LMFDB - Embedded newform 690.3.k.a.277.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,3,Mod(277,690)]

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([0, 1, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("690.277");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	690.k (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:	$18.8011382409$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			277.8
Character	$\chi$	$=$	690.277
Dual form			690.3.k.a.553.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-1.94861 - 4.60466i) q^{5} -2.44949 q^{6} +(-2.18869 - 2.18869i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})$	\(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-1.94861 - 4.60466i) q^{5} -2.44949 q^{6} +(-2.18869 - 2.18869i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(2.65606 - 6.55327i) q^{10} +0.598986 q^{11} +(-2.44949 - 2.44949i) q^{12} +(2.44971 - 2.44971i) q^{13} -4.37738i q^{14} +(8.02608 + 3.25299i) q^{15} -4.00000 q^{16} +(17.9496 + 17.9496i) q^{17} +(3.00000 - 3.00000i) q^{18} +17.4222i q^{19} +(9.20933 - 3.89721i) q^{20} +5.36117 q^{21} +(0.598986 + 0.598986i) q^{22} +(-3.39116 + 3.39116i) q^{23} -4.89898i q^{24} +(-17.4059 + 17.9454i) q^{25} +4.89943 q^{26} +(3.67423 + 3.67423i) q^{27} +(4.37738 - 4.37738i) q^{28} +25.3649i q^{29} +(4.77309 + 11.2791i) q^{30} +49.7350 q^{31} +(-4.00000 - 4.00000i) q^{32} +(-0.733605 + 0.733605i) q^{33} +35.8993i q^{34} +(-5.81329 + 14.3431i) q^{35} +6.00000 q^{36} +(42.3579 + 42.3579i) q^{37} +(-17.4222 + 17.4222i) q^{38} +6.00055i q^{39} +(13.1065 + 5.31212i) q^{40} -59.6411 q^{41} +(5.36117 + 5.36117i) q^{42} +(-37.2918 + 37.2918i) q^{43} +1.19797i q^{44} +(-13.8140 + 5.84582i) q^{45} -6.78233 q^{46} +(3.72350 + 3.72350i) q^{47} +(4.89898 - 4.89898i) q^{48} -39.4193i q^{49} +(-35.3512 + 0.539488i) q^{50} -43.9674 q^{51} +(4.89943 + 4.89943i) q^{52} +(66.2177 - 66.2177i) q^{53} +7.34847i q^{54} +(-1.16719 - 2.75813i) q^{55} +8.75476 q^{56} +(-21.3378 - 21.3378i) q^{57} +(-25.3649 + 25.3649i) q^{58} +106.735i q^{59} +(-6.50599 + 16.0522i) q^{60} +56.8619 q^{61} +(49.7350 + 49.7350i) q^{62} +(-6.56607 + 6.56607i) q^{63} -8.00000i q^{64} +(-16.0536 - 6.50658i) q^{65} -1.46721 q^{66} +(-5.50781 - 5.50781i) q^{67} +(-35.8993 + 35.8993i) q^{68} -8.30662i q^{69} +(-20.1564 + 8.52979i) q^{70} -18.4588 q^{71} +(6.00000 + 6.00000i) q^{72} +(1.41110 - 1.41110i) q^{73} +84.7158i q^{74} +(-0.660735 - 43.2962i) q^{75} -34.8444 q^{76} +(-1.31099 - 1.31099i) q^{77} +(-6.00055 + 6.00055i) q^{78} +123.331i q^{79} +(7.79442 + 18.4187i) q^{80} -9.00000 q^{81} +(-59.6411 - 59.6411i) q^{82} +(34.1108 - 34.1108i) q^{83} +10.7223i q^{84} +(47.6753 - 117.629i) q^{85} -74.5836 q^{86} +(-31.0655 - 31.0655i) q^{87} +(-1.19797 + 1.19797i) q^{88} -55.0628i q^{89} +(-19.6598 - 7.96817i) q^{90} -10.7233 q^{91} +(-6.78233 - 6.78233i) q^{92} +(-60.9127 + 60.9127i) q^{93} +7.44701i q^{94} +(80.2234 - 33.9490i) q^{95} +9.79796 q^{96} +(55.4956 + 55.4956i) q^{97} +(39.4193 - 39.4193i) q^{98} -1.79696i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8}+O(q^{10}) $ 40 * q + 40 * q^2 - 8 * q^5 - 8 * q^7 - 80 * q^8	$ 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8} - 16 q^{10} + 32 q^{11} + 16 q^{13} + 24 q^{15} - 160 q^{16} - 48 q^{17} + 120 q^{18} - 16 q^{20} - 96 q^{21} + 32 q^{22} + 32 q^{26} + 16 q^{28} + 24 q^{30} + 152 q^{31} - 160 q^{32} - 24 q^{33} + 48 q^{35} + 240 q^{36} + 216 q^{37} + 16 q^{38} - 168 q^{41} - 96 q^{42} - 48 q^{43} + 24 q^{45} - 232 q^{47} - 40 q^{50} + 32 q^{52} + 8 q^{53} - 272 q^{55} + 32 q^{56} - 136 q^{58} - 64 q^{61} + 152 q^{62} - 24 q^{63} + 416 q^{65} - 48 q^{66} - 32 q^{67} + 96 q^{68} + 88 q^{70} - 104 q^{71} + 240 q^{72} + 480 q^{73} - 216 q^{75} + 32 q^{76} + 280 q^{77} - 192 q^{78} + 32 q^{80} - 360 q^{81} - 168 q^{82} - 576 q^{83} - 208 q^{85} - 96 q^{86} + 24 q^{87} - 64 q^{88} + 144 q^{91} + 96 q^{93} + 168 q^{95} + 24 q^{97} + 176 q^{98}+O(q^{100}) $ 40 * q + 40 * q^2 - 8 * q^5 - 8 * q^7 - 80 * q^8 - 16 * q^10 + 32 * q^11 + 16 * q^13 + 24 * q^15 - 160 * q^16 - 48 * q^17 + 120 * q^18 - 16 * q^20 - 96 * q^21 + 32 * q^22 + 32 * q^26 + 16 * q^28 + 24 * q^30 + 152 * q^31 - 160 * q^32 - 24 * q^33 + 48 * q^35 + 240 * q^36 + 216 * q^37 + 16 * q^38 - 168 * q^41 - 96 * q^42 - 48 * q^43 + 24 * q^45 - 232 * q^47 - 40 * q^50 + 32 * q^52 + 8 * q^53 - 272 * q^55 + 32 * q^56 - 136 * q^58 - 64 * q^61 + 152 * q^62 - 24 * q^63 + 416 * q^65 - 48 * q^66 - 32 * q^67 + 96 * q^68 + 88 * q^70 - 104 * q^71 + 240 * q^72 + 480 * q^73 - 216 * q^75 + 32 * q^76 + 280 * q^77 - 192 * q^78 + 32 * q^80 - 360 * q^81 - 168 * q^82 - 576 * q^83 - 208 * q^85 - 96 * q^86 + 24 * q^87 - 64 * q^88 + 144 * q^91 + 96 * q^93 + 168 * q^95 + 24 * q^97 + 176 * q^98

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 $

$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$4$			2.00000i			0.500000i
$5$	−1.94861	−	4.60466i	−0.389721	−	0.920933i
$5$	−1.94861	−	4.60466i	−0.389721	−	0.920933i
$6$	−2.44949			−0.408248
$7$	−2.18869	−	2.18869i	−0.312670	−	0.312670i	0.533273	−	0.845943i	$-0.320962\pi$
$7$	−2.18869	−	2.18869i	−0.312670	−	0.312670i	−0.845943	+	0.533273i	$0.820962\pi$
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$		−	3.00000i		−	0.333333i
$10$	2.65606	−	6.55327i	0.265606	−	0.655327i
$11$	0.598986			0.0544533			0.0272266	−	0.999629i	$-0.491332\pi$
$11$	0.598986			0.0544533			0.0272266	+	0.999629i	$0.491332\pi$
$12$	−2.44949	−	2.44949i	−0.204124	−	0.204124i
$13$	2.44971	−	2.44971i	0.188440	−	0.188440i	−0.606582	−	0.795021i	$-0.707460\pi$
$13$	2.44971	−	2.44971i	0.188440	−	0.188440i	0.795021	+	0.606582i	$0.207460\pi$
$14$		−	4.37738i		−	0.312670i
$15$	8.02608	+	3.25299i	0.535072	+	0.216866i
$16$	−4.00000			−0.250000
$17$	17.9496	+	17.9496i	1.05586	+	1.05586i	0.998345	+	0.0575162i	$0.0183181\pi$
$17$	17.9496	+	17.9496i	1.05586	+	1.05586i	0.0575162	+	0.998345i	$0.481682\pi$
$18$	3.00000	−	3.00000i	0.166667	−	0.166667i
$19$			17.4222i			0.916958i	0.888705	+	0.458479i	$0.151606\pi$
$19$			17.4222i			0.916958i	−0.888705	+	0.458479i	$0.848394\pi$
$20$	9.20933	−	3.89721i	0.460466	−	0.194861i
$21$	5.36117			0.255294
$22$	0.598986	+	0.598986i	0.0272266	+	0.0272266i
$23$	−3.39116	+	3.39116i	−0.147442	+	0.147442i
$23$	−3.39116	+	3.39116i	−0.147442	+	0.147442i
$24$		−	4.89898i		−	0.204124i
$25$	−17.4059	+	17.9454i	−0.696235	+	0.717814i
$26$	4.89943			0.188440
$27$	3.67423	+	3.67423i	0.136083	+	0.136083i
$28$	4.37738	−	4.37738i	0.156335	−	0.156335i
$29$			25.3649i			0.874651i	0.899303	+	0.437326i	$0.144074\pi$
$29$			25.3649i			0.874651i	−0.899303	+	0.437326i	$0.855926\pi$
$30$	4.77309	+	11.2791i	0.159103	+	0.375969i
$31$	49.7350			1.60436			0.802178	−	0.597085i	$-0.203675\pi$
$31$	49.7350			1.60436			0.802178	+	0.597085i	$0.203675\pi$
$32$	−4.00000	−	4.00000i	−0.125000	−	0.125000i
$33$	−0.733605	+	0.733605i	−0.0222305	+	0.0222305i
$34$			35.8993i			1.05586i
$35$	−5.81329	+	14.3431i	−0.166094	+	0.409802i
$36$	6.00000			0.166667
$37$	42.3579	+	42.3579i	1.14481	+	1.14481i	0.987559	+	0.157249i	$0.0502625\pi$
$37$	42.3579	+	42.3579i	1.14481	+	1.14481i	0.157249	+	0.987559i	$0.449737\pi$
$38$	−17.4222	+	17.4222i	−0.458479	+	0.458479i
$39$			6.00055i			0.153860i
$40$	13.1065	+	5.31212i	0.327664	+	0.132803i
$41$	−59.6411			−1.45466			−0.727331	−	0.686287i	$-0.759239\pi$
$41$	−59.6411			−1.45466			−0.727331	+	0.686287i	$0.759239\pi$
$42$	5.36117	+	5.36117i	0.127647	+	0.127647i
$43$	−37.2918	+	37.2918i	−0.867251	+	0.867251i	−0.992167	−	0.124916i	$-0.960134\pi$
$43$	−37.2918	+	37.2918i	−0.867251	+	0.867251i	0.124916	+	0.992167i	$0.460134\pi$
$44$			1.19797i			0.0272266i
$45$	−13.8140	+	5.84582i	−0.306978	+	0.129907i
$46$	−6.78233			−0.147442
$47$	3.72350	+	3.72350i	0.0792235	+	0.0792235i	0.745608	−	0.666385i	$-0.232159\pi$
$47$	3.72350	+	3.72350i	0.0792235	+	0.0792235i	−0.666385	+	0.745608i	$0.732159\pi$
$48$	4.89898	−	4.89898i	0.102062	−	0.102062i
$49$		−	39.4193i		−	0.804475i
$50$	−35.3512	+	0.539488i	−0.707024	+	0.0107898i
$51$	−43.9674			−0.862107
$52$	4.89943	+	4.89943i	0.0942198	+	0.0942198i
$53$	66.2177	−	66.2177i	1.24939	−	1.24939i	0.293402	−	0.955989i	$-0.405213\pi$
$53$	66.2177	−	66.2177i	1.24939	−	1.24939i	0.955989	−	0.293402i	$-0.0947874\pi$
$54$			7.34847i			0.136083i
$55$	−1.16719	−	2.75813i	−0.0212216	−	0.0501478i
$56$	8.75476			0.156335
$57$	−21.3378	−	21.3378i	−0.374347	−	0.374347i
$58$	−25.3649	+	25.3649i	−0.437326	+	0.437326i
$59$			106.735i			1.80907i	0.426399	+	0.904535i	$0.359782\pi$
