LMFDB - Embedded newform 804.2.y.a.157.4

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:	$100$
Relative dimension:	$5$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			157.4
Character	$\chi$	$=$	804.157
Dual form			804.2.y.a.169.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 + 0.989821i) q^{3} +(0.716491 + 1.56890i) q^{5} +(0.876788 - 0.836015i) q^{7} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})$	\(q+(-0.142315 + 0.989821i) q^{3} +(0.716491 + 1.56890i) q^{5} +(0.876788 - 0.836015i) q^{7} +(-0.959493 - 0.281733i) q^{9} +(1.67399 + 0.159847i) q^{11} +(-2.11866 - 0.408339i) q^{13} +(-1.65490 + 0.485921i) q^{15} +(4.66679 + 2.40590i) q^{17} +(5.79438 + 5.52493i) q^{19} +(0.702726 + 0.986841i) q^{21} +(0.0433153 - 0.0173408i) q^{23} +(1.32622 - 1.53054i) q^{25} +(0.415415 - 0.909632i) q^{27} +(-4.62547 + 8.01155i) q^{29} +(-5.76539 + 1.11119i) q^{31} +(-0.396454 + 1.63421i) q^{33} +(1.93983 + 0.776592i) q^{35} +(-3.79865 - 6.57946i) q^{37} +(0.705699 - 2.03898i) q^{39} +(-0.368903 - 7.74423i) q^{41} +(-8.13854 + 5.23032i) q^{43} +(-0.245459 - 1.70720i) q^{45} +(8.61679 + 6.77632i) q^{47} +(-0.263238 + 5.52606i) q^{49} +(-3.04556 + 4.27689i) q^{51} +(4.29204 + 2.75832i) q^{53} +(0.948618 + 2.74085i) q^{55} +(-6.29332 + 4.94912i) q^{57} +(3.24071 + 3.73998i) q^{59} +(-13.0837 + 1.24934i) q^{61} +(-1.07680 + 0.555131i) q^{63} +(-0.877361 - 3.61653i) q^{65} +(7.58805 + 3.06945i) q^{67} +(0.0109999 + 0.0453423i) q^{69} +(3.83840 - 1.97884i) q^{71} +(12.8427 - 1.22633i) q^{73} +(1.32622 + 1.53054i) q^{75} +(1.60137 - 1.25933i) q^{77} +(1.13203 + 3.27078i) q^{79} +(0.841254 + 0.540641i) q^{81} +(5.09407 - 7.15362i) q^{83} +(-0.430891 + 9.04552i) q^{85} +(-7.27173 - 5.71855i) q^{87} +(-1.66627 - 11.5892i) q^{89} +(-2.19899 + 1.41321i) q^{91} +(-0.279377 - 5.86485i) q^{93} +(-4.51642 + 13.0493i) q^{95} +(-7.42685 - 12.8637i) q^{97} +(-1.56115 - 0.624990i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q - 10 q^{3} + 2 q^{5} - 3 q^{7} - 10 q^{9}+O(q^{10}) $ 100 * q - 10 * q^3 + 2 * q^5 - 3 * q^7 - 10 * q^9	$ 100 q - 10 q^{3} + 2 q^{5} - 3 q^{7} - 10 q^{9} - 13 q^{11} - 3 q^{13} - 9 q^{15} - 44 q^{17} - 16 q^{19} - 3 q^{21} - 16 q^{23} + 28 q^{25} - 10 q^{27} - 7 q^{29} + 20 q^{31} - 2 q^{33} - 19 q^{35} - 22 q^{37} - 3 q^{39} - 14 q^{41} - 27 q^{43} + 2 q^{45} + 4 q^{47} - 92 q^{49} + 22 q^{51} + 8 q^{53} - 13 q^{55} + 17 q^{57} + 22 q^{59} + 17 q^{61} - 3 q^{63} + 56 q^{65} - 14 q^{67} + 17 q^{69} - q^{71} + 26 q^{73} + 28 q^{75} + 112 q^{77} + 69 q^{79} - 10 q^{81} + 15 q^{83} + 69 q^{85} + 4 q^{87} + 73 q^{89} - 40 q^{91} - 13 q^{93} + 59 q^{95} + 29 q^{97} - 2 q^{99}+O(q^{100}) $ 100 * q - 10 * q^3 + 2 * q^5 - 3 * q^7 - 10 * q^9 - 13 * q^11 - 3 * q^13 - 9 * q^15 - 44 * q^17 - 16 * q^19 - 3 * q^21 - 16 * q^23 + 28 * q^25 - 10 * q^27 - 7 * q^29 + 20 * q^31 - 2 * q^33 - 19 * q^35 - 22 * q^37 - 3 * q^39 - 14 * q^41 - 27 * q^43 + 2 * q^45 + 4 * q^47 - 92 * q^49 + 22 * q^51 + 8 * q^53 - 13 * q^55 + 17 * q^57 + 22 * q^59 + 17 * q^61 - 3 * q^63 + 56 * q^65 - 14 * q^67 + 17 * q^69 - q^71 + 26 * q^73 + 28 * q^75 + 112 * q^77 + 69 * q^79 - 10 * q^81 + 15 * q^83 + 69 * q^85 + 4 * q^87 + 73 * q^89 - 40 * q^91 - 13 * q^93 + 59 * q^95 + 29 * q^97 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{14}{33}\right)$	$1$

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
$5$	0.716491	+	1.56890i	0.320425	+	0.701632i	0.999473	−	0.0324614i	$-0.0103346\pi$
$5$	0.716491	+	1.56890i	0.320425	+	0.701632i	−0.679048	+	0.734094i	$0.737607\pi$
$6$		0			0
$7$	0.876788	−	0.836015i	0.331395	−	0.315984i	−0.506052	−	0.862503i	$-0.668896\pi$
$7$	0.876788	−	0.836015i	0.331395	−	0.315984i	0.837447	+	0.546519i	$0.184047\pi$
$8$		0			0
$9$	−0.959493	−	0.281733i	−0.319831	−	0.0939109i
$10$		0			0
$11$	1.67399	+	0.159847i	0.504728	+	0.0481957i	0.344315	−	0.938854i	$-0.388111\pi$
$11$	1.67399	+	0.159847i	0.504728	+	0.0481957i	0.160413	+	0.987050i	$0.448717\pi$
$12$		0			0
$13$	−2.11866	−	0.408339i	−0.587611	−	0.113253i	−0.113224	−	0.993569i	$-0.536118\pi$
$13$	−2.11866	−	0.408339i	−0.587611	−	0.113253i	−0.474386	+	0.880317i	$0.657330\pi$
$14$		0			0
$15$	−1.65490	+	0.485921i	−0.427292	+	0.125464i
$16$		0			0
$17$	4.66679	+	2.40590i	1.13186	+	0.583516i	0.919271	−	0.393625i	$-0.128779\pi$
$17$	4.66679	+	2.40590i	1.13186	+	0.583516i	0.212592	+	0.977141i	$0.431810\pi$
$18$		0			0
$19$	5.79438	+	5.52493i	1.32932	+	1.26751i	0.937730	+	0.347366i	$0.112924\pi$
$19$	5.79438	+	5.52493i	1.32932	+	1.26751i	0.391592	+	0.920139i	$0.371925\pi$
$20$		0			0
$21$	0.702726	+	0.986841i	0.153347	+	0.215346i
$22$		0			0
$23$	0.0433153	−	0.0173408i	0.00903187	−	0.00361582i	−0.367142	−	0.930165i	$-0.619664\pi$
$23$	0.0433153	−	0.0173408i	0.00903187	−	0.00361582i	0.376174	+	0.926549i	$0.377239\pi$
$24$		0			0
$25$	1.32622	−	1.53054i	0.265245	−	0.306109i
$26$		0			0
$27$	0.415415	−	0.909632i	0.0799467	−	0.175059i
$28$		0			0
$29$	−4.62547	+	8.01155i	−0.858928	+	1.48771i	0.0140239	+	0.999902i	$0.495536\pi$
$29$	−4.62547	+	8.01155i	−0.858928	+	1.48771i	−0.872952	+	0.487806i	$0.837797\pi$
$30$		0			0
$31$	−5.76539	+	1.11119i	−1.03549	+	0.199575i	−0.678553	−	0.734551i	$-0.737393\pi$
$31$	−5.76539	+	1.11119i	−1.03549	+	0.199575i	−0.356942	+	0.934127i	$0.616181\pi$
$32$		0			0
$33$	−0.396454	+	1.63421i	−0.0690138	+	0.284479i
$34$		0			0
$35$	1.93983	+	0.776592i	0.327892	+	0.131268i
$36$		0			0
$37$	−3.79865	−	6.57946i	−0.624495	−	1.08166i	−0.988638	−	0.150314i	$-0.951972\pi$
$37$	−3.79865	−	6.57946i	−0.624495	−	1.08166i	0.364144	−	0.931343i	$-0.381362\pi$
$38$		0			0
$39$	0.705699	−	2.03898i	0.113002	−	0.326499i
$40$		0			0
$41$	−0.368903	−	7.74423i	−0.0576130	−	1.20945i	−0.823820	−	0.566852i	$-0.808161\pi$
$41$	−0.368903	−	7.74423i	−0.0576130	−	1.20945i	0.766207	−	0.642594i	$-0.222142\pi$
$42$		0			0
$43$	−8.13854	+	5.23032i	−1.24112	+	0.797616i	−0.985584	−	0.169184i	$-0.945887\pi$
$43$	−8.13854	+	5.23032i	−1.24112	+	0.797616i	−0.255531	+	0.966801i	$0.582250\pi$
$44$		0			0
$45$	−0.245459	−	1.70720i	−0.0365909	−	0.254495i
$46$		0			0
$47$	8.61679	+	6.77632i	1.25689	+	0.988428i	0.999757	+	0.0220515i	$0.00701978\pi$
$47$	8.61679	+	6.77632i	1.25689	+	0.988428i	0.257132	+	0.966376i	$0.417223\pi$
$48$		0			0
$49$	−0.263238	+	5.52606i	−0.0376055	+	0.789437i
$50$		0			0
$51$	−3.04556	+	4.27689i	−0.426464	+	0.598885i
$52$		0			0
$53$	4.29204	+	2.75832i	0.589557	+	0.378885i	0.801142	−	0.598475i	$-0.204226\pi$
$53$	4.29204	+	2.75832i	0.589557	+	0.378885i	−0.211585	+	0.977360i	$0.567863\pi$
$54$		0			0
$55$	0.948618	+	2.74085i	0.127912	+	0.369576i
$56$		0			0
$57$	−6.29332	+	4.94912i	−0.833570	+	0.655527i
$58$		0			0
$59$	3.24071	+	3.73998i	0.421905	+	0.486904i	0.926416	−	0.376501i	$-0.122873\pi$
$59$	3.24071	+	3.73998i	0.421905	+	0.486904i	−0.504512	+	0.863405i	$0.668327\pi$
$60$		0			0
$61$	−13.0837	+	1.24934i	−1.67519	+	0.159961i	−0.888964	−	0.457976i	$-0.848574\pi$
$61$	−13.0837	+	1.24934i	−1.67519	+	0.159961i	−0.786227	+	0.617938i	$0.787968\pi$
$62$		0			0
$63$	−1.07680	+	0.555131i	−0.135665	+	0.0699400i
$64$		0			0
$65$	−0.877361	−	3.61653i	−0.108823	−	0.448576i
