LMFDB - Embedded newform 690.3.k.a.553.2

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			553.2
Character	$\chi$	$=$	690.553
Dual form			690.3.k.a.277.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(2.69807 - 4.20956i) q^{5} -2.44949 q^{6} +(-5.61863 + 5.61863i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(1.00000 - 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(2.69807 - 4.20956i) q^{5} -2.44949 q^{6} +(-5.61863 + 5.61863i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +(-1.51149 - 6.90763i) q^{10} -12.8664 q^{11} +(-2.44949 + 2.44949i) q^{12} +(9.49626 + 9.49626i) q^{13} +11.2373i q^{14} +(-8.46009 + 1.85119i) q^{15} -4.00000 q^{16} +(-16.0031 + 16.0031i) q^{17} +(3.00000 + 3.00000i) q^{18} +27.2561i q^{19} +(-8.41912 - 5.39614i) q^{20} +13.7628 q^{21} +(-12.8664 + 12.8664i) q^{22} +(-3.39116 - 3.39116i) q^{23} +4.89898i q^{24} +(-10.4408 - 22.7154i) q^{25} +18.9925 q^{26} +(3.67423 - 3.67423i) q^{27} +(11.2373 + 11.2373i) q^{28} -10.8625i q^{29} +(-6.60890 + 10.3113i) q^{30} +11.1289 q^{31} +(-4.00000 + 4.00000i) q^{32} +(15.7581 + 15.7581i) q^{33} +32.0062i q^{34} +(8.49251 + 38.8114i) q^{35} +6.00000 q^{36} +(23.3287 - 23.3287i) q^{37} +(27.2561 + 27.2561i) q^{38} -23.2610i q^{39} +(-13.8153 + 3.02298i) q^{40} -48.0560 q^{41} +(13.7628 - 13.7628i) q^{42} +(19.0800 + 19.0800i) q^{43} +25.7328i q^{44} +(12.6287 + 8.09421i) q^{45} -6.78233 q^{46} +(-56.5992 + 56.5992i) q^{47} +(4.89898 + 4.89898i) q^{48} -14.1380i q^{49} +(-33.1562 - 12.2746i) q^{50} +39.1994 q^{51} +(18.9925 - 18.9925i) q^{52} +(-40.7367 - 40.7367i) q^{53} -7.34847i q^{54} +(-34.7145 + 54.1620i) q^{55} +22.4745 q^{56} +(33.3817 - 33.3817i) q^{57} +(-10.8625 - 10.8625i) q^{58} +63.6669i q^{59} +(3.70238 + 16.9202i) q^{60} +104.528 q^{61} +(11.1289 - 11.1289i) q^{62} +(-16.8559 - 16.8559i) q^{63} +8.00000i q^{64} +(65.5967 - 14.3535i) q^{65} +31.5162 q^{66} +(-3.47681 + 3.47681i) q^{67} +(32.0062 + 32.0062i) q^{68} +8.30662i q^{69} +(47.3039 + 30.3189i) q^{70} -90.8333 q^{71} +(6.00000 - 6.00000i) q^{72} +(6.81243 + 6.81243i) q^{73} -46.6573i q^{74} +(-15.0332 + 40.6079i) q^{75} +54.5121 q^{76} +(72.2917 - 72.2917i) q^{77} +(-23.2610 - 23.2610i) q^{78} -103.414i q^{79} +(-10.7923 + 16.8382i) q^{80} -9.00000 q^{81} +(-48.0560 + 48.0560i) q^{82} +(87.6868 + 87.6868i) q^{83} -27.5255i q^{84} +(24.1885 + 110.543i) q^{85} +38.1600 q^{86} +(-13.3038 + 13.3038i) q^{87} +(25.7328 + 25.7328i) q^{88} -65.1773i q^{89} +(20.7229 - 4.53448i) q^{90} -106.712 q^{91} +(-6.78233 + 6.78233i) q^{92} +(-13.6301 - 13.6301i) q^{93} +113.198i q^{94} +(114.736 + 73.5388i) q^{95} +9.79796 q^{96} +(-121.933 + 121.933i) q^{97} +(-14.1380 - 14.1380i) q^{98} -38.5993i 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 $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	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
$5$	2.69807	−	4.20956i	0.539614	−	0.841912i
$5$	2.69807	−	4.20956i	0.539614	−	0.841912i
$6$	−2.44949			−0.408248
$7$	−5.61863	+	5.61863i	−0.802661	+	0.802661i	−0.983511	−	0.180849i	$-0.942115\pi$
$7$	−5.61863	+	5.61863i	−0.802661	+	0.802661i	0.180849	+	0.983511i	$0.442115\pi$
$8$	−2.00000	−	2.00000i	−0.250000	−	0.250000i
$9$			3.00000i			0.333333i
$10$	−1.51149	−	6.90763i	−0.151149	−	0.690763i
$11$	−12.8664			−1.16967			−0.584837	−	0.811151i	$-0.698842\pi$
$11$	−12.8664			−1.16967			−0.584837	+	0.811151i	$0.698842\pi$
$12$	−2.44949	+	2.44949i	−0.204124	+	0.204124i
$13$	9.49626	+	9.49626i	0.730481	+	0.730481i	0.970715	−	0.240234i	$-0.0772241\pi$
$13$	9.49626	+	9.49626i	0.730481	+	0.730481i	−0.240234	+	0.970715i	$0.577224\pi$
$14$			11.2373i			0.802661i
$15$	−8.46009	+	1.85119i	−0.564006	+	0.123413i
$16$	−4.00000			−0.250000
$17$	−16.0031	+	16.0031i	−0.941358	+	0.941358i	−0.998373	−	0.0570149i	$-0.981842\pi$
$17$	−16.0031	+	16.0031i	−0.941358	+	0.941358i	0.0570149	+	0.998373i	$0.481842\pi$
$18$	3.00000	+	3.00000i	0.166667	+	0.166667i
$19$			27.2561i			1.43453i	0.696800	+	0.717265i	$0.254606\pi$
$19$			27.2561i			1.43453i	−0.696800	+	0.717265i	$0.745394\pi$
$20$	−8.41912	−	5.39614i	−0.420956	−	0.269807i
$21$	13.7628			0.655370
$22$	−12.8664	+	12.8664i	−0.584837	+	0.584837i
$23$	−3.39116	−	3.39116i	−0.147442	−	0.147442i
$23$	−3.39116	−	3.39116i	−0.147442	−	0.147442i
$24$			4.89898i			0.204124i
$25$	−10.4408	−	22.7154i	−0.417633	−	0.908616i
$26$	18.9925			0.730481
$27$	3.67423	−	3.67423i	0.136083	−	0.136083i
$28$	11.2373	+	11.2373i	0.401331	+	0.401331i
$29$		−	10.8625i		−	0.374569i	−0.982306	−	0.187284i	$-0.940031\pi$
$29$		−	10.8625i		−	0.374569i	0.982306	−	0.187284i	$-0.0599686\pi$
$30$	−6.60890	+	10.3113i	−0.220297	+	0.343709i
$31$	11.1289			0.358997			0.179499	−	0.983758i	$-0.442552\pi$
$31$	11.1289			0.358997			0.179499	+	0.983758i	$0.442552\pi$
$32$	−4.00000	+	4.00000i	−0.125000	+	0.125000i
$33$	15.7581	+	15.7581i	0.477518	+	0.477518i
$34$			32.0062i			0.941358i
$35$	8.49251	+	38.8114i	0.242643	+	1.10890i
$36$	6.00000			0.166667
$37$	23.3287	−	23.3287i	0.630504	−	0.630504i	−0.317690	−	0.948195i	$-0.602907\pi$
$37$	23.3287	−	23.3287i	0.630504	−	0.630504i	0.948195	+	0.317690i	$0.102907\pi$
$38$	27.2561	+	27.2561i	0.717265	+	0.717265i
$39$		−	23.2610i		−	0.596435i
$40$	−13.8153	+	3.02298i	−0.345382	+	0.0755746i
$41$	−48.0560			−1.17210			−0.586049	−	0.810276i	$-0.699317\pi$
$41$	−48.0560			−1.17210			−0.586049	+	0.810276i	$0.699317\pi$
$42$	13.7628	−	13.7628i	0.327685	−	0.327685i
$43$	19.0800	+	19.0800i	0.443721	+	0.443721i	0.893260	−	0.449540i	$-0.148412\pi$
$43$	19.0800	+	19.0800i	0.443721	+	0.443721i	−0.449540	+	0.893260i	$0.648412\pi$
$44$			25.7328i			0.584837i
$45$	12.6287	+	8.09421i	0.280637	+	0.179871i
$46$	−6.78233			−0.147442
$47$	−56.5992	+	56.5992i	−1.20424	+	1.20424i	−0.231374	+	0.972865i	$0.574322\pi$
$47$	−56.5992	+	56.5992i	−1.20424	+	1.20424i	−0.972865	+	0.231374i	$0.925678\pi$
$48$	4.89898	+	4.89898i	0.102062	+	0.102062i
$49$		−	14.1380i		−	0.288530i
$50$	−33.1562	−	12.2746i	−0.663124	−	0.245491i
$51$	39.1994			0.768616
$52$	18.9925	−	18.9925i	0.365241	−	0.365241i
$53$	−40.7367	−	40.7367i	−0.768617	−	0.768617i	0.209246	−	0.977863i	$-0.432899\pi$
$53$	−40.7367	−	40.7367i	−0.768617	−	0.768617i	−0.977863	+	0.209246i	$0.932899\pi$
$54$		−	7.34847i		−	0.136083i
$55$	−34.7145	+	54.1620i	−0.631173	+	0.984764i
$56$	22.4745			0.401331
$57$	33.3817	−	33.3817i	0.585644	−	0.585644i
$58$	−10.8625	−	10.8625i	−0.187284	−	0.187284i
$59$			63.6669i			1.07910i	0.841954	+	0.539550i	$0.181406\pi$
$59$			63.6669i			1.07910i	−0.841954	+	0.539550i	$0.818594\pi$
$60$	3.70238	+	16.9202i	0.0617064	+	0.282003i
$61$	104.528			1.71358			0.856788	−	0.515670i	$-0.172457\pi$
$61$	104.528			1.71358			0.856788	+	0.515670i	$0.172457\pi$
$62$	11.1289	−	11.1289i	0.179499	−	0.179499i
$63$	−16.8559	−	16.8559i	−0.267554	−	0.267554i
$64$			8.00000i			0.125000i
$65$	65.5967	−	14.3535i	1.00918	−	0.220823i
$66$	31.5162			0.477518
$67$	−3.47681	+	3.47681i	−0.0518926	+	0.0518926i	−0.732577	−	0.680684i	$-0.761683\pi$
$67$	−3.47681	+	3.47681i	−0.0518926	+	0.0518926i	0.680684	+	0.732577i	$0.261683\pi$
$68$	32.0062	+	32.0062i	0.470679	+	0.470679i
$69$			8.30662i			0.120386i
$70$	47.3039	+	30.3189i	0.675771	+	0.433127i
$71$	−90.8333			−1.27934			−0.639671	−	0.768649i	$-0.720930\pi$
$71$	−90.8333			−1.27934			−0.639671	+	0.768649i	$0.720930\pi$
$72$	6.00000	−	6.00000i	0.0833333	−	0.0833333i
$73$	6.81243	+	6.81243i	0.0933210	+	0.0933210i	0.752226	−	0.658905i	$-0.228980\pi$
$73$	6.81243	+	6.81243i	0.0933210	+	0.0933210i	−0.658905	+	0.752226i	$0.728980\pi$
$74$		−	46.6573i		−	0.630504i
$75$	−15.0332	+	40.6079i	−0.200443	+	0.541439i
$76$	54.5121			0.717265
$77$	72.2917	−	72.2917i	0.938853	−	0.938853i
$78$	−23.2610	−	23.2610i	−0.298218	−	0.298218i
$79$		−	103.414i		−	1.30904i	−0.756045	−	0.654520i	$-0.772871\pi$
$79$		−	103.414i		−	1.30904i	0.756045	−	0.654520i	$-0.227129\pi$
$80$	−10.7923	+	16.8382i	−0.134904	+	0.210478i
$81$	−9.00000			−0.111111
$82$	−48.0560	+	48.0560i	−0.586049	+	0.586049i
