LMFDB - Embedded newform 804.2.o.d.365.12

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			365.12
Character	$\chi$	$=$	804.365
Dual form			804.2.o.d.641.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.869231 + 1.49814i) q^{3} -2.66956 q^{5} +(0.767031 + 0.442845i) q^{7} +(-1.48888 + 2.60447i) q^{9} +O(q^{10})$	\(q+(0.869231 + 1.49814i) q^{3} -2.66956 q^{5} +(0.767031 + 0.442845i) q^{7} +(-1.48888 + 2.60447i) q^{9} +(2.39703 - 4.15178i) q^{11} +(-5.90147 + 3.40722i) q^{13} +(-2.32046 - 3.99938i) q^{15} +(-5.55864 + 3.20928i) q^{17} +(2.50179 + 4.33322i) q^{19} +(0.00328022 + 1.53406i) q^{21} +(1.46659 - 0.846736i) q^{23} +2.12654 q^{25} +(-5.19605 + 0.0333319i) q^{27} +(-5.11405 - 2.95260i) q^{29} +(-5.28723 - 3.05259i) q^{31} +(8.30354 - 0.0177551i) q^{33} +(-2.04763 - 1.18220i) q^{35} +(0.639895 + 1.10833i) q^{37} +(-10.2342 - 5.87960i) q^{39} +(1.45058 - 2.51248i) q^{41} +12.1986i q^{43} +(3.97464 - 6.95278i) q^{45} +(-3.58366 - 2.06903i) q^{47} +(-3.10778 - 5.38283i) q^{49} +(-9.63971 - 5.53804i) q^{51} +5.25036 q^{53} +(-6.39901 + 11.0834i) q^{55} +(-4.31717 + 7.51461i) q^{57} +0.587414i q^{59} +(-5.85867 + 3.38250i) q^{61} +(-2.29539 + 1.33836i) q^{63} +(15.7543 - 9.09576i) q^{65} +(2.91744 - 7.64778i) q^{67} +(2.54334 + 1.46115i) q^{69} +(-1.38128 - 0.797483i) q^{71} +(3.71930 + 6.44202i) q^{73} +(1.84845 + 3.18586i) q^{75} +(3.67719 - 2.12303i) q^{77} +(10.0799 + 5.81963i) q^{79} +(-4.56650 - 7.75546i) q^{81} +(7.12573 - 4.11404i) q^{83} +(14.8391 - 8.56736i) q^{85} +(-0.0218703 - 10.2281i) q^{87} +9.09197i q^{89} -6.03548 q^{91} +(-0.0226109 - 10.5744i) q^{93} +(-6.67867 - 11.5678i) q^{95} +(7.83565 - 4.52391i) q^{97} +(7.24429 + 12.4245i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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
$3$	0.869231	+	1.49814i	0.501851	+	0.864954i
$3$	0.869231	+	1.49814i	0.501851	+	0.864954i
$4$		0			0
$5$	−2.66956			−1.19386			−0.596931	−	0.802292i	$-0.703614\pi$
$5$	−2.66956			−1.19386			−0.596931	+	0.802292i	$0.703614\pi$
$6$		0			0
$7$	0.767031	+	0.442845i	0.289910	+	0.167380i	0.637901	−	0.770118i	$-0.279803\pi$
$7$	0.767031	+	0.442845i	0.289910	+	0.167380i	−0.347991	+	0.937498i	$0.613136\pi$
$8$		0			0
$9$	−1.48888	+	2.60447i	−0.496292	+	0.868156i
$10$		0			0
$11$	2.39703	−	4.15178i	0.722732	−	1.25181i	−0.237169	−	0.971468i	$-0.576220\pi$
$11$	2.39703	−	4.15178i	0.722732	−	1.25181i	0.959901	−	0.280340i	$-0.0904471\pi$
$12$		0			0
$13$	−5.90147	+	3.40722i	−1.63677	+	0.944992i	−0.654840	+	0.755767i	$0.727264\pi$
$13$	−5.90147	+	3.40722i	−1.63677	+	0.944992i	−0.981934	+	0.189225i	$0.939402\pi$
$14$		0			0
$15$	−2.32046	−	3.99938i	−0.599141	−	1.03264i
$16$		0			0
$17$	−5.55864	+	3.20928i	−1.34817	+	0.778365i	−0.987990	−	0.154519i	$-0.950617\pi$
$17$	−5.55864	+	3.20928i	−1.34817	+	0.778365i	−0.360178	+	0.932884i	$0.617284\pi$
$18$		0			0
$19$	2.50179	+	4.33322i	0.573950	+	0.994110i	0.996155	+	0.0876097i	$0.0279228\pi$
$19$	2.50179	+	4.33322i	0.573950	+	0.994110i	−0.422205	+	0.906500i	$0.638744\pi$
$20$		0			0
$21$	0.00328022	+	1.53406i	0.000715803	+	0.334759i
$22$		0			0
$23$	1.46659	−	0.846736i	0.305805	−	0.176557i	−0.339243	−	0.940699i	$-0.610171\pi$
$23$	1.46659	−	0.846736i	0.305805	−	0.176557i	0.645048	+	0.764142i	$0.276837\pi$
$24$		0			0
$25$	2.12654			0.425308
$26$		0			0
$27$	−5.19605	+	0.0333319i	−0.999979	+	0.00641474i
$28$		0			0
$29$	−5.11405	−	2.95260i	−0.949654	−	0.548283i	−0.0566808	−	0.998392i	$-0.518052\pi$
$29$	−5.11405	−	2.95260i	−0.949654	−	0.548283i	−0.892974	+	0.450109i	$0.851385\pi$
$30$		0			0
$31$	−5.28723	−	3.05259i	−0.949615	−	0.548261i	−0.0566539	−	0.998394i	$-0.518043\pi$
$31$	−5.28723	−	3.05259i	−0.949615	−	0.548261i	−0.892961	+	0.450133i	$0.851376\pi$
$32$		0			0
$33$	8.30354	−	0.0177551i	1.44546	−	0.00309077i
$34$		0			0
$35$	−2.04763	−	1.18220i	−0.346113	−	0.199829i
$36$		0			0
$37$	0.639895	+	1.10833i	0.105198	+	0.182208i	0.913819	−	0.406121i	$-0.133119\pi$
$37$	0.639895	+	1.10833i	0.105198	+	0.182208i	−0.808621	+	0.588330i	$0.799786\pi$
$38$		0			0
$39$	−10.2342	−	5.87960i	−1.63879	−	0.941490i
$40$		0			0
$41$	1.45058	−	2.51248i	0.226543	−	0.392384i	−0.730238	−	0.683192i	$-0.760591\pi$
$41$	1.45058	−	2.51248i	0.226543	−	0.392384i	0.956781	+	0.290809i	$0.0939244\pi$
$42$		0			0
$43$			12.1986i			1.86027i	0.367218	+	0.930135i	$0.380310\pi$
$43$			12.1986i			1.86027i	−0.367218	+	0.930135i	$0.619690\pi$
$44$		0			0
$45$	3.97464	−	6.95278i	0.592504	−	1.03646i
$46$		0			0
$47$	−3.58366	−	2.06903i	−0.522730	−	0.301798i	0.215321	−	0.976543i	$-0.430920\pi$
$47$	−3.58366	−	2.06903i	−0.522730	−	0.301798i	−0.738051	+	0.674745i	$0.764254\pi$
$48$		0			0
$49$	−3.10778	−	5.38283i	−0.443968	−	0.768975i
$50$		0			0
$51$	−9.63971	−	5.53804i	−1.34983	−	0.775480i
$52$		0			0
$53$	5.25036			0.721192			0.360596	−	0.932722i	$-0.382573\pi$
$53$	5.25036			0.721192			0.360596	+	0.932722i	$0.382573\pi$
$54$		0			0
$55$	−6.39901	+	11.0834i	−0.862842	+	1.49449i
$56$		0			0
$57$	−4.31717	+	7.51461i	−0.571823	+	0.995335i
$58$		0			0
$59$			0.587414i			0.0764748i	0.999269	+	0.0382374i	$0.0121743\pi$
$59$			0.587414i			0.0764748i	−0.999269	+	0.0382374i	$0.987826\pi$
$60$		0			0
$61$	−5.85867	+	3.38250i	−0.750126	+	0.433085i	−0.825739	−	0.564052i	$-0.809242\pi$
$61$	−5.85867	+	3.38250i	−0.750126	+	0.433085i	0.0756136	+	0.997137i	$0.475908\pi$
$62$		0			0
$63$	−2.29539	+	1.33836i	−0.289192	+	0.168618i
$64$		0			0
$65$	15.7543	−	9.09576i	1.95408	−	1.12819i
$66$		0			0
$67$	2.91744	−	7.64778i	0.356422	−	0.934325i
$67$	2.91744	−	7.64778i	0.356422	−	0.934325i
$68$		0			0
$69$	2.54334	+	1.46115i	0.306182	+	0.175902i
$70$		0			0
$71$	−1.38128	−	0.797483i	−0.163928	−	0.0946439i	0.415792	−	0.909460i	$-0.363505\pi$
$71$	−1.38128	−	0.797483i	−0.163928	−	0.0946439i	−0.579720	+	0.814816i	$0.696838\pi$
$72$		0			0
$73$	3.71930	+	6.44202i	0.435312	+	0.753982i	0.997321	−	0.0731491i	$-0.0233049\pi$
$73$	3.71930	+	6.44202i	0.435312	+	0.753982i	−0.562009	+	0.827131i	$0.689972\pi$
$74$		0			0
$75$	1.84845	+	3.18586i	0.213441	+	0.367872i
$76$		0			0
$77$	3.67719	−	2.12303i	0.419055	−	0.241941i
$78$		0			0
$79$	10.0799	+	5.81963i	1.13408	+	0.654760i	0.944957	−	0.327194i	$-0.106103\pi$
$79$	10.0799	+	5.81963i	1.13408	+	0.654760i	0.189120	+	0.981954i	$0.439437\pi$
$80$		0			0
$81$	−4.56650	−	7.75546i	−0.507389	−	0.861717i
$82$		0			0
$83$	7.12573	−	4.11404i	0.782150	−	0.451575i	−0.0550415	−	0.998484i	$-0.517529\pi$
