LMFDB - Embedded newform 690.3.f.a.229.20

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			229.20
Character	$\chi$	$=$	690.229
Dual form			690.3.f.a.229.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421i q^{2} -1.73205i q^{3} -2.00000 q^{4} +(1.15789 + 4.86408i) q^{5} +2.44949 q^{6} -1.79343 q^{7} -2.82843i q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+1.41421i q^{2} -1.73205i q^{3} -2.00000 q^{4} +(1.15789 + 4.86408i) q^{5} +2.44949 q^{6} -1.79343 q^{7} -2.82843i q^{8} -3.00000 q^{9} +(-6.87885 + 1.63751i) q^{10} -0.382184i q^{11} +3.46410i q^{12} -24.0468i q^{13} -2.53629i q^{14} +(8.42483 - 2.00553i) q^{15} +4.00000 q^{16} +22.1605 q^{17} -4.24264i q^{18} -17.6049i q^{19} +(-2.31579 - 9.72816i) q^{20} +3.10631i q^{21} +0.540489 q^{22} +(-1.50786 + 22.9505i) q^{23} -4.89898 q^{24} +(-22.3186 + 11.2642i) q^{25} +34.0074 q^{26} +5.19615i q^{27} +3.58685 q^{28} -1.79697 q^{29} +(2.83625 + 11.9145i) q^{30} +40.3465 q^{31} +5.65685i q^{32} -0.661961 q^{33} +31.3397i q^{34} +(-2.07660 - 8.72337i) q^{35} +6.00000 q^{36} +42.7110 q^{37} +24.8971 q^{38} -41.6503 q^{39} +(13.7577 - 3.27502i) q^{40} +1.26689 q^{41} -4.39298 q^{42} +16.5675 q^{43} +0.764367i q^{44} +(-3.47368 - 14.5922i) q^{45} +(-32.4569 - 2.13244i) q^{46} -5.75045i q^{47} -6.92820i q^{48} -45.7836 q^{49} +(-15.9300 - 31.5632i) q^{50} -38.3831i q^{51} +48.0937i q^{52} +81.4797 q^{53} -7.34847 q^{54} +(1.85897 - 0.442528i) q^{55} +5.07258i q^{56} -30.4925 q^{57} -2.54131i q^{58} +18.0948 q^{59} +(-16.8497 + 4.01106i) q^{60} -33.1411i q^{61} +57.0586i q^{62} +5.38028 q^{63} -8.00000 q^{64} +(116.966 - 27.8437i) q^{65} -0.936155i q^{66} +116.835 q^{67} -44.3210 q^{68} +(39.7515 + 2.61169i) q^{69} +(12.3367 - 2.93676i) q^{70} +28.3516 q^{71} +8.48528i q^{72} -112.311i q^{73} +60.4025i q^{74} +(19.5101 + 38.6569i) q^{75} +35.2098i q^{76} +0.685419i q^{77} -58.9025i q^{78} +62.0766i q^{79} +(4.63158 + 19.4563i) q^{80} +9.00000 q^{81} +1.79165i q^{82} +148.140 q^{83} -6.21261i q^{84} +(25.6595 + 107.790i) q^{85} +23.4300i q^{86} +3.11245i q^{87} -1.08098 q^{88} -102.736i q^{89} +(20.6365 - 4.91253i) q^{90} +43.1262i q^{91} +(3.01572 - 45.9010i) q^{92} -69.8822i q^{93} +8.13236 q^{94} +(85.6316 - 20.3846i) q^{95} +9.79796 q^{96} -150.611 q^{97} -64.7478i q^{98} +1.14655i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	1.15789	+	4.86408i	0.231579	+	0.972816i
$5$	1.15789	+	4.86408i	0.231579	+	0.972816i
$6$	2.44949			0.408248
$7$	−1.79343			−0.256204			−0.128102	−	0.991761i	$-0.540888\pi$
$7$	−1.79343			−0.256204			−0.128102	+	0.991761i	$0.540888\pi$
$8$		−	2.82843i		−	0.353553i
$9$	−3.00000			−0.333333
$10$	−6.87885	+	1.63751i	−0.687885	+	0.163751i
$11$		−	0.382184i		−	0.0347440i	−0.999849	−	0.0173720i	$-0.994470\pi$
$11$		−	0.382184i		−	0.0347440i	0.999849	−	0.0173720i	$-0.00552995\pi$
$12$			3.46410i			0.288675i
$13$		−	24.0468i		−	1.84976i	−0.380264	−	0.924878i	$-0.624167\pi$
$13$		−	24.0468i		−	1.84976i	0.380264	−	0.924878i	$-0.375833\pi$
$14$		−	2.53629i		−	0.181164i
$15$	8.42483	−	2.00553i	0.561656	−	0.133702i
$16$	4.00000			0.250000
$17$	22.1605			1.30356			0.651779	−	0.758409i	$-0.274023\pi$
$17$	22.1605			1.30356			0.651779	+	0.758409i	$0.274023\pi$
$18$		−	4.24264i		−	0.235702i
$19$		−	17.6049i		−	0.926573i	−0.886209	−	0.463286i	$-0.846670\pi$
$19$		−	17.6049i		−	0.926573i	0.886209	−	0.463286i	$-0.153330\pi$
$20$	−2.31579	−	9.72816i	−0.115789	−	0.486408i
$21$			3.10631i			0.147919i
$22$	0.540489			0.0245677
$23$	−1.50786	+	22.9505i	−0.0655591	+	0.997849i
$23$	−1.50786	+	22.9505i	−0.0655591	+	0.997849i
$24$	−4.89898			−0.204124
$25$	−22.3186	+	11.2642i	−0.892742	+	0.450567i
$26$	34.0074			1.30798
$27$			5.19615i			0.192450i
$28$	3.58685			0.128102
$29$	−1.79697			−0.0619646			−0.0309823	−	0.999520i	$-0.509864\pi$
$29$	−1.79697			−0.0619646			−0.0309823	+	0.999520i	$0.509864\pi$
$30$	2.83625	+	11.9145i	0.0945417	+	0.397151i
$31$	40.3465			1.30150			0.650750	−	0.759292i	$-0.274455\pi$
$31$	40.3465			1.30150			0.650750	+	0.759292i	$0.274455\pi$
$32$			5.65685i			0.176777i
$33$	−0.661961			−0.0200594
$34$			31.3397i			0.921755i
$35$	−2.07660	−	8.72337i	−0.0593314	−	0.249239i
$36$	6.00000			0.166667
$37$	42.7110			1.15435			0.577175	−	0.816620i	$-0.304155\pi$
$37$	42.7110			1.15435			0.577175	+	0.816620i	$0.304155\pi$
$38$	24.8971			0.655186
$39$	−41.6503			−1.06796
$40$	13.7577	−	3.27502i	0.343942	−	0.0818755i
$41$	1.26689			0.0308998			0.0154499	−	0.999881i	$-0.495082\pi$
$41$	1.26689			0.0308998			0.0154499	+	0.999881i	$0.495082\pi$
$42$	−4.39298			−0.104595
$43$	16.5675			0.385291			0.192646	−	0.981268i	$-0.438293\pi$
$43$	16.5675			0.385291			0.192646	+	0.981268i	$0.438293\pi$
$44$			0.764367i			0.0173720i
$45$	−3.47368	−	14.5922i	−0.0771930	−	0.324272i
$46$	−32.4569	−	2.13244i	−0.705586	−	0.0463573i
$47$		−	5.75045i		−	0.122350i	−0.998127	−	0.0611750i	$-0.980515\pi$
$47$		−	5.75045i		−	0.122350i	0.998127	−	0.0611750i	$-0.0194848\pi$
$48$		−	6.92820i		−	0.144338i
$49$	−45.7836			−0.934360
$50$	−15.9300	−	31.5632i	−0.318599	−	0.631264i
$51$		−	38.3831i		−	0.752610i
$52$			48.0937i			0.924878i
$53$	81.4797			1.53735			0.768677	−	0.639637i	$-0.220915\pi$
$53$	81.4797			1.53735			0.768677	+	0.639637i	$0.220915\pi$
$54$	−7.34847			−0.136083
$55$	1.85897	−	0.442528i	0.0337995	−	0.00804597i
$56$			5.07258i			0.0905818i
$57$	−30.4925			−0.534957
$58$		−	2.54131i		−	0.0438156i
$59$	18.0948			0.306691			0.153346	−	0.988173i	$-0.450995\pi$
$59$	18.0948			0.306691			0.153346	+	0.988173i	$0.450995\pi$
$60$	−16.8497	+	4.01106i	−0.280828	+	0.0668511i
$61$		−	33.1411i		−	0.543296i	−0.962397	−	0.271648i	$-0.912431\pi$
$61$		−	33.1411i		−	0.543296i	0.962397	−	0.271648i	$-0.0875687\pi$
$62$			57.0586i			0.920300i
$63$	5.38028			0.0854013
$64$	−8.00000			−0.125000
$65$	116.966	−	27.8437i	1.79947	−	0.428365i
$66$		−	0.936155i		−	0.0141842i
$67$	116.835			1.74381			0.871904	−	0.489677i	$-0.162885\pi$
$67$	116.835			1.74381			0.871904	+	0.489677i	$0.162885\pi$
$68$	−44.3210			−0.651779
$69$	39.7515	+	2.61169i	0.576108	+	0.0378506i
$70$	12.3367	−	2.93676i	0.176239	−	0.0419537i
$71$	28.3516			0.399318			0.199659	−	0.979865i	$-0.436017\pi$
$71$	28.3516			0.399318			0.199659	+	0.979865i	$0.436017\pi$
$72$			8.48528i			0.117851i
$73$		−	112.311i		−	1.53850i	−0.638948	−	0.769250i	$-0.720630\pi$
$73$		−	112.311i		−	1.53850i	0.638948	−	0.769250i	$-0.279370\pi$
$74$			60.4025i			0.816249i
$75$	19.5101	+	38.6569i	0.260135	+	0.515425i
$76$			35.2098i			0.463286i
$77$			0.685419i			0.00890154i
$78$		−	58.9025i		−	0.755160i
$79$			62.0766i			0.785780i	0.919585	+	0.392890i	$0.128525\pi$
$79$			62.0766i			0.785780i	−0.919585	+	0.392890i	$0.871475\pi$
$80$	4.63158	+	19.4563i	0.0578947	+	0.243204i
$81$	9.00000			0.111111
$82$			1.79165i			0.0218494i
$83$	148.140			1.78481			0.892407	−	0.451231i	$-0.149015\pi$
