LMFDB - Embedded newform 804.2.y.b.793.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("804.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.y (of order $33$, degree $20$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$6$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			793.5
Character	$\chi$	$=$	804.793
Dual form			804.2.y.b.73.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.415415 - 0.909632i) q^{3} +(2.10734 - 0.618772i) q^{5} +(0.474282 + 0.0914103i) q^{7} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.415415 - 0.909632i) q^{3} +(2.10734 - 0.618772i) q^{5} +(0.474282 + 0.0914103i) q^{7} +(-0.654861 + 0.755750i) q^{9} +(3.02245 + 2.88190i) q^{11} +(0.287738 + 6.04037i) q^{13} +(-1.43828 - 1.65986i) q^{15} +(0.106025 + 0.0833792i) q^{17} +(4.57644 - 0.882036i) q^{19} +(-0.113874 - 0.469395i) q^{21} +(0.0590758 + 0.00564106i) q^{23} +(-0.148248 + 0.0952734i) q^{25} +(0.959493 + 0.281733i) q^{27} +(-0.202525 - 0.350784i) q^{29} +(0.214233 - 4.49731i) q^{31} +(1.36590 - 3.94650i) q^{33} +(1.05604 - 0.100839i) q^{35} +(-1.16314 + 2.01461i) q^{37} +(5.37498 - 2.77100i) q^{39} +(2.08254 - 0.833724i) q^{41} +(1.26496 - 8.79801i) q^{43} +(-0.912380 + 1.99783i) q^{45} +(0.663038 - 0.931107i) q^{47} +(-6.28199 - 2.51493i) q^{49} +(0.0317999 - 0.131081i) q^{51} +(0.919967 + 6.39851i) q^{53} +(8.15258 + 4.20295i) q^{55} +(-2.70345 - 3.79646i) q^{57} +(8.18366 + 5.25932i) q^{59} +(3.09277 - 2.94895i) q^{61} +(-0.379672 + 0.298577i) q^{63} +(4.34398 + 12.5511i) q^{65} +(1.95922 - 7.94742i) q^{67} +(-0.0194097 - 0.0560806i) q^{69} +(4.67866 - 3.67934i) q^{71} +(-5.09429 + 4.85739i) q^{73} +(0.148248 + 0.0952734i) q^{75} +(1.17006 + 1.64312i) q^{77} +(-6.81475 - 3.51325i) q^{79} +(-0.142315 - 0.989821i) q^{81} +(-1.19490 + 4.92546i) q^{83} +(0.275025 + 0.110103i) q^{85} +(-0.234952 + 0.329944i) q^{87} +(1.25611 - 2.75050i) q^{89} +(-0.415683 + 2.89114i) q^{91} +(-4.17990 + 1.67338i) q^{93} +(9.09834 - 4.69052i) q^{95} +(5.47937 - 9.49054i) q^{97} +(-4.15728 + 0.396972i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9}+O(q^{10}) $ 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9	$ 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9} + 11 q^{11} + 2 q^{13} - 9 q^{15} + 48 q^{17} - 4 q^{19} - q^{21} + 22 q^{23} - 42 q^{25} + 12 q^{27} - q^{29} + 27 q^{31} + 17 q^{35} - 8 q^{37} - 2 q^{39} - 58 q^{41} - 17 q^{43} - 2 q^{45} - 84 q^{47} + 101 q^{49} - 26 q^{51} + 28 q^{53} - 9 q^{55} + 26 q^{57} + 34 q^{59} + 16 q^{61} + 12 q^{63} + 144 q^{65} + 23 q^{67} + 11 q^{69} + 173 q^{71} - 2 q^{73} + 42 q^{75} + 128 q^{77} + 31 q^{79} - 12 q^{81} + 47 q^{83} - 75 q^{85} - 10 q^{87} - 67 q^{89} + 16 q^{91} + 6 q^{93} - 79 q^{95} + 10 q^{97}+O(q^{100}) $ 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9 + 11 * q^11 + 2 * q^13 - 9 * q^15 + 48 * q^17 - 4 * q^19 - q^21 + 22 * q^23 - 42 * q^25 + 12 * q^27 - q^29 + 27 * q^31 + 17 * q^35 - 8 * q^37 - 2 * q^39 - 58 * q^41 - 17 * q^43 - 2 * q^45 - 84 * q^47 + 101 * q^49 - 26 * q^51 + 28 * q^53 - 9 * q^55 + 26 * q^57 + 34 * q^59 + 16 * q^61 + 12 * q^63 + 144 * q^65 + 23 * q^67 + 11 * q^69 + 173 * q^71 - 2 * q^73 + 42 * q^75 + 128 * q^77 + 31 * q^79 - 12 * q^81 + 47 * q^83 - 75 * q^85 - 10 * q^87 - 67 * q^89 + 16 * q^91 + 6 * q^93 - 79 * q^95 + 10 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{13}{33}\right)$	$1$

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
$3$	−0.415415	−	0.909632i	−0.239840	−	0.525176i
$3$	−0.415415	−	0.909632i	−0.239840	−	0.525176i
$4$		0			0
$5$	2.10734	−	0.618772i	0.942433	−	0.276723i	0.225800	−	0.974174i	$-0.427500\pi$
$5$	2.10734	−	0.618772i	0.942433	−	0.276723i	0.716633	+	0.697450i	$0.245682\pi$
$6$		0			0
$7$	0.474282	+	0.0914103i	0.179262	+	0.0345499i	0.278092	−	0.960554i	$-0.410298\pi$
$7$	0.474282	+	0.0914103i	0.179262	+	0.0345499i	−0.0988303	+	0.995104i	$0.531510\pi$
$8$		0			0
$9$	−0.654861	+	0.755750i	−0.218287	+	0.251917i
$10$		0			0
$11$	3.02245	+	2.88190i	0.911303	+	0.868925i	0.991796	−	0.127830i	$-0.0408011\pi$
$11$	3.02245	+	2.88190i	0.911303	+	0.868925i	−0.0804934	+	0.996755i	$0.525650\pi$
$12$		0			0
$13$	0.287738	+	6.04037i	0.0798043	+	1.67530i	0.584035	+	0.811729i	$0.301473\pi$
$13$	0.287738	+	6.04037i	0.0798043	+	1.67530i	−0.504231	+	0.863569i	$0.668224\pi$
$14$		0			0
$15$	−1.43828	−	1.65986i	−0.371362	−	0.428574i
$16$		0			0
$17$	0.106025	+	0.0833792i	0.0257149	+	0.0202224i	0.630934	−	0.775837i	$-0.282672\pi$
$17$	0.106025	+	0.0833792i	0.0257149	+	0.0202224i	−0.605219	+	0.796059i	$0.706914\pi$
$18$		0			0
$19$	4.57644	−	0.882036i	1.04991	−	0.202353i	0.365018	−	0.931001i	$-0.381063\pi$
$19$	4.57644	−	0.882036i	1.04991	−	0.202353i	0.684889	+	0.728648i	$0.259851\pi$
$20$		0			0
$21$	−0.113874	−	0.469395i	−0.0248494	−	0.102430i
$22$		0			0
$23$	0.0590758	+	0.00564106i	0.0123182	+	0.00117624i	0.101213	−	0.994865i	$-0.467728\pi$
$23$	0.0590758	+	0.00564106i	0.0123182	+	0.00117624i	−0.0888951	+	0.996041i	$0.528334\pi$
$24$		0			0
$25$	−0.148248	+	0.0952734i	−0.0296497	+	0.0190547i
$26$		0			0
$27$	0.959493	+	0.281733i	0.184655	+	0.0542195i
$28$		0			0
$29$	−0.202525	−	0.350784i	−0.0376080	−	0.0651389i	0.846609	−	0.532216i	$-0.178640\pi$
$29$	−0.202525	−	0.350784i	−0.0376080	−	0.0651389i	−0.884217	+	0.467077i	$0.845307\pi$
$30$		0			0
$31$	0.214233	−	4.49731i	0.0384775	−	0.807741i	−0.894339	−	0.447390i	$-0.852354\pi$
$31$	0.214233	−	4.49731i	0.0384775	−	0.807741i	0.932817	−	0.360352i	$-0.117343\pi$
$32$		0			0
$33$	1.36590	−	3.94650i	0.237772	−	0.686998i
$34$		0			0
$35$	1.05604	−	0.100839i	0.178503	−	0.0170450i
$36$		0			0
$37$	−1.16314	+	2.01461i	−0.191218	+	0.331200i	−0.945654	−	0.325174i	$-0.894577\pi$
$37$	−1.16314	+	2.01461i	−0.191218	+	0.331200i	0.754436	+	0.656374i	$0.227910\pi$
$38$		0			0
$39$	5.37498	−	2.77100i	0.860686	−	0.443715i
$40$		0			0
$41$	2.08254	−	0.833724i	0.325239	−	0.130206i	−0.203297	−	0.979117i	$-0.565166\pi$
$41$	2.08254	−	0.833724i	0.325239	−	0.130206i	0.528535	+	0.848911i	$0.322741\pi$
$42$		0			0
$43$	1.26496	−	8.79801i	0.192905	−	1.34168i	−0.631365	−	0.775486i	$-0.717505\pi$
$43$	1.26496	−	8.79801i	0.192905	−	1.34168i	0.824270	−	0.566198i	$-0.191586\pi$
$44$		0			0
$45$	−0.912380	+	1.99783i	−0.136010	+	0.297819i
$46$		0			0
$47$	0.663038	−	0.931107i	0.0967141	−	0.135816i	−0.763383	−	0.645946i	$-0.776463\pi$
$47$	0.663038	−	0.931107i	0.0967141	−	0.135816i	0.860097	+	0.510130i	$0.170403\pi$
$48$		0			0
$49$	−6.28199	−	2.51493i	−0.897427	−	0.359276i
$50$		0			0
$51$	0.0317999	−	0.131081i	0.00445288	−	0.0183550i
$52$		0			0
$53$	0.919967	+	6.39851i	0.126367	+	0.878903i	0.950105	+	0.311932i	$0.100976\pi$
$53$	0.919967	+	6.39851i	0.126367	+	0.878903i	−0.823737	+	0.566972i	$0.808115\pi$
$54$		0			0
$55$	8.15258	+	4.20295i	1.09929	+	0.566725i
$56$		0			0
$57$	−2.70345	−	3.79646i	−0.358080	−	0.502854i
$58$		0			0
$59$	8.18366	+	5.25932i	1.06542	+	0.684705i	0.951145	−	0.308744i	$-0.0999087\pi$
$59$	8.18366	+	5.25932i	1.06542	+	0.684705i	0.114276	+	0.993449i	$0.463545\pi$
$60$		0			0
$61$	3.09277	−	2.94895i	0.395989	−	0.377574i	−0.465759	−	0.884912i	$-0.654219\pi$
