LMFDB - Embedded newform 690.2.i.e.323.13

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			323.13
Character	$\chi$	$=$	690.323
Dual form			690.2.i.e.47.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(0.911701 + 1.47268i) q^{3} +1.00000i q^{4} +(-2.23363 + 0.104337i) q^{5} +(-0.396675 + 1.68602i) q^{6} +(-1.29732 + 1.29732i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.33760 + 2.68530i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(0.911701 + 1.47268i) q^{3} +1.00000i q^{4} +(-2.23363 + 0.104337i) q^{5} +(-0.396675 + 1.68602i) q^{6} +(-1.29732 + 1.29732i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.33760 + 2.68530i) q^{9} +(-1.65319 - 1.50564i) q^{10} +0.254719i q^{11} +(-1.47268 + 0.911701i) q^{12} +(0.686574 + 0.686574i) q^{13} -1.83469 q^{14} +(-2.19006 - 3.19431i) q^{15} -1.00000 q^{16} +(-2.14714 - 2.14714i) q^{17} +(-2.84462 + 0.952965i) q^{18} -0.235326i q^{19} +(-0.104337 - 2.23363i) q^{20} +(-3.09331 - 0.727776i) q^{21} +(-0.180113 + 0.180113i) q^{22} +(-0.707107 + 0.707107i) q^{23} +(-1.68602 - 0.396675i) q^{24} +(4.97823 - 0.466101i) q^{25} +0.970962i q^{26} +(-5.17409 + 0.478323i) q^{27} +(-1.29732 - 1.29732i) q^{28} -0.789167 q^{29} +(0.710113 - 3.80733i) q^{30} -2.07999 q^{31} +(-0.707107 - 0.707107i) q^{32} +(-0.375120 + 0.232227i) q^{33} -3.03651i q^{34} +(2.76238 - 3.03310i) q^{35} +(-2.68530 - 1.33760i) q^{36} +(-4.51979 + 4.51979i) q^{37} +(0.166400 - 0.166400i) q^{38} +(-0.385157 + 1.63706i) q^{39} +(1.50564 - 1.65319i) q^{40} +7.61245i q^{41} +(-1.67269 - 2.70192i) q^{42} +(2.43550 + 2.43550i) q^{43} -0.254719 q^{44} +(2.70753 - 6.13753i) q^{45} -1.00000 q^{46} +(2.45797 + 2.45797i) q^{47} +(-0.911701 - 1.47268i) q^{48} +3.63392i q^{49} +(3.84972 + 3.19056i) q^{50} +(1.20451 - 5.11961i) q^{51} +(-0.686574 + 0.686574i) q^{52} +(-2.31783 + 2.31783i) q^{53} +(-3.99686 - 3.32041i) q^{54} +(-0.0265766 - 0.568948i) q^{55} -1.83469i q^{56} +(0.346560 - 0.214547i) q^{57} +(-0.558025 - 0.558025i) q^{58} +10.3269 q^{59} +(3.19431 - 2.19006i) q^{60} +12.2697 q^{61} +(-1.47077 - 1.47077i) q^{62} +(-1.74839 - 5.21899i) q^{63} -1.00000i q^{64} +(-1.60519 - 1.46192i) q^{65} +(-0.429460 - 0.101041i) q^{66} +(1.01439 - 1.01439i) q^{67} +(2.14714 - 2.14714i) q^{68} +(-1.68602 - 0.396675i) q^{69} +(4.09802 - 0.191426i) q^{70} +1.05315i q^{71} +(-0.952965 - 2.84462i) q^{72} +(6.97373 + 6.97373i) q^{73} -6.39195 q^{74} +(5.22508 + 6.90642i) q^{75} +0.235326 q^{76} +(-0.330452 - 0.330452i) q^{77} +(-1.42992 + 0.885227i) q^{78} -12.7539i q^{79} +(2.23363 - 0.104337i) q^{80} +(-5.42164 - 7.18372i) q^{81} +(-5.38282 + 5.38282i) q^{82} +(-8.88336 + 8.88336i) q^{83} +(0.727776 - 3.09331i) q^{84} +(5.01995 + 4.57190i) q^{85} +3.44432i q^{86} +(-0.719484 - 1.16219i) q^{87} +(-0.180113 - 0.180113i) q^{88} +9.41789 q^{89} +(6.25440 - 2.42537i) q^{90} -1.78141 q^{91} +(-0.707107 - 0.707107i) q^{92} +(-1.89633 - 3.06317i) q^{93} +3.47609i q^{94} +(0.0245532 + 0.525631i) q^{95} +(0.396675 - 1.68602i) q^{96} +(2.94241 - 2.94241i) q^{97} +(-2.56957 + 2.56957i) q^{98} +(-0.683996 - 0.340712i) 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
$3$	0.911701	+	1.47268i	0.526371	+	0.850255i
$3$	0.911701	+	1.47268i	0.526371	+	0.850255i
$4$			1.00000i			0.500000i
$5$	−2.23363	+	0.104337i	−0.998911	+	0.0466609i
$5$	−2.23363	+	0.104337i	−0.998911	+	0.0466609i
$6$	−0.396675	+	1.68602i	−0.161942	+	0.688313i
$7$	−1.29732	+	1.29732i	−0.490341	+	0.490341i	−0.908414	−	0.418072i	$-0.862706\pi$
$7$	−1.29732	+	1.29732i	−0.490341	+	0.490341i	0.418072	+	0.908414i	$0.362706\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−1.33760	+	2.68530i	−0.445867	+	0.895099i
$10$	−1.65319	−	1.50564i	−0.522786	−	0.476125i
$11$			0.254719i			0.0768006i	0.999262	+	0.0384003i	$0.0122262\pi$
$11$			0.254719i			0.0768006i	−0.999262	+	0.0384003i	$0.987774\pi$
$12$	−1.47268	+	0.911701i	−0.425128	+	0.263185i
$13$	0.686574	+	0.686574i	0.190421	+	0.190421i	0.795878	−	0.605457i	$-0.207010\pi$
$13$	0.686574	+	0.686574i	0.190421	+	0.190421i	−0.605457	+	0.795878i	$0.707010\pi$
$14$	−1.83469			−0.490341
$15$	−2.19006	−	3.19431i	−0.565471	−	0.824768i
$16$	−1.00000			−0.250000
$17$	−2.14714	−	2.14714i	−0.520758	−	0.520758i	0.397042	−	0.917800i	$-0.370037\pi$
$17$	−2.14714	−	2.14714i	−0.520758	−	0.520758i	−0.917800	+	0.397042i	$0.870037\pi$
$18$	−2.84462	+	0.952965i	−0.670483	+	0.224616i
$19$		−	0.235326i		−	0.0539874i	−0.999636	−	0.0269937i	$-0.991407\pi$
$19$		−	0.235326i		−	0.0539874i	0.999636	−	0.0269937i	$-0.00859340\pi$
$20$	−0.104337	−	2.23363i	−0.0233305	−	0.499455i
$21$	−3.09331	−	0.727776i	−0.675016	−	0.158814i
$22$	−0.180113	+	0.180113i	−0.0384003	+	0.0384003i
$23$	−0.707107	+	0.707107i	−0.147442	+	0.147442i
$23$	−0.707107	+	0.707107i	−0.147442	+	0.147442i
$24$	−1.68602	−	0.396675i	−0.344156	−	0.0809710i
$25$	4.97823	−	0.466101i	0.995646	−	0.0932202i
$26$			0.970962i			0.190421i
$27$	−5.17409	+	0.478323i	−0.995754	+	0.0920533i
$28$	−1.29732	−	1.29732i	−0.245171	−	0.245171i
$29$	−0.789167			−0.146545			−0.0732723	−	0.997312i	$-0.523344\pi$
$29$	−0.789167			−0.146545			−0.0732723	+	0.997312i	$0.523344\pi$
$30$	0.710113	−	3.80733i	0.129648	−	0.695120i
$31$	−2.07999			−0.373577			−0.186788	−	0.982400i	$-0.559808\pi$
$31$	−2.07999			−0.373577			−0.186788	+	0.982400i	$0.559808\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−0.375120	+	0.232227i	−0.0653001	+	0.0404256i
$34$		−	3.03651i		−	0.520758i
$35$	2.76238	−	3.03310i	0.466927	−	0.512687i
$36$	−2.68530	−	1.33760i	−0.447550	−	0.222934i
$37$	−4.51979	+	4.51979i	−0.743049	+	0.743049i	−0.973164	−	0.230114i	$-0.926090\pi$
$37$	−4.51979	+	4.51979i	−0.743049	+	0.743049i	0.230114	+	0.973164i	$0.426090\pi$
$38$	0.166400	−	0.166400i	0.0269937	−	0.0269937i
$39$	−0.385157	+	1.63706i	−0.0616744	+	0.262139i
$40$	1.50564	−	1.65319i	0.238062	−	0.261393i
$41$			7.61245i			1.18887i	0.804145	+	0.594433i	$0.202623\pi$
$41$			7.61245i			1.18887i	−0.804145	+	0.594433i	$0.797377\pi$
$42$	−1.67269	−	2.70192i	−0.258101	−	0.416915i
$43$	2.43550	+	2.43550i	0.371410	+	0.371410i	0.867991	−	0.496580i	$-0.165411\pi$
$43$	2.43550	+	2.43550i	0.371410	+	0.371410i	−0.496580	+	0.867991i	$0.665411\pi$
$44$	−0.254719			−0.0384003
$45$	2.70753	−	6.13753i	0.403615	−	0.914929i
$46$	−1.00000			−0.147442
$47$	2.45797	+	2.45797i	0.358531	+	0.358531i	0.863271	−	0.504740i	$-0.168412\pi$
$47$	2.45797	+	2.45797i	0.358531	+	0.358531i	−0.504740	+	0.863271i	$0.668412\pi$
$48$	−0.911701	−	1.47268i	−0.131593	−	0.212564i
$49$			3.63392i			0.519131i
$50$	3.84972	+	3.19056i	0.544433	+	0.451213i
$51$	1.20451	−	5.11961i	0.168665	−	0.716889i
$52$	−0.686574	+	0.686574i	−0.0952107	+	0.0952107i
$53$	−2.31783	+	2.31783i	−0.318378	+	0.318378i	−0.848144	−	0.529766i	$-0.822280\pi$
$53$	−2.31783	+	2.31783i	−0.318378	+	0.318378i	0.529766	+	0.848144i	$0.322280\pi$
$54$	−3.99686	−	3.32041i	−0.543904	−	0.451850i
$55$	−0.0265766	−	0.568948i	−0.00358359	−	0.0767169i
$56$		−	1.83469i		−	0.245171i
$57$	0.346560	−	0.214547i	0.0459031	−	0.0284174i
$58$	−0.558025	−	0.558025i	−0.0732723	−	0.0732723i
$59$	10.3269			1.34445			0.672224	−	0.740348i	$-0.265339\pi$
$59$	10.3269			1.34445			0.672224	+	0.740348i	$0.265339\pi$
$60$	3.19431	−	2.19006i	0.412384	−	0.282736i
$61$	12.2697			1.57098			0.785490	−	0.618874i	$-0.212411\pi$
$61$	12.2697			1.57098			0.785490	+	0.618874i	$0.212411\pi$
$62$	−1.47077	−	1.47077i	−0.186788	−	0.186788i
$63$	−1.74839	−	5.21899i	−0.220277	−	0.657531i
$64$		−	1.00000i		−	0.125000i
$65$	−1.60519	−	1.46192i	−0.199099	−	0.181329i
$66$	−0.429460	−	0.101041i	−0.0528628	−	0.0124372i
$67$	1.01439	−	1.01439i	0.123927	−	0.123927i	−0.642423	−	0.766350i	$-0.722071\pi$
$67$	1.01439	−	1.01439i	0.123927	−	0.123927i	0.766350	+	0.642423i	$0.222071\pi$
$68$	2.14714	−	2.14714i	0.260379	−	0.260379i
$69$	−1.68602	−	0.396675i	−0.202972	−	0.0477541i
$70$	4.09802	−	0.191426i	0.489807	−	0.0228798i
$71$			1.05315i			0.124985i	0.998045	+	0.0624927i	$0.0199050\pi$
$71$			1.05315i			0.124985i	−0.998045	+	0.0624927i	$0.980095\pi$
$72$	−0.952965	−	2.84462i	−0.112308	−	0.335242i
$73$	6.97373	+	6.97373i	0.816214	+	0.816214i	0.985557	−	0.169343i	$-0.0541646\pi$
$73$	6.97373	+	6.97373i	0.816214	+	0.816214i	−0.169343	+	0.985557i	$0.554165\pi$
$74$	−6.39195			−0.743049
$75$	5.22508	+	6.90642i	0.603340	+	0.797484i
$76$	0.235326			0.0269937
$77$	−0.330452	−	0.330452i	−0.0376585	−	0.0376585i
$78$	−1.42992	+	0.885227i	−0.161907	+	0.100232i
$79$		−	12.7539i		−	1.43492i	−0.696599	−	0.717461i	$-0.745304\pi$