$66$		0			0
$67$	7.58805	+	3.06945i	0.927028	+	0.374993i
$67$	7.58805	+	3.06945i	0.927028	+	0.374993i
$68$		0			0
$69$	0.0109999	+	0.0453423i	0.00132424	+	0.00545857i
$70$		0			0
$71$	3.83840	−	1.97884i	0.455535	−	0.234845i	−0.215159	−	0.976579i	$-0.569027\pi$
$71$	3.83840	−	1.97884i	0.455535	−	0.234845i	0.670694	+	0.741735i	$0.265997\pi$
$72$		0			0
$73$	12.8427	−	1.22633i	1.50313	−	0.143531i	0.689231	−	0.724541i	$-0.257948\pi$
$73$	12.8427	−	1.22633i	1.50313	−	0.143531i	0.813896	+	0.581010i	$0.197342\pi$
$74$		0			0
$75$	1.32622	+	1.53054i	0.153139	+	0.176732i
$76$		0			0
$77$	1.60137	−	1.25933i	0.182493	−	0.143514i
$78$		0			0
$79$	1.13203	+	3.27078i	0.127363	+	0.367991i	0.990597	−	0.136813i	$-0.0436860\pi$
$79$	1.13203	+	3.27078i	0.127363	+	0.367991i	−0.863234	+	0.504804i	$0.831565\pi$
$80$		0			0
$81$	0.841254	+	0.540641i	0.0934726	+	0.0600712i
$82$		0			0
$83$	5.09407	−	7.15362i	0.559147	−	0.785211i	−0.434146	−	0.900843i	$-0.642950\pi$
$83$	5.09407	−	7.15362i	0.559147	−	0.785211i	0.993292	+	0.115631i	$0.0368891\pi$
$84$		0			0
$85$	−0.430891	+	9.04552i	−0.0467367	+	0.981124i
$86$		0			0
$87$	−7.27173	−	5.71855i	−0.779611	−	0.613093i
$88$		0			0
$89$	−1.66627	−	11.5892i	−0.176624	−	1.22845i	−0.864505	−	0.502625i	$-0.832368\pi$
$89$	−1.66627	−	11.5892i	−0.176624	−	1.22845i	0.687881	−	0.725824i	$-0.258541\pi$
$90$		0			0
$91$	−2.19899	+	1.41321i	−0.230517	+	0.148144i
$92$		0			0
$93$	−0.279377	−	5.86485i	−0.0289701	−	0.608156i
$94$		0			0
$95$	−4.51642	+	13.0493i	−0.463375	+	1.33883i
$96$		0			0
$97$	−7.42685	−	12.8637i	−0.754082	−	1.30611i	−0.945829	−	0.324664i	$-0.894749\pi$
$97$	−7.42685	−	12.8637i	−0.754082	−	1.30611i	0.191747	−	0.981444i	$-0.438585\pi$
$98$		0			0
$99$	−1.56115	−	0.624990i	−0.156902	−	0.0628139i
$100$		0			0
$101$	4.46791	−	18.4170i	0.444574	−	1.83256i	−0.101517	−	0.994834i	$-0.532370\pi$
$101$	4.46791	−	18.4170i	0.444574	−	1.83256i	0.546091	−	0.837726i	$-0.316115\pi$
$102$		0			0
$103$	−3.05043	+	0.587922i	−0.300568	+	0.0579297i	−0.337305	−	0.941395i	$-0.609516\pi$
$103$	−3.05043	+	0.587922i	−0.300568	+	0.0579297i	0.0367377	+	0.999325i	$0.488303\pi$
$104$		0			0
$105$	−1.04475	+	1.80957i	−0.101958	+	0.176596i
$106$		0			0
$107$	−7.38237	+	16.1651i	−0.713680	+	1.56274i	0.108874	+	0.994056i	$0.465276\pi$
$107$	−7.38237	+	16.1651i	−0.713680	+	1.56274i	−0.822554	+	0.568687i	$0.807452\pi$
$108$		0			0
$109$	1.96321	−	2.26566i	0.188041	−	0.217011i	−0.653899	−	0.756582i	$-0.726868\pi$
$109$	1.96321	−	2.26566i	0.188041	−	0.217011i	0.841940	+	0.539571i	$0.181413\pi$
$110$		0			0
$111$	7.05310	−	2.82363i	0.669450	−	0.268007i
$112$		0			0
$113$	4.69804	+	6.59747i	0.441954	+	0.620638i	0.974128	−	0.225997i	$-0.0725641\pi$
$113$	4.69804	+	6.59747i	0.441954	+	0.620638i	−0.532174	+	0.846635i	$0.678625\pi$
$114$		0			0
$115$	0.0582411	+	0.0555328i	0.00543101	+	0.00517846i
$116$		0			0
$117$	1.91780	+	0.988694i	0.177301	+	0.0914048i
$118$		0			0
$119$	6.10315	−	1.79205i	0.559475	−	0.164277i
$120$		0			0
$121$	−8.02451	−	1.54660i	−0.729501	−	0.140600i
$122$		0			0
$123$	7.71791	+	0.736971i	0.695900	+	0.0664504i
$124$		0			0
$125$	11.6260	+	3.41369i	1.03986	+	0.305330i
$126$		0			0
$127$	7.82279	−	7.45901i	0.694160	−	0.661880i	−0.258467	−	0.966020i	$-0.583217\pi$
$127$	7.82279	−	7.45901i	0.694160	−	0.661880i	0.952627	+	0.304140i	$0.0983690\pi$
$128$		0			0
$129$	−4.01885	−	8.80005i	−0.353840	−	0.774801i
$130$		0			0
$131$	0.546620	−	3.80183i	0.0477584	−	0.332167i	−0.951909	−	0.306381i	$-0.900882\pi$
$131$	0.546620	−	3.80183i	0.0477584	−	0.332167i	0.999667	−	0.0257864i	$-0.00820898\pi$
$132$		0			0
$133$	9.69936			0.841041
$134$		0			0
$135$	1.72476			0.148444
$136$		0			0
$137$	2.26955	−	15.7851i	0.193901	−	1.34861i	−0.627658	−	0.778489i	$-0.715986\pi$
$137$	2.26955	−	15.7851i	0.193901	−	1.34861i	0.821559	−	0.570123i	$-0.193104\pi$
$138$		0			0
$139$	−3.38632	−	7.41500i	−0.287224	−	0.628932i	0.709935	−	0.704268i	$-0.248724\pi$
$139$	−3.38632	−	7.41500i	−0.287224	−	0.628932i	−0.997158	+	0.0753356i	$0.975997\pi$
$140$		0			0
$141$	−7.93364	+	7.56471i	−0.668133	+	0.637064i
$142$		0			0
$143$	−3.48135	−	1.02222i	−0.291125	−	0.0854821i
$144$		0			0
$145$	−15.8834	−	1.51668i	−1.31905	−	0.125954i
$146$		0			0
$147$	−5.43235	−	1.04700i	−0.448052	−	0.0863550i
$148$		0			0
$149$	17.8169	−	5.23151i	1.45962	−	0.428582i	0.546907	−	0.837193i	$-0.315805\pi$
$149$	17.8169	−	5.23151i	1.45962	−	0.428582i	0.912708	+	0.408612i	$0.133987\pi$
$150$		0			0
$151$	−3.66235	−	1.88807i	−0.298037	−	0.153649i	0.302722	−	0.953079i	$-0.402105\pi$
$151$	−3.66235	−	1.88807i	−0.298037	−	0.153649i	−0.600759	+	0.799430i	$0.705135\pi$
$152$		0			0
$153$	−3.79993	−	3.62323i	−0.307206	−	0.292921i
$154$		0			0
$155$	−5.87419	−	8.24915i	−0.471827	−	0.662588i
$156$		0			0
$157$	−15.6601	+	6.26938i	−1.24982	+	0.500351i	−0.899763	−	0.436379i	$-0.856261\pi$
$157$	−15.6601	+	6.26938i	−1.24982	+	0.500351i	−0.350053	+	0.936730i	$0.613836\pi$
$158$		0			0
$159$	−3.34107	+	3.85580i	−0.264964	+	0.305785i
$160$		0			0
$161$	0.0234811	−	0.0514165i	0.00185057	−	0.00405219i
$162$		0			0
$163$	1.74200	−	3.01723i	0.136444	−	0.236328i	−0.789704	−	0.613488i	$-0.789766\pi$
$163$	1.74200	−	3.01723i	0.136444	−	0.236328i	0.926148	+	0.377160i	$0.123099\pi$
$164$		0			0
$165$	−2.84796	+	0.548899i	−0.221713	+	0.0427317i
$166$		0			0
$167$	0.193898	−	0.799260i	0.0150043	−	0.0618486i	−0.963817	−	0.266564i	$-0.914112\pi$
$167$	0.193898	−	0.799260i	0.0150043	−	0.0618486i	0.978822	+	0.204715i	$0.0656268\pi$
$168$		0			0
$169$	−7.74680	−	3.10135i	−0.595907	−	0.238565i
$170$		0			0
$171$	−4.00311	−	6.93359i	−0.306126	−	0.530225i
$172$		0			0
$173$	0.0427964	−	0.123652i	0.00325375	−	0.00940108i	−0.943362	−	0.331764i	$-0.892356\pi$
$173$	0.0427964	−	0.123652i	0.00325375	−	0.00940108i	0.946616	+	0.322363i	$0.104477\pi$
$174$		0			0
$175$	−0.116742	−	2.45071i	−0.00882483	−	0.185256i
$176$		0			0
$177$	−4.16311	+	2.67547i	−0.312919	+	0.201101i
$178$		0			0
$179$	−1.15135	−	8.00783i	−0.0860561	−	0.598533i	−0.986525	−	0.163612i	$-0.947685\pi$
$179$	−1.15135	−	8.00783i	−0.0860561	−	0.598533i	0.900469	−	0.434921i	$-0.143224\pi$
$180$		0			0
$181$	−1.28979	−	1.01430i	−0.0958694	−	0.0753925i	0.569074	−	0.822286i	$-0.307302\pi$
$181$	−1.28979	−	1.01430i	−0.0958694	−	0.0753925i	−0.664943	+	0.746894i	$0.731544\pi$
$182$		0			0
$183$	0.625378	−	13.1283i	0.0462292	−	0.970471i
$184$		0			0
$185$	7.60080	−	10.6738i	0.558822	−	0.784755i
$186$		0			0
$187$	7.42760	+	4.77343i	0.543160	+	0.349068i
$188$		0			0
$189$	−0.396236	−	1.14485i	−0.0288219	−	0.0832754i
$190$		0			0
$191$	13.6775	−	10.7561i	0.989666	−	0.778282i	0.0145315	−	0.999894i	$-0.495374\pi$
$191$	13.6775	−	10.7561i	0.989666	−	0.778282i	0.975135	+	0.221612i	$0.0711319\pi$
$192$		0			0
$193$	−10.8495	−	12.5210i	−0.780966	−	0.901283i	0.216213	−	0.976346i	$-0.430630\pi$
$193$	−10.8495	−	12.5210i	−0.780966	−	0.901283i	−0.997179	+	0.0750635i	$0.976084\pi$
$194$		0			0
$195$	3.70458	−	0.353745i	0.265291	−	0.0253322i
$196$		0			0
$197$	−9.08214	+	4.68217i	−0.647076	+	0.333591i	−0.750329	−	0.661064i	$-0.770105\pi$
