LMFDB - Embedded newform 690.2.i.e.47.10

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			47.10
Character	$\chi$	$=$	690.47
Dual form			690.2.i.e.323.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-1.12312 - 1.31856i) q^{3} -1.00000i q^{4} +(1.11299 + 1.93940i) q^{5} +(-1.72653 - 0.138191i) q^{6} +(1.56700 + 1.56700i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.477181 + 2.96181i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-1.12312 - 1.31856i) 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} +(-1.31856 + 1.12312i) q^{12} +(1.86804 - 1.86804i) q^{13} +2.21607 q^{14} +(1.30717 - 3.64572i) q^{15} -1.00000 q^{16} +(-4.87994 + 4.87994i) q^{17} +(1.75690 + 2.43173i) 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} +(4.44124 - 2.69729i) q^{27} +(1.56700 - 1.56700i) q^{28} +0.714554 q^{29} +(-1.65360 - 3.50223i) q^{30} +6.39562 q^{31} +(-0.707107 + 0.707107i) q^{32} +(7.47990 - 6.37126i) 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} +(-2.48893 - 2.92202i) q^{42} +(8.81584 - 8.81584i) q^{43} +5.67280 q^{44} +(-6.27521 + 2.37102i) q^{45} -1.00000 q^{46} +(4.01373 - 4.01373i) q^{47} +(1.12312 + 1.31856i) 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} +(5.21927 - 4.44569i) q^{57} +(0.505266 - 0.505266i) q^{58} -7.32082 q^{59} +(-3.64572 - 1.30717i) q^{60} -4.73865 q^{61} +(4.52238 - 4.52238i) q^{62} +(-5.38890 + 3.89341i) 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} +(2.43173 - 1.75690i) q^{72} +(-5.13585 + 5.13585i) q^{73} -4.13458 q^{74} +(8.52537 - 1.52252i) q^{75} +3.95832 q^{76} +(-8.88928 + 8.88928i) q^{77} +(-3.48338 + 2.96708i) 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} +(-0.802533 - 0.942179i) q^{87} +(4.01127 - 4.01127i) q^{88} +8.06770 q^{89} +(-2.76068 + 6.11381i) q^{90} +5.85445 q^{91} +(-0.707107 + 0.707107i) q^{92} +(-7.18308 - 8.43298i) 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 $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

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

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
$3$	−1.12312	−	1.31856i	−0.648436	−	0.761269i
$3$	−1.12312	−	1.31856i	−0.648436	−	0.761269i
$4$		−	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	0.938244	−	0.345974i	$-0.112451\pi$
$7$	1.56700	+	1.56700i	0.592271	+	0.592271i	−0.345974	+	0.938244i	$0.612451\pi$
$8$	−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	$0.673430\pi$
$12$	−1.31856	+	1.12312i	−0.380634	+	0.324218i
$13$	1.86804	−	1.86804i	0.518102	−	0.518102i	−0.398895	−	0.916997i	$-0.630606\pi$
$13$	1.86804	−	1.86804i	0.518102	−	0.518102i	0.916997	+	0.398895i	$0.130606\pi$
$14$	2.21607			0.592271
$15$	1.30717	−	3.64572i	0.337511	−	0.941322i
$16$	−1.00000			−0.250000
$17$	−4.87994	+	4.87994i	−1.18356	+	1.18356i	−0.204744	+	0.978816i	$0.565636\pi$
$17$	−4.87994	+	4.87994i	−1.18356	+	1.18356i	−0.978816	+	0.204744i	$0.934364\pi$
$18$	1.75690	+	2.43173i	0.414104	+	0.573165i
$19$			3.95832i			0.908102i	0.890976	+	0.454051i	$0.150022\pi$
$19$			3.95832i			0.908102i	−0.890976	+	0.454051i	$0.849978\pi$
$20$	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
$27$	4.44124	−	2.69729i	0.854718	−	0.519093i
$28$	1.56700	−	1.56700i	0.296135	−	0.296135i
$29$	0.714554			0.132689			0.0663447	−	0.997797i	$-0.478866\pi$
$29$	0.714554			0.132689			0.0663447	+	0.997797i	$0.478866\pi$
$30$	−1.65360	−	3.50223i	−0.301905	−	0.639416i
$31$	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
$33$	7.47990	−	6.37126i	1.30208	−	1.10909i
$34$			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	0.424699	−	0.905334i	$-0.360380\pi$
$37$	−2.92359	−	2.92359i	−0.480635	−	0.480635i	−0.905334	+	0.424699i	$0.860380\pi$
$38$	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	$-0.124617\pi$
$42$	−2.48893	−	2.92202i	−0.384050	−	0.450877i
$43$	8.81584	−	8.81584i	1.34440	−	1.34440i	0.452782	−	0.891621i	$-0.350431\pi$
$43$	8.81584	−	8.81584i	1.34440	−	1.34440i	0.891621	−	0.452782i	$-0.149569\pi$
$44$	5.67280			0.855207
$45$	−6.27521	+	2.37102i	−0.935453	+	0.353450i
$46$	−1.00000			−0.147442
$47$	4.01373	−	4.01373i	0.585462	−	0.585462i	−0.350937	−	0.936399i	$-0.614137\pi$
$47$	4.01373	−	4.01373i	0.585462	−	0.585462i	0.936399	+	0.350937i	$0.114137\pi$
$48$	1.12312	+	1.31856i	0.162109	+	0.190317i
$49$		−	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	$-0.421104\pi$
$53$	−5.27160	−	5.27160i	−0.724111	−	0.724111i	−0.969440	+	0.245329i	$0.921104\pi$
$54$	1.23316	−	5.04770i	0.167812	−	0.686905i
$55$	−11.0018	+	6.31377i	−1.48348	+	0.851348i
$56$		−	2.21607i		−	0.296135i
$57$	5.21927	−	4.44569i	0.691310	−	0.588846i
$58$	0.505266	−	0.505266i	0.0663447	−	0.0663447i
$59$	−7.32082			−0.953089			−0.476545	−	0.879150i	$-0.658111\pi$
$59$	−7.32082			−0.953089			−0.476545	+	0.879150i	$0.658111\pi$
$60$	−3.64572	−	1.30717i	−0.470661	−	0.168756i
$61$	−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
$63$	−5.38890	+	3.89341i	−0.678937	+	0.490524i
$64$			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	0.971913	−	0.235342i	$-0.0756210\pi$
$67$	6.02909	+	6.02909i	0.736571	+	0.736571i	−0.235342	+	0.971913i	$0.575621\pi$
$68$	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	$-0.0816330\pi$
$72$	2.43173	−	1.75690i	0.286582	−	0.207052i
$73$	−5.13585	+	5.13585i	−0.601106	+	0.601106i	−0.940606	−	0.339500i	$-0.889742\pi$
$73$	−5.13585	+	5.13585i	−0.601106	+	0.601106i	0.339500	+	0.940606i	$0.389742\pi$
$74$	−4.13458			−0.480635
$75$	8.52537	−	1.52252i	0.984425	−	0.175806i
$76$	3.95832			0.454051
$77$	−8.88928	+	8.88928i	−1.01303	+	1.01303i
$78$	−3.48338	+	2.96708i	−0.394415	+	0.335956i
$79$			7.27349i			0.818332i	0.912460	+	0.409166i	$0.134180\pi$
$79$			7.27349i			0.818332i	−0.912460	+	0.409166i	$0.865820\pi$
