LMFDB - Embedded newform 804.2.i.d.37.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(37,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("804.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 11x^{6} + 4x^{5} + 91x^{4} - 6x^{3} + 129x^{2} + 36x + 144 $ x^8 - x^7 + 11x^6 + 4x^5 + 91x^4 - 6x^3 + 129x^2 + 36x + 144
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.4
Root			$1.69181 + 2.93030i$ of defining polynomial
Character	$\chi$	$=$	804.37
Dual form			804.2.i.d.565.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{3} +3.38361 q^{5} +(1.69181 - 2.93030i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{3} +3.38361 q^{5} +(1.69181 - 2.93030i) q^{7} +1.00000 q^{9} +(1.00000 - 1.73205i) q^{11} +(1.53262 + 2.65457i) q^{13} -3.38361 q^{15} +(-1.03262 - 1.78855i) q^{17} +(-3.72442 - 6.45089i) q^{19} +(-1.69181 + 2.93030i) q^{21} +(1.11036 + 1.92321i) q^{23} +6.44885 q^{25} -1.00000 q^{27} +(-2.80217 + 4.85350i) q^{29} +(-2.99398 + 5.18572i) q^{31} +(-1.00000 + 1.73205i) q^{33} +(5.72442 - 9.91499i) q^{35} +(-3.14298 - 5.44380i) q^{37} +(-1.53262 - 2.65457i) q^{39} +(1.92225 - 3.32944i) q^{41} +5.92272 q^{43} +3.38361 q^{45} +(1.92225 - 3.32944i) q^{47} +(-2.22442 - 3.85282i) q^{49} +(1.03262 + 1.78855i) q^{51} +1.93477 q^{53} +(3.38361 - 5.86059i) q^{55} +(3.72442 + 6.45089i) q^{57} +11.6696 q^{59} +(4.98379 + 8.63218i) q^{61} +(1.69181 - 2.93030i) q^{63} +(5.18579 + 8.98204i) q^{65} +(-7.80587 - 2.46342i) q^{67} +(-1.11036 - 1.92321i) q^{69} +(6.65687 - 11.5300i) q^{71} +(2.80587 + 4.85991i) q^{73} -6.44885 q^{75} +(-3.38361 - 5.86059i) q^{77} +(-6.29985 + 10.9117i) q^{79} +1.00000 q^{81} +(-2.03262 - 3.52060i) q^{83} +(-3.49398 - 6.05175i) q^{85} +(2.80217 - 4.85350i) q^{87} -0.837112 q^{89} +10.3716 q^{91} +(2.99398 - 5.18572i) q^{93} +(-12.6020 - 21.8273i) q^{95} +(3.08144 + 5.33722i) q^{97} +(1.00000 - 1.73205i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{3} + 2 q^{5} + q^{7} + 8 q^{9}+O(q^{10}) $ 8 * q - 8 * q^3 + 2 * q^5 + q^7 + 8 * q^9	$ 8 q - 8 q^{3} + 2 q^{5} + q^{7} + 8 q^{9} + 8 q^{11} - 2 q^{15} + 4 q^{17} - 5 q^{19} - q^{21} + q^{23} + 2 q^{25} - 8 q^{27} - 2 q^{29} + 9 q^{31} - 8 q^{33} + 21 q^{35} - 5 q^{37} + 11 q^{41} + 6 q^{43} + 2 q^{45} + 11 q^{47} + 7 q^{49} - 4 q^{51} + 40 q^{53} + 2 q^{55} + 5 q^{57} + 28 q^{59} + 20 q^{61} + q^{63} - 4 q^{65} - 33 q^{67} - q^{69} + 11 q^{71} - 7 q^{73} - 2 q^{75} - 2 q^{77} + 12 q^{79} + 8 q^{81} - 4 q^{83} + 5 q^{85} + 2 q^{87} - 16 q^{89} - 8 q^{91} - 9 q^{93} - 18 q^{95} + 20 q^{97} + 8 q^{99}+O(q^{100}) $ 8 * q - 8 * q^3 + 2 * q^5 + q^7 + 8 * q^9 + 8 * q^11 - 2 * q^15 + 4 * q^17 - 5 * q^19 - q^21 + q^23 + 2 * q^25 - 8 * q^27 - 2 * q^29 + 9 * q^31 - 8 * q^33 + 21 * q^35 - 5 * q^37 + 11 * q^41 + 6 * q^43 + 2 * q^45 + 11 * q^47 + 7 * q^49 - 4 * q^51 + 40 * q^53 + 2 * q^55 + 5 * q^57 + 28 * q^59 + 20 * q^61 + q^63 - 4 * q^65 - 33 * q^67 - q^69 + 11 * q^71 - 7 * q^73 - 2 * q^75 - 2 * q^77 + 12 * q^79 + 8 * q^81 - 4 * q^83 + 5 * q^85 + 2 * q^87 - 16 * q^89 - 8 * q^91 - 9 * q^93 - 18 * q^95 + 20 * q^97 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$		0			0
$5$	3.38361			1.51320			0.756599	−	0.653879i	$-0.226859\pi$
$5$	3.38361			1.51320			0.756599	+	0.653879i	$0.226859\pi$
$6$		0			0
$7$	1.69181	−	2.93030i	0.639443	−	1.10755i	−0.346112	−	0.938193i	$-0.612498\pi$
$7$	1.69181	−	2.93030i	0.639443	−	1.10755i	0.985555	−	0.169355i	$-0.0541684\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	−0.674967	−	0.737848i	$-0.735842\pi$
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	0.976478	+	0.215615i	$0.0691756\pi$
$12$		0			0
$13$	1.53262	+	2.65457i	0.425071	+	0.736245i	0.996427	−	0.0844572i	$-0.0269156\pi$
$13$	1.53262	+	2.65457i	0.425071	+	0.736245i	−0.571356	+	0.820703i	$0.693582\pi$
$14$		0			0
$15$	−3.38361			−0.873646
$16$		0			0
$17$	−1.03262	−	1.78855i	−0.250446	−	0.433786i	0.713202	−	0.700958i	$-0.247244\pi$
$17$	−1.03262	−	1.78855i	−0.250446	−	0.433786i	−0.963649	+	0.267172i	$0.913911\pi$
$18$		0			0
$19$	−3.72442	−	6.45089i	−0.854442	−	1.47994i	−0.877162	−	0.480194i	$-0.840566\pi$
$19$	−3.72442	−	6.45089i	−0.854442	−	1.47994i	0.0227206	−	0.999742i	$-0.492767\pi$
$20$		0			0
$21$	−1.69181	+	2.93030i	−0.369183	+	0.639443i
$22$		0			0
$23$	1.11036	+	1.92321i	0.231527	+	0.401016i	0.958258	−	0.285906i	$-0.0922946\pi$
$23$	1.11036	+	1.92321i	0.231527	+	0.401016i	−0.726731	+	0.686922i	$0.758961\pi$
$24$		0			0
$25$	6.44885			1.28977
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−2.80217	+	4.85350i	−0.520350	+	0.901273i	0.479370	+	0.877613i	$0.340865\pi$
$29$	−2.80217	+	4.85350i	−0.520350	+	0.901273i	−0.999720	+	0.0236598i	$0.992468\pi$
$30$		0			0
$31$	−2.99398	+	5.18572i	−0.537734	+	0.931383i	0.461291	+	0.887249i	$0.347386\pi$
$31$	−2.99398	+	5.18572i	−0.537734	+	0.931383i	−0.999026	+	0.0441344i	$0.985947\pi$
$32$		0			0
$33$	−1.00000	+	1.73205i	−0.174078	+	0.301511i
$34$		0			0
$35$	5.72442	−	9.91499i	0.967604	−	1.67594i
$36$		0			0
$37$	−3.14298	−	5.44380i	−0.516703	−	0.894955i	−0.999812	−	0.0193953i	$-0.993826\pi$
$37$	−3.14298	−	5.44380i	−0.516703	−	0.894955i	0.483109	−	0.875560i	$-0.339507\pi$
$38$		0			0
$39$	−1.53262	−	2.65457i	−0.245415	−	0.425071i
$40$		0			0
$41$	1.92225	−	3.32944i	0.300206	−	0.519971i	−0.675977	−	0.736923i	$-0.736278\pi$
$41$	1.92225	−	3.32944i	0.300206	−	0.519971i	0.976182	+	0.216952i	$0.0696114\pi$
$42$		0			0
$43$	5.92272			0.903207			0.451603	−	0.892219i	$-0.350852\pi$
$43$	5.92272			0.903207			0.451603	+	0.892219i	$0.350852\pi$
$44$		0			0
$45$	3.38361			0.504400
$46$		0			0
$47$	1.92225	−	3.32944i	0.280390	−	0.485649i	−0.691091	−	0.722768i	$-0.742870\pi$
$47$	1.92225	−	3.32944i	0.280390	−	0.485649i	0.971481	+	0.237119i	$0.0762030\pi$
$48$		0			0
$49$	−2.22442	−	3.85282i	−0.317775	−	0.550402i
$50$		0			0
$51$	1.03262	+	1.78855i	0.144595	+	0.250446i
$52$		0			0
$53$	1.93477			0.265761			0.132880	−	0.991132i	$-0.457577\pi$
$53$	1.93477			0.265761			0.132880	+	0.991132i	$0.457577\pi$
$54$		0			0
$55$	3.38361	−	5.86059i	0.456247	−	0.790242i
$56$		0			0
$57$	3.72442	+	6.45089i	0.493312	+	0.854442i
$58$		0			0
$59$	11.6696			1.51925			0.759625	−	0.650362i	$-0.225383\pi$
$59$	11.6696			1.51925			0.759625	+	0.650362i	$0.225383\pi$
$60$		0			0
$61$	4.98379	+	8.63218i	0.638109	+	1.10524i	0.985847	+	0.167645i	$0.0536164\pi$
$61$	4.98379	+	8.63218i	0.638109	+	1.10524i	−0.347738	+	0.937592i	$0.613050\pi$
$62$		0			0
$63$	1.69181	−	2.93030i	0.213148	−	0.369183i
