LMFDB - Embedded newform 804.2.ba.b.41.15

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			41.15
Character	$\chi$	$=$	804.41
Dual form			804.2.ba.b.353.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.774432 + 1.54928i) q^{3} +(-0.177548 + 1.23488i) q^{5} +(0.271050 + 2.83857i) q^{7} +(-1.80051 + 2.39962i) q^{9} +O(q^{10})$	\(q+(0.774432 + 1.54928i) q^{3} +(-0.177548 + 1.23488i) q^{5} +(0.271050 + 2.83857i) q^{7} +(-1.80051 + 2.39962i) q^{9} +(5.62239 - 2.25086i) q^{11} +(0.830910 + 0.871434i) q^{13} +(-2.05066 + 0.681255i) q^{15} +(4.76535 - 1.64930i) q^{17} +(-3.22750 - 0.308189i) q^{19} +(-4.18781 + 2.61821i) q^{21} +(-4.74225 + 0.225901i) q^{23} +(3.30407 + 0.970163i) q^{25} +(-5.11204 - 0.931149i) q^{27} +(-7.03437 + 4.06129i) q^{29} +(-6.90458 + 7.24131i) q^{31} +(7.84136 + 6.96749i) q^{33} +(-3.55340 - 0.169269i) q^{35} +(3.38398 - 5.86123i) q^{37} +(-0.706608 + 1.96218i) q^{39} +(-4.19811 - 0.809119i) q^{41} +(4.51548 + 3.91269i) q^{43} +(-2.64355 - 2.64945i) q^{45} +(2.74131 - 5.31740i) q^{47} +(-1.11049 + 0.214029i) q^{49} +(6.24567 + 6.10557i) q^{51} +(-6.19918 - 7.15424i) q^{53} +(1.78129 + 7.34258i) q^{55} +(-2.02201 - 5.23896i) q^{57} +(1.03031 + 3.50891i) q^{59} +(0.285957 - 0.714285i) q^{61} +(-7.29950 - 4.46045i) q^{63} +(-1.22364 + 0.871349i) q^{65} +(6.77031 - 4.60032i) q^{67} +(-4.02253 - 7.17211i) q^{69} +(13.6640 + 4.72917i) q^{71} +(-7.42126 - 2.97103i) q^{73} +(1.05573 + 5.87024i) q^{75} +(7.91317 + 15.3494i) q^{77} +(5.89134 - 1.42922i) q^{79} +(-2.51632 - 8.64107i) q^{81} +(-4.48418 + 5.70210i) q^{83} +(1.19061 + 6.17745i) q^{85} +(-11.7397 - 7.75298i) q^{87} +(8.56425 - 13.3262i) q^{89} +(-2.24840 + 2.59480i) q^{91} +(-16.5659 - 5.08919i) q^{93} +(0.953612 - 3.93084i) q^{95} +(4.86960 + 2.81147i) q^{97} +(-4.72196 + 17.5443i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.774432	+	1.54928i	0.447118	+	0.894475i
$3$	0.774432	+	1.54928i	0.447118	+	0.894475i
$4$		0			0
$5$	−0.177548	+	1.23488i	−0.0794020	+	0.552253i	0.910826	+	0.412792i	$0.135446\pi$
$5$	−0.177548	+	1.23488i	−0.0794020	+	0.552253i	−0.990228	+	0.139461i	$0.955463\pi$
$6$		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
$9$	−1.80051	+	2.39962i	−0.600170	+	0.799872i
$10$		0			0
$11$	5.62239	−	2.25086i	1.69521	−	0.678661i	0.695989	−	0.718052i	$-0.254966\pi$
$11$	5.62239	−	2.25086i	1.69521	−	0.678661i	0.999224	+	0.0393914i	$0.0125419\pi$
$12$		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
$15$	−2.05066	+	0.681255i	−0.529478	+	0.175899i
$16$		0			0
$17$	4.76535	−	1.64930i	1.15577	−	0.400015i	0.319098	−	0.947722i	$-0.396620\pi$
$17$	4.76535	−	1.64930i	1.15577	−	0.400015i	0.836670	+	0.547707i	$0.184499\pi$
$18$		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
$21$	−4.18781	+	2.61821i	−0.913855	+	0.571340i
$22$		0			0
$23$	−4.74225	+	0.225901i	−0.988828	+	0.0471037i	−0.535758	−	0.844371i	$-0.679974\pi$
$23$	−4.74225	+	0.225901i	−0.988828	+	0.0471037i	−0.453070	+	0.891475i	$0.649671\pi$
$24$		0			0
$25$	3.30407	+	0.970163i	0.660814	+	0.194033i
$26$		0			0
$27$	−5.11204	−	0.931149i	−0.983813	−	0.179200i
$28$		0			0
$29$	−7.03437	+	4.06129i	−1.30625	+	0.754163i	−0.981468	−	0.191626i	$-0.938624\pi$
$29$	−7.03437	+	4.06129i	−1.30625	+	0.754163i	−0.324781	+	0.945789i	$0.605291\pi$
$30$		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
$33$	7.84136	+	6.96749i	1.36501	+	1.21288i
$34$		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
$39$	−0.706608	+	1.96218i	−0.113148	+	0.314200i
$40$		0			0
$41$	−4.19811	−	0.809119i	−0.655634	−	0.126363i	−0.149424	−	0.988773i	$-0.547742\pi$
$41$	−4.19811	−	0.809119i	−0.655634	−	0.126363i	−0.506210	+	0.862410i	$0.668954\pi$
$42$		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
$45$	−2.64355	−	2.64945i	−0.394077	−	0.394957i
$46$		0			0
$47$	2.74131	−	5.31740i	0.399861	−	0.775623i	−0.599838	−	0.800121i	$-0.704768\pi$
$47$	2.74131	−	5.31740i	0.399861	−	0.775623i	0.999700	+	0.0244981i	$0.00779878\pi$
$48$		0			0
$49$	−1.11049	+	0.214029i	−0.158641	+	0.0305755i
$50$		0			0
$51$	6.24567	+	6.10557i	0.874569	+	0.854951i
$52$		0			0
$53$	−6.19918	−	7.15424i	−0.851523	−	0.982710i	0.148458	−	0.988919i	$-0.452569\pi$
$53$	−6.19918	−	7.15424i	−0.851523	−	0.982710i	−0.999981	+	0.00620868i	$0.998024\pi$
$54$		0			0
$55$	1.78129	+	7.34258i	0.240189	+	0.990073i
$56$		0			0
$57$	−2.02201	−	5.23896i	−0.267822	−	0.693917i
$58$		0			0
$59$	1.03031	+	3.50891i	0.134135	+	0.456821i	0.998977	−	0.0452228i	$-0.0143998\pi$
$59$	1.03031	+	3.50891i	0.134135	+	0.456821i	−0.864842	+	0.502044i	$0.832582\pi$
$60$		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
$63$	−7.29950	−	4.46045i	−0.919650	−	0.561964i
