LMFDB - Embedded newform 770.2.l.b.573.2

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:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			573.2
Character	$\chi$	$=$	770.573
Dual form			770.2.l.b.727.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-0.878808 + 0.878808i) q^{3} -1.00000i q^{4} +(0.142676 + 2.23151i) q^{5} -1.24282i q^{6} +(0.993466 - 2.45215i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.45539i q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.878808 + 0.878808i) q^{3} -1.00000i q^{4} +(0.142676 + 2.23151i) q^{5} -1.24282i q^{6} +(0.993466 - 2.45215i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.45539i q^{9} +(-1.67880 - 1.47703i) q^{10} +1.00000 q^{11} +(0.878808 + 0.878808i) q^{12} +(-3.33166 + 3.33166i) q^{13} +(1.03144 + 2.43642i) q^{14} +(-2.08645 - 1.83569i) q^{15} -1.00000 q^{16} +(-0.428381 - 0.428381i) q^{17} +(-1.02912 - 1.02912i) q^{18} +3.00044 q^{19} +(2.23151 - 0.142676i) q^{20} +(1.28190 + 3.02803i) q^{21} +(-0.707107 + 0.707107i) q^{22} +(3.55487 + 3.55487i) q^{23} -1.24282 q^{24} +(-4.95929 + 0.636764i) q^{25} -4.71168i q^{26} +(-3.91544 - 3.91544i) q^{27} +(-2.45215 - 0.993466i) q^{28} +0.740302i q^{29} +(2.77337 - 0.177320i) q^{30} +10.7325i q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.878808 + 0.878808i) q^{33} +0.605822 q^{34} +(5.61374 + 1.86707i) q^{35} +1.45539 q^{36} +(-2.42399 + 2.42399i) q^{37} +(-2.12163 + 2.12163i) q^{38} -5.85578i q^{39} +(-1.47703 + 1.67880i) q^{40} +1.70572i q^{41} +(-3.04758 - 1.23470i) q^{42} +(-8.29161 - 8.29161i) q^{43} -1.00000i q^{44} +(-3.24773 + 0.207649i) q^{45} -5.02735 q^{46} +(-1.30912 - 1.30912i) q^{47} +(0.878808 - 0.878808i) q^{48} +(-5.02605 - 4.87225i) q^{49} +(3.05649 - 3.95701i) q^{50} +0.752930 q^{51} +(3.33166 + 3.33166i) q^{52} +(-4.40443 - 4.40443i) q^{53} +5.53726 q^{54} +(0.142676 + 2.23151i) q^{55} +(2.43642 - 1.03144i) q^{56} +(-2.63681 + 2.63681i) q^{57} +(-0.523473 - 0.523473i) q^{58} -9.46005 q^{59} +(-1.83569 + 2.08645i) q^{60} -3.33840i q^{61} +(-7.58900 - 7.58900i) q^{62} +(3.56884 + 1.44588i) q^{63} +1.00000i q^{64} +(-7.90998 - 6.95929i) q^{65} -1.24282i q^{66} +(-9.80074 + 9.80074i) q^{67} +(-0.428381 + 0.428381i) q^{68} -6.24810 q^{69} +(-5.28973 + 2.64929i) q^{70} +13.7560 q^{71} +(-1.02912 + 1.02912i) q^{72} +(-5.99019 + 5.99019i) q^{73} -3.42804i q^{74} +(3.79867 - 4.91785i) q^{75} -3.00044i q^{76} +(0.993466 - 2.45215i) q^{77} +(4.14066 + 4.14066i) q^{78} +2.34126i q^{79} +(-0.142676 - 2.23151i) q^{80} +2.51565 q^{81} +(-1.20612 - 1.20612i) q^{82} +(6.98186 - 6.98186i) q^{83} +(3.02803 - 1.28190i) q^{84} +(0.894818 - 1.01706i) q^{85} +11.7261 q^{86} +(-0.650584 - 0.650584i) q^{87} +(0.707107 + 0.707107i) q^{88} +6.29246 q^{89} +(2.14966 - 2.44332i) q^{90} +(4.85983 + 11.4796i) q^{91} +(3.55487 - 3.55487i) q^{92} +(-9.43178 - 9.43178i) q^{93} +1.85137 q^{94} +(0.428089 + 6.69551i) q^{95} +1.24282i q^{96} +(-3.67113 - 3.67113i) q^{97} +(6.99916 - 0.108754i) q^{98} +1.45539i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+O(q^{10}) $ 24 * q	$ 24 q + 24 q^{11} - 24 q^{15} - 24 q^{16} - 24 q^{18} - 28 q^{21} + 16 q^{23} + 16 q^{25} - 24 q^{30} + 16 q^{35} - 64 q^{36} - 8 q^{37} + 16 q^{42} + 40 q^{43} - 16 q^{46} + 16 q^{50} - 24 q^{51} - 88 q^{53} + 4 q^{56} - 112 q^{57} + 8 q^{58} - 8 q^{60} + 48 q^{63} - 8 q^{65} - 88 q^{67} - 28 q^{70} + 40 q^{71} - 24 q^{72} + 64 q^{78} - 136 q^{81} + 64 q^{85} + 96 q^{86} + 16 q^{92} - 104 q^{93} + 64 q^{95} - 16 q^{98}+O(q^{100}) $ 24 * q + 24 * q^11 - 24 * q^15 - 24 * q^16 - 24 * q^18 - 28 * q^21 + 16 * q^23 + 16 * q^25 - 24 * q^30 + 16 * q^35 - 64 * q^36 - 8 * q^37 + 16 * q^42 + 40 * q^43 - 16 * q^46 + 16 * q^50 - 24 * q^51 - 88 * q^53 + 4 * q^56 - 112 * q^57 + 8 * q^58 - 8 * q^60 + 48 * q^63 - 8 * q^65 - 88 * q^67 - 28 * q^70 + 40 * q^71 - 24 * q^72 + 64 * q^78 - 136 * q^81 + 64 * q^85 + 96 * q^86 + 16 * q^92 - 104 * q^93 + 64 * 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
$3$	−0.878808	+	0.878808i	−0.507380	+	0.507380i	−0.913721	−	0.406341i	$-0.866804\pi$
$3$	−0.878808	+	0.878808i	−0.507380	+	0.507380i	0.406341	+	0.913721i	$0.366804\pi$
$4$		−	1.00000i		−	0.500000i
$5$	0.142676	+	2.23151i	0.0638065	+	0.997962i
$5$	0.142676	+	2.23151i	0.0638065	+	0.997962i
$6$		−	1.24282i		−	0.507380i
$7$	0.993466	−	2.45215i	0.375495	−	0.926824i
$7$	0.993466	−	2.45215i	0.375495	−	0.926824i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$			1.45539i			0.485131i
$10$	−1.67880	−	1.47703i	−0.530884	−	0.467078i
$11$	1.00000			0.301511
$11$	1.00000			0.301511
$12$	0.878808	+	0.878808i	0.253690	+	0.253690i
$13$	−3.33166	+	3.33166i	−0.924036	+	0.924036i	−0.997312	−	0.0732760i	$-0.976655\pi$
$13$	−3.33166	+	3.33166i	−0.924036	+	0.924036i	0.0732760	+	0.997312i	$0.476655\pi$
$14$	1.03144	+	2.43642i	0.275665	+	0.651160i
$15$	−2.08645	−	1.83569i	−0.538720	−	0.473972i
$16$	−1.00000			−0.250000
$17$	−0.428381	−	0.428381i	−0.103898	−	0.103898i	0.653247	−	0.757145i	$-0.273406\pi$
$17$	−0.428381	−	0.428381i	−0.103898	−	0.103898i	−0.757145	+	0.653247i	$0.773406\pi$
$18$	−1.02912	−	1.02912i	−0.242565	−	0.242565i
$19$	3.00044			0.688348			0.344174	−	0.938906i	$-0.388159\pi$
$19$	3.00044			0.688348			0.344174	+	0.938906i	$0.388159\pi$
$20$	2.23151	−	0.142676i	0.498981	−	0.0319032i
$21$	1.28190	+	3.02803i	0.279734	+	0.660771i
$22$	−0.707107	+	0.707107i	−0.150756	+	0.150756i
$23$	3.55487	+	3.55487i	0.741242	+	0.741242i	0.972817	−	0.231575i	$-0.0743879\pi$
$23$	3.55487	+	3.55487i	0.741242	+	0.741242i	−0.231575	+	0.972817i	$0.574388\pi$
$24$	−1.24282			−0.253690
$25$	−4.95929	+	0.636764i	−0.991857	+	0.127353i
$26$		−	4.71168i		−	0.924036i
$27$	−3.91544	−	3.91544i	−0.753526	−	0.753526i
$28$	−2.45215	−	0.993466i	−0.463412	−	0.187747i
$29$			0.740302i			0.137471i	0.997635	+	0.0687353i	$0.0218964\pi$
$29$			0.740302i			0.137471i	−0.997635	+	0.0687353i	$0.978104\pi$
$30$	2.77337	−	0.177320i	0.506346	−	0.0323741i
$31$			10.7325i			1.92761i	0.266610	+	0.963804i	$0.414096\pi$
$31$			10.7325i			1.92761i	−0.266610	+	0.963804i	$0.585904\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−0.878808	+	0.878808i	−0.152981	+	0.152981i
$34$	0.605822			0.103898
$35$	5.61374	+	1.86707i	0.948895	+	0.315592i
$36$	1.45539			0.242565
$37$	−2.42399	+	2.42399i	−0.398502	+	0.398502i	−0.877704	−	0.479202i	$-0.840926\pi$
$37$	−2.42399	+	2.42399i	−0.398502	+	0.398502i	0.479202	+	0.877704i	$0.340926\pi$
$38$	−2.12163	+	2.12163i	−0.344174	+	0.344174i
$39$		−	5.85578i		−	0.937675i
$40$	−1.47703	+	1.67880i	−0.233539	+	0.265442i
$41$			1.70572i			0.266388i	0.991090	+	0.133194i	$0.0425234\pi$
$41$			1.70572i			0.266388i	−0.991090	+	0.133194i	$0.957477\pi$
$42$	−3.04758	−	1.23470i	−0.470252	−	0.190519i
$43$	−8.29161	−	8.29161i	−1.26446	−	1.26446i	−0.948909	−	0.315549i	$-0.897811\pi$
$43$	−8.29161	−	8.29161i	−1.26446	−	1.26446i	−0.315549	−	0.948909i	$-0.602189\pi$
$44$		−	1.00000i		−	0.150756i
$45$	−3.24773	+	0.207649i	−0.484142	+	0.0309545i
$46$	−5.02735			−0.741242
$47$	−1.30912	−	1.30912i	−0.190955	−	0.190955i	0.605154	−	0.796109i	$-0.293112\pi$
$47$	−1.30912	−	1.30912i	−0.190955	−	0.190955i	−0.796109	+	0.605154i	$0.793112\pi$
$48$	0.878808	−	0.878808i	0.126845	−	0.126845i
$49$	−5.02605	−	4.87225i	−0.718007	−	0.696036i
$50$	3.05649	−	3.95701i	0.432252	−	0.559605i
$51$	0.752930			0.105431
$52$	3.33166	+	3.33166i	0.462018	+	0.462018i
$53$	−4.40443	−	4.40443i	−0.604995	−	0.604995i	0.336638	−	0.941634i	$-0.390710\pi$
$53$	−4.40443	−	4.40443i	−0.604995	−	0.604995i	−0.941634	+	0.336638i	$0.890710\pi$
$54$	5.53726			0.753526
$55$	0.142676	+	2.23151i	0.0192384	+	0.300897i
$56$	2.43642	−	1.03144i	0.325580	−	0.137832i
$57$	−2.63681	+	2.63681i	−0.349254	+	0.349254i
$58$	−0.523473	−	0.523473i	−0.0687353	−	0.0687353i
$59$	−9.46005			−1.23159			−0.615797	−	0.787905i	$-0.711166\pi$
$59$	−9.46005			−1.23159			−0.615797	+	0.787905i	$0.711166\pi$
$60$	−1.83569	+	2.08645i	−0.236986	+	0.269360i
$61$		−	3.33840i		−	0.427438i	−0.976895	−	0.213719i	$-0.931442\pi$
$61$		−	3.33840i		−	0.427438i	0.976895	−	0.213719i	$-0.0685577\pi$
$62$	−7.58900	−	7.58900i	−0.963804	−	0.963804i
$63$	3.56884	+	1.44588i	0.449631	+	0.182164i
$64$			1.00000i			0.125000i
$65$	−7.90998	−	6.95929i	−0.981112	−	0.863193i
$66$		−	1.24282i		−	0.152981i
$67$	−9.80074	+	9.80074i	−1.19735	+	1.19735i	−0.222394	+	0.974957i	$0.571387\pi$
$67$	−9.80074	+	9.80074i	−1.19735	+	1.19735i	−0.974957	+	0.222394i	$0.928613\pi$
$68$	−0.428381	+	0.428381i	−0.0519488	+	0.0519488i
