LMFDB - Embedded newform 810.3.j.g.539.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [810,3,Mod(269,810)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(810, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

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

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

chi := DirichletCharacter("810.269");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	810.j (of order $6$, degree $2$, not 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:	$22.0709014132$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			539.3
Character	$\chi$	$=$	810.539
Dual form			810.3.j.g.269.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-1.24727 + 4.84193i) q^{5} +(0.315907 - 0.182389i) q^{7} +2.82843 q^{8} +O(q^{10})$	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-1.24727 + 4.84193i) q^{5} +(0.315907 - 0.182389i) q^{7} +2.82843 q^{8} +(6.81209 - 1.89618i) q^{10} +(8.32536 - 4.80665i) q^{11} +(-6.62954 - 3.82757i) q^{13} +(-0.446760 - 0.257937i) q^{14} +(-2.00000 - 3.46410i) q^{16} +12.3400 q^{17} +5.36509 q^{19} +(-7.13920 - 7.00227i) q^{20} +(-11.7738 - 6.79763i) q^{22} +(-6.03305 + 10.4495i) q^{23} +(-21.8886 - 12.0784i) q^{25} +10.8260i q^{26} +0.729555i q^{28} +(27.1888 - 15.6975i) q^{29} +(-2.45982 + 4.26054i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(-8.72566 - 15.1133i) q^{34} +(0.489094 + 1.75709i) q^{35} +40.2567i q^{37} +(-3.79369 - 6.57087i) q^{38} +(-3.52781 + 13.6951i) q^{40} +(54.8152 + 31.6476i) q^{41} +(-46.6042 + 26.9070i) q^{43} +19.2266i q^{44} +17.0640 q^{46} +(14.1167 + 24.4509i) q^{47} +(-24.4335 + 42.3200i) q^{49} +(0.684649 + 35.3487i) q^{50} +(13.2591 - 7.65513i) q^{52} -41.6903 q^{53} +(12.8895 + 46.3060i) q^{55} +(0.893519 - 0.515874i) q^{56} +(-38.4508 - 22.1996i) q^{58} +(97.2149 + 56.1271i) q^{59} +(-22.9787 - 39.8003i) q^{61} +6.95743 q^{62} +8.00000 q^{64} +(26.8016 - 27.3258i) q^{65} +(39.9594 + 23.0706i) q^{67} +(-12.3400 + 21.3734i) q^{68} +(1.80614 - 1.84146i) q^{70} +125.617i q^{71} +59.0826i q^{73} +(49.3042 - 28.4658i) q^{74} +(-5.36509 + 9.29261i) q^{76} +(1.75336 - 3.03691i) q^{77} +(-25.3435 - 43.8963i) q^{79} +(19.2675 - 5.36320i) q^{80} -89.5128i q^{82} +(29.5183 + 51.1271i) q^{83} +(-15.3913 + 59.7492i) q^{85} +(65.9083 + 38.0522i) q^{86} +(23.5477 - 13.5953i) q^{88} -8.93057i q^{89} -2.79242 q^{91} +(-12.0661 - 20.8991i) q^{92} +(19.9641 - 34.5788i) q^{94} +(-6.69172 + 25.9774i) q^{95} +(113.714 - 65.6530i) q^{97} +69.1083 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{4} - 24 q^{7}+O(q^{10}) $ 24 * q - 24 * q^4 - 24 * q^7	$ 24 q - 24 q^{4} - 24 q^{7} - 12 q^{10} - 48 q^{13} - 48 q^{16} + 120 q^{22} + 24 q^{25} + 60 q^{34} + 24 q^{43} - 36 q^{49} + 96 q^{52} + 216 q^{55} - 396 q^{58} - 60 q^{61} + 192 q^{64} + 1032 q^{67} - 480 q^{70} - 240 q^{79} - 396 q^{85} - 240 q^{88} + 48 q^{91} - 48 q^{94} + 1440 q^{97}+O(q^{100}) $ 24 * q - 24 * q^4 - 24 * q^7 - 12 * q^10 - 48 * q^13 - 48 * q^16 + 120 * q^22 + 24 * q^25 + 60 * q^34 + 24 * q^43 - 36 * q^49 + 96 * q^52 + 216 * q^55 - 396 * q^58 - 60 * q^61 + 192 * q^64 + 1032 * q^67 - 480 * q^70 - 240 * q^79 - 396 * q^85 - 240 * q^88 + 48 * q^91 - 48 * q^94 + 1440 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.707107	−	1.22474i	−0.353553	−	0.612372i
$2$	−0.707107	−	1.22474i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−1.00000	+	1.73205i	−0.250000	+	0.433013i
$5$	−1.24727	+	4.84193i	−0.249454	+	0.968387i
$5$	−1.24727	+	4.84193i	−0.249454	+	0.968387i
$6$		0			0
$7$	0.315907	−	0.182389i	0.0451295	−	0.0260556i	−0.477265	−	0.878759i	$-0.658372\pi$
$7$	0.315907	−	0.182389i	0.0451295	−	0.0260556i	0.522395	+	0.852704i	$0.325039\pi$
$8$	2.82843			0.353553
$9$		0			0
$10$	6.81209	−	1.89618i	0.681209	−	0.189618i
$11$	8.32536	−	4.80665i	0.756851	−	0.436968i	−0.0713128	−	0.997454i	$-0.522719\pi$
$11$	8.32536	−	4.80665i	0.756851	−	0.436968i	0.828164	+	0.560486i	$0.189386\pi$
$12$		0			0
$13$	−6.62954	−	3.82757i	−0.509965	−	0.294428i	0.222854	−	0.974852i	$-0.428463\pi$
$13$	−6.62954	−	3.82757i	−0.509965	−	0.294428i	−0.732819	+	0.680424i	$0.761796\pi$
$14$	−0.446760	−	0.257937i	−0.0319114	−	0.0184241i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	12.3400			0.725879			0.362940	−	0.931813i	$-0.381773\pi$
$17$	12.3400			0.725879			0.362940	+	0.931813i	$0.381773\pi$
$18$		0			0
$19$	5.36509			0.282373			0.141187	−	0.989983i	$-0.454908\pi$
$19$	5.36509			0.282373			0.141187	+	0.989983i	$0.454908\pi$
$20$	−7.13920	−	7.00227i	−0.356960	−	0.350113i
$21$		0			0
$22$	−11.7738	−	6.79763i	−0.535175	−	0.308983i
$23$	−6.03305	+	10.4495i	−0.262307	+	0.454328i	−0.966854	−	0.255328i	$-0.917816\pi$
$23$	−6.03305	+	10.4495i	−0.262307	+	0.454328i	0.704548	+	0.709656i	$0.251150\pi$
$24$		0			0
$25$	−21.8886	−	12.0784i	−0.875545	−	0.483136i
$26$			10.8260i			0.416384i
$27$		0			0
$28$			0.729555i			0.0260556i
$29$	27.1888	−	15.6975i	0.937545	−	0.541292i	0.0483548	−	0.998830i	$-0.484602\pi$
$29$	27.1888	−	15.6975i	0.937545	−	0.541292i	0.889190	+	0.457539i	$0.151269\pi$
$30$		0			0
$31$	−2.45982	+	4.26054i	−0.0793491	+	0.137437i	−0.902969	−	0.429705i	$-0.858618\pi$
$31$	−2.45982	+	4.26054i	−0.0793491	+	0.137437i	0.823620	+	0.567142i	$0.191951\pi$
$32$	−2.82843	+	4.89898i	−0.0883883	+	0.153093i
$33$		0			0
$34$	−8.72566	−	15.1133i	−0.256637	−	0.444509i
$35$	0.489094	+	1.75709i	0.0139741	+	0.0502025i
$36$		0			0
$37$			40.2567i			1.08802i	0.839079	+	0.544010i	$0.183095\pi$
$37$			40.2567i			1.08802i	−0.839079	+	0.544010i	$0.816905\pi$
$38$	−3.79369	−	6.57087i	−0.0998340	−	0.172918i
$39$		0			0
$40$	−3.52781	+	13.6951i	−0.0881953	+	0.342376i
$41$	54.8152	+	31.6476i	1.33696	+	0.771892i	0.986355	−	0.164633i	$-0.0526441\pi$
$41$	54.8152	+	31.6476i	1.33696	+	0.771892i	0.350601	+	0.936525i	$0.385977\pi$
$42$		0			0
$43$	−46.6042	+	26.9070i	−1.08382	+	0.625743i	−0.931924	−	0.362653i	$-0.881871\pi$
$43$	−46.6042	+	26.9070i	−1.08382	+	0.625743i	−0.151895	+	0.988397i	$0.548538\pi$
$44$			19.2266i			0.436968i
$45$		0			0
$46$	17.0640			0.370957
$47$	14.1167	+	24.4509i	0.300356	+	0.520232i	0.976217	−	0.216797i	$-0.0695611\pi$
$47$	14.1167	+	24.4509i	0.300356	+	0.520232i	−0.675860	+	0.737030i	$0.736228\pi$
$48$		0			0
$49$	−24.4335	+	42.3200i	−0.498642	+	0.863674i
$50$	0.684649	+	35.3487i	0.0136930	+	0.706974i
$51$		0			0
$52$	13.2591	−	7.65513i	0.254982	−	0.147214i
$53$	−41.6903			−0.786610			−0.393305	−	0.919408i	$-0.628668\pi$
$53$	−41.6903			−0.786610			−0.393305	+	0.919408i	$0.628668\pi$
$54$		0			0
$55$	12.8895	+	46.3060i	0.234355	+	0.841928i
$56$	0.893519	−	0.515874i	0.0159557	−	0.00921203i
$57$		0			0
$58$	−38.4508	−	22.1996i	−0.662944	−	0.382751i
$59$	97.2149	+	56.1271i	1.64771	+	0.951306i	0.977979	+	0.208702i	$0.0669240\pi$
$59$	97.2149	+	56.1271i	1.64771	+	0.951306i	0.669731	+	0.742604i	$0.266409\pi$
$60$		0			0
$61$	−22.9787	−	39.8003i	−0.376701	−	0.652465i	0.613879	−	0.789400i	$-0.289608\pi$
$61$	−22.9787	−	39.8003i	−0.376701	−	0.652465i	−0.990580	+	0.136935i	$0.956275\pi$
$62$	6.95743			0.112217
$63$		0			0
$64$	8.00000			0.125000
$65$	26.8016	−	27.3258i	0.412333	−	0.420397i
$66$		0			0
$67$	39.9594	+	23.0706i	0.596409	+	0.344337i	0.767628	−	0.640896i	$-0.221437\pi$
$67$	39.9594	+	23.0706i	0.596409	+	0.344337i	−0.171218	+	0.985233i	$0.554770\pi$
$68$	−12.3400	+	21.3734i	−0.181470	+	0.314315i
