LMFDB - Embedded newform 810.3.j.f.269.1

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			269.1
Root			$2.90379 - 1.67650i$ of defining polynomial
Character	$\chi$	$=$	810.269
Dual form			810.3.j.f.539.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(-3.31368 + 3.74426i) q^{5} +(0.704577 + 0.406788i) q^{7} +2.82843 q^{8} +O(q^{10})$	\(q+(-0.707107 + 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(-3.31368 + 3.74426i) q^{5} +(0.704577 + 0.406788i) q^{7} +2.82843 q^{8} +(-2.24264 - 6.70601i) q^{10} +(13.3161 + 7.68808i) q^{11} +(-5.10300 + 2.94622i) q^{13} +(-0.996422 + 0.575285i) q^{14} +(-2.00000 + 3.46410i) q^{16} +12.8995 q^{17} +1.24264 q^{19} +(9.79894 + 1.99520i) q^{20} +(-18.8319 + 10.8726i) q^{22} +(-2.39949 - 4.15605i) q^{23} +(-3.03902 - 24.8146i) q^{25} -8.33316i q^{26} -1.62715i q^{28} +(36.9592 + 21.3384i) q^{29} +(-2.10660 - 3.64874i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(-9.12132 + 15.7986i) q^{34} +(-3.85786 + 1.29016i) q^{35} +70.3144i q^{37} +(-0.878680 + 1.52192i) q^{38} +(-9.37251 + 10.5904i) q^{40} +(-6.09942 + 3.52150i) q^{41} +(-35.5500 - 20.5248i) q^{43} -30.7523i q^{44} +6.78680 q^{46} +(-39.8995 + 69.1080i) q^{47} +(-24.1690 - 41.8620i) q^{49} +(32.5405 + 13.8245i) q^{50} +(10.2060 + 5.89243i) q^{52} -63.7279 q^{53} +(-72.9117 + 24.3833i) q^{55} +(1.99284 + 1.15057i) q^{56} +(-52.2682 + 30.1770i) q^{58} +(31.7353 - 18.3224i) q^{59} +(41.4706 - 71.8291i) q^{61} +5.95837 q^{62} +8.00000 q^{64} +(5.87830 - 28.8698i) q^{65} +(-77.0786 + 44.5013i) q^{67} +(-12.8995 - 22.3426i) q^{68} +(1.14781 - 5.63718i) q^{70} +69.6982i q^{71} +89.6188i q^{73} +(-86.1172 - 49.7198i) q^{74} +(-1.24264 - 2.15232i) q^{76} +(6.25483 + 10.8337i) q^{77} +(-67.0477 + 116.130i) q^{79} +(-6.34315 - 18.9675i) q^{80} -9.96031i q^{82} +(54.5122 - 94.4179i) q^{83} +(-42.7448 + 48.2991i) q^{85} +(50.2753 - 29.0265i) q^{86} +(37.6638 + 21.7452i) q^{88} +137.514i q^{89} -4.79394 q^{91} +(-4.79899 + 8.31209i) q^{92} +(-56.4264 - 97.7334i) q^{94} +(-4.11772 + 4.65277i) q^{95} +(-78.4877 - 45.3149i) q^{97} +68.3604 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−3.31368	+	3.74426i	−0.662736	+	0.748853i
$5$	−3.31368	+	3.74426i	−0.662736	+	0.748853i
$6$		0			0
$7$	0.704577	+	0.406788i	0.100654	+	0.0581125i	0.549482	−	0.835506i	$-0.314825\pi$
$7$	0.704577	+	0.406788i	0.100654	+	0.0581125i	−0.448828	+	0.893618i	$0.648158\pi$
$8$	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	0.962881	−	0.269926i	$-0.0869992\pi$
$11$	13.3161	+	7.68808i	1.21056	+	0.698917i	0.247678	+	0.968842i	$0.420333\pi$
$12$		0			0
$13$	−5.10300	+	2.94622i	−0.392538	+	0.226632i	−0.683259	−	0.730176i	$-0.739438\pi$
$13$	−5.10300	+	2.94622i	−0.392538	+	0.226632i	0.290721	+	0.956808i	$0.406105\pi$
$14$	−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	$0.489589\pi$
$20$	9.79894	+	1.99520i	0.489947	+	0.0997601i
$21$		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
$25$	−3.03902	−	24.8146i	−0.121561	−	0.992584i
$26$		−	8.33316i		−	0.320506i
$27$		0			0
$28$		−	1.62715i		−	0.0581125i
$29$	36.9592	+	21.3384i	1.27445	+	0.735807i	0.975823	−	0.218562i	$-0.0701366\pi$
$29$	36.9592	+	21.3384i	1.27445	+	0.735807i	0.298631	+	0.954369i	$0.403470\pi$
$30$		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	$0.399116\pi$
$37$			70.3144i			1.90039i	−0.311657	+	0.950195i	$0.600884\pi$
$38$	−0.878680	+	1.52192i	−0.0231231	+	0.0400505i
$39$		0			0
$40$	−9.37251	+	10.5904i	−0.234313	+	0.264759i
$41$	−6.09942	+	3.52150i	−0.148766	+	0.0858903i	−0.572535	−	0.819880i	$-0.694040\pi$
$41$	−6.09942	+	3.52150i	−0.148766	+	0.0858903i	0.423769	+	0.905770i	$0.360707\pi$
$42$		0			0
$43$	−35.5500	−	20.5248i	−0.826745	−	0.477321i	0.0259920	−	0.999662i	$-0.491726\pi$
$43$	−35.5500	−	20.5248i	−0.826745	−	0.477321i	−0.852737	+	0.522341i	$0.825059\pi$