$59$			106.735i			1.80907i	−0.426399	+	0.904535i	$0.640218\pi$
$60$	−6.50599	+	16.0522i	−0.108433	+	0.267536i
$61$	56.8619			0.932163			0.466081	−	0.884742i	$-0.345665\pi$
$61$	56.8619			0.932163			0.466081	+	0.884742i	$0.345665\pi$
$62$	49.7350	+	49.7350i	0.802178	+	0.802178i
$63$	−6.56607	+	6.56607i	−0.104223	+	0.104223i
$64$		−	8.00000i		−	0.125000i
$65$	−16.0536	−	6.50658i	−0.246979	−	0.100101i
$66$	−1.46721			−0.0222305
$67$	−5.50781	−	5.50781i	−0.0822061	−	0.0822061i	0.664808	−	0.747014i	$-0.268513\pi$
$67$	−5.50781	−	5.50781i	−0.0822061	−	0.0822061i	−0.747014	+	0.664808i	$0.768513\pi$
$68$	−35.8993	+	35.8993i	−0.527930	+	0.527930i
$69$		−	8.30662i		−	0.120386i
$70$	−20.1564	+	8.52979i	−0.287948	+	0.121854i
$71$	−18.4588			−0.259983			−0.129992	−	0.991515i	$-0.541495\pi$
$71$	−18.4588			−0.259983			−0.129992	+	0.991515i	$0.541495\pi$
$72$	6.00000	+	6.00000i	0.0833333	+	0.0833333i
$73$	1.41110	−	1.41110i	0.0193302	−	0.0193302i	−0.697376	−	0.716706i	$-0.745649\pi$
$73$	1.41110	−	1.41110i	0.0193302	−	0.0193302i	0.716706	+	0.697376i	$0.245649\pi$
$74$			84.7158i			1.14481i
$75$	−0.660735	−	43.2962i	−0.00880980	−	0.577283i
$76$	−34.8444			−0.458479
$77$	−1.31099	−	1.31099i	−0.0170259	−	0.0170259i
$78$	−6.00055	+	6.00055i	−0.0769301	+	0.0769301i
$79$			123.331i			1.56116i	0.625058	+	0.780578i	$0.285075\pi$
$79$			123.331i			1.56116i	−0.625058	+	0.780578i	$0.714925\pi$
$80$	7.79442	+	18.4187i	0.0974303	+	0.230233i
$81$	−9.00000			−0.111111
$82$	−59.6411	−	59.6411i	−0.727331	−	0.727331i
$83$	34.1108	−	34.1108i	0.410974	−	0.410974i	−0.471104	−	0.882078i	$-0.656144\pi$
$83$	34.1108	−	34.1108i	0.410974	−	0.410974i	0.882078	+	0.471104i	$0.156144\pi$
$84$			10.7223i			0.127647i
$85$	47.6753	−	117.629i	0.560886	−	1.38387i
$86$	−74.5836			−0.867251
$87$	−31.0655	−	31.0655i	−0.357075	−	0.357075i
$88$	−1.19797	+	1.19797i	−0.0136133	+	0.0136133i
$89$		−	55.0628i		−	0.618683i	−0.950951	−	0.309342i	$-0.899891\pi$
$89$		−	55.0628i		−	0.618683i	0.950951	−	0.309342i	$-0.100109\pi$
$90$	−19.6598	−	7.96817i	−0.218442	−	0.0885353i
$91$	−10.7233			−0.117839
$92$	−6.78233	−	6.78233i	−0.0737210	−	0.0737210i
$93$	−60.9127	+	60.9127i	−0.654975	+	0.654975i
$94$			7.44701i			0.0792235i
$95$	80.2234	−	33.9490i	0.844457	−	0.357358i
$96$	9.79796			0.102062
$97$	55.4956	+	55.4956i	0.572120	+	0.572120i	0.932720	−	0.360600i	$-0.117428\pi$
$97$	55.4956	+	55.4956i	0.572120	+	0.572120i	−0.360600	+	0.932720i	$0.617428\pi$
$98$	39.4193	−	39.4193i	0.402238	−	0.402238i
$99$		−	1.79696i		−	0.0181511i
$100$	−35.8907	−	34.8117i	−0.358907	−	0.348117i
$101$	−76.1500			−0.753961			−0.376980	−	0.926221i	$-0.623038\pi$
$101$	−76.1500			−0.753961			−0.376980	+	0.926221i	$0.623038\pi$
$102$	−43.9674	−	43.9674i	−0.431053	−	0.431053i
$103$	−75.4678	+	75.4678i	−0.732697	+	0.732697i	−0.971153	−	0.238456i	$-0.923359\pi$
$103$	−75.4678	+	75.4678i	−0.732697	+	0.732697i	0.238456	+	0.971153i	$0.423359\pi$
$104$			9.79885i			0.0942198i
$105$	−10.4468	−	24.6864i	−0.0994934	−	0.235109i
$106$	132.435			1.24939
$107$	−106.837	−	106.837i	−0.998472	−	0.998472i	0.00152681	−	0.999999i	$-0.499514\pi$
$107$	−106.837	−	106.837i	−0.998472	−	0.998472i	−0.999999	+	0.00152681i	$0.999514\pi$
$108$	−7.34847	+	7.34847i	−0.0680414	+	0.0680414i
$109$			105.073i			0.963970i	0.876179	+	0.481985i	$0.160084\pi$
$109$			105.073i			0.963970i	−0.876179	+	0.481985i	$0.839916\pi$
$110$	1.59094	−	3.92532i	0.0144631	−	0.0356847i
$111$	−103.755			−0.934732
$112$	8.75476	+	8.75476i	0.0781675	+	0.0781675i
$113$	40.8621	−	40.8621i	0.361612	−	0.361612i	−0.502794	−	0.864406i	$-0.667695\pi$
$113$	40.8621	−	40.8621i	0.361612	−	0.361612i	0.864406	+	0.502794i	$0.167695\pi$
$114$		−	42.6755i		−	0.374347i
$115$	22.2232	+	9.00713i	0.193245	+	0.0783229i
$116$	−50.7298			−0.437326
$117$	−7.34914	−	7.34914i	−0.0628132	−	0.0628132i
$118$	−106.735	+	106.735i	−0.904535	+	0.904535i
$119$		−	78.5723i		−	0.660272i
$120$	−22.5582	+	9.54618i	−0.187985	+	0.0795515i
$121$	−120.641			−0.997035
$122$	56.8619	+	56.8619i	0.466081	+	0.466081i
$123$	73.0452	−	73.0452i	0.593863	−	0.593863i
$124$			99.4700i			0.802178i
$125$	116.550	+	45.1797i	0.932396	+	0.361438i
$126$	−13.1321			−0.104223
$127$	119.382	+	119.382i	0.940018	+	0.940018i	0.998300	−	0.0582822i	$-0.0185623\pi$
$127$	119.382	+	119.382i	0.940018	+	0.940018i	−0.0582822	+	0.998300i	$0.518562\pi$
$128$	8.00000	−	8.00000i	0.0625000	−	0.0625000i
$129$		−	91.3459i		−	0.708108i
$130$	−9.54705	−	22.5602i	−0.0734389	−	0.173540i
$131$	167.857			1.28135			0.640675	−	0.767813i	$-0.278655\pi$
$131$	167.857			1.28135			0.640675	+	0.767813i	$0.278655\pi$
$132$	−1.46721	−	1.46721i	−0.0111152	−	0.0111152i
$133$	38.1318	−	38.1318i	0.286705	−	0.286705i
$134$		−	11.0156i		−	0.0822061i
$135$	9.75898	−	24.0783i	0.0722887	−	0.178357i
$136$	−71.7985			−0.527930
$137$	129.149	+	129.149i	0.942694	+	0.942694i	0.998445	−	0.0557511i	$-0.0177553\pi$
$137$	129.149	+	129.149i	0.942694	+	0.942694i	−0.0557511	+	0.998445i	$0.517755\pi$
$138$	8.30662	−	8.30662i	0.0601929	−	0.0601929i
$139$		−	40.2260i		−	0.289396i	−0.989476	−	0.144698i	$-0.953779\pi$
$139$		−	40.2260i		−	0.289396i	0.989476	−	0.144698i	$-0.0462211\pi$
$140$	−28.6861	−	11.6266i	−0.204901	−	0.0830469i
$141$	−9.12068			−0.0646857
$142$	−18.4588	−	18.4588i	−0.129992	−	0.129992i
$143$	1.46734	−	1.46734i	0.0102612	−	0.0102612i
$144$			12.0000i			0.0833333i
$145$	116.797	−	49.4262i	0.805495	−	0.340870i
$146$	2.82221			0.0193302
$147$	48.2786	+	48.2786i	0.328426	+	0.328426i
$148$	−84.7158	+	84.7158i	−0.572404	+	0.572404i
$149$		−	252.884i		−	1.69721i	−0.529028	−	0.848604i	$-0.677443\pi$
$149$		−	252.884i		−	1.69721i	0.529028	−	0.848604i	$-0.322557\pi$
$150$	42.6355	−	43.9570i	0.284237	−	0.293046i
$151$	−24.4657			−0.162024			−0.0810122	−	0.996713i	$-0.525815\pi$
$151$	−24.4657			−0.162024			−0.0810122	+	0.996713i	$0.525815\pi$
$152$	−34.8444	−	34.8444i	−0.229240	−	0.229240i
$153$	53.8489	−	53.8489i	0.351954	−	0.351954i
$154$		−	2.62199i		−	0.0170259i
$155$	−96.9140	−	229.013i	−0.625251	−	1.47750i
$156$	−12.0011			−0.0769301
$157$	45.8667	+	45.8667i	0.292144	+	0.292144i	0.837927	−	0.545783i	$-0.183768\pi$
$157$	45.8667	+	45.8667i	0.292144	+	0.292144i	−0.545783	+	0.837927i	$0.683768\pi$
$158$	−123.331	+	123.331i	−0.780578	+	0.780578i
$159$			162.200i			1.02012i
$160$	−10.6242	+	26.2131i	−0.0664015	+	0.163832i
$161$	14.8444			0.0922013
$162$	−9.00000	−	9.00000i	−0.0555556	−	0.0555556i
$163$	154.258	−	154.258i	0.946368	−	0.946368i	−0.0522652	−	0.998633i	$-0.516644\pi$
$163$	154.258	−	154.258i	0.946368	−	0.946368i	0.998633	+	0.0522652i	$0.0166441\pi$
$164$		−	119.282i		−	0.727331i
$165$	4.80751	+	1.94850i	0.0291364	+	0.0118091i
$166$	68.2216			0.410974
$167$	107.910	+	107.910i	0.646169	+	0.646169i	0.952065	−	0.305896i	$-0.0989559\pi$
$167$	107.910	+	107.910i	0.646169	+	0.646169i	−0.305896	+	0.952065i	$0.598956\pi$
$168$	−10.7223	+	10.7223i	−0.0638235	+	0.0638235i
$169$			156.998i			0.928981i
$170$	165.304	−	69.9535i	0.972377	−	0.411491i
$171$	52.2666			0.305653
$172$	−74.5836	−	74.5836i	−0.433626	−	0.433626i
$173$	167.076	−	167.076i	0.965756	−	0.965756i	−0.0336770	−	0.999433i	$-0.510722\pi$
$173$	167.076	−	167.076i	0.965756	−	0.965756i	0.999433	+	0.0336770i	$0.0107218\pi$
$174$		−	62.1310i		−	0.357075i
$175$	77.3728	−	1.18077i	0.442130	−	0.00674726i
$176$	−2.39594			−0.0136133
$177$	−130.723	−	130.723i	−0.738550	−	0.738550i
$178$	55.0628	−	55.0628i	0.309342	−	0.309342i
$179$			182.846i			1.02149i	0.859733	+	0.510744i	$0.170630\pi$
$179$			182.846i			1.02149i	−0.859733	+	0.510744i	$0.829370\pi$
$180$	−11.6916	−	27.6280i	−0.0649535	−	0.153489i
$181$	−283.532			−1.56648			−0.783238	−	0.621722i	$-0.786433\pi$
$181$	−283.532			−1.56648			−0.783238	+	0.621722i	$0.786433\pi$
$182$	−10.7233	−	10.7233i	−0.0589194	−	0.0589194i
$183$	−69.6413	+	69.6413i	−0.380554	+	0.380554i
$184$		−	13.5647i		−	0.0737210i
$185$	112.505	−	277.583i	0.608135	−	1.50045i
$186$	−121.825			−0.654975
$187$	10.7516	+	10.7516i	0.0574951	+	0.0574951i
$188$	−7.44701	+	7.44701i	−0.0396117	+	0.0396117i
$189$		−	16.0835i		−	0.0850980i
$190$	114.172	+	46.2744i	0.600908	+	0.243549i
$191$	−222.465			−1.16474			−0.582369	−	0.812924i	$-0.697874\pi$
$191$	−222.465			−1.16474			−0.582369	+	0.812924i	$0.697874\pi$
$192$	9.79796	+	9.79796i	0.0510310	+	0.0510310i
$193$	155.059	−	155.059i	0.803415	−	0.803415i	−0.180213	−	0.983628i	$-0.557679\pi$
$193$	155.059	−	155.059i	0.803415	−	0.803415i	0.983628	+	0.180213i	$0.0576786\pi$
