LMFDB - Embedded newform 380.2.k.d.343.19

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			343.19
Character	$\chi$	$=$	380.343
Dual form			380.2.k.d.267.19

$q$-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 $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

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

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 $

$2$	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	−0.978759	−	0.205017i	$-0.934275\pi$
$3$	−1.34016	+	1.34016i	−0.773742	+	0.773742i	0.205017	+	0.978759i	$0.434275\pi$
$4$	−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	0.826564	−	0.562842i	$-0.190292\pi$
$7$	0.697742	+	0.697742i	0.263722	+	0.263722i	−0.562842	+	0.826564i	$0.690292\pi$
$8$	−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	$0.253814\pi$
$11$			4.74628i			1.43106i	−0.698584	+	0.715528i	$0.746186\pi$
$12$	3.09189	+	2.19282i	0.892551	+	0.633013i
$13$	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	$0.306562\pi$
$18$	−0.639785	−	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	−0.435662	+	0.900110i	$0.643486\pi$
$23$	−6.40614	+	6.40614i	−1.33577	+	1.33577i	−0.900110	+	0.435662i	$0.856514\pi$
$24$	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	$0.0588636\pi$
$29$			1.98037i			0.367746i	−0.982950	+	0.183873i	$0.941136\pi$
$30$	−1.22805	−	5.86622i	−0.224210	−	1.07102i
$31$		−	9.29923i		−	1.67019i	−0.550106	−	0.835095i	$-0.685413\pi$
$31$		−	9.29923i		−	1.67019i	0.550106	−	0.835095i	$-0.314587\pi$
$32$	−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	−0.998158	−	0.0606627i	$-0.980679\pi$
$37$	−5.70256	+	5.70256i	−0.937496	+	0.937496i	0.0606627	+	0.998158i	$0.480679\pi$
$38$	−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	−0.547569	−	0.836760i	$-0.684447\pi$
$43$	1.89635	−	1.89635i	0.289191	−	0.289191i	0.836760	+	0.547569i	$0.184447\pi$
$44$	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	0.783223	−	0.621741i	$-0.213574\pi$
$47$	1.10706	+	1.10706i	0.161482	+	0.161482i	−0.621741	+	0.783223i	$0.713574\pi$
$48$	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	0.706797	−	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
$58$	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	0.961226	+	0.275761i	$0.0889297\pi$
$67$	10.1252	+	10.1252i	1.23699	+	1.23699i	0.275761	+	0.961226i	$0.411070\pi$
$68$	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	$-0.814065\pi$
$71$		−	9.29365i		−	1.10295i	0.834190	−	0.551477i	$-0.185935\pi$
$72$	−0.850361	+	1.44262i	−0.100216	+	0.170015i
$73$	−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
$78$	−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	−0.815360	−	0.578954i	$-0.803461\pi$
$83$	−2.15376	+	2.15376i	−0.236406	+	0.236406i	0.578954	+	0.815360i	$0.303461\pi$
$84$	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	$0.141906\pi$
$89$			8.13569i			0.862381i	−0.902261	+	0.431191i	$0.858094\pi$
$90$	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	−0.989107	−	0.147197i	$-0.952975\pi$
$97$	−8.29185	+	8.29185i	−0.841910	+	0.841910i	0.147197	+	0.989107i	$0.452975\pi$
$98$	−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	−0.846237	−	0.532806i	$-0.821138\pi$
$103$	−3.18098	+	3.18098i	−0.313432	+	0.313432i	0.532806	+	0.846237i	$0.321138\pi$
$104$	−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	$0.0339613\pi$
$107$	11.3868	+	11.3868i	1.10080	+	1.10080i	0.106490	+	0.994314i	$0.466039\pi$
$108$	−5.28018	+	7.44508i	−0.508086	+	0.716403i
$109$			10.1057i			0.967951i	0.875082	+	0.483975i	$0.160808\pi$
$109$			10.1057i			0.967951i	−0.875082	+	0.483975i	$0.839192\pi$
$110$	−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	0.881123	−	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
