LMFDB - Embedded newform 804.2.ba.b.41.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(41,804)]

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, 33, 53]))

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

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

chi := DirichletCharacter("804.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.ba (of order $66$, 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:	$440$
Relative dimension:	$22$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			41.17
Character	$\chi$	$=$	804.41
Dual form			804.2.ba.b.353.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.08756 + 1.34804i) q^{3} +(0.177548 - 1.23488i) q^{5} +(0.271050 + 2.83857i) q^{7} +(-0.634425 + 2.93215i) q^{9} +O(q^{10})$	\(q+(1.08756 + 1.34804i) q^{3} +(0.177548 - 1.23488i) q^{5} +(0.271050 + 2.83857i) q^{7} +(-0.634425 + 2.93215i) q^{9} +(-5.62239 + 2.25086i) q^{11} +(0.830910 + 0.871434i) q^{13} +(1.85776 - 1.10366i) q^{15} +(-4.76535 + 1.64930i) q^{17} +(-3.22750 - 0.308189i) q^{19} +(-3.53172 + 3.45250i) q^{21} +(4.74225 - 0.225901i) q^{23} +(3.30407 + 0.970163i) q^{25} +(-4.64263 + 2.33366i) q^{27} +(7.03437 - 4.06129i) q^{29} +(-6.90458 + 7.24131i) q^{31} +(-9.14894 - 5.13125i) q^{33} +(3.55340 + 0.169269i) q^{35} +(3.38398 - 5.86123i) q^{37} +(-0.271063 + 2.06784i) q^{39} +(4.19811 + 0.809119i) q^{41} +(4.51548 + 3.91269i) q^{43} +(3.50820 + 1.30403i) q^{45} +(-2.74131 + 5.31740i) q^{47} +(-1.11049 + 0.214029i) q^{49} +(-7.40594 - 4.63017i) q^{51} +(6.19918 + 7.15424i) q^{53} +(1.78129 + 7.34258i) q^{55} +(-3.09465 - 4.68597i) q^{57} +(-1.03031 - 3.50891i) q^{59} +(0.285957 - 0.714285i) q^{61} +(-8.49506 - 1.00610i) q^{63} +(1.22364 - 0.871349i) q^{65} +(6.77031 - 4.60032i) q^{67} +(5.46201 + 6.14706i) q^{69} +(-13.6640 - 4.72917i) q^{71} +(-7.42126 - 2.97103i) q^{73} +(2.28556 + 5.50913i) q^{75} +(-7.91317 - 15.3494i) q^{77} +(5.89134 - 1.42922i) q^{79} +(-8.19501 - 3.72046i) q^{81} +(4.48418 - 5.70210i) q^{83} +(1.19061 + 6.17745i) q^{85} +(13.1251 + 5.06571i) q^{87} +(-8.56425 + 13.3262i) q^{89} +(-2.24840 + 2.59480i) q^{91} +(-17.2707 - 1.43228i) q^{93} +(-0.953612 + 3.93084i) q^{95} +(4.86960 + 2.81147i) q^{97} +(-3.03289 - 17.9137i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q - 12 q^{7} + 4 q^{9}+O(q^{10}) $ 440 * q - 12 * q^7 + 4 * q^9	$ 440 q - 12 q^{7} + 4 q^{9} - 2 q^{15} - 10 q^{19} + 22 q^{21} - 68 q^{25} + 50 q^{31} + 11 q^{33} - 22 q^{37} - 45 q^{39} + 22 q^{43} + 22 q^{45} - 18 q^{49} - 6 q^{51} + 126 q^{55} - 183 q^{57} - 56 q^{61} - 141 q^{63} - 12 q^{67} + 33 q^{69} + 356 q^{73} + 165 q^{75} + 228 q^{79} + 24 q^{81} - 6 q^{85} + 75 q^{87} - 4 q^{91} - 75 q^{93} + 12 q^{97} + 88 q^{99}+O(q^{100}) $ 440 * q - 12 * q^7 + 4 * q^9 - 2 * q^15 - 10 * q^19 + 22 * q^21 - 68 * q^25 + 50 * q^31 + 11 * q^33 - 22 * q^37 - 45 * q^39 + 22 * q^43 + 22 * q^45 - 18 * q^49 - 6 * q^51 + 126 * q^55 - 183 * q^57 - 56 * q^61 - 141 * q^63 - 12 * q^67 + 33 * q^69 + 356 * q^73 + 165 * q^75 + 228 * q^79 + 24 * q^81 - 6 * q^85 + 75 * q^87 - 4 * q^91 - 75 * q^93 + 12 * q^97 + 88 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{53}{66}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.08756	+	1.34804i	0.627903	+	0.778291i
$3$	1.08756	+	1.34804i	0.627903	+	0.778291i
$4$		0			0
$5$	0.177548	−	1.23488i	0.0794020	−	0.552253i	−0.910826	−	0.412792i	$-0.864554\pi$
$5$	0.177548	−	1.23488i	0.0794020	−	0.552253i	0.990228	−	0.139461i	$-0.0445371\pi$
$6$		0			0
$7$	0.271050	+	2.83857i	0.102447	+	1.07288i	0.889793	+	0.456365i	$0.150849\pi$
$7$	0.271050	+	2.83857i	0.102447	+	1.07288i	−0.787345	+	0.616512i	$0.788545\pi$
$8$		0			0
$9$	−0.634425	+	2.93215i	−0.211475	+	0.977383i
$10$		0			0
$11$	−5.62239	+	2.25086i	−1.69521	+	0.678661i	−0.999224	−	0.0393914i	$-0.987458\pi$
$11$	−5.62239	+	2.25086i	−1.69521	+	0.678661i	−0.695989	+	0.718052i	$0.745034\pi$
$12$		0			0
$13$	0.830910	+	0.871434i	0.230453	+	0.241692i	0.828800	−	0.559545i	$-0.189024\pi$
$13$	0.830910	+	0.871434i	0.230453	+	0.241692i	−0.598347	+	0.801237i	$0.704176\pi$
$14$		0			0
$15$	1.85776	−	1.10366i	0.479671	−	0.284964i
$16$		0			0
$17$	−4.76535	+	1.64930i	−1.15577	+	0.400015i	−0.836670	−	0.547707i	$-0.815501\pi$
$17$	−4.76535	+	1.64930i	−1.15577	+	0.400015i	−0.319098	+	0.947722i	$0.603380\pi$
$18$		0			0
$19$	−3.22750	−	0.308189i	−0.740439	−	0.0707034i	−0.281982	−	0.959420i	$-0.590992\pi$
$19$	−3.22750	−	0.308189i	−0.740439	−	0.0707034i	−0.458457	+	0.888716i	$0.651598\pi$
$20$		0			0
$21$	−3.53172	+	3.45250i	−0.770684	+	0.753397i
$22$		0			0
$23$	4.74225	−	0.225901i	0.988828	−	0.0471037i	0.453070	−	0.891475i	$-0.350329\pi$
$23$	4.74225	−	0.225901i	0.988828	−	0.0471037i	0.535758	+	0.844371i	$0.320026\pi$
$24$		0			0
$25$	3.30407	+	0.970163i	0.660814	+	0.194033i
$26$		0			0
$27$	−4.64263	+	2.33366i	−0.893475	+	0.449113i
$28$		0			0
$29$	7.03437	−	4.06129i	1.30625	−	0.754163i	0.324781	−	0.945789i	$-0.394709\pi$
$29$	7.03437	−	4.06129i	1.30625	−	0.754163i	0.981468	+	0.191626i	$0.0613760\pi$
$30$		0			0
$31$	−6.90458	+	7.24131i	−1.24010	+	1.30058i	−0.302378	+	0.953188i	$0.597780\pi$
$31$	−6.90458	+	7.24131i	−1.24010	+	1.30058i	−0.937721	+	0.347390i	$0.887068\pi$
$32$		0			0
$33$	−9.14894	−	5.13125i	−1.59263	−	0.893236i
$34$		0			0
$35$	3.55340	+	0.169269i	0.600634	+	0.0286117i
$36$		0			0
$37$	3.38398	−	5.86123i	0.556323	−	0.963580i	−0.441476	−	0.897273i	$-0.645545\pi$
$37$	3.38398	−	5.86123i	0.556323	−	0.963580i	0.997799	−	0.0663071i	$-0.0211217\pi$
$38$		0			0
$39$	−0.271063	+	2.06784i	−0.0434048	+	0.331119i
$40$		0			0
$41$	4.19811	+	0.809119i	0.655634	+	0.126363i	0.506210	−	0.862410i	$-0.331046\pi$
$41$	4.19811	+	0.809119i	0.655634	+	0.126363i	0.149424	+	0.988773i	$0.452258\pi$
$42$		0			0
$43$	4.51548	+	3.91269i	0.688604	+	0.596679i	0.927257	−	0.374426i	$-0.122160\pi$
$43$	4.51548	+	3.91269i	0.688604	+	0.596679i	−0.238652	+	0.971105i	$0.576706\pi$
$44$		0			0
$45$	3.50820	+	1.30403i	0.522971	+	0.194394i
$46$		0			0
$47$	−2.74131	+	5.31740i	−0.399861	+	0.775623i	−0.999700	−	0.0244981i	$-0.992201\pi$
$47$	−2.74131	+	5.31740i	−0.399861	+	0.775623i	0.599838	+	0.800121i	$0.295232\pi$
$48$		0			0
$49$	−1.11049	+	0.214029i	−0.158641	+	0.0305755i
$50$		0			0
$51$	−7.40594	−	4.63017i	−1.03704	−	0.648353i
$52$		0			0
$53$	6.19918	+	7.15424i	0.851523	+	0.982710i	0.999981	−	0.00620868i	$-0.00197630\pi$
$53$	6.19918	+	7.15424i	0.851523	+	0.982710i	−0.148458	+	0.988919i	$0.547431\pi$
$54$		0			0
$55$	1.78129	+	7.34258i	0.240189	+	0.990073i
$56$		0			0
$57$	−3.09465	−	4.68597i	−0.409896	−	0.620672i
$58$		0			0
$59$	−1.03031	−	3.50891i	−0.134135	−	0.456821i	0.864842	−	0.502044i	$-0.167418\pi$
$59$	−1.03031	−	3.50891i	−0.134135	−	0.456821i	−0.998977	+	0.0452228i	$0.985600\pi$
$60$		0			0
$61$	0.285957	−	0.714285i	0.0366130	−	0.0914548i	−0.908935	−	0.416939i	$-0.863103\pi$
$61$	0.285957	−	0.714285i	0.0366130	−	0.0914548i	0.945548	+	0.325484i	$0.105527\pi$
$62$		0			0
$63$	−8.49506	−	1.00610i	−1.07028	−	0.126756i
$64$		0			0
$65$	1.22364	−	0.871349i	0.151774	−	0.108078i