$194$			110.991i			0.572120i
$195$	27.6305	−	11.6927i	0.141695	−	0.0599626i
$196$	78.8386			0.402238
$197$	−195.127	−	195.127i	−0.990491	−	0.990491i	0.00946412	−	0.999955i	$-0.496987\pi$
$197$	−195.127	−	195.127i	−0.990491	−	0.990491i	−0.999955	+	0.00946412i	$0.996987\pi$
$198$	1.79696	−	1.79696i	0.00907555	−	0.00907555i
$199$			161.566i			0.811887i	0.913898	+	0.405944i	$0.133057\pi$
$199$			161.566i			0.811887i	−0.913898	+	0.405944i	$0.866943\pi$
$200$	−1.07898	−	70.7024i	−0.00539488	−	0.353512i
$201$	13.4913			0.0671210
$202$	−76.1500	−	76.1500i	−0.376980	−	0.376980i
$203$	55.5158	−	55.5158i	0.273477	−	0.273477i
$204$		−	87.9349i		−	0.431053i
$205$	116.217	+	274.627i	0.566913	+	1.33965i
$206$	−150.936			−0.732697
$207$	10.1735	+	10.1735i	0.0491473	+	0.0491473i
$208$	−9.79885	+	9.79885i	−0.0471099	+	0.0471099i
$209$			10.4357i			0.0499314i
$210$	14.2396	−	35.1332i	0.0678075	−	0.167301i
$211$	253.473			1.20130			0.600648	−	0.799514i	$-0.294909\pi$
$211$	253.473			1.20130			0.600648	+	0.799514i	$0.294909\pi$
$212$	132.435	+	132.435i	0.624695	+	0.624695i
$213$	22.6073	−	22.6073i	0.106138	−	0.106138i
$214$		−	213.673i		−	0.998472i
$215$	244.383	+	99.0492i	1.13667	+	0.460694i
$216$	−14.6969			−0.0680414
$217$	−108.854	−	108.854i	−0.501634	−	0.501634i
$218$	−105.073	+	105.073i	−0.481985	+	0.481985i
$219$			3.45648i			0.0157830i
$220$	5.51626	−	2.33438i	0.0250739	−	0.0106108i
$221$	87.9429			0.397932
$222$	−103.755	−	103.755i	−0.467366	−	0.467366i
$223$	−148.276	+	148.276i	−0.664913	+	0.664913i	−0.956534	−	0.291621i	$-0.905805\pi$
$223$	−148.276	+	148.276i	−0.664913	+	0.664913i	0.291621	+	0.956534i	$0.405805\pi$
$224$			17.5095i			0.0781675i
$225$	53.8361	+	52.2176i	0.239271	+	0.232078i
$226$	81.7243			0.361612
$227$	−125.826	−	125.826i	−0.554298	−	0.554298i	0.373380	−	0.927678i	$-0.378199\pi$
$227$	−125.826	−	125.826i	−0.554298	−	0.554298i	−0.927678	+	0.373380i	$0.878199\pi$
$228$	42.6755	−	42.6755i	0.187173	−	0.187173i
$229$			8.02492i			0.0350433i	0.999846	+	0.0175217i	$0.00557760\pi$
$229$			8.02492i			0.0350433i	−0.999846	+	0.0175217i	$0.994422\pi$
$230$	13.2161	+	31.2304i	0.0574613	+	0.135784i
$231$	3.21127			0.0139016
$232$	−50.7298	−	50.7298i	−0.218663	−	0.218663i
$233$	301.851	−	301.851i	1.29550	−	1.29550i	0.364165	−	0.931334i	$-0.381354\pi$
$233$	301.851	−	301.851i	1.29550	−	1.29550i	0.931334	−	0.364165i	$-0.118646\pi$
$234$		−	14.6983i		−	0.0628132i
$235$	9.88984	−	24.4011i	0.0420844	−	0.103835i
$236$	−213.470			−0.904535
$237$	−151.049	−	151.049i	−0.637339	−	0.637339i
$238$	78.5723	−	78.5723i	0.330136	−	0.330136i
$239$		−	74.3262i		−	0.310988i	−0.987837	−	0.155494i	$-0.950303\pi$
$239$		−	74.3262i		−	0.310988i	0.987837	−	0.155494i	$-0.0496970\pi$
$240$	−32.1043	−	13.0120i	−0.133768	−	0.0542166i
$241$	−259.415			−1.07641			−0.538206	−	0.842813i	$-0.680898\pi$
$241$	−259.415			−1.07641			−0.538206	+	0.842813i	$0.680898\pi$
$242$	−120.641	−	120.641i	−0.498517	−	0.498517i
$243$	11.0227	−	11.0227i	0.0453609	−	0.0453609i
$244$			113.724i			0.466081i
$245$	−181.513	+	76.8127i	−0.740868	+	0.313521i
$246$	146.090			0.593863
$247$	42.6794	+	42.6794i	0.172791	+	0.172791i
$248$	−99.4700	+	99.4700i	−0.401089	+	0.401089i
$249$			83.5541i			0.335559i
$250$	71.3698	+	161.729i	0.285479	+	0.646917i
$251$	−461.482			−1.83857			−0.919287	−	0.393587i	$-0.871234\pi$
$251$	−461.482			−1.83857			−0.919287	+	0.393587i	$0.871234\pi$
$252$	−13.1321	−	13.1321i	−0.0521116	−	0.0521116i
$253$	−2.03126	+	2.03126i	−0.00802870	+	0.00802870i
$254$			238.765i			0.940018i
$255$	85.6752	+	202.455i	0.335981	+	0.793942i
$256$	16.0000			0.0625000
$257$	35.4321	+	35.4321i	0.137868	+	0.137868i	0.772673	−	0.634805i	$-0.218919\pi$
$257$	35.4321	+	35.4321i	0.137868	+	0.137868i	−0.634805	+	0.772673i	$0.718919\pi$
$258$	91.3459	−	91.3459i	0.354054	−	0.354054i
$259$		−	185.417i		−	0.715894i
$260$	13.0132	−	32.1073i	0.0500506	−	0.123490i
$261$	76.0947			0.291550
$262$	167.857	+	167.857i	0.640675	+	0.640675i
$263$	27.5897	−	27.5897i	0.104904	−	0.104904i	−0.652707	−	0.757611i	$-0.726367\pi$
$263$	27.5897	−	27.5897i	0.104904	−	0.104904i	0.757611	+	0.652707i	$0.226367\pi$
$264$		−	2.93442i		−	0.0111152i
$265$	−433.943	−	175.878i	−1.63752	−	0.663691i
$266$	76.2636			0.286705
$267$	67.4379	+	67.4379i	0.252576	+	0.252576i
$268$	11.0156	−	11.0156i	0.0411031	−	0.0411031i
$269$		−	208.728i		−	0.775939i	−0.921672	−	0.387970i	$-0.873177\pi$
$269$		−	208.728i		−	0.775939i	0.921672	−	0.387970i	$-0.126823\pi$
$270$	33.8372	−	14.3193i	0.125323	−	0.0530343i
$271$	210.239			0.775789			0.387895	−	0.921704i	$-0.373202\pi$
$271$	210.239			0.775789			0.387895	+	0.921704i	$0.373202\pi$
$272$	−71.7985	−	71.7985i	−0.263965	−	0.263965i
$273$	13.1333	−	13.1333i	0.0481075	−	0.0481075i
$274$			258.298i			0.942694i
$275$	−10.4259	+	10.7490i	−0.0379123	+	0.0390873i
$276$	16.6132			0.0601929
$277$	30.9260	+	30.9260i	0.111646	+	0.111646i	0.760723	−	0.649077i	$-0.224845\pi$
$277$	30.9260	+	30.9260i	0.111646	+	0.111646i	−0.649077	+	0.760723i	$0.724845\pi$
$278$	40.2260	−	40.2260i	0.144698	−	0.144698i
$279$		−	149.205i		−	0.534785i
$280$	−17.0596	−	40.3127i	−0.0609270	−	0.143974i
$281$	−438.208			−1.55946			−0.779729	−	0.626117i	$-0.784643\pi$
$281$	−438.208			−1.55946			−0.779729	+	0.626117i	$0.784643\pi$
$282$	−9.12068	−	9.12068i	−0.0323428	−	0.0323428i
$283$	118.312	−	118.312i	0.418064	−	0.418064i	−0.466472	−	0.884536i	$-0.654475\pi$
$283$	118.312	−	118.312i	0.418064	−	0.418064i	0.884536	+	0.466472i	$0.154475\pi$
$284$		−	36.9176i		−	0.129992i
$285$	−56.6743	+	139.832i	−0.198857	+	0.490639i
$286$	2.93469			0.0102612
$287$	130.536	+	130.536i	0.454829	+	0.454829i
$288$	−12.0000	+	12.0000i	−0.0416667	+	0.0416667i
$289$			355.379i			1.22968i
$290$	166.223	+	67.3706i	0.573183	+	0.232312i
$291$	−135.936			−0.467134
$292$	2.82221	+	2.82221i	0.00966509	+	0.00966509i
$293$	−24.6895	+	24.6895i	−0.0842646	+	0.0842646i	−0.747983	−	0.663718i	$-0.768977\pi$
$293$	−24.6895	+	24.6895i	−0.0842646	+	0.0842646i	0.663718	+	0.747983i	$0.268977\pi$
$294$			96.5571i			0.328426i
$295$	491.480	−	207.985i	1.66603	−	0.705033i
$296$	−169.432			−0.572404
$297$	2.20082	+	2.20082i	0.00741015	+	0.00741015i
$298$	252.884	−	252.884i	0.848604	−	0.848604i
$299$			16.6148i			0.0555678i
$300$	86.5925	−	1.32147i	0.288642	−	0.00440490i
$301$	163.240			0.542327
$302$	−24.4657	−	24.4657i	−0.0810122	−	0.0810122i
$303$	93.2643	−	93.2643i	0.307803	−	0.307803i
$304$		−	69.6888i		−	0.229240i
$305$	−110.801	−	261.830i	−0.363284	−	0.858459i
$306$	107.698			0.351954
$307$	243.804	+	243.804i	0.794148	+	0.794148i	0.982166	−	0.188017i	$-0.0602061\pi$
$307$	243.804	+	243.804i	0.794148	+	0.794148i	−0.188017	+	0.982166i	$0.560206\pi$
$308$	2.62199	−	2.62199i	0.00851295	−	0.00851295i
$309$		−	184.858i		−	0.598245i
$310$	132.099	−	325.927i	0.426126	−	1.05138i
$311$	−481.852			−1.54936			−0.774682	−	0.632350i	$-0.782090\pi$
$311$	−481.852			−1.54936			−0.774682	+	0.632350i	$0.782090\pi$
$312$	−12.0011	−	12.0011i	−0.0384651	−	0.0384651i
$313$	60.0172	−	60.0172i	0.191748	−	0.191748i	−0.604703	−	0.796451i	$-0.706708\pi$
$313$	60.0172	−	60.0172i	0.191748	−	0.191748i	0.796451	+	0.604703i	$0.206708\pi$
$314$			91.7333i			0.292144i
$315$	43.0292	+	17.4399i	0.136601	+	0.0553646i
$316$	−246.663			−0.780578
$317$	−13.7241	−	13.7241i	−0.0432936	−	0.0432936i	0.685129	−	0.728422i	$-0.259746\pi$
$317$	−13.7241	−	13.7241i	−0.0432936	−	0.0432936i	−0.728422	+	0.685129i	$0.759746\pi$
$318$	−162.200	+	162.200i	−0.510062	+	0.510062i
$319$			15.1932i			0.0476276i
$320$	−36.8373	+	15.5888i	−0.115117	+	0.0487152i
$321$	261.695			0.815249
$322$	14.8444	+	14.8444i	0.0461007	+	0.0461007i
$323$	−312.722	+	312.722i	−0.968180	+	0.968180i
$324$		−	18.0000i		−	0.0555556i
$325$	1.32159	+	86.6004i	0.00406643	+	0.266463i
$326$	308.516			0.946368
$327$	−128.687	−	128.687i	−0.393539	−	0.393539i
$328$	119.282	−	119.282i	0.363665	−	0.363665i
$329$		−	16.2992i		−	0.0495416i
$330$	2.85902	+	6.75601i	0.00866368	+	0.0204728i
$331$	521.875			1.57666			0.788331	−	0.615251i	$-0.210945\pi$
$331$	521.875			1.57666			0.788331	+	0.615251i	$0.210945\pi$
$332$	68.2216	+	68.2216i	0.205487	+	0.205487i
$333$	127.074	−	127.074i	0.381603	−	0.381603i
$334$			215.820i			0.646169i
$335$	−14.6291	+	36.0942i	−0.0436688	+	0.107744i
$336$	−21.4447			−0.0638235
$337$	−280.503	−	280.503i	−0.832354	−	0.832354i	0.155484	−	0.987838i	$-0.450306\pi$
$337$	−280.503	−	280.503i	−0.832354	−	0.832354i	−0.987838	+	0.155484i	$0.950306\pi$
