LMFDB - Embedded newform 690.3.k.a.277.2

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			277.2
Character	$\chi$	$=$	690.277
Dual form			690.3.k.a.553.2

$q$-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 $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

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

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
$5$	2.69807	+	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	0.180849	−	0.983511i	$-0.442115\pi$
$7$	−5.61863	−	5.61863i	−0.802661	−	0.802661i	−0.983511	+	0.180849i	$0.942115\pi$
$8$	−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	−0.240234	−	0.970715i	$-0.577224\pi$
$13$	9.49626	−	9.49626i	0.730481	−	0.730481i	0.970715	+	0.240234i	$0.0772241\pi$
$14$		−	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	0.0570149	−	0.998373i	$-0.481842\pi$
$17$	−16.0031	−	16.0031i	−0.941358	−	0.941358i	−0.998373	+	0.0570149i	$0.981842\pi$
$18$	3.00000	−	3.00000i	0.166667	−	0.166667i
$19$		−	27.2561i		−	1.43453i	−0.696800	−	0.717265i	$-0.745394\pi$
$19$		−	27.2561i		−	1.43453i	0.696800	−	0.717265i	$-0.254606\pi$
$20$	−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	$0.0599686\pi$
$29$			10.8625i			0.374569i	−0.982306	+	0.187284i	$0.940031\pi$
$30$	−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	0.948195	−	0.317690i	$-0.102907\pi$
$37$	23.3287	+	23.3287i	0.630504	+	0.630504i	−0.317690	+	0.948195i	$0.602907\pi$
$38$	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	−0.449540	−	0.893260i	$-0.648412\pi$
$43$	19.0800	−	19.0800i	0.443721	−	0.443721i	0.893260	+	0.449540i	$0.148412\pi$
$44$		−	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	−0.972865	−	0.231374i	$-0.925678\pi$
$47$	−56.5992	−	56.5992i	−1.20424	−	1.20424i	−0.231374	−	0.972865i	$-0.574322\pi$
$48$	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	−0.977863	−	0.209246i	$-0.932899\pi$
$53$	−40.7367	+	40.7367i	−0.768617	+	0.768617i	0.209246	+	0.977863i	$0.432899\pi$
$54$			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	$-0.818594\pi$
$59$		−	63.6669i		−	1.07910i	0.841954	−	0.539550i	$-0.181406\pi$
$60$	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	0.680684	−	0.732577i	$-0.261683\pi$
$67$	−3.47681	−	3.47681i	−0.0518926	−	0.0518926i	−0.732577	+	0.680684i	$0.761683\pi$
$68$	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	−0.658905	−	0.752226i	$-0.728980\pi$
$73$	6.81243	−	6.81243i	0.0933210	−	0.0933210i	0.752226	+	0.658905i	$0.228980\pi$
$74$			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	$0.227129\pi$
$79$			103.414i			1.30904i	−0.756045	+	0.654520i	$0.772871\pi$
$80$	−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	0.0581608	−	0.998307i	$-0.481476\pi$
$83$	87.6868	−	87.6868i	1.05647	−	1.05647i	0.998307	−	0.0581608i	$-0.0185236\pi$
$84$			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	$0.119329\pi$
$89$			65.1773i			0.732329i	−0.930550	+	0.366165i	$0.880671\pi$
$90$	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	−0.952497	−	0.304547i	$-0.901495\pi$
$97$	−121.933	−	121.933i	−1.25704	−	1.25704i	−0.304547	−	0.952497i	$-0.598505\pi$
$98$	−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	−0.726797	−	0.686853i	$-0.758992\pi$
$103$	−4.11421	+	4.11421i	−0.0399438	+	0.0399438i	0.686853	+	0.726797i	$0.258992\pi$
$104$			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	0.813399	−	0.581706i	$-0.197615\pi$
$107$	24.7912	+	24.7912i	0.231693	+	0.231693i	−0.581706	+	0.813399i	$0.697615\pi$
$108$	−7.34847	+	7.34847i	−0.0680414	+	0.0680414i
$109$			0.116226i			0.00106629i	1.00000		0.000533145i	$0.000169705\pi$
$109$			0.116226i			0.00106629i	−1.00000		0.000533145i	$0.999830\pi$
$110$	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	0.430335	−	0.902669i	$-0.358396\pi$