$44$		−	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
$50$	32.5405	+	13.8245i	0.650809	+	0.276491i
$51$		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	−0.206336	−	0.978481i	$-0.566154\pi$
$59$	31.7353	−	18.3224i	0.537886	−	0.310549i	0.744222	+	0.667932i	$0.232821\pi$
$60$		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
$65$	5.87830	−	28.8698i	0.0904354	−	0.444151i
$66$		0			0
$67$	−77.0786	+	44.5013i	−1.15043	+	0.664199i	−0.948991	−	0.315303i	$-0.897894\pi$
$67$	−77.0786	+	44.5013i	−1.15043	+	0.664199i	−0.201435	+	0.979502i	$0.564561\pi$
$68$	−12.8995	−	22.3426i	−0.189698	−	0.328567i
$69$		0			0
$70$	1.14781	−	5.63718i	0.0163973	−	0.0805311i
$71$			69.6982i			0.981665i	0.871254	+	0.490833i	$0.163307\pi$
$71$			69.6982i			0.981665i	−0.871254	+	0.490833i	$0.836693\pi$
$72$		0			0
$73$			89.6188i			1.22766i	0.789440	+	0.613828i	$0.210371\pi$
$73$			89.6188i			1.22766i	−0.789440	+	0.613828i	$0.789629\pi$
$74$	−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
$85$	−42.7448	+	48.2991i	−0.502880	+	0.568225i
$86$	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	$0.281020\pi$
$89$			137.514i			1.54510i	−0.634953	+	0.772551i	$0.718980\pi$
$90$		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
$95$	−4.11772	+	4.65277i	−0.0433444	+	0.0489766i
$96$		0			0
$97$	−78.4877	−	45.3149i	−0.809152	−	0.467164i	0.0375094	−	0.999296i	$-0.488058\pi$
$97$	−78.4877	−	45.3149i	−0.809152	−	0.467164i	−0.846661	+	0.532132i	$0.821391\pi$
$98$	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	0.271456	−	0.962451i	$-0.412495\pi$
$101$	−43.0586	−	24.8599i	−0.426323	−	0.246138i	−0.697779	+	0.716313i	$0.745828\pi$
$102$		0			0
$103$	−111.582	+	64.4220i	−1.08332	+	0.625456i	−0.931790	−	0.362997i	$-0.881754\pi$
$103$	−111.582	+	64.4220i	−1.08332	+	0.625456i	−0.151531	+	0.988453i	$0.548420\pi$
$104$	−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	$0.334547\pi$
$110$	21.6930	−	106.540i	0.197209	−	0.968544i
$111$		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
$115$	23.5125	+	4.78748i	0.204457	+	0.0416302i
$116$		−	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	$-0.823512\pi$
$127$		−	133.725i		−	1.05296i	0.850189	−	0.526478i	$-0.176488\pi$
$128$	−5.65685	+	9.79796i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	31.2015	+	27.6134i	0.240012	+	0.212411i
$131$	−53.5064	+	30.8919i	−0.408446	+	0.235816i	−0.690122	−	0.723693i	$-0.742443\pi$
$131$	−53.5064	+	30.8919i	−0.408446	+	0.235816i	0.281676	+	0.959510i	$0.409110\pi$
$132$		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	$-0.394240\pi$
$140$	6.09248	+	5.39186i	0.0435177	+	0.0385133i
$141$		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	−0.936647	−	0.350274i	$-0.886089\pi$
$149$	−164.142	+	94.7675i	−1.10163	+	0.636023i	−0.164978	+	0.986297i	$0.552755\pi$
$150$		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
$155$	20.6425	+	4.20310i	0.133177	+	0.0271167i
$156$		0			0
$157$	98.0242	−	56.5943i	0.624358	−	0.360473i	−0.154206	−	0.988039i	$-0.549282\pi$
$157$	98.0242	−	56.5943i	0.624358	−	0.360473i	0.778564	+	0.627566i	$0.215949\pi$
$158$	−94.8198	−	164.233i	−0.600125	−	1.03945i
$159$		0			0
$160$	27.7156	+	5.64328i	0.173222	+	0.0352705i
$161$		−	3.90434i		−	0.0242506i
$162$		0			0
$163$		−	152.414i		−	0.935053i	−0.883979	−	0.467527i	$-0.845145\pi$
$163$		−	152.414i		−	0.935053i	0.883979	−	0.467527i	$-0.154855\pi$
$164$	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
$175$	7.95305	−	18.7200i	0.0454460	−	0.106972i
$176$	−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	$-0.892700\pi$
$179$		−	118.407i		−	0.661492i	0.943720	−	0.330746i	$-0.107300\pi$
$180$		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
$185$	−263.276	−	233.000i	−1.42311	−	1.25946i
