LMFDB - Embedded newform 804.2.y.b.169.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(49,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 0, 46]))

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

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

chi := DirichletCharacter("804.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.y (of order $33$, degree $20$, 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:	$120$
Relative dimension:	$6$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			169.1
Character	$\chi$	$=$	804.169
Dual form			804.2.y.b.157.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.142315 + 0.989821i) q^{3} +(-1.67835 + 3.67507i) q^{5} +(2.54620 + 2.42780i) q^{7} +(-0.959493 + 0.281733i) q^{9} +O(q^{10})$	\(q+(0.142315 + 0.989821i) q^{3} +(-1.67835 + 3.67507i) q^{5} +(2.54620 + 2.42780i) q^{7} +(-0.959493 + 0.281733i) q^{9} +(5.23241 - 0.499635i) q^{11} +(-2.29438 + 0.442205i) q^{13} +(-3.87652 - 1.13825i) q^{15} +(-1.39626 + 0.719822i) q^{17} +(-0.391195 + 0.373004i) q^{19} +(-2.04072 + 2.86579i) q^{21} +(7.68293 + 3.07578i) q^{23} +(-7.41501 - 8.55738i) q^{25} +(-0.415415 - 0.909632i) q^{27} +(-0.551633 - 0.955456i) q^{29} +(-7.91988 - 1.52643i) q^{31} +(1.23920 + 5.10805i) q^{33} +(-13.1957 + 5.28278i) q^{35} +(5.09972 - 8.83298i) q^{37} +(-0.764229 - 2.20809i) q^{39} +(-0.441935 + 9.27736i) q^{41} +(-7.98049 - 5.12875i) q^{43} +(0.574977 - 3.99905i) q^{45} +(-3.79700 + 2.98600i) q^{47} +(0.255863 + 5.37124i) q^{49} +(-0.911204 - 1.27961i) q^{51} +(-4.24648 + 2.72905i) q^{53} +(-6.94562 + 20.0681i) q^{55} +(-0.424880 - 0.334129i) q^{57} +(2.79526 - 3.22590i) q^{59} +(4.29709 + 0.410322i) q^{61} +(-3.12705 - 1.61211i) q^{63} +(2.22563 - 9.17419i) q^{65} +(4.22580 - 7.01018i) q^{67} +(-1.95108 + 8.04245i) q^{69} +(13.0777 + 6.74203i) q^{71} +(6.99211 + 0.667666i) q^{73} +(7.41501 - 8.55738i) q^{75} +(14.5358 + 11.4311i) q^{77} +(-2.12207 + 6.13133i) q^{79} +(0.841254 - 0.540641i) q^{81} +(-9.30173 - 13.0624i) q^{83} +(-0.301986 - 6.33947i) q^{85} +(0.867226 - 0.681994i) q^{87} +(0.140072 - 0.974221i) q^{89} +(-6.91553 - 4.44434i) q^{91} +(0.383778 - 8.05650i) q^{93} +(-0.714254 - 2.06370i) q^{95} +(0.846818 - 1.46673i) q^{97} +(-4.87970 + 1.95354i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9}+O(q^{10}) $ 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9	$ 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9} + 11 q^{11} + 2 q^{13} - 9 q^{15} + 48 q^{17} - 4 q^{19} - q^{21} + 22 q^{23} - 42 q^{25} + 12 q^{27} - q^{29} + 27 q^{31} + 17 q^{35} - 8 q^{37} - 2 q^{39} - 58 q^{41} - 17 q^{43} - 2 q^{45} - 84 q^{47} + 101 q^{49} - 26 q^{51} + 28 q^{53} - 9 q^{55} + 26 q^{57} + 34 q^{59} + 16 q^{61} + 12 q^{63} + 144 q^{65} + 23 q^{67} + 11 q^{69} + 173 q^{71} - 2 q^{73} + 42 q^{75} + 128 q^{77} + 31 q^{79} - 12 q^{81} + 47 q^{83} - 75 q^{85} - 10 q^{87} - 67 q^{89} + 16 q^{91} + 6 q^{93} - 79 q^{95} + 10 q^{97}+O(q^{100}) $ 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9 + 11 * q^11 + 2 * q^13 - 9 * q^15 + 48 * q^17 - 4 * q^19 - q^21 + 22 * q^23 - 42 * q^25 + 12 * q^27 - q^29 + 27 * q^31 + 17 * q^35 - 8 * q^37 - 2 * q^39 - 58 * q^41 - 17 * q^43 - 2 * q^45 - 84 * q^47 + 101 * q^49 - 26 * q^51 + 28 * q^53 - 9 * q^55 + 26 * q^57 + 34 * q^59 + 16 * q^61 + 12 * q^63 + 144 * q^65 + 23 * q^67 + 11 * q^69 + 173 * q^71 - 2 * q^73 + 42 * q^75 + 128 * q^77 + 31 * q^79 - 12 * q^81 + 47 * q^83 - 75 * q^85 - 10 * q^87 - 67 * q^89 + 16 * q^91 + 6 * q^93 - 79 * q^95 + 10 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{19}{33}\right)$	$1$

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
$3$	0.142315	+	0.989821i	0.0821655	+	0.571474i
$3$	0.142315	+	0.989821i	0.0821655	+	0.571474i
$4$		0			0
$5$	−1.67835	+	3.67507i	−0.750581	+	1.64354i	0.0147373	+	0.999891i	$0.495309\pi$
$5$	−1.67835	+	3.67507i	−0.750581	+	1.64354i	−0.765318	+	0.643652i	$0.777418\pi$
$6$		0			0
$7$	2.54620	+	2.42780i	0.962373	+	0.917621i	0.996649	−	0.0817916i	$-0.0260642\pi$
$7$	2.54620	+	2.42780i	0.962373	+	0.917621i	−0.0342765	+	0.999412i	$0.510913\pi$
$8$		0			0
$9$	−0.959493	+	0.281733i	−0.319831	+	0.0939109i
$10$		0			0
$11$	5.23241	−	0.499635i	1.57763	−	0.150646i	0.730832	−	0.682558i	$-0.239132\pi$
$11$	5.23241	−	0.499635i	1.57763	−	0.150646i	0.846800	+	0.531912i	$0.178526\pi$
$12$		0			0
$13$	−2.29438	+	0.442205i	−0.636346	+	0.122646i	−0.497214	−	0.867628i	$-0.665644\pi$
$13$	−2.29438	+	0.442205i	−0.636346	+	0.122646i	−0.139133	+	0.990274i	$0.544431\pi$
$14$		0			0
$15$	−3.87652	−	1.13825i	−1.00091	−	0.293895i
$16$		0			0
$17$	−1.39626	+	0.719822i	−0.338643	+	0.174582i	−0.619157	−	0.785267i	$-0.712525\pi$
$17$	−1.39626	+	0.719822i	−0.338643	+	0.174582i	0.280514	+	0.959850i	$0.409495\pi$
$18$		0			0
$19$	−0.391195	+	0.373004i	−0.0897463	+	0.0855729i	−0.733624	−	0.679555i	$-0.762173\pi$
$19$	−0.391195	+	0.373004i	−0.0897463	+	0.0855729i	0.643878	+	0.765128i	$0.277324\pi$
$20$		0			0
$21$	−2.04072	+	2.86579i	−0.445322	+	0.625368i
$22$		0			0
$23$	7.68293	+	3.07578i	1.60200	+	0.641344i	0.988890	−	0.148652i	$-0.0474935\pi$
$23$	7.68293	+	3.07578i	1.60200	+	0.641344i	0.613111	+	0.789997i	$0.289918\pi$
$24$		0			0
$25$	−7.41501	−	8.55738i	−1.48300	−	1.71148i
$26$		0			0
$27$	−0.415415	−	0.909632i	−0.0799467	−	0.175059i
$28$		0			0
$29$	−0.551633	−	0.955456i	−0.102436	−	0.177424i	0.810252	−	0.586082i	$-0.199330\pi$
$29$	−0.551633	−	0.955456i	−0.102436	−	0.177424i	−0.912688	+	0.408658i	$0.865997\pi$
$30$		0			0
$31$	−7.91988	−	1.52643i	−1.42245	−	0.274155i	−0.580743	−	0.814087i	$-0.697238\pi$
$31$	−7.91988	−	1.52643i	−1.42245	−	0.274155i	−0.841709	+	0.539932i	$0.818450\pi$
$32$		0			0
$33$	1.23920	+	5.10805i	0.215717	+	0.889197i
$34$		0			0
$35$	−13.1957	+	5.28278i	−2.23049	+	0.892953i
$36$		0			0
$37$	5.09972	−	8.83298i	0.838389	−	1.45213i	−0.0528518	−	0.998602i	$-0.516831\pi$
$37$	5.09972	−	8.83298i	0.838389	−	1.45213i	0.891241	−	0.453530i	$-0.149836\pi$
$38$		0			0
$39$	−0.764229	−	2.20809i	−0.122375	−	0.353578i
$40$		0			0
$41$	−0.441935	+	9.27736i	−0.0690187	+	1.44888i	0.653184	+	0.757199i	$0.273433\pi$
$41$	−0.441935	+	9.27736i	−0.0690187	+	1.44888i	−0.722203	+	0.691681i	$0.756870\pi$
$42$		0			0
$43$	−7.98049	−	5.12875i	−1.21701	−	0.782127i	−0.235194	−	0.971948i	$-0.575573\pi$
$43$	−7.98049	−	5.12875i	−1.21701	−	0.782127i	−0.981819	+	0.189822i	$0.939209\pi$
$44$		0			0
$45$	0.574977	−	3.99905i	0.0857125	−	0.596144i
$46$		0			0
$47$	−3.79700	+	2.98600i	−0.553850	+	0.435552i	−0.855452	−	0.517881i	$-0.826721\pi$
$47$	−3.79700	+	2.98600i	−0.553850	+	0.435552i	0.301602	+	0.953434i	$0.402478\pi$
$48$		0			0
$49$	0.255863	+	5.37124i	0.0365519	+	0.767319i
$50$		0			0
$51$	−0.911204	−	1.27961i	−0.127594	−	0.179181i
$52$		0			0
$53$	−4.24648	+	2.72905i	−0.583299	+	0.374863i	−0.798761	−	0.601649i	$-0.794511\pi$
$53$	−4.24648	+	2.72905i	−0.583299	+	0.374863i	0.215462	+	0.976512i	$0.430874\pi$
$54$		0			0
$55$	−6.94562	+	20.0681i	−0.936548	+	2.70598i
$56$		0			0
$57$	−0.424880	−	0.334129i	−0.0562767	−	0.0442565i
$58$		0			0
$59$	2.79526	−	3.22590i	0.363911	−	0.419976i	−0.544035	−	0.839063i	$-0.683104\pi$
