LMFDB - Embedded newform 135.3.l.a.73.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [135,3,Mod(37,135)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(135, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([4, 3])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("135.37"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	135.l (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.67848356886$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			73.4
Character	$\chi$	$=$	135.73
Dual form			135.3.l.a.37.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.238965 - 0.891829i) q^{2} +(2.72585 - 1.57377i) q^{4} +(3.51824 + 3.55274i) q^{5} +(2.96175 + 11.0534i) q^{7} +(-4.66637 - 4.66637i) q^{8} +(2.32770 - 3.98665i) q^{10} +(1.30484 - 2.26005i) q^{11} +(-0.764853 + 2.85447i) q^{13} +(9.15000 - 5.28276i) q^{14} +(3.24857 - 5.62669i) q^{16} +(13.6850 - 13.6850i) q^{17} -11.4465i q^{19} +(15.1814 + 4.14733i) q^{20} +(-2.32738 - 0.623621i) q^{22} +(-2.89082 + 10.7887i) q^{23} +(-0.243925 + 24.9988i) q^{25} +2.72847 q^{26} +(25.4688 + 25.4688i) q^{28} +(-23.0262 - 13.2942i) q^{29} +(-21.8787 - 37.8950i) q^{31} +(-31.2919 - 8.38463i) q^{32} +(-15.4750 - 8.93448i) q^{34} +(-28.8498 + 49.4110i) q^{35} +(14.4324 - 14.4324i) q^{37} +(-10.2083 + 2.73530i) q^{38} +(0.160974 - 32.9958i) q^{40} +(0.924605 + 1.60146i) q^{41} +(-49.0742 + 13.1494i) q^{43} -8.21405i q^{44} +10.3125 q^{46} +(16.4309 + 61.3211i) q^{47} +(-70.9709 + 40.9750i) q^{49} +(22.3529 - 5.75630i) q^{50} +(2.40740 + 8.98455i) q^{52} +(-6.43481 - 6.43481i) q^{53} +(12.6201 - 3.31564i) q^{55} +(37.7587 - 65.4000i) q^{56} +(-6.35367 + 23.7122i) q^{58} +(-49.5170 + 28.5886i) q^{59} +(16.8393 - 29.1666i) q^{61} +(-28.5676 + 28.5676i) q^{62} +3.92205i q^{64} +(-12.8321 + 7.32540i) q^{65} +(31.4072 + 8.41554i) q^{67} +(15.7663 - 58.8405i) q^{68} +(50.9602 + 13.9216i) q^{70} +63.3498 q^{71} +(-50.9063 - 50.9063i) q^{73} +(-16.3201 - 9.42239i) q^{74} +(-18.0141 - 31.2013i) q^{76} +(28.8458 + 7.72922i) q^{77} +(59.5972 + 34.4084i) q^{79} +(31.4194 - 8.25473i) q^{80} +(1.20728 - 1.20728i) q^{82} +(-101.841 + 27.2882i) q^{83} +(96.7668 + 0.472089i) q^{85} +(23.4540 + 40.6236i) q^{86} +(-16.6351 + 4.45735i) q^{88} -136.887i q^{89} -33.8170 q^{91} +(9.09897 + 33.9578i) q^{92} +(50.7615 - 29.3072i) q^{94} +(40.6663 - 40.2715i) q^{95} +(-9.45952 - 35.3034i) q^{97} +(53.5023 + 53.5023i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 2 q^{2} + 2 q^{5} - 2 q^{7} + 24 q^{8} - 8 q^{10} - 8 q^{11} - 2 q^{13} + 28 q^{16} - 28 q^{17} + 114 q^{20} + 14 q^{22} - 82 q^{23} - 8 q^{25} + 112 q^{26} - 88 q^{28} - 4 q^{31} + 14 q^{32} - 352 q^{35}+ \cdots + 1876 q^{98}+O(q^{100}) $ 40 * q + 2 * q^2 + 2 * q^5 - 2 * q^7 + 24 * q^8 - 8 * q^10 - 8 * q^11 - 2 * q^13 + 28 * q^16 - 28 * q^17 + 114 * q^20 + 14 * q^22 - 82 * q^23 - 8 * q^25 + 112 * q^26 - 88 * q^28 - 4 * q^31 + 14 * q^32 - 352 * q^35 - 92 * q^37 - 330 * q^38 + 30 * q^40 + 28 * q^41 - 2 * q^43 - 136 * q^46 - 64 * q^47 + 458 * q^50 - 74 * q^52 + 608 * q^53 + 224 * q^55 + 192 * q^56 + 30 * q^58 + 92 * q^61 + 100 * q^62 + 326 * q^65 - 80 * q^67 - 626 * q^68 - 102 * q^70 - 248 * q^71 - 8 * q^73 - 96 * q^76 - 338 * q^77 - 1444 * q^80 + 104 * q^82 - 370 * q^83 - 98 * q^85 + 328 * q^86 - 210 * q^88 + 152 * q^91 - 388 * q^92 + 360 * q^95 + 292 * q^97 + 1876 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.238965	−	0.891829i	−0.119482	−	0.445914i	0.880101	−	0.474787i	$-0.157475\pi$
$2$	−0.238965	−	0.891829i	−0.119482	−	0.445914i	−0.999583	+	0.0288727i	$0.990808\pi$
$3$		0			0
$3$		0			0
$4$	2.72585	−	1.57377i	0.681462	−	0.393442i
$5$	3.51824	+	3.55274i	0.703649	+	0.710548i
$5$	3.51824	+	3.55274i	0.703649	+	0.710548i
$6$		0			0
$7$	2.96175	+	11.0534i	0.423108	+	1.57906i	0.768021	+	0.640425i	$0.221242\pi$
$7$	2.96175	+	11.0534i	0.423108	+	1.57906i	−0.344913	+	0.938635i	$0.612091\pi$
$8$	−4.66637	−	4.66637i	−0.583296	−	0.583296i
$9$		0			0
$10$	2.32770	−	3.98665i	0.232770	−	0.398665i
$11$	1.30484	−	2.26005i	0.118622	−	0.205459i	−0.800600	−	0.599199i	$-0.795486\pi$
$11$	1.30484	−	2.26005i	0.118622	−	0.205459i	0.919222	+	0.393740i	$0.128819\pi$
$12$		0			0
$13$	−0.764853	+	2.85447i	−0.0588349	+	0.219575i	−0.989084	−	0.147354i	$-0.952924\pi$
$13$	−0.764853	+	2.85447i	−0.0588349	+	0.219575i	0.930249	+	0.366929i	$0.119591\pi$
$14$	9.15000	−	5.28276i	0.653572	−	0.377340i
$15$		0			0
$16$	3.24857	−	5.62669i	0.203036	−	0.351668i
$17$	13.6850	−	13.6850i	0.805003	−	0.805003i	−0.178870	−	0.983873i	$-0.557244\pi$
$17$	13.6850	−	13.6850i	0.805003	−	0.805003i	0.983873	+	0.178870i	$0.0572441\pi$
$18$		0			0
$19$		−	11.4465i		−	0.602446i	−0.953554	−	0.301223i	$-0.902605\pi$
$19$		−	11.4465i		−	0.602446i	0.953554	−	0.301223i	$-0.0973948\pi$
$20$	15.1814	+	4.14733i	0.759069	+	0.207366i
$21$		0			0
$22$	−2.32738	−	0.623621i	−0.105790	−	0.0283464i
$23$	−2.89082	+	10.7887i	−0.125688	+	0.469074i	−0.999863	−	0.0165366i	$-0.994736\pi$
$23$	−2.89082	+	10.7887i	−0.125688	+	0.469074i	0.874175	+	0.485611i	$0.161403\pi$
$24$		0			0
$25$	−0.243925	+	24.9988i	−0.00975701	+	0.999952i
$26$	2.72847			0.104941
$27$		0			0
$28$	25.4688	+	25.4688i	0.909601	+	0.909601i
$29$	−23.0262	−	13.2942i	−0.794005	−	0.458419i	0.0473654	−	0.998878i	$-0.484917\pi$
$29$	−23.0262	−	13.2942i	−0.794005	−	0.458419i	−0.841371	+	0.540458i	$0.818251\pi$
$30$		0			0
$31$	−21.8787	−	37.8950i	−0.705764	−	1.22242i	−0.966415	−	0.256985i	$-0.917271\pi$
$31$	−21.8787	−	37.8950i	−0.705764	−	1.22242i	0.260652	−	0.965433i	$-0.416063\pi$
$32$	−31.2919	−	8.38463i	−0.977870	−	0.262020i
$33$		0			0
$34$	−15.4750	−	8.93448i	−0.455146	−	0.262779i
$35$	−28.8498	+	49.4110i	−0.824279	+	1.41174i
$36$		0			0
$37$	14.4324	−	14.4324i	0.390065	−	0.390065i	−0.484646	−	0.874711i	$-0.661051\pi$
$37$	14.4324	−	14.4324i	0.390065	−	0.390065i	0.874711	+	0.484646i	$0.161051\pi$
$38$	−10.2083	+	2.73530i	−0.268639	+	0.0719817i
$39$		0			0
$40$	0.160974	−	32.9958i	0.00402435	−	0.824896i
$41$	0.924605	+	1.60146i	0.0225513	+	0.0390601i	0.877081	−	0.480343i	$-0.159488\pi$
$41$	0.924605	+	1.60146i	0.0225513	+	0.0390601i	−0.854529	+	0.519403i	$0.826154\pi$
$42$		0			0
$43$	−49.0742	+	13.1494i	−1.14126	+	0.305800i	−0.779458	−	0.626455i	$-0.784505\pi$
$43$	−49.0742	+	13.1494i	−1.14126	+	0.305800i	−0.361803	+	0.932255i	$0.617839\pi$
$44$		−	8.21405i		−	0.186683i
$45$		0			0
$46$	10.3125			0.224184
$47$	16.4309	+	61.3211i	0.349594	+	1.30470i	0.887152	+	0.461477i	$0.152680\pi$
$47$	16.4309	+	61.3211i	0.349594	+	1.30470i	−0.537558	+	0.843227i	$0.680653\pi$
$48$		0			0
$49$	−70.9709	+	40.9750i	−1.44838	+	0.836225i
$50$	22.3529	−	5.75630i	0.447059	−	0.115126i
$51$		0			0
$52$	2.40740	+	8.98455i	0.0462962	+	0.172780i
$53$	−6.43481	−	6.43481i	−0.121412	−	0.121412i	0.643790	−	0.765202i	$-0.277361\pi$
$53$	−6.43481	−	6.43481i	−0.121412	−	0.121412i	−0.765202	+	0.643790i	$0.777361\pi$
$54$		0			0
$55$	12.6201	−	3.31564i	0.229456	−	0.0602844i
$56$	37.7587	−	65.4000i	0.674262	−	1.16786i
$57$		0			0
$58$	−6.35367	+	23.7122i	−0.109546	+	0.408831i
$59$	−49.5170	+	28.5886i	−0.839271	+	0.484553i	−0.857016	−	0.515289i	$-0.827684\pi$
$59$	−49.5170	+	28.5886i	−0.839271	+	0.484553i	0.0177457	+	0.999843i	$0.494351\pi$
$60$		0			0
$61$	16.8393	−	29.1666i	0.276055	−	0.478141i	−0.694346	−	0.719641i	$-0.744306\pi$
$61$	16.8393	−	29.1666i	0.276055	−	0.478141i	0.970401	+	0.241501i	$0.0776396\pi$
$62$	−28.5676	+	28.5676i	−0.460768	+	0.460768i
$63$		0			0
$64$			3.92205i			0.0612820i
$65$	−12.8321	+	7.32540i	−0.197417	+	0.112698i
$66$		0			0
$67$	31.4072	+	8.41554i	0.468765	+	0.125605i	0.485466	−	0.874255i	$-0.338650\pi$
$67$	31.4072	+	8.41554i	0.468765	+	0.125605i	−0.0167016	+	0.999861i	$0.505317\pi$
