LMFDB - Embedded newform 380.2.k.d.267.19

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			267.19
Character	$\chi$	$=$	380.267
Dual form			380.2.k.d.343.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.912296 + 1.08061i) q^{2} +(-1.34016 - 1.34016i) q^{3} +(-0.335432 + 1.97167i) q^{4} +(-2.21942 - 0.272360i) q^{5} +(0.225567 - 2.67081i) q^{6} +(0.697742 - 0.697742i) q^{7} +(-2.43662 + 1.43628i) q^{8} +0.592060i q^{9} +O(q^{10})$	\(q+(0.912296 + 1.08061i) 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} +(-2.43662 + 1.43628i) q^{8} +0.592060i q^{9} +(-1.73045 - 2.64680i) q^{10} -4.74628i q^{11} +(3.09189 - 2.19282i) 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} +(-0.639785 + 0.540133i) q^{18} -1.00000 q^{19} +(1.28147 - 4.28460i) q^{20} -1.87017 q^{21} +(5.12887 - 4.33001i) 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} +(1.14167 + 1.60976i) q^{28} -1.98037i q^{29} +(-1.22805 + 5.86622i) q^{30} +9.29923i q^{31} +(-2.01454 - 5.28598i) 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} +(-0.912296 - 1.08061i) q^{38} -8.85828 q^{39} +(5.79906 - 2.52406i) q^{40} +9.41542 q^{41} +(-1.70615 - 2.02093i) 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} +(3.28640 + 6.83173i) q^{48} +6.02631i q^{49} +(3.11971 + 6.34566i) q^{50} +2.76258i q^{51} +(5.40766 + 7.62482i) 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} +(2.14001 - 1.80669i) q^{58} -3.02457 q^{59} +(-7.45943 + 4.02468i) q^{60} -0.724786 q^{61} +(-10.0488 + 8.48365i) 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} +(2.37791 - 1.68645i) q^{68} +17.1705i q^{69} +(-3.05419 - 0.639373i) q^{70} +9.29365i q^{71} +(-0.850361 - 1.44262i) 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} +(-8.08137 - 9.57234i) q^{78} +0.319115 q^{79} +(8.01798 + 3.96383i) q^{80} +10.4256 q^{81} +(8.58965 + 10.1744i) 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} +(6.81696 + 11.5649i) q^{88} -8.13569i q^{89} +(1.56706 - 1.02453i) q^{90} -4.61198i q^{91} +(14.7796 - 10.4820i) 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} +(-6.51209 + 5.49778i) 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} + 2 q^{10} + 22 q^{12} - 2 q^{13} - 2 q^{15} + 16 q^{16} - 20 q^{17} - 2 q^{18} - 52 q^{19} - 12 q^{20} - 16 q^{21} - 36 q^{22} - 20 q^{23} - 16 q^{25} + 8 q^{27} - 24 q^{28} + 40 q^{30} + 2 q^{32} + 8 q^{33} + 20 q^{34} - 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} + 64 q^{39} - 36 q^{40} - 4 q^{41} - 60 q^{42} + 28 q^{43} - 8 q^{44} + 12 q^{45} - 8 q^{46} + 4 q^{47} - 2 q^{48} + 46 q^{50} + 74 q^{52} - 2 q^{53} + 24 q^{54} + 12 q^{56} - 2 q^{57} - 20 q^{58} - 28 q^{59} - 110 q^{60} - 4 q^{61} - 32 q^{62} - 44 q^{63} - 24 q^{64} + 10 q^{65} + 36 q^{66} - 6 q^{67} + 28 q^{68} + 124 q^{70} + 124 q^{72} + 8 q^{73} + 88 q^{74} - 2 q^{75} + 12 q^{77} - 40 q^{78} + 52 q^{79} - 120 q^{80} - 24 q^{81} - 80 q^{82} + 76 q^{83} - 40 q^{84} + 12 q^{85} - 8 q^{86} - 12 q^{87} + 20 q^{88} + 78 q^{90} + 8 q^{92} + 24 q^{93} + 32 q^{94} - 4 q^{95} - 4 q^{96} - 10 q^{97} - 122 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 + 2 * q^10 + 22 * q^12 - 2 * q^13 - 2 * q^15 + 16 * q^16 - 20 * q^17 - 2 * q^18 - 52 * q^19 - 12 * q^20 - 16 * q^21 - 36 * q^22 - 20 * q^23 - 16 * q^25 + 8 * q^27 - 24 * q^28 + 40 * q^30 + 2 * q^32 + 8 * q^33 + 20 * q^34 - 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 + 64 * q^39 - 36 * q^40 - 4 * q^41 - 60 * q^42 + 28 * q^43 - 8 * q^44 + 12 * q^45 - 8 * q^46 + 4 * q^47 - 2 * q^48 + 46 * q^50 + 74 * q^52 - 2 * q^53 + 24 * q^54 + 12 * q^56 - 2 * q^57 - 20 * q^58 - 28 * q^59 - 110 * q^60 - 4 * q^61 - 32 * q^62 - 44 * q^63 - 24 * q^64 + 10 * q^65 + 36 * q^66 - 6 * q^67 + 28 * q^68 + 124 * q^70 + 124 * q^72 + 8 * q^73 + 88 * q^74 - 2 * q^75 + 12 * q^77 - 40 * q^78 + 52 * q^79 - 120 * q^80 - 24 * q^81 - 80 * q^82 + 76 * q^83 - 40 * q^84 + 12 * q^85 - 8 * q^86 - 12 * q^87 + 20 * q^88 + 78 * q^90 + 8 * q^92 + 24 * q^93 + 32 * q^94 - 4 * q^95 - 4 * q^96 - 10 * q^97 - 122 * q^98 - 128 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.912296	+	1.08061i	0.645091	+	0.764106i
$2$	0.912296	+	1.08061i	0.645091	+	0.764106i
$3$	−1.34016	−	1.34016i	−0.773742	−	0.773742i	0.205017	−	0.978759i	$-0.434275\pi$
$3$	−1.34016	−	1.34016i	−0.773742	−	0.773742i	−0.978759	+	0.205017i	$0.934275\pi$
$4$	−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	$-0.690292\pi$
$7$	0.697742	−	0.697742i	0.263722	−	0.263722i	0.826564	+	0.562842i	$0.190292\pi$
$8$	−2.43662	+	1.43628i	−0.861475	+	0.507800i
$9$			0.592060i			0.197353i
$10$	−1.73045	−	2.64680i	−0.547217	−	0.836991i
$11$		−	4.74628i		−	1.43106i	−0.698584	−	0.715528i	$-0.746186\pi$
$11$		−	4.74628i		−	1.43106i	0.698584	−	0.715528i	$-0.253814\pi$
$12$	3.09189	−	2.19282i	0.892551	−	0.633013i
$13$	3.30493	−	3.30493i	0.916623	−	0.916623i	−0.0801589	−	0.996782i	$-0.525543\pi$
$13$	3.30493	−	3.30493i	0.916623	−	0.916623i	0.996782	+	0.0801589i	$0.0255428\pi$
$14$	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	0.570983	−	0.820962i	$-0.306562\pi$
$17$	−1.03069	−	1.03069i	−0.249979	−	0.249979i	−0.820962	+	0.570983i	$0.806562\pi$
$18$	−0.639785	+	0.540133i	−0.150799	+	0.127311i
$19$	−1.00000			−0.229416
$19$	−1.00000			−0.229416
$20$	1.28147	−	4.28460i	0.286545	−	0.958067i
$21$	−1.87017			−0.408105
$22$	5.12887	−	4.33001i	1.09348	−	0.923161i
$23$	−6.40614	−	6.40614i	−1.33577	−	1.33577i	−0.900110	−	0.435662i	$-0.856514\pi$
$23$	−6.40614	−	6.40614i	−1.33577	−	1.33577i	−0.435662	−	0.900110i	$-0.643486\pi$
$24$	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
