LMFDB - Embedded newform 966.2.y.c.121.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(25,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 44, 6]))

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

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

chi := DirichletCharacter("966.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.y (of order $33$, degree $20$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$8$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			121.8
Character	$\chi$	$=$	966.121
Dual form			966.2.y.c.487.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.580057 + 0.814576i) q^{2} +(-0.235759 - 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(0.141678 + 2.97420i) q^{5} +(0.654861 - 0.755750i) q^{6} +(-2.12708 - 1.57338i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +O(q^{10})$	\(q+(0.580057 + 0.814576i) q^{2} +(-0.235759 - 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(0.141678 + 2.97420i) q^{5} +(0.654861 - 0.755750i) q^{6} +(-2.12708 - 1.57338i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +(-2.34053 + 1.84061i) q^{10} +(0.243786 - 0.342349i) q^{11} +(0.995472 + 0.0950560i) q^{12} +(0.340126 + 2.36563i) q^{13} +(0.0478129 - 2.64532i) q^{14} +(2.85696 - 0.838878i) q^{15} +(-0.786053 - 0.618159i) q^{16} +(-2.06788 - 0.398550i) q^{17} +(-0.888835 - 0.458227i) q^{18} +(-4.09198 + 0.788665i) q^{19} +(-2.85696 - 0.838878i) q^{20} +(-1.02755 + 2.43806i) q^{21} +0.420279 q^{22} +(-1.73720 + 4.47014i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-3.84841 + 0.367479i) q^{25} +(-1.72969 + 1.64926i) q^{26} +(0.654861 + 0.755750i) q^{27} +(2.18255 - 1.49549i) q^{28} +(-0.812390 + 0.937548i) q^{29} +(2.34053 + 1.84061i) q^{30} +(-5.11967 - 4.88160i) q^{31} +(0.0475819 - 0.998867i) q^{32} +(-0.390174 - 0.156202i) q^{33} +(-0.874836 - 1.91562i) q^{34} +(4.37819 - 6.54927i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(-4.58138 + 2.36186i) q^{37} +(-3.01601 - 2.87576i) q^{38} +(2.21875 - 0.888255i) q^{39} +(-0.973867 - 2.81381i) q^{40} +(-1.22448 + 0.786923i) q^{41} +(-2.58202 + 0.577193i) q^{42} +(-9.89797 - 2.90631i) q^{43} +(0.243786 + 0.342349i) q^{44} +(-1.48878 - 2.57865i) q^{45} +(-4.64894 + 1.17785i) q^{46} +(-0.412301 + 0.714126i) q^{47} +(-0.415415 + 0.909632i) q^{48} +(2.04893 + 6.69342i) q^{49} +(-2.53164 - 2.92166i) q^{50} +(0.100204 + 2.10355i) q^{51} +(-2.34676 - 0.452301i) q^{52} +(8.04428 - 3.22044i) q^{53} +(-0.235759 + 0.971812i) q^{54} +(1.05275 + 0.676563i) q^{55} +(2.48419 + 0.910382i) q^{56} +(1.73116 + 3.79070i) q^{57} +(-1.23494 - 0.117922i) q^{58} +(1.72739 - 1.35843i) q^{59} +(-0.141678 + 2.97420i) q^{60} +(-2.69989 + 11.1291i) q^{61} +(1.00673 - 7.00197i) q^{62} +(2.61159 + 0.423794i) q^{63} +(0.841254 - 0.540641i) q^{64} +(-6.98765 + 1.34676i) q^{65} +(-0.0990845 - 0.408432i) q^{66} +(7.40963 - 0.707534i) q^{67} +(1.05297 - 1.82379i) q^{68} +(4.75369 + 0.634360i) q^{69} +(7.87447 - 0.232580i) q^{70} +(2.85888 - 6.26008i) q^{71} +(0.723734 - 0.690079i) q^{72} +(-1.63720 + 4.73038i) q^{73} +(-4.58138 - 2.36186i) q^{74} +(1.26442 + 3.65329i) q^{75} +(0.593067 - 4.12487i) q^{76} +(-1.05720 + 0.344635i) q^{77} +(2.01056 + 1.29211i) q^{78} +(-1.35873 - 0.543953i) q^{79} +(1.72716 - 2.42546i) q^{80} +(0.580057 - 0.814576i) q^{81} +(-1.35127 - 0.540969i) q^{82} +(1.49868 + 0.963143i) q^{83} +(-1.96789 - 1.76845i) q^{84} +(0.892394 - 6.20673i) q^{85} +(-3.37398 - 9.74848i) q^{86} +(1.10265 + 0.568454i) q^{87} +(-0.137460 + 0.397164i) q^{88} +(-9.24850 + 8.81843i) q^{89} +(1.23693 - 2.70849i) q^{90} +(2.99856 - 5.56702i) q^{91} +(-3.65610 - 3.10370i) q^{92} +(-3.53698 + 6.12624i) q^{93} +(-0.820868 + 0.0783834i) q^{94} +(-2.92539 - 12.0586i) q^{95} +(-0.981929 + 0.189251i) q^{96} +(-13.3989 + 8.61097i) q^{97} +(-4.26380 + 5.55158i) q^{98} +(-0.0598119 + 0.416001i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} + 16 q^{6} - 2 q^{7} - 16 q^{8} + 8 q^{9}+O(q^{10}) $ 160 * q + 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 + 16 * q^6 - 2 * q^7 - 16 * q^8 + 8 * q^9	\( 160 q + 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} + 16 q^{6} - 2 q^{7} - 16 q^{8} + 8 q^{9} + 2 q^{10} + 8 q^{11} - 8 q^{12} - 4 q^{13} + 9 q^{14} - 18 q^{15} + 8 q^{16} - 21 q^{17} + 8 q^{18} + 4 q^{19} + 18 q^{20} - 15 q^{21} + 116 q^{22} + 14 q^{23} + 80 q^{24} + 2 q^{25} + 2 q^{26} + 16 q^{27} - 18 q^{28} - 46 q^{29} - 2 q^{30} + q^{31} + 8 q^{32} - 8 q^{33} - 68 q^{34} - 84 q^{35} - 16 q^{36} + 19 q^{37} - 7 q^{38} - 2 q^{39} - 9 q^{40} + 38 q^{41} + 2 q^{42} + 28 q^{43} + 8 q^{44} + 24 q^{45} - 8 q^{46} - 26 q^{47} + 16 q^{48} - 6 q^{49} - 4 q^{50} + 21 q^{51} + 2 q^{52} - 20 q^{53} - 8 q^{54} + 46 q^{55} - 2 q^{56} - 14 q^{57} - 21 q^{58} + 36 q^{59} - 2 q^{60} + 40 q^{61} - 24 q^{62} - 2 q^{63} - 16 q^{64} - 10 q^{65} - 8 q^{66} + 6 q^{67} + 34 q^{68} + 6 q^{69} - 20 q^{70} + 132 q^{71} + 8 q^{72} - 36 q^{73} + 19 q^{74} - 2 q^{75} - 8 q^{76} - 75 q^{77} - 18 q^{78} + 34 q^{79} + 2 q^{80} + 8 q^{81} + 47 q^{82} + 74 q^{83} + 13 q^{84} + 2 q^{85} + 30 q^{86} + 10 q^{87} - 3 q^{88} - 12 q^{89} - 4 q^{90} - 30 q^{91} - 50 q^{92} + 10 q^{93} - 4 q^{94} + 27 q^{95} - 8 q^{96} + 24 q^{97} + 7 q^{98} - 16 q^{99}+O(q^{100}) \) 160 * q + 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 + 16 * q^6 - 2 * q^7 - 16 * q^8 + 8 * q^9 + 2 * q^10 + 8 * q^11 - 8 * q^12 - 4 * q^13 + 9 * q^14 - 18 * q^15 + 8 * q^16 - 21 * q^17 + 8 * q^18 + 4 * q^19 + 18 * q^20 - 15 * q^21 + 116 * q^22 + 14 * q^23 + 80 * q^24 + 2 * q^25 + 2 * q^26 + 16 * q^27 - 18 * q^28 - 46 * q^29 - 2 * q^30 + q^31 + 8 * q^32 - 8 * q^33 - 68 * q^34 - 84 * q^35 - 16 * q^36 + 19 * q^37 - 7 * q^38 - 2 * q^39 - 9 * q^40 + 38 * q^41 + 2 * q^42 + 28 * q^43 + 8 * q^44 + 24 * q^45 - 8 * q^46 - 26 * q^47 + 16 * q^48 - 6 * q^49 - 4 * q^50 + 21 * q^51 + 2 * q^52 - 20 * q^53 - 8 * q^54 + 46 * q^55 - 2 * q^56 - 14 * q^57 - 21 * q^58 + 36 * q^59 - 2 * q^60 + 40 * q^61 - 24 * q^62 - 2 * q^63 - 16 * q^64 - 10 * q^65 - 8 * q^66 + 6 * q^67 + 34 * q^68 + 6 * q^69 - 20 * q^70 + 132 * q^71 + 8 * q^72 - 36 * q^73 + 19 * q^74 - 2 * q^75 - 8 * q^76 - 75 * q^77 - 18 * q^78 + 34 * q^79 + 2 * q^80 + 8 * q^81 + 47 * q^82 + 74 * q^83 + 13 * q^84 + 2 * q^85 + 30 * q^86 + 10 * q^87 - 3 * q^88 - 12 * q^89 - 4 * q^90 - 30 * q^91 - 50 * q^92 + 10 * q^93 - 4 * q^94 + 27 * q^95 - 8 * q^96 + 24 * q^97 + 7 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{9}{11}\right)$

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 $

$2$	0.580057	+	0.814576i	0.410162	+	0.575992i
$2$	0.580057	+	0.814576i	0.410162	+	0.575992i
$3$	−0.235759	−	0.971812i	−0.136115	−	0.561076i
$3$	−0.235759	−	0.971812i	−0.136115	−	0.561076i
$4$	−0.327068	+	0.945001i	−0.163534	+	0.472500i
$5$	0.141678	+	2.97420i	0.0633605	+	1.33010i	0.776961	+	0.629548i	$0.216760\pi$
$5$	0.141678	+	2.97420i	0.0633605	+	1.33010i	−0.713601	+	0.700553i	$0.752937\pi$
$6$	0.654861	−	0.755750i	0.267346	−	0.308533i
$7$	−2.12708	−	1.57338i	−0.803960	−	0.594683i
$7$	−2.12708	−	1.57338i	−0.803960	−	0.594683i
$8$	−0.959493	+	0.281733i	−0.339232	+	0.0996075i
$9$	−0.888835	+	0.458227i	−0.296278	+	0.152742i
$10$	−2.34053	+	1.84061i	−0.740140	+	0.582052i
$11$	0.243786	−	0.342349i	0.0735042	−	0.103222i	−0.776187	−	0.630503i	$-0.782849\pi$
$11$	0.243786	−	0.342349i	0.0735042	−	0.103222i	0.849691	+	0.527280i	$0.176788\pi$
$12$	0.995472	+	0.0950560i	0.287368	+	0.0274403i
$13$	0.340126	+	2.36563i	0.0943339	+	0.656106i	0.981045	+	0.193782i	$0.0620754\pi$
$13$	0.340126	+	2.36563i	0.0943339	+	0.656106i	−0.886711	+	0.462325i	$0.847015\pi$
$14$	0.0478129	−	2.64532i	0.0127785	−	0.706991i
$15$	2.85696	−	0.838878i	0.737663	−	0.216597i
$16$	−0.786053	−	0.618159i	−0.196513	−	0.154540i
$17$	−2.06788	−	0.398550i	−0.501533	−	0.0966626i	−0.0677910	−	0.997700i	$-0.521595\pi$
$17$	−2.06788	−	0.398550i	−0.501533	−	0.0966626i	−0.433742	+	0.901037i	$0.642807\pi$
$18$	−0.888835	−	0.458227i	−0.209501	−	0.108005i
$19$	−4.09198	+	0.788665i	−0.938765	+	0.180932i	−0.635611	−	0.772009i	$-0.719252\pi$
$19$	−4.09198	+	0.788665i	−0.938765	+	0.180932i	−0.303154	+	0.952942i	$0.598040\pi$
$20$	−2.85696	−	0.838878i	−0.638835	−	0.187579i
$21$	−1.02755	+	2.43806i	−0.224231	+	0.532028i
$22$	0.420279			0.0896038
$23$	−1.73720	+	4.47014i	−0.362232	+	0.932088i
$23$	−1.73720	+	4.47014i	−0.362232	+	0.932088i
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−3.84841	+	0.367479i	−0.769682	+	0.0734957i
$26$	−1.72969	+	1.64926i	−0.339220	+	0.323446i
$27$	0.654861	+	0.755750i	0.126028	+	0.145444i
$28$	2.18255	−	1.49549i	0.412463	−	0.282621i
$29$	−0.812390	+	0.937548i	−0.150857	+	0.174098i	−0.826148	−	0.563453i	$-0.809473\pi$
$29$	−0.812390	+	0.937548i	−0.150857	+	0.174098i	0.675291	+	0.737551i	$0.264018\pi$
$30$	2.34053	+	1.84061i	0.427320	+	0.336048i
$31$	−5.11967	−	4.88160i	−0.919520	−	0.876761i	0.0731860	−	0.997318i	$-0.476683\pi$
$31$	−5.11967	−	4.88160i	−0.919520	−	0.876761i	−0.992706	+	0.120557i	$0.961532\pi$
$32$	0.0475819	−	0.998867i	0.00841137	−	0.176576i
$33$	−0.390174	−	0.156202i	−0.0679205	−	0.0271913i
$34$	−0.874836	−	1.91562i	−0.150033	−	0.328527i
$35$	4.37819	−	6.54927i	0.740049	−	1.10703i
$36$	−0.142315	−	0.989821i	−0.0237191	−	0.164970i
$37$	−4.58138	+	2.36186i	−0.753173	+	0.388288i	−0.791653	−	0.610971i	$-0.790779\pi$
$37$	−4.58138	+	2.36186i	−0.753173	+	0.388288i	0.0384791	+	0.999259i	$0.487749\pi$
$38$	−3.01601	−	2.87576i	−0.489261	−	0.466510i
$39$	2.21875	−	0.888255i	0.355285	−	0.142235i
$40$	−0.973867	−	2.81381i	−0.153982	−	0.444902i
$41$	−1.22448	+	0.786923i	−0.191231	+	0.122897i	−0.632753	−	0.774354i	$-0.718075\pi$
$41$	−1.22448	+	0.786923i	−0.191231	+	0.122897i	0.441522	+	0.897250i	$0.354439\pi$
$42$	−2.58202	+	0.577193i	−0.398415	+	0.0890627i
$43$	−9.89797	−	2.90631i	−1.50943	−	0.443208i	−0.580745	−	0.814085i	$-0.697239\pi$
$43$	−9.89797	−	2.90631i	−1.50943	−	0.443208i	−0.928682	+	0.370878i	$0.879057\pi$
$44$	0.243786	+	0.342349i	0.0367521	+	0.0516111i
$45$	−1.48878	−	2.57865i	−0.221935	−	0.384402i
$46$	−4.64894	+	1.17785i	−0.685449	+	0.173664i
