LMFDB - Embedded newform 804.2.y.a.121.2

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			121.2
Character	$\chi$	$=$	804.121
Dual form			804.2.y.a.505.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.654861 + 0.755750i) q^{3} +(-1.55544 + 0.999620i) q^{5} +(-0.0528822 - 0.0211708i) q^{7} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(q+(-0.654861 + 0.755750i) q^{3} +(-1.55544 + 0.999620i) q^{5} +(-0.0528822 - 0.0211708i) q^{7} +(-0.142315 - 0.989821i) q^{9} +(-0.204418 - 4.29125i) q^{11} +(-0.838025 + 0.0800217i) q^{13} +(0.263134 - 1.83013i) q^{15} +(-0.924879 - 3.81240i) q^{17} +(-0.100587 + 0.0402688i) q^{19} +(0.0506303 - 0.0261017i) q^{21} +(3.78325 + 0.729162i) q^{23} +(-0.656925 + 1.43846i) q^{25} +(0.841254 + 0.540641i) q^{27} +(3.47014 - 6.01046i) q^{29} +(6.04742 + 0.577459i) q^{31} +(3.37698 + 2.65568i) q^{33} +(0.103418 - 0.0199321i) q^{35} +(-0.653613 - 1.13209i) q^{37} +(0.488313 - 0.685740i) q^{39} +(7.23841 - 6.90181i) q^{41} +(3.80231 + 1.11646i) q^{43} +(1.21081 + 1.39735i) q^{45} +(-1.91593 - 5.53572i) q^{47} +(-5.06379 - 4.82831i) q^{49} +(3.48689 + 1.79762i) q^{51} +(0.910035 - 0.267210i) q^{53} +(4.60758 + 6.47044i) q^{55} +(0.0354371 - 0.102389i) q^{57} +(-0.781719 - 1.71172i) q^{59} +(0.339191 - 7.12050i) q^{61} +(-0.0134294 + 0.0553568i) q^{63} +(1.22351 - 0.962176i) q^{65} +(-6.41223 + 5.08757i) q^{67} +(-3.02856 + 2.38169i) q^{69} +(0.332088 - 1.36889i) q^{71} +(0.491530 - 10.3185i) q^{73} +(-0.656925 - 1.43846i) q^{75} +(-0.0800393 + 0.231259i) q^{77} +(7.40178 + 10.3944i) q^{79} +(-0.959493 + 0.281733i) q^{81} +(-13.7014 - 7.06355i) q^{83} +(5.24955 + 5.00543i) q^{85} +(2.26994 + 6.55857i) q^{87} +(2.03978 + 2.35403i) q^{89} +(0.0460107 + 0.0135100i) q^{91} +(-4.39663 + 4.19218i) q^{93} +(0.116203 - 0.163184i) q^{95} +(-2.38709 - 4.13456i) q^{97} +(-4.21848 + 0.813046i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{26}{33}\right)$	$1$

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
$3$	−0.654861	+	0.755750i	−0.378084	+	0.436332i
$3$	−0.654861	+	0.755750i	−0.378084	+	0.436332i
$4$		0			0
$5$	−1.55544	+	0.999620i	−0.695613	+	0.447044i	−0.840077	−	0.542466i	$-0.817491\pi$
$5$	−1.55544	+	0.999620i	−0.695613	+	0.447044i	0.144464	+	0.989510i	$0.453854\pi$
$6$		0			0
$7$	−0.0528822	−	0.0211708i	−0.0199876	−	0.00800182i	0.361647	−	0.932315i	$-0.382215\pi$
$7$	−0.0528822	−	0.0211708i	−0.0199876	−	0.00800182i	−0.381635	+	0.924313i	$0.624639\pi$
$8$		0			0
$9$	−0.142315	−	0.989821i	−0.0474383	−	0.329940i
$10$		0			0
$11$	−0.204418	−	4.29125i	−0.0616342	−	1.29386i	−0.791880	−	0.610677i	$-0.790897\pi$
$11$	−0.204418	−	4.29125i	−0.0616342	−	1.29386i	0.730246	−	0.683185i	$-0.239406\pi$
$12$		0			0
$13$	−0.838025	+	0.0800217i	−0.232426	+	0.0221940i	−0.210619	−	0.977568i	$-0.567548\pi$
$13$	−0.838025	+	0.0800217i	−0.232426	+	0.0221940i	−0.0218071	+	0.999762i	$0.506942\pi$
$14$		0			0
$15$	0.263134	−	1.83013i	0.0679408	−	0.472539i
$16$		0			0
$17$	−0.924879	−	3.81240i	−0.224316	−	0.924644i	−0.966954	−	0.254951i	$-0.917941\pi$
$17$	−0.924879	−	3.81240i	−0.224316	−	0.924644i	0.742638	−	0.669693i	$-0.233574\pi$
$18$		0			0
$19$	−0.100587	+	0.0402688i	−0.0230762	+	0.00923830i	−0.383172	−	0.923677i	$-0.625168\pi$
$19$	−0.100587	+	0.0402688i	−0.0230762	+	0.00923830i	0.360096	+	0.932915i	$0.382744\pi$
$20$		0			0
$21$	0.0506303	−	0.0261017i	0.0110484	−	0.00569587i
$22$		0			0
$23$	3.78325	+	0.729162i	0.788862	+	0.152041i	0.567743	−	0.823206i	$-0.307817\pi$
$23$	3.78325	+	0.729162i	0.788862	+	0.152041i	0.221119	+	0.975247i	$0.429029\pi$
$24$		0			0
$25$	−0.656925	+	1.43846i	−0.131385	+	0.287693i
$26$		0			0
$27$	0.841254	+	0.540641i	0.161899	+	0.104046i
$28$		0			0
$29$	3.47014	−	6.01046i	0.644389	−	1.11611i	−0.340053	−	0.940406i	$-0.610445\pi$
$29$	3.47014	−	6.01046i	0.644389	−	1.11611i	0.984442	−	0.175708i	$-0.0562215\pi$
$30$		0			0
$31$	6.04742	+	0.577459i	1.08615	+	0.103715i	0.622739	−	0.782429i	$-0.286020\pi$
$31$	6.04742	+	0.577459i	1.08615	+	0.103715i	0.463410	+	0.886144i	$0.346626\pi$
$32$		0			0
$33$	3.37698	+	2.65568i	0.587856	+	0.462295i
$34$		0			0
$35$	0.103418	−	0.0199321i	0.0174808	−	0.00336915i
$36$		0			0
$37$	−0.653613	−	1.13209i	−0.107453	−	0.186115i	0.807285	−	0.590162i	$-0.200936\pi$
$37$	−0.653613	−	1.13209i	−0.107453	−	0.186115i	−0.914738	+	0.404048i	$0.867603\pi$
$38$		0			0
$39$	0.488313	−	0.685740i	0.0781927	−	0.109806i
$40$		0			0
$41$	7.23841	−	6.90181i	1.13045	−	1.07788i	0.134236	−	0.990949i	$-0.457142\pi$
$41$	7.23841	−	6.90181i	1.13045	−	1.07788i	0.996214	−	0.0869329i	$-0.0277066\pi$
$42$		0			0
$43$	3.80231	+	1.11646i	0.579847	+	0.170258i	0.558487	−	0.829513i	$-0.311382\pi$
$43$	3.80231	+	1.11646i	0.579847	+	0.170258i	0.0213602	+	0.999772i	$0.493200\pi$
$44$		0			0
$45$	1.21081	+	1.39735i	0.180496	+	0.208304i
$46$		0			0
$47$	−1.91593	−	5.53572i	−0.279467	−	0.807468i	−0.994149	−	0.108018i	$-0.965550\pi$
$47$	−1.91593	−	5.53572i	−0.279467	−	0.807468i	0.714682	−	0.699450i	$-0.246572\pi$
$48$		0			0
$49$	−5.06379	−	4.82831i	−0.723399	−	0.689759i
$50$		0			0
$51$	3.48689	+	1.79762i	0.488262	+	0.251717i
$52$		0			0
$53$	0.910035	−	0.267210i	0.125003	−	0.0367042i	−0.218633	−	0.975807i	$-0.570160\pi$
$53$	0.910035	−	0.267210i	0.125003	−	0.0367042i	0.343636	+	0.939103i	$0.388341\pi$
$54$		0			0
$55$	4.60758	+	6.47044i	0.621286	+	0.872474i
$56$		0			0
$57$	0.0354371	−	0.102389i	0.00469376	−	0.0135617i
$58$		0			0
$59$	−0.781719	−	1.71172i	−0.101771	−	0.222848i	0.851896	−	0.523710i	$-0.175453\pi$
$59$	−0.781719	−	1.71172i	−0.101771	−	0.222848i	−0.953667	+	0.300863i	$0.902725\pi$
$60$		0			0
$61$	0.339191	−	7.12050i	0.0434290	−	0.911687i	−0.867073	−	0.498181i	$-0.834001\pi$
$61$	0.339191	−	7.12050i	0.0434290	−	0.911687i	0.910502	−	0.413505i	$-0.135696\pi$
$62$		0			0
$63$	−0.0134294	+	0.0553568i	−0.00169195	+	0.00697431i
$64$		0			0
$65$	1.22351	−	0.962176i	0.151757	−	0.119343i
$66$		0			0
$67$	−6.41223	+	5.08757i	−0.783378	+	0.621546i
$67$	−6.41223	+	5.08757i	−0.783378	+	0.621546i
$68$		0			0
$69$	−3.02856	+	2.38169i	−0.364596	+	0.286722i
$70$		0			0
$71$	0.332088	−	1.36889i	0.0394116	−	0.162457i	−0.948705	−	0.316162i	$-0.897606\pi$
$71$	0.332088	−	1.36889i	0.0394116	−	0.162457i	0.988117	+	0.153705i	$0.0491207\pi$
$72$		0			0
$73$	0.491530	−	10.3185i	0.0575293	−	1.20769i	−0.766916	−	0.641747i	$-0.778210\pi$
$73$	0.491530	−	10.3185i	0.0575293	−	1.20769i	0.824446	−	0.565941i	$-0.191487\pi$
$74$		0			0
$75$	−0.656925	−	1.43846i	−0.0758551	−	0.166100i
$76$		0			0
$77$	−0.0800393	+	0.231259i	−0.00912133	+	0.0263544i
$78$		0			0
$79$	7.40178	+	10.3944i	0.832766	+	1.16946i	0.983505	+	0.180882i	$0.0578953\pi$
$79$	7.40178	+	10.3944i	0.832766	+	1.16946i	−0.150739	+	0.988574i	$0.548165\pi$
$80$		0			0
$81$	−0.959493	+	0.281733i	−0.106610	+	0.0313036i
$82$		0			0
