LMFDB - Embedded newform 380.2.k.c.343.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(267,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("380.267");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			343.20
Character	$\chi$	$=$	380.343
Dual form			380.2.k.c.267.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.08061 - 0.912296i) q^{2} +(1.34016 - 1.34016i) q^{3} +(0.335432 - 1.97167i) q^{4} +(-2.21942 + 0.272360i) q^{5} +(0.225567 - 2.67081i) q^{6} +(-0.697742 - 0.697742i) q^{7} +(-1.43628 - 2.43662i) q^{8} -0.592060i q^{9} +O(q^{10})$	\(q+(1.08061 - 0.912296i) q^{2} +(1.34016 - 1.34016i) q^{3} +(0.335432 - 1.97167i) q^{4} +(-2.21942 + 0.272360i) q^{5} +(0.225567 - 2.67081i) q^{6} +(-0.697742 - 0.697742i) q^{7} +(-1.43628 - 2.43662i) q^{8} -0.592060i q^{9} +(-2.14985 + 2.31908i) q^{10} -4.74628i q^{11} +(-2.19282 - 3.09189i) q^{12} +(3.30493 + 3.30493i) q^{13} +(-1.39053 - 0.117439i) q^{14} +(-2.60937 + 3.33938i) q^{15} +(-3.77497 - 1.32272i) q^{16} +(-1.03069 + 1.03069i) q^{17} +(-0.540133 - 0.639785i) q^{18} +1.00000 q^{19} +(-0.207460 + 4.46732i) q^{20} -1.87017 q^{21} +(-4.33001 - 5.12887i) q^{22} +(6.40614 - 6.40614i) q^{23} +(-5.19030 - 1.34062i) q^{24} +(4.85164 - 1.20896i) q^{25} +(6.58642 + 0.556264i) q^{26} +(3.22703 + 3.22703i) q^{27} +(-1.60976 + 1.14167i) q^{28} +1.98037i q^{29} +(0.226796 + 5.98909i) q^{30} +9.29923i q^{31} +(-5.28598 + 2.01454i) q^{32} +(-6.36077 - 6.36077i) q^{33} +(-0.173479 + 2.05407i) q^{34} +(1.73862 + 1.35854i) q^{35} +(-1.16735 - 0.198596i) q^{36} +(-5.70256 + 5.70256i) q^{37} +(1.08061 - 0.912296i) q^{38} +8.85828 q^{39} +(3.85134 + 5.01669i) q^{40} +9.41542 q^{41} +(-2.02093 + 1.70615i) q^{42} +(-1.89635 + 1.89635i) q^{43} +(-9.35809 - 1.59205i) q^{44} +(0.161254 + 1.31403i) q^{45} +(1.07824 - 12.7668i) q^{46} +(-1.10706 - 1.10706i) q^{47} +(-6.83173 + 3.28640i) q^{48} -6.02631i q^{49} +(4.13979 - 5.73255i) q^{50} +2.76258i q^{51} +(7.62482 - 5.40766i) q^{52} +(-0.00450773 - 0.00450773i) q^{53} +(6.43116 + 0.543151i) q^{54} +(1.29270 + 10.5340i) q^{55} +(-0.697982 + 2.70228i) q^{56} +(1.34016 - 1.34016i) q^{57} +(1.80669 + 2.14001i) q^{58} +3.02457 q^{59} +(5.70890 + 6.26496i) q^{60} -0.724786 q^{61} +(8.48365 + 10.0488i) q^{62} +(-0.413105 + 0.413105i) q^{63} +(-3.87422 + 6.99931i) q^{64} +(-8.23516 - 6.43490i) q^{65} +(-12.6764 - 1.07060i) q^{66} +(-10.1252 - 10.1252i) q^{67} +(1.68645 + 2.37791i) q^{68} -17.1705i q^{69} +(3.11816 - 0.118079i) q^{70} +9.29365i q^{71} +(-1.44262 + 0.850361i) q^{72} +(-4.54609 - 4.54609i) q^{73} +(-0.959817 + 11.3647i) q^{74} +(4.88177 - 8.12218i) q^{75} +(0.335432 - 1.97167i) q^{76} +(-3.31168 + 3.31168i) q^{77} +(9.57234 - 8.08137i) q^{78} -0.319115 q^{79} +(8.73850 + 1.90753i) q^{80} +10.4256 q^{81} +(10.1744 - 8.58965i) q^{82} +(2.15376 - 2.15376i) q^{83} +(-0.627316 + 3.68736i) q^{84} +(2.00681 - 2.56825i) q^{85} +(-0.319181 + 3.77925i) q^{86} +(2.65402 + 2.65402i) q^{87} +(-11.5649 + 6.81696i) q^{88} +8.13569i q^{89} +(1.37303 + 1.27284i) q^{90} -4.61198i q^{91} +(-10.4820 - 14.7796i) q^{92} +(12.4625 + 12.4625i) q^{93} +(-2.20627 - 0.186333i) q^{94} +(-2.21942 + 0.272360i) q^{95} +(-4.38426 + 9.78387i) q^{96} +(-8.29185 + 8.29185i) q^{97} +(-5.49778 - 6.51209i) q^{98} -2.81008 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 2 q^{2} - 2 q^{3} + 4 q^{5} - 4 q^{6} - 4 q^{7} + 4 q^{8}+O(q^{10}) $ 52 * q - 2 * q^2 - 2 * q^3 + 4 * q^5 - 4 * q^6 - 4 * q^7 + 4 * q^8	$ 52 q - 2 q^{2} - 2 q^{3} + 4 q^{5} - 4 q^{6} - 4 q^{7} + 4 q^{8} - 18 q^{10} - 38 q^{12} - 2 q^{13} + 2 q^{15} + 16 q^{16} - 20 q^{17} + 2 q^{18} + 52 q^{19} + 20 q^{20} - 16 q^{21} + 20 q^{22} + 20 q^{23} - 16 q^{25} - 8 q^{27} - 8 q^{28} - 48 q^{30} - 42 q^{32} + 8 q^{33} - 20 q^{34} + 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} - 64 q^{39} + 60 q^{40} - 4 q^{41} + 60 q^{42} - 28 q^{43} + 8 q^{44} + 12 q^{45} - 8 q^{46} - 4 q^{47} - 18 q^{48} - 42 q^{50} - 54 q^{52} - 2 q^{53} - 24 q^{54} + 12 q^{56} - 2 q^{57} - 12 q^{58} + 28 q^{59} + 90 q^{60} - 4 q^{61} + 56 q^{62} + 44 q^{63} + 24 q^{64} + 10 q^{65} + 36 q^{66} + 6 q^{67} - 60 q^{68} - 32 q^{70} - 24 q^{72} + 8 q^{73} - 88 q^{74} + 2 q^{75} + 12 q^{77} + 64 q^{78} - 52 q^{79} - 8 q^{80} - 24 q^{81} + 56 q^{82} - 76 q^{83} + 40 q^{84} + 12 q^{85} - 8 q^{86} + 12 q^{87} - 40 q^{88} - 94 q^{90} - 48 q^{92} + 24 q^{93} - 32 q^{94} + 4 q^{95} - 4 q^{96} - 10 q^{97} + 58 q^{98} + 128 q^{99}+O(q^{100}) $ 52 * q - 2 * q^2 - 2 * q^3 + 4 * q^5 - 4 * q^6 - 4 * q^7 + 4 * q^8 - 18 * q^10 - 38 * q^12 - 2 * q^13 + 2 * q^15 + 16 * q^16 - 20 * q^17 + 2 * q^18 + 52 * q^19 + 20 * q^20 - 16 * q^21 + 20 * q^22 + 20 * q^23 - 16 * q^25 - 8 * q^27 - 8 * q^28 - 48 * q^30 - 42 * q^32 + 8 * q^33 - 20 * q^34 + 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 - 64 * q^39 + 60 * q^40 - 4 * q^41 + 60 * q^42 - 28 * q^43 + 8 * q^44 + 12 * q^45 - 8 * q^46 - 4 * q^47 - 18 * q^48 - 42 * q^50 - 54 * q^52 - 2 * q^53 - 24 * q^54 + 12 * q^56 - 2 * q^57 - 12 * q^58 + 28 * q^59 + 90 * q^60 - 4 * q^61 + 56 * q^62 + 44 * q^63 + 24 * q^64 + 10 * q^65 + 36 * q^66 + 6 * q^67 - 60 * q^68 - 32 * q^70 - 24 * q^72 + 8 * q^73 - 88 * q^74 + 2 * q^75 + 12 * q^77 + 64 * q^78 - 52 * q^79 - 8 * q^80 - 24 * q^81 + 56 * q^82 - 76 * q^83 + 40 * q^84 + 12 * q^85 - 8 * q^86 + 12 * q^87 - 40 * q^88 - 94 * q^90 - 48 * q^92 + 24 * q^93 - 32 * q^94 + 4 * q^95 - 4 * q^96 - 10 * q^97 + 58 * q^98 + 128 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.08061	−	0.912296i	0.764106	−	0.645091i
$2$	1.08061	−	0.912296i	0.764106	−	0.645091i
$3$	1.34016	−	1.34016i	0.773742	−	0.773742i	−0.205017	−	0.978759i	$-0.565725\pi$
$3$	1.34016	−	1.34016i	0.773742	−	0.773742i	0.978759	+	0.205017i	$0.0657248\pi$
$4$	0.335432	−	1.97167i	0.167716	−	0.985835i
$5$	−2.21942	+	0.272360i	−0.992554	+	0.121803i
$5$	−2.21942	+	0.272360i	−0.992554	+	0.121803i
$6$	0.225567	−	2.67081i	0.0920873	−	1.09035i
$7$	−0.697742	−	0.697742i	−0.263722	−	0.263722i	0.562842	−	0.826564i	$-0.309708\pi$
$7$	−0.697742	−	0.697742i	−0.263722	−	0.263722i	−0.826564	+	0.562842i	$0.809708\pi$
$8$	−1.43628	−	2.43662i	−0.507800	−	0.861475i
$9$		−	0.592060i		−	0.197353i
$10$	−2.14985	+	2.31908i	−0.679843	+	0.733358i
$11$		−	4.74628i		−	1.43106i	−0.698584	−	0.715528i	$-0.746186\pi$
$11$		−	4.74628i		−	1.43106i	0.698584	−	0.715528i	$-0.253814\pi$
$12$	−2.19282	−	3.09189i	−0.633013	−	0.892551i
$13$	3.30493	+	3.30493i	0.916623	+	0.916623i	0.996782	−	0.0801589i	$-0.0255428\pi$
$13$	3.30493	+	3.30493i	0.916623	+	0.916623i	−0.0801589	+	0.996782i	$0.525543\pi$
$14$	−1.39053	−	0.117439i	−0.371636	−	0.0313870i
$15$	−2.60937	+	3.33938i	−0.673737	+	0.862225i
$16$	−3.77497	−	1.32272i	−0.943743	−	0.330681i
$17$	−1.03069	+	1.03069i	−0.249979	+	0.249979i	−0.820962	−	0.570983i	$-0.806562\pi$
$17$	−1.03069	+	1.03069i	−0.249979	+	0.249979i	0.570983	+	0.820962i	$0.306562\pi$
$18$	−0.540133	−	0.639785i	−0.127311	−	0.150799i
$19$	1.00000			0.229416
$19$	1.00000			0.229416
$20$	−0.207460	+	4.46732i	−0.0463895	+	0.998923i
$21$	−1.87017			−0.408105
$22$	−4.33001	−	5.12887i	−0.923161	−	1.09348i
$23$	6.40614	−	6.40614i	1.33577	−	1.33577i	0.435662	−	0.900110i	$-0.356514\pi$
$23$	6.40614	−	6.40614i	1.33577	−	1.33577i	0.900110	−	0.435662i	$-0.143486\pi$
$24$	−5.19030	−	1.34062i	−1.05947	−	0.273653i
$25$	4.85164	−	1.20896i	0.970328	−	0.241793i
$26$	6.58642	+	0.556264i	1.29170	+	0.109092i
$27$	3.22703	+	3.22703i	0.621042	+	0.621042i
