LMFDB - Embedded newform 819.2.bm.h.478.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(478,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 5]))

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

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

chi := DirichletCharacter("819.478");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.bm (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			478.3
Character	$\chi$	$=$	819.478
Dual form			819.2.bm.h.550.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.24196i q^{2} -3.02638 q^{4} +(-0.550805 - 0.318007i) q^{5} +(0.958080 - 2.46619i) q^{7} +2.30110i q^{8} +O(q^{10})$	\(q-2.24196i q^{2} -3.02638 q^{4} +(-0.550805 - 0.318007i) q^{5} +(0.958080 - 2.46619i) q^{7} +2.30110i q^{8} +(-0.712960 + 1.23488i) q^{10} +(-2.45100 - 1.41508i) q^{11} +(3.56752 + 0.522308i) q^{13} +(-5.52909 - 2.14798i) q^{14} -0.893779 q^{16} -4.82375 q^{17} +(1.33734 - 0.772111i) q^{19} +(1.66695 + 0.962411i) q^{20} +(-3.17256 + 5.49504i) q^{22} +0.194503 q^{23} +(-2.29774 - 3.97981i) q^{25} +(1.17099 - 7.99823i) q^{26} +(-2.89952 + 7.46362i) q^{28} +(-3.94391 - 6.83106i) q^{29} +(-2.83734 + 1.63814i) q^{31} +6.60603i q^{32} +10.8147i q^{34} +(-1.31198 + 1.05371i) q^{35} +11.2730i q^{37} +(-1.73104 - 2.99825i) q^{38} +(0.731768 - 1.26746i) q^{40} +(5.31403 - 3.06805i) q^{41} +(0.769777 - 1.33329i) q^{43} +(7.41765 + 4.28258i) q^{44} -0.436067i q^{46} +(-5.32055 - 3.07182i) q^{47} +(-5.16416 - 4.72561i) q^{49} +(-8.92257 + 5.15145i) q^{50} +(-10.7967 - 1.58070i) q^{52} +(3.88327 + 6.72602i) q^{53} +(0.900014 + 1.55887i) q^{55} +(5.67496 + 2.20464i) q^{56} +(-15.3150 + 8.84210i) q^{58} +9.86985i q^{59} +(3.40433 + 5.89647i) q^{61} +(3.67264 + 6.36119i) q^{62} +13.0229 q^{64} +(-1.79891 - 1.42219i) q^{65} +(-6.59441 - 3.80728i) q^{67} +14.5985 q^{68} +(2.36238 + 2.94141i) q^{70} +(-3.59586 - 2.07607i) q^{71} +(4.59778 - 2.65453i) q^{73} +25.2736 q^{74} +(-4.04729 + 2.33670i) q^{76} +(-5.83812 + 4.68886i) q^{77} +(1.64247 - 2.84485i) q^{79} +(0.492298 + 0.284228i) q^{80} +(-6.87845 - 11.9138i) q^{82} -15.4589i q^{83} +(2.65695 + 1.53399i) q^{85} +(-2.98919 - 1.72581i) q^{86} +(3.25626 - 5.64000i) q^{88} -2.22739i q^{89} +(4.70608 - 8.29776i) q^{91} -0.588639 q^{92} +(-6.88690 + 11.9285i) q^{94} -0.982148 q^{95} +(-5.19089 - 2.99696i) q^{97} +(-10.5946 + 11.5778i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 44 q^{4} + 8 q^{7}+O(q^{10}) $ 36 * q - 44 * q^4 + 8 * q^7	$ 36 q - 44 q^{4} + 8 q^{7} + 8 q^{10} + 52 q^{16} - 36 q^{19} + 2 q^{22} + 22 q^{25} + 16 q^{28} - 18 q^{31} - 34 q^{40} + 4 q^{43} + 12 q^{49} + 74 q^{52} - 22 q^{55} + 84 q^{58} - 54 q^{61} - 100 q^{64} + 36 q^{67} - 72 q^{70} - 30 q^{73} + 42 q^{76} + 40 q^{79} + 18 q^{82} + 12 q^{88} + 32 q^{91} - 56 q^{94} - 36 q^{97}+O(q^{100}) $ 36 * q - 44 * q^4 + 8 * q^7 + 8 * q^10 + 52 * q^16 - 36 * q^19 + 2 * q^22 + 22 * q^25 + 16 * q^28 - 18 * q^31 - 34 * q^40 + 4 * q^43 + 12 * q^49 + 74 * q^52 - 22 * q^55 + 84 * q^58 - 54 * q^61 - 100 * q^64 + 36 * q^67 - 72 * q^70 - 30 * q^73 + 42 * q^76 + 40 * q^79 + 18 * q^82 + 12 * q^88 + 32 * q^91 - 56 * q^94 - 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$		−	2.24196i		−	1.58530i	−0.609674	−	0.792652i	$-0.708700\pi$
$2$		−	2.24196i		−	1.58530i	0.609674	−	0.792652i	$-0.291300\pi$
$3$		0			0
$3$		0			0
$4$	−3.02638			−1.51319
$5$	−0.550805	−	0.318007i	−0.246327	−	0.142217i	0.371754	−	0.928331i	$-0.378756\pi$
$5$	−0.550805	−	0.318007i	−0.246327	−	0.142217i	−0.618081	+	0.786114i	$0.712090\pi$
$6$		0			0
$7$	0.958080	−	2.46619i	0.362120	−	0.932131i
$7$	0.958080	−	2.46619i	0.362120	−	0.932131i
$8$			2.30110i			0.813563i
$9$		0			0
$10$	−0.712960	+	1.23488i	−0.225458	+	0.390504i
$11$	−2.45100	−	1.41508i	−0.739004	−	0.426664i	0.0827034	−	0.996574i	$-0.473645\pi$
$11$	−2.45100	−	1.41508i	−0.739004	−	0.426664i	−0.821707	+	0.569910i	$0.806978\pi$
$12$		0			0
$13$	3.56752	+	0.522308i	0.989452	+	0.144862i
$13$	3.56752	+	0.522308i	0.989452	+	0.144862i
$14$	−5.52909	−	2.14798i	−1.47771	−	0.574071i
$15$		0			0
$16$	−0.893779			−0.223445
$17$	−4.82375			−1.16993			−0.584966	−	0.811058i	$-0.698892\pi$
$17$	−4.82375			−1.16993			−0.584966	+	0.811058i	$0.698892\pi$
$18$		0			0
$19$	1.33734	−	0.772111i	0.306806	−	0.177134i	−0.338690	−	0.940898i	$-0.609984\pi$
$19$	1.33734	−	0.772111i	0.306806	−	0.177134i	0.645496	+	0.763763i	$0.276651\pi$
$20$	1.66695	+	0.962411i	0.372740	+	0.215202i
$21$		0			0
$22$	−3.17256	+	5.49504i	−0.676392	+	1.17155i
$23$	0.194503			0.0405566			0.0202783	−	0.999794i	$-0.493545\pi$
$23$	0.194503			0.0405566			0.0202783	+	0.999794i	$0.493545\pi$
$24$		0			0
$25$	−2.29774	−	3.97981i	−0.459549	−	0.795961i
$26$	1.17099	−	7.99823i	0.229651	−	1.56858i
$27$		0			0
$28$	−2.89952	+	7.46362i	−0.547957	+	1.41049i
$29$	−3.94391	−	6.83106i	−0.732367	−	1.26850i	−0.955869	−	0.293793i	$-0.905082\pi$
$29$	−3.94391	−	6.83106i	−0.732367	−	1.26850i	0.223502	−	0.974703i	$-0.428251\pi$
$30$		0			0
$31$	−2.83734	+	1.63814i	−0.509601	+	0.294218i	−0.732669	−	0.680585i	$-0.761726\pi$
$31$	−2.83734	+	1.63814i	−0.509601	+	0.294218i	0.223069	+	0.974803i	$0.428393\pi$
$32$			6.60603i			1.16779i
$33$		0			0
$34$			10.8147i			1.85470i
$35$	−1.31198	+	1.05371i	−0.221765	+	0.178110i
$36$		0			0
$37$			11.2730i			1.85327i	0.375960	+	0.926636i	$0.377313\pi$
$37$			11.2730i			1.85327i	−0.375960	+	0.926636i	$0.622687\pi$
$38$	−1.73104	−	2.99825i	−0.280812	−	0.486381i
$39$		0			0
$40$	0.731768	−	1.26746i	0.115703	−	0.200403i
$41$	5.31403	−	3.06805i	0.829911	−	0.479150i	−0.0239109	−	0.999714i	$-0.507612\pi$
$41$	5.31403	−	3.06805i	0.829911	−	0.479150i	0.853822	+	0.520565i	$0.174278\pi$
$42$		0			0
$43$	0.769777	−	1.33329i	0.117390	−	0.203325i	−0.801343	−	0.598206i	$-0.795881\pi$
$43$	0.769777	−	1.33329i	0.117390	−	0.203325i	0.918733	+	0.394880i	$0.129214\pi$
$44$	7.41765	+	4.28258i	1.11825	+	0.645624i
$45$		0			0
$46$		−	0.436067i		−	0.0642946i
$47$	−5.32055	−	3.07182i	−0.776082	−	0.448071i	0.0589577	−	0.998260i	$-0.481222\pi$
$47$	−5.32055	−	3.07182i	−0.776082	−	0.448071i	−0.835040	+	0.550189i	$0.814556\pi$
$48$		0			0
$49$	−5.16416	−	4.72561i	−0.737738	−	0.675087i
$50$	−8.92257	+	5.15145i	−1.26184	+	0.728524i
$51$		0			0
$52$	−10.7967	−	1.58070i	−1.49723	−	0.219204i
$53$	3.88327	+	6.72602i	0.533408	+	0.923890i	0.999239	+	0.0390160i	$0.0124223\pi$
$53$	3.88327	+	6.72602i	0.533408	+	0.923890i	−0.465830	+	0.884874i	$0.654244\pi$
$54$		0			0
$55$	0.900014	+	1.55887i	0.121358	+	0.210198i
$56$	5.67496	+	2.20464i	0.758348	+	0.294608i
$57$		0			0
$58$	−15.3150	+	8.84210i	−2.01095	+	1.16102i
$59$			9.86985i			1.28494i	0.766309	+	0.642472i	$0.222091\pi$
$59$			9.86985i			1.28494i	−0.766309	+	0.642472i	$0.777909\pi$
$60$		0			0
$61$	3.40433	+	5.89647i	0.435880	+	0.754966i	0.997367	−	0.0725196i	$-0.0231040\pi$
$61$	3.40433	+	5.89647i	0.435880	+	0.754966i	−0.561487	+	0.827485i	$0.689771\pi$
$62$	3.67264	+	6.36119i	0.466425	+	0.807872i
$63$		0			0
$64$	13.0229			1.62786
$65$	−1.79891	−	1.42219i	−0.223127	−	0.176401i
$66$		0			0
$67$	−6.59441	−	3.80728i	−0.805635	−	0.465134i	0.0398028	−	0.999208i	$-0.487327\pi$
$67$	−6.59441	−	3.80728i	−0.805635	−	0.465134i	−0.845438	+	0.534074i	$0.820660\pi$
$68$	14.5985			1.77033
$69$		0			0
$70$	2.36238	+	2.94141i	0.282358	+	0.351566i