$64$		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
$69$	−4.02253	−	7.17211i	−0.484256	−	0.863421i
$70$		0			0
$71$	13.6640	+	4.72917i	1.62162	+	0.561250i	0.978810	−	0.204772i	$-0.0656454\pi$
$71$	13.6640	+	4.72917i	1.62162	+	0.561250i	0.642814	+	0.766022i	$0.277767\pi$
$72$		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
$75$	1.05573	+	5.87024i	0.121905	+	0.677837i
$76$		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
$81$	−2.51632	−	8.64107i	−0.279591	−	0.960119i
$82$		0			0
$83$	−4.48418	+	5.70210i	−0.492203	+	0.625887i	−0.967174	−	0.254114i	$-0.918216\pi$
$83$	−4.48418	+	5.70210i	−0.492203	+	0.625887i	0.474971	+	0.880001i	$0.342458\pi$
$84$		0			0
$85$	1.19061	+	6.17745i	0.129139	+	0.670038i
$86$		0			0
$87$	−11.7397	−	7.75298i	−1.25863	−	0.831207i
$88$		0			0
$89$	8.56425	−	13.3262i	0.907809	−	1.41258i	−0.00311057	−	0.999995i	$-0.500990\pi$
$89$	8.56425	−	13.3262i	0.907809	−	1.41258i	0.910920	−	0.412584i	$-0.135374\pi$
$90$		0			0
$91$	−2.24840	+	2.59480i	−0.235697	+	0.272009i
$92$		0			0
$93$	−16.5659	−	5.08919i	−1.71781	−	0.527725i
$94$		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
$99$	−4.72196	+	17.5443i	−0.474575	+	1.76327i
$100$		0			0
$101$	4.60755	−	6.47040i	0.458468	−	0.643829i	−0.519034	−	0.854754i	$-0.673708\pi$
$101$	4.60755	−	6.47040i	0.458468	−	0.643829i	0.977502	+	0.210925i	$0.0676476\pi$
$102$		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
$105$	−2.48962	−	5.63628i	−0.242962	−	0.550045i
$106$		0			0
$107$	1.97204	−	0.283536i	0.190644	−	0.0274105i	−0.0463313	−	0.998926i	$-0.514753\pi$
$107$	1.97204	−	0.283536i	0.190644	−	0.0274105i	0.236975	+	0.971516i	$0.423844\pi$
$108$		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
$111$	11.7013	+	0.703600i	1.11064	+	0.0667828i
$112$		0			0
$113$	−16.4421	+	12.9302i	−1.54674	+	1.21637i	−0.662779	+	0.748815i	$0.730623\pi$
$113$	−16.4421	+	12.9302i	−1.54674	+	1.21637i	−0.883963	+	0.467557i	$0.845134\pi$
$114$		0			0
$115$	0.563019	−	5.89620i	0.0525017	−	0.549823i
$116$		0			0
$117$	−3.58717	+	0.424840i	−0.331634	+	0.0392765i
$118$		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
$123$	−1.99760	−	7.13063i	−0.180117	−	0.642947i
$124$		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
$129$	−2.56490	+	10.0258i	−0.225827	+	0.882725i
$130$		0			0
$131$	−12.1678	−	18.9335i	−1.06311	−	1.65423i	−0.685138	−	0.728414i	$-0.740258\pi$
$131$	−12.1678	−	18.9335i	−1.06311	−	1.65423i	−0.377972	−	0.925817i	$-0.623378\pi$
$132$		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	−0.478420	−	0.878131i	$-0.658790\pi$
$137$	1.42346	−	0.914800i	0.121614	−	0.0781566i	0.600034	+	0.799975i	$0.295154\pi$
$138$		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
$141$	10.3611	+	0.129082i	0.872561	+	0.0108707i
$142$		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
$147$	−1.19158	−	1.55470i	−0.0982803	−	0.128229i
$148$		0			0
$149$	7.36263	−	3.36240i	0.603170	−	0.275459i	−0.0903335	−	0.995912i	$-0.528793\pi$
$149$	7.36263	−	3.36240i	0.603170	−	0.275459i	0.693504	+	0.720453i	$0.256066\pi$
$150$		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
$153$	−4.62237	+	14.4046i	−0.373697	+	1.16454i
$154$		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
$159$	6.28304	−	15.1447i	0.498278	−	1.20105i
$160$		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
$165$	−9.99620	+	8.44604i	−0.778203	+	0.657523i
$166$		0			0
$167$	−7.94281	−	5.65605i	−0.614633	−	0.437678i	0.229876	−	0.973220i	$-0.426168\pi$
$167$	−7.94281	−	5.65605i	−0.614633	−	0.437678i	−0.844509	+	0.535542i	$0.820107\pi$
$168$		0			0
$169$	0.549580	−	11.5371i	0.0422754	−	0.887470i
$170$		0			0
$171$	6.55069	−	7.18987i	0.500943	−	0.549823i
$172$		0			0
$173$	8.60933	+	2.08860i	0.654555	+	0.158793i	0.549265	−	0.835648i	$-0.314908\pi$
$173$	8.60933	+	2.08860i	0.654555	+	0.158793i	0.105290	+	0.994442i	$0.466423\pi$
$174$		0			0
$175$	−1.85830	+	9.64179i	−0.140474	+	0.728851i
$176$		0			0
$177$	−4.63836	+	4.31364i	−0.348641	+	0.324233i
$178$		0			0
$179$	15.4083	+	9.90233i	1.15167	+	0.740135i	0.969971	−	0.243219i	$-0.0782035\pi$
$179$	15.4083	+	9.90233i	1.15167	+	0.740135i	0.181700	+	0.983354i	$0.441840\pi$
$180$		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
$183$	1.32808	−	0.110139i	0.0981744	−	0.00814174i
$184$		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
$189$	1.25751	−	14.7633i	0.0914702	−	1.07387i
$190$		0			0
$191$	−11.9859	+	6.17917i	−0.867271	+	0.447109i	−0.833629	−	0.552325i	$-0.813741\pi$
$191$	−11.9859	+	6.17917i	−0.867271	+	0.447109i	−0.0336417	+	0.999434i	$0.510710\pi$
$192$		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
$195$	−2.29758	−	1.22095i	−0.164533	−	0.0874343i
$196$		0			0
