LMFDB - Embedded newform 961.2.k.a.5.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(5,961)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(961, base_ring=CyclotomicField(186)) chi = DirichletCharacter(H, H._module([88])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("961.5"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.k (of order $93$, degree $60$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$4920$
Relative dimension:	$82$ over $\Q(\zeta_{93})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{93}]$

Embedding invariants

Embedding label			5.11
Character	$\chi$	$=$	961.5
Dual form			961.2.k.a.769.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.67939 - 1.44171i) q^{2} +(-0.222135 - 2.62407i) q^{3} +(0.438970 + 2.86545i) q^{4} +(-0.0342144 - 0.0205319i) q^{5} +(-3.41010 + 4.72709i) q^{6} +(1.12782 + 1.68021i) q^{7} +(1.05238 - 1.68839i) q^{8} +(-3.87909 + 0.661492i) q^{9} +(0.0278583 + 0.0838081i) q^{10} +(3.15032 - 2.03828i) q^{11} +(7.42162 - 1.78840i) q^{12} +(1.19428 - 1.43967i) q^{13} +(0.528326 - 4.44771i) q^{14} +(-0.0462768 + 0.0943417i) q^{15} +(1.33033 - 0.417394i) q^{16} +(5.59328 - 0.760410i) q^{17} +(7.46819 + 4.48162i) q^{18} +(3.15605 + 3.10319i) q^{19} +(0.0438138 - 0.107052i) q^{20} +(4.15846 - 3.33271i) q^{21} +(-8.22922 - 1.11877i) q^{22} +(-4.59847 - 2.55236i) q^{23} +(-4.66423 - 2.38648i) q^{24} +(-2.35158 - 4.41069i) q^{25} +(-4.08124 + 0.695963i) q^{26} +(0.617237 + 2.38391i) q^{27} +(-4.31947 + 3.96926i) q^{28} +(-7.26854 - 4.03437i) q^{29} +(0.213730 - 0.0917188i) q^{30} +(0.833660 + 5.50500i) q^{31} +(-6.49247 - 2.78614i) q^{32} +(-6.04840 - 7.81388i) q^{33} +(-10.4896 - 6.78685i) q^{34} +(-0.00408977 - 0.0806435i) q^{35} +(-3.59828 - 10.8250i) q^{36} +(9.37697 + 1.59903i) q^{37} +(-0.826345 - 9.76158i) q^{38} +(-4.04308 - 2.81407i) q^{39} +(-0.0706724 + 0.0361599i) q^{40} +(7.49813 + 0.253387i) q^{41} +(-11.7885 - 0.398373i) q^{42} +(1.85544 - 5.58187i) q^{43} +(7.22349 + 8.13232i) q^{44} +(0.146302 + 0.0570125i) q^{45} +(4.04286 + 10.9161i) q^{46} +(-0.563107 - 0.312550i) q^{47} +(-1.39079 - 3.39817i) q^{48} +(1.10032 - 2.68847i) q^{49} +(-2.40971 + 10.7976i) q^{50} +(-3.23783 - 14.5082i) q^{51} +(4.64954 + 2.79016i) q^{52} +(-9.43442 - 4.43172i) q^{53} +(2.40032 - 4.89339i) q^{54} +(-0.149636 + 0.00505671i) q^{55} +(4.02375 - 0.135976i) q^{56} +(7.44193 - 8.97104i) q^{57} +(6.39032 + 17.2544i) q^{58} +(9.55433 + 1.62928i) q^{59} +(-0.290645 - 0.0911906i) q^{60} +(-6.38240 + 6.71428i) q^{61} +(6.53657 - 10.4469i) q^{62} +(-5.48636 - 5.77164i) q^{63} +(5.65853 + 11.5357i) q^{64} +(-0.0704204 + 0.0247366i) q^{65} +(-1.10773 + 21.8426i) q^{66} +(-3.26524 + 7.97810i) q^{67} +(4.63419 + 15.6934i) q^{68} +(-5.67609 + 12.6337i) q^{69} +(-0.109396 + 0.141328i) q^{70} +(7.87274 - 7.74087i) q^{71} +(-2.96543 + 7.24557i) q^{72} +(-6.66180 - 4.97898i) q^{73} +(-13.4423 - 16.2043i) q^{74} +(-11.0516 + 7.15047i) q^{75} +(-7.50662 + 10.4057i) q^{76} +(6.97773 + 2.99438i) q^{77} +(2.73284 + 10.5549i) q^{78} +(0.826318 - 0.617584i) q^{79} +(-0.0540863 - 0.0130333i) q^{80} +(-5.01965 + 1.76325i) q^{81} +(-12.2270 - 11.2357i) q^{82} +(2.87763 - 15.3097i) q^{83} +(11.3751 + 10.4529i) q^{84} +(-0.206983 - 0.0888234i) q^{85} +(-11.1634 + 6.69912i) q^{86} +(-8.97187 + 19.9693i) q^{87} +(-0.126081 - 7.46402i) q^{88} +(4.84972 + 9.88683i) q^{89} +(-0.163503 - 0.306672i) q^{90} +(3.76587 + 0.382951i) q^{91} +(5.29505 - 14.2971i) q^{92} +(14.2603 - 3.41043i) q^{93} +(0.495070 + 1.33673i) q^{94} +(-0.0442681 - 0.170973i) q^{95} +(-5.86882 + 17.6556i) q^{96} +(-0.272045 + 1.77581i) q^{97} +(-5.72386 + 2.92864i) q^{98} +(-10.8721 + 9.99060i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4920 q - 58 q^{2} - 64 q^{3} - 226 q^{4} - 60 q^{5} - 56 q^{6} - 60 q^{7} - 56 q^{8} + 18 q^{9} - 61 q^{10} - 64 q^{11} - 72 q^{12} - 64 q^{13} - 65 q^{14} + 66 q^{15} - 234 q^{16} - 68 q^{17} - 70 q^{18}+ \cdots - 86 q^{99}+O(q^{100}) $ 4920 * q - 58 * q^2 - 64 * q^3 - 226 * q^4 - 60 * q^5 - 56 * q^6 - 60 * q^7 - 56 * q^8 + 18 * q^9 - 61 * q^10 - 64 * q^11 - 72 * q^12 - 64 * q^13 - 65 * q^14 + 66 * q^15 - 234 * q^16 - 68 * q^17 - 70 * q^18 - 56 * q^19 - 57 * q^20 - 68 * q^21 + 76 * q^22 - 46 * q^23 + 72 * q^24 + 10 * q^25 + 56 * q^26 - 58 * q^27 - 49 * q^28 - 46 * q^29 - 74 * q^30 - 42 * q^31 - 86 * q^32 - 90 * q^33 - 64 * q^34 - 202 * q^35 + 34 * q^36 - 60 * q^37 - 61 * q^38 - 58 * q^39 + 62 * q^40 - 56 * q^41 - 730 * q^42 + 60 * q^43 - 88 * q^44 - 58 * q^45 + 108 * q^46 + 34 * q^47 - 68 * q^48 + 10 * q^49 + 104 * q^50 - 60 * q^51 - 48 * q^52 - 56 * q^53 - 58 * q^54 - 64 * q^55 - 500 * q^56 - 64 * q^57 - 62 * q^58 - 64 * q^59 + 82 * q^60 + 124 * q^61 + 383 * q^62 + 30 * q^63 + 48 * q^64 - 64 * q^65 - 18 * q^66 - 58 * q^67 - 300 * q^68 - 50 * q^69 - 80 * q^70 - 68 * q^71 - 55 * q^72 - 370 * q^73 - 64 * q^74 - 54 * q^75 + 261 * q^76 - 34 * q^77 - 98 * q^78 - 84 * q^79 + 480 * q^80 + 20 * q^81 + 299 * q^82 - 68 * q^83 + 288 * q^84 + 198 * q^85 - 88 * q^86 + 101 * q^87 - 44 * q^88 - 46 * q^89 - 55 * q^90 + 453 * q^91 - 46 * q^92 - 40 * q^93 - 768 * q^94 + 61 * q^95 - 64 * q^96 - 102 * q^97 - 51 * q^98 - 86 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{44}{93}\right)$

Coefficient data

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

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

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

$2$	−1.67939	−	1.44171i	−1.18751	−	1.01944i	−0.999304	−	0.0373122i	$-0.988120\pi$
$2$	−1.67939	−	1.44171i	−1.18751	−	1.01944i	−0.188204	−	0.982130i	$-0.560267\pi$
$3$	−0.222135	−	2.62407i	−0.128250	−	1.51501i	−0.711483	−	0.702703i	$-0.751976\pi$
$3$	−0.222135	−	2.62407i	−0.128250	−	1.51501i	0.583233	−	0.812305i	$-0.301787\pi$
$4$	0.438970	+	2.86545i	0.219485	+	1.43272i
$5$	−0.0342144	−	0.0205319i	−0.0153011	−	0.00918212i	0.506884	−	0.862014i	$-0.330797\pi$
$5$	−0.0342144	−	0.0205319i	−0.0153011	−	0.00918212i	−0.522185	+	0.852832i	$0.674883\pi$
$6$	−3.41010	+	4.72709i	−1.39217	+	1.92983i
$7$	1.12782	+	1.68021i	0.426275	+	0.635059i	0.980317	−	0.197430i	$-0.0632594\pi$
$7$	1.12782	+	1.68021i	0.426275	+	0.635059i	−0.554042	+	0.832489i	$0.686915\pi$
$8$	1.05238	−	1.68839i	0.372073	−	0.596936i
$9$	−3.87909	+	0.661492i	−1.29303	+	0.220497i
$10$	0.0278583	+	0.0838081i	0.00880957	+	0.0265025i
$11$	3.15032	−	2.03828i	0.949856	−	0.614566i	0.0269694	−	0.999636i	$-0.491414\pi$
$11$	3.15032	−	2.03828i	0.949856	−	0.614566i	0.922887	+	0.385071i	$0.125823\pi$
$12$	7.42162	−	1.78840i	2.14244	−	0.516268i
$13$	1.19428	−	1.43967i	0.331233	−	0.399292i	−0.577690	−	0.816256i	$-0.696046\pi$
$13$	1.19428	−	1.43967i	0.331233	−	0.399292i	0.908923	+	0.416964i	$0.136906\pi$
$14$	0.528326	−	4.44771i	0.141201	−	1.18870i
$15$	−0.0462768	+	0.0943417i	−0.0119486	+	0.0243589i
$16$	1.33033	−	0.417394i	0.332583	−	0.104349i
$17$	5.59328	−	0.760410i	1.35657	−	0.184426i	0.580081	−	0.814559i	$-0.303021\pi$
$17$	5.59328	−	0.760410i	1.35657	−	0.184426i	0.776488	+	0.630132i	$0.216999\pi$
$18$	7.46819	+	4.48162i	1.76027	+	1.05633i
$19$	3.15605	+	3.10319i	0.724048	+	0.711921i	0.966050	−	0.258355i	$-0.0831803\pi$
$19$	3.15605	+	3.10319i	0.724048	+	0.711921i	−0.242002	+	0.970276i	$0.577804\pi$
$20$	0.0438138	−	0.107052i	0.00979707	−	0.0239376i
$21$	4.15846	−	3.33271i	0.907450	−	0.727256i
$22$	−8.22922	−	1.11877i	−1.75448	−	0.238522i
$23$	−4.59847	−	2.55236i	−0.958847	−	0.532203i	−0.0735813	−	0.997289i	$-0.523443\pi$
$23$	−4.59847	−	2.55236i	−0.958847	−	0.532203i	−0.885266	+	0.465086i	$0.846023\pi$
$24$	−4.66423	−	2.38648i	−0.952082	−	0.487137i
$25$	−2.35158	−	4.41069i	−0.470316	−	0.882137i
$26$	−4.08124	+	0.695963i	−0.800396	+	0.136490i
$27$	0.617237	+	2.38391i	0.118787	+	0.458784i
$28$	−4.31947	+	3.96926i	−0.816303	+	0.750120i
$29$	−7.26854	−	4.03437i	−1.34973	−	0.749163i	−0.366311	−	0.930492i	$-0.619379\pi$
$29$	−7.26854	−	4.03437i	−1.34973	−	0.749163i	−0.983422	+	0.181329i	$0.941960\pi$
$30$	0.213730	−	0.0917188i	0.0390216	−	0.0167455i
$31$	0.833660	+	5.50500i	0.149730	+	0.988727i
$31$	0.833660	+	5.50500i	0.149730	+	0.988727i
$32$	−6.49247	−	2.78614i	−1.14772	−	0.492524i
$33$	−6.04840	−	7.81388i	−1.05289	−	1.36022i
$34$	−10.4896	−	6.78685i	−1.79895	−	1.16394i
$35$	−0.00408977	−	0.0806435i	−0.000691298	−	0.0136312i
$36$	−3.59828	−	10.8250i	−0.599713	−	1.80416i
$37$	9.37697	+	1.59903i	1.54156	+	0.262879i	0.875575	−	0.483082i	$-0.160483\pi$
$37$	9.37697	+	1.59903i	1.54156	+	0.262879i	0.665989	+	0.745961i	$0.268010\pi$
$38$	−0.826345	−	9.76158i	−0.134051	−	1.58354i
$39$	−4.04308	−	2.81407i	−0.647411	−	0.450611i
$40$	−0.0706724	+	0.0361599i	−0.0111743	+	0.00571738i
$41$	7.49813	+	0.253387i	1.17101	+	0.0395725i	0.612877	−	0.790178i	$-0.290012\pi$
$41$	7.49813	+	0.253387i	1.17101	+	0.0395725i	0.558134	+	0.829751i	$0.311517\pi$
$42$	−11.7885	−	0.398373i	−1.81900	−	0.0614702i
$43$	1.85544	−	5.58187i	0.282953	−	0.851227i	−0.706671	−	0.707542i	$-0.749804\pi$
$43$	1.85544	−	5.58187i	0.282953	−	0.851227i	0.989624	−	0.143684i	$-0.0458950\pi$
$44$	7.22349	+	8.13232i	1.08898	+	1.22599i
$45$	0.146302	+	0.0570125i	0.0218095	+	0.00849891i
$46$	4.04286	+	10.9161i	0.596088	+	1.60948i
$47$	−0.563107	−	0.312550i	−0.0821376	−	0.0455901i	0.443698	−	0.896177i	$-0.353666\pi$
$47$	−0.563107	−	0.312550i	−0.0821376	−	0.0455901i	−0.525835	+	0.850587i	$0.676247\pi$
$48$	−1.39079	−	3.39817i	−0.200743	−	0.490483i
$49$	1.10032	−	2.68847i	0.157189	−	0.384067i
$50$	−2.40971	+	10.7976i	−0.340784	+	1.52700i
$51$	−3.23783	−	14.5082i	−0.453387	−	2.03156i
$52$	4.64954	+	2.79016i	0.644775	+	0.386926i
$53$	−9.43442	−	4.43172i	−1.29592	−	0.608743i	−0.351099	−	0.936338i	$-0.614192\pi$
$53$	−9.43442	−	4.43172i	−1.29592	−	0.608743i	−0.944818	+	0.327595i	$0.893762\pi$
$54$	2.40032	−	4.89339i	0.326643	−	0.665906i
$55$	−0.149636	+	0.00505671i	−0.0201769	+	0.000681846i
