LMFDB - Embedded newform 804.2.s.b.5.19

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			5.19
Character	$\chi$	$=$	804.5
Dual form			804.2.s.b.161.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.61142 + 0.635084i) q^{3} +(-2.05430 + 0.603197i) q^{5} +(-2.91035 - 2.52183i) q^{7} +(2.19334 + 2.04677i) q^{9} +O(q^{10})$	\(q+(1.61142 + 0.635084i) q^{3} +(-2.05430 + 0.603197i) q^{5} +(-2.91035 - 2.52183i) q^{7} +(2.19334 + 2.04677i) q^{9} +(-5.36557 + 1.57547i) q^{11} +(3.44974 + 5.36790i) q^{13} +(-3.69342 - 0.332650i) q^{15} +(0.764837 + 0.109967i) q^{17} +(-5.19155 - 5.99137i) q^{19} +(-3.08821 - 5.91204i) q^{21} +(-4.69664 + 2.14488i) q^{23} +(-0.349969 + 0.224911i) q^{25} +(2.23451 + 4.69116i) q^{27} +8.43272i q^{29} +(-1.76539 + 2.74699i) q^{31} +(-9.64674 - 0.868839i) q^{33} +(7.49988 + 3.42508i) q^{35} -5.40444 q^{37} +(2.14991 + 10.8408i) q^{39} +(1.28169 - 8.91433i) q^{41} +(0.443176 + 0.0637191i) q^{43} +(-5.74038 - 2.88167i) q^{45} +(-3.17052 + 1.44793i) q^{47} +(1.11429 + 7.75005i) q^{49} +(1.16263 + 0.662939i) q^{51} +(0.119970 + 0.834409i) q^{53} +(10.0722 - 6.47299i) q^{55} +(-4.56074 - 12.9517i) q^{57} +(6.01354 - 9.35726i) q^{59} +(2.74338 - 9.34309i) q^{61} +(-1.22177 - 11.4880i) q^{63} +(-10.3247 - 8.94641i) q^{65} +(7.35766 + 3.58676i) q^{67} +(-8.93042 + 0.473545i) q^{69} +(-7.24102 + 1.04110i) q^{71} +(6.32300 + 1.85660i) q^{73} +(-0.706783 + 0.140167i) q^{75} +(19.5887 + 8.94588i) q^{77} +(1.27332 + 1.98132i) q^{79} +(0.621459 + 8.97852i) q^{81} +(2.86458 + 9.75587i) q^{83} +(-1.63754 + 0.235442i) q^{85} +(-5.35549 + 13.5886i) q^{87} +(3.49281 + 1.59511i) q^{89} +(3.49699 - 24.3221i) q^{91} +(-4.58935 + 3.30539i) q^{93} +(14.2790 + 9.17653i) q^{95} +1.22491i q^{97} +(-14.9931 - 7.52655i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	1.61142	+	0.635084i	0.930353	+	0.366666i
$3$	1.61142	+	0.635084i	0.930353	+	0.366666i
$4$		0			0
$5$	−2.05430	+	0.603197i	−0.918711	+	0.269758i	−0.706703	−	0.707510i	$-0.749818\pi$
$5$	−2.05430	+	0.603197i	−0.918711	+	0.269758i	−0.212007	+	0.977268i	$0.568000\pi$
$6$		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
$9$	2.19334	+	2.04677i	0.731113	+	0.682257i
$10$		0			0
$11$	−5.36557	+	1.57547i	−1.61778	+	0.475023i	−0.960421	−	0.278554i	$-0.910145\pi$
$11$	−5.36557	+	1.57547i	−1.61778	+	0.475023i	−0.657360	+	0.753577i	$0.728327\pi$
$12$		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
$15$	−3.69342	−	0.332650i	−0.953636	−	0.0858898i
$16$		0			0
$17$	0.764837	+	0.109967i	0.185500	+	0.0266709i	0.234439	−	0.972131i	$-0.424675\pi$
$17$	0.764837	+	0.109967i	0.185500	+	0.0266709i	−0.0489385	+	0.998802i	$0.515584\pi$
$18$		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
$21$	−3.08821	−	5.91204i	−0.673903	−	1.29011i
$22$		0			0
$23$	−4.69664	+	2.14488i	−0.979316	+	0.447239i	−0.839750	−	0.542974i	$-0.817298\pi$
$23$	−4.69664	+	2.14488i	−0.979316	+	0.447239i	−0.139567	+	0.990213i	$0.544571\pi$
$24$		0			0
$25$	−0.349969	+	0.224911i	−0.0699937	+	0.0449822i
$26$		0			0
$27$	2.23451	+	4.69116i	0.430032	+	0.902813i
$28$		0			0
$29$			8.43272i			1.56592i	0.622074	+	0.782959i	$0.286290\pi$
$29$			8.43272i			1.56592i	−0.622074	+	0.782959i	$0.713710\pi$
$30$		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
$33$	−9.64674	−	0.868839i	−1.67928	−	0.151245i
$34$		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
$39$	2.14991	+	10.8408i	0.344261	+	1.73592i
$40$		0			0
$41$	1.28169	−	8.91433i	0.200166	−	1.39218i	−0.603623	−	0.797270i	$-0.706277\pi$
$41$	1.28169	−	8.91433i	0.200166	−	1.39218i	0.803789	−	0.594915i	$-0.202814\pi$
$42$		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
$45$	−5.74038	−	2.88167i	−0.855725	−	0.429573i
$46$		0			0
$47$	−3.17052	+	1.44793i	−0.462467	+	0.211202i	−0.633002	−	0.774150i	$-0.718178\pi$
$47$	−3.17052	+	1.44793i	−0.462467	+	0.211202i	0.170535	+	0.985352i	$0.445450\pi$
$48$		0			0
$49$	1.11429	+	7.75005i	0.159184	+	1.10715i
$50$		0			0
$51$	1.16263	+	0.662939i	0.162801	+	0.0928300i
$52$		0			0
$53$	0.119970	+	0.834409i	0.0164791	+	0.114615i	0.996401	−	0.0847686i	$-0.0270151\pi$
$53$	0.119970	+	0.834409i	0.0164791	+	0.114615i	−0.979922	+	0.199384i	$0.936106\pi$
$54$		0			0
$55$	10.0722	−	6.47299i	1.35813	−	0.872818i
$56$		0			0
$57$	−4.56074	−	12.9517i	−0.604084	−	1.71549i
$58$		0			0
$59$	6.01354	−	9.35726i	0.782897	−	1.21821i	−0.188808	−	0.982014i	$-0.560462\pi$
$59$	6.01354	−	9.35726i	0.782897	−	1.21821i	0.971705	−	0.236197i	$-0.0759012\pi$