$69$	−6.24810			−0.752183
$70$	−5.28973	+	2.64929i	−0.632244	+	0.316651i
$71$	13.7560			1.63254			0.816268	−	0.577673i	$-0.196039\pi$
$71$	13.7560			1.63254			0.816268	+	0.577673i	$0.196039\pi$
$72$	−1.02912	+	1.02912i	−0.121283	+	0.121283i
$73$	−5.99019	+	5.99019i	−0.701098	+	0.701098i	−0.964646	−	0.263548i	$-0.915107\pi$
$73$	−5.99019	+	5.99019i	−0.701098	+	0.701098i	0.263548	+	0.964646i	$0.415107\pi$
$74$		−	3.42804i		−	0.398502i
$75$	3.79867	−	4.91785i	0.438632	−	0.567865i
$76$		−	3.00044i		−	0.344174i
$77$	0.993466	−	2.45215i	0.113216	−	0.279448i
$78$	4.14066	+	4.14066i	0.468837	+	0.468837i
$79$			2.34126i			0.263412i	0.991289	+	0.131706i	$0.0420455\pi$
$79$			2.34126i			0.263412i	−0.991289	+	0.131706i	$0.957955\pi$
$80$	−0.142676	−	2.23151i	−0.0159516	−	0.249491i
$81$	2.51565			0.279517
$82$	−1.20612	−	1.20612i	−0.133194	−	0.133194i
$83$	6.98186	−	6.98186i	0.766358	−	0.766358i	−0.211105	−	0.977463i	$-0.567706\pi$
$83$	6.98186	−	6.98186i	0.766358	−	0.766358i	0.977463	+	0.211105i	$0.0677062\pi$
$84$	3.02803	−	1.28190i	0.330385	−	0.139867i
$85$	0.894818	−	1.01706i	0.0970566	−	0.110315i
$86$	11.7261			1.26446
$87$	−0.650584	−	0.650584i	−0.0697499	−	0.0697499i
$88$	0.707107	+	0.707107i	0.0753778	+	0.0753778i
$89$	6.29246			0.666999			0.333500	−	0.942750i	$-0.391770\pi$
$89$	6.29246			0.666999			0.333500	+	0.942750i	$0.391770\pi$
$90$	2.14966	−	2.44332i	0.226594	−	0.257548i
$91$	4.85983	+	11.4796i	0.509448	+	1.20339i
$92$	3.55487	−	3.55487i	0.370621	−	0.370621i
$93$	−9.43178	−	9.43178i	−0.978030	−	0.978030i
$94$	1.85137			0.190955
$95$	0.428089	+	6.69551i	0.0439210	+	0.686945i
$96$			1.24282i			0.126845i
$97$	−3.67113	−	3.67113i	−0.372747	−	0.372747i	0.495730	−	0.868477i	$-0.334901\pi$
$97$	−3.67113	−	3.67113i	−0.372747	−	0.372747i	−0.868477	+	0.495730i	$0.834901\pi$
$98$	6.99916	−	0.108754i	0.707021	−	0.0109858i
$99$			1.45539i			0.146272i
$100$	0.636764	+	4.95929i	0.0636764	+	0.495929i
$101$			0.468416i			0.0466091i	0.999728	+	0.0233046i	$0.00741874\pi$
$101$			0.468416i			0.0466091i	−0.999728	+	0.0233046i	$0.992581\pi$
$102$	−0.532402	+	0.532402i	−0.0527156	+	0.0527156i
$103$	−5.43017	+	5.43017i	−0.535051	+	0.535051i	−0.922071	−	0.387020i	$-0.873504\pi$
$103$	−5.43017	+	5.43017i	−0.535051	+	0.535051i	0.387020	+	0.922071i	$0.373504\pi$
$104$	−4.71168			−0.462018
$105$	−6.57419	+	3.29260i	−0.641576	+	0.321325i
$106$	6.22881			0.604995
$107$	−10.8554	+	10.8554i	−1.04943	+	1.04943i	−0.0507191	+	0.998713i	$0.516151\pi$
$107$	−10.8554	+	10.8554i	−1.04943	+	1.04943i	−0.998713	+	0.0507191i	$0.983849\pi$
$108$	−3.91544	+	3.91544i	−0.376763	+	0.376763i
$109$		−	2.13253i		−	0.204259i	−0.994771	−	0.102130i	$-0.967434\pi$
$109$		−	2.13253i		−	0.204259i	0.994771	−	0.102130i	$-0.0325657\pi$
$110$	−1.67880	−	1.47703i	−0.160068	−	0.140829i
$111$		−	4.26045i		−	0.404384i
$112$	−0.993466	+	2.45215i	−0.0938737	+	0.231706i
$113$	13.4583	+	13.4583i	1.26605	+	1.26605i	0.948112	+	0.317936i	$0.102990\pi$
$113$	13.4583	+	13.4583i	1.26605	+	1.26605i	0.317936	+	0.948112i	$0.397010\pi$
$114$		−	3.72901i		−	0.349254i
$115$	−7.42555	+	8.43993i	−0.692436	+	0.787028i
$116$	0.740302			0.0687353
$117$	−4.84887	−	4.84887i	−0.448278	−	0.448278i
$118$	6.68927	−	6.68927i	0.615797	−	0.615797i
$119$	−1.47604	+	0.624872i	−0.135308	+	0.0572819i
$120$	−0.177320	−	2.77337i	−0.0161871	−	0.253173i
$121$	1.00000			0.0909091
$122$	2.36060	+	2.36060i	0.213719	+	0.213719i
$123$	−1.49900	−	1.49900i	−0.135160	−	0.135160i
$124$	10.7325			0.963804
$125$	−2.12852	−	10.9759i	−0.190380	−	0.981710i
$126$	−3.54594	+	1.50116i	−0.315898	+	0.133734i
$127$	−3.07988	+	3.07988i	−0.273295	+	0.273295i	−0.830425	−	0.557130i	$-0.811903\pi$
$127$	−3.07988	+	3.07988i	−0.273295	+	0.273295i	0.557130	+	0.830425i	$0.311903\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	14.5735			1.28312
$130$	10.5142	−	0.672241i	0.922153	−	0.0589594i
$131$			1.06786i			0.0932993i	0.998911	+	0.0466497i	$0.0148544\pi$
$131$			1.06786i			0.0932993i	−0.998911	+	0.0466497i	$0.985146\pi$
$132$	0.878808	+	0.878808i	0.0764904	+	0.0764904i
$133$	2.98083	−	7.35752i	0.258471	−	0.637978i
$134$		−	13.8603i		−	1.19735i
$135$	8.17870	−	9.29598i	0.703911	−	0.800070i
$136$		−	0.605822i		−	0.0519488i
$137$	1.79047	−	1.79047i	0.152971	−	0.152971i	−0.626473	−	0.779443i	$-0.715502\pi$
$137$	1.79047	−	1.79047i	0.152971	−	0.152971i	0.779443	+	0.626473i	$0.215502\pi$
$138$	4.41807	−	4.41807i	0.376091	−	0.376091i
$139$	20.5103			1.73966			0.869829	−	0.493353i	$-0.164229\pi$
$139$	20.5103			1.73966			0.869829	+	0.493353i	$0.164229\pi$
$140$	1.86707	−	5.61374i	0.157796	−	0.474447i
$141$	2.30093			0.193773
$142$	−9.72696	+	9.72696i	−0.816268	+	0.816268i
$143$	−3.33166	+	3.33166i	−0.278607	+	0.278607i
$144$		−	1.45539i		−	0.121283i
$145$	−1.65199	+	0.105623i	−0.137191	+	0.00877152i
$146$		−	8.47140i		−	0.701098i
$147$	8.69871	−	0.135162i	0.717457	−	0.0111479i
$148$	2.42399	+	2.42399i	0.199251	+	0.199251i
$149$		−	2.73385i		−	0.223966i	−0.993710	−	0.111983i	$-0.964280\pi$
$149$		−	2.73385i		−	0.223966i	0.993710	−	0.111983i	$-0.0357202\pi$
$150$	0.791385	+	6.16351i	0.0646163	+	0.503249i
$151$	17.1990			1.39964			0.699819	−	0.714320i	$-0.253264\pi$
$151$	17.1990			1.39964			0.699819	+	0.714320i	$0.253264\pi$
$152$	2.12163	+	2.12163i	0.172087	+	0.172087i
$153$	0.623463	−	0.623463i	0.0504040	−	0.0504040i
$154$	1.03144	+	2.43642i	0.0831161	+	0.196332i
$155$	−23.9496	+	1.53126i	−1.92368	+	0.122994i
$156$	−5.85578			−0.468837
$157$	−4.53073	−	4.53073i	−0.361591	−	0.361591i	0.502807	−	0.864399i	$-0.332301\pi$
$157$	−4.53073	−	4.53073i	−0.361591	−	0.361591i	−0.864399	+	0.502807i	$0.832301\pi$
$158$	−1.65552	−	1.65552i	−0.131706	−	0.131706i
$159$	7.74130			0.613925
$160$	1.67880	+	1.47703i	0.132721	+	0.116769i
$161$	12.2487	−	5.18542i	0.965334	−	0.408669i
$162$	−1.77883	+	1.77883i	−0.139758	+	0.139758i
$163$	10.9892	+	10.9892i	0.860737	+	0.860737i	0.991424	−	0.130687i	$-0.0417181\pi$
$163$	10.9892	+	10.9892i	0.860737	+	0.860737i	−0.130687	+	0.991424i	$0.541718\pi$
$164$	1.70572			0.133194
$165$	−2.08645	−	1.83569i	−0.162430	−	0.142908i
$166$			9.87384i			0.766358i
$167$	7.95098	+	7.95098i	0.615265	+	0.615265i	0.944313	−	0.329048i	$-0.106728\pi$
$167$	7.95098	+	7.95098i	0.615265	+	0.615265i	−0.329048	+	0.944313i	$0.606728\pi$
$168$	−1.23470	+	3.04758i	−0.0952593	+	0.235126i
$169$		−	9.19989i		−	0.707684i
$170$	0.0864361	+	1.35190i	0.00662934	+	0.103686i
$171$			4.36682i			0.333939i
$172$	−8.29161	+	8.29161i	−0.632229	+	0.632229i
$173$	13.8769	−	13.8769i	1.05504	−	1.05504i	0.0566474	−	0.998394i	$-0.481959\pi$
$173$	13.8769	−	13.8769i	1.05504	−	1.05504i	0.998394	−	0.0566474i	$-0.0180411\pi$
$174$	0.920064			0.0697499
$175$	−3.36544	+	12.7935i	−0.254404	+	0.967098i
$176$	−1.00000			−0.0753778
$177$	8.31357	−	8.31357i	0.624886	−	0.624886i
$178$	−4.44944	+	4.44944i	−0.333500	+	0.333500i
$179$			4.44278i			0.332069i	0.986120	+	0.166035i	$0.0530964\pi$
$179$			4.44278i			0.332069i	−0.986120	+	0.166035i	$0.946904\pi$
$180$	0.207649	+	3.24773i	0.0154772	+	0.242071i
$181$			8.32007i			0.618426i	0.950993	+	0.309213i	$0.100066\pi$
$181$			8.32007i			0.618426i	−0.950993	+	0.309213i	$0.899934\pi$
$182$	−11.5537	−	4.68089i	−0.856419	−	0.346971i
$183$	2.93381	+	2.93381i	0.216873	+	0.216873i
$184$			5.02735i			0.370621i
$185$	−5.75501	−	5.06332i	−0.423117	−	0.372263i
$186$	13.3386			0.978030
$187$	−0.428381	−	0.428381i	−0.0313263	−	0.0313263i
$188$	−1.30912	+	1.30912i	−0.0954774	+	0.0954774i
$189$	−13.4911	+	5.71137i	−0.981331	+	0.415441i
$190$	−5.03715	−	4.43174i	−0.365433	−	0.321512i
$191$	−1.06316			−0.0769279			−0.0384639	−	0.999260i	$-0.512246\pi$
$191$	−1.06316			−0.0769279			−0.0384639	+	0.999260i	$0.512246\pi$
$192$	−0.878808	−	0.878808i	−0.0634225	−	0.0634225i
$193$	16.4522	+	16.4522i	1.18426	+	1.18426i	0.978631	+	0.205624i	$0.0659224\pi$
$193$	16.4522	+	16.4522i	1.18426	+	1.18426i	0.205624	+	0.978631i	$0.434078\pi$
$194$	5.19176			0.372747
$195$	13.0672	−	0.835476i	0.935764	−	0.0598297i
$196$	−4.87225	+	5.02605i	−0.348018	+	0.359004i
$197$	−5.45862	+	5.45862i	−0.388911	+	0.388911i	−0.874299	−	0.485388i	$-0.838678\pi$
$197$	−5.45862	+	5.45862i	−0.388911	+	0.388911i	0.485388	+	0.874299i	$0.338678\pi$
$198$	−1.02912	−	1.02912i	−0.0731362	−	0.0731362i
$199$	13.1447			0.931805			0.465902	−	0.884836i	$-0.345730\pi$
$199$	13.1447			0.931805			0.465902	+	0.884836i	$0.345730\pi$
$200$	−3.95701	−	3.05649i	−0.279803	−	0.216126i
$201$		−	17.2259i		−	1.21502i
