LMFDB - Embedded newform 804.2.i.e.565.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(37,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("804.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 8x^{6} - 9x^{5} + 54x^{4} - 50x^{3} + 85x^{2} + 24x + 9 $ x^8 - x^7 + 8x^6 - 9x^5 + 54x^4 - 50x^3 + 85x^2 + 24x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			565.2
Root			$1.13858 - 1.97209i$ of defining polynomial
Character	$\chi$	$=$	804.565
Dual form			804.2.i.e.37.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{3} -2.18550 q^{5} +(1.80395 + 3.12454i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{3} -2.18550 q^{5} +(1.80395 + 3.12454i) q^{7} +1.00000 q^{9} +(-0.565964 - 0.980278i) q^{11} +(-2.34979 + 4.06996i) q^{13} -2.18550 q^{15} +(-1.13858 + 1.97209i) q^{17} +(-1.37658 + 2.38430i) q^{19} +(1.80395 + 3.12454i) q^{21} +(1.50000 - 2.59808i) q^{23} -0.223598 q^{25} +1.00000 q^{27} +(-0.407251 - 0.705379i) q^{29} +(2.98837 + 5.17602i) q^{31} +(-0.565964 - 0.980278i) q^{33} +(-3.94254 - 6.82868i) q^{35} +(-3.81246 + 6.60337i) q^{37} +(-2.34979 + 4.06996i) q^{39} +(3.20455 + 5.55044i) q^{41} +0.854758 q^{43} -2.18550 q^{45} +(2.07262 + 3.58988i) q^{47} +(-3.00850 + 5.21088i) q^{49} +(-1.13858 + 1.97209i) q^{51} +8.44157 q^{53} +(1.23691 + 2.14240i) q^{55} +(-1.37658 + 2.38430i) q^{57} -3.75315 q^{59} +(-0.712284 + 1.23371i) q^{61} +(1.80395 + 3.12454i) q^{63} +(5.13546 - 8.89488i) q^{65} +(2.71786 - 7.72096i) q^{67} +(1.50000 - 2.59808i) q^{69} +(2.63193 + 4.55863i) q^{71} +(1.27051 - 2.20059i) q^{73} -0.223598 q^{75} +(2.04195 - 3.53675i) q^{77} +(-4.20455 - 7.28249i) q^{79} +1.00000 q^{81} +(-0.716174 + 1.24045i) q^{83} +(2.48837 - 4.30999i) q^{85} +(-0.407251 - 0.705379i) q^{87} +0.527396 q^{89} -16.9557 q^{91} +(2.98837 + 5.17602i) q^{93} +(3.00850 - 5.21088i) q^{95} +(6.98945 - 12.1061i) q^{97} +(-0.565964 - 0.980278i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{3} - 6 q^{5} + 8 q^{9}+O(q^{10}) $ 8 * q + 8 * q^3 - 6 * q^5 + 8 * q^9	$ 8 q + 8 q^{3} - 6 q^{5} + 8 q^{9} + 3 q^{11} - 2 q^{13} - 6 q^{15} - q^{17} + 4 q^{19} + 12 q^{23} + 18 q^{25} + 8 q^{27} - 9 q^{29} - q^{31} + 3 q^{33} - 9 q^{35} + 14 q^{37} - 2 q^{39} + 10 q^{41} + 8 q^{43} - 6 q^{45} + 16 q^{47} + 6 q^{49} - q^{51} - 12 q^{53} + 4 q^{55} + 4 q^{57} + 4 q^{61} - 22 q^{65} + 20 q^{67} + 12 q^{69} + 6 q^{71} - 13 q^{73} + 18 q^{75} - 5 q^{77} - 18 q^{79} + 8 q^{81} - 15 q^{83} - 5 q^{85} - 9 q^{87} - 4 q^{89} - 34 q^{91} - q^{93} - 6 q^{95} + 30 q^{97} + 3 q^{99}+O(q^{100}) $ 8 * q + 8 * q^3 - 6 * q^5 + 8 * q^9 + 3 * q^11 - 2 * q^13 - 6 * q^15 - q^17 + 4 * q^19 + 12 * q^23 + 18 * q^25 + 8 * q^27 - 9 * q^29 - q^31 + 3 * q^33 - 9 * q^35 + 14 * q^37 - 2 * q^39 + 10 * q^41 + 8 * q^43 - 6 * q^45 + 16 * q^47 + 6 * q^49 - q^51 - 12 * q^53 + 4 * q^55 + 4 * q^57 + 4 * q^61 - 22 * q^65 + 20 * q^67 + 12 * q^69 + 6 * q^71 - 13 * q^73 + 18 * q^75 - 5 * q^77 - 18 * q^79 + 8 * q^81 - 15 * q^83 - 5 * q^85 - 9 * q^87 - 4 * q^89 - 34 * q^91 - q^93 - 6 * q^95 + 30 * q^97 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$		0			0
$5$	−2.18550			−0.977384			−0.488692	−	0.872456i	$-0.662526\pi$
$5$	−2.18550			−0.977384			−0.488692	+	0.872456i	$0.662526\pi$
$6$		0			0
$7$	1.80395	+	3.12454i	0.681831	+	1.18097i	0.974422	+	0.224728i	$0.0721492\pi$
$7$	1.80395	+	3.12454i	0.681831	+	1.18097i	−0.292591	+	0.956238i	$0.594517\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	−0.565964	−	0.980278i	−0.170644	−	0.295565i	0.768001	−	0.640449i	$-0.221252\pi$
$11$	−0.565964	−	0.980278i	−0.170644	−	0.295565i	−0.938645	+	0.344884i	$0.887918\pi$
$12$		0			0
$13$	−2.34979	+	4.06996i	−0.651714	+	1.12880i	0.330992	+	0.943633i	$0.392617\pi$
$13$	−2.34979	+	4.06996i	−0.651714	+	1.12880i	−0.982707	+	0.185169i	$0.940717\pi$
$14$		0			0
$15$	−2.18550			−0.564293
$16$		0			0
$17$	−1.13858	+	1.97209i	−0.276147	+	0.478301i	−0.970424	−	0.241407i	$-0.922391\pi$
$17$	−1.13858	+	1.97209i	−0.276147	+	0.478301i	0.694277	+	0.719708i	$0.255724\pi$
$18$		0			0
$19$	−1.37658	+	2.38430i	−0.315808	+	0.546995i	−0.979609	−	0.200914i	$-0.935609\pi$
$19$	−1.37658	+	2.38430i	−0.315808	+	0.546995i	0.663801	+	0.747909i	$0.268942\pi$
$20$		0			0
$21$	1.80395	+	3.12454i	0.393655	+	0.681831i
$22$		0			0
$23$	1.50000	−	2.59808i	0.312772	−	0.541736i	−0.666190	−	0.745782i	$-0.732076\pi$
$23$	1.50000	−	2.59808i	0.312772	−	0.541736i	0.978961	+	0.204046i	$0.0654092\pi$
$24$		0			0
$25$	−0.223598			−0.0447196
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	−0.407251	−	0.705379i	−0.0756246	−	0.130986i	0.825733	−	0.564061i	$-0.190762\pi$
$29$	−0.407251	−	0.705379i	−0.0756246	−	0.130986i	−0.901358	+	0.433075i	$0.857428\pi$
$30$		0			0
$31$	2.98837	+	5.17602i	0.536728	+	0.929640i	0.999078	+	0.0429422i	$0.0136731\pi$
$31$	2.98837	+	5.17602i	0.536728	+	0.929640i	−0.462350	+	0.886698i	$0.652994\pi$
$32$		0			0
$33$	−0.565964	−	0.980278i	−0.0985216	−	0.170644i
$34$		0			0
$35$	−3.94254	−	6.82868i	−0.666411	−	1.15426i
$36$		0			0
$37$	−3.81246	+	6.60337i	−0.626764	+	1.08559i	0.361433	+	0.932398i	$0.382288\pi$
$37$	−3.81246	+	6.60337i	−0.626764	+	1.08559i	−0.988197	+	0.153189i	$0.951046\pi$
$38$		0			0
$39$	−2.34979	+	4.06996i	−0.376267	+	0.651714i
$40$		0			0
$41$	3.20455	+	5.55044i	0.500466	+	0.866833i	1.00000		0.000538550i	$0.000171426\pi$
$41$	3.20455	+	5.55044i	0.500466	+	0.866833i	−0.499534	+	0.866295i	$0.666495\pi$
$42$		0			0
$43$	0.854758			0.130349			0.0651747	−	0.997874i	$-0.479240\pi$
$43$	0.854758			0.130349			0.0651747	+	0.997874i	$0.479240\pi$
$44$		0			0
$45$	−2.18550			−0.325795
$46$		0			0
$47$	2.07262	+	3.58988i	0.302323	+	0.523638i	0.976662	−	0.214784i	$-0.0689046\pi$
$47$	2.07262	+	3.58988i	0.302323	+	0.523638i	−0.674339	+	0.738422i	$0.735571\pi$
$48$		0			0
$49$	−3.00850	+	5.21088i	−0.429786	+	0.744411i
$50$		0			0
$51$	−1.13858	+	1.97209i	−0.159434	+	0.276147i
$52$		0			0
$53$	8.44157			1.15954			0.579770	−	0.814781i	$-0.303143\pi$
$53$	8.44157			1.15954			0.579770	+	0.814781i	$0.303143\pi$
$54$		0			0
$55$	1.23691	+	2.14240i	0.166785	+	0.288881i
$56$		0			0
$57$	−1.37658	+	2.38430i	−0.182332	+	0.315808i
$58$		0			0
$59$	−3.75315			−0.488619			−0.244309	−	0.969697i	$-0.578561\pi$
$59$	−3.75315			−0.488619			−0.244309	+	0.969697i	$0.578561\pi$
$60$		0			0
$61$	−0.712284	+	1.23371i	−0.0911986	+	0.157961i	−0.908016	−	0.418936i	$-0.862403\pi$
$61$	−0.712284	+	1.23371i	−0.0911986	+	0.157961i	0.816817	+	0.576897i	$0.195736\pi$
$62$		0			0
