LMFDB - Embedded newform 429.2.j.a.122.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(122,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("429.122");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.j (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			122.9
Character	$\chi$	$=$	429.122
Dual form			429.2.j.a.320.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.43233 - 1.43233i) q^{2} +(0.643764 - 1.60797i) q^{3} +2.10314i q^{4} +(-2.03215 - 2.03215i) q^{5} +(-3.22523 + 1.38106i) q^{6} +(-3.19246 - 3.19246i) q^{7} +(0.147729 - 0.147729i) q^{8} +(-2.17114 - 2.07031i) q^{9} +O(q^{10})$	\(q+(-1.43233 - 1.43233i) q^{2} +(0.643764 - 1.60797i) q^{3} +2.10314i q^{4} +(-2.03215 - 2.03215i) q^{5} +(-3.22523 + 1.38106i) q^{6} +(-3.19246 - 3.19246i) q^{7} +(0.147729 - 0.147729i) q^{8} +(-2.17114 - 2.07031i) q^{9} +5.82141i q^{10} +(0.707107 - 0.707107i) q^{11} +(3.38178 + 1.35393i) q^{12} +(2.71230 + 2.37559i) q^{13} +9.14530i q^{14} +(-4.57585 + 1.95941i) q^{15} +3.78308 q^{16} +6.40537 q^{17} +(0.144419 + 6.07515i) q^{18} +(3.07168 - 3.07168i) q^{19} +(4.27389 - 4.27389i) q^{20} +(-7.18856 + 3.07818i) q^{21} -2.02562 q^{22} -7.60050 q^{23} +(-0.142441 - 0.332646i) q^{24} +3.25924i q^{25} +(-0.482285 - 7.28754i) q^{26} +(-4.72669 + 2.15833i) q^{27} +(6.71418 - 6.71418i) q^{28} +4.02775i q^{29} +(9.36065 + 3.74761i) q^{30} +(1.47642 - 1.47642i) q^{31} +(-5.71408 - 5.71408i) q^{32} +(-0.681796 - 1.59222i) q^{33} +(-9.17460 - 9.17460i) q^{34} +12.9751i q^{35} +(4.35414 - 4.56620i) q^{36} +(-3.14530 - 3.14530i) q^{37} -8.79931 q^{38} +(5.56596 - 2.83198i) q^{39} -0.600413 q^{40} +(2.66742 + 2.66742i) q^{41} +(14.7054 + 5.88742i) q^{42} -2.03705i q^{43} +(1.48714 + 1.48714i) q^{44} +(0.204898 + 8.61923i) q^{45} +(10.8864 + 10.8864i) q^{46} +(1.19202 - 1.19202i) q^{47} +(2.43541 - 6.08309i) q^{48} +13.3835i q^{49} +(4.66830 - 4.66830i) q^{50} +(4.12355 - 10.2996i) q^{51} +(-4.99619 + 5.70435i) q^{52} -10.2747i q^{53} +(9.86162 + 3.67874i) q^{54} -2.87389 q^{55} -0.943236 q^{56} +(-2.96173 - 6.91660i) q^{57} +(5.76907 - 5.76907i) q^{58} +(-7.79191 + 7.79191i) q^{59} +(-4.12091 - 9.62366i) q^{60} +3.03703 q^{61} -4.22944 q^{62} +(0.321889 + 13.5406i) q^{63} +8.80274i q^{64} +(-0.684251 - 10.3393i) q^{65} +(-1.30402 + 3.25714i) q^{66} +(-5.64400 + 5.64400i) q^{67} +13.4714i q^{68} +(-4.89293 + 12.2214i) q^{69} +(18.5846 - 18.5846i) q^{70} +(-1.16698 - 1.16698i) q^{71} +(-0.626584 + 0.0148952i) q^{72} +(-3.59580 - 3.59580i) q^{73} +9.01021i q^{74} +(5.24076 + 2.09818i) q^{75} +(6.46016 + 6.46016i) q^{76} -4.51481 q^{77} +(-12.0286 - 3.91596i) q^{78} -11.4106 q^{79} +(-7.68778 - 7.68778i) q^{80} +(0.427657 + 8.98983i) q^{81} -7.64125i q^{82} +(4.41707 + 4.41707i) q^{83} +(-6.47385 - 15.1185i) q^{84} +(-13.0166 - 13.0166i) q^{85} +(-2.91772 + 2.91772i) q^{86} +(6.47650 + 2.59292i) q^{87} -0.208920i q^{88} +(3.71362 - 3.71362i) q^{89} +(12.0521 - 12.6391i) q^{90} +(-1.07494 - 16.2429i) q^{91} -15.9849i q^{92} +(-1.42357 - 3.32451i) q^{93} -3.41472 q^{94} -12.4842 q^{95} +(-12.8666 + 5.50955i) q^{96} +(8.15196 - 8.15196i) q^{97} +(19.1696 - 19.1696i) q^{98} +(-2.99915 + 0.0712963i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 12 q^{6} - 16 q^{7}+O(q^{10}) $ 96 * q + 12 * q^6 - 16 * q^7	$ 96 q + 12 q^{6} - 16 q^{7} + 16 q^{13} - 16 q^{15} - 120 q^{16} - 28 q^{18} - 24 q^{19} + 24 q^{24} - 24 q^{27} + 56 q^{28} + 48 q^{31} - 16 q^{34} - 16 q^{37} + 80 q^{40} + 52 q^{42} + 4 q^{45} - 56 q^{46} + 28 q^{48} + 4 q^{54} + 4 q^{57} + 48 q^{58} + 4 q^{60} - 96 q^{61} - 36 q^{63} + 20 q^{66} - 16 q^{67} + 48 q^{70} - 16 q^{72} - 16 q^{73} - 88 q^{76} + 80 q^{78} + 16 q^{79} + 32 q^{81} + 52 q^{84} - 8 q^{85} - 48 q^{87} - 16 q^{91} - 36 q^{93} - 16 q^{94} - 108 q^{96} - 48 q^{97}+O(q^{100}) $ 96 * q + 12 * q^6 - 16 * q^7 + 16 * q^13 - 16 * q^15 - 120 * q^16 - 28 * q^18 - 24 * q^19 + 24 * q^24 - 24 * q^27 + 56 * q^28 + 48 * q^31 - 16 * q^34 - 16 * q^37 + 80 * q^40 + 52 * q^42 + 4 * q^45 - 56 * q^46 + 28 * q^48 + 4 * q^54 + 4 * q^57 + 48 * q^58 + 4 * q^60 - 96 * q^61 - 36 * q^63 + 20 * q^66 - 16 * q^67 + 48 * q^70 - 16 * q^72 - 16 * q^73 - 88 * q^76 + 80 * q^78 + 16 * q^79 + 32 * q^81 + 52 * q^84 - 8 * q^85 - 48 * q^87 - 16 * q^91 - 36 * q^93 - 16 * q^94 - 108 * q^96 - 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.43233	−	1.43233i	−1.01281	−	1.01281i	−0.999917	−	0.0128934i	$-0.995896\pi$
$2$	−1.43233	−	1.43233i	−1.01281	−	1.01281i	−0.0128934	−	0.999917i	$-0.504104\pi$
$3$	0.643764	−	1.60797i	0.371677	−	0.928362i
$3$	0.643764	−	1.60797i	0.371677	−	0.928362i
$4$			2.10314i			1.05157i
$5$	−2.03215	−	2.03215i	−0.908803	−	0.908803i	0.0873723	−	0.996176i	$-0.472153\pi$
$5$	−2.03215	−	2.03215i	−0.908803	−	0.908803i	−0.996176	+	0.0873723i	$0.972153\pi$
$6$	−3.22523	+	1.38106i	−1.31669	+	0.563816i
$7$	−3.19246	−	3.19246i	−1.20663	−	1.20663i	−0.972110	−	0.234524i	$-0.924647\pi$
$7$	−3.19246	−	3.19246i	−1.20663	−	1.20663i	−0.234524	−	0.972110i	$-0.575353\pi$
$8$	0.147729	−	0.147729i	0.0522301	−	0.0522301i
$9$	−2.17114	−	2.07031i	−0.723712	−	0.690102i
$10$			5.82141i			1.84089i
$11$	0.707107	−	0.707107i	0.213201	−	0.213201i
$11$	0.707107	−	0.707107i	0.213201	−	0.213201i
$12$	3.38178	+	1.35393i	0.976237	+	0.390845i
$13$	2.71230	+	2.37559i	0.752257	+	0.658870i
$13$	2.71230	+	2.37559i	0.752257	+	0.658870i
$14$			9.14530i			2.44418i
$15$	−4.57585	+	1.95941i	−1.18148	+	0.505917i
$16$	3.78308			0.945771
$17$	6.40537			1.55353			0.776765	−	0.629791i	$-0.216859\pi$
$17$	6.40537			1.55353			0.776765	+	0.629791i	$0.216859\pi$
$18$	0.144419	+	6.07515i	0.0340399	+	1.43193i
$19$	3.07168	−	3.07168i	0.704691	−	0.704691i	−0.260723	−	0.965414i	$-0.583961\pi$
$19$	3.07168	−	3.07168i	0.704691	−	0.704691i	0.965414	+	0.260723i	$0.0839609\pi$
$20$	4.27389	−	4.27389i	0.955670	−	0.955670i
$21$	−7.18856	+	3.07818i	−1.56867	+	0.671715i
$22$	−2.02562			−0.431864
$23$	−7.60050			−1.58481			−0.792407	−	0.609993i	$-0.791172\pi$
$23$	−7.60050			−1.58481			−0.792407	+	0.609993i	$0.791172\pi$
$24$	−0.142441	−	0.332646i	−0.0290757	−	0.0679011i
$25$			3.25924i			0.651847i
$26$	−0.482285	−	7.28754i	−0.0945839	−	1.42920i
$27$	−4.72669	+	2.15833i	−0.909652	+	0.415371i
$28$	6.71418	−	6.71418i	1.26886	−	1.26886i
$29$			4.02775i			0.747935i	0.927442	+	0.373967i	$0.122003\pi$
$29$			4.02775i			0.747935i	−0.927442	+	0.373967i	$0.877997\pi$
$30$	9.36065	+	3.74761i	1.70901	+	0.684218i
$31$	1.47642	−	1.47642i	0.265173	−	0.265173i	−0.561979	−	0.827152i	$-0.689960\pi$
$31$	1.47642	−	1.47642i	0.265173	−	0.265173i	0.827152	+	0.561979i	$0.189960\pi$
$32$	−5.71408	−	5.71408i	−1.01012	−	1.01012i
$33$	−0.681796	−	1.59222i	−0.118686	−	0.277169i
$34$	−9.17460	−	9.17460i	−1.57343	−	1.57343i
$35$			12.9751i			2.19319i
$36$	4.35414	−	4.56620i	0.725691	−	0.761033i
$37$	−3.14530	−	3.14530i	−0.517084	−	0.517084i	0.399604	−	0.916688i	$-0.369148\pi$
$37$	−3.14530	−	3.14530i	−0.517084	−	0.517084i	−0.916688	+	0.399604i	$0.869148\pi$
$38$	−8.79931			−1.42744
$39$	5.56596	−	2.83198i	0.891266	−	0.453480i
$40$	−0.600413			−0.0949337
$41$	2.66742	+	2.66742i	0.416581	+	0.416581i	0.884023	−	0.467443i	$-0.154825\pi$
$41$	2.66742	+	2.66742i	0.416581	+	0.416581i	−0.467443	+	0.884023i	$0.654825\pi$
$42$	14.7054	+	5.88742i	2.26909	+	0.908448i
$43$		−	2.03705i		−	0.310647i	−0.987864	−	0.155323i	$-0.950358\pi$
$43$		−	2.03705i		−	0.310647i	0.987864	−	0.155323i	$-0.0496419\pi$
$44$	1.48714	+	1.48714i	0.224195	+	0.224195i
$45$	0.204898	+	8.61923i	0.0305443	+	1.28488i
$46$	10.8864	+	10.8864i	1.60512	+	1.60512i
$47$	1.19202	−	1.19202i	0.173873	−	0.173873i	−0.614805	−	0.788679i	$-0.710765\pi$
$47$	1.19202	−	1.19202i	0.173873	−	0.173873i	0.788679	+	0.614805i	$0.210765\pi$
$48$	2.43541	−	6.08309i	0.351522	−	0.878018i
$49$			13.3835i			1.91193i
$50$	4.66830	−	4.66830i	0.660198	−	0.660198i
$51$	4.12355	−	10.2996i	0.577412	−	1.44224i
$52$	−4.99619	+	5.70435i	−0.692847	+	0.791051i
$53$		−	10.2747i		−	1.41134i	−0.708539	−	0.705671i	$-0.750646\pi$
$53$		−	10.2747i		−	1.41134i	0.708539	−	0.705671i	$-0.249354\pi$
$54$	9.86162	+	3.67874i	1.34200	+	0.500613i
$55$	−2.87389			−0.387515
$56$	−0.943236			−0.126045
$57$	−2.96173	−	6.91660i	−0.392290	−	0.916126i
$58$	5.76907	−	5.76907i	0.757516	−	0.757516i
$59$	−7.79191	+	7.79191i	−1.01442	+	1.01442i	−0.0145252	+	0.999895i	$0.504624\pi$
$59$	−7.79191	+	7.79191i	−1.01442	+	1.01442i	−0.999895	+	0.0145252i	$0.995376\pi$
$60$	−4.12091	−	9.62366i	−0.532007	−	1.24241i
$61$	3.03703			0.388852			0.194426	−	0.980917i	$-0.437716\pi$
$61$	3.03703			0.388852			0.194426	+	0.980917i	$0.437716\pi$
$62$	−4.22944			−0.537140