$113$	150.629	−	150.629i	1.33300	−	1.33300i	0.902669	−	0.430335i	$-0.141604\pi$
$114$			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	−0.971582	−	0.236705i	$-0.923932\pi$
$127$	−153.452	−	153.452i	−1.20829	−	1.20829i	−0.236705	−	0.971582i	$-0.576068\pi$
$128$	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	0.840621	−	0.541624i	$-0.182190\pi$
$137$	40.9626	+	40.9626i	0.298997	+	0.298997i	−0.541624	+	0.840621i	$0.682190\pi$
$138$	8.30662	−	8.30662i	0.0601929	−	0.0601929i
$139$		−	148.538i		−	1.06862i	−0.845290	−	0.534308i	$-0.820572\pi$
$139$		−	148.538i		−	1.06862i	0.845290	−	0.534308i	$-0.179428\pi$
$140$	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	$0.0117204\pi$
$149$			10.9701i			0.0736249i	−0.999322	+	0.0368125i	$0.988280\pi$
$150$	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	0.935484	−	0.353370i	$-0.114964\pi$
$157$	91.3919	+	91.3919i	0.582114	+	0.582114i	−0.353370	+	0.935484i	$0.614964\pi$
$158$	−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	−0.543473	−	0.839427i	$-0.682891\pi$
$163$	48.2405	−	48.2405i	0.295954	−	0.295954i	0.839427	+	0.543473i	$0.182891\pi$
$164$		−	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	0.983371	+	0.181609i	$0.0581305\pi$
$167$	194.552	+	194.552i	1.16498	+	1.16498i	0.181609	+	0.983371i	$0.441869\pi$
$168$	−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	−0.971426	−	0.237344i	$-0.923723\pi$
$173$	−126.996	+	126.996i	−0.734081	+	0.734081i	0.237344	+	0.971426i	$0.423723\pi$
$174$		−	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	$0.288165\pi$
$179$			281.606i			1.57322i	−0.617453	+	0.786608i	$0.711835\pi$
$180$	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	−0.349728	−	0.936851i	$-0.613726\pi$
$193$	113.315	−	113.315i	0.587123	−	0.587123i	0.936851	+	0.349728i	$0.113726\pi$
$194$		−	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	0.846842	−	0.531845i	$-0.178501\pi$
$197$	62.0545	+	62.0545i	0.314997	+	0.314997i	−0.531845	+	0.846842i	$0.678501\pi$
$198$	−38.5993	+	38.5993i	−0.194946	+	0.194946i
$199$			132.815i			0.667412i	0.942677	+	0.333706i	$0.108299\pi$
$199$			132.815i			0.667412i	−0.942677	+	0.333706i	$0.891701\pi$
$200$	−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	−0.732490	−	0.680778i	$-0.761642\pi$
$223$	−11.5319	+	11.5319i	−0.0517127	+	0.0517127i	0.680778	+	0.732490i	$0.261642\pi$
$224$			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	0.968575	−	0.248722i	$-0.0800105\pi$
$227$	163.407	+	163.407i	0.719853	+	0.719853i	−0.248722	+	0.968575i	$0.580011\pi$
$228$	−66.7635	+	66.7635i	−0.292822	+	0.292822i
$229$			154.404i			0.674251i	0.941460	+	0.337126i	$0.109455\pi$
$229$			154.404i			0.674251i	−0.941460	+	0.337126i	$0.890545\pi$
$230$	−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	−0.120009	+	0.992773i	$0.538292\pi$
$233$	−259.278	+	259.278i	−1.11278	+	1.11278i	−0.992773	+	0.120009i	$0.961708\pi$
$234$		−	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	$-0.940030\pi$
$239$		−	89.5241i		−	0.374578i	0.982305	−	0.187289i	$-0.0599701\pi$
$240$	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	0.443024	−	0.896510i	$-0.353906\pi$
$257$	−116.546	−	116.546i	−0.453486	−	0.453486i	−0.896510	+	0.443024i	$0.853906\pi$
$258$	−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	0.0186010	−	0.999827i	$-0.494079\pi$
$263$	267.847	−	267.847i	1.01843	−	1.01843i	0.999827	−	0.0186010i	$-0.00592123\pi$
$264$			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	$-0.903054\pi$
$269$		−	161.335i		−	0.599757i	0.953977	−	0.299879i	$-0.0969462\pi$
$270$	−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	0.977081	−	0.212867i	$-0.0682800\pi$
