LMFDB - Embedded newform 144.3.v.a.115.25

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,3,Mod(43,144)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 8]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("144.43");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	144.v (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.92371580679$
Analytic rank:	$0$
Dimension:	$184$
Relative dimension:	$46$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			115.25
Character	$\chi$	$=$	144.115
Dual form			144.3.v.a.139.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.232149 + 1.98648i) q^{2} +(0.171846 - 2.99507i) q^{3} +(-3.89221 + 0.922317i) q^{4} +(0.828901 + 0.222103i) q^{5} +(5.98955 - 0.353933i) q^{6} +(5.23163 - 9.06144i) q^{7} +(-2.73574 - 7.51769i) q^{8} +(-8.94094 - 1.02938i) q^{9} +O(q^{10})$	\(q+(0.232149 + 1.98648i) q^{2} +(0.171846 - 2.99507i) q^{3} +(-3.89221 + 0.922317i) q^{4} +(0.828901 + 0.222103i) q^{5} +(5.98955 - 0.353933i) q^{6} +(5.23163 - 9.06144i) q^{7} +(-2.73574 - 7.51769i) q^{8} +(-8.94094 - 1.02938i) q^{9} +(-0.248776 + 1.69816i) q^{10} +(7.04151 - 1.88677i) q^{11} +(2.09355 + 11.8160i) q^{12} +(1.87144 - 6.98432i) q^{13} +(19.2149 + 8.28893i) q^{14} +(0.807660 - 2.44445i) q^{15} +(14.2987 - 7.17971i) q^{16} +10.9027 q^{17} +(-0.0307736 - 18.0000i) q^{18} +(5.61772 - 5.61772i) q^{19} +(-3.43111 - 0.0999640i) q^{20} +(-26.2407 - 17.2263i) q^{21} +(5.38270 + 13.5498i) q^{22} +(8.49079 + 14.7065i) q^{23} +(-22.9862 + 6.90185i) q^{24} +(-21.0129 - 12.1318i) q^{25} +(14.3087 + 2.09618i) q^{26} +(-4.61955 + 26.6019i) q^{27} +(-12.0051 + 40.0943i) q^{28} +(-8.49945 + 2.27742i) q^{29} +(5.04336 + 1.03692i) q^{30} +(-6.67353 + 3.85297i) q^{31} +(17.5818 + 26.7373i) q^{32} +(-4.44095 - 21.4141i) q^{33} +(2.53105 + 21.6580i) q^{34} +(6.34908 - 6.34908i) q^{35} +(35.7495 - 4.23980i) q^{36} +(-36.7870 + 36.7870i) q^{37} +(12.4636 + 9.85534i) q^{38} +(-20.5969 - 6.80534i) q^{39} +(-0.597951 - 6.83904i) q^{40} +(70.5661 - 40.7414i) q^{41} +(28.1280 - 56.1256i) q^{42} +(-44.8228 + 12.0102i) q^{43} +(-25.6669 + 13.8382i) q^{44} +(-7.18252 - 2.83907i) q^{45} +(-27.2430 + 20.2809i) q^{46} +(21.0600 + 12.1590i) q^{47} +(-19.0466 - 44.0594i) q^{48} +(-30.2398 - 52.3770i) q^{49} +(19.2215 - 44.5581i) q^{50} +(1.87359 - 32.6544i) q^{51} +(-0.842296 + 28.9105i) q^{52} +(-69.3816 + 69.3816i) q^{53} +(-53.9165 - 3.00106i) q^{54} +6.25577 q^{55} +(-82.4335 - 14.5400i) q^{56} +(-15.8601 - 17.7909i) q^{57} +(-6.49719 - 16.3553i) q^{58} +(2.35159 - 8.77626i) q^{59} +(-0.889023 + 10.2593i) q^{60} +(3.80652 - 1.01995i) q^{61} +(-9.20309 - 12.3624i) q^{62} +(-56.1034 + 75.6325i) q^{63} +(-49.0315 + 41.1329i) q^{64} +(3.10248 - 5.37365i) q^{65} +(41.5077 - 13.7931i) q^{66} +(121.375 + 32.5224i) q^{67} +(-42.4357 + 10.0558i) q^{68} +(45.5061 - 22.9033i) q^{69} +(14.0863 + 11.1384i) q^{70} +89.0591 q^{71} +(16.7215 + 70.0314i) q^{72} -82.8383i q^{73} +(-81.6168 - 64.5367i) q^{74} +(-39.9466 + 60.8504i) q^{75} +(-16.6840 + 27.0467i) q^{76} +(19.7417 - 73.6771i) q^{77} +(8.73712 - 42.4953i) q^{78} +(59.4445 + 34.3203i) q^{79} +(13.4468 - 2.77549i) q^{80} +(78.8807 + 18.4073i) q^{81} +(97.3138 + 130.720i) q^{82} +(1.87483 + 6.99695i) q^{83} +(118.022 + 42.8462i) q^{84} +(9.03727 + 2.42153i) q^{85} +(-34.2637 - 86.2515i) q^{86} +(5.36044 + 25.8478i) q^{87} +(-33.4479 - 47.7742i) q^{88} +144.573i q^{89} +(3.97235 - 14.9270i) q^{90} +(-53.4973 - 53.4973i) q^{91} +(-46.6120 - 49.4095i) q^{92} +(10.3931 + 20.6498i) q^{93} +(-19.2646 + 44.6580i) q^{94} +(5.90424 - 3.40882i) q^{95} +(83.1014 - 48.0640i) q^{96} +(48.6538 - 84.2708i) q^{97} +(97.0257 - 72.2301i) q^{98} +(-64.8999 + 9.62105i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q - 2 q^{2} - 4 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} - 4 q^{7} - 8 q^{8}+O(q^{10}) $ 184 * q - 2 * q^2 - 4 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 - 4 * q^7 - 8 * q^8	\( 184 q - 2 q^{2} - 4 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} - 4 q^{7} - 8 q^{8} - 8 q^{10} - 2 q^{11} + 56 q^{12} - 2 q^{13} + 14 q^{14} - 2 q^{16} - 16 q^{17} + 38 q^{18} - 8 q^{19} - 44 q^{20} + 14 q^{21} - 2 q^{22} - 4 q^{23} + 120 q^{24} - 104 q^{26} - 52 q^{27} + 56 q^{28} - 2 q^{29} - 130 q^{30} - 182 q^{32} - 8 q^{33} - 10 q^{34} + 92 q^{35} - 2 q^{36} - 8 q^{37} - 254 q^{38} + 184 q^{39} - 2 q^{40} - 252 q^{42} - 2 q^{43} - 140 q^{44} - 54 q^{45} + 176 q^{46} + 162 q^{48} - 480 q^{49} - 96 q^{50} - 120 q^{51} - 2 q^{52} - 8 q^{53} + 94 q^{54} - 16 q^{55} + 260 q^{56} + 88 q^{58} + 142 q^{59} - 434 q^{60} - 2 q^{61} - 636 q^{62} + 244 q^{64} - 4 q^{65} - 100 q^{66} - 2 q^{67} - 112 q^{68} + 14 q^{69} - 100 q^{70} - 16 q^{71} + 98 q^{72} + 82 q^{74} - 296 q^{75} + 154 q^{76} + 194 q^{77} + 228 q^{78} + 592 q^{80} - 8 q^{81} - 420 q^{82} + 238 q^{83} - 22 q^{84} - 52 q^{85} - 170 q^{86} - 456 q^{87} - 26 q^{88} + 808 q^{90} + 188 q^{91} + 176 q^{92} + 26 q^{93} - 18 q^{94} - 202 q^{96} - 4 q^{97} + 408 q^{98} - 38 q^{99}+O(q^{100}) \) 184 * q - 2 * q^2 - 4 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 - 4 * q^7 - 8 * q^8 - 8 * q^10 - 2 * q^11 + 56 * q^12 - 2 * q^13 + 14 * q^14 - 2 * q^16 - 16 * q^17 + 38 * q^18 - 8 * q^19 - 44 * q^20 + 14 * q^21 - 2 * q^22 - 4 * q^23 + 120 * q^24 - 104 * q^26 - 52 * q^27 + 56 * q^28 - 2 * q^29 - 130 * q^30 - 182 * q^32 - 8 * q^33 - 10 * q^34 + 92 * q^35 - 2 * q^36 - 8 * q^37 - 254 * q^38 + 184 * q^39 - 2 * q^40 - 252 * q^42 - 2 * q^43 - 140 * q^44 - 54 * q^45 + 176 * q^46 + 162 * q^48 - 480 * q^49 - 96 * q^50 - 120 * q^51 - 2 * q^52 - 8 * q^53 + 94 * q^54 - 16 * q^55 + 260 * q^56 + 88 * q^58 + 142 * q^59 - 434 * q^60 - 2 * q^61 - 636 * q^62 + 244 * q^64 - 4 * q^65 - 100 * q^66 - 2 * q^67 - 112 * q^68 + 14 * q^69 - 100 * q^70 - 16 * q^71 + 98 * q^72 + 82 * q^74 - 296 * q^75 + 154 * q^76 + 194 * q^77 + 228 * q^78 + 592 * q^80 - 8 * q^81 - 420 * q^82 + 238 * q^83 - 22 * q^84 - 52 * q^85 - 170 * q^86 - 456 * q^87 - 26 * q^88 + 808 * q^90 + 188 * q^91 + 176 * q^92 + 26 * q^93 - 18 * q^94 - 202 * q^96 - 4 * q^97 + 408 * q^98 - 38 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.232149	+	1.98648i	0.116074	+	0.993241i
$2$	0.232149	+	1.98648i	0.116074	+	0.993241i
$3$	0.171846	−	2.99507i	0.0572821	−	0.998358i
$3$	0.171846	−	2.99507i	0.0572821	−	0.998358i
$4$	−3.89221	+	0.922317i	−0.973054	+	0.230579i
$5$	0.828901	+	0.222103i	0.165780	+	0.0444207i	0.340754	−	0.940152i	$-0.389318\pi$
$5$	0.828901	+	0.222103i	0.165780	+	0.0444207i	−0.174974	+	0.984573i	$0.555984\pi$
$6$	5.98955	−	0.353933i	0.998259	−	0.0589888i
$7$	5.23163	−	9.06144i	0.747375	−	1.29449i	−0.201701	−	0.979447i	$-0.564647\pi$
$7$	5.23163	−	9.06144i	0.747375	−	1.29449i	0.949077	−	0.315045i	$-0.102020\pi$
$8$	−2.73574	−	7.51769i	−0.341967	−	0.939712i
$9$	−8.94094	−	1.02938i	−0.993438	−	0.114376i
$10$	−0.248776	+	1.69816i	−0.0248776	+	0.169816i
$11$	7.04151	−	1.88677i	0.640137	−	0.171524i	0.0758716	−	0.997118i	$-0.475826\pi$
$11$	7.04151	−	1.88677i	0.640137	−	0.171524i	0.564266	+	0.825593i	$0.309159\pi$
$12$	2.09355	+	11.8160i	0.174462	+	0.984664i
$13$	1.87144	−	6.98432i	0.143957	−	0.537255i	−0.855843	−	0.517236i	$-0.826961\pi$
$13$	1.87144	−	6.98432i	0.143957	−	0.537255i	0.999800	−	0.0200186i	$-0.00637255\pi$
$14$	19.2149	+	8.28893i	1.37249	+	0.592066i
$15$	0.807660	−	2.44445i	0.0538440	−	0.162963i
$16$	14.2987	−	7.17971i	0.893666	−	0.448732i
$17$	10.9027			0.641336			0.320668	−	0.947192i	$-0.396093\pi$
$17$	10.9027			0.641336			0.320668	+	0.947192i	$0.396093\pi$
$18$	−0.0307736	−	18.0000i	−0.00170964	−	0.999999i
$19$	5.61772	−	5.61772i	0.295669	−	0.295669i	−0.543646	−	0.839315i	$-0.682956\pi$
$19$	5.61772	−	5.61772i	0.295669	−	0.295669i	0.839315	+	0.543646i	$0.182956\pi$
$20$	−3.43111	−	0.0999640i	−0.171556	−	0.00499820i
$21$	−26.2407	−	17.2263i	−1.24956	−	0.820299i
$22$	5.38270	+	13.5498i	0.244668	+	0.615901i
$23$	8.49079	+	14.7065i	0.369165	+	0.639412i	0.989435	−	0.144976i	$-0.0463105\pi$
$23$	8.49079	+	14.7065i	0.369165	+	0.639412i	−0.620271	+	0.784388i	$0.712977\pi$
$24$	−22.9862	+	6.90185i	−0.957757	+	0.287577i
$25$	−21.0129	−	12.1318i	−0.840516	−	0.485272i
$26$	14.3087	+	2.09618i	0.550333	+	0.0806225i
$27$	−4.61955	+	26.6019i	−0.171094	+	0.985255i
$28$	−12.0051	+	40.0943i	−0.428753	+	1.43194i
$29$	−8.49945	+	2.27742i	−0.293084	+	0.0785317i	−0.402365	−	0.915479i	$-0.631812\pi$
$29$	−8.49945	+	2.27742i	−0.293084	+	0.0785317i	0.109281	+	0.994011i	$0.465145\pi$
$30$	5.04336	+	1.03692i	0.168112	+	0.0345641i
$31$	−6.67353	+	3.85297i	−0.215275	+	0.124289i	−0.603761	−	0.797166i	$-0.706332\pi$
$31$	−6.67353	+	3.85297i	−0.215275	+	0.124289i	0.388485	+	0.921455i	$0.372998\pi$
$32$	17.5818	+	26.7373i	0.549431	+	0.835539i
$33$	−4.44095	−	21.4141i	−0.134574	−	0.648911i
$34$	2.53105	+	21.6580i	0.0744426	+	0.637001i
$35$	6.34908	−	6.34908i	0.181402	−	0.181402i
$36$	35.7495	−	4.23980i	0.993041	−	0.117772i
$37$	−36.7870	+	36.7870i	−0.994244	+	0.994244i	−0.999984	−	0.00573969i	$-0.998173\pi$
$37$	−36.7870	+	36.7870i	−0.994244	+	0.994244i	0.00573969	+	0.999984i	$0.498173\pi$
$38$	12.4636	+	9.85534i	0.327990	+	0.259351i
$39$	−20.5969	−	6.80534i	−0.528127	−	0.174496i
$40$	−0.597951	−	6.83904i	−0.0149488	−	0.170976i
$41$	70.5661	−	40.7414i	1.72112	−	0.993692i	0.804490	−	0.593966i	$-0.202439\pi$
$41$	70.5661	−	40.7414i	1.72112	−	0.993692i	0.916635	−	0.399726i	$-0.130895\pi$
$42$	28.1280	−	56.1256i	0.669713	−	1.33632i
$43$	−44.8228	+	12.0102i	−1.04239	+	0.279308i	−0.739104	−	0.673591i	$-0.764751\pi$
$43$	−44.8228	+	12.0102i	−1.04239	+	0.279308i	−0.303287	+	0.952899i	$0.598084\pi$
$44$	−25.6669	+	13.8382i	−0.583338	+	0.314505i
$45$	−7.18252	−	2.83907i	−0.159612	−	0.0630904i
$46$	−27.2430	+	20.2809i	−0.592239	+	0.440889i
$47$	21.0600	+	12.1590i	0.448085	+	0.258702i	0.707021	−	0.707192i	$-0.250039\pi$