$83$	7.12573	−	4.11404i	0.782150	−	0.451575i	0.837192	+	0.546909i	$0.184196\pi$
$84$		0			0
$85$	14.8391	−	8.56736i	1.60953	−	0.929261i
$86$		0			0
$87$	−0.0218703	−	10.2281i	−0.00234474	−	1.09656i
$88$		0			0
$89$			9.09197i			0.963747i	0.876241	+	0.481874i	$0.160044\pi$
$89$			9.09197i			0.963747i	−0.876241	+	0.481874i	$0.839956\pi$
$90$		0			0
$91$	−6.03548			−0.632691
$92$		0			0
$93$	−0.0226109	−	10.5744i	−0.00234465	−	1.09652i
$94$		0			0
$95$	−6.67867	−	11.5678i	−0.685217	−	1.18683i
$96$		0			0
$97$	7.83565	−	4.52391i	0.795589	−	0.459334i	−0.0463372	−	0.998926i	$-0.514755\pi$
$97$	7.83565	−	4.52391i	0.795589	−	0.459334i	0.841927	+	0.539592i	$0.181422\pi$
$98$		0			0
$99$	7.24429	+	12.4245i	0.728079	+	1.24871i
$100$		0			0
$101$	−6.83885	+	11.8452i	−0.680491	+	1.17865i	0.294340	+	0.955701i	$0.404900\pi$
$101$	−6.83885	+	11.8452i	−0.680491	+	1.17865i	−0.974831	+	0.222945i	$0.928433\pi$
$102$		0			0
$103$	0.0432333	−	0.0748822i	0.00425990	−	0.00737836i	−0.863888	−	0.503685i	$-0.831977\pi$
$103$	0.0432333	−	0.0748822i	0.00425990	−	0.00737836i	0.868147	+	0.496306i	$0.165311\pi$
$104$		0			0
$105$	−0.00875674	−	4.09526i	−0.000854570	−	0.399656i
$106$		0			0
$107$			16.7666i			1.62089i	0.585816	+	0.810444i	$0.300774\pi$
$107$			16.7666i			1.62089i	−0.585816	+	0.810444i	$0.699226\pi$
$108$		0			0
$109$			3.22325i			0.308732i	0.988014	+	0.154366i	$0.0493334\pi$
$109$			3.22325i			0.308732i	−0.988014	+	0.154366i	$0.950667\pi$
$110$		0			0
$111$	−1.10422	+	1.92205i	−0.104808	+	0.182433i
$112$		0			0
$113$	−7.19242	+	12.4576i	−0.676606	+	1.17192i	0.299391	+	0.954130i	$0.403216\pi$
$113$	−7.19242	+	12.4576i	−0.676606	+	1.17192i	−0.975997	+	0.217785i	$0.930117\pi$
$114$		0			0
$115$	−3.91515	+	2.26041i	−0.365089	+	0.210784i
$116$		0			0
$117$	−0.0874259	−	20.4431i	−0.00808253	−	1.88997i
$118$		0			0
$119$	−5.68486			−0.521131
$120$		0			0
$121$	−5.99151	−	10.3776i	−0.544683	−	0.943418i
$122$		0			0
$123$	5.02495	−	0.0107447i	0.453084	−	0.000968814i
$124$		0			0
$125$	7.67087			0.686103
$126$		0			0
$127$	1.64965	−	2.85728i	0.146383	−	0.253542i	−0.783505	−	0.621385i	$-0.786570\pi$
$127$	1.64965	−	2.85728i	0.146383	−	0.253542i	0.929888	+	0.367843i	$0.119904\pi$
$128$		0			0
$129$	−18.2753	+	10.6034i	−1.60905	+	0.933578i
$130$		0			0
$131$			7.00155i			0.611729i	0.952075	+	0.305864i	$0.0989454\pi$
$131$			7.00155i			0.611729i	−0.952075	+	0.305864i	$0.901055\pi$
$132$		0			0
$133$			4.43162i			0.384270i
$134$		0			0
$135$	13.8711	−	0.0889816i	1.19384	−	0.00765831i
$136$		0			0
$137$	−1.93779			−0.165557			−0.0827785	−	0.996568i	$-0.526379\pi$
$137$	−1.93779			−0.165557			−0.0827785	+	0.996568i	$0.526379\pi$
$138$		0			0
$139$			13.8960i			1.17865i	0.807898	+	0.589323i	$0.200605\pi$
$139$			13.8960i			1.17865i	−0.807898	+	0.589323i	$0.799395\pi$
$140$		0			0
$141$	−0.0153256	−	7.16730i	−0.00129065	−	0.603595i
$142$		0			0
$143$			32.6688i			2.73190i
$144$		0			0
$145$	13.6522	+	7.88212i	1.13376	+	0.654575i
$146$		0			0
$147$	5.36288	−	9.33482i	0.442323	−	0.769923i
$148$		0			0
$149$		−	16.0183i		−	1.31227i	−0.754644	−	0.656134i	$-0.772191\pi$
$149$		−	16.0183i		−	1.31227i	0.754644	−	0.656134i	$-0.227809\pi$
$150$		0			0
$151$	3.32600	+	5.76080i	0.270666	+	0.468807i	0.969033	−	0.246933i	$-0.0794228\pi$
$151$	3.32600	+	5.76080i	0.270666	+	0.468807i	−0.698367	+	0.715740i	$0.746089\pi$
$152$		0			0
$153$	−0.0823471	−	19.2555i	−0.00665737	−	1.55672i
$154$		0			0
$155$	14.1146	+	8.14905i	1.13371	+	0.654548i
$156$		0			0
$157$	10.0978	+	17.4899i	0.805893	+	1.39585i	0.915686	+	0.401894i	$0.131648\pi$
$157$	10.0978	+	17.4899i	0.805893	+	1.39585i	−0.109793	+	0.993954i	$0.535019\pi$
$158$		0			0
$159$	4.56377	+	7.86579i	0.361931	+	0.623798i
$160$		0			0
$161$	1.49989			0.118208
$162$		0			0
$163$	4.14521	−	7.17971i	0.324678	−	0.562358i	−0.656769	−	0.754091i	$-0.728078\pi$
$163$	4.14521	−	7.17971i	0.324678	−	0.562358i	0.981447	+	0.191733i	$0.0614109\pi$
$164$		0			0
$165$	−22.1668	+	0.0473984i	−1.72568	+	0.00368996i
$166$		0			0
$167$	−9.82527	−	5.67262i	−0.760302	−	0.438961i	0.0691020	−	0.997610i	$-0.477987\pi$
$167$	−9.82527	−	5.67262i	−0.760302	−	0.438961i	−0.829404	+	0.558649i	$0.811320\pi$
$168$		0			0
$169$	16.7183	−	28.9569i	1.28602	−	2.22745i
$170$		0			0
$171$	−15.0106	+	0.0641935i	−1.14789	+	0.00490900i
$172$		0			0
$173$	−13.7279	+	7.92578i	−1.04371	+	0.602586i	−0.920882	−	0.389842i	$-0.872530\pi$
$173$	−13.7279	+	7.92578i	−1.04371	+	0.602586i	−0.122828	+	0.992428i	$0.539196\pi$
$174$		0			0
$175$	1.63112	+	0.941728i	0.123301	+	0.0711880i
$176$		0			0
$177$	−0.880031	+	0.510598i	−0.0661472	+	0.0383789i
$178$		0			0
$179$	10.8008			0.807289			0.403645	−	0.914916i	$-0.367743\pi$
$179$	10.8008			0.807289			0.403645	+	0.914916i	$0.367743\pi$
$180$		0			0
$181$	4.46568	−	7.73479i	0.331932	−	0.574922i	−0.650959	−	0.759113i	$-0.725633\pi$
$181$	4.46568	−	7.73479i	0.331932	−	0.574922i	0.982891	+	0.184191i	$0.0589664\pi$
$182$		0			0
$183$	−10.1600	−	5.83696i	−0.751050	−	0.431480i
$184$		0			0
$185$	−1.70824	−	2.95875i	−0.125592	−	0.217532i
$186$		0			0
$187$			30.7710i			2.25020i
$188$		0			0
$189$	−4.00029	−	2.27548i	−0.290978	−	0.165517i
$190$		0			0
$191$	−8.44762	−	14.6317i	−0.611249	−	1.05871i	−0.991030	−	0.133637i	$-0.957334\pi$
$191$	−8.44762	−	14.6317i	−0.611249	−	1.05871i	0.379782	−	0.925076i	$-0.375999\pi$
$192$		0			0
$193$	24.5120			1.76441			0.882207	−	0.470862i	$-0.156057\pi$
$193$	24.5120			1.76441			0.882207	+	0.470862i	$0.156057\pi$
$194$		0			0
$195$	27.3209	+	15.6959i	1.95649	+	1.12401i
$196$		0			0
$197$	−11.1465	+	19.3064i	−0.794159	+	1.37552i	0.129213	+	0.991617i	$0.458755\pi$
$197$	−11.1465	+	19.3064i	−0.794159	+	1.37552i	−0.923372	+	0.383906i	$0.874579\pi$
$198$		0			0
$199$	−3.86657	−	6.69709i	−0.274094	−	0.474744i	0.695812	−	0.718224i	$-0.255045\pi$
$199$	−3.86657	−	6.69709i	−0.274094	−	0.474744i	−0.969906	+	0.243479i	$0.921711\pi$
$200$		0			0
$201$	13.9934	−	2.27693i	0.987019	−	0.160602i
$202$		0			0
$203$	−2.61509	−	4.52946i	−0.183543	−	0.317906i
$204$		0			0
$205$	−3.87241	+	6.70721i	−0.270461	+	0.468452i
$206$		0			0
$207$	0.0217264	+	5.08037i	0.00151009	+	0.353110i
$208$		0			0
$209$	23.9874			1.65925
$210$		0			0
$211$	−5.91693	−	10.2484i	−0.407338	−	0.705531i	0.587252	−	0.809404i	$-0.300210\pi$
$211$	−5.91693	−	10.2484i	−0.407338	−	0.705531i	−0.994591	+	0.103873i	$0.966876\pi$