$186$		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	0.982453	−	0.186510i	$-0.0597177\pi$
$191$	250.622	+	144.697i	1.31216	+	0.757574i	0.329704	+	0.944084i	$0.393051\pi$
$192$		0			0
$193$	110.707	−	63.9165i	0.573609	−	0.331173i	−0.184980	−	0.982742i	$-0.559222\pi$
$193$	110.707	−	63.9165i	0.573609	−	0.331173i	0.758590	+	0.651569i	$0.225889\pi$
$194$	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	$0.371426\pi$
$200$	−8.59565	−	70.1863i	−0.0429783	−	0.350931i
$201$		0			0
$202$	60.8941	−	35.1572i	0.301456	−	0.174046i
$203$	17.3604	+	30.0691i	0.0855192	+	0.148124i
$204$		0			0
$205$	7.02611	−	34.5070i	0.0342737	−	0.168327i
$206$		−	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
$220$	115.145	+	101.903i	0.523386	+	0.463197i
$221$	−65.8261	+	38.0047i	−0.297856	+	0.171967i
$222$		0			0
$223$	307.289	+	177.413i	1.37798	+	0.795575i	0.991916	−	0.126899i	$-0.0405024\pi$
$223$	307.289	+	177.413i	1.37798	+	0.795575i	0.386060	+	0.922474i	$0.373836\pi$
$224$		−	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	$0.673669\pi$
$230$	−22.4893	+	25.4116i	−0.0977795	+	0.110485i
$231$		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	−0.278279	−	0.960500i	$-0.589764\pi$
$239$	99.0414	−	57.1816i	0.414399	−	0.239253i	0.692678	+	0.721247i	$0.256431\pi$
$240$		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
$245$	236.831	+	48.2221i	0.966657	+	0.196825i
$246$		0			0
$247$	−6.34119	+	3.66109i	−0.0256728	+	0.0148222i
$248$	−5.95837	−	10.3202i	−0.0240257	−	0.0416137i
$249$		0			0
$250$	−159.592	+	76.0299i	−0.638366	+	0.304120i
$251$			229.631i			0.914866i	0.889244	+	0.457433i	$0.151231\pi$
$251$			229.631i			0.914866i	−0.889244	+	0.457433i	$0.848769\pi$
$252$		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
$265$	211.174	−	238.614i	0.796883	−	0.900431i
$266$	−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	$0.138500\pi$
$269$			226.772i			0.843019i	−0.906824	+	0.421509i	$0.861500\pi$
$270$		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
$275$	150.309	−	353.799i	0.546577	−	1.28654i
$276$		0			0
$277$	173.694	+	100.282i	0.627053	+	0.362029i	0.779610	−	0.626266i	$-0.215417\pi$
$277$	173.694	+	100.282i	0.627053	+	0.362029i	−0.152557	+	0.988295i	$0.548751\pi$
$278$	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	0.289562	−	0.957159i	$-0.406490\pi$
$281$	−110.878	−	64.0152i	−0.394582	−	0.227812i	−0.684144	+	0.729347i	$0.739824\pi$
$282$		0			0
$283$	363.934	−	210.118i	1.28599	−	0.742465i	0.308051	−	0.951370i	$-0.400323\pi$
$283$	363.934	−	210.118i	1.28599	−	0.742465i	0.977936	+	0.208905i	$0.0669898\pi$
$284$	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
$290$	60.2093	−	295.703i	0.207618	−	1.01967i
$291$		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
$295$	−36.5569	+	179.540i	−0.123922	+	0.608610i
$296$			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	$0.0614766\pi$
$307$			117.849i			0.383872i	−0.981407	+	0.191936i	$0.938523\pi$
$308$	12.5097	−	21.6674i	0.0406158	−	0.0703486i
$309$		0			0
$310$	−19.7441	+	22.3097i	−0.0636908	+	0.0719668i
$311$	432.429	−	249.663i	1.39045	−	0.802774i	0.397081	−	0.917783i	$-0.370023\pi$
$311$	432.429	−	249.663i	1.39045	−	0.802774i	0.993364	+	0.115009i	$0.0366898\pi$
$312$		0			0
$313$	−425.916	−	245.903i	−1.36076	−	0.785633i	−0.371031	−	0.928620i	$-0.620996\pi$
$313$	−425.916	−	245.903i	−1.36076	−	0.785633i	−0.989724	+	0.142988i	$0.954329\pi$
$314$			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
$320$	−26.5095	+	29.9541i	−0.0828421	+	0.0936066i
$321$		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
$335$	88.7892	−	436.066i	0.265042	−	1.30169i
$336$		0			0
$337$	391.563	−	226.069i	1.16191	−	0.670828i	0.210148	−	0.977670i	$-0.432605\pi$
$337$	391.563	−	226.069i	1.16191	−	0.670828i	0.951761	+	0.306841i	$0.0992721\pi$
