LMFDB - Embedded newform 810.2.s.a.557.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [810,2,Mod(17,810)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(810, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([22, 9]))

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

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

chi := DirichletCharacter("810.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	810.s (of order $36$, degree $12$, 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:	$6.46788256372$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$18$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 270)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			557.4
Character	$\chi$	$=$	810.557
Dual form			810.2.s.a.413.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.819152 - 0.573576i) q^{2} +(0.342020 + 0.939693i) q^{4} +(-0.377073 - 2.20405i) q^{5} +(-0.0768670 - 0.164842i) q^{7} +(0.258819 - 0.965926i) q^{8} +(-0.955308 + 2.02173i) q^{10} +(2.21054 + 2.63442i) q^{11} +(3.54611 + 5.06437i) q^{13} +(-0.0315836 + 0.179120i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(0.798593 + 2.98039i) q^{17} +(0.822477 - 0.474857i) q^{19} +(1.94216 - 1.10816i) q^{20} +(-0.299728 - 3.42591i) q^{22} +(-0.772585 - 0.360262i) q^{23} +(-4.71563 + 1.66217i) q^{25} -6.18246i q^{26} +(0.128611 - 0.128611i) q^{28} +(-1.73494 - 9.83931i) q^{29} +(7.86334 - 2.86202i) q^{31} +(0.996195 - 0.0871557i) q^{32} +(1.05531 - 2.89945i) q^{34} +(-0.334334 + 0.231576i) q^{35} +(5.53359 - 1.48272i) q^{37} +(-0.946100 - 0.0827730i) q^{38} +(-2.22654 - 0.206224i) q^{40} +(6.60088 + 1.16391i) q^{41} +(-0.0740273 + 0.846136i) q^{43} +(-1.71950 + 2.97826i) q^{44} +(0.426226 + 0.738246i) q^{46} +(-8.64098 + 4.02935i) q^{47} +(4.47825 - 5.33697i) q^{49} +(4.81620 + 1.34320i) q^{50} +(-3.54611 + 5.06437i) q^{52} +(-1.10856 - 1.10856i) q^{53} +(4.97285 - 5.86551i) q^{55} +(-0.179120 + 0.0315836i) q^{56} +(-4.22242 + 9.05501i) q^{58} +(8.77368 + 7.36199i) q^{59} +(0.112705 + 0.0410214i) q^{61} +(-8.08286 - 2.16580i) q^{62} +(-0.866025 - 0.500000i) q^{64} +(9.82496 - 9.72543i) q^{65} +(5.25146 - 3.67711i) q^{67} +(-2.52751 + 1.76978i) q^{68} +(0.406697 + 0.00207050i) q^{70} +(6.13397 + 3.54145i) q^{71} +(11.9795 + 3.20990i) q^{73} +(-5.38331 - 1.95936i) q^{74} +(0.727523 + 0.610464i) q^{76} +(0.264345 - 0.566890i) q^{77} +(-8.96689 + 1.58110i) q^{79} +(1.70559 + 1.44602i) q^{80} +(-4.73953 - 4.73953i) q^{82} +(-2.40418 + 3.43353i) q^{83} +(6.26778 - 2.88396i) q^{85} +(0.545964 - 0.650654i) q^{86} +(3.11679 - 1.45338i) q^{88} +(-1.77224 - 3.06962i) q^{89} +(0.562241 - 0.973831i) q^{91} +(0.0742962 - 0.849209i) q^{92} +(9.38942 + 1.65561i) q^{94} +(-1.35674 - 1.63372i) q^{95} +(-8.66511 - 0.758099i) q^{97} +(-6.72953 + 1.80317i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 24 q^{11} + 24 q^{20} - 24 q^{23} + 36 q^{25} + 108 q^{35} + 36 q^{38} + 72 q^{41} + 48 q^{47} + 48 q^{50} + 12 q^{56} + 36 q^{61} - 24 q^{65} - 72 q^{67} - 36 q^{68} + 240 q^{77} + 60 q^{83} - 72 q^{86}+ \cdots - 72 q^{97}+O(q^{100}) $ 216 * q - 24 * q^11 + 24 * q^20 - 24 * q^23 + 36 * q^25 + 108 * q^35 + 36 * q^38 + 72 * q^41 + 48 * q^47 + 48 * q^50 + 12 * q^56 + 36 * q^61 - 24 * q^65 - 72 * q^67 - 36 * q^68 + 240 * q^77 + 60 * q^83 - 72 * q^86 + 48 * q^92 + 60 * q^95 - 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{17}{18}\right)$

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 $

$2$	−0.819152	−	0.573576i	−0.579228	−	0.405580i
$2$	−0.819152	−	0.573576i	−0.579228	−	0.405580i
$3$		0			0
$3$		0			0
$4$	0.342020	+	0.939693i	0.171010	+	0.469846i
$5$	−0.377073	−	2.20405i	−0.168632	−	0.985679i
$5$	−0.377073	−	2.20405i	−0.168632	−	0.985679i
$6$		0			0
$7$	−0.0768670	−	0.164842i	−0.0290530	−	0.0623044i	0.891246	−	0.453521i	$-0.149832\pi$
$7$	−0.0768670	−	0.164842i	−0.0290530	−	0.0623044i	−0.920299	+	0.391216i	$0.872054\pi$
$8$	0.258819	−	0.965926i	0.0915064	−	0.341506i
$9$		0			0
$10$	−0.955308	+	2.02173i	−0.302095	+	0.639327i
$11$	2.21054	+	2.63442i	0.666504	+	0.794308i	0.988304	−	0.152499i	$-0.0487322\pi$
$11$	2.21054	+	2.63442i	0.666504	+	0.794308i	−0.321800	+	0.946808i	$0.604288\pi$
$12$		0			0
$13$	3.54611	+	5.06437i	0.983514	+	1.40460i	0.913399	+	0.407065i	$0.133448\pi$
$13$	3.54611	+	5.06437i	0.983514	+	1.40460i	0.0701152	+	0.997539i	$0.477663\pi$
$14$	−0.0315836	+	0.179120i	−0.00844108	+	0.0478717i
$15$		0			0
$16$	−0.766044	+	0.642788i	−0.191511	+	0.160697i
$17$	0.798593	+	2.98039i	0.193687	+	0.722850i	0.992603	+	0.121407i	$0.0387407\pi$
$17$	0.798593	+	2.98039i	0.193687	+	0.722850i	−0.798916	+	0.601443i	$0.794593\pi$
$18$		0			0
$19$	0.822477	−	0.474857i	0.188689	−	0.108940i	−0.402680	−	0.915341i	$-0.631921\pi$
$19$	0.822477	−	0.474857i	0.188689	−	0.108940i	0.591369	+	0.806401i	$0.298588\pi$
$20$	1.94216	−	1.10816i	0.434280	−	0.247792i
$21$		0			0
$22$	−0.299728	−	3.42591i	−0.0639023	−	0.730406i
$23$	−0.772585	−	0.360262i	−0.161095	−	0.0751198i	0.340398	−	0.940281i	$-0.389438\pi$
$23$	−0.772585	−	0.360262i	−0.161095	−	0.0751198i	−0.501493	+	0.865161i	$0.667216\pi$
$24$		0			0
$25$	−4.71563	+	1.66217i	−0.943126	+	0.332435i
$26$		−	6.18246i		−	1.21248i
$27$		0			0
$28$	0.128611	−	0.128611i	0.0243051	−	0.0243051i
$29$	−1.73494	−	9.83931i	−0.322170	−	1.82711i	−0.528861	−	0.848708i	$-0.677381\pi$
$29$	−1.73494	−	9.83931i	−0.322170	−	1.82711i	0.206692	−	0.978406i	$-0.433730\pi$
$30$		0			0
$31$	7.86334	−	2.86202i	1.41230	−	0.514034i	0.480494	−	0.876998i	$-0.340457\pi$
$31$	7.86334	−	2.86202i	1.41230	−	0.514034i	0.931803	+	0.362963i	$0.118235\pi$
$32$	0.996195	−	0.0871557i	0.176104	−	0.0154071i
$33$		0			0
$34$	1.05531	−	2.89945i	0.180984	−	0.497251i
$35$	−0.334334	+	0.231576i	−0.0565128	+	0.0391435i
$36$		0			0
$37$	5.53359	−	1.48272i	0.909717	−	0.243758i	0.226533	−	0.974004i	$-0.427261\pi$
$37$	5.53359	−	1.48272i	0.909717	−	0.243758i	0.683185	+	0.730246i	$0.260594\pi$
$38$	−0.946100	−	0.0827730i	−0.153478	−	0.0134276i
$39$		0			0
$40$	−2.22654	−	0.206224i	−0.352047	−	0.0326069i
$41$	6.60088	+	1.16391i	1.03088	+	0.181773i	0.663406	−	0.748259i	$-0.269110\pi$
$41$	6.60088	+	1.16391i	1.03088	+	0.181773i	0.367478	+	0.930032i	$0.380221\pi$
$42$		0			0
$43$	−0.0740273	+	0.846136i	−0.0112891	+	0.129035i	−0.999748	−	0.0224555i	$-0.992852\pi$
$43$	−0.0740273	+	0.846136i	−0.0112891	+	0.129035i	0.988459	+	0.151490i	$0.0484072\pi$
$44$	−1.71950	+	2.97826i	−0.259224	+	0.448989i
$45$		0			0
$46$	0.426226	+	0.738246i	0.0628437	+	0.108848i
$47$	−8.64098	+	4.02935i	−1.26042	+	0.587742i	−0.933929	−	0.357460i	$-0.883643\pi$
$47$	−8.64098	+	4.02935i	−1.26042	+	0.587742i	−0.326488	+	0.945201i	$0.605865\pi$
$48$		0			0
$49$	4.47825	−	5.33697i	0.639750	−	0.762424i
$50$	4.81620	+	1.34320i	0.681114	+	0.189958i
$51$		0			0
$52$	−3.54611	+	5.06437i	−0.491757	+	0.702302i
$53$	−1.10856	−	1.10856i	−0.152273	−	0.152273i	0.626859	−	0.779132i	$-0.284340\pi$
$53$	−1.10856	−	1.10856i	−0.152273	−	0.152273i	−0.779132	+	0.626859i	$0.784340\pi$
$54$		0			0
$55$	4.97285	−	5.86551i	0.670539	−	0.790905i
$56$	−0.179120	+	0.0315836i	−0.0239359	+	0.00422054i
$57$		0			0
$58$	−4.22242	+	9.05501i	−0.554431	+	1.18898i
$59$	8.77368	+	7.36199i	1.14224	+	0.958449i	0.999510	−	0.0313129i	$-0.00996885\pi$
$59$	8.77368	+	7.36199i	1.14224	+	0.958449i	0.142726	+	0.989762i	$0.454413\pi$
$60$		0			0
$61$	0.112705	+	0.0410214i	0.0144304	+	0.00525225i	0.349225	−	0.937039i	$-0.386445\pi$
$61$	0.112705	+	0.0410214i	0.0144304	+	0.00525225i	−0.334795	+	0.942291i	$0.608667\pi$
$62$	−8.08286	−	2.16580i	−1.02652	−	0.275056i
$63$		0			0
$64$	−0.866025	−	0.500000i	−0.108253	−	0.0625000i
$65$	9.82496	−	9.72543i	1.21864	−	1.20629i
$66$		0			0
$67$	5.25146	−	3.67711i	0.641568	−	0.449231i	−0.206983	−	0.978345i	$-0.566364\pi$
$67$	5.25146	−	3.67711i	0.641568	−	0.449231i	0.848551	+	0.529114i	$0.177476\pi$
