LMFDB - Embedded newform 639.2.z.a.530.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [639,2,Mod(35,639)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(639, base_ring=CyclotomicField(70))

chi = DirichletCharacter(H, H._module([35, 29]))

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

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

chi := DirichletCharacter("639.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 639 = 3^{2} \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	639.z (of order $70$, degree $24$, 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:	$5.10244068916$
Analytic rank:	$0$
Dimension:	$576$
Relative dimension:	$24$ over $\Q(\zeta_{70})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{70}]$

Embedding invariants

Embedding label			530.13
Character	$\chi$	$=$	639.530
Dual form			639.2.z.a.170.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.101824 + 0.271308i) q^{2} +(1.44290 - 1.26063i) q^{4} +(0.133137 + 0.183248i) q^{5} +(-1.23575 + 0.815710i) q^{7} +(0.999308 + 0.537751i) q^{8} +O(q^{10})$	\(q+(0.101824 + 0.271308i) q^{2} +(1.44290 - 1.26063i) q^{4} +(0.133137 + 0.183248i) q^{5} +(-1.23575 + 0.815710i) q^{7} +(0.999308 + 0.537751i) q^{8} +(-0.0361601 + 0.0547802i) q^{10} +(0.0814888 - 0.0852306i) q^{11} +(2.93071 - 2.80205i) q^{13} +(-0.347137 - 0.252210i) q^{14} +(0.470245 - 3.47149i) q^{16} +(2.00647 + 6.17527i) q^{17} +(7.01242 + 0.631129i) q^{19} +(0.423112 + 0.0965725i) q^{20} +(0.0314212 + 0.0134301i) q^{22} +(3.06602 - 3.84467i) q^{23} +(1.52923 - 4.70649i) q^{25} +(1.05863 + 0.509810i) q^{26} +(-0.754758 + 2.73481i) q^{28} +(-7.84698 + 3.35396i) q^{29} +(-4.48459 + 0.607479i) q^{31} +(3.20244 - 0.730936i) q^{32} +(-1.47109 + 1.17316i) q^{34} +(-0.314001 - 0.117847i) q^{35} +(-5.76969 - 7.23496i) q^{37} +(0.542799 + 1.96679i) q^{38} +(0.0345036 + 0.254716i) q^{40} +(10.3412 - 4.98004i) q^{41} +(6.36882 + 1.75768i) q^{43} +(0.0101365 - 0.225706i) q^{44} +(1.35528 + 0.440358i) q^{46} +(1.62906 - 0.973316i) q^{47} +(-1.88949 + 4.42067i) q^{49} +(1.43262 - 0.0643390i) q^{50} +(0.696397 - 7.73761i) q^{52} +(-2.03207 - 1.77536i) q^{53} +(0.0264675 + 0.00358527i) q^{55} +(-1.67354 + 0.150621i) q^{56} +(-1.70896 - 1.78743i) q^{58} +(-12.6331 + 2.29256i) q^{59} +(4.83129 + 3.18911i) q^{61} +(-0.621451 - 1.15485i) q^{62} +(-3.33541 - 5.05293i) q^{64} +(0.903656 + 0.163989i) q^{65} +(4.43218 + 5.07304i) q^{67} +(10.6798 + 6.38091i) q^{68} -0.0971906i q^{70} +(-5.19473 + 6.63436i) q^{71} +(-1.59463 + 0.598476i) q^{73} +(1.37541 - 2.30205i) q^{74} +(10.9139 - 7.92938i) q^{76} +(-0.0311761 + 0.171795i) q^{77} +(-7.66558 + 14.2450i) q^{79} +(0.698751 - 0.376014i) q^{80} +(2.40410 + 2.29855i) q^{82} +(2.67721 + 14.7526i) q^{83} +(-0.864469 + 1.18984i) q^{85} +(0.171623 + 1.90688i) q^{86} +(0.127265 - 0.0413510i) q^{88} +(-0.278916 + 0.319245i) q^{89} +(-1.33596 + 5.85323i) q^{91} +(-0.422720 - 9.41259i) q^{92} +(0.429944 + 0.342869i) q^{94} +(0.817962 + 1.36904i) q^{95} +(-0.454465 + 0.943705i) q^{97} +(-1.39176 - 0.0625039i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 576 q - 24 q^{4}+O(q^{10}) $ 576 * q - 24 * q^4	$ 576 q - 24 q^{4} - 16 q^{10} + 76 q^{16} - 8 q^{19} + 20 q^{22} + 168 q^{25} - 20 q^{28} - 28 q^{31} + 40 q^{37} + 32 q^{40} + 52 q^{43} - 20 q^{46} - 208 q^{52} - 92 q^{55} + 56 q^{58} + 56 q^{61} - 144 q^{64} - 16 q^{67} - 44 q^{73} - 336 q^{76} + 88 q^{79} - 124 q^{82} + 60 q^{85} - 260 q^{88} + 80 q^{91} + 56 q^{94} - 56 q^{97}+O(q^{100}) $ 576 * q - 24 * q^4 - 16 * q^10 + 76 * q^16 - 8 * q^19 + 20 * q^22 + 168 * q^25 - 20 * q^28 - 28 * q^31 + 40 * q^37 + 32 * q^40 + 52 * q^43 - 20 * q^46 - 208 * q^52 - 92 * q^55 + 56 * q^58 + 56 * q^61 - 144 * q^64 - 16 * q^67 - 44 * q^73 - 336 * q^76 + 88 * q^79 - 124 * q^82 + 60 * q^85 - 260 * q^88 + 80 * q^91 + 56 * q^94 - 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/639\mathbb{Z}\right)^\times$.

$n$	$433$	$569$
$\chi(n)$	$e\left(\frac{57}{70}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.101824	+	0.271308i	0.0720001	+	0.191844i	0.967308	−	0.253604i	$-0.0816160\pi$
$2$	0.101824	+	0.271308i	0.0720001	+	0.191844i	−0.895308	+	0.445448i	$0.853045\pi$
$3$		0			0
$3$		0			0
$4$	1.44290	−	1.26063i	0.721452	−	0.630313i
$5$	0.133137	+	0.183248i	0.0595409	+	0.0819510i	0.837749	−	0.546055i	$-0.183871\pi$
$5$	0.133137	+	0.183248i	0.0595409	+	0.0819510i	−0.778208	+	0.628006i	$0.783871\pi$
$6$		0			0
$7$	−1.23575	+	0.815710i	−0.467069	+	0.308309i	−0.762424	−	0.647078i	$-0.775991\pi$
$7$	−1.23575	+	0.815710i	−0.467069	+	0.308309i	0.295355	+	0.955388i	$0.404562\pi$
$8$	0.999308	+	0.537751i	0.353309	+	0.190124i
$9$		0			0
$10$	−0.0361601	+	0.0547802i	−0.0114348	+	0.0173230i
$11$	0.0814888	−	0.0852306i	0.0245698	−	0.0256980i	−0.710396	−	0.703802i	$-0.751484\pi$
$11$	0.0814888	−	0.0852306i	0.0245698	−	0.0256980i	0.734966	+	0.678104i	$0.237198\pi$
$12$		0			0
$13$	2.93071	−	2.80205i	0.812833	−	0.777147i	−0.165054	−	0.986285i	$-0.552780\pi$
$13$	2.93071	−	2.80205i	0.812833	−	0.777147i	0.977886	+	0.209137i	$0.0670655\pi$
$14$	−0.347137	−	0.252210i	−0.0927762	−	0.0674058i
$15$		0			0
$16$	0.470245	−	3.47149i	0.117561	−	0.867873i
$17$	2.00647	+	6.17527i	0.486639	+	1.49772i	0.829592	+	0.558369i	$0.188573\pi$
$17$	2.00647	+	6.17527i	0.486639	+	1.49772i	−0.342953	+	0.939353i	$0.611427\pi$
$18$		0			0
$19$	7.01242	+	0.631129i	1.60876	+	0.144791i	0.857239	−	0.514919i	$-0.172178\pi$
$19$	7.01242	+	0.631129i	1.60876	+	0.144791i	0.751520	+	0.659710i	$0.229321\pi$
$20$	0.423112	+	0.0965725i	0.0946106	+	0.0215943i
$21$		0			0
$22$	0.0314212	+	0.0134301i	0.00669902	+	0.00286330i
$23$	3.06602	−	3.84467i	0.639309	−	0.801668i	−0.351607	−	0.936148i	$-0.614365\pi$
$23$	3.06602	−	3.84467i	0.639309	−	0.801668i	0.990916	+	0.134479i	$0.0429361\pi$
$24$		0			0
$25$	1.52923	−	4.70649i	0.305846	−	0.941298i
$26$	1.05863	+	0.509810i	0.207615	+	0.0999820i
$27$		0			0
$28$	−0.754758	+	2.73481i	−0.142636	+	0.516830i
$29$	−7.84698	+	3.35396i	−1.45715	+	0.622814i	−0.968353	−	0.249585i	$-0.919706\pi$
$29$	−7.84698	+	3.35396i	−1.45715	+	0.622814i	−0.488794	+	0.872399i	$0.662563\pi$
$30$		0			0
$31$	−4.48459	+	0.607479i	−0.805457	+	0.109107i	−0.525376	−	0.850870i	$-0.676075\pi$
$31$	−4.48459	+	0.607479i	−0.805457	+	0.109107i	−0.280080	+	0.959977i	$0.590361\pi$
$32$	3.20244	−	0.730936i	0.566117	−	0.129212i
$33$		0			0
$34$	−1.47109	+	1.17316i	−0.252290	+	0.201195i
$35$	−0.314001	−	0.117847i	−0.0530759	−	0.0199197i
$36$		0			0
$37$	−5.76969	−	7.23496i	−0.948531	−	1.18942i	−0.981789	−	0.189974i	$-0.939160\pi$
$37$	−5.76969	−	7.23496i	−0.948531	−	1.18942i	0.0332578	−	0.999447i	$-0.489412\pi$
$38$	0.542799	+	1.96679i	0.0880536	+	0.319055i
$39$		0			0
$40$	0.0345036	+	0.254716i	0.00545550	+	0.0402741i
$41$	10.3412	−	4.98004i	1.61502	−	0.777752i	0.615076	−	0.788468i	$-0.289125\pi$
$41$	10.3412	−	4.98004i	1.61502	−	0.777752i	0.999943	+	0.0107157i	$0.00341097\pi$
$42$		0			0
$43$	6.36882	+	1.75768i	0.971236	+	0.268044i	0.715430	−	0.698684i	$-0.246231\pi$
$43$	6.36882	+	1.75768i	0.971236	+	0.268044i	0.255806	+	0.966728i	$0.417659\pi$
$44$	0.0101365	−	0.225706i	0.00152813	−	0.0340265i
$45$		0			0
$46$	1.35528	+	0.440358i	0.199825	+	0.0649272i
$47$	1.62906	−	0.973316i	0.237622	−	0.141973i	−0.389152	−	0.921174i	$-0.627232\pi$
$47$	1.62906	−	0.973316i	0.237622	−	0.141973i	0.626774	+	0.779201i	$0.284375\pi$
$48$		0			0
$49$	−1.88949	+	4.42067i	−0.269927	+	0.631525i
$50$	1.43262	−	0.0643390i	0.202603	−	0.00909891i
$51$		0			0
$52$	0.696397	−	7.73761i	0.0965729	−	1.07301i
$53$	−2.03207	−	1.77536i	−0.279126	−	0.243865i	0.506979	−	0.861959i	$-0.330762\pi$