$83$	87.6868	+	87.6868i	1.05647	+	1.05647i	0.998307	+	0.0581608i	$0.0185236\pi$
$83$	87.6868	+	87.6868i	1.05647	+	1.05647i	0.0581608	+	0.998307i	$0.481476\pi$
$84$		−	27.5255i		−	0.327685i
$85$	24.1885	+	110.543i	0.284571	+	1.30051i
$86$	38.1600			0.443721
$87$	−13.3038	+	13.3038i	−0.152917	+	0.152917i
$88$	25.7328	+	25.7328i	0.292419	+	0.292419i
$89$		−	65.1773i		−	0.732329i	−0.930550	−	0.366165i	$-0.880671\pi$
$89$		−	65.1773i		−	0.732329i	0.930550	−	0.366165i	$-0.119329\pi$
$90$	20.7229	−	4.53448i	0.230254	−	0.0503831i
$91$	−106.712			−1.17266
$92$	−6.78233	+	6.78233i	−0.0737210	+	0.0737210i
$93$	−13.6301	−	13.6301i	−0.146560	−	0.146560i
$94$			113.198i			1.20424i
$95$	114.736	+	73.5388i	1.20775	+	0.774093i
$96$	9.79796			0.102062
$97$	−121.933	+	121.933i	−1.25704	+	1.25704i	−0.304547	+	0.952497i	$0.598505\pi$
$97$	−121.933	+	121.933i	−1.25704	+	1.25704i	−0.952497	+	0.304547i	$0.901495\pi$
$98$	−14.1380	−	14.1380i	−0.144265	−	0.144265i
$99$		−	38.5993i		−	0.389892i
$100$	−45.4308	+	20.8817i	−0.454308	+	0.208817i
$101$	−129.221			−1.27941			−0.639705	−	0.768620i	$-0.720944\pi$
$101$	−129.221			−1.27941			−0.639705	+	0.768620i	$0.720944\pi$
$102$	39.1994	−	39.1994i	0.384308	−	0.384308i
$103$	−4.11421	−	4.11421i	−0.0399438	−	0.0399438i	0.686853	−	0.726797i	$-0.258992\pi$
$103$	−4.11421	−	4.11421i	−0.0399438	−	0.0399438i	−0.726797	+	0.686853i	$0.758992\pi$
$104$		−	37.9850i		−	0.365241i
$105$	37.1329	−	57.9353i	0.353647	−	0.551764i
$106$	−81.4734			−0.768617
$107$	24.7912	−	24.7912i	0.231693	−	0.231693i	−0.581706	−	0.813399i	$-0.697615\pi$
$107$	24.7912	−	24.7912i	0.231693	−	0.231693i	0.813399	+	0.581706i	$0.197615\pi$
$108$	−7.34847	−	7.34847i	−0.0680414	−	0.0680414i
$109$		−	0.116226i		−	0.00106629i	−1.00000		0.000533145i	$-0.999830\pi$
$109$		−	0.116226i		−	0.00106629i	1.00000		0.000533145i	$-0.000169705\pi$
$110$	19.4475	+	88.8765i	0.176795	+	0.807968i
$111$	−57.1433			−0.514805
$112$	22.4745	−	22.4745i	0.200665	−	0.200665i
$113$	150.629	+	150.629i	1.33300	+	1.33300i	0.902669	+	0.430335i	$0.141604\pi$
$113$	150.629	+	150.629i	1.33300	+	1.33300i	0.430335	+	0.902669i	$0.358396\pi$
$114$		−	66.7635i		−	0.585644i
$115$	−23.4249	+	5.12572i	−0.203695	+	0.0445715i
$116$	−21.7250			−0.187284
$117$	−28.4888	+	28.4888i	−0.243494	+	0.243494i
$118$	63.6669	+	63.6669i	0.539550	+	0.539550i
$119$		−	179.831i		−	1.51118i
$120$	20.6226	+	13.2178i	0.171855	+	0.110148i
$121$	44.5449			0.368139
$122$	104.528	−	104.528i	0.856788	−	0.856788i
$123$	58.8564	+	58.8564i	0.478507	+	0.478507i
$124$		−	22.2578i		−	0.179499i
$125$	−123.792	−	17.3364i	−0.990336	−	0.138691i
$126$	−33.7118			−0.267554
$127$	−153.452	+	153.452i	−1.20829	+	1.20829i	−0.236705	+	0.971582i	$0.576068\pi$
$127$	−153.452	+	153.452i	−1.20829	+	1.20829i	−0.971582	+	0.236705i	$0.923932\pi$
$128$	8.00000	+	8.00000i	0.0625000	+	0.0625000i
$129$		−	46.7362i		−	0.362296i
$130$	51.2431	−	79.9502i	0.394178	−	0.615001i
$131$	−233.897			−1.78548			−0.892738	−	0.450576i	$-0.851219\pi$
$131$	−233.897			−1.78548			−0.892738	+	0.450576i	$0.851219\pi$
$132$	31.5162	−	31.5162i	0.238759	−	0.238759i
$133$	−153.142	−	153.142i	−1.15144	−	1.15144i
$134$			6.95361i			0.0518926i
$135$	−5.55358	−	25.3803i	−0.0411376	−	0.188002i
$136$	64.0124			0.470679
$137$	40.9626	−	40.9626i	0.298997	−	0.298997i	−0.541624	−	0.840621i	$-0.682190\pi$
$137$	40.9626	−	40.9626i	0.298997	−	0.298997i	0.840621	+	0.541624i	$0.182190\pi$
$138$	8.30662	+	8.30662i	0.0601929	+	0.0601929i
$139$			148.538i			1.06862i	0.845290	+	0.534308i	$0.179428\pi$
$139$			148.538i			1.06862i	−0.845290	+	0.534308i	$0.820572\pi$
$140$	77.6229	−	16.9850i	0.554449	−	0.121322i
$141$	138.639			0.983257
$142$	−90.8333	+	90.8333i	−0.639671	+	0.639671i
$143$	−122.183	−	122.183i	−0.854426	−	0.854426i
$144$		−	12.0000i		−	0.0833333i
$145$	−45.7264	−	29.3078i	−0.315354	−	0.202123i
$146$	13.6249			0.0933210
$147$	−17.3154	+	17.3154i	−0.117792	+	0.117792i
$148$	−46.6573	−	46.6573i	−0.315252	−	0.315252i
$149$		−	10.9701i		−	0.0736249i	−0.999322	−	0.0368125i	$-0.988280\pi$
$149$		−	10.9701i		−	0.0736249i	0.999322	−	0.0368125i	$-0.0117204\pi$
$150$	25.5747	+	55.6411i	0.170498	+	0.370941i
$151$	−109.516			−0.725269			−0.362635	−	0.931931i	$-0.618123\pi$
$151$	−109.516			−0.725269			−0.362635	+	0.931931i	$0.618123\pi$
$152$	54.5121	−	54.5121i	0.358633	−	0.358633i
$153$	−48.0093	−	48.0093i	−0.313786	−	0.313786i
$154$		−	144.583i		−	0.938853i
$155$	30.0266	−	46.8479i	0.193720	−	0.302244i
$156$	−46.5220			−0.298218
$157$	91.3919	−	91.3919i	0.582114	−	0.582114i	−0.353370	−	0.935484i	$-0.614964\pi$
$157$	91.3919	−	91.3919i	0.582114	−	0.582114i	0.935484	+	0.353370i	$0.114964\pi$
$158$	−103.414	−	103.414i	−0.654520	−	0.654520i
$159$			99.7841i			0.627573i
$160$	6.04597	+	27.6305i	0.0377873	+	0.172691i
$161$	38.1074			0.236692
$162$	−9.00000	+	9.00000i	−0.0555556	+	0.0555556i
$163$	48.2405	+	48.2405i	0.295954	+	0.295954i	0.839427	−	0.543473i	$-0.182891\pi$
$163$	48.2405	+	48.2405i	0.295954	+	0.295954i	−0.543473	+	0.839427i	$0.682891\pi$
$164$			96.1120i			0.586049i
$165$	108.851	−	23.8182i	0.659704	−	0.144353i
$166$	175.374			1.05647
$167$	194.552	−	194.552i	1.16498	−	1.16498i	0.181609	−	0.983371i	$-0.441869\pi$
$167$	194.552	−	194.552i	1.16498	−	1.16498i	0.983371	−	0.181609i	$-0.0581305\pi$
$168$	−27.5255	−	27.5255i	−0.163843	−	0.163843i
$169$			11.3578i			0.0672057i
$170$	134.732	+	86.3549i	0.792541	+	0.507970i
$171$	−81.7682			−0.478177
$172$	38.1600	−	38.1600i	0.221860	−	0.221860i
$173$	−126.996	−	126.996i	−0.734081	−	0.734081i	0.237344	−	0.971426i	$-0.423723\pi$
$173$	−126.996	−	126.996i	−0.734081	−	0.734081i	−0.971426	+	0.237344i	$0.923723\pi$
$174$			26.6076i			0.152917i
$175$	186.293	+	68.9662i	1.06453	+	0.394093i
$176$	51.4657			0.292419
$177$	77.9757	−	77.9757i	0.440541	−	0.440541i
$178$	−65.1773	−	65.1773i	−0.366165	−	0.366165i
$179$		−	281.606i		−	1.57322i	−0.617453	−	0.786608i	$-0.711835\pi$
$179$		−	281.606i		−	1.57322i	0.617453	−	0.786608i	$-0.288165\pi$
$180$	16.1884	−	25.2574i	0.0899357	−	0.140319i
$181$	−153.271			−0.846803			−0.423402	−	0.905942i	$-0.639164\pi$
$181$	−153.271			−0.846803			−0.423402	+	0.905942i	$0.639164\pi$
$182$	−106.712	+	106.712i	−0.586329	+	0.586329i
$183$	−128.020	−	128.020i	−0.699564	−	0.699564i
$184$			13.5647i			0.0737210i
$185$	−35.2611	−	161.146i	−0.190600	−	0.871059i
$186$	−27.2602			−0.146560
$187$	205.903	−	205.903i	1.10108	−	1.10108i
$188$	113.198	+	113.198i	0.602119	+	0.602119i
$189$			41.2883i			0.218457i
$190$	188.275	−	41.1973i	0.990921	−	0.216828i
$191$	−326.257			−1.70815			−0.854076	−	0.520148i	$-0.825877\pi$
$191$	−326.257			−1.70815			−0.854076	+	0.520148i	$0.825877\pi$
$192$	9.79796	−	9.79796i	0.0510310	−	0.0510310i
$193$	113.315	+	113.315i	0.587123	+	0.587123i	0.936851	−	0.349728i	$-0.113726\pi$
$193$	113.315	+	113.315i	0.587123	+	0.587123i	−0.349728	+	0.936851i	$0.613726\pi$
$194$			243.867i			1.25704i
$195$	−97.9186	−	62.7598i	−0.502146	−	0.321845i
$196$	−28.2760			−0.144265
$197$	62.0545	−	62.0545i	0.314997	−	0.314997i	−0.531845	−	0.846842i	$-0.678501\pi$
$197$	62.0545	−	62.0545i	0.314997	−	0.314997i	0.846842	+	0.531845i	$0.178501\pi$
$198$	−38.5993	−	38.5993i	−0.194946	−	0.194946i
$199$		−	132.815i		−	0.667412i	−0.942677	−	0.333706i	$-0.891701\pi$
$199$		−	132.815i		−	0.667412i	0.942677	−	0.333706i	$-0.108299\pi$
$200$	−24.5491	+	66.3124i	−0.122746	+	0.331562i
$201$	8.51640			0.0423702
$202$	−129.221	+	129.221i	−0.639705	+	0.639705i
$203$	61.0324	+	61.0324i	0.300652	+	0.300652i
$204$		−	78.3988i		−	0.384308i
$205$	−129.659	+	202.295i	−0.632481	+	0.986804i
$206$	−8.22842			−0.0399438
$207$	10.1735	−	10.1735i	0.0491473	−	0.0491473i
$208$	−37.9850	−	37.9850i	−0.182620	−	0.182620i
$209$		−	350.688i		−	1.67793i
$210$	−20.8023	−	95.0682i	−0.0990587	−	0.452706i
$211$	−202.742			−0.960861			−0.480430	−	0.877033i	$-0.659520\pi$
$211$	−202.742			−0.960861			−0.480430	+	0.877033i	$0.659520\pi$
$212$	−81.4734	+	81.4734i	−0.384308	+	0.384308i
