LMFDB - Embedded newform 180.3.m.c.107.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [180,3,Mod(107,180)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(180, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 1]))

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

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

chi := DirichletCharacter("180.107");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	180.m (of order $4$, degree $2$, 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:	$4.90464475849$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			107.12
Character	$\chi$	$=$	180.107
Dual form			180.3.m.c.143.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.321406 + 1.97401i) q^{2} +(-3.79340 + 1.26891i) q^{4} +(-0.196879 - 4.99612i) q^{5} +(8.42491 - 8.42491i) q^{7} +(-3.72406 - 7.08035i) q^{8} +O(q^{10})$	\(q+(0.321406 + 1.97401i) q^{2} +(-3.79340 + 1.26891i) q^{4} +(-0.196879 - 4.99612i) q^{5} +(8.42491 - 8.42491i) q^{7} +(-3.72406 - 7.08035i) q^{8} +(9.79910 - 1.99442i) q^{10} +0.926135 q^{11} +(8.10283 - 8.10283i) q^{13} +(19.3386 + 13.9230i) q^{14} +(12.7797 - 9.62698i) q^{16} +(-20.7351 + 20.7351i) q^{17} +13.8492 q^{19} +(7.08649 + 18.7025i) q^{20} +(0.297665 + 1.82820i) q^{22} +(22.9961 - 22.9961i) q^{23} +(-24.9225 + 1.96726i) q^{25} +(18.5993 + 13.3907i) q^{26} +(-21.2686 + 42.6495i) q^{28} -12.0204 q^{29} -27.6605i q^{31} +(23.1112 + 22.1331i) q^{32} +(-47.5956 - 34.2668i) q^{34} +(-43.7506 - 40.4332i) q^{35} +(14.0127 + 14.0127i) q^{37} +(4.45122 + 27.3384i) q^{38} +(-34.6411 + 19.9998i) q^{40} -10.4392i q^{41} +(44.6417 + 44.6417i) q^{43} +(-3.51320 + 1.17519i) q^{44} +(52.7854 + 38.0033i) q^{46} +(-8.50432 - 8.50432i) q^{47} -92.9583i q^{49} +(-11.8936 - 48.5648i) q^{50} +(-20.4555 + 41.0190i) q^{52} +(7.70260 + 7.70260i) q^{53} +(-0.182336 - 4.62709i) q^{55} +(-91.0262 - 28.2764i) q^{56} +(-3.86343 - 23.7284i) q^{58} +12.6960i q^{59} -13.7631 q^{61} +(54.6019 - 8.89024i) q^{62} +(-36.2627 + 52.7353i) q^{64} +(-42.0780 - 38.8874i) q^{65} +(-75.3408 + 75.3408i) q^{67} +(52.3454 - 104.968i) q^{68} +(65.7537 - 99.3594i) q^{70} -13.5090 q^{71} +(-43.6527 + 43.6527i) q^{73} +(-23.1574 + 32.1649i) q^{74} +(-52.5356 + 17.5735i) q^{76} +(7.80261 - 7.80261i) q^{77} -71.8441 q^{79} +(-50.6136 - 61.9537i) q^{80} +(20.6070 - 3.35521i) q^{82} +(-21.6393 + 21.6393i) q^{83} +(107.677 + 99.5128i) q^{85} +(-73.7749 + 102.471i) q^{86} +(-3.44899 - 6.55736i) q^{88} +98.6190 q^{89} -136.531i q^{91} +(-58.0532 + 116.413i) q^{92} +(14.0542 - 19.5209i) q^{94} +(-2.72662 - 69.1924i) q^{95} +(-27.6349 - 27.6349i) q^{97} +(183.500 - 29.8773i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q+O(q^{10}) $ 40 * q	$ 40 q + 16 q^{10} - 40 q^{13} + 184 q^{16} + 112 q^{22} + 32 q^{28} - 264 q^{37} + 40 q^{40} - 160 q^{46} - 328 q^{52} - 720 q^{58} - 128 q^{61} + 464 q^{70} - 664 q^{73} + 576 q^{76} + 320 q^{82} + 608 q^{85} + 544 q^{88} + 360 q^{97}+O(q^{100}) $ 40 * q + 16 * q^10 - 40 * q^13 + 184 * q^16 + 112 * q^22 + 32 * q^28 - 264 * q^37 + 40 * q^40 - 160 * q^46 - 328 * q^52 - 720 * q^58 - 128 * q^61 + 464 * q^70 - 664 * q^73 + 576 * q^76 + 320 * q^82 + 608 * q^85 + 544 * q^88 + 360 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$

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 $

$2$	0.321406	+	1.97401i	0.160703	+	0.987003i
$2$	0.321406	+	1.97401i	0.160703	+	0.987003i
$3$		0			0
$3$		0			0
$4$	−3.79340	+	1.26891i	−0.948349	+	0.317228i
$5$	−0.196879	−	4.99612i	−0.0393758	−	0.999224i
$5$	−0.196879	−	4.99612i	−0.0393758	−	0.999224i
$6$		0			0
$7$	8.42491	−	8.42491i	1.20356	−	1.20356i	0.230483	−	0.973076i	$-0.425970\pi$
$7$	8.42491	−	8.42491i	1.20356	−	1.20356i	0.973076	−	0.230483i	$-0.0740305\pi$
$8$	−3.72406	−	7.08035i	−0.465508	−	0.885044i
$9$		0			0
$10$	9.79910	−	1.99442i	0.979910	−	0.199442i
$11$	0.926135			0.0841941			0.0420971	−	0.999114i	$-0.486596\pi$
$11$	0.926135			0.0841941			0.0420971	+	0.999114i	$0.486596\pi$
$12$		0			0
$13$	8.10283	−	8.10283i	0.623294	−	0.623294i	−0.323078	−	0.946372i	$-0.604718\pi$
$13$	8.10283	−	8.10283i	0.623294	−	0.623294i	0.946372	+	0.323078i	$0.104718\pi$
$14$	19.3386	+	13.9230i	1.38133	+	0.994501i
$15$		0			0
$16$	12.7797	−	9.62698i	0.798732	−	0.601687i
$17$	−20.7351	+	20.7351i	−1.21971	+	1.21971i	−0.251980	+	0.967732i	$0.581082\pi$
$17$	−20.7351	+	20.7351i	−1.21971	+	1.21971i	−0.967732	+	0.251980i	$0.918918\pi$
$18$		0			0
$19$	13.8492			0.728906			0.364453	−	0.931222i	$-0.381256\pi$
$19$	13.8492			0.728906			0.364453	+	0.931222i	$0.381256\pi$
$20$	7.08649	+	18.7025i	0.354324	+	0.935123i
$21$		0			0
$22$	0.297665	+	1.82820i	0.0135302	+	0.0830998i
$23$	22.9961	−	22.9961i	0.999828	−	0.999828i	−0.000171559	−	1.00000i	$-0.500055\pi$
$23$	22.9961	−	22.9961i	0.999828	−	0.999828i	1.00000		0.000171559i	$5.46090e-5\pi$
$24$		0			0
$25$	−24.9225	+	1.96726i	−0.996899	+	0.0786905i
$26$	18.5993	+	13.3907i	0.715359	+	0.515028i
$27$		0			0
$28$	−21.2686	+	42.6495i	−0.759591	+	1.52320i
$29$	−12.0204			−0.414497			−0.207249	−	0.978288i	$-0.566451\pi$
$29$	−12.0204			−0.414497			−0.207249	+	0.978288i	$0.566451\pi$
$30$		0			0
$31$		−	27.6605i		−	0.892273i	−0.894965	−	0.446137i	$-0.852800\pi$
$31$		−	27.6605i		−	0.892273i	0.894965	−	0.446137i	$-0.147200\pi$
$32$	23.1112	+	22.1331i	0.722225	+	0.691658i
$33$		0			0
$34$	−47.5956	−	34.2668i	−1.39987	−	1.00785i
$35$	−43.7506	−	40.4332i	−1.25002	−	1.15523i
$36$		0			0
$37$	14.0127	+	14.0127i	0.378722	+	0.378722i	0.870641	−	0.491919i	$-0.163704\pi$
$37$	14.0127	+	14.0127i	0.378722	+	0.378722i	−0.491919	+	0.870641i	$0.663704\pi$
$38$	4.45122	+	27.3384i	0.117137	+	0.719432i
$39$		0			0
$40$	−34.6411	+	19.9998i	−0.866028	+	0.499996i
$41$		−	10.4392i		−	0.254614i	−0.991863	−	0.127307i	$-0.959367\pi$
$41$		−	10.4392i		−	0.254614i	0.991863	−	0.127307i	$-0.0406333\pi$
$42$		0			0
$43$	44.6417	+	44.6417i	1.03818	+	1.03818i	0.999242	+	0.0389383i	$0.0123976\pi$
$43$	44.6417	+	44.6417i	1.03818	+	1.03818i	0.0389383	+	0.999242i	$0.487602\pi$
$44$	−3.51320	+	1.17519i	−0.0798454	+	0.0267088i
$45$		0			0
$46$	52.7854	+	38.0033i	1.14751	+	0.826158i
$47$	−8.50432	−	8.50432i	−0.180943	−	0.180943i	0.610824	−	0.791767i	$-0.290838\pi$
$47$	−8.50432	−	8.50432i	−0.180943	−	0.180943i	−0.791767	+	0.610824i	$0.790838\pi$
$48$		0			0
$49$		−	92.9583i		−	1.89711i
$50$	−11.8936	−	48.5648i	−0.237872	−	0.971296i
$51$		0			0
$52$	−20.4555	+	41.0190i	−0.393374	+	0.788827i
$53$	7.70260	+	7.70260i	0.145332	+	0.145332i	0.776029	−	0.630697i	$-0.217231\pi$
$53$	7.70260	+	7.70260i	0.145332	+	0.145332i	−0.630697	+	0.776029i	$0.717231\pi$
$54$		0			0
$55$	−0.182336	−	4.62709i	−0.00331521	−	0.0841288i
$56$	−91.0262	−	28.2764i	−1.62547	−	0.504936i
$57$		0			0
$58$	−3.86343	−	23.7284i	−0.0666109	−	0.409110i
$59$			12.6960i			0.215187i	0.994195	+	0.107594i	$0.0343145\pi$
$59$			12.6960i			0.215187i	−0.994195	+	0.107594i	$0.965685\pi$
$60$		0			0
$61$	−13.7631			−0.225624			−0.112812	−	0.993616i	$-0.535986\pi$
$61$	−13.7631			−0.225624			−0.112812	+	0.993616i	$0.535986\pi$
$62$	54.6019	−	8.89024i	0.880676	−	0.143391i
$63$		0			0
$64$	−36.2627	+	52.7353i	−0.566605	+	0.823989i
$65$	−42.0780	−	38.8874i	−0.647354	−	0.598268i
$66$		0			0
$67$	−75.3408	+	75.3408i	−1.12449	+	1.12449i	−0.133431	+	0.991058i	$0.542599\pi$
$67$	−75.3408	+	75.3408i	−1.12449	+	1.12449i	−0.991058	+	0.133431i	$0.957401\pi$
