LMFDB - Embedded newform 810.3.j.f.269.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("810.269");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$22.0709014132$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.81622204416.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 14x^{6} + 165x^{4} - 434x^{2} + 961 $ x^8 - 14x^6 + 165x^4 - 434*x^2 + 961
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 270)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.2
Root			$-2.90379 + 1.67650i$ of defining polynomial
Character	$\chi$	$=$	810.269
Dual form			810.3.j.f.539.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(4.89947 - 0.997601i) q^{5} +(-0.704577 - 0.406788i) q^{7} +2.82843 q^{8} +O(q^{10})$	\(q+(-0.707107 + 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(4.89947 - 0.997601i) q^{5} +(-0.704577 - 0.406788i) q^{7} +2.82843 q^{8} +(-2.24264 + 6.70601i) q^{10} +(-13.3161 - 7.68808i) q^{11} +(5.10300 - 2.94622i) q^{13} +(0.996422 - 0.575285i) q^{14} +(-2.00000 + 3.46410i) q^{16} +12.8995 q^{17} +1.24264 q^{19} +(-6.62736 - 7.48853i) q^{20} +(18.8319 - 10.8726i) q^{22} +(-2.39949 - 4.15605i) q^{23} +(23.0096 - 9.77543i) q^{25} +8.33316i q^{26} +1.62715i q^{28} +(-36.9592 - 21.3384i) q^{29} +(-2.10660 - 3.64874i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(-9.12132 + 15.7986i) q^{34} +(-3.85786 - 1.29016i) q^{35} -70.3144i q^{37} +(-0.878680 + 1.52192i) q^{38} +(13.8578 - 2.82164i) q^{40} +(6.09942 - 3.52150i) q^{41} +(35.5500 + 20.5248i) q^{43} +30.7523i q^{44} +6.78680 q^{46} +(-39.8995 + 69.1080i) q^{47} +(-24.1690 - 41.8620i) q^{49} +(-4.29783 + 35.0931i) q^{50} +(-10.2060 - 5.89243i) q^{52} -63.7279 q^{53} +(-72.9117 - 24.3833i) q^{55} +(-1.99284 - 1.15057i) q^{56} +(52.2682 - 30.1770i) q^{58} +(-31.7353 + 18.3224i) q^{59} +(41.4706 - 71.8291i) q^{61} +5.95837 q^{62} +8.00000 q^{64} +(22.0628 - 19.5257i) q^{65} +(77.0786 - 44.5013i) q^{67} +(-12.8995 - 22.3426i) q^{68} +(4.30803 - 3.81262i) q^{70} -69.6982i q^{71} -89.6188i q^{73} +(86.1172 + 49.7198i) q^{74} +(-1.24264 - 2.15232i) q^{76} +(6.25483 + 10.8337i) q^{77} +(-67.0477 + 116.130i) q^{79} +(-6.34315 + 18.9675i) q^{80} +9.96031i q^{82} +(54.5122 - 94.4179i) q^{83} +(63.2007 - 12.8685i) q^{85} +(-50.2753 + 29.0265i) q^{86} +(-37.6638 - 21.7452i) q^{88} -137.514i q^{89} -4.79394 q^{91} +(-4.79899 + 8.31209i) q^{92} +(-56.4264 - 97.7334i) q^{94} +(6.08828 - 1.23966i) q^{95} +(78.4877 + 45.3149i) q^{97} +68.3604 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} + 12 q^{5}+O(q^{10}) $ 8 * q - 8 * q^4 + 12 * q^5	$ 8 q - 8 q^{4} + 12 q^{5} + 16 q^{10} - 16 q^{16} + 24 q^{17} - 24 q^{19} + 24 q^{20} + 60 q^{23} + 12 q^{25} + 68 q^{31} - 56 q^{34} - 144 q^{35} - 24 q^{38} - 16 q^{40} + 224 q^{46} - 240 q^{47} + 180 q^{49} + 96 q^{50} - 408 q^{53} - 176 q^{55} + 196 q^{61} + 240 q^{62} + 64 q^{64} - 24 q^{65} - 24 q^{68} - 80 q^{70} + 24 q^{76} - 312 q^{77} - 180 q^{79} - 96 q^{80} + 108 q^{83} - 20 q^{85} + 912 q^{91} + 120 q^{92} - 112 q^{94} - 60 q^{95} + 1056 q^{98}+O(q^{100}) $ 8 * q - 8 * q^4 + 12 * q^5 + 16 * q^10 - 16 * q^16 + 24 * q^17 - 24 * q^19 + 24 * q^20 + 60 * q^23 + 12 * q^25 + 68 * q^31 - 56 * q^34 - 144 * q^35 - 24 * q^38 - 16 * q^40 + 224 * q^46 - 240 * q^47 + 180 * q^49 + 96 * q^50 - 408 * q^53 - 176 * q^55 + 196 * q^61 + 240 * q^62 + 64 * q^64 - 24 * q^65 - 24 * q^68 - 80 * q^70 + 24 * q^76 - 312 * q^77 - 180 * q^79 - 96 * q^80 + 108 * q^83 - 20 * q^85 + 912 * q^91 + 120 * q^92 - 112 * q^94 - 60 * q^95 + 1056 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.707107	+	1.22474i	−0.353553	+	0.612372i
$2$	−0.707107	+	1.22474i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−1.00000	−	1.73205i	−0.250000	−	0.433013i
$5$	4.89947	−	0.997601i	0.979894	−	0.199520i
$5$	4.89947	−	0.997601i	0.979894	−	0.199520i
$6$		0			0
$7$	−0.704577	−	0.406788i	−0.100654	−	0.0581125i	0.448828	−	0.893618i	$-0.351842\pi$
$7$	−0.704577	−	0.406788i	−0.100654	−	0.0581125i	−0.549482	+	0.835506i	$0.685175\pi$
$8$	2.82843			0.353553
$9$		0			0
$10$	−2.24264	+	6.70601i	−0.224264	+	0.670601i
$11$	−13.3161	−	7.68808i	−1.21056	−	0.698917i	−0.247678	−	0.968842i	$-0.579667\pi$
$11$	−13.3161	−	7.68808i	−1.21056	−	0.698917i	−0.962881	+	0.269926i	$0.913001\pi$
$12$		0			0
$13$	5.10300	−	2.94622i	0.392538	−	0.226632i	−0.290721	−	0.956808i	$-0.593895\pi$
$13$	5.10300	−	2.94622i	0.392538	−	0.226632i	0.683259	+	0.730176i	$0.260562\pi$
$14$	0.996422	−	0.575285i	0.0711730	−	0.0410918i
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	12.8995			0.758794			0.379397	−	0.925234i	$-0.376131\pi$
$17$	12.8995			0.758794			0.379397	+	0.925234i	$0.376131\pi$
$18$		0			0
$19$	1.24264			0.0654021			0.0327011	−	0.999465i	$-0.489589\pi$
$19$	1.24264			0.0654021			0.0327011	+	0.999465i	$0.489589\pi$
$20$	−6.62736	−	7.48853i	−0.331368	−	0.374426i
$21$		0			0
$22$	18.8319	−	10.8726i	0.855994	−	0.494209i
$23$	−2.39949	−	4.15605i	−0.104326	−	0.180698i	0.809137	−	0.587620i	$-0.199935\pi$
$23$	−2.39949	−	4.15605i	−0.104326	−	0.180698i	−0.913463	+	0.406923i	$0.866602\pi$
$24$		0			0
$25$	23.0096	−	9.77543i	0.920383	−	0.391017i
$26$			8.33316i			0.320506i
$27$		0			0
$28$			1.62715i			0.0581125i
$29$	−36.9592	−	21.3384i	−1.27445	−	0.735807i	−0.298631	−	0.954369i	$-0.596530\pi$
$29$	−36.9592	−	21.3384i	−1.27445	−	0.735807i	−0.975823	+	0.218562i	$0.929863\pi$
$30$		0			0
$31$	−2.10660	−	3.64874i	−0.0679549	−	0.117701i	0.830046	−	0.557695i	$-0.188314\pi$
$31$	−2.10660	−	3.64874i	−0.0679549	−	0.117701i	−0.898001	+	0.439994i	$0.854981\pi$
$32$	−2.82843	−	4.89898i	−0.0883883	−	0.153093i
$33$		0			0
$34$	−9.12132	+	15.7986i	−0.268274	+	0.464664i
$35$	−3.85786	−	1.29016i	−0.110225	−	0.0368616i
$36$		0			0
$37$		−	70.3144i		−	1.90039i	−0.311657	−	0.950195i	$-0.600884\pi$
$37$		−	70.3144i		−	1.90039i	0.311657	−	0.950195i	$-0.399116\pi$
$38$	−0.878680	+	1.52192i	−0.0231231	+	0.0400505i
$39$		0			0
$40$	13.8578	−	2.82164i	0.346445	−	0.0705410i
$41$	6.09942	−	3.52150i	0.148766	−	0.0858903i	−0.423769	−	0.905770i	$-0.639293\pi$
$41$	6.09942	−	3.52150i	0.148766	−	0.0858903i	0.572535	+	0.819880i	$0.305960\pi$
$42$		0			0
$43$	35.5500	+	20.5248i	0.826745	+	0.477321i	0.852737	−	0.522341i	$-0.174941\pi$
$43$	35.5500	+	20.5248i	0.826745	+	0.477321i	−0.0259920	+	0.999662i	$0.508274\pi$
$44$			30.7523i			0.698917i
$45$		0			0
$46$	6.78680			0.147539
$47$	−39.8995	+	69.1080i	−0.848925	+	1.47038i	0.0332427	+	0.999447i	$0.489417\pi$
$47$	−39.8995	+	69.1080i	−0.848925	+	1.47038i	−0.882168	+	0.470935i	$0.843917\pi$
$48$		0			0
$49$	−24.1690	−	41.8620i	−0.493246	−	0.854327i
$50$	−4.29783	+	35.0931i	−0.0859565	+	0.701863i
$51$		0			0
$52$	−10.2060	−	5.89243i	−0.196269	−	0.113316i
$53$	−63.7279			−1.20241			−0.601207	−	0.799093i	$-0.705313\pi$
$53$	−63.7279			−1.20241			−0.601207	+	0.799093i	$0.705313\pi$
$54$		0			0
$55$	−72.9117	−	24.3833i	−1.32567	−	0.443333i
$56$	−1.99284	−	1.15057i	−0.0355865	−	0.0205459i
$57$		0			0
$58$	52.2682	−	30.1770i	0.901175	−	0.520294i
$59$	−31.7353	+	18.3224i	−0.537886	+	0.310549i	−0.744222	−	0.667932i	$-0.767179\pi$
$59$	−31.7353	+	18.3224i	−0.537886	+	0.310549i	0.206336	+	0.978481i	$0.433846\pi$
$60$		0			0
$61$	41.4706	−	71.8291i	0.679845	−	1.17753i	−0.295182	−	0.955441i	$-0.595380\pi$
$61$	41.4706	−	71.8291i	0.679845	−	1.17753i	0.975027	−	0.222086i	$-0.0712864\pi$
$62$	5.95837			0.0961027
$63$		0			0
$64$	8.00000			0.125000
$65$	22.0628	−	19.5257i	0.339428	−	0.300395i
$66$		0			0