$80$	−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	0.974924	+	0.222537i	$0.0714339\pi$
$83$	10.9094	+	10.9094i	1.19746	+	1.19746i	0.222537	+	0.974924i	$0.428566\pi$
$84$	−3.82612	−	0.306241i	−0.417464	−	0.0334137i
$85$	−14.8955	−	4.03281i	−1.61564	−	0.437420i
$86$		−	12.4675i		−	1.34440i
$87$	−0.802533	−	0.942179i	−0.0860406	−	0.101012i
$88$	4.01127	−	4.01127i	0.427603	−	0.427603i
$89$	8.06770			0.855175			0.427587	−	0.903974i	$-0.359364\pi$
$89$	8.06770			0.855175			0.427587	+	0.903974i	$0.359364\pi$
$90$	−2.76068	+	6.11381i	−0.291001	+	0.644452i
$91$	5.85445			0.613713
$92$	−0.707107	+	0.707107i	−0.0737210	+	0.0737210i
$93$	−7.18308	−	8.43298i	−0.744850	−	0.874459i
$94$		−	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	0.691202	−	0.722661i	$-0.257081\pi$
$97$	−0.309834	−	0.309834i	−0.0314589	−	0.0314589i	−0.722661	+	0.691202i	$0.757081\pi$
$98$	−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	$-0.0619787\pi$
$102$	9.09972	−	7.75100i	0.901007	−	0.767463i
$103$	7.73444	−	7.73444i	0.762097	−	0.762097i	−0.214604	−	0.976701i	$-0.568846\pi$
$103$	7.73444	−	7.73444i	0.762097	−	0.762097i	0.976701	+	0.214604i	$0.0688462\pi$
$104$	−2.64181			−0.259051
$105$	7.76120	−	3.66451i	0.757415	−	0.357619i
$106$	−7.45518			−0.724111
$107$	6.15366	−	6.15366i	0.594897	−	0.594897i	−0.344053	−	0.938950i	$-0.611800\pi$
$107$	6.15366	−	6.15366i	0.594897	−	0.594897i	0.938950	+	0.344053i	$0.111800\pi$
$108$	−2.69729	−	4.44124i	−0.259547	−	0.427359i
$109$			8.34777i			0.799571i	0.916609	+	0.399786i	$0.130915\pi$
$109$			8.34777i			0.799571i	−0.916609	+	0.399786i	$0.869085\pi$
$110$	−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	$-0.0444982\pi$
$113$	9.04524	+	9.04524i	0.850904	+	0.850904i	−0.139340	+	0.990245i	$0.544498\pi$
$114$	0.547004	−	6.83416i	0.0512316	−	0.640078i
$115$	0.584357	−	2.15836i	0.0544915	−	0.201268i
$116$		−	0.714554i		−	0.0663447i
$117$	4.64139	+	6.42418i	0.429096	+	0.593915i
$118$	−5.17660	+	5.17660i	−0.476545	+	0.476545i
$119$	−15.2937			−1.40198
$120$	−3.50223	+	1.65360i	−0.319708	+	0.150953i
$121$	−21.1806			−1.92551
$122$	−3.35073	+	3.35073i	−0.303361	+	0.303361i
$123$	−6.44314	+	5.48816i	−0.580958	+	0.494851i
$124$		−	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	0.358899	−	0.933376i	$-0.383152\pi$
$127$	−6.47403	−	6.47403i	−0.574477	−	0.574477i	−0.933376	+	0.358899i	$0.883152\pi$
$128$	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	$0.647821\pi$
$132$	−6.37126	−	7.47990i	−0.554547	−	0.651042i
$133$	−6.20270	+	6.20270i	−0.537842	+	0.537842i
$134$	8.52642			0.736571
$135$	10.1742	+	5.61127i	0.875653	+	0.482941i
$136$	6.90128			0.591780
$137$	4.59633	−	4.59633i	0.392691	−	0.392691i	−0.482954	−	0.875646i	$-0.660436\pi$
$137$	4.59633	−	4.59633i	0.392691	−	0.392691i	0.875646	+	0.482954i	$0.160436\pi$
$138$	1.12312	+	1.31856i	0.0956067	+	0.112243i
$139$		−	3.93595i		−	0.333843i	−0.985970	−	0.166921i	$-0.946617\pi$
$139$		−	3.93595i		−	0.333843i	0.985970	−	0.166921i	$-0.0533826\pi$
$140$	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
$147$	−2.75448	+	2.34622i	−0.227186	+	0.193513i
$148$	−2.92359	+	2.92359i	−0.240318	+	0.240318i
$149$	−8.75534			−0.717265			−0.358633	−	0.933479i	$-0.616757\pi$
$149$	−8.75534			−0.717265			−0.358633	+	0.933479i	$0.616757\pi$
$150$	4.95176	−	7.10493i	0.404309	−	0.580115i
$151$	−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
$153$	−12.1248	−	16.7821i	−0.980234	−	1.35675i
$154$			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	0.0656901	−	0.997840i	$-0.479075\pi$
$157$	−11.6798	−	11.6798i	−0.932150	−	0.932150i	−0.997840	+	0.0656901i	$0.979075\pi$
$158$	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
$162$	−8.04068	+	4.04321i	−0.631735	+	0.317664i
$163$	7.42502	−	7.42502i	0.581572	−	0.581572i	−0.353763	−	0.935335i	$-0.615098\pi$
$163$	7.42502	−	7.42502i	0.581572	−	0.581572i	0.935335	+	0.353763i	$0.115098\pi$
$164$	−4.88651			−0.381572
$165$	20.6814	+	7.41534i	1.61005	+	0.577283i
$166$	15.4282			1.19746
$167$	16.1431	−	16.1431i	1.24919	−	1.24919i	0.293107	−	0.956080i	$-0.405311\pi$
$167$	16.1431	−	16.1431i	1.24919	−	1.24919i	0.956080	−	0.293107i	$-0.0946894\pi$
$168$	−2.92202	+	2.48893i	−0.225439	+	0.192025i
$169$			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	$-0.160289\pi$
$173$	5.17329	+	5.17329i	0.393318	+	0.393318i	−0.482550	+	0.875868i	$0.660289\pi$
$174$	−1.23370	−	0.0987448i	−0.0935264	−	0.00748583i
$175$	−10.7176	+	2.81206i	−0.810174	+	0.212572i
$176$		−	5.67280i		−	0.427603i
$177$	8.22219	+	9.65291i	0.618018	+	0.725557i
$178$	5.70473	−	5.70473i	0.427587	−	0.427587i
$179$	5.95726			0.445266			0.222633	−	0.974902i	$-0.428535\pi$
$179$	5.95726			0.445266			0.222633	+	0.974902i	$0.428535\pi$
$180$	2.37102	+	6.27521i	0.176725	+	0.467727i
$181$	−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
$183$	5.32209	+	6.24818i	0.393421	+	0.461878i
$184$			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	$-0.228845\pi$
$192$	1.31856	−	1.12312i	0.0951586	−	0.0810546i
$193$	16.1230	−	16.1230i	1.16056	−	1.16056i	0.176208	−	0.984353i	$-0.443617\pi$
$193$	16.1230	−	16.1230i	1.16056	−	1.16056i	0.984353	−	0.176208i	$-0.0563830\pi$
$194$	−0.438172			−0.0314589
$195$	−4.36851	−	9.25223i	−0.312835	−	0.662566i
$196$	−2.08902			−0.149215
$197$	18.1766	−	18.1766i	1.29503	−	1.29503i	0.363393	−	0.931636i	$-0.381618\pi$
$197$	18.1766	−	18.1766i	1.29503	−	1.29503i	0.931636	−	0.363393i	$-0.118382\pi$
$198$	−13.7947	+	9.96651i	−0.980348	+	0.708289i
$199$		−	0.617379i		−	0.0437648i	−0.999761	−	0.0218824i	$-0.993034\pi$
$199$		−	0.617379i		−	0.0437648i	0.999761	−	0.0218824i	$-0.00696594\pi$
$200$	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
$207$	2.43173	−	1.75690i	0.169017	−	0.122113i
$208$	−1.86804	+	1.86804i	−0.129525	+	0.129525i
$209$	−22.4548			−1.55323