$66$		0			0
$67$	6.77031	−	4.60032i	0.827125	−	0.562018i
$67$	6.77031	−	4.60032i	0.827125	−	0.562018i
$68$		0			0
$69$	5.46201	+	6.14706i	0.657549	+	0.740020i
$70$		0			0
$71$	−13.6640	−	4.72917i	−1.62162	−	0.561250i	−0.642814	−	0.766022i	$-0.722233\pi$
$71$	−13.6640	−	4.72917i	−1.62162	−	0.561250i	−0.978810	+	0.204772i	$0.934355\pi$
$72$		0			0
$73$	−7.42126	−	2.97103i	−0.868593	−	0.347732i	−0.105810	−	0.994386i	$-0.533743\pi$
$73$	−7.42126	−	2.97103i	−0.868593	−	0.347732i	−0.762783	+	0.646654i	$0.776168\pi$
$74$		0			0
$75$	2.28556	+	5.50913i	0.263914	+	0.636140i
$76$		0			0
$77$	−7.91317	−	15.3494i	−0.901790	−	1.74923i
$78$		0			0
$79$	5.89134	−	1.42922i	0.662827	−	0.160800i	0.109788	−	0.993955i	$-0.464983\pi$
$79$	5.89134	−	1.42922i	0.662827	−	0.160800i	0.553040	+	0.833155i	$0.313468\pi$
$80$		0			0
$81$	−8.19501	−	3.72046i	−0.910557	−	0.413385i
$82$		0			0
$83$	4.48418	−	5.70210i	0.492203	−	0.625887i	−0.474971	−	0.880001i	$-0.657542\pi$
$83$	4.48418	−	5.70210i	0.492203	−	0.625887i	0.967174	+	0.254114i	$0.0817840\pi$
$84$		0			0
$85$	1.19061	+	6.17745i	0.129139	+	0.670038i
$86$		0			0
$87$	13.1251	+	5.06571i	1.40716	+	0.543101i
$88$		0			0
$89$	−8.56425	+	13.3262i	−0.907809	+	1.41258i	0.00311057	+	0.999995i	$0.499010\pi$
$89$	−8.56425	+	13.3262i	−0.907809	+	1.41258i	−0.910920	+	0.412584i	$0.864626\pi$
$90$		0			0
$91$	−2.24840	+	2.59480i	−0.235697	+	0.272009i
$92$		0			0
$93$	−17.2707	−	1.43228i	−1.79089	−	0.148521i
$94$		0			0
$95$	−0.953612	+	3.93084i	−0.0978385	+	0.403296i
$96$		0			0
$97$	4.86960	+	2.81147i	0.494433	+	0.285461i	0.726412	−	0.687260i	$-0.241187\pi$
$97$	4.86960	+	2.81147i	0.494433	+	0.285461i	−0.231979	+	0.972721i	$0.574520\pi$
$98$		0			0
$99$	−3.03289	−	17.9137i	−0.304817	−	1.80039i
$100$		0			0
$101$	−4.60755	+	6.47040i	−0.458468	+	0.643829i	−0.977502	−	0.210925i	$-0.932352\pi$
$101$	−4.60755	+	6.47040i	−0.458468	+	0.643829i	0.519034	+	0.854754i	$0.326292\pi$
$102$		0			0
$103$	−0.947981	−	0.903898i	−0.0934073	−	0.0890637i	0.641937	−	0.766757i	$-0.278131\pi$
$103$	−0.947981	−	0.903898i	−0.0934073	−	0.0890637i	−0.735344	+	0.677694i	$0.762980\pi$
$104$		0			0
$105$	3.63635	+	4.97422i	0.354872	+	0.485434i
$106$		0			0
$107$	−1.97204	+	0.283536i	−0.190644	+	0.0274105i	−0.236975	−	0.971516i	$-0.576156\pi$
$107$	−1.97204	+	0.283536i	−0.190644	+	0.0274105i	0.0463313	+	0.998926i	$0.485247\pi$
$108$		0			0
$109$	−0.666913	+	2.27130i	−0.0638787	+	0.217551i	−0.985247	−	0.171141i	$-0.945255\pi$
$109$	−0.666913	+	2.27130i	−0.0638787	+	0.217551i	0.921368	+	0.388692i	$0.127073\pi$
$110$		0			0
$111$	11.5815	−	1.81270i	1.09926	−	0.172053i
$112$		0			0
$113$	16.4421	−	12.9302i	1.54674	−	1.21637i	0.662779	−	0.748815i	$-0.269377\pi$
$113$	16.4421	−	12.9302i	1.54674	−	1.21637i	0.883963	−	0.467557i	$-0.154866\pi$
$114$		0			0
$115$	0.563019	−	5.89620i	0.0525017	−	0.549823i
$116$		0			0
$117$	−3.08233	+	1.88349i	−0.284961	+	0.174129i
$118$		0			0
$119$	−5.97331	−	13.0797i	−0.547572	−	1.19902i
$120$		0			0
$121$	18.5838	−	17.7196i	1.68943	−	1.61087i
$122$		0			0
$123$	3.47497	+	6.53918i	0.313327	+	0.589618i
$124$		0			0
$125$	4.37597	−	9.58203i	0.391398	−	0.857043i
$126$		0			0
$127$	9.97022	−	0.952041i	0.884714	−	0.0844800i	0.357202	−	0.934027i	$-0.383731\pi$
$127$	9.97022	−	0.952041i	0.884714	−	0.0844800i	0.527513	+	0.849547i	$0.323125\pi$
$128$		0			0
$129$	−0.363601	+	10.3423i	−0.0320133	+	0.910592i
$130$		0			0
$131$	12.1678	+	18.9335i	1.06311	+	1.65423i	0.685138	+	0.728414i	$0.259742\pi$
$131$	12.1678	+	18.9335i	1.06311	+	1.65423i	0.377972	+	0.925817i	$0.376622\pi$
$132$		0			0
$133$		−	9.24501i		−	0.801644i
$134$		0			0
$135$	2.05749	+	6.14741i	0.177080	+	0.529085i
$136$		0			0
$137$	−1.42346	+	0.914800i	−0.121614	+	0.0781566i	−0.600034	−	0.799975i	$-0.704846\pi$
$137$	−1.42346	+	0.914800i	−0.121614	+	0.0781566i	0.478420	+	0.878131i	$0.341210\pi$
$138$		0			0
$139$	19.3972	+	2.78890i	1.64525	+	0.236551i	0.901772	−	0.432211i	$-0.142267\pi$
$139$	19.3972	+	2.78890i	1.64525	+	0.236551i	0.743476	+	0.668762i	$0.233176\pi$
$140$		0			0
$141$	−10.1494	+	2.08760i	−0.854735	+	0.175807i
$142$		0			0
$143$	−6.63318	−	3.02927i	−0.554694	−	0.253320i
$144$		0			0
$145$	−3.76625	−	9.40764i	−0.312770	−	0.781262i
$146$		0			0
$147$	−1.49624	−	1.26421i	−0.123408	−	0.104270i
$148$		0			0
$149$	−7.36263	+	3.36240i	−0.603170	+	0.275459i	−0.693504	−	0.720453i	$-0.743934\pi$
$149$	−7.36263	+	3.36240i	−0.603170	+	0.275459i	0.0903335	+	0.995912i	$0.471207\pi$
$150$		0			0
$151$	4.84507	+	13.9989i	0.394286	+	1.13922i	0.951181	+	0.308633i	$0.0998714\pi$
$151$	4.84507	+	13.9989i	0.394286	+	1.13922i	−0.556895	+	0.830583i	$0.688007\pi$
$152$		0			0
$153$	−1.81275	−	15.0191i	−0.146552	−	1.21422i
$154$		0			0
$155$	7.71622	+	9.81197i	0.619782	+	0.788117i
$156$		0			0
$157$	−0.180626	−	3.79180i	−0.0144155	−	0.302619i	−0.994548	−	0.104277i	$-0.966747\pi$
$157$	−0.180626	−	3.79180i	−0.0144155	−	0.302619i	0.980133	−	0.198342i	$-0.0635557\pi$
$158$		0			0
$159$	−2.90222	+	16.1374i	−0.230161	+	1.27978i
$160$		0			0
$161$	1.92662	+	13.4000i	0.151839	+	1.05606i
$162$		0			0
$163$	3.69900	+	6.40685i	0.289728	+	0.501823i	0.973745	−	0.227643i	$-0.0731019\pi$
$163$	3.69900	+	6.40685i	0.289728	+	0.501823i	−0.684017	+	0.729466i	$0.739769\pi$
$164$		0			0
$165$	−7.96083	+	10.3868i	−0.619750	+	0.808608i
$166$		0			0
$167$	7.94281	+	5.65605i	0.614633	+	0.437678i	0.844509	−	0.535542i	$-0.179893\pi$
$167$	7.94281	+	5.65605i	0.614633	+	0.437678i	−0.229876	+	0.973220i	$0.573832\pi$
$168$		0			0
$169$	0.549580	−	11.5371i	0.0422754	−	0.887470i
$170$		0			0
$171$	2.95126	−	9.26799i	0.225689	−	0.708741i
$172$		0			0
$173$	−8.60933	−	2.08860i	−0.654555	−	0.158793i	−0.105290	−	0.994442i	$-0.533577\pi$
$173$	−8.60933	−	2.08860i	−0.654555	−	0.158793i	−0.549265	+	0.835648i	$0.685092\pi$
$174$		0			0
$175$	−1.85830	+	9.64179i	−0.140474	+	0.728851i
$176$		0			0
$177$	3.60963	−	5.20505i	0.271316	−	0.391235i
$178$		0			0
$179$	−15.4083	−	9.90233i	−1.15167	−	0.740135i	−0.181700	−	0.983354i	$-0.558160\pi$
$179$	−15.4083	−	9.90233i	−1.15167	−	0.740135i	−0.969971	+	0.243219i	$0.921797\pi$
$180$		0			0
$181$	4.72348	+	2.43512i	0.351094	+	0.181001i	0.624747	−	0.780827i	$-0.285202\pi$
$181$	4.72348	+	2.43512i	0.351094	+	0.181001i	−0.273654	+	0.961828i	$0.588232\pi$
$182$		0			0
$183$	1.27388	−	0.391347i	0.0941679	−	0.0289292i
$184$		0			0
$185$	−6.63707	−	5.21945i	−0.487967	−	0.383741i
$186$		0			0
$187$	23.0803	−	19.9992i	1.68780	−	1.46249i
$188$		0			0
$189$	−7.88263	−	12.5459i	−0.573377	−	0.912578i
$190$		0			0
$191$	11.9859	−	6.17917i	0.867271	−	0.447109i	0.0336417	−	0.999434i	$-0.489290\pi$
$191$	11.9859	−	6.17917i	0.867271	−	0.447109i	0.833629	+	0.552325i	$0.186259\pi$
$192$		0			0
$193$	1.59036	−	0.466972i	0.114477	−	0.0336134i	−0.223992	−	0.974591i	$-0.571909\pi$
$193$	1.59036	−	0.466972i	0.114477	−	0.0336134i	0.338469	+	0.940977i	$0.390091\pi$
$194$		0			0
$195$	2.50539	+	0.701870i	0.179415	+	0.0502619i
$196$		0			0
$197$	0.0834813	−	0.241203i	0.00594779	−	0.0171850i	−0.941988	−	0.335647i	$-0.891045\pi$