$63$	0.321889	+	13.5406i	0.0405543	+	1.70596i
$64$			8.80274i			1.10034i
$65$	−0.684251	−	10.3393i	−0.0848709	−	1.28244i
$66$	−1.30402	+	3.25714i	−0.160514	+	0.400926i
$67$	−5.64400	+	5.64400i	−0.689524	+	0.689524i	−0.962127	−	0.272603i	$-0.912116\pi$
$67$	−5.64400	+	5.64400i	−0.689524	+	0.689524i	0.272603	+	0.962127i	$0.412116\pi$
$68$			13.4714i			1.63364i
$69$	−4.89293	+	12.2214i	−0.589039	+	1.47128i
$70$	18.5846	−	18.5846i	2.22128	−	2.22128i
$71$	−1.16698	−	1.16698i	−0.138495	−	0.138495i	0.634460	−	0.772956i	$-0.281222\pi$
$71$	−1.16698	−	1.16698i	−0.138495	−	0.138495i	−0.772956	+	0.634460i	$0.781222\pi$
$72$	−0.626584	+	0.0148952i	−0.0738436	+	0.00175542i
$73$	−3.59580	−	3.59580i	−0.420857	−	0.420857i	0.464642	−	0.885499i	$-0.346183\pi$
$73$	−3.59580	−	3.59580i	−0.420857	−	0.420857i	−0.885499	+	0.464642i	$0.846183\pi$
$74$			9.01021i			1.04742i
$75$	5.24076	+	2.09818i	0.605150	+	0.242277i
$76$	6.46016	+	6.46016i	0.741031	+	0.741031i
$77$	−4.51481			−0.514511
$78$	−12.0286	−	3.91596i	−1.36197	−	0.443395i
$79$	−11.4106			−1.28379			−0.641895	−	0.766792i	$-0.721852\pi$
$79$	−11.4106			−1.28379			−0.641895	+	0.766792i	$0.721852\pi$
$80$	−7.68778	−	7.68778i	−0.859520	−	0.859520i
$81$	0.427657	+	8.98983i	0.0475174	+	0.998870i
$82$		−	7.64125i		−	0.843835i
$83$	4.41707	+	4.41707i	0.484836	+	0.484836i	0.906672	−	0.421836i	$-0.138614\pi$
$83$	4.41707	+	4.41707i	0.484836	+	0.484836i	−0.421836	+	0.906672i	$0.638614\pi$
$84$	−6.47385	−	15.1185i	−0.706355	−	1.64957i
$85$	−13.0166	−	13.0166i	−1.41185	−	1.41185i
$86$	−2.91772	+	2.91772i	−0.314626	+	0.314626i
$87$	6.47650	+	2.59292i	0.694354	+	0.277990i
$88$		−	0.208920i		−	0.0222710i
$89$	3.71362	−	3.71362i	0.393643	−	0.393643i	−0.482341	−	0.875984i	$-0.660213\pi$
$89$	3.71362	−	3.71362i	0.393643	−	0.393643i	0.875984	+	0.482341i	$0.160213\pi$
$90$	12.0521	−	12.6391i	1.27040	−	1.33227i
$91$	−1.07494	−	16.2429i	−0.112685	−	1.70271i
$92$		−	15.9849i		−	1.66654i
$93$	−1.42357	−	3.32451i	−0.147618	−	0.344735i
$94$	−3.41472			−0.352201
$95$	−12.4842			−1.28085
$96$	−12.8666	+	5.50955i	−1.31319	+	0.562316i
$97$	8.15196	−	8.15196i	0.827706	−	0.827706i	−0.159493	−	0.987199i	$-0.550986\pi$
$97$	8.15196	−	8.15196i	0.827706	−	0.827706i	0.987199	+	0.159493i	$0.0509859\pi$
$98$	19.1696	−	19.1696i	1.93643	−	1.93643i
$99$	−2.99915	+	0.0712963i	−0.301426	+	0.00716555i
$100$	−6.85463			−0.685463
$101$	6.73261			0.669920			0.334960	−	0.942232i	$-0.391277\pi$
$101$	6.73261			0.669920			0.334960	+	0.942232i	$0.391277\pi$
$102$	−20.6588	+	8.84620i	−2.04552	+	0.875905i
$103$		−	2.49825i		−	0.246160i	−0.992397	−	0.123080i	$-0.960723\pi$
$103$		−	2.49825i		−	0.246160i	0.992397	−	0.123080i	$-0.0392771\pi$
$104$	0.751628	−	0.0497423i	0.0737032	−	0.00487764i
$105$	20.8635	+	8.35289i	2.03607	+	0.815158i
$106$	−14.7168	+	14.7168i	−1.42942	+	1.42942i
$107$		−	5.82782i		−	0.563397i	−0.959503	−	0.281698i	$-0.909102\pi$
$107$		−	5.82782i		−	0.563397i	0.959503	−	0.281698i	$-0.0908978\pi$
$108$	−4.53927	−	9.94089i	−0.436791	−	0.956562i
$109$	−6.32234	+	6.32234i	−0.605570	+	0.605570i	−0.941785	−	0.336215i	$-0.890853\pi$
$109$	−6.32234	+	6.32234i	−0.605570	+	0.605570i	0.336215	+	0.941785i	$0.390853\pi$
$110$	4.11636	+	4.11636i	0.392479	+	0.392479i
$111$	−7.08237	+	3.03271i	−0.672229	+	0.287853i
$112$	−12.0773	−	12.0773i	−1.14120	−	1.14120i
$113$			0.0682002i			0.00641573i	0.999995	+	0.00320787i	$0.00102110\pi$
$113$			0.0682002i			0.00641573i	−0.999995	+	0.00320787i	$0.998979\pi$
$114$	−5.66468	+	14.1490i	−0.530546	+	1.32518i
$115$	15.4453	+	15.4453i	1.44028	+	1.44028i
$116$	−8.47092			−0.786505
$117$	−0.970577	−	10.7730i	−0.0897299	−	0.995966i
$118$	22.3212			2.05483
$119$	−20.4488	−	20.4488i	−1.87454	−	1.87454i
$120$	−0.386525	+	0.965447i	−0.0352847	+	0.0881328i
$121$		−	1.00000i		−	0.0909091i
$122$	−4.35003	−	4.35003i	−0.393834	−	0.393834i
$123$	6.00632	−	2.57194i	0.541572	−	0.231904i
$124$	3.10512	+	3.10512i	0.278848	+	0.278848i
$125$	−3.53748	+	3.53748i	−0.316402	+	0.316402i
$126$	18.9336	−	19.8557i	1.68674	−	1.76888i
$127$		−	12.6162i		−	1.11950i	−0.828660	−	0.559752i	$-0.810896\pi$
$127$		−	12.6162i		−	1.11950i	0.828660	−	0.559752i	$-0.189104\pi$
$128$	1.18026	−	1.18026i	0.104321	−	0.104321i
$129$	−3.27551	−	1.31138i	−0.288392	−	0.115460i
$130$	−13.8293	+	15.7894i	−1.21291	+	1.38482i
$131$		−	4.32229i		−	0.377641i	−0.982012	−	0.188820i	$-0.939534\pi$
$131$		−	4.32229i		−	0.377641i	0.982012	−	0.188820i	$-0.0604664\pi$
$132$	3.34865	−	1.43391i	0.291463	−	0.124806i
$133$	−19.6124			−1.70061
$134$	16.1681			1.39671
$135$	13.9914	+	5.21928i	1.20419	+	0.449204i
$136$	0.946258	−	0.946258i	0.0811409	−	0.0811409i
$137$	8.50908	−	8.50908i	0.726980	−	0.726980i	−0.243037	−	0.970017i	$-0.578144\pi$
$137$	8.50908	−	8.50908i	0.726980	−	0.726980i	0.970017	+	0.243037i	$0.0781438\pi$
$138$	24.5133	−	10.4968i	2.08671	−	0.893543i
$139$	1.06503			0.0903349			0.0451674	−	0.998979i	$-0.485618\pi$
$139$	1.06503			0.0903349			0.0451674	+	0.998979i	$0.485618\pi$
$140$	−27.2884			−2.30629
$141$	−1.14935	−	2.68410i	−0.0967926	−	0.226042i
$142$			3.34301i			0.280539i
$143$	3.59768	−	0.238092i	0.300853	−	0.0199103i
$144$	−8.21359	−	7.83215i	−0.684466	−	0.652679i
$145$	8.18498	−	8.18498i	0.679726	−	0.679726i
$146$			10.3007i			0.852496i
$147$	21.5203	+	8.61584i	1.77497	+	0.710623i
$148$	6.61500	−	6.61500i	0.543749	−	0.543749i
$149$	−5.28091	−	5.28091i	−0.432629	−	0.432629i	0.456893	−	0.889522i	$-0.348962\pi$
$149$	−5.28091	−	5.28091i	−0.432629	−	0.432629i	−0.889522	+	0.456893i	$0.848962\pi$
$150$	−4.50121	−	10.5118i	−0.367522	−	0.858283i
$151$	16.7224	+	16.7224i	1.36085	+	1.36085i	0.872831	+	0.488022i	$0.162281\pi$
$151$	16.7224	+	16.7224i	1.36085	+	1.36085i	0.488022	+	0.872831i	$0.337719\pi$
$152$		−	0.907551i		−	0.0736121i
$153$	−13.9069	−	13.2611i	−1.12431	−	1.07209i
$154$	6.46670	+	6.46670i	0.521102	+	0.521102i
$155$	−6.00061			−0.481980
$156$	5.95605	+	11.7060i	0.476866	+	0.937229i
$157$	−20.1620			−1.60911			−0.804553	−	0.593881i	$-0.797595\pi$
$157$	−20.1620			−1.60911			−0.804553	+	0.593881i	$0.797595\pi$
$158$	16.3437	+	16.3437i	1.30024	+	1.30024i
$159$	−16.5215	−	6.61450i	−1.31024	−	0.524564i
$160$			23.2237i			1.83600i
$161$	24.2642	+	24.2642i	1.91229	+	1.91229i
$162$	12.2639	−	13.4890i	0.963540	−	1.05979i
$163$	−12.8534	−	12.8534i	−1.00676	−	1.00676i	−0.999977	−	0.00677853i	$-0.997842\pi$
$163$	−12.8534	−	12.8534i	−1.00676	−	1.00676i	−0.00677853	−	0.999977i	$-0.502158\pi$
$164$	−5.60995	+	5.60995i	−0.438064	+	0.438064i
$165$	−1.85011	+	4.62113i	−0.144031	+	0.359754i
$166$		−	12.6534i		−	0.982094i
$167$	−6.34869	+	6.34869i	−0.491276	+	0.491276i	−0.908708	−	0.417432i	$-0.862930\pi$
$167$	−6.34869	+	6.34869i	−0.491276	+	0.491276i	0.417432	+	0.908708i	$0.362930\pi$
$168$	−0.607221	+	1.51669i	−0.0468481	+	0.117016i
$169$	1.71316	+	12.8866i	0.131782	+	0.991279i
$170$			37.2883i			2.85988i
$171$	−13.0283	+	0.309712i	−0.996302	+	0.0236842i
$172$	4.28419			0.326666
$173$	24.1503			1.83611			0.918056	−	0.396451i	$-0.129758\pi$
$173$	24.1503			1.83611			0.918056	+	0.396451i	$0.129758\pi$
$174$	−5.56257	−	12.9904i	−0.421697	−	0.984801i
$175$	10.4050	−	10.4050i	0.786542	−	0.786542i
$176$	2.67504	−	2.67504i	0.201639	−	0.201639i
$177$	7.51300	+	17.5453i	0.564712	+	1.31879i
$178$	−10.6383			−0.797371
$179$	4.14742			0.309993			0.154997	−	0.987915i	$-0.450463\pi$
$179$	4.14742			0.309993			0.154997	+	0.987915i	$0.450463\pi$
$180$	−18.1274	+	0.430928i	−1.35114	+	0.0321195i
$181$		−	1.10514i		−	0.0821442i	−0.999156	−	0.0410721i	$-0.986923\pi$
$181$		−	1.10514i		−	0.0821442i	0.999156	−	0.0410721i	$-0.0130773\pi$
$182$	−21.7255	+	24.8048i	−1.61040	+	1.83865i
$183$	1.95513	−	4.88346i	0.144528	−	0.360996i
$184$	−1.12281	+	1.12281i	−0.0827749	+	0.0827749i
$185$			12.7834i			0.939855i
$186$	−2.72276	+	6.80082i	−0.199643	+	0.498660i
$187$	4.52928	−	4.52928i	0.331214	−	0.331214i
$188$	2.50697	+	2.50697i	0.182840	+	0.182840i
$189$	21.9801	+	8.19937i	1.59882	+	0.596417i
$190$	17.8815	+	17.8815i	1.29726	+	1.29726i
$191$		−	11.1227i		−	0.804809i	−0.915462	−	0.402404i	$-0.868175\pi$
$191$		−	11.1227i		−	0.804809i	0.915462	−	0.402404i	$-0.131825\pi$
$192$	14.1545	+	5.66689i	1.02152	+	0.408972i
$193$	10.7250	+	10.7250i	0.772005	+	0.772005i	0.978457	−	0.206452i	$-0.0661917\pi$
$193$	10.7250	+	10.7250i	0.772005	+	0.772005i	−0.206452	+	0.978457i	$0.566192\pi$
$194$	−23.3526			−1.67662
$195$	−17.0658	−	5.55584i	−1.22211	−	0.397862i
$196$	−28.1474			−2.01053
$197$	2.51064	+	2.51064i	0.178876	+	0.178876i	0.790866	−	0.611990i	$-0.209631\pi$
$197$	2.51064	+	2.51064i	0.178876	+	0.178876i	−0.611990	+	0.790866i	$0.709631\pi$