$53$	−2.03207	−	1.77536i	−0.279126	−	0.243865i	−0.786104	+	0.618094i	$0.787905\pi$
$54$		0			0
$55$	0.0264675	+	0.00358527i	0.00356888	+	0.000483438i
$56$	−1.67354	+	0.150621i	−0.223636	+	0.0201276i
$57$		0			0
$58$	−1.70896	−	1.78743i	−0.224398	−	0.234702i
$59$	−12.6331	+	2.29256i	−1.64468	+	0.298466i	−0.920383	−	0.391018i	$-0.872123\pi$
$59$	−12.6331	+	2.29256i	−1.64468	+	0.298466i	−0.724301	+	0.689484i	$0.757837\pi$
$60$		0			0
$61$	4.83129	+	3.18911i	0.618583	+	0.408323i	0.820961	−	0.570984i	$-0.193438\pi$
$61$	4.83129	+	3.18911i	0.618583	+	0.408323i	−0.202378	+	0.979308i	$0.564867\pi$
$62$	−0.621451	−	1.15485i	−0.0789244	−	0.146666i
$63$		0			0
$64$	−3.33541	−	5.05293i	−0.416926	−	0.631616i
$65$	0.903656	+	0.163989i	0.112085	+	0.0203404i
$66$		0			0
$67$	4.43218	+	5.07304i	0.541477	+	0.619770i	0.957097	−	0.289768i	$-0.0935783\pi$
$67$	4.43218	+	5.07304i	0.541477	+	0.619770i	−0.415620	+	0.909538i	$0.636435\pi$
$68$	10.6798	+	6.38091i	1.29512	+	0.773799i
$69$		0			0
$70$		−	0.0971906i		−	0.0116165i
$71$	−5.19473	+	6.63436i	−0.616501	+	0.787354i
$71$	−5.19473	+	6.63436i	−0.616501	+	0.787354i
$72$		0			0
$73$	−1.59463	+	0.598476i	−0.186638	+	0.0700463i	−0.442944	−	0.896549i	$-0.646066\pi$
$73$	−1.59463	+	0.598476i	−0.186638	+	0.0700463i	0.256306	+	0.966596i	$0.417494\pi$
$74$	1.37541	−	2.30205i	0.159888	−	0.267608i
$75$		0			0
$76$	10.9139	−	7.92938i	1.25191	−	0.909563i
$77$	−0.0311761	+	0.171795i	−0.00355285	+	0.0195778i
$78$		0			0
$79$	−7.66558	+	14.2450i	−0.862445	+	1.60269i	−0.0661296	+	0.997811i	$0.521065\pi$
$79$	−7.66558	+	14.2450i	−0.862445	+	1.60269i	−0.796316	+	0.604881i	$0.793221\pi$
$80$	0.698751	−	0.376014i	0.0781227	−	0.0420396i
$81$		0			0
$82$	2.40410	+	2.29855i	0.265488	+	0.253833i
$83$	2.67721	+	14.7526i	0.293862	+	1.61931i	0.706014	+	0.708198i	$0.250492\pi$
$83$	2.67721	+	14.7526i	0.293862	+	1.61931i	−0.412152	+	0.911115i	$0.635223\pi$
$84$		0			0
$85$	−0.864469	+	1.18984i	−0.0937648	+	0.129056i
$86$	0.171623	+	1.90688i	0.0185065	+	0.205625i
$87$		0			0
$88$	0.127265	−	0.0413510i	0.0135665	−	0.00440803i
$89$	−0.278916	+	0.319245i	−0.0295650	+	0.0338399i	−0.767664	−	0.640853i	$-0.778581\pi$
$89$	−0.278916	+	0.319245i	−0.0295650	+	0.0338399i	0.738099	+	0.674693i	$0.235724\pi$
$90$		0			0
$91$	−1.33596	+	5.85323i	−0.140047	+	0.613585i
$92$	−0.422720	−	9.41259i	−0.0440716	−	0.981330i
$93$		0			0
$94$	0.429944	+	0.342869i	0.0443454	+	0.0353643i
$95$	0.817962	+	1.36904i	0.0839212	+	0.140460i
$96$		0			0
$97$	−0.454465	+	0.943705i	−0.0461439	+	0.0958188i	−0.922766	−	0.385360i	$-0.874077\pi$
$97$	−0.454465	+	0.943705i	−0.0461439	+	0.0958188i	0.876622	+	0.481179i	$0.159791\pi$
$98$	−1.39176	−	0.0625039i	−0.140589	−	0.00631385i
$99$		0			0
$100$	−3.72659	−	8.71879i	−0.372659	−	0.871879i
$101$	−6.21873	−	12.9133i	−0.618787	−	1.28492i	−0.941048	−	0.338273i	$-0.890157\pi$
$101$	−6.21873	−	12.9133i	−0.618787	−	1.28492i	0.322261	−	0.946651i	$-0.395557\pi$
$102$		0			0
$103$	−1.91909	−	8.40810i	−0.189094	−	0.828475i	−0.977095	−	0.212802i	$-0.931741\pi$
$103$	−1.91909	−	8.40810i	−0.189094	−	0.828475i	0.788001	−	0.615673i	$-0.211116\pi$
$104$	4.43548	−	1.22412i	0.434935	−	0.120034i
$105$		0			0
$106$	0.274758	−	0.732089i	0.0266868	−	0.0711068i
$107$	−0.0825208	+	0.219876i	−0.00797759	+	0.0212562i	−0.940163	−	0.340724i	$-0.889328\pi$
$107$	−0.0825208	+	0.219876i	−0.00797759	+	0.0212562i	0.932186	+	0.361980i	$0.117899\pi$
$108$		0			0
$109$	−7.94811	+	2.19354i	−0.761291	+	0.210103i	−0.625063	−	0.780574i	$-0.714927\pi$
$109$	−7.94811	+	2.19354i	−0.761291	+	0.210103i	−0.136228	+	0.990677i	$0.543498\pi$
$110$	0.00172231	+	0.00754591i	0.000164215	+	0.000719475i
$111$		0			0
$112$	2.25062	+	4.67347i	0.212664	+	0.441601i
$113$	−7.50812	−	17.5661i	−0.706304	−	1.65248i	−0.756709	−	0.653752i	$-0.773194\pi$
$113$	−7.50812	−	17.5661i	−0.706304	−	1.65248i	0.0504044	−	0.998729i	$-0.483949\pi$
$114$		0			0
$115$	1.11273	+	0.0499727i	0.103763	+	0.00465998i
$116$	−7.09434	+	14.7315i	−0.658693	+	1.36779i
$117$		0			0
$118$	−1.90833	−	3.19401i	−0.175676	−	0.294033i
$119$	−7.51671	−	5.99438i	−0.689056	−	0.549504i
$120$		0			0
$121$	0.492889	+	10.9750i	0.0448081	+	0.997730i
$122$	−0.373290	+	1.63549i	−0.0337961	+	0.148070i
$123$		0			0
$124$	−5.70503	+	6.52993i	−0.512327	+	0.586405i
$125$	2.14316	−	0.696354i	0.191690	−	0.0622838i
$126$		0			0
$127$	1.06969	+	11.8852i	0.0949197	+	1.05464i	0.892384	+	0.451277i	$0.149032\pi$
$127$	1.06969	+	11.8852i	0.0949197	+	1.05464i	−0.797464	+	0.603366i	$0.793826\pi$
$128$	4.89278	−	6.73434i	0.432465	−	0.595237i
$129$		0			0
$130$	0.0475218	+	0.261867i	0.00416794	+	0.0229673i
$131$	−12.0322	−	11.5040i	−1.05126	−	1.00511i	−0.999979	−	0.00642069i	$-0.997956\pi$
$131$	−12.0322	−	11.5040i	−1.05126	−	1.00511i	−0.0512781	−	0.998684i	$-0.516329\pi$
$132$		0			0
$133$	−9.18040	+	4.94018i	−0.796041	+	0.428368i
$134$	−0.925054	+	1.71904i	−0.0799125	+	0.148502i
$135$		0			0
$136$	−1.31568	+	7.24997i	−0.112818	+	0.621680i
$137$	6.30201	−	4.57868i	0.538417	−	0.391183i	−0.285080	−	0.958504i	$-0.592020\pi$
$137$	6.30201	−	4.57868i	0.538417	−	0.391183i	0.823497	+	0.567321i	$0.192020\pi$
$138$		0			0
$139$	−5.21495	+	8.72836i	−0.442326	+	0.740330i	−0.995703	−	0.0926014i	$-0.970482\pi$
$139$	−5.21495	+	8.72836i	−0.442326	+	0.740330i	0.553377	+	0.832931i	$0.313339\pi$
$140$	−0.601634	+	0.225797i	−0.0508474	+	0.0190833i
$141$		0			0
$142$	−2.32890	−	0.733837i	−0.195437	−	0.0615822i
$143$		−	0.478121i		−	0.0399825i
$144$		0			0
$145$	−1.65933	−	0.991405i	−0.137800	−	0.0823317i
$146$	−0.324742	−	0.371698i	−0.0268759	−	0.0307619i
$147$		0			0
$148$	−17.4457	−	3.16593i	−1.43403	−	0.260238i
$149$	2.24282	+	3.39772i	0.183739	+	0.278352i	0.914756	−	0.404007i	$-0.132383\pi$
$149$	2.24282	+	3.39772i	0.183739	+	0.278352i	−0.731017	+	0.682359i	$0.760954\pi$
$150$		0			0
$151$	−7.43731	−	13.8208i	−0.605240	−	1.12472i	−0.980261	−	0.197707i	$-0.936650\pi$
$151$	−7.43731	−	13.8208i	−0.605240	−	1.12472i	0.375021	−	0.927016i	$-0.377635\pi$
$152$	6.66818	+	4.40162i	0.540860	+	0.357019i
$153$		0			0
$154$	−0.0497837	+	0.00903441i	−0.00401168	+	0.000728013i
$155$	−0.708386	−	0.740914i	−0.0568990	−	0.0595117i
$156$		0			0
$157$	−3.06213	+	0.275596i	−0.244384	+	0.0219950i	−0.211154	−	0.977453i	$-0.567722\pi$
$157$	−3.06213	+	0.275596i	−0.244384	+	0.0219950i	−0.0332300	+	0.999448i	$0.510579\pi$
$158$	−4.64533	−	0.629252i	−0.369562	−	0.0500606i
$159$		0			0
$160$	0.560307	+	0.489525i	0.0442962	+	0.0387004i
$161$	−0.652694	+	7.25202i	−0.0514395	+	0.571539i
$162$		0			0
$163$	2.87132	−	0.128951i	0.224899	−	0.0101002i	0.0678697	−	0.997694i	$-0.478380\pi$
$163$	2.87132	−	0.128951i	0.224899	−	0.0101002i	0.157029	+	0.987594i	$0.449808\pi$
$164$	8.64333	−	20.2221i	0.674930	−	1.57908i
$165$		0			0
$166$	−3.72991	+	2.22851i	−0.289497	+	0.172966i
$167$	−17.9409	−	5.82934i	−1.38830	−	0.451088i	−0.482915	−	0.875668i	$-0.660422\pi$
$167$	−17.9409	−	5.82934i	−1.38830	−	0.451088i	−0.905390	+	0.424580i	$0.860422\pi$
$168$		0			0
$169$	0.154358	−	3.43705i	0.0118737	−	0.264389i
$170$	−0.410836	−	0.113384i	−0.0315097	−	0.00869612i
$171$		0			0
$172$	11.4054	−	5.49254i	0.869651	−	0.418802i
$173$	−1.09491	−	8.08293i	−0.0832443	−	0.614534i	−0.983731	−	0.179650i	$-0.942504\pi$
$173$	−1.09491	−	8.08293i	−0.0832443	−	0.614534i	0.900486	−	0.434884i	$-0.143211\pi$
$174$		0			0
$175$	1.94939	+	7.06344i	0.147360	+	0.533946i
$176$	−0.257557	−	0.322967i	−0.0194141	−	0.0243445i
$177$		0			0
$178$	−0.115014	−	0.0431654i	−0.00862065	−	0.00323538i
$179$	−9.74934	+	7.77484i	−0.728700	+	0.581119i	−0.915997	−	0.401184i	$-0.868599\pi$