$71$	−3.59586	−	2.07607i	−0.426750	−	0.246384i	0.271211	−	0.962520i	$-0.412576\pi$
$71$	−3.59586	−	2.07607i	−0.426750	−	0.246384i	−0.697961	+	0.716136i	$0.745909\pi$
$72$		0			0
$73$	4.59778	−	2.65453i	0.538129	−	0.310689i	−0.206191	−	0.978512i	$-0.566107\pi$
$73$	4.59778	−	2.65453i	0.538129	−	0.310689i	0.744320	+	0.667823i	$0.232774\pi$
$74$	25.2736			2.93800
$75$		0			0
$76$	−4.04729	+	2.33670i	−0.464256	+	0.268038i
$77$	−5.83812	+	4.68886i	−0.665315	+	0.534345i
$78$		0			0
$79$	1.64247	−	2.84485i	0.184793	−	0.320070i	−0.758714	−	0.651424i	$-0.774172\pi$
$79$	1.64247	−	2.84485i	0.184793	−	0.320070i	0.943507	+	0.331354i	$0.107505\pi$
$80$	0.492298	+	0.284228i	0.0550406	+	0.0317777i
$81$		0			0
$82$	−6.87845	−	11.9138i	−0.759598	−	1.31566i
$83$		−	15.4589i		−	1.69683i	−0.529329	−	0.848417i	$-0.677556\pi$
$83$		−	15.4589i		−	1.69683i	0.529329	−	0.848417i	$-0.322444\pi$
$84$		0			0
$85$	2.65695	+	1.53399i	0.288186	+	0.166384i
$86$	−2.98919	−	1.72581i	−0.322332	−	0.186099i
$87$		0			0
$88$	3.25626	−	5.64000i	0.347118	−	0.601226i
$89$		−	2.22739i		−	0.236103i	−0.993007	−	0.118052i	$-0.962335\pi$
$89$		−	2.22739i		−	0.236103i	0.993007	−	0.118052i	$-0.0376648\pi$
$90$		0			0
$91$	4.70608	−	8.29776i	0.493331	−	0.869841i
$92$	−0.588639			−0.0613699
$93$		0			0
$94$	−6.88690	+	11.9285i	−0.710330	+	1.23033i
$95$	−0.982148			−0.100766
$96$		0			0
$97$	−5.19089	−	2.99696i	−0.527055	−	0.304295i	0.212761	−	0.977104i	$-0.431754\pi$
$97$	−5.19089	−	2.99696i	−0.527055	−	0.304295i	−0.739816	+	0.672809i	$0.765088\pi$
$98$	−10.5946	+	11.5778i	−1.07022	+	1.16954i
$99$		0			0
$100$	6.95385	+	12.0444i	0.695385	+	1.20444i
$101$	6.41787	−	11.1161i	0.638602	−	1.10609i	−0.347138	−	0.937814i	$-0.612846\pi$
$101$	6.41787	−	11.1161i	0.638602	−	1.10609i	0.985740	−	0.168277i	$-0.0538203\pi$
$102$		0			0
$103$	8.92913	−	15.4657i	0.879813	−	1.52388i	0.0282671	−	0.999600i	$-0.491001\pi$
$103$	8.92913	−	15.4657i	0.879813	−	1.52388i	0.851546	−	0.524280i	$-0.175666\pi$
$104$	−1.20189	+	8.20924i	−0.117855	+	0.804982i
$105$		0			0
$106$	15.0795	−	8.70613i	1.46465	−	0.845614i
$107$	2.07850			0.200936			0.100468	−	0.994940i	$-0.467966\pi$
$107$	2.07850			0.200936			0.100468	+	0.994940i	$0.467966\pi$
$108$		0			0
$109$	8.68240	−	5.01278i	0.831623	−	0.480138i	−0.0227851	−	0.999740i	$-0.507253\pi$
$109$	8.68240	−	5.01278i	0.831623	−	0.480138i	0.854408	+	0.519603i	$0.173920\pi$
$110$	3.49492	−	2.01780i	0.333228	−	0.192389i
$111$		0			0
$112$	−0.856312	+	2.20423i	−0.0809139	+	0.208280i
$113$	0.0915059	−	0.158493i	0.00860815	−	0.0149098i	−0.861689	−	0.507436i	$-0.830593\pi$
$113$	0.0915059	−	0.158493i	0.00860815	−	0.0149098i	0.870297	+	0.492527i	$0.163927\pi$
$114$		0			0
$115$	−0.107133	−	0.0618533i	−0.00999021	−	0.00576785i
$116$	11.9358	+	20.6734i	1.10821	+	1.91948i
$117$		0			0
$118$	22.1278			2.03703
$119$	−4.62154	+	11.8963i	−0.423656	+	1.09053i
$120$		0			0
$121$	−1.49507	−	2.58954i	−0.135916	−	0.235413i
$122$	13.2196	−	7.63237i	1.19685	−	0.691002i
$123$		0			0
$124$	8.58686	−	4.95763i	0.771123	−	0.445208i
$125$			6.10287i			0.545857i
$126$		0			0
$127$	−6.69375	−	11.5939i	−0.593975	−	1.02879i	−0.993691	−	0.112155i	$-0.964225\pi$
$127$	−6.69375	−	11.5939i	−0.593975	−	1.02879i	0.399716	−	0.916639i	$-0.369109\pi$
$128$		−	15.9847i		−	1.41286i
$129$		0			0
$130$	−3.18849	+	4.03308i	−0.279649	+	0.353725i
$131$	8.28999	−	14.3587i	0.724300	−	1.25452i	−0.234962	−	0.972005i	$-0.575496\pi$
$131$	8.28999	−	14.3587i	0.724300	−	1.25452i	0.959262	−	0.282520i	$-0.0911702\pi$
$132$		0			0
$133$	−0.622896	−	4.03787i	−0.0540119	−	0.350127i
$134$	−8.53577	+	14.7844i	−0.737378	+	1.27718i
$135$		0			0
$136$		−	11.1000i		−	0.951814i
$137$			18.6411i			1.59261i	0.604894	+	0.796306i	$0.293216\pi$
$137$			18.6411i			1.59261i	−0.604894	+	0.796306i	$0.706784\pi$
$138$		0			0
$139$	−1.74420	+	3.02104i	−0.147941	+	0.256241i	−0.930466	−	0.366377i	$-0.880598\pi$
$139$	−1.74420	+	3.02104i	−0.147941	+	0.256241i	0.782525	+	0.622619i	$0.213931\pi$
$140$	3.97056	−	3.18893i	0.335573	−	0.269514i
$141$		0			0
$142$	−4.65446	+	8.06177i	−0.390594	+	0.676529i
$143$	−8.00487	−	6.32852i	−0.669401	−	0.529217i
$144$		0			0
$145$			5.01678i			0.416621i
$146$	−5.95135	−	10.3080i	−0.492537	−	0.853099i
$147$		0			0
$148$		−	34.1164i		−	2.80435i
$149$	−7.16146	+	4.13467i	−0.586690	+	0.338726i	−0.763788	−	0.645468i	$-0.776662\pi$
$149$	−7.16146	+	4.13467i	−0.586690	+	0.338726i	0.177098	+	0.984193i	$0.443329\pi$
$150$		0			0
$151$	2.12170	−	1.22496i	0.172661	−	0.0996860i	−0.411179	−	0.911555i	$-0.634883\pi$
$151$	2.12170	−	1.22496i	0.172661	−	0.0996860i	0.583840	+	0.811869i	$0.301550\pi$
$152$	1.77671	+	3.07735i	0.144110	+	0.249606i
$153$		0			0
$154$	10.5122	+	13.0888i	0.847099	+	1.05473i
$155$	2.08376			0.167371
$156$		0			0
$157$	−1.81721	−	3.14750i	−0.145029	−	0.251198i	0.784355	−	0.620313i	$-0.212994\pi$
$157$	−1.81721	−	3.14750i	−0.145029	−	0.251198i	−0.929384	+	0.369115i	$0.879661\pi$
$158$	−6.37803	−	3.68236i	−0.507409	−	0.292953i
$159$		0			0
$160$	2.10076	−	3.63863i	0.166080	−	0.287659i
$161$	0.186349	−	0.479680i	0.0146864	−	0.0378041i
$162$		0			0
$163$	7.01241	−	4.04862i	0.549255	−	0.317112i	−0.199567	−	0.979884i	$-0.563953\pi$
$163$	7.01241	−	4.04862i	0.549255	−	0.317112i	0.748821	+	0.662772i	$0.230620\pi$
$164$	−16.0823	+	9.28510i	−1.25581	+	0.725045i
$165$		0			0
$166$	−34.6582			−2.69000
$167$	14.3939	−	8.31033i	1.11383	−	0.643073i	0.174015	−	0.984743i	$-0.444326\pi$
$167$	14.3939	−	8.31033i	1.11383	−	0.643073i	0.939820	+	0.341670i	$0.110993\pi$
$168$		0			0
$169$	12.4544	+	3.72669i	0.958030	+	0.286669i
$170$	3.43914	−	5.95676i	0.263770	−	0.456863i
$171$		0			0
$172$	−2.32964	+	4.03505i	−0.177633	+	0.307670i
$173$	−11.6107	−	20.1103i	−0.882746	−	1.52896i	−0.848276	−	0.529554i	$-0.822359\pi$
$173$	−11.6107	−	20.1103i	−0.882746	−	1.52896i	−0.0344695	−	0.999406i	$-0.510974\pi$
$174$		0			0
$175$	−12.0164	+	1.85369i	−0.908352	+	0.140126i
$176$	2.19065	+	1.26477i	0.165126	+	0.0953358i
$177$		0			0
$178$	−4.99372			−0.374295
$179$	0.871591	−	1.50964i	0.0651458	−	0.112836i	−0.831613	−	0.555356i	$-0.812582\pi$
$179$	0.871591	−	1.50964i	0.0651458	−	0.112836i	0.896759	+	0.442520i	$0.145915\pi$
$180$		0			0
$181$	−7.72648			−0.574305			−0.287152	−	0.957885i	$-0.592709\pi$
$181$	−7.72648			−0.574305			−0.287152	+	0.957885i	$0.592709\pi$
$182$	−18.6032	−	10.5508i	−1.37896	−	0.782080i
$183$		0			0
$184$			0.447571i			0.0329954i
$185$	3.58490	−	6.20923i	0.263567	−	0.456512i
$186$		0			0
$187$	11.8230	+	6.82601i	0.864584	+	0.499168i
$188$	16.1020	+	9.29651i	1.17436	+	0.678017i
$189$		0			0
$190$			2.20194i			0.159745i
$191$	12.5661	+	21.7651i	0.909251	+	1.57487i	0.815107	+	0.579311i	$0.196678\pi$
$191$	12.5661	+	21.7651i	0.909251	+	1.57487i	0.0941446	+	0.995559i	$0.469988\pi$
$192$		0			0
$193$	9.54557	+	5.51114i	0.687105	+	0.396700i	0.802527	−	0.596616i	$-0.203489\pi$
$193$	9.54557	+	5.51114i	0.687105	+	0.396700i	−0.115422	+	0.993317i	$0.536822\pi$
$194$	−6.71907	+	11.6378i	−0.482401	+	0.835543i
$195$		0			0
$196$	15.6287	+	14.3015i	1.11634	+	1.02154i
$197$	−9.96350	+	5.75243i	−0.709870	+	0.409843i	−0.811013	−	0.585028i	$-0.801083\pi$
$197$	−9.96350	+	5.75243i	−0.709870	+	0.409843i	0.101143	+	0.994872i	$0.467750\pi$
$198$		0			0