$198$	4.39790	+	4.19366i	0.312545	+	0.298030i
$199$		−	14.3078i		−	1.01425i	−0.861872	−	0.507127i	$-0.830708\pi$
$199$		−	14.3078i		−	1.01425i	0.861872	−	0.507127i	$-0.169292\pi$
$200$	0.481484	+	0.481484i	0.0340460	+	0.0340460i
$201$	5.44198	+	12.7088i	0.383847	+	0.896409i
$202$	−9.64332	−	9.64332i	−0.678502	−	0.678502i
$203$	12.8584	−	12.8584i	0.902484	−	0.902484i
$204$	21.6616	+	8.67239i	1.51661	+	0.607189i
$205$		−	10.8412i		−	0.757180i
$206$	−3.57832	+	3.57832i	−0.249313	+	0.249313i
$207$	16.5017	+	15.7354i	1.14695	+	1.09368i
$208$	10.2609	+	8.98705i	0.711463	+	0.623140i
$209$		−	4.34401i		−	0.300481i
$210$	−17.9194	−	41.8475i	−1.23655	−	2.88776i
$211$	−1.70289			−0.117232			−0.0586158	−	0.998281i	$-0.518669\pi$
$211$	−1.70289			−0.117232			−0.0586158	+	0.998281i	$0.518669\pi$
$212$	21.6092			1.48412
$213$	−2.62773	+	1.12521i	−0.180049	+	0.0770982i
$214$	−8.34736	+	8.34736i	−0.570614	+	0.570614i
$215$	−4.13957	+	4.13957i	−0.282317	+	0.282317i
$216$	−0.379421	+	1.01712i	−0.0258163	+	0.0692060i
$217$	−9.42681			−0.639934
$218$	18.1114			1.22666
$219$	−8.09679	+	3.46709i	−0.547130	+	0.234284i
$220$		−	6.04419i		−	0.407499i
$221$	17.3733	+	15.2165i	1.16865	+	1.02357i
$222$	14.4881	+	5.80045i	0.972381	+	0.389301i
$223$	−2.60181	+	2.60181i	−0.174230	+	0.174230i	−0.788835	−	0.614605i	$-0.789315\pi$
$223$	−2.60181	+	2.60181i	−0.174230	+	0.174230i	0.614605	+	0.788835i	$0.289315\pi$
$224$			36.4839i			2.43768i
$225$	6.74762	−	7.07624i	0.449841	−	0.471750i
$226$	0.0976852	−	0.0976852i	0.00649792	−	0.00649792i
$227$	−18.5101	−	18.5101i	−1.22856	−	1.22856i	−0.964509	−	0.264050i	$-0.914942\pi$
$227$	−18.5101	−	18.5101i	−1.22856	−	1.22856i	−0.264050	−	0.964509i	$-0.585058\pi$
$228$	14.5466	−	6.22893i	0.963370	−	0.412521i
$229$	−12.0794	−	12.0794i	−0.798232	−	0.798232i	0.184584	−	0.982817i	$-0.440906\pi$
$229$	−12.0794	−	12.0794i	−0.798232	−	0.798232i	−0.982817	+	0.184584i	$0.940906\pi$
$230$		−	44.2456i		−	2.91747i
$231$	−2.90648	+	7.25968i	−0.191232	+	0.477652i
$232$	0.595015	+	0.595015i	0.0390647	+	0.0390647i
$233$	−14.4525			−0.946818			−0.473409	−	0.880843i	$-0.656977\pi$
$233$	−14.4525			−0.946818			−0.473409	+	0.880843i	$0.656977\pi$
$234$	−14.0403	+	16.8207i	−0.917845	+	1.09960i
$235$	−4.84470			−0.316033
$236$	−16.3875	−	16.3875i	−1.06673	−	1.06673i
$237$	−7.34572	+	18.3479i	−0.477156	+	1.19182i
$238$			58.5790i			3.79711i
$239$	2.78259	+	2.78259i	0.179990	+	0.179990i	0.791352	−	0.611361i	$-0.209378\pi$
$239$	2.78259	+	2.78259i	0.179990	+	0.179990i	−0.611361	+	0.791352i	$0.709378\pi$
$240$	−17.3108	+	7.41260i	−1.11741	+	0.478482i
$241$	−5.06652	−	5.06652i	−0.326363	−	0.326363i	0.524839	−	0.851202i	$-0.324126\pi$
$241$	−5.06652	−	5.06652i	−0.326363	−	0.326363i	−0.851202	+	0.524839i	$0.824126\pi$
$242$	−1.43233	+	1.43233i	−0.0920737	+	0.0920737i
$243$	14.7307	+	5.09967i	0.944974	+	0.327144i
$244$			6.38730i			0.408905i
$245$	27.1973	−	27.1973i	1.73757	−	1.73757i
$246$	−12.2869	−	4.91916i	−0.783384	−	0.313634i
$247$	15.6283	−	1.03427i	0.994408	−	0.0658093i
$248$		−	0.436220i		−	0.0277000i
$249$	9.94606	−	4.25896i	0.630306	−	0.269901i
$250$	10.1337			0.640911
$251$	18.8616			1.19053			0.595266	−	0.803529i	$-0.297047\pi$
$251$	18.8616			1.19053			0.595266	+	0.803529i	$0.297047\pi$
$252$	−28.4778	+	0.676978i	−1.79393	+	0.0426456i
$253$	−5.37436	+	5.37436i	−0.337883	+	0.337883i
$254$	−18.0705	+	18.0705i	−1.13385	+	1.13385i
$255$	−29.3100	+	12.5507i	−1.83546	+	0.785957i
$256$	14.2244			0.889027
$257$	0.732279			0.0456783			0.0228391	−	0.999739i	$-0.492729\pi$
$257$	0.732279			0.0456783			0.0228391	+	0.999739i	$0.492729\pi$
$258$	2.81328	+	6.56993i	0.175147	+	0.409026i
$259$			20.0824i			1.24786i
$260$	21.7451	−	1.43908i	1.34857	−	0.0892477i
$261$	8.33868	−	8.74479i	0.516152	−	0.541289i
$262$	−6.19095	+	6.19095i	−0.382478	+	0.382478i
$263$		−	3.59373i		−	0.221599i	−0.993843	−	0.110799i	$-0.964659\pi$
$263$		−	3.59373i		−	0.221599i	0.993843	−	0.110799i	$-0.0353411\pi$
$264$	−0.335937	−	0.134495i	−0.0206755	−	0.00827762i
$265$	−20.8798	+	20.8798i	−1.28263	+	1.28263i
$266$	28.0914	+	28.0914i	1.72239	+	1.72239i
$267$	−3.58069	−	8.36208i	−0.219135	−	0.511751i
$268$	−11.8701	−	11.8701i	−0.725083	−	0.725083i
$269$			18.1072i			1.10402i	0.833839	+	0.552008i	$0.186138\pi$
$269$			18.1072i			1.10402i	−0.833839	+	0.552008i	$0.813862\pi$
$270$	−12.5645	−	27.5160i	−0.764653	−	1.67457i
$271$	−10.5152	−	10.5152i	−0.638752	−	0.638752i	0.311496	−	0.950248i	$-0.399170\pi$
$271$	−10.5152	−	10.5152i	−0.638752	−	0.638752i	−0.950248	+	0.311496i	$0.899170\pi$
$272$	24.2320			1.46928
$273$	−26.8100	−	8.72810i	−1.62262	−	0.528248i
$274$	−24.3756			−1.47258
$275$	2.30463	+	2.30463i	0.138974	+	0.138974i
$276$	−25.7032	−	10.2905i	−1.54715	−	0.619416i
$277$		−	9.78417i		−	0.587874i	−0.955825	−	0.293937i	$-0.905034\pi$
$277$		−	9.78417i		−	0.587874i	0.955825	−	0.293937i	$-0.0949656\pi$
$278$	−1.52548	−	1.52548i	−0.0914921	−	0.0914921i
$279$	−6.26215	+	0.148865i	−0.374905	+	0.00891231i
$280$	1.91679	+	1.91679i	0.114550	+	0.114550i
$281$	0.402171	−	0.402171i	0.0239915	−	0.0239915i	−0.695009	−	0.719001i	$-0.744600\pi$
$281$	0.402171	−	0.402171i	0.0239915	−	0.0239915i	0.719001	+	0.695009i	$0.244600\pi$
$282$	−2.19827	+	5.49077i	−0.130905	+	0.326970i
$283$		−	5.71582i		−	0.339770i	−0.985464	−	0.169885i	$-0.945660\pi$
$283$		−	5.71582i		−	0.339770i	0.985464	−	0.169885i	$-0.0543396\pi$
$284$	2.45433	−	2.45433i	0.145637	−	0.145637i
$285$	−8.03687	+	20.0742i	−0.476063	+	1.18909i
$286$	−5.49409	−	4.81204i	−0.324873	−	0.284542i
$287$		−	17.0312i		−	1.00532i
$288$	0.576141	+	24.2360i	0.0339494	+	1.42812i
$289$	24.0287			1.41345
$290$	−23.4472			−1.37687
$291$	−7.86017	−	18.3561i	−0.460771	−	1.07605i
$292$	7.56247	−	7.56247i	0.442560	−	0.442560i
$293$	11.5921	−	11.5921i	0.677217	−	0.677217i	−0.282153	−	0.959370i	$-0.591048\pi$
$293$	11.5921	−	11.5921i	0.677217	−	0.677217i	0.959370	+	0.282153i	$0.0910485\pi$
$294$	−18.4835	−	43.1649i	−1.07798	−	2.51743i
$295$	31.6686			1.84382
$296$	−0.929303			−0.0540146
$297$	−1.81610	+	4.86845i	−0.105381	+	0.282496i
$298$			15.1280i			0.876342i
$299$	−20.6148	−	18.0557i	−1.19219	−	1.04419i
$300$	−4.41276	+	11.0220i	−0.254771	+	0.636358i
$301$	−6.50318	+	6.50318i	−0.374837	+	0.374837i
$302$		−	47.9041i		−	2.75657i
$303$	4.33421	−	10.8258i	0.248994	−	0.621928i
$304$	11.6204	−	11.6204i	0.666476	−	0.666476i
$305$	−6.17169	−	6.17169i	−0.353390	−	0.353390i
$306$	0.925058	+	38.9135i	0.0528821	+	2.22454i
$307$	13.4444	+	13.4444i	0.767311	+	0.767311i	0.977632	−	0.210321i	$-0.0674510\pi$
$307$	13.4444	+	13.4444i	0.767311	+	0.767311i	−0.210321	+	0.977632i	$0.567451\pi$
$308$		−	9.49528i		−	0.541044i
$309$	−4.01711	−	1.60828i	−0.228525	−	0.0914920i
$310$	8.59485	+	8.59485i	0.488155	+	0.488155i
$311$	12.3388			0.699670			0.349835	−	0.936811i	$-0.386238\pi$
$311$	12.3388			0.699670			0.349835	+	0.936811i	$0.386238\pi$
$312$	0.403887	−	1.24062i	0.0228656	−	0.0702362i
$313$	−0.997216			−0.0563660			−0.0281830	−	0.999603i	$-0.508972\pi$
$313$	−0.997216			−0.0563660			−0.0281830	+	0.999603i	$0.508972\pi$
$314$	28.8787	+	28.8787i	1.62972	+	1.62972i
$315$	26.8624	−	28.1706i	1.51352	−	1.58724i
$316$		−	23.9980i		−	1.34999i
$317$	−1.66001	−	1.66001i	−0.0932353	−	0.0932353i	0.658951	−	0.752186i	$-0.271001\pi$
$317$	−1.66001	−	1.66001i	−0.0932353	−	0.0932353i	−0.752186	+	0.658951i	$0.771001\pi$
$318$	14.1900	+	33.1383i	0.795737	+	1.85831i
$319$	2.84805	+	2.84805i	0.159460	+	0.159460i
$320$	17.8885	−	17.8885i	0.999995	−	0.999995i
$321$	−9.37096	−	3.75174i	−0.523036	−	0.209402i
$322$		−	69.5088i		−	3.87358i
$323$	19.6752	−	19.6752i	1.09476	−	1.09476i
$324$	−18.9069	+	0.899422i	−1.05038	+	0.0499679i
$325$	−7.74261	+	8.84003i	−0.429482	+	0.490357i
$326$			36.8206i			2.03930i
$327$	6.09604	+	14.2362i	0.337112	+	0.787265i
$328$	0.788110			0.0435161
$329$	−7.61091			−0.419603
$330$	9.26894	−	3.96902i	0.510239	−	0.218487i
$331$	16.0962	−	16.0962i	0.884727	−	0.884727i	−0.109284	−	0.994011i	$-0.534856\pi$
$331$	16.0962	−	16.0962i	0.884727	−	0.884727i	0.994011	+	0.109284i	$0.0348558\pi$
$332$	−9.28970	+	9.28970i	−0.509839	+	0.509839i
$333$	0.317135	+	13.3406i	0.0173789	+	0.731060i
$334$	18.1868			0.995139
$335$	22.9389			1.25328
$336$	−27.1949	+	11.6450i	−1.48361	+	0.635288i
$337$			23.3201i			1.27033i	0.772378	+	0.635163i	$0.219067\pi$
$337$			23.3201i			1.27033i	−0.772378	+	0.635163i	$0.780933\pi$
$338$	16.0041	−	20.9117i	0.870508	−	1.13745i
$339$	0.109664	+	0.0439048i	0.00595612	+	0.00238458i
$340$	27.3758	−	27.3758i	1.48466	−	1.48466i
$341$		−	2.08797i		−	0.113070i
$342$	19.1045	+	18.2173i	1.03305	+	0.985077i
