LMFDB - Embedded newform 690.2.i.e.323.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(47,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("690.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.i (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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			323.6
Character	$\chi$	$=$	690.323
Dual form			690.2.i.e.47.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(1.31856 - 1.12312i) q^{3} +1.00000i q^{4} +(-1.11299 + 1.93940i) q^{5} +(-1.72653 - 0.138191i) q^{6} +(1.56700 - 1.56700i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.477181 - 2.96181i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(1.31856 - 1.12312i) q^{3} +1.00000i q^{4} +(-1.11299 + 1.93940i) q^{5} +(-1.72653 - 0.138191i) q^{6} +(1.56700 - 1.56700i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.477181 - 2.96181i) q^{9} +(2.15836 - 0.584357i) q^{10} +5.67280i q^{11} +(1.12312 + 1.31856i) q^{12} +(1.86804 + 1.86804i) q^{13} -2.21607 q^{14} +(0.710643 + 3.80723i) q^{15} -1.00000 q^{16} +(4.87994 + 4.87994i) q^{17} +(-2.43173 + 1.75690i) q^{18} -3.95832i q^{19} +(-1.93940 - 1.11299i) q^{20} +(0.306241 - 3.82612i) q^{21} +(4.01127 - 4.01127i) q^{22} +(0.707107 - 0.707107i) q^{23} +(0.138191 - 1.72653i) q^{24} +(-2.52251 - 4.31705i) q^{25} -2.64181i q^{26} +(-2.69729 - 4.44124i) q^{27} +(1.56700 + 1.56700i) q^{28} -0.714554 q^{29} +(2.18962 - 3.19462i) q^{30} +6.39562 q^{31} +(0.707107 + 0.707107i) q^{32} +(6.37126 + 7.47990i) q^{33} -6.90128i q^{34} +(1.29498 + 4.78309i) q^{35} +(2.96181 + 0.477181i) q^{36} +(-2.92359 + 2.92359i) q^{37} +(-2.79896 + 2.79896i) q^{38} +(4.56117 + 0.365074i) q^{39} +(0.584357 + 2.15836i) q^{40} -4.88651i q^{41} +(-2.92202 + 2.48893i) q^{42} +(8.81584 + 8.81584i) q^{43} -5.67280 q^{44} +(5.21302 + 4.22190i) q^{45} -1.00000 q^{46} +(-4.01373 - 4.01373i) q^{47} +(-1.31856 + 1.12312i) q^{48} +2.08902i q^{49} +(-1.26894 + 4.83630i) q^{50} +(11.9153 + 0.953694i) q^{51} +(-1.86804 + 1.86804i) q^{52} +(5.27160 - 5.27160i) q^{53} +(-1.23316 + 5.04770i) q^{54} +(-11.0018 - 6.31377i) q^{55} -2.21607i q^{56} +(-4.44569 - 5.21927i) q^{57} +(0.505266 + 0.505266i) q^{58} +7.32082 q^{59} +(-3.80723 + 0.710643i) q^{60} -4.73865 q^{61} +(-4.52238 - 4.52238i) q^{62} +(-3.89341 - 5.38890i) q^{63} -1.00000i q^{64} +(-5.70199 + 1.54376i) q^{65} +(0.783929 - 9.79425i) q^{66} +(6.02909 - 6.02909i) q^{67} +(-4.87994 + 4.87994i) q^{68} +(0.138191 - 1.72653i) q^{69} +(2.46647 - 4.29784i) q^{70} -4.27468i q^{71} +(-1.75690 - 2.43173i) q^{72} +(-5.13585 - 5.13585i) q^{73} +4.13458 q^{74} +(-8.17466 - 2.85919i) q^{75} +3.95832 q^{76} +(8.88928 + 8.88928i) q^{77} +(-2.96708 - 3.48338i) q^{78} -7.27349i q^{79} +(1.11299 - 1.93940i) q^{80} +(-8.54460 - 2.82664i) q^{81} +(-3.45528 + 3.45528i) q^{82} +(-10.9094 + 10.9094i) q^{83} +(3.82612 + 0.306241i) q^{84} +(-14.8955 + 4.03281i) q^{85} -12.4675i q^{86} +(-0.942179 + 0.802533i) q^{87} +(4.01127 + 4.01127i) q^{88} -8.06770 q^{89} +(-0.700822 - 6.67150i) q^{90} +5.85445 q^{91} +(0.707107 + 0.707107i) q^{92} +(8.43298 - 7.18308i) q^{93} +5.67627i q^{94} +(7.67675 + 4.40558i) q^{95} +(1.72653 + 0.138191i) q^{96} +(-0.309834 + 0.309834i) q^{97} +(1.47716 - 1.47716i) q^{98} +(16.8017 + 2.70695i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{3} - 4 q^{6} - 8 q^{7}+O(q^{10}) $ 32 * q + 4 * q^3 - 4 * q^6 - 8 * q^7	$ 32 q + 4 q^{3} - 4 q^{6} - 8 q^{7} - 8 q^{10} - 4 q^{12} - 4 q^{15} - 32 q^{16} + 8 q^{18} - 32 q^{21} - 8 q^{22} + 4 q^{27} - 8 q^{28} + 20 q^{30} - 24 q^{31} + 20 q^{36} - 32 q^{37} - 16 q^{40} + 8 q^{42} + 144 q^{43} + 36 q^{45} - 32 q^{46} - 4 q^{48} + 12 q^{51} - 64 q^{55} + 52 q^{57} + 16 q^{58} + 4 q^{60} - 24 q^{61} - 116 q^{63} + 12 q^{66} - 16 q^{67} - 80 q^{70} - 8 q^{72} + 40 q^{73} + 44 q^{75} + 24 q^{76} - 36 q^{78} - 108 q^{81} - 32 q^{82} - 80 q^{85} + 68 q^{87} - 8 q^{88} + 16 q^{90} + 120 q^{91} + 12 q^{93} + 4 q^{96} - 8 q^{97}+O(q^{100}) $ 32 * q + 4 * q^3 - 4 * q^6 - 8 * q^7 - 8 * q^10 - 4 * q^12 - 4 * q^15 - 32 * q^16 + 8 * q^18 - 32 * q^21 - 8 * q^22 + 4 * q^27 - 8 * q^28 + 20 * q^30 - 24 * q^31 + 20 * q^36 - 32 * q^37 - 16 * q^40 + 8 * q^42 + 144 * q^43 + 36 * q^45 - 32 * q^46 - 4 * q^48 + 12 * q^51 - 64 * q^55 + 52 * q^57 + 16 * q^58 + 4 * q^60 - 24 * q^61 - 116 * q^63 + 12 * q^66 - 16 * q^67 - 80 * q^70 - 8 * q^72 + 40 * q^73 + 44 * q^75 + 24 * q^76 - 36 * q^78 - 108 * q^81 - 32 * q^82 - 80 * q^85 + 68 * q^87 - 8 * q^88 + 16 * q^90 + 120 * q^91 + 12 * q^93 + 4 * q^96 - 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	1.31856	−	1.12312i	0.761269	−	0.648436i
$3$	1.31856	−	1.12312i	0.761269	−	0.648436i
$4$			1.00000i			0.500000i
$5$	−1.11299	+	1.93940i	−0.497744	+	0.867324i
$5$	−1.11299	+	1.93940i	−0.497744	+	0.867324i
$6$	−1.72653	−	0.138191i	−0.704853	−	0.0564162i
$7$	1.56700	−	1.56700i	0.592271	−	0.592271i	−0.345974	−	0.938244i	$-0.612451\pi$
$7$	1.56700	−	1.56700i	0.592271	−	0.592271i	0.938244	+	0.345974i	$0.112451\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	0.477181	−	2.96181i	0.159060	−	0.987269i
$10$	2.15836	−	0.584357i	0.682534	−	0.184790i
$11$			5.67280i			1.71041i	0.518287	+	0.855207i	$0.326570\pi$
$11$			5.67280i			1.71041i	−0.518287	+	0.855207i	$0.673430\pi$
$12$	1.12312	+	1.31856i	0.324218	+	0.380634i
$13$	1.86804	+	1.86804i	0.518102	+	0.518102i	0.916997	−	0.398895i	$-0.130606\pi$
$13$	1.86804	+	1.86804i	0.518102	+	0.518102i	−0.398895	+	0.916997i	$0.630606\pi$
$14$	−2.21607			−0.592271
$15$	0.710643	+	3.80723i	0.183487	+	0.983022i
$16$	−1.00000			−0.250000
$17$	4.87994	+	4.87994i	1.18356	+	1.18356i	0.978816	+	0.204744i	$0.0656362\pi$
$17$	4.87994	+	4.87994i	1.18356	+	1.18356i	0.204744	+	0.978816i	$0.434364\pi$
$18$	−2.43173	+	1.75690i	−0.573165	+	0.414104i
$19$		−	3.95832i		−	0.908102i	−0.890976	−	0.454051i	$-0.849978\pi$
$19$		−	3.95832i		−	0.908102i	0.890976	−	0.454051i	$-0.150022\pi$
$20$	−1.93940	−	1.11299i	−0.433662	−	0.248872i
$21$	0.306241	−	3.82612i	0.0668273	−	0.834927i
$22$	4.01127	−	4.01127i	0.855207	−	0.855207i
$23$	0.707107	−	0.707107i	0.147442	−	0.147442i
$23$	0.707107	−	0.707107i	0.147442	−	0.147442i
$24$	0.138191	−	1.72653i	0.0282081	−	0.352426i
$25$	−2.52251	−	4.31705i	−0.504501	−	0.863411i
$26$		−	2.64181i		−	0.518102i
$27$	−2.69729	−	4.44124i	−0.519093	−	0.854718i
$28$	1.56700	+	1.56700i	0.296135	+	0.296135i
$29$	−0.714554			−0.132689			−0.0663447	−	0.997797i	$-0.521134\pi$
$29$	−0.714554			−0.132689			−0.0663447	+	0.997797i	$0.521134\pi$
$30$	2.18962	−	3.19462i	0.399767	−	0.583255i
$31$	6.39562			1.14869			0.574343	−	0.818615i	$-0.305257\pi$
$31$	6.39562			1.14869			0.574343	+	0.818615i	$0.305257\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	6.37126	+	7.47990i	1.10909	+	1.30208i
$34$		−	6.90128i		−	1.18356i
$35$	1.29498	+	4.78309i	0.218891	+	0.808490i
$36$	2.96181	+	0.477181i	0.493634	+	0.0795302i
$37$	−2.92359	+	2.92359i	−0.480635	+	0.480635i	−0.905334	−	0.424699i	$-0.860380\pi$
$37$	−2.92359	+	2.92359i	−0.480635	+	0.480635i	0.424699	+	0.905334i	$0.360380\pi$
$38$	−2.79896	+	2.79896i	−0.454051	+	0.454051i
$39$	4.56117	+	0.365074i	0.730371	+	0.0584587i
$40$	0.584357	+	2.15836i	0.0923949	+	0.341267i
$41$		−	4.88651i		−	0.763144i	−0.924339	−	0.381572i	$-0.875383\pi$
$41$		−	4.88651i		−	0.763144i	0.924339	−	0.381572i	$-0.124617\pi$
$42$	−2.92202	+	2.48893i	−0.450877	+	0.384050i
$43$	8.81584	+	8.81584i	1.34440	+	1.34440i	0.891621	+	0.452782i	$0.149569\pi$
$43$	8.81584	+	8.81584i	1.34440	+	1.34440i	0.452782	+	0.891621i	$0.350431\pi$
$44$	−5.67280			−0.855207
$45$	5.21302	+	4.22190i	0.777110	+	0.629364i
$46$	−1.00000			−0.147442
$47$	−4.01373	−	4.01373i	−0.585462	−	0.585462i	0.350937	−	0.936399i	$-0.385863\pi$
$47$	−4.01373	−	4.01373i	−0.585462	−	0.585462i	−0.936399	+	0.350937i	$0.885863\pi$
$48$	−1.31856	+	1.12312i	−0.190317	+	0.162109i
$49$			2.08902i			0.298431i
$50$	−1.26894	+	4.83630i	−0.179455	+	0.683956i
$51$	11.9153	+	0.953694i	1.66847	+	0.133544i
$52$	−1.86804	+	1.86804i	−0.259051	+	0.259051i
$53$	5.27160	−	5.27160i	0.724111	−	0.724111i	−0.245329	−	0.969440i	$-0.578896\pi$
$53$	5.27160	−	5.27160i	0.724111	−	0.724111i	0.969440	+	0.245329i	$0.0788961\pi$
$54$	−1.23316	+	5.04770i	−0.167812	+	0.686905i
$55$	−11.0018	−	6.31377i	−1.48348	−	0.851348i
$56$		−	2.21607i		−	0.296135i
$57$	−4.44569	−	5.21927i	−0.588846	−	0.691310i
$58$	0.505266	+	0.505266i	0.0663447	+	0.0663447i
$59$	7.32082			0.953089			0.476545	−	0.879150i	$-0.341889\pi$
$59$	7.32082			0.953089			0.476545	+	0.879150i	$0.341889\pi$
$60$	−3.80723	+	0.710643i	−0.491511	+	0.0917436i
$61$	−4.73865			−0.606722			−0.303361	−	0.952876i	$-0.598109\pi$
$61$	−4.73865			−0.606722			−0.303361	+	0.952876i	$0.598109\pi$
$62$	−4.52238	−	4.52238i	−0.574343	−	0.574343i
$63$	−3.89341	−	5.38890i	−0.490524	−	0.678937i