$61$	3.09277	−	2.94895i	0.395989	−	0.377574i	0.861748	+	0.507337i	$0.169370\pi$
$62$		0			0
$63$	−0.379672	+	0.298577i	−0.0478342	+	0.0376172i
$64$		0			0
$65$	4.34398	+	12.5511i	0.538804	+	1.55677i
$66$		0			0
$67$	1.95922	−	7.94742i	0.239356	−	0.970932i
$67$	1.95922	−	7.94742i	0.239356	−	0.970932i
$68$		0			0
$69$	−0.0194097	−	0.0560806i	−0.00233665	−	0.00675131i
$70$		0			0
$71$	4.67866	−	3.67934i	0.555254	−	0.436657i	−0.300692	−	0.953721i	$-0.597218\pi$
$71$	4.67866	−	3.67934i	0.555254	−	0.436657i	0.855947	+	0.517064i	$0.172975\pi$
$72$		0			0
$73$	−5.09429	+	4.85739i	−0.596241	+	0.568515i	−0.926934	−	0.375223i	$-0.877566\pi$
$73$	−5.09429	+	4.85739i	−0.596241	+	0.568515i	0.330693	+	0.943738i	$0.392718\pi$
$74$		0			0
$75$	0.148248	+	0.0952734i	0.0171182	+	0.0110012i
$76$		0			0
$77$	1.17006	+	1.64312i	0.133340	+	0.187250i
$78$		0			0
$79$	−6.81475	−	3.51325i	−0.766719	−	0.395271i	0.0300553	−	0.999548i	$-0.490432\pi$
$79$	−6.81475	−	3.51325i	−0.766719	−	0.395271i	−0.796774	+	0.604277i	$0.793462\pi$
$80$		0			0
$81$	−0.142315	−	0.989821i	−0.0158128	−	0.109980i
$82$		0			0
$83$	−1.19490	+	4.92546i	−0.131158	+	0.540640i	0.867880	+	0.496775i	$0.165482\pi$
$83$	−1.19490	+	4.92546i	−0.131158	+	0.540640i	−0.999037	+	0.0438654i	$0.986033\pi$
$84$		0			0
$85$	0.275025	+	0.110103i	0.0298306	+	0.0119424i
$86$		0			0
$87$	−0.234952	+	0.329944i	−0.0251895	+	0.0353737i
$88$		0			0
$89$	1.25611	−	2.75050i	0.133147	−	0.291552i	−0.831301	−	0.555822i	$-0.812404\pi$
$89$	1.25611	−	2.75050i	0.133147	−	0.291552i	0.964449	+	0.264270i	$0.0851309\pi$
$90$		0			0
$91$	−0.415683	+	2.89114i	−0.0435755	+	0.303074i
$92$		0			0
$93$	−4.17990	+	1.67338i	−0.433435	+	0.173521i
$94$		0			0
$95$	9.09834	−	4.69052i	0.933470	−	0.481237i
$96$		0			0
$97$	5.47937	−	9.49054i	0.556345	−	0.963619i	−0.441452	−	0.897285i	$-0.645536\pi$
$97$	5.47937	−	9.49054i	0.556345	−	0.963619i	0.997797	−	0.0663338i	$-0.0211302\pi$
$98$		0			0
$99$	−4.15728	+	0.396972i	−0.417822	+	0.0398972i
$100$		0			0
$101$	0.748085	−	2.16145i	0.0744372	−	0.215072i	−0.901644	−	0.432480i	$-0.857639\pi$
$101$	0.748085	−	2.16145i	0.0744372	−	0.215072i	0.976081	+	0.217407i	$0.0697600\pi$
$102$		0			0
$103$	0.434157	−	9.11408i	0.0427788	−	0.898037i	−0.870865	−	0.491522i	$-0.836441\pi$
$103$	0.434157	−	9.11408i	0.0427788	−	0.898037i	0.913644	−	0.406515i	$-0.133256\pi$
$104$		0			0
$105$	−0.530420	−	0.918715i	−0.0517637	−	0.0896574i
$106$		0			0
$107$	−7.13214	−	2.09419i	−0.689490	−	0.202453i	−0.0818260	−	0.996647i	$-0.526075\pi$
$107$	−7.13214	−	2.09419i	−0.689490	−	0.202453i	−0.607664	+	0.794194i	$0.707893\pi$
$108$		0			0
$109$	−2.63278	+	1.69199i	−0.252175	+	0.162063i	−0.660621	−	0.750719i	$-0.729707\pi$
$109$	−2.63278	+	1.69199i	−0.252175	+	0.162063i	0.408446	+	0.912782i	$0.366071\pi$
$110$		0			0
$111$	2.31574	+	0.221126i	0.219800	+	0.0209884i
$112$		0			0
$113$	3.08211	+	12.7046i	0.289941	+	1.19515i	0.911339	+	0.411657i	$0.135050\pi$
$113$	3.08211	+	12.7046i	0.289941	+	1.19515i	−0.621398	+	0.783495i	$0.713435\pi$
$114$		0			0
$115$	0.127984	−	0.0246668i	0.0119345	−	0.00230019i
$116$		0			0
$117$	−4.75344	−	3.73814i	−0.439455	−	0.345592i
$118$		0			0
$119$	0.0426642	+	0.0492371i	0.00391102	+	0.00451355i
$120$		0			0
$121$	0.306453	+	6.43325i	0.0278594	+	0.584841i
$122$		0			0
$123$	−1.62350	−	1.54801i	−0.146386	−	0.139579i
$124$		0			0
$125$	−7.44484	+	8.59181i	−0.665887	+	0.768475i
$126$		0			0
$127$	−9.42316	−	1.81617i	−0.836171	−	0.161159i	−0.246846	−	0.969055i	$-0.579394\pi$
$127$	−9.42316	−	1.81617i	−0.836171	−	0.161159i	−0.589325	+	0.807896i	$0.700606\pi$
$128$		0			0
$129$	−8.52843	+	2.50417i	−0.750887	+	0.220480i
$130$		0			0
$131$	−3.48887	−	7.63957i	−0.304824	−	0.667472i	0.693785	−	0.720182i	$-0.255942\pi$
$131$	−3.48887	−	7.63957i	−0.304824	−	0.667472i	−0.998610	+	0.0527094i	$0.983214\pi$
$132$		0			0
$133$	2.25115			0.195199
$134$		0			0
$135$	2.19631			0.189028
$136$		0			0
$137$	9.39297	+	20.5677i	0.802495	+	1.75722i	0.636780	+	0.771046i	$0.280266\pi$
$137$	9.39297	+	20.5677i	0.802495	+	1.75722i	0.165716	+	0.986174i	$0.447007\pi$
$138$		0			0
$139$	−9.73845	+	2.85947i	−0.826004	+	0.242537i	−0.667300	−	0.744789i	$-0.732550\pi$
$139$	−9.73845	+	2.85947i	−0.826004	+	0.242537i	−0.158705	+	0.987326i	$0.550732\pi$
$140$		0			0
$141$	−1.12240	−	0.216325i	−0.0945232	−	0.0182179i
$142$		0			0
$143$	−16.5381	+	19.0860i	−1.38298	+	1.59605i
$144$		0			0
$145$	−0.643845	−	0.613905i	−0.0534684	−	0.0509820i
$146$		0			0
$147$	0.321973	+	6.75904i	0.0265559	+	0.557476i
$148$		0			0
$149$	−12.8096	−	14.7831i	−1.04940	−	1.21108i	−0.976897	−	0.213709i	$-0.931446\pi$
$149$	−12.8096	−	14.7831i	−1.04940	−	1.21108i	−0.0725063	−	0.997368i	$-0.523100\pi$
$150$		0			0
$151$	−2.17354	−	1.70929i	−0.176880	−	0.139100i	0.525794	−	0.850612i	$-0.323768\pi$
$151$	−2.17354	−	1.70929i	−0.176880	−	0.139100i	−0.702674	+	0.711512i	$0.748011\pi$
$152$		0			0
$153$	−0.132446	+	0.0255268i	−0.0107076	+	0.00206372i
$154$		0			0
$155$	−2.33135	−	9.60995i	−0.187258	−	0.771889i
$156$		0			0
$157$	−16.2488	−	1.55157i	−1.29679	−	0.123829i	−0.576269	−	0.817260i	$-0.695492\pi$
$157$	−16.2488	−	1.55157i	−1.29679	−	0.123829i	−0.720523	+	0.693431i	$0.756098\pi$
$158$		0			0
$159$	5.43812	−	3.49487i	0.431271	−	0.277161i
$160$		0			0
$161$	0.0275029	+	0.00807559i	0.00216753	+	0.000636446i
$162$		0			0
$163$	−0.220703	−	0.382270i	−0.0172868	−	0.0299417i	0.857253	−	0.514896i	$-0.172170\pi$
$163$	−0.220703	−	0.382270i	−0.0172868	−	0.0299417i	−0.874539	+	0.484954i	$0.838836\pi$
$164$		0			0
$165$	0.436431	−	9.16181i	0.0339761	−	0.713246i
$166$		0			0
$167$	−2.92282	+	8.44494i	−0.226175	+	0.653489i	0.773628	+	0.633640i	$0.218440\pi$
$167$	−2.92282	+	8.44494i	−0.226175	+	0.653489i	−0.999803	+	0.0198492i	$0.993681\pi$
$168$		0			0
$169$	−23.4622	+	2.24036i	−1.80478	+	0.172336i
$170$		0			0
$171$	−2.33033	+	4.03625i	−0.178205	+	0.308660i
$172$		0			0
$173$	−21.6314	+	11.1518i	−1.64461	+	0.847853i	−0.648355	+	0.761338i	$0.724543\pi$
$173$	−21.6314	+	11.1518i	−1.64461	+	0.847853i	−0.996251	+	0.0865151i	$0.972427\pi$
$174$		0			0
$175$	−0.0790205	+	0.0316350i	−0.00597339	+	0.00239138i
$176$		0			0
$177$	1.38443	−	9.62891i	0.104060	−	0.723754i
$178$		0			0
$179$	−2.69567	+	5.90270i	−0.201484	+	0.441189i	−0.983221	−	0.182420i	$-0.941607\pi$
$179$	−2.69567	+	5.90270i	−0.201484	+	0.441189i	0.781737	+	0.623609i	$0.214334\pi$
$180$		0			0
$181$	11.6405	−	16.3468i	0.865231	−	1.21505i	−0.110016	−	0.993930i	$-0.535090\pi$
$181$	11.6405	−	16.3468i	0.865231	−	1.21505i	0.975247	−	0.221117i	$-0.0709703\pi$
$182$		0			0
$183$	−3.96724	−	1.58824i	−0.293267	−	0.117406i
$184$		0			0
$185$	−1.20454	+	4.96519i	−0.0885597	+	0.365048i
$186$		0			0
$187$	0.0801656	+	0.557564i	0.00586229	+	0.0407731i
$188$		0			0
$189$	0.429317	+	0.221328i	0.0312282	+	0.0160993i
$190$		0			0
$191$	4.20722	+	5.90822i	0.304424	+	0.427504i	0.938243	−	0.345978i	$-0.112453\pi$
$191$	4.20722	+	5.90822i	0.304424	+	0.427504i	−0.633819	+	0.773482i	$0.718513\pi$
$192$		0			0
$193$	−2.10693	−	1.35404i	−0.151660	−	0.0974660i	0.462610	−	0.886562i	$-0.346913\pi$
$193$	−2.10693	−	1.35404i	−0.151660	−	0.0974660i	−0.614270	+	0.789096i	$0.710549\pi$