$199$	0.250926			0.0177877			0.00889383	−	0.999960i	$-0.497169\pi$
$199$	0.250926			0.0177877			0.00889383	+	0.999960i	$0.497169\pi$
$200$	9.15795	−	5.28735i	0.647565	−	0.373872i
$201$		0			0
$202$	−24.9218	−	14.3886i	−1.75349	−	1.01238i
$203$	−20.6253	+	3.18173i	−1.44761	+	0.223314i
$204$		0			0
$205$	−3.90266			−0.272573
$206$	−34.6735	−	20.0187i	−2.41581	−	1.39477i
$207$		0			0
$208$	−3.18857	−	0.466828i	−0.221088	−	0.0323687i
$209$	−4.37041			−0.302308
$210$		0			0
$211$	−2.62918	−	4.55387i	−0.181000	−	0.313501i	0.761221	−	0.648492i	$-0.224600\pi$
$211$	−2.62918	−	4.55387i	−0.181000	−	0.313501i	−0.942221	+	0.334991i	$0.891267\pi$
$212$	−11.7523	−	20.3555i	−0.807148	−	1.39802i
$213$		0			0
$214$		−	4.65991i		−	0.318545i
$215$	−0.847993	+	0.489589i	−0.0578327	+	0.0333897i
$216$		0			0
$217$	1.32156	+	8.56687i	0.0897131	+	0.581557i
$218$	−11.2385	−	19.4656i	−0.761165	−	1.31838i
$219$		0			0
$220$	−2.72379	−	4.71774i	−0.183638	−	0.318070i
$221$	−17.2088	−	2.51949i	−1.15759	−	0.169479i
$222$		0			0
$223$	1.21469	−	0.701303i	0.0813419	−	0.0469627i	−0.458777	−	0.888551i	$-0.651712\pi$
$223$	1.21469	−	0.701303i	0.0813419	−	0.0469627i	0.540119	+	0.841588i	$0.318379\pi$
$224$	16.2917	+	6.32910i	1.08854	+	0.422881i
$225$		0			0
$226$	−0.355335	−	0.205153i	−0.0236365	−	0.0136465i
$227$		−	10.2151i		−	0.678003i	−0.940786	−	0.339002i	$-0.889911\pi$
$227$		−	10.2151i		−	0.678003i	0.940786	−	0.339002i	$-0.110089\pi$
$228$		0			0
$229$	2.61602	+	1.51036i	0.172872	+	0.0998074i	0.583939	−	0.811797i	$-0.301511\pi$
$229$	2.61602	+	1.51036i	0.172872	+	0.0998074i	−0.411068	+	0.911605i	$0.634844\pi$
$230$	−0.138673	+	0.240188i	−0.00914380	+	0.0158375i
$231$		0			0
$232$	15.7190	−	9.07536i	1.03200	−	0.595827i
$233$	9.89754	−	17.1430i	0.648409	−	1.12308i	−0.335093	−	0.942185i	$-0.608768\pi$
$233$	9.89754	−	17.1430i	0.648409	−	1.12308i	0.983503	−	0.180893i	$-0.0578988\pi$
$234$		0			0
$235$	1.95372	+	3.38395i	0.127447	+	0.220745i
$236$		−	29.8699i		−	1.94437i
$237$		0			0
$238$	26.6710	+	10.3613i	1.72882	+	0.671624i
$239$			14.3439i			0.927830i	0.885880	+	0.463915i	$0.153556\pi$
$239$			14.3439i			0.927830i	−0.885880	+	0.463915i	$0.846444\pi$
$240$		0			0
$241$		−	5.51238i		−	0.355083i	−0.984113	−	0.177542i	$-0.943186\pi$
$241$		−	5.51238i		−	0.355083i	0.984113	−	0.177542i	$-0.0568144\pi$
$242$	−5.80565	+	3.35190i	−0.373202	+	0.215468i
$243$		0			0
$244$	−10.3028	−	17.8450i	−0.659569	−	1.14241i
$245$	1.34167	+	4.24513i	0.0857160	+	0.271212i
$246$		0			0
$247$	5.17425	−	2.05602i	0.329230	−	0.130821i
$248$	−3.76952	−	6.52901i	−0.239365	−	0.414592i
$249$		0			0
$250$	13.6824			0.865350
$251$	−3.85017	+	6.66869i	−0.243021	+	0.420924i	−0.961573	−	0.274548i	$-0.911472\pi$
$251$	−3.85017	+	6.66869i	−0.243021	+	0.420924i	0.718553	+	0.695473i	$0.244805\pi$
$252$		0			0
$253$	−0.476726	−	0.275238i	−0.0299715	−	0.0173040i
$254$	−25.9931	+	15.0071i	−1.63095	+	0.941631i
$255$		0			0
$256$	−9.79133			−0.611958
$257$	18.1969			1.13509			0.567544	−	0.823343i	$-0.307894\pi$
$257$	18.1969			1.13509			0.567544	+	0.823343i	$0.307894\pi$
$258$		0			0
$259$	27.8014	+	10.8005i	1.72749	+	0.671107i
$260$	5.44418	+	4.30408i	0.337634	+	0.266928i
$261$		0			0
$262$	−32.1916	−	18.5858i	−1.98880	−	1.14824i
$263$	−1.68741	+	2.92267i	−0.104050	+	0.180220i	−0.913350	−	0.407176i	$-0.866513\pi$
$263$	−1.68741	+	2.92267i	−0.104050	+	0.180220i	0.809300	+	0.587396i	$0.199847\pi$
$264$		0			0
$265$		−	4.93963i		−	0.303439i
$266$	−9.05273	+	1.39651i	−0.555058	+	0.0856254i
$267$		0			0
$268$	19.9572	+	11.5223i	1.21908	+	0.703836i
$269$	16.3659			0.997846			0.498923	−	0.866646i	$-0.333729\pi$
$269$	16.3659			0.997846			0.498923	+	0.866646i	$0.333729\pi$
$270$		0			0
$271$		−	24.0551i		−	1.46124i	−0.682784	−	0.730620i	$-0.739231\pi$
$271$		−	24.0551i		−	1.46124i	0.682784	−	0.730620i	$-0.260769\pi$
$272$	4.31137			0.261415
$273$		0			0
$274$	41.7925			2.52478
$275$			13.0060i			0.784291i
$276$		0			0
$277$	−24.8115			−1.49078			−0.745389	−	0.666630i	$-0.767736\pi$
$277$	−24.8115			−1.49078			−0.745389	+	0.666630i	$0.767736\pi$
$278$	6.77305	+	3.91042i	0.406221	+	0.234532i
$279$		0			0
$280$	−2.42470	−	3.01901i	−0.144904	−	0.180420i
$281$		−	9.75382i		−	0.581864i	−0.956744	−	0.290932i	$-0.906035\pi$
$281$		−	9.75382i		−	0.581864i	0.956744	−	0.290932i	$-0.0939654\pi$
$282$		0			0
$283$	12.6563	−	21.9213i	0.752336	−	1.30308i	−0.194351	−	0.980932i	$-0.562260\pi$
$283$	12.6563	−	21.9213i	0.752336	−	1.30308i	0.946688	−	0.322153i	$-0.104407\pi$
$284$	10.8824	+	6.28298i	0.645754	+	0.372826i
$285$		0			0
$286$	−14.1883	+	17.9466i	−0.838970	+	1.06120i
$287$	−2.47513	−	16.0448i	−0.146103	−	0.947096i
$288$		0			0
$289$	6.26858			0.368740
$290$	11.2474			0.660470
$291$		0			0
$292$	−13.9146	+	8.03362i	−0.814292	+	0.470132i
$293$	5.39788	+	3.11647i	0.315347	+	0.182066i	0.649317	−	0.760518i	$-0.275055\pi$
$293$	5.39788	+	3.11647i	0.315347	+	0.182066i	−0.333970	+	0.942584i	$0.608388\pi$
$294$		0			0
$295$	3.13868	−	5.43636i	0.182741	−	0.316517i
$296$	−25.9404			−1.50775
$297$		0			0
$298$	9.26977	+	16.0557i	0.536983	+	0.930082i
$299$	0.693892	+	0.101590i	0.0401288	+	0.00587512i
$300$		0			0
$301$	−2.55064	−	3.17581i	−0.147017	−	0.183051i
$302$	−2.74632	−	4.75676i	−0.158033	−	0.273721i
$303$		0			0
$304$	−1.19528	+	0.690097i	−0.0685542	+	0.0395798i
$305$		−	4.33041i		−	0.247958i
$306$		0			0
$307$		−	0.591812i		−	0.0337765i	−0.999857	−	0.0168883i	$-0.994624\pi$
$307$		−	0.591812i		−	0.0337765i	0.999857	−	0.0168883i	$-0.00537596\pi$
$308$	17.6684	−	14.1903i	1.00675	−	0.808565i
$309$		0			0
$310$		−	4.67170i		−	0.265335i
$311$	16.7999	+	29.0984i	0.952638	+	1.65002i	0.739684	+	0.672955i	$0.234975\pi$
$311$	16.7999	+	29.0984i	0.952638	+	1.65002i	0.212954	+	0.977062i	$0.431692\pi$
$312$		0			0
$313$	−7.80427	+	13.5174i	−0.441123	+	0.764048i	−0.997773	−	0.0666992i	$-0.978753\pi$
$313$	−7.80427	+	13.5174i	−0.441123	+	0.764048i	0.556650	+	0.830747i	$0.312087\pi$
$314$	−7.05657	+	4.07411i	−0.398225	+	0.229916i
$315$		0			0
$316$	−4.97075	+	8.60959i	−0.279626	+	0.484327i
$317$	23.0473	+	13.3063i	1.29446	+	0.747359i	0.979442	−	0.201726i	$-0.0646550\pi$
$317$	23.0473	+	13.3063i	1.29446	+	0.747359i	0.315021	+	0.949085i	$0.397988\pi$
$318$		0			0
$319$			22.3239i			1.24990i
$320$	−7.17307	−	4.14137i	−0.400987	−	0.231510i
$321$		0			0
$322$	−1.07542	−	0.417787i	−0.0599310	−	0.0232824i
$323$	−6.45098	+	3.72447i	−0.358942	+	0.207235i
$324$		0			0
$325$	−6.11855	−	15.3982i	−0.339396	−	0.854137i
$326$	−9.07684	−	15.7215i	−0.502720	−	0.870736i
$327$		0			0
$328$	7.05991	+	12.2281i	0.389819	+	0.675186i
$329$	−12.6732	+	10.1784i	−0.698697	+	0.561155i
$330$		0			0
$331$	27.4901	−	15.8714i	1.51099	−	0.872372i	0.511075	−	0.859536i	$-0.329247\pi$
$331$	27.4901	−	15.8714i	1.51099	−	0.872372i	0.999918	−	0.0128360i	$-0.00408593\pi$
$332$			46.7845i			2.56763i
$333$		0			0
$334$	−18.6314	−	32.2706i	−1.01947	−	1.76577i
$335$	2.42149	+	4.19414i	0.132300	+	0.229150i
$336$		0			0
$337$	−25.9329			−1.41266			−0.706328	−	0.707885i	$-0.749649\pi$
$337$	−25.9329			−1.41266			−0.706328	+	0.707885i	$0.749649\pi$
$338$	8.35509	−	27.9222i	0.454457	−	1.51877i
$339$		0			0
$340$	−8.04093	−	4.64243i	−0.436081	−	0.251771i
$341$	9.27240			0.502129
$342$		0			0
$343$	−16.6019	+	8.20828i	−0.896420	+	0.443206i