$69$		0			0
$70$	1.80614	−	1.84146i	0.0258020	−	0.0263066i
$71$			125.617i			1.76926i	0.466295	+	0.884629i	$0.345588\pi$
$71$			125.617i			1.76926i	−0.466295	+	0.884629i	$0.654412\pi$
$72$		0			0
$73$			59.0826i			0.809351i	0.914460	+	0.404676i	$0.132616\pi$
$73$			59.0826i			0.809351i	−0.914460	+	0.404676i	$0.867384\pi$
$74$	49.3042	−	28.4658i	0.666273	−	0.384673i
$75$		0			0
$76$	−5.36509	+	9.29261i	−0.0705933	+	0.122271i
$77$	1.75336	−	3.03691i	0.0227709	−	0.0394404i
$78$		0			0
$79$	−25.3435	−	43.8963i	−0.320804	−	0.555649i	0.659850	−	0.751397i	$-0.270620\pi$
$79$	−25.3435	−	43.8963i	−0.320804	−	0.555649i	−0.980654	+	0.195748i	$0.937287\pi$
$80$	19.2675	−	5.36320i	0.240844	−	0.0670400i
$81$		0			0
$82$		−	89.5128i		−	1.09162i
$83$	29.5183	+	51.1271i	0.355642	+	0.615990i	0.987228	−	0.159316i	$-0.0509290\pi$
$83$	29.5183	+	51.1271i	0.355642	+	0.615990i	−0.631586	+	0.775306i	$0.717596\pi$
$84$		0			0
$85$	−15.3913	+	59.7492i	−0.181074	+	0.702932i
$86$	65.9083	+	38.0522i	0.766376	+	0.442467i
$87$		0			0
$88$	23.5477	−	13.5953i	0.267587	−	0.154492i
$89$		−	8.93057i		−	0.100344i	−0.998741	−	0.0501718i	$-0.984023\pi$
$89$		−	8.93057i		−	0.100344i	0.998741	−	0.0501718i	$-0.0159769\pi$
$90$		0			0
$91$	−2.79242			−0.0306860
$92$	−12.0661	−	20.8991i	−0.131153	−	0.227164i
$93$		0			0
$94$	19.9641	−	34.5788i	0.212384	−	0.367860i
$95$	−6.69172	+	25.9774i	−0.0704391	+	0.273447i
$96$		0			0
$97$	113.714	−	65.6530i	1.17231	−	0.676835i	0.218089	−	0.975929i	$-0.430018\pi$
$97$	113.714	−	65.6530i	1.17231	−	0.676835i	0.954224	+	0.299093i	$0.0966842\pi$
$98$	69.1083			0.705187
$99$		0			0
$100$	42.8090	−	25.8338i	0.428090	−	0.258338i
$101$	−9.48116	+	5.47395i	−0.0938729	+	0.0541975i	−0.546202	−	0.837654i	$-0.683927\pi$
$101$	−9.48116	+	5.47395i	−0.0938729	+	0.0541975i	0.452329	+	0.891851i	$0.350593\pi$
$102$		0			0
$103$	−45.4294	−	26.2287i	−0.441063	−	0.254648i	0.262986	−	0.964800i	$-0.415293\pi$
$103$	−45.4294	−	26.2287i	−0.441063	−	0.254648i	−0.704048	+	0.710152i	$0.748626\pi$
$104$	−18.7512	−	10.8260i	−0.180300	−	0.104096i
$105$		0			0
$106$	29.4795	+	51.0600i	0.278109	+	0.481698i
$107$	−189.947			−1.77521			−0.887603	−	0.460608i	$-0.847631\pi$
$107$	−189.947			−1.77521			−0.887603	+	0.460608i	$0.847631\pi$
$108$		0			0
$109$	142.655			1.30876			0.654382	−	0.756164i	$-0.272929\pi$
$109$	142.655			1.30876			0.654382	+	0.756164i	$0.272929\pi$
$110$	47.5988	−	48.5297i	0.432717	−	0.441179i
$111$		0			0
$112$	−1.26363	−	0.729555i	−0.0112824	−	0.00651389i
$113$	40.8390	−	70.7352i	0.361407	−	0.625975i	−0.626786	−	0.779192i	$-0.715630\pi$
$113$	40.8390	−	70.7352i	0.361407	−	0.625975i	0.988193	+	0.153216i	$0.0489632\pi$
$114$		0			0
$115$	−43.0712	−	42.2450i	−0.374532	−	0.367348i
$116$			62.7898i			0.541292i
$117$		0			0
$118$		−	158.751i		−	1.34535i
$119$	3.89827	−	2.25067i	0.0327586	−	0.0189132i
$120$		0			0
$121$	−14.2922	+	24.7548i	−0.118117	+	0.204585i
$122$	−32.4968	+	56.2862i	−0.266368	+	0.461362i
$123$		0			0
$124$	−4.91964	−	8.52107i	−0.0396745	−	0.0687183i
$125$	85.7838	−	90.9183i	0.686271	−	0.727346i
$126$		0			0
$127$		−	83.4011i		−	0.656701i	−0.944556	−	0.328351i	$-0.893507\pi$
$127$		−	83.4011i		−	0.656701i	0.944556	−	0.328351i	$-0.106493\pi$
$128$	−5.65685	−	9.79796i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−52.4187	−	13.5029i	−0.403221	−	0.103869i
$131$	98.6364	+	56.9478i	0.752950	+	0.434716i	0.826759	−	0.562557i	$-0.190182\pi$
$131$	98.6364	+	56.9478i	0.752950	+	0.434716i	−0.0738090	+	0.997272i	$0.523516\pi$
$132$		0			0
$133$	1.69487	−	0.978533i	0.0127434	−	0.00735739i
$134$		−	65.2535i		−	0.486966i
$135$		0			0
$136$	34.9027			0.256637
$137$	76.3672	+	132.272i	0.557425	+	0.965488i	0.997710	+	0.0676304i	$0.0215439\pi$
$137$	76.3672	+	132.272i	0.557425	+	0.965488i	−0.440286	+	0.897858i	$0.645123\pi$
$138$		0			0
$139$	−50.2751	+	87.0790i	−0.361691	+	0.626467i	−0.988239	−	0.152915i	$-0.951134\pi$
$139$	−50.2751	+	87.0790i	−0.361691	+	0.626467i	0.626548	+	0.779383i	$0.284467\pi$
$140$	−3.53246	−	0.909953i	−0.0252318	−	0.00649966i
$141$		0			0
$142$	153.849	−	88.8249i	1.08345	−	0.625527i
$143$	−73.5911			−0.514623
$144$		0			0
$145$	42.0943	+	151.225i	0.290305	+	1.04293i
$146$	72.3612	−	41.7777i	0.495624	−	0.286149i
$147$		0			0
$148$	−69.7267	−	40.2567i	−0.471126	−	0.272005i
$149$	−22.4980	−	12.9892i	−0.150993	−	0.0871761i	0.422600	−	0.906316i	$-0.361118\pi$
$149$	−22.4980	−	12.9892i	−0.150993	−	0.0871761i	−0.573593	+	0.819140i	$0.694451\pi$
$150$		0			0
$151$	77.9769	+	135.060i	0.516403	+	0.894437i	0.999819	+	0.0190456i	$0.00606276\pi$
$151$	77.9769	+	135.060i	0.516403	+	0.894437i	−0.483415	+	0.875391i	$0.660604\pi$
$152$	15.1748			0.0998340
$153$		0			0
$154$	−4.95925			−0.0322029
$155$	−17.5612	−	17.2243i	−0.113298	−	0.111125i
$156$		0			0
$157$	218.848	+	126.352i	1.39394	+	0.804790i	0.993748	−	0.111643i	$-0.0356114\pi$
$157$	218.848	+	126.352i	1.39394	+	0.804790i	0.400188	+	0.916433i	$0.368945\pi$
$158$	−35.8412	+	62.0787i	−0.226843	+	0.392903i
$159$		0			0
$160$	−20.1927	−	19.8054i	−0.126204	−	0.123784i
$161$			4.40144i			0.0273382i
$162$		0			0
$163$			156.387i			0.959430i	0.877424	+	0.479715i	$0.159260\pi$
$163$			156.387i			0.959430i	−0.877424	+	0.479715i	$0.840740\pi$
$164$	−109.630	+	63.2951i	−0.668478	+	0.385946i
$165$		0			0
$166$	41.7451	−	72.3047i	0.251477	−	0.435570i
$167$	160.031	−	277.182i	0.958268	−	1.65977i	0.231564	−	0.972820i	$-0.425616\pi$
$167$	160.031	−	277.182i	0.958268	−	1.65977i	0.726705	−	0.686950i	$-0.241051\pi$
$168$		0			0
$169$	−55.1995	−	95.6083i	−0.326624	−	0.565729i
$170$	84.0608	−	23.3987i	0.494475	−	0.137640i
$171$		0			0
$172$		−	107.628i		−	0.625743i
$173$	19.8360	+	34.3570i	0.114659	+	0.198595i	0.917643	−	0.397405i	$-0.130089\pi$
$173$	19.8360	+	34.3570i	0.114659	+	0.198595i	−0.802984	+	0.596000i	$0.796756\pi$
$174$		0			0
$175$	−9.11773	+	0.176596i	−0.0521013	+	0.00100912i
$176$	−33.3015	−	19.2266i	−0.189213	−	0.109242i
$177$		0			0
$178$	−10.9377	+	6.31487i	−0.0614476	+	0.0354768i
$179$		−	51.3204i		−	0.286706i	−0.989672	−	0.143353i	$-0.954212\pi$
$179$		−	51.3204i		−	0.286706i	0.989672	−	0.143353i	$-0.0457884\pi$
$180$		0			0
$181$	−298.058			−1.64673			−0.823363	−	0.567515i	$-0.807905\pi$
$181$	−298.058			−1.64673			−0.823363	+	0.567515i	$0.807905\pi$
$182$	1.97454	+	3.42000i	0.0108491	+	0.0187912i
$183$		0			0
$184$	−17.0640	+	29.5558i	−0.0927394	+	0.160629i
$185$	−194.920	−	50.2110i	−1.05362	−	0.271411i
$186$		0			0
$187$	102.735	−	59.3138i	0.549383	−	0.317186i
$188$	−56.4670			−0.300356
$189$		0			0
$190$	36.5475	−	10.1732i	0.192355	−	0.0535430i
$191$	−186.106	+	107.448i	−0.974377	+	0.562557i	−0.900568	−	0.434716i	$-0.856849\pi$
$191$	−186.106	+	107.448i	−0.974377	+	0.562557i	−0.0738091	+	0.997272i	$0.523516\pi$
$192$		0			0
$193$	152.179	+	87.8608i	0.788494	+	0.455237i	0.839432	−	0.543464i	$-0.182888\pi$
$193$	152.179	+	87.8608i	0.788494	+	0.455237i	−0.0509379	+	0.998702i	$0.516221\pi$
$194$	−160.816	−	92.8474i	−0.828951	−	0.478595i
$195$		0			0
$196$	−48.8669	−	84.6400i	−0.249321	−	0.431837i
$197$	−147.580			−0.749136			−0.374568	−	0.927200i	$-0.622209\pi$
$197$	−147.580			−0.749136			−0.374568	+	0.927200i	$0.622209\pi$
$198$		0			0
$199$	−192.973			−0.969716			−0.484858	−	0.874593i	$-0.661129\pi$
$199$	−192.973			−0.969716			−0.484858	+	0.874593i	$0.661129\pi$
