1.90289	−	2.24025i
$549$	3.14645	+	1.06016i	0.134287	+	0.0452466i
$550$	−23.3487	−	10.8023i	−0.995594	−	0.460611i
$551$	−13.3378	−	25.1578i	−0.568211	−	1.07176i
$552$	−84.2775	+	18.5509i	−3.58709	+	0.789578i
$553$	0.509648	−	1.27912i	0.0216724	−	0.0543937i
$554$	−9.98253	+	3.36351i	−0.424117	+	0.142902i
$555$	9.70293	+	1.05526i	0.411867	+	0.0447932i
$556$	−5.95485	+	109.831i	−0.252542	+	4.65786i
$557$	−0.276773	−	5.10478i	−0.0117273	−	0.216297i	−0.998523	−	0.0543278i	$-0.982698\pi$
$557$	−0.276773	−	5.10478i	−0.0117273	−	0.216297i	0.986796	−	0.161969i	$-0.0517844\pi$
$558$	3.43692	−	0.373787i	0.145496	−	0.0158237i
$559$	−0.949556	+	0.439312i	−0.0401620	+	0.0185809i
$560$	3.32933	+	2.53089i	0.140690	+	0.106950i
$561$	17.7844	+	13.5194i	0.750858	+	0.570788i
$562$	−32.9550	+	15.2466i	−1.39012	+	0.643140i
$563$	33.5628	−	3.65018i	1.41450	−	0.153837i	0.631270	−	0.775563i	$-0.282534\pi$
$563$	33.5628	−	3.65018i	1.41450	−	0.153837i	0.783234	+	0.621727i	$0.213569\pi$
$564$	−1.43818	−	26.5256i	−0.0605583	−	1.11693i
$565$	0.247135	−	4.55813i	0.0103970	−	0.191762i
$566$	24.2848	+	2.64113i	1.02077	+	0.111015i
$567$	−4.87077	+	1.64115i	−0.204553	+	0.0689219i
$568$	9.37634	−	23.5328i	0.393422	−	0.987416i
$569$	7.00852	−	1.54269i	0.293812	−	0.0646730i	−0.0656183	−	0.997845i	$-0.520902\pi$
$569$	7.00852	−	1.54269i	0.293812	−	0.0646730i	0.359431	+	0.933172i	$0.382971\pi$
$570$	6.66895	+	12.5790i	0.279332	+	0.526875i
$571$	34.0296	+	15.7438i	1.42409	+	0.658856i	0.972401	−	0.233318i	$-0.0749582\pi$
$571$	34.0296	+	15.7438i	1.42409	+	0.658856i	0.451693	+	0.892174i	$0.350820\pi$
$572$	2.70377	+	0.911008i	0.113050	+	0.0380911i
$573$	29.2667	−	34.4554i	1.22263	−	1.43940i
$574$	4.40913	+	2.65288i	0.184033	+	0.110729i
$575$	−4.53031	−	16.3167i	−0.188927	−	0.680453i
$576$	106.438	+	23.4288i	4.43492	+	0.976200i
$577$	−4.94090	+	7.28728i	−0.205692	+	0.303373i	−0.916517	−	0.399996i	$-0.869012\pi$
$577$	−4.94090	+	7.28728i	−0.205692	+	0.303373i	0.710825	+	0.703369i	$0.248322\pi$
$578$	10.5576	+	10.0007i	0.439140	+	0.415975i
$579$	6.48544	−	3.90216i	0.269526	−	0.162168i
$580$	−2.53743	+	15.4776i	−0.105361	+	0.642673i
$581$	2.61510	+	3.85698i	0.108493	+	0.160014i
$582$	6.38530	+	16.0259i	0.264679	+	0.664294i
$583$	−10.6133	−	12.4949i	−0.439556	−	0.517485i
$584$	−17.5254	−	106.900i	−0.725206	−	4.42356i
$585$	0.252916	−	0.239575i	0.0104568	−	0.00990521i
$586$	8.59728	−	30.9646i	0.355150	−	1.27914i
$587$	−13.7524	+	25.9397i	−0.567622	+	1.07065i	0.419056	+	0.907960i	$0.362361\pi$
$587$	−13.7524	+	25.9397i	−0.567622	+	1.07065i	−0.986678	+	0.162687i	$0.947984\pi$
$588$	−73.0149	+	55.5045i	−3.01108	+	2.28897i
$589$	1.98245			0.0816853
$590$	−5.66666	+	7.81471i	−0.233293	+	0.321726i
$591$	15.6840			0.645153
$592$	115.183	−	87.5600i	4.73400	−	3.59869i
$593$	−11.9254	+	22.4937i	−0.489718	+	0.923707i	0.508324	+	0.861166i	$0.330265\pi$
$593$	−11.9254	+	22.4937i	−0.489718	+	0.923707i	−0.998042	+	0.0625409i	$0.980080\pi$
$594$	−0.224551	+	0.808759i	−0.00921343	+	0.0331838i
$595$	0.871844	−	0.825855i	0.0357421	−	0.0338567i
$596$	4.79076	+	29.2224i	0.196237	+	1.19699i
$597$	−20.0786	−	23.6383i	−0.821762	−	0.967453i
$598$	0.942081	+	2.36444i	0.0385246	+	0.0966893i
$599$	−17.6632	−	26.0512i	−0.721698	−	1.06442i	−0.994741	−	0.102423i	$-0.967341\pi$
$599$	−17.6632	−	26.0512i	−0.721698	−	1.06442i	0.273043	−	0.962002i	$-0.411970\pi$
$600$	−18.9397	+	115.527i	−0.773209	+	4.71637i
$601$	−2.99384	+	1.80133i	−0.122121	+	0.0734778i	−0.575304	−	0.817940i	$-0.695116\pi$
$601$	−2.99384	+	1.80133i	−0.122121	+	0.0734778i	0.453183	+	0.891418i	$0.350289\pi$
$602$	4.49988	+	4.26251i	0.183401	+	0.173727i
$603$	−7.58688	+	11.1898i	−0.308962	+	0.455684i
$604$	−30.0583	−	6.61633i	−1.22305	−	0.269215i
$605$	0.879278	+	3.16687i	0.0357477	+	0.128752i
$606$	−77.4713	−	46.6129i	−3.14706	−	1.89352i
$607$	−3.69432	+	4.34929i	−0.149948	+	0.176532i	−0.832008	−	0.554764i	$-0.812809\pi$
$607$	−3.69432	+	4.34929i	−0.149948	+	0.176532i	0.682060	+	0.731296i	$0.261084\pi$
$608$	111.655	+	37.6209i	4.52820	+	1.52573i
$609$	7.57415	+	3.50418i	0.306920	+	0.141996i
$610$	−0.665739	−	1.25572i	−0.0269550	−	0.0508425i
$611$	−0.493338	+	0.108592i	−0.0199583	+	0.00439316i
$612$	28.8650	−	72.4458i	1.16680	−	2.92845i
$613$	34.0157	−	11.4612i	1.37388	−	0.462915i	0.466984	−	0.884266i	$-0.345340\pi$