$68$	−2.52751	+	1.76978i	−0.306506	+	0.214618i
$69$		0			0
$70$	0.406697	+	0.00207050i	0.0486096	+	0.000247473i
$71$	6.13397	+	3.54145i	0.727969	+	0.420293i	0.817679	−	0.575675i	$-0.195261\pi$
$71$	6.13397	+	3.54145i	0.727969	+	0.420293i	−0.0897098	+	0.995968i	$0.528594\pi$
$72$		0			0
$73$	11.9795	+	3.20990i	1.40210	+	0.375691i	0.879097	−	0.476643i	$-0.158146\pi$
$73$	11.9795	+	3.20990i	1.40210	+	0.375691i	0.522999	+	0.852333i	$0.324813\pi$
$74$	−5.38331	−	1.95936i	−0.625797	−	0.227771i
$75$		0			0
$76$	0.727523	+	0.610464i	0.0834526	+	0.0700251i
$77$	0.264345	−	0.566890i	0.0301249	−	0.0646031i
$78$		0			0
$79$	−8.96689	+	1.58110i	−1.00885	+	0.177888i	−0.653567	−	0.756869i	$-0.726728\pi$
$79$	−8.96689	+	1.58110i	−1.00885	+	0.177888i	−0.355287	+	0.934757i	$0.615617\pi$
$80$	1.70559	+	1.44602i	0.190691	+	0.161670i
$81$		0			0
$82$	−4.73953	−	4.73953i	−0.523394	−	0.523394i
$83$	−2.40418	+	3.43353i	−0.263893	+	0.376878i	−0.929130	−	0.369754i	$-0.879442\pi$
$83$	−2.40418	+	3.43353i	−0.263893	+	0.376878i	0.665236	+	0.746633i	$0.268331\pi$
$84$		0			0
$85$	6.26778	−	2.88396i	0.679837	−	0.312809i
$86$	0.545964	−	0.650654i	0.0588728	−	0.0701618i
$87$		0			0
$88$	3.11679	−	1.45338i	0.332251	−	0.154931i
$89$	−1.77224	−	3.06962i	−0.187857	−	0.325379i	0.756678	−	0.653787i	$-0.226821\pi$
$89$	−1.77224	−	3.06962i	−0.187857	−	0.325379i	−0.944536	+	0.328409i	$0.893488\pi$
$90$		0			0
$91$	0.562241	−	0.973831i	0.0589389	−	0.102085i
$92$	0.0742962	−	0.849209i	0.00774591	−	0.0885362i
$93$		0			0
$94$	9.38942	+	1.65561i	0.968444	+	0.170763i
$95$	−1.35674	−	1.63372i	−0.139199	−	0.167616i
$96$		0			0
$97$	−8.66511	−	0.758099i	−0.879808	−	0.0769733i	−0.361706	−	0.932292i	$-0.617806\pi$
$97$	−8.66511	−	0.758099i	−0.879808	−	0.0769733i	−0.518102	+	0.855319i	$0.673361\pi$
$98$	−6.72953	+	1.80317i	−0.679785	+	0.182148i
$99$		0			0
$100$	−3.17477	−	3.86275i	−0.317477	−	0.386275i
$101$	1.87082	−	5.14003i	0.186153	−	0.511452i	−0.811150	−	0.584838i	$-0.801158\pi$
$101$	1.87082	−	5.14003i	0.186153	−	0.511452i	0.997304	+	0.0733854i	$0.0233803\pi$
$102$		0			0
$103$	−15.7114	+	1.37457i	−1.54809	+	0.135441i	−0.828911	−	0.559380i	$-0.811039\pi$
$103$	−15.7114	+	1.37457i	−1.54809	+	0.135441i	−0.719183	+	0.694821i	$0.755484\pi$
$104$	5.80961	−	2.11452i	0.569679	−	0.207346i
$105$		0			0
$106$	0.272236	+	1.54393i	0.0264419	+	0.149960i
$107$	5.00063	−	5.00063i	0.483429	−	0.483429i	−0.422796	−	0.906225i	$-0.638951\pi$
$107$	5.00063	−	5.00063i	0.483429	−	0.483429i	0.906225	+	0.422796i	$0.138951\pi$
$108$		0			0
$109$		−	10.5083i		−	1.00651i	−0.864137	−	0.503256i	$-0.832135\pi$
$109$		−	10.5083i		−	1.00651i	0.864137	−	0.503256i	$-0.167865\pi$
$110$	−7.43784	+	1.95243i	−0.709170	+	0.186157i
$111$		0			0
$112$	0.164842	+	0.0768670i	0.0155761	+	0.00726325i
$113$	0.303819	+	3.47267i	0.0285809	+	0.326681i	0.997003	+	0.0773644i	$0.0246505\pi$
$113$	0.303819	+	3.47267i	0.0285809	+	0.326681i	−0.968422	+	0.249317i	$0.919794\pi$
$114$		0			0
$115$	−0.502713	+	1.83866i	−0.0468782	+	0.171456i
$116$	8.65255	−	4.99555i	0.803369	−	0.463825i
$117$		0			0
$118$	−2.96431	−	11.0630i	−0.272887	−	1.01843i
$119$	0.429907	−	0.360735i	0.0394095	−	0.0330685i
$120$		0			0
$121$	−0.143553	+	0.814128i	−0.0130502	+	0.0740116i
$122$	−0.0687939	−	0.0982478i	−0.00622831	−	0.00889494i
$123$		0			0
$124$	5.37884	+	6.41026i	0.483034	+	0.575658i
$125$	5.44164	+	9.76670i	0.486715	+	0.873561i
$126$		0			0
$127$	0.453065	−	1.69086i	0.0402030	−	0.150040i	−0.942907	−	0.333057i	$-0.891920\pi$
$127$	0.453065	−	1.69086i	0.0402030	−	0.150040i	0.983110	+	0.183017i	$0.0585865\pi$
$128$	0.422618	+	0.906308i	0.0373545	+	0.0801070i
$129$		0			0
$130$	−13.6264	+	2.33124i	−1.19512	+	0.204463i
$131$	0.268507	+	0.737717i	0.0234596	+	0.0644546i	0.950870	−	0.309592i	$-0.100192\pi$
$131$	0.268507	+	0.737717i	0.0234596	+	0.0644546i	−0.927410	+	0.374046i	$0.877970\pi$
$132$		0			0
$133$	−0.141498	−	0.0990777i	−0.0122694	−	0.00859113i
$134$	−6.41085			−0.553813
$135$		0			0
$136$	3.08553			0.264582
$137$	−4.25306	−	2.97803i	−0.363364	−	0.254430i	0.377609	−	0.925965i	$-0.376746\pi$
$137$	−4.25306	−	2.97803i	−0.363364	−	0.254430i	−0.740973	+	0.671535i	$0.765635\pi$
$138$		0			0
$139$	0.952250	+	2.61629i	0.0807688	+	0.221910i	0.973503	−	0.228672i	$-0.0734384\pi$
$139$	0.952250	+	2.61629i	0.0807688	+	0.221910i	−0.892735	+	0.450583i	$0.851216\pi$
$140$	−0.331959	−	0.234968i	−0.0280557	−	0.0198584i
$141$		0			0
$142$	−2.99336	−	6.41929i	−0.251198	−	0.538695i
$143$	−5.50286	+	20.5370i	−0.460173	+	1.71739i
$144$		0			0
$145$	−21.0321	+	7.53402i	−1.74662	+	0.625666i
$146$	−7.97192	−	9.50057i	−0.659761	−	0.786272i
$147$		0			0
$148$	3.28590	+	4.69276i	0.270100	+	0.385742i
$149$	−1.98047	+	11.2318i	−0.162247	+	0.920146i	0.789611	+	0.613607i	$0.210282\pi$
$149$	−1.98047	+	11.2318i	−0.162247	+	0.920146i	−0.951858	+	0.306539i	$0.900829\pi$
$150$		0			0
$151$	4.01482	−	3.36883i	0.326721	−	0.274152i	−0.464641	−	0.885499i	$-0.653817\pi$
$151$	4.01482	−	3.36883i	0.326721	−	0.274152i	0.791362	+	0.611347i	$0.209372\pi$
$152$	−0.245804	−	0.917353i	−0.0199373	−	0.0744072i
$153$		0			0
$154$	−0.541694	+	0.312747i	−0.0436509	+	0.0252019i
$155$	−9.27308	−	16.2520i	−0.744832	−	1.30539i
$156$		0			0
$157$	−0.0323122	−	0.369330i	−0.00257880	−	0.0294758i	0.994796	−	0.101884i	$-0.0324871\pi$
$157$	−0.0323122	−	0.369330i	−0.00257880	−	0.0294758i	−0.997375	+	0.0724083i	$0.976932\pi$
$158$	8.25213	+	3.84803i	0.656504	+	0.306133i
$159$		0			0
$160$	−0.567734	−	2.16279i	−0.0448833	−	0.170984i
$161$			0.155047i			0.0122194i
$162$		0			0
$163$	−13.5925	+	13.5925i	−1.06465	+	1.06465i	−0.0668902	+	0.997760i	$0.521308\pi$
$163$	−13.5925	+	13.5925i	−1.06465	+	1.06465i	−0.997760	+	0.0668902i	$0.978692\pi$
$164$	1.16391	+	6.60088i	0.0908864	+	0.515442i
$165$		0			0
$166$	3.93878	−	1.43360i	0.305709	−	0.111269i
$167$	13.0724	−	1.14369i	1.01158	−	0.0885014i	0.430701	−	0.902495i	$-0.358266\pi$
$167$	13.0724	−	1.14369i	1.01158	−	0.0885014i	0.580874	+	0.813993i	$0.302711\pi$
$168$		0			0
$169$	−8.62670	+	23.7017i	−0.663592	+	1.82320i
$170$	−6.78844	−	1.23265i	−0.520649	−	0.0945401i
$171$		0			0
$172$	−0.820427	+	0.219833i	−0.0625570	+	0.0167621i
$173$	5.69949	+	0.498641i	0.433324	+	0.0379110i	0.301732	−	0.953393i	$-0.402435\pi$
$173$	5.69949	+	0.498641i	0.433324	+	0.0379110i	0.131593	+	0.991304i	$0.457991\pi$
$174$		0			0
$175$	0.636472	+	0.649567i	0.0481128	+	0.0491027i
$176$	−3.38675	−	0.597175i	−0.255286	−	0.0450138i
$177$		0			0
$178$	−0.308922	+	3.53100i	−0.0231547	+	0.264660i
$179$	−11.6897	+	20.2472i	−0.873730	+	1.51334i	−0.0156200	+	0.999878i	$0.504972\pi$
$179$	−11.6897	+	20.2472i	−0.873730	+	1.51334i	−0.858110	+	0.513466i	$0.828361\pi$
$180$		0			0
$181$	−11.8112	−	20.4576i	−0.877918	−	1.52060i	−0.853622	−	0.520893i	$-0.825599\pi$
$181$	−11.8112	−	20.4576i	−0.877918	−	1.52060i	−0.0242958	−	0.999705i	$-0.507734\pi$
$182$	−1.01913	+	0.475227i	−0.0755428	+	0.0352262i
$183$		0			0
$184$	−0.547946	+	0.653017i	−0.0403951	+	0.0481410i
$185$	−5.35456	−	11.6372i	−0.393675	−	0.855584i
$186$		0			0
$187$	−6.08628	+	8.69211i	−0.445073	+	0.635630i
$188$	−6.74174	−	6.74174i	−0.491692	−	0.491692i
$189$		0			0
$190$	0.174314	+	2.11646i	0.0126460	+	0.153544i
$191$	22.5323	−	3.97306i	1.63038	−	0.287480i	0.717762	−	0.696289i	$-0.245167\pi$
$191$	22.5323	−	3.97306i	1.63038	−	0.287480i	0.912620	+	0.408808i	$0.134056\pi$
$192$		0			0
$193$	0.679718	−	1.45766i	0.0489272	−	0.104925i	−0.880325	−	0.474372i	$-0.842675\pi$
$193$	0.679718	−	1.45766i	0.0489272	−	0.104925i	0.929252	+	0.369447i	$0.120453\pi$
$194$	6.66321	+	5.59110i	0.478391	+	0.401418i
$195$		0			0
$196$	6.54676	+	2.38283i	0.467626	+	0.170202i
$197$	−17.6351	−	4.72531i	−1.25645	−	0.336664i	−0.431624	−	0.902053i	$-0.642059\pi$
$197$	−17.6351	−	4.72531i	−1.25645	−	0.336664i	−0.824824	+	0.565389i	$0.808726\pi$
$198$		0			0