$200$	−61.9104	−	34.1629i	−0.309552	−	0.170814i
$201$		0			0
$202$	13.4084	+	7.74134i	0.0663781	+	0.0383234i
$203$	5.72608	−	9.91787i	0.0282073	−	0.0488565i
$204$		0			0
$205$	−221.605	+	225.938i	−1.08100	+	1.10214i
$206$			74.1860i			0.360126i
$207$		0			0
$208$			30.6205i			0.147214i
$209$	44.6663	−	25.7881i	0.213715	−	0.123388i
$210$		0			0
$211$	191.949	−	332.466i	0.909712	−	1.57567i	0.0952487	−	0.995454i	$-0.469635\pi$
$211$	191.949	−	332.466i	0.909712	−	1.57567i	0.814464	−	0.580215i	$-0.197031\pi$
$212$	41.6903	−	72.2097i	0.196652	−	0.340612i
$213$		0			0
$214$	134.313	+	232.637i	0.627630	+	1.08709i
$215$	−72.1537	−	259.215i	−0.335598	−	1.20565i
$216$		0			0
$217$			1.79458i			0.00826994i
$218$	−100.872	−	174.716i	−0.462718	−	0.801451i
$219$		0			0
$220$	−93.0939	−	23.9808i	−0.423154	−	0.109003i
$221$	−81.8082	−	47.2320i	−0.370173	−	0.213719i
$222$		0			0
$223$	−299.254	+	172.774i	−1.34195	+	0.774773i	−0.987093	−	0.160149i	$-0.948803\pi$
$223$	−299.254	+	172.774i	−1.34195	+	0.774773i	−0.354853	+	0.934922i	$0.615469\pi$
$224$			2.06349i			0.00921203i
$225$		0			0
$226$	−115.510			−0.511107
$227$	136.398	+	236.248i	0.600872	+	1.04074i	0.992689	+	0.120697i	$0.0385130\pi$
$227$	136.398	+	236.248i	0.600872	+	1.04074i	−0.391818	+	0.920043i	$0.628154\pi$
$228$		0			0
$229$	−0.0521213	+	0.0902767i	−0.000227604	+	0.000394221i	−0.866139	−	0.499803i	$-0.833406\pi$
$229$	−0.0521213	+	0.0902767i	−0.000227604	+	0.000394221i	0.865912	+	0.500197i	$0.166739\pi$
$230$	−21.2835	+	82.6230i	−0.0925368	+	0.359230i
$231$		0			0
$232$	76.9015	−	44.3991i	0.331472	−	0.191375i
$233$	317.302			1.36181			0.680905	−	0.732372i	$-0.261587\pi$
$233$	317.302			1.36181			0.680905	+	0.732372i	$0.261587\pi$
$234$		0			0
$235$	−135.997	+	37.8554i	−0.578711	+	0.161087i
$236$	−194.430	+	112.254i	−0.823855	+	0.475653i
$237$		0			0
$238$	−5.51299	−	3.18293i	−0.0231638	−	0.0133736i
$239$	−167.164	−	96.5123i	−0.699432	−	0.403817i	0.107704	−	0.994183i	$-0.465650\pi$
$239$	−167.164	−	96.5123i	−0.699432	−	0.403817i	−0.807136	+	0.590366i	$0.798983\pi$
$240$		0			0
$241$	157.363	+	272.561i	0.652959	+	1.13096i	0.982401	+	0.186783i	$0.0598061\pi$
$241$	157.363	+	272.561i	0.652959	+	1.13096i	−0.329442	+	0.944176i	$0.606861\pi$
$242$	40.4245			0.167043
$243$		0			0
$244$	91.9149			0.376701
$245$	−174.436	−	171.090i	−0.711982	−	0.698325i
$246$		0			0
$247$	−35.5681	−	20.5352i	−0.144000	−	0.0831387i
$248$	−6.95743	+	12.0506i	−0.0280541	+	0.0485912i
$249$		0			0
$250$	−172.010	−	40.7744i	−0.688040	−	0.163097i
$251$			57.1694i			0.227767i	0.993494	+	0.113883i	$0.0363290\pi$
$251$			57.1694i			0.227767i	−0.993494	+	0.113883i	$0.963671\pi$
$252$		0			0
$253$			115.995i			0.458479i
$254$	−102.145	+	58.9735i	−0.402146	+	0.232179i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	35.8560	−	62.1044i	0.139517	−	0.241651i	−0.787797	−	0.615935i	$-0.788778\pi$
$257$	35.8560	−	62.1044i	0.139517	−	0.241651i	0.927314	+	0.374284i	$0.122112\pi$
$258$		0			0
$259$	7.34238	+	12.7174i	0.0283490	+	0.0491018i
$260$	20.5280	+	73.7476i	0.0789538	+	0.283645i
$261$		0			0
$262$		−	161.073i		−	0.614781i
$263$	−114.235	−	197.861i	−0.434353	−	0.752322i	0.562889	−	0.826532i	$-0.309690\pi$
$263$	−114.235	−	197.861i	−0.434353	−	0.752322i	−0.997243	+	0.0742102i	$0.976356\pi$
$264$		0			0
$265$	51.9991	−	201.862i	0.196223	−	0.761742i
$266$	−2.39691	−	1.38385i	−0.00901093	−	0.00520246i
$267$		0			0
$268$	−79.9188	+	46.1412i	−0.298205	+	0.172169i
$269$		−	8.79629i		−	0.0326999i	−0.999866	−	0.0163500i	$-0.994795\pi$
$269$		−	8.79629i		−	0.0326999i	0.999866	−	0.0163500i	$-0.00520459\pi$
$270$		0			0
$271$	0.783006			0.00288932			0.00144466	−	0.999999i	$-0.499540\pi$
$271$	0.783006			0.00288932			0.00144466	+	0.999999i	$0.499540\pi$
$272$	−24.6799	−	42.7468i	−0.0907349	−	0.157158i
$273$		0			0
$274$	108.000	−	187.061i	0.394159	−	0.682703i
$275$	−240.287	+	4.65399i	−0.873773	+	0.0169236i
$276$		0			0
$277$	408.921	−	236.091i	1.47625	−	0.852313i	0.476609	−	0.879115i	$-0.341866\pi$
$277$	408.921	−	236.091i	1.47625	−	0.852313i	0.999641	+	0.0268020i	$0.00853238\pi$
$278$	142.199			0.511509
$279$		0			0
$280$	1.38337	+	4.96979i	0.00494059	+	0.0177493i
$281$	−205.633	+	118.722i	−0.731790	+	0.422499i	−0.819076	−	0.573684i	$-0.805514\pi$
$281$	−205.633	+	118.722i	−0.731790	+	0.422499i	0.0872870	+	0.996183i	$0.472180\pi$
$282$		0			0
$283$	−230.663	−	133.173i	−0.815064	−	0.470577i	0.0336474	−	0.999434i	$-0.489288\pi$
$283$	−230.663	−	133.173i	−0.815064	−	0.470577i	−0.848711	+	0.528856i	$0.822621\pi$
$284$	−217.576	−	125.617i	−0.766111	−	0.442315i
$285$		0			0
$286$	52.0368	+	90.1303i	0.181947	+	0.315141i
$287$	23.0886			0.0804482
$288$		0			0
$289$	−136.726			−0.473099
$290$	155.447	−	158.487i	0.536025	−	0.546507i
$291$		0			0
$292$	−102.334	−	59.0826i	−0.350459	−	0.202338i
$293$	−165.793	+	287.162i	−0.565847	+	0.980075i	0.431124	+	0.902293i	$0.358117\pi$
$293$	−165.793	+	287.162i	−0.565847	+	0.980075i	−0.996970	+	0.0777821i	$0.975216\pi$
$294$		0			0
$295$	−393.017	+	400.703i	−1.33226	+	1.35831i
$296$			113.863i			0.384673i
$297$		0			0
$298$			36.7391i			0.123286i
$299$	79.9927	−	46.1838i	0.267534	−	0.154461i
$300$		0			0
$301$	−9.81506	+	17.0002i	−0.0326082	+	0.0564790i
$302$	110.276	−	191.004i	0.365152	−	0.632462i
$303$		0			0
$304$	−10.7302	−	18.5852i	−0.0352967	−	0.0611356i
$305$	221.371	−	61.6197i	0.725807	−	0.202032i
$306$		0			0
$307$		−	414.087i		−	1.34882i	−0.738358	−	0.674409i	$-0.764399\pi$
$307$		−	414.087i		−	1.34882i	0.738358	−	0.674409i	$-0.235601\pi$
$308$	3.50672	+	6.07381i	0.0113855	+	0.0197202i
$309$		0			0
$310$	−8.67779	+	33.6874i	−0.0279929	+	0.108669i
$311$	−427.244	−	246.669i	−1.37377	−	0.793149i	−0.382374	−	0.924008i	$-0.624893\pi$
$311$	−427.244	−	246.669i	−1.37377	−	0.793149i	−0.991401	+	0.130858i	$0.958227\pi$
$312$		0			0
$313$	−95.3452	+	55.0476i	−0.304617	+	0.175871i	−0.644515	−	0.764591i	$-0.722941\pi$
$313$	−95.3452	+	55.0476i	−0.304617	+	0.175871i	0.339898	+	0.940462i	$0.389607\pi$
$314$		−	357.377i		−	1.13814i
$315$		0			0
$316$	101.374			0.320804
$317$	−49.7880	−	86.2353i	−0.157060	−	0.272036i	0.776747	−	0.629812i	$-0.216868\pi$
$317$	−49.7880	−	86.2353i	−0.157060	−	0.272036i	−0.933807	+	0.357777i	$0.883535\pi$
$318$		0			0
$319$	150.904	−	261.374i	0.473055	−	0.819355i
$320$	−9.97816	+	38.7355i	−0.0311817	+	0.121048i
$321$		0			0
$322$	5.39065	−	3.11229i	0.0167411	−	0.00966550i
$323$	66.2050			0.204969
$324$		0			0
$325$	98.8807	+	163.854i	0.304248	+	0.504167i
$326$	191.534	−	110.582i	0.587528	−	0.339210i
$327$		0			0
$328$	155.041	+	89.5128i	0.472685	+	0.272905i
$329$	8.91915	+	5.14948i	0.0271099	+	0.0156519i
$330$		0			0
$331$	−99.4038	−	172.172i	−0.300314	−	0.520158i	0.675893	−	0.736999i	$-0.263758\pi$
$331$	−99.4038	−	172.172i	−0.300314	−	0.520158i	−0.976207	+	0.216841i	$0.930425\pi$
$332$	−118.073			−0.355642
$333$		0			0
$334$	−452.636			−1.35520
$335$	−161.546	+	164.706i	−0.482228	+	0.491658i
$336$		0			0
$337$	281.276	+	162.395i	0.834648	+	0.481884i	0.855441	−	0.517900i	$-0.173286\pi$
$337$	281.276	+	162.395i	0.834648	+	0.481884i	−0.0207935	+	0.999784i	$0.506619\pi$
$338$	−78.0638	+	135.211i	−0.230958	+	0.400031i
$339$		0			0
$340$	−88.0974	−	86.4076i	−0.259110	−	0.254140i
$341$			47.2940i			0.138692i
$342$		0			0
$343$			35.6997i			0.104081i
$344$	−131.817	+	76.1044i	−0.383188	+	0.221234i