$64$		0			0
$65$	5.18579	+	8.98204i	0.643218	+	1.11409i
$66$		0			0
$67$	−7.80587	−	2.46342i	−0.953639	−	0.300954i
$67$	−7.80587	−	2.46342i	−0.953639	−	0.300954i
$68$		0			0
$69$	−1.11036	−	1.92321i	−0.133672	−	0.231527i
$70$		0			0
$71$	6.65687	−	11.5300i	0.790025	−	1.36836i	−0.135926	−	0.990719i	$-0.543401\pi$
$71$	6.65687	−	11.5300i	0.790025	−	1.36836i	0.925951	−	0.377644i	$-0.123266\pi$
$72$		0			0
$73$	2.80587	+	4.85991i	0.328402	+	0.568809i	0.982195	−	0.187864i	$-0.0601566\pi$
$73$	2.80587	+	4.85991i	0.328402	+	0.568809i	−0.653793	+	0.756674i	$0.726823\pi$
$74$		0			0
$75$	−6.44885			−0.744649
$76$		0			0
$77$	−3.38361	−	5.86059i	−0.385599	−	0.667877i
$78$		0			0
$79$	−6.29985	+	10.9117i	−0.708788	+	1.22766i	0.256519	+	0.966539i	$0.417424\pi$
$79$	−6.29985	+	10.9117i	−0.708788	+	1.22766i	−0.965307	+	0.261118i	$0.915909\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	−2.03262	−	3.52060i	−0.223109	−	0.386436i	0.732642	−	0.680615i	$-0.238287\pi$
$83$	−2.03262	−	3.52060i	−0.223109	−	0.386436i	−0.955750	+	0.294179i	$0.904954\pi$
$84$		0			0
$85$	−3.49398	−	6.05175i	−0.378975	−	0.656404i
$86$		0			0
$87$	2.80217	−	4.85350i	0.300424	−	0.520350i
$88$		0			0
$89$	−0.837112			−0.0887337			−0.0443668	−	0.999015i	$-0.514127\pi$
$89$	−0.837112			−0.0887337			−0.0443668	+	0.999015i	$0.514127\pi$
$90$		0			0
$91$	10.3716			1.08724
$92$		0			0
$93$	2.99398	−	5.18572i	0.310461	−	0.537734i
$94$		0			0
$95$	−12.6020	−	21.8273i	−1.29294	−	2.23944i
$96$		0			0
$97$	3.08144	+	5.33722i	0.312873	+	0.541912i	0.978983	−	0.203941i	$-0.0653752\pi$
$97$	3.08144	+	5.33722i	0.312873	+	0.541912i	−0.666110	+	0.745854i	$0.732042\pi$
$98$		0			0
$99$	1.00000	−	1.73205i	0.100504	−	0.174078i
$100$		0			0
$101$	5.09785	−	8.82974i	0.507255	−	0.878592i	−0.492710	−	0.870194i	$-0.663994\pi$
$101$	5.09785	−	8.82974i	0.507255	−	0.878592i	0.999965	−	0.00839785i	$-0.00267315\pi$
$102$		0			0
$103$	−1.65919	+	2.87380i	−0.163485	+	0.283164i	−0.936116	−	0.351691i	$-0.885607\pi$
$103$	−1.65919	+	2.87380i	−0.163485	+	0.283164i	0.772631	+	0.634855i	$0.218940\pi$
$104$		0			0
$105$	−5.72442	+	9.91499i	−0.558647	+	0.967604i
$106$		0			0
$107$	8.15084			0.787972			0.393986	−	0.919116i	$-0.371096\pi$
$107$	8.15084			0.787972			0.393986	+	0.919116i	$0.371096\pi$
$108$		0			0
$109$	−17.3063			−1.65765			−0.828823	−	0.559511i	$-0.810989\pi$
$109$	−17.3063			−1.65765			−0.828823	+	0.559511i	$0.810989\pi$
$110$		0			0
$111$	3.14298	+	5.44380i	0.298318	+	0.516703i
$112$		0			0
$113$	−6.14066	+	10.6359i	−0.577664	+	1.00054i	0.418082	+	0.908409i	$0.362702\pi$
$113$	−6.14066	+	10.6359i	−0.577664	+	1.00054i	−0.995747	+	0.0921348i	$0.970631\pi$
$114$		0			0
$115$	3.75704	+	6.50739i	0.350346	+	0.606817i
$116$		0			0
$117$	1.53262	+	2.65457i	0.141690	+	0.245415i
$118$		0			0
$119$	−6.98796			−0.640585
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$		0			0
$123$	−1.92225	+	3.32944i	−0.173324	+	0.300206i
$124$		0			0
$125$	4.90235			0.438479
$126$		0			0
$127$	−9.49768	+	16.4505i	−0.842782	+	1.45974i	0.0447507	+	0.998998i	$0.485751\pi$
$127$	−9.49768	+	16.4505i	−0.842782	+	1.45974i	−0.887533	+	0.460744i	$0.847583\pi$
$128$		0			0
$129$	−5.92272			−0.521467
$130$		0			0
$131$	−6.87732			−0.600874			−0.300437	−	0.953802i	$-0.597133\pi$
$131$	−6.87732			−0.600874			−0.300437	+	0.953802i	$0.597133\pi$
$132$		0			0
$133$	−25.2040			−2.18547
$134$		0			0
$135$	−3.38361			−0.291215
$136$		0			0
$137$	1.51873			0.129754			0.0648770	−	0.997893i	$-0.479335\pi$
$137$	1.51873			0.129754			0.0648770	+	0.997893i	$0.479335\pi$
$138$		0			0
$139$	−10.9301			−0.927080			−0.463540	−	0.886076i	$-0.653421\pi$
$139$	−10.9301			−0.927080			−0.463540	+	0.886076i	$0.653421\pi$
$140$		0			0
$141$	−1.92225	+	3.32944i	−0.161883	+	0.280390i
$142$		0			0
$143$	6.13047			0.512655
$144$		0			0
$145$	−9.48147	+	16.4224i	−0.787393	+	1.36380i
$146$		0			0
$147$	2.22442	+	3.85282i	0.183467	+	0.317775i
$148$		0			0
$149$	24.0365			1.96915			0.984573	−	0.174973i	$-0.0559837\pi$
$149$	24.0365			1.96915			0.984573	+	0.174973i	$0.0559837\pi$
$150$		0			0
$151$	−1.90604	−	3.30136i	−0.155112	−	0.268661i	0.777988	−	0.628279i	$-0.216240\pi$
$151$	−1.90604	−	3.30136i	−0.155112	−	0.268661i	−0.933100	+	0.359618i	$0.882907\pi$
$152$		0			0
$153$	−1.03262	−	1.78855i	−0.0834821	−	0.144595i
$154$		0			0
$155$	−10.1305	+	17.5465i	−0.813699	+	1.40937i
$156$		0			0
$157$	−1.83711	−	3.18197i	−0.146617	−	0.253949i	0.783358	−	0.621571i	$-0.213505\pi$
$157$	−1.83711	−	3.18197i	−0.146617	−	0.253949i	−0.929975	+	0.367622i	$0.880172\pi$
$158$		0			0
$159$	−1.93477			−0.153437
$160$		0			0
$161$	7.51408			0.592193
$162$		0			0
$163$	−7.03631	+	12.1873i	−0.551127	+	0.954579i	0.447067	+	0.894501i	$0.352469\pi$
$163$	−7.03631	+	12.1873i	−0.551127	+	0.954579i	−0.998194	+	0.0600790i	$0.980865\pi$
$164$		0			0
$165$	−3.38361	+	5.86059i	−0.263414	+	0.456247i
$166$		0			0
$167$	−11.1835	+	19.3703i	−0.865402	+	1.49892i	0.00124506	+	0.999999i	$0.499604\pi$
$167$	−11.1835	+	19.3703i	−0.865402	+	1.49892i	−0.866647	+	0.498921i	$0.833730\pi$
$168$		0			0
$169$	1.80217	−	3.12145i	0.138629	−	0.240112i
$170$		0			0
$171$	−3.72442	−	6.45089i	−0.284814	−	0.493312i
$172$		0			0
$173$	2.30819	+	3.99791i	0.175489	+	0.303955i	0.940330	−	0.340263i	$-0.110516\pi$
$173$	2.30819	+	3.99791i	0.175489	+	0.303955i	−0.764842	+	0.644218i	$0.777183\pi$
$174$		0			0
$175$	10.9102	−	18.8970i	0.824734	−	1.42848i
$176$		0			0
$177$	−11.6696			−0.877139
$178$		0			0
$179$	8.37157			0.625721			0.312860	−	0.949799i	$-0.398713\pi$
$179$	8.37157			0.625721			0.312860	+	0.949799i	$0.398713\pi$
$180$		0			0
$181$	−1.70802	+	2.95837i	−0.126956	+	0.219894i	−0.922496	−	0.386007i	$-0.873854\pi$
$181$	−1.70802	+	2.95837i	−0.126956	+	0.219894i	0.795540	+	0.605901i	$0.207187\pi$
$182$		0			0
$183$	−4.98379	−	8.63218i	−0.368412	−	0.638109i
$184$		0			0
$185$	−10.6346	−	18.4197i	−0.781874	−	1.35425i
$186$		0			0
$187$	−4.13047			−0.302050
$188$		0			0
$189$	−1.69181	+	2.93030i	−0.123061	+	0.213148i
$190$		0			0
$191$	4.36119	+	7.55380i	0.315564	+	0.546573i	0.979557	−	0.201165i	$-0.0644729\pi$
$191$	4.36119	+	7.55380i	0.315564	+	0.546573i	−0.663993	+	0.747739i	$0.731140\pi$
$192$		0			0
$193$	−4.69460			−0.337925			−0.168962	−	0.985623i	$-0.554042\pi$
$193$	−4.69460			−0.337925			−0.168962	+	0.985623i	$0.554042\pi$
$194$		0			0
$195$	−5.18579	−	8.98204i	−0.371362	−	0.643218i
$196$		0			0
$197$	−6.47128	+	11.2086i	−0.461059	+	0.798578i	−0.999014	−	0.0443955i	$-0.985864\pi$