$197$	0.0834813	−	0.241203i	0.00594779	−	0.0171850i	0.947936	+	0.318462i	$0.103166\pi$
$198$		0			0
$199$	−3.88124	−	5.45044i	−0.275134	−	0.386371i	0.653770	−	0.756694i	$-0.273187\pi$
$199$	−3.88124	−	5.45044i	−0.275134	−	0.386371i	−0.928903	+	0.370322i	$0.879247\pi$
$200$		0			0
$201$	13.5645	+	4.12353i	0.956768	+	0.290851i
$202$		0			0
$203$	13.4349	+	18.8667i	0.942946	+	1.32418i
$204$		0			0
$205$	1.74453	−	5.04048i	0.121843	−	0.352042i
$206$		0			0
$207$	−2.34623	+	14.0483i	−0.163074	+	0.976425i
$208$		0			0
$209$	18.8399	−	5.53191i	1.30319	−	0.382650i
$210$		0			0
$211$	1.54063	−	0.794251i	0.106061	−	0.0546785i	−0.404380	−	0.914591i	$-0.632512\pi$
$211$	1.54063	−	0.794251i	0.106061	−	0.0546785i	0.510441	+	0.859913i	$0.329482\pi$
$212$		0			0
$213$	−8.48536	−	23.5629i	−0.581407	−	1.61451i
$214$		0			0
$215$	5.63340	−	4.88136i	0.384194	−	0.332906i
$216$		0			0
$217$	−22.4264	−	17.6363i	−1.52240	−	1.19723i
$218$		0			0
$219$	−4.06601	−	13.2353i	−0.274755	−	0.894361i
$220$		0			0
$221$	−5.39684	−	2.78227i	−0.363031	−	0.187155i
$222$		0			0
$223$	−20.0793	−	12.9042i	−1.34461	−	0.864130i	−0.347326	−	0.937745i	$-0.612910\pi$
$223$	−20.0793	−	12.9042i	−1.34461	−	0.864130i	−0.997287	+	0.0736148i	$0.976546\pi$
$224$		0			0
$225$	−4.94085	+	9.07254i	−0.329390	+	0.604836i
$226$		0			0
$227$	3.87856	−	20.1239i	0.257429	−	1.33567i	−0.591134	−	0.806574i	$-0.701319\pi$
$227$	3.87856	−	20.1239i	0.257429	−	1.33567i	0.848563	−	0.529095i	$-0.177468\pi$
$228$		0			0
$229$	−5.04776	−	1.22457i	−0.333565	−	0.0809220i	0.0654785	−	0.997854i	$-0.479143\pi$
$229$	−5.04776	−	1.22457i	−0.333565	−	0.0809220i	−0.399044	+	0.916932i	$0.630658\pi$
$230$		0			0
$231$	12.0856	−	27.3607i	0.795173	−	1.80020i
$232$		0			0
$233$	−0.778718	+	16.3473i	−0.0510155	+	1.07095i	0.817703	+	0.575641i	$0.195247\pi$
$233$	−0.778718	+	16.3473i	−0.0510155	+	1.07095i	−0.868718	+	0.495307i	$0.835056\pi$
$234$		0			0
$235$	6.07961	+	4.32927i	0.396590	+	0.282411i
$236$		0			0
$237$	8.33384	+	6.38740i	0.541341	+	0.414906i
$238$		0			0
$239$	1.49234	+	2.58480i	0.0965313	+	0.167197i	0.910247	−	0.414066i	$-0.135892\pi$
$239$	1.49234	+	2.58480i	0.0965313	+	0.167197i	−0.813715	+	0.581264i	$0.802559\pi$
$240$		0			0
$241$	−3.09140	−	21.5012i	−0.199135	−	1.38501i	−0.806802	−	0.590821i	$-0.798804\pi$
$241$	−3.09140	−	21.5012i	−0.199135	−	1.38501i	0.607668	−	0.794191i	$-0.292105\pi$
$242$		0			0
$243$	−3.89724	−	15.0934i	−0.250008	−	0.968244i
$244$		0			0
$245$	0.0671338	+	1.40931i	0.00428902	+	0.0900376i
$246$		0			0
$247$	−2.41320	−	3.06863i	−0.153548	−	0.195252i
$248$		0			0
$249$	12.5635	−	0.156521i	0.796178	−	0.00991910i
$250$		0			0
$251$	−4.13319	−	11.9421i	−0.260885	−	0.753776i	−0.997034	−	0.0769577i	$-0.975479\pi$
$251$	−4.13319	−	11.9421i	−0.260885	−	0.753776i	0.736150	−	0.676819i	$-0.236642\pi$
$252$		0			0
$253$	−26.1543	+	11.9443i	−1.64431	+	0.750930i
$254$		0			0
$255$	−7.03259	+	8.32333i	−0.440398	+	0.521227i
$256$		0			0
$257$	−0.837662	−	2.09238i	−0.0522519	−	0.130519i	0.899945	−	0.436003i	$-0.143606\pi$
$257$	−0.837662	−	2.09238i	−0.0522519	−	0.130519i	−0.952197	+	0.305484i	$0.901182\pi$
$258$		0			0
$259$	17.5547	+	8.01697i	1.09080	+	0.498150i
$260$		0			0
$261$	7.44554	+	23.2024i	0.460868	+	1.43619i
$262$		0			0
$263$	−12.2448	−	1.76054i	−0.755047	−	0.108559i	−0.245967	−	0.969278i	$-0.579105\pi$
$263$	−12.2448	−	1.76054i	−0.755047	−	0.108559i	−0.509081	+	0.860719i	$0.670015\pi$
$264$		0			0
$265$	9.93524	−	6.38499i	0.610317	−	0.392227i
$266$		0			0
$267$	−27.2785	+	2.94813i	−1.66941	+	0.180423i
$268$		0			0
$269$			26.0117i			1.58596i	0.609246	+	0.792981i	$0.291472\pi$
$269$			26.0117i			1.58596i	−0.609246	+	0.792981i	$0.708528\pi$
$270$		0			0
$271$	5.96421	+	9.28049i	0.362300	+	0.563749i	0.973775	−	0.227514i	$-0.0730599\pi$
$271$	5.96421	+	9.28049i	0.362300	+	0.563749i	−0.611475	+	0.791264i	$0.709423\pi$
$272$		0			0
$273$	−5.94316	−	0.208942i	−0.359697	−	0.0126457i
$274$		0			0
$275$	−20.7605	+	1.98238i	−1.25190	+	0.119542i
$276$		0			0
$277$	12.6487	−	27.6969i	0.759990	−	1.66414i	0.0124546	−	0.999922i	$-0.496035\pi$
$277$	12.6487	−	27.6969i	0.759990	−	1.66414i	0.747535	−	0.664223i	$-0.231237\pi$
$278$		0			0
$279$	−16.8522	−	24.8393i	−1.00891	−	1.48709i
$280$		0			0
$281$	1.23763	−	1.18007i	0.0738306	−	0.0703973i	−0.652265	−	0.757991i	$-0.726181\pi$
$281$	1.23763	−	1.18007i	0.0738306	−	0.0703973i	0.726096	+	0.687593i	$0.241333\pi$
$282$		0			0
$283$	6.29421	+	13.7824i	0.374152	+	0.819278i	0.999250	+	0.0387317i	$0.0123318\pi$
$283$	6.29421	+	13.7824i	0.374152	+	0.819278i	−0.625098	+	0.780546i	$0.714941\pi$
$284$		0			0
$285$	−6.33604	+	2.98952i	−0.375315	+	0.177084i
$286$		0			0
$287$	−1.15884	+	12.1359i	−0.0684041	+	0.716360i
$288$		0			0
$289$	6.62548	−	5.21034i	0.389734	−	0.306490i
$290$		0			0
$291$	1.50602	+	9.62206i	0.0882842	+	0.564055i
$292$		0			0
$293$	−4.96968	+	16.9252i	−0.290332	+	0.988779i	0.677152	+	0.735844i	$0.263214\pi$
$293$	−4.96968	+	16.9252i	−0.290332	+	0.988779i	−0.967483	+	0.252935i	$0.918604\pi$
$294$		0			0
$295$	−4.51599	+	0.649302i	−0.262931	+	0.0378038i
$296$		0			0
$297$	20.8499	−	23.5707i	1.20984	−	1.36771i
$298$		0			0
$299$	4.13724	+	3.94485i	0.239263	+	0.228137i
$300$		0			0
$301$	−9.88250	+	13.8780i	−0.569618	+	0.799916i
$302$		0			0
$303$	−13.7333	+	0.825785i	−0.788960	+	0.0474401i
$304$		0			0
$305$	−0.831282	−	0.479941i	−0.0475991	−	0.0274813i
$306$		0			0
$307$	2.13694	−	8.80857i	0.121961	−	0.502732i	−0.877759	−	0.479102i	$-0.840963\pi$
$307$	2.13694	−	8.80857i	0.121961	−	0.502732i	0.999721	−	0.0236299i	$-0.00752233\pi$
$308$		0			0
$309$	0.187504	−	2.26096i	0.0106668	−	0.128621i
$310$		0			0
$311$	15.3682	−	17.7358i	0.871450	−	1.00571i	−0.128452	−	0.991716i	$-0.541001\pi$
$311$	15.3682	−	17.7358i	0.871450	−	1.00571i	0.999902	−	0.0139911i	$-0.00445366\pi$
$312$		0			0
$313$	−1.83055	+	2.84839i	−0.103469	+	0.161000i	−0.889127	−	0.457660i	$-0.848688\pi$
$313$	−1.83055	+	2.84839i	−0.103469	+	0.161000i	0.785659	+	0.618660i	$0.212324\pi$
$314$		0			0
$315$	−2.75069	+	10.3117i	−0.154984	+	0.580999i
$316$		0			0
$317$	1.89899	+	9.85288i	0.106658	+	0.553393i	0.995466	+	0.0951144i	$0.0303217\pi$
$317$	1.89899	+	9.85288i	0.106658	+	0.553393i	−0.888809	+	0.458279i	$0.848466\pi$
$318$		0			0
$319$	−30.4085	+	38.6676i	−1.70255	+	2.16497i
$320$		0			0
$321$	−2.52693	−	2.35002i	−0.141039	−	0.131166i
$322$		0			0
$323$	15.8885	−	3.85450i	0.884058	−	0.214470i
$324$		0			0
$325$	1.89995	+	3.68540i	0.105391	+	0.204429i
$326$		0			0
$327$	−3.78711	+	1.57115i	−0.209428	+	0.0868847i
$328$		0			0
$329$	−15.8368	−	6.34011i	−0.873113	−	0.349542i
$330$		0			0
$331$	23.5013	+	8.13388i	1.29175	+	0.447079i	0.884629	−	0.466296i	$-0.154412\pi$
$331$	23.5013	+	8.13388i	1.29175	+	0.447079i	0.407120	+	0.913375i	$0.366533\pi$
$332$		0			0
$333$	15.0391	+	13.6409i	0.824139	+	0.747514i
$334$		0			0
$335$	−4.47876	−	9.17727i	−0.244701	−	0.501408i
$336$		0			0
$337$	−27.8821	+	19.8548i	−1.51884	+	1.08156i	−0.549598	+	0.835429i	$0.685219\pi$