$197$	−0.0834813	+	0.241203i	−0.00594779	+	0.0171850i	−0.947936	−	0.318462i	$-0.896834\pi$
$197$	−0.0834813	+	0.241203i	−0.00594779	+	0.0171850i	0.941988	+	0.335647i	$0.108955\pi$
$198$		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
$201$	12.3703	+	6.92645i	0.872534	+	0.488554i
$202$		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
$207$	7.99640	−	11.7863i	0.555788	−	0.819206i
$208$		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
$213$	3.25508	+	24.8318i	0.223034	+	1.70145i
$214$		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
$219$	−1.14432	−	13.7984i	−0.0773262	−	0.932412i
$220$		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
$225$	−8.27704	+	6.18172i	−0.551802	+	0.412114i
$226$		0			0
$227$	−3.87856	+	20.1239i	−0.257429	+	1.33567i	0.591134	+	0.806574i	$0.298681\pi$
$227$	−3.87856	+	20.1239i	−0.257429	+	1.33567i	−0.848563	+	0.529095i	$0.822532\pi$
$228$		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
$231$	−17.6523	+	24.1468i	−1.16143	+	1.58874i
$232$		0			0
$233$	0.778718	−	16.3473i	0.0510155	−	1.07095i	−0.817703	−	0.575641i	$-0.804753\pi$
$233$	0.778718	−	16.3473i	0.0510155	−	1.07095i	0.868718	−	0.495307i	$-0.164944\pi$
$234$		0			0
$235$	6.07961	+	4.32927i	0.396590	+	0.282411i
$236$		0			0
$237$	6.77670	+	8.02047i	0.440194	+	0.520986i
$238$		0			0
$239$	−1.49234	−	2.58480i	−0.0965313	−	0.167197i	0.813715	−	0.581264i	$-0.197441\pi$
$239$	−1.49234	−	2.58480i	−0.0965313	−	0.167197i	−0.910247	+	0.414066i	$0.864108\pi$
$240$		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
$243$	11.4387	−	10.5904i	0.733792	−	0.679374i
$244$		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
$249$	−12.3068	−	2.53135i	−0.779913	−	0.160418i
$250$		0			0
$251$	4.13319	+	11.9421i	0.260885	+	0.753776i	0.997034	+	0.0769577i	$0.0245207\pi$
$251$	4.13319	+	11.9421i	0.260885	+	0.753776i	−0.736150	+	0.676819i	$0.763358\pi$
$252$		0			0
$253$	−26.1543	+	11.9443i	−1.64431	+	0.750930i
$254$		0			0
$255$	−8.64853	+	6.62859i	−0.541592	+	0.415098i
$256$		0			0
$257$	0.837662	+	2.09238i	0.0522519	+	0.130519i	0.952197	−	0.305484i	$-0.0988181\pi$
$257$	0.837662	+	2.09238i	0.0522519	+	0.130519i	−0.899945	+	0.436003i	$0.856394\pi$
$258$		0			0
$259$	17.5547	+	8.01697i	1.09080	+	0.498150i
$260$		0			0
$261$	2.91991	−	24.1922i	0.180738	−	1.49746i
$262$		0			0
$263$	12.2448	+	1.76054i	0.755047	+	0.108559i	0.509081	−	0.860719i	$-0.329985\pi$
$263$	12.2448	+	1.76054i	0.755047	+	0.108559i	0.245967	+	0.969278i	$0.420895\pi$
$264$		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	$-0.708528\pi$
$269$		−	26.0117i		−	1.58596i	0.609246	−	0.792981i	$-0.291472\pi$
$270$		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
$273$	−5.76129	−	1.47390i	−0.348689	−	0.0892048i
$274$		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
$279$	−4.94461	−	29.6064i	−0.296026	−	1.77249i
$280$		0			0
$281$	−1.23763	+	1.18007i	−0.0738306	+	0.0703973i	−0.726096	−	0.687593i	$-0.758667\pi$
$281$	−1.23763	+	1.18007i	−0.0738306	+	0.0703973i	0.652265	+	0.757991i	$0.273819\pi$
$282$		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
$285$	6.82847	−	1.56676i	0.404483	−	0.0928069i
$286$		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
$291$	−0.584562	+	9.72164i	−0.0342676	+	0.569893i
$292$		0			0
$293$	4.96968	−	16.9252i	0.290332	−	0.988779i	−0.677152	−	0.735844i	$-0.736786\pi$
$293$	4.96968	−	16.9252i	0.290332	−	0.988779i	0.967483	−	0.252935i	$-0.0813960\pi$
$294$		0			0
$295$	−4.51599	+	0.649302i	−0.262931	+	0.0378038i
$296$		0			0
$297$	−30.8378	+	6.27123i	−1.78939	+	0.363894i
$298$		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
$303$	13.5927	+	2.12748i	0.780878	+	0.122221i
$304$		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
$309$	0.666241	−	2.16869i	0.0379011	−	0.123372i
$310$		0			0
$311$	−15.3682	+	17.7358i	−0.871450	+	1.00571i	0.128452	+	0.991716i	$0.458999\pi$
$311$	−15.3682	+	17.7358i	−0.871450	+	1.00571i	−0.999902	+	0.0139911i	$0.995546\pi$
$312$		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
$315$	6.80411	−	8.22202i	0.383368	−	0.463259i
$316$		0			0
$317$	−1.89899	−	9.85288i	−0.106658	−	0.553393i	−0.995466	−	0.0951144i	$-0.969678\pi$
$317$	−1.89899	−	9.85288i	−0.106658	−	0.553393i	0.888809	−	0.458279i	$-0.151534\pi$
$318$		0			0
$319$	−30.4085	+	38.6676i	−1.70255	+	2.16497i
$320$		0			0
$321$	1.96648	+	2.83565i	0.109758	+	0.158271i
$322$		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
$327$	−4.03535	+	0.725733i	−0.223155	+	0.0401331i
$328$		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
$333$	7.97181	+	18.6735i	0.436852	+	1.02330i
$334$		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
$339$	−32.7657	−	15.4598i	−1.77959	−	0.839660i