$28$	1.14167	+	1.60976i	0.215756	+	0.304217i
$29$		−	1.98037i		−	0.367746i	−0.982950	−	0.183873i	$-0.941136\pi$
$29$		−	1.98037i		−	0.367746i	0.982950	−	0.183873i	$-0.0588636\pi$
$30$	−1.22805	+	5.86622i	−0.224210	+	1.07102i
$31$			9.29923i			1.67019i	0.550106	+	0.835095i	$0.314587\pi$
$31$			9.29923i			1.67019i	−0.550106	+	0.835095i	$0.685413\pi$
$32$	−2.01454	−	5.28598i	−0.356124	−	0.934439i
$33$	−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	0.0606627	−	0.998158i	$-0.480679\pi$
$37$	−5.70256	−	5.70256i	−0.937496	−	0.937496i	−0.998158	+	0.0606627i	$0.980679\pi$
$38$	−0.912296	−	1.08061i	−0.147994	−	0.175298i
$39$	−8.85828			−1.41846
$40$	5.79906	−	2.52406i	0.916912	−	0.399089i
$41$	9.41542			1.47044			0.735221	−	0.677828i	$-0.237078\pi$
$41$	9.41542			1.47044			0.735221	+	0.677828i	$0.237078\pi$
$42$	−1.70615	−	2.02093i	−0.263265	−	0.311836i
$43$	1.89635	+	1.89635i	0.289191	+	0.289191i	0.836760	−	0.547569i	$-0.184447\pi$
$43$	1.89635	+	1.89635i	0.289191	+	0.289191i	−0.547569	+	0.836760i	$0.684447\pi$
$44$	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	$-0.713574\pi$
$47$	1.10706	−	1.10706i	0.161482	−	0.161482i	0.783223	+	0.621741i	$0.213574\pi$
$48$	3.28640	+	6.83173i	0.474351	+	0.986075i
$49$			6.02631i			0.860902i
$50$	3.11971	+	6.34566i	0.441194	+	0.897412i
$51$			2.76258i			0.386838i
$52$	5.40766	+	7.62482i	0.749907	+	1.05737i
$53$	−0.00450773	+	0.00450773i	−0.000619185	+	0.000619185i	−0.707416	−	0.706797i	$-0.750139\pi$
$53$	−0.00450773	+	0.00450773i	−0.000619185	+	0.000619185i	0.706797	+	0.707416i	$0.250139\pi$
$54$	−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
$58$	2.14001	−	1.80669i	0.280997	−	0.237230i
$59$	−3.02457			−0.393765			−0.196883	−	0.980427i	$-0.563082\pi$
$59$	−3.02457			−0.393765			−0.196883	+	0.980427i	$0.563082\pi$
$60$	−7.45943	+	4.02468i	−0.963009	+	0.519584i
$61$	−0.724786			−0.0927993			−0.0463997	−	0.998923i	$-0.514775\pi$
$61$	−0.724786			−0.0927993			−0.0463997	+	0.998923i	$0.514775\pi$
$62$	−10.0488	+	8.48365i	−1.27620	+	1.07742i
$63$	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	0.275761	−	0.961226i	$-0.411070\pi$
$67$	10.1252	−	10.1252i	1.23699	−	1.23699i	0.961226	−	0.275761i	$-0.0889297\pi$
$68$	2.37791	−	1.68645i	0.288364	−	0.204512i
$69$			17.1705i			2.06709i
$70$	−3.05419	−	0.639373i	−0.365046	−	0.0764197i
$71$			9.29365i			1.10295i	0.834190	+	0.551477i	$0.185935\pi$
$71$			9.29365i			1.10295i	−0.834190	+	0.551477i	$0.814065\pi$
$72$	−0.850361	−	1.44262i	−0.100216	−	0.170015i
$73$	−4.54609	+	4.54609i	−0.532079	+	0.532079i	−0.921191	−	0.389112i	$-0.872782\pi$
$73$	−4.54609	+	4.54609i	−0.532079	+	0.532079i	0.389112	+	0.921191i	$0.372782\pi$
$74$	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
$78$	−8.08137	−	9.57234i	−0.915035	−	1.08385i
$79$	0.319115			0.0359032			0.0179516	−	0.999839i	$-0.494286\pi$
$79$	0.319115			0.0359032			0.0179516	+	0.999839i	$0.494286\pi$
$80$	8.01798	+	3.96383i	0.896438	+	0.443170i
$81$	10.4256			1.15840
$82$	8.58965	+	10.1744i	0.948568	+	1.12357i
$83$	−2.15376	−	2.15376i	−0.236406	−	0.236406i	0.578954	−	0.815360i	$-0.303461\pi$
$83$	−2.15376	−	2.15376i	−0.236406	−	0.236406i	−0.815360	+	0.578954i	$0.803461\pi$
$84$	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
$88$	6.81696	+	11.5649i	0.726690	+	1.23282i
$89$		−	8.13569i		−	0.862381i	−0.902261	−	0.431191i	$-0.858094\pi$
$89$		−	8.13569i		−	0.862381i	0.902261	−	0.431191i	$-0.141906\pi$
$90$	1.56706	−	1.02453i	0.165183	−	0.107995i
$91$		−	4.61198i		−	0.483467i
$92$	14.7796	−	10.4820i	1.54088	−	1.09282i
$93$	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	0.147197	−	0.989107i	$-0.452975\pi$
$97$	−8.29185	−	8.29185i	−0.841910	−	0.841910i	−0.989107	+	0.147197i	$0.952975\pi$
$98$	−6.51209	+	5.49778i	−0.657820	+	0.555360i
$99$	2.81008			0.282423
$100$	−4.01107	+	9.16031i	−0.401107	+	0.916031i
$101$	2.37691			0.236512			0.118256	−	0.992983i	$-0.462270\pi$
$101$	2.37691			0.236512			0.118256	+	0.992983i	$0.462270\pi$
$102$	−2.98527	+	2.52029i	−0.295585	+	0.249546i
$103$	−3.18098	−	3.18098i	−0.313432	−	0.313432i	0.532806	−	0.846237i	$-0.321138\pi$
$103$	−3.18098	−	3.18098i	−0.313432	−	0.313432i	−0.846237	+	0.532806i	$0.821138\pi$
$104$	−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	0.106490	−	0.994314i	$-0.466039\pi$
$107$	11.3868	−	11.3868i	1.10080	−	1.10080i	0.994314	−	0.106490i	$-0.0339613\pi$
$108$	−5.28018	−	7.44508i	−0.508086	−	0.716403i
$109$		−	10.1057i		−	0.967951i	−0.875082	−	0.483975i	$-0.839192\pi$
$109$		−	10.1057i		−	0.967951i	0.875082	−	0.483975i	$-0.160808\pi$
$110$	−12.5624	+	8.21320i	−1.19778	+	0.783098i
$111$			15.2847i			1.45076i
$112$	−3.55688	+	1.71104i	−0.336093	+	0.161678i
$113$	4.33960	−	4.33960i	0.408236	−	0.408236i	−0.472887	−	0.881123i	$-0.656788\pi$
$113$	4.33960	−	4.33960i	0.408236	−	0.408236i	0.881123	+	0.472887i	$0.156788\pi$
$114$	−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
$118$	−2.75930	−	3.26838i	−0.254014	−	0.300878i
$119$	−1.43831			−0.131850
$120$	−11.1543	−	4.38903i	−1.01825	−	0.400662i
$121$	−11.5271			−1.04792
$122$	−0.661219	−	0.783210i	−0.0598640	−	0.0709085i
$123$	−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	$-0.867430\pi$
$127$	−5.74713	+	5.74713i	−0.509976	+	0.509976i	0.404543	+	0.914519i	$0.367430\pi$
$128$	11.0980	−	2.19892i	0.980930	−	0.194359i
$129$		−	5.08283i		−	0.447518i
$130$	−14.4665	−	3.02846i	−1.26880	−	0.265614i
$131$			8.12224i			0.709644i	0.934934	+	0.354822i	$0.115458\pi$
$131$			8.12224i			0.709644i	−0.934934	+	0.354822i	$0.884542\pi$
$132$	−10.4077	−	14.6750i	−0.905877	−	1.27729i