$179$	−9.74934	+	7.77484i	−0.728700	+	0.581119i	0.187297	+	0.982303i	$0.440027\pi$
$180$		0			0
$181$	−11.0968	+	2.53276i	−0.824816	+	0.188259i	−0.614039	−	0.789276i	$-0.710456\pi$
$181$	−11.0968	+	2.53276i	−0.824816	+	0.188259i	−0.210776	+	0.977534i	$0.567599\pi$
$182$	−1.72406	+	0.233540i	−0.127796	+	0.0173111i
$183$		0			0
$184$	5.13137	−	2.19325i	0.378290	−	0.161689i
$185$	0.557630	−	2.02053i	0.0409978	−	0.148552i
$186$		0			0
$187$	0.689826	+	0.332203i	0.0504451	+	0.0242931i
$188$	1.12358	−	3.45803i	0.0819457	−	0.252203i
$189$		0			0
$190$	−0.288143	+	0.361320i	−0.0209041	+	0.0262129i
$191$	−4.16847	−	1.78169i	−0.301620	−	0.128918i	0.236893	−	0.971536i	$-0.423871\pi$
$191$	−4.16847	−	1.78169i	−0.301620	−	0.128918i	−0.538513	+	0.842617i	$0.681014\pi$
$192$		0			0
$193$	−3.30663	−	0.754717i	−0.238017	−	0.0543257i	0.101849	−	0.994800i	$-0.467524\pi$
$193$	−3.30663	−	0.754717i	−0.238017	−	0.0543257i	−0.339865	+	0.940474i	$0.610381\pi$
$194$	−0.302310	−	0.0272084i	−0.0217046	−	0.00195345i
$195$		0			0
$196$	2.84647	+	8.76054i	0.203319	+	0.625753i
$197$	−2.26280	+	16.7047i	−0.161218	+	1.19016i	0.711768	+	0.702415i	$0.247895\pi$
$197$	−2.26280	+	16.7047i	−0.161218	+	1.19016i	−0.872986	+	0.487745i	$0.837819\pi$
$198$		0			0
$199$	12.2011	+	8.86461i	0.864912	+	0.628395i	0.929217	−	0.369535i	$-0.120483\pi$
$199$	12.2011	+	8.86461i	0.864912	+	0.628395i	−0.0643048	+	0.997930i	$0.520483\pi$
$200$	4.05909	−	3.88089i	0.287021	−	0.274420i
$201$		0			0
$202$	2.87027	−	3.00207i	0.201952	−	0.211225i
$203$	6.96102	−	10.5455i	0.488568	−	0.740149i
$204$		0			0
$205$	2.28938	+	1.23197i	0.159897	+	0.0860443i
$206$	2.08577	−	1.37681i	0.145323	−	0.0959268i
$207$		0			0
$208$	−8.34912	−	11.4916i	−0.578908	−	0.796798i
$209$	0.625225	−	0.546242i	0.0432477	−	0.0377844i
$210$		0			0
$211$	6.59596	+	17.5749i	0.454084	+	1.20990i	0.941583	+	0.336780i	$0.109338\pi$
$211$	6.59596	+	17.5749i	0.454084	+	1.20990i	−0.487499	+	0.873124i	$0.662091\pi$
$212$	−5.17014			−0.355087
$213$		0			0
$214$	−0.0680566			−0.00465225
$215$	0.525836	+	1.40109i	0.0358617	+	0.0955533i
$216$		0			0
$217$	5.04630	−	4.40882i	0.342565	−	0.299290i
$218$	−1.40443	−	1.93303i	−0.0951200	−	0.130921i
$219$		0			0
$220$	0.0427098	−	0.0281925i	0.00287949	−	0.00190074i
$221$	23.1837	+	12.4757i	1.55951	+	0.839207i
$222$		0			0
$223$	−3.08926	+	4.68004i	−0.206872	+	0.313398i	−0.923167	−	0.384400i	$-0.874408\pi$
$223$	−3.08926	+	4.68004i	−0.206872	+	0.313398i	0.716294	+	0.697798i	$0.245837\pi$
$224$	−3.36117	+	3.51551i	−0.224578	+	0.234890i
$225$		0			0
$226$	4.00132	−	3.82566i	0.266164	−	0.254479i
$227$	10.0781	+	7.32214i	0.668904	+	0.485988i	0.869658	−	0.493654i	$-0.164339\pi$
$227$	10.0781	+	7.32214i	0.668904	+	0.485988i	−0.200754	+	0.979642i	$0.564339\pi$
$228$		0			0
$229$	0.388999	−	2.87171i	0.0257058	−	0.189768i	−0.973544	−	0.228500i	$-0.926618\pi$
$229$	0.388999	−	2.87171i	0.0257058	−	0.189768i	0.999250	+	0.0387327i	$0.0123321\pi$
$230$	0.0997440	+	0.306981i	0.00657693	+	0.0202417i
$231$		0			0
$232$	−9.64514	−	0.868078i	−0.633234	−	0.0569921i
$233$	−13.6513	−	3.11582i	−0.894327	−	0.204124i	−0.249429	−	0.968393i	$-0.580243\pi$
$233$	−13.6513	−	3.11582i	−0.894327	−	0.204124i	−0.644898	+	0.764269i	$0.723100\pi$
$234$		0			0
$235$	0.395246	+	0.168936i	0.0257830	+	0.0110202i
$236$	−15.3382	+	19.2335i	−0.998433	+	1.25200i
$237$		0			0
$238$	0.860943	−	2.64971i	0.0558067	−	0.171755i
$239$	11.9527	+	5.75614i	0.773159	+	0.372334i	0.778494	−	0.627652i	$-0.215984\pi$
$239$	11.9527	+	5.75614i	0.773159	+	0.372334i	−0.00533498	+	0.999986i	$0.501698\pi$
$240$		0			0
$241$	5.36006	−	19.4217i	0.345272	−	1.25106i	−0.560804	−	0.827948i	$-0.689508\pi$
$241$	5.36006	−	19.4217i	0.345272	−	1.25106i	0.906076	−	0.423115i	$-0.139063\pi$
$242$	−2.92742	+	1.25124i	−0.188182	+	0.0804328i
$243$		0			0
$244$	10.9913	−	1.48888i	0.703649	−	0.0953157i
$245$	−1.06164	+	0.242312i	−0.0678257	+	0.0154808i
$246$		0			0
$247$	22.3198	−	17.7995i	1.42018	−	1.13255i
$248$	−4.80816	−	1.80453i	−0.305319	−	0.114588i
$249$		0			0
$250$	0.407150	+	0.510550i	0.0257504	+	0.0322900i
$251$	1.12836	+	4.08852i	0.0712215	+	0.258065i	0.990899	−	0.134610i	$-0.0429782\pi$
$251$	1.12836	+	4.08852i	0.0712215	+	0.258065i	−0.919677	+	0.392675i	$0.871550\pi$
$252$		0			0
$253$	−0.0778370	−	0.574616i	−0.00489357	−	0.0361258i
$254$	−3.11564	+	1.50041i	−0.195492	+	0.0941442i
$255$		0			0
$256$	−9.34735	−	2.57971i	−0.584210	−	0.161232i
$257$	−0.154121	+	3.43178i	−0.00961383	+	0.214069i	0.988436	+	0.151641i	$0.0484557\pi$
$257$	−0.154121	+	3.43178i	−0.00961383	+	0.214069i	−0.998049	+	0.0624277i	$0.980116\pi$
$258$		0			0
$259$	13.0315	+	4.23419i	0.809739	+	0.263100i
$260$	1.51062	−	0.902552i	0.0936845	−	0.0559739i
$261$		0			0
$262$	1.89595	−	4.43580i	0.117132	−	0.274045i
$263$	30.1383	−	1.35351i	1.85841	−	0.0834613i	0.912730	−	0.408562i	$-0.133970\pi$
$263$	30.1383	−	1.35351i	1.85841	−	0.0834613i	0.945679	+	0.325101i	$0.105398\pi$
$264$		0			0
$265$	0.0547875	−	0.608739i	0.00336557	−	0.0373945i
$266$	−2.27509	−	1.98769i	−0.139495	−	0.121873i
$267$		0			0
$268$	12.7904	+	1.73258i	0.781298	+	0.105834i
$269$	13.9797	−	1.25820i	0.852359	−	0.0767137i	0.345161	−	0.938543i	$-0.387824\pi$
$269$	13.9797	−	1.25820i	0.852359	−	0.0767137i	0.507198	+	0.861830i	$0.330681\pi$
$270$		0			0
$271$	2.00787	+	2.10006i	0.121969	+	0.127570i	0.780960	−	0.624582i	$-0.214730\pi$
$271$	2.00787	+	2.10006i	0.121969	+	0.127570i	−0.658990	+	0.752151i	$0.729016\pi$
$272$	22.3809	−	4.06154i	1.35704	−	0.246267i
$273$		0			0
$274$	1.88392	+	1.24357i	0.113812	+	0.0751267i
$275$	−0.276522	−	0.513863i	−0.0166749	−	0.0309871i
$276$		0			0
$277$	8.98210	+	13.6073i	0.539682	+	0.817583i	0.997441	−	0.0714930i	$-0.0227764\pi$
$277$	8.98210	+	13.6073i	0.539682	+	0.817583i	−0.457759	+	0.889076i	$0.651348\pi$
$278$	−2.89908	−	0.526105i	−0.173875	−	0.0315537i
$279$		0			0
$280$	−0.250412	−	0.286620i	−0.0149650	−	0.0171288i
$281$	−17.1030	−	10.2186i	−1.02028	−	0.609588i	−0.0976275	−	0.995223i	$-0.531125\pi$
$281$	−17.1030	−	10.2186i	−1.02028	−	0.609588i	−0.922652	+	0.385635i	$0.873983\pi$
$282$		0			0
$283$		−	10.2358i		−	0.608453i	−0.952600	−	0.304227i	$-0.901602\pi$
$283$		−	10.2358i		−	0.608453i	0.952600	−	0.304227i	$-0.0983980\pi$
$284$	0.867961	+	16.1214i	0.0515040	+	0.956627i
$285$		0			0
$286$	0.129718	−	0.0486840i	0.00767039	−	0.00287874i
$287$	−8.71680	+	14.5895i	−0.514536	+	0.861189i
$288$		0			0
$289$	−20.3547	+	14.7886i	−1.19734	+	0.869916i
$290$	0.100017	−	0.551138i	0.00587319	−	0.0323639i
$291$		0			0
$292$	−1.54645	+	2.87378i	−0.0904989	+	0.168175i
$293$	−9.79508	+	5.27096i	−0.572235	+	0.307933i	−0.734276	−	0.678851i	$-0.762478\pi$
$293$	−9.79508	+	5.27096i	−0.572235	+	0.307933i	0.162041	+	0.986784i	$0.448192\pi$
$294$		0			0
$295$	−2.10204	−	2.00976i	−0.122386	−	0.117013i
$296$	−1.87509	−	10.3326i	−0.108988	−	0.600571i
$297$		0			0
$298$	−0.693457	+	0.954462i	−0.0401709	+	0.0552905i
$299$	−1.78732	−	19.8587i	−0.103363	−	1.14846i
$300$		0			0
$301$	−9.30401	+	3.02306i	−0.536274	+	0.174246i
$302$	2.99241	−	3.42509i	0.172194	−	0.197092i
$303$		0			0
$304$	5.48852	−	24.0468i	0.314788	−	1.37918i
$305$	0.0588283	+	1.30991i	0.00336850	+	0.0750054i
$306$		0			0
$307$	−23.2516	−	18.5425i	−1.32704	−	1.05828i	−0.993294	−	0.115615i	$-0.963116\pi$
$307$	−23.2516	−	18.5425i	−1.32704	−	1.05828i	−0.333745	−	0.942663i	$-0.608312\pi$
$308$	0.171585	+	0.287184i	0.00977695	+	0.0163639i
$309$		0			0
$310$	0.128885	−	0.267633i	0.00732020	−	0.0152005i
$311$	−9.40801	−	0.422514i	−0.533479	−	0.0239586i	−0.223504	−	0.974703i	$-0.571749\pi$
$311$	−9.40801	−	0.422514i	−0.533479	−	0.0239586i	−0.309976	+	0.950745i	$0.600321\pi$
