LMFDB - Embedded newform 770.2.l.c.573.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(573,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 2, 0]))

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

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

chi := DirichletCharacter("770.573");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.l (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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			573.3
Character	$\chi$	$=$	770.573
Dual form			770.2.l.c.727.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-0.903547 + 0.903547i) q^{3} -1.00000i q^{4} +(-1.41673 - 1.72999i) q^{5} -1.27781i q^{6} +(1.36406 + 2.26701i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.36720i q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.903547 + 0.903547i) q^{3} -1.00000i q^{4} +(-1.41673 - 1.72999i) q^{5} -1.27781i q^{6} +(1.36406 + 2.26701i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.36720i q^{9} +(2.22507 + 0.221508i) q^{10} -1.00000 q^{11} +(0.903547 + 0.903547i) q^{12} +(4.51196 - 4.51196i) q^{13} +(-2.56755 - 0.638484i) q^{14} +(2.84321 + 0.283045i) q^{15} -1.00000 q^{16} +(-4.77930 - 4.77930i) q^{17} +(-0.966759 - 0.966759i) q^{18} +6.06268 q^{19} +(-1.72999 + 1.41673i) q^{20} +(-3.28084 - 0.815861i) q^{21} +(0.707107 - 0.707107i) q^{22} +(1.28935 + 1.28935i) q^{23} -1.27781 q^{24} +(-0.985742 + 4.90187i) q^{25} +6.38087i q^{26} +(-3.94598 - 3.94598i) q^{27} +(2.26701 - 1.36406i) q^{28} +7.55147i q^{29} +(-2.21060 + 1.81031i) q^{30} +7.78472i q^{31} +(0.707107 - 0.707107i) q^{32} +(0.903547 - 0.903547i) q^{33} +6.75895 q^{34} +(1.98941 - 5.57156i) q^{35} +1.36720 q^{36} +(4.82324 - 4.82324i) q^{37} +(-4.28696 + 4.28696i) q^{38} +8.15354i q^{39} +(0.221508 - 2.22507i) q^{40} +5.27619i q^{41} +(2.89681 - 1.74301i) q^{42} +(6.22344 + 6.22344i) q^{43} +1.00000i q^{44} +(2.36525 - 1.93696i) q^{45} -1.82342 q^{46} +(4.65334 + 4.65334i) q^{47} +(0.903547 - 0.903547i) q^{48} +(-3.27869 + 6.18468i) q^{49} +(-2.76912 - 4.16317i) q^{50} +8.63665 q^{51} +(-4.51196 - 4.51196i) q^{52} +(4.24814 + 4.24814i) q^{53} +5.58045 q^{54} +(1.41673 + 1.72999i) q^{55} +(-0.638484 + 2.56755i) q^{56} +(-5.47792 + 5.47792i) q^{57} +(-5.33970 - 5.33970i) q^{58} +1.55180 q^{59} +(0.283045 - 2.84321i) q^{60} -0.913067i q^{61} +(-5.50463 - 5.50463i) q^{62} +(-3.09947 + 1.86495i) q^{63} +1.00000i q^{64} +(-14.1979 - 1.41342i) q^{65} +1.27781i q^{66} +(-8.57879 + 8.57879i) q^{67} +(-4.77930 + 4.77930i) q^{68} -2.32998 q^{69} +(2.53296 + 5.34641i) q^{70} +6.02338 q^{71} +(-0.966759 + 0.966759i) q^{72} +(-2.79071 + 2.79071i) q^{73} +6.82109i q^{74} +(-3.53841 - 5.31974i) q^{75} -6.06268i q^{76} +(-1.36406 - 2.26701i) q^{77} +(-5.76542 - 5.76542i) q^{78} -6.11533i q^{79} +(1.41673 + 1.72999i) q^{80} +3.02914 q^{81} +(-3.73083 - 3.73083i) q^{82} +(5.04120 - 5.04120i) q^{83} +(-0.815861 + 3.28084i) q^{84} +(-1.49716 + 15.0391i) q^{85} -8.80128 q^{86} +(-6.82312 - 6.82312i) q^{87} +(-0.707107 - 0.707107i) q^{88} +7.76249 q^{89} +(-0.302847 + 3.04212i) q^{90} +(16.3832 + 4.07409i) q^{91} +(1.28935 - 1.28935i) q^{92} +(-7.03386 - 7.03386i) q^{93} -6.58082 q^{94} +(-8.58919 - 10.4884i) q^{95} +1.27781i q^{96} +(-6.01682 - 6.01682i) q^{97} +(-2.05484 - 6.69161i) q^{98} -1.36720i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q+O(q^{10}) $ 40 * q	$ 40 q - 40 q^{11} + 56 q^{15} - 40 q^{16} - 8 q^{18} - 4 q^{21} - 32 q^{25} - 24 q^{30} + 48 q^{35} - 48 q^{36} - 8 q^{37} - 40 q^{42} - 8 q^{43} + 32 q^{46} + 16 q^{50} - 8 q^{51} + 56 q^{53} + 4 q^{56} + 32 q^{57} - 8 q^{58} + 8 q^{60} - 16 q^{63} + 8 q^{65} - 24 q^{67} - 4 q^{70} - 24 q^{71} - 8 q^{72} - 16 q^{78} - 24 q^{81} + 96 q^{85} - 96 q^{86} + 64 q^{91} + 24 q^{93} - 112 q^{95} + 16 q^{98}+O(q^{100}) $ 40 * q - 40 * q^11 + 56 * q^15 - 40 * q^16 - 8 * q^18 - 4 * q^21 - 32 * q^25 - 24 * q^30 + 48 * q^35 - 48 * q^36 - 8 * q^37 - 40 * q^42 - 8 * q^43 + 32 * q^46 + 16 * q^50 - 8 * q^51 + 56 * q^53 + 4 * q^56 + 32 * q^57 - 8 * q^58 + 8 * q^60 - 16 * q^63 + 8 * q^65 - 24 * q^67 - 4 * q^70 - 24 * q^71 - 8 * q^72 - 16 * q^78 - 24 * q^81 + 96 * q^85 - 96 * q^86 + 64 * q^91 + 24 * q^93 - 112 * q^95 + 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−0.903547	+	0.903547i	−0.521663	+	0.521663i	−0.918074	−	0.396410i	$-0.870256\pi$
$3$	−0.903547	+	0.903547i	−0.521663	+	0.521663i	0.396410	+	0.918074i	$0.370256\pi$
$4$		−	1.00000i		−	0.500000i
$5$	−1.41673	−	1.72999i	−0.633582	−	0.773676i
$5$	−1.41673	−	1.72999i	−0.633582	−	0.773676i
$6$		−	1.27781i		−	0.521663i
$7$	1.36406	+	2.26701i	0.515566	+	0.856850i
$7$	1.36406	+	2.26701i	0.515566	+	0.856850i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$			1.36720i			0.455735i
$10$	2.22507	+	0.221508i	0.703629	+	0.0700470i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$	0.903547	+	0.903547i	0.260832	+	0.260832i
$13$	4.51196	−	4.51196i	1.25139	−	1.25139i	0.296296	−	0.955096i	$-0.404249\pi$
$13$	4.51196	−	4.51196i	1.25139	−	1.25139i	0.955096	−	0.296296i	$-0.0957514\pi$
$14$	−2.56755	−	0.638484i	−0.686208	−	0.170642i
$15$	2.84321	+	0.283045i	0.734115	+	0.0730820i
$16$	−1.00000			−0.250000
$17$	−4.77930	−	4.77930i	−1.15915	−	1.15915i	−0.984659	−	0.174492i	$-0.944172\pi$
$17$	−4.77930	−	4.77930i	−1.15915	−	1.15915i	−0.174492	−	0.984659i	$-0.555828\pi$
$18$	−0.966759	−	0.966759i	−0.227867	−	0.227867i
$19$	6.06268			1.39087			0.695437	−	0.718587i	$-0.255211\pi$
$19$	6.06268			1.39087			0.695437	+	0.718587i	$0.255211\pi$
$20$	−1.72999	+	1.41673i	−0.386838	+	0.316791i
$21$	−3.28084	−	0.815861i	−0.715939	−	0.178035i
$22$	0.707107	−	0.707107i	0.150756	−	0.150756i
$23$	1.28935	+	1.28935i	0.268848	+	0.268848i	0.828636	−	0.559788i	$-0.189117\pi$
$23$	1.28935	+	1.28935i	0.268848	+	0.268848i	−0.559788	+	0.828636i	$0.689117\pi$
$24$	−1.27781			−0.260832
$25$	−0.985742	+	4.90187i	−0.197148	+	0.980374i
$26$			6.38087i			1.25139i
$27$	−3.94598	−	3.94598i	−0.759403	−	0.759403i
$28$	2.26701	−	1.36406i	0.428425	−	0.257783i
$29$			7.55147i			1.40227i	0.713027	+	0.701137i	$0.247324\pi$
$29$			7.55147i			1.40227i	−0.713027	+	0.701137i	$0.752676\pi$
$30$	−2.21060	+	1.81031i	−0.403598	+	0.330516i
$31$			7.78472i			1.39818i	0.715036	+	0.699088i	$0.246411\pi$
$31$			7.78472i			1.39818i	−0.715036	+	0.699088i	$0.753589\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	0.903547	−	0.903547i	0.157287	−	0.157287i
$34$	6.75895			1.15915
$35$	1.98941	−	5.57156i	0.336271	−	0.941765i
$36$	1.36720			0.227867
$37$	4.82324	−	4.82324i	0.792935	−	0.792935i	−0.189035	−	0.981970i	$-0.560536\pi$
$37$	4.82324	−	4.82324i	0.792935	−	0.792935i	0.981970	+	0.189035i	$0.0605360\pi$
$38$	−4.28696	+	4.28696i	−0.695437	+	0.695437i
$39$			8.15354i			1.30561i
$40$	0.221508	−	2.22507i	0.0350235	−	0.351814i
$41$			5.27619i			0.824003i	0.911183	+	0.412001i	$0.135170\pi$
$41$			5.27619i			0.824003i	−0.911183	+	0.412001i	$0.864830\pi$
$42$	2.89681	−	1.74301i	0.446987	−	0.268952i
$43$	6.22344	+	6.22344i	0.949066	+	0.949066i	0.998764	−	0.0496984i	$-0.0158260\pi$
$43$	6.22344	+	6.22344i	0.949066	+	0.949066i	−0.0496984	+	0.998764i	$0.515826\pi$
$44$			1.00000i			0.150756i
$45$	2.36525	−	1.93696i	0.352591	−	0.288745i
$46$	−1.82342			−0.268848
$47$	4.65334	+	4.65334i	0.678760	+	0.678760i	0.959720	−	0.280960i	$-0.0906527\pi$
$47$	4.65334	+	4.65334i	0.678760	+	0.678760i	−0.280960	+	0.959720i	$0.590653\pi$
$48$	0.903547	−	0.903547i	0.130416	−	0.130416i
$49$	−3.27869	+	6.18468i	−0.468384	+	0.883525i
$50$	−2.76912	−	4.16317i	−0.391613	−	0.588761i
$51$	8.63665			1.20937
$52$	−4.51196	−	4.51196i	−0.625696	−	0.625696i
$53$	4.24814	+	4.24814i	0.583527	+	0.583527i	0.935871	−	0.352344i	$-0.114615\pi$
$53$	4.24814	+	4.24814i	0.583527	+	0.583527i	−0.352344	+	0.935871i	$0.614615\pi$
$54$	5.58045			0.759403
$55$	1.41673	+	1.72999i	0.191032	+	0.233272i
$56$	−0.638484	+	2.56755i	−0.0853211	+	0.343104i
$57$	−5.47792	+	5.47792i	−0.725568	+	0.725568i
$58$	−5.33970	−	5.33970i	−0.701137	−	0.701137i
$59$	1.55180			0.202027			0.101013	−	0.994885i	$-0.467792\pi$
$59$	1.55180			0.202027			0.101013	+	0.994885i	$0.467792\pi$
$60$	0.283045	−	2.84321i	0.0365410	−	0.367057i
$61$		−	0.913067i		−	0.116906i	−0.998290	−	0.0584531i	$-0.981383\pi$
$61$		−	0.913067i		−	0.116906i	0.998290	−	0.0584531i	$-0.0186168\pi$
$62$	−5.50463	−	5.50463i	−0.699088	−	0.699088i
$63$	−3.09947	+	1.86495i	−0.390496	+	0.234961i
$64$			1.00000i			0.125000i
$65$	−14.1979	−	1.41342i	−1.76103	−	0.175313i
$66$			1.27781i			0.157287i
