LMFDB - Embedded newform 690.3.f.a.229.4

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			229.4
Character	$\chi$	$=$	690.229
Dual form			690.3.f.a.229.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421i q^{2} -1.73205i q^{3} -2.00000 q^{4} +(1.71908 + 4.69518i) q^{5} +2.44949 q^{6} +12.9397 q^{7} -2.82843i q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+1.41421i q^{2} -1.73205i q^{3} -2.00000 q^{4} +(1.71908 + 4.69518i) q^{5} +2.44949 q^{6} +12.9397 q^{7} -2.82843i q^{8} -3.00000 q^{9} +(-6.63999 + 2.43115i) q^{10} +18.3935i q^{11} +3.46410i q^{12} +7.60366i q^{13} +18.2995i q^{14} +(8.13230 - 2.97754i) q^{15} +4.00000 q^{16} -19.9407 q^{17} -4.24264i q^{18} -24.3487i q^{19} +(-3.43816 - 9.39037i) q^{20} -22.4122i q^{21} -26.0123 q^{22} +(22.9301 + 1.79238i) q^{23} -4.89898 q^{24} +(-19.0895 + 16.1428i) q^{25} -10.7532 q^{26} +5.19615i q^{27} -25.8794 q^{28} +32.2461 q^{29} +(4.21087 + 11.5008i) q^{30} +3.18657 q^{31} +5.65685i q^{32} +31.8584 q^{33} -28.2004i q^{34} +(22.2444 + 60.7542i) q^{35} +6.00000 q^{36} -11.0170 q^{37} +34.4342 q^{38} +13.1699 q^{39} +(13.2800 - 4.86230i) q^{40} -60.4391 q^{41} +31.6956 q^{42} +50.3599 q^{43} -36.7869i q^{44} +(-5.15724 - 14.0856i) q^{45} +(-2.53481 + 32.4280i) q^{46} +79.4647i q^{47} -6.92820i q^{48} +118.435 q^{49} +(-22.8294 - 26.9967i) q^{50} +34.5383i q^{51} -15.2073i q^{52} -92.1165 q^{53} -7.34847 q^{54} +(-86.3608 + 31.6199i) q^{55} -36.5989i q^{56} -42.1731 q^{57} +45.6028i q^{58} +5.16200 q^{59} +(-16.2646 + 5.95507i) q^{60} +10.5265i q^{61} +4.50650i q^{62} -38.8190 q^{63} -8.00000 q^{64} +(-35.7006 + 13.0713i) q^{65} +45.0546i q^{66} -72.2321 q^{67} +39.8814 q^{68} +(3.10449 - 39.7160i) q^{69} +(-85.9194 + 31.4583i) q^{70} -8.94916 q^{71} +8.48528i q^{72} +70.6321i q^{73} -15.5805i q^{74} +(27.9602 + 33.0640i) q^{75} +48.6973i q^{76} +238.006i q^{77} +18.6251i q^{78} +1.35260i q^{79} +(6.87633 + 18.7807i) q^{80} +9.00000 q^{81} -85.4739i q^{82} +135.372 q^{83} +44.8244i q^{84} +(-34.2797 - 93.6253i) q^{85} +71.2197i q^{86} -55.8518i q^{87} +52.0246 q^{88} +41.9425i q^{89} +(19.9200 - 7.29345i) q^{90} +98.3889i q^{91} +(-45.8601 - 3.58476i) q^{92} -5.51931i q^{93} -112.380 q^{94} +(114.321 - 41.8573i) q^{95} +9.79796 q^{96} +165.650 q^{97} +167.493i q^{98} -55.1804i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	1.71908	+	4.69518i	0.343816	+	0.939037i
$5$	1.71908	+	4.69518i	0.343816	+	0.939037i
$6$	2.44949			0.408248
$7$	12.9397			1.84853			0.924263	−	0.381757i	$-0.124681\pi$
$7$	12.9397			1.84853			0.924263	+	0.381757i	$0.124681\pi$
$8$		−	2.82843i		−	0.353553i
$9$	−3.00000			−0.333333
$10$	−6.63999	+	2.43115i	−0.663999	+	0.243115i
$11$			18.3935i			1.67213i	0.548627	+	0.836067i	$0.315151\pi$
$11$			18.3935i			1.67213i	−0.548627	+	0.836067i	$0.684849\pi$
$12$			3.46410i			0.288675i
$13$			7.60366i			0.584897i	0.956281	+	0.292448i	$0.0944699\pi$
$13$			7.60366i			0.584897i	−0.956281	+	0.292448i	$0.905530\pi$
$14$			18.2995i			1.30710i
$15$	8.13230	−	2.97754i	0.542153	−	0.198502i
$16$	4.00000			0.250000
$17$	−19.9407			−1.17298			−0.586491	−	0.809956i	$-0.699491\pi$
$17$	−19.9407			−1.17298			−0.586491	+	0.809956i	$0.699491\pi$
$18$		−	4.24264i		−	0.235702i
$19$		−	24.3487i		−	1.28151i	−0.767746	−	0.640754i	$-0.778622\pi$
$19$		−	24.3487i		−	1.28151i	0.767746	−	0.640754i	$-0.221378\pi$
$20$	−3.43816	−	9.39037i	−0.171908	−	0.469518i
$21$		−	22.4122i		−	1.06725i
$22$	−26.0123			−1.18238
$23$	22.9301	+	1.79238i	0.996959	+	0.0779296i
$23$	22.9301	+	1.79238i	0.996959	+	0.0779296i
$24$	−4.89898			−0.204124
$25$	−19.0895	+	16.1428i	−0.763581	+	0.645712i
$26$	−10.7532			−0.413584
$27$			5.19615i			0.192450i
$28$	−25.8794			−0.924263
$29$	32.2461			1.11193			0.555967	−	0.831205i	$-0.312348\pi$
$29$	32.2461			1.11193			0.555967	+	0.831205i	$0.312348\pi$
$30$	4.21087	+	11.5008i	0.140362	+	0.383360i
$31$	3.18657			0.102793			0.0513963	−	0.998678i	$-0.483633\pi$
$31$	3.18657			0.102793			0.0513963	+	0.998678i	$0.483633\pi$
$32$			5.65685i			0.176777i
$33$	31.8584			0.965407
$34$		−	28.2004i		−	0.829424i
$35$	22.2444	+	60.7542i	0.635553	+	1.73583i
$36$	6.00000			0.166667
$37$	−11.0170			−0.297758			−0.148879	−	0.988855i	$-0.547567\pi$
$37$	−11.0170			−0.297758			−0.148879	+	0.988855i	$0.547567\pi$
$38$	34.4342			0.906163
$39$	13.1699			0.337690
$40$	13.2800	−	4.86230i	0.332000	−	0.121557i
$41$	−60.4391			−1.47413			−0.737063	−	0.675824i	$-0.763788\pi$
$41$	−60.4391			−1.47413			−0.737063	+	0.675824i	$0.763788\pi$
$42$	31.6956			0.754657
$43$	50.3599			1.17116			0.585581	−	0.810614i	$-0.300867\pi$
$43$	50.3599			1.17116			0.585581	+	0.810614i	$0.300867\pi$
$44$		−	36.7869i		−	0.836067i
$45$	−5.15724	−	14.0856i	−0.114605	−	0.313012i
$46$	−2.53481	+	32.4280i	−0.0551045	+	0.704956i
$47$			79.4647i			1.69074i	0.534182	+	0.845369i	$0.320620\pi$
$47$			79.4647i			1.69074i	−0.534182	+	0.845369i	$0.679380\pi$
$48$		−	6.92820i		−	0.144338i
$49$	118.435			2.41705
$50$	−22.8294	−	26.9967i	−0.456588	−	0.539933i
$51$			34.5383i			0.677222i
$52$		−	15.2073i		−	0.292448i
$53$	−92.1165			−1.73805			−0.869024	−	0.494770i	$-0.835252\pi$
$53$	−92.1165			−1.73805			−0.869024	+	0.494770i	$0.835252\pi$
$54$	−7.34847			−0.136083
$55$	−86.3608	+	31.6199i	−1.57020	+	0.574907i
$56$		−	36.5989i		−	0.653552i
$57$	−42.1731			−0.739879
$58$			45.6028i			0.786256i
$59$	5.16200			0.0874916			0.0437458	−	0.999043i	$-0.486071\pi$
$59$	5.16200			0.0874916			0.0437458	+	0.999043i	$0.486071\pi$
$60$	−16.2646	+	5.95507i	−0.271077	+	0.0992512i
$61$			10.5265i			0.172565i	0.996271	+	0.0862827i	$0.0274988\pi$
$61$			10.5265i			0.172565i	−0.996271	+	0.0862827i	$0.972501\pi$
$62$			4.50650i			0.0726854i
$63$	−38.8190			−0.616175
$64$	−8.00000			−0.125000
$65$	−35.7006	+	13.0713i	−0.549240	+	0.201097i
$66$			45.0546i			0.682646i
$67$	−72.2321			−1.07809			−0.539046	−	0.842276i	$-0.681215\pi$
$67$	−72.2321			−1.07809			−0.539046	+	0.842276i	$0.681215\pi$
$68$	39.8814			0.586491
$69$	3.10449	−	39.7160i	0.0449927	−	0.575594i
$70$	−85.9194	+	31.4583i	−1.22742	+	0.449404i
$71$	−8.94916			−0.126045			−0.0630223	−	0.998012i	$-0.520074\pi$
$71$	−8.94916			−0.126045			−0.0630223	+	0.998012i	$0.520074\pi$
$72$			8.48528i			0.117851i
$73$			70.6321i			0.967564i	0.875189	+	0.483782i	$0.160737\pi$
$73$			70.6321i			0.967564i	−0.875189	+	0.483782i	$0.839263\pi$
$74$		−	15.5805i		−	0.210547i
$75$	27.9602	+	33.0640i	0.372802	+	0.440854i
$76$			48.6973i			0.640754i
$77$			238.006i			3.09098i
$78$			18.6251i			0.238783i
$79$			1.35260i			0.0171215i	0.999963	+	0.00856076i	$0.00272501\pi$
$79$			1.35260i			0.0171215i	−0.999963	+	0.00856076i	$0.997275\pi$
$80$	6.87633	+	18.7807i	0.0859541	+	0.234759i
$81$	9.00000			0.111111
$82$		−	85.4739i		−	1.04236i
$83$	135.372			1.63099			0.815494	−	0.578765i	$-0.196465\pi$
$83$	135.372			1.63099			0.815494	+	0.578765i	$0.196465\pi$