$202$	−0.331220	−	0.331220i	−0.0233046	−	0.0233046i
$203$	1.81533	+	0.735465i	0.127411	+	0.0516195i
$204$		−	0.752930i		−	0.0527156i
$205$	−3.80633	+	0.243364i	−0.265845	+	0.0169973i
$206$		−	7.67943i		−	0.535051i
$207$	−5.17374	+	5.17374i	−0.359600	+	0.359600i
$208$	3.33166	−	3.33166i	0.231009	−	0.231009i
$209$	3.00044			0.207545
$210$	2.32044	−	6.97688i	0.160125	−	0.481450i
$211$	−17.8252			−1.22714			−0.613569	−	0.789641i	$-0.710267\pi$
$211$	−17.8252			−1.22714			−0.613569	+	0.789641i	$0.710267\pi$
$212$	−4.40443	+	4.40443i	−0.302498	+	0.302498i
$213$	−12.0889	+	12.0889i	−0.828316	+	0.828316i
$214$		−	15.3519i		−	1.04943i
$215$	17.3198	−	19.6858i	1.18120	−	1.34256i
$216$		−	5.53726i		−	0.376763i
$217$	26.3176	+	10.6623i	1.78656	+	0.723807i
$218$	1.50793	+	1.50793i	0.102130	+	0.102130i
$219$		−	10.5284i		−	0.711446i
$220$	2.23151	−	0.142676i	0.150448	−	0.00961918i
$221$	2.85444			0.192010
$222$	3.01259	+	3.01259i	0.202192	+	0.202192i
$223$	20.8214	−	20.8214i	1.39430	−	1.39430i	0.578908	−	0.815393i	$-0.303479\pi$
$223$	20.8214	−	20.8214i	1.39430	−	1.39430i	0.815393	−	0.578908i	$-0.196521\pi$
$224$	−1.03144	−	2.43642i	−0.0689162	−	0.162790i
$225$	−0.926742	−	7.21771i	−0.0617828	−	0.481181i
$226$	−19.0329			−1.26605
$227$	10.2646	+	10.2646i	0.681283	+	0.681283i	0.960289	−	0.279007i	$-0.0900051\pi$
$227$	10.2646	+	10.2646i	0.681283	+	0.681283i	−0.279007	+	0.960289i	$0.590005\pi$
$228$	2.63681	+	2.63681i	0.174627	+	0.174627i
$229$	−18.2001			−1.20270			−0.601348	−	0.798987i	$-0.705369\pi$
$229$	−18.2001			−1.20270			−0.601348	+	0.798987i	$0.705369\pi$
$230$	−0.717280	−	11.2186i	−0.0472960	−	0.739732i
$231$	1.28190	+	3.02803i	0.0843429	+	0.199230i
$232$	−0.523473	+	0.523473i	−0.0343677	+	0.0343677i
$233$	5.19484	+	5.19484i	0.340326	+	0.340326i	0.856490	−	0.516164i	$-0.172641\pi$
$233$	5.19484	+	5.19484i	0.340326	+	0.340326i	−0.516164	+	0.856490i	$0.672641\pi$
$234$	6.85734			0.448278
$235$	2.73454	−	3.10809i	0.178381	−	0.202750i
$236$			9.46005i			0.615797i
$237$	−2.05751	−	2.05751i	−0.133650	−	0.133650i
$238$	0.601864	−	1.48557i	0.0390131	−	0.0962949i
$239$			28.7508i			1.85974i	0.367892	+	0.929868i	$0.380079\pi$
$239$			28.7508i			1.85974i	−0.367892	+	0.929868i	$0.619921\pi$
$240$	2.08645	+	1.83569i	0.134680	+	0.118493i
$241$			17.8073i			1.14707i	0.819182	+	0.573534i	$0.194428\pi$
$241$			17.8073i			1.14707i	−0.819182	+	0.573534i	$0.805572\pi$
$242$	−0.707107	+	0.707107i	−0.0454545	+	0.0454545i
$243$	9.53553	−	9.53553i	0.611705	−	0.611705i
$244$	−3.33840			−0.213719
$245$	10.1554	−	11.9108i	0.648804	−	0.760956i
$246$	2.11990			0.135160
$247$	−9.99643	+	9.99643i	−0.636058	+	0.636058i
$248$	−7.58900	+	7.58900i	−0.481902	+	0.481902i
$249$			12.2714i			0.777670i
$250$	9.26619	+	6.25601i	0.586045	+	0.395665i
$251$			2.78304i			0.175664i	0.996135	+	0.0878321i	$0.0279939\pi$
$251$			2.78304i			0.175664i	−0.996135	+	0.0878321i	$0.972006\pi$
$252$	1.44588	−	3.56884i	0.0910821	−	0.224816i
$253$	3.55487	+	3.55487i	0.223493	+	0.223493i
$254$		−	4.35561i		−	0.273295i
$255$	0.107425	+	1.68017i	0.00672719	+	0.105216i
$256$	1.00000			0.0625000
$257$	−17.6226	−	17.6226i	−1.09927	−	1.09927i	−0.994496	−	0.104775i	$-0.966588\pi$
$257$	−17.6226	−	17.6226i	−1.09927	−	1.09927i	−0.104775	−	0.994496i	$-0.533412\pi$
$258$	−10.3050	+	10.3050i	−0.641561	+	0.641561i
$259$	3.53583	+	8.35214i	0.219706	+	0.518977i
$260$	−6.95929	+	7.90998i	−0.431597	+	0.490556i
$261$	−1.07743			−0.0666913
$262$	−0.755091	−	0.755091i	−0.0466497	−	0.0466497i
$263$	−2.14151	−	2.14151i	−0.132051	−	0.132051i	0.637992	−	0.770043i	$-0.279765\pi$
$263$	−2.14151	−	2.14151i	−0.132051	−	0.132051i	−0.770043	+	0.637992i	$0.779765\pi$
$264$	−1.24282			−0.0764904
$265$	9.20014	−	10.4569i	0.565160	−	0.642365i
$266$	3.09478	+	7.31032i	0.189753	+	0.448224i
$267$	−5.52986	+	5.52986i	−0.338422	+	0.338422i
$268$	9.80074	+	9.80074i	0.598675	+	0.598675i
$269$	−13.1203			−0.799962			−0.399981	−	0.916523i	$-0.630983\pi$
$269$	−13.1203			−0.799962			−0.399981	+	0.916523i	$0.630983\pi$
$270$	0.790032	+	12.3565i	0.0480798	+	0.751990i
$271$		−	9.30142i		−	0.565021i	−0.959264	−	0.282511i	$-0.908833\pi$
$271$		−	9.30142i		−	0.565021i	0.959264	−	0.282511i	$-0.0911672\pi$
$272$	0.428381	+	0.428381i	0.0259744	+	0.0259744i
$273$	−14.3592	−	5.81751i	−0.869060	−	0.352092i
$274$			2.53211i			0.152971i
$275$	−4.95929	+	0.636764i	−0.299056	+	0.0383983i
$276$			6.24810i			0.376091i
$277$	8.01892	−	8.01892i	0.481810	−	0.481810i	−0.423899	−	0.905709i	$-0.639339\pi$
$277$	8.01892	−	8.01892i	0.481810	−	0.481810i	0.905709	+	0.423899i	$0.139339\pi$
$278$	−14.5029	+	14.5029i	−0.869829	+	0.869829i
$279$	−15.6200			−0.935143
$280$	2.64929	+	5.28973i	0.158326	+	0.316122i
$281$	13.8558			0.826568			0.413284	−	0.910602i	$-0.364382\pi$
$281$	13.8558			0.826568			0.413284	+	0.910602i	$0.364382\pi$
$282$	−1.62700	+	1.62700i	−0.0968866	+	0.0968866i
$283$	−0.449718	+	0.449718i	−0.0267329	+	0.0267329i	−0.720347	−	0.693614i	$-0.756017\pi$
$283$	−0.449718	+	0.449718i	−0.0267329	+	0.0267329i	0.693614	+	0.720347i	$0.256017\pi$
$284$		−	13.7560i		−	0.816268i
$285$	−6.26028	−	5.50786i	−0.370827	−	0.326258i
$286$		−	4.71168i		−	0.278607i
$287$	4.18267	+	1.69457i	0.246895	+	0.100027i
$288$	1.02912	+	1.02912i	0.0606414	+	0.0606414i
$289$		−	16.6330i		−	0.978411i
$290$	1.09345	−	1.24282i	0.0642095	−	0.0729810i
$291$	6.45244			0.378248
$292$	5.99019	+	5.99019i	0.350549	+	0.350549i
$293$	12.1194	−	12.1194i	0.708025	−	0.708025i	−0.258094	−	0.966120i	$-0.583095\pi$
$293$	12.1194	−	12.1194i	0.708025	−	0.708025i	0.966120	+	0.258094i	$0.0830946\pi$
$294$	−6.05534	+	6.24649i	−0.353155	+	0.364303i
$295$	−1.34972	−	21.1102i	−0.0785836	−	1.22908i
$296$	−3.42804			−0.199251
$297$	−3.91544	−	3.91544i	−0.227197	−	0.227197i
$298$	1.93312	+	1.93312i	0.111983	+	0.111983i
$299$	−23.6872			−1.36987
$300$	−4.91785	−	3.79867i	−0.283932	−	0.219316i
$301$	−28.5697	+	12.0948i	−1.64673	+	0.697133i
$302$	−12.1616	+	12.1616i	−0.699819	+	0.699819i
$303$	−0.411648	−	0.411648i	−0.0236485	−	0.0236485i
$304$	−3.00044			−0.172087
$305$	7.44967	−	0.476308i	0.426567	−	0.0272733i
$306$			0.881710i			0.0504040i
$307$	1.99609	+	1.99609i	0.113923	+	0.113923i	0.761770	−	0.647847i	$-0.224331\pi$
$307$	1.99609	+	1.99609i	0.113923	+	0.113923i	−0.647847	+	0.761770i	$0.724331\pi$
$308$	−2.45215	−	0.993466i	−0.139724	−	0.0566080i
$309$		−	9.54416i		−	0.542948i
$310$	15.8522	−	18.0177i	0.900344	−	1.02334i
$311$		−	22.0116i		−	1.24816i	−0.781360	−	0.624081i	$-0.785474\pi$
$311$		−	22.0116i		−	1.24816i	0.781360	−	0.624081i	$-0.214526\pi$
$312$	4.14066	−	4.14066i	0.234419	−	0.234419i
$313$	−3.84995	+	3.84995i	−0.217612	+	0.217612i	−0.807491	−	0.589879i	$-0.799175\pi$
$313$	−3.84995	+	3.84995i	−0.217612	+	0.217612i	0.589879	+	0.807491i	$0.299175\pi$
$314$	6.40741			0.361591
$315$	−2.71732	+	8.17019i	−0.153104	+	0.460338i
$316$	2.34126			0.131706
$317$	2.43142	−	2.43142i	0.136562	−	0.136562i	−0.635521	−	0.772083i	$-0.719215\pi$
$317$	2.43142	−	2.43142i	0.136562	−	0.136562i	0.772083	+	0.635521i	$0.219215\pi$
$318$	−5.47393	+	5.47393i	−0.306963	+	0.306963i
$319$			0.740302i			0.0414490i
$320$	−2.23151	+	0.142676i	−0.124745	+	0.00797581i
$321$		−	19.0796i		−	1.06492i
$322$	−4.99450	+	12.3278i	−0.278333	+	0.687001i
$323$	−1.28533	−	1.28533i	−0.0715177	−	0.0715177i
$324$		−	2.51565i		−	0.139758i
$325$	14.4012	−	18.6441i	0.798833	−	1.03419i
$326$	−15.5410			−0.860737
$327$	1.87408	+	1.87408i	0.103637	+	0.103637i
$328$	−1.20612	+	1.20612i	−0.0665971	+	0.0665971i
$329$	−4.51072	+	1.90959i	−0.248684	+	0.105279i
$330$	2.77337	−	0.177320i	0.152669	−	0.00976116i
$331$	0.698720			0.0384051			0.0192026	−	0.999816i	$-0.493887\pi$
$331$	0.698720			0.0384051			0.0192026	+	0.999816i	$0.493887\pi$
$332$	−6.98186	−	6.98186i	−0.383179	−	0.383179i
$333$	−3.52786	−	3.52786i	−0.193326	−	0.193326i
$334$	−11.2444			−0.615265
$335$	−23.2688	−	20.4721i	−1.27131	−	1.11851i
$336$	−1.28190	−	3.02803i	−0.0699334	−	0.165193i
$337$	17.7014	−	17.7014i	0.964257	−	0.964257i	−0.0351259	−	0.999383i	$-0.511183\pi$
$337$	17.7014	−	17.7014i	0.964257	−	0.964257i	0.999383	+	0.0351259i	$0.0111832\pi$
$338$	6.50531	+	6.50531i	0.353842	+	0.353842i
$339$	−23.6545			−1.28474
$340$	−1.01706	−	0.894818i	−0.0551577	−	0.0485283i
$341$			10.7325i			0.581196i
$342$	−3.08781	−	3.08781i	−0.166969	−	0.166969i
$343$	−16.9407	+	7.48420i	−0.914711	+	0.404109i
$344$		−	11.7261i		−	0.632229i
$345$	−0.891451	−	13.9427i	−0.0479941	−	0.750650i
$346$			19.6249i			1.05504i