$133$	−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	0.886734	−	0.462281i	$-0.152969\pi$
$137$	4.96810	+	4.96810i	0.424453	+	0.424453i	−0.462281	+	0.886734i	$0.652969\pi$
$138$	−18.5546	+	15.6646i	−1.57947	+	1.33346i
$139$	4.21496			0.357508			0.178754	−	0.983894i	$-0.442793\pi$
$139$	4.21496			0.357508			0.178754	+	0.983894i	$0.442793\pi$
$140$	−2.09541	−	3.88368i	−0.177095	−	0.328231i
$141$	−2.96728			−0.249890
$142$	−10.0428	+	8.47856i	−0.842774	+	0.711505i
$143$	−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
$148$	13.1564	−	9.33075i	1.08145	−	0.766983i
$149$		−	7.03834i		−	0.576603i	−0.957540	−	0.288302i	$-0.906909\pi$
$149$		−	7.03834i		−	0.576603i	0.957540	−	0.288302i	$-0.0930906\pi$
$150$	4.32328	−	12.6851i	0.352995	−	1.03574i
$151$			16.8075i			1.36777i	0.729589	+	0.683886i	$0.239711\pi$
$151$			16.8075i			1.36777i	−0.729589	+	0.683886i	$0.760289\pi$
$152$	2.43662	−	1.43628i	0.197636	−	0.116497i
$153$	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	0.996990	−	0.0775322i	$-0.0247040\pi$
$157$	11.5208	+	11.5208i	0.919458	+	0.919458i	−0.0775322	+	0.996990i	$0.524704\pi$
$158$	0.291127	+	0.344839i	0.0231608	+	0.0274339i
$159$	0.0120822			0.000958178
$160$	3.03142	+	12.2805i	0.239655	+	0.970858i
$161$	−8.93967			−0.704544
$162$	9.51127	+	11.2660i	0.747276	+	0.885144i
$163$	8.50009	+	8.50009i	0.665778	+	0.665778i	0.956736	−	0.290958i	$-0.0939739\pi$
$163$	8.50009	+	8.50009i	0.665778	+	0.665778i	−0.290958	+	0.956736i	$0.593974\pi$
$164$	−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	$-0.526768\pi$
$167$	11.7917	−	11.7917i	0.912471	−	0.912471i	0.996466	+	0.0839953i	$0.0267681\pi$
$168$	4.55690	−	2.68608i	0.351572	−	0.207236i
$169$		−	8.84515i		−	0.680396i
$170$	−0.944468	+	4.51158i	−0.0724374	+	0.346023i
$171$		−	0.592060i		−	0.0452759i
$172$	−4.37508	+	3.10288i	−0.333597	+	0.236593i
$173$	−14.0451	+	14.0451i	−1.06783	+	1.06783i	−0.0703074	+	0.997525i	$0.522398\pi$
$173$	−14.0451	+	14.0451i	−1.06783	+	1.06783i	−0.997525	+	0.0703074i	$0.977602\pi$
$174$	−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
$178$	8.79150	−	7.42215i	0.658951	−	0.556314i
$179$	8.86640			0.662706			0.331353	−	0.943507i	$-0.392495\pi$
$179$	8.86640			0.662706			0.331353	+	0.943507i	$0.392495\pi$
$180$	2.53674	+	0.758706i	0.189078	+	0.0565506i
$181$	5.73740			0.426457			0.213229	−	0.977002i	$-0.431602\pi$
$181$	5.73740			0.426457			0.213229	+	0.977002i	$0.431602\pi$
$182$	4.98375	−	4.20749i	0.369420	−	0.311880i
$183$	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
$188$	1.81142	+	2.55411i	0.132111	+	0.186278i
$189$			4.50326i			0.327564i
$190$	1.73045	+	2.64680i	0.125540	+	0.192019i
$191$		−	3.42146i		−	0.247568i	−0.992309	−	0.123784i	$-0.960497\pi$
$191$		−	3.42146i		−	0.247568i	0.992309	−	0.123784i	$-0.0395030\pi$
$192$	−14.5723	+	4.18812i	−1.05166	+	0.302252i
$193$	14.1458	−	14.1458i	1.01824	−	1.01824i	0.0184059	−	0.999831i	$-0.494141\pi$
$193$	14.1458	−	14.1458i	1.01824	−	1.01824i	0.999831	−	0.0184059i	$-0.00585912\pi$
$194$	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	0.552557	−	0.833475i	$-0.313652\pi$
$197$	−3.94287	−	3.94287i	−0.280918	−	0.280918i	−0.833475	+	0.552557i	$0.813652\pi$
$198$	2.56362	+	3.03660i	0.182189	+	0.215801i
$199$	22.6493			1.60557			0.802785	−	0.596269i	$-0.203351\pi$
$199$	22.6493			1.60557			0.802785	+	0.596269i	$0.203351\pi$
$200$	−13.5580	+	4.02251i	−0.958696	+	0.284434i
$201$	−27.1387			−1.91422
$202$	2.16845	+	2.56851i	0.152571	+	0.180720i
$203$	−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
$208$	−16.8475	+	8.10451i	−1.16817	+	0.561946i
$209$			4.74628i			0.328307i
$210$	3.23624	+	4.94997i	0.223322	+	0.341580i
$211$		−	23.7055i		−	1.63196i	−0.578083	−	0.815978i	$-0.696199\pi$
$211$		−	23.7055i		−	1.63196i	0.578083	−	0.815978i	$-0.303801\pi$
$212$	−0.00737572	−	0.0103998i	−0.000506567	−	0.000714261i
$213$	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
$218$	10.9203	−	9.21939i	0.739617	−	0.624416i
$219$	12.1850			0.823384
$220$	−20.3359	−	6.08221i	−1.37105	−	0.410062i
$221$	−6.81272			−0.458273
$222$	−16.5168	+	13.9442i	−1.10853	+	0.935871i
$223$	12.4637	+	12.4637i	0.834631	+	0.834631i	0.988146	−	0.153515i	$-0.0490594\pi$
$223$	12.4637	+	12.4637i	0.834631	+	0.834631i	−0.153515	+	0.988146i	$0.549059\pi$
$224$	−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	$-0.736975\pi$
$227$	0.871636	−	0.871636i	0.0578525	−	0.0578525i	0.735441	+	0.677589i	$0.236975\pi$
$228$	−3.09189	+	2.19282i	−0.204765	+	0.145223i
$229$			10.1929i			0.673563i	0.941583	+	0.336782i	$0.109338\pi$
$229$			10.1929i			0.673563i	−0.941583	+	0.336782i	$0.890662\pi$
$230$	−5.87024	+	28.0413i	−0.387072	+	1.84899i
$231$			8.87635i			0.584021i
$232$	2.84436	+	4.82542i	0.186742	+	0.316804i
$233$	−5.24568	+	5.24568i	−0.343656	+	0.343656i	−0.857740	−	0.514084i	$-0.828132\pi$
$233$	−5.24568	+	5.24568i	−0.343656	+	0.343656i	0.514084	+	0.857740i	$0.328132\pi$
$234$	−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
$238$	−1.31216	−	1.55425i	−0.0850550	−	0.100747i
$239$	−0.785993			−0.0508417			−0.0254208	−	0.999677i	$-0.508093\pi$
$239$	−0.785993			−0.0508417			−0.0254208	+	0.999677i	$0.508093\pi$
$240$	−5.43321	−	16.0576i	−0.350712	−	1.03651i
$241$	18.3499			1.18202			0.591009	−	0.806665i	$-0.298730\pi$
$241$	18.3499			1.18202			0.591009	+	0.806665i	$0.298730\pi$
$242$	−10.5162	−	12.4563i	−0.676004	−	0.800723i
$243$	−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
$248$	−13.3563	−	22.6587i	−0.848123	−	1.43883i
$249$			5.77276i			0.365834i
$250$	−5.19565	−	14.9334i	−0.328602	−	0.944469i
