LMFDB - Embedded newform 804.2.o.d.641.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(365,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("804.365");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.o (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			641.1
Character	$\chi$	$=$	804.641
Dual form			804.2.o.d.365.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.72171 + 0.188968i) q^{3} +3.09374 q^{5} +(-1.38610 + 0.800262i) q^{7} +(2.92858 - 0.650697i) q^{9} +O(q^{10})$	\(q+(-1.72171 + 0.188968i) q^{3} +3.09374 q^{5} +(-1.38610 + 0.800262i) q^{7} +(2.92858 - 0.650697i) q^{9} +(2.72317 + 4.71667i) q^{11} +(-3.69642 - 2.13413i) q^{13} +(-5.32653 + 0.584618i) q^{15} +(1.10628 + 0.638709i) q^{17} +(0.117880 - 0.204175i) q^{19} +(2.23523 - 1.63975i) q^{21} +(4.09358 + 2.36343i) q^{23} +4.57123 q^{25} +(-4.91921 + 1.67372i) q^{27} +(-1.17099 + 0.676069i) q^{29} +(-1.21571 + 0.701891i) q^{31} +(-5.57981 - 7.60615i) q^{33} +(-4.28822 + 2.47580i) q^{35} +(3.33128 - 5.76994i) q^{37} +(6.76745 + 2.97585i) q^{39} +(3.91001 + 6.77233i) q^{41} +7.91208i q^{43} +(9.06028 - 2.01309i) q^{45} +(0.523745 - 0.302384i) q^{47} +(-2.21916 + 3.84370i) q^{49} +(-2.02538 - 0.890622i) q^{51} +8.20758 q^{53} +(8.42478 + 14.5922i) q^{55} +(-0.164374 + 0.373806i) q^{57} +13.8714i q^{59} +(7.23406 + 4.17658i) q^{61} +(-3.53856 + 3.24556i) q^{63} +(-11.4358 - 6.60244i) q^{65} +(6.48268 - 4.99749i) q^{67} +(-7.49458 - 3.29559i) q^{69} +(11.3188 - 6.53491i) q^{71} +(-3.23694 + 5.60654i) q^{73} +(-7.87035 + 0.863817i) q^{75} +(-7.54914 - 4.35850i) q^{77} +(-8.34701 + 4.81915i) q^{79} +(8.15319 - 3.81124i) q^{81} +(-12.5094 - 7.22228i) q^{83} +(3.42253 + 1.97600i) q^{85} +(1.88835 - 1.38528i) q^{87} -2.12681i q^{89} +6.83145 q^{91} +(1.96047 - 1.43818i) q^{93} +(0.364692 - 0.631664i) q^{95} +(2.75058 + 1.58805i) q^{97} +(11.0441 + 12.0412i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{9}+O(q^{10}) $ 36 * q + 4 * q^9	$ 36 q + 4 q^{9} - 36 q^{13} + 18 q^{15} + 16 q^{21} + 76 q^{25} + 6 q^{31} + 4 q^{33} + 42 q^{37} - 21 q^{39} + 2 q^{49} + 18 q^{51} + 20 q^{55} + 18 q^{57} - 24 q^{61} - 12 q^{63} - 8 q^{67} + 3 q^{69} + 14 q^{73} + 72 q^{79} - 12 q^{81} - 18 q^{85} - 21 q^{87} - 68 q^{91} + 9 q^{93} - 48 q^{97} + 15 q^{99}+O(q^{100}) $ 36 * q + 4 * q^9 - 36 * q^13 + 18 * q^15 + 16 * q^21 + 76 * q^25 + 6 * q^31 + 4 * q^33 + 42 * q^37 - 21 * q^39 + 2 * q^49 + 18 * q^51 + 20 * q^55 + 18 * q^57 - 24 * q^61 - 12 * q^63 - 8 * q^67 + 3 * q^69 + 14 * q^73 + 72 * q^79 - 12 * q^81 - 18 * q^85 - 21 * q^87 - 68 * q^91 + 9 * q^93 - 48 * q^97 + 15 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.72171	+	0.188968i	−0.994031	+	0.109101i
$3$	−1.72171	+	0.188968i	−0.994031	+	0.109101i
$4$		0			0
$5$	3.09374			1.38356			0.691782	−	0.722107i	$-0.256826\pi$
$5$	3.09374			1.38356			0.691782	+	0.722107i	$0.256826\pi$
$6$		0			0
$7$	−1.38610	+	0.800262i	−0.523895	+	0.302471i	−0.738527	−	0.674224i	$-0.764478\pi$
$7$	−1.38610	+	0.800262i	−0.523895	+	0.302471i	0.214632	+	0.976695i	$0.431145\pi$
$8$		0			0
$9$	2.92858	−	0.650697i	0.976194	−	0.216899i
$10$		0			0
$11$	2.72317	+	4.71667i	0.821067	+	1.42213i	0.904889	+	0.425648i	$0.139954\pi$
$11$	2.72317	+	4.71667i	0.821067	+	1.42213i	−0.0838221	+	0.996481i	$0.526713\pi$
$12$		0			0
$13$	−3.69642	−	2.13413i	−1.02520	−	0.591901i	−0.109596	−	0.993976i	$-0.534956\pi$
$13$	−3.69642	−	2.13413i	−1.02520	−	0.591901i	−0.915607	+	0.402075i	$0.868289\pi$
$14$		0			0
$15$	−5.32653	+	0.584618i	−1.37530	+	0.150948i
$16$		0			0
$17$	1.10628	+	0.638709i	0.268311	+	0.154910i	0.628120	−	0.778116i	$-0.283825\pi$
$17$	1.10628	+	0.638709i	0.268311	+	0.154910i	−0.359809	+	0.933026i	$0.617158\pi$
$18$		0			0
$19$	0.117880	−	0.204175i	0.0270436	−	0.0468409i	−0.852187	−	0.523238i	$-0.824724\pi$
$19$	0.117880	−	0.204175i	0.0270436	−	0.0468409i	0.879230	+	0.476397i	$0.158057\pi$
$20$		0			0
$21$	2.23523	−	1.63975i	0.487768	−	0.357822i
$22$		0			0
$23$	4.09358	+	2.36343i	0.853570	+	0.492809i	0.861854	−	0.507157i	$-0.169303\pi$
$23$	4.09358	+	2.36343i	0.853570	+	0.492809i	−0.00828347	+	0.999966i	$0.502637\pi$
$24$		0			0
$25$	4.57123			0.914247
$26$		0			0
$27$	−4.91921	+	1.67372i	−0.946703	+	0.322108i
$28$		0			0
$29$	−1.17099	+	0.676069i	−0.217447	+	0.125543i	−0.604767	−	0.796402i	$-0.706734\pi$
$29$	−1.17099	+	0.676069i	−0.217447	+	0.125543i	0.387321	+	0.921945i	$0.373401\pi$
$30$		0			0
$31$	−1.21571	+	0.701891i	−0.218348	+	0.126063i	−0.605185	−	0.796085i	$-0.706901\pi$
$31$	−1.21571	+	0.701891i	−0.218348	+	0.126063i	0.386837	+	0.922148i	$0.373568\pi$
$32$		0			0
$33$	−5.57981	−	7.60615i	−0.971321	−	1.32406i
$34$		0			0
$35$	−4.28822	+	2.47580i	−0.724841	+	0.418487i
$36$		0			0
$37$	3.33128	−	5.76994i	0.547659	−	0.948573i	−0.450776	−	0.892637i	$-0.648853\pi$
$37$	3.33128	−	5.76994i	0.547659	−	0.948573i	0.998434	−	0.0559354i	$-0.0178141\pi$
$38$		0			0
$39$	6.76745	+	2.97585i	1.08366	+	0.476517i
$40$		0			0
$41$	3.91001	+	6.77233i	0.610640	+	1.05766i	0.991133	+	0.132876i	$0.0424212\pi$
$41$	3.91001	+	6.77233i	0.610640	+	1.05766i	−0.380492	+	0.924784i	$0.624245\pi$
$42$		0			0
$43$			7.91208i			1.20658i	0.797521	+	0.603291i	$0.206144\pi$
$43$			7.91208i			1.20658i	−0.797521	+	0.603291i	$0.793856\pi$
$44$		0			0
$45$	9.06028	−	2.01309i	1.35063	−	0.300093i
$46$		0			0
$47$	0.523745	−	0.302384i	0.0763961	−	0.0441073i	−0.461315	−	0.887236i	$-0.652622\pi$
$47$	0.523745	−	0.302384i	0.0763961	−	0.0441073i	0.537711	+	0.843129i	$0.319289\pi$
$48$		0			0
$49$	−2.21916	+	3.84370i	−0.317023	+	0.549100i
$50$		0			0
$51$	−2.02538	−	0.890622i	−0.283611	−	0.124712i
$52$		0			0
$53$	8.20758			1.12740			0.563699	−	0.825980i	$-0.309378\pi$
$53$	8.20758			1.12740			0.563699	+	0.825980i	$0.309378\pi$
$54$		0			0
$55$	8.42478	+	14.5922i	1.13600	+	1.96761i
$56$		0			0
$57$	−0.164374	+	0.373806i	−0.0217718	+	0.0495118i
$58$		0			0
$59$			13.8714i			1.80590i	0.429746	+	0.902950i	$0.358603\pi$
$59$			13.8714i			1.80590i	−0.429746	+	0.902950i	$0.641397\pi$
$60$		0			0
$61$	7.23406	+	4.17658i	0.926226	+	0.534757i	0.885616	−	0.464418i	$-0.153737\pi$
$61$	7.23406	+	4.17658i	0.926226	+	0.534757i	0.0406100	+	0.999175i	$0.487070\pi$
$62$		0			0
$63$	−3.53856	+	3.24556i	−0.445817	+	0.408902i
$64$		0			0
$65$	−11.4358	−	6.60244i	−1.41843	−	0.818932i
$66$		0			0
$67$	6.48268	−	4.99749i	0.791985	−	0.610540i
$67$	6.48268	−	4.99749i	0.791985	−	0.610540i
$68$		0			0
$69$	−7.49458	−	3.29559i	−0.902241	−	0.396742i
$70$		0			0
$71$	11.3188	−	6.53491i	1.34329	−	0.775551i	0.356004	−	0.934484i	$-0.384139\pi$