$47$	21.0600	+	12.1590i	0.448085	+	0.258702i	−0.258936	+	0.965894i	$0.583372\pi$
$48$	−19.0466	−	44.0594i	−0.396804	−	0.917903i
$49$	−30.2398	−	52.3770i	−0.617140	−	1.06892i
$50$	19.2215	−	44.5581i	0.384429	−	0.891162i
$51$	1.87359	−	32.6544i	0.0367370	−	0.640283i
$52$	−0.842296	+	28.9105i	−0.0161980	+	0.555971i
$53$	−69.3816	+	69.3816i	−1.30909	+	1.30909i	−0.387014	+	0.922074i	$0.626493\pi$
$53$	−69.3816	+	69.3816i	−1.30909	+	1.30909i	−0.922074	+	0.387014i	$0.873507\pi$
$54$	−53.9165	−	3.00106i	−0.998455	−	0.0555751i
$55$	6.25577			0.113741
$56$	−82.4335	−	14.5400i	−1.47203	−	0.259644i
$57$	−15.8601	−	17.7909i	−0.278247	−	0.312120i
$58$	−6.49719	−	16.3553i	−0.112020	−	0.281988i
$59$	2.35159	−	8.77626i	0.0398575	−	0.148750i	−0.943129	−	0.332426i	$-0.892133\pi$
$59$	2.35159	−	8.77626i	0.0398575	−	0.148750i	0.982987	+	0.183676i	$0.0587996\pi$
$60$	−0.889023	+	10.2593i	−0.0148170	+	0.170988i
$61$	3.80652	−	1.01995i	0.0624020	−	0.0167206i	−0.227483	−	0.973782i	$-0.573050\pi$
$61$	3.80652	−	1.01995i	0.0624020	−	0.0167206i	0.289885	+	0.957061i	$0.406383\pi$
$62$	−9.20309	−	12.3624i	−0.148437	−	0.199393i
$63$	−56.1034	+	75.6325i	−0.890530	+	1.20052i
$64$	−49.0315	+	41.1329i	−0.766117	+	0.642701i
$65$	3.10248	−	5.37365i	0.0477305	−	0.0826716i
$66$	41.5077	−	13.7931i	0.628905	−	0.208987i
$67$	121.375	+	32.5224i	1.81157	+	0.485409i	0.995685	−	0.0928006i	$-0.0295819\pi$
$67$	121.375	+	32.5224i	1.81157	+	0.485409i	0.815888	+	0.578210i	$0.196249\pi$
$68$	−42.4357	+	10.0558i	−0.624054	+	0.147879i
$69$	45.5061	−	22.9033i	0.659508	−	0.331932i
$70$	14.0863	+	11.1384i	0.201232	+	0.159120i
$71$	89.0591			1.25435			0.627177	−	0.778877i	$-0.284210\pi$
$71$	89.0591			1.25435			0.627177	+	0.778877i	$0.284210\pi$
$72$	16.7215	+	70.0314i	0.232243	+	0.972658i
$73$		−	82.8383i		−	1.13477i	−0.823452	−	0.567386i	$-0.807955\pi$
$73$		−	82.8383i		−	1.13477i	0.823452	−	0.567386i	$-0.192045\pi$
$74$	−81.6168	−	64.5367i	−1.10293	−	0.872117i
$75$	−39.9466	+	60.8504i	−0.532622	+	0.811338i
$76$	−16.6840	+	27.0467i	−0.219527	+	0.355877i
$77$	19.7417	−	73.6771i	0.256386	−	0.956846i
$78$	8.73712	−	42.4953i	0.112014	−	0.544811i
$79$	59.4445	+	34.3203i	0.752462	+	0.434434i	0.826583	−	0.562815i	$-0.190282\pi$
$79$	59.4445	+	34.3203i	0.752462	+	0.434434i	−0.0741205	+	0.997249i	$0.523615\pi$
$80$	13.4468	−	2.77549i	0.168085	−	0.0346936i
$81$	78.8807	+	18.4073i	0.973836	+	0.227251i
$82$	97.3138	+	130.720i	1.18675	+	1.59415i
$83$	1.87483	+	6.99695i	0.0225883	+	0.0843006i	0.976300	−	0.216422i	$-0.0694388\pi$
$83$	1.87483	+	6.99695i	0.0225883	+	0.0843006i	−0.953712	+	0.300723i	$0.902772\pi$
$84$	118.022	+	42.8462i	1.40503	+	0.510073i
$85$	9.03727	+	2.42153i	0.106321	+	0.0284886i
$86$	−34.2637	−	86.2515i	−0.398415	−	1.00292i
$87$	5.36044	+	25.8478i	0.0616143	+	0.297102i
$88$	−33.4479	−	47.7742i	−0.380089	−	0.542889i
$89$			144.573i			1.62442i	0.583367	+	0.812208i	$0.301735\pi$
$89$			144.573i			1.62442i	−0.583367	+	0.812208i	$0.698265\pi$
$90$	3.97235	−	14.9270i	0.0441372	−	0.165856i
$91$	−53.4973	−	53.4973i	−0.587882	−	0.587882i
$92$	−46.6120	−	49.4095i	−0.506652	−	0.537060i
$93$	10.3931	+	20.6498i	0.111754	+	0.222041i
$94$	−19.2646	+	44.6580i	−0.204942	+	0.475085i
$95$	5.90424	−	3.40882i	0.0621499	−	0.0358823i
$96$	83.1014	−	48.0640i	0.865640	−	0.500667i
$97$	48.6538	−	84.2708i	0.501585	−	0.868771i	−0.498413	−	0.866940i	$-0.666084\pi$
$97$	48.6538	−	84.2708i	0.501585	−	0.868771i	0.999998	−	0.00183136i	$-0.000582939\pi$
$98$	97.0257	−	72.2301i	0.990058	−	0.737042i
$99$	−64.8999	+	9.62105i	−0.655555	+	0.0971823i
$100$	92.9760	+	27.8390i	0.929760	+	0.278390i
$101$	39.6775	+	148.079i	0.392847	+	1.46612i	0.825417	+	0.564524i	$0.190940\pi$
$101$	39.6775	+	148.079i	0.392847	+	1.46612i	−0.432570	+	0.901601i	$0.642393\pi$
$102$	65.3024	−	3.85883i	0.640219	−	0.0378316i
$103$	88.3701	+	153.062i	0.857962	+	1.48603i	0.873869	+	0.486161i	$0.161603\pi$
$103$	88.3701	+	153.062i	0.857962	+	1.48603i	−0.0159070	+	0.999873i	$0.505064\pi$
$104$	−57.6257	+	5.03833i	−0.554094	+	0.0484455i
$105$	−17.9249	−	20.1070i	−0.170713	−	0.191495i
$106$	−153.932	−	121.718i	−1.45219	−	1.14829i
$107$	−15.4533	−	15.4533i	−0.144424	−	0.144424i	0.631198	−	0.775622i	$-0.282563\pi$
$107$	−15.4533	−	15.4533i	−0.144424	−	0.144424i	−0.775622	+	0.631198i	$0.782563\pi$
$108$	−6.55510	−	107.801i	−0.0606954	−	0.998156i
$109$	−84.1975	−	84.1975i	−0.772454	−	0.772454i	0.206081	−	0.978535i	$-0.433929\pi$
$109$	−84.1975	−	84.1975i	−0.772454	−	0.772454i	−0.978535	+	0.206081i	$0.933929\pi$
$110$	1.45227	+	12.4270i	0.0132024	+	0.112972i
$111$	103.858	+	116.502i	0.935659	+	1.04956i
$112$	9.74669	−	167.128i	0.0870240	−	1.49222i
$113$	44.6315	+	77.3041i	0.394969	+	0.684107i	0.993097	−	0.117294i	$-0.0374219\pi$
$113$	44.6315	+	77.3041i	0.394969	+	0.684107i	−0.598128	+	0.801401i	$0.704089\pi$
$114$	31.6593	−	35.6359i	0.277713	−	0.312596i
$115$	3.77166	+	14.0760i	0.0327971	+	0.122400i
$116$	30.9812	−	16.7034i	0.267079	−	0.143995i
$117$	−23.9220	+	60.5199i	−0.204461	+	0.517264i
$118$	17.9798	+	2.63400i	0.152371	+	0.0223220i
$119$	57.0389	−	98.7943i	0.479319	−	0.830204i
$120$	−20.5862	+	0.615643i	−0.171552	+	0.00513036i
$121$	−58.7661	+	33.9286i	−0.485670	+	0.280402i
$122$	2.90980	+	7.32480i	0.0238508	+	0.0600393i
$123$	−109.897	−	218.352i	−0.893471	−	1.77522i
$124$	22.4212	−	21.1517i	0.180816	−	0.170578i
$125$	−29.8930	−	29.8930i	−0.239144	−	0.239144i
$126$	−163.267	−	93.8903i	−1.29577	−	0.745161i
$127$		−	95.7663i		−	0.754065i	−0.926200	−	0.377033i	$-0.876944\pi$
$127$		−	95.7663i		−	0.754065i	0.926200	−	0.377033i	$-0.123056\pi$
$128$	−93.0923	−	87.8512i	−0.727283	−	0.686337i
$129$	28.2689	+	136.312i	0.219139	+	1.05668i
$130$	11.3949	+	4.91553i	0.0876531	+	0.0378118i
$131$	−126.942	−	34.0140i	−0.969023	−	0.259649i	−0.260607	−	0.965445i	$-0.583923\pi$
$131$	−126.942	−	34.0140i	−0.969023	−	0.259649i	−0.708415	+	0.705796i	$0.750589\pi$
$132$	37.0357	+	79.2522i	0.280574	+	0.600395i
$133$	−21.5148	−	80.2944i	−0.161766	−	0.603717i
$134$	−36.4281	+	248.660i	−0.271851	+	1.85567i
$135$	−9.73751	+	21.0243i	−0.0721297	+	0.155736i
$136$	−29.8270	−	81.9633i	−0.219316	−	0.602671i
$137$	−58.5672	−	33.8138i	−0.427498	−	0.246816i	0.270782	−	0.962641i	$-0.412718\pi$
$137$	−58.5672	−	33.8138i	−0.427498	−	0.246816i	−0.698280	+	0.715825i	$0.746051\pi$
$138$	56.0611	+	85.0800i	0.406240	+	0.616522i
$139$	46.8794	−	174.956i	0.337262	−	1.25868i	−0.564134	−	0.825684i	$-0.690790\pi$
$139$	46.8794	−	174.956i	0.337262	−	1.25868i	0.901396	−	0.432996i	$-0.142544\pi$
$140$	−18.8561	+	30.5678i	−0.134686	+	0.218342i
$141$	40.0362	−	60.9868i	0.283945	−	0.432531i
$142$	20.6750	+	176.914i	0.145598	+	1.24588i
$143$		−	52.7111i		−	0.368609i
$144$	−135.234	+	49.4746i	−0.939126	+	0.343573i
$145$	−7.55102			−0.0520760
$146$	164.557	−	19.2308i	1.12710	−	0.131718i
$147$	−162.069	+	81.5698i	−1.10251	+	0.554897i
$148$	109.254	−	177.112i	0.738200	−	1.19670i
$149$	115.680	+	30.9963i	0.776374	+	0.208029i	0.625186	−	0.780476i	$-0.285023\pi$
$149$	115.680	+	30.9963i	0.776374	+	0.208029i	0.151189	+	0.988505i	$0.451690\pi$
$150$	−130.152	−	65.2269i	−0.867677	−	0.434846i
$151$	62.0746	−	107.516i	0.411090	−	0.712028i	−0.583919	−	0.811812i	$-0.698482\pi$
$151$	62.0746	−	107.516i	0.411090	−	0.712028i	0.995009	+	0.0997832i	$0.0318149\pi$
$152$	−57.6009	−	26.8637i	−0.378953	−	0.176735i
$153$	−97.4805	−	11.2231i	−0.637127	−	0.0733534i
$154$	150.941	+	22.1125i	0.980138	+	0.143588i
$155$	−6.38745	+	1.71151i	−0.0412094	+	0.0110420i
$156$	86.4444	+	7.49090i	0.554131	+	0.0480186i
$157$	−79.3946	+	296.305i	−0.505698	+	1.88729i	−0.0465835	+	0.998914i	$0.514833\pi$
$157$	−79.3946	+	296.305i	−0.505698	+	1.88729i	−0.459115	+	0.888377i	$0.651833\pi$
$158$	−54.3767	+	126.053i	−0.344156	+	0.797803i
$159$	195.880	+	219.726i	1.23195	+	1.38193i
$160$	8.63512	+	26.0675i	0.0539695	+	0.162922i
$161$	177.683			1.10362
$162$	−18.2537	+	160.968i	−0.112677	+	0.993632i
$163$	174.457	−	174.457i	1.07029	−	1.07029i	0.0729500	−	0.997336i	$-0.476759\pi$
$163$	174.457	−	174.457i	1.07029	−	1.07029i	0.997336	−	0.0729500i	$-0.0232413\pi$
$164$	−237.082	+	223.658i	−1.44562	+	1.36377i
$165$	1.07503	−	18.7365i	0.00651534	−	0.113555i
$166$	−13.4641	+	5.34864i	−0.0811088	+	0.0322207i
$167$	−107.460	−	186.127i	−0.643476	−	1.11453i	−0.984651	−	0.174533i	$-0.944158\pi$
$167$	−107.460	−	186.127i	−0.643476	−	1.11453i	0.341176	−	0.939999i	$-0.389175\pi$
$168$	−57.7144	+	244.396i	−0.343538	+	1.45474i
$169$	101.080	+	58.3585i	0.598106	+	0.345317i
$170$	−2.71233	+	18.5145i	−0.0159549	+	0.108909i
$171$	−56.0104	+	44.4449i	−0.327546	+	0.259911i
$172$	163.383	−	88.0873i	0.949900	−	0.512135i
$173$	−166.639	+	44.6509i	−0.963234	+	0.258098i	−0.705969	−	0.708243i	$-0.749488\pi$
$173$	−166.639	+	44.6509i	−0.963234	+	0.258098i	−0.257265	+	0.966341i	$0.582821\pi$
$174$	−50.1018	+	16.6490i	−0.287942	+	0.0956837i
$175$	−219.863	+	126.938i	−1.25636	+	0.725360i
$176$	87.1377	−	77.5343i	0.495101	−	0.440536i
$177$	−25.8815	−	8.55136i	−0.146223	−	0.0483128i
$178$	−287.192	+	33.5624i	−1.61344	+	0.188553i
$179$	−70.8708	+	70.8708i	−0.395926	+	0.395926i	−0.876793	−	0.480867i	$-0.840322\pi$
$179$	−70.8708	+	70.8708i	−0.395926	+	0.395926i	0.480867	+	0.876793i	$0.340322\pi$
$180$	30.5744	+	4.42570i	0.169858	+	0.0245872i
$181$	4.33948	−	4.33948i	0.0239750	−	0.0239750i	−0.695018	−	0.718993i	$-0.744603\pi$
$181$	4.33948	−	4.33948i	0.0239750	−	0.0239750i	0.718993	+	0.695018i	$0.244603\pi$
$182$	93.8521	−	118.691i	0.515671	−	0.652147i
$183$	−2.40070	−	11.5761i	−0.0131186	−	0.0632573i
$184$	87.3302	−	104.064i	0.474621	−	0.565566i
$185$	−38.6633	+	22.3223i	−0.208991	+	0.120661i
$186$	−38.6078	+	25.4395i	−0.207569	+	0.136772i
$187$	76.7715	−	20.5709i	0.410543	−	0.110005i
$188$	−93.1845	−	27.9014i	−0.495662	−	0.148412i
$189$	216.884	+	181.031i	1.14753	+	0.957835i