$347$	18.3897	−	18.3897i	0.987210	−	0.987210i	−0.0127090	−	0.999919i	$-0.504046\pi$
$347$	18.3897	−	18.3897i	0.987210	−	0.987210i	0.999919	+	0.0127090i	$0.00404552\pi$
$348$	−0.650584	+	0.650584i	−0.0348749	+	0.0348749i
$349$	−9.74711			−0.521751			−0.260876	−	0.965372i	$-0.584011\pi$
$349$	−9.74711			−0.521751			−0.260876	+	0.965372i	$0.584011\pi$
$350$	−6.66665	−	11.4261i	−0.356347	−	0.610751i
$351$	26.0898			1.39257
$352$	0.707107	−	0.707107i	0.0376889	−	0.0376889i
$353$	−22.6587	+	22.6587i	−1.20600	+	1.20600i	−0.233687	+	0.972312i	$0.575079\pi$
$353$	−22.6587	+	22.6587i	−1.20600	+	1.20600i	−0.972312	+	0.233687i	$0.924921\pi$
$354$			11.7572i			0.624886i
$355$	1.96264	+	30.6967i	0.104166	+	1.62921i
$356$		−	6.29246i		−	0.333500i
$357$	0.748010	−	1.84629i	0.0395889	−	0.0977163i
$358$	−3.14152	−	3.14152i	−0.166035	−	0.166035i
$359$		−	15.1281i		−	0.798430i	−0.916857	−	0.399215i	$-0.869283\pi$
$359$		−	15.1281i		−	0.798430i	0.916857	−	0.399215i	$-0.130717\pi$
$360$	−2.44332	−	2.14966i	−0.128774	−	0.113297i
$361$	−9.99737			−0.526177
$362$	−5.88318	−	5.88318i	−0.309213	−	0.309213i
$363$	−0.878808	+	0.878808i	−0.0461255	+	0.0461255i
$364$	11.4796	−	4.85983i	0.601695	−	0.254724i
$365$	−14.2218	−	12.5125i	−0.744404	−	0.654935i
$366$	−4.14903			−0.216873
$367$	6.41466	+	6.41466i	0.334843	+	0.334843i	0.854422	−	0.519579i	$-0.173911\pi$
$367$	6.41466	+	6.41466i	0.334843	+	0.334843i	−0.519579	+	0.854422i	$0.673911\pi$
$368$	−3.55487	−	3.55487i	−0.185311	−	0.185311i
$369$	−2.48249			−0.129233
$370$	7.64972	−	0.489098i	0.397690	−	0.0254270i
$371$	−15.1760	+	6.42466i	−0.787897	+	0.333552i
$372$	−9.43178	+	9.43178i	−0.489015	+	0.489015i
$373$	19.8077	+	19.8077i	1.02561	+	1.02561i	0.999663	+	0.0259425i	$0.00825869\pi$
$373$	19.8077	+	19.8077i	1.02561	+	1.02561i	0.0259425	+	0.999663i	$0.491741\pi$
$374$	0.605822			0.0313263
$375$	11.5162	+	7.77511i	0.594695	+	0.401505i
$376$		−	1.85137i		−	0.0954774i
$377$	−2.46643	−	2.46643i	−0.127028	−	0.127028i
$378$	5.50108	−	13.5782i	0.282945	−	0.698386i
$379$		−	7.06555i		−	0.362933i	−0.983397	−	0.181466i	$-0.941916\pi$
$379$		−	7.06555i		−	0.362933i	0.983397	−	0.181466i	$-0.0580843\pi$
$380$	6.69551	−	0.428089i	0.343473	−	0.0219605i
$381$		−	5.41325i		−	0.277329i
$382$	0.751771	−	0.751771i	0.0384639	−	0.0384639i
$383$	17.3382	−	17.3382i	0.885939	−	0.885939i	−0.108191	−	0.994130i	$-0.534506\pi$
$383$	17.3382	−	17.3382i	0.885939	−	0.885939i	0.994130	+	0.108191i	$0.0345059\pi$
$384$	1.24282			0.0634225
$385$	5.61374	+	1.86707i	0.286103	+	0.0951547i
$386$	−23.2669			−1.18426
$387$	12.0675	−	12.0675i	0.613428	−	0.613428i
$388$	−3.67113	+	3.67113i	−0.186373	+	0.186373i
$389$			22.2613i			1.12869i	0.825538	+	0.564346i	$0.190872\pi$
$389$			22.2613i			1.12869i	−0.825538	+	0.564346i	$0.809128\pi$
$390$	−8.64916	+	9.83070i	−0.437967	+	0.497797i
$391$		−	3.04568i		−	0.154027i
$392$	−0.108754	−	6.99916i	−0.00549289	−	0.353511i
$393$	−0.938444	−	0.938444i	−0.0473382	−	0.0473382i
$394$		−	7.71965i		−	0.388911i
$395$	−5.22454	+	0.334040i	−0.262875	+	0.0168074i
$396$	1.45539			0.0731362
$397$	−23.9130	−	23.9130i	−1.20016	−	1.20016i	−0.974117	−	0.226043i	$-0.927421\pi$
$397$	−23.9130	−	23.9130i	−1.20016	−	1.20016i	−0.226043	−	0.974117i	$-0.572579\pi$
$398$	−9.29472	+	9.29472i	−0.465902	+	0.465902i
$399$	3.84626	+	9.08542i	0.192554	+	0.454840i
$400$	4.95929	−	0.636764i	0.247964	−	0.0318382i
$401$	−8.86304			−0.442599			−0.221300	−	0.975206i	$-0.571030\pi$
$401$	−8.86304			−0.442599			−0.221300	+	0.975206i	$0.571030\pi$
$402$	12.1806	+	12.1806i	0.607512	+	0.607512i
$403$	−35.7569	−	35.7569i	−1.78118	−	1.78118i
$404$	0.468416			0.0233046
$405$	0.358922	+	5.61371i	0.0178350	+	0.278947i
$406$	−1.80368	+	0.763580i	−0.0895154	+	0.0378958i
$407$	−2.42399	+	2.42399i	−0.120153	+	0.120153i
$408$	0.532402	+	0.532402i	0.0263578	+	0.0263578i
$409$	−7.23846			−0.357919			−0.178959	−	0.983856i	$-0.557273\pi$
$409$	−7.23846			−0.357919			−0.178959	+	0.983856i	$0.557273\pi$
$410$	2.51940	−	2.86356i	0.124424	−	0.141421i
$411$			3.14697i			0.155228i
$412$	5.43017	+	5.43017i	0.267525	+	0.267525i
$413$	−9.39824	+	23.1974i	−0.462457	+	1.14147i
$414$		−	7.31677i		−	0.359600i
$415$	16.5762	+	14.5840i	0.813695	+	0.715898i
$416$			4.71168i			0.231009i
$417$	−18.0246	+	18.0246i	−0.882668	+	0.882668i
$418$	−2.12163	+	2.12163i	−0.103772	+	0.103772i
$419$	37.8132			1.84729			0.923647	−	0.383245i	$-0.125194\pi$
$419$	37.8132			1.84729			0.923647	+	0.383245i	$0.125194\pi$
$420$	3.29260	+	6.57419i	0.160663	+	0.320788i
$421$	14.1279			0.688553			0.344277	−	0.938868i	$-0.388124\pi$
$421$	14.1279			0.688553			0.344277	+	0.938868i	$0.388124\pi$
$422$	12.6043	−	12.6043i	0.613569	−	0.613569i
$423$	1.90528	−	1.90528i	0.0926381	−	0.0926381i
$424$		−	6.22881i		−	0.302498i
$425$	2.39724	+	1.85169i	0.116283	+	0.0898200i
$426$		−	17.0963i		−	0.828316i
$427$	−8.18624	−	3.31658i	−0.396160	−	0.160501i
$428$	10.8554	+	10.8554i	0.524716	+	0.524716i
$429$		−	5.85578i		−	0.282720i
$430$	1.67303	+	26.1669i	0.0806806	+	1.26188i
$431$	−4.41857			−0.212835			−0.106418	−	0.994322i	$-0.533938\pi$
$431$	−4.41857			−0.212835			−0.106418	+	0.994322i	$0.533938\pi$
$432$	3.91544	+	3.91544i	0.188381	+	0.188381i
$433$	−17.5629	+	17.5629i	−0.844021	+	0.844021i	−0.989379	−	0.145358i	$-0.953567\pi$
$433$	−17.5629	+	17.5629i	−0.844021	+	0.844021i	0.145358	+	0.989379i	$0.453567\pi$
$434$	−26.1488	+	11.0699i	−1.25518	+	0.531374i
$435$	1.35896	−	1.54461i	0.0651573	−	0.0740582i
$436$	−2.13253			−0.102130
$437$	10.6662	+	10.6662i	0.510232	+	0.510232i
$438$	7.44474	+	7.44474i	0.355723	+	0.355723i
$439$	−10.1649			−0.485142			−0.242571	−	0.970134i	$-0.577991\pi$
$439$	−10.1649			−0.485142			−0.242571	+	0.970134i	$0.577991\pi$
$440$	−1.47703	+	1.67880i	−0.0704146	+	0.0800338i
$441$	7.09104	−	7.31488i	0.337668	−	0.348328i
$442$	−2.01839	+	2.01839i	−0.0960052	+	0.0960052i
$443$	23.5318	+	23.5318i	1.11803	+	1.11803i	0.992030	+	0.125999i	$0.0402136\pi$
$443$	23.5318	+	23.5318i	1.11803	+	1.11803i	0.125999	+	0.992030i	$0.459786\pi$
$444$	−4.26045			−0.202192
$445$	0.897780	+	14.0417i	0.0425588	+	0.665640i
$446$			29.4458i			1.39430i
$447$	2.40253	+	2.40253i	0.113636	+	0.113636i
$448$	2.45215	+	0.993466i	0.115853	+	0.0469369i
$449$			24.5008i			1.15626i	0.815943	+	0.578132i	$0.196218\pi$
$449$			24.5008i			1.15626i	−0.815943	+	0.578132i	$0.803782\pi$
$450$	5.75900	+	4.44839i	0.271482	+	0.209699i
$451$			1.70572i			0.0803191i
$452$	13.4583	−	13.4583i	0.633024	−	0.633024i
$453$	−15.1147	+	15.1147i	−0.710148	+	0.710148i
$454$	−14.5163			−0.681283
$455$	−24.9235	+	12.4826i	−1.16843	+	0.585194i
$456$	−3.72901			−0.174627
$457$	−15.5332	+	15.5332i	−0.726613	+	0.726613i	−0.969944	−	0.243330i	$-0.921760\pi$
$457$	−15.5332	+	15.5332i	−0.726613	+	0.726613i	0.243330	+	0.969944i	$0.421760\pi$
$458$	12.8694	−	12.8694i	0.601348	−	0.601348i
$459$			3.35460i			0.156579i
$460$	8.43993	+	7.42555i	0.393514	+	0.346218i
$461$			33.8712i			1.57754i	0.614690	+	0.788769i	$0.289281\pi$
$461$			33.8712i			1.57754i	−0.614690	+	0.788769i	$0.710719\pi$
$462$	−3.04758	−	1.23470i	−0.141786	−	0.0574435i
$463$	−8.11414	−	8.11414i	−0.377096	−	0.377096i	0.492957	−	0.870053i	$-0.335916\pi$
$463$	−8.11414	−	8.11414i	−0.377096	−	0.377096i	−0.870053	+	0.492957i	$0.835916\pi$
$464$		−	0.740302i		−	0.0343677i
$465$	19.7014	−	22.3928i	0.913633	−	1.03844i
$466$	−7.34662			−0.340326
$467$	−14.1457	−	14.1457i	−0.654587	−	0.654587i	0.299507	−	0.954094i	$-0.403178\pi$
$467$	−14.1457	−	14.1457i	−0.654587	−	0.654587i	−0.954094	+	0.299507i	$0.903178\pi$
$468$	−4.84887	+	4.84887i	−0.224139	+	0.224139i
$469$	14.2962	+	33.7696i	0.660135	+	1.55933i
$470$	0.264146	+	4.13136i	0.0121841	+	0.190566i
$471$	7.96328			0.366928
$472$	−6.68927	−	6.68927i	−0.307898	−	0.307898i
$473$	−8.29161	−	8.29161i	−0.381249	−	0.381249i
$474$	2.90976			0.133650
$475$	−14.8800	+	1.91057i	−0.682743	+	0.0876631i
$476$	0.624872	+	1.47604i	0.0286409	+	0.0676540i
$477$	6.41018	−	6.41018i	0.293502	−	0.293502i
$478$	−20.3299	−	20.3299i	−0.929868	−	0.929868i
$479$	2.08890			0.0954444			0.0477222	−	0.998861i	$-0.484804\pi$
$479$	2.08890			0.0954444			0.0477222	+	0.998861i	$0.484804\pi$
$480$	−2.77337	+	0.177320i	−0.126587	+	0.00809353i
$481$		−	16.1518i		−	0.736460i
$482$	−12.5917	−	12.5917i	−0.573534	−	0.573534i
$483$	−6.20728	+	15.3213i	−0.282441	+	0.697142i
$484$		−	1.00000i		−	0.0454545i
$485$	7.66839	−	8.71595i	0.348203	−	0.395771i
$486$			13.4853i			0.611705i
$487$	−14.7176	+	14.7176i	−0.666919	+	0.666919i	−0.957002	−	0.290083i	$-0.906317\pi$
