LMFDB - Embedded newform 690.3.k.a.277.6

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			277.6
Character	$\chi$	$=$	690.277
Dual form			690.3.k.a.553.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(2.62353 + 4.25642i) q^{5} -2.44949 q^{6} +(0.185981 + 0.185981i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})$	\(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(2.62353 + 4.25642i) q^{5} -2.44949 q^{6} +(0.185981 + 0.185981i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(-1.63289 + 6.87995i) q^{10} +17.6358 q^{11} +(-2.44949 - 2.44949i) q^{12} +(16.7901 - 16.7901i) q^{13} +0.371963i q^{14} +(-8.42618 - 1.99988i) q^{15} -4.00000 q^{16} +(19.8067 + 19.8067i) q^{17} +(3.00000 - 3.00000i) q^{18} +16.2208i q^{19} +(-8.51284 + 5.24705i) q^{20} -0.455559 q^{21} +(17.6358 + 17.6358i) q^{22} +(3.39116 - 3.39116i) q^{23} -4.89898i q^{24} +(-11.2342 + 22.3337i) q^{25} +33.5803 q^{26} +(3.67423 + 3.67423i) q^{27} +(-0.371963 + 0.371963i) q^{28} -5.94151i q^{29} +(-6.42630 - 10.4261i) q^{30} -4.19616 q^{31} +(-4.00000 - 4.00000i) q^{32} +(-21.5994 + 21.5994i) q^{33} +39.6134i q^{34} +(-0.303688 + 1.27954i) q^{35} +6.00000 q^{36} +(-45.9154 - 45.9154i) q^{37} +(-16.2208 + 16.2208i) q^{38} +41.1273i q^{39} +(-13.7599 - 3.26579i) q^{40} -37.8568 q^{41} +(-0.455559 - 0.455559i) q^{42} +(-24.5503 + 24.5503i) q^{43} +35.2717i q^{44} +(12.7693 - 7.87058i) q^{45} +6.78233 q^{46} +(30.1312 + 30.1312i) q^{47} +(4.89898 - 4.89898i) q^{48} -48.9308i q^{49} +(-33.5679 + 11.0994i) q^{50} -48.5163 q^{51} +(33.5803 + 33.5803i) q^{52} +(-54.4809 + 54.4809i) q^{53} +7.34847i q^{54} +(46.2681 + 75.0656i) q^{55} -0.743925 q^{56} +(-19.8664 - 19.8664i) q^{57} +(5.94151 - 5.94151i) q^{58} -87.7441i q^{59} +(3.99976 - 16.8524i) q^{60} +20.2409 q^{61} +(-4.19616 - 4.19616i) q^{62} +(0.557944 - 0.557944i) q^{63} -8.00000i q^{64} +(115.515 + 27.4165i) q^{65} -43.1988 q^{66} +(5.03763 + 5.03763i) q^{67} +(-39.6134 + 39.6134i) q^{68} +8.30662i q^{69} +(-1.58323 + 0.975853i) q^{70} +42.6028 q^{71} +(6.00000 + 6.00000i) q^{72} +(25.5335 - 25.5335i) q^{73} -91.8308i q^{74} +(-13.5940 - 41.1121i) q^{75} -32.4416 q^{76} +(3.27994 + 3.27994i) q^{77} +(-41.1273 + 41.1273i) q^{78} +85.8118i q^{79} +(-10.4941 - 17.0257i) q^{80} -9.00000 q^{81} +(-37.8568 - 37.8568i) q^{82} +(-49.0744 + 49.0744i) q^{83} -0.911118i q^{84} +(-32.3423 + 136.269i) q^{85} -49.1006 q^{86} +(7.27683 + 7.27683i) q^{87} +(-35.2717 + 35.2717i) q^{88} -64.8558i q^{89} +(20.6398 + 4.89868i) q^{90} +6.24530 q^{91} +(6.78233 + 6.78233i) q^{92} +(5.13922 - 5.13922i) q^{93} +60.2624i q^{94} +(-69.0426 + 42.5557i) q^{95} +9.79796 q^{96} +(-63.8100 - 63.8100i) q^{97} +(48.9308 - 48.9308i) q^{98} -52.9075i 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
$5$	2.62353	+	4.25642i	0.524705	+	0.851284i
$5$	2.62353	+	4.25642i	0.524705	+	0.851284i
$6$	−2.44949			−0.408248
$7$	0.185981	+	0.185981i	0.0265688	+	0.0265688i	0.720266	−	0.693698i	$-0.244020\pi$
$7$	0.185981	+	0.185981i	0.0265688	+	0.0265688i	−0.693698	+	0.720266i	$0.744020\pi$
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$		−	3.00000i		−	0.333333i
$10$	−1.63289	+	6.87995i	−0.163289	+	0.687995i
$11$	17.6358			1.60326			0.801629	−	0.597821i	$-0.203967\pi$
$11$	17.6358			1.60326			0.801629	+	0.597821i	$0.203967\pi$
$12$	−2.44949	−	2.44949i	−0.204124	−	0.204124i
$13$	16.7901	−	16.7901i	1.29155	−	1.29155i	0.357719	−	0.933829i	$-0.383554\pi$
$13$	16.7901	−	16.7901i	1.29155	−	1.29155i	0.933829	−	0.357719i	$-0.116446\pi$
$14$			0.371963i			0.0265688i
$15$	−8.42618	−	1.99988i	−0.561745	−	0.133325i
$16$	−4.00000			−0.250000
$17$	19.8067	+	19.8067i	1.16510	+	1.16510i	0.983343	+	0.181758i	$0.0581786\pi$
$17$	19.8067	+	19.8067i	1.16510	+	1.16510i	0.181758	+	0.983343i	$0.441821\pi$
$18$	3.00000	−	3.00000i	0.166667	−	0.166667i
$19$			16.2208i			0.853727i	0.904316	+	0.426863i	$0.140382\pi$
$19$			16.2208i			0.853727i	−0.904316	+	0.426863i	$0.859618\pi$
$20$	−8.51284	+	5.24705i	−0.425642	+	0.262353i
$21$	−0.455559			−0.0216933
$22$	17.6358	+	17.6358i	0.801629	+	0.801629i
$23$	3.39116	−	3.39116i	0.147442	−	0.147442i
$23$	3.39116	−	3.39116i	0.147442	−	0.147442i
$24$		−	4.89898i		−	0.204124i
$25$	−11.2342	+	22.3337i	−0.449369	+	0.893346i
$26$	33.5803			1.29155
$27$	3.67423	+	3.67423i	0.136083	+	0.136083i
$28$	−0.371963	+	0.371963i	−0.0132844	+	0.0132844i
$29$		−	5.94151i		−	0.204880i	−0.994739	−	0.102440i	$-0.967335\pi$
$29$		−	5.94151i		−	0.204880i	0.994739	−	0.102440i	$-0.0326649\pi$
$30$	−6.42630	−	10.4261i	−0.214210	−	0.347535i
$31$	−4.19616			−0.135360			−0.0676799	−	0.997707i	$-0.521560\pi$
$31$	−4.19616			−0.135360			−0.0676799	+	0.997707i	$0.521560\pi$
$32$	−4.00000	−	4.00000i	−0.125000	−	0.125000i
$33$	−21.5994	+	21.5994i	−0.654528	+	0.654528i
$34$			39.6134i			1.16510i
$35$	−0.303688	+	1.27954i	−0.00867680	+	0.0365583i
$36$	6.00000			0.166667
$37$	−45.9154	−	45.9154i	−1.24096	−	1.24096i	−0.959604	−	0.281353i	$-0.909217\pi$
$37$	−45.9154	−	45.9154i	−1.24096	−	1.24096i	−0.281353	−	0.959604i	$-0.590783\pi$
$38$	−16.2208	+	16.2208i	−0.426863	+	0.426863i
$39$			41.1273i			1.05454i
$40$	−13.7599	−	3.26579i	−0.343997	−	0.0816447i
$41$	−37.8568			−0.923336			−0.461668	−	0.887053i	$-0.652749\pi$
$41$	−37.8568			−0.923336			−0.461668	+	0.887053i	$0.652749\pi$
$42$	−0.455559	−	0.455559i	−0.0108466	−	0.0108466i
$43$	−24.5503	+	24.5503i	−0.570937	+	0.570937i	−0.932390	−	0.361453i	$-0.882281\pi$
$43$	−24.5503	+	24.5503i	−0.570937	+	0.570937i	0.361453	+	0.932390i	$0.382281\pi$
$44$			35.2717i			0.801629i
$45$	12.7693	−	7.87058i	0.283761	−	0.174902i
$46$	6.78233			0.147442
$47$	30.1312	+	30.1312i	0.641089	+	0.641089i	0.950823	−	0.309734i	$-0.100240\pi$
$47$	30.1312	+	30.1312i	0.641089	+	0.641089i	−0.309734	+	0.950823i	$0.600240\pi$
$48$	4.89898	−	4.89898i	0.102062	−	0.102062i
$49$		−	48.9308i		−	0.998588i
$50$	−33.5679	+	11.0994i	−0.671358	+	0.221989i
$51$	−48.5163			−0.951301
$52$	33.5803	+	33.5803i	0.645774	+	0.645774i
$53$	−54.4809	+	54.4809i	−1.02794	+	1.02794i	−0.0283437	+	0.999598i	$0.509023\pi$
$53$	−54.4809	+	54.4809i	−1.02794	+	1.02794i	−0.999598	+	0.0283437i	$0.990977\pi$
$54$			7.34847i			0.136083i
$55$	46.2681	+	75.0656i	0.841238	+	1.36483i
$56$	−0.743925			−0.0132844
$57$	−19.8664	−	19.8664i	−0.348533	−	0.348533i
$58$	5.94151	−	5.94151i	0.102440	−	0.102440i
$59$		−	87.7441i		−	1.48719i	−0.668631	−	0.743594i	$-0.733119\pi$
$59$		−	87.7441i		−	1.48719i	0.668631	−	0.743594i	$-0.266881\pi$
$60$	3.99976	−	16.8524i	0.0666627	−	0.280873i
$61$	20.2409			0.331818			0.165909	−	0.986141i	$-0.446944\pi$
$61$	20.2409			0.331818			0.165909	+	0.986141i	$0.446944\pi$
$62$	−4.19616	−	4.19616i	−0.0676799	−	0.0676799i
$63$	0.557944	−	0.557944i	0.00885625	−	0.00885625i
$64$		−	8.00000i		−	0.125000i
$65$	115.515	+	27.4165i	1.77716	+	0.421793i
$66$	−43.1988			−0.654528
$67$	5.03763	+	5.03763i	0.0751885	+	0.0751885i	0.743701	−	0.668512i	$-0.233069\pi$
$67$	5.03763	+	5.03763i	0.0751885	+	0.0751885i	−0.668512	+	0.743701i	$0.733069\pi$
$68$	−39.6134	+	39.6134i	−0.582550	+	0.582550i
$69$			8.30662i			0.120386i
$70$	−1.58323	+	0.975853i	−0.0226176	+	0.0139408i
$71$	42.6028			0.600039			0.300020	−	0.953933i	$-0.403007\pi$
$71$	42.6028			0.600039			0.300020	+	0.953933i	$0.403007\pi$
$72$	6.00000	+	6.00000i	0.0833333	+	0.0833333i
$73$	25.5335	−	25.5335i	0.349773	−	0.349773i	−0.510252	−	0.860025i	$-0.670448\pi$
$73$	25.5335	−	25.5335i	0.349773	−	0.349773i	0.860025	+	0.510252i	$0.170448\pi$
$74$		−	91.8308i		−	1.24096i
$75$	−13.5940	−	41.1121i	−0.181253	−	0.548161i
$76$	−32.4416			−0.426863
$77$	3.27994	+	3.27994i	0.0425966	+	0.0425966i
$78$	−41.1273	+	41.1273i	−0.527272	+	0.527272i
$79$			85.8118i			1.08623i	0.839660	+	0.543113i	$0.182754\pi$
$79$			85.8118i			1.08623i	−0.839660	+	0.543113i	$0.817246\pi$
$80$	−10.4941	−	17.0257i	−0.131176	−	0.212821i
$81$	−9.00000			−0.111111
$82$	−37.8568	−	37.8568i	−0.461668	−	0.461668i
$83$	−49.0744	+	49.0744i	−0.591258	+	0.591258i	−0.937971	−	0.346713i	$-0.887298\pi$
