LMFDB - Embedded newform 690.3.f.a.229.26

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,3,Mod(229,690)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("690.229");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	690.f (of order $2$, degree $1$, 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:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			229.26
Character	$\chi$	$=$	690.229
Dual form			690.3.f.a.229.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} +1.73205i q^{3} -2.00000 q^{4} +(4.76030 - 1.52956i) q^{5} +2.44949 q^{6} -5.00987 q^{7} +2.82843i q^{8} -3.00000 q^{9} +O(q^{10})$	\(q-1.41421i q^{2} +1.73205i q^{3} -2.00000 q^{4} +(4.76030 - 1.52956i) q^{5} +2.44949 q^{6} -5.00987 q^{7} +2.82843i q^{8} -3.00000 q^{9} +(-2.16312 - 6.73208i) q^{10} +0.0576902i q^{11} -3.46410i q^{12} -4.70984i q^{13} +7.08502i q^{14} +(2.64927 + 8.24508i) q^{15} +4.00000 q^{16} -12.7478 q^{17} +4.24264i q^{18} -27.4834i q^{19} +(-9.52060 + 3.05911i) q^{20} -8.67734i q^{21} +0.0815863 q^{22} +(19.0086 - 12.9489i) q^{23} -4.89898 q^{24} +(20.3209 - 14.5623i) q^{25} -6.66071 q^{26} -5.19615i q^{27} +10.0197 q^{28} -49.2705 q^{29} +(11.6603 - 3.74663i) q^{30} -19.1734 q^{31} -5.65685i q^{32} -0.0999224 q^{33} +18.0281i q^{34} +(-23.8485 + 7.66287i) q^{35} +6.00000 q^{36} +27.0395 q^{37} -38.8673 q^{38} +8.15768 q^{39} +(4.32624 + 13.4642i) q^{40} +37.5883 q^{41} -12.2716 q^{42} +42.1364 q^{43} -0.115380i q^{44} +(-14.2809 + 4.58867i) q^{45} +(-18.3126 - 26.8822i) q^{46} -89.2480i q^{47} +6.92820i q^{48} -23.9012 q^{49} +(-20.5942 - 28.7381i) q^{50} -22.0799i q^{51} +9.41967i q^{52} +90.8728 q^{53} -7.34847 q^{54} +(0.0882405 + 0.274623i) q^{55} -14.1700i q^{56} +47.6026 q^{57} +69.6789i q^{58} -84.9868 q^{59} +(-5.29854 - 16.4902i) q^{60} -108.398i q^{61} +27.1152i q^{62} +15.0296 q^{63} -8.00000 q^{64} +(-7.20396 - 22.4202i) q^{65} +0.141312i q^{66} -59.1930 q^{67} +25.4956 q^{68} +(22.4282 + 32.9238i) q^{69} +(10.8369 + 33.7268i) q^{70} -124.781 q^{71} -8.48528i q^{72} -73.2318i q^{73} -38.2396i q^{74} +(25.2226 + 35.1969i) q^{75} +54.9667i q^{76} -0.289020i q^{77} -11.5367i q^{78} +82.2106i q^{79} +(19.0412 - 6.11823i) q^{80} +9.00000 q^{81} -53.1579i q^{82} -16.6525 q^{83} +17.3547i q^{84} +(-60.6835 + 19.4985i) q^{85} -59.5899i q^{86} -85.3389i q^{87} -0.163173 q^{88} -129.739i q^{89} +(6.48936 + 20.1962i) q^{90} +23.5956i q^{91} +(-38.0171 + 25.8979i) q^{92} -33.2092i q^{93} -126.216 q^{94} +(-42.0374 - 130.829i) q^{95} +9.79796 q^{96} -96.0557 q^{97} +33.8015i q^{98} -0.173071i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 96 q^{4} - 144 q^{9}+O(q^{10}) $ 48 * q - 96 * q^4 - 144 * q^9	$ 48 q - 96 q^{4} - 144 q^{9} + 192 q^{16} + 96 q^{25} + 64 q^{26} - 152 q^{29} - 8 q^{31} + 56 q^{35} + 288 q^{36} - 48 q^{39} + 40 q^{41} - 160 q^{46} + 424 q^{49} + 96 q^{50} + 32 q^{55} + 360 q^{59} - 384 q^{64} + 192 q^{69} - 496 q^{70} - 152 q^{71} + 144 q^{75} + 432 q^{81} - 136 q^{85} + 256 q^{94} + 496 q^{95}+O(q^{100}) $ 48 * q - 96 * q^4 - 144 * q^9 + 192 * q^16 + 96 * q^25 + 64 * q^26 - 152 * q^29 - 8 * q^31 + 56 * q^35 + 288 * q^36 - 48 * q^39 + 40 * q^41 - 160 * q^46 + 424 * q^49 + 96 * q^50 + 32 * q^55 + 360 * q^59 - 384 * q^64 + 192 * q^69 - 496 * q^70 - 152 * q^71 + 144 * q^75 + 432 * q^81 - 136 * q^85 + 256 * q^94 + 496 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$		−	1.41421i		−	0.707107i
$2$		−	1.41421i		−	0.707107i
$3$			1.73205i			0.577350i
$3$			1.73205i			0.577350i
$4$	−2.00000			−0.500000
$5$	4.76030	−	1.52956i	0.952060	−	0.305911i
$5$	4.76030	−	1.52956i	0.952060	−	0.305911i
$6$	2.44949			0.408248
$7$	−5.00987			−0.715695			−0.357848	−	0.933780i	$-0.616489\pi$
$7$	−5.00987			−0.715695			−0.357848	+	0.933780i	$0.616489\pi$
$8$			2.82843i			0.353553i
$9$	−3.00000			−0.333333
$10$	−2.16312	−	6.73208i	−0.216312	−	0.673208i
$11$			0.0576902i			0.00524457i	0.999997	+	0.00262228i	$0.000834700\pi$
$11$			0.0576902i			0.00524457i	−0.999997	+	0.00262228i	$0.999165\pi$
$12$		−	3.46410i		−	0.288675i
$13$		−	4.70984i		−	0.362295i	−0.983456	−	0.181148i	$-0.942019\pi$
$13$		−	4.70984i		−	0.362295i	0.983456	−	0.181148i	$-0.0579812\pi$
$14$			7.08502i			0.506073i
$15$	2.64927	+	8.24508i	0.176618	+	0.549672i
$16$	4.00000			0.250000
$17$	−12.7478			−0.749872			−0.374936	−	0.927051i	$-0.622335\pi$
$17$	−12.7478			−0.749872			−0.374936	+	0.927051i	$0.622335\pi$
$18$			4.24264i			0.235702i
$19$		−	27.4834i		−	1.44649i	−0.690590	−	0.723246i	$-0.742649\pi$
$19$		−	27.4834i		−	1.44649i	0.690590	−	0.723246i	$-0.257351\pi$
$20$	−9.52060	+	3.05911i	−0.476030	+	0.152956i
$21$		−	8.67734i		−	0.413207i
$22$	0.0815863			0.00370847
$23$	19.0086	−	12.9489i	0.826459	−	0.562997i
$23$	19.0086	−	12.9489i	0.826459	−	0.562997i
$24$	−4.89898			−0.204124
$25$	20.3209	−	14.5623i	0.812836	−	0.582492i
$26$	−6.66071			−0.256181
$27$		−	5.19615i		−	0.192450i
$28$	10.0197			0.357848
$29$	−49.2705			−1.69898			−0.849491	−	0.527604i	$-0.823091\pi$
$29$	−49.2705			−1.69898			−0.849491	+	0.527604i	$0.823091\pi$
$30$	11.6603	−	3.74663i	0.388677	−	0.124888i
$31$	−19.1734			−0.618496			−0.309248	−	0.950981i	$-0.600077\pi$
$31$	−19.1734			−0.618496			−0.309248	+	0.950981i	$0.600077\pi$
$32$		−	5.65685i		−	0.176777i
$33$	−0.0999224			−0.00302795
$34$			18.0281i			0.530239i
$35$	−23.8485	+	7.66287i	−0.681385	+	0.218939i
$36$	6.00000			0.166667
$37$	27.0395			0.730796			0.365398	−	0.930851i	$-0.380933\pi$
$37$	27.0395			0.730796			0.365398	+	0.930851i	$0.380933\pi$
$38$	−38.8673			−1.02282
$39$	8.15768			0.209171
$40$	4.32624	+	13.4642i	0.108156	+	0.336604i
$41$	37.5883			0.916788			0.458394	−	0.888749i	$-0.348425\pi$
$41$	37.5883			0.916788			0.458394	+	0.888749i	$0.348425\pi$
$42$	−12.2716			−0.292181
$43$	42.1364			0.979917			0.489959	−	0.871746i	$-0.337012\pi$
$43$	42.1364			0.979917			0.489959	+	0.871746i	$0.337012\pi$
$44$		−	0.115380i		−	0.00262228i
$45$	−14.2809	+	4.58867i	−0.317353	+	0.101970i
$46$	−18.3126	−	26.8822i	−0.398099	−	0.584395i
$47$		−	89.2480i		−	1.89889i	−0.313926	−	0.949447i	$-0.601645\pi$
$47$		−	89.2480i		−	1.89889i	0.313926	−	0.949447i	$-0.398355\pi$
$48$			6.92820i			0.144338i
$49$	−23.9012			−0.487781
$50$	−20.5942	−	28.7381i	−0.411884	−	0.574762i
$51$		−	22.0799i		−	0.432939i
$52$			9.41967i			0.181148i
$53$	90.8728			1.71458			0.857291	−	0.514833i	$-0.172146\pi$
$53$	90.8728			1.71458			0.857291	+	0.514833i	$0.172146\pi$
$54$	−7.34847			−0.136083
$55$	0.0882405	+	0.274623i	0.00160437	+	0.00499314i
$56$		−	14.1700i		−	0.253036i
$57$	47.6026			0.835133
$58$			69.6789i			1.20136i
$59$	−84.9868			−1.44045			−0.720227	−	0.693739i	$-0.755962\pi$
$59$	−84.9868			−1.44045			−0.720227	+	0.693739i	$0.755962\pi$
$60$	−5.29854	−	16.4902i	−0.0883090	−	0.274836i
$61$		−	108.398i		−	1.77702i	−0.458859	−	0.888509i	$-0.651742\pi$
$61$		−	108.398i		−	1.77702i	0.458859	−	0.888509i	$-0.348258\pi$
$62$			27.1152i			0.437343i
$63$	15.0296			0.238565
$64$	−8.00000			−0.125000
$65$	−7.20396	−	22.4202i	−0.110830	−	0.344927i
$66$			0.141312i			0.00214109i
$67$	−59.1930			−0.883478			−0.441739	−	0.897144i	$-0.645638\pi$