$197$	−6.47128	+	11.2086i	−0.461059	+	0.798578i	0.537955	+	0.842974i	$0.319197\pi$
$198$		0			0
$199$	1.87343	+	3.24487i	0.132804	+	0.230023i	0.924756	−	0.380560i	$-0.124269\pi$
$199$	1.87343	+	3.24487i	0.132804	+	0.230023i	−0.791953	+	0.610583i	$0.790935\pi$
$200$		0			0
$201$	7.80587	+	2.46342i	0.550584	+	0.173756i
$202$		0			0
$203$	9.48147	+	16.4224i	0.665468	+	1.15263i
$204$		0			0
$205$	6.50417	−	11.2655i	0.454271	−	0.786820i
$206$		0			0
$207$	1.11036	+	1.92321i	0.0771756	+	0.133672i
$208$		0			0
$209$	−14.8977			−1.03050
$210$		0			0
$211$	−7.77325	−	13.4637i	−0.535133	−	0.926877i	−0.999157	−	0.0410545i	$-0.986928\pi$
$211$	−7.77325	−	13.4637i	−0.535133	−	0.926877i	0.464024	−	0.885823i	$-0.346405\pi$
$212$		0			0
$213$	−6.65687	+	11.5300i	−0.456121	+	0.790025i
$214$		0			0
$215$	20.0402			1.36673
$216$		0			0
$217$	10.1305	+	17.5465i	0.687701	+	1.19113i
$218$		0			0
$219$	−2.80587	−	4.85991i	−0.189603	−	0.328402i
$220$		0			0
$221$	3.16521	−	5.48231i	0.212915	−	0.368780i
$222$		0			0
$223$	0.514083			0.0344255			0.0172128	−	0.999852i	$-0.494521\pi$
$223$	0.514083			0.0344255			0.0172128	+	0.999852i	$0.494521\pi$
$224$		0			0
$225$	6.44885			0.429923
$226$		0			0
$227$	−13.9981	+	24.2455i	−0.929089	+	1.60923i	−0.144241	+	0.989543i	$0.546074\pi$
$227$	−13.9981	+	24.2455i	−0.929089	+	1.60923i	−0.784849	+	0.619688i	$0.787259\pi$
$228$		0			0
$229$	3.75334	+	6.50098i	0.248028	+	0.429597i	0.962979	−	0.269578i	$-0.0868842\pi$
$229$	3.75334	+	6.50098i	0.248028	+	0.429597i	−0.714951	+	0.699175i	$0.753551\pi$
$230$		0			0
$231$	3.38361	+	5.86059i	0.222626	+	0.385599i
$232$		0			0
$233$	8.95534	−	15.5111i	0.586684	−	1.01617i	−0.407979	−	0.912991i	$-0.633767\pi$
$233$	8.95534	−	15.5111i	0.586684	−	1.01617i	0.994663	−	0.103175i	$-0.0329002\pi$
$234$		0			0
$235$	6.50417	−	11.2655i	0.424285	−	0.734883i
$236$		0			0
$237$	6.29985	−	10.9117i	0.409219	−	0.708788i
$238$		0			0
$239$	−3.65919	+	6.33790i	−0.236693	+	0.409965i	−0.959763	−	0.280810i	$-0.909397\pi$
$239$	−3.65919	+	6.33790i	−0.236693	+	0.409965i	0.723070	+	0.690775i	$0.242730\pi$
$240$		0			0
$241$	29.9833			1.93139			0.965697	−	0.259670i	$-0.0836139\pi$
$241$	29.9833			1.93139			0.965697	+	0.259670i	$0.0836139\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	−7.52659	−	13.0364i	−0.480857	−	0.832868i
$246$		0			0
$247$	11.4162	−	19.7735i	0.726397	−	1.25816i
$248$		0			0
$249$	2.03262	+	3.52060i	0.128812	+	0.223109i
$250$		0			0
$251$	−13.4917	−	23.3682i	−0.851586	−	1.47499i	−0.879777	−	0.475387i	$-0.842308\pi$
$251$	−13.4917	−	23.3682i	−0.851586	−	1.47499i	0.0281911	−	0.999603i	$-0.491025\pi$
$252$		0			0
$253$	4.44145			0.279232
$254$		0			0
$255$	3.49398	+	6.05175i	0.218801	+	0.378975i
$256$		0			0
$257$	12.6221	−	21.8622i	0.787346	−	1.36372i	−0.140241	−	0.990117i	$-0.544788\pi$
$257$	12.6221	−	21.8622i	0.787346	−	1.36372i	0.927587	−	0.373606i	$-0.121879\pi$
$258$		0			0
$259$	−21.2693			−1.32161
$260$		0			0
$261$	−2.80217	+	4.85350i	−0.173450	+	0.300424i
$262$		0			0
$263$	11.0532			0.681569			0.340784	−	0.940141i	$-0.389307\pi$
$263$	11.0532			0.681569			0.340784	+	0.940141i	$0.389307\pi$
$264$		0			0
$265$	6.54650			0.402148
$266$		0			0
$267$	0.837112			0.0512304
$268$		0			0
$269$	−20.0161			−1.22040			−0.610202	−	0.792246i	$-0.708912\pi$
$269$	−20.0161			−1.22040			−0.610202	+	0.792246i	$0.708912\pi$
$270$		0			0
$271$	−23.8736			−1.45022			−0.725109	−	0.688634i	$-0.758211\pi$
$271$	−23.8736			−1.45022			−0.725109	+	0.688634i	$0.758211\pi$
$272$		0			0
$273$	−10.3716			−0.627716
$274$		0			0
$275$	6.44885	−	11.1697i	0.388880	−	0.673560i
$276$		0			0
$277$	−17.8325			−1.07145			−0.535724	−	0.844393i	$-0.679961\pi$
$277$	−17.8325			−1.07145			−0.535724	+	0.844393i	$0.679961\pi$
$278$		0			0
$279$	−2.99398	+	5.18572i	−0.179245	+	0.310461i
$280$		0			0
$281$	−5.63649	−	9.76269i	−0.336245	−	0.582393i	0.647478	−	0.762084i	$-0.275824\pi$
$281$	−5.63649	−	9.76269i	−0.336245	−	0.582393i	−0.983723	+	0.179691i	$0.942490\pi$
$282$		0			0
$283$	−18.5673			−1.10371			−0.551855	−	0.833940i	$-0.686080\pi$
$283$	−18.5673			−1.10371			−0.551855	+	0.833940i	$0.686080\pi$
$284$		0			0
$285$	12.6020	+	21.8273i	0.746479	+	1.29294i
$286$		0			0
$287$	−6.50417	−	11.2655i	−0.383929	−	0.664984i
$288$		0			0
$289$	6.36740	−	11.0287i	0.374553	−	0.648745i
$290$		0			0
$291$	−3.08144	−	5.33722i	−0.180637	−	0.312873i
$292$		0			0
$293$	−33.8000			−1.97462			−0.987310	−	0.158806i	$-0.949236\pi$
$293$	−33.8000			−1.97462			−0.987310	+	0.158806i	$0.949236\pi$
$294$		0			0
$295$	39.4853			2.29893
$296$		0			0
$297$	−1.00000	+	1.73205i	−0.0580259	+	0.100504i
$298$		0			0
$299$	−3.40352	+	5.89507i	−0.196831	+	0.340921i
$300$		0			0
$301$	10.0201	−	17.3553i	0.577549	−	1.00034i
$302$		0			0
$303$	−5.09785	+	8.82974i	−0.292864	+	0.507255i
$304$		0			0
$305$	16.8632	+	29.2080i	0.965585	+	1.67244i
$306$		0			0
$307$	1.95117	+	3.37953i	0.111359	+	0.192880i	0.916319	−	0.400450i	$-0.131146\pi$
$307$	1.95117	+	3.37953i	0.111359	+	0.192880i	−0.804959	+	0.593330i	$0.797813\pi$
$308$		0			0
$309$	1.65919	−	2.87380i	0.0943880	−	0.163485i
$310$		0			0
$311$	26.6071			1.50875			0.754375	−	0.656444i	$-0.227940\pi$
$311$	26.6071			1.50875			0.754375	+	0.656444i	$0.227940\pi$
$312$		0			0
$313$	20.8482			1.17841			0.589205	−	0.807984i	$-0.299441\pi$
$313$	20.8482			1.17841			0.589205	+	0.807984i	$0.299441\pi$
$314$		0			0
$315$	5.72442	−	9.91499i	0.322535	−	0.558647i
$316$		0			0
$317$	3.90002	+	6.75504i	0.219047	+	0.379401i	0.954517	−	0.298157i	$-0.0963719\pi$
$317$	3.90002	+	6.75504i	0.219047	+	0.379401i	−0.735470	+	0.677557i	$0.763039\pi$
$318$		0			0
$319$	5.60434	+	9.70700i	0.313783	+	0.543488i
$320$		0			0
$321$	−8.15084			−0.454936
$322$		0			0
$323$	−7.69181	+	13.3226i	−0.427984	+	0.741289i
$324$		0			0
$325$	9.88361	+	17.1189i	0.548244	+	0.949587i
$326$		0			0
$327$	17.3063			0.957043
$328$		0			0
$329$	−6.50417	−	11.2655i	−0.358586	−	0.621090i
$330$		0			0
$331$	10.0569	−	17.4190i	0.552777	−	0.957437i	−0.445296	−	0.895383i	$-0.646902\pi$
$331$	10.0569	−	17.4190i	0.552777	−	0.957437i	0.998073	−	0.0620538i	$-0.0197650\pi$
$332$		0			0
$333$	−3.14298	−	5.44380i	−0.172234	−	0.298318i
$334$		0			0
$335$	−26.4121	−	8.33525i	−1.44304	−	0.455403i
$336$		0			0
$337$	12.0819	+	20.9265i	0.658144	+	1.13994i	0.981096	+	0.193523i	$0.0619914\pi$
$337$	12.0819	+	20.9265i	0.658144	+	1.13994i	−0.322952	+	0.946415i	$0.604675\pi$
$338$		0			0