$190$	8.14221	+	10.9373i	0.0428538	+	0.0575648i
$191$	−199.278	−	115.053i	−1.04334	−	0.602373i	−0.122563	−	0.992461i	$-0.539111\pi$
$191$	−199.278	−	115.053i	−1.04334	−	0.602373i	−0.920778	+	0.390087i	$0.872445\pi$
$192$	114.770	+	153.921i	0.597761	+	0.801674i
$193$	−125.936	−	218.127i	−0.652518	−	1.13019i	−0.982510	−	0.186210i	$-0.940379\pi$
$193$	−125.936	−	218.127i	−0.652518	−	1.13019i	0.329992	−	0.943984i	$-0.392954\pi$
$194$	178.697	+	77.0864i	0.921120	+	0.397353i
$195$	−15.5613	−	10.2156i	−0.0798017	−	0.0523877i
$196$	166.008	+	175.972i	0.846980	+	0.897814i
$197$	−129.669	+	129.669i	−0.658219	+	0.658219i	−0.954959	−	0.296739i	$-0.904101\pi$
$197$	−129.669	+	129.669i	−0.658219	+	0.658219i	0.296739	+	0.954959i	$0.404101\pi$
$198$	−34.1784	−	126.689i	−0.172618	−	0.639843i
$199$	−205.292			−1.03162			−0.515810	−	0.856703i	$-0.672509\pi$
$199$	−205.292			−1.03162			−0.515810	+	0.856703i	$0.672509\pi$
$200$	−33.7174	+	191.158i	−0.168587	+	0.955789i
$201$	118.265	−	357.939i	0.588383	−	1.78079i
$202$	−284.944	+	113.195i	−1.41062	+	0.560371i
$203$	−23.8292	+	88.9319i	−0.117385	+	0.438088i
$204$	22.8253	+	128.826i	0.111889	+	0.631500i
$205$	67.5411	−	18.0976i	0.329469	−	0.0882809i
$206$	−283.539	+	211.079i	−1.37640	+	1.02465i
$207$	−60.7770	−	140.230i	−0.293609	−	0.677439i
$208$	−23.3863	−	113.303i	−0.112434	−	0.544725i
$209$	28.9579	−	50.1565i	0.138554	−	0.239983i
$210$	35.7810	−	40.2753i	0.170386	−	0.191787i
$211$	96.4890	+	25.8542i	0.457294	+	0.122532i	0.480110	−	0.877208i	$-0.340597\pi$
$211$	96.4890	+	25.8542i	0.457294	+	0.122532i	−0.0228164	+	0.999740i	$0.507263\pi$
$212$	206.056	−	334.040i	0.971964	−	1.57566i
$213$	15.3045	−	266.739i	0.0718520	−	1.25229i
$214$	27.1103	−	34.2852i	0.126683	−	0.160211i
$215$	−39.8212			−0.185215
$216$	212.623	−	38.0474i	0.984364	−	0.176145i
$217$			80.6291i			0.371563i
$218$	147.710	−	186.803i	0.677570	−	0.856894i
$219$	−248.107	−	14.2354i	−1.13291	−	0.0650020i
$220$	−24.3488	+	5.76981i	−0.110676	+	0.0262264i
$221$	20.4038	−	76.1480i	0.0923248	−	0.344561i
$222$	−207.318	+	233.358i	−0.933863	+	1.05116i
$223$	−10.8479	−	6.26305i	−0.0486454	−	0.0280854i	0.475480	−	0.879726i	$-0.342274\pi$
$223$	−10.8479	−	6.26305i	−0.0486454	−	0.0280854i	−0.524125	+	0.851641i	$0.675608\pi$
$224$	334.259	−	19.4369i	1.49223	−	0.0867720i
$225$	175.387	+	130.100i	0.779496	+	0.578222i
$226$	−143.202	+	106.606i	−0.633637	+	0.471707i
$227$	−57.2643	−	213.713i	−0.252265	−	0.941468i	−0.969591	−	0.244730i	$-0.921301\pi$
$227$	−57.2643	−	213.713i	−0.252265	−	0.941468i	0.717326	−	0.696738i	$-0.245366\pi$
$228$	78.1397	+	54.6178i	0.342718	+	0.239552i
$229$	−35.7878	−	9.58932i	−0.156279	−	0.0418748i	0.179831	−	0.983697i	$-0.442445\pi$
$229$	−35.7878	−	9.58932i	−0.156279	−	0.0418748i	−0.336110	+	0.941823i	$0.609111\pi$
$230$	−27.0862	+	10.7601i	−0.117766	+	0.0467829i
$231$	−217.276	−	71.7890i	−0.940588	−	0.310775i
$232$	40.3732	+	57.6658i	0.174022	+	0.248560i
$233$			3.99805i			0.0171590i	0.999963	+	0.00857951i	$0.00273098\pi$
$233$			3.99805i			0.0171590i	−0.999963	+	0.00857951i	$0.997269\pi$
$234$	−125.775	−	33.4710i	−0.537500	−	0.143038i
$235$	14.7561	+	14.7561i	0.0627919	+	0.0627919i
$236$	−1.05840	+	36.3280i	−0.00448475	+	0.153932i
$237$	113.007	−	172.143i	0.476824	−	0.726342i
$238$	209.495	+	90.3718i	0.880229	+	0.379713i
$239$	14.3118	−	8.26293i	0.0598821	−	0.0345729i	−0.469760	−	0.882794i	$-0.655660\pi$
$239$	14.3118	−	8.26293i	0.0598821	−	0.0345729i	0.529642	+	0.848221i	$0.322326\pi$
$240$	−6.00202	−	40.7512i	−0.0250084	−	0.169797i
$241$	23.6755	−	41.0071i	0.0982384	−	0.170154i	−0.812717	−	0.582658i	$-0.802013\pi$
$241$	23.6755	−	41.0071i	0.0982384	−	0.170154i	0.910956	+	0.412505i	$0.135346\pi$
$242$	−81.0410	−	108.861i	−0.334880	−	0.449840i
$243$	68.6866	−	233.090i	0.282661	−	0.959220i
$244$	−13.8751	+	7.48070i	−0.0568650	+	0.0306586i
$245$	−13.4327	−	50.1317i	−0.0548275	−	0.204619i
$246$	408.240	−	268.998i	1.65951	−	1.09349i
$247$	−28.7227	−	49.7491i	−0.116286	−	0.201414i
$248$	47.2225	+	39.6289i	0.190413	+	0.159794i
$249$	21.2786	−	4.41284i	0.0854560	−	0.0177223i
$250$	52.4423	−	66.3216i	0.209769	−	0.265286i
$251$	144.761	+	144.761i	0.576738	+	0.576738i	0.934003	−	0.357265i	$-0.116291\pi$
$251$	144.761	+	144.761i	0.576738	+	0.576738i	−0.357265	+	0.934003i	$0.616291\pi$
$252$	148.609	−	346.123i	0.589719	−	1.37350i
$253$	87.5356	+	87.5356i	0.345991	+	0.345991i
$254$	190.238	−	22.2320i	0.748968	−	0.0875276i
$255$	8.80568	−	26.6512i	0.0345321	−	0.104514i
$256$	152.903	−	205.321i	0.597279	−	0.802034i
$257$	125.090	+	216.663i	0.486732	+	0.843045i	0.999884	−	0.0152528i	$-0.00485531\pi$
$257$	125.090	+	216.663i	0.486732	+	0.843045i	−0.513151	+	0.858298i	$0.671522\pi$
$258$	−264.218	+	87.8002i	−1.02410	+	0.340311i
$259$	140.888	+	525.800i	0.543967	+	2.03011i
$260$	−7.11930	+	23.7769i	−0.0273819	+	0.0914495i
$261$	78.3374	−	11.6131i	0.300143	−	0.0444945i
$262$	38.0988	−	260.064i	0.145415	−	0.992611i
$263$	44.5421	−	77.1492i	0.169362	−	0.293343i	−0.768834	−	0.639449i	$-0.779163\pi$
$263$	44.5421	−	77.1492i	0.169362	−	0.293343i	0.938196	+	0.346105i	$0.112496\pi$
$264$	−148.835	+	91.9690i	−0.563770	+	0.348367i
$265$	−72.9204	+	42.1006i	−0.275171	+	0.158870i
$266$	154.509	−	61.3790i	0.580860	−	0.230748i
$267$	433.007	+	24.8443i	1.62175	+	0.0930500i
$268$	−502.415	−	14.6377i	−1.87468	−	0.0546181i
$269$	−137.619	−	137.619i	−0.511595	−	0.511595i	0.403420	−	0.915015i	$-0.367821\pi$
$269$	−137.619	−	137.619i	−0.511595	−	0.511595i	−0.915015	+	0.403420i	$0.867821\pi$
$270$	−44.0249	−	14.4626i	−0.163055	−	0.0535653i
$271$			334.184i			1.23315i	0.787295	+	0.616576i	$0.211481\pi$
$271$			334.184i			1.23315i	−0.787295	+	0.616576i	$0.788519\pi$
$272$	155.894	−	78.2783i	0.573140	−	0.287788i
$273$	−169.422	+	151.035i	−0.620592	+	0.553242i
$274$	53.5742	−	124.192i	0.195526	−	0.453257i
$275$	−170.852	−	45.7797i	−0.621281	−	0.166472i
$276$	−155.995	+	131.116i	−0.565200	+	0.475056i
$277$	35.0205	+	130.698i	0.126428	+	0.471835i	0.999887	−	0.0150632i	$-0.00479494\pi$
$277$	35.0205	+	130.698i	0.126428	+	0.471835i	−0.873459	+	0.486898i	$0.838128\pi$
$278$	358.431	+	52.5092i	1.28932	+	0.188882i
$279$	63.6338	−	27.5795i	0.228078	−	0.0988512i
$280$	−65.0998	−	30.3610i	−0.232499	−	0.108432i
$281$	87.7929	+	50.6873i	0.312430	+	0.180382i	0.648013	−	0.761629i	$-0.275600\pi$
$281$	87.7929	+	50.6873i	0.312430	+	0.180382i	−0.335583	+	0.942011i	$0.608933\pi$
$282$	130.443	+	65.3731i	0.462565	+	0.231820i
$283$	−79.2038	+	295.592i	−0.279872	+	1.04450i	0.672634	+	0.739976i	$0.265163\pi$
$283$	−79.2038	+	295.592i	−0.279872	+	1.04450i	−0.952506	+	0.304521i	$0.901504\pi$
$284$	−346.637	+	82.1408i	−1.22055	+	0.289228i
$285$	−9.19504	−	18.2694i	−0.0322633	−	0.0641033i
$286$	104.710	−	12.2368i	0.366118	−	0.0427860i
$287$		−	852.575i		−	2.97064i
$288$	−129.675	−	257.155i	−0.450259	−	0.892898i
$289$	−170.131			−0.588688
$290$	−1.75296	−	15.0000i	−0.00604469	−	0.0517240i
$291$	−244.036	−	160.203i	−0.838613	−	0.550527i
$292$	76.4032	+	322.424i	0.261655	+	1.10419i
$293$	−148.791	−	39.8684i	−0.507819	−	0.136070i	−0.00419275	−	0.999991i	$-0.501335\pi$
$293$	−148.791	−	39.8684i	−0.507819	−	0.136070i	−0.503627	+	0.863921i	$0.668001\pi$
$294$	−199.661	−	303.012i	−0.679119	−	1.03065i
$295$	3.89848	−	6.75236i	0.0132152	−	0.0228893i
$296$	377.193	+	175.914i	1.27430	+	0.594304i
$297$	17.6629	+	196.033i	0.0594712	+	0.660045i
$298$	−34.7187	+	236.991i	−0.116506	+	0.795273i
$299$	118.605	−	31.7800i	0.396671	−	0.106288i
$300$	99.3574	−	273.686i	0.331191	−	0.912287i
$301$	−125.666	+	468.993i	−0.417496	+	1.55812i
$302$	227.990	+	98.3502i	0.754932	+	0.325663i
$303$	450.325	−	93.3904i	1.48622	−	0.308219i
$304$	39.9922	−	120.659i	0.131553	−	0.396906i
$305$	3.38176			0.0110877
$306$	−0.335515	−	196.249i	−0.00109646	−	0.641335i
$307$	−98.8548	+	98.8548i	−0.322003	+	0.322003i	−0.849535	−	0.527532i	$-0.823117\pi$
$307$	−98.8548	+	98.8548i	−0.322003	+	0.322003i	0.527532	+	0.849535i	$0.323117\pi$
$308$	−8.88533	+	304.975i	−0.0288485	+	0.990179i
$309$	473.617	−	238.372i	1.53274	−	0.771430i
$310$	−4.88273	−	12.2912i	−0.0157507	−	0.0396491i
$311$	258.528	+	447.784i	0.831280	+	1.43982i	0.897024	+	0.441982i	$0.145725\pi$
$311$	258.528	+	447.784i	0.831280	+	1.43982i	−0.0657442	+	0.997837i	$0.520942\pi$
$312$	5.18741	+	173.459i	0.0166263	+	0.555959i
$313$	−70.6134	−	40.7686i	−0.225602	−	0.130251i	0.382940	−	0.923773i	$-0.374912\pi$
$313$	−70.6134	−	40.7686i	−0.225602	−	0.130251i	−0.608541	+	0.793522i	$0.708245\pi$
$314$	−607.035	−	88.9292i	−1.93323	−	0.283214i
$315$	−63.3024	+	50.2311i	−0.200960	+	0.159464i
$316$	−263.025	−	78.7553i	−0.832358	−	0.249226i
$317$	−224.100	+	60.0475i	−0.706941	+	0.189424i	−0.594338	−	0.804216i	$-0.702586\pi$
$317$	−224.100	+	60.0475i	−0.706941	+	0.189424i	−0.112604	+	0.993640i	$0.535919\pi$
$318$	−391.008	+	440.121i	−1.22959	+	1.38403i
$319$	−55.5520	+	32.0730i	−0.174144	+	0.100542i
$320$	−49.7780	+	23.2050i	−0.155556	+	0.0725157i
$321$	−48.9394	+	43.6283i	−0.152459	+	0.135914i
$322$	41.2487	+	352.963i	0.128102	+	1.09616i
$323$	61.2483	−	61.2483i	0.189623	−	0.189623i
$324$	−323.998	+	1.10785i	−0.999994	+	0.00341928i
$325$	−124.057	+	124.057i	−0.381713	+	0.381713i
$326$	387.054	+	306.055i	1.18728	+	0.938818i
$327$	−266.647	+	237.709i	−0.815433	+	0.726938i
$328$	−499.332	−	419.037i	−1.52235	−	1.27755i
$329$	220.356	−	127.223i	0.669776	−	0.386695i
$330$	37.4693	−	2.21412i	0.113543	−	0.00670946i
$331$	446.744	−	119.705i	1.34968	−	0.361646i	0.489663	−	0.871912i	$-0.337120\pi$
$331$	446.744	−	119.705i	1.34968	−	0.361646i	0.860017	+	0.510266i	$0.170453\pi$
$332$	−13.7506	−	25.5044i	−0.0414176	−	0.0768206i
$333$	366.778	−	291.042i	1.10144	−	0.874001i
$334$	344.791	−	256.677i	1.03231	−	0.768494i
$335$	93.3848	+	53.9158i	0.278761	+	0.160943i
$336$	−498.886	−	57.9124i	−1.48478	−	0.172358i