$47$	−0.412301	+	0.714126i	−0.0601403	+	0.104166i	−0.894528	−	0.447012i	$-0.852488\pi$
$47$	−0.412301	+	0.714126i	−0.0601403	+	0.104166i	0.834388	+	0.551178i	$0.185821\pi$
$48$	−0.415415	+	0.909632i	−0.0599600	+	0.131294i
$49$	2.04893	+	6.69342i	0.292705	+	0.956203i
$50$	−2.53164	−	2.92166i	−0.358028	−	0.413186i
$51$	0.100204	+	2.10355i	0.0140314	+	0.294555i
$52$	−2.34676	−	0.452301i	−0.325437	−	0.0627229i
$53$	8.04428	−	3.22044i	1.10497	−	0.442362i	0.253800	−	0.967257i	$-0.418320\pi$
$53$	8.04428	−	3.22044i	1.10497	−	0.442362i	0.851167	+	0.524895i	$0.175895\pi$
$54$	−0.235759	+	0.971812i	−0.0320827	+	0.132247i
$55$	1.05275	+	0.676563i	0.141953	+	0.0912278i
$56$	2.48419	+	0.910382i	0.331964	+	0.121655i
$57$	1.73116	+	3.79070i	0.229297	+	0.502091i
$58$	−1.23494	−	0.117922i	−0.162155	−	0.0154839i
$59$	1.72739	−	1.35843i	0.224887	−	0.176853i	−0.499358	−	0.866396i	$-0.666431\pi$
$59$	1.72739	−	1.35843i	0.224887	−	0.176853i	0.724245	+	0.689543i	$0.242188\pi$
$60$	−0.141678	+	2.97420i	−0.0182906	+	0.383967i
$61$	−2.69989	+	11.1291i	−0.345686	+	1.42494i	0.488072	+	0.872804i	$0.337700\pi$
$61$	−2.69989	+	11.1291i	−0.345686	+	1.42494i	−0.833757	+	0.552131i	$0.813815\pi$
$62$	1.00673	−	7.00197i	0.127855	−	0.889251i
$63$	2.61159	+	0.423794i	0.329029	+	0.0533931i
$64$	0.841254	−	0.540641i	0.105157	−	0.0675801i
$65$	−6.98765	+	1.34676i	−0.866711	+	0.167045i
$66$	−0.0990845	−	0.408432i	−0.0121965	−	0.0502745i
$67$	7.40963	−	0.707534i	0.905231	−	0.0864390i	0.367953	−	0.929844i	$-0.380059\pi$
$67$	7.40963	−	0.707534i	0.905231	−	0.0864390i	0.537278	+	0.843405i	$0.319453\pi$
$68$	1.05297	−	1.82379i	0.127691	−	0.221167i
$69$	4.75369	+	0.634360i	0.572277	+	0.0763679i
$70$	7.87447	−	0.232580i	0.941180	−	0.0277986i
$71$	2.85888	−	6.26008i	0.339287	−	0.742935i	−0.660683	−	0.750665i	$-0.729733\pi$
$71$	2.85888	−	6.26008i	0.339287	−	0.742935i	0.999970	+	0.00773004i	$0.00246057\pi$
$72$	0.723734	−	0.690079i	0.0852929	−	0.0813266i
$73$	−1.63720	+	4.73038i	−0.191620	+	0.553649i	−0.999356	−	0.0358956i	$-0.988572\pi$
$73$	−1.63720	+	4.73038i	−0.191620	+	0.553649i	0.807736	+	0.589545i	$0.200693\pi$
$74$	−4.58138	−	2.36186i	−0.532574	−	0.274561i
$75$	1.26442	+	3.65329i	0.146002	+	0.421846i
$76$	0.593067	−	4.12487i	0.0680295	−	0.473155i
$77$	−1.05720	+	0.344635i	−0.120479	+	0.0392749i
$78$	2.01056	+	1.29211i	0.227651	+	0.146302i
$79$	−1.35873	−	0.543953i	−0.152869	−	0.0611995i	0.293966	−	0.955816i	$-0.405025\pi$
$79$	−1.35873	−	0.543953i	−0.152869	−	0.0611995i	−0.446835	+	0.894616i	$0.647449\pi$
$80$	1.72716	−	2.42546i	0.193102	−	0.271174i
$81$	0.580057	−	0.814576i	0.0644508	−	0.0905084i
$82$	−1.35127	−	0.540969i	−0.149223	−	0.0597400i
$83$	1.49868	+	0.963143i	0.164501	+	0.105719i	0.620301	−	0.784364i	$-0.287010\pi$
$83$	1.49868	+	0.963143i	0.164501	+	0.105719i	−0.455800	+	0.890082i	$0.650647\pi$
$84$	−1.96789	−	1.76845i	−0.214714	−	0.192954i
$85$	0.892394	−	6.20673i	0.0967937	−	0.673215i
$86$	−3.37398	−	9.74848i	−0.363826	−	1.05121i
$87$	1.10265	+	0.568454i	0.118216	+	0.0609447i
$88$	−0.137460	+	0.397164i	−0.0146533	+	0.0423378i
$89$	−9.24850	+	8.81843i	−0.980339	+	0.934751i	−0.997879	−	0.0650949i	$-0.979265\pi$
$89$	−9.24850	+	8.81843i	−0.980339	+	0.934751i	0.0175402	+	0.999846i	$0.494416\pi$
$90$	1.23693	−	2.70849i	0.130384	−	0.285500i
$91$	2.99856	−	5.56702i	0.314335	−	0.583582i
$92$	−3.65610	−	3.10370i	−0.381175	−	0.323583i
$93$	−3.53698	+	6.12624i	−0.366768	+	0.635261i
$94$	−0.820868	+	0.0783834i	−0.0846661	+	0.00808463i
$95$	−2.92539	−	12.0586i	−0.300139	−	1.23719i
$96$	−0.981929	+	0.189251i	−0.100218	+	0.0193154i
$97$	−13.3989	+	8.61097i	−1.36046	+	0.874312i	−0.998327	−	0.0578163i	$-0.981586\pi$
$97$	−13.3989	+	8.61097i	−1.36046	+	0.874312i	−0.362129	+	0.932128i	$0.617950\pi$
$98$	−4.26380	+	5.55158i	−0.430709	+	0.560794i
$99$	−0.0598119	+	0.416001i	−0.00601133	+	0.0418097i
$100$	0.911424	−	3.75694i	0.0911424	−	0.375694i
$101$	−0.295856	+	6.21079i	−0.0294388	+	0.617997i	0.935152	+	0.354246i	$0.115263\pi$
$101$	−0.295856	+	6.21079i	−0.0294388	+	0.617997i	−0.964591	+	0.263750i	$0.915040\pi$
$102$	−1.65537	+	1.30180i	−0.163907	+	0.128898i
$103$	11.3888	+	1.08750i	1.12217	+	0.107154i	0.639603	−	0.768705i	$-0.279099\pi$
$103$	11.3888	+	1.08750i	1.12217	+	0.107154i	0.482566	+	0.875859i	$0.339705\pi$
$104$	−0.992822	−	2.17398i	−0.0973542	−	0.213176i
$105$	−7.39685	−	2.71073i	−0.721859	−	0.264540i
$106$	7.28944	+	4.68464i	0.708013	+	0.455012i
$107$	−1.88047	+	7.75138i	−0.181791	+	0.749355i	0.805784	+	0.592209i	$0.201744\pi$
$107$	−1.88047	+	7.75138i	−0.181791	+	0.749355i	−0.987576	+	0.157145i	$0.949771\pi$
$108$	−0.928368	+	0.371662i	−0.0893322	+	0.0357632i
$109$	13.5405	+	2.60971i	1.29694	+	0.249965i	0.790581	−	0.612358i	$-0.209779\pi$
$109$	13.5405	+	2.60971i	1.29694	+	0.249965i	0.506360	+	0.862322i	$0.330991\pi$
$110$	0.0595445	+	1.24999i	0.00567734	+	0.119182i
$111$	3.37539	+	3.89540i	0.320377	+	0.369735i
$112$	0.699396	+	2.55164i	0.0660868	+	0.241107i
$113$	6.14941	−	13.4653i	0.578488	−	1.26671i	−0.363665	−	0.931530i	$-0.618475\pi$
$113$	6.14941	−	13.4653i	0.578488	−	1.26671i	0.942153	−	0.335182i	$-0.108798\pi$
$114$	−2.08365	+	3.60898i	−0.195151	+	0.338012i
$115$	−13.5412	−	4.53346i	−1.26272	−	0.422747i
$116$	−0.620277	−	1.07435i	−0.0575912	−	0.0997509i
$117$	−1.38631	−	1.94680i	−0.128164	−	0.179981i
$118$	2.10853	+	0.619120i	0.194106	+	0.0569947i
$119$	3.77146	+	4.10131i	0.345729	+	0.375966i
$120$	−2.50489	+	1.60980i	−0.228664	+	0.146954i
$121$	3.53998	+	10.2281i	0.321816	+	0.929826i
$122$	−10.6316	+	4.25624i	−0.962539	+	0.385342i
$123$	1.05342	+	1.00444i	0.0949839	+	0.0905670i
$124$	6.28760	−	3.24148i	0.564643	−	0.291094i
$125$	0.480571	+	3.34244i	0.0429835	+	0.298957i
$126$	1.16966	+	2.37316i	0.104201	+	0.211418i
$127$	0.556471	+	1.21850i	0.0493788	+	0.108125i	0.932713	−	0.360618i	$-0.117434\pi$
$127$	0.556471	+	1.21850i	0.0493788	+	0.108125i	−0.883335	+	0.468743i	$0.844707\pi$
$128$	0.928368	+	0.371662i	0.0820569	+	0.0328506i
$129$	−0.490847	+	10.3042i	−0.0432167	+	0.907230i
$130$	−5.15027	−	4.91077i	−0.451709	−	0.430703i
$131$	−3.55222	−	2.79349i	−0.310358	−	0.244069i	0.450814	−	0.892618i	$-0.351134\pi$
$131$	−3.55222	−	2.79349i	−0.310358	−	0.244069i	−0.761173	+	0.648549i	$0.775376\pi$
$132$	0.275224	−	0.317626i	0.0239552	−	0.0276458i
$133$	9.94484	+	4.76070i	0.862327	+	0.412805i
$134$	4.87435	+	5.62530i	0.421080	+	0.485952i
$135$	−2.15497	+	2.05476i	−0.185470	+	0.176845i
$136$	2.09640	−	0.200182i	0.179765	−	0.0171654i
$137$	−11.3680	−	19.6900i	−0.971237	−	1.68223i	−0.691831	−	0.722059i	$-0.743196\pi$
$137$	−11.3680	−	19.6900i	−0.971237	−	1.68223i	−0.279406	−	0.960173i	$-0.590138\pi$
$138$	2.24068	+	4.24021i	0.190739	+	0.360950i
$139$	15.8088			1.34089			0.670443	−	0.741961i	$-0.266104\pi$
$139$	15.8088			1.34089			0.670443	+	0.741961i	$0.266104\pi$
$140$	4.75710	+	6.27945i	0.402048	+	0.530710i
$141$	0.791200	+	0.232317i	0.0666310	+	0.0195646i
$142$	6.75763	−	1.30243i	0.567087	−	0.109297i
$143$	0.892788	+	0.460264i	0.0746587	+	0.0384892i
$144$	0.981929	+	0.189251i	0.0818274	+	0.0157709i
$145$	−2.90355	−	2.28338i	−0.241127	−	0.189624i
$146$	−4.80292	+	1.41027i	−0.397493	+	0.116714i
$147$	6.02169	−	3.56921i	0.496661	−	0.294383i
$148$	−0.733542	−	5.10189i	−0.0602967	−	0.419373i
$149$	13.7663	+	1.31453i	1.12778	+	0.107690i	0.642226	−	0.766515i	$-0.278011\pi$
$149$	13.7663	+	1.31453i	1.12778	+	0.107690i	0.485556	+	0.874205i	$0.338617\pi$
$150$	−2.24245	+	3.14908i	−0.183095	+	0.257122i
$151$	2.81533	−	2.21400i	0.229108	−	0.180173i	−0.497005	−	0.867748i	$-0.665567\pi$
$151$	2.81533	−	2.21400i	0.229108	−	0.180173i	0.726114	+	0.687575i	$0.241325\pi$
$152$	3.70404	−	1.90956i	0.300437	−	0.154886i
$153$	2.02063	−	0.593310i	0.163358	−	0.0479662i
$154$	−0.893967	−	0.661260i	−0.0720379	−	0.0532858i
$155$	13.7935	−	15.9185i	1.10792	−	1.27861i
$156$	0.113718	+	2.38724i	0.00910477	+	0.191133i
$157$	−2.20708	+	6.37693i	−0.176144	+	0.508935i	−0.998167	−	0.0605196i	$-0.980724\pi$
$157$	−2.20708	+	6.37693i	−0.176144	+	0.508935i	0.822023	+	0.569454i	$0.192845\pi$
$158$	−0.345049	−	1.42231i	−0.0274506	−	0.113153i
$159$	−5.02617	−	7.05827i	−0.398602	−	0.559758i
$160$	2.97757			0.235397
$161$	10.7284	−	6.77505i	0.845517	−	0.533949i
$162$	1.00000			0.0785674
$163$	5.26674	+	7.39610i	0.412523	+	0.579307i	0.967599	−	0.252492i	$-0.0812502\pi$
$163$	5.26674	+	7.39610i	0.412523	+	0.579307i	−0.555076	+	0.831800i	$0.687311\pi$
$164$	−0.343156	−	1.41451i	−0.0267960	−	0.110455i
$165$	0.409296	−	1.18258i	0.0318637	−	0.0920640i
$166$	0.0847664	+	1.77947i	0.00657915	+	0.138113i
$167$	−5.75199	+	6.63815i	−0.445103	+	0.513676i	−0.933320	−	0.359046i	$-0.883102\pi$
$167$	−5.75199	+	6.63815i	−0.445103	+	0.513676i	0.488217	+	0.872722i	$0.337647\pi$
$168$	0.299050	−	2.62880i	0.0230722	−	0.202816i
$169$	6.99291	−	2.05330i	0.537916	−	0.157946i
$170$	5.57349	−	2.87334i	0.427468	−	0.220375i
$171$	3.27571	−	2.57605i	0.250500	−	0.196995i
$172$	5.98377	−	8.40303i	0.456258	−	0.640725i
$173$	19.5569	+	1.86746i	1.48688	+	0.141980i	0.806656	−	0.591021i	$-0.201275\pi$
$173$	19.5569	+	1.86746i	1.48688	+	0.141980i	0.680227	+	0.733001i	$0.261881\pi$
$174$	0.176549	+	1.22793i	0.0133842	+	0.0930888i
$175$	8.76406	+	5.27337i	0.662501	+	0.398629i
$176$	−0.403255	+	0.118406i	−0.0303965	+	0.00892521i
$177$	−1.72739	−	1.35843i	−0.129838	−	0.102106i
$178$	−12.5479	−	2.41842i	−0.940507	−	0.181268i
$179$	5.54023	+	2.85619i	0.414096	+	0.213481i	0.652669	−	0.757643i	$-0.273649\pi$
$179$	5.54023	+	2.85619i	0.414096	+	0.213481i	−0.238573	+	0.971125i	$0.576680\pi$
$180$	2.92376	−	0.563509i	0.217924	−	0.0420015i
$181$	−20.5954	−	6.04736i	−1.53084	−	0.449497i	−0.595536	−	0.803329i	$-0.703060\pi$
$181$	−20.5954	−	6.04736i	−1.53084	−	0.449497i	−0.935309	+	0.353832i	$0.884878\pi$
$182$	6.27410	−	0.786633i	0.465067	−	0.0583091i
$183$	11.4519			0.846550
$184$	0.407451	−	4.77849i	0.0300377	−	0.352275i
$185$	−7.67373	−	13.2913i	−0.564184	−	0.977195i
$186$	−7.04194	+	0.672424i	−0.516340	+	0.0493045i
$187$	−0.640562	+	0.610775i	−0.0468425	+	0.0446643i
$188$	−0.539999	−	0.623192i	−0.0393835	−	0.0454510i