$118$	−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	0.404543	−	0.914519i	$-0.367430\pi$
$127$	−5.74713	−	5.74713i	−0.509976	−	0.509976i	−0.914519	+	0.404543i	$0.867430\pi$
$128$	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	$-0.884542\pi$
$131$		−	8.12224i		−	0.709644i	0.934934	−	0.354822i	$-0.115458\pi$
$132$	−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	−0.462281	−	0.886734i	$-0.652969\pi$
$137$	4.96810	−	4.96810i	0.424453	−	0.424453i	0.886734	+	0.462281i	$0.152969\pi$
$138$	−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	$0.0930906\pi$
$149$			7.03834i			0.576603i	−0.957540	+	0.288302i	$0.906909\pi$
$150$	4.32328	+	12.6851i	0.352995	+	1.03574i
$151$		−	16.8075i		−	1.36777i	−0.729589	−	0.683886i	$-0.760289\pi$
$151$		−	16.8075i		−	1.36777i	0.729589	−	0.683886i	$-0.239711\pi$
$152$	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	−0.0775322	−	0.996990i	$-0.524704\pi$
$157$	11.5208	−	11.5208i	0.919458	−	0.919458i	0.996990	+	0.0775322i	$0.0247040\pi$
$158$	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	−0.290958	−	0.956736i	$-0.593974\pi$
$163$	8.50009	−	8.50009i	0.665778	−	0.665778i	0.956736	+	0.290958i	$0.0939739\pi$
$164$	−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	0.996466	−	0.0839953i	$-0.0267681\pi$
$167$	11.7917	+	11.7917i	0.912471	+	0.912471i	−0.0839953	+	0.996466i	$0.526768\pi$
$168$	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	−0.997525	−	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
$178$	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	$0.0395030\pi$
$191$			3.42146i			0.247568i	−0.992309	+	0.123784i	$0.960497\pi$
$192$	−14.5723	−	4.18812i	−1.05166	−	0.302252i
$193$	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	$0.313652\pi$
$198$	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	$0.303801\pi$
$211$			23.7055i			1.63196i	−0.578083	+	0.815978i	$0.696199\pi$
$212$	−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	−0.153515	−	0.988146i	$-0.549059\pi$
$223$	12.4637	−	12.4637i	0.834631	−	0.834631i	0.988146	+	0.153515i	$0.0490594\pi$
$224$	−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	0.735441	−	0.677589i	$-0.236975\pi$
$227$	0.871636	+	0.871636i	0.0578525	+	0.0578525i	−0.677589	+	0.735441i	$0.736975\pi$
$228$	−3.09189	−	2.19282i	−0.204765	−	0.145223i
$229$		−	10.1929i		−	0.673563i	−0.941583	−	0.336782i	$-0.890662\pi$
$229$		−	10.1929i		−	0.673563i	0.941583	−	0.336782i	$-0.109338\pi$
$230$	−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	0.514084	−	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
$238$	−1.31216	+	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	$-0.917712\pi$
$251$		−	8.10035i		−	0.511290i	0.966771	−	0.255645i	$-0.0822878\pi$
$252$	−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	−0.407036	−	0.913412i	$-0.633438\pi$
$257$	8.11783	−	8.11783i	0.506376	−	0.506376i	0.913412	+	0.407036i	$0.133438\pi$
$258$	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	−0.907745	−	0.419523i	$-0.862197\pi$
$263$	−7.91763	+	7.91763i	−0.488222	+	0.488222i	0.419523	+	0.907745i	$0.362197\pi$
$264$	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	$0.182526\pi$
$269$			17.7957i			1.08502i	−0.840049	+	0.542510i	$0.817474\pi$
$270$	14.1255	−	2.95707i	0.859650	−	0.179962i
$271$			16.0644i			0.975843i	0.872888	+	0.487921i	$0.162245\pi$
$271$			16.0644i			0.975843i	−0.872888	+	0.487921i	$0.837755\pi$
$272$	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	−0.937684	−	0.347489i	$-0.887034\pi$
$277$	−9.82279	+	9.82279i	−0.590195	+	0.590195i	0.347489	+	0.937684i	$0.387034\pi$
$278$	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	−0.934661	−	0.355541i	$-0.884297\pi$
$283$	−9.74230	+	9.74230i	−0.579120	+	0.579120i	0.355541	+	0.934661i	$0.384297\pi$
