LMFDB - Embedded newform 804.2.s.b.5.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(5,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 5]))

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

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

chi := DirichletCharacter("804.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.s (of order $22$, degree $10$, 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:	$200$
Relative dimension:	$20$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			5.14
Character	$\chi$	$=$	804.5
Dual form			804.2.s.b.161.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.575290 - 1.63372i) q^{3} +(2.05430 - 0.603197i) q^{5} +(-2.91035 - 2.52183i) q^{7} +(-2.33808 - 1.87973i) q^{9} +O(q^{10})$	\(q+(0.575290 - 1.63372i) q^{3} +(2.05430 - 0.603197i) q^{5} +(-2.91035 - 2.52183i) q^{7} +(-2.33808 - 1.87973i) q^{9} +(5.36557 - 1.57547i) q^{11} +(3.44974 + 5.36790i) q^{13} +(0.196364 - 3.70316i) q^{15} +(-0.764837 - 0.109967i) q^{17} +(-5.19155 - 5.99137i) q^{19} +(-5.79426 + 3.30391i) q^{21} +(4.69664 - 2.14488i) q^{23} +(-0.349969 + 0.224911i) q^{25} +(-4.41602 + 2.73838i) q^{27} -8.43272i q^{29} +(-1.76539 + 2.74699i) q^{31} +(0.512878 - 9.67219i) q^{33} +(-7.49988 - 3.42508i) q^{35} -5.40444 q^{37} +(10.7543 - 2.54781i) q^{39} +(-1.28169 + 8.91433i) q^{41} +(0.443176 + 0.0637191i) q^{43} +(-5.93697 - 2.45120i) q^{45} +(3.17052 - 1.44793i) q^{47} +(1.11429 + 7.75005i) q^{49} +(-0.619659 + 1.18627i) q^{51} +(-0.119970 - 0.834409i) q^{53} +(10.0722 - 6.47299i) q^{55} +(-12.7749 + 5.03476i) q^{57} +(-6.01354 + 9.35726i) q^{59} +(2.74338 - 9.34309i) q^{61} +(2.06428 + 11.3669i) q^{63} +(10.3247 + 8.94641i) q^{65} +(7.35766 + 3.58676i) q^{67} +(-0.802207 - 8.90692i) q^{69} +(7.24102 - 1.04110i) q^{71} +(6.32300 + 1.85660i) q^{73} +(0.166108 + 0.701140i) q^{75} +(-19.5887 - 8.94588i) q^{77} +(1.27332 + 1.98132i) q^{79} +(1.93326 + 8.78991i) q^{81} +(-2.86458 - 9.75587i) q^{83} +(-1.63754 + 0.235442i) q^{85} +(-13.7767 - 4.85127i) q^{87} +(-3.49281 - 1.59511i) q^{89} +(3.49699 - 24.3221i) q^{91} +(3.47221 + 4.46447i) q^{93} +(-14.2790 - 9.17653i) q^{95} +1.22491i q^{97} +(-15.5066 - 6.40222i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 200 q - 10 q^{9}+O(q^{10}) $ 200 * q - 10 * q^9	$ 200 q - 10 q^{9} + 2 q^{15} + 6 q^{19} - 10 q^{21} - 20 q^{25} - 44 q^{31} - 5 q^{33} + 78 q^{39} - 22 q^{43} - 22 q^{45} - 16 q^{49} + 36 q^{55} + 66 q^{57} + 176 q^{61} + 132 q^{63} + 46 q^{67} - 26 q^{73} - 165 q^{75} - 44 q^{79} + 42 q^{81} - 66 q^{87} - 20 q^{91} + 84 q^{93} - 55 q^{99}+O(q^{100}) $ 200 * q - 10 * q^9 + 2 * q^15 + 6 * q^19 - 10 * q^21 - 20 * q^25 - 44 * q^31 - 5 * q^33 + 78 * q^39 - 22 * q^43 - 22 * q^45 - 16 * q^49 + 36 * q^55 + 66 * q^57 + 176 * q^61 + 132 * q^63 + 46 * q^67 - 26 * q^73 - 165 * q^75 - 44 * q^79 + 42 * q^81 - 66 * q^87 - 20 * q^91 + 84 * q^93 - 55 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{5}{22}\right)$	$1$

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
$3$	0.575290	−	1.63372i	0.332144	−	0.943229i
$3$	0.575290	−	1.63372i	0.332144	−	0.943229i
$4$		0			0
$5$	2.05430	−	0.603197i	0.918711	−	0.269758i	0.212007	−	0.977268i	$-0.432000\pi$
$5$	2.05430	−	0.603197i	0.918711	−	0.269758i	0.706703	+	0.707510i	$0.250182\pi$
$6$		0			0
$7$	−2.91035	−	2.52183i	−1.10001	−	0.953162i	−0.100879	−	0.994899i	$-0.532166\pi$
$7$	−2.91035	−	2.52183i	−1.10001	−	0.953162i	−0.999129	+	0.0417366i	$0.986711\pi$
$8$		0			0
$9$	−2.33808	−	1.87973i	−0.779361	−	0.626576i
$10$		0			0
$11$	5.36557	−	1.57547i	1.61778	−	0.475023i	0.657360	−	0.753577i	$-0.271673\pi$
$11$	5.36557	−	1.57547i	1.61778	−	0.475023i	0.960421	+	0.278554i	$0.0898551\pi$
$12$		0			0
$13$	3.44974	+	5.36790i	0.956786	+	1.48879i	0.870292	+	0.492536i	$0.163930\pi$
$13$	3.44974	+	5.36790i	0.956786	+	1.48879i	0.0864941	+	0.996252i	$0.472434\pi$
$14$		0			0
$15$	0.196364	−	3.70316i	0.0507010	−	0.956153i
$16$		0			0
$17$	−0.764837	−	0.109967i	−0.185500	−	0.0266709i	0.0489385	−	0.998802i	$-0.484416\pi$
$17$	−0.764837	−	0.109967i	−0.185500	−	0.0266709i	−0.234439	+	0.972131i	$0.575325\pi$
$18$		0			0
$19$	−5.19155	−	5.99137i	−1.19102	−	1.37451i	−0.909893	−	0.414844i	$-0.863836\pi$
$19$	−5.19155	−	5.99137i	−1.19102	−	1.37451i	−0.281130	−	0.959670i	$-0.590709\pi$
$20$		0			0
$21$	−5.79426	+	3.30391i	−1.26441	+	0.720972i
$22$		0			0
$23$	4.69664	−	2.14488i	0.979316	−	0.447239i	0.139567	−	0.990213i	$-0.455429\pi$
$23$	4.69664	−	2.14488i	0.979316	−	0.447239i	0.839750	+	0.542974i	$0.182702\pi$
$24$		0			0
$25$	−0.349969	+	0.224911i	−0.0699937	+	0.0449822i
$26$		0			0
$27$	−4.41602	+	2.73838i	−0.849864	+	0.527002i
$28$		0			0
$29$		−	8.43272i		−	1.56592i	−0.622074	−	0.782959i	$-0.713710\pi$
$29$		−	8.43272i		−	1.56592i	0.622074	−	0.782959i	$-0.286290\pi$
$30$		0			0
$31$	−1.76539	+	2.74699i	−0.317073	+	0.493375i	−0.962808	−	0.270187i	$-0.912915\pi$
$31$	−1.76539	+	2.74699i	−0.317073	+	0.493375i	0.645735	+	0.763561i	$0.276551\pi$
$32$		0			0
$33$	0.512878	−	9.67219i	0.0892806	−	1.68371i
$34$		0			0
$35$	−7.49988	−	3.42508i	−1.26771	−	0.578944i
$36$		0			0
$37$	−5.40444			−0.888484			−0.444242	−	0.895907i	$-0.646527\pi$
$37$	−5.40444			−0.888484			−0.444242	+	0.895907i	$0.646527\pi$
$38$		0			0
$39$	10.7543	−	2.54781i	1.72206	−	0.407976i
$40$		0			0
$41$	−1.28169	+	8.91433i	−0.200166	+	1.39218i	0.603623	+	0.797270i	$0.293723\pi$
$41$	−1.28169	+	8.91433i	−0.200166	+	1.39218i	−0.803789	+	0.594915i	$0.797186\pi$
$42$		0			0
$43$	0.443176	+	0.0637191i	0.0675837	+	0.00971707i	0.176024	−	0.984386i	$-0.443676\pi$
$43$	0.443176	+	0.0637191i	0.0675837	+	0.00971707i	−0.108440	+	0.994103i	$0.534586\pi$
$44$		0			0
$45$	−5.93697	−	2.45120i	−0.885030	−	0.365403i
$46$		0			0
$47$	3.17052	−	1.44793i	0.462467	−	0.211202i	−0.170535	−	0.985352i	$-0.554550\pi$
$47$	3.17052	−	1.44793i	0.462467	−	0.211202i	0.633002	+	0.774150i	$0.281822\pi$
$48$		0			0
$49$	1.11429	+	7.75005i	0.159184	+	1.10715i
$50$		0			0
$51$	−0.619659	+	1.18627i	−0.0867696	+	0.166111i
$52$		0			0
$53$	−0.119970	−	0.834409i	−0.0164791	−	0.114615i	0.979922	−	0.199384i	$-0.0638940\pi$
$53$	−0.119970	−	0.834409i	−0.0164791	−	0.114615i	−0.996401	+	0.0847686i	$0.972985\pi$
$54$		0			0
$55$	10.0722	−	6.47299i	1.35813	−	0.872818i
$56$		0			0
$57$	−12.7749	+	5.03476i	−1.69207	+	0.666870i
$58$		0			0
$59$	−6.01354	+	9.35726i	−0.782897	+	1.21821i	0.188808	+	0.982014i	$0.439538\pi$
$59$	−6.01354	+	9.35726i	−0.782897	+	1.21821i	−0.971705	+	0.236197i	$0.924099\pi$
$60$		0			0
$61$	2.74338	−	9.34309i	0.351254	−	1.19626i	−0.574618	−	0.818422i	$-0.694849\pi$
$61$	2.74338	−	9.34309i	0.351254	−	1.19626i	0.925872	−	0.377838i	$-0.123332\pi$
$62$		0			0
$63$	2.06428	+	11.3669i	0.260075	+	1.43209i
$64$		0			0
$65$	10.3247	+	8.94641i	1.28062	+	1.10967i
$66$		0			0
$67$	7.35766	+	3.58676i	0.898881	+	0.438192i
$67$	7.35766	+	3.58676i	0.898881	+	0.438192i
$68$		0			0