$79$		−	12.7539i		−	1.43492i	0.696599	−	0.717461i	$-0.254696\pi$
$80$	2.23363	−	0.104337i	0.249728	−	0.0116652i
$81$	−5.42164	−	7.18372i	−0.602405	−	0.798191i
$82$	−5.38282	+	5.38282i	−0.594433	+	0.594433i
$83$	−8.88336	+	8.88336i	−0.975075	+	0.975075i	−0.999697	−	0.0246219i	$-0.992162\pi$
$83$	−8.88336	+	8.88336i	−0.975075	+	0.975075i	0.0246219	+	0.999697i	$0.492162\pi$
$84$	0.727776	−	3.09331i	0.0794069	−	0.337508i
$85$	5.01995	+	4.57190i	0.544490	+	0.495892i
$86$			3.44432i			0.371410i
$87$	−0.719484	−	1.16219i	−0.0771368	−	0.124600i
$88$	−0.180113	−	0.180113i	−0.0192001	−	0.0192001i
$89$	9.41789			0.998294			0.499147	−	0.866517i	$-0.333647\pi$
$89$	9.41789			0.998294			0.499147	+	0.866517i	$0.333647\pi$
$90$	6.25440	−	2.42537i	0.659272	−	0.255657i
$91$	−1.78141			−0.186743
$92$	−0.707107	−	0.707107i	−0.0737210	−	0.0737210i
$93$	−1.89633	−	3.06317i	−0.196640	−	0.317635i
$94$			3.47609i			0.358531i
$95$	0.0245532	+	0.525631i	0.00251910	+	0.0539286i
$96$	0.396675	−	1.68602i	0.0404855	−	0.172078i
$97$	2.94241	−	2.94241i	0.298757	−	0.298757i	−0.541770	−	0.840527i	$-0.682246\pi$
$97$	2.94241	−	2.94241i	0.298757	−	0.298757i	0.840527	+	0.541770i	$0.182246\pi$
$98$	−2.56957	+	2.56957i	−0.259566	+	0.259566i
$99$	−0.683996	−	0.340712i	−0.0687441	−	0.0342429i
$100$	0.466101	+	4.97823i	0.0466101	+	0.497823i
$101$			15.2340i			1.51584i	0.652350	+	0.757918i	$0.273783\pi$
$101$			15.2340i			1.51584i	−0.652350	+	0.757918i	$0.726217\pi$
$102$	4.47183	−	2.76839i	0.442777	−	0.274112i
$103$	−1.33242	−	1.33242i	−0.131288	−	0.131288i	0.638409	−	0.769697i	$-0.279593\pi$
$103$	−1.33242	−	1.33242i	−0.131288	−	0.131288i	−0.769697	+	0.638409i	$0.779593\pi$
$104$	−0.970962			−0.0952107
$105$	6.98526	+	1.30284i	0.681692	+	0.127144i
$106$	−3.27790			−0.318378
$107$	−0.890386	−	0.890386i	−0.0860768	−	0.0860768i	0.662757	−	0.748834i	$-0.269386\pi$
$107$	−0.890386	−	0.890386i	−0.0860768	−	0.0860768i	−0.748834	+	0.662757i	$0.769386\pi$
$108$	−0.478323	−	5.17409i	−0.0460266	−	0.497877i
$109$		−	11.3456i		−	1.08672i	−0.839501	−	0.543358i	$-0.817153\pi$
$109$		−	11.3456i		−	1.08672i	0.839501	−	0.543358i	$-0.182847\pi$
$110$	0.383515	−	0.421099i	0.0365667	−	0.0401503i
$111$	−10.7769	−	2.53553i	−1.02290	−	0.240662i
$112$	1.29732	−	1.29732i	0.122585	−	0.122585i
$113$	2.39356	−	2.39356i	0.225167	−	0.225167i	−0.585503	−	0.810670i	$-0.699103\pi$
$113$	2.39356	−	2.39356i	0.225167	−	0.225167i	0.810670	+	0.585503i	$0.199103\pi$
$114$	0.396763	+	0.0933479i	0.0371602	+	0.00874283i
$115$	1.50564	−	1.65319i	0.140402	−	0.154161i
$116$		−	0.789167i		−	0.0732723i
$117$	−2.76202	+	0.925292i	−0.255349	+	0.0855433i
$118$	7.30222	+	7.30222i	0.672224	+	0.672224i
$119$	5.57106			0.510698
$120$	3.80733	+	0.710113i	0.347560	+	0.0648242i
$121$	10.9351			0.994102
$122$	8.67602	+	8.67602i	0.785490	+	0.785490i
$123$	−11.2107	+	6.94028i	−1.01084	+	0.625784i
$124$		−	2.07999i		−	0.186788i
$125$	−11.0709	+	1.56051i	−0.990211	+	0.139576i
$126$	2.45408	−	4.92668i	0.218627	−	0.438904i
$127$	−11.6705	+	11.6705i	−1.03559	+	1.03559i	−0.0362444	+	0.999343i	$0.511539\pi$
$127$	−11.6705	+	11.6705i	−1.03559	+	1.03559i	−0.999343	+	0.0362444i	$0.988461\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	−1.36628	+	5.80717i	−0.120294	+	0.511293i
$130$	−0.101307	−	2.16877i	−0.00888523	−	0.190214i
$131$			7.84601i			0.685509i	0.939425	+	0.342755i	$0.111360\pi$
$131$			7.84601i			0.685509i	−0.939425	+	0.342755i	$0.888640\pi$
$132$	−0.232227	−	0.375120i	−0.0202128	−	0.0326500i
$133$	0.305293	+	0.305293i	0.0264722	+	0.0264722i
$134$	1.43456			0.123927
$135$	11.5071	−	1.60825i	0.990374	−	0.138416i
$136$	3.03651			0.260379
$137$	0.446558	+	0.446558i	0.0381520	+	0.0381520i	0.725925	−	0.687773i	$-0.241412\pi$
$137$	0.446558	+	0.446558i	0.0381520	+	0.0381520i	−0.687773	+	0.725925i	$0.741412\pi$
$138$	−0.911701	−	1.47268i	−0.0776092	−	0.125363i
$139$		−	12.5052i		−	1.06067i	−0.847787	−	0.530337i	$-0.822065\pi$
$139$		−	12.5052i		−	1.06067i	0.847787	−	0.530337i	$-0.177935\pi$
$140$	3.03310	+	2.76238i	0.256343	+	0.233464i
$141$	−1.37888	+	5.86074i	−0.116123	+	0.493563i
$142$	−0.744687	+	0.744687i	−0.0624927	+	0.0624927i
$143$	−0.174883	+	0.174883i	−0.0146245	+	0.0146245i
$144$	1.33760	−	2.68530i	0.111467	−	0.223775i
$145$	1.76271	−	0.0823393i	0.146385	−	0.00683791i
$146$			9.86235i			0.816214i
$147$	−5.35162	+	3.31305i	−0.441394	+	0.273255i
$148$	−4.51979	−	4.51979i	−0.371525	−	0.371525i
$149$	10.1715			0.833281			0.416640	−	0.909071i	$-0.363207\pi$
$149$	10.1715			0.833281			0.416640	+	0.909071i	$0.363207\pi$
$150$	−1.18889	+	8.57826i	−0.0970722	+	0.700412i
$151$	−14.1211			−1.14916			−0.574581	−	0.818448i	$-0.694835\pi$
$151$	−14.1211			−1.14916			−0.574581	+	0.818448i	$0.694835\pi$
$152$	0.166400	+	0.166400i	0.0134968	+	0.0134968i
$153$	8.63773	−	2.89369i	0.698319	−	0.233941i
$154$		−	0.467330i		−	0.0376585i
$155$	4.64593	−	0.217020i	0.373170	−	0.0174314i
$156$	−1.63706	−	0.385157i	−0.131069	−	0.0308372i
$157$	−10.7816	+	10.7816i	−0.860465	+	0.860465i	−0.991392	−	0.130927i	$-0.958205\pi$
$157$	−10.7816	+	10.7816i	−0.860465	+	0.860465i	0.130927	+	0.991392i	$0.458205\pi$
$158$	9.01834	−	9.01834i	0.717461	−	0.717461i
$159$	−5.52660	−	1.30026i	−0.438288	−	0.103118i
$160$	1.65319	+	1.50564i	0.130696	+	0.119031i
$161$		−	1.83469i		−	0.144594i
$162$	1.24597	−	8.91334i	0.0978930	−	0.700298i
$163$	−1.35354	−	1.35354i	−0.106017	−	0.106017i	0.652108	−	0.758126i	$-0.273885\pi$
$163$	−1.35354	−	1.35354i	−0.106017	−	0.106017i	−0.758126	+	0.652108i	$0.773885\pi$
$164$	−7.61245			−0.594433
$165$	0.813651	−	0.557850i	0.0633427	−	0.0434285i
$166$	−12.5630			−0.975075
$167$	5.90252	+	5.90252i	0.456751	+	0.456751i	0.897587	−	0.440837i	$-0.145318\pi$
$167$	5.90252	+	5.90252i	0.456751	+	0.456751i	−0.440837	+	0.897587i	$0.645318\pi$
$168$	2.70192	−	1.67269i	0.208458	−	0.129051i
$169$		−	12.0572i		−	0.927479i
$170$	0.316821	+	6.78246i	0.0242990	+	0.520191i
$171$	0.631919	+	0.314772i	0.0483241	+	0.0240712i
$172$	−2.43550	+	2.43550i	−0.185705	+	0.185705i
$173$	12.9677	−	12.9677i	0.985916	−	0.985916i	−0.0139865	−	0.999902i	$-0.504452\pi$
$173$	12.9677	−	12.9677i	0.985916	−	0.985916i	0.999902	+	0.0139865i	$0.00445217\pi$
$174$	0.313043	−	1.33055i	0.0237317	−	0.100869i
$175$	−5.85368	+	7.06304i	−0.442496	+	0.533916i
$176$		−	0.254719i		−	0.0192001i
$177$	9.41504	+	15.2083i	0.707678	+	1.14312i
$178$	6.65945	+	6.65945i	0.499147	+	0.499147i
$179$	17.1909			1.28491			0.642455	−	0.766323i	$-0.277916\pi$
$179$	17.1909			1.28491			0.642455	+	0.766323i	$0.277916\pi$
$180$	6.13753	+	2.70753i	0.457464	+	0.201808i
$181$	−15.0456			−1.11833			−0.559166	−	0.829055i	$-0.688879\pi$
$181$	−15.0456			−1.11833			−0.559166	+	0.829055i	$0.688879\pi$
$182$	−1.25965	−	1.25965i	−0.0933714	−	0.0933714i
$183$	11.1863	+	18.0695i	0.826918	+	1.33573i
$184$		−	1.00000i		−	0.0737210i
$185$	9.62397	−	10.5671i	0.707568	−	0.776911i
$186$	0.825080	−	3.50689i	0.0604978	−	0.257138i
$187$	0.546917	−	0.546917i	0.0399945	−	0.0399945i
$188$	−2.45797	+	2.45797i	−0.179266	+	0.179266i
$189$	6.09192	−	7.33299i	0.443122	−	0.533397i
$190$	−0.354315	+	0.389039i	−0.0257047	+	0.0282238i
$191$		−	2.26357i		−	0.163786i	−0.996641	−	0.0818932i	$-0.973903\pi$
$191$		−	2.26357i		−	0.163786i	0.996641	−	0.0818932i	$-0.0260966\pi$
$192$	1.47268	−	0.911701i	0.106282	−	0.0657964i
$193$	1.03012	+	1.03012i	0.0741495	+	0.0741495i	0.743209	−	0.669059i	$-0.233303\pi$
$193$	1.03012	+	1.03012i	0.0741495	+	0.0741495i	−0.669059	+	0.743209i	$0.733303\pi$
$194$	4.16120			0.298757
$195$	0.689493	−	3.69677i	0.0493756	−	0.264731i
$196$	−3.63392			−0.259566
$197$	−0.571573	−	0.571573i	−0.0407229	−	0.0407229i	0.686452	−	0.727175i	$-0.259167\pi$
$197$	−0.571573	−	0.571573i	−0.0407229	−	0.0407229i	−0.727175	+	0.686452i	$0.759167\pi$
$198$	−0.242738	−	0.724578i	−0.0172506	−	0.0514935i
$199$		−	18.8518i		−	1.33637i	−0.743996	−	0.668184i	$-0.767072\pi$
$199$		−	18.8518i		−	1.33637i	0.743996	−	0.668184i	$-0.232928\pi$
$200$	−3.19056	+	3.84972i	−0.225606	+	0.272216i
$201$	2.41869	+	0.569054i	0.170601	+	0.0401380i
$202$	−10.7720	+	10.7720i	−0.757918	+	0.757918i
$203$	1.02380	−	1.02380i	0.0718568	−	0.0718568i
$204$	5.11961	+	1.20451i	0.358444	+	0.0843326i
$205$	−0.794260	−	17.0034i	−0.0554736	−	1.18757i
$206$		−	1.88433i		−	0.131288i
$207$	−0.952965	−	2.84462i	−0.0662356	−	0.197715i
$208$	−0.686574	−	0.686574i	−0.0476053	−	0.0476053i
$209$	0.0599418			0.00414626
$210$	4.01808	+	5.86057i	0.277274	+	0.404418i
$211$	4.60366			0.316929			0.158465	−	0.987365i	$-0.449346\pi$