$251$			8.10035i			0.511290i	0.966771	+	0.255645i	$0.0822878\pi$
$251$			8.10035i			0.511290i	−0.966771	+	0.255645i	$0.917712\pi$
$252$	−0.953075	+	0.675938i	−0.0600381	+	0.0425801i
$253$	−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	0.913412	−	0.407036i	$-0.133438\pi$
$257$	8.11783	+	8.11783i	0.506376	+	0.506376i	−0.407036	+	0.913412i	$0.633438\pi$
$258$	5.49255	−	4.63704i	0.341951	−	0.288690i
$259$	−7.95784			−0.494476
$260$	−9.92516	−	18.3955i	−0.615532	−	1.14084i
$261$	1.17250			0.0725759
$262$	−8.77697	+	7.40989i	−0.542243	+	0.457784i
$263$	−7.91763	−	7.91763i	−0.488222	−	0.488222i	0.419523	−	0.907745i	$-0.362197\pi$
$263$	−7.91763	−	7.91763i	−0.488222	−	0.488222i	−0.907745	+	0.419523i	$0.862197\pi$
$264$	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
$268$	16.5672	+	23.3598i	1.01200	+	1.42693i
$269$		−	17.7957i		−	1.08502i	−0.840049	−	0.542510i	$-0.817474\pi$
$269$		−	17.7957i		−	1.08502i	0.840049	−	0.542510i	$-0.182526\pi$
$270$	14.1255	+	2.95707i	0.859650	+	0.179962i
$271$		−	16.0644i		−	0.975843i	−0.872888	−	0.487921i	$-0.837755\pi$
$271$		−	16.0644i		−	0.975843i	0.872888	−	0.487921i	$-0.162245\pi$
$272$	2.52750	+	5.25414i	0.153252	+	0.318579i
$273$	−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	0.347489	−	0.937684i	$-0.387034\pi$
$277$	−9.82279	−	9.82279i	−0.590195	−	0.590195i	−0.937684	+	0.347489i	$0.887034\pi$
$278$	3.84529	+	4.55472i	0.230625	+	0.273174i
$279$	−5.50569			−0.329617
$280$	2.28511	−	5.80739i	0.136561	−	0.347058i
$281$	10.4171			0.621431			0.310715	−	0.950503i	$-0.399431\pi$
$281$	10.4171			0.621431			0.310715	+	0.950503i	$0.399431\pi$
$282$	−2.70704	−	3.20648i	−0.161202	−	0.190943i
$283$	−9.74230	−	9.74230i	−0.579120	−	0.579120i	0.355541	−	0.934661i	$-0.384297\pi$
$283$	−9.74230	−	9.74230i	−0.579120	−	0.579120i	−0.934661	+	0.355541i	$0.884297\pi$
$284$	−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
$288$	3.12962	−	1.19273i	0.184414	−	0.0702822i
$289$		−	14.8754i		−	0.875021i
$290$	−5.24165	+	3.42694i	−0.307800	+	0.201237i
$291$			22.2248i			1.30284i
$292$	−7.43848	−	10.4883i	−0.435304	−	0.613781i
$293$	−17.9213	+	17.9213i	−1.04697	+	1.04697i	−0.0481339	+	0.998841i	$0.515327\pi$
$293$	−17.9213	+	17.9213i	−1.04697	+	1.04697i	−0.998841	+	0.0481339i	$0.984673\pi$
$294$	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
$298$	7.60569	−	6.42105i	0.440586	−	0.371961i
$299$	−42.3437			−2.44880
$300$	17.6518	−	6.90080i	1.01913	−	0.398418i
$301$	2.64633			0.152532
$302$	−18.1623	+	15.3334i	−1.04512	+	0.882337i
$303$	−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	$-0.807721\pi$
$307$	−4.46875	+	4.46875i	−0.255045	+	0.255045i	0.567990	+	0.823035i	$0.307721\pi$
$308$	7.64038	−	5.41869i	0.435351	−	0.308759i
$309$			8.52605i			0.485030i
$310$	24.6132	−	16.0919i	1.39793	−	0.913956i
$311$		−	0.594436i		−	0.0337074i	−0.999858	−	0.0168537i	$-0.994635\pi$
$311$		−	0.594436i		−	0.0337074i	0.999858	−	0.0168537i	$-0.00536495\pi$
$312$	21.5842	−	12.7229i	1.22197	−	0.720294i
$313$	14.2529	−	14.2529i	0.805624	−	0.805624i	−0.178344	−	0.983968i	$-0.557074\pi$
$313$	14.2529	−	14.2529i	0.805624	−	0.805624i	0.983968	+	0.178344i	$0.0570740\pi$
$314$	−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	0.418416	−	0.908256i	$-0.362585\pi$
$317$	−8.72134	−	8.72134i	−0.489840	−	0.489840i	−0.908256	+	0.418416i	$0.862585\pi$
$318$	0.0110225	+	0.0130561i	0.000618112	+	0.000732150i
$319$	−9.39940			−0.526265
$320$	−10.5049	+	14.4792i	−0.587240	+	0.809413i
$321$	−30.5203			−1.70348
$322$	−8.15562	−	9.66028i	−0.454495	−	0.538347i
$323$	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
$328$	−22.9418	+	13.5231i	−1.26675	+	0.746690i
$329$		−	1.54489i		−	0.0851725i
$330$	27.8427	+	5.82867i	1.53269	+	0.320858i
$331$			12.5175i			0.688023i	0.938966	+	0.344011i	$0.111786\pi$
$331$			12.5175i			0.688023i	−0.938966	+	0.344011i	$0.888214\pi$
$332$	4.96894	−	3.52406i	0.272706	−	0.193408i
$333$	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	0.375098	−	0.926985i	$-0.377609\pi$
$337$	−10.1313	−	10.1313i	−0.551887	−	0.551887i	−0.926985	+	0.375098i	$0.877609\pi$
$338$	9.55815	−	8.06939i	0.519895	−	0.438917i
$339$	−11.6315			−0.631738
$340$	−5.73689	+	3.09530i	−0.311127	+	0.167866i
$341$	44.1367			2.39014
$342$	0.639785	−	0.540133i	0.0345956	−	0.0292071i
$343$	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	$-0.755847\pi$
$347$	−0.483917	+	0.483917i	−0.0259781	+	0.0259781i	0.693998	+	0.719976i	$0.255847\pi$
$348$	−4.34261	−	6.12309i	−0.232788	−	0.328232i
$349$			12.0418i			0.644582i	0.946641	+	0.322291i	$0.104453\pi$
$349$			12.0418i			0.644582i	−0.946641	+	0.322291i	$0.895547\pi$
$350$	6.60439	+	2.25088i	0.353019	+	0.120314i
$351$			21.3302i			1.13852i
$352$	−25.0887	+	9.56157i	−1.33723	+	0.509633i
$353$	−19.3284	+	19.3284i	−1.02875	+	1.02875i	−0.0291749	+	0.999574i	$0.509288\pi$
$353$	−19.3284	+	19.3284i	−1.02875	+	1.02875i	−0.999574	+	0.0291749i	$0.990712\pi$
$354$	−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
$358$	8.08878	+	9.58112i	0.427505	+	0.506378i
$359$	−23.7453			−1.25323			−0.626614	−	0.779330i	$-0.715560\pi$
$359$	−23.7453			−1.25323			−0.626614	+	0.779330i	$0.715560\pi$
$360$	1.49439	+	3.43339i	0.0787614	+	0.180956i
$361$	1.00000			0.0526316
$362$	5.23420	+	6.19988i	0.275104	+	0.325859i
$363$	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	$-0.912712\pi$
$367$	−13.2536	+	13.2536i	−0.691835	+	0.691835i	0.270801	+	0.962635i	$0.412712\pi$
$368$	15.7094	+	32.6565i	0.818910	+	1.70234i
$369$			5.57449i			0.290196i