$56$	4.02375	−	0.135976i	0.537696	−	0.0181706i
$57$	7.44193	−	8.97104i	0.985707	−	1.18824i
$58$	6.39032	+	17.2544i	0.839091	+	2.26561i
$59$	9.55433	+	1.62928i	1.24387	+	0.212114i	0.752356	−	0.658757i	$-0.228918\pi$
$59$	9.55433	+	1.62928i	1.24387	+	0.212114i	0.491512	+	0.870871i	$0.336444\pi$
$60$	−0.290645	−	0.0911906i	−0.0375222	−	0.0117727i
$61$	−6.38240	+	6.71428i	−0.817182	+	0.859675i	−0.992170	−	0.124896i	$-0.960140\pi$
$61$	−6.38240	+	6.71428i	−0.817182	+	0.859675i	0.174988	+	0.984571i	$0.444011\pi$
$62$	6.53657	−	10.4469i	0.830145	−	1.32676i
$63$	−5.48636	−	5.77164i	−0.691216	−	0.727159i
$64$	5.65853	+	11.5357i	0.707316	+	1.44196i
$65$	−0.0704204	+	0.0247366i	−0.00873458	+	0.00306820i
$66$	−1.10773	+	21.8426i	−0.136352	+	2.68864i
$67$	−3.26524	+	7.97810i	−0.398912	+	0.974680i	0.587326	+	0.809350i	$0.300181\pi$
$67$	−3.26524	+	7.97810i	−0.398912	+	0.974680i	−0.986238	+	0.165330i	$0.947131\pi$
$68$	4.63419	+	15.6934i	0.561978	+	1.90311i
$69$	−5.67609	+	12.6337i	−0.683321	+	1.52092i
$70$	−0.109396	+	0.141328i	−0.0130753	+	0.0168919i
$71$	7.87274	−	7.74087i	0.934322	−	0.918673i	−0.0625233	−	0.998044i	$-0.519915\pi$
$71$	7.87274	−	7.74087i	0.934322	−	0.918673i	0.996845	+	0.0793709i	$0.0252911\pi$
$72$	−2.96543	+	7.24557i	−0.349479	+	0.853899i
$73$	−6.66180	−	4.97898i	−0.779705	−	0.582746i	0.133119	−	0.991100i	$-0.457501\pi$
$73$	−6.66180	−	4.97898i	−0.779705	−	0.582746i	−0.912824	+	0.408354i	$0.866103\pi$
$74$	−13.4423	−	16.2043i	−1.56263	−	1.88371i
$75$	−11.0516	+	7.15047i	−1.27613	+	0.825666i
$76$	−7.50662	+	10.4057i	−0.861068	+	1.19362i
$77$	6.97773	+	2.99438i	0.795186	+	0.341241i
$78$	2.73284	+	10.5549i	0.309433	+	1.19510i
$79$	0.826318	−	0.617584i	0.0929680	−	0.0694837i	−0.551170	−	0.834393i	$-0.685818\pi$
$79$	0.826318	−	0.617584i	0.0929680	−	0.0694837i	0.644138	+	0.764909i	$0.277216\pi$
$80$	−0.0540863	−	0.0130333i	−0.00604704	−	0.00145717i
$81$	−5.01965	+	1.76325i	−0.557739	+	0.195917i
$82$	−12.2270	−	11.2357i	−1.35024	−	1.24077i
$83$	2.87763	−	15.3097i	0.315861	−	1.68046i	−0.351863	−	0.936052i	$-0.614452\pi$
$83$	2.87763	−	15.3097i	0.315861	−	1.68046i	0.667724	−	0.744409i	$-0.267269\pi$
$84$	11.3751	+	10.4529i	1.24113	+	1.14050i
$85$	−0.206983	−	0.0888234i	−0.0224505	−	0.00963425i
$86$	−11.1634	+	6.69912i	−1.20378	+	0.722385i
$87$	−8.97187	+	19.9693i	−0.961885	+	2.14094i
$88$	−0.126081	−	7.46402i	−0.0134403	−	0.795667i
$89$	4.84972	+	9.88683i	0.514070	+	1.04800i	0.986059	+	0.166398i	$0.0532136\pi$
$89$	4.84972	+	9.88683i	0.514070	+	1.04800i	−0.471989	+	0.881604i	$0.656464\pi$
$90$	−0.163503	−	0.306672i	−0.0172348	−	0.0323260i
$91$	3.76587	+	0.382951i	0.394770	+	0.0401442i
$92$	5.29505	−	14.2971i	0.552047	−	1.49057i
$93$	14.2603	−	3.41043i	1.47873	−	0.353646i
$94$	0.495070	+	1.33673i	0.0510626	+	0.137873i
$95$	−0.0442681	−	0.170973i	−0.00454181	−	0.0175415i
$96$	−5.86882	+	17.6556i	−0.598984	+	1.80197i
$97$	−0.272045	+	1.77581i	−0.0276219	+	0.180306i	−0.998159	−	0.0606434i	$-0.980685\pi$
$97$	−0.272045	+	1.77581i	−0.0276219	+	0.180306i	0.970538	+	0.240950i	$0.0774589\pi$
$98$	−5.72386	+	2.92864i	−0.578198	+	0.295838i
$99$	−10.8721	+	9.99060i	−1.09268	+	1.00409i
$100$	11.6063	−	8.67448i	1.16063	−	0.867448i
$101$	6.02736	+	5.17432i	0.599745	+	0.514864i	0.898216	−	0.439555i	$-0.144864\pi$
$101$	6.02736	+	5.17432i	0.599745	+	0.514864i	−0.298471	+	0.954419i	$0.596477\pi$
$102$	−15.4791	+	29.0330i	−1.53266	+	2.87469i
$103$	−1.38991	−	1.27722i	−0.136952	−	0.125848i	0.605219	−	0.796059i	$-0.293085\pi$
$103$	−1.38991	−	1.27722i	−0.136952	−	0.125848i	−0.742171	+	0.670211i	$0.766204\pi$
$104$	−1.17389	−	3.53149i	−0.115109	−	0.346291i
$105$	−0.210706	+	0.0286456i	−0.0205628	+	0.00279552i
$106$	9.45482	+	21.0443i	0.918333	+	2.04400i
$107$	1.08526	+	1.30825i	0.104916	+	0.126473i	0.819507	−	0.573069i	$-0.194247\pi$
$107$	1.08526	+	1.30825i	0.104916	+	0.126473i	−0.714591	+	0.699543i	$0.753387\pi$
$108$	−6.56002	+	2.81512i	−0.631238	+	0.270885i
$109$	−2.55066	+	4.09216i	−0.244309	+	0.391958i	−0.947860	−	0.318687i	$-0.896758\pi$
$109$	−2.55066	+	4.09216i	−0.244309	+	0.391958i	0.703551	+	0.710645i	$0.251597\pi$
$110$	0.258587	+	0.207239i	0.0246553	+	0.0197595i
$111$	2.11302	−	24.9610i	0.200559	−	2.36920i
$112$	2.20168	+	1.76449i	0.208039	+	0.166729i
$113$	6.57289	+	0.893588i	0.618325	+	0.0840617i	0.437149	−	0.899389i	$-0.355988\pi$
$113$	6.57289	+	0.893588i	0.618325	+	0.0840617i	0.181176	+	0.983451i	$0.442010\pi$
$114$	−25.4315	+	4.33677i	−2.38188	+	0.406176i
$115$	0.104929	+	0.181742i	0.00978468	+	0.0169476i
$116$	8.36959	−	22.5986i	0.777097	−	2.09822i
$117$	−3.68038	+	6.37461i	−0.340251	+	0.589333i
$118$	−13.6965	−	16.5107i	−1.26087	−	1.51994i
$119$	7.58584	+	8.54027i	0.695393	+	0.782885i
$120$	0.110585	+	0.177417i	0.0100950	+	0.0161959i
$121$	1.26188	−	2.80865i	0.114716	−	0.255332i
$122$	20.3986	−	2.07433i	1.84680	−	0.187801i
$123$	−1.00069	−	19.7319i	−0.0902291	−	1.77917i
$124$	−15.4083	+	4.80534i	−1.38371	+	0.431532i
$125$	−0.0202069	+	0.398446i	−0.00180736	+	0.0356381i
$126$	0.892701	+	17.6026i	0.0795282	+	1.56816i
$127$	−12.2549	−	18.2572i	−1.08745	−	1.62006i	−0.726037	−	0.687656i	$-0.758640\pi$
$127$	−12.2549	−	18.2572i	−1.08745	−	1.62006i	−0.361409	−	0.932407i	$-0.617704\pi$
$128$	3.58650	−	13.8519i	0.317005	−	1.22434i
$129$	−15.0594	−	3.62889i	−1.32590	−	0.319506i
$130$	0.153926	+	0.0599834i	0.0135002	+	0.00526089i
$131$	−20.9100	+	2.84273i	−1.82691	+	0.248370i	−0.965661	−	0.259806i	$-0.916341\pi$
$131$	−20.9100	+	2.84273i	−1.82691	+	0.248370i	−0.861253	+	0.508176i	$0.830320\pi$
$132$	19.7352	−	20.7614i	1.71773	−	1.80705i
$133$	−1.65456	+	8.80267i	−0.143468	+	0.763288i
$134$	16.9857	−	8.69082i	1.46734	−	0.750772i
$135$	0.0278277	−	0.0942370i	0.00239503	−	0.00811063i
$136$	4.60239	−	10.2439i	0.394652	−	0.878405i
$137$	14.4830	−	4.01211i	1.23737	−	0.342777i	0.413996	−	0.910279i	$-0.364133\pi$
$137$	14.4830	−	4.01211i	1.23737	−	0.342777i	0.823372	+	0.567501i	$0.192090\pi$
$138$	27.7464	−	13.0336i	2.36193	−	1.10949i
$139$	−2.83077	+	7.64329i	−0.240102	+	0.648296i	−0.999998	−	0.00174885i	$-0.999443\pi$
$139$	−2.83077	+	7.64329i	−0.240102	+	0.648296i	0.759896	+	0.650045i	$0.225250\pi$
$140$	0.229284	−	0.0471191i	0.0193781	−	0.00398229i
$141$	−0.695067	+	1.54706i	−0.0585352	+	0.130286i
$142$	−24.3815	+	1.64975i	−2.04605	+	0.138444i
$143$	0.827901	−	6.96968i	0.0692325	−	0.582834i
$144$	−4.88438	+	2.49912i	−0.407032	+	0.208260i
$145$	0.165855	+	0.287270i	0.0137735	+	0.0238565i
$146$	4.00951	+	17.9660i	0.331830	+	1.48688i
$147$	−7.29916	−	2.29013i	−0.602024	−	0.188886i
$148$	−0.465729	+	27.5711i	−0.0382826	+	2.26633i
$149$	−10.8091	+	2.60470i	−0.885519	+	0.213385i	−0.651320	−	0.758803i	$-0.725784\pi$
$149$	−10.8091	+	2.60470i	−0.885519	+	0.213385i	−0.234199	+	0.972189i	$0.575247\pi$
$150$	28.8688	+	3.92474i	2.35713	+	0.320453i
$151$	−11.5246	−	14.8886i	−0.937862	−	1.21162i	−0.977185	−	0.212391i	$-0.931875\pi$
$151$	−11.5246	−	14.8886i	−0.937862	−	1.21162i	0.0393227	−	0.999227i	$-0.487480\pi$
$152$	8.56078	−	2.06291i	0.694371	−	0.167324i
$153$	−21.1938	+	6.64961i	−1.71342	+	0.537589i
$154$	−7.40130	−	15.0886i	−0.596414	−	1.21587i
$155$	0.0845047	−	0.205467i	0.00678758	−	0.0165035i
$156$	6.28876	−	12.8205i	0.503504	−	1.02646i
$157$	−0.564958	+	3.68785i	−0.0450885	+	0.294322i	−0.999997	−	0.00257898i	$-0.999179\pi$
$157$	−0.564958	+	3.68785i	−0.0450885	+	0.294322i	0.954908	+	0.296901i	$0.0959533\pi$
$158$	−2.27809	−	0.154145i	−0.181235	−	0.0122631i
$159$	−9.53343	+	25.7410i	−0.756050	+	2.04140i
$160$	0.164931	+	0.228628i	0.0130389	+	0.0180747i
$161$	−0.897741	−	10.6050i	−0.0707519	−	0.835790i
$162$	10.9720	+	4.27569i	0.862045	+	0.335930i
$163$	13.2744	+	13.9647i	1.03973	+	1.09380i	0.995498	+	0.0947781i	$0.0302141\pi$
$163$	13.2744	+	13.9647i	1.03973	+	1.09380i	0.0442352	+	0.999021i	$0.485915\pi$
$164$	2.56539	+	21.5967i	0.200323	+	1.68642i
$165$	0.0465085	+	0.391532i	0.00362068	+	0.0304807i
$166$	−26.9048	+	21.5623i	−2.08822	+	1.67356i
$167$	−6.46844	−	9.63660i	−0.500543	−	0.745702i	0.491599	−	0.870822i	$-0.336413\pi$
$167$	−6.46844	−	9.63660i	−0.500543	−	0.745702i	−0.992142	+	0.125120i	$0.960069\pi$
$168$	−1.25063	−	10.5284i	−0.0964878	−	0.812283i
$169$	1.75509	+	9.33755i	0.135007	+	0.718273i
$170$	0.219548	+	0.447578i	0.0168385	+	0.0343277i
$171$	−14.2954	−	9.94987i	−1.09319	−	0.760885i
$172$	16.8090	+	2.86640i	1.28168	+	0.218561i
$173$	4.85851	+	21.7703i	0.369386	+	1.65516i	0.702058	+	0.712120i	$0.252265\pi$
$173$	4.85851	+	21.7703i	0.369386	+	1.65516i	−0.332672	+	0.943042i	$0.607950\pi$
$174$	43.8572	−	20.6015i	3.32481	−	1.56179i
$175$	4.75872	−	8.92560i	0.359726	−	0.674712i
$176$	3.34020	−	4.02652i	0.251777	−	0.303510i
$177$	2.15299	−	25.4332i	0.161828	−	1.91167i
$178$	6.10936	−	23.5957i	0.457916	−	1.76858i
$179$	−10.5634	−	19.8131i	−0.789548	−	1.48090i	−0.874771	−	0.484536i	$-0.838988\pi$
$179$	−10.5634	−	19.8131i	−0.789548	−	1.48090i	0.0852236	−	0.996362i	$-0.472840\pi$
$180$	−0.0991437	+	0.444248i	−0.00738974	+	0.0331123i
$181$	−0.963126	+	0.623151i	−0.0715886	+	0.0463184i	−0.578522	−	0.815667i	$-0.696370\pi$
$181$	−0.963126	+	0.623151i	−0.0715886	+	0.0463184i	0.506934	+	0.861985i	$0.330779\pi$
$182$	−5.77226	−	6.07241i	−0.427868	−	0.450117i
$183$	19.0365	+	15.2564i	1.40722	+	1.12778i
$184$	−9.14872	+	5.07796i	−0.674453	+	0.374352i
$185$	−0.287996	−	0.247236i	−0.0211739	−	0.0181772i
$186$	−28.8655	−	14.8318i	−2.11652	−	1.08752i
$187$	16.0707	−	13.7962i	1.17520	−	1.00888i
$188$	0.648407	−	1.75075i	0.0472900	−	0.127687i
$189$	−3.30934	+	3.72570i	−0.240719	+	0.271005i
$190$	−0.172150	+	0.350953i	−0.0124891	+	0.0254608i
$191$	1.63183	−	19.2768i	0.118075	−	1.39482i	−0.652655	−	0.757656i	$-0.726345\pi$
$191$	1.63183	−	19.2768i	0.118075	−	1.39482i	0.770730	−	0.637162i	$-0.219892\pi$
$192$	29.0135	−	17.4109i	2.09387	−	1.25652i