$613$	34.0157	−	11.4612i	1.37388	−	0.462915i	0.906898	+	0.421351i	$0.138444\pi$
$614$	−24.8246	−	2.69983i	−1.00184	−	0.108956i
$615$	0.199861	−	3.68622i	0.00805918	−	0.148643i
$616$	−0.589979	−	10.8815i	−0.0237709	−	0.438429i
$617$	4.59512	−	0.499749i	0.184992	−	0.0201191i	−0.0151538	−	0.999885i	$-0.504824\pi$
$617$	4.59512	−	0.499749i	0.184992	−	0.0201191i	0.200146	+	0.979766i	$0.435858\pi$
$618$	66.5033	−	30.7677i	2.67516	−	1.23766i
$619$	28.5385	+	21.6944i	1.14706	+	0.871973i	0.993235	−	0.116125i	$-0.0370474\pi$
$619$	28.5385	+	21.6944i	1.14706	+	0.871973i	0.153826	+	0.988098i	$0.450840\pi$
$620$	−0.869297	−	0.660822i	−0.0349118	−	0.0265393i
$621$	−0.501423	+	0.231983i	−0.0201214	+	0.00930916i
$622$	−11.7070	+	1.27322i	−0.469409	+	0.0510513i
$623$	0.407781	+	7.52107i	0.0163374	+	0.301325i
$624$	0.565292	−	10.4262i	0.0226298	−	0.417382i
$625$	−21.8092	−	2.37189i	−0.872368	−	0.0948757i
$626$	26.9181	−	9.06978i	1.07587	−	0.362501i
$627$	8.14865	−	20.4516i	0.325426	−	0.816757i
$628$	−46.8502	+	10.3125i	−1.86953	+	0.411514i
$629$	−19.4609	−	36.7071i	−0.775955	−	1.46361i
$630$	−1.87307	−	0.866576i	−0.0746250	−	0.0345252i
$631$	−5.22943	−	1.76200i	−0.208180	−	0.0701441i	0.213279	−	0.976991i	$-0.431586\pi$
$631$	−5.22943	−	1.76200i	−0.208180	−	0.0701441i	−0.421460	+	0.906847i	$0.638482\pi$
$632$	−15.9756	+	18.8080i	−0.635477	+	0.748141i
$633$	−53.5845	−	32.2407i	−2.12979	−	1.28145i
$634$	18.4756	+	66.5430i	0.733759	+	2.64276i
$635$	−7.81595	−	1.72042i	−0.310166	−	0.0682728i
$636$	−64.9347	+	95.7716i	−2.57483	+	3.79759i
$637$	1.26618	+	1.19939i	0.0501680	+	0.0475217i
$638$	28.1635	−	16.9454i	1.11500	−	0.670876i
$639$	−1.20014	+	7.32056i	−0.0474770	+	0.289597i
$640$	−13.2421	−	19.5306i	−0.523440	−	0.772016i
$641$	−12.6621	−	31.7796i	−0.500125	−	1.25522i	−0.934974	−	0.354715i	$-0.884578\pi$
$641$	−12.6621	−	31.7796i	−0.500125	−	1.25522i	0.434850	−	0.900503i	$-0.356802\pi$
$642$	63.6318	+	74.9132i	2.51135	+	2.95659i
$643$	−6.94337	−	42.3527i	−0.273820	−	1.67023i	−0.662659	−	0.748922i	$-0.730572\pi$
$643$	−6.94337	−	42.3527i	−0.273820	−	1.67023i	0.388839	−	0.921306i	$-0.372876\pi$
$644$	8.07720	−	7.65113i	0.318286	−	0.301497i
$645$	1.18963	−	4.28465i	0.0468416	−	0.168708i
$646$	28.3882	−	53.5459i	1.11692	−	2.10673i
$647$	−19.9736	+	15.1835i	−0.785242	+	0.596925i	−0.919077	−	0.394078i	$-0.871064\pi$
$647$	−19.9736	+	15.1835i	−0.785242	+	0.596925i	0.133835	+	0.991004i	$0.457271\pi$
$648$	92.1163			3.61867
$649$	14.8823	−	1.14459i	0.584183	−	0.0449292i
$650$	3.45287			0.135433
$651$	−0.462547	+	0.351619i	−0.0181287	+	0.0137810i
$652$	12.8898	−	24.3127i	0.504803	−	0.952160i
$653$	−7.01168	+	25.2538i	−0.274388	+	0.988257i	0.690009	+	0.723800i	$0.257606\pi$
$653$	−7.01168	+	25.2538i	−0.274388	+	0.988257i	−0.964398	+	0.264457i	$0.914807\pi$
$654$	−42.7342	+	40.4800i	−1.67104	+	1.58289i
$655$	0.0136046	+	0.0829843i	0.000531575	+	0.00324247i
$656$	−35.4284	−	41.7095i	−1.38325	−	1.62848i
$657$	11.7418	+	29.4697i	0.458092	+	1.14972i
$658$	1.67941	+	2.47694i	0.0654700	+	0.0965611i
$659$	−1.20967	+	7.37866i	−0.0471221	+	0.287432i	−0.999866	−	0.0163412i	$-0.994798\pi$
$659$	−1.20967	+	7.37866i	−0.0471221	+	0.287432i	0.952744	+	0.303773i	$0.0982465\pi$
$660$	−10.3904	+	6.25171i	−0.404446	+	0.243347i
$661$	−32.4775	−	30.7643i	−1.26323	−	1.19659i	−0.970689	−	0.240340i	$-0.922741\pi$
$661$	−32.4775	−	30.7643i	−1.26323	−	1.19659i	−0.292540	−	0.956253i	$-0.594500\pi$
$662$	−6.27457	+	9.25429i	−0.243868	+	0.359678i
$663$	−2.92820	−	0.644546i	−0.113722	−	0.0250321i
$664$	−22.3428	−	80.4717i	−0.867071	−	3.12291i
$665$	−1.01405	−	0.610134i	−0.0393232	−	0.0236600i
$666$	−46.2240	+	54.4191i	−1.79114	+	2.10870i
$667$	20.5024	+	6.90807i	0.793856	+	0.267481i
$668$	−67.3443	−	31.1568i	−2.60563	−	1.20549i
$669$	24.0017	+	45.2719i	0.927957	+	1.75031i
$670$	5.65183	−	1.24406i	0.218349	−	0.0480623i
$671$	−0.813452	+	2.04161i	−0.0314030	+	0.0788155i
$672$	−32.7242	+	11.0261i	−1.26236	+	0.425339i
$673$	0.342285	+	0.0372257i	0.0131941	+	0.00143495i	0.114714	−	0.993399i	$-0.463405\pi$
$673$	0.342285	+	0.0372257i	0.0131941	+	0.00143495i	−0.101520	+	0.994834i	$0.532370\pi$
$674$	−2.41640	+	44.5679i	−0.0930763	+	1.71669i
$675$	0.0405777	+	0.748412i	0.00156184	+	0.0288064i
$676$	72.3738	−	7.87113i	2.78361	−	0.302736i
$677$	17.6552	−	8.16815i	0.678544	−	0.313928i	−0.0501756	−	0.998740i	$-0.515978\pi$