$68$	52.3454	−	104.968i	0.769786	−	1.54364i
$69$		0			0
$70$	65.7537	−	99.3594i	0.939339	−	1.41942i
$71$	−13.5090			−0.190268			−0.0951340	−	0.995464i	$-0.530328\pi$
$71$	−13.5090			−0.190268			−0.0951340	+	0.995464i	$0.530328\pi$
$72$		0			0
$73$	−43.6527	+	43.6527i	−0.597983	+	0.597983i	−0.939775	−	0.341793i	$-0.888966\pi$
$73$	−43.6527	+	43.6527i	−0.597983	+	0.597983i	0.341793	+	0.939775i	$0.388966\pi$
$74$	−23.1574	+	32.1649i	−0.312938	+	0.434661i
$75$		0			0
$76$	−52.5356	+	17.5735i	−0.691257	+	0.231230i
$77$	7.80261	−	7.80261i	0.101333	−	0.101333i
$78$		0			0
$79$	−71.8441			−0.909418			−0.454709	−	0.890640i	$-0.650257\pi$
$79$	−71.8441			−0.909418			−0.454709	+	0.890640i	$0.650257\pi$
$80$	−50.6136	−	61.9537i	−0.632671	−	0.774421i
$81$		0			0
$82$	20.6070	−	3.35521i	0.251305	−	0.0409172i
$83$	−21.6393	+	21.6393i	−0.260715	+	0.260715i	−0.825344	−	0.564630i	$-0.809019\pi$
$83$	−21.6393	+	21.6393i	−0.260715	+	0.260715i	0.564630	+	0.825344i	$0.309019\pi$
$84$		0			0
$85$	107.677	+	99.5128i	1.26679	+	1.17074i
$86$	−73.7749	+	102.471i	−0.857848	+	1.19152i
$87$		0			0
$88$	−3.44899	−	6.55736i	−0.0391930	−	0.0745155i
$89$	98.6190			1.10808			0.554039	−	0.832491i	$-0.313086\pi$
$89$	98.6190			1.10808			0.554039	+	0.832491i	$0.313086\pi$
$90$		0			0
$91$		−	136.531i		−	1.50034i
$92$	−58.0532	+	116.413i	−0.631013	+	1.26536i
$93$		0			0
$94$	14.0542	−	19.5209i	0.149513	−	0.207669i
$95$	−2.72662	−	69.1924i	−0.0287012	−	0.728341i
$96$		0			0
$97$	−27.6349	−	27.6349i	−0.284896	−	0.284896i	0.550162	−	0.835058i	$-0.314566\pi$
$97$	−27.6349	−	27.6349i	−0.284896	−	0.284896i	−0.835058	+	0.550162i	$0.814566\pi$
$98$	183.500	−	29.8773i	1.87245	−	0.304871i
$99$		0			0
$100$	92.0446	−	39.0871i	0.920446	−	0.390871i
$101$		−	19.7959i		−	0.195999i	−0.995186	−	0.0979994i	$-0.968756\pi$
$101$		−	19.7959i		−	0.195999i	0.995186	−	0.0979994i	$-0.0312443\pi$
$102$		0			0
$103$	115.307	+	115.307i	1.11948	+	1.11948i	0.991817	+	0.127668i	$0.0407492\pi$
$103$	115.307	+	115.307i	1.11948	+	1.11948i	0.127668	+	0.991817i	$0.459251\pi$
$104$	−87.5463	−	27.1954i	−0.841791	−	0.261494i
$105$		0			0
$106$	−12.7293	+	17.6806i	−0.120088	+	0.166799i
$107$	112.849	+	112.849i	1.05467	+	1.05467i	0.998417	+	0.0562485i	$0.0179139\pi$
$107$	112.849	+	112.849i	1.05467	+	1.05467i	0.0562485	+	0.998417i	$0.482086\pi$
$108$		0			0
$109$			78.9131i			0.723974i	0.932183	+	0.361987i	$0.117901\pi$
$109$			78.9131i			0.723974i	−0.932183	+	0.361987i	$0.882099\pi$
$110$	9.07529	−	1.84711i	0.0825026	−	0.0167919i
$111$		0			0
$112$	26.5615	−	188.775i	0.237156	−	1.68549i
$113$	88.5756	+	88.5756i	0.783855	+	0.783855i	0.980479	−	0.196624i	$-0.0629978\pi$
$113$	88.5756	+	88.5756i	0.783855	+	0.783855i	−0.196624	+	0.980479i	$0.562998\pi$
$114$		0			0
$115$	−119.419	−	110.364i	−1.03842	−	0.959684i
$116$	45.5982	−	15.2529i	0.393088	−	0.131490i
$117$		0			0
$118$	−25.0620	+	4.08058i	−0.212390	+	0.0345812i
$119$			349.383i			2.93599i
$120$		0			0
$121$	−120.142			−0.992911
$122$	−4.42353	−	27.1684i	−0.0362585	−	0.222692i
$123$		0			0
$124$	35.0988	+	104.927i	0.283054	+	0.846187i
$125$	14.7354	+	124.128i	0.117883	+	0.993027i
$126$		0			0
$127$	−53.9089	+	53.9089i	−0.424479	+	0.424479i	−0.886743	−	0.462263i	$-0.847037\pi$
$127$	−53.9089	+	53.9089i	−0.424479	+	0.424479i	0.462263	+	0.886743i	$0.347037\pi$
$128$	−115.755	−	54.6334i	−0.904335	−	0.426823i
$129$		0			0
$130$	63.2399	−	95.5608i	0.486461	−	0.735083i
$131$	206.237			1.57433			0.787164	−	0.616743i	$-0.211548\pi$
$131$	206.237			1.57433			0.787164	+	0.616743i	$0.211548\pi$
$132$		0			0
$133$	116.678	−	116.678i	0.877281	−	0.877281i
$134$	−172.938	−	124.508i	−1.29058	−	0.929165i
$135$		0			0
$136$	224.031	+	69.5930i	1.64728	+	0.511713i
$137$	48.3968	−	48.3968i	0.353261	−	0.353261i	−0.508060	−	0.861321i	$-0.669637\pi$
$137$	48.3968	−	48.3968i	0.353261	−	0.353261i	0.861321	+	0.508060i	$0.169637\pi$
$138$		0			0
$139$	161.857			1.16444			0.582220	−	0.813031i	$-0.302184\pi$
$139$	161.857			1.16444			0.582220	+	0.813031i	$0.302184\pi$
$140$	217.270	+	97.8635i	1.55193	+	0.699025i
$141$		0			0
$142$	−4.34188	−	26.6669i	−0.0305766	−	0.187795i
$143$	7.50431	−	7.50431i	0.0524777	−	0.0524777i
$144$		0			0
$145$	2.36657	+	60.0555i	0.0163211	+	0.414176i
$146$	−100.201	−	72.1405i	−0.686308	−	0.494113i
$147$		0			0
$148$	−70.9367	−	35.3748i	−0.479302	−	0.239019i
$149$	−101.983			−0.684451			−0.342225	−	0.939618i	$-0.611181\pi$
$149$	−101.983			−0.684451			−0.342225	+	0.939618i	$0.611181\pi$
$150$		0			0
$151$		−	172.705i		−	1.14374i	−0.820343	−	0.571872i	$-0.806217\pi$
$151$		−	172.705i		−	1.14374i	0.820343	−	0.571872i	$-0.193783\pi$
$152$	−51.5753	−	98.0573i	−0.339311	−	0.645114i
$153$		0			0
$154$	17.9102	+	12.8946i	0.116300	+	0.0837311i
$155$	−138.195	+	5.44576i	−0.891581	+	0.0351339i
$156$		0			0
$157$	139.421	+	139.421i	0.888033	+	0.888033i	0.994334	−	0.106301i	$-0.0339008\pi$
$157$	139.421	+	139.421i	0.888033	+	0.888033i	−0.106301	+	0.994334i	$0.533901\pi$
$158$	−23.0911	−	141.821i	−0.146146	−	0.897599i
$159$		0			0
$160$	106.029	−	119.824i	0.662684	−	0.748899i
$161$		−	387.480i		−	2.40671i
$162$		0			0
$163$	−76.9546	−	76.9546i	−0.472114	−	0.472114i	0.430484	−	0.902598i	$-0.358343\pi$
$163$	−76.9546	−	76.9546i	−0.472114	−	0.472114i	−0.902598	+	0.430484i	$0.858343\pi$
$164$	13.2464	+	39.5999i	0.0807707	+	0.241463i
$165$		0			0
$166$	−49.6711	−	35.7611i	−0.299224	−	0.215428i
$167$	−139.697	−	139.697i	−0.836511	−	0.836511i	0.151886	−	0.988398i	$-0.451465\pi$
$167$	−139.697	−	139.697i	−0.836511	−	0.836511i	−0.988398	+	0.151886i	$0.951465\pi$
$168$		0			0
$169$			37.6884i			0.223008i
$170$	−161.831	+	244.540i	−0.951946	+	1.43847i
$171$		0			0
$172$	−225.990	−	112.697i	−1.31390	−	0.655217i
$173$	72.1643	+	72.1643i	0.417135	+	0.417135i	0.884215	−	0.467080i	$-0.154694\pi$
$173$	72.1643	+	72.1643i	0.417135	+	0.417135i	−0.467080	+	0.884215i	$0.654694\pi$
$174$		0			0
$175$	−193.396	+	226.544i	−1.10512	+	1.29454i
$176$	11.8357	−	8.91589i	0.0672486	−	0.0506585i
$177$		0			0
$178$	31.6967	+	194.674i	0.178071	+	1.09368i
$179$		−	153.167i		−	0.855683i	−0.903854	−	0.427841i	$-0.859274\pi$
$179$		−	153.167i		−	0.855683i	0.903854	−	0.427841i	$-0.140726\pi$
$180$		0			0
$181$	−133.965			−0.740141			−0.370070	−	0.929004i	$-0.620666\pi$
$181$	−133.965			−0.740141			−0.370070	+	0.929004i	$0.620666\pi$
$182$	269.513	−	43.8819i	1.48084	−	0.241109i
$183$		0			0
$184$	−248.459	−	77.1814i	−1.35032	−	0.419464i
$185$	67.2504	−	72.7680i	0.363516	−	0.393341i
$186$		0			0
$187$	−19.2035	+	19.2035i	−0.102693	+	0.102693i
$188$	43.0515	+	21.4690i	0.228997	+	0.114197i
$189$		0			0
$190$	135.710	−	27.6212i	0.714262	−	0.145375i
$191$	−50.8782			−0.266378			−0.133189	−	0.991091i	$-0.542522\pi$
$191$	−50.8782			−0.266378			−0.133189	+	0.991091i	$0.542522\pi$
$192$		0			0
$193$	156.068	−	156.068i	0.808644	−	0.808644i	−0.175785	−	0.984429i	$-0.556246\pi$
$193$	156.068	−	156.068i	0.808644	−	0.808644i	0.984429	+	0.175785i	$0.0562462\pi$
$194$	45.6695	−	63.4335i	0.235410	−	0.326977i
$195$		0			0
$196$	117.956	+	352.628i	0.601817	+	1.79912i
$197$	−216.939	+	216.939i	−1.10121	+	1.10121i	−0.106950	+	0.994264i	$0.534109\pi$
$197$	−216.939	+	216.939i	−1.10121	+	1.10121i	−0.994264	+	0.106950i	$0.965891\pi$
$198$		0			0
$199$	149.940			0.753465			0.376733	−	0.926322i	$-0.377048\pi$
