LMFDB - Embedded newform 729.2.g.c.55.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(28,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([44]))

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

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

chi := DirichletCharacter("729.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.g (of order $27$, degree $18$, not 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:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			55.6
Character	$\chi$	$=$	729.55
Dual form			729.2.g.c.676.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.311913 - 0.723096i) q^{2} +(0.946905 + 1.00366i) q^{4} +(0.161980 + 2.78108i) q^{5} +(4.84803 + 1.14900i) q^{7} +(2.50111 - 0.910331i) q^{8} +O(q^{10})$	\(q+(0.311913 - 0.723096i) q^{2} +(0.946905 + 1.00366i) q^{4} +(0.161980 + 2.78108i) q^{5} +(4.84803 + 1.14900i) q^{7} +(2.50111 - 0.910331i) q^{8} +(2.06152 + 0.750330i) q^{10} +(-1.45131 - 0.954539i) q^{11} +(-2.15633 - 0.252038i) q^{13} +(2.34301 - 3.14720i) q^{14} +(-0.0385876 + 0.662524i) q^{16} +(-3.39468 + 2.84848i) q^{17} +(-1.63306 - 1.37030i) q^{19} +(-2.63789 + 2.79600i) q^{20} +(-1.14291 + 0.751701i) q^{22} +(-0.659824 + 0.156381i) q^{23} +(-2.74200 + 0.320494i) q^{25} +(-0.854835 + 1.48062i) q^{26} +(3.43741 + 5.95378i) q^{28} +(-3.43613 - 4.61552i) q^{29} +(1.68658 - 5.63358i) q^{31} +(5.22407 + 2.62363i) q^{32} +(1.00088 + 3.34316i) q^{34} +(-2.41020 + 13.6689i) q^{35} +(0.131814 + 0.747552i) q^{37} +(-1.50023 + 0.753445i) q^{38} +(2.93684 + 6.80835i) q^{40} +(0.0489024 + 0.113369i) q^{41} +(2.27552 - 1.14281i) q^{43} +(-0.416216 - 2.36048i) q^{44} +(-0.0927292 + 0.525894i) q^{46} +(-0.487133 - 1.62714i) q^{47} +(15.9278 + 7.99922i) q^{49} +(-0.623519 + 2.08270i) q^{50} +(-1.78887 - 2.40288i) q^{52} +(-5.02192 - 8.69822i) q^{53} +(2.41957 - 4.19082i) q^{55} +(13.1715 - 1.53952i) q^{56} +(-4.40924 + 1.04501i) q^{58} +(9.71683 - 6.39086i) q^{59} +(-5.43508 + 5.76085i) q^{61} +(-3.54755 - 2.97675i) q^{62} +(2.50983 - 2.10599i) q^{64} +(0.351659 - 6.03775i) q^{65} +(-0.277935 + 0.373331i) q^{67} +(-6.07334 - 0.709872i) q^{68} +(9.13216 + 6.00632i) q^{70} +(11.4588 + 4.17067i) q^{71} +(-2.01159 + 0.732160i) q^{73} +(0.581667 + 0.137858i) q^{74} +(-0.171036 - 2.93658i) q^{76} +(-5.93921 - 6.29519i) q^{77} +(2.77777 - 6.43960i) q^{79} -1.84879 q^{80} +0.0972297 q^{82} +(-1.31099 + 3.03921i) q^{83} +(-8.47172 - 8.97950i) q^{85} +(-0.116596 - 2.00188i) q^{86} +(-4.49883 - 1.06624i) q^{88} +(-4.72182 + 1.71860i) q^{89} +(-10.1643 - 3.69952i) q^{91} +(-0.781744 - 0.514161i) q^{92} +(-1.32852 - 0.155282i) q^{94} +(3.54640 - 4.76364i) q^{95} +(0.436507 - 7.49453i) q^{97} +(10.7523 - 9.02224i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10}) $ 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8	$ 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} - 63 q^{20} + 9 q^{22} + 36 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28} - 45 q^{29} + 9 q^{31} + 63 q^{32} + 9 q^{34} + 9 q^{35} - 18 q^{37} - 9 q^{38} + 9 q^{40} - 27 q^{41} + 9 q^{43} + 54 q^{44} - 18 q^{46} + 63 q^{47} + 9 q^{49} - 225 q^{50} + 27 q^{52} + 45 q^{53} - 9 q^{55} + 99 q^{56} + 9 q^{58} - 117 q^{59} + 9 q^{61} + 81 q^{62} - 18 q^{64} + 81 q^{65} + 36 q^{67} - 18 q^{68} + 63 q^{70} - 90 q^{71} - 18 q^{73} + 81 q^{74} + 90 q^{76} + 81 q^{77} + 63 q^{79} - 288 q^{80} - 36 q^{82} + 45 q^{83} + 63 q^{85} + 81 q^{86} + 90 q^{88} - 81 q^{89} - 18 q^{91} - 63 q^{92} + 63 q^{94} + 153 q^{95} + 36 q^{97} + 81 q^{98}+O(q^{100}) $ 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8 - 18 * q^10 + 9 * q^11 + 9 * q^13 + 9 * q^14 + 9 * q^16 - 18 * q^17 - 18 * q^19 - 63 * q^20 + 9 * q^22 + 36 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 - 45 * q^29 + 9 * q^31 + 63 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 - 9 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 + 63 * q^47 + 9 * q^49 - 225 * q^50 + 27 * q^52 + 45 * q^53 - 9 * q^55 + 99 * q^56 + 9 * q^58 - 117 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 + 81 * q^65 + 36 * q^67 - 18 * q^68 + 63 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 + 90 * q^76 + 81 * q^77 + 63 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 + 63 * q^85 + 81 * q^86 + 90 * q^88 - 81 * q^89 - 18 * q^91 - 63 * q^92 + 63 * q^94 + 153 * q^95 + 36 * q^97 + 81 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{17}{27}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.311913	−	0.723096i	0.220556	−	0.511306i	−0.771630	−	0.636071i	$-0.780558\pi$
$2$	0.311913	−	0.723096i	0.220556	−	0.511306i	0.992186	+	0.124765i	$0.0398177\pi$
$3$		0			0
$3$		0			0
$4$	0.946905	+	1.00366i	0.473452	+	0.501830i
$5$	0.161980	+	2.78108i	0.0724395	+	1.24374i	0.817179	+	0.576384i	$0.195537\pi$
$5$	0.161980	+	2.78108i	0.0724395	+	1.24374i	−0.744740	+	0.667355i	$0.767426\pi$
$6$		0			0
$7$	4.84803	+	1.14900i	1.83238	+	0.434283i	0.993866	−	0.110592i	$-0.0352746\pi$
$7$	4.84803	+	1.14900i	1.83238	+	0.434283i	0.838518	+	0.544875i	$0.183423\pi$
$8$	2.50111	−	0.910331i	0.884277	−	0.321851i
$9$		0			0
$10$	2.06152	+	0.750330i	0.651909	+	0.237275i
$11$	−1.45131	−	0.954539i	−0.437585	−	0.287804i	0.311540	−	0.950233i	$-0.399155\pi$
$11$	−1.45131	−	0.954539i	−0.437585	−	0.287804i	−0.749125	+	0.662429i	$0.769526\pi$
$12$		0			0
$13$	−2.15633	−	0.252038i	−0.598057	−	0.0699029i	−0.188322	−	0.982107i	$-0.560305\pi$
$13$	−2.15633	−	0.252038i	−0.598057	−	0.0699029i	−0.409735	+	0.912205i	$0.634379\pi$
$14$	2.34301	−	3.14720i	0.626195	−	0.841126i
$15$		0			0
$16$	−0.0385876	+	0.662524i	−0.00964691	+	0.165631i
$17$	−3.39468	+	2.84848i	−0.823331	+	0.690857i	−0.953750	−	0.300602i	$-0.902812\pi$
$17$	−3.39468	+	2.84848i	−0.823331	+	0.690857i	0.130419	+	0.991459i	$0.458368\pi$
$18$		0			0
$19$	−1.63306	−	1.37030i	−0.374650	−	0.314369i	0.435948	−	0.899972i	$-0.356413\pi$
$19$	−1.63306	−	1.37030i	−0.374650	−	0.314369i	−0.810598	+	0.585603i	$0.800858\pi$
$20$	−2.63789	+	2.79600i	−0.589849	+	0.625204i
$21$		0			0
$22$	−1.14291	+	0.751701i	−0.243668	+	0.160263i
$23$	−0.659824	+	0.156381i	−0.137583	+	0.0326077i	−0.298830	−	0.954306i	$-0.596596\pi$
$23$	−0.659824	+	0.156381i	−0.137583	+	0.0326077i	0.161247	+	0.986914i	$0.448448\pi$
$24$		0			0
$25$	−2.74200	+	0.320494i	−0.548401	+	0.0640989i
$26$	−0.854835	+	1.48062i	−0.167647	+	0.290373i
$27$		0			0
$28$	3.43741	+	5.95378i	0.649610	+	1.12516i
$29$	−3.43613	−	4.61552i	−0.638073	−	0.857080i	0.359016	−	0.933331i	$-0.383112\pi$
$29$	−3.43613	−	4.61552i	−0.638073	−	0.857080i	−0.997089	+	0.0762510i	$0.975705\pi$
$30$		0			0
$31$	1.68658	−	5.63358i	0.302919	−	1.01182i	−0.662050	−	0.749459i	$-0.730313\pi$
$31$	1.68658	−	5.63358i	0.302919	−	1.01182i	0.964970	−	0.262362i	$-0.0845013\pi$
$32$	5.22407	+	2.62363i	0.923494	+	0.463796i
$33$		0			0
$34$	1.00088	+	3.34316i	0.171649	+	0.573347i
$35$	−2.41020	+	13.6689i	−0.407397	+	2.31047i
$36$		0			0
$37$	0.131814	+	0.747552i	0.0216700	+	0.122897i	0.993724	−	0.111861i	$-0.0356813\pi$
$37$	0.131814	+	0.747552i	0.0216700	+	0.122897i	−0.972054	+	0.234758i	$0.924570\pi$
$38$	−1.50023	+	0.753445i	−0.243370	+	0.122225i
$39$		0			0
$40$	2.93684	+	6.80835i	0.464355	+	1.07650i
$41$	0.0489024	+	0.113369i	0.00763727	+	0.0177052i	0.921992	−	0.387209i	$-0.126561\pi$
$41$	0.0489024	+	0.113369i	0.00763727	+	0.0177052i	−0.914355	+	0.404914i	$0.867301\pi$
$42$		0			0
$43$	2.27552	−	1.14281i	0.347014	−	0.174277i	−0.266751	−	0.963765i	$-0.585950\pi$
$43$	2.27552	−	1.14281i	0.347014	−	0.174277i	0.613766	+	0.789488i	$0.289654\pi$
$44$	−0.416216	−	2.36048i	−0.0627469	−	0.355855i
$45$		0			0
$46$	−0.0927292	+	0.525894i	−0.0136722	+	0.0775388i
$47$	−0.487133	−	1.62714i	−0.0710556	−	0.237342i	0.915083	−	0.403265i	$-0.132125\pi$
$47$	−0.487133	−	1.62714i	−0.0710556	−	0.237342i	−0.986139	+	0.165923i	$0.946940\pi$
$48$		0			0
$49$	15.9278	+	7.99922i	2.27539	+	1.14275i
$50$	−0.623519	+	2.08270i	−0.0881789	+	0.294538i
$51$		0			0
$52$	−1.78887	−	2.40288i	−0.248072	−	0.333219i
$53$	−5.02192	−	8.69822i	−0.689814	−	1.19479i	−0.971898	−	0.235403i	$-0.924359\pi$
$53$	−5.02192	−	8.69822i	−0.689814	−	1.19479i	0.282084	−	0.959390i	$-0.408974\pi$
$54$		0			0
