LMFDB - Embedded newform 144.5.q.c.65.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,5,Mod(65,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("144.65");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	144.q (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$14.8852746841$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 6x^{6} + 121x^{5} + 1104x^{4} - 1647x^{3} + 6529x^{2} + 85254x + 440076 $ x^8 - 3x^7 + 6x^6 + 121x^5 + 1104x^4 - 1647x^3 + 6529x^2 + 85254*x + 440076
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{6} $
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.3
Root			$-3.41053 + 2.74723i$ of defining polynomial
Character	$\chi$	$=$	144.65
Dual form			144.5.q.c.113.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.23662 + 7.94047i) q^{3} +(-34.8718 + 20.1332i) q^{5} +(7.38688 - 12.7945i) q^{7} +(-45.1021 + 67.2815i) q^{9} +O(q^{10})$	\(q+(4.23662 + 7.94047i) q^{3} +(-34.8718 + 20.1332i) q^{5} +(7.38688 - 12.7945i) q^{7} +(-45.1021 + 67.2815i) q^{9} +(70.7125 + 40.8259i) q^{11} +(-139.053 - 240.848i) q^{13} +(-307.606 - 191.601i) q^{15} +10.8854i q^{17} -532.815 q^{19} +(132.889 + 4.45005i) q^{21} +(702.045 - 405.326i) q^{23} +(498.193 - 862.895i) q^{25} +(-725.327 - 73.0855i) q^{27} +(-257.640 - 148.749i) q^{29} +(97.5447 + 168.952i) q^{31} +(-24.5946 + 734.454i) q^{33} +594.887i q^{35} -2097.18 q^{37} +(1323.33 - 2124.53i) q^{39} +(-1359.41 + 784.854i) q^{41} +(-46.0863 + 79.8239i) q^{43} +(218.196 - 3254.27i) q^{45} +(-1849.15 - 1067.61i) q^{47} +(1091.37 + 1890.30i) q^{49} +(-86.4353 + 46.1174i) q^{51} -2579.42i q^{53} -3287.82 q^{55} +(-2257.33 - 4230.80i) q^{57} +(-1349.04 + 778.868i) q^{59} +(-2685.97 + 4652.24i) q^{61} +(527.666 + 1074.06i) q^{63} +(9698.07 + 5599.19i) q^{65} +(457.641 + 792.658i) q^{67} +(6192.77 + 3857.35i) q^{69} +8215.93i q^{71} -3438.63 q^{73} +(8962.45 + 300.125i) q^{75} +(1044.69 - 603.152i) q^{77} +(2316.17 - 4011.73i) q^{79} +(-2492.60 - 6069.07i) q^{81} +(5195.52 + 2999.63i) q^{83} +(-219.158 - 379.593i) q^{85} +(89.6101 - 2675.98i) q^{87} +8434.43i q^{89} -4108.69 q^{91} +(-928.301 + 1490.34i) q^{93} +(18580.2 - 10727.3i) q^{95} +(3015.58 - 5223.13i) q^{97} +(-5936.10 + 2916.31i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 9 q^{3} - 9 q^{5} - 13 q^{7} + 21 q^{9}+O(q^{10}) $ 8 * q + 9 * q^3 - 9 * q^5 - 13 * q^7 + 21 * q^9	$ 8 q + 9 q^{3} - 9 q^{5} - 13 q^{7} + 21 q^{9} + 18 q^{11} - 5 q^{13} - 225 q^{15} - 562 q^{19} - 1167 q^{21} + 1719 q^{23} + 353 q^{25} - 648 q^{27} + 2115 q^{29} - 187 q^{31} + 3258 q^{33} + 16 q^{37} + 8265 q^{39} - 7920 q^{41} + 68 q^{43} + 5679 q^{45} - 13689 q^{47} - 327 q^{49} - 10449 q^{51} + 1818 q^{55} - 21861 q^{57} + 20052 q^{59} - 1937 q^{61} - 5559 q^{63} + 25965 q^{65} - 154 q^{67} + 21645 q^{69} - 7802 q^{73} + 30297 q^{75} - 25641 q^{77} + 2195 q^{79} + 19701 q^{81} - 37017 q^{83} - 3042 q^{85} - 22455 q^{87} - 15830 q^{91} - 36489 q^{93} + 37116 q^{95} + 7282 q^{97} + 10035 q^{99}+O(q^{100}) $ 8 * q + 9 * q^3 - 9 * q^5 - 13 * q^7 + 21 * q^9 + 18 * q^11 - 5 * q^13 - 225 * q^15 - 562 * q^19 - 1167 * q^21 + 1719 * q^23 + 353 * q^25 - 648 * q^27 + 2115 * q^29 - 187 * q^31 + 3258 * q^33 + 16 * q^37 + 8265 * q^39 - 7920 * q^41 + 68 * q^43 + 5679 * q^45 - 13689 * q^47 - 327 * q^49 - 10449 * q^51 + 1818 * q^55 - 21861 * q^57 + 20052 * q^59 - 1937 * q^61 - 5559 * q^63 + 25965 * q^65 - 154 * q^67 + 21645 * q^69 - 7802 * q^73 + 30297 * q^75 - 25641 * q^77 + 2195 * q^79 + 19701 * q^81 - 37017 * q^83 - 3042 * q^85 - 22455 * q^87 - 15830 * q^91 - 36489 * q^93 + 37116 * q^95 + 7282 * q^97 + 10035 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$

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			0
$2$		0			0
$3$	4.23662	+	7.94047i	0.470736	+	0.882274i
$3$	4.23662	+	7.94047i	0.470736	+	0.882274i
$4$		0			0
$5$	−34.8718	+	20.1332i	−1.39487	+	0.805329i	−0.993849	−	0.110740i	$-0.964678\pi$
$5$	−34.8718	+	20.1332i	−1.39487	+	0.805329i	−0.401021	+	0.916069i	$0.631345\pi$
$6$		0			0
$7$	7.38688	−	12.7945i	0.150753	−	0.261111i	−0.780752	−	0.624841i	$-0.785164\pi$
$7$	7.38688	−	12.7945i	0.150753	−	0.261111i	0.931504	+	0.363730i	$0.118497\pi$
$8$		0			0
$9$	−45.1021	+	67.2815i	−0.556816	+	0.830636i
$10$		0			0
$11$	70.7125	+	40.8259i	0.584400	+	0.337404i	0.762880	−	0.646540i	$-0.223785\pi$
$11$	70.7125	+	40.8259i	0.584400	+	0.337404i	−0.178480	+	0.983944i	$0.557118\pi$
$12$		0			0
$13$	−139.053	−	240.848i	−0.822801	−	1.42513i	−0.903588	−	0.428402i	$-0.859077\pi$
$13$	−139.053	−	240.848i	−0.822801	−	1.42513i	0.0807868	−	0.996731i	$-0.474257\pi$
$14$		0			0
$15$	−307.606	−	191.601i	−1.36714	−	0.851561i
$16$		0			0
$17$			10.8854i			0.0376658i	0.999823	+	0.0188329i	$0.00599505\pi$
$17$			10.8854i			0.0376658i	−0.999823	+	0.0188329i	$0.994005\pi$
$18$		0			0
$19$	−532.815			−1.47594			−0.737971	−	0.674833i	$-0.764216\pi$
$19$	−532.815			−1.47594			−0.737971	+	0.674833i	$0.764216\pi$
$20$		0			0
$21$	132.889	+	4.45005i	0.301336	+	0.0100908i
$22$		0			0
$23$	702.045	−	405.326i	1.32712	−	0.766211i	0.342264	−	0.939604i	$-0.388806\pi$
$23$	702.045	−	405.326i	1.32712	−	0.766211i	0.984853	+	0.173393i	$0.0554730\pi$
$24$		0			0
$25$	498.193	−	862.895i	0.797109	−	1.38063i
$26$		0			0
$27$	−725.327	−	73.0855i	−0.994962	−	0.100254i
$28$		0			0
$29$	−257.640	−	148.749i	−0.306350	−	0.176871i	0.338942	−	0.940807i	$-0.389931\pi$
$29$	−257.640	−	148.749i	−0.306350	−	0.176871i	−0.645292	+	0.763936i	$0.723264\pi$
$30$		0			0
$31$	97.5447	+	168.952i	0.101503	+	0.175809i	0.912304	−	0.409513i	$-0.134301\pi$
$31$	97.5447	+	168.952i	0.101503	+	0.175809i	−0.810801	+	0.585322i	$0.800968\pi$
$32$		0			0
$33$	−24.5946	+	734.454i	−0.0225845	+	0.674429i
$34$		0			0
$35$			594.887i			0.485622i
$36$		0			0
$37$	−2097.18			−1.53191			−0.765954	−	0.642896i	$-0.777733\pi$
$37$	−2097.18			−1.53191			−0.765954	+	0.642896i	$0.777733\pi$
$38$		0			0
$39$	1323.33	−	2124.53i	0.870037	−	1.39680i
$40$		0			0
$41$	−1359.41	+	784.854i	−0.808689	+	0.466897i	−0.846500	−	0.532388i	$-0.821295\pi$
$41$	−1359.41	+	784.854i	−0.808689	+	0.466897i	0.0378113	+	0.999285i	$0.487961\pi$
$42$		0			0
$43$	−46.0863	+	79.8239i	−0.0249250	+	0.0431714i	−0.878219	−	0.478259i	$-0.841268\pi$
$43$	−46.0863	+	79.8239i	−0.0249250	+	0.0431714i	0.853294	+	0.521430i	$0.174601\pi$
$44$		0			0
$45$	218.196	−	3254.27i	0.107751	−	1.60705i
$46$		0			0
$47$	−1849.15	−	1067.61i	−0.837098	−	0.483299i	0.0191789	−	0.999816i	$-0.493895\pi$
$47$	−1849.15	−	1067.61i	−0.837098	−	0.483299i	−0.856277	+	0.516517i	$0.827228\pi$
$48$		0			0
$49$	1091.37	+	1890.30i	0.454547	+	0.787299i
$50$		0			0
$51$	−86.4353	+	46.1174i	−0.0332315	+	0.0177306i
$52$		0			0
$53$		−	2579.42i		−	0.918271i	−0.888366	−	0.459135i	$-0.848159\pi$
$53$		−	2579.42i		−	0.918271i	0.888366	−	0.459135i	$-0.151841\pi$
$54$		0			0
$55$	−3287.82			−1.08688
$56$		0			0