$212$		0			0
$213$	−0.00590707	−	2.76256i	−0.000404746	−	0.189287i
$214$		0			0
$215$		−	32.5649i		−	2.22091i
$216$		0			0
$217$	−2.70365	−	4.68286i	−0.183536	−	0.317893i
$218$		0			0
$219$	−6.41815	+	11.1717i	−0.433698	+	0.754911i
$220$		0			0
$221$	21.8694	−	37.8790i	1.47110	−	2.54802i
$222$		0			0
$223$	7.01373			0.469674			0.234837	−	0.972035i	$-0.424544\pi$
$223$	7.01373			0.469674			0.234837	+	0.972035i	$0.424544\pi$
$224$		0			0
$225$	−3.16615	+	5.53850i	−0.211077	+	0.369234i
$226$		0			0
$227$	−3.74588	−	2.16268i	−0.248623	−	0.143542i	0.370511	−	0.928828i	$-0.379183\pi$
$227$	−3.74588	−	2.16268i	−0.248623	−	0.143542i	−0.619133	+	0.785286i	$0.712516\pi$
$228$		0			0
$229$	0.261357	−	0.150895i	0.0172710	−	0.00997139i	−0.491340	−	0.870968i	$-0.663493\pi$
$229$	0.261357	−	0.150895i	0.0172710	−	0.00997139i	0.508611	+	0.860997i	$0.330159\pi$
$230$		0			0
$231$	6.37693	+	3.66357i	0.419571	+	0.241045i
$232$		0			0
$233$	12.7168	−	22.0262i	0.833106	−	1.44298i	−0.0624566	−	0.998048i	$-0.519893\pi$
$233$	12.7168	−	22.0262i	0.833106	−	1.44298i	0.895563	−	0.444935i	$-0.146773\pi$
$234$		0			0
$235$	9.56678	+	5.52338i	0.624068	+	0.360306i
$236$		0			0
$237$	0.0431068	+	20.1597i	0.00280009	+	1.30952i
$238$		0			0
$239$	−0.837087	+	1.44988i	−0.0541466	+	0.0937847i	−0.891828	−	0.452374i	$-0.850577\pi$
$239$	−0.837087	+	1.44988i	−0.0541466	+	0.0937847i	0.837682	+	0.546159i	$0.183911\pi$
$240$		0			0
$241$	−12.1313			−0.781444			−0.390722	−	0.920509i	$-0.627775\pi$
$241$	−12.1313			−0.781444			−0.390722	+	0.920509i	$0.627775\pi$
$242$		0			0
$243$	7.64945	−	13.5826i	0.490713	−	0.871321i
$244$		0			0
$245$	8.29639	+	14.3698i	0.530037	+	0.918051i
$246$		0			0
$247$	−29.5285	−	17.0483i	−1.87885	−	1.08476i
$248$		0			0
$249$	12.3573	+	7.09932i	0.783114	+	0.449901i
$250$		0			0
$251$	6.13618	+	10.6282i	0.387312	+	0.670845i	0.992087	−	0.125552i	$-0.0400702\pi$
$251$	6.13618	+	10.6282i	0.387312	+	0.670845i	−0.604775	+	0.796397i	$0.706737\pi$
$252$		0			0
$253$		−	8.11861i		−	0.510412i
$254$		0			0
$255$	25.7338	+	14.7841i	1.61151	+	0.925817i
$256$		0			0
$257$	−23.4922	−	13.5632i	−1.46540	−	0.846050i	−0.466149	−	0.884706i	$-0.654359\pi$
$257$	−23.4922	−	13.5632i	−1.46540	−	0.846050i	−0.999253	+	0.0386567i	$0.987692\pi$
$258$		0			0
$259$			1.13350i			0.0704321i
$260$		0			0
$261$	15.3041	−	8.92332i	0.947301	−	0.552339i
$262$		0			0
$263$			16.0693i			0.990875i	0.868644	+	0.495437i	$0.164992\pi$
$263$			16.0693i			0.990875i	−0.868644	+	0.495437i	$0.835008\pi$
$264$		0			0
$265$	−14.0161			−0.861004
$266$		0			0
$267$	−13.6211	+	7.90302i	−0.833597	+	0.483657i
$268$		0			0
$269$		−	7.74125i		−	0.471992i	−0.971754	−	0.235996i	$-0.924165\pi$
$269$		−	7.74125i		−	0.471992i	0.971754	−	0.235996i	$-0.0758353\pi$
$270$		0			0
$271$		−	17.0339i		−	1.03474i	−0.855762	−	0.517369i	$-0.826911\pi$
$271$		−	17.0339i		−	1.03474i	0.855762	−	0.517369i	$-0.173089\pi$
$272$		0			0
$273$	−5.24623	−	9.04203i	−0.317516	−	0.547248i
$274$		0			0
$275$	5.09738	−	8.82892i	0.307384	−	0.532404i
$276$		0			0
$277$	4.64989			0.279385			0.139693	−	0.990195i	$-0.455389\pi$
$277$	4.64989			0.279385			0.139693	+	0.990195i	$0.455389\pi$
$278$		0			0
$279$	15.8224	−	9.22551i	0.947262	−	0.552317i
$280$		0			0
$281$	9.56232	+	16.5624i	0.570440	+	0.988031i	0.996521	+	0.0833459i	$0.0265606\pi$
$281$	9.56232	+	16.5624i	0.570440	+	0.988031i	−0.426081	+	0.904685i	$0.640106\pi$
$282$		0			0
$283$	20.5705			1.22279			0.611396	−	0.791325i	$-0.290608\pi$
$283$	20.5705			1.22279			0.611396	+	0.791325i	$0.290608\pi$
$284$		0			0
$285$	11.5249	−	20.0607i	0.682678	−	1.18829i
$286$		0			0
$287$	2.22528	−	1.28477i	0.131354	−	0.0758374i
$288$		0			0
$289$	12.0990	−	20.9560i	0.711704	−	1.23271i
$290$		0			0
$291$	13.5885	+	7.80661i	0.796570	+	0.457632i
$292$		0			0
$293$			27.9889i			1.63513i	0.575837	+	0.817564i	$0.304676\pi$
$293$			27.9889i			1.63513i	−0.575837	+	0.817564i	$0.695324\pi$
$294$		0			0
$295$		−	1.56814i		−	0.0913004i
$296$		0			0
$297$	−12.3167	+	21.6527i	−0.714687	+	1.25642i
$298$		0			0
$299$	−5.77003	+	9.99398i	−0.333689	+	0.577967i
$300$		0			0
$301$	−5.40210	+	9.35671i	−0.311372	+	0.539312i
$302$		0			0
$303$	−23.6904	+	0.0506564i	−1.36098	+	0.00291013i
$304$		0			0
$305$	15.6401	−	9.02979i	0.895547	−	0.517044i
$306$		0			0
$307$	0.231235	+	0.400510i	0.0131973	+	0.0228583i	0.872549	−	0.488527i	$-0.162466\pi$
$307$	0.231235	+	0.400510i	0.0131973	+	0.0228583i	−0.859351	+	0.511386i	$0.829132\pi$
$308$		0			0
$309$	0.149764		0.000320235i	0.00851978		1.82175e-5i
$310$		0			0
$311$	9.65840			0.547678			0.273839	−	0.961776i	$-0.411707\pi$
$311$	9.65840			0.547678			0.273839	+	0.961776i	$0.411707\pi$
$312$		0			0
$313$			13.1989i			0.746047i	0.927822	+	0.373024i	$0.121679\pi$
$313$			13.1989i			0.746047i	−0.927822	+	0.373024i	$0.878321\pi$
$314$		0			0
$315$	6.12768	−	3.57284i	0.345255	−	0.201307i
$316$		0			0
$317$	−12.0664	+	6.96656i	−0.677718	+	0.391281i	−0.798995	−	0.601338i	$-0.794635\pi$
$317$	−12.0664	+	6.96656i	−0.677718	+	0.391281i	0.121276	+	0.992619i	$0.461301\pi$
$318$		0			0
$319$	−24.5170	+	14.1549i	−1.37269	+	0.792523i
$320$		0			0
$321$	−25.1188	+	14.5740i	−1.40199	+	0.813443i
$322$		0			0
$323$	−27.8131	−	16.0579i	−1.54756	−	0.893485i
$324$		0			0
$325$	−12.5497	+	7.24558i	−0.696133	+	0.401913i
$326$		0			0
$327$	−4.82890	+	2.80175i	−0.267039	+	0.154937i
$328$		0			0
$329$	−1.83252	−	3.17401i	−0.101030	−	0.174989i
$330$		0			0
$331$	−2.55961	−	1.47779i	−0.140689	−	0.0812269i	0.428003	−	0.903777i	$-0.359217\pi$
$331$	−2.55961	−	1.47779i	−0.140689	−	0.0812269i	−0.568692	+	0.822550i	$0.692551\pi$
$332$		0			0
$333$	−3.83933	+	0.0164191i	−0.210394	+	0.000899760i
$334$		0			0
$335$	−7.78828	+	20.4162i	−0.425519	+	1.11546i
$336$		0			0
$337$	10.9976	−	6.34948i	0.599078	−	0.345878i	−0.169601	−	0.985513i	$-0.554248\pi$
$337$	10.9976	−	6.34948i	0.599078	−	0.345878i	0.768679	+	0.639635i	$0.220914\pi$
$338$		0			0
$339$	−24.9152	+	0.0532753i	−1.35321	+	0.00289352i
$340$		0			0
$341$	−25.3473	+	14.6343i	−1.37263	+	0.792491i
$342$		0			0
$343$		−	11.7049i		−	0.632005i
$344$		0			0
$345$	−6.78959	−	3.90064i	−0.365539	−	0.210003i
$346$		0			0
$347$	−17.3954	+	30.1298i	−0.933836	+	1.61745i	−0.157141	+	0.987576i	$0.550228\pi$
$347$	−17.3954	+	30.1298i	−0.933836	+	1.61745i	−0.776696	+	0.629876i	$0.783106\pi$
$348$		0			0
$349$	−34.3154			−1.83686			−0.918430	−	0.395582i	$-0.870543\pi$