$194$		0			0
$195$	9.61233	−	9.16533i	0.688353	−	0.656343i
$196$		0			0
$197$	15.7977	−	12.4234i	1.12554	−	0.885133i	0.131196	−	0.991356i	$-0.458118\pi$
$197$	15.7977	−	12.4234i	1.12554	−	0.885133i	0.994342	+	0.106223i	$0.0338758\pi$
$198$		0			0
$199$	5.02946	+	14.5317i	0.356529	+	1.03012i	0.970564	+	0.240843i	$0.0774240\pi$
$199$	5.02946	+	14.5317i	0.356529	+	1.03012i	−0.614035	+	0.789279i	$0.710455\pi$
$200$		0			0
$201$	−8.04311	+	1.51931i	−0.567318	+	0.107164i
$202$		0			0
$203$	−0.0639887	−	0.184883i	−0.00449113	−	0.0129763i
$204$		0			0
$205$	3.87275	−	3.04556i	0.270484	−	0.212711i
$206$		0			0
$207$	−0.0429497	+	0.0409524i	−0.00298521	+	0.00284639i
$208$		0			0
$209$	16.3740	+	10.5229i	1.13261	+	0.727886i
$210$		0			0
$211$	−7.81143	−	10.9696i	−0.537761	−	0.755180i	0.452895	−	0.891564i	$-0.350391\pi$
$211$	−7.81143	−	10.9696i	−0.537761	−	0.755180i	−0.990656	+	0.136384i	$0.956452\pi$
$212$		0			0
$213$	−5.29043	−	2.72740i	−0.362494	−	0.186879i
$214$		0			0
$215$	−2.77825	−	19.3232i	−0.189475	−	1.31783i
$216$		0			0
$217$	0.512708	−	2.11341i	0.0348049	−	0.143468i
$218$		0			0
$219$	6.53469	+	2.61609i	0.441573	+	0.176779i
$220$		0			0
$221$	−0.473134	+	0.664424i	−0.0318264	+	0.0446940i
$222$		0			0
$223$	−2.11515	+	4.63154i	−0.141641	+	0.310151i	−0.967136	−	0.254258i	$-0.918169\pi$
$223$	−2.11515	+	4.63154i	−0.141641	+	0.310151i	0.825495	+	0.564409i	$0.190896\pi$
$224$		0			0
$225$	0.0250792	−	0.174429i	0.00167194	−	0.0116286i
$226$		0			0
$227$	16.1695	−	6.47329i	1.07321	−	0.429647i	0.233315	−	0.972401i	$-0.425043\pi$
$227$	16.1695	−	6.47329i	1.07321	−	0.429647i	0.839892	+	0.542754i	$0.182618\pi$
$228$		0			0
$229$	4.30231	−	2.21799i	0.284304	−	0.146569i	−0.310176	−	0.950679i	$-0.600388\pi$
$229$	4.30231	−	2.21799i	0.284304	−	0.146569i	0.594481	+	0.804110i	$0.297358\pi$
$230$		0			0
$231$	1.00857	−	1.74690i	0.0663591	−	0.114937i
$232$		0			0
$233$	−4.34168	+	0.414580i	−0.284433	+	0.0271601i	−0.236297	−	0.971681i	$-0.575934\pi$
$233$	−4.34168	+	0.414580i	−0.284433	+	0.0271601i	−0.0481355	+	0.998841i	$0.515328\pi$
$234$		0			0
$235$	0.821107	−	2.37243i	0.0535631	−	0.154760i
$236$		0			0
$237$	−0.364813	+	7.65837i	−0.0236971	+	0.497464i
$238$		0			0
$239$	3.76281	+	6.51737i	0.243396	+	0.421574i	0.961679	−	0.274177i	$-0.0884053\pi$
$239$	3.76281	+	6.51737i	0.243396	+	0.421574i	−0.718284	+	0.695750i	$0.755072\pi$
$240$		0			0
$241$	−12.4339	−	3.65093i	−0.800940	−	0.235177i	−0.144450	−	0.989512i	$-0.546141\pi$
$241$	−12.4339	−	3.65093i	−0.800940	−	0.235177i	−0.656490	+	0.754335i	$0.727959\pi$
$242$		0			0
$243$	−0.841254	+	0.540641i	−0.0539664	+	0.0346821i
$244$		0			0
$245$	−14.7945	−	1.41270i	−0.945184	−	0.0902542i
$246$		0			0
$247$	6.64464	+	27.3896i	0.422788	+	1.74276i
$248$		0			0
$249$	4.97674	−	0.959188i	0.315388	−	0.0607861i
$250$		0			0
$251$	−17.5290	−	13.7849i	−1.10642	−	0.870097i	−0.114059	−	0.993474i	$-0.536385\pi$
$251$	−17.5290	−	13.7849i	−1.10642	−	0.870097i	−0.992360	+	0.123377i	$0.960628\pi$
$252$		0			0
$253$	0.162297	+	0.187300i	0.0102035	+	0.0117755i
$254$		0			0
$255$	−0.0140959	−	0.295910i	−0.000882720	−	0.0185306i
$256$		0			0
$257$	6.85758	+	6.53869i	0.427764	+	0.407872i	0.873138	−	0.487472i	$-0.162081\pi$
$257$	6.85758	+	6.53869i	0.427764	+	0.407872i	−0.445374	+	0.895344i	$0.646929\pi$
$258$		0			0
$259$	−0.735810	+	0.849170i	−0.0457210	+	0.0527649i
$260$		0			0
$261$	0.397730	+	0.0766562i	0.0246189	+	0.00474490i
$262$		0			0
$263$	15.6817	−	4.60455i	0.966972	−	0.283929i	0.240136	−	0.970739i	$-0.422808\pi$
$263$	15.6817	−	4.60455i	0.966972	−	0.283929i	0.726836	+	0.686811i	$0.240990\pi$
$264$		0			0
$265$	5.89791	+	12.9146i	0.362306	+	0.793338i
$266$		0			0
$267$	−3.02375			−0.185050
$268$		0			0
$269$	−3.53092			−0.215284			−0.107642	−	0.994190i	$-0.534330\pi$
$269$	−3.53092			−0.215284			−0.107642	+	0.994190i	$0.534330\pi$
$270$		0			0
$271$	5.58754	+	12.2350i	0.339419	+	0.743224i	0.999971	−	0.00755614i	$-0.00240522\pi$
$271$	5.58754	+	12.2350i	0.339419	+	0.743224i	−0.660553	+	0.750780i	$0.729678\pi$
$272$		0			0
$273$	2.80256	−	0.822905i	0.169618	−	0.0498045i
$274$		0			0
$275$	−0.722642	−	0.139278i	−0.0435769	−	0.00839876i
$276$		0			0
$277$	−12.4578	+	14.3771i	−0.748519	+	0.863838i	−0.994424	−	0.105457i	$-0.966370\pi$
$277$	−12.4578	+	14.3771i	−0.748519	+	0.863838i	0.245904	+	0.969294i	$0.420915\pi$
$278$		0			0
$279$	3.25855	+	3.10702i	0.195084	+	0.186012i
$280$		0			0
$281$	−1.29052	−	27.0914i	−0.0769860	−	1.61614i	−0.625658	−	0.780098i	$-0.715169\pi$
$281$	−1.29052	−	27.0914i	−0.0769860	−	1.61614i	0.548672	−	0.836038i	$-0.315134\pi$
$282$		0			0
$283$	−7.26894	−	8.38880i	−0.432094	−	0.498663i	0.497389	−	0.867527i	$-0.334292\pi$
$283$	−7.26894	−	8.38880i	−0.432094	−	0.498663i	−0.929483	+	0.368865i	$0.879747\pi$
$284$		0			0
$285$	−8.04624	−	6.32763i	−0.476618	−	0.374817i
$286$		0			0
$287$	1.06392	−	0.205054i	0.0628014	−	0.0121040i
$288$		0			0
$289$	−4.00361	−	16.5031i	−0.235507	−	0.970772i
$290$		0			0
$291$	−10.9091	−	1.04169i	−0.639504	−	0.0610652i
$292$		0			0
$293$	−9.12464	+	5.86405i	−0.533067	+	0.342581i	−0.779322	−	0.626624i	$-0.784436\pi$
$293$	−9.12464	+	5.86405i	−0.533067	+	0.342581i	0.246255	+	0.969205i	$0.420800\pi$
$294$		0			0
$295$	20.5001	+	6.01937i	1.19356	+	0.350461i
$296$		0			0
$297$	2.08809	+	3.61668i	0.121163	+	0.209861i
$298$		0			0
$299$	−0.0170757	+	0.358463i	−0.000987513	+	0.0207305i
$300$		0			0
$301$	1.40418	−	4.05711i	0.0809355	−	0.233848i
$302$		0			0
$303$	−2.27689	+	0.217416i	−0.130804	+	0.0124903i
$304$		0			0
$305$	4.69280	−	8.12817i	0.268709	−	0.465418i
$306$		0			0
$307$	25.9285	−	13.3671i	1.47982	−	0.762899i	0.486004	−	0.873957i	$-0.338454\pi$
$307$	25.9285	−	13.3671i	1.47982	−	0.762899i	0.993814	+	0.111058i	$0.0354239\pi$
$308$		0			0
$309$	−8.47081	+	3.39120i	−0.481888	+	0.192919i
$310$		0			0
$311$	3.52137	−	24.4917i	0.199679	−	1.38880i	−0.605538	−	0.795816i	$-0.707042\pi$
$311$	3.52137	−	24.4917i	0.199679	−	1.38880i	0.805217	−	0.592980i	$-0.202049\pi$
$312$		0			0
$313$	−4.47873	+	9.80705i	−0.253153	+	0.554327i	−0.992954	−	0.118498i	$-0.962192\pi$
$313$	−4.47873	+	9.80705i	−0.253153	+	0.554327i	0.739802	+	0.672825i	$0.234919\pi$
$314$		0			0
$315$	−0.615348	+	0.864135i	−0.0346709	+	0.0486885i
$316$		0			0
$317$	13.5378	+	5.41972i	0.760359	+	0.304402i	0.719249	−	0.694753i	$-0.244486\pi$
$317$	13.5378	+	5.41972i	0.760359	+	0.304402i	0.0411103	+	0.999155i	$0.486911\pi$
$318$		0			0
$319$	0.398802	−	1.64388i	0.0223286	−	0.0920398i
$320$		0			0
$321$	1.05786	+	7.35758i	0.0590440	+	0.410660i
$322$		0			0
$323$	0.558762	+	0.288062i	0.0310903	+	0.0160282i
$324$		0			0
$325$	−0.618144	−	0.868061i	−0.0342884	−	0.0481514i
$326$		0			0
$327$	2.63278	+	1.69199i	0.145593	+	0.0935671i
$328$		0			0
$329$	0.399580	−	0.380999i	0.0220296	−	0.0210051i
$330$		0			0
$331$	6.32159	−	4.97136i	0.347466	−	0.273250i	−0.429138	−	0.903239i	$-0.641183\pi$
$331$	6.32159	−	4.97136i	0.347466	−	0.273250i	0.776605	+	0.629988i	$0.216940\pi$
$332$		0			0
$333$	−0.760849	−	2.19833i	−0.0416942	−	0.120468i
$334$		0			0
$335$	−0.788897	−	17.9603i	−0.0431021	−	0.981273i
$336$		0			0