$68$	15.7663	−	58.8405i	0.231857	−	0.865301i
$69$		0			0
$70$	50.9602	+	13.9216i	0.728003	+	0.198879i
$71$	63.3498			0.892251			0.446126	−	0.894970i	$-0.352803\pi$
$71$	63.3498			0.892251			0.446126	+	0.894970i	$0.352803\pi$
$72$		0			0
$73$	−50.9063	−	50.9063i	−0.697347	−	0.697347i	0.266491	−	0.963838i	$-0.414136\pi$
$73$	−50.9063	−	50.9063i	−0.697347	−	0.697347i	−0.963838	+	0.266491i	$0.914136\pi$
$74$	−16.3201	−	9.42239i	−0.220541	−	0.127330i
$75$		0			0
$76$	−18.0141	−	31.2013i	−0.237028	−	0.410544i
$77$	28.8458	+	7.72922i	0.374621	+	0.100379i
$78$		0			0
$79$	59.5972	+	34.4084i	0.754395	+	0.435550i	0.827280	−	0.561790i	$-0.189887\pi$
$79$	59.5972	+	34.4084i	0.754395	+	0.435550i	−0.0728850	+	0.997340i	$0.523221\pi$
$80$	31.4194	−	8.25473i	0.392743	−	0.103184i
$81$		0			0
$82$	1.20728	−	1.20728i	0.0147230	−	0.0147230i
$83$	−101.841	+	27.2882i	−1.22700	+	0.328773i	−0.813410	−	0.581691i	$-0.802391\pi$
$83$	−101.841	+	27.2882i	−1.22700	+	0.328773i	−0.413589	+	0.910464i	$0.635725\pi$
$84$		0			0
$85$	96.7668	+	0.472089i	1.13843	+	0.00555398i
$86$	23.4540	+	40.6236i	0.272721	+	0.472367i
$87$		0			0
$88$	−16.6351	+	4.45735i	−0.189035	+	0.0506517i
$89$		−	136.887i		−	1.53806i	−0.639213	−	0.769029i	$-0.720740\pi$
$89$		−	136.887i		−	1.53806i	0.639213	−	0.769029i	$-0.279260\pi$
$90$		0			0
$91$	−33.8170			−0.371615
$92$	9.09897	+	33.9578i	0.0989019	+	0.369107i
$93$		0			0
$94$	50.7615	−	29.3072i	0.540016	−	0.311778i
$95$	40.6663	−	40.2715i	0.428067	−	0.423910i
$96$		0			0
$97$	−9.45952	−	35.3034i	−0.0975209	−	0.363953i	0.899869	−	0.436161i	$-0.143662\pi$
$97$	−9.45952	−	35.3034i	−0.0975209	−	0.363953i	−0.997390	+	0.0722080i	$0.976995\pi$
$98$	53.5023	+	53.5023i	0.545941	+	0.545941i
$99$		0			0
$100$	38.6774	+	68.5268i	0.386774	+	0.685268i
$101$	48.3142	−	83.6827i	0.478359	−	0.828541i	−0.521334	−	0.853353i	$-0.674565\pi$
$101$	48.3142	−	83.6827i	0.478359	−	0.828541i	0.999692	+	0.0248116i	$0.00789858\pi$
$102$		0			0
$103$	−6.87754	+	25.6673i	−0.0667723	+	0.249198i	−0.991242	−	0.132058i	$-0.957842\pi$
$103$	−6.87754	+	25.6673i	−0.0667723	+	0.249198i	0.924470	+	0.381255i	$0.124508\pi$
$104$	16.8891	−	9.75093i	0.162395	−	0.0937589i
$105$		0			0
$106$	−4.20106	+	7.27645i	−0.0396326	+	0.0686457i
$107$	43.8389	−	43.8389i	0.409709	−	0.409709i	−0.471928	−	0.881637i	$-0.656442\pi$
$107$	43.8389	−	43.8389i	0.409709	−	0.409709i	0.881637	+	0.471928i	$0.156442\pi$
$108$		0			0
$109$		−	13.1212i		−	0.120378i	−0.998187	−	0.0601892i	$-0.980830\pi$
$109$		−	13.1212i		−	0.120378i	0.998187	−	0.0601892i	$-0.0191704\pi$
$110$	−5.97274	−	10.4626i	−0.0542977	−	0.0951149i
$111$		0			0
$112$	71.8156	+	19.2429i	0.641211	+	0.171812i
$113$	8.41629	−	31.4100i	0.0744805	−	0.277965i	−0.918635	−	0.395108i	$-0.870707\pi$
$113$	8.41629	−	31.4100i	0.0744805	−	0.277965i	0.993115	+	0.117143i	$0.0373737\pi$
$114$		0			0
$115$	−48.5001	+	27.6869i	−0.421740	+	0.240756i
$116$	−83.6877			−0.721446
$117$		0			0
$118$	37.3290	+	37.3290i	0.316347	+	0.316347i
$119$	191.798	+	110.735i	1.61175	+	0.930545i
$120$		0			0
$121$	57.0948	+	98.8911i	0.471858	+	0.817282i
$122$	−30.0356	−	8.04801i	−0.246193	−	0.0659673i
$123$		0			0
$124$	−119.276	−	68.8639i	−0.961902	−	0.555354i
$125$	−89.6725	+	87.0853i	−0.717380	+	0.696682i
$126$		0			0
$127$	−108.223	+	108.223i	−0.852153	+	0.852153i	−0.990398	−	0.138245i	$-0.955854\pi$
$127$	−108.223	+	108.223i	−0.852153	+	0.852153i	0.138245	+	0.990398i	$0.455854\pi$
$128$	−121.670	+	32.6013i	−0.950544	+	0.254697i
$129$		0			0
$130$	9.59943	+	9.69355i	0.0738418	+	0.0745658i
$131$	3.28859	+	5.69601i	0.0251038	+	0.0434810i	0.878304	−	0.478102i	$-0.158675\pi$
$131$	3.28859	+	5.69601i	0.0251038	+	0.0434810i	−0.853201	+	0.521583i	$0.825342\pi$
$132$		0			0
$133$	126.523	−	33.9016i	0.951298	−	0.254900i
$134$		−	30.0209i		−	0.224036i
$135$		0			0
$136$	−127.719			−0.939110
$137$	−22.5393	−	84.1178i	−0.164520	−	0.613998i	−0.998101	−	0.0616003i	$-0.980380\pi$
$137$	−22.5393	−	84.1178i	−0.164520	−	0.613998i	0.833581	−	0.552398i	$-0.186287\pi$
$138$		0			0
$139$	−75.7500	+	43.7343i	−0.544964	+	0.314635i	−0.747088	−	0.664725i	$-0.768549\pi$
$139$	−75.7500	+	43.7343i	−0.544964	+	0.314635i	0.202124	+	0.979360i	$0.435215\pi$
$140$	−0.878589	+	180.090i	−0.00627564	+	1.28635i
$141$		0			0
$142$	−15.1384	−	56.4972i	−0.106608	−	0.397868i
$143$	5.45322	+	5.45322i	0.0381344	+	0.0381344i
$144$		0			0
$145$	−33.7809	−	128.578i	−0.232972	−	0.886745i
$146$	−33.2349	+	57.5646i	−0.227636	+	0.394278i
$147$		0			0
$148$	16.6273	−	62.0538i	0.112346	−	0.419282i
$149$	−144.963	+	83.6946i	−0.972909	+	0.561709i	−0.900122	−	0.435638i	$-0.856523\pi$
$149$	−144.963	+	83.6946i	−0.972909	+	0.561709i	−0.0727869	+	0.997348i	$0.523189\pi$
$150$		0			0
$151$	124.775	−	216.117i	0.826325	−	1.43124i	−0.0745766	−	0.997215i	$-0.523761\pi$
$151$	124.775	−	216.117i	0.826325	−	1.43124i	0.900902	−	0.434022i	$-0.142906\pi$
$152$	−53.4135	+	53.4135i	−0.351404	+	0.351404i
$153$		0			0
$154$		−	27.5726i		−	0.179043i
$155$	57.6565	−	211.053i	0.371977	−	1.36163i
$156$		0			0
$157$	−48.3954	−	12.9675i	−0.308251	−	0.0825957i	0.101377	−	0.994848i	$-0.467675\pi$
$157$	−48.3954	−	12.9675i	−0.308251	−	0.0825957i	−0.409629	+	0.912252i	$0.634342\pi$
$158$	16.4448	−	61.3729i	0.104081	−	0.388436i
$159$		0			0
$160$	−80.3040	−	140.671i	−0.501900	−	0.879194i
$161$	−127.814			−0.793875
$162$		0			0
$163$	−23.5188	−	23.5188i	−0.144287	−	0.144287i	0.631273	−	0.775560i	$-0.282533\pi$
$163$	−23.5188	−	23.5188i	−0.144287	−	0.144287i	−0.775560	+	0.631273i	$0.782533\pi$
$164$	5.04066	+	2.91023i	0.0307358	+	0.0177453i
$165$		0			0
$166$	48.6728	+	84.3037i	0.293210	+	0.507854i
$167$	−106.889	−	28.6408i	−0.640052	−	0.171502i	−0.0758252	−	0.997121i	$-0.524159\pi$
$167$	−106.889	−	28.6408i	−0.640052	−	0.171502i	−0.564227	+	0.825620i	$0.690826\pi$
$168$		0			0
$169$	138.795	+	80.1335i	0.821274	+	0.474163i
$170$	−22.7028	−	86.4122i	−0.133546	−	0.508307i
$171$		0			0
$172$	−113.075	+	113.075i	−0.657411	+	0.657411i
$173$	65.8811	−	17.6528i	0.380816	−	0.102039i	−0.0633327	−	0.997992i	$-0.520173\pi$
$173$	65.8811	−	17.6528i	0.380816	−	0.102039i	0.444149	+	0.895953i	$0.353506\pi$
$174$		0			0
$175$	−277.045	+	71.3441i	−1.58311	+	0.407681i
$176$	−8.47772	−	14.6838i	−0.0481688	−	0.0834309i
$177$		0			0
$178$	−122.080	+	32.7112i	−0.685843	+	0.183771i
$179$			303.920i			1.69788i	0.528490	+	0.848939i	$0.322758\pi$
$179$			303.920i			1.69788i	−0.528490	+	0.848939i	$0.677242\pi$
$180$		0			0
$181$	172.576			0.953460			0.476730	−	0.879050i	$-0.341822\pi$
$181$	172.576			0.953460			0.476730	+	0.879050i	$0.341822\pi$
$182$	8.08107	+	30.1589i	0.0444015	+	0.165708i
$183$		0			0
$184$	63.8337	−	36.8544i	0.346922	−	0.200296i
$185$	102.051	+	0.497870i	0.551628	+	0.00269119i
$186$		0			0
$187$	−13.0721	−	48.7856i	−0.0699041	−	0.260886i
$188$	141.293	+	141.293i	0.751561	+	0.751561i
$189$		0			0
$190$	−45.6331	−	26.6439i	−0.240174	−	0.140231i
$191$	−143.618	+	248.754i	−0.751927	+	1.30238i	0.194960	+	0.980811i	$0.437542\pi$
$191$	−143.618	+	248.754i	−0.751927	+	1.30238i	−0.946887	+	0.321565i	$0.895791\pi$
$192$		0			0
$193$	9.52264	−	35.5390i	0.0493401	−	0.184140i	−0.936858	−	0.349711i	$-0.886280\pi$
$193$	9.52264	−	35.5390i	0.0493401	−	0.184140i	0.986198	+	0.165571i	$0.0529466\pi$
$194$	−29.2241	+	16.8725i	−0.150640	+	0.0869719i
$195$		0			0
$196$	−128.970	+	223.383i	−0.658013	+	1.13971i
$197$	226.659	−	226.659i	1.15056	−	1.15056i	0.164114	−	0.986441i	$-0.447524\pi$
$197$	226.659	−	226.659i	1.15056	−	1.15056i	0.986441	−	0.164114i	$-0.0524764\pi$
$198$		0			0
$199$			107.508i			0.540240i	0.962827	+	0.270120i	$0.0870633\pi$
$199$			107.508i			0.540240i	−0.962827	+	0.270120i	$0.912937\pi$