$67$	77.0786	−	44.5013i	1.15043	−	0.664199i	0.201435	−	0.979502i	$-0.435439\pi$
$67$	77.0786	−	44.5013i	1.15043	−	0.664199i	0.948991	+	0.315303i	$0.102106\pi$
$68$	−12.8995	−	22.3426i	−0.189698	−	0.328567i
$69$		0			0
$70$	4.30803	−	3.81262i	0.0615434	−	0.0544660i
$71$		−	69.6982i		−	0.981665i	−0.871254	−	0.490833i	$-0.836693\pi$
$71$		−	69.6982i		−	0.981665i	0.871254	−	0.490833i	$-0.163307\pi$
$72$		0			0
$73$		−	89.6188i		−	1.22766i	−0.789440	−	0.613828i	$-0.789629\pi$
$73$		−	89.6188i		−	1.22766i	0.789440	−	0.613828i	$-0.210371\pi$
$74$	86.1172	+	49.7198i	1.16375	+	0.671889i
$75$		0			0
$76$	−1.24264	−	2.15232i	−0.0163505	−	0.0283200i
$77$	6.25483	+	10.8337i	0.0812316	+	0.140697i
$78$		0			0
$79$	−67.0477	+	116.130i	−0.848705	+	1.47000i	0.0336586	+	0.999433i	$0.489284\pi$
$79$	−67.0477	+	116.130i	−0.848705	+	1.47000i	−0.882364	+	0.470567i	$0.844049\pi$
$80$	−6.34315	+	18.9675i	−0.0792893	+	0.237093i
$81$		0			0
$82$			9.96031i			0.121467i
$83$	54.5122	−	94.4179i	0.656773	−	1.13756i	−0.324673	−	0.945826i	$-0.605254\pi$
$83$	54.5122	−	94.4179i	0.656773	−	1.13756i	0.981446	−	0.191738i	$-0.0614125\pi$
$84$		0			0
$85$	63.2007	−	12.8685i	0.743537	−	0.151395i
$86$	−50.2753	+	29.0265i	−0.584597	+	0.337517i
$87$		0			0
$88$	−37.6638	−	21.7452i	−0.427997	−	0.247104i
$89$		−	137.514i		−	1.54510i	−0.634953	−	0.772551i	$-0.718980\pi$
$89$		−	137.514i		−	1.54510i	0.634953	−	0.772551i	$-0.281020\pi$
$90$		0			0
$91$	−4.79394			−0.0526807
$92$	−4.79899	+	8.31209i	−0.0521629	+	0.0903489i
$93$		0			0
$94$	−56.4264	−	97.7334i	−0.600281	−	1.03972i
$95$	6.08828	−	1.23966i	0.0640871	−	0.0130490i
$96$		0			0
$97$	78.4877	+	45.3149i	0.809152	+	0.467164i	0.846661	−	0.532132i	$-0.178609\pi$
$97$	78.4877	+	45.3149i	0.809152	+	0.467164i	−0.0375094	+	0.999296i	$0.511942\pi$
$98$	68.3604			0.697555
$99$		0			0
$100$	−39.9411	−	30.0783i	−0.399411	−	0.300783i
$101$	43.0586	+	24.8599i	0.426323	+	0.246138i	0.697779	−	0.716313i	$-0.254172\pi$
$101$	43.0586	+	24.8599i	0.426323	+	0.246138i	−0.271456	+	0.962451i	$0.587505\pi$
$102$		0			0
$103$	111.582	−	64.4220i	1.08332	−	0.625456i	0.151531	−	0.988453i	$-0.451580\pi$
$103$	111.582	−	64.4220i	1.08332	−	0.625456i	0.931790	+	0.362997i	$0.118246\pi$
$104$	14.4335	−	8.33316i	0.138783	−	0.0801265i
$105$		0			0
$106$	45.0624	−	78.0504i	0.425117	−	0.736325i
$107$	−6.42641			−0.0600599			−0.0300299	−	0.999549i	$-0.509560\pi$
$107$	−6.42641			−0.0600599			−0.0300299	+	0.999549i	$0.509560\pi$
$108$		0			0
$109$	108.279			0.993387			0.496694	−	0.867926i	$-0.334547\pi$
$109$	108.279			0.993387			0.496694	+	0.867926i	$0.334547\pi$
$110$	81.4197	−	72.0566i	0.740179	−	0.655060i
$111$		0			0
$112$	2.81831	−	1.62715i	0.0251635	−	0.0145281i
$113$	−15.2132	−	26.3500i	−0.134630	−	0.233186i	0.790826	−	0.612041i	$-0.209651\pi$
$113$	−15.2132	−	26.3500i	−0.134630	−	0.233186i	−0.925456	+	0.378855i	$0.876318\pi$
$114$		0			0
$115$	−15.9023	−	17.9687i	−0.138281	−	0.156249i
$116$			85.3536i			0.735807i
$117$		0			0
$118$		−	51.8235i		−	0.439182i
$119$	−9.08869	−	5.24736i	−0.0763755	−	0.0440954i
$120$		0			0
$121$	57.7132	+	99.9622i	0.476969	+	0.826134i
$122$	58.6482	+	101.582i	0.480723	+	0.832637i
$123$		0			0
$124$	−4.21320	+	7.29748i	−0.0339774	+	0.0588507i
$125$	102.983	−	70.8488i	0.823862	−	0.566790i
$126$		0			0
$127$			133.725i			1.05296i	0.850189	+	0.526478i	$0.176488\pi$
$127$			133.725i			1.05296i	−0.850189	+	0.526478i	$0.823512\pi$
$128$	−5.65685	+	9.79796i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	8.31317	+	40.8281i	0.0639475	+	0.314062i
$131$	53.5064	−	30.8919i	0.408446	−	0.235816i	−0.281676	−	0.959510i	$-0.590890\pi$
$131$	53.5064	−	30.8919i	0.408446	−	0.235816i	0.690122	+	0.723693i	$0.257557\pi$
$132$		0			0
$133$	−0.875536	−	0.505491i	−0.00658298	−	0.00380068i
$134$			125.869i			0.939319i
$135$		0			0
$136$	36.4853			0.268274
$137$	−81.9594	+	141.958i	−0.598244	+	1.03619i	0.394836	+	0.918751i	$0.370801\pi$
$137$	−81.9594	+	141.958i	−0.598244	+	1.03619i	−0.993080	+	0.117437i	$0.962532\pi$
$138$		0			0
$139$	−91.1249	−	157.833i	−0.655575	−	1.13549i	−0.981749	−	0.190179i	$-0.939093\pi$
$139$	−91.1249	−	157.833i	−0.655575	−	1.13549i	0.326175	−	0.945310i	$-0.394240\pi$
$140$	1.62325	+	7.97217i	0.0115946	+	0.0569441i
$141$		0			0
$142$	85.3625	+	49.2841i	0.601145	+	0.347071i
$143$	−90.6030			−0.633588
$144$		0			0
$145$	−202.368	−	67.6763i	−1.39564	−	0.466733i
$146$	109.760	+	63.3701i	0.751782	+	0.434042i
$147$		0			0
$148$	−121.788	+	70.3144i	−0.822893	+	0.475097i
$149$	164.142	−	94.7675i	1.10163	−	0.636023i	0.164978	−	0.986297i	$-0.447245\pi$
$149$	164.142	−	94.7675i	1.10163	−	0.636023i	0.936647	+	0.350274i	$0.113911\pi$
$150$		0			0
$151$	56.6690	−	98.1537i	0.375292	−	0.650024i	−0.615079	−	0.788466i	$-0.710876\pi$
$151$	56.6690	−	98.1537i	0.375292	−	0.650024i	0.990371	+	0.138441i	$0.0442092\pi$
$152$	3.51472			0.0231231
$153$		0			0
$154$	−17.6913			−0.114879
$155$	−13.9612	−	15.7753i	−0.0900724	−	0.101776i
$156$		0			0
$157$	−98.0242	+	56.5943i	−0.624358	+	0.360473i	−0.778564	−	0.627566i	$-0.784051\pi$
$157$	−98.0242	+	56.5943i	−0.624358	+	0.360473i	0.154206	+	0.988039i	$0.450718\pi$
$158$	−94.8198	−	164.233i	−0.600125	−	1.03945i
$159$		0			0
$160$	−18.7450	−	21.1808i	−0.117156	−	0.132380i
$161$			3.90434i			0.0242506i
$162$		0			0
$163$			152.414i			0.935053i	0.883979	+	0.467527i	$0.154855\pi$
$163$			152.414i			0.935053i	−0.883979	+	0.467527i	$0.845145\pi$
$164$	−12.1988	−	7.04300i	−0.0743832	−	0.0429451i
$165$		0			0
$166$	77.0919	+	133.527i	0.464409	+	0.804380i
$167$	52.9264	+	91.6712i	0.316925	+	0.548929i	0.979845	−	0.199761i	$-0.0640165\pi$
$167$	52.9264	+	91.6712i	0.316925	+	0.548929i	−0.662920	+	0.748690i	$0.730683\pi$
$168$		0			0
$169$	−67.1396	+	116.289i	−0.397276	+	0.688102i
$170$	−28.9289	+	86.5041i	−0.170170	+	0.508848i
$171$		0			0
$172$		−	82.0993i		−	0.477321i
$173$	55.0061	−	95.2734i	0.317954	−	0.550713i	−0.662107	−	0.749410i	$-0.730337\pi$
$173$	55.0061	−	95.2734i	0.317954	−	0.550713i	0.980061	+	0.198697i	$0.0636708\pi$
$174$		0			0
$175$	−20.1885	−	2.47247i	−0.115363	−	0.0141284i
$176$	53.2646	−	30.7523i	0.302640	−	0.174729i
$177$		0			0
$178$	168.420	+	97.2371i	0.946178	+	0.546276i
$179$			118.407i			0.661492i	0.943720	+	0.330746i	$0.107300\pi$
$179$			118.407i			0.661492i	−0.943720	+	0.330746i	$0.892700\pi$
$180$		0			0
$181$	172.397			0.952469			0.476235	−	0.879318i	$-0.342001\pi$
$181$	172.397			0.952469			0.476235	+	0.879318i	$0.342001\pi$
$182$	3.38983	−	5.87135i	0.0186254	−	0.0322602i
$183$		0			0
$184$	−6.78680	−	11.7551i	−0.0368848	−	0.0638863i
$185$	−70.1457	−	344.503i	−0.379166	−	1.86218i
$186$		0			0
$187$	−171.772	−	99.1724i	−0.918565	−	0.530334i
$188$	159.598			0.848925
$189$		0			0
$190$	−2.78680	+	8.33316i	−0.0146674	+	0.0438587i
$191$	−250.622	−	144.697i	−1.31216	−	0.757574i	−0.329704	−	0.944084i	$-0.606949\pi$
$191$	−250.622	−	144.697i	−1.31216	−	0.757574i	−0.982453	+	0.186510i	$0.940282\pi$
$192$		0			0
$193$	−110.707	+	63.9165i	−0.573609	+	0.331173i	−0.758590	−	0.651569i	$-0.774111\pi$
$193$	−110.707	+	63.9165i	−0.573609	+	0.331173i	0.184980	+	0.982742i	$0.440778\pi$
$194$	−110.998	+	64.0850i	−0.572157	+	0.330335i
$195$		0			0
$196$	−48.3381	+	83.7240i	−0.246623	+	0.427163i
$197$	−280.414			−1.42342			−0.711711	−	0.702472i	$-0.752080\pi$
$197$	−280.414			−1.42342			−0.711711	+	0.702472i	$0.752080\pi$
$198$		0			0
$199$	156.426			0.786062			0.393031	−	0.919525i	$-0.371426\pi$
$199$	156.426			0.786062			0.393031	+	0.919525i	$0.371426\pi$