$64$		−	1.00000i		−	0.125000i
$65$	−5.70199	+	1.54376i	−0.707244	+	0.191480i
$66$	0.783929	−	9.79425i	0.0964950	−	1.20559i
$67$	6.02909	−	6.02909i	0.736571	−	0.736571i	−0.235342	−	0.971913i	$-0.575621\pi$
$67$	6.02909	−	6.02909i	0.736571	−	0.736571i	0.971913	+	0.235342i	$0.0756210\pi$
$68$	−4.87994	+	4.87994i	−0.591780	+	0.591780i
$69$	0.138191	−	1.72653i	0.0166362	−	0.207850i
$70$	2.46647	−	4.29784i	0.294799	−	0.513691i
$71$		−	4.27468i		−	0.507311i	−0.967295	−	0.253656i	$-0.918367\pi$
$71$		−	4.27468i		−	0.507311i	0.967295	−	0.253656i	$-0.0816330\pi$
$72$	−1.75690	−	2.43173i	−0.207052	−	0.286582i
$73$	−5.13585	−	5.13585i	−0.601106	−	0.601106i	0.339500	−	0.940606i	$-0.389742\pi$
$73$	−5.13585	−	5.13585i	−0.601106	−	0.601106i	−0.940606	+	0.339500i	$0.889742\pi$
$74$	4.13458			0.480635
$75$	−8.17466	−	2.85919i	−0.943928	−	0.330151i
$76$	3.95832			0.454051
$77$	8.88928	+	8.88928i	1.01303	+	1.01303i
$78$	−2.96708	−	3.48338i	−0.335956	−	0.394415i
$79$		−	7.27349i		−	0.818332i	−0.912460	−	0.409166i	$-0.865820\pi$
$79$		−	7.27349i		−	0.818332i	0.912460	−	0.409166i	$-0.134180\pi$
$80$	1.11299	−	1.93940i	0.124436	−	0.216831i
$81$	−8.54460	−	2.82664i	−0.949400	−	0.314071i
$82$	−3.45528	+	3.45528i	−0.381572	+	0.381572i
$83$	−10.9094	+	10.9094i	−1.19746	+	1.19746i	−0.222537	+	0.974924i	$0.571434\pi$
$83$	−10.9094	+	10.9094i	−1.19746	+	1.19746i	−0.974924	+	0.222537i	$0.928566\pi$
$84$	3.82612	+	0.306241i	0.417464	+	0.0334137i
$85$	−14.8955	+	4.03281i	−1.61564	+	0.437420i
$86$		−	12.4675i		−	1.34440i
$87$	−0.942179	+	0.802533i	−0.101012	+	0.0860406i
$88$	4.01127	+	4.01127i	0.427603	+	0.427603i
$89$	−8.06770			−0.855175			−0.427587	−	0.903974i	$-0.640636\pi$
$89$	−8.06770			−0.855175			−0.427587	+	0.903974i	$0.640636\pi$
$90$	−0.700822	−	6.67150i	−0.0738731	−	0.703237i
$91$	5.85445			0.613713
$92$	0.707107	+	0.707107i	0.0737210	+	0.0737210i
$93$	8.43298	−	7.18308i	0.874459	−	0.744850i
$94$			5.67627i			0.585462i
$95$	7.67675	+	4.40558i	0.787618	+	0.452002i
$96$	1.72653	+	0.138191i	0.176213	+	0.0141040i
$97$	−0.309834	+	0.309834i	−0.0314589	+	0.0314589i	−0.722661	−	0.691202i	$-0.757081\pi$
$97$	−0.309834	+	0.309834i	−0.0314589	+	0.0314589i	0.691202	+	0.722661i	$0.257081\pi$
$98$	1.47716	−	1.47716i	0.149215	−	0.149215i
$99$	16.8017	+	2.70695i	1.68864	+	0.272059i
$100$	4.31705	−	2.52251i	0.431705	−	0.252251i
$101$		−	3.88898i		−	0.386968i	−0.981103	−	0.193484i	$-0.938021\pi$
$101$		−	3.88898i		−	0.386968i	0.981103	−	0.193484i	$-0.0619787\pi$
$102$	−7.75100	−	9.09972i	−0.767463	−	0.901007i
$103$	7.73444	+	7.73444i	0.762097	+	0.762097i	0.976701	−	0.214604i	$-0.0688462\pi$
$103$	7.73444	+	7.73444i	0.762097	+	0.762097i	−0.214604	+	0.976701i	$0.568846\pi$
$104$	2.64181			0.259051
$105$	7.07951	+	4.85235i	0.690889	+	0.473541i
$106$	−7.45518			−0.724111
$107$	−6.15366	−	6.15366i	−0.594897	−	0.594897i	0.344053	−	0.938950i	$-0.388200\pi$
$107$	−6.15366	−	6.15366i	−0.594897	−	0.594897i	−0.938950	+	0.344053i	$0.888200\pi$
$108$	4.44124	−	2.69729i	0.427359	−	0.259547i
$109$		−	8.34777i		−	0.799571i	−0.916609	−	0.399786i	$-0.869085\pi$
$109$		−	8.34777i		−	0.799571i	0.916609	−	0.399786i	$-0.130915\pi$
$110$	3.31494	+	12.2440i	0.316067	+	1.16742i
$111$	−0.571361	+	7.13847i	−0.0542312	+	0.677554i
$112$	−1.56700	+	1.56700i	−0.148068	+	0.148068i
$113$	−9.04524	+	9.04524i	−0.850904	+	0.850904i	−0.990245	−	0.139340i	$-0.955502\pi$
$113$	−9.04524	+	9.04524i	−0.850904	+	0.850904i	0.139340	+	0.990245i	$0.455502\pi$
$114$	−0.547004	+	6.83416i	−0.0512316	+	0.640078i
$115$	0.584357	+	2.15836i	0.0544915	+	0.201268i
$116$		−	0.714554i		−	0.0663447i
$117$	6.42418	−	4.64139i	0.593915	−	0.429096i
$118$	−5.17660	−	5.17660i	−0.476545	−	0.476545i
$119$	15.2937			1.40198
$120$	3.19462	+	2.18962i	0.291627	+	0.199884i
$121$	−21.1806			−1.92551
$122$	3.35073	+	3.35073i	0.303361	+	0.303361i
$123$	−5.48816	−	6.44314i	−0.494851	−	0.580958i
$124$			6.39562i			0.574343i
$125$	11.1800	−	0.0872994i	0.999970	−	0.00780829i
$126$	−1.05747	+	6.56358i	−0.0942068	+	0.584730i
$127$	−6.47403	+	6.47403i	−0.574477	+	0.574477i	−0.933376	−	0.358899i	$-0.883152\pi$
$127$	−6.47403	+	6.47403i	−0.574477	+	0.574477i	0.358899	+	0.933376i	$0.383152\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	21.5255	+	1.72289i	1.89521	+	0.151692i
$130$	5.12352	+	2.94031i	0.449362	+	0.257882i
$131$			20.4667i			1.78819i	0.447879	+	0.894094i	$0.352179\pi$
$131$			20.4667i			1.78819i	−0.447879	+	0.894094i	$0.647821\pi$
$132$	−7.47990	+	6.37126i	−0.651042	+	0.554547i
$133$	−6.20270	−	6.20270i	−0.537842	−	0.537842i
$134$	−8.52642			−0.736571
$135$	11.6154	−	0.288049i	0.999693	−	0.0247914i
$136$	6.90128			0.591780
$137$	−4.59633	−	4.59633i	−0.392691	−	0.392691i	0.482954	−	0.875646i	$-0.339564\pi$
$137$	−4.59633	−	4.59633i	−0.392691	−	0.392691i	−0.875646	+	0.482954i	$0.839564\pi$
$138$	−1.31856	+	1.12312i	−0.112243	+	0.0956067i
$139$			3.93595i			0.333843i	0.985970	+	0.166921i	$0.0533826\pi$
$139$			3.93595i			0.333843i	−0.985970	+	0.166921i	$0.946617\pi$
$140$	−4.78309	+	1.29498i	−0.404245	+	0.109446i
$141$	−9.80025	−	0.784409i	−0.825330	−	0.0660591i
$142$	−3.02266	+	3.02266i	−0.253656	+	0.253656i
$143$	−10.5970	+	10.5970i	−0.886168	+	0.886168i
$144$	−0.477181	+	2.96181i	−0.0397651	+	0.246817i
$145$	0.795291	−	1.38580i	0.0660453	−	0.115085i
$146$			7.26319i			0.601106i
$147$	2.34622	+	2.75448i	0.193513	+	0.227186i
$148$	−2.92359	−	2.92359i	−0.240318	−	0.240318i
$149$	8.75534			0.717265			0.358633	−	0.933479i	$-0.383243\pi$
$149$	8.75534			0.717265			0.358633	+	0.933479i	$0.383243\pi$
$150$	3.75860	+	7.80211i	0.306889	+	0.637039i
$151$	−2.00457			−0.163130			−0.0815650	−	0.996668i	$-0.525992\pi$
$151$	−2.00457			−0.163130			−0.0815650	+	0.996668i	$0.525992\pi$
$152$	−2.79896	−	2.79896i	−0.227025	−	0.227025i
$153$	16.7821	−	12.1248i	1.35675	−	0.980234i
$154$		−	12.5713i		−	1.01303i
$155$	−7.11826	+	12.4036i	−0.571752	+	0.996283i
$156$	−0.365074	+	4.56117i	−0.0292293	+	0.365186i
$157$	−11.6798	+	11.6798i	−0.932150	+	0.932150i	−0.997840	−	0.0656901i	$-0.979075\pi$
$157$	−11.6798	+	11.6798i	−0.932150	+	0.932150i	0.0656901	+	0.997840i	$0.479075\pi$
$158$	−5.14314	+	5.14314i	−0.409166	+	0.409166i
$159$	1.03024	−	12.8716i	0.0817031	−	1.02078i
$160$	−2.15836	+	0.584357i	−0.170634	+	0.0461975i
$161$		−	2.21607i		−	0.174651i
$162$	4.04321	+	8.04068i	0.317664	+	0.631735i
$163$	7.42502	+	7.42502i	0.581572	+	0.581572i	0.935335	−	0.353763i	$-0.115098\pi$
$163$	7.42502	+	7.42502i	0.581572	+	0.581572i	−0.353763	+	0.935335i	$0.615098\pi$
$164$	4.88651			0.381572
$165$	−21.5976	+	4.03133i	−1.68137	+	0.313839i
$166$	15.4282			1.19746
$167$	−16.1431	−	16.1431i	−1.24919	−	1.24919i	−0.956080	−	0.293107i	$-0.905311\pi$
$167$	−16.1431	−	16.1431i	−1.24919	−	1.24919i	−0.293107	−	0.956080i	$-0.594689\pi$
$168$	−2.48893	−	2.92202i	−0.192025	−	0.225439i
$169$		−	6.02083i		−	0.463141i
$170$	13.3843	+	7.68105i	1.02653	+	0.589110i
$171$	−11.7238	−	1.88884i	−0.896541	−	0.144443i
$172$	−8.81584	+	8.81584i	−0.672202	+	0.672202i
$173$	−5.17329	+	5.17329i	−0.393318	+	0.393318i	−0.875868	−	0.482550i	$-0.839711\pi$
$173$	−5.17329	+	5.17329i	−0.393318	+	0.393318i	0.482550	+	0.875868i	$0.339711\pi$
$174$	1.23370	+	0.0987448i	0.0935264	+	0.00748583i
$175$	−10.7176	−	2.81206i	−0.810174	−	0.212572i
$176$		−	5.67280i		−	0.427603i
$177$	9.65291	−	8.22219i	0.725557	−	0.618018i
$178$	5.70473	+	5.70473i	0.427587	+	0.427587i
$179$	−5.95726			−0.445266			−0.222633	−	0.974902i	$-0.571465\pi$
$179$	−5.95726			−0.445266			−0.222633	+	0.974902i	$0.571465\pi$
$180$	−4.22190	+	5.21302i	−0.314682	+	0.388555i
$181$	−1.45319			−0.108015			−0.0540074	−	0.998541i	$-0.517199\pi$
$181$	−1.45319			−0.108015			−0.0540074	+	0.998541i	$0.517199\pi$
$182$	−4.13972	−	4.13972i	−0.306857	−	0.306857i
$183$	−6.24818	+	5.32209i	−0.461878	+	0.393421i
$184$		−	1.00000i		−	0.0737210i
$185$	−2.41607	−	8.92392i	−0.177633	−	0.656100i
$186$	−11.0422	−	0.883816i	−0.809655	−	0.0648045i
$187$	−27.6829	+	27.6829i	−2.02438	+	2.02438i
$188$	4.01373	−	4.01373i	0.292731	−	0.292731i
$189$	−11.1861	−	2.73278i	−0.813668	−	0.198780i
$190$	−2.31307	−	8.54350i	−0.167808	−	0.619810i
$191$		−	18.2037i		−	1.31717i	−0.752506	−	0.658586i	$-0.771155\pi$
$191$		−	18.2037i		−	1.31717i	0.752506	−	0.658586i	$-0.228845\pi$
$192$	−1.12312	−	1.31856i	−0.0810546	−	0.0951586i
$193$	16.1230	+	16.1230i	1.16056	+	1.16056i	0.984353	+	0.176208i	$0.0563830\pi$
$193$	16.1230	+	16.1230i	1.16056	+	1.16056i	0.176208	+	0.984353i	$0.443617\pi$
$194$	0.438172			0.0314589
$195$	−5.78455	+	8.43958i	−0.414241	+	0.604371i
$196$	−2.08902			−0.149215
$197$	−18.1766	−	18.1766i	−1.29503	−	1.29503i	−0.931636	−	0.363393i	$-0.881618\pi$
$197$	−18.1766	−	18.1766i	−1.29503	−	1.29503i	−0.363393	−	0.931636i	$-0.618382\pi$