$370$	−5.22552	+	24.9615i	−0.271662	+	1.29769i
$371$			0.00629047i			0.000326585i
$372$	20.3915	+	28.7522i	1.05725	+	1.49073i
$373$	−8.99990	+	8.99990i	−0.465997	+	0.465997i	−0.900615	−	0.434618i	$-0.856883\pi$
$373$	−8.99990	+	8.99990i	−0.465997	+	0.465997i	0.434618	+	0.900615i	$0.356883\pi$
$374$	−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
$378$	−4.86627	+	4.10831i	−0.250294	+	0.211309i
$379$	1.33948			0.0688044			0.0344022	−	0.999408i	$-0.489047\pi$
$379$	1.33948			0.0688044			0.0344022	+	0.999408i	$0.489047\pi$
$380$	−1.28147	+	4.28460i	−0.0657380	+	0.219796i
$381$	15.4042			0.789179
$382$	3.69726	−	3.12138i	0.189168	−	0.159704i
$383$	2.40611	+	2.40611i	0.122946	+	0.122946i	0.765903	−	0.642956i	$-0.222292\pi$
$383$	2.40611	+	2.40611i	0.122946	+	0.122946i	−0.642956	+	0.765903i	$0.722292\pi$
$384$	−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
$388$	19.1302	−	13.5674i	0.971186	−	0.688783i
$389$			26.3685i			1.33693i	0.743742	+	0.668467i	$0.233049\pi$
$389$			26.3685i			1.33693i	−0.743742	+	0.668467i	$0.766951\pi$
$390$	15.3288	+	23.4461i	0.776205	+	1.18724i
$391$			13.2055i			0.667830i
$392$	−8.65545	−	14.6838i	−0.437166	−	0.741645i
$393$	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	0.977405	−	0.211373i	$-0.0677935\pi$
$397$	15.2631	+	15.2631i	0.766032	+	0.766032i	−0.211373	+	0.977405i	$0.567793\pi$
$398$	20.6629	+	24.4751i	1.03574	+	1.22683i
$399$	1.87017			0.0936257
$400$	−16.7157	−	10.9812i	−0.835783	−	0.549059i
$401$	−13.0632			−0.652343			−0.326171	−	0.945311i	$-0.605759\pi$
$401$	−13.0632			−0.652343			−0.326171	+	0.945311i	$0.605759\pi$
$402$	−24.7585	−	29.3263i	−1.23484	−	1.46267i
$403$	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
$408$	−3.96782	−	6.73135i	−0.196437	−	0.333251i
$409$		−	30.5100i		−	1.50862i	−0.656517	−	0.754312i	$-0.727971\pi$
$409$		−	30.5100i		−	1.50862i	0.656517	−	0.754312i	$-0.272029\pi$
$410$	−16.2929	−	24.9207i	−0.804650	−	1.23075i
$411$		−	13.3161i		−	0.656834i
$412$	7.33885	−	5.20485i	0.361559	−	0.256424i
$413$	−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
$418$	−5.12887	+	4.33001i	−0.250861	+	0.211788i
$419$	−9.78783			−0.478167			−0.239083	−	0.970999i	$-0.576847\pi$
$419$	−9.78783			−0.478167			−0.239083	+	0.970999i	$0.576847\pi$
$420$	−2.39657	+	8.01295i	−0.116941	+	0.390992i
$421$	26.7931			1.30582			0.652909	−	0.757437i	$-0.273549\pi$
$421$	26.7931			1.30582			0.652909	+	0.757437i	$0.273549\pi$
$422$	25.6164	−	21.6264i	1.24699	−	1.05276i
$423$	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
$428$	18.6315	+	26.2705i	0.900589	+	1.26983i
$429$			42.0438i			2.02989i
$430$	1.73771	−	8.30080i	0.0838000	−	0.400300i
$431$		−	2.45196i		−	0.118107i	−0.998255	−	0.0590534i	$-0.981192\pi$
$431$		−	2.45196i		−	0.118107i	0.998255	−	0.0590534i	$-0.0188082\pi$
$432$	16.4504	−	7.91346i	0.791470	−	0.380737i
$433$	20.7659	−	20.7659i	0.997948	−	0.997948i	−0.00205006	−	0.999998i	$-0.500653\pi$
$433$	20.7659	−	20.7659i	0.997948	−	0.997948i	0.999998	+	0.00205006i	$0.000652555\pi$
$434$	−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
$438$	11.1163	+	13.1672i	0.531157	+	0.629153i
$439$	−24.9711			−1.19180			−0.595902	−	0.803057i	$-0.703205\pi$
$439$	−24.9711			−1.19180			−0.595902	+	0.803057i	$0.703205\pi$
$440$	−11.9799	−	27.5239i	−0.571118	−	1.31215i
$441$	−3.56794			−0.169902
$442$	−6.21521	−	7.36188i	−0.295628	−	0.350169i
$443$	−14.4843	−	14.4843i	−0.688170	−	0.688170i	0.273657	−	0.961827i	$-0.411767\pi$
$443$	−14.4843	−	14.4843i	−0.688170	−	0.688170i	−0.961827	+	0.273657i	$0.911767\pi$
$444$	−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
$448$	−2.18051	−	7.58693i	−0.103019	−	0.358449i
$449$		−	33.6613i		−	1.58857i	−0.607543	−	0.794286i	$-0.707845\pi$
$449$		−	33.6613i		−	1.58857i	0.607543	−	0.794286i	$-0.292155\pi$
$450$	−3.75701	+	1.84706i	−0.177107	+	0.0870711i
$451$		−	44.6882i		−	2.10428i
$452$	7.10063	+	10.0119i	0.333985	+	0.470921i
$453$	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	0.856919	−	0.515451i	$-0.172376\pi$
$457$	7.29974	+	7.29974i	0.341468	+	0.341468i	−0.515451	+	0.856919i	$0.672376\pi$
$458$	−11.0145	+	9.29890i	−0.514674	+	0.434509i
$459$	6.65212			0.310495
$460$	−35.6570	+	19.2385i	−1.66252	+	0.896999i
$461$	−0.951158			−0.0442999			−0.0221499	−	0.999755i	$-0.507051\pi$
$461$	−0.951158			−0.0442999			−0.0221499	+	0.999755i	$0.507051\pi$
$462$	−9.59187	+	8.09786i	−0.446254	+	0.376747i
$463$	−13.1374	−	13.1374i	−0.610549	−	0.610549i	0.332540	−	0.943089i	$-0.392094\pi$
$463$	−13.1374	−	13.1374i	−0.610549	−	0.610549i	−0.943089	+	0.332540i	$0.892094\pi$
$464$	−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	$-0.523849\pi$
$467$	19.9319	−	19.9319i	0.922339	−	0.922339i	0.997194	+	0.0748550i	$0.0238494\pi$
$468$	−4.51435	+	3.20165i	−0.208676	+	0.147997i
$469$		−	14.1295i		−	0.652441i
$470$	−4.84589	−	1.01445i	−0.223524	−	0.0467932i
$471$		−	30.8794i		−	1.42285i
$472$	7.36972	−	4.34411i	0.339219	−	0.199954i
$473$	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
$478$	−0.717058	−	0.849352i	−0.0327975	−	0.0388484i
$479$	−29.5471			−1.35004			−0.675021	−	0.737799i	$-0.735865\pi$
$479$	−29.5471			−1.35004			−0.675021	+	0.737799i	$0.735865\pi$
$480$	12.3952	−	20.5204i	0.565763	−	0.936625i
$481$	−37.6932			−1.71866
$482$	16.7405	+	19.8290i	0.762509	+	0.903188i
$483$	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	0.379742	−	0.925092i	$-0.376013\pi$
$487$	28.7952	−	28.7952i	1.30483	−	1.30483i	0.925092	−	0.379742i	$-0.123987\pi$
$488$	1.76603	−	1.04099i	0.0799443	−	0.0471235i
$489$		−	22.7830i		−	1.03028i