$28$	−1.60976	+	1.14167i	−0.304217	+	0.215756i
$29$			1.98037i			0.367746i	0.982950	+	0.183873i	$0.0588636\pi$
$29$			1.98037i			0.367746i	−0.982950	+	0.183873i	$0.941136\pi$
$30$	0.226796	+	5.98909i	0.0414071	+	1.09345i
$31$			9.29923i			1.67019i	0.550106	+	0.835095i	$0.314587\pi$
$31$			9.29923i			1.67019i	−0.550106	+	0.835095i	$0.685413\pi$
$32$	−5.28598	+	2.01454i	−0.934439	+	0.356124i
$33$	−6.36077	−	6.36077i	−1.10727	−	1.10727i
$34$	−0.173479	+	2.05407i	−0.0297513	+	0.352269i
$35$	1.73862	+	1.35854i	0.293880	+	0.229636i
$36$	−1.16735	−	0.198596i	−0.194558	−	0.0330993i
$37$	−5.70256	+	5.70256i	−0.937496	+	0.937496i	−0.998158	−	0.0606627i	$-0.980679\pi$
$37$	−5.70256	+	5.70256i	−0.937496	+	0.937496i	0.0606627	+	0.998158i	$0.480679\pi$
$38$	1.08061	−	0.912296i	0.175298	−	0.147994i
$39$	8.85828			1.41846
$40$	3.85134	+	5.01669i	0.608950	+	0.793209i
$41$	9.41542			1.47044			0.735221	−	0.677828i	$-0.237078\pi$
$41$	9.41542			1.47044			0.735221	+	0.677828i	$0.237078\pi$
$42$	−2.02093	+	1.70615i	−0.311836	+	0.263265i
$43$	−1.89635	+	1.89635i	−0.289191	+	0.289191i	−0.836760	−	0.547569i	$-0.815553\pi$
$43$	−1.89635	+	1.89635i	−0.289191	+	0.289191i	0.547569	+	0.836760i	$0.315553\pi$
$44$	−9.35809	−	1.59205i	−1.41079	−	0.240011i
$45$	0.161254	+	1.31403i	0.0240383	+	0.195884i
$46$	1.07824	−	12.7668i	0.158978	−	1.88237i
$47$	−1.10706	−	1.10706i	−0.161482	−	0.161482i	0.621741	−	0.783223i	$-0.286426\pi$
$47$	−1.10706	−	1.10706i	−0.161482	−	0.161482i	−0.783223	+	0.621741i	$0.786426\pi$
$48$	−6.83173	+	3.28640i	−0.986075	+	0.474351i
$49$		−	6.02631i		−	0.860902i
$50$	4.13979	−	5.73255i	0.585455	−	0.810705i
$51$			2.76258i			0.386838i
$52$	7.62482	−	5.40766i	1.05737	−	0.749907i
$53$	−0.00450773	−	0.00450773i	−0.000619185	−	0.000619185i	0.706797	−	0.707416i	$-0.250139\pi$
$53$	−0.00450773	−	0.00450773i	−0.000619185	−	0.000619185i	−0.707416	+	0.706797i	$0.750139\pi$
$54$	6.43116	+	0.543151i	0.875170	+	0.0739135i
$55$	1.29270	+	10.5340i	0.174307	+	1.42040i
$56$	−0.697982	+	2.70228i	−0.0932717	+	0.361108i
$57$	1.34016	−	1.34016i	0.177509	−	0.177509i
$58$	1.80669	+	2.14001i	0.237230	+	0.280997i
$59$	3.02457			0.393765			0.196883	−	0.980427i	$-0.436918\pi$
$59$	3.02457			0.393765			0.196883	+	0.980427i	$0.436918\pi$
$60$	5.70890	+	6.26496i	0.737015	+	0.808802i
$61$	−0.724786			−0.0927993			−0.0463997	−	0.998923i	$-0.514775\pi$
$61$	−0.724786			−0.0927993			−0.0463997	+	0.998923i	$0.514775\pi$
$62$	8.48365	+	10.0488i	1.07742	+	1.27620i
$63$	−0.413105	+	0.413105i	−0.0520463	+	0.0520463i
$64$	−3.87422	+	6.99931i	−0.484278	+	0.874914i
$65$	−8.23516	−	6.43490i	−1.02145	−	0.798151i
$66$	−12.6764	−	1.07060i	−1.56036	−	0.131782i
$67$	−10.1252	−	10.1252i	−1.23699	−	1.23699i	−0.961226	−	0.275761i	$-0.911070\pi$
$67$	−10.1252	−	10.1252i	−1.23699	−	1.23699i	−0.275761	−	0.961226i	$-0.588930\pi$
$68$	1.68645	+	2.37791i	0.204512	+	0.288364i
$69$		−	17.1705i		−	2.06709i
$70$	3.11816	−	0.118079i	0.372692	−	0.0141132i
$71$			9.29365i			1.10295i	0.834190	+	0.551477i	$0.185935\pi$
$71$			9.29365i			1.10295i	−0.834190	+	0.551477i	$0.814065\pi$
$72$	−1.44262	+	0.850361i	−0.170015	+	0.100216i
$73$	−4.54609	−	4.54609i	−0.532079	−	0.532079i	0.389112	−	0.921191i	$-0.372782\pi$
$73$	−4.54609	−	4.54609i	−0.532079	−	0.532079i	−0.921191	+	0.389112i	$0.872782\pi$
$74$	−0.959817	+	11.3647i	−0.111576	+	1.32112i
$75$	4.88177	−	8.12218i	0.563698	−	0.937869i
$76$	0.335432	−	1.97167i	0.0384767	−	0.226166i
$77$	−3.31168	+	3.31168i	−0.377401	+	0.377401i
$78$	9.57234	−	8.08137i	1.08385	−	0.915035i
$79$	−0.319115			−0.0359032			−0.0179516	−	0.999839i	$-0.505714\pi$
$79$	−0.319115			−0.0359032			−0.0179516	+	0.999839i	$0.505714\pi$
$80$	8.73850	+	1.90753i	0.976994	+	0.213268i
$81$	10.4256			1.15840
$82$	10.1744	−	8.58965i	1.12357	−	0.948568i
$83$	2.15376	−	2.15376i	0.236406	−	0.236406i	−0.578954	−	0.815360i	$-0.696539\pi$
$83$	2.15376	−	2.15376i	0.236406	−	0.236406i	0.815360	+	0.578954i	$0.196539\pi$
$84$	−0.627316	+	3.68736i	−0.0684458	+	0.402324i
$85$	2.00681	−	2.56825i	0.217669	−	0.278566i
$86$	−0.319181	+	3.77925i	−0.0344182	+	0.407527i
$87$	2.65402	+	2.65402i	0.284541	+	0.284541i
$88$	−11.5649	+	6.81696i	−1.23282	+	0.726690i
$89$			8.13569i			0.862381i	0.902261	+	0.431191i	$0.141906\pi$
$89$			8.13569i			0.862381i	−0.902261	+	0.431191i	$0.858094\pi$
$90$	1.37303	+	1.27284i	0.144731	+	0.134169i
$91$		−	4.61198i		−	0.483467i
$92$	−10.4820	−	14.7796i	−1.09282	−	1.54088i
$93$	12.4625	+	12.4625i	1.29230	+	1.29230i
$94$	−2.20627	−	0.186333i	−0.227560	−	0.0192188i
$95$	−2.21942	+	0.272360i	−0.227708	+	0.0279436i
$96$	−4.38426	+	9.78387i	−0.447466	+	0.998563i
$97$	−8.29185	+	8.29185i	−0.841910	+	0.841910i	−0.989107	−	0.147197i	$-0.952975\pi$
$97$	−8.29185	+	8.29185i	−0.841910	+	0.841910i	0.147197	+	0.989107i	$0.452975\pi$
$98$	−5.49778	−	6.51209i	−0.555360	−	0.657820i
$99$	−2.81008			−0.282423
$100$	−0.756281	−	9.97136i	−0.0756281	−	0.997136i
$101$	2.37691			0.236512			0.118256	−	0.992983i	$-0.462270\pi$
$101$	2.37691			0.236512			0.118256	+	0.992983i	$0.462270\pi$
$102$	2.52029	+	2.98527i	0.249546	+	0.295585i
$103$	3.18098	−	3.18098i	0.313432	−	0.313432i	−0.532806	−	0.846237i	$-0.678862\pi$
$103$	3.18098	−	3.18098i	0.313432	−	0.313432i	0.846237	+	0.532806i	$0.178862\pi$
$104$	3.30607	−	12.7997i	0.324186	−	1.25511i
$105$	4.15070	−	0.509361i	0.405066	−	0.0497085i
$106$	−0.00898348		0.000758711i	−0.000872553		7.36925e-5i
$107$	−11.3868	−	11.3868i	−1.10080	−	1.10080i	−0.994314	−	0.106490i	$-0.966039\pi$
$107$	−11.3868	−	11.3868i	−1.10080	−	1.10080i	−0.106490	−	0.994314i	$-0.533961\pi$
$108$	7.44508	−	5.28018i	0.716403	−	0.508086i
$109$			10.1057i			0.967951i	0.875082	+	0.483975i	$0.160808\pi$
$109$			10.1057i			0.967951i	−0.875082	+	0.483975i	$0.839192\pi$
$110$	11.0070	+	10.2038i	1.04948	+	0.972893i
$111$			15.2847i			1.45076i
$112$	1.71104	+	3.55688i	0.161678	+	0.336093i
$113$	4.33960	+	4.33960i	0.408236	+	0.408236i	0.881123	−	0.472887i	$-0.156788\pi$
$113$	4.33960	+	4.33960i	0.408236	+	0.408236i	−0.472887	+	0.881123i	$0.656788\pi$
$114$	0.225567	−	2.67081i	0.0211263	−	0.250144i
$115$	−12.4731	+	15.9627i	−1.16312	+	1.48853i
$116$	3.90465	+	0.664282i	0.362537	+	0.0616770i
$117$	1.95672	−	1.95672i	0.180899	−	0.180899i
$118$	3.26838	−	2.75930i	0.300878	−	0.254014i
$119$	1.43831			0.131850
$120$	11.8846	+	1.56177i	1.08491	+	0.142569i
$121$	−11.5271			−1.04792
$122$	−0.783210	+	0.661219i	−0.0709085	+	0.0598640i
$123$	12.6182	−	12.6182i	1.13774	−	1.13774i
$124$	18.3350	+	3.11926i	1.64653	+	0.280118i
$125$	−10.4385	+	4.00459i	−0.933652	+	0.358181i
$126$	−0.0695310	+	0.823279i	−0.00619432	+	0.0733435i
$127$	5.74713	+	5.74713i	0.509976	+	0.509976i	0.914519	−	0.404543i	$-0.132570\pi$
$127$	5.74713	+	5.74713i	0.509976	+	0.509976i	−0.404543	+	0.914519i	$0.632570\pi$
$128$	2.19892	+	11.0980i	0.194359	+	0.980930i
$129$			5.08283i			0.447518i
$130$	−14.7695	+	0.559296i	−1.29537	+	0.0490535i
$131$			8.12224i			0.709644i	0.934934	+	0.354822i	$0.115458\pi$
$131$			8.12224i			0.709644i	−0.934934	+	0.354822i	$0.884542\pi$
$132$	−14.6750	+	10.4077i	−1.27729	+	0.905877i
$133$	−0.697742	−	0.697742i	−0.0605019	−	0.0605019i
$134$	−20.1785	−	1.70420i	−1.74316	−	0.147221i
$135$	−8.04104	−	6.28321i	−0.692062	−	0.540773i
$136$	3.99175	+	1.03104i	0.342290	+	0.0884112i
$137$	4.96810	−	4.96810i	0.424453	−	0.424453i	−0.462281	−	0.886734i	$-0.652969\pi$
$137$	4.96810	−	4.96810i	0.424453	−	0.424453i	0.886734	+	0.462281i	$0.152969\pi$
