LMFDB - Embedded newform 690.3.f.a.229.37

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			229.37
Character	$\chi$	$=$	690.229
Dual form			690.3.f.a.229.39

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} -1.73205i q^{3} -2.00000 q^{4} +(-4.99818 - 0.134731i) q^{5} -2.44949 q^{6} +11.0735 q^{7} +2.82843i q^{8} -3.00000 q^{9} +O(q^{10})$	\(q-1.41421i q^{2} -1.73205i q^{3} -2.00000 q^{4} +(-4.99818 - 0.134731i) q^{5} -2.44949 q^{6} +11.0735 q^{7} +2.82843i q^{8} -3.00000 q^{9} +(-0.190538 + 7.06850i) q^{10} -9.44141i q^{11} +3.46410i q^{12} +22.3707i q^{13} -15.6603i q^{14} +(-0.233360 + 8.65711i) q^{15} +4.00000 q^{16} -29.3065 q^{17} +4.24264i q^{18} +31.8609i q^{19} +(9.99637 + 0.269461i) q^{20} -19.1799i q^{21} -13.3522 q^{22} +(-20.6810 + 10.0645i) q^{23} +4.89898 q^{24} +(24.9637 + 1.34682i) q^{25} +31.6370 q^{26} +5.19615i q^{27} -22.1470 q^{28} +21.8003 q^{29} +(12.2430 + 0.330021i) q^{30} -33.9150 q^{31} -5.65685i q^{32} -16.3530 q^{33} +41.4457i q^{34} +(-55.3475 - 1.49194i) q^{35} +6.00000 q^{36} -7.59191 q^{37} +45.0582 q^{38} +38.7472 q^{39} +(0.381076 - 14.1370i) q^{40} +55.7647 q^{41} -27.1245 q^{42} +22.0768 q^{43} +18.8828i q^{44} +(14.9946 + 0.404192i) q^{45} +(14.2334 + 29.2474i) q^{46} +77.2646i q^{47} -6.92820i q^{48} +73.6229 q^{49} +(1.90469 - 35.3040i) q^{50} +50.7604i q^{51} -44.7414i q^{52} +39.1954 q^{53} +7.34847 q^{54} +(-1.27205 + 47.1899i) q^{55} +31.3207i q^{56} +55.1848 q^{57} -30.8302i q^{58} +70.2950 q^{59} +(0.466721 - 17.3142i) q^{60} -31.9143i q^{61} +47.9630i q^{62} -33.2206 q^{63} -8.00000 q^{64} +(3.01402 - 111.813i) q^{65} +23.1266i q^{66} -21.9858 q^{67} +58.6131 q^{68} +(17.4322 + 35.8206i) q^{69} +(-2.10993 + 78.2732i) q^{70} -31.2687 q^{71} -8.48528i q^{72} +64.0595i q^{73} +10.7366i q^{74} +(2.33276 - 43.2384i) q^{75} -63.7219i q^{76} -104.550i q^{77} -54.7968i q^{78} -8.93982i q^{79} +(-19.9927 - 0.538922i) q^{80} +9.00000 q^{81} -78.8632i q^{82} -6.63429 q^{83} +38.3598i q^{84} +(146.479 + 3.94849i) q^{85} -31.2213i q^{86} -37.7592i q^{87} +26.7043 q^{88} +153.281i q^{89} +(0.571614 - 21.2055i) q^{90} +247.723i q^{91} +(41.3621 - 20.1290i) q^{92} +58.7425i q^{93} +109.269 q^{94} +(4.29264 - 159.247i) q^{95} -9.79796 q^{96} -71.0282 q^{97} -104.119i q^{98} +28.3242i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−4.99818	−	0.134731i	−0.999637	−	0.0269461i
$5$	−4.99818	−	0.134731i	−0.999637	−	0.0269461i
$6$	−2.44949			−0.408248
$7$	11.0735			1.58193			0.790966	−	0.611860i	$-0.209578\pi$
$7$	11.0735			1.58193			0.790966	+	0.611860i	$0.209578\pi$
$8$			2.82843i			0.353553i
$9$	−3.00000			−0.333333
$10$	−0.190538	+	7.06850i	−0.0190538	+	0.706850i
$11$		−	9.44141i		−	0.858310i	−0.903231	−	0.429155i	$-0.858811\pi$
$11$		−	9.44141i		−	0.858310i	0.903231	−	0.429155i	$-0.141189\pi$
$12$			3.46410i			0.288675i
$13$			22.3707i			1.72082i	0.509599	+	0.860412i	$0.329794\pi$
$13$			22.3707i			1.72082i	−0.509599	+	0.860412i	$0.670206\pi$
$14$		−	15.6603i		−	1.11859i
$15$	−0.233360	+	8.65711i	−0.0155574	+	0.577141i
$16$	4.00000			0.250000
$17$	−29.3065			−1.72391			−0.861957	−	0.506982i	$-0.830761\pi$
$17$	−29.3065			−1.72391			−0.861957	+	0.506982i	$0.830761\pi$
$18$			4.24264i			0.235702i
$19$			31.8609i			1.67689i	0.544985	+	0.838446i	$0.316535\pi$
$19$			31.8609i			1.67689i	−0.544985	+	0.838446i	$0.683465\pi$
$20$	9.99637	+	0.269461i	0.499818	+	0.0134731i
$21$		−	19.1799i		−	0.913329i
$22$	−13.3522			−0.606917
$23$	−20.6810	+	10.0645i	−0.899176	+	0.437588i
$23$	−20.6810	+	10.0645i	−0.899176	+	0.437588i
$24$	4.89898			0.204124
$25$	24.9637	+	1.34682i	0.998548	+	0.0538727i
$26$	31.6370			1.21681
$27$			5.19615i			0.192450i
$28$	−22.1470			−0.790966
$29$	21.8003			0.751733			0.375867	−	0.926674i	$-0.377345\pi$
$29$	21.8003			0.751733			0.375867	+	0.926674i	$0.377345\pi$
$30$	12.2430	+	0.330021i	0.408100	+	0.0110007i
$31$	−33.9150			−1.09403			−0.547016	−	0.837122i	$-0.684236\pi$
$31$	−33.9150			−1.09403			−0.547016	+	0.837122i	$0.684236\pi$
$32$		−	5.65685i		−	0.176777i
$33$	−16.3530			−0.495545
$34$			41.4457i			1.21899i
$35$	−55.3475	−	1.49194i	−1.58136	−	0.0426269i
$36$	6.00000			0.166667
$37$	−7.59191			−0.205187			−0.102593	−	0.994723i	$-0.532714\pi$
$37$	−7.59191			−0.205187			−0.102593	+	0.994723i	$0.532714\pi$
$38$	45.0582			1.18574
$39$	38.7472			0.993518
$40$	0.381076	−	14.1370i	0.00952689	−	0.353425i
$41$	55.7647			1.36011			0.680057	−	0.733159i	$-0.261955\pi$
$41$	55.7647			1.36011			0.680057	+	0.733159i	$0.261955\pi$
$42$	−27.1245			−0.645821
$43$	22.0768			0.513413			0.256707	−	0.966489i	$-0.417363\pi$
$43$	22.0768			0.513413			0.256707	+	0.966489i	$0.417363\pi$
$44$			18.8828i			0.429155i
$45$	14.9946	+	0.404192i	0.333212	+	0.00898204i
$46$	14.2334	+	29.2474i	0.309421	+	0.635813i
$47$			77.2646i			1.64393i	0.569539	+	0.821964i	$0.307122\pi$
$47$			77.2646i			1.64393i	−0.569539	+	0.821964i	$0.692878\pi$
$48$		−	6.92820i		−	0.144338i
$49$	73.6229			1.50251
$50$	1.90469	−	35.3040i	0.0380937	−	0.706080i
$51$			50.7604i			0.995302i
$52$		−	44.7414i		−	0.860412i
$53$	39.1954			0.739535			0.369768	−	0.929124i	$-0.379437\pi$
$53$	39.1954			0.739535			0.369768	+	0.929124i	$0.379437\pi$
$54$	7.34847			0.136083
$55$	−1.27205	+	47.1899i	−0.0231281	+	0.857998i
$56$			31.3207i			0.559297i
$57$	55.1848			0.968154
$58$		−	30.8302i		−	0.531556i
$59$	70.2950			1.19144			0.595720	−	0.803192i	$-0.296867\pi$
$59$	70.2950			1.19144			0.595720	+	0.803192i	$0.296867\pi$
$60$	0.466721	−	17.3142i	0.00777868	−	0.288570i
$61$		−	31.9143i		−	0.523185i	−0.965178	−	0.261592i	$-0.915752\pi$
$61$		−	31.9143i		−	0.523185i	0.965178	−	0.261592i	$-0.0842476\pi$
$62$			47.9630i			0.773597i
$63$	−33.2206			−0.527311
$64$	−8.00000			−0.125000
$65$	3.01402	−	111.813i	0.0463695	−	1.72020i
$66$			23.1266i			0.350403i
$67$	−21.9858			−0.328147			−0.164073	−	0.986448i	$-0.552463\pi$
$67$	−21.9858			−0.328147			−0.164073	+	0.986448i	$0.552463\pi$
$68$	58.6131			0.861957
$69$	17.4322	+	35.8206i	0.252641	+	0.519139i
$70$	−2.10993	+	78.2732i	−0.0301418	+	1.11819i
$71$	−31.2687			−0.440404			−0.220202	−	0.975454i	$-0.570672\pi$
$71$	−31.2687			−0.440404			−0.220202	+	0.975454i	$0.570672\pi$
$72$		−	8.48528i		−	0.117851i
$73$			64.0595i			0.877527i	0.898602	+	0.438764i	$0.144583\pi$
$73$			64.0595i			0.877527i	−0.898602	+	0.438764i	$0.855417\pi$
$74$			10.7366i			0.145089i
$75$	2.33276	−	43.2384i	0.0311034	−	0.576512i
$76$		−	63.7219i		−	0.838446i
$77$		−	104.550i		−	1.35779i
$78$		−	54.7968i		−	0.702524i
$79$		−	8.93982i		−	0.113162i	−0.998398	−	0.0565812i	$-0.981980\pi$
$79$		−	8.93982i		−	0.113162i	0.998398	−	0.0565812i	$-0.0180200\pi$
$80$	−19.9927	−	0.538922i	−0.249909	−	0.00673653i
$81$	9.00000			0.111111
$82$		−	78.8632i		−	0.961746i
$83$	−6.63429			−0.0799312			−0.0399656	−	0.999201i	$-0.512725\pi$