$284$	−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	−0.998841	−	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
$298$	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	0.567990	−	0.823035i	$-0.307721\pi$
$307$	−4.46875	−	4.46875i	−0.255045	−	0.255045i	−0.823035	+	0.567990i	$0.807721\pi$
$308$	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	$0.00536495\pi$
$311$			0.594436i			0.0337074i	−0.999858	+	0.0168537i	$0.994635\pi$
$312$	21.5842	+	12.7229i	1.22197	+	0.720294i
$313$	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	$0.362585\pi$
$318$	0.0110225	−	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	$-0.888214\pi$
$331$		−	12.5175i		−	0.688023i	0.938966	−	0.344011i	$-0.111786\pi$
$332$	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	−0.926985	−	0.375098i	$-0.877609\pi$
$337$	−10.1313	+	10.1313i	−0.551887	+	0.551887i	0.375098	+	0.926985i	$0.377609\pi$
$338$	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	0.693998	−	0.719976i	$-0.255847\pi$
$347$	−0.483917	−	0.483917i	−0.0259781	−	0.0259781i	−0.719976	+	0.693998i	$0.755847\pi$
$348$	−4.34261	+	6.12309i	−0.232788	+	0.328232i
$349$		−	12.0418i		−	0.644582i	−0.946641	−	0.322291i	$-0.895547\pi$
$349$		−	12.0418i		−	0.644582i	0.946641	−	0.322291i	$-0.104453\pi$
$350$	6.60439	−	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	−0.999574	−	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
$358$	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	0.270801	−	0.962635i	$-0.412712\pi$
$367$	−13.2536	−	13.2536i	−0.691835	−	0.691835i	−0.962635	+	0.270801i	$0.912712\pi$
$368$	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	0.434618	−	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
$378$	−4.86627	−	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	−0.642956	−	0.765903i	$-0.722292\pi$
$383$	2.40611	−	2.40611i	0.122946	−	0.122946i	0.765903	+	0.642956i	$0.222292\pi$
$384$	−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	$-0.766951\pi$
$389$		−	26.3685i		−	1.33693i	0.743742	−	0.668467i	$-0.233049\pi$
$390$	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	−0.211373	−	0.977405i	$-0.567793\pi$
$397$	15.2631	−	15.2631i	0.766032	−	0.766032i	0.977405	+	0.211373i	$0.0677935\pi$
$398$	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	$0.272029\pi$
$409$			30.5100i			1.50862i	−0.656517	+	0.754312i	$0.727971\pi$
$410$	−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	$0.0188082\pi$
$431$			2.45196i			0.118107i	−0.998255	+	0.0590534i	$0.981192\pi$
$432$	16.4504	+	7.91346i	0.791470	+	0.380737i
$433$	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
$438$	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	−0.961827	−	0.273657i	$-0.911767\pi$
$443$	−14.4843	+	14.4843i	−0.688170	+	0.688170i	0.273657	+	0.961827i	$0.411767\pi$
$444$	−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	$0.292155\pi$
$449$			33.6613i			1.58857i	−0.607543	+	0.794286i	$0.707845\pi$
$450$	−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	−0.515451	−	0.856919i	$-0.672376\pi$
$457$	7.29974	−	7.29974i	0.341468	−	0.341468i	0.856919	+	0.515451i	$0.172376\pi$
$458$	−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	−0.943089	−	0.332540i	$-0.892094\pi$
$463$	−13.1374	+	13.1374i	−0.610549	+	0.610549i	0.332540	+	0.943089i	$0.392094\pi$
$464$	−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	0.997194	−	0.0748550i	$-0.0238494\pi$
$467$	19.9319	+	19.9319i	0.922339	+	0.922339i	−0.0748550	+	0.997194i	$0.523849\pi$
$468$	−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	0.925092	+	0.379742i	$0.123987\pi$
$487$	28.7952	+	28.7952i	1.30483	+	1.30483i	0.379742	+	0.925092i	$0.376013\pi$
$488$	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	$-0.979506\pi$