$67$	−8.57879	+	8.57879i	−1.04807	+	1.04807i	−0.0492814	+	0.998785i	$0.515693\pi$
$67$	−8.57879	+	8.57879i	−1.04807	+	1.04807i	−0.998785	+	0.0492814i	$0.984307\pi$
$68$	−4.77930	+	4.77930i	−0.579575	+	0.579575i
$69$	−2.32998			−0.280496
$70$	2.53296	+	5.34641i	0.302747	+	0.639018i
$71$	6.02338			0.714843			0.357422	−	0.933943i	$-0.383656\pi$
$71$	6.02338			0.714843			0.357422	+	0.933943i	$0.383656\pi$
$72$	−0.966759	+	0.966759i	−0.113934	+	0.113934i
$73$	−2.79071	+	2.79071i	−0.326627	+	0.326627i	−0.851303	−	0.524675i	$-0.824187\pi$
$73$	−2.79071	+	2.79071i	−0.326627	+	0.326627i	0.524675	+	0.851303i	$0.324187\pi$
$74$			6.82109i			0.792935i
$75$	−3.53841	−	5.31974i	−0.408580	−	0.614270i
$76$		−	6.06268i		−	0.695437i
$77$	−1.36406	−	2.26701i	−0.155449	−	0.258350i
$78$	−5.76542	−	5.76542i	−0.652805	−	0.652805i
$79$		−	6.11533i		−	0.688029i	−0.938964	−	0.344014i	$-0.888213\pi$
$79$		−	6.11533i		−	0.688029i	0.938964	−	0.344014i	$-0.111787\pi$
$80$	1.41673	+	1.72999i	0.158395	+	0.193419i
$81$	3.02914			0.336571
$82$	−3.73083	−	3.73083i	−0.412001	−	0.412001i
$83$	5.04120	−	5.04120i	0.553344	−	0.553344i	−0.374060	−	0.927404i	$-0.622035\pi$
$83$	5.04120	−	5.04120i	0.553344	−	0.553344i	0.927404	+	0.374060i	$0.122035\pi$
$84$	−0.815861	+	3.28084i	−0.0890177	+	0.357970i
$85$	−1.49716	+	15.0391i	−0.162390	+	1.63122i
$86$	−8.80128			−0.949066
$87$	−6.82312	−	6.82312i	−0.731515	−	0.731515i
$88$	−0.707107	−	0.707107i	−0.0753778	−	0.0753778i
$89$	7.76249			0.822822			0.411411	−	0.911450i	$-0.365036\pi$
$89$	7.76249			0.822822			0.411411	+	0.911450i	$0.365036\pi$
$90$	−0.302847	+	3.04212i	−0.0319229	+	0.320668i
$91$	16.3832	+	4.07409i	1.71743	+	0.427080i
$92$	1.28935	−	1.28935i	0.134424	−	0.134424i
$93$	−7.03386	−	7.03386i	−0.729377	−	0.729377i
$94$	−6.58082			−0.678760
$95$	−8.58919	−	10.4884i	−0.881233	−	1.07609i
$96$			1.27781i			0.130416i
$97$	−6.01682	−	6.01682i	−0.610916	−	0.610916i	0.332269	−	0.943185i	$-0.392186\pi$
$97$	−6.01682	−	6.01682i	−0.610916	−	0.610916i	−0.943185	+	0.332269i	$0.892186\pi$
$98$	−2.05484	−	6.69161i	−0.207571	−	0.675954i
$99$		−	1.36720i		−	0.137409i
$100$	4.90187	+	0.985742i	0.490187	+	0.0985742i
$101$			11.9147i			1.18555i	0.805367	+	0.592777i	$0.201968\pi$
$101$			11.9147i			1.18555i	−0.805367	+	0.592777i	$0.798032\pi$
$102$	−6.10703	+	6.10703i	−0.604686	+	0.604686i
$103$	4.70655	−	4.70655i	0.463750	−	0.463750i	−0.436133	−	0.899882i	$-0.643652\pi$
$103$	4.70655	−	4.70655i	0.463750	−	0.463750i	0.899882	+	0.436133i	$0.143652\pi$
$104$	6.38087			0.625696
$105$	3.23664	+	6.83169i	0.315864	+	0.666705i
$106$	−6.00777			−0.583527
$107$	−6.67198	+	6.67198i	−0.645005	+	0.645005i	−0.951782	−	0.306777i	$-0.900750\pi$
$107$	−6.67198	+	6.67198i	−0.645005	+	0.645005i	0.306777	+	0.951782i	$0.400750\pi$
$108$	−3.94598	+	3.94598i	−0.379702	+	0.379702i
$109$		−	4.01592i		−	0.384655i	−0.981331	−	0.192328i	$-0.938396\pi$
$109$		−	4.01592i		−	0.384655i	0.981331	−	0.192328i	$-0.0616037\pi$
$110$	−2.22507	−	0.221508i	−0.212152	−	0.0211200i
$111$			8.71604i			0.827290i
$112$	−1.36406	−	2.26701i	−0.128891	−	0.214213i
$113$	−2.80703	−	2.80703i	−0.264064	−	0.264064i	0.562639	−	0.826703i	$-0.309786\pi$
$113$	−2.80703	−	2.80703i	−0.264064	−	0.264064i	−0.826703	+	0.562639i	$0.809786\pi$
$114$		−	7.74695i		−	0.725568i
$115$	0.403902	−	4.05723i	0.0376640	−	0.378339i
$116$	7.55147			0.701137
$117$	6.16877	+	6.16877i	0.570303	+	0.570303i
$118$	−1.09729	+	1.09729i	−0.101013	+	0.101013i
$119$	4.31548	−	17.3540i	0.395600	−	1.59084i
$120$	1.81031	+	2.21060i	0.165258	+	0.201799i
$121$	1.00000			0.0909091
$122$	0.645636	+	0.645636i	0.0584531	+	0.0584531i
$123$	−4.76729	−	4.76729i	−0.429852	−	0.429852i
$124$	7.78472			0.699088
$125$	9.87672	−	5.23931i	0.883401	−	0.468618i
$126$	0.872938	−	3.51037i	0.0777675	−	0.312729i
$127$	6.14002	−	6.14002i	0.544839	−	0.544839i	−0.380105	−	0.924943i	$-0.624112\pi$
$127$	6.14002	−	6.14002i	0.544839	−	0.544839i	0.924943	+	0.380105i	$0.124112\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−11.2463			−0.990186
$130$	11.0389	−	9.03998i	0.968172	−	0.792859i
$131$		−	3.78268i		−	0.330495i	−0.986252	−	0.165247i	$-0.947158\pi$
$131$		−	3.78268i		−	0.330495i	0.986252	−	0.165247i	$-0.0528422\pi$
$132$	−0.903547	−	0.903547i	−0.0786437	−	0.0786437i
$133$	8.26985	+	13.7442i	0.717087	+	1.19177i
$134$		−	12.1322i		−	1.04807i
$135$	−1.23612	+	12.4169i	−0.106388	+	1.06868i
$136$		−	6.75895i		−	0.579575i
$137$	12.1143	−	12.1143i	1.03500	−	1.03500i	0.0356308	−	0.999365i	$-0.488656\pi$
$137$	12.1143	−	12.1143i	1.03500	−	1.03500i	0.999365	−	0.0356308i	$-0.0113440\pi$
$138$	1.64754	−	1.64754i	0.140248	−	0.140248i
$139$	11.2832			0.957027			0.478513	−	0.878080i	$-0.341176\pi$
$139$	11.2832			0.957027			0.478513	+	0.878080i	$0.341176\pi$
$140$	−5.57156	−	1.98941i	−0.470883	−	0.168136i
$141$	−8.40904			−0.708169
$142$	−4.25917	+	4.25917i	−0.357422	+	0.357422i
$143$	−4.51196	+	4.51196i	−0.377309	+	0.377309i
$144$		−	1.36720i		−	0.113934i
$145$	13.0640	−	10.6984i	1.08491	−	0.888455i
$146$		−	3.94665i		−	0.326627i
$147$	−2.62570	−	8.55060i	−0.216564	−	0.705241i
$148$	−4.82324	−	4.82324i	−0.396468	−	0.396468i
$149$			12.3218i			1.00944i	0.863282	+	0.504721i	$0.168405\pi$
$149$			12.3218i			1.00944i	−0.863282	+	0.504721i	$0.831595\pi$
$150$	6.26365	+	1.25959i	0.511425	+	0.102845i
$151$	−1.30380			−0.106101			−0.0530507	−	0.998592i	$-0.516894\pi$
$151$	−1.30380			−0.106101			−0.0530507	+	0.998592i	$0.516894\pi$
$152$	4.28696	+	4.28696i	0.347719	+	0.347719i
$153$	6.53428	−	6.53428i	0.528265	−	0.528265i
$154$	2.56755	+	0.638484i	0.206899	+	0.0514505i
$155$	13.4675	−	11.0289i	1.08174	−	0.885859i
$156$	8.15354			0.652805
$157$	−4.57812	−	4.57812i	−0.365374	−	0.365374i	0.500413	−	0.865787i	$-0.333181\pi$
$157$	−4.57812	−	4.57812i	−0.365374	−	0.365374i	−0.865787	+	0.500413i	$0.833181\pi$
$158$	4.32419	+	4.32419i	0.344014	+	0.344014i
$159$	−7.67679			−0.608809
$160$	−2.22507	−	0.221508i	−0.175907	−	0.0175118i
$161$	−1.16422	+	4.68172i	−0.0917536	+	0.368971i
$162$	−2.14193	+	2.14193i	−0.168286	+	0.168286i
$163$	7.74337	+	7.74337i	0.606508	+	0.606508i	0.942032	−	0.335524i	$-0.108913\pi$
$163$	7.74337	+	7.74337i	0.606508	+	0.606508i	−0.335524	+	0.942032i	$0.608913\pi$
$164$	5.27619			0.412001
$165$	−2.84321	−	0.283045i	−0.221344	−	0.0220350i
$166$			7.12934i			0.553344i
$167$	−2.03274	−	2.03274i	−0.157298	−	0.157298i	0.624070	−	0.781368i	$-0.285478\pi$
$167$	−2.03274	−	2.03274i	−0.157298	−	0.157298i	−0.781368	+	0.624070i	$0.785478\pi$
$168$	−1.74301	−	2.89681i	−0.134476	−	0.223494i
$169$		−	27.7155i		−	2.13196i
$170$	−9.57562	−	11.6929i	−0.734417	−	0.896807i
$171$			8.28892i			0.633870i
$172$	6.22344	−	6.22344i	0.474533	−	0.474533i
$173$	−12.5579	+	12.5579i	−0.954759	+	0.954759i	−0.999020	−	0.0442614i	$-0.985907\pi$
$173$	−12.5579	+	12.5579i	−0.954759	+	0.954759i	0.0442614	+	0.999020i	$0.485907\pi$
$174$	9.64934			0.731515
$175$	−12.4572	+	4.45175i	−0.941676	+	0.336520i
$176$	1.00000			0.0753778
$177$	−1.40212	+	1.40212i	−0.105390	+	0.105390i
$178$	−5.48891	+	5.48891i	−0.411411	+	0.411411i
$179$		−	15.0363i		−	1.12387i	−0.827182	−	0.561934i	$-0.810058\pi$
$179$		−	15.0363i		−	1.12387i	0.827182	−	0.561934i	$-0.189942\pi$
$180$	−1.93696	−	2.36525i	−0.144373	−	0.176295i
$181$			13.8733i			1.03119i	0.856832	+	0.515596i	$0.172430\pi$
$181$			13.8733i			1.03119i	−0.856832	+	0.515596i	$0.827570\pi$
$182$	−14.4655	+	8.70389i	−1.07226	+	0.645175i
$183$	0.824999	+	0.824999i	0.0609857	+	0.0609857i
$184$			1.82342i			0.134424i
$185$	−15.1774	−	1.51093i	−1.11586	−	0.111086i
$186$	9.94738			0.729377
$187$	4.77930	+	4.77930i	0.349497	+	0.349497i
$188$	4.65334	−	4.65334i	0.339380	−	0.339380i
$189$	3.56303	−	14.3281i	0.259172	−	1.04222i
$190$	13.4899	+	1.34293i	0.978659	+	0.0974267i
$191$	2.93911			0.212666			0.106333	−	0.994331i	$-0.466089\pi$
$191$	2.93911			0.212666			0.106333	+	0.994331i	$0.466089\pi$
$192$	−0.903547	−	0.903547i	−0.0652079	−	0.0652079i
$193$	11.5176	+	11.5176i	0.829053	+	0.829053i	0.987386	−	0.158333i	$-0.0506118\pi$
$193$	11.5176	+	11.5176i	0.829053	+	0.829053i	−0.158333	+	0.987386i	$0.550612\pi$
$194$	8.50907			0.610916
$195$	14.1056	−	11.5514i	1.01012	−	0.827211i
$196$	6.18468	+	3.27869i	0.441763	+	0.234192i
$197$	16.3524	−	16.3524i	1.16506	−	1.16506i	0.181711	−	0.983352i	$-0.441836\pi$
$197$	16.3524	−	16.3524i	1.16506	−	1.16506i	0.983352	−	0.181711i	$-0.0581636\pi$
$198$	0.966759	+	0.966759i	0.0687046	+	0.0687046i