$55$	2.41957	−	4.19082i	0.326255	−	0.565090i
$56$	13.1715	−	1.53952i	1.76011	−	0.205727i
$57$		0			0
$58$	−4.40924	+	1.04501i	−0.578961	+	0.137216i
$59$	9.71683	−	6.39086i	1.26502	−	0.832019i	0.273491	−	0.961875i	$-0.411822\pi$
$59$	9.71683	−	6.39086i	1.26502	−	0.832019i	0.991533	+	0.129855i	$0.0414512\pi$
$60$		0			0
$61$	−5.43508	+	5.76085i	−0.695891	+	0.737601i	−0.974889	−	0.222690i	$-0.928516\pi$
$61$	−5.43508	+	5.76085i	−0.695891	+	0.737601i	0.278998	+	0.960292i	$0.409998\pi$
$62$	−3.54755	−	2.97675i	−0.450540	−	0.378048i
$63$		0			0
$64$	2.50983	−	2.10599i	0.313728	−	0.263249i
$65$	0.351659	−	6.03775i	0.0436179	−	0.748891i
$66$		0			0
$67$	−0.277935	+	0.373331i	−0.0339551	+	0.0456097i	−0.818777	−	0.574112i	$-0.805347\pi$
$67$	−0.277935	+	0.373331i	−0.0339551	+	0.0456097i	0.784821	+	0.619722i	$0.212755\pi$
$68$	−6.07334	−	0.709872i	−0.736501	−	0.0860846i
$69$		0			0
$70$	9.13216	+	6.00632i	1.09150	+	0.717892i
$71$	11.4588	+	4.17067i	1.35991	+	0.494968i	0.916027	−	0.401116i	$-0.131378\pi$
$71$	11.4588	+	4.17067i	1.35991	+	0.494968i	0.443885	+	0.896084i	$0.353600\pi$
$72$		0			0
$73$	−2.01159	+	0.732160i	−0.235439	+	0.0856928i	−0.457045	−	0.889443i	$-0.651092\pi$
$73$	−2.01159	+	0.732160i	−0.235439	+	0.0856928i	0.221606	+	0.975136i	$0.428870\pi$
$74$	0.581667	+	0.137858i	0.0676174	+	0.0160256i
$75$		0			0
$76$	−0.171036	−	2.93658i	−0.0196192	−	0.336849i
$77$	−5.93921	−	6.29519i	−0.676835	−	0.717404i
$78$		0			0
$79$	2.77777	−	6.43960i	0.312524	−	0.724512i	−0.687475	−	0.726208i	$-0.741281\pi$
$79$	2.77777	−	6.43960i	0.312524	−	0.724512i	0.999999	+	0.00169654i	$0.000540027\pi$
$80$	−1.84879			−0.206701
$81$		0			0
$82$	0.0972297			0.0107372
$83$	−1.31099	+	3.03921i	−0.143899	+	0.333596i	−0.974889	−	0.222692i	$-0.928516\pi$
$83$	−1.31099	+	3.03921i	−0.143899	+	0.333596i	0.830989	+	0.556288i	$0.187775\pi$
$84$		0			0
$85$	−8.47172	−	8.97950i	−0.918887	−	0.973963i
$86$	−0.116596	−	2.00188i	−0.0125729	−	0.215868i
$87$		0			0
$88$	−4.49883	−	1.06624i	−0.479577	−	0.113662i
$89$	−4.72182	+	1.71860i	−0.500512	+	0.182171i	−0.579924	−	0.814670i	$-0.696918\pi$
$89$	−4.72182	+	1.71860i	−0.500512	+	0.182171i	0.0794124	+	0.996842i	$0.474696\pi$
$90$		0			0
$91$	−10.1643	−	3.69952i	−1.06551	−	0.387815i
$92$	−0.781744	−	0.514161i	−0.0815024	−	0.0536050i
$93$		0			0
$94$	−1.32852	−	0.155282i	−0.137026	−	0.0160161i
$95$	3.54640	−	4.76364i	0.363853	−	0.488739i
$96$		0			0
$97$	0.436507	−	7.49453i	0.0443206	−	0.760955i	−0.900800	−	0.434234i	$-0.857019\pi$
$97$	0.436507	−	7.49453i	0.0443206	−	0.760955i	0.945121	−	0.326721i	$-0.105944\pi$
$98$	10.7523	−	9.02224i	1.08615	−	0.911384i
$99$		0			0
$100$	−2.91808	−	2.44856i	−0.291808	−	0.244856i
$101$	−1.55076	+	1.64371i	−0.154307	+	0.163555i	−0.799915	−	0.600113i	$-0.795122\pi$
$101$	−1.55076	+	1.64371i	−0.154307	+	0.163555i	0.645609	+	0.763668i	$0.276604\pi$
$102$		0			0
$103$	0.223770	−	0.147176i	0.0220487	−	0.0145017i	−0.538437	−	0.842666i	$-0.680985\pi$
$103$	0.223770	−	0.147176i	0.0220487	−	0.0145017i	0.560485	+	0.828164i	$0.310615\pi$
$104$	−5.62265	+	1.33259i	−0.551347	+	0.130672i
$105$		0			0
$106$	−7.85606	+	0.918241i	−0.763048	+	0.0891875i
$107$	4.97987	−	8.62539i	0.481423	−	0.833848i	−0.518350	−	0.855169i	$-0.673454\pi$
$107$	4.97987	−	8.62539i	0.481423	−	0.833848i	0.999773	+	0.0213201i	$0.00678691\pi$
$108$		0			0
$109$	6.70725	+	11.6173i	0.642438	+	1.11273i	0.984887	+	0.173198i	$0.0554102\pi$
$109$	6.70725	+	11.6173i	0.642438	+	1.11273i	−0.342449	+	0.939536i	$0.611256\pi$
$110$	−2.27567	−	3.05676i	−0.216977	−	0.291450i
$111$		0			0
$112$	−0.948317	+	3.16760i	−0.0896075	+	0.299310i
$113$	0.358445	+	0.180018i	0.0337196	+	0.0169346i	0.465579	−	0.885006i	$-0.345846\pi$
$113$	0.358445	+	0.180018i	0.0337196	+	0.0169346i	−0.431859	+	0.901941i	$0.642142\pi$
$114$		0			0
$115$	−0.541787	−	1.80970i	−0.0505219	−	0.168755i
$116$	1.37873	−	7.81916i	0.128012	−	0.725991i
$117$		0			0
$118$	−1.59040	−	9.01960i	−0.146408	−	0.830322i
$119$	−19.7304	+	9.90899i	−1.80869	+	0.908356i
$120$		0			0
$121$	−3.16173	−	7.32972i	−0.287430	−	0.666338i
$122$	2.47037	+	5.72697i	0.223657	+	0.518496i
$123$		0			0
$124$	7.25124	−	3.64171i	0.651180	−	0.327035i
$125$	1.08327	+	6.14355i	0.0968909	+	0.549495i
$126$		0			0
$127$	−1.81470	+	10.2917i	−0.161029	+	0.913239i	0.792037	+	0.610474i	$0.209021\pi$
$127$	−1.81470	+	10.2917i	−0.161029	+	0.913239i	−0.953065	+	0.302765i	$0.902090\pi$
$128$	2.61325	+	8.72885i	0.230981	+	0.771529i
$129$		0			0
$130$	−4.25619	−	2.13754i	−0.373292	−	0.187474i
$131$	−3.85774	+	12.8857i	−0.337052	+	1.12583i	0.606632	+	0.794983i	$0.292520\pi$
$131$	−3.85774	+	12.8857i	−0.337052	+	1.12583i	−0.943684	+	0.330849i	$0.892665\pi$
$132$		0			0
$133$	−6.34265	−	8.51965i	−0.549977	−	0.738748i
$134$	0.183263	+	0.317421i	0.0158315	+	0.0274210i
$135$		0			0
$136$	−5.89743	+	10.2146i	−0.505700	+	0.875898i
$137$	14.2020	−	1.65997i	1.21335	−	0.141821i	0.514757	−	0.857336i	$-0.327882\pi$
$137$	14.2020	−	1.65997i	1.21335	−	0.141821i	0.698597	+	0.715515i	$0.253808\pi$
$138$		0			0
$139$	−0.315089	+	0.0746776i	−0.0267255	+	0.00633407i	−0.243957	−	0.969786i	$-0.578446\pi$
$139$	−0.315089	+	0.0746776i	−0.0267255	+	0.00633407i	0.217231	+	0.976120i	$0.430297\pi$
$140$	−16.0012	+	10.5241i	−1.35235	+	0.889451i
$141$		0			0
$142$	6.58996	−	6.98495i	0.553017	−	0.586164i
$143$	2.88891	+	2.42408i	0.241583	+	0.202712i
$144$		0			0
$145$	12.2796	−	10.3038i	1.01976	−	0.855682i
$146$	−0.0980204	+	1.68295i	−0.00811223	+	0.139282i
$147$		0			0
$148$	−0.625474	+	0.840157i	−0.0514136	+	0.0690605i
$149$	3.05716	+	0.357331i	0.250452	+	0.0292737i	0.240393	−	0.970676i	$-0.422724\pi$
$149$	3.05716	+	0.357331i	0.250452	+	0.0292737i	0.0100596	+	0.999949i	$0.496798\pi$
$150$		0			0
$151$	−10.4653	−	6.88317i	−0.851658	−	0.560144i	0.0469497	−	0.998897i	$-0.485050\pi$
$151$	−10.4653	−	6.88317i	−0.851658	−	0.560144i	−0.898608	+	0.438753i	$0.855420\pi$
$152$	−5.33190	−	1.94065i	−0.432474	−	0.157408i
$153$		0			0
$154$	−6.40455	+	2.33106i	−0.516093	+	0.187843i
$155$	15.9407	+	3.77801i	1.28038	+	0.303457i
$156$		0			0
$157$	−0.338473	−	5.81136i	−0.0270131	−	0.463797i	−0.984507	−	0.175344i	$-0.943896\pi$
$157$	−0.338473	−	5.81136i	−0.0270131	−	0.463797i	0.957494	−	0.288453i	$-0.0931408\pi$
$158$	−3.79003	−	4.01720i	−0.301518	−	0.319591i
$159$		0			0
$160$	−6.45034	+	14.9536i	−0.509944	+	1.18218i
$161$	−3.37853			−0.266265
$162$		0			0
$163$	−6.75084			−0.528767			−0.264383	−	0.964418i	$-0.585168\pi$
$163$	−6.75084			−0.528767			−0.264383	+	0.964418i	$0.585168\pi$
$164$	−0.0674776	+	0.156431i	−0.00526912	+	0.0122152i
$165$		0			0
$166$	1.78873	+	1.89594i	0.138832	+	0.147153i
$167$	1.01103	+	17.3588i	0.0782362	+	1.34326i	0.777718	+	0.628614i	$0.216377\pi$
$167$	1.01103	+	17.3588i	0.0782362	+	1.34326i	−0.699482	+	0.714651i	$0.746586\pi$
$168$		0			0
$169$	−8.06337	−	1.91105i	−0.620259	−	0.147004i
$170$	−9.13549	+	3.32504i	−0.700660	+	0.255019i
$171$		0			0
$172$	3.30170	+	1.20172i	0.251752	+	0.0916303i
$173$	11.4838	+	7.55304i	0.873100	+	0.574247i	0.905080	−	0.425242i	$-0.139811\pi$
$173$	11.4838	+	7.55304i	0.873100	+	0.574247i	−0.0319801	+	0.999489i	$0.510181\pi$
$174$		0			0
$175$	−13.6616	−	1.59681i	−1.03272	−	0.120707i
$176$	0.688407	−	0.924691i	0.0518907	−	0.0697012i
$177$		0			0
$178$	−0.230084	+	3.95038i	−0.0172455	+	0.296094i
$179$	1.66053	−	1.39335i	0.124114	−	0.104144i	−0.578618	−	0.815599i	$-0.696408\pi$
$179$	1.66053	−	1.39335i	0.124114	−	0.104144i	0.702732	+	0.711455i	$0.251963\pi$
$180$		0			0
$181$	−17.7173	−	14.8665i	−1.31691	−	1.10502i	−0.986950	−	0.161028i	$-0.948519\pi$
$181$	−17.7173	−	14.8665i	−1.31691	−	1.10502i	−0.329963	−	0.943994i	$-0.607036\pi$
$182$	−5.84550	+	6.19587i	−0.433297	+	0.459268i
$183$		0			0
$184$	−1.50794	+	0.991785i	−0.111167	+	0.0731154i
$185$	−2.05766	+	0.487673i	−0.151282	+	0.0358544i
$186$		0			0
$187$	7.64570	−	0.893654i	0.559109	−	0.0653505i
$188$	1.17182	−	2.02966i	0.0854640	−	0.148028i
$189$		0			0
$190$	−2.33840	−	4.05023i	−0.169646	−	0.293835i
$191$	−13.0701	−	17.5562i	−0.945719	−	1.27032i	−0.962730	−	0.270465i	$-0.912822\pi$
$191$	−13.0701	−	17.5562i	−0.945719	−	1.27032i	0.0170111	−	0.999855i	$-0.494585\pi$
$192$		0			0
