LMFDB - Embedded newform 805.2.u.d.36.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [805,2,Mod(36,805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(805, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 14]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("805.36");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 805 = 5 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	805.u (of order $11$, degree $10$, 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:	$6.42795736271$
Analytic rank:	$0$
Dimension:	$130$
Relative dimension:	$13$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			36.13
Character	$\chi$	$=$	805.36
Dual form			805.2.u.d.246.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.80777 + 2.08628i) q^{2} +(1.16685 + 0.749889i) q^{3} +(-0.799893 + 5.56338i) q^{4} +(0.415415 - 0.909632i) q^{5} +(0.544920 + 3.79000i) q^{6} +(0.959493 + 0.281733i) q^{7} +(-8.40814 + 5.40358i) q^{8} +(-0.447039 - 0.978878i) q^{9} +O(q^{10})$	\(q+(1.80777 + 2.08628i) q^{2} +(1.16685 + 0.749889i) q^{3} +(-0.799893 + 5.56338i) q^{4} +(0.415415 - 0.909632i) q^{5} +(0.544920 + 3.79000i) q^{6} +(0.959493 + 0.281733i) q^{7} +(-8.40814 + 5.40358i) q^{8} +(-0.447039 - 0.978878i) q^{9} +(2.64872 - 0.777734i) q^{10} +(-2.75025 + 3.17396i) q^{11} +(-5.10527 + 5.89180i) q^{12} +(5.34656 - 1.56989i) q^{13} +(1.14677 + 2.51108i) q^{14} +(1.16685 - 0.749889i) q^{15} +(-15.6875 - 4.60627i) q^{16} +(0.0345049 + 0.239987i) q^{17} +(1.23407 - 2.70223i) q^{18} +(-0.0204131 + 0.141976i) q^{19} +(4.72834 + 3.03872i) q^{20} +(0.908317 + 1.04825i) q^{21} -11.5936 q^{22} +(2.60112 + 4.02917i) q^{23} -13.8631 q^{24} +(-0.654861 - 0.755750i) q^{25} +(12.9406 + 8.31640i) q^{26} +(0.804611 - 5.59619i) q^{27} +(-2.33488 + 5.11266i) q^{28} +(-1.28497 - 8.93715i) q^{29} +(3.67387 + 1.07875i) q^{30} +(-5.97932 + 3.84267i) q^{31} +(-10.4455 - 22.8725i) q^{32} +(-5.58925 + 1.64115i) q^{33} +(-0.438302 + 0.505827i) q^{34} +(0.654861 - 0.755750i) q^{35} +(5.80345 - 1.70405i) q^{36} +(-1.16649 - 2.55425i) q^{37} +(-0.333104 + 0.214073i) q^{38} +(7.41587 + 2.17750i) q^{39} +(1.42240 + 9.89304i) q^{40} +(3.14172 - 6.87940i) q^{41} +(-0.544920 + 3.79000i) q^{42} +(5.98239 + 3.84465i) q^{43} +(-15.4580 - 17.8395i) q^{44} -1.07613 q^{45} +(-3.70374 + 12.7105i) q^{46} +11.3201 q^{47} +(-14.8508 - 17.1387i) q^{48} +(0.841254 + 0.540641i) q^{49} +(0.392866 - 2.73244i) q^{50} +(-0.139701 + 0.305903i) q^{51} +(4.45722 + 31.0006i) q^{52} +(11.2148 + 3.29297i) q^{53} +(13.1298 - 8.43799i) q^{54} +(1.74464 + 3.82022i) q^{55} +(-9.58991 + 2.81585i) q^{56} +(-0.130286 + 0.150358i) q^{57} +(16.3224 - 18.8371i) q^{58} +(1.97910 - 0.581117i) q^{59} +(3.23856 + 7.09146i) q^{60} +(-9.91541 + 6.37225i) q^{61} +(-18.8261 - 5.52784i) q^{62} +(-0.153149 - 1.06517i) q^{63} +(15.2513 - 33.3958i) q^{64} +(0.793017 - 5.51555i) q^{65} +(-13.5280 - 8.69389i) q^{66} +(2.42115 + 2.79416i) q^{67} -1.36274 q^{68} +(0.0136868 + 6.65199i) q^{69} +2.76054 q^{70} +(-4.28023 - 4.93965i) q^{71} +(9.04821 + 5.81493i) q^{72} +(1.28807 - 8.95872i) q^{73} +(3.22013 - 7.05111i) q^{74} +(-0.197396 - 1.37292i) q^{75} +(-0.773539 - 0.227132i) q^{76} +(-3.53305 + 2.27055i) q^{77} +(8.86333 + 19.4080i) q^{78} +(-8.40121 + 2.46682i) q^{79} +(-10.7068 + 12.3564i) q^{80} +(3.02125 - 3.48671i) q^{81} +(20.0318 - 5.88188i) q^{82} +(-4.14920 - 9.08547i) q^{83} +(-6.55838 + 4.21482i) q^{84} +(0.232633 + 0.0683073i) q^{85} +(2.79378 + 19.4312i) q^{86} +(5.20251 - 11.3919i) q^{87} +(5.97374 - 41.5483i) q^{88} +(0.526142 + 0.338131i) q^{89} +(-1.94539 - 2.24510i) q^{90} +5.57227 q^{91} +(-24.4964 + 11.2481i) q^{92} -9.85855 q^{93} +(20.4642 + 23.6169i) q^{94} +(0.120666 + 0.0775475i) q^{95} +(4.96348 - 34.5217i) q^{96} +(-3.10211 + 6.79267i) q^{97} +(0.392866 + 2.73244i) q^{98} +(4.33639 + 1.27328i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 130 q + 2 q^{2} + 2 q^{3} - 16 q^{4} - 13 q^{5} + 5 q^{6} + 13 q^{7} - 7 q^{8} - 39 q^{9}+O(q^{10}) $ 130 * q + 2 * q^2 + 2 * q^3 - 16 * q^4 - 13 * q^5 + 5 * q^6 + 13 * q^7 - 7 * q^8 - 39 * q^9	\( 130 q + 2 q^{2} + 2 q^{3} - 16 q^{4} - 13 q^{5} + 5 q^{6} + 13 q^{7} - 7 q^{8} - 39 q^{9} + 2 q^{10} + 2 q^{11} - 5 q^{12} + 13 q^{13} - 2 q^{14} + 2 q^{15} - 6 q^{16} - 51 q^{17} + q^{18} - 9 q^{19} - 16 q^{20} - 2 q^{21} + 34 q^{22} - 10 q^{23} - 76 q^{24} - 13 q^{25} - 31 q^{26} + 14 q^{27} + 27 q^{28} + 3 q^{29} + 5 q^{30} + 6 q^{31} + 22 q^{32} - 58 q^{33} + q^{34} + 13 q^{35} + 193 q^{36} - 36 q^{37} + 4 q^{38} - 2 q^{39} - 29 q^{40} - 34 q^{41} - 5 q^{42} - 22 q^{43} + 8 q^{44} + 170 q^{45} - 198 q^{46} - 14 q^{47} - 120 q^{48} - 13 q^{49} + 2 q^{50} - 6 q^{51} + 33 q^{52} - 18 q^{53} + 188 q^{54} - 31 q^{55} - 15 q^{56} - 9 q^{57} + 114 q^{58} + 46 q^{59} - 16 q^{60} - 56 q^{61} - 146 q^{62} + 17 q^{63} - 109 q^{64} + 2 q^{65} - 14 q^{66} - 10 q^{67} + 86 q^{68} - 6 q^{69} - 2 q^{70} - 25 q^{72} + 64 q^{73} + 79 q^{74} + 2 q^{75} + 32 q^{76} - 13 q^{77} - 64 q^{78} - 118 q^{79} - 17 q^{80} + 23 q^{81} + 129 q^{82} - 117 q^{83} - 72 q^{84} - 7 q^{85} + 74 q^{86} - 51 q^{87} - 40 q^{88} - 35 q^{89} + 100 q^{90} + 42 q^{91} + 76 q^{92} - 90 q^{93} - 7 q^{94} + 2 q^{95} + 393 q^{96} - 4 q^{97} + 2 q^{98} - 40 q^{99}+O(q^{100}) \) 130 * q + 2 * q^2 + 2 * q^3 - 16 * q^4 - 13 * q^5 + 5 * q^6 + 13 * q^7 - 7 * q^8 - 39 * q^9 + 2 * q^10 + 2 * q^11 - 5 * q^12 + 13 * q^13 - 2 * q^14 + 2 * q^15 - 6 * q^16 - 51 * q^17 + q^18 - 9 * q^19 - 16 * q^20 - 2 * q^21 + 34 * q^22 - 10 * q^23 - 76 * q^24 - 13 * q^25 - 31 * q^26 + 14 * q^27 + 27 * q^28 + 3 * q^29 + 5 * q^30 + 6 * q^31 + 22 * q^32 - 58 * q^33 + q^34 + 13 * q^35 + 193 * q^36 - 36 * q^37 + 4 * q^38 - 2 * q^39 - 29 * q^40 - 34 * q^41 - 5 * q^42 - 22 * q^43 + 8 * q^44 + 170 * q^45 - 198 * q^46 - 14 * q^47 - 120 * q^48 - 13 * q^49 + 2 * q^50 - 6 * q^51 + 33 * q^52 - 18 * q^53 + 188 * q^54 - 31 * q^55 - 15 * q^56 - 9 * q^57 + 114 * q^58 + 46 * q^59 - 16 * q^60 - 56 * q^61 - 146 * q^62 + 17 * q^63 - 109 * q^64 + 2 * q^65 - 14 * q^66 - 10 * q^67 + 86 * q^68 - 6 * q^69 - 2 * q^70 - 25 * q^72 + 64 * q^73 + 79 * q^74 + 2 * q^75 + 32 * q^76 - 13 * q^77 - 64 * q^78 - 118 * q^79 - 17 * q^80 + 23 * q^81 + 129 * q^82 - 117 * q^83 - 72 * q^84 - 7 * q^85 + 74 * q^86 - 51 * q^87 - 40 * q^88 - 35 * q^89 + 100 * q^90 + 42 * q^91 + 76 * q^92 - 90 * q^93 - 7 * q^94 + 2 * q^95 + 393 * q^96 - 4 * q^97 + 2 * q^98 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/805\mathbb{Z}\right)^\times$.

$n$	$162$	$281$	$346$
$\chi(n)$	$1$	$e\left(\frac{7}{11}\right)$	$1$

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 $

$2$	1.80777	+	2.08628i	1.27829	+	1.47522i	0.803728	+	0.594997i	$0.202847\pi$
$2$	1.80777	+	2.08628i	1.27829	+	1.47522i	0.474558	+	0.880224i	$0.342608\pi$
$3$	1.16685	+	0.749889i	0.673681	+	0.432949i	0.832251	−	0.554399i	$-0.187052\pi$
$3$	1.16685	+	0.749889i	0.673681	+	0.432949i	−0.158570	+	0.987348i	$0.550688\pi$
$4$	−0.799893	+	5.56338i	−0.399946	+	2.78169i
$5$	0.415415	−	0.909632i	0.185779	−	0.406800i
$5$	0.415415	−	0.909632i	0.185779	−	0.406800i
$6$	0.544920	+	3.79000i	0.222463	+	1.54726i
$7$	0.959493	+	0.281733i	0.362654	+	0.106485i
$7$	0.959493	+	0.281733i	0.362654	+	0.106485i
$8$	−8.40814	+	5.40358i	−2.97273	+	1.91045i
$9$	−0.447039	−	0.978878i	−0.149013	−	0.326293i
$10$	2.64872	−	0.777734i	0.837599	−	0.245941i
$11$	−2.75025	+	3.17396i	−0.829231	+	0.956984i	−0.999597	−	0.0283971i	$-0.990960\pi$
$11$	−2.75025	+	3.17396i	−0.829231	+	0.956984i	0.170366	+	0.985381i	$0.445505\pi$
$12$	−5.10527	+	5.89180i	−1.47376	+	1.70082i
$13$	5.34656	−	1.56989i	1.48287	−	0.435409i	0.562610	−	0.826722i	$-0.309797\pi$
$13$	5.34656	−	1.56989i	1.48287	−	0.435409i	0.920258	+	0.391313i	$0.127979\pi$
$14$	1.14677	+	2.51108i	0.306487	+	0.671113i
$15$	1.16685	−	0.749889i	0.301280	−	0.193621i
$16$	−15.6875	−	4.60627i	−3.92188	−	1.15157i
$17$	0.0345049	+	0.239987i	0.00836866	+	0.0582053i	0.993578	−	0.113151i	$-0.0360943\pi$
$17$	0.0345049	+	0.239987i	0.00836866	+	0.0582053i	−0.985209	+	0.171356i	$0.945185\pi$
$18$	1.23407	−	2.70223i	0.290873	−	0.636923i
$19$	−0.0204131	+	0.141976i	−0.00468309	+	0.0325716i	−0.992029	−	0.126010i	$-0.959783\pi$
$19$	−0.0204131	+	0.141976i	−0.00468309	+	0.0325716i	0.987346	+	0.158581i	$0.0506920\pi$
$20$	4.72834	+	3.03872i	1.05729	+	0.679478i
$21$	0.908317	+	1.04825i	0.198211	+	0.228748i
$22$	−11.5936			−2.47176
$23$	2.60112	+	4.02917i	0.542371	+	0.840139i
$23$	2.60112	+	4.02917i	0.542371	+	0.840139i
$24$	−13.8631			−2.82980
$25$	−0.654861	−	0.755750i	−0.130972	−	0.151150i
$26$	12.9406	+	8.31640i	2.53785	+	1.63098i
$27$	0.804611	−	5.59619i	0.154848	−	1.07699i
$28$	−2.33488	+	5.11266i	−0.441250	+	0.966203i
$29$	−1.28497	−	8.93715i	−0.238613	−	1.65959i	−0.658926	−	0.752208i	$-0.728989\pi$
$29$	−1.28497	−	8.93715i	−0.238613	−	1.65959i	0.420313	−	0.907379i	$-0.361920\pi$
$30$	3.67387	+	1.07875i	0.670755	+	0.196951i
$31$	−5.97932	+	3.84267i	−1.07392	+	0.690164i	−0.953144	−	0.302516i	$-0.902173\pi$
$31$	−5.97932	+	3.84267i	−1.07392	+	0.690164i	−0.120772	+	0.992680i	$0.538537\pi$
$32$	−10.4455	−	22.8725i	−1.84652	−	4.04332i
$33$	−5.58925	+	1.64115i	−0.972963	+	0.285688i
$34$	−0.438302	+	0.505827i	−0.0751681	+	0.0867486i
$35$	0.654861	−	0.755750i	0.110692	−	0.127745i
$36$	5.80345	−	1.70405i	0.967242	−	0.284008i
$37$	−1.16649	−	2.55425i	−0.191769	−	0.419916i	0.789185	−	0.614156i	$-0.210503\pi$
$37$	−1.16649	−	2.55425i	−0.191769	−	0.419916i	−0.980954	+	0.194240i	$0.937776\pi$
$38$	−0.333104	+	0.214073i	−0.0540366	+	0.0347272i
$39$	7.41587	+	2.17750i	1.18749	+	0.348679i
$40$	1.42240	+	9.89304i	0.224902	+	1.56423i
$41$	3.14172	−	6.87940i	0.490654	−	1.07438i	−0.488742	−	0.872429i	$-0.662544\pi$
$41$	3.14172	−	6.87940i	0.490654	−	1.07438i	0.979395	−	0.201953i	$-0.0647288\pi$