$339$	6.14066	−	10.6359i	0.333515	−	0.577664i
$340$		0			0
$341$	5.98796	+	10.3714i	0.324266	+	0.561645i
$342$		0			0
$343$	8.63211			0.466090
$344$		0			0
$345$	−3.75704	−	6.50739i	−0.202272	−	0.350346i
$346$		0			0
$347$	−6.04048	+	10.4624i	−0.324270	+	0.561652i	−0.981364	−	0.192156i	$-0.938452\pi$
$347$	−6.04048	+	10.4624i	−0.324270	+	0.561652i	0.657094	+	0.753808i	$0.271785\pi$
$348$		0			0
$349$	3.09026			0.165418			0.0827089	−	0.996574i	$-0.473643\pi$
$349$	3.09026			0.165418			0.0827089	+	0.996574i	$0.473643\pi$
$350$		0			0
$351$	−1.53262	−	2.65457i	−0.0818050	−	0.141690i
$352$		0			0
$353$	−1.31606	−	2.27948i	−0.0700466	−	0.121324i	0.828875	−	0.559434i	$-0.188981\pi$
$353$	−1.31606	−	2.27948i	−0.0700466	−	0.121324i	−0.898922	+	0.438110i	$0.855648\pi$
$354$		0			0
$355$	22.5243	−	39.0132i	1.19546	−	2.07060i
$356$		0			0
$357$	6.98796			0.369842
$358$		0			0
$359$	−18.1017			−0.955373			−0.477686	−	0.878530i	$-0.658524\pi$
$359$	−18.1017			−0.955373			−0.477686	+	0.878530i	$0.658524\pi$
$360$		0			0
$361$	−18.2427	+	31.5972i	−0.960141	+	1.66301i
$362$		0			0
$363$	−3.50000	−	6.06218i	−0.183702	−	0.318182i
$364$		0			0
$365$	9.49398	+	16.4441i	0.496938	+	0.860721i
$366$		0			0
$367$	−1.61685	+	2.80047i	−0.0843991	+	0.146183i	−0.905135	−	0.425124i	$-0.860230\pi$
$367$	−1.61685	+	2.80047i	−0.0843991	+	0.146183i	0.820736	+	0.571308i	$0.193564\pi$
$368$		0			0
$369$	1.92225	−	3.32944i	0.100069	−	0.173324i
$370$		0			0
$371$	3.27325	−	5.66944i	0.169939	−	0.294343i
$372$		0			0
$373$	−14.9241	+	25.8493i	−0.772740	+	1.33843i	0.163315	+	0.986574i	$0.447781\pi$
$373$	−14.9241	+	25.8493i	−0.772740	+	1.33843i	−0.936056	+	0.351852i	$0.885552\pi$
$374$		0			0
$375$	−4.90235			−0.253156
$376$		0			0
$377$	−17.1786			−0.884744
$378$		0			0
$379$	−11.0717	−	19.1768i	−0.568716	−	0.985045i	−0.996693	−	0.0812559i	$-0.974107\pi$
$379$	−11.0717	−	19.1768i	−0.568716	−	0.985045i	0.427977	−	0.903790i	$-0.359226\pi$
$380$		0			0
$381$	9.49768	−	16.4505i	0.486581	−	0.842782i
$382$		0			0
$383$	15.0731	+	26.1074i	0.770199	+	1.33402i	0.937453	+	0.348111i	$0.113177\pi$
$383$	15.0731	+	26.1074i	0.770199	+	1.33402i	−0.167254	+	0.985914i	$0.553490\pi$
$384$		0			0
$385$	−11.4488	−	19.8300i	−0.583487	−	1.01063i
$386$		0			0
$387$	5.92272			0.301069
$388$		0			0
$389$	3.31838	+	5.74760i	0.168249	+	0.291415i	0.937804	−	0.347165i	$-0.112856\pi$
$389$	3.31838	+	5.74760i	0.168249	+	0.291415i	−0.769556	+	0.638580i	$0.779522\pi$
$390$		0			0
$391$	2.29316	−	3.97187i	0.115970	−	0.200866i
$392$		0			0
$393$	6.87732			0.346915
$394$		0			0
$395$	−21.3163	+	36.9208i	−1.07254	+	1.85769i
$396$		0			0
$397$	0.518731			0.0260344			0.0130172	−	0.999915i	$-0.495856\pi$
$397$	0.518731			0.0260344			0.0130172	+	0.999915i	$0.495856\pi$
$398$		0			0
$399$	25.2040			1.26178
$400$		0			0
$401$	−10.6973			−0.534200			−0.267100	−	0.963669i	$-0.586065\pi$
$401$	−10.6973			−0.534200			−0.267100	+	0.963669i	$0.586065\pi$
$402$		0			0
$403$	−18.3545			−0.914302
$404$		0			0
$405$	3.38361			0.168133
$406$		0			0
$407$	−12.5719			−0.623167
$408$		0			0
$409$	5.12795	−	8.88187i	0.253561	−	0.439180i	−0.710943	−	0.703250i	$-0.751732\pi$
$409$	5.12795	−	8.88187i	0.253561	−	0.439180i	0.964504	+	0.264070i	$0.0850649\pi$
$410$		0			0
$411$	−1.51873			−0.0749135
$412$		0			0
$413$	19.7427	−	34.1953i	0.971473	−	1.68264i
$414$		0			0
$415$	−6.87759	−	11.9123i	−0.337608	−	0.584754i
$416$		0			0
$417$	10.9301			0.535250
$418$		0			0
$419$	7.41391	+	12.8413i	0.362193	+	0.627337i	0.988321	−	0.152383i	$-0.0486948\pi$
$419$	7.41391	+	12.8413i	0.362193	+	0.627337i	−0.626128	+	0.779720i	$0.715361\pi$
$420$		0			0
$421$	−5.44468	−	9.43047i	−0.265358	−	0.459613i	0.702300	−	0.711881i	$-0.252157\pi$
$421$	−5.44468	−	9.43047i	−0.265358	−	0.459613i	−0.967657	+	0.252269i	$0.918823\pi$
$422$		0			0
$423$	1.92225	−	3.32944i	0.0934632	−	0.161883i
$424$		0			0
$425$	−6.65919	−	11.5341i	−0.323018	−	0.559484i
$426$		0			0
$427$	33.7264			1.63214
$428$		0			0
$429$	−6.13047			−0.295982
$430$		0			0
$431$	18.4671	−	31.9860i	0.889529	−	1.54071i	0.0490954	−	0.998794i	$-0.484366\pi$
$431$	18.4671	−	31.9860i	0.889529	−	1.54071i	0.840433	−	0.541915i	$-0.182301\pi$
$432$		0			0
$433$	−19.1913	+	33.2404i	−0.922276	+	1.59743i	−0.126392	+	0.991980i	$0.540340\pi$
$433$	−19.1913	+	33.2404i	−0.922276	+	1.59743i	−0.795884	+	0.605449i	$0.792994\pi$
$434$		0			0
$435$	9.48147	−	16.4224i	0.454601	−	0.787393i
$436$		0			0
$437$	8.27093	−	14.3257i	0.395652	−	0.685290i
$438$		0			0
$439$	10.5308	+	18.2398i	0.502606	+	0.870539i	0.999995	+	0.00301154i	$0.000958603\pi$
$439$	10.5308	+	18.2398i	0.502606	+	0.870539i	−0.497390	+	0.867527i	$0.665708\pi$
$440$		0			0
$441$	−2.22442	−	3.85282i	−0.105925	−	0.183467i
$442$		0			0
$443$	−6.91993	+	11.9857i	−0.328776	+	0.569456i	−0.982269	−	0.187476i	$-0.939969\pi$
$443$	−6.91993	+	11.9857i	−0.328776	+	0.569456i	0.653493	+	0.756932i	$0.273303\pi$
$444$		0			0
$445$	−2.83246			−0.134272
$446$		0			0
$447$	−24.0365			−1.13689
$448$		0			0
$449$	14.6900	−	25.4437i	0.693262	−	1.20076i	−0.277502	−	0.960725i	$-0.589506\pi$
$449$	14.6900	−	25.4437i	0.693262	−	1.20076i	0.970763	−	0.240039i	$-0.0771603\pi$
$450$		0			0
$451$	−3.84451	−	6.65888i	−0.181031	−	0.313555i
$452$		0			0
$453$	1.90604	+	3.30136i	0.0895537	+	0.155112i
$454$		0			0
$455$	35.0934			1.64520
$456$		0			0
$457$	1.94079	−	3.36154i	0.0907862	−	0.157246i	−0.817056	−	0.576558i	$-0.804395\pi$
$457$	1.94079	−	3.36154i	0.0907862	−	0.157246i	0.907842	+	0.419312i	$0.137729\pi$
$458$		0			0
$459$	1.03262	+	1.78855i	0.0481984	+	0.0834821i
$460$		0			0
$461$	3.40399			0.158540			0.0792698	−	0.996853i	$-0.474741\pi$
$461$	3.40399			0.158540			0.0792698	+	0.996853i	$0.474741\pi$
$462$		0			0
$463$	−15.3894	−	26.6551i	−0.715204	−	1.23877i	−0.962881	−	0.269927i	$-0.913001\pi$
$463$	−15.3894	−	26.6551i	−0.715204	−	1.23877i	0.247677	−	0.968843i	$-0.420333\pi$
$464$		0			0
$465$	10.1305	−	17.5465i	0.469789	−	0.813699i
$466$		0			0
$467$	−13.0983	−	22.6870i	−0.606118	−	1.04983i	−0.991874	−	0.127226i	$-0.959393\pi$
$467$	−13.0983	−	22.6870i	−0.606118	−	1.04983i	0.385756	−	0.922601i	$-0.373941\pi$
$468$		0			0
$469$	−20.4246	+	18.7059i	−0.943119	+	0.863757i
$470$		0			0
$471$	1.83711	+	3.18197i	0.0846496	+	0.146617i
$472$		0			0
$473$	5.92272	−	10.2585i	0.272327	−	0.471684i
$474$		0			0
$475$	−24.0182	−	41.6008i	−1.10203	−	1.90878i
$476$		0			0
$477$	1.93477			0.0885869
$478$		0			0