$59$	2.79526	−	3.22590i	0.363911	−	0.419976i	0.907946	+	0.419086i	$0.137650\pi$
$60$		0			0
$61$	4.29709	+	0.410322i	0.550186	+	0.0525364i	0.366447	−	0.930439i	$-0.380574\pi$
$61$	4.29709	+	0.410322i	0.550186	+	0.0525364i	0.183738	+	0.982975i	$0.441180\pi$
$62$		0			0
$63$	−3.12705	−	1.61211i	−0.393971	−	0.203106i
$64$		0			0
$65$	2.22563	−	9.17419i	0.276056	−	1.13792i
$66$		0			0
$67$	4.22580	−	7.01018i	0.516263	−	0.856430i
$67$	4.22580	−	7.01018i	0.516263	−	0.856430i
$68$		0			0
$69$	−1.95108	+	8.04245i	−0.234882	+	0.968198i
$70$		0			0
$71$	13.0777	+	6.74203i	1.55204	+	0.800132i	0.999445	−	0.0333182i	$-0.0106075\pi$
$71$	13.0777	+	6.74203i	1.55204	+	0.800132i	0.552595	+	0.833450i	$0.313638\pi$
$72$		0			0
$73$	6.99211	+	0.667666i	0.818365	+	0.0781444i	0.495837	−	0.868416i	$-0.334861\pi$
$73$	6.99211	+	0.667666i	0.818365	+	0.0781444i	0.322528	+	0.946560i	$0.395467\pi$
$74$		0			0
$75$	7.41501	−	8.55738i	0.856212	−	0.988121i
$76$		0			0
$77$	14.5358	+	11.4311i	1.65651	+	1.30269i
$78$		0			0
$79$	−2.12207	+	6.13133i	−0.238752	+	0.689829i	0.760431	+	0.649419i	$0.224988\pi$
$79$	−2.12207	+	6.13133i	−0.238752	+	0.689829i	−0.999183	+	0.0404102i	$0.987134\pi$
$80$		0			0
$81$	0.841254	−	0.540641i	0.0934726	−	0.0600712i
$82$		0			0
$83$	−9.30173	−	13.0624i	−1.02100	−	1.43379i	−0.897274	−	0.441473i	$-0.854456\pi$
$83$	−9.30173	−	13.0624i	−1.02100	−	1.43379i	−0.123723	−	0.992317i	$-0.539483\pi$
$84$		0			0
$85$	−0.301986	−	6.33947i	−0.0327550	−	0.687612i
$86$		0			0
$87$	0.867226	−	0.681994i	0.0929763	−	0.0731174i
$88$		0			0
$89$	0.140072	−	0.974221i	0.0148476	−	0.103267i	−0.981050	−	0.193755i	$-0.937933\pi$
$89$	0.140072	−	0.974221i	0.0148476	−	0.103267i	0.995898	+	0.0904874i	$0.0288425\pi$
$90$		0			0
$91$	−6.91553	−	4.44434i	−0.724945	−	0.465894i
$92$		0			0
$93$	0.383778	−	8.05650i	0.0397959	−	0.835420i
$94$		0			0
$95$	−0.714254	−	2.06370i	−0.0732809	−	0.211731i
$96$		0			0
$97$	0.846818	−	1.46673i	0.0859814	−	0.148924i	−0.819828	−	0.572610i	$-0.805931\pi$
$97$	0.846818	−	1.46673i	0.0859814	−	0.148924i	0.905809	+	0.423686i	$0.139264\pi$
$98$		0			0
$99$	−4.87970	+	1.95354i	−0.490428	+	0.196338i
$100$		0			0
$101$	2.16283	+	8.91531i	0.215210	+	0.887106i	0.972289	+	0.233783i	$0.0751105\pi$
$101$	2.16283	+	8.91531i	0.215210	+	0.887106i	−0.757079	+	0.653323i	$0.773374\pi$
$102$		0			0
$103$	6.23895	+	1.20246i	0.614742	+	0.118482i	0.487111	−	0.873340i	$-0.338051\pi$
$103$	6.23895	+	1.20246i	0.614742	+	0.118482i	0.127631	+	0.991822i	$0.459263\pi$
$104$		0			0
$105$	−7.10696	−	12.3096i	−0.693568	−	1.20130i
$106$		0			0
$107$	4.52537	+	9.90918i	0.437484	+	0.957957i	0.992053	+	0.125819i	$0.0401558\pi$
$107$	4.52537	+	9.90918i	0.437484	+	0.957957i	−0.554569	+	0.832138i	$0.687117\pi$
$108$		0			0
$109$	7.16502	+	8.26887i	0.686284	+	0.792014i	0.986831	−	0.161753i	$-0.0517148\pi$
$109$	7.16502	+	8.26887i	0.686284	+	0.792014i	−0.300547	+	0.953767i	$0.597169\pi$
$110$		0			0
$111$	9.46884	+	3.79075i	0.898742	+	0.359802i
$112$		0			0
$113$	3.20300	−	4.49799i	0.301313	−	0.423135i	−0.635965	−	0.771718i	$-0.719398\pi$
$113$	3.20300	−	4.49799i	0.301313	−	0.423135i	0.937278	+	0.348583i	$0.113337\pi$
$114$		0			0
$115$	−24.1984	+	23.0731i	−2.25651	+	2.15158i
$116$		0			0
$117$	2.07686	−	1.07069i	0.192006	−	0.0989857i
$118$		0			0
$119$	−5.30274	−	1.55702i	−0.486101	−	0.142732i
$120$		0			0
$121$	16.3273	−	3.14682i	1.48430	−	0.286075i
$122$		0			0
$123$	−9.24583	+	0.882869i	−0.833668	+	0.0796056i
$124$		0			0
$125$	24.5114	−	7.19719i	2.19236	−	0.643736i
$126$		0			0
$127$	−7.42001	−	7.07497i	−0.658420	−	0.627802i	0.285343	−	0.958425i	$-0.407892\pi$
$127$	−7.42001	−	7.07497i	−0.658420	−	0.627802i	−0.943763	+	0.330624i	$0.892741\pi$
$128$		0			0
$129$	3.94080	−	8.62915i	0.346968	−	0.759755i
$130$		0			0
$131$	−2.62424	−	18.2520i	−0.229281	−	1.59469i	−0.701147	−	0.713016i	$-0.747328\pi$
$131$	−2.62424	−	18.2520i	−0.229281	−	1.59469i	0.471866	−	0.881670i	$-0.343581\pi$
$132$		0			0
$133$	−1.90164			−0.164893
$134$		0			0
$135$	4.04018			0.347723
$136$		0			0
$137$	−0.663672	−	4.61594i	−0.0567013	−	0.394366i	−0.998333	−	0.0577207i	$-0.981617\pi$
$137$	−0.663672	−	4.61594i	−0.0567013	−	0.394366i	0.941631	−	0.336645i	$-0.109292\pi$
$138$		0			0
$139$	−4.01197	+	8.78500i	−0.340291	+	0.745134i	−0.999979	−	0.00640560i	$-0.997961\pi$
$139$	−4.01197	+	8.78500i	−0.340291	+	0.745134i	0.659688	+	0.751539i	$0.270688\pi$
$140$		0			0
$141$	−3.49597	−	3.33340i	−0.294414	−	0.280723i
$142$		0			0
$143$	−11.7842	+	3.46015i	−0.985444	+	0.289352i
$144$		0			0
$145$	4.43721	−	0.423702i	0.368490	−	0.0351865i
$146$		0			0
$147$	−5.28015	+	1.01767i	−0.435500	+	0.0839357i
$148$		0			0
$149$	−9.87527	−	2.89964i	−0.809014	−	0.237548i	−0.149035	−	0.988832i	$-0.547617\pi$
$149$	−9.87527	−	2.89964i	−0.809014	−	0.237548i	−0.659979	+	0.751284i	$0.729435\pi$
$150$		0			0
$151$	15.7758	−	8.13301i	1.28382	−	0.661855i	0.324958	−	0.945728i	$-0.394650\pi$
$151$	15.7758	−	8.13301i	1.28382	−	0.661855i	0.958862	+	0.283873i	$0.0916195\pi$
$152$		0			0
$153$	1.13690	−	1.08404i	0.0919133	−	0.0876391i
$154$		0			0
$155$	18.9021	−	26.5442i	1.51825	−	2.13209i
$156$		0			0
$157$	9.48751	+	3.79822i	0.757186	+	0.303131i	0.717946	−	0.696098i	$-0.245082\pi$
$157$	9.48751	+	3.79822i	0.757186	+	0.303131i	0.0392392	+	0.999230i	$0.487507\pi$
$158$		0			0
$159$	−3.30560	−	3.81487i	−0.262151	−	0.302539i
$160$		0			0
$161$	12.0949	+	26.4841i	0.953211	+	2.08724i
$162$		0			0
$163$	−4.18083	−	7.24141i	−0.327468	−	0.567191i	0.654541	−	0.756027i	$-0.272862\pi$
$163$	−4.18083	−	7.24141i	−0.327468	−	0.567191i	−0.982009	+	0.188836i	$0.939529\pi$
$164$		0			0
$165$	−20.8523	−	4.01894i	−1.62335	−	0.312874i
$166$		0			0
$167$	3.94678	+	16.2688i	0.305411	+	1.25892i	0.893109	+	0.449840i	$0.148519\pi$
$167$	3.94678	+	16.2688i	0.305411	+	1.25892i	−0.587698	+	0.809080i	$0.699966\pi$
$168$		0			0
$169$	−7.00015	+	2.80244i	−0.538473	+	0.215572i
$170$		0			0
$171$	0.270262	−	0.468107i	0.0206674	−	0.0357970i
$172$		0			0
$173$	−6.72267	−	19.4239i	−0.511115	−	1.47677i	−0.845316	−	0.534267i	$-0.820588\pi$
$173$	−6.72267	−	19.4239i	−0.511115	−	1.47677i	0.334201	−	0.942502i	$-0.391534\pi$
$174$		0			0
$175$	1.89548	−	39.7909i	0.143284	−	3.00791i
$176$		0			0
$177$	3.59087	+	2.30771i	0.269906	+	0.173458i
$178$		0			0
$179$	−2.11934	+	14.7403i	−0.158407	+	1.10174i	0.743163	+	0.669110i	$0.233325\pi$
$179$	−2.11934	+	14.7403i	−0.158407	+	1.10174i	−0.901570	+	0.432633i	$0.857585\pi$
$180$		0			0
$181$	11.1141	−	8.74019i	0.826102	−	0.649654i	−0.112885	−	0.993608i	$-0.536009\pi$
$181$	11.1141	−	8.74019i	0.826102	−	0.649654i	0.938986	+	0.343955i	$0.111767\pi$
$182$		0			0
$183$	0.205394	+	4.31174i	0.0151831	+	0.318733i
$184$		0			0
$185$	23.9027	+	33.5667i	1.75736	+	2.46787i
$186$		0			0
$187$	−6.94616	+	4.46402i	−0.507953	+	0.326442i
$188$		0			0
$189$	1.15067	−	3.32465i	0.0836990	−	0.241833i
$190$		0			0
$191$	10.2641	+	8.07177i	0.742684	+	0.584053i	0.916173	−	0.400783i	$-0.131262\pi$
$191$	10.2641	+	8.07177i	0.742684	+	0.584053i	−0.173490	+	0.984836i	$0.555504\pi$
$192$		0			0