$42$	−0.544920	+	3.79000i	−0.0840830	+	0.584810i
$43$	5.98239	+	3.84465i	0.912305	+	0.586303i	0.910416	−	0.413695i	$-0.135762\pi$
$43$	5.98239	+	3.84465i	0.912305	+	0.586303i	0.00188999	+	0.999998i	$0.499398\pi$
$44$	−15.4580	−	17.8395i	−2.33038	−	2.68940i
$45$	−1.07613			−0.160419
$46$	−3.70374	+	12.7105i	−0.546086	+	1.87406i
$47$	11.3201			1.65121			0.825605	−	0.564248i	$-0.190834\pi$
$47$	11.3201			1.65121			0.825605	+	0.564248i	$0.190834\pi$
$48$	−14.8508	−	17.1387i	−2.14353	−	2.47376i
$49$	0.841254	+	0.540641i	0.120179	+	0.0772344i
$50$	0.392866	−	2.73244i	0.0555596	−	0.386426i
$51$	−0.139701	+	0.305903i	−0.0195621	+	0.0428350i
$52$	4.45722	+	31.0006i	0.618105	+	4.29901i
$53$	11.2148	+	3.29297i	1.54047	+	0.452324i	0.938237	−	0.345994i	$-0.112458\pi$
$53$	11.2148	+	3.29297i	1.54047	+	0.452324i	0.602237	+	0.798317i	$0.294276\pi$
$54$	13.1298	−	8.43799i	1.78673	−	1.14826i
$55$	1.74464	+	3.82022i	0.235247	+	0.515119i
$56$	−9.58991	+	2.81585i	−1.28151	+	0.376284i
$57$	−0.130286	+	0.150358i	−0.0172567	+	0.0199153i
$58$	16.3224	−	18.8371i	2.14324	−	2.47343i
$59$	1.97910	−	0.581117i	0.257657	−	0.0756550i	−0.150353	−	0.988632i	$-0.548041\pi$
$59$	1.97910	−	0.581117i	0.257657	−	0.0756550i	0.408010	+	0.912977i	$0.366223\pi$
$60$	3.23856	+	7.09146i	0.418096	+	0.915503i
$61$	−9.91541	+	6.37225i	−1.26954	+	0.815883i	−0.989560	−	0.144123i	$-0.953964\pi$
$61$	−9.91541	+	6.37225i	−1.26954	+	0.815883i	−0.279979	+	0.960006i	$0.590327\pi$
$62$	−18.8261	−	5.52784i	−2.39092	−	0.702037i
$63$	−0.153149	−	1.06517i	−0.0192949	−	0.134199i
$64$	15.2513	−	33.3958i	1.90642	−	4.17447i
$65$	0.793017	−	5.51555i	0.0983616	−	0.684120i
$66$	−13.5280	−	8.69389i	−1.66518	−	1.07014i
$67$	2.42115	+	2.79416i	0.295791	+	0.341361i	0.884119	−	0.467261i	$-0.154759\pi$
$67$	2.42115	+	2.79416i	0.295791	+	0.341361i	−0.588328	+	0.808622i	$0.700214\pi$
$68$	−1.36274			−0.165256
$69$	0.0136868	+	6.65199i	0.00164770	+	0.800805i
$70$	2.76054			0.329948
$71$	−4.28023	−	4.93965i	−0.507970	−	0.586228i	0.442608	−	0.896715i	$-0.354053\pi$
$71$	−4.28023	−	4.93965i	−0.507970	−	0.586228i	−0.950578	+	0.310487i	$0.899508\pi$
$72$	9.04821	+	5.81493i	1.06634	+	0.685296i
$73$	1.28807	−	8.95872i	0.150757	−	1.04854i	−0.764198	−	0.644982i	$-0.776865\pi$
$73$	1.28807	−	8.95872i	0.150757	−	1.04854i	0.914955	−	0.403557i	$-0.132226\pi$
$74$	3.22013	−	7.05111i	0.374333	−	0.819675i
$75$	−0.197396	−	1.37292i	−0.0227933	−	0.158531i
$76$	−0.773539	−	0.227132i	−0.0887310	−	0.0260538i
$77$	−3.53305	+	2.27055i	−0.402629	+	0.258754i
$78$	8.86333	+	19.4080i	1.00357	+	2.19752i
$79$	−8.40121	+	2.46682i	−0.945210	+	0.277539i	−0.717791	−	0.696258i	$-0.754847\pi$
$79$	−8.40121	+	2.46682i	−0.945210	+	0.277539i	−0.227419	+	0.973797i	$0.573029\pi$
$80$	−10.7068	+	12.3564i	−1.19706	+	1.38148i
$81$	3.02125	−	3.48671i	0.335694	−	0.387412i
$82$	20.0318	−	5.88188i	2.21215	−	0.649545i
$83$	−4.14920	−	9.08547i	−0.455434	−	0.997260i	−0.988505	−	0.151190i	$-0.951689\pi$
$83$	−4.14920	−	9.08547i	−0.455434	−	0.997260i	0.533071	−	0.846070i	$-0.321038\pi$
$84$	−6.55838	+	4.21482i	−0.715578	+	0.459874i
$85$	0.232633	+	0.0683073i	0.0252326	+	0.00740897i
$86$	2.79378	+	19.4312i	0.301261	+	2.09532i
$87$	5.20251	−	11.3919i	0.557767	−	1.22134i
$88$	5.97374	−	41.5483i	0.636803	−	4.42906i
$89$	0.526142	+	0.338131i	0.0557709	+	0.0358418i	0.568229	−	0.822870i	$-0.307629\pi$
$89$	0.526142	+	0.338131i	0.0557709	+	0.0358418i	−0.512458	+	0.858712i	$0.671265\pi$
$90$	−1.94539	−	2.24510i	−0.205062	−	0.236654i
$91$	5.57227			0.584133
$92$	−24.4964	+	11.2481i	−2.55392	+	1.17270i
$93$	−9.85855			−1.02228
$94$	20.4642	+	23.6169i	2.11072	+	2.43590i
$95$	0.120666	+	0.0775475i	0.0123801	+	0.00795621i
$96$	4.96348	−	34.5217i	0.506583	−	3.52336i
$97$	−3.10211	+	6.79267i	−0.314971	+	0.689691i	−0.999217	−	0.0395606i	$-0.987404\pi$
$97$	−3.10211	+	6.79267i	−0.314971	+	0.689691i	0.684246	+	0.729251i	$0.260131\pi$
$98$	0.392866	+	2.73244i	0.0396854	+	0.276018i
$99$	4.33639	+	1.27328i	0.435823	+	0.127969i
$100$	4.72834	−	3.03872i	0.472834	−	0.303872i
$101$	2.20741	+	4.83354i	0.219645	+	0.480956i	0.987091	−	0.160158i	$-0.0512002\pi$
$101$	2.20741	+	4.83354i	0.219645	+	0.480956i	−0.767446	+	0.641113i	$0.778473\pi$
$102$	−0.890747	+	0.261547i	−0.0881971	+	0.0258970i
$103$	−10.2308	+	11.8070i	−1.00807	+	1.16338i	−0.0215458	+	0.999768i	$0.506859\pi$
$103$	−10.2308	+	11.8070i	−1.00807	+	1.16338i	−0.986525	+	0.163608i	$0.947687\pi$
$104$	−36.4715	+	42.0904i	−3.57633	+	4.12730i
$105$	1.33085	−	0.390774i	0.129878	−	0.0381356i
$106$	13.4038	+	29.3501i	1.30189	+	2.85074i
$107$	0.128892	−	0.0828341i	0.0124605	−	0.00800788i	−0.534396	−	0.845234i	$-0.679461\pi$
$107$	0.128892	−	0.0828341i	0.0124605	−	0.00800788i	0.546856	+	0.837227i	$0.315824\pi$
$108$	30.4901	+	8.95271i	2.93391	+	0.861475i
$109$	−0.847710	−	5.89595i	−0.0811959	−	0.564730i	−0.989290	−	0.145964i	$-0.953372\pi$
$109$	−0.847710	−	5.89595i	−0.0811959	−	0.564730i	0.908094	−	0.418766i	$-0.137537\pi$
$110$	−4.81614	+	10.5459i	−0.459201	+	1.00551i
$111$	0.554289	−	3.85516i	0.0526108	−	0.365916i
$112$	−13.7543	−	8.83937i	−1.29966	−	0.835242i
$113$	−11.3184	−	13.0621i	−1.06474	−	1.22878i	−0.972466	−	0.233046i	$-0.925131\pi$
$113$	−11.3184	−	13.0621i	−1.06474	−	1.22878i	−0.0922772	−	0.995733i	$-0.529415\pi$
$114$	−0.549214			−0.0514386
$115$	4.74560	−	0.692284i	0.442530	−	0.0645558i
$116$	50.7486			4.71189
$117$	−3.92685	−	4.53183i	−0.363037	−	0.418967i
$118$	4.79014	+	3.07843i	0.440968	+	0.283393i
$119$	−0.0345049	+	0.239987i	−0.00316305	+	0.0219995i
$120$	−5.75895	+	12.6103i	−0.525718	+	1.15116i
$121$	−0.944667	−	6.57030i	−0.0858788	−	0.597300i
$122$	−31.2191	−	9.16674i	−2.82644	−	0.829918i
$123$	8.82470	−	5.67129i	0.795696	−	0.511363i
$124$	−16.5954	−	36.3389i	−1.49031	−	3.26333i
$125$	−0.959493	+	0.281733i	−0.0858197	+	0.0251989i
$126$	1.94539	−	2.24510i	0.173309	−	0.200009i
$127$	1.99928	−	2.30729i	0.177407	−	0.204739i	−0.660081	−	0.751195i	$-0.729478\pi$
$127$	1.99928	−	2.30729i	0.177407	−	0.204739i	0.837488	+	0.546456i	$0.184023\pi$
$128$	48.9914	−	14.3852i	4.33027	−	1.27148i
$129$	4.09749	+	8.97226i	0.360764	+	0.789963i
$130$	12.9406	−	8.31640i	1.13496	−	0.729396i
$131$	8.97435	+	2.63511i	0.784093	+	0.230230i	0.649188	−	0.760628i	$-0.275109\pi$
$131$	8.97435	+	2.63511i	0.784093	+	0.230230i	0.134905	+	0.990859i	$0.456927\pi$
$132$	−4.65954	−	32.4078i	−0.405561	−	2.82074i
$133$	−0.0595856	+	0.130474i	−0.00516672	+	0.0113135i
$134$	−1.45250	+	10.1024i	−0.125477	+	0.872714i
$135$	−4.75623	−	3.05664i	−0.409351	−	0.263074i
$136$	−1.58691	−	1.83139i	−0.136076	−	0.157040i
$137$	5.79432			0.495043			0.247521	−	0.968882i	$-0.420384\pi$
$137$	5.79432			0.495043			0.247521	+	0.968882i	$0.420384\pi$
$138$	−13.8531	+	12.0538i	−1.17926	+	1.02609i
$139$	−8.93384			−0.757758			−0.378879	−	0.925446i	$-0.623690\pi$
$139$	−8.93384			−0.757758			−0.378879	+	0.925446i	$0.623690\pi$
$140$	3.68070	+	4.24775i	0.311076	+	0.359001i
$141$	13.2089	+	8.48884i	1.11239	+	0.714889i
$142$	2.56781	−	17.8595i	0.215486	−	1.49874i
$143$	−9.72159	+	21.2873i	−0.812960	+	1.78014i
$144$	2.50395	+	17.4154i	0.208663	+	1.45128i
$145$	−8.66331	−	2.54378i	−0.719449	−	0.211249i
$146$	21.0189	−	13.5080i	1.73954	−	1.11793i
$147$	0.576196	+	1.26169i	0.0475239	+	0.104063i
$148$	15.1433	−	4.44648i	1.24477	−	0.365498i
$149$	9.12899	−	10.5354i	0.747876	−	0.863095i	−0.246485	−	0.969147i	$-0.579275\pi$
$149$	9.12899	−	10.5354i	0.747876	−	0.863095i	0.994361	+	0.106052i	$0.0338209\pi$
$150$	2.50745	−	2.89375i	0.204732	−	0.236273i
$151$	−21.8096	+	6.40389i	−1.77484	+	0.521141i	−0.994549	−	0.104271i	$-0.966749\pi$
$151$	−21.8096	+	6.40389i	−1.77484	+	0.521141i	−0.780294	+	0.625412i	$0.784931\pi$
$152$	−0.595544	−	1.30406i	−0.0483050	−	0.105773i
$153$	0.219493	−	0.141059i	0.0177449	−	0.0114040i
$154$	−11.1239	−	3.26629i	−0.896393	−	0.263205i
$155$	1.01152	+	7.03528i	0.0812473	+	0.565087i
$156$	−18.0461	+	39.5155i	−1.44485	+	3.16377i
$157$	−0.443610	+	3.08538i	−0.0354039	+	0.246240i	−0.999836	−	0.0180897i	$-0.994242\pi$
$157$	−0.443610	+	3.08538i	−0.0354039	+	0.246240i	0.964432	+	0.264330i	$0.0851506\pi$
$158$	−20.3339	−	13.0678i	−1.61768	−	1.03962i
$159$	10.6167	+	12.2523i	0.841956	+	0.971668i
$160$	−25.1448			−1.98787
$161$	1.36061	+	4.59878i	0.107231	+	0.362434i
$162$	12.7360			1.00063
$163$	−7.38243	−	8.51977i	−0.578236	−	0.667320i	0.388988	−	0.921243i	$-0.372825\pi$
$163$	−7.38243	−	8.51977i	−0.578236	−	0.667320i	−0.967225	+	0.253922i	$0.918279\pi$
$164$	35.7596	+	22.9813i	2.79236	+	1.79454i
$165$	−0.829013	+	5.76591i	−0.0645386	+	0.448876i
$166$	11.4540	−	25.0808i	0.889005	−	1.94665i
$167$	0.755847	+	5.25703i	0.0584892	+	0.406801i	0.997942	+	0.0641229i	$0.0204250\pi$
$167$	0.755847	+	5.25703i	0.0584892	+	0.406801i	−0.939453	+	0.342678i	$0.888666\pi$
$168$	−13.3016	−	3.90569i	−1.02624	−	0.301331i
$169$	15.1848	−	9.75868i	1.16806	−	0.750668i
$170$	0.278039	+	0.608821i	0.0213246	+	0.0466945i
$171$	0.148103	−	0.0434870i	0.0113257	−	0.00332553i
$172$	−26.1745	+	30.2070i	−1.99579	+	2.30326i
$173$	3.96547	−	4.57639i	0.301489	−	0.347937i	−0.584710	−	0.811243i	$-0.698792\pi$
$173$	3.96547	−	4.57639i	0.301489	−	0.347937i	0.886198	+	0.463306i	$0.153337\pi$
$174$	33.1716	−	9.74006i	2.51473	−	0.738392i
$175$	−0.415415	−	0.909632i	−0.0314024	−	0.0687617i
$176$	57.7647	−	37.1231i	4.35418	−	2.79826i
$177$	2.74509	+	0.806032i	0.206334	+	0.0605851i
$178$	0.245709	+	1.70894i	0.0184166	+	0.128091i
$179$	−1.00241	+	2.19496i	−0.0749234	+	0.164059i	−0.943387	−	0.331693i	$-0.892380\pi$
$179$	−1.00241	+	2.19496i	−0.0749234	+	0.164059i	0.868464	+	0.495752i	$0.165108\pi$
$180$	0.860785	−	5.98689i	0.0641591	−	0.446237i
$181$	−0.915854	−	0.588584i	−0.0680749	−	0.0437491i	0.506161	−	0.862439i	$-0.331064\pi$
$181$	−0.915854	−	0.588584i	−0.0680749	−	0.0437491i	−0.574236	+	0.818690i	$0.694701\pi$