$199$	−15.7021			−1.11309			−0.556547	−	0.830816i	$-0.687874\pi$
$199$	−15.7021			−1.11309			−0.556547	+	0.830816i	$0.687874\pi$
$200$	−4.16317	+	2.76912i	−0.294381	+	0.195806i
$201$		−	15.5027i		−	1.09348i
$202$	−8.42494	−	8.42494i	−0.592777	−	0.592777i
$203$	−17.1193	+	10.3007i	−1.20154	+	0.722964i
$204$		−	8.63665i		−	0.604686i
$205$	9.12777	−	7.47495i	0.637511	−	0.522073i
$206$			6.65606i			0.463750i
$207$	−1.76280	+	1.76280i	−0.122523	+	0.122523i
$208$	−4.51196	+	4.51196i	−0.312848	+	0.312848i
$209$	−6.06268			−0.419364
$210$	−7.11939	−	2.54208i	−0.491284	−	0.175420i
$211$	6.03962			0.415784			0.207892	−	0.978152i	$-0.433340\pi$
$211$	6.03962			0.415784			0.207892	+	0.978152i	$0.433340\pi$
$212$	4.24814	−	4.24814i	0.291763	−	0.291763i
$213$	−5.44241	+	5.44241i	−0.372908	+	0.372908i
$214$		−	9.43561i		−	0.645005i
$215$	1.94955	−	19.5834i	0.132959	−	1.33558i
$216$		−	5.58045i		−	0.379702i
$217$	−17.6480	+	10.6188i	−1.19803	+	0.720852i
$218$	2.83969	+	2.83969i	0.192328	+	0.192328i
$219$		−	5.04307i		−	0.340779i
$220$	1.72999	−	1.41673i	0.116636	−	0.0955160i
$221$	−43.1280			−2.90110
$222$	−6.16317	−	6.16317i	−0.413645	−	0.413645i
$223$	5.52624	−	5.52624i	0.370064	−	0.370064i	−0.497436	−	0.867501i	$-0.665725\pi$
$223$	5.52624	−	5.52624i	0.370064	−	0.370064i	0.867501	+	0.497436i	$0.165725\pi$
$224$	2.56755	+	0.638484i	0.171552	+	0.0426605i
$225$	−6.70185	−	1.34771i	−0.446790	−	0.0898474i
$226$	3.96975			0.264064
$227$	−8.48532	−	8.48532i	−0.563190	−	0.563190i	0.367022	−	0.930212i	$-0.380377\pi$
$227$	−8.48532	−	8.48532i	−0.563190	−	0.563190i	−0.930212	+	0.367022i	$0.880377\pi$
$228$	5.47792	+	5.47792i	0.362784	+	0.362784i
$229$	−15.3666			−1.01545			−0.507727	−	0.861518i	$-0.669514\pi$
$229$	−15.3666			−1.01545			−0.507727	+	0.861518i	$0.669514\pi$
$230$	2.58329	+	3.15450i	0.170337	+	0.208001i
$231$	3.28084	+	0.815861i	0.215864	+	0.0536797i
$232$	−5.33970	+	5.33970i	−0.350568	+	0.350568i
$233$	−8.25655	−	8.25655i	−0.540905	−	0.540905i	0.382889	−	0.923794i	$-0.374929\pi$
$233$	−8.25655	−	8.25655i	−0.540905	−	0.540905i	−0.923794	+	0.382889i	$0.874929\pi$
$234$	−8.72395			−0.570303
$235$	1.45771	−	14.6428i	0.0950903	−	0.955190i
$236$		−	1.55180i		−	0.101013i
$237$	5.52549	+	5.52549i	0.358919	+	0.358919i
$238$	9.21961	+	15.3226i	0.597618	+	0.993218i
$239$			16.8327i			1.08881i	0.838821	+	0.544407i	$0.183245\pi$
$239$			16.8327i			1.08881i	−0.838821	+	0.544407i	$0.816755\pi$
$240$	−2.84321	−	0.283045i	−0.183529	−	0.0182705i
$241$			18.0615i			1.16344i	0.813388	+	0.581721i	$0.197621\pi$
$241$			18.0615i			1.16344i	−0.813388	+	0.581721i	$0.802379\pi$
$242$	−0.707107	+	0.707107i	−0.0454545	+	0.0454545i
$243$	9.10095	−	9.10095i	0.583827	−	0.583827i
$244$	−0.913067			−0.0584531
$245$	15.3445	−	3.08992i	0.980321	−	0.197408i
$246$	6.74196			0.429852
$247$	27.3546	−	27.3546i	1.74053	−	1.74053i
$248$	−5.50463	+	5.50463i	−0.349544	+	0.349544i
$249$			9.10993i			0.577319i
$250$	−3.27915	+	10.6886i	−0.207392	+	0.676009i
$251$		−	8.99865i		−	0.567990i	−0.958826	−	0.283995i	$-0.908340\pi$
$251$		−	8.99865i		−	0.567990i	0.958826	−	0.283995i	$-0.0916599\pi$
$252$	1.86495	+	3.09947i	0.117481	+	0.195248i
$253$	−1.28935	−	1.28935i	−0.0810608	−	0.0810608i
$254$			8.68330i			0.544839i
$255$	−12.2358	−	14.9413i	−0.766237	−	0.935662i
$256$	1.00000			0.0625000
$257$	−6.62646	−	6.62646i	−0.413347	−	0.413347i	0.469556	−	0.882903i	$-0.344414\pi$
$257$	−6.62646	−	6.62646i	−0.413347	−	0.413347i	−0.882903	+	0.469556i	$0.844414\pi$
$258$	7.95237	−	7.95237i	0.495093	−	0.495093i
$259$	17.5135	+	4.35516i	1.08824	+	0.270616i
$260$	−1.41342	+	14.1979i	−0.0876563	+	0.880515i
$261$	−10.3244			−0.639065
$262$	2.67476	+	2.67476i	0.165247	+	0.165247i
$263$	−3.70702	−	3.70702i	−0.228585	−	0.228585i	0.583517	−	0.812101i	$-0.301676\pi$
$263$	−3.70702	−	3.70702i	−0.228585	−	0.228585i	−0.812101	+	0.583517i	$0.801676\pi$
$264$	1.27781			0.0786437
$265$	1.33077	−	13.3677i	0.0817486	−	0.821172i
$266$	−15.5663	−	3.87093i	−0.954429	−	0.237342i
$267$	−7.01378	+	7.01378i	−0.429236	+	0.429236i
$268$	8.57879	+	8.57879i	0.524033	+	0.524033i
$269$	0.172624			0.0105251			0.00526255	−	0.999986i	$-0.498325\pi$
$269$	0.172624			0.0105251			0.00526255	+	0.999986i	$0.498325\pi$
$270$	−7.90600	−	9.65414i	−0.481144	−	0.587532i
$271$		−	1.31360i		−	0.0797953i	−0.999204	−	0.0398976i	$-0.987297\pi$
$271$		−	1.31360i		−	0.0797953i	0.999204	−	0.0398976i	$-0.0127032\pi$
$272$	4.77930	+	4.77930i	0.289788	+	0.289788i
$273$	−18.4842	+	11.1219i	−1.11871	+	0.673128i
$274$			17.1322i			1.03500i
$275$	0.985742	−	4.90187i	0.0594425	−	0.295594i
$276$			2.32998i			0.140248i
$277$	6.74454	−	6.74454i	0.405240	−	0.405240i	−0.474835	−	0.880075i	$-0.657492\pi$
$277$	6.74454	−	6.74454i	0.405240	−	0.405240i	0.880075	+	0.474835i	$0.157492\pi$
$278$	−7.97841	+	7.97841i	−0.478513	+	0.478513i
$279$	−10.6433			−0.637197
$280$	5.34641	−	2.53296i	0.319509	−	0.151374i
$281$	0.293644			0.0175173			0.00875867	−	0.999962i	$-0.497212\pi$
$281$	0.293644			0.0175173			0.00875867	+	0.999962i	$0.497212\pi$
$282$	5.94609	−	5.94609i	0.354084	−	0.354084i
$283$	12.1941	−	12.1941i	0.724866	−	0.724866i	−0.244726	−	0.969592i	$-0.578698\pi$
$283$	12.1941	−	12.1941i	0.724866	−	0.724866i	0.969592	+	0.244726i	$0.0786980\pi$
$284$		−	6.02338i		−	0.357422i
$285$	17.2375	+	1.71601i	1.02106	+	0.101648i
$286$		−	6.38087i		−	0.377309i
$287$	−11.9612	+	7.19703i	−0.706047	+	0.424828i
$288$	0.966759	+	0.966759i	0.0569668	+	0.0569668i
$289$			28.6834i			1.68726i
$290$	−1.67271	+	16.8026i	−0.0982251	+	0.986680i
$291$	10.8730			0.637385
$292$	2.79071	+	2.79071i	0.163314	+	0.163314i
$293$	−16.5925	+	16.5925i	−0.969342	+	0.969342i	−0.999544	−	0.0302022i	$-0.990385\pi$
$293$	−16.5925	+	16.5925i	−0.969342	+	0.969342i	0.0302022	+	0.999544i	$0.490385\pi$
$294$	7.90283	+	4.18954i	0.460903	+	0.244339i
$295$	−2.19848	−	2.68460i	−0.128000	−	0.156303i
$296$	6.82109			0.396468
$297$	3.94598	+	3.94598i	0.228969	+	0.228969i
$298$	−8.71284	−	8.71284i	−0.504721	−	0.504721i
$299$	11.6350			0.672869
$300$	−5.31974	+	3.53841i	−0.307135	+	0.204290i
$301$	−5.61948	+	22.5978i	−0.323901	+	1.30251i
$302$	0.921922	−	0.921922i	0.0530507	−	0.0530507i
$303$	−10.7655	−	10.7655i	−0.618460	−	0.618460i
$304$	−6.06268			−0.347719
$305$	−1.57960	+	1.29357i	−0.0904475	+	0.0740696i
$306$			9.24086i			0.528265i
$307$	11.9789	+	11.9789i	0.683670	+	0.683670i	0.960825	−	0.277155i	$-0.0893915\pi$
$307$	11.9789	+	11.9789i	0.683670	+	0.683670i	−0.277155	+	0.960825i	$0.589392\pi$
$308$	−2.26701	+	1.36406i	−0.129175	+	0.0777245i
$309$			8.50517i			0.483842i
$310$	−1.72438	+	17.3215i	−0.0979381	+	0.983797i
$311$			2.03050i			0.115139i	0.998342	+	0.0575695i	$0.0183351\pi$
$311$			2.03050i			0.115139i	−0.998342	+	0.0575695i	$0.981665\pi$
$312$	−5.76542	+	5.76542i	−0.326403	+	0.326403i
$313$	−1.38288	+	1.38288i	−0.0781648	+	0.0781648i	−0.745108	−	0.666944i	$-0.767602\pi$
$313$	−1.38288	+	1.38288i	−0.0781648	+	0.0781648i	0.666944	+	0.745108i	$0.267602\pi$
$314$	6.47444			0.365374
$315$	7.61746	+	2.71992i	0.429195	+	0.153250i
$316$	−6.11533			−0.344014
$317$	−0.758491	+	0.758491i	−0.0426011	+	0.0426011i	−0.728086	−	0.685485i	$-0.759590\pi$
$317$	−0.758491	+	0.758491i	−0.0426011	+	0.0426011i	0.685485	+	0.728086i	$0.259590\pi$
$318$	5.42831	−	5.42831i	0.304404	−	0.304404i
$319$		−	7.55147i		−	0.422801i
$320$	1.72999	−	1.41673i	0.0967095	−	0.0791977i
$321$		−	12.0569i		−	0.672951i
$322$	−2.48725	−	4.13371i	−0.138609	−	0.230363i
$323$	−28.9754	−	28.9754i	−1.61223	−	1.61223i
$324$		−	3.02914i		−	0.168286i
$325$	17.6694	+	26.5647i	0.980122	+	1.47354i
$326$	−10.9508			−0.606508
$327$	3.62858	+	3.62858i	0.200661	+	0.200661i
$328$	−3.73083	+	3.73083i	−0.206001	+	0.206001i
$329$	−4.20175	+	16.8966i	−0.231650	+	0.931541i
$330$	2.21060	−	1.81031i	0.121689	−	0.0996544i
$331$	21.9453			1.20622			0.603111	−	0.797657i	$-0.293927\pi$
$331$	21.9453			1.20622			0.603111	+	0.797657i	$0.293927\pi$
$332$	−5.04120	−	5.04120i	−0.276672	−	0.276672i
$333$	6.59435	+	6.59435i	0.361368	+	0.361368i
$334$	2.87473			0.157298
$335$	26.9951	+	2.68739i	1.47490	+	0.146828i
$336$	3.28084	+	0.815861i	0.178985	+	0.0445089i
$337$	−24.9600	+	24.9600i	−1.35966	+	1.35966i	−0.485320	+	0.874337i	$0.661297\pi$
$337$	−24.9600	+	24.9600i	−1.35966	+	1.35966i	−0.874337	+	0.485320i	$0.838703\pi$
$338$	19.5978	+	19.5978i	1.06598	+	1.06598i
$339$	5.07258			0.275505
$340$	15.0391	+	1.49716i	0.815612	+	0.0811951i
$341$		−	7.78472i		−	0.421566i
$342$	−5.86115	−	5.86115i	−0.316935	−	0.316935i