$200$	117.792	−	115.515i	0.588960	−	0.577577i
$201$		0			0
$202$	−86.1760	−	23.0908i	−0.426614	−	0.114311i
$203$	78.7481	−	293.892i	0.387922	−	1.44774i
$204$		0			0
$205$	−2.43660	+	8.91922i	−0.0118858	+	0.0435084i
$206$	24.5344			0.119099
$207$		0			0
$208$	13.5765	+	13.5765i	0.0652718	+	0.0652718i
$209$	−25.8695	−	14.9358i	−0.123778	−	0.0714631i
$210$		0			0
$211$	45.5871	+	78.9591i	0.216053	+	0.374214i	0.953598	−	0.301084i	$-0.0973484\pi$
$211$	45.5871	+	78.9591i	0.216053	+	0.374214i	−0.737545	+	0.675298i	$0.764015\pi$
$212$	−27.6672	−	7.41341i	−0.130506	−	0.0349689i
$213$		0			0
$214$	−49.5727	−	28.6208i	−0.231648	−	0.133742i
$215$	−219.371	−	128.085i	−1.02033	−	0.595745i
$216$		0			0
$217$	354.070	−	354.070i	1.63166	−	1.63166i
$218$	−11.7019	+	3.13551i	−0.0536784	+	0.0143831i
$219$		0			0
$220$	29.1824	−	28.8990i	0.132647	−	0.131359i
$221$	28.5965	+	49.5306i	0.129396	+	0.224120i
$222$		0			0
$223$	229.262	−	61.4305i	1.02808	−	0.275473i	0.294914	−	0.955524i	$-0.404709\pi$
$223$	229.262	−	61.4305i	1.02808	−	0.275473i	0.733165	+	0.680051i	$0.238042\pi$
$224$		−	370.715i		−	1.65498i
$225$		0			0
$226$	−30.0236			−0.132848
$227$	31.7905	+	118.644i	0.140046	+	0.522660i	0.999926	+	0.0121631i	$0.00387174\pi$
$227$	31.7905	+	118.644i	0.140046	+	0.522660i	−0.859880	+	0.510497i	$0.829462\pi$
$228$		0			0
$229$	285.203	−	164.662i	1.24543	−	0.719048i	0.275234	−	0.961377i	$-0.411245\pi$
$229$	285.203	−	164.662i	1.24543	−	0.719048i	0.970194	+	0.242329i	$0.0779114\pi$
$230$	36.2818	+	36.6376i	0.157747	+	0.159294i
$231$		0			0
$232$	45.4131	+	169.484i	0.195746	+	0.730534i
$233$	227.098	+	227.098i	0.974670	+	0.974670i	0.999687	−	0.0250170i	$-0.00796398\pi$
$233$	227.098	+	227.098i	0.974670	+	0.974670i	−0.0250170	+	0.999687i	$0.507964\pi$
$234$		0			0
$235$	−160.050	+	274.117i	−0.681063	+	1.16646i
$236$	−89.9838	+	155.856i	−0.381287	+	0.660409i
$237$		0			0
$238$	52.9235	−	197.513i	0.222367	−	0.829887i
$239$	123.443	−	71.2696i	0.516496	−	0.298199i	−0.219004	−	0.975724i	$-0.570281\pi$
$239$	123.443	−	71.2696i	0.516496	−	0.298199i	0.735500	+	0.677525i	$0.236947\pi$
$240$		0			0
$241$	−228.867	+	396.410i	−0.949656	+	1.64485i	−0.203509	+	0.979073i	$0.565234\pi$
$241$	−228.867	+	396.410i	−0.949656	+	1.64485i	−0.746148	+	0.665780i	$0.768099\pi$
$242$	74.5503	−	74.5503i	0.308059	−	0.308059i
$243$		0			0
$244$		−	106.005i		−	0.434446i
$245$	−395.266	−	107.981i	−1.61333	−	0.440738i
$246$		0			0
$247$	32.6736	+	8.75487i	0.132282	+	0.0354448i
$248$	−74.7380	+	278.926i	−0.301363	+	1.12470i
$249$		0			0
$250$	99.0937	+	59.1622i	0.396375	+	0.236649i
$251$	−102.580			−0.408684			−0.204342	−	0.978900i	$-0.565506\pi$
$251$	−102.580			−0.408684			−0.204342	+	0.978900i	$0.565506\pi$
$252$		0			0
$253$	20.6109	+	20.6109i	0.0814660	+	0.0814660i
$254$	122.378	+	70.6552i	0.481805	+	0.278170i
$255$		0			0
$256$	65.9936	+	114.304i	0.257788	+	0.446501i
$257$	108.426	+	29.0526i	0.421890	+	0.113045i	0.463517	−	0.886088i	$-0.346587\pi$
$257$	108.426	+	29.0526i	0.421890	+	0.113045i	−0.0416268	+	0.999133i	$0.513254\pi$
$258$		0			0
$259$	202.273	+	116.782i	0.780975	+	0.450896i
$260$	−23.4499	+	40.1627i	−0.0901921	+	0.154472i
$261$		0			0
$262$	4.29401	−	4.29401i	0.0163893	−	0.0163893i
$263$	143.911	−	38.5609i	0.547191	−	0.146619i	0.0253757	−	0.999678i	$-0.491922\pi$
$263$	143.911	−	38.5609i	0.547191	−	0.146619i	0.521815	+	0.853059i	$0.325255\pi$
$264$		0			0
$265$	0.221980	−	45.5005i	0.000837659	−	0.171700i
$266$	−60.4689	−	104.735i	−0.227327	−	0.393742i
$267$		0			0
$268$	98.8554	−	26.4882i	0.368864	−	0.0988367i
$269$			31.0843i			0.115555i	0.998329	+	0.0577774i	$0.0184014\pi$
$269$			31.0843i			0.115555i	−0.998329	+	0.0577774i	$0.981599\pi$
$270$		0			0
$271$	4.22458			0.0155889			0.00779444	−	0.999970i	$-0.497519\pi$
$271$	4.22458			0.0155889			0.00779444	+	0.999970i	$0.497519\pi$
$272$	−32.5447	−	121.458i	−0.119650	−	0.446538i
$273$		0			0
$274$	−69.6325	+	40.2024i	−0.254133	+	0.146724i
$275$	56.1802	+	33.1707i	0.204292	+	0.120621i
$276$		0			0
$277$	−35.9912	−	134.321i	−0.129932	−	0.484913i	0.870035	−	0.492990i	$-0.164096\pi$
$277$	−35.9912	−	134.321i	−0.129932	−	0.484913i	−0.999967	+	0.00807616i	$0.997429\pi$
$278$	57.1051	+	57.1051i	0.205414	+	0.205414i
$279$		0			0
$280$	365.193	−	95.9462i	1.30426	−	0.342665i
$281$	251.702	−	435.961i	0.895737	−	1.55146i	0.0628471	−	0.998023i	$-0.479982\pi$
$281$	251.702	−	435.961i	0.895737	−	1.55146i	0.832890	−	0.553439i	$-0.186685\pi$
$282$		0			0
$283$	−37.9311	+	141.561i	−0.134032	+	0.500214i	0.865968	+	0.500099i	$0.166703\pi$
$283$	−37.9311	+	141.561i	−0.134032	+	0.500214i	−1.00000		0.000114837i	$0.999963\pi$
$284$	172.682	−	99.6980i	0.608035	−	0.351049i
$285$		0			0
$286$	3.56021	−	6.16647i	0.0124483	−	0.0215611i
$287$	−14.9632	+	14.9632i	−0.0521365	+	0.0521365i
$288$		0			0
$289$		−	85.5611i		−	0.296059i
$290$	−106.597	+	60.8524i	−0.367576	+	0.209836i
$291$		0			0
$292$	−218.878	−	58.6481i	−0.749581	−	0.200850i
$293$	88.7756	−	331.315i	0.302988	−	1.13077i	−0.631675	−	0.775234i	$-0.717632\pi$
$293$	88.7756	−	331.315i	0.302988	−	1.13077i	0.934663	−	0.355535i	$-0.115701\pi$
$294$		0			0
$295$	−275.781	−	75.3391i	−0.934850	−	0.255387i
$296$	−134.694			−0.455047
$297$		0			0
$298$	109.282	+	109.282i	0.366720	+	0.366720i
$299$	−28.5850	−	16.5035i	−0.0956019	−	0.0551958i
$300$		0			0
$301$	−290.692	−	503.493i	−0.965753	−	1.67273i
$302$	−222.556	−	59.6337i	−0.736941	−	0.197463i
$303$		0			0
$304$	−64.4057	−	37.1847i	−0.211861	−	0.122318i
$305$	162.866	−	42.7894i	0.533987	−	0.140293i
$306$		0			0
$307$	−19.2282	+	19.2282i	−0.0626327	+	0.0626327i	−0.737729	−	0.675097i	$-0.764102\pi$
$307$	−19.2282	+	19.2282i	−0.0626327	+	0.0626327i	0.675097	+	0.737729i	$0.264102\pi$
$308$	90.7934	−	24.3280i	0.294784	−	0.0789870i
$309$		0			0
$310$	−202.001	−	0.985487i	−0.651616	−	0.00317899i
$311$	275.689	+	477.507i	0.886459	+	1.53539i	0.844032	+	0.536293i	$0.180176\pi$
$311$	275.689	+	477.507i	0.886459	+	1.53539i	0.0424271	+	0.999100i	$0.486491\pi$
$312$		0			0
$313$	−463.260	+	124.130i	−1.48006	+	0.396582i	−0.906368	−	0.422488i	$-0.861157\pi$
$313$	−463.260	+	124.130i	−1.48006	+	0.396582i	−0.573694	+	0.819070i	$0.694490\pi$
$314$			46.2592i			0.147322i
$315$		0			0
$316$	216.604			0.685455
$317$	72.3487	+	270.009i	0.228229	+	0.851763i	0.981085	+	0.193578i	$0.0620092\pi$
$317$	72.3487	+	270.009i	0.228229	+	0.851763i	−0.752856	+	0.658186i	$0.771324\pi$
$318$		0			0
$319$	−60.0908	+	34.6934i	−0.188372	+	0.108757i
$320$	−13.9340	+	13.7987i	−0.0435438	+	0.0431210i
$321$		0			0
$322$	30.5430	+	113.988i	0.0948541	+	0.354000i
$323$	−156.646	−	156.646i	−0.484971	−	0.484971i
$324$		0			0
$325$	−71.1718	−	19.8167i	−0.218990	−	0.0609744i
$326$	−15.3545	+	26.5949i	−0.0470998	+	0.0815793i
$327$		0			0
$328$	3.15847	−	11.7876i	0.00962948	−	0.0359377i
$329$	−629.143	+	363.236i	−1.91229	+	1.10406i
$330$		0			0
$331$	−61.1788	+	105.965i	−0.184830	+	0.320136i	−0.943519	−	0.331317i	$-0.892507\pi$
$331$	−61.1788	+	105.965i	−0.184830	+	0.320136i	0.758689	+	0.651453i	$0.225840\pi$
$332$	−234.657	+	234.657i	−0.706800	+	0.706800i
$333$		0			0
$334$			102.171i			0.305900i
$335$	80.6001	+	141.190i	0.240597	+	0.421462i
$336$		0			0
$337$	−319.193	−	85.5276i	−0.947161	−	0.253791i	−0.248004	−	0.968759i	$-0.579775\pi$
$337$	−319.193	−	85.5276i	−0.947161	−	0.253791i	−0.699157	+	0.714968i	$0.746441\pi$
$338$	38.2982	−	142.931i	0.113308	−	0.422872i
$339$		0			0
$340$	264.514	−	151.002i	0.777983	−	0.444122i
$341$	−114.192			−0.334875
$342$		0			0
$343$	−266.621	−	266.621i	−0.777321	−	0.777321i
$344$	290.358	+	167.638i	0.844065	+	0.487321i
$345$		0			0
$346$	−31.4865	−	54.5363i	−0.0910016	−	0.157619i