$69$	−0.802207	−	8.90692i	−0.0965744	−	1.07227i
$70$		0			0
$71$	7.24102	−	1.04110i	0.859351	−	0.123556i	0.301469	−	0.953476i	$-0.402523\pi$
$71$	7.24102	−	1.04110i	0.859351	−	0.123556i	0.557882	+	0.829920i	$0.311614\pi$
$72$		0			0
$73$	6.32300	+	1.85660i	0.740051	+	0.217298i	0.629965	−	0.776624i	$-0.283069\pi$
$73$	6.32300	+	1.85660i	0.740051	+	0.217298i	0.110086	+	0.993922i	$0.464887\pi$
$74$		0			0
$75$	0.166108	+	0.701140i	0.0191805	+	0.0809607i
$76$		0			0
$77$	−19.5887	−	8.94588i	−2.23234	−	1.01948i
$78$		0			0
$79$	1.27332	+	1.98132i	0.143259	+	0.222916i	0.905467	−	0.424417i	$-0.139521\pi$
$79$	1.27332	+	1.98132i	0.143259	+	0.222916i	−0.762208	+	0.647332i	$0.775885\pi$
$80$		0			0
$81$	1.93326	+	8.78991i	0.214806	+	0.976657i
$82$		0			0
$83$	−2.86458	−	9.75587i	−0.314429	−	1.07085i	−0.953424	−	0.301635i	$-0.902468\pi$
$83$	−2.86458	−	9.75587i	−0.314429	−	1.07085i	0.638995	−	0.769211i	$-0.279350\pi$
$84$		0			0
$85$	−1.63754	+	0.235442i	−0.177616	+	0.0255373i
$86$		0			0
$87$	−13.7767	−	4.85127i	−1.47702	−	0.520110i
$88$		0			0
$89$	−3.49281	−	1.59511i	−0.370238	−	0.169082i	0.221603	−	0.975137i	$-0.428871\pi$
$89$	−3.49281	−	1.59511i	−0.370238	−	0.169082i	−0.591840	+	0.806055i	$0.701598\pi$
$90$		0			0
$91$	3.49699	−	24.3221i	0.366584	−	2.54965i
$92$		0			0
$93$	3.47221	+	4.46447i	0.360051	+	0.462944i
$94$		0			0
$95$	−14.2790	−	9.17653i	−1.46499	−	0.941493i
$96$		0			0
$97$			1.22491i			0.124371i	0.998065	+	0.0621853i	$0.0198070\pi$
$97$			1.22491i			0.124371i	−0.998065	+	0.0621853i	$0.980193\pi$
$98$		0			0
$99$	−15.5066	−	6.40222i	−1.55847	−	0.643447i
$100$		0			0
$101$	−1.40427	−	1.62061i	−0.139730	−	0.161257i	0.681571	−	0.731752i	$-0.261297\pi$
$101$	−1.40427	−	1.62061i	−0.139730	−	0.161257i	−0.821301	+	0.570495i	$0.806752\pi$
$102$		0			0
$103$	−2.30070	−	1.47857i	−0.226695	−	0.145688i	0.422364	−	0.906426i	$-0.361201\pi$
$103$	−2.30070	−	1.47857i	−0.226695	−	0.145688i	−0.649058	+	0.760739i	$0.724837\pi$
$104$		0			0
$105$	−9.91023	+	10.2823i	−0.967140	+	1.00345i
$106$		0			0
$107$	0.573320	−	1.95255i	0.0554249	−	0.188760i	−0.927127	−	0.374746i	$-0.877730\pi$
$107$	0.573320	−	1.95255i	0.0554249	−	0.188760i	0.982552	+	0.185986i	$0.0595480\pi$
$108$		0			0
$109$	8.11037	+	12.6200i	0.776832	+	1.20877i	0.973586	+	0.228322i	$0.0733237\pi$
$109$	8.11037	+	12.6200i	0.776832	+	1.20877i	−0.196754	+	0.980453i	$0.563040\pi$
$110$		0			0
$111$	−3.10912	+	8.82934i	−0.295105	+	0.838044i
$112$		0			0
$113$	18.3068	+	5.37535i	1.72216	+	0.505671i	0.985366	−	0.170451i	$-0.0545224\pi$
$113$	18.3068	+	5.37535i	1.72216	+	0.505671i	0.736790	+	0.676121i	$0.236341\pi$
$114$		0			0
$115$	8.35451	−	7.23922i	0.779062	−	0.675061i
$116$		0			0
$117$	2.02441	−	19.0352i	0.187157	−	1.75980i
$118$		0			0
$119$	1.94862	+	2.24883i	0.178630	+	0.206150i
$120$		0			0
$121$	17.0534	−	10.9596i	1.55031	−	0.996325i
$122$		0			0
$123$	13.8262	+	7.22225i	1.24666	+	0.651208i
$124$		0			0
$125$	−7.59364	+	8.76353i	−0.679196	+	0.783834i
$126$		0			0
$127$	2.98832	−	3.44871i	0.265171	−	0.306024i	−0.607512	−	0.794310i	$-0.707832\pi$
$127$	2.98832	−	3.44871i	0.265171	−	0.306024i	0.872683	+	0.488287i	$0.162378\pi$
$128$		0			0
$129$	0.359054	−	0.687369i	0.0316130	−	0.0605195i
$130$		0			0
$131$	2.81078	−	1.28364i	0.245579	−	0.112152i	−0.288824	−	0.957382i	$-0.593264\pi$
$131$	2.81078	−	1.28364i	0.245579	−	0.112152i	0.534402	+	0.845230i	$0.320537\pi$
$132$		0			0
$133$			30.5292i			2.64721i
$134$		0			0
$135$	−7.42005	+	8.28919i	−0.638616	+	0.713420i
$136$		0			0
$137$	3.57227	+	7.82217i	0.305199	+	0.668293i	0.998635	−	0.0522248i	$-0.0166312\pi$
$137$	3.57227	+	7.82217i	0.305199	+	0.668293i	−0.693436	+	0.720518i	$0.743904\pi$
$138$		0			0
$139$	4.95108	+	16.8618i	0.419945	+	1.43020i	0.849705	+	0.527259i	$0.176780\pi$
$139$	4.95108	+	16.8618i	0.419945	+	1.43020i	−0.429759	+	0.902943i	$0.641402\pi$
$140$		0			0
$141$	−0.541539	−	6.01272i	−0.0456058	−	0.506362i
$142$		0			0
$143$	26.9668	+	23.3669i	2.25508	+	1.95404i
$144$		0			0
$145$	−5.08659	−	17.3233i	−0.422418	−	1.43863i
$146$		0			0
$147$	13.3024	+	2.63809i	1.09717	+	0.217586i
$148$		0			0
$149$	10.0243	−	8.68614i	0.821226	−	0.711596i	−0.139160	−	0.990270i	$-0.544440\pi$
$149$	10.0243	−	8.68614i	0.821226	−	0.711596i	0.960386	+	0.278674i	$0.0898948\pi$
$150$		0			0
$151$	−1.31762	+	9.16424i	−0.107226	+	0.745775i	0.863285	+	0.504717i	$0.168403\pi$
$151$	−1.31762	+	9.16424i	−0.107226	+	0.745775i	−0.970511	+	0.241057i	$0.922506\pi$
$152$		0			0
$153$	1.58154	+	1.69480i	0.127860	+	0.137016i
$154$		0			0
$155$	−1.96965	+	6.70802i	−0.158206	+	0.538802i
$156$		0			0
$157$	2.04478	+	4.47745i	0.163192	+	0.357340i	0.973508	−	0.228653i	$-0.0734321\pi$
$157$	2.04478	+	4.47745i	0.163192	+	0.357340i	−0.810316	+	0.585992i	$0.800705\pi$
$158$		0			0
$159$	−1.43221	−	0.284030i	−0.113582	−	0.0225251i
$160$		0			0
$161$	−19.0779	−	5.60177i	−1.50355	−	0.441481i
$162$		0			0
$163$	7.70377			0.603406			0.301703	−	0.953402i	$-0.402445\pi$
$163$	7.70377			0.603406			0.301703	+	0.953402i	$0.402445\pi$
$164$		0			0
$165$	−4.78063	−	20.1789i	−0.372172	−	1.57093i
$166$		0			0
$167$	13.1265	−	11.3742i	1.01576	−	0.880161i	0.0229352	−	0.999737i	$-0.492699\pi$
$167$	13.1265	−	11.3742i	1.01576	−	0.880161i	0.992825	+	0.119576i	$0.0381534\pi$
$168$		0			0
$169$	−11.5133	+	25.2105i	−0.885636	+	1.93927i
$170$		0			0
$171$	0.876135	+	23.7670i	0.0669997	+	1.81751i
$172$		0			0
$173$	−2.04209	+	3.17755i	−0.155257	+	0.241585i	−0.910165	−	0.414246i	$-0.864045\pi$
$173$	−2.04209	+	3.17755i	−0.155257	+	0.241585i	0.754908	+	0.655831i	$0.227682\pi$
$174$		0			0
$175$	1.58572	+	0.227992i	0.119869	+	0.0172346i
$176$		0			0
$177$	11.8276	+	15.2076i	0.889017	+	1.14307i
$178$		0			0
$179$	−2.71308	+	5.94082i	−0.202785	+	0.444037i	−0.983514	−	0.180833i	$-0.942121\pi$
$179$	−2.71308	+	5.94082i	−0.202785	+	0.444037i	0.780729	+	0.624870i	$0.214848\pi$
$180$		0			0
$181$	−3.14530	−	6.88725i	−0.233788	−	0.511925i	0.755982	−	0.654592i	$-0.227160\pi$
$181$	−3.14530	−	6.88725i	−0.233788	−	0.511925i	−0.989771	+	0.142667i	$0.954432\pi$
$182$		0			0
$183$	−13.6858	−	9.85690i	−1.01168	−	0.728643i
$184$		0			0
$185$	−11.1023	+	3.25994i	−0.816260	+	0.239675i
$186$		0			0
$187$	−4.27704	+	0.614945i	−0.312768	+	0.0449693i
$188$		0			0
$189$	19.7579	+	3.16681i	1.43718	+	0.230352i
$190$		0			0
$191$	−1.20933	+	2.64807i	−0.0875041	+	0.191607i	−0.948325	−	0.317301i	$-0.897223\pi$
$191$	−1.20933	+	2.64807i	−0.0875041	+	0.191607i	0.860821	+	0.508908i	$0.169951\pi$
$192$		0			0
$193$	4.28043	+	2.75087i	0.308112	+	0.198012i	0.685554	−	0.728021i	$-0.259560\pi$
$193$	4.28043	+	2.75087i	0.308112	+	0.198012i	−0.377442	+	0.926033i	$0.623196\pi$
$194$		0			0
$195$	20.5556	−	11.7209i	1.47202	−	0.839351i
$196$		0			0
$197$	0.0858349	+	0.596995i	0.00611548	+	0.0425341i	0.992651	−	0.121015i	$-0.0386149\pi$
$197$	0.0858349	+	0.596995i	0.00611548	+	0.0425341i	−0.986535	+	0.163549i	$0.947706\pi$