$83$	−13.7014	−	7.06355i	−1.50392	−	0.775326i	−0.507647	−	0.861565i	$-0.669485\pi$
$83$	−13.7014	−	7.06355i	−1.50392	−	0.775326i	−0.996274	+	0.0862394i	$0.972515\pi$
$84$		0			0
$85$	5.24955	+	5.00543i	0.569393	+	0.542915i
$86$		0			0
$87$	2.26994	+	6.55857i	0.243363	+	0.703153i
$88$		0			0
$89$	2.03978	+	2.35403i	0.216216	+	0.249527i	0.853488	−	0.521112i	$-0.174483\pi$
$89$	2.03978	+	2.35403i	0.216216	+	0.249527i	−0.637272	+	0.770639i	$0.719937\pi$
$90$		0			0
$91$	0.0460107	+	0.0135100i	0.00482324	+	0.00141623i
$92$		0			0
$93$	−4.39663	+	4.19218i	−0.455910	+	0.434709i
$94$		0			0
$95$	0.116203	−	0.163184i	0.0119222	−	0.0167423i
$96$		0			0
$97$	−2.38709	−	4.13456i	−0.242372	−	0.419801i	0.719017	−	0.694992i	$-0.244592\pi$
$97$	−2.38709	−	4.13456i	−0.242372	−	0.419801i	−0.961389	+	0.275191i	$0.911259\pi$
$98$		0			0
$99$	−4.21848	+	0.813046i	−0.423973	+	0.0817142i
$100$		0			0
$101$	−10.7333	−	8.44079i	−1.06801	−	0.839890i	−0.0803887	−	0.996764i	$-0.525616\pi$
$101$	−10.7333	−	8.44079i	−1.06801	−	0.839890i	−0.987619	+	0.156873i	$0.949859\pi$
$102$		0			0
$103$	2.74947	+	0.262542i	0.270913	+	0.0258691i	0.229628	−	0.973278i	$-0.426249\pi$
$103$	2.74947	+	0.262542i	0.270913	+	0.0258691i	0.0412846	+	0.999147i	$0.486855\pi$
$104$		0			0
$105$	−0.0526605	+	0.0912107i	−0.00513914	+	0.00890126i
$106$		0			0
$107$	9.42262	+	6.05555i	0.910919	+	0.585412i	0.910009	−	0.414587i	$-0.136074\pi$
$107$	9.42262	+	6.05555i	0.910919	+	0.585412i	0.000909570		1.00000i	$0.499710\pi$
$108$		0			0
$109$	−0.745649	+	1.63274i	−0.0714203	+	0.156389i	−0.941975	−	0.335683i	$-0.891033\pi$
$109$	−0.745649	+	1.63274i	−0.0714203	+	0.156389i	0.870555	+	0.492072i	$0.163760\pi$
$110$		0			0
$111$	1.28360	+	0.247394i	0.121834	+	0.0234816i
$112$		0			0
$113$	−9.60284	+	4.95061i	−0.903359	+	0.465714i	−0.846330	−	0.532658i	$-0.821193\pi$
$113$	−9.60284	+	4.95061i	−0.903359	+	0.465714i	−0.0570290	+	0.998373i	$0.518163\pi$
$114$		0			0
$115$	−6.61350	+	2.64765i	−0.616712	+	0.246894i
$116$		0			0
$117$	0.198471	+	0.818107i	0.0183486	+	0.0756340i
$118$		0			0
$119$	−0.0318021	+	0.221189i	−0.00291530	+	0.0202763i
$120$		0			0
$121$	−7.42287	+	0.708798i	−0.674807	+	0.0644362i
$122$		0			0
$123$	0.475890	+	9.99016i	0.0429095	+	0.900782i
$124$		0			0
$125$	−1.73178	−	12.0448i	−0.154895	−	1.07732i
$126$		0			0
$127$	16.7453	+	6.70379i	1.48590	+	0.594865i	0.965811	−	0.259246i	$-0.0834742\pi$
$127$	16.7453	+	6.70379i	1.48590	+	0.594865i	0.520090	+	0.854112i	$0.325898\pi$
$128$		0			0
$129$	−3.33375	+	2.14247i	−0.293520	+	0.188634i
$130$		0			0
$131$	−5.31814	+	6.13746i	−0.464648	+	0.536232i	−0.938915	−	0.344149i	$-0.888168\pi$
$131$	−5.31814	+	6.13746i	−0.464648	+	0.536232i	0.474267	+	0.880381i	$0.342713\pi$
$132$		0			0
$133$	0.00617176			0.000535160
$134$		0			0
$135$	−1.84895			−0.159133
$136$		0			0
$137$	1.64947	−	1.90359i	0.140924	−	0.162635i	−0.680900	−	0.732376i	$-0.738411\pi$
$137$	1.64947	−	1.90359i	0.140924	−	0.162635i	0.821824	+	0.569741i	$0.192957\pi$
$138$		0			0
$139$	1.61732	−	1.03939i	0.137179	−	0.0881598i	−0.470251	−	0.882533i	$-0.655837\pi$
$139$	1.61732	−	1.03939i	0.137179	−	0.0881598i	0.607431	+	0.794373i	$0.292200\pi$
$140$		0			0
$141$	5.43829	+	2.17716i	0.457986	+	0.183350i
$142$		0			0
$143$	0.514700	+	3.57982i	0.0430414	+	0.299360i
$144$		0			0
$145$	0.610583	+	12.8177i	0.0507062	+	1.06445i
$146$		0			0
$147$	6.96507	−	0.665084i	0.574470	−	0.0548552i
$148$		0			0
$149$	0.748974	−	5.20923i	0.0613584	−	0.426757i	−0.935869	−	0.352347i	$-0.885384\pi$
$149$	0.748974	−	5.20923i	0.0613584	−	0.426757i	0.997228	−	0.0744097i	$-0.0237073\pi$
$150$		0			0
$151$	−0.977812	−	4.03060i	−0.0795732	−	0.328005i	0.918086	−	0.396380i	$-0.129734\pi$
$151$	−0.977812	−	4.03060i	−0.0795732	−	0.328005i	−0.997660	+	0.0683748i	$0.978219\pi$
$152$		0			0
$153$	−3.64197	+	1.45803i	−0.294436	+	0.117874i
$154$		0			0
$155$	−9.98364	+	5.14692i	−0.801905	+	0.413411i
$156$		0			0
$157$	−14.5166	−	2.79784i	−1.15855	−	0.223292i	−0.426463	−	0.904505i	$-0.640240\pi$
$157$	−14.5166	−	2.79784i	−1.15855	−	0.223292i	−0.732085	+	0.681213i	$0.761453\pi$
$158$		0			0
$159$	−0.394002	+	0.862744i	−0.0312464	+	0.0684201i
$160$		0			0
$161$	−0.184630	−	0.118654i	−0.0145508	−	0.00935126i
$162$		0			0
$163$	−1.68437	+	2.91741i	−0.131930	+	0.228510i	−0.924421	−	0.381375i	$-0.875451\pi$
$163$	−1.68437	+	2.91741i	−0.131930	+	0.228510i	0.792490	+	0.609884i	$0.208784\pi$
$164$		0			0
$165$	−7.90736	−	0.755061i	−0.615587	−	0.0587814i
$166$		0			0
$167$	−2.04875	−	1.61116i	−0.158537	−	0.124675i	0.535739	−	0.844383i	$-0.320033\pi$
$167$	−2.04875	−	1.61116i	−0.158537	−	0.124675i	−0.694276	+	0.719709i	$0.744275\pi$
$168$		0			0
$169$	−12.0692	+	2.32615i	−0.928399	+	0.178934i
$170$		0			0
$171$	0.0541739	+	0.0938319i	0.00414278	+	0.00717551i
$172$		0			0
$173$	−4.02278	+	5.64921i	−0.305847	+	0.429501i	−0.938682	−	0.344785i	$-0.887952\pi$
$173$	−4.02278	+	5.64921i	−0.305847	+	0.429501i	0.632835	+	0.774287i	$0.281891\pi$
$174$		0			0
$175$	0.0651931	−	0.0621615i	0.00492813	−	0.00469897i
$176$		0			0
$177$	1.80555	+	0.530158i	0.135714	+	0.0398491i
$178$		0			0
$179$	2.95821	+	3.41396i	0.221107	+	0.255171i	0.855456	−	0.517876i	$-0.173277\pi$
$179$	2.95821	+	3.41396i	0.221107	+	0.255171i	−0.634349	+	0.773047i	$0.718732\pi$
$180$		0			0
$181$	−3.80177	−	10.9845i	−0.282583	−	0.816470i	−0.993565	−	0.113260i	$-0.963871\pi$
$181$	−3.80177	−	10.9845i	−0.282583	−	0.816470i	0.710982	−	0.703210i	$-0.248251\pi$
$182$		0			0
$183$	5.15919	+	4.91928i	0.381378	+	0.363644i
$184$		0			0
$185$	2.14832	+	1.10753i	0.157947	+	0.0814275i
$186$		0			0
$187$	−16.1709	+	4.74821i	−1.18254	+	0.347224i
$188$		0			0
$189$	−0.0330415	−	0.0464003i	−0.00240342	−	0.00337513i
$190$		0			0
$191$	3.38638	−	9.78432i	0.245030	−	0.707968i	−0.753682	−	0.657239i	$-0.771724\pi$
$191$	3.38638	−	9.78432i	0.245030	−	0.707968i	0.998712	−	0.0507292i	$-0.0161546\pi$
$192$		0			0
$193$	7.58070	+	16.5994i	0.545671	+	1.19485i	0.958774	+	0.284169i	$0.0917175\pi$
$193$	7.58070	+	16.5994i	0.545671	+	1.19485i	−0.413103	+	0.910684i	$0.635555\pi$
$194$		0			0
$195$	−0.0740621	+	1.55476i	−0.00530370	+	0.111338i
$196$		0			0
$197$	2.95218	−	12.1691i	0.210334	−	0.867010i	−0.764598	−	0.644508i	$-0.777062\pi$
$197$	2.95218	−	12.1691i	0.210334	−	0.867010i	0.974932	−	0.222502i	$-0.0714224\pi$
$198$		0			0
$199$	7.51586	−	5.91054i	0.532785	−	0.418987i	−0.315186	−	0.949030i	$-0.602067\pi$
$199$	7.51586	−	5.91054i	0.532785	−	0.418987i	0.847971	+	0.530043i	$0.177824\pi$
$200$		0			0
$201$	0.354187	−	8.17769i	0.0249824	−	0.576810i
$202$		0			0
$203$	−0.310755	+	0.244380i	−0.0218107	+	0.0171521i
$204$		0			0
$205$	−4.35972	+	17.9710i	−0.304496	+	1.25515i
$206$		0			0
$207$	0.183327	−	3.84851i	0.0127421	−	0.267490i
$208$		0			0
$209$	0.193365	+	0.423411i	0.0133754	+	0.0292879i
$210$		0			0
$211$	−2.82151	+	8.15222i	−0.194241	+	0.561222i	−0.999497	−	0.0317049i	$-0.989906\pi$