$200$	65.0809	−	27.6491i	0.325405	−	0.138245i
$201$		0			0
$202$	−60.8941	+	35.1572i	−0.301456	+	0.174046i
$203$	17.3604	+	30.0691i	0.0855192	+	0.148124i
$204$		0			0
$205$	26.3709	−	23.3383i	0.128638	−	0.113845i
$206$			182.213i			0.884528i
$207$		0			0
$208$			23.5697i			0.113316i
$209$	−16.5472	−	9.55352i	−0.0791731	−	0.0457106i
$210$		0			0
$211$	−11.2538	−	19.4921i	−0.0533355	−	0.0923798i	0.838125	−	0.545478i	$-0.183652\pi$
$211$	−11.2538	−	19.4921i	−0.0533355	−	0.0923798i	−0.891460	+	0.453098i	$0.850319\pi$
$212$	63.7279	+	110.380i	0.300603	+	0.520660i
$213$		0			0
$214$	4.54416	−	7.87071i	0.0212344	−	0.0367790i
$215$	194.652	+	65.0959i	0.905357	+	0.302772i
$216$		0			0
$217$			3.42776i			0.0157961i
$218$	−76.5650	+	132.614i	−0.351215	+	0.608323i
$219$		0			0
$220$	30.6786	+	150.670i	0.139448	+	0.684864i
$221$	65.8261	−	38.0047i	0.297856	−	0.171967i
$222$		0			0
$223$	−307.289	−	177.413i	−1.37798	−	0.795575i	−0.386060	−	0.922474i	$-0.626164\pi$
$223$	−307.289	−	177.413i	−1.37798	−	0.795575i	−0.991916	+	0.126899i	$0.959498\pi$
$224$			4.60228i			0.0205459i
$225$		0			0
$226$	43.0294			0.190396
$227$	−207.549	+	359.485i	−0.914312	+	1.58363i	−0.106406	+	0.994323i	$0.533934\pi$
$227$	−207.549	+	359.485i	−0.914312	+	1.58363i	−0.807906	+	0.589312i	$0.799399\pi$
$228$		0			0
$229$	110.110	+	190.716i	0.480830	+	0.832823i	0.999758	−	0.0219954i	$-0.00700192\pi$
$229$	110.110	+	190.716i	0.480830	+	0.832823i	−0.518928	+	0.854818i	$0.673669\pi$
$230$	33.2517	−	6.77052i	0.144573	−	0.0294370i
$231$		0			0
$232$	−104.536	−	60.3541i	−0.450588	−	0.260147i
$233$	−10.0345			−0.0430665			−0.0215332	−	0.999768i	$-0.506855\pi$
$233$	−10.0345			−0.0430665			−0.0215332	+	0.999768i	$0.506855\pi$
$234$		0			0
$235$	−126.544	+	378.396i	−0.538486	+	1.61020i
$236$	63.4706	+	36.6448i	0.268943	+	0.155274i
$237$		0			0
$238$	12.8533	−	7.42088i	0.0540056	−	0.0311802i
$239$	−99.0414	+	57.1816i	−0.414399	+	0.239253i	−0.692678	−	0.721247i	$-0.743569\pi$
$239$	−99.0414	+	57.1816i	−0.414399	+	0.239253i	0.278279	+	0.960500i	$0.410236\pi$
$240$		0			0
$241$	31.8604	−	55.1838i	0.132201	−	0.228978i	−0.792324	−	0.610101i	$-0.791129\pi$
$241$	31.8604	−	55.1838i	0.132201	−	0.228978i	0.924525	+	0.381122i	$0.124462\pi$
$242$	−163.238			−0.674535
$243$		0			0
$244$	−165.882			−0.679845
$245$	−160.177	−	180.991i	−0.653784	−	0.738737i
$246$		0			0
$247$	6.34119	−	3.66109i	0.0256728	−	0.0148222i
$248$	−5.95837	−	10.3202i	−0.0240257	−	0.0416137i
$249$		0			0
$250$	13.9519	+	176.225i	0.0558076	+	0.704901i
$251$		−	229.631i		−	0.914866i	−0.889244	−	0.457433i	$-0.848769\pi$
$251$		−	229.631i		−	0.914866i	0.889244	−	0.457433i	$-0.151231\pi$
$252$		0			0
$253$			73.7901i			0.291660i
$254$	−163.779	−	94.5581i	−0.644801	−	0.372276i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	194.114	+	336.215i	0.755306	+	1.30823i	0.945222	+	0.326429i	$0.105845\pi$
$257$	194.114	+	336.215i	0.755306	+	1.30823i	−0.189915	+	0.981800i	$0.560821\pi$
$258$		0			0
$259$	−28.6030	+	49.5419i	−0.110436	+	0.191281i
$260$	−55.8823	−	18.6883i	−0.214932	−	0.0718780i
$261$		0			0
$262$			87.3755i			0.333494i
$263$	113.439	−	196.481i	0.431325	−	0.747078i	−0.565662	−	0.824637i	$-0.691379\pi$
$263$	113.439	−	196.481i	0.431325	−	0.747078i	0.996988	+	0.0775594i	$0.0247127\pi$
$264$		0			0
$265$	−312.233	+	63.5750i	−1.17824	+	0.239906i
$266$	1.23819	−	0.714872i	0.00465487	−	0.00268749i
$267$		0			0
$268$	−154.157	−	89.0027i	−0.575213	−	0.332100i
$269$		−	226.772i		−	0.843019i	−0.906824	−	0.421509i	$-0.861500\pi$
$269$		−	226.772i		−	0.843019i	0.906824	−	0.421509i	$-0.138500\pi$
$270$		0			0
$271$	322.889			1.19147			0.595737	−	0.803180i	$-0.296860\pi$
$271$	322.889			1.19147			0.595737	+	0.803180i	$0.296860\pi$
$272$	−25.7990	+	44.6852i	−0.0948492	+	0.164284i
$273$		0			0
$274$	−115.908	−	200.759i	−0.423022	−	0.732696i
$275$	−381.553	−	46.7285i	−1.38747	−	0.169922i
$276$		0			0
$277$	−173.694	−	100.282i	−0.627053	−	0.362029i	0.152557	−	0.988295i	$-0.451249\pi$
$277$	−173.694	−	100.282i	−0.627053	−	0.362029i	−0.779610	+	0.626266i	$0.784583\pi$
$278$	257.740			0.927123
$279$		0			0
$280$	−10.9117	−	3.64911i	−0.0389703	−	0.0130326i
$281$	110.878	+	64.0152i	0.394582	+	0.227812i	0.684144	−	0.729347i	$-0.260176\pi$
$281$	110.878	+	64.0152i	0.394582	+	0.227812i	−0.289562	+	0.957159i	$0.593510\pi$
$282$		0			0
$283$	−363.934	+	210.118i	−1.28599	+	0.742465i	−0.977936	−	0.208905i	$-0.933010\pi$
$283$	−363.934	+	210.118i	−1.28599	+	0.742465i	−0.308051	+	0.951370i	$0.599677\pi$
$284$	−120.721	+	69.6982i	−0.425073	+	0.245416i
$285$		0			0
$286$	64.0660	−	110.966i	0.224007	−	0.387992i
$287$	−5.73001			−0.0199652
$288$		0			0
$289$	−122.603			−0.424232
$290$	225.982	−	199.994i	0.779247	−	0.689635i
$291$		0			0
$292$	−155.224	+	89.6188i	−0.531590	+	0.306914i
$293$	68.7168	+	119.021i	0.234528	+	0.406215i	0.959135	−	0.282947i	$-0.0913121\pi$
$293$	68.7168	+	119.021i	0.234528	+	0.406215i	−0.724607	+	0.689162i	$0.757979\pi$
$294$		0			0
$295$	−137.208	+	121.429i	−0.465111	+	0.411624i
$296$		−	198.879i		−	0.671889i
$297$		0			0
$298$			268.043i			0.899473i
$299$	−24.4892	−	14.1389i	−0.0819038	−	0.0472872i
$300$		0			0
$301$	−16.6985	−	28.9226i	−0.0554767	−	0.0960885i
$302$	80.1421	+	138.810i	0.265371	+	0.459637i
$303$		0			0
$304$	−2.48528	+	4.30463i	−0.00817527	+	0.0141600i
$305$	131.527	−	393.296i	0.431236	−	1.28949i
$306$		0			0
$307$		−	117.849i		−	0.383872i	−0.981407	−	0.191936i	$-0.938523\pi$
$307$		−	117.849i		−	0.383872i	0.981407	−	0.191936i	$-0.0614766\pi$
$308$	12.5097	−	21.6674i	0.0406158	−	0.0703486i
$309$		0			0
$310$	29.1928	−	5.94408i	0.0941705	−	0.0191744i
$311$	−432.429	+	249.663i	−1.39045	+	0.802774i	−0.993364	−	0.115009i	$-0.963310\pi$
$311$	−432.429	+	249.663i	−1.39045	+	0.802774i	−0.397081	+	0.917783i	$0.629977\pi$
$312$		0			0
$313$	425.916	+	245.903i	1.36076	+	0.785633i	0.989724	−	0.142988i	$-0.0456710\pi$
$313$	425.916	+	245.903i	1.36076	+	0.785633i	0.371031	+	0.928620i	$0.379004\pi$
$314$		−	160.073i		−	0.509786i
$315$		0			0
$316$	268.191			0.848705
$317$	−120.700	+	209.058i	−0.380756	+	0.659488i	−0.991170	−	0.132594i	$-0.957669\pi$
$317$	−120.700	+	209.058i	−0.380756	+	0.659488i	0.610415	+	0.792082i	$0.291003\pi$
$318$		0			0
$319$	328.103	+	568.290i	1.02853	+	1.78147i
$320$	39.1957	−	7.98081i	0.122487	−	0.0249400i
$321$		0			0
$322$	−4.78182	−	2.76079i	−0.0148504	−	0.00857387i
$323$	16.0294			0.0496267
$324$		0			0
$325$	88.6173	−	117.675i	0.272669	−	0.362078i
$326$	−186.668	−	107.773i	−0.572601	−	0.330591i
$327$		0			0
$328$	17.2518	−	9.96031i	0.0525968	−	0.0303668i
$329$	56.2245	−	32.4612i	0.170895	−	0.0986664i
$330$		0			0
$331$	43.9045	−	76.0449i	0.132642	−	0.229743i	−0.792052	−	0.610453i	$-0.790987\pi$
$331$	43.9045	−	76.0449i	0.132642	−	0.229743i	0.924694	+	0.380711i	$0.124321\pi$
$332$	−218.049			−0.656773
$333$		0			0
$334$	−149.698			−0.448199
$335$	333.250	−	294.927i	0.994775	−	0.880378i
$336$		0			0
$337$	−391.563	+	226.069i	−1.16191	+	0.670828i	−0.951761	−	0.306841i	$-0.900728\pi$
$337$	−391.563	+	226.069i	−1.16191	+	0.670828i	−0.210148	+	0.977670i	$0.567395\pi$
$338$	−94.9497	−	164.458i	−0.280916	−	0.486561i
$339$		0			0
$340$	−85.4897	−	96.5982i	−0.251440	−	0.284112i
$341$			64.7829i			0.189979i
$342$		0			0
$343$			79.1919i			0.230880i
$344$	100.551	+	58.0529i	0.292298	+	0.168759i
$345$		0			0
$346$	77.7904	+	134.737i	0.224828	+	0.389413i
$347$	94.7056	+	164.035i	0.272927	+	0.472723i	0.969610	−	0.244656i	$-0.0786750\pi$