$182$	10.0734	+	11.6253i	0.746689	+	0.861725i
$183$	−16.3483			−1.20850
$184$	−43.6425	−	19.8224i	−3.21737	−	1.46133i
$185$	−2.80800			−0.206448
$186$	−17.8220	−	20.5677i	−1.30677	−	1.50809i
$187$	−0.856604	−	0.550506i	−0.0626411	−	0.0402570i
$188$	−9.05489	+	62.9781i	−0.660395	+	4.59315i
$189$	2.34865	−	5.14282i	0.170839	−	0.374085i
$190$	0.0563512	+	0.391931i	0.00408815	+	0.0284337i
$191$	−8.45870	−	2.48370i	−0.612050	−	0.179714i	−0.0390065	−	0.999239i	$-0.512419\pi$
$191$	−8.45870	−	2.48370i	−0.612050	−	0.179714i	−0.573044	+	0.819525i	$0.694237\pi$
$192$	42.8392	−	27.5311i	3.09165	−	1.98688i
$193$	5.80224	+	12.7051i	0.417654	+	0.914536i	0.995171	+	0.0981567i	$0.0312946\pi$
$193$	5.80224	+	12.7051i	0.417654	+	0.914536i	−0.577516	+	0.816379i	$0.695978\pi$
$194$	−19.7793	+	5.80772i	−1.42007	+	0.416970i
$195$	5.06139	−	5.84115i	0.362453	−	0.418294i
$196$	−3.68070	+	4.24775i	−0.262907	+	0.303411i
$197$	−2.75547	+	0.809080i	−0.196319	+	0.0576445i	−0.378414	−	0.925636i	$-0.623530\pi$
$197$	−2.75547	+	0.809080i	−0.196319	+	0.0576445i	0.182095	+	0.983281i	$0.441712\pi$
$198$	5.18278	+	11.3487i	0.368324	+	0.806517i
$199$	0.843446	−	0.542050i	0.0597903	−	0.0384249i	−0.510404	−	0.859935i	$-0.670504\pi$
$199$	0.843446	−	0.542050i	0.0597903	−	0.0384249i	0.570194	+	0.821510i	$0.306868\pi$
$200$	9.58991	+	2.81585i	0.678109	+	0.199111i
$201$	0.729813	+	5.07596i	0.0514771	+	0.358031i
$202$	−6.09363	+	13.3432i	−0.428747	+	0.938824i
$203$	1.28497	−	8.93715i	0.0901871	−	0.627265i
$204$	−1.59011	−	1.02190i	−0.111330	−	0.0715474i
$205$	−4.95260	−	5.71561i	−0.345905	−	0.399196i
$206$	−43.1276			−3.00484
$207$	2.78126	−	4.34737i	0.193311	−	0.302163i
$208$	−91.1055			−6.31703
$209$	−0.394485	−	0.455260i	−0.0272871	−	0.0314910i
$210$	3.22114	+	2.07010i	0.222280	+	0.142850i
$211$	−1.78128	+	12.3891i	−0.122629	+	0.852901i	0.831931	+	0.554880i	$0.187236\pi$
$211$	−1.78128	+	12.3891i	−0.122629	+	0.852901i	−0.954559	+	0.298021i	$0.903673\pi$
$212$	−27.2907	+	59.7582i	−1.87433	+	4.10421i
$213$	−1.29020	−	8.97353i	−0.0884030	−	0.614856i
$214$	0.405823	+	0.119160i	0.0277415	+	0.00814563i
$215$	5.98239	−	3.84465i	0.407995	−	0.262203i
$216$	23.4742	+	51.4014i	1.59722	+	3.49742i
$217$	−6.81972	+	2.00245i	−0.462953	+	0.135935i
$218$	10.7681	−	12.4271i	0.729310	−	0.841668i
$219$	8.22103	−	9.48758i	0.555526	−	0.641111i
$220$	−22.6489	+	6.65031i	−1.52699	+	0.448363i
$221$	0.561235	+	1.22893i	0.0377527	+	0.0826669i
$222$	9.04497	−	5.81285i	0.607058	−	0.390133i
$223$	−4.05920	−	1.19189i	−0.271824	−	0.0798147i	0.142980	−	0.989726i	$-0.454332\pi$
$223$	−4.05920	−	1.19189i	−0.271824	−	0.0798147i	−0.414804	+	0.909911i	$0.636150\pi$
$224$	−3.57847	−	24.8888i	−0.239097	−	1.66295i
$225$	−0.447039	+	0.978878i	−0.0298026	+	0.0652586i
$226$	6.79015	−	47.2265i	0.451674	−	3.14146i
$227$	−10.3364	−	6.64281i	−0.686052	−	0.440899i	0.150629	−	0.988590i	$-0.451870\pi$
$227$	−10.3364	−	6.64281i	−0.686052	−	0.440899i	−0.836680	+	0.547692i	$0.815507\pi$
$228$	−0.732281	−	0.845097i	−0.0484965	−	0.0559679i
$229$	9.69108			0.640404			0.320202	−	0.947349i	$-0.396249\pi$
$229$	9.69108			0.640404			0.320202	+	0.947349i	$0.396249\pi$
$230$	10.0233	+	8.64915i	0.660914	+	0.570308i
$231$	−5.82521			−0.383270
$232$	59.0968	+	68.2014i	3.87990	+	4.47764i
$233$	−20.7613	−	13.3425i	−1.36012	−	0.874096i	−0.361813	−	0.932251i	$-0.617842\pi$
$233$	−20.7613	−	13.3425i	−1.36012	−	0.874096i	−0.998308	+	0.0581545i	$0.981478\pi$
$234$	2.35581	−	16.3850i	0.154004	−	1.07112i
$235$	4.70255	−	10.2971i	0.306761	−	0.671712i
$236$	1.64990	+	11.4753i	0.107400	+	0.746980i
$237$	−11.6528	−	3.42157i	−0.756931	−	0.222255i
$238$	−0.563055	+	0.361854i	−0.0364975	+	0.0234555i
$239$	−5.45922	−	11.9540i	−0.353128	−	0.773241i	−0.999944	−	0.0105956i	$-0.996627\pi$
$239$	−5.45922	−	11.9540i	−0.353128	−	0.773241i	0.646816	−	0.762646i	$-0.276100\pi$
$240$	−21.7592	+	6.38907i	−1.40455	+	0.412413i
$241$	4.09224	−	4.72269i	0.263604	−	0.304215i	−0.608482	−	0.793568i	$-0.708221\pi$
$241$	4.09224	−	4.72269i	0.263604	−	0.304215i	0.872086	+	0.489352i	$0.162767\pi$
$242$	11.9997	−	13.8484i	0.771372	−	0.890211i
$243$	−10.1342	+	2.97566i	−0.650108	+	0.190889i
$244$	−27.5199	−	60.2603i	−1.76178	−	3.85777i
$245$	0.841254	−	0.540641i	0.0537457	−	0.0345403i
$246$	27.7849	+	8.15839i	1.77150	+	0.520160i
$247$	0.113747	+	0.791130i	0.00723757	+	0.0503384i
$248$	29.5107	−	64.6194i	1.87393	−	4.10334i
$249$	1.97161	−	13.7128i	0.124946	−	0.869015i
$250$	−2.32231	−	1.49246i	−0.146876	−	0.0943915i
$251$	12.6223	+	14.5670i	0.796715	+	0.919458i	0.998196	−	0.0600340i	$-0.0191209\pi$
$251$	12.6223	+	14.5670i	0.796715	+	0.919458i	−0.201481	+	0.979492i	$0.564575\pi$
$252$	6.04846			0.381017
$253$	−19.9421	−	2.82538i	−1.25375	−	0.177630i
$254$	8.42788			0.528812
$255$	0.220225	+	0.254154i	0.0137910	+	0.0159157i
$256$	56.8058	+	36.5069i	3.55036	+	2.28168i
$257$	−0.413199	+	2.87386i	−0.0257746	+	0.179266i	−0.998642	−	0.0520969i	$-0.983410\pi$
$257$	−0.413199	+	2.87386i	−0.0257746	+	0.179266i	0.972867	+	0.231363i	$0.0743186\pi$
$258$	−11.3113	+	24.7683i	−0.704210	+	1.54201i
$259$	−0.399620	−	2.77942i	−0.0248312	−	0.172705i
$260$	30.0508	+	8.82370i	1.86367	+	0.547223i
$261$	−8.17395	+	5.25308i	−0.505955	+	0.325158i
$262$	10.7260	+	23.4867i	0.662654	+	1.45101i
$263$	8.37190	−	2.45821i	0.516233	−	0.151580i	−0.0132302	−	0.999912i	$-0.504211\pi$
$263$	8.37190	−	2.45821i	0.516233	−	0.151580i	0.529464	+	0.848333i	$0.322393\pi$
$264$	38.1271	−	44.0010i	2.34656	−	2.70807i
$265$	7.65419	−	8.83341i	0.470193	−	0.542632i
$266$	−0.379922	+	0.111555i	−0.0232945	+	0.00683989i
$267$	0.360368	+	0.789096i	0.0220542	+	0.0482919i
$268$	−17.4816	+	11.2348i	−1.06786	+	0.686272i
$269$	−9.50865	−	2.79199i	−0.579753	−	0.170231i	−0.0213088	−	0.999773i	$-0.506783\pi$
$269$	−9.50865	−	2.79199i	−0.579753	−	0.170231i	−0.558444	+	0.829542i	$0.688601\pi$
$270$	−2.22116	−	15.4485i	−0.135176	−	0.940167i
$271$	8.03965	−	17.6044i	0.488374	−	1.06939i	−0.491701	−	0.870764i	$-0.663625\pi$
$271$	8.03965	−	17.6044i	0.488374	−	1.06939i	0.980075	−	0.198626i	$-0.0636480\pi$
$272$	0.564148	−	3.92373i	0.0342065	−	0.237911i
$273$	6.50201	+	4.17859i	0.393519	+	0.252900i
$274$	10.4748	+	12.0886i	0.632806	+	0.730297i
$275$	4.19975			0.253254
$276$	−37.0184	−	5.24473i	−2.22825	−	0.315696i
$277$	−6.54415			−0.393200			−0.196600	−	0.980484i	$-0.562990\pi$
$277$	−6.54415			−0.393200			−0.196600	+	0.980484i	$0.562990\pi$
$278$	−16.1503	−	18.6385i	−0.968632	−	1.11786i
$279$	6.43450	+	4.13520i	0.385223	+	0.247568i
$280$	−1.42240	+	9.89304i	−0.0850049	+	0.591222i
$281$	−9.26604	+	20.2898i	−0.552765	+	1.21039i	0.402713	+	0.915326i	$0.368067\pi$
$281$	−9.26604	+	20.2898i	−0.552765	+	1.21039i	−0.955478	+	0.295061i	$0.904660\pi$
$282$	6.16856	+	42.9033i	0.367333	+	2.55485i
$283$	−22.7789	−	6.68849i	−1.35407	−	0.397589i	−0.477398	−	0.878687i	$-0.658420\pi$
$283$	−22.7789	−	6.68849i	−1.35407	−	0.397589i	−0.876667	+	0.481098i	$0.840238\pi$
$284$	30.9048	−	19.8613i	1.83387	−	1.17855i
$285$	0.0826475	+	0.180973i	0.00489561	+	0.0107199i
$286$	−61.9857	+	18.2006i	−3.66529	+	1.07623i
$287$	4.95260	−	5.71561i	0.292343	−	0.337382i
$288$	−17.7198	+	20.4498i	−1.04415	+	1.20501i
$289$	16.2550	−	4.77289i	0.956175	−	0.280758i
$290$	−10.3542	−	22.6726i	−0.608022	−	1.33138i
$291$	−8.71344	+	5.59979i	−0.510791	+	0.328265i
$292$	48.8104	+	14.3320i	2.85641	+	0.838719i
$293$	2.53415	+	17.6254i	0.148047	+	1.02969i	0.919412	+	0.393295i	$0.128665\pi$
$293$	2.53415	+	17.6254i	0.148047	+	1.02969i	−0.771366	+	0.636392i	$0.780426\pi$
$294$	−1.59061	+	3.48296i	−0.0927665	+	0.203130i
$295$	0.293547	−	2.04166i	0.0170909	−	0.118870i
$296$	23.6101	+	15.1733i	1.37231	+	0.881929i
$297$	15.5492	+	17.9447i	0.902256	+	1.04126i
$298$	38.4829			2.22926
$299$	20.2324	+	17.4587i	1.17007	+	1.00966i
$300$	7.79596			0.450100
$301$	4.65690	+	5.37434i	0.268419	+	0.309772i
$302$	−52.7871	−	33.9242i	−3.03756	−	1.95212i
$303$	−1.04891	+	7.29533i	−0.0602583	+	0.419106i
$304$	0.974213	−	2.13323i	0.0558749	−	0.122349i
$305$	1.67739	+	11.6665i	0.0960471	+	0.668022i
$306$	0.691081	+	0.202920i	0.0395065	+	0.0116001i
$307$	3.27564	−	2.10513i	0.186951	−	0.120146i	−0.443818	−	0.896117i	$-0.646376\pi$
$307$	3.27564	−	2.10513i	0.186951	−	0.120146i	0.630768	+	0.775971i	$0.282740\pi$
$308$	−9.80588	−	21.4719i	−0.558742	−	1.22347i
$309$	−20.7917	+	6.10501i	−1.18280	+	0.347302i
$310$	−12.8490	+	14.8285i	−0.729771	+	0.842201i
$311$	−0.427275	+	0.493101i	−0.0242285	+	0.0279612i	−0.767735	−	0.640768i	$-0.778616\pi$
$311$	−0.427275	+	0.493101i	−0.0242285	+	0.0279612i	0.743506	+	0.668729i	$0.233161\pi$
$312$	−74.1200	+	21.7636i	−4.19622	+	1.23212i
$313$	2.30285	+	5.04254i	0.130165	+	0.285021i	0.963482	−	0.267775i	$-0.0862882\pi$
$313$	2.30285	+	5.04254i	0.130165	+	0.285021i	−0.833317	+	0.552796i	$0.813561\pi$
$314$	−7.23889	+	4.65216i	−0.408514	+	0.262536i
$315$	−1.03254	−	0.303180i	−0.0581768	−	0.0170822i
$316$	−7.00377	−	48.7123i	−0.393993	−	2.74028i
$317$	3.46083	−	7.57816i	0.194380	−	0.425632i	−0.787197	−	0.616702i	$-0.788468\pi$
$317$	3.46083	−	7.57816i	0.194380	−	0.425632i	0.981576	+	0.191070i	$0.0611957\pi$
$318$	−6.36917	+	44.2986i	−0.357166	+	2.48414i
$319$	31.9001	+	20.5010i	1.78606	+	1.14783i
$320$	−24.0422	−	27.7462i	−1.34400	−	1.55106i
$321$	0.212515			0.0118614
$322$	−7.13466	+	11.1521i	−0.397599	+	0.621484i
$323$	−0.0347767			−0.00193503
$324$	16.9812	+	19.5973i	0.943400	+	1.08874i
$325$	−4.68769	−	3.01260i	−0.260026	−	0.167109i
$326$	4.42889	−	30.8036i	0.245293	−	1.70605i
$327$	3.43216	−	7.51539i	0.189799	−	0.415602i
$328$	10.7574	+	74.8194i	0.593979	+	4.13121i
$329$	10.8616	+	3.18925i	0.598818	+	0.175829i
$330$	−13.5280	+	8.69389i	−0.744690	+	0.478583i
$331$	−3.64033	−	7.97121i	−0.200091	−	0.438137i	0.782813	−	0.622257i	$-0.213784\pi$