$60$		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
$63$	−1.22177	−	11.4880i	−0.153928	−	1.44736i
$64$		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
$69$	−8.93042	+	0.473545i	−1.07510	+	0.0570081i
$70$		0			0
$71$	−7.24102	+	1.04110i	−0.859351	+	0.123556i	−0.557882	−	0.829920i	$-0.688386\pi$
$71$	−7.24102	+	1.04110i	−0.859351	+	0.123556i	−0.301469	+	0.953476i	$0.597477\pi$
$72$		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
$75$	−0.706783	+	0.140167i	−0.0816123	+	0.0161850i
$76$		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
$81$	0.621459	+	8.97852i	0.0690510	+	0.997613i
$82$		0			0
$83$	2.86458	+	9.75587i	0.314429	+	1.07085i	0.953424	+	0.301635i	$0.0975323\pi$
$83$	2.86458	+	9.75587i	0.314429	+	1.07085i	−0.638995	+	0.769211i	$0.720650\pi$
$84$		0			0
$85$	−1.63754	+	0.235442i	−0.177616	+	0.0255373i
$86$		0			0
$87$	−5.35549	+	13.5886i	−0.574168	+	1.45686i
$88$		0			0
$89$	3.49281	+	1.59511i	0.370238	+	0.169082i	0.591840	−	0.806055i	$-0.298402\pi$
$89$	3.49281	+	1.59511i	0.370238	+	0.169082i	−0.221603	+	0.975137i	$0.571129\pi$
$90$		0			0
$91$	3.49699	−	24.3221i	0.366584	−	2.54965i
$92$		0			0
$93$	−4.58935	+	3.30539i	−0.475893	+	0.342753i
$94$		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
$99$	−14.9931	−	7.52655i	−1.50687	−	0.756446i
$100$		0			0
$101$	1.40427	+	1.62061i	0.139730	+	0.161257i	0.821301	−	0.570495i	$-0.193248\pi$
$101$	1.40427	+	1.62061i	0.139730	+	0.161257i	−0.681571	+	0.731752i	$0.738703\pi$
$102$		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	−0.982552	−	0.185986i	$-0.940452\pi$
$107$	−0.573320	+	1.95255i	−0.0554249	+	0.188760i	0.927127	+	0.374746i	$0.122270\pi$
$108$		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
$111$	−8.70881	−	3.43227i	−0.826604	−	0.325777i
$112$		0			0
$113$	−18.3068	−	5.37535i	−1.72216	−	0.505671i	−0.736790	−	0.676121i	$-0.763659\pi$
$113$	−18.3068	−	5.37535i	−1.72216	−	0.505671i	−0.985366	+	0.170451i	$0.945478\pi$
$114$		0			0
$115$	8.35451	−	7.23922i	0.779062	−	0.675061i
$116$		0			0
$117$	−3.42042	+	18.8345i	−0.316218	+	1.74125i
$118$		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
$123$	7.72668	−	13.5507i	0.696691	−	1.22183i
$124$		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
$129$	0.673675	+	0.384132i	0.0593138	+	0.0338209i
$130$		0			0
$131$	−2.81078	+	1.28364i	−0.245579	+	0.112152i	−0.534402	−	0.845230i	$-0.679463\pi$
$131$	−2.81078	+	1.28364i	−0.245579	+	0.112152i	0.288824	+	0.957382i	$0.406736\pi$
$132$		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	0.693436	−	0.720518i	$-0.256096\pi$
$137$	−3.57227	−	7.82217i	−0.305199	−	0.668293i	−0.998635	+	0.0522248i	$0.983369\pi$
$138$		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
$141$	−6.02858	+	0.319672i	−0.507698	+	0.0269212i
$142$		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
$147$	−3.12634	+	13.1962i	−0.257856	+	1.08841i
$148$		0			0
$149$	−10.0243	+	8.68614i	−0.821226	+	0.711596i	−0.960386	−	0.278674i	$-0.910105\pi$
$149$	−10.0243	+	8.68614i	−0.821226	+	0.711596i	0.139160	+	0.990270i	$0.455560\pi$
$150$		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
$153$	1.45247	+	1.80664i	0.117425	+	0.146058i
$154$		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
$159$	−0.336598	+	1.42077i	−0.0266940	+	0.112675i
$160$		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
$165$	20.3414	−	4.03402i	1.58357	−	0.314048i
$166$		0			0
$167$	−13.1265	+	11.3742i	−1.01576	+	0.880161i	−0.992825	−	0.119576i	$-0.961847\pi$
$167$	−13.1265	+	11.3742i	−1.01576	+	0.880161i	−0.0229352	+	0.999737i	$0.507301\pi$
$168$		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	−0.754908	−	0.655831i	$-0.772318\pi$
$173$	2.04209	−	3.17755i	0.155257	−	0.241585i	0.910165	+	0.414246i	$0.135955\pi$
$174$		0			0
$175$	1.58572	+	0.227992i	0.119869	+	0.0172346i
$176$		0			0
$177$	15.6330	−	11.2594i	1.17505	−	0.846305i
$178$		0			0
$179$	2.71308	−	5.94082i	0.202785	−	0.444037i	−0.780729	−	0.624870i	$-0.785152\pi$
$179$	2.71308	−	5.94082i	0.202785	−	0.444037i	0.983514	+	0.180833i	$0.0578792\pi$
$180$		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
$183$	10.3544	−	13.3134i	0.765417	−	0.984151i
$184$		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
$189$	5.32709	−	19.2880i	0.387489	−	1.40299i
$190$		0			0
$191$	1.20933	−	2.64807i	0.0875041	−	0.191607i	−0.860821	−	0.508908i	$-0.830049\pi$
$191$	1.20933	−	2.64807i	0.0875041	−	0.191607i	0.948325	+	0.317301i	$0.102777\pi$
$192$		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