$349$	−34.3154			−1.83686			−0.918430	+	0.395582i	$0.870543\pi$
$350$		0			0
$351$	30.5508	−	17.9008i	1.63068	−	0.955472i
$352$		0			0
$353$	−11.2119	−	19.4195i	−0.596747	−	1.03360i	−0.993298	−	0.115583i	$-0.963126\pi$
$353$	−11.2119	−	19.4195i	−0.596747	−	1.03360i	0.396551	−	0.918013i	$-0.370207\pi$
$354$		0			0
$355$	3.68741	+	2.12893i	0.195707	+	0.112992i
$356$		0			0
$357$	−4.94146	−	8.51675i	−0.261530	−	0.450754i
$358$		0			0
$359$		−	24.3510i		−	1.28520i	−0.766203	−	0.642599i	$-0.777856\pi$
$359$		−	24.3510i		−	1.28520i	0.766203	−	0.642599i	$-0.222144\pi$
$360$		0			0
$361$	−3.01789	+	5.22714i	−0.158836	+	0.275113i
$362$		0			0
$363$	10.3391	−	17.9967i	0.542664	−	0.944580i
$364$		0			0
$365$	−9.92890	−	17.1974i	−0.519702	−	0.900151i
$366$		0			0
$367$	−17.9252	−	10.3491i	−0.935687	−	0.540219i	−0.0470815	−	0.998891i	$-0.514992\pi$
$367$	−17.9252	−	10.3491i	−0.935687	−	0.540219i	−0.888606	+	0.458672i	$0.848325\pi$
$368$		0			0
$369$	4.38394	+	7.51876i	0.228219	+	0.391411i
$370$		0			0
$371$	4.02718	+	2.32510i	0.209081	+	0.120713i
$372$		0			0
$373$	−14.8627	−	8.58099i	−0.769562	−	0.444307i	0.0631565	−	0.998004i	$-0.479883\pi$
$373$	−14.8627	−	8.58099i	−0.769562	−	0.444307i	−0.832718	+	0.553697i	$0.813217\pi$
$374$		0			0
$375$	6.66776	+	11.4921i	0.344321	+	0.593448i
$376$		0			0
$377$	40.2405			2.07249
$378$		0			0
$379$	−8.38111	+	4.83883i	−0.430508	+	0.248554i	−0.699563	−	0.714571i	$-0.746622\pi$
$379$	−8.38111	+	4.83883i	−0.430508	+	0.248554i	0.269055	+	0.963125i	$0.413289\pi$
$380$		0			0
$381$	5.71454	−	0.0122192i	0.292765	−	0.000626008i
$382$		0			0
$383$	−6.59191	−	11.4175i	−0.336831	−	0.583408i	0.647004	−	0.762487i	$-0.276022\pi$
$383$	−6.59191	−	11.4175i	−0.336831	−	0.583408i	−0.983835	+	0.179079i	$0.942688\pi$
$384$		0			0
$385$	−9.81648	+	5.66755i	−0.500294	+	0.288845i
$386$		0			0
$387$	−31.7709	−	18.1622i	−1.61500	−	0.923237i
$388$		0			0
$389$	−4.79644	+	2.76923i	−0.243189	+	0.140405i	−0.616642	−	0.787244i	$-0.711507\pi$
$389$	−4.79644	+	2.76923i	−0.243189	+	0.140405i	0.373452	+	0.927649i	$0.378174\pi$
$390$		0			0
$391$	−5.43483	+	9.41340i	−0.274851	+	0.476056i
$392$		0			0
$393$	−10.4893	+	6.08597i	−0.529117	+	0.306996i
$394$		0			0
$395$	−26.9089	−	15.5358i	−1.35393	−	0.781693i
$396$		0			0
$397$	−11.8894			−0.596714			−0.298357	−	0.954454i	$-0.596439\pi$
$397$	−11.8894			−0.596714			−0.298357	+	0.954454i	$0.596439\pi$
$398$		0			0
$399$	−6.63921	+	3.85210i	−0.332376	+	0.192846i
$400$		0			0
$401$	−23.8611			−1.19157			−0.595783	−	0.803146i	$-0.703158\pi$
$401$	−23.8611			−1.19157			−0.595783	+	0.803146i	$0.703158\pi$
$402$		0			0
$403$	41.6033			2.07241
$404$		0			0
$405$	12.1905	+	20.7036i	0.605752	+	1.02877i
$406$		0			0
$407$	6.13539			0.304120
$408$		0			0
$409$	9.72849	+	5.61675i	0.481043	+	0.277730i	0.720851	−	0.693090i	$-0.243751\pi$
$409$	9.72849	+	5.61675i	0.481043	+	0.277730i	−0.239808	+	0.970820i	$0.577084\pi$
$410$		0			0
$411$	−1.68439	−	2.90310i	−0.0830849	−	0.143199i
$412$		0			0
$413$	−0.260134	+	0.450565i	−0.0128003	+	0.0221708i
$414$		0			0
$415$	−19.0225	+	10.9827i	−0.933780	+	0.539118i
$416$		0			0
$417$	−20.8183	+	12.0789i	−1.01947	+	0.591504i
$418$		0			0
$419$	−13.0009	+	7.50607i	−0.635135	+	0.366695i	−0.782738	−	0.622351i	$-0.786178\pi$
$419$	−13.0009	+	7.50607i	−0.635135	+	0.366695i	0.147603	+	0.989047i	$0.452844\pi$
$420$		0			0
$421$	12.3082	+	21.3184i	0.599863	+	1.03899i	0.992841	+	0.119445i	$0.0381116\pi$
$421$	12.3082	+	21.3184i	0.599863	+	1.03899i	−0.392978	+	0.919548i	$0.628555\pi$
$422$		0			0
$423$	10.7243	−	6.25300i	0.521435	−	0.304031i
$424$		0			0
$425$	−11.8207	+	6.82466i	−0.573386	+	0.331045i
$426$		0			0
$427$	−5.99171			−0.289959
$428$		0			0
$429$	−48.9426	+	28.3967i	−2.36297	+	1.37101i
$430$		0			0
$431$	28.4860	+	16.4464i	1.37212	+	0.792195i	0.991195	−	0.132410i	$-0.0422716\pi$
$431$	28.4860	+	16.4464i	1.37212	+	0.792195i	0.380927	+	0.924605i	$0.375605\pi$
$432$		0			0
$433$	−5.46719	−	3.15648i	−0.262736	−	0.151691i	0.362846	−	0.931849i	$-0.381805\pi$
$433$	−5.46719	−	3.15648i	−0.262736	−	0.151691i	−0.625582	+	0.780158i	$0.715138\pi$
$434$		0			0
$435$	0.0583840	+	27.3044i	0.00279930	+	1.30915i
$436$		0			0
$437$	7.33819	+	4.23671i	0.351033	+	0.202669i
$438$		0			0
$439$	7.84323	+	13.5849i	0.374337	+	0.648371i	0.990228	−	0.139461i	$-0.0445370\pi$
$439$	7.84323	+	13.5849i	0.374337	+	0.648371i	−0.615891	+	0.787832i	$0.711204\pi$
$440$		0			0
$441$	18.6465	−	0.0797426i	0.887928	−	0.00379726i
$442$		0			0
$443$	4.22784	−	7.32284i	0.200871	−	0.347918i	−0.747938	−	0.663768i	$-0.768956\pi$
$443$	4.22784	−	7.32284i	0.200871	−	0.347918i	0.948809	+	0.315850i	$0.102290\pi$
$444$		0			0
$445$		−	24.2716i		−	1.15058i
$446$		0			0
$447$	23.9977	−	13.9236i	1.13505	−	0.658563i
$448$		0			0
$449$	8.74757	+	5.05041i	0.412823	+	0.238344i	0.692002	−	0.721896i	$-0.256729\pi$
$449$	8.74757	+	5.05041i	0.412823	+	0.238344i	−0.279179	+	0.960239i	$0.590062\pi$
$450$		0			0
$451$	−6.95417	−	12.0450i	−0.327459	−	0.567176i
$452$		0			0
$453$	−5.73945	+	9.99029i	−0.269663	+	0.469385i
$454$		0			0
$455$	16.1121			0.755346
$456$		0			0
$457$	1.61348	−	2.79462i	0.0754753	−	0.130727i	−0.825818	−	0.563937i	$-0.809286\pi$
$457$	1.61348	−	2.79462i	0.0754753	−	0.130727i	0.901293	+	0.433210i	$0.142619\pi$
$458$		0			0
$459$	28.7760	−	16.8609i	1.34315	−	0.786997i
$460$		0			0
$461$		−	27.3169i		−	1.27227i	−0.771576	−	0.636137i	$-0.780531\pi$
$461$		−	27.3169i		−	1.27227i	0.771576	−	0.636137i	$-0.219469\pi$
$462$		0			0
$463$	−19.1655	+	11.0652i	−0.890695	+	0.514243i	−0.874170	−	0.485621i	$-0.838594\pi$
$463$	−19.1655	+	11.0652i	−0.890695	+	0.514243i	−0.0165250	+	0.999863i	$0.505260\pi$
$464$		0			0
$465$	0.0603612	+	28.2291i	0.00279918	+	1.30909i
$466$		0			0
$467$	16.1193	−	9.30648i	0.745912	−	0.430653i	−0.0783028	−	0.996930i	$-0.524950\pi$
$467$	16.1193	−	9.30648i	0.745912	−	0.430653i	0.824215	+	0.566277i	$0.191617\pi$
$468$		0			0
$469$	5.62455	−	4.57411i	0.259718	−	0.211213i
$470$		0			0
$471$	−17.4251	+	30.3308i	−0.802907	+	1.39757i
$472$		0			0
$473$	50.6459	+	29.2404i	2.32870	+	1.34448i
$474$		0			0
$475$	5.32015	+	9.21477i	0.244105	+	0.422803i
$476$		0			0
$477$	−7.81713	+	13.6744i	−0.357922	+	0.626107i
$478$		0			0
$479$	9.27106	−	5.35265i	0.423605	−	0.244569i	−0.273013	−	0.962010i	$-0.588020\pi$
$479$	9.27106	−	5.35265i	0.423605	−	0.244569i	0.696619	+	0.717442i	$0.254687\pi$