$340$		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
$345$	9.57085	−	3.69393i	0.515277	−	0.198875i
$346$		0			0
$347$	−3.60288	−	14.8513i	−0.193413	−	0.797258i	−0.982998	−	0.183617i	$-0.941219\pi$
$347$	−3.60288	−	14.8513i	−0.193413	−	0.797258i	0.789585	−	0.613641i	$-0.210296\pi$
$348$		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
$351$	−3.43621	−	5.22851i	−0.183412	−	0.279077i
$352$		0			0
$353$	5.06534	−	0.976265i	0.269601	−	0.0519613i	−0.0526590	−	0.998613i	$-0.516770\pi$
$353$	5.06534	−	0.976265i	0.269601	−	0.0519613i	0.322260	+	0.946651i	$0.395558\pi$
$354$		0			0
$355$	−8.26597	+	16.0337i	−0.438712	+	0.850982i
$356$		0			0
$357$	−15.6382	+	19.3837i	−0.827660	+	1.02589i
$358$		0			0
$359$	14.2243	+	12.3254i	0.750730	+	0.650511i	0.943741	−	0.330685i	$-0.107280\pi$
$359$	14.2243	+	12.3254i	0.750730	+	0.650511i	−0.193011	+	0.981197i	$0.561825\pi$
$360$		0			0
$361$	−8.33487	−	1.60641i	−0.438677	−	0.0845481i
$362$		0			0
$363$	41.8444	+	15.0688i	2.19626	+	0.790905i
$364$		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
$369$	9.50031	−	8.61702i	0.494566	−	0.448584i
$370$		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
$375$	−18.2341	+	0.641049i	−0.941605	+	0.0331036i
$376$		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
$381$	9.19623	+	14.7093i	0.471137	+	0.753582i
$382$		0			0
$383$	−12.6317	−	1.20618i	−0.645447	−	0.0616327i	−0.232801	−	0.972524i	$-0.574789\pi$
$383$	−12.6317	−	1.20618i	−0.645447	−	0.0616327i	−0.412646	+	0.910892i	$0.635395\pi$
$384$		0			0
$385$	−20.3596	+	7.04652i	−1.03762	+	0.359124i
$386$		0			0
$387$	−17.5191	+	3.79059i	−0.890547	+	0.192686i
$388$		0			0
$389$	16.4064	+	17.2065i	0.831837	+	0.872406i	0.993429	−	0.114452i	$-0.0365112\pi$
$389$	16.4064	+	17.2065i	0.831837	+	0.872406i	−0.161591	+	0.986858i	$0.551663\pi$
$390$		0			0
$391$	−22.2259	+	8.89792i	−1.12401	+	0.449987i
$392$		0			0
$393$	19.9101	−	33.5141i	1.00433	−	1.69056i
$394$		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
$399$	14.3231	−	7.15963i	0.717050	−	0.358430i
$400$		0			0
$401$	−9.84306			−0.491539			−0.245770	−	0.969328i	$-0.579041\pi$
$401$	−9.84306			−0.491539			−0.245770	+	0.969328i	$0.579041\pi$
$402$		0			0
$403$	−12.0474			−0.600124
$404$		0			0
$405$	11.1174	−	1.57313i	0.552429	−	0.0781697i
$406$		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
$411$	2.51965	+	1.49688i	0.124285	+	0.0738355i
$412$		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
$417$	10.7010	+	32.2114i	0.524032	+	1.57740i
$418$		0			0
$419$	9.38589	−	3.24849i	0.458531	−	0.158699i	−0.0880313	−	0.996118i	$-0.528058\pi$
$419$	9.38589	−	3.24849i	0.458531	−	0.158699i	0.546562	+	0.837419i	$0.315936\pi$
$420$		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
$423$	7.82397	+	16.1521i	0.380414	+	0.785344i
$424$		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
$429$	0.443767	+	12.6226i	0.0214253	+	0.609424i
$430$		0			0
$431$	6.87919	−	3.97170i	0.331359	−	0.191310i	−0.325085	−	0.945685i	$-0.605393\pi$
$431$	6.87919	−	3.97170i	0.331359	−	0.191310i	0.656444	+	0.754375i	$0.272060\pi$
$432$		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
$435$	11.6583	−	13.1205i	0.558974	−	0.629082i
$436$		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
$441$	1.48586	−	3.05010i	0.0707550	−	0.145243i
$442$		0			0
$443$	9.59946	+	1.85014i	0.456084	+	0.0879030i	0.412119	−	0.911130i	$-0.364789\pi$
$443$	9.59946	+	1.85014i	0.456084	+	0.0879030i	0.0439651	+	0.999033i	$0.486001\pi$
$444$		0			0
$445$	14.9357	+	12.9418i	0.708019	+	0.613502i
$446$		0			0
$447$	10.9111	+	8.80280i	0.516079	+	0.416358i
$448$		0			0
$449$	−12.6532	+	24.5438i	−0.597141	+	1.15829i	0.375683	+	0.926748i	$0.377408\pi$
$449$	−12.6532	+	24.5438i	−0.597141	+	1.15829i	−0.972824	+	0.231544i	$0.925622\pi$
$450$		0			0
$451$	−25.4246	+	4.90019i	−1.19720	+	0.230741i
$452$		0			0
$453$	−17.9360	+	18.3476i	−0.842707	+	0.862043i
$454$		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
$459$	−25.8964	+	3.99406i	−1.20874	+	0.186427i
$460$		0			0
$461$	−7.46037	−	25.4077i	−0.347464	−	1.18335i	−0.929077	−	0.369888i	$-0.879396\pi$
$461$	−7.46037	−	25.4077i	−0.347464	−	1.18335i	0.581613	−	0.813466i	$-0.302422\pi$
$462$		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
$465$	9.22577	−	19.5533i	0.427835	−	0.906761i
$466$		0			0
$467$	−21.5349	+	15.3349i	−0.996516	+	0.709616i	−0.957145	−	0.289609i	$-0.906475\pi$
$467$	−21.5349	+	15.3349i	−0.996516	+	0.709616i	−0.0393712	+	0.999225i	$0.512535\pi$
$468$		0			0
$469$	14.8934	+	17.9711i	0.687713	+	0.829826i
$470$		0			0
$471$	5.73466	−	3.21633i	0.264239	−	0.148201i
$472$		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