$83$	148.140			1.78481			0.892407	+	0.451231i	$0.149015\pi$
$84$		−	6.21261i		−	0.0739597i
$85$	25.6595	+	107.790i	0.301877	+	1.26812i
$86$			23.4300i			0.272442i
$87$			3.11245i			0.0357753i
$88$	−1.08098			−0.0122838
$89$		−	102.736i		−	1.15434i	−0.816623	−	0.577171i	$-0.804157\pi$
$89$		−	102.736i		−	1.15434i	0.816623	−	0.577171i	$-0.195843\pi$
$90$	20.6365	−	4.91253i	0.229295	−	0.0545837i
$91$			43.1262i			0.473915i
$92$	3.01572	−	45.9010i	0.0327796	−	0.498924i
$93$		−	69.8822i		−	0.751422i
$94$	8.13236			0.0865145
$95$	85.6316	−	20.3846i	0.901385	−	0.214575i
$96$	9.79796			0.102062
$97$	−150.611			−1.55269			−0.776343	−	0.630310i	$-0.782928\pi$
$97$	−150.611			−1.55269			−0.776343	+	0.630310i	$0.782928\pi$
$98$		−	64.7478i		−	0.660692i
$99$			1.14655i			0.0115813i
$100$	44.6371	−	22.5284i	0.446371	−	0.225284i
$101$	−105.835			−1.04787			−0.523937	−	0.851757i	$-0.675537\pi$
$101$	−105.835			−1.04787			−0.523937	+	0.851757i	$0.675537\pi$
$102$	54.2819			0.532175
$103$	−110.093			−1.06886			−0.534432	−	0.845211i	$-0.679474\pi$
$103$	−110.093			−1.06886			−0.534432	+	0.845211i	$0.679474\pi$
$104$	−68.0147			−0.653988
$105$	−15.1093	+	3.59678i	−0.143898	+	0.0342550i
$106$			115.230i			1.08707i
$107$	145.434			1.35920			0.679599	−	0.733584i	$-0.262154\pi$
$107$	145.434			1.35920			0.679599	+	0.733584i	$0.262154\pi$
$108$		−	10.3923i		−	0.0962250i
$109$			108.845i			0.998578i	0.866435	+	0.499289i	$0.166405\pi$
$109$			108.845i			0.998578i	−0.866435	+	0.499289i	$0.833595\pi$
$110$	0.625830	+	2.62898i	0.00568936	+	0.0238998i
$111$		−	73.9776i		−	0.666465i
$112$	−7.17371			−0.0640510
$113$	−56.0495			−0.496013			−0.248007	−	0.968758i	$-0.579775\pi$
$113$	−56.0495			−0.496013			−0.248007	+	0.968758i	$0.579775\pi$
$114$		−	43.1230i		−	0.378272i
$115$	−113.379	+	19.2399i	−0.985905	+	0.167304i
$116$	3.59395			0.0309823
$117$			72.1405i			0.616585i
$118$			25.5899i			0.216863i
$119$	−39.7432			−0.333977
$120$	−5.67250	−	23.8290i	−0.0472709	−	0.198575i
$121$	120.854			0.998793
$122$	46.8686			0.384169
$123$		−	2.19432i		−	0.0178400i
$124$	−80.6930			−0.650750
$125$	−80.6325	−	95.5165i	−0.645060	−	0.764132i
$126$			7.60887i			0.0603878i
$127$		−	67.2083i		−	0.529199i	−0.964358	−	0.264599i	$-0.914760\pi$
$127$		−	67.2083i		−	0.529199i	0.964358	−	0.264599i	$-0.0852397\pi$
$128$		−	11.3137i		−	0.0883883i
$129$		−	28.6958i		−	0.222448i
$130$	39.3769	+	165.415i	0.302899	+	1.27242i
$131$	−144.689			−1.10450			−0.552249	−	0.833679i	$-0.686230\pi$
$131$	−144.689			−1.10450			−0.552249	+	0.833679i	$0.686230\pi$
$132$	1.32392			0.0100297
$133$			31.5731i			0.237392i
$134$			165.230i			1.23306i
$135$	−25.2745	+	6.01660i	−0.187219	+	0.0445674i
$136$		−	62.6793i		−	0.460877i
$137$	−66.2233			−0.483381			−0.241691	−	0.970353i	$-0.577702\pi$
$137$	−66.2233			−0.483381			−0.241691	+	0.970353i	$0.577702\pi$
$138$	−3.69349	+	56.2171i	−0.0267644	+	0.407370i
$139$	58.2706			0.419213			0.209606	−	0.977786i	$-0.432782\pi$
$139$	58.2706			0.419213			0.209606	+	0.977786i	$0.432782\pi$
$140$	4.15320	+	17.4467i	0.0296657	+	0.124620i
$141$	−9.96007			−0.0706388
$142$			40.0952i			0.282360i
$143$	−9.19030			−0.0642679
$144$	−12.0000			−0.0833333
$145$	−2.08071	−	8.74063i	−0.0143497	−	0.0602802i
$146$	158.831			1.08788
$147$			79.2996i			0.539453i
$148$	−85.4220			−0.577175
$149$		−	178.281i		−	1.19652i	−0.801303	−	0.598259i	$-0.795860\pi$
$149$		−	178.281i		−	1.19652i	0.801303	−	0.598259i	$-0.204140\pi$
$150$	−54.6691	+	27.5915i	−0.364461	+	0.183943i
$151$	216.913			1.43651			0.718257	−	0.695778i	$-0.244940\pi$
$151$	216.913			1.43651			0.718257	+	0.695778i	$0.244940\pi$
$152$	−49.7941			−0.327593
$153$	−66.4815			−0.434519
$154$	−0.969328			−0.00629434
$155$	46.7170	+	196.249i	0.301400	+	1.26612i
$156$	83.3007			0.533979
$157$	−132.164			−0.841810			−0.420905	−	0.907105i	$-0.638287\pi$
$157$	−132.164			−0.841810			−0.420905	+	0.907105i	$0.638287\pi$
$158$	−87.7896			−0.555631
$159$		−	141.127i		−	0.887592i
$160$	−27.5154	+	6.55004i	−0.171971	+	0.0409378i
$161$	2.70424	−	41.1601i	0.0167965	−	0.255653i
$162$			12.7279i			0.0785674i
$163$			98.3005i			0.603070i	0.953455	+	0.301535i	$0.0974991\pi$
$163$			98.3005i			0.603070i	−0.953455	+	0.301535i	$0.902501\pi$
$164$	−2.53378			−0.0154499
$165$	−0.766482	−	3.21983i	−0.00464534	−	0.0195141i
$166$			209.501i			1.26205i
$167$			69.3323i			0.415164i	0.978218	+	0.207582i	$0.0665593\pi$
$167$			69.3323i			0.415164i	−0.978218	+	0.207582i	$0.933441\pi$
$168$	8.78596			0.0522974
$169$	−409.250			−2.42160
$170$	−152.439	+	36.2880i	−0.896698	+	0.213459i
$171$			52.8146i			0.308858i
$172$	−33.1350			−0.192646
$173$		−	337.945i		−	1.95344i	−0.214522	−	0.976719i	$-0.568819\pi$
$173$		−	337.945i		−	1.95344i	0.214522	−	0.976719i	$-0.431181\pi$
$174$	−4.40167			−0.0252970
$175$	40.0267	−	20.2015i	0.228724	−	0.115437i
$176$		−	1.52873i		−	0.00868599i
$177$		−	31.3411i		−	0.177068i
$178$	145.291			0.816243
$179$	−135.350			−0.756146			−0.378073	−	0.925776i	$-0.623413\pi$
$179$	−135.350			−0.756146			−0.378073	+	0.925776i	$0.623413\pi$
$180$	6.94737	+	29.1845i	0.0385965	+	0.162136i
$181$			275.222i			1.52057i	0.649592	+	0.760283i	$0.274940\pi$
$181$			275.222i			1.52057i	−0.649592	+	0.760283i	$0.725060\pi$
$182$	−60.9897			−0.335108
$183$	−57.4020			−0.313672
$184$	64.9139	+	4.26487i	0.352793	+	0.0231787i
$185$	49.4548	+	207.750i	0.267323	+	1.12297i
$186$	98.8284			0.531335
$187$		−	8.46938i		−	0.0452908i
$188$			11.5009i			0.0611750i
$189$		−	9.31892i		−	0.0493065i
$190$	28.8282	+	121.101i	0.151727	+	0.637375i
$191$		−	43.3590i		−	0.227010i	−0.993537	−	0.113505i	$-0.963792\pi$
$191$		−	43.3590i		−	0.227010i	0.993537	−	0.113505i	$-0.0362079\pi$
$192$			13.8564i			0.0721688i
$193$			41.4539i			0.214787i	0.994217	+	0.107394i	$0.0342505\pi$
$193$			41.4539i			0.214787i	−0.994217	+	0.107394i	$0.965749\pi$
$194$		−	212.996i		−	1.09792i
$195$	−48.2267	−	202.591i	−0.247316	−	1.03893i
$196$	91.5672			0.467180
$197$			208.208i			1.05689i	0.848966	+	0.528447i	$0.177226\pi$
$197$			208.208i			1.05689i	−0.848966	+	0.528447i	$0.822774\pi$
$198$	−1.62147			−0.00818923
$199$			270.493i			1.35926i	0.733554	+	0.679631i	$0.237860\pi$
$199$			270.493i			1.35926i	−0.733554	+	0.679631i	$0.762140\pi$
$200$	31.8599	+	63.1264i	0.159300	+	0.315632i
$201$		−	202.364i		−	1.00679i
$202$		−	149.674i		−	0.740959i
$203$	3.22274			0.0158756
$204$			76.7662i			0.376305i
$205$	1.46693	+	6.16226i	0.00715574	+	0.0300598i
$206$		−	155.695i		−	0.755801i
$207$	4.52358	−	68.8516i	0.0218530	−	0.332616i
$208$		−	96.1873i		−	0.462439i
$209$	−6.72830			−0.0321928
$210$	−5.08661	−	21.3678i	−0.0242220	−	0.101752i
$211$	20.2818			0.0961222			0.0480611	−	0.998844i	$-0.484696\pi$
$211$	20.2818			0.0961222			0.0480611	+	0.998844i	$0.484696\pi$
$212$	−162.959			−0.768677
$213$		−	49.1063i		−	0.230546i
$214$			205.675i			0.961098i
$215$	19.1834	+	80.5857i	0.0892253	+	0.374817i