$312$		0			0
$313$	−7.81354	−	18.2807i	−0.441648	−	1.03329i	−0.981489	−	0.191519i	$-0.938659\pi$
$313$	−7.81354	−	18.2807i	−0.441648	−	1.03329i	0.539841	−	0.841767i	$-0.318484\pi$
$314$	−0.386568	−	0.802716i	−0.0218153	−	0.0452999i
$315$		0			0
$316$	6.89698	+	30.2176i	0.387985	+	1.69988i
$317$	6.00898	−	1.65837i	0.337498	−	0.0931435i	−0.0931799	−	0.995649i	$-0.529703\pi$
$317$	6.00898	−	1.65837i	0.337498	−	0.0931435i	0.430678	+	0.902506i	$0.358275\pi$
$318$		0			0
$319$	−0.353581	+	0.942112i	−0.0197967	+	0.0527482i
$320$	0.481871	−	1.28394i	0.0269374	−	0.0717745i
$321$		0			0
$322$	−2.03399	+	0.561345i	−0.113350	+	0.0312826i
$323$	10.1728	+	44.5699i	0.566029	+	2.47993i
$324$		0			0
$325$	−8.70606	−	18.0783i	−0.482925	−	1.00280i
$326$	0.327353	+	0.765880i	0.0181304	+	0.0424182i
$327$		0			0
$328$	13.0120	+	0.584371i	0.718469	+	0.0322665i
$329$	−1.21916	+	2.53161i	−0.0672144	+	0.139572i
$330$		0			0
$331$	10.6559	+	17.8349i	0.585700	+	0.980296i	0.997612	+	0.0690724i	$0.0220040\pi$
$331$	10.6559	+	17.8349i	0.585700	+	0.980296i	−0.411912	+	0.911224i	$0.635139\pi$
$332$	22.4605	+	17.9117i	1.23268	+	0.983031i
$333$		0			0
$334$	−0.245256	−	5.46106i	−0.0134198	−	0.298816i
$335$	−0.339535	+	1.48760i	−0.0185508	+	0.0812762i
$336$		0			0
$337$	14.2067	−	16.2609i	0.773891	−	0.885789i	−0.222120	−	0.975019i	$-0.571298\pi$
$337$	14.2067	−	16.2609i	0.773891	−	0.885789i	0.996011	+	0.0892299i	$0.0284406\pi$
$338$	0.948216	−	0.308094i	0.0515762	−	0.0167581i
$339$		0			0
$340$	0.252598	+	2.80660i	0.0136991	+	0.152209i
$341$	−0.313668	+	0.431727i	−0.0169861	+	0.0233793i
$342$		0			0
$343$	−3.12177	−	17.2024i	−0.168560	−	0.928842i
$344$	5.41922	+	5.18130i	0.292185	+	0.279357i
$345$		0			0
$346$	2.08148	−	1.12009i	0.111901	−	0.0602164i
$347$	8.05878	−	14.9757i	0.432618	−	0.803939i	−0.567189	−	0.823588i	$-0.691969\pi$
$347$	8.05878	−	14.9757i	0.432618	−	0.803939i	0.999807	+	0.0196485i	$0.00625473\pi$
$348$		0			0
$349$	2.87488	−	15.8419i	0.153889	−	0.847997i	−0.810942	−	0.585126i	$-0.801045\pi$
$349$	2.87488	−	15.8419i	0.153889	−	0.847997i	0.964831	−	0.262871i	$-0.0846693\pi$
$350$	−1.71787	+	1.24811i	−0.0918242	+	0.0667142i
$351$		0			0
$352$	0.198665	−	0.332509i	0.0105889	−	0.0177228i
$353$	32.0759	−	12.0383i	1.70723	−	0.640733i	0.709288	−	0.704919i	$-0.249017\pi$
$353$	32.0759	−	12.0383i	1.70723	−	0.640733i	0.997938	+	0.0641864i	$0.0204452\pi$
$354$		0			0
$355$	−1.90735	−	0.0686417i	−0.101231	−	0.00364312i
$356$			0.812248i			0.0430491i
$357$		0			0
$358$	−3.10209	−	1.85341i	−0.163950	−	0.0979558i
$359$	−0.747865	−	0.856001i	−0.0394708	−	0.0451780i	0.732997	−	0.680232i	$-0.238121\pi$
$359$	−0.747865	−	0.856001i	−0.0394708	−	0.0451780i	−0.772468	+	0.635054i	$0.780978\pi$
$360$		0			0
$361$	30.0810	+	5.45890i	1.58321	+	0.287311i
$362$	−1.81707	−	2.75274i	−0.0955030	−	0.144681i
$363$		0			0
$364$	5.45107	+	10.1298i	0.285714	+	0.530945i
$365$	−0.321975	−	0.212534i	−0.0168529	−	0.0111245i
$366$		0			0
$367$	−6.73390	+	1.22202i	−0.351506	+	0.0637890i	−0.351438	−	0.936211i	$-0.614307\pi$
$367$	−6.73390	+	1.22202i	−0.351506	+	0.0637890i	−6.79933e−5		1.00000i	$0.500022\pi$
$368$	−11.9049	−	12.4516i	−0.620588	−	0.649084i
$369$		0			0
$370$	0.604965	−	0.0544478i	0.0314506	−	0.00283061i
$371$	3.95930	+	0.536324i	0.205557	+	0.0278445i
$372$		0			0
$373$	−6.95150	−	6.07335i	−0.359935	−	0.314466i	0.458907	−	0.888484i	$-0.348241\pi$
$373$	−6.95150	−	6.07335i	−0.359935	−	0.314466i	−0.818843	+	0.574018i	$0.805384\pi$
$374$	−0.0198887	+	0.220981i	−0.00102842	+	0.0114267i
$375$		0			0
$376$	2.15133	−	0.0966163i	0.110946	−	0.00498261i
$377$	−13.5993	+	31.8171i	−0.700398	+	1.63866i
$378$		0			0
$379$	3.82413	−	2.28481i	0.196432	−	0.117363i	−0.411315	−	0.911493i	$-0.634930\pi$
$379$	3.82413	−	2.28481i	0.196432	−	0.117363i	0.607747	+	0.794130i	$0.292073\pi$
$380$	2.90609	+	0.944245i	0.149079	+	0.0484387i
$381$		0			0
$382$	0.0589380	−	1.31236i	0.00301553	−	0.0671460i
$383$	6.89996	+	1.90427i	0.352571	+	0.0973035i	0.437836	−	0.899055i	$-0.355745\pi$
$383$	6.89996	+	1.90427i	0.352571	+	0.0973035i	−0.0852648	+	0.996358i	$0.527174\pi$
$384$		0			0
$385$	−0.0356317	+	0.0171593i	−0.00181596	+	0.000874521i
$386$	−0.131932	−	0.973963i	−0.00671518	−	0.0495734i
$387$		0			0
$388$	0.533912	+	1.93459i	0.0271053	+	0.0982137i
$389$	−15.7989	−	19.8111i	−0.801034	−	1.00446i	−0.999702	−	0.0243982i	$-0.992233\pi$
$389$	−15.7989	−	19.8111i	−0.801034	−	1.00446i	0.198668	−	0.980067i	$-0.436338\pi$
$390$		0			0
$391$	29.8937	+	11.2193i	1.51179	+	0.567384i
$392$	−4.26540	+	3.40154i	−0.215435	+	0.171804i
$393$		0			0
$394$	−4.76252	+	1.08701i	−0.239932	+	0.0547630i
$395$	−3.63095	+	0.491846i	−0.182693	+	0.0247474i
$396$		0			0
$397$	18.0445	−	7.71260i	0.905628	−	0.387084i	0.110747	−	0.993849i	$-0.464676\pi$
$397$	18.0445	−	7.71260i	0.905628	−	0.387084i	0.794882	+	0.606765i	$0.207533\pi$
$398$	−1.16268	+	4.21288i	−0.0582799	+	0.211172i
$399$		0			0
$400$	−15.6194	−	7.52192i	−0.780971	−	0.376096i
$401$	2.73477	−	8.41677i	0.136568	−	0.420313i	−0.859263	−	0.511535i	$-0.829077\pi$
$401$	2.73477	−	8.41677i	0.136568	−	0.420313i	0.995831	+	0.0912215i	$0.0290771\pi$
$402$		0			0
$403$	−11.4409	+	14.3464i	−0.569910	+	0.714644i
$404$	−25.2519	−	10.7932i	−1.25633	−	0.536981i
$405$		0			0
$406$	3.56987	+	0.814800i	0.177170	+	0.0404379i
$407$	−1.08680	−	0.0978142i	−0.0538709	−	0.00484847i
$408$		0			0
$409$	−9.89385	−	30.4501i	−0.489219	−	1.50566i	−0.825775	−	0.563999i	$-0.809262\pi$
$409$	−9.89385	−	30.4501i	−0.489219	−	1.50566i	0.336556	−	0.941664i	$-0.390738\pi$
$410$	−0.101130	+	0.746570i	−0.00499444	+	0.0368704i
$411$		0			0
$412$	−13.3685	−	9.71281i	−0.658621	−	0.478516i
$413$	13.7412	−	13.1379i	0.676160	−	0.646476i
$414$		0			0
$415$	−2.34696	+	2.45472i	−0.115208	+	0.120498i
$416$	7.33730	−	11.1155i	0.359741	−	0.544984i
$417$		0			0
$418$	0.211862	+	0.114008i	0.0103625	+	0.00557632i
$419$	−14.5297	+	9.59096i	−0.709822	+	0.468549i	−0.853512	−	0.521074i	$-0.825532\pi$
$419$	−14.5297	+	9.59096i	−0.709822	+	0.468549i	0.143690	+	0.989623i	$0.454103\pi$
$420$		0			0
$421$	16.2710	+	22.3951i	0.792998	+	1.09147i	0.993728	+	0.111822i	$0.0356687\pi$
$421$	16.2710	+	22.3951i	0.792998	+	1.09147i	−0.200730	+	0.979647i	$0.564331\pi$
$422$	−4.09657	+	3.57907i	−0.199418	+	0.174226i
$423$		0			0
$424$	−1.07596	−	2.86688i	−0.0522531	−	0.139228i
$425$	32.1322			1.55864
$426$		0			0
$427$	−8.57164			−0.414811
$428$	0.158112	+	0.421287i	0.00764262	+	0.0203637i
$429$		0			0
$430$	−0.326583	+	0.285327i	−0.0157492	+	0.0137597i
$431$	6.56912	+	9.04162i	0.316424	+	0.435520i	0.937371	−	0.348332i	$-0.113252\pi$
$431$	6.56912	+	9.04162i	0.316424	+	0.435520i	−0.620947	+	0.783852i	$0.713252\pi$
$432$		0			0
$433$	8.57642	−	5.66124i	0.412156	−	0.272062i	−0.327760	−	0.944761i	$-0.606294\pi$
$433$	8.57642	−	5.66124i	0.412156	−	0.272062i	0.739916	+	0.672699i	$0.234865\pi$
$434$	1.70998	+	0.920179i	0.0820816	+	0.0441700i
$435$		0			0
$436$	−8.70312	+	13.1847i	−0.416804	+	0.631431i
$437$	23.9267	−	25.0254i	1.14457	−	1.19713i
$438$		0			0
$439$	−4.46018	+	4.26437i	−0.212873	+	0.203527i	−0.789965	−	0.613152i	$-0.789901\pi$
$439$	−4.46018	+	4.26437i	−0.212873	+	0.203527i	0.577093	+	0.816679i	$0.304187\pi$
$440$	0.0245212	+	0.0178157i	0.00116900	+	0.000849331i
$441$		0			0
$442$	−1.02411	+	7.56025i	−0.0487117	+	0.359604i
$443$	0.557778	+	1.71667i	0.0265009	+	0.0815612i	0.963432	−	0.267952i	$-0.0863469\pi$
$443$	0.557778	+	1.71667i	0.0265009	+	0.0815612i	−0.936931	+	0.349513i	$0.886347\pi$
$444$		0			0
$445$	−0.0956351	−	0.00860731i	−0.00453354	−	0.000408026i
$446$	−1.58429	−	0.361604i	−0.0750183	−	0.0171224i