$343$	−18.4931	+	1.00344i	−0.998531	+	0.0541806i
$344$			8.80128i			0.474533i
$345$	3.30095	+	4.03084i	0.177717	+	0.217013i
$346$		−	17.7595i		−	0.954759i
$347$	−2.67023	+	2.67023i	−0.143345	+	0.143345i	−0.775138	−	0.631792i	$-0.782320\pi$
$347$	−2.67023	+	2.67023i	−0.143345	+	0.143345i	0.631792	+	0.775138i	$0.282320\pi$
$348$	−6.82312	+	6.82312i	−0.365757	+	0.365757i
$349$	30.6454			1.64041			0.820205	−	0.572069i	$-0.193859\pi$
$349$	30.6454			1.64041			0.820205	+	0.572069i	$0.193859\pi$
$350$	5.66071	−	11.9564i	0.302578	−	0.639098i
$351$	−35.6082			−1.90062
$352$	−0.707107	+	0.707107i	−0.0376889	+	0.0376889i
$353$	23.8875	−	23.8875i	1.27140	−	1.27140i	0.326051	−	0.945352i	$-0.394282\pi$
$353$	23.8875	−	23.8875i	1.27140	−	1.27140i	0.945352	−	0.326051i	$-0.105718\pi$
$354$		−	1.98290i		−	0.105390i
$355$	−8.53351	−	10.4204i	−0.452912	−	0.553057i
$356$		−	7.76249i		−	0.411411i
$357$	11.7809	+	19.5794i	0.623511	+	1.03625i
$358$	10.6323	+	10.6323i	0.561934	+	0.561934i
$359$		−	13.4959i		−	0.712286i	−0.934432	−	0.356143i	$-0.884092\pi$
$359$		−	13.4959i		−	0.712286i	0.934432	−	0.356143i	$-0.115908\pi$
$360$	3.04212	+	0.302847i	0.160334	+	0.0159614i
$361$	17.7561			0.934532
$362$	−9.80989	−	9.80989i	−0.515596	−	0.515596i
$363$	−0.903547	+	0.903547i	−0.0474239	+	0.0474239i
$364$	4.07409	−	16.3832i	0.213540	−	0.858715i
$365$	8.78158	+	0.874216i	0.459649	+	0.0457586i
$366$	−1.16672			−0.0609857
$367$	−20.1156	−	20.1156i	−1.05003	−	1.05003i	−0.998681	−	0.0513475i	$-0.983648\pi$
$367$	−20.1156	−	20.1156i	−1.05003	−	1.05003i	−0.0513475	−	0.998681i	$-0.516352\pi$
$368$	−1.28935	−	1.28935i	−0.0672120	−	0.0672120i
$369$	−7.21363			−0.375526
$370$	11.8004	−	9.66365i	0.613475	−	0.502389i
$371$	−3.83587	+	15.4253i	−0.199148	+	0.800841i
$372$	−7.03386	+	7.03386i	−0.364689	+	0.364689i
$373$	−13.8116	−	13.8116i	−0.715137	−	0.715137i	0.252468	−	0.967605i	$-0.418758\pi$
$373$	−13.8116	−	13.8116i	−0.715137	−	0.715137i	−0.967605	+	0.252468i	$0.918758\pi$
$374$	−6.75895			−0.349497
$375$	−4.19013	+	13.6581i	−0.216377	+	0.705299i
$376$			6.58082i			0.339380i
$377$	34.0719	+	34.0719i	1.75479	+	1.75479i
$378$	7.61207	+	12.6510i	0.391522	+	0.650695i
$379$		−	5.38208i		−	0.276459i	−0.990400	−	0.138229i	$-0.955859\pi$
$379$		−	5.38208i		−	0.276459i	0.990400	−	0.138229i	$-0.0441411\pi$
$380$	−10.4884	+	8.58919i	−0.538043	+	0.440616i
$381$			11.0956i			0.568445i
$382$	−2.07826	+	2.07826i	−0.106333	+	0.106333i
$383$	15.2507	−	15.2507i	0.779273	−	0.779273i	−0.200434	−	0.979707i	$-0.564235\pi$
$383$	15.2507	−	15.2507i	0.779273	−	0.779273i	0.979707	+	0.200434i	$0.0642354\pi$
$384$	1.27781			0.0652079
$385$	−1.98941	+	5.57156i	−0.101390	+	0.283953i
$386$	−16.2883			−0.829053
$387$	−8.50871	+	8.50871i	−0.432522	+	0.432522i
$388$	−6.01682	+	6.01682i	−0.305458	+	0.305458i
$389$			0.769292i			0.0390047i	0.999810	+	0.0195023i	$0.00620818\pi$
$389$			0.769292i			0.0390047i	−0.999810	+	0.0195023i	$0.993792\pi$
$390$	−1.80608	+	18.1422i	−0.0914542	+	0.918665i
$391$		−	12.3244i		−	0.623271i
$392$	−6.69161	+	2.05484i	−0.337977	+	0.103785i
$393$	3.41783	+	3.41783i	0.172407	+	0.172407i
$394$			23.1258i			1.16506i
$395$	−10.5795	+	8.66379i	−0.532311	+	0.435922i
$396$	−1.36720			−0.0687046
$397$	−22.4072	−	22.4072i	−1.12459	−	1.12459i	−0.991043	−	0.133543i	$-0.957364\pi$
$397$	−22.4072	−	22.4072i	−1.12459	−	1.12459i	−0.133543	−	0.991043i	$-0.542636\pi$
$398$	11.1031	−	11.1031i	0.556547	−	0.556547i
$399$	−19.8907	−	4.94631i	−0.995781	−	0.247625i
$400$	0.985742	−	4.90187i	0.0492871	−	0.245093i
$401$	−4.50377			−0.224908			−0.112454	−	0.993657i	$-0.535871\pi$
$401$	−4.50377			−0.224908			−0.112454	+	0.993657i	$0.535871\pi$
$402$	10.9621	+	10.9621i	0.546738	+	0.546738i
$403$	35.1243	+	35.1243i	1.74967	+	1.74967i
$404$	11.9147			0.592777
$405$	−4.29148	−	5.24039i	−0.213245	−	0.260397i
$406$	4.82150	−	19.3888i	0.239287	−	0.962251i
$407$	−4.82324	+	4.82324i	−0.239079	+	0.239079i
$408$	6.10703	+	6.10703i	0.302343	+	0.302343i
$409$	−12.9747			−0.641556			−0.320778	−	0.947154i	$-0.603944\pi$
$409$	−12.9747			−0.641556			−0.320778	+	0.947154i	$0.603944\pi$
$410$	−1.16872	+	11.7399i	−0.0577189	+	0.579792i
$411$			21.8917i			1.07984i
$412$	−4.70655	−	4.70655i	−0.231875	−	0.231875i
$413$	2.11674	+	3.51794i	0.104158	+	0.173107i
$414$		−	2.49298i		−	0.122523i
$415$	−15.8633	−	1.57921i	−0.778697	−	0.0775202i
$416$		−	6.38087i		−	0.312848i
$417$	−10.1949	+	10.1949i	−0.499246	+	0.499246i
$418$	4.28696	−	4.28696i	0.209682	−	0.209682i
$419$	−13.6879			−0.668696			−0.334348	−	0.942450i	$-0.608516\pi$
$419$	−13.6879			−0.668696			−0.334348	+	0.942450i	$0.608516\pi$
$420$	6.83169	−	3.23664i	0.333352	−	0.157932i
$421$	−28.2277			−1.37573			−0.687866	−	0.725838i	$-0.741452\pi$
$421$	−28.2277			−1.37573			−0.687866	+	0.725838i	$0.741452\pi$
$422$	−4.27065	+	4.27065i	−0.207892	+	0.207892i
$423$	−6.36207	+	6.36207i	−0.309334	+	0.309334i
$424$			6.00777i			0.291763i
$425$	28.1387	−	18.7163i	1.36493	−	0.907876i
$426$		−	7.69673i		−	0.372908i
$427$	2.06993	−	1.24548i	0.100171	−	0.0602728i
$428$	6.67198	+	6.67198i	0.322502	+	0.322502i
$429$		−	8.15354i		−	0.393656i
$430$	12.4690	+	15.2261i	0.601311	+	0.734269i
$431$	22.9860			1.10720			0.553598	−	0.832784i	$-0.313255\pi$
$431$	22.9860			1.10720			0.553598	+	0.832784i	$0.313255\pi$
$432$	3.94598	+	3.94598i	0.189851	+	0.189851i
$433$	−3.58733	+	3.58733i	−0.172396	+	0.172396i	−0.788031	−	0.615635i	$-0.788899\pi$
$433$	−3.58733	+	3.58733i	−0.172396	+	0.172396i	0.615635	+	0.788031i	$0.288899\pi$
$434$	4.97042	−	19.9877i	0.238588	−	0.959440i
$435$	−2.13741	+	21.4705i	−0.102481	+	1.02943i
$436$	−4.01592			−0.192328
$437$	7.81692	+	7.81692i	0.373934	+	0.373934i
$438$	3.56599	+	3.56599i	0.170390	+	0.170390i
$439$	−29.7935			−1.42197			−0.710984	−	0.703208i	$-0.751750\pi$
$439$	−29.7935			−1.42197			−0.710984	+	0.703208i	$0.751750\pi$
$440$	−0.221508	+	2.22507i	−0.0105600	+	0.106076i
$441$	−8.45571	−	4.48263i	−0.402653	−	0.213459i
$442$	30.4961	−	30.4961i	1.45055	−	1.45055i
$443$	20.7036	+	20.7036i	0.983659	+	0.983659i	0.999869	−	0.0162100i	$-0.00516002\pi$
$443$	20.7036	+	20.7036i	0.983659	+	0.983659i	−0.0162100	+	0.999869i	$0.505160\pi$
$444$	8.71604			0.413645
$445$	−10.9974	−	13.4290i	−0.521325	−	0.636598i
$446$			7.81528i			0.370064i
$447$	−11.1333	−	11.1333i	−0.526589	−	0.526589i
$448$	−2.26701	+	1.36406i	−0.107106	+	0.0644457i
$449$		−	22.6538i		−	1.06910i	−0.845137	−	0.534550i	$-0.820481\pi$
$449$		−	22.6538i		−	1.06910i	0.845137	−	0.534550i	$-0.179519\pi$
$450$	5.69190	−	3.78595i	0.268319	−	0.178471i
$451$		−	5.27619i		−	0.248446i
$452$	−2.80703	+	2.80703i	−0.132032	+	0.132032i
$453$	1.17804	−	1.17804i	0.0553492	−	0.0553492i
$454$	12.0001			0.563190
$455$	−16.1625	−	34.1148i	−0.757711	−	1.59932i
$456$	−7.74695			−0.362784
$457$	−13.4113	+	13.4113i	−0.627353	+	0.627353i	−0.947401	−	0.320048i	$-0.896301\pi$
$457$	−13.4113	+	13.4113i	−0.627353	+	0.627353i	0.320048	+	0.947401i	$0.396301\pi$
$458$	10.8658	−	10.8658i	0.507727	−	0.507727i
$459$			37.7180i			1.76053i
$460$	−4.05723	−	0.403902i	−0.189169	−	0.0188320i
$461$		−	21.3588i		−	0.994780i	−0.867527	−	0.497390i	$-0.834292\pi$
$461$		−	21.3588i		−	0.994780i	0.867527	−	0.497390i	$-0.165708\pi$
$462$	−2.89681	+	1.74301i	−0.134772	+	0.0810920i
$463$	17.8048	+	17.8048i	0.827459	+	0.827459i	0.987165	−	0.159705i	$-0.0510544\pi$
$463$	17.8048	+	17.8048i	0.827459	+	0.827459i	−0.159705	+	0.987165i	$0.551054\pi$
$464$		−	7.55147i		−	0.350568i
$465$	−2.20343	+	22.1336i	−0.102181	+	1.02642i
$466$	11.6765			0.540905
$467$	−5.93179	−	5.93179i	−0.274491	−	0.274491i	0.556414	−	0.830905i	$-0.312177\pi$
$467$	−5.93179	−	5.93179i	−0.274491	−	0.274491i	−0.830905	+	0.556414i	$0.812177\pi$
$468$	6.16877	−	6.16877i	0.285151	−	0.285151i
$469$	−31.1502	−	7.74625i	−1.43838	−	0.357689i
$470$	9.32326	+	11.3848i	0.430050	+	0.525140i
$471$	8.27309			0.381204
$472$	1.09729	+	1.09729i	0.0505067	+	0.0505067i
$473$	−6.22344	−	6.22344i	−0.286154	−	0.286154i
$474$	−7.81423			−0.358919
$475$	−5.97624	+	29.7185i	−0.274209	+	1.36358i
$476$	−17.3540	−	4.31548i	−0.795418	−	0.197800i
$477$	−5.80807	+	5.80807i	−0.265933	+	0.265933i
$478$	−11.9025	−	11.9025i	−0.544407	−	0.544407i
$479$	−20.3027			−0.927655			−0.463827	−	0.885926i	$-0.653524\pi$
$479$	−20.3027			−0.927655			−0.463827	+	0.885926i	$0.653524\pi$
$480$	2.21060	−	1.81031i	0.100900	−	0.0826291i
$481$		−	43.5245i		−	1.98455i
$482$	−12.7714	−	12.7714i	−0.581721	−	0.581721i
$483$	−3.17823	−	5.28209i	−0.144614	−	0.240343i