$347$	−343.816	−	92.1251i	−0.990823	−	0.265490i	−0.273227	−	0.961950i	$-0.588091\pi$
$347$	−343.816	−	92.1251i	−0.990823	−	0.265490i	−0.717596	+	0.696459i	$0.754758\pi$
$348$		0			0
$349$	−43.1516	−	24.9136i	−0.123644	−	0.0713857i	0.436903	−	0.899509i	$-0.356075\pi$
$349$	−43.1516	−	24.9136i	−0.123644	−	0.0713857i	−0.560546	+	0.828123i	$0.689409\pi$
$350$	129.831	+	230.028i	0.370945	+	0.657222i
$351$		0			0
$352$	−59.7804	+	59.7804i	−0.169831	+	0.169831i
$353$	−606.831	+	162.600i	−1.71907	+	0.460623i	−0.977619	−	0.210385i	$-0.932528\pi$
$353$	−606.831	+	162.600i	−1.71907	+	0.460623i	−0.741450	+	0.671008i	$0.765862\pi$
$354$		0			0
$355$	222.880	+	225.065i	0.627831	+	0.633987i
$356$	−215.429	−	373.134i	−0.605137	−	1.04813i
$357$		0			0
$358$	271.045	−	72.6263i	0.757109	−	0.202867i
$359$			81.3046i			0.226475i	0.993568	+	0.113238i	$0.0361221\pi$
$359$			81.3046i			0.226475i	−0.993568	+	0.113238i	$0.963878\pi$
$360$		0			0
$361$	229.978			0.637059
$362$	−41.2397	−	153.908i	−0.113922	−	0.425162i
$363$		0			0
$364$	−92.1799	+	53.2201i	−0.253241	+	0.146209i
$365$	1.75610	−	359.958i	0.00481123	−	0.986186i
$366$		0			0
$367$	15.5484	+	58.0273i	0.0423661	+	0.158113i	0.983868	−	0.178894i	$-0.0572521\pi$
$367$	15.5484	+	58.0273i	0.0423661	+	0.158113i	−0.941502	+	0.337007i	$0.890585\pi$
$368$	51.3136	+	51.3136i	0.139439	+	0.139439i
$369$		0			0
$370$	−23.9426	−	91.1312i	−0.0647098	−	0.246301i
$371$	52.0684	−	90.1851i	0.140346	−	0.243086i
$372$		0			0
$373$	−50.4882	+	188.424i	−0.135357	+	0.505159i	0.864639	+	0.502393i	$0.167547\pi$
$373$	−50.4882	+	188.424i	−0.135357	+	0.505159i	−0.999996	+	0.00276585i	$0.999120\pi$
$374$	−40.3846	+	23.3161i	−0.107980	+	0.0623425i
$375$		0			0
$376$	209.474	−	362.820i	0.557112	−	0.964946i
$377$	55.5594	−	55.5594i	0.147372	−	0.147372i
$378$		0			0
$379$			145.837i			0.384795i	0.981317	+	0.192398i	$0.0616263\pi$
$379$			145.837i			0.384795i	−0.981317	+	0.192398i	$0.938374\pi$
$380$	47.4722	−	173.773i	0.124927	−	0.457298i
$381$		0			0
$382$	256.166	+	68.6394i	0.670591	+	0.179684i
$383$	−195.458	+	729.460i	−0.510335	+	1.90459i	−0.0934803	+	0.995621i	$0.529799\pi$
$383$	−195.458	+	729.460i	−0.510335	+	1.90459i	−0.416854	+	0.908973i	$0.636867\pi$
$384$		0			0
$385$	74.0268	+	129.675i	0.192277	+	0.336818i
$386$	−33.9703			−0.0880059
$387$		0			0
$388$	−81.3446	−	81.3446i	−0.209651	−	0.209651i
$389$	37.3613	+	21.5705i	0.0960444	+	0.0554512i	0.547253	−	0.836967i	$-0.315674\pi$
$389$	37.3613	+	21.5705i	0.0960444	+	0.0554512i	−0.451209	+	0.892419i	$0.649007\pi$
$390$		0			0
$391$	108.083	+	187.205i	0.276427	+	0.478785i
$392$	522.381	+	139.972i	1.33260	+	0.357070i
$393$		0			0
$394$	−256.305	−	147.978i	−0.650520	−	0.375578i
$395$	87.4331	+	332.791i	0.221350	+	0.842508i
$396$		0			0
$397$	−89.7953	+	89.7953i	−0.226185	+	0.226185i	−0.811097	−	0.584912i	$-0.801129\pi$
$397$	−89.7953	+	89.7953i	−0.226185	+	0.226185i	0.584912	+	0.811097i	$0.301129\pi$
$398$	95.8785	−	25.6906i	0.240901	−	0.0645491i
$399$		0			0
$400$	139.868	+	82.5829i	0.349670	+	0.206457i
$401$	144.777	+	250.762i	0.361041	+	0.625341i	0.988132	−	0.153604i	$-0.0490882\pi$
$401$	144.777	+	250.762i	0.361041	+	0.625341i	−0.627092	+	0.778946i	$0.715755\pi$
$402$		0			0
$403$	124.904	−	33.4679i	0.309936	−	0.0830470i
$404$		−	304.142i		−	0.752826i
$405$		0			0
$406$	−280.919			−0.691919
$407$	−13.7859	−	51.4498i	−0.0338721	−	0.126412i
$408$		0			0
$409$	−178.588	+	103.108i	−0.436646	+	0.252098i	−0.702174	−	0.712006i	$-0.747787\pi$
$409$	−178.588	+	103.108i	−0.436646	+	0.252098i	0.265528	+	0.964103i	$0.414454\pi$
$410$	8.53667	+	0.0416472i	0.0208212	+	0.000101579i
$411$		0			0
$412$	21.6473	+	80.7889i	0.0525421	+	0.196090i
$413$	−462.659	−	462.659i	−1.12024	−	1.12024i
$414$		0			0
$415$	−455.249	−	265.808i	−1.09699	−	0.640501i
$416$	47.8673	−	82.9087i	0.115066	−	0.199300i
$417$		0			0
$418$	−7.13826	+	26.6403i	−0.0170772	+	0.0637329i
$419$	621.108	−	358.597i	1.48236	−	0.855839i	0.482558	−	0.875864i	$-0.339708\pi$
$419$	621.108	−	358.597i	1.48236	−	0.855839i	0.999799	+	0.0200248i	$0.00637453\pi$
$420$		0			0
$421$	124.562	−	215.747i	0.295871	−	0.512463i	−0.679316	−	0.733846i	$-0.737724\pi$
$421$	124.562	−	215.747i	0.295871	−	0.512463i	0.975187	+	0.221382i	$0.0710569\pi$
$422$	59.5243	−	59.5243i	0.141053	−	0.141053i
$423$		0			0
$424$			60.0544i			0.141638i
$425$	338.772	+	345.448i	0.797110	+	0.812819i
$426$		0			0
$427$	372.264	+	99.7479i	0.871814	+	0.233602i
$428$	50.5058	−	188.490i	0.118004	−	0.440398i
$429$		0			0
$430$	−61.8080	+	226.250i	−0.143739	+	0.526162i
$431$	234.096			0.543146			0.271573	−	0.962418i	$-0.412456\pi$
$431$	234.096			0.543146			0.271573	+	0.962418i	$0.412456\pi$
$432$		0			0
$433$	372.915	+	372.915i	0.861236	+	0.861236i	0.991482	−	0.130245i	$-0.0415765\pi$
$433$	372.915	+	372.915i	0.861236	+	0.861236i	−0.130245	+	0.991482i	$0.541577\pi$
$434$	−400.380	−	231.159i	−0.922534	−	0.532625i
$435$		0			0
$436$	−20.6498	−	35.7665i	−0.0473619	−	0.0820332i
$437$	123.493	+	33.0897i	0.282592	+	0.0757202i
$438$		0			0
$439$	−558.854	−	322.654i	−1.27302	−	0.734976i	−0.297461	−	0.954734i	$-0.596140\pi$
$439$	−558.854	−	322.654i	−1.27302	−	0.734976i	−0.975554	+	0.219758i	$0.929473\pi$
$440$	−74.3620	−	43.4180i	−0.169005	−	0.0986773i
$441$		0			0
$442$	37.3393	−	37.3393i	0.0844780	−	0.0844780i
$443$	265.585	−	71.1633i	0.599515	−	0.160640i	0.0537167	−	0.998556i	$-0.482893\pi$
$443$	265.585	−	71.1633i	0.599515	−	0.160640i	0.545798	+	0.837917i	$0.316227\pi$
$444$		0			0
$445$	486.325	−	481.603i	1.09286	−	1.08225i
$446$	−109.571	−	189.782i	−0.245675	−	0.425521i
$447$		0			0
$448$	−43.3520	+	11.6161i	−0.0967679	+	0.0259289i
$449$			190.668i			0.424651i	0.977199	+	0.212325i	$0.0681036\pi$
$449$			190.668i			0.424651i	−0.977199	+	0.212325i	$0.931896\pi$
$450$		0			0
$451$	4.82584			0.0107003
$452$	−26.4906	−	98.8642i	−0.0586075	−	0.218726i
$453$		0			0
$454$	98.2131	−	56.7034i	0.216328	−	0.124897i
$455$	−118.976	−	120.143i	−0.261486	−	0.264050i
$456$		0			0
$457$	80.9404	+	302.074i	0.177112	+	0.660993i	0.996182	+	0.0872988i	$0.0278235\pi$
$457$	80.9404	+	302.074i	0.177112	+	0.660993i	−0.819070	+	0.573694i	$0.805510\pi$
$458$	−215.004	−	215.004i	−0.469441	−	0.469441i
$459$		0			0
$460$	−88.6310	+	151.798i	−0.192676	+	0.329996i
$461$	110.361	−	191.151i	0.239395	−	0.414645i	−0.721146	−	0.692784i	$-0.756384\pi$
$461$	110.361	−	191.151i	0.239395	−	0.414645i	0.960541	+	0.278139i	$0.0897174\pi$
$462$		0			0
$463$	74.7605	−	279.010i	0.161470	−	0.602613i	−0.836994	−	0.547211i	$-0.815689\pi$
$463$	74.7605	−	279.010i	0.161470	−	0.602613i	0.998464	−	0.0554018i	$-0.0176440\pi$
$464$	−149.604	+	86.3740i	−0.322423	+	0.186151i
$465$		0			0
$466$	148.264	−	256.801i	0.318163	−	0.551075i
$467$	249.664	−	249.664i	0.534613	−	0.534613i	−0.387329	−	0.921942i	$-0.626602\pi$
$467$	249.664	−	249.664i	0.534613	−	0.534613i	0.921942	+	0.387329i	$0.126602\pi$
$468$		0			0
$469$			372.082i			0.793352i
$470$	282.712	+	77.2327i	0.601515	+	0.164325i
$471$		0			0
$472$	364.470	+	97.6593i	0.772181	+	0.206905i
$473$	−34.3157	+	128.068i	−0.0725490	+	0.270756i
$474$		0			0
$475$	286.148	+	2.79208i	0.602417	+	0.00587807i
$476$	697.084			1.46446
$477$		0			0
$478$	−93.0588	−	93.0588i	−0.194684	−	0.194684i
$479$	−757.971	−	437.615i	−1.58240	−	0.913600i	−0.994508	−	0.104663i	$-0.966624\pi$
$479$	−757.971	−	437.615i	−1.58240	−	0.913600i	−0.587895	−	0.808938i	$-0.700043\pi$
$480$		0			0
$481$	30.1582	+	52.2355i	0.0626989	+	0.108598i
$482$	408.221	+	109.382i	0.846931	+	0.226934i
$483$		0			0
$484$	311.263	+	179.708i	0.643106	+	0.371298i
$485$	92.1430	−	157.813i	0.189986	−	0.325388i
$486$		0			0
$487$	−241.500	+	241.500i	−0.495894	+	0.495894i	−0.910157	−	0.414263i	$-0.864039\pi$