$197$	−9.08214	+	4.68217i	−0.647076	+	0.333591i	0.103253	+	0.994655i	$0.467075\pi$
$198$		0			0
$199$	0.999843	+	4.12141i	0.0708770	+	0.292159i	0.996208	−	0.0870007i	$-0.0277283\pi$
$199$	0.999843	+	4.12141i	0.0708770	+	0.292159i	−0.925331	+	0.379160i	$0.876213\pi$
$200$		0			0
$201$	−4.11810	+	7.07399i	−0.290468	+	0.498960i
$202$		0			0
$203$	2.64222	+	10.8914i	0.185448	+	0.764426i
$204$		0			0
$205$	11.8856	−	6.12745i	0.830126	−	0.427959i
$206$		0			0
$207$	−0.0464462	+	0.00443508i	−0.00322824	+	0.000308259i
$208$		0			0
$209$	8.81660	+	10.1749i	0.609857	+	0.703813i
$210$		0			0
$211$	11.9840	−	9.42431i	0.825012	−	0.648796i	−0.113694	−	0.993516i	$-0.536268\pi$
$211$	11.9840	−	9.42431i	0.825012	−	0.648796i	0.938706	+	0.344719i	$0.112026\pi$
$212$		0			0
$213$	1.41243	+	4.08095i	0.0967782	+	0.279622i
$214$		0			0
$215$	−14.0370	−	9.02105i	−0.957317	−	0.615231i
$216$		0			0
$217$	−4.12605	+	5.79423i	−0.280095	+	0.393338i
$218$		0			0
$219$	−0.613861	+	12.8865i	−0.0414809	+	0.870791i
$220$		0			0
$221$	−8.90493	−	7.00291i	−0.599010	−	0.471067i
$222$		0			0
$223$	1.13685	+	7.90694i	0.0761288	+	0.529488i	0.991824	+	0.127614i	$0.0407318\pi$
$223$	1.13685	+	7.90694i	0.0761288	+	0.529488i	−0.915695	+	0.401874i	$0.868359\pi$
$224$		0			0
$225$	−1.70371	+	1.09491i	−0.113581	+	0.0729938i
$226$		0			0
$227$	0.908781	+	19.0777i	0.0603179	+	1.26623i	0.802753	+	0.596311i	$0.203368\pi$
$227$	0.908781	+	19.0777i	0.0603179	+	1.26623i	−0.742435	+	0.669918i	$0.766329\pi$
$228$		0			0
$229$	6.33089	−	18.2919i	0.418357	−	1.20876i	−0.517285	−	0.855813i	$-0.673057\pi$
$229$	6.33089	−	18.2919i	0.418357	−	1.20876i	0.935642	−	0.352950i	$-0.114822\pi$
$230$		0			0
$231$	1.01861	+	1.76429i	0.0670199	+	0.116082i
$232$		0			0
$233$	20.0956	+	8.04506i	1.31651	+	0.527050i	0.920336	−	0.391128i	$-0.127915\pi$
$233$	20.0956	+	8.04506i	1.31651	+	0.527050i	0.396170	+	0.918177i	$0.370339\pi$
$234$		0			0
$235$	−4.45749	+	18.3740i	−0.290775	+	1.19859i
$236$		0			0
$237$	−3.39859	+	0.655024i	−0.220762	+	0.0425484i
$238$		0			0
$239$	−1.21384	+	2.10243i	−0.0785166	+	0.135995i	−0.902610	−	0.430459i	$-0.858352\pi$
$239$	−1.21384	+	2.10243i	−0.0785166	+	0.135995i	0.824094	+	0.566454i	$0.191685\pi$
$240$		0			0
$241$	8.41300	−	18.4219i	0.541929	−	1.18666i	−0.418522	−	0.908207i	$-0.637452\pi$
$241$	8.41300	−	18.4219i	0.541929	−	1.18666i	0.960450	−	0.278452i	$-0.0898212\pi$
$242$		0			0
$243$	−0.654861	+	0.755750i	−0.0420093	+	0.0484814i
$244$		0			0
$245$	−8.85842	+	3.54638i	−0.565944	+	0.226570i
$246$		0			0
$247$	−10.0203	−	14.0715i	−0.637575	−	0.895349i
$248$		0			0
$249$	6.35584	+	6.06028i	0.402785	+	0.384055i
$250$		0			0
$251$	3.14135	+	1.61948i	0.198280	+	0.102221i	0.554507	−	0.832179i	$-0.312907\pi$
$251$	3.14135	+	1.61948i	0.198280	+	0.102221i	−0.356227	+	0.934399i	$0.615937\pi$
$252$		0			0
$253$	0.0752815	−	0.0221046i	0.00473290	−	0.00138971i
$254$		0			0
$255$	−8.89213	−	1.71382i	−0.556847	−	0.107323i
$256$		0			0
$257$	0.684894	+	0.0653994i	0.0427225	+	0.00407950i	0.116395	−	0.993203i	$-0.462866\pi$
$257$	0.684894	+	0.0653994i	0.0427225	+	0.00407950i	−0.0736729	+	0.997282i	$0.523472\pi$
$258$		0			0
$259$	−8.83114	−	2.59306i	−0.548740	−	0.161125i
$260$		0			0
$261$	6.69522	−	6.38388i	0.414424	−	0.395152i
$262$		0			0
$263$	−5.24072	−	11.4756i	−0.323157	−	0.707614i	0.676426	−	0.736511i	$-0.263528\pi$
$263$	−5.24072	−	11.4756i	−0.323157	−	0.707614i	−0.999582	+	0.0288965i	$0.990801\pi$
$264$		0			0
$265$	−1.25232	+	8.71008i	−0.0769294	+	0.535056i
$266$		0			0
$267$	11.7083			0.716538
$268$		0			0
$269$	−23.7264			−1.44663			−0.723313	−	0.690521i	$-0.757381\pi$
$269$	−23.7264			−1.44663			−0.723313	+	0.690521i	$0.757381\pi$
$270$		0			0
$271$	3.32935	−	23.1561i	0.202243	−	1.40663i	−0.595364	−	0.803456i	$-0.702992\pi$
$271$	3.32935	−	23.1561i	0.202243	−	1.40663i	0.797607	−	0.603177i	$-0.206099\pi$
$272$		0			0
$273$	−1.08587	−	2.37773i	−0.0657200	−	0.143907i
$274$		0			0
$275$	2.46474	−	2.35013i	0.148630	−	0.141718i
$276$		0			0
$277$	−7.42564	−	2.18036i	−0.446163	−	0.131005i	0.0509304	−	0.998702i	$-0.483781\pi$
$277$	−7.42564	−	2.18036i	−0.446163	−	0.131005i	−0.497094	+	0.867697i	$0.665600\pi$
$278$		0			0
$279$	5.84491	+	0.558121i	0.349926	+	0.0334138i
$280$		0			0
$281$	−15.6492	−	3.01614i	−0.933555	−	0.179928i	−0.300277	−	0.953852i	$-0.597079\pi$
$281$	−15.6492	−	3.01614i	−0.933555	−	0.179928i	−0.633278	+	0.773924i	$0.718291\pi$
$282$		0			0
$283$	24.9902	−	7.33780i	1.48552	−	0.436187i	0.564408	−	0.825496i	$-0.309104\pi$
$283$	24.9902	−	7.33780i	1.48552	−	0.436187i	0.921107	+	0.389309i	$0.127286\pi$
$284$		0			0
$285$	−12.2738	−	6.32757i	−0.727035	−	0.374813i
$286$		0			0
$287$	−6.79775	−	6.48164i	−0.401258	−	0.382599i
$288$		0			0
$289$	6.12961	+	8.60784i	0.360566	+	0.506344i
$290$		0			0
$291$	13.7897	−	5.52056i	0.808366	−	0.323621i
$292$		0			0
$293$	−7.66469	+	8.84552i	−0.447776	+	0.516761i	−0.934097	−	0.357019i	$-0.883793\pi$
$293$	−7.66469	+	8.84552i	−0.447776	+	0.516761i	0.486321	+	0.873780i	$0.338339\pi$
$294$		0			0
$295$	−3.54570	+	7.76401i	−0.206439	+	0.452038i
$296$		0			0
$297$	0.840804	−	1.45631i	0.0487884	−	0.0845039i
$298$		0			0
$299$	−0.0988515	+	0.0190521i	−0.00571673	+	0.00110181i
$300$		0			0
$301$	−2.76314	+	11.3898i	−0.159265	+	0.656498i
$302$		0			0
$303$	17.5937	+	7.04345i	1.01073	+	0.404636i
$304$		0			0
$305$	−11.3344	−	19.6318i	−0.649007	−	1.12411i
$306$		0			0
$307$	−2.03524	+	5.88044i	−0.116157	+	0.335615i	−0.988061	−	0.154063i	$-0.950764\pi$
$307$	−2.03524	+	5.88044i	−0.116157	+	0.335615i	0.871904	+	0.489677i	$0.162885\pi$
$308$		0			0
$309$	−0.147817	−	3.10305i	−0.00840899	−	0.176526i
$310$		0			0
$311$	1.04785	−	0.673415i	0.0594183	−	0.0381859i	−0.510594	−	0.859822i	$-0.670575\pi$
$311$	1.04785	−	0.673415i	0.0594183	−	0.0381859i	0.570013	+	0.821636i	$0.306938\pi$
$312$		0			0
$313$	2.91117	+	20.2477i	0.164549	+	1.14447i	0.889923	+	0.456110i	$0.150758\pi$
$313$	2.91117	+	20.2477i	0.164549	+	1.14447i	−0.725374	+	0.688355i	$0.758333\pi$
$314$		0			0
$315$	−1.64246	−	1.29165i	−0.0925424	−	0.0727762i
$316$		0			0
$317$	−1.09006	+	22.8832i	−0.0612238	+	1.28525i	0.734092	+	0.679050i	$0.237608\pi$
$317$	−1.09006	+	22.8832i	−0.0612238	+	1.28525i	−0.795315	+	0.606196i	$0.792695\pi$
$318$		0			0
$319$	−9.02363	+	12.6719i	−0.505226	+	0.709491i
$320$		0			0
$321$	−14.9500	−	9.60776i	−0.834426	−	0.536253i
$322$		0			0
$323$	13.7487	+	39.7243i	0.765000	+	2.21032i
$324$		0			0
$325$	−3.43480	+	2.70116i	−0.190529	+	0.149833i
$326$		0			0
$327$	1.96321	+	2.26566i	0.108566	+	0.125291i
$328$		0			0
$329$	13.2202	−	1.26238i	0.728853	−	0.0695971i
$330$		0			0
$331$	16.8535	−	8.68856i	0.926350	−	0.477567i	0.0720816	−	0.997399i	$-0.477036\pi$
$331$	16.8535	−	8.68856i	0.926350	−	0.477567i	0.854268	+	0.519832i	$0.174005\pi$
$332$		0			0
$333$	1.79113	+	7.38315i	0.0981535	+	0.404594i
$334$		0			0
$335$	0.621123	+	14.1041i	0.0339356	+	0.770589i
$336$		0			0
$337$	−0.895578	−	3.69162i	−0.0487852	−	0.201096i	0.942203	−	0.335041i	$-0.108750\pi$
$337$	−0.895578	−	3.69162i	−0.0487852	−	0.201096i	−0.990989	+	0.133946i	$0.957235\pi$
$338$		0			0