$447$		0			0
$448$	8.24344	+	3.52342i	0.389466	+	0.166466i
$449$	−14.1001	+	17.6809i	−0.665423	+	0.834414i	−0.993922	−	0.110091i	$-0.964886\pi$
$449$	−14.1001	+	17.6809i	−0.665423	+	0.834414i	0.328499	+	0.944504i	$0.393457\pi$
$450$		0			0
$451$	0.418237	−	1.28720i	0.0196940	−	0.0606119i
$452$	−32.9778	−	15.8813i	−1.55114	−	0.746992i
$453$		0			0
$454$	−0.960370	+	3.47982i	−0.0450724	+	0.163316i
$455$	−1.25046	+	0.534472i	−0.0586224	+	0.0250564i
$456$		0			0
$457$	9.96839	−	1.35031i	0.466301	−	0.0631648i	0.102686	−	0.994714i	$-0.467256\pi$
$457$	9.96839	−	1.35031i	0.466301	−	0.0631648i	0.363616	+	0.931549i	$0.381542\pi$
$458$	0.818725	−	0.186869i	0.0382565	−	0.00873180i
$459$		0			0
$460$	1.66856	−	1.33063i	0.0777969	−	0.0620410i
$461$	22.5063	+	8.44676i	1.04822	+	0.393405i	0.815269	−	0.579083i	$-0.196589\pi$
$461$	22.5063	+	8.44676i	1.04822	+	0.393405i	0.232955	+	0.972488i	$0.425161\pi$
$462$		0			0
$463$	15.4607	+	19.3870i	0.718518	+	0.900993i	0.998253	−	0.0590845i	$-0.0188182\pi$
$463$	15.4607	+	19.3870i	0.718518	+	0.900993i	−0.279735	+	0.960077i	$0.590247\pi$
$464$	7.95323	+	28.8179i	0.369220	+	1.33784i
$465$		0			0
$466$	−0.544677	−	4.02097i	−0.0252317	−	0.186268i
$467$	−26.6963	+	12.8563i	−1.23536	+	0.594917i	−0.933549	−	0.358451i	$-0.883305\pi$
$467$	−26.6963	+	12.8563i	−1.23536	+	0.594917i	−0.301810	+	0.953368i	$0.597591\pi$
$468$		0			0
$469$	−9.61518	−	2.65362i	−0.443988	−	0.122533i
$470$	−0.00558839	+	0.124435i	−0.000257773	+	0.00573977i
$471$		0			0
$472$	−13.8571	−	4.50246i	−0.637827	−	0.207242i
$473$	0.668795	−	0.399587i	0.0307512	−	0.0183730i
$474$		0			0
$475$	13.6940	−	32.0387i	0.628324	−	1.47004i
$476$	−18.4026	+	0.826459i	−0.843480	+	0.0378807i
$477$		0			0
$478$	−0.344615	+	3.82898i	−0.0157623	+	0.175134i
$479$	9.33960	+	8.15977i	0.426737	+	0.372829i	0.844346	−	0.535798i	$-0.179989\pi$
$479$	9.33960	+	8.15977i	0.426737	+	0.372829i	−0.417609	+	0.908627i	$0.637132\pi$
$480$		0			0
$481$	−37.1820	−	5.03664i	−1.69535	−	0.229651i
$482$	5.81505	−	0.523364i	0.264868	−	0.0238386i
$483$		0			0
$484$	14.5466	+	15.2146i	0.661209	+	0.691571i
$485$	−0.233438	+	0.0423628i	−0.0105999	+	0.00192360i
$486$		0			0
$487$	23.6386	+	15.6037i	1.07117	+	0.707073i	0.958077	−	0.286512i	$-0.0924958\pi$
$487$	23.6386	+	15.6037i	1.07117	+	0.707073i	0.113092	+	0.993584i	$0.463924\pi$
$488$	3.11300	+	5.78493i	0.140919	+	0.261871i
$489$		0			0
$490$	−0.173841	−	0.263358i	−0.00785335	−	0.0118973i
$491$	−13.0236	−	2.36344i	−0.587747	−	0.106660i	−0.123467	−	0.992349i	$-0.539401\pi$
$491$	−13.0236	−	2.36344i	−0.587747	−	0.106660i	−0.464280	+	0.885688i	$0.653687\pi$
$492$		0			0
$493$	−36.4563	−	41.7276i	−1.64191	−	1.87931i
$494$	7.10181	+	4.24314i	0.319526	+	0.190908i
$495$		0			0
$496$			15.8539i			0.711861i
$497$	1.00766	−	12.4358i	0.0451997	−	0.557821i
$498$		0			0
$499$	11.6377	−	4.36771i	0.520976	−	0.195526i	−0.0770127	−	0.997030i	$-0.524538\pi$
$499$	11.6377	−	4.36771i	0.520976	−	0.195526i	0.597989	+	0.801505i	$0.295967\pi$
$500$	2.21453	−	3.70649i	0.0990366	−	0.165759i
$501$		0			0
$502$	−0.994354	+	0.722441i	−0.0443802	+	0.0322441i
$503$	−0.910599	+	5.01782i	−0.0406016	+	0.223733i	−0.997850	−	0.0655324i	$-0.979125\pi$
$503$	−0.910599	+	5.01782i	−0.0406016	+	0.223733i	0.957249	+	0.289266i	$0.0934111\pi$
$504$		0			0
$505$	1.53840	−	2.85882i	0.0684577	−	0.127216i
$506$	0.147972	−	0.0796272i	0.00657816	−	0.00353986i
$507$		0			0
$508$	16.5263	+	15.8008i	0.733236	+	0.701045i
$509$	−4.20136	−	23.1514i	−0.186222	−	1.02617i	−0.932672	−	0.360726i	$-0.882529\pi$
$509$	−4.20136	−	23.1514i	−0.186222	−	1.02617i	0.746450	−	0.665442i	$-0.231757\pi$
$510$		0			0
$511$	1.48238	−	2.04032i	0.0655767	−	0.0902586i
$512$	−1.74422	−	19.3799i	−0.0770844	−	0.856477i
$513$		0			0
$514$	−0.946762	+	0.307622i	−0.0417599	+	0.0135686i
$515$	1.28526	−	1.47110i	0.0566355	−	0.0648246i
$516$		0			0
$517$	0.0497935	−	0.218160i	0.00218992	−	0.00959465i
$518$	0.178144	+	3.96669i	0.00782721	+	0.174286i
$519$		0			0
$520$	0.814845	+	0.649817i	0.0357333	+	0.0284964i
$521$	22.7941	+	38.1509i	0.998629	+	1.67142i	0.695581	+	0.718448i	$0.255147\pi$
$521$	22.7941	+	38.1509i	0.998629	+	1.67142i	0.303048	+	0.952975i	$0.401996\pi$
$522$		0			0
$523$	−2.87912	+	5.97855i	−0.125895	+	0.261424i	−0.954384	−	0.298581i	$-0.903487\pi$
$523$	−2.87912	+	5.97855i	−0.125895	+	0.261424i	0.828489	+	0.560005i	$0.189201\pi$
$524$	−31.8635	−	1.43099i	−1.39196	−	0.0625131i
$525$		0			0
$526$	3.43601	+	8.03895i	0.149817	+	0.350515i
$527$	−12.7495	−	26.4747i	−0.555378	−	1.15325i
$528$		0			0
$529$	−0.263007	−	1.15231i	−0.0114351	−	0.0501003i
$530$	0.170734	−	0.0471197i	0.00741623	−	0.00204675i
$531$		0			0
$532$	−7.01870	+	18.7013i	−0.304299	+	0.810802i
$533$	16.3526	−	43.5715i	0.708312	−	1.88729i
$534$		0			0
$535$	−0.0512784	+	0.0141519i	−0.00221696	+	0.000611842i
$536$	1.70108	+	7.45293i	0.0734756	+	0.321918i
$537$		0			0
$538$	1.76483	+	3.66470i	0.0760870	+	0.157996i
$539$	0.222804	+	0.521277i	0.00959687	+	0.0224530i
$540$		0			0
$541$	−33.4375	−	1.50168i	−1.43759	−	0.0645622i	−0.687637	−	0.726055i	$-0.741352\pi$
$541$	−33.4375	−	1.50168i	−1.43759	−	0.0645622i	−0.749952	+	0.661493i	$0.769923\pi$
$542$	−0.365316	+	0.758586i	−0.0156917	+	0.0325841i
$543$		0			0
$544$	10.9393	+	18.3093i	0.469019	+	0.785005i
$545$	−1.46015	−	1.16443i	−0.0625461	−	0.0498788i
$546$		0			0
$547$	1.61615	+	35.9864i	0.0691016	+	1.53867i	0.671821	+	0.740713i	$0.265512\pi$
$547$	1.61615	+	35.9864i	0.0691016	+	1.53867i	−0.602720	+	0.797953i	$0.705916\pi$
$548$	3.32119	−	14.5511i	0.141874	−	0.621591i
$549$		0			0
$550$	0.111259	−	0.127346i	0.00474409	−	0.00543004i
$551$	−57.1431	+	18.5669i	−2.43438	+	0.790977i
$552$		0			0
$553$	−2.14709	−	23.8562i	−0.0913037	−	1.01447i
$554$	−2.77718	+	3.82246i	−0.117991	+	0.162401i
$555$		0			0
$556$	3.47853	+	19.1683i	0.147522	+	0.812916i
$557$	−8.72776	−	8.34459i	−0.369807	−	0.353572i	0.483164	−	0.875530i	$-0.339487\pi$
$557$	−8.72776	−	8.34459i	−0.369807	−	0.353572i	−0.852971	+	0.521958i	$0.825202\pi$
$558$		0			0
$559$	23.5903	−	12.6945i	0.997762	−	0.536919i
$560$	−0.556761	+	1.03464i	−0.0235275	+	0.0437214i
$561$		0			0
$562$	1.03089	−	5.68067i	0.0434854	−	0.239624i
$563$	9.86430	−	7.16683i	0.415731	−	0.302046i	−0.360187	−	0.932880i	$-0.617287\pi$
$563$	9.86430	−	7.16683i	0.415731	−	0.302046i	0.775918	+	0.630834i	$0.217287\pi$
$564$		0			0
$565$	2.21934	−	3.71455i	0.0933685	−	0.156272i
$566$	2.77704	−	1.04224i	0.116728	−	0.0438087i
$567$		0			0
$568$	−8.75877	+	3.83630i	−0.367510	+	0.160968i
$569$			39.6281i			1.66130i	0.556797	+	0.830649i	$0.312030\pi$
$569$			39.6281i			1.66130i	−0.556797	+	0.830649i	$0.687970\pi$
$570$		0			0
$571$	−8.20148	−	4.90016i	−0.343221	−	0.205065i	0.330936	−	0.943653i	$-0.392636\pi$
$571$	−8.20148	−	4.90016i	−0.343221	−	0.205065i	−0.674157	+	0.738588i	$0.735493\pi$
$572$	−0.602732	−	0.689882i	−0.0252015	−	0.0288454i
$573$		0			0
$574$	−4.84581	−	0.879385i	−0.202260	−	0.0367048i
$575$	−13.4062	−	20.3096i	−0.559078	−	0.846968i
$576$		0			0
$577$	19.8763	+	36.9363i	0.827460	+	1.53768i	0.843073	+	0.537800i	$0.180744\pi$
$577$	19.8763	+	36.9363i	0.827460	+	1.53768i	−0.0156129	+	0.999878i	$0.504970\pi$
$578$	−6.08484	−	4.01657i	−0.253096	−	0.167067i
$579$		0			0
$580$	−3.64405	+	0.661297i	−0.151311	+	0.0274589i
$581$	−15.3422	−	16.0467i	−0.636503	−	0.665730i
$582$		0			0
$583$	−0.316906	+	0.0285220i	−0.0131249	+	0.00118126i
$584$	−1.91536	−	0.259453i	−0.0792582	−	0.0107362i
$585$		0			0
$586$	−2.42742	−	2.12078i	−0.100276	−	0.0876084i
$587$	1.24580	−	13.8420i	0.0514198	−	0.571321i	−0.928420	−	0.371534i	$-0.878832\pi$