$487$	−241.500	+	241.500i	−0.495894	+	0.495894i	0.414263	+	0.910157i	$0.364039\pi$
$488$	−214.681	+	57.5235i	−0.439919	+	0.117876i
$489$		0			0
$490$	−1.84565	+	378.314i	−0.00376663	+	0.772069i
$491$	14.2377	+	24.6604i	0.0289973	+	0.0502248i	0.880160	−	0.474677i	$-0.157435\pi$
$491$	14.2377	+	24.6604i	0.0289973	+	0.0502248i	−0.851163	+	0.524902i	$0.824102\pi$
$492$		0			0
$493$	−497.045	+	133.183i	−1.00821	+	0.270148i
$494$		−	31.2314i		−	0.0632214i
$495$		0			0
$496$	−284.298			−0.573181
$497$	187.627	+	700.232i	0.377518	+	1.40892i
$498$		0			0
$499$	409.907	−	236.660i	0.821457	−	0.474269i	−0.0294615	−	0.999566i	$-0.509379\pi$
$499$	409.907	−	236.660i	0.821457	−	0.474269i	0.850919	+	0.525297i	$0.176046\pi$
$500$	−107.381	+	378.505i	−0.214763	+	0.757010i
$501$		0			0
$502$	24.5130	+	91.4836i	0.0488306	+	0.182238i
$503$	−58.9981	−	58.9981i	−0.117292	−	0.117292i	0.646024	−	0.763317i	$-0.276430\pi$
$503$	−58.9981	−	58.9981i	−0.117292	−	0.117292i	−0.763317	+	0.646024i	$0.776430\pi$
$504$		0			0
$505$	467.284	−	122.768i	0.925315	−	0.243105i
$506$	13.4561	−	23.3067i	0.0265931	−	0.0460606i
$507$		0			0
$508$	−124.682	+	465.319i	−0.245437	+	0.915983i
$509$	388.655	−	224.390i	0.763565	−	0.440844i	−0.0670093	−	0.997752i	$-0.521346\pi$
$509$	388.655	−	224.390i	0.763565	−	0.440844i	0.830574	+	0.556908i	$0.188012\pi$
$510$		0			0
$511$	411.917	−	713.461i	0.806100	−	1.39621i
$512$	−270.104	+	270.104i	−0.527546	+	0.527546i
$513$		0			0
$514$		−	103.640i		−	0.201634i
$515$	−115.386	+	65.8698i	−0.224051	+	0.127903i
$516$		0			0
$517$	160.028	+	42.8794i	0.309532	+	0.0829389i
$518$	55.8136	−	208.299i	0.107748	−	0.402122i
$519$		0			0
$520$	94.0625	+	25.6965i	0.180889	+	0.0494163i
$521$	548.131			1.05208			0.526038	−	0.850461i	$-0.323677\pi$
$521$	548.131			1.05208			0.526038	+	0.850461i	$0.323677\pi$
$522$		0			0
$523$	−237.559	−	237.559i	−0.454224	−	0.454224i	0.442530	−	0.896754i	$-0.354081\pi$
$523$	−237.559	−	237.559i	−0.454224	−	0.454224i	−0.896754	+	0.442530i	$0.854081\pi$
$524$	17.9284	+	10.3510i	0.0342145	+	0.0197538i
$525$		0			0
$526$	−68.7794	−	119.129i	−0.130759	−	0.226482i
$527$	−818.005	−	219.184i	−1.55219	−	0.415909i
$528$		0			0
$529$	350.088	+	202.124i	0.661793	+	0.382086i
$530$	−40.6317	+	10.6750i	−0.0766635	+	0.0201416i
$531$		0			0
$532$	291.528	−	291.528i	0.547985	−	0.547985i
$533$	−5.27851	+	1.41437i	−0.00990340	+	0.00265361i
$534$		0			0
$535$	309.984	+	1.51229i	0.579409	+	0.00282672i
$536$	−107.288	−	185.828i	−0.200164	−	0.346694i
$537$		0			0
$538$	27.7218	−	7.42804i	0.0515276	−	0.0138068i
$539$			213.863i			0.396778i
$540$		0			0
$541$	−694.204			−1.28319			−0.641593	−	0.767045i	$-0.721726\pi$
$541$	−694.204			−1.28319			−0.641593	+	0.767045i	$0.721726\pi$
$542$	−1.00953	−	3.76761i	−0.00186260	−	0.00695130i
$543$		0			0
$544$	−542.975	+	313.487i	−0.998115	+	0.576262i
$545$	46.6163	−	46.1637i	0.0855346	−	0.0847040i
$546$		0			0
$547$	−229.183	−	855.323i	−0.418982	−	1.56366i	−0.776724	−	0.629841i	$-0.783120\pi$
$547$	−229.183	−	855.323i	−0.418982	−	1.56366i	0.357742	−	0.933820i	$-0.383547\pi$
$548$	−193.821	−	193.821i	−0.353687	−	0.353687i
$549$		0			0
$550$	16.1575	−	58.0297i	0.0293772	−	0.105509i
$551$	−152.171	+	263.568i	−0.276173	+	0.478345i
$552$		0			0
$553$	−203.819	+	760.662i	−0.368569	+	1.37552i
$554$	−111.191	+	64.1960i	−0.200705	+	0.115877i
$555$		0			0
$556$	−137.655	+	238.426i	−0.247581	+	0.428824i
$557$	−598.653	+	598.653i	−1.07478	+	1.07478i	−0.0778138	+	0.996968i	$0.524794\pi$
$557$	−598.653	+	598.653i	−1.07478	+	1.07478i	−0.996968	+	0.0778138i	$0.975206\pi$
$558$		0			0
$559$		−	150.138i		−	0.268584i
$560$	184.300	+	322.844i	0.329107	+	0.576506i
$561$		0			0
$562$	−448.950	−	120.296i	−0.798844	−	0.214050i
$563$	−80.5980	+	300.796i	−0.143158	+	0.534273i	0.856672	+	0.515861i	$0.172528\pi$
$563$	−80.5980	+	300.796i	−0.143158	+	0.534273i	−0.999830	+	0.0184123i	$0.994139\pi$
$564$		0			0
$565$	141.202	−	80.6072i	0.249915	−	0.142668i
$566$	135.312			0.239067
$567$		0			0
$568$	−295.614	−	295.614i	−0.520447	−	0.520447i
$569$	−20.4998	−	11.8356i	−0.0360278	−	0.0208006i	0.481878	−	0.876238i	$-0.339955\pi$
$569$	−20.4998	−	11.8356i	−0.0360278	−	0.0208006i	−0.517906	+	0.855438i	$0.673288\pi$
$570$		0			0
$571$	22.7049	+	39.3260i	0.0397633	+	0.0688721i	0.885222	−	0.465169i	$-0.154006\pi$
$571$	22.7049	+	39.3260i	0.0397633	+	0.0688721i	−0.845459	+	0.534041i	$0.820673\pi$
$572$	23.4468	+	6.28254i	0.0409909	+	0.0109835i
$573$		0			0
$574$	16.9203	+	9.76892i	0.0294778	+	0.0170190i
$575$	−269.000	−	74.8988i	−0.467825	−	0.130259i
$576$		0			0
$577$	−333.577	+	333.577i	−0.578124	+	0.578124i	−0.934386	−	0.356262i	$-0.884051\pi$
$577$	−333.577	+	333.577i	−0.578124	+	0.578124i	0.356262	+	0.934386i	$0.384051\pi$
$578$	−76.3059	+	20.4461i	−0.132017	+	0.0353739i
$579$		0			0
$580$	−294.434	−	297.321i	−0.507644	−	0.512622i
$581$	−603.256	−	1044.87i	−1.03831	−	1.79840i
$582$		0			0
$583$	−22.9394	+	6.14658i	−0.0393471	+	0.0105430i
$584$			475.096i			0.813520i
$585$		0			0
$586$	−316.691			−0.540428
$587$	−201.489	−	751.967i	−0.343252	−	1.28103i	−0.894641	−	0.446786i	$-0.852568\pi$
$587$	−201.489	−	751.967i	−0.343252	−	1.28103i	0.551388	−	0.834249i	$-0.314098\pi$
$588$		0			0
$589$	−433.764	+	250.434i	−0.736441	+	0.425184i
$590$	−1.28773	+	263.953i	−0.00218258	+	0.447377i
$591$		0			0
$592$	−34.3219	−	128.091i	−0.0579763	−	0.216370i
$593$	464.151	+	464.151i	0.782717	+	0.782717i	0.980289	−	0.197571i	$-0.0633054\pi$
$593$	464.151	+	464.151i	0.782717	+	0.782717i	−0.197571	+	0.980289i	$0.563305\pi$
$594$		0			0
$595$	281.381	+	1071.00i	0.472910	+	1.80000i
$596$	−263.432	+	456.278i	−0.442000	+	0.765567i
$597$		0			0
$598$	−7.88753	+	29.4367i	−0.0131899	+	0.0492252i
$599$	402.592	−	232.437i	0.672108	−	0.388042i	−0.124767	−	0.992186i	$-0.539818\pi$
$599$	402.592	−	232.437i	0.672108	−	0.388042i	0.796875	+	0.604145i	$0.206485\pi$
$600$		0			0
$601$	−305.138	+	528.514i	−0.507717	+	0.879392i	0.492243	+	0.870458i	$0.336177\pi$
$601$	−305.138	+	528.514i	−0.507717	+	0.879392i	−0.999960	+	0.00893383i	$0.997156\pi$
$602$	−379.564	+	379.564i	−0.630505	+	0.630505i
$603$		0			0
$604$		−	785.469i		−	1.30045i
$605$	−150.461	+	550.766i	−0.248696	+	0.910357i
$606$		0			0
$607$	81.5905	+	21.8621i	0.134416	+	0.0360167i	0.325400	−	0.945577i	$-0.394501\pi$
$607$	81.5905	+	21.8621i	0.134416	+	0.0360167i	−0.190984	+	0.981593i	$0.561168\pi$
$608$	−95.9744	+	358.181i	−0.157853	+	0.589114i
$609$		0			0
$610$	−77.0800	−	135.024i	−0.126361	−	0.221350i
$611$	−187.606			−0.307048
$612$		0			0
$613$	463.301	+	463.301i	0.755793	+	0.755793i	0.975554	−	0.219760i	$-0.0705276\pi$
$613$	463.301	+	463.301i	0.755793	+	0.755793i	−0.219760	+	0.975554i	$0.570528\pi$
$614$	21.7432	+	12.5534i	0.0354123	+	0.0204453i
$615$		0			0
$616$	−98.5380	−	170.673i	−0.159964	−	0.277066i
$617$	650.709	+	174.357i	1.05463	+	0.282588i	0.744165	−	0.667995i	$-0.232847\pi$
$617$	650.709	+	174.357i	1.05463	+	0.282588i	0.310468	+	0.950584i	$0.399514\pi$
$618$		0			0
$619$	−759.400	−	438.440i	−1.22682	−	0.708303i	−0.260455	−	0.965486i	$-0.583872\pi$
$619$	−759.400	−	438.440i	−1.22682	−	0.708303i	−0.966363	+	0.257183i	$0.917206\pi$
$620$	−174.986	−	666.036i	−0.282235	−	1.07425i
$621$		0			0
$622$	359.975	−	359.975i	0.578737	−	0.578737i
$623$	1513.07	−	405.426i	2.42869	−	0.650765i
$624$		0			0
$625$	−624.881	−	12.1957i	−0.999810	−	0.0195131i
$626$	221.405	+	383.485i	0.353683	+	0.612597i
$627$		0			0
$628$	−152.326	+	40.8157i	−0.242558	+	0.0649932i
$629$		−	395.016i		−	0.628007i
$630$		0			0
$631$	1077.51			1.70762			0.853812	−	0.520581i	$-0.174285\pi$
$631$	1077.51			1.70762			0.853812	+	0.520581i	$0.174285\pi$