$339$	−7.19892	+	3.71130i	−0.390992	+	0.201570i
$340$		0			0
$341$	−9.82884	+	0.938541i	−0.532262	+	0.0508248i
$342$		0			0
$343$	9.94251	+	11.4743i	0.536845	+	0.619552i
$344$		0			0
$345$	−0.0632561	+	0.0497451i	−0.00340559	+	0.00267819i
$346$		0			0
$347$	−7.10132	−	20.5179i	−0.381219	−	1.10146i	−0.958544	−	0.284945i	$-0.908025\pi$
$347$	−7.10132	−	20.5179i	−0.381219	−	1.10146i	0.577325	−	0.816514i	$-0.304097\pi$
$348$		0			0
$349$	−11.9007	−	7.64811i	−0.637029	−	0.409394i	0.181877	−	0.983321i	$-0.441783\pi$
$349$	−11.9007	−	7.64811i	−0.637029	−	0.409394i	−0.818906	+	0.573927i	$0.805419\pi$
$350$		0			0
$351$	−1.25156	+	1.75757i	−0.0668034	+	0.0938123i
$352$		0			0
$353$	1.14788	−	24.0970i	0.0610956	−	1.28256i	−0.735284	−	0.677759i	$-0.762951\pi$
$353$	1.14788	−	24.0970i	0.0610956	−	1.28256i	0.796380	−	0.604797i	$-0.206746\pi$
$354$		0			0
$355$	5.85477	+	4.60424i	0.310739	+	0.244368i
$356$		0			0
$357$	0.905237	+	6.29606i	0.0479102	+	0.333223i
$358$		0			0
$359$	−27.9928	+	17.9899i	−1.47740	+	0.949469i	−0.480013	+	0.877261i	$0.659368\pi$
$359$	−27.9928	+	17.9899i	−1.47740	+	0.949469i	−0.997390	+	0.0722079i	$0.976995\pi$
$360$		0			0
$361$	2.14593	+	45.0485i	0.112943	+	2.37098i
$362$		0			0
$363$	2.67286	−	7.72273i	0.140289	−	0.405338i
$364$		0			0
$365$	11.1257	+	19.2703i	0.582345	+	1.00865i
$366$		0			0
$367$	−12.9112	−	5.16886i	−0.673958	−	0.269812i	0.00933476	−	0.999956i	$-0.497029\pi$
$367$	−12.9112	−	5.16886i	−0.673958	−	0.269812i	−0.683293	+	0.730144i	$0.739453\pi$
$368$		0			0
$369$	−1.82784	+	7.53447i	−0.0951537	+	0.392229i
$370$		0			0
$371$	6.06921	−	1.16974i	0.315097	−	0.0607301i
$372$		0			0
$373$	7.97714	−	13.8168i	0.413041	−	0.715407i	−0.582180	−	0.813060i	$-0.697800\pi$
$373$	7.97714	−	13.8168i	0.413041	−	0.715407i	0.995221	+	0.0976527i	$0.0311334\pi$
$374$		0			0
$375$	−5.03350	+	11.0218i	−0.259929	+	0.569164i
$376$		0			0
$377$	13.0712	−	15.0850i	0.673203	−	0.776917i
$378$		0			0
$379$	18.7141	−	7.49201i	0.961281	−	0.384839i	0.162666	−	0.986681i	$-0.447991\pi$
$379$	18.7141	−	7.49201i	0.961281	−	0.384839i	0.798615	+	0.601842i	$0.205566\pi$
$380$		0			0
$381$	6.26979	+	8.80469i	0.321211	+	0.451078i
$382$		0			0
$383$	−14.0193	−	13.3674i	−0.716354	−	0.683042i	0.241467	−	0.970409i	$-0.422372\pi$
$383$	−14.0193	−	13.3674i	−0.716354	−	0.683042i	−0.957820	+	0.287367i	$0.907220\pi$
$384$		0			0
$385$	3.12313	+	1.61009i	0.159169	+	0.0820576i
$386$		0			0
$387$	9.28242	−	2.72556i	0.471852	−	0.138548i
$388$		0			0
$389$	20.9086	+	4.02981i	1.06011	+	0.204320i	0.689364	−	0.724415i	$-0.257890\pi$
$389$	20.9086	+	4.02981i	1.06011	+	0.204320i	0.370746	+	0.928734i	$0.379102\pi$
$390$		0			0
$391$	0.243864	+	0.0232862i	0.0123327	+	0.00117763i
$392$		0			0
$393$	3.68534	+	1.08211i	0.185901	+	0.0545854i
$394$		0			0
$395$	−4.32042	+	4.11952i	−0.217384	+	0.207275i
$396$		0			0
$397$	0.461234	+	1.00996i	0.0231487	+	0.0506885i	0.920853	−	0.389909i	$-0.127494\pi$
$397$	0.461234	+	1.00996i	0.0231487	+	0.0506885i	−0.897705	+	0.440598i	$0.854766\pi$
$398$		0			0
$399$	−1.38036	+	9.60064i	−0.0691046	+	0.480633i
$400$		0			0
$401$	−17.5050			−0.874158			−0.437079	−	0.899423i	$-0.643987\pi$
$401$	−17.5050			−0.874158			−0.437079	+	0.899423i	$0.643987\pi$
$402$		0			0
$403$	12.6687			0.631071
$404$		0			0
$405$	−0.245459	+	1.70720i	−0.0121970	+	0.0848317i
$406$		0			0
$407$	−5.30721	−	11.6212i	−0.263069	−	0.576040i
$408$		0			0
$409$	−22.9091	+	21.8438i	−1.13278	+	1.08011i	−0.136798	+	0.990599i	$0.543681\pi$
$409$	−22.9091	+	21.8438i	−1.13278	+	1.08011i	−0.995986	+	0.0895088i	$0.971470\pi$
$410$		0			0
$411$	15.3014	+	4.49291i	0.754764	+	0.221619i
$412$		0			0
$413$	5.96810	+	0.569884i	0.293671	+	0.0280422i
$414$		0			0
$415$	14.8731	+	2.86656i	0.730094	+	0.140714i
$416$		0			0
$417$	7.82145	−	2.29658i	0.383018	−	0.112464i
$418$		0			0
$419$	−25.6222	−	13.2091i	−1.25172	−	0.645309i	−0.300492	−	0.953784i	$-0.597151\pi$
$419$	−25.6222	−	13.2091i	−1.25172	−	0.645309i	−0.951232	+	0.308476i	$0.900181\pi$
$420$		0			0
$421$	2.63123	+	2.50887i	0.128238	+	0.122275i	0.751485	−	0.659751i	$-0.229338\pi$
$421$	2.63123	+	2.50887i	0.128238	+	0.122275i	−0.623246	+	0.782026i	$0.714187\pi$
$422$		0			0
$423$	−6.35864	−	8.92946i	−0.309168	−	0.434165i
$424$		0			0
$425$	9.87154	−	3.95197i	0.478840	−	0.191699i
$426$		0			0
$427$	−10.4271	+	12.0335i	−0.504604	+	0.582344i
$428$		0			0
$429$	1.50726	−	3.30044i	0.0727712	−	0.159347i
$430$		0			0
$431$	−6.61319	+	11.4544i	−0.318546	+	0.551738i	−0.980185	−	0.198085i	$-0.936528\pi$
$431$	−6.61319	+	11.4544i	−0.318546	+	0.551738i	0.661639	+	0.749823i	$0.269861\pi$
$432$		0			0
$433$	26.3519	−	5.07892i	1.26639	−	0.244077i	0.488550	−	0.872536i	$-0.337526\pi$
$433$	26.3519	−	5.07892i	1.26639	−	0.244077i	0.777843	+	0.628458i	$0.216314\pi$
$434$		0			0
$435$	3.76169	−	15.5059i	0.180359	−	0.743451i
$436$		0			0
$437$	0.346792	+	0.138835i	0.0165893	+	0.00664136i
$438$		0			0
$439$	−0.424603	−	0.735434i	−0.0202652	−	0.0351003i	0.855715	−	0.517447i	$-0.173118\pi$
$439$	−0.424603	−	0.735434i	−0.0202652	−	0.0351003i	−0.875980	+	0.482347i	$0.839784\pi$
$440$		0			0
$441$	1.80945	−	5.22805i	0.0861641	−	0.248955i
$442$		0			0
$443$	1.42134	+	29.8376i	0.0675299	+	1.41763i	0.737554	+	0.675288i	$0.235981\pi$
$443$	1.42134	+	29.8376i	0.0675299	+	1.41763i	−0.670024	+	0.742340i	$0.733716\pi$
$444$		0			0
$445$	16.9883	−	10.9177i	0.805324	−	0.517551i
$446$		0			0
$447$	2.64265	+	18.3800i	0.124993	+	0.869346i
$448$		0			0
$449$	13.3229	+	10.4772i	0.628745	+	0.494450i	0.880941	−	0.473226i	$-0.156911\pi$
$449$	13.3229	+	10.4772i	0.628745	+	0.494450i	−0.252197	+	0.967676i	$0.581153\pi$
$450$		0			0
$451$	0.620350	−	13.0228i	0.0292112	−	0.613218i
$452$		0			0
$453$	2.39006	−	3.35637i	0.112295	−	0.157696i
$454$		0			0
$455$	−3.79274	−	2.43744i	−0.177806	−	0.114269i
$456$		0			0
$457$	4.93413	+	14.2562i	0.230809	+	0.666879i	0.999624	+	0.0274079i	$0.00872530\pi$
$457$	4.93413	+	14.2562i	0.230809	+	0.666879i	−0.768815	+	0.639471i	$0.779153\pi$
$458$		0			0
$459$	4.12714	−	3.24562i	0.192638	−	0.151492i
$460$		0			0
$461$	13.2307	+	15.2690i	0.616213	+	0.711148i	0.974983	−	0.222278i	$-0.0713493\pi$
$461$	13.2307	+	15.2690i	0.616213	+	0.711148i	−0.358770	+	0.933426i	$0.616804\pi$
$462$		0			0
$463$	−33.2390	+	3.17394i	−1.54475	+	0.147505i	−0.832341	−	0.554264i	$-0.813000\pi$
$463$	−33.2390	+	3.17394i	−1.54475	+	0.147505i	−0.712404	+	0.701769i	$0.752394\pi$
$464$		0			0
$465$	9.00117	−	4.64043i	0.417419	−	0.215195i
$466$		0			0
$467$	2.83341	+	11.6795i	0.131114	+	0.540461i	0.999042	+	0.0437697i	$0.0139368\pi$
$467$	2.83341	+	11.6795i	0.131114	+	0.540461i	−0.867927	+	0.496691i	$0.834548\pi$
$468$		0			0
$469$	9.21921	−	3.65247i	0.425704	−	0.168655i
$470$		0			0
$471$	−3.97689	−	16.3930i	−0.183246	−	0.755348i
$472$		0			0
$473$	−14.4599	+	7.45460i	−0.664867	+	0.342763i
$474$		0			0
$475$	16.1408	−	1.54126i	0.740590	−	0.0707178i
$476$		0			0
$477$	−3.34107	−	3.85580i	−0.152977	−	0.176545i
$478$		0			0
$479$	−3.79268	+	2.98259i	−0.173292	+	0.136278i	−0.701038	−	0.713124i	$-0.747280\pi$