$490$	15.9504	−	10.4282i	0.720567	−	0.471100i
$491$			2.85127i			0.128676i	0.997928	+	0.0643380i	$0.0204936\pi$
$491$			2.85127i			0.128676i	−0.997928	+	0.0643380i	$0.979506\pi$
$492$	29.1114	−	20.6463i	1.31244	−	0.930809i
$493$	−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
$498$	−6.23810	+	5.26647i	−0.279536	+	0.235996i
$499$	−12.2247			−0.547252			−0.273626	−	0.961836i	$-0.588223\pi$
$499$	−12.2247			−0.547252			−0.273626	+	0.961836i	$0.588223\pi$
$500$	11.3972	−	19.2381i	0.509696	−	0.860354i
$501$	−31.6056			−1.41203
$502$	−8.75331	+	7.38992i	−0.390680	+	0.329828i
$503$	22.0965	+	22.0965i	0.985234	+	0.985234i	0.999893	−	0.0146587i	$-0.00466618\pi$
$503$	22.0965	+	22.0965i	0.985234	+	0.985234i	−0.0146587	+	0.999893i	$0.504666\pi$
$504$	−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
$508$	−9.40368	−	13.2592i	−0.417221	−	0.588283i
$509$			5.44703i			0.241435i	0.992687	+	0.120718i	$0.0385196\pi$
$509$			5.44703i			0.241435i	−0.992687	+	0.120718i	$0.961480\pi$
$510$	7.31198	−	4.78051i	0.323780	−	0.211684i
$511$			6.34399i			0.280642i
$512$	0.612936	+	22.6191i	0.0270882	+	0.999633i
$513$	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
$518$	−7.25990	−	8.59931i	−0.318982	−	0.377832i
$519$	37.6455			1.65245
$520$	10.8237	−	27.5074i	0.474649	−	1.20628i
$521$	−14.5598			−0.637877			−0.318938	−	0.947775i	$-0.603326\pi$
$521$	−14.5598			−0.637877			−0.318938	+	0.947775i	$0.603326\pi$
$522$	1.06967	+	1.26701i	0.0468180	+	0.0554557i
$523$	−1.82937	−	1.82937i	−0.0799929	−	0.0799929i	0.665978	−	0.745971i	$-0.268014\pi$
$523$	−1.82937	−	1.82937i	−0.0799929	−	0.0799929i	−0.745971	+	0.665978i	$0.768014\pi$
$524$	−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
$528$	32.4253	−	15.5982i	1.41113	−	0.678823i
$529$			59.0772i			2.56857i
$530$	0.0197315	+	0.00413064i	0.000857080	+	0.000179424i
$531$		−	1.79072i		−	0.0777108i
$532$	−1.14167	−	1.60976i	−0.0494978	−	0.0697921i
$533$	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
$538$	19.2301	−	16.2349i	0.829071	−	0.699936i
$539$	28.6025			1.23200
$540$	9.69119	+	17.9619i	0.417043	+	0.772956i
$541$	−36.8551			−1.58452			−0.792262	−	0.610181i	$-0.791097\pi$
$541$	−36.8551			−1.58452			−0.792262	+	0.610181i	$0.791097\pi$
$542$	17.3593	−	14.6555i	0.745647	−	0.629507i
$543$	−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	$-0.825796\pi$
$547$	−7.80179	+	7.80179i	−0.333580	+	0.333580i	0.520364	+	0.853944i	$0.325796\pi$
$548$	−11.4619	+	8.12899i	−0.489629	+	0.347253i
$549$		−	0.429116i		−	0.0183142i
$550$	30.1182	−	14.8070i	1.28425	−	0.631374i
$551$			1.98037i			0.0843668i
$552$	−24.6616	−	41.8380i	−1.04967	−	1.78074i
$553$	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	0.668648	−	0.743579i	$-0.266873\pi$
$557$	−1.76844	−	1.76844i	−0.0749310	−	0.0749310i	−0.743579	+	0.668648i	$0.766873\pi$
$558$	−5.02282	−	5.94950i	−0.212633	−	0.251863i
$559$	12.5346			0.530158
$560$	8.36022	−	2.82875i	0.353284	−	0.119537i
$561$	13.1120			0.553587
$562$	9.50346	+	11.2568i	0.400879	+	0.474839i
$563$	6.91763	+	6.91763i	0.291543	+	0.291543i	0.837690	−	0.546146i	$-0.183906\pi$
$563$	6.91763	+	6.91763i	0.291543	+	0.291543i	−0.546146	+	0.837690i	$0.683906\pi$
$564$	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
$568$	−13.3482	−	22.6451i	−0.560080	−	0.950167i
$569$			8.71597i			0.365392i	0.983169	+	0.182696i	$0.0584825\pi$
$569$			8.71597i			0.365392i	−0.983169	+	0.182696i	$0.941518\pi$
$570$	1.22805	−	5.86622i	0.0514374	−	0.245709i
$571$		−	44.1078i		−	1.84586i	−0.384973	−	0.922928i	$-0.625789\pi$
$571$		−	44.1078i		−	1.84586i	0.384973	−	0.922928i	$-0.374211\pi$
$572$	36.1895	−	25.6662i	1.51316	−	1.07316i
$573$	−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	0.468348	−	0.883544i	$-0.344850\pi$
$577$	−9.97337	−	9.97337i	−0.415197	−	0.415197i	−0.883544	+	0.468348i	$0.844850\pi$
$578$	16.0744	−	13.5707i	0.668609	−	0.564468i
$579$	−37.9153			−1.57570
$580$	−8.48512	−	2.53779i	−0.352325	−	0.105376i
$581$	−3.00553			−0.124691
$582$	−24.0163	+	20.2756i	−0.995510	+	0.840451i
$583$	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	$-0.797582\pi$
$587$	−5.10277	+	5.10277i	−0.210614	+	0.210614i	0.593914	+	0.804528i	$0.297582\pi$
$588$	13.2146	+	18.6327i	0.544962	+	0.768399i
$589$		−	9.29923i		−	0.383168i
$590$	5.23387	+	8.00542i	0.215475	+	0.329578i
$591$			10.5682i			0.434716i
$592$	13.9841	+	29.0699i	0.574742	+	1.19477i
$593$	3.54561	−	3.54561i	0.145601	−	0.145601i	−0.630549	−	0.776150i	$-0.717170\pi$
$593$	3.54561	−	3.54561i	0.145601	−	0.145601i	0.776150	+	0.630549i	$0.217170\pi$
$594$	−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
$598$	−38.6300	−	45.7570i	−1.57970	−	1.87114i
$599$	30.4232			1.24306			0.621529	−	0.783391i	$-0.286512\pi$
$599$	30.4232			1.24306			0.621529	+	0.783391i	$0.286512\pi$
$600$	23.5607	+	12.7791i	0.961862	+	0.521704i
$601$	26.2371			1.07023			0.535117	−	0.844778i	$-0.320268\pi$
$601$	26.2371			1.07023			0.535117	+	0.844778i	$0.320268\pi$
$602$	2.41423	+	2.85965i	0.0983968	+	0.116550i
$603$	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	$-0.752496\pi$
$607$	−0.273256	+	0.273256i	−0.0110911	+	0.0110911i	0.701539	+	0.712631i	$0.252496\pi$
$608$	2.01454	+	5.28598i	0.0817005	+	0.214375i
$609$			3.70364i			0.150079i
$610$	1.25421	+	1.91836i	0.0507813	+	0.0776722i
$611$		−	7.31754i		−	0.296036i
$612$	0.998481	+	1.40786i	0.0403612	+	0.0569095i
$613$	−6.40183	+	6.40183i	−0.258567	+	0.258567i	−0.824471	−	0.565904i	$-0.808527\pi$
$613$	−6.40183	+	6.40183i	−0.258567	+	0.258567i	0.565904	+	0.824471i	$0.308527\pi$