$343$	20.3792	−	20.3792i	1.10037	−	1.10037i
$344$	−0.300931	−	0.300931i	−0.0162251	−	0.0162251i
$345$	34.7788	−	14.8925i	1.87243	−	0.801784i
$346$	−34.5912	−	34.5912i	−1.85963	−	1.85963i
$347$		−	8.91343i		−	0.478498i	−0.970958	−	0.239249i	$-0.923099\pi$
$347$		−	8.91343i		−	0.478498i	0.970958	−	0.239249i	$-0.0769012\pi$
$348$	−5.45328	+	13.6210i	−0.292326	+	0.730162i
$349$	19.1772	+	19.1772i	1.02653	+	1.02653i	0.999638	+	0.0268957i	$0.00856220\pi$
$349$	19.1772	+	19.1772i	1.02653	+	1.02653i	0.0268957	+	0.999638i	$0.491438\pi$
$350$	−29.8067			−1.59324
$351$	−17.9475	−	5.37463i	−0.957968	−	0.286876i
$352$	−8.08093			−0.430715
$353$	−25.1831	−	25.1831i	−1.34036	−	1.34036i	−0.895696	−	0.444666i	$-0.853322\pi$
$353$	−25.1831	−	25.1831i	−1.34036	−	1.34036i	−0.444666	−	0.895696i	$-0.646678\pi$
$354$	14.3696	−	35.8918i	0.763734	−	1.90763i
$355$			4.74296i			0.251730i
$356$	7.81026	+	7.81026i	0.413943	+	0.413943i
$357$	−46.0454	+	19.7169i	−2.43698	+	1.04353i
$358$	−5.94048	−	5.94048i	−0.313964	−	0.313964i
$359$	−14.3410	+	14.3410i	−0.756890	+	0.756890i	−0.975755	−	0.218865i	$-0.929764\pi$
$359$	−14.3410	+	14.3410i	−0.756890	+	0.756890i	0.218865	+	0.975755i	$0.429764\pi$
$360$	1.30358	+	1.24304i	0.0687046	+	0.0655140i
$361$			0.129613i			0.00682172i
$362$	−1.58292	+	1.58292i	−0.0831965	+	0.0831965i
$363$	−1.60797	−	0.643764i	−0.0843965	−	0.0337889i
$364$	34.1610	−	2.26075i	1.79052	−	0.118496i
$365$			14.6144i			0.764952i
$366$	−9.79512	+	4.19433i	−0.511999	+	0.219241i
$367$	−14.9760			−0.781740			−0.390870	−	0.920446i	$-0.627826\pi$
$367$	−14.9760			−0.781740			−0.390870	+	0.920446i	$0.627826\pi$
$368$	−28.7533			−1.49887
$369$	−0.268951	−	11.3137i	−0.0140010	−	0.588968i
$370$	18.3101	−	18.3101i	0.951895	−	0.951895i
$371$	−32.8016	+	32.8016i	−1.70297	+	1.70297i
$372$	6.99190	−	2.99397i	0.362513	−	0.155230i
$373$	−0.335215			−0.0173568			−0.00867839	−	0.999962i	$-0.502762\pi$
$373$	−0.335215			−0.0173568			−0.00867839	+	0.999962i	$0.502762\pi$
$374$	−12.9748			−0.670913
$375$	3.41086	+	7.96548i	0.176136	+	0.411335i
$376$		−	0.352190i		−	0.0181628i
$377$	−9.56828	+	10.9245i	−0.492791	+	0.562639i
$378$	−19.7386	−	43.2270i	−1.01524	−	2.22336i
$379$	17.8144	−	17.8144i	0.915065	−	0.915065i	−0.0816000	−	0.996665i	$-0.526003\pi$
$379$	17.8144	−	17.8144i	0.915065	−	0.915065i	0.996665	+	0.0816000i	$0.0260030\pi$
$380$		−	26.2560i		−	1.34690i
$381$	−20.2864	−	8.12184i	−1.03931	−	0.416095i
$382$	−15.9313	+	15.9313i	−0.815119	+	0.815119i
$383$	2.24012	+	2.24012i	0.114465	+	0.114465i	0.762019	−	0.647554i	$-0.224208\pi$
$383$	2.24012	+	2.24012i	0.114465	+	0.114465i	−0.647554	+	0.762019i	$0.724208\pi$
$384$	−1.13801	−	2.65763i	−0.0580740	−	0.135622i
$385$	9.17476	+	9.17476i	0.467589	+	0.467589i
$386$		−	30.7236i		−	1.56379i
$387$	−4.21731	+	4.42270i	−0.214378	+	0.224819i
$388$	17.1447	+	17.1447i	0.870391	+	0.870391i
$389$	12.4306			0.630255			0.315127	−	0.949049i	$-0.397953\pi$
$389$	12.4306			0.630255			0.315127	+	0.949049i	$0.397953\pi$
$390$	16.4861	+	32.4017i	0.834807	+	1.64072i
$391$	−48.6840			−2.46205
$392$	1.97714	+	1.97714i	0.0998604	+	0.0998604i
$393$	−6.95012	−	2.78254i	−0.350587	−	0.140360i
$394$		−	7.19214i		−	0.362335i
$395$	23.1880	+	23.1880i	1.16671	+	1.16671i
$396$	−0.149946	−	6.30763i	−0.00753507	−	0.316971i
$397$	17.9978	+	17.9978i	0.903286	+	0.903286i	0.995719	−	0.0924329i	$-0.0294644\pi$
$397$	17.9978	+	17.9978i	0.903286	+	0.903286i	−0.0924329	+	0.995719i	$0.529464\pi$
$398$	−20.4935	+	20.4935i	−1.02725	+	1.02725i
$399$	−12.6257	+	31.5361i	−0.632078	+	1.57878i
$400$			12.3300i			0.616498i
$401$	−16.3446	+	16.3446i	−0.816212	+	0.816212i	−0.985557	−	0.169345i	$-0.945835\pi$
$401$	−16.3446	+	16.3446i	−0.816212	+	0.816212i	0.169345	+	0.985557i	$0.445835\pi$
$402$	10.4085	−	25.9979i	0.519127	−	1.29666i
$403$	7.51187	−	0.497131i	0.374193	−	0.0247639i
$404$			14.1596i			0.704467i
$405$	17.3996	−	19.1377i	0.864593	−	0.950961i
$406$	−36.8350			−1.82809
$407$	−4.44812			−0.220485
$408$	−0.912387	−	2.13072i	−0.0451699	−	0.105486i
$409$	12.1452	−	12.1452i	0.600541	−	0.600541i	−0.339915	−	0.940456i	$-0.610398\pi$
$409$	12.1452	−	12.1452i	0.600541	−	0.600541i	0.940456	+	0.339915i	$0.110398\pi$
$410$	−15.5281	+	15.5281i	−0.766880	+	0.766880i
$411$	−8.20450	−	19.1602i	−0.404698	−	0.945102i
$412$	5.25416			0.258854
$413$	49.7506			2.44807
$414$	−1.09766	−	46.1741i	−0.0539470	−	2.26933i
$415$		−	17.9522i		−	0.881241i
$416$	−1.92401	−	29.0726i	−0.0943323	−	1.42540i
$417$	0.685630	−	1.71254i	0.0335754	−	0.0838635i
$418$	−6.22205	+	6.22205i	−0.304330	+	0.304330i
$419$		−	29.5654i		−	1.44437i	−0.691702	−	0.722183i	$-0.743139\pi$
$419$		−	29.5654i		−	1.44437i	0.691702	−	0.722183i	$-0.256861\pi$
$420$	−17.5673	+	43.8789i	−0.857196	+	2.14107i
$421$	16.8456	−	16.8456i	0.821003	−	0.821003i	−0.165248	−	0.986252i	$-0.552843\pi$
$421$	16.8456	−	16.8456i	0.821003	−	0.821003i	0.986252	+	0.165248i	$0.0528426\pi$
$422$	2.43909	+	2.43909i	0.118733	+	0.118733i
$423$	−5.05586	+	0.120189i	−0.245825	+	0.00584378i
$424$	−1.51787	−	1.51787i	−0.0737145	−	0.0737145i
$425$			20.8766i			1.01266i
$426$	5.37546	+	2.15211i	0.260442	+	0.104270i
$427$	−9.69559	−	9.69559i	−0.469203	−	0.469203i
$428$	12.2567			0.592451
$429$	1.93321	−	5.93824i	0.0933364	−	0.286701i
$430$	11.8585			0.571866
$431$	−10.3791	−	10.3791i	−0.499942	−	0.499942i	0.411478	−	0.911420i	$-0.365013\pi$
$431$	−10.3791	−	10.3791i	−0.499942	−	0.499942i	−0.911420	+	0.411478i	$0.865013\pi$
$432$	−17.8815	+	8.16515i	−0.860323	+	0.392846i
$433$			13.2501i			0.636760i	0.947963	+	0.318380i	$0.103139\pi$
$433$			13.2501i			0.636760i	−0.947963	+	0.318380i	$0.896861\pi$
$434$	13.5023	+	13.5023i	0.648132	+	0.648132i
$435$	−7.89201	−	18.4304i	−0.378393	−	0.883670i
$436$	−13.2968	−	13.2968i	−0.636799	−	0.636799i
$437$	−23.3463	+	23.3463i	−1.11680	+	1.11680i
$438$	16.5633	+	6.63125i	0.791425	+	0.316853i
$439$		−	2.74857i		−	0.131182i	−0.997847	−	0.0655911i	$-0.979107\pi$
$439$		−	2.74857i		−	0.131182i	0.997847	−	0.0655911i	$-0.0208933\pi$
$440$	−0.424556	+	0.424556i	−0.0202399	+	0.0202399i
$441$	27.7080	−	29.0575i	1.31943	−	1.38369i
$442$	−3.08921	−	46.6794i	−0.146939	−	2.22031i
$443$			3.54064i			0.168221i	0.996456	+	0.0841104i	$0.0268048\pi$
$443$			3.54064i			0.168221i	−0.996456	+	0.0841104i	$0.973195\pi$
$444$	−6.37822	−	14.8952i	−0.302697	−	0.706896i
$445$	−15.0932			−0.715488
$446$	7.45331			0.352924
$447$	−11.8912	+	5.09188i	−0.562435	+	0.240838i
$448$	28.1023	−	28.1023i	1.32771	−	1.32771i
$449$	1.63352	−	1.63352i	0.0770908	−	0.0770908i	−0.667510	−	0.744601i	$-0.732640\pi$
$449$	1.63352	−	1.63352i	0.0770908	−	0.0770908i	0.744601	+	0.667510i	$0.232640\pi$
$450$	−19.8003	+	0.470697i	−0.933397	+	0.0221889i
$451$	3.77230			0.177631
$452$	−0.143434			−0.00674659
$453$	37.6545	−	16.1239i	1.76916	−	0.757566i
$454$			53.0252i			2.48859i
$455$	−30.8234	+	35.1923i	−1.44502	+	1.64984i
$456$	−1.45931	−	0.584249i	−0.0683387	−	0.0273599i
$457$	−12.8904	+	12.8904i	−0.602990	+	0.602990i	−0.941105	−	0.338115i	$-0.890211\pi$
$457$	−12.8904	+	12.8904i	−0.602990	+	0.602990i	0.338115	+	0.941105i	$0.390211\pi$
$458$			34.6035i			1.61692i
$459$	−30.2762	+	13.8249i	−1.41317	+	0.645291i
$460$	−32.4837	+	32.4837i	−1.51456	+	1.51456i
$461$	−15.6997	−	15.6997i	−0.731209	−	0.731209i	0.239650	−	0.970859i	$-0.422967\pi$
$461$	−15.6997	−	15.6997i	−0.731209	−	0.731209i	−0.970859	+	0.239650i	$0.922967\pi$
$462$	14.5613	−	6.23523i	0.677453	−	0.290089i
$463$	8.71852	+	8.71852i	0.405184	+	0.405184i	0.880055	−	0.474871i	$-0.157505\pi$
$463$	8.71852	+	8.71852i	0.405184	+	0.405184i	−0.474871	+	0.880055i	$0.657505\pi$
$464$			15.2373i			0.707375i
$465$	−3.86298	+	9.64880i	−0.179141	+	0.447452i
$466$	20.7008	+	20.7008i	0.958947	+	0.958947i
$467$	−4.91346			−0.227368			−0.113684	−	0.993517i	$-0.536265\pi$
$467$	−4.91346			−0.227368			−0.113684	+	0.993517i	$0.536265\pi$
$468$	22.6572	−	2.04126i	1.04733	−	0.0943572i
$469$	36.0364			1.66401
$470$	6.93921	+	6.93921i	0.320082	+	0.320082i
$471$	−12.9796	+	32.4199i	−0.598068	+	1.49383i
$472$			2.30218i			0.105966i
$473$	−1.44041	−	1.44041i	−0.0662301	−	0.0662301i
$474$	36.8017	−	15.7587i	1.69036	−	0.723821i
$475$	10.0113	+	10.0113i	0.459351	+	0.459351i
$476$	43.0068	−	43.0068i	1.97121	−	1.97121i
$477$	−21.2718	+	22.3078i	−0.973971	+	1.02141i
$478$		−	7.97116i		−	0.364592i
$479$	−15.2636	+	15.2636i	−0.697413	+	0.697413i	−0.963852	−	0.266439i	$-0.914153\pi$
$479$	−15.2636	+	15.2636i	−0.697413	+	0.697413i	0.266439	+	0.963852i	$0.414153\pi$
$480$	37.3430	+	14.9506i	1.70447	+	0.682398i
$481$	−1.05906	−	16.0029i	−0.0482892	−	0.729671i
$482$			14.5138i			0.661088i