$198$		0			0
$199$	−6.87755	+	7.93711i	−0.487536	+	0.562647i	−0.945206	−	0.326475i	$-0.894139\pi$
$199$	−6.87755	+	7.93711i	−0.487536	+	0.562647i	0.457669	+	0.889123i	$0.348684\pi$
$200$		0			0
$201$	10.0925	−	9.95693i	0.711874	−	0.702308i
$202$		0			0
$203$	−21.2659	+	24.5422i	−1.49257	+	1.72252i
$204$		0			0
$205$	2.74413	+	19.0858i	0.191658	+	1.33301i
$206$		0			0
$207$	−15.0129	−	3.81348i	−1.04347	−	0.265055i
$208$		0			0
$209$	−37.2949	−	23.9679i	−2.57974	−	1.65790i
$210$		0			0
$211$	4.15574	−	9.09981i	0.286093	−	0.626457i	−0.710955	−	0.703238i	$-0.751737\pi$
$211$	4.15574	−	9.09981i	0.286093	−	0.626457i	0.997048	+	0.0767810i	$0.0244642\pi$
$212$		0			0
$213$	2.46482	−	12.4287i	0.168887	−	0.851603i
$214$		0			0
$215$	0.948852	−	0.136424i	0.0647111	−	0.00930406i
$216$		0			0
$217$	12.0653	−	3.54270i	0.819049	−	0.240494i
$218$		0			0
$219$	6.67072	−	9.26192i	0.450766	−	0.625863i
$220$		0			0
$221$	−2.04820	−	4.48493i	−0.137777	−	0.301689i
$222$		0			0
$223$	4.61874	−	10.1136i	0.309294	−	0.677259i	−0.689604	−	0.724186i	$-0.742216\pi$
$223$	4.61874	−	10.1136i	0.309294	−	0.677259i	0.998898	+	0.0469270i	$0.0149428\pi$
$224$		0			0
$225$	1.24103	+	0.131985i	0.0827351	+	0.00879897i
$226$		0			0
$227$	16.6970	+	2.40067i	1.10822	+	0.159338i	0.672035	−	0.740519i	$-0.265420\pi$
$227$	16.6970	+	2.40067i	1.10822	+	0.159338i	0.436185	+	0.899857i	$0.356329\pi$
$228$		0			0
$229$	−9.00592	+	14.0135i	−0.595128	+	0.926037i	0.404805	+	0.914403i	$0.367340\pi$
$229$	−9.00592	+	14.0135i	−0.595128	+	0.926037i	−0.999932	+	0.0116336i	$0.996297\pi$
$230$		0			0
$231$	−25.8843	+	26.8560i	−1.70306	+	1.76700i
$232$		0			0
$233$	−5.65669	+	12.3864i	−0.370582	+	0.811461i	0.628842	+	0.777533i	$0.283529\pi$
$233$	−5.65669	+	12.3864i	−0.370582	+	0.811461i	−0.999424	+	0.0339285i	$0.989198\pi$
$234$		0			0
$235$	5.63981	−	4.88692i	0.367900	−	0.318787i
$236$		0			0
$237$	3.96944	−	0.940408i	0.257843	−	0.0610861i
$238$		0			0
$239$	−5.75934			−0.372540			−0.186270	−	0.982499i	$-0.559640\pi$
$239$	−5.75934			−0.372540			−0.186270	+	0.982499i	$0.559640\pi$
$240$		0			0
$241$	−11.5227	−	3.38337i	−0.742242	−	0.217942i	−0.111316	−	0.993785i	$-0.535507\pi$
$241$	−11.5227	−	3.38337i	−0.742242	−	0.217942i	−0.630926	+	0.775843i	$0.717325\pi$
$242$		0			0
$243$	15.4724	+	1.89835i	0.992557	+	0.121779i
$244$		0			0
$245$	6.96389	+	15.2488i	0.444906	+	0.974209i
$246$		0			0
$247$	14.2516	−	48.5364i	0.906806	−	3.08830i
$248$		0			0
$249$	−17.5863	−	0.932533i	−1.11449	−	0.0590969i
$250$		0			0
$251$	0.484711	−	3.37124i	0.0305947	−	0.212791i	−0.968789	−	0.247886i	$-0.920264\pi$
$251$	0.484711	−	3.37124i	0.0305947	−	0.212791i	0.999384	+	0.0350948i	$0.0111733\pi$
$252$		0			0
$253$	21.8209	−	18.9079i	1.37187	−	1.18873i
$254$		0			0
$255$	−0.557412	+	2.81072i	−0.0349065	+	0.176014i
$256$		0			0
$257$	7.42734	+	25.2952i	0.463305	+	1.57787i	0.777736	+	0.628591i	$0.216368\pi$
$257$	7.42734	+	25.2952i	0.463305	+	1.57787i	−0.314431	+	0.949280i	$0.601814\pi$
$258$		0			0
$259$	15.7288	+	13.6291i	0.977339	+	0.846869i
$260$		0			0
$261$	−15.8512	+	19.7164i	−0.981166	+	1.22041i
$262$		0			0
$263$	−6.36513	−	21.6777i	−0.392491	−	1.33670i	−0.884674	−	0.466210i	$-0.845619\pi$
$263$	−6.36513	−	21.6777i	−0.392491	−	1.33670i	0.492183	−	0.870492i	$-0.336199\pi$
$264$		0			0
$265$	−0.749767	−	1.64176i	−0.0460578	−	0.100853i
$266$		0			0
$267$	−4.61535	+	4.78863i	−0.282455	+	0.293059i
$268$		0			0
$269$		−	19.6323i		−	1.19700i	−0.801123	−	0.598500i	$-0.795764\pi$
$269$		−	19.6323i		−	1.19700i	0.801123	−	0.598500i	$-0.204236\pi$
$270$		0			0
$271$	−18.3397	+	8.37545i	−1.11406	+	0.508773i	−0.885445	−	0.464745i	$-0.846146\pi$
$271$	−18.3397	+	8.37545i	−1.11406	+	0.508773i	−0.228612	+	0.973518i	$0.573419\pi$
$272$		0			0
$273$	−37.7237	−	19.7054i	−2.28315	−	1.19262i
$274$		0			0
$275$	−1.52344	+	1.75814i	−0.0918669	+	0.106020i
$276$		0			0
$277$	−2.81170	+	3.24488i	−0.168939	+	0.194966i	−0.833906	−	0.551907i	$-0.813900\pi$
$277$	−2.81170	+	3.24488i	−0.168939	+	0.194966i	0.664967	+	0.746873i	$0.268446\pi$
$278$		0			0
$279$	9.29122	−	3.10426i	0.556251	−	0.185847i
$280$		0			0
$281$	−2.96094	+	1.90288i	−0.176635	+	0.113516i	−0.625971	−	0.779847i	$-0.715297\pi$
$281$	−2.96094	+	1.90288i	−0.176635	+	0.113516i	0.449336	+	0.893363i	$0.351661\pi$
$282$		0			0
$283$	2.64597	+	3.05361i	0.157286	+	0.181518i	0.828923	−	0.559362i	$-0.188954\pi$
$283$	2.64597	+	3.05361i	0.157286	+	0.181518i	−0.671637	+	0.740880i	$0.734408\pi$
$284$		0			0
$285$	−23.2064	+	18.0487i	−1.37463	+	1.06911i
$286$		0			0
$287$	26.2106	−	22.7116i	1.54716	−	1.34062i
$288$		0			0
$289$	−15.7385	−	4.62124i	−0.925794	−	0.271838i
$290$		0			0
$291$	2.00116	+	0.704678i	0.117310	+	0.0413089i
$292$		0			0
$293$	8.56693	+	13.3304i	0.500485	+	0.778771i	0.995955	−	0.0898548i	$-0.0286403\pi$
$293$	8.56693	+	13.3304i	0.500485	+	0.778771i	−0.495469	+	0.868625i	$0.665004\pi$
$294$		0			0
$295$	−6.70935	+	22.8500i	−0.390634	+	1.33038i
$296$		0			0
$297$	−19.3802	+	21.6503i	−1.12456	+	1.25628i
$298$		0			0
$299$	27.7157	+	17.8118i	1.60284	+	1.03008i
$300$		0			0
$301$	−1.12911	−	1.30306i	−0.0650807	−	0.0751071i
$302$		0			0
$303$	−3.45549	+	1.36186i	−0.198513	+	0.0782368i
$304$		0			0
$305$		−	20.8483i		−	1.19377i
$306$		0			0
$307$	8.05757	+	5.17828i	0.459870	+	0.295540i	0.749989	−	0.661450i	$-0.230059\pi$
$307$	8.05757	+	5.17828i	0.459870	+	0.295540i	−0.290119	+	0.956990i	$0.593695\pi$
$308$		0			0
$309$	−3.73914	+	2.90809i	−0.212712	+	0.165436i
$310$		0			0
$311$	−2.80597	+	19.5159i	−0.159112	+	1.10665i	0.741163	+	0.671325i	$0.234275\pi$
$311$	−2.80597	+	19.5159i	−0.159112	+	1.10665i	−0.900275	+	0.435322i	$0.856634\pi$
$312$		0			0
$313$	26.7398	+	12.2117i	1.51142	+	0.690245i	0.986927	−	0.161167i	$-0.0515259\pi$
$313$	26.7398	+	12.2117i	1.51142	+	0.690245i	0.524498	+	0.851412i	$0.324253\pi$
$314$		0			0
$315$	11.0971	+	22.1059i	0.625252	+	1.24552i
$316$		0			0
$317$	−5.12090	+	0.736274i	−0.287618	+	0.0413533i	−0.284614	−	0.958642i	$-0.591865\pi$
$317$	−5.12090	+	0.736274i	−0.287618	+	0.0413533i	−0.00300432	+	0.999995i	$0.500956\pi$
$318$		0			0
$319$	−13.2855	−	45.2464i	−0.743847	−	2.53331i
$320$		0			0
$321$	−2.86009	−	2.05993i	−0.159635	−	0.114974i
$322$		0			0
$323$	3.31184	+	5.15332i	0.184276	+	0.286738i
$324$		0			0
$325$	−2.41460	−	1.10271i	−0.133938	−	0.0611675i
$326$		0			0
$327$	25.2833	−	5.98992i	1.39817	−	0.331243i
$328$		0			0
$329$	−12.8787	−	3.78154i	−0.710027	−	0.208483i
$330$		0			0
$331$	−26.9910	+	3.88072i	−1.48356	+	0.213303i	−0.836007	−	0.548719i	$-0.815116\pi$
$331$	−26.9910	+	3.88072i	−1.48356	+	0.213303i	−0.647551	+	0.762022i	$0.724207\pi$
$332$		0			0
$333$	12.6360	+	10.1589i	0.692449	+	0.556702i
$334$		0			0
$335$	17.2784	+	2.93016i	0.944017	+	0.160092i
$336$		0			0
$337$	−17.4251	−	15.0990i	−0.949207	−	0.822493i	0.0350227	−	0.999387i	$-0.488850\pi$
$337$	−17.4251	−	15.0990i	−0.949207	−	0.822493i	−0.984230	+	0.176894i	$0.943395\pi$