$211$	−2.82151	+	8.15222i	−0.194241	+	0.561222i	0.805257	+	0.592927i	$0.202028\pi$
$212$		0			0
$213$	0.817064	+	1.14741i	0.0559843	+	0.0786190i
$214$		0			0
$215$	−7.03030	+	2.06428i	−0.479462	+	0.140783i
$216$		0			0
$217$	−0.307576	−	0.158566i	−0.0208796	−	0.0107642i
$218$		0			0
$219$	7.47631	+	7.12865i	0.505202	+	0.481710i
$220$		0			0
$221$	1.08015	+	3.12088i	0.0726586	+	0.209933i
$222$		0			0
$223$	10.2961	+	11.8824i	0.689479	+	0.795701i	0.987291	−	0.158923i	$-0.0508022\pi$
$223$	10.2961	+	11.8824i	0.689479	+	0.795701i	−0.297812	+	0.954625i	$0.596257\pi$
$224$		0			0
$225$	1.51731	+	0.445523i	0.101154	+	0.0297016i
$226$		0			0
$227$	−18.0950	+	17.2535i	−1.20101	+	1.14516i	−0.215324	+	0.976543i	$0.569081\pi$
$227$	−18.0950	+	17.2535i	−1.20101	+	1.14516i	−0.985682	+	0.168614i	$0.946071\pi$
$228$		0			0
$229$	−15.7530	+	22.1219i	−1.04098	+	1.46186i	−0.160942	+	0.986964i	$0.551453\pi$
$229$	−15.7530	+	22.1219i	−1.04098	+	1.46186i	−0.880043	+	0.474894i	$0.842486\pi$
$230$		0			0
$231$	−0.122359	−	0.211932i	−0.00805062	−	0.0139441i
$232$		0			0
$233$	8.90855	−	1.71698i	0.583618	−	0.112483i	0.111108	−	0.993808i	$-0.464560\pi$
$233$	8.90855	−	1.71698i	0.583618	−	0.112483i	0.472510	+	0.881325i	$0.343348\pi$
$234$		0			0
$235$	8.51373	+	6.69527i	0.555374	+	0.436751i
$236$		0			0
$237$	−12.7027	−	1.21296i	−0.825127	−	0.0787901i
$238$		0			0
$239$	5.48500	−	9.50029i	0.354795	−	0.614523i	−0.632288	−	0.774733i	$-0.717884\pi$
$239$	5.48500	−	9.50029i	0.354795	−	0.614523i	0.987083	+	0.160211i	$0.0512174\pi$
$240$		0			0
$241$	−6.96608	−	4.47683i	−0.448725	−	0.288378i	0.296696	−	0.954972i	$-0.404115\pi$
$241$	−6.96608	−	4.47683i	−0.448725	−	0.288378i	−0.745421	+	0.666594i	$0.767751\pi$
$242$		0			0
$243$	0.415415	−	0.909632i	0.0266489	−	0.0583529i
$244$		0			0
$245$	12.7029	+	2.44828i	0.811558	+	0.156415i
$246$		0			0
$247$	0.0810717	−	0.0417954i	0.00515847	−	0.00265938i
$248$		0			0
$249$	14.3108	−	5.72917i	0.906908	−	0.363071i
$250$		0			0
$251$	−1.98211	−	8.17037i	−0.125110	−	0.515709i	−0.999533	−	0.0305461i	$-0.990275\pi$
$251$	−1.98211	−	8.17037i	−0.125110	−	0.515709i	0.874424	−	0.485163i	$-0.161240\pi$
$252$		0			0
$253$	2.35565	−	16.3839i	0.148099	−	1.03005i
$254$		0			0
$255$	−7.22058	+	0.689481i	−0.452170	+	0.0431770i
$256$		0			0
$257$	−0.139002	−	2.91802i	−0.00867073	−	0.182021i	−0.999048	−	0.0436265i	$-0.986109\pi$
$257$	−0.139002	−	2.91802i	−0.00867073	−	0.182021i	0.990377	−	0.138394i	$-0.0441942\pi$
$258$		0			0
$259$	0.0105972	+	0.0737050i	0.000658477	+	0.00457981i
$260$		0			0
$261$	−6.44313	−	2.57944i	−0.398820	−	0.159663i
$262$		0			0
$263$	−11.8343	+	7.60544i	−0.729734	+	0.468971i	−0.852011	−	0.523525i	$-0.824617\pi$
$263$	−11.8343	+	7.60544i	−0.729734	+	0.468971i	0.122277	+	0.992496i	$0.460980\pi$
$264$		0			0
$265$	−1.14839	+	1.32532i	−0.0705453	+	0.0814137i
$266$		0			0
$267$	−3.11483			−0.190625
$268$		0			0
$269$	1.30645			0.0796554			0.0398277	−	0.999207i	$-0.487319\pi$
$269$	1.30645			0.0796554			0.0398277	+	0.999207i	$0.487319\pi$
$270$		0			0
$271$	13.2566	−	15.2990i	0.805283	−	0.929346i	−0.193376	−	0.981125i	$-0.561944\pi$
$271$	13.2566	−	15.2990i	0.805283	−	0.929346i	0.998659	+	0.0517790i	$0.0164891\pi$
$272$		0			0
$273$	−0.0403408	+	0.0259254i	−0.00244153	+	0.00156908i
$274$		0			0
$275$	6.30710	+	2.52498i	0.380332	+	0.152262i
$276$		0			0
$277$	−1.06158	−	7.38348i	−0.0637844	−	0.443630i	−0.996540	−	0.0831199i	$-0.973512\pi$
$277$	−1.06158	−	7.38348i	−0.0637844	−	0.443630i	0.932755	−	0.360511i	$-0.117398\pi$
$278$		0			0
$279$	−0.289057	−	6.06805i	−0.0173054	−	0.363285i
$280$		0			0
$281$	11.8355	−	1.13015i	0.706045	−	0.0674191i	0.264144	−	0.964483i	$-0.414910\pi$
$281$	11.8355	−	1.13015i	0.706045	−	0.0674191i	0.441901	+	0.897064i	$0.354304\pi$
$282$		0			0
$283$	1.39848	−	9.72664i	0.0831310	−	0.578189i	−0.905098	−	0.425204i	$-0.860202\pi$
$283$	1.39848	−	9.72664i	0.0831310	−	0.578189i	0.988229	−	0.152985i	$-0.0488885\pi$
$284$		0			0
$285$	0.0472296	+	0.194683i	0.00279764	+	0.0115320i
$286$		0			0
$287$	−0.528900	+	0.211740i	−0.0312200	+	0.0124986i
$288$		0			0
$289$	1.43118	−	0.737827i	0.0841873	−	0.0434016i
$290$		0			0
$291$	4.68790	+	0.903519i	0.274810	+	0.0529652i
$292$		0			0
$293$	−4.70447	+	10.3014i	−0.274838	+	0.601812i	−0.995840	−	0.0911216i	$-0.970955\pi$
$293$	−4.70447	+	10.3014i	−0.274838	+	0.601812i	0.721001	+	0.692934i	$0.243682\pi$
$294$		0			0
$295$	2.92699	+	1.88106i	0.170416	+	0.109520i
$296$		0			0
$297$	2.14806	−	3.72055i	0.124643	−	0.215888i
$298$		0			0
$299$	−3.22881	−	0.308314i	−0.186727	−	0.0178302i
$300$		0			0
$301$	−0.177438	−	0.139539i	−0.0102274	−	0.00804289i
$302$		0			0
$303$	13.4080	−	2.58417i	0.770268	−	0.148457i
$304$		0			0
$305$	6.59020	+	11.4146i	0.377354	+	0.653596i
$306$		0			0
$307$	−9.77495	+	13.7270i	−0.557886	+	0.783441i	−0.993148	−	0.116863i	$-0.962716\pi$
$307$	−9.77495	+	13.7270i	−0.557886	+	0.783441i	0.435262	+	0.900304i	$0.356656\pi$
$308$		0			0
$309$	−1.99893	+	1.90598i	−0.113715	+	0.108427i
$310$		0			0
$311$	−5.84489	−	1.71621i	−0.331433	−	0.0973176i	0.111782	−	0.993733i	$-0.464344\pi$
$311$	−5.84489	−	1.71621i	−0.331433	−	0.0973176i	−0.443215	+	0.896415i	$0.646162\pi$
$312$		0			0
$313$	9.18856	+	10.6042i	0.519368	+	0.599382i	0.953472	−	0.301480i	$-0.0974807\pi$
$313$	9.18856	+	10.6042i	0.519368	+	0.599382i	−0.434105	+	0.900862i	$0.642935\pi$
$314$		0			0
$315$	−0.0344472	−	0.0995285i	−0.00194088	−	0.00560780i
$316$		0			0
$317$	−8.12910	−	7.75109i	−0.456576	−	0.435344i	0.426562	−	0.904459i	$-0.359725\pi$
$317$	−8.12910	−	7.75109i	−0.456576	−	0.435344i	−0.883137	+	0.469114i	$0.844573\pi$
$318$		0			0
$319$	−26.5018	−	13.6626i	−1.48381	−	0.764959i
$320$		0			0
$321$	−10.7470	+	3.15560i	−0.599838	+	0.176128i
$322$		0			0
$323$	0.246551	+	0.346233i	0.0137185	+	0.0192649i
$324$		0			0
$325$	0.435411	−	1.25804i	0.0241523	−	0.0697834i
$326$		0			0
$327$	−0.745649	−	1.63274i	−0.0412345	−	0.0902910i
$328$		0			0
$329$	−0.0158772	+	0.333303i	−0.000875337	+	0.0183756i
$330$		0			0
$331$	7.12674	−	29.3768i	0.391721	−	1.61470i	−0.345070	−	0.938577i	$-0.612145\pi$
$331$	7.12674	−	29.3768i	0.391721	−	1.61470i	0.736792	−	0.676120i	$-0.236340\pi$
$332$		0			0
$333$	−1.02755	+	0.808074i	−0.0563094	+	0.0442822i
$334$		0			0
$335$	4.88819	−	14.3232i	0.267070	−	0.782560i
$336$		0			0
$337$	11.9080	−	9.36457i	0.648671	−	0.510121i	−0.238749	−	0.971081i	$-0.576737\pi$
$337$	11.9080	−	9.36457i	0.648671	−	0.510121i	0.887421	+	0.460960i	$0.152495\pi$
$338$		0			0
$339$	2.54710	−	10.4993i	0.138340	−	0.570244i
$340$		0			0
$341$	1.24182	−	26.0691i	0.0672485	−	1.41172i
$342$		0			0
$343$	0.331206	+	0.725241i	0.0178835	+	0.0391593i
$344$		0			0
$345$	2.32996	−	6.73199i	0.125441	−	0.362438i
$346$		0			0
$347$	7.50628	+	10.5411i	0.402958	+	0.565875i	0.965338	−	0.261004i	$-0.0840535\pi$