$211$	4.60366			0.316929			0.158465	+	0.987365i	$0.449346\pi$
$212$	−2.31783	−	2.31783i	−0.159189	−	0.159189i
$213$	−1.55095	+	0.960155i	−0.106270	+	0.0657887i
$214$		−	1.25920i		−	0.0860768i
$215$	−5.69413	−	5.18590i	−0.388336	−	0.353675i
$216$	3.32041	−	3.99686i	0.225925	−	0.271952i
$217$	2.69841	−	2.69841i	0.183180	−	0.183180i
$218$	8.02258	−	8.02258i	0.543358	−	0.543358i
$219$	−3.91215	+	16.6281i	−0.264359	+	1.12362i
$220$	0.568948	−	0.0265766i	0.0383585	−	0.00179179i
$221$		−	2.94834i		−	0.198327i
$222$	−5.82755	−	9.41333i	−0.391120	−	0.631781i
$223$	7.68075	+	7.68075i	0.514341	+	0.514341i	0.915854	−	0.401512i	$-0.131515\pi$
$223$	7.68075	+	7.68075i	0.514341	+	0.514341i	−0.401512	+	0.915854i	$0.631515\pi$
$224$	1.83469			0.122585
$225$	−5.40727	+	13.9915i	−0.360484	+	0.932765i
$226$	3.38500			0.225167
$227$	0.512571	+	0.512571i	0.0340205	+	0.0340205i	0.723912	−	0.689892i	$-0.242342\pi$
$227$	0.512571	+	0.512571i	0.0340205	+	0.0340205i	−0.689892	+	0.723912i	$0.742342\pi$
$228$	0.214547	+	0.346560i	0.0142087	+	0.0229515i
$229$		−	16.3029i		−	1.07733i	−0.842521	−	0.538664i	$-0.818929\pi$
$229$		−	16.3029i		−	1.07733i	0.842521	−	0.538664i	$-0.181071\pi$
$230$	2.23363	−	0.104337i	0.147281	−	0.00687978i
$231$	0.185378	−	0.787925i	0.0121970	−	0.0518417i
$232$	0.558025	−	0.558025i	0.0366361	−	0.0366361i
$233$	6.11748	−	6.11748i	0.400769	−	0.400769i	−0.477735	−	0.878504i	$-0.658542\pi$
$233$	6.11748	−	6.11748i	0.400769	−	0.400769i	0.878504	+	0.477735i	$0.158542\pi$
$234$	−2.60732	−	1.29876i	−0.170446	−	0.0849026i
$235$	−5.74665	−	5.23373i	−0.374870	−	0.341411i
$236$			10.3269i			0.672224i
$237$	18.7824	−	11.6277i	1.22005	−	0.755301i
$238$	3.93933	+	3.93933i	0.255349	+	0.255349i
$239$	5.10225			0.330037			0.165019	−	0.986290i	$-0.447232\pi$
$239$	5.10225			0.330037			0.165019	+	0.986290i	$0.447232\pi$
$240$	2.19006	+	3.19431i	0.141368	+	0.206192i
$241$	12.6977			0.817933			0.408966	−	0.912549i	$-0.365889\pi$
$241$	12.6977			0.817933			0.408966	+	0.912549i	$0.365889\pi$
$242$	7.73230	+	7.73230i	0.497051	+	0.497051i
$243$	5.63643	−	14.5338i	0.361577	−	0.932342i
$244$			12.2697i			0.785490i
$245$	−0.379152	−	8.11684i	−0.0242231	−	0.518566i
$246$	−12.8347	−	3.01967i	−0.818312	−	0.192527i
$247$	0.161568	−	0.161568i	0.0102804	−	0.0102804i
$248$	1.47077	−	1.47077i	0.0933942	−	0.0933942i
$249$	−21.1813	−	4.98342i	−1.34231	−	0.315811i
$250$	−8.93176	−	6.72486i	−0.564894	−	0.425317i
$251$			21.8369i			1.37833i	0.724602	+	0.689167i	$0.242024\pi$
$251$			21.8369i			1.37833i	−0.724602	+	0.689167i	$0.757976\pi$
$252$	5.21899	−	1.74839i	0.328766	−	0.110138i
$253$	−0.180113	−	0.180113i	−0.0113236	−	0.0113236i
$254$	−16.5045			−1.03559
$255$	−2.15627	+	11.5610i	−0.135031	+	0.723978i
$256$	1.00000			0.0625000
$257$	2.12293	+	2.12293i	0.132425	+	0.132425i	0.770212	−	0.637787i	$-0.220150\pi$
$257$	2.12293	+	2.12293i	0.132425	+	0.132425i	−0.637787	+	0.770212i	$0.720150\pi$
$258$	−5.07240	+	3.14019i	−0.315794	+	0.195500i
$259$		−	11.7272i		−	0.728695i
$260$	1.46192	−	1.60519i	0.0906643	−	0.0995496i
$261$	1.05559	−	2.11915i	0.0653394	−	0.131172i
$262$	−5.54797	+	5.54797i	−0.342755	+	0.342755i
$263$	−19.7112	+	19.7112i	−1.21544	+	1.21544i	−0.246234	+	0.969210i	$0.579193\pi$
$263$	−19.7112	+	19.7112i	−1.21544	+	1.21544i	−0.969210	+	0.246234i	$0.920807\pi$
$264$	0.101041	−	0.429460i	0.00621862	−	0.0264314i
$265$	4.93534	−	5.41901i	0.303176	−	0.332887i
$266$			0.431749i			0.0264722i
$267$	8.58630	+	13.8696i	0.525473	+	0.848804i
$268$	1.01439	+	1.01439i	0.0619635	+	0.0619635i
$269$	−24.6404			−1.50235			−0.751176	−	0.660102i	$-0.770513\pi$
$269$	−24.6404			−1.50235			−0.751176	+	0.660102i	$0.770513\pi$
$270$	9.27396	+	6.99955i	0.564395	+	0.425979i
$271$	−27.5909			−1.67603			−0.838014	−	0.545649i	$-0.816283\pi$
$271$	−27.5909			−1.67603			−0.838014	+	0.545649i	$0.816283\pi$
$272$	2.14714	+	2.14714i	0.130189	+	0.130189i
$273$	−1.62412	−	2.62346i	−0.0982960	−	0.158779i
$274$			0.631528i			0.0381520i
$275$	0.118725	+	1.26805i	0.00715937	+	0.0764662i
$276$	0.396675	−	1.68602i	0.0238771	−	0.101486i
$277$	21.0838	−	21.0838i	1.26680	−	1.26680i	0.319076	−	0.947729i	$-0.396628\pi$
$277$	21.0838	−	21.0838i	1.26680	−	1.26680i	0.947729	−	0.319076i	$-0.103372\pi$
$278$	8.84248	−	8.84248i	0.530337	−	0.530337i
$279$	2.78219	−	5.58538i	0.166566	−	0.334388i
$280$	0.191426	+	4.09802i	0.0114399	+	0.244904i
$281$		−	17.6206i		−	1.05115i	−0.850746	−	0.525577i	$-0.823849\pi$
$281$		−	17.6206i		−	1.05115i	0.850746	−	0.525577i	$-0.176151\pi$
$282$	−5.11918	+	3.16915i	−0.304843	+	0.188720i
$283$	17.7774	+	17.7774i	1.05676	+	1.05676i	0.998289	+	0.0584697i	$0.0186221\pi$
$283$	17.7774	+	17.7774i	1.05676	+	1.05676i	0.0584697	+	0.998289i	$0.481378\pi$
$284$	−1.05315			−0.0624927
$285$	−0.751704	+	0.515377i	−0.0445271	+	0.0305283i
$286$	−0.247322			−0.0146245
$287$	−9.87579	−	9.87579i	−0.582950	−	0.582950i
$288$	2.84462	−	0.952965i	0.167621	−	0.0561540i
$289$		−	7.77958i		−	0.457622i
$290$	1.30465	+	1.18820i	0.0766114	+	0.0697735i
$291$	7.01584	+	1.65064i	0.411276	+	0.0967625i
$292$	−6.97373	+	6.97373i	−0.408107	+	0.408107i
$293$	−4.75775	+	4.75775i	−0.277951	+	0.277951i	−0.832291	−	0.554340i	$-0.812971\pi$
$293$	−4.75775	+	4.75775i	−0.277951	+	0.277951i	0.554340	+	0.832291i	$0.312971\pi$
$294$	−6.12684	−	1.44149i	−0.357325	−	0.0840691i
$295$	−23.0665	+	1.07748i	−1.34298	+	0.0627332i
$296$		−	6.39195i		−	0.371525i
$297$	−0.121838	−	1.31794i	−0.00706974	−	0.0764745i
$298$	7.19233	+	7.19233i	0.416640	+	0.416640i
$299$	−0.970962			−0.0561522
$300$	−6.90642	+	5.22508i	−0.398742	+	0.301670i
$301$	−6.31925			−0.364236
$302$	−9.98515	−	9.98515i	−0.574581	−	0.574581i
$303$	−22.4348	+	13.8888i	−1.28885	+	0.797892i
$304$			0.235326i			0.0134968i
$305$	−27.4061	+	1.28019i	−1.56927	+	0.0733034i
$306$	8.15394	+	4.06165i	0.466130	+	0.232189i
$307$	−23.0519	+	23.0519i	−1.31564	+	1.31564i	−0.398451	+	0.917190i	$0.630452\pi$
$307$	−23.0519	+	23.0519i	−1.31564	+	1.31564i	−0.917190	+	0.398451i	$0.869548\pi$
$308$	0.330452	−	0.330452i	0.0188292	−	0.0188292i
$309$	0.747468	−	3.17701i	0.0425220	−	0.180734i
$310$	3.43862	+	3.13171i	0.195301	+	0.177869i
$311$		−	24.8240i		−	1.40764i	−0.710377	−	0.703821i	$-0.751476\pi$
$311$		−	24.8240i		−	1.40764i	0.710377	−	0.703821i	$-0.248524\pi$
$312$	−0.885227	−	1.42992i	−0.0501161	−	0.0809533i
$313$	2.31611	+	2.31611i	0.130914	+	0.130914i	0.769528	−	0.638614i	$-0.220492\pi$
$313$	2.31611	+	2.31611i	0.130914	+	0.130914i	−0.638614	+	0.769528i	$0.720492\pi$
$314$	−15.2475			−0.860465
$315$	4.44980	+	11.4749i	0.250718	+	0.646537i
$316$	12.7539			0.717461
$317$	22.5014	+	22.5014i	1.26381	+	1.26381i	0.949233	+	0.314574i	$0.101862\pi$
$317$	22.5014	+	22.5014i	1.26381	+	1.26381i	0.314574	+	0.949233i	$0.398138\pi$
$318$	−2.98847	−	4.82732i	−0.167585	−	0.270703i
$319$		−	0.201016i		−	0.0112547i
$320$	0.104337	+	2.23363i	0.00583261	+	0.124864i
$321$	0.499492	−	2.12302i	0.0278789	−	0.118496i
$322$	1.29732	−	1.29732i	0.0722969	−	0.0722969i
$323$	−0.505277	+	0.505277i	−0.0281144	+	0.0281144i
$324$	7.18372	−	5.42164i	0.399095	−	0.301202i
$325$	3.73793	+	3.09791i	0.207343	+	0.171841i
$326$		−	1.91419i		−	0.106017i
$327$	16.7086	−	10.3438i	0.923985	−	0.572015i
$328$	−5.38282	−	5.38282i	−0.297216	−	0.297216i
$329$	−6.37754			−0.351605
$330$	0.969798	+	0.180879i	0.0533856	+	0.00995707i
$331$	−9.35497			−0.514196			−0.257098	−	0.966385i	$-0.582766\pi$
$331$	−9.35497			−0.514196			−0.257098	+	0.966385i	$0.582766\pi$
$332$	−8.88336	−	8.88336i	−0.487537	−	0.487537i
$333$	−6.09130	−	18.1827i	−0.333801	−	0.996404i
$334$			8.34742i			0.456751i
$335$	−2.15993	+	2.37161i	−0.118010	+	0.129575i
$336$	3.09331	+	0.727776i	0.168754	+	0.0397034i
$337$	19.5467	−	19.5467i	1.06477	−	1.06477i	0.0670235	−	0.997751i	$-0.478650\pi$
$337$	19.5467	−	19.5467i	1.06477	−	1.06477i	0.997751	−	0.0670235i	$-0.0213503\pi$
$338$	8.52575	−	8.52575i	0.463740	−	0.463740i
$339$	5.70717	+	1.34275i	0.309971	+	0.0729280i
$340$	−4.57190	+	5.01995i	−0.247946	+	0.272245i
$341$		−	0.529812i		−	0.0286909i
$342$	0.224257	+	0.669412i	0.0121264	+	0.0361976i
$343$	−13.7956	−	13.7956i	−0.744893	−	0.744893i
$344$	−3.44432			−0.185705
$345$	3.80733	+	0.710113i	0.204980	+	0.0382312i
$346$	18.3391			0.985916
$347$	−20.1751	−	20.1751i	−1.08306	−	1.08306i	−0.996223	−	0.0868324i	$-0.972326\pi$
$347$	−20.1751	−	20.1751i	−1.08306	−	1.08306i	−0.0868324	−	0.996223i	$-0.527674\pi$
$348$	1.16219	−	0.719484i	0.0623001	−	0.0385684i
$349$		−	3.34945i		−	0.179292i	−0.995974	−	0.0896460i	$-0.971426\pi$