$83$	−6.63429			−0.0799312			−0.0399656	+	0.999201i	$0.512725\pi$
$84$			38.3598i			0.456664i
$85$	146.479	+	3.94849i	1.72329	+	0.0464528i
$86$		−	31.2213i		−	0.363038i
$87$		−	37.7592i		−	0.434013i
$88$	26.7043			0.303458
$89$			153.281i			1.72226i	0.508383	+	0.861131i	$0.330243\pi$
$89$			153.281i			1.72226i	−0.508383	+	0.861131i	$0.669757\pi$
$90$	0.571614	−	21.2055i	0.00635126	−	0.235617i
$91$			247.723i			2.72223i
$92$	41.3621	−	20.1290i	0.449588	−	0.218794i
$93$			58.7425i			0.631639i
$94$	109.269			1.16243
$95$	4.29264	−	159.247i	0.0451857	−	1.67628i
$96$	−9.79796			−0.102062
$97$	−71.0282			−0.732249			−0.366125	−	0.930566i	$-0.619316\pi$
$97$	−71.0282			−0.732249			−0.366125	+	0.930566i	$0.619316\pi$
$98$		−	104.119i		−	1.06243i
$99$			28.3242i			0.286103i
$100$	−49.9274	−	2.69363i	−0.499274	−	0.0269363i
$101$	−138.006			−1.36639			−0.683196	−	0.730235i	$-0.739410\pi$
$101$	−138.006			−1.36639			−0.683196	+	0.730235i	$0.739410\pi$
$102$	71.7860			0.703785
$103$	−14.2828			−0.138668			−0.0693338	−	0.997594i	$-0.522087\pi$
$103$	−14.2828			−0.138668			−0.0693338	+	0.997594i	$0.522087\pi$
$104$	−63.2739			−0.608403
$105$	−2.58412	+	95.8647i	−0.0246107	+	0.912997i
$106$		−	55.4306i		−	0.522930i
$107$	−175.517			−1.64035			−0.820173	−	0.572116i	$-0.806123\pi$
$107$	−175.517			−1.64035			−0.820173	+	0.572116i	$0.806123\pi$
$108$		−	10.3923i		−	0.0962250i
$109$		−	162.959i		−	1.49503i	−0.664243	−	0.747517i	$-0.731246\pi$
$109$		−	162.959i		−	1.49503i	0.664243	−	0.747517i	$-0.268754\pi$
$110$	66.7366	+	1.79895i	0.606696	+	0.0163540i
$111$			13.1496i			0.118465i
$112$	44.2941			0.395483
$113$	66.7137			0.590387			0.295194	−	0.955437i	$-0.404616\pi$
$113$	66.7137			0.590387			0.295194	+	0.955437i	$0.404616\pi$
$114$		−	78.0431i		−	0.684588i
$115$	104.724	−	47.5179i	0.910641	−	0.413199i
$116$	−43.6005			−0.375867
$117$		−	67.1121i		−	0.573608i
$118$		−	99.4121i		−	0.842476i
$119$	−324.527			−2.72711
$120$	−24.4860	−	0.660042i	−0.204050	−	0.00550035i
$121$	31.8598			0.263304
$122$	−45.1336			−0.369948
$123$		−	96.5873i		−	0.785262i
$124$	67.8299			0.547016
$125$	−124.592	−	10.0950i	−0.996734	−	0.0807601i
$126$			46.9810i			0.372865i
$127$			32.5760i			0.256504i	0.991742	+	0.128252i	$0.0409366\pi$
$127$			32.5760i			0.256504i	−0.991742	+	0.128252i	$0.959063\pi$
$128$			11.3137i			0.0883883i
$129$		−	38.2381i		−	0.296419i
$130$	−158.127	−	4.26247i	−1.21636	−	0.0327882i
$131$	120.875			0.922708			0.461354	−	0.887216i	$-0.347364\pi$
$131$	120.875			0.922708			0.461354	+	0.887216i	$0.347364\pi$
$132$	32.7060			0.247773
$133$			352.813i			2.65273i
$134$			31.0926i			0.232035i
$135$	0.700081	−	25.9713i	0.00518578	−	0.192380i
$136$		−	82.8914i		−	0.609495i
$137$	17.4362			0.127271			0.0636356	−	0.997973i	$-0.479730\pi$
$137$	17.4362			0.127271			0.0636356	+	0.997973i	$0.479730\pi$
$138$	50.6580	−	24.6529i	0.367087	−	0.178644i
$139$	−140.316			−1.00947			−0.504734	−	0.863275i	$-0.668409\pi$
$139$	−140.316			−1.00947			−0.504734	+	0.863275i	$0.668409\pi$
$140$	110.695	+	2.98388i	0.790679	+	0.0213135i
$141$	133.826			0.949122
$142$			44.2206i			0.311413i
$143$	211.211			1.47700
$144$	−12.0000			−0.0833333
$145$	−108.962	−	2.93716i	−0.751460	−	0.0202563i
$146$	90.5938			0.620506
$147$		−	127.519i		−	0.867474i
$148$	15.1838			0.102593
$149$			32.9711i			0.221283i	0.993860	+	0.110641i	$0.0352905\pi$
$149$			32.9711i			0.221283i	−0.993860	+	0.110641i	$0.964710\pi$
$150$	−61.1483	−	3.29901i	−0.407655	−	0.0219934i
$151$	241.409			1.59873			0.799366	−	0.600844i	$-0.205169\pi$
$151$	241.409			1.59873			0.799366	+	0.600844i	$0.205169\pi$
$152$	−90.1164			−0.592871
$153$	87.9196			0.574638
$154$	−147.856			−0.960101
$155$	169.513	+	4.56938i	1.09363	+	0.0294799i
$156$	−77.4944			−0.496759
$157$	−67.8434			−0.432123			−0.216062	−	0.976380i	$-0.569321\pi$
$157$	−67.8434			−0.432123			−0.216062	+	0.976380i	$0.569321\pi$
$158$	−12.6428			−0.0800178
$159$		−	67.8884i		−	0.426971i
$160$	−0.762151	+	28.2740i	−0.00476345	+	0.176713i
$161$	−229.012	+	111.450i	−1.42243	+	0.692234i
$162$		−	12.7279i		−	0.0785674i
$163$			222.059i			1.36232i	0.732133	+	0.681162i	$0.238525\pi$
$163$			222.059i			1.36232i	−0.732133	+	0.681162i	$0.761475\pi$
$164$	−111.529			−0.680057
$165$	81.7353	+	2.20325i	0.495365	+	0.0133530i
$166$			9.38230i			0.0565199i
$167$			223.321i			1.33725i	0.743599	+	0.668626i	$0.233117\pi$
$167$			223.321i			1.33725i	−0.743599	+	0.668626i	$0.766883\pi$
$168$	54.2490			0.322910
$169$	−331.449			−1.96124
$170$	5.58400	−	207.153i	0.0328471	−	1.21855i
$171$		−	95.5828i		−	0.558964i
$172$	−44.1536			−0.256707
$173$			30.8477i			0.178310i	0.996018	+	0.0891551i	$0.0284167\pi$
$173$			30.8477i			0.178310i	−0.996018	+	0.0891551i	$0.971583\pi$
$174$	−53.3995			−0.306894
$175$	276.436	+	14.9140i	1.57963	+	0.0852229i
$176$		−	37.7656i		−	0.214577i
$177$		−	121.755i		−	0.687879i
$178$	216.773			1.21782
$179$	55.2209			0.308497			0.154248	−	0.988032i	$-0.450704\pi$
$179$	55.2209			0.308497			0.154248	+	0.988032i	$0.450704\pi$
$180$	−29.9891	−	0.808384i	−0.166606	−	0.00449102i
$181$			45.7487i			0.252755i	0.991982	+	0.126378i	$0.0403351\pi$
$181$			45.7487i			0.252755i	−0.991982	+	0.126378i	$0.959665\pi$
$182$	350.333			1.92491
$183$	−55.2771			−0.302061
$184$	−28.4667	−	58.4948i	−0.154711	−	0.317907i
$185$	37.9458	+	1.02286i	0.205112	+	0.00552899i
$186$	83.0744			0.446636
$187$			276.695i			1.47965i
$188$		−	154.529i		−	0.821964i
$189$			57.5397i			0.304443i
$190$	−225.209	−	6.07072i	−1.18531	−	0.0319511i
$191$		−	140.527i		−	0.735745i	−0.929876	−	0.367873i	$-0.880086\pi$
$191$		−	140.527i		−	0.735745i	0.929876	−	0.367873i	$-0.119914\pi$
$192$			13.8564i			0.0721688i
$193$			171.323i			0.887683i	0.896105	+	0.443842i	$0.146385\pi$
$193$			171.323i			0.887683i	−0.896105	+	0.443842i	$0.853615\pi$
$194$			100.449i			0.517779i
$195$	−193.666	−	5.22044i	−0.993158	−	0.0267715i
$196$	−147.246			−0.751254
$197$		−	47.7742i		−	0.242509i	−0.992621	−	0.121254i	$-0.961308\pi$
$197$		−	47.7742i		−	0.242509i	0.992621	−	0.121254i	$-0.0386916\pi$
$198$	40.0565			0.202306
$199$			45.4098i			0.228190i	0.993470	+	0.114095i	$0.0363968\pi$
$199$			45.4098i			0.228190i	−0.993470	+	0.114095i	$0.963603\pi$
$200$	−3.80937	+	70.6080i	−0.0190469	+	0.353040i
$201$			38.0806i			0.189456i
$202$			195.169i			0.966185i
$203$	241.406			1.18919
$204$		−	101.521i		−	0.497651i
$205$	−278.722	−	7.51321i	−1.35962	−	0.0366498i
$206$			20.1989i			0.0980528i
$207$	62.0431	−	30.1935i	0.299725	−	0.145863i
$208$			89.4829i			0.430206i
$209$	300.812			1.43929
$210$	135.573	+	3.65450i	0.645586	+	0.0174024i
$211$	−125.035			−0.592585			−0.296293	−	0.955097i	$-0.595750\pi$
$211$	−125.035			−0.592585			−0.296293	+	0.955097i	$0.595750\pi$
$212$	−78.3907			−0.369768
$213$			54.1589i			0.254267i
$214$			248.219i			1.15990i
$215$	−110.344	−	2.97442i	−0.513227	−	0.0138345i