$277$	211.687	+	211.687i	0.764215	+	0.764215i	−0.212867	+	0.977081i	$0.568280\pi$
$278$	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	−0.000983541	−	1.00000i	$-0.500313\pi$
$283$	282.722	−	282.722i	0.999016	−	0.999016i	1.00000		0.000983541i	$0.000313071\pi$
$284$		−	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	0.0374575	−	0.999298i	$-0.488074\pi$
$293$	303.769	−	303.769i	1.03676	−	1.03676i	0.999298	−	0.0374575i	$-0.0119259\pi$
$294$		−	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	−0.959038	−	0.283276i	$-0.908579\pi$
$307$	−381.391	−	381.391i	−1.24231	−	1.24231i	−0.283276	−	0.959038i	$-0.591421\pi$
$308$	−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	−0.800475	−	0.599366i	$-0.795419\pi$
$313$	−62.9469	+	62.9469i	−0.201108	+	0.201108i	0.599366	+	0.800475i	$0.295419\pi$
$314$			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	0.442383	−	0.896826i	$-0.354133\pi$
$317$	−144.059	−	144.059i	−0.454444	−	0.454444i	−0.896826	+	0.442383i	$0.854133\pi$
$318$	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	0.954589	−	0.297926i	$-0.0962950\pi$
$337$	221.295	+	221.295i	0.656662	+	0.656662i	−0.297926	+	0.954589i	$0.596295\pi$
$338$	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	0.715195	−	0.698925i	$-0.246338\pi$
$347$	5.64579	+	5.64579i	0.0162703	+	0.0162703i	−0.698925	+	0.715195i	$0.746338\pi$
$348$	26.6076	−	26.6076i	0.0764586	−	0.0764586i
$349$		−	356.420i		−	1.02126i	−0.859800	−	0.510631i	$-0.829412\pi$
$349$		−	356.420i		−	1.02126i	0.859800	−	0.510631i	$-0.170588\pi$
$350$	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	−0.322297	−	0.946639i	$-0.604455\pi$
$353$	220.393	−	220.393i	0.624341	−	0.624341i	0.946639	+	0.322297i	$0.104455\pi$
$354$			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	$0.156620\pi$
$359$			339.199i			0.944844i	−0.881373	+	0.472422i	$0.843380\pi$
$360$	−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	0.752422	−	0.658681i	$-0.228885\pi$
$367$	34.4028	+	34.4028i	0.0937407	+	0.0937407i	−0.658681	+	0.752422i	$0.728885\pi$
$368$	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	−0.597614	−	0.801784i	$-0.703885\pi$
$373$	76.1551	−	76.1551i	0.204169	−	0.204169i	0.801784	+	0.597614i	$0.203885\pi$
$374$			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	$-0.957053\pi$
$379$		−	101.960i		−	0.269024i	0.990912	−	0.134512i	$-0.0429468\pi$
$380$	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	0.499267	−	0.866448i	$-0.333603\pi$
$383$	523.069	−	523.069i	1.36572	−	1.36572i	0.866448	−	0.499267i	$-0.166397\pi$
$384$			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	$0.00331591\pi$
$389$			8.10447i			0.0208341i	−0.999946	+	0.0104171i	$0.996684\pi$
$390$	−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	0.645763	−	0.763538i	$-0.276540\pi$
$397$	−46.7570	−	46.7570i	−0.117776	−	0.117776i	−0.763538	+	0.645763i	$0.776540\pi$
$398$	−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	$0.0790852\pi$
$409$			201.150i			0.491810i	−0.969294	+	0.245905i	$0.920915\pi$
$410$	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	$-0.889615\pi$
$419$		−	284.817i		−	0.679753i	0.940470	−	0.339877i	$-0.110385\pi$
$420$	−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	0.299003	−	0.954252i	$-0.403346\pi$
$433$	542.660	−	542.660i	1.25326	−	1.25326i	0.954252	−	0.299003i	$-0.0966541\pi$
$434$		−	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	$0.186043\pi$
$439$			484.445i			1.10352i	−0.834003	+	0.551760i	$0.813957\pi$
$440$	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	0.210190	−	0.977661i	$-0.432592\pi$
$443$	526.218	−	526.218i	1.18785	−	1.18785i	0.977661	−	0.210190i	$-0.0674082\pi$
$444$		−	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	$-0.757160\pi$