$614$	−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	0.991047	−	0.133517i	$-0.0426269\pi$
$617$	21.3006	+	21.3006i	0.857530	+	0.857530i	−0.133517	+	0.991047i	$0.542627\pi$
$618$	−9.21333	+	7.77828i	−0.370615	+	0.312888i
$619$	−21.5289			−0.865320			−0.432660	−	0.901557i	$-0.642425\pi$
$619$	−21.5289			−0.865320			−0.432660	+	0.901557i	$0.642425\pi$
$620$	39.8435	+	11.9167i	1.60015	+	0.478585i
$621$	41.3456			1.65914
$622$	0.642353	−	0.542302i	0.0257560	−	0.0217443i
$623$	−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
$628$	−26.5796	+	18.8507i	−1.06064	+	0.752226i
$629$			11.7551i			0.468708i
$630$	0.378547	−	1.80826i	0.0150817	−	0.0720429i
$631$		−	33.6642i		−	1.34015i	−0.742294	−	0.670074i	$-0.766262\pi$
$631$		−	33.6642i		−	1.34015i	0.742294	−	0.670074i	$-0.233738\pi$
$632$	−0.777562	+	0.458337i	−0.0309297	+	0.0182317i
$633$	−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
$638$	−8.57503	−	10.1571i	−0.339489	−	0.402123i
$639$	−5.50240			−0.217671
$640$	−25.2299	+	1.85769i	−0.997300	+	0.0734315i
$641$	−11.4028			−0.450383			−0.225192	−	0.974314i	$-0.572301\pi$
$641$	−11.4028			−0.450383			−0.225192	+	0.974314i	$0.572301\pi$
$642$	−27.8435	−	32.9805i	−1.09890	−	1.30164i
$643$	31.2371	+	31.2371i	1.23187	+	1.23187i	0.963244	+	0.268629i	$0.0865704\pi$
$643$	31.2371	+	31.2371i	1.23187	+	1.23187i	0.268629	+	0.963244i	$0.413430\pi$
$644$	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	0.0416381	−	0.999133i	$-0.486742\pi$
$647$	26.4732	−	26.4732i	1.04077	−	1.04077i	0.999133	−	0.0416381i	$-0.0132576\pi$
$648$	−25.4033	+	14.9741i	−0.997937	+	0.588238i
$649$			14.3554i			0.563500i
$650$	31.2824	+	10.6615i	1.22700	+	0.418180i
$651$		−	17.3912i		−	0.681613i
$652$	−19.6106	+	13.9082i	−0.768010	+	0.544686i
$653$	−17.1865	+	17.1865i	−0.672558	+	0.672558i	−0.958305	−	0.285747i	$-0.907758\pi$
$653$	−17.1865	+	17.1865i	−0.672558	+	0.672558i	0.285747	+	0.958305i	$0.407758\pi$
$654$	−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
$658$	1.66942	−	1.40940i	0.0650808	−	0.0549440i
$659$	46.1104			1.79621			0.898104	−	0.439783i	$-0.144945\pi$
$659$	46.1104			1.79621			0.898104	+	0.439783i	$0.144945\pi$
$660$	19.1022	+	35.4045i	0.743554	+	1.37812i
$661$	8.33816			0.324317			0.162158	−	0.986765i	$-0.448154\pi$
$661$	8.33816			0.324317			0.162158	+	0.986765i	$0.448154\pi$
$662$	−13.5265	+	11.4196i	−0.525722	+	0.443837i
$663$	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
$668$	19.2941	+	27.2047i	0.746510	+	1.05258i
$669$		−	33.4067i		−	1.29158i
$670$	−44.3204	−	9.27816i	−1.71225	−	0.358447i
$671$			3.44003i			0.132801i
$672$	3.76754	+	9.88570i	0.145336	+	0.381349i
$673$	−0.923216	+	0.923216i	−0.0355873	+	0.0355873i	−0.724677	−	0.689089i	$-0.758011\pi$
$673$	−0.923216	+	0.923216i	−0.0355873	+	0.0355873i	0.689089	+	0.724677i	$0.258011\pi$
$674$	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	0.775702	−	0.631099i	$-0.217396\pi$
$677$	3.76247	+	3.76247i	0.144603	+	0.144603i	−0.631099	+	0.775702i	$0.717396\pi$
$678$	−10.6114	−	12.5691i	−0.407528	−	0.482715i
$679$	−11.5711			−0.444060
$680$	−8.57855	−	3.37551i	−0.328972	−	0.129445i
$681$	−2.33626			−0.0895259
$682$	40.2657	+	47.6945i	1.54185	+	1.82632i
$683$	−13.9942	−	13.9942i	−0.535473	−	0.535473i	0.386723	−	0.922196i	$-0.373607\pi$
$683$	−13.9942	−	13.9942i	−0.535473	−	0.535473i	−0.922196	+	0.386723i	$0.873607\pi$
$684$	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
$688$	−4.65032	−	9.66702i	−0.177292	−	0.368552i
$689$			0.0297955i			0.00113512i
$690$	45.4469	−	29.7127i	1.73013	−	1.13114i
$691$			10.1227i			0.385087i	0.981288	+	0.192544i	$0.0616737\pi$
$691$			10.1227i			0.385087i	−0.981288	+	0.192544i	$0.938326\pi$
$692$	−22.9812	−	32.4036i	−0.873614	−	1.23180i
$693$	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
$698$	−13.0125	+	10.9857i	−0.492529	+	0.415814i
$699$	14.0601			0.531802
$700$	3.59284	+	9.19023i	0.135797	+	0.347358i
$701$	−21.0307			−0.794320			−0.397160	−	0.917749i	$-0.630004\pi$
$701$	−21.0307			−0.794320			−0.397160	+	0.917749i	$0.630004\pi$
$702$	−23.0496	+	19.4595i	−0.869952	+	0.734450i
$703$	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
$708$	−9.35163	+	6.63234i	−0.351456	+	0.249259i
$709$		−	24.7345i		−	0.928924i	−0.885593	−	0.464462i	$-0.846248\pi$
$709$		−	24.7345i		−	0.928924i	0.885593	−	0.464462i	$-0.153752\pi$
$710$	24.5984	−	16.0822i	0.923162	−	0.603555i
$711$			0.188935i			0.00708562i
$712$	11.6851	+	19.8236i	0.437917	+	0.742920i
$713$	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
$718$	−21.6627	−	25.6594i	−0.808446	−	0.957599i
$719$	26.9815			1.00624			0.503120	−	0.864216i	$-0.332185\pi$
$719$	26.9815			1.00624			0.503120	+	0.864216i	$0.332185\pi$
$720$	−2.34682	+	4.74712i	−0.0874610	+	0.176915i
$721$	−4.43901			−0.165317
$722$	0.912296	+	1.08061i	0.0339521	+	0.0402161i
$723$	−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	−0.0989427	+	0.995093i	$0.531546\pi$
$727$	−29.4984	+	29.4984i	−1.09404	+	1.09404i	−0.995093	+	0.0989427i	$0.968454\pi$
$728$	6.62408	+	11.2376i	0.245505	+	0.416495i
$729$		−	19.7758i		−	0.732437i
$730$	19.8994	+	4.16579i	0.736508	+	0.154183i
$731$		−	3.90910i		−	0.144583i
$732$	−2.24096	+	1.58933i	−0.0828281	+	0.0587432i
$733$	−19.4831	+	19.4831i	−0.719625	+	0.719625i	−0.968528	−	0.248904i	$-0.919930\pi$
$733$	−19.4831	+	19.4831i	−0.719625	+	0.719625i	0.248904	+	0.968528i	$0.419930\pi$
$734$	−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
$738$	−6.02384	+	5.08558i	−0.221741	+	0.187203i
$739$	37.1086			1.36506			0.682532	−	0.730856i	$-0.260879\pi$
$739$	37.1086			1.36506			0.682532	+	0.730856i	$0.260879\pi$
