LMFDB - Embedded newform 729.2.g.b.55.3

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			55.3
Character	$\chi$	$=$	729.55
Dual form			729.2.g.b.676.3

$q$-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	−0.992186	−	0.124765i	$-0.960182\pi$
$2$	−0.311913	+	0.723096i	−0.220556	+	0.511306i	0.771630	+	0.636071i	$0.219442\pi$
$3$		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	$-0.804463\pi$
$5$	−0.161980	−	2.78108i	−0.0724395	−	1.24374i	0.744740	−	0.667355i	$-0.232574\pi$
$6$		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	0.749125	−	0.662429i	$-0.230474\pi$
$11$	1.45131	+	0.954539i	0.437585	+	0.287804i	−0.311540	+	0.950233i	$0.600845\pi$
$12$		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	−0.130419	−	0.991459i	$-0.541632\pi$
$17$	3.39468	−	2.84848i	0.823331	−	0.690857i	0.953750	+	0.300602i	$0.0971877\pi$
$18$		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	−0.161247	−	0.986914i	$-0.551552\pi$
$23$	0.659824	−	0.156381i	0.137583	−	0.0326077i	0.298830	+	0.954306i	$0.403404\pi$
$24$		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	0.997089	−	0.0762510i	$-0.0242950\pi$
$29$	3.43613	+	4.61552i	0.638073	+	0.857080i	−0.359016	+	0.933331i	$0.616888\pi$
$30$		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	0.914355	−	0.404914i	$-0.132699\pi$
$41$	−0.0489024	−	0.113369i	−0.00763727	−	0.0177052i	−0.921992	+	0.387209i	$0.873439\pi$
$42$		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	0.986139	−	0.165923i	$-0.0530604\pi$
$47$	0.487133	+	1.62714i	0.0710556	+	0.237342i	−0.915083	+	0.403265i	$0.867875\pi$
$48$		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	$0.0756410\pi$
$53$	5.02192	+	8.69822i	0.689814	+	1.19479i	−0.282084	+	0.959390i	$0.591026\pi$
$54$		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	−0.991533	−	0.129855i	$-0.958549\pi$
$59$	−9.71683	+	6.39086i	−1.26502	+	0.832019i	−0.273491	+	0.961875i	$0.588178\pi$
$60$		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	−0.443885	−	0.896084i	$-0.646400\pi$
$71$	−11.4588	−	4.17067i	−1.35991	−	0.494968i	−0.916027	+	0.401116i	$0.868622\pi$
$72$		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	−0.830989	−	0.556288i	$-0.812225\pi$
$83$	1.31099	−	3.03921i	0.143899	−	0.333596i	0.974889	+	0.222692i	$0.0714843\pi$
$84$		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	−0.0794124	−	0.996842i	$-0.525304\pi$
$89$	4.72182	−	1.71860i	0.500512	−	0.182171i	0.579924	+	0.814670i	$0.303082\pi$
$90$		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	−0.645609	−	0.763668i	$-0.723396\pi$
$101$	1.55076	−	1.64371i	0.154307	−	0.163555i	0.799915	+	0.600113i	$0.204878\pi$
$102$		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	−0.999773	−	0.0213201i	$-0.993213\pi$
$107$	−4.97987	+	8.62539i	−0.481423	+	0.833848i	0.518350	+	0.855169i	$0.326546\pi$
$108$		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	0.431859	−	0.901941i	$-0.357858\pi$
$113$	−0.358445	−	0.180018i	−0.0337196	−	0.0169346i	−0.465579	+	0.885006i	$0.654154\pi$
$114$		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	$-0.707480\pi$
$131$	3.85774	−	12.8857i	0.337052	−	1.12583i	0.943684	−	0.330849i	$-0.107335\pi$
$132$		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	−0.698597	−	0.715515i	$-0.746192\pi$
$137$	−14.2020	+	1.65997i	−1.21335	+	0.141821i	−0.514757	+	0.857336i	$0.672118\pi$
$138$		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	−0.0100596	−	0.999949i	$-0.503202\pi$
$149$	−3.05716	−	0.357331i	−0.250452	−	0.0292737i	−0.240393	+	0.970676i	$0.577276\pi$
$150$		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	$-0.783623\pi$
$167$	−1.01103	−	17.3588i	−0.0782362	−	1.34326i	0.699482	−	0.714651i	$-0.253414\pi$
$168$		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	0.0319801	−	0.999489i	$-0.489819\pi$
$173$	−11.4838	−	7.55304i	−0.873100	−	0.574247i	−0.905080	+	0.425242i	$0.860189\pi$
$174$		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	−0.702732	−	0.711455i	$-0.748037\pi$
$179$	−1.66053	+	1.39335i	−0.124114	+	0.104144i	0.578618	+	0.815599i	$0.303592\pi$
$180$		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	$0.0871775\pi$
$191$	13.0701	+	17.5562i	0.945719	+	1.27032i	−0.0170111	+	0.999855i	$0.505415\pi$