$57$	−2257.33	−	4230.80i	−0.694778	−	1.30218i
$58$		0			0
$59$	−1349.04	+	778.868i	−0.387544	+	0.223748i	−0.681095	−	0.732195i	$-0.738496\pi$
$59$	−1349.04	+	778.868i	−0.387544	+	0.223748i	0.293552	+	0.955943i	$0.405163\pi$
$60$		0			0
$61$	−2685.97	+	4652.24i	−0.721842	+	1.25027i	0.238419	+	0.971162i	$0.423371\pi$
$61$	−2685.97	+	4652.24i	−0.721842	+	1.25027i	−0.960261	+	0.279105i	$0.909962\pi$
$62$		0			0
$63$	527.666	+	1074.06i	0.132947	+	0.270612i
$64$		0			0
$65$	9698.07	+	5599.19i	2.29540	+	1.32525i
$66$		0			0
$67$	457.641	+	792.658i	0.101947	+	0.176578i	0.912487	−	0.409106i	$-0.134159\pi$
$67$	457.641	+	792.658i	0.101947	+	0.176578i	−0.810540	+	0.585684i	$0.800826\pi$
$68$		0			0
$69$	6192.77	+	3857.35i	1.30073	+	0.810198i
$70$		0			0
$71$			8215.93i			1.62982i	0.579587	+	0.814910i	$0.303214\pi$
$71$			8215.93i			1.62982i	−0.579587	+	0.814910i	$0.696786\pi$
$72$		0			0
$73$	−3438.63			−0.645267			−0.322634	−	0.946524i	$-0.604568\pi$
$73$	−3438.63			−0.645267			−0.322634	+	0.946524i	$0.604568\pi$
$74$		0			0
$75$	8962.45	+	300.125i	1.59332	+	0.0533555i
$76$		0			0
$77$	1044.69	−	603.152i	0.176200	−	0.101729i
$78$		0			0
$79$	2316.17	−	4011.73i	0.371122	−	0.642802i	−0.618617	−	0.785693i	$-0.712307\pi$
$79$	2316.17	−	4011.73i	0.371122	−	0.642802i	0.989738	+	0.142891i	$0.0456399\pi$
$80$		0			0
$81$	−2492.60	−	6069.07i	−0.379912	−	0.925023i
$82$		0			0
$83$	5195.52	+	2999.63i	0.754176	+	0.435424i	0.827201	−	0.561907i	$-0.189932\pi$
$83$	5195.52	+	2999.63i	0.754176	+	0.435424i	−0.0730250	+	0.997330i	$0.523265\pi$
$84$		0			0
$85$	−219.158	−	379.593i	−0.0303333	−	0.0525389i
$86$		0			0
$87$	89.6101	−	2675.98i	0.0118391	−	0.353544i
$88$		0			0
$89$			8434.43i			1.06482i	0.846487	+	0.532409i	$0.178713\pi$
$89$			8434.43i			1.06482i	−0.846487	+	0.532409i	$0.821287\pi$
$90$		0			0
$91$	−4108.69			−0.496158
$92$		0			0
$93$	−928.301	+	1490.34i	−0.107330	+	0.172313i
$94$		0			0
$95$	18580.2	−	10727.3i	2.05875	−	1.18862i
$96$		0			0
$97$	3015.58	−	5223.13i	0.320499	−	0.555121i	−0.660092	−	0.751185i	$-0.729483\pi$
$97$	3015.58	−	5223.13i	0.320499	−	0.555121i	0.980591	+	0.196064i	$0.0628160\pi$
$98$		0			0
$99$	−5936.10	+	2916.31i	−0.605663	+	0.297552i
$100$		0			0
$101$	5181.24	+	2991.39i	0.507915	+	0.293245i	0.731976	−	0.681330i	$-0.238598\pi$
$101$	5181.24	+	2991.39i	0.507915	+	0.293245i	−0.224061	+	0.974575i	$0.571931\pi$
$102$		0			0
$103$	−765.718	−	1326.26i	−0.0721763	−	0.125013i	0.827679	−	0.561202i	$-0.189661\pi$
$103$	−765.718	−	1326.26i	−0.0721763	−	0.125013i	−0.899855	+	0.436189i	$0.856328\pi$
$104$		0			0
$105$	−4723.68	+	2520.31i	−0.428452	+	0.228600i
$106$		0			0
$107$			20499.8i			1.79053i	0.445536	+	0.895264i	$0.353013\pi$
$107$			20499.8i			1.79053i	−0.445536	+	0.895264i	$0.646987\pi$
$108$		0			0
$109$	−9404.21			−0.791534			−0.395767	−	0.918351i	$-0.629521\pi$
$109$	−9404.21			−0.791534			−0.395767	+	0.918351i	$0.629521\pi$
$110$		0			0
$111$	−8884.96	−	16652.6i	−0.721124	−	1.35156i
$112$		0			0
$113$	2598.59	−	1500.29i	0.203507	−	0.117495i	−0.394783	−	0.918774i	$-0.629180\pi$
$113$	2598.59	−	1500.29i	0.203507	−	0.117495i	0.598290	+	0.801279i	$0.295847\pi$
$114$		0			0
$115$	−16321.0	+	28268.8i	−1.23410	+	2.13753i
$116$		0			0
$117$	22476.2	+	1507.01i	1.64192	+	0.110089i
$118$		0			0
$119$	139.273	+	80.4092i	0.00983496	+	0.00567822i
$120$		0			0
$121$	−3987.00	−	6905.69i	−0.272317	−	0.471668i
$122$		0			0
$123$	−11991.4	−	7469.20i	−0.792610	−	0.493701i
$124$		0			0
$125$			14954.4i			0.957081i
$126$		0			0
$127$	−9817.40			−0.608680			−0.304340	−	0.952563i	$-0.598436\pi$
$127$	−9817.40			−0.608680			−0.304340	+	0.952563i	$0.598436\pi$
$128$		0			0
$129$	−829.089	−	27.7636i	−0.0498221	−	0.00166839i
$130$		0			0
$131$	553.194	−	319.387i	0.0322356	−	0.0186112i	−0.483796	−	0.875181i	$-0.660742\pi$
$131$	553.194	−	319.387i	0.0322356	−	0.0186112i	0.516031	+	0.856570i	$0.327409\pi$
$132$		0			0
$133$	−3935.84	+	6817.07i	−0.222502	+	0.385385i
$134$		0			0
$135$	26764.9	−	12054.6i	1.46858	−	0.661429i
$136$		0			0
$137$	−27716.3	−	16002.0i	−1.47670	−	0.852575i	−0.477050	−	0.878876i	$-0.658294\pi$
$137$	−27716.3	−	16002.0i	−1.47670	−	0.852575i	−0.999654	+	0.0263010i	$0.991627\pi$
$138$		0			0
$139$	−2792.13	−	4836.11i	−0.144513	−	0.250303i	0.784678	−	0.619903i	$-0.212828\pi$
$139$	−2792.13	−	4836.11i	−0.144513	−	0.250303i	−0.929191	+	0.369600i	$0.879495\pi$
$140$		0			0
$141$	643.154	−	19206.2i	0.0323502	−	0.966056i
$142$		0			0
$143$		−	22707.9i		−	1.11047i
$144$		0			0
$145$	11979.2			0.569758
$146$		0			0
$147$	−10386.2	+	16674.5i	−0.480642	+	0.771645i
$148$		0			0
$149$	−7118.75	+	4110.01i	−0.320650	+	0.185127i	−0.651682	−	0.758492i	$-0.725936\pi$
$149$	−7118.75	+	4110.01i	−0.320650	+	0.185127i	0.331032	+	0.943619i	$0.392603\pi$
$150$		0			0
$151$	10236.0	−	17729.2i	0.448927	−	0.777564i	−0.549389	−	0.835566i	$-0.685140\pi$
$151$	10236.0	−	17729.2i	0.448927	−	0.777564i	0.998316	+	0.0580020i	$0.0184730\pi$
$152$		0			0
$153$	−732.387	−	490.955i	−0.0312865	−	0.0209729i
$154$		0			0
$155$	−6803.11	−	3927.78i	−0.283168	−	0.163487i
$156$		0			0
$157$	−12896.9	−	22338.2i	−0.523224	−	0.906250i	−0.999635	−	0.0270273i	$-0.991396\pi$
$157$	−12896.9	−	22338.2i	−0.523224	−	0.906250i	0.476411	−	0.879223i	$-0.341937\pi$
$158$		0			0
$159$	20481.8	−	10928.0i	0.810167	−	0.432263i
$160$		0			0
$161$		−	11976.4i		−	0.462034i
$162$		0			0
$163$	16488.3			0.620584			0.310292	−	0.950641i	$-0.399573\pi$
$163$	16488.3			0.620584			0.310292	+	0.950641i	$0.399573\pi$
$164$		0			0
$165$	−13929.3	−	26106.9i	−0.511635	−	0.958930i
$166$		0			0
$167$	−34263.0	+	19781.8i	−1.22855	+	0.709304i	−0.966727	−	0.255812i	$-0.917657\pi$
$167$	−34263.0	+	19781.8i	−1.22855	+	0.709304i	−0.261824	+	0.965116i	$0.584324\pi$
$168$		0			0
$169$	−24391.2	+	42246.8i	−0.854004	+	1.47918i
$170$		0			0
$171$	24031.1	−	35848.6i	0.821828	−	1.22597i
$172$		0			0
$173$	4204.22	+	2427.31i	0.140473	+	0.0811022i	0.568589	−	0.822621i	$-0.307489\pi$
$173$	4204.22	+	2427.31i	0.140473	+	0.0811022i	−0.428116	+	0.903724i	$0.640823\pi$
$174$		0			0
$175$	−7360.19	−	12748.2i	−0.240333	−	0.416268i
$176$		0			0
$177$	−11900.0	−	7412.24i	−0.379838	−	0.236593i
$178$		0			0
$179$		−	4764.02i		−	0.148685i	−0.997233	−	0.0743425i	$-0.976314\pi$
$179$		−	4764.02i		−	0.148685i	0.997233	−	0.0743425i	$-0.0236858\pi$
$180$		0			0
$181$	3741.40			0.114203			0.0571014	−	0.998368i	$-0.481814\pi$
$181$	3741.40			0.114203			0.0571014	+	0.998368i	$0.481814\pi$
$182$		0			0
$183$	−48320.5	−	1618.10i	−1.44288	−	0.0483174i
$184$		0			0
$185$	73132.4	−	42223.0i	2.13681	−	1.23369i
$186$		0			0
$187$	−444.406	+	769.734i	−0.0127086	+	0.0220119i
$188$		0			0
$189$	−6293.00	+	8740.29i	−0.176171	+	0.244682i
$190$		0			0
$191$	−9003.63	−	5198.25i	−0.246803	−	0.142492i	0.371496	−	0.928434i	$-0.378845\pi$
$191$	−9003.63	−	5198.25i	−0.246803	−	0.142492i	−0.618300	+	0.785943i	$0.712178\pi$