$347$	7.50628	+	10.5411i	0.402958	+	0.565875i	−0.562380	+	0.826879i	$0.690114\pi$
$348$		0			0
$349$	25.9299	−	7.61370i	1.38799	−	0.407552i	0.499450	−	0.866343i	$-0.333535\pi$
$349$	25.9299	−	7.61370i	1.38799	−	0.407552i	0.888544	+	0.458790i	$0.151717\pi$
$350$		0			0
$351$	−0.748255	−	0.385752i	−0.0399389	−	0.0205899i
$352$		0			0
$353$	22.8030	+	21.7426i	1.21368	+	1.15724i	0.982881	+	0.184240i	$0.0589824\pi$
$353$	22.8030	+	21.7426i	1.21368	+	1.15724i	0.230799	+	0.973001i	$0.425866\pi$
$354$		0			0
$355$	0.851823	+	2.46118i	0.0452101	+	0.130626i
$356$		0			0
$357$	−0.146337	−	0.168882i	−0.00774499	−	0.00893820i
$358$		0			0
$359$	18.0046	+	5.28663i	0.950247	+	0.279018i	0.719890	−	0.694089i	$-0.244192\pi$
$359$	18.0046	+	5.28663i	0.950247	+	0.279018i	0.230357	+	0.973106i	$0.426011\pi$
$360$		0			0
$361$	−13.7425	+	13.1034i	−0.723287	+	0.689653i
$362$		0			0
$363$	4.32527	−	6.07400i	0.227018	−	0.318802i
$364$		0			0
$365$	9.55003	+	16.5411i	0.499871	+	0.865802i
$366$		0			0
$367$	16.2217	−	3.12648i	0.846768	−	0.163201i	0.252629	−	0.967563i	$-0.418705\pi$
$367$	16.2217	−	3.12648i	0.846768	−	0.163201i	0.594139	+	0.804362i	$0.297493\pi$
$368$		0			0
$369$	−7.86170	−	6.18251i	−0.409264	−	0.321848i
$370$		0			0
$371$	−0.0537817	−	0.00513553i	−0.00279221	−	0.000266623i
$372$		0			0
$373$	5.40351	−	9.35915i	0.279783	−	0.484598i	−0.691548	−	0.722331i	$-0.743071\pi$
$373$	5.40351	−	9.35915i	0.279783	−	0.484598i	0.971331	+	0.237732i	$0.0764041\pi$
$374$		0			0
$375$	10.2369	+	6.57887i	0.528632	+	0.339731i
$376$		0			0
$377$	−2.42710	+	5.31460i	−0.125002	+	0.273716i
$378$		0			0
$379$	10.9717	+	2.11463i	0.563580	+	0.108621i	0.463081	−	0.886316i	$-0.346744\pi$
$379$	10.9717	+	2.11463i	0.563580	+	0.108621i	0.100499	+	0.994937i	$0.467956\pi$
$380$		0			0
$381$	−16.0322	+	8.26517i	−0.821354	+	0.423438i
$382$		0			0
$383$	13.6171	−	5.45146i	0.695801	−	0.278557i	0.00332154	−	0.999994i	$-0.498943\pi$
$383$	13.6171	−	5.45146i	0.695801	−	0.278557i	0.692479	+	0.721438i	$0.256518\pi$
$384$		0			0
$385$	−0.106674	−	0.439717i	−0.00543663	−	0.0224101i
$386$		0			0
$387$	0.563970	−	3.92250i	0.0286682	−	0.199392i
$388$		0			0
$389$	−0.536972	+	0.0512747i	−0.0272256	+	0.00259973i	−0.108660	−	0.994079i	$-0.534656\pi$
$389$	−0.536972	+	0.0512747i	−0.0272256	+	0.00259973i	0.0814344	+	0.996679i	$0.474050\pi$
$390$		0			0
$391$	−0.719190	−	15.0977i	−0.0363710	−	0.763521i
$392$		0			0
$393$	−1.15574	−	8.03836i	−0.0582995	−	0.405482i
$394$		0			0
$395$	−21.9034	−	8.76881i	−1.10208	−	0.441207i
$396$		0			0
$397$	16.8795	−	10.8478i	0.847156	−	0.544434i	−0.0435306	−	0.999052i	$-0.513861\pi$
$397$	16.8795	−	10.8478i	0.847156	−	0.544434i	0.890686	+	0.454618i	$0.150224\pi$
$398$		0			0
$399$	−0.00404165	+	0.00466431i	−0.000202335	+	0.000233507i
$400$		0			0
$401$	−19.4240			−0.969990			−0.484995	−	0.874517i	$-0.661179\pi$
$401$	−19.4240			−0.969990			−0.484995	+	0.874517i	$0.661179\pi$
$402$		0			0
$403$	−5.11410			−0.254752
$404$		0			0
$405$	1.21081	−	1.39735i	0.0601655	−	0.0694347i
$406$		0			0
$407$	−4.72448	+	3.03624i	−0.234184	+	0.150501i
$408$		0			0
$409$	−22.6666	−	9.07433i	−1.12079	−	0.448697i	−0.264084	−	0.964500i	$-0.585069\pi$
$409$	−22.6666	−	9.07433i	−1.12079	−	0.448697i	−0.856707	+	0.515803i	$0.827494\pi$
$410$		0			0
$411$	0.358465	+	2.49318i	0.0176818	+	0.122979i
$412$		0			0
$413$	0.00510034	+	0.107069i	0.000250971	+	0.00526854i
$414$		0			0
$415$	28.3725	−	2.70925i	1.39275	−	0.132992i
$416$		0			0
$417$	−0.273602	+	1.90294i	−0.0133983	+	0.0931876i
$418$		0			0
$419$	−8.16514	−	33.6572i	−0.398893	−	1.64426i	−0.717636	−	0.696419i	$-0.754776\pi$
$419$	−8.16514	−	33.6572i	−0.398893	−	1.64426i	0.318742	−	0.947841i	$-0.396740\pi$
$420$		0			0
$421$	4.48055	−	1.79374i	0.218369	−	0.0874216i	−0.259899	−	0.965636i	$-0.583689\pi$
$421$	4.48055	−	1.79374i	0.218369	−	0.0874216i	0.478267	+	0.878214i	$0.341265\pi$
$422$		0			0
$423$	−5.20671	+	2.68424i	−0.253159	+	0.130512i
$424$		0			0
$425$	6.09158	+	1.17406i	0.295485	+	0.0569501i
$426$		0			0
$427$	−0.168684	+	0.369367i	−0.00816319	+	0.0178749i
$428$		0			0
$429$	−3.04250	−	1.95530i	−0.146894	−	0.0944027i
$430$		0			0
$431$	−6.06769	+	10.5096i	−0.292270	+	0.506227i	−0.974346	−	0.225054i	$-0.927744\pi$
$431$	−6.06769	+	10.5096i	−0.292270	+	0.506227i	0.682076	+	0.731281i	$0.261077\pi$
$432$		0			0
$433$	16.8220	+	1.60631i	0.808416	+	0.0771944i	0.491075	−	0.871117i	$-0.336604\pi$
$433$	16.8220	+	1.60631i	0.808416	+	0.0771944i	0.317341	+	0.948312i	$0.397210\pi$
$434$		0			0
$435$	−10.0868	−	7.93238i	−0.483627	−	0.380328i
$436$		0			0
$437$	−0.409907	+	0.0790030i	−0.0196085	+	0.00377923i
$438$		0			0
$439$	−6.42496	−	11.1284i	−0.306647	−	0.531128i	0.670980	−	0.741475i	$-0.265874\pi$
$439$	−6.42496	−	11.1284i	−0.306647	−	0.531128i	−0.977627	+	0.210348i	$0.932540\pi$
$440$		0			0
$441$	−4.05852	+	5.69939i	−0.193263	+	0.271399i
$442$		0			0
$443$	−2.97468	+	2.83635i	−0.141331	+	0.134759i	−0.757447	−	0.652896i	$-0.773554\pi$
$443$	−2.97468	+	2.83635i	−0.141331	+	0.134759i	0.616116	+	0.787655i	$0.288705\pi$
$444$		0			0
$445$	−5.52589	−	1.62255i	−0.261952	−	0.0769162i
$446$		0			0
$447$	3.44640	+	3.97736i	0.163009	+	0.188123i
$448$		0			0
$449$	9.58213	+	27.6857i	0.452209	+	1.30657i	0.908925	+	0.416959i	$0.136904\pi$
$449$	9.58213	+	27.6857i	0.452209	+	1.30657i	−0.456717	+	0.889612i	$0.650975\pi$
$450$		0			0
$451$	−31.0971	−	29.6510i	−1.46430	−	1.39621i
$452$		0			0
$453$	3.68645	+	1.90050i	0.173205	+	0.0892932i
$454$		0			0
$455$	−0.0850717	+	0.0249793i	−0.00398822	+	0.00117105i
$456$		0			0
$457$	−17.0320	−	23.9182i	−0.796726	−	1.11884i	−0.990461	−	0.137791i	$-0.956000\pi$
$457$	−17.0320	−	23.9182i	−0.796726	−	1.11884i	0.193736	−	0.981054i	$-0.437940\pi$
$458$		0			0
$459$	1.28308	−	3.70723i	0.0598892	−	0.173038i
$460$		0			0
$461$	6.66251	+	14.5889i	0.310304	+	0.679471i	0.998959	−	0.0456183i	$-0.0145258\pi$
$461$	6.66251	+	14.5889i	0.310304	+	0.679471i	−0.688655	+	0.725089i	$0.741799\pi$
$462$		0			0
$463$	0.152564	−	3.20272i	0.00709026	−	0.148843i	−0.992546	−	0.121871i	$-0.961111\pi$
$463$	0.152564	−	3.20272i	0.00709026	−	0.148843i	0.999636	−	0.0269718i	$-0.00858643\pi$
$464$		0			0
$465$	2.64811	−	10.9156i	0.122803	−	0.506201i
$466$		0			0
$467$	−13.4433	+	10.5719i	−0.622082	+	0.489211i	−0.878746	−	0.477290i	$-0.841619\pi$
$467$	−13.4433	+	10.5719i	−0.622082	+	0.489211i	0.256664	+	0.966501i	$0.417377\pi$
$468$		0			0
$469$	0.446801	−	0.133290i	0.0206313	−	0.00615474i
$470$		0			0
$471$	11.6208	−	9.13869i	0.535458	−	0.421089i
$472$		0			0
$473$	4.01375	−	16.5449i	0.184552	−	0.760735i
$474$		0			0
$475$	0.00815258	−	0.171144i	0.000374066	−	0.00785262i
$476$		0			0
$477$	−0.394002	−	0.862744i	−0.0180401	−	0.0395023i
$478$		0			0
$479$	−3.96474	+	11.4553i	−0.181153	+	0.523408i	−0.998617	−	0.0525717i	$-0.983258\pi$