$449$		−	620.540i		−	1.38205i	0.722831	−	0.691025i	$-0.242840\pi$
$450$	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	0.703884	−	0.710315i	$-0.251448\pi$
$457$	−2.93906	−	2.93906i	−0.00643119	−	0.00643119i	−0.710315	+	0.703884i	$0.751448\pi$
$458$	−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	−0.339595	+	0.940572i	$0.610290\pi$
$463$	−592.717	+	592.717i	−1.28017	+	1.28017i	−0.940572	+	0.339595i	$0.889710\pi$
$464$		−	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	0.219884	−	0.975526i	$-0.429432\pi$
$467$	−352.885	−	352.885i	−0.755642	−	0.755642i	−0.975526	+	0.219884i	$0.929432\pi$
$468$	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	$0.0536652\pi$
$479$			160.749i			0.335593i	−0.985822	+	0.167797i	$0.946335\pi$
$480$	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	0.454363	−	0.890817i	$-0.349867\pi$
$487$	−212.553	−	212.553i	−0.436454	−	0.436454i	−0.890817	+	0.454363i	$0.849867\pi$
$488$	−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	$0.0920338\pi$
$499$			284.551i			0.570242i	−0.958492	+	0.285121i	$0.907966\pi$
$500$	−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	−0.819063	−	0.573704i	$-0.805506\pi$
$503$	−123.416	+	123.416i	−0.245359	+	0.245359i	0.573704	+	0.819063i	$0.305506\pi$
$504$		−	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	$0.163993\pi$
$509$			501.577i			0.985416i	−0.870195	+	0.492708i	$0.836007\pi$
$510$	−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	−0.917481	−	0.397779i	$-0.869781\pi$
$523$	−271.805	+	271.805i	−0.519703	+	0.519703i	0.397779	+	0.917481i	$0.369781\pi$
$524$		−	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	0.0251176	−	0.999685i	$-0.492004\pi$
$547$	−533.088	−	533.088i	−0.974567	−	0.974567i	−0.999685	+	0.0251176i	$0.992004\pi$
$548$	−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	0.306507	−	0.951868i	$-0.400840\pi$
$557$	−359.466	−	359.466i	−0.645361	−	0.645361i	−0.951868	+	0.306507i	$0.900840\pi$
$558$	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	−0.942587	−	0.333959i	$-0.891615\pi$
$563$	−342.658	+	342.658i	−0.608628	+	0.608628i	0.333959	+	0.942587i	$0.391615\pi$
$564$			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	$0.0667454\pi$
$569$			236.879i			0.416307i	−0.978096	+	0.208154i	$0.933255\pi$
$570$	−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	0.892963	−	0.450131i	$-0.148623\pi$
$577$	255.514	+	255.514i	0.442832	+	0.442832i	−0.450131	+	0.892963i	$0.648623\pi$
$578$	−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	0.996124	−	0.0879655i	$-0.0280365\pi$
$587$	533.089	+	533.089i	0.908158	+	0.908158i	−0.0879655	+	0.996124i	$0.528037\pi$
$588$	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	−0.240156	−	0.970734i	$-0.577199\pi$
$593$	433.233	−	433.233i	0.730579	−	0.730579i	0.970734	+	0.240156i	$0.0771985\pi$
$594$		−	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	$0.0296773\pi$
$599$			111.533i			0.186198i	−0.995657	+	0.0930989i	$0.970323\pi$
$600$	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	0.710387	−	0.703811i	$-0.248520\pi$
$607$	3.99156	+	3.99156i	0.00657588	+	0.00657588i	−0.703811	+	0.710387i	$0.748520\pi$
$608$	−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	−0.632315	−	0.774712i	$-0.717895\pi$
$613$	87.2893	−	87.2893i	0.142397	−	0.142397i	0.774712	+	0.632315i	$0.217895\pi$
$614$		−	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	0.284385	−	0.958710i	$-0.408211\pi$
$617$	−416.059	−	416.059i	−0.674325	−	0.674325i	−0.958710	+	0.284385i	$0.908211\pi$
$618$	10.0777	−	10.0777i	0.0163070	−	0.0163070i
$619$		−	248.948i		−	0.402178i	−0.979573	−	0.201089i	$-0.935552\pi$
$619$		−	248.948i		−	0.402178i	0.979573	−	0.201089i	$-0.0644480\pi$