$199$	149.940			0.753465			0.376733	+	0.926322i	$0.377048\pi$
$200$	106.742	+	169.134i	0.533709	+	0.845668i
$201$		0			0
$202$	39.0772	−	6.36251i	0.193451	−	0.0314976i
$203$	−101.271	+	101.271i	−0.498872	+	0.498872i
$204$		0			0
$205$	−52.1554	+	2.05525i	−0.254416	+	0.0100256i
$206$	−190.556	+	264.677i	−0.925030	+	1.28484i
$207$		0			0
$208$	25.5460	−	181.558i	0.122818	−	0.872873i
$209$	12.8262			0.0613696
$210$		0			0
$211$			241.207i			1.14316i	0.820546	+	0.571581i	$0.193670\pi$
$211$			241.207i			1.14316i	−0.820546	+	0.571581i	$0.806330\pi$
$212$	−38.9930	−	19.4451i	−0.183929	−	0.0917221i
$213$		0			0
$214$	−186.495	+	259.035i	−0.871470	+	1.21045i
$215$	214.247	−	231.825i	0.996496	−	1.07825i
$216$		0			0
$217$	−233.037	−	233.037i	−1.07390	−	1.07390i
$218$	−155.775	+	25.3631i	−0.714564	+	0.116345i
$219$		0			0
$220$	6.56305	+	17.3210i	0.0298320	+	0.0787318i
$221$			336.026i			1.52048i
$222$		0			0
$223$	88.4922	+	88.4922i	0.396826	+	0.396826i	0.877112	−	0.480286i	$-0.159467\pi$
$223$	88.4922	+	88.4922i	0.396826	+	0.396826i	−0.480286	+	0.877112i	$0.659467\pi$
$224$	381.179	−	8.24066i	1.70169	−	0.0367887i
$225$		0			0
$226$	−146.380	+	203.318i	−0.647700	+	0.899635i
$227$	−188.659	−	188.659i	−0.831097	−	0.831097i	0.156570	−	0.987667i	$-0.449956\pi$
$227$	−188.659	−	188.659i	−0.831097	−	0.831097i	−0.987667	+	0.156570i	$0.949956\pi$
$228$		0			0
$229$		−	82.3589i		−	0.359646i	−0.983699	−	0.179823i	$-0.942448\pi$
$229$		−	82.3589i		−	0.359646i	0.983699	−	0.179823i	$-0.0575525\pi$
$230$	179.477	−	271.204i	0.780333	−	1.17915i
$231$		0			0
$232$	44.7648	+	85.1088i	0.192952	+	0.366848i
$233$	−49.4864	−	49.4864i	−0.212388	−	0.212388i	0.592893	−	0.805281i	$-0.297986\pi$
$233$	−49.4864	−	49.4864i	−0.212388	−	0.212388i	−0.805281	+	0.592893i	$0.797986\pi$
$234$		0			0
$235$	−40.8143	+	44.1629i	−0.173678	+	0.187927i
$236$	−16.1102	−	48.1611i	−0.0682634	−	0.204072i
$237$		0			0
$238$	−689.684	+	112.294i	−2.89783	+	0.471822i
$239$		−	226.369i		−	0.947151i	−0.880753	−	0.473576i	$-0.842963\pi$
$239$		−	226.369i		−	0.947151i	0.880753	−	0.473576i	$-0.157037\pi$
$240$		0			0
$241$	−373.458			−1.54962			−0.774810	−	0.632195i	$-0.782154\pi$
$241$	−373.458			−1.54962			−0.774810	+	0.632195i	$0.782154\pi$
$242$	−38.6144	−	237.162i	−0.159564	−	0.980006i
$243$		0			0
$244$	52.2088	−	17.4642i	0.213971	−	0.0715744i
$245$	−464.431	+	18.3015i	−1.89564	+	0.0747001i
$246$		0			0
$247$	112.218	−	112.218i	0.454323	−	0.454323i
$248$	−195.846	+	103.009i	−0.789701	+	0.415360i
$249$		0			0
$250$	−240.294	+	68.9833i	−0.961177	+	0.275933i
$251$	96.1891			0.383223			0.191612	−	0.981471i	$-0.438629\pi$
$251$	96.1891			0.383223			0.191612	+	0.981471i	$0.438629\pi$
$252$		0			0
$253$	21.2975	−	21.2975i	0.0841797	−	0.0841797i
$254$	−123.743	−	89.0898i	−0.487177	−	0.350747i
$255$		0			0
$256$	70.6423	−	246.060i	0.275947	−	0.961173i
$257$	198.484	−	198.484i	0.772313	−	0.772313i	−0.206198	−	0.978510i	$-0.566109\pi$
$257$	198.484	−	198.484i	0.772313	−	0.772313i	0.978510	+	0.206198i	$0.0661090\pi$
$258$		0			0
$259$	236.112			0.911628
$260$	208.963	+	94.1222i	0.803705	+	0.362008i
$261$		0			0
$262$	66.2858	+	407.113i	0.252999	+	1.55387i
$263$	−128.902	+	128.902i	−0.490121	+	0.490121i	−0.908344	−	0.418223i	$-0.862653\pi$
$263$	−128.902	+	128.902i	−0.490121	+	0.490121i	0.418223	+	0.908344i	$0.362653\pi$
$264$		0			0
$265$	36.9667	−	39.9996i	0.139497	−	0.150942i
$266$	267.825	+	192.823i	1.00686	+	0.724897i
$267$		0			0
$268$	190.197	−	381.398i	0.709688	−	1.42313i
$269$	226.791			0.843091			0.421545	−	0.906807i	$-0.361488\pi$
$269$	226.791			0.843091			0.421545	+	0.906807i	$0.361488\pi$
$270$		0			0
$271$		−	512.514i		−	1.89120i	−0.325336	−	0.945598i	$-0.605477\pi$
$271$		−	512.514i		−	1.89120i	0.325336	−	0.945598i	$-0.394523\pi$
$272$	−65.3723	+	464.605i	−0.240339	+	1.70811i
$273$		0			0
$274$	111.090	+	79.9805i	0.405440	+	0.291900i
$275$	−23.0816	+	1.82195i	−0.0839330	+	0.00662527i
$276$		0			0
$277$	351.545	+	351.545i	1.26911	+	1.26911i	0.946546	+	0.322568i	$0.104546\pi$
$277$	351.545	+	351.545i	1.26911	+	1.26911i	0.322568	+	0.946546i	$0.395454\pi$
$278$	52.0218	+	319.507i	0.187129	+	1.14931i
$279$		0			0
$280$	−123.351	+	460.345i	−0.440541	+	1.64409i
$281$			57.4724i			0.204528i	0.994757	+	0.102264i	$0.0326087\pi$
$281$			57.4724i			0.204528i	−0.994757	+	0.102264i	$0.967391\pi$
$282$		0			0
$283$	154.244	+	154.244i	0.545032	+	0.545032i	0.925000	−	0.379968i	$-0.124065\pi$
$283$	154.244	+	154.244i	0.545032	+	0.545032i	−0.379968	+	0.925000i	$0.624065\pi$
$284$	51.2451	−	17.1418i	0.180441	−	0.0603584i
$285$		0			0
$286$	17.2255	+	12.4016i	0.0602290	+	0.0433623i
$287$	−87.9491	−	87.9491i	−0.306443	−	0.306443i
$288$		0			0
$289$		−	570.890i		−	1.97540i
$290$	−117.789	+	23.9738i	−0.406170	+	0.0826682i
$291$		0			0
$292$	110.201	−	220.984i	0.377399	−	0.756793i
$293$	−311.937	−	311.937i	−1.06463	−	1.06463i	−0.997762	−	0.0668701i	$-0.978699\pi$
$293$	−311.937	−	311.937i	−1.06463	−	1.06463i	−0.0668701	−	0.997762i	$-0.521301\pi$
$294$		0			0
$295$	63.4309	−	2.49958i	0.215020	−	0.00847315i
$296$	47.0307	−	151.399i	0.158887	−	0.511483i
$297$		0			0
$298$	−32.7780	−	201.315i	−0.109993	−	0.675555i
$299$		−	372.666i		−	1.24637i
$300$		0			0
$301$	752.205			2.49902
$302$	340.922	−	55.5085i	1.12888	−	0.183803i
$303$		0			0
$304$	176.989	−	133.326i	0.582201	−	0.438573i
$305$	2.70966	+	68.7620i	0.00888412	+	0.225449i
$306$		0			0
$307$	23.3022	−	23.3022i	0.0759028	−	0.0759028i	−0.668136	−	0.744039i	$-0.732908\pi$
$307$	23.3022	−	23.3022i	0.0759028	−	0.0759028i	0.744039	+	0.668136i	$0.232908\pi$
$308$	−19.6976	+	39.4992i	−0.0639531	+	0.128244i
$309$		0			0
$310$	−55.1667	−	271.048i	−0.177957	−	0.874347i
$311$	329.170			1.05842			0.529212	−	0.848489i	$-0.322488\pi$
$311$	329.170			1.05842			0.529212	+	0.848489i	$0.322488\pi$
$312$		0			0
$313$	−312.415	+	312.415i	−0.998129	+	0.998129i	−0.999998	−	0.00186882i	$-0.999405\pi$
$313$	−312.415	+	312.415i	−0.998129	+	0.998129i	0.00186882	+	0.999998i	$0.499405\pi$
$314$	−230.407	+	320.029i	−0.733781	+	1.01920i
$315$		0			0
$316$	272.533	−	91.1639i	0.862446	−	0.288493i
$317$	−80.4615	+	80.4615i	−0.253822	+	0.253822i	−0.822535	−	0.568714i	$-0.807441\pi$
$317$	−80.4615	+	80.4615i	−0.253822	+	0.253822i	0.568714	+	0.822535i	$0.307441\pi$
$318$		0			0
$319$	−11.1325			−0.0348982
$320$	270.612	+	170.791i	0.845661	+	0.533720i
$321$		0			0
$322$	764.887	−	124.538i	2.37542	−	0.386764i
$323$	−287.165	+	287.165i	−0.889055	+	0.889055i
$324$		0			0
$325$	−186.002	+	217.883i	−0.572314	+	0.670409i
$326$	127.175	−	176.642i	0.390108	−	0.541848i
$327$		0			0
$328$	−73.9130	+	38.8761i	−0.225344	+	0.118525i
$329$	−143.296			−0.435551
$330$		0			0
$331$		−	85.3025i		−	0.257711i	−0.991663	−	0.128856i	$-0.958870\pi$
$331$		−	85.3025i		−	0.257711i	0.991663	−	0.128856i	$-0.0411304\pi$
$332$	54.6281	−	109.545i	0.164542	−	0.329954i
$333$		0			0
$334$	230.864	−	320.663i	0.691209	−	0.960069i
$335$	391.245	+	361.579i	1.16789	+	1.07934i
$336$		0			0
$337$	−95.6561	−	95.6561i	−0.283846	−	0.283846i	0.550795	−	0.834641i	$-0.314325\pi$
$337$	−95.6561	−	95.6561i	−0.283846	−	0.283846i	−0.834641	+	0.550795i	$0.814325\pi$
$338$	−74.3971	+	12.1133i	−0.220110	+	0.0358381i
$339$		0			0
$340$	−534.736	−	240.858i	−1.57275	−	0.708407i
$341$		−	25.6173i		−	0.0751242i