$337$	−27.8821	+	19.8548i	−1.51884	+	1.08156i	−0.969237	+	0.246129i	$0.920841\pi$
$338$		0			0
$339$	35.3122	+	8.10223i	1.91790	+	0.440053i
$340$		0			0
$341$	22.5210	−	56.2547i	1.21958	−	3.04636i
$342$		0			0
$343$	4.71495	+	16.0576i	0.254583	+	0.867031i
$344$		0			0
$345$	8.56063	−	5.65350i	0.460889	−	0.304374i
$346$		0			0
$347$	3.60288	+	14.8513i	0.193413	+	0.797258i	0.982998	+	0.183617i	$0.0587806\pi$
$347$	3.60288	+	14.8513i	0.193413	+	0.797258i	−0.789585	+	0.613641i	$0.789704\pi$
$348$		0			0
$349$	12.8926	+	14.8788i	0.690123	+	0.796445i	0.987383	−	0.158352i	$-0.0506181\pi$
$349$	12.8926	+	14.8788i	0.690123	+	0.796445i	−0.297259	+	0.954797i	$0.596073\pi$
$350$		0			0
$351$	−5.89124	−	2.10668i	−0.314451	−	0.112447i
$352$		0			0
$353$	−5.06534	+	0.976265i	−0.269601	+	0.0519613i	−0.322260	−	0.946651i	$-0.604442\pi$
$353$	−5.06534	+	0.976265i	−0.269601	+	0.0519613i	0.0526590	+	0.998613i	$0.483230\pi$
$354$		0			0
$355$	−8.26597	+	16.0337i	−0.438712	+	0.850982i
$356$		0			0
$357$	11.1357	−	22.2772i	0.589362	−	1.17904i
$358$		0			0
$359$	−14.2243	−	12.3254i	−0.750730	−	0.650511i	0.193011	−	0.981197i	$-0.438175\pi$
$359$	−14.2243	−	12.3254i	−0.750730	−	0.650511i	−0.943741	+	0.330685i	$0.892720\pi$
$360$		0			0
$361$	−8.33487	−	1.60641i	−0.438677	−	0.0845481i
$362$		0			0
$363$	44.0977	+	5.78055i	2.31453	+	0.303400i
$364$		0			0
$365$	−4.98648	+	8.63683i	−0.261004	+	0.452073i
$366$		0			0
$367$	−24.4248	−	1.16350i	−1.27497	−	0.0607341i	−0.600851	−	0.799361i	$-0.705172\pi$
$367$	−24.4248	−	1.16350i	−1.27497	−	0.0607341i	−0.674115	+	0.738627i	$0.735475\pi$
$368$		0			0
$369$	−5.03584	+	11.7962i	−0.262155	+	0.614083i
$370$		0			0
$371$	−18.6275	+	19.5359i	−0.967091	+	1.01426i
$372$		0			0
$373$	−12.1758	+	7.02967i	−0.630437	+	0.363983i	−0.780921	−	0.624630i	$-0.785250\pi$
$373$	−12.1758	+	7.02967i	−0.630437	+	0.363983i	0.150485	+	0.988612i	$0.451917\pi$
$374$		0			0
$375$	17.6761	−	4.52206i	0.912789	−	0.233518i
$376$		0			0
$377$	9.38408	+	2.75541i	0.483305	+	0.141911i
$378$		0			0
$379$	15.7523	−	0.750375i	0.809142	−	0.0385442i	0.361067	−	0.932540i	$-0.382413\pi$
$379$	15.7523	−	0.750375i	0.809142	−	0.0385442i	0.448075	+	0.893996i	$0.352110\pi$
$380$		0			0
$381$	12.1266	+	12.4049i	0.621265	+	0.635520i
$382$		0			0
$383$	12.6317	+	1.20618i	0.645447	+	0.0616327i	0.412646	−	0.910892i	$-0.364605\pi$
$383$	12.6317	+	1.20618i	0.645447	+	0.0616327i	0.232801	+	0.972524i	$0.425211\pi$
$384$		0			0
$385$	−20.3596	+	7.04652i	−1.03762	+	0.359124i
$386$		0			0
$387$	−14.3373	+	10.7578i	−0.728807	+	0.546848i
$388$		0			0
$389$	−16.4064	−	17.2065i	−0.831837	−	0.872406i	0.161591	−	0.986858i	$-0.448337\pi$
$389$	−16.4064	−	17.2065i	−0.831837	−	0.872406i	−0.993429	+	0.114452i	$0.963489\pi$
$390$		0			0
$391$	−22.2259	+	8.89792i	−1.12401	+	0.449987i
$392$		0			0
$393$	−12.2899	+	36.9941i	−0.619944	+	1.86611i
$394$		0			0
$395$	−0.718915	−	7.52882i	−0.0361726	−	0.378816i
$396$		0			0
$397$	−2.30702	+	16.0457i	−0.115786	+	0.805311i	0.846328	+	0.532663i	$0.178809\pi$
$397$	−2.30702	+	16.0457i	−0.115786	+	0.805311i	−0.962114	+	0.272648i	$0.912101\pi$
$398$		0			0
$399$	12.4626	−	10.0545i	0.623912	−	0.503355i
$400$		0			0
$401$	9.84306			0.491539			0.245770	−	0.969328i	$-0.420959\pi$
$401$	9.84306			0.491539			0.245770	+	0.969328i	$0.420959\pi$
$402$		0			0
$403$	−12.0474			−0.600124
$404$		0			0
$405$	−6.04931	+	9.45925i	−0.300593	+	0.470034i
$406$		0			0
$407$	−5.83323	+	40.5710i	−0.289142	+	2.01103i
$408$		0			0
$409$	−0.952292	−	9.97285i	−0.0470878	−	0.493126i	−0.987998	−	0.154469i	$-0.950633\pi$
$409$	−0.952292	−	9.97285i	−0.0470878	−	0.493126i	0.940910	−	0.338657i	$-0.109973\pi$
$410$		0			0
$411$	−2.78128	−	0.923977i	−0.137191	−	0.0455764i
$412$		0			0
$413$	9.68100	−	3.87569i	0.476371	−	0.190710i
$414$		0			0
$415$	−6.24522	−	6.54980i	−0.306566	−	0.321517i
$416$		0			0
$417$	17.3361	+	29.1813i	0.848951	+	1.42901i
$418$		0			0
$419$	−9.38589	+	3.24849i	−0.458531	+	0.158699i	−0.546562	−	0.837419i	$-0.684064\pi$
$419$	−9.38589	+	3.24849i	−0.458531	+	0.158699i	0.0880313	+	0.996118i	$0.471942\pi$
$420$		0			0
$421$	26.5655	+	2.53670i	1.29472	+	0.123631i	0.719573	−	0.694417i	$-0.244338\pi$
$421$	26.5655	+	2.53670i	1.29472	+	0.123631i	0.575150	+	0.818048i	$0.304944\pi$
$422$		0			0
$423$	−13.8523	−	11.4114i	−0.673520	−	0.554843i
$424$		0			0
$425$	−17.3452	+	0.826252i	−0.841364	+	0.0400791i
$426$		0			0
$427$	2.10505	+	0.618100i	0.101871	+	0.0299119i
$428$		0			0
$429$	−3.13040	−	12.2363i	−0.151137	−	0.590774i
$430$		0			0
$431$	−6.87919	+	3.97170i	−0.331359	+	0.191310i	−0.656444	−	0.754375i	$-0.727940\pi$
$431$	−6.87919	+	3.97170i	−0.331359	+	0.191310i	0.325085	+	0.945685i	$0.394607\pi$
$432$		0			0
$433$	−8.68654	+	9.11018i	−0.417448	+	0.437807i	−0.898559	−	0.438853i	$-0.855385\pi$
$433$	−8.68654	+	9.11018i	−0.417448	+	0.437807i	0.481111	+	0.876660i	$0.340234\pi$
$434$		0			0
$435$	8.58586	−	15.3084i	0.411660	−	0.733983i
$436$		0			0
$437$	−15.3752	−	0.732413i	−0.735497	−	0.0350361i
$438$		0			0
$439$	−2.96472	+	5.13504i	−0.141498	+	0.245082i	−0.928061	−	0.372428i	$-0.878525\pi$
$439$	−2.96472	+	5.13504i	−0.141498	+	0.245082i	0.786563	+	0.617510i	$0.211859\pi$
$440$		0			0
$441$	0.0769563	−	3.39190i	0.00366459	−	0.161519i
$442$		0			0
$443$	−9.59946	−	1.85014i	−0.456084	−	0.0879030i	−0.0439651	−	0.999033i	$-0.513999\pi$
$443$	−9.59946	−	1.85014i	−0.456084	−	0.0879030i	−0.412119	+	0.911130i	$0.635211\pi$
$444$		0			0
$445$	14.9357	+	12.9418i	0.708019	+	0.613502i
$446$		0			0
$447$	−12.5400	−	6.26831i	−0.593120	−	0.296481i
$448$		0			0
$449$	12.6532	−	24.5438i	0.597141	−	1.15829i	−0.375683	−	0.926748i	$-0.622592\pi$
$449$	12.6532	−	24.5438i	0.597141	−	1.15829i	0.972824	−	0.231544i	$-0.0743778\pi$
$450$		0			0
$451$	−25.4246	+	4.90019i	−1.19720	+	0.230741i
$452$		0			0
$453$	−13.6018	+	21.7560i	−0.639068	+	1.02219i
$454$		0			0
$455$	2.80505	+	3.23720i	0.131503	+	0.151762i
$456$		0			0
$457$	−6.78293	−	27.9596i	−0.317292	−	1.30790i	−0.877513	−	0.479552i	$-0.840799\pi$
$457$	−6.78293	−	27.9596i	−0.317292	−	1.30790i	0.560221	−	0.828343i	$-0.310716\pi$
$458$		0			0
$459$	18.2749	−	18.7778i	0.852998	−	0.876474i
$460$		0			0
$461$	7.46037	+	25.4077i	0.347464	+	1.18335i	0.929077	+	0.369888i	$0.120604\pi$
$461$	7.46037	+	25.4077i	0.347464	+	1.18335i	−0.581613	+	0.813466i	$0.697578\pi$
$462$		0			0
$463$	−5.24553	+	13.1027i	−0.243781	+	0.608935i	−0.998912	−	0.0466391i	$-0.985149\pi$
$463$	−5.24553	+	13.1027i	−0.243781	+	0.608935i	0.755131	+	0.655574i	$0.227573\pi$
$464$		0			0
$465$	−4.83508	+	21.0729i	−0.224221	+	0.977232i
$466$		0			0
$467$	21.5349	−	15.3349i	0.996516	−	0.709616i	0.0393712	−	0.999225i	$-0.487465\pi$
$467$	21.5349	−	15.3349i	0.996516	−	0.709616i	0.957145	+	0.289609i	$0.0935251\pi$
$468$		0			0
$469$	14.8934	+	17.9711i	0.687713	+	0.829826i
$470$		0			0
$471$	4.91506	−	4.36730i	0.226474	−	0.201235i
$472$		0			0
$473$	−34.1947	−	11.8349i	−1.57227	−	0.544169i
$474$		0			0
$475$	−10.3649	−	4.14948i	−0.475574	−	0.190391i
$476$		0			0
$477$	−24.9102	+	13.6381i	−1.14056	+	0.624446i
$478$		0			0