$491$		−	2.85127i		−	0.128676i	0.997928	−	0.0643380i	$-0.0204936\pi$
$492$	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	−0.0146587	−	0.999893i	$-0.504666\pi$
$503$	22.0965	−	22.0965i	0.985234	−	0.985234i	0.999893	+	0.0146587i	$0.00466618\pi$
$504$	−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	$-0.961480\pi$
$509$		−	5.44703i		−	0.241435i	0.992687	−	0.120718i	$-0.0385196\pi$
$510$	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	−0.745971	−	0.665978i	$-0.768014\pi$
$523$	−1.82937	+	1.82937i	−0.0799929	+	0.0799929i	0.665978	+	0.745971i	$0.268014\pi$
$524$	−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	0.520364	−	0.853944i	$-0.325796\pi$
$547$	−7.80179	−	7.80179i	−0.333580	−	0.333580i	−0.853944	+	0.520364i	$0.825796\pi$
$548$	−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	−0.743579	−	0.668648i	$-0.766873\pi$
$557$	−1.76844	+	1.76844i	−0.0749310	+	0.0749310i	0.668648	+	0.743579i	$0.266873\pi$
$558$	−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	−0.546146	−	0.837690i	$-0.683906\pi$
$563$	6.91763	−	6.91763i	0.291543	−	0.291543i	0.837690	+	0.546146i	$0.183906\pi$
$564$	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	$-0.941518\pi$
$569$		−	8.71597i		−	0.365392i	0.983169	−	0.182696i	$-0.0584825\pi$
$570$	1.22805	+	5.86622i	0.0514374	+	0.245709i
$571$			44.1078i			1.84586i	0.384973	+	0.922928i	$0.374211\pi$
$571$			44.1078i			1.84586i	−0.384973	+	0.922928i	$0.625789\pi$
$572$	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	−0.883544	−	0.468348i	$-0.844850\pi$
$577$	−9.97337	+	9.97337i	−0.415197	+	0.415197i	0.468348	+	0.883544i	$0.344850\pi$
$578$	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	0.593914	−	0.804528i	$-0.297582\pi$
$587$	−5.10277	−	5.10277i	−0.210614	−	0.210614i	−0.804528	+	0.593914i	$0.797582\pi$
$588$	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	0.776150	−	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
$598$	−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	0.701539	−	0.712631i	$-0.252496\pi$
$607$	−0.273256	−	0.273256i	−0.0110911	−	0.0110911i	−0.712631	+	0.701539i	$0.752496\pi$
$608$	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	0.565904	−	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	$0.0426269\pi$
$618$	−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	$0.233738\pi$
$631$			33.6642i			1.34015i	−0.742294	+	0.670074i	$0.766262\pi$
$632$	−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	0.268629	−	0.963244i	$-0.413430\pi$
$643$	31.2371	−	31.2371i	1.23187	−	1.23187i	0.963244	−	0.268629i	$-0.0865704\pi$
$644$	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	$0.0132576\pi$
$647$	26.4732	+	26.4732i	1.04077	+	1.04077i	0.0416381	+	0.999133i	$0.486742\pi$
$648$	−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	0.285747	−	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
$658$	1.66942	+	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	0.689089	−	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	$0.217396\pi$
$678$	−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	−0.922196	−	0.386723i	$-0.873607\pi$
$683$	−13.9942	+	13.9942i	−0.535473	+	0.535473i	0.386723	+	0.922196i	$0.373607\pi$
$684$	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	$-0.938326\pi$
$691$		−	10.1227i		−	0.385087i	0.981288	−	0.192544i	$-0.0616737\pi$
$692$	−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	$0.153752\pi$
$709$			24.7345i			0.928924i	−0.885593	+	0.464462i	$0.846248\pi$
$710$	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	−0.995093	−	0.0989427i	$-0.968454\pi$
$727$	−29.4984	−	29.4984i	−1.09404	−	1.09404i	−0.0989427	−	0.995093i	$-0.531546\pi$