$479$	−3.96474	+	11.4553i	−0.181153	+	0.523408i	0.817464	+	0.575980i	$0.195379\pi$
$480$		0			0
$481$	0.638336	+	0.896418i	0.0291056	+	0.0408731i
$482$		0			0
$483$	0.210579	−	0.0618317i	0.00958170	−	0.00281344i
$484$		0			0
$485$	7.84595	+	4.04487i	0.356266	+	0.183668i
$486$		0			0
$487$	−11.7396	−	11.1937i	−0.531974	−	0.507236i	0.375797	−	0.926702i	$-0.377369\pi$
$487$	−11.7396	−	11.1937i	−0.531974	−	0.507236i	−0.907771	+	0.419466i	$0.862217\pi$
$488$		0			0
$489$	−1.10181	−	3.18346i	−0.0498254	−	0.143961i
$490$		0			0
$491$	11.9255	+	13.7628i	0.538190	+	0.621104i	0.958090	−	0.286466i	$-0.0924805\pi$
$491$	11.9255	+	13.7628i	0.538190	+	0.621104i	−0.419901	+	0.907570i	$0.637935\pi$
$492$		0			0
$493$	−26.1238	−	7.67063i	−1.17655	−	0.345468i
$494$		0			0
$495$	5.74886	−	5.48152i	0.258392	−	0.246376i
$496$		0			0
$497$	−0.0465420	+	0.0653591i	−0.00208770	+	0.00293176i
$498$		0			0
$499$	3.73274	+	6.46529i	0.167100	+	0.289426i	0.937399	−	0.348257i	$-0.113226\pi$
$499$	3.73274	+	6.46529i	0.167100	+	0.289426i	−0.770299	+	0.637683i	$0.779893\pi$
$500$		0			0
$501$	2.55928	−	0.493260i	0.114340	−	0.0220372i
$502$		0			0
$503$	33.9707	+	26.7148i	1.51468	+	1.19116i	0.922891	+	0.385061i	$0.125820\pi$
$503$	33.9707	+	26.7148i	1.51468	+	1.19116i	0.591787	+	0.806095i	$0.298423\pi$
$504$		0			0
$505$	25.1326	+	2.39988i	1.11839	+	0.106793i
$506$		0			0
$507$	6.14566	−	10.6446i	0.272938	−	0.472743i
$508$		0			0
$509$	26.0682	+	16.7530i	1.15545	+	0.742564i	0.970718	−	0.240224i	$-0.0772209\pi$
$509$	26.0682	+	16.7530i	1.15545	+	0.742564i	0.184735	+	0.982788i	$0.440857\pi$
$510$		0			0
$511$	−0.244444	+	0.535258i	−0.0108136	+	0.0236784i
$512$		0			0
$513$	−0.106390	−	0.0205050i	−0.00469722	−	0.000905316i
$514$		0			0
$515$	−4.53907	+	2.34005i	−0.200015	+	0.103115i
$516$		0			0
$517$	−23.3635	+	9.35334i	−1.02753	+	0.411360i
$518$		0			0
$519$	−1.63502	−	6.73966i	−0.0717696	−	0.295838i
$520$		0			0
$521$	0.982875	−	6.83605i	0.0430606	−	0.299493i	−0.956898	−	0.290423i	$-0.906204\pi$
$521$	0.982875	−	6.83605i	0.0430606	−	0.299493i	0.999959	−	0.00906957i	$-0.00288697\pi$
$522$		0			0
$523$	20.5887	−	1.96598i	0.900279	−	0.0859663i	0.365357	−	0.930867i	$-0.380947\pi$
$523$	20.5887	−	1.96598i	0.900279	−	0.0859663i	0.534922	+	0.844901i	$0.320341\pi$
$524$		0			0
$525$	0.00428612	+	0.0899768i	0.000187062	+	0.00392691i
$526$		0			0
$527$	−3.39163	−	23.5893i	−0.147742	−	1.02757i
$528$		0			0
$529$	−7.57116	−	3.03104i	−0.329181	−	0.131784i
$530$		0			0
$531$	−1.58305	+	1.01737i	−0.0686986	+	0.0441499i
$532$		0			0
$533$	−5.51368	+	6.36313i	−0.238824	+	0.275618i
$534$		0			0
$535$	−20.7096			−0.895352
$536$		0			0
$537$	−4.51732			−0.194937
$538$		0			0
$539$	−19.6844	+	22.7170i	−0.847867	+	0.978490i
$540$		0			0
$541$	36.1407	−	23.2262i	1.55381	−	0.998574i	0.569529	−	0.821971i	$-0.307126\pi$
$541$	36.1407	−	23.2262i	1.55381	−	0.998574i	0.984282	−	0.176603i	$-0.0565108\pi$
$542$		0			0
$543$	10.7911	+	4.32012i	0.463093	+	0.185394i
$544$		0			0
$545$	−0.472312	−	3.28500i	−0.0202316	−	0.140714i
$546$		0			0
$547$	2.05485	+	43.1365i	0.0878588	+	1.84438i	0.427724	+	0.903910i	$0.359316\pi$
$547$	2.05485	+	43.1365i	0.0878588	+	1.84438i	−0.339865	+	0.940474i	$0.610381\pi$
$548$		0			0
$549$	−7.09630	+	0.677614i	−0.302862	+	0.0289199i
$550$		0			0
$551$	−0.107016	+	0.744310i	−0.00455902	+	0.0317087i
$552$		0			0
$553$	−0.171365	−	0.706378i	−0.00728720	−	0.0300382i
$554$		0			0
$555$	−2.24387	+	0.898309i	−0.0952469	+	0.0381311i
$556$		0			0
$557$	26.1154	−	13.4634i	1.10655	−	0.570464i	0.194645	−	0.980874i	$-0.437644\pi$
$557$	26.1154	−	13.4634i	1.10655	−	0.570464i	0.911901	+	0.410409i	$0.134614\pi$
$558$		0			0
$559$	−3.27577	−	0.631354i	−0.138550	−	0.0267034i
$560$		0			0
$561$	7.00124	−	15.3306i	0.295593	−	0.647258i
$562$		0			0
$563$	4.17489	+	2.68304i	0.175951	+	0.113077i	0.625652	−	0.780103i	$-0.284833\pi$
$563$	4.17489	+	2.68304i	0.175951	+	0.113077i	−0.449701	+	0.893179i	$0.648469\pi$
$564$		0			0
$565$	9.98791	−	17.2996i	0.420194	−	0.727798i
$566$		0			0
$567$	0.0567046	+	0.00541463i	0.00238137	+	0.000227393i
$568$		0			0
$569$	13.7788	+	10.8358i	0.577638	+	0.454260i	0.863739	−	0.503940i	$-0.168117\pi$
$569$	13.7788	+	10.8358i	0.577638	+	0.454260i	−0.286100	+	0.958200i	$0.592359\pi$
$570$		0			0
$571$	−39.0293	+	7.52228i	−1.63333	+	0.314798i	−0.921742	−	0.387804i	$-0.873234\pi$
$571$	−39.0293	+	7.52228i	−1.63333	+	0.314798i	−0.711583	+	0.702602i	$0.752022\pi$
$572$		0			0
$573$	5.17688	+	8.96662i	0.216267	+	0.374586i
$574$		0			0
$575$	−3.53418	+	4.96306i	−0.147386	+	0.206974i
$576$		0			0
$577$	22.0558	−	21.0302i	0.918195	−	0.875497i	−0.0743680	−	0.997231i	$-0.523694\pi$
$577$	22.0558	−	21.0302i	0.918195	−	0.875497i	0.992563	+	0.121734i	$0.0388455\pi$
$578$		0			0
$579$	−17.5093	−	5.14120i	−0.727662	−	0.213661i
$580$		0			0
$581$	0.575018	+	0.663606i	0.0238558	+	0.0275310i
$582$		0			0
$583$	−1.33269	−	3.85057i	−0.0551946	−	0.159474i
$584$		0			0
$585$	−1.12651	−	1.07412i	−0.0465753	−	0.0444094i
$586$		0			0
$587$	−3.77413	−	1.94570i	−0.155775	−	0.0803076i	0.378576	−	0.925570i	$-0.376414\pi$
$587$	−3.77413	−	1.94570i	−0.155775	−	0.0803076i	−0.534351	+	0.845262i	$0.679444\pi$
$588$		0			0
$589$	−0.631543	+	0.185438i	−0.0260223	+	0.00764083i
$590$		0			0
$591$	7.26349	+	10.2002i	0.298780	+	0.419578i
$592$		0			0
$593$	−5.59935	+	16.1783i	−0.229938	+	0.664362i	0.769724	+	0.638376i	$0.220394\pi$
$593$	−5.59935	+	16.1783i	−0.229938	+	0.664362i	−0.999662	+	0.0259855i	$0.991728\pi$
$594$		0			0
$595$	−0.171638	−	0.375836i	−0.00703649	−	0.0154078i
$596$		0			0
$597$	−0.454955	+	9.55068i	−0.0186201	+	0.390883i
$598$		0			0
$599$	2.44079	−	10.0611i	0.0997278	−	0.411083i	−0.899963	−	0.435967i	$-0.856406\pi$
$599$	2.44079	−	10.0611i	0.0997278	−	0.411083i	0.999690	+	0.0248837i	$0.00792154\pi$
$600$		0			0
$601$	18.0365	−	14.1841i	0.735726	−	0.578581i	−0.178426	−	0.983953i	$-0.557100\pi$
$601$	18.0365	−	14.1841i	0.735726	−	0.578581i	0.914152	+	0.405372i	$0.132858\pi$
$602$		0			0
$603$	5.94834	+	5.62292i	0.242235	+	0.228983i
$604$		0			0
$605$	10.8373	−	8.52254i	0.440599	−	0.346491i
$606$		0			0
$607$	−0.165510	+	0.682242i	−0.00671785	+	0.0276913i	−0.975072	−	0.221889i	$-0.928778\pi$
$607$	−0.165510	+	0.682242i	−0.00671785	+	0.0276913i	0.968354	+	0.249581i	$0.0802928\pi$
$608$		0			0
$609$	0.0188108	−	0.394888i	0.000762254	−	0.0160017i
$610$		0			0
$611$	2.04858	+	4.48576i	0.0828765	+	0.181474i
$612$		0			0
$613$	−2.73304	+	7.89660i	−0.110386	+	0.318941i	−0.986641	−	0.162907i	$-0.947913\pi$
$613$	−2.73304	+	7.89660i	−0.110386	+	0.318941i	0.876255	+	0.481848i	$0.160034\pi$
$614$		0			0
$615$	−10.7266	−	15.0634i	−0.432537	−	0.607414i
$616$		0			0
$617$	−12.3079	+	3.61393i	−0.495497	+	0.145491i	−0.519928	−	0.854210i	$-0.674041\pi$
$617$	−12.3079	+	3.61393i	−0.495497	+	0.145491i	0.0244301	+	0.999702i	$0.492223\pi$