$216$	14.6969			0.0680414
$217$	−72.3585			−0.333449
$218$	−153.930			−0.706102
$219$	−194.528			−0.888254
$220$	−3.71794	+	0.885057i	−0.0168997	+	0.00402299i
$221$		−	532.890i		−	2.41126i
$222$	104.620			0.471262
$223$		−	195.211i		−	0.875386i	−0.899124	−	0.437693i	$-0.855796\pi$
$223$		−	195.211i		−	0.875386i	0.899124	−	0.437693i	$-0.144204\pi$
$224$		−	10.1452i		−	0.0452909i
$225$	66.9557	−	33.7926i	0.297581	−	0.150189i
$226$		−	79.2660i		−	0.350734i
$227$	89.0856			0.392448			0.196224	−	0.980559i	$-0.437132\pi$
$227$	89.0856			0.392448			0.196224	+	0.980559i	$0.437132\pi$
$228$	60.9851			0.267479
$229$		−	240.109i		−	1.04851i	−0.851561	−	0.524255i	$-0.824344\pi$
$229$		−	240.109i		−	1.04851i	0.851561	−	0.524255i	$-0.175656\pi$
$230$	−27.2094	−	160.342i	−0.118302	−	0.697140i
$231$	1.18718			0.00513931
$232$			5.08261i			0.0219078i
$233$		−	366.956i		−	1.57492i	−0.616367	−	0.787459i	$-0.711396\pi$
$233$		−	366.956i		−	1.57492i	0.616367	−	0.787459i	$-0.288604\pi$
$234$	−102.022			−0.435992
$235$	27.9706	−	6.65841i	0.119024	−	0.0283337i
$236$	−36.1895			−0.153346
$237$	107.520			0.453670
$238$		−	56.2054i		−	0.236157i
$239$	312.460			1.30737			0.653683	−	0.756769i	$-0.273223\pi$
$239$	312.460			1.30737			0.653683	+	0.756769i	$0.273223\pi$
$240$	33.6993	−	8.02213i	0.140414	−	0.0334255i
$241$		−	187.089i		−	0.776302i	−0.921596	−	0.388151i	$-0.873114\pi$
$241$		−	187.089i		−	0.776302i	0.921596	−	0.388151i	$-0.126886\pi$
$242$			170.913i			0.706253i
$243$		−	15.5885i		−	0.0641500i
$244$			66.2822i			0.271648i
$245$	−53.0126	−	222.695i	−0.216378	−	0.908960i
$246$	3.10324			0.0126148
$247$	−423.342			−1.71393
$248$		−	114.117i		−	0.460150i
$249$		−	256.585i		−	1.03046i
$250$	135.081	−	114.032i	0.540323	−	0.456126i
$251$			100.664i			0.401051i	0.979688	+	0.200525i	$0.0642649\pi$
$251$			100.664i			0.401051i	−0.979688	+	0.200525i	$0.935735\pi$
$252$	−10.7606			−0.0427006
$253$	8.77131	+	0.576279i	0.0346692	+	0.00227778i
$254$	95.0468			0.374200
$255$	186.698	−	44.4436i	0.732151	−	0.174289i
$256$	16.0000			0.0625000
$257$		−	43.1857i		−	0.168038i	−0.996464	−	0.0840188i	$-0.973224\pi$
$257$		−	43.1857i		−	0.168038i	0.996464	−	0.0840188i	$-0.0267756\pi$
$258$	40.5820			0.157294
$259$	−76.5990			−0.295749
$260$	−233.931	+	55.6874i	−0.899736	+	0.214182i
$261$	5.39092			0.0206549
$262$		−	204.621i		−	0.780998i
$263$	−149.557			−0.568657			−0.284329	−	0.958727i	$-0.591771\pi$
$263$	−149.557			−0.568657			−0.284329	+	0.958727i	$0.591771\pi$
$264$			1.87231i			0.00709208i
$265$	94.3450	+	396.324i	0.356019	+	1.49556i
$266$	−44.6511			−0.167861
$267$	−177.945			−0.666459
$268$	−233.670			−0.871904
$269$	7.50830			0.0279119			0.0139560	−	0.999903i	$-0.495558\pi$
$269$	7.50830			0.0279119			0.0139560	+	0.999903i	$0.495558\pi$
$270$	−8.50875	−	35.7435i	−0.0315139	−	0.132384i
$271$	−333.946			−1.23227			−0.616136	−	0.787640i	$-0.711303\pi$
$271$	−333.946			−1.23227			−0.616136	+	0.787640i	$0.711303\pi$
$272$	88.6420			0.325890
$273$	74.6968			0.273615
$274$		−	93.6538i		−	0.341802i
$275$	4.30499	+	8.52979i	0.0156545	+	0.0310174i
$276$	−79.5029	−	5.22338i	−0.288054	−	0.0189253i
$277$		−	17.8761i		−	0.0645347i	−0.999479	−	0.0322674i	$-0.989727\pi$
$277$		−	17.8761i		−	0.0645347i	0.999479	−	0.0322674i	$-0.0102728\pi$
$278$			82.4070i			0.296428i
$279$	−121.040			−0.433833
$280$	−24.6734	+	5.87351i	−0.0881194	+	0.0209768i
$281$			375.566i			1.33654i	0.743921	+	0.668268i	$0.232964\pi$
$281$			375.566i			1.33654i	−0.743921	+	0.668268i	$0.767036\pi$
$282$		−	14.0857i		−	0.0499492i
$283$	−401.091			−1.41728			−0.708642	−	0.705568i	$-0.750692\pi$
$283$	−401.091			−1.41728			−0.708642	+	0.705568i	$0.750692\pi$
$284$	−56.7031			−0.199659
$285$	−35.3072	−	148.318i	−0.123885	−	0.520415i
$286$		−	12.9971i		−	0.0454442i
$287$	−2.27208			−0.00791664
$288$		−	16.9706i		−	0.0589256i
$289$	202.087			0.699264
$290$	12.3611	−	2.94256i	0.0426245	−	0.0101468i
$291$			260.865i			0.896444i
$292$			224.621i			0.769250i
$293$	−79.9606			−0.272903			−0.136452	−	0.990647i	$-0.543570\pi$
$293$	−79.9606			−0.272903			−0.136452	+	0.990647i	$0.543570\pi$
$294$	−112.147			−0.381451
$295$	20.9518	+	88.0144i	0.0710232	+	0.298354i
$296$		−	120.805i		−	0.408125i
$297$	1.98588			0.00668648
$298$	252.127			0.846065
$299$	551.887	+	36.2593i	1.84578	+	0.121268i
$300$	−39.0203	−	77.3138i	−0.130068	−	0.257713i
$301$	−29.7126			−0.0987131
$302$			306.762i			1.01577i
$303$			183.312i			0.604991i
$304$		−	70.4195i		−	0.231643i
$305$	161.201	−	38.3739i	0.528527	−	0.125816i
$306$		−	94.0190i		−	0.307252i
$307$		−	245.949i		−	0.801137i	−0.916267	−	0.400568i	$-0.868813\pi$
$307$		−	245.949i		−	0.801137i	0.916267	−	0.400568i	$-0.131187\pi$
$308$		−	1.37084i		−	0.00445077i
$309$			190.687i			0.617109i
$310$	−277.538	+	66.0678i	−0.895282	+	0.213122i
$311$	−426.643			−1.37184			−0.685921	−	0.727676i	$-0.740601\pi$
$311$	−426.643			−1.37184			−0.685921	+	0.727676i	$0.740601\pi$
$312$			117.805i			0.377580i
$313$	−330.486			−1.05587			−0.527933	−	0.849286i	$-0.677033\pi$
$313$	−330.486			−1.05587			−0.527933	+	0.849286i	$0.677033\pi$
$314$		−	186.908i		−	0.595250i
$315$	6.22980	+	26.1701i	0.0197771	+	0.0830798i
$316$		−	124.153i		−	0.392890i
$317$		−	45.8757i		−	0.144718i	−0.997379	−	0.0723591i	$-0.976947\pi$
$317$		−	45.8757i		−	0.144718i	0.997379	−	0.0723591i	$-0.0230528\pi$
$318$	199.584			0.627622
$319$			0.686774i			0.00215290i
$320$	−9.26316	−	38.9126i	−0.0289474	−	0.121602i
$321$		−	251.899i		−	0.784733i
$322$	58.2092	+	3.82437i	0.180774	+	0.0118769i
$323$		−	390.133i		−	1.20784i
$324$	−18.0000			−0.0555556
$325$	270.868	+	536.691i	0.833440	+	1.65136i
$326$	−139.018			−0.426435
$327$	188.525			0.576530
$328$		−	3.58331i		−	0.0109247i
$329$			10.3130i			0.0313465i
$330$	4.55353	−	1.08397i	0.0137986	−	0.00328475i
$331$	−528.078			−1.59540			−0.797701	−	0.603053i	$-0.793951\pi$
$331$	−528.078			−1.59540			−0.797701	+	0.603053i	$0.793951\pi$
$332$	−296.279			−0.892407
$333$	−128.133			−0.384784
$334$	−98.0507			−0.293565
$335$	135.283	+	568.295i	0.403829	+	1.69640i
$336$			12.4252i			0.0369798i
$337$	478.649			1.42032			0.710162	−	0.704039i	$-0.248622\pi$
$337$	478.649			1.42032			0.710162	+	0.704039i	$0.248622\pi$
$338$		−	578.767i		−	1.71233i
$339$			97.0806i			0.286373i
$340$	−51.3190	−	215.581i	−0.150938	−	0.634061i
$341$		−	15.4198i		−	0.0452193i
$342$	−74.6912			−0.218395
$343$	169.988			0.495590
$344$		−	46.8600i		−	0.136221i
$345$	33.3245	+	196.378i	0.0965929	+	0.569213i
$346$	477.926			1.38129
$347$			45.8278i			0.132069i	0.997817	+	0.0660344i	$0.0210347\pi$
$347$			45.8278i			0.132069i	−0.997817	+	0.0660344i	$0.978965\pi$
$348$		−	6.22490i		−	0.0178877i
$349$	38.0051			0.108897			0.0544486	−	0.998517i	$-0.482660\pi$
$349$	38.0051			0.108897			0.0544486	+	0.998517i	$0.482660\pi$
$350$	28.5692	+	56.6063i	0.0816264	+	0.161732i