$632$	−117.540	−	438.665i	−0.185981	−	0.694090i
$633$		0			0
$634$	223.513	−	129.045i	0.352544	−	0.203541i
$635$	−765.246	−	3.73335i	−1.20511	−	0.00587929i
$636$		0			0
$637$	−62.6798	−	233.924i	−0.0983984	−	0.367228i
$638$	45.3002	+	45.3002i	0.0710034	+	0.0710034i
$639$		0			0
$640$	−543.887	−	317.561i	−0.849824	−	0.496190i
$641$	332.614	−	576.105i	0.518899	−	0.898759i	−0.480860	−	0.876797i	$-0.659675\pi$
$641$	332.614	−	576.105i	0.518899	−	0.898759i	0.999759	−	0.0219617i	$-0.00699118\pi$
$642$		0			0
$643$	287.192	−	1071.82i	0.446644	−	1.66690i	−0.264915	−	0.964272i	$-0.585344\pi$
$643$	287.192	−	1071.82i	0.446644	−	1.66690i	0.711559	−	0.702626i	$-0.247989\pi$
$644$	−348.401	+	201.150i	−0.540996	+	0.312344i
$645$		0			0
$646$	−102.268	+	177.134i	−0.158310	+	0.274201i
$647$	231.177	−	231.177i	0.357306	−	0.357306i	−0.505513	−	0.862819i	$-0.668697\pi$
$647$	231.177	−	231.177i	0.357306	−	0.357306i	0.862819	+	0.505513i	$0.168697\pi$
$648$		0			0
$649$			149.214i			0.229914i
$650$	−0.665544	+	68.2086i	−0.00102391	+	0.104936i
$651$		0			0
$652$	−101.122	−	27.0955i	−0.155094	−	0.0415574i
$653$	−174.987	+	653.059i	−0.267974	+	1.00009i	0.692432	+	0.721484i	$0.256539\pi$
$653$	−174.987	+	653.059i	−0.267974	+	1.00009i	−0.960405	+	0.278607i	$0.910127\pi$
$654$		0			0
$655$	−8.66637	+	31.7235i	−0.0132311	+	0.0484328i
$656$	12.0146			0.0183149
$657$		0			0
$658$	474.287	+	474.287i	0.720802	+	0.720802i
$659$	−138.847	−	80.1633i	−0.210693	−	0.121644i	0.390940	−	0.920416i	$-0.372150\pi$
$659$	−138.847	−	80.1633i	−0.210693	−	0.121644i	−0.601634	+	0.798772i	$0.705483\pi$
$660$		0			0
$661$	−471.803	−	817.186i	−0.713771	−	1.23629i	−0.963432	−	0.267954i	$-0.913652\pi$
$661$	−471.803	−	817.186i	−0.713771	−	1.23629i	0.249660	−	0.968333i	$-0.419681\pi$
$662$	109.122	+	29.2392i	0.164837	+	0.0441679i
$663$		0			0
$664$	602.564	+	347.891i	0.907476	+	0.523931i
$665$	565.581	+	330.228i	0.850498	+	0.496583i
$666$		0			0
$667$	209.991	−	209.991i	0.314829	−	0.314829i
$668$	−336.436	+	90.1478i	−0.503647	+	0.134952i
$669$		0			0
$670$	106.656	−	105.621i	0.159189	−	0.157643i
$671$	−43.9452	−	76.1153i	−0.0654921	−	0.113436i
$672$		0			0
$673$	549.114	−	147.135i	0.815919	−	0.218625i	0.173358	−	0.984859i	$-0.444538\pi$
$673$	549.114	−	147.135i	0.815919	−	0.218625i	0.642562	+	0.766234i	$0.277872\pi$
$674$			305.104i			0.452676i
$675$		0			0
$676$	504.446			0.746222
$677$	−76.2369	−	284.520i	−0.112610	−	0.420266i	0.886487	−	0.462753i	$-0.153138\pi$
$677$	−76.2369	−	284.520i	−0.112610	−	0.420266i	−0.999097	+	0.0424873i	$0.986472\pi$
$678$		0			0
$679$	362.207	−	209.120i	0.533441	−	0.307983i
$680$	−449.347	−	453.752i	−0.660804	−	0.667283i
$681$		0			0
$682$	27.2880	+	101.840i	0.0400117	+	0.149326i
$683$	−449.659	−	449.659i	−0.658359	−	0.658359i	0.296632	−	0.954992i	$-0.404136\pi$
$683$	−449.659	−	449.659i	−0.658359	−	0.658359i	−0.954992	+	0.296632i	$0.904136\pi$
$684$		0			0
$685$	219.550	−	376.023i	0.320511	−	0.548939i
$686$	−174.067	+	301.493i	−0.253742	+	0.439495i
$687$		0			0
$688$	−85.4335	+	318.842i	−0.124177	+	0.463433i
$689$	23.2897	−	13.4463i	0.0338021	−	0.0195157i
$690$		0			0
$691$	−465.762	+	806.723i	−0.674040	+	1.16747i	0.302708	+	0.953083i	$0.402109\pi$
$691$	−465.762	+	806.723i	−0.674040	+	1.16747i	−0.976748	+	0.214388i	$0.931224\pi$
$692$	151.800	−	151.800i	0.219365	−	0.219365i
$693$		0			0
$694$			328.639i			0.473544i
$695$	−421.883	−	115.252i	−0.607027	−	0.165831i
$696$		0			0
$697$	34.5694	+	9.26283i	0.0495974	+	0.0132896i
$698$	−11.9069	+	44.4373i	−0.0170587	+	0.0636638i
$699$		0			0
$700$	−642.903	+	630.478i	−0.918432	+	0.900682i
$701$	−1256.95			−1.79308			−0.896539	−	0.442964i	$-0.853927\pi$
$701$	−1256.95			−1.79308			−0.896539	+	0.442964i	$0.853927\pi$
$702$		0			0
$703$	−165.200	−	165.200i	−0.234993	−	0.234993i
$704$	8.86400	+	5.11763i	0.0125909	+	0.00726937i
$705$		0			0
$706$	290.023	+	502.334i	0.410797	+	0.711521i
$707$	1068.07	+	286.190i	1.51071	+	0.404795i
$708$		0			0
$709$	631.908	+	364.832i	0.891267	+	0.514573i	0.874357	−	0.485284i	$-0.161284\pi$
$709$	631.908	+	364.832i	0.891267	+	0.514573i	0.0169102	+	0.999857i	$0.494617\pi$
$710$	147.459	−	252.554i	0.207689	−	0.355709i
$711$		0			0
$712$	−638.766	+	638.766i	−0.897144	+	0.897144i
$713$	472.085	−	126.495i	0.662111	−	0.177412i
$714$		0			0
$715$	−0.188118	+	38.5597i	−0.000263102	+	0.0539296i
$716$	478.300	+	828.440i	0.668017	+	1.15704i
$717$		0			0
$718$	72.5097	−	19.4289i	0.100988	−	0.0270598i
$719$		−	806.713i		−	1.12199i	−0.827818	−	0.560997i	$-0.810418\pi$
$719$		−	806.713i		−	1.12199i	0.827818	−	0.560997i	$-0.189582\pi$
$720$		0			0
$721$	−304.082			−0.421750
$722$	−54.9567	−	205.101i	−0.0761173	−	0.284074i
$723$		0			0
$724$	470.417	−	271.595i	0.649747	−	0.375131i
$725$	337.955	−	572.384i	0.466144	−	0.789495i
$726$		0			0
$727$	306.191	+	1142.72i	0.421171	+	1.57183i	0.772145	+	0.635446i	$0.219184\pi$
$727$	306.191	+	1142.72i	0.421171	+	1.57183i	−0.350974	+	0.936385i	$0.614150\pi$
$728$	157.802	+	157.802i	0.216762	+	0.216762i
$729$		0			0
$730$	−321.440	+	84.4511i	−0.440329	+	0.115686i
$731$	−491.633	+	851.533i	−0.672548	+	1.16489i
$732$		0			0
$733$	264.670	−	987.760i	0.361077	−	1.34756i	−0.511585	−	0.859233i	$-0.670941\pi$
$733$	264.670	−	987.760i	0.361077	−	1.34756i	0.872662	−	0.488325i	$-0.162392\pi$
$734$	48.0349	−	27.7330i	0.0654426	−	0.0377833i
$735$		0			0
$736$	180.918	−	313.360i	0.245813	−	0.425761i
$737$	60.0009	−	60.0009i	0.0814123	−	0.0814123i
$738$		0			0
$739$		−	808.791i		−	1.09444i	−0.836989	−	0.547220i	$-0.815686\pi$
$739$		−	808.791i		−	1.09444i	0.836989	−	0.547220i	$-0.184314\pi$
$740$	278.960	−	159.248i	0.376972	−	0.215200i
$741$		0			0
$742$	−92.8721	−	24.8850i	−0.125165	−	0.0335378i
$743$	164.727	−	614.769i	0.221705	−	0.827415i	−0.761993	−	0.647586i	$-0.775779\pi$
$743$	164.727	−	614.769i	0.221705	−	0.827415i	0.983698	−	0.179829i	$-0.0575545\pi$
$744$		0			0
$745$	−807.362	−	220.559i	−1.08371	−	0.296052i
$746$	180.107			0.241431
$747$		0			0
$748$	−112.410	−	112.410i	−0.150280	−	0.150280i
$749$	614.409	+	354.729i	0.820306	+	0.473604i
$750$		0			0
$751$	709.826	+	1229.46i	0.945175	+	1.63709i	0.755401	+	0.655263i	$0.227442\pi$
$751$	709.826	+	1229.46i	0.945175	+	1.63709i	0.189774	+	0.981828i	$0.439224\pi$
$752$	398.412	+	106.754i	0.529803	+	0.141960i
$753$		0			0
$754$	−62.8262	−	36.2727i	−0.0833239	−	0.0481071i
$755$	1206.80	−	317.058i	1.59841	−	0.419945i
$756$		0			0
$757$	582.278	−	582.278i	0.769192	−	0.769192i	−0.208772	−	0.977964i	$-0.566947\pi$
$757$	582.278	−	582.278i	0.769192	−	0.769192i	0.977964	+	0.208772i	$0.0669467\pi$
$758$	130.062	−	34.8500i	0.171586	−	0.0459762i
$759$		0			0
$760$	−377.686	−	1.84259i	−0.496955	−	0.00242446i
$761$	73.5291	+	127.356i	0.0966217	+	0.167354i	0.910284	−	0.413984i	$-0.135863\pi$
$761$	73.5291	+	127.356i	0.0966217	+	0.167354i	−0.813663	+	0.581337i	$0.802530\pi$
$762$		0			0
$763$	145.035	−	38.8619i	0.190085	−	0.0509330i
$764$			904.087i			1.18336i
$765$		0			0
$766$	697.261			0.910262
$767$	−43.7322	−	163.211i	−0.0570172	−	0.212791i
$768$		0			0
$769$	−798.259	+	460.875i	−1.03805	+	0.599317i	−0.919280	−	0.393605i	$-0.871228\pi$
$769$	−798.259	+	460.875i	−1.03805	+	0.599317i	−0.118768	+	0.992922i	$0.537894\pi$
$770$	97.9582	−	97.0070i	0.127218	−	0.125983i
$771$		0			0
$772$	−29.9729	−	111.860i	−0.0388250	−	0.144897i
$773$	−646.946	−	646.946i	−0.836928	−	0.836928i	0.151525	−	0.988453i	$-0.451582\pi$
$773$	−646.946	−	646.946i	−0.836928	−	0.836928i	−0.988453	+	0.151525i	$0.951582\pi$
$774$		0			0
$775$	952.666	−	537.697i	1.22925	−	0.693803i
$776$	−120.597	+	208.880i	−0.155409	+	0.269176i
$777$		0			0
$778$	10.3092	−	38.4744i	0.0132509	−	0.0494530i