$338$	−94.9497	−	164.458i	−0.280916	−	0.486561i
$339$		0			0
$340$	126.401	+	25.7371i	0.371769	+	0.0756974i
$341$		−	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
$355$	−260.969	−	230.958i	−0.735123	−	0.650585i
$356$	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	$-0.964623\pi$
$359$		−	79.6346i		−	0.221823i	0.993830	−	0.110912i	$-0.0353771\pi$
$360$		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
$365$	−335.557	−	296.968i	−0.919333	−	0.813612i
$366$		0			0
$367$	−412.188	−	237.977i	−1.12313	−	0.648438i	−0.180930	−	0.983496i	$-0.557911\pi$
$367$	−412.188	−	237.977i	−1.12313	−	0.648438i	−0.942197	+	0.335058i	$0.891244\pi$
$368$	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	−0.426558	−	0.904460i	$-0.640274\pi$
$373$	53.5064	−	30.8919i	0.143449	−	0.0828201i	0.570007	+	0.821640i	$0.306941\pi$
$374$	−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	$0.560133\pi$
$380$	12.1766	+	2.47932i	0.0320436	+	0.00652452i
$381$		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
$385$	−61.2907	−	12.4797i	−0.159197	−	0.0324147i
$386$			180.783i			0.468350i
$387$		0			0
$388$			181.260i			0.467164i
$389$	−356.005	−	205.539i	−0.915179	−	0.528379i	−0.0330850	−	0.999453i	$-0.510533\pi$
$389$	−356.005	−	205.539i	−0.915179	−	0.528379i	−0.882094	+	0.471074i	$0.843867\pi$
$390$		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	$-0.804555\pi$
$397$		−	457.462i		−	1.15230i	0.817345	−	0.576149i	$-0.195445\pi$
$398$	−110.610	+	191.582i	−0.277915	+	0.481363i
$399$		0			0
$400$	92.0383	+	39.1017i	0.230096	+	0.0977543i
$401$	−404.679	+	233.642i	−1.00917	+	0.582647i	−0.910950	−	0.412517i	$-0.864650\pi$
$401$	−404.679	+	233.642i	−1.00917	+	0.582647i	−0.0982247	+	0.995164i	$0.531316\pi$
$402$		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	$0.648579\pi$
$410$	37.2940	+	33.0053i	0.0909611	+	0.0805007i
$411$		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	−0.0783720	−	0.996924i	$-0.524972\pi$
$419$	312.492	−	180.417i	0.745804	−	0.430590i	0.824176	+	0.566334i	$0.191639\pi$
$420$		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
$425$	−39.2018	−	320.096i	−0.0922396	−	0.753167i
$426$		0			0
$427$	58.4384	−	33.7394i	0.136858	−	0.0790151i
$428$	6.42641	+	11.1309i	0.0150150	+	0.0260067i
$429$		0			0
$430$	−57.9137	+	284.429i	−0.134683	+	0.661462i
$431$		−	655.947i		−	1.52192i	−0.648800	−	0.760959i	$-0.724729\pi$
$431$		−	655.947i		−	1.52192i	0.648800	−	0.760959i	$-0.275271\pi$
$432$		0			0
$433$			164.372i			0.379612i	0.981822	+	0.189806i	$0.0607859\pi$
$433$			164.372i			0.379612i	−0.981822	+	0.189806i	$0.939214\pi$
$434$	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
$445$	−514.889	−	455.678i	−1.15705	−	1.02400i
$446$	−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	$-0.846783\pi$
$449$		−	415.749i		−	0.925944i	0.886373	−	0.462972i	$-0.153217\pi$
$450$		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
$455$	15.8856	−	17.9498i	0.0349134	−	0.0394501i
$456$		0			0
$457$	−262.962	−	151.821i	−0.575410	−	0.332213i	0.183897	−	0.982946i	$-0.441129\pi$
$457$	−262.962	−	151.821i	−0.575410	−	0.332213i	−0.759307	+	0.650732i	$0.774462\pi$
$458$	−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	0.0398803	−	0.999204i	$-0.487302\pi$
$461$	−371.343	−	214.395i	−0.805516	−	0.465065i	−0.845396	+	0.534140i	$0.820636\pi$
$462$		0			0
$463$	−705.364	+	407.242i	−1.52346	+	0.879572i	−0.523850	+	0.851811i	$0.675505\pi$
$463$	−705.364	+	407.242i	−1.52346	+	0.879572i	−0.999615	+	0.0277616i	$0.991162\pi$
$464$	−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
$470$	552.919	+	112.582i	1.17642	+	0.239536i
$471$		0			0
$472$	89.7610	−	51.8235i	0.190172	−	0.109796i
$473$	−315.593	−	546.623i	−0.667215	−	1.15565i
$474$		0			0
$475$	−3.77641	−	30.8356i	−0.00795034	−	0.0649171i