$84$			44.8244i			0.533623i
$85$	−34.2797	−	93.6253i	−0.403291	−	1.10147i
$86$			71.2197i			0.828136i
$87$		−	55.8518i		−	0.641975i
$88$	52.0246			0.591189
$89$			41.9425i			0.471263i	0.971842	+	0.235632i	$0.0757159\pi$
$89$			41.9425i			0.471263i	−0.971842	+	0.235632i	$0.924284\pi$
$90$	19.9200	−	7.29345i	0.221333	−	0.0810383i
$91$			98.3889i			1.08120i
$92$	−45.8601	−	3.58476i	−0.498479	−	0.0389648i
$93$		−	5.51931i		−	0.0593474i
$94$	−112.380			−1.19553
$95$	114.321	−	41.8573i	1.20338	−	0.440604i
$96$	9.79796			0.102062
$97$	165.650			1.70773			0.853867	−	0.520491i	$-0.174251\pi$
$97$	165.650			1.70773			0.853867	+	0.520491i	$0.174251\pi$
$98$			167.493i			1.70911i
$99$		−	55.1804i		−	0.557378i
$100$	38.1790	−	32.2856i	0.381790	−	0.322856i
$101$	20.2266			0.200264			0.100132	−	0.994974i	$-0.468074\pi$
$101$	20.2266			0.200264			0.100132	+	0.994974i	$0.468074\pi$
$102$	−48.8445			−0.478868
$103$	10.1077			0.0981328			0.0490664	−	0.998796i	$-0.484375\pi$
$103$	10.1077			0.0981328			0.0490664	+	0.998796i	$0.484375\pi$
$104$	21.5064			0.206792
$105$	105.229	−	38.5284i	1.00218	−	0.366937i
$106$		−	130.272i		−	1.22899i
$107$	−59.9270			−0.560065			−0.280033	−	0.959990i	$-0.590345\pi$
$107$	−59.9270			−0.560065			−0.280033	+	0.959990i	$0.590345\pi$
$108$		−	10.3923i		−	0.0962250i
$109$		−	44.0489i		−	0.404118i	−0.979373	−	0.202059i	$-0.935237\pi$
$109$		−	44.0489i		−	0.404118i	0.979373	−	0.202059i	$-0.0647633\pi$
$110$	−44.7173	−	122.133i	−0.406521	−	1.11030i
$111$			19.0821i			0.171911i
$112$	51.7587			0.462131
$113$	162.943			1.44197			0.720987	−	0.692948i	$-0.243689\pi$
$113$	162.943			1.44197			0.720987	+	0.692948i	$0.243689\pi$
$114$		−	59.6418i		−	0.523174i
$115$	31.0031	+	110.742i	0.269592	+	0.962975i
$116$	−64.4921			−0.555967
$117$		−	22.8110i		−	0.194966i
$118$			7.30017i			0.0618659i
$119$	−258.026			−2.16829
$120$	−8.42175	−	23.0016i	−0.0701812	−	0.191680i
$121$	−217.320			−1.79603
$122$	−14.8867			−0.122022
$123$			104.684i			0.851087i
$124$	−6.37315			−0.0513963
$125$	−108.610	−	61.8780i	−0.868879	−	0.495024i
$126$		−	54.8984i		−	0.435702i
$127$		−	78.3423i		−	0.616869i	−0.951246	−	0.308434i	$-0.900195\pi$
$127$		−	78.3423i		−	0.616869i	0.951246	−	0.308434i	$-0.0998050\pi$
$128$		−	11.3137i		−	0.0883883i
$129$		−	87.2260i		−	0.676170i
$130$	−18.4856	−	50.4882i	−0.142197	−	0.388371i
$131$	243.523			1.85896			0.929479	−	0.368876i	$-0.120257\pi$
$131$	243.523			1.85896			0.929479	+	0.368876i	$0.120257\pi$
$132$	−63.7169			−0.482704
$133$		−	315.064i		−	2.36890i
$134$		−	102.152i		−	0.762326i
$135$	−24.3969	+	8.93261i	−0.180718	+	0.0661675i
$136$			56.4008i			0.414712i
$137$	68.6757			0.501282			0.250641	−	0.968080i	$-0.419359\pi$
$137$	68.6757			0.501282			0.250641	+	0.968080i	$0.419359\pi$
$138$	56.1669	+	4.39042i	0.407007	+	0.0318146i
$139$	−136.802			−0.984184			−0.492092	−	0.870543i	$-0.663768\pi$
$139$	−136.802			−0.984184			−0.492092	+	0.870543i	$0.663768\pi$
$140$	−44.4887	−	121.508i	−0.317777	−	0.867917i
$141$	137.637			0.976148
$142$		−	12.6560i		−	0.0891270i
$143$	−139.858			−0.978026
$144$	−12.0000			−0.0833333
$145$	55.4336	+	151.401i	0.382301	+	1.04415i
$146$	−99.8889			−0.684171
$147$		−	205.136i		−	1.39548i
$148$	22.0341			0.148879
$149$		−	147.155i		−	0.987620i	−0.869570	−	0.493810i	$-0.835604\pi$
$149$		−	147.155i		−	0.987620i	0.869570	−	0.493810i	$-0.164396\pi$
$150$	−46.7596	+	39.5417i	−0.311731	+	0.263611i
$151$	−4.21892			−0.0279398			−0.0139699	−	0.999902i	$-0.504447\pi$
$151$	−4.21892			−0.0279398			−0.0139699	+	0.999902i	$0.504447\pi$
$152$	−68.8684			−0.453082
$153$	59.8221			0.390994
$154$	−336.591			−2.18565
$155$	5.47798	+	14.9616i	0.0353418	+	0.0965261i
$156$	−26.3398			−0.168845
$157$	−127.989			−0.815216			−0.407608	−	0.913157i	$-0.633637\pi$
$157$	−127.989			−0.815216			−0.407608	+	0.913157i	$0.633637\pi$
$158$	−1.91287			−0.0121067
$159$			159.550i			1.00346i
$160$	−26.5600	+	9.72459i	−0.166000	+	0.0607787i
$161$	296.707	+	23.1928i	1.84290	+	0.144055i
$162$			12.7279i			0.0785674i
$163$		−	53.8931i		−	0.330633i	−0.986241	−	0.165316i	$-0.947136\pi$
$163$		−	53.8931i		−	0.330633i	0.986241	−	0.165316i	$-0.0528645\pi$
$164$	120.878			0.737063
$165$	54.7672	+	149.581i	0.331923	+	0.906553i
$166$			191.445i			1.15328i
$167$			189.614i			1.13541i	0.823232	+	0.567705i	$0.192169\pi$
$167$			189.614i			1.13541i	−0.823232	+	0.567705i	$0.807831\pi$
$168$	−63.3912			−0.377329
$169$	111.184			0.657896
$170$	132.406	−	48.4788i	0.778860	−	0.285169i
$171$			73.0460i			0.427169i
$172$	−100.720			−0.585581
$173$		−	73.4027i		−	0.424293i	−0.977238	−	0.212147i	$-0.931955\pi$
$173$		−	73.4027i		−	0.424293i	0.977238	−	0.212147i	$-0.0680454\pi$
$174$	78.9864			0.453945
$175$	−247.012	+	208.883i	−1.41150	+	1.19362i
$176$			73.5739i			0.418034i
$177$		−	8.94085i		−	0.0505133i
$178$	−59.3156			−0.333234
$179$	−279.042			−1.55889			−0.779447	−	0.626468i	$-0.784500\pi$
$179$	−279.042			−1.55889			−0.779447	+	0.626468i	$0.784500\pi$
$180$	10.3145	+	28.1711i	0.0573027	+	0.156506i
$181$		−	151.434i		−	0.836654i	−0.908296	−	0.418327i	$-0.862617\pi$
$181$		−	151.434i		−	0.836654i	0.908296	−	0.418327i	$-0.137383\pi$
$182$	−139.143			−0.764521
$183$	18.2324			0.0996307
$184$	5.06962	−	64.8560i	0.0275523	−	0.352478i
$185$	−18.9392	−	51.7271i	−0.102374	−	0.279606i
$186$	7.80548			0.0419649
$187$		−	366.779i		−	1.96138i
$188$		−	158.929i		−	0.845369i
$189$			67.2365i			0.355749i
$190$	59.1952	+	161.675i	0.311554	+	0.850921i
$191$		−	296.805i		−	1.55395i	−0.629530	−	0.776976i	$-0.716752\pi$
$191$		−	296.805i		−	1.55395i	0.629530	−	0.776976i	$-0.283248\pi$
$192$			13.8564i			0.0721688i
$193$			26.9147i			0.139455i	0.997566	+	0.0697273i	$0.0222129\pi$
$193$			26.9147i			0.139455i	−0.997566	+	0.0697273i	$0.977787\pi$
$194$			234.265i			1.20755i
$195$	22.6402	+	61.8352i	0.116103	+	0.317104i
$196$	−236.870			−1.20852
$197$			61.5882i			0.312630i	0.987707	+	0.156315i	$0.0499615\pi$
$197$			61.5882i			0.312630i	−0.987707	+	0.156315i	$0.950038\pi$
$198$	78.0369			0.394126
$199$		−	35.3336i		−	0.177556i	−0.996051	−	0.0887780i	$-0.971704\pi$
$199$		−	35.3336i		−	0.177556i	0.996051	−	0.0887780i	$-0.0282962\pi$
$200$	45.6588	+	53.9933i	0.228294	+	0.269967i
$201$			125.110i			0.622437i
$202$			28.6048i			0.141608i
$203$	417.254			2.05544
$204$		−	69.0766i		−	0.338611i
$205$	−103.900	−	283.773i	−0.506828	−	1.38426i
$206$			14.2944i			0.0693904i
$207$	−68.7902	−	5.37714i	−0.332320	−	0.0259765i
$208$			30.4146i			0.146224i
$209$	447.856			2.14285
$210$	54.4873	+	148.817i	0.259464	+	0.708651i
$211$	−142.017			−0.673064			−0.336532	−	0.941672i	$-0.609254\pi$
$211$	−142.017			−0.673064			−0.336532	+	0.941672i	$0.609254\pi$
$212$	184.233			0.869024
$213$			15.5004i			0.0727719i
$214$		−	84.7496i		−	0.396026i
$215$	86.5728	+	236.449i	0.402664	+	1.09976i