$71$	11.3188	−	6.53491i	1.34329	−	0.775551i	0.987289	+	0.158933i	$0.0508055\pi$
$72$		0			0
$73$	−3.23694	+	5.60654i	−0.378855	+	0.656196i	−0.990896	−	0.134630i	$-0.957015\pi$
$73$	−3.23694	+	5.60654i	−0.378855	+	0.656196i	0.612041	+	0.790826i	$0.290349\pi$
$74$		0			0
$75$	−7.87035	+	0.863817i	−0.908789	+	0.0997450i
$76$		0			0
$77$	−7.54914	−	4.35850i	−0.860305	−	0.496697i
$78$		0			0
$79$	−8.34701	+	4.81915i	−0.939112	+	0.542197i	−0.889682	−	0.456581i	$-0.849074\pi$
$79$	−8.34701	+	4.81915i	−0.939112	+	0.542197i	−0.0494304	+	0.998778i	$0.515741\pi$
$80$		0			0
$81$	8.15319	−	3.81124i	0.905910	−	0.423471i
$82$		0			0
$83$	−12.5094	−	7.22228i	−1.37308	−	0.792748i	−0.381765	−	0.924259i	$-0.624684\pi$
$83$	−12.5094	−	7.22228i	−1.37308	−	0.792748i	−0.991315	+	0.131511i	$0.958017\pi$
$84$		0			0
$85$	3.42253	+	1.97600i	0.371226	+	0.214327i
$86$		0			0
$87$	1.88835	−	1.38528i	0.202452	−	0.148517i
$88$		0			0
$89$		−	2.12681i		−	0.225441i	−0.993627	−	0.112721i	$-0.964043\pi$
$89$		−	2.12681i		−	0.225441i	0.993627	−	0.112721i	$-0.0359565\pi$
$90$		0			0
$91$	6.83145			0.716131
$92$		0			0
$93$	1.96047	−	1.43818i	0.203291	−	0.149133i
$94$		0			0
$95$	0.364692	−	0.631664i	0.0374166	−	0.0648074i
$96$		0			0
$97$	2.75058	+	1.58805i	0.279280	+	0.161242i	0.633097	−	0.774072i	$-0.281783\pi$
$97$	2.75058	+	1.58805i	0.279280	+	0.161242i	−0.353818	+	0.935314i	$0.615117\pi$
$98$		0			0
$99$	11.0441	+	12.0412i	1.10998	+	1.21019i
$100$		0			0
$101$	2.10535	+	3.64656i	0.209490	+	0.362847i	0.951554	−	0.307482i	$-0.0994864\pi$
$101$	2.10535	+	3.64656i	0.209490	+	0.362847i	−0.742064	+	0.670329i	$0.766153\pi$
$102$		0			0
$103$	−0.638994	−	1.10677i	−0.0629620	−	0.109053i	0.832826	−	0.553535i	$-0.186721\pi$
$103$	−0.638994	−	1.10677i	−0.0629620	−	0.109053i	−0.895788	+	0.444481i	$0.853388\pi$
$104$		0			0
$105$	6.91523	−	5.07296i	0.674857	−	0.495070i
$106$		0			0
$107$		−	7.73405i		−	0.747679i	−0.927493	−	0.373840i	$-0.878041\pi$
$107$		−	7.73405i		−	0.747679i	0.927493	−	0.373840i	$-0.121959\pi$
$108$		0			0
$109$		−	3.97936i		−	0.381154i	−0.981672	−	0.190577i	$-0.938964\pi$
$109$		−	3.97936i		−	0.381154i	0.981672	−	0.190577i	$-0.0610359\pi$
$110$		0			0
$111$	−4.64517	+	10.5637i	−0.440900	+	1.00266i
$112$		0			0
$113$	−1.84973	−	3.20382i	−0.174008	−	0.301390i	0.765810	−	0.643067i	$-0.222338\pi$
$113$	−1.84973	−	3.20382i	−0.174008	−	0.301390i	−0.939817	+	0.341677i	$0.889005\pi$
$114$		0			0
$115$	12.6645	+	7.31184i	1.18097	+	0.681833i
$116$		0			0
$117$	−12.2139	−	3.84472i	−1.12918	−	0.355445i
$118$		0			0
$119$	−2.04454			−0.187423
$120$		0			0
$121$	−9.33131	+	16.1623i	−0.848301	+	1.46930i
$122$		0			0
$123$	−8.01166	−	10.9211i	−0.722387	−	0.984725i
$124$		0			0
$125$	−1.32649			−0.118645
$126$		0			0
$127$	−9.10719	−	15.7741i	−0.808132	−	1.39973i	−0.914156	−	0.405362i	$-0.867145\pi$
$127$	−9.10719	−	15.7741i	−0.808132	−	1.39973i	0.106024	−	0.994364i	$-0.466188\pi$
$128$		0			0
$129$	−1.49513	−	13.6223i	−0.131639	−	1.19938i
$130$		0			0
$131$			3.50688i			0.306397i	0.988195	+	0.153199i	$0.0489575\pi$
$131$			3.50688i			0.306397i	−0.988195	+	0.153199i	$0.951043\pi$
$132$		0			0
$133$			0.377341i			0.0327196i
$134$		0			0
$135$	−15.2188	+	5.17806i	−1.30982	+	0.445656i
$136$		0			0
$137$	16.4673			1.40690			0.703450	−	0.710745i	$-0.251642\pi$
$137$	16.4673			1.40690			0.703450	+	0.710745i	$0.251642\pi$
$138$		0			0
$139$		−	20.9672i		−	1.77841i	−0.457506	−	0.889207i	$-0.651257\pi$
$139$		−	20.9672i		−	1.77841i	0.457506	−	0.889207i	$-0.348743\pi$
$140$		0			0
$141$	−0.844597	+	0.619590i	−0.0711279	+	0.0521789i
$142$		0			0
$143$		−	23.2464i		−	1.94396i
$144$		0			0
$145$	−3.62273	+	2.09158i	−0.300851	+	0.173697i
$146$		0			0
$147$	3.09442	−	7.03709i	0.255223	−	0.580409i
$148$		0			0
$149$		−	4.30917i		−	0.353021i	−0.984299	−	0.176511i	$-0.943519\pi$
$149$		−	4.30917i		−	0.353021i	0.984299	−	0.176511i	$-0.0564810\pi$
$150$		0			0
$151$	10.5111	−	18.2058i	0.855383	−	1.48157i	−0.0209071	−	0.999781i	$-0.506655\pi$
$151$	10.5111	−	18.2058i	0.855383	−	1.48157i	0.876290	−	0.481785i	$-0.160011\pi$
$152$		0			0
$153$	3.65543	+	1.15066i	0.295524	+	0.0930254i
$154$		0			0
$155$	−3.76110	+	2.17147i	−0.302098	+	0.174417i
$156$		0			0
$157$	−9.90585	+	17.1574i	−0.790573	+	1.36931i	0.135040	+	0.990840i	$0.456884\pi$
$157$	−9.90585	+	17.1574i	−0.790573	+	1.36931i	−0.925613	+	0.378472i	$0.876449\pi$
$158$		0			0
$159$	−14.1311	+	1.55097i	−1.12067	+	0.123000i
$160$		0			0
$161$	−7.56545			−0.596241
$162$		0			0
$163$	−9.37120	−	16.2314i	−0.734009	−	1.27134i	−0.955157	−	0.296101i	$-0.904314\pi$
$163$	−9.37120	−	16.2314i	−0.734009	−	1.27134i	0.221148	−	0.975240i	$-0.429020\pi$
$164$		0			0
$165$	−17.2625	−	23.5315i	−1.34388	−	1.83192i
$166$		0			0
$167$	−11.8538	+	6.84379i	−0.917274	+	0.529589i	−0.882764	−	0.469816i	$-0.844320\pi$
$167$	−11.8538	+	6.84379i	−0.917274	+	0.529589i	−0.0345098	+	0.999404i	$0.510987\pi$
$168$		0			0
$169$	2.60902	+	4.51895i	0.200694	+	0.347611i
$170$		0			0
$171$	0.212367	−	0.674648i	0.0162401	−	0.0515916i
$172$		0			0
$173$	−13.7355	−	7.93017i	−1.04429	−	0.602920i	−0.123243	−	0.992377i	$-0.539329\pi$
$173$	−13.7355	−	7.93017i	−1.04429	−	0.602920i	−0.921045	+	0.389457i	$0.872663\pi$
$174$		0			0
$175$	−6.33616	+	3.65819i	−0.478969	+	0.276533i
$176$		0			0
$177$	−2.62125	−	23.8825i	−0.197025	−	1.79512i
$178$		0			0
$179$	−15.9844			−1.19473			−0.597363	−	0.801971i	$-0.703785\pi$
$179$	−15.9844			−1.19473			−0.597363	+	0.801971i	$0.703785\pi$
$180$		0			0
$181$	3.73838	+	6.47507i	0.277872	+	0.481288i	0.970856	−	0.239665i	$-0.0770376\pi$
$181$	3.73838	+	6.47507i	0.277872	+	0.481288i	−0.692984	+	0.720953i	$0.743704\pi$
$182$		0			0
$183$	−13.2442	−	5.82387i	−0.979039	−	0.430513i
$184$		0			0
$185$	10.3061	−	17.8507i	0.757720	−	1.31241i
$186$		0			0
$187$			6.95725i			0.508765i
$188$		0			0
$189$	5.47908	−	6.25660i	0.398545	−	0.455100i
$190$		0			0
$191$	0.582685	−	1.00924i	0.0421616	−	0.0730261i	−0.844175	−	0.536068i	$-0.819909\pi$
$191$	0.582685	−	1.00924i	0.0421616	−	0.0730261i	0.886336	+	0.463042i	$0.153242\pi$
$192$		0			0
$193$	20.8603			1.50156			0.750778	−	0.660554i	$-0.229679\pi$
$193$	20.8603			1.50156			0.750778	+	0.660554i	$0.229679\pi$
$194$		0			0
$195$	20.9367	+	9.20651i	1.49931	+	0.659292i
$196$		0			0
$197$	−9.33029	−	16.1605i	−0.664755	−	1.15139i	−0.979352	−	0.202165i	$-0.935202\pi$
$197$	−9.33029	−	16.1605i	−0.664755	−	1.15139i	0.314596	−	0.949226i	$-0.398131\pi$
$198$		0			0
$199$	4.17340	−	7.22854i	0.295844	−	0.512418i	−0.679337	−	0.733827i	$-0.737732\pi$
$199$	4.17340	−	7.22854i	0.295844	−	0.512418i	0.975181	+	0.221409i	$0.0710657\pi$