$213$	111.248	+	111.248i	0.522289	+	0.522289i
$214$		−	49.5823i		−	0.231693i
$215$	131.798	−	28.8392i	0.613012	−	0.134136i
$216$	−14.6969			−0.0680414
$217$	−62.5293	+	62.5293i	−0.288153	+	0.288153i
$218$	−0.116226	−	0.116226i	−0.000533145	−	0.000533145i
$219$		−	16.6870i		−	0.0761962i
$220$	108.324	+	69.4290i	0.492382	+	0.315587i
$221$	−303.939			−1.37529
$222$	−57.1433	+	57.1433i	−0.257402	+	0.257402i
$223$	−11.5319	−	11.5319i	−0.0517127	−	0.0517127i	0.680778	−	0.732490i	$-0.261642\pi$
$223$	−11.5319	−	11.5319i	−0.0517127	−	0.0517127i	−0.732490	+	0.680778i	$0.761642\pi$
$224$		−	44.9490i		−	0.200665i
$225$	68.1462	−	31.3225i	0.302872	−	0.139211i
$226$	301.259			1.33300
$227$	163.407	−	163.407i	0.719853	−	0.719853i	−0.248722	−	0.968575i	$-0.580011\pi$
$227$	163.407	−	163.407i	0.719853	−	0.719853i	0.968575	+	0.248722i	$0.0800105\pi$
$228$	−66.7635	−	66.7635i	−0.292822	−	0.292822i
$229$		−	154.404i		−	0.674251i	−0.941460	−	0.337126i	$-0.890545\pi$
$229$		−	154.404i		−	0.674251i	0.941460	−	0.337126i	$-0.109455\pi$
$230$	−18.2992	+	28.5506i	−0.0795618	+	0.124133i
$231$	−177.078			−0.766570
$232$	−21.7250	+	21.7250i	−0.0936422	+	0.0936422i
$233$	−259.278	−	259.278i	−1.11278	−	1.11278i	−0.992773	−	0.120009i	$-0.961708\pi$
$233$	−259.278	−	259.278i	−1.11278	−	1.11278i	−0.120009	−	0.992773i	$-0.538292\pi$
$234$			56.9775i			0.243494i
$235$	85.5493	+	390.967i	0.364039	+	1.66369i
$236$	127.334			0.539550
$237$	−126.656	+	126.656i	−0.534413	+	0.534413i
$238$	−179.831	−	179.831i	−0.755592	−	0.755592i
$239$			89.5241i			0.374578i	0.982305	+	0.187289i	$0.0599701\pi$
$239$			89.5241i			0.374578i	−0.982305	+	0.187289i	$0.940030\pi$
$240$	33.8404	−	7.40477i	0.141001	−	0.0308532i
$241$	−153.366			−0.636373			−0.318187	−	0.948028i	$-0.603074\pi$
$241$	−153.366			−0.636373			−0.318187	+	0.948028i	$0.603074\pi$
$242$	44.5449	−	44.5449i	0.184070	−	0.184070i
$243$	11.0227	+	11.0227i	0.0453609	+	0.0453609i
$244$		−	209.056i		−	0.856788i
$245$	−59.5148	−	38.1453i	−0.242917	−	0.155695i
$246$	117.713			0.478507
$247$	−258.831	+	258.831i	−1.04790	+	1.04790i
$248$	−22.2578	−	22.2578i	−0.0897493	−	0.0897493i
$249$		−	214.788i		−	0.862603i
$250$	−141.128	+	106.456i	−0.564513	+	0.425822i
$251$	−190.513			−0.759016			−0.379508	−	0.925188i	$-0.623907\pi$
$251$	−190.513			−0.759016			−0.379508	+	0.925188i	$0.623907\pi$
$252$	−33.7118	+	33.7118i	−0.133777	+	0.133777i
$253$	43.6322	+	43.6322i	0.172459	+	0.172459i
$254$			306.905i			1.20829i
$255$	105.763	−	165.012i	0.414756	−	0.647107i
$256$	16.0000			0.0625000
$257$	−116.546	+	116.546i	−0.453486	+	0.453486i	−0.896510	−	0.443024i	$-0.853906\pi$
$257$	−116.546	+	116.546i	−0.453486	+	0.453486i	0.443024	+	0.896510i	$0.353906\pi$
$258$	−46.7362	−	46.7362i	−0.181148	−	0.181148i
$259$			262.150i			1.01216i
$260$	−28.7070	−	131.193i	−0.110412	−	0.504590i
$261$	32.5875			0.124856
$262$	−233.897	+	233.897i	−0.892738	+	0.892738i
$263$	267.847	+	267.847i	1.01843	+	1.01843i	0.999827	+	0.0186010i	$0.00592123\pi$
$263$	267.847	+	267.847i	1.01843	+	1.01843i	0.0186010	+	0.999827i	$0.494079\pi$
$264$		−	63.0323i		−	0.238759i
$265$	−281.394	+	61.5732i	−1.06186	+	0.232352i
$266$	−306.284			−1.15144
$267$	−79.8256	+	79.8256i	−0.298972	+	0.298972i
$268$	6.95361	+	6.95361i	0.0259463	+	0.0259463i
$269$			161.335i			0.599757i	0.953977	+	0.299879i	$0.0969462\pi$
$269$			161.335i			0.599757i	−0.953977	+	0.299879i	$0.903054\pi$
$270$	−30.9338	−	19.8267i	−0.114570	−	0.0734322i
$271$	182.280			0.672620			0.336310	−	0.941751i	$-0.390821\pi$
$271$	182.280			0.672620			0.336310	+	0.941751i	$0.390821\pi$
$272$	64.0124	−	64.0124i	0.235340	−	0.235340i
$273$	130.695	+	130.695i	0.478736	+	0.478736i
$274$		−	81.9252i		−	0.298997i
$275$	134.336	+	292.266i	0.488495	+	1.06278i
$276$	16.6132			0.0601929
$277$	211.687	−	211.687i	0.764215	−	0.764215i	−0.212867	−	0.977081i	$-0.568280\pi$
$277$	211.687	−	211.687i	0.764215	−	0.764215i	0.977081	+	0.212867i	$0.0682800\pi$
$278$	148.538	+	148.538i	0.534308	+	0.534308i
$279$			33.3868i			0.119666i
$280$	60.6378	−	94.6079i	0.216564	−	0.337885i
$281$	195.698			0.696433			0.348216	−	0.937414i	$-0.386787\pi$
$281$	195.698			0.696433			0.348216	+	0.937414i	$0.386787\pi$
$282$	138.639	−	138.639i	0.491628	−	0.491628i
$283$	282.722	+	282.722i	0.999016	+	0.999016i	1.00000		0.000983541i	$-0.000313071\pi$
$283$	282.722	+	282.722i	0.999016	+	0.999016i	−0.000983541		1.00000i	$0.500313\pi$
$284$			181.667i			0.639671i
$285$	−50.4562	−	230.589i	−0.177039	−	0.809083i
$286$	−244.366			−0.854426
$287$	270.009	−	270.009i	0.940798	−	0.940798i
$288$	−12.0000	−	12.0000i	−0.0416667	−	0.0416667i
$289$		−	223.198i		−	0.772311i
$290$	−75.0342	+	16.4186i	−0.258738	+	0.0566158i
$291$	298.674			1.02637
$292$	13.6249	−	13.6249i	0.0466605	−	0.0466605i
$293$	303.769	+	303.769i	1.03676	+	1.03676i	0.999298	+	0.0374575i	$0.0119259\pi$
$293$	303.769	+	303.769i	1.03676	+	1.03676i	0.0374575	+	0.999298i	$0.488074\pi$
$294$			34.6309i			0.117792i
$295$	268.010	+	171.778i	0.908508	+	0.582298i
$296$	−93.3147			−0.315252
$297$	−47.2743	+	47.2743i	−0.159173	+	0.159173i
$298$	−10.9701	−	10.9701i	−0.0368125	−	0.0368125i
$299$		−	64.4067i		−	0.215407i
$300$	81.2158	+	30.0664i	0.270719	+	0.100221i
$301$	−214.407			−0.712315
$302$	−109.516	+	109.516i	−0.362635	+	0.362635i
$303$	158.262	+	158.262i	0.522317	+	0.522317i
$304$		−	109.024i		−	0.358633i
$305$	282.024	−	440.017i	0.924669	−	1.44268i
$306$	−96.0186			−0.313786
$307$	−381.391	+	381.391i	−1.24231	+	1.24231i	−0.283276	+	0.959038i	$0.591421\pi$
$307$	−381.391	+	381.391i	−1.24231	+	1.24231i	−0.959038	+	0.283276i	$0.908579\pi$
$308$	−144.583	−	144.583i	−0.469426	−	0.469426i
$309$			10.0777i			0.0326139i
$310$	−16.8213	−	76.8745i	−0.0542622	−	0.247982i
$311$	34.0026			0.109333			0.0546666	−	0.998505i	$-0.482590\pi$
$311$	34.0026			0.109333			0.0546666	+	0.998505i	$0.482590\pi$
$312$	−46.5220	+	46.5220i	−0.149109	+	0.149109i
$313$	−62.9469	−	62.9469i	−0.201108	−	0.201108i	0.599366	−	0.800475i	$-0.295419\pi$
$313$	−62.9469	−	62.9469i	−0.201108	−	0.201108i	−0.800475	+	0.599366i	$0.795419\pi$
$314$		−	182.784i		−	0.582114i
$315$	−116.434	+	25.4775i	−0.369633	+	0.0808811i
$316$	−206.828			−0.654520
$317$	−144.059	+	144.059i	−0.454444	+	0.454444i	−0.896826	−	0.442383i	$-0.854133\pi$
$317$	−144.059	+	144.059i	−0.454444	+	0.454444i	0.442383	+	0.896826i	$0.354133\pi$
$318$	99.7841	+	99.7841i	0.313786	+	0.313786i
$319$			139.762i			0.438124i
$320$	33.6765	+	21.5846i	0.105239	+	0.0674518i
$321$	−60.7257			−0.189177
$322$	38.1074	−	38.1074i	0.118346	−	0.118346i
$323$	−436.181	−	436.181i	−1.35041	−	1.35041i
$324$			18.0000i			0.0555556i
$325$	116.562	−	314.860i	0.358653	−	0.968800i
$326$	96.4810			0.295954
$327$	−0.142347	+	0.142347i	−0.000435311	+	0.000435311i
$328$	96.1120	+	96.1120i	0.293025	+	0.293025i
$329$		−	636.020i		−	1.93319i
$330$	85.0329	−	132.669i	0.257675	−	0.402028i
$331$	133.019			0.401871			0.200936	−	0.979604i	$-0.435602\pi$
$331$	133.019			0.401871			0.200936	+	0.979604i	$0.435602\pi$
$332$	175.374	−	175.374i	0.528234	−	0.528234i
$333$	69.9860	+	69.9860i	0.210168	+	0.210168i
$334$		−	389.103i		−	1.16498i
$335$	5.25517	+	24.0165i	0.0156871	+	0.0716911i
$336$	−55.0511			−0.163843
$337$	221.295	−	221.295i	0.656662	−	0.656662i	−0.297926	−	0.954589i	$-0.596295\pi$
$337$	221.295	−	221.295i	0.656662	−	0.656662i	0.954589	+	0.297926i	$0.0962950\pi$
$338$	11.3578	+	11.3578i	0.0336028	+	0.0336028i
$339$		−	368.965i		−	1.08839i
$340$	221.087	−	48.3771i	0.650256	−	0.142286i
$341$	−143.189			−0.419910
$342$	−81.7682	+	81.7682i	−0.239088	+	0.239088i
$343$	−195.877	−	195.877i	−0.571069	−	0.571069i
$344$		−	76.3199i		−	0.221860i
$345$	34.9673	+	22.4119i	0.101354	+	0.0649619i
$346$	−253.992			−0.734081
$347$	5.64579	−	5.64579i	0.0162703	−	0.0162703i	−0.698925	−	0.715195i	$-0.746338\pi$
$347$	5.64579	−	5.64579i	0.0162703	−	0.0162703i	0.715195	+	0.698925i	$0.246338\pi$
$348$	26.6076	+	26.6076i	0.0764586	+	0.0764586i
$349$			356.420i			1.02126i	0.859800	+	0.510631i	$0.170588\pi$