$337$	−204.678	−	354.513i	−0.607353	−	1.05197i	−0.991675	−	0.128767i	$-0.958898\pi$
$337$	−204.678	−	354.513i	−0.607353	−	1.05197i	0.384322	−	0.923199i	$-0.374435\pi$
$338$	−92.4625	+	214.341i	−0.273558	+	0.634146i
$339$	239.201	−	120.390i	0.705608	−	0.355134i
$340$	−37.4084	−	1.08988i	−0.110025	−	0.00320552i
$341$	−39.7221	+	39.7221i	−0.116487	+	0.116487i
$342$	−101.292	−	100.946i	−0.296174	−	0.295163i
$343$	−120.115			−0.350189
$344$	212.913	+	304.107i	0.618933	+	0.884033i
$345$	42.8069	−	8.87750i	0.124078	−	0.0257319i
$346$	−127.383	−	320.660i	−0.368160	−	0.926764i
$347$	−27.8673	+	104.002i	−0.0803093	+	0.299718i	−0.994385	−	0.105826i	$-0.966251\pi$
$347$	−27.8673	+	104.002i	−0.0803093	+	0.299718i	0.914075	+	0.405544i	$0.132918\pi$
$348$	−44.7039	−	95.6613i	−0.128460	−	0.274889i
$349$	292.371	−	78.3405i	0.837739	−	0.224471i	0.185652	−	0.982616i	$-0.440560\pi$
$349$	292.371	−	78.3405i	0.837739	−	0.224471i	0.652087	+	0.758144i	$0.273894\pi$
$350$	−303.201	−	407.286i	−0.866289	−	1.16367i
$351$	177.151	+	82.0482i	0.504703	+	0.233756i
$352$	174.249	+	155.098i	0.495026	+	0.440619i
$353$	−96.7331	+	167.547i	−0.274032	+	0.474637i	−0.969890	−	0.243542i	$-0.921691\pi$
$353$	−96.7331	+	167.547i	−0.274032	+	0.474637i	0.695859	+	0.718179i	$0.255024\pi$
$354$	10.9788	−	53.3982i	0.0310135	−	0.150842i
$355$	73.8212	+	19.7803i	0.207947	+	0.0557193i
$356$	−133.342	−	562.709i	−0.374557	−	1.58064i
$357$	−286.094	−	187.813i	−0.801385	−	0.526087i
$358$	−157.236	−	124.331i	−0.439207	−	0.347293i
$359$	43.2253			0.120405			0.0602024	−	0.998186i	$-0.480825\pi$
$359$	43.2253			0.120405			0.0602024	+	0.998186i	$0.480825\pi$
$360$	−1.69376	+	61.7630i	−0.00470489	+	0.171564i
$361$			297.883i			0.825159i
$362$	9.62770	+	7.61289i	0.0265959	+	0.0210301i
$363$	91.5200	+	181.839i	0.252121	+	0.500935i
$364$	257.564	+	158.881i	0.707595	+	0.436488i
$365$	18.3987	−	68.6648i	0.0504073	−	0.188123i
$366$	22.4383	−	7.45632i	0.0613070	−	0.0203725i
$367$	−314.433	−	181.538i	−0.856767	−	0.494655i	0.00616149	−	0.999981i	$-0.498039\pi$
$367$	−314.433	−	181.538i	−0.856767	−	0.494655i	−0.862928	+	0.505327i	$0.831372\pi$
$368$	226.995	+	149.321i	0.616835	+	0.405765i
$369$	−672.866	+	291.626i	−1.82348	+	0.790315i
$370$	−53.3184	−	71.6219i	−0.144104	−	0.193573i
$371$	265.719	+	991.677i	0.716224	+	2.67298i
$372$	−59.4979	−	70.7879i	−0.159940	−	0.190290i
$373$	254.904	+	68.3014i	0.683390	+	0.183114i	0.583779	−	0.811913i	$-0.301573\pi$
$373$	254.904	+	68.3014i	0.683390	+	0.183114i	0.0996110	+	0.995026i	$0.468240\pi$
$374$	58.6860	+	147.730i	0.156915	+	0.394999i
$375$	−94.6689	+	84.3948i	−0.252450	+	0.225053i
$376$	33.7930	−	191.587i	0.0898750	−	0.509539i
$377$			63.6249i			0.168766i
$378$	−309.265	+	472.861i	−0.818162	+	1.25096i
$379$	−31.8574	−	31.8574i	−0.0840565	−	0.0840565i	0.663828	−	0.747885i	$-0.268931\pi$
$379$	−31.8574	−	31.8574i	−0.0840565	−	0.0840565i	−0.747885	+	0.663828i	$0.768931\pi$
$380$	−19.8366	+	18.7134i	−0.0522015	+	0.0492459i
$381$	−286.827	−	16.4571i	−0.752827	−	0.0431944i
$382$	182.289	−	422.572i	0.477196	−	1.10621i
$383$	−195.603	+	112.932i	−0.510714	+	0.294861i	−0.733127	−	0.680092i	$-0.761940\pi$
$383$	−195.603	+	112.932i	−0.510714	+	0.294861i	0.222413	+	0.974952i	$0.428607\pi$
$384$	−279.118	+	263.721i	−0.726871	+	0.686775i
$385$	32.7279	−	56.6863i	0.0850074	−	0.147237i
$386$	404.070	−	300.807i	1.04681	−	0.779294i
$387$	413.121	−	61.2429i	1.06750	−	0.158250i
$388$	−111.646	+	372.874i	−0.287749	+	0.961016i
$389$	−122.847	−	458.472i	−0.315802	−	1.17859i	−0.923240	−	0.384223i	$-0.874469\pi$
$389$	−122.847	−	458.472i	−0.315802	−	1.17859i	0.607438	−	0.794367i	$-0.292197\pi$
$390$	16.6806	−	33.2838i	0.0427706	−	0.0853432i
$391$	92.5726	+	160.340i	0.236759	+	0.410078i
$392$	−311.026	+	370.624i	−0.793433	+	0.945468i
$393$	−123.689	+	374.355i	−0.314730	+	0.952558i
$394$	−287.688	−	227.483i	−0.730173	−	0.577368i
$395$	41.6510	+	41.6510i	0.105446	+	0.105446i
$396$	243.731	−	97.3055i	0.615481	−	0.245721i
$397$	−122.223	−	122.223i	−0.307868	−	0.307868i	0.536214	−	0.844082i	$-0.319854\pi$
$397$	−122.223	−	122.223i	−0.307868	−	0.307868i	−0.844082	+	0.536214i	$0.819854\pi$
$398$	−47.6583	−	407.809i	−0.119744	−	1.02465i
$399$	−244.185	+	50.6402i	−0.611992	+	0.126918i
$400$	−387.559	−	22.6019i	−0.968897	−	0.0565048i
$401$	−108.307	−	187.593i	−0.270092	−	0.467813i	0.698793	−	0.715324i	$-0.253721\pi$
$401$	−108.307	−	187.593i	−0.270092	−	0.467813i	−0.968885	+	0.247511i	$0.920387\pi$
$402$	738.495	+	151.836i	1.83705	+	0.377702i
$403$	14.4212	+	53.8207i	0.0357846	+	0.133550i
$404$	−291.009	−	539.758i	−0.720319	−	1.33604i
$405$	61.2960	+	32.7775i	0.151348	+	0.0809322i
$406$	−182.193	−	26.6909i	−0.448752	−	0.0657411i
$407$	−189.628	+	328.445i	−0.465916	+	0.806989i
$408$	−250.612	+	75.2489i	−0.614244	+	0.184434i
$409$	467.836	−	270.105i	1.14385	−	0.660403i	0.196471	−	0.980510i	$-0.437052\pi$
$409$	467.836	−	270.105i	1.14385	−	0.660403i	0.947382	+	0.320106i	$0.103719\pi$
$410$	51.6301	+	129.968i	0.125927	+	0.316995i
$411$	−111.339	+	169.602i	−0.270899	+	0.412658i
$412$	−485.127	−	514.243i	−1.17749	−	1.24816i
$413$	−67.2230	−	67.2230i	−0.162767	−	0.162767i
$414$	264.455	−	153.286i	0.638780	−	0.370257i
$415$			6.21618i			0.0149787i
$416$	219.645	−	72.7595i	0.527992	−	0.174903i
$417$	−515.952	−	170.473i	−1.23729	−	0.408808i
$418$	106.358	+	45.8805i	0.254444	+	0.109762i
$419$	−442.215	−	118.491i	−1.05540	−	0.282795i	−0.310921	−	0.950436i	$-0.600638\pi$
$419$	−442.215	−	118.491i	−1.05540	−	0.282795i	−0.744484	+	0.667641i	$0.767304\pi$
$420$	88.3126	+	61.7284i	0.210268	+	0.146972i
$421$	65.6458	+	244.993i	0.155928	+	0.581932i	0.999024	+	0.0441687i	$0.0140639\pi$
$421$	65.6458	+	244.993i	0.155928	+	0.581932i	−0.843096	+	0.537763i	$0.819269\pi$
$422$	−28.9590	+	197.676i	−0.0686232	+	0.468426i
$423$	−175.780	−	130.392i	−0.415555	−	0.308255i
$424$	711.400	+	331.780i	1.67783	+	0.782500i
$425$	−229.097	−	132.269i	−0.539053	−	0.311222i
$426$	533.424	−	31.5210i	1.25217	−	0.0739929i
$427$	10.6720	−	39.8286i	0.0249931	−	0.0932754i
$428$	74.4005	+	45.8948i	0.173833	+	0.107231i
$429$	−157.874	−	9.05820i	−0.368004	−	0.0211147i
$430$	−9.24443	−	79.1041i	−0.0214987	−	0.183963i
$431$		−	191.766i		−	0.444933i	−0.974940	−	0.222467i	$-0.928589\pi$
$431$		−	191.766i		−	0.444933i	0.974940	−	0.222467i	$-0.0714108\pi$
$432$	124.940	+	413.538i	0.289214	+	0.957264i
$433$	−671.361			−1.55049			−0.775244	−	0.631662i	$-0.782373\pi$
$433$	−671.361			−1.55049			−0.775244	+	0.631662i	$0.782373\pi$
$434$	−160.168	+	18.7179i	−0.369051	+	0.0431289i
$435$	−1.29761	+	22.6159i	−0.00298302	+	0.0519905i
$436$	405.371	+	250.058i	0.929751	+	0.573527i
$437$	130.316	+	34.9180i	0.298205	+	0.0799038i
$438$	−29.3192	−	496.164i	−0.0669388	−	1.13280i
$439$	316.677	−	548.501i	0.721360	−	1.24943i	−0.239094	−	0.970996i	$-0.576851\pi$
$439$	316.677	−	548.501i	0.721360	−	1.24943i	0.960455	−	0.278436i	$-0.0898161\pi$
$440$	−17.1142	−	47.0290i	−0.0388958	−	0.106884i
$441$	216.457	+	499.427i	0.490831	+	1.13249i
$442$	156.003	+	22.8541i	0.352948	+	0.0517061i
$443$	578.144	−	154.913i	1.30507	−	0.349691i	0.461702	−	0.887035i	$-0.347239\pi$
$443$	578.144	−	154.913i	1.30507	−	0.349691i	0.843363	+	0.537344i	$0.180572\pi$
$444$	−511.690	−	357.659i	−1.15245	−	0.805538i
$445$	−32.1102	+	119.837i	−0.0721577	+	0.269296i
$446$	9.92310	−	23.0031i	0.0222491	−	0.0515765i
$447$	112.715	−	341.143i	0.252160	−	0.763183i
$448$	116.209	+	659.488i	0.259395	+	1.47207i
$449$	375.940			0.837284			0.418642	−	0.908151i	$-0.362506\pi$
$449$	375.940			0.837284			0.418642	+	0.908151i	$0.362506\pi$
$450$	−217.725	+	378.605i	−0.483834	+	0.841344i
$451$	420.023	−	420.023i	0.931314	−	0.931314i
$452$	−245.014	−	259.720i	−0.542067	−	0.574601i
$453$	−311.352	−	204.394i	−0.687311	−	0.451201i
$454$	411.243	−	163.368i	0.905822	−	0.359840i
$455$	−32.4620	−	56.2259i	−0.0713451	−	0.123573i
$456$	−90.3572	+	167.902i	−0.198152	+	0.368207i
$457$	−149.241	−	86.1645i	−0.326568	−	0.188544i	0.327749	−	0.944765i	$-0.393710\pi$
$457$	−149.241	−	86.1645i	−0.326568	−	0.188544i	−0.654316	+	0.756221i	$0.727043\pi$
$458$	10.7409	−	73.3180i	0.0234518	−	0.160083i
$459$	−50.3656	+	290.033i	−0.109729	+	0.631879i
$460$	−27.6627	−	51.3083i	−0.0601363	−	0.111540i
$461$	111.874	−	29.9765i	0.242676	−	0.0650249i	−0.135431	−	0.990787i	$-0.543242\pi$
$461$	111.874	−	29.9765i	0.242676	−	0.0650249i	0.378107	+	0.925762i	$0.376575\pi$
$462$	92.1673	−	448.280i	0.199496	−	0.970303i
$463$	−291.279	+	168.170i	−0.629111	+	0.363218i	−0.780408	−	0.625271i	$-0.784988\pi$
$463$	−291.279	+	168.170i	−0.629111	+	0.363218i	0.151297	+	0.988488i	$0.451655\pi$
$464$	−105.180	+	93.5877i	−0.226680	+	0.201698i
$465$	4.02845	+	19.4250i	0.00866333	+	0.0417742i
$466$	−7.94206	+	0.928142i	−0.0170430	+	0.00199172i
$467$	−230.097	+	230.097i	−0.492713	+	0.492713i	−0.909160	−	0.416447i	$-0.863275\pi$
$467$	−230.097	+	230.097i	−0.492713	+	0.492713i	0.416447	+	0.909160i	$0.363275\pi$
$468$	37.2909	−	257.620i	0.0796815	−	0.550470i
$469$	929.691	−	929.691i	1.98228	−	1.98228i
$470$	−25.8871	+	32.7383i	−0.0550790	+	0.0696560i
$471$	873.811	+	288.712i	1.85523	+	0.612976i
$472$	−72.4106	+	6.33100i	−0.153412	+	0.0134131i
$473$	−292.960	+	169.140i	−0.619365	+	0.357591i
$474$	368.193	+	184.524i	0.776779	+	0.389291i
$475$	−186.197	+	49.8915i	−0.391995	+	0.105035i
$476$	−130.888	+	437.137i	−0.274975	+	0.918354i
$477$	691.757	−	548.917i	1.45022	−	1.15077i
$478$	19.7366	+	26.5119i	0.0412900	+	0.0554643i
$479$	156.572	+	90.3968i	0.326872	+	0.188720i	0.654452	−	0.756104i	$-0.272900\pi$
$479$	156.572	+	90.3968i	0.326872	+	0.188720i	−0.327579	+	0.944824i	$0.606233\pi$
$480$	79.5580	−	21.3832i	0.165746	−	0.0445484i
$481$	188.087	+	325.777i	0.391034	+	0.677291i
$482$	86.9560	+	37.5111i	0.180407	+	0.0778239i
$483$	30.5341	−	532.172i	0.0632175	−	1.10181i
$484$	197.437	−	186.258i	0.407928	−	0.384832i