$338$		0			0
$339$	19.3135	−	26.8158i	1.04897	−	1.45643i
$340$		0			0
$341$	−5.14449	+	17.5205i	−0.278590	+	0.948789i
$342$		0			0
$343$	1.72751	−	2.68805i	0.0932766	−	0.145141i
$344$		0			0
$345$	−7.02060	−	17.8136i	−0.377976	−	0.959051i
$346$		0			0
$347$	10.3251	−	6.63554i	0.554280	−	0.356214i	−0.233321	−	0.972400i	$-0.574959\pi$
$347$	10.3251	−	6.63554i	0.554280	−	0.356214i	0.787601	+	0.616185i	$0.211323\pi$
$348$		0			0
$349$	−3.49322	−	24.2959i	−0.186988	−	1.30053i	−0.839754	−	0.542968i	$-0.817301\pi$
$349$	−3.49322	−	24.2959i	−0.186988	−	1.30053i	0.652766	−	0.757560i	$-0.273609\pi$
$350$		0			0
$351$	−29.9335	−	14.2581i	−1.59773	−	0.761039i
$352$		0			0
$353$	−3.07084	−	21.3582i	−0.163444	−	1.13678i	−0.892079	−	0.451879i	$-0.850754\pi$
$353$	−3.07084	−	21.3582i	−0.163444	−	1.13678i	0.728635	−	0.684902i	$-0.240155\pi$
$354$		0			0
$355$	14.2472	−	6.50649i	0.756165	−	0.345329i
$356$		0			0
$357$	4.79499	−	1.88977i	0.253778	−	0.100017i
$358$		0			0
$359$	−19.9608	−	2.86993i	−1.05349	−	0.151469i	−0.406255	−	0.913760i	$-0.633166\pi$
$359$	−19.9608	−	2.86993i	−1.05349	−	0.151469i	−0.647235	+	0.762291i	$0.724075\pi$
$360$		0			0
$361$	−6.24031	+	43.4023i	−0.328437	+	2.28433i
$362$		0			0
$363$	−8.09421	−	34.1655i	−0.424836	−	1.79322i
$364$		0			0
$365$	14.1092			0.738510
$366$		0			0
$367$	5.59358	+	2.55450i	0.291983	+	0.133344i	0.556021	−	0.831168i	$-0.312327\pi$
$367$	5.59358	+	2.55450i	0.291983	+	0.133344i	−0.264039	+	0.964512i	$0.585055\pi$
$368$		0			0
$369$	19.7532	−	18.4332i	1.02831	−	0.959595i
$370$		0			0
$371$	−1.75508	+	2.73096i	−0.0911194	+	0.141785i
$372$		0			0
$373$		−	9.15585i		−	0.474072i	−0.971501	−	0.237036i	$-0.923824\pi$
$373$		−	9.15585i		−	0.474072i	0.971501	−	0.237036i	$-0.0761759\pi$
$374$		0			0
$375$	9.94861	+	17.4475i	0.513744	+	0.900983i
$376$		0			0
$377$	45.2660	−	29.0907i	2.33132	−	1.49825i
$378$		0			0
$379$	8.36305	−	3.81928i	0.429581	−	0.196183i	−0.188877	−	0.982001i	$-0.560485\pi$
$379$	8.36305	−	3.81928i	0.429581	−	0.196183i	0.618458	+	0.785818i	$0.287758\pi$
$380$		0			0
$381$	−3.91507	−	6.86610i	−0.200575	−	0.351761i
$382$		0			0
$383$	−13.2261	−	15.2638i	−0.675824	−	0.779942i	0.309452	−	0.950915i	$-0.399854\pi$
$383$	−13.2261	−	15.2638i	−0.675824	−	0.779942i	−0.985276	+	0.170973i	$0.945309\pi$
$384$		0			0
$385$	−45.6373	−	6.56165i	−2.32589	−	0.334413i
$386$		0			0
$387$	−0.916408	−	0.982031i	−0.0465836	−	0.0499194i
$388$		0			0
$389$	3.16294	+	4.92163i	0.160367	+	0.249536i	0.912133	−	0.409893i	$-0.134434\pi$
$389$	3.16294	+	4.92163i	0.160367	+	0.249536i	−0.751766	+	0.659430i	$0.770798\pi$
$390$		0			0
$391$	−3.82803	+	1.12401i	−0.193592	+	0.0568437i
$392$		0			0
$393$	−0.480093	−	5.33048i	−0.0242175	−	0.268887i
$394$		0			0
$395$	3.81089	+	3.30216i	0.191747	+	0.166150i
$396$		0			0
$397$	−1.73367	+	0.509053i	−0.0870107	+	0.0255486i	−0.324948	−	0.945732i	$-0.605347\pi$
$397$	−1.73367	+	0.509053i	−0.0870107	+	0.0255486i	0.237937	+	0.971280i	$0.423529\pi$
$398$		0			0
$399$	49.8761	+	17.5631i	2.49693	+	0.879256i
$400$		0			0
$401$	23.9896			1.19798			0.598992	−	0.800755i	$-0.295568\pi$
$401$	23.9896			1.19798			0.598992	+	0.800755i	$0.295568\pi$
$402$		0			0
$403$	−20.8357			−1.03790
$404$		0			0
$405$	9.27353	+	16.8910i	0.460805	+	0.839319i
$406$		0			0
$407$	−28.9979	+	8.51455i	−1.43737	+	0.422050i
$408$		0			0
$409$	6.86757	+	5.95079i	0.339580	+	0.294247i	0.807910	−	0.589306i	$-0.200599\pi$
$409$	6.86757	+	5.95079i	0.339580	+	0.294247i	−0.468330	+	0.883553i	$0.655144\pi$
$410$		0			0
$411$	14.8343	−	1.33606i	0.731724	−	0.0659031i
$412$		0			0
$413$	41.0989	−	12.0677i	2.02235	−	0.593814i
$414$		0			0
$415$	−11.7694	−	18.3136i	−0.577738	−	0.898977i
$416$		0			0
$417$	30.3958	+	1.61177i	1.48849	+	0.0789287i
$418$		0			0
$419$	−30.2736	−	4.35269i	−1.47896	−	0.212643i	−0.644880	−	0.764284i	$-0.723093\pi$
$419$	−30.2736	−	4.35269i	−1.47896	−	0.212643i	−0.834082	+	0.551641i	$0.814002\pi$
$420$		0			0
$421$	11.1131	+	12.8253i	0.541622	+	0.625065i	0.958910	−	0.283709i	$-0.0915651\pi$
$421$	11.1131	+	12.8253i	0.541622	+	0.625065i	−0.417289	+	0.908774i	$0.637020\pi$
$422$		0			0
$423$	−10.1346	−	2.57433i	−0.492763	−	0.125168i
$424$		0			0
$425$	0.292402	−	0.133535i	0.0141836	−	0.00647742i
$426$		0			0
$427$	−31.5459	+	20.2733i	−1.52661	+	0.981094i
$428$		0			0
$429$	53.6887	−	30.6135i	2.59211	−	1.47803i
$430$		0			0
$431$		−	15.4336i		−	0.743410i	−0.928351	−	0.371705i	$-0.878773\pi$
$431$		−	15.4336i		−	0.743410i	0.928351	−	0.371705i	$-0.121227\pi$
$432$		0			0
$433$	−12.6950	+	19.7538i	−0.610084	+	0.949309i	0.389516	+	0.921020i	$0.372642\pi$
$433$	−12.6950	+	19.7538i	−0.610084	+	0.949309i	−0.999600	+	0.0282893i	$0.990994\pi$
$434$		0			0
$435$	−31.2278	−	1.65588i	−1.49726	−	0.0793935i
$436$		0			0
$437$	−37.2336	−	17.0040i	−1.78112	−	0.813412i
$438$		0			0
$439$	−36.2970			−1.73236			−0.866180	−	0.499733i	$-0.833432\pi$
$439$	−36.2970			−1.73236			−0.866180	+	0.499733i	$0.833432\pi$
$440$		0			0
$441$	11.9627	−	20.2148i	0.569651	−	0.962610i
$442$		0			0
$443$	−1.80487	+	12.5531i	−0.0857518	+	0.596417i	0.900956	+	0.433911i	$0.142867\pi$
$443$	−1.80487	+	12.5531i	−0.0857518	+	0.596417i	−0.986708	+	0.162506i	$0.948042\pi$
$444$		0			0
$445$	−8.13745	−	1.16999i	−0.385752	−	0.0554628i
$446$		0			0
$447$	−8.42381	−	21.3740i	−0.398433	−	1.01096i
$448$		0			0
$449$	−9.35902	+	4.27412i	−0.441680	+	0.201708i	−0.623826	−	0.781563i	$-0.714423\pi$
$449$	−9.35902	+	4.27412i	−0.441680	+	0.201708i	0.182147	+	0.983271i	$0.441695\pi$
$450$		0			0
$451$	7.16731	+	49.8497i	0.337495	+	2.34733i
$452$		0			0
$453$	14.2138	+	7.42472i	0.667822	+	0.348844i
$454$		0			0
$455$	−7.48715	−	52.0743i	−0.351003	−	2.44128i
$456$		0			0
$457$	−17.7520	+	11.4085i	−0.830403	+	0.533668i	−0.885406	−	0.464818i	$-0.846120\pi$
$457$	−17.7520	+	11.4085i	−0.830403	+	0.533668i	0.0550027	+	0.998486i	$0.482483\pi$
$458$		0			0
$459$	3.67867	−	1.60880i	0.171706	−	0.0750924i
$460$		0			0
$461$	19.4412	−	30.2511i	0.905468	−	1.40894i	−0.00708430	−	0.999975i	$-0.502255\pi$
$461$	19.4412	−	30.2511i	0.905468	−	1.40894i	0.912552	−	0.408960i	$-0.134109\pi$
$462$		0			0
$463$	7.61122	−	25.9214i	0.353723	−	1.20467i	−0.570011	−	0.821637i	$-0.693061\pi$
$463$	7.61122	−	25.9214i	0.353723	−	1.20467i	0.923734	−	0.383034i	$-0.125121\pi$
$464$		0			0
$465$	9.82591	+	7.07692i	0.455666	+	0.328185i
$466$		0			0
$467$	−28.5506	−	24.7392i	−1.32116	−	1.14479i	−0.978707	−	0.205261i	$-0.934196\pi$
$467$	−28.5506	−	24.7392i	−1.32116	−	1.14479i	−0.342457	−	0.939534i	$-0.611259\pi$
$468$		0			0
$469$	−12.3681	−	28.9935i	−0.571108	−	1.33879i
$470$		0			0
$471$	8.49125	−	0.764769i	0.391256	−	0.0352387i
$472$		0			0
$473$	2.47828	−	0.356323i	0.113951	−	0.0163837i
$474$		0			0
$475$	3.16440	+	0.929153i	0.145193	+	0.0426325i
$476$		0			0
$477$	−1.28796	+	2.17643i	−0.0589717	+	0.0996518i
$478$		0			0