$138$	−15.6646	−	18.5546i	−1.33346	−	1.57947i
$139$	−4.21496			−0.357508			−0.178754	−	0.983894i	$-0.557207\pi$
$139$	−4.21496			−0.357508			−0.178754	+	0.983894i	$0.557207\pi$
$140$	3.26179	−	2.97228i	0.275672	−	0.251204i
$141$	−2.96728			−0.249890
$142$	8.47856	+	10.0428i	0.711505	+	0.842774i
$143$	15.6861	−	15.6861i	1.31174	−	1.31174i
$144$	−0.783132	+	2.23501i	−0.0652610	+	0.186251i
$145$	−0.539375	−	4.39528i	−0.0447927	−	0.365008i
$146$	−9.05992	−	0.765167i	−0.749804	−	0.0633256i
$147$	−8.07622	−	8.07622i	−0.666116	−	0.666116i
$148$	9.33075	+	13.1564i	0.766983	+	1.08145i
$149$			7.03834i			0.576603i	0.957540	+	0.288302i	$0.0930906\pi$
$149$			7.03834i			0.576603i	−0.957540	+	0.288302i	$0.906909\pi$
$150$	−2.13455	−	13.2305i	−0.174285	−	1.08027i
$151$			16.8075i			1.36777i	0.729589	+	0.683886i	$0.239711\pi$
$151$			16.8075i			1.36777i	−0.729589	+	0.683886i	$0.760289\pi$
$152$	−1.43628	−	2.43662i	−0.116497	−	0.197636i
$153$	0.610229	+	0.610229i	0.0493341	+	0.0493341i
$154$	−0.557399	+	6.59986i	−0.0449165	+	0.531832i
$155$	−2.53274	−	20.6389i	−0.203435	−	1.65775i
$156$	2.97135	−	17.4656i	0.237899	−	1.39837i
$157$	11.5208	−	11.5208i	0.919458	−	0.919458i	−0.0775322	−	0.996990i	$-0.524704\pi$
$157$	11.5208	−	11.5208i	0.919458	−	0.919458i	0.996990	+	0.0775322i	$0.0247040\pi$
$158$	−0.344839	+	0.291127i	−0.0274339	+	0.0231608i
$159$	−0.0120822			−0.000958178
$160$	11.1831	−	5.91080i	0.884104	−	0.467290i
$161$	−8.93967			−0.704544
$162$	11.2660	−	9.51127i	0.885144	−	0.747276i
$163$	−8.50009	+	8.50009i	−0.665778	+	0.665778i	−0.956736	−	0.290958i	$-0.906026\pi$
$163$	−8.50009	+	8.50009i	−0.665778	+	0.665778i	0.290958	+	0.956736i	$0.406026\pi$
$164$	3.15824	−	18.5641i	0.246617	−	1.44961i
$165$	15.8496	+	12.3848i	1.23389	+	0.964155i
$166$	0.362506	−	4.29223i	0.0281359	−	0.333142i
$167$	−11.7917	−	11.7917i	−0.912471	−	0.912471i	0.0839953	−	0.996466i	$-0.473232\pi$
$167$	−11.7917	−	11.7917i	−0.912471	−	0.912471i	−0.996466	+	0.0839953i	$0.973232\pi$
$168$	2.68608	+	4.55690i	0.207236	+	0.351572i
$169$			8.84515i			0.680396i
$170$	−0.174424	−	4.60608i	−0.0133777	−	0.353270i
$171$		−	0.592060i		−	0.0452759i
$172$	3.10288	+	4.37508i	0.236593	+	0.333597i
$173$	−14.0451	−	14.0451i	−1.06783	−	1.06783i	−0.997525	−	0.0703074i	$-0.977602\pi$
$173$	−14.0451	−	14.0451i	−1.06783	−	1.06783i	−0.0703074	−	0.997525i	$-0.522398\pi$
$174$	5.28921	+	0.446707i	0.400974	+	0.0338647i
$175$	−4.22874	−	2.54165i	−0.319663	−	0.192131i
$176$	−6.27801	+	17.9170i	−0.473223	+	1.35055i
$177$	4.05341	−	4.05341i	0.304673	−	0.304673i
$178$	7.42215	+	8.79150i	0.556314	+	0.658951i
$179$	−8.86640			−0.662706			−0.331353	−	0.943507i	$-0.607505\pi$
$179$	−8.86640			−0.662706			−0.331353	+	0.943507i	$0.607505\pi$
$180$	2.64492	+	0.122829i	0.197141	+	0.00915511i
$181$	5.73740			0.426457			0.213229	−	0.977002i	$-0.431602\pi$
$181$	5.73740			0.426457			0.213229	+	0.977002i	$0.431602\pi$
$182$	−4.20749	−	4.98375i	−0.311880	−	0.369420i
$183$	−0.971329	+	0.971329i	−0.0718027	+	0.0718027i
$184$	−24.8103	−	6.40834i	−1.82904	−	0.472429i
$185$	11.1032	−	14.2095i	0.816325	−	1.04471i
$186$	24.8365	+	2.09760i	1.82110	+	0.153803i
$187$	4.89194	+	4.89194i	0.357734	+	0.357734i
$188$	−2.55411	+	1.81142i	−0.186278	+	0.132111i
$189$		−	4.50326i		−	0.327564i
$190$	−2.14985	+	2.31908i	−0.155967	+	0.168244i
$191$		−	3.42146i		−	0.247568i	−0.992309	−	0.123784i	$-0.960497\pi$
$191$		−	3.42146i		−	0.247568i	0.992309	−	0.123784i	$-0.0395030\pi$
$192$	4.18812	+	14.5723i	0.302252	+	1.05166i
$193$	14.1458	+	14.1458i	1.01824	+	1.01824i	0.999831	+	0.0184059i	$0.00585912\pi$
$193$	14.1458	+	14.1458i	1.01824	+	1.01824i	0.0184059	+	0.999831i	$0.494141\pi$
$194$	−1.39563	+	16.5249i	−0.100200	+	1.18642i
$195$	−19.6602	+	2.41264i	−1.40790	+	0.172773i
$196$	−11.8819	−	2.02142i	−0.848707	−	0.144387i
$197$	−3.94287	+	3.94287i	−0.280918	+	0.280918i	−0.833475	−	0.552557i	$-0.813652\pi$
$197$	−3.94287	+	3.94287i	−0.280918	+	0.280918i	0.552557	+	0.833475i	$0.313652\pi$
$198$	−3.03660	+	2.56362i	−0.215801	+	0.182189i
$199$	−22.6493			−1.60557			−0.802785	−	0.596269i	$-0.796649\pi$
$199$	−22.6493			−1.60557			−0.802785	+	0.596269i	$0.796649\pi$
$200$	−9.91408	−	10.0852i	−0.701031	−	0.713131i
$201$	−27.1387			−1.91422
$202$	2.56851	−	2.16845i	0.180720	−	0.152571i
$203$	1.38179	−	1.38179i	0.0969827	−	0.0969827i
$204$	5.44689	+	0.926658i	0.381359	+	0.0648790i
$205$	−20.8968	+	2.56439i	−1.45949	+	0.179105i
$206$	0.535402	−	6.33940i	0.0373032	−	0.441687i
$207$	−3.79282	−	3.79282i	−0.263619	−	0.263619i
$208$	−8.10451	−	16.8475i	−0.561946	−	1.16817i
$209$		−	4.74628i		−	0.328307i
$210$	4.02059	−	4.33708i	0.277447	−	0.299287i
$211$		−	23.7055i		−	1.63196i	−0.578083	−	0.815978i	$-0.696199\pi$
$211$		−	23.7055i		−	1.63196i	0.578083	−	0.815978i	$-0.303801\pi$
$212$	−0.0103998	+	0.00737572i	−0.000714261	+	0.000506567i
$213$	12.4550	+	12.4550i	0.853402	+	0.853402i
$214$	−22.6928	−	1.91655i	−1.55125	−	0.131013i
$215$	3.69231	−	4.72529i	0.251813	−	0.322262i
$216$	3.22813	−	12.4979i	0.219647	−	0.850377i
$217$	6.48846	−	6.48846i	0.440465	−	0.440465i
$218$	9.21939	+	10.9203i	0.624416	+	0.739617i
$219$	−12.1850			−0.823384
$220$	21.2031	+	0.984662i	1.42952	+	0.0663859i
$221$	−6.81272			−0.458273
$222$	13.9442	+	16.5168i	0.935871	+	1.10853i
$223$	−12.4637	+	12.4637i	−0.834631	+	0.834631i	−0.988146	−	0.153515i	$-0.950941\pi$
$223$	−12.4637	+	12.4637i	−0.834631	+	0.834631i	0.153515	+	0.988146i	$0.450941\pi$
$224$	5.09388	+	2.28262i	0.340349	+	0.152514i
$225$	−0.715778	−	2.87246i	−0.0477186	−	0.191497i
$226$	8.64842	+	0.730413i	0.575284	+	0.0485863i
$227$	−0.871636	−	0.871636i	−0.0578525	−	0.0578525i	0.677589	−	0.735441i	$-0.263025\pi$
$227$	−0.871636	−	0.871636i	−0.0578525	−	0.0578525i	−0.735441	+	0.677589i	$0.763025\pi$
$228$	−2.19282	−	3.09189i	−0.145223	−	0.204765i
$229$		−	10.1929i		−	0.673563i	−0.941583	−	0.336782i	$-0.890662\pi$
$229$		−	10.1929i		−	0.673563i	0.941583	−	0.336782i	$-0.109338\pi$
$230$	1.08412	+	28.6286i	0.0714844	+	1.88771i
$231$			8.87635i			0.584021i
$232$	4.82542	−	2.84436i	0.316804	−	0.186742i
$233$	−5.24568	−	5.24568i	−0.343656	−	0.343656i	0.514084	−	0.857740i	$-0.328132\pi$
$233$	−5.24568	−	5.24568i	−0.343656	−	0.343656i	−0.857740	+	0.514084i	$0.828132\pi$
$234$	0.329341	−	3.89955i	0.0215297	−	0.254922i
$235$	2.75856	+	2.15552i	0.179948	+	0.140610i
$236$	1.01454	−	5.96345i	0.0660408	−	0.388188i
$237$	−0.427665	+	0.427665i	−0.0277798	+	0.0277798i
$238$	1.55425	−	1.31216i	0.100747	−	0.0850550i
$239$	0.785993			0.0508417			0.0254208	−	0.999677i	$-0.491907\pi$
$239$	0.785993			0.0508417			0.0254208	+	0.999677i	$0.491907\pi$
$240$	14.2674	−	9.15460i	0.920955	−	0.590927i
$241$	18.3499			1.18202			0.591009	−	0.806665i	$-0.298730\pi$
$241$	18.3499			1.18202			0.591009	+	0.806665i	$0.298730\pi$
$242$	−12.4563	+	10.5162i	−0.800723	+	0.676004i
$243$	4.29096	−	4.29096i	0.275265	−	0.275265i
$244$	−0.243117	+	1.42904i	−0.0155639	+	0.0914848i
$245$	1.64133	+	13.3749i	0.104861	+	0.854492i
$246$	2.12381	−	25.1468i	0.135409	−	1.60330i
$247$	3.30493	+	3.30493i	0.210288	+	0.210288i
$248$	22.6587	−	13.3563i	1.43883	−	0.848123i
$249$		−	5.77276i		−	0.365834i
$250$	−7.62662	+	13.8504i	−0.482350	+	0.875979i
$251$			8.10035i			0.511290i	0.966771	+	0.255645i	$0.0822878\pi$
$251$			8.10035i			0.511290i	−0.966771	+	0.255645i	$0.917712\pi$
$252$	0.675938	+	0.953075i	0.0425801	+	0.0600381i
$253$	−30.4053	−	30.4053i	−1.91156	−	1.91156i
$254$	11.4535	+	0.967319i	0.718656	+	0.0606950i