$216$	14.6969			0.0680414
$217$	41.2332			0.190015
$218$	62.2945			0.285755
$219$	122.338			0.558623
$220$	172.722	−	63.2398i	0.785098	−	0.287453i
$221$		−	151.622i		−	0.686074i
$222$	−26.9861			−0.121559
$223$		−	122.920i		−	0.551211i	−0.961271	−	0.275605i	$-0.911122\pi$
$223$		−	122.920i		−	0.551211i	0.961271	−	0.275605i	$-0.0888783\pi$
$224$			73.1979i			0.326776i
$225$	57.2685	−	48.4284i	0.254527	−	0.215237i
$226$			230.436i			1.01963i
$227$	284.494			1.25328			0.626639	−	0.779310i	$-0.284430\pi$
$227$	284.494			1.25328			0.626639	+	0.779310i	$0.284430\pi$
$228$	84.3462			0.369940
$229$		−	427.020i		−	1.86472i	−0.361536	−	0.932358i	$-0.617747\pi$
$229$		−	427.020i		−	1.86472i	0.361536	−	0.932358i	$-0.382253\pi$
$230$	−156.613	+	43.8450i	−0.680926	+	0.190630i
$231$	412.238			1.78458
$232$		−	91.2056i		−	0.393128i
$233$		−	377.271i		−	1.61919i	−0.586988	−	0.809595i	$-0.699687\pi$
$233$		−	377.271i		−	1.61919i	0.586988	−	0.809595i	$-0.300313\pi$
$234$	32.2596			0.137861
$235$	−373.101	+	136.606i	−1.58767	+	0.581304i
$236$	−10.3240			−0.0437458
$237$	2.34277			0.00988511
$238$		−	364.904i		−	1.53321i
$239$	112.849			0.472171			0.236086	−	0.971732i	$-0.424135\pi$
$239$	112.849			0.472171			0.236086	+	0.971732i	$0.424135\pi$
$240$	32.5292	−	11.9101i	0.135538	−	0.0496256i
$241$			149.271i			0.619380i	0.950838	+	0.309690i	$0.100225\pi$
$241$			149.271i			0.619380i	−0.950838	+	0.309690i	$0.899775\pi$
$242$		−	307.337i		−	1.26999i
$243$		−	15.5885i		−	0.0641500i
$244$		−	21.0530i		−	0.0862827i
$245$	203.600	+	556.075i	0.831020	+	2.26970i
$246$	−148.045			−0.601809
$247$	185.139			0.749550
$248$		−	9.01299i		−	0.0363427i
$249$		−	234.471i		−	0.941652i
$250$	87.5087	−	153.598i	0.350035	−	0.614390i
$251$		−	357.872i		−	1.42579i	−0.701273	−	0.712893i	$-0.747385\pi$
$251$		−	357.872i		−	1.42579i	0.701273	−	0.712893i	$-0.252615\pi$
$252$	77.6381			0.308088
$253$	−32.9681	+	421.763i	−0.130309	+	1.66705i
$254$	110.793			0.436192
$255$	−162.164	+	59.3742i	−0.635936	+	0.232840i
$256$	16.0000			0.0625000
$257$		−	58.9536i		−	0.229391i	−0.993401	−	0.114696i	$-0.963411\pi$
$257$		−	58.9536i		−	0.229391i	0.993401	−	0.114696i	$-0.0365893\pi$
$258$	123.356			0.478125
$259$	−142.557			−0.550413
$260$	71.4011	−	26.1426i	0.274620	−	0.100549i
$261$	−96.7382			−0.370644
$262$			344.394i			1.31448i
$263$	−121.126			−0.460557			−0.230278	−	0.973125i	$-0.573964\pi$
$263$	−121.126			−0.460557			−0.230278	+	0.973125i	$0.573964\pi$
$264$		−	90.1093i		−	0.341323i
$265$	−158.356	−	432.504i	−0.597569	−	1.63209i
$266$	445.568			1.67507
$267$	72.6465			0.272084
$268$	144.464			0.539046
$269$	313.321			1.16476			0.582381	−	0.812916i	$-0.302121\pi$
$269$	313.321			1.16476			0.582381	+	0.812916i	$0.302121\pi$
$270$	−12.6326	−	34.5024i	−0.0467875	−	0.127787i
$271$	−17.1800			−0.0633948			−0.0316974	−	0.999498i	$-0.510091\pi$
$271$	−17.1800			−0.0633948			−0.0316974	+	0.999498i	$0.510091\pi$
$272$	−79.7628			−0.293246
$273$	170.415			0.624229
$274$			97.1221i			0.354460i
$275$	−296.922	−	351.123i	−1.07972	−	1.27681i
$276$	−6.20899	+	79.4320i	−0.0224963	+	0.287797i
$277$			268.440i			0.969098i	0.874764	+	0.484549i	$0.161016\pi$
$277$			268.440i			0.969098i	−0.874764	+	0.484549i	$0.838984\pi$
$278$		−	193.467i		−	0.695923i
$279$	−9.55972			−0.0342642
$280$	171.839	−	62.9166i	0.613710	−	0.224702i
$281$			386.651i			1.37598i	0.725719	+	0.687991i	$0.241507\pi$
$281$			386.651i			1.37598i	−0.725719	+	0.687991i	$0.758493\pi$
$282$			194.648i			0.690241i
$283$	−54.5729			−0.192837			−0.0964185	−	0.995341i	$-0.530739\pi$
$283$	−54.5729			−0.192837			−0.0964185	+	0.995341i	$0.530739\pi$
$284$	17.8983			0.0630223
$285$	−72.4990	−	198.011i	−0.254383	−	0.694774i
$286$		−	197.789i		−	0.691569i
$287$	−782.063			−2.72496
$288$		−	16.9706i		−	0.0589256i
$289$	108.632			0.375888
$290$	−214.114	+	78.3950i	−0.738323	+	0.270327i
$291$		−	286.915i		−	0.985961i
$292$		−	141.264i		−	0.483782i
$293$	−87.8588			−0.299859			−0.149930	−	0.988697i	$-0.547905\pi$
$293$	−87.8588			−0.299859			−0.149930	+	0.988697i	$0.547905\pi$
$294$	290.106			0.986755
$295$	8.87390	+	24.2366i	0.0300810	+	0.0821578i
$296$			31.1609i			0.105273i
$297$	−95.5753			−0.321802
$298$	208.109			0.698353
$299$	−13.6286	+	174.352i	−0.0455808	+	0.583118i
$300$	−55.9203	−	66.1280i	−0.186401	−	0.220427i
$301$	651.641			2.16492
$302$		−	5.96645i		−	0.0197565i
$303$		−	35.0336i		−	0.115622i
$304$		−	97.3946i		−	0.320377i
$305$	−49.4238	+	18.0959i	−0.162045	+	0.0593308i
$306$			84.6012i			0.276475i
$307$		−	436.714i		−	1.42252i	−0.702928	−	0.711261i	$-0.748124\pi$
$307$		−	436.714i		−	1.42252i	0.702928	−	0.711261i	$-0.251876\pi$
$308$		−	476.011i		−	1.54549i
$309$		−	17.5070i		−	0.0566570i
$310$	−21.1588	+	7.74703i	−0.0682543	+	0.0249904i
$311$	−95.4124			−0.306792			−0.153396	−	0.988165i	$-0.549021\pi$
$311$	−95.4124			−0.306792			−0.153396	+	0.988165i	$0.549021\pi$
$312$		−	37.2502i		−	0.119392i
$313$	277.575			0.886820			0.443410	−	0.896319i	$-0.353769\pi$
$313$	277.575			0.886820			0.443410	+	0.896319i	$0.353769\pi$
$314$		−	181.004i		−	0.576445i
$315$	−66.7331	−	182.263i	−0.211851	−	0.578611i
$316$		−	2.70520i		−	0.00856076i
$317$		−	43.9312i		−	0.138584i	−0.997596	−	0.0692921i	$-0.977926\pi$
$317$		−	43.9312i		−	0.138584i	0.997596	−	0.0692921i	$-0.0220741\pi$
$318$	−225.638			−0.709555
$319$			593.117i			1.85930i
$320$	−13.7527	−	37.5615i	−0.0429770	−	0.117380i
$321$			103.797i			0.323354i
$322$	−32.7996	+	419.608i	−0.101862	+	1.30313i
$323$			485.529i			1.50319i
$324$	−18.0000			−0.0555556
$325$	−122.744	−	145.150i	−0.377675	−	0.446616i
$326$	76.2164			0.233793
$327$	−76.2949			−0.233318
$328$			170.948i			0.521182i
$329$			1028.25i			3.12537i
$330$	−211.540	+	77.4526i	−0.641030	+	0.234705i
$331$	−449.865			−1.35911			−0.679554	−	0.733626i	$-0.737827\pi$
$331$	−449.865			−1.35911			−0.679554	+	0.733626i	$0.737827\pi$
$332$	−270.744			−0.815494
$333$	33.0511			0.0992527
$334$	−268.154			−0.802857
$335$	−124.173	−	339.143i	−0.370666	−	1.01237i
$336$		−	89.6487i		−	0.266812i
$337$	199.863			0.593066			0.296533	−	0.955023i	$-0.404170\pi$
$337$	199.863			0.593066			0.296533	+	0.955023i	$0.404170\pi$
$338$			157.239i			0.465203i
$339$		−	282.226i		−	0.832525i
$340$	68.5594	+	187.251i	0.201645	+	0.550737i
$341$			58.6122i			0.171883i
$342$	−103.303			−0.302054
$343$	898.470			2.61945
$344$		−	142.439i		−	0.414068i
$345$	191.811	−	53.6989i	0.555974	−	0.155649i
$346$	103.807			0.300021
$347$		−	290.365i		−	0.836786i	−0.908266	−	0.418393i	$-0.862594\pi$
$347$		−	290.365i		−	0.836786i	0.908266	−	0.418393i	$-0.137406\pi$
$348$			111.704i			0.320987i
$349$	−126.648			−0.362888			−0.181444	−	0.983401i	$-0.558077\pi$
$349$	−126.648			−0.362888			−0.181444	+	0.983401i	$0.558077\pi$
$350$	−295.405	−	349.328i	−0.844014	−	0.998080i