$479$	29.6370	+	13.5348i	1.35415	+	0.618420i	0.954490	−	0.298243i	$-0.0964005\pi$
$479$	29.6370	+	13.5348i	1.35415	+	0.618420i	0.399661	+	0.916663i	$0.369128\pi$
$480$		0			0
$481$	−18.6439	−	29.0105i	−0.850089	−	1.32276i
$482$		0			0
$483$	−20.1270	+	27.9452i	−0.915812	+	1.27155i
$484$		0			0
$485$	0.738860	+	2.51633i	0.0335499	+	0.114261i
$486$		0			0
$487$	2.23477	−	0.321312i	0.101267	−	0.0145600i	−0.0914949	−	0.995806i	$-0.529165\pi$
$487$	2.23477	−	0.321312i	0.101267	−	0.0145600i	0.192762	+	0.981246i	$0.438255\pi$
$488$		0			0
$489$	4.43191	−	12.5858i	0.200418	−	0.569150i
$490$		0			0
$491$	−3.36878	−	1.53847i	−0.152031	−	0.0694303i	0.337946	−	0.941165i	$-0.390268\pi$
$491$	−3.36878	−	1.53847i	−0.152031	−	0.0694303i	−0.489977	+	0.871735i	$0.662995\pi$
$492$		0			0
$493$	−0.927321	+	6.44966i	−0.0417645	+	0.290478i
$494$		0			0
$495$	−35.7170	−	3.79854i	−1.60536	−	0.170732i
$496$		0			0
$497$	−23.6994	−	15.2307i	−1.06306	−	0.683188i
$498$		0			0
$499$			8.44924i			0.378240i	0.981954	+	0.189120i	$0.0605635\pi$
$499$			8.44924i			0.378240i	−0.981954	+	0.189120i	$0.939436\pi$
$500$		0			0
$501$	−11.0307	−	27.9885i	−0.492815	−	1.25043i
$502$		0			0
$503$	−3.25435	−	3.75572i	−0.145104	−	0.167459i	0.678545	−	0.734559i	$-0.262611\pi$
$503$	−3.25435	−	3.75572i	−0.145104	−	0.167459i	−0.823649	+	0.567100i	$0.808065\pi$
$504$		0			0
$505$	−3.86234	−	2.48218i	−0.171872	−	0.110455i
$506$		0			0
$507$	34.5635	+	33.3128i	1.53502	+	1.47948i
$508$		0			0
$509$	−3.15472	+	10.7440i	−0.139831	+	0.476219i	−0.999394	−	0.0348099i	$-0.988917\pi$
$509$	−3.15472	+	10.7440i	−0.139831	+	0.476219i	0.859563	+	0.511029i	$0.170736\pi$
$510$		0			0
$511$	−13.7201	−	21.3489i	−0.606941	−	0.944418i
$512$		0			0
$513$	39.3327	+	12.2416i	1.73658	+	0.540478i
$514$		0			0
$515$	−5.61819	−	1.64965i	−0.247567	−	0.0726923i
$516$		0			0
$517$	14.7305	−	12.7640i	0.647845	−	0.561361i
$518$		0			0
$519$	4.01644	+	5.16421i	0.176302	+	0.226684i
$520$		0			0
$521$	2.87894	+	3.32248i	0.126129	+	0.145560i	0.815301	−	0.579037i	$-0.196571\pi$
$521$	2.87894	+	3.32248i	0.126129	+	0.145560i	−0.689173	+	0.724597i	$0.742026\pi$
$522$		0			0
$523$	−5.19011	+	3.33548i	−0.226948	+	0.145850i	−0.649174	−	0.760640i	$-0.724885\pi$
$523$	−5.19011	+	3.33548i	−0.226948	+	0.145850i	0.422226	+	0.906491i	$0.361249\pi$
$524$		0			0
$525$	1.28472	−	2.45946i	0.0560699	−	0.107340i
$526$		0			0
$527$	1.65231	−	1.90687i	0.0719759	−	0.0830646i
$528$		0			0
$529$	2.39607	−	2.76522i	0.104177	−	0.120227i
$530$		0			0
$531$	31.6492	−	10.5742i	1.37346	−	0.458882i
$532$		0			0
$533$	−52.2728	+	23.8722i	−2.26418	+	1.03402i
$534$		0			0
$535$		−	4.35694i		−	0.188367i
$536$		0			0
$537$	8.14482	+	7.85011i	0.351475	+	0.338757i
$538$		0			0
$539$	18.1888	+	39.8279i	0.783447	+	1.71551i
$540$		0			0
$541$	−4.93169	−	16.7958i	−0.212030	−	0.722108i	−0.994985	−	0.100029i	$-0.968107\pi$
$541$	−4.93169	−	16.7958i	−0.212030	−	0.722108i	0.782955	−	0.622079i	$-0.213712\pi$
$542$		0			0
$543$	−13.0613	+	1.17637i	−0.560514	+	0.0504830i
$544$		0			0
$545$	24.2734	+	21.0331i	1.03976	+	0.900957i
$546$		0			0
$547$	−6.70920	−	22.8494i	−0.286865	−	0.976971i	−0.969270	−	0.245998i	$-0.920884\pi$
$547$	−6.70920	−	22.8494i	−0.286865	−	0.976971i	0.682406	−	0.730974i	$-0.260934\pi$
$548$		0			0
$549$	−23.9767	+	16.6881i	−1.02330	+	0.712231i
$550$		0			0
$551$	−50.5235	+	43.7789i	−2.15238	+	1.86504i
$552$		0			0
$553$	1.29076	−	8.97740i	0.0548885	−	0.381758i
$554$		0			0
$555$	−1.06124	+	20.0135i	−0.0450470	+	0.849526i
$556$		0			0
$557$	10.2018	−	34.7442i	0.432264	−	1.47216i	−0.399347	−	0.916800i	$-0.630763\pi$
$557$	10.2018	−	34.7442i	0.432264	−	1.47216i	0.831612	−	0.555358i	$-0.187419\pi$
$558$		0			0
$559$	1.18681	+	2.59874i	0.0501965	+	0.109915i
$560$		0			0
$561$	−1.45589	+	7.34126i	−0.0614677	+	0.309948i
$562$		0			0
$563$	−4.92173	−	1.44515i	−0.207426	−	0.0609059i	0.176369	−	0.984324i	$-0.443565\pi$
$563$	−4.92173	−	1.44515i	−0.207426	−	0.0609059i	−0.383795	+	0.923418i	$0.625383\pi$
$564$		0			0
$565$	40.8500			1.71857
$566$		0			0
$567$	16.5402	−	30.4570i	0.694624	−	1.27907i
$568$		0			0
$569$	24.4368	−	21.1746i	1.02445	−	0.887687i	0.0307191	−	0.999528i	$-0.490220\pi$
$569$	24.4368	−	21.1746i	1.02445	−	0.887687i	0.993726	+	0.111841i	$0.0356748\pi$
$570$		0			0
$571$	−1.79742	+	3.93581i	−0.0752198	+	0.164708i	−0.943506	−	0.331355i	$-0.892494\pi$
$571$	−1.79742	+	3.93581i	−0.0752198	+	0.164708i	0.868286	+	0.496063i	$0.165222\pi$
$572$		0			0
$573$	3.63048	+	3.49911i	0.151666	+	0.146178i
$574$		0			0
$575$	−1.16127	+	1.80697i	−0.0484282	+	0.0753557i
$576$		0			0
$577$	12.8650	+	1.84971i	0.535577	+	0.0770043i	0.404796	−	0.914407i	$-0.367342\pi$
$577$	12.8650	+	1.84971i	0.535577	+	0.0770043i	0.130781	+	0.991411i	$0.458252\pi$
$578$		0			0
$579$	6.95664	−	5.41048i	0.289108	−	0.224852i
$580$		0			0
$581$	−16.2657	+	35.6169i	−0.674815	+	1.47764i
$582$		0			0
$583$	−1.95830	−	4.28807i	−0.0811044	−	0.177594i
$584$		0			0
$585$	−7.32320	−	40.3251i	−0.302777	−	1.66724i
$586$		0			0
$587$	−10.5178	+	3.08830i	−0.434116	+	0.127468i	−0.491487	−	0.870885i	$-0.663546\pi$
$587$	−10.5178	+	3.08830i	−0.434116	+	0.127468i	0.0573709	+	0.998353i	$0.481728\pi$
$588$		0			0
$589$	25.6233	−	3.68408i	1.05579	−	0.151800i
$590$		0			0
$591$	1.02470	+	0.203215i	0.0421506	+	0.00835915i
$592$		0			0
$593$	−6.86975	+	15.0427i	−0.282107	+	0.617728i	−0.996643	−	0.0818707i	$-0.973911\pi$
$593$	−6.86975	+	15.0427i	−0.282107	+	0.617728i	0.714536	+	0.699599i	$0.246638\pi$
$594$		0			0
$595$	5.35954	+	3.44437i	0.219720	+	0.141205i
$596$		0			0
$597$	9.01043	+	15.8021i	0.368773	+	0.646738i
$598$		0			0
$599$	5.87718	+	40.8767i	0.240135	+	1.67018i	0.651456	+	0.758686i	$0.274158\pi$
$599$	5.87718	+	40.8767i	0.240135	+	1.67018i	−0.411321	+	0.911490i	$0.634933\pi$
$600$		0			0
$601$	−16.6168	+	19.1768i	−0.677812	+	0.782236i	−0.985577	−	0.169226i	$-0.945873\pi$
$601$	−16.6168	+	19.1768i	−0.677812	+	0.782236i	0.307766	+	0.951462i	$0.400419\pi$
$602$		0			0
$603$	−10.4607	−	22.2165i	−0.425992	−	0.904727i
$604$		0			0
$605$	28.4221	−	32.8008i	1.15552	−	1.33354i
$606$		0			0
$607$	2.41607	+	16.8041i	0.0980651	+	0.682058i	0.978250	+	0.207428i	$0.0665092\pi$
$607$	2.41607	+	16.8041i	0.0980651	+	0.682058i	−0.880185	+	0.474630i	$0.842582\pi$
$608$		0			0
$609$	27.8609	+	48.8614i	1.12898	+	1.97996i
$610$		0			0
$611$	18.7098	+	12.0241i	0.756917	+	0.486441i
$612$		0			0
$613$	5.03209	−	11.0187i	0.203244	−	0.445043i	−0.780372	−	0.625315i	$-0.784970\pi$
$613$	5.03209	−	11.0187i	0.203244	−	0.445043i	0.983617	+	0.180272i	$0.0576978\pi$
$614$		0			0
$615$	32.7595	+	6.49675i	1.32099	+	0.261974i
$616$		0			0
$617$	9.54492	−	1.37235i	0.384264	−	0.0552488i	0.0525240	−	0.998620i	$-0.483273\pi$
$617$	9.54492	−	1.37235i	0.384264	−	0.0552488i	0.331740	+	0.943371i	$0.392364\pi$
$618$		0			0
$619$	−38.3872	+	11.2715i	−1.54291	+	0.453040i	−0.938973	−	0.343990i	$-0.888221\pi$