$63$	1.80395	+	3.12454i	0.227277	+	0.393655i
$64$		0			0
$65$	5.13546	−	8.89488i	0.636976	−	1.10327i
$66$		0			0
$67$	2.71786	−	7.72096i	0.332040	−	0.943265i
$67$	2.71786	−	7.72096i	0.332040	−	0.943265i
$68$		0			0
$69$	1.50000	−	2.59808i	0.180579	−	0.312772i
$70$		0			0
$71$	2.63193	+	4.55863i	0.312352	+	0.541010i	0.978871	−	0.204478i	$-0.0655497\pi$
$71$	2.63193	+	4.55863i	0.312352	+	0.541010i	−0.666519	+	0.745488i	$0.732216\pi$
$72$		0			0
$73$	1.27051	−	2.20059i	0.148702	−	0.257560i	−0.782046	−	0.623221i	$-0.785824\pi$
$73$	1.27051	−	2.20059i	0.148702	−	0.257560i	0.930748	+	0.365661i	$0.119157\pi$
$74$		0			0
$75$	−0.223598			−0.0258189
$76$		0			0
$77$	2.04195	−	3.53675i	0.232701	−	0.403050i
$78$		0			0
$79$	−4.20455	−	7.28249i	−0.473049	−	0.819344i	0.526476	−	0.850190i	$-0.323513\pi$
$79$	−4.20455	−	7.28249i	−0.473049	−	0.819344i	−0.999524	+	0.0308460i	$0.990180\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	−0.716174	+	1.24045i	−0.0786103	+	0.136157i	−0.902651	−	0.430374i	$-0.858382\pi$
$83$	−0.716174	+	1.24045i	−0.0786103	+	0.136157i	0.824040	+	0.566531i	$0.191715\pi$
$84$		0			0
$85$	2.48837	−	4.30999i	0.269902	−	0.467484i
$86$		0			0
$87$	−0.407251	−	0.705379i	−0.0436619	−	0.0756246i
$88$		0			0
$89$	0.527396			0.0559038			0.0279519	−	0.999609i	$-0.491101\pi$
$89$	0.527396			0.0559038			0.0279519	+	0.999609i	$0.491101\pi$
$90$		0			0
$91$	−16.9557			−1.77744
$92$		0			0
$93$	2.98837	+	5.17602i	0.309880	+	0.536728i
$94$		0			0
$95$	3.00850	−	5.21088i	0.308666	−	0.534625i
$96$		0			0
$97$	6.98945	−	12.1061i	0.709671	−	1.22919i	−0.255308	−	0.966860i	$-0.582177\pi$
$97$	6.98945	−	12.1061i	0.709671	−	1.22919i	0.964979	−	0.262327i	$-0.0844899\pi$
$98$		0			0
$99$	−0.565964	−	0.980278i	−0.0568815	−	0.0985216i
$100$		0			0
$101$	−7.80006	−	13.5101i	−0.776135	−	1.34431i	−0.934154	−	0.356870i	$-0.883844\pi$
$101$	−7.80006	−	13.5101i	−0.776135	−	1.34431i	0.158019	−	0.987436i	$-0.449489\pi$
$102$		0			0
$103$	7.56207	+	13.0979i	0.745113	+	1.29057i	0.950142	+	0.311818i	$0.100938\pi$
$103$	7.56207	+	13.0979i	0.745113	+	1.29057i	−0.205029	+	0.978756i	$0.565729\pi$
$104$		0			0
$105$	−3.94254	−	6.82868i	−0.384752	−	0.666411i
$106$		0			0
$107$	−5.50414			−0.532106			−0.266053	−	0.963958i	$-0.585720\pi$
$107$	−5.50414			−0.532106			−0.266053	+	0.963958i	$0.585720\pi$
$108$		0			0
$109$	3.25023			0.311315			0.155658	−	0.987811i	$-0.450250\pi$
$109$	3.25023			0.311315			0.155658	+	0.987811i	$0.450250\pi$
$110$		0			0
$111$	−3.81246	+	6.60337i	−0.361862	+	0.626764i
$112$		0			0
$113$	−5.09444	−	8.82382i	−0.479244	−	0.830076i	0.520472	−	0.853879i	$-0.325756\pi$
$113$	−5.09444	−	8.82382i	−0.479244	−	0.830076i	−0.999717	+	0.0238029i	$0.992423\pi$
$114$		0			0
$115$	−3.27825	+	5.67809i	−0.305698	+	0.529485i
$116$		0			0
$117$	−2.34979	+	4.06996i	−0.217238	+	0.376267i
$118$		0			0
$119$	−8.21582			−0.753143
$120$		0			0
$121$	4.85937	−	8.41668i	0.441761	−	0.765152i
$122$		0			0
$123$	3.20455	+	5.55044i	0.288944	+	0.500466i
$124$		0			0
$125$	11.4162			1.02109
$126$		0			0
$127$	2.70731	+	4.68921i	0.240235	+	0.416100i	0.960781	−	0.277307i	$-0.0894420\pi$
$127$	2.70731	+	4.68921i	0.240235	+	0.416100i	−0.720546	+	0.693407i	$0.756109\pi$
$128$		0			0
$129$	0.854758			0.0752573
$130$		0			0
$131$	−18.6171			−1.62659			−0.813293	−	0.581854i	$-0.802327\pi$
$131$	−18.6171			−1.62659			−0.813293	+	0.581854i	$0.802327\pi$
$132$		0			0
$133$	−9.93311			−0.861310
$134$		0			0
$135$	−2.18550			−0.188098
$136$		0			0
$137$	13.6017			1.16207			0.581034	−	0.813879i	$-0.302648\pi$
$137$	13.6017			1.16207			0.581034	+	0.813879i	$0.302648\pi$
$138$		0			0
$139$	5.78787			0.490921			0.245460	−	0.969407i	$-0.421061\pi$
$139$	5.78787			0.490921			0.245460	+	0.969407i	$0.421061\pi$
$140$		0			0
$141$	2.07262	+	3.58988i	0.174546	+	0.302323i
$142$		0			0
$143$	5.31958			0.444846
$144$		0			0
$145$	0.890046	+	1.54161i	0.0739143	+	0.128023i
$146$		0			0
$147$	−3.00850	+	5.21088i	−0.248137	+	0.429786i
$148$		0			0
$149$	3.08605			0.252819			0.126409	−	0.991978i	$-0.459655\pi$
$149$	3.08605			0.252819			0.126409	+	0.991978i	$0.459655\pi$
$150$		0			0
$151$	1.25920	−	2.18099i	0.102472	−	0.177487i	−0.810231	−	0.586111i	$-0.800658\pi$
$151$	1.25920	−	2.18099i	0.102472	−	0.177487i	0.912703	+	0.408625i	$0.133991\pi$
$152$		0			0
$153$	−1.13858	+	1.97209i	−0.0920491	+	0.159434i
$154$		0			0
$155$	−6.53109	−	11.3122i	−0.524589	−	0.908616i
$156$		0			0
$157$	−2.61953	+	4.53717i	−0.209062	+	0.362105i	−0.951419	−	0.307899i	$-0.900374\pi$
$157$	−2.61953	+	4.53717i	−0.209062	+	0.362105i	0.742358	+	0.670004i	$0.233708\pi$
$158$		0			0
$159$	8.44157			0.669460
$160$		0			0
$161$	10.8237			0.853029
$162$		0			0
$163$	−1.01516	−	1.75831i	−0.0795134	−	0.137721i	0.823527	−	0.567278i	$-0.192003\pi$
$163$	−1.01516	−	1.75831i	−0.0795134	−	0.137721i	−0.903040	+	0.429556i	$0.858670\pi$
$164$		0			0
$165$	1.23691	+	2.14240i	0.0962935	+	0.166785i
$166$		0			0
$167$	2.36218	+	4.09142i	0.182791	+	0.316604i	0.942830	−	0.333274i	$-0.108153\pi$
$167$	2.36218	+	4.09142i	0.182791	+	0.316604i	−0.760039	+	0.649878i	$0.774820\pi$
$168$		0			0
$169$	−4.54302	−	7.86875i	−0.349463	−	0.605288i
$170$		0			0
$171$	−1.37658	+	2.38430i	−0.105269	+	0.182332i
$172$		0			0
$173$	10.7194	−	18.5665i	0.814977	−	1.41158i	−0.0943671	−	0.995537i	$-0.530083\pi$
$173$	10.7194	−	18.5665i	0.814977	−	1.41158i	0.909344	−	0.416044i	$-0.136584\pi$
$174$		0			0
$175$	−0.403361	−	0.698641i	−0.0304912	−	0.0528123i
$176$		0			0
$177$	−3.75315			−0.282104
$178$		0			0
$179$	−24.7447			−1.84951			−0.924755	−	0.380564i	$-0.875730\pi$
$179$	−24.7447			−1.84951			−0.924755	+	0.380564i	$0.875730\pi$
$180$		0			0
$181$	9.63654	+	16.6910i	0.716278	+	1.24063i	0.962464	+	0.271408i	$0.0874892\pi$
$181$	9.63654	+	16.6910i	0.716278	+	1.24063i	−0.246186	+	0.969223i	$0.579177\pi$
$182$		0			0
$183$	−0.712284	+	1.23371i	−0.0526535	+	0.0911986i
$184$		0			0
$185$	8.33212	−	14.4316i	0.612589	−	1.06104i
$186$		0			0
$187$	2.57759			0.188492
$188$		0			0
$189$	1.80395	+	3.12454i	0.131218	+	0.227277i
$190$		0			0
$191$	4.17776	−	7.23610i	0.302292	−	0.523586i	−0.674363	−	0.738400i	$-0.735581\pi$
$191$	4.17776	−	7.23610i	0.302292	−	0.523586i	0.976655	+	0.214815i	$0.0689148\pi$
$192$		0			0
$193$	18.0610			1.30006			0.650028	−	0.759910i	$-0.274757\pi$
$193$	18.0610			1.30006			0.650028	+	0.759910i	$0.274757\pi$
$194$		0			0
$195$	5.13546	−	8.89488i	0.367758	−	0.636976i
$196$		0			0
$197$	3.03252	+	5.25248i	0.216058	+	0.374224i	0.953599	−	0.301078i	$-0.0973466\pi$
