LMFDB - Embedded newform 144.3.v.a.43.7

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			43.7
Character	$\chi$	$=$	144.43
Dual form			144.3.v.a.67.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.83642 + 0.792194i) q^{2} +(2.99507 + 0.171846i) q^{3} +(2.74486 - 2.90960i) q^{4} +(-0.222103 + 0.828901i) q^{5} +(-5.63634 + 2.05710i) q^{6} +(5.23163 - 9.06144i) q^{7} +(-2.73574 + 7.51769i) q^{8} +(8.94094 + 1.02938i) q^{9} +O(q^{10})$	\(q+(-1.83642 + 0.792194i) q^{2} +(2.99507 + 0.171846i) q^{3} +(2.74486 - 2.90960i) q^{4} +(-0.222103 + 0.828901i) q^{5} +(-5.63634 + 2.05710i) 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} +(-1.88677 - 7.04151i) q^{11} +(8.72105 - 8.24277i) q^{12} +(-6.98432 - 1.87144i) q^{13} +(-2.42903 + 20.7851i) q^{14} +(-0.807660 + 2.44445i) q^{15} +(-0.931516 - 15.9729i) q^{16} +10.9027 q^{17} +(-17.2348 + 5.19258i) q^{18} +(5.61772 + 5.61772i) q^{19} +(1.80213 + 2.92145i) q^{20} +(17.2263 - 26.2407i) q^{21} +(9.04313 + 11.4365i) q^{22} +(8.49079 + 14.7065i) q^{23} +(-9.48563 + 22.0459i) q^{24} +(21.0129 + 12.1318i) q^{25} +(14.3087 - 2.09618i) q^{26} +(26.6019 + 4.61955i) q^{27} +(-12.0051 - 40.0943i) q^{28} +(2.27742 + 8.49945i) q^{29} +(-0.453281 - 5.12886i) q^{30} +(6.67353 - 3.85297i) q^{31} +(14.3643 + 28.5949i) q^{32} +(-4.44095 - 21.4141i) q^{33} +(-20.0219 + 8.63706i) q^{34} +(6.34908 + 6.34908i) q^{35} +(27.5367 - 23.1890i) q^{36} +(-36.7870 - 36.7870i) q^{37} +(-14.7668 - 5.86615i) q^{38} +(-20.5969 - 6.80534i) q^{39} +(-5.62381 - 3.93736i) q^{40} +(-70.5661 + 40.7414i) q^{41} +(-10.8470 + 61.8354i) q^{42} +(12.0102 + 44.8228i) q^{43} +(-25.6669 - 13.8382i) q^{44} +(-2.83907 + 7.18252i) q^{45} +(-27.2430 - 20.2809i) q^{46} +(-21.0600 - 12.1590i) q^{47} +(-0.0450846 - 48.0000i) q^{48} +(-30.2398 - 52.3770i) q^{49} +(-48.1992 - 5.63276i) q^{50} +(32.6544 + 1.87359i) q^{51} +(-24.6161 + 15.1847i) q^{52} +(-69.3816 - 69.3816i) q^{53} +(-52.5117 + 12.5904i) q^{54} +6.25577 q^{55} +(53.8088 + 64.1195i) q^{56} +(15.8601 + 17.7909i) q^{57} +(-10.9155 - 13.8044i) q^{58} +(-8.77626 - 2.35159i) q^{59} +(4.89546 + 9.05964i) q^{60} +(-1.01995 - 3.80652i) 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} +(25.1195 + 35.8071i) q^{66} +(-32.5224 + 121.375i) q^{67} +(29.9264 - 31.7225i) q^{68} +(22.9033 + 45.5061i) q^{69} +(-16.6893 - 6.62986i) q^{70} +89.0591 q^{71} +(-32.1987 + 64.3991i) q^{72} +82.8383i q^{73} +(96.6988 + 38.4139i) q^{74} +(60.8504 + 39.9466i) q^{75} +(31.7651 - 0.925464i) q^{76} +(-73.6771 - 19.7417i) q^{77} +(43.2157 - 3.81934i) 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} +(-6.99695 + 1.87483i) q^{83} +(-29.0661 - 122.148i) q^{84} +(-2.42153 + 9.03727i) q^{85} +(-57.5642 - 72.7990i) q^{86} +(5.36044 + 25.8478i) q^{87} +(58.0976 + 5.07959i) q^{88} -144.573i q^{89} +(-0.476234 - 15.4392i) q^{90} +(-53.4973 + 53.4973i) q^{91} +(66.0959 + 15.6624i) q^{92} +(20.6498 - 10.3931i) q^{93} +(48.3072 + 5.64539i) q^{94} +(-5.90424 + 3.40882i) q^{95} +(38.1081 + 88.1123i) q^{96} +(48.6538 - 84.2708i) q^{97} +(97.0257 + 72.2301i) q^{98} +(-9.62105 - 64.8999i) 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 $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.83642	+	0.792194i	−0.918209	+	0.396097i
$2$	−1.83642	+	0.792194i	−0.918209	+	0.396097i
$3$	2.99507	+	0.171846i	0.998358	+	0.0572821i
$3$	2.99507	+	0.171846i	0.998358	+	0.0572821i
$4$	2.74486	−	2.90960i	0.686214	−	0.727399i
$5$	−0.222103	+	0.828901i	−0.0444207	+	0.165780i	−0.984573	−	0.174974i	$-0.944016\pi$
$5$	−0.222103	+	0.828901i	−0.0444207	+	0.165780i	0.940152	+	0.340754i	$0.110682\pi$
$6$	−5.63634	+	2.05710i	−0.939390	+	0.342850i
$7$	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
$11$	−1.88677	−	7.04151i	−0.171524	−	0.640137i	−0.997118	−	0.0758716i	$-0.975826\pi$
$11$	−1.88677	−	7.04151i	−0.171524	−	0.640137i	0.825593	−	0.564266i	$-0.190841\pi$
$12$	8.72105	−	8.24277i	0.726755	−	0.686897i
$13$	−6.98432	−	1.87144i	−0.537255	−	0.143957i	−0.0200186	−	0.999800i	$-0.506373\pi$
$13$	−6.98432	−	1.87144i	−0.537255	−	0.143957i	−0.517236	+	0.855843i	$0.673039\pi$
$14$	−2.42903	+	20.7851i	−0.173502	+	1.48465i
$15$	−0.807660	+	2.44445i	−0.0538440	+	0.162963i
$16$	−0.931516	−	15.9729i	−0.0582198	−	0.998304i
$17$	10.9027			0.641336			0.320668	−	0.947192i	$-0.396093\pi$
$17$	10.9027			0.641336			0.320668	+	0.947192i	$0.396093\pi$
$18$	−17.2348	+	5.19258i	−0.957487	+	0.288477i
$19$	5.61772	+	5.61772i	0.295669	+	0.295669i	0.839315	−	0.543646i	$-0.182956\pi$
$19$	5.61772	+	5.61772i	0.295669	+	0.295669i	−0.543646	+	0.839315i	$0.682956\pi$
$20$	1.80213	+	2.92145i	0.0901063	+	0.146072i
$21$	17.2263	−	26.2407i	0.820299	−	1.24956i
$22$	9.04313	+	11.4365i	0.411051	+	0.519839i
$23$	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	$0.712977\pi$
$24$	−9.48563	+	22.0459i	−0.395234	+	0.918580i
$25$	21.0129	+	12.1318i	0.840516	+	0.485272i
$26$	14.3087	−	2.09618i	0.550333	−	0.0806225i
$27$	26.6019	+	4.61955i	0.985255	+	0.171094i
$28$	−12.0051	−	40.0943i	−0.428753	−	1.43194i
$29$	2.27742	+	8.49945i	0.0785317	+	0.293084i	0.994011	−	0.109281i	$-0.0348548\pi$
$29$	2.27742	+	8.49945i	0.0785317	+	0.293084i	−0.915479	+	0.402365i	$0.868188\pi$
$30$	−0.453281	−	5.12886i	−0.0151094	−	0.170962i
$31$	6.67353	−	3.85297i	0.215275	−	0.124289i	−0.388485	−	0.921455i	$-0.627002\pi$
$31$	6.67353	−	3.85297i	0.215275	−	0.124289i	0.603761	+	0.797166i	$0.293668\pi$
$32$	14.3643	+	28.5949i	0.448883	+	0.893591i
$33$	−4.44095	−	21.4141i	−0.134574	−	0.648911i
$34$	−20.0219	+	8.63706i	−0.588880	+	0.254031i
$35$	6.34908	+	6.34908i	0.181402	+	0.181402i
$36$	27.5367	−	23.1890i	0.764908	−	0.644139i
$37$	−36.7870	−	36.7870i	−0.994244	−	0.994244i	0.00573969	−	0.999984i	$-0.498173\pi$
$37$	−36.7870	−	36.7870i	−0.994244	−	0.994244i	−0.999984	+	0.00573969i	$0.998173\pi$
$38$	−14.7668	−	5.86615i	−0.388600	−	0.154372i
$39$	−20.5969	−	6.80534i	−0.528127	−	0.174496i
$40$	−5.62381	−	3.93736i	−0.140595	−	0.0984340i
$41$	−70.5661	+	40.7414i	−1.72112	+	0.993692i	−0.804490	+	0.593966i	$0.797561\pi$
$41$	−70.5661	+	40.7414i	−1.72112	+	0.993692i	−0.916635	+	0.399726i	$0.869105\pi$
$42$	−10.8470	+	61.8354i	−0.258261	+	1.47227i
$43$	12.0102	+	44.8228i	0.279308	+	1.04239i	0.952899	+	0.303287i	$0.0980842\pi$
$43$	12.0102	+	44.8228i	0.279308	+	1.04239i	−0.673591	+	0.739104i	$0.735249\pi$
$44$	−25.6669	−	13.8382i	−0.583338	−	0.314505i
$45$	−2.83907	+	7.18252i	−0.0630904	+	0.159612i
$46$	−27.2430	−	20.2809i	−0.592239	−	0.440889i
$47$	−21.0600	−	12.1590i	−0.448085	−	0.258702i	0.258936	−	0.965894i	$-0.416628\pi$
$47$	−21.0600	−	12.1590i	−0.448085	−	0.258702i	−0.707021	+	0.707192i	$0.749961\pi$
$48$	−0.0450846	−	48.0000i	−0.000939263	−	1.00000i
$49$	−30.2398	−	52.3770i	−0.617140	−	1.06892i
$50$	−48.1992	−	5.63276i	−0.963983	−	0.112655i
$51$	32.6544	+	1.87359i	0.640283	+	0.0367370i
$52$	−24.6161	+	15.1847i	−0.473386	+	0.292014i
$53$	−69.3816	−	69.3816i	−1.30909	−	1.30909i	−0.922074	−	0.387014i	$-0.873507\pi$
$53$	−69.3816	−	69.3816i	−1.30909	−	1.30909i	−0.387014	−	0.922074i	$-0.626493\pi$
$54$	−52.5117	+	12.5904i	−0.972439	+	0.233156i
$55$	6.25577			0.113741
$56$	53.8088	+	64.1195i	0.960872	+	1.14499i
$57$	15.8601	+	17.7909i	0.278247	+	0.312120i
$58$	−10.9155	−	13.8044i	−0.188198	−	0.238006i
$59$	−8.77626	−	2.35159i	−0.148750	−	0.0398575i	0.183676	−	0.982987i	$-0.441200\pi$
$59$	−8.77626	−	2.35159i	−0.148750	−	0.0398575i	−0.332426	+	0.943129i	$0.607867\pi$
$60$	4.89546	+	9.05964i	0.0815910	+	0.150994i
$61$	−1.01995	−	3.80652i	−0.0167206	−	0.0624020i	0.957061	−	0.289885i	$-0.0936170\pi$
$61$	−1.01995	−	3.80652i	−0.0167206	−	0.0624020i	−0.973782	+	0.227483i	$0.926950\pi$
$62$	−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
$66$	25.1195	+	35.8071i	0.380599	+	0.542532i
$67$	−32.5224	+	121.375i	−0.485409	+	1.81157i	0.0928006	+	0.995685i	$0.470418\pi$
$67$	−32.5224	+	121.375i	−0.485409	+	1.81157i	−0.578210	+	0.815888i	$0.696249\pi$
$68$	29.9264	−	31.7225i	0.440094	−	0.466507i
$69$	22.9033	+	45.5061i	0.331932	+	0.659508i
$70$	−16.6893	−	6.62986i	−0.238418	−	0.0947122i
$71$	89.0591			1.25435			0.627177	−	0.778877i	$-0.284210\pi$
$71$	89.0591			1.25435			0.627177	+	0.778877i	$0.284210\pi$
$72$	−32.1987	+	64.3991i	−0.447204	+	0.894432i
$73$			82.8383i			1.13477i	0.823452	+	0.567386i	$0.192045\pi$