$351$	−39.5098			−0.112563
$352$	−104.049			−0.295594
$353$			497.700i			1.40992i	0.709249	+	0.704958i	$0.249034\pi$
$353$			497.700i			1.40992i	−0.709249	+	0.704958i	$0.750966\pi$
$354$	12.6443			0.0357183
$355$	−15.3843	−	42.0180i	−0.0433362	−	0.118360i
$356$		−	83.8849i		−	0.235632i
$357$			446.915i			1.25186i
$358$		−	394.625i		−	1.10231i
$359$		−	329.021i		−	0.916494i	−0.888825	−	0.458247i	$-0.848477\pi$
$359$		−	329.021i		−	0.916494i	0.888825	−	0.458247i	$-0.151523\pi$
$360$	−39.8400	+	14.5869i	−0.110667	+	0.0405191i
$361$	−231.857			−0.642264
$362$	214.161			0.591604
$363$			376.409i			1.03694i
$364$		−	196.778i		−	0.540598i
$365$	−331.631	+	121.422i	−0.908578	+	0.332664i
$366$			25.7845i			0.0704496i
$367$	172.395			0.469742			0.234871	−	0.972027i	$-0.424533\pi$
$367$	172.395			0.469742			0.234871	+	0.972027i	$0.424533\pi$
$368$	91.7202	+	7.16952i	0.249240	+	0.0194824i
$369$	181.317			0.491375
$370$	73.1531	−	26.7841i	0.197711	−	0.0723894i
$371$	−1191.96			−3.21282
$372$			11.0386i			0.0296737i
$373$	175.718			0.471095			0.235548	−	0.971863i	$-0.424312\pi$
$373$	175.718			0.471095			0.235548	+	0.971863i	$0.424312\pi$
$374$	518.704			1.38691
$375$	−107.176	+	188.118i	−0.285802	+	0.501648i
$376$	224.760			0.597766
$377$			245.188i			0.650366i
$378$	−95.0868			−0.251552
$379$		−	423.074i		−	1.11629i	−0.829744	−	0.558145i	$-0.811513\pi$
$379$		−	423.074i		−	1.11629i	0.829744	−	0.558145i	$-0.188487\pi$
$380$	−228.643	+	83.7147i	−0.601692	+	0.220302i
$381$	−135.693			−0.356149
$382$	419.746			1.09881
$383$	401.734			1.04891			0.524457	−	0.851437i	$-0.324268\pi$
$383$	401.734			1.04891			0.524457	+	0.851437i	$0.324268\pi$
$384$	−19.5959			−0.0510310
$385$	−1117.48	+	409.151i	−2.90255	+	1.06273i
$386$	−38.0632			−0.0986092
$387$	−151.080			−0.390387
$388$	−331.300			−0.853867
$389$			346.765i			0.891427i	0.895176	+	0.445714i	$0.147050\pi$
$389$			346.765i			0.891427i	−0.895176	+	0.445714i	$0.852950\pi$
$390$	−87.4482	+	32.0180i	−0.224226	+	0.0820975i
$391$	−457.241	−	35.7413i	−1.16942	−	0.0914100i
$392$		−	334.985i		−	0.854555i
$393$		−	421.795i		−	1.07327i
$394$	−87.0988			−0.221063
$395$	−6.35071	+	2.32523i	−0.0160777	+	0.00588666i
$396$			110.361i			0.278689i
$397$			98.9151i			0.249157i	0.992210	+	0.124578i	$0.0397578\pi$
$397$			98.9151i			0.249157i	−0.992210	+	0.124578i	$0.960242\pi$
$398$	49.9693			0.125551
$399$	−545.707			−1.36769
$400$	−76.3581	+	64.5712i	−0.190895	+	0.161428i
$401$		−	625.874i		−	1.56078i	−0.625291	−	0.780392i	$-0.715020\pi$
$401$		−	625.874i		−	1.56078i	0.625291	−	0.780392i	$-0.284980\pi$
$402$	−176.932			−0.440129
$403$			24.2296i			0.0601231i
$404$	−40.4533			−0.100132
$405$	15.4717	+	42.2567i	0.0382018	+	0.104337i
$406$			590.086i			1.45341i
$407$		−	202.642i		−	0.497891i
$408$	97.6891			0.239434
$409$	410.570			1.00384			0.501920	−	0.864914i	$-0.332627\pi$
$409$	410.570			1.00384			0.501920	+	0.864914i	$0.332627\pi$
$410$	401.316	−	146.937i	0.978818	−	0.358382i
$411$		−	118.950i		−	0.289415i
$412$	−20.2154			−0.0490664
$413$	66.7946			0.161730
$414$	7.60443	−	97.2840i	0.0183682	−	0.234985i
$415$	232.716	+	635.597i	0.560761	+	1.53156i
$416$	−43.0128			−0.103396
$417$			236.947i			0.568219i
$418$			633.365i			1.51523i
$419$		−	36.3204i		−	0.0866834i	−0.999060	−	0.0433417i	$-0.986200\pi$
$419$		−	36.3204i		−	0.0866834i	0.999060	−	0.0433417i	$-0.0138004\pi$
$420$	−210.459	+	77.0567i	−0.501092	+	0.183468i
$421$		−	545.508i		−	1.29574i	−0.761750	−	0.647871i	$-0.775659\pi$
$421$		−	545.508i		−	1.29574i	0.761750	−	0.647871i	$-0.224341\pi$
$422$		−	200.842i		−	0.475928i
$423$		−	238.394i		−	0.563580i
$424$			260.545i			0.614493i
$425$	380.658	−	321.899i	0.895667	−	0.757409i
$426$	−21.9209			−0.0514575
$427$			136.209i			0.318992i
$428$	119.854			0.280033
$429$			242.241i			0.564663i
$430$	−334.390	+	122.432i	−0.777650	+	0.284727i
$431$		−	156.738i		−	0.363662i	−0.983330	−	0.181831i	$-0.941798\pi$
$431$		−	156.738i		−	0.363662i	0.983330	−	0.181831i	$-0.0582024\pi$
$432$			20.7846i			0.0481125i
$433$	−10.8320			−0.0250162			−0.0125081	−	0.999922i	$-0.503982\pi$
$433$	−10.8320			−0.0250162			−0.0125081	+	0.999922i	$0.503982\pi$
$434$			58.3126i			0.134361i
$435$	262.235	−	96.0138i	0.602838	−	0.220721i
$436$			88.0978i			0.202059i
$437$	43.6421	−	558.316i	0.0998674	−	1.27761i
$438$			173.013i			0.395006i
$439$	10.1988			0.0232319			0.0116159	−	0.999933i	$-0.496302\pi$
$439$	10.1988			0.0232319			0.0116159	+	0.999933i	$0.496302\pi$
$440$	89.4345	+	244.265i	0.203260	+	0.555148i
$441$	−355.306			−0.805682
$442$	214.426			0.485127
$443$			23.7800i			0.0536794i	0.999640	+	0.0268397i	$0.00854437\pi$
$443$			23.7800i			0.0536794i	−0.999640	+	0.0268397i	$0.991456\pi$
$444$		−	38.1642i		−	0.0859553i
$445$	−196.928	+	72.1025i	−0.442534	+	0.162028i
$446$	173.835			0.389765
$447$	−254.881			−0.570203
$448$	−103.517			−0.231066
$449$	−417.771			−0.930448			−0.465224	−	0.885193i	$-0.654026\pi$
$449$	−417.771			−0.930448			−0.465224	+	0.885193i	$0.654026\pi$
$450$	68.4881	+	80.9900i	0.152196	+	0.179978i
$451$		−	1111.69i		−	2.46494i
$452$	−325.886			−0.720987
$453$			7.30738i			0.0161311i
$454$			402.335i			0.886201i
$455$	−461.954	+	169.138i	−1.01528	+	0.371733i
$456$			119.284i			0.261587i
$457$	197.215			0.431543			0.215772	−	0.976444i	$-0.430773\pi$
$457$	197.215			0.431543			0.215772	+	0.976444i	$0.430773\pi$
$458$	603.898			1.31855
$459$		−	103.615i		−	0.225741i
$460$	−62.0062	−	221.484i	−0.134796	−	0.481487i
$461$	−791.818			−1.71761			−0.858805	−	0.512303i	$-0.828792\pi$
$461$	−791.818			−1.71761			−0.858805	+	0.512303i	$0.828792\pi$
$462$			582.992i			1.26189i
$463$			225.166i			0.486320i	0.969986	+	0.243160i	$0.0781840\pi$
$463$			225.166i			0.486320i	−0.969986	+	0.243160i	$0.921816\pi$
$464$	128.984			0.277983
$465$	25.9142	−	9.48814i	0.0557294	−	0.0204046i
$466$	533.542			1.14494
$467$	−4.35994			−0.00933607			−0.00466803	−	0.999989i	$-0.501486\pi$
$467$	−4.35994			−0.00933607			−0.00466803	+	0.999989i	$0.501486\pi$
$468$			45.6219i			0.0974828i
$469$	−934.661			−1.99288
$470$	−193.191	−	527.645i	−0.411044	−	1.12265i
$471$			221.683i			0.470665i
$472$		−	14.6003i		−	0.0309329i
$473$			926.294i			1.95834i
$474$			3.31318i			0.00698983i
$475$	393.056	+	464.804i	0.827486	+	0.978535i
$476$	516.053			1.08414
$477$	276.350			0.579349
$478$			159.593i			0.333876i
$479$			262.797i			0.548637i	0.961639	+	0.274318i	$0.0884522\pi$
$479$			262.797i			0.548637i	−0.961639	+	0.274318i	$0.911548\pi$
$480$	16.8435	+	46.0032i	0.0350906	+	0.0958401i
$481$		−	83.7698i		−	0.174158i
$482$	−211.100			−0.437968
$483$	40.1712	−	513.912i	0.0831701	−	1.06400i
$484$	434.640			0.898016
$485$	284.766	+	777.758i	0.587147	+	1.60363i
$486$	22.0454			0.0453609
$487$		−	320.366i		−	0.657835i	−0.944359	−	0.328917i	$-0.893316\pi$
$487$		−	320.366i		−	0.657835i	0.944359	−	0.328917i	$-0.106684\pi$