$200$		0			0
$201$	−10.2169	+	9.82925i	−0.720647	+	0.693302i
$202$		0			0
$203$	1.08207	−	1.87419i	0.0759461	−	0.131543i
$204$		0			0
$205$	12.0965	+	20.9518i	0.844859	+	1.46334i
$206$		0			0
$207$	13.5263	+	4.25782i	0.940140	+	0.295939i
$208$		0			0
$209$	1.28403			0.0888185
$210$		0			0
$211$	1.30463	−	2.25969i	0.0898145	−	0.155563i	−0.817618	−	0.575761i	$-0.804706\pi$
$211$	1.30463	−	2.25969i	0.0898145	−	0.155563i	0.907433	+	0.420198i	$0.138039\pi$
$212$		0			0
$213$	−18.2528	+	13.3901i	−1.25066	+	0.917476i
$214$		0			0
$215$			24.4779i			1.66938i
$216$		0			0
$217$	1.12339	−	1.94578i	0.0762610	−	0.132088i
$218$		0			0
$219$	4.51362	−	10.2645i	0.305002	−	0.693613i
$220$		0			0
$221$	−2.72617	−	4.72187i	−0.183382	−	0.317628i
$222$		0			0
$223$	20.1726			1.35086			0.675429	−	0.737425i	$-0.263958\pi$
$223$	20.1726			1.35086			0.675429	+	0.737425i	$0.263958\pi$
$224$		0			0
$225$	13.3872	−	2.97449i	0.892482	−	0.198299i
$226$		0			0
$227$	−9.98643	+	5.76567i	−0.662822	+	0.382681i	−0.793352	−	0.608764i	$-0.791666\pi$
$227$	−9.98643	+	5.76567i	−0.662822	+	0.382681i	0.130529	+	0.991444i	$0.458332\pi$
$228$		0			0
$229$	−12.7449	−	7.35827i	−0.842207	−	0.486248i	0.0158068	−	0.999875i	$-0.494968\pi$
$229$	−12.7449	−	7.35827i	−0.842207	−	0.486248i	−0.858014	+	0.513627i	$0.828302\pi$
$230$		0			0
$231$	13.8211	+	6.07753i	0.909359	+	0.399872i
$232$		0			0
$233$	3.97386	+	6.88293i	0.260336	+	0.450916i	0.966331	−	0.257301i	$-0.0828333\pi$
$233$	3.97386	+	6.88293i	0.260336	+	0.450916i	−0.705995	+	0.708217i	$0.749500\pi$
$234$		0			0
$235$	1.62033	−	0.935499i	0.105699	−	0.0610252i
$236$		0			0
$237$	13.4605	−	9.87451i	0.874352	−	0.641418i
$238$		0			0
$239$	13.8741	+	24.0307i	0.897442	+	1.55442i	0.830752	+	0.556642i	$0.187911\pi$
$239$	13.8741	+	24.0307i	0.897442	+	1.55442i	0.0666902	+	0.997774i	$0.478756\pi$
$240$		0			0
$241$	−1.22462			−0.0788850			−0.0394425	−	0.999222i	$-0.512558\pi$
$241$	−1.22462			−0.0788850			−0.0394425	+	0.999222i	$0.512558\pi$
$242$		0			0
$243$	−13.3172	+	8.10255i	−0.854301	+	0.519779i
$244$		0			0
$245$	−6.86551	+	11.8914i	−0.438621	+	0.759714i
$246$		0			0
$247$	−0.871472	+	0.503144i	−0.0554504	+	0.0320143i
$248$		0			0
$249$	22.9023	+	10.0708i	1.45137	+	0.638212i
$250$		0			0
$251$	−1.29071	+	2.23557i	−0.0814687	+	0.141108i	−0.903881	−	0.427784i	$-0.859294\pi$
$251$	−1.29071	+	2.23557i	−0.0814687	+	0.141108i	0.822412	+	0.568892i	$0.192628\pi$
$252$		0			0
$253$			25.7441i			1.61852i
$254$		0			0
$255$	−6.26601	−	2.75535i	−0.392393	−	0.172547i
$256$		0			0
$257$	7.44518	−	4.29848i	0.464418	−	0.268132i	−0.249482	−	0.968379i	$-0.580260\pi$
$257$	7.44518	−	4.29848i	0.464418	−	0.268132i	0.713900	+	0.700248i	$0.246927\pi$
$258$		0			0
$259$			10.6636i			0.662603i
$260$		0			0
$261$	−2.98941	+	2.74188i	−0.185040	+	0.169718i
$262$		0			0
$263$		−	11.6279i		−	0.717009i	−0.933528	−	0.358505i	$-0.883287\pi$
$263$		−	11.6279i		−	0.717009i	0.933528	−	0.358505i	$-0.116713\pi$
$264$		0			0
$265$	25.3921			1.55983
$266$		0			0
$267$	0.401899	+	3.66175i	0.0245958	+	0.224096i
$268$		0			0
$269$		−	3.35461i		−	0.204534i	−0.994757	−	0.102267i	$-0.967390\pi$
$269$		−	3.35461i		−	0.204534i	0.994757	−	0.102267i	$-0.0326096\pi$
$270$		0			0
$271$			3.39129i			0.206006i	0.994681	+	0.103003i	$0.0328452\pi$
$271$			3.39129i			0.206006i	−0.994681	+	0.103003i	$0.967155\pi$
$272$		0			0
$273$	−11.7618	+	1.29093i	−0.711856	+	0.0781304i
$274$		0			0
$275$	12.4482	+	21.5610i	0.750658	+	1.30018i
$276$		0			0
$277$	−24.5468			−1.47488			−0.737438	−	0.675415i	$-0.763965\pi$
$277$	−24.5468			−1.47488			−0.737438	+	0.675415i	$0.763965\pi$
$278$		0			0
$279$	−3.10359	+	2.84661i	−0.185807	+	0.170422i
$280$		0			0
$281$	5.71395	−	9.89685i	0.340865	−	0.590396i	−0.643728	−	0.765254i	$-0.722613\pi$
$281$	5.71395	−	9.89685i	0.340865	−	0.590396i	0.984594	+	0.174858i	$0.0559466\pi$
$282$		0			0
$283$	−7.61687			−0.452776			−0.226388	−	0.974037i	$-0.572692\pi$
$283$	−7.61687			−0.452776			−0.226388	+	0.974037i	$0.572692\pi$
$284$		0			0
$285$	−0.508529	+	1.15646i	−0.0301227	+	0.0685027i
$286$		0			0
$287$	−10.8393	−	6.25806i	−0.639822	−	0.369402i
$288$		0			0
$289$	−7.68410	−	13.3093i	−0.452006	−	0.782897i
$290$		0			0
$291$	−5.03580	−	2.21439i	−0.295204	−	0.129810i
$292$		0			0
$293$			7.97510i			0.465910i	0.972487	+	0.232955i	$0.0748395\pi$
$293$			7.97510i			0.465910i	−0.972487	+	0.232955i	$0.925160\pi$
$294$		0			0
$295$			42.9145i			2.49858i
$296$		0			0
$297$	−21.2902	−	18.6445i	−1.23538	−	1.08186i
$298$		0			0
$299$	−10.0877	−	17.4725i	−0.583388	−	1.01046i
$300$		0			0
$301$	−6.33174	−	10.9669i	−0.364955	−	0.632121i
$302$		0			0
$303$	−4.31388	−	5.88049i	−0.247826	−	0.337825i
$304$		0			0
$305$	22.3803	+	12.9213i	1.28149	+	0.739870i
$306$		0			0
$307$	8.59740	−	14.8911i	0.490679	−	0.849882i	−0.509263	−	0.860611i	$-0.670082\pi$
$307$	8.59740	−	14.8911i	0.490679	−	0.849882i	0.999942	+	0.0107293i	$0.00341530\pi$
$308$		0			0
$309$	1.30931	+	1.78479i	0.0744840	+	0.101533i
$310$		0			0
$311$	8.51233			0.482690			0.241345	−	0.970439i	$-0.422411\pi$
$311$	8.51233			0.482690			0.241345	+	0.970439i	$0.422411\pi$
$312$		0			0
$313$		−	16.1984i		−	0.915589i	−0.889058	−	0.457794i	$-0.848640\pi$
$313$		−	16.1984i		−	0.915589i	0.889058	−	0.457794i	$-0.151360\pi$
$314$		0			0
$315$	−10.9474	+	10.0409i	−0.616816	+	0.565742i
$316$		0			0
$317$	20.5239	+	11.8495i	1.15274	+	0.665534i	0.949553	−	0.313607i	$-0.101537\pi$
$317$	20.5239	+	11.8495i	1.15274	+	0.665534i	0.203185	+	0.979140i	$0.434871\pi$
$318$		0			0
$319$	−6.37759	−	3.68210i	−0.357076	−	0.206158i
$320$		0			0
$321$	1.46149	+	13.3158i	0.0815723	+	0.743216i
$322$		0			0
$323$	0.260817	−	0.150583i	0.0145122	−	0.00837864i
$324$		0			0
$325$	−16.8972	−	9.75561i	−0.937288	−	0.541144i
$326$		0			0
$327$	0.751972	+	6.85132i	0.0415842	+	0.378879i
$328$		0			0
$329$	−0.483974	+	0.838267i	−0.0266823	+	0.0462152i
$330$		0			0
$331$	−20.6692	+	11.9334i	−1.13608	+	0.655917i	−0.945457	−	0.325746i	$-0.894385\pi$
$331$	−20.6692	+	11.9334i	−1.13608	+	0.655917i	−0.190624	+	0.981663i	$0.561051\pi$
$332$		0			0
$333$	6.00144	−	19.0654i	0.328877	−	1.04478i
$334$		0			0
$335$	20.0557	−	15.4609i	1.09576	−	0.844721i
$336$		0			0
$337$	−25.3487	−	14.6351i	−1.38083	−	0.797223i	−0.388573	−	0.921418i	$-0.627032\pi$
$337$	−25.3487	−	14.6351i	−1.38083	−	0.797223i	−0.992258	+	0.124194i	$0.960365\pi$
$338$		0			0
$339$	3.79012	+	5.16652i	0.205851	+	0.280607i
$340$		0			0
$341$	−6.62117	−	3.82274i	−0.358557	−	0.207013i
$342$		0			0
$343$		−	18.3073i		−	0.988502i