$73$			82.8383i			1.13477i	−0.823452	+	0.567386i	$0.807955\pi$
$74$	96.6988	+	38.4139i	1.30674	+	0.519106i
$75$	60.8504	+	39.9466i	0.811338	+	0.532622i
$76$	31.7651	−	0.925464i	0.417962	−	0.0121772i
$77$	−73.6771	−	19.7417i	−0.956846	−	0.256386i
$78$	43.2157	−	3.81934i	0.554048	−	0.0489659i
$79$	−59.4445	−	34.3203i	−0.752462	−	0.434434i	0.0741205	−	0.997249i	$-0.476385\pi$
$79$	−59.4445	−	34.3203i	−0.752462	−	0.434434i	−0.826583	+	0.562815i	$0.809718\pi$
$80$	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
$83$	−6.99695	+	1.87483i	−0.0843006	+	0.0225883i	−0.300723	−	0.953712i	$-0.597228\pi$
$83$	−6.99695	+	1.87483i	−0.0843006	+	0.0225883i	0.216422	+	0.976300i	$0.430561\pi$
$84$	−29.0661	−	122.148i	−0.346025	−	1.45415i
$85$	−2.42153	+	9.03727i	−0.0284886	+	0.106321i
$86$	−57.5642	−	72.7990i	−0.669351	−	0.846500i
$87$	5.36044	+	25.8478i	0.0616143	+	0.297102i
$88$	58.0976	+	5.07959i	0.660200	+	0.0577226i
$89$		−	144.573i		−	1.62442i	−0.583367	−	0.812208i	$-0.698265\pi$
$89$		−	144.573i		−	1.62442i	0.583367	−	0.812208i	$-0.301735\pi$
$90$	−0.476234	−	15.4392i	−0.00529149	−	0.171547i
$91$	−53.4973	+	53.4973i	−0.587882	+	0.587882i
$92$	66.0959	+	15.6624i	0.718434	+	0.170243i
$93$	20.6498	−	10.3931i	0.222041	−	0.111754i
$94$	48.3072	+	5.64539i	0.513907	+	0.0600573i
$95$	−5.90424	+	3.40882i	−0.0621499	+	0.0358823i
$96$	38.1081	+	88.1123i	0.396959	+	0.917836i
$97$	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
$99$	−9.62105	−	64.8999i	−0.0971823	−	0.655555i
$100$	92.9760	−	27.8390i	0.929760	−	0.278390i
$101$	−148.079	+	39.6775i	−1.46612	+	0.392847i	−0.901601	−	0.432570i	$-0.857607\pi$
$101$	−148.079	+	39.6775i	−1.46612	+	0.392847i	−0.564524	+	0.825417i	$0.690940\pi$
$102$	−61.4514	+	22.4279i	−0.602465	+	0.219882i
$103$	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	$0.505064\pi$
$104$	33.1762	−	47.3862i	0.319002	−	0.455636i
$105$	17.9249	+	20.1070i	0.170713	+	0.191495i
$106$	182.377	+	72.4499i	1.72054	+	0.683490i
$107$	−15.4533	+	15.4533i	−0.144424	+	0.144424i	−0.775622	−	0.631198i	$-0.782563\pi$
$107$	−15.4533	+	15.4533i	−0.144424	+	0.144424i	0.631198	+	0.775622i	$0.282563\pi$
$108$	86.4594	−	64.7208i	0.800550	−	0.599266i
$109$	−84.1975	+	84.1975i	−0.772454	+	0.772454i	−0.978535	−	0.206081i	$-0.933929\pi$
$109$	−84.1975	+	84.1975i	−0.772454	+	0.772454i	0.206081	+	0.978535i	$0.433929\pi$
$110$	−11.4882	+	4.95578i	−0.104438	+	0.0450526i
$111$	−103.858	−	116.502i	−0.935659	−	1.04956i
$112$	−149.611	−	75.1232i	−1.33581	−	0.670743i
$113$	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	$0.704089\pi$
$114$	−43.2196	−	20.1072i	−0.379119	−	0.176379i
$115$	−14.0760	+	3.77166i	−0.122400	+	0.0327971i
$116$	30.9812	+	16.7034i	0.267079	+	0.143995i
$117$	−60.5199	−	23.9220i	−0.517264	−	0.204461i
$118$	17.9798	−	2.63400i	0.152371	−	0.0223220i
$119$	57.0389	−	98.7943i	0.479319	−	0.830204i
$120$	−16.1671	−	12.7591i	−0.134726	−	0.106326i
$121$	58.7661	−	33.9286i	0.485670	−	0.280402i
$122$	4.88856	+	6.18236i	0.0400702	+	0.0506751i
$123$	−218.352	+	109.897i	−1.77522	+	0.893471i
$124$	7.10731	−	29.9931i	0.0573171	−	0.241880i
$125$	−29.8930	+	29.8930i	−0.239144	+	0.239144i
$126$	−43.1136	+	183.337i	−0.342172	+	1.45506i
$127$			95.7663i			0.754065i	0.926200	+	0.377033i	$0.123056\pi$
$127$			95.7663i			0.754065i	−0.926200	+	0.377033i	$0.876944\pi$
$128$	122.627	+	36.6947i	0.958027	+	0.286677i
$129$	28.2689	+	136.312i	0.219139	+	1.05668i
$130$	−1.44047	+	12.3260i	−0.0110806	+	0.0948157i
$131$	34.0140	−	126.942i	0.259649	−	0.969023i	−0.705796	−	0.708415i	$-0.749411\pi$
$131$	34.0140	−	126.942i	0.259649	−	0.969023i	0.965445	−	0.260607i	$-0.0839228\pi$
$132$	−74.4961	−	45.8572i	−0.564365	−	0.347403i
$133$	80.2944	−	21.5148i	0.603717	−	0.161766i
$134$	−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	0.698280	−	0.715825i	$-0.253949\pi$
$137$	58.5672	+	33.8138i	0.427498	+	0.246816i	−0.270782	+	0.962641i	$0.587282\pi$
$138$	−78.1096	−	65.4243i	−0.566012	−	0.474089i
$139$	−174.956	−	46.8794i	−1.25868	−	0.337262i	−0.432996	−	0.901396i	$-0.642544\pi$
$139$	−174.956	−	46.8794i	−1.25868	−	0.337262i	−0.825684	+	0.564134i	$0.809210\pi$
$140$	35.9006	−	1.04595i	0.256433	−	0.00747106i
$141$	−60.9868	−	40.0362i	−0.432531	−	0.283945i
$142$	−163.550	+	70.5521i	−1.15176	+	0.496846i
$143$			52.7111i			0.368609i
$144$	8.11358	−	143.771i	0.0563443	−	0.998411i
$145$	−7.55102			−0.0520760
$146$	−65.6240	−	152.126i	−0.449480	−	1.04196i
$147$	−81.5698	−	162.069i	−0.554897	−	1.10251i
$148$	−208.011	+	6.06030i	−1.40548	+	0.0409480i
$149$	−30.9963	+	115.680i	−0.208029	+	0.776374i	0.780476	+	0.625186i	$0.214977\pi$
$149$	−30.9963	+	115.680i	−0.208029	+	0.776374i	−0.988505	+	0.151189i	$0.951690\pi$
$150$	−143.392	−	25.1534i	−0.955947	−	0.167689i
$151$	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
$155$	1.71151	+	6.38745i	0.0110420	+	0.0412094i
$156$	−76.3365	+	41.2491i	−0.489336	+	0.264418i
$157$	296.305	+	79.3946i	1.88729	+	0.505698i	0.998914	+	0.0465835i	$0.0148334\pi$
$157$	296.305	+	79.3946i	1.88729	+	0.505698i	0.888377	+	0.459115i	$0.151833\pi$
$158$	136.353	+	15.9348i	0.862996	+	0.100853i
$159$	−195.880	−	219.726i	−1.23195	−	1.38193i
$160$	−26.8927	+	5.55552i	−0.168079	+	0.0347220i
$161$	177.683			1.10362
$162$	−159.440	+	28.6853i	−0.984198	+	0.177070i
$163$	174.457	+	174.457i	1.07029	+	1.07029i	0.997336	+	0.0729500i	$0.0232413\pi$
$163$	174.457	+	174.457i	1.07029	+	1.07029i	0.0729500	+	0.997336i	$0.476759\pi$
$164$	−75.1529	+	317.148i	−0.458250	+	1.93383i
$165$	18.7365	+	1.07503i	0.113555	+	0.00651534i
$166$	11.3641	−	8.98590i	0.0684584	−	0.0541319i
$167$	−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	$-0.389175\pi$
$168$	150.143	+	201.290i	0.893706	+	1.19815i
$169$	−101.080	−	58.3585i	−0.598106	−	0.345317i
$170$	−2.71233	−	18.5145i	−0.0159549	−	0.108909i
$171$	44.4449	+	56.0104i	0.259911	+	0.327546i
$172$	163.383	+	88.0873i	0.949900	+	0.512135i
$173$	44.6509	+	166.639i	0.258098	+	0.963234i	0.966341	+	0.257265i	$0.0828214\pi$
$173$	44.6509	+	166.639i	0.258098	+	0.963234i	−0.708243	+	0.705969i	$0.750512\pi$
$174$	−30.3205	−	43.2209i	−0.174256	−	0.248396i
$175$	219.863	−	126.938i	1.25636	−	0.725360i
$176$	−110.715	+	36.6963i	−0.629065	+	0.208502i
$177$	−25.8815	−	8.55136i	−0.146223	−	0.0483128i
$178$	114.530	+	265.497i	0.643427	+	1.49155i
$179$	−70.8708	−	70.8708i	−0.395926	−	0.395926i	0.480867	−	0.876793i	$-0.340322\pi$
$179$	−70.8708	−	70.8708i	−0.395926	−	0.395926i	−0.876793	+	0.480867i	$0.840322\pi$
$180$	13.1054	+	27.9756i	0.0728078	+	0.155420i
$181$	4.33948	+	4.33948i	0.0239750	+	0.0239750i	0.718993	−	0.695018i	$-0.244603\pi$
$181$	4.33948	+	4.33948i	0.0239750	+	0.0239750i	−0.695018	+	0.718993i	$0.744603\pi$
$182$	55.8631	−	140.624i	0.306940	−	0.772657i
$183$	−2.40070	−	11.5761i	−0.0131186	−	0.0632573i
$184$	−133.787	+	23.5981i	−0.727105	+	0.128250i
$185$	38.6633	−	22.3223i	0.208991	−	0.120661i
$186$	−29.6884	+	35.4447i	−0.159615	+	0.190563i
$187$	−20.5709	−	76.7715i	−0.110005	−	0.410543i
$188$	−93.1845	+	27.9014i	−0.495662	+	0.148412i
$189$	181.031	−	216.884i	0.957835	−	1.14753i
$190$	8.14221	−	10.9373i	0.0428538	−	0.0575648i
$191$	199.278	+	115.053i	1.04334	+	0.602373i	0.920778	−	0.390087i	$-0.127555\pi$
$191$	199.278	+	115.053i	1.04334	+	0.602373i	0.122563	+	0.992461i	$0.460889\pi$
$192$	−139.784	−	131.622i	−0.728044	−	0.685531i
$193$	−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	$-0.392954\pi$
$194$	−22.5898	+	193.300i	−0.116442	+	0.996389i
$195$	10.2156	−	15.5613i	0.0523877	−	0.0798017i
$196$	−235.400	−	55.7815i	−1.20102	−	0.284599i
$197$	−129.669	−	129.669i	−0.658219	−	0.658219i	0.296739	−	0.954959i	$-0.404101\pi$
$197$	−129.669	−	129.669i	−0.658219	−	0.658219i	−0.954959	+	0.296739i	$0.904101\pi$
$198$	69.0816	+	111.562i	0.348897	+	0.563442i
$199$	−205.292			−1.03162			−0.515810	−	0.856703i	$-0.672509\pi$
$199$	−205.292			−1.03162			−0.515810	+	0.856703i	$0.672509\pi$
$200$	−148.689	+	124.779i	−0.743445	+	0.623895i
$201$	−118.265	+	357.939i	−0.588383	+	1.78079i
$202$	240.502	−	190.171i	1.19060	−	0.941443i
$203$	88.9319	+	23.8292i	0.438088	+	0.117385i
$204$	95.0831	−	89.8685i	0.466094	−	0.440532i
$205$	−18.0976	−	67.5411i	−0.0882809	−	0.329469i
$206$	−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
$210$	−48.8463	−	22.7249i	−0.232601	−	0.108214i
$211$	−25.8542	+	96.4890i	−0.122532	+	0.457294i	−0.999740	−	0.0228164i	$-0.992737\pi$