$351$	124.951			0.355986
$352$	2.16196			0.00614192
$353$			332.010i			0.940540i	0.882523	+	0.470270i	$0.155843\pi$
$353$			332.010i			0.940540i	−0.882523	+	0.470270i	$0.844157\pi$
$354$	44.3230			0.125206
$355$	32.8281	+	137.904i	0.0924736	+	0.388463i
$356$			205.473i			0.577171i
$357$			68.8373i			0.192822i
$358$		−	191.414i		−	0.534676i
$359$		−	384.549i		−	1.07117i	−0.844482	−	0.535584i	$-0.820091\pi$
$359$		−	384.549i		−	1.07117i	0.844482	−	0.535584i	$-0.179909\pi$
$360$	−41.2731	+	9.82506i	−0.114647	+	0.0272918i
$361$	51.0681			0.141463
$362$	−389.223			−1.07520
$363$		−	209.325i		−	0.576653i
$364$		−	86.2525i		−	0.236957i
$365$	546.287	−	130.044i	1.49668	−	0.356284i
$366$		−	81.1787i		−	0.221800i
$367$	158.946			0.433096			0.216548	−	0.976272i	$-0.430520\pi$
$367$	158.946			0.433096			0.216548	+	0.976272i	$0.430520\pi$
$368$	−6.03144	+	91.8021i	−0.0163898	+	0.249462i
$369$	−3.80067			−0.0102999
$370$	−293.802	+	69.9397i	−0.794061	+	0.189026i
$371$	−146.128			−0.393876
$372$			139.764i			0.375711i
$373$	353.352			0.947324			0.473662	−	0.880707i	$-0.342932\pi$
$373$	353.352			0.947324			0.473662	+	0.880707i	$0.342932\pi$
$374$	11.9775			0.0320254
$375$	−165.439	+	139.660i	−0.441172	+	0.372425i
$376$	−16.2647			−0.0432573
$377$			43.2115i			0.114619i
$378$	13.1789			0.0348649
$379$			494.663i			1.30518i	0.757712	+	0.652589i	$0.226317\pi$
$379$			494.663i			1.30518i	−0.757712	+	0.652589i	$0.773683\pi$
$380$	−171.263	+	40.7692i	−0.450692	+	0.107287i
$381$	−116.408			−0.305533
$382$	61.3189			0.160521
$383$	329.711			0.860864			0.430432	−	0.902623i	$-0.358361\pi$
$383$	329.711			0.860864			0.430432	+	0.902623i	$0.358361\pi$
$384$	−19.5959			−0.0510310
$385$	−3.33393	+	0.793642i	−0.00865956	+	0.00206141i
$386$	−58.6247			−0.151878
$387$	−49.7025			−0.128430
$388$	301.221			0.776343
$389$			318.459i			0.818660i	0.912386	+	0.409330i	$0.134238\pi$
$389$			318.459i			0.818660i	−0.912386	+	0.409330i	$0.865762\pi$
$390$	286.506	−	68.2028i	0.734632	−	0.174879i
$391$	−33.4149	+	508.595i	−0.0854601	+	1.30075i
$392$			129.496i			0.330346i
$393$			250.609i			0.637682i
$394$	−294.451			−0.747337
$395$	−301.946	+	71.8782i	−0.764420	+	0.181970i
$396$		−	2.29310i		−	0.00579066i
$397$		−	68.2935i		−	0.172024i	−0.996294	−	0.0860119i	$-0.972588\pi$
$397$		−	68.2935i		−	0.172024i	0.996294	−	0.0860119i	$-0.0274123\pi$
$398$	−382.535			−0.961143
$399$	54.6862			0.137058
$400$	−89.2742	+	45.0567i	−0.223186	+	0.112642i
$401$			486.040i			1.21207i	0.795438	+	0.606035i	$0.207241\pi$
$401$			486.040i			1.21207i	−0.795438	+	0.606035i	$0.792759\pi$
$402$	286.186			0.711906
$403$		−	970.206i		−	2.40746i
$404$	211.671			0.523937
$405$	10.4211	+	43.7767i	0.0257310	+	0.108091i
$406$			4.55765i			0.0112257i
$407$		−	16.3234i		−	0.0401067i
$408$	−108.564			−0.266088
$409$	−124.021			−0.303230			−0.151615	−	0.988440i	$-0.548447\pi$
$409$	−124.021			−0.303230			−0.151615	+	0.988440i	$0.548447\pi$
$410$	−8.71475	+	2.07455i	−0.0212555	+	0.00505987i
$411$			114.702i			0.279080i
$412$	220.186			0.534432
$413$	−32.4517			−0.0785754
$414$	97.3708	+	6.39731i	0.235195	+	0.0154524i
$415$	171.530	+	720.563i	0.413325	+	1.73630i
$416$	136.029			0.326994
$417$		−	100.928i		−	0.242033i
$418$		−	9.51525i		−	0.0227638i
$419$			628.400i			1.49976i	0.661573	+	0.749881i	$0.269889\pi$
$419$			628.400i			1.49976i	−0.661573	+	0.749881i	$0.730111\pi$
$420$	30.2187	−	7.19355i	0.0719492	−	0.0171275i
$421$			258.480i			0.613966i	0.951715	+	0.306983i	$0.0993195\pi$
$421$			258.480i			0.613966i	−0.951715	+	0.306983i	$0.900681\pi$
$422$			28.6828i			0.0679687i
$423$			17.2513i			0.0407833i
$424$		−	230.460i		−	0.543537i
$425$	−494.590	+	249.620i	−1.16374	+	0.587341i
$426$	69.4468			0.163021
$427$			59.4361i			0.139195i
$428$	−290.868			−0.679599
$429$			15.9181i			0.0371051i
$430$	−113.965	+	27.1295i	−0.265036	+	0.0630918i
$431$			360.875i			0.837298i	0.908148	+	0.418649i	$0.137496\pi$
$431$			360.875i			0.837298i	−0.908148	+	0.418649i	$0.862504\pi$
$432$			20.7846i			0.0481125i
$433$	527.704			1.21872			0.609358	−	0.792896i	$-0.291427\pi$
$433$	527.704			1.21872			0.609358	+	0.792896i	$0.291427\pi$
$434$		−	102.330i		−	0.235784i
$435$	−15.1392	+	3.60389i	−0.0348028	+	0.00828481i
$436$		−	217.690i		−	0.499289i
$437$	404.041	+	26.5457i	0.924579	+	0.0607453i
$438$		−	275.103i		−	0.628090i
$439$	678.504			1.54557			0.772784	−	0.634669i	$-0.218864\pi$
$439$	678.504			1.54557			0.772784	+	0.634669i	$0.218864\pi$
$440$	−1.25166	−	5.25797i	−0.00284468	−	0.0119499i
$441$	137.351			0.311453
$442$	753.620			1.70502
$443$		−	296.200i		−	0.668624i	−0.942462	−	0.334312i	$-0.891496\pi$
$443$		−	296.200i		−	0.668624i	0.942462	−	0.334312i	$-0.108504\pi$
$444$			147.955i			0.333232i
$445$	499.718	−	118.958i	1.12296	−	0.267321i
$446$	276.070			0.618991
$447$	−308.792			−0.690810
$448$	14.3474			0.0320255
$449$	535.630			1.19294			0.596470	−	0.802635i	$-0.296569\pi$
$449$	535.630			1.19294			0.596470	+	0.802635i	$0.296569\pi$
$450$	47.7899	+	94.6896i	0.106200	+	0.210421i
$451$		−	0.484185i		−	0.00107358i
$452$	112.099			0.248007
$453$		−	375.705i		−	0.829371i
$454$			125.986i			0.277502i
$455$	−209.770	+	49.9356i	−0.461032	+	0.109749i
$456$			86.2460i			0.189136i
$457$	−198.709			−0.434813			−0.217406	−	0.976081i	$-0.569760\pi$
$457$	−198.709			−0.434813			−0.217406	+	0.976081i	$0.569760\pi$
$458$	339.565			0.741409
$459$			115.149i			0.250870i
$460$	226.758	−	38.4799i	0.492953	−	0.0836519i
$461$	−677.481			−1.46959			−0.734795	−	0.678290i	$-0.762722\pi$
$461$	−677.481			−1.46959			−0.734795	+	0.678290i	$0.762722\pi$
$462$			1.67893i			0.00363404i
$463$		−	317.422i		−	0.685576i	−0.939413	−	0.342788i	$-0.888629\pi$
$463$		−	317.422i		−	0.685576i	0.939413	−	0.342788i	$-0.111371\pi$
$464$	−7.18790			−0.0154912
$465$	339.913	−	80.9162i	0.730995	−	0.174013i
$466$	518.954			1.11364
$467$	−231.177			−0.495025			−0.247512	−	0.968885i	$-0.579613\pi$
$467$	−231.177			−0.495025			−0.247512	+	0.968885i	$0.579613\pi$
$468$		−	144.281i		−	0.308293i
$469$	−209.535			−0.446770
$470$	9.41642	+	39.5565i	0.0200349	+	0.0841627i
$471$			228.915i			0.486019i
$472$		−	51.1797i		−	0.108432i
$473$		−	6.33183i		−	0.0133865i
$474$			152.056i			0.320793i
$475$	198.305	+	392.916i	0.417484	+	0.827191i
$476$	79.4865			0.166988
$477$	−244.439			−0.512451
$478$			441.886i			0.924447i
$479$			603.191i			1.25927i	0.776891	+	0.629636i	$0.216796\pi$
$479$			603.191i			1.25927i	−0.776891	+	0.629636i	$0.783204\pi$
$480$	11.3450	+	47.6581i	0.0236354	+	0.0992876i
$481$		−	1027.06i		−	2.13527i
$482$	264.583			0.548928
$483$	−71.2914	−	4.68388i	−0.147601	−	0.00969747i
$484$	−241.708			−0.499396
$485$	−174.391	−	732.582i	−0.359570	−	1.51048i
$486$	22.0454			0.0453609
$487$		−	432.259i		−	0.887596i	−0.896127	−	0.443798i	$-0.853631\pi$
$487$		−	432.259i		−	0.887596i	0.896127	−	0.443798i	$-0.146369\pi$