$337$	6.60932	+	19.0964i	0.360033	+	1.04025i	0.969002	+	0.247052i	$0.0794619\pi$
$337$	6.60932	+	19.0964i	0.360033	+	1.04025i	−0.608970	+	0.793194i	$0.708417\pi$
$338$		0			0
$339$	10.2762	−	8.08129i	0.558126	−	0.438915i
$340$		0			0
$341$	13.6083	−	12.9755i	0.736932	−	0.702663i
$342$		0			0
$343$	−5.59388	−	3.59497i	−0.302041	−	0.194110i
$344$		0			0
$345$	−0.0756040	−	0.106171i	−0.00407038	−	0.00571605i
$346$		0			0
$347$	−23.5321	−	12.1316i	−1.26327	−	0.651261i	−0.309243	−	0.950983i	$-0.600076\pi$
$347$	−23.5321	−	12.1316i	−1.26327	−	0.651261i	−0.954026	+	0.299722i	$0.903106\pi$
$348$		0			0
$349$	4.25964	+	29.6264i	0.228013	+	1.58587i	0.706462	+	0.707750i	$0.250290\pi$
$349$	4.25964	+	29.6264i	0.228013	+	1.58587i	−0.478449	+	0.878115i	$0.658801\pi$
$350$		0			0
$351$	−1.42569	+	5.87676i	−0.0760975	+	0.313678i
$352$		0			0
$353$	19.7201	+	7.89475i	1.04960	+	0.420195i	0.831379	−	0.555705i	$-0.187552\pi$
$353$	19.7201	+	7.89475i	1.04960	+	0.420195i	0.218217	+	0.975900i	$0.429976\pi$
$354$		0			0
$355$	7.58287	−	10.6487i	0.402457	−	0.565172i
$356$		0			0
$357$	0.0270643	−	0.0592625i	0.00143239	−	0.00313650i
$358$		0			0
$359$	−4.37756	+	30.4466i	−0.231039	+	1.60691i	0.462586	+	0.886575i	$0.346922\pi$
$359$	−4.37756	+	30.4466i	−0.231039	+	1.60691i	−0.693625	+	0.720337i	$0.743987\pi$
$360$		0			0
$361$	2.52679	−	1.01157i	0.132989	−	0.0532407i
$362$		0			0
$363$	5.72458	−	2.95123i	0.300463	−	0.154899i
$364$		0			0
$365$	−7.72980	+	13.3884i	−0.404596	+	0.700781i
$366$		0			0
$367$	−3.77148	+	0.360133i	−0.196870	+	0.0187988i	−0.193025	−	0.981194i	$-0.561830\pi$
$367$	−3.77148	+	0.360133i	−0.196870	+	0.0187988i	−0.00384471	+	0.999993i	$0.501224\pi$
$368$		0			0
$369$	−0.733689	+	2.11985i	−0.0381943	+	0.110355i
$370$		0			0
$371$	−0.148566	+	3.11879i	−0.00771318	+	0.161920i
$372$		0			0
$373$	−13.3966	−	23.2035i	−0.693648	−	1.20143i	−0.970634	−	0.240559i	$-0.922669\pi$
$373$	−13.3966	−	23.2035i	−0.693648	−	1.20143i	0.276987	−	0.960874i	$-0.410664\pi$
$374$		0			0
$375$	10.9081	+	3.20290i	0.563291	+	0.165397i
$376$		0			0
$377$	2.06059	−	1.32426i	0.106126	−	0.0682029i
$378$		0			0
$379$	36.7380	+	3.50806i	1.88711	+	0.180197i	0.973851	−	0.227189i	$-0.0729535\pi$
$379$	36.7380	+	3.50806i	1.88711	+	0.180197i	0.913256	+	0.407386i	$0.133560\pi$
$380$		0			0
$381$	2.26248	+	9.32607i	0.115910	+	0.477789i
$382$		0			0
$383$	−36.3599	+	7.00779i	−1.85790	+	0.358082i	−0.990274	−	0.139130i	$-0.955569\pi$
$383$	−36.3599	+	7.00779i	−1.85790	+	0.358082i	−0.867629	+	0.497211i	$0.834357\pi$
$384$		0			0
$385$	3.48243	+	2.73861i	0.177481	+	0.139573i
$386$		0			0
$387$	5.82072	+	6.71746i	0.295884	+	0.341468i
$388$		0			0
$389$	−0.170793	−	3.58538i	−0.00865953	−	0.181786i	−0.999053	−	0.0435084i	$-0.986146\pi$
$389$	−0.170793	−	3.58538i	−0.00865953	−	0.181786i	0.990394	−	0.138277i	$-0.0441566\pi$
$390$		0			0
$391$	0.00579318	+	0.00552379i	0.000292974	+	0.000279350i
$392$		0			0
$393$	−5.49987	+	6.34718i	−0.277432	+	0.320173i
$394$		0			0
$395$	−16.5349	−	3.18684i	−0.831962	−	0.160347i
$396$		0			0
$397$	13.0116	−	3.82054i	0.653032	−	0.191748i	0.0615983	−	0.998101i	$-0.480380\pi$
$397$	13.0116	−	3.82054i	0.653032	−	0.191748i	0.591434	+	0.806353i	$0.298562\pi$
$398$		0			0
$399$	−0.935161	−	2.04772i	−0.0468166	−	0.102514i
$400$		0			0
$401$	7.02365			0.350744			0.175372	−	0.984502i	$-0.443887\pi$
$401$	7.02365			0.350744			0.175372	+	0.984502i	$0.443887\pi$
$402$		0			0
$403$	27.2271			1.35628
$404$		0			0
$405$	−0.912380	−	1.99783i	−0.0453365	−	0.0992732i
$406$		0			0
$407$	−9.32142	+	2.73702i	−0.462046	+	0.135669i
$408$		0			0
$409$	−22.4899	−	4.33457i	−1.11205	−	0.214331i	−0.400041	−	0.916497i	$-0.631004\pi$
$409$	−22.4899	−	4.33457i	−1.11205	−	0.214331i	−0.712013	+	0.702167i	$0.752216\pi$
$410$		0			0
$411$	14.8071	−	17.0883i	0.730380	−	0.842903i
$412$		0			0
$413$	3.40060	+	3.24247i	0.167333	+	0.159551i
$414$		0			0
$415$	0.529664	+	11.1190i	0.0260002	+	0.545811i
$416$		0			0
$417$	6.64656	+	7.67054i	0.325483	+	0.375628i
$418$		0			0
$419$	11.6102	+	9.13039i	0.567197	+	0.446049i	0.860123	−	0.510086i	$-0.170387\pi$
$419$	11.6102	+	9.13039i	0.567197	+	0.446049i	−0.292926	+	0.956135i	$0.594629\pi$
$420$		0			0
$421$	−4.52663	+	0.872437i	−0.220614	+	0.0425200i	−0.298361	−	0.954453i	$-0.596440\pi$
$421$	−4.52663	+	0.872437i	−0.220614	+	0.0425200i	0.0777461	+	0.996973i	$0.475228\pi$
$422$		0			0
$423$	0.269486	+	1.11084i	0.0131029	+	0.0540107i
$424$		0			0
$425$	−0.0236619	−	0.00225944i	−0.00114777	−	0.000109599i
$426$		0			0
$427$	1.73641	−	1.11592i	0.0840307	−	0.0540033i
$428$		0			0
$429$	24.2314	+	7.11497i	1.16990	+	0.343514i
$430$		0			0
$431$	5.60380	+	9.70606i	0.269925	+	0.467525i	0.968842	−	0.247678i	$-0.0796676\pi$
$431$	5.60380	+	9.70606i	0.269925	+	0.467525i	−0.698917	+	0.715203i	$0.746334\pi$
$432$		0			0
$433$	1.01682	−	21.3457i	0.0488652	−	1.02581i	−0.832694	−	0.553733i	$-0.813203\pi$
$433$	1.01682	−	21.3457i	0.0488652	−	1.02581i	0.881559	−	0.472073i	$-0.156494\pi$
$434$		0			0
$435$	−0.290965	+	0.840688i	−0.0139507	+	0.0403079i
$436$		0			0
$437$	0.275332	−	0.0262910i	0.0131709	−	0.00125767i
$438$		0			0
$439$	−8.96338	+	15.5250i	−0.427799	+	0.740969i	−0.996677	−	0.0814524i	$-0.974044\pi$
$439$	−8.96338	+	15.5250i	−0.427799	+	0.740969i	0.568878	+	0.822422i	$0.307377\pi$
$440$		0			0
$441$	6.01448	−	3.10068i	0.286404	−	0.147652i
$442$		0			0
$443$	−8.06760	+	3.22978i	−0.383303	+	0.153451i	−0.555308	−	0.831645i	$-0.687400\pi$
$443$	−8.06760	+	3.22978i	−0.383303	+	0.153451i	0.172005	+	0.985096i	$0.444975\pi$
$444$		0			0
$445$	0.945125	−	6.57349i	0.0448032	−	0.311613i
$446$		0			0
$447$	−8.12585	+	17.7931i	−0.384340	+	0.841587i
$448$		0			0
$449$	21.3969	−	30.0478i	1.00978	−	1.41804i	0.103866	−	0.994591i	$-0.466879\pi$
$449$	21.3969	−	30.0478i	1.00978	−	1.41804i	0.905918	−	0.423452i	$-0.139182\pi$
$450$		0			0
$451$	8.69709	+	3.48179i	0.409530	+	0.163951i
$452$		0			0
$453$	−0.651905	+	2.68719i	−0.0306292	+	0.126255i
$454$		0			0
$455$	0.912969	+	6.34984i	0.0428007	+	0.297685i
$456$		0			0
$457$	8.79847	+	4.53593i	0.411575	+	0.212182i	0.651564	−	0.758594i	$-0.274113\pi$
$457$	8.79847	+	4.53593i	0.411575	+	0.212182i	−0.239989	+	0.970776i	$0.577144\pi$
$458$		0			0
$459$	0.0782399	+	0.109873i	0.00365193	+	0.00512841i
$460$		0			0
$461$	24.3709	+	15.6623i	1.13507	+	0.729464i	0.966612	−	0.256245i	$-0.0824854\pi$
$461$	24.3709	+	15.6623i	1.13507	+	0.729464i	0.168456	+	0.985709i	$0.446122\pi$
$462$		0			0
$463$	−4.62922	+	4.41396i	−0.215138	+	0.205134i	−0.789983	−	0.613128i	$-0.789911\pi$
$463$	−4.62922	+	4.41396i	−0.215138	+	0.205134i	0.574845	+	0.818262i	$0.305062\pi$
$464$		0			0
$465$	−7.77304	+	6.11278i	−0.360466	+	0.283474i
$466$		0			0
$467$	−2.20524	−	6.37162i	−0.102046	−	0.294844i	0.882408	−	0.470485i	$-0.155921\pi$
$467$	−2.20524	−	6.37162i	−0.102046	−	0.294844i	−0.984454	+	0.175642i	$0.943800\pi$
$468$		0			0
$469$	1.65570	−	3.59022i	0.0764530	−	0.165781i
$470$		0			0
$471$	5.33862	+	15.4249i	0.245991	+	0.710744i
$472$		0			0
$473$	29.1783	−	22.9460i	1.34162	−	1.05506i
$474$		0			0
$475$	−0.594414	+	0.566773i	−0.0272736	+	0.0260053i
$476$		0			0
$477$	−5.43812	−	3.49487i	−0.248995	−	0.160019i