$483$	54.6366	−	23.3957i	2.48605	−	1.06454i
$484$	2.10314			0.0955972
$485$	−33.1320			−1.50444
$486$	−13.7948	−	28.4036i	−0.625745	−	1.28841i
$487$	5.48767	−	5.48767i	0.248670	−	0.248670i	−0.571755	−	0.820425i	$-0.693737\pi$
$487$	5.48767	−	5.48767i	0.248670	−	0.248670i	0.820425	+	0.571755i	$0.193737\pi$
$488$	0.448658	−	0.448658i	0.0203098	−	0.0203098i
$489$	−28.9424	+	12.3933i	−1.30882	+	0.560445i
$490$	−77.9111			−3.51966
$491$	−3.83279			−0.172971			−0.0864856	−	0.996253i	$-0.527564\pi$
$491$	−3.83279			−0.172971			−0.0864856	+	0.996253i	$0.527564\pi$
$492$	5.40915	+	12.6321i	0.243863	+	0.569500i
$493$			25.7992i			1.16194i
$494$	−23.8664	−	20.9035i	−1.07380	−	0.940494i
$495$	6.23960	+	5.94983i	0.280449	+	0.267425i
$496$	5.58543	−	5.58543i	0.250793	−	0.250793i
$497$			7.45108i			0.334227i
$498$	−20.3463	−	8.14580i	−0.911739	−	0.365022i
$499$	−0.560718	+	0.560718i	−0.0251012	+	0.0251012i	−0.719546	−	0.694445i	$-0.755650\pi$
$499$	−0.560718	+	0.560718i	−0.0251012	+	0.0251012i	0.694445	+	0.719546i	$0.255650\pi$
$500$	−7.43982	−	7.43982i	−0.332719	−	0.332719i
$501$	6.12144	+	14.2956i	0.273486	+	0.638678i
$502$	−27.0160	−	27.0160i	−1.20578	−	1.20578i
$503$		−	28.4251i		−	1.26741i	−0.773574	−	0.633706i	$-0.781533\pi$
$503$		−	28.4251i		−	1.26741i	0.773574	−	0.633706i	$-0.218467\pi$
$504$	2.04789	+	1.95279i	0.0912204	+	0.0869841i
$505$	−13.6816	−	13.6816i	−0.608825	−	0.608825i
$506$	15.3957			0.684423
$507$	21.8242	+	5.54123i	0.969246	+	0.246095i
$508$	26.5336			1.17724
$509$	−1.66904	−	1.66904i	−0.0739789	−	0.0739789i	0.669149	−	0.743128i	$-0.266659\pi$
$509$	−1.66904	−	1.66904i	−0.0739789	−	0.0739789i	−0.743128	+	0.669149i	$0.766659\pi$
$510$	59.9584	+	24.0048i	2.65500	+	1.06295i
$511$			22.9589i			1.01564i
$512$	−22.7346	−	22.7346i	−1.00474	−	1.00474i
$513$	−7.88917	+	21.1486i	−0.348315	+	0.933732i
$514$	−1.04886	−	1.04886i	−0.0462634	−	0.0462634i
$515$	−5.07681	+	5.07681i	−0.223711	+	0.223711i
$516$	2.75801	−	6.88885i	0.121415	−	0.303265i
$517$		−	1.68576i		−	0.0741398i
$518$	28.7647	−	28.7647i	1.26385	−	1.26385i
$519$	15.5471	−	38.8329i	0.682441	−	1.70458i
$520$	−1.62850	−	1.42634i	−0.0714146	−	0.0625489i
$521$		−	8.68260i		−	0.380392i	−0.981746	−	0.190196i	$-0.939088\pi$
$521$		−	8.68260i		−	0.380392i	0.981746	−	0.190196i	$-0.0609123\pi$
$522$	−24.4692	+	0.581685i	−1.07099	+	0.0254597i
$523$	−17.2478			−0.754196			−0.377098	−	0.926173i	$-0.623078\pi$
$523$	−17.2478			−0.754196			−0.377098	+	0.926173i	$0.623078\pi$
$524$	9.09038			0.397115
$525$	−10.0325	−	23.4292i	−0.437856	−	1.02254i
$526$	−5.14741	+	5.14741i	−0.224438	+	0.224438i
$527$	9.45702	−	9.45702i	0.411954	−	0.411954i
$528$	−2.57929	−	6.02349i	−0.112249	−	0.262139i
$529$	34.7676			1.51163
$530$	59.8134			2.59813
$531$	33.0489	−	0.785644i	1.43420	−	0.0340940i
$532$		−	41.2476i		−	1.78831i
$533$	0.898156	+	13.5715i	0.0389035	+	0.587848i
$534$	−6.84853	+	17.1060i	−0.296365	+	0.740249i
$535$	−11.8430	+	11.8430i	−0.512017	+	0.512017i
$536$			1.66756i			0.0720278i
$537$	2.66996	−	6.66893i	0.115217	−	0.287786i
$538$	25.9355	−	25.9355i	1.11816	−	1.11816i
$539$	9.46359	+	9.46359i	0.407626	+	0.407626i
$540$	−10.9769	+	29.4258i	−0.472370	+	1.26628i
$541$	23.2895	+	23.2895i	1.00129	+	1.00129i	0.999999	+	0.00129335i	$0.000411685\pi$
$541$	23.2895	+	23.2895i	1.00129	+	1.00129i	0.00129335	+	0.999999i	$0.499588\pi$
$542$			30.1224i			1.29387i
$543$	−1.77703	−	0.711448i	−0.0762596	−	0.0305312i
$544$	−36.6008	−	36.6008i	−1.56925	−	1.56925i
$545$	25.6958			1.10069
$546$	25.8993	+	50.9023i	1.10839	+	2.17842i
$547$	23.1396			0.989376			0.494688	−	0.869071i	$-0.335282\pi$
$547$	23.1396			0.989376			0.494688	+	0.869071i	$0.335282\pi$
$548$	17.8958	+	17.8958i	0.764470	+	0.764470i
$549$	−6.59381	−	6.28759i	−0.281417	−	0.268348i
$550$		−	6.60198i		−	0.281509i
$551$	12.3719	+	12.3719i	0.527063	+	0.527063i
$552$	1.08262	+	2.52828i	0.0460795	+	0.107611i
$553$	36.4278	+	36.4278i	1.54907	+	1.54907i
$554$	−14.0142	+	14.0142i	−0.595405	+	0.595405i
$555$	20.5553	+	8.22950i	0.872526	+	0.349323i
$556$			2.23991i			0.0949934i
$557$	12.4599	−	12.4599i	0.527944	−	0.527944i	−0.392015	−	0.919959i	$-0.628222\pi$
$557$	12.4599	−	12.4599i	0.527944	−	0.527944i	0.919959	+	0.392015i	$0.128222\pi$
$558$	9.18270	+	8.75625i	0.388734	+	0.370682i
$559$	4.83918	−	5.52508i	0.204676	−	0.233686i
$560$			49.0858i			2.07425i
$561$	−4.36716	−	10.1987i	−0.184381	−	0.430591i
$562$	−1.15208			−0.0485977
$563$	32.4436			1.36733			0.683667	−	0.729794i	$-0.260384\pi$
$563$	32.4436			1.36733			0.683667	+	0.729794i	$0.260384\pi$
$564$	5.64504	−	2.41724i	0.237699	−	0.101784i
$565$	0.138593	−	0.138593i	0.00583064	−	0.00583064i
$566$	−8.18693	+	8.18693i	−0.344123	+	0.344123i
$567$	27.3344	−	30.0649i	1.14794	−	1.26261i
$568$	−0.344794			−0.0144672
$569$	−23.0824			−0.967663			−0.483831	−	0.875161i	$-0.660755\pi$
$569$	−23.0824			−0.967663			−0.483831	+	0.875161i	$0.660755\pi$
$570$	40.2643	−	17.2414i	1.68649	−	0.722164i
$571$		−	30.6094i		−	1.28096i	−0.767974	−	0.640481i	$-0.778735\pi$
$571$		−	30.6094i		−	1.28096i	0.767974	−	0.640481i	$-0.221265\pi$
$572$	0.500741	+	7.56642i	0.0209371	+	0.316368i
$573$	−17.8849	−	7.16038i	−0.747154	−	0.299129i
$574$	−24.3943	+	24.3943i	−1.01820	+	1.01820i
$575$		−	24.7718i		−	1.03306i
$576$	18.2244	−	19.1119i	0.759349	−	0.796331i
$577$	−26.1454	+	26.1454i	−1.08845	+	1.08845i	−0.0927588	+	0.995689i	$0.529569\pi$
$577$	−26.1454	+	26.1454i	−1.08845	+	1.08845i	−0.995689	+	0.0927588i	$0.970431\pi$
$578$	−34.4171	−	34.4171i	−1.43156	−	1.43156i
$579$	24.1499	−	10.3411i	1.00364	−	0.429763i
$580$	17.2142	+	17.2142i	0.714779	+	0.714779i
$581$		−	28.2026i		−	1.17004i
$582$	−15.0336	+	37.5503i	−0.623161	+	1.55651i
$583$	−7.26533	−	7.26533i	−0.300899	−	0.300899i
$584$	−1.06241			−0.0439627
$585$	−19.9200	+	23.8647i	−0.823591	+	0.986684i
$586$	−33.2074			−1.37178
$587$	26.1257	+	26.1257i	1.07832	+	1.07832i	0.996660	+	0.0816650i	$0.0260237\pi$
$587$	26.1257	+	26.1257i	1.07832	+	1.07832i	0.0816650	+	0.996660i	$0.473976\pi$
$588$	−18.1203	+	45.2602i	−0.747269	+	1.86650i
$589$		−	9.07017i		−	0.373730i
$590$	−45.3599	−	45.3599i	−1.86744	−	1.86744i
$591$	5.65330	−	2.42078i	0.232546	−	0.0995775i
$592$	−11.8989	−	11.8989i	−0.489043	−	0.489043i
$593$	−0.916747	+	0.916747i	−0.0376463	+	0.0376463i	−0.725679	−	0.688033i	$-0.758474\pi$
$593$	−0.916747	+	0.916747i	−0.0376463	+	0.0376463i	0.688033	+	0.725679i	$0.258474\pi$
$594$	9.57448	−	4.37196i	0.392846	−	0.179384i
$595$			83.1101i			3.40718i
$596$	11.1065	−	11.1065i	0.454939	−	0.454939i
$597$	−23.0065	−	9.21085i	−0.941594	−	0.376975i
$598$	3.66561	+	55.3889i	0.149898	+	2.26502i
$599$		−	28.3360i		−	1.15778i	−0.815407	−	0.578888i	$-0.803487\pi$
$599$		−	28.3360i		−	1.15778i	0.815407	−	0.578888i	$-0.196513\pi$
$600$	1.08417	−	0.464249i	0.0442612	−	0.0189529i
$601$	−33.3834			−1.36174			−0.680868	−	0.732406i	$-0.738397\pi$
$601$	−33.3834			−1.36174			−0.680868	+	0.732406i	$0.738397\pi$
$602$	18.6294			0.759277
$603$	23.9387	−	0.569074i	0.974859	−	0.0231745i
$604$	−35.1696	+	35.1696i	−1.43103	+	1.43103i
$605$	−2.03215	+	2.03215i	−0.0826185	+	0.0826185i
$606$	−21.7142	+	9.29814i	−0.882079	+	0.377711i
$607$	−31.2969			−1.27030			−0.635151	−	0.772388i	$-0.719062\pi$
$607$	−31.2969			−1.27030			−0.635151	+	0.772388i	$0.719062\pi$
$608$	−35.1036			−1.42364
$609$	−12.3982	−	28.9537i	−0.502399	−	1.17326i
$610$			17.6798i			0.715835i
$611$	6.06484	−	0.401368i	0.245357	−	0.0162376i
$612$	27.8899	−	29.2482i	1.12738	−	1.18229i
$613$	−22.3908	+	22.3908i	−0.904355	+	0.904355i	−0.995809	−	0.0914539i	$-0.970849\pi$
$613$	−22.3908	+	22.3908i	−0.904355	+	0.904355i	0.0914539	+	0.995809i	$0.470849\pi$
$614$		−	38.5136i		−	1.55428i
$615$	−17.4323	−	6.97916i	−0.702937	−	0.281427i
$616$	−0.666968	+	0.666968i	−0.0268729	+	0.0268729i
$617$	−4.96083	−	4.96083i	−0.199715	−	0.199715i	0.600163	−	0.799878i	$-0.295103\pi$
$617$	−4.96083	−	4.96083i	−0.199715	−	0.199715i	−0.799878	+	0.600163i	$0.795103\pi$
$618$	3.45023	+	8.05742i	0.138789	+	0.324117i
$619$	−13.6872	−	13.6872i	−0.550137	−	0.550137i	0.376344	−	0.926480i	$-0.377181\pi$
$619$	−13.6872	−	13.6872i	−0.550137	−	0.550137i	−0.926480	+	0.376344i	$0.877181\pi$
$620$		−	12.6201i		−	0.506836i
$621$	35.9252	−	16.4044i	1.44163	−	0.658285i
$622$	−17.6733	−	17.6733i	−0.708633	−	0.708633i
$623$	−23.7111			−0.949966
$624$	21.0565	−	10.7136i	0.842934	−	0.428888i
$625$	30.6736			1.22694
$626$	1.42834	+	1.42834i	0.0570880	+	0.0570880i
$627$	−6.98503	−	2.79652i	−0.278955	−	0.111682i
$628$		−	42.4036i		−	1.69209i
$629$	−20.1468	−	20.1468i	−0.803305	−	0.803305i
$630$	−78.8254	+	1.87385i	−3.14048	+	0.0746560i