$193$	2.06918	−	6.91153i	0.148943	−	0.497503i	−0.850659	−	0.525717i	$-0.823797\pi$
$193$	2.06918	−	6.91153i	0.148943	−	0.497503i	0.999602	+	0.0282144i	$0.00898211\pi$
$194$	−5.28312	−	2.65328i	−0.379306	−	0.190494i
$195$		0			0
$196$	7.05357	+	23.5606i	0.503827	+	1.68290i
$197$	2.84835	−	16.1538i	0.202936	−	1.15091i	−0.697718	−	0.716373i	$-0.745801\pi$
$197$	2.84835	−	16.1538i	0.202936	−	1.15091i	0.900654	−	0.434537i	$-0.143088\pi$
$198$		0			0
$199$	−1.40107	−	7.94587i	−0.0993193	−	0.563268i	−0.993338	−	0.115238i	$-0.963237\pi$
$199$	−1.40107	−	7.94587i	−0.0993193	−	0.563268i	0.894019	−	0.448030i	$-0.147874\pi$
$200$	−6.56631	+	3.29772i	−0.464308	+	0.233184i
$201$		0			0
$202$	0.704859	+	1.63405i	0.0495937	+	0.114971i
$203$	−11.3552	−	26.3243i	−0.796979	−	1.84760i
$204$		0			0
$205$	−0.307366	+	0.154365i	−0.0214674	+	0.0107813i
$206$	−0.0366255	−	0.207713i	−0.00255182	−	0.0144721i
$207$		0			0
$208$	0.250189	−	1.41889i	0.0173475	−	0.0983824i
$209$	1.06207	+	3.54755i	0.0734646	+	0.245389i
$210$		0			0
$211$	−21.3780	−	10.7364i	−1.47172	−	0.739125i	−0.481215	−	0.876603i	$-0.659804\pi$
$211$	−21.3780	−	10.7364i	−1.47172	−	0.739125i	−0.990505	+	0.137477i	$0.956101\pi$
$212$	3.97478	−	13.2767i	0.272989	−	0.911847i
$213$		0			0
$214$	−4.68370	−	6.29130i	−0.320171	−	0.430065i
$215$	3.54684	+	6.14331i	0.241893	+	0.418970i
$216$		0			0
$217$	14.6496	−	25.3739i	0.994481	−	1.72249i
$218$	10.4925	−	1.22640i	0.710642	−	0.0830621i
$219$		0			0
$220$	6.49727	−	1.53988i	0.438046	−	0.103819i
$221$	8.03796	−	5.28665i	0.540692	−	0.355619i
$222$		0			0
$223$	−8.21140	+	8.70358i	−0.549876	+	0.582835i	−0.941383	−	0.337341i	$-0.890473\pi$
$223$	−8.21140	+	8.70358i	−0.549876	+	0.582835i	0.391507	+	0.920175i	$0.371954\pi$
$224$	22.3119	+	18.7219i	1.49078	+	1.25091i
$225$		0			0
$226$	0.241974	−	0.203040i	0.0160959	−	0.0135060i
$227$	1.46018	−	25.0704i	0.0969158	−	1.66398i	−0.503278	−	0.864125i	$-0.667873\pi$
$227$	1.46018	−	25.0704i	0.0969158	−	1.66398i	0.600194	−	0.799855i	$-0.295090\pi$
$228$		0			0
$229$	−15.3910	+	20.6737i	−1.01706	+	1.36615i	−0.0880481	+	0.996116i	$0.528063\pi$
$229$	−15.3910	+	20.6737i	−1.01706	+	1.36615i	−0.929016	+	0.370038i	$0.879344\pi$
$230$	−1.47757	−	0.172704i	−0.0974284	−	0.0113877i
$231$		0			0
$232$	−12.7958	−	8.41593i	−0.840085	−	0.552533i
$233$	−8.58260	−	3.12381i	−0.562265	−	0.204648i	0.0452226	−	0.998977i	$-0.485600\pi$
$233$	−8.58260	−	3.12381i	−0.562265	−	0.204648i	−0.607488	+	0.794329i	$0.707823\pi$
$234$		0			0
$235$	4.44630	−	1.61832i	0.290044	−	0.105568i
$236$	15.6152	+	3.70086i	1.01646	+	0.240906i
$237$		0			0
$238$	1.01097	+	17.3577i	0.0655317	+	1.12514i
$239$	14.9323	+	15.8273i	0.965890	+	1.02378i	0.999703	+	0.0243558i	$0.00775345\pi$
$239$	14.9323	+	15.8273i	0.965890	+	1.02378i	−0.0338130	+	0.999428i	$0.510765\pi$
$240$		0			0
$241$	5.49154	−	12.7308i	0.353741	−	0.820064i	−0.644710	−	0.764427i	$-0.723022\pi$
$241$	5.49154	−	12.7308i	0.353741	−	0.820064i	0.998451	−	0.0556368i	$-0.0177189\pi$
$242$	−6.28628			−0.404097
$243$		0			0
$244$	−10.9284			−0.699622
$245$	−19.6665	+	45.5922i	−1.25645	+	2.91278i
$246$		0			0
$247$	3.17604	+	3.36641i	0.202087	+	0.214199i
$248$	−0.910086	−	15.6256i	−0.0577905	−	0.992225i
$249$		0			0
$250$	4.78026	+	1.13294i	0.302330	+	0.0716536i
$251$	−10.0143	+	3.64492i	−0.632099	+	0.230065i	−0.638144	−	0.769917i	$-0.720298\pi$
$251$	−10.0143	+	3.64492i	−0.632099	+	0.230065i	0.00604584	+	0.999982i	$0.498076\pi$
$252$		0			0
$253$	1.10688	+	0.402871i	0.0695888	+	0.0253283i
$254$	6.87585	+	4.52232i	0.431429	+	0.283755i
$255$		0			0
$256$	13.6353	+	1.59374i	0.852206	+	0.0996086i
$257$	−0.701983	+	0.942927i	−0.0437885	+	0.0588181i	−0.823478	−	0.567348i	$-0.807969\pi$
$257$	−0.701983	+	0.942927i	−0.0437885	+	0.0588181i	0.779690	+	0.626166i	$0.215377\pi$
$258$		0			0
$259$	−0.219904	+	3.77561i	−0.0136642	+	0.234605i
$260$	6.39284	−	5.36423i	0.396467	−	0.332675i
$261$		0			0
$262$	8.11435	+	6.80875i	0.501306	+	0.420646i
$263$	−6.40456	+	6.78844i	−0.394922	+	0.418593i	−0.894072	−	0.447922i	$-0.852164\pi$
$263$	−6.40456	+	6.78844i	−0.394922	+	0.418593i	0.499150	+	0.866515i	$0.333646\pi$
$264$		0			0
$265$	23.3770	−	15.3753i	1.43604	−	0.944499i
$266$	−8.13889	+	1.92895i	−0.499027	+	0.118272i
$267$		0			0
$268$	−0.637875	+	0.0745569i	−0.0389644	+	0.00455429i
$269$	−1.25116	+	2.16707i	−0.0762845	+	0.132129i	−0.901644	−	0.432479i	$-0.857639\pi$
$269$	−1.25116	+	2.16707i	−0.0762845	+	0.132129i	0.825360	+	0.564607i	$0.190972\pi$
$270$		0			0
$271$	−2.76243	−	4.78467i	−0.167806	−	0.290648i	0.769842	−	0.638234i	$-0.220335\pi$
$271$	−2.76243	−	4.78467i	−0.167806	−	0.290648i	−0.937648	+	0.347586i	$0.887002\pi$
$272$	−1.75619	−	2.35897i	−0.106485	−	0.143034i
$273$		0			0
$274$	3.22946	−	10.7871i	0.195099	−	0.651675i
$275$	4.28541	+	2.15221i	0.258420	+	0.129783i
$276$		0			0
$277$	−7.66146	−	25.5911i	−0.460333	−	1.53762i	−0.801722	−	0.597696i	$-0.796083\pi$
$277$	−7.66146	−	25.5911i	−0.460333	−	1.53762i	0.341390	−	0.939922i	$-0.389102\pi$
$278$	−0.0442815	+	0.251133i	−0.00265583	+	0.0150620i
$279$		0			0
$280$	6.41505	+	36.3816i	0.383373	+	2.17421i
$281$	28.1325	−	14.1287i	1.67824	−	0.842846i	0.684774	−	0.728756i	$-0.259901\pi$
$281$	28.1325	−	14.1287i	1.67824	−	0.842846i	0.993470	−	0.114090i	$-0.0363952\pi$
$282$		0			0
$283$	2.65029	+	6.14405i	0.157543	+	0.365226i	0.978646	−	0.205555i	$-0.0658999\pi$
$283$	2.65029	+	6.14405i	0.157543	+	0.365226i	−0.821102	+	0.570781i	$0.806641\pi$
$284$	6.66448	+	15.4500i	0.395464	+	0.916789i
$285$		0			0
$286$	2.65393	−	1.33286i	0.156930	−	0.0788134i
$287$	0.106819	+	0.605803i	0.00630535	+	0.0357594i
$288$		0			0
$289$	0.458026	−	2.59759i	0.0269427	−	0.152800i
$290$	−3.62047	−	12.0932i	−0.212601	−	0.710137i
$291$		0			0
$292$	−2.63963	−	1.32567i	−0.154472	−	0.0775790i
$293$	−1.07661	+	3.59613i	−0.0628962	+	0.210088i	−0.983661	−	0.180030i	$-0.942381\pi$
$293$	−1.07661	+	3.59613i	−0.0628962	+	0.210088i	0.920765	+	0.390118i	$0.127566\pi$
$294$		0			0
$295$	19.3475	+	25.9882i	1.12645	+	1.51309i
$296$	1.01020	+	1.74972i	0.0587167	+	0.101700i
$297$		0			0
$298$	1.21195	−	2.09916i	0.0702066	−	0.121601i
$299$	1.46221	−	0.170908i	0.0845617	−	0.00988385i
$300$		0			0
$301$	12.3449	−	2.92580i	0.711549	−	0.168640i
$302$	−8.24148	+	5.42050i	−0.474244	+	0.311915i
$303$		0			0
$304$	0.970873	−	1.02907i	0.0556834	−	0.0590209i
$305$	−16.9018	−	14.1823i	−0.967793	−	0.812075i
$306$		0			0
$307$	−22.9491	+	19.2566i	−1.30977	+	1.09903i	−0.321406	+	0.946942i	$0.604155\pi$
$307$	−22.9491	+	19.2566i	−1.30977	+	1.09903i	−0.988367	+	0.152088i	$0.951400\pi$
$308$	0.694371	−	11.9219i	0.0395655	−	0.679313i
$309$		0			0
$310$	7.70397	−	10.3482i	0.437556	−	0.587740i
$311$	−4.41818	−	0.516411i	−0.250532	−	0.0292830i	−0.0101001	−	0.999949i	$-0.503215\pi$
$311$	−4.41818	−	0.516411i	−0.250532	−	0.0292830i	−0.240432	+	0.970666i	$0.577289\pi$
$312$		0			0
$313$	26.0864	+	17.1573i	1.47449	+	0.969789i	0.995776	+	0.0918201i	$0.0292685\pi$
$313$	26.0864	+	17.1573i	1.47449	+	0.969789i	0.478717	+	0.877969i	$0.341102\pi$
$314$	−4.30775	−	1.56789i	−0.243100	−	0.0884812i
$315$		0			0
$316$	9.09346	−	3.30975i	0.511547	−	0.186188i
$317$	−27.0789	−	6.41782i	−1.52090	−	0.360461i	−0.616575	−	0.787297i	$-0.711480\pi$
$317$	−27.0789	−	6.41782i	−1.52090	−	0.360461i	−0.904329	+	0.426836i	$0.859628\pi$
$318$		0			0
$319$	0.581178	+	9.97845i	0.0325397	+	0.558686i
$320$	6.26349	+	6.63891i	0.350140	+	0.371126i
$321$		0			0
$322$	−1.05381	+	2.44300i	−0.0587264	+	0.136143i
$323$	9.44699			0.525644
$324$		0			0
$325$	5.99343			0.332456
$326$	−2.10568	+	4.88151i	−0.116623	+	0.270362i
$327$		0			0
$328$	0.225513	+	0.239030i	0.0124519	+	0.0131982i
$329$	−0.492047	−	8.44812i	−0.0271274	−	0.465760i
$330$		0			0
$331$	0.191772	+	0.0454508i	0.0105408	+	0.00249820i	0.235883	−	0.971781i	$-0.424202\pi$
$331$	0.191772	+	0.0454508i	0.0105408	+	0.00249820i	−0.225342	+	0.974280i	$0.572350\pi$
$332$	−4.29171	+	1.56206i	−0.235538	+	0.0857289i
$333$		0			0
$334$	12.8674	+	4.68336i	0.704075	+	0.256262i
$335$	−1.08329	−	0.712488i	−0.0591862	−	0.0389274i
$336$		0			0
$337$	17.7835	+	2.07859i	0.968730	+	0.113228i	0.585718	−	0.810515i	$-0.300813\pi$