$197$	3.03252	+	5.25248i	0.216058	+	0.374224i	−0.737541	+	0.675302i	$0.764013\pi$
$198$		0			0
$199$	−2.14709	+	3.71886i	−0.152203	+	0.263623i	−0.932037	−	0.362363i	$-0.881970\pi$
$199$	−2.14709	+	3.71886i	−0.152203	+	0.263623i	0.779834	+	0.625986i	$0.215303\pi$
$200$		0			0
$201$	2.71786	−	7.72096i	0.191703	−	0.544595i
$202$		0			0
$203$	1.46932	−	2.54494i	0.103126	−	0.178620i
$204$		0			0
$205$	−7.00353	−	12.1305i	−0.489148	−	0.847229i
$206$		0			0
$207$	1.50000	−	2.59808i	0.104257	−	0.180579i
$208$		0			0
$209$	3.11637			0.215564
$210$		0			0
$211$	6.41078	−	11.1038i	0.441337	−	0.764417i	−0.556452	−	0.830880i	$-0.687838\pi$
$211$	6.41078	−	11.1038i	0.441337	−	0.764417i	0.997789	+	0.0664621i	$0.0211711\pi$
$212$		0			0
$213$	2.63193	+	4.55863i	0.180337	+	0.312352i
$214$		0			0
$215$	−1.86807			−0.127402
$216$		0			0
$217$	−10.7818	+	18.6746i	−0.731915	+	1.26771i
$218$		0			0
$219$	1.27051	−	2.20059i	0.0858532	−	0.148702i
$220$		0			0
$221$	−5.35087	−	9.26798i	−0.359938	−	0.623431i
$222$		0			0
$223$	−6.42457			−0.430221			−0.215110	−	0.976590i	$-0.569011\pi$
$223$	−6.42457			−0.430221			−0.215110	+	0.976590i	$0.569011\pi$
$224$		0			0
$225$	−0.223598			−0.0149065
$226$		0			0
$227$	−13.5227	−	23.4220i	−0.897533	−	1.55457i	−0.830638	−	0.556812i	$-0.812024\pi$
$227$	−13.5227	−	23.4220i	−0.897533	−	1.55457i	−0.0668945	−	0.997760i	$-0.521309\pi$
$228$		0			0
$229$	4.91744	−	8.51726i	0.324954	−	0.562836i	−0.656549	−	0.754283i	$-0.727985\pi$
$229$	4.91744	−	8.51726i	0.324954	−	0.562836i	0.981503	+	0.191447i	$0.0613179\pi$
$230$		0			0
$231$	2.04195	−	3.53675i	0.134350	−	0.232701i
$232$		0			0
$233$	−13.0159	−	22.5442i	−0.852699	−	1.47692i	−0.878764	−	0.477257i	$-0.841631\pi$
$233$	−13.0159	−	22.5442i	−0.852699	−	1.47692i	0.0260649	−	0.999660i	$-0.491702\pi$
$234$		0			0
$235$	−4.52971	−	7.84569i	−0.295486	−	0.511796i
$236$		0			0
$237$	−4.20455	−	7.28249i	−0.273115	−	0.473049i
$238$		0			0
$239$	−7.40352	−	12.8233i	−0.478894	−	0.829468i	0.520813	−	0.853671i	$-0.325629\pi$
$239$	−7.40352	−	12.8233i	−0.478894	−	0.829468i	−0.999707	+	0.0242023i	$0.992295\pi$
$240$		0			0
$241$	4.90833			0.316173			0.158087	−	0.987425i	$-0.449467\pi$
$241$	4.90833			0.316173			0.158087	+	0.987425i	$0.449467\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	6.57508	−	11.3884i	0.420066	−	0.727576i
$246$		0			0
$247$	−6.46932	−	11.2052i	−0.411633	−	0.712970i
$248$		0			0
$249$	−0.716174	+	1.24045i	−0.0453857	+	0.0786103i
$250$		0			0
$251$	−14.5007	+	25.1160i	−0.915277	+	1.58531i	−0.108783	+	0.994066i	$0.534695\pi$
$251$	−14.5007	+	25.1160i	−0.915277	+	1.58531i	−0.806495	+	0.591241i	$0.798638\pi$
$252$		0			0
$253$	−3.39578			−0.213491
$254$		0			0
$255$	2.48837	−	4.30999i	0.155828	−	0.269902i
$256$		0			0
$257$	11.5007	+	19.9198i	0.717395	+	1.24257i	0.962028	+	0.272949i	$0.0879992\pi$
$257$	11.5007	+	19.9198i	0.717395	+	1.24257i	−0.244633	+	0.969616i	$0.578668\pi$
$258$		0			0
$259$	−27.5100			−1.70939
$260$		0			0
$261$	−0.407251	−	0.705379i	−0.0252082	−	0.0436619i
$262$		0			0
$263$	10.0148			0.617542			0.308771	−	0.951136i	$-0.400082\pi$
$263$	10.0148			0.617542			0.308771	+	0.951136i	$0.400082\pi$
$264$		0			0
$265$	−18.4490			−1.13332
$266$		0			0
$267$	0.527396			0.0322761
$268$		0			0
$269$	5.82157			0.354947			0.177474	−	0.984126i	$-0.443208\pi$
$269$	5.82157			0.354947			0.177474	+	0.984126i	$0.443208\pi$
$270$		0			0
$271$	5.00769			0.304196			0.152098	−	0.988365i	$-0.451397\pi$
$271$	5.00769			0.304196			0.152098	+	0.988365i	$0.451397\pi$
$272$		0			0
$273$	−16.9557			−1.02620
$274$		0			0
$275$	0.126548	+	0.219188i	0.00763115	+	0.0132175i
$276$		0			0
$277$	10.6806			0.641738			0.320869	−	0.947124i	$-0.396025\pi$
$277$	10.6806			0.641738			0.320869	+	0.947124i	$0.396025\pi$
$278$		0			0
$279$	2.98837	+	5.17602i	0.178909	+	0.309880i
$280$		0			0
$281$	3.86884	−	6.70103i	0.230796	−	0.399750i	−0.727247	−	0.686376i	$-0.759200\pi$
$281$	3.86884	−	6.70103i	0.230796	−	0.399750i	0.958042	+	0.286626i	$0.0925338\pi$
$282$		0			0
$283$	21.1300			1.25605			0.628024	−	0.778194i	$-0.283864\pi$
$283$	21.1300			1.25605			0.628024	+	0.778194i	$0.283864\pi$
$284$		0			0
$285$	3.00850	−	5.21088i	0.178208	−	0.308666i
$286$		0			0
$287$	−11.5617	+	20.0255i	−0.682467	+	1.18207i
$288$		0			0
$289$	5.90725	+	10.2317i	0.347485	+	0.601862i
$290$		0			0
$291$	6.98945	−	12.1061i	0.409729	−	0.709671i
$292$		0			0
$293$	25.3133			1.47882			0.739410	−	0.673255i	$-0.235104\pi$
$293$	25.3133			1.47882			0.739410	+	0.673255i	$0.235104\pi$
$294$		0			0
$295$	8.20250			0.477568
$296$		0			0
$297$	−0.565964	−	0.980278i	−0.0328405	−	0.0568815i
$298$		0			0
$299$	7.04937	+	12.2099i	0.407676	+	0.706115i
$300$		0			0
$301$	1.54195	+	2.67073i	0.0888762	+	0.153938i
$302$		0			0
$303$	−7.80006	−	13.5101i	−0.448102	−	0.776135i
$304$		0			0
$305$	1.55669	−	2.69627i	0.0891361	−	0.154388i
$306$		0			0
$307$	10.2180	−	17.6981i	0.583173	−	1.01009i	−0.411927	−	0.911217i	$-0.635144\pi$
$307$	10.2180	−	17.6981i	0.583173	−	1.01009i	0.995100	−	0.0988688i	$-0.0315224\pi$
$308$		0			0
$309$	7.56207	+	13.0979i	0.430191	+	0.745113i
$310$		0			0
$311$	10.7441			0.609245			0.304622	−	0.952473i	$-0.401470\pi$
$311$	10.7441			0.609245			0.304622	+	0.952473i	$0.401470\pi$
$312$		0			0
$313$	−12.9811			−0.733733			−0.366866	−	0.930274i	$-0.619569\pi$
$313$	−12.9811			−0.733733			−0.366866	+	0.930274i	$0.619569\pi$
$314$		0			0
$315$	−3.94254	−	6.82868i	−0.222137	−	0.384752i
$316$		0			0
$317$	−16.1746	+	28.0152i	−0.908456	+	1.57349i	−0.0922456	+	0.995736i	$0.529404\pi$
$317$	−16.1746	+	28.0152i	−0.908456	+	1.57349i	−0.816210	+	0.577755i	$0.803929\pi$
$318$		0			0
$319$	−0.460978	+	0.798438i	−0.0258098	+	0.0447039i
$320$		0			0
$321$	−5.50414			−0.307211
$322$		0			0
$323$	−3.13469	−	5.42945i	−0.174419	−	0.302103i
$324$		0			0
$325$	0.525408	−	0.910034i	0.0291444	−	0.0504796i
$326$		0			0
$327$	3.25023			0.179738
$328$		0			0
$329$	−7.47783	+	12.9520i	−0.412266	+	0.714066i
$330$		0			0
$331$	13.6683	+	23.6742i	0.751277	+	1.30125i	0.947204	+	0.320632i	$0.103895\pi$
$331$	13.6683	+	23.6742i	0.751277	+	1.30125i	−0.195927	+	0.980619i	$0.562771\pi$
$332$		0			0
$333$	−3.81246	+	6.60337i	−0.208921	+	0.361862i
$334$		0			0
$335$	−5.93988	+	16.8741i	−0.324530	+	0.921933i
$336$		0			0
$337$	−12.8820	+	22.3122i	−0.701725	+	1.21542i	0.266136	+	0.963936i	$0.414253\pi$
$337$	−12.8820	+	22.3122i	−0.701725	+	1.21542i	−0.967861	+	0.251487i	$0.919080\pi$