$728$	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	0.248904	−	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
$738$	−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	−0.442288	−	0.896873i	$-0.645833\pi$
$743$	12.3911	−	12.3911i	0.454586	−	0.454586i	0.896873	+	0.442288i	$0.145833\pi$
$744$	−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	$-0.974858\pi$
$751$		−	4.32457i		−	0.157806i	0.996882	−	0.0789029i	$-0.0251417\pi$
$752$	−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	−0.630177	−	0.776452i	$-0.717017\pi$
$757$	4.02457	−	4.02457i	0.146275	−	0.146275i	0.776452	+	0.630177i	$0.217017\pi$
$758$	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	$0.357878\pi$
$769$			50.0247i			1.80394i	−0.431802	+	0.901968i	$0.642122\pi$
$770$	−3.03464	−	14.4960i	−0.109361	−	0.522401i
$771$			21.7584i			0.783609i
$772$	23.1459	−	32.6358i	0.833039	−	1.17459i
$773$	−0.732635	−	0.732635i	−0.0263510	−	0.0263510i	0.693809	−	0.720160i	$-0.255931\pi$
$773$	−0.732635	−	0.732635i	−0.0263510	−	0.0263510i	−0.720160	+	0.693809i	$0.755931\pi$
$774$	−2.23754	+	0.188974i	−0.0804267	+	0.00679254i
$775$	−11.2424	−	45.1165i	−0.403840	−	1.62063i
$776$	32.1135	−	8.29470i	1.15281	−	0.297762i
$777$	10.6648	−	10.6648i	0.382597	−	0.382597i
$778$	−28.4940	−	24.0558i	−1.02156	−	0.862443i
$779$	−9.41542			−0.337342
$780$	−11.3516	−	37.9542i	−0.406453	−	1.35898i
$781$	44.1102			1.57839
$782$	−14.2700	−	12.0473i	−0.510293	−	0.430811i
$783$	6.39072	−	6.39072i	0.228386	−	0.228386i
$784$	7.97115	+	22.7491i	0.284684	+	0.812470i
$785$	−22.4316	+	28.7072i	−0.800619	+	1.02460i
$786$	21.6930	−	1.83211i	0.773763	−	0.0653491i
$787$	13.7218	+	13.7218i	0.489128	+	0.489128i	0.908031	−	0.418903i	$-0.137585\pi$
$787$	13.7218	+	13.7218i	0.489128	+	0.489128i	−0.418903	+	0.908031i	$0.637585\pi$
$788$	9.09661	+	6.45147i	0.324053	+	0.229824i
$789$		−	21.2218i		−	0.755516i
$790$	−0.552213	+	0.844633i	−0.0196469	+	0.0300507i
$791$			6.05585i			0.215321i
$792$	−6.84709	−	4.03605i	−0.243301	−	0.143415i
$793$	−2.39537	−	2.39537i	−0.0850620	−	0.0850620i
$794$	−2.56898	−	30.4179i	−0.0911697	−	1.07949i
$795$	−0.0268154	+	0.00329070i	−0.000951044	+	0.000116709i
$796$	−7.59732	−	44.6570i	−0.269280	−	1.58283i
$797$	−23.8669	+	23.8669i	−0.845410	+	0.845410i	−0.989556	−	0.144146i	$-0.953956\pi$
$797$	−23.8669	+	23.8669i	−0.845410	+	0.845410i	0.144146	+	0.989556i	$0.453956\pi$
$798$	1.70615	−	2.02093i	0.0603971	−	0.0715400i
$799$	−2.28208			−0.0807341
$800$	−3.38327	+	28.0812i	−0.119617	+	0.992820i
$801$	4.81681			0.170194
$802$	−11.9175	+	14.1162i	−0.420820	+	0.498459i
$803$	21.5770	−	21.5770i	0.761435	−	0.761435i
$804$	9.10320	+	53.5086i	0.321045	+	1.88710i
$805$	19.8409	−	2.43481i	0.699298	−	0.0858158i
$806$	−5.17282	−	61.2486i	−0.182205	−	2.15739i
$807$	−23.8490	−	23.8490i	−0.839526	−	0.839526i
$808$	−5.79163	−	3.41390i	−0.203749	−	0.120101i
$809$		−	55.6290i		−	1.95581i	−0.209043	−	0.977906i	$-0.567035\pi$
$809$		−	55.6290i		−	1.95581i	0.209043	−	0.977906i	$-0.432965\pi$
$810$	−18.0411	+	27.5946i	−0.633899	+	0.969574i
$811$		−	10.2643i		−	0.360427i	−0.983628	−	0.180213i	$-0.942321\pi$
$811$		−	10.2643i		−	0.360427i	0.983628	−	0.180213i	$-0.0576788\pi$
$812$	3.18793	+	2.26094i	0.111875	+	0.0793434i
$813$	−21.5289	−	21.5289i	−0.755050	−	0.755050i
$814$	−53.9398	+	4.55556i	−1.89059	+	0.159672i
$815$	−16.5502	+	21.1803i	−0.579727	+	0.741915i
$816$	3.65413	+	10.4286i	0.127920	+	0.365076i
$817$	−1.89635	+	1.89635i	−0.0663449	+	0.0663449i
$818$	32.9694	+	27.8342i	1.15275	+	0.973199i
$819$	2.73057			0.0954137
$820$	12.0656	+	40.3414i	0.421348	+	1.40878i
$821$	1.32813			0.0463522			0.0231761	−	0.999731i	$-0.492622\pi$
$821$	1.32813			0.0463522			0.0231761	+	0.999731i	$0.492622\pi$
$822$	14.3895	+	12.1482i	0.501891	+	0.423718i