$479$	14.2559	+	27.6526i	0.651368	+	1.26348i	0.950932	+	0.309401i	$0.100129\pi$
$479$	14.2559	+	27.6526i	0.651368	+	1.26348i	−0.299563	+	0.954076i	$0.596841\pi$
$480$		0			0
$481$	7.91946	−	1.92124i	0.361096	−	0.0876010i
$482$		0			0
$483$	−15.9684	+	17.1704i	−0.726586	+	0.781282i
$484$		0			0
$485$	4.33640	−	5.51418i	0.196906	−	0.250386i
$486$		0			0
$487$	1.33028	+	6.90213i	0.0602806	+	0.312765i	0.999536	−	0.0304531i	$-0.00969504\pi$
$487$	1.33028	+	6.90213i	0.0602806	+	0.312765i	−0.939256	+	0.343218i	$0.888483\pi$
$488$		0			0
$489$	−4.61381	+	11.9542i	−0.208644	+	0.540589i
$490$		0			0
$491$	−9.07689	+	14.1239i	−0.409634	+	0.637403i	−0.983365	−	0.181641i	$-0.941859\pi$
$491$	−9.07689	+	14.1239i	−0.409634	+	0.637403i	0.573731	+	0.819044i	$0.305496\pi$
$492$		0			0
$493$	−26.8229	+	30.9553i	−1.20804	+	1.39416i
$494$		0			0
$495$	−22.6596	+	0.564693i	−1.01848	+	0.0253811i
$496$		0			0
$497$	9.72043	−	40.0681i	0.436021	−	1.79730i
$498$		0			0
$499$	−28.5971	−	16.5105i	−1.28018	−	0.739113i	−0.303300	−	0.952895i	$-0.598089\pi$
$499$	−28.5971	−	16.5105i	−1.28018	−	0.739113i	−0.976881	+	0.213782i	$0.931422\pi$
$500$		0			0
$501$	1.01370	+	16.8585i	0.0452889	+	0.753183i
$502$		0			0
$503$	2.49099	−	3.49810i	0.111068	−	0.155973i	−0.755300	−	0.655379i	$-0.772509\pi$
$503$	2.49099	−	3.49810i	0.111068	−	0.155973i	0.866368	+	0.499406i	$0.166448\pi$
$504$		0			0
$505$	7.17207	+	6.83856i	0.319153	+	0.304312i
$506$		0			0
$507$	16.1502	−	11.8064i	0.717255	−	0.524343i
$508$		0			0
$509$	21.5661	−	3.10074i	0.955903	−	0.137438i	0.353327	−	0.935500i	$-0.385050\pi$
$509$	21.5661	−	3.10074i	0.955903	−	0.137438i	0.602576	+	0.798062i	$0.294141\pi$
$510$		0			0
$511$	6.42192	−	21.8710i	0.284089	−	0.967518i
$512$		0			0
$513$	15.7033	−	6.10108i	0.693318	−	0.269369i
$514$		0			0
$515$	−1.28451	+	1.01015i	−0.0566024	+	0.0445126i
$516$		0			0
$517$	3.44396	−	36.0668i	0.151465	−	1.58622i
$518$		0			0
$519$	−6.54764	−	13.8772i	−0.287410	−	0.609141i
$520$		0			0
$521$	4.00476	+	8.76920i	0.175452	+	0.384186i	0.976844	−	0.213954i	$-0.0686342\pi$
$521$	4.00476	+	8.76920i	0.175452	+	0.384186i	−0.801392	+	0.598139i	$0.795907\pi$
$522$		0			0
$523$	−6.02032	+	5.74036i	−0.263250	+	0.251009i	−0.810195	−	0.586160i	$-0.800639\pi$
$523$	−6.02032	+	5.74036i	−0.263250	+	0.251009i	0.546945	+	0.837168i	$0.315791\pi$
$524$		0			0
$525$	−15.0185	+	7.98096i	−0.655462	+	0.348318i
$526$		0			0
$527$	20.9596	−	45.8952i	0.913015	−	1.99922i
$528$		0			0
$529$	−0.457938	+	0.0437278i	−0.0199104	+	0.00190121i
$530$		0			0
$531$	10.9423	−	0.794879i	0.474856	−	0.0344948i
$532$		0			0
$533$	2.78316	+	4.33068i	0.120552	+	0.187582i
$534$		0			0
$535$			2.48556i			0.107460i
$536$		0			0
$537$	−3.40874	−	31.5404i	−0.147098	−	1.36107i
$538$		0			0
$539$	5.76183	−	3.70290i	0.248180	−	0.159495i
$540$		0			0
$541$	−2.16925	−	0.311891i	−0.0932634	−	0.0134092i	0.0955251	−	0.995427i	$-0.469547\pi$
$541$	−2.16925	−	0.311891i	−0.0932634	−	0.0134092i	−0.188788	+	0.982018i	$0.560456\pi$
$542$		0			0
$543$	1.85443	+	9.01579i	0.0795810	+	0.386905i
$544$		0			0
$545$	2.68636	+	1.22682i	0.115071	+	0.0525512i
$546$		0			0
$547$	−9.88563	−	24.6931i	−0.422679	−	1.05580i	−0.975007	−	0.222174i	$-0.928685\pi$
$547$	−9.88563	−	24.6931i	−0.422679	−	1.05580i	0.552328	−	0.833627i	$-0.313740\pi$
$548$		0			0
$549$	1.91297	+	1.29163i	0.0816437	+	0.0551254i
$550$		0			0
$551$	−23.9551	+	10.9399i	−1.02052	+	0.466056i
$552$		0			0
$553$	5.65379	+	16.3356i	0.240424	+	0.694659i
$554$		0			0
$555$	−0.182185	−	14.6235i	−0.00773333	−	0.620733i
$556$		0			0
$557$	5.97109	+	7.59286i	0.253003	+	0.321720i	0.895919	−	0.444217i	$-0.146518\pi$
$557$	5.97109	+	7.59286i	0.253003	+	0.321720i	−0.642916	+	0.765937i	$0.722276\pi$
$558$		0			0
$559$	0.342313	+	7.18603i	0.0144783	+	0.303937i
$560$		0			0
$561$	52.0609	+	9.36284i	2.19801	+	0.395300i
$562$		0			0
$563$	−1.64096	−	11.4132i	−0.0691584	−	0.481007i	−0.994738	−	0.102454i	$-0.967331\pi$
$563$	−1.64096	−	11.4132i	−0.0691584	−	0.481007i	0.925579	−	0.378553i	$-0.123578\pi$
$564$		0			0
$565$	−13.0479	−	22.5997i	−0.548930	−	0.950775i
$566$		0			0
$567$	8.33951	−	24.2705i	0.350227	−	1.01927i
$568$		0			0
$569$	11.1066	+	7.90898i	0.465613	+	0.331562i	0.788669	−	0.614818i	$-0.210771\pi$
$569$	11.1066	+	7.90898i	0.465613	+	0.331562i	−0.323056	+	0.946380i	$0.604710\pi$
$570$		0			0
$571$	−0.284062	+	5.96320i	−0.0118876	+	0.249552i	0.985100	+	0.171985i	$0.0550182\pi$
$571$	−0.284062	+	5.96320i	−0.0118876	+	0.249552i	−0.996987	+	0.0775669i	$0.975285\pi$
$572$		0			0
$573$	21.3652	+	9.43728i	0.892543	+	0.394248i
$574$		0			0
$575$	15.8879	+	3.85436i	0.662571	+	0.160738i
$576$		0			0
$577$	4.96863	−	25.7797i	0.206847	−	1.07322i	−0.718910	−	0.695103i	$-0.755359\pi$
$577$	4.96863	−	25.7797i	0.206847	−	1.07322i	0.925757	−	0.378119i	$-0.123429\pi$
$578$		0			0
$579$	2.35911	+	1.63601i	0.0980414	+	0.0679903i
$580$		0			0
$581$	17.4012	+	11.1831i	0.721924	+	0.463953i
$582$		0			0
$583$	−50.9574	−	26.2704i	−2.11044	−	1.08801i
$584$		0			0
$585$	1.77862	+	4.14070i	0.0735369	+	0.171197i
$586$		0			0
$587$	23.1431	+	18.1999i	0.955217	+	0.751191i	0.968576	−	0.248720i	$-0.0800098\pi$
$587$	23.1431	+	18.1999i	0.955217	+	0.751191i	−0.0133582	+	0.999911i	$0.504252\pi$
$588$		0			0
$589$	24.5162	−	21.2434i	1.01017	−	0.875320i
$590$		0			0
$591$	0.415943	−	0.149787i	0.0171096	−	0.00616141i
$592$		0			0
$593$	−33.4171	+	17.2277i	−1.37227	+	0.707457i	−0.977424	−	0.211288i	$-0.932234\pi$
$593$	−33.4171	+	17.2277i	−1.37227	+	0.707457i	−0.394851	+	0.918745i	$0.629204\pi$
$594$		0			0
$595$	−17.2124	+	5.05401i	−0.705639	+	0.207194i
$596$		0			0
$597$	3.12633	−	11.1597i	0.127952	−	0.456738i
$598$		0			0
$599$	1.91514	−	5.53343i	0.0782505	−	0.226090i	−0.899090	−	0.437764i	$-0.855770\pi$
$599$	1.91514	−	5.53343i	0.0782505	−	0.226090i	0.977340	+	0.211674i	$0.0678916\pi$
$600$		0			0
$601$	−6.08524	−	8.54552i	−0.248222	−	0.348579i	0.671601	−	0.740913i	$-0.265607\pi$
$601$	−6.08524	−	8.54552i	−0.248222	−	0.348579i	−0.919823	+	0.392334i	$0.871668\pi$
$602$		0			0
$603$	9.19356	+	22.7701i	0.374391	+	0.927271i
$604$		0			0
$605$	−18.5820	−	26.0947i	−0.755464	−	1.06090i
$606$		0			0
$607$	−13.1542	+	38.0064i	−0.533911	+	1.54263i	0.279027	+	0.960283i	$0.409988\pi$
$607$	−13.1542	+	38.0064i	−0.533911	+	1.54263i	−0.812938	+	0.582350i	$0.802133\pi$
$608$		0			0
$609$	−10.8218	+	38.6295i	−0.438521	+	1.56535i
$610$		0			0
$611$	−6.91155	+	2.02941i	−0.279611	+	0.0821013i
$612$		0			0
$613$	1.05817	−	0.545524i	0.0427390	−	0.0220335i	−0.436725	−	0.899595i	$-0.643862\pi$
$613$	1.05817	−	0.545524i	0.0427390	−	0.0220335i	0.479464	+	0.877562i	$0.340831\pi$
$614$		0			0
$615$	8.69205	−	3.13013i	0.350497	−	0.126219i
$616$		0			0
$617$	−6.20162	+	5.37373i	−0.249668	+	0.216338i	−0.770699	−	0.637199i	$-0.780093\pi$
$617$	−6.20162	+	5.37373i	−0.249668	+	0.216338i	0.521031	+	0.853537i	$0.325547\pi$
$618$		0			0
$619$	−30.7540	−	24.1852i	−1.23611	−	0.972086i	−1.00000		0.000359445i	$-0.999886\pi$
$619$	−30.7540	−	24.1852i	−1.23611	−	0.972086i	−0.236108	−	0.971727i	$-0.575872\pi$