$192$		0			0
$193$	21606.1	+	37422.9i	0.580045	+	1.00467i	0.995473	+	0.0950419i	$0.0302985\pi$
$193$	21606.1	+	37422.9i	0.580045	+	1.00467i	−0.415428	+	0.909626i	$0.636368\pi$
$194$		0			0
$195$	−3373.10	+	100729.i	−0.0887073	+	2.64902i
$196$		0			0
$197$			49899.7i			1.28578i	0.765960	+	0.642889i	$0.222264\pi$
$197$			49899.7i			1.28578i	−0.765960	+	0.642889i	$0.777736\pi$
$198$		0			0
$199$	7613.76			0.192262			0.0961310	−	0.995369i	$-0.469353\pi$
$199$	7613.76			0.192262			0.0961310	+	0.995369i	$0.469353\pi$
$200$		0			0
$201$	−4355.22	+	6992.07i	−0.107800	+	0.173067i
$202$		0			0
$203$	−3806.32	+	2197.58i	−0.0923662	+	0.0533276i
$204$		0			0
$205$	31603.3	−	54738.5i	0.752011	−	1.30252i
$206$		0			0
$207$	−4392.76	+	65515.7i	−0.102517	+	1.52899i
$208$		0			0
$209$	−37676.6	−	21752.6i	−0.862541	−	0.497988i
$210$		0			0
$211$	−28097.7	−	48666.7i	−0.631112	−	1.09312i	−0.987325	−	0.158713i	$-0.949266\pi$
$211$	−28097.7	−	48666.7i	−0.631112	−	1.09312i	0.356213	−	0.934405i	$-0.384068\pi$
$212$		0			0
$213$	−65238.3	+	34807.8i	−1.43795	+	0.767215i
$214$		0			0
$215$		−	3711.47i		−	0.0802913i
$216$		0			0
$217$	2882.21			0.0612076
$218$		0			0
$219$	−14568.2	−	27304.3i	−0.303750	−	0.569303i
$220$		0			0
$221$	2621.72	−	1513.65i	0.0536788	−	0.0309915i
$222$		0			0
$223$	18961.1	−	32841.6i	0.381289	−	0.660412i	−0.609958	−	0.792434i	$-0.708814\pi$
$223$	18961.1	−	32841.6i	0.381289	−	0.660412i	0.991247	+	0.132022i	$0.0421469\pi$
$224$		0			0
$225$	35587.4	+	72437.6i	0.702960	+	1.43087i
$226$		0			0
$227$	−8461.24	−	4885.10i	−0.164203	−	0.0948029i	0.415646	−	0.909526i	$-0.363555\pi$
$227$	−8461.24	−	4885.10i	−0.164203	−	0.0948029i	−0.579850	+	0.814723i	$0.696889\pi$
$228$		0			0
$229$	−18965.0	−	32848.4i	−0.361645	−	0.626387i	0.626587	−	0.779352i	$-0.284451\pi$
$229$	−18965.0	−	32848.4i	−0.361645	−	0.626387i	−0.988232	+	0.152964i	$0.951118\pi$
$230$		0			0
$231$	9215.26	+	5740.00i	0.172696	+	0.107569i
$232$		0			0
$233$			3372.35i			0.0621185i	0.999518	+	0.0310592i	$0.00988805\pi$
$233$			3372.35i			0.0621185i	−0.999518	+	0.0310592i	$0.990112\pi$
$234$		0			0
$235$	85977.4			1.55686
$236$		0			0
$237$	41667.7	+	1395.32i	0.741828	+	0.0248415i
$238$		0			0
$239$	64618.9	−	37307.7i	1.13126	−	0.653135i	0.187011	−	0.982358i	$-0.440120\pi$
$239$	64618.9	−	37307.7i	1.13126	−	0.653135i	0.944252	+	0.329223i	$0.106787\pi$
$240$		0			0
$241$	12127.1	−	21004.7i	0.208796	−	0.361645i	−0.742540	−	0.669802i	$-0.766379\pi$
$241$	12127.1	−	21004.7i	0.208796	−	0.361645i	0.951336	+	0.308157i	$0.0997122\pi$
$242$		0			0
$243$	37631.1	−	45504.8i	0.637285	−	0.770628i
$244$		0			0
$245$	−76115.8	−	43945.5i	−1.26807	−	0.732120i
$246$		0			0
$247$	74089.7	+	128327.i	1.21441	+	2.10341i
$248$		0			0
$249$	−1807.06	+	53963.1i	−0.0291456	+	0.870359i
$250$		0			0
$251$			25543.7i			0.405449i	0.979236	+	0.202724i	$0.0649795\pi$
$251$			25543.7i			0.405449i	−0.979236	+	0.202724i	$0.935020\pi$
$252$		0			0
$253$	66191.1			1.03409
$254$		0			0
$255$	2085.66	−	3348.41i	0.0320747	−	0.0514942i
$256$		0			0
$257$	18961.7	−	10947.6i	0.287086	−	0.165749i	−0.349541	−	0.936921i	$-0.613662\pi$
$257$	18961.7	−	10947.6i	0.287086	−	0.165749i	0.636627	+	0.771172i	$0.280329\pi$
$258$		0			0
$259$	−15491.6	+	26832.3i	−0.230939	+	0.399998i
$260$		0			0
$261$	21628.2	−	10625.6i	0.317496	−	0.155981i
$262$		0			0
$263$	−6539.22	−	3775.42i	−0.0945397	−	0.0545825i	0.451985	−	0.892026i	$-0.350716\pi$
$263$	−6539.22	−	3775.42i	−0.0945397	−	0.0545825i	−0.546524	+	0.837443i	$0.684049\pi$
$264$		0			0
$265$	51932.1	+	89949.0i	0.739510	+	1.28087i
$266$		0			0
$267$	−66973.3	+	35733.5i	−0.939462	+	0.501248i
$268$		0			0
$269$			106275.i			1.46868i	0.678780	+	0.734342i	$0.262509\pi$
$269$			106275.i			1.46868i	−0.678780	+	0.734342i	$0.737491\pi$
$270$		0			0
$271$	−82971.5			−1.12977			−0.564885	−	0.825170i	$-0.691080\pi$
$271$	−82971.5			−1.12977			−0.564885	+	0.825170i	$0.691080\pi$
$272$		0			0
$273$	−17406.9	−	32624.9i	−0.233559	−	0.437748i
$274$		0			0
$275$	70456.9	−	40678.3i	0.931661	−	0.537895i
$276$		0			0
$277$	32616.8	−	56494.0i	0.425091	−	0.736280i	−0.571338	−	0.820715i	$-0.693575\pi$
$277$	32616.8	−	56494.0i	0.425091	−	0.736280i	0.996429	+	0.0844353i	$0.0269086\pi$
$278$		0			0
$279$	−15766.8	−	1057.15i	−0.202552	−	0.0135809i
$280$		0			0
$281$	−82142.7	−	47425.1i	−1.04029	−	0.600614i	−0.120378	−	0.992728i	$-0.538410\pi$
$281$	−82142.7	−	47425.1i	−1.04029	−	0.600614i	−0.919917	+	0.392114i	$0.871744\pi$
$282$		0			0
$283$	52834.0	+	91511.3i	0.659692	+	1.14262i	0.980695	+	0.195542i	$0.0626465\pi$
$283$	52834.0	+	91511.3i	0.659692	+	1.14262i	−0.321004	+	0.947078i	$0.604020\pi$
$284$		0			0
$285$	163897.	+	102088.i	2.01781	+	1.25685i
$286$		0			0
$287$			23190.5i			0.281544i
$288$		0			0
$289$	83402.5			0.998581
$290$		0			0
$291$	54250.0	+	1816.66i	0.640639	+	0.0214530i
$292$		0			0
$293$	−61404.7	+	35452.0i	−0.715264	+	0.412958i	−0.813007	−	0.582254i	$-0.802171\pi$
$293$	−61404.7	+	35452.0i	−0.715264	+	0.412958i	0.0977432	+	0.995212i	$0.468838\pi$
$294$		0			0
$295$	31362.3	−	54321.0i	0.360382	−	0.624200i
$296$		0			0
$297$	−48305.9	−	34780.2i	−0.547630	−	0.394293i
$298$		0			0
$299$	−195243.	−	112724.i	−2.18391	−	1.26088i
$300$		0			0
$301$	680.869	+	1179.30i	0.00751503	+	0.0130164i
$302$		0			0
$303$	−1802.09	+	53814.9i	−0.0196287	+	0.586162i
$304$		0			0
$305$		−	216309.i		−	2.32528i
$306$		0			0
$307$	−27339.7			−0.290079			−0.145040	−	0.989426i	$-0.546331\pi$
$307$	−27339.7			−0.290079			−0.145040	+	0.989426i	$0.546331\pi$
$308$		0			0
$309$	7287.09	−	11699.0i	0.0763198	−	0.122527i
$310$		0			0
$311$	−88117.5	+	50874.6i	−0.911048	+	0.525994i	−0.880768	−	0.473548i	$-0.842973\pi$
$311$	−88117.5	+	50874.6i	−0.911048	+	0.525994i	−0.0302797	+	0.999541i	$0.509640\pi$
$312$		0			0
$313$	22810.8	−	39509.5i	0.232837	−	0.403286i	−0.725805	−	0.687901i	$-0.758532\pi$
$313$	22810.8	−	39509.5i	0.232837	−	0.403286i	0.958642	+	0.284615i	$0.0918658\pi$
$314$		0			0
$315$	−40024.9	−	26830.6i	−0.403375	−	0.270402i
$316$		0			0
$317$	20556.7	+	11868.4i	0.204567	+	0.118107i	0.598784	−	0.800911i	$-0.295651\pi$
$317$	20556.7	+	11868.4i	0.204567	+	0.118107i	−0.394217	+	0.919017i	$0.628984\pi$
$318$		0			0
$319$	−12145.6	−	21036.8i	−0.119354	−	0.206727i
$320$		0			0
$321$	−162778.	+	86849.7i	−1.57974	+	0.842866i
$322$		0			0
$323$		−	5799.91i		−	0.0555925i
$324$		0			0
$325$	−277102.			−2.62345
$326$		0			0
$327$	−39842.1	−	74673.9i	−0.372603	−	0.698350i
$328$		0			0
$329$	−27318.9	+	15772.6i	−0.252389	+	0.145717i
$330$		0			0
$331$	63701.2	−	110334.i	0.581422	−	1.00705i	−0.413889	−	0.910327i	$-0.635830\pi$
$331$	63701.2	−	110334.i	0.581422	−	1.00705i	0.995311	−	0.0967256i	$-0.0308369\pi$
$332$		0			0
$333$	94587.3	−	141102.i	0.852991	−	1.27246i
$334$		0			0
$335$	−31917.5	−	18427.6i	−0.284406	−	0.164202i