$487$	−14.7176	+	14.7176i	−0.666919	+	0.666919i	0.290083	+	0.957002i	$0.406317\pi$
$488$	2.36060	−	2.36060i	0.106859	−	0.106859i
$489$	−19.3147			−0.873442
$490$	1.24129	+	15.6032i	0.0560759	+	0.704880i
$491$	32.4688			1.46530			0.732649	−	0.680607i	$-0.238284\pi$
$491$	32.4688			1.46530			0.732649	+	0.680607i	$0.238284\pi$
$492$	−1.49900	+	1.49900i	−0.0675800	+	0.0675800i
$493$	0.317132	−	0.317132i	0.0142829	−	0.0142829i
$494$		−	14.1371i		−	0.636058i
$495$	−3.24773	+	0.207649i	−0.145974	+	0.00933313i
$496$		−	10.7325i		−	0.481902i
$497$	13.6661	−	33.7317i	0.613009	−	1.51307i
$498$	−8.67721	−	8.67721i	−0.388835	−	0.388835i
$499$			3.76425i			0.168511i	0.996444	+	0.0842556i	$0.0268512\pi$
$499$			3.76425i			0.168511i	−0.996444	+	0.0842556i	$0.973149\pi$
$500$	−10.9759	+	2.12852i	−0.490855	+	0.0951901i
$501$	−13.9748			−0.624347
$502$	−1.96791	−	1.96791i	−0.0878321	−	0.0878321i
$503$	18.2650	−	18.2650i	0.814394	−	0.814394i	−0.170895	−	0.985289i	$-0.554666\pi$
$503$	18.2650	−	18.2650i	0.814394	−	0.814394i	0.985289	+	0.170895i	$0.0546659\pi$
$504$	1.50116	+	3.54594i	0.0668668	+	0.157949i
$505$	−1.04528	+	0.0668315i	−0.0465141	+	0.00297396i
$506$	−5.02735			−0.223493
$507$	8.08494	+	8.08494i	0.359065	+	0.359065i
$508$	3.07988	+	3.07988i	0.136648	+	0.136648i
$509$	10.5877			0.469290			0.234645	−	0.972081i	$-0.424607\pi$
$509$	10.5877			0.469290			0.234645	+	0.972081i	$0.424607\pi$
$510$	−1.26402	−	1.11210i	−0.0559718	−	0.0492446i
$511$	8.73777	+	20.6399i	0.386536	+	0.913054i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−11.7480	−	11.7480i	−0.518688	−	0.518688i
$514$	24.9222			1.09927
$515$	−12.8922	−	11.3427i	−0.568100	−	0.499821i
$516$		−	14.5735i		−	0.641561i
$517$	−1.30912	−	1.30912i	−0.0575750	−	0.0575750i
$518$	−8.40607	−	3.40565i	−0.369341	−	0.149635i
$519$			24.3903i			1.07061i
$520$	−0.672241	−	10.5142i	−0.0294797	−	0.461076i
$521$			3.10236i			0.135917i	0.997688	+	0.0679585i	$0.0216485\pi$
$521$			3.10236i			0.135917i	−0.997688	+	0.0679585i	$0.978351\pi$
$522$	0.761859	−	0.761859i	0.0333456	−	0.0333456i
$523$	18.6913	−	18.6913i	0.817314	−	0.817314i	−0.168404	−	0.985718i	$-0.553861\pi$
$523$	18.6913	−	18.6913i	0.817314	−	0.817314i	0.985718	+	0.168404i	$0.0538614\pi$
$524$	1.06786			0.0466497
$525$	−8.28546	−	14.2006i	−0.361607	−	0.619766i
$526$	3.02855			0.132051
$527$	4.59759	−	4.59759i	0.200274	−	0.200274i
$528$	0.878808	−	0.878808i	0.0382452	−	0.0382452i
$529$			2.27423i			0.0988797i
$530$	0.888699	+	13.8997i	0.0386026	+	0.603763i
$531$		−	13.7681i		−	0.597484i
$532$	−7.35752	−	2.98083i	−0.318989	−	0.129236i
$533$	−5.68287	−	5.68287i	−0.246152	−	0.246152i
$534$		−	7.82041i		−	0.338422i
$535$	−25.7728	−	22.6752i	−1.11425	−	0.980333i
$536$	−13.8603			−0.598675
$537$	−3.90435	−	3.90435i	−0.168485	−	0.168485i
$538$	9.27749	−	9.27749i	0.399981	−	0.399981i
$539$	−5.02605	−	4.87225i	−0.216487	−	0.209863i
$540$	−9.29598	−	8.17870i	−0.400035	−	0.351955i
$541$	−13.1368			−0.564794			−0.282397	−	0.959298i	$-0.591130\pi$
$541$	−13.1368			−0.564794			−0.282397	+	0.959298i	$0.591130\pi$
$542$	6.57710	+	6.57710i	0.282511	+	0.282511i
$543$	−7.31175	−	7.31175i	−0.313777	−	0.313777i
$544$	−0.605822			−0.0259744
$545$	4.75877	−	0.304260i	0.203843	−	0.0130331i
$546$	14.2671	−	6.03990i	0.610576	−	0.258484i
$547$	−17.7180	+	17.7180i	−0.757565	+	0.757565i	−0.975879	−	0.218314i	$-0.929944\pi$
$547$	−17.7180	+	17.7180i	−0.757565	+	0.757565i	0.218314	+	0.975879i	$0.429944\pi$
$548$	−1.79047	−	1.79047i	−0.0764853	−	0.0764853i
$549$	4.85868			0.207363
$550$	3.05649	−	3.95701i	0.130329	−	0.168727i
$551$			2.22123i			0.0946276i
$552$	−4.41807	−	4.41807i	−0.188046	−	0.188046i
$553$	5.74110	+	2.32596i	0.244137	+	0.0989098i
$554$			11.3405i			0.481810i
$555$	9.50724	−	0.607862i	0.403560	−	0.0258023i
$556$		−	20.5103i		−	0.869829i
$557$	16.9291	−	16.9291i	0.717311	−	0.717311i	−0.250743	−	0.968054i	$-0.580675\pi$
$557$	16.9291	−	16.9291i	0.717311	−	0.717311i	0.968054	+	0.250743i	$0.0806749\pi$
$558$	11.0450	−	11.0450i	0.467571	−	0.467571i
$559$	55.2496			2.33681
$560$	−5.61374	−	1.86707i	−0.237224	−	0.0788981i
$561$	0.752930			0.0317887
$562$	−9.79754	+	9.79754i	−0.413284	+	0.413284i
$563$	14.3182	−	14.3182i	0.603439	−	0.603439i	−0.337785	−	0.941223i	$-0.609678\pi$
$563$	14.3182	−	14.3182i	0.603439	−	0.603439i	0.941223	+	0.337785i	$0.109678\pi$
$564$		−	2.30093i		−	0.0968866i
$565$	−28.1121	+	31.9525i	−1.18269	+	1.34425i
$566$		−	0.635997i		−	0.0267329i
$567$	2.49921	−	6.16875i	0.104957	−	0.259063i
$568$	9.72696	+	9.72696i	0.408134	+	0.408134i
$569$		−	20.7798i		−	0.871134i	−0.900156	−	0.435567i	$-0.856548\pi$
$569$		−	20.7798i		−	0.871134i	0.900156	−	0.435567i	$-0.143452\pi$
$570$	8.32133	−	0.532039i	0.348542	−	0.0222847i
$571$	−12.5810			−0.526500			−0.263250	−	0.964728i	$-0.584794\pi$
$571$	−12.5810			−0.526500			−0.263250	+	0.964728i	$0.584794\pi$
$572$	3.33166	+	3.33166i	0.139304	+	0.139304i
$573$	0.934318	−	0.934318i	0.0390317	−	0.0390317i
$574$	−4.15584	+	1.75935i	−0.173461	+	0.0734339i
$575$	−19.8932	−	15.3660i	−0.829606	−	0.640807i
$576$	−1.45539			−0.0606414
$577$	18.8363	+	18.8363i	0.784166	+	0.784166i	0.980531	−	0.196365i	$-0.0629137\pi$
$577$	18.8363	+	18.8363i	0.784166	+	0.784166i	−0.196365	+	0.980531i	$0.562914\pi$
$578$	11.7613	+	11.7613i	0.489205	+	0.489205i
$579$	−28.9166			−1.20173
$580$	0.105623	+	1.65199i	0.00438576	+	0.0685953i
$581$	−10.1843	−	24.0568i	−0.422516	−	0.998043i
$582$	−4.56256	+	4.56256i	−0.189124	+	0.189124i
$583$	−4.40443	−	4.40443i	−0.182413	−	0.182413i
$584$	−8.47140			−0.350549
$585$	10.1285	−	11.5121i	0.418762	−	0.475968i
$586$			17.1395i			0.708025i
$587$	30.1247	+	30.1247i	1.24338	+	1.24338i	0.958589	+	0.284792i	$0.0919245\pi$
$587$	30.1247	+	30.1247i	1.24338	+	1.24338i	0.284792	+	0.958589i	$0.408076\pi$
$588$	−0.135162	−	8.69871i	−0.00557397	−	0.358729i
$589$			32.2021i			1.32687i
$590$	15.8816	+	13.9728i	0.653834	+	0.575250i
$591$		−	9.59416i		−	0.394651i
$592$	2.42399	−	2.42399i	0.0996255	−	0.0996255i
$593$	5.56951	−	5.56951i	0.228712	−	0.228712i	−0.583442	−	0.812155i	$-0.698295\pi$
$593$	5.56951	−	5.56951i	0.228712	−	0.228712i	0.812155	+	0.583442i	$0.198295\pi$
$594$	5.53726			0.227197
$595$	−1.60500	−	3.20464i	−0.0657987	−	0.131377i
$596$	−2.73385			−0.111983
$597$	−11.5517	+	11.5517i	−0.472779	+	0.472779i
$598$	16.7494	−	16.7494i	0.684934	−	0.684934i
$599$		−	41.6323i		−	1.70105i	−0.525936	−	0.850524i	$-0.676285\pi$
$599$		−	41.6323i		−	1.70105i	0.525936	−	0.850524i	$-0.323715\pi$
$600$	6.16351	−	0.791385i	0.251624	−	0.0323082i
$601$			14.2367i			0.580727i	0.956916	+	0.290363i	$0.0937762\pi$
$601$			14.2367i			0.580727i	−0.956916	+	0.290363i	$0.906224\pi$
$602$	11.6495	−	28.7541i	0.474798	−	1.17193i
$603$	−14.2639	−	14.2639i	−0.580872	−	0.580872i
$604$		−	17.1990i		−	0.699819i
$605$	0.142676	+	2.23151i	0.00580059	+	0.0907238i
$606$	0.582158			0.0236485
$607$	14.9312	+	14.9312i	0.606038	+	0.606038i	0.941908	−	0.335870i	$-0.109030\pi$
$607$	14.9312	+	14.9312i	0.606038	+	0.606038i	−0.335870	+	0.941908i	$0.609030\pi$
$608$	2.12163	−	2.12163i	0.0860435	−	0.0860435i
$609$	−2.24166	+	0.948994i	−0.0908366	+	0.0384552i
$610$	−4.93091	+	5.60451i	−0.199647	+	0.226920i
$611$	8.72308			0.352898
$612$	−0.623463	−	0.623463i	−0.0252020	−	0.0252020i
$613$	−17.7824	−	17.7824i	−0.718225	−	0.718225i	0.250017	−	0.968242i	$-0.419564\pi$
$613$	−17.7824	−	17.7824i	−0.718225	−	0.718225i	−0.968242	+	0.250017i	$0.919564\pi$
$614$	−2.82289			−0.113923
$615$	3.13116	−	3.55890i	0.126261	−	0.143509i
$616$	2.43642	−	1.03144i	0.0981660	−	0.0415580i
$617$	−9.09669	+	9.09669i	−0.366219	+	0.366219i	−0.866096	−	0.499877i	$-0.833378\pi$
$617$	−9.09669	+	9.09669i	−0.366219	+	0.366219i	0.499877	+	0.866096i	$0.333378\pi$
$618$	6.74874	+	6.74874i	0.271474	+	0.271474i
$619$	35.9649			1.44555			0.722776	−	0.691083i	$-0.242866\pi$
$619$	35.9649			1.44555			0.722776	+	0.691083i	$0.242866\pi$
$620$	1.53126	+	23.9496i	0.0614969	+	0.961840i
$621$		−	27.8377i		−	1.11709i
$622$	15.5645	+	15.5645i	0.624081	+	0.624081i
$623$	6.25134	−	15.4300i	0.250455	−	0.618191i
$624$			5.85578i			0.234419i
$625$	24.1891	−	6.31579i	0.967562	−	0.252632i
$626$		−	5.44465i		−	0.217612i
$627$	−2.63681	+	2.63681i	−0.105304	+	0.105304i
$628$	−4.53073	+	4.53073i	−0.180796	+	0.180796i
$629$	2.07679			0.0828069
$630$	−3.85576	−	7.69864i	−0.153617	−	0.306721i
$631$	11.7313			0.467015			0.233508	−	0.972355i	$-0.424980\pi$
$631$	11.7313			0.467015			0.233508	+	0.972355i	$0.424980\pi$