$337$	17.7835	+	2.07859i	0.968730	+	0.113228i	0.383012	+	0.923743i	$0.374887\pi$
$338$	−3.89695	+	5.23451i	−0.211966	+	0.284720i
$339$		0			0
$340$	0.990455	−	17.0055i	0.0537150	−	0.922251i
$341$	−7.82522	+	6.56614i	−0.423759	+	0.355576i
$342$		0			0
$343$	41.3103	+	34.6635i	2.23055	+	1.87165i
$344$	4.65101	−	4.92978i	0.250766	−	0.265796i
$345$		0			0
$346$	9.04353	−	5.94803i	0.486183	−	0.319768i
$347$	21.9243	−	5.19616i	1.17696	−	0.278944i	0.404819	−	0.914397i	$-0.367335\pi$
$347$	21.9243	−	5.19616i	1.17696	−	0.278944i	0.772140	+	0.635453i	$0.219186\pi$
$348$		0			0
$349$	11.7759	−	1.37641i	0.630349	−	0.0736773i	0.205082	−	0.978745i	$-0.434254\pi$
$349$	11.7759	−	1.37641i	0.630349	−	0.0736773i	0.425268	+	0.905068i	$0.360180\pi$
$350$	−5.41587	+	9.38056i	−0.289490	+	0.501412i
$351$		0			0
$352$	−5.07737	−	8.79426i	−0.270625	−	0.468736i
$353$	−11.2290	−	15.0832i	−0.597661	−	0.802798i	0.395634	−	0.918408i	$-0.370525\pi$
$353$	−11.2290	−	15.0832i	−0.597661	−	0.802798i	−0.993295	+	0.115610i	$0.963118\pi$
$354$		0			0
$355$	−9.74289	+	32.5435i	−0.517099	+	1.72723i
$356$	−6.19601	−	3.11175i	−0.328388	−	0.164922i
$357$		0			0
$358$	−0.489585	−	1.63533i	−0.0258754	−	0.0864297i
$359$	−1.61227	+	9.14366i	−0.0850926	+	0.482584i	0.912244	+	0.409647i	$0.134348\pi$
$359$	−1.61227	+	9.14366i	−0.0850926	+	0.482584i	−0.997337	+	0.0729368i	$0.976763\pi$
$360$		0			0
$361$	−2.51015	−	14.2358i	−0.132113	−	0.749251i
$362$	−16.2762	+	8.17421i	−0.855458	+	0.429627i
$363$		0			0
$364$	−5.91160	−	13.7046i	−0.309852	−	0.718318i
$365$	−2.36204	−	5.47581i	−0.123635	−	0.286617i
$366$		0			0
$367$	−26.1118	+	13.1138i	−1.36302	+	0.684536i	−0.971810	−	0.235764i	$-0.924241\pi$
$367$	−26.1118	+	13.1138i	−1.36302	+	0.684536i	−0.391213	+	0.920300i	$0.627945\pi$
$368$	−0.0781452	−	0.443183i	−0.00407360	−	0.0231025i
$369$		0			0
$370$	−0.289175	+	1.63999i	−0.0150335	+	0.0852593i
$371$	−14.3521	−	47.9395i	−0.745126	−	2.48889i
$372$		0			0
$373$	4.97275	+	2.49741i	0.257479	+	0.129311i	0.572857	−	0.819655i	$-0.305835\pi$
$373$	4.97275	+	2.49741i	0.257479	+	0.129311i	−0.315378	+	0.948966i	$0.602131\pi$
$374$	1.73860	−	5.80732i	0.0899007	−	0.300289i
$375$		0			0
$376$	−2.69961	−	3.62620i	−0.139222	−	0.187007i
$377$	6.24612	+	10.8186i	0.321692	+	0.557186i
$378$		0			0
$379$	−14.7919	+	25.6203i	−0.759808	+	1.31603i	0.183140	+	0.983087i	$0.441374\pi$
$379$	−14.7919	+	25.6203i	−0.759808	+	1.31603i	−0.942948	+	0.332940i	$0.891959\pi$
$380$	8.13918	−	0.951334i	0.417531	−	0.0488024i
$381$		0			0
$382$	−16.7715	+	3.97493i	−0.858107	+	0.203375i
$383$	10.3490	−	6.80665i	0.528810	−	0.347804i	−0.256861	−	0.966448i	$-0.582688\pi$
$383$	10.3490	−	6.80665i	0.528810	−	0.347804i	0.785671	+	0.618645i	$0.212318\pi$
$384$		0			0
$385$	16.5454	−	17.5371i	0.843233	−	0.893775i
$386$	−4.35230	−	3.65201i	−0.221526	−	0.185883i
$387$		0			0
$388$	7.93530	−	6.65850i	0.402854	−	0.338034i
$389$	−1.08026	+	18.5473i	−0.0547712	+	0.940386i	0.853261	+	0.521485i	$0.174622\pi$
$389$	−1.08026	+	18.5473i	−0.0547712	+	0.940386i	−0.908032	+	0.418901i	$0.862415\pi$
$390$		0			0
$391$	1.79444	−	2.41036i	0.0907489	−	0.121897i
$392$	47.1191	+	5.50743i	2.37987	+	0.278167i
$393$		0			0
$394$	−10.7923	−	7.09821i	−0.543708	−	0.357603i
$395$	18.3590	+	6.68214i	0.923743	+	0.336215i
$396$		0			0
$397$	9.59694	−	3.49300i	0.481657	−	0.175309i	−0.0897688	−	0.995963i	$-0.528613\pi$
$397$	9.59694	−	3.49300i	0.481657	−	0.175309i	0.571426	+	0.820654i	$0.306391\pi$
$398$	−6.18264	−	1.46531i	−0.309908	−	0.0734495i
$399$		0			0
$400$	−0.106528	−	1.82901i	−0.00532639	−	0.0914505i
$401$	−1.38543	−	1.46847i	−0.0691851	−	0.0733319i	0.691856	−	0.722035i	$-0.256793\pi$
$401$	−1.38543	−	1.46847i	−0.0691851	−	0.0733319i	−0.761041	+	0.648703i	$0.775312\pi$
$402$		0			0
$403$	−5.05670	+	11.7228i	−0.251892	+	0.583952i
$404$	−3.11815			−0.155134
$405$		0			0
$406$	−22.5768			−1.12047
$407$	0.522266	−	1.21075i	0.0258878	−	0.0600146i
$408$		0			0
$409$	0.596821	+	0.632593i	0.0295109	+	0.0312797i	0.741961	−	0.670443i	$-0.233896\pi$
$409$	0.596821	+	0.632593i	0.0295109	+	0.0312797i	−0.712450	+	0.701723i	$0.752414\pi$
$410$	0.0157492	+	0.270404i	0.000777800	+	0.0133543i
$411$		0			0
$412$	0.359603	+	0.0852276i	0.0177164	+	0.00419886i
$413$	54.4506	−	19.8184i	2.67934	−	0.975200i
$414$		0			0
$415$	−8.66465	−	3.15367i	−0.425331	−	0.154808i
$416$	−10.6035	−	6.97406i	−0.519881	−	0.341931i
$417$		0			0
$418$	2.89649	+	0.338551i	0.141672	+	0.0165591i
$419$	−15.0749	+	20.2492i	−0.736459	+	0.989236i	0.263241	+	0.964730i	$0.415209\pi$
$419$	−15.0749	+	20.2492i	−0.736459	+	0.989236i	−0.999700	+	0.0245058i	$0.992199\pi$
$420$		0			0
$421$	−0.974084	+	16.7244i	−0.0474740	+	0.815096i	0.887594	+	0.460627i	$0.152375\pi$
$421$	−0.974084	+	16.7244i	−0.0474740	+	0.815096i	−0.935068	+	0.354469i	$0.884662\pi$
$422$	−14.4315	+	12.1095i	−0.702516	+	0.589481i
$423$		0			0
$424$	−20.4787	−	17.1836i	−0.994532	−	0.834511i
$425$	8.39531	−	8.89850i	0.407232	−	0.431641i
$426$		0			0
$427$	−32.9687	+	21.6838i	−1.59547	+	1.04935i
$428$	13.3724	−	3.16933i	0.646381	−	0.153195i
$429$		0			0
$430$	5.54851	−	0.648528i	0.267573	−	0.0312748i
$431$	−13.1811	+	22.8303i	−0.634911	+	1.09970i	0.351623	+	0.936142i	$0.385630\pi$
$431$	−13.1811	+	22.8303i	−0.634911	+	1.09970i	−0.986534	+	0.163556i	$0.947703\pi$
$432$		0			0
$433$	6.29345	+	10.9006i	0.302444	+	0.523848i	0.976689	−	0.214660i	$-0.0688642\pi$
$433$	6.29345	+	10.9006i	0.302444	+	0.523848i	−0.674245	+	0.738508i	$0.735531\pi$
$434$	−13.7784	−	18.5075i	−0.661382	−	0.888390i
$435$		0			0
$436$	−5.30869	+	17.7323i	−0.254240	+	0.849222i
$437$	1.29182	+	0.648777i	0.0617962	+	0.0310352i
$438$		0			0
$439$	−2.52350	−	8.42909i	−0.120440	−	0.402299i	0.876414	−	0.481559i	$-0.159929\pi$
$439$	−2.52350	−	8.42909i	−0.120440	−	0.402299i	−0.996854	+	0.0792605i	$0.974744\pi$
$440$	2.23659	−	12.6843i	0.106625	−	0.604702i
$441$		0			0
$442$	−1.31561	−	7.46120i	−0.0625772	−	0.354893i
$443$	−13.6033	+	6.83182i	−0.646311	+	0.324590i	−0.741582	−	0.670862i	$-0.765924\pi$
$443$	−13.6033	+	6.83182i	−0.646311	+	0.324590i	0.0952714	+	0.995451i	$0.469628\pi$
$444$		0			0
$445$	−5.54442	−	12.8534i	−0.262831	−	0.609310i
$446$	3.73228	+	8.65240i	0.176729	+	0.409703i
$447$		0			0
$448$	14.5875	−	7.32613i	0.689195	−	0.346127i
$449$	−0.214786	−	1.21811i	−0.0101364	−	0.0574862i	0.979320	−	0.202317i	$-0.0648472\pi$
$449$	−0.214786	−	1.21811i	−0.0101364	−	0.0574862i	−0.989456	+	0.144831i	$0.953736\pi$
$450$		0			0
$451$	0.0372423	−	0.211212i	0.00175367	−	0.00994557i
$452$	0.158736	+	0.530217i	0.00746633	+	0.0249393i
$453$		0			0
$454$	−17.6728	−	8.87564i	−0.829428	−	0.416554i
$455$	8.64225	−	28.8671i	0.405155	−	1.35331i
$456$		0			0
$457$	18.5032	+	24.8541i	0.865542	+	1.16263i	0.985471	+	0.169843i	$0.0543259\pi$
$457$	18.5032	+	24.8541i	0.865542	+	1.16263i	−0.119929	+	0.992782i	$0.538267\pi$
$458$	10.1484	+	17.5776i	0.474204	+	0.821345i
$459$		0			0
$460$	1.30330	−	2.25738i	0.0607666	−	0.105251i
$461$	16.8270	−	1.96679i	0.783710	−	0.0916026i	0.285179	−	0.958474i	$-0.407947\pi$
$461$	16.8270	−	1.96679i	0.783710	−	0.0916026i	0.498531	+	0.866872i	$0.333873\pi$
$462$		0			0
$463$	34.7253	−	8.23005i	1.61382	−	0.382483i	0.678030	−	0.735034i	$-0.262834\pi$
$463$	34.7253	−	8.23005i	1.61382	−	0.382483i	0.935792	+	0.352551i	$0.114686\pi$
$464$	3.19048	−	2.09841i	0.148114	−	0.0974164i
$465$		0			0
$466$	−4.93584	+	5.23169i	−0.228649	+	0.242353i
$467$	−32.1894	−	27.0101i	−1.48955	−	1.24988i	−0.895195	−	0.445675i	$-0.852964\pi$
$467$	−32.1894	−	27.0101i	−1.48955	−	1.24988i	−0.594353	−	0.804204i	$-0.702592\pi$
$468$		0			0
$469$	−1.77640	+	1.49057i	−0.0820263	+	0.0688282i
$470$	0.216658	−	3.71988i	0.00999370	−	0.171585i
$471$		0			0
$472$	18.4851	−	24.8298i	0.850846	−	1.14288i
$473$	−4.39334	−	0.513508i	−0.202006	−	0.0236111i
$474$		0			0
$475$	4.91703	+	3.23398i	0.225609	+	0.148385i
$476$	−28.6281	−	10.4198i	−1.31217	−	0.477590i
$477$		0			0
$478$	16.1023	−	5.86074i	0.736500	−	0.268064i
$479$	35.1181	+	8.32315i	1.60459	+	0.380295i	0.932785	−	0.360434i	$-0.117371\pi$
$479$	35.1181	+	8.32315i	1.60459	+	0.380295i	0.671804	+	0.740729i	$0.265520\pi$
$480$		0			0
$481$	−0.0958213	−	1.64519i	−0.00436908	−	0.0750141i