$211$	−25.8542	+	96.4890i	−0.122532	+	0.457294i	0.877208	+	0.480110i	$0.159403\pi$
$212$	−392.315	+	11.4299i	−1.85054	+	0.0539148i
$213$	266.739	+	15.3045i	1.25229	+	0.0718520i
$214$	16.1367	−	40.6208i	0.0754052	−	0.189817i
$215$	−39.8212			−0.185215
$216$	−107.504	+	187.347i	−0.497704	+	0.867347i
$217$		−	80.6291i		−	0.371563i
$218$	87.9210	−	221.322i	0.403307	−	1.01524i
$219$	−14.2354	+	248.107i	−0.0650020	+	1.13291i
$220$	17.1712	−	18.2018i	0.0780509	−	0.0827354i
$221$	−76.1480	−	20.4038i	−0.344561	−	0.0923248i
$222$	283.019	+	131.670i	1.27486	+	0.593107i
$223$	10.8479	+	6.26305i	0.0486454	+	0.0280854i	0.524125	−	0.851641i	$-0.324392\pi$
$223$	10.8479	+	6.26305i	0.0486454	+	0.0280854i	−0.475480	+	0.879726i	$0.657726\pi$
$224$	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
$227$	213.713	−	57.2643i	0.941468	−	0.252265i	0.244730	−	0.969591i	$-0.421301\pi$
$227$	213.713	−	57.2643i	0.941468	−	0.252265i	0.696738	+	0.717326i	$0.254634\pi$
$228$	95.2979	+	2.68688i	0.417973	+	0.0117846i
$229$	9.58932	−	35.7878i	0.0418748	−	0.156279i	−0.941823	−	0.336110i	$-0.890889\pi$
$229$	9.58932	−	35.7878i	0.0418748	−	0.156279i	0.983697	+	0.179831i	$0.0575552\pi$
$230$	22.8616	−	18.0773i	0.0993983	−	0.0785970i
$231$	−217.276	−	71.7890i	−0.940588	−	0.310775i
$232$	−70.1267	−	6.13131i	−0.302270	−	0.0264281i
$233$		−	3.99805i		−	0.0171590i	−0.999963	−	0.00857951i	$-0.997269\pi$
$233$		−	3.99805i		−	0.0171590i	0.999963	−	0.00857951i	$-0.00273098\pi$
$234$	130.091	−	4.01275i	0.555943	−	0.0171485i
$235$	14.7561	−	14.7561i	0.0627919	−	0.0627919i
$236$	−30.9318	+	19.0806i	−0.131067	+	0.0808500i
$237$	−172.143	−	113.007i	−0.726342	−	0.476824i
$238$	−26.4830	+	226.613i	−0.111273	+	0.952157i
$239$	−14.3118	+	8.26293i	−0.0598821	+	0.0345729i	−0.529642	−	0.848221i	$-0.677674\pi$
$239$	−14.3118	+	8.26293i	−0.0598821	+	0.0345729i	0.469760	+	0.882794i	$0.344340\pi$
$240$	39.7972	+	10.6236i	0.165822	+	0.0442649i
$241$	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
$243$	233.090	+	68.6866i	0.959220	+	0.282661i
$244$	−13.8751	−	7.48070i	−0.0568650	−	0.0306586i
$245$	50.1317	−	13.4327i	0.204619	−	0.0548275i
$246$	313.926	−	374.794i	1.27612	−	1.52355i
$247$	−28.7227	−	49.7491i	−0.116286	−	0.201414i
$248$	10.7084	+	60.7103i	0.0431790	+	0.244800i
$249$	−21.2786	+	4.41284i	−0.0854560	+	0.0177223i
$250$	31.2150	−	78.5772i	0.124860	−	0.314309i
$251$	144.761	−	144.761i	0.576738	−	0.576738i	−0.357265	−	0.934003i	$-0.616291\pi$
$251$	144.761	−	144.761i	0.576738	−	0.576738i	0.934003	+	0.357265i	$0.116291\pi$
$252$	−66.0643	−	370.839i	−0.262160	−	1.47158i
$253$	87.5356	−	87.5356i	0.345991	−	0.345991i
$254$	−75.8655	−	175.867i	−0.298683	−	0.692389i
$255$	−8.80568	+	26.6512i	−0.0345321	+	0.104514i
$256$	−254.265	+	29.7580i	−0.993221	+	0.116242i
$257$	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	$0.671522\pi$
$258$	−159.899	−	227.931i	−0.619763	−	0.883452i
$259$	−525.800	+	140.888i	−2.03011	+	0.543967i
$260$	−7.11930	−	23.7769i	−0.0273819	−	0.0914495i
$261$	11.6131	+	78.3374i	0.0444945	+	0.300143i
$262$	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	$0.112496\pi$
$264$	173.134	+	25.1976i	0.655810	+	0.0954454i
$265$	72.9204	−	42.1006i	0.275171	−	0.158870i
$266$	−130.410	+	103.119i	−0.490264	+	0.387665i
$267$	24.8443	−	433.007i	0.0930500	−	1.62175i
$268$	263.884	+	427.785i	0.984642	+	1.59621i
$269$	−137.619	+	137.619i	−0.511595	+	0.511595i	−0.915015	−	0.403420i	$-0.867821\pi$
$269$	−137.619	+	137.619i	−0.511595	+	0.511595i	0.403420	+	0.915015i	$0.367821\pi$
$270$	1.22681	−	46.3234i	0.00454375	−	0.171568i
$271$		−	334.184i		−	1.23315i	−0.787295	−	0.616576i	$-0.788519\pi$
$271$		−	334.184i		−	1.23315i	0.787295	−	0.616576i	$-0.211481\pi$
$272$	−10.1561	−	174.147i	−0.0373384	−	0.640248i
$273$	−169.422	+	151.035i	−0.620592	+	0.553242i
$274$	−134.341	−	15.6996i	−0.490295	−	0.0572980i
$275$	45.7797	−	170.852i	0.166472	−	0.621281i
$276$	195.271	+	58.2684i	0.707502	+	0.211117i
$277$	−130.698	+	35.0205i	−0.471835	+	0.126428i	−0.486898	−	0.873459i	$-0.661872\pi$
$277$	−130.698	+	35.0205i	−0.471835	+	0.126428i	0.0150632	+	0.999887i	$0.495205\pi$
$278$	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	0.335583	−	0.942011i	$-0.391067\pi$
$281$	−87.7929	−	50.6873i	−0.312430	−	0.180382i	−0.648013	+	0.761629i	$0.724400\pi$
$282$	143.714	+	25.2098i	0.509623	+	0.0893964i
$283$	295.592	+	79.2038i	1.04450	+	0.279872i	0.739976	−	0.672634i	$-0.234837\pi$
$283$	295.592	+	79.2038i	1.04450	+	0.279872i	0.304521	+	0.952506i	$0.401504\pi$
$284$	244.455	−	259.126i	0.860756	−	0.912416i
$285$	−18.2694	+	9.19504i	−0.0641033	+	0.0322633i
$286$	−41.7574	−	96.7996i	−0.146005	−	0.338460i
$287$			852.575i			2.97064i
$288$	98.9948	+	270.452i	0.343732	+	0.939068i
$289$	−170.131			−0.588688
$290$	13.8668	−	5.98188i	0.0478167	−	0.0206272i
$291$	160.203	−	244.036i	0.550527	−	0.838613i
$292$	241.026	+	227.379i	0.825432	+	0.778696i
$293$	39.8684	−	148.791i	0.136070	−	0.507819i	−0.863921	−	0.503627i	$-0.831999\pi$
$293$	39.8684	−	148.791i	0.136070	−	0.507819i	0.999991	−	0.00419275i	$-0.00133460\pi$
$294$	278.187	+	233.008i	0.946213	+	0.792544i
$295$	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
$299$	−31.7800	−	118.605i	−0.106288	−	0.396671i
$300$	283.254	−	67.4023i	0.944180	−	0.224674i
$301$	468.993	+	125.666i	1.55812	+	0.417496i
$302$	−28.8210	+	246.620i	−0.0954339	+	0.816622i
$303$	−450.325	+	93.3904i	−1.48622	+	0.308219i
$304$	84.4980	−	94.9640i	0.277954	−	0.312382i
$305$	3.38176			0.0110877
$306$	−187.906	+	56.6132i	−0.614071	+	0.185010i
$307$	−98.8548	−	98.8548i	−0.322003	−	0.322003i	0.527532	−	0.849535i	$-0.323117\pi$
$307$	−98.8548	−	98.8548i	−0.322003	−	0.322003i	−0.849535	+	0.527532i	$0.823117\pi$
$308$	−259.674	+	160.183i	−0.843096	+	0.520073i
$309$	238.372	+	473.617i	0.771430	+	1.53274i
$310$	−8.20316	−	10.3742i	−0.0264618	−	0.0334651i
$311$	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	$0.520942\pi$
$312$	107.508	−	136.224i	0.344578	−	0.436615i
$313$	70.6134	+	40.7686i	0.225602	+	0.130251i	0.608541	−	0.793522i	$-0.291755\pi$
$313$	70.6134	+	40.7686i	0.225602	+	0.130251i	−0.382940	+	0.923773i	$0.625088\pi$
$314$	−607.035	+	88.9292i	−1.93323	+	0.283214i
$315$	50.2311	+	63.3024i	0.159464	+	0.200960i
$316$	−263.025	+	78.7553i	−0.832358	+	0.249226i
$317$	60.0475	+	224.100i	0.189424	+	0.706941i	0.993640	+	0.112604i	$0.0359190\pi$
$317$	60.0475	+	224.100i	0.189424	+	0.706941i	−0.804216	+	0.594338i	$0.797414\pi$
$318$	533.784	+	248.334i	1.67856	+	0.780924i
$319$	55.5520	−	32.0730i	0.174144	−	0.100542i
$320$	44.9851	−	31.5065i	0.140579	−	0.0984578i
$321$	−48.9394	+	43.6283i	−0.152459	+	0.135914i
$322$	−326.299	+	140.759i	−1.01335	+	0.437140i
$323$	61.2483	+	61.2483i	0.189623	+	0.189623i
$324$	270.074	−	178.986i	0.833563	−	0.552425i
$325$	−124.057	−	124.057i	−0.381713	−	0.381713i
$326$	−458.578	−	182.172i	−1.40668	−	0.558809i
$327$	−266.647	+	237.709i	−0.815433	+	0.726938i
$328$	−113.231	−	641.952i	−0.345216	−	1.95717i
$329$	−220.356	+	127.223i	−0.669776	+	0.386695i
$330$	−35.2597	+	12.8687i	−0.106847	+	0.0389962i
$331$	−119.705	−	446.744i	−0.361646	−	1.34968i	−0.871912	−	0.489663i	$-0.837120\pi$
$331$	−119.705	−	446.744i	−0.361646	−	1.34968i	0.510266	−	0.860017i	$-0.329547\pi$
$332$	−13.7506	+	25.5044i	−0.0414176	+	0.0768206i
$333$	−291.042	−	366.778i	−0.874001	−	1.10144i
$334$	344.791	+	256.677i	1.03231	+	0.768494i
$335$	−93.3848	−	53.9158i	−0.278761	−	0.160943i
$336$	−435.185	−	250.709i	−1.29519	−	0.746159i
$337$	−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	$-0.374435\pi$
$338$	231.856	+	27.0957i	0.685965	+	0.0801648i
$339$	120.390	+	239.201i	0.355134	+	0.705608i
$340$	19.6481	+	31.8517i	0.0577884	+	0.0936814i
$341$	−39.7221	−	39.7221i	−0.116487	−	0.116487i
$342$	−125.990	−	67.6496i	−0.368393	−	0.197806i
$343$	−120.115			−0.350189
$344$	−369.821	−	32.3342i	−1.07506	−	0.0939947i
$345$	−42.8069	+	8.87750i	−0.124078	+	0.0257319i
$346$	−214.008	−	270.647i	−0.618521	−	0.782218i
$347$	104.002	+	27.8673i	0.299718	+	0.0803093i	0.405544	−	0.914075i	$-0.367082\pi$
$347$	104.002	+	27.8673i	0.299718	+	0.0803093i	−0.105826	+	0.994385i	$0.533749\pi$
$348$	89.9205	+	55.3519i	0.258392	+	0.159057i
$349$	−78.3405	−	292.371i	−0.224471	−	0.837739i	−0.982616	−	0.185652i	$-0.940560\pi$