$480$		0			0
$481$	−7.55264	−	4.36052i	−0.344371	−	0.198823i
$482$		0			0
$483$	1.30375	+	2.24706i	0.0593228	+	0.102245i
$484$		0			0
$485$	−20.9177	+	12.0768i	−0.949824	+	0.548381i
$486$		0			0
$487$	−37.0488	+	21.3902i	−1.67884	+	0.969280i	−0.716442	+	0.697647i	$0.754231\pi$
$487$	−37.0488	+	21.3902i	−1.67884	+	0.969280i	−0.962401	+	0.271634i	$0.912436\pi$
$488$		0			0
$489$	14.3594	−	0.0307041i	0.649354	−	0.00138849i
$490$		0			0
$491$		−	4.04352i		−	0.182481i	−0.995829	−	0.0912407i	$-0.970917\pi$
$491$		−	4.04352i		−	0.182481i	0.995829	−	0.0912407i	$-0.0290833\pi$
$492$		0			0
$493$	37.9028			1.70706
$494$		0			0
$495$	−19.3391	−	33.1678i	−0.869226	−	1.49078i
$496$		0			0
$497$	−0.706324	−	1.22339i	−0.0316830	−	0.0548765i
$498$		0			0
$499$	−30.1152	+	17.3870i	−1.34814	+	0.778349i	−0.987986	−	0.154544i	$-0.950609\pi$
$499$	−30.1152	+	17.3870i	−1.34814	+	0.778349i	−0.360154	+	0.932893i	$0.617276\pi$
$500$		0			0
$501$	−0.0420179	−	19.6505i	−0.00187722	−	0.877919i
$502$		0			0
$503$	9.58680	−	16.6048i	0.427454	−	0.740373i	−0.569192	−	0.822205i	$-0.692744\pi$
$503$	9.58680	−	16.6048i	0.427454	−	0.740373i	0.996646	+	0.0818321i	$0.0260771\pi$
$504$		0			0
$505$	18.2567	−	31.6216i	0.812413	−	1.40714i
$506$		0			0
$507$	57.9136	−	0.123835i	2.57203	−	0.00549969i
$508$		0			0
$509$		−	17.0124i		−	0.754061i	−0.926201	−	0.377031i	$-0.876945\pi$
$509$		−	17.0124i		−	0.754061i	0.926201	−	0.377031i	$-0.123055\pi$
$510$		0			0
$511$			6.58831i			0.291450i
$512$		0			0
$513$	−13.1438	−	22.4322i	−0.580315	−	0.990408i
$514$		0			0
$515$	−0.115414	+	0.199902i	−0.00508574	+	0.00880875i
$516$		0			0
$517$	−17.1803	+	9.91903i	−0.755587	+	0.436239i
$518$		0			0
$519$	−23.8067	−	13.6770i	−1.04500	−	0.600353i
$520$		0			0
$521$	−4.28481			−0.187721			−0.0938605	−	0.995585i	$-0.529921\pi$
$521$	−4.28481			−0.187721			−0.0938605	+	0.995585i	$0.529921\pi$
$522$		0			0
$523$	−14.2199	−	24.6296i	−0.621793	−	1.07698i	−0.989152	−	0.146897i	$-0.953071\pi$
$523$	−14.2199	−	24.6296i	−0.621793	−	1.07698i	0.367359	−	0.930079i	$-0.380262\pi$
$524$		0			0
$525$	0.00697552	+	3.26224i	0.000304437	+	0.142376i
$526$		0			0
$527$	39.1864			1.70699
$528$		0			0
$529$	−10.0661	+	17.4350i	−0.437656	+	0.758042i
$530$		0			0
$531$	−1.52990	−	0.874586i	−0.0663920	−	0.0379538i
$532$		0			0
$533$			19.7698i			0.856324i
$534$		0			0
$535$		−	44.7594i		−	1.93512i
$536$		0			0
$537$	9.38838	+	16.1811i	0.405139	+	0.698268i
$538$		0			0
$539$	−29.7977			−1.28348
$540$		0			0
$541$			19.5488i			0.840468i	0.907416	+	0.420234i	$0.138052\pi$
$541$			19.5488i			0.840468i	−0.907416	+	0.420234i	$0.861948\pi$
$542$		0			0
$543$	15.4695	−	0.0330780i	0.663862	−	0.00141951i
$544$		0			0
$545$		−	8.60466i		−	0.368583i
$546$		0			0
$547$	−28.8062	−	16.6313i	−1.23167	−	0.711103i	−0.264289	−	0.964444i	$-0.585137\pi$
$547$	−28.8062	−	16.6313i	−1.23167	−	0.711103i	−0.967377	+	0.253341i	$0.918471\pi$
$548$		0			0
$549$	−0.0867918	−	20.2948i	−0.00370418	−	0.866163i
$550$		0			0
$551$		−	29.5471i		−	1.25875i
$552$		0			0
$553$	5.15439	+	8.92767i	0.219187	+	0.379643i
$554$		0			0
$555$	2.94779	−	5.13102i	0.125127	−	0.217800i
$556$		0			0
$557$	−10.6629	−	6.15624i	−0.451802	−	0.260848i	0.256789	−	0.966468i	$-0.417336\pi$
$557$	−10.6629	−	6.15624i	−0.451802	−	0.260848i	−0.708591	+	0.705619i	$0.750669\pi$
$558$		0			0
$559$	−41.5633	−	71.9898i	−1.75794	−	3.04484i
$560$		0			0
$561$	−46.0994	+	26.7471i	−1.94632	+	1.12926i
$562$		0			0
$563$	−44.2623			−1.86543			−0.932717	−	0.360610i	$-0.882569\pi$
$563$	−44.2623			−1.86543			−0.932717	+	0.360610i	$0.882569\pi$
$564$		0			0
$565$	19.2006	−	33.2564i	0.807774	−	1.39911i
$566$		0			0
$567$	−0.0681773	−	7.97093i	−0.00286318	−	0.334747i
$568$		0			0
$569$	−27.8744	−	16.0933i	−1.16856	−	0.674667i	−0.215218	−	0.976566i	$-0.569046\pi$
$569$	−27.8744	−	16.0933i	−1.16856	−	0.674667i	−0.953340	+	0.301899i	$0.902379\pi$
$570$		0			0
$571$	2.23640	−	3.87355i	0.0935903	−	0.162103i	−0.815429	−	0.578857i	$-0.803499\pi$
$571$	2.23640	−	3.87355i	0.0935903	−	0.162103i	0.909019	+	0.416754i	$0.136832\pi$
$572$		0			0
$573$	14.5775	−	25.3741i	0.608983	−	1.06002i
$574$		0			0
$575$	3.11876	−	1.80062i	0.130061	−	0.0750909i
$576$		0			0
$577$	19.6185	+	11.3267i	0.816729	+	0.471538i	0.849287	−	0.527931i	$-0.177032\pi$
$577$	19.6185	+	11.3267i	0.816729	+	0.471538i	−0.0325585	+	0.999470i	$0.510366\pi$
$578$		0			0
$579$	21.3066	+	36.7226i	0.885472	+	1.52614i
$580$		0			0
$581$	7.28754			0.302338
$582$		0			0
$583$	12.5853	−	21.7983i	0.521228	−	0.902794i
$584$		0			0
$585$	0.233389	+	54.5741i	0.00964943	+	2.25636i
$586$		0			0
$587$	5.41622	+	9.38117i	0.223551	+	0.387202i	0.955884	−	0.293745i	$-0.0949017\pi$
$587$	5.41622	+	9.38117i	0.223551	+	0.387202i	−0.732333	+	0.680947i	$0.761568\pi$
$588$		0			0
$589$		−	30.5477i		−	1.25870i
$590$		0			0
$591$	−38.6127	+	0.0825641i	−1.58831	+	0.00339623i
$592$		0			0
$593$	1.57009	+	2.71947i	0.0644758	+	0.111675i	0.896461	−	0.443122i	$-0.146129\pi$
$593$	1.57009	+	2.71947i	0.0644758	+	0.111675i	−0.831986	+	0.554797i	$0.812796\pi$
$594$		0			0
$595$	15.1761			0.622158
$596$		0			0
$597$	6.67227	−	11.6140i	0.273078	−	0.475329i
$598$		0			0
$599$	−13.9261	+	24.1207i	−0.569006	+	0.985547i	0.427659	+	0.903940i	$0.359338\pi$
$599$	−13.9261	+	24.1207i	−0.569006	+	0.985547i	−0.996665	+	0.0816064i	$0.973995\pi$
$600$		0			0
$601$	2.16618	+	3.75193i	0.0883601	+	0.153044i	0.906818	−	0.421522i	$-0.138504\pi$
$601$	2.16618	+	3.75193i	0.0883601	+	0.153044i	−0.818458	+	0.574566i	$0.805171\pi$
$602$		0			0
$603$	15.5747	+	18.9850i	0.634250	+	0.773128i
$604$		0			0
$605$	15.9947	+	27.7036i	0.650276	+	1.12631i
$606$		0			0
$607$	18.4717	−	31.9940i	0.749744	−	1.29860i	−0.198201	−	0.980161i	$-0.563510\pi$
$607$	18.4717	−	31.9940i	0.749744	−	1.29860i	0.947945	−	0.318434i	$-0.103157\pi$
$608$		0			0
$609$	4.51268	−	7.85493i	0.182863	−	0.318298i
$610$		0			0
$611$	28.1985			1.14079
$612$		0			0
$613$	−2.55105	−	4.41856i	−0.103036	−	0.178464i	0.809898	−	0.586571i	$-0.199522\pi$
$613$	−2.55105	−	4.41856i	−0.103036	−	0.178464i	−0.912934	+	0.408107i	$0.866189\pi$
$614$		0			0
$615$	−13.4144	+	0.0286835i	−0.540921	+	0.00115663i
$616$		0			0
$617$		−	15.7934i		−	0.635819i	−0.948121	−	0.317909i	$-0.897019\pi$
$617$		−	15.7934i		−	0.635819i	0.948121	−	0.317909i	$-0.102981\pi$
$618$		0			0
$619$	22.6888	+	39.2981i	0.911940	+	1.57953i	0.811321	+	0.584601i	$0.198749\pi$