$677$	17.6552	−	8.16815i	0.678544	−	0.313928i	0.728719	+	0.684813i	$0.240116\pi$
$678$	53.7511	+	40.8605i	2.06430	+	1.56924i
$679$	−1.14156	−	0.867792i	−0.0438091	−	0.0333028i
$680$	−19.5333	+	9.03708i	−0.749069	+	0.346556i
$681$	−1.68949	+	0.183743i	−0.0647414	+	0.00704106i
$682$	0.123888	+	2.28498i	0.00474391	+	0.0874963i
$683$	−0.744241	+	13.7267i	−0.0284776	+	0.525239i	0.949141	+	0.314852i	$0.101955\pi$
$683$	−0.744241	+	13.7267i	−0.0284776	+	0.525239i	−0.977618	+	0.210386i	$0.932528\pi$
$684$	−76.4014	−	8.30915i	−2.92128	−	0.317708i
$685$	5.26997	−	1.77566i	0.201355	−	0.0678445i
$686$	7.82762	−	19.6458i	0.298860	−	0.750082i
$687$	21.3359	−	4.69638i	0.814014	−	0.179178i
$688$	−30.8770	−	58.2402i	−1.17717	−	2.22039i
$689$	1.99695	+	0.923888i	0.0760778	+	0.0351973i
$690$	−10.2513	−	3.45405i	−0.390259	−	0.131494i
$691$	−12.4402	+	14.6457i	−0.473247	+	0.557149i	−0.946051	−	0.324019i	$-0.894966\pi$
$691$	−12.4402	+	14.6457i	−0.473247	+	0.557149i	0.472804	+	0.881168i	$0.343242\pi$
$692$	66.4016	+	39.9525i	2.52421	+	1.51877i
$693$	0.853750	+	3.07493i	0.0324313	+	0.116807i
$694$	10.5082	+	2.31304i	0.398888	+	0.0878018i
$695$	−4.98871	+	7.35779i	−0.189232	+	0.279097i
$696$	−108.586	−	102.858i	−4.11594	−	3.89883i
$697$	−13.4651	+	8.10165i	−0.510025	+	0.306872i
$698$	−2.55969	+	15.6134i	−0.0968857	+	0.590977i
$699$	−15.5674	−	22.9602i	−0.588812	−	0.868433i
$700$	−5.58660	−	14.0213i	−0.211153	−	0.529955i
$701$	−4.90487	−	5.77446i	−0.185254	−	0.218098i	0.661693	−	0.749775i	$-0.269838\pi$
$701$	−4.90487	−	5.77446i	−0.185254	−	0.218098i	−0.846948	+	0.531676i	$0.821562\pi$
$702$	−0.0182253	−	0.111169i	−0.000687870	−	0.00419582i
$703$	−29.7247	+	28.1567i	−1.12109	+	1.06195i
$704$	−19.2991	+	69.5092i	−0.727364	+	2.61973i
$705$	1.00565	−	1.89686i	0.0378750	−	0.0714398i
$706$	19.6706	−	14.9532i	0.740311	−	0.562770i
$707$	7.51537			0.282645
$708$	−35.8853	−	99.0502i	−1.34865	−	3.72253i
$709$	39.9384			1.49992			0.749960	−	0.661483i	$-0.230073\pi$
$709$	39.9384			1.49992			0.749960	+	0.661483i	$0.230073\pi$
$710$	2.52799	−	1.92173i	0.0948737	−	0.0721211i
$711$	3.38496	−	6.38471i	0.126946	−	0.239445i
$712$	36.1140	−	130.071i	1.35343	−	4.87461i
$713$	−1.09353	+	1.03585i	−0.0409530	+	0.0387927i
$714$	2.87365	+	17.5285i	0.107544	+	0.655988i
$715$	0.149281	+	0.175747i	0.00558278	+	0.00657255i
$716$	9.86470	+	24.7585i	0.368661	+	0.925269i
$717$	9.26572	+	13.6659i	0.346035	+	0.510363i
$718$	−9.15303	+	55.8310i	−0.341588	+	2.08359i
$719$	28.8259	−	17.3440i	1.07503	−	0.646822i	0.136014	−	0.990707i	$-0.456571\pi$
$719$	28.8259	−	17.3440i	1.07503	−	0.646822i	0.939012	+	0.343885i	$0.111743\pi$
$720$	15.9349	+	15.0943i	0.593858	+	0.562533i
$721$	−3.41811	+	5.04134i	−0.127297	+	0.187749i
$722$	−7.07517	−	1.55736i	−0.263311	−	0.0579590i
$723$	7.83978	+	28.2363i	0.291565	+	1.05012i
$724$	92.2199	+	55.4869i	3.42733	+	2.06215i
$725$	19.0009	−	22.3696i	0.705677	−	0.830788i
$726$	−46.0686	−	15.5223i	−1.70977	−	0.576088i
$727$	−16.3607	−	7.56925i	−0.606784	−	0.280728i	0.0923415	−	0.995727i	$-0.470565\pi$
$727$	−16.3607	−	7.56925i	−0.606784	−	0.280728i	−0.699125	+	0.714999i	$0.746427\pi$
$728$	0.685096	+	1.29223i	0.0253914	+	0.0478932i
$729$	−25.2286	+	5.55324i	−0.934394	+	0.205676i
$730$	5.02624	−	12.6149i	0.186029	−	0.466899i
$731$	−17.9379	+	6.04398i	−0.663457	+	0.223545i
$732$	15.4205	+	1.67708i	0.569959	+	0.0619868i
$733$	1.92477	−	35.5003i	0.0710929	−	1.31123i	−0.717605	−	0.696451i	$-0.754761\pi$
$733$	1.92477	−	35.5003i	0.0710929	−	1.31123i	0.788698	−	0.614781i	$-0.210756\pi$
$734$	4.74167	+	87.4550i	0.175018	+	3.22802i
$735$	−7.36908	+	0.801435i	−0.271812	+	0.0295614i
$736$	−81.2468	+	37.5888i	−2.99480	+	1.38554i
$737$	−7.12387	−	5.41543i	−0.262411	−	0.199480i
$738$	21.4996	+	16.3436i	0.791411	+	0.601615i
$739$	−28.5154	+	13.1926i	−1.04895	+	0.485298i	−0.867156	−	0.498037i	$-0.834054\pi$
$739$	−28.5154	+	13.1926i	−1.04895	+	0.485298i	−0.181799	+	0.983336i	$0.558192\pi$
$740$	22.4198	−	2.43831i	0.824170	−	0.0896339i
$741$	0.159967	+	2.95042i	0.00587654	+	0.108386i
$742$	0.705705	−	13.0160i	0.0259073	−	0.477831i
$743$	−33.4440	−	3.63726i	−1.22694	−	0.133438i	−0.528393	−	0.849000i	$-0.677205\pi$
$743$	−33.4440	−	3.63726i	−1.22694	−	0.133438i	−0.698550	+	0.715562i	$0.746171\pi$
$744$	9.86802	−	3.32492i	0.361779	−	0.121898i