$779$	18.3311	−	10.5835i	0.0235316	−	0.0135860i
$780$		0			0
$781$	82.6613	−	143.174i	0.105840	−	0.183321i
$782$	141.127	−	141.127i	0.180469	−	0.180469i
$783$		0			0
$784$			532.441i			0.679134i
$785$	−124.197	−	217.559i	−0.158212	−	0.277146i
$786$		0			0
$787$	−105.372	−	28.2343i	−0.133890	−	0.0358758i	0.191251	−	0.981541i	$-0.438745\pi$
$787$	−105.372	−	28.2343i	−0.133890	−	0.0358758i	−0.325142	+	0.945665i	$0.605412\pi$
$788$	261.129	−	974.548i	0.331382	−	1.23674i
$789$		0			0
$790$	275.899	−	157.501i	0.349239	−	0.199368i
$791$	372.115			0.470436
$792$		0			0
$793$	70.3755	+	70.3755i	0.0887459	+	0.0887459i
$794$	101.540	+	58.6241i	0.127884	+	0.0738339i
$795$		0			0
$796$	169.192	+	293.050i	0.212553	+	0.368153i
$797$	−863.511	−	231.377i	−1.08345	−	0.290310i	−0.327443	−	0.944871i	$-0.606187\pi$
$797$	−863.511	−	231.377i	−1.08345	−	0.290310i	−0.756009	+	0.654561i	$0.772854\pi$
$798$		0			0
$799$	1064.04	+	614.324i	1.33171	+	0.768866i
$800$	217.239	−	780.214i	0.271548	−	0.975267i
$801$		0			0
$802$	189.040	−	189.040i	0.235711	−	0.235711i
$803$	−181.475	+	48.6261i	−0.225996	+	0.0605556i
$804$		0			0
$805$	−449.681	−	454.090i	−0.558609	−	0.564087i
$806$	−59.6953	−	103.395i	−0.0740637	−	0.128282i
$807$		0			0
$808$	−615.946	+	165.042i	−0.762310	+	0.204260i
$809$			920.002i			1.13721i	0.822611	+	0.568604i	$0.192516\pi$
$809$			920.002i			1.13721i	−0.822611	+	0.568604i	$0.807484\pi$
$810$		0			0
$811$	−174.196			−0.214792			−0.107396	−	0.994216i	$-0.534251\pi$
$811$	−174.196			−0.214792			−0.107396	+	0.994216i	$0.534251\pi$
$812$	−247.862	−	925.035i	−0.305249	−	1.13921i
$813$		0			0
$814$	−42.5901	+	24.5894i	−0.0523220	+	0.0302081i
$815$	0.811319	−	166.301i	0.000995483	−	0.204050i
$816$		0			0
$817$	150.514	+	561.727i	0.184228	+	0.687548i
$818$	134.631	+	134.631i	0.164585	+	0.164585i
$819$		0			0
$820$	7.39500	+	28.1471i	0.00901829	+	0.0343257i
$821$	−425.992	+	737.840i	−0.518869	+	0.898708i	0.480890	+	0.876781i	$0.340314\pi$
$821$	−425.992	+	737.840i	−0.518869	+	0.898708i	−0.999760	+	0.0219274i	$0.993020\pi$
$822$		0			0
$823$	−53.4313	+	199.408i	−0.0649226	+	0.242295i	−0.990760	−	0.135628i	$-0.956695\pi$
$823$	−53.4313	+	199.408i	−0.0649226	+	0.242295i	0.925837	+	0.377923i	$0.123361\pi$
$824$	151.866	−	87.6802i	0.184304	−	0.106408i
$825$		0			0
$826$	−302.054	+	523.172i	−0.365682	+	0.633380i
$827$	66.1579	−	66.1579i	0.0799974	−	0.0799974i	−0.665976	−	0.745973i	$-0.731985\pi$
$827$	66.1579	−	66.1579i	0.0799974	−	0.0799974i	0.745973	+	0.665976i	$0.231985\pi$
$828$		0			0
$829$			71.1280i			0.0857998i	0.999079	+	0.0428999i	$0.0136596\pi$
$829$			71.1280i			0.0857998i	−0.999079	+	0.0428999i	$0.986340\pi$
$830$	−128.267	+	469.523i	−0.154538	+	0.565690i
$831$		0			0
$832$	−11.1954	−	2.99979i	−0.0134560	−	0.00360552i
$833$	−410.494	+	1531.98i	−0.492790	+	1.83912i
$834$		0			0
$835$	−274.307	−	480.513i	−0.328512	−	0.575465i
$836$	−94.0219			−0.112466
$837$		0			0
$838$	−468.230	−	468.230i	−0.558747	−	0.558747i
$839$	327.523	+	189.096i	0.390373	+	0.225382i	0.682322	−	0.731052i	$-0.260970\pi$
$839$	327.523	+	189.096i	0.390373	+	0.225382i	−0.291949	+	0.956434i	$0.594304\pi$
$840$		0			0
$841$	−67.0308	−	116.101i	−0.0797037	−	0.138051i
$842$	−222.175	−	59.5317i	−0.263866	−	0.0707027i
$843$		0			0
$844$	248.527	+	143.487i	0.294463	+	0.170008i
$845$	203.622	+	775.033i	0.240973	+	0.917199i
$846$		0			0
$847$	−923.984	+	923.984i	−1.09089	+	1.09089i
$848$	−57.1106	+	15.3028i	−0.0673475	+	0.0180457i
$849$		0			0
$850$	227.126	−	384.676i	0.267207	−	0.452560i
$851$	113.985	+	197.428i	0.133943	+	0.231996i
$852$		0			0
$853$	629.719	−	168.733i	0.738240	−	0.197811i	0.129944	−	0.991521i	$-0.458520\pi$
$853$	629.719	−	168.733i	0.738240	−	0.197811i	0.608296	+	0.793711i	$0.291854\pi$
$854$		−	355.832i		−	0.416665i
$855$		0			0
$856$	−409.137			−0.477963
$857$	145.445	+	542.809i	0.169714	+	0.633382i	0.997392	+	0.0721782i	$0.0229950\pi$
$857$	145.445	+	542.809i	0.169714	+	0.633382i	−0.827677	+	0.561204i	$0.810338\pi$
$858$		0			0
$859$	468.778	−	270.649i	0.545725	−	0.315075i	−0.201671	−	0.979453i	$-0.564637\pi$
$859$	468.778	−	270.649i	0.545725	−	0.315075i	0.747396	+	0.664379i	$0.231304\pi$
$860$	−799.549	−	3.90070i	−0.929709	−	0.00453570i
$861$		0			0
$862$	−55.9407	−	208.774i	−0.0648964	−	0.242197i
$863$	−24.2188	−	24.2188i	−0.0280635	−	0.0280635i	0.692936	−	0.720999i	$-0.256317\pi$
$863$	−24.2188	−	24.2188i	−0.0280635	−	0.0280635i	−0.720999	+	0.692936i	$0.756317\pi$
$864$		0			0
$865$	294.502	+	171.952i	0.340464	+	0.198788i
$866$	243.463	−	421.690i	0.281135	−	0.486940i
$867$		0			0
$868$	407.916	−	1522.36i	0.469950	−	1.75388i
$869$	155.529	−	89.7949i	0.178975	−	0.103331i
$870$		0			0
$871$	−48.0438	+	83.2144i	−0.0551594	+	0.0955389i
$872$	−61.2285	+	61.2285i	−0.0702162	+	0.0702162i
$873$		0			0
$874$		−	118.041i		−	0.135059i
$875$	−1228.18	−	733.262i	−1.40363	−	0.838014i
$876$		0			0
$877$	−1200.73	−	321.735i	−1.36913	−	0.366858i	−0.501972	−	0.864884i	$-0.667392\pi$
$877$	−1200.73	−	321.735i	−1.36913	−	0.366858i	−0.867162	+	0.498025i	$0.834059\pi$
$878$	−154.206	+	575.505i	−0.175633	+	0.655472i
$879$		0			0
$880$	22.3412	−	81.7804i	0.0253877	−	0.0929323i
$881$	−1074.75			−1.21993			−0.609963	−	0.792430i	$-0.708816\pi$
$881$	−1074.75			−1.21993			−0.609963	+	0.792430i	$0.708816\pi$
$882$		0			0
$883$	285.903	+	285.903i	0.323786	+	0.323786i	0.850217	−	0.526432i	$-0.176470\pi$
$883$	285.903	+	285.903i	0.323786	+	0.323786i	−0.526432	+	0.850217i	$0.676470\pi$
$884$	155.899	+	90.0086i	0.176357	+	0.101820i
$885$		0			0
$886$	−126.931	−	219.851i	−0.143263	−	0.248139i
$887$	−1036.58	−	277.751i	−1.16864	−	0.313135i	−0.378226	−	0.925713i	$-0.623466\pi$
$887$	−1036.58	−	277.751i	−1.16864	−	0.313135i	−0.790410	+	0.612578i	$0.790132\pi$
$888$		0			0
$889$	−1516.77	−	875.708i	−1.70615	−	0.985048i
$890$	−545.722	−	318.632i	−0.613170	−	0.358014i
$891$		0			0
$892$	528.255	−	528.255i	0.592214	−	0.592214i
$893$	701.910	−	188.076i	0.786013	−	0.210612i
$894$		0			0
$895$	−1079.75	+	1069.27i	−1.20642	+	1.19471i
$896$	−720.711	−	1248.31i	−0.804365	−	1.39320i
$897$		0			0
$898$	170.043	−	45.5630i	0.189358	−	0.0507383i
$899$			1163.43i			1.29414i
$900$		0			0
$901$	−176.122			−0.195473
$902$	−1.15321	−	4.30382i	−0.00127850	−	0.00477142i
$903$		0			0
$904$	−185.844	+	107.297i	−0.205580	+	0.118692i
$905$	607.165	+	613.119i	0.670901	+	0.677479i
$906$		0			0
$907$	−442.672	−	1652.08i	−0.488062	−	1.82147i	−0.565858	−	0.824503i	$-0.691455\pi$
$907$	−442.672	−	1652.08i	−0.488062	−	1.82147i	0.0777954	−	0.996969i	$-0.475212\pi$
$908$	273.374	+	273.374i	0.301073	+	0.301073i
$909$		0			0
$910$	−78.7157	+	134.816i	−0.0865008	+	0.148150i
$911$	203.177	−	351.913i	0.223026	−	0.386293i	−0.732699	−	0.680553i	$-0.761740\pi$
$911$	203.177	−	351.913i	0.223026	−	0.386293i	0.955726	+	0.294260i	$0.0950730\pi$
$912$		0			0
$913$	−71.2133	+	265.772i	−0.0779993	+	0.291097i
$914$	250.056	−	144.370i	0.273584	−	0.157954i
$915$		0			0
$916$	518.280	−	897.687i	0.565808	−	0.980008i
$917$	−53.2204	+	53.2204i	−0.0580375	+	0.0580375i
$918$		0			0
$919$		−	975.596i		−	1.06158i	−0.847502	−	0.530792i	$-0.821895\pi$
$919$		−	975.596i		−	1.06158i	0.847502	−	0.530792i	$-0.178105\pi$
$920$	355.517	+	97.1218i	0.386431	+	0.105567i
$921$		0			0
$922$	−196.847	−	52.7449i	−0.213500	−	0.0572071i
$923$	−48.4533	+	180.830i	−0.0524955	+	0.195916i
$924$		0			0
$925$	357.272	+	364.313i	0.386240	+	0.393852i
$926$	−266.694			−0.288007
$927$		0			0
$928$	609.065	+	609.065i	0.656320	+	0.656320i
$929$	−1121.09	−	647.262i	−1.20677	−	0.696730i	−0.244719	−	0.969594i	$-0.578696\pi$
$929$	−1121.09	−	647.262i	−1.20677	−	0.696730i	−0.962052	+	0.272864i	$0.912029\pi$
$930$		0			0