$216$	−14.6969			−0.0680414
$217$	−375.558			−1.73068
$218$	−230.458			−1.05715
$219$	110.954			0.506641
$220$	2.54409	−	94.3798i	0.0115641	−	0.428999i
$221$		−	655.608i		−	2.96655i
$222$	18.5963			0.0837672
$223$		−	398.218i		−	1.78573i	−0.450324	−	0.892865i	$-0.648692\pi$
$223$		−	398.218i		−	1.78573i	0.450324	−	0.892865i	$-0.351308\pi$
$224$		−	62.6413i		−	0.279649i
$225$	−74.8911	−	4.04045i	−0.332849	−	0.0179576i
$226$		−	94.3475i		−	0.417467i
$227$	−120.751			−0.531945			−0.265972	−	0.963981i	$-0.585693\pi$
$227$	−120.751			−0.531945			−0.265972	+	0.963981i	$0.585693\pi$
$228$	−110.370			−0.484077
$229$			2.35749i			0.0102947i	0.999987	+	0.00514735i	$0.00163846\pi$
$229$			2.35749i			0.0102947i	−0.999987	+	0.00514735i	$0.998362\pi$
$230$	−67.2005	−	148.102i	−0.292176	−	0.643920i
$231$	−181.085			−0.783919
$232$			61.6605i			0.265778i
$233$			80.4920i			0.345459i	0.984969	+	0.172730i	$0.0552587\pi$
$233$			80.4920i			0.345459i	−0.984969	+	0.172730i	$0.944741\pi$
$234$	−94.9109			−0.405602
$235$	10.4099	−	386.183i	0.0442975	−	1.64333i
$236$	−140.590			−0.595720
$237$	−15.4842			−0.0653343
$238$			458.950i			1.92836i
$239$	−177.239			−0.741584			−0.370792	−	0.928716i	$-0.620914\pi$
$239$	−177.239			−0.741584			−0.370792	+	0.928716i	$0.620914\pi$
$240$	−0.933441	+	34.6284i	−0.00388934	+	0.144285i
$241$			373.299i			1.54896i	0.632600	+	0.774479i	$0.281988\pi$
$241$			373.299i			1.54896i	−0.632600	+	0.774479i	$0.718012\pi$
$242$		−	45.0566i		−	0.186184i
$243$		−	15.5885i		−	0.0641500i
$244$			63.8285i			0.261592i
$245$	−367.981	−	9.91926i	−1.50196	−	0.0404868i
$246$	−136.595			−0.555264
$247$	−712.752			−2.88564
$248$		−	95.9260i		−	0.386798i
$249$			11.4909i			0.0461483i
$250$	−14.2765	+	176.199i	−0.0571060	+	0.704797i
$251$		−	78.0057i		−	0.310780i	−0.987853	−	0.155390i	$-0.950337\pi$
$251$		−	78.0057i		−	0.310780i	0.987853	−	0.155390i	$-0.0496633\pi$
$252$	66.4411			0.263655
$253$	95.0232	+	195.258i	0.375586	+	0.771771i
$254$	46.0694			0.181375
$255$	6.83898	−	253.710i	0.0268195	−	0.994940i
$256$	16.0000			0.0625000
$257$			163.162i			0.634872i	0.948280	+	0.317436i	$0.102822\pi$
$257$			163.162i			0.634872i	−0.948280	+	0.317436i	$0.897178\pi$
$258$	−54.0768			−0.209600
$259$	−84.0692			−0.324592
$260$	−6.02804	+	223.626i	−0.0231848	+	0.860100i
$261$	−65.4008			−0.250578
$262$		−	170.943i		−	0.652453i
$263$	−40.0337			−0.152219			−0.0761097	−	0.997099i	$-0.524250\pi$
$263$	−40.0337			−0.152219			−0.0761097	+	0.997099i	$0.524250\pi$
$264$		−	46.2533i		−	0.175202i
$265$	−195.906	−	5.28082i	−0.739267	−	0.0199276i
$266$	498.953			1.87576
$267$	265.491			0.994348
$268$	43.9716			0.164073
$269$	−284.506			−1.05764			−0.528822	−	0.848733i	$-0.677366\pi$
$269$	−284.506			−1.05764			−0.528822	+	0.848733i	$0.677366\pi$
$270$	−36.7290	−	0.990064i	−0.136033	−	0.00366690i
$271$	−443.178			−1.63534			−0.817671	−	0.575685i	$-0.804735\pi$
$271$	−443.178			−1.63534			−0.817671	+	0.575685i	$0.804735\pi$
$272$	−117.226			−0.430978
$273$	429.068			1.57168
$274$		−	24.6585i		−	0.0899944i
$275$	12.7158	−	235.692i	0.0462394	−	0.857063i
$276$	−34.8645	−	71.6412i	−0.126321	−	0.259570i
$277$		−	314.272i		−	1.13456i	−0.823526	−	0.567279i	$-0.807996\pi$
$277$		−	314.272i		−	1.13456i	0.823526	−	0.567279i	$-0.192004\pi$
$278$			198.437i			0.713802i
$279$	101.745			0.364677
$280$	4.21985	−	156.546i	0.0150709	−	0.559094i
$281$			71.4214i			0.254169i	0.991892	+	0.127084i	$0.0405619\pi$
$281$			71.4214i			0.254169i	−0.991892	+	0.127084i	$0.959438\pi$
$282$		−	189.259i		−	0.671131i
$283$	203.792			0.720113			0.360057	−	0.932930i	$-0.382757\pi$
$283$	203.792			0.720113			0.360057	+	0.932930i	$0.382757\pi$
$284$	62.5373			0.220202
$285$	−275.824	−	7.43508i	−0.967802	−	0.0260880i
$286$		−	298.697i		−	1.04440i
$287$	617.512			2.15161
$288$			16.9706i			0.0589256i
$289$	569.873			1.97188
$290$	−4.15378	+	154.095i	−0.0143234	+	0.531363i
$291$			123.024i			0.422764i
$292$		−	128.119i		−	0.438764i
$293$	36.5407			0.124712			0.0623562	−	0.998054i	$-0.480139\pi$
$293$	36.5407			0.124712			0.0623562	+	0.998054i	$0.480139\pi$
$294$	−180.339			−0.613397
$295$	−351.347	−	9.47089i	−1.19101	−	0.0321047i
$296$		−	21.4732i		−	0.0725445i
$297$	49.0590			0.165182
$298$	46.6282			0.156470
$299$	−225.150	−	462.650i	−0.753011	−	1.54732i
$300$	−4.66551	+	86.4768i	−0.0155517	+	0.288256i
$301$	244.468			0.812185
$302$		−	341.403i		−	1.13047i
$303$			239.033i			0.788887i
$304$			127.444i			0.419223i
$305$	−4.29983	+	159.513i	−0.0140978	+	0.522995i
$306$		−	124.337i		−	0.406330i
$307$		−	128.731i		−	0.419319i	−0.977774	−	0.209659i	$-0.932764\pi$
$307$		−	128.731i		−	0.419319i	0.977774	−	0.209659i	$-0.0672355\pi$
$308$			209.099i			0.678894i
$309$			24.7385i			0.0800598i
$310$	6.46209	−	239.728i	0.0208454	−	0.773316i
$311$	−480.481			−1.54495			−0.772477	−	0.635043i	$-0.780982\pi$
$311$	−480.481			−1.54495			−0.772477	+	0.635043i	$0.780982\pi$
$312$			109.594i			0.351262i
$313$	262.271			0.837926			0.418963	−	0.908003i	$-0.362394\pi$
$313$	262.271			0.837926			0.418963	+	0.908003i	$0.362394\pi$
$314$			95.9450i			0.305557i
$315$	166.043	+	4.47583i	0.527119	+	0.0142090i
$316$			17.8796i			0.0565812i
$317$		−	361.397i		−	1.14005i	−0.821626	−	0.570027i	$-0.806933\pi$
$317$		−	361.397i		−	1.14005i	0.821626	−	0.570027i	$-0.193067\pi$
$318$	−96.0086			−0.301914
$319$		−	205.825i		−	0.645220i
$320$	39.9855	+	1.07784i	0.124955	+	0.00336827i
$321$			304.004i			0.947054i
$322$	157.614	+	323.872i	0.489483	+	1.00581i
$323$		−	933.734i		−	2.89082i
$324$	−18.0000			−0.0555556
$325$	−30.1293	+	558.456i	−0.0927054	+	1.71833i
$326$	314.039			0.963309
$327$	−282.253			−0.863158
$328$			157.726i			0.480873i
$329$			855.592i			2.60058i
$330$	3.11586	−	115.591i	0.00944201	−	0.350276i
$331$	219.463			0.663032			0.331516	−	0.943450i	$-0.392440\pi$
$331$	219.463			0.663032			0.331516	+	0.943450i	$0.392440\pi$
$332$	13.2686			0.0399656
$333$	22.7757			0.0683956
$334$	315.824			0.945580
$335$	109.889	+	2.96216i	0.328027	+	0.00884228i
$336$		−	76.7196i		−	0.228332i
$337$	477.616			1.41726			0.708629	−	0.705581i	$-0.249314\pi$
$337$	477.616			1.41726			0.708629	+	0.705581i	$0.249314\pi$
$338$			468.740i			1.38680i
$339$		−	115.552i		−	0.340860i
$340$	−292.959	−	7.89697i	−0.861644	−	0.0232264i
$341$			320.205i			0.939018i
$342$	−135.175			−0.395247
$343$	272.662			0.794934
$344$			62.4426i			0.181519i
$345$	−82.3035	−	181.387i	−0.238561	−	0.525759i
$346$	43.6252			0.126084
$347$		−	333.470i		−	0.961008i	−0.876993	−	0.480504i	$-0.840454\pi$
$347$		−	333.470i		−	0.961008i	0.876993	−	0.480504i	$-0.159546\pi$
$348$			75.5183i			0.217007i
$349$	−106.304			−0.304596			−0.152298	−	0.988335i	$-0.548667\pi$
$349$	−106.304			−0.304596			−0.152298	+	0.988335i	$0.548667\pi$
$350$	21.0916	−	390.940i	0.0602617	−	1.11697i
$351$	−116.242			−0.331173