$192$		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	$0.254199\pi$
$197$	−2.84835	+	16.1538i	−0.202936	+	1.15091i	−0.900654	+	0.434537i	$0.856912\pi$
$198$		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	$0.332127\pi$
$227$	−1.46018	+	25.0704i	−0.0969158	+	1.66398i	−0.600194	+	0.799855i	$0.704910\pi$
$228$		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	0.607488	−	0.794329i	$-0.292177\pi$
$233$	8.58260	+	3.12381i	0.562265	+	0.204648i	−0.0452226	+	0.998977i	$0.514400\pi$
$234$		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	$-0.992247\pi$
$239$	−14.9323	−	15.8273i	−0.965890	−	1.02378i	0.0338130	−	0.999428i	$-0.489235\pi$
$240$		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	−0.00604584	−	0.999982i	$-0.501924\pi$
$251$	10.0143	−	3.64492i	0.632099	−	0.230065i	0.638144	+	0.769917i	$0.279702\pi$
$252$		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	−0.779690	−	0.626166i	$-0.784623\pi$
$257$	0.701983	−	0.942927i	0.0437885	−	0.0588181i	0.823478	+	0.567348i	$0.192031\pi$
$258$		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	−0.499150	−	0.866515i	$-0.666354\pi$
$263$	6.40456	−	6.78844i	0.394922	−	0.418593i	0.894072	+	0.447922i	$0.147836\pi$
$264$		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	−0.825360	−	0.564607i	$-0.809028\pi$
$269$	1.25116	−	2.16707i	0.0762845	−	0.132129i	0.901644	+	0.432479i	$0.142361\pi$
$270$		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	$0.740099\pi$
$281$	−28.1325	+	14.1287i	−1.67824	+	0.842846i	−0.993470	+	0.114090i	$0.963605\pi$
$282$		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	−0.920765	−	0.390118i	$-0.872434\pi$
$293$	1.07661	−	3.59613i	0.0628962	−	0.210088i	0.983661	+	0.180030i	$0.0576194\pi$
$294$		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	0.240432	−	0.970666i	$-0.422711\pi$
$311$	4.41818	+	0.516411i	0.250532	+	0.0292830i	0.0101001	+	0.999949i	$0.496785\pi$
$312$		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	0.904329	−	0.426836i	$-0.140372\pi$
$317$	27.0789	+	6.41782i	1.52090	+	0.360461i	0.616575	+	0.787297i	$0.288520\pi$
$318$		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	−0.772140	−	0.635453i	$-0.780814\pi$
$347$	−21.9243	+	5.19616i	−1.17696	+	0.278944i	−0.404819	+	0.914397i	$0.632665\pi$
$348$		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	0.993295	−	0.115610i	$-0.0368824\pi$
$353$	11.2290	+	15.0832i	0.597661	+	0.802798i	−0.395634	+	0.918408i	$0.629475\pi$
$354$		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	$-0.865652\pi$
$359$	1.61227	−	9.14366i	0.0850926	−	0.482584i	0.997337	−	0.0729368i	$-0.0232371\pi$
$360$		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	−0.785671	−	0.618645i	$-0.787682\pi$
$383$	−10.3490	+	6.80665i	−0.528810	+	0.347804i	0.256861	+	0.966448i	$0.417312\pi$
$384$		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	$-0.825378\pi$
$389$	1.08026	−	18.5473i	0.0547712	−	0.940386i	0.908032	−	0.418901i	$-0.137585\pi$
$390$		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	0.761041	−	0.648703i	$-0.224688\pi$
$401$	1.38543	+	1.46847i	0.0691851	+	0.0733319i	−0.691856	+	0.722035i	$0.743207\pi$
$402$		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	$-0.584791\pi$
$419$	15.0749	−	20.2492i	0.736459	−	0.989236i	0.999700	−	0.0245058i	$-0.00780121\pi$
$420$		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	$-0.614370\pi$
$431$	13.1811	−	22.8303i	0.634911	−	1.09970i	0.986534	−	0.163556i	$-0.0522966\pi$
$432$		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	−0.0952714	−	0.995451i	$-0.530372\pi$
$443$	13.6033	−	6.83182i	0.646311	−	0.324590i	0.741582	+	0.670862i	$0.234076\pi$
$444$		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	0.989456	−	0.144831i	$-0.0462639\pi$
$449$	0.214786	+	1.21811i	0.0101364	+	0.0574862i	−0.979320	+	0.202317i	$0.935153\pi$
$450$		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	−0.498531	−	0.866872i	$-0.666127\pi$
$461$	−16.8270	+	1.96679i	−0.783710	+	0.0916026i	−0.285179	+	0.958474i	$0.592053\pi$
$462$		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	$0.147036\pi$
$467$	32.1894	+	27.0101i	1.48955	+	1.24988i	0.594353	+	0.804204i	$0.297408\pi$