$198$	−9.96651	−	13.7947i	−0.708289	−	0.980348i
$199$			0.617379i			0.0437648i	0.999761	+	0.0218824i	$0.00696594\pi$
$199$			0.617379i			0.0437648i	−0.999761	+	0.0218824i	$0.993034\pi$
$200$	−4.83630	−	1.26894i	−0.341978	−	0.0897274i
$201$	1.17827	−	14.7211i	0.0831090	−	1.03835i
$202$	−2.74992	+	2.74992i	−0.193484	+	0.193484i
$203$	−1.11971	+	1.11971i	−0.0785880	+	0.0785880i
$204$	−0.953694	+	11.9153i	−0.0667719	+	0.834235i
$205$	9.47687	+	5.43863i	0.661893	+	0.379851i
$206$		−	10.9381i		−	0.762097i
$207$	−1.75690	−	2.43173i	−0.122113	−	0.169017i
$208$	−1.86804	−	1.86804i	−0.129525	−	0.129525i
$209$	22.4548			1.55323
$210$	−1.57484	−	8.43710i	−0.108674	−	0.582215i
$211$	−9.86494			−0.679130			−0.339565	−	0.940583i	$-0.610280\pi$
$211$	−9.86494			−0.679130			−0.339565	+	0.940583i	$0.610280\pi$
$212$	5.27160	+	5.27160i	0.362055	+	0.362055i
$213$	−4.80100	−	5.63641i	−0.328959	−	0.386200i
$214$			8.70259i			0.594897i
$215$	−26.9093	+	7.28546i	−1.83520	+	0.496864i
$216$	−5.04770	−	1.23316i	−0.343453	−	0.0839060i
$217$	10.0219	−	10.0219i	0.680334	−	0.680334i
$218$	−5.90276	+	5.90276i	−0.399786	+	0.399786i
$219$	−12.5401	−	1.00371i	−0.847383	−	0.0678242i
$220$	6.31377	−	11.0018i	0.425674	−	0.741741i
$221$			18.2319i			1.22641i
$222$	5.45168	−	4.64365i	0.365892	−	0.311661i
$223$	−3.88670	−	3.88670i	−0.260273	−	0.260273i	0.564892	−	0.825165i	$-0.308918\pi$
$223$	−3.88670	−	3.88670i	−0.260273	−	0.260273i	−0.825165	+	0.564892i	$0.808918\pi$
$224$	2.21607			0.148068
$225$	−13.9900	+	5.41116i	−0.932665	+	0.360744i
$226$	12.7919			0.850904
$227$	17.3335	+	17.3335i	1.15046	+	1.15046i	0.986460	+	0.164003i	$0.0524406\pi$
$227$	17.3335	+	17.3335i	1.15046	+	1.15046i	0.164003	+	0.986460i	$0.447559\pi$
$228$	5.21927	−	4.44569i	0.345655	−	0.294423i
$229$		−	7.33027i		−	0.484398i	−0.970227	−	0.242199i	$-0.922131\pi$
$229$		−	7.33027i		−	0.484398i	0.970227	−	0.242199i	$-0.0778687\pi$
$230$	1.11299	−	1.93940i	0.0733884	−	0.127880i
$231$	21.7048	+	1.73724i	1.42807	+	0.114302i
$232$	−0.505266	+	0.505266i	−0.0331723	+	0.0331723i
$233$	5.63455	−	5.63455i	0.369131	−	0.369131i	−0.498029	−	0.867160i	$-0.665943\pi$
$233$	5.63455	−	5.63455i	0.369131	−	0.369131i	0.867160	+	0.498029i	$0.165943\pi$
$234$	−7.82454	−	1.26062i	−0.511506	−	0.0824095i
$235$	12.2514	−	3.31697i	0.799196	−	0.216375i
$236$			7.32082i			0.476545i
$237$	−8.16904	−	9.59051i	−0.530636	−	0.622971i
$238$	−10.8143	−	10.8143i	−0.700988	−	0.700988i
$239$	−2.57538			−0.166588			−0.0832938	−	0.996525i	$-0.526544\pi$
$239$	−2.57538			−0.166588			−0.0832938	+	0.996525i	$0.526544\pi$
$240$	−0.710643	−	3.80723i	−0.0458718	−	0.245756i
$241$	19.0373			1.22630			0.613150	−	0.789966i	$-0.289902\pi$
$241$	19.0373			1.22630			0.613150	+	0.789966i	$0.289902\pi$
$242$	14.9770	+	14.9770i	0.962756	+	0.962756i
$243$	−14.4412	+	5.86957i	−0.926403	+	0.376533i
$244$		−	4.73865i		−	0.303361i
$245$	−4.05143	−	2.32505i	−0.258836	−	0.148542i
$246$	−0.675271	+	8.43670i	−0.0430537	+	0.537904i
$247$	7.39432	−	7.39432i	0.470489	−	0.470489i
$248$	4.52238	−	4.52238i	0.287172	−	0.287172i
$249$	−2.13204	+	26.6373i	−0.135112	+	1.68807i
$250$	−7.96718	−	7.84372i	−0.503889	−	0.496081i
$251$		−	4.04938i		−	0.255595i	−0.991800	−	0.127797i	$-0.959209\pi$
$251$		−	4.04938i		−	0.255595i	0.991800	−	0.127797i	$-0.0407907\pi$
$252$	5.38890	−	3.89341i	0.339469	−	0.245262i
$253$	4.01127	+	4.01127i	0.252187	+	0.252187i
$254$	9.15566			0.574477
$255$	−15.1112	+	22.0469i	−0.946297	+	1.38063i
$256$	1.00000			0.0625000
$257$	4.10051	+	4.10051i	0.255783	+	0.255783i	0.823336	−	0.567554i	$-0.192110\pi$
$257$	4.10051	+	4.10051i	0.255783	+	0.255783i	−0.567554	+	0.823336i	$0.692110\pi$
$258$	−14.0025	−	16.4391i	−0.871760	−	1.02345i
$259$			9.16253i			0.569332i
$260$	−1.54376	−	5.70199i	−0.0957400	−	0.353622i
$261$	−0.340972	+	2.11637i	−0.0211056	+	0.131000i
$262$	14.4722	−	14.4722i	0.894094	−	0.894094i
$263$	−13.1034	+	13.1034i	−0.807991	+	0.807991i	−0.984330	−	0.176338i	$-0.943575\pi$
$263$	−13.1034	+	13.1034i	−0.807991	+	0.807991i	0.176338	+	0.984330i	$0.443575\pi$
$264$	9.79425	+	0.783929i	0.602795	+	0.0482475i
$265$	4.35648	+	16.0910i	0.267617	+	0.988460i
$266$			8.77194i			0.537842i
$267$	−10.6377	+	9.06104i	−0.651018	+	0.554526i
$268$	6.02909	+	6.02909i	0.368285	+	0.368285i
$269$	−8.38175			−0.511044			−0.255522	−	0.966803i	$-0.582247\pi$
$269$	−8.38175			−0.511044			−0.255522	+	0.966803i	$0.582247\pi$
$270$	−8.41699	−	8.00963i	−0.512242	−	0.487451i
$271$	−5.96566			−0.362388			−0.181194	−	0.983447i	$-0.557996\pi$
$271$	−5.96566			−0.362388			−0.181194	+	0.983447i	$0.557996\pi$
$272$	−4.87994	−	4.87994i	−0.295890	−	0.295890i
$273$	7.71942	−	6.57528i	0.467201	−	0.397954i
$274$			6.50020i			0.392691i
$275$	24.4898	−	14.3097i	1.47679	−	0.862906i
$276$	1.72653	+	0.138191i	0.103925	+	0.00831811i
$277$	0.912280	−	0.912280i	0.0548136	−	0.0548136i	−0.679169	−	0.733982i	$-0.737660\pi$
$277$	0.912280	−	0.912280i	0.0548136	−	0.0548136i	0.733982	+	0.679169i	$0.237660\pi$
$278$	2.78313	−	2.78313i	0.166921	−	0.166921i
$279$	3.05187	−	18.9426i	0.182711	−	1.13406i
$280$	4.29784	+	2.46647i	0.256845	+	0.147400i
$281$		−	28.8512i		−	1.72112i	−0.509353	−	0.860558i	$-0.670115\pi$
$281$		−	28.8512i		−	1.72112i	0.509353	−	0.860558i	$-0.329885\pi$
$282$	6.37516	+	7.48448i	0.379635	+	0.445694i
$283$	−17.7013	−	17.7013i	−1.05223	−	1.05223i	−0.998558	−	0.0536753i	$-0.982906\pi$
$283$	−17.7013	−	17.7013i	−1.05223	−	1.05223i	−0.0536753	−	0.998558i	$-0.517094\pi$
$284$	4.27468			0.253656
$285$	15.0702	−	2.81296i	0.892684	−	0.166625i
$286$	14.9865			0.886168
$287$	−7.65716	−	7.65716i	−0.451988	−	0.451988i
$288$	2.43173	−	1.75690i	0.143291	−	0.103526i
$289$			30.6277i			1.80163i
$290$	−1.54227	+	0.417554i	−0.0905650	+	0.0245196i
$291$	−0.0605514	+	0.756517i	−0.00354958	+	0.0443478i
$292$	5.13585	−	5.13585i	0.300553	−	0.300553i
$293$	23.0340	−	23.0340i	1.34566	−	1.34566i	0.455348	−	0.890313i	$-0.349515\pi$
$293$	23.0340	−	23.0340i	1.34566	−	1.34566i	0.890313	−	0.455348i	$-0.150485\pi$
$294$	0.288683	−	3.60675i	0.0168363	−	0.210350i
$295$	−8.14799	+	14.1980i	−0.474395	+	0.826637i
$296$			4.13458i			0.240318i
$297$	25.1943	−	15.3012i	1.46192	−	0.887864i
$298$	−6.19096	−	6.19096i	−0.358633	−	0.358633i
$299$	2.64181			0.152780
$300$	2.85919	−	8.17466i	0.165075	−	0.471964i
$301$	27.6289			1.59250
$302$	1.41745	+	1.41745i	0.0815650	+	0.0815650i
$303$	−4.36781	−	5.12784i	−0.250924	−	0.294587i
$304$			3.95832i			0.227025i
$305$	5.27407	−	9.19011i	0.301992	−	0.526224i
$306$	−20.4403	−	3.29316i	−1.16849	−	0.188257i
$307$	8.12472	−	8.12472i	0.463702	−	0.463702i	−0.436164	−	0.899867i	$-0.643663\pi$
$307$	8.12472	−	8.12472i	0.463702	−	0.463702i	0.899867	+	0.436164i	$0.143663\pi$
$308$	−8.88928	+	8.88928i	−0.506514	+	0.506514i
$309$	18.8850	+	1.51155i	1.07433	+	0.0859892i
$310$	13.8041	−	3.73732i	0.784018	−	0.212266i
$311$		−	12.7900i		−	0.725256i	−0.931934	−	0.362628i	$-0.881880\pi$
$311$		−	12.7900i		−	0.725256i	0.931934	−	0.362628i	$-0.118120\pi$
$312$	3.48338	−	2.96708i	0.197207	−	0.167978i
$313$	−3.96504	−	3.96504i	−0.224117	−	0.224117i	0.586112	−	0.810230i	$-0.300658\pi$
$313$	−3.96504	−	3.96504i	−0.224117	−	0.224117i	−0.810230	+	0.586112i	$0.800658\pi$
$314$	16.5177			0.932150
$315$	14.7845	−	1.55307i	0.833014	−	0.0875058i
$316$	7.27349			0.409166
$317$	0.469818	+	0.469818i	0.0263876	+	0.0263876i	0.720177	−	0.693790i	$-0.244060\pi$
$317$	0.469818	+	0.469818i	0.0263876	+	0.0263876i	−0.693790	+	0.720177i	$0.744060\pi$
$318$	−9.83007	+	8.37309i	−0.551243	+	0.469540i
$319$		−	4.05352i		−	0.226954i
$320$	1.93940	+	1.11299i	0.108415	+	0.0622180i
$321$	−15.0253	−	1.20262i	−0.838630	−	0.0671237i
$322$	−1.56700	+	1.56700i	−0.0873256	+	0.0873256i
$323$	19.3164	−	19.3164i	1.07479	−	1.07479i
$324$	2.82664	−	8.54460i	0.157035	−	0.474700i
$325$	3.35229	−	12.7766i	0.185952	−	0.708718i
$326$		−	10.5006i		−	0.581572i
$327$	−9.37559	−	11.0070i	−0.518471	−	0.608689i
$328$	−3.45528	−	3.45528i	−0.190786	−	0.190786i
$329$	−12.5790			−0.693505
$330$	18.1224	+	12.4213i	0.997606	+	0.683767i
$331$	−21.1336			−1.16161			−0.580805	−	0.814043i	$-0.697262\pi$
$331$	−21.1336			−1.16161			−0.580805	+	0.814043i	$0.697262\pi$
$332$	−10.9094	−	10.9094i	−0.598731	−	0.598731i
$333$	7.26402	+	10.0542i	0.398066	+	0.550966i
$334$			22.8297i			1.24919i
$335$	4.98247	+	18.4031i	0.272222	+	1.00547i
$336$	−0.306241	+	3.82612i	−0.0167068	+	0.208732i
$337$	10.8685	−	10.8685i	0.592045	−	0.592045i	−0.346138	−	0.938183i	$-0.612507\pi$
$337$	10.8685	−	10.8685i	0.592045	−	0.592045i	0.938183	+	0.346138i	$0.112507\pi$
$338$	−4.25737	+	4.25737i	−0.231570	+	0.231570i
$339$	−1.76772	+	22.0856i	−0.0960095	+	1.19952i
$340$	−4.03281	−	14.8955i	−0.218710	−	0.807820i
$341$			36.2810i			1.96473i
$342$	6.95436	+	9.62558i	0.376049	+	0.520492i