$83$	−49.0744	+	49.0744i	−0.591258	+	0.591258i	0.346713	+	0.937971i	$0.387298\pi$
$84$		−	0.911118i		−	0.0108466i
$85$	−32.3423	+	136.269i	−0.380497	+	1.60317i
$86$	−49.1006			−0.570937
$87$	7.27683	+	7.27683i	0.0836418	+	0.0836418i
$88$	−35.2717	+	35.2717i	−0.400815	+	0.400815i
$89$		−	64.8558i		−	0.728717i	−0.931259	−	0.364358i	$-0.881288\pi$
$89$		−	64.8558i		−	0.728717i	0.931259	−	0.364358i	$-0.118712\pi$
$90$	20.6398	+	4.89868i	0.229332	+	0.0544298i
$91$	6.24530			0.0686297
$92$	6.78233	+	6.78233i	0.0737210	+	0.0737210i
$93$	5.13922	−	5.13922i	0.0552604	−	0.0552604i
$94$			60.2624i			0.641089i
$95$	−69.0426	+	42.5557i	−0.726764	+	0.447955i
$96$	9.79796			0.102062
$97$	−63.8100	−	63.8100i	−0.657835	−	0.657835i	0.297032	−	0.954868i	$-0.404003\pi$
$97$	−63.8100	−	63.8100i	−0.657835	−	0.657835i	−0.954868	+	0.297032i	$0.904003\pi$
$98$	48.9308	−	48.9308i	0.499294	−	0.499294i
$99$		−	52.9075i		−	0.534420i
$100$	−44.6673	−	22.4685i	−0.446673	−	0.224685i
$101$	193.561			1.91645			0.958224	−	0.286017i	$-0.0923315\pi$
$101$	193.561			1.91645			0.958224	+	0.286017i	$0.0923315\pi$
$102$	−48.5163	−	48.5163i	−0.475650	−	0.475650i
$103$	−40.0309	+	40.0309i	−0.388650	+	0.388650i	−0.874206	−	0.485556i	$-0.838617\pi$
$103$	−40.0309	+	40.0309i	−0.388650	+	0.388650i	0.485556	+	0.874206i	$0.338617\pi$
$104$			67.1605i			0.645774i
$105$	−1.19517	−	1.93905i	−0.0113826	−	0.0184672i
$106$	−108.962			−1.02794
$107$	−10.8053	−	10.8053i	−0.100984	−	0.100984i	0.654810	−	0.755794i	$-0.272749\pi$
$107$	−10.8053	−	10.8053i	−0.100984	−	0.100984i	−0.755794	+	0.654810i	$0.772749\pi$
$108$	−7.34847	+	7.34847i	−0.0680414	+	0.0680414i
$109$			159.431i			1.46267i	0.682019	+	0.731334i	$0.261102\pi$
$109$			159.431i			1.46267i	−0.682019	+	0.731334i	$0.738898\pi$
$110$	−28.7975	+	121.334i	−0.261795	+	1.10303i
$111$	112.469			1.01324
$112$	−0.743925	−	0.743925i	−0.00664219	−	0.00664219i
$113$	−18.9925	+	18.9925i	−0.168075	+	0.168075i	−0.786133	−	0.618058i	$-0.787920\pi$
$113$	−18.9925	+	18.9925i	−0.168075	+	0.168075i	0.618058	+	0.786133i	$0.287920\pi$
$114$		−	39.7327i		−	0.348533i
$115$	23.3310	+	5.53742i	0.202879	+	0.0481514i
$116$	11.8830			0.102440
$117$	−50.3704	−	50.3704i	−0.430516	−	0.430516i
$118$	87.7441	−	87.7441i	0.743594	−	0.743594i
$119$			7.36736i			0.0619106i
$120$	20.8521	−	12.8526i	0.173768	−	0.107105i
$121$	190.023			1.57044
$122$	20.2409	+	20.2409i	0.165909	+	0.165909i
$123$	46.3649	−	46.3649i	0.376950	−	0.376950i
$124$		−	8.39231i		−	0.0676799i
$125$	−124.535	+	10.7753i	−0.996278	+	0.0862025i
$126$	1.11589			0.00885625
$127$	60.8528	+	60.8528i	0.479156	+	0.479156i	0.904862	−	0.425706i	$-0.139974\pi$
$127$	60.8528	+	60.8528i	0.479156	+	0.479156i	−0.425706	+	0.904862i	$0.639974\pi$
$128$	8.00000	−	8.00000i	0.0625000	−	0.0625000i
$129$		−	60.1357i		−	0.466168i
$130$	88.0987	+	142.932i	0.677682	+	1.09947i
$131$	−51.5356			−0.393401			−0.196701	−	0.980464i	$-0.563023\pi$
$131$	−51.5356			−0.393401			−0.196701	+	0.980464i	$0.563023\pi$
$132$	−43.1988	−	43.1988i	−0.327264	−	0.327264i
$133$	−3.01677	+	3.01677i	−0.0226825	+	0.0226825i
$134$			10.0753i			0.0751885i
$135$	−5.99964	+	25.2785i	−0.0444418	+	0.187248i
$136$	−79.2269			−0.582550
$137$	−140.637	−	140.637i	−1.02655	−	1.02655i	−0.999638	−	0.0269071i	$-0.991434\pi$
$137$	−140.637	−	140.637i	−1.02655	−	1.02655i	−0.0269071	−	0.999638i	$-0.508566\pi$
$138$	−8.30662	+	8.30662i	−0.0601929	+	0.0601929i
$139$		−	96.0813i		−	0.691232i	−0.938376	−	0.345616i	$-0.887670\pi$
$139$		−	96.0813i		−	0.691232i	0.938376	−	0.345616i	$-0.112330\pi$
$140$	−2.55908	−	0.607376i	−0.0182792	−	0.00433840i
$141$	−73.8061			−0.523447
$142$	42.6028	+	42.6028i	0.300020	+	0.300020i
$143$	296.108	−	296.108i	2.07069	−	2.07069i
$144$			12.0000i			0.0833333i
$145$	25.2896	−	15.5877i	0.174411	−	0.107501i
$146$	51.0669			0.349773
$147$	59.9278	+	59.9278i	0.407672	+	0.407672i
$148$	91.8308	−	91.8308i	0.620479	−	0.620479i
$149$			34.1953i			0.229499i	0.993394	+	0.114749i	$0.0366065\pi$
$149$			34.1953i			0.229499i	−0.993394	+	0.114749i	$0.963394\pi$
$150$	27.5181	−	54.7061i	0.183454	−	0.364707i
$151$	182.642			1.20955			0.604776	−	0.796395i	$-0.293263\pi$
$151$	182.642			1.20955			0.604776	+	0.796395i	$0.293263\pi$
$152$	−32.4416	−	32.4416i	−0.213432	−	0.213432i
$153$	59.4201	−	59.4201i	0.388367	−	0.388367i
$154$			6.55987i			0.0425966i
$155$	−11.0087	−	17.8606i	−0.0710240	−	0.115230i
$156$	−82.2545			−0.527272
$157$	−67.8885	−	67.8885i	−0.432411	−	0.432411i	0.457037	−	0.889448i	$-0.348911\pi$
$157$	−67.8885	−	67.8885i	−0.432411	−	0.432411i	−0.889448	+	0.457037i	$0.848911\pi$
$158$	−85.8118	+	85.8118i	−0.543113	+	0.543113i
$159$		−	133.450i		−	0.839311i
$160$	6.53158	−	27.5198i	0.0408224	−	0.171999i
$161$	1.26139			0.00783470
$162$	−9.00000	−	9.00000i	−0.0555556	−	0.0555556i
$163$	−109.843	+	109.843i	−0.673883	+	0.673883i	−0.958609	−	0.284726i	$-0.908098\pi$
$163$	−109.843	+	109.843i	−0.673883	+	0.673883i	0.284726	+	0.958609i	$0.408098\pi$
$164$		−	75.7135i		−	0.461668i
$165$	−148.603	−	35.2696i	−0.900623	−	0.213755i
$166$	−98.1488			−0.591258
$167$	22.5337	+	22.5337i	0.134932	+	0.134932i	0.771347	−	0.636415i	$-0.219583\pi$
$167$	22.5337	+	22.5337i	0.134932	+	0.134932i	−0.636415	+	0.771347i	$0.719583\pi$
$168$	0.911118	−	0.911118i	0.00542332	−	0.00542332i
$169$		−	394.817i		−	2.33620i
$170$	−168.611	+	103.927i	−0.991832	+	0.611334i
$171$	48.6624			0.284576
$172$	−49.1006	−	49.1006i	−0.285469	−	0.285469i
$173$	−9.88896	+	9.88896i	−0.0571616	+	0.0571616i	−0.735110	−	0.677948i	$-0.762869\pi$
$173$	−9.88896	+	9.88896i	−0.0571616	+	0.0571616i	0.677948	+	0.735110i	$0.262869\pi$
$174$			14.5537i			0.0836418i
$175$	−6.24300	+	2.06429i	−0.0356743	+	0.0117959i
$176$	−70.5434			−0.400815
$177$	107.464	+	107.464i	0.607142	+	0.607142i
$178$	64.8558	−	64.8558i	0.364358	−	0.364358i
$179$		−	285.992i		−	1.59772i	−0.601517	−	0.798860i	$-0.705437\pi$
$179$		−	285.992i		−	1.59772i	0.601517	−	0.798860i	$-0.294563\pi$
$180$	15.7412	+	25.5385i	0.0874508	+	0.141881i
$181$	−133.675			−0.738539			−0.369269	−	0.929322i	$-0.620392\pi$
$181$	−133.675			−0.738539			−0.369269	+	0.929322i	$0.620392\pi$
$182$	6.24530	+	6.24530i	0.0343148	+	0.0343148i
$183$	−24.7900	+	24.7900i	−0.135464	+	0.135464i
$184$			13.5647i			0.0737210i
$185$	74.9751	−	315.896i	0.405271	−	1.70754i
$186$	10.2784			0.0552604
$187$	349.308	+	349.308i	1.86796	+	1.86796i
$188$	−60.2624	+	60.2624i	−0.320545	+	0.320545i
$189$			1.36668i			0.00723110i
$190$	−111.598	−	26.4869i	−0.587360	−	0.139405i
$191$	106.774			0.559028			0.279514	−	0.960142i	$-0.409827\pi$
$191$	106.774			0.559028			0.279514	+	0.960142i	$0.409827\pi$
$192$	9.79796	+	9.79796i	0.0510310	+	0.0510310i
$193$	33.3322	−	33.3322i	0.172706	−	0.172706i	−0.615461	−	0.788167i	$-0.711030\pi$
$193$	33.3322	−	33.3322i	0.172706	−	0.172706i	0.788167	+	0.615461i	$0.211030\pi$
$194$		−	127.620i		−	0.657835i
$195$	−175.055	+	107.898i	−0.897717	+	0.553325i
$196$	97.8616			0.499294
$197$	−178.442	−	178.442i	−0.905798	−	0.905798i	0.0901317	−	0.995930i	$-0.471271\pi$
$197$	−178.442	−	178.442i	−0.905798	−	0.905798i	−0.995930	+	0.0901317i	$0.971271\pi$
$198$	52.9075	−	52.9075i	0.267210	−	0.267210i
$199$			91.0351i			0.457463i	0.973490	+	0.228731i	$0.0734578\pi$
$199$			91.0351i			0.457463i	−0.973490	+	0.228731i	$0.926542\pi$
$200$	−22.1989	−	67.1358i	−0.110994	−	0.335679i
$201$	−12.3396			−0.0613912
$202$	193.561	+	193.561i	0.958224	+	0.958224i
$203$	1.10501	−	1.10501i	0.00544340	−	0.00544340i
$204$		−	97.0327i		−	0.475650i
$205$	−99.3182	−	161.134i	−0.484479	−	0.786021i
$206$	−80.0619			−0.388650
$207$	−10.1735	−	10.1735i	−0.0491473	−	0.0491473i
$208$	−67.1605	+	67.1605i	−0.322887	+	0.322887i
$209$			286.068i			1.36875i
$210$	0.743880	−	3.13422i	0.00354229	−	0.0149249i
$211$	384.346			1.82154			0.910772	−	0.412909i	$-0.135487\pi$
$211$	384.346			1.82154			0.910772	+	0.412909i	$0.135487\pi$
$212$	−108.962	−	108.962i	−0.513971	−	0.513971i
$213$	−52.1775	+	52.1775i	−0.244965	+	0.244965i
$214$		−	21.6106i		−	0.100984i