$485$	59.0460	−	59.0460i	0.121744	−	0.121744i
$486$	478.975	+	82.3331i	0.985546	+	0.169410i
$487$	−157.394			−0.323192			−0.161596	−	0.986857i	$-0.551664\pi$
$487$	−157.394			−0.323192			−0.161596	+	0.986857i	$0.551664\pi$
$488$	−18.0813	−	25.8259i	−0.0370519	−	0.0529220i
$489$	−492.531	−	552.490i	−1.00722	−	1.12984i
$490$	96.4672	−	38.3219i	0.196872	−	0.0782079i
$491$	−199.608	+	744.948i	−0.406534	+	1.51721i	0.394674	+	0.918821i	$0.370857\pi$
$491$	−199.608	+	744.948i	−0.406534	+	1.51721i	−0.801209	+	0.598385i	$0.795809\pi$
$492$	629.132	+	748.513i	1.27872	+	1.52137i
$493$	−92.6670	+	24.8301i	−0.187966	+	0.0503652i
$494$	92.1578	−	68.6062i	0.186554	−	0.138879i
$495$	−55.9325	−	6.43959i	−0.112995	−	0.0130093i
$496$	−67.7594	+	103.006i	−0.136612	+	0.207674i
$497$	465.924	−	807.005i	0.937473	−	1.62375i
$498$	13.7058	+	41.2450i	0.0275217	+	0.0828213i
$499$	−472.231	−	126.534i	−0.946355	−	0.253575i	−0.247540	−	0.968878i	$-0.579622\pi$
$499$	−472.231	−	126.534i	−0.946355	−	0.253575i	−0.698815	+	0.715302i	$0.746289\pi$
$500$	143.921	+	88.7792i	0.287842	+	0.177558i
$501$	−575.930	+	289.867i	−1.14956	+	0.578576i
$502$	−253.959	+	321.171i	−0.505895	+	0.639783i
$503$	92.0334			0.182969			0.0914845	−	0.995807i	$-0.470839\pi$
$503$	92.0334			0.182969			0.0914845	+	0.995807i	$0.470839\pi$
$504$	722.066	+	214.857i	1.43267	+	0.426304i
$505$			131.555i			0.260505i
$506$	−153.567	+	194.209i	−0.303491	+	0.383813i
$507$	192.158	−	292.713i	0.379010	−	0.577343i
$508$	88.3269	+	372.743i	0.173872	+	0.733746i
$509$	179.077	−	668.325i	0.351822	−	1.31302i	−0.532616	−	0.846357i	$-0.678791\pi$
$509$	179.077	−	668.325i	0.351822	−	1.31302i	0.884437	−	0.466659i	$-0.154543\pi$
$510$	54.9862	+	11.3053i	0.107816	+	0.0221672i
$511$	−750.635	−	433.379i	−1.46895	−	0.848100i
$512$	443.362	+	256.075i	0.865941	+	0.500146i
$513$	123.490	+	175.393i	0.240722	+	0.341897i
$514$	−401.357	+	298.787i	−0.780850	+	0.581298i
$515$	39.2546	+	146.500i	0.0762225	+	0.284466i
$516$	−235.751	−	504.481i	−0.456882	−	0.977676i
$517$	171.235	+	45.8824i	0.331210	+	0.0887474i
$518$	−1011.78	+	401.934i	−1.95325	+	0.775935i
$519$	105.096	+	506.771i	0.202498	+	0.976436i
$520$	−48.8851	−	8.62259i	−0.0940097	−	0.0165819i
$521$			871.991i			1.67369i	0.547442	+	0.836844i	$0.315602\pi$
$521$			871.991i			1.67369i	−0.547442	+	0.836844i	$0.684398\pi$
$522$	41.2551	+	152.920i	0.0790327	+	0.292950i
$523$	−59.7664	−	59.7664i	−0.114276	−	0.114276i	0.647656	−	0.761933i	$-0.275749\pi$
$523$	−59.7664	−	59.7664i	−0.114276	−	0.114276i	−0.761933	+	0.647656i	$0.775749\pi$
$524$	525.457	+	15.3090i	1.00278	+	0.0292156i
$525$	342.406	+	680.320i	0.652202	+	1.29585i
$526$	163.596	+	70.5720i	0.311019	+	0.134167i
$527$	−72.7596	+	42.0078i	−0.138064	+	0.0797111i
$528$	−217.247	−	274.308i	−0.411452	−	0.519522i
$529$	120.313	−	208.388i	0.227435	−	0.393929i
$530$	−100.560	−	135.081i	−0.189737	−	0.254871i
$531$	−30.0596	+	76.0473i	−0.0566094	+	0.143215i
$532$	157.797	+	292.680i	0.296611	+	0.550150i
$533$	−152.490	−	569.101i	−0.286098	−	1.06773i
$534$	51.1692	+	865.928i	0.0958224	+	1.62159i
$535$	−9.37704	−	16.2415i	−0.0175272	−	0.0303580i
$536$	−87.5575	−	1001.44i	−0.163354	−	1.86835i
$537$	200.084	+	224.442i	0.372596	+	0.417955i
$538$	241.429	−	305.325i	0.448753	−	0.567519i
$539$	−311.757	−	311.757i	−0.578399	−	0.578399i
$540$	18.5094	−	90.8122i	0.0342767	−	0.168171i
$541$	−199.007	−	199.007i	−0.367851	−	0.367851i	0.498842	−	0.866693i	$-0.333759\pi$
$541$	−199.007	−	199.007i	−0.367851	−	0.367851i	−0.866693	+	0.498842i	$0.833759\pi$
$542$	−663.851	+	77.5804i	−1.22482	+	0.143137i
$543$	−12.2513	−	13.7428i	−0.0225623	−	0.0253090i
$544$	191.689	+	291.509i	0.352370	+	0.535861i
$545$	−51.0908	−	88.4919i	−0.0937446	−	0.162370i
$546$	−339.359	−	301.490i	−0.621537	−	0.552180i
$547$	−101.528	−	378.909i	−0.185610	−	0.692705i	−0.994499	−	0.104744i	$-0.966598\pi$
$547$	−101.528	−	378.909i	−0.185610	−	0.692705i	0.808890	−	0.587961i	$-0.200069\pi$
$548$	259.143	+	77.5929i	0.472889	+	0.141593i
$549$	−35.0838	+	5.20097i	−0.0639049	+	0.00947354i
$550$	51.2775	−	350.023i	0.0932318	−	0.636405i
$551$	−34.9536	+	60.5414i	−0.0634366	+	0.109875i
$552$	−296.673	−	279.443i	−0.537450	−	0.506238i
$553$	621.983	−	359.102i	1.12474	−	0.649371i
$554$	−251.500	+	99.9090i	−0.453971	+	0.180341i
$555$	60.2127	+	119.636i	0.108491	+	0.215559i
$556$	−21.0994	+	724.206i	−0.0379486	+	1.30253i
$557$	−112.934	−	112.934i	−0.202755	−	0.202755i	0.598425	−	0.801179i	$-0.295794\pi$
$557$	−112.934	−	112.934i	−0.202755	−	0.202755i	−0.801179	+	0.598425i	$0.795794\pi$
$558$	69.5586	+	120.005i	0.124657	+	0.215062i
$559$			335.533i			0.600238i
$560$	45.1988	−	136.368i	0.0807121	−	0.243514i
$561$	−48.4184	−	233.471i	−0.0863073	−	0.416170i
$562$	−80.3083	+	186.166i	−0.142897	+	0.331256i
$563$	−251.958	−	67.5119i	−0.447528	−	0.119915i	0.0280147	−	0.999608i	$-0.491081\pi$
$563$	−251.958	−	67.5119i	−0.447528	−	0.119915i	−0.475542	+	0.879693i	$0.657748\pi$
$564$	−99.5802	+	274.300i	−0.176561	+	0.486347i
$565$	19.8256	+	73.9903i	0.0350896	+	0.130956i
$566$	−605.576	−	88.7154i	−1.06992	−	0.156741i
$567$	579.472	−	618.473i	1.02200	−	1.09078i
$568$	−243.642	−	669.520i	−0.428948	−	1.17873i
$569$	−467.191	−	269.733i	−0.821073	−	0.474047i	0.0297132	−	0.999558i	$-0.490541\pi$
$569$	−467.191	−	269.733i	−0.821073	−	0.474047i	−0.850786	+	0.525512i	$0.823874\pi$
$570$	34.1573	−	22.5070i	0.0599251	−	0.0394860i
$571$	182.270	−	680.242i	0.319212	−	1.19132i	−0.600791	−	0.799406i	$-0.705148\pi$
$571$	182.270	−	680.242i	0.319212	−	1.19132i	0.920003	−	0.391910i	$-0.128186\pi$
$572$	48.6164	+	205.163i	0.0849936	+	0.358676i
$573$	−378.838	+	577.081i	−0.661149	+	1.00712i
$574$	1693.62	−	197.924i	2.95056	−	0.344815i
$575$		−	412.034i		−	0.716581i
$576$	480.729	−	317.294i	0.834599	−	0.550858i
$577$	488.442			0.846519			0.423260	−	0.906008i	$-0.360886\pi$
$577$	488.442			0.846519			0.423260	+	0.906008i	$0.360886\pi$
$578$	−39.4956	−	337.962i	−0.0683316	−	0.584709i
$579$	−674.950	+	339.703i	−1.16572	+	0.586707i
$580$	29.3902	−	6.96444i	0.0506728	−	0.0120077i
$581$	73.2108	+	19.6168i	0.126008	+	0.0337638i
$582$	261.588	−	521.964i	0.449464	−	0.896846i
$583$	−357.645	+	619.458i	−0.613455	+	1.06254i
$584$	−622.753	+	226.624i	−1.06636	+	0.388055i
$585$	−33.2706	+	44.8519i	−0.0568729	+	0.0766698i
$586$	44.6563	−	304.826i	0.0762053	−	0.520181i
$587$	283.400	−	75.9368i	0.482794	−	0.129364i	−0.00920939	−	0.999958i	$-0.502931\pi$
$587$	283.400	−	75.9368i	0.482794	−	0.129364i	0.492003	+	0.870593i	$0.336265\pi$
$588$	555.576	−	466.967i	0.944857	−	0.794161i
$589$	−15.8451	+	59.1349i	−0.0269018	+	0.100399i
$590$	14.3185	+	6.17670i	0.0242686	+	0.0104690i
$591$	366.086	+	410.652i	0.619434	+	0.694843i
$592$	−261.885	+	790.125i	−0.442373	+	1.33467i
$593$	−428.045			−0.721830			−0.360915	−	0.932599i	$-0.617536\pi$
$593$	−428.045			−0.721830			−0.360915	+	0.932599i	$0.617536\pi$
$594$	−385.316	+	80.5960i	−0.648680	+	0.135683i
$595$	69.2222	−	69.2222i	0.116340	−	0.116340i
$596$	−478.839	−	13.9508i	−0.803421	−	0.0234073i
$597$	−35.2787	+	614.866i	−0.0590933	+	1.02993i
$598$	90.6643	+	228.228i	0.151613	+	0.381653i
$599$	−310.190	−	537.265i	−0.517846	−	0.896936i	−0.999785	−	0.0207311i	$-0.993401\pi$
$599$	−310.190	−	537.265i	−0.517846	−	0.896936i	0.481939	−	0.876205i	$-0.339933\pi$
$600$	566.738	+	133.836i	0.944563	+	0.223060i
$601$	−484.136	−	279.516i	−0.805550	−	0.465085i	0.0398580	−	0.999205i	$-0.487309\pi$
$601$	−484.136	−	279.516i	−0.805550	−	0.465085i	−0.845408	+	0.534121i	$0.820643\pi$
$602$	−960.818	−	140.758i	−1.59604	−	0.233817i
$603$	−1051.73	−	415.723i	−1.74417	−	0.689424i
$604$	−142.443	+	475.729i	−0.235833	+	0.787631i
$605$	−56.2469	+	15.0713i	−0.0929702	+	0.0249113i
$606$	290.061	+	872.881i	0.478648	+	1.44040i
$607$	749.119	−	432.504i	1.23413	−	0.712527i	0.266244	−	0.963906i	$-0.414217\pi$
$607$	749.119	−	432.504i	1.23413	−	0.712527i	0.967889	+	0.251378i	$0.0808838\pi$
$608$	248.972	+	51.4329i	0.409493	+	0.0845936i
$609$	262.263	+	86.6529i	0.430645	+	0.142287i
$610$	0.785071	+	6.71781i	0.00128700	+	0.0110128i
$611$	124.335	−	124.335i	0.203494	−	0.203494i
$612$	389.766	−	46.2253i	0.636873	−	0.0755315i
$613$	180.243	−	180.243i	0.294034	−	0.294034i	−0.544638	−	0.838671i	$-0.683333\pi$
$613$	180.243	−	180.243i	0.294034	−	0.294034i	0.838671	+	0.544638i	$0.183333\pi$
$614$	−219.322	−	173.424i	−0.357202	−	0.282450i
$615$	−42.5969	−	205.401i	−0.0692633	−	0.333985i
$616$	−607.890	+	53.1490i	−0.986835	+	0.0862809i
$617$	395.767	−	228.496i	0.641437	−	0.370334i	−0.143731	−	0.989617i	$-0.545910\pi$
$617$	395.767	−	228.496i	0.641437	−	0.370334i	0.785168	+	0.619283i	$0.212577\pi$
$618$	583.471	+	885.493i	0.944128	+	1.43284i
$619$	284.547	−	76.2441i	0.459688	−	0.123173i	−0.0215411	−	0.999768i	$-0.506857\pi$
$619$	284.547	−	76.2441i	0.459688	−	0.123173i	0.481229	+	0.876595i	$0.340191\pi$
$620$	23.2828	−	12.5528i	0.0375529	−	0.0202465i
$621$	−430.443	+	157.934i	−0.693145	+	0.254321i
$622$	−829.497	+	617.513i	−1.33360	+	0.992787i
$623$	1310.04	+	756.353i	2.10279	+	1.21405i
$624$	−343.369	+	50.5730i	−0.550271	+	0.0810464i
$625$	285.156	+	493.904i	0.456249	+	0.790247i
$626$	64.5934	−	149.737i	0.103184	−	0.239196i
$627$	−145.246	−	95.3502i	−0.231653	−	0.152074i
$628$	35.7338	−	1226.51i	0.0569010	−	1.95304i
$629$	−401.078	+	401.078i	−0.637644	+	0.637644i
$630$	−114.479	−	114.088i	−0.181712	−	0.181092i
$631$	−660.355			−1.04652			−0.523261	−	0.852173i	$-0.675285\pi$
$631$	−660.355			−1.04652			−0.523261	+	0.852173i	$0.675285\pi$
$632$	95.3850	−	540.777i	0.150926	−	0.855660i
$633$	94.0164	−	284.549i	0.148525	−	0.449524i
$634$	−171.308	−	431.231i	−0.270202	−	0.680175i
$635$	21.2700	−	79.3808i	0.0334961	−	0.125009i
$636$	−965.065	−	674.557i	−1.51740	−	1.06062i
$637$	−422.409	+	113.184i	−0.663123	+	0.177683i
$638$	−76.6086	−	102.907i	−0.120076	−	0.161297i