$476$		−	20.9894i		−	0.0440954i
$477$		0			0
$478$			161.734i			0.338355i
$479$	297.816	+	171.944i	0.621746	+	0.358965i	0.777549	−	0.628823i	$-0.216463\pi$
$479$	297.816	+	171.944i	0.621746	+	0.358965i	−0.155802	+	0.987788i	$0.549796\pi$
$480$		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	$0.0999233\pi$
$487$			300.759i			0.617576i	−0.951131	+	0.308788i	$0.900077\pi$
$488$	117.296	−	203.163i	0.240362	−	0.416319i
$489$		0			0
$490$	−226.525	+	255.959i	−0.462295	+	0.522366i
$491$	−150.614	+	86.9568i	−0.306749	+	0.177101i	−0.645471	−	0.763785i	$-0.723339\pi$
$491$	−150.614	+	86.9568i	−0.306749	+	0.177101i	0.338722	+	0.940886i	$0.390005\pi$
$492$		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	$0.556992\pi$
$500$	19.7310	−	249.220i	0.0394619	−	0.498440i
$501$		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	−0.930167	−	0.367136i	$-0.880338\pi$
$509$	−548.347	+	316.588i	−1.07730	+	0.621981i	−0.147135	+	0.989116i	$0.547005\pi$
$510$		0			0
$511$	−36.4558	+	63.1434i	−0.0713422	+	0.123568i
$512$	22.6274			0.0441942
$513$		0			0
$514$	−549.037			−1.06816
$515$	128.535	−	631.267i	0.249582	−	1.22576i
$516$		0			0
$517$	−1062.62	+	613.501i	−2.05535	+	1.18666i
$518$	−40.4508	−	70.0628i	−0.0780903	−	0.135256i
$519$		0			0
$520$	16.6263	−	81.6561i	0.0319737	−	0.157031i
$521$			92.3966i			0.177345i	0.996061	+	0.0886723i	$0.0282624\pi$
$521$			92.3966i			0.177345i	−0.996061	+	0.0886723i	$0.971738\pi$
$522$		0			0
$523$			818.552i			1.56511i	0.622582	+	0.782554i	$0.286084\pi$
$523$			818.552i			1.56511i	−0.622582	+	0.782554i	$0.713916\pi$
$524$	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
$535$	21.2951	−	24.0622i	0.0398039	−	0.0449760i
$536$	−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
$545$	−358.803	+	405.426i	−0.658354	+	0.743901i
$546$		0			0
$547$	292.151	+	168.673i	0.534096	+	0.308360i	0.742683	−	0.669643i	$-0.233553\pi$
$547$	292.151	+	168.673i	0.534096	+	0.308360i	−0.208587	+	0.978004i	$0.566886\pi$
$548$	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
$560$	3.24649	−	15.9443i	0.00579731	−	0.0284720i
$561$		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
$565$	149.073	+	30.3534i	0.263846	+	0.0537229i
$566$			594.302i			1.05000i
$567$		0			0
$568$			197.136i			0.347071i
$569$	57.6129	+	33.2628i	0.101253	+	0.0584584i	0.549771	−	0.835315i	$-0.314715\pi$
$569$	57.6129	+	33.2628i	0.101253	+	0.0584584i	−0.448518	+	0.893774i	$0.648048\pi$
$570$		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	$0.311430\pi$
$577$			957.356i			1.65920i	−0.558361	+	0.829598i	$0.688570\pi$
$578$	86.6934	−	150.157i	0.149989	−	0.259788i
$579$		0			0
$580$	319.586	+	282.835i	0.551011	+	0.487646i
$581$	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
$590$	−194.041	−	171.727i	−0.328883	−	0.291062i
$591$		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	0.339304	−	0.940677i	$-0.389808\pi$
$599$	792.840	−	457.746i	1.32361	−	0.764184i	0.984302	+	0.176492i	$0.0564751\pi$
$600$		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
$605$	−565.528	−	115.150i	−0.934757	−	0.190330i
$606$		0			0
$607$	−190.433	+	109.946i	−0.313727	+	0.181131i	−0.648593	−	0.761135i	$-0.724642\pi$
$607$	−190.433	+	109.946i	−0.313727	+	0.181131i	0.334866	+	0.942266i	$0.391309\pi$
$608$	−3.51472	−	6.08767i	−0.00578079	−	0.0100126i
$609$		0			0
$610$	−574.690	−	117.015i	−0.942115	−	0.191828i
$611$		−	470.210i		−	0.769575i
$612$		0			0
$613$		−	862.066i		−	1.40631i	−0.711038	−	0.703154i	$-0.751775\pi$
$613$		−	862.066i		−	1.40631i	0.711038	−	0.703154i	$-0.248225\pi$
$614$	−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
$625$	−606.529	+	150.824i	−0.970446	+	0.241319i
$626$	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
$635$	500.703	+	443.123i	0.788509	+	0.697832i