$338$		0			0
$339$	−5.09444	−	8.82382i	−0.276692	−	0.479244i
$340$		0			0
$341$	3.38262	−	5.85887i	0.183179	−	0.317276i
$342$		0			0
$343$	3.54656			0.191496
$344$		0			0
$345$	−3.27825	+	5.67809i	−0.176495	+	0.305698i
$346$		0			0
$347$	17.3005	+	29.9653i	0.928738	+	1.60862i	0.785436	+	0.618943i	$0.212439\pi$
$347$	17.3005	+	29.9653i	0.928738	+	1.60862i	0.143302	+	0.989679i	$0.454228\pi$
$348$		0			0
$349$	23.1427			1.23880			0.619400	−	0.785076i	$-0.287376\pi$
$349$	23.1427			1.23880			0.619400	+	0.785076i	$0.287376\pi$
$350$		0			0
$351$	−2.34979	+	4.06996i	−0.125422	+	0.217238i
$352$		0			0
$353$	−10.3143	+	17.8649i	−0.548975	+	0.950852i	0.449370	+	0.893346i	$0.351648\pi$
$353$	−10.3143	+	17.8649i	−0.548975	+	0.950852i	−0.998345	+	0.0575068i	$0.981685\pi$
$354$		0			0
$355$	−5.75207	−	9.96288i	−0.305288	−	0.528775i
$356$		0			0
$357$	−8.21582			−0.434827
$358$		0			0
$359$	2.39618			0.126466			0.0632328	−	0.997999i	$-0.479859\pi$
$359$	2.39618			0.126466			0.0632328	+	0.997999i	$0.479859\pi$
$360$		0			0
$361$	5.71008	+	9.89015i	0.300531	+	0.520534i
$362$		0			0
$363$	4.85937	−	8.41668i	0.255051	−	0.441761i
$364$		0			0
$365$	−2.77670	+	4.80939i	−0.145339	+	0.251735i
$366$		0			0
$367$	4.93076	+	8.54032i	0.257383	+	0.445801i	0.965540	−	0.260254i	$-0.0838063\pi$
$367$	4.93076	+	8.54032i	0.257383	+	0.445801i	−0.708157	+	0.706055i	$0.750473\pi$
$368$		0			0
$369$	3.20455	+	5.55044i	0.166822	+	0.288944i
$370$		0			0
$371$	15.2282	+	26.3760i	0.790609	+	1.36938i
$372$		0			0
$373$	−15.0760	−	26.1123i	−0.780603	−	1.35204i	−0.931591	−	0.363509i	$-0.881579\pi$
$373$	−15.0760	−	26.1123i	−0.780603	−	1.35204i	0.150987	−	0.988536i	$-0.451755\pi$
$374$		0			0
$375$	11.4162			0.589528
$376$		0			0
$377$	3.82782			0.197143
$378$		0			0
$379$	−12.0416	+	20.8566i	−0.618535	+	1.07133i	0.371218	+	0.928546i	$0.378940\pi$
$379$	−12.0416	+	20.8566i	−0.618535	+	1.07133i	−0.989753	+	0.142788i	$0.954393\pi$
$380$		0			0
$381$	2.70731	+	4.68921i	0.138700	+	0.240235i
$382$		0			0
$383$	−8.32869	+	14.4257i	−0.425576	+	0.737120i	−0.996474	−	0.0839013i	$-0.973262\pi$
$383$	−8.32869	+	14.4257i	−0.425576	+	0.737120i	0.570898	+	0.821021i	$0.306595\pi$
$384$		0			0
$385$	−4.46267	+	7.72957i	−0.227439	+	0.393935i
$386$		0			0
$387$	0.854758			0.0434498
$388$		0			0
$389$	4.25848	−	7.37590i	0.215913	−	0.373973i	−0.737641	−	0.675193i	$-0.764060\pi$
$389$	4.25848	−	7.37590i	0.215913	−	0.373973i	0.953555	+	0.301220i	$0.0973938\pi$
$390$		0			0
$391$	3.41575	+	5.91626i	0.172742	+	0.299198i
$392$		0			0
$393$	−18.6171			−0.939110
$394$		0			0
$395$	9.18903	+	15.9159i	0.462350	+	0.800814i
$396$		0			0
$397$	−9.18356			−0.460910			−0.230455	−	0.973083i	$-0.574021\pi$
$397$	−9.18356			−0.460910			−0.230455	+	0.973083i	$0.574021\pi$
$398$		0			0
$399$	−9.93311			−0.497278
$400$		0			0
$401$	−25.3190			−1.26437			−0.632184	−	0.774818i	$-0.717841\pi$
$401$	−25.3190			−1.26437			−0.632184	+	0.774818i	$0.717841\pi$
$402$		0			0
$403$	−28.0882			−1.39917
$404$		0			0
$405$	−2.18550			−0.108598
$406$		0			0
$407$	8.63085			0.427815
$408$		0			0
$409$	−3.95381	−	6.84820i	−0.195503	−	0.338622i	0.751562	−	0.659662i	$-0.229301\pi$
$409$	−3.95381	−	6.84820i	−0.195503	−	0.338622i	−0.947065	+	0.321041i	$0.895967\pi$
$410$		0			0
$411$	13.6017			0.670920
$412$		0			0
$413$	−6.77051	−	11.7269i	−0.333155	−	0.577042i
$414$		0			0
$415$	1.56520	−	2.71100i	0.0768325	−	0.133078i
$416$		0			0
$417$	5.78787			0.283433
$418$		0			0
$419$	−6.87330	+	11.9049i	−0.335782	+	0.581592i	−0.983635	−	0.180174i	$-0.942334\pi$
$419$	−6.87330	+	11.9049i	−0.335782	+	0.581592i	0.647852	+	0.761766i	$0.275667\pi$
$420$		0			0
$421$	−2.09659	+	3.63141i	−0.102182	+	0.176984i	−0.912583	−	0.408891i	$-0.865916\pi$
$421$	−2.09659	+	3.63141i	−0.102182	+	0.176984i	0.810402	+	0.585875i	$0.199249\pi$
$422$		0			0
$423$	2.07262	+	3.58988i	0.100774	+	0.174546i
$424$		0			0
$425$	0.254585	−	0.440955i	0.0123492	−	0.0213894i
$426$		0			0
$427$	−5.13971			−0.248728
$428$		0			0
$429$	5.31958			0.256832
$430$		0			0
$431$	13.1294	+	22.7407i	0.632419	+	1.09538i	0.987056	+	0.160378i	$0.0512714\pi$
$431$	13.1294	+	22.7407i	0.632419	+	1.09538i	−0.354636	+	0.935004i	$0.615395\pi$
$432$		0			0
$433$	3.29125	+	5.70061i	0.158167	+	0.273954i	0.934208	−	0.356729i	$-0.116108\pi$
$433$	3.29125	+	5.70061i	0.158167	+	0.273954i	−0.776040	+	0.630683i	$0.782775\pi$
$434$		0			0
$435$	0.890046	+	1.54161i	0.0426744	+	0.0739143i
$436$		0			0
$437$	4.12973	+	7.15289i	0.197552	+	0.342169i
$438$		0			0
$439$	−5.05260	+	8.75137i	−0.241148	+	0.417680i	−0.961041	−	0.276404i	$-0.910857\pi$
$439$	−5.05260	+	8.75137i	−0.241148	+	0.417680i	0.719894	+	0.694084i	$0.244190\pi$
$440$		0			0
$441$	−3.00850	+	5.21088i	−0.143262	+	0.248137i
$442$		0			0
$443$	−11.6255	−	20.1360i	−0.552345	−	0.956690i	−0.998105	−	0.0615373i	$-0.980400\pi$
$443$	−11.6255	−	20.1360i	−0.552345	−	0.956690i	0.445759	−	0.895153i	$-0.352934\pi$
$444$		0			0
$445$	−1.15262			−0.0546395
$446$		0			0
$447$	3.08605			0.145965
$448$		0			0
$449$	5.08558	+	8.80848i	0.240003	+	0.415698i	0.960715	−	0.277537i	$-0.0895181\pi$
$449$	5.08558	+	8.80848i	0.240003	+	0.415698i	−0.720712	+	0.693235i	$0.756185\pi$
$450$		0			0
$451$	3.62732	−	6.28269i	0.170804	−	0.295841i
$452$		0			0
$453$	1.25920	−	2.18099i	0.0591622	−	0.102472i
$454$		0			0
$455$	37.0565			1.73724
$456$		0			0
$457$	−16.1162	−	27.9141i	−0.753885	−	1.30577i	−0.945927	−	0.324380i	$-0.894844\pi$
$457$	−16.1162	−	27.9141i	−0.753885	−	1.30577i	0.192042	−	0.981387i	$-0.438489\pi$
$458$		0			0
$459$	−1.13858	+	1.97209i	−0.0531446	+	0.0920491i
$460$		0			0
$461$	2.07313			0.0965554			0.0482777	−	0.998834i	$-0.484627\pi$
$461$	2.07313			0.0965554			0.0482777	+	0.998834i	$0.484627\pi$
$462$		0			0
$463$	18.3737	−	31.8242i	0.853899	−	1.47900i	−0.0237646	−	0.999718i	$-0.507565\pi$
$463$	18.3737	−	31.8242i	0.853899	−	1.47900i	0.877663	−	0.479278i	$-0.159101\pi$
$464$		0			0
$465$	−6.53109	−	11.3122i	−0.302872	−	0.524589i
$466$		0			0
$467$	−8.03109	+	13.9102i	−0.371634	+	0.643690i	−0.989817	−	0.142345i	$-0.954536\pi$
$467$	−8.03109	+	13.9102i	−0.371634	+	0.643690i	0.618183	+	0.786034i	$0.287869\pi$
$468$		0			0
$469$	29.0274	−	5.43619i	1.34036	−	0.251020i
$470$		0			0
$471$	−2.61953	+	4.53717i	−0.120702	+	0.209062i
$472$		0			0
$473$	−0.483762	−	0.837901i	−0.0222434	−	0.0385267i
$474$		0			0
$475$	0.307799	−	0.533124i	0.0141228	−	0.0244614i
$476$		0			0
$477$	8.44157			0.386513
$478$		0			0