$619$	−38.3872	+	11.2715i	−1.54291	+	0.453040i	−0.603940	+	0.797030i	$0.706403\pi$
$620$		0			0
$621$	−14.8669	+	22.3330i	−0.596590	+	0.896194i
$622$		0			0
$623$	6.14269	+	13.4506i	0.246102	+	0.538888i
$624$		0			0
$625$	−9.44940	+	20.6913i	−0.377976	+	0.827652i
$626$		0			0
$627$	−60.6123	+	47.1408i	−2.42062	+	1.88262i
$628$		0			0
$629$	4.13352	+	0.594310i	0.164814	+	0.0236967i
$630$		0			0
$631$	−12.1271	+	18.8702i	−0.482774	+	0.751210i	−0.994134	−	0.108156i	$-0.965505\pi$
$631$	−12.1271	+	18.8702i	−0.482774	+	0.751210i	0.511360	+	0.859366i	$0.329142\pi$
$632$		0			0
$633$	−12.4758	−	12.0244i	−0.495868	−	0.477925i
$634$		0			0
$635$	4.05866	−	8.88723i	0.161063	−	0.352679i
$636$		0			0
$637$	−37.7575	+	32.7171i	−1.49601	+	1.29630i
$638$		0			0
$639$	−18.8871	−	11.1770i	−0.747162	−	0.442154i
$640$		0			0
$641$	44.6524			1.76366			0.881831	−	0.471565i	$-0.156311\pi$
$641$	44.6524			1.76366			0.881831	+	0.471565i	$0.156311\pi$
$642$		0			0
$643$	−10.6277	−	3.12056i	−0.419114	−	0.123063i	0.0653743	−	0.997861i	$-0.479176\pi$
$643$	−10.6277	−	3.12056i	−0.419114	−	0.123063i	−0.484488	+	0.874798i	$0.660994\pi$
$644$		0			0
$645$	0.322986	−	1.62864i	0.0127176	−	0.0641277i
$646$		0			0
$647$	−6.78193	−	14.8504i	−0.266625	−	0.583828i	0.728207	−	0.685357i	$-0.240354\pi$
$647$	−6.78193	−	14.8504i	−0.266625	−	0.583828i	−0.994833	+	0.101529i	$0.967627\pi$
$648$		0			0
$649$	−17.5240	+	59.6812i	−0.687877	+	2.34269i
$650$		0			0
$651$	1.15329	−	21.7495i	0.0452009	−	0.852429i
$652$		0			0
$653$	−3.18187	+	22.1304i	−0.124516	+	0.866029i	0.827823	+	0.560989i	$0.189579\pi$
$653$	−3.18187	+	22.1304i	−0.124516	+	0.866029i	−0.952340	+	0.305040i	$0.901330\pi$
$654$		0			0
$655$	4.99989	−	4.33243i	0.195362	−	0.169282i
$656$		0			0
$657$	−11.2938	−	16.2264i	−0.440612	−	0.633052i
$658$		0			0
$659$	−10.0400	−	34.1930i	−0.391101	−	1.33197i	−0.886269	−	0.463171i	$-0.846712\pi$
$659$	−10.0400	−	34.1930i	−0.391101	−	1.33197i	0.495168	−	0.868797i	$-0.335107\pi$
$660$		0			0
$661$	3.86237	+	3.34676i	0.150229	+	0.130174i	0.726733	−	0.686920i	$-0.241038\pi$
$661$	3.86237	+	3.34676i	0.150229	+	0.130174i	−0.576504	+	0.817094i	$0.695583\pi$
$662$		0			0
$663$	−8.50543	+	0.766047i	−0.330323	+	0.0297508i
$664$		0			0
$665$	18.4151	+	62.7160i	0.714106	+	2.43202i
$666$		0			0
$667$	−18.0872	−	39.6054i	−0.700339	−	1.53353i
$668$		0			0
$669$	−13.8657	−	13.3640i	−0.536080	−	0.516683i
$670$		0			0
$671$		−	54.4531i		−	2.10214i
$672$		0			0
$673$	−2.83398	+	1.29423i	−0.109242	+	0.0498890i	−0.469286	−	0.883046i	$-0.655489\pi$
$673$	−2.83398	+	1.29423i	−0.109242	+	0.0498890i	0.360045	+	0.932935i	$0.382761\pi$
$674$		0			0
$675$	0.929577	−	1.95156i	0.0357794	−	0.0751156i
$676$		0			0
$677$	−15.1871	+	17.5269i	−0.583689	+	0.673613i	−0.968394	−	0.249427i	$-0.919758\pi$
$677$	−15.1871	+	17.5269i	−0.583689	+	0.673613i	0.384705	+	0.923040i	$0.374303\pi$
$678$		0			0
$679$	3.08901	−	3.56491i	0.118545	−	0.136809i
$680$		0			0
$681$	13.5276	−	25.8972i	0.518381	−	0.992381i
$682$		0			0
$683$	−22.4208	+	14.4090i	−0.857909	+	0.551344i	−0.894032	−	0.448003i	$-0.852135\pi$
$683$	−22.4208	+	14.4090i	−0.857909	+	0.551344i	0.0361235	+	0.999347i	$0.488499\pi$
$684$		0			0
$685$	12.0568	+	13.9143i	0.460667	+	0.531638i
$686$		0			0
$687$	17.7131	+	22.7750i	0.675796	+	0.868919i
$688$		0			0
$689$	4.06516	−	3.52248i	0.154870	−	0.134196i
$690$		0			0
$691$	−37.8298	−	11.1078i	−1.43911	−	0.422562i	−0.533187	−	0.845997i	$-0.679006\pi$
$691$	−37.8298	−	11.1078i	−1.43911	−	0.422562i	−0.905926	+	0.423435i	$0.860824\pi$
$692$		0			0
$693$	28.9843	+	57.7377i	1.10102	+	2.19327i
$694$		0			0
$695$	20.3420	+	31.6528i	0.771616	+	1.20066i
$696$		0			0
$697$	1.96056	−	6.67707i	0.0742617	−	0.252912i
$698$		0			0
$699$	16.9817	+	16.3672i	0.642307	+	0.619066i
$700$		0			0
$701$	−26.6339	−	17.1166i	−1.00595	−	0.646483i	−0.0696066	−	0.997575i	$-0.522174\pi$
$701$	−26.6339	−	17.1166i	−1.00595	−	0.646483i	−0.936341	+	0.351091i	$0.885811\pi$
$702$		0			0
$703$	28.0574	+	32.3800i	1.05820	+	1.22123i
$704$		0			0
$705$	−4.73933	−	12.0253i	−0.178494	−	0.452898i
$706$		0			0
$707$			8.25788i			0.310570i
$708$		0			0
$709$	−27.0527	−	17.3857i	−1.01599	−	0.652935i	−0.0770512	−	0.997027i	$-0.524550\pi$
$709$	−27.0527	−	17.3857i	−1.01599	−	0.652935i	−0.938936	+	0.344092i	$0.888187\pi$
$710$		0			0
$711$	0.747219	−	7.02597i	0.0280229	−	0.263494i
$712$		0			0
$713$	−2.39940	+	16.6882i	−0.0898582	+	0.624977i
$714$		0			0
$715$	69.4927	+	31.7363i	2.59888	+	1.18687i
$716$		0			0
$717$	−3.31329	+	9.40914i	−0.123737	+	0.351391i
$718$		0			0
$719$	−10.6376	+	1.52946i	−0.396717	+	0.0570393i	−0.337786	−	0.941223i	$-0.609678\pi$
$719$	−10.6376	+	1.52946i	−0.396717	+	0.0570393i	−0.0589305	+	0.998262i	$0.518769\pi$
$720$		0			0
$721$	2.96713	+	10.1051i	0.110502	+	0.376334i
$722$		0			0
$723$	−12.1564	+	16.8784i	−0.452100	+	0.627716i
$724$		0			0
$725$	1.89661	+	2.95119i	0.0704385	+	0.109604i
$726$		0			0
$727$	−4.85499	−	2.21720i	−0.180062	−	0.0822314i	0.323344	−	0.946281i	$-0.395193\pi$
$727$	−4.85499	−	2.21720i	−0.180062	−	0.0822314i	−0.503406	+	0.864050i	$0.667920\pi$
$728$		0			0
$729$	12.0025	−	24.1855i	0.444538	−	0.895760i
$730$		0			0
$731$	−0.331951	−	0.0974695i	−0.0122776	−	0.00360504i
$732$		0			0
$733$	27.6536	−	3.97598i	1.02141	−	0.146856i	0.388795	−	0.921324i	$-0.372891\pi$
$733$	27.6536	−	3.97598i	1.02141	−	0.146856i	0.632613	+	0.774468i	$0.281982\pi$
$734$		0			0
$735$	28.9185	−	2.60456i	1.06667	−	0.0960707i
$736$		0			0
$737$	45.1289	+	7.65321i	1.66234	+	0.281909i
$738$		0			0
$739$	−10.7060	−	9.27680i	−0.393826	−	0.341252i	0.435328	−	0.900272i	$-0.356632\pi$
$739$	−10.7060	−	9.27680i	−0.393826	−	0.341252i	−0.829155	+	0.559019i	$0.811178\pi$
$740$		0			0
$741$	−71.0961	−	51.2056i	−2.61178	−	1.88108i
$742$		0			0
$743$	11.1004	−	37.8045i	0.407234	−	1.38691i	−0.459517	−	0.888169i	$-0.651977\pi$
$743$	11.1004	−	37.8045i	0.407234	−	1.38691i	0.866751	−	0.498742i	$-0.166204\pi$
$744$		0			0
$745$	15.3535	−	23.8906i	0.562510	−	0.875283i
$746$		0			0
$747$	−11.6407	+	28.1946i	−0.425912	+	1.03159i
$748$		0			0
$749$	−6.59255	+	4.23677i	−0.240887	+	0.154808i
$750$		0			0
$751$	−1.92313	−	13.3756i	−0.0701758	−	0.488084i	−0.994353	−	0.106120i	$-0.966157\pi$
$751$	−1.92313	−	13.3756i	−0.0701758	−	0.488084i	0.924177	−	0.381963i	$-0.124752\pi$
$752$		0			0
$753$	−5.22882	−	2.73133i	−0.190549	−	0.0995351i
$754$		0			0
$755$	2.82105	+	19.6209i	0.102669	+	0.714076i
$756$		0			0
$757$	36.5661	−	16.6992i	1.32902	−	0.606942i	0.380828	−	0.924646i	$-0.375639\pi$
$757$	36.5661	−	16.6992i	1.32902	−	0.606942i	0.948190	+	0.317704i	$0.102912\pi$
$758$		0			0
$759$	−18.3369	−	46.5268i	−0.665588	−	1.68882i
$760$		0			0
$761$	−1.08944	−	0.156638i	−0.0394923	−	0.00567813i	0.122540	−	0.992464i	$-0.460896\pi$
$761$	−1.08944	−	0.156638i	−0.0394923	−	0.00567813i	−0.162033	+	0.986785i	$0.551805\pi$
$762$		0			0
$763$	8.22145	−	57.1815i	0.297637	−	2.07011i