$338$	−156.998	+	156.998i	−0.464491	+	0.464491i
$339$			100.091i			0.295255i
$340$	235.258	+	95.3505i	0.691934	+	0.280443i
$341$	29.7906			0.0873624
$342$	52.2666	+	52.2666i	0.152826	+	0.152826i
$343$	−193.522	+	193.522i	−0.564205	+	0.564205i
$344$		−	149.167i		−	0.433626i
$345$	−38.2492	+	16.1863i	−0.110867	+	0.0469169i
$346$	334.151			0.965756
$347$	−64.7394	−	64.7394i	−0.186569	−	0.186569i	0.607642	−	0.794211i	$-0.292116\pi$
$347$	−64.7394	−	64.7394i	−0.186569	−	0.186569i	−0.794211	+	0.607642i	$0.792116\pi$
$348$	62.1310	−	62.1310i	0.178537	−	0.178537i
$349$			534.997i			1.53294i	0.642278	+	0.766472i	$0.277989\pi$
$349$			534.997i			1.53294i	−0.642278	+	0.766472i	$0.722011\pi$
$350$	78.5536	+	76.1921i	0.224439	+	0.217692i
$351$	18.0016			0.0512867
$352$	−2.39594	−	2.39594i	−0.00680666	−	0.00680666i
$353$	−8.45263	+	8.45263i	−0.0239451	+	0.0239451i	−0.718978	−	0.695033i	$-0.755390\pi$
$353$	−8.45263	+	8.45263i	−0.0239451	+	0.0239451i	0.695033	+	0.718978i	$0.255390\pi$
$354$		−	261.447i		−	0.738550i
$355$	35.9689	+	84.9966i	0.101321	+	0.239427i
$356$	110.126			0.309342
$357$	96.2311	+	96.2311i	0.269555	+	0.269555i
$358$	−182.846	+	182.846i	−0.510744	+	0.510744i
$359$		−	29.7289i		−	0.0828104i	−0.999142	−	0.0414052i	$-0.986817\pi$
$359$		−	29.7289i		−	0.0828104i	0.999142	−	0.0414052i	$-0.0131834\pi$
$360$	15.9363	−	39.3196i	0.0442676	−	0.109221i
$361$	57.4667			0.159187
$362$	−283.532	−	283.532i	−0.783238	−	0.783238i
$363$	147.755	−	147.755i	0.407038	−	0.407038i
$364$		−	21.4466i		−	0.0589194i
$365$	−9.24734	−	3.74797i	−0.0253352	−	0.0102684i
$366$	−139.283			−0.380554
$367$	−287.976	−	287.976i	−0.784674	−	0.784674i	0.195941	−	0.980616i	$-0.437224\pi$
$367$	−287.976	−	287.976i	−0.784674	−	0.784674i	−0.980616	+	0.195941i	$0.937224\pi$
$368$	13.5647	−	13.5647i	0.0368605	−	0.0368605i
$369$			178.923i			0.484887i
$370$	390.088	−	165.078i	1.05429	−	0.446156i
$371$	−289.860			−0.781294
$372$	−121.825	−	121.825i	−0.327488	−	0.327488i
$373$	−198.584	+	198.584i	−0.532395	+	0.532395i	−0.921285	−	0.388889i	$-0.872859\pi$
$373$	−198.584	+	198.584i	−0.532395	+	0.532395i	0.388889	+	0.921285i	$0.372859\pi$
$374$			21.5032i			0.0574951i
$375$	−198.077	+	87.4098i	−0.528206	+	0.233093i
$376$	−14.8940			−0.0396117
$377$	62.1367	+	62.1367i	0.164819	+	0.164819i
$378$	16.0835	−	16.0835i	0.0425490	−	0.0425490i
$379$			533.203i			1.40687i	0.710761	+	0.703434i	$0.248351\pi$
$379$			533.203i			1.40687i	−0.710761	+	0.703434i	$0.751649\pi$
$380$	67.8980	+	160.447i	0.178679	+	0.422229i
$381$	−292.426			−0.767521
$382$	−222.465	−	222.465i	−0.582369	−	0.582369i
$383$	120.598	−	120.598i	0.314877	−	0.314877i	−0.531919	−	0.846795i	$-0.678529\pi$
$383$	120.598	−	120.598i	0.314877	−	0.314877i	0.846795	+	0.531919i	$0.178529\pi$
$384$			19.5959i			0.0510310i
$385$	−3.48208	+	8.59130i	−0.00904436	+	0.0223151i
$386$	310.118			0.803415
$387$	111.875	+	111.875i	0.289084	+	0.289084i
$388$	−110.991	+	110.991i	−0.286060	+	0.286060i
$389$		−	292.831i		−	0.752778i	−0.926462	−	0.376389i	$-0.877166\pi$
$389$		−	292.831i		−	0.752778i	0.926462	−	0.376389i	$-0.122834\pi$
$390$	39.3232	+	15.9378i	0.100829	+	0.0408662i
$391$	−121.740			−0.311356
$392$	78.8386	+	78.8386i	0.201119	+	0.201119i
$393$	−205.582	+	205.582i	−0.523109	+	0.523109i
$394$		−	390.253i		−	0.990491i
$395$	567.899	−	240.324i	1.43772	−	0.608416i
$396$	3.59392			0.00907555
$397$	−221.984	−	221.984i	−0.559153	−	0.559153i	0.369913	−	0.929066i	$-0.379387\pi$
$397$	−221.984	−	221.984i	−0.559153	−	0.559153i	−0.929066	+	0.369913i	$0.879387\pi$
$398$	−161.566	+	161.566i	−0.405944	+	0.405944i
$399$			93.4034i			0.234094i
$400$	69.6235	−	71.7814i	0.174059	−	0.179454i
$401$	−453.324			−1.13048			−0.565242	−	0.824925i	$-0.691217\pi$
$401$	−453.324			−1.13048			−0.565242	+	0.824925i	$0.691217\pi$
$402$	13.4913	+	13.4913i	0.0335605	+	0.0335605i
$403$	121.837	−	121.837i	0.302324	−	0.302324i
$404$		−	152.300i		−	0.376980i
$405$	17.5375	+	41.4420i	0.0433024	+	0.102326i
$406$	111.032			0.273477
$407$	25.3718	+	25.3718i	0.0623386	+	0.0623386i
$408$	87.9349	−	87.9349i	0.215527	−	0.215527i
$409$		−	685.562i		−	1.67619i	−0.545523	−	0.838096i	$-0.683669\pi$
$409$		−	685.562i		−	1.67619i	0.545523	−	0.838096i	$-0.316331\pi$
$410$	−158.410	+	390.844i	−0.386367	+	0.953279i
$411$	−316.349			−0.769706
$412$	−150.936	−	150.936i	−0.366349	−	0.366349i
$413$	233.610	−	233.610i	0.565642	−	0.565642i
$414$			20.3470i			0.0491473i
$415$	−223.537	−	90.6003i	−0.538644	−	0.218314i
$416$	−19.5977			−0.0471099
$417$	49.2666	+	49.2666i	0.118145	+	0.118145i
$418$	−10.4357	+	10.4357i	−0.0249657	+	0.0249657i
$419$			526.496i			1.25655i	0.777990	+	0.628277i	$0.216239\pi$
$419$			526.496i			1.25655i	−0.777990	+	0.628277i	$0.783761\pi$
$420$	49.3728	−	20.8936i	0.117554	−	0.0497467i
$421$	−23.9389			−0.0568620			−0.0284310	−	0.999596i	$-0.509051\pi$
$421$	−23.9389			−0.0568620			−0.0284310	+	0.999596i	$0.509051\pi$
$422$	253.473	+	253.473i	0.600648	+	0.600648i
$423$	11.1705	−	11.1705i	0.0264078	−	0.0264078i
$424$			264.871i			0.624695i
$425$	−634.541	+	9.68361i	−1.49304	+	0.0227850i
$426$	45.2146			0.106138
$427$	−124.453	−	124.453i	−0.291459	−	0.291459i
$428$	213.673	−	213.673i	0.499236	−	0.499236i
$429$			3.59425i			0.00837819i
$430$	145.334	+	343.433i	0.337986	+	0.798680i
$431$	118.968			0.276027			0.138013	−	0.990430i	$-0.455928\pi$
$431$	118.968			0.276027			0.138013	+	0.990430i	$0.455928\pi$
$432$	−14.6969	−	14.6969i	−0.0340207	−	0.0340207i
$433$	−402.728	+	402.728i	−0.930089	+	0.930089i	−0.997711	−	0.0676224i	$-0.978459\pi$
$433$	−402.728	+	402.728i	−0.930089	+	0.930089i	0.0676224	+	0.997711i	$0.478459\pi$
$434$		−	217.709i		−	0.501634i
$435$	−82.5118	+	203.581i	−0.189682	+	0.468002i
$436$	−210.146			−0.481985
$437$	−59.0816	−	59.0816i	−0.135198	−	0.135198i
$438$	−3.45648	+	3.45648i	−0.00789151	+	0.00789151i
$439$			517.562i			1.17896i	0.807784	+	0.589479i	$0.200667\pi$
$439$			517.562i			1.17896i	−0.807784	+	0.589479i	$0.799333\pi$
$440$	7.85064	+	3.18188i	0.0178424	+	0.00723155i
$441$	−118.258			−0.268158
$442$	87.9429	+	87.9429i	0.198966	+	0.198966i
$443$	256.263	−	256.263i	0.578472	−	0.578472i	−0.356010	−	0.934482i	$-0.615863\pi$
$443$	256.263	−	256.263i	0.578472	−	0.578472i	0.934482	+	0.356010i	$0.115863\pi$
$444$		−	207.510i		−	0.467366i
$445$	−253.546	+	107.296i	−0.569766	+	0.241114i
$446$	−296.551			−0.664913
$447$	309.718	+	309.718i	0.692882	+	0.692882i
$448$	−17.5095	+	17.5095i	−0.0390837	+	0.0390837i
$449$			347.606i			0.774178i	0.922042	+	0.387089i	$0.126519\pi$
$449$			347.606i			0.774178i	−0.922042	+	0.387089i	$0.873481\pi$
$450$	1.61846	+	106.054i	0.00359658	+	0.235675i
$451$	−35.7242			−0.0792111
$452$	81.7243	+	81.7243i	0.180806	+	0.180806i
$453$	29.9642	−	29.9642i	0.0661462	−	0.0661462i
$454$		−	251.651i		−	0.554298i
$455$	20.8955	+	49.3773i	0.0459242	+	0.108522i
$456$	85.3510			0.187173
$457$	−112.362	−	112.362i	−0.245868	−	0.245868i	0.573405	−	0.819272i	$-0.305622\pi$
$457$	−112.362	−	112.362i	−0.245868	−	0.245868i	−0.819272	+	0.573405i	$0.805622\pi$
$458$	−8.02492	+	8.02492i	−0.0175217	+	0.0175217i
$459$			131.902i			0.287369i
$460$	−18.0143	+	44.4464i	−0.0391614	+	0.0966227i
$461$	131.722			0.285730			0.142865	−	0.989742i	$-0.454369\pi$
$461$	131.722			0.285730			0.142865	+	0.989742i	$0.454369\pi$
$462$	3.21127	+	3.21127i	0.00695079	+	0.00695079i
$463$	304.225	−	304.225i	0.657074	−	0.657074i	−0.297613	−	0.954687i	$-0.596190\pi$
$463$	304.225	−	304.225i	0.657074	−	0.657074i	0.954687	+	0.297613i	$0.0961904\pi$
$464$		−	101.460i		−	0.218663i
$465$	399.177	+	161.788i	0.858446	+	0.347931i
$466$	603.703			1.29550
$467$	−153.989	−	153.989i	−0.329741	−	0.329741i	0.522747	−	0.852488i	$-0.324907\pi$
$467$	−153.989	−	153.989i	−0.329741	−	0.329741i	−0.852488	+	0.522747i	$0.824907\pi$
$468$	14.6983	−	14.6983i	0.0314066	−	0.0314066i
$469$			24.1098i			0.0514067i
$470$	34.2910	−	14.5113i	0.0729595	−	0.0308751i
$471$	−112.350			−0.238535
$472$	−213.470	−	213.470i	−0.452268	−	0.452268i
$473$	−22.3373	+	22.3373i	−0.0472247	+	0.0472247i
$474$		−	302.099i		−	0.637339i
$475$	−312.648	−	303.249i	−0.658206	−	0.638418i
$476$	157.145			0.330136
$477$	−198.653	−	198.653i	−0.416464	−	0.416464i
$478$	74.3262	−	74.3262i	0.155494	−	0.155494i
$479$			644.063i			1.34460i	0.740280	+	0.672299i	$0.234693\pi$
$479$			644.063i			1.34460i	−0.740280	+	0.672299i	$0.765307\pi$
$480$	−19.0924	−	45.1163i	−0.0397758	−	0.0939923i
$481$	207.529			0.431454
$482$	−259.415	−	259.415i	−0.538206	−	0.538206i