$193$	−8.38577	+	9.67769i	−0.603621	+	0.696615i	−0.972511	−	0.232858i	$-0.925192\pi$
$193$	−8.38577	+	9.67769i	−0.603621	+	0.696615i	0.368890	+	0.929473i	$0.379738\pi$
$194$		0			0
$195$	9.39755	+	0.897357i	0.672973	+	0.0642611i
$196$		0			0
$197$	7.62815	+	3.93259i	0.543483	+	0.280185i	0.708028	−	0.706184i	$-0.249585\pi$
$197$	7.62815	+	3.93259i	0.543483	+	0.280185i	−0.164544	+	0.986370i	$0.552615\pi$
$198$		0			0
$199$	−0.678186	+	2.79552i	−0.0480753	+	0.198169i	−0.990785	−	0.135446i	$-0.956753\pi$
$199$	−0.678186	+	2.79552i	−0.0480753	+	0.198169i	0.942709	+	0.333615i	$0.108269\pi$
$200$		0			0
$201$	7.54022	+	3.18513i	0.531846	+	0.224662i
$202$		0			0
$203$	0.915086	−	3.77203i	0.0642264	−	0.264745i
$204$		0			0
$205$	−33.3533	−	17.1948i	−2.32949	−	1.20094i
$206$		0			0
$207$	−8.23826	−	0.786659i	−0.572599	−	0.0546765i
$208$		0			0
$209$	−1.86053	+	2.14716i	−0.128695	+	0.148522i
$210$		0			0
$211$	12.0964	+	9.51273i	0.832752	+	0.654883i	0.940687	−	0.339275i	$-0.110182\pi$
$211$	12.0964	+	9.51273i	0.832752	+	0.654883i	−0.107936	+	0.994158i	$0.534424\pi$
$212$		0			0
$213$	−4.81225	+	13.9041i	−0.329730	+	0.952693i
$214$		0			0
$215$	32.2426	−	20.7211i	2.19893	−	1.41316i
$216$		0			0
$217$	−16.4597	−	23.1144i	−1.11736	−	1.56911i
$218$		0			0
$219$	0.334211	+	7.01596i	0.0225839	+	0.474095i
$220$		0			0
$221$	2.88524	−	2.26898i	0.194082	−	0.152628i
$222$		0			0
$223$	0.617833	−	4.29713i	0.0413732	−	0.287757i	−0.958622	−	0.284682i	$-0.908112\pi$
$223$	0.617833	−	4.29713i	0.0413732	−	0.287757i	0.999995	−	0.00307510i	$-0.000978837\pi$
$224$		0			0
$225$	9.52554	+	6.12169i	0.635036	+	0.408113i
$226$		0			0
$227$	0.396759	−	8.32899i	0.0263338	−	0.552815i	−0.946695	−	0.322131i	$-0.895601\pi$
$227$	0.396759	−	8.32899i	0.0263338	−	0.552815i	0.973029	−	0.230683i	$-0.0740962\pi$
$228$		0			0
$229$	−2.30699	−	6.66562i	−0.152451	−	0.440477i	0.842753	−	0.538300i	$-0.180933\pi$
$229$	−2.30699	−	6.66562i	−0.152451	−	0.440477i	−0.995204	+	0.0978231i	$0.968812\pi$
$230$		0			0
$231$	−9.24605	+	16.0146i	−0.608345	+	1.05369i
$232$		0			0
$233$	3.30554	−	1.32334i	0.216553	−	0.0866948i	−0.260849	−	0.965379i	$-0.584003\pi$
$233$	3.30554	−	1.32334i	0.216553	−	0.0866948i	0.477402	+	0.878685i	$0.341578\pi$
$234$		0			0
$235$	−4.60106	−	18.9658i	−0.300140	−	1.23719i
$236$		0			0
$237$	−6.37093	−	1.22790i	−0.413836	−	0.0797604i
$238$		0			0
$239$	−0.700503	−	1.21331i	−0.0453118	−	0.0784823i	0.842480	−	0.538728i	$-0.181095\pi$
$239$	−0.700503	−	1.21331i	−0.0453118	−	0.0784823i	−0.887792	+	0.460245i	$0.847761\pi$
$240$		0			0
$241$	−2.71668	−	5.94869i	−0.174997	−	0.383189i	0.801727	−	0.597690i	$-0.203915\pi$
$241$	−2.71668	−	5.94869i	−0.174997	−	0.383189i	−0.976724	+	0.214501i	$0.931187\pi$
$242$		0			0
$243$	0.654861	+	0.755750i	0.0420093	+	0.0484814i
$244$		0			0
$245$	−20.1691	−	8.07450i	−1.28856	−	0.515861i
$246$		0			0
$247$	0.732606	−	1.02880i	0.0466146	−	0.0654610i
$248$		0			0
$249$	11.6057	−	11.0660i	0.735483	−	0.701281i
$250$		0			0
$251$	−15.4514	+	7.96576i	−0.975285	+	0.502794i	−0.870749	−	0.491727i	$-0.836366\pi$
$251$	−15.4514	+	7.96576i	−0.975285	+	0.502794i	−0.104535	+	0.994521i	$0.533335\pi$
$252$		0			0
$253$	41.7370	+	12.2551i	2.62398	+	0.770471i
$254$		0			0
$255$	6.23197	−	1.20111i	0.390261	−	0.0752166i
$256$		0			0
$257$	28.9862	−	2.76785i	1.80811	−	0.172654i	0.864264	−	0.503038i	$-0.167785\pi$
$257$	28.9862	−	2.76785i	1.80811	−	0.172654i	0.943846	+	0.330385i	$0.107179\pi$
$258$		0			0
$259$	34.4296	−	10.1094i	2.13935	−	0.628170i
$260$		0			0
$261$	0.798471	+	0.761341i	0.0494241	+	0.0471258i
$262$		0			0
$263$	−9.83483	+	21.5353i	−0.606442	+	1.32792i	0.318539	+	0.947910i	$0.396808\pi$
$263$	−9.83483	+	21.5353i	−0.606442	+	1.32792i	−0.924981	+	0.380013i	$0.875920\pi$
$264$		0			0
$265$	−2.90237	−	20.1864i	−0.178291	−	1.24004i
$266$		0			0
$267$	0.984240			0.0602345
$268$		0			0
$269$	3.13815			0.191336			0.0956681	−	0.995413i	$-0.469501\pi$
$269$	3.13815			0.191336			0.0956681	+	0.995413i	$0.469501\pi$
$270$		0			0
$271$	4.10986	+	28.5847i	0.249656	+	1.73640i	0.600200	+	0.799850i	$0.295088\pi$
$271$	4.10986	+	28.5847i	0.249656	+	1.73640i	−0.350544	+	0.936546i	$0.614003\pi$
$272$		0			0
$273$	3.41492	−	7.47764i	0.206681	−	0.452567i
$274$		0			0
$275$	−43.0739	−	41.0709i	−2.59746	−	2.47667i
$276$		0			0
$277$	21.7647	−	6.39071i	1.30772	−	0.383980i	0.447671	−	0.894198i	$-0.352253\pi$
$277$	21.7647	−	6.39071i	1.30772	−	0.383980i	0.860045	+	0.510218i	$0.170435\pi$
$278$		0			0
$279$	8.02911	−	0.766687i	0.480690	−	0.0459004i
$280$		0			0
$281$	7.94088	−	1.53048i	0.473713	−	0.0913007i	0.0531937	−	0.998584i	$-0.483060\pi$
$281$	7.94088	−	1.53048i	0.473713	−	0.0913007i	0.420520	+	0.907283i	$0.361848\pi$
$282$		0			0
$283$	−4.11994	−	1.20972i	−0.244905	−	0.0719106i	0.156976	−	0.987602i	$-0.449825\pi$
$283$	−4.11994	−	1.20972i	−0.244905	−	0.0719106i	−0.401881	+	0.915692i	$0.631644\pi$
$284$		0			0
$285$	1.94105	−	1.00068i	0.114978	−	0.0592751i
$286$		0			0
$287$	−23.6488	+	22.5491i	−1.39594	+	1.33103i
$288$		0			0
$289$	−8.42957	+	11.8377i	−0.495857	+	0.696334i
$290$		0			0
$291$	1.57232	+	0.629461i	0.0921709	+	0.0368997i
$292$		0			0
$293$	4.90890	+	5.66517i	0.286781	+	0.330963i	0.880800	−	0.473488i	$-0.157005\pi$
$293$	4.90890	+	5.66517i	0.286781	+	0.330963i	−0.594020	+	0.804451i	$0.702460\pi$
$294$		0			0
$295$	7.16400	+	15.6870i	0.417104	+	0.913330i
$296$		0			0
$297$	−2.62811	−	4.55201i	−0.152498	−	0.264135i
$298$		0			0
$299$	−18.9877	−	3.65957i	−1.09809	−	0.211639i
$300$		0			0
$301$	−7.86836	−	32.4338i	−0.453525	−	1.86945i
$302$		0			0
$303$	−8.51676	+	3.40960i	−0.489275	+	0.195876i
$304$		0			0
$305$	−8.71998	+	15.1035i	−0.499305	+	0.864821i
$306$		0			0
$307$	4.92971	+	14.2435i	0.281353	+	0.812917i	0.993799	+	0.111190i	$0.0354662\pi$
$307$	4.92971	+	14.2435i	0.281353	+	0.812917i	−0.712446	+	0.701727i	$0.752413\pi$
$308$		0			0
$309$	−0.302325	+	6.34657i	−0.0171986	+	0.361044i
$310$		0			0
$311$	−10.3488	−	6.65074i	−0.586824	−	0.377129i	0.213279	−	0.976991i	$-0.431586\pi$
$311$	−10.3488	−	6.65074i	−0.586824	−	0.377129i	−0.800103	+	0.599862i	$0.795222\pi$
$312$		0			0
$313$	0.957129	−	6.65698i	0.0541001	−	0.376275i	−0.944727	−	0.327858i	$-0.893673\pi$
$313$	0.957129	−	6.65698i	0.0541001	−	0.376275i	0.998827	−	0.0484169i	$-0.0154176\pi$
$314$		0			0
$315$	11.1729	−	8.78646i	0.629521	−	0.495061i
$316$		0			0
$317$	−1.51000	−	31.6987i	−0.0848099	−	1.78038i	−0.495505	−	0.868605i	$-0.665017\pi$
$317$	−1.51000	−	31.6987i	−0.0848099	−	1.78038i	0.410695	−	0.911773i	$-0.365286\pi$
$318$		0			0
$319$	−3.36375	−	4.72373i	−0.188334	−	0.264478i
$320$		0			0
$321$	−9.16429	+	5.88953i	−0.511501	+	0.328722i
$322$		0			0
$323$	0.277714	−	0.802401i	0.0154524	−	0.0446468i
$324$		0			0
$325$	20.7970	+	16.3549i	1.15361	+	0.907207i
$326$		0			0
$327$	−7.16502	+	8.26887i	−0.396226	+	0.457269i
$328$		0			0
$329$	−16.9173	−	1.61541i	−0.932682	−	0.0890604i
$330$		0			0
$331$	8.11228	+	4.18217i	0.445891	+	0.229873i	0.666523	−	0.745484i	$-0.267782\pi$
$331$	8.11228	+	4.18217i	0.445891	+	0.229873i	−0.220632	+	0.975357i	$0.570812\pi$
$332$		0			0
$333$	−2.40461	+	9.91194i	−0.131772	+	0.543171i