$189$	−0.203857	−	2.63789i	−0.0148284	−	0.191878i
$190$	8.12577	−	9.37764i	0.589505	−	0.680325i
$191$	−0.671337	−	0.527945i	−0.0485762	−	0.0382008i	0.593576	−	0.804778i	$-0.297716\pi$
$191$	−0.671337	−	0.527945i	−0.0485762	−	0.0382008i	−0.642152	+	0.766577i	$0.721958\pi$
$192$	−0.723734	−	0.690079i	−0.0522310	−	0.0498022i
$193$	−0.176300	+	3.70099i	−0.0126904	+	0.266403i	0.983601	+	0.180359i	$0.0577258\pi$
$193$	−0.176300	+	3.70099i	−0.0126904	+	0.266403i	−0.996291	+	0.0860447i	$0.972577\pi$
$194$	−14.7864	−	5.91960i	−1.06160	−	0.425002i
$195$	2.95620	+	6.47317i	0.211698	+	0.463553i
$196$	−6.99543	−	0.252961i	−0.499673	−	0.0180686i
$197$	−2.46461	−	17.1417i	−0.175596	−	1.22130i	−0.866807	−	0.498644i	$-0.833831\pi$
$197$	−2.46461	−	17.1417i	−0.175596	−	1.22130i	0.691211	−	0.722653i	$-0.257078\pi$
$198$	−0.373559	+	0.192583i	−0.0265477	+	0.0136863i
$199$	2.29157	+	2.18501i	0.162445	+	0.154891i	0.766942	−	0.641716i	$-0.221777\pi$
$199$	2.29157	+	2.18501i	0.162445	+	0.154891i	−0.604497	+	0.796607i	$0.706626\pi$
$200$	3.58899	−	1.43682i	0.253780	−	0.101598i
$201$	−2.43448	−	7.03396i	−0.171715	−	0.496137i
$202$	−5.23077	+	3.36161i	−0.368036	+	0.236522i
$203$	3.20314	−	0.716038i	0.224816	−	0.0502560i
$204$	−2.02063	−	0.593310i	−0.141472	−	0.0415400i
$205$	−2.51395	−	3.53034i	−0.175582	−	0.246570i
$206$	5.72029	+	9.90784i	0.398552	+	0.690312i
$207$	−0.504247	−	4.76925i	−0.0350476	−	0.331486i
$208$	1.19498	−	2.06976i	0.0828567	−	0.143512i
$209$	−0.727568	+	1.59315i	−0.0503269	+	0.110201i
$210$	−2.08250	−	7.59767i	−0.143706	−	0.524289i
$211$	7.06507	+	8.15352i	0.486379	+	0.561312i	0.944895	−	0.327375i	$-0.106164\pi$
$211$	7.06507	+	8.15352i	0.486379	+	0.561312i	−0.458515	+	0.888687i	$0.651619\pi$
$212$	0.412296	+	8.65515i	0.0283166	+	0.594438i
$213$	−6.75763	−	1.30243i	−0.463025	−	0.0892407i
$214$	−7.40487	+	2.96446i	−0.506186	+	0.202646i
$215$	7.24160	−	29.8503i	0.493873	−	2.03577i
$216$	−0.841254	−	0.540641i	−0.0572401	−	0.0367859i
$217$	3.20933	+	18.4388i	0.217863	+	1.25170i
$218$	5.72843	+	12.5435i	0.387978	+	0.849554i
$219$	4.98302	+	0.475821i	0.336721	+	0.0321530i
$220$	−0.983674	+	0.773570i	−0.0663193	+	0.0521541i
$221$	0.239483	−	5.02738i	0.0161094	−	0.338178i
$222$	−1.21519	+	5.00906i	−0.0815579	+	0.336186i
$223$	−1.73505	+	12.0675i	−0.116187	+	0.808102i	0.845504	+	0.533969i	$0.179300\pi$
$223$	−1.73505	+	12.0675i	−0.116187	+	0.808102i	−0.961692	+	0.274133i	$0.911609\pi$
$224$	−1.67281	+	2.04981i	−0.111769	+	0.136958i
$225$	3.25222	−	2.09007i	0.216814	−	0.139338i
$226$	14.5355	−	2.80150i	0.966890	−	0.186353i
$227$	2.07277	+	8.54406i	0.137574	+	0.567089i	0.998314	+	0.0580439i	$0.0184863\pi$
$227$	2.07277	+	8.54406i	0.137574	+	0.567089i	−0.860740	+	0.509045i	$0.829999\pi$
$228$	−4.14842	+	0.396126i	−0.274736	+	0.0262341i
$229$	9.47063	−	16.4036i	0.625837	−	1.08398i	−0.362541	−	0.931968i	$-0.618091\pi$
$229$	9.47063	−	16.4036i	0.625837	−	1.08398i	0.988378	−	0.152014i	$-0.0485758\pi$
$230$	−4.16181	−	13.6600i	−0.274422	−	0.900713i
$231$	0.584165	+	0.946146i	0.0384352	+	0.0622519i
$232$	0.515344	−	1.12845i	0.0338340	−	0.0740862i
$233$	4.45367	−	4.24656i	0.291770	−	0.278202i	−0.530029	−	0.847979i	$-0.677819\pi$
$233$	4.45367	−	4.24656i	0.291770	−	0.278202i	0.821799	+	0.569778i	$0.192971\pi$
$234$	0.781677	−	2.25851i	0.0510998	−	0.147643i
$235$	−2.18237	−	1.12509i	−0.142362	−	0.0733926i
$236$	0.718747	+	2.07668i	0.0467865	+	0.135181i
$237$	−0.208287	+	1.44867i	−0.0135297	+	0.0941012i
$238$	−1.15316	+	5.45113i	−0.0747485	+	0.353345i
$239$	18.1281	+	11.6502i	1.17261	+	0.753590i	0.974013	−	0.226492i	$-0.0727256\pi$
$239$	18.1281	+	11.6502i	1.17261	+	0.753590i	0.198596	+	0.980082i	$0.436362\pi$
$240$	−2.76428	−	1.10665i	−0.178433	−	0.0714340i
$241$	−5.25129	+	7.37440i	−0.338265	+	0.475027i	−0.948313	−	0.317338i	$-0.897211\pi$
$241$	−5.25129	+	7.37440i	−0.338265	+	0.475027i	0.610047	+	0.792365i	$0.291150\pi$
$242$	−6.27817	+	8.81645i	−0.403576	+	0.566743i
$243$	−0.928368	−	0.371662i	−0.0595548	−	0.0238422i
$244$	−9.63396	−	6.19137i	−0.616751	−	0.396362i
$245$	−19.6173	+	7.04224i	−1.25330	+	0.449912i
$246$	−0.207145	+	1.44072i	−0.0132071	+	0.0918571i
$247$	−3.25747	−	9.41185i	−0.207268	−	0.598862i
$248$	6.28760	+	3.24148i	0.399263	+	0.205834i
$249$	0.582666	−	1.68350i	0.0369250	−	0.106688i
$250$	−2.44391	+	2.33027i	−0.154567	+	0.147379i
$251$	3.65701	−	8.00773i	0.230828	−	0.505443i	−0.758406	−	0.651782i	$-0.774022\pi$
$251$	3.65701	−	8.00773i	0.230828	−	0.505443i	0.989235	+	0.146339i	$0.0467489\pi$
$252$	−1.25465	+	2.32934i	−0.0790357	+	0.146735i
$253$	1.10684	+	1.68449i	0.0695866	+	0.105903i
$254$	−0.669777	+	1.16009i	−0.0420256	+	0.0727904i
$255$	−6.24216	+	0.596054i	−0.390900	+	0.0373264i
$256$	0.235759	+	0.971812i	0.0147349	+	0.0607382i
$257$	−5.08040	+	0.979166i	−0.316906	+	0.0610787i	−0.345224	−	0.938520i	$-0.612197\pi$
$257$	−5.08040	+	0.979166i	−0.316906	+	0.0610787i	0.0283177	+	0.999599i	$0.490985\pi$
$258$	−8.67824	+	5.57716i	−0.540283	+	0.347219i
$259$	13.4611	+	2.18439i	0.836430	+	0.135731i
$260$	1.01275	−	7.04381i	0.0628079	−	0.436839i
$261$	0.292471	−	1.20558i	0.0181035	−	0.0746238i
$262$	0.215025	−	4.51393i	0.0132843	−	0.278872i
$263$	−22.7542	+	17.8941i	−1.40309	+	1.10340i	−0.422711	+	0.906265i	$0.638921\pi$
$263$	−22.7542	+	17.8941i	−1.40309	+	1.10340i	−0.980376	+	0.197135i	$0.936836\pi$
$264$	0.418376	+	0.0399501i	0.0257493	+	0.00245876i
$265$	10.7179	+	23.4690i	0.658397	+	1.44169i
$266$	1.89062	+	10.8623i	0.115921	+	0.666011i
$267$	10.7503	+	6.90878i	0.657905	+	0.422810i
$268$	−1.75483	+	7.23352i	−0.107193	+	0.441858i
$269$	20.9053	−	8.36923i	1.27462	−	0.510281i	0.367058	−	0.930198i	$-0.380365\pi$
$269$	20.9053	−	8.36923i	1.27462	−	0.510281i	0.907563	+	0.419917i	$0.137941\pi$
$270$	−2.92376	−	0.563509i	−0.177934	−	0.0342940i
$271$	−0.125557	−	2.63577i	−0.00762704	−	0.160111i	−0.999468	−	0.0326268i	$-0.989613\pi$
$271$	−0.125557	−	2.63577i	−0.00762704	−	0.160111i	0.991841	−	0.127485i	$-0.0406903\pi$
$272$	1.37909	+	1.59156i	0.0836198	+	0.0965023i
$273$	−6.11703	−	1.60156i	−0.370220	−	0.0969309i
$274$	9.44491	−	20.6815i	0.570588	−	1.24941i
$275$	−0.812382	+	1.40709i	−0.0489885	+	0.0848505i
$276$	−2.15425	+	4.28476i	−0.129671	+	0.257912i
$277$	3.22333	+	5.58298i	0.193671	+	0.335449i	0.946464	−	0.322809i	$-0.104627\pi$
$277$	3.22333	+	5.58298i	0.193671	+	0.335449i	−0.752793	+	0.658258i	$0.771294\pi$
$278$	9.17000	+	12.8775i	0.549980	+	0.772339i
$279$	6.78742	+	1.99297i	0.406352	+	0.119316i
$280$	−2.35570	+	7.51745i	−0.140780	+	0.449254i
$281$	9.13502	−	5.87072i	0.544949	−	0.350218i	−0.239022	−	0.971014i	$-0.576827\pi$
$281$	9.13502	−	5.87072i	0.544949	−	0.350218i	0.783972	+	0.620796i	$0.213191\pi$
$282$	0.269701	+	0.779249i	0.0160605	+	0.0464036i
$283$	−25.7355	+	10.3029i	−1.52982	+	0.612446i	−0.975527	−	0.219879i	$-0.929434\pi$
$283$	−25.7355	+	10.3029i	−1.52982	+	0.612446i	−0.554289	+	0.832324i	$0.687010\pi$
$284$	4.98073	+	4.74912i	0.295552	+	0.281808i
$285$	−11.0290	+	5.68586i	−0.653303	+	0.336801i
$286$	0.142948	+	0.994223i	0.00845267	+	0.0587896i
$287$	3.84269	+	0.252722i	0.226827	+	0.0149177i
$288$	0.415415	+	0.909632i	0.0244786	+	0.0536006i
$289$	−11.6650	−	4.66996i	−0.686176	−	0.274703i
$290$	0.175760	−	3.68965i	0.0103210	−	0.216664i
$291$	11.5272	+	10.9911i	0.675734	+	0.644311i
$292$	−3.93474	−	3.09431i	−0.230263	−	0.181081i
$293$	−9.38311	+	10.8287i	−0.548167	+	0.632619i	−0.960455	−	0.278435i	$-0.910184\pi$
$293$	−9.38311	+	10.8287i	−0.548167	+	0.632619i	0.412288	+	0.911054i	$0.364730\pi$
$294$	6.40031	+	2.83478i	0.373274	+	0.165328i
$295$	4.28498	+	4.94513i	0.249481	+	0.287917i
$296$	3.73038	−	3.55691i	0.216824	−	0.206741i
$297$	0.418376	−	0.0399501i	0.0242766	−	0.00231814i
$298$	6.91448	+	11.9762i	0.400545	+	0.693764i
$299$	−11.1655	−	2.58916i	−0.645720	−	0.149735i
$300$	−3.86592			−0.223199
$301$	16.4810	+	21.7553i	0.949951	+	1.25395i
$302$	3.43652	+	1.00905i	0.197750	+	0.0580646i
$303$	6.10547	−	1.17673i	0.350750	−	0.0676015i
$304$	3.70404	+	1.90956i	0.212441	+	0.109521i
$305$	−33.4826	−	6.45325i	−1.91721	−	0.369512i
$306$	1.65537	+	1.30180i	0.0946315	+	0.0744190i
$307$	−22.2757	+	6.54073i	−1.27134	+	0.373299i	−0.846704	−	0.532065i	$-0.821416\pi$
$307$	−22.2757	+	6.54073i	−1.27134	+	0.373299i	−0.424637	+	0.905364i	$0.639598\pi$
$308$	0.0200948	−	1.11177i	0.00114500	−	0.0633491i
$309$	−1.62816	−	11.3241i	−0.0926231	−	0.644208i
$310$	20.9679	+	2.00219i	1.19089	+	0.113717i
$311$	0.0208502	−	0.0292800i	0.00118230	−	0.00166031i	−0.813984	−	0.580887i	$-0.802706\pi$
$311$	0.0208502	−	0.0292800i	0.00118230	−	0.00166031i	0.815167	+	0.579226i	$0.196645\pi$
$312$	−1.87863	+	1.47737i	−0.106356	+	0.0836396i
$313$	−20.4655	+	10.5507i	−1.15678	+	0.596359i	−0.926325	−	0.376725i	$-0.877050\pi$
$313$	−20.4655	+	10.5507i	−1.15678	+	0.596359i	−0.230450	+	0.973084i	$0.574020\pi$
$314$	−6.47473	+	1.90115i	−0.365390	+	0.107288i
$315$	−0.890442	+	7.82742i	−0.0501707	+	0.441025i
$316$	0.958433	−	1.10609i	0.0539161	−	0.0622224i
$317$	−0.620634	−	13.0287i	−0.0348583	−	0.731765i	−0.946873	−	0.321607i	$-0.895777\pi$
$317$	−0.620634	−	13.0287i	−0.0348583	−	0.731765i	0.912015	−	0.410157i	$-0.134526\pi$
$318$	2.83403	−	8.18840i	0.158925	−	0.459183i
$319$	0.122920	+	0.506682i	0.00688218	+	0.0283687i
$320$	1.72716	+	2.42546i	0.0965511	+	0.135587i
$321$	7.97622			0.445189
$322$	11.7419	+	4.80919i	0.654349	+	0.268006i
$323$	8.77603			0.488311
$324$	0.580057	+	0.814576i	0.0322254	+	0.0452542i
$325$	−2.17826	−	8.97891i	−0.120828	−	0.498060i
$326$	−2.96968	+	8.58032i	−0.164475	+	0.475220i
$327$	−0.656138	−	13.7740i	−0.0362845	−	0.761706i
$328$	0.953175	−	1.10002i	0.0526303	−	0.0607386i
$329$	2.00059	−	0.870296i	0.110296	−	0.0479810i
$330$	1.20072	−	0.352563i	0.0660974	−	0.0194079i
$331$	−9.62779	+	4.96347i	−0.529191	+	0.272817i	−0.702048	−	0.712130i	$-0.747731\pi$
$331$	−9.62779	+	4.96347i	−0.529191	+	0.272817i	0.172856	+	0.984947i	$0.444700\pi$
$332$	−1.40034	+	1.10124i	−0.0768537	+	0.0604384i
$333$	2.98982	−	4.19862i	0.163841	−	0.230083i
$334$	−8.74377	−	0.834928i	−0.478438	−	0.0456852i