$479$	−3.79268	+	2.98259i	−0.173292	+	0.136278i	0.527746	+	0.849402i	$0.323037\pi$
$480$		0			0
$481$	5.36141	+	15.4908i	0.244459	+	0.706319i
$482$		0			0
$483$	0.0475515	+	0.0305595i	0.00216367	+	0.00139050i
$484$		0			0
$485$	14.8605	−	20.8687i	0.674781	−	0.947598i
$486$		0			0
$487$	0.0166973	−	0.350519i	0.000756627	−	0.0158835i	−0.998457	−	0.0555222i	$-0.982318\pi$
$487$	0.0166973	−	0.350519i	0.000756627	−	0.0158835i	0.999214	+	0.0396386i	$0.0126207\pi$
$488$		0			0
$489$	2.73861	+	2.15366i	0.123844	+	0.0973920i
$490$		0			0
$491$	2.79693	+	19.4531i	0.126224	+	0.877906i	0.950280	+	0.311398i	$0.100797\pi$
$491$	2.79693	+	19.4531i	0.126224	+	0.877906i	−0.824056	+	0.566509i	$0.808294\pi$
$492$		0			0
$493$	−40.8611	+	26.2598i	−1.84029	+	1.18268i
$494$		0			0
$495$	−0.138005	−	2.89708i	−0.00620287	−	0.130214i
$496$		0			0
$497$	1.71113	−	4.94398i	0.0767546	−	0.221768i
$498$		0			0
$499$	−4.19759	−	7.27044i	−0.187910	−	0.325470i	0.756643	−	0.653828i	$-0.226838\pi$
$499$	−4.19759	−	7.27044i	−0.187910	−	0.325470i	−0.944553	+	0.328358i	$0.893505\pi$
$500$		0			0
$501$	0.763530	+	0.305671i	0.0341120	+	0.0136564i
$502$		0			0
$503$	−0.153132	+	0.631218i	−0.00682781	+	0.0281446i	−0.975124	−	0.221662i	$-0.928852\pi$
$503$	−0.153132	+	0.631218i	−0.00682781	+	0.0281446i	0.968296	+	0.249807i	$0.0803670\pi$
$504$		0			0
$505$	32.0956	−	6.18592i	1.42824	−	0.275270i
$506$		0			0
$507$	4.17227	−	7.22658i	0.185297	−	0.320944i
$508$		0			0
$509$	1.64251	−	3.59658i	0.0728028	−	0.159416i	−0.869732	−	0.493525i	$-0.835708\pi$
$509$	1.64251	−	3.59658i	0.0728028	−	0.159416i	0.942534	+	0.334109i	$0.108435\pi$
$510$		0			0
$511$	10.2351	−	11.8119i	0.452775	−	0.522530i
$512$		0			0
$513$	7.43272	−	2.97561i	0.328163	−	0.131377i
$514$		0			0
$515$	−3.10800	−	4.36457i	−0.136955	−	0.192326i
$516$		0			0
$517$	13.3413	+	12.7209i	0.586749	+	0.559464i
$518$		0			0
$519$	0.116303	+	0.0599583i	0.00510513	+	0.00263188i
$520$		0			0
$521$	−21.3689	+	6.27449i	−0.936190	+	0.274890i	−0.714026	−	0.700119i	$-0.753130\pi$
$521$	−21.3689	+	6.27449i	−0.936190	+	0.274890i	−0.222164	+	0.975009i	$0.571312\pi$
$522$		0			0
$523$	24.3287	+	4.68897i	1.06382	+	0.205034i	0.690989	−	0.722865i	$-0.257175\pi$
$523$	24.3287	+	4.68897i	1.06382	+	0.205034i	0.372830	+	0.927900i	$0.378387\pi$
$524$		0			0
$525$	2.44238	+	0.233219i	0.106594	+	0.0101785i
$526$		0			0
$527$	−29.5793	−	8.68526i	−1.28849	−	0.378336i
$528$		0			0
$529$	−16.6443	+	15.8703i	−0.723666	+	0.690014i
$530$		0			0
$531$	−2.05577	−	4.50150i	−0.0892126	−	0.195348i
$532$		0			0
$533$	−2.38069	+	16.5580i	−0.103119	+	0.717208i
$534$		0			0
$535$	−30.6508			−1.32515
$536$		0			0
$537$	8.09018			0.349117
$538$		0			0
$539$	−1.32398	+	9.20850i	−0.0570280	+	0.396638i
$540$		0			0
$541$	−0.150579	−	0.329723i	−0.00647391	−	0.0141759i	0.906367	−	0.422490i	$-0.138844\pi$
$541$	−0.150579	−	0.329723i	−0.00647391	−	0.0141759i	−0.912841	+	0.408314i	$0.866117\pi$
$542$		0			0
$543$	1.18753	−	1.13231i	0.0509620	−	0.0485922i
$544$		0			0
$545$	4.96121	+	1.45674i	0.212515	+	0.0624000i
$546$		0			0
$547$	32.1134	+	3.06645i	1.37307	+	0.131112i	0.755367	−	0.655301i	$-0.227458\pi$
$547$	32.1134	+	3.06645i	1.37307	+	0.131112i	0.617700	+	0.786414i	$0.288064\pi$
$548$		0			0
$549$	12.9057	+	2.48736i	0.550800	+	0.106158i
$550$		0			0
$551$	−71.0649	+	20.8666i	−3.02747	+	0.888945i
$552$		0			0
$553$	3.72697	+	1.92138i	0.158487	+	0.0817056i
$554$		0			0
$555$	9.48347	+	9.04247i	0.402551	+	0.383832i
$556$		0			0
$557$	−4.01517	−	5.63851i	−0.170128	−	0.238911i	0.720705	−	0.693241i	$-0.243818\pi$
$557$	−4.01517	−	5.63851i	−0.170128	−	0.238911i	−0.890833	+	0.454330i	$0.849879\pi$
$558$		0			0
$559$	19.3785	−	7.75800i	0.819625	−	0.328128i
$560$		0			0
$561$	−5.78190	+	6.67267i	−0.244112	+	0.281720i
$562$		0			0
$563$	−17.2961	+	37.8732i	−0.728944	+	1.59617i	0.0719847	+	0.997406i	$0.477067\pi$
$563$	−17.2961	+	37.8732i	−0.728944	+	1.59617i	−0.800929	+	0.598759i	$0.795661\pi$
$564$		0			0
$565$	−6.98465	+	12.0978i	−0.293847	+	0.508957i
$566$		0			0
$567$	1.18958	−	0.229274i	0.0499579	−	0.00962859i
$568$		0			0
$569$	5.97022	−	24.6096i	0.250285	−	1.03169i	−0.698461	−	0.715648i	$-0.746132\pi$
$569$	5.97022	−	24.6096i	0.250285	−	1.03169i	0.948746	−	0.316040i	$-0.102353\pi$
$570$		0			0
$571$	−33.7268	−	13.5022i	−1.41142	−	0.565049i	−0.464231	−	0.885714i	$-0.653669\pi$
$571$	−33.7268	−	13.5022i	−1.41142	−	0.565049i	−0.947192	+	0.320666i	$0.896093\pi$
$572$		0			0
$573$	8.70009	+	15.0690i	0.363451	+	0.629516i
$574$		0			0
$575$	0.0309049	−	0.0892939i	0.00128882	−	0.00372381i
$576$		0			0
$577$	0.647215	+	13.5867i	0.0269439	+	0.565623i	0.971467	+	0.237176i	$0.0762219\pi$
$577$	0.647215	+	13.5867i	0.0269439	+	0.565623i	−0.944523	+	0.328446i	$0.893475\pi$
$578$		0			0
$579$	13.9376	−	8.95717i	0.579228	−	0.372247i
$580$		0			0
$581$	−1.51412	−	10.5309i	−0.0628162	−	0.436896i
$582$		0			0
$583$	6.74393	+	5.30348i	0.279305	+	0.219648i
$584$		0			0
$585$	−0.177073	+	3.71722i	−0.00732107	+	0.153688i
$586$		0			0
$587$	25.4066	−	35.6785i	1.04864	−	1.47261i	0.175913	−	0.984406i	$-0.443712\pi$
$587$	25.4066	−	35.6785i	1.04864	−	1.47261i	0.872729	−	0.488206i	$-0.162348\pi$
$588$		0			0
$589$	−39.5461	−	25.4147i	−1.62947	−	1.04720i
$590$		0			0
$591$	−3.34199	−	9.65604i	−0.137471	−	0.397197i
$592$		0			0
$593$	6.27045	−	4.93114i	0.257497	−	0.202498i	−0.481063	−	0.876686i	$-0.659749\pi$
$593$	6.27045	−	4.93114i	0.257497	−	0.202498i	0.738559	+	0.674189i	$0.235507\pi$
$594$		0			0
$595$	7.18439	+	8.29123i	0.294531	+	0.339907i
$596$		0			0
$597$	−4.22175	+	0.403128i	−0.172785	+	0.0164989i
$598$		0			0
$599$	−9.93382	+	5.12124i	−0.405885	+	0.209248i	−0.649065	−	0.760733i	$-0.724840\pi$
$599$	−9.93382	+	5.12124i	−0.405885	+	0.209248i	0.243180	+	0.969981i	$0.421809\pi$
$600$		0			0
$601$	−3.84261	−	15.8395i	−0.156743	−	0.646105i	−0.994917	−	0.100701i	$-0.967891\pi$
$601$	−3.84261	−	15.8395i	−0.156743	−	0.646105i	0.838173	−	0.545404i	$-0.183624\pi$
$602$		0			0
$603$	−6.41592	−	5.08291i	−0.261276	−	0.206992i
$604$		0			0
$605$	−3.32304	−	13.6978i	−0.135101	−	0.556893i
$606$		0			0
$607$	−39.1232	+	20.1694i	−1.58796	+	0.818650i	−0.588008	+	0.808855i	$0.700088\pi$
$607$	−39.1232	+	20.1694i	−1.58796	+	0.818650i	−0.999952	+	0.00979553i	$0.996882\pi$
$608$		0			0
$609$	−11.1566	+	1.06532i	−0.452087	+	0.0431690i
$610$		0			0
$611$	−15.4890	−	17.8753i	−0.626619	−	0.723157i
$612$		0			0
$613$	13.1570	−	10.3468i	0.531408	−	0.417904i	−0.316069	−	0.948736i	$-0.602363\pi$
$613$	13.1570	−	10.3468i	0.531408	−	0.417904i	0.847477	+	0.530832i	$0.178121\pi$
$614$		0			0
$615$	4.37358	+	12.6366i	0.176360	+	0.509558i
$616$		0			0
$617$	16.8558	+	10.8326i	0.678589	+	0.436103i	0.834013	−	0.551745i	$-0.186038\pi$
$617$	16.8558	+	10.8326i	0.678589	+	0.436103i	−0.155424	+	0.987848i	$0.549674\pi$
$618$		0			0
$619$	11.5645	−	16.2401i	0.464817	−	0.652745i	−0.513926	−	0.857835i	$-0.671809\pi$
$619$	11.5645	−	16.2401i	0.464817	−	0.652745i	0.978743	+	0.205090i	$0.0657487\pi$
$620$		0			0
$621$	0.00222005	−	0.0466047i	8.90877e−5	−	0.00187018i
$622$		0			0
$623$	−11.1497	−	8.76821i	−0.446702	−	0.351291i
$624$		0			0