$344$	3.06805	+	1.77134i	0.165418	+	0.0955041i
$345$		0			0
$346$	−45.0865	+	26.0307i	−2.42387	+	1.39942i
$347$	23.5492			1.26419			0.632094	−	0.774892i	$-0.282196\pi$
$347$	23.5492			1.26419			0.632094	+	0.774892i	$0.282196\pi$
$348$		0			0
$349$	2.49824	−	1.44236i	0.133728	−	0.0772078i	−0.431644	−	0.902044i	$-0.642066\pi$
$349$	2.49824	−	1.44236i	0.133728	−	0.0772078i	0.565371	+	0.824836i	$0.308733\pi$
$350$	4.15590	+	26.9402i	0.222142	+	1.44002i
$351$		0			0
$352$	9.34808	−	16.1914i	0.498254	−	0.863002i
$353$	8.84648	+	5.10752i	0.470851	+	0.271846i	0.716596	−	0.697489i	$-0.245699\pi$
$353$	8.84648	+	5.10752i	0.470851	+	0.271846i	−0.245745	+	0.969335i	$0.579033\pi$
$354$		0			0
$355$	1.32041	+	2.28702i	0.0700801	+	0.121382i
$356$			6.74094i			0.357269i
$357$		0			0
$358$	−3.38455	−	1.95407i	−0.178879	−	0.103276i
$359$	23.5410	+	13.5914i	1.24245	+	0.717327i	0.969592	−	0.244728i	$-0.0786987\pi$
$359$	23.5410	+	13.5914i	1.24245	+	0.717327i	0.272855	+	0.962055i	$0.412032\pi$
$360$		0			0
$361$	−8.30769	+	14.3893i	−0.437247	+	0.757334i
$362$			17.3225i			0.910448i
$363$		0			0
$364$	−14.2424	+	25.1122i	−0.746504	+	1.31624i
$365$	−3.37664			−0.176741
$366$		0			0
$367$	2.41056	−	4.17522i	0.125830	−	0.217945i	−0.796227	−	0.604998i	$-0.793174\pi$
$367$	2.41056	−	4.17522i	0.125830	−	0.217945i	0.922057	+	0.387054i	$0.126507\pi$
$368$	−0.173842			−0.00906216
$369$		0			0
$370$	−13.9208	−	8.03720i	−0.723710	−	0.417834i
$371$	20.3081	−	3.13280i	1.05434	−	0.162647i
$372$		0			0
$373$	5.11919	+	8.86669i	0.265061	+	0.459100i	0.967580	−	0.252566i	$-0.0812745\pi$
$373$	5.11919	+	8.86669i	0.265061	+	0.459100i	−0.702518	+	0.711666i	$0.747941\pi$
$374$	15.3036	−	26.5067i	0.791333	−	1.37063i
$375$		0			0
$376$	7.06859	−	12.2431i	0.364534	−	0.631392i
$377$	−10.5021	−	26.4299i	−0.540884	−	1.36121i
$378$		0			0
$379$	−1.39862	+	0.807493i	−0.0718422	+	0.0414781i	−0.535491	−	0.844541i	$-0.679873\pi$
$379$	−1.39862	+	0.807493i	−0.0718422	+	0.0414781i	0.463649	+	0.886019i	$0.346540\pi$
$380$	2.97235			0.152479
$381$		0			0
$382$	48.7965	−	28.1727i	2.49665	−	1.44144i
$383$	−26.8406	+	15.4964i	−1.37149	+	0.791831i	−0.991116	−	0.133001i	$-0.957539\pi$
$383$	−26.8406	+	15.4964i	−1.37149	+	0.791831i	−0.380376	+	0.924832i	$0.624205\pi$
$384$		0			0
$385$	4.70675	−	0.726081i	0.239878	−	0.0370045i
$386$	12.3557	−	21.4008i	0.628891	−	1.08927i
$387$		0			0
$388$	15.7096	+	9.06995i	0.797535	+	0.460457i
$389$	−5.67028	−	9.82120i	−0.287494	−	0.497955i	0.685717	−	0.727869i	$-0.259489\pi$
$389$	−5.67028	−	9.82120i	−0.287494	−	0.497955i	−0.973211	+	0.229914i	$0.926156\pi$
$390$		0			0
$391$	−0.938233			−0.0474485
$392$	10.8741	−	11.8833i	0.549226	−	0.600196i
$393$		0			0
$394$	12.8967	+	22.3378i	0.649727	+	1.12536i
$395$	−1.80936	+	1.04464i	−0.0910390	+	0.0525614i
$396$		0			0
$397$	−15.7923	+	9.11768i	−0.792592	+	0.457603i	−0.840874	−	0.541230i	$-0.817959\pi$
$397$	−15.7923	+	9.11768i	−0.792592	+	0.457603i	0.0482822	+	0.998834i	$0.484625\pi$
$398$		−	0.562566i		−	0.0281989i
$399$		0			0
$400$	2.05367	+	3.55707i	0.102684	+	0.177853i
$401$			24.1902i			1.20800i	0.796983	+	0.604002i	$0.206428\pi$
$401$			24.1902i			1.20800i	−0.796983	+	0.604002i	$0.793572\pi$
$402$		0			0
$403$	−10.9779	+	4.36212i	−0.546846	+	0.217293i
$404$	−19.4229	+	33.6415i	−0.966326	+	1.67373i
$405$		0			0
$406$	7.13331	+	46.2410i	0.354020	+	2.29490i
$407$	15.9523	−	27.6301i	0.790724	−	1.36957i
$408$		0			0
$409$		−	7.35938i		−	0.363898i	−0.983308	−	0.181949i	$-0.941759\pi$
$409$		−	7.35938i		−	0.363898i	0.983308	−	0.181949i	$-0.0582406\pi$
$410$			8.74959i			0.432112i
$411$		0			0
$412$	−27.0229	+	46.8051i	−1.33132	+	2.30592i
$413$	24.3409	+	9.45611i	1.19774	+	0.465305i
$414$		0			0
$415$	−4.91604	+	8.51483i	−0.241319	+	0.417977i
$416$	−3.45038	+	23.5671i	−0.169169	+	1.15547i
$417$		0			0
$418$			9.79828i			0.479249i
$419$	−9.55449	−	16.5489i	−0.466767	−	0.808465i	0.532512	−	0.846423i	$-0.321248\pi$
$419$	−9.55449	−	16.5489i	−0.466767	−	0.808465i	−0.999279	+	0.0379576i	$0.987915\pi$
$420$		0			0
$421$		−	33.9039i		−	1.65238i	−0.563393	−	0.826189i	$-0.690504\pi$
$421$		−	33.9039i		−	1.65238i	0.563393	−	0.826189i	$-0.309496\pi$
$422$	−10.2096	+	5.89451i	−0.496995	+	0.286940i
$423$		0			0
$424$	−15.4773	+	8.93581i	−0.751643	+	0.433961i
$425$	11.0837	+	19.1976i	0.537640	+	0.931220i
$426$		0			0
$427$	17.8034	−	2.74642i	0.861568	−	0.132909i
$428$	−6.29033			−0.304055
$429$		0			0
$430$	1.09764	+	1.90117i	0.0529329	+	0.0916824i
$431$	−18.2755	−	10.5513i	−0.880299	−	0.508241i	−0.00954172	−	0.999954i	$-0.503037\pi$
$431$	−18.2755	−	10.5513i	−0.880299	−	0.508241i	−0.870757	+	0.491714i	$0.836371\pi$
$432$		0			0
$433$	−16.0407	+	27.7833i	−0.770865	+	1.33518i	0.166224	+	0.986088i	$0.446843\pi$
$433$	−16.0407	+	27.7833i	−0.770865	+	1.33518i	−0.937089	+	0.349090i	$0.886491\pi$
$434$	19.2066	−	2.96288i	0.921945	−	0.142223i
$435$		0			0
$436$	−26.2762	+	15.1706i	−1.25840	+	0.726540i
$437$	0.260115	−	0.150178i	0.0124430	−	0.00718397i
$438$		0			0
$439$	16.4573			0.785465			0.392733	−	0.919653i	$-0.371530\pi$
$439$	16.4573			0.785465			0.392733	+	0.919653i	$0.371530\pi$
$440$	−3.58712	+	2.07103i	−0.171009	+	0.0987324i
$441$		0			0
$442$	−5.64859	+	38.5815i	−0.268676	+	1.83513i
$443$	−0.361627	+	0.626356i	−0.0171814	+	0.0297591i	−0.874488	−	0.485047i	$-0.838803\pi$
$443$	−0.361627	+	0.626356i	−0.0171814	+	0.0297591i	0.857307	+	0.514806i	$0.172136\pi$
$444$		0			0
$445$	−0.708327	+	1.22686i	−0.0335779	+	0.0581587i
$446$	−1.57229	−	2.72329i	−0.0744503	−	0.128952i
$447$		0			0
$448$	12.4770	−	32.1169i	0.589481	−	1.51738i
$449$	10.1092	+	5.83656i	0.477083	+	0.275444i	0.719200	−	0.694803i	$-0.244508\pi$
$449$	10.1092	+	5.83656i	0.477083	+	0.275444i	−0.242117	+	0.970247i	$0.577842\pi$
$450$		0			0
$451$	−17.3662			−0.817743
$452$	−0.276932	+	0.479660i	−0.0130258	+	0.0225613i
$453$		0			0
$454$	−22.9019			−1.07484
$455$	−5.23088	+	3.07388i	−0.245227	+	0.144106i
$456$		0			0
$457$			24.1042i			1.12755i	0.825930	+	0.563773i	$0.190651\pi$
$457$			24.1042i			1.12755i	−0.825930	+	0.563773i	$0.809349\pi$
$458$	3.38617	−	5.86501i	0.158225	−	0.274054i
$459$		0			0
$460$	0.324225	+	0.187192i	0.0151171	+	0.00872785i
$461$	30.4133	+	17.5591i	1.41649	+	0.817809i	0.995988	−	0.0894835i	$-0.0285216\pi$
$461$	30.4133	+	17.5591i	1.41649	+	0.817809i	0.420499	+	0.907293i	$0.361855\pi$
$462$		0			0
$463$		−	13.5882i		−	0.631496i	−0.948843	−	0.315748i	$-0.897745\pi$
$463$		−	13.5882i		−	0.631496i	0.948843	−	0.315748i	$-0.102255\pi$
$464$	3.52499	+	6.10546i	0.163643	+	0.283439i
$465$		0			0
$466$	−38.4340	−	22.1899i	−1.78042	−	1.02793i
$467$	4.33263	−	7.50434i	0.200490	−	0.347259i	−0.748196	−	0.663477i	$-0.769080\pi$
$467$	4.33263	−	7.50434i	0.200490	−	0.347259i	0.948686	+	0.316218i	$0.102413\pi$
$468$		0			0
$469$	−15.7074	+	12.6154i	−0.725302	+	0.582523i
$470$	7.58668	−	4.38017i	0.349947	−	0.202042i
$471$		0			0
$472$	−22.7116			−1.04538
$473$	−3.77344	+	2.17860i	−0.173503	+	0.100172i
$474$		0			0
$475$	−6.14571	−	3.54823i	−0.281984	−	0.162804i
$476$	13.9865	−	36.0027i	0.641072	−	1.65018i
$477$		0			0
$478$	32.1585			1.47089
$479$	−16.2438	−	9.37835i	−0.742197	−	0.428508i	0.0806707	−	0.996741i	$-0.474294\pi$
$479$	−16.2438	−	9.37835i	−0.742197	−	0.428508i	−0.822868	+	0.568233i	$0.807627\pi$
$480$		0			0