$215$	−168.905	−	40.0881i	−0.785603	−	0.186456i
$216$	−14.6969			−0.0680414
$217$	−0.780406	−	0.780406i	−0.00359634	−	0.00359634i
$218$	−159.431	+	159.431i	−0.731334	+	0.731334i
$219$			62.5439i			0.285589i
$220$	−150.131	+	92.5362i	−0.682414	+	0.420619i
$221$	665.115			3.00957
$222$	112.469	+	112.469i	0.506619	+	0.506619i
$223$	−260.988	+	260.988i	−1.17035	+	1.17035i	−0.188223	+	0.982126i	$0.560273\pi$
$223$	−260.988	+	260.988i	−1.17035	+	1.17035i	−0.982126	+	0.188223i	$0.939727\pi$
$224$		−	1.48785i		−	0.00664219i
$225$	67.0010	+	33.7027i	0.297782	+	0.149790i
$226$	−37.9849			−0.168075
$227$	58.0060	+	58.0060i	0.255533	+	0.255533i	0.823234	−	0.567701i	$-0.192167\pi$
$227$	58.0060	+	58.0060i	0.255533	+	0.255533i	−0.567701	+	0.823234i	$0.692167\pi$
$228$	39.7327	−	39.7327i	0.174266	−	0.174266i
$229$		−	55.6940i		−	0.243205i	−0.992579	−	0.121603i	$-0.961197\pi$
$229$		−	55.6940i		−	0.243205i	0.992579	−	0.121603i	$-0.0388033\pi$
$230$	17.7936	+	28.8684i	0.0773635	+	0.125515i
$231$	−8.03417			−0.0347800
$232$	11.8830	+	11.8830i	0.0512199	+	0.0512199i
$233$	156.415	−	156.415i	0.671310	−	0.671310i	−0.286708	−	0.958018i	$-0.592561\pi$
$233$	156.415	−	156.415i	0.671310	−	0.671310i	0.958018	+	0.286708i	$0.0925609\pi$
$234$		−	100.741i		−	0.430516i
$235$	−49.2011	+	207.301i	−0.209366	+	0.882132i
$236$	175.488			0.743594
$237$	−105.098	−	105.098i	−0.443450	−	0.443450i
$238$	−7.36736	+	7.36736i	−0.0309553	+	0.0309553i
$239$		−	299.721i		−	1.25406i	−0.778995	−	0.627031i	$-0.784270\pi$
$239$		−	299.721i		−	1.25406i	0.778995	−	0.627031i	$-0.215730\pi$
$240$	33.7047	+	7.99952i	0.140436	+	0.0333313i
$241$	317.414			1.31707			0.658536	−	0.752549i	$-0.271176\pi$
$241$	317.414			1.31707			0.658536	+	0.752549i	$0.271176\pi$
$242$	190.023	+	190.023i	0.785219	+	0.785219i
$243$	11.0227	−	11.0227i	0.0453609	−	0.0453609i
$244$			40.4819i			0.165909i
$245$	208.270	−	128.371i	0.850082	−	0.523964i
$246$	92.7298			0.376950
$247$	272.350	+	272.350i	1.10263	+	1.10263i
$248$	8.39231	−	8.39231i	0.0338400	−	0.0338400i
$249$		−	120.207i		−	0.482760i
$250$	−135.310	−	113.759i	−0.541240	−	0.455038i
$251$	178.565			0.711416			0.355708	−	0.934597i	$-0.384240\pi$
$251$	178.565			0.711416			0.355708	+	0.934597i	$0.384240\pi$
$252$	1.11589	+	1.11589i	0.00442813	+	0.00442813i
$253$	59.8061	−	59.8061i	0.236388	−	0.236388i
$254$			121.706i			0.479156i
$255$	−127.284	−	206.506i	−0.499152	−	0.809827i
$256$	16.0000			0.0625000
$257$	−329.851	−	329.851i	−1.28347	−	1.28347i	−0.938682	−	0.344784i	$-0.887952\pi$
$257$	−329.851	−	329.851i	−1.28347	−	1.28347i	−0.344784	−	0.938682i	$-0.612048\pi$
$258$	60.1357	−	60.1357i	0.233084	−	0.233084i
$259$		−	17.0788i		−	0.0659414i
$260$	−54.8330	+	231.030i	−0.210896	+	0.888578i
$261$	−17.8245			−0.0682932
$262$	−51.5356	−	51.5356i	−0.196701	−	0.196701i
$263$	25.7719	−	25.7719i	0.0979919	−	0.0979919i	−0.656411	−	0.754403i	$-0.727926\pi$
$263$	25.7719	−	25.7719i	0.0979919	−	0.0979919i	0.754403	+	0.656411i	$0.227926\pi$
$264$		−	86.3976i		−	0.327264i
$265$	−374.826	−	88.9616i	−1.41444	−	0.335704i
$266$	−6.03353			−0.0226825
$267$	79.4318	+	79.4318i	0.297497	+	0.297497i
$268$	−10.0753	+	10.0753i	−0.0375943	+	0.0375943i
$269$		−	349.179i		−	1.29806i	−0.760761	−	0.649032i	$-0.775174\pi$
$269$		−	349.179i		−	1.29806i	0.760761	−	0.649032i	$-0.224826\pi$
$270$	−31.2782	+	19.2789i	−0.115845	+	0.0714033i
$271$	−479.592			−1.76971			−0.884856	−	0.465866i	$-0.845743\pi$
$271$	−479.592			−1.76971			−0.884856	+	0.465866i	$0.845743\pi$
$272$	−79.2269	−	79.2269i	−0.291275	−	0.291275i
$273$	−7.64890	+	7.64890i	−0.0280179	+	0.0280179i
$274$		−	281.273i		−	1.02655i
$275$	−198.125	+	393.873i	−0.720455	+	1.43227i
$276$	−16.6132			−0.0601929
$277$	31.3729	+	31.3729i	0.113260	+	0.113260i	0.761465	−	0.648206i	$-0.224480\pi$
$277$	31.3729	+	31.3729i	0.113260	+	0.113260i	−0.648206	+	0.761465i	$0.724480\pi$
$278$	96.0813	−	96.0813i	0.345616	−	0.345616i
$279$			12.5885i			0.0451199i
$280$	−1.95171	−	3.16646i	−0.00697038	−	0.0113088i
$281$	−398.612			−1.41855			−0.709275	−	0.704932i	$-0.750977\pi$
$281$	−398.612			−1.41855			−0.709275	+	0.704932i	$0.750977\pi$
$282$	−73.8061	−	73.8061i	−0.261724	−	0.261724i
$283$	−155.860	+	155.860i	−0.550741	+	0.550741i	−0.926655	−	0.375913i	$-0.877329\pi$
$283$	−155.860	+	155.860i	−0.550741	+	0.550741i	0.375913	+	0.926655i	$0.377329\pi$
$284$			85.2056i			0.300020i
$285$	32.4397	−	136.679i	0.113823	−	0.479577i
$286$	592.216			2.07069
$287$	−7.04065	−	7.04065i	−0.0245319	−	0.0245319i
$288$	−12.0000	+	12.0000i	−0.0416667	+	0.0416667i
$289$			495.612i			1.71492i
$290$	40.8773	+	9.70186i	0.140956	+	0.0334547i
$291$	156.302			0.537120
$292$	51.0669	+	51.0669i	0.174887	+	0.174887i
$293$	−102.859	+	102.859i	−0.351054	+	0.351054i	−0.860502	−	0.509448i	$-0.829850\pi$
$293$	−102.859	+	102.859i	−0.351054	+	0.351054i	0.509448	+	0.860502i	$0.329850\pi$
$294$			119.856i			0.407672i
$295$	373.476	−	230.199i	1.26602	−	0.780335i
$296$	183.662			0.620479
$297$	64.7982	+	64.7982i	0.218176	+	0.218176i
$298$	−34.1953	+	34.1953i	−0.114749	+	0.114749i
$299$		−	113.876i		−	0.380857i
$300$	82.2242	−	27.1879i	0.274081	−	0.0906264i
$301$	−9.13179			−0.0303382
$302$	182.642	+	182.642i	0.604776	+	0.604776i
$303$	−237.063	+	237.063i	−0.782387	+	0.782387i
$304$		−	64.8833i		−	0.213432i
$305$	53.1026	+	86.1539i	0.174107	+	0.282472i
$306$	118.840			0.388367
$307$	165.629	+	165.629i	0.539508	+	0.539508i	0.923385	−	0.383876i	$-0.125411\pi$
$307$	165.629	+	165.629i	0.539508	+	0.539508i	−0.383876	+	0.923385i	$0.625411\pi$
$308$	−6.55987	+	6.55987i	−0.0212983	+	0.0212983i
$309$		−	98.0554i		−	0.317331i
$310$	6.85188	−	28.8693i	0.0221028	−	0.0931268i
$311$	−176.951			−0.568974			−0.284487	−	0.958680i	$-0.591823\pi$
$311$	−176.951			−0.568974			−0.284487	+	0.958680i	$0.591823\pi$
$312$	−82.2545	−	82.2545i	−0.263636	−	0.263636i
$313$	11.6544	−	11.6544i	0.0372345	−	0.0372345i	−0.688244	−	0.725479i	$-0.741618\pi$
$313$	11.6544	−	11.6544i	0.0372345	−	0.0372345i	0.725479	+	0.688244i	$0.241618\pi$
$314$		−	135.777i		−	0.432411i
$315$	3.83862	+	0.911064i	0.0121861	+	0.00289227i
$316$	−171.624			−0.543113
$317$	−225.841	−	225.841i	−0.712431	−	0.712431i	0.254612	−	0.967043i	$-0.418052\pi$
$317$	−225.841	−	225.841i	−0.712431	−	0.712431i	−0.967043	+	0.254612i	$0.918052\pi$
$318$	133.450	−	133.450i	0.419656	−	0.419656i
$319$		−	104.784i		−	0.328475i
$320$	34.0514	−	20.9882i	0.106411	−	0.0655881i
$321$	26.4675			0.0824533
$322$	1.26139	+	1.26139i	0.00391735	+	0.00391735i
$323$	−321.281	+	321.281i	−0.994678	+	0.994678i
$324$		−	18.0000i		−	0.0555556i
$325$	186.361	+	563.609i	0.573418	+	1.73418i
$326$	−219.686			−0.673883
$327$	−195.262	−	195.262i	−0.597132	−	0.597132i
$328$	75.7135	−	75.7135i	0.230834	−	0.230834i
$329$			11.2077i			0.0340659i
$330$	−113.333	−	183.872i	−0.343434	−	0.557189i
$331$	−217.937			−0.658421			−0.329211	−	0.944257i	$-0.606783\pi$
$331$	−217.937			−0.658421			−0.329211	+	0.944257i	$0.606783\pi$
$332$	−98.1488	−	98.1488i	−0.295629	−	0.295629i
$333$	−137.746	+	137.746i	−0.413652	+	0.413652i
$334$			45.0674i			0.134932i
$335$	−8.22592	+	34.6586i	−0.0245550	+	0.103459i
$336$	1.82224			0.00542332
$337$	253.634	+	253.634i	0.752622	+	0.752622i	0.974968	−	0.222346i	$-0.0713715\pi$
$337$	253.634	+	253.634i	0.752622	+	0.752622i	−0.222346	+	0.974968i	$0.571371\pi$
$338$	394.817	−	394.817i	1.16810	−	1.16810i
$339$		−	46.5219i		−	0.137233i
$340$	−272.538	−	64.6846i	−0.801583	−	0.190249i
$341$	−74.0027			−0.217017
$342$	48.6624	+	48.6624i	0.142288	+	0.142288i
$343$	18.2133	−	18.2133i	0.0531000	−	0.0531000i
$344$		−	98.2012i		−	0.285469i
$345$	−35.3565	+	21.7926i	−0.102483	+	0.0631671i
$346$	−19.7779			−0.0571616
$347$	−52.2309	−	52.2309i	−0.150521	−	0.150521i	0.627830	−	0.778351i	$-0.283943\pi$
$347$	−52.2309	−	52.2309i	−0.150521	−	0.150521i	−0.778351	+	0.627830i	$0.783943\pi$
$348$	−14.5537	+	14.5537i	−0.0418209	+	0.0418209i
$349$		−	413.853i		−	1.18583i	−0.805266	−	0.592913i	$-0.797978\pi$
$349$		−	413.853i		−	1.18583i	0.805266	−	0.592913i	$-0.202022\pi$