$488$	29.7734			0.0610111
$489$	−93.3456			−0.190891
$490$	−786.409	+	287.934i	−1.60492	+	0.587620i
$491$	179.242			0.365055			0.182528	−	0.983201i	$-0.441572\pi$
$491$	179.242			0.365055			0.182528	+	0.983201i	$0.441572\pi$
$492$		−	209.367i		−	0.425543i
$493$	−643.009			−1.30428
$494$			261.826i			0.530012i
$495$	259.082	−	94.8597i	0.523399	−	0.191636i
$496$	12.7463			0.0256982
$497$	−115.799			−0.232997
$498$	331.593			0.665848
$499$	−14.9582			−0.0299763			−0.0149882	−	0.999888i	$-0.504771\pi$
$499$	−14.9582			−0.0299763			−0.0149882	+	0.999888i	$0.504771\pi$
$500$	217.220	+	123.756i	0.434440	+	0.247512i
$501$	328.420			0.655530
$502$	506.108			1.00818
$503$	694.560			1.38084			0.690418	−	0.723411i	$-0.257427\pi$
$503$	694.560			1.38084			0.690418	+	0.723411i	$0.257427\pi$
$504$			109.797i			0.217851i
$505$	34.7713	+	94.9678i	0.0688540	+	0.188055i
$506$	−596.463	−	46.6239i	−1.17878	−	0.0921422i
$507$		−	192.577i		−	0.379836i
$508$			156.685i			0.308434i
$509$	−401.121			−0.788057			−0.394028	−	0.919098i	$-0.628919\pi$
$509$	−401.121			−0.788057			−0.394028	+	0.919098i	$0.628919\pi$
$510$	−83.9678	−	229.334i	−0.164643	−	0.449675i
$511$			913.957i			1.78857i
$512$			22.6274i			0.0441942i
$513$	126.519			0.246626
$514$	83.3730			0.162204
$515$	17.3759	+	47.4574i	0.0337397	+	0.0921503i
$516$			174.452i			0.338085i
$517$	−1461.63			−2.82714
$518$		−	201.606i		−	0.389201i
$519$	−127.137			−0.244966
$520$	36.9712	+	100.976i	0.0710985	+	0.194186i
$521$		−	832.880i		−	1.59862i	−0.600920	−	0.799309i	$-0.705199\pi$
$521$		−	832.880i		−	1.59862i	0.600920	−	0.799309i	$-0.294801\pi$
$522$		−	136.808i		−	0.262085i
$523$	303.690			0.580670			0.290335	−	0.956925i	$-0.406233\pi$
$523$	303.690			0.580670			0.290335	+	0.956925i	$0.406233\pi$
$524$	−487.047			−0.929479
$525$	361.796	+	427.838i	0.689134	+	0.814929i
$526$		−	171.299i		−	0.325663i
$527$	−63.5425			−0.120574
$528$	127.434			0.241352
$529$	522.575	+	82.1988i	0.987854	+	0.155385i
$530$	611.653	−	223.949i	1.15406	−	0.422545i
$531$	−15.4860			−0.0291639
$532$			630.128i			1.18445i
$533$		−	459.558i		−	0.862211i
$534$			102.738i			0.192393i
$535$	−103.019	−	281.368i	−0.192560	−	0.525922i
$536$			204.303i			0.381163i
$537$			483.315i			0.900028i
$538$			443.103i			0.823612i
$539$			2178.44i			4.04162i
$540$	48.7938	−	17.8652i	0.0903589	−	0.0330837i
$541$	802.731			1.48379			0.741896	−	0.670515i	$-0.233927\pi$
$541$	802.731			1.48379			0.741896	+	0.670515i	$0.233927\pi$
$542$		−	24.2962i		−	0.0448269i
$543$	−262.292			−0.483043
$544$		−	112.802i		−	0.207356i
$545$	206.818	−	75.7236i	0.379482	−	0.138942i
$546$			241.003i			0.441397i
$547$			555.494i			1.01553i	0.861496	+	0.507764i	$0.169528\pi$
$547$			555.494i			1.01553i	−0.861496	+	0.507764i	$0.830472\pi$
$548$	−137.351			−0.250641
$549$		−	31.5795i		−	0.0575218i
$550$	496.562	−	419.912i	0.902840	−	0.763476i
$551$		−	785.148i		−	1.42495i
$552$	−112.334	−	8.78084i	−0.203503	−	0.0159073i
$553$			17.5022i			0.0316496i
$554$	−379.632			−0.685256
$555$	−89.5939	+	32.8037i	−0.161430	+	0.0591057i
$556$	273.603			0.492092
$557$	697.030			1.25140			0.625700	−	0.780064i	$-0.284813\pi$
$557$	697.030			1.25140			0.625700	+	0.780064i	$0.284813\pi$
$558$		−	13.5195i		−	0.0242285i
$559$			382.920i			0.685008i
$560$	88.9774	+	243.017i	0.158888	+	0.433958i
$561$	−635.280			−1.13241
$562$	−546.807			−0.972966
$563$	−24.7377			−0.0439390			−0.0219695	−	0.999759i	$-0.506994\pi$
$563$	−24.7377			−0.0439390			−0.0219695	+	0.999759i	$0.506994\pi$
$564$	−275.274			−0.488074
$565$	280.113	+	765.048i	0.495775	+	1.35407i
$566$		−	77.1777i		−	0.136356i
$567$	116.457			0.205392
$568$			25.3121i			0.0445635i
$569$		−	475.965i		−	0.836495i	−0.908333	−	0.418247i	$-0.862645\pi$
$569$		−	475.965i		−	0.836495i	0.908333	−	0.418247i	$-0.137355\pi$
$570$	280.029	−	102.529i	0.491279	−	0.179876i
$571$			558.821i			0.978671i	0.872096	+	0.489336i	$0.162761\pi$
$571$			558.821i			0.978671i	−0.872096	+	0.489336i	$0.837239\pi$
$572$	279.715			0.489013
$573$	−514.081			−0.897175
$574$		−	1106.00i		−	1.92684i
$575$	−466.658	+	335.940i	−0.811579	+	0.584243i
$576$	24.0000			0.0416667
$577$			1114.51i			1.93156i	0.259365	+	0.965779i	$0.416487\pi$
$577$			1114.51i			1.93156i	−0.259365	+	0.965779i	$0.583513\pi$
$578$			153.628i			0.265793i
$579$	46.6177			0.0805141
$580$	−110.867	−	302.802i	−0.191150	−	0.522073i
$581$	1751.67			3.01492
$582$	405.758			0.697179
$583$		−	1694.34i		−	2.90625i
$584$	199.778			0.342085
$585$	107.102	−	39.2139i	0.183080	−	0.0670323i
$586$		−	124.251i		−	0.212032i
$587$			396.273i			0.675082i	0.941311	+	0.337541i	$0.109595\pi$
$587$			396.273i			0.675082i	−0.941311	+	0.337541i	$0.890405\pi$
$588$			410.272i			0.697741i
$589$		−	77.5888i		−	0.131730i
$590$	−34.2757	+	12.5496i	−0.0580943	+	0.0212705i
$591$	106.674			0.180497
$592$	−44.0682			−0.0744395
$593$		−	888.386i		−	1.49812i	−0.662501	−	0.749061i	$-0.730505\pi$
$593$		−	888.386i		−	1.49812i	0.662501	−	0.749061i	$-0.269495\pi$
$594$		−	135.164i		−	0.227549i
$595$	−443.568	−	1211.48i	−0.745493	−	2.03610i
$596$			294.311i			0.493810i
$597$	−61.1997			−0.102512
$598$	−246.571	−	19.2738i	−0.412327	−	0.0322305i
$599$	−902.768			−1.50713			−0.753563	−	0.657376i	$-0.771666\pi$
$599$	−902.768			−1.50713			−0.753563	+	0.657376i	$0.771666\pi$
$600$	93.5192	−	79.0833i	0.155865	−	0.131806i
$601$	685.970			1.14138			0.570691	−	0.821165i	$-0.306675\pi$
$601$	685.970			1.14138			0.570691	+	0.821165i	$0.306675\pi$
$602$			921.560i			1.53083i
$603$	216.696			0.359364
$604$	8.43783			0.0139699
$605$	−373.591	−	1020.36i	−0.617505	−	1.68654i
$606$	49.5450			0.0817574
$607$		−	790.719i		−	1.30267i	−0.758791	−	0.651334i	$-0.774210\pi$
$607$		−	790.719i		−	1.30267i	0.758791	−	0.651334i	$-0.225790\pi$
$608$	137.737			0.226541
$609$		−	722.705i		−	1.18671i
$610$	−25.5915	−	69.8959i	−0.0419532	−	0.114583i
$611$	−604.222			−0.988907
$612$	−119.644			−0.195497
$613$	563.868			0.919850			0.459925	−	0.887958i	$-0.347876\pi$
$613$	563.868			0.919850			0.459925	+	0.887958i	$0.347876\pi$
$614$	617.607			1.00587
$615$	−491.509	+	179.960i	−0.799202	+	0.292618i
$616$	673.182			1.09283
$617$	−803.130			−1.30167			−0.650835	−	0.759219i	$-0.725581\pi$
$617$	−803.130			−1.30167			−0.650835	+	0.759219i	$0.725581\pi$
$618$	24.7587			0.0400625
$619$		−	242.335i		−	0.391494i	−0.980654	−	0.195747i	$-0.937287\pi$
$619$		−	242.335i		−	0.391494i	0.980654	−	0.195747i	$-0.0627131\pi$
$620$	−10.9560	−	29.9231i	−0.0176709	−	0.0482631i
$621$	−9.31348	+	119.148i	−0.0149976	+	0.191865i
$622$		−	134.934i		−	0.216935i
$623$			542.722i			0.871142i
$624$	52.6797			0.0844226
$625$	103.819	−	616.317i	0.166111	−	0.986107i
$626$			392.550i			0.627076i
$627$		−	775.710i		−	1.23718i
$628$	255.978			0.407608
$629$	219.688			0.349265
$630$	257.758	−	94.3748i	0.409140	−	0.149801i