$479$	−13.1600	+	22.7939i	−0.601298	+	1.04148i	0.391327	+	0.920252i	$0.372016\pi$
$479$	−13.1600	+	22.7939i	−0.601298	+	1.04148i	−0.992625	+	0.121227i	$0.961317\pi$
$480$		0			0
$481$	−17.9169	−	31.0331i	−0.816942	−	1.41499i
$482$		0			0
$483$	10.8237			0.492497
$484$		0			0
$485$	−15.2754	+	26.4578i	−0.693622	+	1.20139i
$486$		0			0
$487$	−15.9159	+	27.5671i	−0.721217	+	1.24918i	0.239296	+	0.970947i	$0.423083\pi$
$487$	−15.9159	+	27.5671i	−0.721217	+	1.24918i	−0.960512	+	0.278237i	$0.910250\pi$
$488$		0			0
$489$	−1.01516	−	1.75831i	−0.0459071	−	0.0795134i
$490$		0			0
$491$	−26.7413			−1.20682			−0.603409	−	0.797432i	$-0.706191\pi$
$491$	−26.7413			−1.20682			−0.603409	+	0.797432i	$0.706191\pi$
$492$		0			0
$493$	1.85476			0.0835341
$494$		0			0
$495$	1.23691	+	2.14240i	0.0555951	+	0.0962935i
$496$		0			0
$497$	−9.49575	+	16.4471i	−0.425943	+	0.737754i
$498$		0			0
$499$	14.3686	−	24.8871i	0.643227	−	1.11410i	−0.341481	−	0.939889i	$-0.610929\pi$
$499$	14.3686	−	24.8871i	0.643227	−	1.11410i	0.984708	−	0.174213i	$-0.0557380\pi$
$500$		0			0
$501$	2.36218	+	4.09142i	0.105535	+	0.182791i
$502$		0			0
$503$	−8.86776	−	15.3594i	−0.395394	−	0.684842i	0.597757	−	0.801677i	$-0.296059\pi$
$503$	−8.86776	−	15.3594i	−0.395394	−	0.684842i	−0.993151	+	0.116835i	$0.962725\pi$
$504$		0			0
$505$	17.0470	+	29.5263i	0.758583	+	1.31390i
$506$		0			0
$507$	−4.54302	−	7.86875i	−0.201763	−	0.349463i
$508$		0			0
$509$	−3.99222			−0.176952			−0.0884760	−	0.996078i	$-0.528200\pi$
$509$	−3.99222			−0.176952			−0.0884760	+	0.996078i	$0.528200\pi$
$510$		0			0
$511$	9.16778			0.405559
$512$		0			0
$513$	−1.37658	+	2.38430i	−0.0607773	+	0.105269i
$514$		0			0
$515$	−16.5269	−	28.6254i	−0.728262	−	1.26139i
$516$		0			0
$517$	2.34606	−	4.06349i	0.103179	−	0.178712i
$518$		0			0
$519$	10.7194	−	18.5665i	0.470527	−	0.814977i
$520$		0			0
$521$	20.2631			0.887744			0.443872	−	0.896090i	$-0.353604\pi$
$521$	20.2631			0.887744			0.443872	+	0.896090i	$0.353604\pi$
$522$		0			0
$523$	12.0162	−	20.8127i	0.525433	−	0.910077i	−0.474128	−	0.880456i	$-0.657237\pi$
$523$	12.0162	−	20.8127i	0.525433	−	0.910077i	0.999561	−	0.0296213i	$-0.00943013\pi$
$524$		0			0
$525$	−0.403361	−	0.698641i	−0.0176041	−	0.0304912i
$526$		0			0
$527$	−13.6101			−0.592864
$528$		0			0
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$		0			0
$531$	−3.75315			−0.162873
$532$		0			0
$533$	−30.1201			−1.30464
$534$		0			0
$535$	12.0293			0.520072
$536$		0			0
$537$	−24.7447			−1.06781
$538$		0			0
$539$	6.81081			0.293362
$540$		0			0
$541$	−14.3994			−0.619078			−0.309539	−	0.950887i	$-0.600175\pi$
$541$	−14.3994			−0.619078			−0.309539	+	0.950887i	$0.600175\pi$
$542$		0			0
$543$	9.63654	+	16.6910i	0.413543	+	0.716278i
$544$		0			0
$545$	−7.10336			−0.304275
$546$		0			0
$547$	3.88728	+	6.73297i	0.166208	+	0.287881i	0.937084	−	0.349105i	$-0.113514\pi$
$547$	3.88728	+	6.73297i	0.166208	+	0.287881i	−0.770876	+	0.636986i	$0.780181\pi$
$548$		0			0
$549$	−0.712284	+	1.23371i	−0.0303995	+	0.0526535i
$550$		0			0
$551$	2.24245			0.0955314
$552$		0			0
$553$	15.1696	−	26.2746i	0.645078	−	1.11731i
$554$		0			0
$555$	8.33212	−	14.4316i	0.353679	−	0.612589i
$556$		0			0
$557$	23.5989	+	40.8745i	0.999917	+	1.73191i	0.511098	+	0.859522i	$0.329239\pi$
$557$	23.5989	+	40.8745i	0.999917	+	1.73191i	0.488819	+	0.872385i	$0.337428\pi$
$558$		0			0
$559$	−2.00850	+	3.47883i	−0.0849506	+	0.147139i
$560$		0			0
$561$	2.57759			0.108826
$562$		0			0
$563$	−15.8315			−0.667218			−0.333609	−	0.942711i	$-0.608267\pi$
$563$	−15.8315			−0.667218			−0.333609	+	0.942711i	$0.608267\pi$
$564$		0			0
$565$	11.1339	+	19.2845i	0.468406	+	0.811303i
$566$		0			0
$567$	1.80395	+	3.12454i	0.0757590	+	0.131218i
$568$		0			0
$569$	5.88231	+	10.1885i	0.246599	+	0.427123i	0.962580	−	0.270998i	$-0.0873535\pi$
$569$	5.88231	+	10.1885i	0.246599	+	0.427123i	−0.715981	+	0.698120i	$0.754020\pi$
$570$		0			0
$571$	−9.77573	−	16.9321i	−0.409102	−	0.708585i	0.585688	−	0.810537i	$-0.300825\pi$
$571$	−9.77573	−	16.9321i	−0.409102	−	0.708585i	−0.994789	+	0.101952i	$0.967491\pi$
$572$		0			0
$573$	4.17776	−	7.23610i	0.174529	−	0.302292i
$574$		0			0
$575$	−0.335397	+	0.580925i	−0.0139870	+	0.0242262i
$576$		0			0
$577$	12.3131	+	21.3269i	0.512600	+	0.887849i	0.999893	+	0.0146105i	$0.00465083\pi$
$577$	12.3131	+	21.3269i	0.512600	+	0.887849i	−0.487294	+	0.873238i	$0.662016\pi$
$578$		0			0
$579$	18.0610			0.750588
$580$		0			0
$581$	−5.16778			−0.214396
$582$		0			0
$583$	−4.77762	−	8.27508i	−0.197869	−	0.342719i
$584$		0			0
$585$	5.13546	−	8.89488i	0.212325	−	0.367758i
$586$		0			0
$587$	8.91622	−	15.4433i	0.368012	−	0.637415i	−0.621243	−	0.783618i	$-0.713372\pi$
$587$	8.91622	−	15.4433i	0.368012	−	0.637415i	0.989255	+	0.146203i	$0.0467053\pi$
$588$		0			0
$589$	−16.4549			−0.678012
$590$		0			0
$591$	3.03252	+	5.25248i	0.124741	+	0.216058i
$592$		0			0
$593$	17.3150	−	29.9905i	0.711043	−	1.23156i	−0.253423	−	0.967355i	$-0.581557\pi$
$593$	17.3150	−	29.9905i	0.711043	−	1.23156i	0.964466	−	0.264207i	$-0.0851101\pi$
$594$		0			0
$595$	17.9557			0.736110
$596$		0			0
$597$	−2.14709	+	3.71886i	−0.0878744	+	0.152203i
$598$		0			0
$599$	11.9671	+	20.7277i	0.488963	+	0.846909i	0.999919	−	0.0126975i	$-0.00404184\pi$
$599$	11.9671	+	20.7277i	0.488963	+	0.846909i	−0.510956	+	0.859607i	$0.670709\pi$
$600$		0			0
$601$	19.4301	−	33.6539i	0.792570	−	1.37277i	−0.131800	−	0.991276i	$-0.542076\pi$
$601$	19.4301	−	33.6539i	0.792570	−	1.37277i	0.924371	−	0.381496i	$-0.124591\pi$
$602$		0			0
$603$	2.71786	−	7.72096i	0.110680	−	0.314422i
$604$		0			0
$605$	−10.6201	+	18.3946i	−0.431770	+	0.747848i
$606$		0			0
$607$	−4.56273	−	7.90288i	−0.185195	−	0.320768i	0.758447	−	0.651735i	$-0.225958\pi$
$607$	−4.56273	−	7.90288i	−0.185195	−	0.320768i	−0.943642	+	0.330967i	$0.892625\pi$
$608$		0			0
$609$	1.46932	−	2.54494i	0.0595400	−	0.103126i
$610$		0			0
$611$	−19.4809			−0.788113
$612$		0			0
$613$	−19.0733	+	33.0360i	−0.770365	+	1.33431i	0.166998	+	0.985957i	$0.446593\pi$
$613$	−19.0733	+	33.0360i	−0.770365	+	1.33431i	−0.937363	+	0.348354i	$0.886741\pi$
$614$		0			0
$615$	−7.00353	−	12.1305i	−0.282410	−	0.489148i
$616$		0			0
$617$	−8.17903			−0.329275			−0.164638	−	0.986354i	$-0.552645\pi$
$617$	−8.17903			−0.329275			−0.164638	+	0.986354i	$0.552645\pi$
$618$		0			0
$619$	8.84104	−	15.3131i	0.355351	−	0.615487i	−0.631827	−	0.775110i	$-0.717695\pi$
$619$	8.84104	−	15.3131i	0.355351	−	0.615487i	0.987178	+	0.159623i	$0.0510278\pi$
$620$		0			0