$336$		0			0
$337$	8353.80	+	14469.2i	0.0735571	+	0.127405i	0.900458	−	0.434943i	$-0.143232\pi$
$337$	8353.80	+	14469.2i	0.0735571	+	0.127405i	−0.826901	+	0.562348i	$0.809898\pi$
$338$		0			0
$339$	22922.3	+	14277.8i	0.199461	+	0.124240i
$340$		0			0
$341$			15929.4i			0.136990i
$342$		0			0
$343$	67719.0			0.575602
$344$		0			0
$345$	−293614.	−	9832.21i	−2.46682	−	0.0826063i
$346$		0			0
$347$	153069.	−	88374.3i	1.27124	−	0.733951i	0.296019	−	0.955182i	$-0.404341\pi$
$347$	153069.	−	88374.3i	1.27124	−	0.733951i	0.975221	+	0.221231i	$0.0710074\pi$
$348$		0			0
$349$	−49219.9	+	85251.3i	−0.404101	+	0.699923i	−0.994216	−	0.107396i	$-0.965749\pi$
$349$	−49219.9	+	85251.3i	−0.404101	+	0.699923i	0.590116	+	0.807319i	$0.299082\pi$
$350$		0			0
$351$	83256.8	+	184856.i	0.675780	+	1.50044i
$352$		0			0
$353$	108285.	+	62518.3i	0.868997	+	0.501716i	0.867015	−	0.498282i	$-0.166036\pi$
$353$	108285.	+	62518.3i	0.868997	+	0.501716i	0.00198242	+	0.999998i	$0.499369\pi$
$354$		0			0
$355$	−165413.	−	286504.i	−1.31254	−	2.27339i
$356$		0			0
$357$	−48.4406	+	1446.56i	−0.000380079	+	0.0113501i
$358$		0			0
$359$			130777.i			1.01471i	0.861737	+	0.507356i	$0.169377\pi$
$359$			130777.i			1.01471i	−0.861737	+	0.507356i	$0.830623\pi$
$360$		0			0
$361$	153571.			1.17840
$362$		0			0
$363$	37943.0	−	60915.4i	0.287951	−	0.462289i
$364$		0			0
$365$	119911.	−	69230.7i	0.900064	−	0.519652i
$366$		0			0
$367$	−64119.3	+	111058.i	−0.476054	+	0.824550i	−0.999624	−	0.0274329i	$-0.991267\pi$
$367$	−64119.3	+	111058.i	−0.476054	+	0.824550i	0.523569	+	0.851983i	$0.324600\pi$
$368$		0			0
$369$	8505.93	−	126861.i	0.0624696	−	0.931702i
$370$		0			0
$371$	−33002.3	−	19053.9i	−0.239771	−	0.138432i
$372$		0			0
$373$	−31604.2	−	54740.0i	−0.227157	−	0.393448i	0.729807	−	0.683653i	$-0.239610\pi$
$373$	−31604.2	−	54740.0i	−0.227157	−	0.393448i	−0.956964	+	0.290205i	$0.906276\pi$
$374$		0			0
$375$	−118745.	+	63356.1i	−0.844408	+	0.450532i
$376$		0			0
$377$			82736.1i			0.582120i
$378$		0			0
$379$	101202.			0.704547			0.352273	−	0.935897i	$-0.385409\pi$
$379$	101202.			0.704547			0.352273	+	0.935897i	$0.385409\pi$
$380$		0			0
$381$	−41592.6	−	77954.8i	−0.286527	−	0.537023i
$382$		0			0
$383$	16878.5	−	9744.83i	0.115063	−	0.0664319i	−0.441364	−	0.897328i	$-0.645505\pi$
$383$	16878.5	−	9744.83i	0.115063	−	0.0664319i	0.556427	+	0.830896i	$0.312172\pi$
$384$		0			0
$385$	−24286.8	+	42065.9i	−0.163851	+	0.283798i
$386$		0			0
$387$	−3292.08	−	6700.98i	−0.0219811	−	0.0447421i
$388$		0			0
$389$	49519.1	+	28589.9i	0.327245	+	0.188935i	0.654617	−	0.755960i	$-0.272830\pi$
$389$	49519.1	+	28589.9i	0.327245	+	0.188935i	−0.327372	+	0.944895i	$0.606163\pi$
$390$		0			0
$391$	4412.14	+	7642.04i	0.0288599	+	0.0499869i
$392$		0			0
$393$	4879.76	+	3039.50i	0.0315946	+	0.0196796i
$394$		0			0
$395$			186528.i			1.19550i
$396$		0			0
$397$	−75878.7			−0.481436			−0.240718	−	0.970595i	$-0.577383\pi$
$397$	−75878.7			−0.481436			−0.240718	+	0.970595i	$0.577383\pi$
$398$		0			0
$399$	−70805.4	−	2371.05i	−0.444755	−	0.0148935i
$400$		0			0
$401$	210130.	−	121319.i	1.30677	−	0.754464i	0.325215	−	0.945640i	$-0.394563\pi$
$401$	210130.	−	121319.i	1.30677	−	0.754464i	0.981556	+	0.191176i	$0.0612300\pi$
$402$		0			0
$403$	27127.9	−	46986.8i	0.167034	−	0.289312i
$404$		0			0
$405$	209111.	+	161455.i	1.27488	+	0.984332i
$406$		0			0
$407$	−148297.	−	85619.2i	−0.895248	−	0.516871i
$408$		0			0
$409$	−60915.8	−	105509.i	−0.364153	−	0.630731i	0.624487	−	0.781035i	$-0.285308\pi$
$409$	−60915.8	−	105509.i	−0.364153	−	0.630731i	−0.988640	+	0.150304i	$0.951975\pi$
$410$		0			0
$411$	9640.02	−	287874.i	0.0570682	−	1.70420i
$412$		0			0
$413$			23013.6i			0.134923i
$414$		0			0
$415$	−241569.			−1.40264
$416$		0			0
$417$	26571.8	−	42659.6i	0.152809	−	0.245326i
$418$		0			0
$419$	107882.	−	62285.6i	0.614498	−	0.354780i	−0.160226	−	0.987080i	$-0.551222\pi$
$419$	107882.	−	62285.6i	0.614498	−	0.354780i	0.774724	+	0.632300i	$0.217889\pi$
$420$		0			0
$421$	−12647.9	+	21906.8i	−0.0713600	+	0.123599i	−0.899498	−	0.436926i	$-0.856067\pi$
$421$	−12647.9	+	21906.8i	−0.0713600	+	0.123599i	0.828138	+	0.560525i	$0.189401\pi$
$422$		0			0
$423$	155231.	−	76262.2i	0.867555	−	0.426215i
$424$		0			0
$425$	9392.97	+	5423.03i	0.0520026	+	0.0300237i
$426$		0			0
$427$	39682.0	+	68731.2i	0.217639	+	0.376962i
$428$		0			0
$429$	180311.	−	96204.8i	0.979735	−	0.522735i
$430$		0			0
$431$			153800.i			0.827944i	0.910290	+	0.413972i	$0.135859\pi$
$431$			153800.i			0.827944i	−0.910290	+	0.413972i	$0.864141\pi$
$432$		0			0
$433$	112975.			0.602569			0.301285	−	0.953534i	$-0.402585\pi$
$433$	112975.			0.602569			0.301285	+	0.953534i	$0.402585\pi$
$434$		0			0
$435$	50751.2	+	95120.2i	0.268205	+	0.502683i
$436$		0			0
$437$	−374060.	+	215963.i	−1.95875	+	1.13088i
$438$		0			0
$439$	−89083.3	+	154297.i	−0.462239	+	0.800622i	−0.999072	−	0.0430665i	$-0.986287\pi$
$439$	−89083.3	+	154297.i	−0.462239	+	0.800622i	0.536833	+	0.843689i	$0.319621\pi$
$440$		0			0
$441$	−176406.	−	11827.8i	−0.907058	−	0.0608173i
$442$		0			0
$443$	258569.	+	149285.i	1.31756	+	0.760691i	0.983335	−	0.181804i	$-0.0581935\pi$
$443$	258569.	+	149285.i	1.31756	+	0.760691i	0.334221	+	0.942495i	$0.391527\pi$
$444$		0			0
$445$	−169812.	−	294123.i	−0.857529	−	1.48528i
$446$		0			0
$447$	−62794.9	−	39113.7i	−0.314275	−	0.195755i
$448$		0			0
$449$			201956.i			1.00176i	0.865516	+	0.500881i	$0.166991\pi$
$449$			201956.i			1.00176i	−0.865516	+	0.500881i	$0.833009\pi$
$450$		0			0
$451$	−128169.			−0.630131
$452$		0			0
$453$	184145.	+	6166.43i	0.897351	+	0.0300495i
$454$		0			0
$455$	143277.	−	82721.1i	0.692076	−	0.399570i
$456$		0			0
$457$	−147659.	+	255752.i	−0.707011	+	1.22458i	0.258949	+	0.965891i	$0.416624\pi$
$457$	−147659.	+	255752.i	−0.707011	+	1.22458i	−0.965961	+	0.258689i	$0.916710\pi$
$458$		0			0
$459$	795.565	−	7895.48i	0.00377616	−	0.0374760i
$460$		0			0
$461$	−171120.	−	98796.4i	−0.805193	−	0.464878i	0.0400909	−	0.999196i	$-0.487235\pi$
$461$	−171120.	−	98796.4i	−0.805193	−	0.464878i	−0.845284	+	0.534318i	$0.820569\pi$
$462$		0			0
$463$	43231.3	+	74878.8i	0.201668	+	0.349299i	0.949066	−	0.315078i	$-0.102031\pi$
$463$	43231.3	+	74878.8i	0.201668	+	0.349299i	−0.747398	+	0.664376i	$0.768697\pi$
$464$		0			0
$465$	2366.20	−	70660.4i	0.0109432	−	0.326791i
$466$		0			0
$467$		−	249159.i		−	1.14247i	−0.820788	−	0.571233i	$-0.806465\pi$
$467$		−	249159.i		−	1.14247i	0.820788	−	0.571233i	$-0.193535\pi$
$468$		0			0
$469$	13522.2			0.0614753
$470$		0			0
$471$	122736.	−	197046.i	0.553261	−	0.888231i
$472$		0			0
$473$	−6517.76	+	3763.03i	−0.0291324	+	0.0168196i
$474$		0			0
$475$	−265445.	+	459763.i	−1.17649	+	2.03773i
$476$		0			0
$477$	173547.	+	116337.i	0.762749	+	0.511308i
$478$		0			0
$479$	363916.	+	210107.i	1.58610	+	0.915734i	0.993941	+	0.109911i	$0.0350566\pi$