$199$	16.1145	+	9.30374i	1.14233	+	0.659524i	0.947006	−	0.321215i	$-0.104091\pi$
$199$	16.1145	+	9.30374i	1.14233	+	0.659524i	0.195323	+	0.980739i	$0.437424\pi$
$200$	0.385041	+	4.98515i	0.0272265	+	0.352503i
$201$		0			0
$202$	−4.48069	+	3.13741i	−0.315260	+	0.220747i
$203$	−1.48857	+	1.04231i	−0.104477	+	0.0731557i
$204$		0			0
$205$	0.0763018	−	14.9875i	0.00532915	−	1.04677i
$206$	13.6585	+	7.88573i	0.951632	+	0.549425i
$207$		0			0
$208$	−5.97179	−	1.60014i	−0.414069	−	0.110950i
$209$	3.06909	+	1.11706i	0.212294	+	0.0772686i
$210$		0			0
$211$	6.49482	+	5.44980i	0.447122	+	0.375180i	0.838367	−	0.545107i	$-0.183511\pi$
$211$	6.49482	+	5.44980i	0.447122	+	0.375180i	−0.391245	+	0.920287i	$0.627955\pi$
$212$	0.662559	−	1.42086i	0.0455047	−	0.0975852i
$213$		0			0
$214$	−6.96451	+	1.22803i	−0.476084	+	0.0839465i
$215$	1.89284	−	0.155896i	0.129090	−	0.0106320i
$216$		0			0
$217$	−1.07621	−	1.07621i	−0.0730581	−	0.0730581i
$218$	−6.02731	+	8.60789i	−0.408221	+	0.583000i
$219$		0			0
$220$	7.21259	+	2.66683i	0.486273	+	0.179798i
$221$	−12.2619	+	14.6132i	−0.824824	+	0.982987i
$222$		0			0
$223$	−8.57594	+	3.99903i	−0.574288	+	0.267795i	−0.687990	−	0.725720i	$-0.741507\pi$
$223$	−8.57594	+	3.99903i	−0.574288	+	0.267795i	0.113702	+	0.993515i	$0.463729\pi$
$224$	−0.0909414	−	0.157515i	−0.00607628	−	0.0105244i
$225$		0			0
$226$	1.74297	−	3.01891i	0.115940	−	0.200815i
$227$	−1.08696	+	12.4240i	−0.0721439	+	0.824608i	0.870796	+	0.491645i	$0.163604\pi$
$227$	−1.08696	+	12.4240i	−0.0721439	+	0.824608i	−0.942940	+	0.332963i	$0.891951\pi$
$228$		0			0
$229$	−10.2443	−	1.80635i	−0.676962	−	0.119367i	−0.175412	−	0.984495i	$-0.556126\pi$
$229$	−10.2443	−	1.80635i	−0.676962	−	0.119367i	−0.501550	+	0.865128i	$0.667237\pi$
$230$	1.46641	−	1.21780i	0.0966921	−	0.0802990i
$231$		0			0
$232$	−9.95308	−	0.870782i	−0.653452	−	0.0571696i
$233$	−16.5139	+	4.42489i	−1.08186	+	0.289884i	−0.755359	−	0.655311i	$-0.772537\pi$
$233$	−16.5139	+	4.42489i	−1.08186	+	0.289884i	−0.326504	+	0.945196i	$0.605871\pi$
$234$		0			0
$235$	12.1392	+	17.5257i	0.791872	+	1.14325i
$236$	−3.91723	+	10.7625i	−0.254990	+	0.700580i
$237$		0			0
$238$	−0.559069	+	0.0489122i	−0.0362390	+	0.00317050i
$239$	−6.68620	+	2.43358i	−0.432494	+	0.157415i	−0.549088	−	0.835765i	$-0.685025\pi$
$239$	−6.68620	+	2.43358i	−0.432494	+	0.157415i	0.116594	+	0.993180i	$0.462802\pi$
$240$		0			0
$241$	−4.36162	−	24.7360i	−0.280957	−	1.59339i	−0.719380	−	0.694617i	$-0.755574\pi$
$241$	−4.36162	−	24.7360i	−0.280957	−	1.59339i	0.438423	−	0.898769i	$-0.355537\pi$
$242$	0.584556	−	0.584556i	0.0375767	−	0.0375767i
$243$		0			0
$244$			0.119938i			0.00767827i
$245$	−13.4516	−	7.85783i	−0.859388	−	0.502019i
$246$		0			0
$247$	5.32145	+	2.48143i	0.338596	+	0.157890i
$248$	−0.729319	−	8.33615i	−0.0463118	−	0.529346i
$249$		0			0
$250$	1.14442	−	11.1216i	0.0723793	−	0.703393i
$251$	−16.5915	+	9.57908i	−1.04724	+	0.604626i	−0.921876	−	0.387484i	$-0.873344\pi$
$251$	−16.5915	+	9.57908i	−1.04724	+	0.604626i	−0.125367	+	0.992110i	$0.540011\pi$
$252$		0			0
$253$	−0.758749	−	2.83169i	−0.0477021	−	0.178027i
$254$	−1.34097	+	1.12520i	−0.0841397	+	0.0706016i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−5.34643	−	7.63550i	−0.333501	−	0.476289i	0.617020	−	0.786947i	$-0.288340\pi$
$257$	−5.34643	−	7.63550i	−0.333501	−	0.476289i	−0.950522	+	0.310658i	$0.899451\pi$
$258$		0			0
$259$	−0.669766	−	0.798195i	−0.0416172	−	0.0495975i
$260$	12.4992	+	5.90615i	0.775171	+	0.366284i
$261$		0			0
$262$	0.203189	−	0.758311i	0.0125531	−	0.0468486i
$263$	11.9957	+	25.7248i	0.739684	+	1.58626i	0.808408	+	0.588622i	$0.200329\pi$
$263$	11.9957	+	25.7248i	0.739684	+	1.58626i	−0.0687239	+	0.997636i	$0.521893\pi$
$264$		0			0
$265$	−2.02532	+	2.86134i	−0.124414	+	0.175771i
$266$	0.0590794	+	0.162319i	0.00362239	+	0.00995244i
$267$		0			0
$268$	5.25146	+	3.67711i	0.320784	+	0.224615i
$269$	9.81443			0.598396			0.299198	−	0.954191i	$-0.403281\pi$
$269$	9.81443			0.598396			0.299198	+	0.954191i	$0.403281\pi$
$270$		0			0
$271$	7.52718			0.457244			0.228622	−	0.973515i	$-0.426578\pi$
$271$	7.52718			0.457244			0.228622	+	0.973515i	$0.426578\pi$
$272$	−2.52751	−	1.76978i	−0.153253	−	0.107309i
$273$		0			0
$274$	1.77578	+	4.87891i	0.107279	+	0.294746i
$275$	−14.8030	−	8.74866i	−0.892653	−	0.527564i
$276$		0			0
$277$	10.7436	+	23.0397i	0.645520	+	1.38432i	0.907830	+	0.419339i	$0.137738\pi$
$277$	10.7436	+	23.0397i	0.645520	+	1.38432i	−0.262309	+	0.964984i	$0.584484\pi$
$278$	0.720602	−	2.68932i	0.0432188	−	0.161295i
$279$		0			0
$280$	0.137153	+	0.382878i	0.00819646	+	0.0228814i
$281$	−1.86726	−	2.22532i	−0.111392	−	0.132751i	0.707468	−	0.706746i	$-0.249838\pi$
$281$	−1.86726	−	2.22532i	−0.111392	−	0.132751i	−0.818859	+	0.573994i	$0.805393\pi$
$282$		0			0
$283$	4.49746	+	6.42304i	0.267346	+	0.381810i	0.930269	−	0.366878i	$-0.119573\pi$
$283$	4.49746	+	6.42304i	0.267346	+	0.381810i	−0.662923	+	0.748688i	$0.730684\pi$
$284$	−1.22993	+	6.97530i	−0.0729831	+	0.413908i
$285$		0			0
$286$	16.2872	−	13.6666i	0.963083	−	0.808122i
$287$	−0.315528	−	1.17757i	−0.0186251	−	0.0695097i
$288$		0			0
$289$	6.47747	−	3.73977i	0.381027	−	0.219986i
$290$	21.5498	+	5.89200i	1.26545	+	0.345990i
$291$		0			0
$292$	1.08091	+	12.3549i	0.0632558	+	0.723017i
$293$	−17.7250	−	8.26532i	−1.03551	−	0.482865i	−0.170887	−	0.985291i	$-0.554663\pi$
$293$	−17.7250	−	8.26532i	−1.03551	−	0.482865i	−0.864620	+	0.502426i	$0.832441\pi$
$294$		0			0
$295$	12.9178	−	22.1136i	0.752106	−	1.28750i
$296$		−	5.72880i		−	0.332980i
$297$		0			0
$298$	8.06461	−	8.06461i	0.467171	−	0.467171i
$299$	−0.915170	−	5.19019i	−0.0529256	−	0.300156i
$300$		0			0
$301$	0.145169	−	0.0528372i	0.00836740	−	0.00304548i
$302$	−5.22103	+	0.456781i	−0.300436	+	0.0262848i
$303$		0			0
$304$	−0.324821	+	0.892439i	−0.0186298	+	0.0511849i
$305$	0.0479148	−	0.263876i	0.00274359	−	0.0151095i
$306$		0			0
$307$	6.90951	−	1.85140i	0.394347	−	0.105665i	−0.0561960	−	0.998420i	$-0.517897\pi$
$307$	6.90951	−	1.85140i	0.394347	−	0.105665i	0.450543	+	0.892755i	$0.351230\pi$
$308$	0.623114	+	0.0545154i	0.0355052	+	0.00310630i
$309$		0			0
$310$	−1.72568	+	18.6317i	−0.0980121	+	1.05821i
$311$	−14.3002	−	2.52150i	−0.810888	−	0.142981i	−0.247195	−	0.968966i	$-0.579509\pi$
$311$	−14.3002	−	2.52150i	−0.810888	−	0.142981i	−0.563693	+	0.825984i	$0.690620\pi$
$312$		0			0
$313$	0.332302	−	3.79823i	0.0187828	−	0.214688i	−0.981003	−	0.193992i	$-0.937856\pi$
$313$	0.332302	−	3.79823i	0.0187828	−	0.214688i	0.999786	−	0.0206959i	$-0.00658819\pi$
$314$	−0.185371	+	0.321071i	−0.0104611	+	0.0181191i
$315$		0			0
$316$	−4.55261	−	7.88535i	−0.256104	−	0.443586i
$317$	22.9410	−	10.6976i	1.28850	−	0.600836i	0.347003	−	0.937864i	$-0.387199\pi$
$317$	22.9410	−	10.6976i	1.28850	−	0.600836i	0.941495	+	0.337028i	$0.109422\pi$
$318$		0			0
$319$	22.0858	−	26.3208i	1.23657	−	1.47368i
$320$	−0.775468	+	2.09730i	−0.0433500	+	0.117242i
$321$		0			0
$322$	0.0889310	−	0.127007i	0.00495593	−	0.00707781i
$323$	2.07208	+	2.07208i	0.115294	+	0.115294i
$324$		0			0
$325$	−25.1400	−	17.9875i	−1.39452	−	0.997765i
$326$	18.9307	−	3.33800i	1.04848	−	0.184875i
$327$		0			0
$328$	2.83269	−	6.07472i	0.156409	−	0.335420i
$329$	1.32841	+	1.11467i	0.0732377	+	0.0614538i
$330$		0			0
$331$	−28.3592	−	10.3219i	−1.55876	−	0.567344i	−0.588312	−	0.808634i	$-0.700207\pi$
$331$	−28.3592	−	10.3219i	−1.55876	−	0.567344i	−0.970453	+	0.241290i	$0.922429\pi$
$332$	−4.04874	−	1.08486i	−0.222203	−	0.0595392i
$333$		0			0
$334$	−11.3643	−	6.56118i	−0.621827	−	0.359012i
$335$	−10.0847	−	10.1879i	−0.550986	−	0.556625i
$336$		0			0
$337$	−16.9382	+	11.8602i	−0.922680	+	0.646067i	−0.935301	−	0.353853i	$-0.884871\pi$
$337$	−16.9382	+	11.8602i	−0.922680	+	0.646067i	0.0126212	+	0.999920i	$0.495982\pi$
$338$	20.6613	−	14.4672i	1.12383	−	0.786911i
$339$		0			0