$764$		0			0
$765$	4.27126	+	2.52764i	0.154428	+	0.0913869i
$766$		0			0
$767$	−70.9740			−2.56272
$768$		0			0
$769$	32.1287	+	14.6727i	1.15859	+	0.529111i	0.899577	−	0.436763i	$-0.143875\pi$
$769$	32.1287	+	14.6727i	1.15859	+	0.529111i	0.259014	+	0.965874i	$0.416602\pi$
$770$		0			0
$771$	45.5981	+	2.41789i	1.64218	+	0.0870781i
$772$		0			0
$773$	9.47518	−	14.7437i	0.340798	−	0.530293i	−0.627977	−	0.778232i	$-0.716117\pi$
$773$	9.47518	−	14.7437i	0.340798	−	0.530293i	0.968776	+	0.247939i	$0.0797533\pi$
$774$		0			0
$775$		−	1.35842i		−	0.0487958i
$776$		0			0
$777$	31.3147	−	17.8558i	1.12341	−	0.640572i
$778$		0			0
$779$	60.0630	−	38.6001i	2.15198	−	1.38299i
$780$		0			0
$781$	37.2120	−	16.9941i	1.33155	−	0.608098i
$782$		0			0
$783$	23.0920	+	37.2391i	0.825242	+	1.33082i
$784$		0			0
$785$	6.90138	+	7.96462i	0.246321	+	0.284269i
$786$		0			0
$787$	49.2286	+	7.07800i	1.75481	+	0.252304i	0.943278	−	0.332004i	$-0.107725\pi$
$787$	49.2286	+	7.07800i	1.75481	+	0.252304i	0.811532	+	0.584308i	$0.198634\pi$
$788$		0			0
$789$	−39.0770	−	2.07210i	−1.39118	−	0.0737687i
$790$		0			0
$791$	−39.7233	−	61.8107i	−1.41240	−	2.19774i
$792$		0			0
$793$	59.6167	−	17.5051i	2.11705	−	0.621623i
$794$		0			0
$795$	−3.11351	+	0.280420i	−0.110425	+	0.00994548i
$796$		0			0
$797$	32.8459	+	28.4612i	1.16346	+	1.00815i	0.999766	+	0.0216353i	$0.00688726\pi$
$797$	32.8459	+	28.4612i	1.16346	+	1.00815i	0.163697	+	0.986511i	$0.447658\pi$
$798$		0			0
$799$	−2.58415	+	0.758776i	−0.0914208	+	0.0268436i
$800$		0			0
$801$	5.16811	+	10.2950i	0.182606	+	0.363758i
$802$		0			0
$803$	36.8515			1.30046
$804$		0			0
$805$	−42.5706			−1.50042
$806$		0			0
$807$	−32.0736	−	11.2942i	−1.12904	−	0.397576i
$808$		0			0
$809$	−47.5514	+	13.9624i	−1.67182	+	0.490890i	−0.974220	−	0.225598i	$-0.927566\pi$
$809$	−47.5514	+	13.9624i	−1.67182	+	0.490890i	−0.697599	+	0.716489i	$0.745748\pi$
$810$		0			0
$811$	13.4463	+	11.6513i	0.472165	+	0.409133i	0.858172	−	0.513363i	$-0.171600\pi$
$811$	13.4463	+	11.6513i	0.472165	+	0.409133i	−0.386007	+	0.922496i	$0.626146\pi$
$812$		0			0
$813$	3.13250	+	34.7802i	0.109862	+	1.21980i
$814$		0			0
$815$	15.8259	−	4.64689i	0.554356	−	0.162773i
$816$		0			0
$817$	−1.91901	−	2.98603i	−0.0671375	−	0.104468i
$818$		0			0
$819$	−53.8952	+	50.2937i	−1.88325	+	1.75740i
$820$		0			0
$821$	−12.9571	−	1.86295i	−0.452205	−	0.0650173i	−0.0875506	−	0.996160i	$-0.527904\pi$
$821$	−12.9571	−	1.86295i	−0.452205	−	0.0650173i	−0.364655	+	0.931143i	$0.618813\pi$
$822$		0			0
$823$	−10.0631	−	11.6135i	−0.350779	−	0.404820i	0.552750	−	0.833347i	$-0.313578\pi$
$823$	−10.0631	−	11.6135i	−0.350779	−	0.404820i	−0.903529	+	0.428527i	$0.859033\pi$
$824$		0			0
$825$	1.99589	+	3.50032i	0.0694881	+	0.121865i
$826$		0			0
$827$	−46.2625	+	21.1274i	−1.60871	+	0.734672i	−0.998348	−	0.0574539i	$-0.981702\pi$
$827$	−46.2625	+	21.1274i	−1.60871	+	0.734672i	−0.610358	+	0.792126i	$0.708975\pi$
$828$		0			0
$829$	19.0814	−	12.2629i	0.662724	−	0.425907i	−0.165572	−	0.986198i	$-0.552947\pi$
$829$	19.0814	−	12.2629i	0.662724	−	0.425907i	0.828296	+	0.560291i	$0.189311\pi$
$830$		0			0
$831$	3.68368	+	6.46028i	0.127785	+	0.224105i
$832$		0			0
$833$		−	6.05006i		−	0.209622i
$834$		0			0
$835$	20.1049	−	31.2839i	0.695759	−	1.08262i
$836$		0			0
$837$	0.273663	−	16.9651i	0.00945919	−	0.586400i
$838$		0			0
$839$	3.91914	+	1.78981i	0.135304	+	0.0617912i	0.481916	−	0.876217i	$-0.339941\pi$
$839$	3.91914	+	1.78981i	0.135304	+	0.0617912i	−0.346613	+	0.938008i	$0.612668\pi$
$840$		0			0
$841$	−42.1108			−1.45210
$842$		0			0
$843$	1.40537	+	5.93205i	0.0484036	+	0.204311i
$844$		0			0
$845$	−8.44478	+	58.7348i	−0.290509	+	2.02054i
$846$		0			0
$847$	−77.2696	−	11.1097i	−2.65502	−	0.381734i
$848$		0			0
$849$	6.51094	−	2.56606i	0.223455	−	0.0880668i
$850$		0			0
$851$	−25.3827	+	11.5919i	−0.870107	+	0.397364i
$852$		0			0
$853$	7.93994	+	55.2235i	0.271858	+	1.89082i	0.429102	+	0.903256i	$0.358830\pi$
$853$	7.93994	+	55.2235i	0.271858	+	1.89082i	−0.157244	+	0.987560i	$0.550261\pi$
$854$		0			0
$855$	16.1360	+	48.2960i	0.551840	+	1.65169i
$856$		0			0
$857$	−0.620121	−	4.31304i	−0.0211829	−	0.147330i	0.976485	−	0.215585i	$-0.0691660\pi$
$857$	−0.620121	−	4.31304i	−0.0211829	−	0.147330i	−0.997668	+	0.0682549i	$0.978257\pi$
$858$		0			0
$859$	−12.6256	+	8.11399i	−0.430780	+	0.276846i	−0.738010	−	0.674790i	$-0.764234\pi$
$859$	−12.6256	+	8.11399i	−0.430780	+	0.276846i	0.307230	+	0.951635i	$0.400598\pi$
$860$		0			0
$861$	−22.0257	−	55.8865i	−0.750634	−	1.90461i
$862$		0			0
$863$	−7.96768	+	12.3979i	−0.271223	+	0.422031i	−0.949970	−	0.312341i	$-0.898887\pi$
$863$	−7.96768	+	12.3979i	−0.271223	+	0.422031i	0.678747	+	0.734372i	$0.262523\pi$
$864$		0			0
$865$	−2.27837	+	7.75942i	−0.0774670	+	0.263828i
$866$		0			0
$867$	−16.6040	+	23.0537i	−0.563902	+	0.782946i
$868$		0			0
$869$	9.95357	+	8.62482i	0.337652	+	0.292577i
$870$		0			0
$871$	6.12866	+	51.8686i	0.207662	+	1.75750i
$872$		0			0
$873$	2.30249	−	2.86394i	0.0779276	−	0.0969295i
$874$		0			0
$875$	44.2003	−	6.35504i	1.49424	−	0.214840i
$876$		0			0
$877$	13.0905	+	3.84372i	0.442035	+	0.129793i	0.495174	−	0.868794i	$-0.335104\pi$
$877$	13.0905	+	3.84372i	0.442035	+	0.129793i	−0.0531390	+	0.998587i	$0.516923\pi$
$878$		0			0
$879$	26.7066	−	6.32711i	0.900792	−	0.213408i
$880$		0			0
$881$	−2.02893	−	0.926582i	−0.0683565	−	0.0312173i	0.380943	−	0.924598i	$-0.375599\pi$
$881$	−2.02893	−	0.926582i	−0.0683565	−	0.0312173i	−0.449300	+	0.893381i	$0.648327\pi$
$882$		0			0
$883$	14.3438	+	22.3194i	0.482708	+	0.751108i	0.994127	−	0.108223i	$-0.0345162\pi$
$883$	14.3438	+	22.3194i	0.482708	+	0.751108i	−0.511419	+	0.859332i	$0.670880\pi$
$884$		0			0
$885$	33.4706	+	24.1066i	1.12510	+	0.810333i
$886$		0			0
$887$	−1.43120	−	4.87420i	−0.0480548	−	0.163660i	0.931970	−	0.362536i	$-0.118089\pi$
$887$	−1.43120	−	4.87420i	−0.0480548	−	0.163660i	−0.980025	+	0.198876i	$0.936271\pi$
$888$		0			0
$889$	−17.3941	+	2.50090i	−0.583380	+	0.0838774i
$890$		0			0
$891$	24.2213	+	44.1171i	0.811444	+	1.47798i
$892$		0			0
$893$	−25.1349	−	11.4787i	−0.841109	−	0.384122i
$894$		0			0
$895$	−1.99000	+	13.8407i	−0.0665183	+	0.462645i
$896$		0			0
$897$	45.0441	−	35.0327i	1.50398	−	1.16971i
$898$		0			0
$899$	23.1647	+	14.8870i	0.772584	+	0.496510i
$900$		0			0
$901$			0.651380i			0.0217006i
$902$		0			0
$903$	−2.77840	+	1.09501i	−0.0924593	+	0.0364396i
$904$		0			0
$905$	−10.6158	−	12.2512i	−0.352880	−	0.407245i
$906$		0			0
$907$	36.4465	+	23.4228i	1.21019	+	0.777740i	0.980690	−	0.195569i	$-0.0626555\pi$
$907$	36.4465	+	23.4228i	1.21019	+	0.777740i	0.229497	+	0.973309i	$0.426292\pi$
$908$		0			0
$909$	0.236987	+	6.42877i	0.00786037	+	0.213229i
$910$		0			0
$911$	15.9034	−	54.1621i	0.526904	−	1.79447i	−0.0765404	−	0.997066i	$-0.524387\pi$
$911$	15.9034	−	54.1621i	0.526904	−	1.79447i	0.603445	−	0.797405i	$-0.293794\pi$
$912$		0			0
$913$	−30.7402	−	47.8327i	−1.01735	−	1.58303i