$349$			356.420i			1.02126i	−0.859800	+	0.510631i	$0.829412\pi$
$350$	255.259	−	117.326i	0.729311	−	0.335218i
$351$	69.7829			0.198812
$352$	51.4657	−	51.4657i	0.146209	−	0.146209i
$353$	220.393	+	220.393i	0.624341	+	0.624341i	0.946639	−	0.322297i	$-0.104455\pi$
$353$	220.393	+	220.393i	0.624341	+	0.624341i	−0.322297	+	0.946639i	$0.604455\pi$
$354$		−	155.951i		−	0.440541i
$355$	−245.075	+	382.369i	−0.690351	+	1.07709i
$356$	−130.355			−0.366165
$357$	−220.247	+	220.247i	−0.616938	+	0.616938i
$358$	−281.606	−	281.606i	−0.786608	−	0.786608i
$359$		−	339.199i		−	0.944844i	−0.881373	−	0.472422i	$-0.843380\pi$
$359$		−	339.199i		−	0.944844i	0.881373	−	0.472422i	$-0.156620\pi$
$360$	−9.06895	−	41.4458i	−0.0251915	−	0.115127i
$361$	−381.893			−1.05788
$362$	−153.271	+	153.271i	−0.423402	+	0.423402i
$363$	−54.5561	−	54.5561i	−0.150292	−	0.150292i
$364$			213.424i			0.586329i
$365$	47.0578	−	10.2969i	0.128925	−	0.0282108i
$366$	−256.040			−0.699564
$367$	34.4028	−	34.4028i	0.0937407	−	0.0937407i	−0.658681	−	0.752422i	$-0.728885\pi$
$367$	34.4028	−	34.4028i	0.0937407	−	0.0937407i	0.752422	+	0.658681i	$0.228885\pi$
$368$	13.5647	+	13.5647i	0.0368605	+	0.0368605i
$369$		−	144.168i		−	0.390699i
$370$	−196.407	−	125.885i	−0.530830	−	0.340229i
$371$	457.769			1.23388
$372$	−27.2602	+	27.2602i	−0.0732800	+	0.0732800i
$373$	76.1551	+	76.1551i	0.204169	+	0.204169i	0.801784	−	0.597614i	$-0.203885\pi$
$373$	76.1551	+	76.1551i	0.204169	+	0.204169i	−0.597614	+	0.801784i	$0.703885\pi$
$374$		−	411.805i		−	1.10108i
$375$	130.381	+	172.846i	0.347682	+	0.460923i
$376$	226.397			0.602119
$377$	103.153	−	103.153i	0.273616	−	0.273616i
$378$	41.2883	+	41.2883i	0.109228	+	0.109228i
$379$			101.960i			0.269024i	0.990912	+	0.134512i	$0.0429468\pi$
$379$			101.960i			0.269024i	−0.990912	+	0.134512i	$0.957053\pi$
$380$	147.078	−	229.472i	0.387046	−	0.603874i
$381$	375.880			0.986562
$382$	−326.257	+	326.257i	−0.854076	+	0.854076i
$383$	523.069	+	523.069i	1.36572	+	1.36572i	0.866448	+	0.499267i	$0.166397\pi$
$383$	523.069	+	523.069i	1.36572	+	1.36572i	0.499267	+	0.866448i	$0.333603\pi$
$384$		−	19.5959i		−	0.0510310i
$385$	−109.268	−	499.364i	−0.283814	−	1.29705i
$386$	226.630			0.587123
$387$	−57.2400	+	57.2400i	−0.147907	+	0.147907i
$388$	243.867	+	243.867i	0.628522	+	0.628522i
$389$		−	8.10447i		−	0.0208341i	−0.999946	−	0.0104171i	$-0.996684\pi$
$389$		−	8.10447i		−	0.0208341i	0.999946	−	0.0104171i	$-0.00331591\pi$
$390$	−160.678	+	35.1588i	−0.411996	+	0.0901507i
$391$	108.538			0.277591
$392$	−28.2760	+	28.2760i	−0.0721326	+	0.0721326i
$393$	286.465	+	286.465i	0.728917	+	0.728917i
$394$		−	124.109i		−	0.314997i
$395$	−435.328	−	279.019i	−1.10210	−	0.706376i
$396$	−77.1985			−0.194946
$397$	−46.7570	+	46.7570i	−0.117776	+	0.117776i	−0.763538	−	0.645763i	$-0.776540\pi$
$397$	−46.7570	+	46.7570i	−0.117776	+	0.117776i	0.645763	+	0.763538i	$0.276540\pi$
$398$	−132.815	−	132.815i	−0.333706	−	0.333706i
$399$			375.119i			0.940148i
$400$	41.7633	+	90.8616i	0.104408	+	0.227154i
$401$	212.655			0.530311			0.265156	−	0.964206i	$-0.414577\pi$
$401$	212.655			0.530311			0.265156	+	0.964206i	$0.414577\pi$
$402$	8.51640	−	8.51640i	0.0211851	−	0.0211851i
$403$	105.683	+	105.683i	0.262241	+	0.262241i
$404$			258.441i			0.639705i
$405$	−24.2826	+	37.8861i	−0.0599571	+	0.0935458i
$406$	122.065			0.300652
$407$	−300.156	+	300.156i	−0.737485	+	0.737485i
$408$	−78.3988	−	78.3988i	−0.192154	−	0.192154i
$409$		−	201.150i		−	0.491810i	−0.969294	−	0.245905i	$-0.920915\pi$
$409$		−	201.150i		−	0.491810i	0.969294	−	0.245905i	$-0.0790852\pi$
$410$	72.6363	+	331.953i	0.177162	+	0.809642i
$411$	−100.337			−0.244130
$412$	−8.22842	+	8.22842i	−0.0199719	+	0.0199719i
$413$	−357.721	−	357.721i	−0.866152	−	0.866152i
$414$		−	20.3470i		−	0.0491473i
$415$	605.709	−	132.538i	1.45954	−	0.319369i
$416$	−75.9700			−0.182620
$417$	181.921	−	181.921i	0.436260	−	0.436260i
$418$	−350.688	−	350.688i	−0.838967	−	0.838967i
$419$			284.817i			0.679753i	0.940470	+	0.339877i	$0.110385\pi$
$419$			284.817i			0.679753i	−0.940470	+	0.339877i	$0.889615\pi$
$420$	−115.871	−	74.2659i	−0.275882	−	0.176824i
$421$	−162.868			−0.386860			−0.193430	−	0.981114i	$-0.561961\pi$
$421$	−162.868			−0.386860			−0.193430	+	0.981114i	$0.561961\pi$
$422$	−202.742	+	202.742i	−0.480430	+	0.480430i
$423$	−169.798	−	169.798i	−0.401413	−	0.401413i
$424$			162.947i			0.384308i
$425$	530.602	+	196.431i	1.24848	+	0.462190i
$426$	222.495			0.522289
$427$	−587.305	+	587.305i	−1.37542	+	1.37542i
$428$	−49.5823	−	49.5823i	−0.115847	−	0.115847i
$429$			299.286i			0.697636i
$430$	102.958	−	160.637i	0.239438	−	0.373574i
$431$	740.079			1.71712			0.858561	−	0.512712i	$-0.171359\pi$
$431$	740.079			1.71712			0.858561	+	0.512712i	$0.171359\pi$
$432$	−14.6969	+	14.6969i	−0.0340207	+	0.0340207i
$433$	542.660	+	542.660i	1.25326	+	1.25326i	0.954252	+	0.299003i	$0.0966541\pi$
$433$	542.660	+	542.660i	1.25326	+	1.25326i	0.299003	+	0.954252i	$0.403346\pi$
$434$			125.059i			0.288153i
$435$	20.1086	+	91.8977i	0.0462266	+	0.211259i
$436$	−0.232451			−0.000533145
$437$	92.4298	−	92.4298i	0.211510	−	0.211510i
$438$	−16.6870	−	16.6870i	−0.0380981	−	0.0380981i
$439$		−	484.445i		−	1.10352i	−0.834003	−	0.551760i	$-0.813957\pi$
$439$		−	484.445i		−	1.10352i	0.834003	−	0.551760i	$-0.186043\pi$
$440$	177.753	−	38.8950i	0.403984	−	0.0883977i
$441$	42.4140			0.0961768
$442$	−303.939	+	303.939i	−0.687645	+	0.687645i
$443$	526.218	+	526.218i	1.18785	+	1.18785i	0.977661	+	0.210190i	$0.0674082\pi$
$443$	526.218	+	526.218i	1.18785	+	1.18785i	0.210190	+	0.977661i	$0.432592\pi$
$444$			114.287i			0.257402i
$445$	−274.368	−	175.853i	−0.616557	−	0.395175i
$446$	−23.0638			−0.0517127
$447$	−13.4356	+	13.4356i	−0.0300572	+	0.0300572i
$448$	−44.9490	−	44.9490i	−0.100333	−	0.100333i
$449$			620.540i			1.38205i	0.722831	+	0.691025i	$0.242840\pi$
$449$			620.540i			1.38205i	−0.722831	+	0.691025i	$0.757160\pi$
$450$	36.8237	−	99.4687i	0.0818304	−	0.221041i
$451$	618.309			1.37097
$452$	301.259	−	301.259i	0.666502	−	0.666502i
$453$	134.129	+	134.129i	0.296090	+	0.296090i
$454$		−	326.813i		−	0.719853i
$455$	−287.916	+	449.210i	−0.632783	+	0.987275i
$456$	−133.527			−0.292822
$457$	−2.93906	+	2.93906i	−0.00643119	+	0.00643119i	−0.710315	−	0.703884i	$-0.751448\pi$
$457$	−2.93906	+	2.93906i	−0.00643119	+	0.00643119i	0.703884	+	0.710315i	$0.251448\pi$
$458$	−154.404	−	154.404i	−0.337126	−	0.337126i
$459$			117.598i			0.256205i
$460$	10.2514	+	46.8498i	0.0222857	+	0.101847i
$461$	336.573			0.730093			0.365046	−	0.930989i	$-0.381053\pi$
$461$	336.573			0.730093			0.365046	+	0.930989i	$0.381053\pi$
$462$	−177.078	+	177.078i	−0.383285	+	0.383285i
$463$	−592.717	−	592.717i	−1.28017	−	1.28017i	−0.940572	−	0.339595i	$-0.889710\pi$
$463$	−592.717	−	592.717i	−1.28017	−	1.28017i	−0.339595	−	0.940572i	$-0.610290\pi$
$464$			43.4500i			0.0936422i
$465$	−94.1516	+	20.6018i	−0.202477	+	0.0443049i
$466$	−518.556			−1.11278
$467$	−352.885	+	352.885i	−0.755642	+	0.755642i	−0.975526	−	0.219884i	$-0.929432\pi$
$467$	−352.885	+	352.885i	−0.755642	+	0.755642i	0.219884	+	0.975526i	$0.429432\pi$
$468$	56.9775	+	56.9775i	0.121747	+	0.121747i
$469$		−	39.0698i		−	0.0833044i
$470$	476.516	+	305.417i	1.01386	+	0.649824i
$471$	−223.864			−0.475294
$472$	127.334	−	127.334i	0.269775	−	0.269775i
$473$	−245.491	−	245.491i	−0.519009	−	0.519009i
$474$			253.312i			0.534413i
$475$	619.132	−	284.576i	1.30344	−	0.599107i
$476$	−359.662			−0.755592
$477$	122.210	−	122.210i	0.256206	−	0.256206i
$478$	89.5241	+	89.5241i	0.187289	+	0.187289i
$479$		−	160.749i		−	0.335593i	−0.985822	−	0.167797i	$-0.946335\pi$
$479$		−	160.749i		−	0.335593i	0.985822	−	0.167797i	$-0.0536652\pi$
$480$	26.4356	−	41.2451i	0.0550741	−	0.0859273i
$481$	443.070			0.921143
$482$	−153.366	+	153.366i	−0.318187	+	0.318187i
$483$	−46.6718	−	46.6718i	−0.0966291	−	0.0966291i
$484$		−	89.0897i		−	0.184070i
$485$	184.301	+	842.270i	0.380002	+	1.73664i
$486$	22.0454			0.0453609