$340$	4.85374	+	4.90342i	0.263231	+	0.265925i
$341$	24.9220	+	14.3887i	1.34960	+	0.779194i
$342$		0			0
$343$	−2.45378	−	0.657489i	−0.132492	−	0.0355011i
$344$	0.798145	+	0.290501i	0.0430331	+	0.0156628i
$345$		0			0
$346$	−4.38274	−	3.67756i	−0.235618	−	0.197707i
$347$	6.33169	−	13.5783i	0.339903	−	0.728924i	−0.659844	−	0.751402i	$-0.729378\pi$
$347$	6.33169	−	13.5783i	0.339903	−	0.728924i	0.999747	+	0.0224782i	$0.00715563\pi$
$348$		0			0
$349$	29.0560	−	5.12336i	1.55533	−	0.274247i	0.671127	−	0.741343i	$-0.265811\pi$
$349$	29.0560	−	5.12336i	1.55533	−	0.274247i	0.884207	+	0.467096i	$0.154700\pi$
$350$	−0.148791	−	0.897160i	−0.00795322	−	0.0479552i
$351$		0			0
$352$	2.43174	+	2.43174i	0.129612	+	0.129612i
$353$	9.33441	−	13.3309i	0.496821	−	0.709533i	−0.489933	−	0.871760i	$-0.662979\pi$
$353$	9.33441	−	13.3309i	0.496821	−	0.709533i	0.986753	+	0.162227i	$0.0518676\pi$
$354$		0			0
$355$	5.49256	−	14.8549i	0.291515	−	0.788419i
$356$	2.27835	−	2.71523i	0.120752	−	0.143907i
$357$		0			0
$358$	21.1889	−	9.88057i	1.11987	−	0.522204i
$359$	−16.7566	−	29.0233i	−0.884379	−	1.53179i	−0.846423	−	0.532510i	$-0.821249\pi$
$359$	−16.7566	−	29.0233i	−0.884379	−	1.53179i	−0.0379559	−	0.999279i	$-0.512085\pi$
$360$		0			0
$361$	−9.04902	+	15.6734i	−0.476264	+	0.824914i
$362$	−2.05882	+	23.5325i	−0.108209	+	1.23684i
$363$		0			0
$364$	1.10740	+	0.195264i	0.0580435	+	0.0102346i
$365$	2.55761	−	27.6138i	0.133872	−	1.44537i
$366$		0			0
$367$	−16.0908	−	1.40776i	−0.839932	−	0.0734846i	−0.340934	−	0.940087i	$-0.610743\pi$
$367$	−16.0908	−	1.40776i	−0.839932	−	0.0734846i	−0.498999	+	0.866603i	$0.666299\pi$
$368$	0.823406	−	0.220631i	0.0429230	−	0.0115012i
$369$		0			0
$370$	−2.28863	+	12.6039i	−0.118980	+	0.655245i
$371$	−0.0975258	+	0.267950i	−0.00506329	+	0.0139113i
$372$		0			0
$373$	−20.5516	+	1.79803i	−1.06412	+	0.0930986i	−0.605745	−	0.795659i	$-0.707125\pi$
$373$	−20.5516	+	1.79803i	−1.06412	+	0.0930986i	−0.458377	+	0.888758i	$0.651569\pi$
$374$	9.97118	−	3.62921i	0.515597	−	0.187662i
$375$		0			0
$376$	1.65561	+	9.38942i	0.0853814	+	0.484222i
$377$	43.6777	−	43.6777i	2.24951	−	2.24951i
$378$		0			0
$379$			37.5407i			1.92833i	0.265296	+	0.964167i	$0.414530\pi$
$379$			37.5407i			1.92833i	−0.265296	+	0.964167i	$0.585470\pi$
$380$	1.07116	−	1.83368i	0.0549494	−	0.0940660i
$381$		0			0
$382$	−20.7363	−	9.66947i	−1.06096	−	0.494733i
$383$	−2.96219	−	33.8580i	−0.151361	−	1.73006i	−0.569771	−	0.821804i	$-0.692968\pi$
$383$	−2.96219	−	33.8580i	−0.151361	−	1.73006i	0.418410	−	0.908258i	$-0.362588\pi$
$384$		0			0
$385$	−1.34913	−	0.368870i	−0.0687580	−	0.0187993i
$386$	−1.39287	+	0.804175i	−0.0708953	+	0.0409314i
$387$		0			0
$388$	−2.25126	−	8.40182i	−0.114291	−	0.426538i
$389$	−7.34911	+	6.16663i	−0.372615	+	0.312661i	−0.809795	−	0.586713i	$-0.800422\pi$
$389$	−7.34911	+	6.16663i	−0.372615	+	0.312661i	0.437180	+	0.899374i	$0.355977\pi$
$390$		0			0
$391$	0.456741	−	2.59030i	0.0230984	−	0.130997i
$392$	−3.99606	−	5.70697i	−0.201832	−	0.288245i
$393$		0			0
$394$	11.7355	+	13.9858i	0.591226	+	0.704596i
$395$	6.86600	+	19.1672i	0.345466	+	0.964408i
$396$		0			0
$397$	−0.0296335	+	0.110594i	−0.00148726	+	0.00555054i	−0.966665	−	0.256043i	$-0.917581\pi$
$397$	−0.0296335	+	0.110594i	−0.00148726	+	0.00555054i	0.965178	+	0.261593i	$0.0842479\pi$
$398$	−7.86386	−	16.8641i	−0.394180	−	0.845321i
$399$		0			0
$400$	2.54396	−	4.30445i	0.127198	−	0.215222i
$401$	9.28961	+	25.5230i	0.463901	+	1.27456i	0.922529	+	0.385929i	$0.126119\pi$
$401$	9.28961	+	25.5230i	0.463901	+	1.27456i	−0.458628	+	0.888628i	$0.651659\pi$
$402$		0			0
$403$	42.3786	+	29.6738i	2.11103	+	1.47816i
$404$	5.46991			0.272138
$405$		0			0
$406$	1.81721			0.0901866
$407$	16.1384	+	11.3002i	0.799949	+	0.560130i
$408$		0			0
$409$	−7.22114	−	19.8399i	−0.357062	−	0.981020i	−0.980043	−	0.198784i	$-0.936301\pi$
$409$	−7.22114	−	19.8399i	−0.357062	−	0.981020i	0.622981	−	0.782237i	$-0.285921\pi$
$410$	−8.65899	+	12.2333i	−0.427637	+	0.604159i
$411$		0			0
$412$	−6.66531	−	14.2938i	−0.328376	−	0.704205i
$413$	0.539158	−	2.01216i	0.0265302	−	0.0990121i
$414$		0			0
$415$	8.47420	+	4.00423i	0.415982	+	0.196560i
$416$	3.97401	+	4.73604i	0.194842	+	0.232203i
$417$		0			0
$418$	−1.87334	−	2.67540i	−0.0916279	−	0.130858i
$419$	−3.55100	+	20.1387i	−0.173478	+	0.983840i	0.766409	+	0.642353i	$0.222042\pi$
$419$	−3.55100	+	20.1387i	−0.173478	+	0.983840i	−0.939886	+	0.341487i	$0.889069\pi$
$420$		0			0
$421$	−18.7621	+	15.7433i	−0.914411	+	0.767282i	−0.972953	−	0.231003i	$-0.925799\pi$
$421$	−18.7621	+	15.7433i	−0.914411	+	0.767282i	0.0585424	+	0.998285i	$0.481355\pi$
$422$	−2.19437	−	8.18949i	−0.106820	−	0.398658i
$423$		0			0
$424$	−1.35771	+	0.783874i	−0.0659362	+	0.0380683i
$425$	−8.71979	−	12.7270i	−0.422972	−	0.617351i
$426$		0			0
$427$	−0.00190128	−	0.0217317i	−9.20094e−5	−	0.00105167i
$428$	6.40937	+	2.98874i	0.309808	+	0.144466i
$429$		0			0
$430$	−1.63994	−	0.957984i	−0.0790849	−	0.0461981i
$431$		−	20.2854i		−	0.977112i	−0.872532	−	0.488556i	$-0.837524\pi$
$431$		−	20.2854i		−	0.977112i	0.872532	−	0.488556i	$-0.162476\pi$
$432$		0			0
$433$	17.3173	−	17.3173i	0.832217	−	0.832217i	−0.155603	−	0.987820i	$-0.549732\pi$
$433$	17.3173	−	17.3173i	0.832217	−	0.832217i	0.987820	+	0.155603i	$0.0497321\pi$
$434$	0.264292	+	1.49887i	0.0126864	+	0.0719482i
$435$		0			0
$436$	9.87456	−	3.59405i	0.472906	−	0.172124i
$437$	−0.806506	+	0.0705601i	−0.0385804	+	0.00337535i
$438$		0			0
$439$	0.00392325	−	0.0107791i	0.000187247	−	0.000514456i	−0.939599	−	0.342277i	$-0.888802\pi$
$439$	0.00392325	−	0.0107791i	0.000187247	−	0.000514456i	0.939786	+	0.341763i	$0.111024\pi$
$440$	−4.37858	−	6.32151i	−0.208740	−	0.301366i
$441$		0			0
$442$	18.4261	−	4.93726i	0.876441	−	0.234842i
$443$	−0.701451	−	0.0613690i	−0.0333269	−	0.00291573i	0.0704801	−	0.997513i	$-0.477547\pi$
$443$	−0.701451	−	0.0613690i	−0.0333269	−	0.00291573i	−0.103807	+	0.994597i	$0.533102\pi$
$444$		0			0
$445$	−6.09731	+	5.06357i	−0.289040	+	0.240036i
$446$	9.31875	+	1.64315i	0.441256	+	0.0778053i
$447$		0			0
$448$	−0.0158521	+	0.181191i	−0.000748943	+	0.00856046i
$449$	18.9080	−	32.7496i	0.892324	−	1.54555i	0.0552412	−	0.998473i	$-0.482407\pi$
$449$	18.9080	−	32.7496i	0.892324	−	1.54555i	0.837082	−	0.547077i	$-0.184259\pi$
$450$		0			0
$451$	11.5253	+	19.9624i	0.542705	+	0.939993i
$452$	−3.15933	+	1.47322i	−0.148602	+	0.0692944i
$453$		0			0
$454$	8.01648	−	9.55367i	0.376232	−	0.448376i
$455$	−2.35837	−	0.872000i	−0.110562	−	0.0408800i
$456$		0			0
$457$	3.17168	−	4.52963i	0.148365	−	0.211887i	−0.738090	−	0.674703i	$-0.764272\pi$
$457$	3.17168	−	4.52963i	0.148365	−	0.211887i	0.886455	+	0.462816i	$0.153161\pi$
$458$	7.35556	+	7.35556i	0.343703	+	0.343703i
$459$		0			0
$460$	−1.89971	+	0.156462i	−0.0885744	+	0.00729508i
$461$	−11.5780	+	2.04152i	−0.539242	+	0.0950830i	−0.436635	−	0.899639i	$-0.643830\pi$
$461$	−11.5780	+	2.04152i	−0.539242	+	0.0950830i	−0.102608	+	0.994722i	$0.532719\pi$
$462$		0			0
$463$	−7.97565	+	17.1038i	−0.370660	+	0.794882i	0.629185	+	0.777256i	$0.283389\pi$
$463$	−7.97565	+	17.1038i	−0.370660	+	0.794882i	−0.999845	+	0.0176267i	$0.994389\pi$
$464$	7.65363	+	6.42215i	0.355311	+	0.298141i
$465$		0			0
$466$	16.0654	+	5.84734i	0.744217	+	0.270873i
$467$	−13.3031	−	3.56456i	−0.615595	−	0.164948i	−0.0624706	−	0.998047i	$-0.519898\pi$
$467$	−13.3031	−	3.56456i	−0.615595	−	0.164948i	−0.553125	+	0.833099i	$0.686565\pi$
$468$		0			0
$469$	−1.00981	−	0.583012i	−0.0466285	−	0.0269210i
$470$	0.108535	−	21.3190i	0.00500637	−	0.983372i
$471$		0			0
$472$	9.38193	−	6.56930i	0.431838	−	0.302376i
$473$	−2.39272	+	1.67540i	−0.110017	+	0.0770351i
$474$		0			0
$475$	−3.08920	+	3.60635i	−0.141742	+	0.165471i
$476$	0.486017	+	0.280602i	0.0222766	+	0.0128614i
$477$		0			0
$478$	6.87285	+	1.84158i	0.314357	+	0.0842317i
$479$	−27.9319	−	10.1664i	−1.27624	−	0.464515i	−0.387055	−	0.922057i	$-0.626508\pi$