$587$	1.24580	−	13.8420i	0.0514198	−	0.571321i	0.979839	−	0.199787i	$-0.0640251\pi$
$588$		0			0
$589$	−31.8312	+	1.42954i	−1.31158	+	0.0589033i
$590$	0.331225	−	0.774940i	0.0136363	−	0.0319038i
$591$		0			0
$592$	−27.8293	+	16.6272i	−1.14378	+	0.683375i
$593$	44.8814	+	14.5829i	1.84306	+	0.598846i	0.997932	+	0.0642795i	$0.0204749\pi$
$593$	44.8814	+	14.5829i	1.84306	+	0.598846i	0.845126	+	0.534566i	$0.179525\pi$
$594$		0			0
$595$	0.0977017	−	2.17550i	0.00400538	−	0.0891867i
$596$	7.51943	+	2.07523i	0.308008	+	0.0850048i
$597$		0			0
$598$	5.20584	−	2.50700i	0.212883	−	0.102519i
$599$	1.00980	+	7.45464i	0.0412593	+	0.304588i	0.999807	+	0.0196556i	$0.00625698\pi$
$599$	1.00980	+	7.45464i	0.0412593	+	0.304588i	−0.958548	+	0.284933i	$0.908029\pi$
$600$		0			0
$601$	−2.24797	−	8.14535i	−0.0916968	−	0.332256i	0.903691	−	0.428184i	$-0.140847\pi$
$601$	−2.24797	−	8.14535i	−0.0916968	−	0.332256i	−0.995388	+	0.0959284i	$0.969418\pi$
$602$	−1.76755	−	2.21643i	−0.0720398	−	0.0903350i
$603$		0			0
$604$	−28.1542	−	10.5665i	−1.14558	−	0.429943i
$605$	−1.94553	+	1.55151i	−0.0790971	+	0.0630778i
$606$		0			0
$607$	−44.1402	+	10.0747i	−1.79160	+	0.408920i	−0.983614	−	0.180287i	$-0.942297\pi$
$607$	−44.1402	+	10.0747i	−1.79160	+	0.408920i	−0.807982	+	0.589207i	$0.799440\pi$
$608$	22.9182	−	3.10448i	0.929454	−	0.125903i
$609$		0			0
$610$	−0.349399	+	0.149341i	−0.0141468	+	0.00604662i
$611$	2.04702	−	7.41719i	0.0828134	−	0.300068i
$612$		0			0
$613$	−23.8442	−	11.4828i	−0.963059	−	0.463785i	−0.114813	−	0.993387i	$-0.536627\pi$
$613$	−23.8442	−	11.4828i	−0.963059	−	0.463785i	−0.848246	+	0.529602i	$0.822341\pi$
$614$	2.66317	−	8.19641i	0.107477	−	0.330780i
$615$		0			0
$616$	−0.123537	+	0.154911i	−0.00497746	+	0.00624153i
$617$	−33.9589	−	14.5147i	−1.36713	−	0.584341i	−0.420688	−	0.907205i	$-0.638211\pi$
$617$	−33.9589	−	14.5147i	−1.36713	−	0.584341i	−0.946445	+	0.322865i	$0.895354\pi$
$618$		0			0
$619$	7.82654	+	1.78636i	0.314575	+	0.0717997i	0.376894	−	0.926257i	$-0.376992\pi$
$619$	7.82654	+	1.78636i	0.314575	+	0.0717997i	−0.0623183	+	0.998056i	$0.519849\pi$
$620$	−1.95615	−	0.176057i	−0.0785608	−	0.00707060i
$621$		0			0
$622$	−0.843325	−	2.59549i	−0.0338143	−	0.104070i
$623$	0.0842584	−	0.622020i	0.00337574	−	0.0249207i
$624$		0			0
$625$	−19.6050	−	14.2438i	−0.784198	−	0.569753i
$626$	4.16409	−	3.98128i	0.166431	−	0.159124i
$627$		0			0
$628$	−4.07093	+	4.25786i	−0.162448	+	0.169907i
$629$	33.1011	−	50.1461i	1.31983	−	1.99946i
$630$		0			0
$631$	9.03722	+	4.86313i	0.359766	+	0.193598i	0.643759	−	0.765228i	$-0.277374\pi$
$631$	9.03722	+	4.86313i	0.359766	+	0.193598i	−0.283994	+	0.958826i	$0.591659\pi$
$632$	−15.3206	+	10.1130i	−0.609419	+	0.402274i
$633$		0			0
$634$	1.06178	+	1.46142i	0.0421688	+	0.0580404i
$635$	−2.03553	+	1.77839i	−0.0807775	+	0.0705732i
$636$		0			0
$637$	6.84939	+	18.2501i	0.271383	+	0.723096i
$638$	−0.291605			−0.0115448
$639$		0			0
$640$	1.88547			0.0745296
$641$	2.46098	+	6.55727i	0.0972030	+	0.258997i	0.975837	−	0.218499i	$-0.0701161\pi$
$641$	2.46098	+	6.55727i	0.0972030	+	0.258997i	−0.878634	+	0.477496i	$0.841545\pi$
$642$		0			0
$643$	3.48846	−	3.04778i	0.137571	−	0.120193i	−0.586403	−	0.810020i	$-0.699456\pi$
$643$	3.48846	−	3.04778i	0.137571	−	0.120193i	0.723974	+	0.689827i	$0.242313\pi$
$644$	8.20031	+	11.2868i	0.323138	+	0.444761i
$645$		0			0
$646$	−11.0563	+	7.29822i	−0.435006	+	0.287145i
$647$	5.76029	+	3.09974i	0.226460	+	0.121863i	0.583165	−	0.812354i	$-0.301814\pi$
$647$	5.76029	+	3.09974i	0.226460	+	0.121863i	−0.356705	+	0.934217i	$0.616100\pi$
$648$		0			0
$649$	−0.834056	+	1.26354i	−0.0327396	+	0.0495983i
$650$	4.01831	−	4.20282i	0.157611	−	0.164848i
$651$		0			0
$652$	3.98047	−	3.80572i	0.155887	−	0.149044i
$653$	−15.2680	−	11.0928i	−0.597481	−	0.434096i	0.247503	−	0.968887i	$-0.420390\pi$
$653$	−15.2680	−	11.0928i	−0.597481	−	0.434096i	−0.844984	+	0.534792i	$0.820390\pi$
$654$		0			0
$655$	0.506141	−	3.73648i	0.0197766	−	0.145996i
$656$	−12.4253	−	38.2411i	−0.485126	−	1.49306i
$657$		0			0
$658$	−0.810984	−	0.0729899i	−0.0316155	−	0.00284544i
$659$	−32.0480	−	7.31475i	−1.24841	−	0.284942i	−0.453275	−	0.891371i	$-0.649744\pi$
$659$	−32.0480	−	7.31475i	−1.24841	−	0.284942i	−0.795138	+	0.606429i	$0.792602\pi$
$660$		0			0
$661$	−3.32207	−	1.41992i	−0.129214	−	0.0552286i	0.327447	−	0.944870i	$-0.393812\pi$
$661$	−3.32207	−	1.41992i	−0.129214	−	0.0552286i	−0.456661	+	0.889641i	$0.650955\pi$
$662$	−3.75374	+	4.70704i	−0.145893	+	0.182944i
$663$		0			0
$664$	−5.25789	+	16.1821i	−0.204046	+	0.627988i
$665$	−2.12753	−	1.02457i	−0.0825022	−	0.0397310i
$666$		0			0
$667$	−11.1641	+	40.4523i	−0.432277	+	1.56632i
$668$	−33.2355	+	14.2055i	−1.28592	+	0.549629i
$669$		0			0
$670$	−0.438170	+	0.0593541i	−0.0169280	+	0.00229305i
$671$	0.665505	−	0.151897i	0.0256915	−	0.00586392i
$672$		0			0
$673$	−25.0948	+	20.0125i	−0.967335	+	0.771424i	−0.973531	−	0.228557i	$-0.926599\pi$
$673$	−25.0948	+	20.0125i	−0.967335	+	0.771424i	0.00619565	+	0.999981i	$0.498028\pi$
$674$	5.85830	+	2.19866i	0.225653	+	0.0846891i
$675$		0			0
$676$	−4.11011	−	5.15392i	−0.158081	−	0.198228i
$677$	3.12034	+	11.3063i	0.119925	+	0.434537i	0.999121	−	0.0419228i	$-0.0133484\pi$
$677$	3.12034	+	11.3063i	0.119925	+	0.434537i	−0.879196	+	0.476460i	$0.841920\pi$
$678$		0			0
$679$	−0.208186	−	1.53689i	−0.00798946	−	0.0589805i
$680$	−1.50371	+	0.724148i	−0.0576646	+	0.0277698i
$681$		0			0
$682$	−0.149070	−	0.0411406i	−0.00570817	−	0.00157536i
$683$	1.25709	−	27.9912i	0.0481011	−	1.07105i	−0.819275	−	0.573401i	$-0.805624\pi$
$683$	1.25709	−	27.9912i	0.0481011	−	1.07105i	0.867376	−	0.497653i	$-0.165805\pi$
$684$		0			0
$685$	1.67807	+	0.545237i	0.0641157	+	0.0208324i
$686$	4.34927	−	2.59857i	0.166056	−	0.0992139i
$687$		0			0
$688$	9.09669	−	21.2828i	0.346808	−	0.811398i
$689$	−10.9300	+	0.490869i	−0.416401	+	0.0187006i
$690$		0			0
$691$	−0.842343	+	9.35919i	−0.0320442	+	0.356040i	0.963913	+	0.266216i	$0.0857734\pi$
$691$	−0.842343	+	9.35919i	−0.0320442	+	0.356040i	−0.995958	+	0.0898244i	$0.971369\pi$
$692$	−11.7694	−	10.2826i	−0.447406	−	0.390886i
$693$		0			0
$694$	4.88361	+	0.661529i	0.185379	+	0.0251113i
$695$	−2.29376	+	0.206442i	−0.0870072	+	0.00783079i
$696$		0			0
$697$	51.5023	+	53.8672i	1.95079	+	2.04036i
$698$	4.59076	−	0.833100i	0.173763	−	0.0315333i
$699$		0			0
$700$	11.7171	+	7.73441i	0.442866	+	0.292333i
$701$	−1.95338	−	3.62999i	−0.0737782	−	0.137103i	0.841034	−	0.540982i	$-0.181947\pi$
$701$	−1.95338	−	3.62999i	−0.0737782	−	0.137103i	−0.914812	+	0.403879i	$0.867662\pi$
$702$		0			0
$703$	−35.8933	−	54.3760i	−1.35374	−	2.05083i
$704$	−0.702462	−	0.127478i	−0.0264750	−	0.00480451i
$705$		0			0
$706$	6.53215	+	7.47665i	0.245841	+	0.281388i
$707$	18.2183	+	10.8849i	0.685170	+	0.409370i
$708$		0			0
$709$		−	36.3116i		−	1.36371i	−0.731487	−	0.681855i	$-0.761174\pi$
$709$		−	36.3116i		−	1.36371i	0.731487	−	0.681855i	$-0.238826\pi$
$710$	−0.175590	−	0.524467i	−0.00658977	−	0.0196829i
$711$		0			0
$712$	−0.450397	+	0.169037i	−0.0168793	+	0.00633492i
$713$	−11.4143	+	19.1043i	−0.427469	+	0.715462i
$714$		0			0
$715$	0.0876147	−	0.0636558i	0.00327660	−	0.00238059i
$716$	−4.26619	+	23.5086i	−0.159435	+	0.878559i
$717$		0			0
$718$	0.156089	−	0.290063i	0.00582521	−	0.0108250i
$719$	13.9205	−	7.49092i	0.519145	−	0.279364i	−0.193241	−	0.981151i	$-0.561900\pi$
$719$	13.9205	−	7.49092i	0.519145	−	0.279364i	0.712387	+	0.701787i	$0.247614\pi$
$720$		0			0
$721$	9.23009	+	8.82487i	0.343746	+	0.328655i
$722$	1.58191	+	8.71706i	0.0588727	+	0.324416i
$723$		0			0
$724$	−12.8187	+	17.6434i	−0.476402	+	0.655712i
$725$	3.78553	+	42.0607i	0.140591	+	1.56209i