$479$	18.4666	+	31.9851i	0.843762	+	1.46144i	0.886692	+	0.462360i	$0.152997\pi$
$479$	18.4666	+	31.9851i	0.843762	+	1.46144i	−0.0429303	+	0.999078i	$0.513669\pi$
$480$		0			0
$481$	9.63397	−	16.6865i	0.439271	−	0.760840i
$482$		0			0
$483$	−7.51408			−0.341903
$484$		0			0
$485$	10.4264	+	18.0591i	0.473439	+	0.820021i
$486$		0			0
$487$	6.84313	+	11.8527i	0.310092	+	0.537095i	0.978382	−	0.206806i	$-0.0663068\pi$
$487$	6.84313	+	11.8527i	0.310092	+	0.537095i	−0.668290	+	0.743901i	$0.732973\pi$
$488$		0			0
$489$	7.03631	−	12.1873i	0.318193	−	0.551127i
$490$		0			0
$491$	0.727413			0.0328277			0.0164138	−	0.999865i	$-0.494775\pi$
$491$	0.727413			0.0328277			0.0164138	+	0.999865i	$0.494775\pi$
$492$		0			0
$493$	11.5743			0.521279
$494$		0			0
$495$	3.38361	−	5.86059i	0.152082	−	0.263414i
$496$		0			0
$497$	−22.5243	−	39.0132i	−1.01035	−	1.74998i
$498$		0			0
$499$	13.2087	+	22.8781i	0.591302	+	1.02416i	0.994057	+	0.108857i	$0.0347191\pi$
$499$	13.2087	+	22.8781i	0.591302	+	1.02416i	−0.402756	+	0.915308i	$0.631948\pi$
$500$		0			0
$501$	11.1835	−	19.3703i	0.499640	−	0.865402i
$502$		0			0
$503$	−15.6346	+	27.0800i	−0.697114	+	1.20744i	0.272349	+	0.962199i	$0.412199\pi$
$503$	−15.6346	+	27.0800i	−0.697114	+	1.20744i	−0.969463	+	0.245238i	$0.921134\pi$
$504$		0			0
$505$	17.2492	−	29.8764i	0.767578	−	1.32948i
$506$		0			0
$507$	−1.80217	+	3.12145i	−0.0800372	+	0.138629i
$508$		0			0
$509$	37.7505			1.67326			0.836632	−	0.547766i	$-0.184522\pi$
$509$	37.7505			1.67326			0.836632	+	0.547766i	$0.184522\pi$
$510$		0			0
$511$	18.9880			0.839978
$512$		0			0
$513$	3.72442	+	6.45089i	0.164437	+	0.284814i
$514$		0			0
$515$	−5.61406	+	9.72384i	−0.247385	+	0.428484i
$516$		0			0
$517$	−3.84451	−	6.65888i	−0.169081	−	0.292857i
$518$		0			0
$519$	−2.30819	−	3.99791i	−0.101318	−	0.175489i
$520$		0			0
$521$	−10.2860			−0.450636			−0.225318	−	0.974285i	$-0.572342\pi$
$521$	−10.2860			−0.450636			−0.225318	+	0.974285i	$0.572342\pi$
$522$		0			0
$523$	−3.64947	−	6.32107i	−0.159580	−	0.276401i	0.775137	−	0.631793i	$-0.217681\pi$
$523$	−3.64947	−	6.32107i	−0.159580	−	0.276401i	−0.934717	+	0.355392i	$0.884347\pi$
$524$		0			0
$525$	−10.9102	+	18.8970i	−0.476161	+	0.824734i
$526$		0			0
$527$	12.3665			0.538694
$528$		0			0
$529$	9.03419	−	15.6477i	0.392791	−	0.680334i
$530$		0			0
$531$	11.6696			0.506416
$532$		0			0
$533$	11.7843			0.510435
$534$		0			0
$535$	27.5793			1.19236
$536$		0			0
$537$	−8.37157			−0.361260
$538$		0			0
$539$	−8.89770			−0.383251
$540$		0			0
$541$	−28.2485			−1.21450			−0.607249	−	0.794512i	$-0.707727\pi$
$541$	−28.2485			−1.21450			−0.607249	+	0.794512i	$0.707727\pi$
$542$		0			0
$543$	1.70802	−	2.95837i	0.0732981	−	0.126956i
$544$		0			0
$545$	−58.5580			−2.50835
$546$		0			0
$547$	−1.13444	+	1.96490i	−0.0485050	+	0.0840132i	−0.889259	−	0.457405i	$-0.848779\pi$
$547$	−1.13444	+	1.96490i	−0.0485050	+	0.0840132i	0.840754	+	0.541418i	$0.182112\pi$
$548$		0			0
$549$	4.98379	+	8.63218i	0.212703	+	0.368412i
$550$		0			0
$551$	41.7459			1.77843
$552$		0			0
$553$	21.3163	+	36.9208i	0.906459	+	1.57003i
$554$		0			0
$555$	10.6346	+	18.4197i	0.451415	+	0.781874i
$556$		0			0
$557$	12.2711	−	21.2542i	0.519944	−	0.900570i	−0.479787	−	0.877385i	$-0.659286\pi$
$557$	12.2711	−	21.2542i	0.519944	−	0.900570i	0.999731	−	0.0231848i	$-0.00738060\pi$
$558$		0			0
$559$	9.07726	+	15.7223i	0.383927	+	0.664982i
$560$		0			0
$561$	4.13047			0.174388
$562$		0			0
$563$	−27.9509			−1.17799			−0.588995	−	0.808137i	$-0.700476\pi$
$563$	−27.9509			−1.17799			−0.588995	+	0.808137i	$0.700476\pi$
$564$		0			0
$565$	−20.7776	+	35.9879i	−0.874121	+	1.51402i
$566$		0			0
$567$	1.69181	−	2.93030i	0.0710492	−	0.123061i
$568$		0			0
$569$	−7.28317	+	12.6148i	−0.305326	+	0.528841i	−0.977334	−	0.211704i	$-0.932099\pi$
$569$	−7.28317	+	12.6148i	−0.305326	+	0.528841i	0.672008	+	0.740544i	$0.265432\pi$
$570$		0			0
$571$	−11.2529	+	19.4905i	−0.470918	+	0.815653i	−0.999447	−	0.0332620i	$-0.989410\pi$
$571$	−11.2529	+	19.4905i	−0.470918	+	0.815653i	0.528529	+	0.848915i	$0.322744\pi$
$572$		0			0
$573$	−4.36119	−	7.55380i	−0.182191	−	0.315564i
$574$		0			0
$575$	7.16056	+	12.4025i	0.298616	+	0.517218i
$576$		0			0
$577$	11.5833	−	20.0628i	0.482219	−	0.835227i	−0.517573	−	0.855639i	$-0.673164\pi$
$577$	11.5833	−	20.0628i	0.482219	−	0.835227i	0.999792	+	0.0204120i	$0.00649779\pi$
$578$		0			0
$579$	4.69460			0.195101
$580$		0			0
$581$	−13.7552			−0.570661
$582$		0			0
$583$	1.93477	−	3.35111i	0.0801298	−	0.138789i
$584$		0			0
$585$	5.18579	+	8.98204i	0.214406	+	0.371362i
$586$		0			0
$587$	−6.22859	−	10.7882i	−0.257081	−	0.445278i	0.708377	−	0.705834i	$-0.249428\pi$
$587$	−6.22859	−	10.7882i	−0.257081	−	0.445278i	−0.965459	+	0.260556i	$0.916094\pi$
$588$		0			0
$589$	44.6034			1.83785
$590$		0			0
$591$	6.47128	−	11.2086i	0.266193	−	0.461059i
$592$		0			0
$593$	16.9181	+	29.3030i	0.694742	+	1.20333i	0.970268	+	0.242035i	$0.0778148\pi$
$593$	16.9181	+	29.3030i	0.694742	+	1.20333i	−0.275526	+	0.961294i	$0.588852\pi$
$594$		0			0
$595$	−23.6446			−0.969332
$596$		0			0
$597$	−1.87343	−	3.24487i	−0.0766742	−	0.132804i
$598$		0			0
$599$	−14.0349	+	24.3092i	−0.573452	+	0.993248i	0.422756	+	0.906244i	$0.361063\pi$
$599$	−14.0349	+	24.3092i	−0.573452	+	0.993248i	−0.996208	+	0.0870046i	$0.972271\pi$
$600$		0			0
$601$	−14.7059	−	25.4713i	−0.599866	−	1.03900i	−0.992840	−	0.119449i	$-0.961887\pi$
$601$	−14.7059	−	25.4713i	−0.599866	−	1.03900i	0.392975	−	0.919549i	$-0.371446\pi$
$602$		0			0
$603$	−7.80587	−	2.46342i	−0.317880	−	0.100318i
$604$		0			0
$605$	11.8427	+	20.5121i	0.481472	+	0.833934i
$606$		0			0
$607$	9.59553	−	16.6199i	0.389470	−	0.674583i	−0.602908	−	0.797811i	$-0.705991\pi$
$607$	9.59553	−	16.6199i	0.389470	−	0.674583i	0.992378	+	0.123228i	$0.0393247\pi$
$608$		0			0
$609$	−9.48147	−	16.4224i	−0.384208	−	0.665468i
$610$		0			0
$611$	11.7843			0.476742
$612$		0			0
$613$	−15.0574	−	26.0801i	−0.608161	−	1.05337i	−0.991543	−	0.129776i	$-0.958574\pi$
$613$	−15.0574	−	26.0801i	−0.608161	−	1.05337i	0.383382	−	0.923590i	$-0.374759\pi$
$614$		0			0
$615$	−6.50417	+	11.2655i	−0.262273	+	0.454271i
$616$		0			0
$617$	−20.7579			−0.835683			−0.417841	−	0.908520i	$-0.637213\pi$
$617$	−20.7579			−0.835683			−0.417841	+	0.908520i	$0.637213\pi$
$618$		0			0
$619$	0.359344	+	0.622402i	0.0144433	+	0.0250165i	0.873157	−	0.487440i	$-0.162069\pi$
$619$	0.359344	+	0.622402i	0.0144433	+	0.0250165i	−0.858713	+	0.512456i	$0.828736\pi$
$620$		0			0