$349$		−	3.34945i		−	0.179292i	0.995974	−	0.0896460i	$-0.0285736\pi$
$350$	−9.13350	+	0.855150i	−0.488206	+	0.0457097i
$351$	−3.88080	−	3.22399i	−0.207142	−	0.172084i
$352$	0.180113	−	0.180113i	0.00960007	−	0.00960007i
$353$	−0.587472	+	0.587472i	−0.0312680	+	0.0312680i	−0.722568	−	0.691300i	$-0.757038\pi$
$353$	−0.587472	+	0.587472i	−0.0312680	+	0.0312680i	0.691300	+	0.722568i	$0.257038\pi$
$354$	−4.09643	+	17.4113i	−0.217723	+	0.925401i
$355$	−0.109882	−	2.35234i	−0.00583194	−	0.124849i
$356$			9.41789i			0.499147i
$357$	5.07914	+	8.20442i	0.268817	+	0.434224i
$358$	12.1558	+	12.1558i	0.642455	+	0.642455i
$359$	−22.1203			−1.16746			−0.583731	−	0.811947i	$-0.698408\pi$
$359$	−22.1203			−1.16746			−0.583731	+	0.811947i	$0.698408\pi$
$360$	2.42537	+	6.25440i	0.127828	+	0.329636i
$361$	18.9446			0.997085
$362$	−10.6389	−	10.6389i	−0.559166	−	0.559166i
$363$	9.96956	+	16.1040i	0.523266	+	0.845240i
$364$		−	1.78141i		−	0.0933714i
$365$	−16.3044	−	14.8491i	−0.853410	−	0.777240i
$366$	−4.86711	+	20.6870i	−0.254408	+	1.08133i
$367$	−10.1692	+	10.1692i	−0.530827	+	0.530827i	−0.920818	−	0.389992i	$-0.872478\pi$
$367$	−10.1692	+	10.1692i	−0.530827	+	0.530827i	0.389992	+	0.920818i	$0.372478\pi$
$368$	0.707107	−	0.707107i	0.0368605	−	0.0368605i
$369$	−20.4417	−	10.1824i	−1.06415	−	0.530076i
$370$	14.2773	−	0.666917i	0.742240	−	0.0346714i
$371$		−	6.01393i		−	0.312228i
$372$	3.06317	−	1.89633i	0.158818	−	0.0983200i
$373$	6.32688	+	6.32688i	0.327594	+	0.327594i	0.851671	−	0.524077i	$-0.175590\pi$
$373$	6.32688	+	6.32688i	0.327594	+	0.327594i	−0.524077	+	0.851671i	$0.675590\pi$
$374$	0.773457			0.0399945
$375$	−12.3915	−	14.8812i	−0.639894	−	0.768463i
$376$	−3.47609			−0.179266
$377$	−0.541821	−	0.541821i	−0.0279052	−	0.0279052i
$378$	9.49284	−	0.877573i	0.488259	−	0.0451375i
$379$			29.7415i			1.52772i	0.645382	+	0.763860i	$0.276698\pi$
$379$			29.7415i			1.52772i	−0.645382	+	0.763860i	$0.723302\pi$
$380$	−0.525631	+	0.0245532i	−0.0269643	+	0.00125955i
$381$	−27.8269	−	6.54695i	−1.42562	−	0.335410i
$382$	1.60059	−	1.60059i	0.0818932	−	0.0818932i
$383$	11.8299	−	11.8299i	0.604479	−	0.604479i	−0.337019	−	0.941498i	$-0.609419\pi$
$383$	11.8299	−	11.8299i	0.604479	−	0.604479i	0.941498	+	0.337019i	$0.109419\pi$
$384$	1.68602	+	0.396675i	0.0860391	+	0.0202428i
$385$	0.772586	+	0.703630i	0.0393747	+	0.0358603i
$386$			1.45681i			0.0741495i
$387$	−9.79777	+	3.28231i	−0.498049	+	0.166849i
$388$	2.94241	+	2.94241i	0.149378	+	0.149378i
$389$	−33.8998			−1.71879			−0.859394	−	0.511315i	$-0.829159\pi$
$389$	−33.8998			−1.71879			−0.859394	+	0.511315i	$0.829159\pi$
$390$	3.10156	−	2.12647i	0.157053	−	0.107678i
$391$	3.03651			0.153563
$392$	−2.56957	−	2.56957i	−0.129783	−	0.129783i
$393$	−11.5547	+	7.15322i	−0.582858	+	0.360832i
$394$		−	0.808326i		−	0.0407229i
$395$	1.33070	+	28.4874i	0.0669547	+	1.43336i
$396$	0.340712	−	0.683996i	0.0171214	−	0.0343721i
$397$	−1.01644	+	1.01644i	−0.0510138	+	0.0510138i	−0.732153	−	0.681140i	$-0.761485\pi$
$397$	−1.01644	+	1.01644i	−0.0510138	+	0.0510138i	0.681140	+	0.732153i	$0.261485\pi$
$398$	13.3302	−	13.3302i	0.668184	−	0.668184i
$399$	−0.171264	+	0.727936i	−0.00857394	+	0.0364424i
$400$	−4.97823	+	0.466101i	−0.248911	+	0.0233050i
$401$		−	21.8339i		−	1.09033i	−0.838327	−	0.545167i	$-0.816466\pi$
$401$		−	21.8339i		−	1.09033i	0.838327	−	0.545167i	$-0.183534\pi$
$402$	1.30789	+	2.11265i	0.0652316	+	0.105370i
$403$	−1.42806	−	1.42806i	−0.0711370	−	0.0711370i
$404$	−15.2340			−0.757918
$405$	12.8595	+	15.4801i	0.638993	+	0.769213i
$406$	1.44788			0.0718568
$407$	−1.15128	−	1.15128i	−0.0570666	−	0.0570666i
$408$	2.76839	+	4.47183i	0.137056	+	0.221389i
$409$			32.4433i			1.60422i	0.597177	+	0.802109i	$0.296289\pi$
$409$			32.4433i			1.60422i	−0.597177	+	0.802109i	$0.703711\pi$
$410$	11.4616	−	12.5849i	0.566049	−	0.621522i
$411$	−0.250512	+	1.06477i	−0.0123568	+	0.0525210i
$412$	1.33242	−	1.33242i	0.0656438	−	0.0656438i
$413$	−13.3973	+	13.3973i	−0.659238	+	0.659238i
$414$	1.33760	−	2.68530i	0.0657395	−	0.131975i
$415$	18.9153	−	20.7690i	0.928515	−	1.01951i
$416$		−	0.970962i		−	0.0476053i
$417$	18.4162	−	11.4010i	0.901843	−	0.558308i
$418$	0.0423853	+	0.0423853i	0.00207313	+	0.00207313i
$419$	11.6777			0.570495			0.285248	−	0.958454i	$-0.407924\pi$
$419$	11.6777			0.570495			0.285248	+	0.958454i	$0.407924\pi$
$420$	−1.30284	+	6.98526i	−0.0635719	+	0.340846i
$421$	31.0857			1.51502			0.757512	−	0.652822i	$-0.226415\pi$
$421$	31.0857			1.51502			0.757512	+	0.652822i	$0.226415\pi$
$422$	3.25528	+	3.25528i	0.158465	+	0.158465i
$423$	−9.88815	+	3.31259i	−0.480778	+	0.161064i
$424$		−	3.27790i		−	0.159189i
$425$	−11.6897	−	9.68817i	−0.567036	−	0.469945i
$426$	−1.77562	−	0.417757i	−0.0860291	−	0.0202404i
$427$	−15.9178	+	15.9178i	−0.770316	+	0.770316i
$428$	0.890386	−	0.890386i	0.0430384	−	0.0430384i
$429$	−0.416989	−	0.0981066i	−0.0201324	−	0.00473663i
$430$	−0.359370	−	7.69334i	−0.0173303	−	0.371006i
$431$		−	17.3722i		−	0.836791i	−0.908265	−	0.418395i	$-0.862593\pi$
$431$		−	17.3722i		−	0.836791i	0.908265	−	0.418395i	$-0.137407\pi$
$432$	5.17409	−	0.478323i	0.248939	−	0.0230133i
$433$	−3.43595	−	3.43595i	−0.165121	−	0.165121i	0.619710	−	0.784831i	$-0.287250\pi$
$433$	−3.43595	−	3.43595i	−0.165121	−	0.165121i	−0.784831	+	0.619710i	$0.787250\pi$
$434$	3.81613			0.183180
$435$	1.72832	+	2.52085i	0.0828668	+	0.120865i
$436$	11.3456			0.543358
$437$	0.166400	+	0.166400i	0.00796001	+	0.00796001i
$438$	−14.5241	+	8.99152i	−0.693990	+	0.429631i
$439$		−	12.2984i		−	0.586971i	−0.955964	−	0.293486i	$-0.905185\pi$
$439$		−	12.2984i		−	0.586971i	0.955964	−	0.293486i	$-0.0948153\pi$
$440$	0.421099	+	0.383515i	0.0200751	+	0.0182833i
$441$	−9.75815	−	4.86073i	−0.464674	−	0.231464i
$442$	2.08479	−	2.08479i	0.0991634	−	0.0991634i
$443$	11.2303	−	11.2303i	0.533567	−	0.533567i	−0.388065	−	0.921632i	$-0.626856\pi$
$443$	11.2303	−	11.2303i	0.533567	−	0.533567i	0.921632	+	0.388065i	$0.126856\pi$
$444$	2.53553	−	10.7769i	0.120331	−	0.511450i
$445$	−21.0361	+	0.982634i	−0.997207	+	0.0465813i
$446$			10.8622i			0.514341i
$447$	9.27336	+	14.9794i	0.438615	+	0.708501i
$448$	1.29732	+	1.29732i	0.0612926	+	0.0612926i
$449$	−4.18538			−0.197520			−0.0987601	−	0.995111i	$-0.531488\pi$
$449$	−4.18538			−0.197520			−0.0987601	+	0.995111i	$0.531488\pi$
$450$	−13.7170	+	6.06995i	−0.646625	+	0.286140i
$451$	−1.93903			−0.0913056
$452$	2.39356	+	2.39356i	0.112584	+	0.112584i
$453$	−12.8743	−	20.7960i	−0.604885	−	0.977080i
$454$			0.724884i			0.0340205i
$455$	3.97902	−	0.185867i	0.186539	−	0.00871359i
$456$	−0.0933479	+	0.396763i	−0.00437141	+	0.0185801i
$457$	7.32848	−	7.32848i	0.342812	−	0.342812i	−0.514612	−	0.857423i	$-0.672064\pi$
$457$	7.32848	−	7.32848i	0.342812	−	0.342812i	0.857423	+	0.514612i	$0.172064\pi$
$458$	11.5279	−	11.5279i	0.538664	−	0.538664i
$459$	12.1365	+	10.0825i	0.566484	+	0.470609i
$460$	1.65319	+	1.50564i	0.0770806	+	0.0702008i
$461$			11.7310i			0.546367i	0.961962	+	0.273184i	$0.0880767\pi$
$461$			11.7310i			0.546367i	−0.961962	+	0.273184i	$0.911923\pi$
$462$	0.688229	−	0.426065i	0.0320193	−	0.0198223i
$463$	−19.3473	−	19.3473i	−0.899144	−	0.899144i	0.0962167	−	0.995360i	$-0.469326\pi$
$463$	−19.3473	−	19.3473i	−0.899144	−	0.899144i	−0.995360	+	0.0962167i	$0.969326\pi$
$464$	0.789167			0.0366361
$465$	4.55530	+	6.64413i	0.211247	+	0.308114i
$466$	8.65142			0.400769
$467$	−18.8596	−	18.8596i	−0.872719	−	0.872719i	0.120049	−	0.992768i	$-0.461695\pi$
$467$	−18.8596	−	18.8596i	−0.872719	−	0.872719i	−0.992768	+	0.120049i	$0.961695\pi$
$468$	−0.925292	−	2.76202i	−0.0427717	−	0.127674i
$469$			2.63197i			0.121533i
$470$	−0.362685	−	7.76430i	−0.0167294	−	0.358141i
$471$	−25.7075	−	6.04830i	−1.18454	−	0.278691i
$472$	−7.30222	+	7.30222i	−0.336112	+	0.336112i
$473$	−0.620368	+	0.620368i	−0.0285245	+	0.0285245i
$474$	21.5032	+	5.05914i	0.987675	+	0.232374i
$475$	−0.109685	−	1.17150i	−0.00503272	−	0.0537523i
$476$			5.57106i			0.255349i
$477$	−3.12373	−	9.32439i	−0.143026	−	0.426934i
$478$	3.60784	+	3.60784i	0.165019	+	0.165019i
$479$	31.9961			1.46194			0.730970	−	0.682410i	$-0.239068\pi$
$479$	31.9961			1.46194			0.730970	+	0.682410i	$0.239068\pi$
$480$	−0.710113	+	3.80733i	−0.0324121	+	0.173780i
$481$	−6.20634			−0.282985
$482$	8.97865	+	8.97865i	0.408966	+	0.408966i
$483$	2.70192	−	1.67269i	0.122942	−	0.0761099i
$484$			10.9351i			0.497051i
$485$	−6.26526	+	6.87927i	−0.284491	+	0.312371i
$486$	14.2625	−	6.29137i	0.646960	−	0.285382i
$487$	5.57401	−	5.57401i	0.252583	−	0.252583i	−0.569446	−	0.822029i	$-0.692842\pi$