$625$	1.53309	+	10.6629i	0.0613238	+	0.426516i
$626$		0			0
$627$	−11.3261	+	7.27882i	−0.452320	+	0.290688i
$628$		0			0
$629$	−1.89801	−	39.8441i	−0.0756786	−	1.58869i
$630$		0			0
$631$	13.5820	−	39.2425i	0.540689	−	1.56222i	−0.261534	−	0.965194i	$-0.584228\pi$
$631$	13.5820	−	39.2425i	0.540689	−	1.56222i	0.802223	−	0.597024i	$-0.203650\pi$
$632$		0			0
$633$	7.62289	+	13.2032i	0.302983	+	0.524781i
$634$		0			0
$635$	17.3074	+	6.92883i	0.686823	+	0.274962i
$636$		0			0
$637$	2.81421	−	11.6004i	0.111503	−	0.459623i
$638$		0			0
$639$	−4.24042	+	0.817275i	−0.167749	+	0.0323309i
$640$		0			0
$641$	0.758272	−	1.31337i	0.0299499	−	0.0518748i	−0.850662	−	0.525713i	$-0.823799\pi$
$641$	0.758272	−	1.31337i	0.0299499	−	0.0518748i	0.880612	+	0.473838i	$0.157132\pi$
$642$		0			0
$643$	−4.67752	+	10.2423i	−0.184463	+	0.403918i	−0.979161	−	0.203088i	$-0.934902\pi$
$643$	−4.67752	+	10.2423i	−0.184463	+	0.403918i	0.794697	+	0.607006i	$0.207630\pi$
$644$		0			0
$645$	10.9269	−	12.6103i	0.430247	−	0.496531i
$646$		0			0
$647$	0.935250	−	0.374418i	0.0367685	−	0.0147199i	−0.353205	−	0.935546i	$-0.614908\pi$
$647$	0.935250	−	0.374418i	0.0367685	−	0.0147199i	0.389974	+	0.920826i	$0.372484\pi$
$648$		0			0
$649$	4.82710	+	6.77872i	0.189480	+	0.266088i
$650$		0			0
$651$	−5.14806	−	4.90866i	−0.201768	−	0.192386i
$652$		0			0
$653$	−14.4575	−	7.45335i	−0.565765	−	0.291672i	0.151517	−	0.988455i	$-0.451584\pi$
$653$	−14.4575	−	7.45335i	−0.565765	−	0.291672i	−0.717283	+	0.696782i	$0.754614\pi$
$654$		0			0
$655$	6.35632	−	1.86639i	0.248362	−	0.0729257i
$656$		0			0
$657$	−12.6680	−	2.44156i	−0.494226	−	0.0952542i
$658$		0			0
$659$	−13.8122	−	1.31890i	−0.538046	−	0.0513772i	−0.177504	−	0.984120i	$-0.556802\pi$
$659$	−13.8122	−	1.31890i	−0.538046	−	0.0513772i	−0.360542	+	0.932743i	$0.617408\pi$
$660$		0			0
$661$	−2.70203	−	0.793387i	−0.105097	−	0.0308592i	0.228761	−	0.973483i	$-0.426532\pi$
$661$	−2.70203	−	0.793387i	−0.105097	−	0.0308592i	−0.333858	+	0.942623i	$0.608351\pi$
$662$		0			0
$663$	8.19893	−	7.81767i	0.318420	−	0.303613i
$664$		0			0
$665$	6.94951	+	15.2173i	0.269490	+	0.590102i
$666$		0			0
$667$	−0.0614268	+	0.427233i	−0.00237845	+	0.0165425i
$668$		0			0
$669$	−7.98825			−0.308843
$670$		0			0
$671$	−22.1017			−0.853225
$672$		0			0
$673$	−3.91313	+	27.2164i	−0.150840	+	1.04912i	0.763976	+	0.645244i	$0.223244\pi$
$673$	−3.91313	+	27.2164i	−0.150840	+	1.04912i	−0.914816	+	0.403871i	$0.867665\pi$
$674$		0			0
$675$	−0.841299	−	1.84219i	−0.0323816	−	0.0709058i
$676$		0			0
$677$	−35.0785	+	33.4473i	−1.34818	+	1.28548i	−0.422908	+	0.906173i	$0.638991\pi$
$677$	−35.0785	+	33.4473i	−1.34818	+	1.28548i	−0.925269	+	0.379312i	$0.876161\pi$
$678$		0			0
$679$	−17.2660	−	5.06975i	−0.662608	−	0.194559i
$680$		0			0
$681$	−19.0128	−	1.81550i	−0.728572	−	0.0695702i
$682$		0			0
$683$	−7.06039	−	1.36078i	−0.270158	−	0.0520688i	0.0523728	−	0.998628i	$-0.483322\pi$
$683$	−7.06039	−	1.36078i	−0.270158	−	0.0520688i	−0.322531	+	0.946559i	$0.604534\pi$
$684$		0			0
$685$	26.3913	−	7.74919i	1.00836	−	0.296081i
$686$		0			0
$687$	17.2047	+	8.86966i	0.656402	+	0.338399i
$688$		0			0
$689$	−7.96704	−	7.59656i	−0.303520	−	0.289406i
$690$		0			0
$691$	−25.4202	−	35.6977i	−0.967030	−	1.35800i	−0.933505	−	0.358566i	$-0.883266\pi$
$691$	−25.4202	−	35.6977i	−0.967030	−	1.35800i	−0.0335254	−	0.999438i	$-0.510673\pi$
$692$		0			0
$693$	−1.89130	+	0.757162i	−0.0718445	+	0.0287622i
$694$		0			0
$695$	9.20711	−	10.6256i	0.349245	−	0.403051i
$696$		0			0
$697$	16.9102	−	37.0282i	0.640521	−	1.40254i
$698$		0			0
$699$	−10.8231	+	18.7461i	−0.409366	+	0.709043i
$700$		0			0
$701$	34.8051	−	6.70814i	1.31457	−	0.253363i	0.516687	−	0.856174i	$-0.327165\pi$
$701$	34.8051	−	6.70814i	1.31457	−	0.253363i	0.797884	+	0.602811i	$0.205953\pi$
$702$		0			0
$703$	14.3402	−	59.1112i	0.540851	−	2.22942i
$704$		0			0
$705$	−17.5526	−	7.02702i	−0.661071	−	0.264653i
$706$		0			0
$707$	−11.4795	−	19.8830i	−0.431730	−	0.747779i
$708$		0			0
$709$	9.84461	−	28.4441i	0.369722	−	1.06824i	−0.594716	−	0.803936i	$-0.702736\pi$
$709$	9.84461	−	28.4441i	0.369722	−	1.06824i	0.964439	−	0.264307i	$-0.0851431\pi$
$710$		0			0
$711$	−0.164687	−	3.45721i	−0.00617626	−	0.129656i
$712$		0			0
$713$	−0.230461	+	0.148108i	−0.00863083	+	0.00554670i
$714$		0			0
$715$	−0.890605	−	6.19429i	−0.0333067	−	0.231653i
$716$		0			0
$717$	−1.90828	−	1.50069i	−0.0712661	−	0.0560443i
$718$		0			0
$719$	1.10316	−	23.1582i	0.0411410	−	0.863656i	−0.880130	−	0.474734i	$-0.842544\pi$
$719$	1.10316	−	23.1582i	0.0411410	−	0.863656i	0.921271	−	0.388922i	$-0.127153\pi$
$720$		0			0
$721$	−2.18307	+	3.06569i	−0.0813017	+	0.114172i
$722$		0			0
$723$	17.0371	+	10.9491i	0.633616	+	0.407200i
$724$		0			0
$725$	6.12762	+	17.7046i	0.227574	+	0.657533i
$726$		0			0
$727$	15.0880	−	11.8653i	0.559583	−	0.440061i	−0.297882	−	0.954603i	$-0.596280\pi$
$727$	15.0880	−	11.8653i	0.559583	−	0.440061i	0.857465	+	0.514542i	$0.172038\pi$
$728$		0			0
$729$	−0.654861	−	0.755750i	−0.0242541	−	0.0279907i
$730$		0			0
$731$	−50.5645	+	4.82832i	−1.87019	+	0.178582i
$732$		0			0
$733$	46.1031	−	23.7678i	1.70286	−	0.877884i	0.719894	−	0.694084i	$-0.244191\pi$
$733$	46.1031	−	23.7678i	1.70286	−	0.877884i	0.982964	−	0.183800i	$-0.0588397\pi$
$734$		0			0
$735$	−2.24960	−	9.27296i	−0.0829776	−	0.342038i
$736$		0			0
$737$	12.2117	+	6.35116i	0.449824	+	0.233948i
$738$		0			0
$739$	8.81206	+	36.3238i	0.324157	+	1.33619i	0.867816	+	0.496886i	$0.165523\pi$
$739$	8.81206	+	36.3238i	0.324157	+	1.33619i	−0.543659	+	0.839306i	$0.682961\pi$
$740$		0			0
$741$	15.3543	−	7.91570i	0.564055	−	0.290791i
$742$		0			0
$743$	38.6284	−	3.68857i	1.41714	−	0.135320i	0.641804	−	0.766869i	$-0.278186\pi$
$743$	38.6284	−	3.68857i	1.41714	−	0.135320i	0.775336	+	0.631549i	$0.217580\pi$
$744$		0			0
$745$	20.9733	+	24.2045i	0.768404	+	0.886785i
$746$		0			0
$747$	−6.90313	+	5.42868i	−0.252572	+	0.198625i
$748$		0			0
$749$	7.04153	+	20.3452i	0.257292	+	0.743396i
$750$		0			0
$751$	−32.7928	−	21.0746i	−1.19663	−	0.769025i	−0.218257	−	0.975891i	$-0.570037\pi$
$751$	−32.7928	−	21.0746i	−1.19663	−	0.769025i	−0.978369	+	0.206867i	$0.933673\pi$
$752$		0			0
$753$	−2.05006	+	2.87890i	−0.0747082	+	0.104913i
$754$		0			0
$755$	0.338149	−	7.09863i	0.0123065	−	0.258346i
$756$		0			0
$757$	16.1549	+	12.7043i	0.587159	+	0.461747i	0.867006	−	0.498298i	$-0.166041\pi$
$757$	16.1549	+	12.7043i	0.587159	+	0.461747i	−0.279847	+	0.960045i	$0.590284\pi$
$758$		0			0
$759$	0.0111660	+	0.0776610i	0.000405299	+	0.00281892i
$760$		0			0
$761$	−3.26200	+	2.09636i	−0.118247	+	0.0759929i	−0.598428	−	0.801177i	$-0.704208\pi$
$761$	−3.26200	+	2.09636i	−0.118247	+	0.0759929i	0.480180	+	0.877170i	$0.340571\pi$
$762$		0			0
$763$	−0.172812	−	3.62777i	−0.00625622	−	0.131334i
$764$		0			0
$765$	2.96185	−	8.55772i	0.107086	−	0.309405i
$766$		0			0
$767$	−5.33879	−	9.24706i	−0.192773	−	0.333892i
$768$		0			0
$769$	22.8747	+	9.15764i	0.824882	+	0.330233i	0.745412	−	0.666604i	$-0.232253\pi$
$769$	22.8747	+	9.15764i	0.824882	+	0.330233i	0.0794704	+	0.996837i	$0.474677\pi$
$770$		0			0