$488$	−93.7371			−0.192084
$489$	170.261			0.348183
$490$	314.939	−	74.9712i	0.642732	−	0.153002i
$491$	−457.843			−0.932471			−0.466235	−	0.884661i	$-0.654390\pi$
$491$	−457.843			−0.932471			−0.466235	+	0.884661i	$0.654390\pi$
$492$			4.38864i			0.00892000i
$493$	−39.8218			−0.0807745
$494$		−	598.695i		−	1.21193i
$495$	−5.57692	+	1.32759i	−0.0112665	+	0.00268199i
$496$	161.386			0.325375
$497$	−50.8465			−0.102307
$498$	362.866			0.728647
$499$	232.828			0.466589			0.233294	−	0.972406i	$-0.425049\pi$
$499$	232.828			0.466589			0.233294	+	0.972406i	$0.425049\pi$
$500$	161.265	+	191.033i	0.322530	+	0.382066i
$501$	120.087			0.239695
$502$	−142.360			−0.283586
$503$	874.235			1.73804			0.869021	−	0.494775i	$-0.164750\pi$
$503$	874.235			1.73804			0.869021	+	0.494775i	$0.164750\pi$
$504$		−	15.2177i		−	0.0301939i
$505$	−122.546	−	514.792i	−0.242666	−	1.01939i
$506$	−0.814982	+	12.4045i	−0.00161064	+	0.0245148i
$507$			708.842i			1.39811i
$508$			134.417i			0.264599i
$509$	670.805			1.31789			0.658944	−	0.752192i	$-0.271003\pi$
$509$	670.805			1.31789			0.658944	+	0.752192i	$0.271003\pi$
$510$	62.8527	+	264.032i	0.123241	+	0.517709i
$511$			201.421i			0.394170i
$512$			22.6274i			0.0441942i
$513$	91.4776			0.178319
$514$	61.0738			0.118821
$515$	−127.476	−	535.501i	−0.247526	−	1.03981i
$516$			57.3916i			0.111224i
$517$	−2.19773			−0.00425092
$518$		−	108.327i		−	0.209126i
$519$	−585.338			−1.12782
$520$	−78.7539	−	330.829i	−0.151450	−	0.636210i
$521$		−	251.816i		−	0.483332i	−0.970359	−	0.241666i	$-0.922306\pi$
$521$		−	251.816i		−	0.483332i	0.970359	−	0.241666i	$-0.0776939\pi$
$522$			7.62392i			0.0146052i
$523$	−755.642			−1.44482			−0.722411	−	0.691464i	$-0.756966\pi$
$523$	−755.642			−1.44482			−0.722411	+	0.691464i	$0.756966\pi$
$524$	289.378			0.552249
$525$	−34.9900	−	69.3283i	−0.0666477	−	0.132054i
$526$		−	211.505i		−	0.402102i
$527$	894.098			1.69658
$528$	−2.64785			−0.00501486
$529$	−524.453	−	69.2123i	−0.991404	−	0.130836i
$530$	−560.487	+	133.424i	−1.05752	+	0.251743i
$531$	−54.2843			−0.102230
$532$		−	63.1461i		−	0.118696i
$533$		−	30.4647i		−	0.0571571i
$534$		−	251.652i		−	0.471258i
$535$	168.398	+	707.404i	0.314762	+	1.32225i
$536$		−	330.460i		−	0.616529i
$537$			234.433i			0.436561i
$538$			10.6183i			0.0197367i
$539$			17.4977i			0.0324634i
$540$	50.5490	−	12.0332i	0.0936093	−	0.0222837i
$541$	−422.567			−0.781085			−0.390543	−	0.920585i	$-0.627713\pi$
$541$	−422.567			−0.781085			−0.390543	+	0.920585i	$0.627713\pi$
$542$		−	472.270i		−	0.871348i
$543$	476.699			0.877899
$544$			125.359i			0.230439i
$545$	−529.431	+	126.031i	−0.971433	+	0.231250i
$546$			105.637i			0.193475i
$547$			962.341i			1.75931i	0.475615	+	0.879653i	$0.342226\pi$
$547$			962.341i			1.75931i	−0.475615	+	0.879653i	$0.657774\pi$
$548$	132.447			0.241691
$549$			99.4232i			0.181099i
$550$	−12.0629	+	6.08817i	−0.0219326	+	0.0110694i
$551$			31.6355i			0.0574147i
$552$	7.38697	−	112.434i	0.0133822	−	0.203685i
$553$		−	111.330i		−	0.201320i
$554$	25.2807			0.0456329
$555$	359.833	−	85.6583i	0.648348	−	0.154339i
$556$	−116.541			−0.209606
$557$	157.867			0.283424			0.141712	−	0.989908i	$-0.454739\pi$
$557$	157.867			0.283424			0.141712	+	0.989908i	$0.454739\pi$
$558$		−	171.176i		−	0.306767i
$559$		−	398.396i		−	0.712695i
$560$	−8.30640	−	34.8935i	−0.0148329	−	0.0623098i
$561$	−14.6694			−0.0261486
$562$	−531.131			−0.945073
$563$	−417.217			−0.741060			−0.370530	−	0.928820i	$-0.620824\pi$
$563$	−417.217			−0.741060			−0.370530	+	0.928820i	$0.620824\pi$
$564$	19.9201			0.0353194
$565$	−64.8994	−	272.629i	−0.114866	−	0.482530i
$566$		−	567.229i		−	1.00217i
$567$	−16.1408			−0.0284671
$568$		−	80.1903i		−	0.141180i
$569$		−	93.8235i		−	0.164892i	−0.996596	−	0.0824460i	$-0.973727\pi$
$569$		−	93.8235i		−	0.164892i	0.996596	−	0.0824460i	$-0.0262732\pi$
$570$	209.754	−	49.9319i	0.367989	−	0.0875998i
$571$			781.206i			1.36814i	0.729418	+	0.684068i	$0.239791\pi$
$571$			781.206i			1.36814i	−0.729418	+	0.684068i	$0.760209\pi$
$572$	18.3806			0.0321339
$573$	−75.1000			−0.131065
$574$		−	3.21320i		−	0.00559791i
$575$	−224.866	−	529.207i	−0.391071	−	0.920361i
$576$	24.0000			0.0416667
$577$		−	877.034i		−	1.51999i	−0.649929	−	0.759995i	$-0.725201\pi$
$577$		−	877.034i		−	1.51999i	0.649929	−	0.759995i	$-0.274799\pi$
$578$			285.795i			0.494454i
$579$	71.8003			0.124007
$580$	4.16141	+	17.4813i	0.00717485	+	0.0301401i
$581$	−265.678			−0.457276
$582$	−368.919			−0.633882
$583$		−	31.1402i		−	0.0534138i
$584$	−317.662			−0.543942
$585$	−350.897	+	83.5311i	−0.599824	+	0.142788i
$586$		−	113.081i		−	0.192972i
$587$			820.156i			1.39720i	0.715513	+	0.698600i	$0.246193\pi$
$587$			820.156i			1.39720i	−0.715513	+	0.698600i	$0.753807\pi$
$588$		−	158.599i		−	0.269726i
$589$		−	710.296i		−	1.20593i
$590$	−124.471	+	29.6304i	−0.210968	+	0.0502210i
$591$	360.627			0.610198
$592$	170.844			0.288588
$593$			423.705i			0.714510i	0.934007	+	0.357255i	$0.116287\pi$
$593$			423.705i			0.714510i	−0.934007	+	0.357255i	$0.883713\pi$
$594$			2.80846i			0.00472805i
$595$	−46.0185	−	193.314i	−0.0773420	−	0.324898i
$596$			356.562i			0.598259i
$597$	468.508			0.784770
$598$	−51.2783	+	780.486i	−0.0857497	+	1.30516i
$599$	874.974			1.46073			0.730363	−	0.683060i	$-0.239351\pi$
$599$	874.974			1.46073			0.730363	+	0.683060i	$0.239351\pi$
$600$	109.338	−	55.1830i	0.182230	−	0.0919717i
$601$	−644.991			−1.07320			−0.536598	−	0.843838i	$-0.680291\pi$
$601$	−644.991			−1.07320			−0.536598	+	0.843838i	$0.680291\pi$
$602$		−	42.0200i		−	0.0698007i
$603$	−350.505			−0.581269
$604$	−433.827			−0.718257
$605$	139.936	+	587.843i	0.231299	+	0.971642i
$606$	−259.243			−0.427793
$607$		−	251.491i		−	0.414318i	−0.978307	−	0.207159i	$-0.933578\pi$
$607$		−	251.491i		−	0.414318i	0.978307	−	0.207159i	$-0.0664217\pi$
$608$	99.5883			0.163796
$609$		−	5.58195i		−	0.00916577i
$610$	54.2689	+	227.972i	0.0889653	+	0.373725i
$611$	−138.280			−0.226318
$612$	132.963			0.217260
$613$	986.481			1.60927			0.804634	−	0.593771i	$-0.202361\pi$
$613$	986.481			1.60927			0.804634	+	0.593771i	$0.202361\pi$
$614$	347.824			0.566489
$615$	10.6733	−	2.54079i	0.0173550	−	0.00413137i
$616$	1.93866			0.00314717
$617$	−192.369			−0.311782			−0.155891	−	0.987774i	$-0.549825\pi$
$617$	−192.369			−0.311782			−0.155891	+	0.987774i	$0.549825\pi$
$618$	−269.672			−0.436362
$619$		−	864.558i		−	1.39670i	−0.715756	−	0.698351i	$-0.753918\pi$
$619$		−	864.558i		−	1.39670i	0.715756	−	0.698351i	$-0.246082\pi$
$620$	−93.4340	−	392.497i	−0.150700	−	0.633060i
$621$	−119.254	−	7.83507i	−0.192036	−	0.0126169i
$622$		−	603.364i		−	0.970039i
$623$			184.250i			0.295747i
$624$	−166.601			−0.266989
$625$	371.236	−	502.801i	0.593978	−	0.804481i
$626$		−	467.377i		−	0.746609i
$627$			11.6538i			0.0185865i
$628$	264.328			0.420905
$629$	946.496			1.50476
$630$	−37.0101	+	8.81027i	−0.0587463	+	0.0139846i