$745$	−0.885844	+	2.22330i	−0.0324548	+	0.0814554i
$746$	−48.8692	+	10.7569i	−1.78923	+	0.393839i
$747$	11.4558	+	21.6080i	0.419148	+	0.790596i
$748$	46.8477	+	21.6740i	1.71292	+	0.792481i
$749$	−7.74245	−	2.60873i	−0.282903	−	0.0953211i
$750$	−19.4114	+	22.8528i	−0.708803	+	0.834467i
$751$	0.111877	+	0.0673144i	0.00408247	+	0.00245634i	0.517594	−	0.855627i	$-0.326828\pi$
$751$	0.111877	+	0.0673144i	0.00408247	+	0.00245634i	−0.513511	+	0.858083i	$0.671656\pi$
$752$	−8.51453	−	30.6666i	−0.310493	−	1.11830i
$753$	21.3378	+	4.69681i	0.777594	+	0.171161i
$754$	−2.47563	+	3.65128i	−0.0901571	+	0.132972i
$755$	−1.80589	−	1.71063i	−0.0657230	−	0.0622562i
$756$	−0.421945	+	0.253876i	−0.0153460	+	0.00923338i
$757$	2.98239	−	18.1918i	0.108397	−	0.661191i	−0.875604	−	0.483029i	$-0.839537\pi$
$757$	2.98239	−	18.1918i	0.108397	−	0.661191i	0.984001	−	0.178162i	$-0.0570152\pi$
$758$	21.0083	+	30.9849i	0.763056	+	1.12542i
$759$	6.19128	+	15.5389i	0.224729	+	0.564028i
$760$	13.7310	+	16.1654i	0.498077	+	0.586381i
$761$	2.85579	+	17.4196i	0.103522	+	0.631459i	0.986717	+	0.162451i	$0.0519401\pi$
$761$	2.85579	+	17.4196i	0.103522	+	0.631459i	−0.883194	+	0.469008i	$0.844612\pi$
$762$	85.9388	−	81.4055i	3.11323	−	2.94901i
$763$	1.30897	−	4.71449i	0.0473879	−	0.170676i
$764$	48.9288	−	92.2896i	1.77018	−	3.33892i
$765$	5.01754	−	3.81424i	0.181410	−	0.137904i
$766$	−77.7261			−2.80836
$767$	−1.74831	+	0.978120i	−0.0631279	+	0.0353179i
$768$	168.130			6.06685
$769$	−12.0412	+	9.15349i	−0.434217	+	0.330083i	−0.799343	−	0.600875i	$-0.794819\pi$
$769$	−12.0412	+	9.15349i	−0.434217	+	0.330083i	0.365126	+	0.930958i	$0.381026\pi$
$770$	0.639873	−	1.20693i	0.0230594	−	0.0434947i
$771$	7.14979	−	25.7512i	0.257493	−	0.927407i
$772$	12.6968	−	12.0271i	0.456968	−	0.432863i
$773$	−3.71417	−	22.6555i	−0.133590	−	0.814860i	−0.965587	−	0.260080i	$-0.916251\pi$
$773$	−3.71417	−	22.6555i	−0.133590	−	0.814860i	0.831997	−	0.554779i	$-0.187197\pi$
$774$	21.0597	+	24.7934i	0.756976	+	0.891182i
$775$	0.756339	+	1.89827i	0.0271685	+	0.0681878i
$776$	14.4222	+	21.2712i	0.517727	+	0.763590i
$777$	1.94135	−	11.8417i	0.0696456	−	0.424819i
$778$	−67.8834	+	40.8441i	−2.43374	+	1.46433i
$779$	11.2429	+	10.6499i	0.402820	+	0.381571i
$780$	0.913339	−	1.34707i	0.0327028	−	0.0482330i
$781$	−4.79541	−	1.05555i	−0.171593	−	0.0377706i
$782$	12.3191	+	44.3693i	0.440530	+	1.58664i
$783$	−0.820510	−	0.493685i	−0.0293226	−	0.0176429i
$784$	−71.1375	+	83.7496i	−2.54063	+	2.99106i
$785$	−3.67413	−	1.23796i	−0.131135	−	0.0441846i
$786$	−1.12885	−	0.522263i	−0.0402649	−	0.0186285i
$787$	−8.72867	−	16.4640i	−0.311143	−	0.586879i	0.677787	−	0.735258i	$-0.262939\pi$
$787$	−8.72867	−	16.4640i	−0.311143	−	0.586879i	−0.988930	+	0.148380i	$0.952594\pi$
$788$	35.3926	−	7.79050i	1.26081	−	0.277525i
$789$	−15.6434	+	39.2621i	−0.556921	+	1.39777i
$790$	−2.93148	+	0.987729i	−0.104297	+	0.0351418i
$791$	−5.57941	−	0.606798i	−0.198381	−	0.0215752i
$792$	3.09641	−	57.1100i	0.110026	−	2.02931i
$793$	−0.0159690	−	0.294531i	−0.000567075	−	0.0104591i
$794$	−49.6903	+	5.40414i	−1.76344	+	0.191786i
$795$	−8.48733	+	3.92666i	−0.301015	+	0.139264i
$796$	−57.0510	−	43.3690i	−2.02212	−	1.53718i
$797$	−1.91562	−	1.45622i	−0.0678548	−	0.0515819i	0.570697	−	0.821161i	$-0.306673\pi$
$797$	−1.91562	−	1.45622i	−0.0678548	−	0.0515819i	−0.638552	+	0.769579i	$0.720466\pi$
$798$	15.8867	−	7.34996i	0.562382	−	0.260186i
$799$	−9.08552	+	0.988110i	−0.321423	+	0.0349568i
$800$	6.57490	+	121.267i	0.232458	+	4.28743i
$801$	−2.14017	+	39.4732i	−0.0756193	+	1.39472i
$802$	53.3083	+	5.79763i	1.88238	+	0.204721i
$803$	−19.8984	+	6.70454i	−0.702198	+	0.236598i
$804$	−23.3776	+	58.6734i	−0.824466	+	2.06925i
$805$	0.878156	−	0.193297i	0.0309509	−	0.00681282i
$806$	−0.143861	−	0.271351i	−0.00506730	−	0.00955793i
$807$	−48.0860	−	22.2470i	−1.69271	−	0.783131i
$808$	−127.640	−	43.0071i	−4.49038	−	1.51298i
$809$	19.3198	−	22.7450i	0.679247	−	0.799672i	−0.309239	−	0.950984i	$-0.600074\pi$
$809$	19.3198	−	22.7450i	0.679247	−	0.799672i	0.988486	+	0.151313i	$0.0483501\pi$
$810$	9.89434	+	5.95323i	0.347652	+	0.209175i
$811$	−6.09940	−	21.9681i	−0.214179	−	0.771403i	−0.990075	−	0.140542i	$-0.955116\pi$
$811$	−6.09940	−	21.9681i	−0.214179	−	0.771403i	0.775896	−	0.630861i	$-0.217298\pi$
$812$	18.8324	+	4.14533i	0.660889	+	0.145473i