$483$	−18.1806	+	18.1806i	−0.0376410	+	0.0376410i
$484$		−	241.282i		−	0.498517i
$485$	147.400	−	363.678i	0.303917	−	0.749851i
$486$	22.0454			0.0453609
$487$	−331.877	−	331.877i	−0.681472	−	0.681472i	0.278860	−	0.960332i	$-0.410044\pi$
$487$	−331.877	−	331.877i	−0.681472	−	0.681472i	−0.960332	+	0.278860i	$0.910044\pi$
$488$	−113.724	+	113.724i	−0.233041	+	0.233041i
$489$			377.853i			0.772706i
$490$	−258.325	−	104.700i	−0.527194	−	0.213673i
$491$	584.577			1.19058			0.595292	−	0.803509i	$-0.297036\pi$
$491$	584.577			1.19058			0.595292	+	0.803509i	$0.297036\pi$
$492$	146.090	+	146.090i	0.296932	+	0.296932i
$493$	−455.290	+	455.290i	−0.923510	+	0.923510i
$494$			85.3588i			0.172791i
$495$	−8.27439	+	3.50156i	−0.0167159	+	0.00707387i
$496$	−198.940			−0.401089
$497$	40.4006	+	40.4006i	0.0812889	+	0.0812889i
$498$	−83.5541	+	83.5541i	−0.167779	+	0.167779i
$499$			366.222i			0.733911i	0.930238	+	0.366956i	$0.119600\pi$
$499$			366.222i			0.733911i	−0.930238	+	0.366956i	$0.880400\pi$
$500$	−90.3595	+	233.099i	−0.180719	+	0.466198i
$501$	−264.325			−0.527595
$502$	−461.482	−	461.482i	−0.919287	−	0.919287i
$503$	−391.814	+	391.814i	−0.778954	+	0.778954i	−0.979653	−	0.200699i	$-0.935679\pi$
$503$	−391.814	+	391.814i	−0.778954	+	0.778954i	0.200699	+	0.979653i	$0.435679\pi$
$504$		−	26.2643i		−	0.0521116i
$505$	148.386	+	350.645i	0.293834	+	0.694347i
$506$	−4.06252			−0.00802870
$507$	−192.282	−	192.282i	−0.379255	−	0.379255i
$508$	−238.765	+	238.765i	−0.470009	+	0.470009i
$509$		−	154.418i		−	0.303376i	−0.988428	−	0.151688i	$-0.951529\pi$
$509$		−	154.418i		−	0.303376i	0.988428	−	0.151688i	$-0.0484709\pi$
$510$	−116.780	+	288.131i	−0.228981	+	0.564962i
$511$	−6.17693			−0.0120879
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$	−64.0133	+	64.0133i	−0.124782	+	0.124782i
$514$			70.8643i			0.137868i
$515$	494.561	+	200.447i	0.960313	+	0.389217i
$516$	182.692			0.354054
$517$	2.23033	+	2.23033i	0.00431398	+	0.00431398i
$518$	185.417	−	185.417i	0.357947	−	0.357947i
$519$			409.250i			0.788536i
$520$	45.1204	−	19.0941i	0.0867701	−	0.0367194i
$521$	−568.142			−1.09048			−0.545242	−	0.838279i	$-0.683562\pi$
$521$	−568.142			−1.09048			−0.545242	+	0.838279i	$0.683562\pi$
$522$	76.0947	+	76.0947i	0.145775	+	0.145775i
$523$	−179.943	+	179.943i	−0.344059	+	0.344059i	−0.857891	−	0.513832i	$-0.828225\pi$
$523$	−179.943	+	179.943i	−0.344059	+	0.344059i	0.513832	+	0.857891i	$0.328225\pi$
$524$			335.713i			0.640675i
$525$	−93.3158	+	96.2081i	−0.177744	+	0.183254i
$526$	55.1794			0.104904
$527$	892.725	+	892.725i	1.69398	+	1.69398i
$528$	2.93442	−	2.93442i	0.00555762	−	0.00555762i
$529$		−	23.0000i		−	0.0434783i
$530$	−258.065	−	609.821i	−0.486914	−	1.15061i
$531$	320.205			0.603023
$532$	76.2636	+	76.2636i	0.143353	+	0.143353i
$533$	−146.104	+	146.104i	−0.274116	+	0.274116i
$534$			134.876i			0.252576i
$535$	−283.764	+	700.129i	−0.530400	+	1.30865i
$536$	22.0312			0.0411031
$537$	−223.940	−	223.940i	−0.417021	−	0.417021i
$538$	208.728	−	208.728i	0.387970	−	0.387970i
$539$		−	23.6116i		−	0.0438063i
$540$	48.1565	+	19.5180i	0.0891787	+	0.0361444i
$541$	257.058			0.475153			0.237576	−	0.971369i	$-0.423647\pi$
$541$	257.058			0.475153			0.237576	+	0.971369i	$0.423647\pi$
$542$	210.239	+	210.239i	0.387895	+	0.387895i
$543$	347.255	−	347.255i	0.639511	−	0.639511i
$544$		−	143.597i		−	0.263965i
$545$	483.825	−	204.745i	0.887752	−	0.375680i
$546$	26.2667			0.0481075
$547$	254.464	+	254.464i	0.465200	+	0.465200i	0.900355	−	0.435155i	$-0.143307\pi$
$547$	254.464	+	254.464i	0.465200	+	0.465200i	−0.435155	+	0.900355i	$0.643307\pi$
$548$	−258.298	+	258.298i	−0.471347	+	0.471347i
$549$		−	170.586i		−	0.310721i
$550$	−21.1749	+	0.323146i	−0.0384998	+	0.000587538i
$551$	−441.912			−0.802019
$552$	16.6132	+	16.6132i	0.0300965	+	0.0300965i
$553$	269.934	−	269.934i	0.488126	−	0.488126i
$554$			61.8520i			0.111646i
$555$	202.178	+	477.758i	0.364285	+	0.860825i
$556$	80.4521			0.144698
$557$	40.9023	+	40.9023i	0.0734333	+	0.0734333i	0.742870	−	0.669436i	$-0.233464\pi$
$557$	40.9023	+	40.9023i	0.0734333	+	0.0734333i	−0.669436	+	0.742870i	$0.733464\pi$
$558$	149.205	−	149.205i	0.267393	−	0.267393i
$559$			182.709i			0.326849i
$560$	23.2531	−	57.3723i	0.0415235	−	0.102451i
$561$	−26.3359			−0.0469445
$562$	−438.208	−	438.208i	−0.779729	−	0.779729i
$563$	−220.043	+	220.043i	−0.390840	+	0.390840i	−0.874987	−	0.484147i	$-0.839130\pi$
$563$	−220.043	+	220.043i	−0.390840	+	0.390840i	0.484147	+	0.874987i	$0.339130\pi$
$564$		−	18.2414i		−	0.0323428i
$565$	−267.781	−	108.532i	−0.473948	−	0.192092i
$566$	236.624			0.418064
$567$	19.6982	+	19.6982i	0.0347411	+	0.0347411i
$568$	36.9176	−	36.9176i	0.0649958	−	0.0649958i
$569$		−	187.836i		−	0.330116i	−0.986284	−	0.165058i	$-0.947219\pi$
$569$		−	187.836i		−	0.330116i	0.986284	−	0.165058i	$-0.0527811\pi$
$570$	−196.506	+	83.1578i	−0.344748	+	0.145891i
$571$	72.3367			0.126684			0.0633421	−	0.997992i	$-0.479824\pi$
$571$	72.3367			0.126684			0.0633421	+	0.997992i	$0.479824\pi$
$572$	2.93469	+	2.93469i	0.00513058	+	0.00513058i
$573$	272.463	−	272.463i	0.475503	−	0.475503i
$574$			261.072i			0.454829i
$575$	−1.82949	−	119.882i	−0.00318172	−	0.208490i
$576$	−24.0000			−0.0416667
$577$	−229.527	−	229.527i	−0.397794	−	0.397794i	0.479660	−	0.877454i	$-0.340760\pi$
$577$	−229.527	−	229.527i	−0.397794	−	0.397794i	−0.877454	+	0.479660i	$0.840760\pi$
$578$	−355.379	+	355.379i	−0.614842	+	0.614842i
$579$			379.816i			0.655986i
$580$	98.8523	+	233.594i	0.170435	+	0.402748i
$581$	−149.316			−0.256998
$582$	−135.936	−	135.936i	−0.233567	−	0.233567i
$583$	39.6635	−	39.6635i	0.0680334	−	0.0680334i
$584$			5.64441i			0.00966509i
$585$	−19.5197	+	48.1609i	−0.0333671	+	0.0823263i
$586$	−49.3790			−0.0842646
$587$	−381.748	−	381.748i	−0.650337	−	0.650337i	0.302737	−	0.953074i	$-0.402100\pi$
$587$	−381.748	−	381.748i	−0.650337	−	0.650337i	−0.953074	+	0.302737i	$0.902100\pi$
$588$	−96.5571	+	96.5571i	−0.164213	+	0.164213i
$589$			866.494i			1.47113i
$590$	699.464	+	283.495i	1.18553	+	0.480500i
$591$	477.961			0.808733
$592$	−169.432	−	169.432i	−0.286202	−	0.286202i
$593$	−46.1542	+	46.1542i	−0.0778317	+	0.0778317i	−0.744951	−	0.667119i	$-0.767527\pi$
$593$	−46.1542	+	46.1542i	−0.0778317	+	0.0778317i	0.667119	+	0.744951i	$0.267527\pi$
$594$			4.40163i			0.00741015i
$595$	−361.799	+	153.107i	−0.608066	+	0.257322i
$596$	505.768			0.848604
$597$	−197.877	−	197.877i	−0.331451	−	0.331451i
$598$	−16.6148	+	16.6148i	−0.0277839	+	0.0277839i
$599$			109.193i			0.182292i	0.995838	+	0.0911461i	$0.0290530\pi$
$599$			109.193i			0.182292i	−0.995838	+	0.0911461i	$0.970947\pi$
$600$	87.9139	+	85.2710i	0.146523	+	0.142118i
$601$	−966.016			−1.60735			−0.803674	−	0.595070i	$-0.797124\pi$
$601$	−966.016			−1.60735			−0.803674	+	0.595070i	$0.797124\pi$
$602$	163.240	+	163.240i	0.271163	+	0.271163i
$603$	−16.5234	+	16.5234i	−0.0274020	+	0.0274020i
$604$		−	48.9314i		−	0.0810122i
$605$	235.082	+	555.512i	0.388566	+	0.918202i
$606$	186.529			0.307803
$607$	399.940	+	399.940i	0.658880	+	0.658880i	0.955115	−	0.296235i	$-0.0957313\pi$
$607$	399.940	+	399.940i	0.658880	+	0.658880i	−0.296235	+	0.955115i	$0.595731\pi$
$608$	69.6888	−	69.6888i	0.114620	−	0.114620i
$609$			135.985i			0.223293i
$610$	151.029	−	372.632i	0.247588	−	0.610871i
$611$	18.2430			0.0298577
$612$	107.698	+	107.698i	0.175977	+	0.175977i
$613$	−8.23463	+	8.23463i	−0.0134333	+	0.0134333i	−0.713792	−	0.700358i	$-0.753024\pi$
$613$	−8.23463	+	8.23463i	−0.0134333	+	0.0134333i	0.700358	+	0.713792i	$0.253024\pi$
$614$			487.607i			0.794148i
$615$	−478.685	−	194.012i	−0.778349	−	0.315467i
$616$	5.24398			0.00851295
$617$	456.432	+	456.432i	0.739761	+	0.739761i	0.972532	−	0.232771i	$-0.0747792\pi$
$617$	456.432	+	456.432i	0.739761	+	0.739761i	−0.232771	+	0.972532i	$0.574779\pi$
$618$	184.858	−	184.858i	0.299122	−	0.299122i
$619$			695.598i			1.12375i	0.827224	+	0.561873i	$0.189919\pi$
$619$			695.598i			1.12375i	−0.827224	+	0.561873i	$0.810081\pi$
$620$	458.026	−	193.828i	0.738752	−	0.312626i
$621$	−24.9199			−0.0401286
$622$	−481.852	−	481.852i	−0.774682	−	0.774682i
$623$	−120.515	+	120.515i	−0.193444	+	0.193444i
$624$		−	24.0022i		−	0.0384651i
$625$	−19.0715	−	624.709i	−0.0305145	−	0.999534i
$626$	120.034			0.191748
$627$	−12.7810	−	12.7810i	−0.0203844	−	0.0203844i
$628$	−91.7333	+	91.7333i	−0.146072	+	0.146072i
$629$			1520.62i			2.41752i
$630$	25.5894	+	60.4691i	0.0406180	+	0.0959826i
$631$	920.371			1.45859			0.729296	−	0.684199i	$-0.239848\pi$