$631$	8.80054	+	8.80054i	0.350344	+	0.350344i	0.860238	−	0.509894i	$-0.170315\pi$
$631$	8.80054	+	8.80054i	0.350344	+	0.350344i	−0.509894	+	0.860238i	$0.670315\pi$
$632$	−1.68567	+	1.68567i	−0.0670524	+	0.0670524i
$633$	−1.09626	+	2.73819i	−0.0435723	+	0.108833i
$634$			4.75536i			0.188859i
$635$	−25.6379	+	25.6379i	−1.01741	+	1.01741i
$636$	13.9112	−	34.7469i	0.551616	−	1.37780i
$637$	−31.7938	+	36.3002i	−1.25972	+	1.43827i
$638$		−	8.15870i		−	0.323006i
$639$	0.117665	+	4.94969i	0.00465475	+	0.195807i
$640$	−4.79692			−0.189615
$641$	−23.7780			−0.939174			−0.469587	−	0.882886i	$-0.655597\pi$
$641$	−23.7780			−0.939174			−0.469587	+	0.882886i	$0.655597\pi$
$642$	8.04858	+	18.7960i	0.317652	+	0.741821i
$643$	31.5256	−	31.5256i	1.24325	−	1.24325i	0.284600	−	0.958646i	$-0.408139\pi$
$643$	31.5256	−	31.5256i	1.24325	−	1.24325i	0.958646	−	0.284600i	$-0.0918609\pi$
$644$	−51.0311	+	51.0311i	−2.01091	+	2.01091i
$645$	3.99140	+	9.32122i	0.157161	+	0.367023i
$646$	−56.3628			−2.21756
$647$	6.69601			0.263247			0.131624	−	0.991300i	$-0.457981\pi$
$647$	6.69601			0.263247			0.131624	+	0.991300i	$0.457981\pi$
$648$	1.39124	+	1.26488i	0.0546529	+	0.0496892i
$649$			11.0194i			0.432550i
$650$	23.7518	−	1.57188i	0.931623	−	0.0616542i
$651$	−6.06865	+	15.1580i	−0.237849	+	0.594090i
$652$	27.0325	−	27.0325i	1.05867	−	1.05867i
$653$		−	48.3682i		−	1.89279i	−0.323008	−	0.946396i	$-0.604694\pi$
$653$		−	48.3682i		−	1.89279i	0.323008	−	0.946396i	$-0.395306\pi$
$654$	11.6594	−	29.1225i	0.455920	−	1.13878i
$655$	−8.78353	+	8.78353i	−0.343201	+	0.343201i
$656$	10.0911	+	10.0911i	0.393990	+	0.393990i
$657$	0.362558	+	15.2514i	0.0141447	+	0.595013i
$658$	10.9013	+	10.9013i	0.424978	+	0.424978i
$659$		−	1.57798i		−	0.0614694i	−0.999528	−	0.0307347i	$-0.990215\pi$
$659$		−	1.57798i		−	0.0614694i	0.999528	−	0.0307347i	$-0.00978470\pi$
$660$	−9.71887	−	3.89103i	−0.378307	−	0.151458i
$661$	−5.28760	−	5.28760i	−0.205664	−	0.205664i	0.596758	−	0.802421i	$-0.296455\pi$
$661$	−5.28760	−	5.28760i	−0.205664	−	0.205664i	−0.802421	+	0.596758i	$0.796455\pi$
$662$	−46.1101			−1.79212
$663$	35.6520	−	18.1399i	1.38461	−	0.704495i
$664$	1.30506			0.0506460
$665$	39.8552	+	39.8552i	1.54552	+	1.54552i
$666$	18.6539	−	19.5624i	0.722824	−	0.758027i
$667$		−	30.6129i		−	1.18534i
$668$	−13.3522	−	13.3522i	−0.516611	−	0.516611i
$669$	2.50868	+	5.85859i	0.0969912	+	0.226506i
$670$	−32.8560	−	32.8560i	−1.26934	−	1.26934i
$671$	2.14751	−	2.14751i	0.0829036	−	0.0829036i
$672$	58.6650	+	23.4870i	2.26305	+	0.906032i
$673$			16.3866i			0.631658i	0.948816	+	0.315829i	$0.102283\pi$
$673$			16.3866i			0.631658i	−0.948816	+	0.315829i	$0.897717\pi$
$674$	33.4021	−	33.4021i	1.28660	−	1.28660i
$675$	−7.03451	−	15.4054i	−0.270759	−	0.592954i
$676$	−27.1024	+	3.60302i	−1.04240	+	0.138578i
$677$			9.56767i			0.367715i	0.982953	+	0.183858i	$0.0588586\pi$
$677$			9.56767i			0.367715i	−0.982953	+	0.183858i	$0.941141\pi$
$678$	−0.0941886	−	0.219961i	−0.00361729	−	0.00844755i
$679$	−52.0495			−1.99748
$680$	−3.84587			−0.147482
$681$	−41.6798	+	17.8475i	−1.59717	+	0.683920i
$682$	−2.99067	+	2.99067i	−0.114519	+	0.114519i
$683$	−12.0934	+	12.0934i	−0.462741	+	0.462741i	−0.899553	−	0.436812i	$-0.856107\pi$
$683$	−12.0934	+	12.0934i	−0.462741	+	0.462741i	0.436812	+	0.899553i	$0.356107\pi$
$684$	−0.651366	−	27.4004i	−0.0249056	−	1.04768i
$685$	−34.5834			−1.32136
$686$	−58.3794			−2.22894
$687$	−27.1997	+	11.6471i	−1.03773	+	0.444364i
$688$		−	7.70632i		−	0.293801i
$689$	24.4085	−	27.8682i	0.929891	−	1.06169i
$690$	−71.1456	−	28.4837i	−2.70847	−	1.08436i
$691$	−7.66129	+	7.66129i	−0.291449	+	0.291449i	−0.837653	−	0.546203i	$-0.816073\pi$
$691$	−7.66129	+	7.66129i	−0.291449	+	0.291449i	0.546203	+	0.837653i	$0.316073\pi$
$692$			50.7914i			1.93080i
$693$	9.80227	+	9.34705i	0.372357	+	0.355065i
$694$	−12.7670	+	12.7670i	−0.484628	+	0.484628i
$695$	−2.16430	−	2.16430i	−0.0820966	−	0.0820966i
$696$	1.33982	−	0.573717i	0.0507856	−	0.0217467i
$697$	17.0858	+	17.0858i	0.647171	+	0.647171i
$698$		−	54.9363i		−	2.07937i
$699$	−9.30403	+	23.2393i	−0.351911	+	0.878990i
$700$	21.8831	+	21.8831i	0.827103	+	0.827103i
$701$	18.3010			0.691219			0.345609	−	0.938378i	$-0.387672\pi$
$701$	18.3010			0.691219			0.345609	+	0.938378i	$0.387672\pi$
$702$	18.0085	+	33.4050i	0.679688	+	1.26079i
$703$	−19.3227			−0.728768
$704$	6.22448	+	6.22448i	0.234594	+	0.234594i
$705$	−3.11884	+	7.79013i	−0.117462	+	0.293393i
$706$			72.1411i			2.71507i
$707$	−21.4936	−	21.4936i	−0.808348	−	0.808348i
$708$	−36.9002	+	15.8009i	−1.38679	+	0.593834i
$709$	5.22958	+	5.22958i	0.196401	+	0.196401i	0.798455	−	0.602054i	$-0.205651\pi$
$709$	5.22958	+	5.22958i	0.196401	+	0.196401i	−0.602054	+	0.798455i	$0.705651\pi$
$710$	6.79348	−	6.79348i	0.254955	−	0.254955i
$711$	24.7739	+	23.6234i	0.929094	+	0.885947i
$712$		−	1.09722i		−	0.0411200i
$713$	−11.2215	+	11.2215i	−0.420250	+	0.420250i
$714$	94.1933	+	37.7111i	3.52509	+	1.41130i
$715$	−7.79485	−	6.82718i	−0.291511	−	0.255322i
$716$			8.72261i			0.325979i
$717$	6.26564	−	2.68298i	0.233995	−	0.100198i
$718$	41.0821			1.53317
$719$	−21.7187			−0.809972			−0.404986	−	0.914323i	$-0.632724\pi$
$719$	−21.7187			−0.809972			−0.404986	+	0.914323i	$0.632724\pi$
$720$	0.775145	+	32.6073i	0.0288880	+	1.21520i
$721$	−7.97555	+	7.97555i	−0.297025	+	0.297025i
$722$	0.185648	−	0.185648i	0.00690911	−	0.00690911i
$723$	−11.4084	+	4.88516i	−0.424285	+	0.181681i
$724$	2.32426			0.0863804
$725$	−13.1274			−0.487539
$726$	1.38106	+	3.22523i	0.0512560	+	0.119699i
$727$			30.8919i			1.14572i	0.819654	+	0.572859i	$0.194166\pi$
$727$			30.8919i			1.14572i	−0.819654	+	0.572859i	$0.805834\pi$
$728$	−2.55834	−	2.24074i	−0.0948184	−	0.0830473i
$729$	17.6832	−	20.4035i	0.654934	−	0.755686i
$730$	20.9326	−	20.9326i	0.774751	−	0.774751i
$731$		−	13.0480i		−	0.482599i
$732$	10.2706	+	4.11192i	0.379612	+	0.151981i
$733$	25.9723	−	25.9723i	0.959310	−	0.959310i	−0.0398938	−	0.999204i	$-0.512702\pi$
$733$	25.9723	−	25.9723i	0.959310	−	0.959310i	0.999204	+	0.0398938i	$0.0127020\pi$
$734$	21.4506	+	21.4506i	0.791755	+	0.791755i
$735$	−26.2238	−	61.2411i	−0.967280	−	2.25891i
$736$	43.4299	+	43.4299i	1.60085	+	1.60085i
$737$			7.98182i			0.294014i
$738$	−15.8197	+	16.5902i	−0.582332	+	0.610693i
$739$	−21.0696	−	21.0696i	−0.775058	−	0.775058i	0.203928	−	0.978986i	$-0.434629\pi$
$739$	−21.0696	−	21.0696i	−0.775058	−	0.775058i	−0.978986	+	0.203928i	$0.934629\pi$
$740$	−26.8853			−0.988323
$741$	8.39789	−	25.7957i	0.308504	−	0.947630i
$742$	93.9655			3.44958
$743$	15.0407	+	15.0407i	0.551788	+	0.551788i	0.926957	−	0.375168i	$-0.122415\pi$
$743$	15.0407	+	15.0407i	0.551788	+	0.551788i	−0.375168	+	0.926957i	$0.622415\pi$
$744$	−0.701429	−	0.280823i	−0.0257156	−	0.0102955i
$745$			21.4632i			0.786349i
$746$	0.480139	+	0.480139i	0.0175791	+	0.0175791i
$747$	−0.445365	−	18.7347i	−0.0162950	−	0.685468i
$748$	9.52570	+	9.52570i	0.348294	+	0.348294i
$749$	−18.6051	+	18.6051i	−0.679814	+	0.679814i
$750$	6.52371	−	16.2947i	0.238212	−	0.594997i
$751$		−	27.8284i		−	1.01547i	−0.861513	−	0.507736i	$-0.830482\pi$
$751$		−	27.8284i		−	1.01547i	0.861513	−	0.507736i	$-0.169518\pi$
$752$	4.50950	−	4.50950i	0.164444	−	0.164444i
$753$	12.1424	−	30.3289i	0.442494	−	1.10524i
$754$	29.3524	−	1.94252i	1.06895	−	0.0707426i
$755$		−	67.9649i		−	2.47350i
$756$	−17.2444	+	46.2273i	−0.627174	+	1.68127i
$757$	−6.11486			−0.222249			−0.111124	−	0.993807i	$-0.535445\pi$
$757$	−6.11486			−0.222249			−0.111124	+	0.993807i	$0.535445\pi$
$758$	−51.0323			−1.85357
$759$	5.18199	+	12.1016i	0.188094	+	0.439262i
$760$	−1.84428	+	1.84428i	−0.0668989	+	0.0668989i
$761$	3.01579	−	3.01579i	0.109322	−	0.109322i	−0.650330	−	0.759652i	$-0.725369\pi$
$761$	3.01579	−	3.01579i	0.109322	−	0.109322i	0.759652	+	0.650330i	$0.225369\pi$
$762$	17.4237	+	40.6900i	0.631194	+	1.47404i
$763$	40.3676			1.46140
$764$	23.3925			0.846312
$765$	1.31244	+	55.2093i	0.0474515	+	1.99610i
$766$		−	6.41719i		−	0.231862i
$767$	−39.6444	+	2.62364i	−1.43147	+	0.0947342i
$768$	9.15718	−	22.8725i	0.330431	−	0.825339i
$769$	5.42297	−	5.42297i	0.195557	−	0.195557i	−0.602535	−	0.798092i	$-0.705843\pi$
$769$	5.42297	−	5.42297i	0.195557	−	0.195557i	0.798092	+	0.602535i	$0.205843\pi$
$770$		−	26.2826i		−	0.947158i
$771$	0.471415	−	1.17748i	0.0169776	−	0.0424060i
$772$	−22.5562	+	22.5562i	−0.811817	+	0.811817i
$773$	−15.2230	−	15.2230i	−0.547535	−	0.547535i	0.378192	−	0.925727i	$-0.376546\pi$
$773$	−15.2230	−	15.2230i	−0.547535	−	0.547535i	−0.925727	+	0.378192i	$0.876546\pi$
$774$	12.3753	−	0.294189i	0.444823	−	0.0105744i
$775$	4.81201	+	4.81201i	0.172852	+	0.172852i