$823$	−13.3218	+	13.3218i	−0.464370	+	0.464370i	−0.900085	−	0.435715i	$-0.856496\pi$
$823$	−13.3218	+	13.3218i	−0.464370	+	0.464370i	0.435715	+	0.900085i	$0.356496\pi$
$824$	12.3196	−	3.18207i	0.429174	−	0.110853i
$825$	−38.5501	−	23.1702i	−1.34214	−	0.806684i
$826$	−4.20576	+	0.355203i	−0.146337	+	0.0123591i
$827$	0.0744113	+	0.0744113i	0.00258753	+	0.00258753i	0.708399	−	0.705812i	$-0.249418\pi$
$827$	0.0744113	+	0.0744113i	0.00258753	+	0.00258753i	−0.705812	+	0.708399i	$0.749418\pi$
$828$	6.20595	−	8.75042i	0.215672	−	0.304098i
$829$			27.2990i			0.948132i	0.880489	+	0.474066i	$0.157214\pi$
$829$			27.2990i			0.948132i	−0.880489	+	0.474066i	$0.842786\pi$
$830$	−1.97359	−	9.42753i	−0.0685042	−	0.327234i
$831$		−	26.3282i		−	0.913317i
$832$	−10.3282	+	35.9363i	−0.358066	+	1.24587i
$833$	6.21126	+	6.21126i	0.215207	+	0.215207i
$834$	0.950754	+	11.2574i	0.0329219	+	0.389810i
$835$	−29.3824	−	22.9592i	−1.01682	−	0.794535i
$836$	−9.35809	+	1.59205i	−0.323656	+	0.0550624i
$837$	−30.0088	+	30.0088i	−1.03726	+	1.03726i
$838$	−8.92939	+	10.5768i	−0.308461	+	0.365370i
$839$	35.2499			1.21696			0.608482	−	0.793568i	$-0.291779\pi$
$839$	35.2499			1.21696			0.608482	+	0.793568i	$0.291779\pi$
$840$	−10.8452	−	4.72043i	−0.374197	−	0.162870i
$841$	25.0781			0.864763
$842$	24.4433	−	28.9529i	0.842370	−	0.997783i
$843$	−13.9606	+	13.9606i	−0.480827	+	0.480827i
$844$	46.7395	−	7.95160i	1.60884	−	0.273705i
$845$	−2.40907	−	19.6311i	−0.0828745	−	0.675330i
$846$	−0.110320	−	1.30624i	−0.00379290	−	0.0449096i
$847$	−8.04296	−	8.04296i	−0.276359	−	0.276359i
$848$	0.0229790	+	0.0110541i	0.000789104	+	0.000379598i
$849$		−	26.1125i		−	0.896179i
$850$	3.32495	+	9.75586i	0.114045	+	0.334623i
$851$		−	73.0628i		−	2.50456i
$852$	20.3793	−	28.7349i	0.698184	−	0.984443i
$853$	−2.90863	−	2.90863i	−0.0995897	−	0.0995897i	0.655556	−	0.755146i	$-0.272434\pi$
$853$	−2.90863	−	2.90863i	−0.0995897	−	0.0995897i	−0.755146	+	0.655556i	$0.772434\pi$
$854$	−1.00784	+	0.0851183i	−0.0344875	+	0.00291269i
$855$	−0.161254	−	1.31403i	−0.00551476	−	0.0449388i
$856$	−11.3907	−	44.0999i	−0.389327	−	1.50730i
$857$	−1.96804	+	1.96804i	−0.0672271	+	0.0672271i	−0.739921	−	0.672694i	$-0.765137\pi$
$857$	−1.96804	+	1.96804i	−0.0672271	+	0.0672271i	0.672694	+	0.739921i	$0.265137\pi$
$858$	−45.4329	−	38.3564i	−1.55106	−	1.30947i
$859$	−41.5822			−1.41876			−0.709382	−	0.704824i	$-0.751026\pi$
$859$	−41.5822			−1.41876			−0.709382	+	0.704824i	$0.751026\pi$
$860$	10.5552	+	5.69500i	0.359930	+	0.194198i
$861$	−17.6085			−0.600095
$862$	2.64961	+	2.23692i	0.0902462	+	0.0761896i
$863$	−0.751986	+	0.751986i	−0.0255979	+	0.0255979i	−0.719790	−	0.694192i	$-0.755762\pi$
$863$	−0.751986	+	0.751986i	−0.0255979	+	0.0255979i	0.694192	+	0.719790i	$0.255762\pi$
$864$	23.5590	−	10.5570i	0.801493	−	0.359157i
$865$	34.9974	+	27.3467i	1.18995	+	0.929816i
$866$	41.3846	−	3.49518i	1.40630	−	0.118771i
$867$	−19.9354	−	19.9354i	−0.677041	−	0.677041i
$868$	−14.9695	−	10.6167i	−0.508100	−	0.360353i
$869$			1.51461i			0.0513795i
$870$	11.6173	−	2.43200i	0.393863	−	0.0824525i
$871$			66.9260i			2.26770i
$872$	14.5146	−	24.6237i	0.491526	−	0.833865i
$873$	4.90927	+	4.90927i	0.166154	+	0.166154i
$874$	−1.07824	−	12.7668i	−0.0364719	−	0.431844i
$875$	−10.0776	−	4.48924i	−0.340685	−	0.151764i
$876$	−4.08723	−	24.0247i	−0.138095	−	0.811721i
$877$	15.6200	−	15.6200i	0.527449	−	0.527449i	−0.392362	−	0.919811i	$-0.628342\pi$
$877$	15.6200	−	15.6200i	0.527449	−	0.527449i	0.919811	+	0.392362i	$0.128342\pi$
$878$	−22.7810	+	26.9840i	−0.768822	+	0.910665i
$879$	48.0349			1.62018
$880$	18.8134	+	38.0556i	0.634201	+	1.28285i
$881$	23.1977			0.781552			0.390776	−	0.920486i	$-0.372207\pi$
$881$	23.1977			0.781552			0.390776	+	0.920486i	$0.372207\pi$