$343$	14.2425	+	14.2425i	0.769023	+	0.769023i
$344$	12.4675			0.672202
$345$	3.19462	+	2.18962i	0.171992	+	0.117885i
$346$	7.31614			0.393318
$347$	14.4344	+	14.4344i	0.774878	+	0.774878i	0.978955	−	0.204077i	$-0.0654191\pi$
$347$	14.4344	+	14.4344i	0.774878	+	0.774878i	−0.204077	+	0.978955i	$0.565419\pi$
$348$	−0.802533	−	0.942179i	−0.0430203	−	0.0505061i
$349$		−	35.9155i		−	1.92251i	−0.275655	−	0.961257i	$-0.588895\pi$
$349$		−	35.9155i		−	1.92251i	0.275655	−	0.961257i	$-0.411105\pi$
$350$	5.59006	+	9.56691i	0.298801	+	0.511373i
$351$	3.25778	−	13.3351i	0.173888	−	0.711774i
$352$	−4.01127	+	4.01127i	−0.213802	+	0.213802i
$353$	−4.89196	+	4.89196i	−0.260373	+	0.260373i	−0.825206	−	0.564833i	$-0.808941\pi$
$353$	−4.89196	+	4.89196i	−0.260373	+	0.260373i	0.564833	+	0.825206i	$0.308941\pi$
$354$	−12.6396	−	1.01167i	−0.671787	−	0.0537697i
$355$	8.29030	+	4.75768i	0.440003	+	0.252511i
$356$		−	8.06770i		−	0.427587i
$357$	20.1657	−	17.1768i	1.06728	−	0.909092i
$358$	4.21242	+	4.21242i	0.222633	+	0.222633i
$359$	−32.9343			−1.73821			−0.869103	−	0.494630i	$-0.835303\pi$
$359$	−32.9343			−1.73821			−0.869103	+	0.494630i	$0.835303\pi$
$360$	6.67150	−	0.700822i	0.351619	−	0.0369365i
$361$	3.33167			0.175351
$362$	1.02756	+	1.02756i	0.0540074	+	0.0540074i
$363$	−27.9279	+	23.7885i	−1.46583	+	1.24857i
$364$			5.85445i			0.306857i
$365$	15.6766	−	4.24430i	0.820551	−	0.222157i
$366$	8.18142	+	0.654838i	0.427649	+	0.0342289i
$367$	−16.9661	+	16.9661i	−0.885624	+	0.885624i	−0.994099	−	0.108475i	$-0.965403\pi$
$367$	−16.9661	+	16.9661i	−0.885624	+	0.885624i	0.108475	+	0.994099i	$0.465403\pi$
$368$	−0.707107	+	0.707107i	−0.0368605	+	0.0368605i
$369$	−14.4729	−	2.33175i	−0.753429	−	0.121386i
$370$	−4.60174	+	8.01858i	−0.239233	+	0.416866i
$371$		−	16.5212i		−	0.857739i
$372$	7.18308	+	8.43298i	0.372425	+	0.437230i
$373$	−7.20832	−	7.20832i	−0.373233	−	0.373233i	0.495420	−	0.868653i	$-0.335014\pi$
$373$	−7.20832	−	7.20832i	−0.373233	−	0.373233i	−0.868653	+	0.495420i	$0.835014\pi$
$374$	39.1496			2.02438
$375$	14.6434	−	12.6716i	0.756182	−	0.654361i
$376$	−5.67627			−0.292731
$377$	−1.33482	−	1.33482i	−0.0687466	−	0.0687466i
$378$	5.97739	+	9.84212i	0.307444	+	0.506224i
$379$		−	0.269443i		−	0.0138404i	−0.999976	−	0.00692018i	$-0.997797\pi$
$379$		−	0.269443i		−	0.0138404i	0.999976	−	0.00692018i	$-0.00220278\pi$
$380$	−4.40558	+	7.67675i	−0.226001	+	0.393809i
$381$	−1.26523	+	15.8075i	−0.0648197	+	0.809844i
$382$	−12.8719	+	12.8719i	−0.658586	+	0.658586i
$383$	14.7895	−	14.7895i	0.755707	−	0.755707i	−0.219831	−	0.975538i	$-0.570551\pi$
$383$	14.7895	−	14.7895i	0.755707	−	0.755707i	0.975538	+	0.219831i	$0.0705506\pi$
$384$	−0.138191	+	1.72653i	−0.00705202	+	0.0881066i
$385$	−27.1335	+	7.34615i	−1.38285	+	0.374394i
$386$		−	22.8014i		−	1.16056i
$387$	30.3176	−	21.9041i	1.54113	−	1.11345i
$388$	−0.309834	−	0.309834i	−0.0157295	−	0.0157295i
$389$	−34.0408			−1.72594			−0.862970	−	0.505256i	$-0.831398\pi$
$389$	−34.0408			−1.72594			−0.862970	+	0.505256i	$0.831398\pi$
$390$	10.0580	−	1.87739i	0.509306	−	0.0950651i
$391$	6.90128			0.349013
$392$	1.47716	+	1.47716i	0.0746077	+	0.0746077i
$393$	22.9867	+	26.9866i	1.15953	+	1.36129i
$394$			25.7056i			1.29503i
$395$	14.1062	+	8.09533i	0.709759	+	0.407320i
$396$	−2.70695	+	16.8017i	−0.136029	+	0.844319i
$397$	15.3440	−	15.3440i	0.770093	−	0.770093i	−0.208030	−	0.978122i	$-0.566705\pi$
$397$	15.3440	−	15.3440i	0.770093	−	0.770093i	0.978122	+	0.208030i	$0.0667051\pi$
$398$	0.436553	−	0.436553i	0.0218824	−	0.0218824i
$399$	−15.1450	−	1.21220i	−0.758199	−	0.0606860i
$400$	2.52251	+	4.31705i	0.126125	+	0.215853i
$401$		−	11.5244i		−	0.575503i	−0.957705	−	0.287752i	$-0.907092\pi$
$401$		−	11.5244i		−	0.575503i	0.957705	−	0.287752i	$-0.0929078\pi$
$402$	−11.2426	+	9.57624i	−0.560728	+	0.477619i
$403$	11.9473	+	11.9473i	0.595137	+	0.595137i
$404$	3.88898			0.193484
$405$	14.9920	−	13.4253i	0.744959	−	0.667110i
$406$	1.58350			0.0785880
$407$	−16.5849	−	16.5849i	−0.822084	−	0.822084i
$408$	9.09972	−	7.75100i	0.450504	−	0.383732i
$409$		−	14.4328i		−	0.713658i	−0.934170	−	0.356829i	$-0.883858\pi$
$409$		−	14.4328i		−	0.713658i	0.934170	−	0.356829i	$-0.116142\pi$
$410$	−2.85546	−	10.5469i	−0.141021	−	0.520872i
$411$	−11.2228	−	0.898268i	−0.553579	−	0.0443083i
$412$	−7.73444	+	7.73444i	−0.381048	+	0.381048i
$413$	11.4717	−	11.4717i	0.564487	−	0.564487i
$414$	−0.477181	+	2.96181i	−0.0234522	+	0.145565i
$415$	−9.01558	−	33.2997i	−0.442557	−	1.63462i
$416$			2.64181i			0.129525i
$417$	4.42056	+	5.18977i	0.216476	+	0.254144i
$418$	−15.8779	−	15.8779i	−0.776615	−	0.776615i
$419$	−1.59881			−0.0781072			−0.0390536	−	0.999237i	$-0.512434\pi$
$419$	−1.59881			−0.0781072			−0.0390536	+	0.999237i	$0.512434\pi$
$420$	−4.85235	+	7.07951i	−0.236771	+	0.345445i
$421$	−3.21224			−0.156555			−0.0782774	−	0.996932i	$-0.524942\pi$
$421$	−3.21224			−0.156555			−0.0782774	+	0.996932i	$0.524942\pi$
$422$	6.97557	+	6.97557i	0.339565	+	0.339565i
$423$	−13.8032	+	9.97261i	−0.671133	+	0.484885i
$424$		−	7.45518i		−	0.362055i
$425$	8.75729	−	33.3767i	0.424791	−	1.61901i
$426$	−0.590722	+	7.38036i	−0.0286206	+	0.357580i
$427$	−7.42547	+	7.42547i	−0.359344	+	0.359344i
$428$	6.15366	−	6.15366i	0.297449	−	0.297449i
$429$	−2.07099	+	25.8746i	−0.0999885	+	1.24924i
$430$	24.1794	+	13.8762i	1.16603	+	0.669169i
$431$		−	16.9446i		−	0.816195i	−0.912938	−	0.408097i	$-0.866192\pi$
$431$		−	16.9446i		−	0.816195i	0.912938	−	0.408097i	$-0.133808\pi$
$432$	2.69729	+	4.44124i	0.129773	+	0.213679i
$433$	−23.5807	−	23.5807i	−1.13321	−	1.13321i	−0.989639	−	0.143576i	$-0.954140\pi$
$433$	−23.5807	−	23.5807i	−1.13321	−	1.13321i	−0.143576	−	0.989639i	$-0.545860\pi$
$434$	−14.1732			−0.680334
$435$	−0.507793	−	2.72047i	−0.0243468	−	0.130437i
$436$	8.34777			0.399786
$437$	−2.79896	−	2.79896i	−0.133892	−	0.133892i
$438$	8.15747	+	9.57693i	0.389779	+	0.457603i
$439$		−	18.7018i		−	0.892590i	−0.894886	−	0.446295i	$-0.852743\pi$
$439$		−	18.7018i		−	0.892590i	0.894886	−	0.446295i	$-0.147257\pi$
$440$	−12.2440	+	3.31494i	−0.583708	+	0.158033i
$441$	6.18726	+	0.996839i	0.294631	+	0.0474685i
$442$	12.8919	−	12.8919i	0.613205	−	0.613205i
$443$	14.4583	−	14.4583i	0.686934	−	0.686934i	−0.274619	−	0.961553i	$-0.588552\pi$
$443$	14.4583	−	14.4583i	0.686934	−	0.686934i	0.961553	+	0.274619i	$0.0885517\pi$
$444$	−7.13847	−	0.571361i	−0.338777	−	0.0271156i
$445$	8.97927	−	15.6465i	0.425658	−	0.741713i
$446$			5.49662i			0.260273i
$447$	11.5444	−	9.83333i	0.546031	−	0.465101i
$448$	−1.56700	−	1.56700i	−0.0740338	−	0.0740338i
$449$	−21.0282			−0.992382			−0.496191	−	0.868213i	$-0.665268\pi$
$449$	−21.0282			−0.992382			−0.496191	+	0.868213i	$0.665268\pi$
$450$	13.7187	+	6.06614i	0.646704	+	0.285960i
$451$	27.7202			1.30529
$452$	−9.04524	−	9.04524i	−0.425452	−	0.425452i
$453$	−2.64314	+	2.25139i	−0.124186	+	0.105779i
$454$		−	24.5132i		−	1.15046i
$455$	−6.51595	+	11.3541i	−0.305472	+	0.532288i
$456$	−6.83416	−	0.547004i	−0.320039	−	0.0256158i
$457$	−15.3590	+	15.3590i	−0.718465	+	0.718465i	−0.968291	−	0.249826i	$-0.919627\pi$
$457$	−15.3590	+	15.3590i	−0.718465	+	0.718465i	0.249826	+	0.968291i	$0.419627\pi$
$458$	−5.18329	+	5.18329i	−0.242199	+	0.242199i
$459$	8.51039	−	34.8356i	0.397231	−	1.62599i
$460$	−2.15836	+	0.584357i	−0.100634	+	0.0272458i
$461$		−	33.5271i		−	1.56151i	−0.624837	−	0.780756i	$-0.714834\pi$
$461$		−	33.5271i		−	1.56151i	0.624837	−	0.780756i	$-0.285166\pi$
$462$	−14.1192	−	16.5760i	−0.656884	−	0.771186i
$463$	22.9496	+	22.9496i	1.06656	+	1.06656i	0.997621	+	0.0689368i	$0.0219607\pi$
$463$	22.9496	+	22.9496i	1.06656	+	1.06656i	0.0689368	+	0.997621i	$0.478039\pi$
$464$	0.714554			0.0331723
$465$	4.54500	+	24.3496i	0.210769	+	1.12918i
$466$	−7.96845			−0.369131
$467$	17.4583	+	17.4583i	0.807875	+	0.807875i	0.984312	−	0.176437i	$-0.0564571\pi$
$467$	17.4583	+	17.4583i	0.807875	+	0.807875i	−0.176437	+	0.984312i	$0.556457\pi$
$468$	4.64139	+	6.42418i	0.214548	+	0.296958i
$469$		−	18.8952i		−	0.872499i
$470$	−11.0085	−	6.31763i	−0.507786	−	0.291411i
$471$	−2.28260	+	28.5184i	−0.105177	+	1.31406i
$472$	5.17660	−	5.17660i	0.238272	−	0.238272i
$473$	−50.0105	+	50.0105i	−2.29949	+	2.29949i
$474$	−1.00513	+	12.5579i	−0.0461672	+	0.576803i
$475$	−17.0883	+	9.98490i	−0.784065	+	0.458139i
$476$			15.2937i			0.700988i
$477$	−13.0980	−	18.1290i	−0.599715	−	0.830069i
$478$	1.82107	+	1.82107i	0.0832938	+	0.0832938i
$479$	16.3083			0.745147			0.372573	−	0.928003i	$-0.378475\pi$
$479$	16.3083			0.745147			0.372573	+	0.928003i	$0.378475\pi$
$480$	−2.18962	+	3.19462i	−0.0999419	+	0.145814i
$481$	−10.9228			−0.498036
$482$	−13.4614	−	13.4614i	−0.613150	−	0.613150i
$483$	−2.48893	−	2.92202i	−0.113250	−	0.132956i
$484$		−	21.1806i		−	0.962756i
$485$	−0.256049	−	0.945734i	−0.0116266	−	0.0429436i