$813$	28.3648	−	41.8349i	0.994796	−	1.46721i
$814$	−34.3111	−	32.5012i	−1.20260	−	1.13917i
$815$	1.90567	−	1.14661i	0.0667529	−	0.0401639i
$816$	30.5617	−	186.418i	1.06987	−	6.52594i
$817$	10.4683	+	15.4396i	0.366239	+	0.540163i
$818$	9.66450	+	24.2561i	0.337911	+	0.848094i
$819$	−0.277284	−	0.326443i	−0.00968907	−	0.0114069i
$820$	−1.38000	−	8.41762i	−0.0481916	−	0.293956i
$821$	18.2222	−	17.2610i	0.635961	−	0.602414i	−0.300247	−	0.953862i	$-0.597069\pi$
$821$	18.2222	−	17.2610i	0.635961	−	0.602414i	0.936208	+	0.351448i	$0.114310\pi$
$822$	−22.0053	+	79.2561i	−0.767525	+	2.76437i
$823$	14.7380	−	27.7988i	0.513734	−	0.969006i	−0.481950	−	0.876199i	$-0.660071\pi$
$823$	14.7380	−	27.7988i	0.513734	−	0.969006i	0.995684	−	0.0928069i	$-0.0295839\pi$
$824$	86.9023	−	66.0614i	3.02739	−	2.30136i
$825$	22.6920			0.790034
$826$	9.21666	+	7.47693i	0.320689	+	0.260156i
$827$	10.5707			0.367580			0.183790	−	0.982966i	$-0.441163\pi$
$827$	10.5707			0.367580			0.183790	+	0.982966i	$0.441163\pi$
$828$	46.4851	−	35.3370i	1.61547	−	1.22805i
$829$	−23.5498	+	44.4196i	−0.817919	+	1.54276i	0.0218166	+	0.999762i	$0.493055\pi$
$829$	−23.5498	+	44.4196i	−0.817919	+	1.54276i	−0.839735	+	0.542996i	$0.817290\pi$
$830$	2.80079	−	10.0875i	0.0972168	−	0.350143i
$831$	6.74555	−	6.38973i	0.234001	−	0.221657i
$832$	−1.56638	−	9.55452i	−0.0543046	−	0.331243i
$833$	20.4273	+	24.0489i	0.707764	+	0.833244i
$834$	−48.6680	−	122.148i	−1.68524	−	4.22962i
$835$	−3.36546	−	4.96369i	−0.116467	−	0.171775i
$836$	8.22965	−	50.1987i	0.284629	−	1.73616i
$837$	0.0571248	−	0.0343709i	0.00197452	−	0.00118803i
$838$	−29.9423	−	28.3629i	−1.03434	−	0.979779i
$839$	19.2563	−	28.4009i	0.664801	−	0.980508i	−0.334473	−	0.942405i	$-0.608558\pi$
$839$	19.2563	−	28.4009i	0.664801	−	0.980508i	0.999274	−	0.0381028i	$-0.0121314\pi$
$840$	−6.07094	−	1.33632i	−0.209467	−	0.0461073i
$841$	2.27348	+	8.18833i	0.0783959	+	0.282356i
$842$	−90.8658	−	54.6721i	−3.13144	−	1.88413i
$843$	20.7346	−	24.4106i	0.714136	−	0.840746i
$844$	−136.933	−	46.1382i	−4.71344	−	1.58814i
$845$	5.33994	+	2.47052i	0.183700	+	0.0849885i
$846$	7.35690	+	13.8766i	0.252935	+	0.477087i
$847$	3.94639	−	0.868666i	0.135600	−	0.0298477i
$848$	−51.3122	+	128.784i	−1.76207	+	4.42246i
$849$	−20.4188	+	6.87989i	−0.700771	+	0.236117i
$850$	62.1029	+	6.75409i	2.13011	+	0.231663i
$851$	1.68418	−	31.0628i	0.0577328	−	1.06482i
$852$	1.87626	+	34.6057i	0.0642798	+	1.18557i
$853$	26.8140	−	2.91620i	0.918094	−	0.0998488i	0.363145	−	0.931733i	$-0.381703\pi$
$853$	26.8140	−	2.91620i	0.918094	−	0.0998488i	0.554950	+	0.831884i	$0.312738\pi$
$854$	−1.58591	+	0.733722i	−0.0542689	+	0.0251075i
$855$	−4.94467	−	3.75884i	−0.169104	−	0.128550i
$856$	116.569	+	88.6131i	3.98423	+	3.02873i
$857$	52.0485	−	24.0802i	1.77794	−	0.822564i	0.804391	−	0.594101i	$-0.202492\pi$
$857$	52.0485	−	24.0802i	1.77794	−	0.822564i	0.973552	−	0.228464i	$-0.0733702\pi$
$858$	−3.39067	+	0.368758i	−0.115756	+	0.0125892i
$859$	3.06830	+	56.5914i	0.104689	+	1.93088i	0.307294	+	0.951615i	$0.400576\pi$
$859$	3.06830	+	56.5914i	0.104689	+	1.93088i	−0.202605	+	0.979260i	$0.564941\pi$
$860$	0.556264	−	10.2597i	0.0189684	−	0.349852i
$861$	−4.51215	−	0.490725i	−0.153774	−	0.0167239i
$862$	57.2286	−	19.2826i	1.94921	−	0.656767i
$863$	−8.05576	+	20.2184i	−0.274221	+	0.688243i	0.725779	+	0.687928i	$0.241480\pi$
$863$	−8.05576	+	20.2184i	−0.274221	+	0.688243i	−1.00000		0.000315051i	$0.999900\pi$
$864$	3.86963	−	0.851770i	0.131647	−	0.0289778i
$865$	2.93369	+	5.53352i	0.0997483	+	0.188145i
$866$	35.8352	+	16.5791i	1.21773	+	0.563381i
$867$	−12.1555	−	4.09568i	−0.412824	−	0.139097i
$868$	−0.869131	+	1.02322i	−0.0295002	+	0.0347304i
$869$	4.09859	+	2.46604i	0.139035	+	0.0836546i
$870$	−5.01593	−	18.0657i	−0.170056	−	0.612486i
$871$	1.17295	+	0.258185i	0.0397438	+	0.00874826i
$872$	−49.2103	+	72.5798i	−1.66647	+	2.45786i
$873$	−5.46376	−	5.17555i	−0.184920	−	0.175166i
$874$	38.8833	−	23.3953i	1.31525	−	0.791358i
$875$	0.403219	−	2.45953i	0.0136313	−	0.0831472i
$876$	83.1688	+	122.665i	2.81001	+	4.14446i
$877$	10.4297	+	26.1765i	0.352184	+	0.883916i	0.993203	+	0.116391i	$0.0371327\pi$
$877$	10.4297	+	26.1765i	0.352184	+	0.883916i	−0.641019	+	0.767525i	$0.721488\pi$
$878$	33.4931	+	39.4312i	1.13034	+	1.33074i
$879$	4.58578	+	27.9720i	0.154675	+	0.943474i
$880$	−10.5474	+	9.99104i	−0.355553	+	0.336798i