$771$	−0.162204	+	0.668615i	−0.00584165	+	0.0240796i
$772$		0			0
$773$	−36.4667	+	7.02838i	−1.31162	+	0.252793i	−0.796662	−	0.604425i	$-0.793403\pi$
$773$	−36.4667	+	7.02838i	−1.31162	+	0.252793i	−0.514954	+	0.857218i	$0.672191\pi$
$774$		0			0
$775$	−5.94548	+	10.2979i	−0.213568	+	0.369911i
$776$		0			0
$777$	3.82347	−	8.37222i	0.137166	−	0.300352i
$778$		0			0
$779$	40.6488	−	46.9112i	1.45639	−	1.68077i
$780$		0			0
$781$	6.74177	−	2.69900i	0.241240	−	0.0965778i
$782$		0			0
$783$	5.36607	+	7.53559i	0.191768	+	0.269300i
$784$		0			0
$785$	−21.0564	−	20.0772i	−0.751534	−	0.716586i
$786$		0			0
$787$	−2.02179	−	1.04230i	−0.0720689	−	0.0371541i	0.421815	−	0.906682i	$-0.361393\pi$
$787$	−2.02179	−	1.04230i	−0.0720689	−	0.0371541i	−0.493884	+	0.869528i	$0.664423\pi$
$788$		0			0
$789$	12.1046	−	3.55423i	0.430935	−	0.126534i
$790$		0			0
$791$	9.63477	+	1.85695i	0.342573	+	0.0660255i
$792$		0			0
$793$	28.2300	+	2.69564i	1.00248	+	0.0957249i
$794$		0			0
$795$	−8.44320	−	2.47915i	−0.299449	−	0.0879263i
$796$		0			0
$797$	−5.67994	+	5.41581i	−0.201194	+	0.191838i	−0.783977	−	0.620790i	$-0.786812\pi$
$797$	−5.67994	+	5.41581i	−0.201194	+	0.191838i	0.582783	+	0.812628i	$0.301964\pi$
$798$		0			0
$799$	23.9096	+	52.3548i	0.845862	+	1.85218i
$800$		0			0
$801$	−1.66627	+	11.5892i	−0.0588747	+	0.409483i
$802$		0			0
$803$	21.6947			0.765588
$804$		0			0
$805$	0.0974913			0.00343612
$806$		0			0
$807$	3.37662	−	23.4849i	0.118863	−	0.826708i
$808$		0			0
$809$	−0.876764	−	1.91985i	−0.0308254	−	0.0674982i	0.893593	−	0.448878i	$-0.148176\pi$
$809$	−0.876764	−	1.91985i	−0.0308254	−	0.0674982i	−0.924418	+	0.381380i	$0.875449\pi$
$810$		0			0
$811$	−7.17170	+	6.83821i	−0.251833	+	0.240122i	−0.805471	−	0.592635i	$-0.798088\pi$
$811$	−7.17170	+	6.83821i	−0.251833	+	0.240122i	0.553638	+	0.832757i	$0.313239\pi$
$812$		0			0
$813$	22.4466	+	6.59092i	0.787237	+	0.231154i
$814$		0			0
$815$	5.98185	+	0.571197i	0.209535	+	0.0200082i
$816$		0			0
$817$	−76.0549	−	14.6584i	−2.66082	−	0.512832i
$818$		0			0
$819$	2.50807	−	0.736434i	0.0876389	−	0.0257331i
$820$		0			0
$821$	23.6277	+	12.1809i	0.824613	+	0.425118i	0.818250	−	0.574862i	$-0.194944\pi$
$821$	23.6277	+	12.1809i	0.824613	+	0.425118i	0.00636284	+	0.999980i	$0.497975\pi$
$822$		0			0
$823$	−12.7646	−	12.1710i	−0.444946	−	0.424256i	0.434193	−	0.900820i	$-0.357033\pi$
$823$	−12.7646	−	12.1710i	−0.444946	−	0.424256i	−0.879140	+	0.476564i	$0.841882\pi$
$824$		0			0
$825$	1.97544	+	2.77411i	0.0687759	+	0.0965823i
$826$		0			0
$827$	15.1808	−	6.07747i	0.527888	−	0.211334i	−0.0923810	−	0.995724i	$-0.529448\pi$
$827$	15.1808	−	6.07747i	0.527888	−	0.211334i	0.620269	+	0.784389i	$0.287024\pi$
$828$		0			0
$829$	3.48055	−	4.01677i	0.120885	−	0.139508i	−0.692081	−	0.721820i	$-0.743306\pi$
$829$	3.48055	−	4.01677i	0.120885	−	0.139508i	0.812966	+	0.582311i	$0.197852\pi$
$830$		0			0
$831$	3.21495	−	7.03976i	0.111525	−	0.244207i
$832$		0			0
$833$	−14.5236	+	25.1556i	−0.503213	+	0.871590i
$834$		0			0
$835$	1.39288	−	0.268456i	0.0482027	−	0.00929031i
$836$		0			0
$837$	−1.38426	+	5.70599i	−0.0478470	+	0.197228i
$838$		0			0
$839$	−46.3157	−	18.5420i	−1.59899	−	0.640141i	−0.610585	−	0.791951i	$-0.709066\pi$
$839$	−46.3157	−	18.5420i	−1.59899	−	0.640141i	−0.988410	+	0.151810i	$0.951490\pi$
$840$		0			0
$841$	−28.2900	−	48.9996i	−0.975516	−	1.68964i
$842$		0			0
$843$	5.21256	−	15.0607i	0.179530	−	0.518718i
$844$		0			0
$845$	−0.684814	−	14.3760i	−0.0235583	−	0.494550i
$846$		0			0
$847$	−8.32877	+	5.35258i	−0.286180	+	0.183917i
$848$		0			0
$849$	3.70663	+	25.7801i	0.127211	+	0.884772i
$850$		0			0
$851$	−0.278633	−	0.219120i	−0.00955143	−	0.00751133i
$852$		0			0
$853$	−0.108143	+	2.27021i	−0.00370276	+	0.0777304i	−0.999962	−	0.00868067i	$-0.997237\pi$
$853$	−0.108143	+	2.27021i	−0.00370276	+	0.0777304i	0.996260	+	0.0864111i	$0.0275399\pi$
$854$		0			0
$855$	8.00990	−	11.2483i	0.273933	−	0.384685i
$856$		0			0
$857$	−4.68145	−	3.00859i	−0.159915	−	0.102771i	0.458236	−	0.888831i	$-0.348482\pi$
$857$	−4.68145	−	3.00859i	−0.159915	−	0.102771i	−0.618151	+	0.786059i	$0.712118\pi$
$858$		0			0
$859$	−10.3209	−	29.8202i	−0.352144	−	1.01745i	−0.972454	−	0.233096i	$-0.925114\pi$
$859$	−10.3209	−	29.8202i	−0.352144	−	1.01745i	0.620310	−	0.784357i	$-0.287007\pi$
$860$		0			0
$861$	7.38308	−	5.80612i	0.251615	−	0.197872i
$862$		0			0
$863$	−1.19825	−	1.38285i	−0.0407887	−	0.0470727i	0.734989	−	0.678079i	$-0.237187\pi$
$863$	−1.19825	−	1.38285i	−0.0407887	−	0.0470727i	−0.775777	+	0.631007i	$0.782642\pi$
$864$		0			0
$865$	0.224660	−	0.0214525i	0.00763868	−	0.000729406i
$866$		0			0
$867$	−9.39256	+	4.84220i	−0.318988	+	0.164450i
$868$		0			0
$869$	1.37218	+	5.65621i	0.0465480	+	0.191874i
$870$		0			0
$871$	−14.8231	−	9.60161i	−0.502263	−	0.325338i
$872$		0			0
$873$	3.50189	+	14.4350i	0.118521	+	0.488550i
$874$		0			0
$875$	13.0474	−	6.72641i	0.441083	−	0.227394i
$876$		0			0
$877$	−9.00179	+	0.859566i	−0.303969	+	0.0290255i	−0.245926	−	0.969289i	$-0.579092\pi$
$877$	−9.00179	+	0.859566i	−0.303969	+	0.0290255i	−0.0580427	+	0.998314i	$0.518486\pi$
$878$		0			0
$879$	−7.66469	−	8.84552i	−0.258524	−	0.298352i
$880$		0			0
$881$	37.1478	−	29.2134i	1.25154	−	0.984223i	0.251676	−	0.967811i	$-0.419018\pi$
$881$	37.1478	−	29.2134i	1.25154	−	0.984223i	0.999865	−	0.0164119i	$-0.00522429\pi$
$882$		0			0
$883$	0.828410	+	2.39353i	0.0278782	+	0.0805488i	0.958081	−	0.286496i	$-0.0924906\pi$
$883$	0.828410	+	2.39353i	0.0278782	+	0.0805488i	−0.930203	+	0.367045i	$0.880369\pi$
$884$		0			0
$885$	−7.18037	−	4.61455i	−0.241366	−	0.155116i
$886$		0			0
$887$	5.48663	−	7.70489i	0.184223	−	0.258705i	−0.712129	−	0.702049i	$-0.752269\pi$
$887$	5.48663	−	7.70489i	0.184223	−	0.258705i	0.896351	+	0.443344i	$0.146208\pi$
$888$		0			0
$889$	0.623074	−	13.0799i	0.0208972	−	0.438687i
$890$		0			0
$891$	1.32183	+	1.03950i	0.0442831	+	0.0348246i
$892$		0			0
$893$	12.4903	+	86.8717i	0.417971	+	2.90705i
$894$		0			0
$895$	11.7385	−	7.54390i	0.392376	−	0.252165i
$896$		0			0
$897$	−0.00479011	−	0.100557i	−0.000159937	−	0.00335749i
$898$		0			0
$899$	17.7653	−	51.3295i	0.592506	−	1.71193i
$900$		0			0
$901$	13.3938	+	23.1987i	0.446212	+	0.772861i
$902$		0			0
$903$	−10.8807	−	4.35596i	−0.362086	−	0.144957i
$904$		0			0
$905$	0.667213	−	2.75029i	0.0221789	−	0.0914227i
$906$		0			0
$907$	−37.0143	+	7.13391i	−1.22904	+	0.236878i	−0.762128	−	0.647427i	$-0.775845\pi$
$907$	−37.0143	+	7.13391i	−1.22904	+	0.236878i	−0.466911	+	0.884305i	$0.654633\pi$
$908$		0			0
$909$	−9.47560	+	16.4122i	−0.314286	+	0.544359i
$910$		0			0
$911$	−6.69014	+	14.6494i	−0.221654	+	0.485355i	−0.987490	−	0.157681i	$-0.949598\pi$
$911$	−6.69014	+	14.6494i	−0.221654	+	0.485355i	0.765836	+	0.643036i	$0.222325\pi$
$912$		0			0
$913$	9.67092	−	11.1608i	0.320061	−	0.369370i
$914$		0			0
$915$	21.0450	−	8.42515i	0.695727	−	0.278527i
$916$		0			0
$917$	−2.69912	−	3.79038i	−0.0891326	−	0.125169i
$918$		0			0
$919$	34.5708	+	32.9632i	1.14039	+	1.08736i	0.995191	+	0.0979540i	$0.0312298\pi$
$919$	34.5708	+	32.9632i	1.14039	+	1.08736i	0.145196	+	0.989403i	$0.453619\pi$
$920$		0			0