$621$	−1.11036	−	1.92321i	−0.0445573	−	0.0771756i
$622$		0			0
$623$	−1.41623	+	2.45299i	−0.0567401	+	0.0982768i
$624$		0			0
$625$	−15.6566			−0.626264
$626$		0			0
$627$	14.8977			0.594957
$628$		0			0
$629$	−6.49099	+	11.2427i	−0.258813	+	0.448277i
$630$		0			0
$631$	6.85257	+	11.8690i	0.272796	+	0.472497i	0.969577	−	0.244787i	$-0.0787181\pi$
$631$	6.85257	+	11.8690i	0.272796	+	0.472497i	−0.696780	+	0.717285i	$0.745385\pi$
$632$		0			0
$633$	7.77325	+	13.4637i	0.308959	+	0.535133i
$634$		0			0
$635$	−32.1365	+	55.6620i	−1.27530	+	2.20888i
$636$		0			0
$637$	6.81838	−	11.8098i	0.270154	−	0.467921i
$638$		0			0
$639$	6.65687	−	11.5300i	0.263342	−	0.456121i
$640$		0			0
$641$	−4.61658	+	7.99615i	−0.182344	+	0.315829i	−0.942678	−	0.333703i	$-0.891702\pi$
$641$	−4.61658	+	7.99615i	−0.182344	+	0.315829i	0.760334	+	0.649532i	$0.225035\pi$
$642$		0			0
$643$	−11.2031			−0.441807			−0.220904	−	0.975296i	$-0.570901\pi$
$643$	−11.2031			−0.441807			−0.220904	+	0.975296i	$0.570901\pi$
$644$		0			0
$645$	−20.0402			−0.789082
$646$		0			0
$647$	15.1839	+	26.2993i	0.596942	+	1.03393i	0.993270	+	0.115825i	$0.0369510\pi$
$647$	15.1839	+	26.2993i	0.596942	+	1.03393i	−0.396328	+	0.918109i	$0.629716\pi$
$648$		0			0
$649$	11.6696	−	20.2123i	0.458071	−	0.793402i
$650$		0			0
$651$	−10.1305	−	17.5465i	−0.397044	−	0.687701i
$652$		0			0
$653$	−21.2388	−	36.7866i	−0.831138	−	1.43957i	−0.897137	−	0.441753i	$-0.854357\pi$
$653$	−21.2388	−	36.7866i	−0.831138	−	1.43957i	0.0659991	−	0.997820i	$-0.478977\pi$
$654$		0			0
$655$	−23.2702			−0.909242
$656$		0			0
$657$	2.80587	+	4.85991i	0.109467	+	0.189603i
$658$		0			0
$659$	−7.62611	+	13.2088i	−0.297071	+	0.514542i	−0.975465	−	0.220157i	$-0.929343\pi$
$659$	−7.62611	+	13.2088i	−0.297071	+	0.514542i	0.678394	+	0.734699i	$0.262676\pi$
$660$		0			0
$661$	31.7218			1.23384			0.616918	−	0.787027i	$-0.288381\pi$
$661$	31.7218			1.23384			0.616918	+	0.787027i	$0.288381\pi$
$662$		0			0
$663$	−3.16521	+	5.48231i	−0.122927	+	0.212915i
$664$		0			0
$665$	−85.2807			−3.30705
$666$		0			0
$667$	−12.4457			−0.481900
$668$		0			0
$669$	−0.514083			−0.0198756
$670$		0			0
$671$	19.9352			0.769588
$672$		0			0
$673$	−22.7904			−0.878504			−0.439252	−	0.898364i	$-0.644756\pi$
$673$	−22.7904			−0.878504			−0.439252	+	0.898364i	$0.644756\pi$
$674$		0			0
$675$	−6.44885			−0.248216
$676$		0			0
$677$	13.5164	−	23.4111i	0.519478	−	0.899762i	−0.480266	−	0.877123i	$-0.659460\pi$
$677$	13.5164	−	23.4111i	0.519478	−	0.899762i	0.999744	−	0.0226389i	$-0.00720680\pi$
$678$		0			0
$679$	20.8528			0.800259
$680$		0			0
$681$	13.9981	−	24.2455i	0.536410	−	0.929089i
$682$		0			0
$683$	−2.05784	−	3.56428i	−0.0787410	−	0.136383i	0.823966	−	0.566639i	$-0.191757\pi$
$683$	−2.05784	−	3.56428i	−0.0787410	−	0.136383i	−0.902707	+	0.430256i	$0.858423\pi$
$684$		0			0
$685$	5.13880			0.196343
$686$		0			0
$687$	−3.75334	−	6.50098i	−0.143199	−	0.248028i
$688$		0			0
$689$	2.96526	+	5.13597i	0.112967	+	0.195665i
$690$		0			0
$691$	−3.82692	+	6.62843i	−0.145583	+	0.252157i	−0.929590	−	0.368594i	$-0.879839\pi$
$691$	−3.82692	+	6.62843i	−0.145583	+	0.252157i	0.784007	+	0.620752i	$0.213172\pi$
$692$		0			0
$693$	−3.38361	−	5.86059i	−0.128533	−	0.222626i
$694$		0			0
$695$	−36.9833			−1.40286
$696$		0			0
$697$	−7.93981			−0.300742
$698$		0			0
$699$	−8.95534	+	15.5111i	−0.338722	+	0.586684i
$700$		0			0
$701$	−12.9558	+	22.4401i	−0.489334	+	0.847551i	−0.999925	−	0.0122725i	$-0.996093\pi$
$701$	−12.9558	+	22.4401i	−0.489334	+	0.847551i	0.510591	+	0.859824i	$0.329427\pi$
$702$		0			0
$703$	−23.4116	+	40.5501i	−0.882985	+	1.52937i
$704$		0			0
$705$	−6.50417	+	11.2655i	−0.244961	+	0.424285i
$706$		0			0
$707$	−17.2492	−	29.8764i	−0.648722	−	1.12362i
$708$		0			0
$709$	−11.0204	−	19.0879i	−0.413879	−	0.716859i	0.581431	−	0.813596i	$-0.302493\pi$
$709$	−11.0204	−	19.0879i	−0.413879	−	0.716859i	−0.995310	+	0.0967363i	$0.969160\pi$
$710$		0			0
$711$	−6.29985	+	10.9117i	−0.236263	+	0.409219i
$712$		0			0
$713$	−13.2976			−0.497999
$714$		0			0
$715$	20.7431			0.775749
$716$		0			0
$717$	3.65919	−	6.33790i	0.136655	−	0.236693i
$718$		0			0
$719$	12.1705	+	21.0799i	0.453882	+	0.786147i	0.998623	−	0.0524572i	$-0.0167053\pi$
$719$	12.1705	+	21.0799i	0.453882	+	0.786147i	−0.544741	+	0.838604i	$0.683372\pi$
$720$		0			0
$721$	5.61406	+	9.72384i	0.209079	+	0.362135i
$722$		0			0
$723$	−29.9833			−1.11509
$724$		0			0
$725$	−18.0708	+	31.2995i	−0.671132	+	1.16243i
$726$		0			0
$727$	11.4773	+	19.8793i	0.425669	+	0.737281i	0.996483	−	0.0837988i	$-0.0267053\pi$
$727$	11.4773	+	19.8793i	0.425669	+	0.737281i	−0.570813	+	0.821080i	$0.693372\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−6.11590	−	10.5931i	−0.226205	−	0.391798i
$732$		0			0
$733$	12.3815	−	21.4454i	0.457321	−	0.792103i	−0.541498	−	0.840702i	$-0.682143\pi$
$733$	12.3815	−	21.4454i	0.457321	−	0.792103i	0.998818	+	0.0485996i	$0.0154758\pi$
$734$		0			0
$735$	7.52659	+	13.0364i	0.277623	+	0.480857i
$736$		0			0
$737$	−12.0726	+	11.0567i	−0.444701	+	0.407280i
$738$		0			0
$739$	−9.47591	−	16.4128i	−0.348577	−	0.603753i	0.637420	−	0.770517i	$-0.280002\pi$
$739$	−9.47591	−	16.4128i	−0.348577	−	0.603753i	−0.985997	+	0.166763i	$0.946668\pi$
$740$		0			0
$741$	−11.4162	+	19.7735i	−0.419386	+	0.726397i
$742$		0			0
$743$	−10.3637	−	17.9505i	−0.380208	−	0.658539i	0.610884	−	0.791720i	$-0.290814\pi$
$743$	−10.3637	−	17.9505i	−0.380208	−	0.658539i	−0.991092	+	0.133181i	$0.957481\pi$
$744$		0			0
$745$	81.3302			2.97971
$746$		0			0
$747$	−2.03262	−	3.52060i	−0.0743696	−	0.128812i
$748$		0			0
$749$	13.7897	−	23.8844i	0.503863	−	0.872717i
$750$		0			0
$751$	37.0241			1.35103			0.675514	−	0.737348i	$-0.263922\pi$
$751$	37.0241			1.35103			0.675514	+	0.737348i	$0.263922\pi$
$752$		0			0
$753$	13.4917	+	23.3682i	0.491663	+	0.851586i
$754$		0			0
$755$	−6.44932	−	11.1705i	−0.234715	−	0.406538i
$756$		0			0
$757$	−7.58301	+	13.1342i	−0.275609	+	0.477369i	−0.970289	−	0.241950i	$-0.922213\pi$
$757$	−7.58301	+	13.1342i	−0.275609	+	0.477369i	0.694679	+	0.719320i	$0.255546\pi$
$758$		0			0
$759$	−4.44145			−0.161215
$760$		0			0
$761$	−3.28871			−0.119216			−0.0596078	−	0.998222i	$-0.518985\pi$
$761$	−3.28871			−0.119216			−0.0596078	+	0.998222i	$0.518985\pi$
$762$		0			0
$763$	−29.2790	+	50.7127i	−1.05997	+	1.83592i
$764$		0			0
$765$	−3.49398	−	6.05175i	−0.126325	−	0.218801i
$766$		0			0
$767$	17.8850	+	30.9777i	0.645790	+	1.11854i
$768$		0			0
$769$	14.0391	−	24.3164i	0.506263	−	0.876874i	−0.493711	−	0.869626i	$-0.664360\pi$