$350$	−8.30728	−	4.17871i	−0.0237351	−	0.0119392i
$351$	123.382			0.351515
$352$	−70.5434	−	70.5434i	−0.200407	−	0.200407i
$353$	−85.1537	+	85.1537i	−0.241229	+	0.241229i	−0.817358	−	0.576130i	$-0.804562\pi$
$353$	−85.1537	+	85.1537i	−0.241229	+	0.241229i	0.576130	+	0.817358i	$0.304562\pi$
$354$			214.928i			0.607142i
$355$	111.770	+	181.335i	0.314844	+	0.510804i
$356$	129.712			0.364358
$357$	−9.02313	−	9.02313i	−0.0252749	−	0.0252749i
$358$	285.992	−	285.992i	0.798860	−	0.798860i
$359$			574.569i			1.60047i	0.599686	+	0.800236i	$0.295292\pi$
$359$			574.569i			1.60047i	−0.599686	+	0.800236i	$0.704708\pi$
$360$	−9.79737	+	41.2797i	−0.0272149	+	0.114666i
$361$	97.8852			0.271150
$362$	−133.675	−	133.675i	−0.369269	−	0.369269i
$363$	−232.730	+	232.730i	−0.641129	+	0.641129i
$364$			12.4906i			0.0343148i
$365$	175.669	+	41.6934i	0.481284	+	0.114229i
$366$	−49.5799			−0.135464
$367$	−259.433	−	259.433i	−0.706902	−	0.706902i	0.258981	−	0.965882i	$-0.416613\pi$
$367$	−259.433	−	259.433i	−0.706902	−	0.706902i	−0.965882	+	0.258981i	$0.916613\pi$
$368$	−13.5647	+	13.5647i	−0.0368605	+	0.0368605i
$369$			113.570i			0.307779i
$370$	390.871	−	240.921i	1.05641	−	0.651137i
$371$	−20.2649			−0.0546223
$372$	10.2784	+	10.2784i	0.0276302	+	0.0276302i
$373$	80.1444	−	80.1444i	0.214864	−	0.214864i	−0.591466	−	0.806330i	$-0.701451\pi$
$373$	80.1444	−	80.1444i	0.214864	−	0.214864i	0.806330	+	0.591466i	$0.201451\pi$
$374$			698.616i			1.86796i
$375$	139.326	−	165.720i	0.371537	−	0.441921i
$376$	−120.525			−0.320545
$377$	−99.7587	−	99.7587i	−0.264612	−	0.264612i
$378$	−1.36668	+	1.36668i	−0.00361555	+	0.00361555i
$379$		−	715.430i		−	1.88768i	−0.330407	−	0.943838i	$-0.607186\pi$
$379$		−	715.430i		−	1.88768i	0.330407	−	0.943838i	$-0.392814\pi$
$380$	−85.1114	−	138.085i	−0.223977	−	0.363382i
$381$	−149.058			−0.391229
$382$	106.774	+	106.774i	0.279514	+	0.279514i
$383$	262.427	−	262.427i	0.685187	−	0.685187i	−0.275977	−	0.961164i	$-0.589001\pi$
$383$	262.427	−	262.427i	0.685187	−	0.685187i	0.961164	+	0.275977i	$0.0890015\pi$
$384$			19.5959i			0.0510310i
$385$	−5.35579	+	22.5658i	−0.0139111	+	0.0586124i
$386$	66.6643			0.172706
$387$	73.6509	+	73.6509i	0.190312	+	0.190312i
$388$	127.620	−	127.620i	0.328918	−	0.328918i
$389$		−	523.535i		−	1.34585i	−0.739712	−	0.672924i	$-0.765038\pi$
$389$		−	523.535i		−	1.34585i	0.739712	−	0.672924i	$-0.234962\pi$
$390$	−282.953	−	67.1565i	−0.725521	−	0.172196i
$391$	134.336			0.343570
$392$	97.8616	+	97.8616i	0.249647	+	0.249647i
$393$	63.1179	−	63.1179i	0.160605	−	0.160605i
$394$		−	356.884i		−	0.905798i
$395$	−365.251	+	225.129i	−0.924686	+	0.569948i
$396$	105.815			0.267210
$397$	271.071	+	271.071i	0.682799	+	0.682799i	0.960630	−	0.277831i	$-0.0896155\pi$
$397$	271.071	+	271.071i	0.682799	+	0.682799i	−0.277831	+	0.960630i	$0.589616\pi$
$398$	−91.0351	+	91.0351i	−0.228731	+	0.228731i
$399$		−	7.38954i		−	0.0185202i
$400$	44.9369	−	89.3346i	0.112342	−	0.223337i
$401$	275.406			0.686799			0.343399	−	0.939189i	$-0.388422\pi$
$401$	275.406			0.686799			0.343399	+	0.939189i	$0.388422\pi$
$402$	−12.3396	−	12.3396i	−0.0306956	−	0.0306956i
$403$	−70.4540	+	70.4540i	−0.174824	+	0.174824i
$404$			387.123i			0.958224i
$405$	−23.6117	−	38.3078i	−0.0583006	−	0.0945871i
$406$	2.21002			0.00544340
$407$	−809.757	−	809.757i	−1.98958	−	1.98958i
$408$	97.0327	−	97.0327i	0.237825	−	0.237825i
$409$		−	87.9556i		−	0.215050i	−0.994202	−	0.107525i	$-0.965707\pi$
$409$		−	87.9556i		−	0.215050i	0.994202	−	0.107525i	$-0.0342926\pi$
$410$	61.8161	−	260.453i	0.150771	−	0.635250i
$411$	344.488			0.838171
$412$	−80.0619	−	80.0619i	−0.194325	−	0.194325i
$413$	16.3188	−	16.3188i	0.0395127	−	0.0395127i
$414$		−	20.3470i		−	0.0491473i
$415$	−337.629	−	80.1333i	−0.813564	−	0.193092i
$416$	−134.321			−0.322887
$417$	117.675	+	117.675i	0.282194	+	0.282194i
$418$	−286.068	+	286.068i	−0.684373	+	0.684373i
$419$			549.190i			1.31072i	0.755319	+	0.655358i	$0.227482\pi$
$419$			549.190i			1.31072i	−0.755319	+	0.655358i	$0.772518\pi$
$420$	3.87810	−	2.39034i	0.00923358	−	0.00569129i
$421$	−579.831			−1.37727			−0.688636	−	0.725107i	$-0.741790\pi$
$421$	−579.831			−1.37727			−0.688636	+	0.725107i	$0.741790\pi$
$422$	384.346	+	384.346i	0.910772	+	0.910772i
$423$	90.3936	−	90.3936i	0.213696	−	0.213696i
$424$		−	217.924i		−	0.513971i
$425$	−664.870	+	219.843i	−1.56440	+	0.517278i
$426$	−104.355			−0.244965
$427$	3.76443	+	3.76443i	0.00881600	+	0.00881600i
$428$	21.6106	−	21.6106i	0.0504921	−	0.0504921i
$429$			725.314i			1.69071i
$430$	−128.817	−	208.993i	−0.299574	−	0.486030i
$431$	422.783			0.980935			0.490467	−	0.871460i	$-0.336826\pi$
$431$	422.783			0.980935			0.490467	+	0.871460i	$0.336826\pi$
$432$	−14.6969	−	14.6969i	−0.0340207	−	0.0340207i
$433$	356.992	−	356.992i	0.824462	−	0.824462i	−0.162282	−	0.986744i	$-0.551886\pi$
$433$	356.992	−	356.992i	0.824462	−	0.824462i	0.986744	+	0.162282i	$0.0518855\pi$
$434$		−	1.56081i		−	0.00359634i
$435$	−11.8823	+	50.0642i	−0.0273156	+	0.115090i
$436$	−318.862			−0.731334
$437$	55.0075	+	55.0075i	0.125875	+	0.125875i
$438$	−62.5439	+	62.5439i	−0.142794	+	0.142794i
$439$			95.4606i			0.217450i	0.994072	+	0.108725i	$0.0346768\pi$
$439$			95.4606i			0.217450i	−0.994072	+	0.108725i	$0.965323\pi$
$440$	−242.667	−	57.5950i	−0.551517	−	0.130898i
$441$	−146.792			−0.332863
$442$	665.115	+	665.115i	1.50478	+	1.50478i
$443$	−90.7273	+	90.7273i	−0.204802	+	0.204802i	−0.802054	−	0.597252i	$-0.796259\pi$
$443$	−90.7273	+	90.7273i	−0.204802	+	0.204802i	0.597252	+	0.802054i	$0.296259\pi$
$444$			224.939i			0.506619i
$445$	276.053	−	170.151i	0.620345	−	0.382361i
$446$	−521.976			−1.17035
$447$	−41.8805	−	41.8805i	−0.0936924	−	0.0936924i
$448$	1.48785	−	1.48785i	0.00332109	−	0.00332109i
$449$		−	685.452i		−	1.52662i	−0.646033	−	0.763310i	$-0.723573\pi$
$449$		−	685.452i		−	1.52662i	0.646033	−	0.763310i	$-0.276427\pi$
$450$	33.2983	+	100.704i	0.0739962	+	0.223786i
$451$	−667.636			−1.48035
$452$	−37.9849	−	37.9849i	−0.0840375	−	0.0840375i
$453$	−223.690	+	223.690i	−0.493798	+	0.493798i
$454$			116.012i			0.255533i
$455$	16.3847	+	26.5826i	0.0360103	+	0.0584233i
$456$	79.4654			0.174266
$457$	20.7695	+	20.7695i	0.0454474	+	0.0454474i	0.729465	−	0.684018i	$-0.239769\pi$
$457$	20.7695	+	20.7695i	0.0454474	+	0.0454474i	−0.684018	+	0.729465i	$0.739769\pi$
$458$	55.6940	−	55.6940i	0.121603	−	0.121603i
$459$			145.549i			0.317100i
$460$	−11.0748	+	46.6621i	−0.0240757	+	0.101439i
$461$	413.944			0.897926			0.448963	−	0.893550i	$-0.351794\pi$
$461$	413.944			0.897926			0.448963	+	0.893550i	$0.351794\pi$
$462$	−8.03417	−	8.03417i	−0.0173900	−	0.0173900i
$463$	−480.825	+	480.825i	−1.03850	+	1.03850i	−0.0392698	+	0.999229i	$0.512503\pi$
$463$	−480.825	+	480.825i	−1.03850	+	1.03850i	−0.999229	+	0.0392698i	$0.987497\pi$
$464$			23.7660i			0.0512199i
$465$	35.3576	+	8.39181i	0.0760377	+	0.0180469i
$466$	312.831			0.671310
$467$	470.023	+	470.023i	1.00647	+	1.00647i	0.999979	+	0.00649415i	$0.00206717\pi$
$467$	470.023	+	470.023i	1.00647	+	1.00647i	0.00649415	+	0.999979i	$0.497933\pi$
$468$	100.741	−	100.741i	0.215258	−	0.215258i
$469$			1.87381i			0.00399533i
$470$	−256.502	+	158.100i	−0.545749	+	0.336383i
$471$	166.292			0.353062
$472$	175.488	+	175.488i	0.371797	+	0.371797i
$473$	−432.965	+	432.965i	−0.915360	+	0.915360i
$474$		−	210.195i		−	0.443450i
$475$	−362.270	−	182.228i	−0.762674	−	0.383639i
$476$	−14.7347			−0.0309553
$477$	163.443	+	163.443i	0.342647	+	0.342647i
$478$	299.721	−	299.721i	0.627031	−	0.627031i
$479$		−	204.710i		−	0.427370i	−0.976903	−	0.213685i	$-0.931453\pi$
$479$		−	204.710i		−	0.427370i	0.976903	−	0.213685i	$-0.0685465\pi$
$480$	25.7052	+	41.7042i	0.0535525	+	0.0868838i
$481$	−1541.85			−3.20551
$482$	317.414	+	317.414i	0.658536	+	0.658536i
$483$	−1.54488	+	1.54488i	−0.00319850	+	0.00319850i
$484$			380.046i			0.785219i
$485$	104.195	−	439.010i	0.214835	−	0.905174i
$486$	22.0454			0.0453609
$487$	311.497	+	311.497i	0.639625	+	0.639625i	0.950463	−	0.310838i	$-0.100610\pi$