$195$	−10.9557	−	20.9735i	−0.784554	−	1.50194i
$196$		0			0
$197$	−0.0858349	−	0.596995i	−0.00611548	−	0.0425341i	0.986535	−	0.163549i	$-0.0522942\pi$
$197$	−0.0858349	−	0.596995i	−0.00611548	−	0.0425341i	−0.992651	+	0.121015i	$0.961385\pi$
$198$		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
$201$	9.57838	+	10.4525i	0.675607	+	0.737262i
$202$		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
$207$	−14.6914	−	4.90849i	−1.02112	−	0.341163i
$208$		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
$213$	−12.3295	−	2.92100i	−0.844803	−	0.200144i
$214$		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
$219$	9.00990	+	7.00739i	0.608832	+	0.473515i
$220$		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
$225$	−1.22794	−	0.222999i	−0.0818627	−	0.0148666i
$226$		0			0
$227$	−16.6970	−	2.40067i	−1.10822	−	0.159338i	−0.436185	−	0.899857i	$-0.643671\pi$
$227$	−16.6970	−	2.40067i	−1.10822	−	0.159338i	−0.672035	+	0.740519i	$0.734580\pi$
$228$		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	$-0.716471\pi$
$233$	5.65669	−	12.3864i	0.370582	−	0.811461i	0.999424	−	0.0339285i	$-0.0108019\pi$
$234$		0			0
$235$	5.63981	−	4.88692i	0.367900	−	0.318787i
$236$		0			0
$237$	0.793541	+	4.00139i	0.0515460	+	0.259918i
$238$		0			0
$239$	5.75934			0.372540			0.186270	−	0.982499i	$-0.440360\pi$
$239$	5.75934			0.372540			0.186270	+	0.982499i	$0.440360\pi$
$240$		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
$243$	−4.70068	+	14.8628i	−0.301549	+	0.953451i
$244$		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
$249$	−1.57975	+	17.5400i	−0.100113	+	1.11155i
$250$		0			0
$251$	−0.484711	+	3.37124i	−0.0305947	+	0.212791i	−0.999384	−	0.0350948i	$-0.988827\pi$
$251$	−0.484711	+	3.37124i	−0.0305947	+	0.212791i	0.968789	+	0.247886i	$0.0797358\pi$
$252$		0			0
$253$	21.8209	−	18.9079i	1.37187	−	1.18873i
$254$		0			0
$255$	−2.78828	−	0.660577i	−0.174609	−	0.0413669i
$256$		0			0
$257$	−7.42734	−	25.2952i	−0.463305	−	1.57787i	−0.777736	−	0.628591i	$-0.783632\pi$
$257$	−7.42734	−	25.2952i	−0.463305	−	1.57787i	0.314431	−	0.949280i	$-0.398186\pi$
$258$		0			0
$259$	15.7288	+	13.6291i	0.977339	+	0.846869i
$260$		0			0
$261$	−17.2599	+	18.4958i	−1.06836	+	1.14486i
$262$		0			0
$263$	6.36513	+	21.6777i	0.392491	+	1.33670i	0.884674	+	0.466210i	$0.154381\pi$
$263$	6.36513	+	21.6777i	0.392491	+	1.33670i	−0.492183	+	0.870492i	$0.663801\pi$
$264$		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	$0.204236\pi$
$269$			19.6323i			1.19700i	−0.801123	+	0.598500i	$0.795764\pi$
$270$		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
$273$	21.0817	−	36.9722i	1.27592	−	2.23766i
$274$		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
$279$	−9.49456	+	2.41175i	−0.568424	+	0.144387i
$280$		0			0
$281$	2.96094	−	1.90288i	0.176635	−	0.113516i	−0.449336	−	0.893363i	$-0.648339\pi$
$281$	2.96094	−	1.90288i	0.176635	−	0.113516i	0.625971	+	0.779847i	$0.284703\pi$
$282$		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
$285$	17.1815	+	23.8556i	1.01775	+	1.41308i
$286$		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
$291$	−0.777919	+	1.97384i	−0.0456024	+	0.115708i
$292$		0			0
$293$	−8.56693	−	13.3304i	−0.500485	−	0.778771i	0.495469	−	0.868625i	$-0.334996\pi$
$293$	−8.56693	−	13.3304i	−0.500485	−	0.778771i	−0.995955	+	0.0898548i	$0.971360\pi$
$294$		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
$303$	1.23364	+	3.50332i	0.0708708	+	0.201260i
$304$		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
$309$	−2.76837	−	3.84373i	−0.157487	−	0.218662i
$310$		0			0
$311$	2.80597	−	19.5159i	0.159112	−	1.10665i	−0.741163	−	0.671325i	$-0.765725\pi$
$311$	2.80597	−	19.5159i	0.159112	−	1.10665i	0.900275	−	0.435322i	$-0.143366\pi$
$312$		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
$315$	9.43942	+	22.8629i	0.531851	+	1.28818i
$316$		0			0
$317$	5.12090	−	0.736274i	0.287618	−	0.0413533i	0.00300432	−	0.999995i	$-0.499044\pi$
$317$	5.12090	−	0.736274i	0.287618	−	0.0413533i	0.284614	+	0.958642i	$0.408135\pi$
$318$		0			0
$319$	−13.2855	−	45.2464i	−0.743847	−	2.53331i
$320$		0			0
$321$	−2.16389	+	2.78226i	−0.120776	+	0.155291i
$322$		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
$327$	5.05445	+	25.4868i	0.279512	+	1.40942i
$328$		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
$333$	−11.8538	−	11.0616i	−0.649582	−	0.606174i
$334$		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
$339$	−26.0861	−	20.2883i	−1.41680	−	1.10191i
$340$		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