$487$	5.57401	−	5.57401i	0.252583	−	0.252583i	0.822029	+	0.569446i	$0.192842\pi$
$488$	−8.67602	+	8.67602i	−0.392745	+	0.392745i
$489$	0.759313	−	3.22736i	0.0343373	−	0.145946i
$490$	5.47137	−	6.00757i	0.247171	−	0.271394i
$491$		−	10.2383i		−	0.462049i	−0.972948	−	0.231025i	$-0.925792\pi$
$491$		−	10.2383i		−	0.462049i	0.972948	−	0.231025i	$-0.0742078\pi$
$492$	−6.94028	−	11.2107i	−0.312892	−	0.505419i
$493$	1.69445	+	1.69445i	0.0763143	+	0.0763143i
$494$	0.228492			0.0102804
$495$	1.56334	+	0.689660i	0.0702671	+	0.0309979i
$496$	2.07999			0.0933942
$497$	−1.36627	−	1.36627i	−0.0612855	−	0.0612855i
$498$	−11.4537	−	18.5013i	−0.513251	−	0.829062i
$499$			23.8537i			1.06784i	0.845536	+	0.533919i	$0.179281\pi$
$499$			23.8537i			1.06784i	−0.845536	+	0.533919i	$0.820719\pi$
$500$	−1.56051	−	11.0709i	−0.0697882	−	0.495106i
$501$	−3.31122	+	14.0739i	−0.147934	+	0.628775i
$502$	−15.4410	+	15.4410i	−0.689167	+	0.689167i
$503$	−18.1094	+	18.1094i	−0.807460	+	0.807460i	−0.984249	−	0.176789i	$-0.943429\pi$
$503$	−18.1094	+	18.1094i	−0.807460	+	0.807460i	0.176789	+	0.984249i	$0.443429\pi$
$504$	4.92668	+	2.45408i	0.219452	+	0.109314i
$505$	−1.58947	−	34.0271i	−0.0707303	−	1.51418i
$506$		−	0.254719i		−	0.0113236i
$507$	17.7565	−	10.9926i	0.788594	−	0.488198i
$508$	−11.6705	−	11.6705i	−0.517794	−	0.517794i
$509$	33.2985			1.47593			0.737966	−	0.674838i	$-0.235787\pi$
$509$	33.2985			1.47593			0.737966	+	0.674838i	$0.235787\pi$
$510$	−9.69958	+	6.65015i	−0.429505	+	0.294474i
$511$	−18.0943			−0.800447
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	0.112562	+	1.21760i	0.00496972	+	0.0537582i
$514$			3.00228i			0.132425i
$515$	3.11517	+	2.83712i	0.137271	+	0.125019i
$516$	−5.80717	−	1.36628i	−0.255647	−	0.0601470i
$517$	−0.626090	+	0.626090i	−0.0275354	+	0.0275354i
$518$	8.29241	−	8.29241i	0.364348	−	0.364348i
$519$	30.9200	+	7.27467i	1.35724	+	0.319322i
$520$	2.16877	−	0.101307i	0.0951070	−	0.00444262i
$521$		−	39.9278i		−	1.74927i	−0.484782	−	0.874635i	$-0.661101\pi$
$521$		−	39.9278i		−	1.74927i	0.484782	−	0.874635i	$-0.338899\pi$
$522$	2.24488	−	0.752048i	0.0982557	−	0.0329162i
$523$	12.0950	+	12.0950i	0.528876	+	0.528876i	0.920237	−	0.391361i	$-0.127996\pi$
$523$	12.0950	+	12.0950i	0.528876	+	0.528876i	−0.391361	+	0.920237i	$0.627996\pi$
$524$	−7.84601			−0.342755
$525$	−15.7384	−	2.18124i	−0.686882	−	0.0951970i
$526$	−27.8758			−1.21544
$527$	4.46602	+	4.46602i	0.194543	+	0.194543i
$528$	0.375120	−	0.232227i	0.0163250	−	0.0101064i
$529$		−	1.00000i		−	0.0434783i
$530$	7.32163	−	0.342007i	0.318031	−	0.0148558i
$531$	−13.8133	+	27.7308i	−0.599445	+	1.20341i
$532$	−0.305293	+	0.305293i	−0.0132361	+	0.0132361i
$533$	−5.22651	+	5.22651i	−0.226385	+	0.226385i
$534$	−3.73584	+	15.8787i	−0.161666	+	0.687139i
$535$	2.08169	+	1.89589i	0.0899995	+	0.0819666i
$536$			1.43456i			0.0619635i
$537$	15.6730	+	25.3168i	0.676339	+	1.09250i
$538$	−17.4234	−	17.4234i	−0.751176	−	0.751176i
$539$	−0.925627			−0.0398696
$540$	1.60825	+	11.5071i	0.0692079	+	0.495187i
$541$	−2.96852			−0.127627			−0.0638134	−	0.997962i	$-0.520326\pi$
$541$	−2.96852			−0.127627			−0.0638134	+	0.997962i	$0.520326\pi$
$542$	−19.5097	−	19.5097i	−0.838014	−	0.838014i
$543$	−13.7171	−	22.1575i	−0.588658	−	0.950868i
$544$			3.03651i			0.130189i
$545$	1.18377	+	25.3420i	0.0507071	+	1.08553i
$546$	0.706643	−	3.00349i	0.0302415	−	0.128538i
$547$	8.47104	−	8.47104i	0.362195	−	0.362195i	−0.502425	−	0.864621i	$-0.667559\pi$
$547$	8.47104	−	8.47104i	0.362195	−	0.362195i	0.864621	+	0.502425i	$0.167559\pi$
$548$	−0.446558	+	0.446558i	−0.0190760	+	0.0190760i
$549$	−16.4120	+	32.9479i	−0.700449	+	1.40618i
$550$	−0.812694	+	0.980596i	−0.0346534	+	0.0418128i
$551$			0.185711i			0.00791156i
$552$	1.47268	−	0.911701i	0.0626816	−	0.0388046i
$553$	16.5458	+	16.5458i	0.703601	+	0.703601i
$554$	29.8170			1.26680
$555$	24.3362	+	4.53901i	1.03302	+	0.192670i
$556$	12.5052			0.530337
$557$	14.3600	+	14.3600i	0.608454	+	0.608454i	0.942542	−	0.334088i	$-0.108428\pi$
$557$	14.3600	+	14.3600i	0.608454	+	0.608454i	−0.334088	+	0.942542i	$0.608428\pi$
$558$	5.91677	−	1.98215i	0.250477	−	0.0839113i
$559$			3.34430i			0.141449i
$560$	−2.76238	+	3.03310i	−0.116732	+	0.128172i
$561$	1.30406	+	0.306811i	0.0550575	+	0.0129536i
$562$	12.4596	−	12.4596i	0.525577	−	0.525577i
$563$	−13.7798	+	13.7798i	−0.580751	+	0.580751i	−0.935109	−	0.354359i	$-0.884699\pi$
$563$	−13.7798	+	13.7798i	−0.580751	+	0.580751i	0.354359	+	0.935109i	$0.384699\pi$
$564$	−5.86074	−	1.37888i	−0.246782	−	0.0580613i
$565$	−5.09659	+	5.59607i	−0.214415	+	0.235428i
$566$			25.1411i			1.05676i
$567$	16.3532	+	2.28598i	0.686770	+	0.0960019i
$568$	−0.744687	−	0.744687i	−0.0312464	−	0.0312464i
$569$	29.2322			1.22548			0.612739	−	0.790285i	$-0.290068\pi$
$569$	29.2322			1.22548			0.612739	+	0.790285i	$0.290068\pi$
$570$	−0.895962	−	0.167108i	−0.0375277	−	0.00699938i
$571$	−0.323861			−0.0135532			−0.00677659	−	0.999977i	$-0.502157\pi$
$571$	−0.323861			−0.0135532			−0.00677659	+	0.999977i	$0.502157\pi$
$572$	−0.174883	−	0.174883i	−0.00731223	−	0.00731223i
$573$	3.33353	−	2.06370i	0.139260	−	0.0862124i
$574$		−	13.9665i		−	0.582950i
$575$	−3.19056	+	3.84972i	−0.133055	+	0.160544i
$576$	2.68530	+	1.33760i	0.111887	+	0.0557334i
$577$	−16.8926	+	16.8926i	−0.703249	+	0.703249i	−0.965107	−	0.261857i	$-0.915665\pi$
$577$	−16.8926	+	16.8926i	−0.703249	+	0.703249i	0.261857	+	0.965107i	$0.415665\pi$
$578$	5.50099	−	5.50099i	0.228811	−	0.228811i
$579$	−0.577879	+	2.45620i	−0.0240158	+	0.102076i
$580$	0.0823393	+	1.76271i	0.00341895	+	0.0731925i
$581$		−	23.0491i		−	0.956239i
$582$	3.79377	+	6.12813i	0.157257	+	0.254019i
$583$	−0.590394	−	0.590394i	−0.0244516	−	0.0244516i
$584$	−9.86235			−0.408107
$585$	6.07279	−	2.35494i	0.251079	−	0.0973649i
$586$	−6.72848			−0.277951
$587$	13.5739	+	13.5739i	0.560257	+	0.560257i	0.929380	−	0.369124i	$-0.120342\pi$
$587$	13.5739	+	13.5739i	0.560257	+	0.560257i	−0.369124	+	0.929380i	$0.620342\pi$
$588$	−3.31305	−	5.35162i	−0.136628	−	0.220697i
$589$			0.489474i			0.0201684i
$590$	−17.0724	−	15.5486i	−0.702858	−	0.640125i
$591$	0.320643	−	1.36285i	0.0131895	−	0.0560601i
$592$	4.51979	−	4.51979i	0.185762	−	0.185762i
$593$	−12.1444	+	12.1444i	−0.498710	+	0.498710i	−0.911036	−	0.412326i	$-0.864716\pi$
$593$	−12.1444	+	12.1444i	−0.498710	+	0.498710i	0.412326	+	0.911036i	$0.364716\pi$
$594$	0.845770	−	1.01807i	0.0347024	−	0.0417721i
$595$	−12.4437	+	0.581268i	−0.510142	+	0.0238296i
$596$			10.1715i			0.416640i
$597$	27.7628	−	17.1872i	1.13625	−	0.703426i
$598$	−0.686574	−	0.686574i	−0.0280761	−	0.0280761i
$599$	16.7260			0.683406			0.341703	−	0.939808i	$-0.388996\pi$
$599$	16.7260			0.683406			0.341703	+	0.939808i	$0.388996\pi$
$600$	−8.57826	−	1.18889i	−0.350206	−	0.0485361i
$601$	28.9544			1.18108			0.590538	−	0.807010i	$-0.298915\pi$
$601$	28.9544			1.18108			0.590538	+	0.807010i	$0.298915\pi$
$602$	−4.46839	−	4.46839i	−0.182118	−	0.182118i
$603$	1.36708	+	4.08078i	0.0556720	+	0.166182i
$604$		−	14.1211i		−	0.574581i
$605$	−24.4250	+	1.14094i	−0.993019	+	0.0463857i
$606$	−25.6847	−	6.04294i	−1.04337	−	0.245478i
$607$	−21.5740	+	21.5740i	−0.875663	+	0.875663i	−0.993082	−	0.117420i	$-0.962538\pi$
$607$	−21.5740	+	21.5740i	−0.875663	+	0.875663i	0.117420	+	0.993082i	$0.462538\pi$
$608$	−0.166400	+	0.166400i	−0.00674842	+	0.00674842i
$609$	2.44114	+	0.574337i	0.0989200	+	0.0232733i
$610$	−20.2843	−	18.4738i	−0.821286	−	0.747983i
$611$			3.37515i			0.136544i
$612$	2.89369	+	8.63773i	0.116971	+	0.349159i
$613$	0.222524	+	0.222524i	0.00898766	+	0.00898766i	0.711586	−	0.702599i	$-0.247977\pi$
$613$	0.222524	+	0.222524i	0.00898766	+	0.00898766i	−0.702599	+	0.711586i	$0.747977\pi$
$614$	−32.6003			−1.31564
$615$	24.3166	−	16.6717i	0.980538	−	0.672269i
$616$	0.467330			0.0188292
$617$	13.9375	+	13.9375i	0.561104	+	0.561104i	0.929621	−	0.368517i	$-0.120134\pi$
$617$	13.9375	+	13.9375i	0.561104	+	0.561104i	−0.368517	+	0.929621i	$0.620134\pi$
$618$	2.77503	−	1.71795i	0.111628	−	0.0691060i
$619$			28.4695i			1.14429i	0.820154	+	0.572143i	$0.193888\pi$
$619$			28.4695i			1.14429i	−0.820154	+	0.572143i	$0.806112\pi$
$620$	0.217020	+	4.64593i	0.00871572	+	0.186585i
$621$	3.32041	−	3.99686i	0.133243	−	0.160388i
$622$	17.5532	−	17.5532i	0.703821	−	0.703821i
$623$	−12.2180	+	12.2180i	−0.489505	+	0.489505i
$624$	0.385157	−	1.63706i	0.0154186	−	0.0655347i
$625$	24.5655	−	4.64071i	0.982620	−	0.185629i
$626$			3.27547i			0.130914i
$627$	0.0546490	+	0.0882754i	0.00218247	+	0.00352538i