$487$	−212.553	+	212.553i	−0.436454	+	0.436454i	−0.890817	−	0.454363i	$-0.849867\pi$
$487$	−212.553	+	212.553i	−0.436454	+	0.436454i	0.454363	+	0.890817i	$0.349867\pi$
$488$	−209.056	−	209.056i	−0.428394	−	0.428394i
$489$		−	118.165i		−	0.241645i
$490$	−97.6601	+	21.3695i	−0.199306	+	0.0436111i
$491$	−399.924			−0.814510			−0.407255	−	0.913314i	$-0.633514\pi$
$491$	−399.924			−0.814510			−0.407255	+	0.913314i	$0.633514\pi$
$492$	117.713	−	117.713i	0.239254	−	0.239254i
$493$	173.834	+	173.834i	0.352604	+	0.352604i
$494$			517.661i			1.04790i
$495$	−162.486	−	104.144i	−0.328255	−	0.210391i
$496$	−44.5157			−0.0897493
$497$	510.359	−	510.359i	1.02688	−	1.02688i
$498$	−214.788	−	214.788i	−0.431301	−	0.431301i
$499$		−	284.551i		−	0.570242i	−0.958492	−	0.285121i	$-0.907966\pi$
$499$		−	284.551i		−	0.570242i	0.958492	−	0.285121i	$-0.0920338\pi$
$500$	−34.6728	+	247.584i	−0.0693456	+	0.495168i
$501$	−476.552			−0.951202
$502$	−190.513	+	190.513i	−0.379508	+	0.379508i
$503$	−123.416	−	123.416i	−0.245359	−	0.245359i	0.573704	−	0.819063i	$-0.305506\pi$
$503$	−123.416	−	123.416i	−0.245359	−	0.245359i	−0.819063	+	0.573704i	$0.805506\pi$
$504$			67.4236i			0.133777i
$505$	−348.646	+	543.962i	−0.690388	+	1.07715i
$506$	87.2643			0.172459
$507$	13.9104	−	13.9104i	0.0274366	−	0.0274366i
$508$	306.905	+	306.905i	0.604143	+	0.604143i
$509$		−	501.577i		−	0.985416i	−0.870195	−	0.492708i	$-0.836007\pi$
$509$		−	501.577i		−	0.985416i	0.870195	−	0.492708i	$-0.163993\pi$
$510$	−59.2496	−	270.775i	−0.116176	−	0.530932i
$511$	−76.5530			−0.149810
$512$	16.0000	−	16.0000i	0.0312500	−	0.0312500i
$513$	100.145	+	100.145i	0.195215	+	0.195215i
$514$			233.092i			0.453486i
$515$	−28.4194	+	6.21859i	−0.0551834	+	0.0120749i
$516$	−93.4724			−0.181148
$517$	728.230	−	728.230i	1.40857	−	1.40857i
$518$	262.150	+	262.150i	0.506082	+	0.506082i
$519$			311.076i			0.599375i
$520$	−159.900	−	102.486i	−0.307501	−	0.197089i
$521$	−622.530			−1.19488			−0.597438	−	0.801915i	$-0.703814\pi$
$521$	−622.530			−1.19488			−0.597438	+	0.801915i	$0.703814\pi$
$522$	32.5875	−	32.5875i	0.0624282	−	0.0624282i
$523$	−271.805	−	271.805i	−0.519703	−	0.519703i	0.397779	−	0.917481i	$-0.369781\pi$
$523$	−271.805	−	271.805i	−0.519703	−	0.519703i	−0.917481	+	0.397779i	$0.869781\pi$
$524$			467.795i			0.892738i
$525$	−143.695	−	312.627i	−0.273704	−	0.595480i
$526$	535.693			1.01843
$527$	−178.097	+	178.097i	−0.337945	+	0.337945i
$528$	−63.0323	−	63.0323i	−0.119379	−	0.119379i
$529$			23.0000i			0.0434783i
$530$	−219.821	+	342.967i	−0.414756	+	0.647108i
$531$	−191.001			−0.359700
$532$	−306.284	+	306.284i	−0.575721	+	0.575721i
$533$	−456.352	−	456.352i	−0.856196	−	0.856196i
$534$			159.651i			0.298972i
$535$	−37.4716	−	171.248i	−0.0700404	−	0.320090i
$536$	13.9072			0.0259463
$537$	−344.895	+	344.895i	−0.642263	+	0.642263i
$538$	161.335	+	161.335i	0.299879	+	0.299879i
$539$			181.905i			0.337487i
$540$	−50.7605	+	11.1072i	−0.0940010	+	0.0205688i
$541$	1017.17			1.88017			0.940085	−	0.340940i	$-0.110745\pi$
$541$	1017.17			1.88017			0.940085	+	0.340940i	$0.110745\pi$
$542$	182.280	−	182.280i	0.336310	−	0.336310i
$543$	187.718	+	187.718i	0.345706	+	0.345706i
$544$		−	128.025i		−	0.235340i
$545$	−0.489259	−	0.313585i	−0.000897722	−	0.000575385i
$546$	261.390			0.478736
$547$	−533.088	+	533.088i	−0.974567	+	0.974567i	−0.999685	−	0.0251176i	$-0.992004\pi$
$547$	−533.088	+	533.088i	−0.974567	+	0.974567i	0.0251176	+	0.999685i	$0.492004\pi$
$548$	−81.9252	−	81.9252i	−0.149498	−	0.149498i
$549$			313.584i			0.571192i
$550$	426.602	+	157.930i	0.775640	+	0.287145i
$551$	296.069			0.537330
$552$	16.6132	−	16.6132i	0.0300965	−	0.0300965i
$553$	581.046	+	581.046i	1.05072	+	1.05072i
$554$		−	423.375i		−	0.764215i
$555$	−154.177	+	240.548i	−0.277796	+	0.433421i
$556$	297.075			0.534308
$557$	−359.466	+	359.466i	−0.645361	+	0.645361i	−0.951868	−	0.306507i	$-0.900840\pi$
$557$	−359.466	+	359.466i	−0.645361	+	0.645361i	0.306507	+	0.951868i	$0.400840\pi$
$558$	33.3868	+	33.3868i	0.0598329	+	0.0598329i
$559$			362.377i			0.648259i
$560$	−33.9701	−	155.246i	−0.0606608	−	0.277224i
$561$	−504.356			−0.899031
$562$	195.698	−	195.698i	0.348216	−	0.348216i
$563$	−342.658	−	342.658i	−0.608628	−	0.608628i	0.333959	−	0.942587i	$-0.391615\pi$
$563$	−342.658	−	342.658i	−0.608628	−	0.608628i	−0.942587	+	0.333959i	$0.891615\pi$
$564$		−	277.278i		−	0.491628i
$565$	1040.49	−	227.675i	1.84158	−	0.402965i
$566$	565.443			0.999016
$567$	50.5677	−	50.5677i	0.0891846	−	0.0891846i
$568$	181.667	+	181.667i	0.319836	+	0.319836i
$569$		−	236.879i		−	0.416307i	−0.978096	−	0.208154i	$-0.933255\pi$
$569$		−	236.879i		−	0.416307i	0.978096	−	0.208154i	$-0.0667454\pi$
$570$	−281.045	−	180.133i	−0.493061	−	0.316022i
$571$	402.396			0.704722			0.352361	−	0.935864i	$-0.385379\pi$
$571$	402.396			0.704722			0.352361	+	0.935864i	$0.385379\pi$
$572$	−244.366	+	244.366i	−0.427213	+	0.427213i
$573$	399.582	+	399.582i	0.697350	+	0.697350i
$574$		−	540.018i		−	0.940798i
$575$	−41.6251	+	112.438i	−0.0723914	+	0.195545i
$576$	−24.0000			−0.0416667
$577$	255.514	−	255.514i	0.442832	−	0.442832i	−0.450131	−	0.892963i	$-0.648623\pi$
$577$	255.514	−	255.514i	0.442832	−	0.442832i	0.892963	+	0.450131i	$0.148623\pi$
$578$	−223.198	−	223.198i	−0.386156	−	0.386156i
$579$		−	277.564i		−	0.479384i
$580$	−58.6156	+	91.4527i	−0.101061	+	0.157677i
$581$	−985.360			−1.69597
$582$	298.674	−	298.674i	0.513186	−	0.513186i
$583$	524.135	+	524.135i	0.899032	+	0.899032i
$584$		−	27.2497i		−	0.0466605i
$585$	43.0605	+	196.790i	0.0736078	+	0.336393i
$586$	607.539			1.03676
$587$	533.089	−	533.089i	0.908158	−	0.908158i	−0.0879655	−	0.996124i	$-0.528037\pi$
$587$	533.089	−	533.089i	0.908158	−	0.908158i	0.996124	+	0.0879655i	$0.0280365\pi$
$588$	34.6309	+	34.6309i	0.0588960	+	0.0588960i
$589$			303.331i			0.514992i
$590$	439.788	−	96.2320i	0.745403	−	0.163105i
$591$	−152.002			−0.257194
$592$	−93.3147	+	93.3147i	−0.157626	+	0.157626i
$593$	433.233	+	433.233i	0.730579	+	0.730579i	0.970734	−	0.240156i	$-0.0771985\pi$
$593$	433.233	+	433.233i	0.730579	+	0.730579i	−0.240156	+	0.970734i	$0.577199\pi$
$594$			94.5485i			0.159173i
$595$	−757.009	−	485.196i	−1.27228	−	0.815456i
$596$	−21.9402			−0.0368125
$597$	−162.664	+	162.664i	−0.272470	+	0.272470i
$598$	−64.4067	−	64.4067i	−0.107704	−	0.107704i
$599$		−	111.533i		−	0.186198i	−0.995657	−	0.0930989i	$-0.970323\pi$
$599$		−	111.533i		−	0.186198i	0.995657	−	0.0930989i	$-0.0296773\pi$
$600$	111.282	−	51.1494i	0.185470	−	0.0852490i
$601$	523.677			0.871343			0.435671	−	0.900106i	$-0.356511\pi$
$601$	523.677			0.871343			0.435671	+	0.900106i	$0.356511\pi$
$602$	−214.407	+	214.407i	−0.356157	+	0.356157i
$603$	−10.4304	−	10.4304i	−0.0172975	−	0.0172975i
$604$			219.031i			0.362635i
$605$	120.185	−	187.514i	0.198653	−	0.309941i
$606$	316.524			0.522317
$607$	3.99156	−	3.99156i	0.00657588	−	0.00657588i	−0.703811	−	0.710387i	$-0.748520\pi$
$607$	3.99156	−	3.99156i	0.00657588	−	0.00657588i	0.710387	+	0.703811i	$0.248520\pi$
$608$	−109.024	−	109.024i	−0.179316	−	0.179316i
$609$		−	149.498i		−	0.245481i
$610$	−157.993	−	722.042i	−0.259005	−	1.18367i
$611$	−1074.96			−1.75935
$612$	−96.0186	+	96.0186i	−0.156893	+	0.156893i
$613$	87.2893	+	87.2893i	0.142397	+	0.142397i	0.774712	−	0.632315i	$-0.217895\pi$
$613$	87.2893	+	87.2893i	0.142397	+	0.142397i	−0.632315	+	0.774712i	$0.717895\pi$
$614$			762.781i			1.24231i
$615$	406.558	−	88.9609i	0.661070	−	0.144652i
$616$	−289.167			−0.469426
$617$	−416.059	+	416.059i	−0.674325	+	0.674325i	−0.958710	−	0.284385i	$-0.908211\pi$
$617$	−416.059	+	416.059i	−0.674325	+	0.674325i	0.284385	+	0.958710i	$0.408211\pi$
$618$	10.0777	+	10.0777i	0.0163070	+	0.0163070i
$619$			248.948i			0.402178i	0.979573	+	0.201089i	$0.0644480\pi$
$619$			248.948i			0.402178i	−0.979573	+	0.201089i	$0.935552\pi$
$620$	−93.6957	−	60.0532i	−0.151122	−	0.0968600i
$621$	−24.9199			−0.0401286
$622$	34.0026	−	34.0026i	0.0546666	−	0.0546666i