$345$	18.0601	−	6.35960i	0.972324	−	0.342390i
$346$		0			0
$347$	−10.3251	+	6.63554i	−0.554280	+	0.356214i	−0.787601	−	0.616185i	$-0.788677\pi$
$347$	−10.3251	+	6.63554i	−0.554280	+	0.356214i	0.233321	+	0.972400i	$0.425041\pi$
$348$		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
$351$	−17.4732	+	28.1779i	−0.932649	+	1.50403i
$352$		0			0
$353$	3.07084	+	21.3582i	0.163444	+	1.13678i	0.892079	+	0.451879i	$0.149246\pi$
$353$	3.07084	+	21.3582i	0.163444	+	1.13678i	−0.728635	+	0.684902i	$0.759845\pi$
$354$		0			0
$355$	14.2472	−	6.50649i	0.756165	−	0.345329i
$356$		0			0
$357$	−1.71185	−	4.86135i	−0.0906008	−	0.257290i
$358$		0			0
$359$	19.9608	+	2.86993i	1.05349	+	0.151469i	0.647235	−	0.762291i	$-0.275925\pi$
$359$	19.9608	+	2.86993i	1.05349	+	0.151469i	0.406255	+	0.913760i	$0.366834\pi$
$360$		0			0
$361$	−6.24031	+	43.4023i	−0.328437	+	2.28433i
$362$		0			0
$363$	34.4405	−	6.83011i	1.80766	−	0.358488i
$364$		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
$369$	21.0568	−	16.9288i	1.09617	−	0.881279i
$370$		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
$375$	17.8021	−	9.29912i	0.919297	−	0.480204i
$376$		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
$381$	7.00566	−	3.65948i	0.358911	−	0.187481i
$382$		0			0
$383$	13.2261	+	15.2638i	0.675824	+	0.779942i	0.985276	−	0.170973i	$-0.0546910\pi$
$383$	13.2261	+	15.2638i	0.675824	+	0.779942i	−0.309452	+	0.950915i	$0.600146\pi$
$384$		0			0
$385$	−45.6373	−	6.56165i	−2.32589	−	0.334413i
$386$		0			0
$387$	0.841617	+	1.04684i	0.0427818	+	0.0532137i
$388$		0			0
$389$	−3.16294	−	4.92163i	−0.160367	−	0.249536i	0.751766	−	0.659430i	$-0.229202\pi$
$389$	−3.16294	−	4.92163i	−0.160367	−	0.249536i	−0.912133	+	0.409893i	$0.865566\pi$
$390$		0			0
$391$	−3.82803	+	1.12401i	−0.193592	+	0.0568437i
$392$		0			0
$393$	−5.34455	+	0.283400i	−0.269597	+	0.0142957i
$394$		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
$399$	−19.3886	+	49.1952i	−0.970642	+	2.46284i
$400$		0			0
$401$	−23.9896			−1.19798			−0.598992	−	0.800755i	$-0.704432\pi$
$401$	−23.9896			−1.19798			−0.598992	+	0.800755i	$0.704432\pi$
$402$		0			0
$403$	−20.8357			−1.03790
$404$		0			0
$405$	−6.69247	−	18.0697i	−0.332552	−	0.897891i
$406$		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
$411$	−0.788682	−	14.8735i	−0.0389028	−	0.733655i
$412$		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
$417$	−2.73041	+	30.3158i	−0.133709	+	1.48457i
$418$		0			0
$419$	30.2736	+	4.35269i	1.47896	+	0.212643i	0.834082	−	0.551641i	$-0.185998\pi$
$419$	30.2736	+	4.35269i	1.47896	+	0.212643i	0.644880	+	0.764284i	$0.276907\pi$
$420$		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
$423$	−9.91759	−	3.31353i	−0.482210	−	0.161109i
$424$		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
$429$	−28.6149	−	54.7800i	−1.38154	−	2.64480i
$430$		0			0
$431$			15.4336i			0.743410i	0.928351	+	0.371705i	$0.121227\pi$
$431$			15.4336i			0.743410i	−0.928351	+	0.371705i	$0.878773\pi$
$432$		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
$435$	2.80514	−	31.1456i	0.134496	−	1.49332i
$436$		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
$441$	−13.4186	+	19.2792i	−0.638979	+	0.918055i
$442$		0			0
$443$	1.80487	−	12.5531i	0.0857518	−	0.596417i	−0.900956	−	0.433911i	$-0.857133\pi$
$443$	1.80487	−	12.5531i	0.0857518	−	0.596417i	0.986708	−	0.162506i	$-0.0519577\pi$
$444$		0			0
$445$	−8.13745	−	1.16999i	−0.385752	−	0.0554628i
$446$		0			0
$447$	−21.6698	+	7.63071i	−1.02495	+	0.360920i
$448$		0			0
$449$	9.35902	−	4.27412i	0.441680	−	0.201708i	−0.182147	−	0.983271i	$-0.558305\pi$
$449$	9.35902	−	4.27412i	0.441680	−	0.201708i	0.623826	+	0.781563i	$0.285577\pi$
$450$		0			0
$451$	7.16731	+	49.8497i	0.337495	+	2.34733i
$452$		0			0
$453$	−7.94329	+	13.9306i	−0.373208	+	0.654518i
$454$		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
$459$	1.19317	+	3.83369i	0.0556923	+	0.178942i
$460$		0			0
$461$	−19.4412	+	30.2511i	−0.905468	+	1.40894i	0.00708430	+	0.999975i	$0.497745\pi$
$461$	−19.4412	+	30.2511i	−0.905468	+	1.40894i	−0.912552	+	0.408960i	$0.865891\pi$
$462$		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
$465$	7.43409	−	9.55854i	0.344748	−	0.443267i
$466$		0			0
$467$	28.5506	+	24.7392i	1.32116	+	1.14479i	0.978707	+	0.205261i	$0.0658044\pi$
$467$	28.5506	+	24.7392i	1.32116	+	1.14479i	0.342457	+	0.939534i	$0.388741\pi$
$468$		0			0
$469$	−12.3681	−	28.9935i	−0.571108	−	1.33879i
$470$		0			0
$471$	0.451445	+	8.51366i	0.0208015	+	0.392289i