$487$	311.497	+	311.497i	0.639625	+	0.639625i	−0.310838	+	0.950463i	$0.600610\pi$
$488$	−40.4819	+	40.4819i	−0.0829546	+	0.0829546i
$489$		−	269.059i		−	0.550224i
$490$	336.641	+	79.8989i	0.687023	+	0.163059i
$491$	356.163			0.725383			0.362691	−	0.931909i	$-0.381858\pi$
$491$	356.163			0.725383			0.362691	+	0.931909i	$0.381858\pi$
$492$	92.7298	+	92.7298i	0.188475	+	0.188475i
$493$	117.682	−	117.682i	0.238706	−	0.238706i
$494$			544.699i			1.10263i
$495$	225.197	−	138.804i	0.454943	−	0.280413i
$496$	16.7846			0.0338400
$497$	7.92332	+	7.92332i	0.0159423	+	0.0159423i
$498$	120.207	−	120.207i	0.241380	−	0.241380i
$499$			150.466i			0.301535i	0.988569	+	0.150768i	$0.0481745\pi$
$499$			150.466i			0.301535i	−0.988569	+	0.150768i	$0.951826\pi$
$500$	−21.5506	−	249.069i	−0.0431013	−	0.498139i
$501$	−55.1961			−0.110172
$502$	178.565	+	178.565i	0.355708	+	0.355708i
$503$	−577.609	+	577.609i	−1.14833	+	1.14833i	−0.161446	+	0.986881i	$0.551616\pi$
$503$	−577.609	+	577.609i	−1.14833	+	1.14833i	−0.986881	+	0.161446i	$0.948384\pi$
$504$			2.23178i			0.00442813i
$505$	507.813	+	823.878i	1.00557	+	1.63144i
$506$	119.612			0.236388
$507$	483.550	+	483.550i	0.953748	+	0.953748i
$508$	−121.706	+	121.706i	−0.239578	+	0.239578i
$509$			19.0252i			0.0373776i	0.999825	+	0.0186888i	$0.00594918\pi$
$509$			19.0252i			0.0373776i	−0.999825	+	0.0186888i	$0.994051\pi$
$510$	79.2221	−	333.790i	0.155337	−	0.654490i
$511$	9.49749			0.0185861
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$	−59.5991	+	59.5991i	−0.116178	+	0.116178i
$514$		−	659.701i		−	1.28347i
$515$	−275.411	−	65.3663i	−0.534778	−	0.126925i
$516$	120.271			0.233084
$517$	531.389	+	531.389i	1.02783	+	1.02783i
$518$	17.0788	−	17.0788i	0.0329707	−	0.0329707i
$519$		−	24.2229i		−	0.0466723i
$520$	−285.863	+	176.197i	−0.549737	+	0.338841i
$521$	320.453			0.615072			0.307536	−	0.951536i	$-0.400496\pi$
$521$	320.453			0.615072			0.307536	+	0.951536i	$0.400496\pi$
$522$	−17.8245	−	17.8245i	−0.0341466	−	0.0341466i
$523$	−51.9595	+	51.9595i	−0.0993490	+	0.0993490i	−0.755034	−	0.655685i	$-0.772380\pi$
$523$	−51.9595	+	51.9595i	−0.0993490	+	0.0993490i	0.655685	+	0.755034i	$0.272380\pi$
$524$		−	103.071i		−	0.196701i
$525$	5.11786	−	10.1743i	0.00974830	−	0.0193796i
$526$	51.5438			0.0979919
$527$	−83.1121	−	83.1121i	−0.157708	−	0.157708i
$528$	86.3976	−	86.3976i	0.163632	−	0.163632i
$529$		−	23.0000i		−	0.0434783i
$530$	−285.864	−	463.787i	−0.539366	−	0.875071i
$531$	−263.232			−0.495730
$532$	−6.03353	−	6.03353i	−0.0113412	−	0.0113412i
$533$	−635.620	+	635.620i	−1.19253	+	1.19253i
$534$			158.864i			0.297497i
$535$	17.6439	−	74.3400i	0.0329793	−	0.138953i
$536$	−20.1505			−0.0375943
$537$	350.267	+	350.267i	0.652266	+	0.652266i
$538$	349.179	−	349.179i	0.649032	−	0.649032i
$539$		−	862.936i		−	1.60100i
$540$	−50.5571	−	11.9993i	−0.0936242	−	0.0222209i
$541$	179.611			0.331999			0.165999	−	0.986126i	$-0.446915\pi$
$541$	179.611			0.331999			0.165999	+	0.986126i	$0.446915\pi$
$542$	−479.592	−	479.592i	−0.884856	−	0.884856i
$543$	163.718	−	163.718i	0.301507	−	0.301507i
$544$		−	158.454i		−	0.291275i
$545$	−678.605	+	418.271i	−1.24515	+	0.767470i
$546$	−15.2978			−0.0280179
$547$	574.121	+	574.121i	1.04958	+	1.04958i	0.998705	+	0.0508772i	$0.0162017\pi$
$547$	574.121	+	574.121i	1.04958	+	1.04958i	0.0508772	+	0.998705i	$0.483798\pi$
$548$	281.273	−	281.273i	0.513273	−	0.513273i
$549$		−	60.7228i		−	0.110606i
$550$	−591.998	+	195.748i	−1.07636	+	0.355905i
$551$	96.3761			0.174911
$552$	−16.6132	−	16.6132i	−0.0300965	−	0.0300965i
$553$	−15.9594	+	15.9594i	−0.0288597	+	0.0288597i
$554$			62.7459i			0.113260i
$555$	295.066	+	478.717i	0.531651	+	0.862553i
$556$	192.163			0.345616
$557$	−115.816	−	115.816i	−0.207928	−	0.207928i	0.595458	−	0.803386i	$-0.296970\pi$
$557$	−115.816	−	115.816i	−0.207928	−	0.207928i	−0.803386	+	0.595458i	$0.796970\pi$
$558$	−12.5885	+	12.5885i	−0.0225600	+	0.0225600i
$559$			824.405i			1.47479i
$560$	1.21475	−	5.11816i	0.00216920	−	0.00913958i
$561$	−855.627			−1.52518
$562$	−398.612	−	398.612i	−0.709275	−	0.709275i
$563$	617.004	−	617.004i	1.09592	−	1.09592i	0.101040	−	0.994882i	$-0.467783\pi$
$563$	617.004	−	617.004i	1.09592	−	1.09592i	0.994882	−	0.101040i	$-0.0322169\pi$
$564$		−	147.612i		−	0.261724i
$565$	−130.667	−	31.0127i	−0.231269	−	0.0548898i
$566$	−311.720			−0.550741
$567$	−1.67383	−	1.67383i	−0.00295208	−	0.00295208i
$568$	−85.2056	+	85.2056i	−0.150010	+	0.150010i
$569$		−	133.091i		−	0.233903i	−0.993138	−	0.116951i	$-0.962688\pi$
$569$		−	133.091i		−	0.233903i	0.993138	−	0.116951i	$-0.0373122\pi$
$570$	169.119	−	104.240i	0.296700	−	0.182877i
$571$	−70.1411			−0.122839			−0.0614195	−	0.998112i	$-0.519563\pi$
$571$	−70.1411			−0.122839			−0.0614195	+	0.998112i	$0.519563\pi$
$572$	592.216	+	592.216i	1.03534	+	1.03534i
$573$	−130.771	+	130.771i	−0.228222	+	0.228222i
$574$		−	14.0813i		−	0.0245319i
$575$	37.6400	+	113.834i	0.0654608	+	0.197973i
$576$	−24.0000			−0.0416667
$577$	−593.584	−	593.584i	−1.02874	−	1.02874i	−0.999575	−	0.0291673i	$-0.990714\pi$
$577$	−593.584	−	593.584i	−1.02874	−	1.02874i	−0.0291673	−	0.999575i	$-0.509286\pi$
$578$	−495.612	+	495.612i	−0.857460	+	0.857460i
$579$			81.6468i			0.141014i
$580$	31.1754	+	50.5791i	0.0537507	+	0.0872054i
$581$	−18.2538			−0.0314180
$582$	156.302	+	156.302i	0.268560	+	0.268560i
$583$	−960.817	+	960.817i	−1.64806	+	1.64806i
$584$			102.134i			0.174887i
$585$	82.2496	−	346.546i	0.140598	−	0.592386i
$586$	−205.717			−0.351054
$587$	567.035	+	567.035i	0.965989	+	0.965989i	0.999440	−	0.0334516i	$-0.0106500\pi$
$587$	567.035	+	567.035i	0.965989	+	0.965989i	−0.0334516	+	0.999440i	$0.510650\pi$
$588$	−119.856	+	119.856i	−0.203836	+	0.203836i
$589$		−	68.0650i		−	0.115560i
$590$	603.675	+	143.277i	1.02318	+	0.242842i
$591$	437.092			0.739581
$592$	183.662	+	183.662i	0.310239	+	0.310239i
$593$	−47.6862	+	47.6862i	−0.0804152	+	0.0804152i	−0.746170	−	0.665755i	$-0.768110\pi$
$593$	−47.6862	+	47.6862i	−0.0804152	+	0.0804152i	0.665755	+	0.746170i	$0.268110\pi$
$594$			129.596i			0.218176i
$595$	−31.3586	+	19.3284i	−0.0527035	+	0.0324848i
$596$	−68.3906			−0.114749
$597$	−111.495	−	111.495i	−0.186758	−	0.186758i
$598$	113.876	−	113.876i	0.190428	−	0.190428i
$599$			793.250i			1.32429i	0.749376	+	0.662145i	$0.230354\pi$
$599$			793.250i			1.32429i	−0.749376	+	0.662145i	$0.769646\pi$
$600$	109.412	+	55.0363i	0.182354	+	0.0917271i
$601$	−234.950			−0.390931			−0.195465	−	0.980711i	$-0.562622\pi$
$601$	−234.950			−0.390931			−0.195465	+	0.980711i	$0.562622\pi$
$602$	−9.13179	−	9.13179i	−0.0151691	−	0.0151691i
$603$	15.1129	−	15.1129i	0.0250628	−	0.0250628i
$604$			365.285i			0.604776i
$605$	498.530	+	808.818i	0.824017	+	1.33689i
$606$	−474.127			−0.782387
$607$	−643.221	−	643.221i	−1.05967	−	1.05967i	−0.998103	−	0.0615699i	$-0.980389\pi$
$607$	−643.221	−	643.221i	−1.05967	−	1.05967i	−0.0615699	−	0.998103i	$-0.519611\pi$
$608$	64.8833	−	64.8833i	0.106716	−	0.106716i
$609$			2.70671i			0.00444452i
$610$	−33.0513	+	139.256i	−0.0541825	+	0.228289i
$611$	1011.81			1.65600
$612$	118.840	+	118.840i	0.194183	+	0.194183i
$613$	−323.718	+	323.718i	−0.528088	+	0.528088i	−0.920002	−	0.391914i	$-0.871813\pi$
$613$	−323.718	+	323.718i	−0.528088	+	0.528088i	0.391914	+	0.920002i	$0.371813\pi$
$614$			331.258i			0.539508i
$615$	318.988	+	75.7090i	0.518680	+	0.123104i
$616$	−13.1197			−0.0212983
$617$	267.813	+	267.813i	0.434057	+	0.434057i	0.890006	−	0.455949i	$-0.150700\pi$
$617$	267.813	+	267.813i	0.434057	+	0.434057i	−0.455949	+	0.890006i	$0.650700\pi$
$618$	98.0554	−	98.0554i	0.158666	−	0.158666i
$619$		−	508.117i		−	0.820867i	−0.911890	−	0.410434i	$-0.865377\pi$
$619$		−	508.117i		−	0.820867i	0.911890	−	0.410434i	$-0.134623\pi$
$620$	35.7212	−	22.0174i	0.0576148	−	0.0355120i
$621$	24.9199			0.0401286
$622$	−176.951	−	176.951i	−0.284487	−	0.284487i
$623$	12.0620	−	12.0620i	0.0193611	−	0.0193611i
$624$		−	164.509i		−	0.263636i
$625$	−372.584	−	501.803i	−0.596135	−	0.802884i