$349$	−78.3405	−	292.371i	−0.224471	−	0.837739i	0.758144	−	0.652087i	$-0.226106\pi$
$350$	−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	$0.255024\pi$
$354$	54.3035	−	4.79926i	0.153400	−	0.0135572i
$355$	−19.7803	+	73.8212i	−0.0557193	+	0.207947i
$356$	−420.650	−	396.833i	−1.18160	−	1.11470i
$357$	187.813	−	286.094i	0.526087	−	0.801385i
$358$	186.292	+	74.0049i	0.520368	+	0.206718i
$359$	43.2253			0.120405			0.0602024	−	0.998186i	$-0.480825\pi$
$359$	43.2253			0.120405			0.0602024	+	0.998186i	$0.480825\pi$
$360$	−46.2291	−	40.9928i	−0.128414	−	0.113869i
$361$		−	297.883i		−	0.825159i
$362$	−11.4068	−	4.53139i	−0.0315105	−	0.0125176i
$363$	181.839	−	91.5200i	0.500935	−	0.252121i
$364$	8.81316	+	302.498i	0.0242120	+	0.831039i
$365$	−68.6648	−	18.3987i	−0.188123	−	0.0504073i
$366$	13.5792	+	19.3567i	0.0371016	+	0.0528871i
$367$	314.433	+	181.538i	0.856767	+	0.494655i	0.862928	−	0.505327i	$-0.168628\pi$
$367$	314.433	+	181.538i	0.856767	+	0.494655i	−0.00616149	+	0.999981i	$0.501961\pi$
$368$	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
$371$	−991.677	+	265.719i	−2.67298	+	0.716224i
$372$	26.4411	−	88.6103i	0.0710783	−	0.238200i
$373$	−68.3014	+	254.904i	−0.183114	+	0.683390i	0.811913	+	0.583779i	$0.198427\pi$
$373$	−68.3014	+	254.904i	−0.183114	+	0.683390i	−0.995026	+	0.0996110i	$0.968240\pi$
$374$	98.5947	+	124.688i	0.263622	+	0.333392i
$375$	−94.6689	+	84.3948i	−0.252450	+	0.225053i
$376$	149.022	−	125.059i	0.396336	−	0.332603i
$377$		−	63.6249i		−	0.168766i
$378$	−160.634	+	541.700i	−0.424958	+	1.43307i
$379$	−31.8574	+	31.8574i	−0.0840565	+	0.0840565i	−0.747885	−	0.663828i	$-0.768931\pi$
$379$	−31.8574	+	31.8574i	−0.0840565	+	0.0840565i	0.663828	+	0.747885i	$0.268931\pi$
$380$	−6.28802	+	26.5357i	−0.0165474	+	0.0698308i
$381$	−16.4571	+	286.827i	−0.0431944	+	0.752827i
$382$	−457.102	−	53.4189i	−1.19660	−	0.139840i
$383$	195.603	−	112.932i	0.510714	−	0.294861i	−0.222413	−	0.974952i	$-0.571393\pi$
$383$	195.603	−	112.932i	0.510714	−	0.294861i	0.733127	+	0.680092i	$0.238060\pi$
$384$	360.973	+	130.976i	0.940033	+	0.341084i
$385$	32.7279	−	56.6863i	0.0850074	−	0.147237i
$386$	404.070	+	300.807i	1.04681	+	0.779294i
$387$	61.2429	+	413.121i	0.158250	+	1.06750i
$388$	−111.646	−	372.874i	−0.287749	−	0.961016i
$389$	458.472	−	122.847i	1.17859	−	0.315802i	0.384223	−	0.923240i	$-0.374469\pi$
$389$	458.472	−	122.847i	1.17859	−	0.315802i	0.794367	+	0.607438i	$0.207803\pi$
$390$	−6.43250	+	36.6699i	−0.0164936	+	0.0940253i
$391$	92.5726	+	160.340i	0.236759	+	0.410078i
$392$	476.482	−	84.0443i	1.21552	−	0.214399i
$393$	123.689	−	374.355i	0.314730	−	0.952558i
$394$	340.850	+	135.404i	0.865101	+	0.343664i
$395$	41.6510	−	41.6510i	0.105446	−	0.105446i
$396$	−215.241	−	150.148i	−0.543538	−	0.379161i
$397$	−122.223	+	122.223i	−0.307868	+	0.307868i	−0.844082	−	0.536214i	$-0.819854\pi$
$397$	−122.223	+	122.223i	−0.307868	+	0.307868i	0.536214	+	0.844082i	$0.319854\pi$
$398$	377.002	−	162.631i	0.947242	−	0.408621i
$399$	244.185	−	50.6402i	0.611992	−	0.126918i
$400$	174.206	−	346.937i	0.435514	−	0.867342i
$401$	−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	$0.920387\pi$
$402$	−66.3735	−	751.015i	−0.165108	−	1.86820i
$403$	−53.8207	+	14.4212i	−0.133550	+	0.0357846i
$404$	−291.009	+	539.758i	−0.720319	+	1.33604i
$405$	−32.7775	+	61.2960i	−0.0809322	+	0.151348i
$406$	−182.193	+	26.6909i	−0.448752	+	0.0657411i
$407$	−189.628	+	328.445i	−0.465916	+	0.806989i
$408$	−103.419	+	240.360i	−0.253478	+	0.589119i
$409$	−467.836	+	270.105i	−1.14385	+	0.660403i	−0.947382	−	0.320106i	$-0.896281\pi$
$409$	−467.836	+	270.105i	−1.14385	+	0.660403i	−0.196471	+	0.980510i	$0.562948\pi$
$410$	86.7404	+	109.697i	0.211562	+	0.267553i
$411$	169.602	+	111.339i	0.412658	+	0.270899i
$412$	687.911	+	163.011i	1.66969	+	0.395657i
$413$	−67.2230	+	67.2230i	−0.162767	+	0.162767i
$414$	−222.701	−	209.374i	−0.537926	−	0.505733i
$415$		−	6.21618i		−	0.0149787i
$416$	−46.8108	−	226.598i	−0.112526	−	0.544706i
$417$	−515.952	−	170.473i	−1.23729	−	0.408808i
$418$	−13.4451	+	115.049i	−0.0321652	+	0.275236i
$419$	118.491	−	442.215i	0.282795	−	1.05540i	−0.667641	−	0.744484i	$-0.732696\pi$
$419$	118.491	−	442.215i	0.282795	−	1.05540i	0.950436	−	0.310921i	$-0.100638\pi$
$420$	107.705	+	3.03668i	0.256440	+	0.00723020i
$421$	−244.993	+	65.6458i	−0.581932	+	0.155928i	−0.537763	−	0.843096i	$-0.680731\pi$
$421$	−244.993	+	65.6458i	−0.581932	+	0.155928i	−0.0441687	+	0.999024i	$0.514064\pi$
$422$	−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
$426$	−501.968	+	183.203i	−1.17833	+	0.430055i
$427$	−39.8286	−	10.6720i	−0.0932754	−	0.0249931i
$428$	2.54578	+	87.3801i	0.00594809	+	0.204159i
$429$	−9.05820	+	157.874i	−0.0211147	+	0.368004i
$430$	73.1283	−	31.5461i	0.170066	−	0.0733631i
$431$			191.766i			0.444933i	0.974940	+	0.222467i	$0.0714108\pi$
$431$			191.766i			0.444933i	−0.974940	+	0.222467i	$0.928589\pi$
$432$	49.0073	−	429.211i	0.113443	−	0.993545i
$433$	−671.361			−1.55049			−0.775244	−	0.631662i	$-0.782373\pi$
$433$	−671.361			−1.55049			−0.775244	+	0.631662i	$0.782373\pi$
$434$	63.8739	+	148.069i	0.147175	+	0.341172i
$435$	−22.6159	−	1.29761i	−0.0519905	−	0.00298302i
$436$	13.8707	+	476.091i	0.0318136	+	1.09195i
$437$	−34.9180	+	130.316i	−0.0799038	+	0.298205i
$438$	−170.407	−	466.905i	−0.389056	−	1.06599i
$439$	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
$443$	−154.913	−	578.144i	−0.349691	−	1.30507i	−0.887035	−	0.461702i	$-0.847239\pi$
$443$	−154.913	−	578.144i	−0.349691	−	1.30507i	0.537344	−	0.843363i	$-0.319428\pi$
$444$	−624.048	−	17.5948i	−1.40551	−	0.0396279i
$445$	119.837	+	32.1102i	0.269296	+	0.0721577i
$446$	−24.8828	−	2.90791i	−0.0557911	−	0.00651999i
$447$	−112.715	+	341.143i	−0.252160	+	0.763183i
$448$	−629.238	+	229.104i	−1.40455	+	0.511393i
$449$	375.940			0.837284			0.418642	−	0.908151i	$-0.362506\pi$
$449$	375.940			0.837284			0.418642	+	0.908151i	$0.362506\pi$
$450$	−425.147	−	99.9776i	−0.944772	−	0.222172i
$451$	420.023	+	420.023i	0.931314	+	0.931314i
$452$	347.431	+	82.3289i	0.768653	+	0.182144i
$453$	204.394	−	311.352i	0.451201	−	0.687311i
$454$	−347.102	+	274.463i	−0.764542	+	0.604545i
$455$	−32.4620	−	56.2259i	−0.0713451	−	0.123573i
$456$	−177.135	+	70.5602i	−0.388455	+	0.154737i
$457$	149.241	+	86.1645i	0.326568	+	0.188544i	0.654316	−	0.756221i	$-0.272957\pi$
$457$	149.241	+	86.1645i	0.326568	+	0.188544i	−0.327749	+	0.944765i	$0.606290\pi$
$458$	10.7409	+	73.3180i	0.0234518	+	0.160083i
$459$	290.033	+	50.3656i	0.631879	+	0.109729i
$460$	−27.6627	+	51.3083i	−0.0601363	+	0.111540i
$461$	−29.9765	−	111.874i	−0.0650249	−	0.242676i	0.925762	−	0.378107i	$-0.123425\pi$
$461$	−29.9765	−	111.874i	−0.0650249	−	0.242676i	−0.990787	+	0.135431i	$0.956758\pi$
$462$	455.880	−	40.2900i	0.986753	−	0.0872077i
$463$	291.279	−	168.170i	0.629111	−	0.363218i	−0.151297	−	0.988488i	$-0.548345\pi$
$463$	291.279	−	168.170i	0.629111	−	0.363218i	0.780408	+	0.625271i	$0.215012\pi$
$464$	133.639	−	44.2943i	0.288015	−	0.0954618i
$465$	4.02845	+	19.4250i	0.00866333	+	0.0417742i
$466$	3.16723	+	7.34209i	0.00679664	+	0.0157556i
$467$	−230.097	−	230.097i	−0.492713	−	0.492713i	0.416447	−	0.909160i	$-0.363275\pi$
$467$	−230.097	−	230.097i	−0.492713	−	0.492713i	−0.909160	+	0.416447i	$0.863275\pi$
$468$	−235.722	+	110.426i	−0.503679	+	0.235953i
$469$	929.691	+	929.691i	1.98228	+	1.98228i
$470$	−15.4087	+	38.7881i	−0.0327844	+	0.0825278i
$471$	873.811	+	288.712i	1.85523	+	0.612976i
$472$	41.6881	−	59.5439i	0.0883223	−	0.126152i
$473$	292.960	−	169.140i	0.619365	−	0.357591i
$474$	405.650	+	71.1578i	0.855802	+	0.150122i
$475$	49.8915	+	186.197i	0.105035	+	0.391995i
$476$	−130.888	−	437.137i	−0.274975	−	0.918354i
$477$	−548.917	−	691.757i	−1.15077	−	1.45022i
$478$	19.7366	−	26.5119i	0.0412900	−	0.0554643i
$479$	−156.572	−	90.3968i	−0.326872	−	0.188720i	0.327579	−	0.944824i	$-0.393767\pi$
$479$	−156.572	−	90.3968i	−0.326872	−	0.188720i	−0.654452	+	0.756104i	$0.727100\pi$
$480$	−81.5003	+	12.0178i	−0.169792	+	0.0250371i
$481$	188.087	+	325.777i	0.391034	+	0.677291i
$482$	−10.9924	+	94.0617i	−0.0228059	+	0.195149i
$483$	532.172	+	30.5341i	1.10181	+	0.0632175i
$484$	62.5859	−	264.115i	0.129310	−	0.545692i
$485$	59.0460	+	59.0460i	0.121744	+	0.121744i
$486$	−482.464	+	58.5155i	−0.992725	+	0.120402i