$472$		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
$477$	−1.44471	+	2.07569i	−0.0661487	+	0.0950394i
$478$		0			0
$479$	−29.6370	−	13.5348i	−1.35415	−	0.618420i	−0.399661	−	0.916663i	$-0.630872\pi$
$479$	−29.6370	−	13.5348i	−1.35415	−	0.618420i	−0.954490	+	0.298243i	$0.903600\pi$
$480$		0			0
$481$	−18.6439	−	29.0105i	−0.850089	−	1.32276i
$482$		0			0
$483$	27.1848	+	21.1428i	1.23695	+	0.962032i
$484$		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
$489$	12.4140	+	4.89254i	0.561381	+	0.221248i
$490$		0			0
$491$	3.36878	+	1.53847i	0.152031	+	0.0694303i	0.489977	−	0.871735i	$-0.337005\pi$
$491$	3.36878	+	1.53847i	0.152031	+	0.0694303i	−0.337946	+	0.941165i	$0.609732\pi$
$492$		0			0
$493$	−0.927321	+	6.44966i	−0.0417645	+	0.290478i
$494$		0			0
$495$	35.3404	+	6.41797i	1.58843	+	0.288466i
$496$		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
$501$	−28.3759	+	9.99214i	−1.26774	+	0.446416i
$502$		0			0
$503$	3.25435	+	3.75572i	0.145104	+	0.167459i	0.823649	−	0.567100i	$-0.191935\pi$
$503$	3.25435	+	3.75572i	0.145104	+	0.167459i	−0.678545	+	0.734559i	$0.737389\pi$
$504$		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	−0.859563	−	0.511029i	$-0.829264\pi$
$509$	3.15472	−	10.7440i	0.139831	−	0.476219i	0.999394	+	0.0348099i	$0.0110826\pi$
$510$		0			0
$511$	−13.7201	−	21.3489i	−0.606941	−	0.944418i
$512$		0			0
$513$	16.5059	−	37.7422i	0.728751	−	1.66636i
$514$		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
$519$	5.30867	−	3.82347i	0.233025	−	0.167832i
$520$		0			0
$521$	−2.87894	−	3.32248i	−0.126129	−	0.145560i	0.689173	−	0.724597i	$-0.257974\pi$
$521$	−2.87894	−	3.32248i	−0.126129	−	0.145560i	−0.815301	+	0.579037i	$0.803429\pi$
$522$		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
$525$	2.41046	+	1.37445i	0.105201	+	0.0599861i
$526$		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
$531$	32.3419	−	8.21528i	1.40352	−	0.356513i
$532$		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
$543$	−0.694417	−	13.0958i	−0.0298003	−	0.561993i
$544$		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
$549$	25.1403	−	14.8775i	1.07296	−	0.634955i
$550$		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
$555$	19.9608	+	1.79778i	0.847290	+	0.0763117i
$556$		0			0
$557$	−10.2018	+	34.7442i	−0.432264	+	1.47216i	0.399347	+	0.916800i	$0.369237\pi$
$557$	−10.2018	+	34.7442i	−0.432264	+	1.47216i	−0.831612	+	0.555358i	$0.812581\pi$
$558$		0			0
$559$	1.18681	+	2.59874i	0.0501965	+	0.109915i
$560$		0			0
$561$	−7.28264	−	1.72534i	−0.307473	−	0.0728440i
$562$		0			0
$563$	4.92173	+	1.44515i	0.207426	+	0.0609059i	0.383795	−	0.923418i	$-0.374617\pi$
$563$	4.92173	+	1.44515i	0.207426	+	0.0609059i	−0.176369	+	0.984324i	$0.556435\pi$
$564$		0			0
$565$	40.8500			1.71857
$566$		0			0
$567$	20.8336	−	27.6978i	0.874930	−	1.16320i
$568$		0			0
$569$	−24.4368	+	21.1746i	−1.02445	+	0.887687i	−0.993726	−	0.111841i	$-0.964325\pi$
$569$	−24.4368	+	21.1746i	−1.02445	+	0.887687i	−0.0307191	+	0.999528i	$0.509780\pi$
$570$		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
$579$	5.15054	+	7.15123i	0.214049	+	0.297195i
$580$		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
$585$	−4.33432	−	40.7548i	−0.179202	−	1.68500i
$586$		0			0
$587$	10.5178	−	3.08830i	0.434116	−	0.127468i	−0.0573709	−	0.998353i	$-0.518272\pi$
$587$	10.5178	−	3.08830i	0.434116	−	0.127468i	0.491487	+	0.870885i	$0.336454\pi$
$588$		0			0
$589$	25.6233	−	3.68408i	1.05579	−	0.151800i
$590$		0			0
$591$	0.240826	−	1.01652i	0.00990624	−	0.0418141i
$592$		0			0
$593$	6.86975	−	15.0427i	0.282107	−	0.617728i	−0.714536	−	0.699599i	$-0.753362\pi$
$593$	6.86975	−	15.0427i	0.282107	−	0.617728i	0.996643	+	0.0818707i	$0.0260895\pi$
$594$		0			0
$595$	5.35954	+	3.44437i	0.219720	+	0.141205i
$596$		0			0
$597$	−16.1233	+	8.42219i	−0.659884	+	0.344697i
$598$		0			0
$599$	−5.87718	−	40.8767i	−0.240135	−	1.67018i	−0.651456	−	0.758686i	$-0.725842\pi$
$599$	−5.87718	−	40.8767i	−0.240135	−	1.67018i	0.411321	−	0.911490i	$-0.365067\pi$
$600$		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
$603$	8.79656	+	22.9264i	0.358224	+	0.933636i
$604$		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
$609$	49.8546	−	26.0420i	2.02021	−	1.05528i
$610$		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
$615$	−7.69915	+	32.4980i	−0.310460	+	1.31044i
$616$		0			0
$617$	−9.54492	+	1.37235i	−0.384264	+	0.0552488i	−0.331740	−	0.943371i	$-0.607636\pi$
$617$	−9.54492	+	1.37235i	−0.384264	+	0.0552488i	−0.0525240	+	0.998620i	$0.516727\pi$