$345$		0			0
$346$	28.0523	−	48.5881i	0.0810761	−	0.140428i
$347$	220.679	−	382.228i	0.635963	−	1.10152i	−0.350347	−	0.936620i	$-0.613936\pi$
$347$	220.679	−	382.228i	0.635963	−	1.10152i	0.986310	−	0.164901i	$-0.0527304\pi$
$348$		0			0
$349$	0.0673877	+	0.116719i	0.000193088	+	0.000334438i	0.866122	−	0.499833i	$-0.166605\pi$
$349$	0.0673877	+	0.116719i	0.000193088	+	0.000334438i	−0.865929	+	0.500167i	$0.833272\pi$
$350$	6.66350	+	11.0420i	0.0190386	+	0.0315486i
$351$		0			0
$352$			54.3811i			0.154492i
$353$	−261.124	−	452.281i	−0.739729	−	1.28125i	−0.952617	−	0.304172i	$-0.901620\pi$
$353$	−261.124	−	452.281i	−0.739729	−	1.28125i	0.212888	−	0.977077i	$-0.431713\pi$
$354$		0			0
$355$	−608.231	−	156.679i	−1.71333	−	0.441349i
$356$	15.4682	+	8.93057i	0.0434500	+	0.0250859i
$357$		0			0
$358$	−62.8544	+	36.2890i	−0.175571	+	0.101366i
$359$		−	146.484i		−	0.408034i	−0.978967	−	0.204017i	$-0.934600\pi$
$359$		−	146.484i		−	0.408034i	0.978967	−	0.204017i	$-0.0653998\pi$
$360$		0			0
$361$	−332.216			−0.920265
$362$	210.758	+	365.044i	0.582206	+	1.00841i
$363$		0			0
$364$	2.79242	−	4.83662i	0.00767149	−	0.0132874i
$365$	−286.074	−	73.6920i	−0.783765	−	0.201896i
$366$		0			0
$367$	294.167	−	169.838i	0.801546	−	0.462773i	−0.0424654	−	0.999098i	$-0.513521\pi$
$367$	294.167	−	169.838i	0.801546	−	0.462773i	0.844012	+	0.536325i	$0.180188\pi$
$368$	48.2644			0.131153
$369$		0			0
$370$	76.3339	+	274.232i	0.206308	+	0.741168i
$371$	−13.1703	+	7.60385i	−0.0354993	+	0.0204955i
$372$		0			0
$373$	378.262	+	218.390i	1.01411	+	0.585496i	0.912392	−	0.409318i	$-0.134233\pi$
$373$	378.262	+	218.390i	1.01411	+	0.585496i	0.101716	+	0.994813i	$0.467567\pi$
$374$	−145.289	−	83.8824i	−0.388472	−	0.224285i
$375$		0			0
$376$	39.9282	+	69.1577i	0.106192	+	0.183930i
$377$	−240.332			−0.637486
$378$		0			0
$379$	677.751			1.78826			0.894130	−	0.447807i	$-0.147795\pi$
$379$	677.751			1.78826			0.894130	+	0.447807i	$0.147795\pi$
$380$	−38.3025	−	37.5678i	−0.100796	−	0.0988627i
$381$		0			0
$382$	263.194	+	151.955i	0.688989	+	0.397788i
$383$	72.5570	−	125.672i	0.189444	−	0.328127i	−0.755621	−	0.655009i	$-0.772665\pi$
$383$	72.5570	−	125.672i	0.189444	−	0.328127i	0.945065	+	0.326882i	$0.105998\pi$
$384$		0			0
$385$	12.5176	+	12.2775i	0.0325132	+	0.0318896i
$386$		−	248.508i		−	0.643803i
$387$		0			0
$388$			262.612i			0.676835i
$389$	27.6862	−	15.9846i	0.0711728	−	0.0410916i	−0.463991	−	0.885840i	$-0.653583\pi$
$389$	27.6862	−	15.9846i	0.0711728	−	0.0410916i	0.535164	+	0.844748i	$0.320250\pi$
$390$		0			0
$391$	−74.4475	+	128.947i	−0.190403	+	0.329788i
$392$	−69.1083	+	119.699i	−0.176297	+	0.305355i
$393$		0			0
$394$	104.355	+	180.748i	0.264859	+	0.458750i
$395$	244.153	−	67.9612i	0.618109	−	0.172054i
$396$		0			0
$397$		−	399.771i		−	1.00698i	−0.864001	−	0.503490i	$-0.832049\pi$
$397$		−	399.771i		−	1.00698i	0.864001	−	0.503490i	$-0.167951\pi$
$398$	136.453	+	236.343i	0.342846	+	0.593827i
$399$		0			0
$400$	1.93648	+	99.9812i	0.00484120	+	0.249953i
$401$	68.8518	+	39.7516i	0.171700	+	0.0991311i	0.583387	−	0.812194i	$-0.301727\pi$
$401$	68.8518	+	39.7516i	0.171700	+	0.0991311i	−0.411687	+	0.911325i	$0.635060\pi$
$402$		0			0
$403$	32.6150	−	18.8303i	0.0809305	−	0.0467252i
$404$		−	21.8958i		−	0.0541975i
$405$		0			0
$406$	−16.1958			−0.0398912
$407$	193.500	+	335.152i	0.475430	+	0.823469i
$408$		0			0
$409$	−229.459	+	397.434i	−0.561024	+	0.971721i	0.436384	+	0.899761i	$0.356259\pi$
$409$	−229.459	+	397.434i	−0.561024	+	0.971721i	−0.997407	+	0.0719608i	$0.977074\pi$
$410$	433.415	+	111.647i	1.05711	+	0.272309i
$411$		0			0
$412$	90.8589	−	52.4574i	0.220531	−	0.127324i
$413$	40.9478			0.0991472
$414$		0			0
$415$	−284.371	+	79.1561i	−0.685232	+	0.190738i
$416$	37.5023	−	21.6520i	0.0901499	−	0.0520480i
$417$		0			0
$418$	−63.1678	−	36.4699i	−0.151119	−	0.0872486i
$419$	639.066	+	368.965i	1.52522	+	0.880585i	0.999553	+	0.0298924i	$0.00951646\pi$
$419$	639.066	+	368.965i	1.52522	+	0.880585i	0.525664	+	0.850692i	$0.323817\pi$
$420$		0			0
$421$	51.2781	+	88.8163i	0.121801	+	0.210965i	0.920478	−	0.390795i	$-0.127800\pi$
$421$	51.2781	+	88.8163i	0.121801	+	0.210965i	−0.798677	+	0.601760i	$0.794466\pi$
$422$	−542.915			−1.28653
$423$		0			0
$424$	−117.918			−0.278109
$425$	−270.105	−	149.047i	−0.635540	−	0.350698i
$426$		0			0
$427$	−14.5183	−	8.38213i	−0.0340006	−	0.0196303i
$428$	189.947	−	328.998i	0.443802	−	0.768687i
$429$		0			0
$430$	−266.452	+	271.662i	−0.619655	+	0.631773i
$431$		−	251.755i		−	0.584118i	−0.956400	−	0.292059i	$-0.905660\pi$
$431$		−	251.755i		−	0.584118i	0.956400	−	0.292059i	$-0.0943403\pi$
$432$		0			0
$433$			153.868i			0.355353i	0.984089	+	0.177676i	$0.0568581\pi$
$433$			153.868i			0.355353i	−0.984089	+	0.177676i	$0.943142\pi$
$434$	2.19790	−	1.26896i	0.00506428	−	0.00292386i
$435$		0			0
$436$	−142.655	+	247.086i	−0.327191	+	0.566711i
$437$	−32.3679	+	56.0628i	−0.0740683	+	0.128290i
$438$		0			0
$439$	−246.438	−	426.843i	−0.561362	−	0.972308i	−0.997378	−	0.0723691i	$-0.976944\pi$
$439$	−246.438	−	426.843i	−0.561362	−	0.972308i	0.436016	−	0.899939i	$-0.356389\pi$
$440$	36.4570	+	130.973i	0.0828569	+	0.297667i
$441$		0			0
$442$			133.592i			0.302245i
$443$	258.290	+	447.372i	0.583048	+	1.00987i	0.995116	+	0.0987152i	$0.0314733\pi$
$443$	258.290	+	447.372i	0.583048	+	1.00987i	−0.412068	+	0.911153i	$0.635193\pi$
$444$		0			0
$445$	43.2412	+	11.1388i	0.0971713	+	0.0250311i
$446$	423.209	+	244.340i	0.948899	+	0.547847i
$447$		0			0
$448$	2.52725	−	1.45911i	0.00564119	−	0.00325694i
$449$			612.611i			1.36439i	0.731170	+	0.682195i	$0.238974\pi$
$449$			612.611i			1.36439i	−0.731170	+	0.682195i	$0.761026\pi$
$450$		0			0
$451$	608.475			1.34917
$452$	81.6780	+	141.470i	0.180703	+	0.312988i
$453$		0			0
$454$	192.896	−	334.105i	0.424880	−	0.735914i
$455$	3.48290	−	13.5207i	0.00765473	−	0.0297159i
$456$		0			0
$457$	764.584	−	441.433i	1.67305	−	0.965936i	0.707135	−	0.707079i	$-0.249987\pi$
$457$	764.584	−	441.433i	1.67305	−	0.965936i	0.965916	−	0.258857i	$-0.0833460\pi$
$458$	0.147421			0.000321880
$459$		0			0
$460$	116.242	−	32.3564i	0.252699	−	0.0703401i
$461$	297.353	−	171.677i	0.645017	−	0.372401i	−0.141527	−	0.989934i	$-0.545201\pi$
$461$	297.353	−	171.677i	0.645017	−	0.372401i	0.786545	+	0.617534i	$0.211868\pi$
$462$		0			0
$463$	−566.909	−	327.305i	−1.22442	−	0.706922i	−0.258566	−	0.965993i	$-0.583250\pi$
$463$	−566.909	−	327.305i	−1.22442	−	0.706922i	−0.965858	+	0.259072i	$0.916583\pi$
$464$	−108.755	−	62.7898i	−0.234386	−	0.135323i
$465$		0			0
$466$	−224.366	−	388.614i	−0.481473	−	0.833935i
$467$	−861.410			−1.84456			−0.922280	−	0.386522i	$-0.873676\pi$
$467$	−861.410			−1.84456			−0.922280	+	0.386522i	$0.873676\pi$
$468$		0			0
$469$	16.8313			0.0358876
$470$	142.528	+	139.794i	0.303251	+	0.297434i
$471$		0			0
$472$	274.965	+	158.751i	0.582554	+	0.336337i
$473$	−258.665	+	448.020i	−0.546860	+	0.947189i
$474$		0			0
$475$	−117.435	−	64.8017i	−0.247231	−	0.136425i
$476$			9.00268i			0.0189132i
$477$		0			0
$478$			272.978i			0.571084i
$479$	311.459	−	179.821i	0.650227	−	0.375409i	−0.138316	−	0.990388i	$-0.544169\pi$
$479$	311.459	−	179.821i	0.650227	−	0.375409i	0.788543	+	0.614979i	$0.210836\pi$
$480$		0			0
$481$	154.085	−	266.884i	0.320344	−	0.554852i
$482$	222.545	−	385.460i	0.461712	−	0.799709i
$483$		0			0