$882$	−3.25501	+	3.85554i	−0.109602	+	0.129823i
$883$	31.0012	−	31.0012i	1.04327	−	1.04327i	0.0442526	−	0.999020i	$-0.485909\pi$
$883$	31.0012	−	31.0012i	1.04327	−	1.04327i	0.999020	−	0.0442526i	$-0.0140907\pi$
$884$	2.28521	+	13.4324i	0.0768598	+	0.451782i
$885$	−7.89222	+	10.1002i	−0.265294	+	0.339514i
$886$	2.43790	+	28.8659i	0.0819029	+	0.969767i
$887$	15.0265	+	15.0265i	0.504541	+	0.504541i	0.912846	−	0.408305i	$-0.133880\pi$
$887$	15.0265	+	15.0265i	0.504541	+	0.504541i	−0.408305	+	0.912846i	$0.633880\pi$
$888$	−21.9530	+	37.2430i	−0.736696	+	1.24979i
$889$		−	8.02003i		−	0.268983i
$890$	−21.5335	−	14.0784i	−0.721805	−	0.471910i
$891$			49.4830i			1.65774i
$892$	−28.7550	−	20.3936i	−0.962790	−	0.682828i
$893$	−1.10706	−	1.10706i	−0.0370465	−	0.0370465i
$894$	−18.7981	+	1.58762i	−0.628702	+	0.0530978i
$895$	−19.6783	+	2.41486i	−0.657772	+	0.0807198i
$896$	6.20923	+	9.27780i	0.207436	+	0.309949i
$897$	56.7474	−	56.7474i	1.89474	−	1.89474i
$898$	36.3747	+	30.7090i	1.21384	+	1.02477i
$899$	18.4159			0.614206
$900$	−5.42345	+	2.37480i	−0.180782	+	0.0791598i
$901$	0.00929214			0.000309566
$902$	48.2905	+	40.7688i	1.60790	+	1.35745i
$903$	−3.54650	+	3.54650i	−0.118020	+	0.118020i
$904$	−4.34109	−	16.8068i	−0.144383	−	0.558987i
$905$	−12.7337	+	1.56264i	−0.423282	+	0.0519439i
$906$	44.8896	−	3.79120i	1.49136	−	0.125954i
$907$	−31.8884	−	31.8884i	−1.05884	−	1.05884i	−0.998157	−	0.0606790i	$-0.980673\pi$
$907$	−31.8884	−	31.8884i	−1.05884	−	1.05884i	−0.0606790	−	0.998157i	$-0.519327\pi$
$908$	1.42620	−	2.01095i	0.0473303	−	0.0667359i
$909$		−	1.40727i		−	0.0466763i
$910$	−12.2070	−	7.98081i	−0.404657	−	0.264561i
$911$			26.4093i			0.874979i	0.899224	+	0.437489i	$0.144132\pi$
$911$			26.4093i			0.874979i	−0.899224	+	0.437489i	$0.855868\pi$
$912$	−3.28640	+	6.83173i	−0.108824	+	0.226221i
$913$	−10.2223	−	10.2223i	−0.338310	−	0.338310i
$914$	−1.22864	−	14.5477i	−0.0406399	−	0.481195i
$915$	−1.89123	+	2.42034i	−0.0625223	+	0.0800139i
$916$	−20.0970	+	3.41902i	−0.664022	+	0.112967i
$917$	5.66723	−	5.66723i	0.187148	−	0.187148i
$918$	6.06870	−	7.18835i	0.200297	−	0.237251i
$919$	−0.693031			−0.0228610			−0.0114305	−	0.999935i	$-0.503639\pi$
$919$	−0.693031			−0.0228610			−0.0114305	+	0.999935i	$0.503639\pi$
$920$	−53.3191	+	20.9801i	−1.75788	+	0.691694i
$921$	11.9777			0.394678
$922$	−0.867738	+	1.02783i	−0.0285774	+	0.0338498i
$923$	30.7149	−	30.7149i	1.01099	−	1.01099i
$924$	−17.5012	+	2.97742i	−0.575749	+	0.0979498i
$925$	−20.7726	+	34.5610i	−0.682999	+	1.13636i
$926$	2.21121	+	26.1817i	0.0726648	+	0.860384i
$927$	1.88333	+	1.88333i	0.0618567	+	0.0618567i
$928$	−10.4682	−	3.98955i	−0.343636	−	0.130963i
$929$		−	39.3217i		−	1.29010i	−0.764139	−	0.645051i	$-0.776836\pi$
$929$		−	39.3217i		−	1.29010i	0.764139	−	0.645051i	$-0.223164\pi$
$930$	−54.5513	+	11.4199i	−1.78881	+	0.374474i
$931$			6.02631i			0.197504i
$932$	−8.58318	+	12.1023i	−0.281152	+	0.396425i
$933$	−0.796640	−	0.796640i	−0.0260808	−	0.0260808i
$934$	39.7224	−	3.35481i	1.29976	−	0.109773i
$935$	12.1896	+	9.52488i	0.398643	+	0.311497i
$936$	−7.57816	+	1.95739i	−0.247700	+	0.0639792i
$937$	27.9936	−	27.9936i	0.914512	−	0.914512i	−0.0821109	−	0.996623i	$-0.526166\pi$
$937$	27.9936	−	27.9936i	0.914512	−	0.914512i	0.996623	+	0.0821109i	$0.0261662\pi$
$938$	15.2685	+	12.8903i	0.498534	+	0.420883i
$939$	−38.2025			−1.24669
$940$	−3.32466	+	6.16200i	−0.108438	+	0.200982i
$941$	−29.0330			−0.946448			−0.473224	−	0.880942i	$-0.656910\pi$
$941$	−29.0330			−0.946448			−0.473224	+	0.880942i	$0.656910\pi$
$942$	33.3685	+	28.1711i	1.08721	+	0.917865i
$943$	−60.3165	+	60.3165i	−1.96418	+	1.96418i
$944$	11.4177	−	4.00067i	0.371613	−	0.130211i
$945$	1.22651	+	9.99463i	0.0398984	+	0.325125i
$946$	17.9374	−	1.51492i	0.583194	−	0.0492543i