$618$		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
$621$	−20.5567	−	17.2399i	−0.824911	−	0.691813i
$622$		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
$627$	44.8760	+	62.3077i	1.79217	+	2.48833i
$628$		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
$639$	−18.0129	−	12.5372i	−0.712579	−	0.495965i
$640$		0			0
$641$	−44.6524			−1.76366			−0.881831	−	0.471565i	$-0.843689\pi$
$641$	−44.6524			−1.76366			−0.881831	+	0.471565i	$0.843689\pi$
$642$		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
$645$	−1.61564	−	0.382764i	−0.0636157	−	0.0150713i
$646$		0			0
$647$	6.78193	+	14.8504i	0.266625	+	0.583828i	0.994833	−	0.101529i	$-0.0323735\pi$
$647$	6.78193	+	14.8504i	0.266625	+	0.583828i	−0.728207	+	0.685357i	$0.759646\pi$
$648$		0			0
$649$	−17.5240	+	59.6812i	−0.687877	+	2.34269i
$650$		0			0
$651$	21.6922	+	1.95372i	0.850185	+	0.0765725i
$652$		0			0
$653$	3.18187	−	22.1304i	0.124516	−	0.866029i	−0.827823	−	0.560989i	$-0.810421\pi$
$653$	3.18187	−	22.1304i	0.124516	−	0.866029i	0.952340	−	0.305040i	$-0.0986699\pi$
$654$		0			0
$655$	4.99989	−	4.33243i	0.195362	−	0.169282i
$656$		0			0
$657$	10.0684	+	17.0139i	0.392807	+	0.663774i
$658$		0			0
$659$	10.0400	+	34.1930i	0.391101	+	1.33197i	0.886269	+	0.463171i	$0.153288\pi$
$659$	10.0400	+	34.1930i	0.391101	+	1.33197i	−0.495168	+	0.868797i	$0.664893\pi$
$660$		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
$663$	0.452199	+	8.52788i	0.0175620	+	0.331195i
$664$		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
$675$	−1.83710	−	1.13919i	−0.0707101	−	0.0438475i
$676$		0			0
$677$	15.1871	−	17.5269i	0.583689	−	0.673613i	−0.384705	−	0.923040i	$-0.625697\pi$
$677$	15.1871	−	17.5269i	0.583689	−	0.673613i	0.968394	+	0.249427i	$0.0802421\pi$
$678$		0			0
$679$	3.08901	−	3.56491i	0.118545	−	0.136809i
$680$		0			0
$681$	−25.3812	−	14.4725i	−0.972611	−	0.554587i
$682$		0			0
$683$	22.4208	−	14.4090i	0.857909	−	0.551344i	−0.0361235	−	0.999347i	$-0.511501\pi$
$683$	22.4208	−	14.4090i	0.857909	−	0.551344i	0.894032	+	0.448003i	$0.147865\pi$
$684$		0			0
$685$	12.0568	+	13.9143i	0.460667	+	0.531638i
$686$		0			0
$687$	−23.4120	+	16.8621i	−0.893225	+	0.643328i
$688$		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
$693$	24.6546	+	59.7150i	0.936549	+	2.26839i
$694$		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	0.936341	−	0.351091i	$-0.114189\pi$
$701$	26.6339	+	17.1166i	1.00595	+	0.646483i	0.0696066	+	0.997575i	$0.477826\pi$
$702$		0			0
$703$	28.0574	+	32.3800i	1.05820	+	1.22123i
$704$		0			0
$705$	12.1917	−	4.29312i	0.459166	−	0.161688i
$706$		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
$711$	−1.26249	+	6.95188i	−0.0473471	+	0.260716i
$712$		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
$717$	9.28070	+	3.65766i	0.346594	+	0.136598i
$718$		0			0
$719$	10.6376	−	1.52946i	0.396717	−	0.0570393i	0.0589305	−	0.998262i	$-0.481231\pi$
$719$	10.6376	−	1.52946i	0.396717	−	0.0570393i	0.337786	+	0.941223i	$0.390322\pi$
$720$		0			0
$721$	2.96713	+	10.1051i	0.110502	+	0.376334i
$722$		0			0
$723$	−16.4192	−	12.7699i	−0.610635	−	0.474917i
$724$		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
$729$	−17.0139	+	20.9649i	−0.630144	+	0.776478i
$730$		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
$735$	−1.53748	−	28.9948i	−0.0567108	−	1.06949i
$736$		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
$741$	53.7899	−	69.1615i	1.97602	−	2.54071i
$742$		0			0
$743$	−11.1004	+	37.8045i	−0.407234	+	1.38691i	0.459517	+	0.888169i	$0.348023\pi$
$743$	−11.1004	+	37.8045i	−0.407234	+	1.38691i	−0.866751	+	0.498742i	$0.833796\pi$
$744$		0			0
$745$	15.3535	−	23.8906i	0.562510	−	0.875283i
$746$		0			0
$747$	−13.6850	+	27.2610i	−0.500709	+	0.997430i
$748$		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
$753$	−2.92209	+	5.12465i	−0.106487	+	0.186753i
$754$		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
$759$	47.1708	−	16.6105i	1.71219	−	0.602922i
$760$		0			0
$761$	1.08944	+	0.156638i	0.0394923	+	0.00567813i	0.162033	−	0.986785i	$-0.448195\pi$
$761$	1.08944	+	0.156638i	0.0394923	+	0.00567813i	−0.122540	+	0.992464i	$0.539104\pi$
$762$		0			0
$763$	8.22145	−	57.1815i	0.297637	−	2.07011i
$764$		0			0
$765$	−4.07357	−	2.83526i	−0.147280	−	0.102509i
$766$		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
$771$	4.09602	−	45.4781i	0.147514	−	1.63785i
$772$		0			0
$773$	−9.47518	+	14.7437i	−0.340798	+	0.530293i	−0.968776	−	0.247939i	$-0.920247\pi$