$335$	3.15413	+	21.9375i	0.172329	+	1.19857i
$336$	2.31482	−	1.28125i	0.126284	−	0.0698981i
$337$	−15.2132	+	4.46700i	−0.828716	+	0.243333i	−0.668465	−	0.743743i	$-0.733048\pi$
$337$	−15.2132	+	4.46700i	−0.828716	+	0.243333i	−0.160251	+	0.987076i	$0.551230\pi$
$338$	5.72886	+	4.50522i	0.311609	+	0.245052i
$339$	−14.5355	−	2.80150i	−0.789462	−	0.152156i
$340$	5.57349	+	2.87334i	0.302265	+	0.155829i
$341$	−2.91931	+	0.562652i	−0.158090	+	0.0304693i
$342$	3.99849	+	1.17406i	0.216213	+	0.0634860i
$343$	6.17307	−	17.4612i	0.333315	−	0.942816i
$344$	10.3158			0.556193
$345$	−1.21321	+	14.2283i	−0.0653172	+	0.766025i
$346$	9.82293	+	17.0138i	0.528084	+	0.914668i
$347$	−30.1515	+	2.87911i	−1.61861	+	0.154559i	−0.864657	−	0.502363i	$-0.832464\pi$
$347$	−30.1515	+	2.87911i	−1.61861	+	0.154559i	−0.753958	+	0.656922i	$0.771858\pi$
$348$	−0.897831	+	0.856080i	−0.0481288	+	0.0458907i
$349$	−12.6000	−	14.5412i	−0.674465	−	0.778374i	0.310603	−	0.950540i	$-0.399469\pi$
$349$	−12.6000	−	14.5412i	−0.674465	−	0.778374i	−0.985068	+	0.172166i	$0.944924\pi$
$350$	0.788095	+	10.1978i	0.0421254	+	0.545098i
$351$	−1.56509	+	1.80621i	−0.0835381	+	0.0964081i
$352$	−0.330362	−	0.259799i	−0.0176083	−	0.0138473i
$353$	19.3500	+	18.4502i	1.02990	+	0.982004i	0.999846	−	0.0175440i	$-0.00558470\pi$
$353$	19.3500	+	18.4502i	1.02990	+	0.982004i	0.0300505	+	0.999548i	$0.490433\pi$
$354$	0.104563	−	2.19506i	0.00555749	−	0.116666i
$355$	19.0237	+	7.61596i	1.00968	+	0.404213i
$356$	−5.30853	−	11.6241i	−0.281352	−	0.616074i
$357$	3.09654	−	4.63207i	0.163886	−	0.245155i
$358$	0.887067	+	6.16969i	0.0468830	+	0.326078i
$359$	−2.05132	+	1.05753i	−0.108265	+	0.0558143i	−0.511508	−	0.859278i	$-0.670913\pi$
$359$	−2.05132	+	1.05753i	−0.108265	+	0.0558143i	0.403244	+	0.915093i	$0.367883\pi$
$360$	2.15497	+	2.05476i	0.113577	+	0.108295i
$361$	−1.51666	+	0.607181i	−0.0798244	+	0.0319569i
$362$	−7.02048	−	20.2843i	−0.368988	−	1.06612i
$363$	9.10519	−	5.85155i	0.477899	−	0.307127i
$364$	4.28011	+	4.65444i	0.224339	+	0.243959i
$365$	−14.3010	−	4.19916i	−0.748550	−	0.219794i
$366$	6.64276	+	9.32845i	0.347223	+	0.487606i
$367$	−5.35250	−	9.27080i	−0.279398	−	0.483932i	0.691837	−	0.722054i	$-0.256802\pi$
$367$	−5.35250	−	9.27080i	−0.279398	−	0.483932i	−0.971235	+	0.238122i	$0.923468\pi$
$368$	4.12879	−	2.43990i	0.215228	−	0.127188i
$369$	0.727769	−	1.26053i	0.0378861	−	0.0656207i
$370$	6.37556	−	13.9605i	0.331450	−	0.725774i
$371$	−22.1778	−	5.80659i	−1.15141	−	0.301463i
$372$	−4.63246	−	5.34615i	−0.240182	−	0.277185i
$373$	0.885667	+	18.5924i	0.0458581	+	0.962680i	0.898171	+	0.439647i	$0.144896\pi$
$373$	0.885667	+	18.5924i	0.0458581	+	0.962680i	−0.852312	+	0.523033i	$0.824800\pi$
$374$	−0.869085	−	0.167502i	−0.0449393	−	0.00866134i
$375$	3.13492	−	1.25503i	0.161887	−	0.0648097i
$376$	0.194407	−	0.801358i	0.0100258	−	0.0413269i
$377$	−2.49420	−	1.60293i	−0.128458	−	0.0825549i
$378$	2.03051	−	1.69618i	0.104438	−	0.0872421i
$379$	−8.46393	−	18.5334i	−0.434763	−	0.951997i	−0.992530	−	0.122000i	$-0.961069\pi$
$379$	−8.46393	−	18.5334i	−0.434763	−	0.951997i	0.557767	−	0.829997i	$-0.311658\pi$
$380$	12.3522	+	1.17949i	0.633655	+	0.0605067i
$381$	1.05296	−	0.828058i	0.0539448	−	0.0424227i
$382$	0.0406378	−	0.853093i	0.00207921	−	0.0436480i
$383$	−2.41865	+	9.96980i	−0.123587	+	0.509433i	0.876043	+	0.482233i	$0.160174\pi$
$383$	−2.41865	+	9.96980i	−0.123587	+	0.509433i	−0.999630	+	0.0271998i	$0.991341\pi$
$384$	0.142315	−	0.989821i	0.00726247	−	0.0505116i
$385$	−1.17480	−	3.09549i	−0.0598731	−	0.157761i
$386$	−3.11700	+	2.00318i	−0.158651	+	0.101959i
$387$	10.1294	−	1.95229i	0.514907	−	0.0992402i
$388$	−3.75501	−	15.4784i	−0.190632	−	0.785796i
$389$	21.5646	−	2.05917i	1.09337	−	0.104404i	0.467246	−	0.884128i	$-0.345246\pi$
$389$	21.5646	−	2.05917i	1.09337	−	0.104404i	0.626124	+	0.779723i	$0.284640\pi$
$390$	−3.55812	+	6.16285i	−0.180173	+	0.312068i
$391$	5.37389	−	8.55132i	0.271770	−	0.432459i
$392$	−3.85169	−	5.84504i	−0.194540	−	0.295219i
$393$	−1.87728	+	4.11067i	−0.0946964	+	0.207356i
$394$	12.5336	−	11.9508i	0.631435	−	0.602072i
$395$	1.42532	−	4.11819i	0.0717157	−	0.207209i
$396$	−0.373559	−	0.192583i	−0.0187720	−	0.00967766i
$397$	−9.33130	−	26.9610i	−0.468325	−	1.35313i	−0.893922	−	0.448222i	$-0.852057\pi$
$397$	−9.33130	−	26.9610i	−0.468325	−	1.35313i	0.425598	−	0.904913i	$-0.360064\pi$
$398$	−0.450614	+	3.13409i	−0.0225872	+	0.157098i
$399$	2.28192	−	10.7869i	0.114239	−	0.540020i
$400$	3.25222	+	2.09007i	0.162611	+	0.104504i
$401$	−21.9400	−	8.78343i	−1.09563	−	0.438624i	−0.247756	−	0.968823i	$-0.579693\pi$
$401$	−21.9400	−	8.78343i	−1.09563	−	0.438624i	−0.847873	+	0.530199i	$0.822117\pi$
$402$	4.31756	−	6.06316i	0.215340	−	0.302403i
$403$	9.80670	−	13.7716i	0.488507	−	0.686012i
$404$	−5.77244	−	2.31093i	−0.287189	−	0.114973i
$405$	2.50489	+	1.60980i	0.124469	+	0.0799914i
$406$	2.44127	+	2.19386i	0.121158	+	0.108879i
$407$	−0.308292	+	2.14422i	−0.0152815	+	0.106285i
$408$	−0.688783	−	1.99011i	−0.0340998	−	0.0985250i
$409$	25.9862	+	13.3968i	1.28494	+	0.662430i	0.959119	−	0.283003i	$-0.0913305\pi$
$409$	25.9862	+	13.3968i	1.28494	+	0.662430i	0.325817	+	0.945433i	$0.394361\pi$
$410$	1.41750	−	4.09560i	0.0700054	−	0.202267i
$411$	−16.4549	+	15.6897i	−0.811659	+	0.773916i
$412$	−4.75259	+	10.4067i	−0.234143	+	0.512702i
$413$	−5.81163	+	0.171652i	−0.285972	+	0.00844643i
$414$	3.59242	−	3.17718i	0.176558	−	0.156150i
$415$	−2.65224	+	4.59382i	−0.130194	+	0.225502i
$416$	2.37913	−	0.227179i	0.116646	−	0.0111384i
$417$	−3.72707	−	15.3632i	−0.182515	−	0.752338i
$418$	−1.71977	+	0.331459i	−0.0841169	+	0.0162122i
$419$	−0.503887	+	0.323829i	−0.0246165	+	0.0158201i	−0.552891	−	0.833253i	$-0.686475\pi$
$419$	−0.503887	+	0.323829i	−0.0246165	+	0.0158201i	0.528275	+	0.849074i	$0.322839\pi$
$420$	4.98091	−	6.10344i	0.243044	−	0.297817i
$421$	2.16326	−	15.0458i	0.105431	−	0.733289i	−0.866696	−	0.498836i	$-0.833761\pi$
$421$	2.16326	−	15.0458i	0.105431	−	0.733289i	0.972127	−	0.234453i	$-0.0753299\pi$
$422$	−2.54352	+	10.4845i	−0.123817	+	0.510379i
$423$	0.0392361	−	0.823668i	0.00190773	−	0.0400481i
$424$	−6.81113	+	5.35633i	−0.330777	+	0.260126i
$425$	8.10449	+	0.773885i	0.393126	+	0.0375389i
$426$	−2.85888	−	6.26008i	−0.138513	−	0.303302i
$427$	23.2532	−	19.4245i	1.12530	−	0.940018i
$428$	−6.71002	−	4.31227i	−0.324341	−	0.208441i
$429$	0.236807	−	0.976133i	0.0114332	−	0.0471281i
$430$	28.5159	−	11.4160i	1.37516	−	0.550530i
$431$	−6.03976	−	1.16407i	−0.290925	−	0.0560712i	0.0417007	−	0.999130i	$-0.486722\pi$
$431$	−6.03976	−	1.16407i	−0.290925	−	0.0560712i	−0.332626	+	0.943059i	$0.607935\pi$
$432$	−0.0475819	−	0.998867i	−0.00228929	−	0.0480580i
$433$	−15.2321	−	17.5788i	−0.732007	−	0.844782i	0.260689	−	0.965423i	$-0.416050\pi$
$433$	−15.2321	−	17.5788i	−0.732007	−	0.844782i	−0.992696	+	0.120641i	$0.961505\pi$
$434$	−13.1582	+	13.3098i	−0.631612	+	0.638889i
$435$	−1.53447	+	3.36003i	−0.0735724	+	0.161101i
$436$	−6.89483	+	11.9422i	−0.330202	+	0.571927i
$437$	3.58316	−	19.6618i	0.171406	−	0.940551i
$438$	2.50284	+	4.33505i	0.119591	+	0.207137i
$439$	8.89824	+	12.4958i	0.424690	+	0.596393i	0.970377	−	0.241596i	$-0.0776707\pi$
$439$	8.89824	+	12.4958i	0.424690	+	0.596393i	−0.545687	+	0.837989i	$0.683731\pi$
$440$	−1.20072	−	0.352563i	−0.0572420	−	0.0168078i
$441$	−4.88827	−	5.01047i	−0.232775	−	0.238594i
$442$	4.23409	−	2.72109i	0.201395	−	0.129429i
$443$	−5.34974	−	15.4571i	−0.254174	−	0.734387i	−0.997831	−	0.0658262i	$-0.979032\pi$
$443$	−5.34974	−	15.4571i	−0.254174	−	0.734387i	0.743657	−	0.668561i	$-0.233089\pi$
$444$	−4.78514	+	1.91568i	−0.227093	+	0.0909142i
$445$	−27.5380	−	26.2575i	−1.30543	−	1.24472i
$446$	−10.8363	+	5.58653i	−0.513116	+	0.264530i
$447$	−1.96807	−	13.6882i	−0.0930863	−	0.647430i
$448$	−2.64005	−	0.173628i	−0.124731	−	0.00820316i
$449$	2.97890	+	6.52288i	0.140583	+	0.307834i	0.966807	−	0.255508i	$-0.0822427\pi$
$449$	2.97890	+	6.52288i	0.140583	+	0.307834i	−0.826224	+	0.563342i	$0.809515\pi$
$450$	3.58899	+	1.43682i	0.169187	+	0.0677322i
$451$	−0.0291074	+	0.611039i	−0.00137061	+	0.0287727i
$452$	10.7135	+	10.2153i	0.503920	+	0.480486i
$453$	−2.81533	−	2.21400i	−0.132276	−	0.104023i
$454$	−5.75746	+	6.64447i	−0.270211	+	0.311840i
$455$	16.9822	+	8.12958i	0.796140	+	0.381121i
$456$	−2.72900	−	3.14943i	−0.127797	−	0.147485i
$457$	−7.85433	+	7.48909i	−0.367410	+	0.350325i	−0.851183	−	0.524869i	$-0.824114\pi$
$457$	−7.85433	+	7.48909i	−0.367410	+	0.350325i	0.483773	+	0.875193i	$0.339266\pi$
$458$	18.8555	−	1.80048i	0.881059	−	0.0841310i
$459$	−1.05297	−	1.82379i	−0.0491483	−	0.0851273i
$460$	8.71301	−	11.3137i	0.406246	−	0.527503i
$461$	−36.0253			−1.67787			−0.838933	−	0.544234i	$-0.816820\pi$
$461$	−36.0253			−1.67787			−0.838933	+	0.544234i	$0.816820\pi$
$462$	−0.431859	+	1.02467i	−0.0200919	+	0.0476717i
$463$	−25.2791	−	7.42262i	−1.17482	−	0.344958i	−0.364645	−	0.931147i	$-0.618810\pi$
$463$	−25.2791	−	7.42262i	−1.17482	−	0.344958i	−0.810175	+	0.586188i	$0.800628\pi$
$464$	1.21813	−	0.234776i	0.0565505	−	0.0108992i
$465$	−18.7217	−	9.65173i	−0.868200	−	0.447588i
$466$	6.04253	+	1.16460i	0.279915	+	0.0539492i
$467$	−4.45839	−	3.50612i	−0.206310	−	0.162244i	0.509658	−	0.860377i	$-0.329772\pi$
$467$	−4.45839	−	3.50612i	−0.206310	−	0.162244i	−0.715968	+	0.698133i	$0.754014\pi$
$468$	2.29314	−	0.673327i	0.106001	−	0.0311246i
$469$	−16.8741	−	10.1532i	−0.779173	−	0.468832i
$470$	−0.349427	−	2.43032i	−0.0161179	−	0.112102i
$471$	6.71752	+	0.641445i	0.309527	+	0.0295562i
$472$	−1.27470	+	1.79007i	−0.0586729	+	0.0823946i
$473$	−3.40796	+	2.68005i	−0.156698	+	0.123229i
$474$	−1.30087	+	0.670645i	−0.0597510	+	0.0308038i
$475$	15.4578	−	4.53882i	0.709253	−	0.208255i
$476$	−5.10926	+	2.22263i	−0.234183	+	0.101874i
$477$	−5.67435	+	6.54855i	−0.259811	+	0.299837i
$478$	1.02534	+	21.5245i	0.0468979	+	0.984508i
$479$	−3.00590	+	8.68498i	−0.137343	+	0.396827i	−0.992608	−	0.121364i	$-0.961273\pi$
$479$	−3.00590	+	8.68498i	−0.137343	+	0.396827i	0.855265	+	0.518191i	$0.173394\pi$
$480$	−0.701988	−	2.89364i	−0.0320412	−	0.132076i