$626$	23.3088			0.0372345
$627$	−350.360	−	350.360i	−0.558788	−	0.558788i
$628$	135.777	−	135.777i	0.216205	−	0.216205i
$629$		−	1818.87i		−	2.89168i
$630$	2.92756	+	4.74969i	0.00464692	+	0.00753919i
$631$	−15.4171			−0.0244327			−0.0122164	−	0.999925i	$-0.503889\pi$
$631$	−15.4171			−0.0244327			−0.0122164	+	0.999925i	$0.503889\pi$
$632$	−171.624	−	171.624i	−0.271556	−	0.271556i
$633$	−470.726	+	470.726i	−0.743643	+	0.743643i
$634$		−	451.681i		−	0.712431i
$635$	−99.3662	+	418.664i	−0.156482	+	0.659313i
$636$	266.901			0.419656
$637$	−821.555	−	821.555i	−1.28973	−	1.28973i
$638$	104.784	−	104.784i	0.164238	−	0.164238i
$639$		−	127.808i		−	0.200013i
$640$	55.0396	+	13.0632i	0.0859993	+	0.0204112i
$641$	127.618			0.199091			0.0995456	−	0.995033i	$-0.468261\pi$
$641$	127.618			0.199091			0.0995456	+	0.995033i	$0.468261\pi$
$642$	26.4675	+	26.4675i	0.0412267	+	0.0412267i
$643$	732.374	−	732.374i	1.13899	−	1.13899i	0.150364	−	0.988631i	$-0.451955\pi$
$643$	732.374	−	732.374i	1.13899	−	1.13899i	0.988631	−	0.150364i	$-0.0480447\pi$
$644$			2.52277i			0.00391735i
$645$	255.963	−	157.768i	0.396842	−	0.244601i
$646$	−642.562			−0.994678
$647$	830.198	+	830.198i	1.28315	+	1.28315i	0.938865	+	0.344286i	$0.111879\pi$
$647$	830.198	+	830.198i	1.28315	+	1.28315i	0.344286	+	0.938865i	$0.388121\pi$
$648$	18.0000	−	18.0000i	0.0277778	−	0.0277778i
$649$		−	1547.44i		−	2.38435i
$650$	−377.248	+	749.970i	−0.580382	+	1.15380i
$651$	1.91160			0.00293640
$652$	−219.686	−	219.686i	−0.336942	−	0.336942i
$653$	171.573	−	171.573i	0.262745	−	0.262745i	−0.563423	−	0.826168i	$-0.690516\pi$
$653$	171.573	−	171.573i	0.262745	−	0.262745i	0.826168	+	0.563423i	$0.190516\pi$
$654$		−	390.524i		−	0.597132i
$655$	−135.205	−	219.357i	−0.206420	−	0.334896i
$656$	151.427			0.230834
$657$	−76.6004	−	76.6004i	−0.116591	−	0.116591i
$658$	−11.2077	+	11.2077i	−0.0170329	+	0.0170329i
$659$			801.680i			1.21651i	0.793742	+	0.608255i	$0.208130\pi$
$659$			801.680i			1.21651i	−0.793742	+	0.608255i	$0.791870\pi$
$660$	70.5391	−	297.206i	0.106877	−	0.450311i
$661$	−960.626			−1.45329			−0.726646	−	0.687012i	$-0.758922\pi$
$661$	−960.626			−1.45329			−0.726646	+	0.687012i	$0.758922\pi$
$662$	−217.937	−	217.937i	−0.329211	−	0.329211i
$663$	−814.596	+	814.596i	−1.22865	+	1.22865i
$664$		−	196.298i		−	0.295629i
$665$	−20.7552	−	4.92606i	−0.0312108	−	0.00740761i
$666$	−275.493			−0.413652
$667$	−20.1486	−	20.1486i	−0.0302079	−	0.0302079i
$668$	−45.0674	+	45.0674i	−0.0674662	+	0.0674662i
$669$		−	639.287i		−	0.955586i
$670$	−42.8845	+	26.4327i	−0.0640068	+	0.0394518i
$671$	356.966			0.531991
$672$	1.82224	+	1.82224i	0.00271166	+	0.00271166i
$673$	326.569	−	326.569i	0.485243	−	0.485243i	−0.421558	−	0.906801i	$-0.638517\pi$
$673$	326.569	−	326.569i	0.485243	−	0.485243i	0.906801	+	0.421558i	$0.138517\pi$
$674$			507.267i			0.752622i
$675$	−123.336	+	40.7819i	−0.182720	+	0.0604176i
$676$	789.634			1.16810
$677$	676.535	+	676.535i	0.999314	+	0.999314i	1.00000		0.000685886i	$-0.000218324\pi$
$677$	676.535	+	676.535i	0.999314	+	0.999314i	−0.000685886		1.00000i	$0.500218\pi$
$678$	46.5219	−	46.5219i	0.0686163	−	0.0686163i
$679$		−	23.7349i		−	0.0349557i
$680$	−207.854	−	337.223i	−0.305667	−	0.495916i
$681$	−142.085			−0.208642
$682$	−74.0027	−	74.0027i	−0.108508	−	0.108508i
$683$	118.338	−	118.338i	0.173262	−	0.173262i	−0.615149	−	0.788411i	$-0.710904\pi$
$683$	118.338	−	118.338i	0.173262	−	0.173262i	0.788411	+	0.615149i	$0.210904\pi$
$684$			97.3249i			0.142288i
$685$	229.645	−	967.573i	0.335248	−	1.41251i
$686$	36.4266			0.0531000
$687$	68.2109	+	68.2109i	0.0992880	+	0.0992880i
$688$	98.2012	−	98.2012i	0.142734	−	0.142734i
$689$			1829.48i			2.65527i
$690$	−57.1491	−	13.5638i	−0.0828248	−	0.0196577i
$691$	1096.90			1.58741			0.793705	−	0.608302i	$-0.208149\pi$
$691$	1096.90			1.58741			0.793705	+	0.608302i	$0.208149\pi$
$692$	−19.7779	−	19.7779i	−0.0285808	−	0.0285808i
$693$	9.83981	−	9.83981i	0.0141989	−	0.0141989i
$694$		−	104.462i		−	0.150521i
$695$	408.962	−	252.072i	0.588435	−	0.362693i
$696$	−29.1073			−0.0418209
$697$	−749.818	−	749.818i	−1.07578	−	1.07578i
$698$	413.853	−	413.853i	0.592913	−	0.592913i
$699$			383.138i			0.548122i
$700$	−4.12857	−	12.4860i	−0.00589796	−	0.0178371i
$701$	1131.15			1.61362			0.806809	−	0.590813i	$-0.201193\pi$
$701$	1131.15			1.61362			0.806809	+	0.590813i	$0.201193\pi$
$702$	123.382	+	123.382i	0.175757	+	0.175757i
$703$	744.785	−	744.785i	1.05944	−	1.05944i
$704$		−	141.087i		−	0.200407i
$705$	−193.632	−	314.150i	−0.274655	−	0.445602i
$706$	−170.307			−0.241229
$707$	35.9988	+	35.9988i	0.0509177	+	0.0509177i
$708$	−214.928	+	214.928i	−0.303571	+	0.303571i
$709$		−	298.642i		−	0.421215i	−0.977571	−	0.210608i	$-0.932456\pi$
$709$		−	298.642i		−	0.421215i	0.977571	−	0.210608i	$-0.0675443\pi$
$710$	−69.5659	+	293.105i	−0.0979801	+	0.412824i
$711$	257.435			0.362075
$712$	129.712	+	129.712i	0.182179	+	0.182179i
$713$	−14.2299	+	14.2299i	−0.0199577	+	0.0199577i
$714$		−	18.0463i		−	0.0252749i
$715$	2037.21	+	483.513i	2.84924	+	0.676243i
$716$	571.984			0.798860
$717$	367.081	+	367.081i	0.511968	+	0.511968i
$718$	−574.569	+	574.569i	−0.800236	+	0.800236i
$719$		−	403.971i		−	0.561852i	−0.959729	−	0.280926i	$-0.909359\pi$
$719$		−	403.971i		−	0.561852i	0.959729	−	0.280926i	$-0.0906415\pi$
$720$	−51.0770	+	31.4823i	−0.0709403	+	0.0437254i
$721$	−14.8900			−0.0206519
$722$	97.8852	+	97.8852i	0.135575	+	0.135575i
$723$	−388.752	+	388.752i	−0.537693	+	0.537693i
$724$		−	267.351i		−	0.369269i
$725$	132.696	+	66.7483i	0.183028	+	0.0920666i
$726$	−465.460			−0.641129
$727$	−836.080	−	836.080i	−1.15004	−	1.15004i	−0.986544	−	0.163497i	$-0.947723\pi$
$727$	−836.080	−	836.080i	−1.15004	−	1.15004i	−0.163497	−	0.986544i	$-0.552277\pi$
$728$	−12.4906	+	12.4906i	−0.0171574	+	0.0171574i
$729$			27.0000i			0.0370370i
$730$	133.975	+	217.362i	0.183528	+	0.297756i
$731$	−972.522			−1.33040
$732$	−49.5799	−	49.5799i	−0.0677322	−	0.0677322i
$733$	−736.812	+	736.812i	−1.00520	+	1.00520i	−0.00521382	+	0.999986i	$0.501660\pi$
$733$	−736.812	+	736.812i	−1.00520	+	1.00520i	−0.999986	+	0.00521382i	$0.998340\pi$
$734$		−	518.866i		−	0.706902i
$735$	−97.8558	+	412.300i	−0.133137	+	0.560952i
$736$	−27.1293			−0.0368605
$737$	88.8429	+	88.8429i	0.120547	+	0.120547i
$738$	−113.570	+	113.570i	−0.153889	+	0.153889i
$739$			248.799i			0.336670i	0.985730	+	0.168335i	$0.0538391\pi$
$739$			248.799i			0.336670i	−0.985730	+	0.168335i	$0.946161\pi$
$740$	631.791	+	149.950i	0.853772	+	0.202635i
$741$	−667.117			−0.900293
$742$	−20.2649	−	20.2649i	−0.0273111	−	0.0273111i
$743$	127.951	−	127.951i	0.172208	−	0.172208i	−0.615741	−	0.787949i	$-0.711143\pi$
$743$	127.951	−	127.951i	0.172208	−	0.172208i	0.787949	+	0.615741i	$0.211143\pi$
$744$			20.5569i			0.0276302i
$745$	−145.550	+	89.7122i	−0.195368	+	0.120419i
$746$	160.289			0.214864
$747$	147.223	+	147.223i	0.197086	+	0.197086i
$748$	−698.616	+	698.616i	−0.933979	+	0.933979i
$749$		−	4.01917i		−	0.00536605i
$750$	305.046	−	26.3940i	0.406729	−	0.0351920i
$751$	267.001			0.355527			0.177764	−	0.984073i	$-0.443114\pi$
$751$	267.001			0.355527			0.177764	+	0.984073i	$0.443114\pi$
$752$	−120.525	−	120.525i	−0.160272	−	0.160272i
$753$	−218.697	+	218.697i	−0.290434	+	0.290434i
$754$		−	199.517i		−	0.264612i
$755$	479.167	+	777.403i	0.634658	+	1.02967i
$756$	−2.73336			−0.00361555
$757$	159.734	+	159.734i	0.211009	+	0.211009i	0.804696	−	0.593687i	$-0.202328\pi$
$757$	159.734	+	159.734i	0.211009	+	0.211009i	−0.593687	+	0.804696i	$0.702328\pi$
$758$	715.430	−	715.430i	0.943838	−	0.943838i
$759$			146.494i			0.193010i
$760$	52.9738	−	223.197i	0.0697023	−	0.293680i
$761$	−913.192			−1.19999			−0.599995	−	0.800004i	$-0.704831\pi$
$761$	−913.192			−1.19999			−0.599995	+	0.800004i	$0.704831\pi$
$762$	−149.058	−	149.058i	−0.195615	−	0.195615i
$763$	−29.6512	+	29.6512i	−0.0388613	+	0.0388613i
$764$			213.549i			0.279514i
$765$	408.807	+	97.0269i	0.534389	+	0.126832i
$766$	524.853			0.685187