$352$	−53.4087			−0.151729
$353$			365.647i			1.03583i	0.855433	+	0.517914i	$0.173291\pi$
$353$			365.647i			1.03583i	−0.855433	+	0.517914i	$0.826709\pi$
$354$	−172.187			−0.486404
$355$	156.287	+	4.21285i	0.440244	+	0.0118672i
$356$		−	306.563i		−	0.861131i
$357$			562.096i			1.57450i
$358$		−	78.0942i		−	0.218140i
$359$			654.287i			1.82253i	0.411823	+	0.911264i	$0.364892\pi$
$359$			654.287i			1.82253i	−0.411823	+	0.911264i	$0.635108\pi$
$360$	−1.14323	+	42.4110i	−0.00317563	+	0.117808i
$361$	−654.120			−1.81197
$362$	64.6984			0.178725
$363$		−	55.1829i		−	0.152019i
$364$		−	495.445i		−	1.36111i
$365$	8.63078	−	320.181i	0.0236460	−	0.877209i
$366$			78.1737i			0.213589i
$367$	368.184			1.00323			0.501613	−	0.865092i	$-0.332740\pi$
$367$	368.184			1.00323			0.501613	+	0.865092i	$0.332740\pi$
$368$	−82.7242	+	40.2581i	−0.224794	+	0.109397i
$369$	−167.294			−0.453371
$370$	1.44655	−	53.6634i	0.00390959	−	0.145036i
$371$	434.031			1.16989
$372$		−	117.485i		−	0.315820i
$373$	91.4071			0.245059			0.122530	−	0.992465i	$-0.460899\pi$
$373$	91.4071			0.245059			0.122530	+	0.992465i	$0.460899\pi$
$374$	391.306			1.04627
$375$	−17.4851	+	215.799i	−0.0466269	+	0.575464i
$376$	−218.537			−0.581216
$377$			487.687i			1.29360i
$378$	81.3734			0.215274
$379$		−	203.934i		−	0.538084i	−0.963128	−	0.269042i	$-0.913293\pi$
$379$		−	203.934i		−	0.538084i	0.963128	−	0.269042i	$-0.0867070\pi$
$380$	−8.58529	+	318.494i	−0.0225929	+	0.838141i
$381$	56.4232			0.148092
$382$	−198.736			−0.520251
$383$	−398.715			−1.04103			−0.520516	−	0.853852i	$-0.674260\pi$
$383$	−398.715			−1.04103			−0.520516	+	0.853852i	$0.674260\pi$
$384$	19.5959			0.0510310
$385$	−14.0860	+	522.558i	−0.0365871	+	1.35729i
$386$	242.287			0.627687
$387$	−66.2303			−0.171138
$388$	142.056			0.366125
$389$			39.2823i			0.100983i	0.998724	+	0.0504914i	$0.0160788\pi$
$389$			39.2823i			0.100983i	−0.998724	+	0.0504914i	$0.983921\pi$
$390$	−7.38281	+	273.885i	−0.0189303	+	0.702268i
$391$	606.090	−	294.956i	1.55010	−	0.754363i
$392$			208.237i			0.531217i
$393$		−	209.361i		−	0.532726i
$394$	−67.5629			−0.171479
$395$	−1.20447	+	44.6829i	−0.00304929	+	0.113121i
$396$		−	56.6484i		−	0.143052i
$397$			6.66240i			0.0167819i	0.999965	+	0.00839094i	$0.00267095\pi$
$397$			6.66240i			0.0167819i	−0.999965	+	0.00839094i	$0.997329\pi$
$398$	64.2192			0.161355
$399$	611.090			1.53155
$400$	99.8548	+	5.38727i	0.249637	+	0.0134682i
$401$		−	88.5787i		−	0.220895i	−0.993882	−	0.110447i	$-0.964772\pi$
$401$		−	88.5787i		−	0.220895i	0.993882	−	0.110447i	$-0.0352283\pi$
$402$	53.8540			0.133965
$403$		−	758.702i		−	1.88264i
$404$	276.011			0.683196
$405$	−44.9837	−	1.21258i	−0.111071	−	0.00299401i
$406$		−	341.399i		−	0.840885i
$407$			71.6783i			0.176114i
$408$	−143.572			−0.351892
$409$	140.829			0.344325			0.172162	−	0.985069i	$-0.444925\pi$
$409$	140.829			0.344325			0.172162	+	0.985069i	$0.444925\pi$
$410$	−10.6253	+	394.173i	−0.0259153	+	0.961397i
$411$		−	30.2003i		−	0.0734801i
$412$	28.5655			0.0693338
$413$	778.413			1.88478
$414$	−42.7001	−	87.7422i	−0.103140	−	0.211938i
$415$	33.1594	+	0.893842i	0.0799021	+	0.00215383i
$416$	126.548			0.304202
$417$			243.035i			0.582817i
$418$		−	425.413i		−	1.01773i
$419$		−	607.946i		−	1.45095i	−0.688251	−	0.725473i	$-0.741621\pi$
$419$		−	607.946i		−	1.45095i	0.688251	−	0.725473i	$-0.258379\pi$
$420$	5.16824	−	191.729i	0.0123053	−	0.456499i
$421$			197.430i			0.468955i	0.972122	+	0.234477i	$0.0753379\pi$
$421$			197.430i			0.468955i	−0.972122	+	0.234477i	$0.924662\pi$
$422$			176.827i			0.419021i
$423$		−	231.794i		−	0.547976i
$424$			110.861i			0.261465i
$425$	−731.599	−	39.4705i	−1.72141	−	0.0928718i
$426$	76.5923			0.179794
$427$		−	353.403i		−	0.827643i
$428$	351.034			0.820173
$429$		−	365.828i		−	0.852746i
$430$	−4.20646	+	156.050i	−0.00978247	+	0.362906i
$431$			495.113i			1.14875i	0.818591	+	0.574377i	$0.194755\pi$
$431$			495.113i			1.14875i	−0.818591	+	0.574377i	$0.805245\pi$
$432$			20.7846i			0.0481125i
$433$	49.7031			0.114788			0.0573939	−	0.998352i	$-0.481721\pi$
$433$	49.7031			0.114788			0.0573939	+	0.998352i	$0.481721\pi$
$434$			531.120i			1.22378i
$435$	−5.08731	+	188.727i	−0.0116950	+	0.433856i
$436$			325.917i			0.747517i
$437$	−320.665	−	658.918i	−0.733787	−	1.50782i
$438$		−	156.913i		−	0.358249i
$439$	275.213			0.626910			0.313455	−	0.949603i	$-0.398514\pi$
$439$	275.213			0.626910			0.313455	+	0.949603i	$0.398514\pi$
$440$	−133.473	−	3.59789i	−0.303348	−	0.00817702i
$441$	−220.869			−0.500836
$442$	−927.170			−2.09767
$443$			322.324i			0.727594i	0.931478	+	0.363797i	$0.118520\pi$
$443$			322.324i			0.727594i	−0.931478	+	0.363797i	$0.881480\pi$
$444$		−	26.2992i		−	0.0592323i
$445$	20.6517	−	766.128i	0.0464083	−	1.72164i
$446$	−563.165			−1.26270
$447$	57.1076			0.127758
$448$	−88.5882			−0.197741
$449$	159.589			0.355432			0.177716	−	0.984082i	$-0.443129\pi$
$449$	159.589			0.355432			0.177716	+	0.984082i	$0.443129\pi$
$450$	−5.71406	+	105.912i	−0.0126979	+	0.235360i
$451$		−	526.497i		−	1.16740i
$452$	−133.427			−0.295194
$453$		−	418.132i		−	0.923029i
$454$			170.768i			0.376142i
$455$	33.3758	−	1238.16i	0.0733535	−	2.72124i
$456$			156.086i			0.342294i
$457$	−698.342			−1.52810			−0.764051	−	0.645156i	$-0.776792\pi$
$457$	−698.342			−1.52810			−0.764051	+	0.645156i	$0.776792\pi$
$458$	3.33399			0.00727946
$459$		−	152.281i		−	0.331767i
$460$	−209.447	+	95.0358i	−0.455320	+	0.206600i
$461$	808.968			1.75481			0.877405	−	0.479750i	$-0.159273\pi$
$461$	808.968			1.75481			0.877405	+	0.479750i	$0.159273\pi$
$462$			256.093i			0.554314i
$463$			490.949i			1.06036i	0.847884	+	0.530182i	$0.177876\pi$
$463$			490.949i			1.06036i	−0.847884	+	0.530182i	$0.822124\pi$
$464$	87.2011			0.187933
$465$	7.91441	−	293.606i	0.0170202	−	0.631410i
$466$	113.833			0.244277
$467$	−363.574			−0.778532			−0.389266	−	0.921125i	$-0.627271\pi$
$467$	−363.574			−0.778532			−0.389266	+	0.921125i	$0.627271\pi$
$468$			134.224i			0.286804i
$469$	−243.461			−0.519106
$470$	−546.145	−	14.7218i	−1.16201	−	0.0313231i
$471$			117.508i			0.249487i
$472$			198.824i			0.421238i
$473$		−	208.436i		−	0.440668i
$474$			21.8980i			0.0461983i
$475$	−42.9109	+	795.367i	−0.0903386	+	1.67446i
$476$	649.053			1.36356
$477$	−117.586			−0.246512
$478$			250.653i			0.524379i
$479$			231.968i			0.484275i	0.970242	+	0.242138i	$0.0778486\pi$
$479$			231.968i			0.484275i	−0.970242	+	0.242138i	$0.922151\pi$
$480$	48.9720	+	1.32008i	0.102025	+	0.00275018i
$481$		−	169.836i		−	0.353090i
$482$	527.924			1.09528
$483$	193.036	+	396.660i	0.399661	+	0.821243i
$484$	−63.7197			−0.131652
$485$	355.012	+	9.56967i	0.731984	+	0.0197313i
$486$	−22.0454			−0.0453609
$487$		−	126.084i		−	0.258898i	−0.991586	−	0.129449i	$-0.958679\pi$
$487$		−	126.084i		−	0.258898i	0.991586	−	0.129449i	$-0.0413209\pi$