$481$	−7.14553	−	10.0345i	−0.325808	−	0.457533i
$482$	−9.05306			−0.412355
$483$	−9.11339	−	8.82871i	−0.414674	−	0.401720i
$484$	−10.8234			−0.491971
$485$	−27.5091	−	38.6311i	−1.24912	−	1.75415i
$486$	−0.235759	−	0.971812i	−0.0106942	−	0.0440823i
$487$	6.55935	−	18.9520i	0.297233	−	0.858798i	−0.693193	−	0.720752i	$-0.743797\pi$
$487$	6.55935	−	18.9520i	0.297233	−	0.858798i	0.990426	−	0.138046i	$-0.0440821\pi$
$488$	−0.544904	−	11.4389i	−0.0246666	−	0.517816i
$489$	5.94594	−	6.86198i	0.268885	−	0.310309i
$490$	−17.1156	−	11.8948i	−0.773202	−	0.537354i
$491$	23.6954	−	6.95761i	1.06936	−	0.313992i	0.300745	−	0.953704i	$-0.402765\pi$
$491$	23.6954	−	6.95761i	1.06936	−	0.313992i	0.768615	+	0.639712i	$0.220946\pi$
$492$	−1.29373	+	0.666966i	−0.0583260	+	0.0300692i
$493$	2.05358	−	1.61495i	0.0924886	−	0.0727338i
$494$	5.77715	−	8.11287i	0.259926	−	0.365015i
$495$	−1.24574	−	0.118954i	−0.0559920	−	0.00534659i
$496$	1.00673	+	7.00197i	0.0452035	+	0.314398i
$497$	−15.9306	+	8.81757i	−0.714584	+	0.395522i
$498$	1.70932	−	0.501902i	0.0765965	−	0.0224908i
$499$	34.0735	+	26.7957i	1.52534	+	1.19954i	0.912323	+	0.409471i	$0.134287\pi$
$499$	34.0735	+	26.7957i	1.52534	+	1.19954i	0.613017	+	0.790070i	$0.289956\pi$
$500$	−3.31579	−	0.639066i	−0.148287	−	0.0285799i
$501$	7.80712	+	4.02485i	0.348796	+	0.179817i
$502$	8.64418	−	1.66603i	0.385809	−	0.0743585i
$503$	40.3187	+	11.8386i	1.79772	+	0.527859i	0.997423	−	0.0717427i	$-0.0228561\pi$
$503$	40.3187	+	11.8386i	1.79772	+	0.527859i	0.800299	+	0.599602i	$0.204674\pi$
$504$	−2.62520	+	0.329142i	−0.116936	+	0.0146611i
$505$	−18.5140			−0.823863
$506$	−0.730110	+	1.87870i	−0.0324574	+	0.0835186i
$507$	−3.64407	−	6.31171i	−0.161839	−	0.280313i
$508$	−1.33349	+	0.127333i	−0.0591640	+	0.00564948i
$509$	0.270365	−	0.257793i	0.0119837	−	0.0114265i	−0.684063	−	0.729422i	$-0.739789\pi$
$509$	0.270365	−	0.257793i	0.0119837	−	0.0114265i	0.696047	+	0.717996i	$0.254940\pi$
$510$	−4.10634	−	4.73897i	−0.181832	−	0.209845i
$511$	10.9252	−	7.48595i	0.483300	−	0.331159i
$512$	−0.654861	+	0.755750i	−0.0289410	+	0.0333997i
$513$	−3.27571	−	2.57605i	−0.144626	−	0.113735i
$514$	−3.74452	−	3.57040i	−0.165164	−	0.157483i
$515$	−1.62088	+	34.0265i	−0.0714247	+	1.49939i
$516$	−9.57689	−	3.83401i	−0.421599	−	0.168783i
$517$	0.143967	+	0.315245i	0.00633168	+	0.0138644i
$518$	6.02883	+	12.2321i	0.264892	+	0.537449i
$519$	−2.79590	−	19.4459i	−0.122726	−	0.853580i
$520$	6.32517	−	3.26085i	0.277377	−	0.142998i
$521$	5.86482	+	5.59209i	0.256942	+	0.244994i	0.807591	−	0.589743i	$-0.200771\pi$
$521$	5.86482	+	5.59209i	0.256942	+	0.244994i	−0.550648	+	0.834737i	$0.685620\pi$
$522$	1.15169	−	0.461067i	0.0504081	−	0.0201804i
$523$	−10.4619	−	30.2278i	−0.457469	−	1.32177i	−0.904203	−	0.427103i	$-0.859534\pi$
$523$	−10.4619	−	30.2278i	−0.457469	−	1.32177i	0.446734	−	0.894667i	$-0.352587\pi$
$524$	3.80167	−	2.44318i	0.166077	−	0.106731i
$525$	3.05851	−	9.76026i	0.133485	−	0.425973i
$526$	−27.7749	−	8.15544i	−1.21104	−	0.355594i
$527$	8.64128	+	12.1350i	0.376420	+	0.528608i
$528$	0.210140	+	0.363972i	0.00914515	+	0.0158399i
$529$	−16.9642	−	15.5311i	−0.737576	−	0.675264i
$530$	−12.9003	+	22.3439i	−0.560352	+	0.970558i
$531$	−0.912894	+	1.99896i	−0.0396162	+	0.0867474i
$532$	−7.75151	+	7.84081i	−0.336070	+	0.339942i
$533$	−2.27804	−	2.62900i	−0.0986729	−	0.113875i
$534$	0.608043	+	12.7644i	0.0263126	+	0.552369i
$535$	−23.3206	−	4.49467i	−1.00824	−	0.194321i
$536$	−6.91015	+	2.76641i	−0.298473	+	0.119491i
$537$	1.46952	−	6.05743i	0.0634143	−	0.261397i
$538$	18.9437	+	12.1744i	0.816719	+	0.524874i
$539$	2.79099	+	0.930310i	0.120216	+	0.0400713i
$540$	−1.23693	−	2.70849i	−0.0532289	−	0.116555i
$541$	9.51867	+	0.908923i	0.409240	+	0.0390777i	0.297646	−	0.954676i	$-0.403798\pi$
$541$	9.51867	+	0.908923i	0.409240	+	0.0390777i	0.111594	+	0.993754i	$0.464405\pi$
$542$	2.07420	−	1.63117i	0.0890946	−	0.0700647i
$543$	−1.02134	+	21.4406i	−0.0438299	+	0.920103i
$544$	−0.496492	+	2.04657i	−0.0212869	+	0.0877459i
$545$	−5.84340	+	40.6417i	−0.250304	+	1.74090i
$546$	−2.24363	−	5.91178i	−0.0960187	−	0.253001i
$547$	−15.9335	+	10.2398i	−0.681265	+	0.437823i	−0.834971	−	0.550294i	$-0.814516\pi$
$547$	−15.9335	+	10.2398i	−0.681265	+	0.437823i	0.153706	+	0.988117i	$0.450879\pi$
$548$	22.3252	−	4.30283i	0.953686	−	0.183808i
$549$	−2.69989	−	11.1291i	−0.115229	−	0.474978i
$550$	−1.61741	+	0.154444i	−0.0689664	+	0.00658550i
$551$	2.58487	−	4.47713i	0.110119	−	0.190732i
$552$	−4.73985	+	0.730606i	−0.201742	+	0.0310967i
$553$	2.03428	+	3.29483i	0.0865063	+	0.140111i
$554$	−2.67804	+	5.86409i	−0.113779	+	0.249141i
$555$	−11.1075	+	10.5910i	−0.471486	+	0.449561i
$556$	−5.17055	+	14.9393i	−0.219280	+	0.633569i
$557$	19.7508	+	10.1823i	0.836870	+	0.431437i	0.822709	−	0.568463i	$-0.192462\pi$
$557$	19.7508	+	10.1823i	0.836870	+	0.431437i	0.0141615	+	0.999900i	$0.495492\pi$
$558$	2.31367	+	6.68491i	0.0979454	+	0.282995i
$559$	3.50868	−	24.4034i	0.148401	−	1.03215i
$560$	−7.48998	+	2.44165i	−0.316509	+	0.103179i
$561$	0.744576	+	0.478510i	0.0314360	+	0.0202027i
$562$	10.0810	+	4.03581i	0.425240	+	0.170241i
$563$	−8.90896	+	12.5109i	−0.375468	+	0.527271i	−0.958468	−	0.285202i	$-0.907939\pi$
$563$	−8.90896	+	12.5109i	−0.375468	+	0.527271i	0.583000	+	0.812472i	$0.301879\pi$
$564$	−0.478316	+	0.671701i	−0.0201407	+	0.0282837i
$565$	40.9198	+	16.3818i	1.72151	+	0.689188i
$566$	−23.3206	−	14.9872i	−0.980237	−	0.629960i
$567$	−2.51547	+	0.820016i	−0.105640	+	0.0344374i
$568$	−0.979410	+	6.81194i	−0.0410951	+	0.285823i
$569$	−5.71231	−	16.5046i	−0.239472	−	0.691910i	−0.999135	−	0.0415923i	$-0.986757\pi$
$569$	−5.71231	−	16.5046i	−0.239472	−	0.691910i	0.759662	−	0.650318i	$-0.225364\pi$
$570$	−11.0290	−	5.68586i	−0.461955	−	0.238154i
$571$	−8.84959	+	25.5692i	−0.370344	+	1.07004i	0.593790	+	0.804620i	$0.297631\pi$
$571$	−8.84959	+	25.5692i	−0.370344	+	1.07004i	−0.964134	+	0.265418i	$0.914490\pi$
$572$	−0.726952	+	0.693148i	−0.0303954	+	0.0289820i
$573$	−0.354789	+	0.776880i	−0.0148215	+	0.0324546i
$574$	2.02312	+	3.27676i	0.0844433	+	0.136769i
$575$	5.04279	−	17.8413i	0.210299	−	0.744034i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−21.1764	+	2.02210i	−0.881586	+	0.0841813i	−0.526022	−	0.850471i	$-0.676317\pi$
$577$	−21.1764	+	2.02210i	−0.881586	+	0.0841813i	−0.355564	+	0.934652i	$0.615711\pi$
$578$	−2.96232	−	12.2109i	−0.123216	−	0.507905i
$579$	3.63823	−	0.701212i	0.151200	−	0.0291414i
$580$	3.10745	−	1.99704i	0.129030	−	0.0829224i
$581$	−1.67242	−	4.40668i	−0.0693836	−	0.182820i
$582$	−2.26670	+	15.7652i	−0.0939576	+	0.653490i
$583$	0.858564	−	3.53905i	0.0355581	−	0.146572i
$584$	0.238180	−	5.00002i	0.00985597	−	0.206902i
$585$	5.59375	−	4.39897i	0.231273	−	0.181875i
$586$	−14.2635	−	1.36200i	−0.589221	−	0.0562638i
$587$	4.01774	+	8.79763i	0.165830	+	0.363117i	0.974244	−	0.225498i	$-0.0724008\pi$
$587$	4.01774	+	8.79763i	0.165830	+	0.363117i	−0.808414	+	0.588615i	$0.799674\pi$
$588$	1.40340	+	6.85788i	0.0578754	+	0.282814i
$589$	24.7996	+	15.9377i	1.02185	+	0.656702i
$590$	−1.54265	+	6.35890i	−0.0635100	+	0.261792i
$591$	−16.0775	+	6.43645i	−0.661339	+	0.264760i
$592$	5.06121	+	0.975469i	0.208015	+	0.0400915i
$593$	0.227151	+	4.76850i	0.00932799	+	0.195819i	0.998721	+	0.0505565i	$0.0160995\pi$
$593$	0.227151	+	4.76850i	0.00932799	+	0.195819i	−0.989393	+	0.145262i	$0.953597\pi$
$594$	0.275224	+	0.317626i	0.0112926	+	0.0130323i
$595$	−11.6638	+	11.7981i	−0.478168	+	0.483676i
$596$	−5.74476	+	12.5793i	−0.235314	+	0.515267i
$597$	1.58316	−	2.74211i	0.0647943	−	0.112227i
$598$	−4.36758	−	10.5970i	−0.178603	−	0.433345i
$599$	−13.3678	−	23.1538i	−0.546195	−	0.946038i	−0.998531	−	0.0541900i	$-0.982742\pi$
$599$	−13.3678	−	23.1538i	−0.546195	−	0.946038i	0.452335	−	0.891848i	$-0.350591\pi$
$600$	−2.24245	−	3.14908i	−0.0915477	−	0.128561i
$601$	26.3302	+	7.73125i	1.07403	+	0.315364i	0.770489	−	0.637453i	$-0.220012\pi$
$601$	26.3302	+	7.73125i	1.07403	+	0.315364i	0.303543	+	0.952818i	$0.401830\pi$
$602$	−8.16136	+	26.0443i	−0.332632	+	1.06149i
$603$	−6.26173	+	4.02417i	−0.254997	+	0.163877i
$604$	1.17143	+	3.38462i	0.0476647	+	0.137718i
$605$	−29.9188	+	11.9777i	−1.21637	+	0.486962i
$606$	4.50006	+	4.29080i	0.182802	+	0.174302i
$607$	7.78404	−	4.01295i	0.315945	−	0.162881i	−0.292959	−	0.956125i	$-0.594640\pi$
$607$	7.78404	−	4.01295i	0.315945	−	0.162881i	0.608904	+	0.793244i	$0.291610\pi$
$608$	0.593067	+	4.12487i	0.0240521	+	0.167286i
$609$	−1.45102	−	2.94403i	−0.0587984	−	0.119298i
$610$	−14.1652	−	31.0174i	−0.573531	−	1.25586i
$611$	−1.82959	−	0.732457i	−0.0740173	−	0.0296320i
$612$	−0.100204	+	2.10355i	−0.00405052	+	0.0850308i
$613$	1.57059	+	1.49756i	0.0634357	+	0.0604858i	0.721134	−	0.692796i	$-0.243621\pi$
$613$	1.57059	+	1.49756i	0.0634357	+	0.0604858i	−0.657698	+	0.753282i	$0.728470\pi$
$614$	−18.2491	−	14.3512i	−0.736473	−	0.579169i
$615$	−2.83814	+	3.27539i	−0.114445	+	0.132077i
$616$	0.917279	−	0.628522i	0.0369582	−	0.0253239i
$617$	22.2912	+	25.7254i	0.897410	+	1.03567i	0.999165	+	0.0408573i	$0.0130089\pi$
$617$	22.2912	+	25.7254i	0.897410	+	1.03567i	−0.101755	+	0.994810i	$0.532446\pi$
$618$	8.27994	−	7.89491i	0.333068	−	0.317580i
$619$	−27.8747	+	2.66171i	−1.12038	+	0.106983i	−0.638767	−	0.769400i	$-0.720555\pi$
$619$	−27.8747	+	2.66171i	−1.12038	+	0.106983i	−0.481613	+	0.876384i	$0.659949\pi$
$620$	10.5316	+	18.2413i	0.422960	+	0.732588i
$621$	−4.51593	+	1.61443i	−0.181218	+	0.0647847i
$622$	0.0359450			0.00144126
$623$	33.5470	−	4.20606i	1.34403	−	0.168512i
$624$	−2.29314	−	0.673327i	−0.0917991	−	0.0269547i
$625$	−28.8533	+	5.56101i	−1.15413	+	0.222440i
$626$	−20.4655	−	10.5507i	−0.817964	−	0.421690i
$627$	1.71977	+	0.331459i	0.0686812	+	0.0132372i
$628$	−5.30434	−	4.17138i	−0.211666	−	0.166456i
$629$	10.4150	−	3.05813i	0.415275	−	0.121936i
$630$	−6.89254	+	3.81502i	−0.274605	+	0.151994i
$631$	−3.34678	−	23.2774i	−0.133233	−	0.926657i	−0.941301	−	0.337568i	$-0.890396\pi$
$631$	−3.34678	−	23.2774i	−0.133233	−	0.926657i	0.808068	−	0.589089i	$-0.200513\pi$
$632$	1.45694	+	0.139121i	0.0579540	+	0.00553393i