$639$	−796.272	−	91.6761i	−1.24612	−	0.143468i
$640$	−57.6523	−	93.4960i	−0.0900816	−	0.146088i
$641$	−4.38899	+	7.60195i	−0.00684710	+	0.0118595i	−0.869429	−	0.494059i	$-0.835513\pi$
$641$	−4.38899	+	7.60195i	−0.00684710	+	0.0118595i	0.862582	+	0.505918i	$0.168846\pi$
$642$	−98.0279	−	87.0890i	−0.152691	−	0.135653i
$643$	−452.459	−	121.236i	−0.703668	−	0.188547i	−0.110795	−	0.993843i	$-0.535340\pi$
$643$	−452.459	−	121.236i	−0.703668	−	0.188547i	−0.592873	+	0.805296i	$0.702006\pi$
$644$	−691.578	+	163.880i	−1.07388	+	0.254472i
$645$	−6.84312	+	119.267i	−0.0106095	+	0.184911i
$646$	135.887	+	107.450i	0.210352	+	0.166331i
$647$	−651.741			−1.00733			−0.503664	−	0.863900i	$-0.668015\pi$
$647$	−651.741			−1.00733			−0.503664	+	0.863900i	$0.668015\pi$
$648$	−77.4164	−	643.359i	−0.119470	−	0.992838i
$649$		−	66.2351i		−	0.102057i
$650$	−275.236	−	217.637i	−0.423440	−	0.334826i
$651$	241.490	+	13.8558i	0.370953	+	0.0212839i
$652$	−518.118	+	839.927i	−0.794659	+	1.28823i
$653$	−148.436	+	553.971i	−0.227314	+	0.848347i	0.754150	+	0.656702i	$0.228049\pi$
$653$	−148.436	+	553.971i	−0.227314	+	0.848347i	−0.981464	+	0.191645i	$0.938618\pi$
$654$	−534.105	−	474.505i	−0.816675	−	0.725543i
$655$	−97.6677	−	56.3885i	−0.149111	−	0.0860893i
$656$	716.490	−	1089.19i	1.09221	−	1.66035i
$657$	−85.2724	+	740.652i	−0.129791	+	1.12732i
$658$	303.881	+	408.199i	0.461825	+	0.620363i
$659$	182.895	+	682.574i	0.277534	+	1.03577i	0.954124	+	0.299412i	$0.0967906\pi$
$659$	182.895	+	682.574i	0.277534	+	1.03577i	−0.676589	+	0.736360i	$0.736543\pi$
$660$	13.0968	+	73.9180i	0.0198436	+	0.111997i
$661$	−302.694	−	81.1067i	−0.457934	−	0.122703i	0.0224754	−	0.999747i	$-0.492845\pi$
$661$	−302.694	−	81.1067i	−0.457934	−	0.122703i	−0.480409	+	0.877044i	$0.659512\pi$
$662$	341.502	+	859.659i	0.515864	+	1.29858i
$663$	−224.563	−	74.1966i	−0.338707	−	0.111910i
$664$	47.4719	−	33.2362i	0.0714938	−	0.0500545i
$665$		−	71.3346i		−	0.107270i
$666$	663.297	+	661.033i	0.995942	+	0.992543i
$667$	−105.660	−	105.660i	−0.158411	−	0.158411i
$668$	589.927	+	625.333i	0.883124	+	0.936127i
$669$	−20.6225	+	31.4140i	−0.0308258	+	0.0469567i
$670$	−85.4235	+	198.024i	−0.127498	+	0.295558i
$671$	24.8792	−	14.3640i	0.0370778	−	0.0214069i
$672$	−0.773827	−	1004.47i	−0.00115153	−	1.49475i
$673$	−497.699	+	862.039i	−0.739522	+	1.28089i	0.213188	+	0.977011i	$0.431615\pi$
$673$	−497.699	+	862.039i	−0.739522	+	1.28089i	−0.952711	+	0.303879i	$0.901718\pi$
$674$	656.717	−	488.888i	0.974357	−	0.725354i
$675$	419.799	−	502.939i	0.621924	−	0.745095i
$676$	−447.250	−	133.916i	−0.661612	−	0.198101i
$677$	258.107	+	963.267i	0.381250	+	1.42285i	0.843993	+	0.536354i	$0.180199\pi$
$677$	258.107	+	963.267i	0.381250	+	1.42285i	−0.462743	+	0.886493i	$0.653135\pi$
$678$	294.683	+	447.220i	0.434636	+	0.659617i
$679$	−509.077	−	881.747i	−0.749745	−	1.29860i
$680$	−6.51928	−	74.5641i	−0.00958718	−	0.109653i
$681$	−649.927	+	134.785i	−0.954372	+	0.197922i
$682$	−88.1286	−	69.6858i	−0.129221	−	0.102179i
$683$	78.7837	+	78.7837i	0.115350	+	0.115350i	0.762426	−	0.647076i	$-0.224008\pi$
$683$	78.7837	+	78.7837i	0.115350	+	0.115350i	−0.647076	+	0.762426i	$0.724008\pi$
$684$	177.012	−	224.648i	0.258790	−	0.328433i
$685$	−41.0362	−	41.0362i	−0.0599069	−	0.0599069i
$686$	−27.8845	−	238.606i	−0.0406480	−	0.347822i
$687$	−34.8707	+	105.539i	−0.0507580	+	0.153623i
$688$	−554.676	+	493.545i	−0.806216	+	0.717363i
$689$	354.740	+	614.427i	0.514862	+	0.891766i
$690$	27.5726	+	82.9743i	0.0399602	+	0.120253i
$691$	216.618	+	808.428i	0.313484	+	1.16994i	0.925392	+	0.379010i	$0.123736\pi$
$691$	216.618	+	808.428i	0.313484	+	1.16994i	−0.611908	+	0.790929i	$0.709598\pi$
$692$	607.414	−	327.485i	0.877766	−	0.473245i
$693$	−252.352	+	638.421i	−0.364144	+	0.921242i
$694$	−213.068	−	31.2139i	−0.307014	−	0.0449769i
$695$	77.7168	−	134.610i	0.111823	−	0.193683i
$696$	179.651	−	111.011i	0.258120	−	0.159499i
$697$	769.362	−	444.191i	1.10382	−	0.637290i
$698$	223.495	+	562.603i	0.320194	+	0.806021i
$699$	11.9745	+	0.687050i	0.0171309	+	0.000982905i
$700$	738.677	−	696.854i	1.05525	−	0.995505i
$701$	899.718	+	899.718i	1.28348	+	1.28348i	0.938676	+	0.344802i	$0.112054\pi$
$701$	899.718	+	899.718i	1.28348	+	1.28348i	0.344802	+	0.938676i	$0.387946\pi$
$702$	−121.862	+	370.954i	−0.173593	+	0.528424i
$703$			413.318i			0.587935i
$704$	−267.647	+	382.149i	−0.380181	+	0.542825i
$705$	46.7314	−	41.6599i	0.0662857	−	0.0590920i
$706$	−355.285	−	153.263i	−0.503236	−	0.217086i
$707$	1549.38	+	415.156i	2.19149	+	0.587208i
$708$	108.623	+	9.41282i	0.153423	+	0.0132949i
$709$	146.580	+	547.046i	0.206743	+	0.771574i	0.988911	+	0.148507i	$0.0474468\pi$
$709$	146.580	+	547.046i	0.206743	+	0.771574i	−0.782169	+	0.623067i	$0.785887\pi$
$710$	−22.1558	+	151.236i	−0.0312053	+	0.213009i
$711$	−496.161	−	368.047i	−0.697836	−	0.517647i
$712$	1086.86	−	395.514i	1.52648	−	0.555497i
$713$	−113.327	−	65.4294i	−0.158944	−	0.0917664i
$714$	306.671	−	611.922i	0.429511	−	0.857033i
$715$	11.7073	−	43.6923i	0.0163739	−	0.0611081i
$716$	210.479	−	341.209i	0.293965	−	0.476550i
$717$	−22.2887	−	44.2849i	−0.0310860	−	0.0617642i
$718$	10.0347	+	85.8663i	0.0139759	+	0.119591i
$719$			922.935i			1.28364i	0.766856	+	0.641819i	$0.221820\pi$
$719$			922.935i			1.28364i	−0.766856	+	0.641819i	$0.778180\pi$
$720$	−123.084	+	10.9736i	−0.170950	+	0.0152411i
$721$	1849.28			2.56488
$722$	−591.738	+	69.1530i	−0.819582	+	0.0957798i
$723$	−118.751	−	77.9567i	−0.164247	−	0.107824i
$724$	−12.8878	+	20.8926i	−0.0178008	+	0.0288571i
$725$	206.227	+	55.2584i	0.284451	+	0.0762185i
$726$	−339.974	+	224.017i	−0.468284	+	0.308563i
$727$	418.934	−	725.615i	0.576250	−	0.998095i	−0.419654	−	0.907684i	$-0.637849\pi$
$727$	418.934	−	725.615i	0.576250	−	0.998095i	0.995905	−	0.0904109i	$-0.0288180\pi$
$728$	−255.822	+	548.531i	−0.351404	+	0.753477i
$729$	−686.320	−	245.777i	−0.941453	−	0.337143i
$730$	140.672	+	20.6082i	0.192702	+	0.0282304i
$731$	−488.690	+	130.944i	−0.668523	+	0.179130i
$732$	20.0209	+	42.8424i	0.0273509	+	0.0585278i
$733$	−87.6370	+	327.066i	−0.119559	+	0.446201i	−0.999587	−	0.0287201i	$-0.990857\pi$
$733$	−87.6370	+	327.066i	−0.119559	+	0.446201i	0.880028	+	0.474921i	$0.157524\pi$
$734$	287.627	−	666.760i	0.391862	−	0.908392i
$735$	−152.456	+	31.6171i	−0.207424	+	0.0430165i
$736$	−243.928	+	485.586i	−0.331423	+	0.659764i
$737$	916.028			1.24291
$738$	−735.515	−	1268.93i	−0.996633	−	1.71942i
$739$	314.546	−	314.546i	0.425638	−	0.425638i	−0.461502	−	0.887139i	$-0.652689\pi$
$739$	314.546	−	314.546i	0.425638	−	0.425638i	0.887139	+	0.461502i	$0.152689\pi$
$740$	129.898	−	122.543i	0.175537	−	0.165599i
$741$	−153.938	+	77.4773i	−0.207744	+	0.104558i
$742$	−1908.26	+	758.062i	−2.57178	+	1.02165i
$743$	124.479	+	215.603i	0.167535	+	0.290179i	0.937553	−	0.347843i	$-0.113086\pi$
$743$	124.479	+	215.603i	0.167535	+	0.290179i	−0.770018	+	0.638023i	$0.779753\pi$
$744$	126.806	−	134.625i	0.170439	−	0.180947i
$745$	89.0027	+	51.3857i	0.119467	+	0.0689741i
$746$	−76.5038	+	522.219i	−0.102552	+	0.700025i
$747$	−9.56016	−	64.4892i	−0.0127981	−	0.0863309i
$748$	−279.838	+	150.874i	−0.374116	+	0.201703i
$749$	−220.875	+	59.1834i	−0.294894	+	0.0790166i
$750$	−189.626	−	168.466i	−0.252835	−	0.224621i
$751$	231.042	−	133.392i	0.307645	−	0.177619i	−0.338227	−	0.941065i	$-0.609827\pi$
$751$	231.042	−	133.392i	0.307645	−	0.177619i	0.645872	+	0.763445i	$0.276494\pi$
$752$	388.428	+	22.6526i	0.516527	+	0.0301232i
$753$	458.447	−	408.694i	0.608827	−	0.542754i
$754$	−126.390	+	14.7704i	−0.167626	+	0.0195894i
$755$	75.3334	−	75.3334i	0.0997793	−	0.0997793i
$756$	−1011.13	−	504.575i	−1.33747	−	0.667428i
$757$	−680.254	+	680.254i	−0.898619	+	0.898619i	−0.995314	−	0.0966952i	$-0.969173\pi$
$757$	−680.254	+	680.254i	−0.898619	+	0.898619i	0.0966952	+	0.995314i	$0.469173\pi$
$758$	55.8885	−	70.6798i	0.0737315	−	0.0932451i
$759$	277.218	−	247.133i	0.365242	−	0.325603i
$760$	−41.7789	−	35.0607i	−0.0549723	−	0.0461325i
$761$	563.633	−	325.414i	0.740648	−	0.427613i	−0.0816571	−	0.996660i	$-0.526021\pi$
$761$	563.633	−	325.414i	0.740648	−	0.427613i	0.822305	+	0.569047i	$0.192688\pi$
$762$	−33.8948	−	573.597i	−0.0444814	−	0.752752i
$763$	−1203.44	+	322.461i	−1.57725	+	0.422622i
$764$	881.749	+	264.014i	1.15412	+	0.345568i
$765$	−78.3090	−	30.9536i	−0.102365	−	0.0404622i
$766$	−269.746	−	362.345i	−0.352148	−	0.473036i
$767$	−56.8953	−	32.8485i	−0.0741791	−	0.0428273i
$768$	−588.674	−	493.241i	−0.766503	−	0.642240i
$769$	−487.695	−	844.713i	−0.634194	−	1.09846i	−0.986685	−	0.162642i	$-0.947999\pi$
$769$	−487.695	−	844.713i	−0.634194	−	1.09846i	0.352491	−	0.935815i	$-0.385335\pi$
$770$	120.204	+	51.8536i	0.156109	+	0.0673424i
$771$	670.417	−	337.422i	0.869542	−	0.437642i
$772$	691.352	+	732.846i	0.895534	+	0.949282i
$773$	476.130	−	476.130i	0.615951	−	0.615951i	−0.328539	−	0.944490i	$-0.606556\pi$
$773$	476.130	−	476.130i	0.615951	−	0.615951i	0.944490	+	0.328539i	$0.106556\pi$
$774$	217.563	+	806.440i	0.281090	+	1.04191i
$775$	186.974			0.241256
$776$	−766.626	−	135.221i	−0.987920	−	0.174254i
$777$	1599.02	−	331.612i	2.05794	−	0.426785i
$778$	882.226	−	350.467i	1.13397	−	0.450472i
$779$	167.547	−	625.294i	0.215080	−	0.802688i
$780$	69.9901	+	25.4088i	0.0897309	+	0.0325754i
$781$	627.111	−	168.034i	0.802959	−	0.215152i
$782$	−297.023	+	221.116i	−0.379824	+	0.282758i
$783$	−21.3200	−	236.622i	−0.0272287	−	0.302199i
$784$	−808.441	−	531.807i	−1.03117	−	0.678325i
$785$	−131.621	+	227.974i	−0.167670	+	0.290412i
$786$	−772.364	−	158.800i	−0.982652	−	0.202035i
$787$	−1298.13	−	347.832i	−1.64946	−	0.441972i	−0.690000	−	0.723809i	$-0.742390\pi$
$787$	−1298.13	−	347.832i	−1.64946	−	0.441972i	−0.959462	+	0.281837i	$0.909056\pi$
$788$	385.104	−	624.297i	0.488711	−	0.792255i
$789$	−223.413	−	146.665i	−0.283160	−	0.185887i