$488$	90.2672			0.184974
$489$	384.617			0.786538
$490$	−14.0280	+	520.404i	−0.0286285	+	1.06205i
$491$	18.6259			0.0379346			0.0189673	−	0.999820i	$-0.493962\pi$
$491$	18.6259			0.0379346			0.0189673	+	0.999820i	$0.493962\pi$
$492$			193.175i			0.392631i
$493$	−638.890			−1.29592
$494$			1007.98i			2.04045i
$495$	3.81614	−	141.570i	0.00770937	−	0.285999i
$496$	−135.660			−0.273508
$497$	−346.254			−0.696689
$498$	16.2506			0.0326318
$499$	835.929			1.67521			0.837604	−	0.546277i	$-0.183955\pi$
$499$	835.929			1.67521			0.837604	+	0.546277i	$0.183955\pi$
$500$	249.183	+	20.1900i	0.498367	+	0.0403801i
$501$	386.803			0.772062
$502$	−110.317			−0.219754
$503$	455.945			0.906452			0.453226	−	0.891396i	$-0.350273\pi$
$503$	455.945			0.906452			0.453226	+	0.891396i	$0.350273\pi$
$504$		−	93.9620i		−	0.186432i
$505$	689.777	+	18.5936i	1.36590	+	0.0368190i
$506$	276.137	−	134.383i	0.545725	−	0.265579i
$507$			574.086i			1.13232i
$508$		−	65.1519i		−	0.128252i
$509$	−546.234			−1.07315			−0.536576	−	0.843852i	$-0.680283\pi$
$509$	−546.234			−1.07315			−0.536576	+	0.843852i	$0.680283\pi$
$510$	−358.800	−	9.67178i	−0.703529	−	0.0189643i
$511$			709.364i			1.38819i
$512$		−	22.6274i		−	0.0441942i
$513$	−165.554			−0.322718
$514$	230.746			0.448922
$515$	71.3879	+	1.92433i	0.138617	+	0.00373655i
$516$			76.4762i			0.148210i
$517$	729.487			1.41100
$518$			118.892i			0.229521i
$519$	53.4297			0.102947
$520$	316.255	+	8.52494i	0.608182	+	0.0163941i
$521$		−	468.515i		−	0.899261i	−0.893215	−	0.449631i	$-0.851556\pi$
$521$		−	468.515i		−	0.899261i	0.893215	−	0.449631i	$-0.148444\pi$
$522$			92.4907i			0.177185i
$523$	780.495			1.49234			0.746171	−	0.665754i	$-0.231890\pi$
$523$	780.495			1.49234			0.746171	+	0.665754i	$0.231890\pi$
$524$	−241.749			−0.461354
$525$	25.8318	−	478.801i	0.0492035	−	0.912002i
$526$			56.6162i			0.107635i
$527$	993.930			1.88602
$528$	−65.4120			−0.123886
$529$	326.411	−	416.289i	0.617034	−	0.786936i
$530$	−7.46820	+	277.052i	−0.0140909	+	0.522740i
$531$	−210.885			−0.397147
$532$		−	705.626i		−	1.32636i
$533$			1247.50i			2.34052i
$534$		−	375.461i		−	0.703111i
$535$	877.266	+	23.6475i	1.63975	+	0.0442010i
$536$		−	62.1853i		−	0.116017i
$537$		−	95.6455i		−	0.178111i
$538$			402.353i			0.747867i
$539$		−	695.104i		−	1.28962i
$540$	−1.40016	+	51.9427i	−0.00259289	+	0.0961901i
$541$	−190.214			−0.351597			−0.175799	−	0.984426i	$-0.556251\pi$
$541$	−190.214			−0.351597			−0.175799	+	0.984426i	$0.556251\pi$
$542$			626.748i			1.15636i
$543$	79.2390			0.145928
$544$			165.783i			0.304748i
$545$	−21.9555	+	814.497i	−0.0402854	+	1.49449i
$546$		−	606.794i		−	1.11134i
$547$		−	285.722i		−	0.522344i	−0.965292	−	0.261172i	$-0.915891\pi$
$547$		−	285.722i		−	0.522344i	0.965292	−	0.261172i	$-0.0841090\pi$
$548$	−34.8723			−0.0636356
$549$			95.7428i			0.174395i
$550$	−333.319	−	17.9829i	−0.606035	−	0.0326962i
$551$			694.577i			1.26058i
$552$	−101.316	+	49.3058i	−0.183543	+	0.0893222i
$553$		−	98.9953i		−	0.179015i
$554$	−444.448			−0.802253
$555$	1.77165	−	65.7240i	0.00319216	−	0.118422i
$556$	280.632			0.504734
$557$	−65.8064			−0.118144			−0.0590721	−	0.998254i	$-0.518814\pi$
$557$	−65.8064			−0.118144			−0.0590721	+	0.998254i	$0.518814\pi$
$558$		−	143.889i		−	0.257866i
$559$			493.873i			0.883494i
$560$	−221.390	−	5.96777i	−0.395339	−	0.0106567i
$561$	479.250			0.854277
$562$	101.005			0.179724
$563$	−206.928			−0.367545			−0.183772	−	0.982969i	$-0.558831\pi$
$563$	−206.928			−0.367545			−0.183772	+	0.982969i	$0.558831\pi$
$564$	−267.652			−0.474561
$565$	−333.448	−	8.98838i	−0.590173	−	0.0159086i
$566$		−	288.206i		−	0.509197i
$567$	99.6617			0.175770
$568$		−	88.4412i		−	0.155706i
$569$			60.5855i			0.106477i	0.998582	+	0.0532386i	$0.0169544\pi$
$569$			60.5855i			0.106477i	−0.998582	+	0.0532386i	$0.983046\pi$
$570$	−10.5148	+	390.074i	−0.0184470	+	0.684340i
$571$			810.739i			1.41986i	0.704273	+	0.709929i	$0.251273\pi$
$571$			810.739i			1.41986i	−0.704273	+	0.709929i	$0.748727\pi$
$572$	−422.422			−0.738500
$573$	−243.401			−0.424783
$574$		−	873.293i		−	1.52142i
$575$	−529.830	+	223.394i	−0.921444	+	0.388511i
$576$	24.0000			0.0416667
$577$		−	1016.03i		−	1.76088i	−0.474159	−	0.880439i	$-0.657248\pi$
$577$		−	1016.03i		−	1.76088i	0.474159	−	0.880439i	$-0.342752\pi$
$578$		−	805.922i		−	1.39433i
$579$	296.740			0.512504
$580$	217.923	+	5.87433i	0.375730	+	0.0101281i
$581$	−73.4649			−0.126446
$582$	173.983			0.298940
$583$		−	370.059i		−	0.634750i
$584$	−181.188			−0.310253
$585$	−9.04206	+	335.439i	−0.0154565	+	0.573400i
$586$		−	51.6764i		−	0.0881850i
$587$		−	962.245i		−	1.63926i	−0.572894	−	0.819629i	$-0.694179\pi$
$587$		−	962.245i		−	1.63926i	0.572894	−	0.819629i	$-0.305821\pi$
$588$			255.037i			0.433737i
$589$		−	1080.56i		−	1.83457i
$590$	−13.3939	+	496.880i	−0.0227015	+	0.842170i
$591$	−82.7473			−0.140012
$592$	−30.3676			−0.0512967
$593$		−	234.132i		−	0.394826i	−0.980320	−	0.197413i	$-0.936746\pi$
$593$		−	234.132i		−	0.394826i	0.980320	−	0.197413i	$-0.0632539\pi$
$594$		−	69.3799i		−	0.116801i
$595$	1622.04	+	43.7237i	2.72612	+	0.0734851i
$596$		−	65.9422i		−	0.110641i
$597$	78.6521			0.131746
$598$	−654.286	+	318.411i	−1.09412	+	0.532459i
$599$	−129.460			−0.216127			−0.108063	−	0.994144i	$-0.534465\pi$
$599$	−129.460			−0.216127			−0.108063	+	0.994144i	$0.534465\pi$
$600$	122.297	+	6.59803i	0.203828	+	0.0109967i
$601$	−109.440			−0.182097			−0.0910483	−	0.995846i	$-0.529022\pi$
$601$	−109.440			−0.182097			−0.0910483	+	0.995846i	$0.529022\pi$
$602$		−	345.730i		−	0.574302i
$603$	65.9575			0.109382
$604$	−482.817			−0.799366
$605$	−159.241	−	4.29250i	−0.263209	−	0.00709503i
$606$	338.043			0.557827
$607$		−	643.634i		−	1.06035i	−0.847887	−	0.530176i	$-0.822126\pi$
$607$		−	643.634i		−	1.06035i	0.847887	−	0.530176i	$-0.177874\pi$
$608$	180.233			0.296435
$609$		−	418.127i		−	0.686580i
$610$	225.586	+	6.08088i	0.369813	+	0.00996865i
$611$	−1728.46			−2.82891
$612$	−175.839			−0.287319
$613$	−837.840			−1.36679			−0.683393	−	0.730050i	$-0.739497\pi$
$613$	−837.840			−1.36679			−0.683393	+	0.730050i	$0.739497\pi$
$614$	−182.053			−0.296503
$615$	−13.0133	+	482.761i	−0.0211598	+	0.784977i
$616$	295.711			0.480050
$617$	249.042			0.403634			0.201817	−	0.979423i	$-0.435315\pi$
$617$	249.042			0.403634			0.201817	+	0.979423i	$0.435315\pi$
$618$	34.9855			0.0566108
$619$			128.268i			0.207218i	0.994618	+	0.103609i	$0.0330391\pi$
$619$			128.268i			0.207218i	−0.994618	+	0.103609i	$0.966961\pi$
$620$	−339.027	−	9.13877i	−0.546817	−	0.0147400i
$621$	−52.2967	−	107.462i	−0.0842138	−	0.173046i
$622$			679.502i			1.09245i
$623$			1697.36i			2.72450i
$624$	154.989			0.248380
$625$	621.372	+	67.2430i	0.994195	+	0.107589i
$626$		−	370.907i		−	0.592503i
$627$		−	521.022i		−	0.830976i
$628$	135.687			0.216062
$629$	222.493			0.353724