$67$	−59.1930			−0.883478			−0.441739	+	0.897144i	$0.645638\pi$
$68$	25.4956			0.374936
$69$	22.4282	+	32.9238i	0.325046	+	0.477156i
$70$	10.8369	+	33.7268i	0.154813	+	0.481812i
$71$	−124.781			−1.75748			−0.878742	−	0.477297i	$-0.841617\pi$
$71$	−124.781			−1.75748			−0.878742	+	0.477297i	$0.841617\pi$
$72$		−	8.48528i		−	0.117851i
$73$		−	73.2318i		−	1.00318i	−0.865107	−	0.501588i	$-0.832749\pi$
$73$		−	73.2318i		−	1.00318i	0.865107	−	0.501588i	$-0.167251\pi$
$74$		−	38.2396i		−	0.516751i
$75$	25.2226	+	35.1969i	0.336302	+	0.469291i
$76$			54.9667i			0.723246i
$77$		−	0.289020i		−	0.00375351i
$78$		−	11.5367i		−	0.147906i
$79$			82.2106i			1.04064i	0.853971	+	0.520320i	$0.174188\pi$
$79$			82.2106i			1.04064i	−0.853971	+	0.520320i	$0.825812\pi$
$80$	19.0412	−	6.11823i	0.238015	−	0.0764778i
$81$	9.00000			0.111111
$82$		−	53.1579i		−	0.648267i
$83$	−16.6525			−0.200632			−0.100316	−	0.994956i	$-0.531985\pi$
$83$	−16.6525			−0.200632			−0.100316	+	0.994956i	$0.531985\pi$
$84$			17.3547i			0.206603i
$85$	−60.6835	+	19.4985i	−0.713923	+	0.229394i
$86$		−	59.5899i		−	0.692906i
$87$		−	85.3389i		−	0.980907i
$88$	−0.163173			−0.00185423
$89$		−	129.739i		−	1.45774i	−0.684650	−	0.728872i	$-0.740045\pi$
$89$		−	129.739i		−	1.45774i	0.684650	−	0.728872i	$-0.259955\pi$
$90$	6.48936	+	20.1962i	0.0721040	+	0.224403i
$91$			23.5956i			0.259293i
$92$	−38.0171	+	25.8979i	−0.413230	+	0.281498i
$93$		−	33.2092i		−	0.357089i
$94$	−126.216			−1.34272
$95$	−42.0374	−	130.829i	−0.442498	−	1.37715i
$96$	9.79796			0.102062
$97$	−96.0557			−0.990265			−0.495133	−	0.868817i	$-0.664881\pi$
$97$	−96.0557			−0.990265			−0.495133	+	0.868817i	$0.664881\pi$
$98$			33.8015i			0.344913i
$99$		−	0.173071i		−	0.00174819i
$100$	−40.6418	+	29.1246i	−0.406418	+	0.291246i
$101$	97.0685			0.961075			0.480537	−	0.876974i	$-0.340442\pi$
$101$	97.0685			0.961075			0.480537	+	0.876974i	$0.340442\pi$
$102$	−31.2257			−0.306134
$103$	−99.2962			−0.964040			−0.482020	−	0.876160i	$-0.660097\pi$
$103$	−99.2962			−0.964040			−0.482020	+	0.876160i	$0.660097\pi$
$104$	13.3214			0.128091
$105$	−13.2725	−	41.3068i	−0.126405	−	0.393398i
$106$		−	128.514i		−	1.21239i
$107$	37.4899			0.350373			0.175186	−	0.984535i	$-0.443947\pi$
$107$	37.4899			0.350373			0.175186	+	0.984535i	$0.443947\pi$
$108$			10.3923i			0.0962250i
$109$			91.9460i			0.843541i	0.906703	+	0.421771i	$0.138591\pi$
$109$			91.9460i			0.843541i	−0.906703	+	0.421771i	$0.861409\pi$
$110$	0.388375	−	0.124791i	0.00353068	−	0.00113446i
$111$			46.8337i			0.421925i
$112$	−20.0395			−0.178924
$113$	154.478			1.36706			0.683530	−	0.729923i	$-0.260444\pi$
$113$	154.478			1.36706			0.683530	+	0.729923i	$0.260444\pi$
$114$		−	67.3202i		−	0.590528i
$115$	70.6803	−	90.7155i	0.614611	−	0.788830i
$116$	98.5409			0.849491
$117$			14.1295i			0.120765i
$118$			120.189i			1.01855i
$119$	63.8649			0.536680
$120$	−23.3206	+	7.49327i	−0.194338	+	0.0624439i
$121$	120.997			0.999972
$122$	−153.298			−1.25654
$123$			65.1048i			0.529308i
$124$	38.3467			0.309248
$125$	74.4598	−	100.403i	0.595678	−	0.803223i
$126$		−	21.2551i		−	0.168691i
$127$			195.303i			1.53782i	0.639360	+	0.768908i	$0.279199\pi$
$127$			195.303i			1.53782i	−0.639360	+	0.768908i	$0.720801\pi$
$128$			11.3137i			0.0883883i
$129$			72.9825i			0.565756i
$130$	−31.7070	+	10.1879i	−0.243900	+	0.0783688i
$131$	−91.1261			−0.695619			−0.347809	−	0.937565i	$-0.613074\pi$
$131$	−91.1261			−0.695619			−0.347809	+	0.937565i	$0.613074\pi$
$132$	0.199845			0.00151398
$133$			137.688i			1.03525i
$134$			83.7116i			0.624713i
$135$	−7.94781	−	24.7352i	−0.0588727	−	0.183224i
$136$		−	36.0563i		−	0.265120i
$137$	−10.3919			−0.0758532			−0.0379266	−	0.999281i	$-0.512075\pi$
$137$	−10.3919			−0.0758532			−0.0379266	+	0.999281i	$0.512075\pi$
$138$	46.5613	−	31.7183i	0.337400	−	0.229843i
$139$	−149.153			−1.07305			−0.536523	−	0.843886i	$-0.680263\pi$
$139$	−149.153			−1.07305			−0.536523	+	0.843886i	$0.680263\pi$
$140$	47.6969	−	15.3257i	0.340692	−	0.109470i
$141$	154.582			1.09633
$142$			176.468i			1.24273i
$143$	0.271712			0.00190008
$144$	−12.0000			−0.0833333
$145$	−234.542	+	75.3620i	−1.61753	+	0.519738i
$146$	−103.565			−0.709352
$147$		−	41.3982i		−	0.281620i
$148$	−54.0789			−0.365398
$149$			134.100i			0.899998i	0.893029	+	0.449999i	$0.148576\pi$
$149$			134.100i			0.899998i	−0.893029	+	0.449999i	$0.851424\pi$
$150$	49.7759	−	35.6702i	0.331839	−	0.237801i
$151$	−105.581			−0.699215			−0.349607	−	0.936896i	$-0.613685\pi$
$151$	−105.581			−0.699215			−0.349607	+	0.936896i	$0.613685\pi$
$152$	77.7347			0.511412
$153$	38.2435			0.249957
$154$	−0.408736			−0.00265413
$155$	−91.2710	+	29.3268i	−0.588845	+	0.189205i
$156$	−16.3154			−0.104586
$157$	195.183			1.24320			0.621601	−	0.783334i	$-0.286482\pi$
$157$	195.183			1.24320			0.621601	+	0.783334i	$0.286482\pi$
$158$	116.263			0.735844
$159$			157.396i			0.989914i
$160$	−8.65248	−	26.9283i	−0.0540780	−	0.168302i
$161$	−95.2303	+	64.8724i	−0.591493	+	0.402934i
$162$		−	12.7279i		−	0.0785674i
$163$			41.2026i			0.252777i	0.991981	+	0.126388i	$0.0403386\pi$
$163$			41.2026i			0.252777i	−0.991981	+	0.126388i	$0.959661\pi$
$164$	−75.1766			−0.458394
$165$	−0.475661	+	0.152837i	−0.00288279	+	0.000926285i
$166$			23.5502i			0.141868i
$167$			97.6594i			0.584787i	0.956298	+	0.292394i	$0.0944517\pi$
$167$			97.6594i			0.584787i	−0.956298	+	0.292394i	$0.905548\pi$
$168$	24.5432			0.146091
$169$	146.817			0.868742
$170$	27.5751	+	85.8194i	0.162206	+	0.504820i
$171$			82.4501i			0.482164i
$172$	−84.2729			−0.489959
$173$		−	89.7436i		−	0.518749i	−0.965777	−	0.259375i	$-0.916484\pi$
$173$		−	89.7436i		−	0.518749i	0.965777	−	0.259375i	$-0.0835164\pi$
$174$	−120.687			−0.693606
$175$	−101.805	+	72.9552i	−0.581743	+	0.416887i
$176$			0.230761i			0.00131114i
$177$		−	147.201i		−	0.831646i
$178$	−183.479			−1.03078
$179$	281.937			1.57507			0.787533	−	0.616273i	$-0.211358\pi$
$179$	281.937			1.57507			0.787533	+	0.616273i	$0.211358\pi$
$180$	28.5618	−	9.17734i	0.158677	−	0.0509852i
$181$			10.6269i			0.0587123i	0.999569	+	0.0293561i	$0.00934569\pi$
$181$			10.6269i			0.0587123i	−0.999569	+	0.0293561i	$0.990654\pi$
$182$	33.3693			0.183348
$183$	187.751			1.02596
$184$	36.6251	+	53.7643i	0.199049	+	0.292197i
$185$	128.716	−	41.3584i	0.695762	−	0.223559i
$186$	−46.9650			−0.252500
$187$		−	0.735425i		−	0.00393275i
$188$			178.496i			0.949447i
$189$			26.0320i			0.137736i
$190$	−185.020	+	59.4498i	−0.973790	+	0.312894i
$191$		−	228.368i		−	1.19564i	−0.801630	−	0.597821i	$-0.796033\pi$
$191$		−	228.368i		−	1.19564i	0.801630	−	0.597821i	$-0.203967\pi$
$192$		−	13.8564i		−	0.0721688i
$193$			273.933i			1.41934i	0.704534	+	0.709671i	$0.251156\pi$
$193$			273.933i			1.41934i	−0.704534	+	0.709671i	$0.748844\pi$
$194$			135.843i			0.700223i
$195$	38.8330	−	12.4776i	0.199144	−	0.0639878i
$196$	47.8025			0.243890
$197$		−	248.662i		−	1.26225i	−0.775683	−	0.631123i	$-0.782594\pi$
$197$		−	248.662i		−	1.26225i	0.775683	−	0.631123i	$-0.217406\pi$
$198$	−0.244759			−0.00123616
$199$		−	78.8866i		−	0.396415i	−0.980160	−	0.198208i	$-0.936488\pi$