$210$	2.89680	−	8.07919i	0.199898	−	0.557517i
$211$	−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
$213$	−5.63641	+	4.80100i	−0.386200	+	0.328959i
$214$		−	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
$222$	4.64365	+	5.45168i	0.311661	+	0.365892i
$223$	−3.88670	+	3.88670i	−0.260273	+	0.260273i	−0.825165	−	0.564892i	$-0.808918\pi$
$223$	−3.88670	+	3.88670i	−0.260273	+	0.260273i	0.564892	+	0.825165i	$0.308918\pi$
$224$	−2.21607			−0.148068
$225$	−11.5826	−	9.53119i	−0.772172	−	0.635413i
$226$	12.7919			0.850904
$227$	−17.3335	+	17.3335i	−1.15046	+	1.15046i	−0.164003	+	0.986460i	$0.552441\pi$
$227$	−17.3335	+	17.3335i	−1.15046	+	1.15046i	−0.986460	+	0.164003i	$0.947559\pi$
$228$	−4.44569	−	5.21927i	−0.294423	−	0.345655i
$229$			7.33027i			0.484398i	0.970227	+	0.242199i	$0.0778687\pi$
$229$			7.33027i			0.484398i	−0.970227	+	0.242199i	$0.922131\pi$
$230$	−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	$-0.334057\pi$
$233$	−5.63455	−	5.63455i	−0.369131	−	0.369131i	−0.867160	+	0.498029i	$0.834057\pi$
$234$	7.82454	+	1.26062i	0.511506	+	0.0824095i
$235$	12.2514	+	3.31697i	0.799196	+	0.216375i
$236$			7.32082i			0.476545i
$237$	9.59051	−	8.16904i	0.622971	−	0.530636i
$238$	−10.8143	+	10.8143i	−0.700988	+	0.700988i
$239$	2.57538			0.166588			0.0832938	−	0.996525i	$-0.473456\pi$
$239$	2.57538			0.166588			0.0832938	+	0.996525i	$0.473456\pi$
$240$	−1.30717	+	3.64572i	−0.0843778	+	0.235330i
$241$	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
$243$	5.86957	+	14.4412i	0.376533	+	0.926403i
$244$			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	$-0.0407907\pi$
$252$	3.89341	+	5.38890i	0.245262	+	0.339469i
$253$	4.01127	−	4.01127i	0.252187	−	0.252187i
$254$	−9.15566			−0.574477
$255$	11.4120	+	24.1698i	0.714646	+	1.51357i
$256$	1.00000			0.0625000
$257$	−4.10051	+	4.10051i	−0.255783	+	0.255783i	−0.823336	−	0.567554i	$-0.807890\pi$
$257$	−4.10051	+	4.10051i	−0.255783	+	0.255783i	0.567554	+	0.823336i	$0.307890\pi$
$258$	−16.4391	+	14.0025i	−1.02345	+	0.871760i
$259$		−	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	$-0.0564253\pi$
$263$	13.1034	+	13.1034i	0.807991	+	0.807991i	−0.176338	+	0.984330i	$0.556425\pi$
$264$	−9.79425	−	0.783929i	−0.602795	−	0.0482475i
$265$	4.35648	−	16.0910i	0.267617	−	0.988460i
$266$			8.77194i			0.537842i
$267$	−9.06104	−	10.6377i	−0.554526	−	0.651018i
$268$	6.02909	−	6.02909i	0.368285	−	0.368285i
$269$	8.38175			0.511044			0.255522	−	0.966803i	$-0.417753\pi$
$269$	8.38175			0.511044			0.255522	+	0.966803i	$0.417753\pi$
$270$	11.1620	−	3.22646i	0.679297	−	0.196356i
$271$	−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
$273$	−6.57528	−	7.71942i	−0.397954	−	0.467201i
$274$		−	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	0.733982	−	0.679169i	$-0.237660\pi$
$277$	0.912280	+	0.912280i	0.0548136	+	0.0548136i	−0.679169	+	0.733982i	$0.737660\pi$
$278$	−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	$-0.329885\pi$
$282$	−7.48448	+	6.37516i	−0.445694	+	0.379635i
$283$	−17.7013	+	17.7013i	−1.05223	+	1.05223i	−0.0536753	+	0.998558i	$0.517094\pi$
$283$	−17.7013	+	17.7013i	−1.05223	+	1.05223i	−0.998558	+	0.0536753i	$0.982906\pi$
$284$	−4.27468			−0.253656
$285$	14.4310	+	5.17422i	0.854816	+	0.306494i
$286$	14.9865			0.886168
$287$	7.65716	−	7.65716i	0.451988	−	0.451988i
$288$	−1.75690	−	2.43173i	−0.103526	−	0.143291i
$289$		−	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	−0.890313	−	0.455348i	$-0.849515\pi$
$293$	−23.0340	−	23.0340i	−1.34566	−	1.34566i	−0.455348	−	0.890313i	$-0.650485\pi$
$294$	−0.288683	+	3.60675i	−0.0168363	+	0.210350i
$295$	−8.14799	−	14.1980i	−0.474395	−	0.826637i
$296$			4.13458i			0.240318i
$297$	15.3012	+	25.1943i	0.887864	+	1.46192i
$298$	−6.19096	+	6.19096i	−0.358633	+	0.358633i
$299$	−2.64181			−0.152780
$300$	−1.52252	−	8.52537i	−0.0879030	−	0.492212i
$301$	27.6289			1.59250
$302$	−1.41745	+	1.41745i	−0.0815650	+	0.0815650i
$303$	−5.12784	+	4.36781i	−0.294587	+	0.250924i
$304$		−	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	0.899867	−	0.436164i	$-0.143663\pi$
$307$	8.12472	+	8.12472i	0.463702	+	0.463702i	−0.436164	+	0.899867i	$0.643663\pi$
$308$	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	$-0.118120\pi$
$312$	2.96708	+	3.48338i	0.167978	+	0.197207i
$313$	−3.96504	+	3.96504i	−0.224117	+	0.224117i	−0.810230	−	0.586112i	$-0.800658\pi$
$313$	−3.96504	+	3.96504i	−0.224117	+	0.224117i	0.586112	+	0.810230i	$0.300658\pi$
$314$	−16.5177			−0.932150
$315$	−13.5487	−	6.11787i	−0.763380	−	0.344703i
$316$	7.27349			0.409166
$317$	−0.469818	+	0.469818i	−0.0263876	+	0.0263876i	−0.720177	−	0.693790i	$-0.755940\pi$
$317$	−0.469818	+	0.469818i	−0.0263876	+	0.0263876i	0.693790	+	0.720177i	$0.255940\pi$
$318$	8.37309	+	9.83007i	0.469540	+	0.551243i
$319$			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
$327$	11.0070	−	9.37559i	0.608689	−	0.518471i
$328$	−3.45528	+	3.45528i	−0.190786	+	0.190786i
$329$	12.5790			0.693505
$330$	19.8674	−	9.38056i	1.09367	−	0.516383i
$331$	−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
$333$	10.0542	−	7.26402i	0.550966	−	0.398066i
$334$		−	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	0.938183	−	0.346138i	$-0.112507\pi$
$337$	10.8685	+	10.8685i	0.592045	+	0.592045i	−0.346138	+	0.938183i	$0.612507\pi$
$338$	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
$342$	−9.62558	+	6.95436i	−0.520492	+	0.376049i
$343$	14.2425	−	14.2425i	0.769023	−	0.769023i
$344$	−12.4675			−0.672202
$345$	−3.50223	+	1.65360i	−0.188554	+	0.0890270i
$346$	7.31614			0.393318
$347$	−14.4344	+	14.4344i	−0.774878	+	0.774878i	−0.978955	−	0.204077i	$-0.934581\pi$
$347$	−14.4344	+	14.4344i	−0.774878	+	0.774878i	0.204077	+	0.978955i	$0.434581\pi$
$348$	−0.942179	+	0.802533i	−0.0505061	+	0.0430203i