$478$		0			0
$479$	−17.7194	−	24.8834i	−0.809620	−	1.13695i	−0.988221	−	0.153030i	$-0.951097\pi$
$479$	−17.7194	−	24.8834i	−0.809620	−	1.13695i	0.178602	−	0.983921i	$-0.442843\pi$
$480$		0			0
$481$	−12.5037	−	6.44609i	−0.570118	−	0.293916i
$482$		0			0
$483$	−0.00407932	−	0.0283723i	−0.000185615	−	0.00129098i
$484$		0			0
$485$	5.67443	−	23.3903i	0.257663	−	1.06210i
$486$		0			0
$487$	5.47916	+	2.19353i	0.248285	+	0.0993982i	0.492467	−	0.870331i	$-0.336095\pi$
$487$	5.47916	+	2.19353i	0.248285	+	0.0993982i	−0.244182	+	0.969729i	$0.578520\pi$
$488$		0			0
$489$	−0.256041	+	0.359559i	−0.0115786	+	0.0162598i
$490$		0			0
$491$	13.4842	−	29.5262i	0.608532	−	1.33250i	−0.315041	−	0.949078i	$-0.602018\pi$
$491$	13.4842	−	29.5262i	0.608532	−	1.33250i	0.923573	−	0.383422i	$-0.125255\pi$
$492$		0			0
$493$	0.00777529	−	0.0540783i	0.000350182	−	0.00243557i
$494$		0			0
$495$	−8.51518	+	3.40896i	−0.382729	+	0.153222i
$496$		0			0
$497$	2.55533	−	1.31737i	0.114622	−	0.0590919i
$498$		0			0
$499$	11.3516	−	19.6615i	0.508166	−	0.880170i	−0.491789	−	0.870714i	$-0.663657\pi$
$499$	11.3516	−	19.6615i	0.508166	−	0.880170i	0.999955	−	0.00945528i	$-0.00300975\pi$
$500$		0			0
$501$	8.89597	−	0.849462i	0.397443	−	0.0379512i
$502$		0			0
$503$	−7.08610	+	20.4739i	−0.315953	+	0.912887i	0.669481	+	0.742829i	$0.266517\pi$
$503$	−7.08610	+	20.4739i	−0.315953	+	0.912887i	−0.985434	+	0.170058i	$0.945605\pi$
$504$		0			0
$505$	0.239028	−	5.01781i	0.0106366	−	0.223290i
$506$		0			0
$507$	11.7844	+	20.4113i	0.523365	+	0.906496i
$508$		0			0
$509$	−7.97886	−	2.34280i	−0.353657	−	0.103843i	0.100079	−	0.994980i	$-0.468091\pi$
$509$	−7.97886	−	2.34280i	−0.353657	−	0.103843i	−0.453735	+	0.891137i	$0.649909\pi$
$510$		0			0
$511$	−2.86015	+	1.83810i	−0.126525	+	0.0813129i
$512$		0			0
$513$	4.63956	+	0.443024i	0.204841	+	0.0195600i
$514$		0			0
$515$	−4.72462	−	19.4751i	−0.208192	−	0.858177i
$516$		0			0
$517$	4.68736	−	0.903414i	0.206150	−	0.0397321i
$518$		0			0
$519$	19.1300	+	15.0440i	0.839715	+	0.660359i
$520$		0			0
$521$	20.3842	+	23.5246i	0.893047	+	1.03063i	0.999341	+	0.0362968i	$0.0115562\pi$
$521$	20.3842	+	23.5246i	0.893047	+	1.03063i	−0.106294	+	0.994335i	$0.533898\pi$
$522$		0			0
$523$	1.86562	+	39.1641i	0.0815777	+	1.71253i	0.555133	+	0.831762i	$0.312667\pi$
$523$	1.86562	+	39.1641i	0.0815777	+	1.71253i	−0.473555	+	0.880764i	$0.657029\pi$
$524$		0			0
$525$	0.0616025	+	0.0587379i	0.00268855	+	0.00256353i
$526$		0			0
$527$	0.397697	−	0.458966i	0.0173239	−	0.0199929i
$528$		0			0
$529$	−22.5809	−	4.35211i	−0.981778	−	0.189222i
$530$		0			0
$531$	−9.33388	+	2.74067i	−0.405056	+	0.118935i
$532$		0			0
$533$	5.63523	+	12.3394i	0.244089	+	0.534480i
$534$		0			0
$535$	−16.3257			−0.705822
$536$		0			0
$537$	6.48911			0.280026
$538$		0			0
$539$	−11.7392	−	25.7053i	−0.505644	−	1.10721i
$540$		0			0
$541$	35.3740	−	10.3867i	1.52085	−	0.446561i	0.588612	−	0.808416i	$-0.299675\pi$
$541$	35.3740	−	10.3867i	1.52085	−	0.446561i	0.932234	+	0.361855i	$0.117857\pi$
$542$		0			0
$543$	−19.7052	−	3.79787i	−0.845631	−	0.162982i
$544$		0			0
$545$	−4.50122	+	5.19469i	−0.192811	+	0.222516i
$546$		0			0
$547$	−6.00022	−	5.72120i	−0.256551	−	0.244621i	0.550878	−	0.834586i	$-0.314293\pi$
$547$	−6.00022	−	5.72120i	−0.256551	−	0.244621i	−0.807429	+	0.589965i	$0.799141\pi$
$548$		0			0
$549$	0.203334	+	4.26851i	0.00867809	+	0.182176i
$550$		0			0
$551$	−1.23625	−	1.42670i	−0.0526659	−	0.0607797i
$552$		0			0
$553$	−2.91096	−	2.28921i	−0.123787	−	0.0973470i
$554$		0			0
$555$	5.01688	−	0.966925i	0.212955	−	0.0410437i
$556$		0			0
$557$	2.26395	+	9.33212i	0.0959265	+	0.395414i	0.999451	−	0.0331213i	$-0.0105448\pi$
$557$	2.26395	+	9.33212i	0.0959265	+	0.395414i	−0.903525	+	0.428536i	$0.859030\pi$
$558$		0			0
$559$	53.5072	+	5.10932i	2.26311	+	0.216101i
$560$		0			0
$561$	0.473876	−	0.304542i	0.0200071	−	0.0128578i
$562$		0			0
$563$	−0.582858	−	0.171143i	−0.0245645	−	0.00721280i	0.269427	−	0.963021i	$-0.413166\pi$
$563$	−0.582858	−	0.171143i	−0.0245645	−	0.00721280i	−0.293992	+	0.955808i	$0.594984\pi$
$564$		0			0
$565$	14.3563	+	24.8659i	0.603976	+	1.04612i
$566$		0			0
$567$	0.0229826	−	0.482463i	0.000965177	−	0.0202616i
$568$		0			0
$569$	10.8527	−	31.3569i	0.454970	−	1.31455i	−0.451497	−	0.892272i	$-0.649110\pi$
$569$	10.8527	−	31.3569i	0.454970	−	1.31455i	0.906467	−	0.422276i	$-0.138769\pi$
$570$		0			0
$571$	−20.9268	+	1.99827i	−0.875759	+	0.0836249i	−0.523246	−	0.852182i	$-0.675279\pi$
$571$	−20.9268	+	1.99827i	−0.875759	+	0.0836249i	−0.352513	+	0.935807i	$0.614673\pi$
$572$		0			0
$573$	3.62656	−	6.28138i	0.151502	−	0.262409i
$574$		0			0
$575$	−0.00929533	+	0.00479208i	−0.000387642	+	0.000199843i
$576$		0			0
$577$	−8.04078	+	3.21904i	−0.334742	+	0.134010i	−0.532944	−	0.846151i	$-0.678914\pi$
$577$	−8.04078	+	3.21904i	−0.334742	+	0.134010i	0.198202	+	0.980161i	$0.436490\pi$
$578$		0			0
$579$	−0.356429	+	2.47902i	−0.0148127	+	0.103024i
$580$		0			0
$581$	−1.01696	+	2.22683i	−0.0421906	+	0.0923846i
$582$		0			0
$583$	−15.6593	+	21.9904i	−0.648543	+	0.910751i
$584$		0			0
$585$	−12.3302	−	4.93626i	−0.509790	−	0.204089i
$586$		0			0
$587$	8.01395	−	33.0339i	0.330771	−	1.36346i	−0.527193	−	0.849746i	$-0.676755\pi$
$587$	8.01395	−	33.0339i	0.330771	−	1.36346i	0.857964	−	0.513711i	$-0.171730\pi$
$588$		0			0
$589$	−2.98637	−	20.7706i	−0.123051	−	0.855839i
$590$		0			0
$591$	−17.8634	−	9.20920i	−0.734800	−	0.378816i
$592$		0			0
$593$	−10.1218	−	14.2141i	−0.415654	−	0.583704i	0.552671	−	0.833400i	$-0.313609\pi$
$593$	−10.1218	−	14.2141i	−0.415654	−	0.583704i	−0.968324	+	0.249696i	$0.919669\pi$
$594$		0			0
$595$	0.120375	+	0.0773600i	0.00493488	+	0.00317145i
$596$		0			0
$597$	11.1291	−	10.6116i	0.455486	−	0.434305i
$598$		0			0
$599$	−34.2984	+	26.9726i	−1.40140	+	1.10207i	−0.420553	+	0.907268i	$0.638164\pi$
$599$	−34.2984	+	26.9726i	−1.40140	+	1.10207i	−0.980843	+	0.194802i	$0.937594\pi$
$600$		0			0
$601$	−7.55287	−	21.8226i	−0.308088	−	0.890162i	−0.987668	−	0.156561i	$-0.949959\pi$
$601$	−7.55287	−	21.8226i	−0.308088	−	0.890162i	0.679580	−	0.733601i	$-0.262162\pi$
$602$		0			0
$603$	4.72324	+	6.68513i	0.192345	+	0.272240i
$604$		0			0
$605$	4.62652	+	13.3674i	0.188095	+	0.543464i
$606$		0			0
$607$	−29.0363	+	22.8344i	−1.17855	+	0.926818i	−0.998384	−	0.0568190i	$-0.981904\pi$
$607$	−29.0363	+	22.8344i	−1.17855	+	0.926818i	−0.180161	+	0.983637i	$0.557662\pi$
$608$		0			0
$609$	−0.141594	+	0.135009i	−0.00573767	+	0.00547086i
$610$		0			0
$611$	5.81501	+	3.73708i	0.235250	+	0.151186i
$612$		0			0
$613$	8.07328	+	11.3373i	0.326077	+	0.457911i	0.944776	−	0.327717i	$-0.106279\pi$
$613$	8.07328	+	11.3373i	0.326077	+	0.457911i	−0.618699	+	0.785628i	$0.712340\pi$
$614$		0			0
$615$	−4.37914	−	2.25760i	−0.176584	−	0.0910353i
$616$		0			0
$617$	−1.59780	−	11.1129i	−0.0643250	−	0.447390i	−0.996376	−	0.0850622i	$-0.972891\pi$
$617$	−1.59780	−	11.1129i	−0.0643250	−	0.447390i	0.932051	−	0.362328i	$-0.118018\pi$
$618$		0			0
$619$	6.10170	−	25.1516i	0.245248	−	1.01093i	−0.707391	−	0.706823i	$-0.750128\pi$
$619$	6.10170	−	25.1516i	0.245248	−	1.01093i	0.952639	−	0.304104i	$-0.0983570\pi$