$344$		0			0
$345$	−23.1863	−	10.1957i	−1.24831	−	0.548918i
$346$		0			0
$347$	13.6699	+	23.6770i	0.733841	+	1.27105i	0.955230	+	0.295864i	$0.0956076\pi$
$347$	13.6699	+	23.6770i	0.733841	+	1.27105i	−0.221389	+	0.975186i	$0.571059\pi$
$348$		0			0
$349$	23.4301			1.25418			0.627092	−	0.778945i	$-0.284245\pi$
$349$	23.4301			1.25418			0.627092	+	0.778945i	$0.284245\pi$
$350$		0			0
$351$	21.7554	+	4.31146i	1.16122	+	0.230129i
$352$		0			0
$353$	2.16051	−	3.74211i	0.114992	−	0.199172i	−0.802784	−	0.596269i	$-0.796649\pi$
$353$	2.16051	−	3.74211i	0.114992	−	0.199172i	0.917777	+	0.397097i	$0.129982\pi$
$354$		0			0
$355$	35.0174	−	20.2173i	1.85853	−	1.07302i
$356$		0			0
$357$	3.52011	−	0.386352i	0.186304	−	0.0204479i
$358$		0			0
$359$		−	9.88207i		−	0.521556i	−0.965399	−	0.260778i	$-0.916021\pi$
$359$		−	9.88207i		−	0.521556i	0.965399	−	0.260778i	$-0.0839790\pi$
$360$		0			0
$361$	9.47221	+	16.4063i	0.498537	+	0.863492i
$362$		0			0
$363$	13.0117	−	29.5901i	0.682935	−	1.55308i
$364$		0			0
$365$	−10.0143	+	17.3452i	−0.524170	+	0.907889i
$366$		0			0
$367$	−5.33339	+	3.07924i	−0.278401	+	0.160735i	−0.632699	−	0.774398i	$-0.718053\pi$
$367$	−5.33339	+	3.07924i	−0.278401	+	0.160735i	0.354298	+	0.935132i	$0.384720\pi$
$368$		0			0
$369$	15.8575	+	17.2891i	0.825509	+	0.900034i
$370$		0			0
$371$	−11.3765	+	6.56822i	−0.590638	+	0.341005i
$372$		0			0
$373$	14.4681	−	8.35314i	0.749128	−	0.432509i	−0.0762510	−	0.997089i	$-0.524295\pi$
$373$	14.4681	−	8.35314i	0.749128	−	0.432509i	0.825379	+	0.564580i	$0.190962\pi$
$374$		0			0
$375$	2.28383	−	0.250664i	0.117937	−	0.0129443i
$376$		0			0
$377$	5.77128			0.297236
$378$		0			0
$379$	−27.2027	−	15.7055i	−1.39731	−	0.806738i	−0.403201	−	0.915111i	$-0.632102\pi$
$379$	−27.2027	−	15.7055i	−1.39731	−	0.806738i	−0.994110	+	0.108373i	$0.965436\pi$
$380$		0			0
$381$	18.6608	+	25.4375i	0.956019	+	1.30320i
$382$		0			0
$383$	8.06162	−	13.9631i	0.411930	−	0.713483i	−0.583171	−	0.812349i	$-0.698188\pi$
$383$	8.06162	−	13.9631i	0.411930	−	0.713483i	0.995101	+	0.0988664i	$0.0315216\pi$
$384$		0			0
$385$	−23.3551	−	13.4841i	−1.19029	−	0.687212i
$386$		0			0
$387$	5.14837	+	23.1712i	0.261706	+	1.17786i
$388$		0			0
$389$	−16.5719	−	9.56781i	−0.840230	−	0.485107i	0.0171124	−	0.999854i	$-0.494553\pi$
$389$	−16.5719	−	9.56781i	−0.840230	−	0.485107i	−0.857342	+	0.514747i	$0.827886\pi$
$390$		0			0
$391$	3.01909	+	5.22921i	0.152682	+	0.264453i
$392$		0			0
$393$	−0.662688	−	6.03783i	−0.0334282	−	0.304568i
$394$		0			0
$395$	−25.8235	+	14.9092i	−1.29932	+	0.750163i
$396$		0			0
$397$	−9.47362			−0.475467			−0.237734	−	0.971330i	$-0.576405\pi$
$397$	−9.47362			−0.475467			−0.237734	+	0.971330i	$0.576405\pi$
$398$		0			0
$399$	−0.0713054	−	0.649673i	−0.00356974	−	0.0325243i
$400$		0			0
$401$	30.0145			1.49885			0.749427	−	0.662087i	$-0.230329\pi$
$401$	30.0145			1.49885			0.749427	+	0.662087i	$0.230329\pi$
$402$		0			0
$403$	5.99171			0.298468
$404$		0			0
$405$	25.2239	−	11.7910i	1.25338	−	0.585899i
$406$		0			0
$407$	36.2865			1.79866
$408$		0			0
$409$	−14.5475	+	8.39898i	−0.719326	+	0.415303i	−0.814504	−	0.580157i	$-0.802991\pi$
$409$	−14.5475	+	8.39898i	−0.719326	+	0.415303i	0.0951787	+	0.995460i	$0.469658\pi$
$410$		0			0
$411$	−28.3520	+	3.11180i	−1.39850	+	0.153494i
$412$		0			0
$413$	−11.1007	−	19.2270i	−0.546232	−	0.946101i
$414$		0			0
$415$	−38.7007	−	22.3439i	−1.89974	−	1.09682i
$416$		0			0
$417$	3.96213	+	36.0994i	0.194026	+	1.76780i
$418$		0			0
$419$	−9.38665	−	5.41939i	−0.458568	−	0.264754i	0.252874	−	0.967499i	$-0.418624\pi$
$419$	−9.38665	−	5.41939i	−0.458568	−	0.264754i	−0.711442	+	0.702745i	$0.751958\pi$
$420$		0			0
$421$	2.61037	−	4.52130i	0.127222	−	0.220355i	−0.795377	−	0.606115i	$-0.792727\pi$
$421$	2.61037	−	4.52130i	0.127222	−	0.220355i	0.922599	+	0.385760i	$0.126061\pi$
$422$		0			0
$423$	1.33707	−	1.22636i	0.0650106	−	0.0596275i
$424$		0			0
$425$	5.05705	+	2.91969i	0.245303	+	0.141626i
$426$		0			0
$427$	−13.3695			−0.646993
$428$		0			0
$429$	4.39282	+	40.0236i	0.212088	+	1.93236i
$430$		0			0
$431$	−19.0173	+	10.9796i	−0.916031	+	0.528871i	−0.882367	−	0.470562i	$-0.844051\pi$
$431$	−19.0173	+	10.9796i	−0.916031	+	0.528871i	−0.0336644	+	0.999433i	$0.510718\pi$
$432$		0			0
$433$	22.3862	−	12.9247i	1.07581	−	0.621122i	0.146050	−	0.989277i	$-0.453344\pi$
$433$	22.3862	−	12.9247i	1.07581	−	0.621122i	0.929764	+	0.368156i	$0.120011\pi$
$434$		0			0
$435$	5.84205	−	4.28568i	0.280105	−	0.205483i
$436$		0			0
$437$	0.965106	−	0.557204i	0.0461673	−	0.0266547i
$438$		0			0
$439$	19.8324	−	34.3507i	0.946549	−	1.63947i	0.193928	−	0.981016i	$-0.437877\pi$
$439$	19.8324	−	34.3507i	0.946549	−	1.63947i	0.752621	−	0.658455i	$-0.228790\pi$
$440$		0			0
$441$	−3.99791	+	12.7006i	−0.190377	+	0.604790i
$442$		0			0
$443$	8.73288	+	15.1258i	0.414912	+	0.718648i	0.995419	−	0.0956068i	$-0.0304792\pi$
$443$	8.73288	+	15.1258i	0.414912	+	0.718648i	−0.580508	+	0.814255i	$0.697146\pi$
$444$		0			0
$445$		−	6.57980i		−	0.311912i
$446$		0			0
$447$	0.814296	+	7.41916i	0.0385149	+	0.350914i
$448$		0			0
$449$	−8.84785	+	5.10831i	−0.417556	+	0.241076i	−0.694031	−	0.719945i	$-0.744167\pi$
$449$	−8.84785	+	5.10831i	−0.417556	+	0.241076i	0.276475	+	0.961021i	$0.410834\pi$
$450$		0			0
$451$	−21.2952	+	36.8844i	−1.00275	+	1.73682i
$452$		0			0
$453$	−14.6568	+	33.3314i	−0.688637	+	1.56605i
$454$		0			0
$455$	21.1347			0.990812
$456$		0			0
$457$	8.08125	+	13.9971i	0.378025	+	0.654759i	0.990775	−	0.135518i	$-0.0432700\pi$
$457$	8.08125	+	13.9971i	0.378025	+	0.654759i	−0.612750	+	0.790277i	$0.709937\pi$
$458$		0			0
$459$	−6.51103	−	1.29035i	−0.303909	−	0.0602283i
$460$		0			0
$461$			31.4807i			1.46620i	0.680119	+	0.733101i	$0.261928\pi$
$461$			31.4807i			1.46620i	−0.680119	+	0.733101i	$0.738072\pi$
$462$		0			0
$463$	6.83522	+	3.94631i	0.317659	+	0.183401i	0.650349	−	0.759636i	$-0.274623\pi$
$463$	6.83522	+	3.94631i	0.317659	+	0.183401i	−0.332689	+	0.943036i	$0.607956\pi$
$464$		0			0
$465$	6.06518	−	4.44937i	0.281266	−	0.206335i
$466$		0			0
$467$	9.30098	+	5.36992i	0.430398	+	0.248490i	0.699516	−	0.714617i	$-0.253399\pi$
$467$	9.30098	+	5.36992i	0.430398	+	0.248490i	−0.269118	+	0.963107i	$0.586732\pi$
$468$		0			0
$469$	−4.98631	+	12.1148i	−0.230246	+	0.559411i
$470$		0			0
$471$	13.8128	−	31.4121i	0.636461	−	1.44739i
$472$		0			0
$473$	−37.3187	+	21.5459i	−1.71591	+	0.990683i
$474$		0			0
$475$	0.538859	−	0.933332i	0.0247246	−	0.0428242i
$476$		0			0
$477$	24.0366	−	5.34065i	1.10056	−	0.244531i
$478$		0			0
$479$	10.1713	+	5.87238i	0.464737	+	0.268316i	0.714034	−	0.700111i	$-0.246866\pi$