$193$	9.96669	+	12.0146i	0.717418	+	0.864827i	0.995405	−	0.0957575i	$-0.0305273\pi$
$193$	9.96669	+	12.0146i	0.717418	+	0.864827i	−0.277987	+	0.960585i	$0.589667\pi$
$194$	3.01707	−	2.59007i	0.216613	−	0.185956i
$195$	0.0805534	+	0.179293i	0.00576855	+	0.0128395i
$196$	8.18668	+	1.97276i	0.584763	+	0.140911i
$197$	−11.6518	+	0.788412i	−0.830160	+	0.0561720i	−0.476470	−	0.879191i	$-0.658084\pi$
$197$	−11.6518	+	0.788412i	−0.830160	+	0.0561720i	−0.353690	+	0.935363i	$0.615073\pi$
$198$	32.6620	−	1.10376i	2.32119	−	0.0784408i
$199$	−6.94972	−	0.234855i	−0.492653	−	0.0166484i	−0.213594	−	0.976923i	$-0.568517\pi$
$199$	−6.94972	−	0.234855i	−0.492653	−	0.0166484i	−0.279059	+	0.960274i	$0.590022\pi$
$200$	−9.92172	−	0.671345i	−0.701572	−	0.0474712i
$201$	21.6604	+	6.79600i	1.52781	+	0.479353i
$202$	−2.66243	−	17.3794i	−0.187328	−	1.22281i
$203$	−1.41901	−	16.7627i	−0.0995948	−	1.17651i
$204$	40.1513	−	15.6465i	2.81115	−	1.09547i
$205$	−0.251341	−	0.162620i	−0.0175544	−	0.0113579i
$206$	0.492819	+	4.14880i	0.0343363	+	0.289060i
$207$	19.5263	+	6.85898i	1.35717	+	0.476732i
$208$	0.987875	−	2.41372i	0.0684968	−	0.167361i
$209$	16.2678	+	3.34311i	1.12526	+	0.231248i
$210$	0.395156	+	0.255669i	0.0272683	+	0.0176428i
$211$	10.1226	+	8.11251i	0.696866	+	0.558488i	0.908001	−	0.418969i	$-0.137608\pi$
$211$	10.1226	+	8.11251i	0.696866	+	0.558488i	−0.211135	+	0.977457i	$0.567716\pi$
$212$	8.55742	−	28.9792i	0.587726	−	1.99030i
$213$	−22.0614	−	18.9391i	−1.51162	−	1.29769i
$214$	0.0635421	−	3.76169i	0.00434365	−	0.257144i
$215$	−0.178089	+	0.152884i	−0.0121456	+	0.0104266i
$216$	4.67454	+	1.46665i	0.318062	+	0.0997927i
$217$	−8.30933	+	7.60936i	−0.564074	+	0.516557i
$218$	10.1833	−	3.19502i	0.689698	−	0.216394i
$219$	−11.5854	+	18.5870i	−0.782868	+	1.25600i
$220$	−0.0801754	−	0.426554i	−0.00540542	−	0.0287582i
$221$	5.58518	−	8.96059i	0.375700	−	0.602755i
$222$	−39.5351	+	38.8730i	−2.65342	+	2.60898i
$223$	−0.169020	−	0.109357i	−0.0113184	−	0.00732311i	0.537550	−	0.843232i	$-0.319350\pi$
$223$	−0.169020	−	0.109357i	−0.0113184	−	0.00732311i	−0.548869	+	0.835909i	$0.684941\pi$
$224$	−2.64103	−	14.0510i	−0.176461	−	0.938819i
$225$	12.0396	+	15.5539i	0.802642	+	1.03693i
$226$	−9.75015	−	10.9769i	−0.648570	−	0.730171i
$227$	4.87768	−	7.26671i	0.323743	−	0.482308i	−0.632631	−	0.774454i	$-0.718025\pi$
$227$	4.87768	−	7.26671i	0.323743	−	0.482308i	0.956374	+	0.292145i	$0.0943690\pi$
$228$	28.9728	+	17.3864i	1.91877	+	1.15144i
$229$	0.728968	−	1.26261i	0.0481716	−	0.0834356i	−0.840934	−	0.541137i	$-0.817994\pi$
$229$	0.728968	−	1.26261i	0.0481716	−	0.0834356i	0.889106	+	0.457702i	$0.151327\pi$
$230$	0.0858029	−	0.456493i	0.00565767	−	0.0301003i
$231$	6.30746	−	18.9752i	0.415001	−	1.24848i
$232$	−14.4609	+	8.02644i	−0.949403	+	0.526961i
$233$	12.7942	−	16.5287i	0.838173	−	1.08283i	−0.157277	−	0.987554i	$-0.550272\pi$
$233$	12.7942	−	16.5287i	0.838173	−	1.08283i	0.995451	−	0.0952763i	$-0.0303735\pi$
$234$	15.3711	−	5.39941i	1.00484	−	0.352971i
$235$	0.0128491	+	0.0222553i	0.000838184	+	0.00145178i
$236$	−0.474537	+	28.0926i	−0.0308898	+	1.82867i
$237$	−1.80414	−	2.03113i	−0.117191	−	0.131936i
$238$	−0.427010	−	25.2790i	−0.0276790	−	1.63860i
$239$	10.6834	−	12.8786i	0.691054	−	0.833046i	−0.301676	−	0.953411i	$-0.597546\pi$
$239$	10.6834	−	12.8786i	0.691054	−	0.833046i	0.992730	+	0.120364i	$0.0384063\pi$
$240$	−0.0221858	+	0.144822i	−0.00143209	+	0.00934819i
$241$	−20.2072	−	1.36730i	−1.30166	−	0.0880758i	−0.599662	−	0.800253i	$-0.704698\pi$
$241$	−20.2072	−	1.36730i	−1.30166	−	0.0880758i	−0.702000	+	0.712177i	$0.747709\pi$
$242$	−6.16844	+	2.89756i	−0.396523	+	0.186262i
$243$	8.76951	+	19.5189i	0.562564	+	1.25214i
$244$	−22.0411	−	15.3410i	−1.41104	−	0.982110i
$245$	−0.0928462	+	0.0693926i	−0.00593172	+	0.00443333i
$246$	−26.7671	+	34.5803i	−1.70661	+	2.20476i
$247$	8.23676	−	0.837597i	0.524093	−	0.0532950i
$248$	10.1719	+	4.38582i	0.645918	+	0.278500i
$249$	−40.8130	−	4.15028i	−2.58642	−	0.263013i
$250$	0.608378	−	0.640013i	0.0384772	−	0.0404780i
$251$	6.62364	+	3.38902i	0.418080	+	0.213913i	0.651799	−	0.758391i	$-0.274014\pi$
$251$	6.62364	+	3.38902i	0.418080	+	0.213913i	−0.233719	+	0.972304i	$0.575090\pi$
$252$	14.1300	−	18.2544i	0.890106	−	1.14992i
$253$	−19.6891	+	1.33224i	−1.23784	+	0.0837574i
$254$	−5.74080	+	48.3289i	−0.360210	+	3.03243i
$255$	−0.187101	+	0.562869i	−0.0117167	+	0.0352482i
$256$	−4.90188	+	3.41181i	−0.306368	+	0.213238i
$257$	−2.13232	−	1.27960i	−0.133011	−	0.0798190i	0.446500	−	0.894784i	$-0.352670\pi$
$257$	−2.13232	−	1.27960i	−0.133011	−	0.0798190i	−0.579511	+	0.814965i	$0.696756\pi$
$258$	20.0588	+	27.8055i	1.24880	+	1.73110i
$259$	7.88881	+	17.5587i	0.490187	+	1.09104i
$260$	−0.101794	−	0.190927i	−0.00631298	−	0.0118408i
$261$	30.8640	+	10.8416i	1.91044	+	0.671079i
$262$	39.2144	+	25.3721i	2.42267	+	1.56749i
$263$	−0.554639	+	2.14214i	−0.0342005	+	0.132090i	−0.982922	−	0.184023i	$-0.941088\pi$
$263$	−0.554639	+	2.14214i	−0.0342005	+	0.132090i	0.948721	+	0.316114i	$0.102378\pi$
$264$	−19.5581	+	1.98887i	−1.20372	+	0.122406i
$265$	0.231801	+	0.345335i	0.0142394	+	0.0212137i
$266$	15.4695	−	12.3977i	0.948498	−	0.760153i
$267$	24.8665	−	14.9222i	1.52180	−	0.913226i
$268$	−24.2942	−	5.85422i	−1.48400	−	0.357603i
$269$	−4.93830	+	1.92440i	−0.301093	+	0.117333i	−0.508870	−	0.860844i	$-0.669936\pi$
$269$	−4.93830	+	1.92440i	−0.301093	+	0.117333i	0.207776	+	0.978176i	$0.433377\pi$
$270$	−0.182596	+	0.118141i	−0.0111124	+	0.00718984i
$271$	0.122401	+	0.0124469i	0.00743531	+	0.000756097i	0.104885	−	0.994484i	$-0.466552\pi$
$271$	0.122401	+	0.0124469i	0.00743531	+	0.000756097i	−0.0974500	+	0.995240i	$0.531069\pi$
$272$	7.12352	−	3.34620i	0.431927	−	0.202893i
$273$	0.168361	−	9.96697i	0.0101897	−	0.603229i
$274$	−30.1069	−	14.1424i	−1.81883	−	0.854374i
$275$	−16.3984	−	9.10188i	−0.988864	−	0.548864i
$276$	−38.6927	−	10.7187i	−2.32903	−	0.645191i
$277$	5.84245	−	11.9106i	0.351039	−	0.715641i	−0.647899	−	0.761726i	$-0.724352\pi$
$277$	5.84245	−	11.9106i	0.351039	−	0.715641i	0.998938	+	0.0460852i	$0.0146746\pi$
$278$	15.7734	−	8.75493i	0.946023	−	0.525086i
$279$	−6.87536	−	20.8029i	−0.411617	−	1.24544i
$280$	−0.140462	−	0.0779626i	−0.00839419	−	0.00465916i
$281$	−16.4031	+	11.4169i	−0.978527	+	0.681075i	−0.947937	−	0.318457i	$-0.896835\pi$
$281$	−16.4031	+	11.4169i	−0.978527	+	0.681075i	−0.0305895	+	0.999532i	$0.509738\pi$
$282$	3.39770	−	1.59603i	0.202330	−	0.0950424i
$283$	0.598296	−	0.629407i	0.0355650	−	0.0374143i	−0.706769	−	0.707445i	$-0.749848\pi$
$283$	0.598296	−	0.629407i	0.0355650	−	0.0374143i	0.742334	+	0.670030i	$0.233719\pi$
$284$	25.6370	+	19.1609i	1.52127	+	1.13699i
$285$	−0.438813	+	0.154142i	−0.0259930	+	0.00913057i
$286$	−11.4386	+	10.5112i	−0.676380	+	0.621542i
$287$	8.03078	+	12.8842i	0.474042	+	0.760530i
$288$	27.0279	+	6.51297i	1.59263	+	0.383781i
$289$	14.3235	−	3.96792i	0.842559	−	0.233407i
$290$	0.135624	−	0.721553i	0.00796410	−	0.0423711i
$291$	4.72029	+	0.319394i	0.276708	+	0.0187232i
$292$	11.3427	−	21.2746i	0.663780	−	1.24500i
$293$	5.88916	−	5.41169i	0.344048	−	0.316154i	−0.485879	−	0.874026i	$-0.661500\pi$
$293$	5.88916	−	5.41169i	0.344048	−	0.316154i	0.829927	+	0.557872i	$0.188382\pi$
$294$	8.95644	+	14.3693i	0.522350	+	0.838033i
$295$	−0.293443	−	0.251913i	−0.0170849	−	0.0146669i
$296$	12.5679	−	14.1492i	0.730497	−	0.822406i
$297$	6.80358	+	6.25197i	0.394784	+	0.362776i
$298$	21.9080	+	11.2093i	1.26909	+	0.649338i
$299$	−9.16639	+	3.57204i	−0.530106	+	0.206577i
$300$	−25.3406	−	28.5289i	−1.46304	−	1.64712i
$301$	11.4713	−	3.17780i	0.661195	−	0.183165i
$302$	−2.11067	+	41.6190i	−0.121456	+	2.39490i
$303$	12.2389	−	16.9656i	0.703106	−	0.974649i
$304$	5.49385	+	2.81096i	0.315094	+	0.161219i
$305$	0.356226	−	0.0986823i	0.0203974	−	0.00565053i
$306$	45.1795	+	19.3881i	2.58274	+	1.10834i
$307$	9.65563	+	23.5920i	0.551076	+	1.34647i	0.910583	+	0.413326i	$0.135633\pi$
$307$	9.65563	+	23.5920i	0.551076	+	1.34647i	−0.359507	+	0.933142i	$0.617055\pi$
$308$	−5.51722	+	21.3087i	−0.314373	+	1.21418i
$309$	−3.04277	+	3.93093i	−0.173097	+	0.223623i
$310$	−0.438139	+	0.223227i	−0.0248846	+	0.0126785i
$311$	−5.42587	−	7.00965i	−0.307673	−	0.397481i	0.611558	−	0.791200i	$-0.290543\pi$
$311$	−5.42587	−	7.00965i	−0.307673	−	0.397481i	−0.919231	+	0.393719i	$0.871188\pi$
$312$	−9.00611	+	3.86483i	−0.509870	+	0.218803i
$313$	7.42995	−	33.2925i	0.419966	−	1.88181i	−0.0493617	−	0.998781i	$-0.515719\pi$
$313$	7.42995	−	33.2925i	0.419966	−	1.88181i	0.469328	−	0.883024i	$-0.344496\pi$
$314$	6.26559	−	5.37883i	0.353588	−	0.303545i
$315$	0.0692097	+	0.310118i	0.00389952	+	0.0174732i
$316$	2.13238	+	2.09667i	0.119956	+	0.117947i
$317$	−26.3345	+	6.34588i	−1.47909	+	0.356420i	−0.891605	−	0.452814i	$-0.850420\pi$
$317$	−26.3345	+	6.34588i	−1.47909	+	0.356420i	−0.587487	+	0.809234i	$0.699883\pi$
$318$	53.1214	−	29.4848i	2.97890	−	1.65342i
$319$	−31.1214	+	2.10580i	−1.74246	+	0.117902i
$320$	0.0432462	−	0.510866i	0.00241754	−	0.0285583i
$321$	3.19187	−	3.13841i	0.178153	−	0.175169i
$322$	−13.7816	+	19.1042i	−0.768021	+	1.06463i
$323$	20.0124	+	14.9571i	1.11352	+	0.832236i
$324$	−7.25598	−	13.6095i	−0.403110	−	0.756084i
$325$	−9.15836	−	1.88209i	−0.508014	−	0.104400i
$326$	−2.15992	−	42.5900i	−0.119627	−	2.35884i
$327$	11.3047	+	5.78411i	0.625152	+	0.319862i
$328$	8.31872	−	12.3931i	0.459324	−	0.684295i
$329$	−0.109933	−	1.29864i	−0.00606081	−	0.0715961i
$330$	0.486369	−	0.724586i	0.0267737	−	0.0398872i
$331$	1.21048	−	2.27041i	0.0665339	−	0.124793i	−0.846943	−	0.531684i	$-0.821559\pi$
$331$	1.21048	−	2.27041i	0.0665339	−	0.124793i	0.913477	+	0.406891i	$0.133387\pi$
$332$	45.1324	+	1.52518i	2.47696	+	0.0837050i
$333$	−37.4319			−2.05126
$334$	−3.03014	+	25.5092i	−0.165802	+	1.39580i
$335$	0.275523	−	0.205924i	0.0150534	−	0.0112508i