$484$	−28.5844	−	49.5097i	−0.0590587	−	0.102293i
$485$	176.055	+	632.485i	0.363000	+	1.30409i
$486$		0			0
$487$		−	771.071i		−	1.58331i	−0.610970	−	0.791654i	$-0.709220\pi$
$487$		−	771.071i		−	1.58331i	0.610970	−	0.791654i	$-0.290780\pi$
$488$	−64.9937	−	112.572i	−0.133184	−	0.230681i
$489$		0			0
$490$	−86.1967	+	334.618i	−0.175912	+	0.682893i
$491$	137.273	+	79.2546i	0.279578	+	0.161415i	0.633233	−	0.773962i	$-0.281728\pi$
$491$	137.273	+	79.2546i	0.279578	+	0.161415i	−0.353654	+	0.935376i	$0.615061\pi$
$492$		0			0
$493$	335.508	−	193.706i	0.680544	−	0.392912i
$494$			58.0825i			0.117576i
$495$		0			0
$496$	19.6786			0.0396745
$497$	22.9112	+	39.6834i	0.0460990	+	0.0798458i
$498$		0			0
$499$	−317.053	+	549.152i	−0.635377	+	1.10050i	0.351058	+	0.936354i	$0.385822\pi$
$499$	−317.053	+	549.152i	−0.635377	+	1.10050i	−0.986435	+	0.164151i	$0.947511\pi$
$500$	71.6913	+	239.500i	0.143383	+	0.479000i
$501$		0			0
$502$	70.0180	−	40.4249i	0.139478	−	0.0805277i
$503$	212.791			0.423043			0.211522	−	0.977373i	$-0.432158\pi$
$503$	212.791			0.423043			0.211522	+	0.977373i	$0.432158\pi$
$504$		0			0
$505$	−14.6789	−	52.7346i	−0.0290672	−	0.104425i
$506$	142.064	−	82.0209i	0.280760	−	0.162097i
$507$		0			0
$508$	144.455	+	83.4011i	0.284360	+	0.164175i
$509$	850.733	+	491.171i	1.67138	+	0.964973i	0.966866	+	0.255284i	$0.0821691\pi$
$509$	850.733	+	491.171i	1.67138	+	0.964973i	0.704516	+	0.709688i	$0.251164\pi$
$510$		0			0
$511$	10.7760	+	18.6646i	0.0210881	+	0.0365256i
$512$	22.6274			0.0441942
$513$		0			0
$514$	−101.416			−0.197307
$515$	183.660	−	187.252i	0.356622	−	0.363596i
$516$		0			0
$517$	235.054	+	135.709i	0.454650	+	0.262492i
$518$	10.3837	−	17.9851i	0.0200457	−	0.0347202i
$519$		0			0
$520$	75.8065	−	77.2890i	0.145782	−	0.148633i
$521$		−	148.759i		−	0.285525i	−0.989757	−	0.142763i	$-0.954401\pi$
$521$		−	148.759i		−	0.285525i	0.989757	−	0.142763i	$-0.0455986\pi$
$522$		0			0
$523$		−	896.212i		−	1.71360i	−0.515650	−	0.856799i	$-0.672450\pi$
$523$		−	896.212i		−	1.71360i	0.515650	−	0.856799i	$-0.327550\pi$
$524$	−197.273	+	113.896i	−0.376475	+	0.217358i
$525$		0			0
$526$	−161.553	+	279.817i	−0.307134	+	0.531972i
$527$	−30.3541	+	52.5748i	−0.0575979	+	0.0997625i
$528$		0			0
$529$	191.705	+	332.042i	0.362391	+	0.627679i
$530$	−283.998	+	79.0522i	−0.535845	+	0.149155i
$531$		0			0
$532$			3.91413i			0.00735739i
$533$	−242.266	−	419.617i	−0.454533	−	0.787275i
$534$		0			0
$535$	236.915	−	919.711i	0.442832	−	1.71909i
$536$	113.022	+	65.2535i	0.210863	+	0.121742i
$537$		0			0
$538$	−10.7732	+	6.21991i	−0.0200245	+	0.0115612i
$539$			469.773i			0.871563i
$540$		0			0
$541$	513.074			0.948381			0.474190	−	0.880422i	$-0.342741\pi$
$541$	513.074			0.948381			0.474190	+	0.880422i	$0.342741\pi$
$542$	−0.553669	−	0.958983i	−0.00102153	−	0.00176934i
$543$		0			0
$544$	−34.9027	+	60.4532i	−0.0641593	+	0.111127i
$545$	−177.930	+	690.727i	−0.326476	+	1.26739i
$546$		0			0
$547$	489.598	−	282.669i	0.895060	−	0.516763i	0.0194656	−	0.999811i	$-0.493804\pi$
$547$	489.598	−	282.669i	0.895060	−	0.516763i	0.875594	+	0.483048i	$0.160470\pi$
$548$	−305.469			−0.557425
$549$		0			0
$550$	175.609	+	291.000i	0.319289	+	0.529091i
$551$	145.870	−	84.2183i	0.264738	−	0.152846i
$552$		0			0
$553$	−16.0124	−	9.24476i	−0.0289555	−	0.0167175i
$554$	−578.302	−	333.883i	−1.04387	−	0.602676i
$555$		0			0
$556$	−100.550	−	174.158i	−0.180846	−	0.313234i
$557$	487.883			0.875913			0.437956	−	0.898996i	$-0.355702\pi$
$557$	487.883			0.875913			0.437956	+	0.898996i	$0.355702\pi$
$558$		0			0
$559$	411.953			0.736946
$560$	5.10854	−	5.20845i	0.00912240	−	0.00930080i
$561$		0			0
$562$	290.809	+	167.899i	0.517453	+	0.298752i
$563$	−145.172	+	251.445i	−0.257854	+	0.446616i	−0.965667	−	0.259784i	$-0.916349\pi$
$563$	−145.172	+	251.445i	−0.257854	+	0.446616i	0.707813	+	0.706400i	$0.249682\pi$
$564$		0			0
$565$	291.558	+	285.966i	0.516032	+	0.506134i
$566$			376.671i			0.665497i
$567$		0			0
$568$			355.300i			0.625527i
$569$	506.632	−	292.504i	0.890390	−	0.514067i	0.0163200	−	0.999867i	$-0.494805\pi$
$569$	506.632	−	292.504i	0.890390	−	0.514067i	0.874070	+	0.485800i	$0.161472\pi$
$570$		0			0
$571$	−324.738	+	562.462i	−0.568717	+	0.985048i	0.427976	+	0.903790i	$0.359227\pi$
$571$	−324.738	+	562.462i	−0.568717	+	0.985048i	−0.996693	+	0.0812573i	$0.974106\pi$
$572$	73.5911	−	127.464i	0.128656	−	0.222838i
$573$		0			0
$574$	−16.3261	−	28.2777i	−0.0284428	−	0.0492643i
$575$	258.269	−	155.857i	0.449164	−	0.271055i
$576$		0			0
$577$		−	362.217i		−	0.627760i	−0.949463	−	0.313880i	$-0.898371\pi$
$577$		−	362.217i		−	0.627760i	0.949463	−	0.313880i	$-0.101629\pi$
$578$	96.6796	+	167.454i	0.167266	+	0.289713i
$579$		0			0
$580$	−304.024	−	78.3159i	−0.524180	−	0.135027i
$581$	18.6500	+	10.7676i	0.0320999	+	0.0185329i
$582$		0			0
$583$	−347.087	+	200.391i	−0.595347	+	0.343723i
$584$			167.111i			0.286149i
$585$		0			0
$586$	468.933			0.800228
$587$	129.737	+	224.711i	0.221017	+	0.382812i	0.955117	−	0.296229i	$-0.0957291\pi$
$587$	129.737	+	224.711i	0.221017	+	0.382812i	−0.734100	+	0.679041i	$0.762396\pi$
$588$		0			0
$589$	−13.1972	+	22.8582i	−0.0224061	+	0.0388084i
$590$	768.663	+	198.006i	1.30282	+	0.335603i
$591$		0			0
$592$	139.453	−	80.5135i	0.235563	−	0.136002i
$593$	207.377			0.349709			0.174854	−	0.984594i	$-0.444055\pi$
$593$	207.377			0.349709			0.174854	+	0.984594i	$0.444055\pi$
$594$		0			0
$595$	6.03539	+	21.6824i	0.0101435	+	0.0364410i
$596$	44.9961	−	25.9785i	0.0754967	−	0.0435881i
$597$		0			0
$598$	−113.127	−	65.3138i	−0.189175	−	0.109220i
$599$	666.866	+	385.015i	1.11330	+	0.642764i	0.939682	−	0.342050i	$-0.111121\pi$
$599$	666.866	+	385.015i	1.11330	+	0.642764i	0.173617	+	0.984813i	$0.444454\pi$
$600$		0			0
$601$	−349.168	−	604.777i	−0.580979	−	1.00628i	−0.995364	−	0.0961831i	$-0.969337\pi$
$601$	−349.168	−	604.777i	−0.580979	−	1.00628i	0.414385	−	0.910102i	$-0.363997\pi$
$602$	27.7612			0.0461149
$603$		0			0
$604$	−311.908			−0.516403
$605$	−102.035	−	100.078i	−0.168653	−	0.165418i
$606$		0			0
$607$	−835.380	−	482.307i	−1.37624	−	0.794575i	−0.384539	−	0.923109i	$-0.625639\pi$
$607$	−835.380	−	482.307i	−1.37624	−	0.794575i	−0.991705	+	0.128534i	$0.958973\pi$
$608$	−15.1748	+	26.2835i	−0.0249585	+	0.0432294i
$609$		0			0
$610$	−232.002	−	227.552i	−0.380330	−	0.373035i
$611$		−	216.131i		−	0.353734i
$612$		0			0
$613$			123.585i			0.201607i	0.994906	+	0.100803i	$0.0321413\pi$
$613$			123.585i			0.201607i	−0.994906	+	0.100803i	$0.967859\pi$
$614$	−507.151	+	292.804i	−0.825979	+	0.476879i
$615$		0			0
$616$	4.95925	−	8.58967i	0.00805073	−	0.0139443i
$617$	−62.6768	+	108.559i	−0.101583	+	0.175947i	−0.912337	−	0.409440i	$-0.865724\pi$
$617$	−62.6768	+	108.559i	−0.101583	+	0.175947i	0.810754	+	0.585387i	$0.199057\pi$
$618$		0			0
$619$	−88.0358	−	152.482i	−0.142223	−	0.246337i	0.786111	−	0.618086i	$-0.212092\pi$
$619$	−88.0358	−	152.482i	−0.142223	−	0.246337i	−0.928333	+	0.371749i	$0.878758\pi$
$620$	47.3946	−	13.1925i	0.0764429	−	0.0212782i
$621$		0			0
$622$			697.686i			1.12168i
$623$	−1.62884	−	2.82123i	−0.00261451	−	0.00452846i
$624$		0			0
$625$	333.225	+	528.759i	0.533160	+	0.846015i
$626$	134.838	+	77.8490i	0.215397	+	0.124359i
$627$		0			0
$628$	−437.696	+	252.704i	−0.696968	+	0.402395i
$629$			496.766i			0.789771i
$630$		0			0