$630$	6.32978	−	234.820i	0.0100473	−	0.372730i
$631$			927.605i			1.47006i	0.678037	+	0.735028i	$0.262831\pi$
$631$			927.605i			1.47006i	−0.678037	+	0.735028i	$0.737169\pi$
$632$	25.2856			0.0400089
$633$			216.568i			0.342129i
$634$	−511.093			−0.806140
$635$	4.38898	−	162.821i	0.00691178	−	0.256410i
$636$			135.777i			0.213485i
$637$			1647.00i			2.58555i
$638$	−291.081			−0.456239
$639$	93.8060			0.146801
$640$	1.52430	−	56.5480i	0.00238172	−	0.0883563i
$641$			722.264i			1.12678i	0.826192	+	0.563388i	$0.190503\pi$
$641$			722.264i			1.12678i	−0.826192	+	0.563388i	$0.809497\pi$
$642$	429.927			0.669668
$643$	601.221			0.935025			0.467513	−	0.883986i	$-0.345150\pi$
$643$	601.221			0.935025			0.467513	+	0.883986i	$0.345150\pi$
$644$	458.024	−	222.899i	0.711217	−	0.346117i
$645$	−5.15184	+	191.121i	−0.00798735	+	0.296312i
$646$	−1320.50			−2.04412
$647$		−	330.745i		−	0.511198i	−0.966783	−	0.255599i	$-0.917727\pi$
$647$		−	330.745i		−	0.511198i	0.966783	−	0.255599i	$-0.0822727\pi$
$648$			25.4558i			0.0392837i
$649$		−	663.684i		−	1.02263i
$650$	789.776	+	42.6092i	1.21504	+	0.0655526i
$651$			650.486i			0.999210i
$652$		−	444.118i		−	0.681162i
$653$			903.860i			1.38417i	0.721818	+	0.692083i	$0.243307\pi$
$653$			903.860i			1.38417i	−0.721818	+	0.692083i	$0.756693\pi$
$654$			399.166i			0.610345i
$655$	−604.154	−	16.2855i	−0.922373	−	0.0248634i
$656$	223.059			0.340029
$657$		−	192.178i		−	0.292509i
$658$	1209.99			1.83889
$659$		−	897.167i		−	1.36141i	−0.732559	−	0.680703i	$-0.761674\pi$
$659$		−	897.167i		−	1.36141i	0.732559	−	0.680703i	$-0.238326\pi$
$660$	−163.471	−	4.40650i	−0.247683	−	0.00667651i
$661$			154.770i			0.234145i	0.993123	+	0.117072i	$0.0373510\pi$
$661$			154.770i			0.234145i	−0.993123	+	0.117072i	$0.962649\pi$
$662$		−	310.368i		−	0.468834i
$663$	−1135.55			−1.71274
$664$		−	18.7646i		−	0.0282599i
$665$	47.5347	−	1763.42i	0.0714807	−	2.65177i
$666$		−	32.2098i		−	0.0483630i
$667$	−450.852	+	219.409i	−0.675940	+	0.328949i
$668$		−	446.642i		−	0.668626i
$669$	−689.733			−1.03099
$670$	4.18913	−	155.407i	0.00625244	−	0.231950i
$671$	−301.316			−0.449055
$672$	−108.498			−0.161455
$673$		−	274.578i		−	0.407991i	−0.978972	−	0.203996i	$-0.934607\pi$
$673$		−	274.578i		−	0.407991i	0.978972	−	0.203996i	$-0.0653929\pi$
$674$		−	675.451i		−	1.00215i
$675$	−6.99827	+	129.715i	−0.0103678	+	0.192171i
$676$	662.898			0.980618
$677$	32.5312			0.0480520			0.0240260	−	0.999711i	$-0.492352\pi$
$677$	32.5312			0.0480520			0.0240260	+	0.999711i	$0.492352\pi$
$678$	−163.415			−0.241024
$679$	−786.532			−1.15837
$680$	−11.1680	+	414.306i	−0.0164235	+	0.609274i
$681$			209.148i			0.307119i
$682$	452.838			0.663986
$683$		−	1033.83i		−	1.51367i	−0.653608	−	0.756834i	$-0.726745\pi$
$683$		−	1033.83i		−	1.51367i	0.653608	−	0.756834i	$-0.273255\pi$
$684$			191.166i			0.279482i
$685$	−87.1491	−	2.34918i	−0.127225	−	0.00342947i
$686$		−	385.603i		−	0.562103i
$687$	4.08329			0.00594365
$688$	88.3071			0.128353
$689$			876.828i			1.27261i
$690$	−256.520	+	116.395i	−0.371767	+	0.168688i
$691$	529.831			0.766760			0.383380	−	0.923591i	$-0.374760\pi$
$691$	529.831			0.766760			0.383380	+	0.923591i	$0.374760\pi$
$692$		−	61.6953i		−	0.0891551i
$693$			313.649i			0.452596i
$694$	−471.598			−0.679535
$695$	701.326	+	18.9049i	1.00910	+	0.0272013i
$696$	106.799			0.153447
$697$	−1634.27			−2.34472
$698$			150.337i			0.215382i
$699$	139.416			0.199451
$700$	−552.872	−	29.8280i	−0.789817	−	0.0426114i
$701$			105.986i			0.151193i	0.997138	+	0.0755965i	$0.0240861\pi$
$701$			105.986i			0.151193i	−0.997138	+	0.0755965i	$0.975914\pi$
$702$			164.391i			0.234175i
$703$		−	241.885i		−	0.344076i
$704$			75.5313i			0.107289i
$705$	−668.888	−	18.0305i	−0.948778	−	0.0255752i
$706$	517.103			0.732441
$707$	−1528.21			−2.16154
$708$			243.509i			0.343939i
$709$			62.3237i			0.0879036i	0.999034	+	0.0439518i	$0.0139948\pi$
$709$			62.3237i			0.0879036i	−0.999034	+	0.0439518i	$0.986005\pi$
$710$	5.95787	−	221.023i	0.00839136	−	0.311299i
$711$			26.8195i			0.0377208i
$712$	−433.545			−0.608912
$713$	701.397	−	341.338i	0.983727	−	0.478734i
$714$	794.924			1.11334
$715$	−1055.67	−	28.4566i	−1.47646	−	0.0397994i
$716$	−110.442			−0.154248
$717$			306.986i			0.428154i
$718$	925.302			1.28872
$719$	138.262			0.192297			0.0961486	−	0.995367i	$-0.469348\pi$
$719$	138.262			0.192297			0.0961486	+	0.995367i	$0.469348\pi$
$720$	59.9782	+	1.61677i	0.0833031	+	0.00224551i
$721$	−158.160			−0.219363
$722$			925.065i			1.28125i
$723$	646.572			0.894291
$724$		−	91.4974i		−	0.126378i
$725$	544.215	+	29.3610i	0.750642	+	0.0404979i
$726$	−78.0404			−0.107494
$727$	1156.59			1.59090			0.795452	−	0.606016i	$-0.207233\pi$
$727$	1156.59			1.59090			0.795452	+	0.606016i	$0.207233\pi$
$728$	−700.665			−0.962453
$729$	−27.0000			−0.0370370
$730$	−452.805	−	12.2058i	−0.620280	−	0.0167202i
$731$	−646.994			−0.885080
$732$	110.554			0.151030
$733$	−562.996			−0.768071			−0.384036	−	0.923318i	$-0.625466\pi$
$733$	−562.996			−0.768071			−0.384036	+	0.923318i	$0.625466\pi$
$734$		−	520.691i		−	0.709388i
$735$	−17.1807	+	637.362i	−0.0233751	+	0.867159i
$736$	56.9335	+	116.990i	0.0773553	+	0.158953i
$737$			207.577i			0.281651i
$738$			236.590i			0.320582i
$739$	−487.116			−0.659155			−0.329578	−	0.944128i	$-0.606906\pi$
$739$	−487.116			−0.659155			−0.329578	+	0.944128i	$0.606906\pi$
$740$	−75.8915	−	2.04573i	−0.102556	−	0.00276449i
$741$			1234.52i			1.66602i
$742$		−	613.812i		−	0.827240i
$743$	−884.971			−1.19108			−0.595539	−	0.803326i	$-0.703062\pi$
$743$	−884.971			−1.19108			−0.595539	+	0.803326i	$0.703062\pi$
$744$	−166.149			−0.223318
$745$	4.44222	−	164.796i	0.00596271	−	0.221202i
$746$		−	129.269i		−	0.173283i
$747$	19.9029			0.0266437
$748$		−	553.390i		−	0.739826i
$749$	−1943.59			−2.59492
$750$	305.186	+	24.7276i	0.406915	+	0.0329702i
$751$		−	1213.24i		−	1.61550i	−0.589528	−	0.807748i	$-0.700686\pi$
$751$		−	1213.24i		−	1.61550i	0.589528	−	0.807748i	$-0.299314\pi$
$752$			309.058i			0.410982i
$753$	−135.110			−0.179429
$754$	689.694			0.914714
$755$	−1206.60	−	32.5251i	−1.59815	−	0.0430796i
$756$		−	115.079i		−	0.152221i
$757$	193.250			0.255284			0.127642	−	0.991820i	$-0.459259\pi$
$757$	193.250			0.255284			0.127642	+	0.991820i	$0.459259\pi$
$758$	−288.406			−0.380483
$759$	338.197	−	164.585i	0.445582	−	0.216844i
$760$	450.418	+	12.1414i	0.592656	+	0.0159756i
$761$	−418.741			−0.550251			−0.275125	−	0.961408i	$-0.588719\pi$
$761$	−418.741			−0.550251			−0.275125	+	0.961408i	$0.588719\pi$
$762$		−	79.7945i		−	0.104717i
$763$		−	1804.53i		−	2.36504i
$764$			281.055i			0.367873i
$765$	−439.438	−	11.8455i	−0.574429	−	0.0154843i
$766$			563.868i			0.736120i
$767$			1572.55i			2.05026i
$768$		−	27.7128i		−	0.0360844i
$769$			557.012i			0.724333i	0.932113	+	0.362167i	$0.117963\pi$
$769$			557.012i			0.724333i	−0.932113	+	0.362167i	$0.882037\pi$