$479$	10.1713	+	5.87238i	0.464737	+	0.268316i	−0.249297	+	0.968427i	$0.580200\pi$
$480$		0			0
$481$	−24.6276	+	14.2188i	−1.12292	+	0.648319i
$482$		0			0
$483$	13.0255	−	1.42963i	0.592682	−	0.0650504i
$484$		0			0
$485$	8.50960	+	4.91302i	0.386401	+	0.223089i
$486$		0			0
$487$	33.9794	+	19.6180i	1.53975	+	0.888977i	0.998853	+	0.0478904i	$0.0152498\pi$
$487$	33.9794	+	19.6180i	1.53975	+	0.888977i	0.540901	+	0.841087i	$0.318083\pi$
$488$		0			0
$489$	19.2017	+	26.1749i	0.868332	+	1.18367i
$490$		0			0
$491$		−	13.0134i		−	0.587285i	−0.955915	−	0.293643i	$-0.905132\pi$
$491$		−	13.0134i		−	0.587285i	0.955915	−	0.293643i	$-0.0948675\pi$
$492$		0			0
$493$	−1.72725			−0.0777912
$494$		0			0
$495$	34.1677	+	37.2523i	1.53573	+	1.67437i
$496$		0			0
$497$	−10.4593	+	18.1160i	−0.469163	+	0.812614i
$498$		0			0
$499$	−24.1351	−	13.9344i	−1.08043	−	0.623789i	−0.149421	−	0.988774i	$-0.547741\pi$
$499$	−24.1351	−	13.9344i	−1.08043	−	0.623789i	−0.931014	+	0.364985i	$0.881074\pi$
$500$		0			0
$501$	19.1156	−	14.0230i	0.854020	−	0.626503i
$502$		0			0
$503$	−2.68521	−	4.65092i	−0.119728	−	0.207374i	0.799932	−	0.600091i	$-0.204869\pi$
$503$	−2.68521	−	4.65092i	−0.119728	−	0.207374i	−0.919660	+	0.392716i	$0.871535\pi$
$504$		0			0
$505$	6.51339	+	11.2815i	0.289842	+	0.502021i
$506$		0			0
$507$	−5.34591	−	7.28731i	−0.237420	−	0.323641i
$508$		0			0
$509$		−	36.8498i		−	1.63334i	−0.577106	−	0.816669i	$-0.695818\pi$
$509$		−	36.8498i		−	1.63334i	0.577106	−	0.816669i	$-0.304182\pi$
$510$		0			0
$511$		−	10.3616i		−	0.458370i
$512$		0			0
$513$	−0.238147	+	1.20168i	−0.0105145	+	0.0530554i
$514$		0			0
$515$	−1.97688	−	3.42406i	−0.0871119	−	0.150882i
$516$		0			0
$517$	2.85249	+	1.64689i	0.125453	+	0.0724301i
$518$		0			0
$519$	25.1471	+	11.0579i	1.10383	+	0.485388i
$520$		0			0
$521$	−23.8720			−1.04585			−0.522927	−	0.852378i	$-0.675160\pi$
$521$	−23.8720			−1.04585			−0.522927	+	0.852378i	$0.675160\pi$
$522$		0			0
$523$	0.409211	−	0.708774i	0.0178936	−	0.0309925i	−0.856940	−	0.515416i	$-0.827637\pi$
$523$	0.409211	−	0.708774i	0.0178936	−	0.0309925i	0.874834	+	0.484424i	$0.160971\pi$
$524$		0			0
$525$	10.2178	−	7.49567i	0.445940	−	0.327138i
$526$		0			0
$527$	−1.79322			−0.0781137
$528$		0			0
$529$	−0.328401	−	0.568806i	−0.0142783	−	0.0247307i
$530$		0			0
$531$	9.02606	+	40.6235i	0.391698	+	1.76291i
$532$		0			0
$533$		−	33.3778i		−	1.44575i
$534$		0			0
$535$		−	23.9272i		−	1.03446i
$536$		0			0
$537$	27.5204	−	3.02053i	1.18759	−	0.130346i
$538$		0			0
$539$	−24.1726			−1.04119
$540$		0			0
$541$		−	29.2068i		−	1.25570i	−0.778335	−	0.627849i	$-0.783935\pi$
$541$		−	29.2068i		−	1.25570i	0.778335	−	0.627849i	$-0.216065\pi$
$542$		0			0
$543$	−7.66000	−	10.4418i	−0.328722	−	0.448099i
$544$		0			0
$545$		−	12.3111i		−	0.527350i
$546$		0			0
$547$	−6.11997	+	3.53337i	−0.261671	+	0.151076i	−0.625097	−	0.780547i	$-0.714940\pi$
$547$	−6.11997	+	3.53337i	−0.261671	+	0.151076i	0.363425	+	0.931623i	$0.381607\pi$
$548$		0			0
$549$	23.9032	+	7.52429i	1.02016	+	0.321129i
$550$		0			0
$551$			0.318781i			0.0135805i
$552$		0			0
$553$	7.71317	−	13.3596i	0.327997	−	0.568108i
$554$		0			0
$555$	−14.3709	+	32.6813i	−0.610012	+	1.38724i
$556$		0			0
$557$	−12.3055	+	7.10459i	−0.521401	+	0.301031i	−0.737508	−	0.675339i	$-0.763997\pi$
$557$	−12.3055	+	7.10459i	−0.521401	+	0.301031i	0.216107	+	0.976370i	$0.430664\pi$
$558$		0			0
$559$	16.8854	−	29.2464i	0.714177	−	1.23699i
$560$		0			0
$561$	−1.31470	−	11.9784i	−0.0555066	−	0.505728i
$562$		0			0
$563$	−17.0228			−0.717424			−0.358712	−	0.933448i	$-0.616784\pi$
$563$	−17.0228			−0.717424			−0.358712	+	0.933448i	$0.616784\pi$
$564$		0			0
$565$	−5.72258	−	9.91179i	−0.240751	−	0.416992i
$566$		0			0
$567$	−8.25110	+	11.8074i	−0.346514	+	0.495865i
$568$		0			0
$569$	24.1597	−	13.9486i	1.01283	−	0.584755i	0.100808	−	0.994906i	$-0.467857\pi$
$569$	24.1597	−	13.9486i	1.01283	−	0.584755i	0.912018	+	0.410151i	$0.134524\pi$
$570$		0			0
$571$	1.48575	+	2.57339i	0.0621766	+	0.107693i	0.895438	−	0.445186i	$-0.146862\pi$
$571$	1.48575	+	2.57339i	0.0621766	+	0.107693i	−0.833261	+	0.552879i	$0.813529\pi$
$572$		0			0
$573$	−0.812502	+	1.84773i	−0.0339428	+	0.0771900i
$574$		0			0
$575$	18.7127	+	10.8038i	0.780374	+	0.450549i
$576$		0			0
$577$	−29.0883	+	16.7941i	−1.21096	+	0.699149i	−0.962969	−	0.269614i	$-0.913104\pi$
$577$	−29.0883	+	16.7941i	−1.21096	+	0.699149i	−0.247992	+	0.968762i	$0.579771\pi$
$578$		0			0
$579$	−35.9154	+	3.94193i	−1.49259	+	0.163821i
$580$		0			0
$581$	23.1189			0.959132
$582$		0			0
$583$	22.3506	+	38.7124i	0.925668	+	1.60330i
$584$		0			0
$585$	−37.7868	−	11.8946i	−1.56229	−	0.491780i
$586$		0			0
$587$	13.3898	−	23.1918i	0.552656	−	0.957227i	−0.445426	−	0.895319i	$-0.646948\pi$
$587$	13.3898	−	23.1918i	0.552656	−	0.957227i	0.998082	−	0.0619088i	$-0.0197188\pi$
$588$		0			0
$589$			0.330957i			0.0136368i
$590$		0			0
$591$	19.1179	+	26.0606i	0.786405	+	1.07199i
$592$		0			0
$593$	14.1727	−	24.5478i	0.582002	−	1.00806i	−0.413239	−	0.910622i	$-0.635603\pi$
$593$	14.1727	−	24.5478i	0.582002	−	1.00806i	0.995242	−	0.0974354i	$-0.0310639\pi$
$594$		0			0
$595$	−6.32527			−0.259311
$596$		0			0
$597$	−5.81943	+	13.2341i	−0.238173	+	0.541636i
$598$		0			0
$599$	16.7747	+	29.0546i	0.685394	+	1.18714i	0.973313	+	0.229483i	$0.0737035\pi$
$599$	16.7747	+	29.0546i	0.685394	+	1.18714i	−0.287918	+	0.957655i	$0.592963\pi$
$600$		0			0
$601$	3.71989	−	6.44303i	0.151737	−	0.262817i	−0.780129	−	0.625619i	$-0.784847\pi$
$601$	3.71989	−	6.44303i	0.151737	−	0.262817i	0.931866	+	0.362802i	$0.118180\pi$
$602$		0			0
$603$	15.7332	−	18.8538i	0.640706	−	0.767787i
$604$		0			0
$605$	−28.8687	+	50.0020i	−1.17368	+	2.03287i
$606$		0			0
$607$	−17.2851	−	29.9386i	−0.701579	−	1.21517i	−0.967912	−	0.251290i	$-0.919145\pi$
$607$	−17.2851	−	29.9386i	−0.701579	−	1.21517i	0.266332	−	0.963881i	$-0.414188\pi$
$608$		0			0
$609$	−1.50884	+	3.43129i	−0.0611414	+	0.139043i
$610$		0			0
$611$	−2.58131			−0.104429
$612$		0			0
$613$	3.10205	−	5.37290i	0.125290	−	0.217009i	−0.796556	−	0.604565i	$-0.793347\pi$
$613$	3.10205	−	5.37290i	0.125290	−	0.217009i	0.921846	+	0.387555i	$0.126680\pi$
$614$		0			0
$615$	−24.7860	−	33.7872i	−0.999468	−	1.36243i
$616$		0			0
$617$		−	5.72944i		−	0.230659i	−0.993327	−	0.115329i	$-0.963208\pi$
$617$		−	5.72944i		−	0.230659i	0.993327	−	0.115329i	$-0.0367923\pi$
$618$		0			0
$619$	23.1159	−	40.0379i	0.929105	−	1.60926i	0.144283	−	0.989537i	$-0.453913\pi$
$619$	23.1159	−	40.0379i	0.929105	−	1.60926i	0.784822	−	0.619721i	$-0.212754\pi$