$468$		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	−0.671804	−	0.740729i	$-0.734480\pi$
$479$	−35.1181	−	8.32315i	−1.60459	−	0.380295i	−0.932785	+	0.360434i	$0.882629\pi$
$480$		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	$0.144786\pi$
$491$	1.26476	+	21.7151i	0.0570777	+	0.979987i	−0.841246	+	0.540653i	$0.818177\pi$
$492$		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	$-0.374123\pi$
$503$	30.5223	−	25.6113i	1.36092	−	1.14195i	0.975696	−	0.219128i	$-0.0703214\pi$
$504$		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	0.222832	−	0.974857i	$-0.428470\pi$
$509$	19.3907	−	4.59567i	0.859476	−	0.203700i	0.636645	+	0.771157i	$0.280322\pi$
$510$		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	$-0.660392\pi$
$521$	6.17183	−	35.0022i	0.270393	−	1.53347i	0.753226	−	0.657762i	$-0.228497\pi$
$522$		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	0.249013	−	0.968500i	$-0.419894\pi$
$557$	−4.31357	−	1.57001i	−0.182772	−	0.0665235i	−0.431785	+	0.901977i	$0.642116\pi$
$558$		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	0.741547	−	0.670901i	$-0.234092\pi$
$563$	0.680134	+	0.720900i	0.0286642	+	0.0303823i	−0.712883	+	0.701283i	$0.752611\pi$
$564$		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	−0.841457	−	0.540325i	$-0.818301\pi$
$569$	3.07723	−	7.13381i	0.129004	−	0.299065i	0.970461	+	0.241260i	$0.0775606\pi$
$570$		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	−0.561150	−	0.827714i	$-0.689641\pi$
$587$	7.21493	−	7.64738i	0.297792	−	0.315641i	0.858942	+	0.512073i	$0.171122\pi$
$588$		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	$0.361910\pi$
$593$	−14.0175	+	24.2790i	−0.575630	+	0.997020i	−0.995973	+	0.0896551i	$0.971424\pi$
$594$		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	0.819685	−	0.572814i	$-0.194148\pi$
$599$	20.7959	+	10.4441i	0.849699	+	0.426735i	0.0300143	+	0.999549i	$0.490445\pi$
$600$		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	$-0.774046\pi$
$617$	5.79638	−	19.3612i	0.233353	−	0.779454i	0.991809	−	0.127730i	$-0.0407690\pi$
$618$		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	0.679165	−	0.733986i	$-0.262342\pi$
$641$	24.2211	+	5.74051i	0.956676	+	0.226736i	0.277512	+	0.960722i	$0.410490\pi$
$642$		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	$-0.674685\pi$
$647$	−26.5378			−1.04331			−0.521654	+	0.853157i	$0.674685\pi$
$648$		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	0.998541	−	0.0539986i	$-0.0171966\pi$
$653$	0.0123406	+	0.211880i	0.000482926	+	0.00829152i	−0.998058	+	0.0622901i	$0.980160\pi$
$654$		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	0.0263011	−	0.999654i	$-0.491627\pi$
$659$	−22.6208	−	14.8779i	−0.881180	−	0.579561i	−0.907481	+	0.420093i	$0.861998\pi$
$660$		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	0.600369	−	0.799723i	$-0.295021\pi$
$677$	−8.79309	−	11.8112i	−0.337946	−	0.453940i	−0.938314	+	0.345783i	$0.887613\pi$
$678$		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	−0.995931	−	0.0901204i	$-0.971275\pi$
$683$	−0.764140	+	4.33365i	−0.0292390	+	0.165823i	0.966692	+	0.255943i	$0.0823859\pi$
$684$		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	$0.137354\pi$
$701$	21.6147	+	37.4378i	0.816377	+	1.41401i	−0.0919585	+	0.995763i	$0.529313\pi$
$702$		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	0.513831	−	0.857892i	$-0.328226\pi$
$719$	9.54600	+	3.47446i	0.356006	+	0.129576i	−0.157825	+	0.987467i	$0.550448\pi$
$720$		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	−0.980320	−	0.197416i	$-0.936745\pi$
$743$	−13.9026	+	18.6745i	−0.510039	+	0.685101i	0.470281	+	0.882517i	$0.344152\pi$
$744$		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	−0.360944	−	0.932588i	$-0.617545\pi$
$761$	−36.5389	−	18.3505i	−1.32453	−	0.665206i	−0.963591	+	0.267381i	$0.913842\pi$
$762$		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	$0.190748\pi$
$773$	6.74796	+	38.2696i	0.242707	+	1.37646i	−0.583050	+	0.812436i	$0.698141\pi$
$774$		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
$783$

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

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