$479$	363916.	+	210107.i	1.58610	+	0.915734i	0.592157	+	0.805823i	$0.298277\pi$
$480$		0			0
$481$	291620.	+	505101.i	1.26046	+	2.18317i
$482$		0			0
$483$	95098.0	−	50739.3i	0.407640	−	0.217496i
$484$		0			0
$485$			242853.i			1.03243i
$486$		0			0
$487$	394498.			1.66336			0.831680	−	0.555255i	$-0.187379\pi$
$487$	394498.			1.66336			0.831680	+	0.555255i	$0.187379\pi$
$488$		0			0
$489$	69854.7	+	130925.i	0.292131	+	0.547525i
$490$		0			0
$491$	−291929.	+	168545.i	−1.21092	+	0.699123i	−0.962959	−	0.269647i	$-0.913093\pi$
$491$	−291929.	+	168545.i	−1.21092	+	0.699123i	−0.247958	+	0.968771i	$0.579760\pi$
$492$		0			0
$493$	1619.19	−	2804.52i	0.00666199	−	0.0115389i
$494$		0			0
$495$	148288.	−	221210.i	0.605194	−	0.902805i
$496$		0			0
$497$	105118.	+	60690.1i	0.425565	+	0.245700i
$498$		0			0
$499$	227950.	+	394821.i	0.915458	+	1.58562i	0.806230	+	0.591602i	$0.201504\pi$
$499$	227950.	+	394821.i	0.915458	+	1.58562i	0.109227	+	0.994017i	$0.465162\pi$
$500$		0			0
$501$	−302236.	−	188257.i	−1.20412	−	0.750024i
$502$		0			0
$503$			33893.3i			0.133961i	0.997754	+	0.0669804i	$0.0213365\pi$
$503$			33893.3i			0.133961i	−0.997754	+	0.0669804i	$0.978663\pi$
$504$		0			0
$505$	−240905.			−0.944635
$506$		0			0
$507$	−438796.	−	14693.9i	−1.70705	−	0.0571638i
$508$		0			0
$509$	186058.	−	107421.i	0.718147	−	0.414622i	−0.0959233	−	0.995389i	$-0.530580\pi$
$509$	186058.	−	107421.i	0.718147	−	0.414622i	0.814070	+	0.580766i	$0.197247\pi$
$510$		0			0
$511$	−25400.7	+	43995.4i	−0.0972758	+	0.168487i
$512$		0			0
$513$	386465.	+	38941.0i	1.46851	+	0.147970i
$514$		0			0
$515$	53403.9	+	30832.7i	0.201353	+	0.116251i
$516$		0			0
$517$	−87171.9	−	150986.i	−0.326134	−	0.564880i
$518$		0			0
$519$	−1462.27	+	43667.1i	−0.00542868	+	0.162114i
$520$		0			0
$521$		−	256109.i		−	0.943516i	−0.881728	−	0.471758i	$-0.843620\pi$
$521$		−	256109.i		−	0.943516i	0.881728	−	0.471758i	$-0.156380\pi$
$522$		0			0
$523$	−372105.			−1.36038			−0.680192	−	0.733034i	$-0.738104\pi$
$523$	−372105.			−1.36038			−0.680192	+	0.733034i	$0.738104\pi$
$524$		0			0
$525$	70044.5	−	112453.i	0.254130	−	0.407992i
$526$		0			0
$527$	−1839.12	+	1061.81i	−0.00662198	+	0.00382320i
$528$		0			0
$529$	188657.	−	326764.i	0.674159	−	1.16768i
$530$		0			0
$531$	8441.06	−	125894.i	0.0299370	−	0.446494i
$532$		0			0
$533$	378060.	+	218273.i	1.33078	+	0.768327i
$534$		0			0
$535$	−412726.	−	714863.i	−1.44196	−	2.49755i
$536$		0			0
$537$	37828.5	−	20183.3i	0.131181	−	0.0699913i
$538$		0			0
$539$			178224.i			0.613464i
$540$		0			0
$541$	38292.3			0.130833			0.0654164	−	0.997858i	$-0.479162\pi$
$541$	38292.3			0.130833			0.0654164	+	0.997858i	$0.479162\pi$
$542$		0			0
$543$	15850.9	+	29708.5i	0.0537594	+	0.100758i
$544$		0			0
$545$	327941.	−	189337.i	1.10409	−	0.637445i
$546$		0			0
$547$	251103.	−	434923.i	0.839223	−	1.45358i	−0.0513228	−	0.998682i	$-0.516344\pi$
$547$	251103.	−	434923.i	0.839223	−	1.45358i	0.890545	−	0.454894i	$-0.150323\pi$
$548$		0			0
$549$	−191867.	−	390542.i	−0.636584	−	1.29576i
$550$		0			0
$551$	137275.	+	79255.5i	0.452155	+	0.261052i
$552$		0			0
$553$	−34218.6	−	59268.3i	−0.111895	−	0.193808i
$554$		0			0
$555$	645105.	+	401823.i	2.09433	+	1.30451i
$556$		0			0
$557$			601940.i			1.94018i	0.242737	+	0.970092i	$0.421955\pi$
$557$			601940.i			1.94018i	−0.242737	+	0.970092i	$0.578045\pi$
$558$		0			0
$559$	25633.9			0.0820333
$560$		0			0
$561$	−7994.83	−	267.722i	−0.0254029	−	0.000850664i
$562$		0			0
$563$	−135970.	+	78502.5i	−0.428970	+	0.247666i	−0.698908	−	0.715212i	$-0.746330\pi$
$563$	−135970.	+	78502.5i	−0.428970	+	0.247666i	0.269938	+	0.962878i	$0.412997\pi$
$564$		0			0
$565$	−60411.5	+	104636.i	−0.189244	+	0.327781i
$566$		0			0
$567$	−96063.1	−	12940.0i	−0.298807	−	0.0402503i
$568$		0			0
$569$	−422713.	−	244054.i	−1.30563	−	0.753808i	−0.324270	−	0.945965i	$-0.605119\pi$
$569$	−422713.	−	244054.i	−1.30563	−	0.753808i	−0.981364	+	0.192156i	$0.938452\pi$
$570$		0			0
$571$	−85604.0	−	148270.i	−0.262556	−	0.454760i	0.704365	−	0.709838i	$-0.251232\pi$
$571$	−85604.0	−	148270.i	−0.262556	−	0.454760i	−0.966920	+	0.255078i	$0.917899\pi$
$572$		0			0
$573$	3131.56	−	93516.0i	0.00953787	−	0.284824i
$574$		0			0
$575$		−	807721.i		−	2.44301i
$576$		0			0
$577$	−120517.			−0.361990			−0.180995	−	0.983484i	$-0.557932\pi$
$577$	−120517.			−0.361990			−0.180995	+	0.983484i	$0.557932\pi$
$578$		0			0
$579$	−205618.	+	330109.i	−0.613345	+	0.984692i
$580$		0			0
$581$	76757.3	−	44315.9i	0.227388	−	0.131283i
$582$		0			0
$583$	105307.	−	182397.i	0.309828	−	0.536638i
$584$		0			0
$585$	−814125.	+	399966.i	−2.37892	+	1.16872i
$586$		0			0
$587$	−40161.9	−	23187.5i	−0.116557	−	0.0672942i	0.440588	−	0.897709i	$-0.354770\pi$
$587$	−40161.9	−	23187.5i	−0.116557	−	0.0672942i	−0.557145	+	0.830415i	$0.688103\pi$
$588$		0			0
$589$	−51973.3	−	90020.3i	−0.149813	−	0.259484i
$590$		0			0
$591$	−396227.	+	211406.i	−1.13441	+	0.605261i
$592$		0			0
$593$		−	511267.i		−	1.45391i	−0.686683	−	0.726957i	$-0.740934\pi$
$593$		−	511267.i		−	1.45391i	0.686683	−	0.726957i	$-0.259066\pi$
$594$		0			0
$595$	−6475.59			−0.0182913
$596$		0			0
$597$	32256.6	+	60456.9i	0.0905045	+	0.169628i
$598$		0			0
$599$	−558562.	+	322486.i	−1.55675	+	0.898787i	−0.559180	+	0.829046i	$0.688884\pi$
$599$	−558562.	+	322486.i	−1.55675	+	0.898787i	−0.997565	+	0.0697410i	$0.977783\pi$
$600$		0			0
$601$	−296605.	+	513735.i	−0.821163	+	1.42230i	0.0836541	+	0.996495i	$0.473341\pi$
$601$	−296605.	+	513735.i	−0.821163	+	1.42230i	−0.904817	+	0.425801i	$0.859992\pi$
$602$		0			0
$603$	−73971.8	−	4959.73i	−0.203438	−	0.0136403i
$604$		0			0
$605$	278067.	+	160542.i	0.759695	+	0.438610i
$606$		0			0
$607$	220510.	+	381935.i	0.598482	+	1.03660i	0.993045	+	0.117733i	$0.0375626\pi$
$607$	220510.	+	381935.i	0.598482	+	1.03660i	−0.394563	+	0.918869i	$0.629104\pi$
$608$		0			0
$609$	−33575.7	−	20913.6i	−0.0905297	−	0.0563891i
$610$		0			0
$611$			593817.i			1.59063i
$612$		0			0
$613$	−397447.			−1.05769			−0.528845	−	0.848718i	$-0.677375\pi$
$613$	−397447.			−1.05769			−0.528845	+	0.848718i	$0.677375\pi$
$614$		0			0
$615$	568540.	+	19038.6i	1.50318	+	0.0503368i
$616$		0			0
$617$	−1401.15	+	808.953i	−0.00368056	+	0.00212497i	−0.501839	−	0.864961i	$-0.667343\pi$
$617$	−1401.15	+	808.953i	−0.00368056	+	0.00212497i	0.498159	+	0.867086i	$0.334010\pi$
$618$		0			0
$619$	274485.	−	475422.i	0.716370	−	1.24079i	−0.246059	−	0.969255i	$-0.579136\pi$
$619$	274485.	−	475422.i	0.716370	−	1.24079i	0.962429	−	0.271535i	$-0.0875311\pi$
$620$		0			0
$621$	−538835.	+	242684.i	−1.39725	+	0.629301i
$622$		0			0
$623$	107914.	+	62304.1i	0.278036	+	0.160524i
$624$		0			0
$625$	10290.7	+	17824.0i	0.0263442	+	0.0456294i
$626$		0			0
$627$	13104.3	−	391328.i	0.0333335	−	0.995418i
$628$		0			0
$629$		−	22828.7i		−	0.0577005i
$630$		0			0
$631$	−378413.			−0.950403			−0.475202	−	0.879877i	$-0.657625\pi$