$633$	6.25803	−	8.78818i	0.248735	−	0.349299i
$634$	10.2529	−	8.06294i	0.407193	−	0.320220i
$635$	−3.54522	+	1.82769i	−0.140688	+	0.0725297i
$636$	8.31398	−	2.44120i	0.329671	−	0.0968000i
$637$	−15.1372	+	7.12361i	−0.599759	+	0.282248i
$638$	−0.341430	+	0.394032i	−0.0135174	+	0.0155999i
$639$	0.327458	+	6.87420i	0.0129541	+	0.271939i
$640$	−0.973867	+	2.81381i	−0.0384955	+	0.111225i
$641$	11.2246	+	46.2685i	0.443346	+	1.82750i	0.552553	+	0.833478i	$0.313654\pi$
$641$	11.2246	+	46.2685i	0.443346	+	1.82750i	−0.109208	+	0.994019i	$0.534831\pi$
$642$	4.62666	+	6.49724i	0.182600	+	0.256426i
$643$	−31.6385			−1.24770			−0.623850	−	0.781544i	$-0.714432\pi$
$643$	−31.6385			−1.24770			−0.623850	+	0.781544i	$0.714432\pi$
$644$	2.89351	+	12.3543i	0.114020	+	0.486826i
$645$	−30.7161			−1.20945
$646$	5.09060	+	7.14874i	0.200287	+	0.281264i
$647$	−3.30215	−	13.6116i	−0.129821	−	0.535128i	−0.999163	−	0.0409171i	$-0.986972\pi$
$647$	−3.30215	−	13.6116i	−0.129821	−	0.535128i	0.869342	−	0.494211i	$-0.164543\pi$
$648$	−0.327068	+	0.945001i	−0.0128484	+	0.0371231i
$649$	−0.0439458	−	0.922537i	−0.00172503	−	0.0362127i
$650$	6.05049	−	6.98264i	0.237320	−	0.273882i
$651$	17.1624	−	7.46596i	0.672646	−	0.292614i
$652$	−8.71190	+	2.55805i	−0.341185	+	0.100181i
$653$	−17.6077	+	9.07739i	−0.689042	+	0.355226i	−0.766925	−	0.641737i	$-0.778214\pi$
$653$	−17.6077	+	9.07739i	−0.689042	+	0.355226i	0.0778831	+	0.996963i	$0.475184\pi$
$654$	10.8394	−	8.52420i	0.423854	−	0.333323i
$655$	7.80512	−	10.9608i	0.304971	−	0.428272i
$656$	1.44895	+	0.138358i	0.0565719	+	0.00540196i
$657$	−0.712384	−	4.95474i	−0.0277927	−	0.193303i
$658$	1.86938	+	1.12481i	0.0728760	+	0.0438497i
$659$	35.2721	−	10.3568i	1.37400	−	0.403444i	0.490326	−	0.871539i	$-0.336878\pi$
$659$	35.2721	−	10.3568i	1.37400	−	0.403444i	0.883678	+	0.468095i	$0.155059\pi$
$660$	0.983674	+	0.773570i	0.0382895	+	0.0301112i
$661$	−1.05013	−	0.202396i	−0.0408454	−	0.00787231i	0.168788	−	0.985652i	$-0.446015\pi$
$661$	−1.05013	−	0.202396i	−0.0408454	−	0.00787231i	−0.209633	+	0.977780i	$0.567227\pi$
$662$	−9.62779	−	4.96347i	−0.374195	−	0.192911i
$663$	−4.94212	+	0.952516i	−0.191936	+	0.0369927i
$664$	−1.70932	−	0.501902i	−0.0663345	−	0.0194776i
$665$	−12.7503	+	30.2524i	−0.494435	+	1.17314i
$666$	5.15436			0.199727
$667$	−2.77968	−	5.26020i	−0.107630	−	0.203676i
$668$	−4.39177	−	7.60677i	−0.169923	−	0.294315i
$669$	12.1364	−	1.15889i	0.469221	−	0.0448052i
$670$	−16.0402	+	15.2943i	−0.619685	+	0.590869i
$671$	3.15184	+	3.63742i	0.121676	+	0.140421i
$672$	2.38640	+	1.14240i	0.0920576	+	0.0440689i
$673$	−2.68114	+	3.09420i	−0.103350	+	0.119273i	−0.805068	−	0.593182i	$-0.797871\pi$
$673$	−2.68114	+	3.09420i	−0.103350	+	0.119273i	0.701718	+	0.712455i	$0.252417\pi$
$674$	−12.4632	−	9.80120i	−0.480066	−	0.377528i
$675$	−2.79790	−	2.66779i	−0.107691	−	0.102683i
$676$	−0.346783	+	7.27988i	−0.0133378	+	0.279995i
$677$	24.4672	+	9.79520i	0.940351	+	0.376460i	0.790648	−	0.612271i	$-0.209744\pi$
$677$	24.4672	+	9.79520i	0.940351	+	0.376460i	0.149703	+	0.988731i	$0.452168\pi$
$678$	−6.14941	−	13.4653i	−0.236167	−	0.517133i
$679$	42.0490	+	2.76543i	1.61369	+	0.106128i
$680$	0.892394	+	6.20673i	0.0342217	+	0.238017i
$681$	7.81455	−	4.02868i	0.299454	−	0.154379i
$682$	−2.15169	−	2.05163i	−0.0823925	−	0.0785611i
$683$	28.0308	−	11.2218i	1.07257	−	0.429392i	0.232905	−	0.972499i	$-0.425177\pi$
$683$	28.0308	−	11.2218i	1.07257	−	0.429392i	0.839663	+	0.543108i	$0.182753\pi$
$684$	1.36299	+	3.93809i	0.0521151	+	0.150577i
$685$	56.9514	−	36.6004i	2.17600	−	1.39843i
$686$	17.8042	−	5.10005i	0.679767	−	0.194721i
$687$	−18.1740	−	5.33637i	−0.693382	−	0.203595i
$688$	5.98377	+	8.40303i	0.228129	+	0.320363i
$689$	10.3544	+	17.9344i	0.394472	+	0.683246i
$690$	−12.2938	+	7.26496i	−0.468015	+	0.276572i
$691$	6.58345	−	11.4029i	0.250446	−	0.433786i	−0.713202	−	0.700958i	$-0.752756\pi$
$691$	6.58345	−	11.4029i	0.250446	−	0.433786i	0.963649	+	0.267172i	$0.0860893\pi$
$692$	−8.16118	+	17.8705i	−0.310242	+	0.679334i
$693$	0.781754	−	0.790760i	0.0296964	−	0.0300385i
$694$	−19.8348	−	22.8906i	−0.752919	−	0.868915i
$695$	2.23977	+	47.0185i	0.0849592	+	1.78351i
$696$	−1.21813	−	0.234776i	−0.0461733	−	0.00889917i
$697$	2.84569	−	1.13924i	0.107788	−	0.0431519i
$698$	4.53619	−	18.6984i	0.171697	−	0.707746i
$699$	−5.17685	−	3.32696i	−0.195807	−	0.125837i
$700$	−7.84978	+	6.55729i	−0.296694	+	0.247842i
$701$	1.22324	+	2.67851i	0.0462010	+	0.101166i	0.931325	−	0.364189i	$-0.118654\pi$
$701$	1.22324	+	2.67851i	0.0462010	+	0.101166i	−0.885124	+	0.465355i	$0.845927\pi$
$702$	−2.37913	−	0.227179i	−0.0897945	−	0.00857433i
$703$	16.8842	−	13.2779i	0.636799	−	0.500784i
$704$	0.0199977	−	0.419803i	0.000753691	−	0.0158219i
$705$	−0.578861	+	2.38610i	−0.0218012	+	0.0898656i
$706$	−3.80498	+	26.4642i	−0.143202	+	0.995993i
$707$	10.4013	−	12.7453i	0.391180	−	0.479338i
$708$	1.84869	−	1.18808i	0.0694782	−	0.0446509i
$709$	−49.5154	+	9.54332i	−1.85959	+	0.358407i	−0.990641	−	0.136494i	$-0.956417\pi$
$709$	−49.5154	+	9.54332i	−1.85959	+	0.358407i	−0.868950	+	0.494900i	$0.835205\pi$
$710$	4.83108	+	19.9140i	0.181307	+	0.747358i
$711$	1.45694	−	0.139121i	0.0546395	−	0.00521744i
$712$	6.38943	−	11.0668i	0.239454	−	0.414747i
$713$	30.7153	−	14.4053i	1.15030	−	0.539483i
$714$	5.56934	−	0.164496i	0.208427	−	0.00615610i
$715$	−1.24243	+	2.72054i	−0.0464641	+	0.101742i
$716$	−4.51113	+	4.30135i	−0.168589	+	0.160749i
$717$	7.04796	−	20.3637i	0.263211	−	0.760498i
$718$	−2.05132	−	1.05753i	−0.0765547	−	0.0394667i
$719$	−7.08312	−	20.4653i	−0.264156	−	0.763228i	−0.996599	−	0.0824000i	$-0.973741\pi$
$719$	−7.08312	−	20.4653i	−0.264156	−	0.763228i	0.732444	−	0.680828i	$-0.238380\pi$
$720$	−0.423752	+	2.94726i	−0.0157923	+	0.109838i
$721$	−22.5138	−	20.2321i	−0.838457	−	0.753483i
$722$	−1.37435	−	0.883239i	−0.0511479	−	0.0328707i
$723$	8.40457	+	3.36468i	0.312569	+	0.125134i
$724$	12.4509	−	17.4848i	0.462732	−	0.649817i
$725$	2.78188	−	3.90660i	0.103316	−	0.145088i
$726$	10.0481	+	4.02264i	0.372919	+	0.149294i
$727$	−6.91053	−	4.44113i	−0.256298	−	0.164712i	0.406183	−	0.913792i	$-0.366860\pi$
$727$	−6.91053	−	4.44113i	−0.256298	−	0.164712i	−0.662480	+	0.749080i	$0.730496\pi$
$728$	−1.30869	+	6.18631i	−0.0485032	+	0.229280i
$729$	−0.142315	+	0.989821i	−0.00527092	+	0.0366601i
$730$	−4.87488	−	14.0850i	−0.180427	−	0.521310i
$731$	19.3095	+	9.95472i	0.714186	+	0.368189i
$732$	−3.74555	+	10.8221i	−0.138440	+	0.399995i
$733$	−5.42421	+	5.17197i	−0.200348	+	0.191031i	−0.783611	−	0.621252i	$-0.786624\pi$
$733$	−5.42421	+	5.17197i	−0.200348	+	0.191031i	0.583263	+	0.812283i	$0.301776\pi$
$734$	4.44702	−	9.73761i	0.164142	−	0.359422i
$735$	11.4687	+	17.4040i	0.423028	+	0.641956i
$736$	4.38241	+	1.94793i	0.161538	+	0.0718018i
$737$	1.56414	−	2.70917i	0.0576158	−	0.0997935i
$738$	1.44895	−	0.138358i	0.0533365	−	0.00509302i
$739$	1.21181	+	4.99514i	0.0445771	+	0.183749i	0.989747	−	0.142828i	$-0.0456197\pi$
$739$	1.21181	+	4.99514i	0.0445771	+	0.183749i	−0.945170	+	0.326578i	$0.894105\pi$
$740$	15.0701	−	2.90452i	0.553988	−	0.106772i
$741$	−8.37857	+	5.38458i	−0.307794	+	0.197807i
$742$	−8.13448	−	21.4337i	−0.298626	−	0.786855i
$743$	−5.52126	+	38.4012i	−0.202555	+	1.40880i	0.594111	+	0.804383i	$0.297504\pi$
$743$	−5.52126	+	38.4012i	−0.202555	+	1.40880i	−0.796666	+	0.604419i	$0.793405\pi$
$744$	1.66775	−	6.87457i	0.0611427	−	0.252034i
$745$	−1.95926	+	41.1300i	−0.0717819	+	1.50689i
$746$	−14.6312	+	11.5061i	−0.535687	+	0.421269i
$747$	−1.77342	−	0.169341i	−0.0648859	−	0.00619585i
$748$	−0.367675	−	0.805096i	−0.0134435	−	0.0294372i
$749$	16.1958	−	13.5291i	0.591781	−	0.494343i
$750$	2.84076	+	1.82564i	0.103730	+	0.0666630i
$751$	−9.09152	+	37.4758i	−0.331754	+	1.36751i	0.524700	+	0.851287i	$0.324178\pi$
$751$	−9.09152	+	37.4758i	−0.331754	+	1.36751i	−0.856454	+	0.516223i	$0.827338\pi$
$752$	0.765534	−	0.306474i	0.0279161	−	0.0111759i
$753$	−8.64418	−	1.66603i	−0.315011	−	0.0607135i
$754$	−0.141074	−	2.96150i	−0.00513761	−	0.107852i
$755$	6.98375	+	8.05967i	0.254165	+	0.293321i
$756$	2.55948	+	0.670123i	0.0930874	+	0.0243721i
$757$	−13.5606	+	29.6936i	−0.492869	+	1.07923i	0.485853	+	0.874041i	$0.338509\pi$
$757$	−13.5606	+	29.6936i	−0.492869	+	1.07923i	−0.978722	+	0.205192i	$0.934218\pi$
$758$	10.1873	−	17.6449i	0.370020	−	0.640893i
$759$	1.37605	−	1.47277i	0.0499476	−	0.0534583i
$760$	6.20420	+	10.7460i	0.225050	+	0.389798i
$761$	−8.05010	−	11.3048i	−0.291816	−	0.409798i	0.642477	−	0.766305i	$-0.277907\pi$
$761$	−8.05010	−	11.3048i	−0.291816	−	0.409798i	−0.934293	+	0.356507i	$0.883967\pi$
$762$	1.28529	+	0.377396i	0.0465613	+	0.0136716i
$763$	−24.6956	−	26.8554i	−0.894039	−	0.972230i
$764$	0.718481	−	0.461740i	0.0259937	−	0.0167052i
$765$	2.05090	+	5.92568i	0.0741504	+	0.214244i
$766$	−9.52411	+	3.81288i	−0.344120	+	0.137765i
$767$	3.80107	+	3.62432i	0.137249	+	0.130866i
$768$	0.888835	−	0.458227i	0.0320731	−	0.0165348i
$769$	−0.387279	−	2.69358i	−0.0139656	−	0.0971331i	0.981646	−	0.190710i	$-0.0610790\pi$
$769$	−0.387279	−	2.69358i	−0.0139656	−	0.0971331i	−0.995612	+	0.0935769i	$0.970170\pi$
$770$	1.84006	−	2.75252i	0.0663112	−	0.0991939i
$771$	2.14931	+	4.70634i	0.0774057	+	0.169495i
$772$	−3.43978	−	1.37708i	−0.123800	−	0.0495622i
$773$	0.519027	−	10.8957i	0.0186681	−	0.391892i	−0.970126	−	0.242603i	$-0.921999\pi$
$773$	0.519027	−	10.8957i	0.0186681	−	0.391892i	0.988794	−	0.149289i	$-0.0476983\pi$
$774$	7.46592	+	7.11874i	0.268357	+	0.255878i
$775$	21.4965	+	16.9050i	0.772177	+	0.607246i
$776$	10.4302	−	12.0371i	0.374422	−	0.432106i
$777$	−1.05075	−	13.5966i	−0.0376955	−	0.487776i
$778$	14.1861	+	16.3716i	0.508595	+	0.586950i
$779$	4.38992	−	4.18578i	0.157285	−	0.149971i
$780$	−7.08402	+	0.676442i	−0.253649	+	0.0242205i
$781$	−1.44618	−	2.50485i	−0.0517483	−	0.0896307i
$782$	10.0829	−	0.582809i	0.360563	−	0.0208412i
$783$	−1.24055			−0.0443338
$784$	2.52703	−	6.52795i	0.0902510	−	0.233141i
$785$	−19.2789	−	5.66081i	−0.688095	−	0.202043i
$786$	−4.43739	+	0.855236i	−0.158276	+	0.0305053i
$787$	−46.8957	−	24.1764i	−1.67165	−	0.861796i	−0.991705	−	0.128534i	$-0.958973\pi$