$618$		0			0
$619$	3.14935	+	1.62360i	0.126583	+	0.0652581i	0.520355	−	0.853950i	$-0.325800\pi$
$619$	3.14935	+	1.62360i	0.126583	+	0.0652581i	−0.393772	+	0.919208i	$0.628830\pi$
$620$		0			0
$621$	2.78846	+	2.65879i	0.111897	+	0.106694i
$622$		0			0
$623$	−0.0580312	−	0.167670i	−0.00232497	−	0.00671756i
$624$		0			0
$625$	9.55600	+	11.0282i	0.382240	+	0.441129i
$626$		0			0
$627$	−0.446620	−	0.131139i	−0.0178363	−	0.00523721i
$628$		0			0
$629$	−3.71148	+	3.53889i	−0.147986	+	0.141105i
$630$		0			0
$631$	14.0743	−	19.7645i	0.560287	−	0.786814i	−0.433134	−	0.901330i	$-0.642592\pi$
$631$	14.0743	−	19.7645i	0.560287	−	0.786814i	0.993421	+	0.114516i	$0.0365317\pi$
$632$		0			0
$633$	−4.31334	−	7.47092i	−0.171440	−	0.296942i
$634$		0			0
$635$	−32.7475	+	6.31156i	−1.29954	+	0.250466i
$636$		0			0
$637$	4.62995	+	3.64104i	0.183445	+	0.144263i
$638$		0			0
$639$	−1.40221	−	0.133895i	−0.0554708	−	0.00529681i
$640$		0			0
$641$	1.92711	−	3.33786i	0.0761164	−	0.131838i	−0.825455	−	0.564468i	$-0.809081\pi$
$641$	1.92711	−	3.33786i	0.0761164	−	0.131838i	0.901571	+	0.432631i	$0.142415\pi$
$642$		0			0
$643$	40.9786	+	26.3353i	1.61604	+	1.03856i	0.958480	+	0.285161i	$0.0920471\pi$
$643$	40.9786	+	26.3353i	1.61604	+	1.03856i	0.657558	+	0.753404i	$0.271589\pi$
$644$		0			0
$645$	3.04379	−	6.66496i	0.119849	−	0.262433i
$646$		0			0
$647$	−18.2747	−	3.52216i	−0.718452	−	0.138470i	−0.183094	−	0.983095i	$-0.558611\pi$
$647$	−18.2747	−	3.52216i	−0.718452	−	0.138470i	−0.535358	+	0.844625i	$0.679823\pi$
$648$		0			0
$649$	−7.18565	+	3.70446i	−0.282061	+	0.145413i
$650$		0			0
$651$	0.321256	−	0.128611i	0.0125910	−	0.00504068i
$652$		0			0
$653$	4.37223	+	18.0226i	0.171099	+	0.705278i	0.991123	+	0.132949i	$0.0424447\pi$
$653$	4.37223	+	18.0226i	0.171099	+	0.705278i	−0.820024	+	0.572329i	$0.806040\pi$
$654$		0			0
$655$	2.13691	−	14.8626i	0.0834961	−	0.580728i
$656$		0			0
$657$	−10.2834	+	0.981947i	−0.401194	+	0.0383094i
$658$		0			0
$659$	1.76492	+	37.0502i	0.0687515	+	1.44327i	0.725011	+	0.688737i	$0.241835\pi$
$659$	1.76492	+	37.0502i	0.0687515	+	1.44327i	−0.656260	+	0.754535i	$0.727862\pi$
$660$		0			0
$661$	3.05369	+	21.2389i	0.118775	+	0.826097i	0.958908	+	0.283717i	$0.0915676\pi$
$661$	3.05369	+	21.2389i	0.118775	+	0.826097i	−0.840133	+	0.542380i	$0.817523\pi$
$662$		0			0
$663$	−3.06595	−	1.22742i	−0.119072	−	0.0476691i
$664$		0			0
$665$	−0.00959980	+	0.00616942i	−0.000372264	+	0.000239240i
$666$		0			0
$667$	17.5110	−	20.2088i	0.678029	−	0.782487i
$668$		0			0
$669$	−15.7226			−0.607871
$670$		0			0
$671$	−30.6252			−1.18227
$672$		0			0
$673$	−19.8805	+	22.9433i	−0.766335	+	0.884398i	−0.996044	−	0.0888613i	$-0.971677\pi$
$673$	−19.8805	+	22.9433i	−0.766335	+	0.884398i	0.229709	+	0.973259i	$0.426223\pi$
$674$		0			0
$675$	−1.33033	+	0.854953i	−0.0512045	+	0.0329072i
$676$		0			0
$677$	41.2913	+	16.5306i	1.58696	+	0.635321i	0.986415	−	0.164273i	$-0.0525279\pi$
$677$	41.2913	+	16.5306i	1.58696	+	0.635321i	0.600541	+	0.799594i	$0.294952\pi$
$678$		0			0
$679$	0.0387024	+	0.269181i	0.00148526	+	0.0103302i
$680$		0			0
$681$	−1.18965	−	24.9739i	−0.0455877	−	0.957003i
$682$		0			0
$683$	2.65425	−	0.253450i	0.101562	−	0.00969799i	−0.0441513	−	0.999025i	$-0.514058\pi$
$683$	2.65425	−	0.253450i	0.101562	−	0.00969799i	0.145713	+	0.989327i	$0.453452\pi$
$684$		0			0
$685$	−0.662785	+	4.60977i	−0.0253237	+	0.176130i
$686$		0			0
$687$	−6.40265	−	26.3921i	−0.244276	−	1.00692i
$688$		0			0
$689$	−0.741250	+	0.296752i	−0.0282394	+	0.0113053i
$690$		0			0
$691$	−32.2975	+	16.6505i	−1.22865	+	0.633415i	−0.945488	−	0.325656i	$-0.894415\pi$
$691$	−32.2975	+	16.6505i	−1.22865	+	0.633415i	−0.283166	+	0.959071i	$0.591385\pi$
$692$		0			0
$693$	0.240295	+	0.0463131i	0.00912807	+	0.00175929i
$694$		0			0
$695$	−1.47665	+	3.23341i	−0.0560125	+	0.122650i
$696$		0			0
$697$	−33.0072	−	21.2124i	−1.25024	−	0.803477i
$698$		0			0
$699$	−4.53625	+	7.85702i	−0.171577	+	0.297180i
$700$		0			0
$701$	−16.7561	−	1.60001i	−0.632867	−	0.0604315i	−0.226308	−	0.974056i	$-0.572666\pi$
$701$	−16.7561	−	1.60001i	−0.632867	−	0.0604315i	−0.406559	+	0.913624i	$0.633272\pi$
$702$		0			0
$703$	0.111333	+	0.0875530i	0.00419899	+	0.00330212i
$704$		0			0
$705$	−10.6353	+	2.04978i	−0.400547	+	0.0771991i
$706$		0			0
$707$	0.388904	+	0.673601i	0.0146262	+	0.0253334i
$708$		0			0
$709$	−27.4338	+	38.5254i	−1.03030	+	1.44685i	−0.140729	+	0.990048i	$0.544945\pi$
$709$	−27.4338	+	38.5254i	−1.03030	+	1.44685i	−0.889568	+	0.456802i	$0.848995\pi$
$710$		0			0
$711$	9.23517	−	8.80572i	0.346346	−	0.330240i
$712$		0			0
$713$	22.4578	+	6.59422i	0.841053	+	0.246955i
$714$		0			0
$715$	−4.37905	−	5.05369i	−0.163767	−	0.188997i
$716$		0			0
$717$	3.58793	+	10.3666i	0.133994	+	0.387150i
$718$		0			0
$719$	−29.5391	−	28.1655i	−1.10162	−	1.05039i	−0.998446	−	0.0557317i	$-0.982251\pi$
$719$	−29.5391	−	28.1655i	−1.10162	−	1.05039i	−0.103177	−	0.994663i	$-0.532901\pi$
$720$		0			0
$721$	−0.139840	−	0.0720923i	−0.00520790	−	0.00268486i
$722$		0			0
$723$	7.94517	−	2.33291i	0.295484	−	0.0867620i
$724$		0			0
$725$	6.36621	+	8.94009i	0.236435	+	0.332027i
$726$		0			0
$727$	−5.60739	+	16.2015i	−0.207967	+	0.600880i	−0.999953	−	0.00965834i	$-0.996926\pi$
$727$	−5.60739	+	16.2015i	−0.207967	+	0.600880i	0.791987	+	0.610538i	$0.209047\pi$
$728$		0			0
$729$	0.415415	+	0.909632i	0.0153857	+	0.0336901i
$730$		0			0
$731$	0.739715	−	15.5285i	0.0273594	−	0.574344i
$732$		0			0
$733$	−8.67246	+	35.7484i	−0.320325	+	1.32040i	0.552969	+	0.833202i	$0.313495\pi$
$733$	−8.67246	+	35.7484i	−0.320325	+	1.32040i	−0.873293	+	0.487195i	$0.838020\pi$
$734$		0			0
$735$	−10.1689	+	7.99692i	−0.375086	+	0.294971i
$736$		0			0
$737$	23.1428	+	26.4765i	0.852477	+	0.975274i
$738$		0			0
$739$	17.7751	−	13.9785i	0.653868	−	0.514207i	−0.235221	−	0.971942i	$-0.575581\pi$
$739$	17.7751	−	13.9785i	0.653868	−	0.514207i	0.889089	+	0.457735i	$0.151339\pi$
$740$		0			0
$741$	−0.0215039	+	0.0886401i	−0.000789964	+	0.00325628i
$742$		0			0
$743$	−0.955060	+	20.0492i	−0.0350377	+	0.735533i	0.911181	+	0.412006i	$0.135172\pi$
$743$	−0.955060	+	20.0492i	−0.0350377	+	0.735533i	−0.946219	+	0.323527i	$0.895131\pi$
$744$		0			0
$745$	4.04227	+	8.85133i	0.148097	+	0.324288i
$746$		0			0
$747$	−5.04175	+	14.5672i	−0.184468	+	0.532985i
$748$		0			0
$749$	−0.370088	−	0.519715i	−0.0135227	−	0.0189900i
$750$		0			0
$751$	−0.175443	+	0.0515147i	−0.00640201	+	0.00187980i	−0.284932	−	0.958548i	$-0.591971\pi$
$751$	−0.175443	+	0.0515147i	−0.00640201	+	0.00187980i	0.278530	+	0.960428i	$0.410153\pi$
$752$		0			0
$753$	7.47276	+	3.85248i	0.272323	+	0.140392i
$754$		0			0
$755$	5.54999	+	5.29191i	0.201985	+	0.192592i
$756$		0			0
$757$	7.92242	+	22.8903i	0.287945	+	0.831963i	0.992492	+	0.122306i	$0.0390289\pi$
$757$	7.92242	+	22.8903i	0.287945	+	0.831963i	−0.704547	+	0.709657i	$0.748850\pi$