$255$	−0.752417	−	6.13132i	−0.0471182	−	0.383958i
$256$	12.5008	+	9.98649i	0.781300	+	0.624156i
$257$	8.11783	−	8.11783i	0.506376	−	0.506376i	−0.407036	−	0.913412i	$-0.633438\pi$
$257$	8.11783	−	8.11783i	0.506376	−	0.506376i	0.913412	+	0.407036i	$0.133438\pi$
$258$	4.63704	+	5.49255i	0.288690	+	0.341951i
$259$	7.95784			0.494476
$260$	−15.4498	+	14.0786i	−0.958158	+	0.873115i
$261$	1.17250			0.0725759
$262$	7.40989	+	8.77697i	0.457784	+	0.542243i
$263$	7.91763	−	7.91763i	0.488222	−	0.488222i	−0.419523	−	0.907745i	$-0.637803\pi$
$263$	7.91763	−	7.91763i	0.488222	−	0.488222i	0.907745	+	0.419523i	$0.137803\pi$
$264$	−6.36295	+	24.6346i	−0.391613	+	1.51615i
$265$	0.0112323	+	0.00877682i	0.000689993	+	0.000539156i
$266$	−1.39053	−	0.117439i	−0.0852591	−	0.00720066i
$267$	10.9031	+	10.9031i	0.667261	+	0.667261i
$268$	−23.3598	+	16.5672i	−1.42693	+	1.01200i
$269$			17.7957i			1.08502i	0.840049	+	0.542510i	$0.182526\pi$
$269$			17.7957i			1.08502i	−0.840049	+	0.542510i	$0.817474\pi$
$270$	−14.4214	+	0.546112i	−0.877656	+	0.0332353i
$271$		−	16.0644i		−	0.975843i	−0.872888	−	0.487921i	$-0.837755\pi$
$271$		−	16.0644i		−	0.975843i	0.872888	−	0.487921i	$-0.162245\pi$
$272$	5.25414	−	2.52750i	0.318579	−	0.153252i
$273$	−6.18079	−	6.18079i	−0.374079	−	0.374079i
$274$	0.836197	−	9.90095i	0.0505165	−	0.598138i
$275$	−5.73807	−	23.0272i	−0.346019	−	1.38859i
$276$	−33.8546	−	5.75954i	−2.03781	−	0.346684i
$277$	−9.82279	+	9.82279i	−0.590195	+	0.590195i	−0.937684	−	0.347489i	$-0.887034\pi$
$277$	−9.82279	+	9.82279i	−0.590195	+	0.590195i	0.347489	+	0.937684i	$0.387034\pi$
$278$	−4.55472	+	3.84529i	−0.273174	+	0.230625i
$279$	5.50569			0.329617
$280$	0.813119	−	6.18760i	0.0485932	−	0.369780i
$281$	10.4171			0.621431			0.310715	−	0.950503i	$-0.399431\pi$
$281$	10.4171			0.621431			0.310715	+	0.950503i	$0.399431\pi$
$282$	−3.20648	+	2.70704i	−0.190943	+	0.161202i
$283$	9.74230	−	9.74230i	0.579120	−	0.579120i	−0.355541	−	0.934661i	$-0.615703\pi$
$283$	9.74230	−	9.74230i	0.579120	−	0.579120i	0.934661	+	0.355541i	$0.115703\pi$
$284$	18.3240	+	3.11739i	1.08733	+	0.184983i
$285$	−2.60937	+	3.33938i	−0.154566	+	0.197808i
$286$	2.64018	−	31.2609i	0.156117	−	1.84850i
$287$	−6.56954	−	6.56954i	−0.387787	−	0.387787i
$288$	1.19273	+	3.12962i	0.0702822	+	0.184414i
$289$			14.8754i			0.875021i
$290$	−4.59265	−	4.25751i	−0.269690	−	0.250010i
$291$			22.2248i			1.30284i
$292$	−10.4883	+	7.43848i	−0.613781	+	0.435304i
$293$	−17.9213	−	17.9213i	−1.04697	−	1.04697i	−0.998841	−	0.0481339i	$-0.984673\pi$
$293$	−17.9213	−	17.9213i	−1.04697	−	1.04697i	−0.0481339	−	0.998841i	$-0.515327\pi$
$294$	−16.0951	−	1.35934i	−0.938688	−	0.0792781i
$295$	−6.71278	+	0.823773i	−0.390833	+	0.0479619i
$296$	22.0854	+	5.70452i	1.28369	+	0.331569i
$297$	15.3164	−	15.3164i	0.888745	−	0.888745i
$298$	6.42105	+	7.60569i	0.371961	+	0.440586i
$299$	42.3437			2.44880
$300$	−14.3768	−	12.3497i	−0.830043	−	0.713009i
$301$	2.64633			0.152532
$302$	15.3334	+	18.1623i	0.882337	+	1.04512i
$303$	3.18544	−	3.18544i	0.182999	−	0.182999i
$304$	−3.77497	−	1.32272i	−0.216509	−	0.0758634i
$305$	1.60860	−	0.197403i	0.0921083	−	0.0113033i
$306$	1.21613	+	0.102710i	0.0695215	+	0.00587152i
$307$	4.46875	+	4.46875i	0.255045	+	0.255045i	0.823035	−	0.567990i	$-0.192279\pi$
$307$	4.46875	+	4.46875i	0.255045	+	0.255045i	−0.567990	+	0.823035i	$0.692279\pi$
$308$	5.41869	+	7.64038i	0.308759	+	0.435351i
$309$		−	8.52605i		−	0.485030i
$310$	−21.5657	−	19.9919i	−1.22485	−	1.13547i
$311$		−	0.594436i		−	0.0337074i	−0.999858	−	0.0168537i	$-0.994635\pi$
$311$		−	0.594436i		−	0.0337074i	0.999858	−	0.0168537i	$-0.00536495\pi$
$312$	−12.7229	−	21.5842i	−0.720294	−	1.22197i
$313$	14.2529	+	14.2529i	0.805624	+	0.805624i	0.983968	−	0.178344i	$-0.0570740\pi$
$313$	14.2529	+	14.2529i	0.805624	+	0.805624i	−0.178344	+	0.983968i	$0.557074\pi$
$314$	1.93910	−	22.9598i	0.109430	−	1.29570i
$315$	0.804339	−	1.02937i	0.0453194	−	0.0579982i
$316$	−0.107041	+	0.629190i	−0.00602155	+	0.0353947i
$317$	−8.72134	+	8.72134i	−0.489840	+	0.489840i	−0.908256	−	0.418416i	$-0.862585\pi$
$317$	−8.72134	+	8.72134i	−0.489840	+	0.489840i	0.418416	+	0.908256i	$0.362585\pi$
$318$	−0.0130561	+	0.0110225i	−0.000732150	+	0.000618112i
$319$	9.39940			0.526265
$320$	6.69219	−	16.5896i	0.374105	−	0.927386i
$321$	−30.5203			−1.70348
$322$	−9.66028	+	8.15562i	−0.538347	+	0.454495i
$323$	−1.03069	+	1.03069i	−0.0573491	+	0.0573491i
$324$	3.49710	−	20.5559i	0.194283	−	1.14200i
$325$	20.0299	+	12.0388i	1.11106	+	0.667792i
$326$	−1.43068	+	16.9399i	−0.0792379	+	0.938213i
$327$	13.5433	+	13.5433i	0.748944	+	0.748944i
$328$	−13.5231	−	22.9418i	−0.746690	−	1.26675i
$329$			1.54489i			0.0851725i
$330$	28.4259	−	1.07644i	1.56479	−	0.0592559i
$331$			12.5175i			0.688023i	0.938966	+	0.344011i	$0.111786\pi$
$331$			12.5175i			0.688023i	−0.938966	+	0.344011i	$0.888214\pi$
$332$	−3.52406	−	4.96894i	−0.193408	−	0.272706i
$333$	3.37626	+	3.37626i	0.185018	+	0.185018i
$334$	−23.4998	−	1.98470i	−1.28585	−	0.108598i
$335$	25.2297	+	19.7143i	1.37845	+	1.07711i
$336$	7.05985	+	2.47372i	0.385146	+	0.134953i
$337$	−10.1313	+	10.1313i	−0.551887	+	0.551887i	−0.926985	−	0.375098i	$-0.877609\pi$
$337$	−10.1313	+	10.1313i	−0.551887	+	0.551887i	0.375098	+	0.926985i	$0.377609\pi$
$338$	8.06939	+	9.55815i	0.438917	+	0.519895i
$339$	11.6315			0.631738
$340$	−4.39059	−	4.81825i	−0.238113	−	0.261306i
$341$	44.1367			2.39014
$342$	−0.540133	−	0.639785i	−0.0292071	−	0.0345956i
$343$	−9.08901	+	9.08901i	−0.490760	+	0.490760i
$344$	7.34437	+	1.89700i	0.395982	+	0.102279i
$345$	4.67657	+	38.1085i	0.251778	+	2.05169i
$346$	−27.9906	−	2.36398i	−1.50479	−	0.127089i
$347$	0.483917	+	0.483917i	0.0259781	+	0.0259781i	0.719976	−	0.693998i	$-0.244153\pi$
$347$	0.483917	+	0.483917i	0.0259781	+	0.0259781i	−0.693998	+	0.719976i	$0.744153\pi$
$348$	6.12309	−	4.34261i	0.328232	−	0.232788i
$349$		−	12.0418i		−	0.644582i	−0.946641	−	0.322291i	$-0.895547\pi$
$349$		−	12.0418i		−	0.644582i	0.946641	−	0.322291i	$-0.104453\pi$
$350$	−6.88835	+	1.11133i	−0.368198	+	0.0594032i
$351$			21.3302i			1.13852i
$352$	9.56157	+	25.0887i	0.509633	+	1.33723i
$353$	−19.3284	−	19.3284i	−1.02875	−	1.02875i	−0.999574	−	0.0291749i	$-0.990712\pi$
$353$	−19.3284	−	19.3284i	−1.02875	−	1.02875i	−0.0291749	−	0.999574i	$-0.509288\pi$
$354$	0.682242	−	8.07806i	0.0362608	−	0.429344i
$355$	−2.53122	−	20.6265i	−0.134343	−	1.09474i
$356$	16.0409	+	2.72897i	0.850166	+	0.144635i
$357$	1.92757	−	1.92757i	0.102018	−	0.102018i
$358$	−9.58112	+	8.08878i	−0.506378	+	0.427505i
$359$	23.7453			1.25323			0.626614	−	0.779330i	$-0.284440\pi$
$359$	23.7453			1.25323			0.626614	+	0.779330i	$0.284440\pi$
$360$	2.97018	−	2.28022i	0.156542	−	0.120178i
$361$	1.00000			0.0526316
$362$	6.19988	−	5.23420i	0.325859	−	0.275104i
$363$	−15.4482	+	15.4482i	−0.810820	+	0.810820i
$364$	−9.09331	−	1.54701i	−0.476619	−	0.0810852i
$365$	11.3278	+	8.85150i	0.592926	+	0.463308i
$366$	−0.163488	+	1.93577i	−0.00854563	+	0.101184i
$367$	13.2536	+	13.2536i	0.691835	+	0.691835i	0.962635	−	0.270801i	$-0.0872885\pi$
$367$	13.2536	+	13.2536i	0.691835	+	0.691835i	−0.270801	+	0.962635i	$0.587288\pi$
$368$	−32.6565	+	15.7094i	−1.70234	+	0.818910i
$369$		−	5.57449i		−	0.290196i
$370$	−0.965049	−	25.4844i	−0.0501705	−	1.32487i
$371$			0.00629047i			0.000326585i
$372$	28.7522	−	20.3915i	1.49073	−	1.05725i
$373$	−8.99990	−	8.99990i	−0.465997	−	0.465997i	0.434618	−	0.900615i	$-0.356883\pi$