$347$	94.7056	+	164.035i	0.272927	+	0.472723i	−0.696683	+	0.717379i	$0.745342\pi$
$348$		0			0
$349$	77.8970	−	134.922i	0.223200	−	0.386595i	−0.732578	−	0.680684i	$-0.761683\pi$
$349$	77.8970	−	134.922i	0.223200	−	0.386595i	0.955778	+	0.294089i	$0.0950162\pi$
$350$	17.3036	−	22.9775i	0.0494389	−	0.0656500i
$351$		0			0
$352$			86.9807i			0.247104i
$353$	131.693	−	228.100i	0.373069	−	0.646175i	−0.616967	−	0.786989i	$-0.711639\pi$
$353$	131.693	−	228.100i	0.373069	−	0.646175i	0.990036	+	0.140814i	$0.0449721\pi$
$354$		0			0
$355$	−69.5310	−	341.484i	−0.195862	−	0.961928i
$356$	−238.181	+	137.514i	−0.669049	+	0.386275i
$357$		0			0
$358$	−145.018	−	83.7264i	−0.405079	−	0.233873i
$359$			79.6346i			0.221823i	0.993830	+	0.110912i	$0.0353771\pi$
$359$			79.6346i			0.221823i	−0.993830	+	0.110912i	$0.964623\pi$
$360$		0			0
$361$	−359.456			−0.995723
$362$	−121.903	+	211.142i	−0.336749	+	0.583266i
$363$		0			0
$364$	4.79394	+	8.30335i	0.0131702	+	0.0228114i
$365$	−89.4039	−	439.085i	−0.244942	−	1.20297i
$366$		0			0
$367$	412.188	+	237.977i	1.12313	+	0.648438i	0.942197	−	0.335058i	$-0.108756\pi$
$367$	412.188	+	237.977i	1.12313	+	0.648438i	0.180930	+	0.983496i	$0.442089\pi$
$368$	19.1960			0.0521629
$369$		0			0
$370$	471.529	+	157.690i	1.27440	+	0.426189i
$371$	44.9012	+	25.9237i	0.121028	+	0.0698753i
$372$		0			0
$373$	−53.5064	+	30.8919i	−0.143449	+	0.0828201i	−0.570007	−	0.821640i	$-0.693059\pi$
$373$	−53.5064	+	30.8919i	−0.143449	+	0.0828201i	0.426558	+	0.904460i	$0.359726\pi$
$374$	242.922	−	140.251i	0.649523	−	0.375002i
$375$		0			0
$376$	−112.853	+	195.467i	−0.300140	+	0.519859i
$377$	−251.470			−0.667030
$378$		0			0
$379$	−142.345			−0.375581			−0.187791	−	0.982209i	$-0.560133\pi$
$379$	−142.345			−0.375581			−0.187791	+	0.982209i	$0.560133\pi$
$380$	−8.23543	−	9.30555i	−0.0216722	−	0.0244883i
$381$		0			0
$382$	354.433	−	204.632i	0.927835	−	0.535686i
$383$	178.760	+	309.621i	0.466736	+	0.808410i	0.999278	−	0.0379931i	$-0.0120965\pi$
$383$	178.760	+	309.621i	0.466736	+	0.808410i	−0.532542	+	0.846404i	$0.678763\pi$
$384$		0			0
$385$	41.4531	+	46.8395i	0.107670	+	0.121661i
$386$		−	180.783i		−	0.468350i
$387$		0			0
$388$		−	181.260i		−	0.467164i
$389$	356.005	+	205.539i	0.915179	+	0.528379i	0.882094	−	0.471074i	$-0.156133\pi$
$389$	356.005	+	205.539i	0.915179	+	0.528379i	0.0330850	+	0.999453i	$0.489467\pi$
$390$		0			0
$391$	−30.9523	−	53.6109i	−0.0791618	−	0.137112i
$392$	−68.3604	−	118.404i	−0.174389	−	0.302050i
$393$		0			0
$394$	198.283	−	343.436i	0.503256	−	0.871665i
$395$	−212.647	+	635.863i	−0.538346	+	1.60978i
$396$		0			0
$397$			457.462i			1.15230i	0.817345	+	0.576149i	$0.195445\pi$
$397$			457.462i			1.15230i	−0.817345	+	0.576149i	$0.804555\pi$
$398$	−110.610	+	191.582i	−0.277915	+	0.481363i
$399$		0			0
$400$	−12.1561	+	99.2584i	−0.0303902	+	0.248146i
$401$	404.679	−	233.642i	1.00917	−	0.582647i	0.0982247	−	0.995164i	$-0.468684\pi$
$401$	404.679	−	233.642i	1.00917	−	0.582647i	0.910950	+	0.412517i	$0.135350\pi$
$402$		0			0
$403$	−21.5000	−	12.4130i	−0.0533498	−	0.0308015i
$404$		−	99.4396i		−	0.246138i
$405$		0			0
$406$	−49.1026			−0.120942
$407$	−540.583	+	936.317i	−1.32821	+	2.30053i
$408$		0			0
$409$	224.287	+	388.476i	0.548378	+	0.949819i	0.998386	+	0.0567946i	$0.0180880\pi$
$409$	224.287	+	388.476i	0.548378	+	0.949819i	−0.450007	+	0.893025i	$0.648579\pi$
$410$	9.93642	+	48.8002i	0.0242352	+	0.119025i
$411$		0			0
$412$	−223.164	−	128.844i	−0.541661	−	0.312728i
$413$	29.8133			0.0721871
$414$		0			0
$415$	172.889	−	516.979i	0.416601	−	1.24573i
$416$	−28.8669	−	16.6663i	−0.0693916	−	0.0400633i
$417$		0			0
$418$	23.4013	−	13.5107i	0.0559839	−	0.0323223i
$419$	−312.492	+	180.417i	−0.745804	+	0.430590i	−0.824176	−	0.566334i	$-0.808361\pi$
$419$	−312.492	+	180.417i	−0.745804	+	0.430590i	0.0783720	+	0.996924i	$0.475028\pi$
$420$		0			0
$421$	−178.529	+	309.222i	−0.424060	+	0.734494i	−0.996332	−	0.0855699i	$-0.972729\pi$
$421$	−178.529	+	309.222i	−0.424060	+	0.734494i	0.572272	+	0.820064i	$0.306062\pi$
$422$	31.8305			0.0754278
$423$		0			0
$424$	−180.250			−0.425117
$425$	296.812	−	126.098i	0.698381	−	0.296701i
$426$		0			0
$427$	−58.4384	+	33.7394i	−0.136858	+	0.0790151i
$428$	6.42641	+	11.1309i	0.0150150	+	0.0260067i
$429$		0			0
$430$	−217.366	+	192.369i	−0.505501	+	0.447370i
$431$			655.947i			1.52192i	0.648800	+	0.760959i	$0.275271\pi$
$431$			655.947i			1.52192i	−0.648800	+	0.760959i	$0.724729\pi$
$432$		0			0
$433$		−	164.372i		−	0.379612i	−0.981822	−	0.189806i	$-0.939214\pi$
$433$		−	164.372i		−	0.379612i	0.981822	−	0.189806i	$-0.0607859\pi$
$434$	−4.19813	−	2.42379i	−0.00967311	−	0.00558477i
$435$		0			0
$436$	−108.279	−	187.545i	−0.248347	−	0.430149i
$437$	−2.98171	−	5.16447i	−0.00682314	−	0.0118180i
$438$		0			0
$439$	66.1432	−	114.563i	0.150668	−	0.260964i	−0.780805	−	0.624774i	$-0.785191\pi$
$439$	66.1432	−	114.563i	0.150668	−	0.260964i	0.931473	+	0.363810i	$0.118524\pi$
$440$	−206.225	−	68.9664i	−0.468694	−	0.156742i
$441$		0			0
$442$			107.494i			0.243198i
$443$	227.743	−	394.462i	0.514092	−	0.890433i	−0.485775	−	0.874084i	$-0.661462\pi$
$443$	227.743	−	394.462i	0.514092	−	0.890433i	0.999866	−	0.0163489i	$-0.00520425\pi$
$444$		0			0
$445$	−137.184	−	673.746i	−0.308279	−	1.51404i
$446$	434.572	−	250.900i	0.974376	−	0.562556i
$447$		0			0
$448$	−5.63662	−	3.25430i	−0.0125817	−	0.00726407i
$449$			415.749i			0.925944i	0.886373	+	0.462972i	$0.153217\pi$
$449$			415.749i			0.925944i	−0.886373	+	0.462972i	$0.846783\pi$
$450$		0			0
$451$	−108.294			−0.240121
$452$	−30.4264	+	52.7001i	−0.0673151	+	0.116593i
$453$		0			0
$454$	−293.518	−	508.389i	−0.646516	−	1.11980i
$455$	−23.4878	+	4.78244i	−0.0516214	+	0.0105109i
$456$		0			0
$457$	262.962	+	151.821i	0.575410	+	0.332213i	0.759307	−	0.650732i	$-0.225538\pi$
$457$	262.962	+	151.821i	0.575410	+	0.332213i	−0.183897	+	0.982946i	$0.558871\pi$
$458$	−311.439			−0.679997
$459$		0			0
$460$	−15.2203	+	45.5123i	−0.0330877	+	0.0989398i
$461$	371.343	+	214.395i	0.805516	+	0.465065i	0.845396	−	0.534140i	$-0.179364\pi$
$461$	371.343	+	214.395i	0.805516	+	0.465065i	−0.0398803	+	0.999204i	$0.512698\pi$
$462$		0			0
$463$	705.364	−	407.242i	1.52346	−	0.879572i	0.523850	−	0.851811i	$-0.324495\pi$
$463$	705.364	−	407.242i	1.52346	−	0.879572i	0.999615	−	0.0277616i	$-0.00883792\pi$
$464$	147.837	−	85.3536i	0.318614	−	0.183952i
$465$		0			0
$466$	7.09545	−	12.2897i	0.0152263	−	0.0263727i
$467$	607.118			1.30004			0.650019	−	0.759918i	$-0.274761\pi$
$467$	607.118			1.30004			0.650019	+	0.759918i	$0.274761\pi$
$468$		0			0
$469$	−72.4104			−0.154393
$470$	−373.958	−	422.551i	−0.795656	−	0.899044i
$471$		0			0
$472$	−89.7610	+	51.8235i	−0.190172	+	0.109796i
$473$	−315.593	−	546.623i	−0.667215	−	1.15565i
$474$		0			0
$475$	28.5926	−	12.1473i	0.0601950	−	0.0255734i
$476$			20.9894i			0.0440954i
$477$		0			0
$478$		−	161.734i		−	0.338355i
$479$	−297.816	−	171.944i	−0.621746	−	0.358965i	0.155802	−	0.987788i	$-0.450204\pi$
$479$	−297.816	−	171.944i	−0.621746	−	0.358965i	−0.777549	+	0.628823i	$0.783537\pi$
$480$		0			0
$481$	−207.161	−	358.814i	−0.430689	−	0.745975i
$482$	45.0574	+	78.0417i	0.0934801	+	0.161912i
$483$		0			0
$484$	115.426	−	199.924i	0.238484	−	0.413067i
$485$	429.754	+	143.720i	0.886092	+	0.296329i
$486$		0			0
$487$		−	300.759i		−	0.617576i	−0.951131	−	0.308788i	$-0.900077\pi$
$487$		−	300.759i		−	0.617576i	0.951131	−	0.308788i	$-0.0999233\pi$