$628$	−10.7816	−	10.7816i	−0.430232	−	0.430232i
$629$	19.4093			0.773898
$630$	−4.96748	+	11.2605i	−0.197909	+	0.448627i
$631$	14.9930			0.596863			0.298431	−	0.954431i	$-0.403537\pi$
$631$	14.9930			0.596863			0.298431	+	0.954431i	$0.403537\pi$
$632$	9.01834	+	9.01834i	0.358730	+	0.358730i
$633$	4.19716	+	6.77974i	0.166822	+	0.269471i
$634$			31.8218i			1.26381i
$635$	24.8499	−	27.2852i	0.986138	−	1.08278i
$636$	1.30026	−	5.52660i	0.0515588	−	0.219144i
$637$	−2.49495	+	2.49495i	−0.0988536	+	0.0988536i
$638$	0.142139	−	0.142139i	0.00562736	−	0.00562736i
$639$	−2.82801	−	1.40869i	−0.111874	−	0.0557269i
$640$	−1.50564	+	1.65319i	−0.0595156	+	0.0653482i
$641$			5.92967i			0.234208i	0.993120	+	0.117104i	$0.0373611\pi$
$641$			5.92967i			0.234208i	−0.993120	+	0.117104i	$0.962639\pi$
$642$	1.85440	−	1.14801i	0.0731872	−	0.0453083i
$643$	0.231570	+	0.231570i	0.00913224	+	0.00913224i	0.711658	−	0.702526i	$-0.247945\pi$
$643$	0.231570	+	0.231570i	0.00913224	+	0.00913224i	−0.702526	+	0.711658i	$0.747945\pi$
$644$	1.83469			0.0722969
$645$	2.44586	−	13.1136i	0.0963055	−	0.516349i
$646$	−0.714570			−0.0281144
$647$	−25.8635	−	25.8635i	−1.01680	−	1.01680i	−0.999856	−	0.0169438i	$-0.994606\pi$
$647$	−25.8635	−	25.8635i	−1.01680	−	1.01680i	−0.0169438	−	0.999856i	$-0.505394\pi$
$648$	8.91334	+	1.24597i	0.350149	+	0.0489465i
$649$			2.63045i			0.103254i
$650$	0.452566	+	4.83367i	0.0177511	+	0.189592i
$651$	6.43405	+	1.51376i	0.252170	+	0.0593291i
$652$	1.35354	−	1.35354i	0.0530087	−	0.0530087i
$653$	30.6540	−	30.6540i	1.19958	−	1.19958i	0.225292	−	0.974291i	$-0.427667\pi$
$653$	30.6540	−	30.6540i	1.19958	−	1.19958i	0.974291	−	0.225292i	$-0.0723335\pi$
$654$	19.1289	+	4.50054i	0.748000	+	0.175985i
$655$	−0.818629	−	17.5251i	−0.0319865	−	0.684762i
$656$		−	7.61245i		−	0.297216i
$657$	−28.0546	+	9.39847i	−1.09452	+	0.366669i
$658$	−4.50960	−	4.50960i	−0.175803	−	0.175803i
$659$	−3.72086			−0.144944			−0.0724721	−	0.997370i	$-0.523089\pi$
$659$	−3.72086			−0.144944			−0.0724721	+	0.997370i	$0.523089\pi$
$660$	0.557850	+	0.813651i	0.0217143	+	0.0316713i
$661$	35.1235			1.36615			0.683073	−	0.730350i	$-0.260643\pi$
$661$	35.1235			1.36615			0.683073	+	0.730350i	$0.260643\pi$
$662$	−6.61496	−	6.61496i	−0.257098	−	0.257098i
$663$	4.34198	−	2.68801i	0.168628	−	0.104393i
$664$		−	12.5630i		−	0.487537i
$665$	−0.713765	−	0.650059i	−0.0276786	−	0.0252082i
$666$	8.54988	−	17.1643i	0.331301	−	0.665103i
$667$	0.558025	−	0.558025i	0.0216068	−	0.0216068i
$668$	−5.90252	+	5.90252i	−0.228375	+	0.228375i
$669$	−4.30878	+	18.3139i	−0.166587	+	0.708056i
$670$	−3.20428	+	0.149678i	−0.123792	+	0.00578255i
$671$			3.12533i			0.120652i
$672$	1.67269	+	2.70192i	0.0645253	+	0.104229i
$673$	−6.35962	−	6.35962i	−0.245145	−	0.245145i	0.573830	−	0.818975i	$-0.305457\pi$
$673$	−6.35962	−	6.35962i	−0.245145	−	0.245145i	−0.818975	+	0.573830i	$0.805457\pi$
$674$	27.6432			1.06477
$675$	−25.5349	+	4.79285i	−0.982837	+	0.184477i
$676$	12.0572			0.463740
$677$	−1.56497	−	1.56497i	−0.0601469	−	0.0601469i	0.676394	−	0.736540i	$-0.263542\pi$
$677$	−1.56497	−	1.56497i	−0.0601469	−	0.0601469i	−0.736540	+	0.676394i	$0.763542\pi$
$678$	3.08611	+	4.98504i	0.118521	+	0.191449i
$679$			7.63450i			0.292985i
$680$	−6.78246	+	0.316821i	−0.260095	+	0.0121495i
$681$	−0.287544	+	1.22217i	−0.0110187	+	0.0468335i
$682$	0.374633	−	0.374633i	0.0143455	−	0.0143455i
$683$	2.23708	−	2.23708i	0.0855996	−	0.0855996i	−0.663011	−	0.748610i	$-0.730722\pi$
$683$	2.23708	−	2.23708i	0.0855996	−	0.0855996i	0.748610	+	0.663011i	$0.230722\pi$
$684$	−0.314772	+	0.631919i	−0.0120356	+	0.0241620i
$685$	−1.04404	−	0.950853i	−0.0398906	−	0.0363302i
$686$		−	19.5099i		−	0.744893i
$687$	24.0091	−	14.8634i	0.916004	−	0.567074i
$688$	−2.43550	−	2.43550i	−0.0928526	−	0.0928526i
$689$	−3.18272			−0.121252
$690$	2.19006	+	3.19431i	0.0833742	+	0.121605i
$691$	50.0983			1.90583			0.952914	−	0.303242i	$-0.0980690\pi$
$691$	50.0983			1.90583			0.952914	+	0.303242i	$0.0980690\pi$
$692$	12.9677	+	12.9677i	0.492958	+	0.492958i
$693$	1.32937	−	0.445349i	0.0504988	−	0.0169174i
$694$		−	28.5319i		−	1.08306i
$695$	1.30475	+	27.9319i	0.0494920	+	1.05952i
$696$	1.33055	+	0.313043i	0.0504343	+	0.0118659i
$697$	16.3450	−	16.3450i	0.619111	−	0.619111i
$698$	2.36842	−	2.36842i	0.0896460	−	0.0896460i
$699$	14.5864	+	3.43181i	0.551709	+	0.129803i
$700$	−7.06304	−	5.85368i	−0.266958	−	0.221248i
$701$			17.7346i			0.669827i	0.942249	+	0.334913i	$0.108707\pi$
$701$			17.7346i			0.669827i	−0.942249	+	0.334913i	$0.891293\pi$
$702$	−0.464433	−	5.02384i	−0.0175289	−	0.189613i
$703$	1.06362	+	1.06362i	0.0401153	+	0.0401153i
$704$	0.254719			0.00960007
$705$	2.46842	−	13.2346i	0.0929659	−	0.498444i
$706$	−0.830811			−0.0312680
$707$	−19.7633	−	19.7633i	−0.743277	−	0.743277i
$708$	−15.2083	+	9.41504i	−0.571562	+	0.353839i
$709$			38.9851i			1.46411i	0.681243	+	0.732057i	$0.261440\pi$
$709$			38.9851i			1.46411i	−0.681243	+	0.732057i	$0.738560\pi$
$710$	1.58566	−	1.74106i	0.0595087	−	0.0653406i
$711$	34.2479	+	17.0596i	1.28440	+	0.639784i
$712$	−6.65945	+	6.65945i	−0.249573	+	0.249573i
$713$	1.47077	−	1.47077i	0.0550809	−	0.0550809i
$714$	−2.20990	+	9.39289i	−0.0827035	+	0.351520i
$715$	0.372378	−	0.408872i	0.0139261	−	0.0152909i
$716$			17.1909i			0.642455i
$717$	4.65173	+	7.51401i	0.173722	+	0.280616i
$718$	−15.6414	−	15.6414i	−0.583731	−	0.583731i
$719$	24.8193			0.925605			0.462803	−	0.886461i	$-0.346844\pi$
$719$	24.8193			0.925605			0.462803	+	0.886461i	$0.346844\pi$
$720$	−2.70753	+	6.13753i	−0.100904	+	0.228732i
$721$	3.45716			0.128751
$722$	13.3959	+	13.3959i	0.498543	+	0.498543i
$723$	11.5765	+	18.6998i	0.430536	+	0.695451i
$724$		−	15.0456i		−	0.559166i
$725$	−3.92865	+	0.367831i	−0.145906	+	0.0136609i
$726$	−4.33769	+	18.4368i	−0.160987	+	0.684253i
$727$	17.7250	−	17.7250i	0.657385	−	0.657385i	−0.297376	−	0.954761i	$-0.596111\pi$
$727$	17.7250	−	17.7250i	0.657385	−	0.657385i	0.954761	+	0.297376i	$0.0961114\pi$
$728$	1.25965	−	1.25965i	0.0466857	−	0.0466857i
$729$	26.5424	−	4.94977i	0.983052	−	0.183325i
$730$	−1.02901	−	22.0289i	−0.0380853	−	0.815325i
$731$		−	10.4587i		−	0.386830i
$732$	−18.0695	+	11.1863i	−0.667867	+	0.413459i
$733$	0.884740	+	0.884740i	0.0326786	+	0.0326786i	0.723257	−	0.690579i	$-0.242644\pi$
$733$	0.884740	+	0.884740i	0.0326786	+	0.0326786i	−0.690579	+	0.723257i	$0.742644\pi$
$734$	−14.3814			−0.530827
$735$	11.6079	−	7.95850i	0.428163	−	0.293554i
$736$	1.00000			0.0368605
$737$	0.258383	+	0.258383i	0.00951767	+	0.00951767i
$738$	−7.25440	−	21.6545i	−0.267038	−	0.797114i
$739$		−	30.9488i		−	1.13847i	−0.822175	−	0.569235i	$-0.807239\pi$
$739$		−	30.9488i		−	1.13847i	0.822175	−	0.569235i	$-0.192761\pi$
$740$	10.5671	+	9.62397i	0.388456	+	0.353784i
$741$	0.385241	+	0.0906372i	0.0141522	+	0.00332964i
$742$	4.25249	−	4.25249i	0.156114	−	0.156114i
$743$	9.54480	−	9.54480i	0.350165	−	0.350165i	−0.510006	−	0.860171i	$-0.670357\pi$
$743$	9.54480	−	9.54480i	0.350165	−	0.350165i	0.860171	+	0.510006i	$0.170357\pi$
$744$	3.50689	+	0.825080i	0.128569	+	0.0302489i
$745$	−22.7194	+	1.06126i	−0.832373	+	0.0388816i
$746$			8.94756i			0.327594i
$747$	−11.9721	−	35.7368i	−0.438035	−	1.30754i
$748$	0.546917	+	0.546917i	0.0199973	+	0.0199973i
$749$	2.31023			0.0844140
$750$	1.76051	−	19.2847i	0.0642846	−	0.704179i
$751$	36.9921			1.34986			0.674930	−	0.737882i	$-0.264174\pi$
$751$	36.9921			1.34986			0.674930	+	0.737882i	$0.264174\pi$
$752$	−2.45797	−	2.45797i	−0.0896328	−	0.0896328i
$753$	−32.1589	+	19.9088i	−1.17194	+	0.725515i
$754$		−	0.766251i		−	0.0279052i
$755$	31.5414	−	1.47336i	1.14791	−	0.0536209i
$756$	7.33299	+	6.09192i	0.266698	+	0.221561i
$757$	−28.4234	+	28.4234i	−1.03306	+	1.03306i	−0.0336303	+	0.999434i	$0.510707\pi$
$757$	−28.4234	+	28.4234i	−1.03306	+	1.03306i	−0.999434	+	0.0336303i	$0.989293\pi$
$758$	−21.0304	+	21.0304i	−0.763860	+	0.763860i
$759$	0.101041	−	0.429460i	0.00366754	−	0.0155884i
$760$	−0.389039	−	0.354315i	−0.0141119	−	0.0128524i
$761$		−	33.3114i		−	1.20754i	−0.797160	−	0.603768i	$-0.793665\pi$
$761$		−	33.3114i		−	1.20754i	0.797160	−	0.603768i	$-0.206335\pi$
$762$	−15.0472	−	24.3060i	−0.545103	−	0.880513i
$763$	14.7189	+	14.7189i	0.532861	+	0.532861i
$764$	2.26357			0.0818932
$765$	−18.9916	+	7.36468i	−0.686642	+	0.266270i
$766$	16.7300			0.604479
$767$	7.09018	+	7.09018i	0.256011	+	0.256011i
$768$	0.911701	+	1.47268i	0.0328982	+	0.0531409i
$769$			15.4887i			0.558538i	0.960213	+	0.279269i	$0.0900920\pi$
$769$			15.4887i			0.558538i	−0.960213	+	0.279269i	$0.909908\pi$