$477$	28.3291	−	1.99438i	1.29710	−	0.0913163i
$478$		0			0
$479$	−14.2559	−	27.6526i	−0.651368	−	1.26348i	−0.950932	−	0.309401i	$-0.899871\pi$
$479$	−14.2559	−	27.6526i	−0.651368	−	1.26348i	0.299563	−	0.954076i	$-0.403159\pi$
$480$		0			0
$481$	7.91946	−	1.92124i	0.361096	−	0.0876010i
$482$		0			0
$483$	19.2682	−	13.3622i	0.876733	−	0.608002i
$484$		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
$489$	−7.06136	+	10.6924i	−0.319326	+	0.483529i
$490$		0			0
$491$	9.07689	−	14.1239i	0.409634	−	0.637403i	−0.573731	−	0.819044i	$-0.694504\pi$
$491$	9.07689	−	14.1239i	0.409634	−	0.637403i	0.983365	+	0.181641i	$0.0581408\pi$
$492$		0			0
$493$	−26.8229	+	30.9553i	−1.20804	+	1.39416i
$494$		0			0
$495$	−20.8266	−	8.94598i	−0.936087	−	0.402092i
$496$		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
$501$	2.61162	−	16.6858i	0.116678	−	0.745468i
$502$		0			0
$503$	−2.49099	+	3.49810i	−0.111068	+	0.155973i	−0.866368	−	0.499406i	$-0.833552\pi$
$503$	−2.49099	+	3.49810i	−0.111068	+	0.155973i	0.755300	+	0.655379i	$0.227491\pi$
$504$		0			0
$505$	7.17207	+	6.83856i	0.319153	+	0.304312i
$506$		0			0
$507$	18.2998	−	8.08325i	0.812722	−	0.358990i
$508$		0			0
$509$	−21.5661	+	3.10074i	−0.955903	+	0.137438i	−0.602576	−	0.798062i	$-0.705859\pi$
$509$	−21.5661	+	3.10074i	−0.955903	+	0.137438i	−0.353327	+	0.935500i	$0.614950\pi$
$510$		0			0
$511$	6.42192	−	21.8710i	0.284089	−	0.967518i
$512$		0			0
$513$	16.2121	+	4.58076i	0.715784	+	0.202245i
$514$		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
$519$	3.43152	+	14.9557i	0.150627	+	0.656482i
$520$		0			0
$521$	−4.00476	−	8.76920i	−0.175452	−	0.384186i	0.801392	−	0.598139i	$-0.204093\pi$
$521$	−4.00476	−	8.76920i	−0.175452	−	0.384186i	−0.976844	+	0.213954i	$0.931366\pi$
$522$		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
$525$	−16.3769	+	4.58788i	−0.714747	+	0.200232i
$526$		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
$531$	−10.2751	−	3.84548i	−0.445902	−	0.166880i
$532$		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
$543$	−0.114665	+	9.20382i	−0.00492073	+	0.394974i
$544$		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
$549$	1.19914	+	1.97226i	0.0511781	+	0.0841742i
$550$		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
$555$	−2.94641	+	14.3248i	−0.125068	+	0.608052i
$556$		0			0
$557$	−5.97109	−	7.59286i	−0.253003	−	0.321720i	0.642916	−	0.765937i	$-0.277724\pi$
$557$	−5.97109	−	7.59286i	−0.253003	−	0.321720i	−0.895919	+	0.444217i	$0.853482\pi$
$558$		0			0
$559$	0.342313	+	7.18603i	0.0144783	+	0.303937i
$560$		0			0
$561$	48.8584	+	20.2697i	2.06280	+	0.855789i
$562$		0			0
$563$	1.64096	+	11.4132i	0.0691584	+	0.481007i	0.994738	+	0.102454i	$0.0326693\pi$
$563$	1.64096	+	11.4132i	0.0691584	+	0.481007i	−0.925579	+	0.378553i	$0.876422\pi$
$564$		0			0
$565$	−13.0479	−	22.5997i	−0.548930	−	0.950775i
$566$		0			0
$567$	23.8462	−	9.48490i	1.00145	−	0.398329i
$568$		0			0
$569$	−11.1066	−	7.90898i	−0.465613	−	0.331562i	0.323056	−	0.946380i	$-0.395290\pi$
$569$	−11.1066	−	7.90898i	−0.465613	−	0.331562i	−0.788669	+	0.614818i	$0.789229\pi$
$570$		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
$573$	−18.8555	−	13.7841i	−0.787700	−	0.575841i
$574$		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
$579$	1.95510	+	2.10227i	0.0812510	+	0.0873674i
$580$		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
$585$	0.112271	−	4.50514i	0.00464183	−	0.186265i
$586$		0			0
$587$	−23.1431	−	18.1999i	−0.955217	−	0.751191i	0.0133582	−	0.999911i	$-0.495748\pi$
$587$	−23.1431	−	18.1999i	−0.955217	−	0.751191i	−0.968576	+	0.248720i	$0.919990\pi$
$588$		0			0
$589$	24.5162	−	21.2434i	1.01017	−	0.875320i
$590$		0			0
$591$	−0.438341	+	0.0574600i	−0.0180309	+	0.00236359i
$592$		0			0
$593$	33.4171	−	17.2277i	1.37227	−	0.707457i	0.394851	−	0.918745i	$-0.370796\pi$
$593$	33.4171	−	17.2277i	1.37227	−	0.707457i	0.977424	+	0.211288i	$0.0677659\pi$
$594$		0			0
$595$	−17.2124	+	5.05401i	−0.705639	+	0.207194i
$596$		0			0
$597$	5.43848	−	10.2341i	0.222582	−	0.418854i
$598$		0			0
$599$	−1.91514	+	5.53343i	−0.0782505	+	0.226090i	−0.977340	−	0.211674i	$-0.932108\pi$
$599$	−1.91514	+	5.53343i	−0.0782505	+	0.226090i	0.899090	+	0.437764i	$0.144230\pi$
$600$		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
$603$	−1.15102	+	24.5291i	−0.0468733	+	0.998901i
$604$		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
$609$	18.8253	−	35.4254i	0.762840	−	1.43551i
$610$		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
$615$	9.16011	−	1.20075i	0.369371	−	0.0484191i
$616$		0			0
$617$	6.20162	−	5.37373i	0.249668	−	0.216338i	−0.521031	−	0.853537i	$-0.674453\pi$