$620$		0			0
$621$	−21.4894	+	12.1156i	−0.862338	+	0.486181i
$622$		0			0
$623$	−40.1488	−	20.6981i	−1.60853	−	0.829253i
$624$		0			0
$625$	3.42887	+	2.20360i	0.137155	+	0.0881440i
$626$		0			0
$627$	27.9468	+	19.3807i	1.11609	+	0.773991i
$628$		0			0
$629$	−6.45892	+	33.5120i	−0.257534	+	1.33621i
$630$		0			0
$631$	−2.77883	−	0.674138i	−0.110624	−	0.0268370i	0.180065	−	0.983655i	$-0.442369\pi$
$631$	−2.77883	−	0.674138i	−0.110624	−	0.0268370i	−0.290689	+	0.956818i	$0.593884\pi$
$632$		0			0
$633$	2.74621	+	1.21304i	0.109152	+	0.0482139i
$634$		0			0
$635$	0.594544	−	12.4810i	0.0235938	−	0.495294i
$636$		0			0
$637$	−1.10923	−	0.789876i	−0.0439491	−	0.0312960i
$638$		0			0
$639$	22.5355	−	37.0647i	0.891489	−	1.46626i
$640$		0			0
$641$	17.5025	+	30.3151i	0.691305	+	1.19738i	0.971410	+	0.237407i	$0.0762974\pi$
$641$	17.5025	+	30.3151i	0.691305	+	1.19738i	−0.280105	+	0.959969i	$0.590369\pi$
$642$		0			0
$643$	−3.61977	−	25.1761i	−0.142750	−	0.992848i	−0.927710	−	0.373301i	$-0.878226\pi$
$643$	−3.61977	−	25.1761i	−0.142750	−	0.992848i	0.784960	−	0.619546i	$-0.212683\pi$
$644$		0			0
$645$	12.7069	+	2.28527i	0.500335	+	0.0899822i
$646$		0			0
$647$	0.0372958	+	0.782935i	0.00146625	+	0.0307804i	0.999482	−	0.0321861i	$-0.0102469\pi$
$647$	0.0372958	+	0.782935i	0.00146625	+	0.0307804i	−0.998016	+	0.0629665i	$0.979944\pi$
$648$		0			0
$649$	13.6909	+	17.4094i	0.537414	+	0.683377i
$650$		0			0
$651$	−0.615598	−	49.4123i	−0.0241272	−	1.93662i
$652$		0			0
$653$	4.66960	+	13.4919i	0.182735	+	0.527979i	0.998746	−	0.0500571i	$-0.0159403\pi$
$653$	4.66960	+	13.4919i	0.182735	+	0.527979i	−0.816011	+	0.578036i	$0.803819\pi$
$654$		0			0
$655$	25.5409	−	11.6642i	0.997967	−	0.455756i
$656$		0			0
$657$	13.4197	−	19.8754i	0.523554	−	0.775412i
$658$		0			0
$659$	−6.02945	−	15.0608i	−0.234874	−	0.586687i	0.763368	−	0.645964i	$-0.223545\pi$
$659$	−6.02945	−	15.0608i	−0.234874	−	0.586687i	−0.998242	+	0.0592776i	$0.981120\pi$
$660$		0			0
$661$	19.7598	+	9.02398i	0.768566	+	0.350992i	0.760807	−	0.648978i	$-0.224803\pi$
$661$	19.7598	+	9.02398i	0.768566	+	0.350992i	0.00775838	+	0.999970i	$0.497530\pi$
$662$		0			0
$663$	−2.11878	−	10.3010i	−0.0822868	−	0.400059i
$664$		0			0
$665$	−11.4164	−	1.64143i	−0.442710	−	0.0636521i
$666$		0			0
$667$	32.4413	−	20.8488i	1.25613	−	0.807267i
$668$		0			0
$669$	−4.44210	−	41.1019i	−0.171742	−	1.58909i
$670$		0			0
$671$			4.65964i			0.179883i
$672$		0			0
$673$	18.9480	+	29.4836i	0.730391	+	1.13651i	0.985513	+	0.169602i	$0.0542482\pi$
$673$	18.9480	+	29.4836i	0.730391	+	1.13651i	−0.255121	+	0.966909i	$0.582115\pi$
$674$		0			0
$675$	−17.6036	+	3.20647i	−0.677564	+	0.123417i
$676$		0			0
$677$	44.6510	−	4.26366i	1.71608	−	0.163866i	0.809845	−	0.586644i	$-0.199551\pi$
$677$	44.6510	−	4.26366i	1.71608	−	0.163866i	0.906233	+	0.422778i	$0.138945\pi$
$678$		0			0
$679$	−6.66062	+	14.5847i	−0.255611	+	0.559710i
$680$		0			0
$681$	31.3460	−	16.6575i	1.20118	−	0.638316i
$682$		0			0
$683$	4.89897	−	4.67116i	0.187454	−	0.178737i	−0.590541	−	0.807008i	$-0.701085\pi$
$683$	4.89897	−	4.67116i	0.187454	−	0.178737i	0.777995	+	0.628271i	$0.216237\pi$
$684$		0			0
$685$	0.876931	+	1.92021i	0.0335058	+	0.0733675i
$686$		0			0
$687$	−3.83897	−	8.13637i	−0.146466	−	0.310422i
$688$		0			0
$689$	−1.08348	+	11.3467i	−0.0412773	+	0.432275i
$690$		0			0
$691$	16.3921	−	12.8909i	0.623583	−	0.490391i	−0.255658	−	0.966767i	$-0.582292\pi$
$691$	16.3921	−	12.8909i	0.623583	−	0.490391i	0.879242	+	0.476376i	$0.158050\pi$
$692$		0			0
$693$	50.0271	−	13.4646i	1.90037	−	0.511476i
$694$		0			0
$695$	6.88788	−	23.4580i	0.261272	−	0.889811i
$696$		0			0
$697$	−21.3399	+	3.06822i	−0.808308	+	0.116217i
$698$		0			0
$699$	−22.8837	+	16.7289i	−0.865542	+	0.632746i
$700$		0			0
$701$	−25.8412	−	24.6396i	−0.976009	−	0.930623i	0.0215972	−	0.999767i	$-0.493125\pi$
$701$	−25.8412	−	24.6396i	−0.976009	−	0.930623i	−0.997607	+	0.0691436i	$0.977973\pi$
$702$		0			0
$703$	−12.7282	+	17.8742i	−0.480052	+	0.674139i
$704$		0			0
$705$	0.775912	+	12.9039i	0.0292225	+	0.485989i
$706$		0			0
$707$	−19.6155	−	11.3250i	−0.737718	−	0.425922i
$708$		0			0
$709$	5.74258	−	23.6712i	0.215667	−	0.888992i	−0.756366	−	0.654148i	$-0.773027\pi$
$709$	5.74258	−	23.6712i	0.215667	−	0.888992i	0.972033	−	0.234843i	$-0.0754577\pi$
$710$		0			0
$711$	0.453083	+	18.1810i	0.0169919	+	0.681842i
$712$		0			0
$713$	−31.1074	+	35.8999i	−1.16498	+	1.34446i
$714$		0			0
$715$	−4.91848	+	7.65330i	−0.183941	+	0.286217i
$716$		0			0
$717$	−1.86141	+	4.82286i	−0.0695158	+	0.180113i
$718$		0			0
$719$	−0.787928	−	4.08816i	−0.0293847	−	0.152463i	0.964273	−	0.264911i	$-0.0853427\pi$
$719$	−0.787928	−	4.08816i	−0.0293847	−	0.152463i	−0.993658	+	0.112449i	$0.964131\pi$
$720$		0			0
$721$	2.30882	−	2.93591i	0.0859850	−	0.109339i
$722$		0			0
$723$	25.6224	−	27.5512i	0.952906	−	1.02464i
$724$		0			0
$725$	27.1822	−	6.59432i	1.00952	−	0.244907i
$726$		0			0
$727$	−5.16258	−	10.0140i	−0.191470	−	0.371399i	0.773486	−	0.633814i	$-0.218511\pi$
$727$	−5.16258	−	10.0140i	−0.191470	−	0.371399i	−0.964955	+	0.262415i	$0.915481\pi$
$728$		0			0
$729$	16.1081	−	21.6686i	0.596595	−	0.802542i
$730$		0			0
$731$	−27.9711	−	11.1979i	−1.03455	−	0.414170i
$732$		0			0
$733$	5.54878	+	1.92045i	0.204949	+	0.0709336i	0.427614	−	0.903962i	$-0.359354\pi$
$733$	5.54878	+	1.92045i	0.204949	+	0.0709336i	−0.222665	+	0.974895i	$0.571476\pi$
$734$		0			0
$735$	−1.82680	+	1.62321i	−0.0673824	+	0.0598730i
$736$		0			0
$737$	−27.7106	+	41.1038i	−1.02073	+	1.51408i
$738$		0			0
$739$	−11.0929	+	7.89920i	−0.408058	+	0.290577i	−0.765596	−	0.643322i	$-0.777556\pi$
$739$	−11.0929	+	7.89920i	−0.408058	+	0.290577i	0.357538	+	0.933899i	$0.383616\pi$
$740$		0			0
$741$	1.51214	−	6.59041i	0.0555498	−	0.242105i
$742$		0			0
$743$	−7.33380	+	18.3190i	−0.269051	+	0.672057i	−0.999946	−	0.0104334i	$-0.996679\pi$
$743$	−7.33380	+	18.3190i	−0.269051	+	0.672057i	0.730894	+	0.682490i	$0.239103\pi$
$744$		0			0
$745$	2.84492	+	9.68892i	0.104230	+	0.354975i
$746$		0			0
$747$	13.8745	+	16.7658i	0.507643	+	0.613430i
$748$		0			0
$749$	−1.33936	−	5.52091i	−0.0489391	−	0.201730i
$750$		0			0
$751$	−24.5196	−	28.2972i	−0.894734	−	1.03258i	−0.999276	−	0.0380577i	$-0.987883\pi$
$751$	−24.5196	−	28.2972i	−0.894734	−	1.03258i	0.104541	−	0.994521i	$-0.466663\pi$
$752$		0			0
$753$	11.6033	−	18.5594i	0.422847	−	0.676343i
$754$		0			0
$755$	18.1471	−	3.49758i	0.660442	−	0.127290i
$756$		0			0
$757$	9.05969	−	17.5733i	0.329280	−	0.638714i	−0.664842	−	0.746984i	$-0.731501\pi$
$757$	9.05969	−	17.5733i	0.329280	−	0.638714i	0.994121	+	0.108270i	$0.0345313\pi$
$758$		0			0
$759$	−44.5457	−	22.2669i	−1.61691	−	0.808238i
$760$		0			0
$761$	−10.5028	−	9.10074i	−0.380727	−	0.329902i	0.443382	−	0.896333i	$-0.353778\pi$
$761$	−10.5028	−	9.10074i	−0.380727	−	0.329902i	−0.824109	+	0.566431i	$0.808324\pi$
$762$		0			0
$763$	−6.62800	−	1.27744i	−0.239950	−	0.0462465i
$764$		0			0
$765$	−18.8686	−	0.428095i	−0.682194	−	0.0154778i
$766$		0			0
$767$	2.20169	−	3.81344i	0.0794983	−	0.137695i