$621$	1.50000	−	2.59808i	0.0601929	−	0.104257i
$622$		0			0
$623$	0.951398	+	1.64787i	0.0381169	+	0.0660205i
$624$		0			0
$625$	−23.8320			−0.953281
$626$		0			0
$627$	3.11637			0.124456
$628$		0			0
$629$	−8.68161	−	15.0370i	−0.346158	−	0.599564i
$630$		0			0
$631$	−8.44234	+	14.6226i	−0.336084	+	0.582115i	−0.983692	−	0.179859i	$-0.942436\pi$
$631$	−8.44234	+	14.6226i	−0.336084	+	0.582115i	0.647608	+	0.761973i	$0.275769\pi$
$632$		0			0
$633$	6.41078	−	11.1038i	0.254806	−	0.441337i
$634$		0			0
$635$	−5.91683	−	10.2483i	−0.234802	−	0.406690i
$636$		0			0
$637$	−14.1387	−	24.4889i	−0.560196	−	0.970287i
$638$		0			0
$639$	2.63193	+	4.55863i	0.104117	+	0.180337i
$640$		0			0
$641$	16.5337	+	28.6371i	0.653040	+	1.13110i	0.982381	+	0.186888i	$0.0598400\pi$
$641$	16.5337	+	28.6371i	0.653040	+	1.13110i	−0.329341	+	0.944211i	$0.606827\pi$
$642$		0			0
$643$	−13.5197			−0.533165			−0.266583	−	0.963812i	$-0.585895\pi$
$643$	−13.5197			−0.533165			−0.266583	+	0.963812i	$0.585895\pi$
$644$		0			0
$645$	−1.86807			−0.0735553
$646$		0			0
$647$	7.30456	−	12.6519i	0.287172	−	0.497397i	−0.685962	−	0.727638i	$-0.740618\pi$
$647$	7.30456	−	12.6519i	0.287172	−	0.497397i	0.973134	+	0.230241i	$0.0739515\pi$
$648$		0			0
$649$	2.12415	+	3.67913i	0.0833800	+	0.144418i
$650$		0			0
$651$	−10.7818	+	18.6746i	−0.422571	+	0.731915i
$652$		0			0
$653$	11.9736	−	20.7389i	0.468564	−	0.811577i	−0.530790	−	0.847503i	$-0.678105\pi$
$653$	11.9736	−	20.7389i	0.468564	−	0.811577i	0.999354	+	0.0359263i	$0.0114382\pi$
$654$		0			0
$655$	40.6877			1.58980
$656$		0			0
$657$	1.27051	−	2.20059i	0.0495674	−	0.0858532i
$658$		0			0
$659$	11.4716	+	19.8695i	0.446872	+	0.774004i	0.998180	−	0.0602970i	$-0.0192048\pi$
$659$	11.4716	+	19.8695i	0.446872	+	0.774004i	−0.551309	+	0.834301i	$0.685871\pi$
$660$		0			0
$661$	−29.2236			−1.13667			−0.568333	−	0.822799i	$-0.692412\pi$
$661$	−29.2236			−1.13667			−0.568333	+	0.822799i	$0.692412\pi$
$662$		0			0
$663$	−5.35087	−	9.26798i	−0.207810	−	0.359938i
$664$		0			0
$665$	21.7088			0.841831
$666$		0			0
$667$	−2.44351			−0.0946129
$668$		0			0
$669$	−6.42457			−0.248388
$670$		0			0
$671$	1.61251			0.0622501
$672$		0			0
$673$	22.0095			0.848405			0.424203	−	0.905567i	$-0.360554\pi$
$673$	22.0095			0.848405			0.424203	+	0.905567i	$0.360554\pi$
$674$		0			0
$675$	−0.223598			−0.00860629
$676$		0			0
$677$	5.54630	+	9.60648i	0.213162	+	0.369207i	0.952702	−	0.303905i	$-0.0982905\pi$
$677$	5.54630	+	9.60648i	0.213162	+	0.369207i	−0.739541	+	0.673112i	$0.764957\pi$
$678$		0			0
$679$	50.4346			1.93550
$680$		0			0
$681$	−13.5227	−	23.4220i	−0.518191	−	0.897533i
$682$		0			0
$683$	4.44110	−	7.69222i	0.169934	−	0.294335i	−0.768462	−	0.639895i	$-0.778978\pi$
$683$	4.44110	−	7.69222i	0.169934	−	0.294335i	0.938396	+	0.345560i	$0.112311\pi$
$684$		0			0
$685$	−29.7264			−1.13579
$686$		0			0
$687$	4.91744	−	8.51726i	0.187612	−	0.324954i
$688$		0			0
$689$	−19.8359	+	34.3568i	−0.755688	+	1.30889i
$690$		0			0
$691$	3.49431	+	6.05232i	0.132930	+	0.230241i	0.924805	−	0.380442i	$-0.124228\pi$
$691$	3.49431	+	6.05232i	0.132930	+	0.230241i	−0.791875	+	0.610683i	$0.790895\pi$
$692$		0			0
$693$	2.04195	−	3.53675i	0.0775671	−	0.134350i
$694$		0			0
$695$	−12.6494			−0.479819
$696$		0			0
$697$	−14.5946			−0.552810
$698$		0			0
$699$	−13.0159	−	22.5442i	−0.492306	−	0.852699i
$700$		0			0
$701$	−10.1116	−	17.5138i	−0.381910	−	0.661487i	0.609425	−	0.792843i	$-0.291400\pi$
$701$	−10.1116	−	17.5138i	−0.381910	−	0.661487i	−0.991335	+	0.131356i	$0.958067\pi$
$702$		0			0
$703$	−10.4963	−	18.1801i	−0.395874	−	0.685674i
$704$		0			0
$705$	−4.52971	−	7.84569i	−0.170599	−	0.295486i
$706$		0			0
$707$	28.1419	−	48.7432i	1.05839	−	1.83318i
$708$		0			0
$709$	5.76069	−	9.97780i	0.216347	−	0.374724i	−0.737341	−	0.675520i	$-0.763919\pi$
$709$	5.76069	−	9.97780i	0.216347	−	0.374724i	0.953688	+	0.300796i	$0.0972524\pi$
$710$		0			0
$711$	−4.20455	−	7.28249i	−0.157683	−	0.273115i
$712$		0			0
$713$	17.9302			0.671493
$714$		0			0
$715$	−11.6259			−0.434785
$716$		0			0
$717$	−7.40352	−	12.8233i	−0.276489	−	0.478894i
$718$		0			0
$719$	−10.0196	+	17.3544i	−0.373667	+	0.647210i	−0.990127	−	0.140176i	$-0.955233\pi$
$719$	−10.0196	+	17.3544i	−0.373667	+	0.647210i	0.616460	+	0.787387i	$0.288566\pi$
$720$		0			0
$721$	−27.2833	+	47.2560i	−1.01608	+	1.75991i
$722$		0			0
$723$	4.90833			0.182543
$724$		0			0
$725$	0.0910605	+	0.157721i	0.00338190	+	0.00585763i
$726$		0			0
$727$	−1.04953	+	1.81783i	−0.0389248	+	0.0674197i	−0.884831	−	0.465911i	$-0.845727\pi$
$727$	−1.04953	+	1.81783i	−0.0389248	+	0.0674197i	0.845907	+	0.533331i	$0.179060\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−0.973215	+	1.68566i	−0.0359956	+	0.0623463i
$732$		0			0
$733$	−9.75837	−	16.9020i	−0.360434	−	0.624290i	0.627599	−	0.778537i	$-0.284038\pi$
$733$	−9.75837	−	16.9020i	−0.360434	−	0.624290i	−0.988032	+	0.154248i	$0.950705\pi$
$734$		0			0
$735$	6.57508	−	11.3884i	0.242525	−	0.420066i
$736$		0			0
$737$	−9.10690	+	1.70552i	−0.335457	+	0.0628237i
$738$		0			0
$739$	18.7174	−	32.4194i	0.688529	−	1.19257i	−0.283785	−	0.958888i	$-0.591590\pi$
$739$	18.7174	−	32.4194i	0.688529	−	1.19257i	0.972314	−	0.233679i	$-0.0750765\pi$
$740$		0			0
$741$	−6.46932	−	11.2052i	−0.237657	−	0.411633i
$742$		0			0
$743$	24.1292	−	41.7929i	0.885213	−	1.53323i	0.0397444	−	0.999210i	$-0.487346\pi$
$743$	24.1292	−	41.7929i	0.885213	−	1.53323i	0.845469	−	0.534025i	$-0.179321\pi$
$744$		0			0
$745$	−6.74455			−0.247101
$746$		0			0
$747$	−0.716174	+	1.24045i	−0.0262034	+	0.0453857i
$748$		0			0
$749$	−9.92922	−	17.1979i	−0.362806	−	0.628398i
$750$		0			0
$751$	−48.0379			−1.75293			−0.876464	−	0.481467i	$-0.840104\pi$
$751$	−48.0379			−1.75293			−0.876464	+	0.481467i	$0.840104\pi$
$752$		0			0
$753$	−14.5007	+	25.1160i	−0.528436	+	0.915277i
$754$		0			0
$755$	−2.75197	+	4.76656i	−0.100155	+	0.173473i
$756$		0			0
$757$	−2.74512	−	4.75468i	−0.0997729	−	0.172812i	0.811818	−	0.583911i	$-0.198478\pi$
$757$	−2.74512	−	4.75468i	−0.0997729	−	0.172812i	−0.911591	+	0.411099i	$0.865145\pi$
$758$		0			0
$759$	−3.39578			−0.123259
$760$		0			0
$761$	25.1452			0.911514			0.455757	−	0.890104i	$-0.349369\pi$
$761$	25.1452			0.911514			0.455757	+	0.890104i	$0.349369\pi$
$762$		0			0
$763$	5.86326	+	10.1555i	0.212264	+	0.367653i
$764$		0			0
$765$	2.48837	−	4.30999i	0.0899674	−	0.155828i
$766$		0			0
$767$	8.81911	−	15.2752i	0.318440	−	0.551554i
$768$		0			0
$769$	−17.1261	−	29.6633i	−0.617584	−	1.06969i	−0.989925	−	0.141591i	$-0.954778\pi$