$336$	4.14108	−	6.16932i	0.225914	−	0.336564i
$337$	7.14154	+	2.24067i	0.389025	+	0.122057i	0.487589	−	0.873073i	$-0.337877\pi$
$337$	7.14154	+	2.24067i	0.389025	+	0.122057i	−0.0985641	+	0.995131i	$0.531425\pi$
$338$	10.5145	−	18.2117i	0.571916	−	0.990587i
$339$	0.884772	−	17.4462i	0.0480542	−	0.947549i
$340$	0.163659	−	0.632089i	0.00887567	−	0.0342799i
$341$	13.8470	+	15.6433i	0.749859	+	0.847130i
$342$	9.66268	+	37.3195i	0.522498	+	2.01801i
$343$	19.6336	−	4.03481i	1.06011	−	0.217859i
$344$	−7.47174	−	9.00697i	−0.402849	−	0.485623i
$345$	0.453596	−	0.315712i	0.0244208	−	0.0169974i
$346$	23.2270	−	43.5653i	1.24869	−	2.34209i
$347$	−9.75768	+	29.3547i	−0.523819	+	1.57584i	0.266937	+	0.963714i	$0.413988\pi$
$347$	−9.75768	+	29.3547i	−0.523819	+	1.57584i	−0.790757	+	0.612130i	$0.790313\pi$
$348$	−61.1594	−	16.9425i	−3.27849	−	0.908212i
$349$	2.46063	+	5.01633i	0.131714	+	0.268518i	0.953566	−	0.301183i	$-0.0973815\pi$
$349$	2.46063	+	5.01633i	0.131714	+	0.268518i	−0.821852	+	0.569701i	$0.807059\pi$
$350$	−20.8599	+	8.12886i	−1.11501	+	0.434506i
$351$	4.16919	+	1.95843i	0.222535	+	0.104533i
$352$	−26.1323	+	4.45627i	−1.39286	+	0.237520i
$353$	−2.59340	−	6.33658i	−0.138033	−	0.337262i	0.840978	−	0.541069i	$-0.181980\pi$
$353$	−2.59340	−	6.33658i	−0.138033	−	0.337262i	−0.979011	+	0.203807i	$0.934668\pi$
$354$	−40.2829	+	39.6082i	−2.14101	+	2.10515i
$355$	−0.428295	+	0.103207i	−0.0227315	+	0.00547767i
$356$	−26.2013	+	18.2366i	−1.38867	+	0.966540i
$357$	20.7252	−	21.8029i	1.09689	−	1.15393i
$358$	−10.8246	+	48.5032i	−0.572096	+	2.56348i
$359$	−6.52887	−	3.06687i	−0.344581	−	0.161863i	0.245104	−	0.969497i	$-0.421178\pi$
$359$	−6.52887	−	3.06687i	−0.344581	−	0.161863i	−0.589684	+	0.807634i	$0.700748\pi$
$360$	0.250225	−	0.187017i	0.0131880	−	0.00985665i
$361$	0.00997288	+	0.590394i	0.000524888	+	0.0310734i
$362$	2.51587	+	0.342034i	0.132231	+	0.0179769i
$363$	−7.65041	−	2.68736i	−0.401542	−	0.141050i
$364$	0.555777	+	10.9590i	0.0291306	+	0.574407i
$365$	0.125701	+	0.307132i	0.00657951	+	0.0160760i
$366$	−9.97442	−	53.0665i	−0.521371	−	2.77383i
$367$	−1.52465	−	12.8352i	−0.0795859	−	0.669994i	−0.974600	−	0.223955i	$-0.928103\pi$
$367$	−1.52465	−	12.8352i	−0.0795859	−	0.669994i	0.895014	−	0.446039i	$-0.147166\pi$
$368$	−7.18283	−	1.47611i	−0.374431	−	0.0769475i
$369$	−29.2536	+	3.97704i	−1.52288	+	0.207036i
$370$	0.127215	+	0.830413i	0.00661357	+	0.0431711i
$371$	−3.19410	−	20.8500i	−0.165829	−	1.08248i
$372$	16.0323	+	39.3651i	0.831235	+	2.04099i
$373$	2.13220	−	13.9182i	0.110401	−	0.720659i	−0.865252	−	0.501338i	$-0.832841\pi$
$373$	2.13220	−	13.9182i	0.110401	−	0.720659i	0.975653	−	0.219322i	$-0.0703844\pi$
$374$	−46.8790			−2.42406
$375$	1.05004	−	0.0354844i	0.0542237	−	0.00183241i
$376$	−1.12031	+	0.621823i	−0.0577756	+	0.0320681i
$377$	−14.4888	+	5.64612i	−0.746211	+	0.290790i
$378$	10.9290	−	1.48581i	0.562129	−	0.0764219i
$379$	2.82737	+	2.78001i	0.145232	+	0.142800i	0.770081	−	0.637946i	$-0.220216\pi$
$379$	2.82737	+	2.78001i	0.145232	+	0.142800i	−0.624849	+	0.780746i	$0.714839\pi$
$380$	0.470483	−	0.201900i	0.0241353	−	0.0103573i
$381$	−45.1859	+	36.2133i	−2.31494	+	1.85526i
$382$	−30.5320	+	30.0206i	−1.56215	+	1.53599i
$383$	9.48827	+	4.45701i	0.484828	+	0.227743i	0.652049	−	0.758177i	$-0.273910\pi$
$383$	9.48827	+	4.45701i	0.484828	+	0.227743i	−0.167221	+	0.985919i	$0.553479\pi$
$384$	−37.1450	−	6.33424i	−1.89555	−	0.323243i
$385$	−0.177258	−	0.245716i	−0.00903392	−	0.0125229i
$386$	0.583551	−	34.5462i	0.0297019	−	1.75836i
$387$	−3.50508	+	22.8799i	−0.178173	+	1.16305i
$388$	−5.20792			−0.264392
$389$	−2.72360	+	0.0920399i	−0.138092	+	0.00466661i	−0.102740	−	0.994708i	$-0.532761\pi$
$389$	−2.72360	+	0.0920399i	−0.138092	+	0.00466661i	−0.0353526	+	0.999375i	$0.511255\pi$
$390$	0.123208	−	0.417238i	0.00623890	−	0.0211277i
$391$	−27.6613	−	10.7793i	−1.39889	−	0.545134i
$392$	−3.38123	−	4.68708i	−0.170778	−	0.236733i
$393$	12.1044	+	54.2378i	0.610584	+	2.73594i
$394$	20.7047	+	15.4745i	1.04309	+	0.779595i
$395$	−0.0409521	+	0.00416442i	−0.00206052	+	0.000209535i
$396$	−33.4000	−	26.7677i	−1.67842	−	1.34513i
$397$	−0.417656	−	0.115700i	−0.0209616	−	0.00580680i	0.256471	−	0.966552i	$-0.417440\pi$
$397$	−0.417656	−	0.115700i	−0.0209616	−	0.00580680i	−0.277432	+	0.960745i	$0.589483\pi$
$398$	11.3327	+	10.4139i	0.568057	+	0.522001i
$399$	23.4664	+	2.38629i	1.17479	+	0.119464i
$400$	−4.96938	−	4.88614i	−0.248469	−	0.244307i
$401$	11.7358	+	31.6875i	0.586056	+	1.58240i	0.796400	+	0.604770i	$0.206735\pi$
$401$	11.7358	+	31.6875i	0.586056	+	1.58240i	−0.210345	+	0.977627i	$0.567459\pi$
$402$	−26.5784	−	42.6412i	−1.32561	−	2.12675i
$403$	8.92099	+	5.37430i	0.444386	+	0.267713i
$404$	−12.1809	+	19.5424i	−0.606022	+	0.972273i
$405$	0.207947	+	0.0427342i	0.0103330	+	0.00212348i
$406$	−21.7839	+	30.1969i	−1.08111	+	1.49865i
$407$	32.7997	−	14.0755i	1.62582	−	0.697695i
$408$	−27.9030	−	9.80149i	−1.38140	−	0.485246i
$409$	15.1881	+	22.6271i	0.751005	+	1.11884i	0.989050	+	0.147583i	$0.0471493\pi$
$409$	15.1881	+	22.6271i	0.751005	+	1.11884i	−0.238045	+	0.971254i	$0.576507\pi$
$410$	0.187649	+	0.635463i	0.00926733	+	0.0313833i
$411$	−13.7452	−	37.1132i	−0.678003	−	1.83066i
$412$	3.04968	−	4.54337i	0.150247	−	0.223836i
$413$	8.03802	+	17.8908i	0.395525	+	0.880348i
$414$	−22.9035	−	39.6701i	−1.12565	−	1.94968i
$415$	−0.412793	+	0.464730i	−0.0202632	+	0.0228127i
$416$	−11.7649	+	6.01958i	−0.576822	+	0.295134i
$417$	20.6854	+	5.73029i	1.01297	+	0.280613i
$418$	−22.5001	−	29.0678i	−1.10052	−	1.42175i
$419$	−1.45231	−	1.52783i	−0.0709499	−	0.0746393i	0.688356	−	0.725373i	$-0.258333\pi$
$419$	−1.45231	−	1.52783i	−0.0709499	−	0.0746393i	−0.759306	+	0.650733i	$0.774462\pi$
$420$	−0.174576	−	0.591191i	−0.00851843	−	0.0288472i
$421$	−2.17502	−	0.295695i	−0.106004	−	0.0144113i	0.0815167	−	0.996672i	$-0.474024\pi$
$421$	−2.17502	−	0.295695i	−0.106004	−	0.0144113i	−0.187521	+	0.982261i	$0.560045\pi$
$422$	−5.30385	−	28.2179i	−0.258188	−	1.37362i
$423$	2.39109	+	0.839919i	0.116259	+	0.0408383i
$424$	−17.4111	+	11.2651i	−0.845557	+	0.547083i
$425$	−16.5070	−	22.8820i	−0.800705	−	1.10994i
$426$	9.74504	+	63.6123i	0.472149	+	3.08202i
$427$	−18.4796	−	3.15128i	−0.894289	−	0.152501i
$428$	−3.27233	+	3.68404i	−0.158174	+	0.178075i
$429$	−18.4728	−	0.624261i	−0.891877	−	0.0301396i
$430$	0.519495			0.0250523
$431$	0.865009	−	7.28208i	0.0416660	−	0.350765i	−0.956575	−	0.291485i	$-0.905851\pi$
$431$	0.865009	−	7.28208i	0.0416660	−	0.350765i	0.998241	−	0.0592803i	$-0.0188806\pi$
$432$	1.81616	+	2.91376i	0.0873801	+	0.140188i
$433$	−1.24846	−	0.868952i	−0.0599970	−	0.0417591i	0.540888	−	0.841095i	$-0.318088\pi$
$433$	−1.24846	−	0.868952i	−0.0599970	−	0.0417591i	−0.600885	+	0.799335i	$0.705185\pi$
$434$	24.9251	−	0.799447i	1.19644	−	0.0383747i
$435$	0.716974	−	0.499029i	0.0343763	−	0.0239266i
$436$	−12.8455	−	5.51245i	−0.615190	−	0.263999i
$437$	−6.59255	−	22.3253i	−0.315365	−	1.06796i
$438$	46.2535	−	14.5121i	2.21008	−	0.693416i
$439$	17.2416	+	29.8634i	0.822899	+	1.42530i	0.903515	+	0.428557i	$0.140978\pi$
$439$	17.2416	+	29.8634i	0.822899	+	1.42530i	−0.0806160	+	0.996745i	$0.525689\pi$
$440$	−0.148936	+	0.257965i	−0.00710027	+	0.0122980i
$441$	−2.48986	+	11.1567i	−0.118565	+	0.531271i
$442$	−22.2983	+	6.99613i	−1.06062	+	0.332772i
$443$	4.28348	−	14.5058i	0.203514	−	0.689189i	−0.793256	−	0.608888i	$-0.791616\pi$
$443$	4.28348	−	14.5058i	0.203514	−	0.689189i	0.996771	−	0.0803016i	$-0.0255884\pi$
$444$	72.4521	−	4.90240i	3.43842	−	0.232658i
$445$	0.0370648	−	0.437846i	0.00175704	−	0.0207559i
$446$	0.126189	+	0.427331i	0.00597522	+	0.0202347i
$447$	9.23600	+	27.7853i	0.436848	+	1.31420i
$448$	−13.0006	+	22.5177i	−0.614220	+	1.06386i
$449$	1.01306	+	0.103019i	0.0478095	+	0.00486175i	0.125044	−	0.992151i	$-0.460093\pi$
$449$	1.01306	+	0.103019i	0.0478095	+	0.00486175i	−0.0772344	+	0.997013i	$0.524609\pi$
$450$	2.20499	−	43.4787i	0.103944	−	2.04961i
$451$	24.1380	−	14.4851i	1.13661	−	0.682075i
$452$	0.324772	+	19.2265i	0.0152760	+	0.904339i
$453$	−36.5087	+	33.5488i	−1.71533	+	1.57626i
$454$	−18.6680	+	5.17144i	−0.876133	+	0.242708i
$455$	−0.120984	−	0.0904227i	−0.00567182	−	0.00423908i
$456$	−7.31487	−	22.0058i	−0.342550	−	1.03052i
$457$	16.5217	−	3.39530i	0.772854	−	0.158826i	0.201455	−	0.979498i	$-0.435433\pi$
$457$	16.5217	−	3.39530i	0.772854	−	0.158826i	0.571399	+	0.820672i	$0.306401\pi$
$458$	−3.04454	+	1.06945i	−0.142262	+	0.0499723i
$459$	5.26512	+	12.8645i	0.245755	+	0.600464i
$460$	−0.474712	+	0.380448i	−0.0221336	+	0.0177385i
$461$	−25.4515	+	2.58816i	−1.18539	+	0.120543i	−0.673952	−	0.738775i	$-0.735404\pi$
$461$	−25.4515	+	2.58816i	−1.18539	+	0.120543i	−0.511442	+	0.859318i	$0.670888\pi$
$462$	−37.9494	+	22.7732i	−1.76557	+	1.05951i
$463$	−6.32950	−	6.65863i	−0.294157	−	0.309453i	0.561007	−	0.827811i	$-0.310414\pi$
$463$	−6.32950	−	6.65863i	−0.294157	−	0.309453i	−0.855163	+	0.518359i	$0.826543\pi$
$464$	−11.3535	−	2.33320i	−0.527072	−	0.108316i
$465$	−0.557930	−	0.176105i	−0.0258734	−	0.00816667i
$466$	−45.3160	+	9.31266i	−2.09922	+	0.431401i
$467$	12.2561	+	8.53047i	0.567143	+	0.394743i	0.819661	−	0.572849i	$-0.194162\pi$
$467$	12.2561	+	8.53047i	0.567143	+	0.394743i	−0.252518	+	0.967592i	$0.581259\pi$
$468$	−19.8817	−	7.74767i	−0.919031	−	0.358136i
$469$	−17.0875	+	3.51156i	−0.789026	+	0.162149i
$470$	0.0105070	−	0.0559000i	0.000484653	−	0.00257848i
$471$	9.80267	+	0.663289i	0.451683	+	0.0305628i
$472$	12.8057	−	14.4168i	0.589428	−	0.663588i
$473$	−5.53219	−	21.3666i	−0.254370	−	0.982436i
$474$	0.101556	+	6.01210i	0.00466461	+	0.276145i
$475$	6.26550	−	21.2178i	0.287481	−	0.973538i
$476$	−21.1417	+	25.4857i	−0.969029	+	1.16814i
$477$	39.5285	+	10.9503i	1.80989	+	0.501378i
$478$	−36.5088	+	6.22576i	−1.66987	+	0.284760i
$479$	19.2540	+	18.9315i	0.879736	+	0.865001i	0.991682	−	0.128713i	$-0.0410846\pi$