$787$	−46.8957	−	24.1764i	−1.67165	−	0.861796i	−0.679946	−	0.733262i	$-0.737997\pi$
$788$	17.0050	+	3.27745i	0.605779	+	0.116754i
$789$	22.7542	+	17.8941i	0.810073	+	0.637048i
$790$	4.18135	−	1.22775i	0.148766	−	0.0436815i
$791$	−34.2664	+	18.9665i	−1.21837	+	0.674369i
$792$	−0.0598119	−	0.416001i	−0.00212532	−	0.0147820i
$793$	−27.2456	−	2.60164i	−0.967519	−	0.0923869i
$794$	16.5491	−	23.2400i	0.587306	−	0.824756i
$795$	20.2806	−	15.9488i	0.719279	−	0.565647i
$796$	−2.81433	+	1.45089i	−0.0997514	+	0.0514254i
$797$	−36.6624	+	10.7651i	−1.29865	+	0.381318i	−0.856743	−	0.515743i	$-0.827516\pi$
$797$	−36.6624	+	10.7651i	−1.29865	+	0.381318i	−0.441907	+	0.897061i	$0.645698\pi$
$798$	10.1104	−	4.39821i	0.357904	−	0.155695i
$799$	1.13720	−	1.31240i	0.0402313	−	0.0464294i
$800$	0.183948	+	3.86154i	0.00650353	+	0.136526i
$801$	4.17956	−	12.0760i	0.147677	−	0.426686i
$802$	−5.57165	−	22.9667i	−0.196742	−	0.810981i
$803$	1.22032	+	1.71369i	0.0430640	+	0.0604749i
$804$	7.44334			0.262506
$805$	21.6703	+	30.9485i	0.763778	+	1.09079i
$806$	16.9064			0.595504
$807$	−13.0619	−	18.3429i	−0.459802	−	0.645702i
$808$	−1.46591	−	6.04256i	−0.0515705	−	0.212577i
$809$	−8.49586	+	24.5472i	−0.298698	+	0.863032i	0.691377	+	0.722494i	$0.257004\pi$
$809$	−8.49586	+	24.5472i	−0.298698	+	0.863032i	−0.990075	+	0.140538i	$0.955117\pi$
$810$	0.141678	+	2.97420i	0.00497807	+	0.104503i
$811$	15.9212	−	18.3740i	0.559068	−	0.645199i	−0.403904	−	0.914802i	$-0.632347\pi$
$811$	15.9212	−	18.3740i	0.559068	−	0.645199i	0.962972	+	0.269603i	$0.0868924\pi$
$812$	−0.370987	+	3.26116i	−0.0130191	+	0.114444i
$813$	−2.53187	+	0.743423i	−0.0887964	+	0.0260730i
$814$	−1.92546	+	0.992642i	−0.0674872	+	0.0347921i
$815$	−21.2513	+	16.7122i	−0.744400	+	0.585402i
$816$	1.22156	−	1.71544i	0.0427632	−	0.0600525i
$817$	42.7944	+	4.08637i	1.49719	+	0.142964i
$818$	4.16075	+	28.9387i	0.145477	+	1.01182i
$819$	−0.114270	+	6.32219i	−0.00399293	+	0.220915i
$820$	4.15841	−	1.22102i	0.145218	−	0.0426398i
$821$	−8.36523	−	6.57849i	−0.291949	−	0.229591i	0.461432	−	0.887176i	$-0.347336\pi$
$821$	−8.36523	−	6.57849i	−0.291949	−	0.229591i	−0.753381	+	0.657585i	$0.771578\pi$
$822$	−22.3252	−	4.30283i	−0.778681	−	0.150078i
$823$	−6.95545	−	3.58579i	−0.242452	−	0.124993i	0.332719	−	0.943026i	$-0.392034\pi$
$823$	−6.95545	−	3.58579i	−0.242452	−	0.124993i	−0.575171	+	0.818033i	$0.695064\pi$
$824$	−11.2338	+	2.16514i	−0.391349	+	0.0754264i
$825$	1.55895	+	0.457749i	0.0542756	+	0.0159368i
$826$	−3.51090	−	4.63444i	−0.122160	−	0.161253i
$827$	−30.5040			−1.06073			−0.530365	−	0.847770i	$-0.677945\pi$
$827$	−30.5040			−1.06073			−0.530365	+	0.847770i	$0.677945\pi$
$828$	4.67187	+	1.08335i	0.162359	+	0.0376492i
$829$	4.11572	+	7.12863i	0.142945	+	0.247588i	0.928604	−	0.371072i	$-0.121010\pi$
$829$	4.11572	+	7.12863i	0.142945	+	0.247588i	−0.785660	+	0.618659i	$0.787676\pi$
$830$	−5.28047	+	0.504224i	−0.183288	+	0.0175019i
$831$	4.66567	−	4.44871i	0.161850	−	0.154324i
$832$	1.56509	+	1.80621i	0.0542596	+	0.0626189i
$833$	−1.56927	−	14.6578i	−0.0543720	−	0.507861i
$834$	10.3526	−	11.9475i	0.358480	−	0.413708i
$835$	−20.5581	−	16.1671i	−0.711443	−	0.559485i
$836$	−1.26757	−	1.20862i	−0.0438397	−	0.0418010i
$837$	0.336593	−	7.06596i	0.0116344	−	0.244235i
$838$	−0.556066	−	0.222615i	−0.0192090	−	0.00769012i
$839$	13.6049	+	29.7906i	0.469694	+	1.02849i	0.985170	+	0.171582i	$0.0548877\pi$
$839$	13.6049	+	29.7906i	0.469694	+	1.02849i	−0.515476	+	0.856904i	$0.672385\pi$
$840$	7.86092	+	0.516990i	0.271228	+	0.0178378i
$841$	3.90811	+	27.1815i	0.134762	+	0.937294i
$842$	13.5108	−	6.96530i	0.465613	−	0.240040i
$843$	−7.85890	−	7.49344i	−0.270675	−	0.258088i
$844$	−10.0158	+	4.00974i	−0.344759	+	0.138021i
$845$	7.09767	+	20.5074i	0.244167	+	0.705475i
$846$	0.693699	−	0.445813i	0.0238499	−	0.0153274i
$847$	8.56289	−	27.3257i	0.294224	−	0.938922i
$848$	−8.31398	−	2.44120i	−0.285503	−	0.0838313i
$849$	16.0799	+	22.5810i	0.551860	+	0.774979i
$850$	4.07068	+	7.05062i	0.139623	+	0.241834i
$851$	−2.59907	−	24.5824i	−0.0890950	−	0.842674i
$852$	3.44100	−	5.95998i	0.117887	−	0.204186i
$853$	16.6343	−	36.4241i	0.569549	−	1.24714i	−0.377489	−	0.926014i	$-0.623212\pi$
$853$	16.6343	−	36.4241i	0.569549	−	1.24714i	0.947037	−	0.321124i	$-0.104060\pi$
$854$	29.3109	+	7.67419i	1.00300	+	0.262605i
$855$	8.12577	+	9.37764i	0.277895	+	0.320708i
$856$	−0.379524	−	7.96719i	−0.0129719	−	0.272313i
$857$	21.9965	+	4.23947i	0.751385	+	0.144818i	0.550544	−	0.834806i	$-0.314420\pi$
$857$	21.9965	+	4.23947i	0.751385	+	0.144818i	0.200841	+	0.979624i	$0.435633\pi$
$858$	0.932496	−	0.373315i	0.0318349	−	0.0127448i
$859$	12.2588	−	50.5317i	0.418267	−	1.72412i	−0.239500	−	0.970896i	$-0.576984\pi$
$859$	12.2588	−	50.5317i	0.418267	−	1.72412i	0.657767	−	0.753222i	$-0.271501\pi$
$860$	25.8400	+	16.6064i	0.881138	+	0.566273i
$861$	−0.660350	−	3.79395i	−0.0225047	−	0.129298i
$862$	−2.55518	−	5.59507i	−0.0870298	−	0.190569i
$863$	13.4473	+	1.28406i	0.457751	+	0.0437099i	0.321385	−	0.946949i	$-0.395852\pi$
$863$	13.4473	+	1.28406i	0.457751	+	0.0437099i	0.136366	+	0.990659i	$0.456458\pi$
$864$	0.786053	−	0.618159i	0.0267421	−	0.0210302i
$865$	−2.78339	+	58.4306i	−0.0946382	+	1.98670i
$866$	5.48376	−	22.6044i	0.186346	−	0.768128i
$867$	−1.78819	+	12.4372i	−0.0607302	+	0.422388i
$868$	−18.4743	−	2.99791i	−0.627059	−	0.101756i
$869$	−0.517461	+	0.332552i	−0.0175536	+	0.0112810i
$870$	−3.62708	+	0.699062i	−0.122970	+	0.0237004i
$871$	4.19397	+	17.2878i	0.142107	+	0.585774i
$872$	−13.7272	+	1.31079i	−0.464862	+	0.0443889i
$873$	7.96367	−	13.7935i	0.269529	−	0.466839i
$874$	18.0945	−	8.48620i	0.612054	−	0.287050i
$875$	4.23673	−	7.86576i	0.143228	−	0.265911i
$876$	−2.07944	+	4.55333i	−0.0702577	+	0.153843i
$877$	28.9303	−	27.5850i	0.976907	−	0.931479i	−0.0207575	−	0.999785i	$-0.506608\pi$
$877$	28.9303	−	27.5850i	0.976907	−	0.931479i	0.997664	+	0.0683057i	$0.0217593\pi$
$878$	−5.01732	+	14.4966i	−0.169326	+	0.489236i
$879$	12.7356	+	6.56566i	0.429561	+	0.221454i
$880$	−0.409296	−	1.18258i	−0.0137974	−	0.0398649i
$881$	−6.12168	+	42.5772i	−0.206245	+	1.43446i	0.579025	+	0.815310i	$0.303433\pi$
$881$	−6.12168	+	42.5772i	−0.206245	+	1.43446i	−0.785270	+	0.619154i	$0.787476\pi$
$882$	1.24594	−	6.88822i	0.0419530	−	0.231939i
$883$	−27.0142	−	17.3609i	−0.909099	−	0.584242i	0.000376762	−	1.00000i	$-0.499880\pi$
$883$	−27.0142	−	17.3609i	−0.909099	−	0.584242i	−0.909475	+	0.415758i	$0.863516\pi$
$884$	4.67255	+	1.87061i	0.157155	+	0.0629153i
$885$	3.79551	−	5.33005i	0.127585	−	0.179168i
$886$	9.48780	−	13.3237i	0.318749	−	0.447620i
$887$	−5.09354	−	2.03915i	−0.171024	−	0.0684678i	0.284570	−	0.958655i	$-0.408149\pi$
$887$	−5.09354	−	2.03915i	−0.171024	−	0.0684678i	−0.455595	+	0.890187i	$0.650573\pi$
$888$	−4.33612	−	2.78666i	−0.145511	−	0.0935141i
$889$	0.733512	−	3.46739i	0.0246012	−	0.116293i
$890$	5.41507	−	37.6627i	0.181514	−	1.26245i
$891$	−0.137460	−	0.397164i	−0.00460508	−	0.0133055i
$892$	−10.8363	−	5.58653i	−0.362828	−	0.187051i
$893$	1.12392	−	3.24736i	0.0376106	−	0.108669i
$894$	10.0085	−	9.54307i	0.334734	−	0.319168i
$895$	−7.70993	+	16.8824i	−0.257714	+	0.564316i
$896$	−1.38994	−	2.25123i	−0.0464348	−	0.0752084i
$897$	0.116195	+	11.4612i	0.00387965	+	0.382679i
$898$	−3.58545	+	6.21018i	−0.119648	+	0.207236i
$899$	8.73590	−	0.834177i	0.291359	−	0.0278214i
$900$	0.911424	+	3.75694i	0.0303808	+	0.125231i
$901$	−17.9181	+	3.45343i	−0.596938	+	0.115050i
$902$	−0.514622	+	0.330727i	−0.0171350	+	0.0110120i
$903$	17.2565	−	21.1455i	0.574259	−	0.703677i
$904$	−2.10669	+	14.6524i	−0.0700676	+	0.487331i
$905$	15.0681	−	62.1116i	0.500881	−	2.06466i
$906$	0.170420	−	3.57755i	0.00566181	−	0.118856i
$907$	−43.8579	+	34.4902i	−1.45628	+	1.14523i	−0.495259	+	0.868746i	$0.664927\pi$
$907$	−43.8579	+	34.4902i	−1.45628	+	1.14523i	−0.961019	+	0.276484i	$0.910831\pi$
$908$	−8.75208	−	0.835722i	−0.290448	−	0.0277344i
$909$	−2.58298	−	5.65594i	−0.0856721	−	0.187596i
$910$	3.22851	+	18.5489i	0.107024	+	0.614892i
$911$	−3.95473	−	2.54155i	−0.131026	−	0.0842053i	0.473486	−	0.880801i	$-0.342995\pi$
$911$	−3.95473	−	2.54155i	−0.131026	−	0.0842053i	−0.604512	+	0.796596i	$0.706632\pi$
$912$	0.982476	−	4.04982i	0.0325330	−	0.134103i
$913$	0.695088	−	0.278271i	0.0230040	−	0.00920943i
$914$	−10.6564	−	2.05385i	−0.352482	−	0.0679353i
$915$	1.62249	+	34.0602i	0.0536378	+	1.12600i
$916$	12.4039	+	14.3149i	0.409836	+	0.472976i
$917$	3.16061	+	11.5310i	0.104373	+	0.380786i
$918$	0.874836	−	1.91562i	0.0288739	−	0.0632250i
$919$	−19.5274	+	33.8225i	−0.644150	+	1.11570i	0.340347	+	0.940300i	$0.389455\pi$
$919$	−19.5274	+	33.8225i	−0.644150	+	1.11570i	−0.984497	+	0.175401i	$0.943878\pi$
$920$	14.2699	+	0.534831i	0.470465	+	0.0176328i
$921$	11.6080	+	20.1057i	0.382498	+	0.662506i
$922$	−20.8967	−	29.3454i	−0.688197	−	0.966438i
$923$	15.7814	+	4.63383i	0.519451	+	0.152524i
$924$	−1.08517	+	0.242582i	−0.0356995	+	0.00798036i
$925$	16.7631	−	10.7730i	0.551167	−	0.354213i
$926$	−8.61704	−	24.8973i	−0.283173	−	0.818176i
$927$	−10.6211	+	4.25204i	−0.348842	+	0.139655i
$928$	0.897831	+	0.856080i	0.0294727	+	0.0281022i
$929$	−7.81131	+	4.02701i	−0.256281	+	0.132122i	−0.581580	−	0.813489i	$-0.697565\pi$
$929$	−7.81131	+	4.02701i	−0.256281	+	0.132122i	0.325299	+	0.945611i	$0.394535\pi$
$930$	−2.99761	−	20.8488i	−0.0982955	−	0.683660i
$931$	−13.6631	−	25.7734i	−0.447789	−	0.844690i
$932$	2.55635	+	5.59764i	0.0837362	+	0.183357i
$933$	−0.0333702	−	0.0133594i	−0.00109249	−	0.000437368i
$934$	0.269878	−	5.66545i	0.00883069	−	0.185379i
$935$	−1.90732	−	1.81862i	−0.0623759	−	0.0594753i
$936$	1.87863	+	1.47737i	0.0614049	+	0.0482894i
$937$	2.30464	−	2.65970i	0.0752894	−	0.0868887i	−0.716855	−	0.697222i	$-0.754419\pi$
$937$	2.30464	−	2.65970i	0.0752894	−	0.0868887i	0.792145	+	0.610334i	$0.208965\pi$
$938$	−1.51738	−	19.6347i	−0.0495441	−	0.641095i
$939$	15.0782	+	17.4011i	0.492058	+	0.567865i
$940$	1.77699	−	1.69436i	0.0579590	−	0.0552638i
$941$	16.8479	−	1.60878i	0.549227	−	0.0524448i	0.183246	−	0.983067i	$-0.441340\pi$