$481$	−5.88799	+	40.2167i	−0.268469	+	1.83372i
$482$	−12.3585			−0.562915
$483$		0			0
$484$	4.52466	+	7.83695i	0.205667	+	0.356225i
$485$	1.90611	+	3.30148i	0.0865521	+	0.149913i
$486$		0			0
$487$			11.5130i			0.521704i	0.965379	+	0.260852i	$0.0840035\pi$
$487$			11.5130i			0.521704i	−0.965379	+	0.260852i	$0.915997\pi$
$488$	−13.5684	+	7.83372i	−0.614213	+	0.354616i
$489$		0			0
$490$	9.51741	−	3.00796i	0.429953	−	0.135886i
$491$	14.5604	+	25.2193i	0.657099	+	1.13813i	0.981363	+	0.192163i	$0.0615502\pi$
$491$	14.5604	+	25.2193i	0.657099	+	1.13813i	−0.324264	+	0.945967i	$0.605116\pi$
$492$		0			0
$493$	19.0245	+	32.9513i	0.856819	+	1.48405i
$494$	−4.60951	−	11.6005i	−0.207392	−	0.521929i
$495$		0			0
$496$	2.53595	−	1.46413i	0.113868	−	0.0657415i
$497$	−8.56510	+	6.87902i	−0.384197	+	0.308566i
$498$		0			0
$499$	−21.2872	−	12.2902i	−0.952946	−	0.550184i	−0.0589512	−	0.998261i	$-0.518776\pi$
$499$	−21.2872	−	12.2902i	−0.952946	−	0.550184i	−0.893995	+	0.448077i	$0.852109\pi$
$500$		−	18.4696i		−	0.825986i
$501$		0			0
$502$	14.9509	+	8.63193i	0.667293	+	0.385262i
$503$	0.828618	−	1.43521i	0.0369462	−	0.0639928i	−0.846961	−	0.531655i	$-0.821570\pi$
$503$	0.828618	−	1.43521i	0.0369462	−	0.0639928i	0.883907	+	0.467662i	$0.154904\pi$
$504$		0			0
$505$	−7.06999	+	4.08186i	−0.314610	+	0.181640i
$506$	−0.617072	+	1.06880i	−0.0274322	+	0.0475139i
$507$		0			0
$508$	20.2579	+	35.0876i	0.898797	+	1.55676i
$509$			37.5354i			1.66373i	0.554979	+	0.831865i	$0.312726\pi$
$509$			37.5354i			1.66373i	−0.554979	+	0.831865i	$0.687274\pi$
$510$		0			0
$511$	−2.14152	−	13.8822i	−0.0947355	−	0.614114i
$512$		−	10.0177i		−	0.442723i
$513$		0			0
$514$		−	40.7966i		−	1.79946i
$515$	−9.83641	+	5.67906i	−0.433444	+	0.250249i
$516$		0			0
$517$	8.69377	+	15.0581i	0.382352	+	0.662253i
$518$	24.2142	−	62.3295i	1.06391	−	2.73860i
$519$		0			0
$520$	3.27260	−	4.13948i	0.143513	−	0.181528i
$521$	1.21520	+	2.10479i	0.0532389	+	0.0922125i	0.891417	−	0.453185i	$-0.149712\pi$
$521$	1.21520	+	2.10479i	0.0532389	+	0.0922125i	−0.838178	+	0.545397i	$0.816379\pi$
$522$		0			0
$523$	21.8511			0.955484			0.477742	−	0.878500i	$-0.341455\pi$
$523$	21.8511			0.955484			0.477742	+	0.878500i	$0.341455\pi$
$524$	−25.0887	+	43.4549i	−1.09600	+	1.89833i
$525$		0			0
$526$	6.55251	+	3.78309i	0.285703	+	0.164951i
$527$	13.6866	−	7.90196i	0.596198	−	0.344215i
$528$		0			0
$529$	−22.9622			−0.998355
$530$	−11.0745			−0.481044
$531$		0			0
$532$	1.88512	+	12.2201i	0.0817303	+	0.529809i
$533$	20.5604	−	8.16978i	0.890568	−	0.353873i
$534$		0			0
$535$	−1.14485	−	0.660978i	−0.0494961	−	0.0285766i
$536$	8.76096	−	15.1744i	0.378416	−	0.655435i
$537$		0			0
$538$		−	36.6917i		−	1.58189i
$539$	5.97021	+	18.8902i	0.257155	+	0.813658i
$540$		0			0
$541$	−19.5906	−	11.3107i	−0.842267	−	0.486283i	0.0157673	−	0.999876i	$-0.494981\pi$
$541$	−19.5906	−	11.3107i	−0.842267	−	0.486283i	−0.858034	+	0.513593i	$0.828314\pi$
$542$	−53.9305			−2.31651
$543$		0			0
$544$		−	31.8658i		−	1.36624i
$545$	−6.37641			−0.273135
$546$		0			0
$547$	40.3429			1.72494			0.862468	−	0.506111i	$-0.168917\pi$
$547$	40.3429			1.72494			0.862468	+	0.506111i	$0.168917\pi$
$548$		−	56.4149i		−	2.40993i
$549$		0			0
$550$	29.1589			1.24334
$551$	−10.5487	−	6.09028i	−0.449389	−	0.259455i
$552$		0			0
$553$	−5.44230	−	6.77624i	−0.231430	−	0.288155i
$554$			55.6264i			2.36334i
$555$		0			0
$556$	5.27861	−	9.14282i	0.223863	−	0.387742i
$557$	−27.7685	−	16.0321i	−1.17659	−	0.679303i	−0.221365	−	0.975191i	$-0.571051\pi$
$557$	−27.7685	−	16.0321i	−1.17659	−	0.679303i	−0.955223	+	0.295888i	$0.904384\pi$
$558$		0			0
$559$	3.44258	−	4.35449i	0.145606	−	0.184175i
$560$	1.17262	−	0.941785i	0.0495523	−	0.0397977i
$561$		0			0
$562$	−21.8677			−0.922432
$563$	27.8430			1.17344			0.586721	−	0.809789i	$-0.300419\pi$
$563$	27.8430			1.17344			0.586721	+	0.809789i	$0.300419\pi$
$564$		0			0
$565$	−0.100804	+	0.0581991i	−0.00424085	+	0.00244845i
$566$	−49.1466	−	28.3748i	−2.06579	−	1.19268i
$567$		0			0
$568$	4.77725	−	8.27445i	0.200449	−	0.347188i
$569$	−6.11998			−0.256563			−0.128282	−	0.991738i	$-0.540946\pi$
$569$	−6.11998			−0.256563			−0.128282	+	0.991738i	$0.540946\pi$
$570$		0			0
$571$	−17.6586	−	30.5856i	−0.738990	−	1.27997i	−0.952950	−	0.303126i	$-0.901970\pi$
$571$	−17.6586	−	30.5856i	−0.738990	−	1.27997i	0.213960	−	0.976842i	$-0.431364\pi$
$572$	24.2258	+	19.1525i	1.01293	+	0.800806i
$573$		0			0
$574$	−35.9719	+	5.54915i	−1.50144	+	0.231617i
$575$	−0.446917	−	0.774083i	−0.0186377	−	0.0322815i
$576$		0			0
$577$	−36.9193	+	21.3154i	−1.53697	+	0.887371i	−0.537958	+	0.842972i	$0.680804\pi$
$577$	−36.9193	+	21.3154i	−1.53697	+	0.887371i	−0.999014	+	0.0443995i	$0.985863\pi$
$578$		−	14.0539i		−	0.584565i
$579$		0			0
$580$		−	15.1827i		−	0.630426i
$581$	−38.1245	−	14.8109i	−1.58167	−	0.614458i
$582$		0			0
$583$		−	21.9806i		−	0.910344i
$584$	6.10835	+	10.5800i	0.252765	+	0.437802i
$585$		0			0
$586$	6.98699	−	12.1018i	0.288630	−	0.499922i
$587$	−17.0037	+	9.81708i	−0.701817	+	0.405194i	−0.808024	−	0.589150i	$-0.799463\pi$
$587$	−17.0037	+	9.81708i	−0.701817	+	0.405194i	0.106207	+	0.994344i	$0.466129\pi$
$588$		0			0
$589$	−2.52965	+	4.38148i	−0.104232	+	0.180536i
$590$	−12.1881	−	7.03680i	−0.501776	−	0.289701i
$591$		0			0
$592$		−	10.0756i		−	0.414104i
$593$	−21.4032	−	12.3571i	−0.878924	−	0.507447i	−0.00862075	−	0.999963i	$-0.502744\pi$
$593$	−21.4032	−	12.3571i	−0.878924	−	0.507447i	−0.870304	+	0.492516i	$0.836077\pi$
$594$		0			0
$595$	6.32867	−	5.08284i	0.259450	−	0.208376i
$596$	21.6733	−	12.5131i	0.887774	−	0.512556i
$597$		0			0
$598$	0.227762	−	1.55568i	0.00931386	−	0.0636164i
$599$	−11.8622	−	20.5459i	−0.484675	−	0.839481i	0.515170	−	0.857088i	$-0.327729\pi$
$599$	−11.8622	−	20.5459i	−0.484675	−	0.839481i	−0.999845	+	0.0176065i	$0.994395\pi$
$600$		0			0
$601$	22.0116	+	38.1252i	0.897871	+	1.55516i	0.830211	+	0.557450i	$0.188220\pi$
$601$	22.0116	+	38.1252i	0.897871	+	1.55516i	0.0676602	+	0.997708i	$0.478447\pi$
$602$	−7.12005	+	5.71843i	−0.290191	+	0.233066i
$603$		0			0
$604$	−6.42106	+	3.70720i	−0.261269	+	0.150844i
$605$			1.90178i			0.0773183i
$606$		0			0
$607$	−23.4814	−	40.6709i	−0.953079	−	1.65078i	−0.738704	−	0.674030i	$-0.764562\pi$
$607$	−23.4814	−	40.6709i	−0.953079	−	1.65078i	−0.214375	−	0.976751i	$-0.568772\pi$
$608$	5.10059	+	8.83447i	0.206856	+	0.358285i
$609$		0			0
$610$	−9.70860			−0.393090
$611$	−17.3767	−	13.7378i	−0.702987	−	0.555770i
$612$		0			0
$613$	18.4765	+	10.6674i	0.746258	+	0.430852i	0.824340	−	0.566095i	$-0.191546\pi$
$613$	18.4765	+	10.6674i	0.746258	+	0.430852i	−0.0780825	+	0.996947i	$0.524880\pi$
$614$	−1.32682			−0.0535461
$615$		0			0
$616$	−10.7895	−	13.4341i	−0.434723	−	0.541276i
$617$	−17.9964	−	10.3902i	−0.724509	−	0.418295i	0.0919011	−	0.995768i	$-0.470706\pi$
$617$	−17.9964	−	10.3902i	−0.724509	−	0.418295i	−0.816410	+	0.577473i	$0.804039\pi$
$618$		0			0
$619$	15.4782	−	8.93634i	0.622121	−	0.359182i	−0.155573	−	0.987824i	$-0.549722\pi$
$619$	15.4782	−	8.93634i	0.622121	−	0.359182i	0.777694	+	0.628643i	$0.216389\pi$
$620$	−6.30625			−0.253265
$621$		0			0
$622$	65.2373	−	37.6648i	2.61578	−	1.51022i
$623$	−5.49317	−	2.13402i	−0.220079	−	0.0854977i
$624$		0			0
$625$	−9.54796	+	16.5375i	−0.381918	+	0.661502i