$488$	117.296	−	203.163i	0.240362	−	0.416319i
$489$		0			0
$490$	334.930	−	68.1964i	0.683530	−	0.139176i
$491$	150.614	−	86.9568i	0.306749	−	0.177101i	−0.338722	−	0.940886i	$-0.609995\pi$
$491$	150.614	−	86.9568i	0.306749	−	0.177101i	0.645471	+	0.763785i	$0.276661\pi$
$492$		0			0
$493$	−476.755	−	275.254i	−0.967048	−	0.558326i
$494$			10.3551i			0.0209618i
$495$		0			0
$496$	16.8528			0.0339774
$497$	−28.3524	+	49.1078i	−0.0570470	+	0.0988084i
$498$		0			0
$499$	380.805	+	659.574i	0.763136	+	1.32179i	0.941226	+	0.337777i	$0.109675\pi$
$499$	380.805	+	659.574i	0.763136	+	1.32179i	−0.178090	+	0.984014i	$0.556992\pi$
$500$	−225.696	−	107.523i	−0.451393	−	0.215045i
$501$		0			0
$502$	281.240	+	162.374i	0.560239	+	0.323454i
$503$	280.632			0.557917			0.278959	−	0.960303i	$-0.410011\pi$
$503$	280.632			0.557917			0.278959	+	0.960303i	$0.410011\pi$
$504$		0			0
$505$	235.765	+	78.8450i	0.466860	+	0.156129i
$506$	−90.3740	−	52.1774i	−0.178605	−	0.103117i
$507$		0			0
$508$	231.619	−	133.725i	0.455943	−	0.263239i
$509$	548.347	−	316.588i	1.07730	−	0.621981i	0.147135	−	0.989116i	$-0.452995\pi$
$509$	548.347	−	316.588i	1.07730	−	0.621981i	0.930167	+	0.367136i	$0.119662\pi$
$510$		0			0
$511$	−36.4558	+	63.1434i	−0.0713422	+	0.123568i
$512$	22.6274			0.0441942
$513$		0			0
$514$	−549.037			−1.06816
$515$	482.426	−	426.948i	0.936749	−	0.829025i
$516$		0			0
$517$	1062.62	−	613.501i	2.05535	−	1.18666i
$518$	−40.4508	−	70.0628i	−0.0780903	−	0.135256i
$519$		0			0
$520$	62.4031	−	55.2269i	0.120006	−	0.106206i
$521$		−	92.3966i		−	0.177345i	−0.996061	−	0.0886723i	$-0.971738\pi$
$521$		−	92.3966i		−	0.177345i	0.996061	−	0.0886723i	$-0.0282624\pi$
$522$		0			0
$523$		−	818.552i		−	1.56511i	−0.622582	−	0.782554i	$-0.713916\pi$
$523$		−	818.552i		−	1.56511i	0.622582	−	0.782554i	$-0.286084\pi$
$524$	−107.013	−	61.7838i	−0.204223	−	0.117908i
$525$		0			0
$526$	160.426	+	277.867i	0.304993	+	0.528264i
$527$	−27.1741	−	47.0669i	−0.0515638	−	0.0893110i
$528$		0			0
$529$	252.985	−	438.183i	0.478232	−	0.828323i
$530$	142.919	−	427.360i	0.269658	−	0.806340i
$531$		0			0
$532$			2.02196i			0.00380068i
$533$	20.7502	−	35.9404i	0.0389310	−	0.0674304i
$534$		0			0
$535$	−31.4860	+	6.41099i	−0.0588523	+	0.0119832i
$536$	218.011	−	125.869i	0.406737	−	0.234830i
$537$		0			0
$538$	277.738	+	160.352i	0.516241	+	0.298052i
$539$			743.254i			1.37895i
$540$		0			0
$541$	−376.985			−0.696830			−0.348415	−	0.937340i	$-0.613280\pi$
$541$	−376.985			−0.696830			−0.348415	+	0.937340i	$0.613280\pi$
$542$	−228.317	+	395.457i	−0.421250	+	0.729626i
$543$		0			0
$544$	−36.4853	−	63.1944i	−0.0670685	−	0.116166i
$545$	530.511	−	108.019i	0.973414	−	0.198201i
$546$		0			0
$547$	−292.151	−	168.673i	−0.534096	−	0.308360i	0.208587	−	0.978004i	$-0.433114\pi$
$547$	−292.151	−	168.673i	−0.534096	−	0.308360i	−0.742683	+	0.669643i	$0.766447\pi$
$548$	327.838			0.598244
$549$		0			0
$550$	327.029	−	434.263i	0.594599	−	0.789570i
$551$	−45.9270	−	26.5160i	−0.0833520	−	0.0481233i
$552$		0			0
$553$	94.4806	−	54.5484i	0.170851	−	0.0986408i
$554$	245.640	−	141.820i	0.443393	−	0.255993i
$555$		0			0
$556$	−182.250	+	315.666i	−0.327787	+	0.567744i
$557$	−303.338			−0.544593			−0.272296	−	0.962213i	$-0.587783\pi$
$557$	−303.338			−0.544593			−0.272296	+	0.962213i	$0.587783\pi$
$558$		0			0
$559$	241.882			0.432705
$560$	12.1850	−	10.7837i	0.0217589	−	0.0192566i
$561$		0			0
$562$	−156.805	+	90.5311i	−0.279012	+	0.161087i
$563$	117.047	+	202.731i	0.207898	+	0.360090i	0.951052	−	0.309030i	$-0.100004\pi$
$563$	117.047	+	202.731i	0.207898	+	0.360090i	−0.743154	+	0.669120i	$0.766671\pi$
$564$		0			0
$565$	−100.823	−	113.924i	−0.178449	−	0.201636i
$566$		−	594.302i		−	1.05000i
$567$		0			0
$568$		−	197.136i		−	0.347071i
$569$	−57.6129	−	33.2628i	−0.101253	−	0.0584584i	0.448518	−	0.893774i	$-0.351952\pi$
$569$	−57.6129	−	33.2628i	−0.101253	−	0.0584584i	−0.549771	+	0.835315i	$0.685285\pi$
$570$		0			0
$571$	−557.768	−	966.082i	−0.976826	−	1.69191i	−0.673773	−	0.738939i	$-0.735327\pi$
$571$	−557.768	−	966.082i	−0.976826	−	1.69191i	−0.303053	−	0.952974i	$-0.598006\pi$
$572$	90.6030	+	156.929i	0.158397	+	0.274351i
$573$		0			0
$574$	4.05173	−	7.01781i	0.00705877	−	0.0122261i
$575$	−95.8385	−	72.1728i	−0.166676	−	0.125518i
$576$		0			0
$577$		−	957.356i		−	1.65920i	−0.558361	−	0.829598i	$-0.688570\pi$
$577$		−	957.356i		−	1.65920i	0.558361	−	0.829598i	$-0.311430\pi$
$578$	86.6934	−	150.157i	0.149989	−	0.259788i
$579$		0			0
$580$	85.1488	+	418.187i	0.146808	+	0.721012i
$581$	−76.8161	+	44.3498i	−0.132214	+	0.0763335i
$582$		0			0
$583$	848.610	+	489.945i	1.45559	+	0.840387i
$584$		−	253.480i		−	0.434042i
$585$		0			0
$586$	−194.360			−0.331673
$587$	−39.9487	+	69.1932i	−0.0680557	+	0.117876i	−0.898045	−	0.439903i	$-0.855013\pi$
$587$	−39.9487	+	69.1932i	−0.0680557	+	0.117876i	0.829990	+	0.557779i	$0.188346\pi$
$588$		0			0
$589$	−2.61775	−	4.53407i	−0.00444440	−	0.00769792i
$590$	−51.6992	−	253.908i	−0.0876258	−	0.430352i
$591$		0			0
$592$	243.576	+	140.629i	0.411446	+	0.237549i
$593$	213.831			0.360593			0.180296	−	0.983612i	$-0.442294\pi$
$593$	213.831			0.360593			0.180296	+	0.983612i	$0.442294\pi$
$594$		0			0
$595$	−49.7645	−	16.6424i	−0.0836378	−	0.0279704i
$596$	−328.284	−	189.535i	−0.550813	−	0.318012i
$597$		0			0
$598$	34.6330	−	19.9954i	0.0579147	−	0.0334371i
$599$	−792.840	+	457.746i	−1.32361	+	0.764184i	−0.984302	−	0.176492i	$-0.943525\pi$
$599$	−792.840	+	457.746i	−1.32361	+	0.764184i	−0.339304	+	0.940677i	$0.610192\pi$
$600$		0			0
$601$	−239.713	+	415.195i	−0.398857	+	0.690841i	−0.993585	−	0.113086i	$-0.963926\pi$
$601$	−239.713	+	415.195i	−0.398857	+	0.690841i	0.594728	+	0.803927i	$0.297260\pi$
$602$	47.2304			0.0784559
$603$		0			0
$604$	−226.676			−0.375292
$605$	382.486	+	432.187i	0.632209	+	0.714359i
$606$		0			0
$607$	190.433	−	109.946i	0.313727	−	0.181131i	−0.334866	−	0.942266i	$-0.608691\pi$
$607$	190.433	−	109.946i	0.313727	−	0.181131i	0.648593	+	0.761135i	$0.275358\pi$
$608$	−3.51472	−	6.08767i	−0.00578079	−	0.0100126i
$609$		0			0
$610$	388.683	+	439.189i	0.637186	+	0.719982i
$611$			470.210i			0.769575i
$612$		0			0
$613$			862.066i			1.40631i	0.711038	+	0.703154i	$0.248225\pi$
$613$			862.066i			1.40631i	−0.711038	+	0.703154i	$0.751775\pi$
$614$	144.335	+	83.3316i	0.235073	+	0.135719i
$615$		0			0
$616$	17.6913	+	30.6423i	0.0287197	+	0.0497440i
$617$	347.712	+	602.254i	0.563552	+	0.976101i	0.997183	+	0.0750103i	$0.0238990\pi$
$617$	347.712	+	602.254i	0.563552	+	0.976101i	−0.433631	+	0.901091i	$0.642768\pi$
$618$		0			0
$619$	256.037	−	443.468i	0.413629	−	0.716427i	−0.581654	−	0.813436i	$-0.697594\pi$
$619$	256.037	−	443.468i	0.413629	−	0.716427i	0.995283	+	0.0970091i	$0.0309276\pi$
$620$	−13.3625	+	39.9569i	−0.0215524	+	0.0644466i
$621$		0			0
$622$		−	706.153i		−	1.13529i
$623$	−55.9390	+	96.8892i	−0.0897898	+	0.155520i
$624$		0			0
$625$	433.882	−	449.857i	0.694211	−	0.719771i
$626$	−602.337	+	347.759i	−0.962199	+	0.555526i
$627$		0			0
$628$	196.048	+	113.189i	0.312179	+	0.180237i
$629$		−	907.020i		−	1.44200i
$630$		0			0
$631$	−643.375			−1.01961			−0.509806	−	0.860290i	$-0.670283\pi$
$631$	−643.375			−1.01961			−0.509806	+	0.860290i	$0.670283\pi$
$632$	−189.640	+	328.465i	−0.300063	+	0.519724i
$633$		0			0
$634$	−170.695	−	295.652i	−0.269235	−	0.466328i
$635$	133.405	+	655.183i	0.210086	+	1.03178i
$636$		0			0
$637$	−246.669	−	142.415i	−0.387236	−	0.223571i
$638$	−928.014			−1.45457
$639$		0			0