$631$		−	713.068i		−	1.13006i	−0.825070	−	0.565031i	$-0.808864\pi$
$631$		−	713.068i		−	1.13006i	0.825070	−	0.565031i	$-0.191136\pi$
$632$	3.82573			0.00605337
$633$			245.980i			0.388594i
$634$	62.1281			0.0979939
$635$	367.832	−	134.677i	0.579263	−	0.212090i
$636$		−	319.101i		−	0.501731i
$637$			900.541i			1.41372i
$638$	−838.794			−1.31472
$639$	26.8475			0.0420149
$640$	53.1199	−	19.4492i	0.0829999	−	0.0303894i
$641$		−	320.213i		−	0.499553i	−0.968304	−	0.249776i	$-0.919643\pi$
$641$		−	320.213i		−	0.499553i	0.968304	−	0.249776i	$-0.0803571\pi$
$642$	−146.791			−0.228646
$643$	−441.300			−0.686315			−0.343157	−	0.939278i	$-0.611496\pi$
$643$	−441.300			−0.686315			−0.343157	+	0.939278i	$0.611496\pi$
$644$	−593.415	−	46.3857i	−0.921452	−	0.0720274i
$645$	409.542	−	149.949i	0.634949	−	0.232478i
$646$	−686.642			−1.06291
$647$			935.951i			1.44660i	0.690533	+	0.723301i	$0.257376\pi$
$647$			935.951i			1.44660i	−0.690533	+	0.723301i	$0.742624\pi$
$648$		−	25.4558i		−	0.0392837i
$649$			94.9472i			0.146298i
$650$	205.273	−	173.587i	0.315805	−	0.267057i
$651$		−	71.4181i		−	0.109705i
$652$			107.786i			0.165316i
$653$			779.044i			1.19302i	0.802604	+	0.596512i	$0.203447\pi$
$653$			779.044i			1.19302i	−0.802604	+	0.596512i	$0.796553\pi$
$654$		−	107.897i		−	0.164981i
$655$	418.637	+	1143.39i	0.639140	+	1.74563i
$656$	−241.757			−0.368531
$657$		−	211.896i		−	0.322521i
$658$	−1454.16			−2.20997
$659$			990.231i			1.50263i	0.659946	+	0.751313i	$0.270579\pi$
$659$			990.231i			1.50263i	−0.659946	+	0.751313i	$0.729421\pi$
$660$	−109.534	−	299.162i	−0.165961	−	0.453276i
$661$		−	82.8711i		−	0.125372i	−0.998033	−	0.0626862i	$-0.980033\pi$
$661$		−	82.8711i		−	0.125372i	0.998033	−	0.0626862i	$-0.0199667\pi$
$662$		−	636.205i		−	0.961034i
$663$	−262.617			−0.396105
$664$		−	382.890i		−	0.576642i
$665$	1479.28	−	541.620i	2.22449	−	0.814467i
$666$			46.7414i			0.0701822i
$667$	739.404	+	57.7972i	1.10855	+	0.0866525i
$668$		−	379.227i		−	0.567705i
$669$	−212.904			−0.318242
$670$	479.621	−	175.607i	0.715852	−	0.262100i
$671$	−193.619			−0.288553
$672$	126.782			0.188664
$673$		−	461.012i		−	0.685010i	−0.939516	−	0.342505i	$-0.888725\pi$
$673$		−	461.012i		−	0.685010i	0.939516	−	0.342505i	$-0.111275\pi$
$674$			282.649i			0.419361i
$675$	−83.8805	−	99.1920i	−0.124267	−	0.146951i
$676$	−222.369			−0.328948
$677$	−1137.48			−1.68017			−0.840085	−	0.542454i	$-0.817495\pi$
$677$	−1137.48			−1.68017			−0.840085	+	0.542454i	$0.817495\pi$
$678$	399.128			0.588684
$679$	2143.46			3.15679
$680$	−264.812	+	96.9576i	−0.389430	+	0.142585i
$681$		−	492.758i		−	0.723580i
$682$	−82.8901			−0.121540
$683$			27.4834i			0.0402393i	0.999798	+	0.0201196i	$0.00640471\pi$
$683$			27.4834i			0.0402393i	−0.999798	+	0.0201196i	$0.993595\pi$
$684$		−	146.092i		−	0.213585i
$685$	118.059	+	322.445i	0.172349	+	0.470723i
$686$			1270.63i			1.85223i
$687$	−739.621			−1.07659
$688$	201.440			0.292790
$689$		−	700.422i		−	1.01658i
$690$	75.9417	+	271.262i	0.110060	+	0.393133i
$691$	202.309			0.292777			0.146388	−	0.989227i	$-0.453235\pi$
$691$	202.309			0.292777			0.146388	+	0.989227i	$0.453235\pi$
$692$			146.805i			0.212147i
$693$		−	714.017i		−	1.03033i
$694$	410.638			0.591697
$695$	−235.173	−	642.309i	−0.338378	−	0.924185i
$696$	−157.973			−0.226972
$697$	1205.20			1.72912
$698$		−	179.107i		−	0.256600i
$699$	−653.453			−0.934840
$700$	494.024	−	417.766i	0.705749	−	0.596808i
$701$			720.064i			1.02719i	0.858031	+	0.513597i	$0.171687\pi$
$701$			720.064i			1.02719i	−0.858031	+	0.513597i	$0.828313\pi$
$702$		−	55.8752i		−	0.0795944i
$703$			268.250i			0.381579i
$704$		−	147.148i		−	0.209017i
$705$	236.609	+	646.231i	0.335616	+	0.916639i
$706$	−703.855			−0.996961
$707$	261.726			0.370193
$708$			17.8817i			0.0252566i
$709$			1116.63i			1.57493i	0.616357	+	0.787467i	$0.288608\pi$
$709$			1116.63i			1.57493i	−0.616357	+	0.787467i	$0.711392\pi$
$710$	59.4224	−	21.7567i	0.0836935	−	0.0306433i
$711$		−	4.05780i		−	0.00570717i
$712$	118.631			0.166617
$713$	73.0683	+	5.71155i	0.102480	+	0.00801059i
$714$	−632.033			−0.885200
$715$	−240.427	−	656.658i	−0.336261	−	0.918402i
$716$	558.084			0.779447
$717$		−	195.460i		−	0.272608i
$718$	465.307			0.648059
$719$	−276.958			−0.385199			−0.192600	−	0.981277i	$-0.561692\pi$
$719$	−276.958			−0.385199			−0.192600	+	0.981277i	$0.561692\pi$
$720$	−20.6290	−	56.3422i	−0.0286514	−	0.0782531i
$721$	130.790			0.181401
$722$		−	327.896i		−	0.454149i
$723$	258.544			0.357599
$724$			302.869i			0.418327i
$725$	−615.562	+	520.542i	−0.849051	+	0.717989i
$726$	−532.323			−0.733227
$727$	1175.60			1.61706			0.808530	−	0.588455i	$-0.200264\pi$
$727$	1175.60			1.61706			0.808530	+	0.588455i	$0.200264\pi$
$728$	278.286			0.382261
$729$	−27.0000			−0.0370370
$730$	−171.717	−	468.997i	−0.235229	−	0.642462i
$731$	−1004.21			−1.37375
$732$	−36.4648			−0.0498154
$733$	620.255			0.846187			0.423093	−	0.906086i	$-0.360944\pi$
$733$	620.255			0.846187			0.423093	+	0.906086i	$0.360944\pi$
$734$			243.804i			0.332158i
$735$	963.151	−	352.645i	1.31041	−	0.479790i
$736$	−10.1392	+	129.712i	−0.0137761	+	0.176239i
$737$		−	1328.60i		−	1.80271i
$738$			256.422i			0.347455i
$739$	−147.282			−0.199298			−0.0996492	−	0.995023i	$-0.531772\pi$
$739$	−147.282			−0.199298			−0.0996492	+	0.995023i	$0.531772\pi$
$740$	37.8784	+	103.454i	0.0511870	+	0.139803i
$741$		−	320.670i		−	0.432753i
$742$		−	1685.68i		−	2.27181i
$743$	−722.303			−0.972143			−0.486072	−	0.873919i	$-0.661571\pi$
$743$	−722.303			−0.972143			−0.486072	+	0.873919i	$0.661571\pi$
$744$	−15.6110			−0.0209825
$745$	690.922	−	252.972i	0.927412	−	0.339560i
$746$			248.503i			0.333114i
$747$	−406.116			−0.543663
$748$			733.558i			0.980692i
$749$	−775.436			−1.03529
$750$	−266.039	−	151.570i	−0.354719	−	0.202093i
$751$			1411.00i			1.87883i	0.342781	+	0.939415i	$0.388631\pi$
$751$			1411.00i			1.87883i	−0.342781	+	0.939415i	$0.611369\pi$
$752$			317.859i			0.422685i
$753$	−619.853			−0.823178
$754$	−346.748			−0.459878
$755$	−7.25266	−	19.8086i	−0.00960618	−	0.0262365i
$756$		−	134.473i		−	0.177874i
$757$	407.669			0.538532			0.269266	−	0.963066i	$-0.413219\pi$
$757$	407.669			0.538532			0.269266	+	0.963066i	$0.413219\pi$
$758$	598.317			0.789336
$759$	730.516	+	57.1024i	0.962471	+	0.0752338i
$760$	−118.390	−	323.350i	−0.155777	−	0.425460i
$761$	696.139			0.914769			0.457385	−	0.889269i	$-0.348786\pi$
$761$	696.139			0.914769			0.457385	+	0.889269i	$0.348786\pi$
$762$		−	191.899i		−	0.251836i
$763$		−	569.978i		−	0.747023i
$764$			593.610i			0.776976i
$765$	102.839	+	280.876i	0.134430	+	0.367158i
$766$			568.138i			0.741694i
$767$			39.2501i			0.0511735i
$768$		−	27.7128i		−	0.0360844i
$769$		−	320.918i		−	0.417319i	−0.977988	−	0.208659i	$-0.933090\pi$
$769$		−	320.918i		−	0.417319i	0.977988	−	0.208659i	$-0.0669100\pi$