$484$		−	1.00000i		−	0.0454545i
$485$	−1.88483	+	18.9333i	−0.0855857	+	0.859716i
$486$			12.8707i			0.583827i
$487$	1.93767	−	1.93767i	0.0878042	−	0.0878042i	−0.661840	−	0.749645i	$-0.730224\pi$
$487$	1.93767	−	1.93767i	0.0878042	−	0.0878042i	0.749645	+	0.661840i	$0.230224\pi$
$488$	0.645636	−	0.645636i	0.0292265	−	0.0292265i
$489$	−13.9930			−0.632786
$490$	−8.66526	+	13.0351i	−0.391457	+	0.588865i
$491$	3.28230			0.148128			0.0740641	−	0.997253i	$-0.476403\pi$
$491$	3.28230			0.148128			0.0740641	+	0.997253i	$0.476403\pi$
$492$	−4.76729	+	4.76729i	−0.214926	+	0.214926i
$493$	36.0908	−	36.0908i	1.62545	−	1.62545i
$494$			38.6852i			1.74053i
$495$	−2.36525	+	1.93696i	−0.106310	+	0.0870599i
$496$		−	7.78472i		−	0.349544i
$497$	8.21624	+	13.6551i	0.368549	+	0.612514i
$498$	−6.44170	−	6.44170i	−0.288659	−	0.288659i
$499$			34.2199i			1.53189i	0.642904	+	0.765946i	$0.277729\pi$
$499$			34.2199i			1.53189i	−0.642904	+	0.765946i	$0.722271\pi$
$500$	−5.23931	−	9.87672i	−0.234309	−	0.441701i
$501$	3.67336			0.164114
$502$	6.36301	+	6.36301i	0.283995	+	0.283995i
$503$	−24.1925	+	24.1925i	−1.07869	+	1.07869i	−0.0820631	+	0.996627i	$0.526151\pi$
$503$	−24.1925	+	24.1925i	−1.07869	+	1.07869i	−0.996627	+	0.0820631i	$0.973849\pi$
$504$	−3.51037	−	0.872938i	−0.156364	−	0.0388838i
$505$	20.6123	−	16.8799i	0.917234	−	0.751145i
$506$	1.82342			0.0810608
$507$	25.0423	+	25.0423i	1.11217	+	1.11217i
$508$	−6.14002	−	6.14002i	−0.272419	−	0.272419i
$509$	15.1097			0.669726			0.334863	−	0.942267i	$-0.391310\pi$
$509$	15.1097			0.669726			0.334863	+	0.942267i	$0.391310\pi$
$510$	19.2171	+	1.91309i	0.850950	+	0.0847130i
$511$	−10.1333	−	2.51988i	−0.448269	−	0.111473i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−23.9232	−	23.9232i	−1.05623	−	1.05623i
$514$	9.37123			0.413347
$515$	−14.8102	−	1.47437i	−0.652615	−	0.0649686i
$516$			11.2463i			0.495093i
$517$	−4.65334	−	4.65334i	−0.204654	−	0.204654i
$518$	−15.4635	+	9.30436i	−0.679426	+	0.408810i
$519$		−	22.6933i		−	0.996125i
$520$	−9.03998	−	11.0389i	−0.396430	−	0.484086i
$521$		−	12.1371i		−	0.531734i	−0.964010	−	0.265867i	$-0.914342\pi$
$521$		−	12.1371i		−	0.531734i	0.964010	−	0.265867i	$-0.0856582\pi$
$522$	7.30046	−	7.30046i	0.319532	−	0.319532i
$523$	−0.478912	+	0.478912i	−0.0209414	+	0.0209414i	−0.717500	−	0.696559i	$-0.754714\pi$
$523$	−0.478912	+	0.478912i	−0.0209414	+	0.0209414i	0.696559	+	0.717500i	$0.254714\pi$
$524$	−3.78268			−0.165247
$525$	7.23331	−	15.2780i	0.315688	−	0.666788i
$526$	5.24252			0.228585
$527$	37.2055	−	37.2055i	1.62070	−	1.62070i
$528$	−0.903547	+	0.903547i	−0.0393219	+	0.0393219i
$529$		−	19.6752i		−	0.855441i
$530$	8.51140	+	10.3934i	0.369712	+	0.451460i
$531$			2.12162i			0.0920706i
$532$	13.7442	−	8.26985i	0.595885	−	0.358544i
$533$	23.8060	+	23.8060i	1.03115	+	1.03115i
$534$		−	9.91898i		−	0.429236i
$535$	20.9949	+	2.09006i	0.907688	+	0.0903614i
$536$	−12.1322			−0.524033
$537$	13.5860	+	13.5860i	0.586280	+	0.586280i
$538$	−0.122064	+	0.122064i	−0.00526255	+	0.00526255i
$539$	3.27869	−	6.18468i	0.141223	−	0.266393i
$540$	12.4169	+	1.23612i	0.534338	+	0.0531940i
$541$	29.2796			1.25883			0.629414	−	0.777070i	$-0.283295\pi$
$541$	29.2796			1.25883			0.629414	+	0.777070i	$0.283295\pi$
$542$	0.928853	+	0.928853i	0.0398976	+	0.0398976i
$543$	−12.5352	−	12.5352i	−0.537935	−	0.537935i
$544$	−6.75895			−0.289788
$545$	−6.94751	+	5.68948i	−0.297599	+	0.243711i
$546$	5.20591	−	20.9347i	0.222792	−	0.895920i
$547$	14.0735	−	14.0735i	0.601741	−	0.601741i	−0.339034	−	0.940774i	$-0.610100\pi$
$547$	14.0735	−	14.0735i	0.601741	−	0.601741i	0.940774	+	0.339034i	$0.110100\pi$
$548$	−12.1143	−	12.1143i	−0.517498	−	0.517498i
$549$	1.24835			0.0532782
$550$	2.76912	+	4.16317i	0.118076	+	0.177518i
$551$			45.7822i			1.95039i
$552$	−1.64754	−	1.64754i	−0.0701241	−	0.0701241i
$553$	13.8635	−	8.34168i	0.589538	−	0.354724i
$554$			9.53822i			0.405240i
$555$	15.0787	−	12.3483i	0.640055	−	0.524156i
$556$		−	11.2832i		−	0.478513i
$557$	−19.4265	+	19.4265i	−0.823129	+	0.823129i	−0.986556	−	0.163426i	$-0.947745\pi$
$557$	−19.4265	+	19.4265i	−0.823129	+	0.823129i	0.163426	+	0.986556i	$0.447745\pi$
$558$	7.52595	−	7.52595i	0.318599	−	0.318599i
$559$	56.1598			2.37531
$560$	−1.98941	+	5.57156i	−0.0840678	+	0.235441i
$561$	−8.63665			−0.364640
$562$	−0.207638	+	0.207638i	−0.00875867	+	0.00875867i
$563$	−19.1451	+	19.1451i	−0.806868	+	0.806868i	−0.984159	−	0.177291i	$-0.943267\pi$
$563$	−19.1451	+	19.1451i	−0.806868	+	0.806868i	0.177291	+	0.984159i	$0.443267\pi$
$564$			8.40904i			0.354084i
$565$	−0.879331	+	8.83296i	−0.0369938	+	0.371606i
$566$			17.2451i			0.724866i
$567$	4.13193	+	6.86710i	0.173525	+	0.288391i
$568$	4.25917	+	4.25917i	0.178711	+	0.178711i
$569$			42.5991i			1.78585i	0.450209	+	0.892923i	$0.351349\pi$
$569$			42.5991i			1.78585i	−0.450209	+	0.892923i	$0.648651\pi$
$570$	−13.4022	+	10.9754i	−0.561355	+	0.459707i
$571$	1.34853			0.0564343			0.0282172	−	0.999602i	$-0.491017\pi$
$571$	1.34853			0.0564343			0.0282172	+	0.999602i	$0.491017\pi$
$572$	4.51196	+	4.51196i	0.188654	+	0.188654i
$573$	−2.65562	+	2.65562i	−0.110940	+	0.110940i
$574$	3.36877	−	13.5469i	0.140610	−	0.565437i
$575$	−7.59119	+	5.04926i	−0.316575	+	0.210569i
$576$	−1.36720			−0.0569668
$577$	7.01450	+	7.01450i	0.292018	+	0.292018i	0.837877	−	0.545859i	$-0.183797\pi$
$577$	7.01450	+	7.01450i	0.292018	+	0.292018i	−0.545859	+	0.837877i	$0.683797\pi$
$578$	−20.2822	−	20.2822i	−0.843630	−	0.843630i
$579$	−20.8134			−0.864973
$580$	−10.6984	−	13.0640i	−0.444227	−	0.542453i
$581$	18.3050	+	4.55197i	0.759418	+	0.188848i
$582$	−7.68835	+	7.68835i	−0.318692	+	0.318692i
$583$	−4.24814	−	4.24814i	−0.175940	−	0.175940i
$584$	−3.94665			−0.163314
$585$	1.93243	−	19.4114i	0.0798960	−	0.802563i
$586$		−	23.4653i		−	0.969342i
$587$	13.2305	+	13.2305i	0.546080	+	0.546080i	0.925305	−	0.379225i	$-0.123809\pi$
$587$	13.2305	+	13.2305i	0.546080	+	0.546080i	−0.379225	+	0.925305i	$0.623809\pi$
$588$	−8.55060	+	2.62570i	−0.352621	+	0.108282i
$589$			47.1963i			1.94469i
$590$	3.45286	+	0.343736i	0.142152	+	0.0141514i
$591$			29.5504i			1.21554i
$592$	−4.82324	+	4.82324i	−0.198234	+	0.198234i
$593$	−25.2664	+	25.2664i	−1.03757	+	1.03757i	−0.0382996	+	0.999266i	$0.512194\pi$
$593$	−25.2664	+	25.2664i	−1.03757	+	1.03757i	−0.999266	+	0.0382996i	$0.987806\pi$
$594$	−5.58045			−0.228969
$595$	−36.1361	+	17.1202i	−1.48144	+	0.701859i
$596$	12.3218			0.504721
$597$	14.1876	−	14.1876i	0.580660	−	0.580660i
$598$	−8.22718	+	8.22718i	−0.336434	+	0.336434i
$599$		−	13.9693i		−	0.570770i	−0.958413	−	0.285385i	$-0.907879\pi$
$599$		−	13.9693i		−	0.570770i	0.958413	−	0.285385i	$-0.0921214\pi$
$600$	1.25959	−	6.26365i	0.0514226	−	0.255713i
$601$		−	29.7532i		−	1.21366i	−0.794832	−	0.606830i	$-0.792441\pi$
$601$		−	29.7532i		−	1.21366i	0.794832	−	0.606830i	$-0.207559\pi$
$602$	−12.0055	−	19.9526i	−0.489306	−	0.813207i
$603$	−11.7290	−	11.7290i	−0.477640	−	0.477640i
$604$			1.30380i			0.0530507i
$605$	−1.41673	−	1.72999i	−0.0575983	−	0.0703342i
$606$	15.2247			0.618460
$607$	−20.3342	−	20.3342i	−0.825339	−	0.825339i	0.161529	−	0.986868i	$-0.448357\pi$
$607$	−20.3342	−	20.3342i	−0.825339	−	0.825339i	−0.986868	+	0.161529i	$0.948357\pi$
$608$	4.28696	−	4.28696i	0.173859	−	0.173859i
$609$	6.16095	−	24.7752i	0.249654	−	1.00394i
$610$	0.202252	−	2.03164i	0.00818893	−	0.0822586i
$611$	41.9914			1.69879
$612$	−6.53428	−	6.53428i	−0.264133	−	0.264133i
$613$	−24.6878	−	24.6878i	−0.997132	−	0.997132i	0.00286351	−	0.999996i	$-0.499089\pi$
$613$	−24.6878	−	24.6878i	−0.997132	−	0.997132i	−0.999996	+	0.00286351i	$0.999089\pi$
$614$	−16.9407			−0.683670
$615$	−1.49340	+	15.0013i	−0.0602197	+	0.604912i
$616$	0.638484	−	2.56755i	0.0257253	−	0.103450i
$617$	27.4111	−	27.4111i	1.10353	−	1.10353i	0.109550	−	0.993981i	$-0.465059\pi$
$617$	27.4111	−	27.4111i	1.10353	−	1.10353i	0.993981	−	0.109550i	$-0.0349409\pi$
$618$	−6.01407	−	6.01407i	−0.241921	−	0.241921i
$619$	−24.9497			−1.00281			−0.501407	−	0.865211i	$-0.667184\pi$
$619$	−24.9497			−1.00281			−0.501407	+	0.865211i	$0.667184\pi$
$620$	−11.0289	−	13.4675i	−0.442929	−	0.540868i
$621$		−	10.1755i		−	0.408328i
$622$	−1.43578	−	1.43578i	−0.0575695	−	0.0575695i
$623$	10.5885	+	17.5977i	0.424219	+	0.705035i
$624$		−	8.15354i		−	0.326403i
$625$	−23.0566	−	9.66396i	−0.922265	−	0.386558i
$626$		−	1.95568i		−	0.0781648i
$627$	5.47792	−	5.47792i	0.218767	−	0.218767i
$628$	−4.57812	+	4.57812i	−0.182687	+	0.182687i