$342$		0			0
$343$	−370.345	−	370.345i	−1.07972	−	1.07972i
$344$	149.831	−	482.328i	0.435554	−	1.40212i
$345$		0			0
$346$	−119.259	+	165.647i	−0.344678	+	0.478748i
$347$	115.957	+	115.957i	0.334171	+	0.334171i	0.854168	−	0.519997i	$-0.174067\pi$
$347$	115.957	+	115.957i	0.334171	+	0.334171i	−0.519997	+	0.854168i	$0.674067\pi$
$348$		0			0
$349$			91.8490i			0.263178i	0.991304	+	0.131589i	$0.0420079\pi$
$349$			91.8490i			0.263178i	−0.991304	+	0.131589i	$0.957992\pi$
$350$	−509.357	−	308.952i	−1.45531	−	0.882719i
$351$		0			0
$352$	21.4041	+	20.4982i	0.0608071	+	0.0582336i
$353$	85.7655	+	85.7655i	0.242962	+	0.242962i	0.818074	−	0.575113i	$-0.195042\pi$
$353$	85.7655	+	85.7655i	0.242962	+	0.242962i	−0.575113	+	0.818074i	$0.695042\pi$
$354$		0			0
$355$	2.65964	+	67.4928i	0.00749195	+	0.190121i
$356$	−374.101	+	125.139i	−1.05084	+	0.351514i
$357$		0			0
$358$	302.353	−	49.2288i	0.844561	−	0.137511i
$359$			19.9867i			0.0556733i	0.999612	+	0.0278366i	$0.00886182\pi$
$359$			19.9867i			0.0556733i	−0.999612	+	0.0278366i	$0.991138\pi$
$360$		0			0
$361$	−169.199			−0.468696
$362$	−43.0573	−	264.449i	−0.118943	−	0.730521i
$363$		0			0
$364$	173.246	+	517.917i	0.475951	+	1.42285i
$365$	226.689	+	209.500i	0.621065	+	0.573973i
$366$		0			0
$367$	206.308	−	206.308i	0.562147	−	0.562147i	−0.367770	−	0.929917i	$-0.619879\pi$
$367$	206.308	−	206.308i	0.562147	−	0.562147i	0.929917	+	0.367770i	$0.119879\pi$
$368$	72.5004	−	515.266i	0.197012	−	1.40018i
$369$		0			0
$370$	165.259	+	109.365i	0.446646	+	0.295580i
$371$	129.788			0.349832
$372$		0			0
$373$	27.1299	−	27.1299i	0.0727344	−	0.0727344i	−0.669804	−	0.742538i	$-0.733622\pi$
$373$	27.1299	−	27.1299i	0.0727344	−	0.0727344i	0.742538	+	0.669804i	$0.233622\pi$
$374$	−44.0800	−	31.7357i	−0.117861	−	0.0848549i
$375$		0			0
$376$	−28.5429	+	91.8841i	−0.0759121	+	0.244373i
$377$	−97.3994	+	97.3994i	−0.258354	+	0.258354i
$378$		0			0
$379$	−129.731			−0.342298			−0.171149	−	0.985245i	$-0.554748\pi$
$379$	−129.731			−0.342298			−0.171149	+	0.985245i	$0.554748\pi$
$380$	98.1423	+	259.014i	0.258269	+	0.681616i
$381$		0			0
$382$	−16.3525	−	100.434i	−0.0428077	−	0.262916i
$383$	−57.9801	+	57.9801i	−0.151384	+	0.151384i	−0.778736	−	0.627352i	$-0.784139\pi$
$383$	−57.9801	+	57.9801i	−0.151384	+	0.151384i	0.627352	+	0.778736i	$0.284139\pi$
$384$		0			0
$385$	−40.5190	−	37.4466i	−0.105244	−	0.0972640i
$386$	358.241	+	257.918i	0.928085	+	0.668183i
$387$		0			0
$388$	139.897	+	69.7639i	0.360558	+	0.179804i
$389$	592.195			1.52235			0.761176	−	0.648545i	$-0.224622\pi$
$389$	592.195			1.52235			0.761176	+	0.648545i	$0.224622\pi$
$390$		0			0
$391$			953.651i			2.43901i
$392$	−658.177	+	346.183i	−1.67902	+	0.883119i
$393$		0			0
$394$	−497.965	−	358.514i	−1.26387	−	0.909934i
$395$	14.1446	+	358.942i	0.0358090	+	0.908713i
$396$		0			0
$397$	95.1951	+	95.1951i	0.239786	+	0.239786i	0.816762	−	0.576975i	$-0.195767\pi$
$397$	95.1951	+	95.1951i	0.239786	+	0.239786i	−0.576975	+	0.816762i	$0.695767\pi$
$398$	48.1914	+	295.982i	0.121084	+	0.743672i
$399$		0			0
$400$	−299.563	+	265.069i	−0.748909	+	0.662673i
$401$			105.145i			0.262207i	0.991369	+	0.131103i	$0.0418520\pi$
$401$			105.145i			0.262207i	−0.991369	+	0.131103i	$0.958148\pi$
$402$		0			0
$403$	−224.128	−	224.128i	−0.556149	−	0.556149i
$404$	25.1193	+	75.0936i	0.0621764	+	0.185875i
$405$		0			0
$406$	−232.459	−	167.360i	−0.572558	−	0.412218i
$407$	12.9777	+	12.9777i	0.0318861	+	0.0318861i
$408$		0			0
$409$			452.421i			1.10616i	0.833127	+	0.553082i	$0.186548\pi$
$409$			452.421i			1.10616i	−0.833127	+	0.553082i	$0.813452\pi$
$410$	−20.8201	−	102.294i	−0.0507807	−	0.249499i
$411$		0			0
$412$	−583.719	−	291.090i	−1.41679	−	0.706530i
$413$	106.963	+	106.963i	0.258990	+	0.258990i
$414$		0			0
$415$	112.373	+	103.852i	0.270778	+	0.250247i
$416$	366.606	−	7.92562i	0.881265	−	0.0190520i
$417$		0			0
$418$	4.12243	+	25.3191i	0.00986227	+	0.0605720i
$419$			605.395i			1.44486i	0.691445	+	0.722429i	$0.256974\pi$
$419$			605.395i			1.44486i	−0.691445	+	0.722429i	$0.743026\pi$
$420$		0			0
$421$	−103.190			−0.245106			−0.122553	−	0.992462i	$-0.539108\pi$
$421$	−103.190			−0.245106			−0.122553	+	0.992462i	$0.539108\pi$
$422$	−476.144	+	77.5253i	−1.12830	+	0.183709i
$423$		0			0
$424$	25.8522	−	83.2221i	0.0609721	−	0.196279i
$425$	475.979	−	557.562i	1.11995	−	1.31191i
$426$		0			0
$427$	−115.953	+	115.953i	−0.271552	+	0.271552i
$428$	−571.278	−	284.886i	−1.33476	−	0.665621i
$429$		0			0
$430$	526.483	+	348.414i	1.22438	+	0.810266i
$431$	−527.752			−1.22448			−0.612241	−	0.790671i	$-0.709732\pi$
$431$	−527.752			−1.22448			−0.612241	+	0.790671i	$0.709732\pi$
$432$		0			0
$433$	155.637	−	155.637i	0.359438	−	0.359438i	−0.504168	−	0.863606i	$-0.668201\pi$
$433$	155.637	−	155.637i	0.359438	−	0.359438i	0.863606	+	0.504168i	$0.168201\pi$
$434$	385.117	−	534.916i	0.887367	−	1.23253i
$435$		0			0
$436$	−100.134	−	299.349i	−0.229665	−	0.686580i
$437$	318.477	−	318.477i	0.728781	−	0.728781i
$438$		0			0
$439$	−595.270			−1.35597			−0.677984	−	0.735076i	$-0.737146\pi$
$439$	−595.270			−1.35597			−0.677984	+	0.735076i	$0.737146\pi$
$440$	−32.0824	+	18.5226i	−0.0729144	+	0.0420967i
$441$		0			0
$442$	−663.317	+	108.001i	−1.50072	+	0.244345i
$443$	492.767	−	492.767i	1.11234	−	1.11234i	0.119507	−	0.992833i	$-0.461869\pi$
$443$	492.767	−	492.767i	1.11234	−	1.11234i	0.992833	−	0.119507i	$-0.0381315\pi$
$444$		0			0
$445$	−19.4160	−	492.712i	−0.0436314	−	1.10722i
$446$	−146.242	+	203.126i	−0.327897	+	0.455439i
$447$		0			0
$448$	138.780	+	749.801i	0.309777	+	1.67366i
$449$	−159.331			−0.354858			−0.177429	−	0.984134i	$-0.556778\pi$
$449$	−159.331			−0.354858			−0.177429	+	0.984134i	$0.556778\pi$
$450$		0			0
$451$		−	9.66808i		−	0.0214370i
$452$	−448.397	−	223.608i	−0.992030	−	0.494707i
$453$		0			0
$454$	311.778	−	433.050i	0.686736	−	0.953855i
$455$	−682.127	+	26.8801i	−1.49918	+	0.0590772i
$456$		0			0
$457$	−262.705	−	262.705i	−0.574847	−	0.574847i	0.358632	−	0.933479i	$-0.383243\pi$
$457$	−262.705	−	262.705i	−0.574847	−	0.574847i	−0.933479	+	0.358632i	$0.883243\pi$
$458$	162.577	−	26.4706i	0.354971	−	0.0577961i
$459$		0			0
$460$	593.044	+	267.121i	1.28923	+	0.580699i
$461$		−	41.2100i		−	0.0893926i	−0.999001	−	0.0446963i	$-0.985768\pi$
$461$		−	41.2100i		−	0.0893926i	0.999001	−	0.0446963i	$-0.0142320\pi$
$462$		0			0
$463$	85.4456	+	85.4456i	0.184548	+	0.184548i	0.793334	−	0.608786i	$-0.208343\pi$
$463$	85.4456	+	85.4456i	0.184548	+	0.184548i	−0.608786	+	0.793334i	$0.708343\pi$
$464$	−153.618	+	115.720i	−0.331072	+	0.249397i
$465$		0			0
$466$	81.7813	−	113.592i	0.175496	−	0.243759i
$467$	174.003	+	174.003i	0.372598	+	0.372598i	0.868422	−	0.495825i	$-0.165134\pi$
$467$	174.003	+	174.003i	0.372598	+	0.372598i	−0.495825	+	0.868422i	$0.665134\pi$
$468$		0			0
$469$			1269.48i			2.70678i
$470$	−100.296	−	66.3734i	−0.213395	−	0.141220i
$471$		0			0
$472$	89.8924	−	47.2808i	0.190450	−	0.100171i
$473$	41.3443	+	41.3443i	0.0874086	+	0.0874086i
$474$		0			0
$475$	−345.157	+	27.2450i	−0.726646	+	0.0573579i
$476$	−443.337	−	1325.35i	−0.931380	−	2.78435i
$477$		0			0
$478$	446.854	−	72.7563i	0.934841	−	0.152210i
$479$			84.3547i			0.176106i	0.996116	+	0.0880529i	$0.0280645\pi$
$479$			84.3547i			0.176106i	−0.996116	+	0.0880529i	$0.971936\pi$
$480$		0			0
$481$	227.085			0.472110