$199$		−	78.8866i		−	0.396415i	0.980160	−	0.198208i	$-0.0635120\pi$
$200$	41.1884	+	57.4762i	0.205942	+	0.287381i
$201$		−	102.525i		−	0.510076i
$202$		−	137.276i		−	0.679582i
$203$	246.838			1.21595
$204$			44.1597i			0.216469i
$205$	178.932	−	57.4934i	0.872837	−	0.280456i
$206$			140.426i			0.681679i
$207$	−57.0257	+	38.8468i	−0.275486	+	0.187666i
$208$		−	18.8393i		−	0.0905738i
$209$	1.58552			0.00758622
$210$	−58.4166	+	18.7701i	−0.278174	+	0.0893816i
$211$	307.866			1.45908			0.729541	−	0.683937i	$-0.239734\pi$
$211$	307.866			1.45908			0.729541	+	0.683937i	$0.239734\pi$
$212$	−181.746			−0.857291
$213$		−	216.128i		−	1.01468i
$214$		−	53.0187i		−	0.247751i
$215$	200.582	−	64.4501i	0.932940	−	0.299768i
$216$	14.6969			0.0680414
$217$	96.0560			0.442654
$218$	130.031			0.596474
$219$	126.841			0.579184
$220$	−0.176481	−	0.549246i	−0.000802186	−	0.00249657i
$221$			60.0402i			0.271675i
$222$	66.2329			0.298346
$223$			280.640i			1.25847i	0.777213	+	0.629237i	$0.216633\pi$
$223$			280.640i			1.25847i	−0.777213	+	0.629237i	$0.783367\pi$
$224$			28.3401i			0.126518i
$225$	−60.9627	+	43.6869i	−0.270945	+	0.194164i
$226$		−	218.464i		−	0.966657i
$227$	86.1664			0.379588			0.189794	−	0.981824i	$-0.439218\pi$
$227$	86.1664			0.379588			0.189794	+	0.981824i	$0.439218\pi$
$228$	−95.2051			−0.417566
$229$			161.498i			0.705230i	0.935768	+	0.352615i	$0.114707\pi$
$229$			161.498i			0.705230i	−0.935768	+	0.352615i	$0.885293\pi$
$230$	−128.291	−	99.9571i	−0.557787	−	0.434596i
$231$	0.500598			0.00216709
$232$		−	139.358i		−	0.600681i
$233$		−	331.589i		−	1.42313i	−0.702621	−	0.711564i	$-0.747987\pi$
$233$		−	331.589i		−	1.42313i	0.702621	−	0.711564i	$-0.252013\pi$
$234$	19.9821			0.0853938
$235$	−136.510	−	424.847i	−0.580893	−	1.80786i
$236$	169.974			0.720227
$237$	−142.393			−0.600814
$238$		−	90.3186i		−	0.379490i
$239$	−212.907			−0.890823			−0.445411	−	0.895326i	$-0.646943\pi$
$239$	−212.907			−0.890823			−0.445411	+	0.895326i	$0.646943\pi$
$240$	10.5971	+	32.9803i	0.0441545	+	0.137418i
$241$			405.643i			1.68316i	0.540129	+	0.841582i	$0.318375\pi$
$241$			405.643i			1.68316i	−0.540129	+	0.841582i	$0.681625\pi$
$242$		−	171.115i		−	0.707087i
$243$			15.5885i			0.0641500i
$244$			216.796i			0.888509i
$245$	−113.777	+	36.5583i	−0.464396	+	0.149218i
$246$	92.0721			0.374277
$247$	−129.442			−0.524057
$248$		−	54.2305i		−	0.218671i
$249$		−	28.8429i		−	0.115835i
$250$	−141.991	−	105.302i	−0.567965	−	0.421208i
$251$			139.294i			0.554956i	0.960732	+	0.277478i	$0.0894985\pi$
$251$			139.294i			0.554956i	−0.960732	+	0.277478i	$0.910501\pi$
$252$	−30.0592			−0.119283
$253$	0.747027	+	1.09661i	0.00295267	+	0.00433442i
$254$	276.199			1.08740
$255$	−33.7724	−	105.107i	−0.132441	−	0.412184i
$256$	16.0000			0.0625000
$257$		−	36.2902i		−	0.141207i	−0.997504	−	0.0706036i	$-0.977507\pi$
$257$		−	36.2902i		−	0.141207i	0.997504	−	0.0706036i	$-0.0224925\pi$
$258$	103.213			0.400050
$259$	−135.464			−0.523027
$260$	14.4079	+	44.8405i	0.0554151	+	0.172463i
$261$	147.811			0.566327
$262$			128.872i			0.491877i
$263$	−224.831			−0.854869			−0.427435	−	0.904046i	$-0.640583\pi$
$263$	−224.831			−0.854869			−0.427435	+	0.904046i	$0.640583\pi$
$264$		−	0.282623i		−	0.00107054i
$265$	432.582	−	138.995i	1.63238	−	0.524510i
$266$	194.720			0.732030
$267$	224.715			0.841629
$268$	118.386			0.441739
$269$	194.215			0.721989			0.360995	−	0.932568i	$-0.382437\pi$
$269$	194.215			0.721989			0.360995	+	0.932568i	$0.382437\pi$
$270$	−34.9809	+	11.2399i	−0.129559	+	0.0416293i
$271$	17.2004			0.0634701			0.0317350	−	0.999496i	$-0.489897\pi$
$271$	17.2004			0.0634701			0.0317350	+	0.999496i	$0.489897\pi$
$272$	−50.9913			−0.187468
$273$	−40.8689			−0.149703
$274$			14.6964i			0.0536363i
$275$	0.840102	+	1.17232i	0.00305492	+	0.00426297i
$276$	−44.8564	−	65.8476i	−0.162523	−	0.238578i
$277$			211.498i			0.763530i	0.924259	+	0.381765i	$0.124684\pi$
$277$			211.498i			0.763530i	−0.924259	+	0.381765i	$0.875316\pi$
$278$			210.935i			0.758758i
$279$	57.5201			0.206165
$280$	−21.6739	−	67.4536i	−0.0774067	−	0.240906i
$281$			420.172i			1.49527i	0.664108	+	0.747637i	$0.268812\pi$
$281$			420.172i			1.49527i	−0.664108	+	0.747637i	$0.731188\pi$
$282$		−	218.612i		−	0.775220i
$283$	176.413			0.623368			0.311684	−	0.950186i	$-0.399107\pi$
$283$	176.413			0.623368			0.311684	+	0.950186i	$0.399107\pi$
$284$	249.563			0.878742
$285$	226.602	−	72.8108i	0.795096	−	0.255477i
$286$		−	0.384258i		−	0.00134356i
$287$	−188.312			−0.656140
$288$			16.9706i			0.0589256i
$289$	−126.493			−0.437692
$290$	106.578	+	331.693i	0.367510	+	1.14377i
$291$		−	166.373i		−	0.571730i
$292$			146.464i			0.501588i
$293$	78.3017			0.267241			0.133621	−	0.991033i	$-0.457340\pi$
$293$	78.3017			0.267241			0.133621	+	0.991033i	$0.457340\pi$
$294$	−58.5459			−0.199136
$295$	−404.563	+	129.992i	−1.37140	+	0.440651i
$296$			76.4791i			0.258375i
$297$	0.299767			0.00100932
$298$	189.646			0.636395
$299$	−60.9873	−	89.5272i	−0.203971	−	0.299422i
$300$	−50.4453	−	70.3937i	−0.168151	−	0.234646i
$301$	−211.098			−0.701322
$302$			149.315i			0.494419i
$303$			168.128i			0.554877i
$304$		−	109.933i		−	0.361623i
$305$	−165.801	−	516.007i	−0.543610	−	1.69183i
$306$		−	54.0844i		−	0.176746i
$307$			3.03456i			0.00988456i	0.999988	+	0.00494228i	$0.00157318\pi$
$307$			3.03456i			0.00988456i	−0.999988	+	0.00494228i	$0.998427\pi$
$308$			0.578041i			0.00187676i
$309$		−	171.986i		−	0.556589i
$310$	41.4743	+	129.077i	0.133788	+	0.416376i
$311$	−79.5040			−0.255640			−0.127820	−	0.991797i	$-0.540798\pi$
$311$	−79.5040			−0.255640			−0.127820	+	0.991797i	$0.540798\pi$
$312$			23.0734i			0.0739532i
$313$	442.224			1.41286			0.706428	−	0.707785i	$-0.250306\pi$
$313$	442.224			1.41286			0.706428	+	0.707785i	$0.250306\pi$
$314$		−	276.030i		−	0.879077i
$315$	71.5454	−	22.9886i	0.227128	−	0.0729798i
$316$		−	164.421i		−	0.520320i
$317$			152.526i			0.481154i	0.970630	+	0.240577i	$0.0773367\pi$
$317$			152.526i			0.481154i	−0.970630	+	0.240577i	$0.922663\pi$
$318$	222.592			0.699975
$319$		−	2.84242i		−	0.00891042i
$320$	−38.0824	+	12.2365i	−0.119007	+	0.0382389i
$321$			64.9344i			0.202288i
$322$	91.7434	+	134.676i	0.284917	+	0.418248i
$323$			350.353i			1.08468i
$324$	−18.0000			−0.0555556
$325$	−68.5860	−	95.7082i	−0.211034	−	0.294487i
$326$	58.2693			0.178740
$327$	−159.255			−0.487019
$328$			106.316i			0.324133i
$329$			447.121i			1.35903i
$330$	0.216144	+	0.672686i	0.000654982	+	0.00203844i
$331$	231.930			0.700695			0.350347	−	0.936620i	$-0.386064\pi$
$331$	231.930			0.700695			0.350347	+	0.936620i	$0.386064\pi$
$332$	33.3049			0.100316
$333$	−81.1184			−0.243599
$334$	138.111			0.413507
$335$	−281.776	+	90.5391i	−0.841124	+	0.270266i
$336$		−	34.7094i		−	0.103302i
$337$	−58.8185			−0.174536			−0.0872678	−	0.996185i	$-0.527814\pi$
$337$	−58.8185			−0.174536			−0.0872678	+	0.996185i	$0.527814\pi$
$338$		−	207.631i		−	0.614294i
$339$			267.563i			0.789272i
$340$	121.367	−	38.9970i	0.356961	−	0.114697i
$341$		−	1.10612i		−	0.00324374i
$342$	116.602			0.340941
$343$	365.225			1.06480