$620$	−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	−0.954550	−	0.298052i	$-0.903663\pi$
$643$	−422.128	+	422.128i	−0.656498	+	0.656498i	0.298052	+	0.954550i	$0.403663\pi$
$644$			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	0.973664	−	0.227989i	$-0.0732149\pi$
$647$	482.452	+	482.452i	0.745675	+	0.745675i	−0.227989	+	0.973664i	$0.573215\pi$
$648$	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	−0.266303	−	0.963889i	$-0.585802\pi$
$653$	455.524	−	455.524i	0.697586	−	0.697586i	0.963889	+	0.266303i	$0.0858022\pi$
$654$		−	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	$0.0197525\pi$
$659$			81.7349i			0.124029i	−0.998075	+	0.0620143i	$0.980248\pi$
$660$	−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	−0.923441	−	0.383739i	$-0.874636\pi$
$673$	−363.220	+	363.220i	−0.539702	+	0.539702i	0.383739	+	0.923441i	$0.374636\pi$
$674$			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	0.840791	−	0.541360i	$-0.182090\pi$
$677$	202.715	+	202.715i	0.299431	+	0.299431i	−0.541360	+	0.840791i	$0.682090\pi$
$678$	−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	−0.970144	−	0.242530i	$-0.922023\pi$
$683$	−496.960	+	496.960i	−0.727614	+	0.727614i	0.242530	+	0.970144i	$0.422023\pi$
$684$		−	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	$0.0790725\pi$
$709$			348.639i			0.491733i	−0.969304	+	0.245867i	$0.920927\pi$
$710$	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	$-0.840092\pi$
$719$		−	692.400i		−	0.963003i	0.876445	−	0.481502i	$-0.159908\pi$
$720$	−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	0.979168	−	0.203052i	$-0.0650861\pi$
$727$	564.236	+	564.236i	0.776116	+	0.776116i	−0.203052	+	0.979168i	$0.565086\pi$
$728$	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	−0.984111	−	0.177556i	$-0.943181\pi$
$733$	−591.205	+	591.205i	−0.806555	+	0.806555i	0.177556	+	0.984111i	$0.443181\pi$
$734$			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	$0.0560262\pi$
$739$			258.804i			0.350208i	−0.984550	+	0.175104i	$0.943974\pi$
$740$	−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	−0.673270	−	0.739397i	$-0.735111\pi$
$743$	49.1328	−	49.1328i	0.0661276	−	0.0661276i	0.739397	+	0.673270i	$0.235111\pi$
$744$		−	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	−0.996920	−	0.0784198i	$-0.975013\pi$
$757$	−814.033	−	814.033i	−1.07534	−	1.07534i	−0.0784198	−	0.996920i	$-0.524987\pi$
$758$	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	$0.149023\pi$
$769$			694.030i			0.902510i	−0.892395	+	0.451255i	$0.850977\pi$
$770$	−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	−0.943380	−	0.331714i	$-0.892373\pi$
$773$	−472.817	+	472.817i	−0.611665	+	0.611665i	0.331714	+	0.943380i	$0.392373\pi$
$774$		−	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	−0.996721	−	0.0809093i	$-0.974218\pi$
$787$	−848.095	−	848.095i	−1.07763	−	1.07763i	−0.0809093	−	0.996721i	$-0.525782\pi$
$788$	−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	0.609486	−	0.792797i	$-0.291376\pi$
$797$	−146.099	−	146.099i	−0.183312	−	0.183312i	−0.792797	+	0.609486i	$0.791376\pi$
$798$	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	$0.146136\pi$
$809$			717.004i			0.886284i	−0.896451	+	0.443142i	$0.853864\pi$
$810$	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	−0.796504	−	0.604633i	$-0.793320\pi$
$823$	−157.910	+	157.910i	−0.191872	+	0.191872i	0.604633	+	0.796504i	$0.293320\pi$
$824$		−	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	0.990668	+	0.136299i	$0.0435207\pi$
$827$	932.001	+	932.001i	1.12697	+	1.12697i	0.136299	+	0.990668i	$0.456479\pi$
$828$	−20.3470	+	20.3470i	−0.0245737	+	0.0245737i
$829$			1455.66i			1.75592i	0.478732	+	0.877961i	$0.341097\pi$
$829$			1455.66i			1.75592i	−0.478732	+	0.877961i	$0.658903\pi$