$482$	−7.49272	−	7.94182i	−0.341284	−	0.361740i
$483$		0			0
$484$	4.36269	−	10.1139i	0.198304	−	0.459721i
$485$	20.9136			0.949639
$486$		0			0
$487$	27.8890			1.26377			0.631885	−	0.775062i	$-0.282282\pi$
$487$	27.8890			1.26377			0.631885	+	0.775062i	$0.282282\pi$
$488$	−8.34948	+	19.3563i	−0.377963	+	0.876217i
$489$		0			0
$490$	26.8333	+	28.4416i	1.21220	+	1.28486i
$491$	−1.26476	−	21.7151i	−0.0570777	−	0.979987i	−0.898324	−	0.439334i	$-0.855214\pi$
$491$	−1.26476	−	21.7151i	−0.0570777	−	0.979987i	0.841246	−	0.540653i	$-0.181823\pi$
$492$		0			0
$493$	24.8117	+	5.88049i	1.11746	+	0.264844i
$494$	3.42489	−	1.24656i	0.154093	−	0.0560853i
$495$		0			0
$496$	3.66730	+	1.33479i	0.164667	+	0.0599338i
$497$	50.7606	+	33.3858i	2.27692	+	1.49756i
$498$		0			0
$499$	2.96418	+	0.346463i	0.132695	+	0.0155098i	0.182181	−	0.983265i	$-0.441684\pi$
$499$	2.96418	+	0.346463i	0.132695	+	0.0155098i	−0.0494861	+	0.998775i	$0.515758\pi$
$500$	−5.14028	+	6.90459i	−0.229880	+	0.308783i
$501$		0			0
$502$	−0.487976	+	8.37822i	−0.0217794	+	0.373938i
$503$	−30.5223	+	25.6113i	−1.36092	+	1.14195i	−0.385227	+	0.922822i	$0.625877\pi$
$503$	−30.5223	+	25.6113i	−1.36092	+	1.14195i	−0.975696	+	0.219128i	$0.929679\pi$
$504$		0			0
$505$	−4.82249	−	4.04655i	−0.214598	−	0.180069i
$506$	0.636564	−	0.674719i	0.0282987	−	0.0299949i
$507$		0			0
$508$	−12.0477	+	7.92390i	−0.534530	+	0.351566i
$509$	−19.3907	+	4.59567i	−0.859476	+	0.203700i	−0.636645	−	0.771157i	$-0.719678\pi$
$509$	−19.3907	+	4.59567i	−0.859476	+	0.203700i	−0.222832	+	0.974857i	$0.571530\pi$
$510$		0			0
$511$	−10.5935	+	1.23820i	−0.468630	+	0.0547750i
$512$	−3.70618	+	6.41930i	−0.163792	+	0.283695i
$513$		0			0
$514$	0.462869	+	0.801713i	0.0204163	+	0.0353620i
$515$	0.445555	+	0.598484i	0.0196335	+	0.0263723i
$516$		0			0
$517$	−0.846186	+	2.82646i	−0.0372152	+	0.124308i
$518$	2.66154	+	1.33668i	0.116941	+	0.0587301i
$519$		0			0
$520$	−4.61681	−	15.4212i	−0.202461	−	0.676265i
$521$	−6.17183	+	35.0022i	−0.270393	+	1.53347i	0.482833	+	0.875713i	$0.339608\pi$
$521$	−6.17183	+	35.0022i	−0.270393	+	1.53347i	−0.753226	+	0.657762i	$0.771503\pi$
$522$		0			0
$523$	4.17875	+	23.6989i	0.182724	+	1.03628i	0.928845	+	0.370469i	$0.120803\pi$
$523$	4.17875	+	23.6989i	0.182724	+	1.03628i	−0.746121	+	0.665810i	$0.768086\pi$
$524$	−16.5858	+	8.32971i	−0.724555	+	0.363885i
$525$		0			0
$526$	2.91103	+	6.74852i	0.126927	+	0.294249i
$527$	10.3217	+	23.9284i	0.449620	+	1.04234i
$528$		0			0
$529$	−20.1426	+	10.1160i	−0.875767	+	0.439827i
$530$	−3.82623	−	21.6996i	−0.166201	−	0.942571i
$531$		0			0
$532$	2.54496	−	14.4332i	0.110338	−	0.625757i
$533$	−0.0768763	−	0.256785i	−0.00332988	−	0.0111226i
$534$		0			0
$535$	24.7946	+	12.4523i	1.07196	+	0.538360i
$536$	−0.355291	+	1.18676i	−0.0153463	+	0.0512601i
$537$		0			0
$538$	1.17675	+	1.58065i	0.0507332	+	0.0681466i
$539$	−15.4805	−	26.8130i	−0.666792	−	1.15492i
$540$		0			0
$541$	5.32644	−	9.22567i	0.229002	−	0.396642i	−0.728511	−	0.685034i	$-0.759787\pi$
$541$	5.32644	−	9.22567i	0.229002	−	0.396642i	0.957512	+	0.288392i	$0.0931206\pi$
$542$	−4.32142	+	0.505102i	−0.185621	+	0.0216960i
$543$		0			0
$544$	−25.2074	+	5.97426i	−1.08076	+	0.256144i
$545$	−31.2222	+	20.5352i	−1.33741	+	0.879631i
$546$		0			0
$547$	−9.33306	+	9.89247i	−0.399053	+	0.422971i	−0.895476	−	0.445109i	$-0.853165\pi$
$547$	−9.33306	+	9.89247i	−0.399053	+	0.422971i	0.496423	+	0.868081i	$0.334646\pi$
$548$	15.1139	+	12.6821i	0.645636	+	0.541753i
$549$		0			0
$550$	2.89293	−	2.42746i	0.123355	−	0.103507i
$551$	−0.713245	+	12.2460i	−0.0303853	+	0.521695i
$552$		0			0
$553$	20.8659	−	28.0277i	0.887307	−	1.19186i
$554$	−20.8945	−	2.44222i	−0.887723	−	0.103760i
$555$		0			0
$556$	−0.373311	−	0.245530i	−0.0158319	−	0.0104128i
$557$	4.31357	+	1.57001i	0.182772	+	0.0665235i	0.431785	−	0.901977i	$-0.357884\pi$
$557$	4.31357	+	1.57001i	0.182772	+	0.0665235i	−0.249013	+	0.968500i	$0.580106\pi$
$558$		0			0
$559$	−5.19480	+	1.89075i	−0.219717	+	0.0799704i
$560$	−8.96297	−	2.12426i	−0.378755	−	0.0897665i
$561$		0			0
$562$	−1.44149	−	24.7494i	−0.0608056	−	1.04399i
$563$	−0.680134	−	0.720900i	−0.0286642	−	0.0303823i	0.712883	−	0.701283i	$-0.247389\pi$
$563$	−0.680134	−	0.720900i	−0.0286642	−	0.0303823i	−0.741547	+	0.670901i	$0.765908\pi$
$564$		0			0
$565$	−0.442584	+	1.02602i	−0.0186196	+	0.0431652i
$566$	5.26940			0.221489
$567$		0			0
$568$	32.4565			1.36185
$569$	−3.07723	+	7.13381i	−0.129004	+	0.299065i	−0.970461	−	0.241260i	$-0.922439\pi$
$569$	−3.07723	+	7.13381i	−0.129004	+	0.299065i	0.841457	+	0.540325i	$0.181699\pi$
$570$		0			0
$571$	−14.6837	−	15.5638i	−0.614494	−	0.651326i	0.343150	−	0.939281i	$-0.388506\pi$
$571$	−14.6837	−	15.5638i	−0.614494	−	0.651326i	−0.957644	+	0.287955i	$0.907025\pi$
$572$	0.302566	+	5.19486i	0.0126509	+	0.217208i
$573$		0			0
$574$	0.471373	+	0.111717i	0.0196747	+	0.00466299i
$575$	1.75912	−	0.640267i	0.0733604	−	0.0267010i
$576$		0			0
$577$	−8.13925	−	2.96244i	−0.338841	−	0.123328i	0.166995	−	0.985958i	$-0.446594\pi$
$577$	−8.13925	−	2.96244i	−0.338841	−	0.123328i	−0.505836	+	0.862630i	$0.668816\pi$
$578$	−1.73545	−	1.14142i	−0.0721851	−	0.0474769i
$579$		0			0
$580$	21.9691	+	2.56782i	0.912216	+	0.106623i
$581$	−9.84777	+	13.2278i	−0.408554	+	0.548784i
$582$		0			0
$583$	−1.01445	+	17.4174i	−0.0420141	+	0.721355i
$584$	−4.36471	+	3.66243i	−0.180613	+	0.151552i
$585$		0			0
$586$	2.26454	+	1.90017i	0.0935472	+	0.0784954i
$587$	−7.21493	+	7.64738i	−0.297792	+	0.315641i	−0.858942	−	0.512073i	$-0.828878\pi$
$587$	−7.21493	+	7.64738i	−0.297792	+	0.315641i	0.561150	+	0.827714i	$0.310359\pi$
$588$		0			0
$589$	−10.4740	+	6.88885i	−0.431573	+	0.283850i
$590$	24.8267	−	5.88403i	1.02210	−	0.242242i
$591$		0			0
$592$	−0.500358	+	0.0584834i	−0.0205646	+	0.00240365i
$593$	14.0175	−	24.2790i	0.575630	−	0.997020i	−0.420343	−	0.907365i	$-0.638090\pi$
$593$	14.0175	−	24.2790i	0.575630	−	0.997020i	0.995973	−	0.0896551i	$-0.0285765\pi$
$594$		0			0
$595$	−30.7537	−	53.2669i	−1.26078	−	2.18373i
$596$	2.53620	+	3.40671i	0.103887	+	0.139544i
$597$		0			0
$598$	0.332500	−	1.11063i	0.0135969	−	0.0454169i
$599$	−20.7959	−	10.4441i	−0.849699	−	0.426735i	−0.0300143	−	0.999549i	$-0.509555\pi$
$599$	−20.7959	−	10.4441i	−0.849699	−	0.426735i	−0.819685	+	0.572814i	$0.805852\pi$
$600$		0			0
$601$	−6.16371	−	20.5882i	−0.251423	−	0.839811i	−0.986771	−	0.162121i	$-0.948166\pi$
$601$	−6.16371	−	20.5882i	−0.251423	−	0.839811i	0.735348	−	0.677690i	$-0.237019\pi$
$602$	1.73491	−	9.83915i	0.0707096	−	0.401014i
$603$		0			0
$604$	−3.00133	−	17.0214i	−0.122122	−	0.692589i
$605$	19.8724	−	9.98031i	0.807930	−	0.405757i
$606$		0			0
$607$	1.91860	+	4.44782i	0.0778737	+	0.180531i	0.952705	−	0.303896i	$-0.0982874\pi$
$607$	1.91860	+	4.44782i	0.0778737	+	0.180531i	−0.874832	+	0.484427i	$0.839028\pi$
$608$	−4.93607	−	11.4431i	−0.200184	−	0.464079i
$609$		0			0
$610$	−15.5270	+	7.79798i	−0.628672	+	0.315731i
$611$	0.640316	+	3.63141i	0.0259044	+	0.146911i
$612$		0			0
$613$	2.42381	−	13.7461i	0.0978969	−	0.555201i	−0.895924	−	0.444207i	$-0.853485\pi$
$613$	2.42381	−	13.7461i	0.0978969	−	0.555201i	0.993821	−	0.110994i	$-0.0354034\pi$
$614$	6.76622	+	22.6008i	0.273063	+	0.912093i
$615$		0			0
$616$	−20.5853	−	10.3383i	−0.829407	−	0.416544i
$617$	−5.79638	+	19.3612i	−0.233353	+	0.779454i	0.758456	+	0.651725i	$0.225954\pi$
$617$	−5.79638	+	19.3612i	−0.233353	+	0.779454i	−0.991809	+	0.127730i	$0.959231\pi$
$618$		0			0
$619$	−17.2355	−	23.1513i	−0.692753	−	0.930529i	0.307022	−	0.951702i	$-0.400667\pi$
$619$	−17.2355	−	23.1513i	−0.692753	−	0.930529i	−0.999776	+	0.0211729i	$0.993260\pi$
$620$	11.3025	+	19.5764i	0.453917	+	0.786208i
$621$		0			0
$622$	−1.75151	+	3.03370i	−0.0702290	+	0.121640i
$623$	−24.8662	+	2.90644i	−0.996243	+	0.116444i
$624$		0			0
$625$	−30.3415	+	7.19108i	−1.21366	+	0.287643i
$626$	20.5431	−	13.5114i	0.821068	−	0.540025i
$627$		0			0
$628$	5.51213	−	5.84252i	0.219958	−	0.233142i
$629$	−2.57685	−	2.16223i	−0.102746	−	0.0862139i
$630$		0			0
$631$	−35.3851	+	29.6916i	−1.40866	+	1.18200i	−0.451558	+	0.892242i	$0.649132\pi$
$631$	−35.3851	+	29.6916i	−1.40866	+	1.18200i	−0.957099	+	0.289762i	$0.906424\pi$