$617$	6.20162	−	5.37373i	0.249668	−	0.216338i	0.770699	+	0.637199i	$0.219907\pi$
$618$		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
$621$	24.4529	+	3.26093i	0.981262	+	0.130856i
$622$		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
$627$	−23.1607	−	24.9042i	−0.924949	−	0.994577i
$628$		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
$633$	2.42363	+	1.77177i	0.0963305	+	0.0704215i
$634$		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
$639$	−35.9505	+	24.2735i	−1.42218	+	0.960247i
$640$		0			0
$641$	−17.5025	−	30.3151i	−0.691305	−	1.19738i	−0.971410	−	0.237407i	$-0.923703\pi$
$641$	−17.5025	−	30.3151i	−0.691305	−	1.19738i	0.280105	−	0.959969i	$-0.409631\pi$
$642$		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
$645$	−11.9253	−	4.94740i	−0.469557	−	0.194804i
$646$		0			0
$647$	−0.0372958	−	0.782935i	−0.00146625	−	0.0307804i	0.998016	−	0.0629665i	$-0.0200561\pi$
$647$	−0.0372958	−	0.782935i	−0.00146625	−	0.0307804i	−0.999482	+	0.0321861i	$0.989753\pi$
$648$		0			0
$649$	13.6909	+	17.4094i	0.537414	+	0.683377i
$650$		0			0
$651$	9.95581	−	48.4029i	0.390199	−	1.89706i
$652$		0			0
$653$	−4.66960	−	13.4919i	−0.182735	−	0.527979i	0.816011	−	0.578036i	$-0.196181\pi$
$653$	−4.66960	−	13.4919i	−0.182735	−	0.527979i	−0.998746	+	0.0500571i	$0.984060\pi$
$654$		0			0
$655$	25.5409	−	11.6642i	0.997967	−	0.455756i
$656$		0			0
$657$	20.4914	−	12.4588i	0.799445	−	0.486065i
$658$		0			0
$659$	6.02945	+	15.0608i	0.234874	+	0.586687i	0.998242	−	0.0592776i	$-0.0188797\pi$
$659$	6.02945	+	15.0608i	0.234874	+	0.586687i	−0.763368	+	0.645964i	$0.776455\pi$
$660$		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
$663$	−0.131011	+	10.5159i	−0.00508804	+	0.408403i
$664$		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
$675$	−15.9872	−	8.03609i	−0.615347	−	0.309309i
$676$		0			0
$677$	−44.6510	+	4.26366i	−1.71608	+	0.163866i	−0.906233	−	0.422778i	$-0.861055\pi$
$677$	−44.6510	+	4.26366i	−1.71608	+	0.163866i	−0.809845	+	0.586644i	$0.800449\pi$
$678$		0			0
$679$	−6.66062	+	14.5847i	−0.255611	+	0.559710i
$680$		0			0
$681$	−34.1811	+	9.57561i	−1.30982	+	0.366938i
$682$		0			0
$683$	−4.89897	+	4.67116i	−0.187454	+	0.178737i	−0.777995	−	0.628271i	$-0.783763\pi$
$683$	−4.89897	+	4.67116i	−0.187454	+	0.178737i	0.590541	+	0.807008i	$0.298915\pi$
$684$		0			0
$685$	0.876931	+	1.92021i	0.0335058	+	0.0733675i
$686$		0			0
$687$	−2.01194	−	8.76871i	−0.0767604	−	0.334547i
$688$		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
$693$	−51.0805	−	8.64821i	−1.94039	−	0.328518i
$694$		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
$699$	25.9295	−	11.4534i	0.980745	−	0.433208i
$700$		0			0
$701$	25.8412	+	24.6396i	0.976009	+	0.930623i	0.997607	−	0.0691436i	$-0.0220267\pi$
$701$	25.8412	+	24.6396i	0.976009	+	0.930623i	−0.0215972	+	0.999767i	$0.506875\pi$
$702$		0			0
$703$	−12.7282	+	17.8742i	−0.480052	+	0.674139i
$704$		0			0
$705$	−1.99899	+	12.7717i	−0.0752864	+	0.481011i
$706$		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
$711$	−7.17783	+	16.7103i	−0.269190	+	0.626685i
$712$		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
$717$	2.84886	−	4.31380i	0.106393	−	0.161102i
$718$		0			0
$719$	0.787928	+	4.08816i	0.0293847	+	0.152463i	0.993658	−	0.112449i	$-0.0358694\pi$
$719$	0.787928	+	4.08816i	0.0293847	+	0.152463i	−0.964273	+	0.264911i	$0.914657\pi$
$720$		0			0
$721$	2.30882	−	2.93591i	0.0859850	−	0.109339i
$722$		0			0
$723$	30.9172	−	21.4406i	1.14982	−	0.797386i
$724$		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
$729$	25.2659	+	9.52014i	0.935775	+	0.352598i
$730$		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
$735$	2.13142	−	1.19542i	0.0786187	−	0.0440939i
$736$		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
$741$	2.88530	−	6.11515i	0.105994	−	0.224646i
$742$		0			0
$743$	7.33380	−	18.3190i	0.269051	−	0.672057i	−0.730894	−	0.682490i	$-0.760897\pi$
$743$	7.33380	−	18.3190i	0.269051	−	0.672057i	0.999946	+	0.0104334i	$0.00332110\pi$
$744$		0			0
$745$	2.84492	+	9.68892i	0.104230	+	0.354975i
$746$		0			0
$747$	−5.60904	−	21.0270i	−0.205224	−	0.769338i
$748$		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
$753$	−15.3007	+	15.6518i	−0.557588	+	0.570382i
$754$		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
$759$	−38.7597	−	31.2702i	−1.40689	−	1.13504i
$760$		0			0
$761$	10.5028	+	9.10074i	0.380727	+	0.329902i	0.824109	−	0.566431i	$-0.191676\pi$
$761$	10.5028	+	9.10074i	0.380727	+	0.329902i	−0.443382	+	0.896333i	$0.646222\pi$
$762$		0			0
$763$	−6.62800	−	1.27744i	−0.239950	−	0.0462465i
$764$		0			0
$765$	−16.9672	−	8.26557i	−0.613451	−	0.298842i
$766$		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