$486$	14.3619	+	6.06106i	0.651468	+	0.274935i
$487$	−12.6082	+	12.6082i	−0.571334	+	0.571334i	−0.932501	−	0.361167i	$-0.882378\pi$
$487$	−12.6082	+	12.6082i	−0.571334	+	0.571334i	0.361167	+	0.932501i	$0.382378\pi$
$488$	−3.35073	+	3.35073i	−0.151680	+	0.151680i
$489$	18.1295	+	1.45108i	0.819846	+	0.0656202i
$490$	1.22073	+	4.50885i	0.0551470	+	0.203689i
$491$			29.1446i			1.31528i	0.753334	+	0.657638i	$0.228444\pi$
$491$			29.1446i			1.31528i	−0.753334	+	0.657638i	$0.771556\pi$
$492$	6.44314	−	5.48816i	0.290479	−	0.247425i
$493$	−3.48698	−	3.48698i	−0.157046	−	0.157046i
$494$	−10.4571			−0.470489
$495$	−23.9500	+	29.5724i	−1.07647	+	1.32918i
$496$	−6.39562			−0.287172
$497$	−6.69843	−	6.69843i	−0.300466	−	0.300466i
$498$	20.3430	−	17.3278i	0.911590	−	0.776478i
$499$		−	2.64641i		−	0.118469i	−0.998244	−	0.0592347i	$-0.981134\pi$
$499$		−	2.64641i		−	0.118469i	0.998244	−	0.0592347i	$-0.0188660\pi$
$500$	0.0872994	+	11.1800i	0.00390415	+	0.499985i
$501$	−39.4162	−	3.15486i	−1.76099	−	0.140949i
$502$	−2.86334	+	2.86334i	−0.127797	+	0.127797i
$503$	−3.51592	+	3.51592i	−0.156767	+	0.156767i	−0.781133	−	0.624365i	$-0.785358\pi$
$503$	−3.51592	+	3.51592i	−0.156767	+	0.156767i	0.624365	+	0.781133i	$0.285358\pi$
$504$	−6.56358	−	1.05747i	−0.292365	−	0.0471034i
$505$	7.54227	+	4.32839i	0.335626	+	0.192611i
$506$		−	5.67280i		−	0.252187i
$507$	−6.76214	−	7.93880i	−0.300317	−	0.352575i
$508$	−6.47403	−	6.47403i	−0.287239	−	0.287239i
$509$	0.570411			0.0252830			0.0126415	−	0.999920i	$-0.495976\pi$
$509$	0.570411			0.0252830			0.0126415	+	0.999920i	$0.495976\pi$
$510$	26.2747	−	4.90435i	1.16347	−	0.217168i
$511$	−16.0958			−0.712035
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−17.5799	+	10.6767i	−0.776171	+	0.471390i
$514$		−	5.79900i		−	0.255783i
$515$	−23.6085	+	6.39178i	−1.04031	+	0.281655i
$516$	−1.72289	+	21.5255i	−0.0758461	+	0.947606i
$517$	22.7691	−	22.7691i	1.00138	−	1.00138i
$518$	6.47889	−	6.47889i	0.284666	−	0.284666i
$519$	−1.01102	+	12.6315i	−0.0443790	+	0.554463i
$520$	−2.94031	+	5.12352i	−0.128941	+	0.224681i
$521$		−	22.9010i		−	1.00331i	−0.865067	−	0.501656i	$-0.832724\pi$
$521$		−	22.9010i		−	1.00331i	0.865067	−	0.501656i	$-0.167276\pi$
$522$	1.73760	−	1.25540i	0.0760528	−	0.0549472i
$523$	23.8359	+	23.8359i	1.04227	+	1.04227i	0.999066	+	0.0432069i	$0.0137575\pi$
$523$	23.8359	+	23.8359i	1.04227	+	1.04227i	0.0432069	+	0.999066i	$0.486243\pi$
$524$	−20.4667			−0.894094
$525$	−17.2901	+	8.32935i	−0.754600	+	0.363522i
$526$	18.5310			0.807991
$527$	31.2102	+	31.2102i	1.35954	+	1.35954i
$528$	−6.37126	−	7.47990i	−0.277274	−	0.325521i
$529$		−	1.00000i		−	0.0434783i
$530$	8.29753	−	14.4585i	0.360422	−	0.628038i
$531$	3.49336	−	21.6828i	0.151599	−	0.940955i
$532$	6.20270	−	6.20270i	0.268921	−	0.268921i
$533$	9.12821	−	9.12821i	0.395387	−	0.395387i
$534$	13.9291	+	1.11488i	0.602772	+	0.0482457i
$535$	18.7833	−	5.08542i	0.812075	−	0.219862i
$536$		−	8.52642i		−	0.368285i
$537$	−7.85498	+	6.69074i	−0.338967	+	0.288727i
$538$	5.92679	+	5.92679i	0.255522	+	0.255522i
$539$	−11.8506			−0.510440
$540$	0.288049	+	11.6154i	0.0123957	+	0.499846i
$541$	−19.8837			−0.854868			−0.427434	−	0.904047i	$-0.640582\pi$
$541$	−19.8837			−0.854868			−0.427434	+	0.904047i	$0.640582\pi$
$542$	4.21836	+	4.21836i	0.181194	+	0.181194i
$543$	−1.91611	+	1.63211i	−0.0822283	+	0.0700407i
$544$			6.90128i			0.295890i
$545$	16.1896	+	9.29098i	0.693487	+	0.397982i
$546$	−10.1079	−	0.809032i	−0.432577	−	0.0346234i
$547$	1.43836	−	1.43836i	0.0614997	−	0.0614997i	−0.675688	−	0.737188i	$-0.736153\pi$
$547$	1.43836	−	1.43836i	0.0614997	−	0.0614997i	0.737188	+	0.675688i	$0.236153\pi$
$548$	4.59633	−	4.59633i	0.196346	−	0.196346i
$549$	−2.26119	+	14.0350i	−0.0965054	+	0.598998i
$550$	−27.4354	−	7.19842i	−1.16985	−	0.306942i
$551$			2.82844i			0.120495i
$552$	−1.12312	−	1.31856i	−0.0478034	−	0.0561215i
$553$	−11.3976	−	11.3976i	−0.484674	−	0.484674i
$554$	−1.29016			−0.0548136
$555$	−13.2084	−	9.05314i	−0.560665	−	0.384284i
$556$	−3.93595			−0.166921
$557$	4.53628	+	4.53628i	0.192208	+	0.192208i	0.796650	−	0.604441i	$-0.206604\pi$
$557$	4.53628	+	4.53628i	0.192208	+	0.192208i	−0.604441	+	0.796650i	$0.706604\pi$
$558$	−15.5524	+	11.2364i	−0.658387	+	0.475676i
$559$			32.9367i			1.39308i
$560$	−1.29498	−	4.78309i	−0.0547228	−	0.202122i
$561$	−5.41011	+	67.5929i	−0.228415	+	2.85377i
$562$	−20.4008	+	20.4008i	−0.860558	+	0.860558i
$563$	1.12010	−	1.12010i	0.0472067	−	0.0472067i	−0.683109	−	0.730316i	$-0.739373\pi$
$563$	1.12010	−	1.12010i	0.0472067	−	0.0472067i	0.730316	+	0.683109i	$0.239373\pi$
$564$	0.784409	−	9.80025i	0.0330296	−	0.412665i
$565$	−7.47503	−	27.6095i	−0.314477	−	1.16154i
$566$			25.0334i			1.05223i
$567$	−17.8187	+	8.96005i	−0.748317	+	0.376287i
$568$	−3.02266	−	3.02266i	−0.126828	−	0.126828i
$569$	22.6299			0.948693			0.474347	−	0.880338i	$-0.342684\pi$
$569$	22.6299			0.948693			0.474347	+	0.880338i	$0.342684\pi$
$570$	−12.6453	−	8.66721i	−0.529655	−	0.363030i
$571$	46.0793			1.92836			0.964178	−	0.265254i	$-0.0854559\pi$
$571$	46.0793			1.92836			0.964178	+	0.265254i	$0.0854559\pi$
$572$	−10.5970	−	10.5970i	−0.443084	−	0.443084i
$573$	−20.4450	−	24.0026i	−0.854102	−	1.00272i
$574$			10.8289i			0.451988i
$575$	−4.83630	−	1.26894i	−0.201688	−	0.0529183i
$576$	−2.96181	−	0.477181i	−0.123409	−	0.0198825i
$577$	−11.0358	+	11.0358i	−0.459427	+	0.459427i	−0.898467	−	0.439041i	$-0.855318\pi$
$577$	−11.0358	+	11.0358i	−0.459427	+	0.459427i	0.439041	+	0.898467i	$0.355318\pi$
$578$	21.6570	−	21.6570i	0.900813	−	0.900813i
$579$	39.3673	+	3.15095i	1.63605	+	0.130949i
$580$	1.38580	+	0.795291i	0.0575423	+	0.0330227i
$581$			34.1901i			1.41844i
$582$	0.577755	−	0.492122i	0.0239487	−	0.0203991i
$583$	29.9048	+	29.9048i	1.23853	+	1.23853i
$584$	−7.26319			−0.300553
$585$	1.85144	+	17.6248i	0.0765476	+	0.728697i
$586$	−32.5750			−1.34566
$587$	16.2913	+	16.2913i	0.672415	+	0.672415i	0.958272	−	0.285857i	$-0.0922783\pi$
$587$	16.2913	+	16.2913i	0.672415	+	0.672415i	−0.285857	+	0.958272i	$0.592278\pi$
$588$	−2.75448	+	2.34622i	−0.113593	+	0.0967567i
$589$		−	25.3159i		−	1.04312i
$590$	15.8010	−	4.27797i	0.650516	−	0.176121i
$591$	−44.3814	−	3.55228i	−1.82561	−	0.146121i
$592$	2.92359	−	2.92359i	0.120159	−	0.120159i
$593$	23.5367	−	23.5367i	0.966535	−	0.966535i	−0.0329233	−	0.999458i	$-0.510482\pi$
$593$	23.5367	−	23.5367i	0.966535	−	0.966535i	0.999458	+	0.0329233i	$0.0104817\pi$
$594$	−28.6346	−	6.99548i	−1.17489	−	0.287028i
$595$	−17.0218	+	29.6606i	−0.697825	+	1.21597i
$596$			8.75534i			0.358633i
$597$	0.693393	+	0.814049i	0.0283787	+	0.0333168i
$598$	−1.86804	−	1.86804i	−0.0763900	−	0.0763900i
$599$	−3.05690			−0.124901			−0.0624507	−	0.998048i	$-0.519892\pi$
$599$	−3.05690			−0.124901			−0.0624507	+	0.998048i	$0.519892\pi$
$600$	−7.80211	+	3.75860i	−0.318520	+	0.153444i
$601$	−0.352393			−0.0143744			−0.00718721	−	0.999974i	$-0.502288\pi$
$601$	−0.352393			−0.0143744			−0.00718721	+	0.999974i	$0.502288\pi$
$602$	−19.5366	−	19.5366i	−0.796251	−	0.796251i
$603$	−14.9800	−	20.7340i	−0.610034	−	0.844353i
$604$		−	2.00457i		−	0.0815650i
$605$	23.5738	−	41.0776i	0.958413	−	1.67004i
$606$	−0.537421	+	6.71444i	−0.0218312	+	0.272755i
$607$	−4.89133	+	4.89133i	−0.198533	+	0.198533i	−0.799371	−	0.600838i	$-0.794834\pi$
$607$	−4.89133	+	4.89133i	−0.198533	+	0.198533i	0.600838	+	0.799371i	$0.294834\pi$
$608$	2.79896	−	2.79896i	0.113513	−	0.113513i
$609$	−0.218826	+	2.73397i	−0.00886727	+	0.110786i
$610$	−10.2277	+	2.76906i	−0.414108	+	0.112116i
$611$		−	14.9956i		−	0.606659i
$612$	12.1248	+	16.7821i	0.490117	+	0.678375i
$613$	12.5329	+	12.5329i	0.506199	+	0.506199i	0.913358	−	0.407158i	$-0.133480\pi$
$613$	12.5329	+	12.5329i	0.506199	+	0.506199i	−0.407158	+	0.913358i	$0.633480\pi$
$614$	−11.4901			−0.463702
$615$	18.6041	−	3.47256i	0.750188	−	0.140027i
$616$	12.5713			0.506514
$617$	32.9202	+	32.9202i	1.32532	+	1.32532i	0.909403	+	0.415916i	$0.136539\pi$
$617$	32.9202	+	32.9202i	1.32532	+	1.32532i	0.415916	+	0.909403i	$0.363461\pi$
$618$	−12.2849	−	14.4226i	−0.494171	−	0.580160i
$619$		−	35.6199i		−	1.43168i	−0.698262	−	0.715842i	$-0.746043\pi$
$619$		−	35.6199i		−	1.43168i	0.698262	−	0.715842i	$-0.253957\pi$
$620$	−12.4036	−	7.11826i	−0.498142	−	0.285876i
$621$	−5.04770	−	1.23316i	−0.202557	−	0.0494851i
$622$	−9.04391	+	9.04391i	−0.362628	+	0.362628i
$623$	−12.6421	+	12.6421i	−0.506495	+	0.506495i
$624$	−4.56117	−	0.365074i	−0.182593	−	0.0146147i
$625$	−12.2739	+	21.7796i	−0.490957	+	0.871184i
$626$			5.60742i			0.224117i
$627$	29.6079	−	25.2195i	1.18243	−	1.00717i
$628$	−11.6798	−	11.6798i	−0.466075	−	0.466075i
$629$	−28.5339			−1.13772
$630$	−11.5524	−	9.35605i	−0.460260	−	0.372754i
$631$	2.84251			0.113159			0.0565793	−	0.998398i	$-0.481981\pi$