$770$	0.0487598	+	1.04384i	0.00175718	+	0.0376175i
$771$	−1.19093	+	5.06189i	−0.0428903	+	0.182300i
$772$	−1.03012	+	1.03012i	−0.0370748	+	0.0370748i
$773$	−22.3134	+	22.3134i	−0.802556	+	0.802556i	−0.983494	−	0.180938i	$-0.942087\pi$
$773$	−22.3134	+	22.3134i	−0.802556	+	0.802556i	0.180938	+	0.983494i	$0.442087\pi$
$774$	−9.24902	−	4.60713i	−0.332449	−	0.165600i
$775$	−10.3546	+	0.969484i	−0.371950	+	0.0348249i
$776$			4.16120i			0.149378i
$777$	17.2705	−	10.6917i	0.619577	−	0.383564i
$778$	−23.9708	−	23.9708i	−0.859394	−	0.859394i
$779$	1.79141			0.0641838
$780$	3.69677	+	0.689493i	0.132366	+	0.0246878i
$781$	−0.268256			−0.00959896
$782$	2.14714	+	2.14714i	0.0767816	+	0.0767816i
$783$	4.08322	−	0.377476i	0.145922	−	0.0134899i
$784$		−	3.63392i		−	0.129783i
$785$	22.9572	−	25.2070i	0.819377	−	0.899677i
$786$	−13.2285	−	3.11232i	−0.471845	−	0.111013i
$787$	−17.3064	+	17.3064i	−0.616906	+	0.616906i	−0.944737	−	0.327830i	$-0.893683\pi$
$787$	−17.3064	+	17.3064i	−0.616906	+	0.616906i	0.327830	+	0.944737i	$0.393683\pi$
$788$	0.571573	−	0.571573i	0.0203614	−	0.0203614i
$789$	−46.9991	−	11.0577i	−1.67321	−	0.393663i
$790$	−19.2027	+	21.0846i	−0.683202	+	0.750157i
$791$			6.21043i			0.220817i
$792$	0.724578	−	0.242738i	0.0257468	−	0.00862532i
$793$	8.42409	+	8.42409i	0.299148	+	0.299148i
$794$	−1.43747			−0.0510138
$795$	12.4801	+	2.32768i	0.442622	+	0.0825544i
$796$	18.8518			0.668184
$797$	32.5163	+	32.5163i	1.15179	+	1.15179i	0.986194	+	0.165592i	$0.0529535\pi$
$797$	32.5163	+	32.5163i	1.15179	+	1.15179i	0.165592	+	0.986194i	$0.447047\pi$
$798$	−0.635831	+	0.393626i	−0.0225082	+	0.0139342i
$799$		−	10.5552i		−	0.373416i
$800$	−3.84972	−	3.19056i	−0.136108	−	0.112803i
$801$	−12.5974	+	25.2898i	−0.445107	+	0.893572i
$802$	15.4389	−	15.4389i	0.545167	−	0.545167i
$803$	−1.77634	+	1.77634i	−0.0626857	+	0.0626857i
$804$	−0.569054	+	2.41869i	−0.0200690	+	0.0853006i
$805$	0.191426	+	4.09802i	0.00674688	+	0.144436i
$806$		−	2.01959i		−	0.0711370i
$807$	−22.4647	−	36.2876i	−0.790794	−	1.27738i
$808$	−10.7720	−	10.7720i	−0.378959	−	0.378959i
$809$	23.9795			0.843074			0.421537	−	0.906811i	$-0.361491\pi$
$809$	23.9795			0.843074			0.421537	+	0.906811i	$0.361491\pi$
$810$	−1.85306	+	20.0391i	−0.0651098	+	0.704103i
$811$	45.9811			1.61461			0.807307	−	0.590131i	$-0.200924\pi$
$811$	45.9811			1.61461			0.807307	+	0.590131i	$0.200924\pi$
$812$	1.02380	+	1.02380i	0.0359284	+	0.0359284i
$813$	−25.1546	−	40.6327i	−0.882212	−	1.42505i
$814$		−	1.62815i		−	0.0570666i
$815$	3.16453	+	2.88208i	0.110849	+	0.100955i
$816$	−1.20451	+	5.11961i	−0.0421663	+	0.179222i
$817$	0.573136	−	0.573136i	0.0200515	−	0.0200515i
$818$	−22.9409	+	22.9409i	−0.802109	+	0.802109i
$819$	2.38282	−	4.78362i	0.0832625	−	0.167153i
$820$	17.0034	−	0.794260i	0.593785	−	0.0277368i
$821$			9.96541i			0.347795i	0.984764	+	0.173898i	$0.0556362\pi$
$821$			9.96541i			0.347795i	−0.984764	+	0.173898i	$0.944364\pi$
$822$	−0.930041	+	0.575765i	−0.0324389	+	0.0200821i
$823$	−21.9898	−	21.9898i	−0.766516	−	0.766516i	0.210975	−	0.977491i	$-0.432336\pi$
$823$	−21.9898	−	21.9898i	−0.766516	−	0.766516i	−0.977491	+	0.210975i	$0.932336\pi$
$824$	1.88433			0.0656438
$825$	−1.75919	+	1.33092i	−0.0612473	+	0.0463369i
$826$	−18.9466			−0.659238
$827$	−17.8372	−	17.8372i	−0.620260	−	0.620260i	0.325338	−	0.945598i	$-0.394522\pi$
$827$	−17.8372	−	17.8372i	−0.620260	−	0.620260i	−0.945598	+	0.325338i	$0.894522\pi$
$828$	2.84462	−	0.952965i	0.0988574	−	0.0331178i
$829$			32.1993i			1.11833i	0.829058	+	0.559163i	$0.188878\pi$
$829$			32.1993i			1.11833i	−0.829058	+	0.559163i	$0.811122\pi$
$830$	28.0610	−	1.31078i	0.974013	−	0.0454979i
$831$	50.2720	+	11.8277i	1.74392	+	0.410298i
$832$	0.686574	−	0.686574i	0.0238027	−	0.0238027i
$833$	7.80253	−	7.80253i	0.270342	−	0.270342i
$834$	21.0839	+	4.96049i	0.730075	+	0.171768i
$835$	−13.7999	−	12.5682i	−0.477566	−	0.434941i
$836$			0.0599418i			0.00207313i
$837$	10.7620	−	0.994905i	0.371991	−	0.0343890i
$838$	8.25742	+	8.25742i	0.285248	+	0.285248i
$839$	−27.6357			−0.954092			−0.477046	−	0.878878i	$-0.658292\pi$
$839$	−27.6357			−0.954092			−0.477046	+	0.878878i	$0.658292\pi$
$840$	−5.86057	+	4.01808i	−0.202209	+	0.138637i
$841$	−28.3772			−0.978525
$842$	21.9809	+	21.9809i	0.757512	+	0.757512i
$843$	25.9495	−	16.0647i	0.893749	−	0.553297i
$844$			4.60366i			0.158465i
$845$	1.25802	+	26.9314i	0.0432770	+	0.926469i
$846$	−9.33433	−	4.64962i	−0.320921	−	0.159857i
$847$	−14.1864	+	14.1864i	−0.487449	+	0.487449i
$848$	2.31783	−	2.31783i	0.0795945	−	0.0795945i
$849$	−9.97285	+	42.3883i	−0.342267	+	1.45476i
$850$	−1.41532	−	15.1165i	−0.0485452	−	0.518490i
$851$		−	6.39195i		−	0.219113i
$852$	−0.960155	−	1.55095i	−0.0328944	−	0.0531348i
$853$	11.1857	+	11.1857i	0.382990	+	0.382990i	0.872178	−	0.489188i	$-0.162707\pi$
$853$	11.1857	+	11.1857i	0.382990	+	0.382990i	−0.489188	+	0.872178i	$0.662707\pi$
$854$	−22.5112			−0.770316
$855$	−1.44432	−	0.637152i	−0.0493946	−	0.0217901i
$856$	1.25920			0.0430384
$857$	−10.4211	−	10.4211i	−0.355979	−	0.355979i	0.506349	−	0.862328i	$-0.330995\pi$
$857$	−10.4211	−	10.4211i	−0.355979	−	0.355979i	−0.862328	+	0.506349i	$0.830995\pi$
$858$	−0.225484	−	0.364228i	−0.00769790	−	0.0124345i
$859$			29.1495i			0.994567i	0.867588	+	0.497284i	$0.165669\pi$
$859$			29.1495i			0.994567i	−0.867588	+	0.497284i	$0.834331\pi$
$860$	5.18590	−	5.69413i	0.176838	−	0.194168i
$861$	5.54016	−	23.5477i	0.188808	−	0.802504i
$862$	12.2840	−	12.2840i	0.418395	−	0.418395i
$863$	−7.86977	+	7.86977i	−0.267890	+	0.267890i	−0.828250	−	0.560359i	$-0.810663\pi$
$863$	−7.86977	+	7.86977i	−0.267890	+	0.267890i	0.560359	+	0.828250i	$0.310663\pi$
$864$	3.99686	+	3.32041i	0.135976	+	0.112963i
$865$	−27.6121	+	30.3181i	−0.938838	+	1.03085i
$866$		−	4.85917i		−	0.165121i
$867$	11.4569	−	7.09265i	0.389096	−	0.240879i
$868$	2.69841	+	2.69841i	0.0915900	+	0.0915900i
$869$	3.24865			0.110203
$870$	−0.560398	+	3.00462i	−0.0189993	+	0.101866i
$871$	1.39290			0.0471967
$872$	8.02258	+	8.02258i	0.271679	+	0.271679i
$873$	3.96547	+	11.8370i	0.134211	+	0.400623i
$874$			0.235326i			0.00796001i
$875$	12.3380	−	16.3870i	0.417101	−	0.553981i
$876$	−16.6281	−	3.91215i	−0.561811	−	0.132179i
$877$	−12.4703	+	12.4703i	−0.421092	+	0.421092i	−0.885580	−	0.464488i	$-0.846238\pi$
$877$	−12.4703	+	12.4703i	−0.421092	+	0.421092i	0.464488	+	0.885580i	$0.346238\pi$
$878$	8.69629	−	8.69629i	0.293486	−	0.293486i
$879$	−11.3443	−	2.66902i	−0.382634	−	0.0900238i
$880$	0.0265766	+	0.568948i	0.000895897	+	0.0191792i
$881$			24.7836i			0.834981i	0.908681	+	0.417490i	$0.137090\pi$
$881$			24.7836i			0.834981i	−0.908681	+	0.417490i	$0.862910\pi$
$882$	−3.46299	−	10.3371i	−0.116605	−	0.348069i
$883$	−18.5993	−	18.5993i	−0.625916	−	0.625916i	0.321122	−	0.947038i	$-0.395940\pi$
$883$	−18.5993	−	18.5993i	−0.625916	−	0.625916i	−0.947038	+	0.321122i	$0.895940\pi$
$884$	2.94834			0.0991634
$885$	−22.6165	−	32.9873i	−0.760246	−	1.10886i
$886$	15.8820			0.533567
$887$	−10.0096	−	10.0096i	−0.336088	−	0.336088i	0.518805	−	0.854893i	$-0.326377\pi$
$887$	−10.0096	−	10.0096i	−0.336088	−	0.336088i	−0.854893	+	0.518805i	$0.826377\pi$
$888$	9.41333	−	5.82755i	0.315891	−	0.195560i
$889$		−	30.2807i		−	1.01558i
$890$	−15.5696	−	14.1799i	−0.521894	−	0.475313i
$891$	1.82983	−	1.38099i	0.0613015	−	0.0462650i
$892$	−7.68075	+	7.68075i	−0.257171	+	0.257171i
$893$	0.578422	−	0.578422i	0.0193562	−	0.0193562i
$894$	−4.03478	+	17.1493i	−0.134943	+	0.573558i
$895$	−38.3982	+	1.79365i	−1.28351	+	0.0599551i
$896$			1.83469i			0.0612926i
$897$	−0.885227	−	1.42992i	−0.0295569	−	0.0477437i
$898$	−2.95951	−	2.95951i	−0.0987601	−	0.0987601i
$899$	1.64146			0.0547456
$900$	−13.9915	−	5.40727i	−0.466383	−	0.180242i
$901$	9.95340			0.331596
$902$	−1.37110	−	1.37110i	−0.0456528	−	0.0456528i
$903$	−5.76127	−	9.30627i	−0.191723	−	0.309693i
$904$			3.38500i			0.112584i
$905$	33.6064	−	1.56982i	1.11711	−	0.0521824i
$906$	5.60151	−	23.8084i	0.186098	−	0.790983i
$907$	−30.3282	+	30.3282i	−1.00703	+	1.00703i	−0.00705622	+	0.999975i	$0.502246\pi$
$907$	−30.3282	+	30.3282i	−1.00703	+	1.00703i	−0.999975	+	0.00705622i	$0.997754\pi$
$908$	−0.512571	+	0.512571i	−0.0170103	+	0.0170103i
$909$	−40.9077	−	20.3770i	−1.35682	−	0.675862i
$910$	2.94502	+	2.68217i	0.0976265	+	0.0889129i
$911$		−	21.9257i		−	0.726430i	−0.931705	−	0.363215i	$-0.881679\pi$
$911$		−	21.9257i		−	0.726430i	0.931705	−	0.363215i	$-0.118321\pi$
$912$	−0.346560	+	0.214547i	−0.0114758	+	0.00710435i