$636$		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	0.361038	−	0.932551i	$-0.382422\pi$
$641$	−170.542	−	98.4625i	−0.266056	−	0.153608i	−0.627094	+	0.778944i	$0.715756\pi$
$642$		0			0
$643$	205.208	−	118.477i	0.319141	−	0.184256i	−0.331868	−	0.943326i	$-0.607679\pi$
$643$	205.208	−	118.477i	0.319141	−	0.184256i	0.651010	+	0.759069i	$0.274346\pi$
$644$	−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
$650$	−206.784	+	25.3247i	−0.318129	+	0.0389610i
$651$		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
$655$	61.6356	−	302.708i	0.0941002	−	0.462150i
$656$		−	28.1720i		−	0.0429451i
$657$		0			0
$658$		−	91.8143i		−	0.139535i
$659$	−431.945	−	249.384i	−0.655455	−	0.378427i	0.135088	−	0.990834i	$-0.456868\pi$
$659$	−431.945	−	249.384i	−0.655455	−	0.378427i	−0.790543	+	0.612406i	$0.790202\pi$
$660$		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
$670$	471.286	+	417.089i	0.703412	+	0.622521i
$671$	1104.46	−	637.658i	1.64599	−	0.950310i
$672$		0			0
$673$	401.085	+	231.567i	0.595966	+	0.344081i	0.767453	−	0.641105i	$-0.221524\pi$
$673$	401.085	+	231.567i	0.595966	+	0.344081i	−0.171487	+	0.985186i	$0.554857\pi$
$674$			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
$680$	−120.901	+	136.611i	−0.177795	+	0.200898i
$681$		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
$695$	892.927	+	181.813i	1.28479	+	0.261601i
$696$		0			0
$697$	−78.6794	+	45.4256i	−0.112883	+	0.0651730i
$698$	110.163	+	190.808i	0.157827	+	0.273364i
$699$		0			0
$700$	−40.3771	+	4.94495i	−0.0576816	+	0.00706421i
$701$			250.274i			0.357024i	0.983938	+	0.178512i	$0.0571284\pi$
$701$			250.274i			0.357024i	−0.983938	+	0.178512i	$0.942872\pi$
$702$		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
$715$	300.230	−	339.242i	0.419902	−	0.474464i
$716$	−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	$-0.962699\pi$
$719$		−	168.127i		−	0.233834i	0.993142	−	0.116917i	$-0.0373012\pi$
$720$		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
$725$	417.184	−	981.975i	0.575426	−	1.35445i
$726$		0			0
$727$	331.545	+	191.417i	0.456045	+	0.263298i	0.710380	−	0.703819i	$-0.248523\pi$
$727$	331.545	+	191.417i	0.456045	+	0.263298i	−0.254335	+	0.967116i	$0.581857\pi$
$728$	−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	$0.739738\pi$
$733$	−1215.10	+	701.541i	−1.65771	+	0.957082i	−0.973766	+	0.227550i	$0.926928\pi$
$734$	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	$0.291836\pi$
$740$	−140.291	+	689.006i	−0.189583	+	0.931090i
$741$		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
$745$	189.080	−	928.621i	0.253799	−	1.24647i
$746$			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	$-0.826930\pi$
$757$		−	783.221i		−	1.03464i	0.855793	−	0.517319i	$-0.173070\pi$
$758$	100.653	−	174.337i	0.132788	−	0.229996i
$759$		0			0
$760$	−11.6467	+	13.1600i	−0.0153246	+	0.0173158i
$761$	−893.662	+	515.956i	−1.17433	+	0.677997i	−0.954695	−	0.297586i	$-0.903819\pi$
$761$	−893.662	+	515.956i	−1.17433	+	0.677997i	−0.219631	+	0.975583i	$0.570485\pi$
$762$		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	$0.651578\pi$
$770$	58.6235	−	66.2411i	0.0761344	−	0.0860273i
$771$		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
$785$	−112.917	+	554.564i	−0.143843	+	0.706451i
$786$		0			0
$787$	497.037	−	286.965i	0.631559	−	0.364631i	−0.149796	−	0.988717i	$-0.547862\pi$
$787$	497.037	−	286.965i	0.631559	−	0.364631i	0.781356	+	0.624086i	$0.214528\pi$
$788$	280.414	+	485.692i	0.355856	+	0.616360i
$789$		0			0
$790$	929.133	+	189.185i	1.17612	+	0.239474i
$791$		−	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
$805$	14.6189	+	12.9377i	0.0181601	+	0.0160717i
$806$	−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	$-0.979202\pi$
$809$		−	105.645i		−	0.130587i	0.997866	−	0.0652936i	$-0.0207984\pi$