$726$		0			0
$727$	11.8870	−	3.86232i	0.440865	−	0.143246i	−0.0801699	−	0.996781i	$-0.525546\pi$
$727$	11.8870	−	3.86232i	0.440865	−	0.143246i	0.521034	+	0.853536i	$0.325546\pi$
$728$	−4.48261	+	5.13076i	−0.166137	+	0.190159i
$729$		0			0
$730$	0.0248774	−	0.108995i	0.000920756	−	0.00403409i
$731$	1.92466	+	42.8559i	0.0711861	+	1.58508i
$732$		0			0
$733$	1.73590	+	1.38433i	0.0641169	+	0.0511315i	0.655024	−	0.755608i	$-0.272659\pi$
$733$	1.73590	+	1.38433i	0.0641169	+	0.0511315i	−0.590907	+	0.806740i	$0.701230\pi$
$734$	−1.01721	−	1.70253i	−0.0375460	−	0.0628415i
$735$		0			0
$736$	7.00854	−	14.5534i	0.258338	−	0.536445i
$737$	0.793550	+	0.0356384i	0.0292308	+	0.00131276i
$738$		0			0
$739$	−8.54186	−	19.9847i	−0.314217	−	0.735148i	−0.999973	−	0.00731652i	$-0.997671\pi$
$739$	−8.54186	−	19.9847i	−0.314217	−	0.735148i	0.685756	−	0.727832i	$-0.259472\pi$
$740$	−1.74252	−	3.61839i	−0.0640565	−	0.133015i
$741$		0			0
$742$	0.257641	+	1.12880i	0.00945830	+	0.0414395i
$743$	27.6889	−	7.64165i	1.01581	−	0.280345i	0.281790	−	0.959476i	$-0.409072\pi$
$743$	27.6889	−	7.64165i	1.01581	−	0.280345i	0.734017	+	0.679131i	$0.237643\pi$
$744$		0			0
$745$	−0.324023	+	0.863356i	−0.0118713	+	0.0316309i
$746$	0.939920	−	2.50441i	0.0344129	−	0.0916929i
$747$		0			0
$748$	1.41413	−	0.390276i	0.0517059	−	0.0142699i
$749$	−0.0773800	−	0.339024i	−0.00282740	−	0.0123877i
$750$		0			0
$751$	2.84689	+	5.91162i	0.103884	+	0.215718i	0.946432	−	0.322904i	$-0.104659\pi$
$751$	2.84689	+	5.91162i	0.103884	+	0.215718i	−0.842547	+	0.538622i	$0.818945\pi$
$752$	−2.61280	−	6.11295i	−0.0952790	−	0.222916i
$753$		0			0
$754$	−10.0169	−	0.449861i	−0.364796	−	0.0163830i
$755$	1.54246	−	3.20294i	0.0561357	−	0.116567i
$756$		0			0
$757$	−13.1718	−	22.0459i	−0.478739	−	0.801274i	0.519857	−	0.854253i	$-0.325985\pi$
$757$	−13.1718	−	22.0459i	−0.478739	−	0.801274i	−0.998596	+	0.0529798i	$0.983128\pi$
$758$	1.00927	+	0.804869i	0.0366585	+	0.0292342i
$759$		0			0
$760$	0.0811951	+	1.80795i	0.00294526	+	0.0655813i
$761$	3.35363	−	14.6932i	0.121569	−	0.532629i	−0.877065	−	0.480372i	$-0.840502\pi$
$761$	3.35363	−	14.6932i	0.121569	−	0.532629i	0.998634	−	0.0522564i	$-0.0166413\pi$
$762$		0			0
$763$	8.03257	−	9.19402i	0.290799	−	0.332846i
$764$	−8.26074	+	2.68408i	−0.298863	+	0.0971065i
$765$		0			0
$766$	0.185935	+	2.06591i	0.00671812	+	0.0746444i
$767$	−30.6000	+	42.1172i	−1.10490	+	1.52077i
$768$		0			0
$769$	0.176927	+	0.974946i	0.00638014	+	0.0351575i	0.986963	−	0.160950i	$-0.0514557\pi$
$769$	0.176927	+	0.974946i	0.00638014	+	0.0351575i	−0.980582	+	0.196107i	$0.937170\pi$
$770$	−0.00828361	−	0.00791994i	−0.000298521	−	0.000285415i
$771$		0			0
$772$	−5.72257	+	3.07944i	−0.205960	+	0.110832i
$773$	12.3826	−	23.0107i	0.445371	−	0.827637i	−0.554620	−	0.832104i	$-0.687136\pi$
$773$	12.3826	−	23.0107i	0.445371	−	0.827637i	0.999990	+	0.00446699i	$0.00142189\pi$
$774$		0			0
$775$	−3.99888	+	22.0357i	−0.143644	+	0.791544i
$776$	−0.961628	+	0.698664i	−0.0345204	+	0.0250806i
$777$		0			0
$778$	3.76622	−	6.30360i	0.135026	−	0.225995i
$779$	75.6596	−	28.3955i	2.71079	−	1.01738i
$780$		0			0
$781$	0.142138	+	0.983376i	0.00508611	+	0.0351880i
$782$			9.25278i			0.330879i
$783$		0			0
$784$	14.4578	+	8.63813i	0.516350	+	0.308505i
$785$	−0.458186	−	0.524436i	−0.0163534	−	0.0187179i
$786$		0			0
$787$	−17.9936	−	3.26536i	−0.641404	−	0.116398i	−0.151896	−	0.988396i	$-0.548538\pi$
$787$	−17.9936	−	3.26536i	−0.641404	−	0.116398i	−0.489508	+	0.871999i	$0.662824\pi$
$788$	17.7934	+	26.9558i	0.633863	+	0.960261i
$789$		0			0
$790$	−0.503158	−	0.935024i	−0.0179015	−	0.0332667i
$791$	23.6070	+	15.5828i	0.839368	+	0.554062i
$792$		0			0
$793$	23.0951	−	4.19115i	0.820132	−	0.148832i
$794$	3.92984	+	4.11029i	0.139465	+	0.145869i
$795$		0			0
$796$	28.7799	−	2.59024i	1.02008	−	0.0918087i
$797$	−7.65571	−	1.03704i	−0.271179	−	0.0367337i	−0.00261873	−	0.999997i	$-0.500834\pi$
$797$	−7.65571	−	1.03704i	−0.271179	−	0.0367337i	−0.268560	+	0.963263i	$0.586548\pi$
$798$		0			0
$799$	9.27913	+	8.10693i	0.328272	+	0.286803i
$800$	1.45713	−	16.1900i	0.0515172	−	0.572403i
$801$		0			0
$802$	2.56200	−	0.115059i	0.0904673	−	0.00406289i
$803$	−0.0789362	+	0.184681i	−0.00278560	+	0.00651723i
$804$		0			0
$805$	−1.41582	+	0.845910i	−0.0499009	+	0.0298144i
$806$	−5.05723	−	1.64319i	−0.178133	−	0.0578791i
$807$		0			0
$808$	0.729722	−	16.2485i	0.0256715	−	0.571621i
$809$	−18.2938	−	5.04876i	−0.643175	−	0.177505i	−0.0707913	−	0.997491i	$-0.522552\pi$
$809$	−18.2938	−	5.04876i	−0.643175	−	0.177505i	−0.572383	+	0.819986i	$0.693981\pi$
$810$		0			0
$811$	16.1169	−	7.76147i	0.565940	−	0.272542i	−0.128959	−	0.991650i	$-0.541164\pi$
$811$	16.1169	−	7.76147i	0.565940	−	0.272542i	0.694899	+	0.719108i	$0.255449\pi$
$812$	−3.24985	−	23.9914i	−0.114048	−	0.841933i
$813$		0			0
$814$	−0.0841246	−	0.304818i	−0.00294856	−	0.0106839i
$815$	0.405910	+	0.508995i	0.0142184	+	0.0178293i
$816$		0			0
$817$	43.5515	+	16.3452i	1.52367	+	0.571844i
$818$	7.25394	−	5.78482i	0.253628	−	0.202262i
$819$		0			0
$820$	4.85640	−	1.10844i	0.169593	−	0.0387085i
$821$	−13.6590	+	1.85023i	−0.476701	+	0.0645736i	−0.368643	−	0.929571i	$-0.620178\pi$
$821$	−13.6590	+	1.85023i	−0.476701	+	0.0645736i	−0.108058	+	0.994145i	$0.534463\pi$
$822$		0			0
$823$	−40.0181	+	17.1046i	−1.39494	+	0.596227i	−0.953591	−	0.301106i	$-0.902644\pi$
$823$	−40.0181	+	17.1046i	−1.39494	+	0.596227i	−0.441353	+	0.897334i	$0.645501\pi$
$824$	2.60370	−	9.43428i	0.0907040	−	0.328659i
$825$		0			0
$826$	4.96360	+	2.39035i	0.172706	+	0.0831707i
$827$	−14.6302	+	45.0270i	−0.508741	+	1.56574i	0.285648	+	0.958335i	$0.407791\pi$
$827$	−14.6302	+	45.0270i	−0.508741	+	1.56574i	−0.794389	+	0.607409i	$0.792209\pi$
$828$		0			0
$829$	27.4519	−	34.4236i	0.953445	−	1.19558i	−0.0271682	−	0.999631i	$-0.508649\pi$
$829$	27.4519	−	34.4236i	0.953445	−	1.19558i	0.980614	−	0.195952i	$-0.0627796\pi$
$830$	−0.904961	−	0.386799i	−0.0314117	−	0.0134260i
$831$		0			0
$832$	−23.9336	−	5.46270i	−0.829750	−	0.189385i
$833$	−31.0900	−	2.79815i	−1.07721	−	0.0969502i
$834$		0			0
$835$	−1.32039	−	4.06373i	−0.0456938	−	0.140631i
$836$	0.213531	−	1.57635i	0.00738513	−	0.0545192i
$837$		0			0
$838$	−4.08157	−	2.96543i	−0.140995	−	0.102439i
$839$	7.45275	−	7.12556i	0.257298	−	0.246002i	−0.551379	−	0.834255i	$-0.685898\pi$
$839$	7.45275	−	7.12556i	0.257298	−	0.246002i	0.808677	+	0.588253i	$0.200184\pi$
$840$		0			0
$841$	30.2852	−	31.6758i	1.04432	−	1.09227i
$842$	−4.41919	+	6.69479i	−0.152295	+	0.230718i
$843$		0			0
$844$	31.6727	+	17.0438i	1.09022	+	0.586671i
$845$	0.650383	−	0.429314i	0.0223739	−	0.0147689i
$846$		0			0
$847$	−9.56153	−	13.1603i	−0.328538	−	0.452194i
$848$	−7.11873	+	6.21944i	−0.244458	+	0.213577i
$849$		0			0
$850$	3.27181	+	8.71771i	0.112222	+	0.299015i
$851$	−45.5060			−1.55993
$852$		0			0
$853$	−15.8118			−0.541385			−0.270692	−	0.962666i	$-0.587253\pi$
$853$	−15.8118			−0.541385			−0.270692	+	0.962666i	$0.587253\pi$
$854$	−0.872794	−	2.32555i	−0.0298664	−	0.0795787i
$855$		0			0
$856$	−0.200702	+	0.175348i	−0.00685985	+	0.00599327i
$857$	26.1116	+	35.9396i	0.891956	+	1.22767i	0.972964	+	0.230959i	$0.0741862\pi$
$857$	26.1116	+	35.9396i	0.891956	+	1.22767i	−0.0810075	+	0.996713i	$0.525814\pi$
$858$		0			0
$859$	24.1993	−	15.9738i	0.825668	−	0.545019i	−0.0659415	−	0.997823i	$-0.521005\pi$
$859$	24.1993	−	15.9738i	0.825668	−	0.545019i	0.891610	+	0.452805i	$0.149577\pi$
$860$	2.52498	+	1.35875i	0.0861010	+	0.0463329i
$861$		0			0
$862$	−1.78417	+	2.70291i	−0.0607691	+	0.0920613i
$863$	11.3895	−	11.9124i	0.387702	−	0.405504i	−0.499924	−	0.866069i	$-0.666639\pi$