$631$	−378413.			−0.950403			−0.475202	+	0.879877i	$0.657625\pi$
$632$		0			0
$633$	267397.	−	429291.i	0.667343	−	1.07138i
$634$		0			0
$635$	342350.	−	197656.i	0.849030	−	0.490188i
$636$		0			0
$637$	303517.	−	525707.i	0.748004	−	1.29558i
$638$		0			0
$639$	−552780.	−	370555.i	−1.35379	−	0.907510i
$640$		0			0
$641$	−62090.7	−	35848.1i	−0.151116	−	0.0872469i	0.422535	−	0.906346i	$-0.361140\pi$
$641$	−62090.7	−	35848.1i	−0.151116	−	0.0872469i	−0.573651	+	0.819100i	$0.694474\pi$
$642$		0			0
$643$	83582.4	+	144769.i	0.202159	+	0.350149i	0.949224	−	0.314602i	$-0.101871\pi$
$643$	83582.4	+	144769.i	0.202159	+	0.350149i	−0.747065	+	0.664751i	$0.768538\pi$
$644$		0			0
$645$	29470.8	−	15724.1i	0.0708390	−	0.0377960i
$646$		0			0
$647$		−	678022.i		−	1.61970i	−0.586635	−	0.809852i	$-0.699548\pi$
$647$		−	678022.i		−	1.61970i	0.586635	−	0.809852i	$-0.300452\pi$
$648$		0			0
$649$	−127192.			−0.301974
$650$		0			0
$651$	12210.8	+	22886.1i	0.0288126	+	0.0540019i
$652$		0			0
$653$	−256473.	+	148075.i	−0.601472	+	0.347260i	−0.769620	−	0.638502i	$-0.779554\pi$
$653$	−256473.	+	148075.i	−0.601472	+	0.347260i	0.168149	+	0.985762i	$0.446221\pi$
$654$		0			0
$655$	−12860.6	+	22275.2i	−0.0299763	+	0.0519204i
$656$		0			0
$657$	155089.	−	231356.i	0.359295	−	0.535982i
$658$		0			0
$659$	−684065.	−	394945.i	−1.57517	−	0.909423i	−0.995520	−	0.0945561i	$-0.969857\pi$
$659$	−684065.	−	394945.i	−1.57517	−	0.909423i	−0.579648	−	0.814867i	$-0.696810\pi$
$660$		0			0
$661$	212744.	+	368484.i	0.486917	+	0.843365i	0.999887	−	0.0150418i	$-0.00478812\pi$
$661$	212744.	+	368484.i	0.486917	+	0.843365i	−0.512970	+	0.858407i	$0.671455\pi$
$662$		0			0
$663$	23126.4	+	14404.9i	0.0526115	+	0.0327706i
$664$		0			0
$665$		−	316964.i		−	0.716749i
$666$		0			0
$667$	−241167.			−0.542083
$668$		0			0
$669$	341109.	+	11422.7i	0.762151	+	0.0255221i
$670$		0			0
$671$	−379864.	+	219314.i	−0.843690	+	0.487104i
$672$		0			0
$673$	181403.	−	314199.i	0.400511	−	0.693705i	−0.593277	−	0.804998i	$-0.702166\pi$
$673$	181403.	−	314199.i	0.400511	−	0.693705i	0.993788	+	0.111294i	$0.0354994\pi$
$674$		0			0
$675$	−424418.	+	589471.i	−0.931507	+	1.29376i
$676$		0			0
$677$	−747854.	−	431774.i	−1.63170	−	0.942061i	−0.983570	−	0.180528i	$-0.942219\pi$
$677$	−747854.	−	431774.i	−1.63170	−	0.942061i	−0.648127	−	0.761532i	$-0.724447\pi$
$678$		0			0
$679$	−44551.4	−	77165.3i	−0.0966322	−	0.167372i
$680$		0			0
$681$	2942.91	−	87882.5i	0.00634575	−	0.189500i
$682$		0			0
$683$		−	323967.i		−	0.694479i	−0.937776	−	0.347239i	$-0.887119\pi$
$683$		−	323967.i		−	0.694479i	0.937776	−	0.347239i	$-0.112881\pi$
$684$		0			0
$685$	1.28869e6			2.74641
$686$		0			0
$687$	180484.	−	289757.i	0.382406	−	0.613933i
$688$		0			0
$689$	−621248.	+	358678.i	−1.30866	+	0.755554i
$690$		0			0
$691$	−328629.	+	569202.i	−0.688255	+	1.19209i	0.284147	+	0.958781i	$0.408290\pi$
$691$	−328629.	+	569202.i	−0.688255	+	1.19209i	−0.972402	+	0.233312i	$0.925044\pi$
$692$		0			0
$693$	−6536.71	+	97491.7i	−0.0136111	+	0.203002i
$694$		0			0
$695$	194733.	+	112429.i	0.403153	+	0.232760i
$696$		0			0
$697$	−8543.45	−	14797.7i	−0.0175860	−	0.0304599i
$698$		0			0
$699$	−26778.0	+	14287.4i	−0.0548055	+	0.0292414i
$700$		0			0
$701$		−	695995.i		−	1.41635i	−0.706038	−	0.708174i	$-0.749519\pi$
$701$		−	695995.i		−	1.41635i	0.706038	−	0.708174i	$-0.250481\pi$
$702$		0			0
$703$	1.11741e6			2.26101
$704$		0			0
$705$	364254.	+	682701.i	0.732868	+	1.37357i
$706$		0			0
$707$	76546.5	−	44194.1i	0.153139	−	0.0884150i
$708$		0			0
$709$	215242.	−	372810.i	0.428188	−	0.741643i	−0.568525	−	0.822666i	$-0.692486\pi$
$709$	215242.	−	372810.i	0.428188	−	0.741643i	0.996712	+	0.0810236i	$0.0258189\pi$
$710$		0			0
$711$	165451.	+	336773.i	0.327288	+	0.666189i
$712$		0			0
$713$	136961.	+	79074.7i	0.269413	+	0.155546i
$714$		0			0
$715$	457183.	+	791864.i	0.894289	+	1.54895i
$716$		0			0
$717$	570007.	+	355046.i	1.10877	+	0.690631i
$718$		0			0
$719$		−	435311.i		−	0.842059i	−0.907047	−	0.421029i	$-0.861669\pi$
$719$		−	435311.i		−	0.842059i	0.907047	−	0.421029i	$-0.138331\pi$
$720$		0			0
$721$	−22625.1			−0.0435231
$722$		0			0
$723$	218165.	+	7305.67i	0.417358	+	0.0139760i
$724$		0			0
$725$	−256709.	+	148211.i	−0.488388	+	0.281971i
$726$		0			0
$727$	−3053.98	+	5289.64i	−0.00577826	+	0.0100082i	−0.868900	−	0.494988i	$-0.835173\pi$
$727$	−3053.98	+	5289.64i	−0.00577826	+	0.0100082i	0.863122	+	0.504996i	$0.168506\pi$
$728$		0			0
$729$	520758.	+	106022.i	0.979898	+	0.199499i
$730$		0			0
$731$	−868.916	−	501.669i	−0.00162608	−	0.000938820i
$732$		0			0
$733$	184878.	+	320218.i	0.344094	+	0.595989i	0.985189	−	0.171473i	$-0.0548526\pi$
$733$	184878.	+	320218.i	0.344094	+	0.595989i	−0.641094	+	0.767462i	$0.721519\pi$
$734$		0			0
$735$	26473.9	−	790576.i	0.0490054	−	1.46342i
$736$		0			0
$737$			74734.4i			0.137590i
$738$		0			0
$739$	381087.			0.697807			0.348904	−	0.937159i	$-0.386554\pi$
$739$	381087.			0.697807			0.348904	+	0.937159i	$0.386554\pi$
$740$		0			0
$741$	−705088.	+	1.13198e6i	−1.28412	+	2.06159i
$742$		0			0
$743$	370613.	−	213974.i	0.671341	−	0.387599i	−0.125243	−	0.992126i	$-0.539971\pi$
$743$	370613.	−	213974.i	0.671341	−	0.387599i	0.796585	+	0.604527i	$0.206638\pi$
$744$		0			0
$745$	165496.	−	286647.i	0.298177	−	0.516457i
$746$		0			0
$747$	−436149.	+	214273.i	−0.781616	+	0.383995i
$748$		0			0
$749$	262283.	+	151429.i	0.467527	+	0.269927i
$750$		0			0
$751$	−211790.	−	366831.i	−0.375514	−	0.650408i	0.614890	−	0.788613i	$-0.289200\pi$
$751$	−211790.	−	366831.i	−0.375514	−	0.650408i	−0.990404	+	0.138204i	$0.955867\pi$
$752$		0			0
$753$	−202829.	+	108219.i	−0.357717	+	0.190859i
$754$		0			0
$755$			824333.i			1.44614i
$756$		0			0
$757$	−910525.			−1.58891			−0.794457	−	0.607321i	$-0.792244\pi$
$757$	−910525.			−1.58891			−0.794457	+	0.607321i	$0.792244\pi$
$758$		0			0
$759$	280426.	+	525588.i	0.486783	+	0.912351i
$760$		0			0
$761$	−612058.	+	353372.i	−1.05687	+	0.610187i	−0.924566	−	0.381022i	$-0.875572\pi$
$761$	−612058.	+	353372.i	−1.05687	+	0.610187i	−0.132309	+	0.991209i	$0.542239\pi$
$762$		0			0
$763$	−69467.8	+	120322.i	−0.119326	+	0.206678i
$764$		0			0
$765$	35424.1	+	2375.15i	0.0605308	+	0.00405852i
$766$		0			0
$767$	375177.	+	216609.i	0.637743	+	0.368201i
$768$		0			0
$769$	−247932.	−	429430.i	−0.419256	−	0.726173i	0.576609	−	0.817021i	$-0.304376\pi$
$769$	−247932.	−	429430.i	−0.419256	−	0.726173i	−0.995865	+	0.0908474i	$0.971042\pi$
$770$		0			0
$771$	167263.	+	104184.i	0.281378	+	0.175265i
$772$		0			0
$773$		−	834415.i		−	1.39644i	−0.715882	−	0.698221i	$-0.753975\pi$
$773$		−	834415.i		−	1.39644i	0.715882	−	0.698221i	$-0.246025\pi$
$774$		0			0
$775$	194384.			0.323637
$776$		0			0
$777$	−278693.	−	9332.57i	−0.461620	−	0.0154582i
$778$		0			0
$779$	724312.	−	418182.i	1.19358	−	0.689112i
$780$		0			0