$631$	−154.760			−0.245262			−0.122631	−	0.992452i	$-0.539133\pi$
$631$	−154.760			−0.245262			−0.122631	+	0.992452i	$0.539133\pi$
$632$	−71.6824	−	124.157i	−0.113421	−	0.196452i
$633$		0			0
$634$	−70.4108	+	121.955i	−0.111058	+	0.192358i
$635$	403.823	+	104.024i	0.635941	+	0.163817i
$636$		0			0
$637$	323.965	−	187.041i	0.508580	−	0.293629i
$638$	−426.822			−0.669000
$639$		0			0
$640$	54.4967	−	15.1694i	0.0851511	−	0.0237022i
$641$	796.683	−	459.965i	1.24288	−	0.717574i	0.273196	−	0.961958i	$-0.411919\pi$
$641$	796.683	−	459.965i	1.24288	−	0.717574i	0.969679	+	0.244384i	$0.0785857\pi$
$642$		0			0
$643$	−544.318	−	314.262i	−0.846528	−	0.488743i	0.0129497	−	0.999916i	$-0.495878\pi$
$643$	−544.318	−	314.262i	−0.846528	−	0.488743i	−0.859478	+	0.511173i	$0.829211\pi$
$644$	−7.62353	−	4.40144i	−0.0118378	−	0.00683454i
$645$		0			0
$646$	−46.8140	−	81.0842i	−0.0724675	−	0.125517i
$647$	423.162			0.654037			0.327019	−	0.945018i	$-0.393956\pi$
$647$	423.162			0.654037			0.327019	+	0.945018i	$0.393956\pi$
$648$		0			0
$649$	1079.13			1.66276
$650$	130.761	−	236.966i	0.201170	−	0.364563i
$651$		0			0
$652$	−270.870	−	156.387i	−0.415445	−	0.239857i
$653$	−105.321	+	182.421i	−0.161288	+	0.279358i	−0.935331	−	0.353775i	$-0.884898\pi$
$653$	−105.321	+	182.421i	−0.161288	+	0.279358i	0.774043	+	0.633133i	$0.218231\pi$
$654$		0			0
$655$	−398.763	+	406.562i	−0.608799	+	0.620705i
$656$		−	253.180i		−	0.385946i
$657$		0			0
$658$		−	14.5649i		−	0.0221351i
$659$	336.939	−	194.532i	0.511288	−	0.295192i	−0.222075	−	0.975030i	$-0.571283\pi$
$659$	336.939	−	194.532i	0.511288	−	0.295192i	0.733363	+	0.679837i	$0.237950\pi$
$660$		0			0
$661$	−263.498	+	456.392i	−0.398636	+	0.690457i	−0.993558	−	0.113326i	$-0.963849\pi$
$661$	−263.498	+	456.392i	−0.398636	+	0.690457i	0.594922	+	0.803783i	$0.297183\pi$
$662$	−140.578	+	243.489i	−0.212354	+	0.367808i
$663$		0			0
$664$	83.4903	+	144.609i	0.125738	+	0.217785i
$665$	2.62403	+	9.42694i	0.00394591	+	0.0141758i
$666$		0			0
$667$			378.814i			0.567937i
$668$	320.062	+	554.363i	0.479134	+	0.829885i
$669$		0			0
$670$	315.953	+	81.3887i	0.471571	+	0.121476i
$671$	−382.613	−	220.902i	−0.570213	−	0.329212i
$672$		0			0
$673$	−326.464	+	188.484i	−0.485087	+	0.280065i	−0.722534	−	0.691335i	$-0.757023\pi$
$673$	−326.464	+	188.484i	−0.485087	+	0.280065i	0.237447	+	0.971401i	$0.423689\pi$
$674$		−	459.322i		−	0.681487i
$675$		0			0
$676$	220.798			0.326624
$677$	151.338	+	262.125i	0.223542	+	0.387185i	0.955881	−	0.293754i	$-0.0949048\pi$
$677$	151.338	+	262.125i	0.223542	+	0.387185i	−0.732339	+	0.680940i	$0.761571\pi$
$678$		0			0
$679$	23.9488	−	41.4805i	0.0352706	−	0.0610905i
$680$	−43.5330	+	168.996i	−0.0640192	+	0.248524i
$681$		0			0
$682$	57.9231	−	33.4419i	0.0849313	−	0.0490351i
$683$	−665.773			−0.974777			−0.487389	−	0.873185i	$-0.662050\pi$
$683$	−665.773			−0.974777			−0.487389	+	0.873185i	$0.662050\pi$
$684$		0			0
$685$	−735.702	+	204.786i	−1.07402	+	0.298958i
$686$	43.7230	−	25.2435i	0.0637362	−	0.0367981i
$687$		0			0
$688$	186.417	+	107.628i	0.270955	+	0.156436i
$689$	276.388	+	159.572i	0.401143	+	0.231600i
$690$		0			0
$691$	−355.665	−	616.031i	−0.514711	−	0.891506i	−0.999854	−	0.0170712i	$-0.994566\pi$
$691$	−355.665	−	616.031i	−0.514711	−	0.891506i	0.485143	−	0.874435i	$-0.338768\pi$
$692$	−79.3440			−0.114659
$693$		0			0
$694$	−624.175			−0.899388
$695$	−358.924	−	352.040i	−0.516437	−	0.506532i
$696$		0			0
$697$	676.417	+	390.529i	0.970469	+	0.560300i
$698$	0.0953007	−	0.165066i	0.000136534	−	0.000236484i
$699$		0			0
$700$	8.81186	−	15.9690i	0.0125884	−	0.0228128i
$701$		−	792.935i		−	1.13115i	−0.824698	−	0.565574i	$-0.808655\pi$
$701$		−	792.935i		−	1.13115i	0.824698	−	0.565574i	$-0.191345\pi$
$702$		0			0
$703$			215.981i			0.307228i
$704$	66.6029	−	38.4532i	0.0946064	−	0.0546210i
$705$		0			0
$706$	−369.286	+	639.621i	−0.523067	+	0.905979i
$707$	−1.99678	+	3.45852i	−0.00282429	+	0.00489182i
$708$		0			0
$709$	−605.619	−	1048.96i	−0.854188	−	1.47950i	−0.877396	−	0.479766i	$-0.840721\pi$
$709$	−605.619	−	1048.96i	−0.854188	−	1.47950i	0.0232083	−	0.999731i	$-0.492612\pi$
$710$	238.193	+	855.716i	0.335483	+	1.20523i
$711$		0			0
$712$		−	25.2595i		−	0.0354768i
$713$	−29.6805	−	51.4081i	−0.0416276	−	0.0721011i
$714$		0			0
$715$	91.7880	−	356.323i	0.128375	−	0.498354i
$716$	88.8895	+	51.3204i	0.124147	+	0.0716765i
$717$		0			0
$718$	−179.406	+	103.580i	−0.249869	+	0.144262i
$719$			239.649i			0.333309i	0.986015	+	0.166654i	$0.0532964\pi$
$719$			239.649i			0.333309i	−0.986015	+	0.166654i	$0.946704\pi$
$720$		0			0
$721$	−19.1353			−0.0265399
$722$	234.912	+	406.880i	0.325363	+	0.563545i
$723$		0			0
$724$	298.058	−	516.251i	0.411682	−	0.713054i
$725$	−784.726	+	15.1989i	−1.08238	+	0.0209640i
$726$		0			0
$727$	−958.582	+	553.438i	−1.31855	+	0.761262i	−0.983495	−	0.180938i	$-0.942087\pi$
$727$	−958.582	+	553.438i	−1.31855	+	0.761262i	−0.335051	+	0.942200i	$0.608753\pi$
$728$	−7.89816			−0.0108491
$729$		0			0
$730$	112.031	+	402.476i	0.153467	+	0.551337i
$731$	−575.094	+	332.031i	−0.786722	+	0.454214i
$732$		0			0
$733$	−245.992	−	142.023i	−0.335596	−	0.193756i	0.322727	−	0.946492i	$-0.395400\pi$
$733$	−245.992	−	142.023i	−0.335596	−	0.193756i	−0.658323	+	0.752736i	$0.728734\pi$
$734$	−416.016	−	240.187i	−0.566779	−	0.327230i
$735$		0			0
$736$	−34.1281	−	59.1116i	−0.0463697	−	0.0803146i
$737$	443.569			0.601857
$738$		0			0
$739$	−851.158			−1.15177			−0.575885	−	0.817531i	$-0.695342\pi$
$739$	−851.158			−1.15177			−0.575885	+	0.817531i	$0.695342\pi$
$740$	281.888	−	287.401i	0.380930	−	0.388380i
$741$		0			0
$742$	18.6256	+	10.7535i	0.0251018	+	0.0144925i
$743$	469.349	−	812.936i	0.631695	−	1.09413i	−0.355511	−	0.934672i	$-0.615693\pi$
$743$	469.349	−	812.936i	0.631695	−	1.09413i	0.987205	−	0.159455i	$-0.0509736\pi$
$744$		0			0
$745$	90.9542	−	92.7329i	0.122086	−	0.124474i
$746$		−	617.700i		−	0.828016i
$747$		0			0
$748$			237.255i			0.317186i
$749$	−60.0056	+	34.6442i	−0.0801143	+	0.0462540i
$750$		0			0
$751$	353.207	−	611.773i	0.470316	−	0.814611i	−0.529108	−	0.848555i	$-0.677473\pi$
$751$	353.207	−	611.773i	0.470316	−	0.814611i	0.999424	+	0.0339437i	$0.0108067\pi$
$752$	56.4670	−	97.8037i	0.0750891	−	0.130058i
$753$		0			0
$754$	169.941	+	294.346i	0.225385	+	0.390379i
$755$	−751.209	+	209.103i	−0.994979	+	0.276957i
$756$		0			0
$757$			624.266i			0.824658i	0.911035	+	0.412329i	$0.135284\pi$
$757$			624.266i			0.824658i	−0.911035	+	0.412329i	$0.864716\pi$
$758$	−479.242	−	830.072i	−0.632246	−	1.09508i
$759$		0			0
$760$	−18.9270	+	73.4752i	−0.0249040	+	0.0966779i
$761$	−679.179	−	392.124i	−0.892482	−	0.515275i	−0.0177283	−	0.999843i	$-0.505643\pi$
$761$	−679.179	−	392.124i	−0.892482	−	0.515275i	−0.874753	+	0.484568i	$0.838977\pi$
$762$		0			0
$763$	45.0658	−	26.0187i	0.0590639	−	0.0341006i
$764$		−	429.793i		−	0.562557i
$765$		0			0
$766$	−205.222			−0.267914
$767$	−429.660	−	744.193i	−0.560183	−	0.970265i
$768$		0			0
$769$	−338.456	+	586.223i	−0.440125	+	0.762319i	−0.997698	−	0.0678090i	$-0.978399\pi$
$769$	−338.456	+	586.223i	−0.440125	+	0.762319i	0.557573	+	0.830128i	$0.311732\pi$
$770$	6.18552	−	24.0124i	0.00803315	−	0.0311849i
$771$		0			0
$772$	−304.359	+	175.722i	−0.394247	+	0.227619i
$773$	1033.43			1.33691			0.668453	−	0.743754i	$-0.266957\pi$
$773$	1033.43			1.33691			0.668453	+	0.743754i	$0.266957\pi$