$758$		0			0
$759$	10.8395	+	12.5095i	0.393450	+	0.454065i
$760$		0			0
$761$	−45.8252	−	13.4555i	−1.66116	−	0.487761i	−0.689530	−	0.724257i	$-0.742183\pi$
$761$	−45.8252	−	13.4555i	−1.66116	−	0.487761i	−0.971633	+	0.236495i	$0.924001\pi$
$762$		0			0
$763$	0.0739981	−	0.0705571i	0.00267891	−	0.00255434i
$764$		0			0
$765$	4.20740	−	5.90846i	0.152119	−	0.213621i
$766$		0			0
$767$	0.792075	+	1.37191i	0.0286002	+	0.0495370i
$768$		0			0
$769$	−12.3134	+	2.37321i	−0.444032	+	0.0855801i	−0.406366	−	0.913710i	$-0.633204\pi$
$769$	−12.3134	+	2.37321i	−0.444032	+	0.0855801i	−0.0376654	+	0.999290i	$0.511992\pi$
$770$		0			0
$771$	2.29632	+	1.80584i	0.0826999	+	0.0650359i
$772$		0			0
$773$	−41.1930	−	3.93346i	−1.48161	−	0.141477i	−0.677309	−	0.735699i	$-0.736854\pi$
$773$	−41.1930	−	3.93346i	−1.48161	−	0.141477i	−0.804301	+	0.594222i	$0.797460\pi$
$774$		0			0
$775$	−4.80335	+	8.31965i	−0.172542	+	0.298851i
$776$		0			0
$777$	−0.0626422	−	0.0402577i	−0.00224728	−	0.00144424i
$778$		0			0
$779$	−0.450160	+	0.985712i	−0.0161286	+	0.0353168i
$780$		0			0
$781$	−5.94212	−	1.14525i	−0.212626	−	0.0409803i
$782$		0			0
$783$	6.16877	−	3.18022i	0.220454	−	0.113652i
$784$		0			0
$785$	25.3764	−	10.1592i	0.905722	−	0.362597i
$786$		0			0
$787$	−7.00206	−	28.8629i	−0.249596	−	1.02885i	−0.949289	−	0.314406i	$-0.898195\pi$
$787$	−7.00206	−	28.8629i	−0.249596	−	1.02885i	0.699692	−	0.714444i	$-0.253320\pi$
$788$		0			0
$789$	2.00201	−	13.9243i	0.0712733	−	0.495717i
$790$		0			0
$791$	0.612628	−	0.0584989i	0.0217825	−	0.00207998i
$792$		0			0
$793$	0.285544	+	5.99430i	0.0101400	+	0.212864i
$794$		0			0
$795$	−0.249570	−	1.73580i	−0.00885134	−	0.0615624i
$796$		0			0
$797$	18.1932	+	7.28345i	0.644435	+	0.257993i	0.670776	−	0.741660i	$-0.265961\pi$
$797$	18.1932	+	7.28345i	0.644435	+	0.257993i	−0.0263407	+	0.999653i	$0.508385\pi$
$798$		0			0
$799$	−19.3324	+	12.4242i	−0.683931	+	0.439536i
$800$		0			0
$801$	2.03978	−	2.35403i	0.0720721	−	0.0831756i
$802$		0			0
$803$	−44.3797			−1.56613
$804$		0			0
$805$	0.405789			0.0143022
$806$		0			0
$807$	−0.855540	+	0.987346i	−0.0301164	+	0.0347562i
$808$		0			0
$809$	−24.2092	+	15.5583i	−0.851150	+	0.547001i	−0.891933	−	0.452167i	$-0.850651\pi$
$809$	−24.2092	+	15.5583i	−0.851150	+	0.547001i	0.0407832	+	0.999168i	$0.487015\pi$
$810$		0			0
$811$	−7.87389	−	3.15223i	−0.276490	−	0.110690i	0.229274	−	0.973362i	$-0.426365\pi$
$811$	−7.87389	−	3.15223i	−0.276490	−	0.110690i	−0.505763	+	0.862672i	$0.668789\pi$
$812$		0			0
$813$	2.88094	+	20.0374i	0.101039	+	0.702742i
$814$		0			0
$815$	−0.296371	−	6.22159i	−0.0103814	−	0.217933i
$816$		0			0
$817$	−0.427420	+	0.0408137i	−0.0149535	+	0.00142789i
$818$		0			0
$819$	0.00682445	−	0.0474651i	0.000238466	−	0.00165856i
$820$		0			0
$821$	−1.94535	−	8.01883i	−0.0678931	−	0.279859i	0.927738	−	0.373232i	$-0.121750\pi$
$821$	−1.94535	−	8.01883i	−0.0678931	−	0.279859i	−0.995631	+	0.0933726i	$0.970235\pi$
$822$		0			0
$823$	−41.6971	+	16.6930i	−1.45347	+	0.581881i	−0.958006	−	0.286749i	$-0.907426\pi$
$823$	−41.6971	+	16.6930i	−1.45347	+	0.581881i	−0.495462	+	0.868629i	$0.665001\pi$
$824$		0			0
$825$	−6.03853	+	3.11308i	−0.210235	+	0.108383i
$826$		0			0
$827$	−29.3307	−	5.65303i	−1.01993	−	0.196575i	−0.348238	−	0.937406i	$-0.613220\pi$
$827$	−29.3307	−	5.65303i	−1.01993	−	0.196575i	−0.671692	+	0.740831i	$0.734432\pi$
$828$		0			0
$829$	−21.8519	+	47.8490i	−0.758948	+	1.66186i	−0.00936252	+	0.999956i	$0.502980\pi$
$829$	−21.8519	+	47.8490i	−0.758948	+	1.66186i	−0.749585	+	0.661908i	$0.769747\pi$
$830$		0			0
$831$	6.27525	+	4.03286i	0.217686	+	0.139898i
$832$		0			0
$833$	−13.7241	+	23.7708i	−0.475511	+	0.823610i
$834$		0			0
$835$	4.79725	+	0.458082i	0.166016	+	0.0158526i
$836$		0			0
$837$	4.77522	+	3.75527i	0.165056	+	0.129801i
$838$		0			0
$839$	23.2628	−	4.48353i	0.803120	−	0.154789i	0.228857	−	0.973460i	$-0.426501\pi$
$839$	23.2628	−	4.48353i	0.803120	−	0.154789i	0.574262	+	0.818671i	$0.305289\pi$
$840$		0			0
$841$	−9.58375	−	16.5995i	−0.330474	−	0.572398i
$842$		0			0
$843$	−6.89647	+	9.68474i	−0.237527	+	0.333560i
$844$		0			0
$845$	16.4476	−	15.6828i	0.565816	−	0.539504i
$846$		0			0
$847$	0.407544	+	0.119666i	0.0140034	+	0.00411176i
$848$		0			0
$849$	6.43509	+	7.42649i	0.220852	+	0.254877i
$850$		0			0
$851$	−1.64730	−	4.75957i	−0.0564689	−	0.163156i
$852$		0			0
$853$	−18.2922	−	17.4415i	−0.626312	−	0.597187i	0.308978	−	0.951069i	$-0.400013\pi$
$853$	−18.2922	−	17.4415i	−0.626312	−	0.597187i	−0.935290	+	0.353882i	$0.884861\pi$
$854$		0			0
$855$	−0.178060	−	0.0917965i	−0.00608954	−	0.00313938i
$856$		0			0
$857$	−26.2318	+	7.70235i	−0.896061	+	0.263107i	−0.697163	−	0.716913i	$-0.745555\pi$
$857$	−26.2318	+	7.70235i	−0.896061	+	0.263107i	−0.198898	+	0.980020i	$0.563736\pi$
$858$		0			0
$859$	−27.0291	−	37.9570i	−0.922220	−	1.29508i	−0.955304	−	0.295624i	$-0.904472\pi$
$859$	−27.0291	−	37.9570i	−0.922220	−	1.29508i	0.0330843	−	0.999453i	$-0.489467\pi$
$860$		0			0
$861$	0.186334	−	0.538376i	0.00635024	−	0.0183478i
$862$		0			0
$863$	14.0958	+	30.8654i	0.479826	+	1.05067i	0.982511	+	0.186202i	$0.0596180\pi$
$863$	14.0958	+	30.8654i	0.479826	+	1.05067i	−0.502686	+	0.864469i	$0.667655\pi$
$864$		0			0
$865$	0.610132	−	12.8083i	0.0207451	−	0.435494i
$866$		0			0
$867$	−0.379614	+	1.56479i	−0.0128924	+	0.0531431i
$868$		0			0
$869$	43.0917	−	33.8877i	1.46179	−	1.14956i
$870$		0			0
$871$	4.96649	−	4.77663i	0.168283	−	0.161850i
$872$		0			0
$873$	−3.75275	+	2.95120i	−0.127012	+	0.0998830i
$874$		0			0
$875$	−0.163418	+	0.673618i	−0.00552454	+	0.0227724i
$876$		0			0
$877$	0.365399	−	7.67068i	0.0123387	−	0.259020i	−0.984266	−	0.176690i	$-0.943461\pi$
$877$	0.365399	−	7.67068i	0.0123387	−	0.259020i	0.996605	−	0.0823299i	$-0.0262361\pi$
$878$		0			0
$879$	−4.70447	−	10.3014i	−0.158678	−	0.347456i
$880$		0			0
$881$	−13.1853	+	38.0964i	−0.444224	+	1.28350i	0.471562	+	0.881833i	$0.343690\pi$
$881$	−13.1853	+	38.0964i	−0.444224	+	1.28350i	−0.915786	+	0.401667i	$0.868431\pi$
$882$		0			0
$883$	24.0516	+	33.7758i	0.809401	+	1.13665i	0.988262	+	0.152771i	$0.0488196\pi$
$883$	24.0516	+	33.7758i	0.809401	+	1.13665i	−0.178860	+	0.983874i	$0.557241\pi$
$884$		0			0
$885$	−3.33838	+	0.980238i	−0.112219	+	0.0329503i
$886$		0			0
$887$	−8.21818	−	4.23677i	−0.275940	−	0.142257i	0.314703	−	0.949190i	$-0.398095\pi$
$887$	−8.21818	−	4.23677i	−0.275940	−	0.142257i	−0.590642	+	0.806934i	$0.701126\pi$
$888$		0			0
$889$	−0.743601	−	0.709022i	−0.0249396	−	0.0237798i
$890$		0			0
$891$	1.40512	+	4.05984i	0.0470734	+	0.136010i
$892$		0			0
$893$	0.415634	+	0.479667i	0.0139087	+	0.0160514i
$894$		0			0
$895$	−8.01398	−	2.35312i	−0.267878	−	0.0786561i
$896$		0			0
$897$	2.34743	−	2.23827i	0.0783783	−	0.0747336i
$898$		0			0
$899$	24.4562	−	34.3439i	0.815660	−	1.14543i
$900$		0			0
$901$	−1.86039	−	3.22228i	−0.0619784	−	0.107350i