$631$		−	643.458i		−	1.01974i	−0.860251	−	0.509871i	$-0.829693\pi$
$631$		−	643.458i		−	1.01974i	0.860251	−	0.509871i	$-0.170307\pi$
$632$	175.579			0.277815
$633$		−	35.1291i		−	0.0554962i
$634$	64.8780			0.102331
$635$	326.906	−	77.8201i	0.514813	−	0.122551i
$636$			282.254i			0.443796i
$637$			1100.95i			1.72834i
$638$	−0.971245			−0.00152233
$639$	−85.0547			−0.133106
$640$	55.0308	−	13.1001i	0.0859856	−	0.0204689i
$641$			716.907i			1.11842i	0.829026	+	0.559210i	$0.188895\pi$
$641$			716.907i			1.11842i	−0.829026	+	0.559210i	$0.811105\pi$
$642$	356.240			0.554890
$643$	−275.422			−0.428339			−0.214170	−	0.976796i	$-0.568705\pi$
$643$	−275.422			−0.428339			−0.214170	+	0.976796i	$0.568705\pi$
$644$	−5.40847	+	82.3202i	−0.00839825	+	0.127826i
$645$	139.579	−	33.2267i	0.216401	−	0.0515142i
$646$	551.731			0.854073
$647$			593.326i			0.917041i	0.888684	+	0.458521i	$0.151620\pi$
$647$			593.326i			0.917041i	−0.888684	+	0.458521i	$0.848380\pi$
$648$		−	25.4558i		−	0.0392837i
$649$		−	6.91553i		−	0.0106557i
$650$	−758.995	+	383.065i	−1.16768	+	0.589331i
$651$			125.329i			0.192517i
$652$		−	196.601i		−	0.301535i
$653$			376.904i			0.577188i	0.957452	+	0.288594i	$0.0931877\pi$
$653$			376.904i			0.577188i	−0.957452	+	0.288594i	$0.906812\pi$
$654$			266.615i			0.407668i
$655$	−167.535	−	703.780i	−0.255778	−	1.07447i
$656$	5.06756			0.00772494
$657$			336.932i			0.512833i
$658$	−14.5848			−0.0221654
$659$			821.196i			1.24612i	0.782172	+	0.623062i	$0.214112\pi$
$659$			821.196i			1.24612i	−0.782172	+	0.623062i	$0.785888\pi$
$660$	1.53296	+	6.43967i	0.00232267	+	0.00975707i
$661$		−	1108.77i		−	1.67741i	−0.544587	−	0.838705i	$-0.683313\pi$
$661$		−	1108.77i		−	1.67741i	0.544587	−	0.838705i	$-0.316687\pi$
$662$		−	746.816i		−	1.12812i
$663$	−922.992			−1.39214
$664$		−	419.002i		−	0.631027i
$665$	−153.574	+	36.5583i	−0.230938	+	0.0549749i
$666$		−	181.207i		−	0.272083i
$667$	2.70959	−	41.2415i	0.00406235	−	0.0618313i
$668$		−	138.665i		−	0.207582i
$669$	−338.115			−0.505404
$670$	−803.691	+	191.319i	−1.19954	+	0.285550i
$671$	−12.6660			−0.0188763
$672$	−17.5719			−0.0261487
$673$		−	45.4888i		−	0.0675911i	−0.999429	−	0.0337955i	$-0.989240\pi$
$673$		−	45.4888i		−	0.0675911i	0.999429	−	0.0337955i	$-0.0107595\pi$
$674$			676.912i			1.00432i
$675$	−58.5304	−	115.971i	−0.0867117	−	0.171808i
$676$	818.500			1.21080
$677$	−206.922			−0.305645			−0.152822	−	0.988254i	$-0.548836\pi$
$677$	−206.922			−0.305645			−0.152822	+	0.988254i	$0.548836\pi$
$678$	−137.293			−0.202497
$679$	270.109			0.397804
$680$	304.877	−	72.5761i	0.448349	−	0.106730i
$681$		−	154.301i		−	0.226580i
$682$	21.8069			0.0319749
$683$		−	437.345i		−	0.640330i	−0.947362	−	0.320165i	$-0.896262\pi$
$683$		−	437.345i		−	0.640330i	0.947362	−	0.320165i	$-0.103738\pi$
$684$		−	105.629i		−	0.154429i
$685$	−76.6796	−	322.115i	−0.111941	−	0.470241i
$686$			240.399i			0.350435i
$687$	−415.881			−0.605358
$688$	66.2701			0.0963228
$689$		−	1959.33i		−	2.84373i
$690$	−277.721	+	47.1280i	−0.402494	+	0.0683015i
$691$	−552.016			−0.798866			−0.399433	−	0.916762i	$-0.630793\pi$
$691$	−552.016			−0.798866			−0.399433	+	0.916762i	$0.630793\pi$
$692$			675.890i			0.976719i
$693$		−	2.05626i		−	0.00296718i
$694$	−64.8104			−0.0933867
$695$	67.4712	+	283.433i	0.0970809	+	0.407817i
$696$	8.80334			0.0126485
$697$	28.0749			0.0402797
$698$			53.7474i			0.0770020i
$699$	−635.587			−0.909280
$700$	−80.0534	+	40.4030i	−0.114362	+	0.0577186i
$701$		−	645.651i		−	0.921042i	−0.887649	−	0.460521i	$-0.847663\pi$
$701$		−	645.651i		−	0.921042i	0.887649	−	0.460521i	$-0.152337\pi$
$702$			176.707i			0.251720i
$703$		−	751.922i		−	1.06959i
$704$			3.05747i			0.00434300i
$705$	−11.5327	−	48.4466i	−0.0163585	−	0.0687186i
$706$	−469.534			−0.665062
$707$	189.808			0.268470
$708$			62.6821i			0.0885341i
$709$			552.330i			0.779027i	0.921021	+	0.389513i	$0.127357\pi$
$709$			552.330i			0.779027i	−0.921021	+	0.389513i	$0.872643\pi$
$710$	−195.026	+	46.4260i	−0.274685	+	0.0653887i
$711$		−	186.230i		−	0.261927i
$712$	−290.582			−0.408121
$713$	−60.8369	+	925.973i	−0.0853252	+	1.29870i
$714$	−97.3506			−0.136345
$715$	−10.6414	−	44.7024i	−0.0148831	−	0.0625208i
$716$	270.700			0.378073
$717$		−	541.197i		−	0.754808i
$718$	543.835			0.757430
$719$	882.221			1.22701			0.613505	−	0.789691i	$-0.289759\pi$
$719$	882.221			1.22701			0.613505	+	0.789691i	$0.289759\pi$
$720$	−13.8947	−	58.3690i	−0.0192982	−	0.0810680i
$721$	197.444			0.273847
$722$			72.2213i			0.100029i
$723$	−324.047			−0.448198
$724$		−	550.445i		−	0.760283i
$725$	40.1059	−	20.2415i	0.0553185	−	0.0279192i
$726$	296.030			0.407755
$727$	−574.892			−0.790773			−0.395387	−	0.918515i	$-0.629389\pi$
$727$	−574.892			−0.790773			−0.395387	+	0.918515i	$0.629389\pi$
$728$	121.979			0.167554
$729$	−27.0000			−0.0370370
$730$	183.910	+	772.567i	0.251931	+	1.05831i
$731$	367.144			0.502249
$732$	114.804			0.156836
$733$	−563.848			−0.769233			−0.384617	−	0.923076i	$-0.625666\pi$
$733$	−563.848			−0.769233			−0.384617	+	0.923076i	$0.625666\pi$
$734$			224.784i			0.306245i
$735$	−385.719	+	91.8205i	−0.524788	+	0.124926i
$736$	−129.828	−	8.52974i	−0.176396	−	0.0115893i
$737$		−	44.6525i		−	0.0605868i
$738$		−	5.37496i		−	0.00728315i
$739$	1029.01			1.39244			0.696218	−	0.717831i	$-0.254865\pi$
$739$	1029.01			1.39244			0.696218	+	0.717831i	$0.254865\pi$
$740$	−98.9096	−	415.499i	−0.133662	−	0.561486i
$741$			733.249i			0.989540i
$742$		−	206.656i		−	0.278512i
$743$	71.4526			0.0961678			0.0480839	−	0.998843i	$-0.484689\pi$
$743$	71.4526			0.0961678			0.0480839	+	0.998843i	$0.484689\pi$
$744$	−197.657			−0.265668
$745$	867.173	−	206.431i	1.16399	−	0.277088i
$746$			499.715i			0.669860i
$747$	−444.419			−0.594938
$748$			16.9388i			0.0226454i
$749$	−260.826			−0.348232
$750$	−197.508	−	233.967i	−0.263344	−	0.311956i
$751$			579.354i			0.771444i	0.922615	+	0.385722i	$0.126048\pi$
$751$			579.354i			0.771444i	−0.922615	+	0.385722i	$0.873952\pi$
$752$		−	23.0018i		−	0.0305875i
$753$	174.355			0.231547
$754$	−61.1103			−0.0810482
$755$	251.163	+	1055.08i	0.332666	+	1.39746i
$756$			18.6378i			0.0246532i
$757$	1033.03			1.36464			0.682321	−	0.731052i	$-0.260970\pi$
$757$	1033.03			1.36464			0.682321	+	0.731052i	$0.260970\pi$
$758$	−699.559			−0.922900
$759$	0.998145	−	15.1924i	0.00131508	−	0.0200163i
$760$	−57.6564	−	242.203i	−0.0758636	−	0.318688i
$761$	−714.171			−0.938463			−0.469232	−	0.883075i	$-0.655469\pi$
$761$	−714.171			−0.938463			−0.469232	+	0.883075i	$0.655469\pi$
$762$		−	164.626i		−	0.216045i
$763$		−	195.206i		−	0.255840i
$764$			86.7180i			0.113505i
$765$	−76.9785	−	323.371i	−0.100626	−	0.422708i
$766$			466.282i			0.608723i
$767$		−	435.122i		−	0.567304i
$768$		−	27.7128i		−	0.0360844i
$769$			129.899i			0.168919i	0.996427	+	0.0844595i	$0.0269164\pi$
$769$			129.899i			0.168919i	−0.996427	+	0.0844595i	$0.973084\pi$