$773$	−9.47518	+	14.7437i	−0.340798	+	0.530293i	0.627977	+	0.778232i	$0.283883\pi$
$774$		0			0
$775$		−	1.35842i		−	0.0487958i
$776$		0			0
$777$	16.6901	+	31.9512i	0.598752	+	1.14624i
$778$		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
$783$	−39.5592	+	18.8430i	−1.41373	+	0.673395i
$784$		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
$789$	−3.51023	+	38.9742i	−0.124968	+	1.38752i
$790$		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
$795$	−0.165533	−	3.12173i	−0.00587085	−	0.110716i
$796$		0			0
$797$	−32.8459	−	28.4612i	−1.16346	−	1.00815i	−0.999766	−	0.0216353i	$-0.993113\pi$
$797$	−32.8459	−	28.4612i	−1.16346	−	1.00815i	−0.163697	−	0.986511i	$-0.552342\pi$
$798$		0			0
$799$	−2.58415	+	0.758776i	−0.0914208	+	0.0268436i
$800$		0			0
$801$	4.39609	+	10.6476i	0.155328	+	0.376215i
$802$		0			0
$803$	−36.8515			−1.30046
$804$		0			0
$805$	−42.5706			−1.50042
$806$		0			0
$807$	−12.4681	+	31.6358i	−0.438899	+	1.11363i
$808$		0			0
$809$	47.5514	−	13.9624i	1.67182	−	0.490890i	0.697599	−	0.716489i	$-0.254252\pi$
$809$	47.5514	−	13.9624i	1.67182	−	0.490890i	0.974220	+	0.225598i	$0.0724337\pi$
$810$		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
$813$	−34.8720	+	1.84912i	−1.22302	+	0.0648516i
$814$		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
$819$	57.4519	−	46.1891i	2.00753	−	1.61398i
$820$		0			0
$821$	12.9571	+	1.86295i	0.452205	+	0.0650173i	0.364655	−	0.931143i	$-0.381187\pi$
$821$	12.9571	+	1.86295i	0.452205	+	0.0650173i	0.0875506	+	0.996160i	$0.472096\pi$
$822$		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
$825$	3.57147	−	1.86559i	0.124342	−	0.0649516i
$826$		0			0
$827$	46.2625	−	21.1274i	1.60871	−	0.734672i	0.610358	−	0.792126i	$-0.291025\pi$
$827$	46.2625	−	21.1274i	1.60871	−	0.734672i	0.998348	+	0.0574539i	$0.0182982\pi$
$828$		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
$831$	−6.59160	+	3.44319i	−0.228660	+	0.119443i
$832$		0			0
$833$			6.05006i			0.209622i
$834$		0			0
$835$	20.1049	−	31.2839i	0.695759	−	1.08262i
$836$		0			0
$837$	−16.8314	−	2.14351i	−0.581777	−	0.0740904i
$838$		0			0
$839$	−3.91914	−	1.78981i	−0.135304	−	0.0617912i	0.346613	−	0.938008i	$-0.387332\pi$
$839$	−3.91914	−	1.78981i	−0.135304	−	0.0617912i	−0.481916	+	0.876217i	$0.660059\pi$
$840$		0			0
$841$	−42.1108			−1.45210
$842$		0			0
$843$	5.97979	−	1.18589i	0.205955	−	0.0408442i
$844$		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
$849$	2.32446	+	6.60105i	0.0797753	+	0.226547i
$850$		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
$855$	12.5363	+	49.3530i	0.428733	+	1.68784i
$856$		0			0
$857$	0.620121	+	4.31304i	0.0211829	+	0.147330i	0.997668	−	0.0682549i	$-0.0217431\pi$
$857$	0.620121	+	4.31304i	0.0211829	+	0.147330i	−0.976485	+	0.215585i	$0.930834\pi$
$858$		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
$861$	−56.6600	+	19.9520i	−1.93097	+	0.679961i
$862$		0			0
$863$	7.96768	−	12.3979i	0.271223	−	0.422031i	−0.678747	−	0.734372i	$-0.737477\pi$
$863$	7.96768	−	12.3979i	0.271223	−	0.422031i	0.949970	+	0.312341i	$0.101113\pi$
$864$		0			0
$865$	−2.27837	+	7.75942i	−0.0774670	+	0.263828i
$866$		0			0
$867$	−22.4264	−	17.4420i	−0.761641	−	0.592362i
$868$		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
$873$	−2.50711	+	2.68664i	−0.0848527	+	0.0909289i
$874$		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
$879$	−5.33899	−	26.9216i	−0.180080	−	0.908042i
$880$		0			0
$881$	2.02893	+	0.926582i	0.0683565	+	0.0312173i	0.449300	−	0.893381i	$-0.351673\pi$
$881$	2.02893	+	0.926582i	0.0683565	+	0.0312173i	−0.380943	+	0.924598i	$0.624401\pi$
$882$		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
$885$	−25.3232	+	32.5598i	−0.851230	+	1.09449i
$886$		0			0
$887$	1.43120	+	4.87420i	0.0480548	+	0.163660i	0.980025	−	0.198876i	$-0.0637292\pi$
$887$	1.43120	+	4.87420i	0.0480548	+	0.163660i	−0.931970	+	0.362536i	$0.881911\pi$
$888$		0			0
$889$	−17.3941	+	2.50090i	−0.583380	+	0.0838774i
$890$		0			0
$891$	−17.4799	−	47.1958i	−0.585599	−	1.58112i
$892$		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
$897$	−33.3496	−	46.3040i	−1.11351	−	1.54605i
$898$		0			0
$899$	−23.1647	−	14.8870i	−0.772584	−	0.496510i
$900$		0			0
$901$			0.651380i			0.0217006i
$902$		0			0
$903$	−0.991913	−	2.81685i	−0.0330088	−	0.0937390i
$904$		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	$0.475613\pi$
$911$	−15.9034	+	54.1621i	−0.526904	+	1.79447i	−0.603445	+	0.797405i	$0.706206\pi$
$912$		0			0
$913$	−30.7402	−	47.8327i	−1.01735	−	1.58303i