$770$	739.009	+	19.9207i	0.959752	+	0.0258710i
$771$	282.605			0.366543
$772$		−	342.646i		−	0.443842i
$773$	1116.13			1.44390			0.721948	−	0.691947i	$-0.243247\pi$
$773$	1116.13			1.44390			0.721948	+	0.691947i	$0.243247\pi$
$774$			93.6638i			0.121013i
$775$	−846.643	−	45.6773i	−1.09244	−	0.0589384i
$776$		−	200.898i		−	0.258889i
$777$			145.612i			0.187403i
$778$	55.5536			0.0714057
$779$			1776.72i			2.28076i
$780$	387.331	+	10.4409i	0.496579	+	0.0133857i
$781$			295.220i			0.378003i
$782$	−417.131	−	857.140i	−0.533415	−	1.09609i
$783$			113.277i			0.144671i
$784$	294.492			0.375627
$785$	339.094	+	9.14058i	0.431966	+	0.0116440i
$786$	−296.081			−0.376694
$787$	−795.293			−1.01054			−0.505269	−	0.862962i	$-0.668607\pi$
$787$	−795.293			−1.01054			−0.505269	+	0.862962i	$0.668607\pi$
$788$			95.5484i			0.121254i
$789$			69.3404i			0.0878840i
$790$	63.1911	+	1.70337i	0.0799888	+	0.00215617i
$791$	738.756			0.933952
$792$	−80.1130			−0.101153
$793$	713.945			0.900309
$794$	9.42206			0.0118666
$795$	−9.14664	+	339.319i	−0.0115052	+	0.426816i
$796$		−	90.8196i		−	0.114095i
$797$	1372.56			1.72216			0.861080	−	0.508470i	$-0.169789\pi$
$797$	1372.56			1.72216			0.861080	+	0.508470i	$0.169789\pi$
$798$		−	864.212i		−	1.08297i
$799$		−	2264.36i		−	2.83399i
$800$	7.61875	−	141.216i	0.00952343	−	0.176520i
$801$		−	459.844i		−	0.574087i
$802$	−125.269			−0.156196
$803$	604.812			0.753190
$804$		−	76.1611i		−	0.0947278i
$805$	1159.66	−	526.191i	1.44057	−	0.653653i
$806$	−1072.97			−1.33122
$807$			492.779i			0.610631i
$808$		−	390.339i		−	0.483092i
$809$	1416.49			1.75091			0.875454	−	0.483301i	$-0.160562\pi$
$809$	1416.49			1.75091			0.875454	+	0.483301i	$0.160562\pi$
$810$	−1.71484	+	63.6165i	−0.00211709	+	0.0785389i
$811$	268.418			0.330972			0.165486	−	0.986212i	$-0.447081\pi$
$811$	268.418			0.330972			0.165486	+	0.986212i	$0.447081\pi$
$812$	−482.811			−0.594595
$813$			767.607i			0.944166i
$814$	101.368			0.124531
$815$	29.9181	−	1109.89i	0.0367094	−	1.36183i
$816$			203.042i			0.248825i
$817$			703.387i			0.860939i
$818$		−	199.162i		−	0.243475i
$819$		−	743.168i		−	0.907409i
$820$	557.444	+	15.0264i	0.679810	+	0.0183249i
$821$	−1148.66			−1.39910			−0.699549	−	0.714584i	$-0.746616\pi$
$821$	−1148.66			−1.39910			−0.699549	+	0.714584i	$0.746616\pi$
$822$	−42.7097			−0.0519583
$823$			1510.42i			1.83527i	0.397429	+	0.917633i	$0.369902\pi$
$823$			1510.42i			1.83527i	−0.397429	+	0.917633i	$0.630098\pi$
$824$		−	40.3977i		−	0.0490264i
$825$	−408.231	−	22.0245i	−0.494826	−	0.0266964i
$826$		−	1100.84i		−	1.33274i
$827$	578.500			0.699516			0.349758	−	0.936840i	$-0.386264\pi$
$827$	578.500			0.699516			0.349758	+	0.936840i	$0.386264\pi$
$828$	−124.086	+	60.3871i	−0.149863	+	0.0729313i
$829$	1007.46			1.21527			0.607636	−	0.794216i	$-0.292118\pi$
$829$	1007.46			1.21527			0.607636	+	0.794216i	$0.292118\pi$
$830$	1.26408	−	46.8945i	0.00152299	−	0.0564993i
$831$	−544.336			−0.655037
$832$		−	178.966i		−	0.215103i
$833$	−2157.63			−2.59019
$834$	343.703			0.412114
$835$	30.0882	−	1116.20i	0.0360337	−	1.33677i
$836$	−601.624			−0.719646
$837$		−	176.227i		−	0.210546i
$838$	−859.766			−1.02597
$839$		−	128.132i		−	0.152720i	−0.997080	−	0.0763601i	$-0.975670\pi$
$839$		−	128.132i		−	0.152720i	0.997080	−	0.0763601i	$-0.0243299\pi$
$840$	−271.146	−	7.30900i	−0.322793	−	0.00870119i
$841$	−365.749			−0.434897
$842$	279.208			0.331601
$843$	123.706			0.146744
$844$	250.071			0.296293
$845$	1656.64	+	44.6563i	1.96052	+	0.0528477i
$846$	−327.806			−0.387478
$847$	352.801			0.416530
$848$	156.781			0.184884
$849$		−	352.978i		−	0.415758i
$850$	−55.8198	+	1034.64i	−0.0656703	+	1.21722i
$851$	157.009	−	76.4089i	0.184499	−	0.0897872i
$852$		−	108.318i		−	0.127134i
$853$		−	928.585i		−	1.08861i	−0.838887	−	0.544305i	$-0.816793\pi$
$853$		−	928.585i		−	1.08861i	0.838887	−	0.544305i	$-0.183207\pi$
$854$	−499.788			−0.585232
$855$	−12.8779	+	477.741i	−0.0150619	+	0.558761i
$856$		−	496.437i		−	0.579950i
$857$			1165.78i			1.36030i	0.733072	+	0.680151i	$0.238086\pi$
$857$			1165.78i			1.36030i	−0.733072	+	0.680151i	$0.761914\pi$
$858$	−517.359			−0.602983
$859$	894.893			1.04178			0.520892	−	0.853622i	$-0.325599\pi$
$859$	894.893			1.04178			0.520892	+	0.853622i	$0.325599\pi$
$860$	220.688	+	5.94883i	0.256613	+	0.00691725i
$861$		−	1069.56i		−	1.24223i
$862$	700.195			0.812291
$863$		−	314.462i		−	0.364382i	−0.983263	−	0.182191i	$-0.941681\pi$
$863$		−	314.462i		−	0.364382i	0.983263	−	0.182191i	$-0.0583189\pi$
$864$	29.3939			0.0340207
$865$	4.15612	−	154.182i	0.00480477	−	0.178245i
$866$		−	70.2909i		−	0.0811673i
$867$		−	987.048i		−	1.13846i
$868$	751.116			0.865342
$869$	−84.4045			−0.0971283
$870$	266.901	+	7.19455i	0.306782	+	0.00826960i
$871$		−	491.839i		−	0.564683i
$872$	460.917			0.528574
$873$	213.085			0.244083
$874$	−931.850	+	453.489i	−1.06619	+	0.518866i
$875$	−1379.67	−	111.787i	−1.57676	−	0.127757i
$876$	−221.909			−0.253320
$877$			543.927i			0.620213i	0.950702	+	0.310107i	$0.100365\pi$
$877$			543.927i			0.620213i	−0.950702	+	0.310107i	$0.899635\pi$
$878$		−	389.211i		−	0.443292i
$879$		−	63.2904i		−	0.0720027i
$880$	−5.08819	+	188.760i	−0.00578203	+	0.214500i
$881$		−	1012.21i		−	1.14893i	−0.818530	−	0.574464i	$-0.805211\pi$
$881$		−	1012.21i		−	1.14893i	0.818530	−	0.574464i	$-0.194789\pi$
$882$			312.356i			0.354145i
$883$		−	1113.87i		−	1.26146i	−0.776004	−	0.630729i	$-0.782756\pi$
$883$		−	1113.87i		−	1.26146i	0.776004	−	0.630729i	$-0.217244\pi$
$884$			1311.22i			1.48328i
$885$	−16.4041	+	608.552i	−0.0185357	+	0.687629i
$886$	455.835			0.514487
$887$		−	142.275i		−	0.160400i	−0.996779	−	0.0801999i	$-0.974444\pi$
$887$		−	142.275i		−	0.160400i	0.996779	−	0.0801999i	$-0.0255559\pi$
$888$	−37.1926			−0.0418836
$889$			360.731i			0.405771i
$890$	−1083.47	−	29.2059i	−1.21738	−	0.0328156i
$891$		−	84.9727i		−	0.0953677i
$892$			796.436i			0.892865i
$893$	−2461.72			−2.75669
$894$		−	80.7624i		−	0.0903382i
$895$	−276.004	−	7.43995i	−0.308385	−	0.00831279i
$896$			125.283i			0.139824i
$897$	−801.333	+	389.972i	−0.893348	+	0.434751i
$898$		−	225.693i		−	0.251328i
$899$	−739.355			−0.822420
$900$	149.782	+	8.08090i	0.166425	+	0.00897878i
$901$	−1148.68			−1.27489
$902$	−744.579			−0.825476
$903$		−	423.430i		−	0.468915i
$904$			188.695i			0.208733i
$905$	6.16375	−	228.660i	0.00681077	−	0.252663i
$906$	−591.328			−0.652680
$907$	1352.97			1.49169			0.745847	−	0.666117i	$-0.232045\pi$
$907$	1352.97			1.49169			0.745847	+	0.666117i	$0.232045\pi$
$908$	241.503			0.265972
$909$	414.017			0.455464
$910$	−1751.03	−	47.2005i	−1.92421	−	0.0518687i
$911$		−	1639.29i		−	1.79944i	−0.436473	−	0.899718i	$-0.643772\pi$
$911$		−	1639.29i		−	1.79944i	0.436473	−	0.899718i	$-0.356228\pi$
$912$	220.739			0.242038
$913$			62.6370i			0.0686057i