$479$	19.2540	+	18.9315i	0.879736	+	0.865001i	−0.111946	+	0.993714i	$0.535708\pi$
$480$	0.563300	−	0.483577i	0.0257110	−	0.0220722i
$481$	13.5008	−	11.5900i	0.615582	−	0.528460i
$482$	31.9646	+	31.4292i	1.45595	+	1.43156i
$483$	−27.6288	+	4.71147i	−1.25715	+	0.214379i
$484$	8.60197	+	2.38293i	0.390998	+	0.108315i
$485$	0.0457686	−	0.0551727i	0.00207824	−	0.00250526i
$486$	13.4132	−	45.4230i	0.608434	−	2.06043i
$487$	0.0563495	+	3.33589i	0.00255344	+	0.151164i	0.998273	+	0.0587407i	$0.0187085\pi$
$487$	0.0563495	+	3.33589i	0.00255344	+	0.151164i	−0.995720	+	0.0924230i	$0.970539\pi$
$488$	4.61961	+	17.8420i	0.209120	+	0.807668i
$489$	33.6956	−	37.9351i	1.52377	−	1.71548i
$490$	0.255969	+	0.0173199i	0.0115635	+	0.000782434i
$491$	1.33067	−	7.07951i	0.0600524	−	0.319494i	−0.939694	−	0.342016i	$-0.888890\pi$
$491$	1.33067	−	7.07951i	0.0600524	−	0.319494i	0.999746	+	0.0225225i	$0.00716973\pi$
$492$	56.1014	−	11.5291i	2.52925	−	0.519774i
$493$	−43.7227	−	17.0383i	−1.96917	−	0.767365i
$494$	−15.0403	−	10.4684i	−0.676696	−	0.470994i
$495$	0.577107	−	0.118598i	0.0259390	−	0.00533060i
$496$	3.40680	+	6.97551i	0.152970	+	0.313210i
$497$	21.8853	+	4.49754i	0.981690	+	0.201742i
$498$	62.5575	+	65.8104i	2.80327	+	2.94904i
$499$	26.7981	−	16.0814i	1.19965	−	0.719902i	0.232125	−	0.972686i	$-0.425432\pi$
$499$	26.7981	−	16.0814i	1.19965	−	0.719902i	0.967523	+	0.252783i	$0.0813460\pi$
$500$	−1.15059	+	0.117004i	−0.0514562	+	0.00523258i
$501$	−23.8502	+	19.1143i	−1.06555	+	0.853962i
$502$	−6.23769	−	15.2408i	−0.278402	−	0.680232i
$503$	7.65531	−	2.68908i	0.341333	−	0.119900i	−0.155284	−	0.987870i	$-0.549629\pi$
$503$	7.65531	−	2.68908i	0.341333	−	0.119900i	0.496617	+	0.867970i	$0.334575\pi$
$504$	−15.5185	+	3.18914i	−0.691251	+	0.142056i
$505$	−0.0999839	−	0.300789i	−0.00444923	−	0.0133849i
$506$	34.9863	+	26.1485i	1.55533	+	1.16244i
$507$	24.1125	−	6.67968i	1.07087	−	0.296655i
$508$	46.9354	−	43.1301i	2.08242	−	1.91359i
$509$	0.645465	+	38.2115i	0.0286097	+	1.69370i	0.545872	+	0.837869i	$0.316198\pi$
$509$	0.645465	+	38.2115i	0.0286097	+	1.69370i	−0.517262	+	0.855827i	$0.673049\pi$
$510$	1.12571	−	0.675531i	0.0498472	−	0.0299130i
$511$	0.852436	−	16.8086i	0.0377095	−	0.743569i
$512$	−15.3195	−	1.55784i	−0.677031	−	0.0688473i
$513$	−5.44970	+	9.43915i	−0.240610	+	0.416749i
$514$	1.73620	+	5.22313i	0.0765804	+	0.230382i
$515$	0.0213311	+	0.0722367i	0.000939963	+	0.00318313i
$516$	3.78777	−	44.7448i	0.166747	−	1.96978i
$517$	−2.41103	+	0.163140i	−0.106037	+	0.00717490i
$518$	12.0661	−	40.8613i	0.530155	−	1.79534i
$519$	56.0475	−	17.5850i	2.46021	−	0.771896i
$520$	−0.0323442	+	0.144930i	−0.00141839	+	0.00635558i
$521$	−9.82683	+	17.0206i	−0.430521	+	0.745685i	−0.996918	−	0.0784478i	$-0.975004\pi$
$521$	−9.82683	+	17.0206i	−0.430521	+	0.745685i	0.566397	+	0.824133i	$0.308337\pi$
$522$	−36.2023	−	62.7042i	−1.58453	−	2.74449i
$523$	30.1201	−	9.45025i	1.31706	−	0.413231i	0.441901	−	0.897064i	$-0.354304\pi$
$523$	30.1201	−	9.45025i	1.31706	−	0.413231i	0.875160	+	0.483833i	$0.160756\pi$
$524$	−17.3245	−	58.6686i	−0.756826	−	2.56295i
$525$	−24.4785	−	10.5045i	−1.06833	−	0.458456i
$526$	4.01980	−	2.79786i	0.175272	−	0.121993i
$527$	8.84894	+	30.1570i	0.385466	+	1.31366i
$528$	−11.3078	−	7.87049i	−0.492111	−	0.342519i
$529$	2.46520	+	3.95506i	0.107183	+	0.171959i
$530$	0.108587	−	0.914141i	0.00471673	−	0.0397078i
$531$	−38.1399			−1.65513
$532$	−25.9499	−	0.876935i	−1.12507	−	0.0380199i
$533$	9.31963	−	10.4922i	0.403678	−	0.454467i
$534$	−63.2740	−	10.7900i	−2.73813	−	0.466927i
$535$	−0.0102707	−	0.0670434i	−0.000444040	−	0.00289854i
$536$	10.0339	+	13.9090i	0.433397	+	0.600778i
$537$	−49.6444	+	32.1204i	−2.14231	+	1.38610i
$538$	11.0678	+	3.88777i	0.477165	+	0.167614i
$539$	−2.01349	−	10.7123i	−0.0867273	−	0.461412i
$540$	0.282247	+	0.0383716i	0.0121460	+	0.00165125i
$541$	6.82368	+	23.1080i	0.293373	+	0.993491i	0.967076	+	0.254488i	$0.0819071\pi$
$541$	6.82368	+	23.1080i	0.293373	+	0.993491i	−0.673703	+	0.739002i	$0.735297\pi$
$542$	−0.187614	−	0.197369i	−0.00805869	−	0.00847774i
$543$	1.84914	+	2.38889i	0.0793540	+	0.102517i
$544$	−38.4328	−	10.6467i	−1.64779	−	0.456474i
$545$	0.171289	−	0.0876409i	0.00733722	−	0.00375412i
$546$	−14.6522	+	16.4957i	−0.627057	+	0.705951i
$547$	13.3291	+	23.0867i	0.569913	+	0.987118i	0.996574	+	0.0827065i	$0.0263564\pi$
$547$	13.3291	+	23.0867i	0.569913	+	0.987118i	−0.426661	+	0.904412i	$0.640310\pi$
$548$	17.8541	+	39.7391i	0.762689	+	1.69757i
$549$	20.3165	−	30.2672i	0.867086	−	1.29177i
$550$	14.4171	+	38.9274i	0.614748	+	1.65987i
$551$	−10.4205	−	35.2883i	−0.443927	−	1.50333i
$552$	15.3572	+	22.8789i	0.653644	+	0.973791i
$553$	1.96961	+	0.691864i	0.0837562	+	0.0294210i
$554$	−26.9834	+	11.5795i	−1.14642	+	0.491966i
$555$	−0.584792	+	0.810642i	−0.0248230	+	0.0344098i
$556$	−23.1441	−	4.75623i	−0.981527	−	0.201709i
$557$	−23.1652	+	37.1651i	−0.981541	+	1.57474i	−0.174152	+	0.984719i	$0.555718\pi$
$557$	−23.1652	+	37.1651i	−0.981541	+	1.57474i	−0.807389	+	0.590019i	$0.799120\pi$
$558$	−18.4454	+	44.8485i	−0.780855	+	1.89859i
$559$	−5.82012	−	9.33751i	−0.246165	−	0.394935i
$560$	−0.0391009	−	0.105576i	−0.00165231	−	0.00446138i
$561$	−39.7721	−	39.1059i	−1.67918	−	1.65105i
$562$	44.0070	+	4.47508i	1.85632	+	0.188770i
$563$	11.4162	+	10.4906i	0.481137	+	0.442128i	0.880064	−	0.474854i	$-0.157499\pi$
$563$	11.4162	+	10.4906i	0.481137	+	0.442128i	−0.398928	+	0.916982i	$0.630618\pi$
$564$	−4.73813	−	1.31256i	−0.199511	−	0.0552689i
$565$	−0.206540	−	0.165527i	−0.00868921	−	0.00696378i
$566$	−1.91219	+	0.194451i	−0.0803755	+	0.00817339i
$567$	−8.62388	−	6.44543i	−0.362169	−	0.270683i
$568$	−4.78449	−	21.4386i	−0.200753	−	0.899544i
$569$	24.7080	+	34.2503i	1.03581	+	1.43585i	0.895136	+	0.445793i	$0.147078\pi$
$569$	24.7080	+	34.2503i	1.03581	+	1.43585i	0.140677	+	0.990056i	$0.455072\pi$
$570$	0.959165	+	0.373776i	0.0401750	+	0.0156558i
$571$	13.0556	−	44.2120i	0.546359	−	1.85021i	0.0202534	−	0.999795i	$-0.493553\pi$
$571$	13.0556	−	44.2120i	0.546359	−	1.85021i	0.526106	−	0.850419i	$-0.323652\pi$
$572$	20.3347	−	0.687178i	0.850235	−	0.0287324i
$573$	−50.9461			−2.12830
$574$	5.08845	−	33.2156i	0.212388	−	1.38639i
$575$	−0.443994	+	26.2845i	−0.0185158	+	1.09614i
$576$	−29.5807	−	41.0050i	−1.23253	−	1.70854i
$577$	35.0565	+	5.97810i	1.45942	+	0.248872i	0.842731	−	0.538335i	$-0.180946\pi$
$577$	35.0565	+	5.97810i	1.45942	+	0.248872i	0.616690	+	0.787206i	$0.288473\pi$
$578$	−29.7753	−	13.9866i	−1.23849	−	0.581768i
$579$	29.3131	−	28.8221i	1.21821	−	1.19781i
$580$	−0.750351	+	0.601352i	−0.0311566	+	0.0249698i
$581$	28.9690	−	12.4316i	1.20184	−	0.515748i
$582$	−7.46673	−	7.34167i	−0.309506	−	0.304322i
$583$	−38.7545	+	5.26870i	−1.60505	+	0.218207i
$584$	−15.4172	+	6.00793i	−0.637970	+	0.248610i
$585$	0.256804	−	0.142538i	0.0106176	−	0.00589323i
$586$	−17.6923	+	0.597883i	−0.730861	+	0.0246983i
$587$	−14.2044			−0.586279			−0.293140	−	0.956070i	$-0.594700\pi$
$587$	−14.2044			−0.586279			−0.293140	+	0.956070i	$0.594700\pi$
$588$	3.35812	−	21.9206i	0.138486	−	0.903992i
$589$	−14.4520	+	19.9611i	−0.595484	+	0.822482i
$590$	0.129621	+	0.846119i	0.00533640	+	0.0348342i
$591$	4.65713	+	30.4001i	0.191569	+	1.25049i
$592$	13.1419	−	1.78665i	0.540129	−	0.0734309i
$593$	16.5296	+	3.39692i	0.678790	+	0.139495i	0.528224	−	0.849105i	$-0.322858\pi$
$593$	16.5296	+	3.39692i	0.678790	+	0.139495i	0.150566	+	0.988600i	$0.451890\pi$
$594$	−2.41234	−	20.3083i	−0.0989794	−	0.833258i
$595$	−0.0841973	−	0.447951i	−0.00345175	−	0.0183642i
$596$	−12.2085	−	29.8296i	−0.500080	−	1.22187i
$597$	0.927499	+	18.2887i	0.0379600	+	0.748508i
$598$	20.5438	+	7.21641i	0.840098	+	0.295101i
$599$	−8.16472	−	1.11000i	−0.333602	−	0.0453533i	−0.0340116	−	0.999421i	$-0.510828\pi$
$599$	−8.16472	−	1.11000i	−0.333602	−	0.0453533i	−0.299590	+	0.954068i	$0.596850\pi$
$600$	0.442305	+	26.1844i	0.0180570	+	1.06898i
$601$	13.8308	−	10.3371i	0.564172	−	0.421658i	−0.278225	−	0.960516i	$-0.589746\pi$
$601$	13.8308	−	10.3371i	0.564172	−	0.421658i	0.842397	+	0.538858i	$0.181144\pi$
$602$	−23.8463	−	11.2015i	−0.971901	−	0.456540i
$603$	7.38871	−	33.1077i	0.300892	−	1.34825i
$604$	37.6035	−	39.5589i	1.53007	−	1.60963i
$605$	−0.100841	+	0.0701875i	−0.00409978	+	0.00285353i
$606$	−45.0133	+	10.8470i	−1.82854	+	0.440628i
$607$	14.2441	−	14.0055i	0.578150	−	0.568467i	−0.351836	−	0.936062i	$-0.614442\pi$
$607$	14.2441	−	14.0055i	0.578150	−	0.568467i	0.929986	+	0.367595i	$0.119819\pi$
$608$	−11.8447	−	28.9406i	−0.480364	−	1.17370i
$609$	−43.6713	+	7.44716i	−1.76965	+	0.301774i
$610$	−0.740514	−	0.347848i	−0.0299825	−	0.0140840i
$611$	−1.12247	+	0.437415i	−0.0454104	+	0.0176959i
$612$	−28.3576	−	57.8108i	−1.14629	−	2.33686i
$613$	−24.3438	−	6.74374i	−0.983235	−	0.272377i	−0.262000	−	0.965068i	$-0.584382\pi$
$613$	−24.3438	−	6.74374i	−0.983235	−	0.272377i	−0.721235	+	0.692691i	$0.756425\pi$
$614$	17.7973	−	53.5408i	0.718240	−	2.16073i
$615$	−0.370895	+	0.695661i	−0.0149559	+	0.0280517i
$616$	12.3989	−	8.62990i	0.499567	−	0.347709i
$617$	13.1578	+	15.8614i	0.529713	+	0.638555i	0.965160	−	0.261660i	$-0.0842698\pi$
$617$	13.1578	+	15.8614i	0.529713	+	0.638555i	−0.435447	+	0.900214i	$0.643410\pi$
$618$	10.7773	−	2.21478i	0.433525	−	0.0890917i
$619$	2.88452	+	11.1407i	0.115939	+	0.447782i	0.999801	−	0.0199659i	$-0.00635578\pi$
$619$	2.88452	+	11.1407i	0.115939	+	0.447782i	−0.883862	+	0.467748i	$0.845065\pi$
$620$	0.625849	+	0.151950i	0.0251347	+	0.00610245i
$621$	3.24625	−	12.5377i	0.130267	−	0.503122i
$622$	−0.993719	+	19.5945i	−0.0398445	+	0.785666i
$623$	−11.1423	+	19.2991i	−0.446408	+	0.773202i
$624$	−6.55321	−	2.05608i	−0.262338	−	0.0823092i
$625$	−13.9198	+	20.7375i	−0.556792	+	0.829502i
$626$	−60.4759	+	45.1993i	−2.41710	+	1.80653i
$627$	5.15892	−	43.4304i	0.206027	−	1.73444i