$914$		0			0
$915$	−34.0603	−	11.9938i	−1.12600	−	0.396504i
$916$		0			0
$917$	−11.4174	−	3.35246i	−0.377037	−	0.110708i
$918$		0			0
$919$	10.1441	−	8.78994i	0.334624	−	0.289953i	−0.471299	−	0.881973i	$-0.656215\pi$
$919$	10.1441	−	8.78994i	0.334624	−	0.289953i	0.805923	+	0.592020i	$0.201669\pi$
$920$		0			0
$921$	13.0953	−	10.1848i	0.431505	−	0.335600i
$922$		0			0
$923$	30.5682	+	35.2776i	1.00616	+	1.16118i
$924$		0			0
$925$	1.89138	−	1.21552i	0.0621883	−	0.0399660i
$926$		0			0
$927$	2.59992	+	7.78170i	0.0853925	+	0.255585i
$928$		0			0
$929$	−17.3909	+	20.0702i	−0.570578	+	0.658482i	−0.965552	−	0.260210i	$-0.916208\pi$
$929$	−17.3909	+	20.0702i	−0.570578	+	0.658482i	0.394974	+	0.918692i	$0.370754\pi$
$930$		0			0
$931$	40.6485	−	46.9109i	1.33220	−	1.53744i
$932$		0			0
$933$	30.2693	+	15.8115i	0.990974	+	0.517645i
$934$		0			0
$935$	−8.41538	+	3.84318i	−0.275212	+	0.125685i
$936$		0			0
$937$		−	27.3655i		−	0.893991i	−0.894536	−	0.446996i	$-0.852494\pi$
$937$		−	27.3655i		−	0.893991i	0.894536	−	0.446996i	$-0.147506\pi$
$938$		0			0
$939$	35.3336	−	36.6601i	1.15307	−	1.19636i
$940$		0			0
$941$	−6.15785	−	13.4838i	−0.200740	−	0.439560i	0.782312	−	0.622887i	$-0.214040\pi$
$941$	−6.15785	−	13.4838i	−0.200740	−	0.439560i	−0.983052	+	0.183328i	$0.941313\pi$
$942$		0			0
$943$	13.1006	+	44.6164i	0.426613	+	1.45291i
$944$		0			0
$945$	42.4988	−	5.41231i	1.38249	−	0.176062i
$946$		0			0
$947$	12.5601	+	10.8834i	0.408148	+	0.353663i	0.834608	−	0.550844i	$-0.185694\pi$
$947$	12.5601	+	10.8834i	0.408148	+	0.353663i	−0.426460	+	0.904506i	$0.640239\pi$
$948$		0			0
$949$	11.8467	+	40.3460i	0.384559	+	1.30969i
$950$		0			0
$951$	−1.74314	+	8.78968i	−0.0565251	+	0.285025i
$952$		0			0
$953$	−18.4460	+	15.9835i	−0.597524	+	0.517757i	−0.900280	−	0.435311i	$-0.856639\pi$
$953$	−18.4460	+	15.9835i	−0.597524	+	0.517757i	0.302756	+	0.953068i	$0.402093\pi$
$954$		0			0
$955$	−0.887023	+	6.16938i	−0.0287034	+	0.199637i
$956$		0			0
$957$	−81.5630	−	4.32496i	−2.63656	−	0.139806i
$958$		0			0
$959$	9.32966	−	31.7739i	0.301270	−	1.02603i
$960$		0			0
$961$	8.44847	+	18.4996i	0.272531	+	0.596761i
$962$		0			0
$963$	−5.01072	+	3.48753i	−0.161468	+	0.112384i
$964$		0			0
$965$	10.4526	+	3.06916i	0.336481	+	0.0987998i
$966$		0			0
$967$	−7.58311			−0.243856			−0.121928	−	0.992539i	$-0.538908\pi$
$967$	−7.58311			−0.243856			−0.121928	+	0.992539i	$0.538908\pi$
$968$		0			0
$969$	10.3243	−	2.44596i	0.331666	−	0.0785756i
$970$		0			0
$971$	−40.6777	+	35.2474i	−1.30541	+	1.13114i	−0.322597	+	0.946536i	$0.604556\pi$
$971$	−40.6777	+	35.2474i	−1.30541	+	1.13114i	−0.982812	+	0.184607i	$0.940899\pi$
$972$		0			0
$973$	28.1133	−	61.5596i	0.901272	−	1.97351i
$974$		0			0
$975$	−3.19062	+	3.31041i	−0.102182	+	0.106018i
$976$		0			0
$977$	−5.17287	+	8.04914i	−0.165495	+	0.257515i	−0.914089	−	0.405514i	$-0.867093\pi$
$977$	−5.17287	+	8.04914i	−0.165495	+	0.257515i	0.748594	+	0.663028i	$0.230729\pi$
$978$		0			0
$979$	−21.2540	−	3.05586i	−0.679281	−	0.0976658i
$980$		0			0
$981$	4.75940	−	44.7518i	0.151956	−	1.42882i
$982$		0			0
$983$	−13.8124	+	30.2449i	−0.440547	+	0.964664i	0.550950	+	0.834538i	$0.314265\pi$
$983$	−13.8124	+	30.2449i	−0.440547	+	0.964664i	−0.991498	+	0.130126i	$0.958462\pi$
$984$		0			0
$985$	0.536436	+	1.17463i	0.0170923	+	0.0374268i
$986$		0			0
$987$	−13.5870	+	18.8648i	−0.432478	+	0.600472i
$988$		0			0
$989$	2.21811	−	0.651295i	0.0705317	−	0.0207100i
$990$		0			0
$991$	−21.4624	+	3.08583i	−0.681775	+	0.0980245i	−0.474497	−	0.880257i	$-0.657370\pi$
$991$	−21.4624	+	3.08583i	−0.681775	+	0.0980245i	−0.207279	+	0.978282i	$0.566461\pi$
$992$		0			0
$993$	−9.18764	+	46.3282i	−0.291561	+	1.47018i
$994$		0			0
$995$	−9.34090	+	20.4537i	−0.296126	+	0.648427i
$996$		0			0
$997$	−2.67222	−	1.71733i	−0.0846299	−	0.0543884i	0.497641	−	0.867383i	$-0.334200\pi$
$997$	−2.67222	−	1.71733i	−0.0846299	−	0.0543884i	−0.582271	+	0.812994i	$0.697836\pi$
$998$		0			0
$999$	23.8661	−	14.7994i	0.755091	−	0.468233i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.s.b.5.14	✓	200
3.2	odd	2	inner	804.2.s.b.5.19	yes	200
67.27	odd	22	inner	804.2.s.b.161.19	yes	200
201.161	even	22	inner	804.2.s.b.161.14	yes	200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.s.b.5.14	✓	200	1.1	even	1	trivial
804.2.s.b.5.19	yes	200	3.2	odd	2	inner
804.2.s.b.161.14	yes	200	201.161	even	22	inner
804.2.s.b.161.19	yes	200	67.27	odd	22	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.s (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.575290 - 1.63372i) q^{3} +(2.05430 - 0.603197i) q^{5} +(-2.91035 - 2.52183i) q^{7} +(-2.33808 - 1.87973i) q^{9} +O(q^{10})\)	\(q+(0.575290 - 1.63372i) q^{3} +(2.05430 - 0.603197i) q^{5} +(-2.91035 - 2.52183i) q^{7} +(-2.33808 - 1.87973i) q^{9} +(5.36557 - 1.57547i) q^{11} +(3.44974 + 5.36790i) q^{13} +(0.196364 - 3.70316i) q^{15} +(-0.764837 - 0.109967i) q^{17} +(-5.19155 - 5.99137i) q^{19} +(-5.79426 + 3.30391i) q^{21} +(4.69664 - 2.14488i) q^{23} +(-0.349969 + 0.224911i) q^{25} +(-4.41602 + 2.73838i) q^{27} -8.43272i q^{29} +(-1.76539 + 2.74699i) q^{31} +(0.512878 - 9.67219i) q^{33} +(-7.49988 - 3.42508i) q^{35} -5.40444 q^{37} +(10.7543 - 2.54781i) q^{39} +(-1.28169 + 8.91433i) q^{41} +(0.443176 + 0.0637191i) q^{43} +(-5.93697 - 2.45120i) q^{45} +(3.17052 - 1.44793i) q^{47} +(1.11429 + 7.75005i) q^{49} +(-0.619659 + 1.18627i) q^{51} +(-0.119970 - 0.834409i) q^{53} +(10.0722 - 6.47299i) q^{55} +(-12.7749 + 5.03476i) q^{57} +(-6.01354 + 9.35726i) q^{59} +(2.74338 - 9.34309i) q^{61} +(2.06428 + 11.3669i) q^{63} +(10.3247 + 8.94641i) q^{65} +(7.35766 + 3.58676i) q^{67} +(-0.802207 - 8.90692i) q^{69} +(7.24102 - 1.04110i) q^{71} +(6.32300 + 1.85660i) q^{73} +(0.166108 + 0.701140i) q^{75} +(-19.5887 - 8.94588i) q^{77} +(1.27332 + 1.98132i) q^{79} +(1.93326 + 8.78991i) q^{81} +(-2.86458 - 9.75587i) q^{83} +(-1.63754 + 0.235442i) q^{85} +(-13.7767 - 4.85127i) q^{87} +(-3.49281 - 1.59511i) q^{89} +(3.49699 - 24.3221i) q^{91} +(3.47221 + 4.46447i) q^{93} +(-14.2790 - 9.17653i) q^{95} +1.22491i q^{97} +(-15.5066 - 6.40222i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 200 q - 10 q^{9}+O(q^{10}) \) 200 * q - 10 * q^9	\( 200 q - 10 q^{9} + 2 q^{15} + 6 q^{19} - 10 q^{21} - 20 q^{25} - 44 q^{31} - 5 q^{33} + 78 q^{39} - 22 q^{43} - 22 q^{45} - 16 q^{49} + 36 q^{55} + 66 q^{57} + 176 q^{61} + 132 q^{63} + 46 q^{67} - 26 q^{73} - 165 q^{75} - 44 q^{79} + 42 q^{81} - 66 q^{87} - 20 q^{91} + 84 q^{93} - 55 q^{99}+O(q^{100}) \) 200 * q - 10 * q^9 + 2 * q^15 + 6 * q^19 - 10 * q^21 - 20 * q^25 - 44 * q^31 - 5 * q^33 + 78 * q^39 - 22 * q^43 - 22 * q^45 - 16 * q^49 + 36 * q^55 + 66 * q^57 + 176 * q^61 + 132 * q^63 + 46 * q^67 - 26 * q^73 - 165 * q^75 - 44 * q^79 + 42 * q^81 - 66 * q^87 - 20 * q^91 + 84 * q^93 - 55 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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