$344$			119.180i			0.346453i
$345$	157.124	+	122.422i	0.455431	+	0.354846i
$346$	−126.917			−0.366811
$347$		−	195.974i		−	0.564768i	−0.959301	−	0.282384i	$-0.908875\pi$
$347$		−	195.974i		−	0.564768i	0.959301	−	0.282384i	$-0.0911252\pi$
$348$			170.678i			0.490454i
$349$	−48.6448			−0.139383			−0.0696917	−	0.997569i	$-0.522202\pi$
$349$	−48.6448			−0.139383			−0.0696917	+	0.997569i	$0.522202\pi$
$350$	103.174	+	143.974i	0.294783	+	0.411354i
$351$	−24.4730			−0.0697237
$352$	0.326345			0.000927117
$353$			668.062i			1.89253i	0.323395	+	0.946264i	$0.395176\pi$
$353$			668.062i			1.89253i	−0.323395	+	0.946264i	$0.604824\pi$
$354$	−208.174			−0.588063
$355$	−593.997	+	190.860i	−1.67323	+	0.537634i
$356$			259.478i			0.728872i
$357$			110.617i			0.309852i
$358$		−	398.719i		−	1.11374i
$359$		−	463.881i		−	1.29215i	−0.763275	−	0.646074i	$-0.776410\pi$
$359$		−	463.881i		−	1.29215i	0.763275	−	0.646074i	$-0.223590\pi$
$360$	−12.9787	−	40.3925i	−0.0360520	−	0.112201i
$361$	−394.335			−1.09234
$362$	15.0287			0.0415158
$363$			209.572i			0.577334i
$364$		−	47.1913i		−	0.129646i
$365$	−112.012	−	348.605i	−0.306883	−	0.955083i
$366$		−	265.520i		−	0.725464i
$367$	107.592			0.293167			0.146584	−	0.989198i	$-0.453172\pi$
$367$	107.592			0.293167			0.146584	+	0.989198i	$0.453172\pi$
$368$	76.0342	−	51.7957i	0.206615	−	0.140749i
$369$	−112.765			−0.305596
$370$	−58.4896	−	182.032i	−0.158080	−	0.491978i
$371$	−455.261			−1.22712
$372$			66.4185i			0.178544i
$373$	−321.385			−0.861621			−0.430811	−	0.902442i	$-0.641772\pi$
$373$	−321.385			−0.861621			−0.430811	+	0.902442i	$0.641772\pi$
$374$	−1.04005			−0.00278088
$375$	173.903	+	128.968i	0.463741	+	0.343915i
$376$	252.432			0.671361
$377$			232.056i			0.615533i
$378$	36.8148			0.0973938
$379$		−	191.481i		−	0.505228i	−0.967567	−	0.252614i	$-0.918710\pi$
$379$		−	191.481i		−	0.505228i	0.967567	−	0.252614i	$-0.0812902\pi$
$380$	84.0747	+	261.658i	0.221249	+	0.688574i
$381$	−338.274			−0.887858
$382$	−322.960			−0.845446
$383$	161.155			0.420770			0.210385	−	0.977619i	$-0.432528\pi$
$383$	161.155			0.420770			0.210385	+	0.977619i	$0.432528\pi$
$384$	−19.5959			−0.0510310
$385$	−0.442073	−	1.37582i	−0.00114824	−	0.00357357i
$386$	387.400			1.00363
$387$	−126.409			−0.326639
$388$	192.111			0.495133
$389$		−	732.455i		−	1.88292i	−0.337127	−	0.941459i	$-0.609455\pi$
$389$		−	732.455i		−	1.88292i	0.337127	−	0.941459i	$-0.390545\pi$
$390$	−17.6460	−	54.9181i	−0.0452462	−	0.140816i
$391$	−242.318	+	165.071i	−0.619738	+	0.422176i
$392$		−	67.6029i		−	0.172456i
$393$		−	157.835i		−	0.401616i
$394$	−351.662			−0.892543
$395$	125.746	+	391.347i	0.318344	+	0.990753i
$396$			0.346141i			0.000874094i
$397$		−	67.5165i		−	0.170067i	−0.996378	−	0.0850333i	$-0.972900\pi$
$397$		−	67.5165i		−	0.170067i	0.996378	−	0.0850333i	$-0.0270997\pi$
$398$	−111.563			−0.280308
$399$	−238.482			−0.597700
$400$	81.2836	−	58.2492i	0.203209	−	0.145623i
$401$			511.081i			1.27452i	0.770651	+	0.637258i	$0.219931\pi$
$401$			511.081i			1.27452i	−0.770651	+	0.637258i	$0.780069\pi$
$402$	−144.993			−0.360678
$403$			90.3034i			0.224078i
$404$	−194.137			−0.480537
$405$	42.8427	−	13.7660i	0.105784	−	0.0339902i
$406$		−	349.082i		−	0.859808i
$407$			1.55991i			0.00383271i
$408$	62.4513			0.153067
$409$	−654.480			−1.60020			−0.800098	−	0.599870i	$-0.795219\pi$
$409$	−654.480			−1.60020			−0.800098	+	0.599870i	$0.795219\pi$
$410$	−81.3080	−	253.047i	−0.198312	−	0.617189i
$411$		−	17.9993i		−	0.0437939i
$412$	198.592			0.482020
$413$	425.772			1.03093
$414$	54.9377	+	80.6465i	0.132700	+	0.194798i
$415$	−79.2708	+	25.4709i	−0.191014	+	0.0613757i
$416$	−26.6429			−0.0640453
$417$		−	258.341i		−	0.619524i
$418$		−	2.24226i		−	0.00536427i
$419$		−	744.555i		−	1.77698i	−0.458895	−	0.888491i	$-0.651755\pi$
$419$		−	744.555i		−	1.77698i	0.458895	−	0.888491i	$-0.348245\pi$
$420$	26.5450	+	82.6135i	0.0632023	+	0.196699i
$421$		−	367.212i		−	0.872238i	−0.899889	−	0.436119i	$-0.856353\pi$
$421$		−	367.212i		−	0.872238i	0.899889	−	0.436119i	$-0.143647\pi$
$422$		−	435.389i		−	1.03173i
$423$			267.744i			0.632965i
$424$			257.027i			0.606196i
$425$	−259.047	+	185.638i	−0.609523	+	0.436794i
$426$	−305.651			−0.717490
$427$			543.060i			1.27180i
$428$	−74.9798			−0.175186
$429$			0.470618i			0.00109701i
$430$	−91.1462	−	283.666i	−0.211968	−	0.659688i
$431$			87.9048i			0.203955i	0.994787	+	0.101978i	$0.0325170\pi$
$431$			87.9048i			0.203955i	−0.994787	+	0.101978i	$0.967483\pi$
$432$		−	20.7846i		−	0.0481125i
$433$	−544.174			−1.25675			−0.628377	−	0.777909i	$-0.716280\pi$
$433$	−544.174			−1.25675			−0.628377	+	0.777909i	$0.716280\pi$
$434$		−	135.844i		−	0.313004i
$435$	−130.531	−	406.239i	−0.300071	−	0.933883i
$436$		−	183.892i		−	0.421771i
$437$	−355.880	−	522.419i	−0.814371	−	1.19547i
$438$		−	179.381i		−	0.409545i
$439$	289.288			0.658969			0.329485	−	0.944161i	$-0.393125\pi$
$439$	289.288			0.658969			0.329485	+	0.944161i	$0.393125\pi$
$440$	−0.776750	+	0.249582i	−0.00176534	+	0.000567231i
$441$	71.7037			0.162594
$442$	84.9096			0.192103
$443$			529.489i			1.19523i	0.801782	+	0.597617i	$0.203886\pi$
$443$			529.489i			1.19523i	−0.801782	+	0.597617i	$0.796114\pi$
$444$		−	93.6674i		−	0.210963i
$445$	−198.443	−	617.597i	−0.445940	−	1.38786i
$446$	396.885			0.889876
$447$	−232.267			−0.519614
$448$	40.0789			0.0894619
$449$	411.333			0.916109			0.458055	−	0.888924i	$-0.348546\pi$
$449$	411.333			0.916109			0.458055	+	0.888924i	$0.348546\pi$
$450$	61.7826	+	86.2143i	0.137295	+	0.191587i
$451$			2.16848i			0.00480815i
$452$	−308.955			−0.683530
$453$		−	182.872i		−	0.403692i
$454$		−	121.858i		−	0.268409i
$455$	36.0909	+	112.322i	0.0793206	+	0.246862i
$456$			134.640i			0.295264i
$457$	241.436			0.528307			0.264154	−	0.964481i	$-0.414907\pi$
$457$	241.436			0.528307			0.264154	+	0.964481i	$0.414907\pi$
$458$	228.392			0.498673
$459$			66.2396i			0.144313i
$460$	−141.361	+	181.431i	−0.307306	+	0.394415i
$461$	−523.261			−1.13506			−0.567528	−	0.823354i	$-0.692100\pi$
$461$	−523.261			−1.13506			−0.567528	+	0.823354i	$0.692100\pi$
$462$		−	0.707952i		−	0.00153236i
$463$			563.747i			1.21760i	0.793326	+	0.608798i	$0.208348\pi$
$463$			563.747i			1.21760i	−0.793326	+	0.608798i	$0.791652\pi$
$464$	−197.082			−0.424745
$465$	−50.7954	−	158.086i	−0.109237	−	0.339970i
$466$	−468.937			−1.00630
$467$	−579.075			−1.23999			−0.619995	−	0.784606i	$-0.712865\pi$
$467$	−579.075			−1.23999			−0.619995	+	0.784606i	$0.712865\pi$
$468$		−	28.2590i		−	0.0603825i
$469$	296.549			0.632301
$470$	−600.825	+	193.054i	−1.27835	+	0.410754i
$471$			338.067i			0.717763i
$472$		−	240.379i		−	0.509277i
$473$			2.43086i			0.00513924i
$474$			201.374i			0.424840i
$475$	−400.221	−	558.487i	−0.842570	−	1.17576i
$476$	−127.730			−0.268340
$477$	−272.618			−0.571527
$478$			301.095i			0.629907i
$479$		−	775.222i		−	1.61842i	−0.587521	−	0.809209i	$-0.699896\pi$
$479$		−	775.222i		−	1.61842i	0.587521	−	0.809209i	$-0.300104\pi$
$480$	46.6412	−	14.9865i	0.0971692	−	0.0312219i
$481$		−	127.351i		−	0.264764i
$482$	573.665			1.19018