$487$	−157.394			−0.323192			−0.161596	−	0.986857i	$-0.551664\pi$
$487$	−157.394			−0.323192			−0.161596	+	0.986857i	$0.551664\pi$
$488$	31.4066	+	2.74594i	0.0643577	+	0.00562692i
$489$	492.531	+	552.490i	1.00722	+	1.12984i
$490$	−81.4213	+	64.3821i	−0.166166	+	0.131392i
$491$	744.948	+	199.608i	1.51721	+	0.406534i	0.918821	−	0.394674i	$-0.129143\pi$
$491$	744.948	+	199.608i	1.51721	+	0.406534i	0.598385	+	0.801209i	$0.295809\pi$
$492$	−279.589	+	936.968i	−0.568271	+	1.90441i
$493$	24.8301	+	92.6670i	0.0503652	+	0.187966i
$494$	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
$498$	35.5805	−	24.9606i	0.0714467	−	0.0501216i
$499$	126.534	−	472.231i	0.253575	−	0.946355i	−0.715302	−	0.698815i	$-0.753711\pi$
$499$	126.534	−	472.231i	0.253575	−	0.946355i	0.968878	−	0.247540i	$-0.0796223\pi$
$500$	4.92458	+	169.029i	0.00984917	+	0.338058i
$501$	−289.867	−	575.930i	−0.578576	−	1.14956i
$502$	−151.163	+	380.521i	−0.301121	+	0.758009i
$503$	92.0334			0.182969			0.0914845	−	0.995807i	$-0.470839\pi$
$503$	92.0334			0.182969			0.0914845	+	0.995807i	$0.470839\pi$
$504$	415.098	+	628.679i	0.823606	+	1.24738i
$505$		−	131.555i		−	0.260505i
$506$	−91.4067	+	230.097i	−0.180646	+	0.454737i
$507$	−292.713	−	192.158i	−0.577343	−	0.379010i
$508$	278.641	+	262.865i	0.548507	+	0.517450i
$509$	−668.325	−	179.077i	−1.31302	−	0.351822i	−0.466659	−	0.884437i	$-0.654543\pi$
$509$	−668.325	−	179.077i	−1.31302	−	0.351822i	−0.846357	+	0.532616i	$0.821209\pi$
$510$	−4.94199	−	55.9185i	−0.00969017	−	0.109644i
$511$	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
$515$	−146.500	+	39.2546i	−0.284466	+	0.0762225i
$516$	474.206	+	291.905i	0.919004	+	0.565707i
$517$	−45.8824	+	171.235i	−0.0887474	+	0.331210i
$518$	853.977	−	675.264i	1.64860	−	1.30360i
$519$	105.096	+	506.771i	0.202498	+	0.976436i
$520$	31.9099	+	38.0244i	0.0613652	+	0.0731239i
$521$		−	871.991i		−	1.67369i	−0.547442	−	0.836844i	$-0.684398\pi$
$521$		−	871.991i		−	1.67369i	0.547442	−	0.836844i	$-0.315602\pi$
$522$	−83.3849	−	134.660i	−0.159741	−	0.257970i
$523$	−59.7664	+	59.7664i	−0.114276	+	0.114276i	−0.761933	−	0.647656i	$-0.775749\pi$
$523$	−59.7664	+	59.7664i	−0.114276	+	0.114276i	0.647656	+	0.761933i	$0.275749\pi$
$524$	−275.986	−	447.405i	−0.526692	−	0.853826i
$525$	680.320	−	342.406i	1.29585	−	0.652202i
$526$	−20.6808	+	176.964i	−0.0393171	+	0.336434i
$527$	72.7596	−	42.0078i	0.138064	−	0.0797111i
$528$	−337.907	+	90.8822i	−0.639976	+	0.172125i
$529$	120.313	−	208.388i	0.227435	−	0.393929i
$530$	−100.560	+	135.081i	−0.189737	+	0.254871i
$531$	−76.0473	−	30.0596i	−0.143215	−	0.0566094i
$532$	157.797	−	292.680i	0.296611	−	0.550150i
$533$	569.101	−	152.490i	1.06773	−	0.286098i
$534$	297.401	+	814.863i	0.556931	+	1.52596i
$535$	−9.37704	−	16.2415i	−0.0175272	−	0.0303580i
$536$	−823.490	−	576.545i	−1.53636	−	1.07564i
$537$	−200.084	−	224.442i	−0.372596	−	0.417955i
$538$	143.705	−	361.747i	0.267109	−	0.672392i
$539$	−311.757	+	311.757i	−0.578399	+	0.578399i
$540$	34.4442	+	86.0410i	0.0637855	+	0.159335i
$541$	−199.007	+	199.007i	−0.367851	+	0.367851i	−0.866693	−	0.498842i	$-0.833759\pi$
$541$	−199.007	+	199.007i	−0.367851	+	0.367851i	0.498842	+	0.866693i	$0.333759\pi$
$542$	264.739	+	613.702i	0.488448	+	1.13229i
$543$	12.2513	+	13.7428i	0.0225623	+	0.0253090i
$544$	156.609	+	311.762i	0.287885	+	0.573092i
$545$	−51.0908	−	88.4919i	−0.0937446	−	0.162370i
$546$	191.480	−	411.578i	0.350696	−	0.753806i
$547$	378.909	−	101.528i	0.692705	−	0.185610i	0.104744	−	0.994499i	$-0.466598\pi$
$547$	378.909	−	101.528i	0.692705	−	0.185610i	0.587961	+	0.808890i	$0.299931\pi$
$548$	259.143	−	77.5929i	0.472889	−	0.141593i
$549$	−5.20097	−	35.0838i	−0.00947354	−	0.0639049i
$550$	51.2775	+	350.023i	0.0932318	+	0.636405i
$551$	−34.9536	+	60.5414i	−0.0634366	+	0.109875i
$552$	−404.758	+	47.6872i	−0.733258	+	0.0863898i
$553$	−621.983	+	359.102i	−1.12474	+	0.649371i
$554$	212.274	−	167.851i	0.383165	−	0.302980i
$555$	119.636	−	60.2127i	0.215559	−	0.108491i
$556$	−616.631	+	380.376i	−1.10905	+	0.684129i
$557$	−112.934	+	112.934i	−0.202755	+	0.202755i	−0.801179	−	0.598425i	$-0.795794\pi$
$557$	−112.934	+	112.934i	−0.202755	+	0.202755i	0.598425	+	0.801179i	$0.295794\pi$
$558$	−95.0099	+	101.058i	−0.170269	+	0.181107i
$559$		−	335.533i		−	0.600238i
$560$	95.4987	−	107.327i	0.170533	−	0.191656i
$561$	−48.4184	−	233.471i	−0.0863073	−	0.416170i
$562$	201.379	+	23.5340i	0.358325	+	0.0418754i
$563$	67.5119	−	251.958i	0.119915	−	0.447528i	−0.879693	−	0.475542i	$-0.842252\pi$
$563$	67.5119	−	251.958i	0.119915	−	0.447528i	0.999608	+	0.0280147i	$0.00891854\pi$
$564$	−283.889	+	67.5534i	−0.503350	+	0.119776i
$565$	−73.9903	+	19.8256i	−0.130956	+	0.0350896i
$566$	−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	0.850786	−	0.525512i	$-0.176126\pi$
$569$	467.191	+	269.733i	0.821073	+	0.474047i	−0.0297132	+	0.999558i	$0.509459\pi$
$570$	26.2661	−	31.3589i	0.0460808	−	0.0550156i
$571$	−680.242	−	182.270i	−1.19132	−	0.319212i	−0.391910	−	0.920003i	$-0.628186\pi$
$571$	−680.242	−	182.270i	−1.19132	−	0.319212i	−0.799406	+	0.600791i	$0.794852\pi$
$572$	153.368	+	144.684i	0.268126	+	0.252945i
$573$	577.081	+	378.838i	1.00712	+	0.661149i
$574$	−675.404	−	1565.68i	−1.17666	−	2.72767i
$575$			412.034i			0.716581i
$576$	−396.046	−	418.239i	−0.687580	−	0.726109i
$577$	488.442			0.846519			0.423260	−	0.906008i	$-0.360886\pi$
$577$	488.442			0.846519			0.423260	+	0.906008i	$0.360886\pi$
$578$	312.431	−	134.777i	0.540539	−	0.233178i
$579$	−339.703	−	674.950i	−0.586707	−	1.16572i
$580$	−20.7265	+	21.9704i	−0.0357353	+	0.0378801i
$581$	−19.6168	+	73.2108i	−0.0337638	+	0.126008i
$582$	−100.876	+	575.065i	−0.173326	+	0.988083i
$583$	−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
$587$	−75.9368	−	283.400i	−0.129364	−	0.482794i	0.870593	−	0.492003i	$-0.163735\pi$
$587$	−75.9368	−	283.400i	−0.129364	−	0.482794i	−0.999958	+	0.00920939i	$0.997069\pi$
$588$	−695.454	−	207.522i	−1.18275	−	0.352929i
$589$	59.1349	+	15.8451i	0.100399	+	0.0269018i
$590$	−1.81005	+	15.4885i	−0.00306788	+	0.0262517i
$591$	−366.086	−	410.652i	−0.619434	−	0.694843i
$592$	−553.326	+	621.862i	−0.934673	+	1.05044i
$593$	−428.045			−0.721830			−0.360915	−	0.932599i	$-0.617536\pi$
$593$	−428.045			−0.721830			−0.360915	+	0.932599i	$0.617536\pi$
$594$	187.733	+	346.007i	0.316049	+	0.582503i
$595$	69.2222	+	69.2222i	0.116340	+	0.116340i
$596$	251.501	+	407.711i	0.421982	+	0.684079i
$597$	−614.866	−	35.2787i	−1.02993	−	0.0590933i
$598$	152.319	+	192.632i	0.254715	+	0.322127i
$599$	−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	$-0.339933\pi$
$600$	−466.777	+	348.171i	−0.777962	+	0.580285i
$601$	484.136	+	279.516i	0.805550	+	0.465085i	0.845408	−	0.534121i	$-0.179357\pi$
$601$	484.136	+	279.516i	0.805550	+	0.465085i	−0.0398580	+	0.999205i	$0.512691\pi$
$602$	−960.818	+	140.758i	−1.59604	+	0.233817i
$603$	−415.723	+	1051.73i	−0.689424	+	1.74417i
$604$	−142.443	−	475.729i	−0.235833	−	0.787631i
$605$	15.0713	+	56.2469i	0.0249113	+	0.0929702i
$606$	753.001	−	528.248i	1.24258	−	0.871697i
$607$	−749.119	+	432.504i	−1.23413	+	0.712527i	−0.967889	−	0.251378i	$-0.919116\pi$
$607$	−749.119	+	432.504i	−1.23413	+	0.712527i	−0.266244	+	0.963906i	$0.585783\pi$
$608$	−79.9437	+	241.332i	−0.131486	+	0.396928i
$609$	262.263	+	86.6529i	0.430645	+	0.142287i
$610$	−6.21033	+	2.67901i	−0.0101809	+	0.00439182i
$611$	124.335	+	124.335i	0.203494	+	0.203494i
$612$	300.225	−	252.823i	0.490563	−	0.413110i
$613$	180.243	+	180.243i	0.294034	+	0.294034i	0.838671	−	0.544638i	$-0.183333\pi$
$613$	180.243	+	180.243i	0.294034	+	0.294034i	−0.544638	+	0.838671i	$0.683333\pi$
$614$	259.851	+	103.226i	0.423210	+	0.168121i
$615$	−42.5969	−	205.401i	−0.0692633	−	0.333985i
$616$	349.973	−	499.874i	0.568139	−	0.811483i
$617$	−395.767	+	228.496i	−0.641437	+	0.370334i	−0.785168	−	0.619283i	$-0.787423\pi$
$617$	−395.767	+	228.496i	−0.641437	+	0.370334i	0.143731	+	0.989617i	$0.454090\pi$
$618$	−812.947	−	680.921i	−1.31545	−	1.10181i
$619$	−76.2441	−	284.547i	−0.123173	−	0.459688i	0.876595	−	0.481229i	$-0.159809\pi$
$619$	−76.2441	−	284.547i	−0.123173	−	0.459688i	−0.999768	+	0.0215411i	$0.993143\pi$
$620$	23.2828	+	12.5528i	0.0375529	+	0.0202465i
$621$	157.934	+	430.443i	0.254321	+	0.693145i
$622$	−829.497	−	617.513i	−1.33360	−	0.992787i
$623$	−1310.04	−	756.353i	−2.10279	−	1.21405i