$626$	30.3054	+	17.4969i	1.21125	+	0.699315i
$627$		0			0
$628$	5.49957	+	9.52554i	0.219457	+	0.380110i
$629$		−	54.3782i		−	2.16820i
$630$		0			0
$631$	9.76939	+	5.64036i	0.388913	+	0.224539i	0.681689	−	0.731642i	$-0.261246\pi$
$631$	9.76939	+	5.64036i	0.388913	+	0.224539i	−0.292776	+	0.956181i	$0.594579\pi$
$632$	6.54629	+	3.77950i	0.260397	+	0.150341i
$633$		0			0
$634$	29.8323	−	51.6710i	1.18479	−	2.05212i
$635$			8.51465i			0.337894i
$636$		0			0
$637$	−15.9550	−	19.5560i	−0.632161	−	0.774837i
$638$	50.0492			1.98147
$639$		0			0
$640$	−5.08326	+	8.80446i	−0.200933	+	0.348027i
$641$	−34.4207			−1.35953			−0.679767	−	0.733428i	$-0.737919\pi$
$641$	−34.4207			−1.35953			−0.679767	+	0.733428i	$0.737919\pi$
$642$		0			0
$643$	22.9561	+	13.2537i	0.905299	+	0.522674i	0.878916	−	0.476977i	$-0.158268\pi$
$643$	22.9561	+	13.2537i	0.905299	+	0.522674i	0.0263831	+	0.999652i	$0.491601\pi$
$644$	−0.563964	+	1.45169i	−0.0222233	+	0.0572048i
$645$		0			0
$646$	8.35012	+	14.4628i	0.328531	+	0.569032i
$647$	22.0402	−	38.1748i	0.866492	−	1.50081i	0.000933018	−	1.00000i	$-0.499703\pi$
$647$	22.0402	−	38.1748i	0.866492	−	1.50081i	0.865559	−	0.500808i	$-0.166964\pi$
$648$		0			0
$649$	13.9667	−	24.1910i	0.548240	−	0.949579i
$650$	−34.5221	+	13.7175i	−1.35407	+	0.538047i
$651$		0			0
$652$	−21.2222	+	12.2527i	−0.831127	+	0.479851i
$653$	−20.7479			−0.811928			−0.405964	−	0.913889i	$-0.633064\pi$
$653$	−20.7479			−0.811928			−0.405964	+	0.913889i	$0.633064\pi$
$654$		0			0
$655$	−9.13234	+	5.27256i	−0.356830	+	0.206016i
$656$	−4.74957	+	2.74216i	−0.185439	+	0.107063i
$657$		0			0
$658$	22.8196	+	28.4128i	0.889601	+	1.10765i
$659$	−9.83347	+	17.0321i	−0.383058	+	0.663475i	−0.991498	−	0.130125i	$-0.958462\pi$
$659$	−9.83347	+	17.0321i	−0.383058	+	0.663475i	0.608440	+	0.793600i	$0.291796\pi$
$660$		0			0
$661$	29.5589	+	17.0658i	1.14971	+	0.663784i	0.948816	−	0.315829i	$-0.102283\pi$
$661$	29.5589	+	17.0658i	1.14971	+	0.663784i	0.200892	+	0.979613i	$0.435616\pi$
$662$	−35.5831	−	61.6317i	−1.38298	−	2.39538i
$663$		0			0
$664$	35.5725			1.38048
$665$	−0.940977	+	2.42216i	−0.0364895	+	0.0939274i
$666$		0			0
$667$	−0.767102	−	1.32866i	−0.0297023	−	0.0514459i
$668$	−43.5615	+	25.1502i	−1.68544	+	0.973091i
$669$		0			0
$670$	9.40309	−	5.42888i	0.363273	−	0.209736i
$671$		−	19.2696i		−	0.743896i
$672$		0			0
$673$	0.707130	+	1.22479i	0.0272579	+	0.0472120i	0.879333	−	0.476208i	$-0.157989\pi$
$673$	0.707130	+	1.22479i	0.0272579	+	0.0472120i	−0.852075	+	0.523420i	$0.824656\pi$
$674$			58.1405i			2.23949i
$675$		0			0
$676$	−37.6917	−	11.2784i	−1.44968	−	0.433784i
$677$	14.5443	−	25.1916i	0.558985	−	0.968190i	−0.438597	−	0.898684i	$-0.644524\pi$
$677$	14.5443	−	25.1916i	0.558985	−	0.968190i	0.997582	−	0.0695060i	$-0.0221423\pi$
$678$		0			0
$679$	−12.3644	+	9.93038i	−0.474501	+	0.381093i
$680$	−3.52987	+	6.11391i	−0.135364	+	0.234458i
$681$		0			0
$682$		−	20.7884i		−	0.796027i
$683$		−	48.3557i		−	1.85028i	−0.379629	−	0.925139i	$-0.623948\pi$
$683$		−	48.3557i		−	1.85028i	0.379629	−	0.925139i	$-0.376052\pi$
$684$		0			0
$685$	5.92799	−	10.2676i	0.226497	−	0.392304i
$686$	18.4026	+	37.2209i	0.702616	+	1.42110i
$687$		0			0
$688$	−0.688010	+	1.19167i	−0.0262301	+	0.0454319i
$689$	10.3406	+	26.0235i	0.393945	+	0.991415i
$690$		0			0
$691$			35.3305i			1.34403i	0.740536	+	0.672017i	$0.234572\pi$
$691$			35.3305i			1.34403i	−0.740536	+	0.672017i	$0.765428\pi$
$692$	35.1384	+	60.8615i	1.33576	+	2.31361i
$693$		0			0
$694$		−	52.7964i		−	2.00412i
$695$	1.92143	−	1.10934i	0.0728839	−	0.0420795i
$696$		0			0
$697$	−25.6335	+	14.7995i	−0.970940	+	0.560572i
$698$	−3.23372	−	5.60096i	−0.122398	−	0.211999i
$699$		0			0
$700$	36.3661	−	5.60997i	1.37451	−	0.212037i
$701$	21.9517			0.829104			0.414552	−	0.910026i	$-0.363938\pi$
$701$	21.9517			0.829104			0.414552	+	0.910026i	$0.363938\pi$
$702$		0			0
$703$	8.70402	+	15.0758i	0.328278	+	0.568595i
$704$	−31.9191	−	18.4285i	−1.20299	−	0.694549i
$705$		0			0
$706$	11.4509	−	19.8335i	0.430958	−	0.746442i
$707$	−21.2655	−	26.4778i	−0.799771	−	0.995799i
$708$		0			0
$709$	−32.1011	+	18.5336i	−1.20558	+	0.696043i	−0.961791	−	0.273785i	$-0.911724\pi$
$709$	−32.1011	+	18.5336i	−1.20558	+	0.696043i	−0.243791	+	0.969828i	$0.578391\pi$
$710$	5.12740	−	2.96031i	0.192428	−	0.111098i
$711$		0			0
$712$	5.12546			0.192085
$713$	−0.551869	+	0.318622i	−0.0206677	+	0.0119325i
$714$		0			0
$715$	2.39661	+	6.03139i	0.0896280	+	0.225561i
$716$	−2.63777	+	4.56875i	−0.0985780	+	0.170742i
$717$		0			0
$718$	30.4714	−	52.7780i	1.13718	−	1.96966i
$719$	7.65925	+	13.2662i	0.285642	+	0.494746i	0.972765	−	0.231795i	$-0.0744600\pi$
$719$	7.65925	+	13.2662i	0.285642	+	0.494746i	−0.687123	+	0.726541i	$0.741127\pi$
$720$		0			0
$721$	−29.5865	−	36.8383i	−1.10186	−	1.37193i
$722$	32.2603	+	18.6255i	1.20060	+	0.693169i
$723$		0			0
$724$	23.3833			0.869033
$725$	−18.1242	+	31.3920i	−0.673116	+	1.16587i
$726$		0			0
$727$	8.76569			0.325102			0.162551	−	0.986700i	$-0.448028\pi$
$727$	8.76569			0.325102			0.162551	+	0.986700i	$0.448028\pi$
$728$	19.0940	+	10.8292i	0.707671	+	0.401356i
$729$		0			0
$730$			7.57029i			0.280189i
$731$	−3.71321	+	6.43147i	−0.137338	+	0.237877i
$732$		0			0
$733$	37.4473	+	21.6202i	1.38315	+	0.798560i	0.992531	−	0.121994i	$-0.0389290\pi$
$733$	37.4473	+	21.6202i	1.38315	+	0.798560i	0.390615	+	0.920554i	$0.372262\pi$
$734$	−9.36067	−	5.40439i	−0.345509	−	0.199480i
$735$		0			0
$736$			1.28489i			0.0473617i
$737$	10.7752	+	18.6633i	0.396911	+	0.687471i
$738$		0			0
$739$	−3.38615	−	1.95500i	−0.124562	−	0.0719157i	0.436425	−	0.899741i	$-0.356245\pi$
$739$	−3.38615	−	1.95500i	−0.124562	−	0.0719157i	−0.560986	+	0.827825i	$0.689578\pi$
$740$	−10.8493	+	18.7915i	−0.398827	+	0.690789i
$741$		0			0
$742$	−7.02362	−	45.5300i	−0.257845	−	1.67146i
$743$	11.5121	−	6.64653i	0.422339	−	0.243838i	−0.273738	−	0.961804i	$-0.588260\pi$
$743$	11.5121	−	6.64653i	0.422339	−	0.243838i	0.696078	+	0.717967i	$0.254927\pi$
$744$		0			0
$745$	5.25942			0.192690
$746$	19.8788	−	11.4770i	0.727813	−	0.420203i
$747$		0			0
$748$	−35.7809	−	20.6581i	−1.30828	−	0.755336i
$749$	1.99137	−	5.12597i	0.0727631	−	0.187299i
$750$		0			0
$751$	21.1032			0.770067			0.385034	−	0.922903i	$-0.374190\pi$
$751$	21.1032			0.770067			0.385034	+	0.922903i	$0.374190\pi$
$752$	4.75540	+	2.74553i	0.173412	+	0.100119i
$753$		0			0
$754$	−59.2547	+	23.5452i	−2.15793	+	0.857466i
$755$	−1.55819			−0.0567083
$756$		0			0
$757$	−19.5023	−	33.7789i	−0.708822	−	1.22772i	−0.965294	−	0.261165i	$-0.915893\pi$
$757$	−19.5023	−	33.7789i	−0.708822	−	1.22772i	0.256472	−	0.966552i	$-0.417440\pi$
$758$	1.81037	+	3.13565i	0.0657555	+	0.113892i
$759$		0			0
$760$		−	2.26003i		−	0.0819798i
$761$	−1.15217	+	0.665205i	−0.0417661	+	0.0241137i	−0.520738	−	0.853717i	$-0.674343\pi$
$761$	−1.15217	+	0.665205i	−0.0417661	+	0.0241137i	0.478972	+	0.877830i	$0.341010\pi$
$762$		0			0
$763$	−4.04403	−	26.2151i	−0.146404	−	0.949049i
$764$	−38.0298	−	65.8696i	−1.37587	−	2.38308i
$765$		0			0
$766$	34.7424	+	60.1756i	1.25529	+	2.17423i
$767$	−5.15511	+	35.2109i	−0.186140	+	1.27139i
$768$		0			0
$769$	−13.9092	+	8.03049i	−0.501579	+	0.289587i	−0.729365	−	0.684124i	$-0.760185\pi$
$769$	−13.9092	+	8.03049i	−0.501579	+	0.289587i	0.227786	+	0.973711i	$0.426851\pi$