$479$	−27.9319	−	10.1664i	−1.27624	−	0.464515i	−0.889188	+	0.457542i	$0.848730\pi$
$480$		0			0
$481$	27.1318	+	22.7663i	1.23710	+	1.03805i
$482$	−10.6152	+	22.7643i	−0.483507	+	1.03688i
$483$		0			0
$484$	−0.814128	+	0.143553i	−0.0370058	+	0.00652512i
$485$	1.59650	+	19.3842i	0.0724932	+	0.880189i
$486$		0			0
$487$	12.2241	+	12.2241i	0.553928	+	0.553928i	0.927572	−	0.373644i	$-0.121892\pi$
$487$	12.2241	+	12.2241i	0.553928	+	0.553928i	−0.373644	+	0.927572i	$0.621892\pi$
$488$	0.0687939	−	0.0982478i	0.00311415	−	0.00444747i
$489$		0			0
$490$	6.51180	+	14.1523i	0.294173	+	0.639334i
$491$	7.20060	−	8.58134i	0.324959	−	0.387271i	−0.578688	−	0.815549i	$-0.696435\pi$
$491$	7.20060	−	8.58134i	0.324959	−	0.387271i	0.903647	+	0.428278i	$0.140880\pi$
$492$		0			0
$493$	27.9395	−	13.0284i	1.25833	−	0.586769i
$494$	−2.93578	−	5.08493i	−0.132087	−	0.228782i
$495$		0			0
$496$	−4.18400	+	7.24690i	−0.187867	+	0.325395i
$497$	0.112279	−	1.28336i	0.00503641	−	0.0575664i
$498$		0			0
$499$	−24.9478	−	4.39897i	−1.11682	−	0.196925i	−0.415374	−	0.909651i	$-0.636349\pi$
$499$	−24.9478	−	4.39897i	−1.11682	−	0.196925i	−0.701443	+	0.712726i	$0.747460\pi$
$500$	−7.31655	+	8.45388i	−0.327206	+	0.378069i
$501$		0			0
$502$	19.0853	+	1.66974i	0.851817	+	0.0745243i
$503$	33.8781	−	9.07762i	1.51055	−	0.404751i	0.593933	−	0.804515i	$-0.297575\pi$
$503$	33.8781	−	9.07762i	1.51055	−	0.404751i	0.916618	+	0.399764i	$0.130908\pi$
$504$		0			0
$505$	−12.0343	−	2.18520i	−0.535519	−	0.0972402i
$506$	−1.00266	+	2.75478i	−0.0445737	+	0.122465i
$507$		0			0
$508$	1.74385	−	0.152567i	0.0773707	−	0.00676905i
$509$	−8.89067	+	3.23594i	−0.394072	+	0.143430i	−0.531453	−	0.847088i	$-0.678354\pi$
$509$	−8.89067	+	3.23594i	−0.394072	+	0.143430i	0.137381	+	0.990518i	$0.456132\pi$
$510$		0			0
$511$	−0.391704	−	2.22146i	−0.0173279	−	0.0982717i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$			9.32122i			0.411141i
$515$	8.95399	+	34.1104i	0.394560	+	1.50308i
$516$		0			0
$517$	−29.7163	−	13.8569i	−1.30692	−	0.609427i
$518$	0.0908137	+	1.03801i	0.00399012	+	0.0456073i
$519$		0			0
$520$	−6.85116	−	12.0073i	−0.300443	−	0.526555i
$521$	−6.93135	+	4.00181i	−0.303668	+	0.175323i	−0.644089	−	0.764950i	$-0.722764\pi$
$521$	−6.93135	+	4.00181i	−0.303668	+	0.175323i	0.340422	+	0.940273i	$0.389430\pi$
$522$		0			0
$523$	−0.789663	−	2.94706i	−0.0345295	−	0.128866i	0.946510	−	0.322676i	$-0.104582\pi$
$523$	−0.789663	−	2.94706i	−0.0345295	−	0.128866i	−0.981039	+	0.193810i	$0.937916\pi$
$524$	−0.601392	+	0.504628i	−0.0262719	+	0.0220448i
$525$		0			0
$526$	4.92886	−	27.9529i	0.214908	−	1.21881i
$527$	14.8095	+	21.1502i	0.645114	+	0.921318i
$528$		0			0
$529$	−14.3170	−	17.0624i	−0.622479	−	0.741842i
$530$	3.30024	−	1.18220i	0.143353	−	0.0513513i
$531$		0			0
$532$	0.0447076	−	0.166851i	0.00193832	−	0.00723390i
$533$	17.5130	+	37.5567i	0.758571	+	1.62676i
$534$		0			0
$535$	−12.9072	−	9.13600i	−0.558027	−	0.394984i
$536$	−2.19264	−	6.02423i	−0.0947076	−	0.260207i
$537$		0			0
$538$	−8.03951	−	5.62933i	−0.346608	−	0.242697i
$539$	23.9592			1.03200
$540$		0			0
$541$	2.43402			0.104647			0.0523234	−	0.998630i	$-0.483337\pi$
$541$	2.43402			0.104647			0.0523234	+	0.998630i	$0.483337\pi$
$542$	−6.16591	−	4.31742i	−0.264848	−	0.185449i
$543$		0			0
$544$	1.05531	+	2.89945i	0.0452461	+	0.124313i
$545$	−23.1607	+	3.96240i	−0.992097	+	0.169730i
$546$		0			0
$547$	8.69456	+	18.6455i	0.371752	+	0.797225i	0.999818	+	0.0190653i	$0.00606905\pi$
$547$	8.69456	+	18.6455i	0.371752	+	0.797225i	−0.628066	+	0.778160i	$0.716153\pi$
$548$	1.34380	−	5.01512i	0.0574041	−	0.214235i
$549$		0			0
$550$	7.10786	+	15.6571i	0.303080	+	0.667622i
$551$	−6.09921	−	7.26876i	−0.259835	−	0.309659i
$552$		0			0
$553$	0.949890	+	1.35658i	0.0403934	+	0.0576878i
$554$	4.41440	−	25.0353i	0.187550	−	1.06365i
$555$		0			0
$556$	−2.13282	+	1.78964i	−0.0904515	+	0.0758978i
$557$	5.30767	+	19.8085i	0.224893	+	0.839313i	0.982447	+	0.186540i	$0.0597275\pi$
$557$	5.30767	+	19.8085i	0.224893	+	0.839313i	−0.757554	+	0.652772i	$0.773606\pi$
$558$		0			0
$559$	−4.54766	+	2.62559i	−0.192345	+	0.111051i
$560$	0.107261	−	0.392303i	0.00453260	−	0.0165778i
$561$		0			0
$562$	0.253183	+	2.89389i	0.0106799	+	0.122071i
$563$	−9.57025	−	4.46268i	−0.403338	−	0.188080i	0.210354	−	0.977625i	$-0.432538\pi$
$563$	−9.57025	−	4.46268i	−0.403338	−	0.188080i	−0.613692	+	0.789546i	$0.710316\pi$
$564$		0			0
$565$	7.53936	−	1.97908i	0.317183	−	0.0832606i
$566$		−	7.84108i		−	0.329585i
$567$		0			0
$568$	5.00837	−	5.00837i	0.210147	−	0.210147i
$569$	4.75609	+	26.9731i	0.199386	+	1.13077i	0.906033	+	0.423207i	$0.139096\pi$
$569$	4.75609	+	26.9731i	0.199386	+	1.13077i	−0.706647	+	0.707566i	$0.749793\pi$
$570$		0			0
$571$	−14.9025	+	5.42407i	−0.623651	+	0.226990i	−0.634466	−	0.772951i	$-0.718780\pi$
$571$	−14.9025	+	5.42407i	−0.623651	+	0.226990i	0.0108146	+	0.999942i	$0.496558\pi$
$572$	−21.1805	+	1.85306i	−0.885603	+	0.0774802i
$573$		0			0
$574$	−0.416960	+	1.14559i	−0.0174036	+	0.0478159i
$575$	4.24204	+	0.414694i	0.176905	+	0.0172939i
$576$		0			0
$577$	17.9461	−	4.80864i	0.747105	−	0.200186i	0.134872	−	0.990863i	$-0.456938\pi$
$577$	17.9461	−	4.80864i	0.747105	−	0.200186i	0.612234	+	0.790677i	$0.290271\pi$
$578$	−7.45107	−	0.651884i	−0.309924	−	0.0271148i
$579$		0			0
$580$	−14.2731	−	17.1869i	−0.592657	−	0.713648i
$581$	0.750791	+	0.132385i	0.0311481	+	0.00549224i
$582$		0			0
$583$	0.469898	−	5.37096i	0.0194612	−	0.222442i
$584$	6.20105	−	10.7405i	0.256601	−	0.444447i
$585$		0			0
$586$	9.77870	+	16.9372i	0.403955	+	0.699670i
$587$	−14.0015	+	6.52901i	−0.577904	+	0.269481i	−0.689516	−	0.724271i	$-0.742177\pi$
$587$	−14.0015	+	6.52901i	−0.577904	+	0.269481i	0.111611	+	0.993752i	$0.464399\pi$
$588$		0			0
$589$	5.10836	−	6.08791i	0.210486	−	0.250848i
$590$	−23.2655	+	10.7050i	−0.957826	+	0.440719i
$591$		0			0
$592$	−3.28590	+	4.69276i	−0.135050	+	0.192871i
$593$	−12.1315	−	12.1315i	−0.498180	−	0.498180i	0.412691	−	0.910871i	$-0.364589\pi$
$593$	−12.1315	−	12.1315i	−0.498180	−	0.498180i	−0.910871	+	0.412691i	$0.864589\pi$
$594$		0			0
$595$	−0.957183	−	0.811512i	−0.0392407	−	0.0332687i
$596$	−11.2318	+	1.98047i	−0.460073	+	0.0811233i
$597$		0			0
$598$	−2.22730	+	4.77647i	−0.0910813	+	0.195324i
$599$	5.04538	+	4.23358i	0.206149	+	0.172979i	0.740017	−	0.672589i	$-0.234818\pi$
$599$	5.04538	+	4.23358i	0.206149	+	0.172979i	−0.533868	+	0.845568i	$0.679262\pi$
$600$		0			0
$601$	−27.2576	−	9.92094i	−1.11186	−	0.404684i	−0.280184	−	0.959946i	$-0.590396\pi$
$601$	−27.2576	−	9.92094i	−1.11186	−	0.404684i	−0.831675	+	0.555262i	$0.812618\pi$
$602$	−0.149222	−	0.0399838i	−0.00608182	−	0.00162962i
$603$		0			0
$604$	4.53881	+	2.62049i	0.184682	+	0.106626i
$605$	1.84850	+	0.00941077i	0.0751524	+	0.000382602i
$606$		0			0
$607$	31.9580	−	22.3772i	1.29714	−	0.908264i	0.298205	−	0.954502i	$-0.403612\pi$
$607$	31.9580	−	22.3772i	1.29714	−	0.908264i	0.998930	+	0.0462382i	$0.0147233\pi$
$608$	0.777960	−	0.544734i	0.0315505	−	0.0220919i
$609$		0			0
$610$	−0.190602	+	0.188671i	−0.00771726	+	0.00763909i
$611$	−51.0480	−	29.4726i	−2.06518	−	1.19233i
$612$		0			0
$613$	−43.4107	−	11.6319i	−1.75334	−	0.469807i	−0.768008	−	0.640440i	$-0.778752\pi$
$613$	−43.4107	−	11.6319i	−1.75334	−	0.469807i	−0.985335	+	0.170634i	$0.945419\pi$
$614$	−6.72186	−	2.44656i	−0.271272	−	0.0987350i
$615$		0			0
$616$	−0.479156	−	0.402060i	−0.0193058	−	0.0161995i
$617$	−2.38076	+	5.10556i	−0.0958459	+	0.205542i	−0.948385	−	0.317121i	$-0.897284\pi$
$617$	−2.38076	+	5.10556i	−0.0958459	+	0.205542i	0.852539	+	0.522663i	$0.175062\pi$
$618$		0			0
$619$	−9.08289	+	1.60156i	−0.365072	+	0.0643721i	−0.353175	−	0.935557i	$-0.614898\pi$
$619$	−9.08289	+	1.60156i	−0.365072	+	0.0643721i	−0.0118969	+	0.999929i	$0.503787\pi$
$620$	12.1003	−	14.2723i	0.485959	−	0.573191i