$482$	−120.032	−	737.209i	−0.249028	−	1.52948i
$483$		0			0
$484$	455.747	−	152.450i	0.941627	−	0.314980i
$485$	−132.627	+	143.508i	−0.273457	+	0.295893i
$486$		0			0
$487$	−447.915	+	447.915i	−0.919744	+	0.919744i	−0.997010	−	0.0772667i	$-0.975381\pi$
$487$	−447.915	+	447.915i	−0.919744	+	0.919744i	0.0772667	+	0.997010i	$0.475381\pi$
$488$	51.2545	+	97.4474i	0.105030	+	0.199687i
$489$		0			0
$490$	−185.398	−	910.907i	−0.378364	−	1.85899i
$491$	−692.548			−1.41048			−0.705242	−	0.708967i	$-0.749162\pi$
$491$	−692.548			−1.41048			−0.705242	+	0.708967i	$0.749162\pi$
$492$		0			0
$493$	249.245	−	249.245i	0.505567	−	0.505567i
$494$	257.586	+	185.451i	0.521429	+	0.375407i
$495$		0			0
$496$	−266.287	−	353.493i	−0.536869	−	0.712688i
$497$	−113.812	+	113.812i	−0.228999	+	0.228999i
$498$		0			0
$499$	−455.486			−0.912797			−0.456399	−	0.889775i	$-0.650861\pi$
$499$	−455.486			−0.912797			−0.456399	+	0.889775i	$0.650861\pi$
$500$	−213.405	−	452.170i	−0.426811	−	0.904341i
$501$		0			0
$502$	30.9157	+	189.878i	0.0615851	+	0.378243i
$503$	154.316	−	154.316i	0.306791	−	0.306791i	−0.536872	−	0.843664i	$-0.680394\pi$
$503$	154.316	−	154.316i	0.306791	−	0.306791i	0.843664	+	0.536872i	$0.180394\pi$
$504$		0			0
$505$	−98.9026	+	3.89739i	−0.195847	+	0.00771760i
$506$	48.8864	+	35.1962i	0.0966135	+	0.0695577i
$507$		0			0
$508$	136.092	−	272.903i	0.267898	−	0.537211i
$509$	−804.596			−1.58074			−0.790370	−	0.612630i	$-0.790112\pi$
$509$	−804.596			−1.58074			−0.790370	+	0.612630i	$0.790112\pi$
$510$		0			0
$511$			735.541i			1.43941i
$512$	508.429	+	60.3632i	0.993026	+	0.117897i
$513$		0			0
$514$	455.603	+	328.015i	0.886388	+	0.638162i
$515$	553.386	−	598.789i	1.07454	−	1.16270i
$516$		0			0
$517$	−7.87615	−	7.87615i	−0.0152343	−	0.0152343i
$518$	75.8876	+	466.086i	0.146501	+	0.899779i
$519$		0			0
$520$	−118.636	+	442.746i	−0.228146	+	0.851435i
$521$		−	229.718i		−	0.440917i	−0.975396	−	0.220458i	$-0.929245\pi$
$521$		−	229.718i		−	0.440917i	0.975396	−	0.220458i	$-0.0707553\pi$
$522$		0			0
$523$	−316.981	−	316.981i	−0.606083	−	0.606083i	0.335837	−	0.941920i	$-0.390981\pi$
$523$	−316.981	−	316.981i	−0.606083	−	0.606083i	−0.941920	+	0.335837i	$0.890981\pi$
$524$	−782.339	+	261.697i	−1.49301	+	0.499422i
$525$		0			0
$526$	−295.883	−	213.023i	−0.562515	−	0.404987i
$527$	573.543	+	573.543i	1.08832	+	1.08832i
$528$		0			0
$529$		−	528.637i		−	0.999314i
$530$	90.8408	+	60.1163i	0.171398	+	0.113427i
$531$		0			0
$532$	−294.553	+	590.662i	−0.553670	+	1.11027i
$533$	−84.5868	−	84.5868i	−0.158699	−	0.158699i
$534$		0			0
$535$	541.591	−	586.026i	1.01232	−	1.09538i
$536$	814.013	+	252.865i	1.51868	+	0.471764i
$537$		0			0
$538$	72.8921	+	447.688i	0.135487	+	0.832133i
$539$		−	86.0920i		−	0.159725i
$540$		0			0
$541$	−31.7231			−0.0586379			−0.0293189	−	0.999570i	$-0.509334\pi$
$541$	−31.7231			−0.0586379			−0.0293189	+	0.999570i	$0.509334\pi$
$542$	1011.71	−	164.725i	1.86662	−	0.303921i
$543$		0			0
$544$	−938.145	+	20.2816i	−1.72453	+	0.0372824i
$545$	394.260	−	15.5363i	0.723412	−	0.0285070i
$546$		0			0
$547$	597.232	−	597.232i	1.09183	−	1.09183i	0.0964985	−	0.995333i	$-0.469236\pi$
$547$	597.232	−	597.232i	1.09183	−	1.09183i	0.995333	−	0.0964985i	$-0.0307643\pi$
$548$	−122.177	+	244.999i	−0.222950	+	0.447079i
$549$		0			0
$550$	−11.0151	−	44.9776i	−0.0200274	−	0.0817775i
$551$	−166.473			−0.302129
$552$		0			0
$553$	−605.280	+	605.280i	−1.09454	+	1.09454i
$554$	−580.963	+	806.940i	−1.04867	+	1.45657i
$555$		0			0
$556$	−613.988	+	205.383i	−1.10430	+	0.369393i
$557$	557.605	−	557.605i	1.00109	−	1.00109i	0.00108692	−	0.999999i	$-0.499654\pi$
$557$	557.605	−	557.605i	1.00109	−	1.00109i	0.999999	−	0.00108692i	$-0.000345977\pi$
$558$		0			0
$559$	723.449			1.29418
$560$	−948.370	−	95.5388i	−1.69352	−	0.170605i
$561$		0			0
$562$	−113.451	+	18.4720i	−0.201870	+	0.0328683i
$563$	87.4204	−	87.4204i	0.155276	−	0.155276i	−0.625194	−	0.780470i	$-0.714980\pi$
$563$	87.4204	−	87.4204i	0.155276	−	0.155276i	0.780470	+	0.625194i	$0.214980\pi$
$564$		0			0
$565$	425.096	−	459.973i	0.752382	−	0.814112i
$566$	−254.903	+	354.053i	−0.450360	+	0.625536i
$567$		0			0
$568$	50.3085	+	95.6487i	0.0885713	+	0.168396i
$569$	−569.819			−1.00144			−0.500720	−	0.865609i	$-0.666931\pi$
$569$	−569.819			−1.00144			−0.500720	+	0.865609i	$0.666931\pi$
$570$		0			0
$571$		−	265.302i		−	0.464627i	−0.972641	−	0.232314i	$-0.925370\pi$
$571$		−	265.302i		−	0.464627i	0.972641	−	0.232314i	$-0.0746296\pi$
$572$	−18.9445	+	37.9892i	−0.0331198	+	0.0664146i
$573$		0			0
$574$	145.345	−	201.879i	0.253214	−	0.351706i
$575$	−527.879	+	618.358i	−0.918051	+	1.07541i
$576$		0			0
$577$	−83.7550	−	83.7550i	−0.145156	−	0.145156i	0.630794	−	0.775950i	$-0.282729\pi$
$577$	−83.7550	−	83.7550i	−0.145156	−	0.145156i	−0.775950	+	0.630794i	$0.782729\pi$
$578$	1126.94	−	183.487i	1.94972	−	0.317452i
$579$		0			0
$580$	−85.1825	−	224.811i	−0.146866	−	0.387606i
$581$			364.619i			0.627571i
$582$		0			0
$583$	7.13365	+	7.13365i	0.0122361	+	0.0122361i
$584$	471.642	+	146.511i	0.807606	+	0.250875i
$585$		0			0
$586$	515.507	−	716.024i	0.879705	−	1.22188i
$587$	−233.459	−	233.459i	−0.397715	−	0.397715i	0.479712	−	0.877426i	$-0.340741\pi$
$587$	−233.459	−	233.459i	−0.397715	−	0.397715i	−0.877426	+	0.479712i	$0.840741\pi$
$588$		0			0
$589$		−	383.076i		−	0.650383i
$590$	25.3213	+	124.410i	0.0429174	+	0.210864i
$591$		0			0
$592$	313.979	+	44.1783i	0.530369	+	0.0746255i
$593$	605.165	+	605.165i	1.02051	+	1.02051i	0.999785	+	0.0207287i	$0.00659863\pi$
$593$	605.165	+	605.165i	1.02051	+	1.02051i	0.0207287	+	0.999785i	$0.493401\pi$
$594$		0			0
$595$	1745.56	−	68.7861i	2.93371	−	0.115607i
$596$	386.863	−	129.408i	0.649098	−	0.217127i
$597$		0			0
$598$	735.645	−	119.777i	1.23018	−	0.200296i
$599$		−	947.643i		−	1.58204i	−0.611789	−	0.791021i	$-0.709550\pi$
$599$		−	947.643i		−	1.58204i	0.611789	−	0.791021i	$-0.290450\pi$
$600$		0			0
$601$	954.684			1.58849			0.794246	−	0.607596i	$-0.207866\pi$
$601$	954.684			1.58849			0.794246	+	0.607596i	$0.207866\pi$
$602$	241.763	+	1484.86i	0.401600	+	2.46654i
$603$		0			0
$604$	219.148	+	655.140i	0.362828	+	1.08467i
$605$	23.6535	+	600.245i	0.0390966	+	0.992141i
$606$		0			0
$607$	83.9758	−	83.9758i	0.138346	−	0.138346i	−0.634542	−	0.772888i	$-0.718811\pi$
$607$	83.9758	−	83.9758i	0.138346	−	0.138346i	0.772888	+	0.634542i	$0.218811\pi$
$608$	320.072	+	306.526i	0.526434	+	0.504154i
$609$		0			0
$610$	−134.866	+	27.4494i	−0.221091	+	0.0449990i
$611$	−137.818			−0.225561
$612$		0			0
$613$	−363.599	+	363.599i	−0.593147	+	0.593147i	−0.938480	−	0.345333i	$-0.887766\pi$
$613$	−363.599	+	363.599i	−0.593147	+	0.593147i	0.345333	+	0.938480i	$0.387766\pi$
$614$	53.4880	+	38.5091i	0.0871141	+	0.0627185i
$615$		0			0
$616$	−84.3026	−	26.1878i	−0.136855	−	0.0425127i
$617$	−394.223	+	394.223i	−0.638935	+	0.638935i	−0.950293	−	0.311358i	$-0.899216\pi$
$617$	−394.223	+	394.223i	−0.638935	+	0.638935i	0.311358	+	0.950293i	$0.399216\pi$
$618$		0			0
$619$	−393.359			−0.635475			−0.317737	−	0.948179i	$-0.602923\pi$
$619$	−393.359			−0.635475			−0.317737	+	0.948179i	$0.602923\pi$
$620$	517.319	−	196.016i	0.834385	−	0.316154i
$621$		0			0
$622$	105.797	+	649.783i	0.170092	+	1.04467i
$623$	830.856	−	830.856i	1.33364	−	1.33364i
$624$		0			0
$625$	617.260	−	98.0580i	0.987616	−	0.156893i