$640$	−17.9411	+	53.6481i	−0.0280330	+	0.0838251i
$641$	170.542	+	98.4625i	0.266056	+	0.153608i	0.627094	−	0.778944i	$-0.284244\pi$
$641$	170.542	+	98.4625i	0.266056	+	0.153608i	−0.361038	+	0.932551i	$0.617578\pi$
$642$		0			0
$643$	−205.208	+	118.477i	−0.319141	+	0.184256i	−0.651010	−	0.759069i	$-0.725654\pi$
$643$	−205.208	+	118.477i	−0.319141	+	0.184256i	0.331868	+	0.943326i	$0.392321\pi$
$644$	6.76252	−	3.90434i	0.0105008	−	0.00606264i
$645$		0			0
$646$	−11.3345	+	19.6320i	−0.0175457	+	0.0303900i
$647$	−17.3818			−0.0268653			−0.0134326	−	0.999910i	$-0.504276\pi$
$647$	−17.3818			−0.0268653			−0.0134326	+	0.999910i	$0.504276\pi$
$648$		0			0
$649$	563.456			0.868191
$650$	81.4602	+	191.743i	0.125323	+	0.294989i
$651$		0			0
$652$	263.988	−	152.414i	0.404890	−	0.233763i
$653$	−392.852	−	680.439i	−0.601611	−	1.04202i	−0.992577	−	0.121615i	$-0.961193\pi$
$653$	−392.852	−	680.439i	−0.601611	−	1.04202i	0.390967	−	0.920405i	$-0.372141\pi$
$654$		0			0
$655$	231.335	−	204.732i	0.353183	−	0.312568i
$656$			28.1720i			0.0429451i
$657$		0			0
$658$			91.8143i			0.139535i
$659$	431.945	+	249.384i	0.655455	+	0.378427i	0.790543	−	0.612406i	$-0.209798\pi$
$659$	431.945	+	249.384i	0.655455	+	0.378427i	−0.135088	+	0.990834i	$0.543132\pi$
$660$		0			0
$661$	−151.566	−	262.521i	−0.229299	−	0.397157i	0.728302	−	0.685257i	$-0.240310\pi$
$661$	−151.566	−	262.521i	−0.229299	−	0.397157i	−0.957600	+	0.288100i	$0.906977\pi$
$662$	62.0904	+	107.544i	0.0937922	+	0.162453i
$663$		0			0
$664$	154.184	−	267.054i	0.232204	−	0.402190i
$665$	−4.79394	−	1.60320i	−0.00720893	−	0.00241083i
$666$		0			0
$667$			204.805i			0.307055i
$668$	105.853	−	183.342i	0.158462	−	0.274465i
$669$		0			0
$670$	125.567	+	616.690i	0.187413	+	0.920433i
$671$	−1104.46	+	637.658i	−1.64599	+	0.950310i
$672$		0			0
$673$	−401.085	−	231.567i	−0.595966	−	0.344081i	0.171487	−	0.985186i	$-0.445143\pi$
$673$	−401.085	−	231.567i	−0.595966	−	0.344081i	−0.767453	+	0.641105i	$0.778476\pi$
$674$		−	639.420i		−	0.948694i
$675$		0			0
$676$	268.558			0.397276
$677$	155.532	−	269.389i	0.229737	−	0.397916i	−0.727993	−	0.685584i	$-0.759547\pi$
$677$	155.532	−	269.389i	0.229737	−	0.397916i	0.957730	+	0.287668i	$0.0928801\pi$
$678$		0			0
$679$	−36.8671	−	63.8557i	−0.0542962	−	0.0940437i
$680$	178.758	−	36.3978i	0.262880	−	0.0535261i
$681$		0			0
$682$	−79.3425	−	45.8084i	−0.116338	−	0.0671678i
$683$	−232.009			−0.339691			−0.169846	−	0.985471i	$-0.554327\pi$
$683$	−232.009			−0.339691			−0.169846	+	0.985471i	$0.554327\pi$
$684$		0			0
$685$	−259.940	+	777.281i	−0.379475	+	1.13472i
$686$	−96.9898	−	55.9971i	−0.141385	−	0.0816284i
$687$		0			0
$688$	−142.200	+	82.0993i	−0.206686	+	0.119330i
$689$	−325.203	+	187.756i	−0.471993	+	0.272506i
$690$		0			0
$691$	276.452	−	478.829i	0.400075	−	0.692950i	−0.593660	−	0.804716i	$-0.702317\pi$
$691$	276.452	−	478.829i	0.400075	−	0.692950i	0.993735	+	0.111766i	$0.0356507\pi$
$692$	−220.024			−0.317954
$693$		0			0
$694$	−267.868			−0.385977
$695$	−603.918	−	682.391i	−0.868947	−	0.981858i
$696$		0			0
$697$	78.6794	−	45.4256i	0.112883	−	0.0651730i
$698$	110.163	+	190.808i	0.157827	+	0.273364i
$699$		0			0
$700$	15.9061	+	37.4401i	0.0227230	+	0.0534858i
$701$		−	250.274i		−	0.357024i	−0.983938	−	0.178512i	$-0.942872\pi$
$701$		−	250.274i		−	0.357024i	0.983938	−	0.178512i	$-0.0571284\pi$
$702$		0			0
$703$		−	87.3755i		−	0.124290i
$704$	−106.529	−	61.5047i	−0.151320	−	0.0873646i
$705$		0			0
$706$	186.243	+	322.582i	0.263800	+	0.456915i
$707$	−20.2254	−	35.0314i	−0.0286074	−	0.0495494i
$708$		0			0
$709$	−585.286	+	1013.75i	−0.825510	+	1.42982i	0.0760195	+	0.997106i	$0.475779\pi$
$709$	−585.286	+	1013.75i	−0.825510	+	1.42982i	−0.901529	+	0.432718i	$0.857554\pi$
$710$	467.397	+	156.308i	0.658306	+	0.220152i
$711$		0			0
$712$		−	388.949i		−	0.546276i
$713$	−10.1096	+	17.5103i	−0.0141789	+	0.0245586i
$714$		0			0
$715$	−443.907	+	90.3857i	−0.620849	+	0.126414i
$716$	205.087	−	118.407i	0.286434	−	0.165373i
$717$		0			0
$718$	−97.5321	−	56.3102i	−0.135839	−	0.0784264i
$719$			168.127i			0.233834i	0.993142	+	0.116917i	$0.0373012\pi$
$719$			168.127i			0.233834i	−0.993142	+	0.116917i	$0.962699\pi$
$720$		0			0
$721$	−104.824			−0.145387
$722$	254.174	−	440.242i	0.352041	−	0.609753i
$723$		0			0
$724$	−172.397	−	298.600i	−0.238117	−	0.412431i
$725$	−1059.01	−	129.696i	−1.46070	−	0.178891i
$726$		0			0
$727$	−331.545	−	191.417i	−0.456045	−	0.263298i	0.254335	−	0.967116i	$-0.418143\pi$
$727$	−331.545	−	191.417i	−0.456045	−	0.263298i	−0.710380	+	0.703819i	$0.751477\pi$
$728$	−13.5593			−0.0186254
$729$		0			0
$730$	600.985	+	200.983i	0.823267	+	0.275319i
$731$	458.577	+	264.760i	0.627329	+	0.362188i
$732$		0			0
$733$	1215.10	−	701.541i	1.65771	−	0.957082i	0.683948	−	0.729531i	$-0.260262\pi$
$733$	1215.10	−	701.541i	1.65771	−	0.957082i	0.973766	−	0.227550i	$-0.0730716\pi$
$734$	−582.921	+	336.550i	−0.794171	+	0.458515i
$735$		0			0
$736$	−13.5736	+	23.5102i	−0.0184424	+	0.0319431i
$737$	−1368.52			−1.85688
$738$		0			0
$739$	899.125			1.21668			0.608339	−	0.793677i	$-0.291836\pi$
$739$	899.125			1.21668			0.608339	+	0.793677i	$0.291836\pi$
$740$	−526.551	+	465.999i	−0.711556	+	0.629729i
$741$		0			0
$742$	−63.4999	+	36.6617i	−0.0855794	+	0.0494093i
$743$	−158.294	−	274.172i	−0.213046	−	0.369007i	0.739620	−	0.673025i	$-0.235005\pi$
$743$	−158.294	−	274.172i	−0.213046	−	0.369007i	−0.952666	+	0.304017i	$0.901672\pi$
$744$		0			0
$745$	709.669	−	628.059i	0.952576	−	0.843032i
$746$		−	87.3755i		−	0.117125i
$747$		0			0
$748$			396.689i			0.530334i
$749$	4.52790	+	2.61418i	0.00604526	+	0.00349023i
$750$		0			0
$751$	143.216	+	248.058i	0.190701	+	0.330304i	0.945483	−	0.325672i	$-0.105591\pi$
$751$	143.216	+	248.058i	0.190701	+	0.330304i	−0.754782	+	0.655976i	$0.772257\pi$
$752$	−159.598	−	276.432i	−0.212231	−	0.367595i
$753$		0			0
$754$	177.816	−	307.987i	0.235831	−	0.408470i
$755$	179.730	−	537.434i	0.238053	−	0.711833i
$756$		0			0
$757$			783.221i			1.03464i	0.855793	+	0.517319i	$0.173070\pi$
$757$			783.221i			1.03464i	−0.855793	+	0.517319i	$0.826930\pi$
$758$	100.653	−	174.337i	0.132788	−	0.229996i
$759$		0			0
$760$	17.2203	−	3.50629i	0.0226582	−	0.00461354i
$761$	893.662	−	515.956i	1.17433	−	0.677997i	0.219631	−	0.975583i	$-0.429515\pi$
$761$	893.662	−	515.956i	1.17433	−	0.677997i	0.954695	+	0.297586i	$0.0961814\pi$
$762$		0			0
$763$	−76.2910	−	44.0467i	−0.0999883	−	0.0577282i
$764$			578.787i			0.757574i
$765$		0			0
$766$	−505.609			−0.660064
$767$	−107.963	+	186.998i	−0.140761	+	0.243805i
$768$		0			0
$769$	415.625	+	719.883i	0.540475	+	0.936129i	0.998877	+	0.0473845i	$0.0150886\pi$
$769$	415.625	+	719.883i	0.540475	+	0.936129i	−0.458402	+	0.888745i	$0.651578\pi$
$770$	−86.6782	+	17.6489i	−0.112569	+	0.0229207i
$771$		0			0
$772$	221.413	+	127.833i	0.286805	+	0.165587i
$773$	395.360			0.511462			0.255731	−	0.966748i	$-0.417684\pi$
$773$	395.360			0.511462			0.255731	+	0.966748i	$0.417684\pi$
$774$		0			0
$775$	−84.1400	−	63.3631i	−0.108568	−	0.0817588i
$776$	221.997	+	128.170i	0.286078	+	0.165167i
$777$		0			0
$778$	−503.466	+	290.676i	−0.647129	+	0.373620i
$779$	7.57939	−	4.37596i	0.00972964	−	0.00561741i
$780$		0			0
$781$	−535.846	+	928.112i	−0.686102	+	1.18836i
$782$	87.5462			0.111952
$783$		0			0
$784$	193.352			0.246623
$785$	−423.808	+	375.071i	−0.539883	+	0.477797i
$786$		0			0
$787$	−497.037	+	286.965i	−0.631559	+	0.364631i	−0.781356	−	0.624086i	$-0.785472\pi$