$624$	−89.5143	+	335.331i	−0.143452	+	0.537390i
$625$	285.156	+	493.904i	0.456249	+	0.790247i
$626$	−161.972	−	18.9288i	−0.258742	−	0.0302376i
$627$	95.3502	−	145.246i	0.152074	−	0.231653i
$628$	1044.32	−	644.201i	1.66293	−	1.02580i
$629$	−401.078	−	401.078i	−0.637644	−	0.637644i
$630$	−142.393	−	76.4568i	−0.226021	−	0.121360i
$631$	−660.355			−1.04652			−0.523261	−	0.852173i	$-0.675285\pi$
$631$	−660.355			−1.04652			−0.523261	+	0.852173i	$0.675285\pi$
$632$	420.634	−	352.994i	0.665561	−	0.558536i
$633$	−94.0164	+	284.549i	−0.148525	+	0.449524i
$634$	−287.803	−	363.972i	−0.453948	−	0.574089i
$635$	−79.3808	−	21.2700i	−0.125009	−	0.0334961i
$636$	−1176.98	−	33.1844i	−1.85059	−	0.0521767i
$637$	113.184	+	422.409i	0.177683	+	0.663123i
$638$	−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	$0.168846\pi$
$642$	55.3112	−	118.889i	0.0861545	−	0.185186i
$643$	121.236	−	452.459i	0.188547	−	0.703668i	−0.805296	−	0.592873i	$-0.797994\pi$
$643$	121.236	−	452.459i	0.188547	−	0.703668i	0.993843	−	0.110795i	$-0.0353397\pi$
$644$	487.713	−	516.985i	0.757319	−	0.802771i
$645$	−119.267	−	6.84312i	−0.184911	−	0.0106095i
$646$	−160.998	−	63.9569i	−0.249223	−	0.0990046i
$647$	−651.741			−1.00733			−0.503664	−	0.863900i	$-0.668015\pi$
$647$	−651.741			−1.00733			−0.503664	+	0.863900i	$0.668015\pi$
$648$	−354.178	+	542.644i	−0.546570	+	0.837413i
$649$			66.2351i			0.102057i
$650$	326.097	+	129.543i	0.501687	+	0.199297i
$651$	13.8558	−	241.490i	0.0212839	−	0.370953i
$652$	986.457	−	28.7400i	1.51297	−	0.0440798i
$653$	553.971	+	148.436i	0.848347	+	0.227314i	0.656702	−	0.754150i	$-0.271951\pi$
$653$	553.971	+	148.436i	0.848347	+	0.227314i	0.191645	+	0.981464i	$0.438618\pi$
$654$	301.363	−	647.768i	0.460800	−	0.990471i
$655$	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
$659$	−682.574	+	182.895i	−1.03577	+	0.277534i	−0.736360	−	0.676589i	$-0.763457\pi$
$659$	−682.574	+	182.895i	−1.03577	+	0.277534i	−0.299412	+	0.954124i	$0.596791\pi$
$660$	54.5569	−	51.5649i	0.0826620	−	0.0781286i
$661$	81.1067	−	302.694i	0.122703	−	0.457934i	−0.877044	−	0.480409i	$-0.840488\pi$
$661$	81.1067	−	302.694i	0.122703	−	0.457934i	0.999747	+	0.0224754i	$0.00715474\pi$
$662$	573.736	+	725.579i	0.866670	+	1.09604i
$663$	−224.563	−	74.1966i	−0.338707	−	0.111910i
$664$	5.04744	−	57.7299i	0.00760157	−	0.0869427i
$665$			71.3346i			0.107270i
$666$	825.035	+	442.996i	1.23879	+	0.665159i
$667$	−105.660	+	105.660i	−0.158411	+	0.158411i
$668$	−836.518	−	198.225i	−1.25227	−	0.296744i
$669$	31.4140	+	20.6225i	0.0469567	+	0.0308258i
$670$	214.205	+	25.0329i	0.319709	+	0.0373626i
$671$	−24.8792	+	14.3640i	−0.0370778	+	0.0214069i
$672$	997.792	+	115.656i	1.48481	+	0.172108i
$673$	−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
$675$	502.939	+	419.799i	0.745095	+	0.621924i
$676$	−447.250	+	133.916i	−0.661612	+	0.198101i
$677$	−963.267	+	258.107i	−1.42285	+	0.381250i	−0.886493	−	0.462743i	$-0.846865\pi$
$677$	−963.267	+	258.107i	−1.42285	+	0.381250i	−0.536354	+	0.843993i	$0.680199\pi$
$678$	−410.581	−	343.901i	−0.605576	−	0.507228i
$679$	−509.077	−	881.747i	−0.749745	−	1.29860i
$680$	−61.3148	−	42.9279i	−0.0901688	−	0.0631293i
$681$	649.927	−	134.785i	0.954372	−	0.197922i
$682$	104.414	+	41.4787i	0.153100	+	0.0608193i
$683$	78.7837	−	78.7837i	0.115350	−	0.115350i	−0.647076	−	0.762426i	$-0.724008\pi$
$683$	78.7837	−	78.7837i	0.115350	−	0.115350i	0.762426	+	0.647076i	$0.224008\pi$
$684$	284.963	+	24.4240i	0.416612	+	0.0357076i
$685$	−41.0362	+	41.0362i	−0.0599069	+	0.0599069i
$686$	220.581	−	95.1544i	0.321547	−	0.138709i
$687$	34.8707	−	105.539i	0.0507580	−	0.153623i
$688$	704.761	−	233.591i	1.02436	−	0.339522i
$689$	354.740	+	614.427i	0.514862	+	0.891766i
$690$	71.5787	−	50.2142i	0.103737	−	0.0727742i
$691$	−808.428	+	216.618i	−1.16994	+	0.313484i	−0.790929	−	0.611908i	$-0.790402\pi$
$691$	−808.428	+	216.618i	−1.16994	+	0.313484i	−0.379010	+	0.925392i	$0.623736\pi$
$692$	607.414	+	327.485i	0.877766	+	0.473245i
$693$	−638.421	−	252.352i	−0.921242	−	0.364144i
$694$	−213.068	+	31.2139i	−0.307014	+	0.0449769i
$695$	77.7168	−	134.610i	0.111823	−	0.193683i
$696$	−208.981	−	30.4147i	−0.300260	−	0.0436993i
$697$	−769.362	+	444.191i	−1.10382	+	0.637290i
$698$	375.480	+	474.854i	0.537938	+	0.680307i
$699$	0.687050	−	11.9745i	0.000982905	−	0.0171309i
$700$	234.154	−	988.140i	0.334506	−	1.41163i
$701$	899.718	−	899.718i	1.28348	−	1.28348i	0.344802	−	0.938676i	$-0.387946\pi$
$701$	899.718	−	899.718i	1.28348	−	1.28348i	0.938676	−	0.344802i	$-0.112054\pi$
$702$	390.321	+	10.3371i	0.556012	+	0.0147252i
$703$		−	413.318i		−	0.587935i
$704$	−197.127	+	422.864i	−0.280009	+	0.600659i
$705$	46.7314	−	41.6599i	0.0662857	−	0.0590920i
$706$	44.9129	−	384.317i	0.0636160	−	0.544359i
$707$	−415.156	+	1549.38i	−0.587208	+	2.19149i
$708$	−95.9219	+	51.8323i	−0.135483	+	0.0732095i
$709$	−547.046	+	146.580i	−0.771574	+	0.206743i	−0.623067	−	0.782169i	$-0.714113\pi$
$709$	−547.046	+	146.580i	−0.771574	+	0.206743i	−0.148507	+	0.988911i	$0.547447\pi$
$710$	−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
$714$	−118.261	+	674.173i	−0.165632	+	0.944220i
$715$	−43.6923	−	11.7073i	−0.0611081	−	0.0163739i
$716$	−400.735	+	11.6753i	−0.559686	+	0.0163062i
$717$	−44.2849	+	22.2887i	−0.0617642	+	0.0310860i
$718$	−79.3797	+	34.2428i	−0.110557	+	0.0476920i
$719$		−	922.935i		−	1.28364i	−0.766856	−	0.641819i	$-0.778180\pi$
$719$		−	922.935i		−	1.28364i	0.766856	−	0.641819i	$-0.221820\pi$
$720$	117.370	+	38.6574i	0.163014	+	0.0536909i
$721$	1849.28			2.56488
$722$	235.981	+	547.037i	0.326843	+	0.757668i
$723$	77.9567	−	118.751i	0.107824	−	0.164247i
$724$	24.5374	−	0.714887i	0.0338914	−	0.000987413i
$725$	−55.2584	+	206.227i	−0.0762185	+	0.284451i
$726$	−261.431	+	312.121i	−0.360098	+	0.429919i
$727$	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
$731$	130.944	+	488.690i	0.179130	+	0.668523i
$732$	−40.2713	−	24.7896i	−0.0550155	−	0.0338656i
$733$	327.066	+	87.6370i	0.446201	+	0.119559i	0.474921	−	0.880028i	$-0.342476\pi$
$733$	327.066	+	87.6370i	0.446201	+	0.119559i	−0.0287201	+	0.999587i	$0.509143\pi$
$734$	−721.244	−	84.2877i	−0.982622	−	0.114833i
$735$	152.456	−	31.6171i	0.207424	−	0.0430165i
$736$	−298.566	+	454.041i	−0.405661	+	0.616903i
$737$	916.028			1.24291
$738$	1004.64	−	1068.59i	1.36130	−	1.44795i
$739$	314.546	+	314.546i	0.425638	+	0.425638i	0.887139	−	0.461502i	$-0.152689\pi$
$739$	314.546	+	314.546i	0.425638	+	0.425638i	−0.461502	+	0.887139i	$0.652689\pi$
$740$	41.1765	−	173.766i	0.0556439	−	0.234819i
$741$	−77.4773	−	153.938i	−0.104558	−	0.207744i
$742$	1610.63	−	1273.57i	2.17066	−	1.71640i
$743$	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	$0.779753\pi$
$744$	21.6396	+	183.672i	0.0290854	+	0.246871i
$745$	−89.0027	−	51.3857i	−0.119467	−	0.0689741i
$746$	−76.5038	−	522.219i	−0.102552	−	0.700025i
$747$	−64.4892	+	9.56016i	−0.0863309	+	0.0127981i
$748$	−279.838	−	150.874i	−0.374116	−	0.201703i
$749$	59.1834	+	220.875i	0.0790166	+	0.294894i
$750$	106.994	−	229.980i	0.142659	−	0.306640i
$751$	−231.042	+	133.392i	−0.307645	+	0.177619i	−0.645872	−	0.763445i	$-0.723506\pi$
$751$	−231.042	+	133.392i	−0.307645	+	0.177619i	0.338227	+	0.941065i	$0.390173\pi$
$752$	−174.596	+	347.715i	−0.232176	+	0.462387i
$753$	458.447	−	408.694i	0.608827	−	0.542754i
$754$	50.4033	+	116.842i	0.0668478	+	0.154963i
$755$	75.3334	+	75.3334i	0.0997793	+	0.0997793i
$756$	−134.140	−	1122.04i	−0.177434	−	1.48418i
$757$	−680.254	−	680.254i	−0.898619	−	0.898619i	0.0966952	−	0.995314i	$-0.469173\pi$
$757$	−680.254	−	680.254i	−0.898619	−	0.898619i	−0.995314	+	0.0966952i	$0.969173\pi$
$758$	33.2662	−	83.7407i	0.0438869	−	0.110476i
$759$	277.218	−	247.133i	0.365242	−	0.325603i
$760$	−9.47398	−	53.7119i	−0.0124658	−	0.0706736i
$761$	−563.633	+	325.414i	−0.740648	+	0.427613i	−0.822305	−	0.569047i	$-0.807312\pi$
$761$	−563.633	+	325.414i	−0.740648	+	0.427613i	0.0816571	+	0.996660i	$0.473979\pi$
$762$	−197.001	−	539.771i	−0.258531	−	0.708362i
$763$	322.461	+	1203.44i	0.422622	+	1.57725i
$764$	881.749	−	264.014i	1.15412	−	0.345568i
$765$	−30.9536	+	78.3090i	−0.0404622	+	0.102365i
$766$	−269.746	+	362.345i	−0.352148	+	0.473036i
$767$	56.8953	+	32.8485i	0.0741791	+	0.0428273i
$768$	−766.655	+	45.4329i	−0.998249	+	0.0591574i
$769$	−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	$-0.385335\pi$