$914$		0			0
$915$	−13.2404	+	33.5953i	−0.437715	+	1.11063i
$916$		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
$921$	9.69547	+	13.4616i	0.319477	+	0.443575i
$922$		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
$927$	−2.01992	−	7.95200i	−0.0663428	−	0.261178i
$928$		0			0
$929$	17.3909	−	20.0702i	0.570578	−	0.658482i	−0.394974	−	0.918692i	$-0.629246\pi$
$929$	17.3909	−	20.0702i	0.570578	−	0.658482i	0.965552	+	0.260210i	$0.0837919\pi$
$930$		0			0
$931$	40.6485	−	46.9109i	1.33220	−	1.53744i
$932$		0			0
$933$	16.9159	−	29.6663i	0.553800	−	0.971232i
$934$		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	0.983052	−	0.183328i	$-0.0586869\pi$
$941$	6.15785	+	13.4838i	0.200740	+	0.439560i	−0.782312	+	0.622887i	$0.785960\pi$
$942$		0			0
$943$	13.1006	+	44.6164i	0.426613	+	1.45291i
$944$		0			0
$945$	0.690994	+	42.8365i	0.0224781	+	1.39347i
$946$		0			0
$947$	−12.5601	−	10.8834i	−0.408148	−	0.353663i	0.426460	−	0.904506i	$-0.359761\pi$
$947$	−12.5601	−	10.8834i	−0.408148	−	0.353663i	−0.834608	+	0.550844i	$0.814306\pi$
$948$		0			0
$949$	11.8467	+	40.3460i	0.384559	+	1.30969i
$950$		0			0
$951$	8.71950	+	2.06575i	0.282749	+	0.0669866i
$952$		0			0
$953$	18.4460	−	15.9835i	0.597524	−	0.517757i	−0.302756	−	0.953068i	$-0.597907\pi$
$953$	18.4460	−	15.9835i	0.597524	−	0.517757i	0.900280	+	0.435311i	$0.143361\pi$
$954$		0			0
$955$	−0.887023	+	6.16938i	−0.0287034	+	0.199637i
$956$		0			0
$957$	7.32668	−	81.3483i	0.236838	−	2.62962i
$958$		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
$963$	−5.25390	+	3.10914i	−0.169305	+	0.100191i
$964$		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
$969$	−2.06397	−	10.4074i	−0.0663041	−	0.334335i
$970$		0			0
$971$	40.6777	−	35.2474i	1.30541	−	1.13114i	0.322597	−	0.946536i	$-0.395444\pi$
$971$	40.6777	−	35.2474i	1.30541	−	1.13114i	0.982812	−	0.184607i	$-0.0591013\pi$
$972$		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	−0.748594	−	0.663028i	$-0.769271\pi$
$977$	5.17287	−	8.04914i	0.165495	−	0.257515i	0.914089	+	0.405514i	$0.132907\pi$
$978$		0			0
$979$	−21.2540	−	3.05586i	−0.679281	−	0.0976658i
$980$		0			0
$981$	−8.04143	+	44.2799i	−0.256743	+	1.41375i
$982$		0			0
$983$	13.8124	−	30.2449i	0.440547	−	0.964664i	−0.550950	−	0.834538i	$-0.685735\pi$
$983$	13.8124	−	30.2449i	0.440547	−	0.964664i	0.991498	−	0.130126i	$-0.0415381\pi$
$984$		0			0
$985$	0.536436	+	1.17463i	0.0170923	+	0.0374268i
$986$		0			0
$987$	18.3514	+	14.2727i	0.584132	+	0.454305i
$988$		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
$993$	−45.9583	−	10.8881i	−1.45844	−	0.345522i
$994$		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
$999$	−12.0763	−	25.3531i	−0.382077	−	0.802135i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(1.61142 + 0.635084i) q^{3} +(-2.05430 + 0.603197i) q^{5} +(-2.91035 - 2.52183i) q^{7} +(2.19334 + 2.04677i) q^{9} +O(q^{10})\)	\(q+(1.61142 + 0.635084i) q^{3} +(-2.05430 + 0.603197i) q^{5} +(-2.91035 - 2.52183i) q^{7} +(2.19334 + 2.04677i) q^{9} +(-5.36557 + 1.57547i) q^{11} +(3.44974 + 5.36790i) q^{13} +(-3.69342 - 0.332650i) q^{15} +(0.764837 + 0.109967i) q^{17} +(-5.19155 - 5.99137i) q^{19} +(-3.08821 - 5.91204i) q^{21} +(-4.69664 + 2.14488i) q^{23} +(-0.349969 + 0.224911i) q^{25} +(2.23451 + 4.69116i) q^{27} +8.43272i q^{29} +(-1.76539 + 2.74699i) q^{31} +(-9.64674 - 0.868839i) q^{33} +(7.49988 + 3.42508i) q^{35} -5.40444 q^{37} +(2.14991 + 10.8408i) q^{39} +(1.28169 - 8.91433i) q^{41} +(0.443176 + 0.0637191i) q^{43} +(-5.74038 - 2.88167i) q^{45} +(-3.17052 + 1.44793i) q^{47} +(1.11429 + 7.75005i) q^{49} +(1.16263 + 0.662939i) q^{51} +(0.119970 + 0.834409i) q^{53} +(10.0722 - 6.47299i) q^{55} +(-4.56074 - 12.9517i) q^{57} +(6.01354 - 9.35726i) q^{59} +(2.74338 - 9.34309i) q^{61} +(-1.22177 - 11.4880i) q^{63} +(-10.3247 - 8.94641i) q^{65} +(7.35766 + 3.58676i) q^{67} +(-8.93042 + 0.473545i) q^{69} +(-7.24102 + 1.04110i) q^{71} +(6.32300 + 1.85660i) q^{73} +(-0.706783 + 0.140167i) q^{75} +(19.5887 + 8.94588i) q^{77} +(1.27332 + 1.98132i) q^{79} +(0.621459 + 8.97852i) q^{81} +(2.86458 + 9.75587i) q^{83} +(-1.63754 + 0.235442i) q^{85} +(-5.35549 + 13.5886i) q^{87} +(3.49281 + 1.59511i) q^{89} +(3.49699 - 24.3221i) q^{91} +(-4.58935 + 3.30539i) q^{93} +(14.2790 + 9.17653i) q^{95} +1.22491i q^{97} +(-14.9931 - 7.52655i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 200 q - 10 q^{9}+O(q^{10}) \) 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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