$770$	−578.627	−	1580.36i	−0.751464	−	2.05241i
$771$	−102.111			−0.132439
$772$		−	53.8294i		−	0.0697273i
$773$	582.738			0.753865			0.376933	−	0.926241i	$-0.376979\pi$
$773$	582.738			0.753865			0.376933	+	0.926241i	$0.376979\pi$
$774$		−	213.659i		−	0.276045i
$775$	−60.8301	+	51.4403i	−0.0784905	+	0.0663745i
$776$		−	468.529i		−	0.603775i
$777$			246.916i			0.317781i
$778$	−490.400			−0.630334
$779$			1471.61i			1.88910i
$780$	−45.2803	−	123.670i	−0.0580517	−	0.158552i
$781$		−	164.606i		−	0.210763i
$782$	50.5459	−	646.637i	0.0646367	−	0.826902i
$783$			167.555i			0.213992i
$784$	473.741			0.604261
$785$	−220.023	−	600.932i	−0.280285	−	0.765518i
$786$	596.508			0.758916
$787$	463.279			0.588665			0.294333	−	0.955703i	$-0.404903\pi$
$787$	463.279			0.588665			0.294333	+	0.955703i	$0.404903\pi$
$788$		−	123.176i		−	0.156315i
$789$			209.797i			0.265903i
$790$	−3.28837	−	8.98125i	−0.00416250	−	0.0113687i
$791$	2108.43			2.66553
$792$	−156.074			−0.197063
$793$	−80.0399			−0.100933
$794$	−139.887			−0.176180
$795$	−749.119	+	274.280i	−0.942288	+	0.345007i
$796$			70.6673i			0.0887780i
$797$	−831.050			−1.04272			−0.521362	−	0.853336i	$-0.674576\pi$
$797$	−831.050			−1.04272			−0.521362	+	0.853336i	$0.674576\pi$
$798$		−	771.746i		−	0.967100i
$799$		−	1584.58i		−	1.98321i
$800$	−91.3175	−	107.987i	−0.114147	−	0.134983i
$801$		−	125.827i		−	0.157088i
$802$	885.120			1.10364
$803$	−1299.17			−1.61790
$804$		−	250.220i		−	0.311218i
$805$	401.170	+	1432.97i	0.498348	+	1.78008i
$806$	−34.2658			−0.0425135
$807$		−	542.688i		−	0.672476i
$808$		−	57.2096i		−	0.0708040i
$809$	618.152			0.764094			0.382047	−	0.924143i	$-0.375219\pi$
$809$	618.152			0.764094			0.382047	+	0.924143i	$0.375219\pi$
$810$	−59.7599	+	21.8803i	−0.0737777	+	0.0270128i
$811$	−668.575			−0.824383			−0.412192	−	0.911097i	$-0.635237\pi$
$811$	−668.575			−0.824383			−0.412192	+	0.911097i	$0.635237\pi$
$812$	−834.507			−1.02772
$813$			29.7566i			0.0366010i
$814$	286.579			0.352062
$815$	253.038	−	92.6467i	0.310476	−	0.113677i
$816$			138.153i			0.169305i
$817$		−	1226.20i		−	1.50085i
$818$			580.634i			0.709822i
$819$		−	295.167i		−	0.360399i
$820$	207.800	+	567.546i	0.253414	+	0.692129i
$821$	−1377.11			−1.67736			−0.838681	−	0.544623i	$-0.816673\pi$
$821$	−1377.11			−1.67736			−0.838681	+	0.544623i	$0.816673\pi$
$822$	168.220			0.204648
$823$			976.421i			1.18642i	0.805049	+	0.593208i	$0.202139\pi$
$823$			976.421i			1.18642i	−0.805049	+	0.593208i	$0.797861\pi$
$824$		−	28.5888i		−	0.0346952i
$825$	−608.162	+	514.285i	−0.737166	+	0.623375i
$826$			94.4619i			0.114361i
$827$	−438.021			−0.529650			−0.264825	−	0.964296i	$-0.585314\pi$
$827$	−438.021			−0.529650			−0.264825	+	0.964296i	$0.585314\pi$
$828$	137.580	+	10.7543i	0.166160	+	0.0129883i
$829$	541.852			0.653621			0.326810	−	0.945090i	$-0.394026\pi$
$829$	541.852			0.653621			0.326810	+	0.945090i	$0.394026\pi$
$830$	−898.870	+	329.110i	−1.08298	+	0.396518i
$831$	464.952			0.559509
$832$		−	60.8293i		−	0.0731121i
$833$	−2361.68			−2.83515
$834$	−335.094			−0.401791
$835$	−890.271	+	325.961i	−1.06619	+	0.390373i
$836$	−895.713			−1.07143
$837$			16.5579i			0.0197825i
$838$	51.3647			0.0612944
$839$		−	537.167i		−	0.640247i	−0.947376	−	0.320123i	$-0.896276\pi$
$839$		−	537.167i		−	0.640247i	0.947376	−	0.320123i	$-0.103724\pi$
$840$	−108.975	−	297.633i	−0.129732	−	0.354326i
$841$	198.809			0.236395
$842$	771.464			0.916228
$843$	669.699			0.794423
$844$	284.033			0.336532
$845$	191.135	+	522.031i	0.226195	+	0.617789i
$846$	337.140			0.398511
$847$	−2812.05			−3.32001
$848$	−368.466			−0.434512
$849$			94.5230i			0.111335i
$850$	455.234	+	538.332i	0.535569	+	0.633332i
$851$	−252.622	−	19.7467i	−0.296853	−	0.0232042i
$852$		−	31.0008i		−	0.0363859i
$853$		−	198.433i		−	0.232630i	−0.993212	−	0.116315i	$-0.962892\pi$
$853$		−	198.433i		−	0.232630i	0.993212	−	0.116315i	$-0.0371081\pi$
$854$	−192.629			−0.225561
$855$	−342.964	+	125.572i	−0.401128	+	0.146868i
$856$			169.499i			0.198013i
$857$		−	984.927i		−	1.14927i	−0.818409	−	0.574637i	$-0.805143\pi$
$857$		−	984.927i		−	1.14927i	0.818409	−	0.574637i	$-0.194857\pi$
$858$	−342.580			−0.399277
$859$	332.809			0.387437			0.193719	−	0.981057i	$-0.437945\pi$
$859$	332.809			0.387437			0.193719	+	0.981057i	$0.437945\pi$
$860$	−173.146	−	472.898i	−0.201332	−	0.549882i
$861$			1354.57i			1.57326i
$862$	221.661			0.257148
$863$		−	22.3010i		−	0.0258412i	−0.999917	−	0.0129206i	$-0.995887\pi$
$863$		−	22.3010i		−	0.0258412i	0.999917	−	0.0129206i	$-0.00411287\pi$
$864$	−29.3939			−0.0340207
$865$	344.639	−	126.185i	0.398427	−	0.145879i
$866$		−	15.3188i		−	0.0176891i
$867$		−	188.156i		−	0.217019i
$868$	−82.4665			−0.0950075
$869$	−24.8790			−0.0286295
$870$	135.784	+	370.856i	0.156074	+	0.426271i
$871$		−	549.228i		−	0.630572i
$872$	−124.589			−0.142877
$873$	−496.951			−0.569245
$874$	789.578	+	61.7192i	0.903408	+	0.0706169i
$875$	−1405.38	−	800.681i	−1.60615	−	0.915064i
$876$	−244.677			−0.279312
$877$			298.806i			0.340714i	0.985382	+	0.170357i	$0.0544921\pi$
$877$			298.806i			0.340714i	−0.985382	+	0.170357i	$0.945508\pi$
$878$			14.4233i			0.0164274i
$879$			152.176i			0.173124i
$880$	−345.443	+	126.480i	−0.392549	+	0.143727i
$881$			392.975i			0.446056i	0.974812	+	0.223028i	$0.0715941\pi$
$881$			392.975i			0.446056i	−0.974812	+	0.223028i	$0.928406\pi$
$882$		−	502.478i		−	0.569703i
$883$		−	565.810i		−	0.640781i	−0.947286	−	0.320391i	$-0.896186\pi$
$883$		−	565.810i		−	0.640781i	0.947286	−	0.320391i	$-0.103814\pi$
$884$			303.245i			0.343037i
$885$	41.9789	−	15.3701i	0.0474338	−	0.0173673i
$886$	−33.6300			−0.0379571
$887$		−	233.861i		−	0.263654i	−0.991273	−	0.131827i	$-0.957916\pi$
$887$		−	233.861i		−	0.263654i	0.991273	−	0.131827i	$-0.0420844\pi$
$888$	53.9723			0.0607796
$889$		−	1013.72i		−	1.14030i
$890$	−101.968	−	278.498i	−0.114571	−	0.312919i
$891$			165.541i			0.185793i
$892$			245.840i			0.275605i
$893$	1934.86			2.16670
$894$		−	360.456i		−	0.403194i
$895$	−479.696	−	1310.15i	−0.535974	−	1.46386i
$896$		−	146.396i		−	0.163388i
$897$	301.987	+	23.6055i	0.336663	+	0.0263161i
$898$		−	590.818i		−	0.657926i
$899$	102.754			0.114299
$900$	−114.537	+	96.8569i	−0.127263	+	0.107619i
$901$	1836.87			2.03870
$902$	1572.16			1.74297
$903$		−	1128.68i		−	1.24992i
$904$		−	460.873i		−	0.509815i
$905$	711.013	−	260.328i	0.785649	−	0.287655i
$906$	−10.3342			−0.0114064
$907$	−1359.32			−1.49870			−0.749350	−	0.662174i	$-0.769634\pi$
$907$	−1359.32			−1.49870			−0.749350	+	0.662174i	$0.769634\pi$
$908$	−568.988			−0.626639
$909$	−60.6799			−0.0667546
$910$	−239.198	−	653.301i	−0.262855	−	0.717914i
$911$		−	413.072i		−	0.453427i	−0.973961	−	0.226714i	$-0.927202\pi$
$911$		−	413.072i		−	0.453427i	0.973961	−	0.226714i	$-0.0727982\pi$
$912$	−168.692			−0.184970
$913$			2489.96i			2.72723i