$770$	−15.1955	+	130.027i	−0.0197344	+	0.168866i
$771$	337.422	+	670.417i	0.437642	+	0.869542i
$772$	−980.339	−	232.306i	−1.26987	−	0.300914i
$773$	476.130	+	476.130i	0.615951	+	0.615951i	0.944490	−	0.328539i	$-0.106556\pi$
$773$	476.130	+	476.130i	0.615951	+	0.615951i	−0.328539	+	0.944490i	$0.606556\pi$
$774$	−439.740	−	710.147i	−0.568139	−	0.917502i
$775$	186.974			0.241256
$776$	500.418	+	596.307i	0.644869	+	0.768437i
$777$	−1599.02	+	331.612i	−2.05794	+	0.426785i
$778$	−744.626	+	588.797i	−0.957103	+	0.756808i
$779$	−625.294	−	167.547i	−0.802688	−	0.215080i
$780$	−17.2369	−	72.4369i	−0.0220986	−	0.0928679i
$781$	−168.034	−	627.111i	−0.215152	−	0.802959i
$782$	−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
$786$	69.4176	+	785.458i	0.0883176	+	0.999311i
$787$	347.832	−	1298.13i	0.441972	−	1.64946i	−0.281837	−	0.959462i	$-0.590944\pi$
$787$	347.832	−	1298.13i	0.441972	−	1.64946i	0.723809	−	0.690000i	$-0.242390\pi$
$788$	−733.209	+	21.3617i	−0.930468	+	0.0271088i
$789$	146.665	−	223.413i	0.185887	−	0.283160i
$790$	−43.4929	+	109.484i	−0.0550543	+	0.138588i
$791$	933.982			1.18076
$792$	514.218	+	105.221i	0.649266	+	0.132855i
$793$			28.4947i			0.0359328i
$794$	127.629	−	321.278i	0.160741	−	0.404632i
$795$	225.637	−	113.563i	0.283820	−	0.142847i
$796$	−563.498	+	597.318i	−0.707912	+	0.750399i
$797$	−683.590	−	183.168i	−0.857704	−	0.229821i	−0.196941	−	0.980415i	$-0.563101\pi$
$797$	−683.590	−	183.168i	−0.857704	−	0.229821i	−0.660764	+	0.750594i	$0.729767\pi$
$798$	−408.309	+	286.438i	−0.511665	+	0.358945i
$799$	−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
$803$	583.307	−	156.297i	0.726409	−	0.194641i
$804$	716.839	+	1326.60i	0.891591	+	1.65000i
$805$	−39.4639	+	147.281i	−0.0490235	+	0.182958i
$806$	87.4128	−	69.1197i	0.108453	−	0.0857565i
$807$	−435.828	+	388.530i	−0.540060	+	0.481449i
$808$	106.821	−	1221.76i	0.132204	−	1.51208i
$809$			1299.74i			1.60661i	0.595571	+	0.803303i	$0.296926\pi$
$809$			1299.74i			1.60661i	−0.595571	+	0.803303i	$0.703074\pi$
$810$	11.6349	−	138.531i	0.0143641	−	0.171026i
$811$	305.471	−	305.471i	0.376659	−	0.376659i	−0.493236	−	0.869895i	$-0.664186\pi$
$811$	305.471	−	305.471i	0.376659	−	0.376659i	0.869895	+	0.493236i	$0.164186\pi$
$812$	313.439	−	193.348i	0.386008	−	0.238114i
$813$	57.4283	−	1000.91i	0.0706375	−	1.23113i
$814$	88.0436	−	753.383i	0.108162	−	0.925532i
$815$	−183.355	+	105.860i	−0.224975	+	0.129889i
$816$	−0.491544	−	523.330i	−0.000602383	−	0.641336i
$817$	−184.332	+	319.272i	−0.225620	+	0.390786i
$818$	645.166	−	866.642i	0.788711	−	1.05946i
$819$	−533.385	+	423.247i	−0.651264	+	0.516785i
$820$	−246.193	−	132.734i	−0.300235	−	0.161871i
$821$	819.783	−	219.660i	0.998518	−	0.267552i	0.277693	−	0.960670i	$-0.410430\pi$
$821$	819.783	−	219.660i	0.998518	−	0.267552i	0.720824	+	0.693118i	$0.243763\pi$
$822$	−399.663	−	70.1076i	−0.486208	−	0.0852890i
$823$	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	$0.597899\pi$
$824$	−1392.43	+	245.603i	−1.68984	+	0.298062i
$825$	166.474	−	503.848i	0.201787	−	0.610725i
$826$	70.1958	−	176.703i	0.0849828	−	0.213926i
$827$	−980.630	+	980.630i	−1.18577	+	1.18577i	−0.207542	+	0.978226i	$0.566546\pi$
$827$	−980.630	+	980.630i	−1.18577	+	1.18577i	−0.978226	+	0.207542i	$0.933454\pi$
$828$	574.837	+	208.075i	0.694247	+	0.251298i
$829$	11.8666	−	11.8666i	0.0143143	−	0.0143143i	−0.699913	−	0.714228i	$-0.746778\pi$
$829$	11.8666	−	11.8666i	0.0143143	−	0.0143143i	0.714228	+	0.699913i	$0.246778\pi$
$830$	4.92442	+	11.4155i	0.00593304	+	0.0137536i
$831$	−397.469	+	82.4290i	−0.478302	+	0.0991925i
$832$	265.474	+	379.045i	0.319079	+	0.455582i
$833$	−329.696	−	571.051i	−0.395794	−	0.685535i
$834$	1082.55	−	95.6741i	1.29802	−	0.114717i
$835$	178.148	−	47.7346i	0.213351	−	0.0571672i
$836$	−66.4500	−	221.928i	−0.0794857	−	0.265464i
$837$	195.327	−	71.6674i	0.233366	−	0.0856241i
$838$	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	$0.892746\pi$
$840$	−200.196	+	79.7463i	−0.238329	+	0.0949361i
$841$	661.273	−	381.786i	0.786294	−	0.453967i
$842$	397.906	−	314.635i	0.472572	−	0.373676i
$843$	−254.236	−	166.899i	−0.301585	−	0.197982i
$844$	209.778	+	340.074i	0.248552	+	0.402931i
$845$	70.8236	−	70.8236i	0.0838149	−	0.0838149i
$846$	426.101	+	100.202i	0.503665	+	0.118442i
$847$		−	710.008i		−	0.838262i
$848$	−1043.59	+	1172.85i	−1.23065	+	1.38308i
$849$	871.710	+	288.018i	1.02675	+	0.339243i
$850$	−525.502	−	61.4123i	−0.618237	−	0.0722498i
$851$	228.657	−	853.358i	0.268692	−	1.00277i
$852$	776.690	−	734.094i	0.911608	−	0.861612i
$853$	−553.040	+	148.187i	−0.648347	+	0.173724i	−0.567981	−	0.823042i	$-0.692275\pi$
$853$	−553.040	+	148.187i	−0.648347	+	0.173724i	−0.0803654	+	0.996765i	$0.525609\pi$
$854$	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	0.365461	−	0.930826i	$-0.380911\pi$
$857$	−221.044	−	127.620i	−0.257927	−	0.148914i	−0.623389	+	0.781912i	$0.714245\pi$
$858$	−108.432	−	297.098i	−0.126378	−	0.346268i
$859$	73.9507	+	19.8150i	0.0860893	+	0.0230675i	0.301607	−	0.953432i	$-0.402477\pi$
$859$	73.9507	+	19.8150i	0.0860893	+	0.0230675i	−0.215517	+	0.976500i	$0.569144\pi$
$860$	−109.304	+	115.864i	−0.127097	+	0.134725i
$861$	−146.512	+	2553.52i	−0.170165	+	2.96577i
$862$	−151.916	−	352.163i	−0.176237	−	0.408541i
$863$		−	1139.78i		−	1.32072i	−0.750949	−	0.660360i	$-0.770404\pi$
$863$		−	1139.78i		−	1.32072i	0.750949	−	0.660360i	$-0.229596\pi$
$864$	250.021	+	827.034i	0.289376	+	0.957216i
$865$	−148.045			−0.171150
$866$	1232.90	−	531.848i	1.42367	−	0.614143i
$867$	−509.555	−	29.2363i	−0.587722	−	0.0337213i
$868$	−234.598	−	221.315i	−0.270275	−	0.254972i
$869$	−129.509	+	483.334i	−0.149032	+	0.556195i
$870$	42.5602	−	15.5332i	0.0489197	−	0.0178543i
$871$	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
$875$	114.485	+	427.263i	0.130840	+	0.488301i
$876$	682.817	+	722.437i	0.779471	+	0.824700i
$877$	−547.754	−	146.770i	−0.624577	−	0.167355i	−0.0673695	−	0.997728i	$-0.521461\pi$
$877$	−547.754	−	146.770i	−0.624577	−	0.167355i	−0.557208	+	0.830373i	$0.688127\pi$
$878$	−147.032	+	1258.15i	−0.167463	+	1.43297i
$879$	144.978	−	438.789i	0.164935	−	0.499191i
$880$	−5.82735	−	99.9226i	−0.00662199	−	0.113548i
$881$	−80.3510			−0.0912043			−0.0456022	−	0.998960i	$-0.514521\pi$
$881$	−80.3510			−0.0912043			−0.0456022	+	0.998960i	$0.514521\pi$
$882$	793.148	+	745.682i	0.899261	+	0.845444i
$883$	−249.733	−	249.733i	−0.282823	−	0.282823i	0.551411	−	0.834234i	$-0.314090\pi$
$883$	−249.733	−	249.733i	−0.282823	−	0.282823i	−0.834234	+	0.551411i	$0.814090\pi$
$884$	−268.382	+	165.554i	−0.303600	+	0.187279i
$885$	12.8366	−	19.5539i	0.0145046	−	0.0220948i
$886$	742.487	+	938.992i	0.838022	+	1.05981i
$887$	−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	$0.834492\pi$
$888$	1159.95	−	462.056i	1.30625	−	0.520333i
$889$	867.781	+	501.013i	0.976131	+	0.563570i
$890$	−245.508	+	35.9663i	−0.275852	+	0.0404116i
$891$	−19.2142	−	590.170i	−0.0215648	−	0.662368i
$892$	47.9989	−	14.3719i	0.0538105	−	0.0161120i
$893$	−50.0033	−	186.615i	−0.0559948	−	0.208975i
$894$	−63.2589	−	715.773i	−0.0707594	−	0.800641i
$895$	74.4855	−	43.0042i	0.0832240	−	0.0480494i
$896$	974.048	−	919.209i	1.08711	−	1.02590i
$897$	−74.8018	−	360.691i	−0.0833910	−	0.402108i
$898$	−690.383	+	297.818i	−0.768801	+	0.331646i
$899$	47.9465	+	47.9465i	0.0533332	+	0.0533332i
$900$	859.950	−	153.199i	0.955500	−	0.170221i
$901$	−756.448	−	756.448i	−0.839565	−	0.839565i
$902$	−1104.08	−	438.597i	−1.22403	−	0.486250i
$903$	1383.07	+	456.974i	1.53164	+	0.506062i
$904$	−703.249	+	124.043i	−0.777930	+	0.137215i
$905$	−4.56081	+	2.63319i	−0.00503957	+	0.00290960i
$906$	−128.702	+	733.692i	−0.142055	+	0.809815i
$907$	281.964	+	1052.31i	0.310876	+	1.16020i	0.927768	+	0.373157i	$0.121725\pi$
$907$	281.964	+	1052.31i	0.310876	+	1.16020i	−0.616892	+	0.787048i	$0.711609\pi$
$908$	419.996	−	779.001i	0.462551	−	0.857931i
$909$	−1364.80	+	202.325i	−1.50144	+	0.222579i
$910$	104.156	+	77.5380i	0.114457	+	0.0852066i
$911$	1285.69	+	742.296i	1.41130	+	0.814815i	0.995511	−	0.0946462i	$-0.0301720\pi$
$911$	1285.69	+	742.296i	1.41130	+	0.814815i	0.415789	+	0.909461i	$0.363505\pi$
$912$	269.397	−	269.904i	0.295391	−	0.295947i
$913$	26.4032	+	45.7317i	0.0289192	+	0.0500895i
$914$	−342.328	−	40.0059i	−0.374539	−	0.0437702i