$621$		0			0
$622$	10.2677	+	10.2677i	0.411698	+	0.411698i
$623$	−0.369774	+	0.528092i	−0.0148147	+	0.0211576i
$624$		0			0
$625$	19.4744	−	15.6764i	0.778974	−	0.627056i
$626$	−2.45078	+	2.92072i	−0.0979528	+	0.116736i
$627$		0			0
$628$	0.336006	−	0.156682i	0.0134081	−	0.00625229i
$629$	8.83817	+	15.3082i	0.352401	+	0.610377i
$630$		0			0
$631$	9.66695	−	16.7436i	0.384835	−	0.666554i	−0.606911	−	0.794770i	$-0.707592\pi$
$631$	9.66695	−	16.7436i	0.384835	−	0.666554i	0.991746	+	0.128216i	$0.0409250\pi$
$632$	−0.793572	+	9.07057i	−0.0315666	+	0.360808i
$633$		0			0
$634$	−24.9281	−	4.39549i	−0.990021	−	0.174567i
$635$	−3.89757	−	0.360997i	−0.154670	−	0.0143257i
$636$		0			0
$637$	42.9088	+	3.75403i	1.70011	+	0.148740i
$638$	−33.1886	+	8.89285i	−1.31395	+	0.352071i
$639$		0			0
$640$	1.83819	−	1.27321i	0.0726607	−	0.0503282i
$641$	6.18059	−	16.9810i	0.244118	−	0.670710i	−0.755756	−	0.654854i	$-0.772730\pi$
$641$	6.18059	−	16.9810i	0.244118	−	0.670710i	0.999874	−	0.0158565i	$-0.00504749\pi$
$642$		0			0
$643$	−25.6737	+	2.24616i	−1.01247	+	0.0885797i	−0.581299	−	0.813690i	$-0.697455\pi$
$643$	−25.6737	+	2.24616i	−1.01247	+	0.0885797i	−0.431172	+	0.902270i	$0.641900\pi$
$644$	−0.145696	+	0.0530290i	−0.00574123	+	0.00208964i
$645$		0			0
$646$	−0.508853	−	2.88585i	−0.0200205	−	0.113542i
$647$	−9.88031	+	9.88031i	−0.388435	+	0.388435i	−0.874129	−	0.485694i	$-0.838567\pi$
$647$	−9.88031	+	9.88031i	−0.388435	+	0.388435i	0.485694	+	0.874129i	$0.338567\pi$
$648$		0			0
$649$			39.3876i			1.54610i
$650$	10.2763	+	29.1542i	0.403070	+	1.14352i
$651$		0			0
$652$	−17.4217	−	8.12389i	−0.682288	−	0.318156i
$653$	−4.04621	−	46.2484i	−0.158341	−	1.80984i	−0.495731	−	0.868476i	$-0.665100\pi$
$653$	−4.04621	−	46.2484i	−0.158341	−	1.80984i	0.337391	−	0.941365i	$-0.390456\pi$
$654$		0			0
$655$	1.52471	−	0.869974i	0.0595755	−	0.0339927i
$656$	−5.80472	+	3.35136i	−0.226636	+	0.130848i
$657$		0			0
$658$	−0.448823	−	1.67503i	−0.0174969	−	0.0652995i
$659$	3.19816	−	2.68357i	0.124582	−	0.104537i	−0.578368	−	0.815776i	$-0.696310\pi$
$659$	3.19816	−	2.68357i	0.124582	−	0.104537i	0.702950	+	0.711239i	$0.251866\pi$
$660$		0			0
$661$	2.58039	−	14.6341i	0.100365	−	0.569201i	−0.892605	−	0.450839i	$-0.851125\pi$
$661$	2.58039	−	14.6341i	0.100365	−	0.569201i	0.992971	−	0.118361i	$-0.0377642\pi$
$662$	17.3101	+	24.7214i	0.672777	+	0.960825i
$663$		0			0
$664$	2.69428	+	3.21092i	0.104558	+	0.124608i
$665$	−0.165017	+	0.349227i	−0.00639908	+	0.0135424i
$666$		0			0
$667$	−2.20435	+	8.22673i	−0.0853526	+	0.318540i
$668$	5.54575	+	11.8929i	0.214572	+	0.460150i
$669$		0			0
$670$	2.41736	+	14.1298i	0.0933908	+	0.545882i
$671$	0.141072	+	0.387593i	0.00544604	+	0.0149629i
$672$		0			0
$673$	−3.97021	−	2.77997i	−0.153040	−	0.107160i	0.494548	−	0.869150i	$-0.335334\pi$
$673$	−3.97021	−	2.77997i	−0.153040	−	0.107160i	−0.647589	+	0.761990i	$0.724222\pi$
$674$	20.6777			0.796474
$675$		0			0
$676$	−25.2228			−0.970107
$677$	−34.8354	−	24.3920i	−1.33883	−	0.937460i	−0.338838	−	0.940845i	$-0.610034\pi$
$677$	−34.8354	−	24.3920i	−1.33883	−	0.937460i	−0.999994	+	0.00338474i	$0.998923\pi$
$678$		0			0
$679$	0.541095	+	1.48665i	0.0207653	+	0.0570522i
$680$	−1.16347	−	6.80064i	−0.0446170	−	0.260793i
$681$		0			0
$682$	−12.1619	−	26.0813i	−0.465703	−	0.998703i
$683$	−4.24546	+	15.8443i	−0.162448	+	0.606265i	0.835904	+	0.548876i	$0.184944\pi$
$683$	−4.24546	+	15.8443i	−0.162448	+	0.606265i	−0.998352	+	0.0573886i	$0.981723\pi$
$684$		0			0
$685$	−4.95999	+	10.4969i	−0.189511	+	0.401065i
$686$	1.63290	+	1.94602i	0.0623445	+	0.0742992i
$687$		0			0
$688$	−0.487178	−	0.695762i	−0.0185735	−	0.0265257i
$689$	1.68309	−	9.54528i	0.0641206	−	0.363646i
$690$		0			0
$691$	−24.5196	+	20.5744i	−0.932771	+	0.782688i	−0.976313	−	0.216364i	$-0.930580\pi$
$691$	−24.5196	+	20.5744i	−0.932771	+	0.782688i	0.0435418	+	0.999052i	$0.486136\pi$
$692$	1.48077	+	5.52632i	0.0562905	+	0.210079i
$693$		0			0
$694$	−12.9748	+	7.49103i	−0.492518	+	0.284355i
$695$	5.40734	−	3.08533i	0.205112	−	0.117033i
$696$		0			0
$697$	1.80250	+	20.6027i	0.0682746	+	0.780382i
$698$	−26.7399	−	12.4690i	−1.01212	−	0.471960i
$699$		0			0
$700$	−0.392707	+	0.820253i	−0.0148429	+	0.0310027i
$701$			8.63693i			0.326213i	0.986609	+	0.163106i	$0.0521513\pi$
$701$			8.63693i			0.326213i	−0.986609	+	0.163106i	$0.947849\pi$
$702$		0			0
$703$	3.84717	−	3.84717i	0.145099	−	0.145099i
$704$	−0.597175	−	3.38675i	−0.0225069	−	0.127643i
$705$		0			0
$706$	−15.2926	+	5.56605i	−0.575545	+	0.209481i
$707$	−0.991097	+	0.0867098i	−0.0372740	+	0.00326106i
$708$		0			0
$709$	4.25952	−	11.7029i	0.159970	−	0.439513i	−0.833650	−	0.552292i	$-0.813753\pi$
$709$	4.25952	−	11.7029i	0.159970	−	0.439513i	0.993620	+	0.112780i	$0.0359754\pi$
$710$	−13.0197	+	9.01805i	−0.488620	+	0.338442i
$711$		0			0
$712$	−3.42371	+	0.917381i	−0.128309	+	0.0343803i
$713$	−7.10617	−	0.621710i	−0.266128	−	0.0232832i
$714$		0			0
$715$	47.3394	+	4.38462i	1.77039	+	0.163975i
$716$	−23.0242	−	4.05979i	−0.860456	−	0.151722i
$717$		0			0
$718$	−2.92087	+	33.3857i	−0.109006	+	1.24594i
$719$	2.02215	−	3.50246i	0.0754133	−	0.130620i	−0.825853	−	0.563886i	$-0.809306\pi$
$719$	2.02215	−	3.50246i	0.0754133	−	0.130620i	0.901266	+	0.433266i	$0.142639\pi$
$720$		0			0
$721$	1.43428	+	2.48424i	0.0534153	+	0.0925181i
$722$	16.4024	−	7.64856i	0.610434	−	0.284650i
$723$		0			0
$724$	15.1842	−	18.0958i	0.564315	−	0.672524i
$725$	24.5360	+	43.5148i	0.911243	+	1.61610i
$726$		0			0
$727$	7.39684	−	10.5638i	0.274333	−	0.391789i	−0.658217	−	0.752828i	$-0.728689\pi$
$727$	7.39684	−	10.5638i	0.274333	−	0.391789i	0.932551	+	0.361039i	$0.117578\pi$
$728$	−0.795130	−	0.795130i	−0.0294695	−	0.0294695i
$729$		0			0
$730$	−17.9337	+	21.1529i	−0.663755	+	0.782903i
$731$	−2.58093	+	0.455088i	−0.0954593	+	0.0168320i
$732$		0			0
$733$	7.30068	−	15.6564i	0.269657	−	0.578281i	−0.724120	−	0.689674i	$-0.757754\pi$
$733$	7.30068	−	15.6564i	0.269657	−	0.578281i	0.993776	+	0.111394i	$0.0355315\pi$
$734$	12.3733	+	10.3825i	0.456708	+	0.383224i
$735$		0			0
$736$	−0.801044	−	0.291556i	−0.0295269	−	0.0107469i
$737$	21.2957	+	5.70615i	0.784435	+	0.210189i
$738$		0			0
$739$	−22.9689	−	13.2611i	−0.844924	−	0.487817i	0.0140111	−	0.999902i	$-0.495540\pi$
$739$	−22.9689	−	13.2611i	−0.844924	−	0.487817i	−0.858935	+	0.512085i	$0.828873\pi$
$740$	9.10402	−	9.01179i	0.334670	−	0.331280i
$741$		0			0
$742$	0.233578	−	0.163553i	0.00857493	−	0.00600423i
$743$	16.1586	−	11.3143i	0.592800	−	0.415083i	−0.238311	−	0.971189i	$-0.576594\pi$
$743$	16.1586	−	11.3143i	0.592800	−	0.415083i	0.831112	+	0.556106i	$0.187705\pi$
$744$		0			0
$745$	25.5022	+	0.129832i	0.934329	+	0.00475669i
$746$	17.8662	+	10.3151i	0.654128	+	0.377661i
$747$		0			0
$748$	−10.2495	−	2.74636i	−0.374760	−	0.100417i
$749$	−1.20870	−	0.439929i	−0.0441648	−	0.0160747i
$750$		0			0
$751$	21.2071	+	17.7949i	0.773858	+	0.649344i	0.941694	−	0.336471i	$-0.109233\pi$
$751$	21.2071	+	17.7949i	0.773858	+	0.649344i	−0.167836	+	0.985815i	$0.553678\pi$
$752$	4.02935	−	8.64098i	0.146935	−	0.315104i
$753$		0			0
$754$	−60.8311	+	10.7262i	−2.21534	+	0.390624i
$755$	−8.93894	−	7.57854i	−0.325321	−	0.275811i
$756$		0			0
$757$	25.6984	+	25.6984i	0.934023	+	0.934023i	0.997954	−	0.0639309i	$-0.0203637\pi$
$757$	25.6984	+	25.6984i	0.934023	+	0.934023i	−0.0639309	+	0.997954i	$0.520364\pi$
$758$	21.5324	−	30.7515i	0.782093	−	1.11694i
$759$		0			0
$760$	−1.92920	+	0.887673i	−0.0699795	+	0.0321993i
$761$	−22.9130	+	27.3066i	−0.830594	+	0.989863i	0.169397	+	0.985548i	$0.445818\pi$
$761$	−22.9130	+	27.3066i	−0.830594	+	0.989863i	−0.999991	+	0.00431527i	$0.998626\pi$
$762$		0			0
$763$	−1.73221	+	0.807741i	−0.0627101	+	0.0292422i
$764$	11.4400	+	19.8146i	0.413883	+	0.716867i
$765$		0			0
$766$	−16.9937	+	29.4339i	−0.614006	+	1.06349i
$767$	−6.17141	+	70.5396i	−0.222837	+	2.54704i
$768$		0			0