$810$		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
$815$	570.677	+	505.050i	0.700217	+	0.619694i
$816$		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	0.876547	−	0.481316i	$-0.159841\pi$
$821$	737.249	+	425.651i	0.897990	+	0.518454i	0.0214421	+	0.999770i	$0.493174\pi$
$822$		0			0
$823$	970.057	−	560.062i	1.17868	−	0.680513i	0.222974	−	0.974824i	$-0.428424\pi$
$823$	970.057	−	560.062i	1.17868	−	0.680513i	0.955710	+	0.294311i	$0.0950902\pi$
$824$	−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	$0.142231\pi$
$830$	−755.419	−	153.814i	−0.910143	−	0.185318i
$831$		0			0
$832$	−40.8240	+	23.5697i	−0.0490673	+	0.0283290i
$833$	−311.769	−	539.999i	−0.374272	−	0.648258i
$834$		0			0
$835$	−518.623	−	105.599i	−0.621105	−	0.126466i
$836$		−	38.2141i		−	0.0457106i
$837$		0			0
$838$			510.297i			0.608946i
$839$	401.719	+	231.933i	0.478807	+	0.276439i	0.719919	−	0.694058i	$-0.244179\pi$
$839$	401.719	+	231.933i	0.478807	+	0.276439i	−0.241112	+	0.970497i	$0.577512\pi$
$840$		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
$850$	419.756	+	178.330i	0.493830	+	0.209800i
$851$	292.230	−	168.719i	0.343396	−	0.198260i
$852$		0			0
$853$	429.419	+	247.925i	0.503422	+	0.290651i	0.730125	−	0.683313i	$-0.239462\pi$
$853$	429.419	+	247.925i	0.503422	+	0.290651i	−0.226704	+	0.973964i	$0.572795\pi$
$854$			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	$0.794790\pi$
$860$	−307.401	−	272.051i	−0.357443	−	0.316338i
$861$		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
$875$	43.7389	+	91.8105i	0.0499873	+	0.104926i
$876$		0			0
$877$	786.903	−	454.319i	0.897267	−	0.518037i	0.0209544	−	0.999780i	$-0.493330\pi$
$877$	786.903	−	454.319i	0.897267	−	0.518037i	0.876312	+	0.481743i	$0.159996\pi$
$878$	93.5406	+	162.017i	0.106538	+	0.184530i
$879$		0			0
$880$	61.3571	−	301.340i	0.0697240	−	0.342432i
$881$			1226.54i			1.39221i	0.717941	+	0.696104i	$0.245085\pi$
$881$			1226.54i			1.39221i	−0.717941	+	0.696104i	$0.754915\pi$
$882$		0			0
$883$		−	760.022i		−	0.860728i	−0.902656	−	0.430364i	$-0.858385\pi$
$883$		−	760.022i		−	0.860728i	0.902656	−	0.430364i	$-0.141615\pi$
$884$	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
$895$	443.347	+	392.363i	0.495360	+	0.438395i
$896$	−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
$905$	−571.269	+	645.500i	−0.631236	+	0.713259i
$906$		0			0
$907$	−1479.39	−	854.128i	−1.63108	−	0.941707i	−0.983759	−	0.179492i	$-0.942555\pi$
$907$	−1479.39	−	854.128i	−1.63108	−	0.941707i	−0.647324	−	0.762215i	$-0.724112\pi$
$908$	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	0.989816	−	0.142350i	$-0.0454658\pi$
$911$	1240.28	+	716.074i	1.36145	+	0.786031i	0.371630	+	0.928381i	$0.378799\pi$
$912$		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	$0.542451\pi$
$920$	66.5034	+	13.5410i	0.0722863	+	0.0147185i
$921$		0			0
$922$	525.158	−	303.200i	0.569586	−	0.328851i
$923$	−205.346	−	355.670i	−0.222477	−	0.385341i
$924$		0			0
$925$	1744.82	−	213.687i	1.88630	−	0.231013i
$926$		−	1151.85i		−	1.24390i
$927$		0			0
$928$		−	241.416i		−	0.260147i
$929$	−325.628	−	188.002i	−0.350515	−	0.202370i	0.314397	−	0.949292i	$-0.398198\pi$
$929$	−325.628	−	188.002i	−0.350515	−	0.202370i	−0.664912	+	0.746922i	$0.731531\pi$
$930$		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	$-0.929430\pi$
$937$		−	412.076i		−	0.439782i	0.975524	−	0.219891i	$-0.0705701\pi$
$938$	51.2019	−	88.6843i	0.0545862	−	0.0945461i
$939$		0			0
$940$	−528.857	+	597.577i	−0.562614	+	0.635720i
$941$	−289.754	+	167.289i	−0.307921	+	0.177778i	−0.645996	−	0.763341i	$-0.723558\pi$
$941$	−289.754	+	167.289i	−0.307921	+	0.177778i	0.338075	+	0.941119i	$0.390224\pi$
$942$		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
$950$	40.4361	+	17.1789i	0.0425643	+	0.0180831i