$632$	1.08536	−	18.6349i	0.0431732	−	0.741255i
$633$		0			0
$634$	−13.0870	+	17.5789i	−0.519750	+	0.698146i
$635$	−28.9160	−	3.37979i	−1.14750	−	0.134123i
$636$		0			0
$637$	−32.3293	−	21.2633i	−1.28093	−	0.842484i
$638$	7.39666	+	2.69216i	0.292836	+	0.106584i
$639$		0			0
$640$	−23.8524	+	8.68156i	−0.942848	+	0.343169i
$641$	−24.2211	−	5.74051i	−0.956676	−	0.226736i	−0.277512	−	0.960722i	$-0.589510\pi$
$641$	−24.2211	−	5.74051i	−0.956676	−	0.226736i	−0.679165	+	0.733986i	$0.737658\pi$
$642$		0			0
$643$	−0.128744	−	2.21044i	−0.00507715	−	0.0871713i	0.994818	−	0.101675i	$-0.0324202\pi$
$643$	−0.128744	−	2.21044i	−0.00507715	−	0.0871713i	−0.999895	+	0.0145037i	$0.995383\pi$
$644$	−3.19915	−	3.39090i	−0.126064	−	0.133620i
$645$		0			0
$646$	2.94664	−	6.83108i	0.115934	−	0.268765i
$647$	26.5378			1.04331			0.521654	−	0.853157i	$-0.325315\pi$
$647$	26.5378			1.04331			0.521654	+	0.853157i	$0.325315\pi$
$648$		0			0
$649$	−20.2024			−0.793015
$650$	1.86943	−	4.33383i	0.0733251	−	0.169987i
$651$		0			0
$652$	−6.39241	−	6.77556i	−0.250346	−	0.265351i
$653$	−0.0123406	−	0.211880i	−0.000482926	−	0.00829152i	0.998058	−	0.0622901i	$-0.0198404\pi$
$653$	−0.0123406	−	0.211880i	−0.000482926	−	0.00829152i	−0.998541	+	0.0539986i	$0.982803\pi$
$654$		0			0
$655$	−36.4612	−	8.64147i	−1.42466	−	0.337650i
$656$	−0.0769964	+	0.0280244i	−0.00300620	+	0.00109417i
$657$		0			0
$658$	−6.26228	−	2.27928i	−0.244129	−	0.0888558i
$659$	22.6208	+	14.8779i	0.881180	+	0.579561i	0.907481	−	0.420093i	$-0.138002\pi$
$659$	22.6208	+	14.8779i	0.881180	+	0.579561i	−0.0263011	+	0.999654i	$0.508373\pi$
$660$		0			0
$661$	−35.5356	−	4.15352i	−1.38218	−	0.161553i	−0.607705	−	0.794163i	$-0.707910\pi$
$661$	−35.5356	−	4.15352i	−1.38218	−	0.161553i	−0.774471	+	0.632609i	$0.781984\pi$
$662$	0.0926816	−	0.124493i	0.00360217	−	0.00483856i
$663$		0			0
$664$	−0.512241	+	8.79484i	−0.0198788	+	0.341306i
$665$	22.6665	−	19.0195i	0.878969	−	0.737543i
$666$		0			0
$667$	2.98902	+	2.50808i	0.115735	+	0.0971134i
$668$	−16.4650	+	17.4519i	−0.637049	+	0.675233i
$669$		0			0
$670$	−0.853088	+	0.561085i	−0.0329577	+	0.0216766i
$671$	13.3869	−	3.17276i	0.516796	−	0.122483i
$672$		0			0
$673$	28.3593	−	3.31473i	1.09317	−	0.127773i	0.449652	−	0.893204i	$-0.351548\pi$
$673$	28.3593	−	3.31473i	1.09317	−	0.127773i	0.643519	+	0.765430i	$0.277474\pi$
$674$	7.04994	−	12.2109i	0.271554	−	0.470345i
$675$		0			0
$676$	−5.71719	−	9.90247i	−0.219892	−	0.380864i
$677$	8.79309	+	11.8112i	0.337946	+	0.453940i	0.938314	−	0.345783i	$-0.112387\pi$
$677$	8.79309	+	11.8112i	0.337946	+	0.453940i	−0.600369	+	0.799723i	$0.704979\pi$
$678$		0			0
$679$	10.7274	−	35.8322i	0.411682	−	1.37511i
$680$	−29.3631	−	14.7467i	−1.12602	−	0.565509i
$681$		0			0
$682$	2.30716	+	7.70646i	0.0883458	+	0.295095i
$683$	0.764140	−	4.33365i	0.0292390	−	0.165823i	−0.966692	−	0.255943i	$-0.917614\pi$
$683$	0.764140	−	4.33365i	0.0292390	−	0.165823i	0.995931	+	0.0901204i	$0.0287252\pi$
$684$		0			0
$685$	6.91695	+	39.2280i	0.264283	+	1.49882i
$686$	37.9503	−	19.0594i	1.44895	−	0.727690i
$687$		0			0
$688$	0.669333	+	1.55169i	0.0255181	+	0.0591575i
$689$	8.63661	+	20.0219i	0.329029	+	0.762774i
$690$		0			0
$691$	2.70634	−	1.35918i	0.102954	−	0.0517055i	−0.396577	−	0.918001i	$-0.629802\pi$
$691$	2.70634	−	1.35918i	0.102954	−	0.0517055i	0.499531	+	0.866296i	$0.333506\pi$
$692$	3.29341	+	18.6779i	0.125197	+	0.710026i
$693$		0			0
$694$	3.08116	−	17.4741i	0.116959	−	0.663309i
$695$	−0.258723	−	0.864194i	−0.00981391	−	0.0327808i
$696$		0			0
$697$	−0.488936	−	0.245553i	−0.0185198	−	0.00930097i
$698$	2.67779	−	8.94443i	0.101356	−	0.338552i
$699$		0			0
$700$	−11.3336	−	15.2236i	−0.428368	−	0.575398i
$701$	−21.6147	−	37.4378i	−0.816377	−	1.41401i	−0.908335	−	0.418243i	$-0.862646\pi$
$701$	−21.6147	−	37.4378i	−0.816377	−	1.41401i	0.0919585	−	0.995763i	$-0.470687\pi$
$702$		0			0
$703$	0.809112	−	1.40142i	0.0305162	−	0.0528557i
$704$	−5.65278	+	0.660715i	−0.213047	+	0.0249016i
$705$		0			0
$706$	−14.4091	+	3.41502i	−0.542294	+	0.128526i
$707$	−9.40677	+	6.18693i	−0.353778	+	0.232684i
$708$		0			0
$709$	22.0808	−	23.4043i	0.829261	−	0.878966i	−0.164962	−	0.986300i	$-0.552750\pi$
$709$	22.0808	−	23.4043i	0.829261	−	0.878966i	0.994223	+	0.107334i	$0.0342316\pi$
$710$	20.4932	+	17.1958i	0.769095	+	0.645347i
$711$		0			0
$712$	−10.2453	+	8.59684i	−0.383959	+	0.322180i
$713$	−0.231862	+	3.98092i	−0.00868331	+	0.149087i
$714$		0			0
$715$	−6.27363	+	8.42695i	−0.234621	+	0.315150i
$716$	2.97081	+	0.347238i	0.111024	+	0.0129769i
$717$		0			0
$718$	6.10886	+	4.01786i	0.227981	+	0.149945i
$719$	−9.54600	−	3.47446i	−0.356006	−	0.129576i	0.157825	−	0.987467i	$-0.449552\pi$
$719$	−9.54600	−	3.47446i	−0.356006	−	0.129576i	−0.513831	+	0.857892i	$0.671774\pi$
$720$		0			0
$721$	1.25395	−	0.456400i	0.0466995	−	0.0169972i
$722$	−11.0768	−	2.62525i	−0.412235	−	0.0977016i
$723$		0			0
$724$	−1.85559	−	31.8593i	−0.0689626	−	1.18404i
$725$	10.9011	+	11.5545i	0.404857	+	0.429124i
$726$		0			0
$727$	5.58259	−	12.9419i	0.207047	−	0.479989i	−0.782774	−	0.622306i	$-0.786196\pi$
$727$	5.58259	−	12.9419i	0.207047	−	0.479989i	0.989821	+	0.142317i	$0.0454553\pi$
$728$	−28.7900			−1.06703
$729$		0			0
$730$	−4.69629			−0.173818
$731$	−4.46941	+	10.3613i	−0.165307	+	0.383225i
$732$		0			0
$733$	10.7728	+	11.4185i	0.397904	+	0.421753i	0.895086	−	0.445893i	$-0.147114\pi$
$733$	10.7728	+	11.4185i	0.397904	+	0.421753i	−0.497183	+	0.867646i	$0.665632\pi$
$734$	1.33795	+	22.9717i	0.0493846	+	0.847901i
$735$		0			0
$736$	−3.85725	−	0.914186i	−0.142180	−	0.0336973i
$737$	0.759727	−	0.276518i	0.0279849	−	0.0101857i
$738$		0			0
$739$	−3.42025	−	1.24487i	−0.125816	−	0.0457933i	0.278345	−	0.960481i	$-0.410214\pi$
$739$	−3.42025	−	1.24487i	−0.125816	−	0.0457933i	−0.404161	+	0.914688i	$0.632436\pi$
$740$	−2.43786	−	1.60341i	−0.0896176	−	0.0589424i
$741$		0			0
$742$	−39.1415	−	4.57498i	−1.43693	−	0.167953i
$743$	13.9026	−	18.6745i	0.510039	−	0.685101i	−0.470281	−	0.882517i	$-0.655848\pi$
$743$	13.9026	−	18.6745i	0.510039	−	0.685101i	0.980320	+	0.197416i	$0.0632549\pi$
$744$		0			0
$745$	−0.498569	+	8.56010i	−0.0182662	+	0.313618i
$746$	3.35694	−	2.81680i	0.122906	−	0.103130i
$747$		0			0
$748$	8.13668	+	6.82748i	0.297506	+	0.249637i
$749$	34.0532	−	36.0943i	1.24428	−	1.31886i
$750$		0			0
$751$	−6.59964	+	4.34065i	−0.240824	+	0.158393i	−0.664184	−	0.747569i	$-0.731221\pi$
$751$	−6.59964	+	4.34065i	−0.240824	+	0.158393i	0.423360	+	0.905962i	$0.360851\pi$
$752$	1.09681	−	0.259950i	0.0399967	−	0.00947939i
$753$		0			0
$754$	9.77114	−	1.14208i	0.355844	−	0.0415922i
$755$	17.4475	−	30.2200i	0.634980	−	1.09982i
$756$		0			0
$757$	−2.12074	−	3.67323i	−0.0770795	−	0.133506i	0.824909	−	0.565265i	$-0.191226\pi$
$757$	−2.12074	−	3.67323i	−0.0770795	−	0.133506i	−0.901989	+	0.431760i	$0.857893\pi$
$758$	13.9122	+	18.6873i	0.505312	+	0.678752i
$759$		0			0
$760$	4.53346	−	15.1428i	0.164446	−	0.549287i
$761$	36.5389	+	18.3505i	1.32453	+	0.665206i	0.963591	−	0.267381i	$-0.0861583\pi$
$761$	36.5389	+	18.3505i	1.32453	+	0.665206i	0.360944	+	0.932588i	$0.382455\pi$
$762$		0			0
$763$	19.1686	+	64.0276i	0.693951	+	2.31796i
$764$	5.24431	−	29.7420i	0.189733	−	1.07603i
$765$		0			0
$766$	−1.69387	−	9.60642i	−0.0612020	−	0.347094i
$767$	−22.5634	+	11.3318i	−0.814717	+	0.409166i
$768$		0			0
$769$	12.9500	+	30.0215i	0.466989	+	1.08260i	0.975191	+	0.221364i	$0.0710510\pi$
$769$	12.9500	+	30.0215i	0.466989	+	1.08260i	−0.508202	+	0.861238i	$0.669690\pi$
$770$	−7.52030	−	17.4340i	−0.271013	−	0.628278i
$771$		0			0
$772$	8.89615	−	4.46781i	0.320179	−	0.160800i
$773$	−6.74796	−	38.2696i	−0.242707	−	1.37646i	−0.825757	−	0.564025i	$-0.809252\pi$
$773$	−6.74796	−	38.2696i	−0.242707	−	1.37646i	0.583050	−	0.812436i	$-0.301859\pi$
$774$		0			0
$775$	−2.81909	+	15.9878i	−0.101265	+	0.574300i
$776$	−5.73075	−	19.1420i	−0.205722	−	0.687159i
$777$		0			0
$778$	13.0745	+	6.56628i	0.468745	+	0.235413i
$779$	0.0754884	−	0.252149i	0.00270465	−	0.00903417i
$780$		0			0
$781$	−12.6492	−	16.9908i	−0.452624	−	0.607979i
$782$	−1.18321	−	2.04938i	−0.0423115	−	0.0732856i
$783$		0			0
$784$	−5.91429	+	10.2439i	−0.211225	+	0.365852i