$331$	−3.64033	−	7.97121i	−0.200091	−	0.438137i	−0.982904	+	0.184119i	$0.941057\pi$
$332$	53.8648	−	15.8161i	2.95622	−	0.868023i
$333$	−1.97883	+	2.28370i	−0.108439	+	0.125146i
$334$	−9.60122	+	11.0804i	−0.525356	+	0.606293i
$335$	3.54744	−	1.04162i	0.193817	−	0.0569099i
$336$	−9.42070	−	20.6285i	−0.513941	−	1.12537i
$337$	10.7682	−	6.92032i	0.586582	−	0.376974i	−0.213429	−	0.976959i	$-0.568463\pi$
$337$	10.7682	−	6.92032i	0.586582	−	0.376974i	0.800011	+	0.599985i	$0.204827\pi$
$338$	47.8099	+	14.0383i	2.60052	+	0.763581i
$339$	−3.41172	−	23.7290i	−0.185299	−	1.28878i
$340$	−0.566101	+	1.23959i	−0.0307011	+	0.0672261i
$341$	4.24813	−	29.5464i	0.230049	−	1.60003i
$342$	0.358462	+	0.230369i	0.0193834	+	0.0124570i
$343$	0.654861	+	0.755750i	0.0353592	+	0.0408066i
$344$	−71.0756			−3.83214
$345$	6.05655	+	2.75088i	0.326073	+	0.148103i
$346$	16.7163			0.898672
$347$	−4.24102	−	4.89440i	−0.227670	−	0.262745i	0.630409	−	0.776263i	$-0.282887\pi$
$347$	−4.24102	−	4.89440i	−0.227670	−	0.262745i	−0.858079	+	0.513518i	$0.828342\pi$
$348$	59.2160	+	38.0558i	3.17431	+	2.04001i
$349$	−0.00363369	+	0.0252729i	−0.000194507	+	0.00135282i	−0.989918	−	0.141638i	$-0.954763\pi$
$349$	−0.00363369	+	0.0252729i	−0.000194507	+	0.00135282i	0.989724	+	0.142991i	$0.0456721\pi$
$350$	1.14677	−	2.51108i	0.0612974	−	0.134223i
$351$	−4.48351	−	31.1835i	−0.239312	−	1.66445i
$352$	101.324	+	29.7514i	5.40059	+	1.58576i
$353$	1.15189	−	0.740274i	0.0613089	−	0.0394008i	−0.509627	−	0.860395i	$-0.670217\pi$
$353$	1.15189	−	0.740274i	0.0613089	−	0.0394008i	0.570936	+	0.820994i	$0.306580\pi$
$354$	3.28089	+	7.18414i	0.174377	+	0.381833i
$355$	−6.27133	+	1.84143i	−0.332848	+	0.0977329i
$356$	−2.30201	+	2.65666i	−0.122006	+	0.140803i
$357$	−0.220225	+	0.254154i	−0.0116556	+	0.0134512i
$358$	−6.39142	+	1.87669i	−0.337797	+	0.0991862i
$359$	−8.16811	−	17.8857i	−0.431096	−	0.943969i	−0.993148	−	0.116867i	$-0.962715\pi$
$359$	−8.16811	−	17.8857i	−0.431096	−	0.943969i	0.562052	−	0.827102i	$-0.310012\pi$
$360$	9.04821	−	5.81493i	0.476883	−	0.306474i
$361$	18.2106	+	5.34712i	0.958454	+	0.281427i
$362$	−0.427704	−	2.97475i	−0.0224796	−	0.156349i
$363$	3.82471	−	8.37496i	0.200745	−	0.439571i
$364$	−4.45722	+	31.0006i	−0.233622	+	1.62487i
$365$	−7.61406	−	4.89326i	−0.398538	−	0.256125i
$366$	−29.5539	−	34.1071i	−1.54481	−	1.78280i
$367$	15.6001			0.814317			0.407159	−	0.913357i	$-0.366520\pi$
$367$	15.6001			0.814317			0.407159	+	0.913357i	$0.366520\pi$
$368$	−22.2457	−	75.1891i	−1.15964	−	3.91950i
$369$	−8.13856			−0.423677
$370$	−5.07622	−	5.85827i	−0.263900	−	0.304557i
$371$	9.83280	+	6.31916i	0.510494	+	0.328074i
$372$	7.88578	−	54.8468i	0.408859	−	2.84367i
$373$	0.345847	−	0.757299i	0.0179073	−	0.0392115i	−0.900467	−	0.434924i	$-0.856775\pi$
$373$	0.345847	−	0.757299i	0.0179073	−	0.0392115i	0.918374	+	0.395713i	$0.129502\pi$
$374$	−0.400034	−	2.78230i	−0.0206853	−	0.143869i
$375$	−1.33085	−	0.390774i	−0.0687250	−	0.0201795i
$376$	−95.1812	+	61.1692i	−4.90859	+	3.15456i
$377$	−20.9005	−	45.7657i	−1.07643	−	2.35705i
$378$	14.9752	−	4.39711i	0.770240	−	0.226163i
$379$	−0.155681	+	0.179666i	−0.00799682	+	0.00922882i	−0.759734	−	0.650234i	$-0.774671\pi$
$379$	−0.155681	+	0.179666i	−0.00799682	+	0.00922882i	0.751737	+	0.659463i	$0.229216\pi$
$380$	−0.527946	+	0.609282i	−0.0270831	+	0.0312555i
$381$	4.06307	−	1.19302i	0.208157	−	0.0611205i
$382$	−10.1097	−	22.1372i	−0.517257	−	1.13264i
$383$	20.3343	−	13.0681i	1.03904	−	0.667748i	0.0942882	−	0.995545i	$-0.469942\pi$
$383$	20.3343	−	13.0681i	1.03904	−	0.667748i	0.944748	+	0.327797i	$0.106306\pi$
$384$	67.9529	+	19.9528i	3.46771	+	1.01821i
$385$	0.597686	+	4.15700i	0.0304609	+	0.211860i
$386$	−16.0173	+	35.0730i	−0.815260	+	1.78517i
$387$	1.08908	−	7.57474i	0.0553612	−	0.385045i
$388$	−35.3088	−	22.6916i	−1.79253	−	1.15199i
$389$	−16.5179	−	19.0626i	−0.837490	−	0.966515i	0.162306	−	0.986741i	$-0.448107\pi$
$389$	−16.5179	−	19.0626i	−0.837490	−	0.966515i	−0.999795	+	0.0202258i	$0.993561\pi$
$390$	21.3361			1.08039
$391$	−0.877195	+	0.763259i	−0.0443616	+	0.0385997i
$392$	−9.99477			−0.504812
$393$	8.49569	+	9.80455i	0.428551	+	0.494574i
$394$	−6.66922	−	4.28605i	−0.335991	−	0.215928i
$395$	−1.24609	+	8.66676i	−0.0626977	+	0.436072i
$396$	−10.5524	+	23.1065i	−0.530276	+	1.16114i
$397$	4.31587	+	30.0175i	0.216607	+	1.50654i	0.750436	+	0.660943i	$0.229844\pi$
$397$	4.31587	+	30.0175i	0.216607	+	1.50654i	−0.533829	+	0.845593i	$0.679247\pi$
$398$	2.65562	+	0.779761i	0.133114	+	0.0390859i
$399$	−0.167369	+	0.107561i	−0.00837891	+	0.00538480i
$400$	6.79195	+	14.8723i	0.339598	+	0.743615i
$401$	−22.8045	+	6.69600i	−1.13880	+	0.334382i	−0.796161	−	0.605085i	$-0.793139\pi$
$401$	−22.8045	+	6.69600i	−1.13880	+	0.334382i	−0.342640	+	0.939467i	$0.611321\pi$
$402$	−9.27053	+	10.6988i	−0.462372	+	0.533606i
$403$	−25.9362	+	29.9319i	−1.29197	+	1.49102i
$404$	−28.6565	+	8.41431i	−1.42571	+	0.418628i
$405$	−1.91655	−	4.19666i	−0.0952341	−	0.208534i
$406$	20.9683	−	13.4755i	1.04064	−	0.668778i
$407$	11.3152	+	3.32244i	0.560874	+	0.164687i
$408$	−0.478345	−	3.32696i	−0.0236816	−	0.164709i
$409$	6.47883	−	14.1867i	0.320358	−	0.701485i	−0.679113	−	0.734034i	$-0.737635\pi$
$409$	6.47883	−	14.1867i	0.320358	−	0.701485i	0.999470	+	0.0325489i	$0.0103625\pi$
$410$	2.97118	−	20.6650i	0.146736	−	1.02057i
$411$	6.76111	+	4.34510i	0.333501	+	0.214328i
$412$	−57.5031	−	66.3621i	−2.83297	−	3.26943i
$413$	2.06266			0.101497
$414$	14.0977	−	2.05656i	0.692865	−	0.101074i
$415$	−9.98808			−0.490295
$416$	−91.7548	−	105.891i	−4.49865	−	5.19172i
$417$	−10.4245	−	6.69939i	−0.510488	−	0.328071i
$418$	0.236661	−	1.64601i	0.0115755	−	0.0805091i
$419$	3.95315	−	8.65619i	0.193124	−	0.422882i	−0.788154	−	0.615478i	$-0.788963\pi$
$419$	3.95315	−	8.65619i	0.193124	−	0.422882i	0.981278	+	0.192595i	$0.0616904\pi$
$420$	1.10948	+	7.71661i	0.0541372	+	0.376532i
$421$	−34.6115	−	10.1628i	−1.68686	−	0.495307i	−0.709114	−	0.705094i	$-0.750905\pi$
$421$	−34.6115	−	10.1628i	−1.68686	−	0.495307i	−0.977747	+	0.209787i	$0.932723\pi$
$422$	−29.0672	+	18.6804i	−1.41497	+	0.909347i
$423$	−5.06054	−	11.0810i	−0.246052	−	0.538778i
$424$	−112.090	+	32.9125i	−5.44355	+	1.59837i
$425$	0.158774	−	0.183235i	0.00770166	−	0.00888819i
$426$	16.3889	−	18.9138i	0.794044	−	0.916376i
$427$	−11.3090	+	3.32063i	−0.547283	+	0.160697i
$428$	0.357737	+	0.783335i	0.0172919	+	0.0378640i
$429$	−27.3068	+	17.5490i	−1.31838	+	0.847274i
$430$	18.8358	+	5.53068i	0.908342	+	0.266713i
$431$	4.68614	+	32.5928i	0.225723	+	1.56994i	0.715827	+	0.698277i	$0.246050\pi$
$431$	4.68614	+	32.5928i	0.225723	+	1.56994i	−0.490104	+	0.871664i	$0.663041\pi$
$432$	−38.4000	+	84.0842i	−1.84752	+	4.04550i
$433$	−2.35486	+	16.3784i	−0.113167	+	0.787095i	0.851638	+	0.524130i	$0.175609\pi$
$433$	−2.35486	+	16.3784i	−0.113167	+	0.787095i	−0.964805	+	0.262965i	$0.915300\pi$
$434$	−16.5061	−	10.6079i	−0.792320	−	0.509193i
$435$	−8.20124	−	9.46474i	−0.393219	−	0.453799i
$436$	33.4795			1.60338
$437$	−0.625143	+	0.287049i	−0.0299046	+	0.0137314i
$438$	34.6555			1.65590
$439$	−13.3791	−	15.4403i	−0.638550	−	0.736926i	0.340568	−	0.940220i	$-0.389381\pi$
$439$	−13.3791	−	15.4403i	−0.638550	−	0.736926i	−0.979118	+	0.203294i	$0.934835\pi$
$440$	−35.3120	−	22.6937i	−1.68344	−	1.08188i
$441$	0.153149	−	1.06517i	0.00729279	−	0.0507225i
$442$	−1.54931	+	3.39252i	−0.0736932	+	0.161366i
$443$	−4.47233	−	31.1057i	−0.212487	−	1.47788i	−0.764814	−	0.644251i	$-0.777169\pi$
$443$	−4.47233	−	31.1057i	−0.212487	−	1.47788i	0.552327	−	0.833627i	$-0.313740\pi$
$444$	21.0043	+	6.16743i	0.996822	+	0.292693i
$445$	0.526142	−	0.338131i	0.0249415	−	0.0160289i
$446$	−4.85148	−	10.6233i	−0.229724	−	0.503026i
$447$	18.5526	−	5.44752i	0.877506	−	0.257659i
$448$	24.0422	−	27.7462i	1.13589	−	1.31089i
$449$	−5.68109	+	6.55632i	−0.268107	+	0.309412i	−0.873799	−	0.486287i	$-0.838351\pi$
$449$	−5.68109	+	6.55632i	−0.268107	+	0.309412i	0.605692	+	0.795699i	$0.292896\pi$
$450$	−2.85036	+	0.836940i	−0.134367	+	0.0394537i
$451$	13.1944	+	28.8917i	0.621300	+	1.36046i
$452$	81.7228	−	52.5201i	3.84392	−	2.47034i
$453$	−30.2508	−	8.88244i	−1.42131	−	0.417333i
$454$	−4.82711	−	33.5733i	−0.226547	−	1.57567i
$455$	2.31481	−	5.06872i	0.108520	−	0.237625i
$456$	0.282990	−	1.96824i	0.0132522	−	0.0921711i
$457$	14.2189	+	9.13793i	0.665132	+	0.427454i	0.829168	−	0.559000i	$-0.188815\pi$
$457$	14.2189	+	9.13793i	0.665132	+	0.427454i	−0.164036	+	0.986454i	$0.552451\pi$
$458$	17.5192	+	20.2183i	0.818620	+	0.944738i
$459$	1.37077			0.0639823
$460$	0.0554621	+	26.9553i	0.00258593	+	1.25680i
$461$	−2.85969			−0.133189			−0.0665946	−	0.997780i	$-0.521213\pi$
$461$	−2.85969			−0.133189			−0.0665946	+	0.997780i	$0.521213\pi$
$462$	−10.5306	−	12.1530i	−0.489929	−	0.565409i
$463$	−17.2807	−	11.1056i	−0.803103	−	0.516123i	0.0735243	−	0.997293i	$-0.476575\pi$
$463$	−17.2807	−	11.1056i	−0.803103	−	0.516123i	−0.876627	+	0.481171i	$0.840212\pi$
$464$	−21.0090	+	146.121i	−0.975317	+	6.78348i
$465$	−4.09539	+	8.96765i	−0.189919	+	0.415865i
$466$	−9.69556	−	67.4341i	−0.449138	−	3.12382i
$467$	−14.1428	−	4.15272i	−0.654453	−	0.192165i	−0.0623843	−	0.998052i	$-0.519870\pi$
$467$	−14.1428	−	4.15272i	−0.654453	−	0.192165i	−0.592069	+	0.805887i	$0.701689\pi$
$468$	28.3533	−	18.2216i	1.31063	−	0.842292i
$469$	1.53587	+	3.36309i	0.0709200	+	0.155293i
$470$	29.9838	−	8.80405i	1.38305	−	0.406101i
$471$	−2.83132	+	3.26751i	−0.130460	+	0.150559i
$472$	−13.5005	+	15.5804i	−0.621409	+	0.717144i
$473$	−28.6558	+	8.41410i	−1.31759	+	0.386881i
$474$	−13.9272	−	30.4964i	−0.639699	−	1.40075i
$475$	0.120666	−	0.0775475i	0.00553655	−	0.00355812i
$476$	−1.30754	−	0.383927i	−0.0599308	−	0.0175973i
$477$	−1.79004	−	12.4500i	−0.0819605	−	0.570048i
$478$	15.0704	−	32.9996i	0.689304	−	1.50936i