$769$	−17.1261	−	29.6633i	−0.617584	−	1.06969i	0.372341	−	0.928096i	$-0.378555\pi$
$770$		0			0
$771$	11.5007	+	19.9198i	0.414188	+	0.717395i
$772$		0			0
$773$	−18.4599	−	31.9735i	−0.663957	−	1.15001i	−0.979567	−	0.201118i	$-0.935543\pi$
$773$	−18.4599	−	31.9735i	−0.663957	−	1.15001i	0.315610	−	0.948889i	$-0.397791\pi$
$774$		0			0
$775$	−0.668194	−	1.15735i	−0.0240023	−	0.0415731i
$776$		0			0
$777$	−27.5100			−0.986915
$778$		0			0
$779$	−17.6452			−0.632205
$780$		0			0
$781$	2.97915	−	5.16004i	0.106602	−	0.184641i
$782$		0			0
$783$	−0.407251	−	0.705379i	−0.0145540	−	0.0252082i
$784$		0			0
$785$	5.72499	−	9.91597i	0.204334	−	0.353916i
$786$		0			0
$787$	−3.75305	+	6.50048i	−0.133782	+	0.231717i	−0.925131	−	0.379647i	$-0.876045\pi$
$787$	−3.75305	+	6.50048i	−0.133782	+	0.231717i	0.791350	+	0.611364i	$0.209379\pi$
$788$		0			0
$789$	10.0148			0.356538
$790$		0			0
$791$	18.3803	−	31.8356i	0.653527	−	1.13194i
$792$		0			0
$793$	−3.34743	−	5.79792i	−0.118871	−	0.205890i
$794$		0			0
$795$	−18.4490			−0.654320
$796$		0			0
$797$	25.2065	+	43.6589i	0.892860	+	1.54648i	0.836431	+	0.548073i	$0.184638\pi$
$797$	25.2065	+	43.6589i	0.892860	+	1.54648i	0.0564295	+	0.998407i	$0.482028\pi$
$798$		0			0
$799$	−9.43942			−0.333943
$800$		0			0
$801$	0.527396			0.0186346
$802$		0			0
$803$	−2.87625			−0.101501
$804$		0			0
$805$	−23.6552			−0.833737
$806$		0			0
$807$	5.82157			0.204929
$808$		0			0
$809$	26.1340			0.918821			0.459411	−	0.888224i	$-0.348061\pi$
$809$	26.1340			0.918821			0.459411	+	0.888224i	$0.348061\pi$
$810$		0			0
$811$	26.3960	+	45.7193i	0.926890	+	1.60542i	0.788493	+	0.615044i	$0.210862\pi$
$811$	26.3960	+	45.7193i	0.926890	+	1.60542i	0.138397	+	0.990377i	$0.455805\pi$
$812$		0			0
$813$	5.00769			0.175627
$814$		0			0
$815$	2.21863	+	3.84278i	0.0777152	+	0.134607i
$816$		0			0
$817$	−1.17664	+	2.03800i	−0.0411654	+	0.0713005i
$818$		0			0
$819$	−16.9557			−0.592478
$820$		0			0
$821$	−15.4989	+	26.8449i	−0.540916	+	0.936894i	0.457936	+	0.888985i	$0.348589\pi$
$821$	−15.4989	+	26.8449i	−0.540916	+	0.936894i	−0.998852	+	0.0479088i	$0.984744\pi$
$822$		0			0
$823$	25.9398	−	44.9290i	0.904204	−	1.56613i	0.0822216	−	0.996614i	$-0.473798\pi$
$823$	25.9398	−	44.9290i	0.904204	−	1.56613i	0.821982	−	0.569513i	$-0.192868\pi$
$824$		0			0
$825$	0.126548	+	0.219188i	0.00440585	+	0.00763115i
$826$		0			0
$827$	24.7243	−	42.8238i	0.859749	−	1.48913i	−0.0124196	−	0.999923i	$-0.503953\pi$
$827$	24.7243	−	42.8238i	0.859749	−	1.48913i	0.872168	−	0.489206i	$-0.162713\pi$
$828$		0			0
$829$	33.9457			1.17898			0.589492	−	0.807774i	$-0.299328\pi$
$829$	33.9457			1.17898			0.589492	+	0.807774i	$0.299328\pi$
$830$		0			0
$831$	10.6806			0.370507
$832$		0			0
$833$	−6.85087	−	11.8661i	−0.237369	−	0.411134i
$834$		0			0
$835$	−5.16255	−	8.94179i	−0.178657	−	0.309443i
$836$		0			0
$837$	2.98837	+	5.17602i	0.103293	+	0.178909i
$838$		0			0
$839$	−3.19605	−	5.53571i	−0.110340	−	0.191114i	0.805568	−	0.592504i	$-0.201861\pi$
$839$	−3.19605	−	5.53571i	−0.110340	−	0.191114i	−0.915907	+	0.401390i	$0.868527\pi$
$840$		0			0
$841$	14.1683	−	24.5402i	0.488562	−	0.846214i
$842$		0			0
$843$	3.86884	−	6.70103i	0.133250	−	0.230796i
$844$		0			0
$845$	9.92877	+	17.1971i	0.341560	+	0.591599i
$846$		0			0
$847$	35.0643			1.20482
$848$		0			0
$849$	21.1300			0.725179
$850$		0			0
$851$	11.4374	+	19.8101i	0.392068	+	0.679082i
$852$		0			0
$853$	22.9753	−	39.7943i	0.786658	−	1.36253i	−0.141345	−	0.989960i	$-0.545143\pi$
$853$	22.9753	−	39.7943i	0.786658	−	1.36253i	0.928003	−	0.372572i	$-0.121524\pi$
$854$		0			0
$855$	3.00850	−	5.21088i	0.102889	−	0.178208i
$856$		0			0
$857$	45.5691			1.55661			0.778305	−	0.627886i	$-0.216080\pi$
$857$	45.5691			1.55661			0.778305	+	0.627886i	$0.216080\pi$
$858$		0			0
$859$	−7.30472	−	12.6521i	−0.249234	−	0.431686i	0.714080	−	0.700065i	$-0.246845\pi$
$859$	−7.30472	−	12.6521i	−0.249234	−	0.431686i	−0.963313	+	0.268379i	$0.913512\pi$
$860$		0			0
$861$	−11.5617	+	20.0255i	−0.394022	+	0.682467i
$862$		0			0
$863$	−47.6989			−1.62369			−0.811844	−	0.583874i	$-0.801536\pi$
$863$	−47.6989			−1.62369			−0.811844	+	0.583874i	$0.801536\pi$
$864$		0			0
$865$	−23.4271	+	40.5770i	−0.796546	+	1.37966i
$866$		0			0
$867$	5.90725	+	10.2317i	0.200621	+	0.347485i
$868$		0			0
$869$	−4.75924	+	8.24325i	−0.161446	+	0.279633i
$870$		0			0
$871$	25.0376	+	29.2042i	0.848365	+	0.989547i
$872$		0			0
$873$	6.98945	−	12.1061i	0.236557	−	0.409729i
$874$		0			0
$875$	20.5942	+	35.6703i	0.696212	+	1.20588i
$876$		0			0
$877$	2.03533	−	3.52530i	0.0687283	−	0.119041i	−0.829613	−	0.558338i	$-0.811439\pi$
$877$	2.03533	−	3.52530i	0.0687283	−	0.119041i	0.898342	+	0.439297i	$0.144773\pi$
$878$		0			0
$879$	25.3133			0.853798
$880$		0			0
$881$	−17.1155	+	29.6449i	−0.576635	+	0.998762i	0.419226	+	0.907882i	$0.362301\pi$
$881$	−17.1155	+	29.6449i	−0.576635	+	0.998762i	−0.995862	+	0.0908802i	$0.971032\pi$
$882$		0			0
$883$	−15.8440	−	27.4426i	−0.533193	−	0.923518i	−0.999248	−	0.0387624i	$-0.987658\pi$
$883$	−15.8440	−	27.4426i	−0.533193	−	0.923518i	0.466055	−	0.884756i	$-0.345675\pi$
$884$		0			0
$885$	8.20250			0.275724
$886$		0			0
$887$	−2.01925	+	3.49744i	−0.0677998	+	0.117433i	−0.897933	−	0.440133i	$-0.854931\pi$
$887$	−2.01925	+	3.49744i	−0.0677998	+	0.117433i	0.830133	+	0.557566i	$0.188265\pi$
$888$		0			0
$889$	−9.76774	+	16.9182i	−0.327600	+	0.567419i
$890$		0			0
$891$	−0.565964	−	0.980278i	−0.0189605	−	0.0328405i
$892$		0			0
$893$	−11.4125			−0.381904
$894$		0			0
$895$	54.0796			1.80768
$896$		0			0
$897$	7.04937	+	12.2099i	0.235372	+	0.407676i
$898$		0			0
$899$	2.43404	−	4.21587i	0.0811797	−	0.140607i
$900$		0			0
$901$	−9.61144	+	16.6475i	−0.320204	+	0.554609i
$902$		0			0
$903$	1.54195	+	2.67073i	0.0513127	+	0.0888762i
$904$		0			0
$905$	−21.0606	−	36.4781i	−0.700079	−	1.21257i
$906$		0			0
$907$	−6.14974	−	10.6517i	−0.204199	−	0.353683i	0.745678	−	0.666306i	$-0.232126\pi$
$907$	−6.14974	−	10.6517i	−0.204199	−	0.353683i	−0.949877	+	0.312623i	$0.898792\pi$
$908$		0			0
$909$	−7.80006	−	13.5101i	−0.258712	−	0.448102i
$910$		0			0
$911$	−18.6454			−0.617749			−0.308875	−	0.951103i	$-0.599952\pi$
$911$	−18.6454			−0.617749			−0.308875	+	0.951103i	$0.599952\pi$
$912$		0			0
$913$	1.62131			0.0536576
$914$		0			0
$915$	1.55669	−	2.69627i	0.0514627	−	0.0891361i
$916$		0			0
$917$	−33.5845	−	58.1700i	−1.10906	−	1.92094i
$918$		0			0
$919$	−28.5346	+	49.4233i	−0.941269	+	1.63033i	−0.178214	+	0.983992i	$0.557032\pi$