$373$	−8.99990	−	8.99990i	−0.465997	−	0.465997i	−0.900615	+	0.434618i	$0.856883\pi$
$374$	9.74916	+	0.823378i	0.504117	+	0.0425758i
$375$	−8.62253	+	19.3561i	−0.445266	+	0.999546i
$376$	−1.10744	+	4.28754i	−0.0571120	+	0.221113i
$377$	−6.54500	+	6.54500i	−0.337085	+	0.337085i
$378$	−4.10831	−	4.86627i	−0.211309	−	0.250294i
$379$	−1.33948			−0.0688044			−0.0344022	−	0.999408i	$-0.510953\pi$
$379$	−1.33948			−0.0688044			−0.0344022	+	0.999408i	$0.510953\pi$
$380$	−0.207460	+	4.46732i	−0.0106425	+	0.229169i
$381$	15.4042			0.789179
$382$	−3.12138	−	3.69726i	−0.159704	−	0.189168i
$383$	−2.40611	+	2.40611i	−0.122946	+	0.122946i	−0.765903	−	0.642956i	$-0.777708\pi$
$383$	−2.40611	+	2.40611i	−0.122946	+	0.122946i	0.642956	+	0.765903i	$0.277708\pi$
$384$	17.8200	+	11.9261i	0.909371	+	0.608603i
$385$	6.44803	−	8.25197i	0.328622	−	0.420559i
$386$	28.1912	+	2.38092i	1.43490	+	0.121186i
$387$	1.12275	+	1.12275i	0.0570727	+	0.0570727i
$388$	13.5674	+	19.1302i	0.688783	+	0.971186i
$389$		−	26.3685i		−	1.33693i	−0.743742	−	0.668467i	$-0.766951\pi$
$389$		−	26.3685i		−	1.33693i	0.743742	−	0.668467i	$-0.233049\pi$
$390$	−19.0440	+	20.5431i	−0.964329	+	1.04024i
$391$			13.2055i			0.667830i
$392$	−14.6838	+	8.65545i	−0.741645	+	0.437166i
$393$	10.8851	+	10.8851i	0.549081	+	0.549081i
$394$	−0.663637	+	7.85777i	−0.0334336	+	0.395869i
$395$	0.708250	−	0.0869143i	0.0356359	−	0.00437313i
$396$	−0.942591	+	5.54055i	−0.0473670	+	0.278423i
$397$	15.2631	−	15.2631i	0.766032	−	0.766032i	−0.211373	−	0.977405i	$-0.567793\pi$
$397$	15.2631	−	15.2631i	0.766032	−	0.766032i	0.977405	+	0.211373i	$0.0677935\pi$
$398$	−24.4751	+	20.6629i	−1.22683	+	1.03574i
$399$	−1.87017			−0.0936257
$400$	−19.9139	−	1.85358i	−0.995696	−	0.0926790i
$401$	−13.0632			−0.652343			−0.326171	−	0.945311i	$-0.605759\pi$
$401$	−13.0632			−0.652343			−0.326171	+	0.945311i	$0.605759\pi$
$402$	−29.3263	+	24.7585i	−1.46267	+	1.23484i
$403$	−30.7333	+	30.7333i	−1.53094	+	1.53094i
$404$	0.797293	−	4.68649i	0.0396668	−	0.233161i
$405$	−23.1389	+	2.83953i	−1.14978	+	0.141097i
$406$	0.232574	−	2.75378i	0.0115424	−	0.136668i
$407$	27.0659	+	27.0659i	1.34161	+	1.34161i
$408$	6.73135	−	3.96782i	0.333251	−	0.196437i
$409$			30.5100i			1.50862i	0.656517	+	0.754312i	$0.272029\pi$
$409$			30.5100i			1.50862i	−0.656517	+	0.754312i	$0.727971\pi$
$410$	−20.2418	+	21.8351i	−0.999669	+	1.07836i
$411$		−	13.3161i		−	0.656834i
$412$	−5.20485	−	7.33885i	−0.256424	−	0.361559i
$413$	−2.11037	−	2.11037i	−0.103844	−	0.103844i
$414$	−7.55872	−	0.638381i	−0.371491	−	0.0313747i
$415$	−4.19349	+	5.36669i	−0.205850	+	0.263440i
$416$	−24.1277	−	10.8119i	−1.18296	−	0.530097i
$417$	−5.64872	+	5.64872i	−0.276619	+	0.276619i
$418$	−4.33001	−	5.12887i	−0.211788	−	0.250861i
$419$	9.78783			0.478167			0.239083	−	0.970999i	$-0.423153\pi$
$419$	9.78783			0.478167			0.239083	+	0.970999i	$0.423153\pi$
$420$	0.387986	−	8.35466i	0.0189318	−	0.407666i
$421$	26.7931			1.30582			0.652909	−	0.757437i	$-0.273549\pi$
$421$	26.7931			1.30582			0.652909	+	0.757437i	$0.273549\pi$
$422$	−21.6264	−	25.6164i	−1.05276	−	1.24699i
$423$	−0.655447	+	0.655447i	−0.0318689	+	0.0318689i
$424$	−0.00450928	+	0.0174580i	−0.000218990	+	0.000847834i
$425$	−3.75447	+	6.24660i	−0.182118	+	0.303005i
$426$	24.8216	+	2.09634i	1.20261	+	0.101568i
$427$	0.505714	+	0.505714i	0.0244732	+	0.0244732i
$428$	−26.2705	+	18.6315i	−1.26983	+	0.900589i
$429$		−	42.0438i		−	2.02989i
$430$	−0.320921	−	8.47467i	−0.0154762	−	0.408685i
$431$		−	2.45196i		−	0.118107i	−0.998255	−	0.0590534i	$-0.981192\pi$
$431$		−	2.45196i		−	0.118107i	0.998255	−	0.0590534i	$-0.0188082\pi$
$432$	−7.91346	−	16.4504i	−0.380737	−	0.791470i
$433$	20.7659	+	20.7659i	0.997948	+	0.997948i	0.999998	−	0.00205006i	$-0.000652555\pi$
$433$	20.7659	+	20.7659i	0.997948	+	0.997948i	−0.00205006	+	0.999998i	$0.500653\pi$
$434$	1.09209	−	12.9309i	0.0524222	−	0.620702i
$435$	−6.61323	−	5.16753i	−0.317080	−	0.247764i
$436$	19.9251	+	3.38978i	0.954240	+	0.162341i
$437$	6.40614	−	6.40614i	0.306447	−	0.306447i
$438$	−13.1672	+	11.1163i	−0.629153	+	0.531157i
$439$	24.9711			1.19180			0.595902	−	0.803057i	$-0.296795\pi$
$439$	24.9711			1.19180			0.595902	+	0.803057i	$0.296795\pi$
$440$	23.8106	−	18.2795i	1.13513	−	0.871441i
$441$	−3.56794			−0.169902
$442$	−7.36188	+	6.21521i	−0.350169	+	0.295628i
$443$	14.4843	−	14.4843i	0.688170	−	0.688170i	−0.273657	−	0.961827i	$-0.588233\pi$
$443$	14.4843	−	14.4843i	0.688170	−	0.688170i	0.961827	+	0.273657i	$0.0882333\pi$
$444$	30.1364	+	5.12698i	1.43021	+	0.243316i
$445$	−2.21584	−	18.0565i	−0.105041	−	0.855960i
$446$	−2.09781	+	24.8390i	−0.0993340	+	1.17616i
$447$	9.43250	+	9.43250i	0.446142	+	0.446142i
$448$	7.58693	−	2.18051i	0.358449	−	0.103019i
$449$			33.6613i			1.58857i	0.607543	+	0.794286i	$0.292155\pi$
$449$			33.6613i			1.58857i	−0.607543	+	0.794286i	$0.707845\pi$
$450$	−3.39401	−	2.45100i	−0.159995	−	0.115541i
$451$		−	44.6882i		−	2.10428i
$452$	10.0119	−	7.10063i	0.470921	−	0.333985i
$453$	22.5247	+	22.5247i	1.05830	+	1.05830i
$454$	−1.73709	−	0.146708i	−0.0815256	−	0.00688535i
$455$	1.25612	+	10.2359i	0.0588878	+	0.479867i
$456$	−5.19030	−	1.34062i	−0.243058	−	0.0627803i
$457$	7.29974	−	7.29974i	0.341468	−	0.341468i	−0.515451	−	0.856919i	$-0.672376\pi$
$457$	7.29974	−	7.29974i	0.341468	−	0.341468i	0.856919	+	0.515451i	$0.172376\pi$
$458$	−9.29890	−	11.0145i	−0.434509	−	0.514674i
$459$	−6.65212			−0.310495
$460$	27.2893	+	29.9473i	1.27237	+	1.39630i
$461$	−0.951158			−0.0442999			−0.0221499	−	0.999755i	$-0.507051\pi$
$461$	−0.951158			−0.0442999			−0.0221499	+	0.999755i	$0.507051\pi$
$462$	8.09786	+	9.59187i	0.376747	+	0.446254i
$463$	13.1374	−	13.1374i	0.610549	−	0.610549i	−0.332540	−	0.943089i	$-0.607906\pi$
$463$	13.1374	−	13.1374i	0.610549	−	0.610549i	0.943089	+	0.332540i	$0.107906\pi$
$464$	2.61949	−	7.47585i	0.121607	−	0.347058i
$465$	−31.0537	−	24.2651i	−1.44008	−	1.12527i
$466$	−10.4541	−	0.882918i	−0.484279	−	0.0409004i
$467$	−19.9319	−	19.9319i	−0.922339	−	0.922339i	0.0748550	−	0.997194i	$-0.476151\pi$
$467$	−19.9319	−	19.9319i	−0.922339	−	0.922339i	−0.997194	+	0.0748550i	$0.976151\pi$
$468$	−3.20165	−	4.51435i	−0.147997	−	0.208676i
$469$			14.1295i			0.652441i
$470$	4.94739	−	0.187349i	0.228206	−	0.00864177i
$471$		−	30.8794i		−	1.42285i
$472$	−4.34411	−	7.36972i	−0.199954	−	0.339219i
$473$	9.00060	+	9.00060i	0.413848	+	0.413848i
$474$	−0.0719817	+	0.852296i	−0.00330623	+	0.0391473i
$475$	4.85164	−	1.20896i	0.222608	−	0.0554710i
$476$	0.482456	−	2.83587i	0.0221133	−	0.129982i
$477$	−0.00266885	+	0.00266885i	−0.000122198	+	0.000122198i
$478$	0.849352	−	0.717058i	0.0388484	−	0.0327975i
$479$	29.5471			1.35004			0.675021	−	0.737799i	$-0.264135\pi$
$479$	29.5471			1.35004			0.675021	+	0.737799i	$0.264135\pi$
$480$	7.06576	−	22.9086i	0.322506	−	1.04563i
$481$	−37.6932			−1.71866
$482$	19.8290	−	16.7405i	0.903188	−	0.762509i
$483$	−11.9806	+	11.9806i	−0.545135	+	0.545135i
$484$	−3.86657	+	22.7277i	−0.175753	+	1.03308i
$485$	16.1447	−	20.6615i	0.733094	−	0.938189i
$486$	0.722225	−	8.55147i	0.0327608	−	0.387902i
$487$	−28.7952	−	28.7952i	−1.30483	−	1.30483i	−0.925092	−	0.379742i	$-0.876013\pi$
$487$	−28.7952	−	28.7952i	−1.30483	−	1.30483i	−0.379742	−	0.925092i	$-0.623987\pi$
$488$	1.04099	+	1.76603i	0.0471235	+	0.0799443i
$489$			22.7830i			1.03028i
$490$	13.9755	+	12.9557i	0.631349	+	0.585278i
$491$			2.85127i			0.128676i	0.997928	+	0.0643380i	$0.0204936\pi$