$881$	−8.49212	+	30.5858i	−0.286107	+	1.03046i	0.671173	+	0.741301i	$0.265791\pi$
$881$	−8.49212	+	30.5858i	−0.286107	+	1.03046i	−0.957280	+	0.289163i	$0.906623\pi$
$882$	25.4003	−	47.9101i	0.855273	−	1.61322i
$883$	−13.8071	+	10.4959i	−0.464647	+	0.353215i	−0.811155	−	0.584832i	$-0.801161\pi$
$883$	−13.8071	+	10.4959i	−0.464647	+	0.353215i	0.346508	+	0.938047i	$0.387367\pi$
$884$	−6.92796			−0.233012
$885$	1.64203	−	8.35458i	0.0551962	−	0.280836i
$886$	−49.4043			−1.65977
$887$	35.8341	−	27.2404i	1.20319	−	0.914642i	0.205245	−	0.978711i	$-0.434201\pi$
$887$	35.8341	−	27.2404i	1.20319	−	0.914642i	0.997945	+	0.0640687i	$0.0204077\pi$
$888$	−100.737	+	190.009i	−3.38050	+	6.37630i
$889$	−2.63235	+	9.48086i	−0.0882861	+	0.317978i
$890$	12.2852	−	11.6371i	0.411800	−	0.390078i
$891$	−2.88867	−	17.6201i	−0.0967740	−	0.590295i
$892$	76.6495	+	90.2388i	2.56642	+	3.02142i
$893$	3.33360	+	8.36670i	0.111555	+	0.279981i
$894$	−19.8655	−	29.2995i	−0.664403	−	0.979921i
$895$	−0.348473	+	2.12559i	−0.0116482	+	0.0710506i
$896$	−24.8585	+	14.9569i	−0.830465	+	0.499674i
$897$	−1.62986	−	1.54389i	−0.0544195	−	0.0515488i
$898$	28.8932	−	42.6143i	0.964179	−	1.42206i
$899$	−2.54962	−	0.561214i	−0.0850347	−	0.0187176i
$900$	−21.1922	−	76.3273i	−0.706406	−	2.54424i
$901$	34.1097	+	20.5231i	1.13636	+	0.683724i
$902$	−11.5725	+	13.6242i	−0.385322	+	0.453636i
$903$	−5.18094	−	1.74566i	−0.172411	−	0.0580920i
$904$	91.2879	+	42.2343i	3.03619	+	1.40469i
$905$	4.07436	+	7.68507i	0.135436	+	0.255460i
$906$	35.9321	−	7.90925i	1.19376	−	0.262767i
$907$	10.0941	−	25.3343i	0.335169	−	0.841212i	−0.660720	−	0.750633i	$-0.729749\pi$
$907$	10.0941	−	25.3343i	0.335169	−	0.841212i	0.995889	−	0.0905793i	$-0.0288718\pi$
$908$	−3.72125	+	1.25383i	−0.123494	+	0.0416099i
$909$	39.2120	+	4.26457i	1.30058	+	0.141447i
$910$	−0.00992609	+	0.183076i	−0.000329047	+	0.00606891i
$911$	2.18840	+	40.3627i	0.0725050	+	1.33728i	0.777867	+	0.628429i	$0.216302\pi$
$911$	2.18840	+	40.3627i	0.0725050	+	1.33728i	−0.705362	+	0.708847i	$0.749216\pi$
$912$	−185.072	+	20.1278i	−6.12834	+	0.666497i
$913$	−14.6920	+	6.79726i	−0.486236	+	0.224957i
$914$	−76.6870	−	58.2959i	−2.53658	−	1.92826i
$915$	0.998011	+	0.758668i	0.0329932	+	0.0250808i
$916$	45.8139	−	21.1958i	1.51373	−	0.700327i
$917$	0.102783	−	0.0111783i	0.00339418	−	0.000369139i
$918$	−0.110341	−	2.03513i	−0.00364181	−	0.0671692i
$919$	1.90808	−	35.1924i	0.0629417	−	1.16089i	−0.781026	−	0.624498i	$-0.785304\pi$
$919$	1.90808	−	35.1924i	0.0629417	−	1.16089i	0.843968	−	0.536393i	$-0.180214\pi$
$920$	−16.0207	−	1.74236i	−0.528187	−	0.0574437i
$921$	20.8726	−	7.03279i	0.687775	−	0.231738i
$922$	34.4083	−	86.3584i	1.13318	−	2.84406i
$923$	0.643614	−	0.141670i	0.0211848	−	0.00466313i
$924$	6.98340	+	13.1721i	0.229737	+	0.433330i
$925$	−38.3016	−	17.7202i	−1.25935	−	0.582637i
$926$	58.3698	+	19.6671i	1.91815	+	0.646301i
$927$	−20.6950	+	24.3640i	−0.679712	+	0.800219i
$928$	−132.949	−	79.9928i	−4.36427	−	2.62589i
$929$	−2.83215	−	10.2005i	−0.0929199	−	0.334667i	0.902449	−	0.430797i	$-0.141767\pi$
$929$	−2.83215	−	10.2005i	−0.0929199	−	0.334667i	−0.995369	+	0.0961297i	$0.969354\pi$
$930$	1.27482	+	0.280609i	0.0418030	+	0.00920153i
$931$	17.4502	−	25.7372i	0.571908	−	0.843501i
$932$	−46.5341	−	44.0794i	−1.52428	−	1.44387i
$933$	8.90022	−	5.35509i	0.291380	−	0.175318i
$934$	6.95722	−	42.4372i	0.227647	−	1.38859i
$935$	2.34116	+	3.45296i	0.0765642	+	0.112924i
$936$	2.84127	+	7.13106i	0.0928699	+	0.233086i
$937$	−38.5366	−	45.3688i	−1.25894	−	1.48213i	−0.807542	−	0.589810i	$-0.799203\pi$
$937$	−38.5366	−	45.3688i	−1.25894	−	1.48213i	−0.451394	−	0.892325i	$-0.649073\pi$
$938$	−1.15110	−	7.02137i	−0.0375846	−	0.229256i
$939$	−18.1895	+	17.2300i	−0.593593	+	0.562281i
$940$	1.32716	−	4.77998i	0.0432870	−	0.155906i
$941$	−24.0840	+	45.4272i	−0.785116	+	1.48089i	0.0894570	+	0.995991i	$0.471487\pi$
$941$	−24.0840	+	45.4272i	−0.785116	+	1.48089i	−0.874573	+	0.484895i	$0.838858\pi$
$942$	45.6529	−	34.7044i	1.48745	−	1.13073i
$943$	−11.7663			−0.383164
$944$	−67.4992	−	106.654i	−2.19691	−	3.47128i
$945$	−0.0397985			−0.00129464
$946$	−17.1416	+	13.0307i	−0.557320	+	0.423664i
$947$	7.34190	−	13.8483i	0.238580	−	0.450009i	−0.735091	−	0.677969i	$-0.762861\pi$
$947$	7.34190	−	13.8483i	0.238580	−	0.450009i	0.973671	+	0.227960i	$0.0732054\pi$