$629$	−46.1034			−1.83826
$630$	−7.30963	+	3.46308i	−0.291223	+	0.137972i
$631$	−36.9175			−1.46966			−0.734832	−	0.678249i	$-0.762739\pi$
$631$	−36.9175			−1.46966			−0.734832	+	0.678249i	$0.762739\pi$
$632$	4.32419	−	4.32419i	0.172007	−	0.172007i
$633$	−5.45708	+	5.45708i	−0.216899	+	0.216899i
$634$		−	1.07267i		−	0.0426011i
$635$	−19.3209	−	1.92342i	−0.766728	−	0.0763287i
$636$			7.67679i			0.304404i
$637$	13.1117	+	42.6983i	0.519504	+	1.69177i
$638$	5.33970	+	5.33970i	0.211401	+	0.211401i
$639$			8.23519i			0.325779i
$640$	−0.221508	+	2.22507i	−0.00875588	+	0.0879536i
$641$	22.1299			0.874078			0.437039	−	0.899443i	$-0.356027\pi$
$641$	22.1299			0.874078			0.437039	+	0.899443i	$0.356027\pi$
$642$	8.52552	+	8.52552i	0.336475	+	0.336475i
$643$	21.3104	−	21.3104i	0.840400	−	0.840400i	−0.148511	−	0.988911i	$-0.547448\pi$
$643$	21.3104	−	21.3104i	0.840400	−	0.840400i	0.988911	+	0.148511i	$0.0474481\pi$
$644$	4.68172	+	1.16422i	0.184486	+	0.0458768i
$645$	15.9331	+	19.4561i	0.627364	+	0.766083i
$646$	40.9774			1.61223
$647$	30.0056	+	30.0056i	1.17964	+	1.17964i	0.979835	+	0.199806i	$0.0640312\pi$
$647$	30.0056	+	30.0056i	1.17964	+	1.17964i	0.199806	+	0.979835i	$0.435969\pi$
$648$	2.14193	+	2.14193i	0.0841428	+	0.0841428i
$649$	−1.55180			−0.0609134
$650$	−31.2782	−	6.28990i	−1.22683	−	0.246710i
$651$	6.35125	−	25.5404i	0.248925	−	1.00101i
$652$	7.74337	−	7.74337i	0.303254	−	0.303254i
$653$	−19.0791	−	19.0791i	−0.746621	−	0.746621i	0.227222	−	0.973843i	$-0.427036\pi$
$653$	−19.0791	−	19.0791i	−0.746621	−	0.746621i	−0.973843	+	0.227222i	$0.927036\pi$
$654$	−5.13158			−0.200661
$655$	−6.54401	+	5.35905i	−0.255696	+	0.209395i
$656$		−	5.27619i		−	0.206001i
$657$	−3.81546	−	3.81546i	−0.148855	−	0.148855i
$658$	−8.97663	−	14.9188i	−0.349945	−	0.581596i
$659$		−	17.5265i		−	0.682737i	−0.939930	−	0.341368i	$-0.889110\pi$
$659$		−	17.5265i		−	0.682737i	0.939930	−	0.341368i	$-0.110890\pi$
$660$	−0.283045	+	2.84321i	−0.0110175	+	0.110672i
$661$		−	28.8634i		−	1.12265i	−0.827594	−	0.561327i	$-0.810291\pi$
$661$		−	28.8634i		−	1.12265i	0.827594	−	0.561327i	$-0.189709\pi$
$662$	−15.5177	+	15.5177i	−0.603111	+	0.603111i
$663$	38.9682	−	38.9682i	1.51340	−	1.51340i
$664$	7.12934			0.276672
$665$	12.0611	−	33.7786i	0.467711	−	1.30988i
$666$	−9.32581			−0.361368
$667$	−9.73650	+	9.73650i	−0.376999	+	0.376999i
$668$	−2.03274	+	2.03274i	−0.0786492	+	0.0786492i
$669$			9.98644i			0.386098i
$670$	−20.9887	+	17.1881i	−0.810864	+	0.664036i
$671$			0.913067i			0.0352485i
$672$	−2.89681	+	1.74301i	−0.111747	+	0.0672379i
$673$	−14.1089	−	14.1089i	−0.543860	−	0.543860i	0.380798	−	0.924658i	$-0.375649\pi$
$673$	−14.1089	−	14.1089i	−0.543860	−	0.543860i	−0.924658	+	0.380798i	$0.875649\pi$
$674$		−	35.2987i		−	1.35966i
$675$	23.2324	−	15.4529i	0.894214	−	0.594784i
$676$	−27.7155			−1.06598
$677$	−20.5043	−	20.5043i	−0.788044	−	0.788044i	0.193130	−	0.981173i	$-0.438136\pi$
$677$	−20.5043	−	20.5043i	−0.788044	−	0.788044i	−0.981173	+	0.193130i	$0.938136\pi$
$678$	−3.58685	+	3.58685i	−0.137752	+	0.137752i
$679$	5.43291	−	21.8475i	0.208496	−	0.838431i
$680$	−11.6929	+	9.57562i	−0.448403	+	0.367208i
$681$	15.3338			0.587592
$682$	5.50463	+	5.50463i	0.210783	+	0.210783i
$683$	21.7027	+	21.7027i	0.830432	+	0.830432i	0.987576	−	0.157144i	$-0.0502286\pi$
$683$	21.7027	+	21.7027i	0.830432	+	0.830432i	−0.157144	+	0.987576i	$0.550229\pi$
$684$	8.28892			0.316935
$685$	−38.1204	−	3.79493i	−1.45651	−	0.144997i
$686$	12.3670	−	13.7861i	0.472175	−	0.526356i
$687$	13.8845	−	13.8845i	0.529725	−	0.529725i
$688$	−6.22344	−	6.22344i	−0.237266	−	0.237266i
$689$	38.3348			1.46044
$690$	−5.18436	−	0.516109i	−0.197365	−	0.0196479i
$691$		−	32.1941i		−	1.22472i	−0.790578	−	0.612361i	$-0.790220\pi$
$691$		−	32.1941i		−	1.22472i	0.790578	−	0.612361i	$-0.209780\pi$
$692$	12.5579	+	12.5579i	0.477379	+	0.477379i
$693$	3.09947	−	1.86495i	0.117739	−	0.0708435i
$694$		−	3.77627i		−	0.143345i
$695$	−15.9852	−	19.5198i	−0.606355	−	0.740428i
$696$		−	9.64934i		−	0.365757i
$697$	25.2165	−	25.2165i	0.955143	−	0.955143i
$698$	−21.6696	+	21.6696i	−0.820205	+	0.820205i
$699$	14.9204			0.564341
$700$	4.45175	+	12.4572i	0.168260	+	0.470838i
$701$	39.8618			1.50556			0.752780	−	0.658272i	$-0.228712\pi$
$701$	39.8618			1.50556			0.752780	+	0.658272i	$0.228712\pi$
$702$	25.1788	−	25.1788i	0.950311	−	0.950311i
$703$	29.2417	−	29.2417i	1.10287	−	1.10287i
$704$		−	1.00000i		−	0.0376889i
$705$	11.9133	+	14.5476i	0.448683	+	0.547893i
$706$			33.7820i			1.27140i
$707$	−27.0107	+	16.2523i	−1.01584	+	0.611231i
$708$	1.40212	+	1.40212i	0.0526950	+	0.0526950i
$709$		−	4.80833i		−	0.180580i	−0.995915	−	0.0902902i	$-0.971221\pi$
$709$		−	4.80833i		−	0.180580i	0.995915	−	0.0902902i	$-0.0287795\pi$
$710$	13.4024	+	1.33423i	0.502984	+	0.0500727i
$711$	8.36091			0.313559
$712$	5.48891	+	5.48891i	0.205706	+	0.205706i
$713$	−10.0372	+	10.0372i	−0.375897	+	0.375897i
$714$	−22.1751	−	5.51437i	−0.829881	−	0.206370i
$715$	14.1979	+	1.41342i	0.530971	+	0.0528587i
$716$	−15.0363			−0.561934
$717$	−15.2091	−	15.2091i	−0.567994	−	0.567994i
$718$	9.54303	+	9.54303i	0.356143	+	0.356143i
$719$	27.6376			1.03071			0.515354	−	0.856977i	$-0.327660\pi$
$719$	27.6376			1.03071			0.515354	+	0.856977i	$0.327660\pi$
$720$	−2.36525	+	1.93696i	−0.0881477	+	0.0721863i
$721$	17.0898	+	4.24979i	0.636457	+	0.158270i
$722$	−12.5555	+	12.5555i	−0.467266	+	0.467266i
$723$	−16.3194	−	16.3194i	−0.606925	−	0.606925i
$724$	13.8733			0.515596
$725$	−37.0163	−	7.44381i	−1.37475	−	0.276456i
$726$		−	1.27781i		−	0.0474239i
$727$	15.6166	+	15.6166i	0.579186	+	0.579186i	0.934679	−	0.355493i	$-0.115687\pi$
$727$	15.6166	+	15.6166i	0.579186	+	0.579186i	−0.355493	+	0.934679i	$0.615687\pi$
$728$	8.70389	+	14.4655i	0.322587	+	0.536128i
$729$			25.5337i			0.945693i
$730$	−6.82768	+	5.59135i	−0.252704	+	0.206945i
$731$		−	59.4874i		−	2.20022i
$732$	0.824999	−	0.824999i	0.0304928	−	0.0304928i
$733$	−14.1369	+	14.1369i	−0.522157	+	0.522157i	−0.918222	−	0.396065i	$-0.870375\pi$
$733$	−14.1369	+	14.1369i	−0.522157	+	0.522157i	0.396065	+	0.918222i	$0.370375\pi$
$734$	28.4478			1.05003
$735$	−11.0726	+	16.6563i	−0.408417	+	0.614378i
$736$	1.82342			0.0672120
$737$	8.57879	−	8.57879i	0.316004	−	0.316004i
$738$	5.10081	−	5.10081i	0.187763	−	0.187763i
$739$			24.8828i			0.915329i	0.889125	+	0.457665i	$0.151314\pi$
$739$			24.8828i			0.915329i	−0.889125	+	0.457665i	$0.848686\pi$
$740$	−1.51093	+	15.1774i	−0.0555428	+	0.557932i
$741$			49.4323i			1.81594i
$742$	−8.19496	−	13.6197i	−0.300846	−	0.499995i
$743$	−14.7790	−	14.7790i	−0.542190	−	0.542190i	0.381980	−	0.924171i	$-0.375242\pi$
$743$	−14.7790	−	14.7790i	−0.542190	−	0.542190i	−0.924171	+	0.381980i	$0.875242\pi$
$744$		−	9.94738i		−	0.364689i
$745$	21.3166	−	17.4567i	0.780981	−	0.639564i
$746$	19.5325			0.715137
$747$	6.89235	+	6.89235i	0.252178	+	0.252178i
$748$	4.77930	−	4.77930i	0.174749	−	0.174749i
$749$	−24.2264	−	6.02449i	−0.885215	−	0.220130i
$750$	−6.69483	−	12.6206i	−0.244461	−	0.460838i
$751$	−43.4872			−1.58687			−0.793435	−	0.608655i	$-0.791709\pi$
$751$	−43.4872			−1.58687			−0.793435	+	0.608655i	$0.791709\pi$
$752$	−4.65334	−	4.65334i	−0.169690	−	0.169690i
$753$	8.13071	+	8.13071i	0.296299	+	0.296299i
$754$	−48.1850			−1.75479
$755$	1.84713	+	2.25555i	0.0672239	+	0.0820880i
$756$	−14.3281	−	3.56303i	−0.521109	−	0.129586i
$757$	24.1126	−	24.1126i	0.876386	−	0.876386i	−0.116773	−	0.993159i	$-0.537255\pi$
$757$	24.1126	−	24.1126i	0.876386	−	0.876386i	0.993159	+	0.116773i	$0.0372549\pi$
$758$	3.80570	+	3.80570i	0.138229	+	0.138229i
$759$	2.32998			0.0845729
$760$	1.34293	−	13.4899i	0.0487133	−	0.489330i
$761$		−	11.5097i		−	0.417226i	−0.977998	−	0.208613i	$-0.933105\pi$
$761$		−	11.5097i		−	0.417226i	0.977998	−	0.208613i	$-0.0668950\pi$
$762$	−7.84577	−	7.84577i	−0.284222	−	0.284222i
$763$	9.10414	−	5.47795i	0.329592	−	0.198315i
$764$		−	2.93911i		−	0.106333i
$765$	−20.5616	−	2.04693i	−0.743405	−	0.0740068i
$766$			21.5677i			0.779273i
$767$	7.00164	−	7.00164i	0.252815	−	0.252815i
$768$	−0.903547	+	0.903547i	−0.0326040	+	0.0326040i
$769$	−37.8720			−1.36570			−0.682849	−	0.730560i	$-0.739259\pi$
$769$	−37.8720			−1.36570			−0.682849	+	0.730560i	$0.739259\pi$
$770$	−2.53296	−	5.34641i	−0.0912817	−	0.192671i
$771$	11.9746			0.431256
$772$	11.5176	−	11.5176i	0.414527	−	0.414527i
$773$	2.36055	−	2.36055i	0.0849030	−	0.0849030i	−0.663380	−	0.748283i	$-0.730879\pi$
$773$	2.36055	−	2.36055i	0.0849030	−	0.0849030i	0.748283	+	0.663380i	$0.230879\pi$