$334$		0			0
$335$	18.6706	+	27.2957i	1.02008	+	1.49132i
$336$		0			0
$337$	−1.73051	+	7.13327i	−0.0942670	+	0.388574i	−0.999326	−	0.0367125i	$-0.988311\pi$
$337$	−1.73051	+	7.13327i	−0.0942670	+	0.388574i	0.905059	+	0.425286i	$0.139827\pi$
$338$		0			0
$339$	4.90804	+	2.53027i	0.266568	+	0.137425i
$340$		0			0
$341$	−42.2027	−	4.02987i	−2.28540	−	0.218230i
$342$		0			0
$343$	3.73847	−	4.31442i	0.201858	−	0.232957i
$344$		0			0
$345$	−26.2820	−	20.6684i	−1.41498	−	1.11275i
$346$		0			0
$347$	−3.51360	+	10.1519i	−0.188620	+	0.544982i	−0.999172	−	0.0406848i	$-0.987046\pi$
$347$	−3.51360	+	10.1519i	−0.188620	+	0.544982i	0.810552	+	0.585667i	$0.199167\pi$
$348$		0			0
$349$	−23.9207	+	15.3729i	−1.28045	+	0.822892i	−0.990943	−	0.134285i	$-0.957126\pi$
$349$	−23.9207	+	15.3729i	−1.28045	+	0.822892i	−0.289503	+	0.957177i	$0.593490\pi$
$350$		0			0
$351$	1.35536	+	1.90334i	0.0723440	+	0.101593i
$352$		0			0
$353$	0.0931665	+	1.95581i	0.00495875	+	0.104097i	0.999990	+	0.00453124i	$0.00144234\pi$
$353$	0.0931665	+	1.95581i	0.00495875	+	0.104097i	−0.995031	+	0.0995658i	$0.968255\pi$
$354$		0			0
$355$	−46.7265	+	36.7461i	−2.47998	+	1.95028i
$356$		0			0
$357$	0.786518	−	5.47035i	0.0416269	−	0.289522i
$358$		0			0
$359$	−7.39494	−	4.75244i	−0.390290	−	0.250824i	0.330749	−	0.943719i	$-0.392699\pi$
$359$	−7.39494	−	4.75244i	−0.390290	−	0.250824i	−0.721039	+	0.692895i	$0.756335\pi$
$360$		0			0
$361$	−0.890155	+	18.6866i	−0.0468502	+	0.983508i
$362$		0			0
$363$	5.43841	+	15.7132i	0.285442	+	0.824732i
$364$		0			0
$365$	−14.1889	+	24.5760i	−0.742683	+	1.28636i
$366$		0			0
$367$	14.0056	−	5.60698i	0.731084	−	0.292682i	0.0239028	−	0.999714i	$-0.492391\pi$
$367$	14.0056	−	5.60698i	0.731084	−	0.292682i	0.707181	+	0.707032i	$0.249967\pi$
$368$		0			0
$369$	−2.18970	−	9.02607i	−0.113991	−	0.469879i
$370$		0			0
$371$	−17.4379	−	3.36089i	−0.905333	−	0.174489i
$372$		0			0
$373$	−6.66882	−	11.5507i	−0.345298	−	0.598074i	0.640110	−	0.768284i	$-0.278889\pi$
$373$	−6.66882	−	11.5507i	−0.345298	−	0.598074i	−0.985408	+	0.170209i	$0.945556\pi$
$374$		0			0
$375$	10.6123	+	23.2376i	0.548015	+	1.19999i
$376$		0			0
$377$	1.68816	+	1.94824i	0.0869448	+	0.100340i
$378$		0			0
$379$	0.272717	+	0.109180i	0.0140086	+	0.00560818i	0.378656	−	0.925537i	$-0.376386\pi$
$379$	0.272717	+	0.109180i	0.0140086	+	0.00560818i	−0.364648	+	0.931146i	$0.618811\pi$
$380$		0			0
$381$	5.94698	−	8.35136i	0.304673	−	0.427853i
$382$		0			0
$383$	−10.9944	+	10.4832i	−0.561790	+	0.535666i	−0.916878	−	0.399167i	$-0.869299\pi$
$383$	−10.9944	+	10.4832i	−0.561790	+	0.535666i	0.355088	+	0.934833i	$0.384451\pi$
$384$		0			0
$385$	−66.4061	+	34.2347i	−3.38437	+	1.74476i
$386$		0			0
$387$	9.10216	+	2.67263i	0.462689	+	0.135858i
$388$		0			0
$389$	28.4319	−	5.47981i	1.44156	−	0.277837i	0.592257	−	0.805749i	$-0.298237\pi$
$389$	28.4319	−	5.47981i	1.44156	−	0.277837i	0.849299	+	0.527912i	$0.177025\pi$
$390$		0			0
$391$	−12.9414	+	1.23575i	−0.654473	+	0.0624946i
$392$		0			0
$393$	17.6928	−	5.19507i	0.892482	−	0.262057i
$394$		0			0
$395$	−18.9715	−	18.0893i	−0.954561	−	0.910172i
$396$		0			0
$397$	−9.01108	+	19.7315i	−0.452253	+	0.990297i	0.536932	+	0.843626i	$0.319583\pi$
$397$	−9.01108	+	19.7315i	−0.452253	+	0.990297i	−0.989185	+	0.146671i	$0.953144\pi$
$398$		0			0
$399$	−0.270631	−	1.88228i	−0.0135485	−	0.0942320i
$400$		0			0
$401$	−13.0777			−0.653067			−0.326534	−	0.945186i	$-0.605881\pi$
$401$	−13.0777			−0.653067			−0.326534	+	0.945186i	$0.605881\pi$
$402$		0			0
$403$	18.8462			0.938796
$404$		0			0
$405$	0.574977	+	3.99905i	0.0285708	+	0.198715i
$406$		0			0
$407$	22.2706	−	48.7658i	1.10391	−	2.41723i
$408$		0			0
$409$	10.0109	+	9.54534i	0.495006	+	0.471987i	0.895975	−	0.444105i	$-0.146478\pi$
$409$	10.0109	+	9.54534i	0.495006	+	0.471987i	−0.400969	+	0.916091i	$0.631327\pi$
$410$		0			0
$411$	4.47450	−	1.31383i	0.220711	−	0.0648066i
$412$		0			0
$413$	14.9491	−	1.42747i	0.735597	−	0.0702410i
$414$		0			0
$415$	63.6170	−	12.2612i	3.12284	−	0.601878i
$416$		0			0
$417$	−9.26654	−	2.72090i	−0.453784	−	0.133243i
$418$		0			0
$419$	−12.0969	+	6.23638i	−0.590972	+	0.304667i	−0.727650	−	0.685948i	$-0.759388\pi$
$419$	−12.0969	+	6.23638i	−0.590972	+	0.304667i	0.136678	+	0.990615i	$0.456357\pi$
$420$		0			0
$421$	−6.67393	+	6.36358i	−0.325267	+	0.310142i	−0.835064	−	0.550153i	$-0.814569\pi$
$421$	−6.67393	+	6.36358i	−0.325267	+	0.310142i	0.509796	+	0.860295i	$0.329721\pi$
$422$		0			0
$423$	2.80195	−	3.93478i	0.136235	−	0.191316i
$424$		0			0
$425$	16.5131	+	6.61083i	0.801001	+	0.320673i
$426$		0			0
$427$	9.94506	+	11.4772i	0.481275	+	0.555421i
$428$		0			0
$429$	−5.10200	−	11.1718i	−0.246327	−	0.539381i
$430$		0			0
$431$	−3.40149	−	5.89155i	−0.163844	−	0.283786i	0.772400	−	0.635136i	$-0.219056\pi$
$431$	−3.40149	−	5.89155i	−0.163844	−	0.283786i	−0.936244	+	0.351350i	$0.885723\pi$
$432$		0			0
$433$	−30.6733	−	5.91180i	−1.47406	−	0.284103i	−0.611983	−	0.790871i	$-0.709628\pi$
$433$	−30.6733	−	5.91180i	−1.47406	−	0.284103i	−0.862082	+	0.506768i	$0.830840\pi$
$434$		0			0
$435$	1.05087	+	4.33174i	0.0503853	+	0.207691i
$436$		0			0
$437$	−4.15280	+	1.66253i	−0.198655	+	0.0795296i
$438$		0			0
$439$	15.2854	−	26.4750i	0.729530	−	1.26358i	−0.227552	−	0.973766i	$-0.573072\pi$
$439$	15.2854	−	26.4750i	0.729530	−	1.26358i	0.957082	−	0.289817i	$-0.0935945\pi$
$440$		0			0
$441$	−1.75875	−	5.08158i	−0.0837501	−	0.241980i
$442$		0			0
$443$	−0.429360	+	9.01338i	−0.0203995	+	0.428238i	0.965448	+	0.260595i	$0.0839187\pi$
$443$	−0.429360	+	9.01338i	−0.0203995	+	0.428238i	−0.985848	+	0.167643i	$0.946384\pi$
$444$		0			0
$445$	3.34525	+	2.14986i	0.158580	+	0.101913i
$446$		0			0
$447$	1.46473	−	10.1874i	0.0692793	−	0.481848i
$448$		0			0
$449$	13.4050	−	10.5418i	0.632619	−	0.497497i	−0.249592	−	0.968351i	$-0.580297\pi$
$449$	13.4050	−	10.5418i	0.632619	−	0.497497i	0.882211	+	0.470854i	$0.156054\pi$
$450$		0			0
$451$	2.32291	+	48.7638i	0.109381	+	2.29620i
$452$		0			0
$453$	10.2954	+	14.4578i	0.483718	+	0.679288i
$454$		0			0
$455$	27.9400	−	17.9559i	1.30985	−	0.841787i
$456$		0			0
$457$	7.14609	−	20.6473i	0.334280	−	0.965839i	−0.645150	−	0.764056i	$-0.723205\pi$
$457$	7.14609	−	20.6473i	0.334280	−	0.965839i	0.979430	−	0.201783i	$-0.0646736\pi$
$458$		0			0
$459$	1.23480	+	0.971058i	0.0576355	+	0.0453251i
$460$		0			0
$461$	−4.65104	+	5.36759i	−0.216621	+	0.249993i	−0.853651	−	0.520845i	$-0.825617\pi$
$461$	−4.65104	+	5.36759i	−0.216621	+	0.249993i	0.637031	+	0.770838i	$0.280162\pi$
$462$		0			0
$463$	−36.1727	−	3.45408i	−1.68109	−	0.160525i	−0.789617	−	0.613600i	$-0.789721\pi$
$463$	−36.1727	−	3.45408i	−1.68109	−	0.160525i	−0.891472	+	0.453075i	$0.850327\pi$
$464$		0			0
$465$	28.9641	+	14.9320i	1.34318	+	0.692457i
$466$		0			0
$467$	−1.34648	+	5.55027i	−0.0623077	+	0.256836i	−0.994443	−	0.105274i	$-0.966428\pi$
$467$	−1.34648	+	5.55027i	−0.0623077	+	0.256836i	0.932136	+	0.362109i	$0.117943\pi$
$468$		0			0
$469$	27.7790	−	7.58994i	1.28272	−	0.350471i
$470$		0			0
$471$	−2.40935	+	9.93148i	−0.111017	+	0.457619i
$472$		0			0
$473$	−44.3197	−	22.8484i	−2.03782	−	1.05057i