$914$			987.605i			1.08053i
$915$	276.285	+	7.44752i	0.301951	+	0.00813937i
$916$		−	4.71498i		−	0.00514735i
$917$	1338.51			1.45966
$918$	−215.358			−0.234595
$919$			1680.00i			1.82807i	0.405633	+	0.914036i	$0.367051\pi$
$919$			1680.00i			1.82807i	−0.405633	+	0.914036i	$0.632949\pi$
$920$	134.401	+	296.203i	0.146088	+	0.321960i
$921$	−222.968			−0.242094
$922$		−	1144.05i		−	1.24084i
$923$		−	699.503i		−	0.757858i
$924$	362.171			0.391959
$925$	−189.522	−	10.2249i	−0.204889	−	0.0110540i
$926$	694.306			0.749791
$927$	42.8483			0.0462225
$928$		−	123.321i		−	0.132889i
$929$	−193.633			−0.208431			−0.104216	−	0.994555i	$-0.533233\pi$
$929$	−193.633			−0.208431			−0.104216	+	0.994555i	$0.533233\pi$
$930$	−415.221	−	11.1927i	−0.446474	−	0.0120351i
$931$			2345.70i			2.51954i
$932$		−	160.984i		−	0.172730i
$933$			832.217i			0.891979i
$934$			514.172i			0.550505i
$935$	37.2793	−	1382.97i	0.0398709	−	1.47911i
$936$	189.822			0.202801
$937$	128.669			0.137320			0.0686599	−	0.997640i	$-0.478128\pi$
$937$	128.669			0.137320			0.0686599	+	0.997640i	$0.478128\pi$
$938$			344.305i			0.367063i
$939$		−	454.267i		−	0.483777i
$940$	−20.8198	+	772.366i	−0.0221487	+	0.821666i
$941$			1506.94i			1.60142i	0.599051	+	0.800711i	$0.295545\pi$
$941$			1506.94i			1.60142i	−0.599051	+	0.800711i	$0.704455\pi$
$942$	166.182			0.176414
$943$	−1153.27	+	561.244i	−1.22298	+	0.595169i
$944$	281.180			0.297860
$945$	7.75236	−	287.594i	0.00820356	−	0.304332i
$946$	−294.773			−0.311599
$947$			296.571i			0.313169i	0.987665	+	0.156585i	$0.0500484\pi$
$947$			296.571i			0.313169i	−0.987665	+	0.156585i	$0.949952\pi$
$948$	30.9685			0.0326671
$949$	−1433.06			−1.51007
$950$	1124.82	+	60.6851i	1.18402	+	0.0638791i
$951$	−625.958			−0.658210
$952$		−	917.900i		−	0.964180i
$953$	−648.066			−0.680028			−0.340014	−	0.940420i	$-0.610432\pi$
$953$	−648.066			−0.680028			−0.340014	+	0.940420i	$0.610432\pi$
$954$			166.292i			0.174310i
$955$	−18.9333	+	702.382i	−0.0198255	+	0.735478i
$956$	354.477			0.370792
$957$	−356.500			−0.372518
$958$	328.052			0.342434
$959$	193.080			0.201334
$960$	1.86688	−	69.2569i	0.00194467	−	0.0721426i
$961$	189.225			0.196905
$962$	−240.185			−0.249673
$963$	526.551			0.546782
$964$		−	746.597i		−	0.774479i
$965$	23.0824	−	856.303i	0.0239196	−	0.887361i
$966$	560.963	−	272.995i	0.580707	−	0.282603i
$967$		−	847.812i		−	0.876745i	−0.898793	−	0.438372i	$-0.855555\pi$
$967$		−	847.812i		−	0.876745i	0.898793	−	0.438372i	$-0.144445\pi$
$968$			90.1132i			0.0930922i
$969$	−1617.27			−1.66901
$970$	13.5336	−	502.063i	0.0139521	−	0.517591i
$971$		−	968.123i		−	0.997037i	−0.866879	−	0.498519i	$-0.833878\pi$
$971$		−	968.123i		−	0.997037i	0.866879	−	0.498519i	$-0.166122\pi$
$972$			31.1769i			0.0320750i
$973$	−1553.79			−1.59691
$974$	−178.309			−0.183069
$975$	967.274	+	52.1854i	0.992076	+	0.0535235i
$976$		−	127.657i		−	0.130796i
$977$	741.921			0.759387			0.379693	−	0.925112i	$-0.376030\pi$
$977$	741.921			0.759387			0.379693	+	0.925112i	$0.376030\pi$
$978$		−	543.931i		−	0.556166i
$979$	1447.19			1.47823
$980$	735.962	+	19.8385i	0.750981	+	0.0202434i
$981$			488.876i			0.498345i
$982$		−	26.3410i		−	0.0268238i
$983$	−1287.65			−1.30992			−0.654959	−	0.755665i	$-0.727314\pi$
$983$	−1287.65			−1.30992			−0.654959	+	0.755665i	$0.727314\pi$
$984$	273.190			0.277632
$985$	−6.43665	+	238.784i	−0.00653467	+	0.242421i
$986$			903.527i			0.916356i
$987$	1481.93			1.50145
$988$	1425.50			1.44282
$989$	−456.571	+	222.192i	−0.461649	+	0.224663i
$990$	−200.210	−	5.39684i	−0.202232	−	0.00545135i
$991$	−122.228			−0.123338			−0.0616689	−	0.998097i	$-0.519642\pi$
$991$	−122.228			−0.123338			−0.0616689	+	0.998097i	$0.519642\pi$
$992$			191.852i			0.193399i
$993$		−	380.122i		−	0.382801i
$994$			489.678i			0.492633i
$995$	6.11809	−	226.967i	0.00614884	−	0.228107i
$996$		−	22.9818i		−	0.0230741i
$997$		−	1953.85i		−	1.95973i	−0.199660	−	0.979865i	$-0.563984\pi$
$997$		−	1953.85i		−	1.95973i	0.199660	−	0.979865i	$-0.436016\pi$
$998$		−	1182.18i		−	1.18455i
$999$		−	39.4487i		−	0.0394882i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.f.a.229.37	✓	48
5.4	even	2	inner	690.3.f.a.229.40	yes	48
23.22	odd	2	inner	690.3.f.a.229.38	yes	48
115.114	odd	2	inner	690.3.f.a.229.39	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.f.a.229.37	✓	48	1.1	even	1	trivial
690.3.f.a.229.38	yes	48	23.22	odd	2	inner
690.3.f.a.229.39	yes	48	115.114	odd	2	inner
690.3.f.a.229.40	yes	48	5.4	even	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)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} -1.73205i q^{3} -2.00000 q^{4} +(-4.99818 - 0.134731i) q^{5} -2.44949 q^{6} +11.0735 q^{7} +2.82843i q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q-1.41421i q^{2} -1.73205i q^{3} -2.00000 q^{4} +(-4.99818 - 0.134731i) q^{5} -2.44949 q^{6} +11.0735 q^{7} +2.82843i q^{8} -3.00000 q^{9} +(-0.190538 + 7.06850i) q^{10} -9.44141i q^{11} +3.46410i q^{12} +22.3707i q^{13} -15.6603i q^{14} +(-0.233360 + 8.65711i) q^{15} +4.00000 q^{16} -29.3065 q^{17} +4.24264i q^{18} +31.8609i q^{19} +(9.99637 + 0.269461i) q^{20} -19.1799i q^{21} -13.3522 q^{22} +(-20.6810 + 10.0645i) q^{23} +4.89898 q^{24} +(24.9637 + 1.34682i) q^{25} +31.6370 q^{26} +5.19615i q^{27} -22.1470 q^{28} +21.8003 q^{29} +(12.2430 + 0.330021i) q^{30} -33.9150 q^{31} -5.65685i q^{32} -16.3530 q^{33} +41.4457i q^{34} +(-55.3475 - 1.49194i) q^{35} +6.00000 q^{36} -7.59191 q^{37} +45.0582 q^{38} +38.7472 q^{39} +(0.381076 - 14.1370i) q^{40} +55.7647 q^{41} -27.1245 q^{42} +22.0768 q^{43} +18.8828i q^{44} +(14.9946 + 0.404192i) q^{45} +(14.2334 + 29.2474i) q^{46} +77.2646i q^{47} -6.92820i q^{48} +73.6229 q^{49} +(1.90469 - 35.3040i) q^{50} +50.7604i q^{51} -44.7414i q^{52} +39.1954 q^{53} +7.34847 q^{54} +(-1.27205 + 47.1899i) q^{55} +31.3207i q^{56} +55.1848 q^{57} -30.8302i q^{58} +70.2950 q^{59} +(0.466721 - 17.3142i) q^{60} -31.9143i q^{61} +47.9630i q^{62} -33.2206 q^{63} -8.00000 q^{64} +(3.01402 - 111.813i) q^{65} +23.1266i q^{66} -21.9858 q^{67} +58.6131 q^{68} +(17.4322 + 35.8206i) q^{69} +(-2.10993 + 78.2732i) q^{70} -31.2687 q^{71} -8.48528i q^{72} +64.0595i q^{73} +10.7366i q^{74} +(2.33276 - 43.2384i) q^{75} -63.7219i q^{76} -104.550i q^{77} -54.7968i q^{78} -8.93982i q^{79} +(-19.9927 - 0.538922i) q^{80} +9.00000 q^{81} -78.8632i q^{82} -6.63429 q^{83} +38.3598i q^{84} +(146.479 + 3.94849i) q^{85} -31.2213i q^{86} -37.7592i q^{87} +26.7043 q^{88} +153.281i q^{89} +(0.571614 - 21.2055i) q^{90} +247.723i q^{91} +(41.3621 - 20.1290i) q^{92} +58.7425i q^{93} +109.269 q^{94} +(4.29264 - 159.247i) q^{95} -9.79796 q^{96} -71.0282 q^{97} -104.119i q^{98} +28.3242i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 96 q^{4} - 144 q^{9}+O(q^{10}) \) 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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