$628$	−10.8153			−0.431579
$629$	53.6639	+	1.81349i	2.13972	+	0.0723085i
$630$	0.330870	−	0.620590i	0.0131822	−	0.0247249i
$631$	−24.1394	+	35.9625i	−0.960974	+	1.43165i	−0.0597886	+	0.998211i	$0.519043\pi$
$631$	−24.1394	+	35.9625i	−0.960974	+	1.43165i	−0.901185	+	0.433435i	$0.857301\pi$
$632$	−0.173122	−	2.04508i	−0.00688642	−	0.0813490i
$633$	19.0392	−	28.3644i	0.756741	−	1.12738i
$634$	53.3748	+	27.3095i	2.11978	+	1.08460i
$635$	0.0444396	+	0.876274i	0.00176353	+	0.0347739i
$636$	−77.9444	−	16.0180i	−3.09070	−	0.635154i
$637$	−2.55641	−	4.79488i	−0.101289	−	0.189980i
$638$	55.3009	+	41.3315i	2.18938	+	1.63633i
$639$	−25.4186	+	35.2353i	−1.00554	+	1.39389i
$640$	−0.407114	+	0.400296i	−0.0160926	+	0.0158231i
$641$	−1.03328	+	12.2061i	−0.0408122	+	0.482113i	0.946432	+	0.322902i	$0.104659\pi$
$641$	−1.03328	+	12.2061i	−0.0408122	+	0.482113i	−0.987245	+	0.159211i	$0.949105\pi$
$642$	−9.88506	+	0.668864i	−0.390132	+	0.0263980i
$643$	−19.3189	+	10.7228i	−0.761861	+	0.422868i	−0.817753	−	0.575569i	$-0.804780\pi$
$643$	−19.3189	+	10.7228i	−0.761861	+	0.422868i	0.0558917	+	0.998437i	$0.482200\pi$
$644$	29.9939	−	7.22770i	1.18193	−	0.284811i
$645$	0.440739	+	0.433357i	0.0173541	+	0.0170634i
$646$	−12.0448	−	53.9708i	−0.473895	−	2.12345i
$647$	13.9974	−	12.0163i	0.550293	−	0.472411i	−0.331890	−	0.943318i	$-0.607686\pi$
$647$	13.9974	−	12.0163i	0.550293	−	0.472411i	0.882183	+	0.470907i	$0.156073\pi$
$648$	−2.30553	+	10.3307i	−0.0905698	+	0.405830i
$649$	33.4201	−	14.3417i	1.31185	−	0.562961i
$650$	12.6670	+	16.3644i	0.496842	+	0.641866i
$651$	21.8133	+	20.1140i	0.854930	+	0.788329i
$652$	−34.1880	+	44.1672i	−1.33891	+	1.72972i
$653$	−4.36472	+	16.8575i	−0.170805	+	0.659686i	0.824750	+	0.565498i	$0.191316\pi$
$653$	−4.36472	+	16.8575i	−0.170805	+	0.659686i	−0.995554	+	0.0941883i	$0.969974\pi$
$654$	−10.6460	−	26.0119i	−0.416292	−	1.01715i
$655$	0.773788	+	0.332059i	0.0302344	+	0.0129746i
$656$	10.0808	−	2.79259i	0.393588	−	0.109032i
$657$	29.1353	+	14.9072i	1.13668	+	0.581586i
$658$	−1.68763	+	2.33941i	−0.0657909	+	0.0911996i
$659$	0.235086	−	4.63551i	0.00915767	−	0.180574i	−0.990048	−	0.140729i	$-0.955055\pi$
$659$	0.235086	−	4.63551i	0.00915767	−	0.180574i	0.999206	−	0.0398452i	$-0.0126865\pi$
$660$	−1.10150	+	0.305138i	−0.0428757	+	0.0118775i
$661$	17.2212	+	19.3879i	0.669825	+	0.754100i	0.980522	−	0.196409i	$-0.0629279\pi$
$661$	17.2212	+	19.3879i	0.669825	+	0.754100i	−0.310697	+	0.950509i	$0.600562\pi$
$662$	−5.30613	+	2.06774i	−0.206229	+	0.0803651i
$663$	−24.7539	−	12.6654i	−0.961362	−	0.491885i
$664$	−22.8204	−	20.9703i	−0.885605	−	0.813804i
$665$	0.237345	−	0.267207i	0.00920383	−	0.0103618i
$666$	62.8627	+	53.9659i	2.43588	+	2.09114i
$667$	23.1270	+	37.1038i	0.895480	+	1.43667i
$668$	24.7737	−	22.7651i	0.958523	−	0.880810i
$669$	−0.249416	+	0.467812i	−0.00964299	+	0.0180867i
$670$	−0.759594	−	0.0513972i	−0.0293457	−	0.00198565i
$671$	−6.42097	+	34.1612i	−0.247879	+	1.31878i
$672$	−36.2841	+	10.0515i	−1.39969	+	0.387743i
$673$	21.2736	+	5.12634i	0.820036	+	0.197606i	0.622430	−	0.782676i	$-0.286146\pi$
$673$	21.2736	+	5.12634i	0.820036	+	0.197606i	0.197606	+	0.980281i	$0.436683\pi$
$674$	−8.76304	−	14.0590i	−0.337540	−	0.541532i
$675$	9.06320	−	8.32839i	0.348843	−	0.320560i
$676$	−25.9858	+	9.12803i	−0.999454	+	0.351078i
$677$	18.7900	+	14.0435i	0.722157	+	0.539735i	0.895465	−	0.445133i	$-0.146843\pi$
$677$	18.7900	+	14.0435i	0.722157	+	0.539735i	−0.173308	+	0.984868i	$0.555446\pi$
$678$	−26.6382	+	28.0234i	−1.02304	+	1.07623i
$679$	−3.29055	+	1.54570i	−0.126280	+	0.0593186i
$680$	−0.367794	+	0.255992i	−0.0141042	+	0.00981685i
$681$	−20.1519	−	11.1852i	−0.772221	−	0.428618i
$682$	−0.701556	−	46.2345i	−0.0268640	−	1.77041i
$683$	−20.5907	+	11.4288i	−0.787881	+	0.437310i	−0.827193	−	0.561917i	$-0.810064\pi$
$683$	−20.5907	+	11.4288i	−0.787881	+	0.437310i	0.0393122	+	0.999227i	$0.487483\pi$
$684$	22.2356	−	45.3303i	0.850198	−	1.73325i
$685$	−0.577903	−	0.160092i	−0.0220806	−	0.00611679i
$686$	−38.7895	−	21.5299i	−1.48099	−	0.822016i
$687$	−3.47511	−	1.63239i	−0.132584	−	0.0622797i
$688$	0.138517	−	8.20019i	0.00528090	−	0.312629i
$689$	−17.6475	+	8.28973i	−0.672316	+	0.315813i
$690$	−1.21693	−	0.123750i	−0.0463278	−	0.00471107i
$691$	17.8622	−	11.5570i	0.679509	−	0.439649i	−0.157002	−	0.987598i	$-0.550183\pi$
$691$	17.8622	−	11.5570i	0.679509	−	0.439649i	0.836511	+	0.547950i	$0.184591\pi$
$692$	−60.2488	+	23.4783i	−2.29031	+	0.892511i
$693$	−29.0480	−	6.99976i	−1.10344	−	0.265899i
$694$	58.7079	−	35.2303i	2.22852	−	1.33732i
$695$	0.253784	−	0.203390i	0.00962657	−	0.00771501i
$696$	24.2742	+	36.1634i	0.920111	+	1.37077i
$697$	42.1318	−	4.28438i	1.59585	−	0.162283i
$698$	3.09974	−	11.9719i	0.117327	−	0.453143i
$699$	−46.2145	−	29.9012i	−1.74799	−	1.13097i
$700$	27.6647	+	9.71779i	1.04563	+	0.367298i
$701$	−3.86512	−	7.24953i	−0.145984	−	0.273811i	0.798742	−	0.601674i	$-0.205499\pi$
$701$	−3.86512	−	7.24953i	−0.145984	−	0.273811i	−0.944725	+	0.327863i	$0.893671\pi$
$702$	−4.17820	−	9.29973i	−0.157696	−	0.350996i
$703$	24.6321	+	34.1452i	0.929018	+	1.28781i
$704$	41.3392	+	24.8074i	1.55803	+	0.934964i
$705$	0.0555453	−	0.0386607i	0.00209196	−	0.00145604i
$706$	−4.78016	+	14.3805i	−0.179904	+	0.541218i
$707$	−1.89617	+	15.9629i	−0.0713128	+	0.600347i
$708$	73.8224	−	4.99513i	2.77442	−	0.187728i
$709$	−2.54733	+	3.29088i	−0.0956669	+	0.123591i	−0.836191	−	0.548438i	$-0.815223\pi$
$709$	−2.54733	+	3.29088i	−0.0956669	+	0.123591i	0.740524	+	0.672030i	$0.234577\pi$
$710$	0.868069	+	0.444152i	0.0325781	+	0.0166687i
$711$	−2.79684	+	2.94227i	−0.104890	+	0.110344i
$712$	21.7966	+	2.21650i	0.816862	+	0.0830668i
$713$	10.2172	−	27.4424i	0.382636	−	1.02772i
$714$	−66.2391	+	6.73586i	−2.47893	+	0.252083i
$715$	−0.171427	+	0.221465i	−0.00641099	+	0.00828232i
$716$	52.1362	−	38.9663i	1.94842	−	1.45624i
$717$	−36.1675	−	25.1733i	−1.35070	−	0.940114i
$718$	6.54299	+	14.5632i	0.244182	+	0.543494i
$719$	42.5369	−	19.9813i	1.58636	−	0.745176i	0.588372	−	0.808590i	$-0.299769\pi$
$719$	42.5369	−	19.9813i	1.58636	−	0.745176i	0.997987	+	0.0634146i	$0.0201990\pi$
$720$	0.218427	+	0.0147797i	0.00814031	+	0.000550807i
$721$	0.578433	−	3.77581i	0.0215420	−	0.140619i
$722$	0.834429	−	1.00588i	0.0310542	−	0.0374350i
$723$	0.900826	+	53.3289i	0.0335021	+	1.98332i
$724$	−2.20839	−	2.48624i	−0.0820741	−	0.0924004i
$725$	−0.701797	+	41.5464i	−0.0260641	+	1.54299i
$726$	8.97363	+	15.5428i	0.333043	+	0.576847i
$727$	0.594722	−	0.208908i	0.0220570	−	0.00774797i	−0.320366	−	0.947294i	$-0.603806\pi$
$727$	0.594722	−	0.208908i	0.0220570	−	0.00774797i	0.342423	+	0.939546i	$0.388752\pi$
$728$	4.60970	−	5.95525i	0.170847	−	0.220716i
$729$	35.3156	−	19.6017i	1.30798	−	0.725990i
$730$	0.231693	−	0.697019i	0.00857534	−	0.0257978i
$731$	6.13350	−	32.6318i	0.226856	−	1.20693i
$732$	−35.3599	+	61.2451i	−1.30694	+	2.26368i
$733$	−2.07275	−	1.24385i	−0.0765589	−	0.0459426i	0.475763	−	0.879574i	$-0.342172\pi$
$733$	−2.07275	−	1.24385i	−0.0765589	−	0.0459426i	−0.552322	+	0.833631i	$0.686258\pi$
$734$	−15.9442	+	23.7535i	−0.588511	+	0.876756i
$735$	0.202715	+	0.228220i	0.00747727	+	0.00841804i
$736$	22.7442	+	29.3831i	0.838362	+	1.08307i
$737$	5.97509	+	31.7890i	0.220095	+	1.17096i
$738$	54.8619	+	35.4961i	2.01949	+	1.30663i
$739$	−27.3200	+	26.8624i	−1.00498	+	0.988150i	−0.999930	−	0.0118373i	$-0.996232\pi$
$739$	−27.3200	+	26.8624i	−1.00498	+	0.988150i	−0.00505266	+	0.999987i	$0.501608\pi$
$740$	0.582021	−	0.933766i	0.0213955	−	0.0343259i
$741$	−4.02759	−	21.4278i	−0.147957	−	0.787170i
$742$	−24.6954	+	39.6202i	−0.906598	+	1.45450i
$743$	−24.1523	+	7.57784i	−0.886063	+	0.278004i	−0.708167	−	0.706045i	$-0.750477\pi$
$743$	−24.1523	+	7.57784i	−0.886063	+	0.278004i	−0.177896	+	0.984049i	$0.556929\pi$
$744$	9.24916	−	27.6661i	0.339091	−	1.01429i
$745$	0.423307	+	0.132813i	0.0155088	+	0.00486591i
$746$	−23.6468	+	20.3002i	−0.865773	+	0.743241i
$747$	−1.03533	+	61.2914i	−0.0378807	+	2.24253i
$748$	46.5868	+	39.9935i	1.70338	+	1.46231i
$749$	−0.974159	+	3.29893i	−0.0355950	+	0.120540i
$750$	−1.81458	−	1.45426i	−0.0662592	−	0.0531020i
$751$	−5.00346	−	3.23728i	−0.182579	−	0.118130i	0.448712	−	0.893677i	$-0.351883\pi$
$751$	−5.00346	−	3.23728i	−0.182579	−	0.118130i	−0.631290	+	0.775546i	$0.717474\pi$
$752$	−0.879575	−	0.180757i	−0.0320748	−	0.00659154i
$753$	7.42167	−	18.1337i	0.270461	−	0.660829i
$754$	32.4724	+	11.4066i	1.18257	+	0.415403i
$755$	0.0886175	+	0.746027i	0.00322512	+	0.0271507i
$756$	−12.1285	−	7.84725i	−0.441109	−	0.285402i
$757$	−4.73213	+	1.84406i	−0.171992	+	0.0670235i	−0.447540	−	0.894264i	$-0.647700\pi$
$757$	−4.73213	+	1.84406i	−0.171992	+	0.0670235i	0.275548	+	0.961287i	$0.411141\pi$
$758$	−0.740286	−	8.74497i	−0.0268884	−	0.317632i
$759$	7.86953	+	51.3696i	0.285646	+	1.86460i
$760$	−0.335257	−	0.105188i	−0.0121610	−	0.00381555i
$761$	−20.0402	−	1.35600i	−0.726457	−	0.0491551i	−0.300352	−	0.953829i	$-0.597104\pi$
$761$	−20.0402	−	1.35600i	−0.726457	−	0.0491551i	−0.426106	+	0.904673i	$0.640115\pi$
$762$	128.094	+	4.32873i	4.64035	+	0.156813i
$763$	−9.75237	+	0.329566i	−0.353060	+	0.0119311i
$764$	55.9529	−	3.78600i	2.02430	−	0.136973i
$765$	0.861662	+	0.207637i	0.0311535	+	0.00750712i
$766$	−9.50879	−	21.1644i	−0.343566	−	0.764700i
$767$	13.7561	−	11.8092i	0.496705	−	0.426407i
$768$	10.0417	+	12.1050i	0.362349	+	0.436802i
$769$	−17.5345	+	10.5224i	−0.632311	+	0.379446i	−0.794457	−	0.607320i	$-0.792244\pi$
$769$	−17.5345	+	10.5224i	−0.632311	+	0.379446i	0.162146	+	0.986767i	$0.448158\pi$
$770$	−0.0565657	+	0.668209i	−0.00203849	+	0.0240806i
$771$	−2.88409	+	5.87961i	−0.103868	+	0.211749i
$772$	−30.0520	+	33.8330i	−1.08160	+	1.21768i
$773$	8.24364	−	22.2585i	0.296503	−	0.800582i	−0.699773	−	0.714365i	$-0.746716\pi$
$773$	8.24364	−	22.2585i	0.296503	−	0.800582i	0.996276	−	0.0862170i	$-0.0274779\pi$