$767$	−1473.24	−	1473.24i	−1.92078	−	1.92078i
$768$	−19.5959	+	19.5959i	−0.0255155	+	0.0255155i
$769$			638.410i			0.830182i	0.909780	+	0.415091i	$0.136250\pi$
$769$			638.410i			0.830182i	−0.909780	+	0.415091i	$0.863750\pi$
$770$	−27.9216	+	17.2100i	−0.0362618	+	0.0223506i
$771$	807.966			1.04795
$772$	66.6643	+	66.6643i	0.0863528	+	0.0863528i
$773$	−15.4984	+	15.4984i	−0.0200496	+	0.0200496i	−0.717061	−	0.697011i	$-0.754513\pi$
$773$	−15.4984	+	15.4984i	−0.0200496	+	0.0200496i	0.697011	+	0.717061i	$0.254513\pi$
$774$			147.302i			0.190312i
$775$	47.1406	−	93.7155i	0.0608265	−	0.120923i
$776$	255.240			0.328918
$777$	20.9172	+	20.9172i	0.0269205	+	0.0269205i
$778$	523.535	−	523.535i	0.672924	−	0.672924i
$779$		−	614.068i		−	0.788277i
$780$	−215.797	−	350.110i	−0.276663	−	0.448859i
$781$	751.336			0.962018
$782$	134.336	+	134.336i	0.171785	+	0.171785i
$783$	21.8305	−	21.8305i	0.0278806	−	0.0278806i
$784$			195.723i			0.249647i
$785$	110.855	−	467.069i	0.141216	−	0.594993i
$786$	126.236			0.160605
$787$	−857.491	−	857.491i	−1.08957	−	1.08957i	−0.995572	−	0.0939971i	$-0.970036\pi$
$787$	−857.491	−	857.491i	−1.08957	−	1.08957i	−0.0939971	−	0.995572i	$-0.529964\pi$
$788$	356.884	−	356.884i	0.452899	−	0.452899i
$789$			63.1280i			0.0800101i
$790$	−590.381	−	140.122i	−0.747317	−	0.177369i
$791$	−7.06449			−0.00893109
$792$	105.815	+	105.815i	0.133605	+	0.133605i
$793$	339.848	−	339.848i	0.428560	−	0.428560i
$794$			542.142i			0.682799i
$795$	568.021	−	350.111i	0.714492	−	0.440391i
$796$	−182.070			−0.228731
$797$	404.935	+	404.935i	0.508074	+	0.508074i	0.913935	−	0.405861i	$-0.133028\pi$
$797$	404.935	+	404.935i	0.508074	+	0.508074i	−0.405861	+	0.913935i	$0.633028\pi$
$798$	7.38954	−	7.38954i	0.00926008	−	0.00926008i
$799$			1193.60i			1.49387i
$800$	134.272	−	44.3977i	0.167839	−	0.0554971i
$801$	−194.567			−0.242906
$802$	275.406	+	275.406i	0.343399	+	0.343399i
$803$	450.304	−	450.304i	0.560777	−	0.560777i
$804$		−	24.6792i		−	0.0306956i
$805$	3.30928	+	5.36899i	0.00411091	+	0.00666955i
$806$	−140.908			−0.174824
$807$	427.656	+	427.656i	0.529932	+	0.529932i
$808$	−387.123	+	387.123i	−0.479112	+	0.479112i
$809$			123.960i			0.153226i	0.997061	+	0.0766130i	$0.0244106\pi$
$809$			123.960i			0.153226i	−0.997061	+	0.0766130i	$0.975589\pi$
$810$	14.6961	−	61.9195i	0.0181433	−	0.0764438i
$811$	−1376.52			−1.69731			−0.848654	−	0.528948i	$-0.822587\pi$
$811$	−1376.52			−1.69731			−0.848654	+	0.528948i	$0.822587\pi$
$812$	2.21002	+	2.21002i	0.00272170	+	0.00272170i
$813$	587.377	−	587.377i	0.722482	−	0.722482i
$814$		−	1619.51i		−	1.98958i
$815$	−755.714	−	179.362i	−0.927256	−	0.220076i
$816$	194.065			0.237825
$817$	−398.226	−	398.226i	−0.487424	−	0.487424i
$818$	87.9556	−	87.9556i	0.107525	−	0.107525i
$819$		−	18.7359i		−	0.0228766i
$820$	322.269	−	198.636i	0.393011	−	0.242240i
$821$	−95.8252			−0.116718			−0.0583588	−	0.998296i	$-0.518587\pi$
$821$	−95.8252			−0.116718			−0.0583588	+	0.998296i	$0.518587\pi$
$822$	344.488	+	344.488i	0.419085	+	0.419085i
$823$	−87.3148	+	87.3148i	−0.106093	+	0.106093i	−0.758161	−	0.652068i	$-0.773902\pi$
$823$	−87.3148	+	87.3148i	−0.106093	+	0.106093i	0.652068	+	0.758161i	$0.273902\pi$
$824$		−	160.124i		−	0.194325i
$825$	−239.741	−	725.047i	−0.290595	−	0.878844i
$826$	32.6375			0.0395127
$827$	−521.100	−	521.100i	−0.630109	−	0.630109i	0.317986	−	0.948095i	$-0.396993\pi$
$827$	−521.100	−	521.100i	−0.630109	−	0.630109i	−0.948095	+	0.317986i	$0.896993\pi$
$828$	20.3470	−	20.3470i	0.0245737	−	0.0245737i
$829$		−	1479.49i		−	1.78466i	−0.451379	−	0.892332i	$-0.649068\pi$
$829$		−	1479.49i		−	1.78466i	0.451379	−	0.892332i	$-0.350932\pi$
$830$	−257.496	−	417.762i	−0.310236	−	0.503328i
$831$	−76.8477			−0.0924761
$832$	−134.321	−	134.321i	−0.161444	−	0.161444i
$833$	969.159	−	969.159i	1.16346	−	1.16346i
$834$			235.350i			0.282194i
$835$	−36.7952	+	155.031i	−0.0440661	+	0.185666i
$836$	−572.136			−0.684373
$837$	−15.4177	−	15.4177i	−0.0184201	−	0.0184201i
$838$	−549.190	+	549.190i	−0.655358	+	0.655358i
$839$		−	847.105i		−	1.00966i	−0.863219	−	0.504830i	$-0.831555\pi$
$839$		−	847.105i		−	1.00966i	0.863219	−	0.504830i	$-0.168445\pi$
$840$	6.26845	+	1.48776i	0.00746243	+	0.00177114i
$841$	805.698			0.958024
$842$	−579.831	−	579.831i	−0.688636	−	0.688636i
$843$	488.198	−	488.198i	0.579120	−	0.579120i
$844$			768.692i			0.910772i
$845$	1680.51	−	1035.81i	1.98877	−	1.22581i
$846$	180.787			0.213696
$847$	35.3407	+	35.3407i	0.0417246	+	0.0417246i
$848$	217.924	−	217.924i	0.256985	−	0.256985i
$849$		−	381.777i		−	0.449678i
$850$	−884.713	−	445.026i	−1.04084	−	0.523560i
$851$	−311.414			−0.365938
$852$	−104.355	−	104.355i	−0.122483	−	0.122483i
$853$	407.026	−	407.026i	0.477170	−	0.477170i	−0.427055	−	0.904226i	$-0.640449\pi$
$853$	407.026	−	407.026i	0.477170	−	0.477170i	0.904226	+	0.427055i	$0.140449\pi$
$854$			7.52887i			0.00881600i
$855$	127.667	+	207.128i	0.149318	+	0.242255i
$856$	43.2213			0.0504921
$857$	−459.608	−	459.608i	−0.536299	−	0.536299i	0.386141	−	0.922440i	$-0.373808\pi$
$857$	−459.608	−	459.608i	−0.536299	−	0.536299i	−0.922440	+	0.386141i	$0.873808\pi$
$858$	−725.314	+	725.314i	−0.845354	+	0.845354i
$859$		−	718.564i		−	0.836512i	−0.908329	−	0.418256i	$-0.862641\pi$
$859$		−	718.564i		−	0.836512i	0.908329	−	0.418256i	$-0.137359\pi$
$860$	80.1761	−	337.809i	0.0932280	−	0.392802i
$861$	17.2460			0.0200302
$862$	422.783	+	422.783i	0.490467	+	0.490467i
$863$	1031.60	−	1031.60i	1.19537	−	1.19537i	0.219829	−	0.975538i	$-0.429450\pi$
$863$	1031.60	−	1031.60i	1.19537	−	1.19537i	0.975538	−	0.219829i	$-0.0705499\pi$
$864$		−	29.3939i		−	0.0340207i
$865$	−68.0355	−	16.1476i	−0.0786537	−	0.0186678i
$866$	713.984			0.824462
$867$	−606.998	−	606.998i	−0.700113	−	0.700113i
$868$	1.56081	−	1.56081i	0.00179817	−	0.00179817i
$869$			1513.36i			1.74150i
$870$	−61.9465	+	38.1819i	−0.0712029	+	0.0438873i
$871$	169.165			0.194219
$872$	−318.862	−	318.862i	−0.365667	−	0.365667i
$873$	−191.430	+	191.430i	−0.219278	+	0.219278i
$874$			110.015i			0.125875i
$875$	−25.1651	−	21.1571i	−0.0287601	−	0.0241796i
$876$	−125.088			−0.142794
$877$	466.189	+	466.189i	0.531572	+	0.531572i	0.921040	−	0.389468i	$-0.127341\pi$
$877$	466.189	+	466.189i	0.531572	+	0.531572i	−0.389468	+	0.921040i	$0.627341\pi$
$878$	−95.4606	+	95.4606i	−0.108725	+	0.108725i
$879$		−	251.951i		−	0.286634i
$880$	−185.072	−	300.262i	−0.210310	−	0.341207i
$881$	26.2535			0.0297996			0.0148998	−	0.999889i	$-0.495257\pi$
$881$	26.2535			0.0297996			0.0148998	+	0.999889i	$0.495257\pi$
$882$	−146.792	−	146.792i	−0.166431	−	0.166431i
$883$	710.684	−	710.684i	0.804851	−	0.804851i	−0.178998	−	0.983849i	$-0.557286\pi$
$883$	710.684	−	710.684i	0.804851	−	0.804851i	0.983849	+	0.178998i	$0.0572856\pi$
$884$			1330.23i			1.50478i
$885$	−175.478	+	739.348i	−0.198280	+	0.835421i
$886$	−181.455			−0.204802
$887$	−1117.50	−	1117.50i	−1.25986	−	1.25986i	−0.951159	−	0.308700i	$-0.900106\pi$
$887$	−1117.50	−	1117.50i	−1.25986	−	1.25986i	−0.308700	−	0.951159i	$-0.599894\pi$
$888$	−224.939	+	224.939i	−0.253309	+	0.253309i
$889$			22.6350i			0.0254611i
$890$	446.204	+	105.903i	0.501353	+	0.118992i
$891$	−158.723			−0.178140
$892$	−521.976	−	521.976i	−0.585175	−	0.585175i
$893$	−488.753	+	488.753i	−0.547315	+	0.547315i
$894$		−	83.7610i		−	0.0936924i
$895$	1217.30	−	750.307i	1.36011	−	0.838332i
$896$	2.97570			0.00332109
$897$	139.469	+	139.469i	0.155484	+	0.155484i
$898$	685.452	−	685.452i	0.763310	−	0.763310i
$899$			24.9315i			0.0277325i
$900$	−67.4054	+	134.002i	−0.0748949	+	0.148891i
$901$	−2158.18			−2.39531
$902$	−667.636	−	667.636i	−0.740173	−	0.740173i
$903$	11.1841	−	11.1841i	0.0123855	−	0.0123855i
$904$		−	75.9699i		−	0.0840375i
$905$	−350.701	−	568.979i	−0.387515	−	0.628706i
$906$	−447.381			−0.493798
$907$	−751.338	−	751.338i	−0.828377	−	0.828377i	0.158916	−	0.987292i	$-0.449200\pi$
$907$	−751.338	−	751.338i	−0.828377	−	0.828377i	−0.987292	+	0.158916i	$0.949200\pi$
$908$	−116.012	+	116.012i	−0.127766	+	0.127766i
$909$		−	580.684i		−	0.638816i