$474$		0			0
$475$	6.09265	+	0.581778i	0.279550	+	0.0266938i
$476$		0			0
$477$	3.30560	−	3.81487i	0.151353	−	0.174671i
$478$		0			0
$479$	6.92510	+	5.44596i	0.316416	+	0.248832i	0.763717	−	0.645551i	$-0.223372\pi$
$479$	6.92510	+	5.44596i	0.316416	+	0.248832i	−0.447301	+	0.894383i	$0.647615\pi$
$480$		0			0
$481$	−7.79471	+	22.5213i	−0.355408	+	1.02688i
$482$		0			0
$483$	−24.4933	+	15.7409i	−1.11448	+	0.716234i
$484$		0			0
$485$	3.96909	+	5.57381i	0.180227	+	0.253094i
$486$		0			0
$487$	−0.268082	−	5.62774i	−0.0121480	−	0.255017i	−0.996769	−	0.0803159i	$-0.974407\pi$
$487$	−0.268082	−	5.62774i	−0.0121480	−	0.255017i	0.984621	−	0.174701i	$-0.0558960\pi$
$488$		0			0
$489$	6.57271	−	5.16884i	0.297228	−	0.233743i
$490$		0			0
$491$	1.69012	−	11.7550i	0.0762738	−	0.530496i	−0.915482	−	0.402358i	$-0.868191\pi$
$491$	1.69012	−	11.7550i	0.0762738	−	0.530496i	0.991756	−	0.128138i	$-0.0409002\pi$
$492$		0			0
$493$	1.45798	+	0.936988i	0.0656642	+	0.0421998i
$494$		0			0
$495$	1.01045	−	21.2120i	0.0454164	−	0.953407i
$496$		0			0
$497$	16.9302	+	48.9166i	0.759423	+	2.19421i
$498$		0			0
$499$	−4.45174	+	7.71064i	−0.199287	+	0.345176i	−0.948298	−	0.317383i	$-0.897196\pi$
$499$	−4.45174	+	7.71064i	−0.199287	+	0.345176i	0.749010	+	0.662558i	$0.230529\pi$
$500$		0			0
$501$	−15.5416	+	6.22190i	−0.694345	+	0.277974i
$502$		0			0
$503$	−0.818886	−	3.37550i	−0.0365123	−	0.150506i	0.950637	−	0.310304i	$-0.100431\pi$
$503$	−0.818886	−	3.37550i	−0.0365123	−	0.150506i	−0.987150	+	0.159798i	$0.948916\pi$
$504$		0			0
$505$	−36.3944	−	7.01445i	−1.61953	−	0.312139i
$506$		0			0
$507$	−3.77014	−	6.53007i	−0.167438	−	0.290011i
$508$		0			0
$509$	−4.51665	−	9.89009i	−0.200197	−	0.438370i	0.782731	−	0.622360i	$-0.213826\pi$
$509$	−4.51665	−	9.89009i	−0.200197	−	0.438370i	−0.982928	+	0.183990i	$0.941099\pi$
$510$		0			0
$511$	16.1824	+	18.6754i	0.715865	+	0.826153i
$512$		0			0
$513$	0.501805	+	0.200892i	0.0221552	+	0.00886961i
$514$		0			0
$515$	−14.8903	+	20.9105i	−0.656144	+	0.921425i
$516$		0			0
$517$	−18.3756	+	17.5211i	−0.808157	+	0.770576i
$518$		0			0
$519$	18.2694	−	9.41854i	0.801939	−	0.413428i
$520$		0			0
$521$	23.7070	+	6.96100i	1.03862	+	0.304967i	0.756212	−	0.654327i	$-0.227048\pi$
$521$	23.7070	+	6.96100i	1.03862	+	0.304967i	0.282410	+	0.959294i	$0.408866\pi$
$522$		0			0
$523$	2.33956	−	0.450914i	0.102302	−	0.0197171i	−0.137843	−	0.990454i	$-0.544017\pi$
$523$	2.33956	−	0.450914i	0.102302	−	0.0197171i	0.240145	+	0.970737i	$0.422805\pi$
$524$		0			0
$525$	39.6557	−	3.78666i	1.73071	−	0.165263i
$526$		0			0
$527$	12.1570	−	3.56961i	0.529566	−	0.155494i
$528$		0			0
$529$	32.9211	+	31.3902i	1.43135	+	1.36479i
$530$		0			0
$531$	−1.77319	+	3.88274i	−0.0769498	+	0.168497i
$532$		0			0
$533$	−3.08853	−	21.4812i	−0.133779	−	0.930455i
$534$		0			0
$535$	−44.0121			−1.90281
$536$		0			0
$537$	−14.8919			−0.642633
$538$		0			0
$539$	4.02244	+	27.9767i	0.173259	+	1.20504i
$540$		0			0
$541$	13.2116	−	28.9294i	0.568013	−	1.24377i	−0.379836	−	0.925054i	$-0.624020\pi$
$541$	13.2116	−	28.9294i	0.568013	−	1.24377i	0.947849	−	0.318720i	$-0.103253\pi$
$542$		0			0
$543$	10.2329	+	9.75708i	0.439137	+	0.418716i
$544$		0			0
$545$	−42.4141	+	12.4539i	−1.81682	+	0.533467i
$546$		0			0
$547$	8.99779	−	0.859185i	0.384718	−	0.0367361i	0.0990943	−	0.995078i	$-0.468405\pi$
$547$	8.99779	−	0.859185i	0.384718	−	0.0367361i	0.285623	+	0.958342i	$0.407799\pi$
$548$		0			0
$549$	−4.23863	+	0.816928i	−0.180900	+	0.0348656i
$550$		0			0
$551$	0.572185	+	0.168009i	0.0243759	+	0.00715741i
$552$		0			0
$553$	−20.2889	+	10.4596i	−0.862770	+	0.444789i
$554$		0			0
$555$	−29.8233	+	28.4365i	−1.26593	+	1.20706i
$556$		0			0
$557$	3.15958	−	4.43701i	0.133876	−	0.188002i	−0.742196	−	0.670183i	$-0.766216\pi$
$557$	3.15958	−	4.43701i	0.133876	−	0.188002i	0.876072	+	0.482181i	$0.160155\pi$
$558$		0			0
$559$	20.5782	+	8.23828i	0.870366	+	0.348442i
$560$		0			0
$561$	−5.40713	−	6.24016i	−0.228289	−	0.263460i
$562$		0			0
$563$	−8.94352	−	19.5836i	−0.376924	−	0.825349i	−0.999098	−	0.0424697i	$-0.986477\pi$
$563$	−8.94352	−	19.5836i	−0.376924	−	0.825349i	0.622173	−	0.782879i	$-0.286250\pi$
$564$		0			0
$565$	11.1547	+	19.3205i	0.469281	+	0.812819i
$566$		0			0
$567$	3.45457	+	0.665813i	0.145078	+	0.0279615i
$568$		0			0
$569$	−2.04295	−	8.42116i	−0.0856450	−	0.353034i	0.912824	−	0.408354i	$-0.133897\pi$
$569$	−2.04295	−	8.42116i	−0.0856450	−	0.353034i	−0.998469	+	0.0553205i	$0.982382\pi$
$570$		0			0
$571$	−2.48396	+	0.994428i	−0.103951	+	0.0416155i	−0.423055	−	0.906104i	$-0.639042\pi$
$571$	−2.48396	+	0.994428i	−0.103951	+	0.0416155i	0.319104	+	0.947720i	$0.396618\pi$
$572$		0			0
$573$	−6.52888	+	11.3083i	−0.272748	+	0.472413i
$574$		0			0
$575$	−30.6484	−	88.5526i	−1.27813	−	3.69290i
$576$		0			0
$577$	0.932346	−	19.5723i	0.0388141	−	0.814808i	−0.892601	−	0.450848i	$-0.851122\pi$
$577$	0.932346	−	19.5723i	0.0388141	−	0.814808i	0.931415	−	0.363959i	$-0.118575\pi$
$578$		0			0
$579$	−10.7726	−	6.92313i	−0.447694	−	0.287716i
$580$		0			0
$581$	8.02891	−	55.8423i	0.333095	−	2.31673i
$582$		0			0
$583$	−20.8558	+	16.4012i	−0.863759	+	0.679267i
$584$		0			0
$585$	0.449188	+	9.42961i	0.0185716	+	0.389866i
$586$		0			0
$587$	−22.3482	−	31.3837i	−0.922409	−	1.29534i	−0.955225	−	0.295881i	$-0.904387\pi$
$587$	−22.3482	−	31.3837i	−0.922409	−	1.29534i	0.0328153	−	0.999461i	$-0.489553\pi$
$588$		0			0
$589$	3.66758	−	2.35701i	0.151120	−	0.0971190i
$590$		0			0
$591$	−2.80696	+	8.11017i	−0.115463	+	0.333608i
$592$		0			0
$593$	−19.3285	−	15.2001i	−0.793727	−	0.624194i	0.136725	−	0.990609i	$-0.456342\pi$
$593$	−19.3285	−	15.2001i	−0.793727	−	0.624194i	−0.930451	+	0.366415i	$0.880585\pi$
$594$		0			0
$595$	14.6220	−	16.8747i	0.599445	−	0.691796i
$596$		0			0
$597$	−2.86358	−	0.273439i	−0.117199	−	0.0111911i
$598$		0			0
$599$	−2.31677	−	1.19438i	−0.0946607	−	0.0488010i	0.410246	−	0.911975i	$-0.365443\pi$
$599$	−2.31677	−	1.19438i	−0.0946607	−	0.0488010i	−0.504907	+	0.863174i	$0.668473\pi$
$600$		0			0
$601$	1.22099	−	5.03300i	0.0498054	−	0.205301i	−0.941472	−	0.337090i	$-0.890557\pi$
$601$	1.22099	−	5.03300i	0.0498054	−	0.205301i	0.991278	+	0.131790i	$0.0420724\pi$
$602$		0			0
$603$	−2.07963	+	7.91676i	−0.0846890	+	0.322396i
$604$		0			0
$605$	−15.8381	+	65.2854i	−0.643909	+	2.65423i
$606$		0			0
$607$	8.29159	+	4.27461i	0.336545	+	0.173501i	0.618212	−	0.786011i	$-0.287857\pi$
$607$	8.29159	+	4.27461i	0.336545	+	0.173501i	−0.281667	+	0.959512i	$0.590887\pi$
$608$		0			0
$609$	3.86387	+	0.368955i	0.156572	+	0.0149508i
$610$		0			0
$611$	7.39135	−	8.53007i	0.299022	−	0.345090i
$612$		0			0
$613$	25.2903	+	19.8885i	1.02146	+	0.803288i	0.980628	−	0.195878i	$-0.0627556\pi$
$613$	25.2903	+	19.8885i	1.02146	+	0.803288i	0.0408356	+	0.999166i	$0.486998\pi$
$614$		0			0
$615$	12.2731	−	35.4609i	0.494900	−	1.42992i
$616$		0			0
$617$	−16.8964	+	10.8587i	−0.680224	+	0.437153i	−0.834598	−	0.550859i	$-0.814300\pi$
$617$	−16.8964	+	10.8587i	−0.680224	+	0.437153i	0.154375	+	0.988012i	$0.450664\pi$
$618$		0			0
$619$	−20.3543	−	28.5836i	−0.818107	−	1.14887i	−0.986598	−	0.163168i	$-0.947829\pi$