$479$	1.89574	−	13.1852i	0.0866187	−	0.602447i	−0.899564	−	0.436788i	$-0.856116\pi$
$479$	1.89574	−	13.1852i	0.0866187	−	0.602447i	0.986183	−	0.165658i	$-0.0529749\pi$
$480$	−29.3402	−	18.8558i	−1.33919	−	0.860645i
$481$	−10.2466	−	11.8252i	−0.467204	−	0.539182i
$482$	17.2507			0.785747
$483$	−1.86095	+	6.38639i	−0.0846761	+	0.290591i
$484$	37.3087			1.69585
$485$	4.89016	+	5.64355i	0.222051	+	0.256260i
$486$	−24.5283	−	15.7634i	−1.11263	−	0.715042i
$487$	−3.46480	+	24.0982i	−0.157005	+	1.09199i	0.747109	+	0.664702i	$0.231441\pi$
$487$	−3.46480	+	24.0982i	−0.157005	+	1.09199i	−0.904114	+	0.427292i	$0.859468\pi$
$488$	48.9372	−	107.157i	2.21528	−	4.85079i
$489$	−2.22530	−	15.4773i	−0.100632	−	0.699908i
$490$	2.64872	+	0.777734i	0.119657	+	0.0351344i
$491$	4.12184	−	2.64894i	0.186016	−	0.119545i	−0.444319	−	0.895869i	$-0.646554\pi$
$491$	4.12184	−	2.64894i	0.186016	−	0.119545i	0.630334	+	0.776324i	$0.282918\pi$
$492$	24.4927	+	53.6315i	1.10422	+	2.41790i
$493$	2.10046	−	0.616750i	0.0945999	−	0.0277770i
$494$	−1.44489	+	1.66749i	−0.0650086	+	0.0750239i
$495$	2.95961	−	3.41558i	0.133025	−	0.153519i
$496$	111.501	−	32.7397i	5.00654	−	1.47005i
$497$	−2.71519	−	5.94544i	−0.121793	−	0.266689i
$498$	32.1730	−	20.6763i	1.44171	−	0.926528i
$499$	3.69917	+	1.08617i	0.165597	+	0.0486238i	0.363480	−	0.931602i	$-0.381588\pi$
$499$	3.69917	+	1.08617i	0.165597	+	0.0486238i	−0.197883	+	0.980226i	$0.563407\pi$
$500$	−0.799893	−	5.56338i	−0.0357723	−	0.248802i
$501$	−3.06023	+	6.70097i	−0.136721	+	0.299377i
$502$	−7.57243	+	52.6674i	−0.337974	+	2.35066i
$503$	24.6839	+	15.8633i	1.10060	+	0.707312i	0.959225	−	0.282645i	$-0.0912117\pi$
$503$	24.6839	+	15.8633i	1.10060	+	0.707312i	0.141374	+	0.989956i	$0.454848\pi$
$504$	7.04344	+	8.12856i	0.313740	+	0.362075i
$505$	5.31374			0.236458
$506$	−30.1562	−	46.7124i	−1.34061	−	2.07662i
$507$	25.0363			1.11190
$508$	11.2371	+	12.9683i	0.498566	+	0.575376i
$509$	24.8826	+	15.9911i	1.10290	+	0.708791i	0.959735	−	0.280908i	$-0.0906355\pi$
$509$	24.8826	+	15.9911i	1.10290	+	0.708791i	0.143166	+	0.989699i	$0.454272\pi$
$510$	−0.132118	+	0.918902i	−0.00585029	+	0.0406897i
$511$	3.75986	−	8.23294i	0.166326	−	0.364204i
$512$	11.9953	+	83.4288i	0.530120	+	3.68707i
$513$	0.778102	+	0.228471i	0.0343541	+	0.0100873i
$514$	−6.74263	+	4.33323i	−0.297405	+	0.191131i
$515$	6.48998	+	14.2111i	0.285982	+	0.626214i
$516$	−53.1936	+	15.6190i	−2.34172	+	0.687590i
$517$	−31.1332	+	35.9296i	−1.36923	+	1.58018i
$518$	5.07622	−	5.85827i	0.223036	−	0.257398i
$519$	8.05889	−	2.36630i	0.353746	−	0.103869i
$520$	23.1359	+	50.6607i	1.01458	+	2.22162i
$521$	6.49586	−	4.17464i	0.284589	−	0.182894i	−0.390556	−	0.920579i	$-0.627717\pi$
$521$	6.49586	−	4.17464i	0.284589	−	0.182894i	0.675145	+	0.737685i	$0.264081\pi$
$522$	−25.7360	−	7.55677i	−1.12643	−	0.330751i
$523$	2.08922	+	14.5308i	0.0913552	+	0.635390i	0.983130	+	0.182910i	$0.0585515\pi$
$523$	2.08922	+	14.5308i	0.0913552	+	0.635390i	−0.891775	+	0.452480i	$0.850539\pi$
$524$	−21.8386	+	47.8199i	−0.954024	+	2.08902i
$525$	0.197396	−	1.37292i	0.00861507	−	0.0599191i
$526$	20.2630	+	13.0222i	0.883508	+	0.567796i
$527$	−1.12851	−	1.30236i	−0.0491585	−	0.0567319i
$528$	95.2410			4.14483
$529$	−9.46837	+	20.9607i	−0.411668	+	0.911334i
$530$	32.2660			1.40154
$531$	−1.45358	−	1.67752i	−0.0630800	−	0.0727982i
$532$	−0.678215	−	0.435862i	−0.0294043	−	0.0188970i
$533$	5.99746	−	41.7132i	0.259779	−	1.80680i
$534$	−0.994811	+	2.17833i	−0.0430497	+	0.0942657i
$535$	−0.0218047	−	0.151655i	−0.000942701	−	0.00655663i
$536$	−35.4559	−	10.4108i	−1.53146	−	0.449677i
$537$	−2.81564	+	1.80950i	−0.121504	+	0.0780857i
$538$	−11.3646	−	24.8850i	−0.489962	−	1.07287i
$539$	−4.02963	+	1.18321i	−0.173568	+	0.0509643i
$540$	20.8097	−	24.0157i	0.895508	−	1.03347i
$541$	−5.99139	+	6.91443i	−0.257590	+	0.297275i	−0.869784	−	0.493433i	$-0.835742\pi$
$541$	−5.99139	+	6.91443i	−0.257590	+	0.297275i	0.612194	+	0.790708i	$0.290287\pi$
$542$	51.2615	−	15.0517i	2.20187	−	0.646527i
$543$	−0.627292	−	1.37358i	−0.0269197	−	0.0589459i
$544$	5.12867	−	3.29599i	0.219890	−	0.141315i
$545$	−5.71530	−	1.67816i	−0.244817	−	0.0718846i
$546$	3.03644	+	21.1189i	0.129948	+	0.903806i
$547$	2.81686	−	6.16806i	0.120440	−	0.263727i	−0.839804	−	0.542890i	$-0.817330\pi$
$547$	2.81686	−	6.16806i	0.120440	−	0.263727i	0.960244	+	0.279163i	$0.0900571\pi$
$548$	−4.63484	+	32.2360i	−0.197990	+	1.37705i
$549$	10.6702	+	6.85734i	0.455394	+	0.292664i
$550$	7.59217	+	8.76184i	0.323731	+	0.373606i
$551$	1.29509			0.0551728
$552$	−36.0596	−	55.8569i	−1.53480	−	2.37743i
$553$	−8.75589			−0.372338
$554$	−11.8303	−	13.6529i	−0.502622	−	0.580057i
$555$	−3.27652	−	2.10569i	−0.139081	−	0.0893816i
$556$	7.14611	−	49.7023i	0.303063	−	2.10785i
$557$	2.01072	−	4.40287i	0.0851971	−	0.186556i	−0.862238	−	0.506503i	$-0.830938\pi$
$557$	2.01072	−	4.40287i	0.0851971	−	0.186556i	0.947435	+	0.319947i	$0.103665\pi$
$558$	3.00491	+	20.8996i	0.127208	+	0.884752i
$559$	38.0208	+	11.1639i	1.60811	+	0.472184i
$560$	−13.7543	+	8.83937i	−0.581227	+	0.373532i
$561$	−0.586710	−	1.28472i	−0.0247709	−	0.0542407i
$562$	−59.0810	+	17.3477i	−2.49218	+	0.731770i
$563$	−20.6495	+	23.8308i	−0.870272	+	1.00435i	0.129646	+	0.991560i	$0.458616\pi$
$563$	−20.6495	+	23.8308i	−0.870272	+	1.00435i	−0.999918	+	0.0127869i	$0.995930\pi$
$564$	−57.7923	+	66.6959i	−2.43350	+	2.80840i
$565$	−16.5835	+	4.86936i	−0.697674	+	0.204856i
$566$	−27.2250	−	59.6144i	−1.14435	−	2.50578i
$567$	3.88119	−	2.49429i	0.162995	−	0.104750i
$568$	62.6806	+	18.4047i	2.63002	+	0.772243i
$569$	−3.43607	−	23.8984i	−0.144047	−	1.00187i	−0.925727	−	0.378192i	$-0.876546\pi$
$569$	−3.43607	−	23.8984i	−0.144047	−	1.00187i	0.781680	−	0.623680i	$-0.214363\pi$
$570$	−0.228152	+	0.499582i	−0.00955622	+	0.0209252i
$571$	−6.25356	+	43.4944i	−0.261703	+	1.82019i	0.258349	+	0.966052i	$0.416822\pi$
$571$	−6.25356	+	43.4944i	−0.261703	+	1.82019i	−0.520052	+	0.854134i	$0.674088\pi$
$572$	−110.653	−	71.1124i	−4.62664	−	2.97336i
$573$	−8.00754	−	9.24120i	−0.334520	−	0.386057i
$574$	20.8775			0.871411
$575$	1.34167	−	4.60434i	0.0559516	−	0.192014i
$576$	−39.5084			−1.64618
$577$	28.2167	+	32.5638i	1.17468	+	1.35565i	0.921571	+	0.388210i	$0.126907\pi$
$577$	28.2167	+	32.5638i	1.17468	+	1.35565i	0.253106	+	0.967439i	$0.418548\pi$
$578$	39.3428	+	25.2841i	1.63645	+	1.05168i
$579$	−2.75710	+	19.1760i	−0.114581	+	0.796929i
$580$	21.0817	−	46.1625i	0.875371	−	1.91679i
$581$	−1.42145	−	9.88641i	−0.0589717	−	0.410158i
$582$	−27.4346	−	8.05553i	−1.13720	−	0.333912i
$583$	−41.2953	+	26.5389i	−1.71028	+	1.09913i
$584$	37.5789	+	82.2863i	1.55503	+	3.40503i
$585$	−5.75357	+	1.68940i	−0.237881	+	0.0698481i
$586$	−32.1903	+	37.1496i	−1.32977	+	1.53464i
$587$	−15.2550	+	17.6052i	−0.629642	+	0.726645i	−0.977508	−	0.210899i	$-0.932361\pi$
$587$	−15.2550	+	17.6052i	−0.629642	+	0.726645i	0.347866	+	0.937544i	$0.386906\pi$
$588$	−7.48017	+	2.19638i	−0.308477	+	0.0905771i
$589$	−0.423512	−	0.927362i	−0.0174505	−	0.0382113i
$590$	4.79014	−	3.07843i	0.197207	−	0.126737i
$591$	−3.82194	−	1.12222i	−0.157214	−	0.0461621i
$592$	6.53372	+	45.4430i	0.268534	+	1.86770i
$593$	−1.02930	+	2.25386i	−0.0422684	+	0.0925548i	−0.929588	−	0.368600i	$-0.879837\pi$
$593$	−1.02930	+	2.25386i	−0.0422684	+	0.0925548i	0.887320	+	0.461154i	$0.152565\pi$
$594$	−9.32832	+	64.8799i	−0.382745	+	2.66205i
$595$	0.203966	+	0.131081i	0.00836177	+	0.00537379i
$596$	51.3103	+	59.2152i	2.10175	+	2.42555i
$597$	1.39065			0.0569156
$598$	0.151789	+	73.7716i	0.00620713	+	3.01675i
$599$	26.9592			1.10152			0.550762	−	0.834663i	$-0.314337\pi$
$599$	26.9592			1.10152			0.550762	+	0.834663i	$0.314337\pi$
$600$	9.07842	+	10.4771i	0.370625	+	0.427724i
$601$	−27.6154	−	17.7474i	−1.12646	−	0.723930i	−0.161640	−	0.986850i	$-0.551678\pi$
$601$	−27.6154	−	17.7474i	−1.12646	−	0.723930i	−0.964818	+	0.262919i	$0.915315\pi$
$602$	−2.79378	+	19.4312i	−0.113866	+	0.791955i
$603$	1.65279	−	3.61911i	0.0673069	−	0.147382i
$604$	−18.1819	−	126.458i	−0.739810	−	5.14549i
$605$	−6.36899	−	1.87010i	−0.258936	−	0.0760305i
$606$	−17.1163	+	11.0000i	−0.695301	+	0.446843i
$607$	14.1666	+	31.0206i	0.575005	+	1.25909i	0.944089	+	0.329690i	$0.106944\pi$
$607$	14.1666	+	31.0206i	0.575005	+	1.25909i	−0.369084	+	0.929396i	$0.620329\pi$
$608$	3.46057	−	1.01612i	0.140345	−	0.0412090i
$609$	8.20124	−	9.46474i	0.332331	−	0.383530i
$610$	−21.3072	+	24.5899i	−0.862705	+	0.995614i
$611$	60.5237	−	17.7714i	2.44853	−	0.718952i
$612$	0.609196	+	1.33395i	0.0246253	+	0.0539218i
$613$	−38.6946	+	24.8675i	−1.56286	+	1.00439i	−0.581200	+	0.813761i	$0.697416\pi$
$613$	−38.6946	+	24.8675i	−1.56286	+	1.00439i	−0.981662	+	0.190629i	$0.938947\pi$
$614$	10.3135	+	3.02831i	0.416219	+	0.122213i
$615$	−1.49287	−	10.3832i	−0.0601985	−	0.418690i
$616$	17.4373	−	38.1823i	0.702567	−	1.53841i
$617$	−6.14009	+	42.7053i	−0.247191	+	1.71925i	0.367110	+	0.930178i	$0.380347\pi$
$617$	−6.14009	+	42.7053i	−0.247191	+	1.71925i	−0.614301	+	0.789072i	$0.710562\pi$
$618$	−50.3234	−	32.3409i	−2.02431	−	1.30094i
$619$	7.94113	+	9.16455i	0.319181	+	0.368354i	0.892554	−	0.450940i	$-0.148911\pi$
$619$	7.94113	+	9.16455i	0.319181	+	0.368354i	−0.573374	+	0.819294i	$0.694366\pi$
$620$	−39.9490			−1.60439
$621$	24.6409	−	11.3144i	0.988805	−	0.454033i
$622$	−1.80116			−0.0722199
$623$	0.409567	+	0.472665i	0.0164090	+	0.0189369i
$624$	−106.307	−	68.3191i	−4.25567	−	2.73495i
$625$	−0.142315	+	0.989821i	−0.00569259	+	0.0395929i
$626$	−6.35712	+	13.9201i	−0.254081	+	0.556361i
$627$	−0.118911	−	0.827041i	−0.00474883	−	0.0330288i
$628$	−16.8103	−	4.93594i	−0.670803	−	0.196965i
$629$	0.572736	−	0.368075i	0.0228365	−	0.0146761i
$630$	−1.23407	−	2.70223i	−0.0491665	−	0.107660i
$631$	13.4047	−	3.93597i	0.533632	−	0.156689i	−0.00380433	−	0.999993i	$-0.501211\pi$