$781$	−335422.	+	580968.i	−0.549908	+	0.952468i
$782$		0			0
$783$	176002.	+	126721.i	0.287074	+	0.206693i
$784$		0			0
$785$	899478.	+	519314.i	1.45966	+	0.842734i
$786$		0			0
$787$	64818.1	+	112268.i	0.104652	+	0.181262i	0.913596	−	0.406623i	$-0.133294\pi$
$787$	64818.1	+	112268.i	0.104652	+	0.181262i	−0.808944	+	0.587886i	$0.799961\pi$
$788$		0			0
$789$	2274.41	−	67919.5i	0.00365355	−	0.109104i
$790$		0			0
$791$		−	44330.0i		−	0.0708508i
$792$		0			0
$793$	1.49398e6			2.37573
$794$		0			0
$795$	−494221.	+	793445.i	−0.781964	+	1.25540i
$796$		0			0
$797$	−146748.	+	84725.1i	−0.231024	+	0.133382i	−0.611044	−	0.791597i	$-0.709250\pi$
$797$	−146748.	+	84725.1i	−0.231024	+	0.133382i	0.380021	+	0.924978i	$0.375917\pi$
$798$		0			0
$799$	11621.3	−	20128.7i	0.0182038	−	0.0315299i
$800$		0			0
$801$	−567481.	−	380410.i	−0.884477	−	0.592908i
$802$		0			0
$803$	−243154.	−	140385.i	−0.377094	−	0.217716i
$804$		0			0
$805$	241123.	+	417637.i	0.372089	+	0.644477i
$806$		0			0
$807$	−843877.	+	450249.i	−1.29578	+	0.691362i
$808$		0			0
$809$			622158.i			0.950613i	0.879820	+	0.475307i	$0.157663\pi$
$809$			622158.i			0.950613i	−0.879820	+	0.475307i	$0.842337\pi$
$810$		0			0
$811$	−543177.			−0.825846			−0.412923	−	0.910766i	$-0.635492\pi$
$811$	−543177.			−0.825846			−0.412923	+	0.910766i	$0.635492\pi$
$812$		0			0
$813$	−351519.	−	658832.i	−0.531823	−	0.996767i
$814$		0			0
$815$	−574976.	+	331962.i	−0.865634	+	0.499774i
$816$		0			0
$817$	24555.5	−	42531.3i	0.0367878	−	0.0637184i
$818$		0			0
$819$	185310.	−	276439.i	0.276269	−	0.412127i
$820$		0			0
$821$	213399.	+	123206.i	0.316597	+	0.182787i	0.649875	−	0.760041i	$-0.274821\pi$
$821$	213399.	+	123206.i	0.316597	+	0.182787i	−0.333278	+	0.942829i	$0.608155\pi$
$822$		0			0
$823$	8586.13	+	14871.6i	0.0126765	+	0.0219563i	0.872294	−	0.488982i	$-0.162632\pi$
$823$	8586.13	+	14871.6i	0.0126765	+	0.0219563i	−0.859618	+	0.510938i	$0.829298\pi$
$824$		0			0
$825$	621504.	+	387122.i	0.913137	+	0.568775i
$826$		0			0
$827$		−	471086.i		−	0.688794i	−0.938824	−	0.344397i	$-0.888083\pi$
$827$		−	471086.i		−	0.688794i	0.938824	−	0.344397i	$-0.111917\pi$
$828$		0			0
$829$	197808.			0.287829			0.143915	−	0.989590i	$-0.454031\pi$
$829$	197808.			0.287829			0.143915	+	0.989590i	$0.454031\pi$
$830$		0			0
$831$	586774.	+	19649.2i	0.849706	+	0.0284540i
$832$		0			0
$833$	−20576.7	+	11880.0i	−0.0296542	+	0.0171209i
$834$		0			0
$835$	796542.	−	1.37965e6i	1.14245	−	1.97877i
$836$		0			0
$837$	−58403.9	−	129675.i	−0.0833663	−	0.185099i
$838$		0			0
$839$	−216362.	−	124917.i	−0.307367	−	0.177458i	0.338381	−	0.941009i	$-0.390121\pi$
$839$	−216362.	−	124917.i	−0.307367	−	0.177458i	−0.645748	+	0.763551i	$0.723454\pi$
$840$		0			0
$841$	−309388.	−	535876.i	−0.437433	−	0.757656i
$842$		0			0
$843$	28570.1	−	853173.i	0.0402029	−	1.20056i
$844$		0			0
$845$		−	1.96429e6i		−	2.75102i
$846$		0			0
$847$	−117806.			−0.164210
$848$		0			0
$849$	−502804.	+	807226.i	−0.697563	+	1.11990i
$850$		0			0
$851$	−1.47232e6	+	850042.i	−2.03302	+	1.17376i
$852$		0			0
$853$	−96671.0	+	167439.i	−0.132861	+	0.230122i	−0.924778	−	0.380506i	$-0.875750\pi$
$853$	−96671.0	+	167439.i	−0.132861	+	0.230122i	0.791917	+	0.610629i	$0.209083\pi$
$854$		0			0
$855$	−116258.	+	1.73393e6i	−0.159034	+	2.37191i
$856$		0			0
$857$	860714.	+	496934.i	1.17192	+	0.676607i	0.954131	−	0.299389i	$-0.0967829\pi$
$857$	860714.	+	496934.i	1.17192	+	0.676607i	0.217787	+	0.975996i	$0.430116\pi$
$858$		0			0
$859$	−508451.	−	880664.i	−0.689070	−	1.19350i	−0.972139	−	0.234404i	$-0.924686\pi$
$859$	−508451.	−	880664.i	−0.689070	−	1.19350i	0.283070	−	0.959099i	$-0.408647\pi$
$860$		0			0
$861$	−184143.	+	98249.3i	−0.248399	+	0.132533i
$862$		0			0
$863$			17982.7i			0.0241453i	0.999927	+	0.0120727i	$0.00384294\pi$
$863$			17982.7i			0.0241453i	−0.999927	+	0.0120727i	$0.996157\pi$
$864$		0			0
$865$	−195478.			−0.261256
$866$		0			0
$867$	353345.	+	662255.i	0.470068	+	0.881023i
$868$		0			0
$869$	327564.	−	189119.i	0.433768	−	0.250436i
$870$		0			0
$871$	127273.	−	220444.i	0.167765	−	0.290577i
$872$		0			0
$873$	215411.	+	438467.i	0.282644	+	0.575318i
$874$		0			0
$875$	191333.	+	110466.i	0.249905	+	0.144282i
$876$		0			0
$877$	−267680.	−	463636.i	−0.348030	−	0.602806i	0.637869	−	0.770145i	$-0.279816\pi$
$877$	−267680.	−	463636.i	−0.348030	−	0.602806i	−0.985899	+	0.167339i	$0.946483\pi$
$878$		0			0
$879$	−541654.	−	337385.i	−0.701042	−	0.436665i
$880$		0			0
$881$			348052.i			0.448427i	0.974540	+	0.224214i	$0.0719813\pi$
$881$			348052.i			0.448427i	−0.974540	+	0.224214i	$0.928019\pi$
$882$		0			0
$883$	1.28216e6			1.64445			0.822227	−	0.569160i	$-0.192732\pi$
$883$	1.28216e6			1.64445			0.822227	+	0.569160i	$0.192732\pi$
$884$		0			0
$885$	564204.	+	18893.4i	0.720361	+	0.0241226i
$886$		0			0
$887$	−538578.	+	310948.i	−0.684544	+	0.395222i	−0.801565	−	0.597908i	$-0.795999\pi$
$887$	−538578.	+	310948.i	−0.684544	+	0.395222i	0.117021	+	0.993129i	$0.462666\pi$
$888$		0			0
$889$	−72520.0	+	125608.i	−0.0917602	+	0.158933i
$890$		0			0
$891$	71517.0	−	530922.i	0.0900853	−	0.668767i
$892$		0			0
$893$	985254.	+	568837.i	1.23551	+	0.713320i
$894$		0			0
$895$	95915.0	+	166130.i	0.119740	+	0.207396i
$896$		0			0
$897$	67907.8	−	2.02789e6i	0.0843985	−	2.52035i
$898$		0			0
$899$		−	58038.6i		−	0.0718121i
$900$		0			0
$901$	28078.1			0.0345874
$902$		0			0
$903$	−6479.61	+	10402.7i	−0.00794645	+	0.0127576i
$904$		0			0
$905$	−130469.	+	75326.4i	−0.159298	+	0.0919709i
$906$		0			0
$907$	−626846.	+	1.08573e6i	−0.761985	+	1.31980i	0.179841	+	0.983696i	$0.442442\pi$
$907$	−626846.	+	1.08573e6i	−0.761985	+	1.31980i	−0.941826	+	0.336101i	$0.890892\pi$
$908$		0			0
$909$	−434950.	+	213684.i	−0.526395	+	0.258609i
$910$		0			0
$911$	455921.	+	263226.i	0.549355	+	0.317170i	0.748862	−	0.662726i	$-0.230601\pi$
$911$	455921.	+	263226.i	0.549355	+	0.317170i	−0.199507	+	0.979896i	$0.563934\pi$
$912$		0			0
$913$	244925.	+	424223.i	0.293827	+	0.508923i
$914$		0			0
$915$	1.71760e6	−	916420.i	2.05154	−	1.09459i
$916$		0			0
$917$		−	9437.09i		−	0.0112228i
$918$		0			0
$919$	−317984.			−0.376508			−0.188254	−	0.982120i	$-0.560283\pi$
$919$	−317984.			−0.376508			−0.188254	+	0.982120i	$0.560283\pi$
$920$		0			0
$921$	−115828.	−	217090.i	−0.136551	−	0.255930i
$922$		0			0
$923$	1.97879e6	−	1.14245e6i	2.32271	−	1.34102i
$924$		0			0
$925$	−1.04480e6	+	1.80965e6i	−1.22110	+	2.11500i
$926$		0			0
$927$	123768.	+	8298.54i	0.144029	+	0.00965700i
$928$		0			0
$929$	−1.27158e6	−	734148.i	−1.47337	−	0.850652i	−0.473822	−	0.880621i	$-0.657126\pi$
$929$	−1.27158e6	−	734148.i	−1.47337	−	0.850652i	−0.999551	+	0.0299688i	$0.990459\pi$
$930$		0			0
$931$	−581497.	−	1.00718e6i	−0.670885	−	1.16201i
$932$		0			0
$933$	−777289.	−	484157.i	−0.892933	−	0.556190i
$934$		0			0
$935$		−	35789.3i		−	0.0409383i
$936$		0			0
$937$	−672991.			−0.766532			−0.383266	−	0.923638i	$-0.625201\pi$