$910$	−10.1979	+	42.9673i	−0.0112065	+	0.0472168i
$911$	−464.544			−0.509928			−0.254964	−	0.966951i	$-0.582064\pi$
$911$	−464.544			−0.509928			−0.254964	+	0.966951i	$0.582064\pi$
$912$	79.4654	+	79.4654i	0.0871331	+	0.0871331i
$913$	−865.468	+	865.468i	−0.947939	+	0.947939i
$914$			41.5390i			0.0454474i
$915$	−170.554	−	40.4794i	−0.186397	−	0.0442398i
$916$	111.388			0.121603
$917$	−9.58465	−	9.58465i	−0.0104522	−	0.0104522i
$918$	−145.549	+	145.549i	−0.158550	+	0.158550i
$919$			471.275i			0.512813i	0.966569	+	0.256406i	$0.0825386\pi$
$919$			471.275i			0.512813i	−0.966569	+	0.256406i	$0.917461\pi$
$920$	−57.7369	+	35.5872i	−0.0627575	+	0.0386818i
$921$	−405.707			−0.440507
$922$	413.944	+	413.944i	0.448963	+	0.448963i
$923$	715.306	−	715.306i	0.774980	−	0.774980i
$924$		−	16.0683i		−	0.0173900i
$925$	1541.28	−	509.635i	1.66625	−	0.550957i
$926$	−961.650			−1.03850
$927$	120.093	+	120.093i	0.129550	+	0.129550i
$928$	−23.7660	+	23.7660i	−0.0256100	+	0.0256100i
$929$			889.293i			0.957259i	0.878017	+	0.478629i	$0.158866\pi$
$929$			889.293i			0.957259i	−0.878017	+	0.478629i	$0.841134\pi$
$930$	26.9657	+	43.7494i	0.0289954	+	0.0470423i
$931$	793.698			0.852522
$932$	312.831	+	312.831i	0.335655	+	0.335655i
$933$	216.720	−	216.720i	0.232283	−	0.232283i
$934$			940.046i			1.00647i
$935$	−570.384	+	2403.22i	−0.610036	+	2.57029i
$936$	201.482			0.215258
$937$	1186.80	+	1186.80i	1.26660	+	1.26660i	0.947833	+	0.318766i	$0.103268\pi$
$937$	1186.80	+	1186.80i	1.26660	+	1.26660i	0.318766	+	0.947833i	$0.396732\pi$
$938$	−1.87381	+	1.87381i	−0.00199766	+	0.00199766i
$939$			28.5473i			0.0304019i
$940$	−414.602	−	98.4022i	−0.441066	−	0.104683i
$941$	1016.73			1.08048			0.540240	−	0.841511i	$-0.318333\pi$
$941$	1016.73			1.08048			0.540240	+	0.841511i	$0.318333\pi$
$942$	166.292	+	166.292i	0.176531	+	0.176531i
$943$	−128.379	+	128.379i	−0.136138	+	0.136138i
$944$			350.977i			0.371797i
$945$	−5.81715	+	3.58551i	−0.00615572	+	0.00379419i
$946$	−865.931			−0.915360
$947$	182.703	+	182.703i	0.192928	+	0.192928i	0.796960	−	0.604032i	$-0.206440\pi$
$947$	182.703	+	182.703i	0.192928	+	0.192928i	−0.604032	+	0.796960i	$0.706440\pi$
$948$	210.195	−	210.195i	0.221725	−	0.221725i
$949$		−	857.420i		−	0.903498i
$950$	−180.042	−	544.498i	−0.189518	−	0.573156i
$951$	553.194			0.581697
$952$	−14.7347	−	14.7347i	−0.0154776	−	0.0154776i
$953$	1134.24	−	1134.24i	1.19018	−	1.19018i	0.213161	−	0.977017i	$-0.431624\pi$
$953$	1134.24	−	1134.24i	1.19018	−	1.19018i	0.977017	−	0.213161i	$-0.0683760\pi$
$954$			326.886i			0.342647i
$955$	280.125	+	454.477i	0.293325	+	0.475892i
$956$	599.441			0.627031
$957$	128.333	+	128.333i	0.134099	+	0.134099i
$958$	204.710	−	204.710i	0.213685	−	0.213685i
$959$		−	52.3116i		−	0.0545480i
$960$	−15.9990	+	67.4094i	−0.0166657	+	0.0702182i
$961$	−943.392			−0.981678
$962$	−1541.85	−	1541.85i	−1.60276	−	1.60276i
$963$	−32.4159	+	32.4159i	−0.0336614	+	0.0336614i
$964$			634.829i			0.658536i
$965$	229.324	+	54.4279i	0.237641	+	0.0564020i
$966$	−3.08975			−0.00319850
$967$	867.599	+	867.599i	0.897206	+	0.897206i	0.995188	−	0.0979818i	$-0.0312387\pi$
$967$	867.599	+	867.599i	0.897206	+	0.897206i	−0.0979818	+	0.995188i	$0.531239\pi$
$968$	−380.046	+	380.046i	−0.392610	+	0.392610i
$969$		−	786.975i		−	0.812151i
$970$	543.205	−	334.815i	0.560005	−	0.345170i
$971$	1330.51			1.37025			0.685123	−	0.728427i	$-0.259748\pi$
$971$	1330.51			1.37025			0.685123	+	0.728427i	$0.259748\pi$
$972$	22.0454	+	22.0454i	0.0226805	+	0.0226805i
$973$	17.8693	−	17.8693i	0.0183652	−	0.0183652i
$974$			622.994i			0.639625i
$975$	−918.522	−	462.033i	−0.942074	−	0.473880i
$976$	−80.9637			−0.0829546
$977$	−372.655	−	372.655i	−0.381428	−	0.381428i	0.490188	−	0.871617i	$-0.336928\pi$
$977$	−372.655	−	372.655i	−0.381428	−	0.381428i	−0.871617	+	0.490188i	$0.836928\pi$
$978$	269.059	−	269.059i	0.275112	−	0.275112i
$979$		−	1143.79i		−	1.16832i
$980$	256.743	+	416.540i	0.261982	+	0.425041i
$981$	478.293			0.487556
$982$	356.163	+	356.163i	0.362691	+	0.362691i
$983$	−988.350	+	988.350i	−1.00544	+	1.00544i	−0.00545738	+	0.999985i	$0.501737\pi$
$983$	−988.350	+	988.350i	−1.00544	+	1.00544i	−0.999985	+	0.00545738i	$0.998263\pi$
$984$			185.460i			0.188475i
$985$	291.377	−	1227.67i	0.295815	−	1.24637i
$986$	235.364			0.238706
$987$	−13.7265	−	13.7265i	−0.0139073	−	0.0139073i
$988$	−544.699	+	544.699i	−0.551315	+	0.551315i
$989$			166.508i			0.168360i
$990$	364.001	+	86.3924i	0.367678	+	0.0872651i
$991$	−1406.17			−1.41894			−0.709471	−	0.704735i	$-0.751066\pi$
$991$	−1406.17			−1.41894			−0.709471	+	0.704735i	$0.751066\pi$
$992$	16.7846	+	16.7846i	0.0169200	+	0.0169200i
$993$	266.918	−	266.918i	0.268799	−	0.268799i
$994$			15.8466i			0.0159423i
$995$	−387.484	+	238.833i	−0.389431	+	0.240033i
$996$	240.414			0.241380
$997$	−1229.39	−	1229.39i	−1.23309	−	1.23309i	−0.962771	−	0.270319i	$-0.912871\pi$
$997$	−1229.39	−	1229.39i	−1.23309	−	1.23309i	−0.270319	−	0.962771i	$-0.587129\pi$
$998$	−150.466	+	150.466i	−0.150768	+	0.150768i
$999$		−	337.408i		−	0.337746i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.k.a.277.6	✓	40
5.3	odd	4	inner	690.3.k.a.553.6	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.k.a.277.6	✓	40	1.1	even	1	trivial
690.3.k.a.553.6	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)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(2.62353 + 4.25642i) q^{5} -2.44949 q^{6} +(0.185981 + 0.185981i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(2.62353 + 4.25642i) q^{5} -2.44949 q^{6} +(0.185981 + 0.185981i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(-1.63289 + 6.87995i) q^{10} +17.6358 q^{11} +(-2.44949 - 2.44949i) q^{12} +(16.7901 - 16.7901i) q^{13} +0.371963i q^{14} +(-8.42618 - 1.99988i) q^{15} -4.00000 q^{16} +(19.8067 + 19.8067i) q^{17} +(3.00000 - 3.00000i) q^{18} +16.2208i q^{19} +(-8.51284 + 5.24705i) q^{20} -0.455559 q^{21} +(17.6358 + 17.6358i) q^{22} +(3.39116 - 3.39116i) q^{23} -4.89898i q^{24} +(-11.2342 + 22.3337i) q^{25} +33.5803 q^{26} +(3.67423 + 3.67423i) q^{27} +(-0.371963 + 0.371963i) q^{28} -5.94151i q^{29} +(-6.42630 - 10.4261i) q^{30} -4.19616 q^{31} +(-4.00000 - 4.00000i) q^{32} +(-21.5994 + 21.5994i) q^{33} +39.6134i q^{34} +(-0.303688 + 1.27954i) q^{35} +6.00000 q^{36} +(-45.9154 - 45.9154i) q^{37} +(-16.2208 + 16.2208i) q^{38} +41.1273i q^{39} +(-13.7599 - 3.26579i) q^{40} -37.8568 q^{41} +(-0.455559 - 0.455559i) q^{42} +(-24.5503 + 24.5503i) q^{43} +35.2717i q^{44} +(12.7693 - 7.87058i) q^{45} +6.78233 q^{46} +(30.1312 + 30.1312i) q^{47} +(4.89898 - 4.89898i) q^{48} -48.9308i q^{49} +(-33.5679 + 11.0994i) q^{50} -48.5163 q^{51} +(33.5803 + 33.5803i) q^{52} +(-54.4809 + 54.4809i) q^{53} +7.34847i q^{54} +(46.2681 + 75.0656i) q^{55} -0.743925 q^{56} +(-19.8664 - 19.8664i) q^{57} +(5.94151 - 5.94151i) q^{58} -87.7441i q^{59} +(3.99976 - 16.8524i) q^{60} +20.2409 q^{61} +(-4.19616 - 4.19616i) q^{62} +(0.557944 - 0.557944i) q^{63} -8.00000i q^{64} +(115.515 + 27.4165i) q^{65} -43.1988 q^{66} +(5.03763 + 5.03763i) q^{67} +(-39.6134 + 39.6134i) q^{68} +8.30662i q^{69} +(-1.58323 + 0.975853i) q^{70} +42.6028 q^{71} +(6.00000 + 6.00000i) q^{72} +(25.5335 - 25.5335i) q^{73} -91.8308i q^{74} +(-13.5940 - 41.1121i) q^{75} -32.4416 q^{76} +(3.27994 + 3.27994i) q^{77} +(-41.1273 + 41.1273i) q^{78} +85.8118i q^{79} +(-10.4941 - 17.0257i) q^{80} -9.00000 q^{81} +(-37.8568 - 37.8568i) q^{82} +(-49.0744 + 49.0744i) q^{83} -0.911118i q^{84} +(-32.3423 + 136.269i) q^{85} -49.1006 q^{86} +(7.27683 + 7.27683i) q^{87} +(-35.2717 + 35.2717i) q^{88} -64.8558i q^{89} +(20.6398 + 4.89868i) q^{90} +6.24530 q^{91} +(6.78233 + 6.78233i) q^{92} +(5.13922 - 5.13922i) q^{93} +60.2624i q^{94} +(-69.0426 + 42.5557i) q^{95} +9.79796 q^{96} +(-63.8100 - 63.8100i) q^{97} +(48.9308 - 48.9308i) q^{98} -52.9075i 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

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Representations

Groups

Database

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