$776$		−	2.40856i		−	0.0864623i
$777$	32.2920	+	12.9284i	1.15847	+	0.463802i
$778$	−17.8047	−	17.8047i	−0.638328	−	0.638328i
$779$	16.3869			0.587121
$780$	11.6847	−	35.8918i	0.418379	−	1.28513i
$781$	−1.65036			−0.0590546
$782$	69.7315	+	69.7315i	2.49359	+	2.49359i
$783$	−8.69322	−	19.0379i	−0.310670	−	0.680360i
$784$			50.6311i			1.80825i
$785$	40.9722	+	40.9722i	1.46236	+	1.46236i
$786$	5.96935	+	13.9404i	0.212920	+	0.497237i
$787$	33.8082	+	33.8082i	1.20513	+	1.20513i	0.972585	+	0.232549i	$0.0747066\pi$
$787$	33.8082	+	33.8082i	1.20513	+	1.20513i	0.232549	+	0.972585i	$0.425293\pi$
$788$	−5.28023	+	5.28023i	−0.188101	+	0.188101i
$789$	−5.77861	−	2.31351i	−0.205724	−	0.0823633i
$790$		−	66.4256i		−	2.36332i
$791$	0.217726	−	0.217726i	0.00774145	−	0.00774145i
$792$	−0.432529	+	0.453594i	−0.0153692	+	0.0161178i
$793$	8.23735	+	7.21474i	0.292517	+	0.256203i
$794$		−	51.5577i		−	1.82971i
$795$	20.1324	+	47.0157i	0.714022	+	1.66747i
$796$	30.0913			1.06656
$797$	14.2151			0.503526			0.251763	−	0.967789i	$-0.418990\pi$
$797$	14.2151			0.503526			0.251763	+	0.967789i	$0.418990\pi$
$798$	63.2544	−	27.0859i	2.23918	−	0.958830i
$799$	7.63530	−	7.63530i	0.270117	−	0.270117i
$800$	18.6236	−	18.6236i	0.658442	−	0.658442i
$801$	−15.7511	+	0.374438i	−0.556538	+	0.0132301i
$802$	46.8218			1.65334
$803$	−5.08523			−0.179454
$804$	−26.7283	+	11.4452i	−0.942636	+	0.403642i
$805$		−	98.6170i		−	3.47579i
$806$	−11.4715	−	10.0474i	−0.404067	−	0.353905i
$807$	29.1158	+	11.6568i	1.02493	+	0.410338i
$808$	0.994601	−	0.994601i	0.0349899	−	0.0349899i
$809$		−	39.6998i		−	1.39577i	−0.716209	−	0.697885i	$-0.754124\pi$
$809$		−	39.6998i		−	1.39577i	0.716209	−	0.697885i	$-0.245876\pi$
$810$	−52.3335	+	2.48957i	−1.83881	+	0.0874744i
$811$	36.8880	−	36.8880i	1.29531	−	1.29531i	0.363859	−	0.931454i	$-0.381459\pi$
$811$	36.8880	−	36.8880i	1.29531	−	1.29531i	0.931454	−	0.363859i	$-0.118541\pi$
$812$	27.0430	+	27.0430i	0.949025	+	0.949025i
$813$	−23.6774	+	10.1388i	−0.830403	+	0.355583i
$814$	6.37118	+	6.37118i	0.223310	+	0.223310i
$815$			52.2400i			1.82989i
$816$	15.5997	−	38.9644i	0.546100	−	1.36403i
$817$	−6.25714	−	6.25714i	−0.218910	−	0.218910i
$818$	−34.7918			−1.21647
$819$	−31.2939	+	37.4909i	−1.09350	+	1.31004i
$820$	22.8005			0.796228
$821$	3.81230	+	3.81230i	0.133050	+	0.133050i	0.770496	−	0.637445i	$-0.220009\pi$
$821$	3.81230	+	3.81230i	0.133050	+	0.133050i	−0.637445	+	0.770496i	$0.720009\pi$
$822$	−15.6921	+	39.1953i	−0.547327	+	1.36709i
$823$			13.6721i			0.476580i	0.971194	+	0.238290i	$0.0765869\pi$
$823$			13.6721i			0.476580i	−0.971194	+	0.238290i	$0.923413\pi$
$824$	−0.369064	−	0.369064i	−0.0128569	−	0.0128569i
$825$	5.18941	−	2.22214i	0.180672	−	0.0773649i
$826$	−71.2593	−	71.2593i	−2.47943	−	2.47943i
$827$	14.0361	−	14.0361i	0.488082	−	0.488082i	−0.419618	−	0.907701i	$-0.637836\pi$
$827$	14.0361	−	14.0361i	0.488082	−	0.488082i	0.907701	+	0.419618i	$0.137836\pi$
$828$	−33.0937	+	34.7054i	−1.15008	+	1.20610i
$829$		−	57.0060i		−	1.97990i	−0.141417	−	0.989950i	$-0.545166\pi$
$829$		−	57.0060i		−	1.97990i	0.141417	−	0.989950i	$-0.454834\pi$
$830$	−25.7135	+	25.7135i	−0.892530	+	0.892530i
$831$	−15.7327	−	6.29870i	−0.545760	−	0.218499i
$832$	−20.9117	+	23.8757i	−0.724982	+	0.827740i
$833$			85.7265i			2.97025i
$834$	−3.43497	+	1.47087i	−0.118943	+	0.0509322i
$835$	25.8029			0.892947
$836$	9.13605			0.315977
$837$	−3.79198	+	10.1652i	−0.131070	+	0.351360i
$838$	−42.3475	+	42.3475i	−1.46287	+	1.46287i
$839$	26.6956	−	26.6956i	0.921635	−	0.921635i	−0.0755105	−	0.997145i	$-0.524059\pi$
$839$	26.6956	−	26.6956i	0.921635	−	0.921635i	0.997145	+	0.0755105i	$0.0240586\pi$
$840$	4.31611	−	1.84818i	0.148920	−	0.0637684i
$841$	12.7772			0.440594
$842$	−48.2569			−1.66304
$843$	−0.387776	−	0.905582i	−0.0133557	−	0.0311899i
$844$		−	3.58141i		−	0.123277i
$845$	22.7061	−	29.6689i	0.781114	−	1.02064i
$846$	7.41382	+	7.06952i	0.254892	+	0.243055i
$847$	−3.19246	+	3.19246i	−0.109694	+	0.109694i
$848$		−	38.8702i		−	1.33481i
$849$	−9.19086	−	3.67964i	−0.315429	−	0.126285i
$850$	29.9022	−	29.9022i	1.02564	−	1.02564i
$851$	23.9058	+	23.9058i	0.819481	+	0.819481i
$852$	−2.36648	−	5.52649i	−0.0810741	−	0.189334i
$853$	−36.7783	−	36.7783i	−1.25927	−	1.25927i	−0.951444	−	0.307821i	$-0.900400\pi$
$853$	−36.7783	−	36.7783i	−1.25927	−	1.25927i	−0.307821	−	0.951444i	$-0.599600\pi$
$854$			27.7746i			0.950426i
$855$	27.1049	+	25.8461i	0.926967	+	0.883918i
$856$	−0.860938	−	0.860938i	−0.0294262	−	0.0294262i
$857$	29.6413			1.01253			0.506264	−	0.862379i	$-0.331026\pi$
$857$	29.6413			1.01253			0.506264	+	0.862379i	$0.331026\pi$
$858$	−11.2745	+	5.73652i	−0.384906	+	0.195842i
$859$	−17.8477			−0.608957			−0.304478	−	0.952519i	$-0.598482\pi$
$859$	−17.8477			−0.608957			−0.304478	+	0.952519i	$0.598482\pi$
$860$	−8.70610	−	8.70610i	−0.296876	−	0.296876i
$861$	−27.3857	−	10.9641i	−0.933303	−	0.373655i
$862$			29.7325i			1.01269i
$863$	2.44403	+	2.44403i	0.0831959	+	0.0831959i	0.747480	−	0.664284i	$-0.231264\pi$
$863$	2.44403	+	2.44403i	0.0831959	+	0.0831959i	−0.664284	+	0.747480i	$0.731264\pi$
$864$	39.3416	+	14.6758i	1.33843	+	0.499282i
$865$	−49.0769	−	49.0769i	−1.66866	−	1.66866i
$866$	18.9786	−	18.9786i	0.644917	−	0.644917i
$867$	15.4688	−	38.6375i	0.525349	−	1.31220i
$868$		−	19.8259i		−	0.672935i
$869$	−8.06850	+	8.06850i	−0.273705	+	0.273705i
$870$	−15.0945	+	37.7024i	−0.511750	+	1.27823i
$871$	−28.7160	+	1.90041i	−0.973006	+	0.0643930i
$872$			1.86798i			0.0632580i
$873$	−34.5761	+	0.821948i	−1.17022	+	0.0278187i
$874$	66.8791			2.26222
$875$	22.5865			0.763564
$876$	−7.29178	−	17.0287i	−0.246366	−	0.575345i
$877$	3.17140	−	3.17140i	0.107090	−	0.107090i	−0.651531	−	0.758622i	$-0.725873\pi$
$877$	3.17140	−	3.17140i	0.107090	−	0.107090i	0.758622	+	0.651531i	$0.225873\pi$
$878$	−3.93686	+	3.93686i	−0.132863	+	0.132863i
$879$	−11.1772	−	26.1023i	−0.376996	−	0.880409i
$880$	−10.8722			−0.366501
$881$	−42.9744			−1.44785			−0.723923	−	0.689881i	$-0.757663\pi$
$881$	−42.9744			−1.44785			−0.723923	+	0.689881i	$0.757663\pi$
$882$	−81.3070	+	1.93284i	−2.73775	+	0.0650821i
$883$		−	30.2723i		−	1.01874i	−0.860546	−	0.509372i	$-0.829878\pi$
$883$		−	30.2723i		−	1.01874i	0.860546	−	0.509372i	$-0.170122\pi$
$884$	−32.0024	+	36.5384i	−1.07636	+	1.22892i
$885$	20.3871	−	50.9221i	0.685305	−	1.71173i
$886$	5.07136	−	5.07136i	0.170376	−	0.170376i
$887$			14.3213i			0.480863i	0.970666	+	0.240432i	$0.0772890\pi$
$887$			14.3213i			0.480863i	−0.970666	+	0.240432i	$0.922711\pi$
$888$	−0.598252	+	1.49429i	−0.0200760	+	0.0501451i
$889$	−40.2766	+	40.2766i	−1.35083	+	1.35083i
$890$	21.6185	+	21.6185i	0.724654	+	0.724654i
$891$	6.65917	+	6.05437i	0.223091	+	0.202829i
$892$	−5.47197	−	5.47197i	−0.183215	−	0.183215i
$893$		−	7.32297i		−	0.245054i
$894$	24.3254	+	9.73887i	0.813563	+	0.325717i
$895$	−8.42817	−	8.42817i	−0.281723	−	0.281723i
$896$	−7.53585			−0.251755
$897$	−42.3040	+	21.5245i	−1.41249	+	0.718681i
$898$	−4.67949			−0.156157
$899$	5.94666	+	5.94666i	0.198332	+	0.198332i
$900$	14.8823	+	14.1912i	0.496078	+	0.473040i
$901$		−	65.8134i		−	2.19256i
$902$	−5.40318	−	5.40318i	−0.179906	−	0.179906i
$903$	6.27040	+	14.6434i	0.208666	+	0.487303i
$904$	0.0100751	+	0.0100751i	0.000335094	+	0.000335094i
$905$	−2.24580	+	2.24580i	−0.0746530	+	0.0746530i
$906$	−77.0284	−	30.8390i	−2.55910	−	1.02456i
$907$		−	14.9758i		−	0.497262i	−0.968598	−	0.248631i	$-0.920019\pi$
$907$		−	14.9758i		−	0.497262i	0.968598	−	0.248631i	$-0.0799807\pi$
$908$	38.9293	−	38.9293i	1.29191	−	1.29191i
$909$	−14.6174	−	13.9386i	−0.484829	−	0.462313i
$910$	94.5563	−	6.25768i	3.13451	−	0.207440i
$911$			41.6751i			1.38076i	0.723448	+	0.690378i	$0.242556\pi$
$911$			41.6751i			1.38076i	−0.723448	+	0.690378i	$0.757444\pi$
$912$	−11.2045	−	26.1661i	−0.371017	−	0.866445i
$913$	6.24668			0.206735
$914$	36.9267			1.22143
$915$	−13.8970	+	5.95078i	−0.459421	+	0.196727i
$916$	25.4048	−	25.4048i	0.839397	−	0.839397i
$917$	−13.7987	+	13.7987i	−0.455674	+	0.455674i
$918$	63.1673	+	23.5637i	2.08483	+	0.777717i
$919$	−43.9509			−1.44981			−0.724903	−	0.688851i	$-0.758116\pi$
$919$	−43.9509			−1.44981			−0.724903	+	0.688851i	$0.758116\pi$
$920$	4.56344			0.150452
$921$	30.2732	−	12.9631i	0.997534	−	0.427150i
$922$			44.9744i			1.48115i
$923$	−0.392939	−	5.93748i	−0.0129337	−	0.195434i
$924$	−15.2681	−	6.11272i	−0.502284	−	0.201094i
$925$	10.2513	−	10.2513i	0.337060	−	0.337060i
$926$		−	24.9756i		−	0.820749i
$927$	−5.17214	+	5.42404i	−0.169875	+	0.178149i
$928$	23.0149	−	23.0149i	0.755501	−	0.755501i
$929$	35.1726	+	35.1726i	1.15398	+	1.15398i	0.985748	+	0.168227i	$0.0538041\pi$