$631$	13.4047	−	3.93597i	0.533632	−	0.156689i	0.537437	+	0.843304i	$0.319393\pi$
$632$	57.3089	−	66.1380i	2.27963	−	2.63083i
$633$	−11.3689	+	13.1205i	−0.451875	+	0.521492i
$634$	22.0665	−	6.47932i	0.876374	−	0.257327i
$635$	−1.26825	−	2.77709i	−0.0503291	−	0.110205i
$636$	−76.6562	+	49.2639i	−3.03962	+	1.95344i
$637$	5.34656	+	1.56989i	0.211838	+	0.0622013i
$638$	14.8974	+	103.613i	0.589792	+	4.10210i
$639$	−2.92189	+	6.39804i	−0.115588	+	0.253103i
$640$	7.26655	−	50.5399i	0.287235	−	1.99777i
$641$	−9.57686	−	6.15468i	−0.378263	−	0.243095i	0.337669	−	0.941265i	$-0.390362\pi$
$641$	−9.57686	−	6.15468i	−0.378263	−	0.243095i	−0.715932	+	0.698170i	$0.753998\pi$
$642$	0.384178	+	0.443365i	0.0151623	+	0.0174982i
$643$	30.5167			1.20346			0.601732	−	0.798698i	$-0.294478\pi$
$643$	30.5167			1.20346			0.601732	+	0.798698i	$0.294478\pi$
$644$	−26.6731	+	3.89104i	−1.05107	+	0.153328i
$645$	9.86361			0.388379
$646$	−0.0628684	−	0.0725539i	−0.00247352	−	0.00285460i
$647$	−17.0794	−	10.9762i	−0.671459	−	0.431521i	0.159992	−	0.987118i	$-0.448853\pi$
$647$	−17.0794	−	10.9762i	−0.671459	−	0.431521i	−0.831451	+	0.555598i	$0.812490\pi$
$648$	−6.56237	+	45.6423i	−0.257794	+	1.79300i
$649$	−3.59859	+	7.87981i	−0.141257	+	0.309309i
$650$	−2.18916	−	15.2259i	−0.0858657	−	0.597209i
$651$	−9.45921	−	2.77747i	−0.370736	−	0.108858i
$652$	53.3038	−	34.2563i	2.08754	−	1.34158i
$653$	−4.03691	−	8.83960i	−0.157976	−	0.345920i	0.814049	−	0.580796i	$-0.197259\pi$
$653$	−4.03691	−	8.83960i	−0.157976	−	0.345920i	−0.972025	+	0.234876i	$0.924532\pi$
$654$	21.8837	−	6.42564i	0.855722	−	0.251263i
$655$	6.12506	−	7.06870i	0.239326	−	0.276197i
$656$	−80.9741	+	93.4491i	−3.16151	+	3.64857i
$657$	−9.34531	+	2.74403i	−0.364595	+	0.107055i
$658$	12.9816	+	28.4257i	0.506075	+	1.10815i
$659$	13.1292	−	8.43765i	0.511443	−	0.328684i	−0.259336	−	0.965787i	$-0.583504\pi$
$659$	13.1292	−	8.43765i	0.511443	−	0.328684i	0.770779	+	0.637103i	$0.219867\pi$
$660$	−31.4148	−	9.22423i	−1.22282	−	0.359052i
$661$	−3.56402	−	24.7883i	−0.138624	−	0.964152i	−0.933806	−	0.357781i	$-0.883533\pi$
$661$	−3.56402	−	24.7883i	−0.138624	−	0.964152i	0.795181	−	0.606372i	$-0.207376\pi$
$662$	10.0493	−	22.0048i	0.390576	−	0.855242i
$663$	−0.266686	+	1.85484i	−0.0103572	+	0.0720362i
$664$	83.9811	+	53.9714i	3.25910	+	2.09450i
$665$	0.0939308	+	0.108402i	0.00364248	+	0.00420365i
$666$	−8.34170			−0.323234
$667$	32.6669	−	28.4239i	1.26487	−	1.10058i
$668$	−29.8514			−1.15499
$669$	−3.84269	−	4.43470i	−0.148567	−	0.171456i
$670$	8.58607	+	5.51793i	0.331709	+	0.213176i
$671$	7.04461	−	48.9964i	0.271954	−	1.89148i
$672$	14.4883	−	31.7250i	0.558899	−	1.22382i
$673$	3.04684	+	21.1912i	0.117447	+	0.816863i	0.960350	+	0.278797i	$0.0899356\pi$
$673$	3.04684	+	21.1912i	0.117447	+	0.816863i	−0.842903	+	0.538066i	$0.819155\pi$
$674$	33.9042	+	9.95516i	1.30594	+	0.383459i
$675$	−4.75623	+	3.05664i	−0.183067	+	0.117650i
$676$	42.1450	+	92.2846i	1.62096	+	3.54941i
$677$	−12.6556	+	3.71603i	−0.486395	+	0.142818i	−0.515730	−	0.856751i	$-0.672479\pi$
$677$	−12.6556	+	3.71603i	−0.486395	+	0.142818i	0.0293350	+	0.999570i	$0.490661\pi$
$678$	43.3378	−	50.0144i	1.66438	−	1.92079i
$679$	−4.89016	+	5.64355i	−0.187667	+	0.216580i
$680$	−2.32512	+	0.682716i	−0.0891641	+	0.0261810i
$681$	−7.07967	−	15.5023i	−0.271294	−	0.594050i
$682$	69.3216	−	44.5503i	2.65446	−	1.70592i
$683$	−1.10751	−	0.325194i	−0.0423776	−	0.0124432i	0.260475	−	0.965481i	$-0.416121\pi$
$683$	−1.10751	−	0.325194i	−0.0423776	−	0.0124432i	−0.302853	+	0.953037i	$0.597939\pi$
$684$	0.123468	+	0.858737i	0.00472091	+	0.0328346i
$685$	2.40705	−	5.27070i	0.0919686	−	0.201383i
$686$	−0.392866	+	2.73244i	−0.0149997	+	0.104325i
$687$	11.3080	+	7.26724i	0.431429	+	0.277262i
$688$	−76.1393	−	87.8695i	−2.90279	−	3.34999i
$689$	65.1302			2.48126
$690$	5.20973	+	17.6086i	0.198331	+	0.670348i
$691$	−1.03900			−0.0395254			−0.0197627	−	0.999805i	$-0.506291\pi$
$691$	−1.03900			−0.0395254			−0.0197627	+	0.999805i	$0.506291\pi$
$692$	22.2882	+	25.7220i	0.847272	+	0.977803i
$693$	3.80201	+	2.44340i	0.144426	+	0.0928172i
$694$	2.54429	−	17.6959i	0.0965797	−	0.671727i
$695$	−3.71125	+	8.12650i	−0.140776	+	0.308256i
$696$	17.8137	+	123.897i	0.675226	+	4.69630i
$697$	1.75937	+	0.516597i	0.0666408	+	0.0195675i
$698$	−0.0592951	+	0.0381066i	−0.00224435	+	0.00144236i
$699$	−14.2200	−	31.1374i	−0.537849	−	1.17772i
$700$	5.39291	−	1.58350i	0.203833	−	0.0598507i
$701$	−14.6108	+	16.8618i	−0.551842	+	0.636860i	−0.961311	−	0.275464i	$-0.911168\pi$
$701$	−14.6108	+	16.8618i	−0.551842	+	0.636860i	0.409469	+	0.912324i	$0.365714\pi$
$702$	56.9523	−	65.7265i	2.14953	−	2.48069i
$703$	0.386454	−	0.113473i	0.0145754	−	0.00427973i
$704$	64.0518	+	140.254i	2.41404	+	5.28602i
$705$	13.2089	−	8.48884i	0.497476	−	0.319708i
$706$	3.62677	+	1.06491i	0.136495	+	0.0400786i
$707$	0.756223	+	5.25965i	0.0284407	+	0.197809i
$708$	−6.68004	+	14.6272i	−0.251051	+	0.549725i
$709$	0.794134	−	5.52332i	0.0298243	−	0.207433i	−0.969460	−	0.245248i	$-0.921131\pi$
$709$	0.794134	−	5.52332i	0.0298243	−	0.207433i	0.999285	+	0.0378150i	$0.0120398\pi$
$710$	−15.1789	−	9.75486i	−0.569653	−	0.366093i
$711$	6.17038	+	7.12100i	0.231407	+	0.267058i
$712$	−6.25099			−0.234266
$713$	−31.0357	−	14.0964i	−1.16230	−	0.527915i
$714$	−0.928352			−0.0347427
$715$	15.3251	+	17.6861i	0.573127	+	0.661424i
$716$	−11.4096	−	7.33250i	−0.426396	−	0.274028i
$717$	2.59410	−	18.0424i	0.0968785	−	0.673805i
$718$	22.5484	−	49.3741i	0.841498	−	1.84262i
$719$	4.08590	+	28.4180i	0.152378	+	1.05981i	0.912218	+	0.409704i	$0.134368\pi$
$719$	4.08590	+	28.4180i	0.152378	+	1.05981i	−0.759840	+	0.650110i	$0.774723\pi$
$720$	16.8817	+	4.95693i	0.629146	+	0.184734i
$721$	−13.1428	+	8.44636i	−0.489463	+	0.314559i
$722$	21.7650	+	47.6588i	0.810011	+	1.77368i
$723$	8.31653	−	2.44195i	0.309295	−	0.0908172i
$724$	4.00710	−	4.62444i	0.148923	−	0.171866i
$725$	−5.91277	+	6.82370i	−0.219595	+	0.253426i
$726$	24.3867	−	7.16058i	0.905075	−	0.265754i
$727$	−19.8521	−	43.4701i	−0.736275	−	1.61222i	−0.789587	−	0.613639i	$-0.789705\pi$
$727$	−19.8521	−	43.4701i	−0.736275	−	1.61222i	0.0533124	−	0.998578i	$-0.483022\pi$
$728$	−46.8524	+	30.1102i	−1.73647	+	1.11596i
$729$	−27.3366	−	8.02674i	−1.01247	−	0.297287i
$730$	−3.55577	−	24.7309i	−0.131605	−	0.915332i
$731$	−0.716242	+	1.56835i	−0.0264912	+	0.0580076i
$732$	13.0769	−	90.9517i	0.483335	−	3.36167i
$733$	20.7994	+	13.3670i	0.768243	+	0.493720i	0.865113	−	0.501577i	$-0.167247\pi$
$733$	20.7994	+	13.3670i	0.768243	+	0.493720i	−0.0968700	+	0.995297i	$0.530883\pi$
$734$	28.2013	+	32.5461i	1.04093	+	1.20130i
$735$	1.38704			0.0511617
$736$	64.9870	−	101.581i	2.39545	−	3.74431i
$737$	−15.5273			−0.571956
$738$	−14.7126	−	16.9793i	−0.541580	−	0.625017i
$739$	34.1070	+	21.9193i	1.25465	+	0.806313i	0.987542	−	0.157354i	$-0.0502964\pi$
$739$	34.1070	+	21.9193i	1.25465	+	0.806313i	0.267106	+	0.963667i	$0.413933\pi$
$740$	2.24610	−	15.6220i	0.0825683	−	0.574275i
$741$	−0.460534	+	1.00843i	−0.0169181	+	0.0370456i
$742$	4.59192	+	31.9375i	0.168575	+	1.17246i
$743$	12.1849	+	3.57782i	0.447022	+	0.131257i	0.497493	−	0.867468i	$-0.334254\pi$
$743$	12.1849	+	3.57782i	0.447022	+	0.131257i	−0.0504711	+	0.998726i	$0.516072\pi$
$744$	82.8920	−	53.2715i	3.03897	−	1.95303i
$745$	−5.79103	−	12.6806i	−0.212167	−	0.464581i
$746$	2.20515	−	0.647490i	0.0807362	−	0.0237063i
$747$	−7.03872	+	8.12312i	−0.257533	+	0.297209i
$748$	3.74786	−	4.32526i	0.137035	−	0.158147i
$749$	0.147008	−	0.0431656i	0.00537157	−	0.00157724i
$750$	−1.59061	−	3.48296i	−0.0580810	−	0.127180i
$751$	29.5239	−	18.9739i	1.07734	−	0.692366i	0.123401	−	0.992357i	$-0.460620\pi$
$751$	29.5239	−	18.9739i	1.07734	−	0.692366i	0.953942	+	0.299991i	$0.0969836\pi$
$752$	−177.585	−	52.1436i	−6.47585	−	1.90148i
$753$	3.80478	+	26.4628i	0.138654	+	0.964359i
$754$	57.6967	−	126.338i	2.10119	−	4.60096i
$755$	−3.23487	+	22.4990i	−0.117729	+	0.818823i
$756$	26.7328	+	17.1801i	0.972262	+	0.624835i
$757$	−31.2037	−	36.0110i	−1.13412	−	1.30884i	−0.945068	−	0.326872i	$-0.894005\pi$
$757$	−31.2037	−	36.0110i	−1.13412	−	1.30884i	−0.189048	−	0.981968i	$-0.560540\pi$
$758$	−0.656269			−0.0238368
$759$	−21.1508	−	18.2512i	−0.767724	−	0.662476i
$760$	−1.43361			−0.0520026
$761$	35.4358	+	40.8951i	1.28455	+	1.48244i	0.789741	+	0.613441i	$0.210215\pi$
$761$	35.4358	+	40.8951i	1.28455	+	1.48244i	0.494805	+	0.869004i	$0.335239\pi$
$762$	9.83408	+	6.31998i	0.356251	+	0.228949i
$763$	0.847710	−	5.89595i	0.0306892	−	0.213448i
$764$	20.5838	−	45.0722i	0.744696	−	1.63066i
$765$	−0.0371316	−	0.258256i	−0.00134249	−	0.00933725i
$766$	64.0235	+	18.7990i	2.31326	+	0.679235i
$767$	9.66910	−	6.21395i	0.349131	−	0.224373i
$768$	38.9078	+	85.1961i	1.40396	+	3.07425i
$769$	−2.13731	+	0.627569i	−0.0770732	+	0.0226307i	−0.320042	−	0.947403i	$-0.603697\pi$
$769$	−2.13731	+	0.627569i	−0.0770732	+	0.0226307i	0.242969	+	0.970034i	$0.421879\pi$
$770$	−7.59217	+	8.76184i	−0.273603	+	0.315755i
$771$	−2.63722	+	3.04351i	−0.0949771	+	0.109609i
$772$	−75.3246	+	22.1173i	−2.71099	+	0.796019i
$773$	16.1180	+	35.2934i	0.579723	+	1.26942i	0.941457	+	0.337134i	$0.109458\pi$
$773$	16.1180	+	35.2934i	0.579723	+	1.26942i	−0.361734	+	0.932281i	$0.617815\pi$
$774$	17.7718	−	11.4212i	0.638795	−	0.410528i
$775$	6.81972	+	2.00245i	0.244971	+	0.0719301i
$776$	−10.6218	−	73.8762i	−0.381300	−	2.65200i
$777$	1.61796	−	3.54284i	0.0580440	−	0.127099i
$778$	9.90945	−	68.9218i	0.355271	−	2.47096i
$779$	0.912579	+	0.586479i	0.0326965	+	0.0210128i
$780$	28.4480	+	32.8307i	1.01860	+	1.17553i
$781$	27.4499			0.982236
$782$	−3.17814	−	0.450275i	−0.113650	−	0.0161018i
$783$	−51.0479			−1.82430
$784$	−10.7068	−	12.3564i	−0.382387	−	0.441299i
$785$	2.62227	+	1.68523i	0.0935930	+	0.0601486i
$786$	−5.09676	+	35.4487i	−0.181795	+	1.26441i