$483$	−112.362	−	164.944i	−0.232634	−	0.341498i
$484$	−241.993			−0.499986
$485$	−457.254	+	146.923i	−0.942792	+	0.302933i
$486$	22.0454			0.0453609
$487$		−	732.601i		−	1.50431i	−0.658984	−	0.752157i	$-0.729014\pi$
$487$		−	732.601i		−	1.50431i	0.658984	−	0.752157i	$-0.270986\pi$
$488$	306.596			0.628271
$489$	−71.3650			−0.145941
$490$	51.7013	+	160.905i	0.105513	+	0.328378i
$491$	−898.312			−1.82956			−0.914778	−	0.403957i	$-0.867634\pi$
$491$	−898.312			−1.82956			−0.914778	+	0.403957i	$0.867634\pi$
$492$		−	130.210i		−	0.264654i
$493$	628.091			1.27402
$494$			183.059i			0.370564i
$495$	−0.264721	−	0.823868i	−0.000534791	−	0.00166438i
$496$	−76.6935			−0.154624
$497$	625.138			1.25782
$498$	−40.7901			−0.0819077
$499$	277.354			0.555819			0.277909	−	0.960607i	$-0.410359\pi$
$499$	277.354			0.555819			0.277909	+	0.960607i	$0.410359\pi$
$500$	−148.920	+	200.806i	−0.297839	+	0.401612i
$501$	−169.151			−0.337627
$502$	196.991			0.392413
$503$	−188.189			−0.374132			−0.187066	−	0.982347i	$-0.559898\pi$
$503$	−188.189			−0.374132			−0.187066	+	0.982347i	$0.559898\pi$
$504$			42.5101i			0.0843455i
$505$	462.075	−	148.472i	0.915001	−	0.294004i
$506$	1.55084	−	1.05646i	0.00306490	−	0.00208786i
$507$			254.295i			0.501569i
$508$		−	390.605i		−	0.768908i
$509$	695.935			1.36726			0.683630	−	0.729829i	$-0.260400\pi$
$509$	695.935			1.36726			0.683630	+	0.729829i	$0.260400\pi$
$510$	−148.643	+	47.7614i	−0.291458	+	0.0936498i
$511$			366.882i			0.717968i
$512$		−	22.6274i		−	0.0441942i
$513$	−142.808			−0.278378
$514$	−51.3221			−0.0998485
$515$	−472.680	+	151.879i	−0.917824	+	0.294911i
$516$		−	145.965i		−	0.282878i
$517$	5.14874			0.00995888
$518$			191.575i			0.369836i
$519$	155.440			0.299500
$520$	63.4140	−	20.3759i	0.121950	−	0.0391844i
$521$		−	926.782i		−	1.77885i	−0.457079	−	0.889426i	$-0.651104\pi$
$521$		−	926.782i		−	1.77885i	0.457079	−	0.889426i	$-0.348896\pi$
$522$		−	209.037i		−	0.400454i
$523$	42.6407			0.0815311			0.0407655	−	0.999169i	$-0.487020\pi$
$523$	42.6407			0.0815311			0.0407655	+	0.999169i	$0.487020\pi$
$524$	182.252			0.347809
$525$	−126.362	−	176.331i	−0.240690	−	0.335870i
$526$			317.959i			0.604484i
$527$	244.419			0.463793
$528$	−0.399690			−0.000756988
$529$	193.651	−	492.281i	0.366069	−	0.930588i
$530$	−196.569	−	611.763i	−0.370885	−	1.15427i
$531$	254.960			0.480151
$532$		−	275.376i		−	0.517624i
$533$		−	177.035i		−	0.332148i
$534$		−	317.795i		−	0.595121i
$535$	178.463	−	57.3429i	0.333576	−	0.107183i
$536$		−	167.423i		−	0.312357i
$537$			488.329i			0.909365i
$538$		−	274.662i		−	0.510524i
$539$		−	1.37887i		−	0.00255820i
$540$	15.8956	+	49.4705i	0.0294363	+	0.0916120i
$541$	−339.326			−0.627221			−0.313610	−	0.949552i	$-0.601539\pi$
$541$	−339.326			−0.627221			−0.313610	+	0.949552i	$0.601539\pi$
$542$		−	24.3250i		−	0.0448801i
$543$	−18.4064			−0.0338975
$544$			72.1126i			0.132560i
$545$	140.637	+	437.690i	0.258049	+	0.803102i
$546$			57.7973i			0.105856i
$547$			905.630i			1.65563i	0.561001	+	0.827815i	$0.310416\pi$
$547$			905.630i			1.65563i	−0.561001	+	0.827815i	$0.689584\pi$
$548$	20.7838			0.0379266
$549$			325.194i			0.592339i
$550$	1.65791	−	1.18808i	0.00301438	−	0.00216015i
$551$			1354.12i			2.45756i
$552$	−93.1225	+	63.4365i	−0.168700	+	0.114921i
$553$		−	411.864i		−	0.744782i
$554$	299.103			0.539897
$555$	71.6348	+	222.943i	0.129072	+	0.401698i
$556$	298.307			0.536523
$557$	−483.984			−0.868912			−0.434456	−	0.900693i	$-0.643059\pi$
$557$	−483.984			−0.868912			−0.434456	+	0.900693i	$0.643059\pi$
$558$		−	81.3457i		−	0.145781i
$559$		−	198.456i		−	0.355019i
$560$	−95.3939	+	30.6515i	−0.170346	+	0.0547348i
$561$	1.27379			0.00227058
$562$	594.213			1.05732
$563$	350.054			0.621766			0.310883	−	0.950448i	$-0.399375\pi$
$563$	350.054			0.621766			0.310883	+	0.950448i	$0.399375\pi$
$564$	−309.164			−0.548164
$565$	735.360	−	236.282i	1.30152	−	0.418199i
$566$		−	249.486i		−	0.440787i
$567$	−45.0888			−0.0795217
$568$		−	352.935i		−	0.621364i
$569$		−	125.697i		−	0.220908i	−0.993881	−	0.110454i	$-0.964770\pi$
$569$		−	125.697i		−	0.220908i	0.993881	−	0.110454i	$-0.0352305\pi$
$570$	−102.970	−	320.464i	−0.180649	−	0.562218i
$571$			374.097i			0.655161i	0.944823	+	0.327581i	$0.106233\pi$
$571$			374.097i			0.655161i	−0.944823	+	0.327581i	$0.893767\pi$
$572$	−0.543423			−0.000950040
$573$	395.544			0.690304
$574$			266.314i			0.463961i
$575$	197.705	−	539.942i	0.343835	−	0.939030i
$576$	24.0000			0.0416667
$577$		−	399.297i		−	0.692023i	−0.938230	−	0.346012i	$-0.887536\pi$
$577$		−	399.297i		−	0.692023i	0.938230	−	0.346012i	$-0.112464\pi$
$578$			178.888i			0.309495i
$579$	−474.466			−0.819457
$580$	469.084	−	150.724i	0.808766	−	0.259869i
$581$	83.4266			0.143591
$582$	−235.288			−0.404274
$583$			5.24247i			0.00899223i
$584$	207.131			0.354676
$585$	21.6119	+	67.2607i	0.0369434	+	0.114976i
$586$		−	110.735i		−	0.188968i
$587$			27.6368i			0.0470814i	0.999723	+	0.0235407i	$0.00749393\pi$
$587$			27.6368i			0.0470814i	−0.999723	+	0.0235407i	$0.992506\pi$
$588$			82.7963i			0.140810i
$589$			526.948i			0.894649i
$590$	183.837	+	572.138i	0.311587	+	0.969725i
$591$	430.696			0.728758
$592$	108.158			0.182699
$593$		−	466.725i		−	0.787057i	−0.919313	−	0.393528i	$-0.871254\pi$
$593$		−	466.725i		−	0.787057i	0.919313	−	0.393528i	$-0.128746\pi$
$594$		−	0.423935i		−	0.000713695i
$595$	304.016	−	97.6850i	0.510951	−	0.164176i
$596$		−	268.199i		−	0.449999i
$597$	136.636			0.228870
$598$	−126.611	+	86.2491i	−0.211723	+	0.144229i
$599$	−19.5253			−0.0325965			−0.0162983	−	0.999867i	$-0.505188\pi$
$599$	−19.5253			−0.0325965			−0.0162983	+	0.999867i	$0.505188\pi$
$600$	−99.5517	+	71.3404i	−0.165920	+	0.118901i
$601$	−6.59286			−0.0109698			−0.00548491	−	0.999985i	$-0.501746\pi$
$601$	−6.59286			−0.0109698			−0.00548491	+	0.999985i	$0.501746\pi$
$602$			298.538i			0.495910i
$603$	177.579			0.294493
$604$	211.163			0.349607
$605$	575.980	−	185.071i	0.952034	−	0.305903i
$606$	237.768			0.392357
$607$		−	1096.43i		−	1.80632i	−0.429308	−	0.903158i	$-0.641242\pi$
$607$		−	1096.43i		−	1.80632i	0.429308	−	0.903158i	$-0.358758\pi$
$608$	−155.469			−0.255706
$609$			427.537i			0.702031i
$610$	−729.745	+	234.478i	−1.19630	+	0.384390i
$611$	−420.344			−0.687960
$612$	−76.4869			−0.124979
$613$	433.067			0.706472			0.353236	−	0.935534i	$-0.385081\pi$
$613$	433.067			0.706472			0.353236	+	0.935534i	$0.385081\pi$
$614$	4.29152			0.00698944
$615$	99.5815	+	309.919i	0.161921	+	0.503933i
$616$	0.817473			0.00132707
$617$	491.904			0.797252			0.398626	−	0.917114i	$-0.369487\pi$
$617$	491.904			0.797252			0.398626	+	0.917114i	$0.369487\pi$
$618$	−243.225			−0.393568
$619$			346.239i			0.559353i	0.960094	+	0.279676i	$0.0902272\pi$
$619$			346.239i			0.559353i	−0.960094	+	0.279676i	$0.909773\pi$
$620$	182.542	−	58.6535i	0.294423	−	0.0946024i
$621$	−67.2846	−	98.7714i	−0.108349	−	0.159052i
$622$			112.436i			0.180765i
$623$			649.976i			1.04330i
$624$	32.6307			0.0522928
$625$	200.879	−	591.838i	0.321406	−	0.946941i
$626$		−	625.399i		−	0.999040i
$627$			2.74620i			0.00437991i
$628$	−390.366			−0.621601
$629$	−344.694			−0.548003