$491$			2.85127i			0.128676i	−0.997928	+	0.0643380i	$0.979506\pi$
$492$	−20.6463	−	29.1114i	−0.930809	−	1.31244i
$493$	−2.04115	−	2.04115i	−0.0919288	−	0.0919288i
$494$	6.58642	+	0.556264i	0.296337	+	0.0250275i
$495$	6.23674	−	0.765354i	0.280321	−	0.0344001i
$496$	12.3003	−	35.1043i	0.552300	−	1.57623i
$497$	6.48457	−	6.48457i	0.290873	−	0.290873i
$498$	−5.26647	−	6.23810i	−0.235996	−	0.279536i
$499$	12.2247			0.547252			0.273626	−	0.961836i	$-0.411777\pi$
$499$	12.2247			0.547252			0.273626	+	0.961836i	$0.411777\pi$
$500$	4.39431	+	21.9246i	0.196519	+	0.980500i
$501$	−31.6056			−1.41203
$502$	7.38992	+	8.75331i	0.329828	+	0.390680i
$503$	−22.0965	+	22.0965i	−0.985234	+	0.985234i	−0.999893	−	0.0146587i	$-0.995334\pi$
$503$	−22.0965	+	22.0965i	−0.985234	+	0.985234i	0.0146587	+	0.999893i	$0.495334\pi$
$504$	1.59991	+	0.413247i	0.0712657	+	0.0184075i
$505$	−5.27536	+	0.647377i	−0.234751	+	0.0288079i
$506$	−60.5949	−	5.11761i	−2.69377	−	0.227506i
$507$	11.8539	+	11.8539i	0.526451	+	0.526451i
$508$	13.2592	−	9.40368i	0.588283	−	0.417221i
$509$		−	5.44703i		−	0.241435i	−0.992687	−	0.120718i	$-0.961480\pi$
$509$		−	5.44703i		−	0.241435i	0.992687	−	0.120718i	$-0.0385196\pi$
$510$	−6.40664	−	5.93913i	−0.283691	−	0.262989i
$511$			6.34399i			0.280642i
$512$	22.6191	−	0.612936i	0.999633	−	0.0270882i
$513$	3.22703	+	3.22703i	0.142477	+	0.142477i
$514$	1.36634	−	16.1781i	0.0602666	−	0.713584i
$515$	−6.19356	+	7.92631i	−0.272921	+	0.349275i
$516$	10.0217	+	1.70495i	0.441179	+	0.0750560i
$517$	−5.25443	+	5.25443i	−0.231089	+	0.231089i
$518$	8.59931	−	7.25990i	0.377832	−	0.318982i
$519$	−37.6455			−1.65245
$520$	−3.85143	+	29.3082i	−0.168896	+	1.28525i
$521$	−14.5598			−0.637877			−0.318938	−	0.947775i	$-0.603326\pi$
$521$	−14.5598			−0.637877			−0.318938	+	0.947775i	$0.603326\pi$
$522$	1.26701	−	1.06967i	0.0554557	−	0.0468180i
$523$	1.82937	−	1.82937i	0.0799929	−	0.0799929i	−0.665978	−	0.745971i	$-0.731986\pi$
$523$	1.82937	−	1.82937i	0.0799929	−	0.0799929i	0.745971	+	0.665978i	$0.231986\pi$
$524$	16.0144	+	2.72446i	0.699592	+	0.119019i
$525$	−9.07340	+	2.26097i	−0.395996	+	0.0986768i
$526$	1.33264	−	15.7791i	0.0581060	−	0.688001i
$527$	−9.58461	−	9.58461i	−0.417512	−	0.417512i
$528$	15.5982	+	32.4253i	0.678823	+	1.41113i
$529$		−	59.0772i		−	2.56857i
$530$	0.0201448		0.000762847i	0.000875032		3.31359e-5i
$531$		−	1.79072i		−	0.0777108i
$532$	−1.60976	+	1.14167i	−0.0697921	+	0.0494978i
$533$	31.1173	+	31.1173i	1.34784	+	1.34784i
$534$	21.7289	+	1.83514i	0.940301	+	0.0794143i
$535$	28.3734	+	22.1708i	1.22669	+	0.958526i
$536$	−10.1287	+	39.2137i	−0.437491	+	1.69378i
$537$	−11.8824	+	11.8824i	−0.512763	+	0.512763i
$538$	16.2349	+	19.2301i	0.699936	+	0.829071i
$539$	−28.6025			−1.23200
$540$	−15.0856	+	13.7467i	−0.649183	+	0.591563i
$541$	−36.8551			−1.58452			−0.792262	−	0.610181i	$-0.791097\pi$
$541$	−36.8551			−1.58452			−0.792262	+	0.610181i	$0.791097\pi$
$542$	−14.6555	−	17.3593i	−0.629507	−	0.745647i
$543$	7.68903	−	7.68903i	0.329968	−	0.329968i
$544$	3.37184	−	7.52457i	0.144566	−	0.322613i
$545$	−2.75239	−	22.4288i	−0.117900	−	0.960744i
$546$	−12.3177	−	1.04031i	−0.527150	−	0.0445211i
$547$	7.80179	+	7.80179i	0.333580	+	0.333580i	0.853944	−	0.520364i	$-0.174204\pi$
$547$	7.80179	+	7.80179i	0.333580	+	0.333580i	−0.520364	+	0.853944i	$0.674204\pi$
$548$	−8.12899	−	11.4619i	−0.347253	−	0.489629i
$549$			0.429116i			0.0183142i
$550$	−27.2083	−	19.6486i	−1.16016	−	0.837819i
$551$			1.98037i			0.0843668i
$552$	−41.8380	+	24.6616i	−1.78074	+	1.04967i
$553$	0.222660	+	0.222660i	0.00946846	+	0.00946846i
$554$	−1.65331	+	19.5759i	−0.0702423	+	0.831700i
$555$	−4.16295	−	33.9231i	−0.176707	−	1.43996i
$556$	−1.41383	+	8.31051i	−0.0599599	+	0.352444i
$557$	−1.76844	+	1.76844i	−0.0749310	+	0.0749310i	−0.743579	−	0.668648i	$-0.766873\pi$
$557$	−1.76844	+	1.76844i	−0.0749310	+	0.0749310i	0.668648	+	0.743579i	$0.266873\pi$
$558$	5.94950	−	5.02282i	0.251863	−	0.212633i
$559$	−12.5346			−0.530158
$560$	−4.76626	−	7.42818i	−0.201411	−	0.313898i
$561$	13.1120			0.553587
$562$	11.2568	−	9.50346i	0.474839	−	0.400879i
$563$	−6.91763	+	6.91763i	−0.291543	+	0.291543i	−0.837690	−	0.546146i	$-0.816094\pi$
$563$	−6.91763	+	6.91763i	−0.291543	+	0.291543i	0.546146	+	0.837690i	$0.316094\pi$
$564$	−0.995323	+	5.85051i	−0.0419107	+	0.246351i
$565$	−10.8133	−	8.44946i	−0.454920	−	0.355472i
$566$	1.63976	−	19.4155i	0.0689242	−	0.816094i
$567$	−7.27441	−	7.27441i	−0.305497	−	0.305497i
$568$	22.6451	−	13.3482i	0.950167	−	0.560080i
$569$		−	8.71597i		−	0.365392i	−0.983169	−	0.182696i	$-0.941518\pi$
$569$		−	8.71597i		−	0.365392i	0.983169	−	0.182696i	$-0.0584825\pi$
$570$	0.226796	+	5.98909i	0.00949945	+	0.250855i
$571$		−	44.1078i		−	1.84586i	−0.384973	−	0.922928i	$-0.625789\pi$
$571$		−	44.1078i		−	1.84586i	0.384973	−	0.922928i	$-0.374211\pi$
$572$	−25.6662	−	36.1895i	−1.07316	−	1.51316i
$573$	−4.58530	−	4.58530i	−0.191554	−	0.191554i
$574$	−13.0925	−	1.10574i	−0.546469	−	0.0461527i
$575$	23.3355	−	38.8251i	0.973157	−	1.61912i
$576$	4.14401	+	2.29377i	0.172667	+	0.0955738i
$577$	−9.97337	+	9.97337i	−0.415197	+	0.415197i	−0.883544	−	0.468348i	$-0.844850\pi$
$577$	−9.97337	+	9.97337i	−0.415197	+	0.415197i	0.468348	+	0.883544i	$0.344850\pi$
$578$	13.5707	+	16.0744i	0.564468	+	0.668609i
$579$	37.9153			1.57570
$580$	−8.84697	−	0.410848i	−0.367350	−	0.0170596i
$581$	−3.00553			−0.124691
$582$	20.2756	+	24.0163i	0.840451	+	0.995510i
$583$	−0.0213949	+	0.0213949i	−0.000886088	+	0.000886088i
$584$	−4.54765	+	17.6065i	−0.188183	+	0.728563i
$585$	−3.80984	+	4.87571i	−0.157518	+	0.201586i
$586$	−35.7155	−	3.01640i	−1.47539	−	0.124606i
$587$	5.10277	+	5.10277i	0.210614	+	0.210614i	0.804528	−	0.593914i	$-0.202418\pi$
$587$	5.10277	+	5.10277i	0.210614	+	0.210614i	−0.593914	+	0.804528i	$0.702418\pi$
$588$	−18.6327	+	13.2146i	−0.768399	+	0.544962i
$589$			9.29923i			0.383168i
$590$	−6.50237	+	7.01422i	−0.267698	+	0.288771i
$591$			10.5682i			0.434716i
$592$	29.0699	−	13.9841i	1.19477	−	0.574742i
$593$	3.54561	+	3.54561i	0.145601	+	0.145601i	0.776150	−	0.630549i	$-0.217170\pi$
$593$	3.54561	+	3.54561i	0.145601	+	0.145601i	−0.630549	+	0.776150i	$0.717170\pi$
$594$	2.57795	−	30.5240i	0.105774	−	1.25242i
$595$	−3.19221	+	0.391739i	−0.130868	+	0.0160597i
$596$	13.8773	+	2.36089i	0.568436	+	0.0967057i
$597$	−30.3537	+	30.3537i	−1.24230	+	1.24230i
$598$	45.7570	−	38.6300i	1.87114	−	1.57970i
$599$	−30.4232			−1.24306			−0.621529	−	0.783391i	$-0.713488\pi$
$599$	−30.4232			−1.24306			−0.621529	+	0.783391i	$0.713488\pi$
$600$	−26.8022	−	0.229324i	−1.09420	−	0.00936211i
$601$	26.2371			1.07023			0.535117	−	0.844778i	$-0.320268\pi$
$601$	26.2371			1.07023			0.535117	+	0.844778i	$0.320268\pi$
$602$	2.85965	−	2.41423i	0.116550	−	0.0983968i
$603$	−5.99471	+	5.99471i	−0.244123	+	0.244123i
$604$	33.1388	+	5.63777i	1.34840	+	0.229397i
$605$	25.5835	−	3.13953i	1.04012	−	0.127640i
$606$	0.536152	−	6.34829i	0.0217797	−	0.257881i
$607$	0.273256	+	0.273256i	0.0110911	+	0.0110911i	0.712631	−	0.701539i	$-0.247504\pi$
$607$	0.273256	+	0.273256i	0.0110911	+	0.0110911i	−0.701539	+	0.712631i	$0.747504\pi$
$608$	−5.28598	+	2.01454i	−0.214375	+	0.0817005i
$609$		−	3.70364i		−	0.150079i
$610$	1.55818	−	1.68084i	0.0630889	−	0.0680551i
$611$		−	7.31754i		−	0.296036i
$612$	1.40786	−	0.998481i	0.0569095	−	0.0403612i
$613$	−6.40183	−	6.40183i	−0.258567	−	0.258567i	0.565904	−	0.824471i	$-0.308527\pi$
$613$	−6.40183	−	6.40183i	−0.258567	−	0.258567i	−0.824471	+	0.565904i	$0.808527\pi$