$941$	16.8479	−	1.60878i	0.549227	−	0.0524448i	0.365981	+	0.930622i	$0.380733\pi$
$942$	3.37404	+	5.84400i	0.109932	+	0.190408i
$943$	−1.39049	−	6.84062i	−0.0452806	−	0.222761i
$944$	−2.19755			−0.0715241
$945$	7.81671	−	0.980043i	0.254278	−	0.0318808i
$946$	−4.15991	−	1.22146i	−0.135250	−	0.0397131i
$947$	40.7966	−	7.86290i	1.32571	−	0.255510i	0.523232	−	0.852190i	$-0.324726\pi$
$947$	40.7966	−	7.86290i	1.32571	−	0.255510i	0.802479	+	0.596680i	$0.203514\pi$
$948$	−1.30087	−	0.670645i	−0.0422503	−	0.0217815i
$949$	−11.7472	−	2.26408i	−0.381329	−	0.0734951i
$950$	12.6636	+	9.95879i	0.410862	+	0.323106i
$951$	−12.5151	+	3.67477i	−0.405831	+	0.119163i
$952$	−4.77416	−	2.87263i	−0.154732	−	0.0931025i
$953$	4.05161	+	28.1795i	0.131244	+	0.912825i	0.943935	+	0.330130i	$0.107093\pi$
$953$	4.05161	+	28.1795i	0.131244	+	0.912825i	−0.812691	+	0.582695i	$0.801998\pi$
$954$	−8.62573	−	0.823658i	−0.279268	−	0.0266669i
$955$	1.47510	−	2.07149i	0.0477331	−	0.0670317i
$956$	−16.9386	+	13.3206i	−0.547833	+	0.430821i
$957$	0.463420	−	0.238909i	0.0149802	−	0.00772285i
$958$	−8.81817	+	2.58925i	−0.284902	+	0.0836548i
$959$	−6.79922	+	59.7685i	−0.219558	+	1.93003i
$960$	1.94989	−	2.25030i	0.0629325	−	0.0726280i
$961$	0.906009	+	19.0195i	0.0292261	+	0.613532i
$962$	4.02904	−	11.6411i	0.129901	−	0.375326i
$963$	−1.88047	−	7.75138i	−0.0605971	−	0.249785i
$964$	−5.25129	−	7.37440i	−0.169133	−	0.237514i
$965$	−11.0325			−0.355147
$966$	1.90537	−	12.5447i	0.0613043	−	0.403619i
$967$	47.1283			1.51554			0.757772	−	0.652520i	$-0.226288\pi$
$967$	47.1283			1.51554			0.757772	+	0.652520i	$0.226288\pi$
$968$	−6.27817	−	8.81645i	−0.201788	−	0.283372i
$969$	−2.06903	−	8.52865i	−0.0664668	−	0.273980i
$970$	15.5111	−	44.8164i	0.498032	−	1.43897i
$971$	−1.12115	−	23.5359i	−0.0359795	−	0.755303i	−0.942714	−	0.333601i	$-0.891736\pi$
$971$	−1.12115	−	23.5359i	−0.0359795	−	0.755303i	0.906735	−	0.421701i	$-0.138567\pi$
$972$	0.654861	−	0.755750i	0.0210047	−	0.0242407i
$973$	−33.6266	−	24.8733i	−1.07802	−	0.797401i
$974$	19.2426	−	5.65015i	0.616574	−	0.181043i
$975$	−8.21226	+	4.23372i	−0.263003	+	0.135587i
$976$	9.00181	−	7.07910i	0.288141	−	0.226597i
$977$	28.1080	−	39.4721i	0.899254	−	1.26283i	−0.0650106	−	0.997885i	$-0.520708\pi$
$977$	28.1080	−	39.4721i	0.899254	−	1.26283i	0.964265	−	0.264941i	$-0.0853525\pi$
$978$	9.03858	+	0.863080i	0.289022	+	0.0275983i
$979$	0.764329	+	5.31602i	0.0244280	+	0.169901i
$980$	−0.238746	−	20.8416i	−0.00762648	−	0.665761i
$981$	−13.2311	+	3.88499i	−0.422436	+	0.124038i
$982$	19.4122	+	15.2659i	0.619468	+	0.487155i
$983$	47.8260	+	9.21771i	1.52541	+	0.293999i	0.881901	−	0.471436i	$-0.156264\pi$
$983$	47.8260	+	9.21771i	1.52541	+	0.293999i	0.643513	+	0.765435i	$0.277476\pi$
$984$	−1.29373	−	0.666966i	−0.0412427	−	0.0212621i
$985$	50.6337	−	9.75884i	1.61332	−	0.310943i
$986$	2.50670	+	0.736032i	0.0798294	+	0.0234400i
$987$	−1.31742	−	1.73902i	−0.0419340	−	0.0553535i
$988$	9.95962			0.316858
$989$	30.1864	−	39.1965i	0.959871	−	1.24637i
$990$	−0.625705	−	1.08375i	−0.0198862	−	0.0344439i
$991$	10.5243	−	1.00495i	0.334314	−	0.0319231i	0.0734508	−	0.997299i	$-0.476599\pi$
$991$	10.5243	−	1.00495i	0.334314	−	0.0319231i	0.260863	+	0.965376i	$0.415993\pi$
$992$	−5.11967	+	4.88160i	−0.162550	+	0.154991i
$993$	7.09339	+	8.18621i	0.225102	+	0.259782i
$994$	−16.4232	−	7.86197i	−0.520913	−	0.249367i
$995$	−6.17398	+	7.12515i	−0.195728	+	0.225882i
$996$	1.40034	+	1.10124i	0.0443715	+	0.0348941i
$997$	7.88834	+	7.52152i	0.249826	+	0.238209i	0.804636	−	0.593768i	$-0.202360\pi$
$997$	7.88834	+	7.52152i	0.249826	+	0.238209i	−0.554810	+	0.831977i	$0.687209\pi$
$998$	−2.06256	+	43.2985i	−0.0652893	+	1.37059i
$999$	−4.78514	−	1.91568i	−0.151395	−	0.0606095i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.y.c.121.8	✓	160
7.4	even	3	inner	966.2.y.c.949.1	yes	160
23.4	even	11	inner	966.2.y.c.625.1	yes	160
161.4	even	33	inner	966.2.y.c.487.8	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.y.c.121.8	✓	160	1.1	even	1	trivial
966.2.y.c.487.8	yes	160	161.4	even	33	inner
966.2.y.c.625.1	yes	160	23.4	even	11	inner
966.2.y.c.949.1	yes	160	7.4	even	3	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.580057 + 0.814576i) q^{2} +(-0.235759 - 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(0.141678 + 2.97420i) q^{5} +(0.654861 - 0.755750i) q^{6} +(-2.12708 - 1.57338i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +O(q^{10})\)	\(q+(0.580057 + 0.814576i) q^{2} +(-0.235759 - 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(0.141678 + 2.97420i) q^{5} +(0.654861 - 0.755750i) q^{6} +(-2.12708 - 1.57338i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +(-2.34053 + 1.84061i) q^{10} +(0.243786 - 0.342349i) q^{11} +(0.995472 + 0.0950560i) q^{12} +(0.340126 + 2.36563i) q^{13} +(0.0478129 - 2.64532i) q^{14} +(2.85696 - 0.838878i) q^{15} +(-0.786053 - 0.618159i) q^{16} +(-2.06788 - 0.398550i) q^{17} +(-0.888835 - 0.458227i) q^{18} +(-4.09198 + 0.788665i) q^{19} +(-2.85696 - 0.838878i) q^{20} +(-1.02755 + 2.43806i) q^{21} +0.420279 q^{22} +(-1.73720 + 4.47014i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-3.84841 + 0.367479i) q^{25} +(-1.72969 + 1.64926i) q^{26} +(0.654861 + 0.755750i) q^{27} +(2.18255 - 1.49549i) q^{28} +(-0.812390 + 0.937548i) q^{29} +(2.34053 + 1.84061i) q^{30} +(-5.11967 - 4.88160i) q^{31} +(0.0475819 - 0.998867i) q^{32} +(-0.390174 - 0.156202i) q^{33} +(-0.874836 - 1.91562i) q^{34} +(4.37819 - 6.54927i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(-4.58138 + 2.36186i) q^{37} +(-3.01601 - 2.87576i) q^{38} +(2.21875 - 0.888255i) q^{39} +(-0.973867 - 2.81381i) q^{40} +(-1.22448 + 0.786923i) q^{41} +(-2.58202 + 0.577193i) q^{42} +(-9.89797 - 2.90631i) q^{43} +(0.243786 + 0.342349i) q^{44} +(-1.48878 - 2.57865i) q^{45} +(-4.64894 + 1.17785i) q^{46} +(-0.412301 + 0.714126i) q^{47} +(-0.415415 + 0.909632i) q^{48} +(2.04893 + 6.69342i) q^{49} +(-2.53164 - 2.92166i) q^{50} +(0.100204 + 2.10355i) q^{51} +(-2.34676 - 0.452301i) q^{52} +(8.04428 - 3.22044i) q^{53} +(-0.235759 + 0.971812i) q^{54} +(1.05275 + 0.676563i) q^{55} +(2.48419 + 0.910382i) q^{56} +(1.73116 + 3.79070i) q^{57} +(-1.23494 - 0.117922i) q^{58} +(1.72739 - 1.35843i) q^{59} +(-0.141678 + 2.97420i) q^{60} +(-2.69989 + 11.1291i) q^{61} +(1.00673 - 7.00197i) q^{62} +(2.61159 + 0.423794i) q^{63} +(0.841254 - 0.540641i) q^{64} +(-6.98765 + 1.34676i) q^{65} +(-0.0990845 - 0.408432i) q^{66} +(7.40963 - 0.707534i) q^{67} +(1.05297 - 1.82379i) q^{68} +(4.75369 + 0.634360i) q^{69} +(7.87447 - 0.232580i) q^{70} +(2.85888 - 6.26008i) q^{71} +(0.723734 - 0.690079i) q^{72} +(-1.63720 + 4.73038i) q^{73} +(-4.58138 - 2.36186i) q^{74} +(1.26442 + 3.65329i) q^{75} +(0.593067 - 4.12487i) q^{76} +(-1.05720 + 0.344635i) q^{77} +(2.01056 + 1.29211i) q^{78} +(-1.35873 - 0.543953i) q^{79} +(1.72716 - 2.42546i) q^{80} +(0.580057 - 0.814576i) q^{81} +(-1.35127 - 0.540969i) q^{82} +(1.49868 + 0.963143i) q^{83} +(-1.96789 - 1.76845i) q^{84} +(0.892394 - 6.20673i) q^{85} +(-3.37398 - 9.74848i) q^{86} +(1.10265 + 0.568454i) q^{87} +(-0.137460 + 0.397164i) q^{88} +(-9.24850 + 8.81843i) q^{89} +(1.23693 - 2.70849i) q^{90} +(2.99856 - 5.56702i) q^{91} +(-3.65610 - 3.10370i) q^{92} +(-3.53698 + 6.12624i) q^{93} +(-0.820868 + 0.0783834i) q^{94} +(-2.92539 - 12.0586i) q^{95} +(-0.981929 + 0.189251i) q^{96} +(-13.3989 + 8.61097i) q^{97} +(-4.26380 + 5.55158i) q^{98} +(-0.0598119 + 0.416001i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} + 16 q^{6} - 2 q^{7} - 16 q^{8} + 8 q^{9}+O(q^{10}) \) 160 * q + 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 + 16 * q^6 - 2 * q^7 - 16 * q^8 + 8 * q^9	\( 160 q + 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} + 16 q^{6} - 2 q^{7} - 16 q^{8} + 8 q^{9} + 2 q^{10} + 8 q^{11} - 8 q^{12} - 4 q^{13} + 9 q^{14} - 18 q^{15} + 8 q^{16} - 21 q^{17} + 8 q^{18} + 4 q^{19} + 18 q^{20} - 15 q^{21} + 116 q^{22} + 14 q^{23} + 80 q^{24} + 2 q^{25} + 2 q^{26} + 16 q^{27} - 18 q^{28} - 46 q^{29} - 2 q^{30} + q^{31} + 8 q^{32} - 8 q^{33} - 68 q^{34} - 84 q^{35} - 16 q^{36} + 19 q^{37} - 7 q^{38} - 2 q^{39} - 9 q^{40} + 38 q^{41} + 2 q^{42} + 28 q^{43} + 8 q^{44} + 24 q^{45} - 8 q^{46} - 26 q^{47} + 16 q^{48} - 6 q^{49} - 4 q^{50} + 21 q^{51} + 2 q^{52} - 20 q^{53} - 8 q^{54} + 46 q^{55} - 2 q^{56} - 14 q^{57} - 21 q^{58} + 36 q^{59} - 2 q^{60} + 40 q^{61} - 24 q^{62} - 2 q^{63} - 16 q^{64} - 10 q^{65} - 8 q^{66} + 6 q^{67} + 34 q^{68} + 6 q^{69} - 20 q^{70} + 132 q^{71} + 8 q^{72} - 36 q^{73} + 19 q^{74} - 2 q^{75} - 8 q^{76} - 75 q^{77} - 18 q^{78} + 34 q^{79} + 2 q^{80} + 8 q^{81} + 47 q^{82} + 74 q^{83} + 13 q^{84} + 2 q^{85} + 30 q^{86} + 10 q^{87} - 3 q^{88} - 12 q^{89} - 4 q^{90} - 30 q^{91} - 50 q^{92} + 10 q^{93} - 4 q^{94} + 27 q^{95} - 8 q^{96} + 24 q^{97} + 7 q^{98} - 16 q^{99}+O(q^{100}) \) 160 * q + 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 + 16 * q^6 - 2 * q^7 - 16 * q^8 + 8 * q^9 + 2 * q^10 + 8 * q^11 - 8 * q^12 - 4 * q^13 + 9 * q^14 - 18 * q^15 + 8 * q^16 - 21 * q^17 + 8 * q^18 + 4 * q^19 + 18 * q^20 - 15 * q^21 + 116 * q^22 + 14 * q^23 + 80 * q^24 + 2 * q^25 + 2 * q^26 + 16 * q^27 - 18 * q^28 - 46 * q^29 - 2 * q^30 + q^31 + 8 * q^32 - 8 * q^33 - 68 * q^34 - 84 * q^35 - 16 * q^36 + 19 * q^37 - 7 * q^38 - 2 * q^39 - 9 * q^40 + 38 * q^41 + 2 * q^42 + 28 * q^43 + 8 * q^44 + 24 * q^45 - 8 * q^46 - 26 * q^47 + 16 * q^48 - 6 * q^49 - 4 * q^50 + 21 * q^51 + 2 * q^52 - 20 * q^53 - 8 * q^54 + 46 * q^55 - 2 * q^56 - 14 * q^57 - 21 * q^58 + 36 * q^59 - 2 * q^60 + 40 * q^61 - 24 * q^62 - 2 * q^63 - 16 * q^64 - 10 * q^65 - 8 * q^66 + 6 * q^67 + 34 * q^68 + 6 * q^69 - 20 * q^70 + 132 * q^71 + 8 * q^72 - 36 * q^73 + 19 * q^74 - 2 * q^75 - 8 * q^76 - 75 * q^77 - 18 * q^78 + 34 * q^79 + 2 * q^80 + 8 * q^81 + 47 * q^82 + 74 * q^83 + 13 * q^84 + 2 * q^85 + 30 * q^86 + 10 * q^87 - 3 * q^88 - 12 * q^89 - 4 * q^90 - 30 * q^91 - 50 * q^92 + 10 * q^93 - 4 * q^94 + 27 * q^95 - 8 * q^96 + 24 * q^97 + 7 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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