$619$	−20.3543	−	28.5836i	−0.818107	−	1.14887i	0.168491	−	0.985703i	$-0.446111\pi$
$620$		0			0
$621$	−0.393775	−	8.26636i	−0.0158017	−	0.331718i
$622$		0			0
$623$	2.72186	−	2.14050i	0.109049	−	0.0857572i
$624$		0			0
$625$	−6.63129	+	46.1216i	−0.265252	+	1.84487i
$626$		0			0
$627$	−2.39009	−	1.53602i	−0.0954510	−	0.0613426i
$628$		0			0
$629$	−0.762366	+	16.0040i	−0.0303975	+	0.638122i
$630$		0			0
$631$	−7.54574	−	21.8020i	−0.300391	−	0.867923i	−0.989662	−	0.143419i	$-0.954190\pi$
$631$	−7.54574	−	21.8020i	−0.300391	−	0.867923i	0.689271	−	0.724504i	$-0.257931\pi$
$632$		0			0
$633$	−7.69440	+	13.3271i	−0.305825	+	0.529704i
$634$		0			0
$635$	38.4544	−	15.3948i	1.52602	−	0.610925i
$636$		0			0
$637$	−2.96224	−	12.2105i	−0.117368	−	0.483798i
$638$		0			0
$639$	−14.4474	−	2.78451i	−0.571531	−	0.110154i
$640$		0			0
$641$	4.58346	+	7.93878i	0.181036	+	0.313563i	0.942233	−	0.334957i	$-0.108722\pi$
$641$	4.58346	+	7.93878i	0.181036	+	0.313563i	−0.761198	+	0.648520i	$0.775388\pi$
$642$		0			0
$643$	−18.8277	−	41.2268i	−0.742491	−	1.62583i	−0.779414	−	0.626509i	$-0.784483\pi$
$643$	−18.8277	−	41.2268i	−0.742491	−	1.62583i	0.0369234	−	0.999318i	$-0.488244\pi$
$644$		0			0
$645$	25.0987	+	28.9655i	0.988262	+	1.14051i
$646$		0			0
$647$	−5.07457	−	2.03155i	−0.199502	−	0.0798685i	0.269760	−	0.962928i	$-0.413056\pi$
$647$	−5.07457	−	2.03155i	−0.199502	−	0.0798685i	−0.469262	+	0.883059i	$0.655480\pi$
$648$		0			0
$649$	13.0142	−	18.2758i	0.510851	−	0.717389i
$650$		0			0
$651$	20.5367	−	19.5817i	0.804897	−	0.767468i
$652$		0			0
$653$	−15.4472	+	7.96357i	−0.604495	+	0.311639i	−0.733167	−	0.680048i	$-0.761959\pi$
$653$	−15.4472	+	7.96357i	−0.604495	+	0.311639i	0.128672	+	0.991687i	$0.458928\pi$
$654$		0			0
$655$	71.4820	+	20.9890i	2.79303	+	0.820108i
$656$		0			0
$657$	−6.89699	+	1.32929i	−0.269077	+	0.0518604i
$658$		0			0
$659$	22.0552	−	2.10602i	0.859149	−	0.0820388i	0.343825	−	0.939034i	$-0.388277\pi$
$659$	22.0552	−	2.10602i	0.859149	−	0.0820388i	0.515325	+	0.856995i	$0.327671\pi$
$660$		0			0
$661$	−17.7369	+	5.20802i	−0.689885	+	0.202568i	−0.607839	−	0.794060i	$-0.707963\pi$
$661$	−17.7369	+	5.20802i	−0.689885	+	0.202568i	−0.0820456	+	0.996629i	$0.526145\pi$
$662$		0			0
$663$	2.65650	+	2.53296i	0.103170	+	0.0983722i
$664$		0			0
$665$	3.19161	−	6.98866i	0.123766	−	0.271009i
$666$		0			0
$667$	−1.29938	−	9.03740i	−0.0503123	−	0.349930i
$668$		0			0
$669$	4.34131			0.167845
$670$		0			0
$671$	22.6891			0.875904
$672$		0			0
$673$	−6.72494	−	46.7730i	−0.259227	−	1.80297i	−0.538362	−	0.842714i	$-0.680957\pi$
$673$	−6.72494	−	46.7730i	−0.259227	−	1.80297i	0.279135	−	0.960252i	$-0.409952\pi$
$674$		0			0
$675$	−4.70376	+	10.2998i	−0.181048	+	0.396439i
$676$		0			0
$677$	27.5201	+	26.2403i	1.05768	+	1.00850i	0.999948	+	0.0101652i	$0.00323574\pi$
$677$	27.5201	+	26.2403i	1.05768	+	1.00850i	0.0577331	+	0.998332i	$0.481613\pi$
$678$		0			0
$679$	5.71710	−	1.67869i	0.219402	−	0.0644222i
$680$		0			0
$681$	8.30068	−	0.792619i	0.318083	−	0.0303732i
$682$		0			0
$683$	−33.7875	+	6.51202i	−1.29284	+	0.249175i	−0.788879	−	0.614548i	$-0.789338\pi$
$683$	−33.7875	+	6.51202i	−1.29284	+	0.249175i	−0.503965	+	0.863724i	$0.668126\pi$
$684$		0			0
$685$	18.0778	+	5.30812i	0.690717	+	0.202813i
$686$		0			0
$687$	6.26946	−	3.23213i	0.239195	−	0.123313i
$688$		0			0
$689$	8.53623	−	8.13928i	0.325205	−	0.310082i
$690$		0			0
$691$	24.6692	−	34.6431i	0.938461	−	1.31788i	−0.00965323	−	0.999953i	$-0.503073\pi$
$691$	24.6692	−	34.6431i	0.938461	−	1.31788i	0.948114	−	0.317930i	$-0.102988\pi$
$692$		0			0
$693$	−17.1675	−	6.87282i	−0.652138	−	0.261077i
$694$		0			0
$695$	−25.5520	−	29.4886i	−0.969243	−	1.11857i
$696$		0			0
$697$	−6.06099	−	13.2717i	−0.229576	−	0.502702i
$698$		0			0
$699$	1.78030	+	3.08356i	0.0673370	+	0.116631i
$700$		0			0
$701$	12.0481	+	2.32208i	0.455049	+	0.0877036i	0.411625	−	0.911353i	$-0.364961\pi$
$701$	12.0481	+	2.32208i	0.455049	+	0.0877036i	0.0434241	+	0.999057i	$0.486173\pi$
$702$		0			0
$703$	1.29975	+	5.35763i	0.0490209	+	0.202067i
$704$		0			0
$705$	18.1180	−	7.25335i	0.682363	−	0.273177i
$706$		0			0
$707$	−16.1376	+	27.9511i	−0.606915	+	1.05121i
$708$		0			0
$709$	−16.3278	−	47.1760i	−0.613203	−	1.77173i	−0.635642	−	0.771984i	$-0.719264\pi$
$709$	−16.3278	−	47.1760i	−0.613203	−	1.77173i	0.0224389	−	0.999748i	$-0.492857\pi$
$710$		0			0
$711$	0.308720	−	6.48083i	0.0115779	−	0.243050i
$712$		0			0
$713$	−56.1529	−	36.0872i	−2.10294	−	1.35148i
$714$		0			0
$715$	7.06169	−	49.1151i	0.264092	−	1.83680i
$716$		0			0
$717$	1.10127	−	0.866044i	0.0411275	−	0.0323430i
$718$		0			0
$719$	−1.68414	−	35.3545i	−0.0628078	−	1.31850i	−0.781821	−	0.623503i	$-0.785709\pi$
$719$	−1.68414	−	35.3545i	−0.0628078	−	1.31850i	0.719013	−	0.694996i	$-0.244594\pi$
$720$		0			0
$721$	12.9663	+	18.2086i	0.482890	+	0.678124i
$722$		0			0
$723$	5.50152	−	3.53561i	0.204604	−	0.131491i
$724$		0			0
$725$	−4.08584	+	11.8052i	−0.151744	+	0.438436i
$726$		0			0
$727$	−24.5160	−	19.2796i	−0.909248	−	0.715041i	0.0496572	−	0.998766i	$-0.484187\pi$
$727$	−24.5160	−	19.2796i	−0.909248	−	0.715041i	−0.958906	+	0.283725i	$0.908430\pi$
$728$		0			0
$729$	−0.654861	+	0.755750i	−0.0242541	+	0.0279907i
$730$		0			0
$731$	14.8346	+	1.41653i	0.548678	+	0.0523924i
$732$		0			0
$733$	34.5566	+	17.8152i	1.27638	+	0.658019i	0.957132	−	0.289653i	$-0.0935399\pi$
$733$	34.5566	+	17.8152i	1.27638	+	0.658019i	0.319246	+	0.947672i	$0.396570\pi$
$734$		0			0
$735$	5.12195	−	21.1129i	0.188926	−	0.778763i
$736$		0			0
$737$	18.6086	−	38.7915i	0.685456	−	1.42890i
$738$		0			0
$739$	5.59628	−	23.0682i	0.205863	−	0.848577i	−0.771367	−	0.636391i	$-0.780426\pi$
$739$	5.59628	−	23.0682i	0.205863	−	0.848577i	0.977229	−	0.212186i	$-0.0680584\pi$
$740$		0			0
$741$	1.12259	+	0.578735i	0.0412394	+	0.0212604i
$742$		0			0
$743$	0.100586	+	0.00960481i	0.00369015	+	0.000352366i	0.0969010	−	0.995294i	$-0.469107\pi$
$743$	0.100586	+	0.00960481i	0.00369015	+	0.000352366i	−0.0932108	+	0.995646i	$0.529713\pi$
$744$		0			0
$745$	27.2306	−	31.4257i	0.997651	−	1.15135i
$746$		0			0
$747$	12.6051	+	9.91273i	0.461195	+	0.362688i
$748$		0			0
$749$	−12.5350	+	36.2174i	−0.458018	+	1.32336i
$750$		0			0
$751$	33.9577	−	21.8233i	1.23913	−	0.796343i	0.253846	−	0.967245i	$-0.418304\pi$
$751$	33.9577	−	21.8233i	1.23913	−	0.796343i	0.985288	+	0.170902i	$0.0546680\pi$
$752$		0			0
$753$	−10.0836	−	14.1605i	−0.367468	−	0.516037i
$754$		0			0
$755$	3.41204	+	71.6274i	0.124177	+	2.60679i
$756$		0			0
$757$	−13.4066	+	10.5431i	−0.487271	+	0.383194i	−0.831352	−	0.555745i	$-0.812433\pi$
$757$	−13.4066	+	10.5431i	−0.487271	+	0.383194i	0.344081	+	0.938940i	$0.388190\pi$
$758$		0			0
$759$	−6.19056	+	43.0563i	−0.224703	+	1.56284i
$760$		0			0
$761$	31.8627	+	20.4769i	1.15502	+	0.742287i	0.970633	−	0.240567i	$-0.0773333\pi$
$761$	31.8627	+	20.4769i	1.15502	+	0.742287i	0.184388	+	0.982854i	$0.440970\pi$
$762$		0			0
$763$	−1.83157	+	38.4494i	−0.0663073	+	1.39196i
$764$		0			0
$765$	2.07579	+	5.99760i	0.0750503	+	0.216844i
$766$		0			0
$767$	−4.98687	+	8.63751i	−0.180065	+	0.311883i
$768$		0			0