$902$		0			0
$903$	0.221654	−	0.0427203i	0.00737617	−	0.00142164i
$904$		0			0
$905$	16.8937	+	13.2854i	0.561567	+	0.441621i
$906$		0			0
$907$	−39.4336	−	3.76545i	−1.30937	−	0.125030i	−0.583079	−	0.812415i	$-0.698152\pi$
$907$	−39.4336	−	3.76545i	−1.30937	−	0.125030i	−0.726293	+	0.687385i	$0.758758\pi$
$908$		0			0
$909$	−6.82736	+	11.8253i	−0.226449	+	0.392222i
$910$		0			0
$911$	17.3102	+	11.1246i	0.573514	+	0.368575i	0.795019	−	0.606584i	$-0.207461\pi$
$911$	17.3102	+	11.1246i	0.573514	+	0.368575i	−0.221505	+	0.975159i	$0.571097\pi$
$912$		0			0
$913$	−27.5107	+	60.2400i	−0.910471	+	1.99365i
$914$		0			0
$915$	−12.9422	−	2.49441i	−0.427857	−	0.0824626i
$916$		0			0
$917$	0.411170	−	0.211973i	0.0135780	−	0.00699996i
$918$		0			0
$919$	24.1989	−	9.68777i	0.798247	−	0.319570i	0.0635619	−	0.997978i	$-0.479754\pi$
$919$	24.1989	−	9.68777i	0.798247	−	0.319570i	0.734686	+	0.678408i	$0.237330\pi$
$920$		0			0
$921$	−3.97294	−	16.3767i	−0.130913	−	0.539630i
$922$		0			0
$923$	−0.168758	+	1.17374i	−0.00555473	+	0.0386340i
$924$		0			0
$925$	2.05785	−	0.196501i	0.0676616	−	0.00646090i
$926$		0			0
$927$	−0.131420	−	2.75884i	−0.00431640	−	0.0906124i
$928$		0			0
$929$	3.26665	+	22.7201i	0.107175	+	0.745421i	0.970557	+	0.240870i	$0.0774328\pi$
$929$	3.26665	+	22.7201i	0.107175	+	0.745421i	−0.863382	+	0.504551i	$0.831658\pi$
$930$		0			0
$931$	0.703780	+	0.281751i	0.0230655	+	0.00923402i
$932$		0			0
$933$	5.12461	−	3.29339i	0.167772	−	0.107821i
$934$		0			0
$935$	20.4065	−	23.5503i	0.667363	−	0.770178i
$936$		0			0
$937$	38.4600			1.25643			0.628217	−	0.778038i	$-0.283785\pi$
$937$	38.4600			1.25643			0.628217	+	0.778038i	$0.283785\pi$
$938$		0			0
$939$	−14.0313			−0.457895
$940$		0			0
$941$	5.73754	−	6.62147i	0.187038	−	0.215854i	−0.654484	−	0.756076i	$-0.727114\pi$
$941$	5.73754	−	6.62147i	0.187038	−	0.215854i	0.841523	+	0.540222i	$0.181660\pi$
$942$		0			0
$943$	32.4173	−	20.8333i	1.05565	−	0.678426i
$944$		0			0
$945$	0.0977767	+	0.0391439i	0.00318068	+	0.00127335i
$946$		0			0
$947$	−4.36776	−	30.3784i	−0.141933	−	0.987166i	−0.928942	−	0.370225i	$-0.879281\pi$
$947$	−4.36776	−	30.3784i	−0.141933	−	0.987166i	0.787009	−	0.616941i	$-0.211628\pi$
$948$		0			0
$949$	0.413789	+	8.68649i	0.0134321	+	0.281975i
$950$		0			0
$951$	11.1813	−	1.06769i	0.362579	−	0.0346221i
$952$		0			0
$953$	5.77623	−	40.1745i	0.187110	−	1.30138i	−0.652333	−	0.757933i	$-0.726209\pi$
$953$	5.77623	−	40.1745i	0.187110	−	1.30138i	0.839443	−	0.543448i	$-0.182881\pi$
$954$		0			0
$955$	4.51328	+	18.6040i	0.146046	+	0.602011i
$956$		0			0
$957$	27.6805	−	11.0816i	0.894782	−	0.358217i
$958$		0			0
$959$	−0.127528	+	0.0657454i	−0.00411811	+	0.00212303i
$960$		0			0
$961$	5.79807	+	1.11749i	0.187035	+	0.0360480i
$962$		0			0
$963$	4.65293	−	10.1885i	0.149939	−	0.328320i
$964$		0			0
$965$	−28.3844	−	18.2416i	−0.913727	−	0.587217i
$966$		0			0
$967$	21.5027	−	37.2438i	0.691481	−	1.19768i	−0.279872	−	0.960037i	$-0.590292\pi$
$967$	21.5027	−	37.2438i	0.691481	−	1.19768i	0.971353	−	0.237642i	$-0.0763746\pi$
$968$		0			0
$969$	−0.423122	−	0.0404033i	−0.0135926	−	0.00129794i
$970$		0			0
$971$	−45.7089	−	35.9459i	−1.46687	−	1.15356i	−0.955800	−	0.294018i	$-0.905007\pi$
$971$	−45.7089	−	35.9459i	−1.46687	−	1.15356i	−0.511069	−	0.859540i	$-0.670750\pi$
$972$		0			0
$973$	−0.107532	+	0.0207251i	−0.00344732	+	0.000664417i
$974$		0			0
$975$	0.665628	+	1.15290i	0.0213172	+	0.0369224i
$976$		0			0
$977$	−19.4232	+	27.2760i	−0.621402	+	0.872637i	−0.998567	−	0.0535088i	$-0.982959\pi$
$977$	−19.4232	+	27.2760i	−0.621402	+	0.872637i	0.377165	+	0.926146i	$0.376899\pi$
$978$		0			0
$979$	9.68478	−	9.23442i	0.309527	−	0.295133i
$980$		0			0
$981$	1.72224	+	0.505696i	0.0549870	+	0.0161456i
$982$		0			0
$983$	0.402076	+	0.464020i	0.0128242	+	0.0148000i	0.762125	−	0.647429i	$-0.224156\pi$
$983$	0.402076	+	0.464020i	0.0128242	+	0.0148000i	−0.749301	+	0.662229i	$0.769610\pi$
$984$		0			0
$985$	7.57250	+	21.8793i	0.241280	+	0.697132i
$986$		0			0
$987$	−0.241496	−	0.230266i	−0.00768691	−	0.00732945i
$988$		0			0
$989$	13.5710	+	6.99634i	0.431533	+	0.222471i
$990$		0			0
$991$	38.5473	−	11.3185i	1.22449	−	0.359544i	0.395325	−	0.918541i	$-0.370632\pi$
$991$	38.5473	−	11.3185i	1.22449	−	0.359544i	0.829170	+	0.558997i	$0.188814\pi$
$992$		0			0
$993$	17.5345	+	24.6238i	0.556441	+	0.781412i
$994$		0			0
$995$	−5.78217	+	16.7065i	−0.183307	+	0.529631i
$996$		0			0
$997$	10.5963	+	23.2027i	0.335589	+	0.734837i	0.999921	−	0.0126011i	$-0.00401115\pi$
$997$	10.5963	+	23.2027i	0.335589	+	0.734837i	−0.664332	+	0.747438i	$0.731284\pi$
$998$		0			0
$999$	0.0622004	−	1.30575i	0.00196793	−	0.0413120i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.y.a.121.2	✓	100
67.36	even	33	inner	804.2.y.a.505.2	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.y.a.121.2	✓	100	1.1	even	1	trivial
804.2.y.a.505.2	yes	100	67.36	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)

\(f(q)\)	\(=\)	\(q+(-0.654861 + 0.755750i) q^{3} +(-1.55544 + 0.999620i) q^{5} +(-0.0528822 - 0.0211708i) q^{7} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(q+(-0.654861 + 0.755750i) q^{3} +(-1.55544 + 0.999620i) q^{5} +(-0.0528822 - 0.0211708i) q^{7} +(-0.142315 - 0.989821i) q^{9} +(-0.204418 - 4.29125i) q^{11} +(-0.838025 + 0.0800217i) q^{13} +(0.263134 - 1.83013i) q^{15} +(-0.924879 - 3.81240i) q^{17} +(-0.100587 + 0.0402688i) q^{19} +(0.0506303 - 0.0261017i) q^{21} +(3.78325 + 0.729162i) q^{23} +(-0.656925 + 1.43846i) q^{25} +(0.841254 + 0.540641i) q^{27} +(3.47014 - 6.01046i) q^{29} +(6.04742 + 0.577459i) q^{31} +(3.37698 + 2.65568i) q^{33} +(0.103418 - 0.0199321i) q^{35} +(-0.653613 - 1.13209i) q^{37} +(0.488313 - 0.685740i) q^{39} +(7.23841 - 6.90181i) q^{41} +(3.80231 + 1.11646i) q^{43} +(1.21081 + 1.39735i) q^{45} +(-1.91593 - 5.53572i) q^{47} +(-5.06379 - 4.82831i) q^{49} +(3.48689 + 1.79762i) q^{51} +(0.910035 - 0.267210i) q^{53} +(4.60758 + 6.47044i) q^{55} +(0.0354371 - 0.102389i) q^{57} +(-0.781719 - 1.71172i) q^{59} +(0.339191 - 7.12050i) q^{61} +(-0.0134294 + 0.0553568i) q^{63} +(1.22351 - 0.962176i) q^{65} +(-6.41223 + 5.08757i) q^{67} +(-3.02856 + 2.38169i) q^{69} +(0.332088 - 1.36889i) q^{71} +(0.491530 - 10.3185i) q^{73} +(-0.656925 - 1.43846i) q^{75} +(-0.0800393 + 0.231259i) q^{77} +(7.40178 + 10.3944i) q^{79} +(-0.959493 + 0.281733i) q^{81} +(-13.7014 - 7.06355i) q^{83} +(5.24955 + 5.00543i) q^{85} +(2.26994 + 6.55857i) q^{87} +(2.03978 + 2.35403i) q^{89} +(0.0460107 + 0.0135100i) q^{91} +(-4.39663 + 4.19218i) q^{93} +(0.116203 - 0.163184i) q^{95} +(-2.38709 - 4.13456i) q^{97} +(-4.21848 + 0.813046i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 10 q^{3} + 2 q^{5} - 3 q^{7} - 10 q^{9}+O(q^{10}) \) 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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