$620$		0			0
$621$	−24.0929	−	4.77470i	−0.966815	−	0.191602i
$622$		0			0
$623$	1.70201	+	2.94796i	0.0681894	+	0.118108i
$624$		0			0
$625$	−26.9600			−1.07840
$626$		0			0
$627$	−2.21074	+	0.242641i	−0.0882883	+	0.00969016i
$628$		0			0
$629$	7.37063	−	4.25543i	0.293886	−	0.169675i
$630$		0			0
$631$	−0.0252987	−	0.0146062i	−0.00100712	−	0.000581464i	0.499496	−	0.866316i	$-0.333518\pi$
$631$	−0.0252987	−	0.0146062i	−0.00100712	−	0.000581464i	−0.500503	+	0.865735i	$0.666852\pi$
$632$		0			0
$633$	−1.81919	+	4.13706i	−0.0723063	+	0.164434i
$634$		0			0
$635$	−28.1753	−	48.8010i	−1.11810	−	1.93661i
$636$		0			0
$637$	16.4059	−	9.47195i	0.650025	−	0.375292i
$638$		0			0
$639$	28.8958	−	26.5031i	1.14310	−	1.04845i
$640$		0			0
$641$	9.49914	+	16.4530i	0.375193	+	0.649854i	0.990356	−	0.138546i	$-0.0442430\pi$
$641$	9.49914	+	16.4530i	0.375193	+	0.649854i	−0.615163	+	0.788400i	$0.710910\pi$
$642$		0			0
$643$	−38.4133			−1.51487			−0.757437	−	0.652908i	$-0.773549\pi$
$643$	−38.4133			−1.51487			−0.757437	+	0.652908i	$0.773549\pi$
$644$		0			0
$645$	−4.62555	−	42.1439i	−0.182131	−	1.65942i
$646$		0			0
$647$	−9.84720	+	17.0558i	−0.387133	+	0.670534i	−0.992063	−	0.125745i	$-0.959868\pi$
$647$	−9.84720	+	17.0558i	−0.387133	+	0.670534i	0.604929	+	0.796279i	$0.293201\pi$
$648$		0			0
$649$	−65.4267	+	37.7741i	−2.56822	+	1.48276i
$650$		0			0
$651$	−1.56647	+	3.56235i	−0.0613948	+	0.139619i
$652$		0			0
$653$	19.8292	−	34.3452i	0.775976	−	1.34403i	−0.158268	−	0.987396i	$-0.550591\pi$
$653$	19.8292	−	34.3452i	0.775976	−	1.34403i	0.934244	−	0.356634i	$-0.116076\pi$
$654$		0			0
$655$			10.8494i			0.423920i
$656$		0			0
$657$	−5.83148	+	18.5255i	−0.227508	+	0.722748i
$658$		0			0
$659$	−8.48654	+	4.89970i	−0.330588	+	0.190865i	−0.656102	−	0.754672i	$-0.727796\pi$
$659$	−8.48654	+	4.89970i	−0.330588	+	0.190865i	0.325514	+	0.945537i	$0.394463\pi$
$660$		0			0
$661$		−	22.0111i		−	0.856133i	−0.903747	−	0.428067i	$-0.859195\pi$
$661$		−	22.0111i		−	0.856133i	0.903747	−	0.428067i	$-0.140805\pi$
$662$		0			0
$663$	5.58597	+	7.61454i	0.216941	+	0.295724i
$664$		0			0
$665$			1.16740i			0.0452697i
$666$		0			0
$667$	−6.39137			−0.247475
$668$		0			0
$669$	−34.7314	+	3.81198i	−1.34279	+	0.147380i
$670$		0			0
$671$			45.4942i			1.75628i
$672$		0			0
$673$			27.2693i			1.05116i	0.850745	+	0.525578i	$0.176151\pi$
$673$			27.2693i			1.05116i	−0.850745	+	0.525578i	$0.823849\pi$
$674$		0			0
$675$	−22.4869	+	7.65097i	−0.865520	+	0.294486i
$676$		0			0
$677$	12.5178	+	21.6815i	0.481099	+	0.833288i	0.999765	−	0.0216892i	$-0.00690443\pi$
$677$	12.5178	+	21.6815i	0.481099	+	0.833288i	−0.518666	+	0.854977i	$0.673571\pi$
$678$		0			0
$679$	−5.08343			−0.195084
$680$		0			0
$681$	16.1042	−	11.8139i	0.617115	−	0.452711i
$682$		0			0
$683$	3.36151	−	5.82230i	0.128625	−	0.222784i	−0.794519	−	0.607239i	$-0.792277\pi$
$683$	3.36151	−	5.82230i	0.128625	−	0.222784i	0.923144	+	0.384455i	$0.125610\pi$
$684$		0			0
$685$	50.9457			1.94654
$686$		0			0
$687$	23.3335	+	10.2604i	0.890230	+	0.391460i
$688$		0			0
$689$	−30.3387	−	17.5160i	−1.15581	−	0.667308i
$690$		0			0
$691$	15.8629	+	27.4753i	0.603453	+	1.04521i	0.992294	+	0.123907i	$0.0395423\pi$
$691$	15.8629	+	27.4753i	0.603453	+	1.04521i	−0.388841	+	0.921305i	$0.627124\pi$
$692$		0			0
$693$	−24.9444	−	7.85202i	−0.947558	−	0.298274i
$694$		0			0
$695$		−	64.8670i		−	2.46055i
$696$		0			0
$697$			9.98942i			0.378376i
$698$		0			0
$699$	−8.14249	−	11.0995i	−0.307977	−	0.419821i
$700$		0			0
$701$	18.3857	+	31.8450i	0.694418	+	1.20277i	0.970376	+	0.241598i	$0.0776715\pi$
$701$	18.3857	+	31.8450i	0.694418	+	1.20277i	−0.275958	+	0.961170i	$0.588995\pi$
$702$		0			0
$703$	−0.785385	−	1.36033i	−0.0296214	−	0.0513057i
$704$		0			0
$705$	−2.61297	+	1.91685i	−0.0984100	+	0.0721928i
$706$		0			0
$707$	−5.83642	−	3.36966i	−0.219501	−	0.126729i
$708$		0			0
$709$	−13.8280	+	23.9508i	−0.519321	+	0.899490i	0.480427	+	0.877035i	$0.340482\pi$
$709$	−13.8280	+	23.9508i	−0.519321	+	0.899490i	−0.999748	+	0.0224551i	$0.992852\pi$
$710$		0			0
$711$	−21.3091	+	19.5447i	−0.799154	+	0.732982i
$712$		0			0
$713$	−6.63548			−0.248501
$714$		0			0
$715$		−	71.9183i		−	2.68959i
$716$		0			0
$717$	−28.4283	−	38.7522i	−1.06167	−	1.44723i
$718$		0			0
$719$	11.5718	+	6.68101i	0.431557	+	0.249160i	0.700010	−	0.714133i	$-0.253179\pi$
$719$	11.5718	+	6.68101i	0.431557	+	0.249160i	−0.268453	+	0.963293i	$0.586512\pi$
$720$		0			0
$721$	1.77141	+	1.02273i	0.0659709	+	0.0380883i
$722$		0			0
$723$	2.10845	−	0.231415i	0.0784141	−	0.00860641i
$724$		0			0
$725$	−5.35285	+	3.09047i	−0.198800	+	0.114777i
$726$		0			0
$727$	14.1810	+	8.18741i	0.525944	+	0.303654i	0.739363	−	0.673307i	$-0.235127\pi$
$727$	14.1810	+	8.18741i	0.525944	+	0.303654i	−0.213419	+	0.976961i	$0.568460\pi$
$728$		0			0
$729$	21.3973	−	16.4668i	0.792493	−	0.609881i
$730$		0			0
$731$	−5.05352	+	8.75295i	−0.186911	+	0.323739i
$732$		0			0
$733$	−42.1025	+	24.3079i	−1.55509	+	0.897831i	−0.557375	+	0.830261i	$0.688191\pi$
$733$	−42.1025	+	24.3079i	−1.55509	+	0.897831i	−0.997714	+	0.0675706i	$0.978475\pi$
$734$		0			0
$735$	9.57333	−	21.7709i	0.353118	−	0.803033i
$736$		0			0
$737$	41.2249	+	16.9676i	1.51854	+	0.625011i
$738$		0			0
$739$	−6.15543	−	3.55384i	−0.226431	−	0.130730i	0.382493	−	0.923958i	$-0.375065\pi$
$739$	−6.15543	−	3.55384i	−0.226431	−	0.130730i	−0.608925	+	0.793228i	$0.708399\pi$
$740$		0			0
$741$	1.40534	−	1.03095i	0.0516266	−	0.0378729i
$742$		0			0
$743$	−22.9252	−	13.2359i	−0.841046	−	0.485578i	0.0165740	−	0.999863i	$-0.494724\pi$
$743$	−22.9252	−	13.2359i	−0.841046	−	0.485578i	−0.857619	+	0.514285i	$0.828057\pi$
$744$		0			0
$745$		−	13.3315i		−	0.488427i
$746$		0			0
$747$	−41.3342	−	13.0112i	−1.51234	−	0.476056i
$748$		0			0
$749$	6.18927	+	10.7201i	0.226151	+	0.391705i
$750$		0			0
$751$	43.9009			1.60197			0.800984	−	0.598686i	$-0.204310\pi$
$751$	43.9009			1.60197			0.800984	+	0.598686i	$0.204310\pi$
$752$		0			0
$753$	1.79977	−	4.09291i	0.0655874	−	0.149154i
$754$		0			0
$755$	32.5187	−	56.3240i	1.18348	−	2.04984i
$756$		0			0
$757$	44.1206	−	25.4731i	1.60359	−	0.925834i	0.612831	−	0.790214i	$-0.290031\pi$
$757$	44.1206	−	25.4731i	1.60359	−	0.925834i	0.990761	−	0.135620i	$-0.0433025\pi$
$758$		0			0
$759$	−4.86481	−	44.3239i	−0.176581	−	1.60886i
$760$		0			0
$761$		−	13.1323i		−	0.476046i	−0.971260	−	0.238023i	$-0.923501\pi$
$761$		−	13.1323i		−	0.476046i	0.971260	−	0.238023i	$-0.0764993\pi$
$762$		0			0
$763$	3.18453	+	5.51577i	0.115288	+	0.199684i
$764$		0			0
$765$	11.3089	+	3.55985i	0.408876	+	0.128707i