$769$	26.9406	−	10.7854i	0.971502	−	0.388931i	0.169023	−	0.985612i	$-0.445939\pi$
$769$	26.9406	−	10.7854i	0.971502	−	0.388931i	0.802478	+	0.596681i	$0.203514\pi$
$770$		0			0
$771$	6.86484	+	28.2973i	0.247231	+	1.01910i
$772$		0			0
$773$	−14.2944	−	2.75501i	−0.514132	−	0.0990909i	−0.0744154	−	0.997227i	$-0.523709\pi$
$773$	−14.2944	−	2.75501i	−0.514132	−	0.0990909i	−0.439717	+	0.898136i	$0.644921\pi$
$774$		0			0
$775$	45.6637	+	79.0919i	1.64029	+	2.84106i
$776$		0			0
$777$	14.9064	+	32.6404i	0.534763	+	1.17097i
$778$		0			0
$779$	−3.28761	−	3.79410i	−0.117791	−	0.135938i
$780$		0			0
$781$	71.7965	+	28.7430i	2.56908	+	1.02851i
$782$		0			0
$783$	−0.639957	+	0.898694i	−0.0228702	+	0.0321167i
$784$		0			0
$785$	−29.8821	+	28.4925i	−1.06654	+	1.01694i
$786$		0			0
$787$	19.6912	−	10.1515i	0.701915	−	0.361862i	−0.0700358	−	0.997544i	$-0.522311\pi$
$787$	19.6912	−	10.1515i	0.701915	−	0.361862i	0.771951	+	0.635682i	$0.219281\pi$
$788$		0			0
$789$	−22.7157	−	6.66994i	−0.808701	−	0.237456i
$790$		0			0
$791$	19.0757	−	3.67654i	0.678254	−	0.130723i
$792$		0			0
$793$	−10.0406	+	0.958761i	−0.356552	+	0.0340466i
$794$		0			0
$795$	19.5679	−	5.74565i	0.694002	−	0.203777i
$796$		0			0
$797$	−28.2009	−	26.8895i	−0.998928	−	0.952476i	−5.80259e−5	−	1.00000i	$-0.500018\pi$
$797$	−28.2009	−	26.8895i	−0.998928	−	0.952476i	−0.998870	+	0.0475240i	$0.984867\pi$
$798$		0			0
$799$	3.15222	−	6.90240i	0.111517	−	0.244189i
$800$		0			0
$801$	0.140072	+	0.974221i	0.00494920	+	0.0344224i
$802$		0			0
$803$	36.9192			1.30285
$804$		0			0
$805$	−117.631			−4.14593
$806$		0			0
$807$	0.446605	+	3.10621i	0.0157212	+	0.109344i
$808$		0			0
$809$	−1.25179	+	2.74104i	−0.0440107	+	0.0963700i	−0.930360	−	0.366647i	$-0.880506\pi$
$809$	−1.25179	+	2.74104i	−0.0440107	+	0.0963700i	0.886350	+	0.463017i	$0.153233\pi$
$810$		0			0
$811$	6.88371	+	6.56361i	0.241720	+	0.230479i	0.801249	−	0.598331i	$-0.204169\pi$
$811$	6.88371	+	6.56361i	0.241720	+	0.230479i	−0.559529	+	0.828811i	$0.689018\pi$
$812$		0			0
$813$	−27.7088	+	8.13605i	−0.971791	+	0.285344i
$814$		0			0
$815$	33.6296	−	3.21124i	1.17799	−	0.112485i
$816$		0			0
$817$	5.03497	−	0.970411i	0.176151	−	0.0339504i
$818$		0			0
$819$	7.88752	+	2.31599i	0.275612	+	0.0809271i
$820$		0			0
$821$	−27.7396	+	14.3008i	−0.968120	+	0.499101i	−0.868373	−	0.495912i	$-0.834834\pi$
$821$	−27.7396	+	14.3008i	−0.968120	+	0.499101i	−0.0997474	+	0.995013i	$0.531803\pi$
$822$		0			0
$823$	−21.8749	+	20.8577i	−0.762512	+	0.727053i	−0.967820	−	0.251644i	$-0.919029\pi$
$823$	−21.8749	+	20.8577i	−0.762512	+	0.727053i	0.205308	+	0.978697i	$0.434180\pi$
$824$		0			0
$825$	34.5228	−	48.4805i	1.20193	−	1.68787i
$826$		0			0
$827$	−8.06152	−	3.22734i	−0.280326	−	0.112226i	0.227239	−	0.973839i	$-0.427030\pi$
$827$	−8.06152	−	3.22734i	−0.280326	−	0.112226i	−0.507565	+	0.861613i	$0.669454\pi$
$828$		0			0
$829$	6.30535	+	7.27676i	0.218994	+	0.252732i	0.854607	−	0.519275i	$-0.173798\pi$
$829$	6.30535	+	7.27676i	0.218994	+	0.252732i	−0.635613	+	0.772008i	$0.719253\pi$
$830$		0			0
$831$	9.42310	+	20.6337i	0.326884	+	0.715776i
$832$		0			0
$833$	−4.22359	−	7.31546i	−0.146339	−	0.253466i
$834$		0			0
$835$	−66.4132	−	12.8001i	−2.29833	−	0.442966i
$836$		0			0
$837$	1.90154	+	7.83827i	0.0657270	+	0.270930i
$838$		0			0
$839$	10.3139	−	4.12906i	0.356075	−	0.142551i	−0.186726	−	0.982412i	$-0.559788\pi$
$839$	10.3139	−	4.12906i	0.356075	−	0.142551i	0.542802	+	0.839861i	$0.317364\pi$
$840$		0			0
$841$	13.8914	−	24.0606i	0.479014	−	0.829676i
$842$		0			0
$843$	2.64501	+	7.64224i	0.0910989	+	0.263213i
$844$		0			0
$845$	1.44954	−	30.4295i	0.0498656	−	1.04681i
$846$		0			0
$847$	49.2124	+	31.6269i	1.69096	+	1.08671i
$848$		0			0
$849$	0.611081	−	4.25016i	0.0209723	−	0.145865i
$850$		0			0
$851$	66.3491	−	52.1775i	2.27442	−	1.78862i
$852$		0			0
$853$	0.380441	+	7.98643i	0.0130260	+	0.273450i	0.995979	+	0.0895911i	$0.0285560\pi$
$853$	0.380441	+	7.98643i	0.0130260	+	0.273450i	−0.982953	+	0.183859i	$0.941141\pi$
$854$		0			0
$855$	1.26673	+	1.77888i	0.0433214	+	0.0608364i
$856$		0			0
$857$	9.63594	−	6.19264i	0.329158	−	0.211537i	−0.365615	−	0.930766i	$-0.619141\pi$
$857$	9.63594	−	6.19264i	0.329158	−	0.211537i	0.694773	+	0.719229i	$0.255505\pi$
$858$		0			0
$859$	18.5529	−	53.6052i	0.633018	−	1.82899i	0.0783319	−	0.996927i	$-0.475041\pi$
$859$	18.5529	−	53.6052i	0.633018	−	1.82899i	0.554687	−	0.832059i	$-0.312838\pi$
$860$		0			0
$861$	−25.6851	−	20.1990i	−0.875347	−	0.688381i
$862$		0			0
$863$	2.67477	−	3.08684i	0.0910501	−	0.105077i	−0.708396	−	0.705815i	$-0.750581\pi$
$863$	2.67477	−	3.08684i	0.0910501	−	0.105077i	0.799446	+	0.600738i	$0.205126\pi$
$864$		0			0
$865$	82.6671	+	7.89375i	2.81077	+	0.268396i
$866$		0			0
$867$	−12.9168	−	6.65909i	−0.438679	−	0.226155i
$868$		0			0
$869$	−8.04014	+	33.1419i	−0.272743	+	1.12426i
$870$		0			0
$871$	−6.59565	+	17.9527i	−0.223485	+	0.608304i
$872$		0			0
$873$	−0.399290	+	1.64590i	−0.0135139	+	0.0557051i
$874$		0			0
$875$	79.8842	+	41.1831i	2.70058	+	1.39224i
$876$		0			0
$877$	54.0066	+	5.15701i	1.82367	+	0.174140i	0.949975	−	0.312326i	$-0.101108\pi$
$877$	54.0066	+	5.15701i	1.82367	+	0.174140i	0.873700	+	0.486466i	$0.161714\pi$
$878$		0			0
$879$	−4.90890	+	5.66517i	−0.165573	+	0.191081i
$880$		0			0
$881$	18.5534	+	14.5905i	0.625078	+	0.491567i	0.879735	−	0.475464i	$-0.157720\pi$
$881$	18.5534	+	14.5905i	0.625078	+	0.491567i	−0.254657	+	0.967032i	$0.581962\pi$
$882$		0			0
$883$	2.39891	−	6.93119i	0.0807297	−	0.233253i	−0.897412	−	0.441194i	$-0.854555\pi$
$883$	2.39891	−	6.93119i	0.0807297	−	0.233253i	0.978141	+	0.207941i	$0.0666762\pi$
$884$		0			0
$885$	−14.5078	+	9.32357i	−0.487673	+	0.313408i
$886$		0			0
$887$	22.7765	+	31.9852i	0.764761	+	1.07396i	0.994907	+	0.100801i	$0.0321405\pi$
$887$	22.7765	+	31.9852i	0.764761	+	1.07396i	−0.230145	+	0.973156i	$0.573920\pi$
$888$		0			0
$889$	−1.71625	−	36.0286i	−0.0575612	−	1.20836i
$890$		0			0
$891$	4.13166	−	3.24917i	0.138416	−	0.108851i
$892$		0			0
$893$	0.371581	−	2.58440i	0.0124345	−	0.0864838i
$894$		0			0
$895$	−50.6148	−	32.5281i	−1.69187	−	1.08730i
$896$		0			0
$897$	0.920097	−	19.3152i	0.0307212	−	0.644916i
$898$		0			0
$899$	2.91043	+	8.40912i	0.0970681	+	0.280460i
$900$		0			0
$901$	3.96476	−	6.86716i	0.132085	−	0.228778i
$902$		0			0
$903$	30.9839	−	12.4041i	1.03108	−	0.412782i
$904$		0			0
$905$	13.4676	+	55.5141i	0.447677	+	1.84535i
$906$		0			0
$907$	3.86579	+	0.745070i	0.128361	+	0.0247396i	0.253027	−	0.967459i	$-0.418574\pi$
$907$	3.86579	+	0.745070i	0.128361	+	0.0247396i	−0.124666	+	0.992199i	$0.539786\pi$
$908$		0			0
$909$	−4.58695	−	7.94483i	−0.152140	−	0.263514i
$910$		0			0
$911$	−6.49626	−	14.2248i	−0.215231	−	0.471289i	0.770964	−	0.636878i	$-0.219775\pi$
$911$	−6.49626	−	14.2248i	−0.215231	−	0.471289i	−0.986195	+	0.165589i	$0.947047\pi$
$912$		0			0
$913$	−55.1969	−	63.7006i	−1.82675	−	2.10818i
$914$		0			0
$915$	−16.1907	−	6.48178i	−0.535248	−	0.214281i
$916$		0			0
$917$	37.6303	−	52.8444i	1.24266	−	1.74508i
$918$		0			0
$919$	−19.2184	+	18.3248i	−0.633958	+	0.604478i	−0.937350	−	0.348388i	$-0.886729\pi$