$774$	38.8726	−	33.3710i	1.39725	−	1.19950i
$775$	22.3204	−	16.6224i	0.801773	−	0.597096i
$776$	2.71197	+	2.32815i	0.0973541	+	0.0835758i
$777$	44.3229	−	24.6012i	1.59007	−	0.882563i
$778$	4.70669	+	3.77207i	0.168743	+	0.135235i
$779$	22.8782	+	24.0678i	0.819696	+	0.862320i
$780$	−0.478395	+	0.309526i	−0.0171293	+	0.0110828i
$781$	9.02352	−	40.4331i	0.322887	−	1.44681i
$782$	30.9135	+	57.9823i	1.10547	+	2.07344i
$783$	5.13116	−	19.8177i	0.183373	−	0.708227i
$784$	0.341644	−	4.03583i	0.0122016	−	0.144137i
$785$	0.0950481	−	0.114578i	0.00339241	−	0.00408946i
$786$	57.8672	−	108.537i	2.06406	−	3.87140i
$787$	−3.53069	+	1.65850i	−0.125855	+	0.0591193i	−0.487067	−	0.873365i	$-0.661933\pi$
$787$	−3.53069	+	1.65850i	−0.125855	+	0.0591193i	0.361211	+	0.932484i	$0.382363\pi$
$788$	−7.37396	−	33.0416i	−0.262687	−	1.17706i
$789$	5.74434	+	0.979568i	0.204504	+	0.0348735i
$790$	0.0747784	+	0.0520473i	0.00266050	+	0.00185176i
$791$	5.91161	+	12.0516i	0.210193	+	0.428507i
$792$	5.42647	+	28.8702i	0.192821	+	1.02586i
$793$	2.04398	+	17.2072i	0.0725838	+	0.611047i
$794$	0.534602	+	0.796443i	0.0189723	+	0.0282647i
$795$	0.854691	−	0.684974i	0.0303128	−	0.0242935i
$796$	−2.37776	−	20.0171i	−0.0842773	−	0.709489i
$797$	−0.155264	−	1.30709i	−0.00549972	−	0.0462994i	0.989999	−	0.141074i	$-0.0450557\pi$
$797$	−0.155264	−	1.30709i	−0.00549972	−	0.0462994i	−0.995499	+	0.0947750i	$0.969787\pi$
$798$	−35.9688	−	37.8392i	−1.27328	−	1.33949i
$799$	−3.38728	−	1.31998i	−0.119833	−	0.0466977i
$800$	2.97877	+	35.1881i	0.105315	+	1.24409i
$801$	−25.3526	−	35.1439i	−0.895790	−	1.24175i
$802$	25.9752	−	70.1352i	0.917217	−	2.47656i
$803$	−31.1354	−	2.10675i	−1.09874	−	0.0743455i
$804$	−9.96530	+	65.0500i	−0.351449	+	2.29414i
$805$	−0.187024	+	0.381275i	−0.00659174	+	0.0134382i
$806$	−7.23364	−	21.8870i	−0.254794	−	0.770937i
$807$	6.14673	+	12.5310i	0.216375	+	0.441111i
$808$	15.0794	−	4.73118i	0.530490	−	0.166442i
$809$	7.14605	−	1.72200i	0.251242	−	0.0605423i	−0.106682	−	0.994293i	$-0.534023\pi$
$809$	7.14605	−	1.72200i	0.251242	−	0.0605423i	0.357923	+	0.933751i	$0.383485\pi$
$810$	−0.287614	−	0.371566i	−0.0101057	−	0.0130555i
$811$	18.6891	+	2.54079i	0.656262	+	0.0892193i	0.455242	−	0.890368i	$-0.349553\pi$
$811$	18.6891	+	2.54079i	0.656262	+	0.0892193i	0.201020	+	0.979587i	$0.435574\pi$
$812$	47.4097	−	11.4244i	1.66375	−	0.400918i
$813$	0.00547217	−	0.323953i	0.000191918	−	0.0113615i
$814$	−75.3762	−	23.6494i	−2.64194	−	0.828913i
$815$	−0.167455	−	0.750342i	−0.00586570	−	0.0262833i
$816$	−10.3630	−	17.9493i	−0.362779	−	0.628352i
$817$	23.1775	−	11.8589i	0.810878	−	0.414889i
$818$	7.11487	−	59.8965i	0.248766	−	2.09423i
$819$	−14.8615	+	1.00559i	−0.519302	+	0.0351381i
$820$	0.355648	−	0.791590i	0.0124198	−	0.0276435i
$821$	14.1378	−	2.90540i	0.493413	−	0.101399i	0.0518974	−	0.998652i	$-0.483473\pi$
$821$	14.1378	−	2.90540i	0.493413	−	0.101399i	0.441516	+	0.897253i	$0.354441\pi$
$822$	−30.4229	+	82.1442i	−1.06112	+	2.86511i
$823$	−20.8904	+	9.81305i	−0.728194	+	0.342062i	−0.753348	−	0.657622i	$-0.771562\pi$
$823$	−20.8904	+	9.81305i	−0.728194	+	0.342062i	0.0251537	+	0.999684i	$0.491992\pi$
$824$	−3.61916	+	1.00259i	−0.126080	+	0.0349267i
$825$	−20.2413	+	45.0525i	−0.704712	+	1.56853i
$826$	12.2943	−	41.6341i	0.427775	−	1.44864i
$827$	−44.1748	+	22.6023i	−1.53611	+	0.785957i	−0.998366	−	0.0571515i	$-0.981798\pi$
$827$	−44.1748	+	22.6023i	−1.53611	+	0.785957i	−0.537743	+	0.843109i	$0.680723\pi$
$828$	−11.0826	+	58.9623i	−0.385147	+	2.04908i
$829$	4.47513	−	4.70783i	0.155428	−	0.163510i	−0.642453	−	0.766325i	$-0.722083\pi$
$829$	4.47513	−	4.70783i	0.155428	−	0.163510i	0.797881	+	0.602815i	$0.205954\pi$
$830$	1.36325	−	0.185334i	0.0473189	−	0.00643304i
$831$	−32.5522	−	12.6852i	−1.12922	−	0.440046i
$832$	23.3654	+	5.63041i	0.810049	+	0.195199i
$833$	4.11008	−	15.8741i	0.142406	−	0.550003i
$834$	−26.4774	−	39.4456i	−0.916836	−	1.36589i
$835$	0.0234563	+	0.462519i	0.000811739	+	0.0160061i
$836$	−2.43844	+	48.0819i	−0.0843352	+	1.66295i
$837$	−12.6089	+	5.38526i	−0.435826	+	0.186142i
$838$	0.236309	+	4.65962i	0.00816317	+	0.160964i
$839$	53.9266	−	5.48380i	1.86175	−	0.189322i	0.895178	−	0.445708i	$-0.147048\pi$
$839$	53.9266	−	5.48380i	1.86175	−	0.189322i	0.966574	+	0.256386i	$0.0825318\pi$
$840$	−0.173378	+	0.385900i	−0.00598211	+	0.0133148i
$841$	21.2156	+	34.0372i	0.731571	+	1.17370i
$842$	3.22639	+	3.63233i	0.111189	+	0.125178i
$843$	33.6024	+	40.5068i	1.15733	+	1.39513i
$844$	−18.8025	+	32.5668i	−0.647207	+	1.12100i
$845$	0.131668	−	0.355514i	0.00452951	−	0.0122300i
$846$	−2.80466	−	4.85781i	−0.0964262	−	0.167015i
$847$	6.14229	−	1.04743i	0.211052	−	0.0359901i
$848$	−14.4007	−	1.95778i	−0.494521	−	0.0672305i
$849$	−1.78451	−	1.43016i	−0.0612442	−	0.0490829i
$850$	−5.26761	+	62.2261i	−0.180677	+	2.13434i
$851$	−39.0384	−	31.2865i	−1.33822	−	1.07249i
$852$	44.5847	−	71.5295i	1.52745	−	2.45056i
$853$	42.6074	−	18.2843i	1.45885	−	0.626041i	0.489560	−	0.871969i	$-0.337157\pi$
$853$	42.6074	−	18.2843i	1.45885	−	0.626041i	0.969288	+	0.245928i	$0.0790927\pi$
$854$	26.4912	+	31.9344i	0.906509	+	1.09277i
$855$	0.284818	+	0.633939i	0.00974056	+	0.0216802i
$856$	3.35095	−	0.455564i	0.114533	−	0.0155708i
$857$	−5.36869	−	16.1510i	−0.183391	−	0.551708i	0.816272	−	0.577668i	$-0.196037\pi$
$857$	−5.36869	−	16.1510i	−0.183391	−	0.551708i	−0.999663	+	0.0259595i	$0.991736\pi$
$858$	30.1231	+	27.6808i	1.02839	+	0.945008i
$859$	2.39537	−	4.49282i	0.0817290	−	0.153293i	−0.838219	−	0.545334i	$-0.816403\pi$
$859$	2.39537	−	4.49282i	0.0817290	−	0.153293i	0.919948	+	0.392041i	$0.128231\pi$
$860$	−0.516257	−	0.443192i	−0.0176042	−	0.0151127i
$861$	32.0251	−	23.9354i	1.09141	−	0.815715i
$862$	−11.9513	+	10.9824i	−0.407064	+	0.374061i
$863$	3.17732	−	1.62569i	0.108157	−	0.0553393i	−0.400575	−	0.916264i	$-0.631190\pi$
$863$	3.17732	−	1.62569i	0.108157	−	0.0553393i	0.508732	+	0.860925i	$0.330114\pi$
$864$	2.63451	−	17.1972i	0.0896278	−	0.585060i
$865$	0.280753	−	0.844610i	0.00954589	−	0.0287176i
$866$	0.843870	+	3.25922i	0.0286759	+	0.110753i
$867$	−13.5938	−	36.7045i	−0.461671	−	1.24655i
$868$	−25.4518	−	20.4697i	−0.863889	−	0.694785i
$869$	1.34435	−	3.62986i	0.0456040	−	0.123134i
$870$	−1.92353	−	0.195604i	−0.0652139	−	0.00663160i
$871$	7.58621	+	14.2289i	0.257049	+	0.482128i
$872$	4.22490	+	8.61304i	0.143073	+	0.291674i
$873$	−0.119400	−	7.06850i	−0.00404109	−	0.239232i
$874$	−21.1151	+	46.9974i	−0.714230	+	1.58971i
$875$	−0.692262	+	0.415422i	−0.0234027	+	0.0140438i
$876$	−58.3458	−	25.0381i	−1.97132	−	0.845961i
$877$	−33.9418	−	31.1899i	−1.14613	−	1.05321i	−0.997934	−	0.0642514i	$-0.979534\pi$
$877$	−33.9418	−	31.1899i	−1.14613	−	1.05321i	−0.148199	−	0.988958i	$-0.547348\pi$
$878$	14.0989	−	75.0097i	0.475815	−	2.53146i
$879$	−15.5088	−	14.2515i	−0.523100	−	0.480689i
$880$	−0.196955	+	0.0691843i	−0.00663934	+	0.00233220i
$881$	−9.61396	−	2.31670i	−0.323903	−	0.0780515i	0.0690417	−	0.997614i	$-0.478006\pi$
$881$	−9.61396	−	2.31670i	−0.323903	−	0.0780515i	−0.392944	+	0.919562i	$0.628543\pi$
$882$	20.2661	−	15.1468i	0.682396	−	0.510018i
$883$	−0.506812	−	1.95742i	−0.0170556	−	0.0658725i	0.958989	−	0.283444i	$-0.0914769\pi$
$883$	−0.506812	−	1.95742i	−0.0170556	−	0.0658725i	−0.976044	+	0.217571i	$0.930187\pi$
$884$	28.1278	+	12.0706i	0.946041	+	0.405978i
$885$	−0.595853	+	0.825974i	−0.0200294	+	0.0277648i
$886$	−28.1067	+	18.1853i	−0.944264	+	0.610947i
$887$	−16.9689	−	20.4555i	−0.569759	−	0.686829i	0.403909	−	0.914799i	$-0.367651\pi$
$887$	−16.9689	−	20.4555i	−0.569759	−	0.686829i	−0.973668	+	0.227970i	$0.926791\pi$
$888$	−39.9203	−	29.8362i	−1.33964	−	1.00124i
$889$	16.8546	−	41.1816i	0.565285	−	1.38119i
$890$	−0.693492	+	0.681877i	−0.0232459	+	0.0228566i
$891$	−12.2195	+	15.7863i	−0.409368	+	0.528860i
$892$	0.239163	−	0.532322i	0.00800777	−	0.0178235i
$893$	−0.807293	−	2.73385i	−0.0270150	−	0.0914849i
$894$	24.5475	−	59.9780i	0.820992	−	2.00597i
$895$	−0.0453780	+	0.894778i	−0.00151682	+	0.0299091i
$896$	27.3190	−	9.59633i	0.912662	−	0.320591i
$897$	11.4095	+	23.2598i	0.380951	+	0.776621i
$898$	−1.55281	−	1.63355i	−0.0518179	−	0.0545124i
$899$	16.1497	−	43.3766i	0.538623	−	1.44669i
$900$	−39.2839	+	41.3266i	−1.30946	+	1.37755i
$901$	−56.1392	−	17.6138i	−1.87027	−	0.586801i
$902$	−61.4203	−	10.4739i	−2.04507	−	0.348741i
$903$	−10.8869	−	29.3956i	−0.362295	−	0.978225i
$904$	8.42592	−	10.1572i	0.280242	−	0.337824i
$905$	0.0457472	−	0.00154595i	0.00152069	−	5.13892e-5i
$906$	109.680	−	3.70646i	3.64387	−	0.123139i
$907$	24.6704	−	50.2940i	0.819167	−	1.66998i	0.0796728	−	0.996821i	$-0.474612\pi$
$907$	24.6704	−	50.2940i	0.819167	−	1.66998i	0.739494	−	0.673163i	$-0.235065\pi$
$908$	22.9635	+	10.7869i	0.762071	+	0.357975i
$909$	−26.8035	−	16.0846i	−0.889015	−	0.533493i
$910$	0.0728162	+	0.326279i	0.00241383	+	0.0108160i
$911$	−11.0269	+	49.4101i	−0.365339	+	1.63703i	0.348925	+	0.937151i	$0.386547\pi$
$911$	−11.0269	+	49.4101i	−0.365339	+	1.63703i	−0.714263	+	0.699877i	$0.753238\pi$
$912$	6.15577	−	15.0407i	0.203838	−	0.498046i
$913$	−22.1401	−	54.0959i	−0.732731	−	1.79031i
$914$	−32.6415	−	18.1175i	−1.07968	−	0.599273i
$915$	−0.338079	−	0.912842i	−0.0111766	−	0.0301776i
$916$	3.93794	+	1.53457i	0.130113	+	0.0507036i
$917$	−28.3590	−	31.9271i	−0.936498	−	1.05432i
$918$	9.70468	−	29.1953i	0.320302	−	0.963589i
$919$	14.8649	+	0.502334i	0.490346	+	0.0165705i	0.277915	−	0.960606i	$-0.410357\pi$
$919$	14.8649	+	0.502334i	0.490346	+	0.0165705i	0.212431	+	0.977176i	$0.431862\pi$
$920$	0.417278	+	0.0141012i	0.0137572	+	0.000464904i
$921$	59.7623	−	30.5777i	1.96924	−	1.00757i
$922$	46.4743	+	32.3471i	1.53055	+	1.06529i
$923$	−1.74206	−	20.5789i	−0.0573405	−	0.677361i
$924$	57.1412	+	9.74415i	1.87981	+	0.320559i
$925$	−14.9979	−	45.1191i	−0.493126	−	1.48351i