$787$	9.00684	−	19.7222i	0.321059	−	0.703022i	−0.678440	−	0.734656i	$-0.737344\pi$
$787$	9.00684	−	19.7222i	0.321059	−	0.703022i	0.999500	+	0.0316340i	$0.0100711\pi$
$788$	−2.29713	−	15.9769i	−0.0818319	−	0.569154i
$789$	11.6121	+	3.40963i	0.413403	+	0.121386i
$790$	−20.3339	+	13.0678i	−0.723449	+	0.464932i
$791$	−7.17988	−	15.7217i	−0.255287	−	0.559001i
$792$	−43.3412	+	12.7261i	−1.54006	+	0.452203i
$793$	−43.0096	+	49.6357i	−1.52731	+	1.76262i
$794$	−54.8228	+	63.2689i	−1.94559	+	2.24533i
$795$	15.5554	−	4.56747i	0.551692	−	0.161992i
$796$	2.34096	+	5.12599i	0.0829731	+	0.181686i
$797$	21.5210	−	13.8307i	0.762312	−	0.489908i	−0.100809	−	0.994906i	$-0.532143\pi$
$797$	21.5210	−	13.8307i	0.762312	−	0.489908i	0.863121	+	0.504998i	$0.168507\pi$
$798$	−0.526967	−	0.154731i	−0.0186544	−	0.00547743i
$799$	0.390599	+	2.71668i	0.0138184	+	0.0961092i
$800$	−10.4455	+	22.8725i	−0.369305	+	0.808664i
$801$	0.0957832	−	0.666187i	0.00338433	−	0.0235385i
$802$	−55.1949	−	35.4716i	−1.94900	−	1.25255i
$803$	24.8921	+	28.7270i	0.878422	+	1.01375i
$804$	−28.8233			−1.01652
$805$	4.74841	+	0.672749i	0.167360	+	0.0237113i
$806$	−109.333			−3.85109
$807$	−9.00149	−	10.3883i	−0.316868	−	0.365685i
$808$	−44.6786	−	28.7132i	−1.57179	−	1.01013i
$809$	2.00256	−	13.9281i	0.0704064	−	0.489687i	−0.923858	−	0.382736i	$-0.874982\pi$
$809$	2.00256	−	13.9281i	0.0704064	−	0.489687i	0.994264	−	0.106952i	$-0.0341090\pi$
$810$	5.29071	−	11.5850i	0.185897	−	0.407057i
$811$	7.80832	+	54.3081i	0.274187	+	1.90701i	0.402744	+	0.915312i	$0.368056\pi$
$811$	7.80832	+	54.3081i	0.274187	+	1.90701i	−0.128557	+	0.991702i	$0.541035\pi$
$812$	48.6929	+	14.2975i	1.70879	+	0.501745i
$813$	22.5824	−	14.5128i	0.792000	−	0.508987i
$814$	13.5237	+	29.6129i	0.474007	+	1.03793i
$815$	−10.8166	+	3.17605i	−0.378890	+	0.111252i
$816$	3.60064	−	4.15536i	0.126048	−	0.145467i
$817$	−0.667968	+	0.770876i	−0.0233692	+	0.0269695i
$818$	41.3095	−	12.1296i	1.44435	−	0.424101i
$819$	−2.49102	−	5.45458i	−0.0870433	−	0.190598i
$820$	35.7596	−	22.9813i	1.24878	−	0.802543i
$821$	−3.26375	−	0.958325i	−0.113906	−	0.0334458i	0.224283	−	0.974524i	$-0.427996\pi$
$821$	−3.26375	−	0.958325i	−0.113906	−	0.0334458i	−0.338189	+	0.941078i	$0.609814\pi$
$822$	3.15744	+	21.9605i	0.110128	+	0.765960i
$823$	21.0473	−	46.0871i	0.733662	−	1.60650i	−0.0600445	−	0.998196i	$-0.519124\pi$
$823$	21.0473	−	46.0871i	0.733662	−	1.60650i	0.793707	−	0.608301i	$-0.208148\pi$
$824$	22.2220	−	154.558i	0.774141	−	5.38427i
$825$	4.90048	+	3.14934i	0.170613	+	0.109646i
$826$	3.72881	+	4.30327i	0.129742	+	0.149730i
$827$	50.8806			1.76929			0.884646	−	0.466263i	$-0.154400\pi$
$827$	50.8806			1.76929			0.884646	+	0.466263i	$0.154400\pi$
$828$	21.9614	+	18.9506i	0.763210	+	0.658580i
$829$	18.7310			0.650553			0.325277	−	0.945619i	$-0.394543\pi$
$829$	18.7310			0.650553			0.325277	+	0.945619i	$0.394543\pi$
$830$	−18.0561	−	20.8379i	−0.626738	−	0.723294i
$831$	−7.63605	−	4.90739i	−0.264892	−	0.170235i
$832$	29.1144	−	202.495i	1.00936	−	7.02026i
$833$	−0.100719	+	0.220544i	−0.00348971	+	0.00764141i
$834$	−4.86823	−	33.8593i	−0.168573	−	1.17245i
$835$	5.09595	+	1.49631i	0.176353	+	0.0517818i
$836$	2.84833	−	1.83051i	0.0985116	−	0.0633095i
$837$	16.6933	+	36.5533i	0.577005	+	1.26347i
$838$	25.2056	−	7.40103i	0.870713	−	0.255664i
$839$	−19.0777	+	22.0168i	−0.658634	+	0.760105i	−0.982553	−	0.185980i	$-0.940454\pi$
$839$	−19.0777	+	22.0168i	−0.658634	+	0.760105i	0.323919	+	0.946085i	$0.394999\pi$
$840$	−9.07842	+	10.4771i	−0.313235	+	0.361493i
$841$	−50.3962	+	14.7977i	−1.73780	+	0.510264i
$842$	−41.3671	−	90.5813i	−1.42560	−	3.12164i
$843$	−26.0272	+	16.7267i	−0.896424	+	0.576096i
$844$	−67.5004	−	19.8199i	−2.32346	−	0.682229i
$845$	−2.56881	−	17.8665i	−0.0883698	−	0.614626i
$846$	13.9698	−	30.5896i	0.480292	−	1.05169i
$847$	0.944667	−	6.57030i	0.0324591	−	0.225758i
$848$	−160.764	−	103.317i	−5.52067	−	3.54792i
$849$	−21.5639	−	24.8861i	−0.740073	−	0.854090i
$850$	0.669305			0.0229570
$851$	7.25733	−	11.3439i	0.248778	−	0.388863i
$852$	50.9551			1.74569
$853$	1.29831	+	1.49833i	0.0444532	+	0.0513017i	0.777541	−	0.628833i	$-0.216467\pi$
$853$	1.29831	+	1.49833i	0.0444532	+	0.0513017i	−0.733088	+	0.680134i	$0.761921\pi$
$854$	−27.3719	−	17.5909i	−0.936647	−	0.601947i
$855$	0.0219671	−	0.152784i	0.000751258	−	0.00522511i
$856$	−0.636144	+	1.39296i	−0.0217430	+	0.0476105i
$857$	−0.0238183	−	0.165660i	−0.000813618	−	0.00565883i	0.989411	−	0.145144i	$-0.0463644\pi$
$857$	−0.0238183	−	0.165660i	−0.000813618	−	0.00565883i	−0.990224	+	0.139485i	$0.955455\pi$
$858$	−85.9765	−	25.2450i	−2.93519	−	0.861849i
$859$	−43.7621	+	28.1242i	−1.49314	+	0.959585i	−0.497390	+	0.867527i	$0.665708\pi$
$859$	−43.7621	+	28.1242i	−1.49314	+	0.959585i	−0.995754	+	0.0920578i	$0.970656\pi$
$860$	16.6039	+	36.3576i	0.566190	+	1.23978i
$861$	10.0650	−	2.95536i	0.343015	−	0.100718i
$862$	−59.5262	+	68.6969i	−2.02747	+	2.33983i
$863$	3.06650	−	3.53893i	0.104385	−	0.120467i	−0.701153	−	0.713011i	$-0.747331\pi$
$863$	3.06650	−	3.53893i	0.104385	−	0.120467i	0.805538	+	0.592544i	$0.201876\pi$
$864$	−136.403	+	40.0517i	−4.64054	+	1.36258i
$865$	−2.51552	−	5.50822i	−0.0855302	−	0.187285i
$866$	−38.4269	+	24.6955i	−1.30580	+	0.839186i
$867$	22.5463	+	6.62018i	0.765711	+	0.224833i
$868$	−5.68534	−	39.5424i	−0.192973	−	1.34216i
$869$	15.2758	−	33.4494i	0.518198	−	1.13469i
$870$	4.92011	−	34.2201i	0.166807	−	1.16017i
$871$	17.3313	+	11.1382i	0.587250	+	0.377403i
$872$	38.9869	+	44.9933i	1.32026	+	1.52367i
$873$	8.03596			0.271976
$874$	−1.72898	−	0.785303i	−0.0584836	−	0.0265633i
$875$	−1.00000			−0.0338062
$876$	46.2070	+	53.3257i	1.56119	+	1.80171i
$877$	−10.1162	−	6.50126i	−0.341598	−	0.219532i	0.358582	−	0.933498i	$-0.383260\pi$
$877$	−10.1162	−	6.50126i	−0.341598	−	0.219532i	−0.700180	+	0.713967i	$0.746897\pi$
$878$	8.02643	−	55.8251i	0.270879	−	1.88401i
$879$	−10.2601	+	22.4665i	−0.346065	+	0.757778i
$880$	−9.77205	−	67.9661i	−0.329416	−	2.29114i
$881$	37.1523	+	10.9089i	1.25169	+	0.367530i	0.839397	−	0.543519i	$-0.182908\pi$
$881$	37.1523	+	10.9089i	1.25169	+	0.367530i	0.412297	+	0.911050i	$0.364727\pi$
$882$	2.49910	−	1.60608i	0.0841492	−	0.0540794i
$883$	13.5422	+	29.6532i	0.455730	+	0.997910i	0.988440	+	0.151612i	$0.0484465\pi$
$883$	13.5422	+	29.6532i	0.455730	+	0.997910i	−0.532710	+	0.846298i	$0.678826\pi$
$884$	−7.28594	+	2.13935i	−0.245053	+	0.0719540i
$885$	1.87354	−	2.16219i	0.0629785	−	0.0726811i
$886$	56.8103	−	65.5625i	1.90858	−	2.20262i
$887$	5.77941	−	1.69699i	0.194054	−	0.0569793i	−0.183262	−	0.983064i	$-0.558666\pi$
$887$	5.77941	−	1.69699i	0.194054	−	0.0569793i	0.377315	+	0.926085i	$0.376847\pi$
$888$	16.1712	+	35.4099i	0.542668	+	1.18828i
$889$	2.56833	−	1.65057i	0.0861391	−	0.0553582i
$890$	1.65658	+	0.486415i	0.0555286	+	0.0163047i
$891$	2.75747	+	19.1786i	0.0923787	+	0.642508i
$892$	9.87784	−	21.6295i	0.330735	−	0.724208i
$893$	−0.231079	+	1.60719i	−0.00773276	+	0.0537825i
$894$	44.9038	+	28.8579i	1.50181	+	0.965154i
$895$	1.58019	+	1.82364i	0.0528201	+	0.0609576i
$896$	51.0596			1.70578
$897$	10.5161	+	35.5437i	0.351121	+	1.18677i
$898$	−23.9484			−0.799168
$899$	42.0258	+	48.5003i	1.40164	+	1.61758i
$900$	−5.08829	−	3.27004i	−0.169610	−	0.109001i
$901$	−0.403302	+	2.80503i	−0.0134359	+	0.0934491i
$902$	−36.4237	+	79.7568i	−1.21278	+	2.65561i
$903$	1.40374	+	9.76321i	0.0467135	+	0.324899i
$904$	165.749	+	48.6682i	5.51272	+	1.61868i
$905$	−0.915854	+	0.588584i	−0.0304440	+	0.0195652i
$906$	−36.1553	−	79.1690i	−1.20118	−	2.63021i
$907$	−14.1159	+	4.14480i	−0.468710	+	0.137626i	−0.507555	−	0.861620i	$-0.669450\pi$
$907$	−14.1159	+	4.14480i	−0.468710	+	0.137626i	0.0388445	+	0.999245i	$0.487632\pi$
$908$	45.2244	−	52.1918i	1.50083	−	1.73205i
$909$	3.74466	−	4.32156i	0.124202	−	0.143337i
$910$	14.7594	−	4.33375i	0.489269	−	0.143662i
$911$	−6.98834	−	15.3023i	−0.231534	−	0.506989i	0.757830	−	0.652452i	$-0.226260\pi$
$911$	−6.98834	−	15.3023i	−0.231534	−	0.506989i	−0.989364	+	0.145464i	$0.953533\pi$
$912$	2.73645	−	1.75861i	0.0906128	−	0.0582333i
$913$	40.2482	+	11.8179i	1.33202	+	0.391117i
$914$	6.64024	+	46.1839i	0.219639	+	1.52763i
$915$	−6.79132	+	14.8709i	−0.224514	+	0.491618i
$916$	−7.75182	+	53.9151i	−0.256127	+	1.78141i
$917$	7.86843	+	5.05674i	0.259839	+	0.166988i
$918$	2.47804	+	2.85982i	0.0817876	+	0.0943880i
$919$	−18.8258			−0.621006			−0.310503	−	0.950572i	$-0.600497\pi$
$919$	−18.8258			−0.621006			−0.310503	+	0.950572i	$0.600497\pi$
$920$	−36.1609	+	31.4641i	−1.19219	+	1.03734i
$921$	5.40080			0.177962
$922$	−5.16967	−	5.96611i	−0.170254	−	0.196483i
$923$	−30.6392	−	19.6906i	−1.00850	−	0.648124i
$924$	4.65954	−	32.4078i	0.153288	−	1.06614i
$925$	−1.16649	+	2.55425i	−0.0383538	+	0.0839832i
$926$	−8.07010	−	56.1288i	−0.265200	−	1.84451i
$927$	16.1312	+	4.73654i	0.529817	+	0.155568i
$928$	−190.993	+	122.744i	−6.26964	+	4.02925i
$929$	−0.104663	−	0.229180i	−0.00343388	−	0.00751916i	0.907907	−	0.419171i	$-0.137679\pi$
$929$	−0.104663	−	0.229180i	−0.00343388	−	0.00751916i	−0.911341	+	0.411652i	$0.864952\pi$
$930$	−26.1125	+	7.66733i	−0.856263	+	0.251422i
$931$	−0.0939308	+	0.108402i	−0.00307846	+	0.00355273i
$932$	90.8362	−	104.831i	2.97544	−	3.43384i
$933$	−0.868337	+	0.254967i	−0.0284281	+	0.00834724i
$934$	−16.9033	−	37.0131i	−0.553093	−	1.21110i
$935$	−0.856604	+	0.550506i	−0.0280139	+	0.0180035i
$936$	57.5056	+	16.8852i	1.87963	+	0.551909i
$937$	5.70294	+	39.6649i	0.186307	+	1.29579i	0.841469	+	0.540306i	$0.181691\pi$
$937$	5.70294	+	39.6649i	0.186307	+	1.29579i	−0.655162	+	0.755489i	$0.727400\pi$
$938$	−4.23984	+	9.28396i	−0.138436	+	0.303132i
$939$	−1.09426	+	7.61078i	−0.0357100	+	0.248368i
$940$	53.5254	+	34.3987i	1.74581	+	1.12196i
$941$	28.1505	+	32.4874i	0.917680	+	1.05906i	0.998058	+	0.0622945i	$0.0198418\pi$