$921$	−5.53094	−	2.85140i	−0.182251	−	0.0939568i
$922$		0			0
$923$	−8.94031	+	2.62511i	−0.294274	+	0.0864067i
$924$		0			0
$925$	−15.1080	−	2.91183i	−0.496749	−	0.0957405i
$926$		0			0
$927$	3.09250	+	0.295298i	0.101571	+	0.00969886i
$928$		0			0
$929$	−5.57069	−	1.63570i	−0.182768	−	0.0536657i	0.189068	−	0.981964i	$-0.439453\pi$
$929$	−5.57069	−	1.63570i	−0.182768	−	0.0536657i	−0.371836	+	0.928298i	$0.621272\pi$
$930$		0			0
$931$	−32.0564	+	30.5657i	−1.05060	+	1.00175i
$932$		0			0
$933$	0.517435	+	1.13303i	0.0169401	+	0.0370936i
$934$		0			0
$935$	−2.16721	+	15.0733i	−0.0708753	+	0.492948i
$936$		0			0
$937$	−18.0923			−0.591051			−0.295525	−	0.955335i	$-0.595495\pi$
$937$	−18.0923			−0.591051			−0.295525	+	0.955335i	$0.595495\pi$
$938$		0			0
$939$	−20.4559			−0.667552
$940$		0			0
$941$	4.76775	−	33.1604i	0.155424	−	1.08100i	−0.751508	−	0.659723i	$-0.770673\pi$
$941$	4.76775	−	33.1604i	0.155424	−	1.08100i	0.906933	−	0.421276i	$-0.138417\pi$
$942$		0			0
$943$	−0.150271	−	0.329047i	−0.00489349	−	0.0107152i
$944$		0			0
$945$	1.51225	−	1.44193i	0.0491935	−	0.0469059i
$946$		0			0
$947$	30.8436	+	9.05651i	1.00228	+	0.294297i	0.741393	−	0.671072i	$-0.234166\pi$
$947$	30.8436	+	9.05651i	1.00228	+	0.294297i	0.260891	+	0.965368i	$0.415984\pi$
$948$		0			0
$949$	−27.7101	−	2.64600i	−0.899509	−	0.0858927i
$950$		0			0
$951$	−22.4951	−	4.33558i	−0.729454	−	0.140591i
$952$		0			0
$953$	34.7519	−	10.2041i	1.12572	−	0.330542i	0.334698	−	0.942326i	$-0.391366\pi$
$953$	34.7519	−	10.2041i	1.12572	−	0.330542i	0.791025	+	0.611783i	$0.209548\pi$
$954$		0			0
$955$	26.6750	+	13.7519i	0.863182	+	0.445001i
$956$		0			0
$957$	−11.2587	−	10.7352i	−0.363943	−	0.347019i
$958$		0			0
$959$	−11.2067	−	15.7376i	−0.361882	−	0.508192i
$960$		0			0
$961$	3.22560	−	1.29134i	0.104052	−	0.0416560i
$962$		0			0
$963$	11.6376	−	13.4305i	0.375016	−	0.432791i
$964$		0			0
$965$	11.8706	−	25.9930i	0.382128	−	0.836744i
$966$		0			0
$967$	19.8984	−	34.4651i	0.639890	−	1.10832i	−0.345566	−	0.938394i	$-0.612313\pi$
$967$	19.8984	−	34.4651i	0.639890	−	1.10832i	0.985457	−	0.169928i	$-0.0543535\pi$
$968$		0			0
$969$	−41.2767	+	7.95542i	−1.32600	+	0.255565i
$970$		0			0
$971$	−6.93442	+	28.5841i	−0.222536	+	0.917307i	0.745502	+	0.666503i	$0.232210\pi$
$971$	−6.93442	+	28.5841i	−0.222536	+	0.917307i	−0.968038	+	0.250803i	$0.919305\pi$
$972$		0			0
$973$	−9.16813	−	3.67037i	−0.293917	−	0.117667i
$974$		0			0
$975$	−2.18484	−	3.78425i	−0.0699709	−	0.121193i
$976$		0			0
$977$	1.92167	−	5.55230i	0.0614796	−	0.177634i	−0.910078	−	0.414437i	$-0.863978\pi$
$977$	1.92167	−	5.55230i	0.0614796	−	0.177634i	0.971558	+	0.236803i	$0.0760997\pi$
$978$		0			0
$979$	−0.936832	−	19.6665i	−0.0299413	−	0.628545i
$980$		0			0
$981$	−2.52199	+	1.62079i	−0.0805210	+	0.0517477i
$982$		0			0
$983$	−3.41481	−	23.7505i	−0.108915	−	0.757524i	−0.968944	−	0.247278i	$-0.920464\pi$
$983$	−3.41481	−	23.7505i	−0.108915	−	0.757524i	0.860029	−	0.510245i	$-0.170445\pi$
$984$		0			0
$985$	−13.8531	−	10.8942i	−0.441397	−	0.347119i
$986$		0			0
$987$	−0.631904	+	13.2653i	−0.0201137	+	0.422239i
$988$		0			0
$989$	−0.261825	+	0.367682i	−0.00832556	+	0.0116916i
$990$		0			0
$991$	−10.4828	−	6.73688i	−0.332997	−	0.214004i	0.363448	−	0.931615i	$-0.381599\pi$
$991$	−10.4828	−	6.73688i	−0.332997	−	0.214004i	−0.696445	+	0.717610i	$0.745236\pi$
$992$		0			0
$993$	6.20163	+	17.9184i	0.196803	+	0.568624i
$994$		0			0
$995$	−5.74969	+	4.52161i	−0.182277	+	0.143345i
$996$		0			0
$997$	13.4286	+	15.4975i	0.425289	+	0.490810i	0.927441	−	0.373970i	$-0.122004\pi$
$997$	13.4286	+	15.4975i	0.425289	+	0.490810i	−0.502152	+	0.864779i	$0.667458\pi$
$998$		0			0
$999$	−7.56290	+	0.722170i	−0.239280	+	0.0228484i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.y.a.157.4	✓	100
67.35	even	33	inner	804.2.y.a.169.4	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.y.a.157.4	✓	100	1.1	even	1	trivial
804.2.y.a.169.4	yes	100	67.35	even	33	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.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.142315 + 0.989821i) q^{3} +(0.716491 + 1.56890i) q^{5} +(0.876788 - 0.836015i) q^{7} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})\)	\(q+(-0.142315 + 0.989821i) q^{3} +(0.716491 + 1.56890i) q^{5} +(0.876788 - 0.836015i) q^{7} +(-0.959493 - 0.281733i) q^{9} +(1.67399 + 0.159847i) q^{11} +(-2.11866 - 0.408339i) q^{13} +(-1.65490 + 0.485921i) q^{15} +(4.66679 + 2.40590i) q^{17} +(5.79438 + 5.52493i) q^{19} +(0.702726 + 0.986841i) q^{21} +(0.0433153 - 0.0173408i) q^{23} +(1.32622 - 1.53054i) q^{25} +(0.415415 - 0.909632i) q^{27} +(-4.62547 + 8.01155i) q^{29} +(-5.76539 + 1.11119i) q^{31} +(-0.396454 + 1.63421i) q^{33} +(1.93983 + 0.776592i) q^{35} +(-3.79865 - 6.57946i) q^{37} +(0.705699 - 2.03898i) q^{39} +(-0.368903 - 7.74423i) q^{41} +(-8.13854 + 5.23032i) q^{43} +(-0.245459 - 1.70720i) q^{45} +(8.61679 + 6.77632i) q^{47} +(-0.263238 + 5.52606i) q^{49} +(-3.04556 + 4.27689i) q^{51} +(4.29204 + 2.75832i) q^{53} +(0.948618 + 2.74085i) q^{55} +(-6.29332 + 4.94912i) q^{57} +(3.24071 + 3.73998i) q^{59} +(-13.0837 + 1.24934i) q^{61} +(-1.07680 + 0.555131i) q^{63} +(-0.877361 - 3.61653i) q^{65} +(7.58805 + 3.06945i) q^{67} +(0.0109999 + 0.0453423i) q^{69} +(3.83840 - 1.97884i) q^{71} +(12.8427 - 1.22633i) q^{73} +(1.32622 + 1.53054i) q^{75} +(1.60137 - 1.25933i) q^{77} +(1.13203 + 3.27078i) q^{79} +(0.841254 + 0.540641i) q^{81} +(5.09407 - 7.15362i) q^{83} +(-0.430891 + 9.04552i) q^{85} +(-7.27173 - 5.71855i) q^{87} +(-1.66627 - 11.5892i) q^{89} +(-2.19899 + 1.41321i) q^{91} +(-0.279377 - 5.86485i) q^{93} +(-4.51642 + 13.0493i) q^{95} +(-7.42685 - 12.8637i) q^{97} +(-1.56115 - 0.624990i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 10 q^{3} + 2 q^{5} - 3 q^{7} - 10 q^{9}+O(q^{10}) \) 100 * q - 10 * q^3 + 2 * q^5 - 3 * q^7 - 10 * q^9	\( 100 q - 10 q^{3} + 2 q^{5} - 3 q^{7} - 10 q^{9} - 13 q^{11} - 3 q^{13} - 9 q^{15} - 44 q^{17} - 16 q^{19} - 3 q^{21} - 16 q^{23} + 28 q^{25} - 10 q^{27} - 7 q^{29} + 20 q^{31} - 2 q^{33} - 19 q^{35} - 22 q^{37} - 3 q^{39} - 14 q^{41} - 27 q^{43} + 2 q^{45} + 4 q^{47} - 92 q^{49} + 22 q^{51} + 8 q^{53} - 13 q^{55} + 17 q^{57} + 22 q^{59} + 17 q^{61} - 3 q^{63} + 56 q^{65} - 14 q^{67} + 17 q^{69} - q^{71} + 26 q^{73} + 28 q^{75} + 112 q^{77} + 69 q^{79} - 10 q^{81} + 15 q^{83} + 69 q^{85} + 4 q^{87} + 73 q^{89} - 40 q^{91} - 13 q^{93} + 59 q^{95} + 29 q^{97} - 2 q^{99}+O(q^{100}) \) 100 * q - 10 * q^3 + 2 * q^5 - 3 * q^7 - 10 * q^9 - 13 * q^11 - 3 * q^13 - 9 * q^15 - 44 * q^17 - 16 * q^19 - 3 * q^21 - 16 * q^23 + 28 * q^25 - 10 * q^27 - 7 * q^29 + 20 * q^31 - 2 * q^33 - 19 * q^35 - 22 * q^37 - 3 * q^39 - 14 * q^41 - 27 * q^43 + 2 * q^45 + 4 * q^47 - 92 * q^49 + 22 * q^51 + 8 * q^53 - 13 * q^55 + 17 * q^57 + 22 * q^59 + 17 * q^61 - 3 * q^63 + 56 * q^65 - 14 * q^67 + 17 * q^69 - q^71 + 26 * q^73 + 28 * q^75 + 112 * q^77 + 69 * q^79 - 10 * q^81 + 15 * q^83 + 69 * q^85 + 4 * q^87 + 73 * q^89 - 40 * q^91 - 13 * q^93 + 59 * q^95 + 29 * q^97 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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