$769$	14.0391	−	24.3164i	0.506263	−	0.876874i	0.999974	−	0.00724723i	$-0.00230689\pi$
$770$		0			0
$771$	−12.6221	+	21.8622i	−0.454575	+	0.787346i
$772$		0			0
$773$	−3.88983	+	6.73739i	−0.139908	+	0.242327i	−0.927461	−	0.373919i	$-0.878014\pi$
$773$	−3.88983	+	6.73739i	−0.139908	+	0.242327i	0.787554	+	0.616246i	$0.211347\pi$
$774$		0			0
$775$	−19.3077	+	33.4419i	−0.693553	+	1.20127i
$776$		0			0
$777$	21.2693			0.763031
$778$		0			0
$779$	−28.6372			−1.02603
$780$		0			0
$781$	−13.3137	−	23.0601i	−0.476403	−	0.825154i
$782$		0			0
$783$	2.80217	−	4.85350i	0.100141	−	0.173450i
$784$		0			0
$785$	−6.21608	−	10.7666i	−0.221861	−	0.384275i
$786$		0			0
$787$	6.27372	+	10.8664i	0.223634	+	0.387345i	0.955909	−	0.293664i	$-0.0948747\pi$
$787$	6.27372	+	10.8664i	0.223634	+	0.387345i	−0.732275	+	0.681009i	$0.761541\pi$
$788$		0			0
$789$	−11.0532			−0.393504
$790$		0			0
$791$	20.7776	+	35.9879i	0.738767	+	1.27958i
$792$		0			0
$793$	−15.2765	+	26.4596i	−0.542484	+	0.939609i
$794$		0			0
$795$	−6.54650			−0.232181
$796$		0			0
$797$	17.5574	−	30.4102i	0.621913	−	1.07719i	−0.367216	−	0.930136i	$-0.619689\pi$
$797$	17.5574	−	30.4102i	0.621913	−	1.07719i	0.989129	−	0.147050i	$-0.0469778\pi$
$798$		0			0
$799$	−7.93981			−0.280890
$800$		0			0
$801$	−0.837112			−0.0295779
$802$		0			0
$803$	11.2235			0.396068
$804$		0			0
$805$	25.4248			0.896105
$806$		0			0
$807$	20.0161			0.704601
$808$		0			0
$809$	−21.5539			−0.757795			−0.378897	−	0.925439i	$-0.623697\pi$
$809$	−21.5539			−0.757795			−0.378897	+	0.925439i	$0.623697\pi$
$810$		0			0
$811$	15.2003	−	26.3278i	0.533756	−	0.924492i	−0.465466	−	0.885066i	$-0.654113\pi$
$811$	15.2003	−	26.3278i	0.533756	−	0.924492i	0.999222	−	0.0394270i	$-0.0125532\pi$
$812$		0			0
$813$	23.8736			0.837284
$814$		0			0
$815$	−23.8082	+	41.2370i	−0.833964	+	1.44447i
$816$		0			0
$817$	−22.0587	−	38.2068i	−0.771737	−	1.33669i
$818$		0			0
$819$	10.3716			0.362412
$820$		0			0
$821$	−3.88778	−	6.73383i	−0.135684	−	0.235012i	0.790174	−	0.612882i	$-0.209990\pi$
$821$	−3.88778	−	6.73383i	−0.135684	−	0.235012i	−0.925859	+	0.377870i	$0.876657\pi$
$822$		0			0
$823$	−22.2001	−	38.4518i	−0.773848	−	1.34034i	−0.935440	−	0.353487i	$-0.884996\pi$
$823$	−22.2001	−	38.4518i	−0.773848	−	1.34034i	0.161591	−	0.986858i	$-0.448337\pi$
$824$		0			0
$825$	−6.44885	+	11.1697i	−0.224520	+	0.388880i
$826$		0			0
$827$	−14.8026	−	25.6389i	−0.514738	−	0.891553i	−0.999854	−	0.0171026i	$-0.994556\pi$
$827$	−14.8026	−	25.6389i	−0.514738	−	0.891553i	0.485116	−	0.874450i	$-0.338778\pi$
$828$		0			0
$829$	−40.7352			−1.41479			−0.707396	−	0.706817i	$-0.750130\pi$
$829$	−40.7352			−1.41479			−0.707396	+	0.706817i	$0.750130\pi$
$830$		0			0
$831$	17.8325			0.618601
$832$		0			0
$833$	−4.59396	+	7.95697i	−0.159171	+	0.275693i
$834$		0			0
$835$	−37.8405	+	65.5417i	−1.30953	+	2.26816i
$836$		0			0
$837$	2.99398	−	5.18572i	0.103487	−	0.179245i
$838$		0			0
$839$	22.1286	−	38.3279i	0.763965	−	1.32323i	−0.176828	−	0.984242i	$-0.556584\pi$
$839$	22.1286	−	38.3279i	0.763965	−	1.32323i	0.940792	−	0.338984i	$-0.110083\pi$
$840$		0			0
$841$	−1.20432	−	2.08594i	−0.0415283	−	0.0719291i
$842$		0			0
$843$	5.63649	+	9.76269i	0.194131	+	0.336245i
$844$		0			0
$845$	6.09785	−	10.5618i	0.209772	−	0.363337i
$846$		0			0
$847$	23.6853			0.813837
$848$		0			0
$849$	18.5673			0.637227
$850$		0			0
$851$	6.97970	−	12.0892i	0.239261	−	0.414412i
$852$		0			0
$853$	−12.4431	−	21.5521i	−0.426044	−	0.737929i	0.570474	−	0.821316i	$-0.306760\pi$
$853$	−12.4431	−	21.5521i	−0.426044	−	0.737929i	−0.996517	+	0.0833868i	$0.973426\pi$
$854$		0			0
$855$	−12.6020	−	21.8273i	−0.430980	−	0.746479i
$856$		0			0
$857$	43.9870			1.50257			0.751284	−	0.659980i	$-0.229435\pi$
$857$	43.9870			1.50257			0.751284	+	0.659980i	$0.229435\pi$
$858$		0			0
$859$	24.8042	−	42.9622i	0.846309	−	1.46585i	−0.0381711	−	0.999271i	$-0.512153\pi$
$859$	24.8042	−	42.9622i	0.846309	−	1.46585i	0.884480	−	0.466578i	$-0.154513\pi$
$860$		0			0
$861$	6.50417	+	11.2655i	0.221661	+	0.383929i
$862$		0			0
$863$	−49.8616			−1.69731			−0.848654	−	0.528949i	$-0.822586\pi$
$863$	−49.8616			−1.69731			−0.848654	+	0.528949i	$0.822586\pi$
$864$		0			0
$865$	7.81003	+	13.5274i	0.265549	+	0.459945i
$866$		0			0
$867$	−6.36740	+	11.0287i	−0.216248	+	0.374553i
$868$		0			0
$869$	12.5997	+	21.8233i	0.427415	+	0.740305i
$870$		0			0
$871$	−5.42410	−	24.4967i	−0.183788	−	0.830039i
$872$		0			0
$873$	3.08144	+	5.33722i	0.104291	+	0.180637i
$874$		0			0
$875$	8.29382	−	14.3653i	0.280382	−	0.485637i
$876$		0			0
$877$	−3.54699	−	6.14356i	−0.119773	−	0.207453i	0.799905	−	0.600127i	$-0.204883\pi$
$877$	−3.54699	−	6.14356i	−0.119773	−	0.207453i	−0.919678	+	0.392674i	$0.871550\pi$
$878$		0			0
$879$	33.8000			1.14005
$880$		0			0
$881$	13.6150	+	23.5819i	0.458701	+	0.794493i	0.998893	−	0.0470487i	$-0.0149816\pi$
$881$	13.6150	+	23.5819i	0.458701	+	0.794493i	−0.540192	+	0.841542i	$0.681648\pi$
$882$		0			0
$883$	−2.42363	+	4.19785i	−0.0815616	+	0.141269i	−0.903921	−	0.427700i	$-0.859324\pi$
$883$	−2.42363	+	4.19785i	−0.0815616	+	0.141269i	0.822359	+	0.568969i	$0.192657\pi$
$884$		0			0
$885$	−39.4853			−1.32729
$886$		0			0
$887$	14.7369	+	25.5251i	0.494818	+	0.857050i	0.999982	−	0.00597347i	$-0.00190142\pi$
$887$	14.7369	+	25.5251i	0.494818	+	0.857050i	−0.505164	+	0.863023i	$0.668568\pi$
$888$		0			0
$889$	32.1365	+	55.6620i	1.07782	+	1.86684i
$890$		0			0
$891$	1.00000	−	1.73205i	0.0335013	−	0.0580259i
$892$		0			0
$893$	−28.6372			−0.958306
$894$		0			0
$895$	28.3262			0.946839
$896$		0			0
$897$	3.40352	−	5.89507i	0.113640	−	0.196831i
$898$		0			0
$899$	−16.7793	−	29.0626i	−0.559620	−	0.969290i
$900$		0			0
$901$	−1.99787	−	3.46042i	−0.0665588	−	0.115283i
$902$		0			0
$903$	−10.0201	+	17.3553i	−0.333448	+	0.577549i
$904$		0			0
$905$	−5.77927	+	10.0100i	−0.192110	+	0.332744i
$906$		0			0
$907$	−28.0039	+	48.5041i	−0.929854	+	1.61055i	−0.146290	+	0.989242i	$0.546733\pi$
$907$	−28.0039	+	48.5041i	−0.929854	+	1.61055i	−0.783563	+	0.621312i	$0.786600\pi$
$908$		0			0
$909$	5.09785	−	8.82974i	0.169085	−	0.292864i
$910$		0			0
$911$	47.1837			1.56326			0.781632	−	0.623740i	$-0.214387\pi$
$911$	47.1837			1.56326			0.781632	+	0.623740i	$0.214387\pi$
$912$		0			0
$913$	−8.13047			−0.269079
$914$		0			0
$915$	−16.8632	−	29.2080i	−0.557481	−	0.965585i
$916$		0			0
$917$	−11.6351	+	20.1526i	−0.384225	+	0.665497i
$918$		0			0