$914$			278.904i			0.305147i
$915$	31.3430	+	85.6046i	0.0342547	+	0.0935569i
$916$			854.040i			0.932358i
$917$	3151.11			3.43633
$918$	146.534			0.159623
$919$			88.1481i			0.0959174i	0.998849	+	0.0479587i	$0.0152716\pi$
$919$			88.1481i			0.0959174i	−0.998849	+	0.0479587i	$0.984728\pi$
$920$	313.226	−	87.6899i	0.340463	−	0.0953152i
$921$	−756.411			−0.821293
$922$		−	1119.80i		−	1.21453i
$923$		−	68.0464i		−	0.0737230i
$924$	−824.476			−0.892290
$925$	210.310	−	177.846i	0.227362	−	0.192266i
$926$	−318.433			−0.343880
$927$	−30.3230			−0.0327109
$928$			182.411i			0.196564i
$929$	1331.41			1.43317			0.716584	−	0.697501i	$-0.245705\pi$
$929$	1331.41			1.43317			0.716584	+	0.697501i	$0.245705\pi$
$930$	13.4183	+	36.6482i	0.0144282	+	0.0394066i
$931$		−	2883.74i		−	3.09746i
$932$			754.543i			0.809595i
$933$			165.259i			0.177127i
$934$		−	6.16589i		−	0.00660160i
$935$	1722.09	−	630.523i	1.84181	−	0.674356i
$936$	−64.5192			−0.0689307
$937$	547.333			0.584134			0.292067	−	0.956398i	$-0.405657\pi$
$937$	547.333			0.584134			0.292067	+	0.956398i	$0.405657\pi$
$938$		−	1321.81i		−	1.40918i
$939$		−	480.773i		−	0.512006i
$940$	746.203	−	273.213i	0.793833	−	0.290652i
$941$		−	1213.44i		−	1.28952i	−0.764383	−	0.644762i	$-0.776957\pi$
$941$		−	1213.44i		−	1.28952i	0.764383	−	0.644762i	$-0.223043\pi$
$942$	−313.508			−0.332811
$943$	−1385.87	−	108.330i	−1.46964	−	0.114878i
$944$	20.6480			0.0218729
$945$	−315.688	+	115.585i	−0.334061	+	0.122312i
$946$	−1309.98			−1.38475
$947$		−	320.019i		−	0.337929i	−0.985622	−	0.168964i	$-0.945958\pi$
$947$		−	320.019i		−	0.337929i	0.985622	−	0.168964i	$-0.0540423\pi$
$948$	−4.68554			−0.00494256
$949$	−537.063			−0.565925
$950$	−657.332	+	555.865i	−0.691929	+	0.585121i
$951$	−76.0911			−0.0800117
$952$			729.809i			0.766606i
$953$	−9.42027			−0.00988486			−0.00494243	−	0.999988i	$-0.501573\pi$
$953$	−9.42027			−0.00988486			−0.00494243	+	0.999988i	$0.501573\pi$
$954$			390.817i			0.409662i
$955$	1393.55	−	510.232i	1.45922	−	0.534274i
$956$	−225.698			−0.236086
$957$	1027.31			1.07347
$958$	−371.651			−0.387945
$959$	888.641			0.926633
$960$	−65.0584	+	23.8203i	−0.0677692	+	0.0248128i
$961$	−950.846			−0.989434
$962$	118.468			0.123148
$963$	179.781			0.186688
$964$		−	298.541i		−	0.309690i
$965$	−126.370	+	46.2686i	−0.130953	+	0.0479467i
$966$	726.782	+	56.8106i	0.752362	+	0.0588101i
$967$		−	1077.67i		−	1.11445i	−0.830363	−	0.557223i	$-0.811867\pi$
$967$		−	1077.67i		−	1.11445i	0.830363	−	0.557223i	$-0.188133\pi$
$968$			614.673i			0.634993i
$969$	840.962			0.867865
$970$	−1099.92	+	402.720i	−1.13393	+	0.415175i
$971$			492.034i			0.506729i	0.967371	+	0.253365i	$0.0815373\pi$
$971$			492.034i			0.506729i	−0.967371	+	0.253365i	$0.918463\pi$
$972$			31.1769i			0.0320750i
$973$	−1770.17			−1.81929
$974$	453.065			0.465159
$975$	−251.407	+	212.600i	−0.257854	+	0.218051i
$976$			42.1060i			0.0431414i
$977$	528.771			0.541219			0.270610	−	0.962689i	$-0.412775\pi$
$977$	528.771			0.541219			0.270610	+	0.962689i	$0.412775\pi$
$978$		−	132.011i		−	0.134980i
$979$	−771.467			−0.788016
$980$	−407.200	−	1112.15i	−0.415510	−	1.13485i
$981$			132.147i			0.134706i
$982$			253.487i			0.258133i
$983$	−883.852			−0.899137			−0.449569	−	0.893246i	$-0.648422\pi$
$983$	−883.852			−0.899137			−0.449569	+	0.893246i	$0.648422\pi$
$984$	296.090			0.300905
$985$	−289.168	+	105.875i	−0.293571	+	0.107487i
$986$		−	909.352i		−	0.922264i
$987$	1780.98			1.80443
$988$	−370.278			−0.374775
$989$	1154.76	+	90.2642i	1.16760	+	0.0912681i
$990$	134.152	+	366.398i	0.135507	+	0.370099i
$991$	−1016.15			−1.02537			−0.512687	−	0.858576i	$-0.671350\pi$
$991$	−1016.15			−1.02537			−0.512687	+	0.858576i	$0.671350\pi$
$992$			18.0260i			0.0181714i
$993$			779.188i			0.784681i
$994$		−	163.765i		−	0.164753i
$995$	165.898	−	60.7414i	0.166732	−	0.0610466i
$996$			468.943i			0.470826i
$997$			811.334i			0.813776i	0.913478	+	0.406888i	$0.133386\pi$
$997$			811.334i			0.813776i	−0.913478	+	0.406888i	$0.866614\pi$
$998$		−	21.1541i		−	0.0211965i
$999$		−	57.2463i		−	0.0573036i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.f.a.229.4	yes	48
5.4	even	2	inner	690.3.f.a.229.1	✓	48
23.22	odd	2	inner	690.3.f.a.229.3	yes	48
115.114	odd	2	inner	690.3.f.a.229.2	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.f.a.229.1	✓	48	5.4	even	2	inner
690.3.f.a.229.2	yes	48	115.114	odd	2	inner
690.3.f.a.229.3	yes	48	23.22	odd	2	inner
690.3.f.a.229.4	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)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} -1.73205i q^{3} -2.00000 q^{4} +(1.71908 + 4.69518i) q^{5} +2.44949 q^{6} +12.9397 q^{7} -2.82843i q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+1.41421i q^{2} -1.73205i q^{3} -2.00000 q^{4} +(1.71908 + 4.69518i) q^{5} +2.44949 q^{6} +12.9397 q^{7} -2.82843i q^{8} -3.00000 q^{9} +(-6.63999 + 2.43115i) q^{10} +18.3935i q^{11} +3.46410i q^{12} +7.60366i q^{13} +18.2995i q^{14} +(8.13230 - 2.97754i) q^{15} +4.00000 q^{16} -19.9407 q^{17} -4.24264i q^{18} -24.3487i q^{19} +(-3.43816 - 9.39037i) q^{20} -22.4122i q^{21} -26.0123 q^{22} +(22.9301 + 1.79238i) q^{23} -4.89898 q^{24} +(-19.0895 + 16.1428i) q^{25} -10.7532 q^{26} +5.19615i q^{27} -25.8794 q^{28} +32.2461 q^{29} +(4.21087 + 11.5008i) q^{30} +3.18657 q^{31} +5.65685i q^{32} +31.8584 q^{33} -28.2004i q^{34} +(22.2444 + 60.7542i) q^{35} +6.00000 q^{36} -11.0170 q^{37} +34.4342 q^{38} +13.1699 q^{39} +(13.2800 - 4.86230i) q^{40} -60.4391 q^{41} +31.6956 q^{42} +50.3599 q^{43} -36.7869i q^{44} +(-5.15724 - 14.0856i) q^{45} +(-2.53481 + 32.4280i) q^{46} +79.4647i q^{47} -6.92820i q^{48} +118.435 q^{49} +(-22.8294 - 26.9967i) q^{50} +34.5383i q^{51} -15.2073i q^{52} -92.1165 q^{53} -7.34847 q^{54} +(-86.3608 + 31.6199i) q^{55} -36.5989i q^{56} -42.1731 q^{57} +45.6028i q^{58} +5.16200 q^{59} +(-16.2646 + 5.95507i) q^{60} +10.5265i q^{61} +4.50650i q^{62} -38.8190 q^{63} -8.00000 q^{64} +(-35.7006 + 13.0713i) q^{65} +45.0546i q^{66} -72.2321 q^{67} +39.8814 q^{68} +(3.10449 - 39.7160i) q^{69} +(-85.9194 + 31.4583i) q^{70} -8.94916 q^{71} +8.48528i q^{72} +70.6321i q^{73} -15.5805i q^{74} +(27.9602 + 33.0640i) q^{75} +48.6973i q^{76} +238.006i q^{77} +18.6251i q^{78} +1.35260i q^{79} +(6.87633 + 18.7807i) q^{80} +9.00000 q^{81} -85.4739i q^{82} +135.372 q^{83} +44.8244i q^{84} +(-34.2797 - 93.6253i) q^{85} +71.2197i q^{86} -55.8518i q^{87} +52.0246 q^{88} +41.9425i q^{89} +(19.9200 - 7.29345i) q^{90} +98.3889i q^{91} +(-45.8601 - 3.58476i) q^{92} -5.51931i q^{93} -112.380 q^{94} +(114.321 - 41.8573i) q^{95} +9.79796 q^{96} +165.650 q^{97} +167.493i q^{98} -55.1804i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 96 q^{4} - 144 q^{9}+O(q^{10}) \) 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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