$770$	−1.62784	−	10.5523i	−0.0586634	−	0.380280i
$771$		0			0
$772$	−28.8885	−	16.6788i	−1.03972	−	0.600283i
$773$		−	16.7093i		−	0.600993i	−0.953783	−	0.300496i	$-0.902848\pi$
$773$		−	16.7093i		−	0.600993i	0.953783	−	0.300496i	$-0.0971524\pi$
$774$		0			0
$775$	13.0389	+	7.52803i	0.468372	+	0.270415i
$776$	6.89632	−	11.9448i	0.247564	−	0.428793i
$777$		0			0
$778$	−22.0187	+	12.7125i	−0.789410	+	0.455766i
$779$	4.73776	−	8.20604i	0.169748	−	0.294012i
$780$		0			0
$781$	5.87563	+	10.1769i	0.210246	+	0.364158i
$782$			2.10348i			0.0752203i
$783$		0			0
$784$	4.61562	+	4.22365i	0.164844	+	0.150845i
$785$			2.31155i			0.0825026i
$786$		0			0
$787$			39.8860i			1.42178i	0.703301	+	0.710892i	$0.251708\pi$
$787$			39.8860i			1.42178i	−0.703301	+	0.710892i	$0.748292\pi$
$788$	30.1533	−	17.4090i	1.07417	−	0.620171i
$789$		0			0
$790$	2.34203	+	4.05652i	0.0833258	+	0.144325i
$791$	−0.303203	−	0.377520i	−0.0107807	−	0.0134231i
$792$		0			0
$793$	9.06523	+	22.8139i	0.321916	+	0.810145i
$794$	20.4415	+	35.4057i	0.725441	+	1.25650i
$795$		0			0
$796$	−0.759398			−0.0269161
$797$	22.1433	−	38.3532i	0.784354	−	1.35854i	−0.145030	−	0.989427i	$-0.546328\pi$
$797$	22.1433	−	38.3532i	0.784354	−	1.35854i	0.929384	−	0.369114i	$-0.120339\pi$
$798$		0			0
$799$	25.6650	+	14.8177i	0.907963	+	0.524213i
$800$	26.2907	−	15.1789i	0.929517	−	0.536657i
$801$		0			0
$802$	54.2335			1.91505
$803$	−15.0255			−0.530239
$804$		0			0
$805$	−0.255184	+	0.204950i	−0.00899405	+	0.00722353i
$806$	9.77969	+	24.6119i	0.344475	+	0.866918i
$807$		0			0
$808$	25.5793	+	14.7682i	0.899875	+	0.519543i
$809$	0.669668	−	1.15990i	0.0235443	−	0.0407799i	−0.854013	−	0.520251i	$-0.825838\pi$
$809$	0.669668	−	1.15990i	0.0235443	−	0.0407799i	0.877557	+	0.479471i	$0.159172\pi$
$810$		0			0
$811$		−	11.6495i		−	0.409068i	−0.978859	−	0.204534i	$-0.934432\pi$
$811$		−	11.6495i		−	0.409068i	0.978859	−	0.204534i	$-0.0655678\pi$
$812$	62.4199	−	9.62912i	2.19051	−	0.337916i
$813$		0			0
$814$	−61.9456	−	35.7643i	−2.17119	−	1.25354i
$815$	−5.14996			−0.180395
$816$		0			0
$817$		−	2.37741i		−	0.0831751i
$818$	−16.4994			−0.576889
$819$		0			0
$820$	11.8109			0.412455
$821$			47.8476i			1.66989i	0.550331	+	0.834947i	$0.314501\pi$
$821$			47.8476i			1.66989i	−0.550331	+	0.834947i	$0.685499\pi$
$822$		0			0
$823$	−16.9163			−0.589664			−0.294832	−	0.955549i	$-0.595264\pi$
$823$	−16.9163			−0.589664			−0.294832	+	0.955549i	$0.595264\pi$
$824$	35.5882	+	20.5469i	1.23977	+	0.715784i
$825$		0			0
$826$	21.2002	−	54.5713i	0.737650	−	1.89878i
$827$		−	32.2552i		−	1.12162i	−0.827943	−	0.560812i	$-0.810489\pi$
$827$		−	32.2552i		−	1.12162i	0.827943	−	0.560812i	$-0.189511\pi$
$828$		0			0
$829$	15.0241	−	26.0226i	0.521810	−	0.903801i	−0.477868	−	0.878432i	$-0.658590\pi$
$829$	15.0241	−	26.0226i	0.521810	−	0.903801i	0.999678	−	0.0253697i	$-0.00807629\pi$
$830$	19.0899	+	11.0216i	0.662620	+	0.382564i
$831$		0			0
$832$	46.4594	+	6.80196i	1.61069	+	0.235816i
$833$	24.9106	+	22.7952i	0.863103	+	0.789806i
$834$		0			0
$835$	−10.5710			−0.365824
$836$	13.2265			0.457449
$837$		0			0
$838$	−37.1019	+	21.4208i	−1.28166	+	0.739969i
$839$	−2.88921	−	1.66809i	−0.0997466	−	0.0575888i	0.449297	−	0.893383i	$-0.351675\pi$
$839$	−2.88921	−	1.66809i	−0.0997466	−	0.0575888i	−0.549044	+	0.835794i	$0.685008\pi$
$840$		0			0
$841$	−16.6089	+	28.7675i	−0.572722	+	0.991983i
$842$	−76.0113			−2.61952
$843$		0			0
$844$	7.95690	+	13.7818i	0.273888	+	0.474387i
$845$	−5.67482	−	6.01327i	−0.195220	−	0.206863i
$846$		0			0
$847$	−7.81870	+	1.20614i	−0.268654	+	0.0414435i
$848$	−3.47079	−	6.01158i	−0.119187	−	0.206438i
$849$		0			0
$850$	43.0402	−	24.8493i	1.47627	−	0.852324i
$851$			2.19263i			0.0751624i
$852$		0			0
$853$		−	24.7934i		−	0.848909i	−0.905449	−	0.424455i	$-0.860466\pi$
$853$		−	24.7934i		−	0.848909i	0.905449	−	0.424455i	$-0.139534\pi$
$854$	−6.15736	−	39.9146i	−0.210701	−	1.36585i
$855$		0			0
$856$			4.78285i			0.163474i
$857$	0.0352352	+	0.0610292i	0.00120361	+	0.00208472i	0.866627	−	0.498957i	$-0.166284\pi$
$857$	0.0352352	+	0.0610292i	0.00120361	+	0.00208472i	−0.865423	+	0.501042i	$0.832950\pi$
$858$		0			0
$859$	−4.13095	+	7.15501i	−0.140946	+	0.244126i	−0.927853	−	0.372946i	$-0.878348\pi$
$859$	−4.13095	+	7.15501i	−0.140946	+	0.244126i	0.786907	+	0.617072i	$0.211681\pi$
$860$	2.56635	−	1.48168i	0.0875119	−	0.0505250i
$861$		0			0
$862$	−23.6557	+	40.9729i	−0.805716	+	1.39554i
$863$	−8.67178	−	5.00666i	−0.295191	−	0.170429i	0.345090	−	0.938570i	$-0.387849\pi$
$863$	−8.67178	−	5.00666i	−0.295191	−	0.170429i	−0.640280	+	0.768141i	$0.721182\pi$
$864$		0			0
$865$			14.7692i			0.502166i
$866$	62.2889	+	35.9625i	2.11666	+	1.22206i
$867$		0			0
$868$	−3.99953	−	25.9266i	−0.135753	−	0.880007i
$869$	−8.05139	+	4.64847i	−0.273125	+	0.157689i
$870$		0			0
$871$	−21.5371	−	17.0269i	−0.729757	−	0.576933i
$872$	11.5349	+	19.9791i	0.390622	+	0.676578i
$873$		0			0
$874$	−0.336692	−	0.583168i	−0.0113888	−	0.0197260i
$875$	15.0508	+	5.84704i	0.508811	+	0.197666i
$876$		0			0
$877$	−10.3514	+	5.97636i	−0.349540	+	0.201807i	−0.664483	−	0.747304i	$-0.731348\pi$
$877$	−10.3514	+	5.97636i	−0.349540	+	0.201807i	0.314942	+	0.949111i	$0.398015\pi$
$878$		−	36.8967i		−	1.24520i
$879$		0			0
$880$	−0.804414	−	1.39329i	−0.0271168	−	0.0469677i
$881$	16.3037	+	28.2389i	0.549286	+	0.951391i	0.998324	+	0.0578785i	$0.0184336\pi$
$881$	16.3037	+	28.2389i	0.549286	+	0.951391i	−0.449038	+	0.893513i	$0.648233\pi$
$882$		0			0
$883$	−42.6553			−1.43547			−0.717733	−	0.696318i	$-0.754820\pi$
$883$	−42.6553			−1.43547			−0.717733	+	0.696318i	$0.754820\pi$
$884$	52.0805	+	7.62493i	1.75166	+	0.256454i
$885$		0			0
$886$	1.40426	+	0.810752i	0.0471772	+	0.0272378i
$887$	−41.3944			−1.38989			−0.694945	−	0.719063i	$-0.744571\pi$
$887$	−41.3944			−1.38989			−0.694945	+	0.719063i	$0.744571\pi$
$888$		0			0
$889$	−35.0059	+	5.40014i	−1.17406	+	0.181115i
$890$	2.75057	+	1.58804i	0.0921992	+	0.0532312i
$891$		0			0
$892$	−3.67612	+	2.12241i	−0.123086	+	0.0710636i
$893$	−9.48715			−0.317475
$894$		0			0
$895$	−0.960153	+	0.554345i	−0.0320944	+	0.0185297i
$896$	−39.4213	−	15.3146i	−1.31697	−	0.511626i
$897$		0			0
$898$	13.0853	−	22.6645i	0.436663	−	0.756323i
$899$	22.3804	+	12.9213i	0.746429	+	0.430951i
$900$		0			0
$901$	−18.7319	−	32.4447i	−0.624051	−	1.08089i
$902$			38.9344i			1.29637i
$903$		0			0
$904$	0.364709	+	0.210565i	0.0121300	+	0.00700328i
$905$	4.25578	+	2.45708i	0.141467	+	0.0816760i
$906$		0			0
$907$	−17.2145	+	29.8164i	−0.571598	+	0.990037i	0.424804	+	0.905285i	$0.360343\pi$
$907$	−17.2145	+	29.8164i	−0.571598	+	0.990037i	−0.996402	+	0.0847518i	$0.972990\pi$
$908$			30.9149i			1.02595i
$909$		0			0
$910$	6.89151	+	11.7274i	0.228451	+	0.388760i
$911$	16.4687			0.545632			0.272816	−	0.962066i	$-0.412045\pi$
$911$	16.4687			0.545632			0.272816	+	0.962066i	$0.412045\pi$
$912$		0			0
$913$	−21.8756	+	37.8897i	−0.723977	+	1.25397i
$914$	54.0406			1.78750
$915$		0			0
$916$	−7.91708	−	4.57093i	−0.261588	−	0.151028i
$917$	−27.4687	−	34.2015i	−0.907098	−	1.12943i
$918$		0			0
$919$	9.45268	+	16.3725i	0.311815	+	0.540080i	0.978755	−	0.205031i	$-0.0657297\pi$
$919$	9.45268	+	16.3725i	0.311815	+	0.540080i	−0.666940	+	0.745111i	$0.732396\pi$
$920$	0.142331	−	0.246524i	0.00469251	−	0.00812767i
$921$		0			0