$769$	−30.8291	−	5.43600i	−1.11173	−	0.196027i	−0.412520	−	0.910948i	$-0.635351\pi$
$769$	−30.8291	−	5.43600i	−1.11173	−	0.196027i	−0.699205	+	0.714921i	$0.746463\pi$
$770$	0.893567	+	1.07599i	0.0322019	+	0.0387760i
$771$		0			0
$772$	1.60223	+	0.140177i	0.0576655	+	0.00504508i
$773$	−18.1566	+	4.86504i	−0.653047	+	0.174983i	−0.570106	−	0.821571i	$-0.693098\pi$
$773$	−18.1566	+	4.86504i	−0.653047	+	0.174983i	−0.0829408	+	0.996554i	$0.526431\pi$
$774$		0			0
$775$	−32.3234	+	26.5665i	−1.16109	+	0.954296i
$776$	−2.97496	+	8.17364i	−0.106795	+	0.293417i
$777$		0			0
$778$	9.55707	−	0.836136i	0.342638	−	0.0299769i
$779$	5.98176	−	2.17718i	0.214319	−	0.0780057i
$780$		0			0
$781$	4.22973	+	23.9880i	0.151352	+	0.858359i
$782$	−1.85988	+	1.85988i	−0.0665091	+	0.0665091i
$783$		0			0
$784$			6.96692i			0.248819i
$785$	−0.801837	+	0.210482i	−0.0286188	+	0.00751243i
$786$		0			0
$787$	−19.4420	−	9.06596i	−0.693033	−	0.323167i	0.0439920	−	0.999032i	$-0.485992\pi$
$787$	−19.4420	−	9.06596i	−0.693033	−	0.323167i	−0.737025	+	0.675865i	$0.763770\pi$
$788$	−1.59122	−	18.1877i	−0.0566849	−	0.647911i
$789$		0			0
$790$	5.36958	−	19.6391i	0.191041	−	0.698726i
$791$	0.549087	−	0.317016i	0.0195233	−	0.0112718i
$792$		0			0
$793$	0.191918	+	0.716248i	0.00681521	+	0.0254347i
$794$	0.0877083	−	0.0735960i	0.00311265	−	0.00261183i
$795$		0			0
$796$	−3.23115	+	18.3248i	−0.114525	+	0.649505i
$797$	7.01552	+	10.0192i	0.248503	+	0.354899i	0.923952	−	0.382507i	$-0.124939\pi$
$797$	7.01552	+	10.0192i	0.248503	+	0.354899i	−0.675450	+	0.737406i	$0.736050\pi$
$798$		0			0
$799$	−18.9097	−	22.5357i	−0.668976	−	0.797254i
$800$	−4.55282	+	2.06684i	−0.160966	+	0.0730739i
$801$		0			0
$802$	7.02978	−	26.2355i	0.248230	−	0.926408i
$803$	18.0250	+	38.6547i	0.636088	+	1.36410i
$804$		0			0
$805$	0.341730	−	0.0584639i	0.0120444	−	0.00206058i
$806$	−17.6943	−	48.6148i	−0.623256	−	1.71238i
$807$		0			0
$808$	−4.48069	−	3.13741i	−0.157630	−	0.110374i
$809$	−0.0295016			−0.00103722			−0.000518610	−	1.00000i	$-0.500165\pi$
$809$	−0.0295016			−0.00103722			−0.000518610		1.00000i	$0.500165\pi$
$810$		0			0
$811$	−11.5459			−0.405432			−0.202716	−	0.979238i	$-0.564977\pi$
$811$	−11.5459			−0.405432			−0.202716	+	0.979238i	$0.564977\pi$
$812$	−1.48857	−	1.04231i	−0.0522386	−	0.0365779i
$813$		0			0
$814$	−6.73824	−	18.5132i	−0.236175	−	0.648886i
$815$	35.0840	+	24.8332i	1.22894	+	0.869869i
$816$		0			0
$817$	0.340908	+	0.731080i	0.0119269	+	0.0255772i
$818$	−5.46450	+	20.3938i	−0.191062	+	0.713052i
$819$		0			0
$820$	14.1098	−	5.05434i	0.492734	−	0.176505i
$821$	−16.7175	−	19.9231i	−0.583444	−	0.695321i	0.390888	−	0.920438i	$-0.372168\pi$
$821$	−16.7175	−	19.9231i	−0.583444	−	0.695321i	−0.974332	+	0.225117i	$0.927724\pi$
$822$		0			0
$823$	−26.9940	−	38.5515i	−0.940952	−	1.34382i	−0.939035	−	0.343821i	$-0.888279\pi$
$823$	−26.9940	−	38.5515i	−0.940952	−	1.34382i	−0.00191729	−	0.999998i	$-0.500610\pi$
$824$	−2.73869	+	15.5319i	−0.0954066	+	0.541078i
$825$		0			0
$826$	−1.59578	+	1.33902i	−0.0555243	+	0.0465905i
$827$	−9.42010	−	35.1563i	−0.327569	−	1.22250i	−0.911704	−	0.410847i	$-0.865233\pi$
$827$	−9.42010	−	35.1563i	−0.327569	−	1.22250i	0.584135	−	0.811656i	$-0.301434\pi$
$828$		0			0
$829$	28.3943	−	16.3935i	0.986176	−	0.569369i	0.0820471	−	0.996628i	$-0.473854\pi$
$829$	28.3943	−	16.3935i	0.986176	−	0.569369i	0.904129	+	0.427259i	$0.140521\pi$
$830$	−4.64492	−	8.14068i	−0.161228	−	0.282567i
$831$		0			0
$832$	−0.538837	−	6.15893i	−0.0186808	−	0.213522i
$833$	19.4825	+	9.08486i	0.675030	+	0.314772i
$834$		0			0
$835$	−7.45001	−	28.3810i	−0.257818	−	0.982164i
$836$			3.26606i			0.112959i
$837$		0			0
$838$	14.4599	−	14.4599i	0.499509	−	0.499509i
$839$	4.07938	+	23.1353i	0.140836	+	0.798719i	0.970617	+	0.240630i	$0.0773541\pi$
$839$	4.07938	+	23.1353i	0.140836	+	0.798719i	−0.829781	+	0.558089i	$0.811535\pi$
$840$		0			0
$841$	−66.5510	+	24.2226i	−2.29486	+	0.835261i
$842$	24.3990	−	2.13464i	0.840846	−	0.0735645i
$843$		0			0
$844$	−2.89978	+	7.96708i	−0.0998145	+	0.274238i
$845$	55.4924	+	10.0764i	1.90900	+	0.346638i
$846$		0			0
$847$	0.145237	−	0.0389161i	0.00499039	−	0.00133717i
$848$	1.56178	+	0.136638i	0.0536318	+	0.00469217i
$849$		0			0
$850$	−0.157081	+	15.4268i	−0.00538782	+	0.529136i
$851$	−4.80934	−	0.848016i	−0.164862	−	0.0290696i
$852$		0			0
$853$	1.59838	−	18.2695i	0.0547274	−	0.625537i	−0.918458	−	0.395517i	$-0.870565\pi$
$853$	1.59838	−	18.2695i	0.0547274	−	0.625537i	0.973186	−	0.230020i	$-0.0738792\pi$
$854$	−0.0109074	+	0.0188921i	−0.000373243	+	0.000646475i
$855$		0			0
$856$	−3.53598	−	6.12449i	−0.120857	−	0.209331i
$857$	16.1503	−	7.53102i	0.551685	−	0.257255i	−0.126726	−	0.991938i	$-0.540447\pi$
$857$	16.1503	−	7.53102i	0.551685	−	0.257255i	0.678411	+	0.734683i	$0.262669\pi$
$858$		0			0
$859$	12.0032	−	14.3048i	0.409543	−	0.488075i	−0.521362	−	0.853336i	$-0.674576\pi$
$859$	12.0032	−	14.3048i	0.409543	−	0.488075i	0.930905	+	0.365261i	$0.119020\pi$
$860$	0.793883	+	1.72537i	0.0270712	+	0.0588345i
$861$		0			0
$862$	−11.6352	+	16.6168i	−0.396297	+	0.565971i
$863$	−6.68274	−	6.68274i	−0.227483	−	0.227483i	0.584157	−	0.811640i	$-0.301425\pi$
$863$	−6.68274	−	6.68274i	−0.227483	−	0.227483i	−0.811640	+	0.584157i	$0.801425\pi$
$864$		0			0
$865$	−1.05010	−	12.7500i	−0.0357044	−	0.433512i
$866$	−24.1183	+	4.25271i	−0.819573	+	0.144513i
$867$		0			0
$868$	0.643223	−	1.37940i	0.0218324	−	0.0468197i
$869$	−23.9870	−	20.1275i	−0.813703	−	0.682778i
$870$		0			0
$871$	37.2445	+	13.5559i	1.26198	+	0.459324i
$872$	−10.1502	−	2.71975i	−0.343730	−	0.0921022i
$873$		0			0
$874$	0.701122	+	0.404793i	0.0237158	+	0.0136923i
$875$	1.19168	−	1.64775i	0.0402861	−	0.0557041i
$876$		0			0
$877$	9.84965	−	6.89680i	0.332599	−	0.232888i	−0.395333	−	0.918538i	$-0.629371\pi$
$877$	9.84965	−	6.89680i	0.332599	−	0.232888i	0.727932	+	0.685650i	$0.240482\pi$
$878$	−0.00939635	+	0.00657940i	−0.000317112	+	0.000222044i
$879$		0			0
$880$	−0.0391486	+	7.68973i	−0.00131970	+	0.259221i
$881$	18.9372	+	10.9334i	0.638009	+	0.368355i	0.783847	−	0.620954i	$-0.213255\pi$
$881$	18.9372	+	10.9334i	0.638009	+	0.368355i	−0.145838	+	0.989308i	$0.546588\pi$
$882$		0			0
$883$	22.5759	+	6.04920i	0.759740	+	0.203572i	0.617834	−	0.786308i	$-0.288010\pi$
$883$	22.5759	+	6.04920i	0.759740	+	0.203572i	0.141906	+	0.989880i	$0.454677\pi$
$884$	−17.9257	−	6.52442i	−0.602906	−	0.219440i
$885$		0			0
$886$	0.539395	+	0.452606i	0.0181213	+	0.0152056i
$887$	−2.37089	+	5.08439i	−0.0796067	+	0.170717i	−0.942083	−	0.335381i	$-0.891135\pi$
$887$	−2.37089	+	5.08439i	−0.0796067	+	0.170717i	0.862476	+	0.506098i	$0.168913\pi$
$888$		0			0
$889$	−0.313550	+	0.0552874i	−0.0105161	+	0.00185428i
$890$	7.89897	−	0.650567i	0.264774	−	0.0218070i
$891$		0			0
$892$	−6.69100	−	6.69100i	−0.224031	−	0.224031i
$893$	−5.19363	+	7.41728i	−0.173798	+	0.248210i
$894$		0			0
$895$	49.0336	+	18.1300i	1.63901	+	0.606018i
$896$	0.116912	−	0.139330i	0.00390576	−	0.00465470i
$897$		0			0
$898$	−34.2729	+	15.9817i	−1.14370	+	0.533317i
$899$	−41.8027	−	72.4044i	−1.39420	−	2.41482i
$900$		0			0
$901$	2.41866	−	4.18924i	0.0805773	−	0.139564i
$902$	2.00899	−	22.9629i	0.0668921	−	0.764580i
$903$		0			0
$904$	3.43297	+	0.605326i	0.114179	+	0.0201328i
$905$	−40.6357	+	33.7464i	−1.35078	+	1.12177i
$906$		0			0
$907$	−39.3691	−	3.44435i	−1.30723	−	0.114368i	−0.587842	−	0.808976i	$-0.700022\pi$
$907$	−39.3691	−	3.44435i	−1.30723	−	0.114368i	−0.719389	+	0.694608i	$0.755578\pi$
$908$	−12.0465	+	3.22784i	−0.399776	+	0.107120i
$909$		0			0
$910$	1.43171	+	2.06701i	0.0474606	+	0.0685206i
$911$	3.02154	−	8.30162i	0.100108	−	0.275045i	−0.879521	−	0.475860i	$-0.842137\pi$
$911$	3.02154	−	8.30162i	0.100108	−	0.275045i	0.979629	+	0.200815i	$0.0643591\pi$
$912$		0			0
$913$	−14.3599	+	1.25633i	−0.475244	+	0.0415784i
$914$	−5.19617	+	1.89125i	−0.171874	+	0.0625571i