$349$			35.9155i			1.92251i	0.275655	+	0.961257i	$0.411105\pi$
$349$			35.9155i			1.92251i	−0.275655	+	0.961257i	$0.588895\pi$
$350$	−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	$-0.191059\pi$
$353$	4.89196	+	4.89196i	0.260373	+	0.260373i	−0.564833	+	0.825206i	$0.691059\pi$
$354$	12.6396	+	1.01167i	0.671787	+	0.0537697i
$355$	8.29030	−	4.75768i	0.440003	−	0.252511i
$356$		−	8.06770i		−	0.427587i
$357$	17.1768	+	20.1657i	0.909092	+	1.06728i
$358$	4.21242	−	4.21242i	0.222633	−	0.222633i
$359$	32.9343			1.73821			0.869103	−	0.494630i	$-0.164697\pi$
$359$	32.9343			1.73821			0.869103	+	0.494630i	$0.164697\pi$
$360$	6.11381	+	2.76068i	0.322226	+	0.145501i
$361$	3.33167			0.175351
$362$	−1.02756	+	1.02756i	−0.0540074	+	0.0540074i
$363$	23.7885	+	27.9279i	1.24857	+	1.46583i
$364$		−	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	0.108475	−	0.994099i	$-0.465403\pi$
$367$	−16.9661	−	16.9661i	−0.885624	−	0.885624i	−0.994099	+	0.108475i	$0.965403\pi$
$368$	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
$372$	−8.43298	+	7.18308i	−0.437230	+	0.372425i
$373$	−7.20832	+	7.20832i	−0.373233	+	0.373233i	−0.868653	−	0.495420i	$-0.835014\pi$
$373$	−7.20832	+	7.20832i	−0.373233	+	0.373233i	0.495420	+	0.868653i	$0.335014\pi$
$374$	−39.1496			−2.02438
$375$	12.4414	+	14.8395i	0.642472	+	0.766309i
$376$	−5.67627			−0.292731
$377$	1.33482	−	1.33482i	0.0687466	−	0.0687466i
$378$	9.84212	−	5.97739i	0.506224	−	0.307444i
$379$			0.269443i			0.0138404i	0.999976	+	0.00692018i	$0.00220278\pi$
$379$			0.269443i			0.0138404i	−0.999976	+	0.00692018i	$0.997797\pi$
$380$	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	$-0.429449\pi$
$383$	−14.7895	−	14.7895i	−0.755707	−	0.755707i	−0.975538	+	0.219831i	$0.929449\pi$
$384$	0.138191	−	1.72653i	0.00705202	−	0.0881066i
$385$	−27.1335	−	7.34615i	−1.38285	−	0.374394i
$386$		−	22.8014i		−	1.16056i
$387$	21.9041	+	30.3176i	1.11345	+	1.54113i
$388$	−0.309834	+	0.309834i	−0.0157295	+	0.0157295i
$389$	34.0408			1.72594			0.862970	−	0.505256i	$-0.168602\pi$
$389$	34.0408			1.72594			0.862970	+	0.505256i	$0.168602\pi$
$390$	−9.63131	−	3.45331i	−0.487701	−	0.174865i
$391$	6.90128			0.349013
$392$	−1.47716	+	1.47716i	−0.0746077	+	0.0746077i
$393$	26.9866	−	22.9867i	1.36129	−	1.15953i
$394$		−	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	0.978122	−	0.208030i	$-0.0667051\pi$
$397$	15.3440	+	15.3440i	0.770093	+	0.770093i	−0.208030	+	0.978122i	$0.566705\pi$
$398$	−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	$-0.0929078\pi$
$402$	−9.57624	−	11.2426i	−0.477619	−	0.560728i
$403$	11.9473	−	11.9473i	0.595137	−	0.595137i
$404$	−3.88898			−0.193484
$405$	−4.02808	−	19.7174i	−0.200157	−	0.979764i
$406$	1.58350			0.0785880
$407$	16.5849	−	16.5849i	0.822084	−	0.822084i
$408$	−7.75100	−	9.09972i	−0.383732	−	0.450504i
$409$			14.4328i			0.713658i	0.934170	+	0.356829i	$0.116142\pi$
$409$			14.4328i			0.713658i	−0.934170	+	0.356829i	$0.883858\pi$
$410$	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
$417$	−5.18977	+	4.42056i	−0.254144	+	0.216476i
$418$	−15.8779	+	15.8779i	−0.776615	+	0.776615i
$419$	1.59881			0.0781072			0.0390536	−	0.999237i	$-0.487566\pi$
$419$	1.59881			0.0781072			0.0390536	+	0.999237i	$0.487566\pi$
$420$	−3.66451	−	7.76120i	−0.178810	−	0.378708i
$421$	−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
$423$	9.97261	+	13.8032i	0.484885	+	0.671133i
$424$			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	$-0.133808\pi$
$432$	−4.44124	+	2.69729i	−0.213679	+	0.129773i
$433$	−23.5807	+	23.5807i	−1.13321	+	1.13321i	−0.143576	+	0.989639i	$0.545860\pi$
$433$	−23.5807	+	23.5807i	−1.13321	+	1.13321i	−0.989639	+	0.143576i	$0.954140\pi$
$434$	14.1732			0.680334
$435$	0.934047	−	2.60507i	0.0447841	−	0.124903i
$436$	8.34777			0.399786
$437$	2.79896	−	2.79896i	0.133892	−	0.133892i
$438$	9.57693	−	8.15747i	0.457603	−	0.389779i
$439$			18.7018i			0.892590i	0.894886	+	0.446295i	$0.147257\pi$
$439$			18.7018i			0.892590i	−0.894886	+	0.446295i	$0.852743\pi$
$440$	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	$-0.411448\pi$
$443$	−14.4583	−	14.4583i	−0.686934	−	0.686934i	−0.961553	+	0.274619i	$0.911448\pi$
$444$	7.13847	+	0.571361i	0.338777	+	0.0271156i
$445$	8.97927	+	15.6465i	0.425658	+	0.741713i
$446$			5.49662i			0.260273i
$447$	9.83333	+	11.5444i	0.465101	+	0.546031i
$448$	−1.56700	+	1.56700i	−0.0740338	+	0.0740338i
$449$	21.0282			0.992382			0.496191	−	0.868213i	$-0.334732\pi$
$449$	21.0282			0.992382			0.496191	+	0.868213i	$0.334732\pi$
$450$	−14.9297	+	1.45055i	−0.703793	+	0.0683798i
$451$	27.7202			1.30529
$452$	9.04524	−	9.04524i	0.425452	−	0.425452i
$453$	2.25139	+	2.64314i	0.105779	+	0.124186i
$454$			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	0.249826	−	0.968291i	$-0.419627\pi$
$457$	−15.3590	−	15.3590i	−0.718465	−	0.718465i	−0.968291	+	0.249826i	$0.919627\pi$
$458$	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	$-0.285166\pi$
$462$	16.5760	−	14.1192i	0.771186	−	0.656884i
$463$	22.9496	−	22.9496i	1.06656	−	1.06656i	0.0689368	−	0.997621i	$-0.478039\pi$
$463$	22.9496	−	22.9496i	1.06656	−	1.06656i	0.997621	−	0.0689368i	$-0.0219607\pi$
$464$	−0.714554			−0.0331723
$465$	8.36019	−	23.3166i	0.387695	−	1.08128i
$466$	−7.96845			−0.369131
$467$	−17.4583	+	17.4583i	−0.807875	+	0.807875i	−0.984312	−	0.176437i	$-0.943543\pi$
$467$	−17.4583	+	17.4583i	−0.807875	+	0.807875i	0.176437	+	0.984312i	$0.443543\pi$
$468$	6.42418	−	4.64139i	0.296958	−	0.214548i
$469$			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
$477$	18.1290	−	13.0980i	0.830069	−	0.599715i
$478$	1.82107	−	1.82107i	0.0832938	−	0.0832938i
$479$	−16.3083			−0.745147			−0.372573	−	0.928003i	$-0.621525\pi$
$479$	−16.3083			−0.745147			−0.372573	+	0.928003i	$0.621525\pi$