$766$		0			0
$767$	29.6033	−	51.2744i	1.06891	−	1.85141i
$768$		0			0
$769$	20.9102	−	12.0725i	0.754042	−	0.435347i	−0.0731103	−	0.997324i	$-0.523293\pi$
$769$	20.9102	−	12.0725i	0.754042	−	0.435347i	0.827153	+	0.561977i	$0.189959\pi$
$770$		0			0
$771$	−12.0062	+	8.80764i	−0.432392	+	0.317200i
$772$		0			0
$773$	−38.4914	+	22.2230i	−1.38444	+	0.799306i	−0.992681	−	0.120762i	$-0.961466\pi$
$773$	−38.4914	+	22.2230i	−1.38444	+	0.799306i	−0.391758	+	0.920068i	$0.628133\pi$
$774$		0			0
$775$	−5.55730	+	3.20851i	−0.199624	+	0.115253i
$776$		0			0
$777$	−2.01508	−	18.3596i	−0.0722905	−	0.658648i
$778$		0			0
$779$	1.84365			0.0660557
$780$		0			0
$781$	61.6460	+	35.5913i	2.20587	+	1.27356i
$782$		0			0
$783$	4.62878	−	5.28563i	0.165419	−	0.188893i
$784$		0			0
$785$	−30.6461	+	53.0807i	−1.09381	+	1.89453i
$786$		0			0
$787$	9.97228	+	5.75750i	0.355473	+	0.205233i	0.667093	−	0.744974i	$-0.267538\pi$
$787$	9.97228	+	5.75750i	0.355473	+	0.205233i	−0.311620	+	0.950207i	$0.600872\pi$
$788$		0			0
$789$	2.19731	+	20.0200i	0.0782263	+	0.712729i
$790$		0			0
$791$	5.12779	+	2.96053i	0.182323	+	0.105264i
$792$		0			0
$793$	−17.8267	−	30.8768i	−0.633046	−	1.09647i
$794$		0			0
$795$	−43.7179	+	4.79830i	−1.55051	+	0.170178i
$796$		0			0
$797$	−42.2817	+	24.4114i	−1.49769	+	0.864695i	−0.999996	−	0.00265569i	$-0.999155\pi$
$797$	−42.2817	+	24.4114i	−1.49769	+	0.864695i	−0.497698	+	0.867350i	$0.665821\pi$
$798$		0			0
$799$	0.772543			0.0273306
$800$		0			0
$801$	−1.38391	−	6.22854i	−0.0488980	−	0.220075i
$802$		0			0
$803$	−35.2589			−1.24426
$804$		0			0
$805$	−23.4056			−0.824938
$806$		0			0
$807$	0.633913	+	5.77566i	0.0223148	+	0.203313i
$808$		0			0
$809$	19.8060			0.696343			0.348171	−	0.937431i	$-0.386803\pi$
$809$	19.8060			0.696343			0.348171	+	0.937431i	$0.386803\pi$
$810$		0			0
$811$	42.7352	−	24.6732i	1.50063	−	0.866392i	0.500635	−	0.865658i	$-0.333100\pi$
$811$	42.7352	−	24.6732i	1.50063	−	0.866392i	1.00000		0.000733561i	$-0.000233500\pi$
$812$		0			0
$813$	−0.640846	−	5.83883i	−0.0224754	−	0.204777i
$814$		0			0
$815$	−28.9921	−	50.2157i	−1.01555	−	1.75898i
$816$		0			0
$817$	1.61545	+	0.932680i	0.0565174	+	0.0326303i
$818$		0			0
$819$	20.0065	−	4.44521i	0.699083	−	0.155328i
$820$		0			0
$821$	−3.00276	−	1.73364i	−0.104797	−	0.0605046i	0.446685	−	0.894691i	$-0.352604\pi$
$821$	−3.00276	−	1.73364i	−0.104797	−	0.0605046i	−0.551482	+	0.834186i	$0.685938\pi$
$822$		0			0
$823$	−2.25869	+	3.91216i	−0.0787329	+	0.136369i	−0.902703	−	0.430263i	$-0.858421\pi$
$823$	−2.25869	+	3.91216i	−0.0787329	+	0.136369i	0.823971	+	0.566633i	$0.191754\pi$
$824$		0			0
$825$	−25.5066	−	34.7695i	−0.888027	−	1.21052i
$826$		0			0
$827$	−29.4294	−	16.9911i	−1.02336	−	0.590837i	−0.108284	−	0.994120i	$-0.534536\pi$
$827$	−29.4294	−	16.9911i	−1.02336	−	0.590837i	−0.915075	+	0.403283i	$0.867869\pi$
$828$		0			0
$829$	−32.1140			−1.11537			−0.557683	−	0.830054i	$-0.688309\pi$
$829$	−32.1140			−1.11537			−0.557683	+	0.830054i	$0.688309\pi$
$830$		0			0
$831$	42.2626	−	4.63856i	1.46607	−	0.160910i
$832$		0			0
$833$	−4.91001	+	2.83479i	−0.170122	+	0.0982198i
$834$		0			0
$835$	−36.6726	+	21.1729i	−1.26911	+	0.732719i
$836$		0			0
$837$	4.80557	−	5.48751i	0.166105	−	0.189676i
$838$		0			0
$839$	38.5481	−	22.2558i	1.33083	−	0.768354i	0.345402	−	0.938455i	$-0.387743\pi$
$839$	38.5481	−	22.2558i	1.33083	−	0.768354i	0.985427	+	0.170101i	$0.0544094\pi$
$840$		0			0
$841$	−13.5859	+	23.5314i	−0.468478	+	0.811428i
$842$		0			0
$843$	−7.96758	+	18.1193i	−0.274418	+	0.624061i
$844$		0			0
$845$	8.07162	+	13.9805i	0.277672	+	0.480942i
$846$		0			0
$847$		−	29.8700i		−	1.02634i
$848$		0			0
$849$	13.1141	−	1.43934i	0.450073	−	0.0493982i
$850$		0			0
$851$	27.2737	−	15.7465i	0.934931	−	0.539782i
$852$		0			0
$853$	−13.4918	+	23.3684i	−0.461950	+	0.800120i	−0.999058	−	0.0433929i	$-0.986183\pi$
$853$	−13.4918	+	23.3684i	−0.461950	+	0.800120i	0.537108	+	0.843513i	$0.319517\pi$
$854$		0			0
$855$	0.657007	−	2.08718i	0.0224692	−	0.0713802i
$856$		0			0
$857$	−56.1494			−1.91803			−0.959013	−	0.283361i	$-0.908550\pi$
$857$	−56.1494			−1.91803			−0.959013	+	0.283361i	$0.908550\pi$
$858$		0			0
$859$	11.5654	+	20.0318i	0.394606	+	0.683478i	0.993051	−	0.117686i	$-0.0375478\pi$
$859$	11.5654	+	20.0318i	0.394606	+	0.683478i	−0.598445	+	0.801164i	$0.704214\pi$
$860$		0			0
$861$	19.8447	+	8.72630i	0.676305	+	0.297391i
$862$		0			0
$863$			1.39823i			0.0475965i	0.999717	+	0.0237982i	$0.00757593\pi$
$863$			1.39823i			0.0475965i	−0.999717	+	0.0237982i	$0.992424\pi$
$864$		0			0
$865$	−42.4940	−	24.5339i	−1.44484	−	0.834178i
$866$		0			0
$867$	15.7448	+	21.4627i	0.534723	+	0.728910i
$868$		0			0
$869$	−45.4607	−	26.2467i	−1.54215	−	0.890359i
$870$		0			0
$871$	−34.6280	+	4.63795i	−1.17332	+	0.157151i
$872$		0			0
$873$	9.08865	+	2.86094i	0.307604	+	0.0968282i
$874$		0			0
$875$	1.83864	−	1.06154i	0.0621574	−	0.0358866i
$876$		0			0
$877$	−3.53778	+	6.12762i	−0.119462	+	0.206915i	−0.919555	−	0.392962i	$-0.871450\pi$
$877$	−3.53778	+	6.12762i	−0.119462	+	0.206915i	0.800092	+	0.599877i	$0.204784\pi$
$878$		0			0
$879$	−1.50704	−	13.7308i	−0.0508312	−	0.463129i
$880$		0			0
$881$	39.3763	+	22.7339i	1.32662	+	0.765925i	0.984775	−	0.173831i	$-0.0556148\pi$
$881$	39.3763	+	22.7339i	1.32662	+	0.765925i	0.341845	+	0.939756i	$0.388948\pi$
$882$		0			0
$883$	−5.92073	+	3.41833i	−0.199248	+	0.115036i	−0.596305	−	0.802758i	$-0.703365\pi$
$883$	−5.92073	+	3.41833i	−0.199248	+	0.115036i	0.397056	+	0.917794i	$0.370032\pi$
$884$		0			0
$885$	−8.10946	−	73.8863i	−0.272596	−	2.48366i
$886$		0			0
$887$	12.3293	+	7.11832i	0.413977	+	0.239010i	0.692497	−	0.721421i	$-0.256511\pi$
$887$	12.3293	+	7.11832i	0.413977	+	0.239010i	−0.278520	+	0.960430i	$0.589844\pi$
$888$		0			0
$889$	25.2469	+	14.5763i	0.846752	+	0.488873i
$890$		0			0
$891$	40.1789	+	28.0772i	1.34604	+	0.940623i
$892$		0			0
$893$		−	0.142581i		−	0.00477129i
$894$		0			0
$895$	−49.4514			−1.65298
$896$		0			0
$897$	20.6699	+	28.1763i	0.690148	+	0.940779i
$898$		0			0
$899$	0.949054	−	1.64381i	0.0316527	−	0.0548241i
$900$		0			0
$901$	9.07985	+	5.24225i	0.302494	+	0.174645i
$902$		0			0
$903$	12.9738	+	17.6853i	0.431742	+	0.588531i
$904$		0			0
$905$	11.5656	+	20.0322i	0.384453	+	0.665892i
$906$		0			0
$907$	−6.39971	−	11.0846i	−0.212499	−	0.368059i	0.739997	−	0.672610i	$-0.234827\pi$
$907$	−6.39971	−	11.0846i	−0.212499	−	0.368059i	−0.952496	+	0.304551i	$0.901494\pi$
$908$		0			0
$909$	8.53848	+	9.30932i	0.283204	+	0.308771i
$910$		0			0
$911$		−	23.0571i		−	0.763917i	−0.924180	−	0.381958i	$-0.875250\pi$