$620$		0			0
$621$	0.0550936	+	0.0220561i	0.00221083	+	0.000885082i
$622$		0			0
$623$	0.847174	−	1.18969i	0.0339413	−	0.0476639i
$624$		0			0
$625$	−10.0064	+	21.9111i	−0.400258	+	0.876442i
$626$		0			0
$627$	2.76999	−	19.2657i	0.110623	−	0.769397i
$628$		0			0
$629$	−0.291298	+	0.116618i	−0.0116148	+	0.00464988i
$630$		0			0
$631$	6.57686	−	3.39060i	0.261821	−	0.134978i	−0.322319	−	0.946631i	$-0.604462\pi$
$631$	6.57686	−	3.39060i	0.261821	−	0.134978i	0.584140	+	0.811653i	$0.301432\pi$
$632$		0			0
$633$	−6.73333	+	11.6625i	−0.267626	+	0.463542i
$634$		0			0
$635$	−20.9816	+	2.00350i	−0.832631	+	0.0795066i
$636$		0			0
$637$	13.3835	−	38.6692i	0.530275	−	1.53213i
$638$		0			0
$639$	−0.283212	+	5.94535i	−0.0112037	+	0.235194i
$640$		0			0
$641$	−10.7777	−	18.6676i	−0.425695	−	0.737326i	0.570790	−	0.821096i	$-0.306637\pi$
$641$	−10.7777	−	18.6676i	−0.425695	−	0.737326i	−0.996485	+	0.0837702i	$0.973304\pi$
$642$		0			0
$643$	−43.4029	−	12.7442i	−1.71164	−	0.502583i	−0.728440	−	0.685109i	$-0.759755\pi$
$643$	−43.4029	−	12.7442i	−1.71164	−	0.502583i	−0.983201	+	0.182526i	$0.941573\pi$
$644$		0			0
$645$	−16.4228	+	10.5543i	−0.646648	+	0.415576i
$646$		0			0
$647$	−47.0520	−	4.49292i	−1.84980	−	0.176635i	−0.889750	−	0.456448i	$-0.849121\pi$
$647$	−47.0520	−	4.49292i	−1.84980	−	0.176635i	−0.960055	+	0.279813i	$0.909728\pi$
$648$		0			0
$649$	9.57786	+	39.4805i	0.375964	+	1.54974i
$650$		0			0
$651$	−2.13541	+	0.411567i	−0.0836934	+	0.0161306i
$652$		0			0
$653$	−7.81203	−	6.14345i	−0.305708	−	0.240412i	0.453505	−	0.891254i	$-0.350174\pi$
$653$	−7.81203	−	6.14345i	−0.305708	−	0.240412i	−0.759213	+	0.650842i	$0.774416\pi$
$654$		0			0
$655$	−12.0794	−	13.9404i	−0.471982	−	0.544696i
$656$		0			0
$657$	−0.334924	−	7.03092i	−0.0130666	−	0.274302i
$658$		0			0
$659$	−9.76423	−	9.31018i	−0.380361	−	0.362673i	0.475647	−	0.879636i	$-0.342214\pi$
$659$	−9.76423	−	9.31018i	−0.380361	−	0.362673i	−0.856008	+	0.516963i	$0.827062\pi$
$660$		0			0
$661$	13.3705	−	15.4303i	0.520051	−	0.600171i	−0.433593	−	0.901109i	$-0.642754\pi$
$661$	13.3705	−	15.4303i	0.520051	−	0.600171i	0.953644	+	0.300938i	$0.0972998\pi$
$662$		0			0
$663$	0.800928	+	0.154366i	0.0311055	+	0.00599509i
$664$		0			0
$665$	4.74394	−	1.39295i	0.183962	−	0.0540162i
$666$		0			0
$667$	−0.00998554	−	0.0218653i	−0.000386642	−	0.000846627i
$668$		0			0
$669$	5.09166			0.196855
$670$		0			0
$671$	17.8463			0.688949
$672$		0			0
$673$	7.65772	+	16.7681i	0.295183	+	0.646362i	0.997877	−	0.0651314i	$-0.0207467\pi$
$673$	7.65772	+	16.7681i	0.295183	+	0.646362i	−0.702693	+	0.711493i	$0.748019\pi$
$674$		0			0
$675$	−0.169085	+	0.0496478i	−0.00650808	+	0.00191094i
$676$		0			0
$677$	−40.7653	−	7.85687i	−1.56674	−	0.301964i	−0.669262	−	0.743026i	$-0.733390\pi$
$677$	−40.7653	−	7.85687i	−1.56674	−	0.301964i	−0.897477	+	0.441062i	$0.854602\pi$
$678$		0			0
$679$	3.46630	−	4.00032i	0.133024	−	0.153518i
$680$		0			0
$681$	−12.6054	−	12.0192i	−0.483038	−	0.460576i
$682$		0			0
$683$	−2.10518	−	44.1931i	−0.0805523	−	1.69100i	−0.572127	−	0.820165i	$-0.693882\pi$
$683$	−2.10518	−	44.1931i	−0.0805523	−	1.69100i	0.491575	−	0.870835i	$-0.336421\pi$
$684$		0			0
$685$	32.5209	+	37.5312i	1.24256	+	1.43399i
$686$		0			0
$687$	−3.80480	−	2.99213i	−0.145162	−	0.114157i
$688$		0			0
$689$	−38.3847	+	7.39804i	−1.46234	+	0.281843i
$690$		0			0
$691$	1.46240	+	6.02809i	0.0556323	+	0.229320i	0.992840	−	0.119452i	$-0.0381139\pi$
$691$	1.46240	+	6.02809i	0.0556323	+	0.229320i	−0.937208	+	0.348772i	$0.886599\pi$
$692$		0			0
$693$	−2.00801	−	0.191742i	−0.0762779	−	0.00728366i
$694$		0			0
$695$	−18.7529	+	12.0518i	−0.711338	+	0.457149i
$696$		0			0
$697$	0.290318	+	0.0852449i	0.0109966	+	0.00322888i
$698$		0			0
$699$	2.18071	+	3.77711i	0.0824822	+	0.142863i
$700$		0			0
$701$	−1.35044	+	28.3492i	−0.0510054	+	1.07073i	0.817775	+	0.575537i	$0.195207\pi$
$701$	−1.35044	+	28.3492i	−0.0510054	+	1.07073i	−0.868781	+	0.495197i	$0.835096\pi$
$702$		0			0
$703$	−3.54606	+	10.2457i	−0.133742	+	0.386422i
$704$		0			0
$705$	−2.49914	+	0.238639i	−0.0941231	+	0.00898766i
$706$		0			0
$707$	0.552382	−	0.956753i	0.0207745	−	0.0359824i
$708$		0			0
$709$	−3.50226	+	1.80554i	−0.131530	+	0.0678085i	−0.522736	−	0.852495i	$-0.675088\pi$
$709$	−3.50226	+	1.80554i	−0.131530	+	0.0678085i	0.391205	+	0.920303i	$0.372058\pi$
$710$		0			0
$711$	7.11784	−	2.84955i	0.266940	−	0.106867i
$712$		0			0
$713$	0.0380256	−	0.264474i	0.00142407	−	0.00990463i
$714$		0			0
$715$	−23.0415	+	50.4540i	−0.861705	+	1.88687i
$716$		0			0
$717$	4.36529	−	6.13019i	0.163025	−	0.228936i
$718$		0			0
$719$	−14.2817	−	5.71755i	−0.532619	−	0.213229i	0.0897330	−	0.995966i	$-0.471399\pi$
$719$	−14.2817	−	5.71755i	−0.532619	−	0.213229i	−0.622352	+	0.782737i	$0.713823\pi$
$720$		0			0
$721$	1.03903	−	4.28296i	0.0386956	−	0.159506i
$722$		0			0
$723$	1.84424	+	12.8270i	0.0685879	+	0.477039i
$724$		0			0
$725$	0.0634444	+	0.0327079i	0.00235627	+	0.00121474i
$726$		0			0
$727$	−5.98223	−	8.40087i	−0.221869	−	0.311571i	0.688606	−	0.725136i	$-0.258223\pi$
$727$	−5.98223	−	8.40087i	−0.221869	−	0.311571i	−0.910475	+	0.413565i	$0.864284\pi$
$728$		0			0
$729$	0.841254	+	0.540641i	0.0311575	+	0.0200237i
$730$		0			0
$731$	0.867689	−	0.827340i	0.0320926	−	0.0306003i
$732$		0			0
$733$	−39.2262	+	30.8478i	−1.44885	+	1.13939i	−0.484491	+	0.874796i	$0.660995\pi$
$733$	−39.2262	+	30.8478i	−1.44885	+	1.13939i	−0.964360	+	0.264593i	$0.914762\pi$
$734$		0			0
$735$	4.86081	+	14.0444i	0.179294	+	0.518035i
$736$		0			0
$737$	28.8253	−	18.3744i	1.06179	−	0.676830i
$738$		0			0
$739$	12.0190	+	34.7268i	0.442128	+	1.27744i	0.917527	+	0.397674i	$0.130182\pi$
$739$	12.0190	+	34.7268i	0.442128	+	1.27744i	−0.475399	+	0.879770i	$0.657696\pi$
$740$		0			0
$741$	22.1542	−	17.4222i	0.813853	−	0.640021i
$742$		0			0
$743$	14.7421	−	14.0565i	0.540834	−	0.515684i	−0.369682	−	0.929158i	$-0.620533\pi$
$743$	14.7421	−	14.0565i	0.540834	−	0.515684i	0.910516	+	0.413474i	$0.135685\pi$
$744$		0			0
$745$	−36.1416	−	23.2268i	−1.32413	−	0.850964i
$746$		0			0
$747$	−2.93992	−	4.12854i	−0.107566	−	0.151055i
$748$		0			0
$749$	−3.19122	−	1.64519i	−0.116604	−	0.0601138i
$750$		0			0
$751$	−0.557020	−	3.87416i	−0.0203260	−	0.141370i	0.977131	−	0.212637i	$-0.0682050\pi$
$751$	−0.557020	−	3.87416i	−0.0203260	−	0.141370i	−0.997457	+	0.0712664i	$0.977296\pi$
$752$		0			0
$753$	−5.25742	+	21.6714i	−0.191591	+	0.789749i
$754$		0			0
$755$	−5.63806	−	2.25714i	−0.205190	−	0.0821457i
$756$		0			0
$757$	14.6848	−	20.6219i	0.533727	−	0.749514i	−0.456387	−	0.889781i	$-0.650857\pi$
$757$	14.6848	−	20.6219i	0.533727	−	0.749514i	0.990114	+	0.140267i	$0.0447961\pi$
$758$		0			0
$759$	0.102954	−	0.225438i	0.00373699	−	0.00818287i
$760$		0			0
$761$	−1.41798	+	9.86226i	−0.0514017	+	0.357507i	0.947846	+	0.318728i	$0.103256\pi$
$761$	−1.41798	+	9.86226i	−0.0514017	+	0.357507i	−0.999248	+	0.0387784i	$0.987653\pi$
$762$		0			0
$763$	−1.40335	+	0.561815i	−0.0508045	+	0.0203391i
$764$		0			0
$765$	−0.263313	+	0.135747i	−0.00952011	+	0.00490796i
$766$		0			0
$767$	−29.4135	+	50.9456i	−1.06206	+	1.83954i
$768$		0			0