$623$	366.207	+	366.207i	0.587812	+	0.587812i
$624$			93.0439i			0.149109i
$625$	−406.978	+	474.335i	−0.651165	+	0.758936i
$626$	−125.894			−0.201108
$627$	−429.504	+	429.504i	−0.685014	+	0.685014i
$628$	−182.784	−	182.784i	−0.291057	−	0.291057i
$629$			746.662i			1.18706i
$630$	−90.9567	+	141.912i	−0.144376	+	0.225257i
$631$	470.788			0.746098			0.373049	−	0.927812i	$-0.378312\pi$
$631$	470.788			0.746098			0.373049	+	0.927812i	$0.378312\pi$
$632$	−206.828	+	206.828i	−0.327260	+	0.327260i
$633$	248.307	+	248.307i	0.392270	+	0.392270i
$634$			288.117i			0.454444i
$635$	231.942	+	1059.99i	0.365263	+	1.66928i
$636$	199.568			0.313786
$637$	134.258	−	134.258i	0.210766	−	0.210766i
$638$	139.762	+	139.762i	0.219062	+	0.219062i
$639$		−	272.500i		−	0.426448i
$640$	55.2611	−	12.0919i	0.0863454	−	0.0188936i
$641$	1011.49			1.57799			0.788995	−	0.614400i	$-0.210602\pi$
$641$	1011.49			1.57799			0.788995	+	0.614400i	$0.210602\pi$
$642$	−60.7257	+	60.7257i	−0.0945883	+	0.0945883i
$643$	−422.128	−	422.128i	−0.656498	−	0.656498i	0.298052	−	0.954550i	$-0.403663\pi$
$643$	−422.128	−	422.128i	−0.656498	−	0.656498i	−0.954550	+	0.298052i	$0.903663\pi$
$644$		−	76.2148i		−	0.118346i
$645$	−196.739	−	126.098i	−0.305022	−	0.195500i
$646$	−872.363			−1.35041
$647$	482.452	−	482.452i	0.745675	−	0.745675i	−0.227989	−	0.973664i	$-0.573215\pi$
$647$	482.452	−	482.452i	0.745675	−	0.745675i	0.973664	+	0.227989i	$0.0732149\pi$
$648$	18.0000	+	18.0000i	0.0277778	+	0.0277778i
$649$		−	819.165i		−	1.26220i
$650$	−198.298	−	431.422i	−0.305073	−	0.663727i
$651$	153.165			0.235276
$652$	96.4810	−	96.4810i	0.147977	−	0.147977i
$653$	455.524	+	455.524i	0.697586	+	0.697586i	0.963889	−	0.266303i	$-0.0858022\pi$
$653$	455.524	+	455.524i	0.697586	+	0.697586i	−0.266303	+	0.963889i	$0.585802\pi$
$654$			0.284693i			0.000435311i
$655$	−631.071	+	984.605i	−0.963468	+	1.50321i
$656$	192.224			0.293025
$657$	−20.4373	+	20.4373i	−0.0311070	+	0.0311070i
$658$	−636.020	−	636.020i	−0.966596	−	0.966596i
$659$		−	81.7349i		−	0.124029i	−0.998075	−	0.0620143i	$-0.980248\pi$
$659$		−	81.7349i		−	0.124029i	0.998075	−	0.0620143i	$-0.0197525\pi$
$660$	−47.6364	−	217.702i	−0.0721764	−	0.329852i
$661$	−137.438			−0.207925			−0.103962	−	0.994581i	$-0.533152\pi$
$661$	−137.438			−0.207925			−0.103962	+	0.994581i	$0.533152\pi$
$662$	133.019	−	133.019i	0.200936	−	0.200936i
$663$	372.248	+	372.248i	0.561459	+	0.561459i
$664$		−	350.747i		−	0.528234i
$665$	−1057.85	+	231.473i	−1.59075	+	0.348079i
$666$	139.972			0.210168
$667$	−36.8365	+	36.8365i	−0.0552272	+	0.0552272i
$668$	−389.103	−	389.103i	−0.582490	−	0.582490i
$669$			28.2473i			0.0422232i
$670$	29.2717	+	18.7613i	0.0436891	+	0.0280020i
$671$	−1344.90			−2.00433
$672$	−55.0511	+	55.0511i	−0.0819213	+	0.0819213i
$673$	−363.220	−	363.220i	−0.539702	−	0.539702i	0.383739	−	0.923441i	$-0.374636\pi$
$673$	−363.220	−	363.220i	−0.539702	−	0.539702i	−0.923441	+	0.383739i	$0.874636\pi$
$674$		−	442.591i		−	0.656662i
$675$	−121.824	−	45.0996i	−0.180480	−	0.0668142i
$676$	22.7155			0.0336028
$677$	202.715	−	202.715i	0.299431	−	0.299431i	−0.541360	−	0.840791i	$-0.682090\pi$
$677$	202.715	−	202.715i	0.299431	−	0.299431i	0.840791	+	0.541360i	$0.182090\pi$
$678$	−368.965	−	368.965i	−0.544197	−	0.544197i
$679$		−	1370.20i		−	2.01796i
$680$	172.710	−	269.464i	0.253985	−	0.396271i
$681$	−400.263			−0.587758
$682$	−143.189	+	143.189i	−0.209955	+	0.209955i
$683$	−496.960	−	496.960i	−0.727614	−	0.727614i	0.242530	−	0.970144i	$-0.422023\pi$
$683$	−496.960	−	496.960i	−0.727614	−	0.727614i	−0.970144	+	0.242530i	$0.922023\pi$
$684$			163.536i			0.239088i
$685$	−61.9146	−	282.954i	−0.0903863	−	0.413072i
$686$	−391.753			−0.571069
$687$	−189.105	+	189.105i	−0.275262	+	0.275262i
$688$	−76.3199	−	76.3199i	−0.110930	−	0.110930i
$689$		−	773.692i		−	1.12292i
$690$	57.3791	−	12.5554i	0.0831581	−	0.0181962i
$691$	708.102			1.02475			0.512375	−	0.858762i	$-0.328766\pi$
$691$	708.102			1.02475			0.512375	+	0.858762i	$0.328766\pi$
$692$	−253.992	+	253.992i	−0.367041	+	0.367041i
$693$	216.875	+	216.875i	0.312951	+	0.312951i
$694$		−	11.2916i		−	0.0162703i
$695$	625.278	+	400.765i	0.899681	+	0.576640i
$696$	53.2152			0.0764586
$697$	769.045	−	769.045i	1.10336	−	1.10336i
$698$	356.420	+	356.420i	0.510631	+	0.510631i
$699$			635.099i			0.908583i
$700$	137.932	−	372.585i	0.197046	−	0.532264i
$701$	−282.940			−0.403624			−0.201812	−	0.979424i	$-0.564683\pi$
$701$	−282.940			−0.403624			−0.201812	+	0.979424i	$0.564683\pi$
$702$	69.7829	−	69.7829i	0.0994059	−	0.0994059i
$703$	635.848	+	635.848i	0.904478	+	0.904478i
$704$		−	102.931i		−	0.146209i
$705$	374.058	−	583.610i	0.530579	−	0.827816i
$706$	440.785			0.624341
$707$	726.042	−	726.042i	1.02693	−	1.02693i
$708$	−155.951	−	155.951i	−0.220270	−	0.220270i
$709$		−	348.639i		−	0.491733i	−0.969304	−	0.245867i	$-0.920927\pi$
$709$		−	348.639i		−	0.491733i	0.969304	−	0.245867i	$-0.0790725\pi$
$710$	137.294	+	627.443i	0.193372	+	0.883723i
$711$	310.242			0.436347
$712$	−130.355	+	130.355i	−0.183082	+	0.183082i
$713$	−37.7400	−	37.7400i	−0.0529313	−	0.0529313i
$714$			440.494i			0.616938i
$715$	−843.994	+	184.678i	−1.18041	+	0.258291i
$716$	−563.211			−0.786608
$717$	109.644	−	109.644i	0.152921	−	0.152921i
$718$	−339.199	−	339.199i	−0.472422	−	0.472422i
$719$			692.400i			0.963003i	0.876445	+	0.481502i	$0.159908\pi$
$719$			692.400i			0.963003i	−0.876445	+	0.481502i	$0.840092\pi$
$720$	−50.5147	−	32.3768i	−0.0701594	−	0.0449678i
$721$	46.2324			0.0641226
$722$	−381.893	+	381.893i	−0.528938	+	0.528938i
$723$	187.834	+	187.834i	0.259798	+	0.259798i
$724$			306.543i			0.423402i
$725$	−246.746	+	113.414i	−0.340339	+	0.156432i
$726$	−109.112			−0.150292
$727$	564.236	−	564.236i	0.776116	−	0.776116i	−0.203052	−	0.979168i	$-0.565086\pi$
$727$	564.236	−	564.236i	0.776116	−	0.776116i	0.979168	+	0.203052i	$0.0650861\pi$
$728$	213.424	+	213.424i	0.293165	+	0.293165i
$729$		−	27.0000i		−	0.0370370i
$730$	36.7608	−	57.3547i	0.0503573	−	0.0785681i
$731$	−610.677			−0.835400
$732$	−256.040	+	256.040i	−0.349782	+	0.349782i
$733$	−591.205	−	591.205i	−0.806555	−	0.806555i	0.177556	−	0.984111i	$-0.443181\pi$
$733$	−591.205	−	591.205i	−0.806555	−	0.806555i	−0.984111	+	0.177556i	$0.943181\pi$
$734$		−	68.8057i		−	0.0937407i
$735$	26.1721	+	119.609i	0.0356083	+	0.162733i
$736$	27.1293			0.0368605
$737$	44.7341	−	44.7341i	0.0606975	−	0.0606975i
$738$	−144.168	−	144.168i	−0.195350	−	0.195350i
$739$		−	258.804i		−	0.350208i	−0.984550	−	0.175104i	$-0.943974\pi$
$739$		−	258.804i		−	0.350208i	0.984550	−	0.175104i	$-0.0560262\pi$
$740$	−322.292	+	70.5222i	−0.435529	+	0.0953002i
$741$	634.003			0.855605
$742$	457.769	−	457.769i	0.616939	−	0.616939i
$743$	49.1328	+	49.1328i	0.0661276	+	0.0661276i	0.739397	−	0.673270i	$-0.235111\pi$
$743$	49.1328	+	49.1328i	0.0661276	+	0.0661276i	−0.673270	+	0.739397i	$0.735111\pi$
$744$			54.5203i			0.0732800i
$745$	−46.1794	−	29.5981i	−0.0619857	−	0.0397290i
$746$	152.310			0.204169
$747$	−263.061	+	263.061i	−0.352156	+	0.352156i
$748$	−411.805	−	411.805i	−0.550542	−	0.550542i
$749$			278.585i			0.371942i
$750$	303.227	+	42.4653i	0.404303	+	0.0566204i
$751$	−1118.26			−1.48903			−0.744517	−	0.667604i	$-0.767320\pi$
$751$	−1118.26			−1.48903			−0.744517	+	0.667604i	$0.767320\pi$
$752$	226.397	−	226.397i	0.301060	−	0.301060i
$753$	233.330	+	233.330i	0.309867	+	0.309867i
$754$		−	206.306i		−	0.273616i
$755$	−295.481	+	461.013i	−0.391365	+	0.610613i
$756$	82.5766			0.109228
$757$	−814.033	+	814.033i	−1.07534	+	1.07534i	−0.0784198	+	0.996920i	$0.524987\pi$
$757$	−814.033	+	814.033i	−1.07534	+	1.07534i	−0.996920	+	0.0784198i	$0.975013\pi$
$758$	101.960	+	101.960i	0.134512	+	0.134512i
$759$		−	106.877i		−	0.140812i
$760$	−82.3947	−	376.550i	−0.108414	−	0.495460i
$761$	−470.046			−0.617669			−0.308835	−	0.951116i	$-0.599939\pi$
$761$	−470.046			−0.617669			−0.308835	+	0.951116i	$0.599939\pi$
$762$	375.880	−	375.880i	0.493281	−	0.493281i
$763$	0.653028	+	0.653028i	0.000855869	+	0.000855869i