$480$	1.65360	+	3.50223i	0.0754763	+	0.159854i
$481$	−10.9228			−0.498036
$482$	13.4614	−	13.4614i	0.613150	−	0.613150i
$483$	−2.92202	+	2.48893i	−0.132956	+	0.113250i
$484$			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	0.361167	−	0.932501i	$-0.382378\pi$
$487$	−12.6082	−	12.6082i	−0.571334	−	0.571334i	−0.932501	+	0.361167i	$0.882378\pi$
$488$	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	$0.771556\pi$
$492$	5.48816	+	6.44314i	0.247425	+	0.290479i
$493$	−3.48698	+	3.48698i	−0.157046	+	0.157046i
$494$	10.4571			0.470489
$495$	−13.4503	−	35.5980i	−0.604546	−	1.60001i
$496$	−6.39562			−0.287172
$497$	6.69843	−	6.69843i	0.300466	−	0.300466i
$498$	−17.3278	−	20.3430i	−0.776478	−	0.911590i
$499$			2.64641i			0.118469i	0.998244	+	0.0592347i	$0.0188660\pi$
$499$			2.64641i			0.118469i	−0.998244	+	0.0592347i	$0.981134\pi$
$500$	−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	$-0.214642\pi$
$503$	3.51592	+	3.51592i	0.156767	+	0.156767i	−0.624365	+	0.781133i	$0.714642\pi$
$504$	6.56358	+	1.05747i	0.292365	+	0.0471034i
$505$	7.54227	−	4.32839i	0.335626	−	0.192611i
$506$		−	5.67280i		−	0.252187i
$507$	7.93880	−	6.76214i	0.352575	−	0.300317i
$508$	−6.47403	+	6.47403i	−0.287239	+	0.287239i
$509$	−0.570411			−0.0252830			−0.0126415	−	0.999920i	$-0.504024\pi$
$509$	−0.570411			−0.0252830			−0.0126415	+	0.999920i	$0.504024\pi$
$510$	25.1602	+	9.02118i	1.11411	+	0.399465i
$511$	−16.0958			−0.712035
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	10.6767	+	17.5799i	0.471390	+	0.776171i
$514$			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	$-0.167276\pi$
$522$	1.25540	+	1.73760i	0.0549472	+	0.0760528i
$523$	23.8359	−	23.8359i	1.04227	−	1.04227i	0.0432069	−	0.999066i	$-0.486243\pi$
$523$	23.8359	−	23.8359i	1.04227	−	1.04227i	0.999066	−	0.0432069i	$-0.0137575\pi$
$524$	20.4667			0.894094
$525$	15.7451	+	10.9735i	0.687171	+	0.478921i
$526$	18.5310			0.807991
$527$	−31.2102	+	31.2102i	−1.35954	+	1.35954i
$528$	−7.47990	+	6.37126i	−0.325521	+	0.277274i
$529$			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
$537$	−6.69074	−	7.85498i	−0.288727	−	0.338967i
$538$	5.92679	−	5.92679i	0.255522	−	0.255522i
$539$	11.8506			0.510440
$540$	5.61127	−	10.1742i	0.241471	−	0.437826i
$541$	−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
$543$	1.63211	+	1.91611i	0.0700407	+	0.0822283i
$544$		−	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	0.737188	−	0.675688i	$-0.236153\pi$
$547$	1.43836	+	1.43836i	0.0614997	+	0.0614997i	−0.675688	+	0.737188i	$0.736153\pi$
$548$	−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
$552$	1.31856	−	1.12312i	0.0561215	−	0.0478034i
$553$	−11.3976	+	11.3976i	−0.484674	+	0.484674i
$554$	1.29016			0.0548136
$555$	−14.4802	+	6.83695i	−0.614652	+	0.290212i
$556$	−3.93595			−0.166921
$557$	−4.53628	+	4.53628i	−0.192208	+	0.192208i	−0.796650	−	0.604441i	$-0.793396\pi$
$557$	−4.53628	+	4.53628i	−0.192208	+	0.192208i	0.604441	+	0.796650i	$0.293396\pi$
$558$	11.2364	+	15.5524i	0.475676	+	0.658387i
$559$		−	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	$-0.260627\pi$
$563$	−1.12010	−	1.12010i	−0.0472067	−	0.0472067i	−0.730316	+	0.683109i	$0.760627\pi$
$564$	−0.784409	+	9.80025i	−0.0330296	+	0.412665i
$565$	−7.47503	+	27.6095i	−0.314477	+	1.16154i
$566$			25.0334i			1.05223i
$567$	−8.96005	−	17.8187i	−0.376287	−	0.748317i
$568$	−3.02266	+	3.02266i	−0.126828	+	0.126828i
$569$	−22.6299			−0.948693			−0.474347	−	0.880338i	$-0.657316\pi$
$569$	−22.6299			−0.948693			−0.474347	+	0.880338i	$0.657316\pi$
$570$	13.8630	−	6.54550i	0.580655	−	0.274161i
$571$	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
$573$	−24.0026	+	20.4450i	−1.00272	+	0.854102i
$574$		−	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	0.439041	−	0.898467i	$-0.355318\pi$
$577$	−11.0358	−	11.0358i	−0.459427	−	0.459427i	−0.898467	+	0.439041i	$0.855318\pi$
$578$	−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
$582$	0.492122	+	0.577755i	0.0203991	+	0.0239487i
$583$	29.9048	−	29.9048i	1.23853	−	1.23853i
$584$	7.26319			0.300553
$585$	−7.29320	+	16.1515i	−0.301537	+	0.667784i
$586$	−32.5750			−1.34566
$587$	−16.2913	+	16.2913i	−0.672415	+	0.672415i	−0.958272	−	0.285857i	$-0.907722\pi$
$587$	−16.2913	+	16.2913i	−0.672415	+	0.672415i	0.285857	+	0.958272i	$0.407722\pi$
$588$	2.34622	+	2.75448i	0.0967567	+	0.113593i
$589$			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	$-0.489518\pi$
$593$	−23.5367	−	23.5367i	−0.966535	−	0.966535i	−0.999458	+	0.0329233i	$0.989518\pi$
$594$	28.6346	+	6.99548i	1.17489	+	0.287028i
$595$	−17.0218	−	29.6606i	−0.697825	−	1.21597i
$596$			8.75534i			0.358633i
$597$	−0.814049	+	0.693393i	−0.0333168	+	0.0283787i
$598$	−1.86804	+	1.86804i	−0.0763900	+	0.0763900i
$599$	3.05690			0.124901			0.0624507	−	0.998048i	$-0.480108\pi$
$599$	3.05690			0.124901			0.0624507	+	0.998048i	$0.480108\pi$
$600$	−7.10493	−	4.95176i	−0.290058	−	0.202155i
$601$	−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
$603$	−20.7340	+	14.9800i	−0.844353	+	0.610034i
$604$			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	0.600838	−	0.799371i	$-0.294834\pi$
$607$	−4.89133	−	4.89133i	−0.198533	−	0.198533i	−0.799371	+	0.600838i	$0.794834\pi$
$608$	−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
$612$	−16.7821	+	12.1248i	−0.678375	+	0.490117i
$613$	12.5329	−	12.5329i	0.506199	−	0.506199i	−0.407158	−	0.913358i	$-0.633480\pi$
$613$	12.5329	−	12.5329i	0.506199	−	0.506199i	0.913358	+	0.407158i	$0.133480\pi$
$614$	11.4901			0.463702
$615$	−17.8149	−	6.38752i	−0.718364	−	0.257570i
$616$	12.5713			0.506514
$617$	−32.9202	+	32.9202i	−1.32532	+	1.32532i	−0.415916	+	0.909403i	$0.636539\pi$
$617$	−32.9202	+	32.9202i	−1.32532	+	1.32532i	−0.909403	+	0.415916i	$0.863461\pi$