$787$	−497.037	+	286.965i	−0.631559	+	0.364631i	0.149796	+	0.988717i	$0.452138\pi$
$788$	280.414	+	485.692i	0.355856	+	0.616360i
$789$		0			0
$790$	−628.405	−	710.061i	−0.795450	−	0.898811i
$791$			24.7542i			0.0312948i
$792$		0			0
$793$		−	488.725i		−	0.616299i
$794$	−560.275	−	323.475i	−0.705636	−	0.407399i
$795$		0			0
$796$	−156.426	−	270.938i	−0.196516	−	0.340375i
$797$	704.197	+	1219.70i	0.883560	+	1.53037i	0.847356	+	0.531026i	$0.178193\pi$
$797$	704.197	+	1219.70i	0.883560	+	1.53037i	0.0362039	+	0.999344i	$0.488473\pi$
$798$		0			0
$799$	−514.683	+	891.458i	−0.644159	+	1.11572i
$800$	−112.971	−	85.0744i	−0.141213	−	0.106343i
$801$		0			0
$802$			660.838i			0.823988i
$803$	−688.997	+	1193.38i	−0.858029	+	1.48615i
$804$		0			0
$805$	3.89497	+	19.1292i	0.00483848	+	0.0237630i
$806$	30.4055	−	17.5546i	0.0377240	−	0.0217800i
$807$		0			0
$808$	121.788	+	70.3144i	0.150728	+	0.0870228i
$809$			105.645i			0.130587i	0.997866	+	0.0652936i	$0.0207984\pi$
$809$			105.645i			0.130587i	−0.997866	+	0.0652936i	$0.979202\pi$
$810$		0			0
$811$	−1090.81			−1.34502			−0.672508	−	0.740090i	$-0.734783\pi$
$811$	−1090.81			−1.34502			−0.672508	+	0.740090i	$0.734783\pi$
$812$	34.7208	−	60.1382i	0.0427596	−	0.0740618i
$813$		0			0
$814$	−764.500	−	1324.15i	−0.939189	−	1.62672i
$815$	152.048	+	746.746i	0.186562	+	0.916253i
$816$		0			0
$817$	44.1759	+	25.5050i	0.0540709	+	0.0312178i
$818$	−634.379			−0.775524
$819$		0			0
$820$	−66.7939	−	22.3374i	−0.0814560	−	0.0272407i
$821$	−737.249	−	425.651i	−0.897990	−	0.518454i	−0.0214421	−	0.999770i	$-0.506826\pi$
$821$	−737.249	−	425.651i	−0.897990	−	0.518454i	−0.876547	+	0.481316i	$0.840159\pi$
$822$		0			0
$823$	−970.057	+	560.062i	−1.17868	+	0.680513i	−0.955710	−	0.294311i	$-0.904910\pi$
$823$	−970.057	+	560.062i	−1.17868	+	0.680513i	−0.222974	+	0.974824i	$0.571576\pi$
$824$	315.602	−	182.213i	0.383012	−	0.221132i
$825$		0			0
$826$	−21.0812	+	36.5137i	−0.0255220	+	0.0442054i
$827$	1214.63			1.46871			0.734357	−	0.678763i	$-0.237484\pi$
$827$	1214.63			1.46871			0.734357	+	0.678763i	$0.237484\pi$
$828$		0			0
$829$	1495.22			1.80364			0.901821	−	0.432111i	$-0.142231\pi$
$829$	1495.22			1.80364			0.901821	+	0.432111i	$0.142231\pi$
$830$	510.916	+	577.305i	0.615561	+	0.695548i
$831$		0			0
$832$	40.8240	−	23.5697i	0.0490673	−	0.0283290i
$833$	−311.769	−	539.999i	−0.374272	−	0.648258i
$834$		0			0
$835$	350.763	+	396.341i	0.420075	+	0.474660i
$836$			38.2141i			0.0457106i
$837$		0			0
$838$		−	510.297i		−	0.608946i
$839$	−401.719	−	231.933i	−0.478807	−	0.276439i	0.241112	−	0.970497i	$-0.422488\pi$
$839$	−401.719	−	231.933i	−0.478807	−	0.276439i	−0.719919	+	0.694058i	$0.755821\pi$
$840$		0			0
$841$	490.154	+	848.971i	0.582823	+	1.00948i
$842$	−252.479	−	437.306i	−0.299856	−	0.519366i
$843$		0			0
$844$	−22.5076	+	38.9843i	−0.0266677	+	0.0461899i
$845$	−212.938	+	636.734i	−0.251998	+	0.753531i
$846$		0			0
$847$		−	93.9081i		−	0.110871i
$848$	127.456	−	220.760i	0.150302	−	0.260330i
$849$		0			0
$850$	−55.4398	+	452.684i	−0.0652233	+	0.532569i
$851$	−292.230	+	168.719i	−0.343396	+	0.198260i
$852$		0			0
$853$	−429.419	−	247.925i	−0.503422	−	0.290651i	0.226704	−	0.973964i	$-0.427205\pi$
$853$	−429.419	−	247.925i	−0.503422	−	0.290651i	−0.730125	+	0.683313i	$0.760538\pi$
$854$		−	95.4295i		−	0.111744i
$855$		0			0
$856$	−18.1766			−0.0212344
$857$	852.216	−	1476.08i	0.994418	−	1.72238i	0.405834	−	0.913947i	$-0.366981\pi$
$857$	852.216	−	1476.08i	0.994418	−	1.72238i	0.588584	−	0.808436i	$-0.299686\pi$
$858$		0			0
$859$	103.761	+	179.720i	0.120793	+	0.209220i	0.920081	−	0.391729i	$-0.128123\pi$
$859$	103.761	+	179.720i	0.120793	+	0.209220i	−0.799287	+	0.600949i	$0.794790\pi$
$860$	−81.9023	−	402.243i	−0.0952352	−	0.467724i
$861$		0			0
$862$	−803.367	−	463.824i	−0.931981	−	0.538079i
$863$	−117.426			−0.136068			−0.0680338	−	0.997683i	$-0.521673\pi$
$863$	−117.426			−0.136068			−0.0680338	+	0.997683i	$0.521673\pi$
$864$		0			0
$865$	174.456	−	521.663i	0.201683	−	0.603079i
$866$	201.314	+	116.229i	0.232464	+	0.134213i
$867$		0			0
$868$	5.93705	−	3.42776i	0.00683992	−	0.00394903i
$869$	1785.63	−	1030.94i	2.05482	−	1.18635i
$870$		0			0
$871$	262.221	−	454.180i	0.301058	−	0.521447i
$872$	306.260			0.351215
$873$		0			0
$874$	8.43355			0.00964937
$875$	−101.380	+	8.02631i	−0.115863	+	0.00917293i
$876$		0			0
$877$	−786.903	+	454.319i	−0.897267	+	0.518037i	−0.876312	−	0.481743i	$-0.840004\pi$
$877$	−786.903	+	454.319i	−0.897267	+	0.518037i	−0.0209544	+	0.999780i	$0.506670\pi$
$878$	93.5406	+	162.017i	0.106538	+	0.184530i
$879$		0			0
$880$	230.290	−	203.807i	0.261693	−	0.231599i
$881$		−	1226.54i		−	1.39221i	−0.717941	−	0.696104i	$-0.754915\pi$
$881$		−	1226.54i		−	1.39221i	0.717941	−	0.696104i	$-0.245085\pi$
$882$		0			0
$883$			760.022i			0.860728i	0.902656	+	0.430364i	$0.141615\pi$
$883$			760.022i			0.860728i	−0.902656	+	0.430364i	$0.858385\pi$
$884$	−131.652	−	76.0094i	−0.148928	−	0.0859835i
$885$		0			0
$886$	322.077	+	557.853i	0.363518	+	0.629631i
$887$	−298.771	−	517.487i	−0.336833	−	0.583413i	0.647002	−	0.762488i	$-0.276023\pi$
$887$	−298.771	−	517.487i	−0.336833	−	0.583413i	−0.983835	+	0.179076i	$0.942689\pi$
$888$		0			0
$889$	54.3978	−	94.2198i	0.0611899	−	0.105984i
$890$	922.171	+	308.395i	1.03615	+	0.346511i
$891$		0			0
$892$			709.653i			0.795575i
$893$	−49.5807	+	85.8764i	−0.0555215	+	0.0961661i
$894$		0			0
$895$	118.123	+	580.132i	0.131981	+	0.648192i
$896$	7.97138	−	4.60228i	0.00889663	−	0.00513647i
$897$		0			0
$898$	−509.186	−	293.979i	−0.567022	−	0.327370i
$899$			179.806i			0.200007i
$900$		0			0
$901$	−822.058			−0.912384
$902$	76.5757	−	132.633i	0.0848954	−	0.147043i
$903$		0			0
$904$	−43.0294	−	74.5292i	−0.0475989	−	0.0824438i
$905$	844.654	−	171.983i	0.933319	−	0.190037i
$906$		0			0
$907$	1479.39	+	854.128i	1.63108	+	0.941707i	0.983759	+	0.179492i	$0.0574453\pi$
$907$	1479.39	+	854.128i	1.63108	+	0.941707i	0.647324	+	0.762215i	$0.275888\pi$
$908$	830.195			0.914312
$909$		0			0
$910$	10.7511	−	32.1482i	0.0118144	−	0.0353277i
$911$	−1240.28	−	716.074i	−1.36145	−	0.786031i	−0.371630	−	0.928381i	$-0.621201\pi$
$911$	−1240.28	−	716.074i	−1.36145	−	0.786031i	−0.989816	+	0.142350i	$0.954534\pi$
$912$		0			0
$913$	−1451.78	+	838.188i	−1.59013	+	0.918060i
$914$	−371.885	+	214.708i	−0.406876	+	0.234910i
$915$		0			0
$916$	220.220	−	381.433i	0.240415	−	0.416411i
$917$	−50.2658			−0.0548155
$918$		0			0
$919$	−244.398			−0.265939			−0.132969	−	0.991120i	$-0.542451\pi$
$919$	−244.398			−0.265939			−0.132969	+	0.991120i	$0.542451\pi$
$920$	−44.9786	−	50.8231i	−0.0488898	−	0.0552425i
$921$		0			0
$922$	−525.158	+	303.200i	−0.569586	+	0.328851i
$923$	−205.346	−	355.670i	−0.222477	−	0.385341i
$924$		0			0
$925$	−687.353	−	1617.91i	−0.743085	−	1.74909i
$926$			1151.85i			1.24390i
$927$		0			0
$928$			241.416i			0.260147i
$929$	325.628	+	188.002i	0.350515	+	0.202370i	0.664912	−	0.746922i	$-0.268469\pi$
$929$	325.628	+	188.002i	0.350515	+	0.202370i	−0.314397	+	0.949292i	$0.601802\pi$
$930$		0			0
$931$	−30.0334	−	52.0194i	−0.0322593	−	0.0558748i
$932$	10.0345	+	17.3802i	0.0107666	+	0.0186483i
$933$		0			0
$934$	−429.297	+	743.564i	−0.459633	+	0.796107i
$935$	−940.524	−	314.532i	−1.00591	−	0.336398i
$936$		0			0
$937$			412.076i			0.439782i	0.975524	+	0.219891i	$0.0705701\pi$
$937$			412.076i			0.439782i	−0.975524	+	0.219891i	$0.929430\pi$
$938$	51.2019	−	88.6843i	0.0545862	−	0.0945461i
$939$		0			0
$940$	781.945	−	159.215i	0.831857	−	0.169378i