$764$			652.514i			0.854076i
$765$	−331.630	+	72.5656i	−0.433504	+	0.0948570i
$766$	1046.14			1.36572
$767$	−604.597	+	604.597i	−0.788262	+	0.788262i
$768$	−19.5959	−	19.5959i	−0.0255155	−	0.0255155i
$769$		−	694.030i		−	0.902510i	−0.892395	−	0.451255i	$-0.850977\pi$
$769$		−	694.030i		−	0.902510i	0.892395	−	0.451255i	$-0.149023\pi$
$770$	−608.633	−	390.096i	−0.790432	−	0.506618i
$771$	285.478			0.370270
$772$	226.630	−	226.630i	0.293562	−	0.293562i
$773$	−472.817	−	472.817i	−0.611665	−	0.611665i	0.331714	−	0.943380i	$-0.392373\pi$
$773$	−472.817	−	472.817i	−0.611665	−	0.611665i	−0.943380	+	0.331714i	$0.892373\pi$
$774$			114.480i			0.147907i
$775$	−116.195	−	252.798i	−0.149929	−	0.326191i
$776$	487.733			0.628522
$777$	321.067	−	321.067i	0.413214	−	0.413214i
$778$	−8.10447	−	8.10447i	−0.0104171	−	0.0104171i
$779$		−	1309.82i		−	1.68141i
$780$	−125.520	+	195.837i	−0.160922	+	0.251073i
$781$	1168.70			1.49641
$782$	108.538	−	108.538i	0.138796	−	0.138796i
$783$	−39.9114	−	39.9114i	−0.0509724	−	0.0509724i
$784$			56.5520i			0.0721326i
$785$	−138.138	−	631.302i	−0.175972	−	0.804206i
$786$	572.929			0.728917
$787$	−848.095	+	848.095i	−1.07763	+	1.07763i	−0.0809093	+	0.996721i	$0.525782\pi$
$787$	−848.095	+	848.095i	−1.07763	+	1.07763i	−0.996721	+	0.0809093i	$0.974218\pi$
$788$	−124.109	−	124.109i	−0.157499	−	0.157499i
$789$		−	656.087i		−	0.831543i
$790$	−714.347	+	156.310i	−0.904236	+	0.197860i
$791$	−1692.66			−2.13990
$792$	−77.1985	+	77.1985i	−0.0974729	+	0.0974729i
$793$	992.625	+	992.625i	1.25173	+	1.25173i
$794$			93.5140i			0.117776i
$795$	420.047	+	269.224i	0.528361	+	0.338647i
$796$	−265.630			−0.333706
$797$	−146.099	+	146.099i	−0.183312	+	0.183312i	−0.792797	−	0.609486i	$-0.791376\pi$
$797$	−146.099	+	146.099i	−0.183312	+	0.183312i	0.609486	+	0.792797i	$0.291376\pi$
$798$	375.119	+	375.119i	0.470074	+	0.470074i
$799$		−	1811.53i		−	2.26724i
$800$	132.625	+	49.0982i	0.165781	+	0.0613728i
$801$	195.532			0.244110
$802$	212.655	−	212.655i	0.265156	−	0.265156i
$803$	−87.6516	−	87.6516i	−0.109155	−	0.109155i
$804$		−	17.0328i		−	0.0211851i
$805$	102.816	−	160.415i	0.127722	−	0.199274i
$806$	211.366			0.262241
$807$	197.594	−	197.594i	0.244850	−	0.244850i
$808$	258.441	+	258.441i	0.319853	+	0.319853i
$809$		−	717.004i		−	0.886284i	−0.896451	−	0.443142i	$-0.853864\pi$
$809$		−	717.004i		−	0.886284i	0.896451	−	0.443142i	$-0.146136\pi$
$810$	13.6034	+	62.1687i	0.0167944	+	0.0767515i
$811$	45.3065			0.0558650			0.0279325	−	0.999610i	$-0.491108\pi$
$811$	45.3065			0.0558650			0.0279325	+	0.999610i	$0.491108\pi$
$812$	122.065	−	122.065i	0.150326	−	0.150326i
$813$	−223.246	−	223.246i	−0.274596	−	0.274596i
$814$			600.313i			0.737485i
$815$	333.228	−	72.9151i	0.408868	−	0.0894664i
$816$	−156.798			−0.192154
$817$	−520.045	+	520.045i	−0.636530	+	0.636530i
$818$	−201.150	−	201.150i	−0.245905	−	0.245905i
$819$		−	320.136i		−	0.390886i
$820$	404.590	+	259.317i	0.493402	+	0.316240i
$821$	5.96649			0.00726734			0.00363367	−	0.999993i	$-0.498843\pi$
$821$	5.96649			0.00726734			0.00363367	+	0.999993i	$0.498843\pi$
$822$	−100.337	+	100.337i	−0.122065	+	0.122065i
$823$	−157.910	−	157.910i	−0.191872	−	0.191872i	0.604633	−	0.796504i	$-0.293320\pi$
$823$	−157.910	−	157.910i	−0.191872	−	0.191872i	−0.796504	+	0.604633i	$0.793320\pi$
$824$			16.4568i			0.0199719i
$825$	193.424	−	522.479i	0.234453	−	0.633307i
$826$	−715.441			−0.866152
$827$	932.001	−	932.001i	1.12697	−	1.12697i	0.136299	−	0.990668i	$-0.456479\pi$
$827$	932.001	−	932.001i	1.12697	−	1.12697i	0.990668	−	0.136299i	$-0.0435207\pi$
$828$	−20.3470	−	20.3470i	−0.0245737	−	0.0245737i
$829$		−	1455.66i		−	1.75592i	−0.478732	−	0.877961i	$-0.658903\pi$
$829$		−	1455.66i		−	1.75592i	0.478732	−	0.877961i	$-0.341097\pi$
$830$	473.171	−	738.246i	0.570085	−	0.889454i
$831$	−518.526			−0.623979
$832$	−75.9700	+	75.9700i	−0.0913102	+	0.0913102i
$833$	226.252	+	226.252i	0.271611	+	0.271611i
$834$		−	363.841i		−	0.436260i
$835$	−294.063	−	1343.89i	−0.352171	−	1.60945i
$836$	−701.376			−0.838967
$837$	40.8903	−	40.8903i	0.0488534	−	0.0488534i
$838$	284.817	+	284.817i	0.339877	+	0.339877i
$839$			841.130i			1.00254i	0.865291	+	0.501270i	$0.167133\pi$
$839$			841.130i			1.00254i	−0.865291	+	0.501270i	$0.832867\pi$
$840$	−190.136	+	41.6046i	−0.226353	+	0.0495293i
$841$	723.006			0.859698
$842$	−162.868	+	162.868i	−0.193430	+	0.193430i
$843$	−239.680	−	239.680i	−0.284317	−	0.284317i
$844$			405.483i			0.480430i
$845$	47.8112	+	30.6440i	0.0565813	+	0.0362651i
$846$	−339.595			−0.401413
$847$	−250.281	+	250.281i	−0.295491	+	0.295491i
$848$	162.947	+	162.947i	0.192154	+	0.192154i
$849$		−	692.523i		−	0.815693i
$850$	727.033	−	334.171i	0.855333	−	0.393143i
$851$	−158.223			−0.185926
$852$	222.495	−	222.495i	0.261145	−	0.261145i
$853$	125.620	+	125.620i	0.147269	+	0.147269i	0.776897	−	0.629628i	$-0.216793\pi$
$853$	125.620	+	125.620i	0.147269	+	0.147269i	−0.629628	+	0.776897i	$0.716793\pi$
$854$			1174.61i			1.37542i
$855$	−220.616	+	344.208i	−0.258031	+	0.402583i
$856$	−99.1647			−0.115847
$857$	−397.770	+	397.770i	−0.464143	+	0.464143i	−0.900011	−	0.435868i	$-0.856441\pi$
$857$	−397.770	+	397.770i	−0.464143	+	0.464143i	0.435868	+	0.900011i	$0.356441\pi$
$858$	299.286	+	299.286i	0.348818	+	0.348818i
$859$			577.038i			0.671756i	0.941906	+	0.335878i	$0.109033\pi$
$859$			577.038i			0.671756i	−0.941906	+	0.335878i	$0.890967\pi$
$860$	−57.6785	−	263.595i	−0.0670680	−	0.306506i
$861$	−661.384			−0.768158
$862$	740.079	−	740.079i	0.858561	−	0.858561i
$863$	440.196	+	440.196i	0.510076	+	0.510076i	0.914550	−	0.404474i	$-0.132545\pi$
$863$	440.196	+	440.196i	0.510076	+	0.510076i	−0.404474	+	0.914550i	$0.632545\pi$
$864$			29.3939i			0.0340207i
$865$	−877.242	+	191.954i	−1.01415	+	0.221912i
$866$	1085.32			1.25326
$867$	−273.361	+	273.361i	−0.315295	+	0.315295i
$868$	125.059	+	125.059i	0.144077	+	0.144077i
$869$			1330.57i			1.53115i
$870$	112.006	+	71.7891i	0.128743	+	0.0825162i
$871$	−66.0333			−0.0758132
$872$	−0.232451	+	0.232451i	−0.000266572	+	0.000266572i
$873$	−365.800	−	365.800i	−0.419015	−	0.419015i
$874$		−	184.860i		−	0.211510i
$875$	792.948	−	598.134i	0.906226	−	0.683582i
$876$	−33.3740			−0.0380981
$877$	1080.01	−	1080.01i	1.23148	−	1.23148i	0.268086	−	0.963395i	$-0.413609\pi$
$877$	1080.01	−	1080.01i	1.23148	−	1.23148i	0.963395	−	0.268086i	$-0.0863912\pi$
$878$	−484.445	−	484.445i	−0.551760	−	0.551760i
$879$		−	744.080i		−	0.846508i
$880$	138.858	−	216.648i	0.157793	−	0.246191i
$881$	−134.518			−0.152688			−0.0763440	−	0.997082i	$-0.524325\pi$
$881$	−134.518			−0.152688			−0.0763440	+	0.997082i	$0.524325\pi$
$882$	42.4140	−	42.4140i	0.0480884	−	0.0480884i
$883$	448.543	+	448.543i	0.507976	+	0.507976i	0.913905	−	0.405929i	$-0.133052\pi$
$883$	448.543	+	448.543i	0.507976	+	0.507976i	−0.405929	+	0.913905i	$0.633052\pi$
$884$			607.878i			0.687645i
$885$	−117.860	−	538.628i	−0.133175	−	0.608619i
$886$	1052.44			1.18785
$887$	728.517	−	728.517i	0.821327	−	0.821327i	−0.164971	−	0.986298i	$-0.552753\pi$
$887$	728.517	−	728.517i	0.821327	−	0.821327i	0.986298	+	0.164971i	$0.0527532\pi$
$888$	114.287	+	114.287i	0.128701	+	0.128701i
$889$		−	1724.38i		−	1.93969i
$890$	−450.221	+	98.5150i	−0.505866	+	0.110691i
$891$	115.798			0.129964
$892$	−23.0638	+	23.0638i	−0.0258563	+	0.0258563i
$893$	−1542.67	−	1542.67i	−1.72752	−	1.72752i
$894$			26.8712i			0.0300572i
$895$	−1185.44	−	759.792i	−1.32451	−	0.848929i
$896$	−89.8981			−0.100333
$897$	−78.8818	+	78.8818i	−0.0879396	+	0.0879396i
$898$	620.540	+	620.540i	0.691025	+	0.691025i
$899$		−	120.888i		−	0.134469i
$900$	−62.6450	−	136.292i	−0.0696055	−	0.151436i
$901$	1303.83			1.44709
$902$	618.309	−	618.309i	0.685487	−	0.685487i
$903$	262.594	+	262.594i	0.290801	+	0.290801i
$904$		−	602.518i		−	0.666502i
$905$	−413.537	+	645.205i	−0.456947	+	0.712934i
$906$	268.257			0.296090
$907$	176.709	−	176.709i	0.194828	−	0.194828i	−0.602951	−	0.797779i	$-0.706008\pi$