$626$	−717.120	−	516.296i	−1.14556	−	0.824754i
$627$		0			0
$628$	−705.793	−	351.966i	−1.12387	−	0.560456i
$629$	−581.110			−0.923863
$630$		0			0
$631$		−	518.021i		−	0.820952i	−0.911871	−	0.410476i	$-0.865363\pi$
$631$		−	518.021i		−	0.820952i	0.911871	−	0.410476i	$-0.134637\pi$
$632$	267.552	+	508.681i	0.423341	+	0.804875i
$633$		0			0
$634$	−184.692	−	132.971i	−0.291313	−	0.209733i
$635$	279.949	+	258.722i	0.440864	+	0.407436i
$636$		0			0
$637$	−753.225	−	753.225i	−1.18246	−	1.18246i
$638$	−3.57806	−	21.9757i	−0.00560824	−	0.0344446i
$639$		0			0
$640$	−250.165	+	589.082i	−0.390883	+	0.920440i
$641$			592.363i			0.924123i	0.886848	+	0.462062i	$0.152890\pi$
$641$			592.363i			0.924123i	−0.886848	+	0.462062i	$0.847110\pi$
$642$		0			0
$643$	388.120	+	388.120i	0.603609	+	0.603609i	0.941268	−	0.337660i	$-0.109635\pi$
$643$	388.120	+	388.120i	0.603609	+	0.603609i	−0.337660	+	0.941268i	$0.609635\pi$
$644$	491.678	+	1469.86i	0.763475	+	2.28240i
$645$		0			0
$646$	−659.162	−	474.569i	−1.02037	−	0.734627i
$647$	90.0584	+	90.0584i	0.139194	+	0.139194i	0.773270	−	0.634076i	$-0.218620\pi$
$647$	90.0584	+	90.0584i	0.139194	+	0.139194i	−0.634076	+	0.773270i	$0.718620\pi$
$648$		0			0
$649$			11.7582i			0.0181175i
$650$	−489.884	−	297.140i	−0.753668	−	0.457139i
$651$		0			0
$652$	389.568	+	194.271i	0.597497	+	0.297961i
$653$	−855.835	−	855.835i	−1.31062	−	1.31062i	−0.920958	−	0.389662i	$-0.872592\pi$
$653$	−855.835	−	855.835i	−1.31062	−	1.31062i	−0.389662	−	0.920958i	$-0.627408\pi$
$654$		0			0
$655$	−40.6037	−	1030.39i	−0.0619904	−	1.57311i
$656$	−100.498	−	133.410i	−0.153198	−	0.203368i
$657$		0			0
$658$	−46.0562	−	282.868i	−0.0699943	−	0.429890i
$659$			621.519i			0.943124i	0.881833	+	0.471562i	$0.156310\pi$
$659$			621.519i			0.943124i	−0.881833	+	0.471562i	$0.843690\pi$
$660$		0			0
$661$	−1017.87			−1.53989			−0.769944	−	0.638111i	$-0.779716\pi$
$661$	−1017.87			−1.53989			−0.769944	+	0.638111i	$0.779716\pi$
$662$	168.388	−	27.4167i	0.254362	−	0.0414149i
$663$		0			0
$664$	233.800	+	72.6278i	0.352108	+	0.109379i
$665$	−605.911	−	559.968i	−0.911145	−	0.842057i
$666$		0			0
$667$	−276.422	+	276.422i	−0.414426	+	0.414426i
$668$	707.192	+	352.664i	1.05867	+	0.527940i
$669$		0			0
$670$	−588.010	+	888.533i	−0.877627	+	1.32617i
$671$	−12.7465			−0.0189962
$672$		0			0
$673$	−571.637	+	571.637i	−0.849386	+	0.849386i	−0.990056	−	0.140671i	$-0.955074\pi$
$673$	−571.637	+	571.637i	−0.849386	+	0.849386i	0.140671	+	0.990056i	$0.455074\pi$
$674$	158.081	−	219.570i	0.234542	−	0.325772i
$675$		0			0
$676$	−47.8233	−	142.967i	−0.0707445	−	0.211490i
$677$	−339.238	+	339.238i	−0.501090	+	0.501090i	−0.911777	−	0.410687i	$-0.865289\pi$
$677$	−339.238	+	339.238i	−0.501090	+	0.501090i	0.410687	+	0.911777i	$0.365289\pi$
$678$		0			0
$679$	−465.644			−0.685779
$680$	303.588	−	1132.99i	0.446453	−	1.66616i
$681$		0			0
$682$	50.5688	−	8.23356i	0.0741478	−	0.0120727i
$683$	761.676	−	761.676i	1.11519	−	1.11519i	0.122755	−	0.992437i	$-0.460827\pi$
$683$	761.676	−	761.676i	1.11519	−	1.11519i	0.992437	−	0.122755i	$-0.0391730\pi$
$684$		0			0
$685$	−251.324	−	232.268i	−0.366897	−	0.339077i
$686$	612.032	−	850.094i	0.892175	−	1.23920i
$687$		0			0
$688$	1000.27	+	140.743i	1.45389	+	0.204569i
$689$	124.826			0.181169
$690$		0			0
$691$			943.161i			1.36492i	0.730922	+	0.682461i	$0.239090\pi$
$691$			943.161i			1.36492i	−0.730922	+	0.682461i	$0.760910\pi$
$692$	−365.318	−	182.178i	−0.527916	−	0.263262i
$693$		0			0
$694$	−191.631	+	266.170i	−0.276126	+	0.383530i
$695$	−31.8662	−	808.658i	−0.0458507	−	1.16354i
$696$		0			0
$697$	216.457	+	216.457i	0.310556	+	0.310556i
$698$	−181.311	+	29.5208i	−0.259757	+	0.0422934i
$699$		0			0
$700$	446.162	−	1104.77i	0.637375	−	1.57825i
$701$			633.011i			0.903011i	0.892268	+	0.451506i	$0.149113\pi$
$701$			633.011i			0.903011i	−0.892268	+	0.451506i	$0.850887\pi$
$702$		0			0
$703$	194.065	+	194.065i	0.276053	+	0.276053i
$704$	−33.5842	+	48.8401i	−0.0477048	+	0.0693751i
$705$		0			0
$706$	−141.736	+	196.867i	−0.200759	+	0.278848i
$707$	−166.779	−	166.779i	−0.235896	−	0.235896i
$708$		0			0
$709$			53.1207i			0.0749234i	0.999298	+	0.0374617i	$0.0119272\pi$
$709$			53.1207i			0.0749234i	−0.999298	+	0.0374617i	$0.988073\pi$
$710$	−132.376	+	26.9427i	−0.186446	+	0.0379475i
$711$		0			0
$712$	−367.263	−	698.257i	−0.515819	−	0.980698i
$713$	−636.082	−	636.082i	−0.892120	−	0.892120i
$714$		0			0
$715$	−38.9699	−	36.0150i	−0.0545034	−	0.0503707i
$716$	194.356	+	581.024i	0.271447	+	0.811486i
$717$		0			0
$718$	−39.4539	+	6.42384i	−0.0549497	+	0.00894685i
$719$		−	537.990i		−	0.748248i	−0.927379	−	0.374124i	$-0.877943\pi$
$719$		−	537.990i		−	0.748248i	0.927379	−	0.374124i	$-0.122057\pi$
$720$		0			0
$721$	1942.90			2.69473
$722$	−54.3816	−	334.000i	−0.0753208	−	0.462604i
$723$		0			0
$724$	508.184	−	169.991i	0.701912	−	0.234794i
$725$	299.579	−	23.6473i	0.413212	−	0.0326170i
$726$		0			0
$727$	361.181	−	361.181i	0.496810	−	0.496810i	−0.413633	−	0.910444i	$-0.635740\pi$
$727$	361.181	−	361.181i	0.496810	−	0.496810i	0.910444	+	0.413633i	$0.135740\pi$
$728$	−966.689	+	508.451i	−1.32787	+	0.698421i
$729$		0			0
$730$	−340.695	+	514.819i	−0.466706	+	0.705232i
$731$	−1851.30			−2.53256
$732$		0			0
$733$	860.092	−	860.092i	1.17339	−	1.17339i	0.191990	−	0.981397i	$-0.438506\pi$
$733$	860.092	−	860.092i	1.17339	−	1.17339i	0.981397	−	0.191990i	$-0.0614940\pi$
$734$	473.562	+	340.944i	0.645179	+	0.464502i
$735$		0			0
$736$	1040.44	−	22.4931i	1.41364	−	0.0305613i
$737$	−69.7758	+	69.7758i	−0.0946754	+	0.0946754i
$738$		0			0
$739$	−1131.08			−1.53056			−0.765278	−	0.643700i	$-0.777398\pi$
$739$	−1131.08			−1.53056			−0.765278	+	0.643700i	$0.777398\pi$
$740$	−162.771	+	361.373i	−0.219961	+	0.488342i
$741$		0			0
$742$	41.7145	+	256.201i	0.0562189	+	0.345285i
$743$	−605.598	+	605.598i	−0.815071	+	0.815071i	−0.985389	−	0.170318i	$-0.945520\pi$
$743$	−605.598	+	605.598i	−0.815071	+	0.815071i	0.170318	+	0.985389i	$0.445520\pi$
$744$		0			0
$745$	20.0783	+	509.520i	0.0269508	+	0.683920i
$746$	62.2743	+	44.8349i	0.0834777	+	0.0601004i
$747$		0			0
$748$	48.4790	−	97.2142i	0.0648114	−	0.129965i
$749$	1901.49			2.53870
$750$		0			0
$751$		−	376.601i		−	0.501466i	−0.968056	−	0.250733i	$-0.919328\pi$
$751$		−	376.601i		−	0.501466i	0.968056	−	0.250733i	$-0.0806716\pi$
$752$	−190.554	−	26.8118i	−0.253396	−	0.0356540i
$753$		0			0
$754$	−223.572	−	160.962i	−0.296514	−	0.213478i
$755$	−862.858	+	34.0020i	−1.14286	+	0.0450358i
$756$		0			0
$757$	−457.394	−	457.394i	−0.604220	−	0.604220i	0.337210	−	0.941430i	$-0.390517\pi$
$757$	−457.394	−	457.394i	−0.604220	−	0.604220i	−0.941430	+	0.337210i	$0.890517\pi$
$758$	−41.6962	−	256.089i	−0.0550082	−	0.337849i
$759$		0			0
$760$	−479.752	+	276.982i	−0.631253	+	0.364450i
$761$		−	1019.49i		−	1.33968i	−0.742508	−	0.669838i	$-0.766364\pi$
$761$		−	1019.49i		−	1.33968i	0.742508	−	0.669838i	$-0.233636\pi$
$762$		0			0
$763$	664.836	+	664.836i	0.871345	+	0.871345i
$764$	193.001	−	64.5600i	0.252619	−	0.0845026i
$765$		0			0
$766$	−133.088	−	95.8179i	−0.173744	−	0.125089i
$767$	102.874	+	102.874i	0.134125	+	0.134125i
$768$		0			0
$769$		−	158.184i		−	0.205701i	−0.994697	−	0.102851i	$-0.967204\pi$
$769$		−	158.184i		−	0.205701i	0.994697	−	0.102851i	$-0.0327964\pi$
$770$	60.8968	−	92.0202i	0.0790868	−	0.119507i
$771$		0			0