$614$	8.90579	+	0.752149i	0.359408	+	0.0303543i
$615$	−24.5683	+	31.4417i	−0.990690	+	1.26785i
$616$	12.8258	+	3.31281i	0.516765	+	0.133477i
$617$	21.3006	−	21.3006i	0.857530	−	0.857530i	−0.133517	−	0.991047i	$-0.542627\pi$
$617$	21.3006	−	21.3006i	0.857530	−	0.857530i	0.991047	+	0.133517i	$0.0426269\pi$
$618$	−7.77828	−	9.21333i	−0.312888	−	0.370615i
$619$	21.5289			0.865320			0.432660	−	0.901557i	$-0.357575\pi$
$619$	21.5289			0.865320			0.432660	+	0.901557i	$0.357575\pi$
$620$	−41.5426	−	1.92922i	−1.66839	−	0.0774792i
$621$	41.3456			1.65914
$622$	−0.542302	−	0.642353i	−0.0217443	−	0.0257560i
$623$	5.67661	−	5.67661i	0.227429	−	0.227429i
$624$	−33.4397	−	11.7171i	−1.33866	−	0.469058i
$625$	22.0768	−	11.7309i	0.883073	−	0.469236i
$626$	28.4048	+	2.39896i	1.13528	+	0.0958817i
$627$	−6.36077	−	6.36077i	−0.254025	−	0.254025i
$628$	−18.8507	−	26.5796i	−0.752226	−	1.06064i
$629$		−	11.7551i		−	0.468708i
$630$	−0.0699100	−	1.84614i	−0.00278528	−	0.0735519i
$631$		−	33.6642i		−	1.34015i	−0.742294	−	0.670074i	$-0.766262\pi$
$631$		−	33.6642i		−	1.34015i	0.742294	−	0.670074i	$-0.233738\pi$
$632$	0.458337	+	0.777562i	0.0182317	+	0.0309297i
$633$	−31.7692	−	31.7692i	−1.26271	−	1.26271i
$634$	−1.46792	+	17.3808i	−0.0582985	+	0.690280i
$635$	−14.3206	−	11.1900i	−0.568295	−	0.444062i
$636$	−0.00405275	+	0.0238221i	−0.000160702	+	0.000944606i
$637$	19.9166	−	19.9166i	0.789122	−	0.789122i
$638$	10.1571	−	8.57503i	0.402123	−	0.339489i
$639$	5.50240			0.217671
$640$	−7.90298	−	24.0321i	−0.312393	−	0.949953i
$641$	−11.4028			−0.450383			−0.225192	−	0.974314i	$-0.572301\pi$
$641$	−11.4028			−0.450383			−0.225192	+	0.974314i	$0.572301\pi$
$642$	−32.9805	+	27.8435i	−1.30164	+	1.09890i
$643$	−31.2371	+	31.2371i	−1.23187	+	1.23187i	−0.268629	+	0.963244i	$0.586570\pi$
$643$	−31.2371	+	31.2371i	−1.23187	+	1.23187i	−0.963244	+	0.268629i	$0.913430\pi$
$644$	−2.99865	+	17.6261i	−0.118163	+	0.694565i
$645$	−1.38436	−	11.2809i	−0.0545092	−	0.444186i
$646$	−0.173479	+	2.05407i	−0.00682543	+	0.0808161i
$647$	−26.4732	−	26.4732i	−1.04077	−	1.04077i	−0.999133	−	0.0416381i	$-0.986742\pi$
$647$	−26.4732	−	26.4732i	−1.04077	−	1.04077i	−0.0416381	−	0.999133i	$-0.513258\pi$
$648$	−14.9741	−	25.4033i	−0.588238	−	0.997937i
$649$		−	14.3554i		−	0.563500i
$650$	32.6274	−	5.26394i	1.27975	−	0.206469i
$651$		−	17.3912i		−	0.681613i
$652$	13.9082	+	19.6106i	0.544686	+	0.768010i
$653$	−17.1865	−	17.1865i	−0.672558	−	0.672558i	0.285747	−	0.958305i	$-0.407758\pi$
$653$	−17.1865	−	17.1865i	−0.672558	−	0.672558i	−0.958305	+	0.285747i	$0.907758\pi$
$654$	26.9904	+	2.27951i	1.05541	+	0.0891359i
$655$	−2.21218	−	18.0267i	−0.0864369	−	0.704360i
$656$	−35.5429	−	12.4540i	−1.38772	−	0.486247i
$657$	−2.69155	+	2.69155i	−0.105008	+	0.105008i
$658$	1.40940	+	1.66942i	0.0549440	+	0.0650808i
$659$	−46.1104			−1.79621			−0.898104	−	0.439783i	$-0.855055\pi$
$659$	−46.1104			−1.79621			−0.898104	+	0.439783i	$0.855055\pi$
$660$	29.7352	−	27.0960i	1.15744	−	1.05471i
$661$	8.33816			0.324317			0.162158	−	0.986765i	$-0.448154\pi$
$661$	8.33816			0.324317			0.162158	+	0.986765i	$0.448154\pi$
$662$	11.4196	+	13.5265i	0.443837	+	0.525722i
$663$	−9.13013	+	9.13013i	−0.354585	+	0.354585i
$664$	−8.34128	−	2.15450i	−0.323704	−	0.0836107i
$665$	1.73862	+	1.35854i	0.0674208	+	0.0526821i
$666$	6.72856	+	0.568269i	0.260726	+	0.0220200i
$667$	12.6865	+	12.6865i	0.491225	+	0.491225i
$668$	−27.2047	+	19.2941i	−1.05258	+	0.746510i
$669$			33.4067i			1.29158i
$670$	45.2487	−	1.71349i	1.74811	−	0.0661979i
$671$			3.44003i			0.132801i
$672$	9.88570	−	3.76754i	0.381349	−	0.145336i
$673$	−0.923216	−	0.923216i	−0.0355873	−	0.0355873i	0.689089	−	0.724677i	$-0.258011\pi$
$673$	−0.923216	−	0.923216i	−0.0355873	−	0.0355873i	−0.724677	+	0.689089i	$0.758011\pi$
$674$	−1.70523	+	20.1907i	−0.0656831	+	0.777718i
$675$	19.5577	+	11.7550i	0.752777	+	0.452451i
$676$	17.4397	+	2.96695i	0.670759	+	0.114113i
$677$	3.76247	−	3.76247i	0.144603	−	0.144603i	−0.631099	−	0.775702i	$-0.717396\pi$
$677$	3.76247	−	3.76247i	0.144603	−	0.144603i	0.775702	+	0.631099i	$0.217396\pi$
$678$	12.5691	−	10.6114i	0.482715	−	0.407528i
$679$	11.5711			0.444060
$680$	−9.14018	−	1.20112i	−0.350510	−	0.0460609i
$681$	−2.33626			−0.0895259
$682$	47.6945	−	40.2657i	1.82632	−	1.54185i
$683$	13.9942	−	13.9942i	0.535473	−	0.535473i	−0.386723	−	0.922196i	$-0.626393\pi$
$683$	13.9942	−	13.9942i	0.535473	−	0.535473i	0.922196	+	0.386723i	$0.126393\pi$
$684$	−1.16735	−	0.198596i	−0.0446346	−	0.00759351i
$685$	−9.67317	+	12.3794i	−0.369593	+	0.472993i
$686$	−1.52980	+	18.1135i	−0.0584081	+	0.691578i
$687$	−13.6601	−	13.6601i	−0.521164	−	0.521164i
$688$	9.66702	−	4.65032i	0.368552	−	0.177292i
$689$		−	0.0297955i		−	0.00113512i
$690$	39.8198	+	36.9140i	1.51591	+	1.40529i
$691$			10.1227i			0.385087i	0.981288	+	0.192544i	$0.0616737\pi$
$691$			10.1227i			0.385087i	−0.981288	+	0.192544i	$0.938326\pi$
$692$	−32.4036	+	22.9812i	−1.23180	+	0.873614i
$693$	1.96071	+	1.96071i	0.0744812	+	0.0744812i
$694$	0.964402	+	0.0814497i	0.0366082	+	0.00309179i
$695$	9.35475	−	1.14799i	0.354846	−	0.0435456i
$696$	2.65493	−	10.2787i	0.100635	−	0.389614i
$697$	−9.70437	+	9.70437i	−0.367579	+	0.367579i
$698$	−10.9857	−	13.0125i	−0.415814	−	0.492529i
$699$	−14.0601			−0.531802
$700$	−6.42975	+	7.48513i	−0.243022	+	0.282911i
$701$	−21.0307			−0.794320			−0.397160	−	0.917749i	$-0.630004\pi$
$701$	−21.0307			−0.794320			−0.397160	+	0.917749i	$0.630004\pi$
$702$	19.4595	+	23.0496i	0.734450	+	0.869952i
$703$	−5.70256	+	5.70256i	−0.215076	+	0.215076i
$704$	33.2207	+	18.3881i	1.25205	+	0.693029i
$705$	6.58565	−	0.808171i	0.248030	−	0.0304375i
$706$	−38.5198	−	3.25323i	−1.44971	−	0.122437i
$707$	−1.65847	−	1.65847i	−0.0623732	−	0.0623732i
$708$	−6.63234	−	9.35163i	−0.249259	−	0.351456i
$709$			24.7345i			0.928924i	0.885593	+	0.464462i	$0.153752\pi$
$709$			24.7345i			0.928924i	−0.885593	+	0.464462i	$0.846248\pi$
$710$	−21.5527	−	19.9800i	−0.808860	−	0.749835i
$711$			0.188935i			0.00708562i
$712$	19.8236	−	11.6851i	0.742920	−	0.437917i
$713$	59.5721	+	59.5721i	2.23099	+	2.23099i
$714$	0.324435	−	3.84146i	0.0121417	−	0.143763i
$715$	−30.5418	+	39.0863i	−1.14220	+	1.46175i
$716$	−2.97408	+	17.4816i	−0.111147	+	0.653319i
$717$	1.05336	−	1.05336i	0.0393383	−	0.0393383i
$718$	25.6594	−	21.6627i	0.957599	−	0.808446i
$719$	−26.9815			−1.00624			−0.503120	−	0.864216i	$-0.667815\pi$
$719$	−26.9815			−1.00624			−0.503120	+	0.864216i	$0.667815\pi$
$720$	1.12937	−	5.17371i	0.0420891	−	0.192813i
$721$	−4.43901			−0.165317
$722$	1.08061	−	0.912296i	0.0402161	−	0.0339521i
$723$	24.5918	−	24.5918i	0.914578	−	0.914578i
$724$	1.92451	−	11.3123i	0.0715238	−	0.420417i
$725$	2.39420	+	9.60806i	0.0889183	+	0.356834i
$726$	−2.60014	+	30.7868i	−0.0965001	+	1.14261i
$727$	29.4984	+	29.4984i	1.09404	+	1.09404i	0.995093	+	0.0989427i	$0.0315461\pi$
$727$	29.4984	+	29.4984i	1.09404	+	1.09404i	0.0989427	+	0.995093i	$0.468454\pi$
$728$	−11.2376	+	6.62408i	−0.416495	+	0.245505i
$729$			19.7758i			0.732437i
$730$	20.3162	−	0.769337i	0.751935	−	0.0284745i
$731$		−	3.90910i		−	0.144583i
$732$	1.58933	+	2.24096i	0.0587432	+	0.0828281i
$733$	−19.4831	−	19.4831i	−0.719625	−	0.719625i	0.248904	−	0.968528i	$-0.419930\pi$
$733$	−19.4831	−	19.4831i	−0.719625	−	0.719625i	−0.968528	+	0.248904i	$0.919930\pi$
$734$	26.4133	+	2.23076i	0.974931	+	0.0823390i
$735$	20.1242	+	15.7249i	0.742291	+	0.580021i