$618$	−14.4226	+	12.2849i	−0.580160	+	0.494171i
$619$			35.6199i			1.43168i	0.698262	+	0.715842i	$0.253957\pi$
$619$			35.6199i			1.43168i	−0.698262	+	0.715842i	$0.746043\pi$
$620$	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
$627$	25.2195	+	29.6079i	1.00717	+	1.18243i
$628$	−11.6798	+	11.6798i	−0.466075	+	0.466075i
$629$	28.5339			1.13772
$630$	−13.9063	+	5.25435i	−0.554042	+	0.209338i
$631$	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
$633$	11.0796	+	13.0075i	0.440373	+	0.517001i
$634$			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	$-0.0145828\pi$
$642$	−11.4749	+	9.77410i	−0.452877	+	0.385753i
$643$	−3.83141	+	3.83141i	−0.151096	+	0.151096i	−0.778607	−	0.627511i	$-0.784074\pi$
$643$	−3.83141	+	3.83141i	−0.151096	+	0.151096i	0.627511	+	0.778607i	$0.284074\pi$
$644$	−2.21607			−0.0873256
$645$	−20.6163	−	43.6640i	−0.811765	−	1.71927i
$646$	−27.3175			−1.07479
$647$	8.83653	−	8.83653i	0.347400	−	0.347400i	−0.511740	−	0.859140i	$-0.670999\pi$
$647$	8.83653	−	8.83653i	0.347400	−	0.347400i	0.859140	+	0.511740i	$0.170999\pi$
$648$	4.04321	+	8.04068i	0.158832	+	0.315868i
$649$		−	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	$-0.235897\pi$
$653$	1.60062	+	1.60062i	0.0626369	+	0.0626369i	−0.675094	+	0.737731i	$0.735897\pi$
$654$	1.15359	−	14.4127i	0.0451088	−	0.563580i
$655$	−39.6931	+	22.7793i	−1.55094	+	0.890060i
$656$			4.88651i			0.190786i
$657$	−12.7607	−	17.6621i	−0.497841	−	0.689066i
$658$	8.89472	−	8.89472i	0.346752	−	0.346752i
$659$	−24.4088			−0.950831			−0.475415	−	0.879761i	$-0.657702\pi$
$659$	−24.4088			−0.950831			−0.475415	+	0.879761i	$0.657702\pi$
$660$	7.41534	−	20.6814i	0.288642	−	0.805024i
$661$	−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
$663$	24.0398	−	20.4767i	0.933627	−	0.795248i
$664$		−	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
$672$	2.48893	+	2.92202i	0.0960125	+	0.112719i
$673$	0.870095	−	0.870095i	0.0335397	−	0.0335397i	−0.690138	−	0.723678i	$-0.742450\pi$
$673$	0.870095	−	0.870095i	0.0335397	−	0.0335397i	0.723678	+	0.690138i	$0.242450\pi$
$674$	15.3704			0.592045
$675$	0.441276	+	25.9770i	0.0169847	+	0.999856i
$676$	6.02083			0.231570
$677$	−6.92072	+	6.92072i	−0.265985	+	0.265985i	−0.827480	−	0.561495i	$-0.810226\pi$
$677$	−6.92072	+	6.92072i	−0.265985	+	0.265985i	0.561495	+	0.827480i	$0.310226\pi$
$678$	−14.3669	−	16.8668i	−0.551757	−	0.647767i
$679$		−	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	$-0.199184\pi$
$683$	5.87527	+	5.87527i	0.224811	+	0.224811i	−0.585710	+	0.810521i	$0.699184\pi$
$684$	−1.88884	+	11.7238i	−0.0722215	+	0.448270i
$685$	14.0298	+	3.79843i	0.536050	+	0.145131i
$686$		−	20.1419i		−	0.769023i
$687$	9.66538	−	8.23281i	0.368757	−	0.314101i
$688$	−8.81584	+	8.81584i	−0.336101	+	0.336101i
$689$	−19.6952			−0.750326
$690$	−1.30717	+	3.64572i	−0.0497633	+	0.138790i
$691$	−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
$693$	−22.0865	−	30.5701i	−0.838998	−	1.16126i
$694$			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	$-0.0190969\pi$
$702$	−7.12573	−	11.7329i	−0.268943	−	0.442831i
$703$	11.5725	−	11.5725i	0.436466	−	0.436466i
$704$	−5.67280			−0.213802
$705$	−9.38630	−	19.8796i	−0.353508	−	0.748709i
$706$	6.91828			0.260373
$707$	6.09403	−	6.09403i	0.229190	−	0.229190i
$708$	9.65291	−	8.22219i	0.362778	−	0.309009i
$709$		−	11.9551i		−	0.448982i	−0.974476	−	0.224491i	$-0.927928\pi$
$709$		−	11.9551i		−	0.448982i	0.974476	−	0.224491i	$-0.0720719\pi$
$710$	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
$717$	−2.89247	−	3.39578i	−0.108021	−	0.126818i
$718$	23.2881	−	23.2881i	0.869103	−	0.869103i
$719$	19.3497			0.721622			0.360811	−	0.932639i	$-0.382500\pi$
$719$	19.3497			0.721622			0.360811	+	0.932639i	$0.382500\pi$
$720$	6.27521	−	2.37102i	0.233863	−	0.0883626i
$721$	24.2397			0.902735
$722$	2.35585	−	2.35585i	0.0876755	−	0.0876755i
$723$	−21.3813	−	25.1018i	−0.795178	−	0.933544i
$724$			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	0.972562	−	0.232644i	$-0.0747376\pi$
$727$	19.9504	+	19.9504i	0.739918	+	0.739918i	−0.232644	+	0.972562i	$0.574738\pi$
$728$	−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
$732$	6.24818	−	5.32209i	0.230939	−	0.196710i
$733$	3.98501	−	3.98501i	0.147190	−	0.147190i	−0.629672	−	0.776861i	$-0.716811\pi$
$733$	3.98501	−	3.98501i	0.147190	−	0.147190i	0.776861	+	0.629672i	$0.216811\pi$
$734$	−23.9937			−0.885624
$735$	−7.61597	−	2.73071i	−0.280919	−	0.100724i
$736$	1.00000			0.0368605
$737$	−34.2018	+	34.2018i	−1.25984	+	1.25984i
$738$	11.8827	−	8.58508i	0.437407	−	0.316021i
$739$		−	24.8589i		−	0.914450i	−0.889351	−	0.457225i	$-0.848843\pi$
$739$		−	24.8589i		−	0.914450i	0.889351	−	0.457225i	$-0.151157\pi$
$740$	−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	−0.890773	−	0.454449i	$-0.849836\pi$
$743$	−36.6681	−	36.6681i	−1.34522	−	1.34522i	−0.454449	−	0.890773i	$-0.650164\pi$
$744$	−0.883816	+	11.0422i	−0.0324023	+	0.404827i
$745$	−9.74460	−	16.9801i	−0.357015	−	0.622101i
$746$			10.1941i			0.373233i
$747$	−37.5173	+	27.1058i	−1.37268	+	0.991748i
$748$	−27.6829	+	27.6829i	−1.01219	+	1.01219i
$749$	19.2856			0.704680
$750$	19.2905	+	1.69570i	0.704391	+	0.0619182i
$751$	−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
$753$	−5.33934	+	4.54796i	−0.194576	+	0.165737i
$754$		−	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	−0.989483	−	0.144652i	$-0.953794\pi$
$757$	−31.2042	−	31.2042i	−1.13413	−	1.13413i	−0.144652	−	0.989483i	$-0.546206\pi$
$758$	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	$0.982155\pi$
$762$	10.2830	+	12.0723i	0.372512	+	0.437332i
$763$	−13.0810	+	13.0810i	−0.473563	+	0.473563i
$764$	−18.2037			−0.658586
$765$	19.0522	−	42.1931i	0.688835	−	1.52549i
$766$	−20.9155			−0.755707
$767$	−13.6756	+	13.6756i	−0.493797	+	0.493797i