$630$	−32.5108	−	101.180i	−0.0516045	−	0.160604i
$631$		−	54.2092i		−	0.0859100i	−0.999077	−	0.0429550i	$-0.986323\pi$
$631$		−	54.2092i		−	0.0859100i	0.999077	−	0.0429550i	$-0.0136772\pi$
$632$	−232.527			−0.367922
$633$			533.240i			0.842402i
$634$	215.704			0.340228
$635$	298.726	+	929.699i	0.470435	+	1.46409i
$636$		−	314.793i		−	0.494957i
$637$			112.571i			0.176720i
$638$	−4.01979			−0.00630062
$639$	374.344			0.585828
$640$	17.3050	+	53.8566i	0.0270390	+	0.0841510i
$641$		−	409.970i		−	0.639578i	−0.947489	−	0.319789i	$-0.896388\pi$
$641$		−	409.970i		−	0.639578i	0.947489	−	0.319789i	$-0.103612\pi$
$642$	91.8311			0.143039
$643$	−89.6804			−0.139472			−0.0697359	−	0.997565i	$-0.522216\pi$
$643$	−89.6804			−0.139472			−0.0697359	+	0.997565i	$0.522216\pi$
$644$	190.461	−	129.745i	0.295746	−	0.201467i
$645$	111.631	+	347.418i	0.173071	+	0.538633i
$646$	495.474			0.766987
$647$		−	699.081i		−	1.08050i	−0.841506	−	0.540248i	$-0.818330\pi$
$647$		−	699.081i		−	1.08050i	0.841506	−	0.540248i	$-0.181670\pi$
$648$			25.4558i			0.0392837i
$649$		−	4.90291i		−	0.00755456i
$650$	−135.352	+	96.9953i	−0.208234	+	0.149224i
$651$			166.374i			0.255567i
$652$		−	82.4053i		−	0.126388i
$653$		−	976.805i		−	1.49587i	−0.663770	−	0.747937i	$-0.731045\pi$
$653$		−	976.805i		−	1.49587i	0.663770	−	0.747937i	$-0.268955\pi$
$654$			225.221i			0.344374i
$655$	−433.787	+	139.383i	−0.662271	+	0.212798i
$656$	150.353			0.229197
$657$			219.695i			0.334392i
$658$	632.324			0.960979
$659$		−	721.013i		−	1.09410i	−0.837099	−	0.547051i	$-0.815750\pi$
$659$		−	721.013i		−	1.09410i	0.837099	−	0.547051i	$-0.184250\pi$
$660$	0.951321	−	0.305674i	0.00144140	−	0.000463142i
$661$			666.232i			1.00792i	0.863728	+	0.503958i	$0.168123\pi$
$661$			666.232i			1.00792i	−0.863728	+	0.503958i	$0.831877\pi$
$662$		−	327.998i		−	0.495466i
$663$	−103.993			−0.156852
$664$		−	47.1003i		−	0.0709342i
$665$	210.601	+	655.436i	0.316694	+	0.985618i
$666$			114.719i			0.172250i
$667$	−936.560	+	638.000i	−1.40414	+	0.956521i
$668$		−	195.319i		−	0.292394i
$669$	−486.083			−0.726581
$670$	128.042	+	398.492i	0.191107	+	0.594764i
$671$	6.25351			0.00931969
$672$	−49.0865			−0.0730453
$673$		−	768.734i		−	1.14225i	−0.820863	−	0.571125i	$-0.806507\pi$
$673$		−	768.734i		−	1.14225i	0.820863	−	0.571125i	$-0.193493\pi$
$674$			83.1820i			0.123415i
$675$	−75.6679	−	105.591i	−0.112101	−	0.156430i
$676$	−293.635			−0.434371
$677$	−1314.19			−1.94119			−0.970597	−	0.240712i	$-0.922619\pi$
$677$	−1314.19			−1.94119			−0.970597	+	0.240712i	$0.922619\pi$
$678$	378.392			0.558100
$679$	481.226			0.708728
$680$	−55.1501	−	171.639i	−0.0811031	−	0.252410i
$681$			149.245i			0.219155i
$682$	−1.56428			−0.00229367
$683$			168.078i			0.246087i	0.992401	+	0.123044i	$0.0392655\pi$
$683$			168.078i			0.246087i	−0.992401	+	0.123044i	$0.960734\pi$
$684$		−	164.900i		−	0.241082i
$685$	−49.4685	+	15.8950i	−0.0722168	+	0.0232044i
$686$		−	516.507i		−	0.752925i
$687$	−279.722			−0.407165
$688$	168.546			0.244979
$689$		−	427.996i		−	0.621184i
$690$	173.131	−	222.207i	0.250914	−	0.322039i
$691$	374.231			0.541578			0.270789	−	0.962639i	$-0.412715\pi$
$691$	374.231			0.541578			0.270789	+	0.962639i	$0.412715\pi$
$692$			179.487i			0.259375i
$693$			0.867061i			0.00125117i
$694$	−277.150			−0.399351
$695$	−710.015	+	228.139i	−1.02160	+	0.328257i
$696$	241.375			0.346803
$697$	−479.169			−0.687473
$698$			68.7941i			0.0985589i
$699$	574.329			0.821643
$700$	203.610	−	145.910i	0.290872	−	0.208443i
$701$			296.833i			0.423442i	0.977330	+	0.211721i	$0.0679068\pi$
$701$			296.833i			0.423442i	−0.977330	+	0.211721i	$0.932093\pi$
$702$			34.6101i			0.0493021i
$703$		−	743.135i		−	1.05709i
$704$		−	0.461522i		−	0.000655571i
$705$	735.857	−	236.442i	1.04377	−	0.335379i
$706$	944.783			1.33822
$707$	−486.300			−0.687836
$708$			294.403i			0.415823i
$709$		−	9.61801i		−	0.0135656i	−0.999977	−	0.00678280i	$-0.997841\pi$
$709$		−	9.61801i		−	0.0135656i	0.999977	−	0.00678280i	$-0.00215905\pi$
$710$	269.917	+	840.038i	0.380165	+	1.18315i
$711$		−	246.632i		−	0.346880i
$712$	366.958			0.515390
$713$	−364.458	+	248.275i	−0.511161	+	0.348211i
$714$	156.436			0.219099
$715$	1.29343	−	0.415598i	0.00180899	−	0.000581256i
$716$	−563.874			−0.787533
$717$		−	368.765i		−	0.514317i
$718$	−656.027			−0.913687
$719$	118.958			0.165449			0.0827246	−	0.996572i	$-0.473638\pi$
$719$	118.958			0.165449			0.0827246	+	0.996572i	$0.473638\pi$
$720$	−57.1236	+	18.3547i	−0.0793383	+	0.0254926i
$721$	497.460			0.689959
$722$			557.673i			0.772401i
$723$	−702.594			−0.971775
$724$		−	21.2538i		−	0.0293561i
$725$	−1001.22	+	717.491i	−1.38099	+	0.989643i
$726$	296.380			0.408237
$727$	907.207			1.24788			0.623939	−	0.781473i	$-0.285531\pi$
$727$	907.207			1.24788			0.623939	+	0.781473i	$0.285531\pi$
$728$	−66.7386			−0.0916739
$729$	−27.0000			−0.0370370
$730$	−493.002	+	158.409i	−0.675346	+	0.216999i
$731$	−537.148			−0.734812
$732$	−375.502			−0.512981
$733$	823.465			1.12342			0.561709	−	0.827335i	$-0.310144\pi$
$733$	823.465			1.12342			0.561709	+	0.827335i	$0.310144\pi$
$734$		−	152.159i		−	0.207301i
$735$	−63.3209	−	197.068i	−0.0861508	−	0.268119i
$736$	−73.2502	−	107.529i	−0.0995247	−	0.146099i
$737$		−	3.41486i		−	0.00463346i
$738$			159.474i			0.216089i
$739$	44.1107			0.0596897			0.0298449	−	0.999555i	$-0.490499\pi$
$739$	44.1107			0.0596897			0.0298449	+	0.999555i	$0.490499\pi$
$740$	−257.432	+	82.7168i	−0.347881	+	0.111779i
$741$		−	224.200i		−	0.302564i
$742$			643.836i			0.867703i
$743$	−1253.19			−1.68666			−0.843329	−	0.537398i	$-0.819407\pi$
$743$	−1253.19			−1.68666			−0.843329	+	0.537398i	$0.819407\pi$
$744$	93.9299			0.126250
$745$	205.113	+	638.355i	0.275320	+	0.856852i
$746$			454.507i			0.609258i
$747$	49.9574			0.0668774
$748$			1.47085i			0.00196638i
$749$	−187.819			−0.250760
$750$	182.388	−	245.936i	0.243185	−	0.327915i
$751$		−	157.734i		−	0.210032i	−0.994471	−	0.105016i	$-0.966511\pi$
$751$		−	157.734i		−	0.210032i	0.994471	−	0.105016i	$-0.0334895\pi$
$752$		−	356.992i		−	0.474724i
$753$	−241.264			−0.320404
$754$	328.176			0.435247
$755$	−502.599	+	161.493i	−0.665694	+	0.213898i
$756$		−	52.0641i		−	0.0688678i
$757$	1272.67			1.68120			0.840600	−	0.541656i	$-0.182203\pi$
$757$	1272.67			1.68120			0.840600	+	0.541656i	$0.182203\pi$
$758$	−270.795			−0.357250
$759$	−1.89938	+	1.29389i	−0.00250248	+	0.00170473i
$760$	370.040	−	118.900i	0.486895	−	0.156447i
$761$	939.593			1.23468			0.617341	−	0.786696i	$-0.288210\pi$
$761$	939.593			1.23468			0.617341	+	0.786696i	$0.288210\pi$
$762$			478.392i			0.627810i
$763$		−	460.637i		−	0.603718i
$764$			456.735i			0.597821i
$765$	182.050	−	58.4956i	0.237974	−	0.0764648i
$766$		−	227.908i		−	0.297529i
$767$			400.274i			0.521869i
$768$			27.7128i			0.0360844i
$769$			498.410i			0.648127i	0.946035	+	0.324063i	$0.105049\pi$
$769$			498.410i			0.648127i	−0.946035	+	0.324063i	$0.894951\pi$
$770$	−1.94571	+	0.625186i	−0.00252689	+	0.000811929i
$771$	62.8565			0.0815260
$772$		−	547.866i		−	0.709671i
$773$	740.744			0.958272			0.479136	−	0.877741i	$-0.340950\pi$