$770$	−1.12238	−	4.71489i	−0.00145764	−	0.00612323i
$771$	−74.7998			−0.0970166
$772$		−	82.9079i		−	0.107394i
$773$	946.778			1.22481			0.612405	−	0.790544i	$-0.290202\pi$
$773$	946.778			1.22481			0.612405	+	0.790544i	$0.290202\pi$
$774$		−	70.2900i		−	0.0908140i
$775$	−900.476	+	454.471i	−1.16190	+	0.586414i
$776$			425.991i			0.548958i
$777$			132.673i			0.170751i
$778$	−450.369			−0.578880
$779$		−	22.3035i		−	0.0286309i
$780$	96.4534	+	405.181i	0.123658	+	0.519463i
$781$		−	10.8355i		−	0.0138739i
$782$	−719.262	−	47.2558i	−0.919772	−	0.0604294i
$783$		−	9.33735i		−	0.0119251i
$784$	−183.134			−0.233590
$785$	−153.032	−	642.857i	−0.194945	−	0.818926i
$786$	−354.415			−0.450909
$787$	−1533.79			−1.94890			−0.974450	−	0.224603i	$-0.927892\pi$
$787$	−1533.79			−1.94890			−0.974450	+	0.224603i	$0.927892\pi$
$788$		−	416.417i		−	0.528447i
$789$			259.040i			0.328315i
$790$	−101.651	−	427.016i	−0.128672	−	0.540526i
$791$	100.521			0.127081
$792$	3.24294			0.00409462
$793$	−796.938			−1.00497
$794$	96.5815			0.121639
$795$	686.453	−	163.410i	0.863463	−	0.205548i
$796$		−	540.986i		−	0.679631i
$797$	197.370			0.247641			0.123820	−	0.992305i	$-0.460485\pi$
$797$	197.370			0.247641			0.123820	+	0.992305i	$0.460485\pi$
$798$			77.3379i			0.0969147i
$799$		−	127.433i		−	0.159490i
$800$	−63.7199	−	126.253i	−0.0796498	−	0.157816i
$801$			308.209i			0.384781i
$802$	−687.364			−0.857062
$803$	−42.9232			−0.0534536
$804$			404.729i			0.503394i
$805$	203.337	−	34.5054i	0.252593	−	0.0428639i
$806$	1372.08			1.70233
$807$		−	13.0048i		−	0.0161149i
$808$			299.347i			0.370480i
$809$	−86.0327			−0.106345			−0.0531723	−	0.998585i	$-0.516933\pi$
$809$	−86.0327			−0.106345			−0.0531723	+	0.998585i	$0.516933\pi$
$810$	−61.9096	+	14.7376i	−0.0764317	+	0.0181946i
$811$	104.317			0.128628			0.0643138	−	0.997930i	$-0.479514\pi$
$811$	104.317			0.128628			0.0643138	+	0.997930i	$0.479514\pi$
$812$	−6.44549			−0.00793779
$813$			578.411i			0.711452i
$814$	23.0848			0.0283597
$815$	−478.141	+	113.822i	−0.586677	+	0.139658i
$816$		−	153.532i		−	0.188152i
$817$		−	291.669i		−	0.357000i
$818$		−	175.392i		−	0.214416i
$819$		−	129.379i		−	0.157972i
$820$	−2.93385	−	12.3245i	−0.00357787	−	0.0150299i
$821$	971.740			1.18361			0.591803	−	0.806083i	$-0.298416\pi$
$821$	971.740			1.18361			0.591803	+	0.806083i	$0.298416\pi$
$822$	−162.213			−0.197340
$823$			867.841i			1.05448i	0.849715	+	0.527242i	$0.176774\pi$
$823$			867.841i			1.05448i	−0.849715	+	0.527242i	$0.823226\pi$
$824$			311.390i			0.377900i
$825$	14.7740	−	7.45646i	0.0179079	−	0.00903813i
$826$		−	45.8936i		−	0.0555612i
$827$	−778.152			−0.940933			−0.470467	−	0.882418i	$-0.655914\pi$
$827$	−778.152			−0.940933			−0.470467	+	0.882418i	$0.655914\pi$
$828$	−9.04716	+	137.703i	−0.0109265	+	0.166308i
$829$	−1589.70			−1.91761			−0.958805	−	0.284067i	$-0.908316\pi$
$829$	−1589.70			−1.91761			−0.958805	+	0.284067i	$0.908316\pi$
$830$	−1019.03	+	242.580i	−1.22775	+	0.292265i
$831$	−30.9624			−0.0372591
$832$			192.375i			0.231220i
$833$	−1014.59			−1.21799
$834$	142.733			0.171143
$835$	−337.238	+	80.2795i	−0.403878	+	0.0961431i
$836$	13.4566			0.0160964
$837$			209.647i			0.250474i
$838$	−888.692			−1.06049
$839$			678.335i			0.808504i	0.914648	+	0.404252i	$0.132468\pi$
$839$			678.335i			0.808504i	−0.914648	+	0.404252i	$0.867532\pi$
$840$	10.1732	+	42.7356i	0.0121110	+	0.0508758i
$841$	−837.771			−0.996160
$842$	−365.545			−0.434139
$843$	650.500			0.771649
$844$	−40.5636			−0.0480611
$845$	−473.868	−	1990.63i	−0.560791	−	2.35577i
$846$	−24.3971			−0.0288382
$847$	−216.743			−0.255895
$848$	325.919			0.384338
$849$			694.711i			0.818269i
$850$	−353.016	−	699.456i	−0.415313	−	0.822890i
$851$	−64.4022	+	980.239i	−0.0756782	+	1.15187i
$852$			98.2127i			0.115273i
$853$			882.085i			1.03410i	0.855956	+	0.517049i	$0.172969\pi$
$853$			882.085i			1.03410i	−0.855956	+	0.517049i	$0.827031\pi$
$854$	−84.0554			−0.0984255
$855$	−256.895	+	61.1538i	−0.300462	+	0.0715249i
$856$		−	411.350i		−	0.480549i
$857$		−	551.436i		−	0.643450i	−0.946833	−	0.321725i	$-0.895737\pi$
$857$		−	551.436i		−	0.643450i	0.946833	−	0.321725i	$-0.104263\pi$
$858$	−22.5116			−0.0262372
$859$	282.824			0.329248			0.164624	−	0.986356i	$-0.447359\pi$
$859$	282.824			0.329248			0.164624	+	0.986356i	$0.447359\pi$
$860$	−38.3669	−	161.171i	−0.0446126	−	0.187409i
$861$			3.93535i			0.00457068i
$862$	−510.355			−0.592059
$863$		−	127.380i		−	0.147602i	−0.997273	−	0.0738009i	$-0.976487\pi$
$863$		−	127.380i		−	0.147602i	0.997273	−	0.0738009i	$-0.0235129\pi$
$864$	−29.3939			−0.0340207
$865$	1643.79	−	391.305i	1.90034	−	0.452375i
$866$			746.286i			0.861762i
$867$		−	350.026i		−	0.403720i
$868$	144.717			0.166725
$869$	23.7247			0.0273011
$870$	−5.09667	−	21.4101i	−0.00585824	−	0.0246093i
$871$		−	2809.51i		−	3.22562i
$872$	307.860			0.353051
$873$	451.832			0.517562
$874$	−37.5413	+	571.401i	−0.0429534	+	0.653776i
$875$	144.608	+	171.302i	0.165267	+	0.195774i
$876$	389.055			0.444127
$877$		−	795.079i		−	0.906589i	−0.891361	−	0.453295i	$-0.850249\pi$
$877$		−	795.079i		−	0.906589i	0.891361	−	0.453295i	$-0.149751\pi$
$878$			959.550i			1.09288i
$879$			138.496i			0.157561i
$880$	7.43589	−	1.77011i	0.00844987	−	0.00201149i
$881$			291.283i			0.330628i	0.986241	+	0.165314i	$0.0528638\pi$
$881$			291.283i			0.330628i	−0.986241	+	0.165314i	$0.947136\pi$
$882$			194.243i			0.220231i
$883$			1565.87i			1.77335i	0.462396	+	0.886674i	$0.346990\pi$
$883$			1565.87i			1.77335i	−0.462396	+	0.886674i	$0.653010\pi$
$884$			1065.78i			1.20563i
$885$	152.445	−	36.2897i	0.172255	−	0.0410053i
$886$	418.891			0.472788
$887$		−	452.662i		−	0.510329i	−0.966898	−	0.255165i	$-0.917870\pi$
$887$		−	452.662i		−	0.510329i	0.966898	−	0.255165i	$-0.0821297\pi$
$888$	−209.240			−0.235631
$889$			120.533i			0.135583i
$890$	168.232	+	706.708i	0.189025	+	0.794054i
$891$		−	3.43965i		−	0.00386044i
$892$			390.422i			0.437693i
$893$	−101.236			−0.113366
$894$		−	436.698i		−	0.488476i
$895$	−156.721	−	658.354i	−0.175107	−	0.735591i
$896$			20.2903i			0.0226454i
$897$	62.8029	−	955.897i	0.0700143	−	1.06566i
$898$			757.495i			0.843536i
$899$	−72.5017			−0.0806470
$900$	−133.911	+	67.5851i	−0.148790	+	0.0750946i
$901$	1805.63			2.00403
$902$	0.684741			0.000759136
$903$			51.4638i			0.0569920i
$904$			158.532i			0.175367i
$905$	−1338.70	+	318.679i	−1.47923	+	0.352131i
$906$	531.327			0.586454
$907$	656.602			0.723927			0.361964	−	0.932192i	$-0.382106\pi$
$907$	656.602			0.723927			0.361964	+	0.932192i	$0.382106\pi$
$908$	−178.171			−0.196224
$909$	317.506			0.349291
$910$	−70.6197	−	296.659i	−0.0776040	−	0.325999i
$911$		−	176.046i		−	0.193245i	−0.995321	−	0.0966224i	$-0.969196\pi$
$911$		−	176.046i		−	0.193245i	0.995321	−	0.0966224i	$-0.0308039\pi$
$912$	−121.970			−0.133739
$913$		−	56.6165i		−	0.0620115i