$941$	289.754	−	167.289i	0.307921	−	0.177778i	−0.338075	−	0.941119i	$-0.609776\pi$
$941$	289.754	−	167.289i	0.307921	−	0.177778i	0.645996	+	0.763341i	$0.276442\pi$
$942$		0			0
$943$	−29.2711	−	16.8997i	−0.0310404	−	0.0179212i
$944$		−	146.579i		−	0.155274i
$945$		0			0
$946$	892.632			0.943585
$947$	305.566	−	529.256i	0.322667	−	0.558876i	−0.658370	−	0.752694i	$-0.728754\pi$
$947$	305.566	−	529.256i	0.322667	−	0.558876i	0.981037	+	0.193818i	$0.0620871\pi$
$948$		0			0
$949$	−264.037	−	457.325i	−0.278226	−	0.481902i
$950$	−5.34065	+	43.6082i	−0.00562174	+	0.0459033i
$951$		0			0
$952$	−25.7067	−	14.8418i	−0.0270028	−	0.0155901i
$953$	1445.17			1.51644			0.758221	−	0.651997i	$-0.226069\pi$
$953$	1445.17			1.51644			0.758221	+	0.651997i	$0.226069\pi$
$954$		0			0
$955$	−1372.26	−	458.916i	−1.43693	−	0.480540i
$956$	198.083	+	114.363i	0.207199	+	0.119627i
$957$		0			0
$958$	421.176	−	243.166i	0.439641	−	0.253827i
$959$	115.493	−	66.6802i	0.120431	−	0.0695309i
$960$		0			0
$961$	471.624	−	816.878i	0.490764	−	0.850029i
$962$	585.941			0.609086
$963$		0			0
$964$	−127.442			−0.132201
$965$	−478.640	+	423.598i	−0.496000	+	0.438961i
$966$		0			0
$967$	−1024.57	+	591.535i	−1.05953	+	0.611721i	−0.925303	−	0.379229i	$-0.876189\pi$
$967$	−1024.57	+	591.535i	−1.05953	+	0.611721i	−0.134230	+	0.990950i	$0.542856\pi$
$968$	163.238	+	282.736i	0.168634	+	0.292082i
$969$		0			0
$970$	−479.902	+	424.714i	−0.494744	+	0.437850i
$971$			1444.94i			1.48810i	0.668124	+	0.744050i	$0.267097\pi$
$971$			1444.94i			1.48810i	−0.668124	+	0.744050i	$0.732903\pi$
$972$		0			0
$973$			148.274i			0.152388i
$974$	368.354	+	212.669i	0.378186	+	0.218346i
$975$		0			0
$976$	165.882	+	287.316i	0.169961	+	0.294382i
$977$	−623.257	−	1079.51i	−0.637929	−	1.10493i	−0.985886	−	0.167416i	$-0.946458\pi$
$977$	−623.257	−	1079.51i	−0.637929	−	1.10493i	0.347957	−	0.937510i	$-0.386875\pi$
$978$		0			0
$979$	−1057.22	+	1831.16i	−1.07990	+	1.87044i
$980$	−153.308	+	458.425i	−0.156437	+	0.467781i
$981$		0			0
$982$			245.951i			0.250459i
$983$	72.0025	−	124.712i	0.0732477	−	0.126869i	−0.827075	−	0.562091i	$-0.809997\pi$
$983$	72.0025	−	124.712i	0.0732477	−	0.126869i	0.900323	+	0.435222i	$0.143330\pi$
$984$		0			0
$985$	−1373.88	+	279.742i	−1.39480	+	0.284002i
$986$	674.233	−	389.269i	0.683806	−	0.394796i
$987$		0			0
$988$	−12.6824	−	7.32218i	−0.0128364	−	0.00741111i
$989$		−	196.997i		−	0.199188i
$990$		0			0
$991$	725.742			0.732333			0.366167	−	0.930549i	$-0.380670\pi$
$991$	725.742			0.732333			0.366167	+	0.930549i	$0.380670\pi$
$992$	−11.9167	+	20.6404i	−0.0120128	+	0.0208069i
$993$		0			0
$994$	−40.0963	−	69.4489i	−0.0403384	−	0.0698681i
$995$	766.406	−	156.051i	0.770258	−	0.156835i
$996$		0			0
$997$	−763.248	−	440.661i	−0.765545	−	0.441987i	0.0657384	−	0.997837i	$-0.479060\pi$
$997$	−763.248	−	440.661i	−0.765545	−	0.441987i	−0.831283	+	0.555850i	$0.812393\pi$
$998$	−1077.08			−1.07924
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.3.j.f.269.2		8
3.2	odd	2		810.3.j.a.269.3		8
5.4	even	2		810.3.j.a.269.4		8
9.2	odd	6		270.3.b.d.269.1	yes	4
9.4	even	3	inner	810.3.j.f.539.1		8
9.5	odd	6		810.3.j.a.539.4		8
9.7	even	3		270.3.b.a.269.4	yes	4
15.14	odd	2	inner	810.3.j.f.269.1		8
36.7	odd	6		2160.3.c.g.1889.4		4
36.11	even	6		2160.3.c.m.1889.1		4
45.2	even	12		1350.3.d.o.701.2		8
45.4	even	6		810.3.j.a.539.3		8
45.7	odd	12		1350.3.d.o.701.6		8
45.14	odd	6	inner	810.3.j.f.539.2		8
45.29	odd	6		270.3.b.a.269.3	✓	4
45.34	even	6		270.3.b.d.269.2	yes	4
45.38	even	12		1350.3.d.o.701.7		8
45.43	odd	12		1350.3.d.o.701.3		8
180.79	odd	6		2160.3.c.m.1889.2		4
180.119	even	6		2160.3.c.g.1889.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.3.b.a.269.3	✓	4	45.29	odd	6
270.3.b.a.269.4	yes	4	9.7	even	3
270.3.b.d.269.1	yes	4	9.2	odd	6
270.3.b.d.269.2	yes	4	45.34	even	6
810.3.j.a.269.3		8	3.2	odd	2
810.3.j.a.269.4		8	5.4	even	2
810.3.j.a.539.3		8	45.4	even	6
810.3.j.a.539.4		8	9.5	odd	6
810.3.j.f.269.1		8	15.14	odd	2	inner
810.3.j.f.269.2		8	1.1	even	1	trivial
810.3.j.f.539.1		8	9.4	even	3	inner
810.3.j.f.539.2		8	45.14	odd	6	inner
1350.3.d.o.701.2		8	45.2	even	12
1350.3.d.o.701.3		8	45.43	odd	12
1350.3.d.o.701.6		8	45.7	odd	12
1350.3.d.o.701.7		8	45.38	even	12
2160.3.c.g.1889.3		4	180.119	even	6
2160.3.c.g.1889.4		4	36.7	odd	6
2160.3.c.m.1889.1		4	36.11	even	6
2160.3.c.m.1889.2		4	180.79	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:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	810.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(4.89947 - 0.997601i) q^{5} +(-0.704577 - 0.406788i) q^{7} +2.82843 q^{8} +O(q^{10})\)	\(q+(-0.707107 + 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(4.89947 - 0.997601i) q^{5} +(-0.704577 - 0.406788i) q^{7} +2.82843 q^{8} +(-2.24264 + 6.70601i) q^{10} +(-13.3161 - 7.68808i) q^{11} +(5.10300 - 2.94622i) q^{13} +(0.996422 - 0.575285i) q^{14} +(-2.00000 + 3.46410i) q^{16} +12.8995 q^{17} +1.24264 q^{19} +(-6.62736 - 7.48853i) q^{20} +(18.8319 - 10.8726i) q^{22} +(-2.39949 - 4.15605i) q^{23} +(23.0096 - 9.77543i) q^{25} +8.33316i q^{26} +1.62715i q^{28} +(-36.9592 - 21.3384i) q^{29} +(-2.10660 - 3.64874i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(-9.12132 + 15.7986i) q^{34} +(-3.85786 - 1.29016i) q^{35} -70.3144i q^{37} +(-0.878680 + 1.52192i) q^{38} +(13.8578 - 2.82164i) q^{40} +(6.09942 - 3.52150i) q^{41} +(35.5500 + 20.5248i) q^{43} +30.7523i q^{44} +6.78680 q^{46} +(-39.8995 + 69.1080i) q^{47} +(-24.1690 - 41.8620i) q^{49} +(-4.29783 + 35.0931i) q^{50} +(-10.2060 - 5.89243i) q^{52} -63.7279 q^{53} +(-72.9117 - 24.3833i) q^{55} +(-1.99284 - 1.15057i) q^{56} +(52.2682 - 30.1770i) q^{58} +(-31.7353 + 18.3224i) q^{59} +(41.4706 - 71.8291i) q^{61} +5.95837 q^{62} +8.00000 q^{64} +(22.0628 - 19.5257i) q^{65} +(77.0786 - 44.5013i) q^{67} +(-12.8995 - 22.3426i) q^{68} +(4.30803 - 3.81262i) q^{70} -69.6982i q^{71} -89.6188i q^{73} +(86.1172 + 49.7198i) q^{74} +(-1.24264 - 2.15232i) q^{76} +(6.25483 + 10.8337i) q^{77} +(-67.0477 + 116.130i) q^{79} +(-6.34315 + 18.9675i) q^{80} +9.96031i q^{82} +(54.5122 - 94.4179i) q^{83} +(63.2007 - 12.8685i) q^{85} +(-50.2753 + 29.0265i) q^{86} +(-37.6638 - 21.7452i) q^{88} -137.514i q^{89} -4.79394 q^{91} +(-4.79899 + 8.31209i) q^{92} +(-56.4264 - 97.7334i) q^{94} +(6.08828 - 1.23966i) q^{95} +(78.4877 + 45.3149i) q^{97} +68.3604 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} + 12 q^{5}+O(q^{10}) \) 8 * q - 8 * q^4 + 12 * q^5	\( 8 q - 8 q^{4} + 12 q^{5} + 16 q^{10} - 16 q^{16} + 24 q^{17} - 24 q^{19} + 24 q^{20} + 60 q^{23} + 12 q^{25} + 68 q^{31} - 56 q^{34} - 144 q^{35} - 24 q^{38} - 16 q^{40} + 224 q^{46} - 240 q^{47} + 180 q^{49} + 96 q^{50} - 408 q^{53} - 176 q^{55} + 196 q^{61} + 240 q^{62} + 64 q^{64} - 24 q^{65} - 24 q^{68} - 80 q^{70} + 24 q^{76} - 312 q^{77} - 180 q^{79} - 96 q^{80} + 108 q^{83} - 20 q^{85} + 912 q^{91} + 120 q^{92} - 112 q^{94} - 60 q^{95} + 1056 q^{98}+O(q^{100}) \) 8 * q - 8 * q^4 + 12 * q^5 + 16 * q^10 - 16 * q^16 + 24 * q^17 - 24 * q^19 + 24 * q^20 + 60 * q^23 + 12 * q^25 + 68 * q^31 - 56 * q^34 - 144 * q^35 - 24 * q^38 - 16 * q^40 + 224 * q^46 - 240 * q^47 + 180 * q^49 + 96 * q^50 - 408 * q^53 - 176 * q^55 + 196 * q^61 + 240 * q^62 + 64 * q^64 - 24 * q^65 - 24 * q^68 - 80 * q^70 + 24 * q^76 - 312 * q^77 - 180 * q^79 - 96 * q^80 + 108 * q^83 - 20 * q^85 + 912 * q^91 + 120 * q^92 - 112 * q^94 - 60 * q^95 + 1056 * q^98

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