$768$		0			0
$769$	−0.686755	−	0.0327142i	−0.0247650	−	0.00117970i	0.0351958	−	0.999380i	$-0.488795\pi$
$769$	−0.686755	−	0.0327142i	−0.0247650	−	0.00117970i	−0.0599608	+	0.998201i	$0.519098\pi$
$770$		0			0
$771$	1.90960	−	3.40479i	0.0687726	−	0.122620i
$772$		0			0
$773$	15.8781	−	16.6525i	0.571095	−	0.598947i	−0.373320	−	0.927703i	$-0.621781\pi$
$773$	15.8781	−	16.6525i	0.571095	−	0.598947i	0.944415	+	0.328755i	$0.106629\pi$
$774$		0			0
$775$	−29.8385	+	17.2272i	−1.07183	+	0.618821i
$776$		0			0
$777$	8.28461	+	32.3834i	0.297209	+	1.16175i
$778$		0			0
$779$	−13.3000	−	3.90524i	−0.476523	−	0.139920i
$780$		0			0
$781$	87.4693	−	4.16667i	3.12990	−	0.149095i
$782$		0			0
$783$	−23.1803	+	35.2709i	−0.828397	+	1.26048i
$784$		0			0
$785$	−4.71447	−	0.450178i	−0.168267	−	0.0160675i
$786$		0			0
$787$	4.93777	−	1.70898i	0.176013	−	0.0609185i	−0.237640	−	0.971353i	$-0.576374\pi$
$787$	4.93777	−	1.70898i	0.176013	−	0.0609185i	0.413653	+	0.910435i	$0.364253\pi$
$788$		0			0
$789$	−10.9437	−	18.4212i	−0.389606	−	0.655812i
$790$		0			0
$791$	41.1599	+	43.1672i	1.46348	+	1.53485i
$792$		0			0
$793$	0.860056	−	0.344315i	0.0305415	−	0.0122270i
$794$		0			0
$795$	19.4124	+	6.44904i	0.688487	+	0.228724i
$796$		0			0
$797$	−0.971008	−	10.1689i	−0.0343949	−	0.360199i	−0.996242	−	0.0866123i	$-0.972396\pi$
$797$	−0.971008	−	10.1689i	−0.0343949	−	0.360199i	0.961847	−	0.273587i	$-0.0882102\pi$
$798$		0			0
$799$	4.29330	−	29.8606i	0.151886	−	1.05639i
$800$		0			0
$801$	−33.6412	−	33.5662i	−1.18865	−	1.18600i
$802$		0			0
$803$	48.4126			1.70844
$804$		0			0
$805$	16.8893			0.595271
$806$		0			0
$807$	−35.0648	+	28.2893i	−1.23434	+	0.995831i
$808$		0			0
$809$	5.16569	−	35.9281i	0.181616	−	1.26317i	−0.671327	−	0.741161i	$-0.734275\pi$
$809$	5.16569	−	35.9281i	0.181616	−	1.26317i	0.852943	−	0.522005i	$-0.174816\pi$
$810$		0			0
$811$	2.10886	+	22.0850i	0.0740521	+	0.775509i	0.953874	+	0.300206i	$0.0970555\pi$
$811$	2.10886	+	22.0850i	0.0740521	+	0.775509i	−0.879822	+	0.475303i	$0.842338\pi$
$812$		0			0
$813$	−6.02404	+	18.1331i	−0.211272	+	0.635955i
$814$		0			0
$815$	8.56841	−	3.43027i	0.300138	−	0.120157i
$816$		0			0
$817$	−13.3679	−	14.0198i	−0.467683	−	0.490491i
$818$		0			0
$819$	−6.18189	−	8.23886i	−0.216013	−	0.287889i
$820$		0			0
$821$	−14.2922	+	4.94658i	−0.498801	+	0.172637i	−0.564873	−	0.825178i	$-0.691075\pi$
$821$	−14.2922	+	4.94658i	−0.498801	+	0.172637i	0.0660714	+	0.997815i	$0.478954\pi$
$822$		0			0
$823$	−39.3858	−	3.76089i	−1.37290	−	0.131096i	−0.617611	−	0.786484i	$-0.711899\pi$
$823$	−39.3858	−	3.76089i	−1.37290	−	0.131096i	−0.755293	+	0.655387i	$0.772505\pi$
$824$		0			0
$825$	−25.2506	−	25.8300i	−0.879113	−	0.899285i
$826$		0			0
$827$	11.3400	−	0.540190i	0.394330	−	0.0187842i	0.150519	−	0.988607i	$-0.451905\pi$
$827$	11.3400	−	0.540190i	0.394330	−	0.0187842i	0.243811	+	0.969823i	$0.421602\pi$
$828$		0			0
$829$	15.1900	+	4.46019i	0.527571	+	0.154909i	0.534662	−	0.845066i	$-0.320439\pi$
$829$	15.1900	+	4.46019i	0.527571	+	0.154909i	−0.00709080	+	0.999975i	$0.502257\pi$
$830$		0			0
$831$	51.0928	−	13.0710i	1.77239	−	0.453429i
$832$		0			0
$833$	4.93886	−	2.85145i	0.171121	−	0.0987969i
$834$		0			0
$835$	8.39475	−	8.80416i	0.290512	−	0.304680i
$836$		0			0
$837$	15.1567	−	49.7317i	0.523891	−	1.71898i
$838$		0			0
$839$	56.3355	+	2.68359i	1.94492	+	0.0926478i	0.983328	−	0.181842i	$-0.0582060\pi$
$839$	56.3355	+	2.68359i	1.94492	+	0.0926478i	0.961590	+	0.274490i	$0.0885091\pi$
$840$		0			0
$841$	18.4882	−	32.0225i	0.637525	−	1.10423i
$842$		0			0
$843$	2.93678	+	0.384968i	0.101148	+	0.0132590i
$844$		0			0
$845$	−14.1493	−	2.72706i	−0.486751	−	0.0938136i
$846$		0			0
$847$	55.3353	+	47.9483i	1.90134	+	1.64752i
$848$		0			0
$849$	−11.7339	+	23.4740i	−0.402706	+	0.805626i
$850$		0			0
$851$	14.7236	−	28.5599i	0.504720	−	0.979020i
$852$		0			0
$853$	−25.3756	+	4.89075i	−0.868845	+	0.167456i	−0.604145	−	0.796875i	$-0.706485\pi$
$853$	−25.3756	+	4.89075i	−0.868845	+	0.167456i	−0.264700	+	0.964331i	$0.585273\pi$
$854$		0			0
$855$	−10.9208	−	5.28996i	−0.373484	−	0.180913i
$856$		0			0
$857$	20.8721	+	24.0877i	0.712976	+	0.822819i	0.990444	−	0.137916i	$-0.0440406\pi$
$857$	20.8721	+	24.0877i	0.712976	+	0.822819i	−0.277468	+	0.960735i	$0.589495\pi$
$858$		0			0
$859$	6.38080	+	26.3020i	0.217710	+	0.897413i	0.970876	+	0.239583i	$0.0770106\pi$
$859$	6.38080	+	26.3020i	0.217710	+	0.897413i	−0.753166	+	0.657831i	$0.771474\pi$
$860$		0			0
$861$	−17.6200	+	11.6364i	−0.600488	+	0.396567i
$862$		0			0
$863$	−1.52699	−	5.20045i	−0.0519793	−	0.177025i	0.929412	−	0.369044i	$-0.120315\pi$
$863$	−1.52699	−	5.20045i	−0.0519793	−	0.177025i	−0.981391	+	0.192019i	$0.938497\pi$
$864$		0			0
$865$	−4.10773	+	10.2606i	−0.139667	+	0.348871i
$866$		0			0
$867$	14.2294	+	3.26486i	0.483254	+	0.110881i
$868$		0			0
$869$	−29.9064	+	21.2962i	−1.01450	+	0.722426i
$870$		0			0
$871$	9.63439	+	2.07743i	0.326449	+	0.0703909i
$872$		0			0
$873$	−11.3330	+	12.4947i	−0.383565	+	0.422883i
$874$		0			0
$875$	28.3853	+	9.82426i	0.959599	+	0.332121i
$876$		0			0
$877$	16.0800	+	6.43747i	0.542983	+	0.217378i	0.626907	−	0.779094i	$-0.284321\pi$
$877$	16.0800	+	6.43747i	0.542983	+	0.217378i	−0.0839231	+	0.996472i	$0.526745\pi$
$878$		0			0
$879$	−28.2206	+	11.7078i	−0.951858	+	0.394895i
$880$		0			0
$881$	1.39306	+	2.70216i	0.0469334	+	0.0910381i	0.911136	−	0.412106i	$-0.135207\pi$
$881$	1.39306	+	2.70216i	0.0469334	+	0.0910381i	−0.864202	+	0.503144i	$0.832176\pi$
$882$		0			0
$883$	57.1300	−	13.8596i	1.92258	−	0.466413i	0.926691	−	0.375825i	$-0.122641\pi$
$883$	57.1300	−	13.8596i	1.92258	−	0.466413i	0.995888	−	0.0905877i	$-0.0288745\pi$
$884$		0			0
$885$	−5.78670	−	5.38159i	−0.194518	−	0.180900i
$886$		0			0
$887$	−31.9992	+	40.6903i	−1.07443	+	1.36625i	−0.148340	+	0.988936i	$0.547393\pi$
$887$	−31.9992	+	40.6903i	−1.07443	+	1.36625i	−0.926087	+	0.377309i	$0.876849\pi$
$888$		0			0
$889$	5.40486	+	28.0431i	0.181273	+	0.940535i
$890$		0			0
$891$	54.4497	+	2.47202i	1.82414	+	0.0828157i
$892$		0			0
$893$	10.4864	−	16.3171i	0.350912	−	0.546030i
$894$		0			0
$895$	−14.9639	+	17.2692i	−0.500187	+	0.577246i
$896$		0			0
$897$	−0.818320	+	9.86744i	−0.0273229	+	0.329464i
$898$		0			0
$899$	−19.1602	+	78.9796i	−0.639030	+	2.63412i
$900$		0			0
$901$	−41.3408	−	23.8681i	−1.37726	−	0.795163i
$902$		0			0
$903$	−29.4559	+	1.77118i	−0.980232	+	0.0589413i
$904$		0			0
$905$	3.84572	−	5.40056i	0.127836	−	0.179521i
$906$		0			0
$907$	−9.74638	−	9.29315i	−0.323623	−	0.308574i	0.510799	−	0.859700i	$-0.329350\pi$
$907$	−9.74638	−	9.29315i	−0.323623	−	0.308574i	−0.834422	+	0.551126i	$0.814198\pi$
$908$		0			0
$909$	−16.0490	−	17.6150i	−0.532313	−	0.584253i
$910$		0			0
$911$	−48.9168	+	7.03318i	−1.62069	+	0.233020i	−0.892069	−	0.451900i	$-0.850746\pi$
$911$	−48.9168	+	7.03318i	−1.62069	+	0.233020i	−0.728619	+	0.684920i	$0.759837\pi$
$912$		0			0
$913$	−12.3771	+	42.1527i	−0.409624	+	1.39505i
$914$		0			0
$915$	−0.257090	−	1.64257i	−0.00849912	−	0.0543016i
$916$		0			0
$917$	−50.4460	+	39.6712i	−1.66587	+	1.31006i