$768$	−1.12312	−	1.31856i	−0.0405273	−	0.0475793i
$769$			10.4531i			0.376947i	0.982078	+	0.188473i	$0.0603539\pi$
$769$			10.4531i			0.376947i	−0.982078	+	0.188473i	$0.939646\pi$
$770$	−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	$-0.385806\pi$
$773$	−16.2711	−	16.2711i	−0.585231	−	0.585231i	−0.936336	+	0.351105i	$0.885806\pi$
$774$	36.9263	+	5.94925i	1.32729	+	0.213841i
$775$	−16.1330	+	27.6102i	−0.579514	+	0.991789i
$776$			0.438172i			0.0157295i
$777$	−12.0813	+	10.2907i	−0.433415	+	0.369176i
$778$	24.0705	−	24.0705i	0.862970	−	0.862970i
$779$	19.3424			0.693013
$780$	−9.25223	+	4.36851i	−0.331283	+	0.156418i
$781$	24.2494			0.867712
$782$	4.87994	−	4.87994i	0.174506	−	0.174506i
$783$	3.17351	−	1.92736i	0.113412	−	0.0688781i
$784$			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	0.360219	−	0.932868i	$-0.382702\pi$
$787$	−16.0648	−	16.0648i	−0.572649	−	0.572649i	−0.932868	+	0.360219i	$0.882702\pi$
$788$	−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
$792$	9.96651	+	13.7947i	0.354145	+	0.490174i
$793$	−8.85200	+	8.85200i	−0.314344	+	0.314344i
$794$	21.6997			0.770093
$795$	−26.1097	+	12.3279i	−0.926016	+	0.437226i
$796$	−0.617379			−0.0218824
$797$	−27.0509	+	27.0509i	−0.958192	+	0.958192i	−0.999160	−	0.0409681i	$-0.986956\pi$
$797$	−27.0509	+	27.0509i	−0.958192	+	0.958192i	0.0409681	+	0.999160i	$0.486956\pi$
$798$	11.5663	−	9.85198i	0.409442	−	0.348756i
$799$			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
$807$	−9.41375	−	11.0518i	−0.331380	−	0.389042i
$808$	−2.74992	+	2.74992i	−0.0967420	+	0.0967420i
$809$	28.2673			0.993824			0.496912	−	0.867801i	$-0.334467\pi$
$809$	28.2673			0.993824			0.496912	+	0.867801i	$0.334467\pi$
$810$	−16.7906	−	11.0940i	−0.589960	−	0.389803i
$811$	−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
$813$	6.70018	+	7.86606i	0.234986	+	0.275875i
$814$		−	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	$-0.119044\pi$
$822$	−8.57087	+	7.30053i	−0.298944	+	0.254635i
$823$	29.6324	−	29.6324i	1.03292	−	1.03292i	0.0334802	−	0.999439i	$-0.489341\pi$
$823$	29.6324	−	29.6324i	1.03292	−	1.03292i	0.999439	−	0.0334802i	$-0.0106591\pi$
$824$	−10.9381			−0.381048
$825$	8.63697	+	48.3627i	0.300701	+	1.68377i
$826$	−16.2235			−0.564487
$827$	35.5572	−	35.5572i	1.23644	−	1.23644i	0.275001	−	0.961444i	$-0.411322\pi$
$827$	35.5572	−	35.5572i	1.23644	−	1.23644i	0.961444	−	0.275001i	$-0.0886780\pi$
$828$	−1.75690	−	2.43173i	−0.0610563	−	0.0845085i
$829$		−	4.84770i		−	0.168367i	−0.996450	−	0.0841837i	$-0.973172\pi$
$829$		−	4.84770i		−	0.168367i	0.996450	−	0.0841837i	$-0.0268283\pi$
$830$	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
$837$	28.4045	−	17.2508i	0.981803	−	0.596276i
$838$	1.13053	−	1.13053i	0.0390536	−	0.0390536i
$839$	55.2908			1.90885			0.954426	−	0.298448i	$-0.0964691\pi$
$839$	55.2908			1.90885			0.954426	+	0.298448i	$0.0964691\pi$
$840$	−8.07919	−	2.89680i	−0.278759	−	0.0999490i
$841$	−28.4894			−0.982394
$842$	−2.27139	+	2.27139i	−0.0782774	+	0.0782774i
$843$	−38.0419	+	32.4035i	−1.31023	+	1.11603i
$844$			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
$852$	4.80100	+	5.63641i	0.164480	+	0.193100i
$853$	−22.4947	+	22.4947i	−0.770204	+	0.770204i	−0.978142	−	0.207938i	$-0.933325\pi$
$853$	−22.4947	+	22.4947i	−0.770204	+	0.770204i	0.207938	+	0.978142i	$0.433325\pi$
$854$	−10.5012			−0.359344
$855$	−9.38526	−	24.8393i	−0.320969	−	0.849487i
$856$	−8.70259			−0.297449
$857$	22.0175	−	22.0175i	0.752102	−	0.752102i	−0.222769	−	0.974871i	$-0.571510\pi$
$857$	22.0175	−	22.0175i	0.752102	−	0.752102i	0.974871	+	0.222769i	$0.0715097\pi$
$858$	−16.8317	−	19.7605i	−0.574624	−	0.674612i
$859$		−	8.91500i		−	0.304176i	−0.988367	−	0.152088i	$-0.951400\pi$
$859$		−	8.91500i		−	0.304176i	0.988367	−	0.152088i	$-0.0485997\pi$
$860$	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	$-0.283638\pi$
$863$	−4.38216	−	4.38216i	−0.149171	−	0.149171i	−0.777747	+	0.628577i	$0.783638\pi$
$864$	−1.23316	+	5.04770i	−0.0419530	+	0.171726i
$865$	−4.27524	+	15.7909i	−0.145362	+	0.536906i
$866$			33.3481i			1.13321i
$867$	−40.3843	+	34.3987i	−1.37152	+	1.16824i
$868$	10.0219	−	10.0219i	0.340167	−	0.340167i
$869$	−41.2611			−1.39969
$870$	−1.18159	−	2.50253i	−0.0400596	−	0.0848437i
$871$	22.5252			0.763238
$872$	5.90276	−	5.90276i	0.199893	−	0.199893i
$873$	1.06552	−	0.769823i	0.0360623	−	0.0260545i
$874$		−	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	0.535769	−	0.844365i	$-0.320022\pi$
$877$	−9.13881	−	9.13881i	−0.308596	−	0.308596i	−0.844365	+	0.535769i	$0.820022\pi$
$878$	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	$0.915127\pi$
$882$	5.07992	−	3.67018i	0.171050	−	0.123581i
$883$	19.6438	−	19.6438i	0.661066	−	0.661066i	−0.294566	−	0.955631i	$-0.595175\pi$
$883$	19.6438	−	19.6438i	0.661066	−	0.661066i	0.955631	+	0.294566i	$0.0951750\pi$
$884$	18.2319			0.613205
$885$	−9.56959	+	26.6897i	−0.321678	+	0.897163i
$886$	−20.4471			−0.686934
$887$	−3.17206	+	3.17206i	−0.106507	+	0.106507i	−0.758352	−	0.651845i	$-0.773995\pi$
$887$	−3.17206	+	3.17206i	−0.106507	+	0.106507i	0.651845	+	0.758352i	$0.273995\pi$
$888$	5.45168	−	4.64365i	0.182946	−	0.155831i
$889$		−	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
$897$	2.96708	+	3.48338i	0.0990681	+	0.116307i
$898$	14.8692	−	14.8692i	0.496191	−	0.496191i
$899$	4.57001			0.152418
$900$	−9.53119	+	11.5826i	−0.317706	+	0.386086i
$901$	51.4502			1.71406
$902$	19.6011	−	19.6011i	0.652646	−	0.652646i
$903$	−31.0307	−	36.4302i	−1.03264	−	1.21232i
$904$		−	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	0.263822	−	0.964571i	$-0.415017\pi$
$907$	−21.1041	−	21.1041i	−0.700749	−	0.700749i	−0.964571	+	0.263822i	$0.915017\pi$
$908$	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	$0.872285\pi$