$772$	−393.992	+	790.066i	−0.510352	+	1.02340i
$773$	−492.294	−	492.294i	−0.636861	−	0.636861i	0.312919	−	0.949780i	$-0.398693\pi$
$773$	−492.294	−	492.294i	−0.636861	−	0.636861i	−0.949780	+	0.312919i	$0.898693\pi$
$774$		0			0
$775$	54.4154	+	689.368i	0.0702134	+	0.889507i
$776$	−92.7508	+	298.579i	−0.119524	+	0.384767i
$777$		0			0
$778$	190.335	+	1169.00i	0.244646	+	1.50257i
$779$		−	144.574i		−	0.185590i
$780$		0			0
$781$	−12.5112			−0.0160195
$782$	−1882.51	+	306.509i	−2.40731	+	0.391955i
$783$		0			0
$784$	−894.908	−	1187.98i	−1.14146	−	1.51528i
$785$	669.116	−	724.014i	0.852377	−	0.922311i
$786$		0			0
$787$	334.570	−	334.570i	0.425121	−	0.425121i	−0.461841	−	0.886963i	$-0.652811\pi$
$787$	334.570	−	334.570i	0.425121	−	0.425121i	0.886963	+	0.461841i	$0.152811\pi$
$788$	547.660	−	1098.21i	0.695000	−	1.39367i
$789$		0			0
$790$	−704.007	+	143.287i	−0.891148	+	0.181376i
$791$	1492.48			1.88683
$792$		0			0
$793$	−111.520	+	111.520i	−0.140630	+	0.140630i
$794$	−157.319	+	218.512i	−0.198135	+	0.275204i
$795$		0			0
$796$	−568.780	+	190.260i	−0.714548	+	0.239021i
$797$	290.523	−	290.523i	0.364521	−	0.364521i	−0.500954	−	0.865474i	$-0.667017\pi$
$797$	290.523	−	290.523i	0.364521	−	0.364521i	0.865474	+	0.500954i	$0.167017\pi$
$798$		0			0
$799$	352.676			0.441397
$800$	−619.530	−	506.145i	−0.774412	−	0.632681i
$801$		0			0
$802$	−207.557	+	33.7942i	−0.258799	+	0.0421374i
$803$	−40.4283	+	40.4283i	−0.0503466	+	0.0503466i
$804$		0			0
$805$	−1935.90	+	76.2865i	−2.40484	+	0.0947658i
$806$	370.394	−	514.466i	0.459546	−	0.638295i
$807$		0			0
$808$	−140.162	+	73.7211i	−0.173468	+	0.0912390i
$809$	−1107.13			−1.36852			−0.684259	−	0.729239i	$-0.739874\pi$
$809$	−1107.13			−1.36852			−0.684259	+	0.729239i	$0.739874\pi$
$810$		0			0
$811$			591.308i			0.729110i	0.931182	+	0.364555i	$0.118779\pi$
$811$			591.308i			0.729110i	−0.931182	+	0.364555i	$0.881221\pi$
$812$	255.657	−	512.665i	0.314848	−	0.631361i
$813$		0			0
$814$	−21.4469	+	29.7891i	−0.0263475	+	0.0365959i
$815$	−369.324	+	399.625i	−0.453158	+	0.490338i
$816$		0			0
$817$	618.253	+	618.253i	0.756735	+	0.756735i
$818$	−893.081	+	145.411i	−1.09179	+	0.177764i
$819$		0			0
$820$	195.238	−	73.9770i	0.238095	−	0.0902159i
$821$			94.2436i			0.114791i	0.998352	+	0.0573956i	$0.0182796\pi$
$821$			94.2436i			0.114791i	−0.998352	+	0.0573956i	$0.981720\pi$
$822$		0			0
$823$	−998.124	−	998.124i	−1.21279	−	1.21279i	−0.970106	−	0.242681i	$-0.921973\pi$
$823$	−998.124	−	998.124i	−1.21279	−	1.21279i	−0.242681	−	0.970106i	$-0.578027\pi$
$824$	387.003	−	1245.82i	0.469664	−	1.51192i
$825$		0			0
$826$	−176.767	+	245.524i	−0.214004	+	0.297245i
$827$	−89.6511	−	89.6511i	−0.108405	−	0.108405i	0.650824	−	0.759229i	$-0.274424\pi$
$827$	−89.6511	−	89.6511i	−0.108405	−	0.108405i	−0.759229	+	0.650824i	$0.774424\pi$
$828$		0			0
$829$		−	853.356i		−	1.02938i	−0.857376	−	0.514690i	$-0.827907\pi$
$829$		−	853.356i		−	1.02938i	0.857376	−	0.514690i	$-0.172093\pi$
$830$	−168.888	+	255.204i	−0.203479	+	0.307474i
$831$		0			0
$832$	133.475	+	721.136i	0.160426	+	0.866750i
$833$	1927.50	+	1927.50i	2.31393	+	2.31393i
$834$		0			0
$835$	−670.442	+	725.449i	−0.802924	+	0.868801i
$836$	−48.6550	+	16.2754i	−0.0581998	+	0.0194682i
$837$		0			0
$838$	−1195.05	+	194.578i	−1.42608	+	0.232193i
$839$			771.955i			0.920089i	0.887896	+	0.460045i	$0.152167\pi$
$839$			771.955i			0.920089i	−0.887896	+	0.460045i	$0.847833\pi$
$840$		0			0
$841$	−696.510			−0.828192
$842$	−33.1658	−	203.697i	−0.0393893	−	0.241921i
$843$		0			0
$844$	−306.071	−	914.994i	−0.362643	−	1.08412i
$845$	188.296	−	7.42005i	0.222835	−	0.00878112i
$846$		0			0
$847$	−1012.19	+	1012.19i	−1.19503	+	1.19503i
$848$	172.590	+	24.2842i	0.203526	+	0.0286371i
$849$		0			0
$850$	1253.61	+	760.382i	1.47484	+	0.894567i
$851$	644.474			0.757314
$852$		0			0
$853$	−629.940	+	629.940i	−0.738500	+	0.738500i	−0.972288	−	0.233788i	$-0.924888\pi$
$853$	−629.940	+	629.940i	−0.738500	+	0.738500i	0.233788	+	0.972288i	$0.424888\pi$
$854$	−266.159	−	191.623i	−0.311662	−	0.224383i
$855$		0			0
$856$	378.754	−	1219.27i	0.442470	−	1.42438i
$857$	−1097.67	+	1097.67i	−1.28082	+	1.28082i	−0.340624	+	0.940199i	$0.610638\pi$
$857$	−1097.67	+	1097.67i	−1.28082	+	1.28082i	−0.940199	+	0.340624i	$0.889362\pi$
$858$		0			0
$859$	180.577			0.210217			0.105109	−	0.994461i	$-0.466481\pi$
$859$	180.577			0.210217			0.105109	+	0.994461i	$0.466481\pi$
$860$	−518.557	+	1151.26i	−0.602973	+	1.33868i
$861$		0			0
$862$	−169.622	−	1041.78i	−0.196778	−	1.20857i
$863$	−278.185	+	278.185i	−0.322346	+	0.322346i	−0.849667	−	0.527320i	$-0.823197\pi$
$863$	−278.185	+	278.185i	−0.322346	+	0.322346i	0.527320	+	0.849667i	$0.323197\pi$
$864$		0			0
$865$	346.334	−	374.749i	0.400386	−	0.433236i
$866$	357.250	+	257.205i	0.412529	+	0.297003i
$867$		0			0
$868$	1179.71	+	588.298i	1.35911	+	0.677763i
$869$	−66.5373			−0.0765677
$870$		0			0
$871$			1220.95i			1.40178i
$872$	558.733	−	293.877i	0.640749	−	0.337015i
$873$		0			0
$874$	731.036	+	526.315i	0.836426	+	0.602192i
$875$	1169.92	+	921.627i	1.33705	+	1.05329i
$876$		0			0
$877$	833.741	+	833.741i	0.950673	+	0.950673i	0.998839	−	0.0481659i	$-0.0153376\pi$
$877$	833.741	+	833.741i	0.950673	+	0.950673i	−0.0481659	+	0.998839i	$0.515338\pi$
$878$	−191.323	−	1175.07i	−0.217908	−	1.33834i
$879$		0			0
$880$	−46.8751	−	57.3775i	−0.0532671	−	0.0652017i
$881$			538.804i			0.611582i	0.952099	+	0.305791i	$0.0989209\pi$
$881$			538.804i			0.611582i	−0.952099	+	0.305791i	$0.901079\pi$
$882$		0			0
$883$	−844.245	−	844.245i	−0.956110	−	0.956110i	0.0429669	−	0.999076i	$-0.486319\pi$
$883$	−844.245	−	844.245i	−0.956110	−	0.956110i	−0.999076	+	0.0429669i	$0.986319\pi$
$884$	−426.388	−	1274.68i	−0.482339	−	1.44195i
$885$		0			0
$886$	1131.10	+	814.347i	1.27664	+	0.919127i
$887$	539.424	+	539.424i	0.608144	+	0.608144i	0.942461	−	0.334317i	$-0.108505\pi$
$887$	539.424	+	539.424i	0.608144	+	0.608144i	−0.334317	+	0.942461i	$0.608505\pi$
$888$		0			0
$889$			908.355i			1.02177i
$890$	966.377	−	196.688i	1.08582	−	0.220998i
$891$		0			0
$892$	−447.975	−	223.397i	−0.502214	−	0.250445i
$893$	−117.778	−	117.778i	−0.131890	−	0.131890i
$894$		0			0
$895$	−765.242	+	30.1554i	−0.855019	+	0.0336932i
$896$	−1435.51	+	514.943i	−1.60213	+	0.574713i
$897$		0			0
$898$	−51.2100	−	314.521i	−0.0570267	−	0.350246i
$899$			332.490i			0.369845i
$900$		0			0
$901$	−319.429			−0.354527
$902$	19.0848	−	3.10738i	0.0211584	−	0.00344499i
$903$		0			0
$904$	297.285	−	957.008i	0.328856	−	1.05864i
$905$	26.3750	+	669.308i	0.0291436	+	0.739567i
$906$		0			0
$907$	317.006	−	317.006i	0.349510	−	0.349510i	−0.510417	−	0.859927i	$-0.670509\pi$
$907$	317.006	−	317.006i	0.349510	−	0.349510i	0.859927	+	0.510417i	$0.170509\pi$
$908$	955.051	+	476.267i	1.05182	+	0.524523i
$909$		0			0
$910$	−272.301	−	1337.88i	−0.299232	−	1.47020i
$911$	−923.873			−1.01413			−0.507065	−	0.861908i	$-0.669270\pi$
$911$	−923.873			−1.01413			−0.507065	+	0.861908i	$0.669270\pi$
$912$		0			0
$913$	−20.0409	+	20.0409i	−0.0219506	+	0.0219506i
$914$	434.146	−	603.016i	0.474996	−	0.659755i
$915$		0			0
$916$	104.506	+	312.420i	0.114090	+	0.341070i
$917$	1737.53	−	1737.53i	1.89480	−	1.89480i
$918$		0			0
$919$	606.752			0.660231			0.330115	−	0.943941i	$-0.392912\pi$
$919$	606.752			0.660231			0.330115	+	0.943941i	$0.392912\pi$