$947$	−3.93345	−	3.93345i	−0.127820	−	0.127820i	0.640303	−	0.768123i	$-0.278809\pi$
$947$	−3.93345	−	3.93345i	−0.127820	−	0.127820i	−0.768123	+	0.640303i	$0.778809\pi$
$948$	0.986668	+	0.699762i	0.0320455	+	0.0227272i
$949$		−	30.0490i		−	0.975432i
$950$	−3.11971	+	6.34566i	−0.101217	+	0.205880i
$951$		−	23.3760i		−	0.758019i
$952$	3.50462	+	2.06581i	0.113585	+	0.0669533i
$953$	−20.9223	−	20.9223i	−0.677740	−	0.677740i	0.281748	−	0.959488i	$-0.409086\pi$
$953$	−20.9223	−	20.9223i	−0.677740	−	0.677740i	−0.959488	+	0.281748i	$0.909086\pi$
$954$	0.000449202		0.00531876i	1.45435e−5		0.000172201i
$955$	−0.931869	−	7.59365i	−0.0301546	−	0.245725i
$956$	0.263648	+	1.54972i	0.00852697	+	0.0501215i
$957$	12.5967	−	12.5967i	0.407194	−	0.407194i
$958$	−26.9557	+	31.9289i	−0.870899	+	1.03157i
$959$	6.93290			0.223875
$960$	33.4827	+	5.32628i	1.08065	+	0.171905i
$961$	−55.4756			−1.78954
$962$	−34.3873	+	40.7316i	−1.10869	+	1.31324i
$963$	6.74167	−	6.74167i	0.217247	−	0.217247i
$964$	−6.15514	−	36.1799i	−0.198244	−	1.16528i
$965$	−35.2482	−	27.5427i	−1.13468	−	0.886630i
$966$	−2.01649	−	23.8762i	−0.0648795	−	0.768203i
$967$	30.9050	+	30.9050i	0.993839	+	0.993839i	0.999981	−	0.00614252i	$-0.00195524\pi$
$967$	30.9050	+	30.9050i	0.993839	+	0.993839i	−0.00614252	+	0.999981i	$0.501955\pi$
$968$	28.0872	+	16.5561i	0.902757	+	0.532134i
$969$			2.76258i			0.0887468i
$970$	−7.59820	−	36.2955i	−0.243964	−	1.16538i
$971$			5.36484i			0.172166i	0.996288	+	0.0860829i	$0.0274350\pi$
$971$			5.36484i			0.172166i	−0.996288	+	0.0860829i	$0.972565\pi$
$972$	9.89968	+	7.02103i	0.317532	+	0.225200i
$973$	2.94095	+	2.94095i	0.0942826	+	0.0942826i
$974$	57.3861	−	4.84661i	1.83877	−	0.155295i
$975$	−42.9772	+	10.7093i	−1.37637	+	0.342973i
$976$	2.73604	−	0.958692i	0.0875787	−	0.0306870i
$977$	−21.3158	+	21.3158i	−0.681953	+	0.681953i	−0.960440	−	0.278487i	$-0.910167\pi$
$977$	−21.3158	+	21.3158i	−0.681953	+	0.681953i	0.278487	+	0.960440i	$0.410167\pi$
$978$	24.6195	+	20.7848i	0.787244	+	0.664625i
$979$	−38.6142			−1.23412
$980$	25.8204	−	7.72254i	0.824801	−	0.246687i
$981$	5.98318			0.191028
$982$	−3.08111	−	2.60120i	−0.0983222	−	0.0830077i
$983$	0.756505	−	0.756505i	0.0241288	−	0.0241288i	−0.694939	−	0.719068i	$-0.744569\pi$
$983$	0.756505	−	0.756505i	0.0241288	−	0.0241288i	0.719068	+	0.694939i	$0.244569\pi$
$984$	48.8689	−	12.6225i	1.55788	−	0.402391i
$985$	7.67700	−	9.82476i	0.244610	−	0.313043i
$986$	−4.06782	+	0.343553i	−0.129546	+	0.0109409i
$987$	−2.07040	−	2.07040i	−0.0659015	−	0.0659015i
$988$	−5.40766	+	7.62482i	−0.172040	+	0.242578i
$989$			24.2966i			0.772586i
$990$	−4.86270	+	7.43771i	−0.154547	+	0.236386i
$991$			11.1144i			0.353061i	0.984295	+	0.176530i	$0.0564874\pi$
$991$			11.1144i			0.353061i	−0.984295	+	0.176530i	$0.943513\pi$
$992$	49.1556	+	18.7337i	1.56069	+	0.594795i
$993$	16.7754	+	16.7754i	0.532352	+	0.532352i
$994$	−1.09144	−	12.9231i	−0.0346184	−	0.409897i
$995$	−50.2684	+	6.16878i	−1.59361	+	0.195564i
$996$	−11.3820	+	1.93637i	−0.360652	+	0.0613563i
$997$	−34.7183	+	34.7183i	−1.09954	+	1.09954i	−0.105075	+	0.994464i	$0.533508\pi$
$997$	−34.7183	+	34.7183i	−1.09954	+	1.09954i	−0.994464	+	0.105075i	$0.966492\pi$
$998$	−11.1525	+	13.2101i	−0.353027	+	0.418159i
$999$	36.8046			1.16445

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.k.d.343.19	yes	52
4.3	odd	2		380.2.k.c.343.20	yes	52
5.2	odd	4		380.2.k.c.267.20	✓	52
20.7	even	4	inner	380.2.k.d.267.19	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.k.c.267.20	✓	52	5.2	odd	4
380.2.k.c.343.20	yes	52	4.3	odd	2
380.2.k.d.267.19	yes	52	20.7	even	4	inner
380.2.k.d.343.19	yes	52	1.1	even	1	trivial

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

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