$830$	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	$-0.832867\pi$
$839$		−	841.130i		−	1.00254i	0.865291	−	0.501270i	$-0.167133\pi$
$840$	−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	−0.629628	−	0.776897i	$-0.716793\pi$
$853$	125.620	−	125.620i	0.147269	−	0.147269i	0.776897	+	0.629628i	$0.216793\pi$
$854$		−	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	0.435868	−	0.900011i	$-0.356441\pi$
$857$	−397.770	−	397.770i	−0.464143	−	0.464143i	−0.900011	+	0.435868i	$0.856441\pi$
$858$	299.286	−	299.286i	0.348818	−	0.348818i
$859$		−	577.038i		−	0.671756i	−0.941906	−	0.335878i	$-0.890967\pi$
$859$		−	577.038i		−	0.671756i	0.941906	−	0.335878i	$-0.109033\pi$
$860$	−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	−0.404474	−	0.914550i	$-0.632545\pi$
$863$	440.196	−	440.196i	0.510076	−	0.510076i	0.914550	+	0.404474i	$0.132545\pi$
$864$		−	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	0.963395	+	0.268086i	$0.0863912\pi$
$877$	1080.01	+	1080.01i	1.23148	+	1.23148i	0.268086	+	0.963395i	$0.413609\pi$
$878$	−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	−0.405929	−	0.913905i	$-0.633052\pi$
$883$	448.543	−	448.543i	0.507976	−	0.507976i	0.913905	+	0.405929i	$0.133052\pi$
$884$		−	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	0.986298	−	0.164971i	$-0.0527532\pi$
$887$	728.517	+	728.517i	0.821327	+	0.821327i	−0.164971	+	0.986298i	$0.552753\pi$
$888$	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	0.797779	−	0.602951i	$-0.206008\pi$
$907$	176.709	+	176.709i	0.194828	+	0.194828i	−0.602951	+	0.797779i	$0.706008\pi$
$908$	−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	$-0.859976\pi$
$919$		−	782.706i		−	0.851693i	0.904795	−	0.425847i	$-0.140024\pi$
$920$	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	$-0.763122\pi$
$929$		−	1258.54i		−	1.35473i	0.735647	−	0.677365i	$-0.236878\pi$
$930$	−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	0.577808	−	0.816172i	$-0.303908\pi$
$937$	−223.347	−	223.347i	−0.238364	−	0.238364i	−0.816172	+	0.577808i	$0.803908\pi$
$938$	−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	0.924881	−	0.380257i	$-0.124164\pi$
$947$	515.759	+	515.759i	0.544624	+	0.544624i	−0.380257	+	0.924881i	$0.624164\pi$
$948$	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	−0.0172703	+	0.999851i	$0.505498\pi$
$953$	−969.316	+	969.316i	−1.01712	+	1.01712i	−0.999851	+	0.0172703i	$0.994502\pi$
$954$			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	0.842283	−	0.539036i	$-0.181211\pi$
$967$	293.239	+	293.239i	0.303246	+	0.303246i	−0.539036	+	0.842283i	$0.681211\pi$
$968$	−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	0.630021	−	0.776578i	$-0.283046\pi$
$977$	−143.186	−	143.186i	−0.146556	−	0.146556i	−0.776578	+	0.630021i	$0.783046\pi$
$978$	−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	0.0923919	−	0.995723i	$-0.470549\pi$
$983$	1069.62	−	1069.62i	1.08811	−	1.08811i	0.995723	−	0.0923919i	$-0.0294513\pi$
$984$			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	0.662870	−	0.748734i	$-0.269338\pi$
$997$	−85.6067	−	85.6067i	−0.0858643	−	0.0858643i	−0.748734	+	0.662870i	$0.769338\pi$
$998$	−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.277.2	✓	40
5.3	odd	4	inner	690.3.k.a.553.2	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.k.a.277.2	✓	40	1.1	even	1	trivial
690.3.k.a.553.2	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)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(2.69807 + 4.20956i) q^{5} -2.44949 q^{6} +(-5.61863 - 5.61863i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(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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