$937$	−672991.			−0.766532			−0.383266	+	0.923638i	$0.625201\pi$
$938$		0			0
$939$	410365.	+	13741.8i	0.465413	+	0.0155852i
$940$		0			0
$941$	−75861.4	+	43798.6i	−0.0856725	+	0.0494631i	−0.542224	−	0.840234i	$-0.682418\pi$
$941$	−75861.4	+	43798.6i	−0.0856725	+	0.0494631i	0.456552	+	0.889697i	$0.349084\pi$
$942$		0			0
$943$	−636243.	+	1.10200e6i	−0.715483	+	1.23925i
$944$		0			0
$945$	43477.6	−	431488.i	0.0486857	−	0.483175i
$946$		0			0
$947$	−786357.	−	454003.i	−0.876839	−	0.506243i	−0.00722389	−	0.999974i	$-0.502299\pi$
$947$	−786357.	−	454003.i	−0.876839	−	0.506243i	−0.869615	+	0.493731i	$0.835633\pi$
$948$		0			0
$949$	478153.	+	828185.i	0.530927	+	0.919592i
$950$		0			0
$951$	−7149.84	+	213512.i	−0.00790561	+	0.236081i
$952$		0			0
$953$			747370.i			0.822905i	0.911431	+	0.411452i	$0.134978\pi$
$953$			747370.i			0.822905i	−0.911431	+	0.411452i	$0.865022\pi$
$954$		0			0
$955$	418630.			0.459011
$956$		0			0
$957$	115586.	−	185566.i	0.126206	−	0.202617i
$958$		0			0
$959$	−409473.	+	236410.i	−0.445234	+	0.257056i
$960$		0			0
$961$	442731.	−	766832.i	0.479394	−	0.830335i
$962$		0			0
$963$	−1.37925e6	−	924582.i	−1.48728	−	0.996995i
$964$		0			0
$965$	−1.50689e6	−	870001.i	−1.61818	−	0.934254i
$966$		0			0
$967$	162017.	+	280622.i	0.173264	+	0.300102i	0.939559	−	0.342387i	$-0.111235\pi$
$967$	162017.	+	280622.i	0.173264	+	0.300102i	−0.766295	+	0.642489i	$0.777902\pi$
$968$		0			0
$969$	46054.0	−	24572.0i	0.0490478	−	0.0261694i
$970$		0			0
$971$		−	873822.i		−	0.926797i	−0.886150	−	0.463398i	$-0.846630\pi$
$971$		−	873822.i		−	0.926797i	0.886150	−	0.463398i	$-0.153370\pi$
$972$		0			0
$973$	−82500.5			−0.0871427
$974$		0			0
$975$	−1.17397e6	−	2.20032e6i	−1.23495	−	2.31460i
$976$		0			0
$977$	−246498.	+	142316.i	−0.258240	+	0.149095i	−0.623532	−	0.781798i	$-0.714303\pi$
$977$	−246498.	+	142316.i	−0.258240	+	0.149095i	0.365291	+	0.930893i	$0.380969\pi$
$978$		0			0
$979$	−344343.	+	596419.i	−0.359274	+	0.622280i
$980$		0			0
$981$	424150.	−	632730.i	0.440739	−	0.657476i
$982$		0			0
$983$	306.104	+	176.729i	0.000316783	+	0.000182895i	0.500158	−	0.865934i	$-0.333275\pi$
$983$	306.104	+	176.729i	0.000316783	+	0.000182895i	−0.499842	+	0.866117i	$0.666608\pi$
$984$		0			0
$985$	−1.00464e6	−	1.74009e6i	−1.03547	−	1.79349i
$986$		0			0
$987$	−240981.	−	150102.i	−0.247371	−	0.154083i
$988$		0			0
$989$			74719.9i			0.0763913i
$990$		0			0
$991$	−1.22572e6			−1.24808			−0.624041	−	0.781392i	$-0.714510\pi$
$991$	−1.22572e6			−1.24808			−0.624041	+	0.781392i	$0.714510\pi$
$992$		0			0
$993$	1.14598e6	+	38375.3i	1.16219	+	0.0389182i
$994$		0			0
$995$	−265505.	+	153290.i	−0.268180	+	0.154834i
$996$		0			0
$997$	663483.	−	1.14919e6i	0.667482	−	1.15611i	−0.311124	−	0.950369i	$-0.600705\pi$
$997$	663483.	−	1.14919e6i	0.667482	−	1.15611i	0.978606	−	0.205744i	$-0.0659613\pi$
$998$		0			0
$999$	1.52114e6	+	153274.i	1.52419	+	0.153581i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.5.q.c.65.3		8
3.2	odd	2		432.5.q.c.305.4		8
4.3	odd	2		36.5.g.a.29.2	yes	8
9.2	odd	6		1296.5.e.g.161.8		8
9.4	even	3		432.5.q.c.17.4		8
9.5	odd	6	inner	144.5.q.c.113.3		8
9.7	even	3		1296.5.e.g.161.1		8
12.11	even	2		108.5.g.a.89.4		8
36.7	odd	6		324.5.c.a.161.1		8
36.11	even	6		324.5.c.a.161.8		8
36.23	even	6		36.5.g.a.5.2	✓	8
36.31	odd	6		108.5.g.a.17.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.5.g.a.5.2	✓	8	36.23	even	6
36.5.g.a.29.2	yes	8	4.3	odd	2
108.5.g.a.17.4		8	36.31	odd	6
108.5.g.a.89.4		8	12.11	even	2
144.5.q.c.65.3		8	1.1	even	1	trivial
144.5.q.c.113.3		8	9.5	odd	6	inner
324.5.c.a.161.1		8	36.7	odd	6
324.5.c.a.161.8		8	36.11	even	6
432.5.q.c.17.4		8	9.4	even	3
432.5.q.c.305.4		8	3.2	odd	2
1296.5.e.g.161.1		8	9.7	even	3
1296.5.e.g.161.8		8	9.2	odd	6

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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	144.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(4.23662 + 7.94047i) q^{3} +(-34.8718 + 20.1332i) q^{5} +(7.38688 - 12.7945i) q^{7} +(-45.1021 + 67.2815i) q^{9} +O(q^{10})\)	\(q+(4.23662 + 7.94047i) q^{3} +(-34.8718 + 20.1332i) q^{5} +(7.38688 - 12.7945i) q^{7} +(-45.1021 + 67.2815i) q^{9} +(70.7125 + 40.8259i) q^{11} +(-139.053 - 240.848i) q^{13} +(-307.606 - 191.601i) q^{15} +10.8854i q^{17} -532.815 q^{19} +(132.889 + 4.45005i) q^{21} +(702.045 - 405.326i) q^{23} +(498.193 - 862.895i) q^{25} +(-725.327 - 73.0855i) q^{27} +(-257.640 - 148.749i) q^{29} +(97.5447 + 168.952i) q^{31} +(-24.5946 + 734.454i) q^{33} +594.887i q^{35} -2097.18 q^{37} +(1323.33 - 2124.53i) q^{39} +(-1359.41 + 784.854i) q^{41} +(-46.0863 + 79.8239i) q^{43} +(218.196 - 3254.27i) q^{45} +(-1849.15 - 1067.61i) q^{47} +(1091.37 + 1890.30i) q^{49} +(-86.4353 + 46.1174i) q^{51} -2579.42i q^{53} -3287.82 q^{55} +(-2257.33 - 4230.80i) q^{57} +(-1349.04 + 778.868i) q^{59} +(-2685.97 + 4652.24i) q^{61} +(527.666 + 1074.06i) q^{63} +(9698.07 + 5599.19i) q^{65} +(457.641 + 792.658i) q^{67} +(6192.77 + 3857.35i) q^{69} +8215.93i q^{71} -3438.63 q^{73} +(8962.45 + 300.125i) q^{75} +(1044.69 - 603.152i) q^{77} +(2316.17 - 4011.73i) q^{79} +(-2492.60 - 6069.07i) q^{81} +(5195.52 + 2999.63i) q^{83} +(-219.158 - 379.593i) q^{85} +(89.6101 - 2675.98i) q^{87} +8434.43i q^{89} -4108.69 q^{91} +(-928.301 + 1490.34i) q^{93} +(18580.2 - 10727.3i) q^{95} +(3015.58 - 5223.13i) q^{97} +(-5936.10 + 2916.31i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 9 q^{3} - 9 q^{5} - 13 q^{7} + 21 q^{9}+O(q^{10}) \) 8 * q + 9 * q^3 - 9 * q^5 - 13 * q^7 + 21 * q^9	\( 8 q + 9 q^{3} - 9 q^{5} - 13 q^{7} + 21 q^{9} + 18 q^{11} - 5 q^{13} - 225 q^{15} - 562 q^{19} - 1167 q^{21} + 1719 q^{23} + 353 q^{25} - 648 q^{27} + 2115 q^{29} - 187 q^{31} + 3258 q^{33} + 16 q^{37} + 8265 q^{39} - 7920 q^{41} + 68 q^{43} + 5679 q^{45} - 13689 q^{47} - 327 q^{49} - 10449 q^{51} + 1818 q^{55} - 21861 q^{57} + 20052 q^{59} - 1937 q^{61} - 5559 q^{63} + 25965 q^{65} - 154 q^{67} + 21645 q^{69} - 7802 q^{73} + 30297 q^{75} - 25641 q^{77} + 2195 q^{79} + 19701 q^{81} - 37017 q^{83} - 3042 q^{85} - 22455 q^{87} - 15830 q^{91} - 36489 q^{93} + 37116 q^{95} + 7282 q^{97} + 10035 q^{99}+O(q^{100}) \) 8 * q + 9 * q^3 - 9 * q^5 - 13 * q^7 + 21 * q^9 + 18 * q^11 - 5 * q^13 - 225 * q^15 - 562 * q^19 - 1167 * q^21 + 1719 * q^23 + 353 * q^25 - 648 * q^27 + 2115 * q^29 - 187 * q^31 + 3258 * q^33 + 16 * q^37 + 8265 * q^39 - 7920 * q^41 + 68 * q^43 + 5679 * q^45 - 13689 * q^47 - 327 * q^49 - 10449 * q^51 + 1818 * q^55 - 21861 * q^57 + 20052 * q^59 - 1937 * q^61 - 5559 * q^63 + 25965 * q^65 - 154 * q^67 + 21645 * q^69 - 7802 * q^73 + 30297 * q^75 - 25641 * q^77 + 2195 * q^79 + 19701 * q^81 - 37017 * q^83 - 3042 * q^85 - 22455 * q^87 - 15830 * q^91 - 36489 * q^93 + 37116 * q^95 + 7282 * q^97 + 10035 * q^99

Introduction

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