$911$		−	23.0571i		−	0.763917i	0.924180	−	0.381958i	$-0.124750\pi$
$912$		0			0
$913$		−	78.6700i		−	2.60360i
$914$		0			0
$915$	−40.9741	−	18.0175i	−1.35456	−	0.595642i
$916$		0			0
$917$	−2.80642	−	4.86087i	−0.0926762	−	0.160520i
$918$		0			0
$919$	22.8421	+	13.1879i	0.753491	+	0.435028i	0.826954	−	0.562270i	$-0.190072\pi$
$919$	22.8421	+	13.1879i	0.753491	+	0.435028i	−0.0734629	+	0.997298i	$0.523405\pi$
$920$		0			0
$921$	−11.9883	+	27.2629i	−0.395028	+	0.898342i
$922$		0			0
$923$	−55.7854			−1.83620
$924$		0			0
$925$	15.2281	−	26.3758i	0.500695	−	0.867230i
$926$		0			0
$927$	−2.59152	−	2.82548i	−0.0851167	−	0.0928009i
$928$		0			0
$929$	−42.6683			−1.39990			−0.699951	−	0.714190i	$-0.746795\pi$
$929$	−42.6683			−1.39990			−0.699951	+	0.714190i	$0.746795\pi$
$930$		0			0
$931$	0.523191	+	0.906194i	0.0171469	+	0.0296993i
$932$		0			0
$933$	−14.6558	+	1.60856i	−0.479809	+	0.0526618i
$934$		0			0
$935$			21.5239i			0.703908i
$936$		0			0
$937$			60.7057i			1.98317i	0.129465	+	0.991584i	$0.458674\pi$
$937$			60.7057i			1.98317i	−0.129465	+	0.991584i	$0.541326\pi$
$938$		0			0
$939$	3.06098	+	27.8890i	0.0998914	+	0.910123i
$940$		0			0
$941$	6.18642			0.201671			0.100836	−	0.994903i	$-0.467848\pi$
$941$	6.18642			0.201671			0.100836	+	0.994903i	$0.467848\pi$
$942$		0			0
$943$			36.9641i			1.20372i
$944$		0			0
$945$	16.9509	−	19.3563i	0.551411	−	0.629660i
$946$		0			0
$947$			9.92974i			0.322673i	0.986899	+	0.161337i	$0.0515805\pi$
$947$			9.92974i			0.322673i	−0.986899	+	0.161337i	$0.948420\pi$
$948$		0			0
$949$	23.9302	−	13.8161i	0.776806	−	0.448489i
$950$		0			0
$951$	−37.5754	−	16.5230i	−1.21847	−	0.535796i
$952$		0			0
$953$		−	52.6077i		−	1.70413i	−0.523435	−	0.852066i	$-0.675350\pi$
$953$		−	52.6077i		−	1.70413i	0.523435	−	0.852066i	$-0.324650\pi$
$954$		0			0
$955$	1.80268	−	3.12233i	0.0583333	−	0.101036i
$956$		0			0
$957$	11.6762	+	5.13436i	0.377437	+	0.165970i
$958$		0			0
$959$	−22.8253	+	13.1782i	−0.737068	+	0.425546i
$960$		0			0
$961$	−14.5147	+	25.1402i	−0.468216	+	0.810974i
$962$		0			0
$963$	−5.03252	−	22.6498i	−0.162171	−	0.729880i
$964$		0			0
$965$	64.5363			2.07750
$966$		0			0
$967$	0.472680	+	0.818705i	0.0152004	+	0.0263278i	0.873526	−	0.486778i	$-0.161828\pi$
$967$	0.472680	+	0.818705i	0.0152004	+	0.0263278i	−0.858325	+	0.513106i	$0.828495\pi$
$968$		0			0
$969$	−0.420596	+	0.308546i	−0.0135115	+	0.00991192i
$970$		0			0
$971$	50.0989	−	28.9246i	1.60775	−	0.928235i	0.617877	−	0.786275i	$-0.287993\pi$
$971$	50.0989	−	28.9246i	1.60775	−	0.928235i	0.989872	−	0.141960i	$-0.0453403\pi$
$972$		0			0
$973$	16.7792	+	29.0625i	0.537918	+	0.931701i
$974$		0			0
$975$	30.9356	+	13.6033i	0.990732	+	0.435655i
$976$		0			0
$977$	−33.8510	−	19.5439i	−1.08299	−	0.625264i	−0.151288	−	0.988490i	$-0.548342\pi$
$977$	−33.8510	−	19.5439i	−1.08299	−	0.625264i	−0.931701	+	0.363225i	$0.881676\pi$
$978$		0			0
$979$	10.0315	−	5.79166i	0.320607	−	0.185102i
$980$		0			0
$981$	−2.58936	−	11.6539i	−0.0826719	−	0.372080i
$982$		0			0
$983$	−16.2145			−0.517164			−0.258582	−	0.965989i	$-0.583255\pi$
$983$	−16.2145			−0.517164			−0.258582	+	0.965989i	$0.583255\pi$
$984$		0			0
$985$	−28.8655	−	49.9965i	−0.919731	−	1.59302i
$986$		0			0
$987$	0.674858	−	1.53471i	0.0214810	−	0.0488504i
$988$		0			0
$989$	−18.6996	+	32.3887i	−0.594614	+	1.02990i
$990$		0			0
$991$		−	29.7836i		−	0.946107i	−0.881034	−	0.473053i	$-0.843152\pi$
$991$		−	29.7836i		−	0.946107i	0.881034	−	0.473053i	$-0.156848\pi$
$992$		0			0
$993$	33.3314	−	24.4516i	1.05774	−	0.775949i
$994$		0			0
$995$	12.9114	−	22.3632i	0.409319	−	0.708962i
$996$		0			0
$997$	24.2248			0.767207			0.383604	−	0.923498i	$-0.374683\pi$
$997$	24.2248			0.767207			0.383604	+	0.923498i	$0.374683\pi$
$998$		0			0
$999$	−6.72999	+	33.9592i	−0.212928	+	1.07442i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.o.d.641.1	yes	36
3.2	odd	2	inner	804.2.o.d.641.18	yes	36
67.30	odd	6	inner	804.2.o.d.365.18	yes	36
201.164	even	6	inner	804.2.o.d.365.1	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.o.d.365.1	✓	36	201.164	even	6	inner
804.2.o.d.365.18	yes	36	67.30	odd	6	inner
804.2.o.d.641.1	yes	36	1.1	even	1	trivial
804.2.o.d.641.18	yes	36	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.72171 + 0.188968i) q^{3} +3.09374 q^{5} +(-1.38610 + 0.800262i) q^{7} +(2.92858 - 0.650697i) q^{9} +O(q^{10})\)	\(q+(-1.72171 + 0.188968i) q^{3} +3.09374 q^{5} +(-1.38610 + 0.800262i) q^{7} +(2.92858 - 0.650697i) q^{9} +(2.72317 + 4.71667i) q^{11} +(-3.69642 - 2.13413i) q^{13} +(-5.32653 + 0.584618i) q^{15} +(1.10628 + 0.638709i) q^{17} +(0.117880 - 0.204175i) q^{19} +(2.23523 - 1.63975i) q^{21} +(4.09358 + 2.36343i) q^{23} +4.57123 q^{25} +(-4.91921 + 1.67372i) q^{27} +(-1.17099 + 0.676069i) q^{29} +(-1.21571 + 0.701891i) q^{31} +(-5.57981 - 7.60615i) q^{33} +(-4.28822 + 2.47580i) q^{35} +(3.33128 - 5.76994i) q^{37} +(6.76745 + 2.97585i) q^{39} +(3.91001 + 6.77233i) q^{41} +7.91208i q^{43} +(9.06028 - 2.01309i) q^{45} +(0.523745 - 0.302384i) q^{47} +(-2.21916 + 3.84370i) q^{49} +(-2.02538 - 0.890622i) q^{51} +8.20758 q^{53} +(8.42478 + 14.5922i) q^{55} +(-0.164374 + 0.373806i) q^{57} +13.8714i q^{59} +(7.23406 + 4.17658i) q^{61} +(-3.53856 + 3.24556i) q^{63} +(-11.4358 - 6.60244i) q^{65} +(6.48268 - 4.99749i) q^{67} +(-7.49458 - 3.29559i) q^{69} +(11.3188 - 6.53491i) q^{71} +(-3.23694 + 5.60654i) q^{73} +(-7.87035 + 0.863817i) q^{75} +(-7.54914 - 4.35850i) q^{77} +(-8.34701 + 4.81915i) q^{79} +(8.15319 - 3.81124i) q^{81} +(-12.5094 - 7.22228i) q^{83} +(3.42253 + 1.97600i) q^{85} +(1.88835 - 1.38528i) q^{87} -2.12681i q^{89} +6.83145 q^{91} +(1.96047 - 1.43818i) q^{93} +(0.364692 - 0.631664i) q^{95} +(2.75058 + 1.58805i) q^{97} +(11.0441 + 12.0412i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{9}+O(q^{10}) \) 36 * q + 4 * q^9	\( 36 q + 4 q^{9} - 36 q^{13} + 18 q^{15} + 16 q^{21} + 76 q^{25} + 6 q^{31} + 4 q^{33} + 42 q^{37} - 21 q^{39} + 2 q^{49} + 18 q^{51} + 20 q^{55} + 18 q^{57} - 24 q^{61} - 12 q^{63} - 8 q^{67} + 3 q^{69} + 14 q^{73} + 72 q^{79} - 12 q^{81} - 18 q^{85} - 21 q^{87} - 68 q^{91} + 9 q^{93} - 48 q^{97} + 15 q^{99}+O(q^{100}) \) 36 * q + 4 * q^9 - 36 * q^13 + 18 * q^15 + 16 * q^21 + 76 * q^25 + 6 * q^31 + 4 * q^33 + 42 * q^37 - 21 * q^39 + 2 * q^49 + 18 * q^51 + 20 * q^55 + 18 * q^57 - 24 * q^61 - 12 * q^63 - 8 * q^67 + 3 * q^69 + 14 * q^73 + 72 * q^79 - 12 * q^81 - 18 * q^85 - 21 * q^87 - 68 * q^91 + 9 * q^93 - 48 * q^97 + 15 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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