$790$	−73.0697	+	92.4081i	−0.0924932	+	0.116972i
$791$	933.982			1.18076
$792$	249.877	+	461.577i	0.315502	+	0.582799i
$793$		−	28.4947i		−	0.0359328i
$794$	214.420	−	271.168i	0.270051	−	0.341522i
$795$	113.563	+	225.637i	0.142847	+	0.283820i
$796$	799.041	−	189.345i	1.00382	−	0.237870i
$797$	183.168	−	683.590i	0.229821	−	0.857704i	−0.750594	−	0.660764i	$-0.770233\pi$
$797$	183.168	−	683.590i	0.229821	−	0.857704i	0.980415	−	0.196941i	$-0.0631007\pi$
$798$	−157.283	−	473.313i	−0.197096	−	0.593124i
$799$	229.611	+	132.566i	0.287373	+	0.165915i
$800$	−45.0730	−	775.126i	−0.0563412	−	0.968907i
$801$	148.821	−	1292.62i	0.185794	−	1.61376i
$802$	347.506	−	258.699i	0.433300	−	0.322567i
$803$	−156.297	−	583.307i	−0.194641	−	0.726409i
$804$	−130.179	+	1502.25i	−0.161914	+	1.86848i
$805$	147.281	+	39.4639i	0.182958	+	0.0490235i
$806$	−103.566	+	41.1418i	−0.128494	+	0.0510445i
$807$	−435.828	+	388.530i	−0.540060	+	0.481449i
$808$	1004.66	−	703.388i	1.24339	−	0.870530i
$809$		−	1299.74i		−	1.60661i	−0.595571	−	0.803303i	$-0.703074\pi$
$809$		−	1299.74i		−	1.60661i	0.595571	−	0.803303i	$-0.296926\pi$
$810$	−50.8822	+	129.373i	−0.0628175	+	0.159719i
$811$	305.471	+	305.471i	0.376659	+	0.376659i	0.869895	−	0.493236i	$-0.164186\pi$
$811$	305.471	+	305.471i	0.376659	+	0.376659i	−0.493236	+	0.869895i	$0.664186\pi$
$812$	10.7250	−	368.120i	0.0132082	−	0.453350i
$813$	1000.91	+	57.4283i	1.23113	+	0.0706375i
$814$	−696.471	−	300.444i	−0.855615	−	0.369096i
$815$	183.355	−	105.860i	0.224975	−	0.129889i
$816$	−207.660	−	480.366i	−0.254485	−	0.588684i
$817$	−184.332	+	319.272i	−0.225620	+	0.390786i
$818$	645.166	+	866.642i	0.788711	+	1.05946i
$819$	423.247	+	533.385i	0.516785	+	0.651264i
$820$	−246.193	+	132.734i	−0.300235	+	0.161871i
$821$	−219.660	−	819.783i	−0.267552	−	0.998518i	−0.960670	−	0.277693i	$-0.910430\pi$
$821$	−219.660	−	819.783i	−0.267552	−	0.998518i	0.693118	−	0.720824i	$-0.256237\pi$
$822$	−362.759	−	181.801i	−0.441313	−	0.221169i
$823$	554.720	+	960.804i	0.674022	+	1.16744i	0.976754	+	0.214365i	$0.0687681\pi$
$823$	554.720	+	960.804i	0.674022	+	1.16744i	−0.302731	+	0.953076i	$0.597899\pi$
$824$	908.912	−	1083.08i	1.10305	−	1.31441i
$825$	−166.474	+	503.848i	−0.201787	+	0.610725i
$826$	117.931	−	149.143i	0.142774	−	0.180560i
$827$	−980.630	−	980.630i	−1.18577	−	1.18577i	−0.978226	−	0.207542i	$-0.933454\pi$
$827$	−980.630	−	980.630i	−1.18577	−	1.18577i	−0.207542	−	0.978226i	$-0.566546\pi$
$828$	365.894	+	489.749i	0.441900	+	0.591485i
$829$	11.8666	+	11.8666i	0.0143143	+	0.0143143i	0.714228	−	0.699913i	$-0.246778\pi$
$829$	11.8666	+	11.8666i	0.0143143	+	0.0143143i	−0.699913	+	0.714228i	$0.746778\pi$
$830$	−12.3483	+	1.44308i	−0.0148775	+	0.00173865i
$831$	397.469	−	82.4290i	0.478302	−	0.0991925i
$832$	195.526	+	419.429i	0.235007	+	0.504122i
$833$	−329.696	−	571.051i	−0.395794	−	0.685535i
$834$	218.864	−	1064.50i	0.262427	−	1.27638i
$835$	−47.7346	−	178.148i	−0.0571672	−	0.213351i
$836$	−66.4500	+	221.928i	−0.0794857	+	0.265464i
$837$	−71.6674	−	195.327i	−0.0856241	−	0.233366i
$838$	132.721	−	905.959i	0.158378	−	1.08110i
$839$	−636.130	+	1101.81i	−0.758200	+	1.31324i	0.185568	+	0.982631i	$0.440588\pi$
$839$	−636.130	+	1101.81i	−0.758200	+	1.31324i	−0.943768	+	0.330609i	$0.892746\pi$
$840$	−102.121	+	189.761i	−0.121572	+	0.225906i
$841$	−661.273	+	381.786i	−0.786294	+	0.453967i
$842$	−471.435	+	187.279i	−0.559899	+	0.222422i
$843$	166.899	−	254.236i	0.197982	−	0.301585i
$844$	−399.402	−	11.6364i	−0.473225	−	0.0137872i
$845$	70.8236	+	70.8236i	0.0838149	+	0.0838149i
$846$	218.214	−	379.454i	0.257936	−	0.448527i
$847$			710.008i			0.838262i
$848$	−493.924	+	1490.20i	−0.582458	+	1.75732i
$849$	871.710	+	288.018i	1.02675	+	0.339243i
$850$	209.566	−	485.804i	0.246548	−	0.571534i
$851$	−853.358	−	228.657i	−1.00277	−	0.268692i
$852$	186.449	+	1052.32i	0.218837	+	1.23512i
$853$	148.187	+	553.040i	0.173724	+	0.648347i	0.996765	+	0.0803654i	$0.0256087\pi$
$853$	148.187	+	553.040i	0.173724	+	0.648347i	−0.823042	+	0.567981i	$0.807725\pi$
$854$	81.5962	+	11.9536i	0.0955459	+	0.0139972i
$855$	−56.2985	+	24.4003i	−0.0658462	+	0.0285383i
$856$	−73.8971	+	158.450i	−0.0863284	+	0.185105i
$857$	221.044	+	127.620i	0.257927	+	0.148914i	0.623389	−	0.781912i	$-0.285755\pi$
$857$	221.044	+	127.620i	0.257927	+	0.148914i	−0.365461	+	0.930826i	$0.619089\pi$
$858$	−18.6562	−	315.716i	−0.0217438	−	0.367967i
$859$	−19.8150	+	73.9507i	−0.0230675	+	0.0860893i	−0.976500	−	0.215517i	$-0.930856\pi$
$859$	−19.8150	+	73.9507i	−0.0230675	+	0.0860893i	0.953432	+	0.301607i	$0.0975229\pi$
$860$	154.993	−	36.7278i	0.180224	−	0.0427067i
$861$	−2553.52	−	146.512i	−2.96577	−	0.170165i
$862$	380.940	−	44.5182i	0.441926	−	0.0516453i
$863$			1139.78i			1.32072i	0.750949	+	0.660360i	$0.229596\pi$
$863$			1139.78i			1.32072i	−0.750949	+	0.660360i	$0.770404\pi$
$864$	−792.481	+	344.194i	−0.917224	+	0.398373i
$865$	−148.045			−0.171150
$866$	−155.855	−	1333.65i	−0.179972	−	1.54001i
$867$	−29.2363	+	509.555i	−0.0337213	+	0.587722i
$868$	−74.3656	−	313.826i	−0.0856747	−	0.361550i
$869$	483.334	+	129.509i	0.556195	+	0.149032i
$870$	−45.2273	+	2.67256i	−0.0519853	+	0.00307190i
$871$	454.294	−	786.860i	0.521577	−	0.903399i
$872$	−402.629	+	863.313i	−0.461730	+	0.990038i
$873$	−521.757	+	703.376i	−0.597660	+	0.805700i
$874$	−39.1113	+	266.976i	−0.0447498	+	0.305464i
$875$	−427.263	+	114.485i	−0.488301	+	0.130840i
$876$	978.815	−	173.426i	1.11737	−	0.197975i
$877$	146.770	−	547.754i	0.167355	−	0.624577i	−0.830373	−	0.557208i	$-0.811873\pi$
$877$	146.770	−	547.754i	0.167355	−	0.624577i	0.997728	−	0.0673695i	$-0.0214606\pi$
$878$	1163.10	+	501.739i	1.32472	+	0.571457i
$879$	−144.978	+	438.789i	−0.164935	+	0.499191i
$880$	89.4492	−	44.9146i	0.101647	−	0.0510394i
$881$	−80.3510			−0.0912043			−0.0456022	−	0.998960i	$-0.514521\pi$
$881$	−80.3510			−0.0912043			−0.0456022	+	0.998960i	$0.514521\pi$
$882$	−941.853	+	545.928i	−1.06786	+	0.618966i
$883$	−249.733	+	249.733i	−0.282823	+	0.282823i	−0.834234	−	0.551411i	$-0.814090\pi$
$883$	−249.733	+	249.733i	−0.282823	+	0.282823i	0.551411	+	0.834234i	$0.314090\pi$
$884$	−9.18331	+	315.203i	−0.0103884	+	0.356564i
$885$	−19.5539	−	12.8366i	−0.0220948	−	0.0145046i
$886$	441.947	+	1112.51i	0.498812	+	1.25565i
$887$	−3.22889	−	5.59260i	−0.00364023	−	0.00630507i	0.864200	−	0.503149i	$-0.167825\pi$
$887$	−3.22889	−	5.59260i	−0.00364023	−	0.00630507i	−0.867840	+	0.496844i	$0.834492\pi$
$888$	591.695	−	1099.49i	0.666323	−	1.23817i
$889$	−867.781	−	501.013i	−0.976131	−	0.563570i
$890$	−245.508	−	35.9663i	−0.275852	−	0.0404116i
$891$	590.170	−	19.2142i	0.662368	−	0.0215648i
$892$	47.9989	+	14.3719i	0.0538105	+	0.0161120i
$893$	186.615	−	50.0033i	0.208975	−	0.0559948i
$894$	703.841	+	144.711i	0.787294	+	0.161869i
$895$	−74.4855	+	43.0042i	−0.0832240	+	0.0480494i
$896$	−1283.08	+	383.946i	−1.43201	+	0.428511i
$897$	−74.8018	−	360.691i	−0.0833910	−	0.402108i
$898$	87.2740	+	746.798i	0.0971871	+	0.831624i
$899$	47.9465	−	47.9465i	0.0533332	−	0.0533332i
$900$	−802.636	−	344.615i	−0.891818	−	0.382905i
$901$	−756.448	+	756.448i	−0.839565	+	0.839565i
$902$	931.874	+	736.859i	1.03312	+	0.816917i
$903$	1383.07	+	456.974i	1.53164	+	0.506062i
$904$	459.048	−	547.010i	0.507797	−	0.605100i
$905$	4.56081	−	2.63319i	0.00503957	−	0.00290960i
$906$	333.745	−	665.945i	0.368372	−	0.735038i
$907$	−1052.31	+	281.964i	−1.16020	+	0.310876i	−0.787048	−	0.616892i	$-0.788391\pi$
$907$	−1052.31	+	281.964i	−1.16020	+	0.310876i	−0.373157	+	0.927768i	$0.621725\pi$
$908$	419.996	+	779.001i	0.462551	+	0.857931i
$909$	−202.325	−	1364.80i	−0.222579	−	1.50144i
$910$	104.156	−	77.5380i	0.114457	−	0.0852066i
$911$	−1285.69	−	742.296i	−1.41130	−	0.814815i	−0.415789	−	0.909461i	$-0.636495\pi$
$911$	−1285.69	−	742.296i	−1.41130	−	0.814815i	−0.995511	+	0.0946462i	$0.969828\pi$
$912$	−354.511	−	140.515i	−0.388719	−	0.154073i
$913$	26.4032	+	45.7317i	0.0289192	+	0.0500895i
$914$	136.518	−	316.468i	0.149363	−	0.346245i
$915$	0.581143	−	10.1286i	0.000635129	−	0.0110695i
$916$	148.138	+	4.31595i	0.161723	+	0.00471174i
$917$	−972.329	+	972.329i	−1.06034	+	1.06034i
$918$	−587.836	−	32.7197i	−0.640345	−	0.0356423i
$919$	810.953			0.882430			0.441215	−	0.897401i	$-0.354548\pi$
$919$	810.953			0.882430			0.441215	+	0.897401i	$0.354548\pi$
$920$	95.5011	−	66.8626i	0.103806	−	0.0726767i
$921$	279.090	+	313.065i	0.303029	+	0.339919i
$922$	85.5191	+	215.276i	0.0927539	+	0.233488i
$923$	166.669	−	622.017i	0.180573	−	0.673908i
$924$	911.896	+	79.0210i	0.986901	+	0.0855206i
$925$	1219.29	−	326.709i	1.31816	−	0.353199i
$926$	−401.686	−	539.579i	−0.433786	−	0.582699i
$927$	−632.553	−	1459.48i	−0.682365	−	1.57441i
$928$	−210.327	−	187.211i	−0.226646	−	0.201736i
$929$	−358.218	+	620.451i	−0.385595	+	0.667870i	−0.991852	−	0.127399i	$-0.959337\pi$
$929$	−358.218	+	620.451i	−0.385595	+	0.667870i	0.606257	+	0.795269i	$0.292670\pi$
$930$	−37.6522	+	12.5119i	−0.0404863	+	0.0134537i
$931$	−464.118	−	124.360i	−0.498515	−	0.133577i
$932$	−3.68747	−	15.5613i	−0.00395652	−	0.0166967i
$933$	1385.57	−	697.361i	1.48507	−	0.747439i
$934$	−510.500	−	403.666i	−0.546574	−	0.432191i
$935$	68.2049			0.0729464
$936$	520.414	+	14.2716i	0.555998	+	0.0152475i
$937$			1562.33i			1.66737i	0.552238	+	0.833687i	$0.313774\pi$
$937$			1562.33i			1.66737i	−0.552238	+	0.833687i	$0.686226\pi$
$938$	2062.64	+	1630.99i	2.19898	+	1.73879i
$939$	−134.240	+	204.486i	−0.142960	+	0.217770i
$940$	−71.0437	−	43.8241i	−0.0755784	−	0.0466214i
$941$	−324.553	+	1211.25i	−0.344902	+	1.28719i	0.547825	+	0.836593i	$0.315456\pi$
$941$	−324.553	+	1211.25i	−0.344902	+	1.28719i	−0.892727	+	0.450599i	$0.851211\pi$
$942$	−370.666	+	1802.83i	−0.393489	+	1.91384i
$943$	1198.32	+	691.852i	1.27076	+	0.733672i
$944$	−29.3864	−	142.373i	−0.0311297	−	0.150818i
$945$	139.568	+	198.227i	0.147690	+	0.209764i