$915$		0			0
$916$	−1.80635	−	10.2443i	−0.0596833	−	0.338481i
$917$	0.100967	−	0.100967i	0.00333423	−	0.00333423i
$918$		0			0
$919$		−	31.2847i		−	1.03199i	−0.856592	−	0.515994i	$-0.827423\pi$
$919$		−	31.2847i		−	1.03199i	0.856592	−	0.515994i	$-0.172577\pi$
$920$	1.64589	+	0.961463i	0.0542635	+	0.0316985i
$921$		0			0
$922$	10.6551	+	4.96857i	0.350908	+	0.163631i
$923$	3.81653	+	43.6231i	0.125623	+	1.43587i
$924$		0			0
$925$	−23.6298	+	16.1898i	−0.776945	+	0.532316i
$926$	16.3436	−	9.43599i	0.537085	−	0.310086i
$927$		0			0
$928$	−2.58589	−	9.65066i	−0.0848859	−	0.316798i
$929$	8.15050	−	6.83908i	0.267409	−	0.224383i	−0.499216	−	0.866477i	$-0.666379\pi$
$929$	8.15050	−	6.83908i	0.267409	−	0.224383i	0.766626	+	0.642094i	$0.221934\pi$
$930$		0			0
$931$	1.14896	−	6.51606i	0.0376556	−	0.213555i
$932$	−9.80613	−	14.0046i	−0.321211	−	0.458736i
$933$		0			0
$934$	8.85273	+	10.5503i	0.289670	+	0.345216i
$935$	21.4528	+	10.1369i	0.701581	+	0.331511i
$936$		0			0
$937$	8.26547	−	30.8471i	0.270021	−	1.00773i	−0.689084	−	0.724682i	$-0.741987\pi$
$937$	8.26547	−	30.8471i	0.270021	−	1.00773i	0.959105	−	0.283051i	$-0.0913465\pi$
$938$	0.492783	+	1.05678i	0.0160899	+	0.0345050i
$939$		0			0
$940$	−12.3170	+	17.4012i	−0.401735	+	0.567566i
$941$	0.890141	+	2.44564i	0.0290178	+	0.0797257i	0.953356	−	0.301849i	$-0.0976040\pi$
$941$	0.890141	+	2.44564i	0.0290178	+	0.0797257i	−0.924338	+	0.381575i	$0.875382\pi$
$942$		0			0
$943$	−4.68043	−	3.27727i	−0.152416	−	0.106723i
$944$	−11.4532			−0.372771
$945$		0			0
$946$	2.92097			0.0949691
$947$	−7.43119	−	5.20337i	−0.241481	−	0.169087i	0.446571	−	0.894748i	$-0.352645\pi$
$947$	−7.43119	−	5.20337i	−0.241481	−	0.169087i	−0.688052	+	0.725661i	$0.741534\pi$
$948$		0			0
$949$	26.2246	+	72.0514i	0.851285	+	2.33889i
$950$	4.59904	−	1.18226i	0.149213	−	0.0383574i
$951$		0			0
$952$	−0.237175	−	0.508624i	−0.00768689	−	0.0164846i
$953$	2.72977	−	10.1876i	0.0884258	−	0.330010i	−0.907515	−	0.420020i	$-0.862023\pi$
$953$	2.72977	−	10.1876i	0.0884258	−	0.330010i	0.995941	+	0.0900099i	$0.0286899\pi$
$954$		0			0
$955$	−17.2531	−	48.1641i	−0.558298	−	1.55855i
$956$	−4.57363	−	5.45064i	−0.147922	−	0.176286i
$957$		0			0
$958$	17.0493	+	24.3489i	0.550838	+	0.786678i
$959$	−0.163983	+	0.929995i	−0.00529529	+	0.0300311i
$960$		0			0
$961$	29.8936	−	25.0837i	0.964310	−	0.809152i
$962$	−9.16686	−	34.2112i	−0.295552	−	1.10301i
$963$		0			0
$964$	21.7525	−	12.5588i	0.700600	−	0.404492i
$965$	−3.46905	−	0.948485i	−0.111673	−	0.0305328i
$966$		0			0
$967$	−1.27533	−	14.5771i	−0.0410118	−	0.468768i	−0.988735	−	0.149675i	$-0.952177\pi$
$967$	−1.27533	−	14.5771i	−0.0410118	−	0.468768i	0.947723	−	0.319093i	$-0.103378\pi$
$968$	0.749233	+	0.349373i	0.0240813	+	0.0112293i
$969$		0			0
$970$	9.81052	−	16.7943i	0.314997	−	0.539232i
$971$			31.4688i			1.00988i	0.863153	+	0.504942i	$0.168486\pi$
$971$			31.4688i			1.00988i	−0.863153	+	0.504942i	$0.831514\pi$
$972$		0			0
$973$	0.358077	−	0.358077i	0.0114794	−	0.0114794i
$974$	−3.00195	−	17.0249i	−0.0961886	−	0.545513i
$975$		0			0
$976$	−0.112705	+	0.0410214i	−0.00360761	+	0.00131306i
$977$	21.1140	−	1.84724i	0.675497	−	0.0590983i	0.255755	−	0.966742i	$-0.417676\pi$
$977$	21.1140	−	1.84724i	0.675497	−	0.0590983i	0.419742	+	0.907643i	$0.362121\pi$
$978$		0			0
$979$	4.16904	−	11.4544i	0.133243	−	0.366083i
$980$	2.78325	−	15.3279i	0.0889076	−	0.489631i
$981$		0			0
$982$	−10.8204	+	2.89933i	−0.345294	+	0.0925213i
$983$	50.0320	+	4.37723i	1.59577	+	0.139612i	0.850071	−	0.526668i	$-0.176559\pi$
$983$	50.0320	+	4.37723i	1.59577	+	0.139612i	0.745702	+	0.666280i	$0.232114\pi$
$984$		0			0
$985$	−3.76507	+	40.6503i	−0.119965	+	1.29523i
$986$	−30.3594	−	5.35319i	−0.966842	−	0.170480i
$987$		0			0
$988$	−0.511741	+	5.84922i	−0.0162806	+	0.186089i
$989$	0.362023	−	0.627043i	0.0115117	−	0.0199388i
$990$		0			0
$991$	6.89627	+	11.9447i	0.219067	+	0.379436i	0.954523	−	0.298137i	$-0.0963653\pi$
$991$	6.89627	+	11.9447i	0.219067	+	0.379436i	−0.735456	+	0.677573i	$0.763032\pi$
$992$	7.58398	−	3.53647i	0.240792	−	0.112283i
$993$		0			0
$994$	−0.828077	+	0.986864i	−0.0262650	+	0.0313014i
$995$	14.4295	−	39.0254i	0.457446	−	1.23719i
$996$		0			0
$997$	2.14410	−	3.06210i	0.0679045	−	0.0969776i	−0.783763	−	0.621059i	$-0.786703\pi$
$997$	2.14410	−	3.06210i	0.0679045	−	0.0969776i	0.851668	+	0.524082i	$0.175591\pi$
$998$	17.9129	+	17.9129i	0.567023	+	0.567023i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.2.s.a.557.4		216
3.2	odd	2		270.2.r.a.257.13	yes	216
5.3	odd	4	inner	810.2.s.a.233.9		216
15.8	even	4		270.2.r.a.203.11	yes	216
27.2	odd	18	inner	810.2.s.a.737.9		216
27.25	even	9		270.2.r.a.137.11	yes	216
135.83	even	36	inner	810.2.s.a.413.4		216
135.133	odd	36		270.2.r.a.83.13	✓	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.r.a.83.13	✓	216	135.133	odd	36
270.2.r.a.137.11	yes	216	27.25	even	9
270.2.r.a.203.11	yes	216	15.8	even	4
270.2.r.a.257.13	yes	216	3.2	odd	2
810.2.s.a.233.9		216	5.3	odd	4	inner
810.2.s.a.413.4		216	135.83	even	36	inner
810.2.s.a.557.4		216	1.1	even	1	trivial
810.2.s.a.737.9		216	27.2	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	810.s (of order \(36\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.819152 - 0.573576i) q^{2} +(0.342020 + 0.939693i) q^{4} +(-0.377073 - 2.20405i) q^{5} +(-0.0768670 - 0.164842i) q^{7} +(0.258819 - 0.965926i) q^{8} +(-0.955308 + 2.02173i) q^{10} +(2.21054 + 2.63442i) q^{11} +(3.54611 + 5.06437i) q^{13} +(-0.0315836 + 0.179120i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(0.798593 + 2.98039i) q^{17} +(0.822477 - 0.474857i) q^{19} +(1.94216 - 1.10816i) q^{20} +(-0.299728 - 3.42591i) q^{22} +(-0.772585 - 0.360262i) q^{23} +(-4.71563 + 1.66217i) q^{25} -6.18246i q^{26} +(0.128611 - 0.128611i) q^{28} +(-1.73494 - 9.83931i) q^{29} +(7.86334 - 2.86202i) q^{31} +(0.996195 - 0.0871557i) q^{32} +(1.05531 - 2.89945i) q^{34} +(-0.334334 + 0.231576i) q^{35} +(5.53359 - 1.48272i) q^{37} +(-0.946100 - 0.0827730i) q^{38} +(-2.22654 - 0.206224i) q^{40} +(6.60088 + 1.16391i) q^{41} +(-0.0740273 + 0.846136i) q^{43} +(-1.71950 + 2.97826i) q^{44} +(0.426226 + 0.738246i) q^{46} +(-8.64098 + 4.02935i) q^{47} +(4.47825 - 5.33697i) q^{49} +(4.81620 + 1.34320i) q^{50} +(-3.54611 + 5.06437i) q^{52} +(-1.10856 - 1.10856i) q^{53} +(4.97285 - 5.86551i) q^{55} +(-0.179120 + 0.0315836i) q^{56} +(-4.22242 + 9.05501i) q^{58} +(8.77368 + 7.36199i) q^{59} +(0.112705 + 0.0410214i) q^{61} +(-8.08286 - 2.16580i) q^{62} +(-0.866025 - 0.500000i) q^{64} +(9.82496 - 9.72543i) q^{65} +(5.25146 - 3.67711i) q^{67} +(-2.52751 + 1.76978i) q^{68} +(0.406697 + 0.00207050i) q^{70} +(6.13397 + 3.54145i) q^{71} +(11.9795 + 3.20990i) q^{73} +(-5.38331 - 1.95936i) q^{74} +(0.727523 + 0.610464i) q^{76} +(0.264345 - 0.566890i) q^{77} +(-8.96689 + 1.58110i) q^{79} +(1.70559 + 1.44602i) q^{80} +(-4.73953 - 4.73953i) q^{82} +(-2.40418 + 3.43353i) q^{83} +(6.26778 - 2.88396i) q^{85} +(0.545964 - 0.650654i) q^{86} +(3.11679 - 1.45338i) q^{88} +(-1.77224 - 3.06962i) q^{89} +(0.562241 - 0.973831i) q^{91} +(0.0742962 - 0.849209i) q^{92} +(9.38942 + 1.65561i) q^{94} +(-1.35674 - 1.63372i) q^{95} +(-8.66511 - 0.758099i) q^{97} +(-6.72953 + 1.80317i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 24 q^{11} + 24 q^{20} - 24 q^{23} + 36 q^{25} + 108 q^{35} + 36 q^{38} + 72 q^{41} + 48 q^{47} + 48 q^{50} + 12 q^{56} + 36 q^{61} - 24 q^{65} - 72 q^{67} - 36 q^{68} + 240 q^{77} + 60 q^{83} - 72 q^{86}+ \cdots - 72 q^{97}+O(q^{100}) \) 216 * q - 24 * q^11 + 24 * q^20 - 24 * q^23 + 36 * q^25 + 108 * q^35 + 36 * q^38 + 72 * q^41 + 48 * q^47 + 48 * q^50 + 12 * q^56 + 36 * q^61 - 24 * q^65 - 72 * q^67 - 36 * q^68 + 240 * q^77 + 60 * q^83 - 72 * q^86 + 48 * q^92 + 60 * q^95 - 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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