$948$	9.03192	−	32.5300i	0.293343	−	1.05653i
$949$	2.04598	−	1.93806i	0.0664154	−	0.0629120i
$950$	−9.95958	−	60.7508i	−0.323132	−	1.97102i
$951$	−39.4352	−	46.4267i	−1.27877	−	1.50549i
$952$	9.79434	+	24.5819i	0.317436	+	0.796705i
$953$	9.23932	+	13.6270i	0.299291	+	0.441421i	0.947365	−	0.320156i	$-0.103735\pi$
$953$	9.23932	+	13.6270i	0.299291	+	0.441421i	−0.648074	+	0.761578i	$0.724425\pi$
$954$	11.0679	−	67.5114i	0.358337	−	2.18576i
$955$	7.23381	−	4.35244i	0.234081	−	0.140842i
$956$	27.6971	+	26.2361i	0.895790	+	0.848537i
$957$	−16.2696	+	23.9959i	−0.525923	+	0.775678i
$958$	26.0656	+	5.73748i	0.842142	+	0.185370i
$959$	−1.82914	−	6.58796i	−0.0590659	−	0.212736i
$960$	35.2598	+	21.2151i	1.13801	+	0.684715i
$961$	−19.9513	+	23.4885i	−0.643591	+	0.757693i
$962$	6.01105	+	2.02536i	0.193804	+	0.0653002i
$963$	−38.9165	−	18.0047i	−1.25407	−	0.580193i
$964$	31.7167	+	59.8241i	1.02153	+	1.92681i
$965$	1.38040	−	0.303849i	0.0444367	−	0.00978126i
$966$	−4.92277	+	12.3552i	−0.158387	+	0.397523i
$967$	−34.0867	+	11.4851i	−1.09615	+	0.369338i	−0.808559	−	0.588415i	$-0.799752\pi$
$967$	−34.0867	+	11.4851i	−1.09615	+	0.369338i	−0.287595	+	0.957752i	$0.592856\pi$
$968$	−71.9961	−	7.83005i	−2.31404	−	0.251667i
$969$	−2.89411	+	53.3787i	−0.0929723	+	1.71477i
$970$	0.174412	+	3.21683i	0.00560002	+	0.103286i
$971$	8.77295	−	0.954116i	0.281537	−	0.0306190i	0.0337391	−	0.999431i	$-0.489258\pi$
$971$	8.77295	−	0.954116i	0.281537	−	0.0306190i	0.247798	+	0.968812i	$0.420293\pi$
$972$	−111.979	+	51.8070i	−3.59173	+	1.66171i
$973$	8.70085	+	6.61422i	0.278937	+	0.212042i
$974$	−34.1297	−	25.9447i	−1.09359	−	0.831323i
$975$	−2.76411	+	1.27881i	−0.0885224	+	0.0409548i
$976$	18.4751	−	2.00929i	0.591374	−	0.0643158i
$977$	1.18540	+	21.8634i	0.0379242	+	0.699471i	0.954245	+	0.299026i	$0.0966618\pi$
$977$	1.18540	+	21.8634i	0.0379242	+	0.699471i	−0.916321	+	0.400445i	$0.868855\pi$
$978$	−1.78094	+	32.8475i	−0.0569482	+	1.05035i
$979$	−26.0126	−	2.82904i	−0.831365	−	0.0904164i
$980$	−16.2310	+	5.46886i	−0.518481	+	0.174696i
$981$	9.50487	−	23.8554i	0.303467	−	0.761645i
$982$	−56.2274	+	12.3766i	−1.79429	+	0.394952i
$983$	26.6755	+	50.3153i	0.850816	+	1.60481i	0.795192	+	0.606358i	$0.207370\pi$
$983$	26.6755	+	50.3153i	0.850816	+	1.60481i	0.0556239	+	0.998452i	$0.482285\pi$
$984$	73.8257	+	34.1554i	2.35348	+	1.08883i
$985$	2.77559	+	0.935204i	0.0884375	+	0.0297981i
$986$	−51.6685	+	60.8289i	−1.64546	+	1.93719i
$987$	−2.26177	−	1.36086i	−0.0719929	−	0.0433167i
$988$	1.82651	+	6.57848i	0.0581089	+	0.209289i
$989$	−13.8417	−	3.04679i	−0.440140	−	0.0968822i
$990$	4.02345	−	5.93415i	0.127874	−	0.188600i
$991$	19.7502	+	18.7084i	0.627387	+	0.594293i	0.933883	−	0.357579i	$-0.116398\pi$
$991$	19.7502	+	18.7084i	0.627387	+	0.594293i	−0.306496	+	0.951872i	$0.599156\pi$
$992$	9.25607	−	5.56919i	0.293880	−	0.176822i
$993$	1.59551	−	9.73215i	0.0506318	−	0.308841i
$994$	−2.19097	−	3.23144i	−0.0694934	−	0.102495i
$995$	−2.14379	−	5.38051i	−0.0679627	−	0.170574i
$996$	73.9686	+	87.0826i	2.34378	+	2.75932i
$997$	0.497262	+	3.03317i	0.0157485	+	0.0960614i	0.993531	−	0.113560i	$-0.0362253\pi$
$997$	0.497262	+	3.03317i	0.0157485	+	0.0960614i	−0.977783	+	0.209621i	$0.932777\pi$
$998$	8.61909	−	8.16444i	0.272833	−	0.258441i
$999$	−0.368356	+	1.32670i	−0.0116543	+	0.0419749i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	59.2.c.a.26.1	yes	112
3.2	odd	2		531.2.i.a.262.4		112
4.3	odd	2		944.2.m.c.321.1		112
59.5	even	29		3481.2.a.p.1.1		56
59.25	even	29	inner	59.2.c.a.25.1	✓	112
59.54	odd	58		3481.2.a.q.1.56		56
177.143	odd	58		531.2.i.a.379.4		112
236.143	odd	58		944.2.m.c.497.1		112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
59.2.c.a.25.1	✓	112	59.25	even	29	inner
59.2.c.a.26.1	yes	112	1.1	even	1	trivial
531.2.i.a.262.4		112	3.2	odd	2
531.2.i.a.379.4		112	177.143	odd	58
944.2.m.c.321.1		112	4.3	odd	2
944.2.m.c.497.1		112	236.143	odd	58
3481.2.a.p.1.1		56	59.5	even	29
3481.2.a.q.1.56		56	59.54	odd	58