$913$	−2.26276	−	2.26276i	−0.0748863	−	0.0748863i
$914$	10.3640			0.342812
$915$	−26.8715	−	39.1934i	−0.888344	−	1.29569i
$916$	16.3029			0.538664
$917$	−10.1788	−	10.1788i	−0.336133	−	0.336133i
$918$	1.45243	+	15.7112i	0.0479375	+	0.518547i
$919$		−	24.2711i		−	0.800630i	−0.916378	−	0.400315i	$-0.868901\pi$
$919$		−	24.2711i		−	0.800630i	0.916378	−	0.400315i	$-0.131099\pi$
$920$	0.104337	+	2.23363i	0.00343989	+	0.0736407i
$921$	−54.9646	−	12.9317i	−1.81115	−	0.426115i
$922$	−8.29508	+	8.29508i	−0.273184	+	0.273184i
$923$	−0.723063	+	0.723063i	−0.0237999	+	0.0237999i
$924$	0.787925	+	0.185378i	0.0259208	+	0.00609849i
$925$	−20.3939	+	24.6072i	−0.670546	+	0.809081i
$926$		−	27.3612i		−	0.899144i
$927$	5.36021	−	1.79570i	0.176052	−	0.0589786i
$928$	0.558025	+	0.558025i	0.0183181	+	0.0183181i
$929$	6.03998			0.198165			0.0990826	−	0.995079i	$-0.468409\pi$
$929$	6.03998			0.198165			0.0990826	+	0.995079i	$0.468409\pi$
$930$	−1.47703	+	7.91919i	−0.0484336	+	0.259681i
$931$	0.855154			0.0280265
$932$	6.11748	+	6.11748i	0.200385	+	0.200385i
$933$	36.5580	−	22.6321i	1.19685	−	0.740942i
$934$		−	26.6715i		−	0.872719i
$935$	−1.16455	+	1.27867i	−0.0380848	+	0.0418171i
$936$	1.29876	−	2.60732i	0.0424513	−	0.0852230i
$937$	24.7487	−	24.7487i	0.808506	−	0.808506i	−0.175902	−	0.984408i	$-0.556284\pi$
$937$	24.7487	−	24.7487i	0.808506	−	0.808506i	0.984408	+	0.175902i	$0.0562842\pi$
$938$	−1.86108	+	1.86108i	−0.0607665	+	0.0607665i
$939$	−1.29930	+	5.52249i	−0.0424010	+	0.180220i
$940$	5.23373	−	5.74665i	0.170706	−	0.187435i
$941$			19.5391i			0.636957i	0.947930	+	0.318479i	$0.103172\pi$
$941$			19.5391i			0.636957i	−0.947930	+	0.318479i	$0.896828\pi$
$942$	−13.9011	−	22.4547i	−0.452924	−	0.731614i
$943$	−5.38282	−	5.38282i	−0.175289	−	0.175289i
$944$	−10.3269			−0.336112
$945$	−12.8420	+	17.0148i	−0.417750	+	0.553492i
$946$	−0.877332			−0.0285245
$947$	−14.5559	−	14.5559i	−0.473003	−	0.473003i	0.429882	−	0.902885i	$-0.358555\pi$
$947$	−14.5559	−	14.5559i	−0.473003	−	0.473003i	−0.902885	+	0.429882i	$0.858555\pi$
$948$	11.6277	+	18.7824i	0.377650	+	0.610025i
$949$			9.57597i			0.310849i
$950$	0.750819	−	0.905938i	0.0243598	−	0.0293925i
$951$	−12.6229	+	53.6521i	−0.409327	+	1.73979i
$952$	−3.93933	+	3.93933i	−0.127675	+	0.127675i
$953$	−8.38520	+	8.38520i	−0.271623	+	0.271623i	−0.829753	−	0.558130i	$-0.811519\pi$
$953$	−8.38520	+	8.38520i	−0.271623	+	0.271623i	0.558130	+	0.829753i	$0.311519\pi$
$954$	4.38453	−	8.80215i	0.141954	−	0.284980i
$955$	0.236174	+	5.05599i	0.00764242	+	0.163608i
$956$			5.10225i			0.165019i
$957$	0.296033	−	0.183266i	0.00956937	−	0.00592415i
$958$	22.6247	+	22.6247i	0.730970	+	0.730970i
$959$	−1.15866			−0.0374150
$960$	−3.19431	+	2.19006i	−0.103096	+	0.0706839i
$961$	−26.6737			−0.860440
$962$	−4.38855	−	4.38855i	−0.141492	−	0.141492i
$963$	3.58193	−	1.19997i	0.115426	−	0.0386684i
$964$			12.6977i			0.408966i
$965$	−2.40838	−	2.19343i	−0.0775286	−	0.0706089i
$966$	3.09331	+	0.727776i	0.0995257	+	0.0234158i
$967$	22.3141	−	22.3141i	0.717574	−	0.717574i	−0.250534	−	0.968108i	$-0.580606\pi$
$967$	22.3141	−	22.3141i	0.717574	−	0.717574i	0.968108	+	0.250534i	$0.0806060\pi$
$968$	−7.73230	+	7.73230i	−0.248525	+	0.248525i
$969$	−1.20478	−	0.283452i	−0.0387030	−	0.00910580i
$970$	−9.29459	+	0.434167i	−0.298431	+	0.0139403i
$971$		−	36.3642i		−	1.16698i	−0.812120	−	0.583491i	$-0.801686\pi$
$971$		−	36.3642i		−	1.16698i	0.812120	−	0.583491i	$-0.198314\pi$
$972$	14.5338	+	5.63643i	0.466171	+	0.180789i
$973$	16.2232	+	16.2232i	0.520092	+	0.520092i
$974$	7.88284			0.252583
$975$	−1.15436	+	8.32916i	−0.0369692	+	0.266747i
$976$	−12.2697			−0.392745
$977$	1.24875	+	1.24875i	0.0399511	+	0.0399511i	0.726800	−	0.686849i	$-0.241007\pi$
$977$	1.24875	+	1.24875i	0.0399511	+	0.0399511i	−0.686849	+	0.726800i	$0.741007\pi$
$978$	2.81900	−	1.74517i	0.0901418	−	0.0558044i
$979$			2.39891i			0.0766696i
$980$	8.11684	−	0.379152i	0.259283	−	0.0121116i
$981$	30.4664	+	15.1759i	0.972718	+	0.484531i
$982$	7.23959	−	7.23959i	0.231025	−	0.231025i
$983$	−9.65401	+	9.65401i	−0.307915	+	0.307915i	−0.844100	−	0.536185i	$-0.819865\pi$
$983$	−9.65401	+	9.65401i	−0.307915	+	0.307915i	0.536185	+	0.844100i	$0.319865\pi$
$984$	3.01967	−	12.8347i	0.0962637	−	0.409156i
$985$	1.33632	+	1.21705i	0.0425787	+	0.0387783i
$986$			2.39632i			0.0763143i
$987$	−5.81441	−	9.39211i	−0.185075	−	0.298954i
$988$	0.161568	+	0.161568i	0.00514018	+	0.00514018i
$989$	−3.44432			−0.109523
$990$	0.617788	+	1.59311i	0.0196346	+	0.0506325i
$991$	−15.9477			−0.506594			−0.253297	−	0.967389i	$-0.581515\pi$
$991$	−15.9477			−0.506594			−0.253297	+	0.967389i	$0.581515\pi$
$992$	1.47077	+	1.47077i	0.0466971	+	0.0466971i
$993$	−8.52894	−	13.7769i	−0.270658	−	0.437197i
$994$		−	1.93220i		−	0.0612855i
$995$	1.96694	+	42.1080i	0.0623562	+	1.33491i
$996$	4.98342	−	21.1813i	0.157906	−	0.671157i
$997$	−23.7511	+	23.7511i	−0.752204	+	0.752204i	−0.974890	−	0.222686i	$-0.928517\pi$
$997$	−23.7511	+	23.7511i	−0.752204	+	0.752204i	0.222686	+	0.974890i	$0.428517\pi$
$998$	−16.8671	+	16.8671i	−0.533919	+	0.533919i
$999$	21.2239	−	25.5477i	0.671494	−	0.808294i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.i.e.323.13	yes	32
3.2	odd	2	inner	690.2.i.e.323.8	yes	32
5.2	odd	4	inner	690.2.i.e.47.8	✓	32
15.2	even	4	inner	690.2.i.e.47.13	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.i.e.47.8	✓	32	5.2	odd	4	inner
690.2.i.e.47.13	yes	32	15.2	even	4	inner
690.2.i.e.323.8	yes	32	3.2	odd	2	inner
690.2.i.e.323.13	yes	32	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.911701 + 1.47268i) q^{3} +1.00000i q^{4} +(-2.23363 + 0.104337i) q^{5} +(-0.396675 + 1.68602i) q^{6} +(-1.29732 + 1.29732i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.33760 + 2.68530i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.911701 + 1.47268i) q^{3} +1.00000i q^{4} +(-2.23363 + 0.104337i) q^{5} +(-0.396675 + 1.68602i) q^{6} +(-1.29732 + 1.29732i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.33760 + 2.68530i) q^{9} +(-1.65319 - 1.50564i) q^{10} +0.254719i q^{11} +(-1.47268 + 0.911701i) q^{12} +(0.686574 + 0.686574i) q^{13} -1.83469 q^{14} +(-2.19006 - 3.19431i) q^{15} -1.00000 q^{16} +(-2.14714 - 2.14714i) q^{17} +(-2.84462 + 0.952965i) q^{18} -0.235326i q^{19} +(-0.104337 - 2.23363i) q^{20} +(-3.09331 - 0.727776i) q^{21} +(-0.180113 + 0.180113i) q^{22} +(-0.707107 + 0.707107i) q^{23} +(-1.68602 - 0.396675i) q^{24} +(4.97823 - 0.466101i) q^{25} +0.970962i q^{26} +(-5.17409 + 0.478323i) q^{27} +(-1.29732 - 1.29732i) q^{28} -0.789167 q^{29} +(0.710113 - 3.80733i) q^{30} -2.07999 q^{31} +(-0.707107 - 0.707107i) q^{32} +(-0.375120 + 0.232227i) q^{33} -3.03651i q^{34} +(2.76238 - 3.03310i) q^{35} +(-2.68530 - 1.33760i) q^{36} +(-4.51979 + 4.51979i) q^{37} +(0.166400 - 0.166400i) q^{38} +(-0.385157 + 1.63706i) q^{39} +(1.50564 - 1.65319i) q^{40} +7.61245i q^{41} +(-1.67269 - 2.70192i) q^{42} +(2.43550 + 2.43550i) q^{43} -0.254719 q^{44} +(2.70753 - 6.13753i) q^{45} -1.00000 q^{46} +(2.45797 + 2.45797i) q^{47} +(-0.911701 - 1.47268i) q^{48} +3.63392i q^{49} +(3.84972 + 3.19056i) q^{50} +(1.20451 - 5.11961i) q^{51} +(-0.686574 + 0.686574i) q^{52} +(-2.31783 + 2.31783i) q^{53} +(-3.99686 - 3.32041i) q^{54} +(-0.0265766 - 0.568948i) q^{55} -1.83469i q^{56} +(0.346560 - 0.214547i) q^{57} +(-0.558025 - 0.558025i) q^{58} +10.3269 q^{59} +(3.19431 - 2.19006i) q^{60} +12.2697 q^{61} +(-1.47077 - 1.47077i) q^{62} +(-1.74839 - 5.21899i) q^{63} -1.00000i q^{64} +(-1.60519 - 1.46192i) q^{65} +(-0.429460 - 0.101041i) q^{66} +(1.01439 - 1.01439i) q^{67} +(2.14714 - 2.14714i) q^{68} +(-1.68602 - 0.396675i) q^{69} +(4.09802 - 0.191426i) q^{70} +1.05315i q^{71} +(-0.952965 - 2.84462i) q^{72} +(6.97373 + 6.97373i) q^{73} -6.39195 q^{74} +(5.22508 + 6.90642i) q^{75} +0.235326 q^{76} +(-0.330452 - 0.330452i) q^{77} +(-1.42992 + 0.885227i) q^{78} -12.7539i q^{79} +(2.23363 - 0.104337i) q^{80} +(-5.42164 - 7.18372i) q^{81} +(-5.38282 + 5.38282i) q^{82} +(-8.88336 + 8.88336i) q^{83} +(0.727776 - 3.09331i) q^{84} +(5.01995 + 4.57190i) q^{85} +3.44432i q^{86} +(-0.719484 - 1.16219i) q^{87} +(-0.180113 - 0.180113i) q^{88} +9.41789 q^{89} +(6.25440 - 2.42537i) q^{90} -1.78141 q^{91} +(-0.707107 - 0.707107i) q^{92} +(-1.89633 - 3.06317i) q^{93} +3.47609i q^{94} +(0.0245532 + 0.525631i) q^{95} +(0.396675 - 1.68602i) q^{96} +(2.94241 - 2.94241i) q^{97} +(-2.56957 + 2.56957i) q^{98} +(-0.683996 - 0.340712i) 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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