$773$	740.744			0.958272			0.479136	+	0.877741i	$0.340950\pi$
$774$			178.770i			0.230969i
$775$	−389.620	+	279.208i	−0.502736	+	0.360269i
$776$		−	271.687i		−	0.350112i
$777$		−	234.631i		−	0.301970i
$778$	−1035.85			−1.33142
$779$		−	1033.05i		−	1.32613i
$780$	−77.6660	+	24.9553i	−0.0995718	+	0.0319939i
$781$		−	7.19867i		−	0.00921724i
$782$	233.445	+	342.689i	0.298523	+	0.438221i
$783$			256.017i			0.326969i
$784$	−95.6050			−0.121945
$785$	929.129	−	298.543i	1.18360	−	0.380310i
$786$	−223.212			−0.283985
$787$	594.442			0.755326			0.377663	−	0.925943i	$-0.376728\pi$
$787$	594.442			0.755326			0.377663	+	0.925943i	$0.376728\pi$
$788$			497.325i			0.631123i
$789$		−	389.418i		−	0.493559i
$790$	553.449	−	177.831i	0.700568	−	0.225103i
$791$	−773.913			−0.978398
$792$	0.489518			0.000618078
$793$	−510.537			−0.643805
$794$	−95.4827			−0.120255
$795$	240.747	+	749.254i	0.302826	+	0.942457i
$796$			157.773i			0.198208i
$797$	683.732			0.857881			0.428941	−	0.903333i	$-0.358887\pi$
$797$	683.732			0.857881			0.428941	+	0.903333i	$0.358887\pi$
$798$			337.265i			0.422638i
$799$			1137.72i			1.42393i
$800$	−82.3768	−	114.952i	−0.102971	−	0.143691i
$801$			389.217i			0.485914i
$802$	722.777			0.901218
$803$	4.22476			0.00526122
$804$			205.051i			0.255038i
$805$	−354.099	+	454.472i	−0.439874	+	0.564562i
$806$	127.708			0.158447
$807$			336.390i			0.416841i
$808$			274.551i			0.339791i
$809$	285.424			0.352811			0.176405	−	0.984318i	$-0.443553\pi$
$809$	285.424			0.352811			0.176405	+	0.984318i	$0.443553\pi$
$810$	−19.4681	−	60.5887i	−0.0240347	−	0.0748009i
$811$	50.2369			0.0619444			0.0309722	−	0.999520i	$-0.490140\pi$
$811$	50.2369			0.0619444			0.0309722	+	0.999520i	$0.490140\pi$
$812$	−493.677			−0.607976
$813$			29.7919i			0.0366445i
$814$	2.20605			0.00271013
$815$	63.0218	+	196.137i	0.0773273	+	0.240659i
$816$		−	88.3195i		−	0.108235i
$817$		−	1158.05i		−	1.41744i
$818$			925.574i			1.13151i
$819$		−	70.7869i		−	0.0864309i
$820$	−357.863	+	114.987i	−0.436418	+	0.140228i
$821$	659.707			0.803541			0.401771	−	0.915740i	$-0.368395\pi$
$821$	659.707			0.803541			0.401771	+	0.915740i	$0.368395\pi$
$822$	−25.4548			−0.0309669
$823$			468.619i			0.569404i	0.958616	+	0.284702i	$0.0918946\pi$
$823$			468.619i			0.569404i	−0.958616	+	0.284702i	$0.908105\pi$
$824$		−	280.852i		−	0.340840i
$825$	−2.03051	+	1.45510i	−0.00246123	+	0.00176376i
$826$		−	602.133i		−	0.728975i
$827$	258.119			0.312115			0.156057	−	0.987748i	$-0.450121\pi$
$827$	258.119			0.312115			0.156057	+	0.987748i	$0.450121\pi$
$828$	114.051	−	77.6936i	0.137743	−	0.0938328i
$829$	431.473			0.520474			0.260237	−	0.965545i	$-0.416199\pi$
$829$	431.473			0.520474			0.260237	+	0.965545i	$0.416199\pi$
$830$	36.0213	+	112.106i	0.0433992	+	0.135067i
$831$	−366.325			−0.440824
$832$			37.6787i			0.0452869i
$833$	304.689			0.365773
$834$	−365.350			−0.438069
$835$	149.376	+	464.888i	0.178893	+	0.556752i
$836$	−3.17104			−0.00379311
$837$			99.6277i			0.119030i
$838$	−1052.96			−1.25652
$839$			394.707i			0.470449i	0.971941	+	0.235225i	$0.0755826\pi$
$839$			394.707i			0.470449i	−0.971941	+	0.235225i	$0.924417\pi$
$840$	116.833	−	37.5403i	0.139087	−	0.0446908i
$841$	1586.58			1.88654
$842$	−519.317			−0.616766
$843$	−727.759			−0.863297
$844$	−615.733			−0.729541
$845$	698.895	−	224.566i	0.827095	−	0.265758i
$846$	378.647			0.447574
$847$	−606.177			−0.715675
$848$	363.491			0.428645
$849$			305.556i			0.359901i
$850$	262.531	+	366.348i	0.308860	+	0.430998i
$851$	513.981	−	350.132i	0.603973	−	0.411436i
$852$			432.255i			0.507342i
$853$			56.3613i			0.0660743i	0.999454	+	0.0330371i	$0.0105180\pi$
$853$			56.3613i			0.0660743i	−0.999454	+	0.0330371i	$0.989482\pi$
$854$	768.003			0.899300
$855$	126.112	+	392.487i	0.147499	+	0.459049i
$856$			106.037i			0.123875i
$857$			409.448i			0.477769i	0.971048	+	0.238884i	$0.0767817\pi$
$857$			409.448i			0.477769i	−0.971048	+	0.238884i	$0.923218\pi$
$858$	0.665555			0.000775705
$859$	−90.4653			−0.105315			−0.0526573	−	0.998613i	$-0.516769\pi$
$859$	−90.4653			−0.105315			−0.0526573	+	0.998613i	$0.516769\pi$
$860$	−401.164	+	128.900i	−0.466470	+	0.149884i
$861$		−	326.166i		−	0.378823i
$862$	124.316			0.144218
$863$		−	1330.86i		−	1.54213i	−0.636757	−	0.771064i	$-0.719725\pi$
$863$		−	1330.86i		−	1.54213i	0.636757	−	0.771064i	$-0.280275\pi$
$864$	−29.3939			−0.0340207
$865$	−137.268	−	427.206i	−0.158691	−	0.493880i
$866$			769.579i			0.888659i
$867$		−	219.092i		−	0.252702i
$868$	−192.112			−0.221327
$869$	−4.74275			−0.00545771
$870$	−574.509	+	184.598i	−0.660355	+	0.212182i
$871$			278.789i			0.320080i
$872$	−260.063			−0.298237
$873$	288.167			0.330088
$874$	−738.812	+	503.290i	−0.845322	+	0.575847i
$875$	−373.033	+	503.005i	−0.426324	+	0.574863i
$876$	−253.682			−0.289592
$877$			262.275i			0.299059i	0.988757	+	0.149530i	$0.0477759\pi$
$877$			262.275i			0.299059i	−0.988757	+	0.149530i	$0.952224\pi$
$878$		−	409.114i		−	0.465962i
$879$			135.622i			0.154292i
$880$	0.352962	+	1.09849i	0.000401093	+	0.00124829i
$881$			1482.36i			1.68259i	0.540579	+	0.841293i	$0.318205\pi$
$881$			1482.36i			1.68259i	−0.540579	+	0.841293i	$0.681795\pi$
$882$		−	101.404i		−	0.114971i
$883$			476.034i			0.539109i	0.962985	+	0.269555i	$0.0868765\pi$
$883$			476.034i			0.539109i	−0.962985	+	0.269555i	$0.913123\pi$
$884$		−	120.080i		−	0.135837i
$885$	−225.153	−	700.723i	−0.254410	−	0.791777i
$886$	748.810			0.845158
$887$			1007.94i			1.13634i	0.822910	+	0.568172i	$0.192349\pi$
$887$			1007.94i			1.13634i	−0.822910	+	0.568172i	$0.807651\pi$
$888$	−132.466			−0.149173
$889$		−	978.439i		−	1.10061i
$890$	−873.415	+	280.641i	−0.981365	+	0.315327i
$891$			0.519212i			0.000582730i
$892$		−	561.280i		−	0.629237i
$893$	−2452.84			−2.74674
$894$			328.476i			0.367423i
$895$	1342.10	−	431.238i	1.49956	−	0.481831i
$896$		−	56.6802i		−	0.0632591i
$897$	155.066	−	105.633i	0.172871	−	0.117763i
$898$		−	581.713i		−	0.647787i
$899$	944.681			1.05081
$900$	121.925	−	87.3738i	0.135473	−	0.0970820i
$901$	−1158.43			−1.28572
$902$	3.06669			0.00339988
$903$		−	365.632i		−	0.404908i
$904$			436.929i			0.483329i
$905$	16.2545	+	50.5873i	0.0179607	+	0.0558976i
$906$	−258.621			−0.285453
$907$	−312.307			−0.344329			−0.172165	−	0.985068i	$-0.555076\pi$
$907$	−312.307			−0.344329			−0.172165	+	0.985068i	$0.555076\pi$
$908$	−172.333			−0.189794
$909$	−291.206			−0.320358
$910$	158.848	−	51.0402i	0.174558	−	0.0560882i
$911$		−	258.875i		−	0.284166i	−0.989855	−	0.142083i	$-0.954620\pi$
$911$		−	258.875i		−	0.284166i	0.989855	−	0.142083i	$-0.0453799\pi$
$912$	190.410			0.208783
$913$		−	0.960685i		−	0.00105223i
$914$		−	341.443i		−	0.373570i
$915$	893.751	−	287.176i	0.976777	−	0.313853i
$916$		−	322.995i		−	0.352615i
$917$	456.529			0.497851
$918$	93.6770			0.102045
$919$			522.578i			0.568637i	0.958730	+	0.284319i	$0.0917673\pi$
$919$			522.578i			0.568637i	−0.958730	+	0.284319i	$0.908233\pi$
$920$	256.582	+	199.914i	0.278894	+	0.217298i
$921$	−5.25601			−0.00570686
$922$			740.003i			0.802606i
$923$			587.700i			0.636728i
$924$	−1.00120			−0.00108355