$919$	−28.5346	+	49.4233i	−0.941269	+	1.63033i	−0.763055	+	0.646334i	$0.776301\pi$
$920$		0			0
$921$	10.2180	−	17.6981i	0.336695	−	0.583173i
$922$		0			0
$923$	−24.7379			−0.814258
$924$		0			0
$925$	0.852458	−	1.47650i	0.0280286	−	0.0485470i
$926$		0			0
$927$	7.56207	+	13.0979i	0.248371	+	0.430191i
$928$		0			0
$929$	15.9964			0.524825			0.262413	−	0.964956i	$-0.415482\pi$
$929$	15.9964			0.524825			0.262413	+	0.964956i	$0.415482\pi$
$930$		0			0
$931$	−8.28286	−	14.3463i	−0.271460	−	0.470182i
$932$		0			0
$933$	10.7441			0.351748
$934$		0			0
$935$	−5.63332			−0.184229
$936$		0			0
$937$	−7.52546			−0.245846			−0.122923	−	0.992416i	$-0.539227\pi$
$937$	−7.52546			−0.245846			−0.122923	+	0.992416i	$0.539227\pi$
$938$		0			0
$939$	−12.9811			−0.423621
$940$		0			0
$941$	−41.0892			−1.33947			−0.669736	−	0.742600i	$-0.733593\pi$
$941$	−41.0892			−1.33947			−0.669736	+	0.742600i	$0.733593\pi$
$942$		0			0
$943$	19.2273			0.626127
$944$		0			0
$945$	−3.94254	−	6.82868i	−0.128251	−	0.222137i
$946$		0			0
$947$	−13.8156			−0.448948			−0.224474	−	0.974480i	$-0.572066\pi$
$947$	−13.8156			−0.448948			−0.224474	+	0.974480i	$0.572066\pi$
$948$		0			0
$949$	5.97087	+	10.3419i	0.193823	+	0.335711i
$950$		0			0
$951$	−16.1746	+	28.0152i	−0.524497	+	0.908456i
$952$		0			0
$953$	21.1331			0.684567			0.342283	−	0.939597i	$-0.388800\pi$
$953$	21.1331			0.684567			0.342283	+	0.939597i	$0.388800\pi$
$954$		0			0
$955$	−9.13049	+	15.8145i	−0.295456	+	0.511744i
$956$		0			0
$957$	−0.460978	+	0.798438i	−0.0149013	+	0.0258098i
$958$		0			0
$959$	24.5368	+	42.4989i	0.792334	+	1.37236i
$960$		0			0
$961$	−2.36076	+	4.08896i	−0.0761536	+	0.131902i
$962$		0			0
$963$	−5.50414			−0.177369
$964$		0			0
$965$	−39.4722			−1.27065
$966$		0			0
$967$	−12.7523	−	22.0877i	−0.410088	−	0.710293i	0.584811	−	0.811169i	$-0.301169\pi$
$967$	−12.7523	−	22.0877i	−0.410088	−	0.710293i	−0.994899	+	0.100877i	$0.967835\pi$
$968$		0			0
$969$	−3.13469	−	5.42945i	−0.100701	−	0.174419i
$970$		0			0
$971$	−20.9309	−	36.2533i	−0.671704	−	1.16342i	−0.977421	−	0.211302i	$-0.932230\pi$
$971$	−20.9309	−	36.2533i	−0.671704	−	1.16342i	0.305717	−	0.952122i	$-0.401104\pi$
$972$		0			0
$973$	10.4411	+	18.0844i	0.334725	+	0.579761i
$974$		0			0
$975$	0.525408	−	0.910034i	0.0168265	−	0.0291444i
$976$		0			0
$977$	10.8222	−	18.7447i	0.346234	−	0.599695i	−0.639343	−	0.768922i	$-0.720794\pi$
$977$	10.8222	−	18.7447i	0.346234	−	0.599695i	0.985577	+	0.169227i	$0.0541270\pi$
$978$		0			0
$979$	−0.298487	−	0.516994i	−0.00953968	−	0.0165232i
$980$		0			0
$981$	3.25023			0.103772
$982$		0			0
$983$	47.1378			1.50346			0.751731	−	0.659470i	$-0.229219\pi$
$983$	47.1378			1.50346			0.751731	+	0.659470i	$0.229219\pi$
$984$		0			0
$985$	−6.62757	−	11.4793i	−0.211172	−	0.365760i
$986$		0			0
$987$	−7.47783	+	12.9520i	−0.238022	+	0.412266i
$988$		0			0
$989$	1.28214	−	2.22073i	0.0407696	−	0.0706150i
$990$		0			0
$991$	−17.2811			−0.548952			−0.274476	−	0.961594i	$-0.588504\pi$
$991$	−17.2811			−0.548952			−0.274476	+	0.961594i	$0.588504\pi$
$992$		0			0
$993$	13.6683	+	23.6742i	0.433750	+	0.751277i
$994$		0			0
$995$	4.69245	−	8.12757i	0.148761	−	0.257661i
$996$		0			0
$997$	6.73677			0.213356			0.106678	−	0.994294i	$-0.465979\pi$
$997$	6.73677			0.213356			0.106678	+	0.994294i	$0.465979\pi$
$998$		0			0
$999$	−3.81246	+	6.60337i	−0.120621	+	0.208921i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.i.e.565.2	yes	8
3.2	odd	2		2412.2.l.f.1369.3		8
67.37	even	3	inner	804.2.i.e.37.2	✓	8
201.104	odd	6		2412.2.l.f.37.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.i.e.37.2	✓	8	67.37	even	3	inner
804.2.i.e.565.2	yes	8	1.1	even	1	trivial
2412.2.l.f.37.3		8	201.104	odd	6
2412.2.l.f.1369.3		8	3.2	odd	2

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.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{3} -2.18550 q^{5} +(1.80395 + 3.12454i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{3} -2.18550 q^{5} +(1.80395 + 3.12454i) q^{7} +1.00000 q^{9} +(-0.565964 - 0.980278i) q^{11} +(-2.34979 + 4.06996i) q^{13} -2.18550 q^{15} +(-1.13858 + 1.97209i) q^{17} +(-1.37658 + 2.38430i) q^{19} +(1.80395 + 3.12454i) q^{21} +(1.50000 - 2.59808i) q^{23} -0.223598 q^{25} +1.00000 q^{27} +(-0.407251 - 0.705379i) q^{29} +(2.98837 + 5.17602i) q^{31} +(-0.565964 - 0.980278i) q^{33} +(-3.94254 - 6.82868i) q^{35} +(-3.81246 + 6.60337i) q^{37} +(-2.34979 + 4.06996i) q^{39} +(3.20455 + 5.55044i) q^{41} +0.854758 q^{43} -2.18550 q^{45} +(2.07262 + 3.58988i) q^{47} +(-3.00850 + 5.21088i) q^{49} +(-1.13858 + 1.97209i) q^{51} +8.44157 q^{53} +(1.23691 + 2.14240i) q^{55} +(-1.37658 + 2.38430i) q^{57} -3.75315 q^{59} +(-0.712284 + 1.23371i) q^{61} +(1.80395 + 3.12454i) q^{63} +(5.13546 - 8.89488i) q^{65} +(2.71786 - 7.72096i) q^{67} +(1.50000 - 2.59808i) q^{69} +(2.63193 + 4.55863i) q^{71} +(1.27051 - 2.20059i) q^{73} -0.223598 q^{75} +(2.04195 - 3.53675i) q^{77} +(-4.20455 - 7.28249i) q^{79} +1.00000 q^{81} +(-0.716174 + 1.24045i) q^{83} +(2.48837 - 4.30999i) q^{85} +(-0.407251 - 0.705379i) q^{87} +0.527396 q^{89} -16.9557 q^{91} +(2.98837 + 5.17602i) q^{93} +(3.00850 - 5.21088i) q^{95} +(6.98945 - 12.1061i) q^{97} +(-0.565964 - 0.980278i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{3} - 6 q^{5} + 8 q^{9}+O(q^{10}) \) 8 * q + 8 * q^3 - 6 * q^5 + 8 * q^9	\( 8 q + 8 q^{3} - 6 q^{5} + 8 q^{9} + 3 q^{11} - 2 q^{13} - 6 q^{15} - q^{17} + 4 q^{19} + 12 q^{23} + 18 q^{25} + 8 q^{27} - 9 q^{29} - q^{31} + 3 q^{33} - 9 q^{35} + 14 q^{37} - 2 q^{39} + 10 q^{41} + 8 q^{43} - 6 q^{45} + 16 q^{47} + 6 q^{49} - q^{51} - 12 q^{53} + 4 q^{55} + 4 q^{57} + 4 q^{61} - 22 q^{65} + 20 q^{67} + 12 q^{69} + 6 q^{71} - 13 q^{73} + 18 q^{75} - 5 q^{77} - 18 q^{79} + 8 q^{81} - 15 q^{83} - 5 q^{85} - 9 q^{87} - 4 q^{89} - 34 q^{91} - q^{93} - 6 q^{95} + 30 q^{97} + 3 q^{99}+O(q^{100}) \) 8 * q + 8 * q^3 - 6 * q^5 + 8 * q^9 + 3 * q^11 - 2 * q^13 - 6 * q^15 - q^17 + 4 * q^19 + 12 * q^23 + 18 * q^25 + 8 * q^27 - 9 * q^29 - q^31 + 3 * q^33 - 9 * q^35 + 14 * q^37 - 2 * q^39 + 10 * q^41 + 8 * q^43 - 6 * q^45 + 16 * q^47 + 6 * q^49 - q^51 - 12 * q^53 + 4 * q^55 + 4 * q^57 + 4 * q^61 - 22 * q^65 + 20 * q^67 + 12 * q^69 + 6 * q^71 - 13 * q^73 + 18 * q^75 - 5 * q^77 - 18 * q^79 + 8 * q^81 - 15 * q^83 - 5 * q^85 - 9 * q^87 - 4 * q^89 - 34 * q^91 - q^93 - 6 * q^95 + 30 * q^97 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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