$951$		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
$965$	−127.526	+	626.313i	−0.132152	+	0.649030i
$966$		0			0
$967$	1024.57	−	591.535i	1.05953	−	0.611721i	0.134230	−	0.990950i	$-0.457144\pi$
$967$	1024.57	−	591.535i	1.05953	−	0.611721i	0.925303	+	0.379229i	$0.123811\pi$
$968$	163.238	+	282.736i	0.168634	+	0.292082i
$969$		0			0
$970$	−127.862	+	627.965i	−0.131817	+	0.647386i
$971$		−	1444.94i		−	1.48810i	−0.668124	−	0.744050i	$-0.732903\pi$
$971$		−	1444.94i		−	1.48810i	0.668124	−	0.744050i	$-0.267097\pi$
$972$		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
$985$	929.204	−	1049.94i	0.943354	−	1.06593i
$986$	−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
$995$	−518.347	+	585.702i	−0.520952	+	0.588645i
$996$		0			0
$997$	763.248	+	440.661i	0.765545	+	0.441987i	0.831283	−	0.555850i	$-0.187607\pi$
$997$	763.248	+	440.661i	0.765545	+	0.441987i	−0.0657384	+	0.997837i	$0.520940\pi$
$998$	−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.269.1		8
3.2	odd	2		810.3.j.a.269.4		8
5.4	even	2		810.3.j.a.269.3		8
9.2	odd	6		270.3.b.d.269.2	yes	4
9.4	even	3	inner	810.3.j.f.539.2		8
9.5	odd	6		810.3.j.a.539.3		8
9.7	even	3		270.3.b.a.269.3	✓	4
15.14	odd	2	inner	810.3.j.f.269.2		8
36.7	odd	6		2160.3.c.g.1889.3		4
36.11	even	6		2160.3.c.m.1889.2		4
45.2	even	12		1350.3.d.o.701.3		8
45.4	even	6		810.3.j.a.539.4		8
45.7	odd	12		1350.3.d.o.701.7		8
45.14	odd	6	inner	810.3.j.f.539.1		8
45.29	odd	6		270.3.b.a.269.4	yes	4
45.34	even	6		270.3.b.d.269.1	yes	4
45.38	even	12		1350.3.d.o.701.6		8
45.43	odd	12		1350.3.d.o.701.2		8
180.79	odd	6		2160.3.c.m.1889.1		4
180.119	even	6		2160.3.c.g.1889.4		4

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

\(f(q)\)	\(=\)	\(q+(-0.707107 + 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(-3.31368 + 3.74426i) q^{5} +(0.704577 + 0.406788i) q^{7} +2.82843 q^{8} +O(q^{10})\)	\(q+(-0.707107 + 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(-3.31368 + 3.74426i) q^{5} +(0.704577 + 0.406788i) q^{7} +2.82843 q^{8} +(-2.24264 - 6.70601i) q^{10} +(13.3161 + 7.68808i) q^{11} +(-5.10300 + 2.94622i) q^{13} +(-0.996422 + 0.575285i) q^{14} +(-2.00000 + 3.46410i) q^{16} +12.8995 q^{17} +1.24264 q^{19} +(9.79894 + 1.99520i) q^{20} +(-18.8319 + 10.8726i) q^{22} +(-2.39949 - 4.15605i) q^{23} +(-3.03902 - 24.8146i) q^{25} -8.33316i q^{26} -1.62715i q^{28} +(36.9592 + 21.3384i) q^{29} +(-2.10660 - 3.64874i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(-9.12132 + 15.7986i) q^{34} +(-3.85786 + 1.29016i) q^{35} +70.3144i q^{37} +(-0.878680 + 1.52192i) q^{38} +(-9.37251 + 10.5904i) q^{40} +(-6.09942 + 3.52150i) q^{41} +(-35.5500 - 20.5248i) q^{43} -30.7523i q^{44} +6.78680 q^{46} +(-39.8995 + 69.1080i) q^{47} +(-24.1690 - 41.8620i) q^{49} +(32.5405 + 13.8245i) q^{50} +(10.2060 + 5.89243i) q^{52} -63.7279 q^{53} +(-72.9117 + 24.3833i) q^{55} +(1.99284 + 1.15057i) q^{56} +(-52.2682 + 30.1770i) q^{58} +(31.7353 - 18.3224i) q^{59} +(41.4706 - 71.8291i) q^{61} +5.95837 q^{62} +8.00000 q^{64} +(5.87830 - 28.8698i) q^{65} +(-77.0786 + 44.5013i) q^{67} +(-12.8995 - 22.3426i) q^{68} +(1.14781 - 5.63718i) q^{70} +69.6982i q^{71} +89.6188i q^{73} +(-86.1172 - 49.7198i) q^{74} +(-1.24264 - 2.15232i) q^{76} +(6.25483 + 10.8337i) q^{77} +(-67.0477 + 116.130i) q^{79} +(-6.34315 - 18.9675i) q^{80} -9.96031i q^{82} +(54.5122 - 94.4179i) q^{83} +(-42.7448 + 48.2991i) q^{85} +(50.2753 - 29.0265i) q^{86} +(37.6638 + 21.7452i) q^{88} +137.514i q^{89} -4.79394 q^{91} +(-4.79899 + 8.31209i) q^{92} +(-56.4264 - 97.7334i) q^{94} +(-4.11772 + 4.65277i) q^{95} +(-78.4877 - 45.3149i) q^{97} +68.3604 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} + 12 q^{5}+O(q^{10}) \) 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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