$914$		−	281.017i		−	0.307459i
$915$	−66.4655	−	279.208i	−0.0726399	−	0.305145i
$916$			480.218i			0.524255i
$917$	259.490			0.282977
$918$	−162.846			−0.177392
$919$		−	481.329i		−	0.523753i	−0.965101	−	0.261877i	$-0.915659\pi$
$919$		−	481.329i		−	0.523753i	0.965101	−	0.261877i	$-0.0843414\pi$
$920$	54.4187	+	320.685i	0.0591508	+	0.348570i
$921$	−425.996			−0.462536
$922$		−	958.102i		−	1.03916i
$923$		−	681.765i		−	0.738640i
$924$	−2.37436			−0.00256965
$925$	−953.248	+	481.104i	−1.03054	+	0.520113i
$926$	448.902			0.484775
$927$	330.279			0.356288
$928$		−	10.1652i		−	0.0109539i
$929$	409.397			0.440686			0.220343	−	0.975422i	$-0.429282\pi$
$929$	409.397			0.440686			0.220343	+	0.975422i	$0.429282\pi$
$930$	114.433	+	480.709i	0.123046	+	0.516892i
$931$			806.015i			0.865752i
$932$			733.912i			0.787459i
$933$			738.967i			0.792034i
$934$		−	326.933i		−	0.350035i
$935$	41.1957	−	9.80665i	0.0440596	−	0.0104884i
$936$	204.044			0.217996
$937$	89.4309			0.0954439			0.0477219	−	0.998861i	$-0.484804\pi$
$937$	89.4309			0.0954439			0.0477219	+	0.998861i	$0.484804\pi$
$938$		−	296.328i		−	0.315914i
$939$			572.418i			0.609604i
$940$	−55.9413	+	13.3168i	−0.0595120	+	0.0141668i
$941$		−	667.808i		−	0.709679i	−0.934927	−	0.354840i	$-0.884535\pi$
$941$		−	667.808i		−	0.709679i	0.934927	−	0.354840i	$-0.115465\pi$
$942$	−323.735			−0.343668
$943$	−1.91029	+	29.0758i	−0.00202576	+	0.0308333i
$944$	72.3791			0.0766728
$945$	45.3280	−	10.7903i	0.0479661	−	0.0114183i
$946$	8.95456			0.00946571
$947$			1474.86i			1.55740i	0.627396	+	0.778701i	$0.284121\pi$
$947$			1474.86i			1.55740i	−0.627396	+	0.778701i	$0.715879\pi$
$948$	−215.040			−0.226835
$949$	−2700.71			−2.84585
$950$	−555.667	+	280.445i	−0.584912	+	0.295205i
$951$	−79.4590			−0.0835531
$952$			112.411i			0.118079i
$953$	−1738.41			−1.82415			−0.912073	−	0.410029i	$-0.865519\pi$
$953$	−1738.41			−1.82415			−0.912073	+	0.410029i	$0.865519\pi$
$954$		−	345.689i		−	0.362358i
$955$	210.902	−	50.2052i	0.220839	−	0.0525708i
$956$	−624.921			−0.653683
$957$	1.18953			0.00124298
$958$	−853.041			−0.890439
$959$	118.767			0.123844
$960$	−67.3987	+	16.0443i	−0.0702070	+	0.0167128i
$961$	666.841			0.693903
$962$	1452.49			1.50986
$963$	−436.303			−0.453066
$964$			374.177i			0.388151i
$965$	−201.635	+	47.9993i	−0.208949	+	0.0497402i
$966$	6.62400	−	100.821i	0.00685714	−	0.104370i
$967$		−	745.833i		−	0.771285i	−0.922648	−	0.385643i	$-0.873980\pi$
$967$		−	745.833i		−	0.771285i	0.922648	−	0.385643i	$-0.126020\pi$
$968$		−	341.827i		−	0.353127i
$969$	−675.730			−0.697348
$970$	1036.03	−	246.626i	1.06807	−	0.254254i
$971$		−	715.785i		−	0.737162i	−0.929596	−	0.368581i	$-0.879844\pi$
$971$		−	715.785i		−	0.737162i	0.929596	−	0.368581i	$-0.120156\pi$
$972$			31.1769i			0.0320750i
$973$	−104.504			−0.107404
$974$	611.307			0.627625
$975$	929.575	−	469.157i	0.953411	−	0.481187i
$976$		−	132.564i		−	0.135824i
$977$	−1471.89			−1.50654			−0.753268	−	0.657713i	$-0.771524\pi$
$977$	−1471.89			−1.50654			−0.753268	+	0.657713i	$0.771524\pi$
$978$			240.786i			0.246202i
$979$	−39.2642			−0.0401064
$980$	106.025	+	445.390i	0.108189	+	0.454480i
$981$		−	326.535i		−	0.332859i
$982$		−	647.488i		−	0.659356i
$983$	1276.85			1.29894			0.649468	−	0.760389i	$-0.274992\pi$
$983$	1276.85			1.29894			0.649468	+	0.760389i	$0.274992\pi$
$984$	−6.20647			−0.00630739
$985$	−1012.74	+	241.083i	−1.02816	+	0.244755i
$986$		−	56.3166i		−	0.0571162i
$987$	17.8627			0.0180979
$988$	846.683			0.856967
$989$	−24.9815	+	380.233i	−0.0252593	+	0.384462i
$990$	−1.87749	−	7.88695i	−0.00189645	−	0.00796662i
$991$	−157.977			−0.159411			−0.0797057	−	0.996818i	$-0.525398\pi$
$991$	−157.977			−0.159411			−0.0797057	+	0.996818i	$0.525398\pi$
$992$			228.234i			0.230075i
$993$			914.659i			0.921106i
$994$		−	71.9077i		−	0.0723418i
$995$	−1315.70	+	313.203i	−1.32231	+	0.314776i
$996$			513.170i			0.515231i
$997$			710.953i			0.713092i	0.934278	+	0.356546i	$0.116046\pi$
$997$			710.953i			0.713092i	−0.934278	+	0.356546i	$0.883954\pi$
$998$			329.268i			0.329928i
$999$			221.933i			0.222155i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.f.a.229.20	yes	48
5.4	even	2	inner	690.3.f.a.229.17	✓	48
23.22	odd	2	inner	690.3.f.a.229.19	yes	48
115.114	odd	2	inner	690.3.f.a.229.18	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.f.a.229.17	✓	48	5.4	even	2	inner
690.3.f.a.229.18	yes	48	115.114	odd	2	inner
690.3.f.a.229.19	yes	48	23.22	odd	2	inner
690.3.f.a.229.20	yes	48	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	690.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} -1.73205i q^{3} -2.00000 q^{4} +(1.15789 + 4.86408i) q^{5} +2.44949 q^{6} -1.79343 q^{7} -2.82843i q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+1.41421i q^{2} -1.73205i q^{3} -2.00000 q^{4} +(1.15789 + 4.86408i) q^{5} +2.44949 q^{6} -1.79343 q^{7} -2.82843i q^{8} -3.00000 q^{9} +(-6.87885 + 1.63751i) q^{10} -0.382184i q^{11} +3.46410i q^{12} -24.0468i q^{13} -2.53629i q^{14} +(8.42483 - 2.00553i) q^{15} +4.00000 q^{16} +22.1605 q^{17} -4.24264i q^{18} -17.6049i q^{19} +(-2.31579 - 9.72816i) q^{20} +3.10631i q^{21} +0.540489 q^{22} +(-1.50786 + 22.9505i) q^{23} -4.89898 q^{24} +(-22.3186 + 11.2642i) q^{25} +34.0074 q^{26} +5.19615i q^{27} +3.58685 q^{28} -1.79697 q^{29} +(2.83625 + 11.9145i) q^{30} +40.3465 q^{31} +5.65685i q^{32} -0.661961 q^{33} +31.3397i q^{34} +(-2.07660 - 8.72337i) q^{35} +6.00000 q^{36} +42.7110 q^{37} +24.8971 q^{38} -41.6503 q^{39} +(13.7577 - 3.27502i) q^{40} +1.26689 q^{41} -4.39298 q^{42} +16.5675 q^{43} +0.764367i q^{44} +(-3.47368 - 14.5922i) q^{45} +(-32.4569 - 2.13244i) q^{46} -5.75045i q^{47} -6.92820i q^{48} -45.7836 q^{49} +(-15.9300 - 31.5632i) q^{50} -38.3831i q^{51} +48.0937i q^{52} +81.4797 q^{53} -7.34847 q^{54} +(1.85897 - 0.442528i) q^{55} +5.07258i q^{56} -30.4925 q^{57} -2.54131i q^{58} +18.0948 q^{59} +(-16.8497 + 4.01106i) q^{60} -33.1411i q^{61} +57.0586i q^{62} +5.38028 q^{63} -8.00000 q^{64} +(116.966 - 27.8437i) q^{65} -0.936155i q^{66} +116.835 q^{67} -44.3210 q^{68} +(39.7515 + 2.61169i) q^{69} +(12.3367 - 2.93676i) q^{70} +28.3516 q^{71} +8.48528i q^{72} -112.311i q^{73} +60.4025i q^{74} +(19.5101 + 38.6569i) q^{75} +35.2098i q^{76} +0.685419i q^{77} -58.9025i q^{78} +62.0766i q^{79} +(4.63158 + 19.4563i) q^{80} +9.00000 q^{81} +1.79165i q^{82} +148.140 q^{83} -6.21261i q^{84} +(25.6595 + 107.790i) q^{85} +23.4300i q^{86} +3.11245i q^{87} -1.08098 q^{88} -102.736i q^{89} +(20.6365 - 4.91253i) q^{90} +43.1262i q^{91} +(3.01572 - 45.9010i) q^{92} -69.8822i q^{93} +8.13236 q^{94} +(85.6316 - 20.3846i) q^{95} +9.79796 q^{96} -150.611 q^{97} -64.7478i q^{98} +1.14655i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 96 q^{4} - 144 q^{9}+O(q^{10}) \) 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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