$736$	−20.9573	+	46.7682i	−0.772497	+	1.72390i
$737$	−48.0569	+	48.0569i	−1.77020	+	1.77020i
$738$	−5.08558	−	6.02384i	−0.187203	−	0.221741i
$739$	−37.1086			−1.36506			−0.682532	−	0.730856i	$-0.739121\pi$
$739$	−37.1086			−1.36506			−0.682532	+	0.730856i	$0.739121\pi$
$740$	−24.2921	−	26.6582i	−0.892996	−	0.979976i
$741$	8.85828			0.325417
$742$	0.00573877	+	0.00679754i	0.000210677	+	0.000249545i
$743$	−12.3911	+	12.3911i	−0.454586	+	0.454586i	−0.896873	−	0.442288i	$-0.854167\pi$
$743$	−12.3911	+	12.3911i	−0.454586	+	0.454586i	0.442288	+	0.896873i	$0.354167\pi$
$744$	12.4667	−	48.2658i	0.457053	−	1.76951i
$745$	−1.91696	−	15.6210i	−0.0702322	−	0.572310i
$746$	−17.9359	−	1.51480i	−0.656681	−	0.0554609i
$747$	−1.27515	−	1.27515i	−0.0466554	−	0.0466554i
$748$	11.2862	−	8.00437i	0.412664	−	0.292669i
$749$			15.8901i			0.580612i
$750$	8.34092	+	28.7827i	0.304567	+	1.05100i
$751$			4.32457i			0.157806i	0.996882	+	0.0789029i	$0.0251417\pi$
$751$			4.32457i			0.157806i	−0.996882	+	0.0789029i	$0.974858\pi$
$752$	2.71479	+	5.64347i	0.0989983	+	0.205796i
$753$	10.8558	+	10.8558i	0.395606	+	0.395606i
$754$	−1.10161	+	13.0436i	−0.0401183	+	0.475019i
$755$	−4.57769	−	37.3028i	−0.166599	−	1.35759i
$756$	−8.87895	−	1.51054i	−0.322924	−	0.0549378i
$757$	4.02457	−	4.02457i	0.146275	−	0.146275i	−0.630177	−	0.776452i	$-0.717017\pi$
$757$	4.02457	−	4.02457i	0.146275	−	0.146275i	0.776452	+	0.630177i	$0.217017\pi$
$758$	−1.44745	+	1.22200i	−0.0525739	+	0.0443851i
$759$	−81.4959			−2.95812
$760$	3.85134	+	5.01669i	0.139703	+	0.181975i
$761$	35.1030			1.27248			0.636241	−	0.771490i	$-0.280488\pi$
$761$	35.1030			1.27248			0.636241	+	0.771490i	$0.280488\pi$
$762$	16.6459	−	14.0532i	0.603016	−	0.509092i
$763$	7.05117	−	7.05117i	0.255270	−	0.255270i
$764$	−6.74599	−	1.14767i	−0.244061	−	0.0415212i
$765$	−1.52056	−	1.18815i	−0.0549759	−	0.0429577i
$766$	−0.404980	+	4.79515i	−0.0146325	+	0.173256i
$767$	9.99599	+	9.99599i	0.360934	+	0.360934i
$768$	30.1366	−	3.36958i	1.08746	−	0.121589i
$769$			50.0247i			1.80394i	0.431802	+	0.901968i	$0.357878\pi$
$769$			50.0247i			1.80394i	−0.431802	+	0.901968i	$0.642122\pi$

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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.08061 - 0.912296i) q^{2} +(1.34016 - 1.34016i) q^{3} +(0.335432 - 1.97167i) q^{4} +(-2.21942 + 0.272360i) q^{5} +(0.225567 - 2.67081i) q^{6} +(-0.697742 - 0.697742i) q^{7} +(-1.43628 - 2.43662i) q^{8} -0.592060i q^{9} +O(q^{10})\)	\(q+(1.08061 - 0.912296i) q^{2} +(1.34016 - 1.34016i) q^{3} +(0.335432 - 1.97167i) q^{4} +(-2.21942 + 0.272360i) q^{5} +(0.225567 - 2.67081i) q^{6} +(-0.697742 - 0.697742i) q^{7} +(-1.43628 - 2.43662i) q^{8} -0.592060i q^{9} +(-2.14985 + 2.31908i) q^{10} -4.74628i q^{11} +(-2.19282 - 3.09189i) q^{12} +(3.30493 + 3.30493i) q^{13} +(-1.39053 - 0.117439i) q^{14} +(-2.60937 + 3.33938i) q^{15} +(-3.77497 - 1.32272i) q^{16} +(-1.03069 + 1.03069i) q^{17} +(-0.540133 - 0.639785i) q^{18} +1.00000 q^{19} +(-0.207460 + 4.46732i) q^{20} -1.87017 q^{21} +(-4.33001 - 5.12887i) q^{22} +(6.40614 - 6.40614i) q^{23} +(-5.19030 - 1.34062i) q^{24} +(4.85164 - 1.20896i) q^{25} +(6.58642 + 0.556264i) q^{26} +(3.22703 + 3.22703i) q^{27} +(-1.60976 + 1.14167i) q^{28} +1.98037i q^{29} +(0.226796 + 5.98909i) q^{30} +9.29923i q^{31} +(-5.28598 + 2.01454i) q^{32} +(-6.36077 - 6.36077i) q^{33} +(-0.173479 + 2.05407i) q^{34} +(1.73862 + 1.35854i) q^{35} +(-1.16735 - 0.198596i) q^{36} +(-5.70256 + 5.70256i) q^{37} +(1.08061 - 0.912296i) q^{38} +8.85828 q^{39} +(3.85134 + 5.01669i) q^{40} +9.41542 q^{41} +(-2.02093 + 1.70615i) q^{42} +(-1.89635 + 1.89635i) q^{43} +(-9.35809 - 1.59205i) q^{44} +(0.161254 + 1.31403i) q^{45} +(1.07824 - 12.7668i) q^{46} +(-1.10706 - 1.10706i) q^{47} +(-6.83173 + 3.28640i) q^{48} -6.02631i q^{49} +(4.13979 - 5.73255i) q^{50} +2.76258i q^{51} +(7.62482 - 5.40766i) q^{52} +(-0.00450773 - 0.00450773i) q^{53} +(6.43116 + 0.543151i) q^{54} +(1.29270 + 10.5340i) q^{55} +(-0.697982 + 2.70228i) q^{56} +(1.34016 - 1.34016i) q^{57} +(1.80669 + 2.14001i) q^{58} +3.02457 q^{59} +(5.70890 + 6.26496i) q^{60} -0.724786 q^{61} +(8.48365 + 10.0488i) q^{62} +(-0.413105 + 0.413105i) q^{63} +(-3.87422 + 6.99931i) q^{64} +(-8.23516 - 6.43490i) q^{65} +(-12.6764 - 1.07060i) q^{66} +(-10.1252 - 10.1252i) q^{67} +(1.68645 + 2.37791i) q^{68} -17.1705i q^{69} +(3.11816 - 0.118079i) q^{70} +9.29365i q^{71} +(-1.44262 + 0.850361i) q^{72} +(-4.54609 - 4.54609i) q^{73} +(-0.959817 + 11.3647i) q^{74} +(4.88177 - 8.12218i) q^{75} +(0.335432 - 1.97167i) q^{76} +(-3.31168 + 3.31168i) q^{77} +(9.57234 - 8.08137i) q^{78} -0.319115 q^{79} +(8.73850 + 1.90753i) q^{80} +10.4256 q^{81} +(10.1744 - 8.58965i) q^{82} +(2.15376 - 2.15376i) q^{83} +(-0.627316 + 3.68736i) q^{84} +(2.00681 - 2.56825i) q^{85} +(-0.319181 + 3.77925i) q^{86} +(2.65402 + 2.65402i) q^{87} +(-11.5649 + 6.81696i) q^{88} +8.13569i q^{89} +(1.37303 + 1.27284i) q^{90} -4.61198i q^{91} +(-10.4820 - 14.7796i) q^{92} +(12.4625 + 12.4625i) q^{93} +(-2.20627 - 0.186333i) q^{94} +(-2.21942 + 0.272360i) q^{95} +(-4.38426 + 9.78387i) q^{96} +(-8.29185 + 8.29185i) q^{97} +(-5.49778 - 6.51209i) q^{98} -2.81008 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 2 q^{2} - 2 q^{3} + 4 q^{5} - 4 q^{6} - 4 q^{7} + 4 q^{8}+O(q^{10}) \) 52 * q - 2 * q^2 - 2 * q^3 + 4 * q^5 - 4 * q^6 - 4 * q^7 + 4 * q^8	\( 52 q - 2 q^{2} - 2 q^{3} + 4 q^{5} - 4 q^{6} - 4 q^{7} + 4 q^{8} - 18 q^{10} - 38 q^{12} - 2 q^{13} + 2 q^{15} + 16 q^{16} - 20 q^{17} + 2 q^{18} + 52 q^{19} + 20 q^{20} - 16 q^{21} + 20 q^{22} + 20 q^{23} - 16 q^{25} - 8 q^{27} - 8 q^{28} - 48 q^{30} - 42 q^{32} + 8 q^{33} - 20 q^{34} + 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} - 64 q^{39} + 60 q^{40} - 4 q^{41} + 60 q^{42} - 28 q^{43} + 8 q^{44} + 12 q^{45} - 8 q^{46} - 4 q^{47} - 18 q^{48} - 42 q^{50} - 54 q^{52} - 2 q^{53} - 24 q^{54} + 12 q^{56} - 2 q^{57} - 12 q^{58} + 28 q^{59} + 90 q^{60} - 4 q^{61} + 56 q^{62} + 44 q^{63} + 24 q^{64} + 10 q^{65} + 36 q^{66} + 6 q^{67} - 60 q^{68} - 32 q^{70} - 24 q^{72} + 8 q^{73} - 88 q^{74} + 2 q^{75} + 12 q^{77} + 64 q^{78} - 52 q^{79} - 8 q^{80} - 24 q^{81} + 56 q^{82} - 76 q^{83} + 40 q^{84} + 12 q^{85} - 8 q^{86} + 12 q^{87} - 40 q^{88} - 94 q^{90} - 48 q^{92} + 24 q^{93} - 32 q^{94} + 4 q^{95} - 4 q^{96} - 10 q^{97} + 58 q^{98} + 128 q^{99}+O(q^{100}) \) 52 * q - 2 * q^2 - 2 * q^3 + 4 * q^5 - 4 * q^6 - 4 * q^7 + 4 * q^8 - 18 * q^10 - 38 * q^12 - 2 * q^13 + 2 * q^15 + 16 * q^16 - 20 * q^17 + 2 * q^18 + 52 * q^19 + 20 * q^20 - 16 * q^21 + 20 * q^22 + 20 * q^23 - 16 * q^25 - 8 * q^27 - 8 * q^28 - 48 * q^30 - 42 * q^32 + 8 * q^33 - 20 * q^34 + 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 - 64 * q^39 + 60 * q^40 - 4 * q^41 + 60 * q^42 - 28 * q^43 + 8 * q^44 + 12 * q^45 - 8 * q^46 - 4 * q^47 - 18 * q^48 - 42 * q^50 - 54 * q^52 - 2 * q^53 - 24 * q^54 + 12 * q^56 - 2 * q^57 - 12 * q^58 + 28 * q^59 + 90 * q^60 - 4 * q^61 + 56 * q^62 + 44 * q^63 + 24 * q^64 + 10 * q^65 + 36 * q^66 + 6 * q^67 - 60 * q^68 - 32 * q^70 - 24 * q^72 + 8 * q^73 - 88 * q^74 + 2 * q^75 + 12 * q^77 + 64 * q^78 - 52 * q^79 - 8 * q^80 - 24 * q^81 + 56 * q^82 - 76 * q^83 + 40 * q^84 + 12 * q^85 - 8 * q^86 + 12 * q^87 - 40 * q^88 - 94 * q^90 - 48 * q^92 + 24 * q^93 - 32 * q^94 + 4 * q^95 - 4 * q^96 - 10 * q^97 + 58 * q^98 + 128 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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