$920$	−336.691	+	1256.53i	−0.365969	+	1.36579i
$921$		0			0
$922$	81.3487	−	13.2451i	0.0882307	−	0.0143656i
$923$	−109.461	+	109.461i	−0.118593	+	0.118593i
$924$		0			0
$925$	−376.798	−	321.665i	−0.407349	−	0.347746i
$926$	−141.207	+	196.133i	−0.152492	+	0.211806i
$927$		0			0
$928$	−277.806	−	266.049i	−0.299360	−	0.286690i
$929$	−22.4299			−0.0241441			−0.0120720	−	0.999927i	$-0.503843\pi$
$929$	−22.4299			−0.0241441			−0.0120720	+	0.999927i	$0.503843\pi$
$930$		0			0
$931$		−	1287.40i		−	1.38281i
$932$	250.516	+	124.928i	0.268794	+	0.134043i
$933$		0			0
$934$	−287.557	+	399.409i	−0.307877	+	0.427632i
$935$	99.7239	+	92.1624i	0.106657	+	0.0985694i
$936$		0			0
$937$	392.217	+	392.217i	0.418588	+	0.418588i	0.884717	−	0.466129i	$-0.154352\pi$
$937$	392.217	+	392.217i	0.418588	+	0.418588i	−0.466129	+	0.884717i	$0.654352\pi$
$938$	−2505.96	+	408.018i	−2.67160	+	0.434987i
$939$		0			0
$940$	98.7858	−	219.317i	0.105091	−	0.233316i
$941$		−	866.076i		−	0.920378i	−0.887821	−	0.460189i	$-0.847782\pi$
$941$		−	866.076i		−	0.920378i	0.887821	−	0.460189i	$-0.152218\pi$
$942$		0			0
$943$	−240.060	−	240.060i	−0.254570	−	0.254570i
$944$	122.225	+	162.252i	0.129475	+	0.171877i
$945$		0			0
$946$	−68.3256	+	94.9022i	−0.0722258	+	0.100319i
$947$	130.423	+	130.423i	0.137723	+	0.137723i	0.772607	−	0.634885i	$-0.218952\pi$
$947$	130.423	+	130.423i	0.137723	+	0.137723i	−0.634885	+	0.772607i	$0.718952\pi$
$948$		0			0
$949$			707.421i			0.745439i
$950$	−164.717	−	672.585i	−0.173386	−	0.707984i
$951$		0			0
$952$	2473.75	−	1301.12i	2.59848	−	1.36673i
$953$	215.383	+	215.383i	0.226005	+	0.226005i	0.811021	−	0.585017i	$-0.198912\pi$
$953$	215.383	+	215.383i	0.226005	+	0.226005i	−0.585017	+	0.811021i	$0.698912\pi$
$954$		0			0
$955$	10.0168	+	254.194i	0.0104888	+	0.266171i
$956$	287.243	+	858.708i	0.300463	+	0.898230i
$957$		0			0
$958$	−166.517	+	27.1121i	−0.173817	+	0.0283007i
$959$		−	815.477i		−	0.850341i
$960$		0			0
$961$	195.898			0.203848
$962$	72.9864	+	448.267i	0.0758695	+	0.465974i
$963$		0			0
$964$	1416.68	−	473.886i	1.46958	−	0.491583i
$965$	−810.463	−	749.010i	−0.839858	−	0.776176i
$966$		0			0
$967$	765.169	−	765.169i	0.791281	−	0.791281i	−0.190421	−	0.981702i	$-0.560985\pi$
$967$	765.169	−	765.169i	0.791281	−	0.791281i	0.981702	+	0.190421i	$0.0609855\pi$
$968$	447.417	+	850.649i	0.462208	+	0.878770i
$969$		0			0
$970$	−325.913	−	215.682i	−0.335993	−	0.222352i
$971$	1100.34			1.13321			0.566603	−	0.823991i	$-0.308257\pi$
$971$	1100.34			1.13321			0.566603	+	0.823991i	$0.308257\pi$
$972$		0			0
$973$	1363.63	−	1363.63i	1.40147	−	1.40147i
$974$	−1028.15	−	740.225i	−1.05560	−	0.759984i
$975$		0			0
$976$	−175.888	+	132.497i	−0.180213	+	0.135755i
$977$	−410.621	+	410.621i	−0.420288	+	0.420288i	−0.885303	−	0.465015i	$-0.846049\pi$
$977$	−410.621	+	410.621i	−0.420288	+	0.420288i	0.465015	+	0.885303i	$0.346049\pi$
$978$		0			0
$979$	91.3345			0.0932937
$980$	1738.55	−	658.748i	1.77403	−	0.672192i
$981$		0			0
$982$	−222.589	−	1367.09i	−0.226669	−	1.39215i
$983$	−1100.78	+	1100.78i	−1.11982	+	1.11982i	−0.128054	+	0.991767i	$0.540873\pi$
$983$	−1100.78	+	1100.78i	−1.11982	+	1.11982i	−0.991767	+	0.128054i	$0.959127\pi$
$984$		0			0
$985$	1126.57	+	1041.14i	1.14372	+	1.05700i
$986$	572.119	+	411.902i	0.580242	+	0.417750i
$987$		0			0
$988$	−283.292	+	568.081i	−0.286733	+	0.574981i
$989$	2053.17			2.07600
$990$		0			0
$991$		−	708.358i		−	0.714791i	−0.933953	−	0.357395i	$-0.883665\pi$
$991$		−	708.358i		−	0.714791i	0.933953	−	0.357395i	$-0.116335\pi$
$992$	612.211	−	639.267i	0.617148	−	0.644422i
$993$		0			0
$994$	−261.246	−	188.086i	−0.262823	−	0.189222i
$995$	−29.5199	−	749.116i	−0.0296683	−	0.752881i
$996$		0			0
$997$	1022.38	+	1022.38i	1.02546	+	1.02546i	0.999667	+	0.0257920i	$0.00821077\pi$
$997$	1022.38	+	1022.38i	1.02546	+	1.02546i	0.0257920	+	0.999667i	$0.491789\pi$
$998$	−146.396	−	899.132i	−0.146689	−	0.900933i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.3.m.c.107.12	yes	40
3.2	odd	2	inner	180.3.m.c.107.9	yes	40
4.3	odd	2	inner	180.3.m.c.107.2	✓	40
5.3	odd	4	inner	180.3.m.c.143.19	yes	40
12.11	even	2	inner	180.3.m.c.107.19	yes	40
15.8	even	4	inner	180.3.m.c.143.2	yes	40
20.3	even	4	inner	180.3.m.c.143.9	yes	40
60.23	odd	4	inner	180.3.m.c.143.12	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.3.m.c.107.2	✓	40	4.3	odd	2	inner
180.3.m.c.107.9	yes	40	3.2	odd	2	inner
180.3.m.c.107.12	yes	40	1.1	even	1	trivial
180.3.m.c.107.19	yes	40	12.11	even	2	inner
180.3.m.c.143.2	yes	40	15.8	even	4	inner
180.3.m.c.143.9	yes	40	20.3	even	4	inner
180.3.m.c.143.12	yes	40	60.23	odd	4	inner
180.3.m.c.143.19	yes	40	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	180.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.321406 + 1.97401i) q^{2} +(-3.79340 + 1.26891i) q^{4} +(-0.196879 - 4.99612i) q^{5} +(8.42491 - 8.42491i) q^{7} +(-3.72406 - 7.08035i) q^{8} +O(q^{10})\)	\(q+(0.321406 + 1.97401i) q^{2} +(-3.79340 + 1.26891i) q^{4} +(-0.196879 - 4.99612i) q^{5} +(8.42491 - 8.42491i) q^{7} +(-3.72406 - 7.08035i) q^{8} +(9.79910 - 1.99442i) q^{10} +0.926135 q^{11} +(8.10283 - 8.10283i) q^{13} +(19.3386 + 13.9230i) q^{14} +(12.7797 - 9.62698i) q^{16} +(-20.7351 + 20.7351i) q^{17} +13.8492 q^{19} +(7.08649 + 18.7025i) q^{20} +(0.297665 + 1.82820i) q^{22} +(22.9961 - 22.9961i) q^{23} +(-24.9225 + 1.96726i) q^{25} +(18.5993 + 13.3907i) q^{26} +(-21.2686 + 42.6495i) q^{28} -12.0204 q^{29} -27.6605i q^{31} +(23.1112 + 22.1331i) q^{32} +(-47.5956 - 34.2668i) q^{34} +(-43.7506 - 40.4332i) q^{35} +(14.0127 + 14.0127i) q^{37} +(4.45122 + 27.3384i) q^{38} +(-34.6411 + 19.9998i) q^{40} -10.4392i q^{41} +(44.6417 + 44.6417i) q^{43} +(-3.51320 + 1.17519i) q^{44} +(52.7854 + 38.0033i) q^{46} +(-8.50432 - 8.50432i) q^{47} -92.9583i q^{49} +(-11.8936 - 48.5648i) q^{50} +(-20.4555 + 41.0190i) q^{52} +(7.70260 + 7.70260i) q^{53} +(-0.182336 - 4.62709i) q^{55} +(-91.0262 - 28.2764i) q^{56} +(-3.86343 - 23.7284i) q^{58} +12.6960i q^{59} -13.7631 q^{61} +(54.6019 - 8.89024i) q^{62} +(-36.2627 + 52.7353i) q^{64} +(-42.0780 - 38.8874i) q^{65} +(-75.3408 + 75.3408i) q^{67} +(52.3454 - 104.968i) q^{68} +(65.7537 - 99.3594i) q^{70} -13.5090 q^{71} +(-43.6527 + 43.6527i) q^{73} +(-23.1574 + 32.1649i) q^{74} +(-52.5356 + 17.5735i) q^{76} +(7.80261 - 7.80261i) q^{77} -71.8441 q^{79} +(-50.6136 - 61.9537i) q^{80} +(20.6070 - 3.35521i) q^{82} +(-21.6393 + 21.6393i) q^{83} +(107.677 + 99.5128i) q^{85} +(-73.7749 + 102.471i) q^{86} +(-3.44899 - 6.55736i) q^{88} +98.6190 q^{89} -136.531i q^{91} +(-58.0532 + 116.413i) q^{92} +(14.0542 - 19.5209i) q^{94} +(-2.72662 - 69.1924i) q^{95} +(-27.6349 - 27.6349i) q^{97} +(183.500 - 29.8773i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q+O(q^{10}) \) 40 * q	\( 40 q + 16 q^{10} - 40 q^{13} + 184 q^{16} + 112 q^{22} + 32 q^{28} - 264 q^{37} + 40 q^{40} - 160 q^{46} - 328 q^{52} - 720 q^{58} - 128 q^{61} + 464 q^{70} - 664 q^{73} + 576 q^{76} + 320 q^{82} + 608 q^{85} + 544 q^{88} + 360 q^{97}+O(q^{100}) \) 40 * q + 16 * q^10 - 40 * q^13 + 184 * q^16 + 112 * q^22 + 32 * q^28 - 264 * q^37 + 40 * q^40 - 160 * q^46 - 328 * q^52 - 720 * q^58 - 128 * q^61 + 464 * q^70 - 664 * q^73 + 576 * q^76 + 320 * q^82 + 608 * q^85 + 544 * q^88 + 360 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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