$631$	2.84251			0.113159			0.0565793	+	0.998398i	$0.481981\pi$
$632$	−5.14314	−	5.14314i	−0.204583	−	0.204583i
$633$	−13.0075	+	11.0796i	−0.517001	+	0.440373i
$634$		−	0.664424i		−	0.0263876i
$635$	−5.35017	−	19.7612i	−0.212315	−	0.784201i
$636$	12.8716	+	1.03024i	0.510391	+	0.0408516i
$637$	−3.90237	+	3.90237i	−0.154618	+	0.154618i
$638$	−2.86627	+	2.86627i	−0.113477	+	0.113477i
$639$	−12.6608	−	2.03980i	−0.500853	−	0.0806931i
$640$	−0.584357	−	2.15836i	−0.0230987	−	0.0853168i
$641$		−	2.31899i		−	0.0915947i	−0.998951	−	0.0457973i	$-0.985417\pi$
$641$		−	2.31899i		−	0.0915947i	0.998951	−	0.0457973i	$-0.0145828\pi$
$642$	9.77410	+	11.4749i	0.385753	+	0.452877i
$643$	−3.83141	−	3.83141i	−0.151096	−	0.151096i	0.627511	−	0.778607i	$-0.284074\pi$
$643$	−3.83141	−	3.83141i	−0.151096	−	0.151096i	−0.778607	+	0.627511i	$0.784074\pi$
$644$	2.21607			0.0873256
$645$	−27.2990	+	39.8288i	−1.07490	+	1.56826i
$646$	−27.3175			−1.07479
$647$	−8.83653	−	8.83653i	−0.347400	−	0.347400i	0.511740	−	0.859140i	$-0.329001\pi$
$647$	−8.83653	−	8.83653i	−0.347400	−	0.347400i	−0.859140	+	0.511740i	$0.829001\pi$
$648$	−8.04068	+	4.04321i	−0.315868	+	0.158832i
$649$			41.5295i			1.63018i
$650$	−11.4048	+	6.66399i	−0.447335	+	0.261383i
$651$	1.95860	−	24.4704i	0.0767637	−	0.959070i
$652$	−7.42502	+	7.42502i	−0.290786	+	0.290786i
$653$	−1.60062	+	1.60062i	−0.0626369	+	0.0626369i	−0.737731	−	0.675094i	$-0.764103\pi$
$653$	−1.60062	+	1.60062i	−0.0626369	+	0.0626369i	0.675094	+	0.737731i	$0.264103\pi$
$654$	−1.15359	+	14.4127i	−0.0451088	+	0.563580i
$655$	−39.6931	−	22.7793i	−1.55094	−	0.890060i
$656$			4.88651i			0.190786i
$657$	−17.6621	+	12.7607i	−0.689066	+	0.497841i
$658$	8.89472	+	8.89472i	0.346752	+	0.346752i
$659$	24.4088			0.950831			0.475415	−	0.879761i	$-0.342298\pi$
$659$	24.4088			0.950831			0.475415	+	0.879761i	$0.342298\pi$
$660$	−4.03133	−	21.5976i	−0.156919	−	0.840687i
$661$	−32.4790			−1.26329			−0.631643	−	0.775259i	$-0.717619\pi$
$661$	−32.4790			−1.26329			−0.631643	+	0.775259i	$0.717619\pi$
$662$	14.9437	+	14.9437i	0.580805	+	0.580805i
$663$	20.4767	+	24.0398i	0.795248	+	0.933627i
$664$			15.4282i			0.598731i
$665$	18.9330	−	5.12594i	0.734191	−	0.198776i
$666$	1.97294	−	12.2458i	0.0764500	−	0.474516i
$667$	−0.505266	+	0.505266i	−0.0195640	+	0.0195640i
$668$	16.1431	−	16.1431i	0.624593	−	0.624593i
$669$	−9.49008	−	0.759583i	−0.366908	−	0.0293672i
$670$	9.48982	−	16.5361i	0.366624	−	0.638845i
$671$		−	26.8814i		−	1.03774i
$672$	2.92202	−	2.48893i	0.112719	−	0.0960125i
$673$	0.870095	+	0.870095i	0.0335397	+	0.0335397i	0.723678	−	0.690138i	$-0.242450\pi$
$673$	0.870095	+	0.870095i	0.0335397	+	0.0335397i	−0.690138	+	0.723678i	$0.742450\pi$
$674$	−15.3704			−0.592045
$675$	−12.3692	+	22.8474i	−0.476089	+	0.879397i
$676$	6.02083			0.231570
$677$	6.92072	+	6.92072i	0.265985	+	0.265985i	0.827480	−	0.561495i	$-0.189774\pi$
$677$	6.92072	+	6.92072i	0.265985	+	0.265985i	−0.561495	+	0.827480i	$0.689774\pi$
$678$	16.8668	−	14.3669i	0.647767	−	0.551757i
$679$			0.971022i			0.0372644i
$680$	−7.68105	+	13.3843i	−0.294555	+	0.513265i
$681$	42.3228	+	3.38750i	1.62181	+	0.129809i
$682$	25.6546	−	25.6546i	0.982364	−	0.982364i
$683$	−5.87527	+	5.87527i	−0.224811	+	0.224811i	−0.810521	−	0.585710i	$-0.800816\pi$
$683$	−5.87527	+	5.87527i	−0.224811	+	0.224811i	0.585710	+	0.810521i	$0.300816\pi$
$684$	1.88884	−	11.7238i	0.0722215	−	0.448270i
$685$	14.0298	−	3.79843i	0.536050	−	0.145131i
$686$		−	20.1419i		−	0.769023i
$687$	−8.23281	−	9.66538i	−0.314101	−	0.368757i
$688$	−8.81584	−	8.81584i	−0.336101	−	0.336101i
$689$	19.6952			0.750326
$690$	−0.710643	−	3.80723i	−0.0270537	−	0.144939i
$691$	−9.37992			−0.356829			−0.178414	−	0.983955i	$-0.557097\pi$
$691$	−9.37992			−0.356829			−0.178414	+	0.983955i	$0.557097\pi$
$692$	−5.17329	−	5.17329i	−0.196659	−	0.196659i
$693$	30.5701	−	22.0865i	1.16126	−	0.838998i
$694$		−	20.4133i		−	0.774878i
$695$	−7.63336	−	4.38067i	−0.289550	−	0.166168i
$696$	−0.0987448	+	1.23370i	−0.00374291	+	0.0467632i
$697$	23.8459	−	23.8459i	0.903227	−	0.903227i
$698$	−25.3961	+	25.3961i	−0.961257	+	0.961257i
$699$	1.10117	−	13.7578i	0.0416500	−	0.520366i
$700$	2.81206	−	10.7176i	0.106286	−	0.405087i
$701$		−	3.17498i		−	0.119918i	−0.998201	−	0.0599588i	$-0.980903\pi$
$701$		−	3.17498i		−	0.119918i	0.998201	−	0.0599588i	$-0.0190969\pi$
$702$	−11.7329	+	7.12573i	−0.442831	+	0.268943i
$703$	11.5725	+	11.5725i	0.436466	+	0.436466i
$704$	5.67280			0.213802
$705$	12.4289	−	18.1335i	0.468098	−	0.682947i
$706$	6.91828			0.260373
$707$	−6.09403	−	6.09403i	−0.229190	−	0.229190i
$708$	8.22219	+	9.65291i	0.309009	+	0.362778i
$709$			11.9551i			0.448982i	0.974476	+	0.224491i	$0.0720719\pi$
$709$			11.9551i			0.448982i	−0.974476	+	0.224491i	$0.927928\pi$
$710$	−2.49794	−	9.22631i	−0.0937460	−	0.346257i
$711$	−21.5427	−	3.47077i	−0.807914	−	0.130164i
$712$	−5.70473	+	5.70473i	−0.213794	+	0.213794i
$713$	4.52238	−	4.52238i	0.169365	−	0.169365i
$714$	−26.4051	−	2.11346i	−0.988186	−	0.0790941i
$715$	−8.75744	−	32.3462i	−0.327510	−	1.20968i
$716$		−	5.95726i		−	0.222633i
$717$	−3.39578	+	2.89247i	−0.126818	+	0.108021i
$718$	23.2881	+	23.2881i	0.869103	+	0.869103i
$719$	−19.3497			−0.721622			−0.360811	−	0.932639i	$-0.617500\pi$
$719$	−19.3497			−0.721622			−0.360811	+	0.932639i	$0.617500\pi$
$720$	−5.21302	−	4.22190i	−0.194278	−	0.157341i
$721$	24.2397			0.902735
$722$	−2.35585	−	2.35585i	−0.0876755	−	0.0876755i
$723$	25.1018	−	21.3813i	0.933544	−	0.795178i
$724$		−	1.45319i		−	0.0540074i
$725$	1.80247	+	3.08477i	0.0669419	+	0.114565i
$726$	36.5690	+	2.92697i	1.35720	+	0.108630i
$727$	19.9504	−	19.9504i	0.739918	−	0.739918i	−0.232644	−	0.972562i	$-0.574738\pi$
$727$	19.9504	−	19.9504i	0.739918	−	0.739918i	0.972562	+	0.232644i	$0.0747376\pi$
$728$	4.13972	−	4.13972i	0.153428	−	0.153428i
$729$	−12.4493	+	23.9586i	−0.461084	+	0.887356i
$730$	−14.0862	−	8.08386i	−0.521354	−	0.299197i
$731$			86.0416i			3.18236i
$732$	−5.32209	−	6.24818i	−0.196710	−	0.230939i
$733$	3.98501	+	3.98501i	0.147190	+	0.147190i	0.776861	−	0.629672i	$-0.216811\pi$
$733$	3.98501	+	3.98501i	0.147190	+	0.147190i	−0.629672	+	0.776861i	$0.716811\pi$
$734$	23.9937			0.885624
$735$	−7.95336	+	1.48454i	−0.293364	+	0.0547582i
$736$	1.00000			0.0368605
$737$	34.2018	+	34.2018i	1.25984	+	1.25984i
$738$	8.58508	+	11.8827i	0.316021	+	0.437407i
$739$			24.8589i			0.914450i	0.889351	+	0.457225i	$0.151157\pi$
$739$			24.8589i			0.914450i	−0.889351	+	0.457225i	$0.848843\pi$
$740$	8.92392	−	2.41607i	0.328050	−	0.0888165i
$741$	1.44508	−	18.0546i	0.0530864	−	0.663251i
$742$	−11.6823	+	11.6823i	−0.428870	+	0.428870i
$743$	36.6681	−	36.6681i	1.34522	−	1.34522i	0.454449	−	0.890773i	$-0.349836\pi$
$743$	36.6681	−	36.6681i	1.34522	−	1.34522i	0.890773	−	0.454449i	$-0.150164\pi$
$744$	0.883816	−	11.0422i	0.0324023	−	0.404827i
$745$	−9.74460	+	16.9801i	−0.357015	+	0.622101i
$746$			10.1941i			0.373233i
$747$	27.1058	+	37.5173i	0.991748	+	1.37268i
$748$	−27.6829	−	27.6829i	−1.01219	−	1.01219i
$749$	−19.2856			−0.704680
$750$	−19.3147	−	1.39425i	−0.705272	−	0.0509108i
$751$	−15.8379			−0.577935			−0.288967	−	0.957339i	$-0.593312\pi$
$751$	−15.8379			−0.577935			−0.288967	+	0.957339i	$0.593312\pi$
$752$	4.01373	+	4.01373i	0.146366	+	0.146366i
$753$	−4.54796	−	5.33934i	−0.165737	−	0.194576i
$754$			1.88772i			0.0687466i
$755$	2.23107	−	3.88766i	0.0811970	−	0.141486i
$756$	2.73278	−	11.1861i	0.0993902	−	0.406834i
$757$	−31.2042	+	31.2042i	−1.13413	+	1.13413i	−0.144652	+	0.989483i	$0.546206\pi$
$757$	−31.2042	+	31.2042i	−1.13413	+	1.13413i	−0.989483	+	0.144652i	$0.953794\pi$
$758$	−0.190525	+	0.190525i	−0.00692018	+	0.00692018i
$759$	9.79425	+	0.783929i	0.355509	+	0.0284548i
$760$	8.54350	−	2.31307i	0.309905	−	0.0839040i
$761$			3.09150i			0.112067i	0.998429	+	0.0560334i	$0.0178453\pi$
$761$			3.09150i			0.112067i	−0.998429	+	0.0560334i	$0.982155\pi$
$762$	12.0723	−	10.2830i	0.437332	−	0.372512i
$763$	−13.0810	−	13.0810i	−0.473563	−	0.473563i
$764$	18.2037			0.658586
$765$	4.83657	+	46.0419i	0.174866	+	1.66465i
$766$	−20.9155			−0.755707
$767$	13.6756	+	13.6756i	0.493797	+	0.493797i
$768$	1.31856	−	1.12312i	0.0475793	−	0.0405273i
$769$		−	10.4531i		−	0.376947i	−0.982078	−	0.188473i	$-0.939646\pi$
$769$		−	10.4531i		−	0.376947i	0.982078	−	0.188473i	$-0.0603539\pi$
$770$	24.3808	+	13.9918i	0.878623	+	0.504229i
$771$	10.0121	+	0.801368i	0.360578	+	0.0288606i
$772$	−16.1230	+	16.1230i	−0.580280	+	0.580280i
$773$	16.2711	−	16.2711i	0.585231	−	0.585231i	−0.351105	−	0.936336i	$-0.614194\pi$
$773$	16.2711	−	16.2711i	0.585231	−	0.585231i	0.936336	+	0.351105i	$0.114194\pi$
$774$	−36.9263	−	5.94925i	−1.32729	−	0.213841i
$775$	−16.1330	−	27.6102i	−0.579514	−	0.991789i
$776$			0.438172i			0.0157295i
$777$	10.2907	+	12.0813i	0.369176	+	0.433415i