$946$	−404.004	−	542.693i	−0.427066	−	0.573672i
$947$	−450.341	−	1680.70i	−0.475545	−	1.77476i	−0.619309	−	0.785147i	$-0.712587\pi$
$947$	−450.341	−	1680.70i	−0.475545	−	1.77476i	0.143764	−	0.989612i	$-0.454079\pi$
$948$	−281.078	+	774.246i	−0.296496	+	0.816715i
$949$	−578.569	−	155.027i	−0.609662	−	0.163358i
$950$	−142.334	−	358.295i	−0.149825	−	0.377153i
$951$	141.336	+	681.516i	0.148618	+	0.716631i
$952$	−898.749	−	158.526i	−0.944064	−	0.166519i
$953$		−	113.221i		−	0.118805i	−0.998234	−	0.0594025i	$-0.981080\pi$
$953$		−	113.221i		−	0.118805i	0.998234	−	0.0594025i	$-0.0189195\pi$
$954$	1251.00	+	1246.73i	1.31132	+	1.30685i
$955$	−139.628	−	139.628i	−0.146207	−	0.146207i
$956$	−48.0836	+	45.3611i	−0.0502967	+	0.0474489i
$957$	86.5145	+	171.894i	0.0904018	+	0.179617i
$958$	−143.224	+	332.013i	−0.149503	+	0.346568i
$959$	−612.803	+	353.802i	−0.639003	+	0.368928i
$960$	60.9466	+	153.076i	0.0634861	+	0.159455i
$961$	−450.809	+	780.825i	−0.469104	+	0.812513i
$962$	−603.486	+	449.261i	−0.627324	+	0.467007i
$963$	122.260	+	154.075i	0.126957	+	0.159994i
$964$	−54.3284	+	181.445i	−0.0563572	+	0.188221i
$965$	−55.9416	−	208.777i	−0.0579706	−	0.216349i
$966$	1064.24	−	62.8877i	1.10170	−	0.0651011i
$967$	755.790	+	1309.07i	0.781582	+	1.35374i	0.931020	+	0.364969i	$0.118920\pi$
$967$	755.790	+	1309.07i	0.781582	+	1.35374i	−0.149438	+	0.988771i	$0.547746\pi$
$968$	415.834	+	348.966i	0.429580	+	0.360502i
$969$	−172.918	−	193.969i	−0.178450	−	0.200174i
$970$	131.001	+	103.586i	0.135053	+	0.106790i
$971$	559.274	+	559.274i	0.575978	+	0.575978i	0.933793	−	0.357815i	$-0.116478\pi$
$971$	559.274	+	559.274i	0.575978	+	0.575978i	−0.357815	+	0.933793i	$0.616478\pi$
$972$	−52.3598	+	970.589i	−0.0538681	+	0.998548i
$973$	−1340.10	−	1340.10i	−1.37729	−	1.37729i
$974$	−36.5389	−	312.661i	−0.0375142	−	0.321007i
$975$	350.240	+	392.878i	0.359221	+	0.402951i
$976$	47.1051	−	41.9137i	0.0482635	−	0.0429444i
$977$	−437.650	−	758.032i	−0.447953	−	0.775877i	0.550300	−	0.834967i	$-0.314513\pi$
$977$	−437.650	−	758.032i	−0.447953	−	0.775877i	−0.998253	+	0.0590902i	$0.981180\pi$
$978$	983.171	−	1106.66i	1.00529	−	1.13156i
$979$	272.776	+	1018.01i	0.278627	+	1.03985i
$980$	98.5204	+	182.734i	0.100531	+	0.186463i
$981$	666.133	+	839.476i	0.679034	+	0.855735i
$982$	−1526.16	−	223.579i	−1.55414	−	0.227678i
$983$	745.345	−	1290.98i	0.758235	−	1.31330i	−0.185515	−	0.982642i	$-0.559395\pi$
$983$	745.345	−	1290.98i	0.758235	−	1.31330i	0.943750	−	0.330660i	$-0.107271\pi$
$984$	−1340.85	+	1423.53i	−1.36266	+	1.44667i
$985$	−136.283	+	78.6830i	−0.138358	+	0.0798812i
$986$	−70.8370	−	178.317i	−0.0718428	−	0.180849i
$987$	−343.174	−	681.846i	−0.347694	−	0.690827i
$988$	157.679	+	167.143i	0.159594	+	0.169173i
$989$	−557.209	−	557.209i	−0.563407	−	0.563407i
$990$	−0.192513	−	112.604i	−0.000194457	−	0.113741i
$991$		−	690.368i		−	0.696637i	−0.937376	−	0.348319i	$-0.886753\pi$
$991$		−	690.368i		−	0.696637i	0.937376	−	0.348319i	$-0.113247\pi$
$992$	−220.350	−	110.690i	−0.222127	−	0.111583i
$993$	−281.753	−	1358.60i	−0.283739	−	1.36818i
$994$	1711.26	+	738.205i	1.72159	+	0.742661i
$995$	−170.167	−	45.5961i	−0.171022	−	0.0458252i
$996$	−78.7506	+	36.8013i	−0.0790669	+	0.0369491i
$997$	−226.568	−	845.564i	−0.227250	−	0.848108i	−0.981491	−	0.191510i	$-0.938661\pi$
$997$	−226.568	−	845.564i	−0.227250	−	0.848108i	0.754241	−	0.656598i	$-0.228005\pi$
$998$	141.730	−	967.453i	0.142014	−	0.969392i
$999$	−808.664	−	1148.54i	−0.809474	−	1.14969i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.3.v.a.115.25	yes	184
3.2	odd	2		432.3.w.a.19.22		184
9.4	even	3	inner	144.3.v.a.67.7	yes	184
9.5	odd	6		432.3.w.a.307.40		184
16.11	odd	4	inner	144.3.v.a.43.7	✓	184
48.11	even	4		432.3.w.a.235.40		184
144.59	even	12		432.3.w.a.91.22		184
144.139	odd	12	inner	144.3.v.a.139.25	yes	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.3.v.a.43.7	✓	184	16.11	odd	4	inner
144.3.v.a.67.7	yes	184	9.4	even	3	inner
144.3.v.a.115.25	yes	184	1.1	even	1	trivial
144.3.v.a.139.25	yes	184	144.139	odd	12	inner
432.3.w.a.19.22		184	3.2	odd	2
432.3.w.a.91.22		184	144.59	even	12
432.3.w.a.235.40		184	48.11	even	4
432.3.w.a.307.40		184	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	144.v (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.232149 + 1.98648i) q^{2} +(0.171846 - 2.99507i) q^{3} +(-3.89221 + 0.922317i) q^{4} +(0.828901 + 0.222103i) q^{5} +(5.98955 - 0.353933i) q^{6} +(5.23163 - 9.06144i) q^{7} +(-2.73574 - 7.51769i) q^{8} +(-8.94094 - 1.02938i) q^{9} +O(q^{10})\)	\(q+(0.232149 + 1.98648i) q^{2} +(0.171846 - 2.99507i) q^{3} +(-3.89221 + 0.922317i) q^{4} +(0.828901 + 0.222103i) q^{5} +(5.98955 - 0.353933i) q^{6} +(5.23163 - 9.06144i) q^{7} +(-2.73574 - 7.51769i) q^{8} +(-8.94094 - 1.02938i) q^{9} +(-0.248776 + 1.69816i) q^{10} +(7.04151 - 1.88677i) q^{11} +(2.09355 + 11.8160i) q^{12} +(1.87144 - 6.98432i) q^{13} +(19.2149 + 8.28893i) q^{14} +(0.807660 - 2.44445i) q^{15} +(14.2987 - 7.17971i) q^{16} +10.9027 q^{17} +(-0.0307736 - 18.0000i) q^{18} +(5.61772 - 5.61772i) q^{19} +(-3.43111 - 0.0999640i) q^{20} +(-26.2407 - 17.2263i) q^{21} +(5.38270 + 13.5498i) q^{22} +(8.49079 + 14.7065i) q^{23} +(-22.9862 + 6.90185i) q^{24} +(-21.0129 - 12.1318i) q^{25} +(14.3087 + 2.09618i) q^{26} +(-4.61955 + 26.6019i) q^{27} +(-12.0051 + 40.0943i) q^{28} +(-8.49945 + 2.27742i) q^{29} +(5.04336 + 1.03692i) q^{30} +(-6.67353 + 3.85297i) q^{31} +(17.5818 + 26.7373i) q^{32} +(-4.44095 - 21.4141i) q^{33} +(2.53105 + 21.6580i) q^{34} +(6.34908 - 6.34908i) q^{35} +(35.7495 - 4.23980i) q^{36} +(-36.7870 + 36.7870i) q^{37} +(12.4636 + 9.85534i) q^{38} +(-20.5969 - 6.80534i) q^{39} +(-0.597951 - 6.83904i) q^{40} +(70.5661 - 40.7414i) q^{41} +(28.1280 - 56.1256i) q^{42} +(-44.8228 + 12.0102i) q^{43} +(-25.6669 + 13.8382i) q^{44} +(-7.18252 - 2.83907i) q^{45} +(-27.2430 + 20.2809i) q^{46} +(21.0600 + 12.1590i) q^{47} +(-19.0466 - 44.0594i) q^{48} +(-30.2398 - 52.3770i) q^{49} +(19.2215 - 44.5581i) q^{50} +(1.87359 - 32.6544i) q^{51} +(-0.842296 + 28.9105i) q^{52} +(-69.3816 + 69.3816i) q^{53} +(-53.9165 - 3.00106i) q^{54} +6.25577 q^{55} +(-82.4335 - 14.5400i) q^{56} +(-15.8601 - 17.7909i) q^{57} +(-6.49719 - 16.3553i) q^{58} +(2.35159 - 8.77626i) q^{59} +(-0.889023 + 10.2593i) q^{60} +(3.80652 - 1.01995i) q^{61} +(-9.20309 - 12.3624i) q^{62} +(-56.1034 + 75.6325i) q^{63} +(-49.0315 + 41.1329i) q^{64} +(3.10248 - 5.37365i) q^{65} +(41.5077 - 13.7931i) q^{66} +(121.375 + 32.5224i) q^{67} +(-42.4357 + 10.0558i) q^{68} +(45.5061 - 22.9033i) q^{69} +(14.0863 + 11.1384i) q^{70} +89.0591 q^{71} +(16.7215 + 70.0314i) q^{72} -82.8383i q^{73} +(-81.6168 - 64.5367i) q^{74} +(-39.9466 + 60.8504i) q^{75} +(-16.6840 + 27.0467i) q^{76} +(19.7417 - 73.6771i) q^{77} +(8.73712 - 42.4953i) q^{78} +(59.4445 + 34.3203i) q^{79} +(13.4468 - 2.77549i) q^{80} +(78.8807 + 18.4073i) q^{81} +(97.3138 + 130.720i) q^{82} +(1.87483 + 6.99695i) q^{83} +(118.022 + 42.8462i) q^{84} +(9.03727 + 2.42153i) q^{85} +(-34.2637 - 86.2515i) q^{86} +(5.36044 + 25.8478i) q^{87} +(-33.4479 - 47.7742i) q^{88} +144.573i q^{89} +(3.97235 - 14.9270i) q^{90} +(-53.4973 - 53.4973i) q^{91} +(-46.6120 - 49.4095i) q^{92} +(10.3931 + 20.6498i) q^{93} +(-19.2646 + 44.6580i) q^{94} +(5.90424 - 3.40882i) q^{95} +(83.1014 - 48.0640i) q^{96} +(48.6538 - 84.2708i) q^{97} +(97.0257 - 72.2301i) q^{98} +(-64.8999 + 9.62105i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q - 2 q^{2} - 4 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} - 4 q^{7} - 8 q^{8}+O(q^{10}) \) 184 * q - 2 * q^2 - 4 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 - 4 * q^7 - 8 * q^8	\( 184 q - 2 q^{2} - 4 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} - 4 q^{7} - 8 q^{8} - 8 q^{10} - 2 q^{11} + 56 q^{12} - 2 q^{13} + 14 q^{14} - 2 q^{16} - 16 q^{17} + 38 q^{18} - 8 q^{19} - 44 q^{20} + 14 q^{21} - 2 q^{22} - 4 q^{23} + 120 q^{24} - 104 q^{26} - 52 q^{27} + 56 q^{28} - 2 q^{29} - 130 q^{30} - 182 q^{32} - 8 q^{33} - 10 q^{34} + 92 q^{35} - 2 q^{36} - 8 q^{37} - 254 q^{38} + 184 q^{39} - 2 q^{40} - 252 q^{42} - 2 q^{43} - 140 q^{44} - 54 q^{45} + 176 q^{46} + 162 q^{48} - 480 q^{49} - 96 q^{50} - 120 q^{51} - 2 q^{52} - 8 q^{53} + 94 q^{54} - 16 q^{55} + 260 q^{56} + 88 q^{58} + 142 q^{59} - 434 q^{60} - 2 q^{61} - 636 q^{62} + 244 q^{64} - 4 q^{65} - 100 q^{66} - 2 q^{67} - 112 q^{68} + 14 q^{69} - 100 q^{70} - 16 q^{71} + 98 q^{72} + 82 q^{74} - 296 q^{75} + 154 q^{76} + 194 q^{77} + 228 q^{78} + 592 q^{80} - 8 q^{81} - 420 q^{82} + 238 q^{83} - 22 q^{84} - 52 q^{85} - 170 q^{86} - 456 q^{87} - 26 q^{88} + 808 q^{90} + 188 q^{91} + 176 q^{92} + 26 q^{93} - 18 q^{94} - 202 q^{96} - 4 q^{97} + 408 q^{98} - 38 q^{99}+O(q^{100}) \) 184 * q - 2 * q^2 - 4 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 - 4 * q^7 - 8 * q^8 - 8 * q^10 - 2 * q^11 + 56 * q^12 - 2 * q^13 + 14 * q^14 - 2 * q^16 - 16 * q^17 + 38 * q^18 - 8 * q^19 - 44 * q^20 + 14 * q^21 - 2 * q^22 - 4 * q^23 + 120 * q^24 - 104 * q^26 - 52 * q^27 + 56 * q^28 - 2 * q^29 - 130 * q^30 - 182 * q^32 - 8 * q^33 - 10 * q^34 + 92 * q^35 - 2 * q^36 - 8 * q^37 - 254 * q^38 + 184 * q^39 - 2 * q^40 - 252 * q^42 - 2 * q^43 - 140 * q^44 - 54 * q^45 + 176 * q^46 + 162 * q^48 - 480 * q^49 - 96 * q^50 - 120 * q^51 - 2 * q^52 - 8 * q^53 + 94 * q^54 - 16 * q^55 + 260 * q^56 + 88 * q^58 + 142 * q^59 - 434 * q^60 - 2 * q^61 - 636 * q^62 + 244 * q^64 - 4 * q^65 - 100 * q^66 - 2 * q^67 - 112 * q^68 + 14 * q^69 - 100 * q^70 - 16 * q^71 + 98 * q^72 + 82 * q^74 - 296 * q^75 + 154 * q^76 + 194 * q^77 + 228 * q^78 + 592 * q^80 - 8 * q^81 - 420 * q^82 + 238 * q^83 - 22 * q^84 - 52 * q^85 - 170 * q^86 - 456 * q^87 - 26 * q^88 + 808 * q^90 + 188 * q^91 + 176 * q^92 + 26 * q^93 - 18 * q^94 - 202 * q^96 - 4 * q^97 + 408 * q^98 - 38 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more