$912$	−5.21927	+	4.44569i	−0.172827	+	0.147212i
$913$	−61.8868	+	61.8868i	−2.04815	+	2.04815i
$914$	−21.7209			−0.718465
$915$	−6.19424	+	17.2758i	−0.204775	+	0.571120i
$916$	7.33027			0.242199
$917$	−32.0714	+	32.0714i	−1.05909	+	1.05909i
$918$	18.6147	+	30.6503i	0.614378	+	1.01161i
$919$		−	19.1951i		−	0.633186i	−0.948561	−	0.316593i	$-0.897461\pi$
$919$		−	19.1951i		−	0.633186i	0.948561	−	0.316593i	$-0.102539\pi$
$920$	−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
$927$	19.2172	+	26.5986i	0.631175	+	0.873614i
$928$	−0.505266	+	0.505266i	−0.0165862	+	0.0165862i
$929$	12.8738			0.422374			0.211187	−	0.977446i	$-0.432267\pi$
$929$	12.8738			0.422374			0.211187	+	0.977446i	$0.432267\pi$
$930$	−10.5758	−	22.3989i	−0.346795	−	0.734489i
$931$	8.26900			0.271006
$932$	−5.63455	+	5.63455i	−0.184566	+	0.184566i
$933$	−16.8644	+	14.3648i	−0.552114	+	0.470282i
$934$			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	0.495003	−	0.868891i	$-0.335167\pi$
$937$	−11.4449	−	11.4449i	−0.373888	−	0.373888i	−0.868891	+	0.495003i	$0.835167\pi$
$938$	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	$0.678078\pi$
$942$	18.5515	+	21.7796i	0.604440	+	0.709617i
$943$	−3.45528	+	3.45528i	−0.112519	+	0.112519i
$944$	7.32082			0.238272
$945$	7.15006	+	24.7358i	0.232592	+	0.804655i
$946$	70.7255			2.29949
$947$	23.8469	−	23.8469i	0.774920	−	0.774920i	−0.204042	−	0.978962i	$-0.565408\pi$
$947$	23.8469	−	23.8469i	0.774920	−	0.774920i	0.978962	+	0.204042i	$0.0654078\pi$
$948$	−8.16904	−	9.59051i	−0.265318	−	0.311485i
$949$			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	$-0.111854\pi$
$953$	18.3582	+	18.3582i	0.594681	+	0.594681i	−0.344211	+	0.938892i	$0.611854\pi$
$954$	3.55747	−	22.0808i	0.115177	−	0.714892i
$955$	35.3041	−	20.2605i	1.14241	−	0.655615i
$956$		−	2.57538i		−	0.0832938i
$957$	5.34479	−	4.55261i	0.172773	−	0.147165i
$958$	−11.5317	+	11.5317i	−0.372573	+	0.372573i
$959$	14.4049			0.465159
$960$	3.64572	+	1.30717i	0.117665	+	0.0421889i
$961$	9.90392			0.319481
$962$	−7.72357	+	7.72357i	−0.249018	+	0.249018i
$963$	15.2895	+	21.1624i	0.492699	+	0.681948i
$964$		−	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	0.0558497	−	0.998439i	$-0.482213\pi$
$967$	−29.3113	−	29.3113i	−0.942589	−	0.942589i	−0.998439	+	0.0558497i	$0.982213\pi$
$968$	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	$0.671567\pi$
$972$	14.4412	−	5.86957i	0.463202	−	0.188267i
$973$	6.16763	−	6.16763i	0.197725	−	0.197725i
$974$	−17.8308			−0.571334
$975$	13.0816	−	18.7699i	0.418947	−	0.601118i
$976$	4.73865			0.151680
$977$	−4.86247	+	4.86247i	−0.155564	+	0.155564i	−0.780598	−	0.625034i	$-0.785085\pi$
$977$	−4.86247	+	4.86247i	−0.155564	+	0.155564i	0.625034	+	0.780598i	$0.285085\pi$
$978$	−13.8456	+	11.7934i	−0.442733	+	0.377113i
$979$			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	0.992404	+	0.123018i	$0.0392572\pi$
$983$	34.9716	+	34.9716i	1.11542	+	1.11542i	0.123018	+	0.992404i	$0.460743\pi$
$984$	8.43670	+	0.675271i	0.268952	+	0.0215268i
$985$	55.4820	+	15.0212i	1.76780	+	0.478616i
$986$			4.93134i			0.157046i
$987$	−14.1278	−	16.5862i	−0.449694	−	0.527943i
$988$	7.39432	−	7.39432i	0.235245	−	0.235245i
$989$	−12.4675			−0.396443
$990$	−34.6824	−	15.6608i	−1.10228	−	0.497733i
$991$	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
$993$	23.7357	+	27.8659i	0.753230	+	0.884297i
$994$		−	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	0.901651	−	0.432464i	$-0.142356\pi$
$997$	14.8147	+	14.8147i	0.469187	+	0.469187i	−0.432464	+	0.901651i	$0.642356\pi$
$998$	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.47.10	yes	32
3.2	odd	2	inner	690.2.i.e.47.6	✓	32
5.3	odd	4	inner	690.2.i.e.323.6	yes	32
15.8	even	4	inner	690.2.i.e.323.10	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.i.e.47.6	✓	32	3.2	odd	2	inner
690.2.i.e.47.10	yes	32	1.1	even	1	trivial
690.2.i.e.323.6	yes	32	5.3	odd	4	inner
690.2.i.e.323.10	yes	32	15.8	even	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.12312 - 1.31856i) q^{3} -1.00000i q^{4} +(1.11299 + 1.93940i) q^{5} +(-1.72653 - 0.138191i) q^{6} +(1.56700 + 1.56700i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.477181 + 2.96181i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.12312 - 1.31856i) 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} +(-1.31856 + 1.12312i) q^{12} +(1.86804 - 1.86804i) q^{13} +2.21607 q^{14} +(1.30717 - 3.64572i) q^{15} -1.00000 q^{16} +(-4.87994 + 4.87994i) q^{17} +(1.75690 + 2.43173i) 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} +(4.44124 - 2.69729i) q^{27} +(1.56700 - 1.56700i) q^{28} +0.714554 q^{29} +(-1.65360 - 3.50223i) q^{30} +6.39562 q^{31} +(-0.707107 + 0.707107i) q^{32} +(7.47990 - 6.37126i) 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} +(-2.48893 - 2.92202i) q^{42} +(8.81584 - 8.81584i) q^{43} +5.67280 q^{44} +(-6.27521 + 2.37102i) q^{45} -1.00000 q^{46} +(4.01373 - 4.01373i) q^{47} +(1.12312 + 1.31856i) 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} +(5.21927 - 4.44569i) q^{57} +(0.505266 - 0.505266i) q^{58} -7.32082 q^{59} +(-3.64572 - 1.30717i) q^{60} -4.73865 q^{61} +(4.52238 - 4.52238i) q^{62} +(-5.38890 + 3.89341i) 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} +(2.43173 - 1.75690i) q^{72} +(-5.13585 + 5.13585i) q^{73} -4.13458 q^{74} +(8.52537 - 1.52252i) q^{75} +3.95832 q^{76} +(-8.88928 + 8.88928i) q^{77} +(-3.48338 + 2.96708i) 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} +(-0.802533 - 0.942179i) q^{87} +(4.01127 - 4.01127i) q^{88} +8.06770 q^{89} +(-2.76068 + 6.11381i) q^{90} +5.85445 q^{91} +(-0.707107 + 0.707107i) q^{92} +(-7.18308 - 8.43298i) 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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