$918$		0			0
$919$	4.41766	−	46.2638i	0.145725	−	1.52610i	−0.566447	−	0.824098i	$-0.691683\pi$
$919$	4.41766	−	46.2638i	0.145725	−	1.52610i	0.712172	−	0.702005i	$-0.247711\pi$
$920$		0			0
$921$	14.1984	−	6.69917i	0.467852	−	0.220745i
$922$		0			0
$923$	−7.23244	−	15.8368i	−0.238059	−	0.521276i
$924$		0			0
$925$	16.8673	−	16.0829i	0.554592	−	0.528803i
$926$		0			0
$927$	3.25179	−	2.20617i	0.106803	−	0.0724600i
$928$		0			0
$929$	10.8647	−	23.7904i	0.356459	−	0.780536i	−0.643428	−	0.765507i	$-0.722488\pi$
$929$	10.8647	−	23.7904i	0.356459	−	0.780536i	0.999887	−	0.0150297i	$-0.00478427\pi$
$930$		0			0
$931$	3.65005	−	0.348538i	0.119626	−	0.0114229i
$932$		0			0
$933$	40.6224	+	1.42815i	1.32992	+	0.0467555i
$934$		0			0
$935$	−20.5986	−	32.0521i	−0.673647	−	1.04822i
$936$		0			0
$937$			16.9696i			0.554373i	0.960816	+	0.277187i	$0.0894020\pi$
$937$			16.9696i			0.554373i	−0.960816	+	0.277187i	$0.910598\pi$
$938$		0			0
$939$	−5.83057	+	0.630141i	−0.190274	+	0.0205639i
$940$		0			0
$941$	40.2140	−	25.8440i	1.31094	−	0.842490i	0.316582	−	0.948565i	$-0.397465\pi$
$941$	40.2140	−	25.8440i	1.31094	−	0.842490i	0.994358	+	0.106075i	$0.0338284\pi$
$942$		0			0
$943$	20.0913	+	2.88869i	0.654261	+	0.0940686i
$944$		0			0
$945$	−16.8921	+	7.50657i	−0.549501	+	0.244189i
$946$		0			0
$947$	−19.6475	−	8.97272i	−0.638459	−	0.291574i	0.0697639	−	0.997564i	$-0.477775\pi$
$947$	−19.6475	−	8.97272i	−0.638459	−	0.291574i	−0.708223	+	0.705989i	$0.750503\pi$
$948$		0			0
$949$	−3.57735	−	8.93580i	−0.116126	−	0.290068i
$950$		0			0
$951$	−11.2168	+	13.2755i	−0.363730	+	0.430488i
$952$		0			0
$953$	42.6814	−	19.4920i	1.38259	−	0.631407i	0.421292	−	0.906925i	$-0.361577\pi$
$953$	42.6814	−	19.4920i	1.38259	−	0.631407i	0.961296	+	0.275519i	$0.0888495\pi$
$954$		0			0
$955$	−5.50243	−	15.8982i	−0.178054	−	0.514454i
$956$		0			0
$957$	−85.1965	+	1.06141i	−2.75401	+	0.0343106i
$958$		0			0
$959$	−2.98255	−	3.79262i	−0.0963115	−	0.122470i
$960$		0			0
$961$	−3.28838	−	69.0315i	−0.106077	−	2.22682i
$962$		0			0
$963$	0.419740	−	5.96219i	0.0135259	−	0.192129i
$964$		0			0
$965$	−0.294287	−	2.04681i	−0.00947342	−	0.0658891i
$966$		0			0
$967$	−4.27295	−	7.40096i	−0.137409	−	0.237999i	0.789106	−	0.614257i	$-0.210544\pi$
$967$	−4.27295	−	7.40096i	−0.137409	−	0.237999i	−0.926515	+	0.376258i	$0.877211\pi$
$968$		0			0
$969$	22.4757	+	17.2263i	0.722024	+	0.553389i
$970$		0			0
$971$	−4.56380	−	3.24987i	−0.146459	−	0.104293i	0.504479	−	0.863424i	$-0.331685\pi$
$971$	−4.56380	−	3.24987i	−0.146459	−	0.104293i	−0.650938	+	0.759131i	$0.725624\pi$
$972$		0			0
$973$	−2.65885	+	55.8161i	−0.0852388	+	1.78938i
$974$		0			0
$975$	−2.90175	+	6.56931i	−0.0929304	+	0.210386i
$976$		0			0
$977$	30.0350	+	7.28642i	0.960906	+	0.233113i	0.685384	−	0.728182i	$-0.259634\pi$
$977$	30.0350	+	7.28642i	0.960906	+	0.233113i	0.275522	+	0.961295i	$0.411149\pi$
$978$		0			0
$979$	18.1560	−	94.2022i	0.580268	−	3.01072i
$980$		0			0
$981$	−6.23668	−	3.39646i	−0.199122	−	0.108441i
$982$		0			0
$983$	8.30467	+	5.33709i	0.264878	+	0.170227i	0.666338	−	0.745650i	$-0.267861\pi$
$983$	8.30467	+	5.33709i	0.264878	+	0.170227i	−0.401460	+	0.915877i	$0.631497\pi$
$984$		0			0
$985$	−0.283034	−	0.145914i	−0.00901821	−	0.00464921i
$986$		0			0
$987$	−8.67678	−	28.2439i	−0.276185	−	0.899015i
$988$		0			0
$989$	22.2974	+	17.5349i	0.709017	+	0.557577i
$990$		0			0
$991$	−0.0162826	+	0.0141089i	−0.000517233	+	0.000448185i	−0.655119	−	0.755525i	$-0.727382\pi$
$991$	−0.0162826	+	0.0141089i	−0.000517233	+	0.000448185i	0.654602	+	0.755974i	$0.272836\pi$
$992$		0			0
$993$	14.5943	+	40.5268i	0.463136	+	1.28608i
$994$		0			0
$995$	−7.41972	+	3.82513i	−0.235221	+	0.121265i
$996$		0			0
$997$	18.2997	−	5.37328i	0.579558	−	0.170174i	0.0212022	−	0.999775i	$-0.493251\pi$
$997$	18.2997	−	5.37328i	0.579558	−	0.170174i	0.558356	+	0.829602i	$0.311432\pi$
$998$		0			0
$999$	−2.03247	+	35.1086i	−0.0643047	+	1.11079i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.ba.b.41.17	yes	440
3.2	odd	2	inner	804.2.ba.b.41.15	✓	440
67.18	odd	66	inner	804.2.ba.b.353.15	yes	440
201.152	even	66	inner	804.2.ba.b.353.17	yes	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.ba.b.41.15	✓	440	3.2	odd	2	inner
804.2.ba.b.41.17	yes	440	1.1	even	1	trivial
804.2.ba.b.353.15	yes	440	67.18	odd	66	inner
804.2.ba.b.353.17	yes	440	201.152	even	66	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.ba (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(1.08756 + 1.34804i) q^{3} +(0.177548 - 1.23488i) q^{5} +(0.271050 + 2.83857i) q^{7} +(-0.634425 + 2.93215i) q^{9} +O(q^{10})\)	\(q+(1.08756 + 1.34804i) q^{3} +(0.177548 - 1.23488i) q^{5} +(0.271050 + 2.83857i) q^{7} +(-0.634425 + 2.93215i) q^{9} +(-5.62239 + 2.25086i) q^{11} +(0.830910 + 0.871434i) q^{13} +(1.85776 - 1.10366i) q^{15} +(-4.76535 + 1.64930i) q^{17} +(-3.22750 - 0.308189i) q^{19} +(-3.53172 + 3.45250i) q^{21} +(4.74225 - 0.225901i) q^{23} +(3.30407 + 0.970163i) q^{25} +(-4.64263 + 2.33366i) q^{27} +(7.03437 - 4.06129i) q^{29} +(-6.90458 + 7.24131i) q^{31} +(-9.14894 - 5.13125i) q^{33} +(3.55340 + 0.169269i) q^{35} +(3.38398 - 5.86123i) q^{37} +(-0.271063 + 2.06784i) q^{39} +(4.19811 + 0.809119i) q^{41} +(4.51548 + 3.91269i) q^{43} +(3.50820 + 1.30403i) q^{45} +(-2.74131 + 5.31740i) q^{47} +(-1.11049 + 0.214029i) q^{49} +(-7.40594 - 4.63017i) q^{51} +(6.19918 + 7.15424i) q^{53} +(1.78129 + 7.34258i) q^{55} +(-3.09465 - 4.68597i) q^{57} +(-1.03031 - 3.50891i) q^{59} +(0.285957 - 0.714285i) q^{61} +(-8.49506 - 1.00610i) q^{63} +(1.22364 - 0.871349i) q^{65} +(6.77031 - 4.60032i) q^{67} +(5.46201 + 6.14706i) q^{69} +(-13.6640 - 4.72917i) q^{71} +(-7.42126 - 2.97103i) q^{73} +(2.28556 + 5.50913i) q^{75} +(-7.91317 - 15.3494i) q^{77} +(5.89134 - 1.42922i) q^{79} +(-8.19501 - 3.72046i) q^{81} +(4.48418 - 5.70210i) q^{83} +(1.19061 + 6.17745i) q^{85} +(13.1251 + 5.06571i) q^{87} +(-8.56425 + 13.3262i) q^{89} +(-2.24840 + 2.59480i) q^{91} +(-17.2707 - 1.43228i) q^{93} +(-0.953612 + 3.93084i) q^{95} +(4.86960 + 2.81147i) q^{97} +(-3.03289 - 17.9137i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 12 q^{7} + 4 q^{9}+O(q^{10}) \) 440 * q - 12 * q^7 + 4 * q^9	\( 440 q - 12 q^{7} + 4 q^{9} - 2 q^{15} - 10 q^{19} + 22 q^{21} - 68 q^{25} + 50 q^{31} + 11 q^{33} - 22 q^{37} - 45 q^{39} + 22 q^{43} + 22 q^{45} - 18 q^{49} - 6 q^{51} + 126 q^{55} - 183 q^{57} - 56 q^{61} - 141 q^{63} - 12 q^{67} + 33 q^{69} + 356 q^{73} + 165 q^{75} + 228 q^{79} + 24 q^{81} - 6 q^{85} + 75 q^{87} - 4 q^{91} - 75 q^{93} + 12 q^{97} + 88 q^{99}+O(q^{100}) \) 440 * q - 12 * q^7 + 4 * q^9 - 2 * q^15 - 10 * q^19 + 22 * q^21 - 68 * q^25 + 50 * q^31 + 11 * q^33 - 22 * q^37 - 45 * q^39 + 22 * q^43 + 22 * q^45 - 18 * q^49 - 6 * q^51 + 126 * q^55 - 183 * q^57 - 56 * q^61 - 141 * q^63 - 12 * q^67 + 33 * q^69 + 356 * q^73 + 165 * q^75 + 228 * q^79 + 24 * q^81 - 6 * q^85 + 75 * q^87 - 4 * q^91 - 75 * q^93 + 12 * q^97 + 88 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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