$925$	549.466	−	393.757i	0.594018	−	0.425683i
$926$	797.258			0.860970
$927$	297.888			0.321347
$928$			278.716i			0.300340i
$929$	−70.1132			−0.0754717			−0.0377358	−	0.999288i	$-0.512015\pi$
$929$	−70.1132			−0.0754717			−0.0377358	+	0.999288i	$0.512015\pi$
$930$	−223.567	+	71.8356i	−0.240395	+	0.0772426i
$931$			656.886i			0.705571i
$932$			663.178i			0.711564i
$933$		−	137.705i		−	0.147594i
$934$			818.936i			0.876805i
$935$	−1.12487	−	3.50084i	−0.00120307	−	0.00374422i
$936$	−39.9643			−0.0426969
$937$	−142.612			−0.152201			−0.0761004	−	0.997100i	$-0.524247\pi$
$937$	−142.612			−0.152201			−0.0761004	+	0.997100i	$0.524247\pi$
$938$		−	419.384i		−	0.447104i
$939$			765.954i			0.815712i
$940$	273.020	+	849.695i	0.290447	+	0.903931i
$941$			773.453i			0.821948i	0.911647	+	0.410974i	$0.134811\pi$
$941$			773.453i			0.821948i	−0.911647	+	0.410974i	$0.865189\pi$
$942$	478.098			0.507535
$943$	714.499	−	486.728i	0.757687	−	0.516149i
$944$	−339.947			−0.360113
$945$	39.8175	+	123.920i	0.0421349	+	0.131133i
$946$	3.43776			0.00363399
$947$			1508.84i			1.59328i	0.604452	+	0.796642i	$0.293392\pi$
$947$			1508.84i			1.59328i	−0.604452	+	0.796642i	$0.706608\pi$
$948$	284.786			0.300407
$949$	−344.910			−0.363446
$950$	−789.820	+	565.998i	−0.831389	+	0.595787i
$951$	−264.183			−0.277795
$952$			180.637i			0.189745i
$953$	−1589.34			−1.66773			−0.833863	−	0.551971i	$-0.813876\pi$
$953$	−1589.34			−1.66773			−0.833863	+	0.551971i	$0.813876\pi$
$954$			385.541i			0.404131i
$955$	−349.301	−	1087.10i	−0.365760	−	1.13832i
$956$	425.813			0.445411
$957$	4.92322			0.00514443
$958$	−1096.33			−1.14439
$959$	52.0620			0.0542878
$960$	−21.1942	−	65.9607i	−0.0220773	−	0.0687090i
$961$	−593.382			−0.617463
$962$	−180.102			−0.187216
$963$	−112.470			−0.116791
$964$		−	811.285i		−	0.841582i
$965$	418.996	+	1304.00i	0.434193	+	1.35130i
$966$	−233.266	+	158.904i	−0.241476	+	0.164497i
$967$			112.623i			0.116467i	0.998303	+	0.0582333i	$0.0185467\pi$
$967$			112.623i			0.116467i	−0.998303	+	0.0582333i	$0.981453\pi$
$968$			342.230i			0.353544i
$969$	−606.829			−0.626242
$970$	207.780	+	646.655i	0.214206	+	0.666655i
$971$		−	365.265i		−	0.376174i	−0.982152	−	0.188087i	$-0.939771\pi$
$971$		−	365.265i		−	0.376174i	0.982152	−	0.188087i	$-0.0602287\pi$
$972$		−	31.1769i		−	0.0320750i
$973$	747.239			0.767974
$974$	−1036.05			−1.06371
$975$	165.771	−	118.795i	0.170022	−	0.121841i
$976$		−	433.592i		−	0.444254i
$977$	1277.38			1.30745			0.653724	−	0.756733i	$-0.273206\pi$
$977$	1277.38			1.30745			0.653724	+	0.756733i	$0.273206\pi$
$978$			100.925i			0.103196i
$979$	7.48468			0.00764523
$980$	227.554	−	73.1166i	0.232198	−	0.0746088i
$981$		−	275.838i		−	0.281180i
$982$			1270.40i			1.29369i
$983$	1656.92			1.68557			0.842786	−	0.538248i	$-0.180914\pi$
$983$	1656.92			1.68557			0.842786	+	0.538248i	$0.180914\pi$
$984$	−184.144			−0.187138
$985$	−380.343	−	1183.71i	−0.386135	−	1.20173i
$986$		−	888.255i		−	0.900867i
$987$	−774.436			−0.784636
$988$	258.884			0.262029
$989$	800.953	−	545.622i	0.809861	−	0.551690i
$990$	−1.16513	+	0.374373i	−0.00117689	+	0.000378154i
$991$	1467.20			1.48052			0.740260	−	0.672321i	$-0.234702\pi$
$991$	1467.20			1.48052			0.740260	+	0.672321i	$0.234702\pi$
$992$			108.461i			0.109336i
$993$			401.714i			0.404546i
$994$		−	884.079i		−	0.889415i
$995$	−120.662	−	375.524i	−0.121268	−	0.377411i
$996$			57.6859i			0.0579175i
$997$		−	819.233i		−	0.821698i	−0.911703	−	0.410849i	$-0.865232\pi$
$997$		−	819.233i		−	0.821698i	0.911703	−	0.410849i	$-0.134768\pi$
$998$		−	392.237i		−	0.393023i
$999$		−	140.501i		−	0.140642i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.f.a.229.26	yes	48
5.4	even	2	inner	690.3.f.a.229.27	yes	48
23.22	odd	2	inner	690.3.f.a.229.25	✓	48
115.114	odd	2	inner	690.3.f.a.229.28	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.f.a.229.25	✓	48	23.22	odd	2	inner
690.3.f.a.229.26	yes	48	1.1	even	1	trivial
690.3.f.a.229.27	yes	48	5.4	even	2	inner
690.3.f.a.229.28	yes	48	115.114	odd	2	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.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} +1.73205i q^{3} -2.00000 q^{4} +(4.76030 - 1.52956i) q^{5} +2.44949 q^{6} -5.00987 q^{7} +2.82843i q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q-1.41421i q^{2} +1.73205i q^{3} -2.00000 q^{4} +(4.76030 - 1.52956i) q^{5} +2.44949 q^{6} -5.00987 q^{7} +2.82843i q^{8} -3.00000 q^{9} +(-2.16312 - 6.73208i) q^{10} +0.0576902i q^{11} -3.46410i q^{12} -4.70984i q^{13} +7.08502i q^{14} +(2.64927 + 8.24508i) q^{15} +4.00000 q^{16} -12.7478 q^{17} +4.24264i q^{18} -27.4834i q^{19} +(-9.52060 + 3.05911i) q^{20} -8.67734i q^{21} +0.0815863 q^{22} +(19.0086 - 12.9489i) q^{23} -4.89898 q^{24} +(20.3209 - 14.5623i) q^{25} -6.66071 q^{26} -5.19615i q^{27} +10.0197 q^{28} -49.2705 q^{29} +(11.6603 - 3.74663i) q^{30} -19.1734 q^{31} -5.65685i q^{32} -0.0999224 q^{33} +18.0281i q^{34} +(-23.8485 + 7.66287i) q^{35} +6.00000 q^{36} +27.0395 q^{37} -38.8673 q^{38} +8.15768 q^{39} +(4.32624 + 13.4642i) q^{40} +37.5883 q^{41} -12.2716 q^{42} +42.1364 q^{43} -0.115380i q^{44} +(-14.2809 + 4.58867i) q^{45} +(-18.3126 - 26.8822i) q^{46} -89.2480i q^{47} +6.92820i q^{48} -23.9012 q^{49} +(-20.5942 - 28.7381i) q^{50} -22.0799i q^{51} +9.41967i q^{52} +90.8728 q^{53} -7.34847 q^{54} +(0.0882405 + 0.274623i) q^{55} -14.1700i q^{56} +47.6026 q^{57} +69.6789i q^{58} -84.9868 q^{59} +(-5.29854 - 16.4902i) q^{60} -108.398i q^{61} +27.1152i q^{62} +15.0296 q^{63} -8.00000 q^{64} +(-7.20396 - 22.4202i) q^{65} +0.141312i q^{66} -59.1930 q^{67} +25.4956 q^{68} +(22.4282 + 32.9238i) q^{69} +(10.8369 + 33.7268i) q^{70} -124.781 q^{71} -8.48528i q^{72} -73.2318i q^{73} -38.2396i q^{74} +(25.2226 + 35.1969i) q^{75} +54.9667i q^{76} -0.289020i q^{77} -11.5367i q^{78} +82.2106i q^{79} +(19.0412 - 6.11823i) q^{80} +9.00000 q^{81} -53.1579i q^{82} -16.6525 q^{83} +17.3547i q^{84} +(-60.6835 + 19.4985i) q^{85} -59.5899i q^{86} -85.3389i q^{87} -0.163173 q^{88} -129.739i q^{89} +(6.48936 + 20.1962i) q^{90} +23.5956i q^{91} +(-38.0171 + 25.8979i) q^{92} -33.2092i q^{93} -126.216 q^{94} +(-42.0374 - 130.829i) q^{95} +9.79796 q^{96} -96.0557 q^{97} +33.8015i q^{98} -0.173071i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 96 q^{4} - 144 q^{9}+O(q^{10}) \) 48 * q - 96 * q^4 - 144 * q^9	\( 48 q - 96 q^{4} - 144 q^{9} + 192 q^{16} + 96 q^{25} + 64 q^{26} - 152 q^{29} - 8 q^{31} + 56 q^{35} + 288 q^{36} - 48 q^{39} + 40 q^{41} - 160 q^{46} + 424 q^{49} + 96 q^{50} + 32 q^{55} + 360 q^{59} - 384 q^{64} + 192 q^{69} - 496 q^{70} - 152 q^{71} + 144 q^{75} + 432 q^{81} - 136 q^{85} + 256 q^{94} + 496 q^{95}+O(q^{100}) \) 48 * q - 96 * q^4 - 144 * q^9 + 192 * q^16 + 96 * q^25 + 64 * q^26 - 152 * q^29 - 8 * q^31 + 56 * q^35 + 288 * q^36 - 48 * q^39 + 40 * q^41 - 160 * q^46 + 424 * q^49 + 96 * q^50 + 32 * q^55 + 360 * q^59 - 384 * q^64 + 192 * q^69 - 496 * q^70 - 152 * q^71 + 144 * q^75 + 432 * q^81 - 136 * q^85 + 256 * q^94 + 496 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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