$632$	−1.65552	+	1.65552i	−0.0658530	+	0.0658530i
$633$	15.6649	−	15.6649i	0.622625	−	0.622625i
$634$			3.43854i			0.136562i
$635$	−7.31222	−	6.43337i	−0.290176	−	0.255300i
$636$		−	7.74130i		−	0.306963i
$637$	32.9778	−	0.512412i	1.30663	−	0.0203025i
$638$	−0.523473	−	0.523473i	−0.0207245	−	0.0207245i
$639$			20.0204i			0.791994i
$640$	1.47703	−	1.67880i	0.0583847	−	0.0663605i
$641$	−3.06873			−0.121208			−0.0606038	−	0.998162i	$-0.519303\pi$
$641$	−3.06873			−0.121208			−0.0606038	+	0.998162i	$0.519303\pi$
$642$	13.4913	+	13.4913i	0.532461	+	0.532461i
$643$	−24.0422	+	24.0422i	−0.948131	+	0.948131i	−0.998720	−	0.0505890i	$-0.983890\pi$
$643$	−24.0422	+	24.0422i	−0.948131	+	0.948131i	0.0505890	+	0.998720i	$0.483890\pi$
$644$	−5.18542	−	12.2487i	−0.204334	−	0.482667i
$645$	2.07928	+	32.5209i	0.0818715	+	1.28051i
$646$	1.81773			0.0715177
$647$	5.24116	+	5.24116i	0.206051	+	0.206051i	0.802587	−	0.596535i	$-0.203456\pi$
$647$	5.24116	+	5.24116i	0.206051	+	0.206051i	−0.596535	+	0.802587i	$0.703456\pi$
$648$	1.77883	+	1.77883i	0.0698792	+	0.0698792i
$649$	−9.46005			−0.371339
$650$	3.00023	+	23.3666i	0.117679	+	0.916512i
$651$	−32.4983	+	13.7580i	−1.27371	+	0.539217i
$652$	10.9892	−	10.9892i	0.430369	−	0.430369i
$653$	10.1605	+	10.1605i	0.397612	+	0.397612i	0.877390	−	0.479778i	$-0.159283\pi$
$653$	10.1605	+	10.1605i	0.397612	+	0.397612i	−0.479778	+	0.877390i	$0.659283\pi$
$654$	−2.65036			−0.103637
$655$	−2.38294	+	0.152357i	−0.0931092	+	0.00595310i
$656$		−	1.70572i		−	0.0665971i
$657$	−8.71807	−	8.71807i	−0.340124	−	0.340124i
$658$	1.83928	−	4.53984i	0.0717025	−	0.176982i
$659$		−	38.5574i		−	1.50198i	−0.660312	−	0.750992i	$-0.729576\pi$
$659$		−	38.5574i		−	1.50198i	0.660312	−	0.750992i	$-0.270424\pi$
$660$	−1.83569	+	2.08645i	−0.0714540	+	0.0812151i
$661$		−	37.2663i		−	1.44949i	−0.689017	−	0.724745i	$-0.741958\pi$
$661$		−	37.2663i		−	1.44949i	0.689017	−	0.724745i	$-0.258042\pi$
$662$	−0.494070	+	0.494070i	−0.0192026	+	0.0192026i
$663$	−2.50850	+	2.50850i	−0.0974222	+	0.0974222i
$664$	9.87384			0.383179
$665$	16.8437	+	5.60203i	0.653170	+	0.217237i
$666$	4.98915			0.193326
$667$	−2.63168	+	2.63168i	−0.101899	+	0.101899i
$668$	7.95098	−	7.95098i	0.307633	−	0.307633i
$669$			36.5959i			1.41488i
$670$	30.9295	−	1.97753i	1.19491	−	0.0763987i
$671$		−	3.33840i		−	0.128877i
$672$	3.04758	+	1.23470i	0.117563	+	0.0476296i
$673$	−9.66605	−	9.66605i	−0.372599	−	0.372599i	0.495824	−	0.868423i	$-0.334866\pi$
$673$	−9.66605	−	9.66605i	−0.372599	−	0.372599i	−0.868423	+	0.495824i	$0.834866\pi$
$674$			25.0336i			0.964257i
$675$	21.9110	+	16.9246i	0.843354	+	0.651427i
$676$	−9.19989			−0.353842
$677$	24.6218	+	24.6218i	0.946292	+	0.946292i	0.998629	−	0.0523373i	$-0.0166671\pi$
$677$	24.6218	+	24.6218i	0.946292	+	0.946292i	−0.0523373	+	0.998629i	$0.516667\pi$
$678$	16.7262	−	16.7262i	0.642368	−	0.642368i
$679$	−12.6493	+	5.35501i	−0.485435	+	0.205506i
$680$	1.35190	−	0.0864361i	0.0518430	−	0.00331467i
$681$	−18.0412			−0.691338
$682$	−7.58900	−	7.58900i	−0.290598	−	0.290598i
$683$	26.6183	+	26.6183i	1.01852	+	1.01852i	0.999825	+	0.0186977i	$0.00595200\pi$
$683$	26.6183	+	26.6183i	1.01852	+	1.01852i	0.0186977	+	0.999825i	$0.494048\pi$
$684$	4.36682			0.166969
$685$	4.25092	+	3.74001i	0.162419	+	0.142898i
$686$	6.68674	−	17.2710i	0.255301	−	0.659410i
$687$	15.9944	−	15.9944i	0.610224	−	0.610224i
$688$	8.29161	+	8.29161i	0.316115	+	0.316115i
$689$	29.3481			1.11807
$690$	10.4893	+	9.22863i	0.399322	+	0.351328i
$691$		−	7.65479i		−	0.291202i	−0.989343	−	0.145601i	$-0.953488\pi$
$691$		−	7.65479i		−	0.291202i	0.989343	−	0.145601i	$-0.0465116\pi$
$692$	−13.8769	−	13.8769i	−0.527521	−	0.527521i
$693$	3.56884	+	1.44588i	0.135569	+	0.0549246i
$694$			26.0069i			0.987210i
$695$	2.92631	+	45.7689i	0.111001	+	1.73611i
$696$		−	0.920064i		−	0.0348749i
$697$	0.730697	−	0.730697i	0.0276771	−	0.0276771i
$698$	6.89225	−	6.89225i	0.260876	−	0.260876i
$699$	−9.13054			−0.345349
$700$	12.7935	+	3.36544i	0.483549	+	0.127202i
$701$	−50.5152			−1.90793			−0.953966	−	0.299915i	$-0.903042\pi$
$701$	−50.5152			−1.90793			−0.953966	+	0.299915i	$0.903042\pi$
$702$	−18.4483	+	18.4483i	−0.696285	+	0.696285i
$703$	−7.27304	+	7.27304i	−0.274308	+	0.274308i
$704$			1.00000i			0.0376889i
$705$	0.328286	+	5.13455i	0.0123640	+	0.193378i
$706$		−	32.0442i		−	1.20600i
$707$	1.14862	+	0.465355i	0.0431985	+	0.0175015i
$708$	−8.31357	−	8.31357i	−0.312443	−	0.312443i
$709$		−	10.7055i		−	0.402054i	−0.979586	−	0.201027i	$-0.935572\pi$
$709$		−	10.7055i		−	0.402054i	0.979586	−	0.201027i	$-0.0644278\pi$
$710$	−23.0936	−	20.3180i	−0.866688	−	0.762522i
$711$	−3.40745			−0.127789
$712$	4.44944	+	4.44944i	0.166750	+	0.166750i
$713$	−38.1526	+	38.1526i	−1.42882	+	1.42882i
$714$	0.776604	+	1.83445i	0.0290637	+	0.0686526i
$715$	−7.90998	−	6.95929i	−0.295816	−	0.260263i
$716$	4.44278			0.166035
$717$	−25.2665	−	25.2665i	−0.943593	−	0.943593i
$718$	10.6972	+	10.6972i	0.399215	+	0.399215i
$719$	25.2974			0.943434			0.471717	−	0.881750i	$-0.343634\pi$
$719$	25.2974			0.943434			0.471717	+	0.881750i	$0.343634\pi$
$720$	3.24773	−	0.207649i	0.121036	−	0.00773862i
$721$	7.92089	+	18.7103i	0.294989	+	0.696807i
$722$	7.06921	−	7.06921i	0.263089	−	0.263089i
$723$	−15.6492	−	15.6492i	−0.582000	−	0.582000i
$724$	8.32007			0.309213
$725$	−0.471398	−	3.67137i	−0.0175073	−	0.136351i
$726$		−	1.24282i		−	0.0461255i
$727$	−8.06046	−	8.06046i	−0.298946	−	0.298946i	0.541655	−	0.840601i	$-0.317798\pi$
$727$	−8.06046	−	8.06046i	−0.298946	−	0.298946i	−0.840601	+	0.541655i	$0.817798\pi$
$728$	−4.68089	+	11.5537i	−0.173485	+	0.428209i
$729$			24.3068i			0.900250i
$730$	18.9040	−	1.20866i	0.699670	−	0.0447346i
$731$			7.10394i			0.262749i
$732$	2.93381	−	2.93381i	0.108437	−	0.108437i
$733$	4.16885	−	4.16885i	0.153980	−	0.153980i	−0.625913	−	0.779893i	$-0.715273\pi$
$733$	4.16885	−	4.16885i	0.153980	−	0.153980i	0.779893	+	0.625913i	$0.215273\pi$
$734$	−9.07170			−0.334843
$735$	1.54271	+	19.3920i	0.0569036	+	0.715284i
$736$	5.02735			0.185311
$737$	−9.80074	+	9.80074i	−0.361015	+	0.361015i
$738$	1.75538	−	1.75538i	0.0646166	−	0.0646166i
$739$		−	16.4667i		−	0.605739i	−0.953032	−	0.302869i	$-0.902055\pi$
$739$		−	16.4667i		−	0.605739i	0.953032	−	0.302869i	$-0.0979446\pi$
$740$	−5.06332	+	5.75501i	−0.186132	+	0.211559i
$741$		−	17.5699i		−	0.645446i
$742$	6.18811	−	15.2740i	0.227173	−	0.560725i
$743$	−5.44660	−	5.44660i	−0.199816	−	0.199816i	0.600105	−	0.799921i	$-0.295126\pi$
$743$	−5.44660	−	5.44660i	−0.199816	−	0.199816i	−0.799921	+	0.600105i	$0.795126\pi$
$744$		−	13.3386i		−	0.489015i
$745$	6.10062	−	0.390054i	0.223509	−	0.0142905i
$746$	−28.0124			−1.02561
$747$	10.1613	+	10.1613i	0.371784	+	0.371784i
$748$	−0.428381	+	0.428381i	−0.0156632	+	0.0156632i
$749$	15.8346	+	37.4035i	0.578583	+	1.36670i
$750$	−13.6410	+	2.64537i	−0.498100	+	0.0965951i
$751$	17.8988			0.653138			0.326569	−	0.945173i	$-0.394107\pi$
$751$	17.8988			0.653138			0.326569	+	0.945173i	$0.394107\pi$
$752$	1.30912	+	1.30912i	0.0477387	+	0.0477387i
$753$	−2.44576	−	2.44576i	−0.0891285	−	0.0891285i
$754$	3.48806			0.127028
$755$	2.45388	+	38.3798i	0.0893059	+	1.39679i
$756$	5.71137	+	13.4911i	0.207721	+	0.490666i
$757$	14.9509	−	14.9509i	0.543400	−	0.543400i	−0.381124	−	0.924524i	$-0.624463\pi$
$757$	14.9509	−	14.9509i	0.543400	−	0.543400i	0.924524	+	0.381124i	$0.124463\pi$
$758$	4.99609	+	4.99609i	0.181466	+	0.181466i
$759$	−6.24810			−0.226792
$760$	−4.43174	+	5.03715i	−0.160756	+	0.182717i
$761$			31.6758i			1.14825i	0.818768	+	0.574124i	$0.194657\pi$
$761$			31.6758i			1.14825i	−0.818768	+	0.574124i	$0.805343\pi$
$762$	3.82775	+	3.82775i	0.138665	+	0.138665i
$763$	−5.22928	−	2.11860i	−0.189313	−	0.0766983i
$764$			1.06316i			0.0384639i
$765$	1.48022	+	1.30231i	0.0535174	+	0.0470852i
$766$			24.5199i			0.885939i
$767$	31.5177	−	31.5177i	1.13804	−	1.13804i
$768$	−0.878808	+	0.878808i	−0.0317113	+	0.0317113i
$769$	−24.5001			−0.883496			−0.441748	−	0.897139i	$-0.645641\pi$
$769$	−24.5001			−0.883496			−0.441748	+	0.897139i	$0.645641\pi$
$770$	−5.28973	+	2.64929i	−0.190629	+	0.0954740i
$771$	30.9739			1.11550
$772$	16.4522	−	16.4522i	0.592128	−	0.592128i
$773$	14.0018	−	14.0018i	0.503611	−	0.503611i	−0.408947	−	0.912558i	$-0.634104\pi$
$773$	14.0018	−	14.0018i	0.503611	−	0.503611i	0.912558	+	0.408947i	$0.134104\pi$
$774$			17.0661i			0.613428i
$775$	−6.83406	−	53.2254i	−0.245487	−	1.91191i
$776$		−	5.19176i		−	0.186373i