$769$	39.4517	−	3.76719i	1.42267	−	0.135848i	0.644835	−	0.764322i	$-0.276926\pi$
$769$	39.4517	−	3.76719i	1.42267	−	0.135848i	0.777831	+	0.628473i	$0.216320\pi$
$770$		0			0
$771$	3.09906	−	8.95414i	0.111610	−	0.322476i
$772$		0			0
$773$	−0.911187	+	19.1282i	−0.0327731	+	0.687992i	0.921378	+	0.388667i	$0.127064\pi$
$773$	−0.911187	+	19.1282i	−0.0327731	+	0.687992i	−0.954151	+	0.299325i	$0.903239\pi$
$774$		0			0
$775$	0.396715	+	0.687130i	0.0142504	+	0.0246824i
$776$		0			0
$777$	1.07810	+	0.316558i	0.0386766	+	0.0113565i
$778$		0			0
$779$	8.79525	−	5.65236i	0.315122	−	0.202517i
$780$		0			0
$781$	24.7445	+	2.36281i	0.885427	+	0.0845481i
$782$		0			0
$783$	−0.0954942	−	0.393632i	−0.00341268	−	0.0140673i
$784$		0			0
$785$	−35.2018	+	6.78459i	−1.25641	+	0.242152i
$786$		0			0
$787$	15.9450	+	12.5393i	0.568377	+	0.446977i	0.860534	−	0.509394i	$-0.170130\pi$
$787$	15.9450	+	12.5393i	0.568377	+	0.446977i	−0.292156	+	0.956371i	$0.594373\pi$
$788$		0			0
$789$	−10.7028	−	12.3517i	−0.381031	−	0.439733i
$790$		0			0
$791$	0.300455	+	6.30732i	0.0106829	+	0.224262i
$792$		0			0
$793$	18.7027	+	17.8330i	0.664151	+	0.633267i
$794$		0			0
$795$	9.29747	−	10.7298i	0.329747	−	0.380549i
$796$		0			0
$797$	34.6202	+	6.67250i	1.22631	+	0.236352i	0.760974	−	0.648782i	$-0.224721\pi$
$797$	34.6202	+	6.67250i	1.22631	+	0.236352i	0.465336	+	0.885134i	$0.345933\pi$
$798$		0			0
$799$	0.147934	−	0.0434373i	0.00523352	−	0.00153670i
$800$		0			0
$801$	1.25611	+	2.75050i	0.0443824	+	0.0971840i
$802$		0			0
$803$	−29.3958			−1.03735
$804$		0			0
$805$	0.0629551			0.00221888
$806$		0			0
$807$	1.46680	+	3.21184i	0.0516337	+	0.113062i
$808$		0			0
$809$	32.6671	−	9.59193i	1.14851	−	0.337234i	0.348555	−	0.937288i	$-0.386672\pi$
$809$	32.6671	−	9.59193i	1.14851	−	0.337234i	0.799960	+	0.600054i	$0.204854\pi$
$810$		0			0
$811$	−27.3121	−	5.26398i	−0.959059	−	0.184843i	−0.314380	−	0.949297i	$-0.601797\pi$
$811$	−27.3121	−	5.26398i	−0.959059	−	0.184843i	−0.644679	+	0.764454i	$0.723009\pi$
$812$		0			0
$813$	8.80820	−	10.1652i	0.308917	−	0.356509i
$814$		0			0
$815$	−0.701636	−	0.669008i	−0.0245772	−	0.0234343i
$816$		0			0
$817$	−1.97114	−	41.3793i	−0.0689614	−	1.44768i
$818$		0			0
$819$	−1.91276	−	2.20745i	−0.0668374	−	0.0771345i
$820$		0			0
$821$	−14.8838	−	11.7048i	−0.519449	−	0.408499i	0.323716	−	0.946154i	$-0.395068\pi$
$821$	−14.8838	−	11.7048i	−0.519449	−	0.408499i	−0.843165	+	0.537655i	$0.819310\pi$
$822$		0			0
$823$	−53.4499	+	10.3016i	−1.86315	+	0.359092i	−0.991400	−	0.130866i	$-0.958224\pi$
$823$	−53.4499	+	10.3016i	−1.86315	+	0.359092i	−0.871746	+	0.489958i	$0.837012\pi$
$824$		0			0
$825$	0.173505	+	0.715196i	0.00604066	+	0.0248999i
$826$		0			0
$827$	18.8888	+	1.80366i	0.656829	+	0.0627196i	0.418149	−	0.908379i	$-0.362679\pi$
$827$	18.8888	+	1.80366i	0.656829	+	0.0627196i	0.238680	+	0.971098i	$0.423285\pi$
$828$		0			0
$829$	0.895691	−	0.575626i	0.0311086	−	0.0199923i	−0.524994	−	0.851106i	$-0.675932\pi$
$829$	0.895691	−	0.575626i	0.0311086	−	0.0199923i	0.556103	+	0.831114i	$0.312296\pi$
$830$		0			0
$831$	18.2531	+	5.35958i	0.633192	+	0.185922i
$832$		0			0
$833$	−0.456357	−	0.790433i	−0.0158118	−	0.0273869i
$834$		0			0
$835$	−0.933899	+	19.6049i	−0.0323189	+	0.678457i
$836$		0			0
$837$	1.47259	−	4.25478i	0.0509003	−	0.147067i
$838$		0			0
$839$	3.85479	−	0.368088i	0.133082	−	0.0127078i	−0.0283023	−	0.999599i	$-0.509010\pi$
$839$	3.85479	−	0.368088i	0.133082	−	0.0127078i	0.161385	+	0.986892i	$0.448404\pi$
$840$		0			0
$841$	14.4180	−	24.9727i	0.497171	−	0.861126i
$842$		0			0
$843$	−24.1071	+	12.4281i	−0.830292	+	0.428045i
$844$		0			0
$845$	−48.0566	+	19.2389i	−1.65320	+	0.661840i
$846$		0			0
$847$	−0.442720	+	3.07919i	−0.0152120	+	0.105802i
$848$		0			0
$849$	−4.61110	+	10.0969i	−0.158252	+	0.346525i
$850$		0			0
$851$	−0.0800777	+	0.112453i	−0.00274503	+	0.00385485i
$852$		0			0
$853$	−22.6643	−	9.07343i	−0.776012	−	0.310668i	−0.0503609	−	0.998731i	$-0.516037\pi$
$853$	−22.6643	−	9.07343i	−0.776012	−	0.310668i	−0.725651	+	0.688063i	$0.758461\pi$
$854$		0			0
$855$	−2.41329	+	9.94771i	−0.0825327	+	0.340204i
$856$		0			0
$857$	−4.05987	−	28.2370i	−0.138683	−	0.964558i	−0.933722	−	0.358000i	$-0.883459\pi$
$857$	−4.05987	−	28.2370i	−0.138683	−	0.964558i	0.795039	−	0.606558i	$-0.207450\pi$
$858$		0			0
$859$	−40.6918	−	20.9781i	−1.38839	−	0.715762i	−0.408024	−	0.912971i	$-0.633782\pi$
$859$	−40.6918	−	20.9781i	−1.38839	−	0.715762i	−0.980361	+	0.197209i	$0.936812\pi$
$860$		0			0
$861$	−0.628494	−	0.882596i	−0.0214190	−	0.0300788i
$862$		0			0
$863$	32.3334	+	20.7794i	1.10064	+	0.707339i	0.959234	−	0.282613i	$-0.0912012\pi$
$863$	32.3334	+	20.7794i	1.10064	+	0.707339i	0.141406	+	0.989952i	$0.454838\pi$
$864$		0			0
$865$	−38.6844	+	36.8855i	−1.31531	+	1.25415i
$866$		0			0
$867$	−13.3486	+	10.4975i	−0.453342	+	0.356512i
$868$		0			0
$869$	−10.4724	−	30.2580i	−0.355252	−	1.02643i
$870$		0			0
$871$	48.5691	+	9.54762i	1.64570	+	0.323509i
$872$		0			0
$873$	3.58425	+	10.3560i	0.121309	+	0.350498i
$874$		0			0
$875$	−4.31633	+	3.39440i	−0.145919	+	0.114752i
$876$		0			0
$877$	4.56228	−	4.35012i	0.154057	−	0.146893i	−0.609131	−	0.793070i	$-0.708482\pi$
$877$	4.56228	−	4.35012i	0.154057	−	0.146893i	0.763188	+	0.646177i	$0.223633\pi$
$878$		0			0
$879$	9.12464	+	5.86405i	0.307766	+	0.197789i
$880$		0			0
$881$	19.4370	+	27.2954i	0.654849	+	0.919606i	0.999819	−	0.0190074i	$-0.00605059\pi$
$881$	19.4370	+	27.2954i	0.654849	+	0.919606i	−0.344971	+	0.938613i	$0.612111\pi$
$882$		0			0
$883$	−37.0848	−	19.1185i	−1.24800	−	0.643389i	−0.297682	−	0.954665i	$-0.596213\pi$
$883$	−37.0848	−	19.1185i	−1.24800	−	0.643389i	−0.950320	+	0.311276i	$0.899244\pi$
$884$		0			0
$885$	−3.04063	−	21.1481i	−0.102210	−	0.710885i
$886$		0			0
$887$	2.80108	−	11.5462i	0.0940511	−	0.387684i	−0.905257	−	0.424863i	$-0.860322\pi$
$887$	2.80108	−	11.5462i	0.0940511	−	0.387684i	0.999309	+	0.0371794i	$0.0118373\pi$
$888$		0			0
$889$	−4.30322	−	1.72275i	−0.144325	−	0.0577792i
$890$		0			0
$891$	2.42243	−	3.40182i	0.0811543	−	0.113965i
$892$		0			0
$893$	2.21308	−	4.84598i	0.0740580	−	0.162164i
$894$		0			0
$895$	−2.02828	+	14.1070i	−0.0677981	+	0.471546i
$896$		0			0
$897$	0.333163	−	0.133378i	0.0111240	−	0.00445337i
$898$		0			0
$899$	−1.62097	+	0.835669i	−0.0540624	+	0.0278711i
$900$		0			0
$901$	−0.435963	+	0.755110i	−0.0145240	+	0.0251564i
$902$		0			0
$903$	−4.27379	+	0.408097i	−0.142223	+	0.0135806i
$904$		0			0
$905$	14.4156	−	41.6511i	0.479190	−	1.38453i
$906$		0			0
$907$	1.80108	−	37.8093i	0.0598038	−	1.25544i	−0.747083	−	0.664730i	$-0.768546\pi$
$907$	1.80108	−	37.8093i	0.0598038	−	1.25544i	0.806887	−	0.590706i	$-0.201151\pi$
$908$		0			0
$909$	1.14362	+	1.98081i	0.0379316	+	0.0656994i
$910$		0			0
$911$	54.6745	+	16.0539i	1.81145	+	0.531889i	0.998712	−	0.0507418i	$-0.0161586\pi$
$911$	54.6745	+	16.0539i	1.81145	+	0.531889i	0.812737	+	0.582631i	$0.197977\pi$
$912$		0			0
$913$	−17.8062	+	11.4434i	−0.589300	+	0.378720i
$914$		0			0
$915$	−9.34310	−	0.892158i	−0.308873	−	0.0294938i
$916$		0			0
$917$	−0.956374	−	3.94223i	−0.0315823	−	0.130184i
$918$		0			0
$919$	−14.1163	+	2.72070i	−0.465655	+	0.0897476i	−0.416682	−	0.909053i	$-0.636807\pi$