$778$	24.0705	+	24.0705i	0.862970	+	0.862970i
$779$	−19.3424			−0.693013
$780$	−8.43958	−	5.78455i	−0.302185	−	0.207120i
$781$	24.2494			0.867712
$782$	−4.87994	−	4.87994i	−0.174506	−	0.174506i
$783$	1.92736	+	3.17351i	0.0688781	+	0.113412i
$784$		−	2.08902i		−	0.0746077i
$785$	−9.65225	−	35.6513i	−0.344504	−	1.27245i
$786$	2.82832	−	35.3364i	0.100883	−	1.26041i
$787$	−16.0648	+	16.0648i	−0.572649	+	0.572649i	−0.932868	−	0.360219i	$-0.882702\pi$
$787$	−16.0648	+	16.0648i	−0.572649	+	0.572649i	0.360219	+	0.932868i	$0.382702\pi$
$788$	18.1766	−	18.1766i	0.647514	−	0.647514i
$789$	−2.56082	+	31.9944i	−0.0911676	+	1.13903i
$790$	−4.25032	−	15.6988i	−0.151219	−	0.558539i
$791$			28.3478i			1.00793i
$792$	13.7947	−	9.96651i	0.490174	−	0.354145i
$793$	−8.85200	−	8.85200i	−0.314344	−	0.314344i
$794$	−21.6997			−0.770093
$795$	23.8164	+	16.3240i	0.844682	+	0.578952i
$796$	−0.617379			−0.0218824
$797$	27.0509	+	27.0509i	0.958192	+	0.958192i	0.999160	−	0.0409681i	$-0.0130442\pi$
$797$	27.0509	+	27.0509i	0.958192	+	0.958192i	−0.0409681	+	0.999160i	$0.513044\pi$
$798$	9.85198	+	11.5663i	0.348756	+	0.409442i
$799$		−	39.1735i		−	1.38586i
$800$	1.26894	−	4.83630i	0.0448637	−	0.170989i
$801$	−3.84976	+	23.8950i	−0.136024	+	0.844287i
$802$	−8.14901	+	8.14901i	−0.287752	+	0.287752i
$803$	29.1347	−	29.1347i	1.02814	−	1.02814i
$804$	14.7211	+	1.17827i	0.519174	+	0.0415545i
$805$	4.29784	+	2.46647i	0.151479	+	0.0869316i
$806$		−	16.8960i		−	0.595137i
$807$	−11.0518	+	9.41375i	−0.389042	+	0.331380i
$808$	−2.74992	−	2.74992i	−0.0967420	−	0.0967420i
$809$	−28.2673			−0.993824			−0.496912	−	0.867801i	$-0.665533\pi$
$809$	−28.2673			−0.993824			−0.496912	+	0.867801i	$0.665533\pi$
$810$	−20.0941	−	1.10781i	−0.706035	−	0.0389246i
$811$	−9.50384			−0.333725			−0.166862	−	0.985980i	$-0.553364\pi$
$811$	−9.50384			−0.333725			−0.166862	+	0.985980i	$0.553364\pi$
$812$	−1.11971	−	1.11971i	−0.0392940	−	0.0392940i
$813$	−7.86606	+	6.70018i	−0.275875	+	0.234986i
$814$			23.4546i			0.822084i
$815$	−22.6640	+	6.13607i	−0.793886	+	0.214937i
$816$	−11.9153	−	0.953694i	−0.417118	−	0.0333860i
$817$	34.8960	−	34.8960i	1.22086	−	1.22086i
$818$	−10.2056	+	10.2056i	−0.356829	+	0.356829i
$819$	2.79363	−	17.3398i	0.0976175	−	0.605900i
$820$	−5.43863	+	9.47687i	−0.189925	+	0.330947i
$821$		−	20.9357i		−	0.730661i	−0.930878	−	0.365331i	$-0.880956\pi$
$821$		−	20.9357i		−	0.730661i	0.930878	−	0.365331i	$-0.119044\pi$
$822$	7.30053	+	8.57087i	0.254635	+	0.298944i
$823$	29.6324	+	29.6324i	1.03292	+	1.03292i	0.999439	+	0.0334802i	$0.0106591\pi$
$823$	29.6324	+	29.6324i	1.03292	+	1.03292i	0.0334802	+	0.999439i	$0.489341\pi$
$824$	10.9381			0.381048
$825$	16.2196	−	46.3732i	0.564694	−	1.61451i
$826$	−16.2235			−0.564487
$827$	−35.5572	−	35.5572i	−1.23644	−	1.23644i	−0.961444	−	0.275001i	$-0.911322\pi$
$827$	−35.5572	−	35.5572i	−1.23644	−	1.23644i	−0.275001	−	0.961444i	$-0.588678\pi$
$828$	2.43173	−	1.75690i	0.0845085	−	0.0610563i
$829$			4.84770i			0.168367i	0.996450	+	0.0841837i	$0.0268283\pi$
$829$			4.84770i			0.168367i	−0.996450	+	0.0841837i	$0.973172\pi$
$830$	−17.1714	+	29.9214i	−0.596029	+	1.03859i
$831$	0.178288	−	2.22750i	0.00618475	−	0.0772710i
$832$	1.86804	−	1.86804i	0.0647627	−	0.0647627i
$833$	−10.1943	+	10.1943i	−0.353211	+	0.353211i
$834$	0.543912	−	6.79553i	0.0188341	−	0.235310i
$835$	49.2748	−	13.3407i	1.70523	−	0.461674i
$836$			22.4548i			0.776615i
$837$	−17.2508	−	28.4045i	−0.596276	−	0.981803i
$838$	1.13053	+	1.13053i	0.0390536	+	0.0390536i
$839$	−55.2908			−1.90885			−0.954426	−	0.298448i	$-0.903531\pi$
$839$	−55.2908			−1.90885			−0.954426	+	0.298448i	$0.903531\pi$
$840$	8.43710	−	1.57484i	0.291108	−	0.0543371i
$841$	−28.4894			−0.982394
$842$	2.27139	+	2.27139i	0.0782774	+	0.0782774i
$843$	−32.4035	−	38.0419i	−1.11603	−	1.31023i
$844$		−	9.86494i		−	0.339565i
$845$	11.6768	+	6.70112i	0.401693	+	0.230526i
$846$	16.8120	+	2.70861i	0.578009	+	0.0931239i
$847$	−33.1901	+	33.1901i	−1.14042	+	1.14042i
$848$	−5.27160	+	5.27160i	−0.181028	+	0.181028i
$849$	−43.2210	−	3.45939i	−1.48334	−	0.118726i
$850$	−29.7932	+	17.4085i	−1.02190	+	0.597107i
$851$			4.13458i			0.141732i
$852$	5.63641	−	4.80100i	0.193100	−	0.164480i
$853$	−22.4947	−	22.4947i	−0.770204	−	0.770204i	0.207938	−	0.978142i	$-0.433325\pi$
$853$	−22.4947	−	22.4947i	−0.770204	−	0.770204i	−0.978142	+	0.207938i	$0.933325\pi$
$854$	10.5012			0.359344
$855$	16.7117	−	20.6348i	0.571527	−	0.705695i
$856$	−8.70259			−0.297449
$857$	−22.0175	−	22.0175i	−0.752102	−	0.752102i	0.222769	−	0.974871i	$-0.428490\pi$
$857$	−22.0175	−	22.0175i	−0.752102	−	0.752102i	−0.974871	+	0.222769i	$0.928490\pi$
$858$	19.7605	−	16.8317i	0.674612	−	0.574624i
$859$			8.91500i			0.304176i	0.988367	+	0.152088i	$0.0485997\pi$
$859$			8.91500i			0.304176i	−0.988367	+	0.152088i	$0.951400\pi$
$860$	−7.28546	−	26.9093i	−0.248432	−	0.917601i
$861$	−18.6964	−	1.49645i	−0.637170	−	0.0509989i
$862$	−11.9817	+	11.9817i	−0.408097	+	0.408097i
$863$	4.38216	−	4.38216i	0.149171	−	0.149171i	−0.628577	−	0.777747i	$-0.716362\pi$
$863$	4.38216	−	4.38216i	0.149171	−	0.149171i	0.777747	+	0.628577i	$0.216362\pi$
$864$	1.23316	−	5.04770i	0.0419530	−	0.171726i
$865$	−4.27524	−	15.7909i	−0.145362	−	0.536906i
$866$			33.3481i			1.13321i
$867$	34.3987	+	40.3843i	1.16824	+	1.37152i
$868$	10.0219	+	10.0219i	0.340167	+	0.340167i
$869$	41.2611			1.39969
$870$	−1.56460	+	2.28273i	−0.0530449	+	0.0773917i
$871$	22.5252			0.763238
$872$	−5.90276	−	5.90276i	−0.199893	−	0.199893i
$873$	0.769823	+	1.06552i	0.0260545	+	0.0360623i
$874$			3.95832i			0.133892i
$875$	17.3823	−	17.6559i	0.587628	−	0.596877i
$876$	1.00371	−	12.5401i	0.0339121	−	0.423691i
$877$	−9.13881	+	9.13881i	−0.308596	+	0.308596i	−0.844365	−	0.535769i	$-0.820022\pi$
$877$	−9.13881	+	9.13881i	−0.308596	+	0.308596i	0.535769	+	0.844365i	$0.320022\pi$
$878$	−13.2242	+	13.2242i	−0.446295	+	0.446295i
$879$	4.50157	−	56.2417i	0.151834	−	1.89699i
$880$	11.0018	+	6.31377i	0.370871	+	0.212837i
$881$			15.6416i			0.526978i	0.964662	+	0.263489i	$0.0848733\pi$
$881$			15.6416i			0.526978i	−0.964662	+	0.263489i	$0.915127\pi$
$882$	−3.67018	−	5.07992i	−0.123581	−	0.171050i
$883$	19.6438	+	19.6438i	0.661066	+	0.661066i	0.955631	−	0.294566i	$-0.0951750\pi$
$883$	19.6438	+	19.6438i	0.661066	+	0.661066i	−0.294566	+	0.955631i	$0.595175\pi$
$884$	−18.2319			−0.613205
$885$	5.20249	+	27.8720i	0.174880	+	0.936908i
$886$	−20.4471			−0.686934
$887$	3.17206	+	3.17206i	0.106507	+	0.106507i	0.758352	−	0.651845i	$-0.226005\pi$
$887$	3.17206	+	3.17206i	0.106507	+	0.106507i	−0.651845	+	0.758352i	$0.726005\pi$
$888$	4.64365	+	5.45168i	0.155831	+	0.182946i
$889$			20.2896i			0.680492i
$890$	−17.4130	+	4.71442i	−0.583686	+	0.158028i
$891$	16.0349	−	48.4718i	0.537191	−	1.62387i
$892$	3.88670	−	3.88670i	0.130136	−	0.130136i
$893$	−15.8876	+	15.8876i	−0.531660	+	0.531660i
$894$	−15.1163	−	1.20991i	−0.505566	−	0.0404654i
$895$	6.63037	−	11.5535i	0.221629	−	0.386190i
$896$			2.21607i			0.0740338i
$897$	3.48338	−	2.96708i	0.116307	−	0.0990681i
$898$	14.8692	+	14.8692i	0.496191	+	0.496191i
$899$	−4.57001			−0.152418
$900$	−5.41116	−	13.9900i	−0.180372	−	0.466332i
$901$	51.4502			1.71406
$902$	−19.6011	−	19.6011i	−0.652646	−	0.652646i
$903$	36.4302	−	31.0307i	1.21232	−	1.03264i
$904$			12.7919i			0.425452i
$905$	1.61739	−	2.81831i	0.0537637	−	0.0936838i
$906$	3.46096	+	0.277014i	0.114983	+	0.00920317i
$907$	−21.1041	+	21.1041i	−0.700749	+	0.700749i	−0.964571	−	0.263822i	$-0.915017\pi$
$907$	−21.1041	+	21.1041i	−0.700749	+	0.700749i	0.263822	+	0.964571i	$0.415017\pi$
$908$	−17.3335	+	17.3335i	−0.575231	+	0.575231i
$909$	−11.5184	−	1.85575i	−0.382041	−	0.0615513i
$910$	12.6360	−	3.42109i	0.418880	−	0.113408i
$911$			23.5758i			0.781101i	0.920581	+	0.390551i	$0.127715\pi$
$911$			23.5758i			0.781101i	−0.920581	+	0.390551i	$0.872285\pi$
$912$	4.44569	+	5.21927i	0.147212	+	0.172827i
$913$	−61.8868	−	61.8868i	−2.04815	−	2.04815i
$914$	21.7209			0.718465
$915$	−3.36749	−	18.0411i	−0.111326	−	0.596421i
$916$	7.33027			0.242199
$917$	32.0714	+	32.0714i	1.05909	+	1.05909i
$918$	−30.6503	+	18.6147i	−1.01161	+	0.614378i
$919$			19.1951i			0.633186i	0.948561	+	0.316593i	$0.102539\pi$
$919$			19.1951i			0.633186i	−0.948561	+	0.316593i	$0.897461\pi$
$920$	1.93940	+	1.11299i	0.0639400	+	0.0366942i
$921$	1.58783	−	19.8380i	0.0523207	−	0.653684i
$922$	−23.7072	+	23.7072i	−0.780756	+	0.780756i
$923$	7.98529	−	7.98529i	0.262839	−	0.262839i
$924$	−1.73724	+	21.7048i	−0.0571512	+	0.714035i
$925$	19.9961	+	5.24652i	0.657467	+	0.172505i
$926$		−	32.4556i		−	1.06656i
$927$	26.5986	−	19.2172i	0.873614	−	0.631175i
$928$	−0.505266	−	0.505266i	−0.0165862	−	0.0165862i
$929$	−12.8738			−0.422374			−0.211187	−	0.977446i	$-0.567733\pi$
$929$	−12.8738			−0.422374			−0.211187	+	0.977446i	$0.567733\pi$