$785$	16.1071	−	1.88264i	0.574885	−	0.0671945i
$786$		0			0
$787$	2.21966	−	0.526068i	0.0791222	−	0.0187523i	−0.190864	−	0.981616i	$-0.561129\pi$
$787$	2.21966	−	0.526068i	0.0791222	−	0.0187523i	0.269986	+	0.962864i	$0.412981\pi$
$788$	18.9100	−	12.4373i	0.673642	−	0.443061i
$789$		0			0
$790$	10.5583	−	11.1911i	0.375646	−	0.398161i
$791$	1.53091	+	1.28459i	0.0544329	+	0.0456746i
$792$		0			0
$793$	13.1718	−	11.0524i	0.467743	−	0.392483i
$794$	0.467638	−	8.02903i	0.0165958	−	0.284940i
$795$		0			0
$796$	6.64828	−	8.93019i	0.235642	−	0.316522i
$797$	−33.9740	−	3.97099i	−1.20342	−	0.140660i	−0.509346	−	0.860562i	$-0.670113\pi$
$797$	−33.9740	−	3.97099i	−1.20342	−	0.140660i	−0.694076	+	0.719902i	$0.744187\pi$
$798$		0			0
$799$	6.28852	+	4.13602i	0.222472	+	0.146322i
$800$	−15.1653	−	5.51971i	−0.536174	−	0.195151i
$801$		0			0
$802$	−1.49398	+	0.543764i	−0.0527543	+	0.0192010i
$803$	3.61831	+	0.857556i	0.127687	+	0.0302625i
$804$		0			0
$805$	−0.547253	−	9.39598i	−0.0192881	−	0.331165i
$806$	6.89943	+	7.31296i	0.243022	+	0.257588i
$807$		0			0
$808$	−2.38231	+	5.52282i	−0.0838094	+	0.194292i
$809$	−22.5844			−0.794027			−0.397013	−	0.917813i	$-0.629953\pi$
$809$	−22.5844			−0.794027			−0.397013	+	0.917813i	$0.629953\pi$
$810$		0			0
$811$	15.6809			0.550631			0.275315	−	0.961354i	$-0.411218\pi$
$811$	15.6809			0.550631			0.275315	+	0.961354i	$0.411218\pi$
$812$	15.6684	−	36.3234i	0.549852	−	1.27470i
$813$		0			0
$814$	−0.712586	−	0.755297i	−0.0249761	−	0.0264731i
$815$	−1.09350	−	18.7747i	−0.0383036	−	0.657648i
$816$		0			0
$817$	−5.28206	−	1.25187i	−0.184796	−	0.0437975i
$818$	0.643582	−	0.234245i	0.0225023	−	0.00819017i
$819$		0			0
$820$	−0.445977	−	0.162322i	−0.0155742	−	0.00566854i
$821$	−42.7110	−	28.0914i	−1.49062	−	0.980398i	−0.993636	−	0.112640i	$-0.964069\pi$
$821$	−42.7110	−	28.0914i	−1.49062	−	0.980398i	−0.496987	−	0.867758i	$-0.665560\pi$
$822$		0			0
$823$	−3.27526	−	0.382822i	−0.114168	−	0.0133444i	0.0588169	−	0.998269i	$-0.481267\pi$
$823$	−3.27526	−	0.382822i	−0.114168	−	0.0133444i	−0.172985	+	0.984924i	$0.555341\pi$
$824$	0.425695	−	0.571808i	0.0148298	−	0.0199199i
$825$		0			0
$826$	2.65326	−	45.5547i	0.0923187	−	1.58505i
$827$	15.7734	−	13.2354i	0.548494	−	0.460241i	−0.325937	−	0.945392i	$-0.605680\pi$
$827$	15.7734	−	13.2354i	0.548494	−	0.460241i	0.874431	+	0.485151i	$0.161235\pi$
$828$		0			0
$829$	10.1320	+	8.50174i	0.351898	+	0.295278i	0.801552	−	0.597925i	$-0.204008\pi$
$829$	10.1320	+	8.50174i	0.351898	+	0.295278i	−0.449654	+	0.893203i	$0.648453\pi$
$830$	−4.98303	+	5.28170i	−0.172964	+	0.183331i
$831$		0			0
$832$	−5.94279	+	3.90864i	−0.206029	+	0.135508i
$833$	−76.8553	+	18.2150i	−2.66288	+	0.631113i
$834$		0			0
$835$	−48.1125	+	5.62355i	−1.66500	+	0.194611i
$836$	−2.55486	+	4.42514i	−0.0883616	+	0.153047i
$837$		0			0
$838$	9.94002	+	17.2166i	0.343372	+	0.594738i
$839$	3.76755	+	5.06069i	0.130070	+	0.174715i	0.862387	−	0.506249i	$-0.168968\pi$
$839$	3.76755	+	5.06069i	0.130070	+	0.174715i	−0.732317	+	0.680964i	$0.761561\pi$
$840$		0			0
$841$	−1.17876	+	3.93732i	−0.0406468	+	0.135770i
$842$	11.7895	+	5.92091i	0.406293	+	0.204048i
$843$		0			0
$844$	−9.46718	−	31.6226i	−0.325874	−	1.08849i
$845$	4.00870	−	22.7345i	0.137903	−	0.782089i
$846$		0			0
$847$	−6.90630	−	39.1676i	−0.237303	−	1.34581i
$848$	5.95656	−	2.99150i	0.204549	−	0.102728i
$849$		0			0
$850$	−3.81587	−	8.84618i	−0.130883	−	0.303421i
$851$	−0.203877	−	0.472640i	−0.00698881	−	0.0162019i
$852$		0			0
$853$	16.1960	−	8.13394i	0.554540	−	0.278501i	−0.149380	−	0.988780i	$-0.547728\pi$
$853$	16.1960	−	8.13394i	0.554540	−	0.278501i	0.703920	+	0.710279i	$0.251431\pi$
$854$	5.39614	+	30.6030i	0.184652	+	1.04721i
$855$		0			0
$856$	4.60327	−	26.1064i	0.157336	−	0.892299i
$857$	9.75342	+	32.5787i	0.333170	+	1.11287i	0.946409	+	0.322969i	$0.104681\pi$
$857$	9.75342	+	32.5787i	0.333170	+	1.11287i	−0.613239	+	0.789897i	$0.710134\pi$
$858$		0			0
$859$	42.5333	+	21.3610i	1.45122	+	0.728828i	0.987568	−	0.157191i	$-0.0502437\pi$
$859$	42.5333	+	21.3610i	1.45122	+	0.728828i	0.463649	+	0.886019i	$0.346540\pi$
$860$	−2.80728	+	9.37696i	−0.0957274	+	0.319752i
$861$		0			0
$862$	12.3972	+	16.6523i	0.422249	+	0.567179i
$863$	26.7851	+	46.3932i	0.911777	+	1.57924i	0.811553	+	0.584279i	$0.198623\pi$
$863$	26.7851	+	46.3932i	0.911777	+	1.57924i	0.100224	+	0.994965i	$0.468044\pi$
$864$		0			0
$865$	−19.1455	+	33.1610i	−0.650966	+	1.12751i
$866$	9.84517	−	1.15074i	0.334553	−	0.0391036i
$867$		0			0
$868$	39.3386	−	9.32341i	1.33524	−	0.316457i
$869$	−10.1782	+	6.69434i	−0.345273	+	0.227090i
$870$		0			0
$871$	0.693411	−	0.734973i	0.0234953	−	0.0249036i
$872$	27.3512	+	22.9504i	0.926227	+	0.777197i
$873$		0			0
$874$	0.872065	−	0.731749i	0.0294980	−	0.0247518i
$875$	−1.80722	+	31.0288i	−0.0610952	+	1.04896i
$876$		0			0
$877$	−8.57919	+	11.5239i	−0.289699	+	0.389133i	−0.923017	−	0.384758i	$-0.874285\pi$
$877$	−8.57919	+	11.5239i	−0.289699	+	0.389133i	0.633319	+	0.773891i	$0.281692\pi$
$878$	−6.88216	−	0.804409i	−0.232262	−	0.0271475i
$879$		0			0
$880$	2.68315	+	1.76474i	0.0904491	+	0.0594893i
$881$	0.647962	+	0.235839i	0.0218304	+	0.00794561i	0.352912	−	0.935656i	$-0.385191\pi$
$881$	0.647962	+	0.235839i	0.0218304	+	0.00794561i	−0.331082	+	0.943602i	$0.607414\pi$
$882$		0			0
$883$	−23.8383	+	8.67642i	−0.802222	+	0.291985i	−0.710407	−	0.703791i	$-0.751489\pi$
$883$	−23.8383	+	8.67642i	−0.802222	+	0.291985i	−0.0918148	+	0.995776i	$0.529267\pi$
$884$	12.9172	+	3.06143i	0.434452	+	0.102967i
$885$		0			0
$886$	0.697022	+	11.9674i	0.0234169	+	0.402053i
$887$	−28.6258	−	30.3415i	−0.961159	−	1.01877i	−0.999810	−	0.0195164i	$-0.993787\pi$
$887$	−28.6258	−	30.3415i	−0.961159	−	1.01877i	0.0386504	−	0.999253i	$-0.487694\pi$
$888$		0			0
$889$	−20.6229	+	47.8093i	−0.691670	+	1.60347i
$890$	−11.0236			−0.369513
$891$		0			0
$892$	−16.5109			−0.552824
$893$	−1.43415	+	3.32473i	−0.0479920	+	0.111258i
$894$		0			0
$895$	4.14399	+	4.39238i	0.138518	+	0.146821i
$896$	2.63961	+	45.3204i	0.0881832	+	1.51405i
$897$		0			0
$898$	−0.947806	−	0.224634i	−0.0316287	−	0.00749613i
$899$	−31.7972	+	11.5732i	−1.06050	+	0.385989i
$900$		0			0
$901$	41.8245	+	15.2229i	1.39338	+	0.507147i
$902$	−0.141110	−	0.0928095i	−0.00469845	−	0.00309022i
$903$		0			0
$904$	1.06039	+	0.123941i	0.0352679	+	0.00412223i
$905$	38.4753	−	51.6813i	1.27896	−	1.71794i
$906$		0			0
$907$	2.30839	−	39.6335i	0.0766487	−	1.31601i	−0.712442	−	0.701731i	$-0.752411\pi$
$907$	2.30839	−	39.6335i	0.0766487	−	1.31601i	0.789091	−	0.614277i	$-0.210552\pi$
$908$	26.5448	−	22.2737i	0.880920	−	0.739180i
$909$		0			0
$910$	−18.1781	−	15.2532i	−0.602598	−	0.505640i
$911$	−27.0333	+	28.6536i	−0.895653	+	0.949337i	−0.998973	−	0.0453115i	$-0.985572\pi$
$911$	−27.0333	+	28.6536i	−0.895653	+	0.949337i	0.103320	+	0.994648i	$0.467053\pi$
$912$		0			0
$913$	4.80369	−	3.15943i	0.158979	−	0.104562i
$914$	23.7433	−	5.62726i	0.785358	−	0.186133i
$915$		0			0
$916$	−35.3231	+	4.12868i	−1.16711	+	0.136416i
$917$	−33.5082	+	58.0379i	−1.10654	+	1.91658i
$918$		0			0
$919$	7.97650	+	13.8157i	0.263120	+	0.455738i	0.967069	−	0.254513i	$-0.0819150\pi$
$919$	7.97650	+	13.8157i	0.263120	+	0.455738i	−0.703949	+	0.710250i	$0.748582\pi$
$920$	−3.00249	−	4.03305i	−0.0989893	−	0.132966i
$921$		0			0
$922$	3.82638	−	12.7810i	0.126015	−	0.420920i
$923$	−23.6578	−	11.8814i	−0.778706	−	0.391081i
$924$		0			0
$925$	−0.601020	−	2.00755i	−0.0197614	−	0.0660077i
$926$	4.88017	−	27.6768i	0.160372	−	0.909516i
$927$		0			0
$928$	−5.84117	−	33.1269i	−0.191746	−	1.08744i
$929$	−22.4314	+	11.2654i	−0.735949	+	0.369607i	−0.776959	−	0.629551i	$-0.783239\pi$
$929$	−22.4314	+	11.2654i	−0.735949	+	0.369607i	0.0410101	+	0.999159i	$0.486942\pi$
$930$		0			0
$931$	−15.0497	−	34.8890i	−0.493233	−	1.14344i
$932$	−4.99166	−	11.5720i	−0.163507	−	0.379053i
$933$		0			0
$934$	−29.5712	+	14.8512i	−0.967600	+	0.485947i
$935$	3.72378	+	21.1186i	0.121781	+	0.690652i
$936$		0			0
$937$	−6.76540	+	38.3685i	−0.221016	+	1.25344i	0.649140	+	0.760669i	$0.275129\pi$
$937$	−6.76540	+	38.3685i	−0.221016	+	1.25344i	−0.870156	+	0.492776i	$0.835982\pi$
$938$	0.523746	+	1.74943i	0.0171009	+	0.0571211i
$939$		0			0