$631$	920.371			1.45859			0.729296	+	0.684199i	$0.239848\pi$
$632$	−246.663	−	246.663i	−0.390289	−	0.390289i
$633$	−310.440	+	310.440i	−0.490427	+	0.490427i
$634$		−	27.4482i		−	0.0432936i
$635$	317.086	−	782.344i	0.499348	−	1.23204i
$636$	−324.399			−0.510062
$637$	−96.5660	−	96.5660i	−0.151595	−	0.151595i
$638$	−15.1932	+	15.1932i	−0.0238138	+	0.0238138i
$639$			55.3764i			0.0866610i
$640$	−52.4262	−	21.2485i	−0.0819159	−	0.0332007i
$641$	1166.08			1.81915			0.909576	−	0.415539i	$-0.136407\pi$
$641$	1166.08			1.81915			0.909576	+	0.415539i	$0.136407\pi$
$642$	261.695	+	261.695i	0.407624	+	0.407624i
$643$	804.965	−	804.965i	1.25189	−	1.25189i	0.297018	−	0.954872i	$-0.404008\pi$
$643$	804.965	−	804.965i	1.25189	−	1.25189i	0.954872	−	0.297018i	$-0.0959921\pi$
$644$			29.6888i			0.0461007i
$645$	−420.617	+	177.997i	−0.652120	+	0.275965i
$646$	−625.444			−0.968180
$647$	−202.286	−	202.286i	−0.312652	−	0.312652i	0.533284	−	0.845936i	$-0.320958\pi$
$647$	−202.286	−	202.286i	−0.312652	−	0.312652i	−0.845936	+	0.533284i	$0.820958\pi$
$648$	18.0000	−	18.0000i	0.0277778	−	0.0277778i
$649$			63.9329i			0.0985098i
$650$	−85.2788	+	87.9220i	−0.131198	+	0.135265i
$651$	266.638			0.409582
$652$	308.516	+	308.516i	0.473184	+	0.473184i
$653$	192.092	−	192.092i	0.294169	−	0.294169i	−0.544556	−	0.838725i	$-0.683302\pi$
$653$	192.092	−	192.092i	0.294169	−	0.294169i	0.838725	+	0.544556i	$0.183302\pi$
$654$		−	257.375i		−	0.393539i
$655$	−327.087	−	772.924i	−0.499369	−	1.18004i
$656$	238.565			0.363665
$657$	−4.23331	−	4.23331i	−0.00644339	−	0.00644339i
$658$	16.2992	−	16.2992i	0.0247708	−	0.0247708i
$659$		−	955.049i		−	1.44924i	−0.689149	−	0.724620i	$-0.742016\pi$
$659$		−	955.049i		−	1.44924i	0.689149	−	0.724620i	$-0.257984\pi$
$660$	−3.89700	+	9.61503i	−0.00590454	+	0.0145682i
$661$	270.809			0.409696			0.204848	−	0.978794i	$-0.434330\pi$
$661$	270.809			0.409696			0.204848	+	0.978794i	$0.434330\pi$
$662$	521.875	+	521.875i	0.788331	+	0.788331i
$663$	−107.708	+	107.708i	−0.162455	+	0.162455i
$664$			136.443i			0.205487i
$665$	−249.888	−	101.280i	−0.375771	−	0.152301i
$666$	254.147			0.381603
$667$	−86.0165	−	86.0165i	−0.128960	−	0.128960i
$668$	−215.820	+	215.820i	−0.323085	+	0.323085i
$669$		−	363.199i		−	0.542899i
$670$	−50.7232	+	21.4651i	−0.0757063	+	0.0320375i
$671$	34.0595			0.0507593
$672$	−21.4447	−	21.4447i	−0.0319117	−	0.0319117i
$673$	2.52466	−	2.52466i	0.00375136	−	0.00375136i	−0.705229	−	0.708980i	$-0.749156\pi$
$673$	2.52466	−	2.52466i	0.00375136	−	0.00375136i	0.708980	+	0.705229i	$0.249156\pi$
$674$		−	561.007i		−	0.832354i
$675$	−129.889	+	1.98220i	−0.192428	+	0.00293660i
$676$	−313.996			−0.464491
$677$	717.605	+	717.605i	1.05998	+	1.05998i	0.998083	+	0.0618948i	$0.0197143\pi$
$677$	717.605	+	717.605i	1.05998	+	1.05998i	0.0618948	+	0.998083i	$0.480286\pi$
$678$	−100.091	+	100.091i	−0.147627	+	0.147627i
$679$		−	242.925i		−	0.357769i
$680$	139.907	+	330.608i	0.205746	+	0.486188i
$681$	308.209			0.452582
$682$	29.7906	+	29.7906i	0.0436812	+	0.0436812i
$683$	872.239	−	872.239i	1.27707	−	1.27707i	0.334771	−	0.942300i	$-0.391341\pi$
$683$	872.239	−	872.239i	1.27707	−	1.27707i	0.942300	−	0.334771i	$-0.108659\pi$
$684$			104.533i			0.152826i
$685$	343.027	−	846.349i	0.500770	−	1.23555i
$686$	−387.045			−0.564205
$687$	−9.82848	−	9.82848i	−0.0143064	−	0.0143064i
$688$	149.167	−	149.167i	0.216813	−	0.216813i
$689$		−	324.429i		−	0.470869i
$690$	−54.4356	−	22.0629i	−0.0788921	−	0.0319752i
$691$	−596.416			−0.863120			−0.431560	−	0.902084i	$-0.642037\pi$
$691$	−596.416			−0.863120			−0.431560	+	0.902084i	$0.642037\pi$
$692$	334.151	+	334.151i	0.482878	+	0.482878i
$693$	−3.93298	+	3.93298i	−0.00567530	+	0.00567530i
$694$		−	129.479i		−	0.186569i
$695$	−185.227	+	78.3847i	−0.266514	+	0.112784i
$696$	124.262			0.178537
$697$	−1070.54	−	1070.54i	−1.53592	−	1.53592i
$698$	−534.997	+	534.997i	−0.766472	+	0.766472i
$699$			739.382i			1.05777i
$700$	2.36154	+	154.746i	0.00337363	+	0.221065i
$701$	526.896			0.751635			0.375817	−	0.926694i	$-0.377362\pi$
$701$	526.896			0.751635			0.375817	+	0.926694i	$0.377362\pi$
$702$	18.0016	+	18.0016i	0.0256434	+	0.0256434i
$703$	−737.968	+	737.968i	−1.04974	+	1.04974i
$704$		−	4.79189i		−	0.00680666i
$705$	17.7726	+	41.9977i	0.0252094	+	0.0595712i
$706$	−16.9053			−0.0239451
$707$	166.669	+	166.669i	0.235741	+	0.235741i
$708$	261.447	−	261.447i	0.369275	−	0.369275i
$709$		−	934.208i		−	1.31764i	−0.752300	−	0.658821i	$-0.771056\pi$
$709$		−	934.208i		−	1.31764i	0.752300	−	0.658821i	$-0.228944\pi$
$710$	−49.0276	+	120.965i	−0.0690530	+	0.170374i
$711$	369.994			0.520385
$712$	110.126	+	110.126i	0.154671	+	0.154671i
$713$	−168.660	+	168.660i	−0.236549	+	0.236549i
$714$			192.462i			0.269555i
$715$	−9.61591	−	3.89735i	−0.0134488	−	0.00545084i
$716$	−365.693			−0.510744
$717$	91.0306	+	91.0306i	0.126960	+	0.126960i
$718$	29.7289	−	29.7289i	0.0414052	−	0.0414052i
$719$		−	683.253i		−	0.950283i	−0.879909	−	0.475142i	$-0.842397\pi$
$719$		−	683.253i		−	0.950283i	0.879909	−	0.475142i	$-0.157603\pi$
$720$	55.2560	−	23.3833i	0.0767444	−	0.0324768i
$721$	330.351			0.458185
$722$	57.4667	+	57.4667i	0.0795937	+	0.0795937i
$723$	317.718	−	317.718i	0.439443	−	0.439443i
$724$		−	567.064i		−	0.783238i
$725$	−455.182	−	441.498i	−0.627837	−	0.608962i
$726$	295.509			0.407038
$727$	543.867	+	543.867i	0.748098	+	0.748098i	0.974122	−	0.226024i	$-0.0725726\pi$
$727$	543.867	+	543.867i	0.748098	+	0.748098i	−0.226024	+	0.974122i	$0.572573\pi$
$728$	21.4466	−	21.4466i	0.0294597	−	0.0294597i
$729$			27.0000i			0.0370370i
$730$	−5.49937	−	12.9953i	−0.00753338	−	0.0178018i
$731$	−1338.75			−1.83139
$732$	−139.283	−	139.283i	−0.190277	−	0.190277i
$733$	808.113	−	808.113i	1.10247	−	1.10247i	0.108362	−	0.994111i	$-0.465439\pi$
$733$	808.113	−	808.113i	1.10247	−	1.10247i	0.994111	−	0.108362i	$-0.0345607\pi$
$734$		−	575.951i		−	0.784674i
$735$	128.231	−	316.382i	0.174463	−	0.430452i
$736$	27.1293			0.0368605
$737$	−3.29910	−	3.29910i	−0.00447639	−	0.00447639i
$738$	−178.923	+	178.923i	−0.242444	+	0.242444i
$739$		−	1188.76i		−	1.60860i	−0.594223	−	0.804300i	$-0.702540\pi$
$739$		−	1188.76i		−	1.60860i	0.594223	−	0.804300i	$-0.297460\pi$
$740$	555.165	+	225.010i	0.750224	+	0.304068i
$741$	−104.543			−0.141083
$742$	−289.860	−	289.860i	−0.390647	−	0.390647i
$743$	−38.8612	+	38.8612i	−0.0523031	+	0.0523031i	−0.732775	−	0.680471i	$-0.761775\pi$
$743$	−38.8612	+	38.8612i	−0.0523031	+	0.0523031i	0.680471	+	0.732775i	$0.261775\pi$
$744$		−	243.651i		−	0.327488i
$745$	−1164.45	+	492.771i	−1.56301	+	0.661438i
$746$	−397.167			−0.532395
$747$	−102.332	−	102.332i	−0.136991	−	0.136991i
$748$	−21.5032	+	21.5032i	−0.0287475	+	0.0287475i
$749$			467.664i			0.624384i
$750$	−285.487	−	110.667i	−0.380649	−	0.147556i
$751$	−787.039			−1.04799			−0.523994	−	0.851722i	$-0.675559\pi$
$751$	−787.039			−1.04799			−0.523994	+	0.851722i	$0.675559\pi$
$752$	−14.8940	−	14.8940i	−0.0198059	−	0.0198059i
$753$	565.198	−	565.198i	0.750595	−	0.750595i
$754$			124.273i			0.164819i
$755$	47.6740	+	112.656i	0.0631444	+	0.149214i
$756$	32.1670			0.0425490
$757$	582.426	+	582.426i	0.769387	+	0.769387i	0.977998	−	0.208612i	$-0.0668946\pi$
$757$	582.426	+	582.426i	0.769387	+	0.769387i	−0.208612	+	0.977998i	$0.566895\pi$
$758$	−533.203	+	533.203i	−0.703434	+	0.703434i
$759$		−	4.97555i		−	0.00655541i
$760$	−92.5488	+	228.345i	−0.121775	+	0.300454i
$761$	−228.038			−0.299655			−0.149828	−	0.988712i	$-0.547872\pi$
$761$	−228.038			−0.299655			−0.149828	+	0.988712i	$0.547872\pi$
$762$	−292.426	−	292.426i	−0.383761	−	0.383761i
$763$	229.972	−	229.972i	0.301404	−	0.301404i
$764$		−	444.930i		−	0.582369i
$765$	−352.886	−	143.026i	−0.461289	−	0.186962i
$766$	241.196			0.314877
$767$	261.471	+	261.471i	0.340900	+	0.340900i
$768$	−19.5959	+	19.5959i	−0.0255155	+	0.0255155i
$769$		−	63.2584i		−	0.0822606i	−0.999154	−	0.0411303i	$-0.986904\pi$
$769$		−	63.2584i		−	0.0822606i	0.999154	−	0.0411303i	$-0.0130959\pi$
$770$	−12.0734	+	5.10922i	−0.0156797	+	0.00663536i
$771$	−86.7907			−0.112569
$772$	310.118	+	310.118i	0.401708	+	0.401708i
$773$	−268.204	+	268.204i	−0.346965	+	0.346965i	−0.858978	−	0.512013i	$-0.828900\pi$
$773$	−268.204	+	268.204i	−0.346965	+	0.346965i	0.512013	+	0.858978i	$0.328900\pi$
$774$			223.751i			0.289084i
$775$	−865.681	+	892.513i	−1.11701	+	1.15163i
$776$	−221.983			−0.286060
$777$	227.088	+	227.088i	0.292262	+	0.292262i
$778$	292.831	−	292.831i	0.376389	−	0.376389i
$779$		−	1039.08i		−	1.33386i