$930$	14.0039	−	20.4315i	0.459208	−	0.669977i
$931$	8.26900			0.271006
$932$	5.63455	+	5.63455i	0.184566	+	0.184566i
$933$	−14.3648	−	16.8644i	−0.470282	−	0.552114i
$934$		−	24.6898i		−	0.807875i
$935$	−22.8773	−	84.4989i	−0.748168	−	2.76341i
$936$	1.26062	−	7.82454i	0.0412048	−	0.255753i
$937$	−11.4449	+	11.4449i	−0.373888	+	0.373888i	−0.868891	−	0.495003i	$-0.835167\pi$
$937$	−11.4449	+	11.4449i	−0.373888	+	0.373888i	0.495003	+	0.868891i	$0.335167\pi$
$938$	−13.3609	+	13.3609i	−0.436249	+	0.436249i
$939$	−9.68137	−	0.774894i	−0.315939	−	0.0252877i
$940$	3.31697	+	12.2514i	0.108188	+	0.399598i
$941$			51.9983i			1.69509i	0.530720	+	0.847547i	$0.321922\pi$
$941$			51.9983i			1.69509i	−0.530720	+	0.847547i	$0.678078\pi$
$942$	21.7796	−	18.5515i	0.709617	−	0.604440i
$943$	−3.45528	−	3.45528i	−0.112519	−	0.112519i
$944$	−7.32082			−0.238272
$945$	17.7499	−	18.6527i	0.577406	−	0.606772i
$946$	70.7255			2.29949
$947$	−23.8469	−	23.8469i	−0.774920	−	0.774920i	0.204042	−	0.978962i	$-0.434592\pi$
$947$	−23.8469	−	23.8469i	−0.774920	−	0.774920i	−0.978962	+	0.204042i	$0.934592\pi$
$948$	9.59051	−	8.16904i	0.311485	−	0.265318i
$949$		−	19.1880i		−	0.622869i
$950$	19.1436	+	5.02286i	0.621102	+	0.162963i
$951$	1.14715	+	0.0918173i	0.0371988	+	0.00297738i
$952$	10.8143	−	10.8143i	0.350494	−	0.350494i
$953$	−18.3582	+	18.3582i	−0.594681	+	0.594681i	−0.938892	−	0.344211i	$-0.888146\pi$
$953$	−18.3582	+	18.3582i	−0.594681	+	0.594681i	0.344211	+	0.938892i	$0.388146\pi$
$954$	−3.55747	+	22.0808i	−0.115177	+	0.714892i
$955$	35.3041	+	20.2605i	1.14241	+	0.655615i
$956$		−	2.57538i		−	0.0832938i
$957$	−4.55261	−	5.34479i	−0.147165	−	0.172773i
$958$	−11.5317	−	11.5317i	−0.372573	−	0.372573i
$959$	−14.4049			−0.465159
$960$	3.80723	−	0.710643i	0.122878	−	0.0229359i
$961$	9.90392			0.319481
$962$	7.72357	+	7.72357i	0.249018	+	0.249018i
$963$	−21.1624	+	15.2895i	−0.681948	+	0.492699i
$964$			19.0373i			0.613150i
$965$	−49.2137	+	13.3242i	−1.58424	+	0.428920i
$966$	−0.306241	+	3.82612i	−0.00985315	+	0.123103i
$967$	−29.3113	+	29.3113i	−0.942589	+	0.942589i	−0.998439	−	0.0558497i	$-0.982213\pi$
$967$	−29.3113	+	29.3113i	−0.942589	+	0.942589i	0.0558497	+	0.998439i	$0.482213\pi$
$968$	−14.9770	+	14.9770i	−0.481378	+	0.481378i
$969$	3.77503	−	47.1645i	0.121271	−	1.51514i
$970$	−0.487681	+	0.849789i	−0.0156585	+	0.0272851i
$971$			53.4861i			1.71645i	0.513273	+	0.858225i	$0.328433\pi$
$971$			53.4861i			1.71645i	−0.513273	+	0.858225i	$0.671567\pi$
$972$	−5.86957	−	14.4412i	−0.188267	−	0.463202i
$973$	6.16763	+	6.16763i	0.197725	+	0.197725i
$974$	17.8308			0.571334
$975$	−9.92953	−	20.6117i	−0.317999	−	0.660103i
$976$	4.73865			0.151680
$977$	4.86247	+	4.86247i	0.155564	+	0.155564i	0.780598	−	0.625034i	$-0.214915\pi$
$977$	4.86247	+	4.86247i	0.155564	+	0.155564i	−0.625034	+	0.780598i	$0.714915\pi$
$978$	−11.7934	−	13.8456i	−0.377113	−	0.442733i
$979$		−	45.7664i		−	1.46270i
$980$	2.32505	−	4.05143i	0.0742711	−	0.129418i
$981$	−24.7245	−	3.98340i	−0.789392	−	0.127180i
$982$	20.6083	−	20.6083i	0.657638	−	0.657638i
$983$	−34.9716	+	34.9716i	−1.11542	+	1.11542i	−0.123018	+	0.992404i	$0.539257\pi$
$983$	−34.9716	+	34.9716i	−1.11542	+	1.11542i	−0.992404	+	0.123018i	$0.960743\pi$
$984$	−8.43670	−	0.675271i	−0.268952	−	0.0215268i
$985$	55.4820	−	15.0212i	1.76780	−	0.478616i
$986$			4.93134i			0.157046i
$987$	−16.5862	+	14.1278i	−0.527943	+	0.449694i
$988$	7.39432	+	7.39432i	0.235245	+	0.235245i
$989$	12.4675			0.396443
$990$	37.8460	−	3.97562i	1.20283	−	0.126354i
$991$	54.1306			1.71951			0.859757	−	0.510703i	$-0.170615\pi$
$991$	54.1306			1.71951			0.859757	+	0.510703i	$0.170615\pi$
$992$	4.52238	+	4.52238i	0.143586	+	0.143586i
$993$	−27.8659	+	23.7357i	−0.884297	+	0.753230i
$994$			9.47301i			0.300466i
$995$	−1.19734	−	0.687136i	−0.0379583	−	0.0217837i
$996$	−26.6373	−	2.13204i	−0.844034	−	0.0675562i
$997$	14.8147	−	14.8147i	0.469187	−	0.469187i	−0.432464	−	0.901651i	$-0.642356\pi$
$997$	14.8147	−	14.8147i	0.469187	−	0.469187i	0.901651	+	0.432464i	$0.142356\pi$
$998$	−1.87129	+	1.87129i	−0.0592347	+	0.0592347i
$999$	20.8701	+	5.09861i	0.660302	+	0.161313i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.i.e.323.6	yes	32
3.2	odd	2	inner	690.2.i.e.323.10	yes	32
5.2	odd	4	inner	690.2.i.e.47.10	yes	32
15.2	even	4	inner	690.2.i.e.47.6	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.i.e.47.6	✓	32	15.2	even	4	inner
690.2.i.e.47.10	yes	32	5.2	odd	4	inner
690.2.i.e.323.6	yes	32	1.1	even	1	trivial
690.2.i.e.323.10	yes	32	3.2	odd	2	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(1.31856 - 1.12312i) q^{3} +1.00000i q^{4} +(-1.11299 + 1.93940i) q^{5} +(-1.72653 - 0.138191i) q^{6} +(1.56700 - 1.56700i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.477181 - 2.96181i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(1.31856 - 1.12312i) q^{3} +1.00000i q^{4} +(-1.11299 + 1.93940i) q^{5} +(-1.72653 - 0.138191i) q^{6} +(1.56700 - 1.56700i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.477181 - 2.96181i) q^{9} +(2.15836 - 0.584357i) q^{10} +5.67280i q^{11} +(1.12312 + 1.31856i) q^{12} +(1.86804 + 1.86804i) q^{13} -2.21607 q^{14} +(0.710643 + 3.80723i) q^{15} -1.00000 q^{16} +(4.87994 + 4.87994i) q^{17} +(-2.43173 + 1.75690i) q^{18} -3.95832i q^{19} +(-1.93940 - 1.11299i) q^{20} +(0.306241 - 3.82612i) q^{21} +(4.01127 - 4.01127i) q^{22} +(0.707107 - 0.707107i) q^{23} +(0.138191 - 1.72653i) q^{24} +(-2.52251 - 4.31705i) q^{25} -2.64181i q^{26} +(-2.69729 - 4.44124i) q^{27} +(1.56700 + 1.56700i) q^{28} -0.714554 q^{29} +(2.18962 - 3.19462i) q^{30} +6.39562 q^{31} +(0.707107 + 0.707107i) q^{32} +(6.37126 + 7.47990i) q^{33} -6.90128i q^{34} +(1.29498 + 4.78309i) q^{35} +(2.96181 + 0.477181i) q^{36} +(-2.92359 + 2.92359i) q^{37} +(-2.79896 + 2.79896i) q^{38} +(4.56117 + 0.365074i) q^{39} +(0.584357 + 2.15836i) q^{40} -4.88651i q^{41} +(-2.92202 + 2.48893i) q^{42} +(8.81584 + 8.81584i) q^{43} -5.67280 q^{44} +(5.21302 + 4.22190i) q^{45} -1.00000 q^{46} +(-4.01373 - 4.01373i) q^{47} +(-1.31856 + 1.12312i) q^{48} +2.08902i q^{49} +(-1.26894 + 4.83630i) q^{50} +(11.9153 + 0.953694i) q^{51} +(-1.86804 + 1.86804i) q^{52} +(5.27160 - 5.27160i) q^{53} +(-1.23316 + 5.04770i) q^{54} +(-11.0018 - 6.31377i) q^{55} -2.21607i q^{56} +(-4.44569 - 5.21927i) q^{57} +(0.505266 + 0.505266i) q^{58} +7.32082 q^{59} +(-3.80723 + 0.710643i) q^{60} -4.73865 q^{61} +(-4.52238 - 4.52238i) q^{62} +(-3.89341 - 5.38890i) q^{63} -1.00000i q^{64} +(-5.70199 + 1.54376i) q^{65} +(0.783929 - 9.79425i) q^{66} +(6.02909 - 6.02909i) q^{67} +(-4.87994 + 4.87994i) q^{68} +(0.138191 - 1.72653i) q^{69} +(2.46647 - 4.29784i) q^{70} -4.27468i q^{71} +(-1.75690 - 2.43173i) q^{72} +(-5.13585 - 5.13585i) q^{73} +4.13458 q^{74} +(-8.17466 - 2.85919i) q^{75} +3.95832 q^{76} +(8.88928 + 8.88928i) q^{77} +(-2.96708 - 3.48338i) q^{78} -7.27349i q^{79} +(1.11299 - 1.93940i) q^{80} +(-8.54460 - 2.82664i) q^{81} +(-3.45528 + 3.45528i) q^{82} +(-10.9094 + 10.9094i) q^{83} +(3.82612 + 0.306241i) q^{84} +(-14.8955 + 4.03281i) q^{85} -12.4675i q^{86} +(-0.942179 + 0.802533i) q^{87} +(4.01127 + 4.01127i) q^{88} -8.06770 q^{89} +(-0.700822 - 6.67150i) q^{90} +5.85445 q^{91} +(0.707107 + 0.707107i) q^{92} +(8.43298 - 7.18308i) q^{93} +5.67627i q^{94} +(7.67675 + 4.40558i) q^{95} +(1.72653 + 0.138191i) q^{96} +(-0.309834 + 0.309834i) q^{97} +(1.47716 - 1.47716i) q^{98} +(16.8017 + 2.70695i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{3} - 4 q^{6} - 8 q^{7}+O(q^{10}) \) 32 * q + 4 * q^3 - 4 * q^6 - 8 * q^7	\( 32 q + 4 q^{3} - 4 q^{6} - 8 q^{7} - 8 q^{10} - 4 q^{12} - 4 q^{15} - 32 q^{16} + 8 q^{18} - 32 q^{21} - 8 q^{22} + 4 q^{27} - 8 q^{28} + 20 q^{30} - 24 q^{31} + 20 q^{36} - 32 q^{37} - 16 q^{40} + 8 q^{42} + 144 q^{43} + 36 q^{45} - 32 q^{46} - 4 q^{48} + 12 q^{51} - 64 q^{55} + 52 q^{57} + 16 q^{58} + 4 q^{60} - 24 q^{61} - 116 q^{63} + 12 q^{66} - 16 q^{67} - 80 q^{70} - 8 q^{72} + 40 q^{73} + 44 q^{75} + 24 q^{76} - 36 q^{78} - 108 q^{81} - 32 q^{82} - 80 q^{85} + 68 q^{87} - 8 q^{88} + 16 q^{90} + 120 q^{91} + 12 q^{93} + 4 q^{96} - 8 q^{97}+O(q^{100}) \) 32 * q + 4 * q^3 - 4 * q^6 - 8 * q^7 - 8 * q^10 - 4 * q^12 - 4 * q^15 - 32 * q^16 + 8 * q^18 - 32 * q^21 - 8 * q^22 + 4 * q^27 - 8 * q^28 + 20 * q^30 - 24 * q^31 + 20 * q^36 - 32 * q^37 - 16 * q^40 + 8 * q^42 + 144 * q^43 + 36 * q^45 - 32 * q^46 - 4 * q^48 + 12 * q^51 - 64 * q^55 + 52 * q^57 + 16 * q^58 + 4 * q^60 - 24 * q^61 - 116 * q^63 + 12 * q^66 - 16 * q^67 - 80 * q^70 - 8 * q^72 + 40 * q^73 + 44 * q^75 + 24 * q^76 - 36 * q^78 - 108 * q^81 - 32 * q^82 - 80 * q^85 + 68 * q^87 - 8 * q^88 + 16 * q^90 + 120 * q^91 + 12 * q^93 + 4 * q^96 - 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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