$919$	−14.1163	+	2.72070i	−0.465655	+	0.0897476i	−0.0489731	+	0.998800i	$0.515595\pi$
$920$		0			0
$921$	−22.9302	−	18.0325i	−0.755576	−	0.594191i
$922$		0			0
$923$	23.5708	+	27.2021i	0.775842	+	0.895369i
$924$		0			0
$925$	−0.0195059	−	0.409478i	−0.000641349	−	0.0134636i
$926$		0			0
$927$	6.60365	+	6.29657i	0.216892	+	0.206806i
$928$		0			0
$929$	3.05102	−	3.52107i	0.100101	−	0.115522i	−0.703489	−	0.710707i	$-0.748375\pi$
$929$	3.05102	−	3.52107i	0.100101	−	0.115522i	0.803589	+	0.595184i	$0.202921\pi$
$930$		0			0
$931$	−30.9674	−	5.96847i	−1.01491	−	0.195609i
$932$		0			0
$933$	−23.7413	+	6.97106i	−0.777254	+	0.228222i
$934$		0			0
$935$	0.513941	+	1.12537i	0.0168077	+	0.0368037i
$936$		0			0
$937$	−6.91009			−0.225743			−0.112871	−	0.993610i	$-0.536005\pi$
$937$	−6.91009			−0.225743			−0.112871	+	0.993610i	$0.536005\pi$
$938$		0			0
$939$	10.7813			0.351836
$940$		0			0
$941$	3.92553	+	8.59570i	0.127968	+	0.280212i	0.962762	−	0.270352i	$-0.0871401\pi$
$941$	3.92553	+	8.59570i	0.127968	+	0.280212i	−0.834793	+	0.550564i	$0.814413\pi$
$942$		0			0
$943$	0.127731	−	0.0375052i	0.00415949	−	0.00122134i
$944$		0			0
$945$	1.04167	+	0.200765i	0.0338855	+	0.00653090i
$946$		0			0
$947$	−7.20056	+	8.30989i	−0.233987	+	0.270035i	−0.860584	−	0.509308i	$-0.829901\pi$
$947$	−7.20056	+	8.30989i	−0.233987	+	0.270035i	0.626598	+	0.779343i	$0.284447\pi$
$948$		0			0
$949$	−30.8063	−	29.3737i	−1.00001	−	0.953512i
$950$		0			0
$951$	−0.693857	−	14.5659i	−0.0224999	−	0.472330i
$952$		0			0
$953$	20.7017	+	23.8910i	0.670593	+	0.773906i	0.984469	−	0.175558i	$-0.0561730\pi$
$953$	20.7017	+	23.8910i	0.670593	+	0.773906i	−0.313876	+	0.949464i	$0.601628\pi$
$954$		0			0
$955$	12.5219	+	9.84733i	0.405199	+	0.318652i
$956$		0			0
$957$	−1.66100	+	0.320131i	−0.0536924	+	0.0103484i
$958$		0			0
$959$	2.57481	+	10.6135i	0.0831450	+	0.342728i
$960$		0			0
$961$	10.6797	+	1.01979i	0.344507	+	0.0328964i
$962$		0			0
$963$	6.25324	−	4.01871i	0.201508	−	0.129501i
$964$		0			0
$965$	−5.27787	−	1.54972i	−0.169900	−	0.0498873i
$966$		0			0
$967$	18.8016	+	32.5653i	0.604617	+	1.04723i	0.992112	+	0.125356i	$0.0400073\pi$
$967$	18.8016	+	32.5653i	0.604617	+	1.04723i	−0.387495	+	0.921872i	$0.626659\pi$
$968$		0			0
$969$	0.0299121	−	0.627932i	0.000960915	−	0.0201721i
$970$		0			0
$971$	−10.4034	+	30.0586i	−0.333860	+	0.964626i	0.645720	+	0.763574i	$0.276557\pi$
$971$	−10.4034	+	30.0586i	−0.333860	+	0.964626i	−0.979581	+	0.201052i	$0.935564\pi$
$972$		0			0
$973$	−4.88015	+	0.465998i	−0.156451	+	0.0149392i
$974$		0			0
$975$	−0.532830	+	0.922889i	−0.0170642	+	0.0295561i
$976$		0			0
$977$	−8.62459	+	4.44629i	−0.275925	+	0.142249i	−0.590636	−	0.806938i	$-0.701123\pi$
$977$	−8.62459	+	4.44629i	−0.275925	+	0.142249i	0.314710	+	0.949188i	$0.398093\pi$
$978$		0			0
$979$	11.7232	−	4.69325i	0.374674	−	0.149997i
$980$		0			0
$981$	0.445388	−	3.09774i	0.0142201	−	0.0989032i
$982$		0			0
$983$	−9.57327	+	20.9625i	−0.305340	+	0.668601i	−0.998645	−	0.0520434i	$-0.983427\pi$
$983$	−9.57327	+	20.9625i	−0.305340	+	0.668601i	0.693305	+	0.720644i	$0.256154\pi$
$984$		0			0
$985$	25.6039	−	35.9556i	0.815808	−	1.14564i
$986$		0			0
$987$	−0.512560	−	0.205198i	−0.0163150	−	0.00653153i
$988$		0			0
$989$	0.124359	−	0.512614i	0.00395438	−	0.0163002i
$990$		0			0
$991$	−2.68779	−	18.6940i	−0.0853804	−	0.593834i	−0.986929	−	0.161156i	$-0.948478\pi$
$991$	−2.68779	−	18.6940i	−0.0853804	−	0.593834i	0.901549	−	0.432678i	$-0.142431\pi$
$992$		0			0
$993$	−7.14819	−	3.68515i	−0.226841	−	0.116945i
$994$		0			0
$995$	19.5906	+	27.5111i	0.621063	+	0.872161i
$996$		0			0
$997$	−17.5600	−	11.2851i	−0.556132	−	0.357404i	0.232187	−	0.972671i	$-0.425412\pi$
$997$	−17.5600	−	11.2851i	−0.556132	−	0.357404i	−0.788319	+	0.615267i	$0.789048\pi$
$998$		0			0
$999$	−1.68360	+	1.60531i	−0.0532668	+	0.0507898i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.y.b.793.5	yes	120
67.6	even	33	inner	804.2.y.b.73.5	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.y.b.73.5	✓	120	67.6	even	33	inner
804.2.y.b.793.5	yes	120	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.415415 - 0.909632i) q^{3} +(2.10734 - 0.618772i) q^{5} +(0.474282 + 0.0914103i) q^{7} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.415415 - 0.909632i) q^{3} +(2.10734 - 0.618772i) q^{5} +(0.474282 + 0.0914103i) q^{7} +(-0.654861 + 0.755750i) q^{9} +(3.02245 + 2.88190i) q^{11} +(0.287738 + 6.04037i) q^{13} +(-1.43828 - 1.65986i) q^{15} +(0.106025 + 0.0833792i) q^{17} +(4.57644 - 0.882036i) q^{19} +(-0.113874 - 0.469395i) q^{21} +(0.0590758 + 0.00564106i) q^{23} +(-0.148248 + 0.0952734i) q^{25} +(0.959493 + 0.281733i) q^{27} +(-0.202525 - 0.350784i) q^{29} +(0.214233 - 4.49731i) q^{31} +(1.36590 - 3.94650i) q^{33} +(1.05604 - 0.100839i) q^{35} +(-1.16314 + 2.01461i) q^{37} +(5.37498 - 2.77100i) q^{39} +(2.08254 - 0.833724i) q^{41} +(1.26496 - 8.79801i) q^{43} +(-0.912380 + 1.99783i) q^{45} +(0.663038 - 0.931107i) q^{47} +(-6.28199 - 2.51493i) q^{49} +(0.0317999 - 0.131081i) q^{51} +(0.919967 + 6.39851i) q^{53} +(8.15258 + 4.20295i) q^{55} +(-2.70345 - 3.79646i) q^{57} +(8.18366 + 5.25932i) q^{59} +(3.09277 - 2.94895i) q^{61} +(-0.379672 + 0.298577i) q^{63} +(4.34398 + 12.5511i) q^{65} +(1.95922 - 7.94742i) q^{67} +(-0.0194097 - 0.0560806i) q^{69} +(4.67866 - 3.67934i) q^{71} +(-5.09429 + 4.85739i) q^{73} +(0.148248 + 0.0952734i) q^{75} +(1.17006 + 1.64312i) q^{77} +(-6.81475 - 3.51325i) q^{79} +(-0.142315 - 0.989821i) q^{81} +(-1.19490 + 4.92546i) q^{83} +(0.275025 + 0.110103i) q^{85} +(-0.234952 + 0.329944i) q^{87} +(1.25611 - 2.75050i) q^{89} +(-0.415683 + 2.89114i) q^{91} +(-4.17990 + 1.67338i) q^{93} +(9.09834 - 4.69052i) q^{95} +(5.47937 - 9.49054i) q^{97} +(-4.15728 + 0.396972i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9}+O(q^{10}) \) 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9	\( 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9} + 11 q^{11} + 2 q^{13} - 9 q^{15} + 48 q^{17} - 4 q^{19} - q^{21} + 22 q^{23} - 42 q^{25} + 12 q^{27} - q^{29} + 27 q^{31} + 17 q^{35} - 8 q^{37} - 2 q^{39} - 58 q^{41} - 17 q^{43} - 2 q^{45} - 84 q^{47} + 101 q^{49} - 26 q^{51} + 28 q^{53} - 9 q^{55} + 26 q^{57} + 34 q^{59} + 16 q^{61} + 12 q^{63} + 144 q^{65} + 23 q^{67} + 11 q^{69} + 173 q^{71} - 2 q^{73} + 42 q^{75} + 128 q^{77} + 31 q^{79} - 12 q^{81} + 47 q^{83} - 75 q^{85} - 10 q^{87} - 67 q^{89} + 16 q^{91} + 6 q^{93} - 79 q^{95} + 10 q^{97}+O(q^{100}) \) 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9 + 11 * q^11 + 2 * q^13 - 9 * q^15 + 48 * q^17 - 4 * q^19 - q^21 + 22 * q^23 - 42 * q^25 + 12 * q^27 - q^29 + 27 * q^31 + 17 * q^35 - 8 * q^37 - 2 * q^39 - 58 * q^41 - 17 * q^43 - 2 * q^45 - 84 * q^47 + 101 * q^49 - 26 * q^51 + 28 * q^53 - 9 * q^55 + 26 * q^57 + 34 * q^59 + 16 * q^61 + 12 * q^63 + 144 * q^65 + 23 * q^67 + 11 * q^69 + 173 * q^71 - 2 * q^73 + 42 * q^75 + 128 * q^77 + 31 * q^79 - 12 * q^81 + 47 * q^83 - 75 * q^85 - 10 * q^87 - 67 * q^89 + 16 * q^91 + 6 * q^93 - 79 * q^95 + 10 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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