$619$	22.6888	+	39.2981i	0.911940	+	1.57953i	0.100618	+	0.994925i	$0.467918\pi$
$620$		0			0
$621$	−7.59224	+	4.44856i	−0.304666	+	0.178515i
$622$		0			0
$623$	−4.02634	+	6.97382i	−0.161312	+	0.279400i
$624$		0			0
$625$	−31.1105			−1.24442
$626$		0			0
$627$	20.8506	+	35.9367i	0.832694	+	1.43517i
$628$		0			0
$629$	−7.11389	−	4.10720i	−0.283649	−	0.163765i
$630$		0			0
$631$	−32.9816	+	19.0419i	−1.31297	+	0.758046i	−0.982588	−	0.185799i	$-0.940513\pi$
$631$	−32.9816	+	19.0419i	−1.31297	+	0.758046i	−0.330387	+	0.943846i	$0.607179\pi$
$632$		0			0
$633$	10.2104	−	17.7727i	0.405829	−	0.706400i
$634$		0			0
$635$	−4.40384	+	7.62767i	−0.174761	+	0.302695i
$636$		0			0
$637$	36.6809	+	21.1777i	1.45335	+	0.839092i
$638$		0			0
$639$	4.13358	−	2.41015i	0.163522	−	0.0953440i
$640$		0			0
$641$	−3.27214	+	5.66752i	−0.129242	+	0.223854i	−0.923383	−	0.383880i	$-0.874588\pi$
$641$	−3.27214	+	5.66752i	−0.129242	+	0.223854i	0.794141	+	0.607733i	$0.207921\pi$
$642$		0			0
$643$	3.04449			0.120063			0.0600314	−	0.998196i	$-0.480880\pi$
$643$	3.04449			0.120063			0.0600314	+	0.998196i	$0.480880\pi$
$644$		0			0
$645$	48.7869	−	28.3064i	1.92098	−	1.11456i
$646$		0			0
$647$	0.189531	+	0.328277i	0.00745122	+	0.0129059i	0.869727	−	0.493533i	$-0.164295\pi$
$647$	0.189531	+	0.328277i	0.00745122	+	0.0129059i	−0.862276	+	0.506439i	$0.830962\pi$
$648$		0			0
$649$	2.43881	+	1.40805i	0.0957317	+	0.0552707i
$650$		0			0
$651$	4.66550	−	8.12094i	0.182855	−	0.318285i
$652$		0			0
$653$	21.6786	+	37.5485i	0.848350	+	1.46938i	0.882680	+	0.469974i	$0.155737\pi$
$653$	21.6786	+	37.5485i	0.848350	+	1.46938i	−0.0343306	+	0.999411i	$0.510930\pi$
$654$		0			0
$655$		−	18.6911i		−	0.730320i
$656$		0			0
$657$	−22.3156	+	0.0954338i	−0.870615	+	0.00372323i
$658$		0			0
$659$	31.4183	+	18.1394i	1.22388	+	0.706609i	0.965744	−	0.259498i	$-0.0835572\pi$
$659$	31.4183	+	18.1394i	1.22388	+	0.706609i	0.258140	+	0.966108i	$0.416891\pi$
$660$		0			0
$661$		−	4.46606i		−	0.173710i	−0.996221	−	0.0868549i	$-0.972318\pi$
$661$		−	4.46606i		−	0.173710i	0.996221	−	0.0868549i	$-0.0276816\pi$
$662$		0			0
$663$	75.7578	−	0.161990i	2.94219	−	0.00629117i
$664$		0			0
$665$		−	11.8305i		−	0.458766i
$666$		0			0
$667$	−10.0003			−0.387212
$668$		0			0
$669$	6.09655	+	10.5076i	0.235706	+	0.406247i
$670$		0			0
$671$			32.4319i			1.25202i
$672$		0			0
$673$		−	4.22151i		−	0.162727i	−0.996684	−	0.0813636i	$-0.974072\pi$
$673$		−	4.22151i		−	0.162727i	0.996684	−	0.0813636i	$-0.0259275\pi$
$674$		0			0
$675$	−11.0496	+	0.0708817i	−0.425299	+	0.00272824i
$676$		0			0
$677$	2.63905	−	4.57097i	0.101427	−	0.175677i	−0.810846	−	0.585260i	$-0.800993\pi$
$677$	2.63905	−	4.57097i	0.101427	−	0.175677i	0.912273	+	0.409583i	$0.134326\pi$
$678$		0			0
$679$	8.01358			0.307533
$680$		0			0
$681$	−0.0160193	−	7.49174i	−0.000613861	−	0.287084i
$682$		0			0
$683$	20.1597	+	34.9177i	0.771391	+	1.33609i	0.936801	+	0.349864i	$0.113772\pi$
$683$	20.1597	+	34.9177i	0.771391	+	1.33609i	−0.165410	+	0.986225i	$0.552895\pi$
$684$		0			0
$685$	5.17306			0.197652
$686$		0			0
$687$	0.453242	+	0.260389i	0.0172922	+	0.00993444i
$688$		0			0
$689$	−30.9848	+	17.8891i	−1.18043	+	0.681521i
$690$		0			0
$691$	1.47918	−	2.56202i	0.0562708	−	0.0974639i	−0.836518	−	0.547940i	$-0.815412\pi$
$691$	1.47918	−	2.56202i	0.0562708	−	0.0974639i	0.892789	+	0.450476i	$0.148746\pi$
$692$		0			0
$693$	0.0544749	+	12.7381i	0.00206933	+	0.483879i
$694$		0			0
$695$		−	37.0962i		−	1.40714i
$696$		0			0
$697$			18.6213i			0.705332i
$698$		0			0
$699$	44.0522	−	0.0941953i	1.66621	−	0.00356279i
$700$		0			0
$701$	20.1270	−	34.8610i	0.760186	−	1.31668i	−0.182569	−	0.983193i	$-0.558441\pi$
$701$	20.1270	−	34.8610i	0.760186	−	1.31668i	0.942755	−	0.333487i	$-0.108225\pi$
$702$		0			0
$703$	−3.20176	+	5.54561i	−0.120757	+	0.209157i
$704$		0			0
$705$	0.0409125	+	19.1335i	0.00154085	+	0.720610i
$706$		0			0
$707$	−10.4912	+	6.05711i	−0.394563	+	0.227801i
$708$		0			0
$709$	9.12206	+	15.7999i	0.342586	+	0.593377i	0.984912	−	0.173055i	$-0.0553638\pi$
$709$	9.12206	+	15.7999i	0.342586	+	0.593377i	−0.642326	+	0.766432i	$0.722030\pi$
$710$		0			0
$711$	−30.1647	+	17.5881i	−1.13127	+	0.659603i
$712$		0			0
$713$	−10.3389			−0.387196
$714$		0			0
$715$		−	87.2113i		−	3.26152i
$716$		0			0
$717$	−2.89975	+	0.00620042i	−0.108293	+	0.000231559i
$718$		0			0
$719$	−12.8737	+	7.43265i	−0.480109	+	0.277191i	−0.720462	−	0.693494i	$-0.756070\pi$
$719$	−12.8737	+	7.43265i	−0.480109	+	0.277191i	0.240353	+	0.970686i	$0.422737\pi$
$720$		0			0
$721$	0.0663225	−	0.0382913i	0.00246998	−	0.00142604i
$722$		0			0
$723$	−10.5449	−	18.1744i	−0.392168	−	0.675913i
$724$		0			0
$725$	−10.8752	−	6.27881i	−0.403896	−	0.233189i
$726$		0			0
$727$	1.33011	−	0.767938i	0.0493309	−	0.0284812i	−0.475132	−	0.879915i	$-0.657600\pi$
$727$	1.33011	−	0.767938i	0.0493309	−	0.0284812i	0.524463	+	0.851433i	$0.324266\pi$
$728$		0			0
$729$	26.9978	−	0.346389i	0.999918	−	0.0128292i
$730$		0			0
$731$	−39.1488	−	67.8076i	−1.44797	−	2.50796i
$732$		0			0
$733$	43.9650	+	25.3832i	1.62388	+	0.937550i	0.985868	+	0.167527i	$0.0535780\pi$
$733$	43.9650	+	25.3832i	1.62388	+	0.937550i	0.638016	+	0.770023i	$0.279755\pi$
$734$		0			0
$735$	−14.3165	+	24.9198i	−0.528073	+	0.919182i
$736$		0			0
$737$	−24.7587	−	30.4445i	−0.911998	−	1.12144i
$738$		0			0
$739$	8.00593	−	4.62223i	0.294503	−	0.170031i	−0.345468	−	0.938431i	$-0.612280\pi$
$739$	8.00593	−	4.62223i	0.294503	−	0.170031i	0.639971	+	0.768399i	$0.278946\pi$
$740$		0			0
$741$	−0.126279	−	59.0568i	−0.00463898	−	2.16951i
$742$		0			0
$743$	12.0681	−	6.96754i	0.442737	−	0.255614i	−0.262021	−	0.965062i	$-0.584389\pi$
$743$	12.0681	−	6.96754i	0.442737	−	0.255614i	0.704758	+	0.709448i	$0.251056\pi$
$744$		0			0
$745$			42.7617i			1.56667i
$746$		0			0
$747$	0.105562	+	24.6840i	0.00386232	+	0.903141i
$748$		0			0
$749$	−7.42501	+	12.8605i	−0.271304	+	0.469912i
$750$		0			0
$751$	−5.81892			−0.212335			−0.106168	−	0.994348i	$-0.533858\pi$
$751$	−5.81892			−0.212335			−0.106168	+	0.994348i	$0.533858\pi$
$752$		0			0
$753$	−10.5888	+	18.4312i	−0.385877	+	0.671671i
$754$		0			0
$755$	−8.87895	−	15.3788i	−0.323138	−	0.559691i
$756$		0			0
$757$	39.7347	+	22.9409i	1.44418	+	0.833800i	0.998125	−	0.0612044i	$-0.0194942\pi$
$757$	39.7347	+	22.9409i	1.44418	+	0.833800i	0.446058	+	0.895004i	$0.352827\pi$
$758$		0			0
$759$	12.1628	−	7.05694i	0.441483	−	0.256151i