$919$	−19.2184	+	18.3248i	−0.633958	+	0.604478i	0.303392	+	0.952866i	$0.401881\pi$
$920$		0			0
$921$	−13.3969	+	6.90659i	−0.441443	+	0.227580i
$922$		0			0
$923$	−32.9866	−	9.68574i	−1.08577	−	0.318810i
$924$		0			0
$925$	−113.402	+	21.8564i	−3.72862	+	0.718633i
$926$		0			0
$927$	−6.32500	+	0.603964i	−0.207740	+	0.0198368i
$928$		0			0
$929$	10.6157	−	3.11705i	0.348289	−	0.102267i	−0.102909	−	0.994691i	$-0.532815\pi$
$929$	10.6157	−	3.11705i	0.348289	−	0.102267i	0.451198	+	0.892424i	$0.350997\pi$
$930$		0			0
$931$	−2.10358	−	2.00576i	−0.0689422	−	0.0657362i
$932$		0			0
$933$	5.11026	−	11.1899i	0.167303	−	0.366341i
$934$		0			0
$935$	−4.74754	−	33.0198i	−0.155261	−	1.07986i
$936$		0			0
$937$	−11.3025			−0.369235			−0.184618	−	0.982810i	$-0.559105\pi$
$937$	−11.3025			−0.369235			−0.184618	+	0.982810i	$0.559105\pi$
$938$		0			0
$939$	6.72543			0.219476
$940$		0			0
$941$	2.49620	+	17.3615i	0.0813740	+	0.565968i	0.989194	+	0.146609i	$0.0468360\pi$
$941$	2.49620	+	17.3615i	0.0813740	+	0.565968i	−0.907821	+	0.419359i	$0.862255\pi$
$942$		0			0
$943$	−31.9305	+	69.9180i	−1.03980	+	2.27684i
$944$		0			0
$945$	10.2871	+	9.80873i	0.334639	+	0.319078i
$946$		0			0
$947$	−41.6038	+	12.2160i	−1.35194	+	0.396966i	−0.875915	−	0.482465i	$-0.839742\pi$
$947$	−41.6038	+	12.2160i	−1.35194	+	0.396966i	−0.476027	+	0.879431i	$0.657923\pi$
$948$		0			0
$949$	−16.3378	+	1.56007i	−0.530348	+	0.0506421i
$950$		0			0
$951$	31.1612	−	6.00583i	1.01047	−	0.194752i
$952$		0			0
$953$	−13.5105	−	3.96704i	−0.437648	−	0.128505i	0.0554840	−	0.998460i	$-0.482330\pi$
$953$	−13.5105	−	3.96704i	−0.437648	−	0.128505i	−0.493132	+	0.869955i	$0.664148\pi$
$954$		0			0
$955$	−46.8911	+	24.1740i	−1.51736	+	0.782254i
$956$		0			0
$957$	4.19693	−	4.00177i	0.135668	−	0.129359i
$958$		0			0
$959$	9.51671	−	13.3644i	0.307311	−	0.431558i
$960$		0			0
$961$	31.6150	+	12.6567i	1.01984	+	0.408282i
$962$		0			0
$963$	−7.13380	−	8.23284i	−0.229883	−	0.265300i
$964$		0			0
$965$	−21.4920	−	47.0609i	−0.691851	−	1.51494i
$966$		0			0
$967$	−25.1216	−	43.5118i	−0.807855	−	1.39925i	−0.914347	−	0.404932i	$-0.867295\pi$
$967$	−25.1216	−	43.5118i	−0.807855	−	1.39925i	0.106492	−	0.994314i	$-0.466038\pi$
$968$		0			0
$969$	0.833757	+	0.160693i	0.0267841	+	0.00516222i
$970$		0			0
$971$	10.2581	+	42.2843i	0.329197	+	1.35697i	0.860355	+	0.509695i	$0.170242\pi$
$971$	10.2581	+	42.2843i	0.329197	+	1.35697i	−0.531158	+	0.847273i	$0.678243\pi$
$972$		0			0
$973$	−31.5435	+	12.6281i	−1.01124	+	0.404838i
$974$		0			0
$975$	−13.2287	+	22.9128i	−0.423658	+	0.733798i
$976$		0			0
$977$	14.5154	+	41.9395i	0.464388	+	1.34176i	0.897736	+	0.440535i	$0.145211\pi$
$977$	14.5154	+	41.9395i	0.464388	+	1.34176i	−0.433347	+	0.901227i	$0.642668\pi$
$978$		0			0
$979$	0.246159	−	5.16751i	0.00786727	−	0.165154i
$980$		0			0
$981$	−9.20439	−	5.91530i	−0.293874	−	0.188861i
$982$		0			0
$983$	−2.54786	+	17.7208i	−0.0812642	+	0.565205i	0.907989	+	0.418994i	$0.137617\pi$
$983$	−2.54786	+	17.7208i	−0.0812642	+	0.565205i	−0.989253	+	0.146211i	$0.953292\pi$
$984$		0			0
$985$	−27.2553	+	21.4338i	−0.868425	+	0.682937i
$986$		0			0
$987$	−0.808620	−	16.9750i	−0.0257387	−	0.540321i
$988$		0			0
$989$	−45.5386	−	63.9500i	−1.44804	−	2.03349i
$990$		0			0
$991$	43.4662	−	27.9341i	1.38075	−	0.887355i	0.381437	−	0.924395i	$-0.375429\pi$
$991$	43.4662	−	27.9341i	1.38075	−	0.887355i	0.999314	+	0.0370402i	$0.0117930\pi$
$992$		0			0
$993$	−2.98510	+	8.62489i	−0.0947294	+	0.273703i
$994$		0			0
$995$	−9.13551	−	7.18425i	−0.289615	−	0.227756i
$996$		0			0
$997$	−7.37835	+	8.51507i	−0.233675	+	0.269675i	−0.860461	−	0.509516i	$-0.829824\pi$
$997$	−7.37835	+	8.51507i	−0.233675	+	0.269675i	0.626786	+	0.779191i	$0.284370\pi$
$998$		0			0
$999$	−10.1533	−	0.969519i	−0.321235	−	0.0306742i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.y.b.169.1	yes	120
67.23	even	33	inner	804.2.y.b.157.1	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.y.b.157.1	✓	120	67.23	even	33	inner
804.2.y.b.169.1	yes	120	1.1	even	1	trivial

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.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.142315 + 0.989821i) q^{3} +(-1.67835 + 3.67507i) q^{5} +(2.54620 + 2.42780i) q^{7} +(-0.959493 + 0.281733i) q^{9} +O(q^{10})\)	\(q+(0.142315 + 0.989821i) q^{3} +(-1.67835 + 3.67507i) q^{5} +(2.54620 + 2.42780i) q^{7} +(-0.959493 + 0.281733i) q^{9} +(5.23241 - 0.499635i) q^{11} +(-2.29438 + 0.442205i) q^{13} +(-3.87652 - 1.13825i) q^{15} +(-1.39626 + 0.719822i) q^{17} +(-0.391195 + 0.373004i) q^{19} +(-2.04072 + 2.86579i) q^{21} +(7.68293 + 3.07578i) q^{23} +(-7.41501 - 8.55738i) q^{25} +(-0.415415 - 0.909632i) q^{27} +(-0.551633 - 0.955456i) q^{29} +(-7.91988 - 1.52643i) q^{31} +(1.23920 + 5.10805i) q^{33} +(-13.1957 + 5.28278i) q^{35} +(5.09972 - 8.83298i) q^{37} +(-0.764229 - 2.20809i) q^{39} +(-0.441935 + 9.27736i) q^{41} +(-7.98049 - 5.12875i) q^{43} +(0.574977 - 3.99905i) q^{45} +(-3.79700 + 2.98600i) q^{47} +(0.255863 + 5.37124i) q^{49} +(-0.911204 - 1.27961i) q^{51} +(-4.24648 + 2.72905i) q^{53} +(-6.94562 + 20.0681i) q^{55} +(-0.424880 - 0.334129i) q^{57} +(2.79526 - 3.22590i) q^{59} +(4.29709 + 0.410322i) q^{61} +(-3.12705 - 1.61211i) q^{63} +(2.22563 - 9.17419i) q^{65} +(4.22580 - 7.01018i) q^{67} +(-1.95108 + 8.04245i) q^{69} +(13.0777 + 6.74203i) q^{71} +(6.99211 + 0.667666i) q^{73} +(7.41501 - 8.55738i) q^{75} +(14.5358 + 11.4311i) q^{77} +(-2.12207 + 6.13133i) q^{79} +(0.841254 - 0.540641i) q^{81} +(-9.30173 - 13.0624i) q^{83} +(-0.301986 - 6.33947i) q^{85} +(0.867226 - 0.681994i) q^{87} +(0.140072 - 0.974221i) q^{89} +(-6.91553 - 4.44434i) q^{91} +(0.383778 - 8.05650i) q^{93} +(-0.714254 - 2.06370i) q^{95} +(0.846818 - 1.46673i) q^{97} +(-4.87970 + 1.95354i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9}+O(q^{10}) \) 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9	\( 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9} + 11 q^{11} + 2 q^{13} - 9 q^{15} + 48 q^{17} - 4 q^{19} - q^{21} + 22 q^{23} - 42 q^{25} + 12 q^{27} - q^{29} + 27 q^{31} + 17 q^{35} - 8 q^{37} - 2 q^{39} - 58 q^{41} - 17 q^{43} - 2 q^{45} - 84 q^{47} + 101 q^{49} - 26 q^{51} + 28 q^{53} - 9 q^{55} + 26 q^{57} + 34 q^{59} + 16 q^{61} + 12 q^{63} + 144 q^{65} + 23 q^{67} + 11 q^{69} + 173 q^{71} - 2 q^{73} + 42 q^{75} + 128 q^{77} + 31 q^{79} - 12 q^{81} + 47 q^{83} - 75 q^{85} - 10 q^{87} - 67 q^{89} + 16 q^{91} + 6 q^{93} - 79 q^{95} + 10 q^{97}+O(q^{100}) \) 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9 + 11 * q^11 + 2 * q^13 - 9 * q^15 + 48 * q^17 - 4 * q^19 - q^21 + 22 * q^23 - 42 * q^25 + 12 * q^27 - q^29 + 27 * q^31 + 17 * q^35 - 8 * q^37 - 2 * q^39 - 58 * q^41 - 17 * q^43 - 2 * q^45 - 84 * q^47 + 101 * q^49 - 26 * q^51 + 28 * q^53 - 9 * q^55 + 26 * q^57 + 34 * q^59 + 16 * q^61 + 12 * q^63 + 144 * q^65 + 23 * q^67 + 11 * q^69 + 173 * q^71 - 2 * q^73 + 42 * q^75 + 128 * q^77 + 31 * q^79 - 12 * q^81 + 47 * q^83 - 75 * q^85 - 10 * q^87 - 67 * q^89 + 16 * q^91 + 6 * q^93 - 79 * q^95 + 10 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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