$774$		−	12.0331i		−	0.432522i
$775$	−38.1597	−	7.67372i	−1.37074	−	0.275648i
$776$		−	8.50907i		−	0.305458i
$777$	−19.7594	+	11.8892i	−0.708864	+	0.426523i
$778$	−0.543972	−	0.543972i	−0.0195023	−	0.0195023i
$779$			31.9879i			1.14608i
$780$	−11.5514	−	14.1056i	−0.413606	−	0.505060i
$781$	−6.02338			−0.215533
$782$	8.71466	+	8.71466i	0.311635	+	0.311635i
$783$	29.7979	−	29.7979i	1.06489	−	1.06489i
$784$	3.27869	−	6.18468i	0.117096	−	0.220881i
$785$	−1.43414	+	14.4061i	−0.0511867	+	0.514175i
$786$	−4.83355			−0.172407
$787$	−13.6315	−	13.6315i	−0.485909	−	0.485909i	0.421104	−	0.907013i	$-0.361643\pi$
$787$	−13.6315	−	13.6315i	−0.485909	−	0.485909i	−0.907013	+	0.421104i	$0.861643\pi$
$788$	−16.3524	−	16.3524i	−0.582532	−	0.582532i
$789$	6.69894			0.238489
$790$	1.35460	−	13.6070i	0.0481944	−	0.484117i
$791$	2.53462	−	10.1925i	0.0901208	−	0.362405i
$792$	0.966759	−	0.966759i	0.0343523	−	0.0343523i
$793$	−4.11972	−	4.11972i	−0.146295	−	0.146295i
$794$	31.6886			1.12459
$795$	10.8759	+	13.2808i	0.385730	+	0.471021i
$796$			15.7021i			0.556547i
$797$	−1.99769	−	1.99769i	−0.0707619	−	0.0707619i	0.670840	−	0.741602i	$-0.265934\pi$
$797$	−1.99769	−	1.99769i	−0.0707619	−	0.0707619i	−0.741602	+	0.670840i	$0.765934\pi$
$798$	17.5624	−	10.5673i	0.621703	−	0.374078i
$799$		−	44.4795i		−	1.57357i
$800$	2.76912	+	4.16317i	0.0979031	+	0.147190i
$801$			10.6129i			0.374989i
$802$	3.18465	−	3.18465i	0.112454	−	0.112454i
$803$	2.79071	−	2.79071i	0.0984819	−	0.0984819i
$804$	−15.5027			−0.546738
$805$	9.74873	−	4.61865i	0.343598	−	0.162786i
$806$	−49.6733			−1.74967
$807$	−0.155974	+	0.155974i	−0.00549056	+	0.00549056i
$808$	−8.42494	+	8.42494i	−0.296388	+	0.296388i
$809$		−	15.6494i		−	0.550202i	−0.961415	−	0.275101i	$-0.911289\pi$
$809$		−	15.6494i		−	0.550202i	0.961415	−	0.275101i	$-0.0887114\pi$
$810$	6.74005	+	0.670980i	0.236821	+	0.0235758i
$811$			14.4469i			0.507300i	0.967296	+	0.253650i	$0.0816311\pi$
$811$			14.4469i			0.507300i	−0.967296	+	0.253650i	$0.918369\pi$
$812$	10.3007	+	17.1193i	0.361482	+	0.600769i
$813$	1.18690	+	1.18690i	0.0416263	+	0.0416263i
$814$		−	6.82109i		−	0.239079i
$815$	2.42569	−	24.3663i	0.0849682	−	0.853513i
$816$	−8.63665			−0.302343
$817$	37.7307	+	37.7307i	1.32003	+	1.32003i
$818$	9.17448	−	9.17448i	0.320778	−	0.320778i
$819$	−5.57011	+	22.3992i	−0.194635	+	0.782692i
$820$	−7.47495	−	9.12777i	−0.261036	−	0.318755i
$821$	−50.3895			−1.75861			−0.879303	−	0.476263i	$-0.841991\pi$
$821$	−50.3895			−1.75861			−0.879303	+	0.476263i	$0.841991\pi$
$822$	−15.4798	−	15.4798i	−0.539919	−	0.539919i
$823$	12.2979	+	12.2979i	0.428679	+	0.428679i	0.888178	−	0.459499i	$-0.151971\pi$
$823$	12.2979	+	12.2979i	0.428679	+	0.428679i	−0.459499	+	0.888178i	$0.651971\pi$
$824$	6.65606			0.231875
$825$	3.53841	+	5.31974i	0.123191	+	0.185209i
$826$	−3.98432	−	0.990798i	−0.138632	−	0.0344743i
$827$	7.54816	−	7.54816i	0.262475	−	0.262475i	−0.563584	−	0.826059i	$-0.690578\pi$
$827$	7.54816	−	7.54816i	0.262475	−	0.262475i	0.826059	+	0.563584i	$0.190578\pi$
$828$	1.76280	+	1.76280i	0.0612617	+	0.0612617i
$829$	13.1758			0.457616			0.228808	−	0.973472i	$-0.426517\pi$
$829$	13.1758			0.457616			0.228808	+	0.973472i	$0.426517\pi$
$830$	12.3337	−	10.1004i	0.428109	−	0.350589i
$831$			12.1880i			0.422798i
$832$	4.51196	+	4.51196i	0.156424	+	0.156424i
$833$	45.2283	−	13.8886i	1.56707	−	0.481211i
$834$		−	14.4177i		−	0.499246i
$835$	−0.636777	+	6.39648i	−0.0220366	+	0.221359i
$836$			6.06268i			0.209682i
$837$	30.7183	−	30.7183i	1.06178	−	1.06178i
$838$	9.67878	−	9.67878i	0.334348	−	0.334348i
$839$	−33.3835			−1.15253			−0.576263	−	0.817264i	$-0.695490\pi$
$839$	−33.3835			−1.15253			−0.576263	+	0.817264i	$0.695490\pi$
$840$	−2.54208	+	7.11939i	−0.0877102	+	0.245642i
$841$	−28.0248			−0.966371
$842$	19.9600	−	19.9600i	0.687866	−	0.687866i
$843$	−0.265322	+	0.265322i	−0.00913816	+	0.00913816i
$844$		−	6.03962i		−	0.207892i
$845$	−47.9476	+	39.2655i	−1.64945	+	1.35077i
$846$		−	8.99733i		−	0.309334i
$847$	1.36406	+	2.26701i	0.0468696	+	0.0778955i
$848$	−4.24814	−	4.24814i	−0.145882	−	0.145882i
$849$			22.0360i			0.756272i
$850$	−6.66258	+	33.1315i	−0.228525	+	1.13640i
$851$	12.4377			0.426358
$852$	5.44241	+	5.44241i	0.186454	+	0.186454i
$853$	−26.6354	+	26.6354i	−0.911979	+	0.911979i	−0.996428	−	0.0844490i	$-0.973087\pi$
$853$	−26.6354	+	26.6354i	−0.911979	+	0.911979i	0.0844490	+	0.996428i	$0.473087\pi$
$854$	−0.582979	+	2.34435i	−0.0199491	+	0.0802220i
$855$	14.3398	−	11.7432i	0.490410	−	0.401608i
$856$	−9.43561			−0.322502
$857$	11.3454	+	11.3454i	0.387552	+	0.387552i	0.873813	−	0.486261i	$-0.161640\pi$
$857$	11.3454	+	11.3454i	0.387552	+	0.387552i	−0.486261	+	0.873813i	$0.661640\pi$
$858$	5.76542	+	5.76542i	0.196828	+	0.196828i
$859$	46.6811			1.59274			0.796369	−	0.604811i	$-0.206752\pi$
$859$	46.6811			1.59274			0.796369	+	0.604811i	$0.206752\pi$
$860$	−19.5834	−	1.94955i	−0.667790	−	0.0664793i
$861$	4.30464	−	17.3104i	0.146702	−	0.589936i
$862$	−16.2535	+	16.2535i	−0.553598	+	0.553598i
$863$	−9.00736	−	9.00736i	−0.306614	−	0.306614i	0.536981	−	0.843595i	$-0.319565\pi$
$863$	−9.00736	−	9.00736i	−0.306614	−	0.306614i	−0.843595	+	0.536981i	$0.819565\pi$
$864$	−5.58045			−0.189851
$865$	39.5162	+	3.93388i	1.34359	+	0.133756i
$866$		−	5.07325i		−	0.172396i
$867$	−25.9168	−	25.9168i	−0.880182	−	0.880182i
$868$	10.6188	+	17.6480i	0.360426	+	0.599014i
$869$			6.11533i			0.207449i
$870$	−13.6705	−	16.6933i	−0.463474	−	0.565955i
$871$			77.4143i			2.62308i
$872$	2.83969	−	2.83969i	0.0961639	−	0.0961639i
$873$	8.22622	−	8.22622i	0.278416	−	0.278416i
$874$	−11.0548			−0.373934
$875$	25.3500	+	15.2439i	0.856987	+	0.515339i
$876$	−5.04307			−0.170390
$877$	7.42300	−	7.42300i	0.250657	−	0.250657i	−0.570583	−	0.821240i	$-0.693283\pi$
$877$	7.42300	−	7.42300i	0.250657	−	0.250657i	0.821240	+	0.570583i	$0.193283\pi$
$878$	21.0672	−	21.0672i	0.710984	−	0.710984i
$879$		−	29.9841i		−	1.01134i
$880$	−1.41673	−	1.72999i	−0.0477580	−	0.0583180i
$881$			10.2086i			0.343938i	0.985102	+	0.171969i	$0.0550129\pi$
$881$			10.2086i			0.343938i	−0.985102	+	0.171969i	$0.944987\pi$
$882$	9.14879	−	2.80939i	0.308056	−	0.0945971i
$883$	9.26344	+	9.26344i	0.311740	+	0.311740i	0.845583	−	0.533844i	$-0.179253\pi$
$883$	9.26344	+	9.26344i	0.311740	+	0.311740i	−0.533844	+	0.845583i	$0.679253\pi$
$884$			43.1280i			1.45055i
$885$	4.41209	+	0.439229i	0.148311	+	0.0147645i
$886$	−29.2793			−0.983659
$887$	32.3206	+	32.3206i	1.08522	+	1.08522i	0.996013	+	0.0892072i	$0.0284333\pi$
$887$	32.3206	+	32.3206i	1.08522	+	1.08522i	0.0892072	+	0.996013i	$0.471567\pi$
$888$	−6.16317	+	6.16317i	−0.206823	+	0.206823i
$889$	22.2949	+	5.54415i	0.747745	+	0.185945i
$890$	17.2721	+	1.71946i	0.578962	+	0.0576363i
$891$	−3.02914			−0.101480
$892$	−5.52624	−	5.52624i	−0.185032	−	0.185032i
$893$	28.2117	+	28.2117i	0.944070	+	0.944070i
$894$	15.7449			0.526589
$895$	−26.0127	+	21.3024i	−0.869509	+	0.712062i
$896$	0.638484	−	2.56755i	0.0213303	−	0.0857760i
$897$	−10.5128	+	10.5128i	−0.351011	+	0.351011i
$898$	16.0187	+	16.0187i	0.534550	+	0.534550i
$899$	−58.7861			−1.96063
$900$	−1.34771	+	6.70185i	−0.0449237	+	0.223395i
$901$		−	40.6063i		−	1.35279i
$902$	3.73083	+	3.73083i	0.124223	+	0.124223i
$903$	−15.3407	−	25.4956i	−0.510506	−	0.848441i
$904$		−	3.96975i		−	0.132032i
$905$	24.0007	−	19.6547i	0.797809	−	0.653345i
$906$			1.66600i			0.0553492i
$907$	−29.4475	+	29.4475i	−0.977789	+	0.977789i	−0.999759	−	0.0219699i	$-0.993006\pi$
$907$	−29.4475	+	29.4475i	−0.977789	+	0.977789i	0.0219699	+	0.999759i	$0.493006\pi$
$908$	−8.48532	+	8.48532i	−0.281595	+	0.281595i
$909$	−16.2898			−0.540298
$910$	35.5514	+	12.6941i	1.17852	+	0.420807i
$911$	−39.7846			−1.31812			−0.659062	−	0.752089i	$-0.729046\pi$
$911$	−39.7846			−1.31812			−0.659062	+	0.752089i	$0.729046\pi$
$912$	5.47792	−	5.47792i	0.181392	−	0.181392i
$913$	−5.04120	+	5.04120i	−0.166839	+	0.166839i
$914$		−	18.9664i		−	0.627353i
$915$	0.258439	−	2.59604i	0.00854373	−	0.0858226i
$916$			15.3666i			0.507727i
$917$	8.57539	−	5.15980i	0.283184	−	0.170392i
$918$	−26.6707	−	26.6707i	−0.880263	−	0.880263i
$919$			46.3097i			1.52762i	0.645443	+	0.763808i	$0.276673\pi$
$919$			46.3097i			1.52762i	−0.645443	+	0.763808i	$0.723327\pi$
$920$	3.15450	−	2.58329i	0.104001	−	0.0851686i
$921$	−21.6470			−0.713292
$922$	15.1030	+	15.1030i	0.497390	+	0.497390i
$923$	27.1772	−	27.1772i	0.894549	−	0.894549i
$924$	0.815861	−	3.28084i	0.0268399	−	0.107932i