$940$	5.83446	+	2.93018i	0.190299	+	0.0955719i
$941$	−9.48562	+	31.6842i	−0.309222	+	1.03287i	0.652257	+	0.757998i	$0.273822\pi$
$941$	−9.48562	+	31.6842i	−0.309222	+	1.03287i	−0.961480	+	0.274877i	$0.911363\pi$
$942$		0			0
$943$	−0.0499957	−	0.0671559i	−0.00162808	−	0.00218690i
$944$	3.85915	+	6.68424i	0.125605	+	0.217554i
$945$		0			0
$946$	−1.74166	+	3.01664i	−0.0566261	+	0.0980793i
$947$	−14.4062	+	1.68384i	−0.468138	+	0.0547175i	−0.346892	−	0.937905i	$-0.612763\pi$
$947$	−14.4062	+	1.68384i	−0.468138	+	0.0547175i	−0.121246	+	0.992623i	$0.538689\pi$
$948$		0			0
$949$	4.52218	−	1.07178i	0.146796	−	0.0347913i
$950$	3.87217	−	2.54677i	0.125630	−	0.0826280i
$951$		0			0
$952$	−40.3276	+	42.7447i	−1.30702	+	1.38536i
$953$	−4.46031	−	3.74265i	−0.144484	−	0.121236i	0.567681	−	0.823249i	$-0.307841\pi$
$953$	−4.46031	−	3.74265i	−0.144484	−	0.121236i	−0.712165	+	0.702012i	$0.752285\pi$
$954$		0			0
$955$	46.7081	−	39.1928i	1.51144	−	1.26825i
$956$	−1.74578	+	29.9739i	−0.0564626	+	0.969426i
$957$		0			0
$958$	16.9723	−	22.7977i	0.548349	−	0.736560i
$959$	70.7588	+	8.27052i	2.28492	+	0.267069i
$960$		0			0
$961$	−2.99255	−	1.96823i	−0.0965338	−	0.0634913i
$962$	−1.21952	−	0.443868i	−0.0393188	−	0.0143109i
$963$		0			0
$964$	17.9774	−	6.54323i	0.579013	−	0.210743i
$965$	19.5567	+	4.63503i	0.629553	+	0.149207i
$966$		0			0
$967$	2.65664	+	45.6128i	0.0854319	+	1.46681i	0.720017	+	0.693956i	$0.244134\pi$
$967$	2.65664	+	45.6128i	0.0854319	+	1.46681i	−0.634585	+	0.772853i	$0.718829\pi$
$968$	−14.5803	−	15.4542i	−0.468629	−	0.496718i
$969$		0			0
$970$	6.52324	−	15.1226i	0.209449	−	0.485557i
$971$	1.52462			0.0489275			0.0244638	−	0.999701i	$-0.492212\pi$
$971$	1.52462			0.0489275			0.0244638	+	0.999701i	$0.492212\pi$
$972$		0			0
$973$	−1.61337			−0.0517222
$974$	8.69894	−	20.1664i	0.278732	−	0.646173i
$975$		0			0
$976$	−3.60697	−	3.82317i	−0.115456	−	0.122377i
$977$	−1.18583	−	20.3600i	−0.0379382	−	0.651373i	−0.962657	−	0.270723i	$-0.912737\pi$
$977$	−1.18583	−	20.3600i	−0.0379382	−	0.651373i	0.924719	−	0.380650i	$-0.124300\pi$
$978$		0			0
$979$	8.49328	+	2.01294i	0.271446	+	0.0643339i
$980$	−64.3814	+	23.4329i	−2.05659	+	0.748537i
$981$		0			0
$982$	−16.0966	−	5.85868i	−0.513662	−	0.186958i
$983$	−35.2278	−	23.1697i	−1.12359	−	0.738999i	−0.155065	−	0.987904i	$-0.549559\pi$
$983$	−35.2278	−	23.1697i	−1.12359	−	0.738999i	−0.968528	+	0.248906i	$0.919929\pi$
$984$		0			0
$985$	45.3864	+	5.30491i	1.44613	+	0.169029i
$986$	11.9913	−	16.1071i	0.381880	−	0.512954i
$987$		0			0
$988$	−0.371321	+	6.37534i	−0.0118133	+	0.202826i
$989$	−1.32273	+	1.10990i	−0.0420604	+	0.0352929i
$990$		0			0
$991$	−1.19365	−	1.00159i	−0.0379176	−	0.0318167i	0.623632	−	0.781718i	$-0.285656\pi$
$991$	−1.19365	−	1.00159i	−0.0379176	−	0.0318167i	−0.661550	+	0.749901i	$0.730101\pi$
$992$	23.5912	−	25.0053i	0.749023	−	0.793918i
$993$		0			0
$994$	39.9740	−	26.2913i	1.26790	−	0.833911i
$995$	21.8712	−	5.18357i	0.693364	−	0.164330i
$996$		0			0
$997$	51.9826	−	6.07590i	1.64631	−	0.192426i	0.758187	−	0.652037i	$-0.226085\pi$
$997$	51.9826	−	6.07590i	1.64631	−	0.192426i	0.888120	+	0.459612i	$0.152011\pi$
$998$	1.17509	−	2.03532i	0.0371970	−	0.0644270i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.c.55.6		144
3.2	odd	2		729.2.g.b.55.3		144
9.2	odd	6		729.2.g.a.298.6		144
9.4	even	3		81.2.g.a.7.6	✓	144
9.5	odd	6		243.2.g.a.100.3		144
9.7	even	3		729.2.g.d.298.3		144
81.4	even	27		81.2.g.a.58.6	yes	144
81.23	odd	54		729.2.g.a.433.6		144
81.29	odd	54		6561.2.a.d.1.25		72
81.31	even	27	inner	729.2.g.c.676.6		144
81.50	odd	54		729.2.g.b.676.3		144
81.52	even	27		6561.2.a.c.1.48		72
81.58	even	27		729.2.g.d.433.3		144
81.77	odd	54		243.2.g.a.226.3		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.7.6	✓	144	9.4	even	3
81.2.g.a.58.6	yes	144	81.4	even	27
243.2.g.a.100.3		144	9.5	odd	6
243.2.g.a.226.3		144	81.77	odd	54
729.2.g.a.298.6		144	9.2	odd	6
729.2.g.a.433.6		144	81.23	odd	54
729.2.g.b.55.3		144	3.2	odd	2
729.2.g.b.676.3		144	81.50	odd	54
729.2.g.c.55.6		144	1.1	even	1	trivial
729.2.g.c.676.6		144	81.31	even	27	inner
729.2.g.d.298.3		144	9.7	even	3
729.2.g.d.433.3		144	81.58	even	27
6561.2.a.c.1.48		72	81.52	even	27
6561.2.a.d.1.25		72	81.29	odd	54

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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.311913 - 0.723096i) q^{2} +(0.946905 + 1.00366i) q^{4} +(0.161980 + 2.78108i) q^{5} +(4.84803 + 1.14900i) q^{7} +(2.50111 - 0.910331i) q^{8} +O(q^{10})\)	\(q+(0.311913 - 0.723096i) q^{2} +(0.946905 + 1.00366i) q^{4} +(0.161980 + 2.78108i) q^{5} +(4.84803 + 1.14900i) q^{7} +(2.50111 - 0.910331i) q^{8} +(2.06152 + 0.750330i) q^{10} +(-1.45131 - 0.954539i) q^{11} +(-2.15633 - 0.252038i) q^{13} +(2.34301 - 3.14720i) q^{14} +(-0.0385876 + 0.662524i) q^{16} +(-3.39468 + 2.84848i) q^{17} +(-1.63306 - 1.37030i) q^{19} +(-2.63789 + 2.79600i) q^{20} +(-1.14291 + 0.751701i) q^{22} +(-0.659824 + 0.156381i) q^{23} +(-2.74200 + 0.320494i) q^{25} +(-0.854835 + 1.48062i) q^{26} +(3.43741 + 5.95378i) q^{28} +(-3.43613 - 4.61552i) q^{29} +(1.68658 - 5.63358i) q^{31} +(5.22407 + 2.62363i) q^{32} +(1.00088 + 3.34316i) q^{34} +(-2.41020 + 13.6689i) q^{35} +(0.131814 + 0.747552i) q^{37} +(-1.50023 + 0.753445i) q^{38} +(2.93684 + 6.80835i) q^{40} +(0.0489024 + 0.113369i) q^{41} +(2.27552 - 1.14281i) q^{43} +(-0.416216 - 2.36048i) q^{44} +(-0.0927292 + 0.525894i) q^{46} +(-0.487133 - 1.62714i) q^{47} +(15.9278 + 7.99922i) q^{49} +(-0.623519 + 2.08270i) q^{50} +(-1.78887 - 2.40288i) q^{52} +(-5.02192 - 8.69822i) q^{53} +(2.41957 - 4.19082i) q^{55} +(13.1715 - 1.53952i) q^{56} +(-4.40924 + 1.04501i) q^{58} +(9.71683 - 6.39086i) q^{59} +(-5.43508 + 5.76085i) q^{61} +(-3.54755 - 2.97675i) q^{62} +(2.50983 - 2.10599i) q^{64} +(0.351659 - 6.03775i) q^{65} +(-0.277935 + 0.373331i) q^{67} +(-6.07334 - 0.709872i) q^{68} +(9.13216 + 6.00632i) q^{70} +(11.4588 + 4.17067i) q^{71} +(-2.01159 + 0.732160i) q^{73} +(0.581667 + 0.137858i) q^{74} +(-0.171036 - 2.93658i) q^{76} +(-5.93921 - 6.29519i) q^{77} +(2.77777 - 6.43960i) q^{79} -1.84879 q^{80} +0.0972297 q^{82} +(-1.31099 + 3.03921i) q^{83} +(-8.47172 - 8.97950i) q^{85} +(-0.116596 - 2.00188i) q^{86} +(-4.49883 - 1.06624i) q^{88} +(-4.72182 + 1.71860i) q^{89} +(-10.1643 - 3.69952i) q^{91} +(-0.781744 - 0.514161i) q^{92} +(-1.32852 - 0.155282i) q^{94} +(3.54640 - 4.76364i) q^{95} +(0.436507 - 7.49453i) q^{97} +(10.7523 - 9.02224i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10}) \) 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} - 63 q^{20} + 9 q^{22} + 36 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28} - 45 q^{29} + 9 q^{31} + 63 q^{32} + 9 q^{34} + 9 q^{35} - 18 q^{37} - 9 q^{38} + 9 q^{40} - 27 q^{41} + 9 q^{43} + 54 q^{44} - 18 q^{46} + 63 q^{47} + 9 q^{49} - 225 q^{50} + 27 q^{52} + 45 q^{53} - 9 q^{55} + 99 q^{56} + 9 q^{58} - 117 q^{59} + 9 q^{61} + 81 q^{62} - 18 q^{64} + 81 q^{65} + 36 q^{67} - 18 q^{68} + 63 q^{70} - 90 q^{71} - 18 q^{73} + 81 q^{74} + 90 q^{76} + 81 q^{77} + 63 q^{79} - 288 q^{80} - 36 q^{82} + 45 q^{83} + 63 q^{85} + 81 q^{86} + 90 q^{88} - 81 q^{89} - 18 q^{91} - 63 q^{92} + 63 q^{94} + 153 q^{95} + 36 q^{97} + 81 q^{98}+O(q^{100}) \) 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8 - 18 * q^10 + 9 * q^11 + 9 * q^13 + 9 * q^14 + 9 * q^16 - 18 * q^17 - 18 * q^19 - 63 * q^20 + 9 * q^22 + 36 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 - 45 * q^29 + 9 * q^31 + 63 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 - 9 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 + 63 * q^47 + 9 * q^49 - 225 * q^50 + 27 * q^52 + 45 * q^53 - 9 * q^55 + 99 * q^56 + 9 * q^58 - 117 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 + 81 * q^65 + 36 * q^67 - 18 * q^68 + 63 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 + 90 * q^76 + 81 * q^77 + 63 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 + 63 * q^85 + 81 * q^86 + 90 * q^88 - 81 * q^89 - 18 * q^91 - 63 * q^92 + 63 * q^94 + 153 * q^95 + 36 * q^97 + 81 * q^98

Introduction

L-functions

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Database

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