$771$	−2.59296	+	2.91817i	−0.0933831	+	0.105095i
$772$		0			0
$773$	−15.8781	+	16.6525i	−0.571095	+	0.598947i	−0.944415	−	0.328755i	$-0.893371\pi$
$773$	−15.8781	+	16.6525i	−0.571095	+	0.598947i	0.373320	+	0.927703i	$0.378219\pi$
$774$		0			0
$775$	−29.8385	+	17.2272i	−1.07183	+	0.618821i
$776$		0			0
$777$	1.17443	+	33.4057i	0.0421325	+	1.19842i
$778$		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
$783$	39.7416	−	14.2115i	1.42025	−	0.507876i
$784$		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
$789$	6.75521	+	20.3340i	0.240492	+	0.723910i
$790$		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
$795$	17.5863	+	10.4477i	0.623721	+	0.370541i
$796$		0			0
$797$	0.971008	+	10.1689i	0.0343949	+	0.360199i	0.996242	+	0.0866123i	$0.0276041\pi$
$797$	0.971008	+	10.1689i	0.0343949	+	0.360199i	−0.961847	+	0.273587i	$0.911790\pi$
$798$		0			0
$799$	4.29330	−	29.8606i	0.151886	−	1.05639i
$800$		0			0
$801$	16.5578	+	44.5450i	0.585042	+	1.57392i
$802$		0			0
$803$	−48.4126			−1.70844
$804$		0			0
$805$	16.8893			0.595271
$806$		0			0
$807$	40.2993	−	20.1443i	1.41860	−	0.709113i
$808$		0			0
$809$	−5.16569	+	35.9281i	−0.181616	+	1.26317i	0.671327	+	0.741161i	$0.265725\pi$
$809$	−5.16569	+	35.9281i	−0.181616	+	1.26317i	−0.852943	+	0.522005i	$0.825184\pi$
$810$		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
$813$	−9.75916	+	16.4273i	−0.342269	+	0.576131i
$814$		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
$819$	−2.17824	−	10.0673i	−0.0761139	−	0.351779i
$820$		0			0
$821$	14.2922	−	4.94658i	0.498801	−	0.172637i	−0.0660714	−	0.997815i	$-0.521046\pi$
$821$	14.2922	−	4.94658i	0.498801	−	0.172637i	0.564873	+	0.825178i	$0.308925\pi$
$822$		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
$825$	19.1488	+	30.6285i	0.666677	+	1.06635i
$826$		0			0
$827$	−11.3400	+	0.540190i	−0.394330	+	0.0187842i	−0.243811	−	0.969823i	$-0.578398\pi$
$827$	−11.3400	+	0.540190i	−0.394330	+	0.0187842i	−0.150519	+	0.988607i	$0.548095\pi$
$828$		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
$831$	52.7057	−	1.85295i	1.82834	−	0.0642783i
$832$		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
$837$	42.0392	−	30.5887i	1.45309	−	1.05730i
$838$		0			0
$839$	−56.3355	−	2.68359i	−1.94492	−	0.0926478i	−0.961590	−	0.274490i	$-0.911491\pi$
$839$	−56.3355	−	2.68359i	−1.94492	−	0.0926478i	−0.983328	+	0.181842i	$0.941794\pi$
$840$		0			0
$841$	18.4882	−	32.0225i	0.637525	−	1.10423i
$842$		0			0
$843$	−2.78672	−	1.00354i	−0.0959797	−	0.0345637i
$844$		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
$849$	−16.4783	+	20.4250i	−0.565533	+	0.700984i
$850$		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
$855$	7.71552	+	9.36583i	0.263865	+	0.320305i
$856$		0			0
$857$	−20.8721	−	24.0877i	−0.712976	−	0.822819i	0.277468	−	0.960735i	$-0.410505\pi$
$857$	−20.8721	−	24.0877i	−0.712976	−	0.822819i	−0.990444	+	0.137916i	$0.955959\pi$
$858$		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
$861$	19.6993	−	7.60307i	0.671351	−	0.259112i
$862$		0			0
$863$	1.52699	+	5.20045i	0.0519793	+	0.177025i	0.981391	−	0.192019i	$-0.0615034\pi$
$863$	1.52699	+	5.20045i	0.0519793	+	0.177025i	−0.929412	+	0.369044i	$0.879685\pi$
$864$		0			0
$865$	−4.10773	+	10.2606i	−0.139667	+	0.348871i
$866$		0			0
$867$	13.2032	+	6.22965i	0.448405	+	0.211570i
$868$		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
$873$	−15.5142	+	6.62310i	−0.525076	+	0.224158i
$874$		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
$879$	30.0704	−	5.40799i	1.01425	−	0.182407i
$880$		0			0
$881$	−1.39306	−	2.70216i	−0.0469334	−	0.0910381i	0.864202	−	0.503144i	$-0.167824\pi$
$881$	−1.39306	−	2.70216i	−0.0469334	−	0.0910381i	−0.911136	+	0.412106i	$0.864793\pi$
$882$		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
$885$	−4.50328	−	6.49368i	−0.151376	−	0.218283i
$886$		0			0
$887$	31.9992	−	40.6903i	1.07443	−	1.36625i	0.148340	−	0.988936i	$-0.452607\pi$
$887$	31.9992	−	40.6903i	1.07443	−	1.36625i	0.926087	−	0.377309i	$-0.123151\pi$
$888$		0			0
$889$	5.40486	+	28.0431i	0.181273	+	0.940535i
$890$		0			0
$891$	−33.5976	−	42.9195i	−1.12556	−	1.43786i
$892$		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
$897$	2.90765	−	9.46475i	0.0970837	−	0.316019i
$898$		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
$903$	−29.1542	−	4.56313i	−0.970191	−	0.151851i
$904$		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
$909$	7.23053	+	22.7064i	0.239822	+	0.753123i
$910$		0			0
$911$	48.9168	−	7.03318i	1.62069	−	0.233020i	0.728619	−	0.684920i	$-0.240163\pi$
$911$	48.9168	−	7.03318i	1.62069	−	0.233020i	0.892069	+	0.451900i	$0.149254\pi$
$912$		0			0
$913$	−12.3771	+	42.1527i	−0.409624	+	1.39505i
$914$		0			0