$915$	10.1286	+	0.581143i	0.0110695	+	0.000635129i
$916$	−77.8069	−	126.134i	−0.0849420	−	0.137700i
$917$	−972.329	−	972.329i	−1.06034	−	1.06034i
$918$	−572.520	+	137.270i	−0.623660	+	0.149531i
$919$	810.953			0.882430			0.441215	−	0.897401i	$-0.354548\pi$
$919$	810.953			0.882430			0.441215	+	0.897401i	$0.354548\pi$
$920$	10.1541	−	116.138i	0.0110371	−	0.126237i
$921$	−279.090	−	313.065i	−0.303029	−	0.339919i
$922$	143.675	+	181.700i	0.155830	+	0.197071i
$923$	−622.017	−	166.669i	−0.673908	−	0.180573i
$924$	−805.268	+	435.135i	−0.871503	+	0.470925i
$925$	−326.709	−	1219.29i	−0.353199	−	1.31816i
$926$	−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	$0.292670\pi$
$930$	−22.7863	−	32.4811i	−0.0245014	−	0.0349259i
$931$	124.360	−	464.118i	0.133577	−	0.498515i
$932$	−11.6327	−	10.9741i	−0.0124815	−	0.0117748i
$933$	697.361	+	1385.57i	0.747439	+	1.48507i
$934$	604.835	+	240.273i	0.647575	+	0.257251i
$935$	68.2049			0.0729464
$936$	345.405	−	389.526i	0.369022	−	0.416160i
$937$		−	1562.33i		−	1.66737i	−0.552238	−	0.833687i	$-0.686226\pi$
$937$		−	1562.33i		−	1.66737i	0.552238	−	0.833687i	$-0.313774\pi$
$938$	−2443.80	−	970.805i	−2.60533	−	1.03497i
$939$	204.486	+	134.240i	0.217770	+	0.142960i
$940$	−2.43092	−	83.4377i	−0.00258609	−	0.0887635i
$941$	1211.25	+	324.553i	1.28719	+	0.344902i	0.836593	−	0.547825i	$-0.184544\pi$
$941$	1211.25	+	324.553i	1.28719	+	0.344902i	0.450599	+	0.892727i	$0.351211\pi$
$942$	−1833.40	+	162.033i	−1.94628	+	0.172009i
$943$	−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
$947$	1680.70	−	450.341i	1.77476	−	0.475545i	0.785147	−	0.619309i	$-0.212587\pi$
$947$	1680.70	−	450.341i	1.77476	−	0.475545i	0.989612	+	0.143764i	$0.0459207\pi$
$948$	−801.313	+	190.678i	−0.845267	+	0.201137i
$949$	155.027	−	578.569i	0.163358	−	0.609662i
$950$	−239.126	−	302.413i	−0.251712	−	0.318329i
$951$	141.336	+	681.516i	0.148618	+	0.716631i
$952$	586.662	+	699.077i	0.616241	+	0.734324i
$953$			113.221i			0.118805i	0.998234	+	0.0594025i	$0.0189195\pi$
$953$			113.221i			0.118805i	−0.998234	+	0.0594025i	$0.981080\pi$
$954$	1556.05	+	835.507i	1.63108	+	0.875793i
$955$	−139.628	+	139.628i	−0.146207	+	0.146207i
$956$	−15.2421	+	64.3222i	−0.0159436	+	0.0672826i
$957$	171.894	−	86.5145i	0.179617	−	0.0904018i
$958$	359.143	+	41.9710i	0.374888	+	0.0438110i
$959$	612.803	−	353.802i	0.639003	−	0.368928i
$960$	140.148	−	86.6337i	0.145988	−	0.0902435i
$961$	−450.809	+	780.825i	−0.469104	+	0.812513i
$962$	−603.486	−	449.261i	−0.627324	−	0.467007i
$963$	−154.075	+	122.260i	−0.159994	+	0.126957i
$964$	−54.3284	−	181.445i	−0.0563572	−	0.188221i
$965$	208.777	−	55.9416i	0.216349	−	0.0579706i
$966$	−1001.48	+	365.510i	−1.03673	+	0.378375i
$967$	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	$0.547746\pi$
$968$	94.2964	+	534.606i	0.0974136	+	0.552278i
$969$	172.918	+	193.969i	0.178450	+	0.200174i
$970$	−155.209	−	61.6572i	−0.160009	−	0.0635641i
$971$	559.274	−	559.274i	0.575978	−	0.575978i	−0.357815	−	0.933793i	$-0.616478\pi$
$971$	559.274	−	559.274i	0.575978	−	0.575978i	0.933793	+	0.357815i	$0.116478\pi$
$972$	839.650	−	489.664i	0.863838	−	0.503770i
$973$	−1340.10	+	1340.10i	−1.37729	+	1.37729i
$974$	289.042	−	124.687i	0.296757	−	0.128015i
$975$	−350.240	−	392.878i	−0.359221	−	0.402951i
$976$	−59.8509	+	19.8374i	−0.0613226	+	0.0203252i
$977$	−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	$0.981180\pi$
$978$	−1342.17	−	624.422i	−1.37236	−	0.638469i
$979$	−1018.01	+	272.776i	−1.03985	+	0.278627i
$980$	98.5204	−	182.734i	0.100531	−	0.186463i
$981$	−839.476	+	666.133i	−0.855735	+	0.679034i
$982$	−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	$-0.107271\pi$
$984$	−228.817	−	1942.15i	−0.232538	−	1.97373i
$985$	136.283	−	78.6830i	0.138358	−	0.0798812i
$986$	−119.009	−	150.505i	−0.120698	−	0.152642i
$987$	−681.846	+	343.174i	−0.690827	+	0.347694i
$988$	−223.590	−	52.9829i	−0.226305	−	0.0536264i
$989$	−557.209	+	557.209i	−0.563407	+	0.563407i
$990$	−107.817	+	32.4836i	−0.108906	+	0.0328117i
$991$			690.368i			0.696637i	0.937376	+	0.348319i	$0.113247\pi$
$991$			690.368i			0.696637i	−0.937376	+	0.348319i	$0.886753\pi$
$992$	206.035	+	135.484i	0.207697	+	0.136577i
$993$	−281.753	−	1358.60i	−0.283739	−	1.36818i
$994$	−216.327	+	1851.10i	−0.217633	+	1.86227i
$995$	45.5961	−	170.167i	0.0458252	−	0.171022i
$996$	−45.5670	+	74.0247i	−0.0457500	+	0.0743219i
$997$	845.564	−	226.568i	0.848108	−	0.227250i	0.191510	−	0.981491i	$-0.438661\pi$
$997$	845.564	−	226.568i	0.848108	−	0.227250i	0.656598	+	0.754241i	$0.271995\pi$
$998$	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.43.7	✓	184
3.2	odd	2		432.3.w.a.235.40		184
9.4	even	3	inner	144.3.v.a.139.25	yes	184
9.5	odd	6		432.3.w.a.91.22		184
16.3	odd	4	inner	144.3.v.a.115.25	yes	184
48.35	even	4		432.3.w.a.19.22		184
144.67	odd	12	inner	144.3.v.a.67.7	yes	184
144.131	even	12		432.3.w.a.307.40		184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.3.v.a.43.7	✓	184	1.1	even	1	trivial
144.3.v.a.67.7	yes	184	144.67	odd	12	inner
144.3.v.a.115.25	yes	184	16.3	odd	4	inner
144.3.v.a.139.25	yes	184	9.4	even	3	inner
432.3.w.a.19.22		184	48.35	even	4
432.3.w.a.91.22		184	9.5	odd	6
432.3.w.a.235.40		184	3.2	odd	2
432.3.w.a.307.40		184	144.131	even	12

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)

\(f(q)\)	\(=\)	\(q+(-1.83642 + 0.792194i) q^{2} +(2.99507 + 0.171846i) q^{3} +(2.74486 - 2.90960i) q^{4} +(-0.222103 + 0.828901i) q^{5} +(-5.63634 + 2.05710i) q^{6} +(5.23163 - 9.06144i) q^{7} +(-2.73574 + 7.51769i) q^{8} +(8.94094 + 1.02938i) q^{9} +O(q^{10})\)	\(q+(-1.83642 + 0.792194i) q^{2} +(2.99507 + 0.171846i) q^{3} +(2.74486 - 2.90960i) q^{4} +(-0.222103 + 0.828901i) q^{5} +(-5.63634 + 2.05710i) 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} +(-1.88677 - 7.04151i) q^{11} +(8.72105 - 8.24277i) q^{12} +(-6.98432 - 1.87144i) q^{13} +(-2.42903 + 20.7851i) q^{14} +(-0.807660 + 2.44445i) q^{15} +(-0.931516 - 15.9729i) q^{16} +10.9027 q^{17} +(-17.2348 + 5.19258i) q^{18} +(5.61772 + 5.61772i) q^{19} +(1.80213 + 2.92145i) q^{20} +(17.2263 - 26.2407i) q^{21} +(9.04313 + 11.4365i) q^{22} +(8.49079 + 14.7065i) q^{23} +(-9.48563 + 22.0459i) q^{24} +(21.0129 + 12.1318i) q^{25} +(14.3087 - 2.09618i) q^{26} +(26.6019 + 4.61955i) q^{27} +(-12.0051 - 40.0943i) q^{28} +(2.27742 + 8.49945i) q^{29} +(-0.453281 - 5.12886i) q^{30} +(6.67353 - 3.85297i) q^{31} +(14.3643 + 28.5949i) q^{32} +(-4.44095 - 21.4141i) q^{33} +(-20.0219 + 8.63706i) q^{34} +(6.34908 + 6.34908i) q^{35} +(27.5367 - 23.1890i) q^{36} +(-36.7870 - 36.7870i) q^{37} +(-14.7668 - 5.86615i) q^{38} +(-20.5969 - 6.80534i) q^{39} +(-5.62381 - 3.93736i) q^{40} +(-70.5661 + 40.7414i) q^{41} +(-10.8470 + 61.8354i) q^{42} +(12.0102 + 44.8228i) q^{43} +(-25.6669 - 13.8382i) q^{44} +(-2.83907 + 7.18252i) q^{45} +(-27.2430 - 20.2809i) q^{46} +(-21.0600 - 12.1590i) q^{47} +(-0.0450846 - 48.0000i) q^{48} +(-30.2398 - 52.3770i) q^{49} +(-48.1992 - 5.63276i) q^{50} +(32.6544 + 1.87359i) q^{51} +(-24.6161 + 15.1847i) q^{52} +(-69.3816 - 69.3816i) q^{53} +(-52.5117 + 12.5904i) q^{54} +6.25577 q^{55} +(53.8088 + 64.1195i) q^{56} +(15.8601 + 17.7909i) q^{57} +(-10.9155 - 13.8044i) q^{58} +(-8.77626 - 2.35159i) q^{59} +(4.89546 + 9.05964i) q^{60} +(-1.01995 - 3.80652i) 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} +(25.1195 + 35.8071i) q^{66} +(-32.5224 + 121.375i) q^{67} +(29.9264 - 31.7225i) q^{68} +(22.9033 + 45.5061i) q^{69} +(-16.6893 - 6.62986i) q^{70} +89.0591 q^{71} +(-32.1987 + 64.3991i) q^{72} +82.8383i q^{73} +(96.6988 + 38.4139i) q^{74} +(60.8504 + 39.9466i) q^{75} +(31.7651 - 0.925464i) q^{76} +(-73.6771 - 19.7417i) q^{77} +(43.2157 - 3.81934i) 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} +(-6.99695 + 1.87483i) q^{83} +(-29.0661 - 122.148i) q^{84} +(-2.42153 + 9.03727i) q^{85} +(-57.5642 - 72.7990i) q^{86} +(5.36044 + 25.8478i) q^{87} +(58.0976 + 5.07959i) q^{88} -144.573i q^{89} +(-0.476234 - 15.4392i) q^{90} +(-53.4973 + 53.4973i) q^{91} +(66.0959 + 15.6624i) q^{92} +(20.6498 - 10.3931i) q^{93} +(48.3072 + 5.64539i) q^{94} +(-5.90424 + 3.40882i) q^{95} +(38.1081 + 88.1123i) q^{96} +(48.6538 - 84.2708i) q^{97} +(97.0257 + 72.2301i) q^{98} +(-9.62105 - 64.8999i) 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

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