$760$		0			0
$761$			19.1770i			0.695167i	0.937649	+	0.347584i	$0.112998\pi$
$761$			19.1770i			0.695167i	−0.937649	+	0.347584i	$0.887002\pi$
$762$		0			0
$763$	−1.42740	+	2.47233i	−0.0516755	+	0.0895045i
$764$		0			0
$765$	0.219830	+	51.4037i	0.00794798	+	1.85850i
$766$		0			0
$767$	−2.00145	−	3.46661i	−0.0722680	−	0.125172i
$768$		0			0
$769$	−36.6831	−	21.1790i	−1.32283	−	0.763734i	−0.338647	−	0.940913i	$-0.609969\pi$
$769$	−36.6831	−	21.1790i	−1.32283	−	0.763734i	−0.984179	+	0.177179i	$0.943303\pi$
$770$		0			0
$771$	−0.100465	−	46.9842i	−0.00361815	−	1.69210i
$772$		0			0
$773$	19.1042	+	11.0298i	0.687129	+	0.396714i	0.802536	−	0.596604i	$-0.203484\pi$
$773$	19.1042	+	11.0298i	0.687129	+	0.396714i	−0.115407	+	0.993318i	$0.536817\pi$
$774$		0			0
$775$	−11.2435	−	6.49144i	−0.403879	−	0.233180i
$776$		0			0
$777$	−1.69814	+	0.985271i	−0.0609206	+	0.0353464i
$778$		0			0
$779$	14.5162			0.520097
$780$		0			0
$781$	−6.62195	+	3.82318i	−0.236952	+	0.136804i
$782$		0			0
$783$	26.6712	+	15.1714i	0.953152	+	0.542180i
$784$		0			0
$785$	−26.9567	−	46.6904i	−0.962126	−	1.66645i
$786$		0			0
$787$	18.2496	−	10.5364i	0.650528	−	0.375583i	−0.138130	−	0.990414i	$-0.544109\pi$
$787$	18.2496	−	10.5364i	0.650528	−	0.375583i	0.788659	+	0.614831i	$0.210776\pi$
$788$		0			0
$789$	−24.0741	+	13.9679i	−0.857061	+	0.497271i
$790$		0			0
$791$	−11.0336	+	6.37026i	−0.392310	+	0.226500i
$792$		0			0
$793$	23.0499	−	39.9235i	0.818524	−	1.41773i
$794$		0			0
$795$	−12.1833	−	20.9982i	−0.432095	−	0.744729i
$796$		0			0
$797$	6.94721	+	4.01097i	0.246083	+	0.142076i	0.617969	−	0.786202i	$-0.287956\pi$
$797$	6.94721	+	4.01097i	0.246083	+	0.142076i	−0.371886	+	0.928278i	$0.621289\pi$
$798$		0			0
$799$	26.5603			0.939637
$800$		0			0
$801$	−23.6797	−	13.5368i	−0.836683	−	0.478300i
$802$		0			0
$803$	35.6611			1.25845
$804$		0			0
$805$	−4.00405			−0.141124
$806$		0			0
$807$	11.5975	−	6.72893i	0.408252	−	0.236870i
$808$		0			0
$809$	19.8709			0.698623			0.349311	−	0.937007i	$-0.386416\pi$
$809$	19.8709			0.698623			0.349311	+	0.937007i	$0.386416\pi$
$810$		0			0
$811$	−0.712665	−	0.411458i	−0.0250251	−	0.0144482i	0.487435	−	0.873159i	$-0.337933\pi$
$811$	−0.712665	−	0.411458i	−0.0250251	−	0.0144482i	−0.512460	+	0.858711i	$0.671266\pi$
$812$		0			0
$813$	25.5193	−	14.8064i	0.895002	−	0.519284i
$814$		0			0
$815$	−11.0659	+	19.1666i	−0.387621	+	0.671378i
$816$		0			0
$817$	−52.8593	+	30.5183i	−1.84931	+	1.06770i
$818$		0			0
$819$	8.98608	−	15.7192i	0.313999	−	0.549274i
$820$		0			0
$821$	9.55155	−	5.51459i	0.333351	−	0.192461i	−0.323977	−	0.946065i	$-0.605020\pi$
$821$	9.55155	−	5.51459i	0.333351	−	0.192461i	0.657328	+	0.753605i	$0.271687\pi$
$822$		0			0
$823$	−2.64571	−	4.58250i	−0.0922235	−	0.159736i	0.816223	−	0.577737i	$-0.196064\pi$
$823$	−2.64571	−	4.58250i	−0.0922235	−	0.159736i	−0.908446	+	0.418001i	$0.862731\pi$
$824$		0			0
$825$	17.6578	−	0.0377570i	0.614766	−	0.00131453i
$826$		0			0
$827$	−31.4356	+	18.1494i	−1.09312	+	0.631115i	−0.934406	−	0.356209i	$-0.884069\pi$
$827$	−31.4356	+	18.1494i	−1.09312	+	0.631115i	−0.158718	+	0.987324i	$0.550736\pi$
$828$		0			0
$829$	5.65056			0.196252			0.0981261	−	0.995174i	$-0.468715\pi$
$829$	5.65056			0.196252			0.0981261	+	0.995174i	$0.468715\pi$
$830$		0			0
$831$	4.04183	+	6.96621i	0.140210	+	0.241655i
$832$		0			0
$833$	34.5500	+	19.9475i	1.19709	+	0.691138i
$834$		0			0
$835$	26.2291	+	15.1434i	0.907696	+	0.524059i
$836$		0			0
$837$	27.5745	+	15.6851i	0.953113	+	0.542158i
$838$		0			0
$839$	47.8662	+	27.6356i	1.65253	+	0.954086i	0.976029	+	0.217639i	$0.0698357\pi$
$839$	47.8662	+	27.6356i	1.65253	+	0.954086i	0.676496	+	0.736446i	$0.263498\pi$
$840$		0			0
$841$	2.93564	+	5.08467i	0.101229	+	0.175334i
$842$		0			0
$843$	−16.5010	+	28.7223i	−0.568326	+	0.989249i
$844$		0			0
$845$	−44.6304	+	77.3021i	−1.53533	+	2.65927i
$846$		0			0
$847$		−	10.6132i		−	0.364676i
$848$		0			0
$849$	17.8806	+	30.8177i	0.613659	+	1.05766i
$850$		0			0
$851$	1.87693	+	1.08364i	0.0643402	+	0.0371468i
$852$		0			0
$853$	21.5827	+	37.3823i	0.738976	+	1.27994i	0.952957	+	0.303106i	$0.0980236\pi$
$853$	21.5827	+	37.3823i	0.738976	+	1.27994i	−0.213981	+	0.976838i	$0.568643\pi$
$854$		0			0
$855$	40.0716	−	0.171368i	1.37042	−	0.00586067i
$856$		0			0
$857$	−28.9434			−0.988687			−0.494344	−	0.869267i	$-0.664591\pi$
$857$	−28.9434			−0.988687			−0.494344	+	0.869267i	$0.664591\pi$
$858$		0			0
$859$	9.53921	−	16.5224i	0.325474	−	0.563737i	−0.656135	−	0.754644i	$-0.727810\pi$
$859$	9.53921	−	16.5224i	0.325474	−	0.563737i	0.981608	+	0.190907i	$0.0611430\pi$
$860$		0			0
$861$	3.85905	+	2.21703i	0.131516	+	0.0755563i
$862$		0			0
$863$		−	18.0028i		−	0.612824i	−0.951899	−	0.306412i	$-0.900871\pi$
$863$		−	18.0028i		−	0.612824i	0.951899	−	0.306412i	$-0.0991285\pi$
$864$		0			0
$865$	36.6473	−	21.1583i	1.24605	−	0.719405i
$866$		0			0
$867$	41.9120	−	0.0896188i	1.42341	−	0.00304361i
$868$		0			0
$869$	48.3236	−	27.8997i	1.63927	−	0.946431i
$870$		0			0
$871$	8.84043	+	55.0735i	0.299547	+	1.86610i
$872$		0			0
$873$	0.116079	+	27.1432i	0.00392869	+	0.918659i
$874$		0			0
$875$	5.88379	+	3.39701i	0.198909	+	0.114840i
$876$		0			0
$877$	−2.51276	−	4.35223i	−0.0848499	−	0.146964i	0.820477	−	0.571679i	$-0.193708\pi$
$877$	−2.51276	−	4.35223i	−0.0848499	−	0.146964i	−0.905327	+	0.424715i	$0.860374\pi$
$878$		0			0
$879$	−41.9314	+	24.3288i	−1.41431	+	0.820590i
$880$		0			0
$881$	−6.59259	+	3.80623i	−0.222110	+	0.128235i	−0.606927	−	0.794758i	$-0.707598\pi$
$881$	−6.59259	+	3.80623i	−0.222110	+	0.128235i	0.384817	+	0.922993i	$0.374265\pi$
$882$		0			0
$883$	−15.7960	−	9.11982i	−0.531577	−	0.306906i	0.210081	−	0.977684i	$-0.432627\pi$
$883$	−15.7960	−	9.11982i	−0.531577	−	0.306906i	−0.741659	+	0.670778i	$0.765961\pi$
$884$		0			0
$885$	2.34929	−	1.36307i	0.0789706	−	0.0458191i
$886$		0			0
$887$	40.0349	−	23.1142i	1.34424	−	0.776098i	0.356815	−	0.934175i	$-0.383863\pi$
$887$	40.0349	−	23.1142i	1.34424	−	0.776098i	0.987427	+	0.158077i	$0.0505295\pi$
$888$		0			0
$889$	2.53066	−	1.46108i	0.0848758	−	0.0490030i
$890$		0			0
$891$	−43.1450	+	0.369030i	−1.44541	+	0.0123630i
$892$		0			0
$893$		−	20.7051i		−	0.692868i
$894$		0			0
$895$	−28.8333			−0.963792
$896$		0			0
$897$	−19.9879	+	0.0427394i	−0.667377	+	0.00142703i
$898$		0			0
$899$	18.0261	+	31.2221i	0.601204	+	1.04132i
$900$		0			0
$901$	−29.1848	+	16.8499i	−0.972288	+	0.561350i