$907$	176.709	−	176.709i	0.194828	−	0.194828i	0.797779	+	0.602951i	$0.206008\pi$
$908$	−326.813	−	326.813i	−0.359927	−	0.359927i
$909$		−	387.662i		−	0.426470i
$910$	161.294	+	737.127i	0.177246	+	0.810029i
$911$	−1311.05			−1.43914			−0.719569	−	0.694421i	$-0.755661\pi$
$911$	−1311.05			−1.43914			−0.719569	+	0.694421i	$0.755661\pi$
$912$	−133.527	+	133.527i	−0.146411	+	0.146411i
$913$	−1128.22	−	1128.22i	−1.23572	−	1.23572i
$914$			5.87811i			0.00643119i
$915$	−884.317	+	193.502i	−0.966466	+	0.211477i
$916$	−308.807			−0.337126
$917$	1314.18	−	1314.18i	1.43313	−	1.43313i
$918$	117.598	+	117.598i	0.128103	+	0.128103i
$919$			782.706i			0.851693i	0.904795	+	0.425847i	$0.140024\pi$
$919$			782.706i			0.851693i	−0.904795	+	0.425847i	$0.859976\pi$
$920$	57.1013	+	36.5984i	0.0620666	+	0.0397809i
$921$	934.212			1.01435
$922$	336.573	−	336.573i	0.365046	−	0.365046i
$923$	−862.576	−	862.576i	−0.934536	−	0.934536i
$924$			354.155i			0.383285i
$925$	−773.490	−	286.349i	−0.836206	−	0.309567i
$926$	−1185.43			−1.28017
$927$	12.3426	−	12.3426i	0.0133146	−	0.0133146i
$928$	43.4500	+	43.4500i	0.0468211	+	0.0468211i
$929$			1258.54i			1.35473i	0.735647	+	0.677365i	$0.236878\pi$
$929$			1258.54i			1.35473i	−0.735647	+	0.677365i	$0.763122\pi$
$930$	−73.5499	+	114.753i	−0.0790859	+	0.123391i
$931$	385.346			0.413906
$932$	−518.556	+	518.556i	−0.556391	+	0.556391i
$933$	−41.6445	−	41.6445i	−0.0446351	−	0.0446351i
$934$			705.769i			0.755642i
$935$	−311.220	−	1422.30i	−0.332856	−	1.52118i
$936$	113.955			0.121747
$937$	−223.347	+	223.347i	−0.238364	+	0.238364i	−0.816172	−	0.577808i	$-0.803908\pi$
$937$	−223.347	+	223.347i	−0.238364	+	0.238364i	0.577808	+	0.816172i	$0.303908\pi$
$938$	−39.0698	−	39.0698i	−0.0416522	−	0.0416522i
$939$			154.188i			0.164204i
$940$	781.933	−	171.099i	0.831844	−	0.182020i
$941$	1007.84			1.07104			0.535518	−	0.844524i	$-0.320116\pi$
$941$	1007.84			1.07104			0.535518	+	0.844524i	$0.320116\pi$
$942$	−223.864	+	223.864i	−0.237647	+	0.237647i
$943$	162.966	+	162.966i	0.172816	+	0.172816i
$944$		−	254.668i		−	0.269775i
$945$	173.806	+	111.399i	0.183921	+	0.117882i
$946$	−490.982			−0.519009
$947$	515.759	−	515.759i	0.544624	−	0.544624i	−0.380257	−	0.924881i	$-0.624164\pi$
$947$	515.759	−	515.759i	0.544624	−	0.544624i	0.924881	+	0.380257i	$0.124164\pi$
$948$	253.312	+	253.312i	0.267207	+	0.267207i
$949$			129.385i			0.136338i
$950$	334.556	−	903.708i	0.352165	−	0.951272i
$951$	352.870			0.371052
$952$	−359.662	+	359.662i	−0.377796	+	0.377796i
$953$	−969.316	−	969.316i	−1.01712	−	1.01712i	−0.999851	−	0.0172703i	$-0.994502\pi$
$953$	−969.316	−	969.316i	−1.01712	−	1.01712i	−0.0172703	−	0.999851i	$-0.505498\pi$
$954$		−	244.420i		−	0.256206i
$955$	−880.265	+	1373.40i	−0.921743	+	1.43812i
$956$	179.048			0.187289
$957$	171.172	−	171.172i	0.178863	−	0.178863i
$958$	−160.749	−	160.749i	−0.167797	−	0.167797i
$959$			460.307i			0.479987i
$960$	−14.8095	−	67.6807i	−0.0154266	−	0.0705007i
$961$	−837.147			−0.871121
$962$	443.070	−	443.070i	0.460572	−	0.460572i
$963$	74.3735	+	74.3735i	0.0772310	+	0.0772310i
$964$			306.732i			0.318187i
$965$	782.737	−	171.274i	0.811127	−	0.177486i
$966$	−93.3437			−0.0966291
$967$	293.239	−	293.239i	0.303246	−	0.303246i	−0.539036	−	0.842283i	$-0.681211\pi$
$967$	293.239	−	293.239i	0.303246	−	0.303246i	0.842283	+	0.539036i	$0.181211\pi$
$968$	−89.0897	−	89.0897i	−0.0920348	−	0.0920348i
$969$			1068.42i			1.10260i
$970$	1026.57	+	657.969i	1.05832	+	0.678319i
$971$	1223.41			1.25995			0.629976	−	0.776615i	$-0.283065\pi$
$971$	1223.41			1.25995			0.629976	+	0.776615i	$0.283065\pi$
$972$	22.0454	−	22.0454i	0.0226805	−	0.0226805i
$973$	−834.577	−	834.577i	−0.857736	−	0.857736i
$974$			425.106i			0.436454i
$975$	−528.382	+	242.864i	−0.541931	+	0.249091i
$976$	−418.112			−0.428394
$977$	−143.186	+	143.186i	−0.146556	+	0.146556i	−0.776578	−	0.630021i	$-0.783046\pi$
$977$	−143.186	+	143.186i	−0.146556	+	0.146556i	0.630021	+	0.776578i	$0.283046\pi$
$978$	−118.165	−	118.165i	−0.120823	−	0.120823i
$979$			838.599i			0.856587i
$980$	−76.2906	+	119.030i	−0.0778475	+	0.121459i
$981$	0.348677			0.000355430
$982$	−399.924	+	399.924i	−0.407255	+	0.407255i
$983$	1069.62	+	1069.62i	1.08811	+	1.08811i	0.995723	+	0.0923919i	$0.0294513\pi$
$983$	1069.62	+	1069.62i	1.08811	+	1.08811i	0.0923919	+	0.995723i	$0.470549\pi$
$984$		−	235.425i		−	0.239254i
$985$	−93.7948	−	428.649i	−0.0952232	−	0.435177i
$986$	347.667			0.352604
$987$	−778.962	+	778.962i	−0.789222	+	0.789222i
$988$	517.661	+	517.661i	0.523949	+	0.523949i
$989$		−	129.407i		−	0.130846i
$990$	−266.630	+	58.3425i	−0.269323	+	0.0589318i
$991$	135.844			0.137078			0.0685388	−	0.997648i	$-0.478166\pi$
$991$	135.844			0.137078			0.0685388	+	0.997648i	$0.478166\pi$
$992$	−44.5157	+	44.5157i	−0.0448747	+	0.0448747i
$993$	−162.915	−	162.915i	−0.164063	−	0.164063i
$994$		−	1020.72i		−	1.02688i
$995$	−559.093	−	358.344i	−0.561902	−	0.360145i
$996$	−429.576			−0.431301
$997$	−85.6067	+	85.6067i	−0.0858643	+	0.0858643i	−0.748734	−	0.662870i	$-0.769338\pi$
$997$	−85.6067	+	85.6067i	−0.0858643	+	0.0858643i	0.662870	+	0.748734i	$0.269338\pi$
$998$	−284.551	−	284.551i	−0.285121	−	0.285121i
$999$		−	171.430i		−	0.171602i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.k.a.553.2	yes	40
5.2	odd	4	inner	690.3.k.a.277.2	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.k.a.277.2	✓	40	5.2	odd	4	inner
690.3.k.a.553.2	yes	40	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(2.69807 - 4.20956i) q^{5} -2.44949 q^{6} +(-5.61863 + 5.61863i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(2.69807 - 4.20956i) q^{5} -2.44949 q^{6} +(-5.61863 + 5.61863i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +(-1.51149 - 6.90763i) q^{10} -12.8664 q^{11} +(-2.44949 + 2.44949i) q^{12} +(9.49626 + 9.49626i) q^{13} +11.2373i q^{14} +(-8.46009 + 1.85119i) q^{15} -4.00000 q^{16} +(-16.0031 + 16.0031i) q^{17} +(3.00000 + 3.00000i) q^{18} +27.2561i q^{19} +(-8.41912 - 5.39614i) q^{20} +13.7628 q^{21} +(-12.8664 + 12.8664i) q^{22} +(-3.39116 - 3.39116i) q^{23} +4.89898i q^{24} +(-10.4408 - 22.7154i) q^{25} +18.9925 q^{26} +(3.67423 - 3.67423i) q^{27} +(11.2373 + 11.2373i) q^{28} -10.8625i q^{29} +(-6.60890 + 10.3113i) q^{30} +11.1289 q^{31} +(-4.00000 + 4.00000i) q^{32} +(15.7581 + 15.7581i) q^{33} +32.0062i q^{34} +(8.49251 + 38.8114i) q^{35} +6.00000 q^{36} +(23.3287 - 23.3287i) q^{37} +(27.2561 + 27.2561i) q^{38} -23.2610i q^{39} +(-13.8153 + 3.02298i) q^{40} -48.0560 q^{41} +(13.7628 - 13.7628i) q^{42} +(19.0800 + 19.0800i) q^{43} +25.7328i q^{44} +(12.6287 + 8.09421i) q^{45} -6.78233 q^{46} +(-56.5992 + 56.5992i) q^{47} +(4.89898 + 4.89898i) q^{48} -14.1380i q^{49} +(-33.1562 - 12.2746i) q^{50} +39.1994 q^{51} +(18.9925 - 18.9925i) q^{52} +(-40.7367 - 40.7367i) q^{53} -7.34847i q^{54} +(-34.7145 + 54.1620i) q^{55} +22.4745 q^{56} +(33.3817 - 33.3817i) q^{57} +(-10.8625 - 10.8625i) q^{58} +63.6669i q^{59} +(3.70238 + 16.9202i) q^{60} +104.528 q^{61} +(11.1289 - 11.1289i) q^{62} +(-16.8559 - 16.8559i) q^{63} +8.00000i q^{64} +(65.5967 - 14.3535i) q^{65} +31.5162 q^{66} +(-3.47681 + 3.47681i) q^{67} +(32.0062 + 32.0062i) q^{68} +8.30662i q^{69} +(47.3039 + 30.3189i) q^{70} -90.8333 q^{71} +(6.00000 - 6.00000i) q^{72} +(6.81243 + 6.81243i) q^{73} -46.6573i q^{74} +(-15.0332 + 40.6079i) q^{75} +54.5121 q^{76} +(72.2917 - 72.2917i) q^{77} +(-23.2610 - 23.2610i) q^{78} -103.414i q^{79} +(-10.7923 + 16.8382i) q^{80} -9.00000 q^{81} +(-48.0560 + 48.0560i) q^{82} +(87.6868 + 87.6868i) q^{83} -27.5255i q^{84} +(24.1885 + 110.543i) q^{85} +38.1600 q^{86} +(-13.3038 + 13.3038i) q^{87} +(25.7328 + 25.7328i) q^{88} -65.1773i q^{89} +(20.7229 - 4.53448i) q^{90} -106.712 q^{91} +(-6.78233 + 6.78233i) q^{92} +(-13.6301 - 13.6301i) q^{93} +113.198i q^{94} +(114.736 + 73.5388i) q^{95} +9.79796 q^{96} +(-121.933 + 121.933i) q^{97} +(-14.1380 - 14.1380i) q^{98} -38.5993i 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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