$777$	−10.4472	−	4.23261i	−0.374793	−	0.151844i
$778$	−15.7411	−	15.7411i	−0.564346	−	0.564346i
$779$			5.11790i			0.183368i
$780$	−0.835476	−	13.0672i	−0.0299148	−	0.467882i
$781$	13.7560			0.492228
$782$	2.15362	+	2.15362i	0.0770133	+	0.0770133i
$783$	2.89861	−	2.89861i	0.103588	−	0.103588i
$784$	5.02605	+	4.87225i	0.179502	+	0.174009i
$785$	9.46394	−	10.7568i	0.337783	−	0.383926i
$786$	1.32716			0.0473382
$787$	−6.72427	−	6.72427i	−0.239694	−	0.239694i	0.577029	−	0.816723i	$-0.304212\pi$
$787$	−6.72427	−	6.72427i	−0.239694	−	0.239694i	−0.816723	+	0.577029i	$0.804212\pi$
$788$	5.45862	+	5.45862i	0.194455	+	0.194455i
$789$	3.76395			0.134000
$790$	3.45811	−	3.93051i	0.123034	−	0.139841i
$791$	46.3720	−	19.6313i	1.64880	−	0.698010i
$792$	−1.02912	+	1.02912i	−0.0365681	+	0.0365681i
$793$	11.1224	+	11.1224i	0.394968	+	0.394968i
$794$	33.8181			1.20016
$795$	1.10449	+	17.2748i	0.0391724	+	0.612674i
$796$		−	13.1447i		−	0.465902i
$797$	3.84493	+	3.84493i	0.136194	+	0.136194i	0.771917	−	0.635723i	$-0.219298\pi$
$797$	3.84493	+	3.84493i	0.136194	+	0.136194i	−0.635723	+	0.771917i	$0.719298\pi$
$798$	−9.14408	−	3.70465i	−0.323697	−	0.131143i
$799$			1.12160i			0.0396795i
$800$	−3.05649	+	3.95701i	−0.108063	+	0.139901i
$801$			9.15800i			0.323582i
$802$	6.26712	−	6.26712i	0.221300	−	0.221300i
$803$	−5.99019	+	5.99019i	−0.211389	+	0.211389i
$804$	−17.2259			−0.607512
$805$	13.3189	+	26.5933i	0.469431	+	0.937291i
$806$	50.5679			1.78118
$807$	11.5303	−	11.5303i	0.405885	−	0.405885i
$808$	−0.331220	+	0.331220i	−0.0116523	+	0.0116523i
$809$			23.9301i			0.841336i	0.907215	+	0.420668i	$0.138204\pi$
$809$			23.9301i			0.841336i	−0.907215	+	0.420668i	$0.861796\pi$
$810$	−4.22329	−	3.71569i	−0.148391	−	0.130556i
$811$			21.6935i			0.761761i	0.924624	+	0.380880i	$0.124379\pi$
$811$			21.6935i			0.761761i	−0.924624	+	0.380880i	$0.875621\pi$
$812$	0.735465	−	1.81533i	0.0258098	−	0.0637056i
$813$	8.17417	+	8.17417i	0.286680	+	0.286680i
$814$		−	3.42804i		−	0.120153i
$815$	−22.9545	+	26.0903i	−0.804063	+	0.913904i
$816$	−0.752930			−0.0263578
$817$	−24.8785	−	24.8785i	−0.870387	−	0.870387i
$818$	5.11836	−	5.11836i	0.178959	−	0.178959i
$819$	−16.7073	+	7.07296i	−0.583802	+	0.247149i
$820$	0.243364	+	3.80633i	0.00849864	+	0.132923i
$821$	−53.4946			−1.86697			−0.933487	−	0.358612i	$-0.883250\pi$
$821$	−53.4946			−1.86697			−0.933487	+	0.358612i	$0.883250\pi$
$822$	−2.22524	−	2.22524i	−0.0776142	−	0.0776142i
$823$	−4.06287	−	4.06287i	−0.141623	−	0.141623i	0.632741	−	0.774364i	$-0.281930\pi$
$823$	−4.06287	−	4.06287i	−0.141623	−	0.141623i	−0.774364	+	0.632741i	$0.781930\pi$
$824$	−7.67943			−0.267525
$825$	3.79867	−	4.91785i	0.132253	−	0.171218i
$826$	−9.75751	−	23.0486i	−0.339507	−	0.801964i
$827$	24.8478	−	24.8478i	0.864044	−	0.864044i	−0.127761	−	0.991805i	$-0.540779\pi$
$827$	24.8478	−	24.8478i	0.864044	−	0.864044i	0.991805	+	0.127761i	$0.0407790\pi$
$828$	5.17374	+	5.17374i	0.179800	+	0.179800i
$829$	13.5959			0.472204			0.236102	−	0.971728i	$-0.424130\pi$
$829$	13.5959			0.472204			0.236102	+	0.971728i	$0.424130\pi$
$830$	−22.0336	+	1.40876i	−0.764797	+	0.0488986i
$831$			14.0942i			0.488922i
$832$	−3.33166	−	3.33166i	−0.115504	−	0.115504i
$833$	0.0658855	+	4.24025i	0.00228280	+	0.146916i
$834$		−	25.4906i		−	0.882668i
$835$	−16.6083	+	18.8771i	−0.574754	+	0.653270i
$836$		−	3.00044i		−	0.103772i
$837$	42.0223	−	42.0223i	1.45250	−	1.45250i
$838$	−26.7379	+	26.7379i	−0.923647	+	0.923647i
$839$	6.65895			0.229893			0.114946	−	0.993372i	$-0.463330\pi$
$839$	6.65895			0.229893			0.114946	+	0.993372i	$0.463330\pi$
$840$	−6.97688	−	2.32044i	−0.240725	−	0.0800626i
$841$	28.4520			0.981102
$842$	−9.98996	+	9.98996i	−0.344277	+	0.344277i
$843$	−12.1766	+	12.1766i	−0.419384	+	0.419384i
$844$			17.8252i			0.613569i
$845$	20.5297	−	1.31260i	0.706242	−	0.0451548i
$846$			2.69448i			0.0926381i
$847$	0.993466	−	2.45215i	0.0341359	−	0.0842568i
$848$	4.40443	+	4.40443i	0.151249	+	0.151249i
$849$		−	0.790431i		−	0.0271275i
$850$	−3.00445	+	0.385766i	−0.103052	+	0.0132317i
$851$	−17.2340			−0.590773
$852$	12.0889	+	12.0889i	0.414158	+	0.414158i
$853$	29.5495	−	29.5495i	1.01176	−	1.01176i	0.0118259	−	0.999930i	$-0.496236\pi$
$853$	29.5495	−	29.5495i	1.01176	−	1.01176i	0.999930	−	0.0118259i	$-0.00376440\pi$
$854$	8.13373	−	3.44337i	0.278330	−	0.117830i
$855$	−9.74460	+	0.623038i	−0.333258	+	0.0213075i
$856$	−15.3519			−0.524716
$857$	11.2804	+	11.2804i	0.385332	+	0.385332i	0.873019	−	0.487687i	$-0.162159\pi$
$857$	11.2804	+	11.2804i	0.385332	+	0.385332i	−0.487687	+	0.873019i	$0.662159\pi$
$858$	4.14066	+	4.14066i	0.141360	+	0.141360i
$859$	−49.0258			−1.67274			−0.836369	−	0.548168i	$-0.815326\pi$
$859$	−49.0258			−1.67274			−0.836369	+	0.548168i	$0.815326\pi$
$860$	−19.6858	−	17.3198i	−0.671281	−	0.590601i
$861$	−5.16497	+	2.18656i	−0.176022	+	0.0745178i
$862$	3.12440	−	3.12440i	0.106418	−	0.106418i
$863$	−2.43631	−	2.43631i	−0.0829331	−	0.0829331i	0.664423	−	0.747356i	$-0.268677\pi$
$863$	−2.43631	−	2.43631i	−0.0829331	−	0.0829331i	−0.747356	+	0.664423i	$0.768677\pi$
$864$	−5.53726			−0.188381
$865$	32.9464	+	28.9866i	1.12021	+	0.985573i
$866$		−	24.8378i		−	0.844021i
$867$	14.6172	+	14.6172i	0.496426	+	0.496426i
$868$	10.6623	−	26.3176i	0.361904	−	0.893278i
$869$			2.34126i			0.0794217i
$870$	0.131271	+	2.05313i	0.00445049	+	0.0696077i
$871$		−	65.3054i		−	2.21279i
$872$	1.50793	−	1.50793i	0.0510648	−	0.0510648i
$873$	5.34294	−	5.34294i	0.180831	−	0.180831i
$874$	−15.0842			−0.510232
$875$	−29.0290	−	5.68471i	−0.981360	−	0.192178i
$876$	−10.5284			−0.355723
$877$	13.9372	−	13.9372i	0.470625	−	0.470625i	−0.431492	−	0.902117i	$-0.642013\pi$
$877$	13.9372	−	13.9372i	0.470625	−	0.470625i	0.902117	+	0.431492i	$0.142013\pi$
$878$	7.18764	−	7.18764i	0.242571	−	0.242571i
$879$			21.3013i			0.718476i
$880$	−0.142676	−	2.23151i	−0.00480959	−	0.0752242i
$881$			16.5841i			0.558733i	0.960185	+	0.279366i	$0.0901244\pi$
$881$			16.5841i			0.558733i	−0.960185	+	0.279366i	$0.909876\pi$
$882$	0.158279	+	10.1865i	0.00532954	+	0.342998i
$883$	−4.30754	−	4.30754i	−0.144960	−	0.144960i	0.630902	−	0.775862i	$-0.282685\pi$
$883$	−4.30754	−	4.30754i	−0.144960	−	0.144960i	−0.775862	+	0.630902i	$0.782685\pi$
$884$		−	2.85444i		−	0.0960052i
$885$	19.7380	+	17.3657i	0.663484	+	0.583741i
$886$	−33.2790			−1.11803
$887$	21.5263	+	21.5263i	0.722782	+	0.722782i	0.969171	−	0.246389i	$-0.0792442\pi$
$887$	21.5263	+	21.5263i	0.722782	+	0.722782i	−0.246389	+	0.969171i	$0.579244\pi$
$888$	3.01259	−	3.01259i	0.101096	−	0.101096i
$889$	4.49257	+	10.6121i	0.150676	+	0.355918i
$890$	−10.5638	−	9.29415i	−0.354099	−	0.311541i
$891$	2.51565			0.0842775
$892$	−20.8214	−	20.8214i	−0.697150	−	0.697150i
$893$	−3.92793	−	3.92793i	−0.131443	−	0.131443i
$894$	−3.39769			−0.113636
$895$	−9.91412	+	0.633877i	−0.331393	+	0.0211882i
$896$	−2.43642	+	1.03144i	−0.0813950	+	0.0344581i
$897$	20.8165	−	20.8165i	0.695044	−	0.695044i
$898$	−17.3247	−	17.3247i	−0.578132	−	0.578132i
$899$	−7.94527			−0.264990
$900$	−7.21771	+	0.926742i	−0.240590	+	0.0308914i
$901$			3.77355i			0.125715i
$902$	−1.20612	−	1.20612i	−0.0401595	−	0.0401595i
$903$	14.4782	−	35.7363i	0.481806	−	1.18923i
$904$			19.0329i			0.633024i
$905$	−18.5663	+	1.18707i	−0.617166	+	0.0394596i
$906$		−	21.3753i		−	0.710148i
$907$	−24.2252	+	24.2252i	−0.804384	+	0.804384i	−0.983777	−	0.179394i	$-0.942586\pi$
$907$	−24.2252	+	24.2252i	−0.804384	+	0.804384i	0.179394	+	0.983777i	$0.442586\pi$
$908$	10.2646	−	10.2646i	0.340641	−	0.340641i
$909$	−0.681729			−0.0226115
$910$	8.79703	−	26.4501i	0.291619	−	0.876813i
$911$	−16.3633			−0.542140			−0.271070	−	0.962560i	$-0.587378\pi$
$911$	−16.3633			−0.542140			−0.271070	+	0.962560i	$0.587378\pi$
$912$	2.63681	−	2.63681i	0.0873135	−	0.0873135i
$913$	6.98186	−	6.98186i	0.231066	−	0.231066i
$914$		−	21.9673i		−	0.726613i
$915$	−6.12825	+	6.96541i	−0.202594	+	0.230269i
$916$			18.2001i			0.601348i
$917$	2.61855	+	1.06088i	0.0864721	+	0.0350334i
$918$	−2.37206	−	2.37206i	−0.0782896	−	0.0782896i
$919$		−	44.4685i		−	1.46688i	−0.679755	−	0.733439i	$-0.737914\pi$
$919$		−	44.4685i		−	1.46688i	0.679755	−	0.733439i	$-0.262086\pi$
$920$	−11.2186	+	0.717280i	−0.369866	+	0.0236480i
$921$	−3.50836			−0.115604
$922$	−23.9505	−	23.9505i	−0.788769	−	0.788769i
$923$	−45.8303	+	45.8303i	−1.50852	+	1.50852i
$924$	3.02803	−	1.28190i	0.0996150	−	0.0421714i
$925$	10.4778	−	13.5648i	0.344507	−	0.446008i
$926$	11.4751			0.377096
$927$	−7.90304	−	7.90304i	−0.259570	−	0.259570i