$915$	−0.0997896	+	1.65957i	−0.00329894	+	0.0548636i
$916$		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
$921$	15.3018	−	3.51093i	0.504212	−	0.115689i
$922$		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
$927$	3.87586	−	0.647312i	0.127300	−	0.0212605i
$928$		0			0
$929$	−10.8647	+	23.7904i	−0.356459	+	0.780536i	0.643428	+	0.765507i	$0.277512\pi$
$929$	−10.8647	+	23.7904i	−0.356459	+	0.780536i	−0.999887	+	0.0150297i	$0.995216\pi$
$930$		0			0
$931$	3.65005	−	0.348538i	0.119626	−	0.0114229i
$932$		0			0
$933$	−39.3793	−	10.0744i	−1.28922	−	0.329820i
$934$		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	−0.994358	−	0.106075i	$-0.966172\pi$
$941$	−40.2140	+	25.8440i	−1.31094	+	0.842490i	−0.316582	+	0.948565i	$0.602535\pi$
$942$		0			0
$943$	20.0913	+	2.88869i	0.654261	+	0.0940686i
$944$		0			0
$945$	18.0075	+	4.17405i	0.585784	+	0.135782i
$946$		0			0
$947$	19.6475	+	8.97272i	0.638459	+	0.291574i	0.708223	−	0.705989i	$-0.249497\pi$
$947$	19.6475	+	8.97272i	0.638459	+	0.291574i	−0.0697639	+	0.997564i	$0.522225\pi$
$948$		0			0
$949$	−3.57735	−	8.93580i	−0.116126	−	0.290068i
$950$		0			0
$951$	13.7942	−	10.5724i	0.447308	−	0.342835i
$952$		0			0
$953$	−42.6814	+	19.4920i	−1.38259	+	0.631407i	−0.961296	−	0.275519i	$-0.911150\pi$
$953$	−42.6814	+	19.4920i	−1.38259	+	0.631407i	−0.421292	+	0.906925i	$0.638423\pi$
$954$		0			0
$955$	−5.50243	−	15.8982i	−0.178054	−	0.514454i
$956$		0			0
$957$	−83.4560	−	17.1658i	−2.69775	−	0.554891i
$958$		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
$963$	−2.87030	+	5.24265i	−0.0924940	+	0.168942i
$964$		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
$969$	−18.2762	−	21.6306i	−0.587117	−	0.694874i
$970$		0			0
$971$	4.56380	+	3.24987i	0.146459	+	0.104293i	0.650938	−	0.759131i	$-0.274376\pi$
$971$	4.56380	+	3.24987i	0.146459	+	0.104293i	−0.504479	+	0.863424i	$0.668315\pi$
$972$		0			0
$973$	−2.65885	+	55.8161i	−0.0852388	+	1.78938i
$974$		0			0
$975$	−4.23831	+	5.79764i	−0.135735	+	0.185673i
$976$		0			0
$977$	−30.0350	−	7.28642i	−0.960906	−	0.233113i	−0.275522	−	0.961295i	$-0.588851\pi$
$977$	−30.0350	−	7.28642i	−0.960906	−	0.233113i	−0.685384	+	0.728182i	$0.740366\pi$
$978$		0			0
$979$	18.1560	−	94.2022i	0.580268	−	3.01072i
$980$		0			0
$981$	−4.24946	−	5.68983i	−0.135675	−	0.181662i
$982$		0			0
$983$	−8.30467	−	5.33709i	−0.264878	−	0.170227i	0.401460	−	0.915877i	$-0.368503\pi$
$983$	−8.30467	−	5.33709i	−0.264878	−	0.170227i	−0.666338	+	0.745650i	$0.732139\pi$
$984$		0			0
$985$	−0.283034	−	0.145914i	−0.00901821	−	0.00464921i
$986$		0			0
$987$	2.44196	+	29.4456i	0.0777286	+	0.937264i
$988$		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
$993$	5.59853	+	42.7091i	0.177664	+	1.35533i
$994$		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
$999$	−22.7567	+	26.8119i	−0.719991	+	0.848289i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(0.774432 + 1.54928i) q^{3} +(-0.177548 + 1.23488i) q^{5} +(0.271050 + 2.83857i) q^{7} +(-1.80051 + 2.39962i) q^{9} +O(q^{10})\)	\(q+(0.774432 + 1.54928i) q^{3} +(-0.177548 + 1.23488i) q^{5} +(0.271050 + 2.83857i) q^{7} +(-1.80051 + 2.39962i) q^{9} +(5.62239 - 2.25086i) q^{11} +(0.830910 + 0.871434i) q^{13} +(-2.05066 + 0.681255i) q^{15} +(4.76535 - 1.64930i) q^{17} +(-3.22750 - 0.308189i) q^{19} +(-4.18781 + 2.61821i) q^{21} +(-4.74225 + 0.225901i) q^{23} +(3.30407 + 0.970163i) q^{25} +(-5.11204 - 0.931149i) q^{27} +(-7.03437 + 4.06129i) q^{29} +(-6.90458 + 7.24131i) q^{31} +(7.84136 + 6.96749i) q^{33} +(-3.55340 - 0.169269i) q^{35} +(3.38398 - 5.86123i) q^{37} +(-0.706608 + 1.96218i) q^{39} +(-4.19811 - 0.809119i) q^{41} +(4.51548 + 3.91269i) q^{43} +(-2.64355 - 2.64945i) q^{45} +(2.74131 - 5.31740i) q^{47} +(-1.11049 + 0.214029i) q^{49} +(6.24567 + 6.10557i) q^{51} +(-6.19918 - 7.15424i) q^{53} +(1.78129 + 7.34258i) q^{55} +(-2.02201 - 5.23896i) q^{57} +(1.03031 + 3.50891i) q^{59} +(0.285957 - 0.714285i) q^{61} +(-7.29950 - 4.46045i) q^{63} +(-1.22364 + 0.871349i) q^{65} +(6.77031 - 4.60032i) q^{67} +(-4.02253 - 7.17211i) q^{69} +(13.6640 + 4.72917i) q^{71} +(-7.42126 - 2.97103i) q^{73} +(1.05573 + 5.87024i) q^{75} +(7.91317 + 15.3494i) q^{77} +(5.89134 - 1.42922i) q^{79} +(-2.51632 - 8.64107i) q^{81} +(-4.48418 + 5.70210i) q^{83} +(1.19061 + 6.17745i) q^{85} +(-11.7397 - 7.75298i) q^{87} +(8.56425 - 13.3262i) q^{89} +(-2.24840 + 2.59480i) q^{91} +(-16.5659 - 5.08919i) q^{93} +(0.953612 - 3.93084i) q^{95} +(4.86960 + 2.81147i) q^{97} +(-4.72196 + 17.5443i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 12 q^{7} + 4 q^{9}+O(q^{10}) \) 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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