$902$		0			0
$903$	−18.7134	+	0.0400141i	−0.622742	+	0.00133159i
$904$		0			0
$905$	−11.9214	+	20.6485i	−0.396281	+	0.686378i
$906$		0			0
$907$	12.4865	−	21.6273i	0.414609	−	0.718124i	−0.580778	−	0.814062i	$-0.697252\pi$
$907$	12.4865	−	21.6273i	0.414609	−	0.718124i	0.995387	+	0.0959381i	$0.0305851\pi$
$908$		0			0
$909$	−20.6683	−	35.4477i	−0.685525	−	1.17572i
$910$		0			0
$911$		−	7.82418i		−	0.259227i	−0.991565	−	0.129613i	$-0.958626\pi$
$911$		−	7.82418i		−	0.259227i	0.991565	−	0.129613i	$-0.0413736\pi$
$912$		0			0
$913$		−	39.4459i		−	1.30547i
$914$		0			0
$915$	27.1228	+	15.5821i	0.896651	+	0.515128i
$916$		0			0
$917$	−3.10061	+	5.37041i	−0.102391	+	0.177346i
$918$		0			0
$919$	19.5487	−	11.2864i	0.644851	−	0.372305i	−0.141630	−	0.989920i	$-0.545234\pi$
$919$	19.5487	−	11.2864i	0.644851	−	0.372305i	0.786481	+	0.617615i	$0.211901\pi$
$920$		0			0
$921$	−0.399026	+	0.694559i	−0.0131484	+	0.0228865i
$922$		0			0
$923$	10.8688			0.357751
$924$		0			0
$925$	1.36076	+	2.35691i	0.0447416	+	0.0774947i
$926$		0			0
$927$	0.130659	+	0.224090i	0.00429142	+	0.00736008i
$928$		0			0
$929$	−22.2867			−0.731202			−0.365601	−	0.930772i	$-0.619137\pi$
$929$	−22.2867			−0.731202			−0.365601	+	0.930772i	$0.619137\pi$
$930$		0			0
$931$	15.5500	−	26.9334i	0.509630	−	0.882706i
$932$		0			0
$933$	8.39538	+	14.4697i	0.274852	+	0.473716i
$934$		0			0
$935$		−	82.1449i		−	2.68643i
$936$		0			0
$937$			15.4389i			0.504366i	0.967680	+	0.252183i	$0.0811484\pi$
$937$			15.4389i			0.504366i	−0.967680	+	0.252183i	$0.918852\pi$
$938$		0			0
$939$	−19.7739	+	11.4729i	−0.645297	+	0.374404i
$940$		0			0
$941$	−29.8924			−0.974466			−0.487233	−	0.873272i	$-0.661994\pi$
$941$	−29.8924			−0.974466			−0.487233	+	0.873272i	$0.661994\pi$
$942$		0			0
$943$		−	4.91304i		−	0.159990i
$944$		0			0
$945$	10.6790	+	6.07452i	0.347388	+	0.197604i
$946$		0			0
$947$			37.2442i			1.21027i	0.796122	+	0.605136i	$0.206881\pi$
$947$			37.2442i			1.21027i	−0.796122	+	0.605136i	$0.793119\pi$
$948$		0			0
$949$	−43.8987	−	25.3449i	−1.42501	−	0.822732i
$950$		0			0
$951$	−20.9254	−	12.0217i	−0.678554	−	0.389831i
$952$		0			0
$953$			40.6494i			1.31676i	0.752684	+	0.658382i	$0.228759\pi$
$953$			40.6494i			1.31676i	−0.752684	+	0.658382i	$0.771241\pi$
$954$		0			0
$955$	22.5514	+	39.0602i	0.729747	+	1.26396i
$956$		0			0
$957$	−42.5171	−	24.4262i	−1.37438	−	0.789586i
$958$		0			0
$959$	−1.48635	−	0.858144i	−0.0479967	−	0.0277109i
$960$		0			0
$961$	3.13656	+	5.43268i	0.101179	+	0.175248i
$962$		0			0
$963$	−43.6680	−	24.9634i	−1.40718	−	0.804433i
$964$		0			0
$965$	−65.4363			−2.10647
$966$		0			0
$967$	3.93507	−	6.81574i	0.126543	−	0.219180i	−0.795792	−	0.605570i	$-0.792945\pi$
$967$	3.93507	−	6.81574i	0.126543	−	0.219180i	0.922335	+	0.386391i	$0.126278\pi$
$968$		0			0
$969$	−0.118943	−	55.6260i	−0.00382100	−	1.78697i
$970$		0			0
$971$	−33.4335	−	19.3028i	−1.07293	−	0.619457i	−0.143950	−	0.989585i	$-0.545980\pi$
$971$	−33.4335	−	19.3028i	−1.07293	−	0.619457i	−0.928981	+	0.370128i	$0.879314\pi$
$972$		0			0
$973$	−6.15379	+	10.6587i	−0.197282	+	0.341702i
$974$		0			0
$975$	−21.7635	−	12.5032i	−0.696991	−	0.400423i
$976$		0			0
$977$	21.1843	−	12.2308i	0.677745	−	0.391296i	−0.121260	−	0.992621i	$-0.538693\pi$
$977$	21.1843	−	12.2308i	0.677745	−	0.391296i	0.799005	+	0.601324i	$0.205360\pi$
$978$		0			0
$979$	37.7479	+	21.7937i	1.20643	+	0.696531i
$980$		0			0
$981$	−8.39486	−	4.79902i	−0.268027	−	0.153221i
$982$		0			0
$983$	32.0043			1.02078			0.510390	−	0.859943i	$-0.329501\pi$
$983$	32.0043			1.02078			0.510390	+	0.859943i	$0.329501\pi$
$984$		0			0
$985$	29.7564	−	51.5395i	0.948116	−	1.64219i
$986$		0			0
$987$	3.16225	−	5.50433i	0.100656	−	0.175205i
$988$		0			0
$989$	10.3290	+	17.8903i	0.328443	+	0.568880i
$990$		0			0
$991$			36.6991i			1.16578i	0.812550	+	0.582892i	$0.198079\pi$
$991$			36.6991i			1.16578i	−0.812550	+	0.582892i	$0.801921\pi$
$992$		0			0
$993$	−0.0109462	−	5.11922i	−0.000347368	−	0.162453i
$994$		0			0
$995$	10.3220	+	17.8783i	0.327230	+	0.566779i
$996$		0			0
$997$	−14.4622			−0.458022			−0.229011	−	0.973424i	$-0.573549\pi$
$997$	−14.4622			−0.458022			−0.229011	+	0.973424i	$0.573549\pi$
$998$		0			0
$999$	−3.36186	−	5.73760i	−0.106365	−	0.181530i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.o.d.365.12	yes	36
3.2	odd	2	inner	804.2.o.d.365.7	✓	36
67.38	odd	6	inner	804.2.o.d.641.7	yes	36
201.38	even	6	inner	804.2.o.d.641.12	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.o.d.365.7	✓	36	3.2	odd	2	inner
804.2.o.d.365.12	yes	36	1.1	even	1	trivial
804.2.o.d.641.7	yes	36	67.38	odd	6	inner
804.2.o.d.641.12	yes	36	201.38	even	6	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)

\(f(q)\)	\(=\)	\(q+(0.869231 + 1.49814i) q^{3} -2.66956 q^{5} +(0.767031 + 0.442845i) q^{7} +(-1.48888 + 2.60447i) q^{9} +O(q^{10})\)	\(q+(0.869231 + 1.49814i) q^{3} -2.66956 q^{5} +(0.767031 + 0.442845i) q^{7} +(-1.48888 + 2.60447i) q^{9} +(2.39703 - 4.15178i) q^{11} +(-5.90147 + 3.40722i) q^{13} +(-2.32046 - 3.99938i) q^{15} +(-5.55864 + 3.20928i) q^{17} +(2.50179 + 4.33322i) q^{19} +(0.00328022 + 1.53406i) q^{21} +(1.46659 - 0.846736i) q^{23} +2.12654 q^{25} +(-5.19605 + 0.0333319i) q^{27} +(-5.11405 - 2.95260i) q^{29} +(-5.28723 - 3.05259i) q^{31} +(8.30354 - 0.0177551i) q^{33} +(-2.04763 - 1.18220i) q^{35} +(0.639895 + 1.10833i) q^{37} +(-10.2342 - 5.87960i) q^{39} +(1.45058 - 2.51248i) q^{41} +12.1986i q^{43} +(3.97464 - 6.95278i) q^{45} +(-3.58366 - 2.06903i) q^{47} +(-3.10778 - 5.38283i) q^{49} +(-9.63971 - 5.53804i) q^{51} +5.25036 q^{53} +(-6.39901 + 11.0834i) q^{55} +(-4.31717 + 7.51461i) q^{57} +0.587414i q^{59} +(-5.85867 + 3.38250i) q^{61} +(-2.29539 + 1.33836i) q^{63} +(15.7543 - 9.09576i) q^{65} +(2.91744 - 7.64778i) q^{67} +(2.54334 + 1.46115i) q^{69} +(-1.38128 - 0.797483i) q^{71} +(3.71930 + 6.44202i) q^{73} +(1.84845 + 3.18586i) q^{75} +(3.67719 - 2.12303i) q^{77} +(10.0799 + 5.81963i) q^{79} +(-4.56650 - 7.75546i) q^{81} +(7.12573 - 4.11404i) q^{83} +(14.8391 - 8.56736i) q^{85} +(-0.0218703 - 10.2281i) q^{87} +9.09197i q^{89} -6.03548 q^{91} +(-0.0226109 - 10.5744i) q^{93} +(-6.67867 - 11.5678i) q^{95} +(7.83565 - 4.52391i) q^{97} +(7.24429 + 12.4245i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{9}+O(q^{10}) \) 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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