$929$	35.1726	+	35.1726i	1.15398	+	1.15398i	0.168227	+	0.985748i	$0.446196\pi$
$930$	19.3533	−	8.28720i	0.634620	−	0.271748i
$931$	41.1099	+	41.1099i	1.34732	+	1.34732i
$932$		−	30.3957i		−	0.995645i
$933$	7.94329	−	19.8405i	0.260052	−	0.649547i
$934$	7.03770	+	7.03770i	0.230280	+	0.230280i
$935$	−18.4083			−0.602016
$936$	−1.73487	−	1.44810i	−0.0567060	−	0.0473328i
$937$	38.0620			1.24343			0.621716	−	0.783243i	$-0.286436\pi$
$937$	38.0620			1.24343			0.621716	+	0.783243i	$0.286436\pi$
$938$	−51.6161	−	51.6161i	−1.68532	−	1.68532i
$939$	−0.641972	+	1.60349i	−0.0209500	+	0.0523280i
$940$		−	10.1891i		−	0.332331i
$941$	31.5945	+	31.5945i	1.02995	+	1.02995i	0.999537	+	0.0304149i	$0.00968285\pi$
$941$	31.5945	+	31.5945i	1.02995	+	1.02995i	0.0304149	+	0.999537i	$0.490317\pi$
$942$	65.0271	−	27.8450i	2.11870	−	0.907239i
$943$	−20.2737	−	20.2737i	−0.660203	−	0.660203i
$944$	−29.4774	+	29.4774i	−0.959409	+	0.959409i
$945$	−28.0045	−	61.3292i	−0.910986	−	1.99504i
$946$			4.12628i			0.134157i
$947$	3.57293	−	3.57293i	0.116105	−	0.116105i	−0.646667	−	0.762772i	$-0.723838\pi$
$947$	3.57293	−	3.57293i	0.116105	−	0.116105i	0.762772	+	0.646667i	$0.223838\pi$
$948$	−38.5881	−	15.4491i	−1.25328	−	0.501762i
$949$	−1.21075	−	18.2950i	−0.0393028	−	0.593882i
$950$		−	28.6790i		−	0.930471i
$951$	−3.73790	+	1.60059i	−0.121210	+	0.0519027i
$952$	−6.04177			−0.195815
$953$	5.26383			0.170512			0.0852561	−	0.996359i	$-0.472829\pi$
$953$	5.26383			0.170512			0.0852561	+	0.996359i	$0.472829\pi$
$954$	62.4205	−	1.48387i	2.02094	−	0.0480420i
$955$	−22.6029	+	22.6029i	−0.731413	+	0.731413i
$956$	−5.85216	+	5.85216i	−0.189272	+	0.189272i
$957$	6.41305	−	2.74611i	0.207305	−	0.0887690i
$958$	43.7251			1.41269
$959$	−54.3297			−1.75440
$960$	−17.2482	−	40.2800i	−0.556682	−	1.30003i
$961$			26.6404i			0.859367i
$962$	−21.4045	+	24.4384i	−0.690110	+	0.787926i
$963$	−12.0654	+	12.6530i	−0.388801	+	0.407737i
$964$	10.6556	−	10.6556i	0.343193	−	0.343193i
$965$		−	43.5897i		−	1.40320i
$966$	−111.768	−	44.7473i	−3.59608	−	1.43972i
$967$	−30.7764	+	30.7764i	−0.989701	+	0.989701i	−0.999948	−	0.0102462i	$-0.996738\pi$
$967$	−30.7764	+	30.7764i	−0.989701	+	0.989701i	0.0102462	+	0.999948i	$0.496738\pi$
$968$	−0.147729	−	0.147729i	−0.00474819	−	0.00474819i
$969$	−18.9710	−	44.3033i	−0.609435	−	1.42323i
$970$	47.4559	+	47.4559i	1.52372	+	1.52372i
$971$			1.24895i			0.0400808i	0.999799	+	0.0200404i	$0.00637948\pi$
$971$			1.24895i			0.0400808i	−0.999799	+	0.0200404i	$0.993621\pi$
$972$	−10.7253	+	30.9807i	−0.344015	+	0.993706i
$973$	−3.40007	−	3.40007i	−0.109001	−	0.109001i
$974$	−15.7203			−0.503711
$975$	9.23010	+	18.1408i	0.295600	+	0.580970i
$976$	11.4894			0.367765
$977$	0.319487	+	0.319487i	0.0102213	+	0.0102213i	0.712199	−	0.701978i	$-0.247699\pi$
$977$	0.319487	+	0.319487i	0.0102213	+	0.0102213i	−0.701978	+	0.712199i	$0.747699\pi$
$978$	59.2064	+	23.7038i	1.89321	+	0.757964i
$979$		−	5.25185i		−	0.167850i
$980$	57.1997	+	57.1997i	1.82718	+	1.82718i
$981$	26.8158	−	0.637470i	0.856164	−	0.0203529i
$982$	5.48981	+	5.48981i	0.175187	+	0.175187i
$983$	32.9322	−	32.9322i	1.05037	−	1.05037i	0.0517124	−	0.998662i	$-0.483532\pi$
$983$	32.9322	−	32.9322i	1.05037	−	1.05037i	0.998662	−	0.0517124i	$-0.0164679\pi$
$984$	0.507357	−	1.26726i	0.0161739	−	0.0403987i
$985$		−	10.2040i		−	0.325126i
$986$	36.9530	−	36.9530i	1.17682	−	1.17682i
$987$	−4.89963	+	12.2381i	−0.155957	+	0.389544i
$988$	2.17522	+	32.8686i	0.0692031	+	1.04569i
$989$			15.4826i			0.492317i
$990$	−0.415045	−	17.4593i	−0.0131910	−	0.554893i
$991$	57.1228			1.81457			0.907283	−	0.420520i	$-0.138152\pi$
$991$	57.1228			1.81457			0.907283	+	0.420520i	$0.138152\pi$
$992$	−16.8728			−0.535711
$993$	−15.5200	−	36.2443i	−0.492514	−	1.15018i
$994$	10.6724	−	10.6724i	0.338508	−	0.338508i
$995$	−29.0756	+	29.0756i	−0.921757	+	0.921757i
$996$	8.95719	+	20.9179i	0.283819	+	0.662810i
$997$	−36.6271			−1.15999			−0.579997	−	0.814619i	$-0.696946\pi$
$997$	−36.6271			−1.15999			−0.579997	+	0.814619i	$0.696946\pi$
$998$	1.60627			0.0508455
$999$	21.6554	+	8.07826i	0.685148	+	0.255585i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.j.a.122.9	✓	96
3.2	odd	2	inner	429.2.j.a.122.40	yes	96
13.8	odd	4	inner	429.2.j.a.320.40	yes	96
39.8	even	4	inner	429.2.j.a.320.9	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.j.a.122.9	✓	96	1.1	even	1	trivial
429.2.j.a.122.40	yes	96	3.2	odd	2	inner
429.2.j.a.320.9	yes	96	39.8	even	4	inner
429.2.j.a.320.40	yes	96	13.8	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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.43233 - 1.43233i) q^{2} +(0.643764 - 1.60797i) q^{3} +2.10314i q^{4} +(-2.03215 - 2.03215i) q^{5} +(-3.22523 + 1.38106i) q^{6} +(-3.19246 - 3.19246i) q^{7} +(0.147729 - 0.147729i) q^{8} +(-2.17114 - 2.07031i) q^{9} +O(q^{10})\)	\(q+(-1.43233 - 1.43233i) q^{2} +(0.643764 - 1.60797i) q^{3} +2.10314i q^{4} +(-2.03215 - 2.03215i) q^{5} +(-3.22523 + 1.38106i) q^{6} +(-3.19246 - 3.19246i) q^{7} +(0.147729 - 0.147729i) q^{8} +(-2.17114 - 2.07031i) q^{9} +5.82141i q^{10} +(0.707107 - 0.707107i) q^{11} +(3.38178 + 1.35393i) q^{12} +(2.71230 + 2.37559i) q^{13} +9.14530i q^{14} +(-4.57585 + 1.95941i) q^{15} +3.78308 q^{16} +6.40537 q^{17} +(0.144419 + 6.07515i) q^{18} +(3.07168 - 3.07168i) q^{19} +(4.27389 - 4.27389i) q^{20} +(-7.18856 + 3.07818i) q^{21} -2.02562 q^{22} -7.60050 q^{23} +(-0.142441 - 0.332646i) q^{24} +3.25924i q^{25} +(-0.482285 - 7.28754i) q^{26} +(-4.72669 + 2.15833i) q^{27} +(6.71418 - 6.71418i) q^{28} +4.02775i q^{29} +(9.36065 + 3.74761i) q^{30} +(1.47642 - 1.47642i) q^{31} +(-5.71408 - 5.71408i) q^{32} +(-0.681796 - 1.59222i) q^{33} +(-9.17460 - 9.17460i) q^{34} +12.9751i q^{35} +(4.35414 - 4.56620i) q^{36} +(-3.14530 - 3.14530i) q^{37} -8.79931 q^{38} +(5.56596 - 2.83198i) q^{39} -0.600413 q^{40} +(2.66742 + 2.66742i) q^{41} +(14.7054 + 5.88742i) q^{42} -2.03705i q^{43} +(1.48714 + 1.48714i) q^{44} +(0.204898 + 8.61923i) q^{45} +(10.8864 + 10.8864i) q^{46} +(1.19202 - 1.19202i) q^{47} +(2.43541 - 6.08309i) q^{48} +13.3835i q^{49} +(4.66830 - 4.66830i) q^{50} +(4.12355 - 10.2996i) q^{51} +(-4.99619 + 5.70435i) q^{52} -10.2747i q^{53} +(9.86162 + 3.67874i) q^{54} -2.87389 q^{55} -0.943236 q^{56} +(-2.96173 - 6.91660i) q^{57} +(5.76907 - 5.76907i) q^{58} +(-7.79191 + 7.79191i) q^{59} +(-4.12091 - 9.62366i) q^{60} +3.03703 q^{61} -4.22944 q^{62} +(0.321889 + 13.5406i) q^{63} +8.80274i q^{64} +(-0.684251 - 10.3393i) q^{65} +(-1.30402 + 3.25714i) q^{66} +(-5.64400 + 5.64400i) q^{67} +13.4714i q^{68} +(-4.89293 + 12.2214i) q^{69} +(18.5846 - 18.5846i) q^{70} +(-1.16698 - 1.16698i) q^{71} +(-0.626584 + 0.0148952i) q^{72} +(-3.59580 - 3.59580i) q^{73} +9.01021i q^{74} +(5.24076 + 2.09818i) q^{75} +(6.46016 + 6.46016i) q^{76} -4.51481 q^{77} +(-12.0286 - 3.91596i) q^{78} -11.4106 q^{79} +(-7.68778 - 7.68778i) q^{80} +(0.427657 + 8.98983i) q^{81} -7.64125i q^{82} +(4.41707 + 4.41707i) q^{83} +(-6.47385 - 15.1185i) q^{84} +(-13.0166 - 13.0166i) q^{85} +(-2.91772 + 2.91772i) q^{86} +(6.47650 + 2.59292i) q^{87} -0.208920i q^{88} +(3.71362 - 3.71362i) q^{89} +(12.0521 - 12.6391i) q^{90} +(-1.07494 - 16.2429i) q^{91} -15.9849i q^{92} +(-1.42357 - 3.32451i) q^{93} -3.41472 q^{94} -12.4842 q^{95} +(-12.8666 + 5.50955i) q^{96} +(8.15196 - 8.15196i) q^{97} +(19.1696 - 19.1696i) q^{98} +(-2.99915 + 0.0712963i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 12 q^{6} - 16 q^{7}+O(q^{10}) \) 96 * q + 12 * q^6 - 16 * q^7	\( 96 q + 12 q^{6} - 16 q^{7} + 16 q^{13} - 16 q^{15} - 120 q^{16} - 28 q^{18} - 24 q^{19} + 24 q^{24} - 24 q^{27} + 56 q^{28} + 48 q^{31} - 16 q^{34} - 16 q^{37} + 80 q^{40} + 52 q^{42} + 4 q^{45} - 56 q^{46} + 28 q^{48} + 4 q^{54} + 4 q^{57} + 48 q^{58} + 4 q^{60} - 96 q^{61} - 36 q^{63} + 20 q^{66} - 16 q^{67} + 48 q^{70} - 16 q^{72} - 16 q^{73} - 88 q^{76} + 80 q^{78} + 16 q^{79} + 32 q^{81} + 52 q^{84} - 8 q^{85} - 48 q^{87} - 16 q^{91} - 36 q^{93} - 16 q^{94} - 108 q^{96} - 48 q^{97}+O(q^{100}) \) 96 * q + 12 * q^6 - 16 * q^7 + 16 * q^13 - 16 * q^15 - 120 * q^16 - 28 * q^18 - 24 * q^19 + 24 * q^24 - 24 * q^27 + 56 * q^28 + 48 * q^31 - 16 * q^34 - 16 * q^37 + 80 * q^40 + 52 * q^42 + 4 * q^45 - 56 * q^46 + 28 * q^48 + 4 * q^54 + 4 * q^57 + 48 * q^58 + 4 * q^60 - 96 * q^61 - 36 * q^63 + 20 * q^66 - 16 * q^67 + 48 * q^70 - 16 * q^72 - 16 * q^73 - 88 * q^76 + 80 * q^78 + 16 * q^79 + 32 * q^81 + 52 * q^84 - 8 * q^85 - 48 * q^87 - 16 * q^91 - 36 * q^93 - 16 * q^94 - 108 * q^96 - 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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