$919$	−24.0286	−	41.6188i	−0.792631	−	1.37288i	−0.924332	−	0.381588i	$-0.875377\pi$
$919$	−24.0286	−	41.6188i	−0.792631	−	1.37288i	0.131701	−	0.991290i	$-0.457956\pi$
$920$		0			0
$921$	−1.95117	−	3.37953i	−0.0642933	−	0.111359i
$922$		0			0
$923$	40.8097			1.34327
$924$		0			0
$925$	−20.2686	−	35.1063i	−0.666428	−	1.15429i
$926$		0			0
$927$	−1.65919	+	2.87380i	−0.0544950	+	0.0943880i
$928$		0			0
$929$	20.3314			0.667050			0.333525	−	0.942741i	$-0.391762\pi$
$929$	20.3314			0.667050			0.333525	+	0.942741i	$0.391762\pi$
$930$		0			0
$931$	−16.5694	+	28.6990i	−0.543040	+	0.940573i
$932$		0			0
$933$	−26.6071			−0.871077
$934$		0			0
$935$	−13.9759			−0.457061
$936$		0			0
$937$	−34.5904			−1.13002			−0.565009	−	0.825084i	$-0.691128\pi$
$937$	−34.5904			−1.13002			−0.565009	+	0.825084i	$0.691128\pi$
$938$		0			0
$939$	−20.8482			−0.680355
$940$		0			0
$941$	42.9125			1.39891			0.699454	−	0.714678i	$-0.253427\pi$
$941$	42.9125			1.39891			0.699454	+	0.714678i	$0.253427\pi$
$942$		0			0
$943$	8.53760			0.278022
$944$		0			0
$945$	−5.72442	+	9.91499i	−0.186216	+	0.322535i
$946$		0			0
$947$	34.6482			1.12592			0.562958	−	0.826485i	$-0.309663\pi$
$947$	34.6482			1.12592			0.562958	+	0.826485i	$0.309663\pi$
$948$		0			0
$949$	−8.60064	+	14.8968i	−0.279189	+	0.483569i
$950$		0			0
$951$	−3.90002	−	6.75504i	−0.126467	−	0.219047i
$952$		0			0
$953$	−28.9023			−0.936239			−0.468119	−	0.883665i	$-0.655068\pi$
$953$	−28.9023			−0.936239			−0.468119	+	0.883665i	$0.655068\pi$
$954$		0			0
$955$	14.7566	+	25.5591i	0.477511	+	0.827074i
$956$		0			0
$957$	−5.60434	−	9.70700i	−0.181163	−	0.313783i
$958$		0			0
$959$	2.56940	−	4.45033i	0.0829703	−	0.143709i
$960$		0			0
$961$	−2.42781	−	4.20509i	−0.0783164	−	0.135648i
$962$		0			0
$963$	8.15084			0.262657
$964$		0			0
$965$	−15.8847			−0.511347
$966$		0			0
$967$	−14.6309	+	25.3415i	−0.470499	+	0.814928i	−0.999431	−	0.0337360i	$-0.989259\pi$
$967$	−14.6309	+	25.3415i	−0.470499	+	0.814928i	0.528932	+	0.848664i	$0.322593\pi$
$968$		0			0
$969$	7.69181	−	13.3226i	0.247096	−	0.427984i
$970$		0			0
$971$	−17.0761	+	29.5766i	−0.547998	+	0.949160i	0.450414	+	0.892820i	$0.351276\pi$
$971$	−17.0761	+	29.5766i	−0.547998	+	0.949160i	−0.998412	+	0.0563400i	$0.982057\pi$
$972$		0			0
$973$	−18.4917	+	32.0285i	−0.592815	+	1.02679i
$974$		0			0
$975$	−9.88361	−	17.1189i	−0.316529	−	0.548244i
$976$		0			0
$977$	−12.4134	−	21.5007i	−0.397141	−	0.687869i	0.596231	−	0.802813i	$-0.296664\pi$
$977$	−12.4134	−	21.5007i	−0.397141	−	0.687869i	−0.993372	+	0.114944i	$0.963331\pi$
$978$		0			0
$979$	−0.837112	+	1.44992i	−0.0267542	+	0.0463396i
$980$		0			0
$981$	−17.3063			−0.552549
$982$		0			0
$983$	−10.1920			−0.325074			−0.162537	−	0.986702i	$-0.551968\pi$
$983$	−10.1920			−0.325074			−0.162537	+	0.986702i	$0.551968\pi$
$984$		0			0
$985$	−21.8963	+	37.9255i	−0.697674	+	1.20841i
$986$		0			0
$987$	6.50417	+	11.2655i	0.207030	+	0.358586i
$988$		0			0
$989$	6.57637	+	11.3906i	0.209116	+	0.362200i
$990$		0			0
$991$	3.25260			0.103322			0.0516612	−	0.998665i	$-0.483548\pi$
$991$	3.25260			0.103322			0.0516612	+	0.998665i	$0.483548\pi$
$992$		0			0
$993$	−10.0569	+	17.4190i	−0.319146	+	0.552777i
$994$		0			0
$995$	6.33895	+	10.9794i	0.200958	+	0.348070i
$996$		0			0
$997$	44.0619			1.39545			0.697727	−	0.716363i	$-0.254195\pi$
$997$	44.0619			1.39545			0.697727	+	0.716363i	$0.254195\pi$
$998$		0			0
$999$	3.14298	+	5.44380i	0.0994395	+	0.172234i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.i.d.37.4	✓	8
3.2	odd	2		2412.2.l.e.37.1		8
67.29	even	3	inner	804.2.i.d.565.4	yes	8
201.29	odd	6		2412.2.l.e.1369.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.i.d.37.4	✓	8	1.1	even	1	trivial
804.2.i.d.565.4	yes	8	67.29	even	3	inner
2412.2.l.e.37.1		8	3.2	odd	2
2412.2.l.e.1369.1		8	201.29	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{3} +3.38361 q^{5} +(1.69181 - 2.93030i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{3} +3.38361 q^{5} +(1.69181 - 2.93030i) q^{7} +1.00000 q^{9} +(1.00000 - 1.73205i) q^{11} +(1.53262 + 2.65457i) q^{13} -3.38361 q^{15} +(-1.03262 - 1.78855i) q^{17} +(-3.72442 - 6.45089i) q^{19} +(-1.69181 + 2.93030i) q^{21} +(1.11036 + 1.92321i) q^{23} +6.44885 q^{25} -1.00000 q^{27} +(-2.80217 + 4.85350i) q^{29} +(-2.99398 + 5.18572i) q^{31} +(-1.00000 + 1.73205i) q^{33} +(5.72442 - 9.91499i) q^{35} +(-3.14298 - 5.44380i) q^{37} +(-1.53262 - 2.65457i) q^{39} +(1.92225 - 3.32944i) q^{41} +5.92272 q^{43} +3.38361 q^{45} +(1.92225 - 3.32944i) q^{47} +(-2.22442 - 3.85282i) q^{49} +(1.03262 + 1.78855i) q^{51} +1.93477 q^{53} +(3.38361 - 5.86059i) q^{55} +(3.72442 + 6.45089i) q^{57} +11.6696 q^{59} +(4.98379 + 8.63218i) q^{61} +(1.69181 - 2.93030i) q^{63} +(5.18579 + 8.98204i) q^{65} +(-7.80587 - 2.46342i) q^{67} +(-1.11036 - 1.92321i) q^{69} +(6.65687 - 11.5300i) q^{71} +(2.80587 + 4.85991i) q^{73} -6.44885 q^{75} +(-3.38361 - 5.86059i) q^{77} +(-6.29985 + 10.9117i) q^{79} +1.00000 q^{81} +(-2.03262 - 3.52060i) q^{83} +(-3.49398 - 6.05175i) q^{85} +(2.80217 - 4.85350i) q^{87} -0.837112 q^{89} +10.3716 q^{91} +(2.99398 - 5.18572i) q^{93} +(-12.6020 - 21.8273i) q^{95} +(3.08144 + 5.33722i) q^{97} +(1.00000 - 1.73205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{3} + 2 q^{5} + q^{7} + 8 q^{9}+O(q^{10}) \) 8 * q - 8 * q^3 + 2 * q^5 + q^7 + 8 * q^9	\( 8 q - 8 q^{3} + 2 q^{5} + q^{7} + 8 q^{9} + 8 q^{11} - 2 q^{15} + 4 q^{17} - 5 q^{19} - q^{21} + q^{23} + 2 q^{25} - 8 q^{27} - 2 q^{29} + 9 q^{31} - 8 q^{33} + 21 q^{35} - 5 q^{37} + 11 q^{41} + 6 q^{43} + 2 q^{45} + 11 q^{47} + 7 q^{49} - 4 q^{51} + 40 q^{53} + 2 q^{55} + 5 q^{57} + 28 q^{59} + 20 q^{61} + q^{63} - 4 q^{65} - 33 q^{67} - q^{69} + 11 q^{71} - 7 q^{73} - 2 q^{75} - 2 q^{77} + 12 q^{79} + 8 q^{81} - 4 q^{83} + 5 q^{85} + 2 q^{87} - 16 q^{89} - 8 q^{91} - 9 q^{93} - 18 q^{95} + 20 q^{97} + 8 q^{99}+O(q^{100}) \) 8 * q - 8 * q^3 + 2 * q^5 + q^7 + 8 * q^9 + 8 * q^11 - 2 * q^15 + 4 * q^17 - 5 * q^19 - q^21 + q^23 + 2 * q^25 - 8 * q^27 - 2 * q^29 + 9 * q^31 - 8 * q^33 + 21 * q^35 - 5 * q^37 + 11 * q^41 + 6 * q^43 + 2 * q^45 + 11 * q^47 + 7 * q^49 - 4 * q^51 + 40 * q^53 + 2 * q^55 + 5 * q^57 + 28 * q^59 + 20 * q^61 + q^63 - 4 * q^65 - 33 * q^67 - q^69 + 11 * q^71 - 7 * q^73 - 2 * q^75 - 2 * q^77 + 12 * q^79 + 8 * q^81 - 4 * q^83 + 5 * q^85 + 2 * q^87 - 16 * q^89 - 8 * q^91 - 9 * q^93 - 18 * q^95 + 20 * q^97 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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