$931$	469.020	+	812.366i	0.503780	+	0.872573i
$932$	976.435	+	261.635i	1.04768	+	0.280724i
$933$		0			0
$934$	−282.319	−	162.997i	−0.302269	−	0.174515i
$935$	127.332	−	218.081i	0.136184	−	0.233242i
$936$		0			0
$937$	−416.458	+	416.458i	−0.444459	+	0.444459i	−0.893507	−	0.449049i	$-0.851763\pi$
$937$	−416.458	+	416.458i	−0.444459	+	0.444459i	0.449049	+	0.893507i	$0.351763\pi$
$938$	331.834	−	88.9145i	0.353767	−	0.0947916i
$939$		0			0
$940$	−4.87415	+	999.083i	−0.00518527	+	1.06285i
$941$	−6.23741	−	10.8035i	−0.00662849	−	0.0114809i	0.862692	−	0.505729i	$-0.168777\pi$
$941$	−6.23741	−	10.8035i	−0.00662849	−	0.0114809i	−0.869321	+	0.494249i	$0.835443\pi$
$942$		0			0
$943$	−19.9506	+	5.34574i	−0.0211565	+	0.00566886i
$944$			371.489i			0.393526i
$945$		0			0
$946$	122.415			0.129403
$947$	307.908	+	1149.13i	0.325140	+	1.21344i	0.914171	+	0.405329i	$0.132843\pi$
$947$	307.908	+	1149.13i	0.325140	+	1.21344i	−0.589031	+	0.808111i	$0.700490\pi$
$948$		0			0
$949$	184.246	−	106.375i	0.194148	−	0.112091i
$950$	−65.8893	−	255.862i	−0.0693571	−	0.269329i
$951$		0			0
$952$	−378.272	−	1411.73i	−0.397345	−	1.48291i
$953$	943.370	+	943.370i	0.989895	+	0.989895i	0.999949	−	0.0100546i	$-0.00320052\pi$
$953$	943.370	+	943.370i	0.989895	+	0.989895i	−0.0100546	+	0.999949i	$0.503201\pi$
$954$		0			0
$955$	−1389.04	+	364.939i	−1.45449	+	0.382135i
$956$	224.324	−	388.540i	0.234648	−	0.406423i
$957$		0			0
$958$	−209.149	+	780.555i	−0.218318	+	0.814775i
$959$	863.033	−	498.272i	0.899930	−	0.519575i
$960$		0			0
$961$	−476.853	+	825.933i	−0.496204	+	0.859451i
$962$	39.3784	−	39.3784i	0.0409339	−	0.0409339i
$963$		0			0
$964$			1440.74i			1.49454i
$965$	159.764	−	91.2033i	0.165558	−	0.0945112i
$966$		0			0
$967$	266.681	+	71.4571i	0.275782	+	0.0738956i	0.394059	−	0.919085i	$-0.371070\pi$
$967$	266.681	+	71.4571i	0.275782	+	0.0738956i	−0.118277	+	0.992981i	$0.537737\pi$
$968$	195.037	−	727.888i	0.201484	−	0.751950i
$969$		0			0
$970$	−162.761	−	44.4639i	−0.167795	−	0.0458391i
$971$	311.097			0.320388			0.160194	−	0.987086i	$-0.448788\pi$
$971$	311.097			0.320388			0.160194	+	0.987086i	$0.448788\pi$
$972$		0			0
$973$	−707.766	−	707.766i	−0.727406	−	0.727406i
$974$	273.087	+	157.667i	0.280377	+	0.161876i
$975$		0			0
$976$	−109.407	−	189.499i	−0.112098	−	0.194159i
$977$	−608.490	−	163.044i	−0.622815	−	0.166883i	−0.0664079	−	0.997793i	$-0.521154\pi$
$977$	−608.490	−	163.044i	−0.622815	−	0.166883i	−0.556407	+	0.830910i	$0.687821\pi$
$978$		0			0
$979$	−309.371	−	178.616i	−0.316008	−	0.182447i
$980$	−1247.37	+	327.719i	−1.27283	+	0.334407i
$981$		0			0
$982$	18.5905	−	18.5905i	0.0189313	−	0.0189313i
$983$	−305.307	+	81.8068i	−0.310587	+	0.0832216i	−0.410746	−	0.911750i	$-0.634732\pi$
$983$	−305.307	+	81.8068i	−0.310587	+	0.0832216i	0.100159	+	0.994971i	$0.468065\pi$
$984$		0			0
$985$	1602.70	+	7.81899i	1.62711	+	0.00793806i
$986$	237.553	+	411.453i	0.240926	+	0.417295i
$987$		0			0
$988$	102.841	−	27.5563i	0.104091	−	0.0278910i
$989$		−	567.460i		−	0.573771i
$990$		0			0
$991$	−1401.99			−1.41472			−0.707362	−	0.706852i	$-0.750115\pi$
$991$	−1401.99			−1.41472			−0.707362	+	0.706852i	$0.750115\pi$
$992$	366.889	+	1369.25i	0.369848	+	1.38029i
$993$		0			0
$994$	579.651	−	334.662i	0.583150	−	0.336682i
$995$	−381.947	+	378.238i	−0.383866	+	0.380139i
$996$		0			0
$997$	349.692	+	1305.07i	0.350745	+	1.30900i	0.885756	+	0.464152i	$0.153641\pi$
$997$	349.692	+	1305.07i	0.350745	+	1.30900i	−0.535011	+	0.844845i	$0.679693\pi$
$998$	−309.014	−	309.014i	−0.309633	−	0.309633i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.3.l.a.73.4		40
3.2	odd	2		45.3.k.a.43.7	yes	40
5.2	odd	4	inner	135.3.l.a.127.7		40
9.2	odd	6		405.3.g.h.163.7		20
9.4	even	3	inner	135.3.l.a.118.7		40
9.5	odd	6		45.3.k.a.13.4	yes	40
9.7	even	3		405.3.g.g.163.4		20
15.2	even	4		45.3.k.a.7.4	✓	40
15.8	even	4		225.3.o.b.7.7		40
15.14	odd	2		225.3.o.b.43.4		40
45.2	even	12		405.3.g.h.82.7		20
45.7	odd	12		405.3.g.g.82.4		20
45.14	odd	6		225.3.o.b.193.7		40
45.22	odd	12	inner	135.3.l.a.37.4		40
45.23	even	12		225.3.o.b.157.4		40
45.32	even	12		45.3.k.a.22.7	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.k.a.7.4	✓	40	15.2	even	4
45.3.k.a.13.4	yes	40	9.5	odd	6
45.3.k.a.22.7	yes	40	45.32	even	12
45.3.k.a.43.7	yes	40	3.2	odd	2
135.3.l.a.37.4		40	45.22	odd	12	inner
135.3.l.a.73.4		40	1.1	even	1	trivial
135.3.l.a.118.7		40	9.4	even	3	inner
135.3.l.a.127.7		40	5.2	odd	4	inner
225.3.o.b.7.7		40	15.8	even	4
225.3.o.b.43.4		40	15.14	odd	2
225.3.o.b.157.4		40	45.23	even	12
225.3.o.b.193.7		40	45.14	odd	6
405.3.g.g.82.4		20	45.7	odd	12
405.3.g.g.163.4		20	9.7	even	3
405.3.g.h.82.7		20	45.2	even	12
405.3.g.h.163.7		20	9.2	odd	6

Overview	Random
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Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	135.l (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.238965 - 0.891829i) q^{2} +(2.72585 - 1.57377i) q^{4} +(3.51824 + 3.55274i) q^{5} +(2.96175 + 11.0534i) q^{7} +(-4.66637 - 4.66637i) q^{8} +(2.32770 - 3.98665i) q^{10} +(1.30484 - 2.26005i) q^{11} +(-0.764853 + 2.85447i) q^{13} +(9.15000 - 5.28276i) q^{14} +(3.24857 - 5.62669i) q^{16} +(13.6850 - 13.6850i) q^{17} -11.4465i q^{19} +(15.1814 + 4.14733i) q^{20} +(-2.32738 - 0.623621i) q^{22} +(-2.89082 + 10.7887i) q^{23} +(-0.243925 + 24.9988i) q^{25} +2.72847 q^{26} +(25.4688 + 25.4688i) q^{28} +(-23.0262 - 13.2942i) q^{29} +(-21.8787 - 37.8950i) q^{31} +(-31.2919 - 8.38463i) q^{32} +(-15.4750 - 8.93448i) q^{34} +(-28.8498 + 49.4110i) q^{35} +(14.4324 - 14.4324i) q^{37} +(-10.2083 + 2.73530i) q^{38} +(0.160974 - 32.9958i) q^{40} +(0.924605 + 1.60146i) q^{41} +(-49.0742 + 13.1494i) q^{43} -8.21405i q^{44} +10.3125 q^{46} +(16.4309 + 61.3211i) q^{47} +(-70.9709 + 40.9750i) q^{49} +(22.3529 - 5.75630i) q^{50} +(2.40740 + 8.98455i) q^{52} +(-6.43481 - 6.43481i) q^{53} +(12.6201 - 3.31564i) q^{55} +(37.7587 - 65.4000i) q^{56} +(-6.35367 + 23.7122i) q^{58} +(-49.5170 + 28.5886i) q^{59} +(16.8393 - 29.1666i) q^{61} +(-28.5676 + 28.5676i) q^{62} +3.92205i q^{64} +(-12.8321 + 7.32540i) q^{65} +(31.4072 + 8.41554i) q^{67} +(15.7663 - 58.8405i) q^{68} +(50.9602 + 13.9216i) q^{70} +63.3498 q^{71} +(-50.9063 - 50.9063i) q^{73} +(-16.3201 - 9.42239i) q^{74} +(-18.0141 - 31.2013i) q^{76} +(28.8458 + 7.72922i) q^{77} +(59.5972 + 34.4084i) q^{79} +(31.4194 - 8.25473i) q^{80} +(1.20728 - 1.20728i) q^{82} +(-101.841 + 27.2882i) q^{83} +(96.7668 + 0.472089i) q^{85} +(23.4540 + 40.6236i) q^{86} +(-16.6351 + 4.45735i) q^{88} -136.887i q^{89} -33.8170 q^{91} +(9.09897 + 33.9578i) q^{92} +(50.7615 - 29.3072i) q^{94} +(40.6663 - 40.2715i) q^{95} +(-9.45952 - 35.3034i) q^{97} +(53.5023 + 53.5023i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 2 q^{2} + 2 q^{5} - 2 q^{7} + 24 q^{8} - 8 q^{10} - 8 q^{11} - 2 q^{13} + 28 q^{16} - 28 q^{17} + 114 q^{20} + 14 q^{22} - 82 q^{23} - 8 q^{25} + 112 q^{26} - 88 q^{28} - 4 q^{31} + 14 q^{32} - 352 q^{35}+ \cdots + 1876 q^{98}+O(q^{100}) \) 40 * q + 2 * q^2 + 2 * q^5 - 2 * q^7 + 24 * q^8 - 8 * q^10 - 8 * q^11 - 2 * q^13 + 28 * q^16 - 28 * q^17 + 114 * q^20 + 14 * q^22 - 82 * q^23 - 8 * q^25 + 112 * q^26 - 88 * q^28 - 4 * q^31 + 14 * q^32 - 352 * q^35 - 92 * q^37 - 330 * q^38 + 30 * q^40 + 28 * q^41 - 2 * q^43 - 136 * q^46 - 64 * q^47 + 458 * q^50 - 74 * q^52 + 608 * q^53 + 224 * q^55 + 192 * q^56 + 30 * q^58 + 92 * q^61 + 100 * q^62 + 326 * q^65 - 80 * q^67 - 626 * q^68 - 102 * q^70 - 248 * q^71 - 8 * q^73 - 96 * q^76 - 338 * q^77 - 1444 * q^80 + 104 * q^82 - 370 * q^83 - 98 * q^85 + 328 * q^86 - 210 * q^88 + 152 * q^91 - 388 * q^92 + 360 * q^95 + 292 * q^97 + 1876 * q^98

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