$941$	28.1505	+	32.4874i	0.917680	+	1.05906i	−0.0803780	+	0.996764i	$0.525613\pi$
$942$	−11.9353			−0.388873
$943$	35.8902	−	5.23563i	1.16875	−	0.170496i
$944$	−33.7240			−1.09762
$945$	−3.70241	−	4.27281i	−0.120440	−	0.138995i
$946$	−69.3572	−	44.5732i	−2.25500	−	1.44920i
$947$	−3.64541	+	25.3544i	−0.118460	+	0.823906i	0.840793	+	0.541357i	$0.182089\pi$
$947$	−3.64541	+	25.3544i	−0.118460	+	0.823906i	−0.959253	+	0.282549i	$0.908820\pi$
$948$	28.3565	−	62.0920i	0.920975	−	2.01665i
$949$	−7.17747	−	49.9204i	−0.232991	−	1.62049i
$950$	0.379922	+	0.111555i	0.0123263	+	0.00361933i
$951$	9.72105	−	6.24734i	0.315227	−	0.202584i
$952$	−1.00667	−	2.20429i	−0.0326262	−	0.0714414i
$953$	0.250340	−	0.0735064i	0.00810930	−	0.00238110i	−0.277675	−	0.960675i	$-0.589564\pi$
$953$	0.250340	−	0.0735064i	0.00810930	−	0.00238110i	0.285785	+	0.958294i	$0.407746\pi$
$954$	22.7382	−	26.2413i	0.736177	−	0.849594i
$955$	−5.77312	+	6.66254i	−0.186814	+	0.215595i
$956$	70.8715	−	20.8097i	2.29215	−	0.673035i
$957$	21.8492	+	47.8431i	0.706285	+	1.54655i
$958$	30.9350	−	19.8807i	0.999465	−	0.642317i
$959$	5.55961	+	1.63245i	0.179529	+	0.0527146i
$960$	−7.24710	−	50.4047i	−0.233899	−	1.62681i
$961$	8.10821	−	17.7545i	0.261555	−	0.572726i
$962$	6.14715	−	42.7544i	0.198192	−	1.37846i
$963$	−0.138704	−	0.0891400i	−0.00446969	−	0.00287249i
$964$	23.0008	+	26.5443i	0.740805	+	0.854934i
$965$	13.9673			0.449624
$966$	−16.6879	+	7.66267i	−0.536926	+	0.246542i
$967$	38.6228			1.24202			0.621012	−	0.783801i	$-0.286722\pi$
$967$	38.6228			1.24202			0.621012	+	0.783801i	$0.286722\pi$
$968$	43.4461	+	50.1394i	1.39641	+	1.61154i
$969$	−0.0405793	−	0.0260787i	−0.00130359	−	0.000837769i
$970$	−2.93372	+	20.4045i	−0.0941961	+	0.655148i
$971$	3.59448	−	7.87080i	0.115352	−	0.252586i	−0.843146	−	0.537685i	$-0.819299\pi$
$971$	3.59448	−	7.87080i	0.115352	−	0.252586i	0.958498	+	0.285099i	$0.0920264\pi$
$972$	−8.44848	−	58.7605i	−0.270985	−	1.88474i
$973$	−8.57195	−	2.51695i	−0.274804	−	0.0806898i
$974$	−56.5391	+	36.3354i	−1.81163	+	1.16426i
$975$	−3.21072	−	7.03050i	−0.102825	−	0.225156i
$976$	184.901	−	54.2917i	5.91852	−	1.73784i
$977$	−39.3064	+	45.3620i	−1.25752	+	1.45126i	−0.417529	+	0.908664i	$0.637104\pi$
$977$	−39.3064	+	45.3620i	−1.25752	+	1.45126i	−0.839994	+	0.542595i	$0.817442\pi$
$978$	28.2671	−	32.6220i	0.903883	−	1.04314i
$979$	−2.52023	+	0.740007i	−0.0805470	+	0.0236507i
$980$	2.33488	+	5.11266i	0.0745849	+	0.163318i
$981$	−5.39246	+	3.46552i	−0.172168	+	0.110646i
$982$	12.9778	+	3.81062i	0.414137	+	0.121602i
$983$	−1.86348	−	12.9608i	−0.0594357	−	0.413385i	−0.997718	−	0.0675148i	$-0.978493\pi$
$983$	−1.86348	−	12.9608i	−0.0594357	−	0.413385i	0.938283	−	0.345870i	$-0.112416\pi$
$984$	−43.5540	+	95.3700i	−1.38845	+	3.04028i
$985$	−0.408700	+	2.84257i	−0.0130223	+	0.0905718i
$986$	5.08386	+	3.26720i	0.161903	+	0.104049i
$987$	10.2823	+	11.8664i	0.327288	+	0.377710i
$988$	−4.49234			−0.142920
$989$	0.0701718	+	34.1044i	0.00223133	+	1.08446i
$990$	12.4761			0.396518
$991$	−14.8855	−	17.1787i	−0.472852	−	0.545700i	0.468351	−	0.883543i	$-0.344848\pi$
$991$	−14.8855	−	17.1787i	−0.472852	−	0.545700i	−0.941203	+	0.337842i	$0.890303\pi$
$992$	150.348	+	96.6231i	4.77357	+	3.06779i
$993$	1.72980	−	12.0311i	0.0548937	−	0.381794i
$994$	7.49539	−	16.4126i	0.237739	−	0.520577i
$995$	−0.142686	−	0.992401i	−0.00452344	−	0.0314612i
$996$	74.7125	+	21.9376i	2.36736	+	0.695119i
$997$	−6.61335	+	4.25014i	−0.209447	+	0.134603i	−0.641159	−	0.767408i	$-0.721546\pi$
$997$	−6.61335	+	4.25014i	−0.209447	+	0.134603i	0.431712	+	0.902012i	$0.357910\pi$
$998$	4.42118	+	9.68104i	0.139950	+	0.306448i
$999$	−15.2326	+	4.47271i	−0.481939	+	0.141510i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	805.2.u.d.36.13	✓	130
23.16	even	11	inner	805.2.u.d.246.13	yes	130

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.u.d.36.13	✓	130	1.1	even	1	trivial
805.2.u.d.246.13	yes	130	23.16	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 805 = 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	805.u (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.80777 + 2.08628i) q^{2} +(1.16685 + 0.749889i) q^{3} +(-0.799893 + 5.56338i) q^{4} +(0.415415 - 0.909632i) q^{5} +(0.544920 + 3.79000i) q^{6} +(0.959493 + 0.281733i) q^{7} +(-8.40814 + 5.40358i) q^{8} +(-0.447039 - 0.978878i) q^{9} +O(q^{10})\)	\(q+(1.80777 + 2.08628i) q^{2} +(1.16685 + 0.749889i) q^{3} +(-0.799893 + 5.56338i) q^{4} +(0.415415 - 0.909632i) q^{5} +(0.544920 + 3.79000i) q^{6} +(0.959493 + 0.281733i) q^{7} +(-8.40814 + 5.40358i) q^{8} +(-0.447039 - 0.978878i) q^{9} +(2.64872 - 0.777734i) q^{10} +(-2.75025 + 3.17396i) q^{11} +(-5.10527 + 5.89180i) q^{12} +(5.34656 - 1.56989i) q^{13} +(1.14677 + 2.51108i) q^{14} +(1.16685 - 0.749889i) q^{15} +(-15.6875 - 4.60627i) q^{16} +(0.0345049 + 0.239987i) q^{17} +(1.23407 - 2.70223i) q^{18} +(-0.0204131 + 0.141976i) q^{19} +(4.72834 + 3.03872i) q^{20} +(0.908317 + 1.04825i) q^{21} -11.5936 q^{22} +(2.60112 + 4.02917i) q^{23} -13.8631 q^{24} +(-0.654861 - 0.755750i) q^{25} +(12.9406 + 8.31640i) q^{26} +(0.804611 - 5.59619i) q^{27} +(-2.33488 + 5.11266i) q^{28} +(-1.28497 - 8.93715i) q^{29} +(3.67387 + 1.07875i) q^{30} +(-5.97932 + 3.84267i) q^{31} +(-10.4455 - 22.8725i) q^{32} +(-5.58925 + 1.64115i) q^{33} +(-0.438302 + 0.505827i) q^{34} +(0.654861 - 0.755750i) q^{35} +(5.80345 - 1.70405i) q^{36} +(-1.16649 - 2.55425i) q^{37} +(-0.333104 + 0.214073i) q^{38} +(7.41587 + 2.17750i) q^{39} +(1.42240 + 9.89304i) q^{40} +(3.14172 - 6.87940i) q^{41} +(-0.544920 + 3.79000i) q^{42} +(5.98239 + 3.84465i) q^{43} +(-15.4580 - 17.8395i) q^{44} -1.07613 q^{45} +(-3.70374 + 12.7105i) q^{46} +11.3201 q^{47} +(-14.8508 - 17.1387i) q^{48} +(0.841254 + 0.540641i) q^{49} +(0.392866 - 2.73244i) q^{50} +(-0.139701 + 0.305903i) q^{51} +(4.45722 + 31.0006i) q^{52} +(11.2148 + 3.29297i) q^{53} +(13.1298 - 8.43799i) q^{54} +(1.74464 + 3.82022i) q^{55} +(-9.58991 + 2.81585i) q^{56} +(-0.130286 + 0.150358i) q^{57} +(16.3224 - 18.8371i) q^{58} +(1.97910 - 0.581117i) q^{59} +(3.23856 + 7.09146i) q^{60} +(-9.91541 + 6.37225i) q^{61} +(-18.8261 - 5.52784i) q^{62} +(-0.153149 - 1.06517i) q^{63} +(15.2513 - 33.3958i) q^{64} +(0.793017 - 5.51555i) q^{65} +(-13.5280 - 8.69389i) q^{66} +(2.42115 + 2.79416i) q^{67} -1.36274 q^{68} +(0.0136868 + 6.65199i) q^{69} +2.76054 q^{70} +(-4.28023 - 4.93965i) q^{71} +(9.04821 + 5.81493i) q^{72} +(1.28807 - 8.95872i) q^{73} +(3.22013 - 7.05111i) q^{74} +(-0.197396 - 1.37292i) q^{75} +(-0.773539 - 0.227132i) q^{76} +(-3.53305 + 2.27055i) q^{77} +(8.86333 + 19.4080i) q^{78} +(-8.40121 + 2.46682i) q^{79} +(-10.7068 + 12.3564i) q^{80} +(3.02125 - 3.48671i) q^{81} +(20.0318 - 5.88188i) q^{82} +(-4.14920 - 9.08547i) q^{83} +(-6.55838 + 4.21482i) q^{84} +(0.232633 + 0.0683073i) q^{85} +(2.79378 + 19.4312i) q^{86} +(5.20251 - 11.3919i) q^{87} +(5.97374 - 41.5483i) q^{88} +(0.526142 + 0.338131i) q^{89} +(-1.94539 - 2.24510i) q^{90} +5.57227 q^{91} +(-24.4964 + 11.2481i) q^{92} -9.85855 q^{93} +(20.4642 + 23.6169i) q^{94} +(0.120666 + 0.0775475i) q^{95} +(4.96348 - 34.5217i) q^{96} +(-3.10211 + 6.79267i) q^{97} +(0.392866 + 2.73244i) q^{98} +(4.33639 + 1.27328i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 130 q + 2 q^{2} + 2 q^{3} - 16 q^{4} - 13 q^{5} + 5 q^{6} + 13 q^{7} - 7 q^{8} - 39 q^{9}+O(q^{10}) \) 130 * q + 2 * q^2 + 2 * q^3 - 16 * q^4 - 13 * q^5 + 5 * q^6 + 13 * q^7 - 7 * q^8 - 39 * q^9	\( 130 q + 2 q^{2} + 2 q^{3} - 16 q^{4} - 13 q^{5} + 5 q^{6} + 13 q^{7} - 7 q^{8} - 39 q^{9} + 2 q^{10} + 2 q^{11} - 5 q^{12} + 13 q^{13} - 2 q^{14} + 2 q^{15} - 6 q^{16} - 51 q^{17} + q^{18} - 9 q^{19} - 16 q^{20} - 2 q^{21} + 34 q^{22} - 10 q^{23} - 76 q^{24} - 13 q^{25} - 31 q^{26} + 14 q^{27} + 27 q^{28} + 3 q^{29} + 5 q^{30} + 6 q^{31} + 22 q^{32} - 58 q^{33} + q^{34} + 13 q^{35} + 193 q^{36} - 36 q^{37} + 4 q^{38} - 2 q^{39} - 29 q^{40} - 34 q^{41} - 5 q^{42} - 22 q^{43} + 8 q^{44} + 170 q^{45} - 198 q^{46} - 14 q^{47} - 120 q^{48} - 13 q^{49} + 2 q^{50} - 6 q^{51} + 33 q^{52} - 18 q^{53} + 188 q^{54} - 31 q^{55} - 15 q^{56} - 9 q^{57} + 114 q^{58} + 46 q^{59} - 16 q^{60} - 56 q^{61} - 146 q^{62} + 17 q^{63} - 109 q^{64} + 2 q^{65} - 14 q^{66} - 10 q^{67} + 86 q^{68} - 6 q^{69} - 2 q^{70} - 25 q^{72} + 64 q^{73} + 79 q^{74} + 2 q^{75} + 32 q^{76} - 13 q^{77} - 64 q^{78} - 118 q^{79} - 17 q^{80} + 23 q^{81} + 129 q^{82} - 117 q^{83} - 72 q^{84} - 7 q^{85} + 74 q^{86} - 51 q^{87} - 40 q^{88} - 35 q^{89} + 100 q^{90} + 42 q^{91} + 76 q^{92} - 90 q^{93} - 7 q^{94} + 2 q^{95} + 393 q^{96} - 4 q^{97} + 2 q^{98} - 40 q^{99}+O(q^{100}) \) 130 * q + 2 * q^2 + 2 * q^3 - 16 * q^4 - 13 * q^5 + 5 * q^6 + 13 * q^7 - 7 * q^8 - 39 * q^9 + 2 * q^10 + 2 * q^11 - 5 * q^12 + 13 * q^13 - 2 * q^14 + 2 * q^15 - 6 * q^16 - 51 * q^17 + q^18 - 9 * q^19 - 16 * q^20 - 2 * q^21 + 34 * q^22 - 10 * q^23 - 76 * q^24 - 13 * q^25 - 31 * q^26 + 14 * q^27 + 27 * q^28 + 3 * q^29 + 5 * q^30 + 6 * q^31 + 22 * q^32 - 58 * q^33 + q^34 + 13 * q^35 + 193 * q^36 - 36 * q^37 + 4 * q^38 - 2 * q^39 - 29 * q^40 - 34 * q^41 - 5 * q^42 - 22 * q^43 + 8 * q^44 + 170 * q^45 - 198 * q^46 - 14 * q^47 - 120 * q^48 - 13 * q^49 + 2 * q^50 - 6 * q^51 + 33 * q^52 - 18 * q^53 + 188 * q^54 - 31 * q^55 - 15 * q^56 - 9 * q^57 + 114 * q^58 + 46 * q^59 - 16 * q^60 - 56 * q^61 - 146 * q^62 + 17 * q^63 - 109 * q^64 + 2 * q^65 - 14 * q^66 - 10 * q^67 + 86 * q^68 - 6 * q^69 - 2 * q^70 - 25 * q^72 + 64 * q^73 + 79 * q^74 + 2 * q^75 + 32 * q^76 - 13 * q^77 - 64 * q^78 - 118 * q^79 - 17 * q^80 + 23 * q^81 + 129 * q^82 - 117 * q^83 - 72 * q^84 - 7 * q^85 + 74 * q^86 - 51 * q^87 - 40 * q^88 - 35 * q^89 + 100 * q^90 + 42 * q^91 + 76 * q^92 - 90 * q^93 - 7 * q^94 + 2 * q^95 + 393 * q^96 - 4 * q^97 + 2 * q^98 - 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more