$926$	1.02989	+	20.3077i	0.0338443	+	0.667353i
$927$	6.23646	+	4.03504i	0.204832	+	0.132528i
$928$	35.9504	+	46.4441i	1.18013	+	1.52460i
$929$	12.3134	+	5.28409i	0.403989	+	0.173365i	0.586706	−	0.809800i	$-0.300425\pi$
$929$	12.3134	+	5.28409i	0.403989	+	0.173365i	−0.182716	+	0.983166i	$0.558489\pi$
$930$	0.683090	+	1.10012i	0.0223994	+	0.0360744i
$931$	11.8155	−	5.07044i	0.387238	−	0.166177i
$932$	52.9783	+	29.4054i	1.73536	+	0.963205i
$933$	−17.1885	+	15.7950i	−0.562728	+	0.517104i
$934$	−8.28425	−	31.9956i	−0.271069	−	1.04693i
$935$	−0.833109	+	0.142068i	−0.0272456	+	0.00464612i
$936$	6.88966	+	12.9224i	0.225196	+	0.422383i
$937$	17.0164	+	8.70653i	0.555902	+	0.284430i	0.710675	−	0.703520i	$-0.248390\pi$
$937$	17.0164	+	8.70653i	0.555902	+	0.284430i	−0.154774	+	0.987950i	$0.549465\pi$
$938$	33.7592	+	18.7379i	1.10228	+	0.611813i
$939$	−89.0124	−	12.1013i	−2.90481	−	0.394911i
$940$	−0.0581310	+	0.0465879i	−0.00189603	+	0.00151953i
$941$	−5.54328	+	13.5442i	−0.180706	+	0.441527i	−0.989124	−	0.147081i	$-0.953012\pi$
$941$	−5.54328	+	13.5442i	−0.180706	+	0.441527i	0.808418	+	0.588608i	$0.200324\pi$
$942$	−15.5062	−	15.2465i	−0.505221	−	0.496759i
$943$	−33.8332	−	20.3031i	−1.10176	−	0.661160i
$944$	13.3905	−	1.82044i	0.435823	−	0.0592504i
$945$	0.189722	−	0.0595258i	0.00617167	−	0.00193637i
$946$	−21.5137	+	43.8586i	−0.699470	+	1.42597i
$947$	2.11556	−	17.8099i	0.0687466	−	0.578743i	−0.915548	−	0.402209i	$-0.868243\pi$
$947$	2.11556	−	17.8099i	0.0687466	−	0.578743i	0.984294	−	0.176534i	$-0.0564887\pi$
$948$	5.02813	−	6.06127i	0.163306	−	0.196861i
$949$	−15.1241	+	3.64449i	−0.490949	+	0.118305i
$950$	−41.1121	+	26.5999i	−1.33385	+	0.863014i
$951$	22.5018	+	67.6939i	0.729672	+	2.19513i
$952$	22.4025	−	3.82025i	0.726070	−	0.123815i
$953$	13.3605	−	21.4350i	0.432791	−	0.694348i	−0.557986	−	0.829850i	$-0.688426\pi$
$953$	13.3605	−	21.4350i	0.432791	−	0.694348i	0.990777	+	0.135502i	$0.0432646\pi$
$954$	−50.5968	−	75.3784i	−1.63813	−	2.44047i
$955$	−0.451620	+	0.626038i	−0.0146141	+	0.0202581i
$956$	41.5926	+	24.9595i	1.34520	+	0.807247i
$957$	12.4389	+	81.1969i	0.402093	+	2.62472i
$958$	−5.04124	−	59.5519i	−0.162875	−	1.92404i
$959$	23.0754	+	19.8096i	0.745143	+	0.639685i
$960$	−1.35016			−0.0435761
$961$	−29.6100	+	9.17860i	−0.955162	+	0.296084i
$962$	−39.3825			−1.26974
$963$	−5.07522	−	4.35694i	−0.163547	−	0.140400i
$964$	−4.95243	−	58.5029i	−0.159507	−	1.88425i
$965$	−0.0943226	−	0.615705i	−0.00303635	−	0.0198203i
$966$	53.1921	+	31.9203i	1.71143	+	1.02702i
$967$	21.7558	−	30.1581i	0.699621	−	0.969818i	−0.300252	−	0.953860i	$-0.597071\pi$
$967$	21.7558	−	30.1581i	0.699621	−	0.969818i	0.999873	−	0.0159578i	$-0.00507975\pi$
$968$	−3.41412	−	5.08632i	−0.109734	−	0.163480i
$969$	34.8031	−	55.8364i	1.11804	−	1.79372i
$970$	−0.156406	+	0.0266716i	−0.00502190	+	0.000856373i
$971$	−6.70030	−	20.1570i	−0.215023	−	0.646869i	−0.999638	−	0.0268863i	$-0.991441\pi$
$971$	−6.70030	−	20.1570i	−0.215023	−	0.646869i	0.784616	−	0.619982i	$-0.212860\pi$
$972$	−52.0809	+	33.6968i	−1.67049	+	1.08082i
$973$	−16.0349	+	3.86397i	−0.514056	+	0.123873i
$974$	4.71475	−	5.68350i	0.151070	−	0.182111i
$975$	−2.90435	+	24.4503i	−0.0930136	+	0.783035i
$976$	−5.68820	+	11.5962i	−0.182075	+	0.371185i
$977$	−28.6850	+	8.99997i	−0.917713	+	0.287934i	−0.721329	−	0.692593i	$-0.756468\pi$
$977$	−28.6850	+	8.99997i	−0.917713	+	0.287934i	−0.196384	+	0.980527i	$0.562920\pi$
$978$	−111.279	+	15.1285i	−3.55832	+	0.483757i
$979$	35.4303	+	21.2616i	1.13236	+	0.679522i
$980$	−0.239597	−	0.235584i	−0.00765366	−	0.00752547i
$981$	7.18733	−	17.5611i	0.229474	−	0.560684i
$982$	−12.4413	+	9.97082i	−0.397018	+	0.318182i
$983$	−58.3896	−	7.93811i	−1.86234	−	0.253186i	−0.885112	−	0.465379i	$-0.845918\pi$
$983$	−58.3896	−	7.93811i	−1.86234	−	0.253186i	−0.977228	+	0.212192i	$0.931940\pi$
$984$	−34.3683	−	19.0760i	−1.09562	−	0.608119i
$985$	0.414848	+	0.212259i	0.0132182	+	0.00676313i
$986$	48.8632	+	91.6493i	1.55612	+	2.91871i
$987$	−3.38329	+	0.576945i	−0.107691	+	0.0183644i
$988$	6.01578	+	23.2343i	0.191388	+	0.739182i
$989$	−22.7791	+	20.9323i	−0.724334	+	0.665608i
$990$	−1.14017	−	0.632847i	−0.0362370	−	0.0201132i
$991$	22.6319	−	9.71210i	0.718925	−	0.308515i	−0.00347140	−	0.999994i	$-0.501105\pi$
$991$	22.6319	−	9.71210i	0.718925	−	0.308515i	0.722397	+	0.691479i	$0.243040\pi$
$992$	9.92517	−	38.0637i	0.315125	−	1.20852i
$993$	−6.22660	−	2.67204i	−0.197595	−	0.0847948i
$994$	−30.2698	−	39.1054i	−0.960100	−	1.24035i
$995$	0.232958	+	0.150726i	0.00738527	+	0.00477834i
$996$	−6.02330	−	118.769i	−0.190856	−	3.76335i
$997$	10.2305	+	30.7770i	0.324002	+	0.974719i	0.976238	+	0.216703i	$0.0695302\pi$
$997$	10.2305	+	30.7770i	0.324002	+	0.974719i	−0.652236	+	0.758016i	$0.726169\pi$
$998$	−68.1892	−	11.6281i	−2.15849	−	0.368082i
$999$	1.97587	+	23.3408i	0.0625136	+	0.738471i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.k.a.5.11	✓	4920
961.769	even	93	inner	961.2.k.a.769.11	yes	4920

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
961.2.k.a.5.11	✓	4920	1.1	even	1	trivial
961.2.k.a.769.11	yes	4920	961.769	even	93	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.k (of order \(93\), degree \(60\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.67939 - 1.44171i) q^{2} +(-0.222135 - 2.62407i) q^{3} +(0.438970 + 2.86545i) q^{4} +(-0.0342144 - 0.0205319i) q^{5} +(-3.41010 + 4.72709i) q^{6} +(1.12782 + 1.68021i) q^{7} +(1.05238 - 1.68839i) q^{8} +(-3.87909 + 0.661492i) q^{9} +(0.0278583 + 0.0838081i) q^{10} +(3.15032 - 2.03828i) q^{11} +(7.42162 - 1.78840i) q^{12} +(1.19428 - 1.43967i) q^{13} +(0.528326 - 4.44771i) q^{14} +(-0.0462768 + 0.0943417i) q^{15} +(1.33033 - 0.417394i) q^{16} +(5.59328 - 0.760410i) q^{17} +(7.46819 + 4.48162i) q^{18} +(3.15605 + 3.10319i) q^{19} +(0.0438138 - 0.107052i) q^{20} +(4.15846 - 3.33271i) q^{21} +(-8.22922 - 1.11877i) q^{22} +(-4.59847 - 2.55236i) q^{23} +(-4.66423 - 2.38648i) q^{24} +(-2.35158 - 4.41069i) q^{25} +(-4.08124 + 0.695963i) q^{26} +(0.617237 + 2.38391i) q^{27} +(-4.31947 + 3.96926i) q^{28} +(-7.26854 - 4.03437i) q^{29} +(0.213730 - 0.0917188i) q^{30} +(0.833660 + 5.50500i) q^{31} +(-6.49247 - 2.78614i) q^{32} +(-6.04840 - 7.81388i) q^{33} +(-10.4896 - 6.78685i) q^{34} +(-0.00408977 - 0.0806435i) q^{35} +(-3.59828 - 10.8250i) q^{36} +(9.37697 + 1.59903i) q^{37} +(-0.826345 - 9.76158i) q^{38} +(-4.04308 - 2.81407i) q^{39} +(-0.0706724 + 0.0361599i) q^{40} +(7.49813 + 0.253387i) q^{41} +(-11.7885 - 0.398373i) q^{42} +(1.85544 - 5.58187i) q^{43} +(7.22349 + 8.13232i) q^{44} +(0.146302 + 0.0570125i) q^{45} +(4.04286 + 10.9161i) q^{46} +(-0.563107 - 0.312550i) q^{47} +(-1.39079 - 3.39817i) q^{48} +(1.10032 - 2.68847i) q^{49} +(-2.40971 + 10.7976i) q^{50} +(-3.23783 - 14.5082i) q^{51} +(4.64954 + 2.79016i) q^{52} +(-9.43442 - 4.43172i) q^{53} +(2.40032 - 4.89339i) q^{54} +(-0.149636 + 0.00505671i) q^{55} +(4.02375 - 0.135976i) q^{56} +(7.44193 - 8.97104i) q^{57} +(6.39032 + 17.2544i) q^{58} +(9.55433 + 1.62928i) q^{59} +(-0.290645 - 0.0911906i) q^{60} +(-6.38240 + 6.71428i) q^{61} +(6.53657 - 10.4469i) q^{62} +(-5.48636 - 5.77164i) q^{63} +(5.65853 + 11.5357i) q^{64} +(-0.0704204 + 0.0247366i) q^{65} +(-1.10773 + 21.8426i) q^{66} +(-3.26524 + 7.97810i) q^{67} +(4.63419 + 15.6934i) q^{68} +(-5.67609 + 12.6337i) q^{69} +(-0.109396 + 0.141328i) q^{70} +(7.87274 - 7.74087i) q^{71} +(-2.96543 + 7.24557i) q^{72} +(-6.66180 - 4.97898i) q^{73} +(-13.4423 - 16.2043i) q^{74} +(-11.0516 + 7.15047i) q^{75} +(-7.50662 + 10.4057i) q^{76} +(6.97773 + 2.99438i) q^{77} +(2.73284 + 10.5549i) q^{78} +(0.826318 - 0.617584i) q^{79} +(-0.0540863 - 0.0130333i) q^{80} +(-5.01965 + 1.76325i) q^{81} +(-12.2270 - 11.2357i) q^{82} +(2.87763 - 15.3097i) q^{83} +(11.3751 + 10.4529i) q^{84} +(-0.206983 - 0.0888234i) q^{85} +(-11.1634 + 6.69912i) q^{86} +(-8.97187 + 19.9693i) q^{87} +(-0.126081 - 7.46402i) q^{88} +(4.84972 + 9.88683i) q^{89} +(-0.163503 - 0.306672i) q^{90} +(3.76587 + 0.382951i) q^{91} +(5.29505 - 14.2971i) q^{92} +(14.2603 - 3.41043i) q^{93} +(0.495070 + 1.33673i) q^{94} +(-0.0442681 - 0.170973i) q^{95} +(-5.86882 + 17.6556i) q^{96} +(-0.272045 + 1.77581i) q^{97} +(-5.72386 + 2.92864i) q^{98} +(-10.8721 + 9.99060i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4920 q - 58 q^{2} - 64 q^{3} - 226 q^{4} - 60 q^{5} - 56 q^{6} - 60 q^{7} - 56 q^{8} + 18 q^{9} - 61 q^{10} - 64 q^{11} - 72 q^{12} - 64 q^{13} - 65 q^{14} + 66 q^{15} - 234 q^{16} - 68 q^{17} - 70 q^{18}+ \cdots - 86 q^{99}+O(q^{100}) \) 4920 * q - 58 * q^2 - 64 * q^3 - 226 * q^4 - 60 * q^5 - 56 * q^6 - 60 * q^7 - 56 * q^8 + 18 * q^9 - 61 * q^10 - 64 * q^11 - 72 * q^12 - 64 * q^13 - 65 * q^14 + 66 * q^15 - 234 * q^16 - 68 * q^17 - 70 * q^18 - 56 * q^19 - 57 * q^20 - 68 * q^21 + 76 * q^22 - 46 * q^23 + 72 * q^24 + 10 * q^25 + 56 * q^26 - 58 * q^27 - 49 * q^28 - 46 * q^29 - 74 * q^30 - 42 * q^31 - 86 * q^32 - 90 * q^33 - 64 * q^34 - 202 * q^35 + 34 * q^36 - 60 * q^37 - 61 * q^38 - 58 * q^39 + 62 * q^40 - 56 * q^41 - 730 * q^42 + 60 * q^43 - 88 * q^44 - 58 * q^45 + 108 * q^46 + 34 * q^47 - 68 * q^48 + 10 * q^49 + 104 * q^50 - 60 * q^51 - 48 * q^52 - 56 * q^53 - 58 * q^54 - 64 * q^55 - 500 * q^56 - 64 * q^57 - 62 * q^58 - 64 * q^59 + 82 * q^60 + 124 * q^61 + 383 * q^62 + 30 * q^63 + 48 * q^64 - 64 * q^65 - 18 * q^66 - 58 * q^67 - 300 * q^68 - 50 * q^69 - 80 * q^70 - 68 * q^71 - 55 * q^72 - 370 * q^73 - 64 * q^74 - 54 * q^75 + 261 * q^76 - 34 * q^77 - 98 * q^78 - 84 * q^79 + 480 * q^80 + 20 * q^81 + 299 * q^82 - 68 * q^83 + 288 * q^84 + 198 * q^85 - 88 * q^86 + 101 * q^87 - 44 * q^88 - 46 * q^89 - 55 * q^90 + 453 * q^91 - 46 * q^92 - 40 * q^93 - 768 * q^94 + 61 * q^95 - 64 * q^96 - 102 * q^97 - 51 * q^98 - 86 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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