$774$		0			0
$775$	105.303	−	63.5466i	0.135874	−	0.0819956i
$776$	321.633	−	185.695i	0.414475	−	0.239297i
$777$		0			0
$778$	−39.1542	−	22.6057i	−0.0503268	−	0.0290562i
$779$	294.088	+	169.792i	0.377520	+	0.217962i
$780$		0			0
$781$	603.799	+	1045.81i	0.773110	+	1.33907i
$782$	210.569			0.269270
$783$		0			0
$784$	195.468			0.249321
$785$	−884.750	+	902.053i	−1.12707	+	1.14911i
$786$		0			0
$787$	−349.242	−	201.635i	−0.443763	−	0.256207i	0.261429	−	0.965223i	$-0.415806\pi$
$787$	−349.242	−	201.635i	−0.443763	−	0.256207i	−0.705193	+	0.709016i	$0.749140\pi$
$788$	147.580	−	255.616i	0.187284	−	0.324385i
$789$		0			0
$790$	−255.878	−	250.970i	−0.323896	−	0.317683i
$791$		−	29.7943i		−	0.0376666i
$792$		0			0
$793$			351.811i			0.443645i
$794$	−489.618	+	282.681i	−0.616647	+	0.356021i
$795$		0			0
$796$	192.973	−	334.240i	0.242429	−	0.419899i
$797$	−7.31120	+	12.6634i	−0.00917340	+	0.0158888i	−0.870576	−	0.492035i	$-0.836253\pi$
$797$	−7.31120	+	12.6634i	−0.00917340	+	0.0158888i	0.861402	+	0.507923i	$0.169587\pi$
$798$		0			0
$799$	174.200	+	301.723i	0.218022	+	0.377626i
$800$	121.082	−	73.0691i	0.151353	−	0.0913364i
$801$		0			0
$802$		−	112.434i		−	0.140193i
$803$	283.990	+	491.884i	0.353661	+	0.612558i
$804$		0			0
$805$	−21.3115	−	5.48979i	−0.0264739	−	0.00681961i
$806$	−46.1245	−	26.6300i	−0.0572265	−	0.0330397i
$807$		0			0
$808$	−26.8168	+	15.4827i	−0.0331891	+	0.0191617i
$809$			225.767i			0.279069i	0.990217	+	0.139535i	$0.0445607\pi$
$809$			225.767i			0.279069i	−0.990217	+	0.139535i	$0.955439\pi$
$810$		0			0
$811$	198.448			0.244696			0.122348	−	0.992487i	$-0.460958\pi$
$811$	198.448			0.244696			0.122348	+	0.992487i	$0.460958\pi$
$812$	11.4522	+	19.8357i	0.0141037	+	0.0244282i
$813$		0			0
$814$	273.650	−	473.976i	0.336180	−	0.582281i
$815$	−757.216	−	195.057i	−0.929099	−	0.239334i
$816$		0			0
$817$	−250.036	+	144.358i	−0.306042	+	0.176693i
$818$	649.007			0.793407
$819$		0			0
$820$	−169.732	−	609.769i	−0.206990	−	0.743621i
$821$	105.099	−	60.6790i	0.128013	−	0.0739086i	−0.434626	−	0.900611i	$-0.643119\pi$
$821$	105.099	−	60.6790i	0.128013	−	0.0739086i	0.562639	+	0.826703i	$0.309786\pi$
$822$		0			0
$823$	−214.396	−	123.782i	−0.260506	−	0.150403i	0.364059	−	0.931376i	$-0.381390\pi$
$823$	−214.396	−	123.782i	−0.260506	−	0.150403i	−0.624565	+	0.780973i	$0.714724\pi$
$824$	−128.494	−	74.1860i	−0.155939	−	0.0900315i
$825$		0			0
$826$	−28.9545	−	50.1506i	−0.0350538	−	0.0607150i
$827$	−457.912			−0.553703			−0.276851	−	0.960913i	$-0.589291\pi$
$827$	−457.912			−0.553703			−0.276851	+	0.960913i	$0.589291\pi$
$828$		0			0
$829$	−116.297			−0.140286			−0.0701429	−	0.997537i	$-0.522346\pi$
$829$	−116.297			−0.140286			−0.0701429	+	0.997537i	$0.522346\pi$
$830$	298.027	+	292.311i	0.359069	+	0.352182i
$831$		0			0
$832$	−53.0363	−	30.6205i	−0.0637456	−	0.0368035i
$833$	−301.508	+	522.227i	−0.361954	+	0.626923i
$834$		0			0
$835$	1142.49	+	1120.58i	1.36825	+	1.34201i
$836$			103.153i			0.123388i
$837$		0			0
$838$		−	1043.59i		−	1.24533i
$839$	−478.220	+	276.100i	−0.569988	+	0.329083i	−0.757145	−	0.653247i	$-0.773406\pi$
$839$	−478.220	+	276.100i	−0.569988	+	0.329083i	0.187156	+	0.982330i	$0.440073\pi$
$840$		0			0
$841$	72.3203	−	125.262i	0.0859932	−	0.148945i
$842$	72.5182	−	125.605i	0.0861261	−	0.149175i
$843$		0			0
$844$	383.899	+	664.932i	0.454856	+	0.787834i
$845$	531.778	−	148.023i	0.629323	−	0.175175i
$846$		0			0
$847$			10.4270i			0.0123105i
$848$	83.3806	+	144.419i	0.0983262	+	0.170306i
$849$		0			0
$850$	8.44854	+	436.201i	0.00993945	+	0.513178i
$851$	−420.665	−	242.871i	−0.494318	−	0.285395i
$852$		0			0
$853$	238.466	−	137.678i	0.279561	−	0.161405i	−0.353664	−	0.935373i	$-0.615064\pi$
$853$	238.466	−	137.678i	0.279561	−	0.161405i	0.633225	+	0.773968i	$0.281731\pi$
$854$			23.7082i			0.0277614i
$855$		0			0
$856$	−537.252			−0.627630
$857$	−811.725	−	1405.95i	−0.947170	−	1.64055i	−0.751346	−	0.659908i	$-0.770595\pi$
$857$	−811.725	−	1405.95i	−0.947170	−	1.64055i	−0.195824	−	0.980639i	$-0.562738\pi$
$858$		0			0
$859$	511.175	−	885.381i	0.595082	−	1.03071i	−0.398454	−	0.917188i	$-0.630453\pi$
$859$	511.175	−	885.381i	0.595082	−	1.03071i	0.993535	−	0.113523i	$-0.0362136\pi$
$860$	521.127	+	134.241i	0.605961	+	0.156094i
$861$		0			0
$862$	−308.335	+	178.018i	−0.357698	+	0.206517i
$863$	−588.647			−0.682094			−0.341047	−	0.940046i	$-0.610782\pi$
$863$	−588.647			−0.682094			−0.341047	+	0.940046i	$0.610782\pi$
$864$		0			0
$865$	−191.095	+	53.1922i	−0.220919	+	0.0614938i
$866$	188.449	−	108.801i	0.217608	−	0.125636i
$867$		0			0
$868$	−3.10830	−	1.79458i	−0.00358099	−	0.00206748i
$869$	−421.988	−	243.635i	−0.485602	−	0.280363i
$870$		0			0
$871$	−176.608	−	305.895i	−0.202765	−	0.351199i
$872$	403.490			0.462718
$873$		0			0
$874$	91.5502			0.104748
$875$	10.5172	−	44.3677i	0.0120197	−	0.0507060i
$876$		0			0
$877$	528.533	+	305.149i	0.602661	+	0.347946i	0.770088	−	0.637938i	$-0.220213\pi$
$877$	528.533	+	305.149i	0.602661	+	0.347946i	−0.167427	+	0.985884i	$0.553546\pi$
$878$	−348.516	+	603.648i	−0.396943	+	0.687526i
$879$		0			0
$880$	134.630	−	137.263i	0.152988	−	0.155980i
$881$		−	677.101i		−	0.768559i	−0.923217	−	0.384280i	$-0.874450\pi$
$881$		−	677.101i		−	0.768559i	0.923217	−	0.384280i	$-0.125550\pi$
$882$		0			0
$883$		−	760.076i		−	0.860788i	−0.902641	−	0.430394i	$-0.858375\pi$
$883$		−	760.076i		−	0.860788i	0.902641	−	0.430394i	$-0.141625\pi$
$884$	163.616	−	94.4640i	0.185086	−	0.106860i
$885$		0			0
$886$	365.277	−	632.679i	0.412277	−	0.714085i
$887$	−320.061	+	554.363i	−0.360836	+	0.624986i	−0.988099	−	0.153822i	$-0.950842\pi$
$887$	−320.061	+	554.363i	−0.360836	+	0.624986i	0.627263	+	0.778808i	$0.284175\pi$
$888$		0			0
$889$	−15.2114	−	26.3470i	−0.0171107	−	0.0296366i
$890$	−16.9339	−	60.8358i	−0.0190269	−	0.0683549i
$891$		0			0
$892$		−	691.098i		−	0.774773i
$893$	75.7377	+	131.181i	0.0848126	+	0.146900i
$894$		0			0
$895$	248.490	+	64.0103i	0.277642	+	0.0715199i
$896$	−3.57408	−	2.06349i	−0.00398893	−	0.00230301i
$897$		0			0
$898$	750.292	−	433.181i	0.835515	−	0.482385i
$899$			154.452i			0.171804i
$900$		0			0
$901$	−514.456			−0.570984
$902$	−430.257	−	745.227i	−0.477003	−	0.826194i
$903$		0			0
$904$	115.510	−	200.069i	0.127777	−	0.221316i
$905$	371.758	−	1443.17i	0.410783	−	1.59467i
$906$		0			0
$907$	−152.547	+	88.0733i	−0.168189	+	0.0971040i	−0.581732	−	0.813381i	$-0.697625\pi$
$907$	−152.547	+	88.0733i	−0.168189	+	0.0971040i	0.413543	+	0.910485i	$0.364291\pi$
$908$	−545.591			−0.600872
$909$		0			0
$910$	−19.0222	+	5.29492i	−0.0209035	+	0.00581860i
$911$	−1244.54	+	718.538i	−1.36613	+	0.788735i	−0.990431	−	0.138007i	$-0.955930\pi$
$911$	−1244.54	+	718.538i	−1.36613	+	0.788735i	−0.375698	+	0.926742i	$0.622597\pi$
$912$		0			0
$913$	491.501	+	283.768i	0.538336	+	0.310808i
$914$	−1081.29	−	624.280i	−1.18303	−	0.683020i
$915$		0			0
$916$	−0.104243	−	0.180553i	−0.000113802	−	0.000197111i
$917$	41.5465			0.0453070
$918$		0			0
$919$	217.751			0.236944			0.118472	−	0.992957i	$-0.462200\pi$
$919$	217.751			0.236944			0.118472	+	0.992957i	$0.462200\pi$
$920$	−121.824	−	119.487i	−0.132417	−	0.129877i
$921$		0			0
$922$	−420.520	−	242.788i	−0.456096	−	0.263327i
$923$	480.809	−	832.785i	0.520920	−	0.902259i
$924$		0			0
$925$	486.237	−	881.165i	0.525661	−	0.952611i
$926$			925.758i			0.999738i
$927$		0			0