$928$	0.523473	+	0.523473i	0.0171838	+	0.0171838i
$929$	26.7181			0.876592			0.438296	−	0.898831i	$-0.355582\pi$
$929$	26.7181			0.876592			0.438296	+	0.898831i	$0.355582\pi$
$930$	1.90309	+	29.7651i	0.0624046	+	0.976037i
$931$	−15.0804	−	14.6189i	−0.494239	−	0.479115i
$932$	5.19484	−	5.19484i	0.170163	−	0.170163i
$933$	19.3439	+	19.3439i	0.633292	+	0.633292i
$934$	20.0051			0.654587
$935$	0.894818	−	1.01706i	0.0292637	−	0.0332613i
$936$		−	6.85734i		−	0.224139i
$937$	25.3278	+	25.3278i	0.827423	+	0.827423i	0.987160	−	0.159736i	$-0.0510644\pi$
$937$	25.3278	+	25.3278i	0.827423	+	0.827423i	−0.159736	+	0.987160i	$0.551064\pi$
$938$	−33.9876	−	13.7698i	−1.10973	−	0.449599i
$939$		−	6.76674i		−	0.220824i
$940$	−3.10809	−	2.73454i	−0.101375	−	0.0891907i
$941$		−	54.5372i		−	1.77786i	−0.458042	−	0.888931i	$-0.651449\pi$
$941$		−	54.5372i		−	1.77786i	0.458042	−	0.888931i	$-0.348551\pi$
$942$	−5.63089	+	5.63089i	−0.183464	+	0.183464i
$943$	−6.06361	+	6.06361i	−0.197458	+	0.197458i
$944$	9.46005			0.307898
$945$	−14.6698	−	29.2906i	−0.477210	−	0.952824i
$946$	11.7261			0.381249
$947$	−22.5295	+	22.5295i	−0.732110	+	0.732110i	−0.971037	−	0.238927i	$-0.923204\pi$
$947$	−22.5295	+	22.5295i	−0.732110	+	0.732110i	0.238927	+	0.971037i	$0.423204\pi$
$948$	−2.05751	+	2.05751i	−0.0668250	+	0.0668250i
$949$		−	39.9145i		−	1.29568i
$950$	9.17080	−	11.8728i	0.297540	−	0.385203i
$951$			4.27350i			0.138578i
$952$	−1.48557	−	0.601864i	−0.0481475	−	0.0195065i
$953$	−1.71498	−	1.71498i	−0.0555537	−	0.0555537i	0.678784	−	0.734338i	$-0.262507\pi$
$953$	−1.71498	−	1.71498i	−0.0555537	−	0.0555537i	−0.734338	+	0.678784i	$0.762507\pi$
$954$			9.06537i			0.293502i
$955$	−0.151688	−	2.37246i	−0.00490850	−	0.0767711i
$956$	28.7508			0.929868
$957$	−0.650584	−	0.650584i	−0.0210304	−	0.0210304i
$958$	−1.47708	+	1.47708i	−0.0477222	+	0.0477222i
$959$	−2.61173	−	6.16928i	−0.0843372	−	0.199216i
$960$	1.83569	−	2.08645i	0.0592465	−	0.0673400i
$961$	−84.1860			−2.71568
$962$	11.4211	+	11.4211i	0.368230	+	0.368230i
$963$	−15.7989	−	15.7989i	−0.509112	−	0.509112i
$964$	17.8073			0.573534
$965$	−34.3659	+	39.0606i	−1.10628	+	1.25741i
$966$	−6.44456	−	15.2230i	−0.207350	−	0.489791i
$967$	−38.6139	+	38.6139i	−1.24174	+	1.24174i	−0.282459	+	0.959279i	$0.591150\pi$
$967$	−38.6139	+	38.6139i	−1.24174	+	1.24174i	−0.959279	+	0.282459i	$0.908850\pi$
$968$	0.707107	+	0.707107i	0.0227273	+	0.0227273i
$969$	2.25912			0.0725734
$970$	0.740737	+	11.5855i	0.0237836	+	0.371987i
$971$			32.1399i			1.03142i	0.856764	+	0.515709i	$0.172471\pi$
$971$			32.1399i			1.03142i	−0.856764	+	0.515709i	$0.827529\pi$
$972$	−9.53553	−	9.53553i	−0.305852	−	0.305852i
$973$	20.3762	−	50.2942i	0.653233	−	1.61236i
$974$		−	20.8138i		−	0.666919i
$975$	3.72875	+	29.0405i	0.119416	+	0.930040i
$976$			3.33840i			0.106859i
$977$	−10.0123	+	10.0123i	−0.320322	+	0.320322i	−0.848890	−	0.528569i	$-0.822729\pi$
$977$	−10.0123	+	10.0123i	−0.320322	+	0.320322i	0.528569	+	0.848890i	$0.322729\pi$
$978$	13.6576	−	13.6576i	0.436721	−	0.436721i
$979$	6.29246			0.201108
$980$	−11.9108	−	10.1554i	−0.380478	−	0.324402i
$981$	3.10367			0.0990926
$982$	−22.9589	+	22.9589i	−0.732649	+	0.732649i
$983$	−10.2079	+	10.2079i	−0.325580	+	0.325580i	−0.850903	−	0.525323i	$-0.823945\pi$
$983$	−10.2079	+	10.2079i	−0.325580	+	0.325580i	0.525323	+	0.850903i	$0.323945\pi$
$984$		−	2.11990i		−	0.0675800i
$985$	−12.9598	−	11.4022i	−0.412933	−	0.363303i
$986$			0.448492i			0.0142829i
$987$	2.28590	−	5.64222i	0.0727609	−	0.179594i
$988$	9.99643	+	9.99643i	0.318029	+	0.318029i
$989$		−	58.9512i		−	1.87454i
$990$	2.14966	−	2.44332i	0.0683207	−	0.0776538i
$991$	16.0784			0.510748			0.255374	−	0.966842i	$-0.417801\pi$
$991$	16.0784			0.510748			0.255374	+	0.966842i	$0.417801\pi$
$992$	7.58900	+	7.58900i	0.240951	+	0.240951i
$993$	−0.614041	+	0.614041i	−0.0194860	+	0.0194860i
$994$	14.1885	+	33.5153i	0.450033	+	1.06304i
$995$	1.87543	+	29.3326i	0.0594551	+	0.929906i
$996$	12.2714			0.388835
$997$	−4.07073	−	4.07073i	−0.128921	−	0.128921i	0.639702	−	0.768623i	$-0.279058\pi$
$997$	−4.07073	−	4.07073i	−0.128921	−	0.128921i	−0.768623	+	0.639702i	$0.779058\pi$
$998$	−2.66173	−	2.66173i	−0.0842556	−	0.0842556i
$999$	18.9820			0.600563

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.l.b.573.2	✓	24
5.2	odd	4	inner	770.2.l.b.727.5	yes	24
7.6	odd	2	inner	770.2.l.b.573.5	yes	24
35.27	even	4	inner	770.2.l.b.727.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.l.b.573.2	✓	24	1.1	even	1	trivial
770.2.l.b.573.5	yes	24	7.6	odd	2	inner
770.2.l.b.727.2	yes	24	35.27	even	4	inner
770.2.l.b.727.5	yes	24	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)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.878808 + 0.878808i) q^{3} -1.00000i q^{4} +(0.142676 + 2.23151i) q^{5} -1.24282i q^{6} +(0.993466 - 2.45215i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.45539i q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.878808 + 0.878808i) q^{3} -1.00000i q^{4} +(0.142676 + 2.23151i) q^{5} -1.24282i q^{6} +(0.993466 - 2.45215i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.45539i q^{9} +(-1.67880 - 1.47703i) q^{10} +1.00000 q^{11} +(0.878808 + 0.878808i) q^{12} +(-3.33166 + 3.33166i) q^{13} +(1.03144 + 2.43642i) q^{14} +(-2.08645 - 1.83569i) q^{15} -1.00000 q^{16} +(-0.428381 - 0.428381i) q^{17} +(-1.02912 - 1.02912i) q^{18} +3.00044 q^{19} +(2.23151 - 0.142676i) q^{20} +(1.28190 + 3.02803i) q^{21} +(-0.707107 + 0.707107i) q^{22} +(3.55487 + 3.55487i) q^{23} -1.24282 q^{24} +(-4.95929 + 0.636764i) q^{25} -4.71168i q^{26} +(-3.91544 - 3.91544i) q^{27} +(-2.45215 - 0.993466i) q^{28} +0.740302i q^{29} +(2.77337 - 0.177320i) q^{30} +10.7325i q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.878808 + 0.878808i) q^{33} +0.605822 q^{34} +(5.61374 + 1.86707i) q^{35} +1.45539 q^{36} +(-2.42399 + 2.42399i) q^{37} +(-2.12163 + 2.12163i) q^{38} -5.85578i q^{39} +(-1.47703 + 1.67880i) q^{40} +1.70572i q^{41} +(-3.04758 - 1.23470i) q^{42} +(-8.29161 - 8.29161i) q^{43} -1.00000i q^{44} +(-3.24773 + 0.207649i) q^{45} -5.02735 q^{46} +(-1.30912 - 1.30912i) q^{47} +(0.878808 - 0.878808i) q^{48} +(-5.02605 - 4.87225i) q^{49} +(3.05649 - 3.95701i) q^{50} +0.752930 q^{51} +(3.33166 + 3.33166i) q^{52} +(-4.40443 - 4.40443i) q^{53} +5.53726 q^{54} +(0.142676 + 2.23151i) q^{55} +(2.43642 - 1.03144i) q^{56} +(-2.63681 + 2.63681i) q^{57} +(-0.523473 - 0.523473i) q^{58} -9.46005 q^{59} +(-1.83569 + 2.08645i) q^{60} -3.33840i q^{61} +(-7.58900 - 7.58900i) q^{62} +(3.56884 + 1.44588i) q^{63} +1.00000i q^{64} +(-7.90998 - 6.95929i) q^{65} -1.24282i q^{66} +(-9.80074 + 9.80074i) q^{67} +(-0.428381 + 0.428381i) q^{68} -6.24810 q^{69} +(-5.28973 + 2.64929i) q^{70} +13.7560 q^{71} +(-1.02912 + 1.02912i) q^{72} +(-5.99019 + 5.99019i) q^{73} -3.42804i q^{74} +(3.79867 - 4.91785i) q^{75} -3.00044i q^{76} +(0.993466 - 2.45215i) q^{77} +(4.14066 + 4.14066i) q^{78} +2.34126i q^{79} +(-0.142676 - 2.23151i) q^{80} +2.51565 q^{81} +(-1.20612 - 1.20612i) q^{82} +(6.98186 - 6.98186i) q^{83} +(3.02803 - 1.28190i) q^{84} +(0.894818 - 1.01706i) q^{85} +11.7261 q^{86} +(-0.650584 - 0.650584i) q^{87} +(0.707107 + 0.707107i) q^{88} +6.29246 q^{89} +(2.14966 - 2.44332i) q^{90} +(4.85983 + 11.4796i) q^{91} +(3.55487 - 3.55487i) q^{92} +(-9.43178 - 9.43178i) q^{93} +1.85137 q^{94} +(0.428089 + 6.69551i) q^{95} +1.24282i q^{96} +(-3.67113 - 3.67113i) q^{97} +(6.99916 - 0.108754i) q^{98} +1.45539i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 24 * q	\( 24 q + 24 q^{11} - 24 q^{15} - 24 q^{16} - 24 q^{18} - 28 q^{21} + 16 q^{23} + 16 q^{25} - 24 q^{30} + 16 q^{35} - 64 q^{36} - 8 q^{37} + 16 q^{42} + 40 q^{43} - 16 q^{46} + 16 q^{50} - 24 q^{51} - 88 q^{53} + 4 q^{56} - 112 q^{57} + 8 q^{58} - 8 q^{60} + 48 q^{63} - 8 q^{65} - 88 q^{67} - 28 q^{70} + 40 q^{71} - 24 q^{72} + 64 q^{78} - 136 q^{81} + 64 q^{85} + 96 q^{86} + 16 q^{92} - 104 q^{93} + 64 q^{95} - 16 q^{98}+O(q^{100}) \) 24 * q + 24 * q^11 - 24 * q^15 - 24 * q^16 - 24 * q^18 - 28 * q^21 + 16 * q^23 + 16 * q^25 - 24 * q^30 + 16 * q^35 - 64 * q^36 - 8 * q^37 + 16 * q^42 + 40 * q^43 - 16 * q^46 + 16 * q^50 - 24 * q^51 - 88 * q^53 + 4 * q^56 - 112 * q^57 + 8 * q^58 - 8 * q^60 + 48 * q^63 - 8 * q^65 - 88 * q^67 - 28 * q^70 + 40 * q^71 - 24 * q^72 + 64 * q^78 - 136 * q^81 + 64 * q^85 + 96 * q^86 + 16 * q^92 - 104 * q^93 + 64 * q^95 - 16 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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