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:	\( N \)	\(=\)	\( 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	59.c (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.19893 + 1.67159i) q^{2} +(1.14121 - 2.15255i) q^{3} +(1.50605 - 5.42431i) q^{4} +(0.330311 - 0.312887i) q^{5} +(1.08873 + 6.64093i) q^{6} +(-0.362135 - 0.426338i) q^{7} +(3.71073 + 9.31322i) q^{8} +(-1.64754 - 2.42994i) q^{9} +(-0.203314 + 1.24016i) q^{10} +(1.66508 - 1.00184i) q^{11} +(-9.95736 - 9.43211i) q^{12} +(-0.146364 + 0.215870i) q^{13} +(1.50897 + 0.332149i) q^{14} +(-0.296551 - 1.06808i) q^{15} +(-14.0801 - 8.47172i) q^{16} +(-3.05473 + 3.59631i) q^{17} +(7.68469 + 2.58927i) q^{18} +(4.22025 + 1.95250i) q^{19} +(-1.19973 - 2.26293i) q^{20} +(-1.33098 + 0.292971i) q^{21} +(-1.98672 + 4.98630i) q^{22} +(-3.34811 + 1.12811i) q^{23} +(24.2819 + 2.64081i) q^{24} +(-0.259488 + 4.78597i) q^{25} +(-0.0390017 - 0.719343i) q^{26} +(0.155460 - 0.0169073i) q^{27} +(-2.85798 + 1.32224i) q^{28} +(-4.87493 - 3.70583i) q^{29} +(2.43748 + 1.85292i) q^{30} +(0.386926 - 0.179011i) q^{31} +(25.1895 - 2.73952i) q^{32} +(-0.256316 - 4.72747i) q^{33} +(0.705614 - 13.0143i) q^{34} +(-0.253012 - 0.0275168i) q^{35} +(-15.6620 + 5.27715i) q^{36} +(-3.25905 + 8.17960i) q^{37} +(-12.5438 + 2.76110i) q^{38} +(0.297639 + 0.561407i) q^{39} +(4.13968 + 1.91522i) q^{40} +(3.15602 + 1.06339i) q^{41} +(2.43701 - 2.86908i) q^{42} +(3.43733 + 2.06817i) q^{43} +(-2.92661 - 10.5407i) q^{44} +(-1.30450 - 0.287142i) q^{45} +(5.47654 - 8.07730i) q^{46} +(1.40614 + 1.33196i) q^{47} +(-34.3041 + 20.6401i) q^{48} +(1.08185 - 6.59900i) q^{49} +(-7.42956 - 10.9578i) q^{50} +(4.25514 + 10.6796i) q^{51} +(0.950515 + 1.11903i) q^{52} +(-1.36486 - 8.32531i) q^{53} +(-0.313583 + 0.297042i) q^{54} +(0.236529 - 0.851900i) q^{55} +(2.62679 - 4.95466i) q^{56} +(9.01903 - 6.85609i) q^{57} +16.9142 q^{58} +(6.86593 + 3.44368i) q^{59} -6.24020 q^{60} +(-0.900340 + 0.684420i) q^{61} +(-0.551592 + 1.04041i) q^{62} +(-0.439344 + 1.58238i) q^{63} +(-26.9511 + 25.5294i) q^{64} +(0.0191975 + 0.117099i) q^{65} +(8.46598 + 9.96693i) q^{66} +(-1.70447 - 4.27791i) q^{67} +(14.9069 + 21.9860i) q^{68} +(-1.39258 + 8.49438i) q^{69} +(0.602354 - 0.362424i) q^{70} +(-1.83446 - 1.73769i) q^{71} +(16.5170 - 24.3608i) q^{72} +(-10.5528 - 2.32285i) q^{73} +(-6.50647 - 23.4342i) q^{74} +(10.0059 + 6.02034i) q^{75} +(16.9469 - 19.9514i) q^{76} +(-1.03011 - 0.347083i) q^{77} +(-1.59293 - 0.736967i) q^{78} +(1.15299 + 2.17477i) q^{79} +(-7.30150 + 1.60718i) q^{80} +(3.40099 - 8.53584i) q^{81} +(-8.71741 + 2.93724i) q^{82} +(-8.28172 - 0.900691i) q^{83} +(-0.415361 + 7.66089i) q^{84} +(0.116227 + 2.14369i) q^{85} +(-11.0156 + 1.19802i) q^{86} +(-13.5403 + 6.26440i) q^{87} +(15.5090 + 11.7897i) q^{88} +(-10.7195 - 8.14876i) q^{89} +(3.34848 - 1.54917i) q^{90} +(0.145037 - 0.0157737i) q^{91} +(1.07679 + 19.8602i) q^{92} +(0.0562335 - 1.03717i) q^{93} +(-5.31849 - 0.578420i) q^{94} +(2.00491 - 0.675531i) q^{95} +(22.8495 - 57.3479i) q^{96} +(2.50354 - 0.551071i) q^{97} +(8.65188 + 16.3192i) q^{98} +(-5.17770 - 2.39546i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 26 q^{2} - 23 q^{3} - 30 q^{4} - 25 q^{5} - 13 q^{6} - 23 q^{7} - 8 q^{8} - 21 q^{9} - 3 q^{10} - 15 q^{11} + 21 q^{12} - 23 q^{13} + 13 q^{14} + 4 q^{15} - 8 q^{16} - 10 q^{17} + 12 q^{18} - 15 q^{19}+ \cdots + 44 q^{99}+O(q^{100}) \) 112 * q - 26 * q^2 - 23 * q^3 - 30 * q^4 - 25 * q^5 - 13 * q^6 - 23 * q^7 - 8 * q^8 - 21 * q^9 - 3 * q^10 - 15 * q^11 + 21 * q^12 - 23 * q^13 + 13 * q^14 + 4 * q^15 - 8 * q^16 - 10 * q^17 + 12 * q^18 - 15 * q^19 + 7 * q^20 - 12 * q^21 - q^22 + 3 * q^23 + 25 * q^24 - 5 * q^25 + 5 * q^26 + 22 * q^27 + 29 * q^28 - 13 * q^29 + 29 * q^30 + 3 * q^31 + 36 * q^32 + 33 * q^33 + 27 * q^34 + 28 * q^35 + 20 * q^36 - 9 * q^37 + 31 * q^38 + 45 * q^39 + 79 * q^40 + 23 * q^41 + 33 * q^42 + 19 * q^43 + 43 * q^44 + 19 * q^45 - 31 * q^46 + 10 * q^47 - 25 * q^48 - 31 * q^49 - 60 * q^50 - 61 * q^51 - 75 * q^52 - 23 * q^53 - 86 * q^54 - 24 * q^55 - 103 * q^56 - 91 * q^57 + 12 * q^58 - 33 * q^59 - 210 * q^60 - 47 * q^61 - 39 * q^62 - 58 * q^63 - 152 * q^64 - 16 * q^65 - 116 * q^66 - 19 * q^67 - 5 * q^68 - 45 * q^69 + 23 * q^70 - 18 * q^71 - 36 * q^72 + 24 * q^73 + 19 * q^74 + 58 * q^75 + 97 * q^76 + 65 * q^77 + 119 * q^78 + 41 * q^79 + 107 * q^80 + 95 * q^81 + 145 * q^82 + 49 * q^83 + 167 * q^84 + 39 * q^85 + 111 * q^86 + 80 * q^87 + 175 * q^88 + 51 * q^89 + 213 * q^90 + 77 * q^91 + 135 * q^92 + 93 * q^93 + 151 * q^94 + 65 * q^95 + 181 * q^96 + 91 * q^97 + 31 * q^98 + 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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