$928$			177.596i			0.191375i
$929$	254.358	−	146.854i	0.273798	−	0.158077i	−0.356814	−	0.934175i	$-0.616137\pi$
$929$	254.358	−	146.854i	0.273798	−	0.158077i	0.630612	+	0.776098i	$0.282804\pi$
$930$		0			0
$931$	−131.088	+	227.051i	−0.140803	+	0.243878i
$932$	−317.302	+	549.583i	−0.340453	+	0.589681i
$933$		0			0
$934$	609.109	+	1055.01i	0.652150	+	1.12956i
$935$	159.056	+	571.414i	0.170113	+	0.611138i
$936$		0			0
$937$			375.806i			0.401074i	0.979686	+	0.200537i	$0.0642686\pi$
$937$			375.806i			0.401074i	−0.979686	+	0.200537i	$0.935731\pi$
$938$	−11.9015	−	20.6140i	−0.0126882	−	0.0219766i
$939$		0			0
$940$	70.4296	−	273.409i	0.0749251	−	0.290861i
$941$	−962.551	−	555.729i	−1.02290	−	0.590573i	−0.107959	−	0.994155i	$-0.534431\pi$
$941$	−962.551	−	555.729i	−1.02290	−	0.590573i	−0.914943	+	0.403583i	$0.867765\pi$
$942$		0			0
$943$	−661.405	+	381.863i	−0.701384	+	0.404944i
$944$		−	449.016i		−	0.475653i
$945$		0			0
$946$	731.614			0.773377
$947$	908.613	+	1573.76i	0.959465	+	1.66184i	0.723803	+	0.690007i	$0.242393\pi$
$947$	908.613	+	1573.76i	0.959465	+	1.66184i	0.235662	+	0.971835i	$0.424274\pi$
$948$		0			0
$949$	226.143	−	391.691i	0.238296	−	0.412740i
$950$	3.67321	+	189.649i	0.00386653	+	0.199631i
$951$		0			0
$952$	11.0260	−	6.36586i	0.0115819	−	0.00668682i
$953$	−817.241			−0.857545			−0.428773	−	0.903412i	$-0.641054\pi$
$953$	−817.241			−0.857545			−0.428773	+	0.903412i	$0.641054\pi$
$954$		0			0
$955$	−288.133	−	1035.13i	−0.301710	−	1.08391i
$956$	334.328	−	193.025i	0.349716	−	0.201909i
$957$		0			0
$958$	−440.469	−	254.305i	−0.459780	−	0.265454i
$959$	48.2498	+	27.8571i	0.0503127	+	0.0290480i
$960$		0			0
$961$	468.399	+	811.290i	0.487407	+	0.844214i
$962$	−435.819			−0.453034
$963$		0			0
$964$	−629.453			−0.652959
$965$	−615.225	+	627.256i	−0.637539	+	0.650007i
$966$		0			0
$967$	−42.1958	−	24.3618i	−0.0436358	−	0.0251931i	0.478023	−	0.878347i	$-0.341353\pi$
$967$	−42.1958	−	24.3618i	−0.0436358	−	0.0251931i	−0.521659	+	0.853154i	$0.674687\pi$
$968$	−40.4245	+	70.0172i	−0.0417608	+	0.0723319i
$969$		0			0
$970$	650.142	−	662.857i	0.670250	−	0.683357i
$971$		−	260.809i		−	0.268598i	−0.990941	−	0.134299i	$-0.957122\pi$
$971$		−	260.809i		−	0.268598i	0.990941	−	0.134299i	$-0.0428783\pi$
$972$		0			0
$973$			36.6785i			0.0376963i
$974$	−944.365	+	545.229i	−0.969574	+	0.559784i
$975$		0			0
$976$	−91.9149	+	159.201i	−0.0941751	+	0.163116i
$977$	−124.626	+	215.859i	−0.127560	+	0.220941i	−0.922731	−	0.385445i	$-0.874048\pi$
$977$	−124.626	+	215.859i	−0.127560	+	0.220941i	0.795171	+	0.606386i	$0.207381\pi$
$978$		0			0
$979$	−42.9261	−	74.3503i	−0.0438469	−	0.0759451i
$980$	470.772	−	131.041i	0.480379	−	0.133716i
$981$		0			0
$982$		−	224.166i		−	0.228275i
$983$	−294.126	−	509.440i	−0.299212	−	0.518251i	0.676744	−	0.736219i	$-0.263390\pi$
$983$	−294.126	−	509.440i	−0.299212	−	0.518251i	−0.975956	+	0.217968i	$0.930057\pi$
$984$		0			0
$985$	184.072	−	714.571i	0.186875	−	0.725453i
$986$	−474.480	−	273.941i	−0.481218	−	0.277831i
$987$		0			0
$988$	71.1362	−	41.0705i	0.0720002	−	0.0415693i
$989$		−	649.324i		−	0.656546i
$990$		0			0
$991$	−598.851			−0.604289			−0.302145	−	0.953262i	$-0.597703\pi$
$991$	−598.851			−0.604289			−0.302145	+	0.953262i	$0.597703\pi$
$992$	−13.9149	−	24.1012i	−0.0140271	−	0.0242956i
$993$		0			0
$994$	32.4013	−	56.1208i	0.0325969	−	0.0564595i
$995$	240.690	−	934.365i	0.241900	−	0.939060i
$996$		0			0
$997$	−797.523	+	460.450i	−0.799922	+	0.461835i	−0.843444	−	0.537217i	$-0.819476\pi$
$997$	−797.523	+	460.450i	−0.799922	+	0.461835i	0.0435217	+	0.999052i	$0.486142\pi$
$998$	896.761			0.898559
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.3.j.g.539.3		24
3.2	odd	2	inner	810.3.j.g.539.11		24
5.4	even	2		810.3.j.h.539.11		24
9.2	odd	6		810.3.j.h.269.11		24
9.4	even	3		810.3.b.c.809.23	yes	24
9.5	odd	6		810.3.b.c.809.2	yes	24
9.7	even	3		810.3.j.h.269.3		24
15.14	odd	2		810.3.j.h.539.3		24
45.4	even	6		810.3.b.c.809.1	✓	24
45.14	odd	6		810.3.b.c.809.24	yes	24
45.29	odd	6	inner	810.3.j.g.269.3		24
45.34	even	6	inner	810.3.j.g.269.11		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
810.3.b.c.809.1	✓	24	45.4	even	6
810.3.b.c.809.2	yes	24	9.5	odd	6
810.3.b.c.809.23	yes	24	9.4	even	3
810.3.b.c.809.24	yes	24	45.14	odd	6
810.3.j.g.269.3		24	45.29	odd	6	inner
810.3.j.g.269.11		24	45.34	even	6	inner
810.3.j.g.539.3		24	1.1	even	1	trivial
810.3.j.g.539.11		24	3.2	odd	2	inner
810.3.j.h.269.3		24	9.7	even	3
810.3.j.h.269.11		24	9.2	odd	6
810.3.j.h.539.3		24	15.14	odd	2
810.3.j.h.539.11		24	5.4	even	2

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:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	810.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-1.24727 + 4.84193i) q^{5} +(0.315907 - 0.182389i) q^{7} +2.82843 q^{8} +O(q^{10})\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-1.24727 + 4.84193i) q^{5} +(0.315907 - 0.182389i) q^{7} +2.82843 q^{8} +(6.81209 - 1.89618i) q^{10} +(8.32536 - 4.80665i) q^{11} +(-6.62954 - 3.82757i) q^{13} +(-0.446760 - 0.257937i) q^{14} +(-2.00000 - 3.46410i) q^{16} +12.3400 q^{17} +5.36509 q^{19} +(-7.13920 - 7.00227i) q^{20} +(-11.7738 - 6.79763i) q^{22} +(-6.03305 + 10.4495i) q^{23} +(-21.8886 - 12.0784i) q^{25} +10.8260i q^{26} +0.729555i q^{28} +(27.1888 - 15.6975i) q^{29} +(-2.45982 + 4.26054i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(-8.72566 - 15.1133i) q^{34} +(0.489094 + 1.75709i) q^{35} +40.2567i q^{37} +(-3.79369 - 6.57087i) q^{38} +(-3.52781 + 13.6951i) q^{40} +(54.8152 + 31.6476i) q^{41} +(-46.6042 + 26.9070i) q^{43} +19.2266i q^{44} +17.0640 q^{46} +(14.1167 + 24.4509i) q^{47} +(-24.4335 + 42.3200i) q^{49} +(0.684649 + 35.3487i) q^{50} +(13.2591 - 7.65513i) q^{52} -41.6903 q^{53} +(12.8895 + 46.3060i) q^{55} +(0.893519 - 0.515874i) q^{56} +(-38.4508 - 22.1996i) q^{58} +(97.2149 + 56.1271i) q^{59} +(-22.9787 - 39.8003i) q^{61} +6.95743 q^{62} +8.00000 q^{64} +(26.8016 - 27.3258i) q^{65} +(39.9594 + 23.0706i) q^{67} +(-12.3400 + 21.3734i) q^{68} +(1.80614 - 1.84146i) q^{70} +125.617i q^{71} +59.0826i q^{73} +(49.3042 - 28.4658i) q^{74} +(-5.36509 + 9.29261i) q^{76} +(1.75336 - 3.03691i) q^{77} +(-25.3435 - 43.8963i) q^{79} +(19.2675 - 5.36320i) q^{80} -89.5128i q^{82} +(29.5183 + 51.1271i) q^{83} +(-15.3913 + 59.7492i) q^{85} +(65.9083 + 38.0522i) q^{86} +(23.5477 - 13.5953i) q^{88} -8.93057i q^{89} -2.79242 q^{91} +(-12.0661 - 20.8991i) q^{92} +(19.9641 - 34.5788i) q^{94} +(-6.69172 + 25.9774i) q^{95} +(113.714 - 65.6530i) q^{97} +69.1083 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{4} - 24 q^{7}+O(q^{10}) \) 24 * q - 24 * q^4 - 24 * q^7	\( 24 q - 24 q^{4} - 24 q^{7} - 12 q^{10} - 48 q^{13} - 48 q^{16} + 120 q^{22} + 24 q^{25} + 60 q^{34} + 24 q^{43} - 36 q^{49} + 96 q^{52} + 216 q^{55} - 396 q^{58} - 60 q^{61} + 192 q^{64} + 1032 q^{67} - 480 q^{70} - 240 q^{79} - 396 q^{85} - 240 q^{88} + 48 q^{91} - 48 q^{94} + 1440 q^{97}+O(q^{100}) \) 24 * q - 24 * q^4 - 24 * q^7 - 12 * q^10 - 48 * q^13 - 48 * q^16 + 120 * q^22 + 24 * q^25 + 60 * q^34 + 24 * q^43 - 36 * q^49 + 96 * q^52 + 216 * q^55 - 396 * q^58 - 60 * q^61 + 192 * q^64 + 1032 * q^67 - 480 * q^70 - 240 * q^79 - 396 * q^85 - 240 * q^88 + 48 * q^91 - 48 * q^94 + 1440 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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