$922$	39.3668	−	68.1853i	1.29648	−	2.24556i
$923$	−11.7439	−	9.28457i	−0.386557	−	0.305605i
$924$		0			0
$925$	44.8644	−	25.9025i	1.47513	−	0.851668i
$926$	−30.4641			−1.00111
$927$		0			0
$928$	45.1262	−	26.0536i	1.48134	−	0.855251i
$929$	−44.2452	+	25.5450i	−1.45164	+	0.838104i	−0.998575	−	0.0533735i	$-0.983003\pi$
$929$	−44.2452	+	25.5450i	−1.45164	+	0.838104i	−0.453065	+	0.891478i	$0.649669\pi$
$930$		0			0
$931$	−10.5549	−	2.33242i	−0.345923	−	0.0764420i
$932$	−29.9537	+	51.8814i	−0.981167	+	1.69943i
$933$		0			0
$934$	−16.8244	−	9.71358i	−0.550512	−	0.317838i
$935$	−4.34145	−	7.51960i	−0.141980	−	0.245917i
$936$		0			0
$937$	27.8485			0.909771			0.454886	−	0.890550i	$-0.349680\pi$
$937$	27.8485			0.909771			0.454886	+	0.890550i	$0.349680\pi$
$938$	28.2831	+	35.2155i	0.923477	+	1.14983i
$939$		0			0
$940$	−5.91271	−	10.2411i	−0.192851	−	0.334029i
$941$	−21.9410	+	12.6676i	−0.715256	+	0.412953i	−0.813004	−	0.582258i	$-0.802169\pi$
$941$	−21.9410	+	12.6676i	−0.715256	+	0.412953i	0.0977483	+	0.995211i	$0.468836\pi$
$942$		0			0
$943$	1.03359	−	0.596745i	0.0336584	−	0.0194327i
$944$		−	8.82147i		−	0.287114i
$945$		0			0
$946$	4.88433	+	8.45990i	0.158803	+	0.275055i
$947$			46.5881i			1.51391i	0.653468	+	0.756954i	$0.273314\pi$
$947$			46.5881i			1.51391i	−0.653468	+	0.756954i	$0.726686\pi$
$948$		0			0
$949$	17.7891	−	7.06862i	0.577460	−	0.229457i
$950$	−7.95498	+	13.7784i	−0.258094	+	0.447031i
$951$		0			0
$952$	−27.3746	−	10.6347i	−0.887215	−	0.344671i
$953$	−2.02891	+	3.51418i	−0.0657229	+	0.113835i	−0.897014	−	0.442001i	$-0.854269\pi$
$953$	−2.02891	+	3.51418i	−0.0657229	+	0.113835i	0.831292	+	0.555837i	$0.187602\pi$
$954$		0			0
$955$		−	15.9845i		−	0.517245i
$956$		−	43.4101i		−	1.40398i
$957$		0			0
$958$	−21.0259	+	36.4179i	−0.679315	+	1.17661i
$959$	45.9723	+	17.8596i	1.48452	+	0.576717i
$960$		0			0
$961$	−10.1330	+	17.5509i	−0.326872	+	0.566158i
$962$	90.1642	+	13.2006i	2.90701	+	0.425605i
$963$		0			0
$964$			16.6825i			0.537309i
$965$	−3.50516	−	6.07112i	−0.112835	−	0.195436i
$966$		0			0
$967$		−	30.4667i		−	0.979741i	−0.871795	−	0.489871i	$-0.837044\pi$
$967$		−	30.4667i		−	0.979741i	0.871795	−	0.489871i	$-0.162956\pi$
$968$	5.95881	−	3.44032i	0.191524	−	0.110576i
$969$		0			0
$970$	7.40179	−	4.27343i	0.237657	−	0.137211i
$971$	−7.92039	−	13.7185i	−0.254177	−	0.440248i	0.710494	−	0.703703i	$-0.248471\pi$
$971$	−7.92039	−	13.7185i	−0.254177	−	0.440248i	−0.964672	+	0.263455i	$0.915138\pi$
$972$		0			0
$973$	5.77937	+	7.19592i	0.185278	+	0.230691i
$974$	25.8117			0.827060
$975$		0			0
$976$	−3.04272	−	5.27014i	−0.0973950	−	0.168693i
$977$	17.4835	+	10.0941i	0.559346	+	0.322938i	0.752883	−	0.658155i	$-0.228663\pi$
$977$	17.4835	+	10.0941i	0.559346	+	0.322938i	−0.193537	+	0.981093i	$0.561996\pi$
$978$		0			0
$979$	−3.15195	+	5.45933i	−0.100737	+	0.174481i
$980$	−4.06040	−	12.8474i	−0.129705	−	0.410395i
$981$		0			0
$982$	56.5406	−	32.6437i	1.80428	−	1.04170i
$983$	−45.1460	+	26.0651i	−1.43993	+	0.831346i	−0.997844	−	0.0656242i	$-0.979096\pi$
$983$	−45.1460	+	26.0651i	−1.43993	+	0.831346i	−0.442090	+	0.896971i	$0.645763\pi$
$984$		0			0
$985$	7.31726			0.233147
$986$	73.8756	−	42.6521i	2.35268	−	1.35832i
$987$		0			0
$988$	−15.6593	+	6.22230i	−0.498187	+	0.197958i
$989$	0.149724	−	0.259329i	0.00476093	−	0.00824618i
$990$		0			0
$991$	−7.21499	+	12.4967i	−0.229192	+	0.396972i	−0.957569	−	0.288205i	$-0.906942\pi$
$991$	−7.21499	+	12.4967i	−0.229192	+	0.396972i	0.728377	+	0.685176i	$0.240275\pi$
$992$	−10.8216	−	18.7435i	−0.343585	−	0.595107i
$993$		0			0
$994$	15.4225	+	19.2026i	0.489171	+	0.609070i
$995$	−0.138211	−	0.0797963i	−0.00438159	−	0.00252971i
$996$		0			0
$997$	56.3750			1.78541			0.892707	−	0.450637i	$-0.148803\pi$
$997$	56.3750			1.78541			0.892707	+	0.450637i	$0.148803\pi$
$998$	−27.5541	+	47.7250i	−0.872209	+	1.51071i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.bm.h.478.3	✓	36
3.2	odd	2	inner	819.2.bm.h.478.16	yes	36
7.4	even	3		819.2.do.h.361.16	yes	36
13.4	even	6		819.2.do.h.667.16	yes	36
21.11	odd	6		819.2.do.h.361.3	yes	36
39.17	odd	6		819.2.do.h.667.3	yes	36
91.4	even	6	inner	819.2.bm.h.550.16	yes	36
273.95	odd	6	inner	819.2.bm.h.550.3	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.bm.h.478.3	✓	36	1.1	even	1	trivial
819.2.bm.h.478.16	yes	36	3.2	odd	2	inner
819.2.bm.h.550.3	yes	36	273.95	odd	6	inner
819.2.bm.h.550.16	yes	36	91.4	even	6	inner
819.2.do.h.361.3	yes	36	21.11	odd	6
819.2.do.h.361.16	yes	36	7.4	even	3
819.2.do.h.667.3	yes	36	39.17	odd	6
819.2.do.h.667.16	yes	36	13.4	even	6

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.24196i q^{2} -3.02638 q^{4} +(-0.550805 - 0.318007i) q^{5} +(0.958080 - 2.46619i) q^{7} +2.30110i q^{8} +O(q^{10})\)	\(q-2.24196i q^{2} -3.02638 q^{4} +(-0.550805 - 0.318007i) q^{5} +(0.958080 - 2.46619i) q^{7} +2.30110i q^{8} +(-0.712960 + 1.23488i) q^{10} +(-2.45100 - 1.41508i) q^{11} +(3.56752 + 0.522308i) q^{13} +(-5.52909 - 2.14798i) q^{14} -0.893779 q^{16} -4.82375 q^{17} +(1.33734 - 0.772111i) q^{19} +(1.66695 + 0.962411i) q^{20} +(-3.17256 + 5.49504i) q^{22} +0.194503 q^{23} +(-2.29774 - 3.97981i) q^{25} +(1.17099 - 7.99823i) q^{26} +(-2.89952 + 7.46362i) q^{28} +(-3.94391 - 6.83106i) q^{29} +(-2.83734 + 1.63814i) q^{31} +6.60603i q^{32} +10.8147i q^{34} +(-1.31198 + 1.05371i) q^{35} +11.2730i q^{37} +(-1.73104 - 2.99825i) q^{38} +(0.731768 - 1.26746i) q^{40} +(5.31403 - 3.06805i) q^{41} +(0.769777 - 1.33329i) q^{43} +(7.41765 + 4.28258i) q^{44} -0.436067i q^{46} +(-5.32055 - 3.07182i) q^{47} +(-5.16416 - 4.72561i) q^{49} +(-8.92257 + 5.15145i) q^{50} +(-10.7967 - 1.58070i) q^{52} +(3.88327 + 6.72602i) q^{53} +(0.900014 + 1.55887i) q^{55} +(5.67496 + 2.20464i) q^{56} +(-15.3150 + 8.84210i) q^{58} +9.86985i q^{59} +(3.40433 + 5.89647i) q^{61} +(3.67264 + 6.36119i) q^{62} +13.0229 q^{64} +(-1.79891 - 1.42219i) q^{65} +(-6.59441 - 3.80728i) q^{67} +14.5985 q^{68} +(2.36238 + 2.94141i) q^{70} +(-3.59586 - 2.07607i) q^{71} +(4.59778 - 2.65453i) q^{73} +25.2736 q^{74} +(-4.04729 + 2.33670i) q^{76} +(-5.83812 + 4.68886i) q^{77} +(1.64247 - 2.84485i) q^{79} +(0.492298 + 0.284228i) q^{80} +(-6.87845 - 11.9138i) q^{82} -15.4589i q^{83} +(2.65695 + 1.53399i) q^{85} +(-2.98919 - 1.72581i) q^{86} +(3.25626 - 5.64000i) q^{88} -2.22739i q^{89} +(4.70608 - 8.29776i) q^{91} -0.588639 q^{92} +(-6.88690 + 11.9285i) q^{94} -0.982148 q^{95} +(-5.19089 - 2.99696i) q^{97} +(-10.5946 + 11.5778i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 44 q^{4} + 8 q^{7}+O(q^{10}) \) 36 * q - 44 * q^4 + 8 * q^7	\( 36 q - 44 q^{4} + 8 q^{7} + 8 q^{10} + 52 q^{16} - 36 q^{19} + 2 q^{22} + 22 q^{25} + 16 q^{28} - 18 q^{31} - 34 q^{40} + 4 q^{43} + 12 q^{49} + 74 q^{52} - 22 q^{55} + 84 q^{58} - 54 q^{61} - 100 q^{64} + 36 q^{67} - 72 q^{70} - 30 q^{73} + 42 q^{76} + 40 q^{79} + 18 q^{82} + 12 q^{88} + 32 q^{91} - 56 q^{94} - 36 q^{97}+O(q^{100}) \) 36 * q - 44 * q^4 + 8 * q^7 + 8 * q^10 + 52 * q^16 - 36 * q^19 + 2 * q^22 + 22 * q^25 + 16 * q^28 - 18 * q^31 - 34 * q^40 + 4 * q^43 + 12 * q^49 + 74 * q^52 - 22 * q^55 + 84 * q^58 - 54 * q^61 - 100 * q^64 + 36 * q^67 - 72 * q^70 - 30 * q^73 + 42 * q^76 + 40 * q^79 + 18 * q^82 + 12 * q^88 + 32 * q^91 - 56 * q^94 - 36 * q^97

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