$925$	18.8884	+	28.3973i	0.621047	+	0.933699i
$926$	−25.1798			−0.827459
$927$	6.43481	+	6.43481i	0.211347	+	0.211347i
$928$	5.33970	+	5.33970i	0.175284	+	0.175284i
$929$	−0.956653			−0.0313868			−0.0156934	−	0.999877i	$-0.504996\pi$
$929$	−0.956653			−0.0313868			−0.0156934	+	0.999877i	$0.504996\pi$
$930$	−14.0928	−	17.2089i	−0.462120	−	0.564302i
$931$	−19.8776	+	37.4957i	−0.651463	+	1.22887i
$932$	−8.25655	+	8.25655i	−0.270452	+	0.270452i
$933$	−1.83465	−	1.83465i	−0.0600638	−	0.0600638i
$934$	8.38882			0.274491
$935$	1.49716	−	15.0391i	0.0489625	−	0.491832i
$936$			8.72395i			0.285151i
$937$	−17.9858	−	17.9858i	−0.587571	−	0.587571i	0.349402	−	0.936973i	$-0.386385\pi$
$937$	−17.9858	−	17.9858i	−0.587571	−	0.587571i	−0.936973	+	0.349402i	$0.886385\pi$
$938$	27.5039	−	16.5491i	0.898036	−	0.540347i
$939$		−	2.49899i		−	0.0815514i
$940$	−14.6428	−	1.45771i	−0.477595	−	0.0475451i
$941$		−	43.0392i		−	1.40304i	−0.712652	−	0.701518i	$-0.752506\pi$
$941$		−	43.0392i		−	1.40304i	0.712652	−	0.701518i	$-0.247494\pi$
$942$	−5.84996	+	5.84996i	−0.190602	+	0.190602i
$943$	−6.80286	+	6.80286i	−0.221532	+	0.221532i
$944$	−1.55180			−0.0505067
$945$	−29.8354	+	14.1351i	−0.970545	+	0.459814i
$946$	8.80128			0.286154
$947$	−26.4283	+	26.4283i	−0.858806	+	0.858806i	−0.991197	−	0.132392i	$-0.957734\pi$
$947$	−26.4283	+	26.4283i	−0.858806	+	0.858806i	0.132392	+	0.991197i	$0.457734\pi$
$948$	5.52549	−	5.52549i	0.179460	−	0.179460i
$949$			25.1831i			0.817478i
$950$	−16.7883	−	25.2400i	−0.544684	−	0.818893i
$951$		−	1.37067i		−	0.0444469i
$952$	15.3226	−	9.21961i	0.496609	−	0.298809i
$953$	8.40083	+	8.40083i	0.272129	+	0.272129i	0.829957	−	0.557827i	$-0.188365\pi$
$953$	8.40083	+	8.40083i	0.272129	+	0.272129i	−0.557827	+	0.829957i	$0.688365\pi$
$954$		−	8.21385i		−	0.265933i
$955$	−4.16393	−	5.08463i	−0.134742	−	0.164535i
$956$	16.8327			0.544407
$957$	6.82312	+	6.82312i	0.220560	+	0.220560i
$958$	14.3562	−	14.3562i	0.463827	−	0.463827i
$959$	43.9879	+	10.9387i	1.42044	+	0.353228i
$960$	−0.283045	+	2.84321i	−0.00913524	+	0.0917643i
$961$	−29.6018			−0.954897
$962$	30.7765	+	30.7765i	0.992273	+	0.992273i
$963$	−9.12196	−	9.12196i	−0.293951	−	0.293951i
$964$	18.0615			0.581721
$965$	3.60799	−	36.2426i	0.116145	−	1.16669i
$966$	5.98235	+	1.48765i	0.192479	+	0.0478645i
$967$	−33.1683	+	33.1683i	−1.06662	+	1.06662i	−0.0690054	+	0.997616i	$0.521983\pi$
$967$	−33.1683	+	33.1683i	−1.06662	+	1.06662i	−0.997616	+	0.0690054i	$0.978017\pi$
$968$	0.707107	+	0.707107i	0.0227273	+	0.0227273i
$969$	52.3613			1.68209
$970$	−12.0551	−	14.7206i	−0.387065	−	0.472651i
$971$		−	13.3889i		−	0.429671i	−0.976650	−	0.214836i	$-0.931078\pi$
$971$		−	13.3889i		−	0.429671i	0.976650	−	0.214836i	$-0.0689216\pi$
$972$	−9.10095	−	9.10095i	−0.291913	−	0.291913i
$973$	15.3909	+	25.5791i	0.493410	+	0.820028i
$974$			2.74028i			0.0878042i
$975$	−39.9676	−	8.03729i	−1.27999	−	0.257399i
$976$			0.913067i			0.0292265i
$977$	11.4580	−	11.4580i	0.366574	−	0.366574i	−0.499652	−	0.866226i	$-0.666539\pi$
$977$	11.4580	−	11.4580i	0.366574	−	0.366574i	0.866226	+	0.499652i	$0.166539\pi$
$978$	9.89456	−	9.89456i	0.316393	−	0.316393i
$979$	−7.76249			−0.248090
$980$	−3.08992	−	15.3445i	−0.0987040	−	0.490161i
$981$	5.49058			0.175301
$982$	−2.32094	+	2.32094i	−0.0740641	+	0.0740641i
$983$	−24.6936	+	24.6936i	−0.787603	+	0.787603i	−0.981101	−	0.193498i	$-0.938017\pi$
$983$	−24.6936	+	24.6936i	−0.787603	+	0.787603i	0.193498	+	0.981101i	$0.438017\pi$
$984$		−	6.74196i		−	0.214926i
$985$	−51.4566	−	5.12256i	−1.63954	−	0.163218i
$986$			51.0400i			1.62545i
$987$	−11.4704	−	19.0634i	−0.365107	−	0.606794i
$988$	−27.3546	−	27.3546i	−0.870265	−	0.870265i
$989$			16.0484i			0.510309i
$990$	0.302847	−	3.04212i	0.00962510	−	0.0966850i
$991$	45.0226			1.43019			0.715096	−	0.699026i	$-0.246383\pi$
$991$	45.0226			1.43019			0.715096	+	0.699026i	$0.246383\pi$
$992$	5.50463	+	5.50463i	0.174772	+	0.174772i
$993$	−19.8286	+	19.8286i	−0.629242	+	0.629242i
$994$	−15.4654	−	3.84583i	−0.490531	−	0.121982i
$995$	22.2457	+	27.1645i	0.705236	+	0.861173i
$996$	9.10993			0.288659
$997$	−6.59782	−	6.59782i	−0.208955	−	0.208955i	0.594868	−	0.803823i	$-0.297204\pi$
$997$	−6.59782	−	6.59782i	−0.208955	−	0.208955i	−0.803823	+	0.594868i	$0.797204\pi$
$998$	−24.1971	−	24.1971i	−0.765946	−	0.765946i
$999$	−38.0647			−1.20432

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.l.c.573.3	✓	40
5.2	odd	4	inner	770.2.l.c.727.8	yes	40
7.6	odd	2	inner	770.2.l.c.573.8	yes	40
35.27	even	4	inner	770.2.l.c.727.3	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.l.c.573.3	✓	40	1.1	even	1	trivial
770.2.l.c.573.8	yes	40	7.6	odd	2	inner
770.2.l.c.727.3	yes	40	35.27	even	4	inner
770.2.l.c.727.8	yes	40	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.903547 + 0.903547i) q^{3} -1.00000i q^{4} +(-1.41673 - 1.72999i) q^{5} -1.27781i q^{6} +(1.36406 + 2.26701i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.36720i q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.903547 + 0.903547i) q^{3} -1.00000i q^{4} +(-1.41673 - 1.72999i) q^{5} -1.27781i q^{6} +(1.36406 + 2.26701i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.36720i q^{9} +(2.22507 + 0.221508i) q^{10} -1.00000 q^{11} +(0.903547 + 0.903547i) q^{12} +(4.51196 - 4.51196i) q^{13} +(-2.56755 - 0.638484i) q^{14} +(2.84321 + 0.283045i) q^{15} -1.00000 q^{16} +(-4.77930 - 4.77930i) q^{17} +(-0.966759 - 0.966759i) q^{18} +6.06268 q^{19} +(-1.72999 + 1.41673i) q^{20} +(-3.28084 - 0.815861i) q^{21} +(0.707107 - 0.707107i) q^{22} +(1.28935 + 1.28935i) q^{23} -1.27781 q^{24} +(-0.985742 + 4.90187i) q^{25} +6.38087i q^{26} +(-3.94598 - 3.94598i) q^{27} +(2.26701 - 1.36406i) q^{28} +7.55147i q^{29} +(-2.21060 + 1.81031i) q^{30} +7.78472i q^{31} +(0.707107 - 0.707107i) q^{32} +(0.903547 - 0.903547i) q^{33} +6.75895 q^{34} +(1.98941 - 5.57156i) q^{35} +1.36720 q^{36} +(4.82324 - 4.82324i) q^{37} +(-4.28696 + 4.28696i) q^{38} +8.15354i q^{39} +(0.221508 - 2.22507i) q^{40} +5.27619i q^{41} +(2.89681 - 1.74301i) q^{42} +(6.22344 + 6.22344i) q^{43} +1.00000i q^{44} +(2.36525 - 1.93696i) q^{45} -1.82342 q^{46} +(4.65334 + 4.65334i) q^{47} +(0.903547 - 0.903547i) q^{48} +(-3.27869 + 6.18468i) q^{49} +(-2.76912 - 4.16317i) q^{50} +8.63665 q^{51} +(-4.51196 - 4.51196i) q^{52} +(4.24814 + 4.24814i) q^{53} +5.58045 q^{54} +(1.41673 + 1.72999i) q^{55} +(-0.638484 + 2.56755i) q^{56} +(-5.47792 + 5.47792i) q^{57} +(-5.33970 - 5.33970i) q^{58} +1.55180 q^{59} +(0.283045 - 2.84321i) q^{60} -0.913067i q^{61} +(-5.50463 - 5.50463i) q^{62} +(-3.09947 + 1.86495i) q^{63} +1.00000i q^{64} +(-14.1979 - 1.41342i) q^{65} +1.27781i q^{66} +(-8.57879 + 8.57879i) q^{67} +(-4.77930 + 4.77930i) q^{68} -2.32998 q^{69} +(2.53296 + 5.34641i) q^{70} +6.02338 q^{71} +(-0.966759 + 0.966759i) q^{72} +(-2.79071 + 2.79071i) q^{73} +6.82109i q^{74} +(-3.53841 - 5.31974i) q^{75} -6.06268i q^{76} +(-1.36406 - 2.26701i) q^{77} +(-5.76542 - 5.76542i) q^{78} -6.11533i q^{79} +(1.41673 + 1.72999i) q^{80} +3.02914 q^{81} +(-3.73083 - 3.73083i) q^{82} +(5.04120 - 5.04120i) q^{83} +(-0.815861 + 3.28084i) q^{84} +(-1.49716 + 15.0391i) q^{85} -8.80128 q^{86} +(-6.82312 - 6.82312i) q^{87} +(-0.707107 - 0.707107i) q^{88} +7.76249 q^{89} +(-0.302847 + 3.04212i) q^{90} +(16.3832 + 4.07409i) q^{91} +(1.28935 - 1.28935i) q^{92} +(-7.03386 - 7.03386i) q^{93} -6.58082 q^{94} +(-8.58919 - 10.4884i) q^{95} +1.27781i q^{96} +(-6.01682 - 6.01682i) q^{97} +(-2.05484 - 6.69161i) q^{98} -1.36720i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q+O(q^{10}) \) 40 * q	\( 40 q - 40 q^{11} + 56 q^{15} - 40 q^{16} - 8 q^{18} - 4 q^{21} - 32 q^{25} - 24 q^{30} + 48 q^{35} - 48 q^{36} - 8 q^{37} - 40 q^{42} - 8 q^{43} + 32 q^{46} + 16 q^{50} - 8 q^{51} + 56 q^{53} + 4 q^{56} + 32 q^{57} - 8 q^{58} + 8 q^{60} - 16 q^{63} + 8 q^{65} - 24 q^{67} - 4 q^{70} - 24 q^{71} - 8 q^{72} - 16 q^{78} - 24 q^{81} + 96 q^{85} - 96 q^{86} + 64 q^{91} + 24 q^{93} - 112 q^{95} + 16 q^{98}+O(q^{100}) \) 40 * q - 40 * q^11 + 56 * q^15 - 40 * q^16 - 8 * q^18 - 4 * q^21 - 32 * q^25 - 24 * q^30 + 48 * q^35 - 48 * q^36 - 8 * q^37 - 40 * q^42 - 8 * q^43 + 32 * q^46 + 16 * q^50 - 8 * q^51 + 56 * q^53 + 4 * q^56 + 32 * q^57 - 8 * q^58 + 8 * q^60 - 16 * q^63 + 8 * q^65 - 24 * q^67 - 4 * q^70 - 24 * q^71 - 8 * q^72 - 16 * q^78 - 24 * q^81 + 96 * q^85 - 96 * q^86 + 64 * q^91 + 24 * q^93 - 112 * q^95 + 16 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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