$780$	23.3854	+	55.2610i	0.0299813	+	0.0708475i
$781$	−11.0566			−0.0141569
$782$	−121.740	−	121.740i	−0.155678	−	0.155678i
$783$	−93.1965	+	93.1965i	−0.119025	+	0.119025i
$784$			157.677i			0.201119i
$785$	121.824	−	300.577i	0.155190	−	0.382900i
$786$	−411.163			−0.523109
$787$	−133.984	−	133.984i	−0.170247	−	0.170247i	0.616841	−	0.787088i	$-0.288412\pi$
$787$	−133.984	−	133.984i	−0.170247	−	0.170247i	−0.787088	+	0.616841i	$0.788412\pi$
$788$	390.253	−	390.253i	0.495246	−	0.495246i
$789$			67.5806i			0.0856535i
$790$	808.224	+	327.575i	1.02307	+	0.414652i
$791$	−178.869			−0.226130
$792$	3.59392	+	3.59392i	0.00453777	+	0.00453777i
$793$	139.295	−	139.295i	0.175656	−	0.175656i
$794$		−	443.968i		−	0.559153i
$795$	746.875	−	316.063i	0.939465	−	0.397564i
$796$	−323.131			−0.405944
$797$	−1109.95	−	1109.95i	−1.39266	−	1.39266i	−0.819309	−	0.573352i	$-0.805643\pi$
$797$	−1109.95	−	1109.95i	−1.39266	−	1.39266i	−0.573352	−	0.819309i	$-0.694357\pi$
$798$	−93.4034	+	93.4034i	−0.117047	+	0.117047i
$799$			133.671i			0.167298i
$800$	141.405	−	2.15795i	0.176756	−	0.00269744i
$801$	−165.188			−0.206228
$802$	−453.324	−	453.324i	−0.565242	−	0.565242i
$803$	0.845231	−	0.845231i	0.00105259	−	0.00105259i
$804$			26.9826i			0.0335605i
$805$	−28.9259	−	68.3535i	−0.0359328	−	0.0849112i
$806$	243.673			0.302324
$807$	255.638	+	255.638i	0.316776	+	0.316776i
$808$	152.300	−	152.300i	0.188490	−	0.188490i
$809$		−	884.691i		−	1.09356i	−0.837276	−	0.546780i	$-0.815853\pi$
$809$		−	884.691i		−	1.09356i	0.837276	−	0.546780i	$-0.184147\pi$
$810$	−23.9045	+	58.9794i	−0.0295118	+	0.0728141i
$811$	−602.987			−0.743510			−0.371755	−	0.928331i	$-0.621244\pi$
$811$	−602.987			−0.743510			−0.371755	+	0.928331i	$0.621244\pi$
$812$	111.032	+	111.032i	0.136739	+	0.136739i
$813$	−257.489	+	257.489i	−0.316715	+	0.316715i
$814$			50.7436i			0.0623386i
$815$	−1010.89	−	409.718i	−1.24036	−	0.502722i
$816$	175.870			0.215527
$817$	−649.706	−	649.706i	−0.795233	−	0.795233i
$818$	685.562	−	685.562i	0.838096	−	0.838096i
$819$			32.1700i			0.0392796i
$820$	−549.255	+	232.434i	−0.669823	+	0.283456i
$821$	914.000			1.11328			0.556638	−	0.830755i	$-0.312091\pi$
$821$	914.000			1.11328			0.556638	+	0.830755i	$0.312091\pi$
$822$	−316.349	−	316.349i	−0.384853	−	0.384853i
$823$	589.228	−	589.228i	0.715951	−	0.715951i	−0.251822	−	0.967773i	$-0.581030\pi$
$823$	589.228	−	589.228i	0.715951	−	0.715951i	0.967773	+	0.251822i	$0.0810299\pi$
$824$		−	301.871i		−	0.366349i
$825$	−0.395771	−	25.9338i	−0.000479722	−	0.0314350i
$826$	467.220			0.565642
$827$	183.512	+	183.512i	0.221901	+	0.221901i	0.809298	−	0.587398i	$-0.199848\pi$
$827$	183.512	+	183.512i	0.221901	+	0.221901i	−0.587398	+	0.809298i	$0.699848\pi$
$828$	−20.3470	+	20.3470i	−0.0245737	+	0.0245737i
$829$		−	1385.21i		−	1.67094i	−0.549540	−	0.835468i	$-0.685197\pi$
$829$		−	1385.21i		−	1.67094i	0.549540	−	0.835468i	$-0.314803\pi$
$830$	−132.937	−	314.138i	−0.160165	−	0.378479i
$831$	−75.7529			−0.0911587
$832$	−19.5977	−	19.5977i	−0.0235549	−	0.0235549i
$833$	707.562	−	707.562i	0.849414	−	0.849414i
$834$			98.5333i			0.118145i
$835$	286.616	−	707.165i	0.343253	−	0.846904i
$836$	−20.8713			−0.0249657
$837$	182.738	+	182.738i	0.218325	+	0.218325i
$838$	−526.496	+	526.496i	−0.628277	+	0.628277i
$839$			1046.14i			1.24689i	0.781867	+	0.623446i	$0.214268\pi$
$839$			1046.14i			1.24689i	−0.781867	+	0.623446i	$0.785732\pi$
$840$	70.2664	+	28.4792i	0.0836505	+	0.0339038i
$841$	197.623			0.234985
$842$	−23.9389	−	23.9389i	−0.0284310	−	0.0284310i
$843$	536.693	−	536.693i	0.636646	−	0.636646i
$844$			506.947i			0.600648i
$845$	722.922	−	305.927i	0.855529	−	0.362044i
$846$	22.3410			0.0264078
$847$	264.046	+	264.046i	0.311743	+	0.311743i
$848$	−264.871	+	264.871i	−0.312348	+	0.312348i
$849$			289.804i			0.341348i
$850$	−644.225	−	624.858i	−0.757912	−	0.735127i
$851$	−287.285			−0.337585
$852$	45.2146	+	45.2146i	0.0530688	+	0.0530688i
$853$	905.882	−	905.882i	1.06199	−	1.06199i	0.0640479	−	0.997947i	$-0.479599\pi$
$853$	905.882	−	905.882i	1.06199	−	1.06199i	0.997947	−	0.0640479i	$-0.0204011\pi$
$854$		−	248.906i		−	0.291459i
$855$	−101.847	−	240.670i	−0.119119	−	0.281486i
$856$	427.346			0.499236
$857$	390.237	+	390.237i	0.455352	+	0.455352i	0.897126	−	0.441774i	$-0.145651\pi$
$857$	390.237	+	390.237i	0.455352	+	0.455352i	−0.441774	+	0.897126i	$0.645651\pi$
$858$	−3.59425	+	3.59425i	−0.00418910	+	0.00418910i
$859$		−	633.548i		−	0.737542i	−0.929520	−	0.368771i	$-0.879779\pi$
$859$		−	633.548i		−	0.737542i	0.929520	−	0.368771i	$-0.120221\pi$
$860$	−198.098	+	488.767i	−0.230347	+	0.568333i
$861$	−319.746			−0.371366
$862$	118.968	+	118.968i	0.138013	+	0.138013i
$863$	−541.291	+	541.291i	−0.627221	+	0.627221i	−0.947368	−	0.320147i	$-0.896268\pi$
$863$	−541.291	+	541.291i	−0.627221	+	0.627221i	0.320147	+	0.947368i	$0.396268\pi$
$864$		−	29.3939i		−	0.0340207i
$865$	−1094.89	−	443.763i	−1.26577	−	0.513021i
$866$	−805.457			−0.930089
$867$	−435.248	−	435.248i	−0.502016	−	0.502016i
$868$	217.709	−	217.709i	0.250817	−	0.250817i
$869$			73.8738i			0.0850101i
$870$	−286.093	+	121.069i	−0.328842	+	0.139160i
$871$	−26.9851			−0.0309818
$872$	−210.146	−	210.146i	−0.240993	−	0.240993i
$873$	166.487	−	166.487i	0.190707	−	0.190707i
$874$		−	118.163i		−	0.135198i
$875$	−156.206	−	353.975i	−0.178521	−	0.404543i
$876$	−6.91296			−0.00789151
$877$	−351.560	−	351.560i	−0.400867	−	0.400867i	0.477672	−	0.878538i	$-0.341481\pi$
$877$	−351.560	−	351.560i	−0.400867	−	0.400867i	−0.878538	+	0.477672i	$0.841481\pi$
$878$	−517.562	+	517.562i	−0.589479	+	0.589479i
$879$		−	60.4767i		−	0.0688017i
$880$	4.66875	+	11.0325i	0.00530540	+	0.0125370i
$881$	481.444			0.546475			0.273237	−	0.961947i	$-0.411906\pi$
$881$	481.444			0.546475			0.273237	+	0.961947i	$0.411906\pi$
$882$	−118.258	−	118.258i	−0.134079	−	0.134079i
$883$	873.921	−	873.921i	0.989718	−	0.989718i	−0.0102297	−	0.999948i	$-0.503256\pi$
$883$	873.921	−	873.921i	0.989718	−	0.989718i	0.999948	+	0.0102297i	$0.00325626\pi$
$884$			175.886i			0.198966i
$885$	−347.209	+	856.665i	−0.392326	+	0.967983i
$886$	512.526			0.578472
$887$	410.317	+	410.317i	0.462590	+	0.462590i	0.899503	−	0.436914i	$-0.143929\pi$
$887$	410.317	+	410.317i	0.462590	+	0.462590i	−0.436914	+	0.899503i	$0.643929\pi$
$888$	207.510	−	207.510i	0.233683	−	0.233683i
$889$		−	522.581i		−	0.587831i
$890$	−360.841	−	146.250i	−0.405440	−	0.164326i
$891$	−5.39088			−0.00605037
$892$	−296.551	−	296.551i	−0.332456	−	0.332456i
$893$	−64.8717	+	64.8717i	−0.0726446	+	0.0726446i
$894$			619.437i			0.692882i
$895$	841.946	−	356.295i	0.940722	−	0.398095i
$896$	−35.0190			−0.0390837
$897$	−20.3489	−	20.3489i	−0.0226855	−	0.0226855i
$898$	−347.606	+	347.606i	−0.387089	+	0.387089i
$899$			1261.52i			1.40325i
$900$	−104.435	+	107.672i	−0.116039	+	0.119636i
$901$	2377.17			2.63837
$902$	−35.7242	−	35.7242i	−0.0396056	−	0.0396056i
$903$	−199.928	+	199.928i	−0.221404	+	0.221404i
$904$			163.449i			0.180806i
$905$	552.492	+	1305.57i	0.610489	+	1.44262i
$906$	59.9285			0.0661462
$907$	−333.521	−	333.521i	−0.367719	−	0.367719i	0.498926	−	0.866645i	$-0.333728\pi$
$907$	−333.521	−	333.521i	−0.367719	−	0.367719i	−0.866645	+	0.498926i	$0.833728\pi$
$908$	251.651	−	251.651i	0.277149	−	0.277149i
$909$			228.450i			0.251320i
$910$	−28.4818	+	70.2728i	−0.0312986	+	0.0772229i
$911$	−288.138			−0.316288			−0.158144	−	0.987416i	$-0.550551\pi$
$911$	−288.138			−0.316288			−0.158144	+	0.987416i	$0.550551\pi$
$912$	85.3510	+	85.3510i	0.0935867	+	0.0935867i
$913$	20.4319	−	20.4319i	0.0223789	−	0.0223789i
$914$		−	224.723i		−	0.245868i
$915$	456.379	+	184.971i	0.498774	+	0.202155i
$916$	−16.0498			−0.0175217
$917$	−367.386	−	367.386i	−0.400639	−	0.400639i
$918$	−131.902	+	131.902i	−0.143684	+	0.143684i
$919$		−	429.202i		−	0.467032i	−0.972353	−	0.233516i	$-0.924977\pi$
$919$		−	429.202i		−	0.467032i	0.972353	−	0.233516i	$-0.0750231\pi$
$920$	−62.4607	+	26.4322i	−0.0678921	+	0.0287306i
$921$	−597.194			−0.648419
$922$	131.722	+	131.722i	0.142865	+	0.142865i
$923$	−45.2188	+	45.2188i	−0.0489911	+	0.0489911i
$924$			6.42253i			0.00695079i
$925$	−1497.40	+	22.8516i	−1.61881	+	0.0247044i
$926$	608.451			0.657074
$927$	226.403	+	226.403i	0.244232	+	0.244232i
$928$	101.460	−	101.460i	0.109331	−	0.109331i
$929$			27.1291i			0.0292025i	0.999893	+	0.0146013i	$0.00464789\pi$
$929$			27.1291i			0.0292025i	−0.999893	+	0.0146013i	$0.995352\pi$
$930$	237.390	+	560.965i	0.255258	+	0.603188i
$931$	686.771			0.737670