$740$	−31.7409	+	17.1256i	−1.16682	+	0.629548i
$741$	8.85828			0.325417
$742$	−0.00679754	+	0.00573877i	−0.000249545	+	0.000210677i
$743$	12.3911	+	12.3911i	0.454586	+	0.454586i	0.896873	−	0.442288i	$-0.145833\pi$
$743$	12.3911	+	12.3911i	0.454586	+	0.454586i	−0.442288	+	0.896873i	$0.645833\pi$
$744$	−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
$748$	−8.00437	−	11.2862i	−0.292669	−	0.412664i
$749$		−	15.8901i		−	0.580612i
$750$	−13.0501	+	26.9761i	−0.476522	+	0.985028i
$751$			4.32457i			0.157806i	0.996882	+	0.0789029i	$0.0251417\pi$
$751$			4.32457i			0.157806i	−0.996882	+	0.0789029i	$0.974858\pi$
$752$	−5.64347	+	2.71479i	−0.205796	+	0.0989983i
$753$	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	0.776452	−	0.630177i	$-0.217017\pi$
$757$	4.02457	+	4.02457i	0.146275	+	0.146275i	−0.630177	+	0.776452i	$0.717017\pi$
$758$	1.22200	+	1.44745i	0.0443851	+	0.0525739i
$759$	81.4959			2.95812
$760$	−5.79906	+	2.52406i	−0.210354	+	0.0915572i
$761$	35.1030			1.27248			0.636241	−	0.771490i	$-0.280488\pi$
$761$	35.1030			1.27248			0.636241	+	0.771490i	$0.280488\pi$
$762$	14.0532	+	16.6459i	0.509092	+	0.603016i
$763$	−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
$768$	−3.36958	−	30.1366i	−0.121589	−	1.08746i
$769$		−	50.0247i		−	1.80394i	−0.431802	−	0.901968i	$-0.642122\pi$
$769$		−	50.0247i		−	1.80394i	0.431802	−	0.901968i	$-0.357878\pi$
$770$	−3.03464	+	14.4960i	−0.109361	+	0.522401i
$771$		−	21.7584i		−	0.783609i</

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)

\(f(q)\)	\(=\)	\(q+(0.912296 + 1.08061i) q^{2} +(-1.34016 - 1.34016i) q^{3} +(-0.335432 + 1.97167i) q^{4} +(-2.21942 - 0.272360i) q^{5} +(0.225567 - 2.67081i) q^{6} +(0.697742 - 0.697742i) q^{7} +(-2.43662 + 1.43628i) q^{8} +0.592060i q^{9} +O(q^{10})\)	\(q+(0.912296 + 1.08061i) 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} +(-2.43662 + 1.43628i) q^{8} +0.592060i q^{9} +(-1.73045 - 2.64680i) q^{10} -4.74628i q^{11} +(3.09189 - 2.19282i) 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} +(-0.639785 + 0.540133i) q^{18} -1.00000 q^{19} +(1.28147 - 4.28460i) q^{20} -1.87017 q^{21} +(5.12887 - 4.33001i) 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} +(1.14167 + 1.60976i) q^{28} -1.98037i q^{29} +(-1.22805 + 5.86622i) q^{30} +9.29923i q^{31} +(-2.01454 - 5.28598i) 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} +(-0.912296 - 1.08061i) q^{38} -8.85828 q^{39} +(5.79906 - 2.52406i) q^{40} +9.41542 q^{41} +(-1.70615 - 2.02093i) 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} +(3.28640 + 6.83173i) q^{48} +6.02631i q^{49} +(3.11971 + 6.34566i) q^{50} +2.76258i q^{51} +(5.40766 + 7.62482i) 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} +(2.14001 - 1.80669i) q^{58} -3.02457 q^{59} +(-7.45943 + 4.02468i) q^{60} -0.724786 q^{61} +(-10.0488 + 8.48365i) 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} +(2.37791 - 1.68645i) q^{68} +17.1705i q^{69} +(-3.05419 - 0.639373i) q^{70} +9.29365i q^{71} +(-0.850361 - 1.44262i) 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} +(-8.08137 - 9.57234i) q^{78} +0.319115 q^{79} +(8.01798 + 3.96383i) q^{80} +10.4256 q^{81} +(8.58965 + 10.1744i) 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} +(6.81696 + 11.5649i) q^{88} -8.13569i q^{89} +(1.56706 - 1.02453i) q^{90} -4.61198i q^{91} +(14.7796 - 10.4820i) 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} +(-6.51209 + 5.49778i) 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	\( 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{10} + 22 q^{12} - 2 q^{13} - 2 q^{15} + 16 q^{16} - 20 q^{17} - 2 q^{18} - 52 q^{19} - 12 q^{20} - 16 q^{21} - 36 q^{22} - 20 q^{23} - 16 q^{25} + 8 q^{27} - 24 q^{28} + 40 q^{30} + 2 q^{32} + 8 q^{33} + 20 q^{34} - 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} + 64 q^{39} - 36 q^{40} - 4 q^{41} - 60 q^{42} + 28 q^{43} - 8 q^{44} + 12 q^{45} - 8 q^{46} + 4 q^{47} - 2 q^{48} + 46 q^{50} + 74 q^{52} - 2 q^{53} + 24 q^{54} + 12 q^{56} - 2 q^{57} - 20 q^{58} - 28 q^{59} - 110 q^{60} - 4 q^{61} - 32 q^{62} - 44 q^{63} - 24 q^{64} + 10 q^{65} + 36 q^{66} - 6 q^{67} + 28 q^{68} + 124 q^{70} + 124 q^{72} + 8 q^{73} + 88 q^{74} - 2 q^{75} + 12 q^{77} - 40 q^{78} + 52 q^{79} - 120 q^{80} - 24 q^{81} - 80 q^{82} + 76 q^{83} - 40 q^{84} + 12 q^{85} - 8 q^{86} - 12 q^{87} + 20 q^{88} + 78 q^{90} + 8 q^{92} + 24 q^{93} + 32 q^{94} - 4 q^{95} - 4 q^{96} - 10 q^{97} - 122 q^{98} - 128 q^{99}+O(q^{100}) \) 52 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8 + 2 * q^10 + 22 * q^12 - 2 * q^13 - 2 * q^15 + 16 * q^16 - 20 * q^17 - 2 * q^18 - 52 * q^19 - 12 * q^20 - 16 * q^21 - 36 * q^22 - 20 * q^23 - 16 * q^25 + 8 * q^27 - 24 * q^28 + 40 * q^30 + 2 * q^32 + 8 * q^33 + 20 * q^34 - 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 + 64 * q^39 - 36 * q^40 - 4 * q^41 - 60 * q^42 + 28 * q^43 - 8 * q^44 + 12 * q^45 - 8 * q^46 + 4 * q^47 - 2 * q^48 + 46 * q^50 + 74 * q^52 - 2 * q^53 + 24 * q^54 + 12 * q^56 - 2 * q^57 - 20 * q^58 - 28 * q^59 - 110 * q^60 - 4 * q^61 - 32 * q^62 - 44 * q^63 - 24 * q^64 + 10 * q^65 + 36 * q^66 - 6 * q^67 + 28 * q^68 + 124 * q^70 + 124 * q^72 + 8 * q^73 + 88 * q^74 - 2 * q^75 + 12 * q^77 - 40 * q^78 + 52 * q^79 - 120 * q^80 - 24 * q^81 - 80 * q^82 + 76 * q^83 - 40 * q^84 + 12 * q^85 - 8 * q^86 - 12 * q^87 + 20 * q^88 + 78 * q^90 + 8 * q^92 + 24 * q^93 + 32 * q^94 - 4 * q^95 - 4 * q^96 - 10 * q^97 - 122 * q^98 - 128 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

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