$932$	603.703	+	603.703i	0.647750	+	0.647750i
$933$	590.146	−	590.146i	0.632526	−	0.632526i
$934$		−	307.978i		−	0.329741i
$935$	28.5568	−	70.4580i	0.0305421	−	0.0753562i
$936$	29.3966			0.0314066
$937$	−802.055	−	802.055i	−0.855981	−	0.855981i	0.134880	−	0.990862i	$-0.456935\pi$
$937$	−802.055	−	802.055i	−0.855981	−	0.855981i	−0.990862	+	0.134880i	$0.956935\pi$
$938$	−24.1098	+	24.1098i	−0.0257034	+	0.0257034i
$939$			147.012i			0.156562i
$940$	48.8023	+	19.7797i	0.0519173	+	0.0210422i
$941$	674.074			0.716338			0.358169	−	0.933657i	$-0.383401\pi$
$941$	674.074			0.716338			0.358169	+	0.933657i	$0.383401\pi$
$942$	−112.350	−	112.350i	−0.119267	−	0.119267i
$943$	202.253	−	202.253i	0.214478	−	0.214478i
$944$		−	426.941i		−	0.452268i
$945$	−74.0592	+	31.3404i	−0.0783695	+	0.0331645i
$946$	−44.6746			−0.0472247
$947$	2.67835	+	2.67835i	0.00282825	+	0.00282825i	0.708519	−	0.705691i	$-0.249363\pi$
$947$	2.67835	+	2.67835i	0.00282825	+	0.00282825i	−0.705691	+	0.708519i	$0.749363\pi$
$948$	302.099	−	302.099i	0.318670	−	0.318670i
$949$		−	6.91360i		−	0.00728514i
$950$	−9.39907	−	615.896i	−0.00989375	−	0.648312i
$951$	33.6170			0.0353491
$952$	157.145	+	157.145i	0.165068	+	0.165068i
$953$	936.467	−	936.467i	0.982651	−	0.982651i	−0.0172009	−	0.999852i	$-0.505475\pi$
$953$	936.467	−	936.467i	0.982651	−	0.982651i	0.999852	+	0.0172009i	$0.00547548\pi$
$954$		−	397.306i		−	0.416464i
$955$	433.497	+	1024.38i	0.453924	+	1.07265i
$956$	148.652			0.155494
$957$	−18.6078	−	18.6078i	−0.0194439	−	0.0194439i
$958$	−644.063	+	644.063i	−0.672299	+	0.672299i
$959$		−	565.334i		−	0.589504i
$960$	26.0239	−	64.2087i	0.0271083	−	0.0668840i
$961$	1512.57			1.57396
$962$	207.529	+	207.529i	0.215727	+	0.215727i
$963$	−320.510	+	320.510i	−0.332824	+	0.332824i
$964$		−	518.831i		−	0.538206i
$965$	−1016.14	−	411.846i	−1.05300	−	0.426783i
$966$	−36.3612			−0.0376410
$967$	−105.743	−	105.743i	−0.109351	−	0.109351i	0.650314	−	0.759665i	$-0.274637\pi$
$967$	−105.743	−	105.743i	−0.109351	−	0.109351i	−0.759665	+	0.650314i	$0.774637\pi$
$968$	241.282	−	241.282i	0.249259	−	0.249259i
$969$		−	766.010i		−	0.790516i
$970$	511.078	−	216.278i	0.526884	−	0.222967i
$971$	878.547			0.904786			0.452393	−	0.891819i	$-0.350570\pi$
$971$	878.547			0.904786			0.452393	+	0.891819i	$0.350570\pi$
$972$	22.0454	+	22.0454i	0.0226805	+	0.0226805i
$973$	−88.0423	+	88.0423i	−0.0904854	+	0.0904854i
$974$		−	663.754i		−	0.681472i
$975$	−107.682	−	104.445i	−0.110443	−	0.107123i
$976$	−227.448			−0.233041
$977$	1148.93	+	1148.93i	1.17598	+	1.17598i	0.980759	+	0.195222i	$0.0625426\pi$
$977$	1148.93	+	1148.93i	1.17598	+	1.17598i	0.195222	+	0.980759i	$0.437457\pi$
$978$	−377.853	+	377.853i	−0.386353	+	0.386353i
$979$		−	32.9819i		−	0.0336893i
$980$	−153.625	−	363.025i	−0.156761	−	0.370434i
$981$	315.218			0.321323
$982$	584.577	+	584.577i	0.595292	+	0.595292i
$983$	−771.603	+	771.603i	−0.784948	+	0.784948i	−0.980661	−	0.195714i	$-0.937298\pi$
$983$	−771.603	+	771.603i	−0.784948	+	0.784948i	0.195714	+	0.980661i	$0.437298\pi$
$984$			292.181i			0.296932i
$985$	−518.268	+	1278.72i	−0.526160	+	1.29819i
$986$	−910.581			−0.923510
$987$	19.9623	+	19.9623i	0.0202253	+	0.0202253i
$988$	−85.3588	+	85.3588i	−0.0863956	+	0.0863956i
$989$		−	252.925i		−	0.255738i
$990$	−11.7760	−	4.77283i	−0.0118949	−	0.00482104i
$991$	−1364.98			−1.37737			−0.688686	−	0.725060i	$-0.741812\pi$
$991$	−1364.98			−1.37737			−0.688686	+	0.725060i	$0.741812\pi$
$992$	−198.940	−	198.940i	−0.200544	−	0.200544i
$993$	−639.164	+	639.164i	−0.643670	+	0.643670i
$994$			80.8011i			0.0812889i
$995$	743.955	−	314.828i	0.747693	−	0.316410i
$996$	−167.108			−0.167779
$997$	831.293	+	831.293i	0.833794	+	0.833794i	0.988034	−	0.154239i	$-0.0492927\pi$
$997$	831.293	+	831.293i	0.833794	+	0.833794i	−0.154239	+	0.988034i	$0.549293\pi$
$998$	−366.222	+	366.222i	−0.366956	+	0.366956i
$999$			311.266i			0.311577i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.k.a.277.8	✓	40
5.3	odd	4	inner	690.3.k.a.553.8	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.k.a.277.8	✓	40	1.1	even	1	trivial
690.3.k.a.553.8	yes	40	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	690.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-1.94861 - 4.60466i) q^{5} -2.44949 q^{6} +(-2.18869 - 2.18869i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-1.94861 - 4.60466i) q^{5} -2.44949 q^{6} +(-2.18869 - 2.18869i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(2.65606 - 6.55327i) q^{10} +0.598986 q^{11} +(-2.44949 - 2.44949i) q^{12} +(2.44971 - 2.44971i) q^{13} -4.37738i q^{14} +(8.02608 + 3.25299i) q^{15} -4.00000 q^{16} +(17.9496 + 17.9496i) q^{17} +(3.00000 - 3.00000i) q^{18} +17.4222i q^{19} +(9.20933 - 3.89721i) q^{20} +5.36117 q^{21} +(0.598986 + 0.598986i) q^{22} +(-3.39116 + 3.39116i) q^{23} -4.89898i q^{24} +(-17.4059 + 17.9454i) q^{25} +4.89943 q^{26} +(3.67423 + 3.67423i) q^{27} +(4.37738 - 4.37738i) q^{28} +25.3649i q^{29} +(4.77309 + 11.2791i) q^{30} +49.7350 q^{31} +(-4.00000 - 4.00000i) q^{32} +(-0.733605 + 0.733605i) q^{33} +35.8993i q^{34} +(-5.81329 + 14.3431i) q^{35} +6.00000 q^{36} +(42.3579 + 42.3579i) q^{37} +(-17.4222 + 17.4222i) q^{38} +6.00055i q^{39} +(13.1065 + 5.31212i) q^{40} -59.6411 q^{41} +(5.36117 + 5.36117i) q^{42} +(-37.2918 + 37.2918i) q^{43} +1.19797i q^{44} +(-13.8140 + 5.84582i) q^{45} -6.78233 q^{46} +(3.72350 + 3.72350i) q^{47} +(4.89898 - 4.89898i) q^{48} -39.4193i q^{49} +(-35.3512 + 0.539488i) q^{50} -43.9674 q^{51} +(4.89943 + 4.89943i) q^{52} +(66.2177 - 66.2177i) q^{53} +7.34847i q^{54} +(-1.16719 - 2.75813i) q^{55} +8.75476 q^{56} +(-21.3378 - 21.3378i) q^{57} +(-25.3649 + 25.3649i) q^{58} +106.735i q^{59} +(-6.50599 + 16.0522i) q^{60} +56.8619 q^{61} +(49.7350 + 49.7350i) q^{62} +(-6.56607 + 6.56607i) q^{63} -8.00000i q^{64} +(-16.0536 - 6.50658i) q^{65} -1.46721 q^{66} +(-5.50781 - 5.50781i) q^{67} +(-35.8993 + 35.8993i) q^{68} -8.30662i q^{69} +(-20.1564 + 8.52979i) q^{70} -18.4588 q^{71} +(6.00000 + 6.00000i) q^{72} +(1.41110 - 1.41110i) q^{73} +84.7158i q^{74} +(-0.660735 - 43.2962i) q^{75} -34.8444 q^{76} +(-1.31099 - 1.31099i) q^{77} +(-6.00055 + 6.00055i) q^{78} +123.331i q^{79} +(7.79442 + 18.4187i) q^{80} -9.00000 q^{81} +(-59.6411 - 59.6411i) q^{82} +(34.1108 - 34.1108i) q^{83} +10.7223i q^{84} +(47.6753 - 117.629i) q^{85} -74.5836 q^{86} +(-31.0655 - 31.0655i) q^{87} +(-1.19797 + 1.19797i) q^{88} -55.0628i q^{89} +(-19.6598 - 7.96817i) q^{90} -10.7233 q^{91} +(-6.78233 - 6.78233i) q^{92} +(-60.9127 + 60.9127i) q^{93} +7.44701i q^{94} +(80.2234 - 33.9490i) q^{95} +9.79796 q^{96} +(55.4956 + 55.4956i) q^{97} +(39.4193 - 39.4193i) q^{98} -1.79696i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8}+O(q^{10}) \) 40 * q + 40 * q^2 - 8 * q^5 - 8 * q^7 - 80 * q^8	\( 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8} - 16 q^{10} + 32 q^{11} + 16 q^{13} + 24 q^{15} - 160 q^{16} - 48 q^{17} + 120 q^{18} - 16 q^{20} - 96 q^{21} + 32 q^{22} + 32 q^{26} + 16 q^{28} + 24 q^{30} + 152 q^{31} - 160 q^{32} - 24 q^{33} + 48 q^{35} + 240 q^{36} + 216 q^{37} + 16 q^{38} - 168 q^{41} - 96 q^{42} - 48 q^{43} + 24 q^{45} - 232 q^{47} - 40 q^{50} + 32 q^{52} + 8 q^{53} - 272 q^{55} + 32 q^{56} - 136 q^{58} - 64 q^{61} + 152 q^{62} - 24 q^{63} + 416 q^{65} - 48 q^{66} - 32 q^{67} + 96 q^{68} + 88 q^{70} - 104 q^{71} + 240 q^{72} + 480 q^{73} - 216 q^{75} + 32 q^{76} + 280 q^{77} - 192 q^{78} + 32 q^{80} - 360 q^{81} - 168 q^{82} - 576 q^{83} - 208 q^{85} - 96 q^{86} + 24 q^{87} - 64 q^{88} + 144 q^{91} + 96 q^{93} + 168 q^{95} + 24 q^{97} + 176 q^{98}+O(q^{100}) \) 40 * q + 40 * q^2 - 8 * q^5 - 8 * q^7 - 80 * q^8 - 16 * q^10 + 32 * q^11 + 16 * q^13 + 24 * q^15 - 160 * q^16 - 48 * q^17 + 120 * q^18 - 16 * q^20 - 96 * q^21 + 32 * q^22 + 32 * q^26 + 16 * q^28 + 24 * q^30 + 152 * q^31 - 160 * q^32 - 24 * q^33 + 48 * q^35 + 240 * q^36 + 216 * q^37 + 16 * q^38 - 168 * q^41 - 96 * q^42 - 48 * q^43 + 24 * q^45 - 232 * q^47 - 40 * q^50 + 32 * q^52 + 8 * q^53 - 272 * q^55 + 32 * q^56 - 136 * q^58 - 64 * q^61 + 152 * q^62 - 24 * q^63 + 416 * q^65 - 48 * q^66 - 32 * q^67 + 96 * q^68 + 88 * q^70 - 104 * q^71 + 240 * q^72 + 480 * q^73 - 216 * q^75 + 32 * q^76 + 280 * q^77 - 192 * q^78 + 32 * q^80 - 360 * q^81 - 168 * q^82 - 576 * q^83 - 208 * q^85 - 96 * q^86 + 24 * q^87 - 64 * q^88 + 144 * q^91 + 96 * q^93 + 168 * q^95 + 24 * q^97 + 176 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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