$863$	11.3895	−	11.9124i	0.387702	−	0.405504i	0.887626	+	0.460565i	$0.152353\pi$
$864$		0			0
$865$	1.33541	−	1.27678i	0.0454052	−	0.0434118i
$866$	2.40922	+	1.75040i	0.0818686	+	0.0594811i
$867$		0			0
$868$	1.72345	−	12.7230i	0.0584976	−	0.431846i
$869$	0.589454	+	1.81415i	0.0199959	+	0.0615409i
$870$		0			0
$871$	27.2043	+	2.44843i	0.921783	+	0.0829619i
$872$	−9.12219	−	2.08208i	−0.308916	−	0.0705081i
$873$		0			0
$874$	9.22588	+	3.94333i	0.312070	+	0.133385i
$875$	−2.08038	+	2.60871i	−0.0703296	+	0.0881905i
$876$		0			0
$877$	8.54083	−	26.2860i	0.288403	−	0.887614i	−0.696955	−	0.717115i	$-0.745462\pi$
$877$	8.54083	−	26.2860i	0.288403	−	0.887614i	0.985358	−	0.170499i	$-0.0545379\pi$
$878$	−1.61111	−	0.775868i	−0.0543722	−	0.0261843i
$879$		0			0
$880$	0.0248925	−	0.0901958i	0.000839125	−	0.00304050i
$881$	−36.7523	+	15.7087i	−1.23822	+	0.529240i	−0.909703	−	0.415259i	$-0.863691\pi$
$881$	−36.7523	+	15.7087i	−1.23822	+	0.529240i	−0.328515	+	0.944499i	$0.606548\pi$
$882$		0			0
$883$	32.6588	−	4.42394i	1.09906	−	0.148877i	0.437826	−	0.899060i	$-0.355748\pi$
$883$	32.6588	−	4.42394i	1.09906	−	0.148877i	0.661231	+	0.750182i	$0.270034\pi$
$884$	49.1791	−	11.2248i	1.65407	−	0.377531i
$885$		0			0
$886$	−0.408950	+	0.326127i	−0.0137389	+	0.0109564i
$887$	17.2670	+	6.48041i	0.579769	+	0.217591i	0.623992	−	0.781431i	$-0.285510\pi$
$887$	17.2670	+	6.48041i	0.579769	+	0.217591i	−0.0442230	+	0.999022i	$0.514081\pi$
$888$		0			0
$889$	−11.0168	−	13.8146i	−0.369491	−	0.463326i
$890$	−0.00740267	−	0.0268230i	−0.000248138	−	0.000899108i
$891$		0			0
$892$	1.44227	+	10.6472i	0.0482907	+	0.356496i
$893$	12.0379	−	5.79715i	0.402833	−	0.193994i
$894$		0			0
$895$	−2.72273	−	0.751425i	−0.0910107	−	0.0251174i
$896$	−0.552979	+	12.3130i	−0.0184737	+	0.411350i
$897$		0			0
$898$	−6.23269	−	2.02512i	−0.207987	−	0.0675792i
$899$	33.1530	−	19.8080i	1.10572	−	0.660634i
$900$		0			0
$901$	6.88607	−	16.1108i	0.229408	−	0.536727i
$902$	0.391814	−	0.0175964i	0.0130460	−	0.000585896i
$903$		0			0
$904$	1.94327	−	21.5915i	0.0646321	−	0.718121i
$905$	−1.94152	−	1.69625i	−0.0645382	−	0.0563853i
$906$		0			0
$907$	18.4229	+	2.49555i	0.611723	+	0.0828634i	0.433540	−	0.901134i	$-0.357264\pi$
$907$	18.4229	+	2.49555i	0.611723	+	0.0828634i	0.178182	+	0.983998i	$0.442978\pi$
$908$	23.7721	−	2.13953i	0.788906	−	0.0710029i
$909$		0			0
$910$	−0.272332	−	0.284837i	−0.00902773	−	0.00944227i
$911$	20.0877	−	3.64538i	0.665535	−	0.120777i	0.164732	−	0.986338i	$-0.447324\pi$
$911$	20.0877	−	3.64538i	0.665535	−	0.120777i	0.500803	+	0.865561i	$0.333038\pi$
$912$		0			0
$913$	1.47554	+	0.973995i	0.0488332	+	0.0322345i
$914$	1.38137	+	2.56701i	0.0456915	+	0.0849091i
$915$		0			0
$916$	−3.05886	−	4.63397i	−0.101068	−	0.153111i
$917$	24.2526	+	4.40120i	0.800893	+	0.145341i
$918$		0			0
$919$	19.8871	+	22.7626i	0.656015	+	0.750870i	0.980821	−	0.194911i	$-0.0624418\pi$
$919$	19.8871	+	22.7626i	0.656015	+	0.750870i	−0.324806	+	0.945781i	$0.605299\pi$
$920$	1.08509	+	0.648309i	0.0357742	+	0.0213741i
$921$		0			0
$922$			6.96622i			0.229420i
$923$	3.36554	+	33.9993i	0.110778	+	1.11910i
$924$		0			0
$925$	−42.8745	+	16.0911i	−1.40970	+	0.529071i
$926$	−3.68560	+	6.16865i	−0.121116	+	0.202715i
$927$		0			0
$928$	−22.6779	+	16.4765i	−0.744440	+	0.540867i
$929$	−1.67306	+	9.21931i	−0.0548913	+	0.302476i	−0.999683	−	0.0251971i	$-0.991979\pi$
$929$	−1.67306	+	9.21931i	−0.0548913	+	0.302476i	0.944791	+	0.327673i	$0.106264\pi$
$930$		0			0
$931$	−16.0399	+	29.8071i	−0.525686	+	0.976888i
$932$	−23.6254	+	12.7134i	−0.773875	+	0.416440i
$933$		0			0
$934$	−6.20632	−	5.93385i	−0.203077	−	0.194162i
$935$	0.0309662	+	0.170638i	0.00101270	+	0.00558045i
$936$		0			0
$937$	−15.8831	+	21.8612i	−0.518877	+	0.714173i	−0.985385	−	0.170344i	$-0.945512\pi$
$937$	−15.8831	+	21.8612i	−0.518877	+	0.714173i	0.466508	+	0.884517i	$0.345512\pi$
$938$	−0.259103	−	2.87887i	−0.00846002	−	0.0939986i
$939$		0			0
$940$	0.783268	−	0.254499i	0.0255474	−	0.00830085i
$941$	27.1608	−	31.0880i	0.885416	−	1.01344i	−0.114384	−	0.993437i	$-0.536489\pi$
$941$	27.1608	−	31.0880i	0.885416	−	1.01344i	0.999800	−	0.0200036i	$-0.00636776\pi$
$942$		0			0
$943$	12.5596	−	55.0272i	0.408997	−	1.79193i
$944$	2.01797	+	44.9336i	0.0656794	+	1.46246i
$945$		0			0
$946$	0.176510	+	0.140762i	0.00573884	+	0.00457657i
$947$	−23.7230	−	39.7056i	−0.770893	−	1.29026i	−0.951788	−	0.306756i	$-0.900757\pi$
$947$	−23.7230	−	39.7056i	−0.770893	−	1.29026i	0.180895	−	0.983502i	$-0.442101\pi$
$948$		0			0
$949$	−2.99645	+	6.22219i	−0.0972689	+	0.201981i
$950$	10.0867	+	0.452996i	0.327257	+	0.0146971i
$951$		0			0
$952$	−4.28803	−	10.0323i	−0.138976	−	0.325150i
$953$	−7.48923	−	15.5515i	−0.242600	−	0.503764i	0.743744	−	0.668465i	$-0.233048\pi$
$953$	−7.48923	−	15.5515i	−0.242600	−	0.503764i	−0.986344	+	0.164701i	$0.947334\pi$
$954$		0			0
$955$	−0.228488	−	1.00107i	−0.00739371	−	0.0323939i
$956$	24.5030	−	6.76240i	0.792484	−	0.218712i
$957$		0			0
$958$	−1.26282	+	3.36476i	−0.0407998	+	0.108711i
$959$	−4.05282	+	10.7987i	−0.130872	+	0.348708i
$960$		0			0
$961$	−10.1403	+	2.79855i	−0.327107	+	0.0902757i
$962$	−2.41952	−	10.6006i	−0.0780085	−	0.341777i
$963$		0			0
$964$	−16.7495	−	34.7807i	−0.539465	−	1.12021i
$965$	−0.301936	−	0.706415i	−0.00971967	−	0.0227403i
$966$		0			0
$967$	28.2091	+	1.26687i	0.907145	+	0.0407399i	0.493546	−	0.869720i	$-0.335700\pi$
$967$	28.2091	+	1.26687i	0.907145	+	0.0407399i	0.413598	+	0.910459i	$0.364272\pi$
$968$	−5.40928	+	11.2325i	−0.173861	+	0.361026i
$969$		0			0
$970$	−0.0352629	−	0.0590201i	−0.00113222	−	0.00189502i
$971$	−10.8947	−	8.68825i	−0.349628	−	0.278819i	0.432890	−	0.901447i	$-0.357494\pi$
$971$	−10.8947	−	8.68825i	−0.349628	−	0.278819i	−0.782518	+	0.622627i	$0.786065\pi$
$972$		0			0
$973$	−0.675444	−	15.0399i	−0.0216537	−	0.482158i
$974$	−1.82644	+	8.00218i	−0.0585231	+	0.256406i
$975$		0			0
$976$	13.3428	−	15.2721i	0.427094	−	0.488848i
$977$	−3.74029	+	1.21529i	−0.119662	+	0.0388807i	−0.368236	−	0.929732i	$-0.620038\pi$
$977$	−3.74029	+	1.21529i	−0.119662	+	0.0388807i	0.248574	+	0.968613i	$0.420038\pi$
$978$		0			0
$979$	0.00448091	+	0.0497870i	0.000143211	+	0.00159120i
$980$	−1.22638	+	1.68797i	−0.0391752	+	0.0539201i
$981$		0			0
$982$	−0.684891	−	3.77406i	−0.0218558	−	0.120435i
$983$	−37.0567	−	35.4298i	−1.18193	−	1.13004i	−0.988860	−	0.148851i	$-0.952443\pi$
$983$	−37.0567	−	35.4298i	−1.18193	−	1.13004i	−0.193066	−	0.981186i	$-0.561843\pi$
$984$		0			0
$985$	−3.36236	+	1.80937i	−0.107134	+	0.0576512i
$986$	7.60891	−	14.1397i	0.242317	−	0.450300i
$987$		0			0
$988$	9.76686	−	53.8198i	0.310725	−	1.71224i
$989$	26.2846	−	19.0969i	0.835803	−	0.607246i
$990$		0			0
$991$	−17.8266	+	29.8367i	−0.566281	+	0.947795i	0.432649	+	0.901562i	$0.357579\pi$
$991$	−17.8266	+	29.8367i	−0.566281	+	0.947795i	−0.998931	+	0.0462329i	$0.985278\pi$
$992$	−13.9176	+	5.22337i	−0.441884	+	0.165842i
$993$		0			0
$994$	3.47653	−	0.992870i	0.110269	−	0.0314919i
$995$			3.41603i			0.108296i
$996$		0			0
$997$	−23.3259	−	13.9366i	−0.738738	−	0.441376i	0.0936240	−	0.995608i	$-0.470155\pi$
$997$	−23.3259	−	13.9366i	−0.738738	−	0.441376i	−0.832362	+	0.554232i	$0.813012\pi$
$998$	2.36999	+	2.71267i	0.0750207	+	0.0858681i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	639.2.z.a.530.13	yes	576
3.2	odd	2	inner	639.2.z.a.530.12	yes	576
71.28	odd	70	inner	639.2.z.a.170.12	✓	576
213.170	even	70	inner	639.2.z.a.170.13	yes	576

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
639.2.z.a.170.12	✓	576	71.28	odd	70	inner
639.2.z.a.170.13	yes	576	213.170	even	70	inner
639.2.z.a.530.12	yes	576	3.2	odd	2	inner
639.2.z.a.530.13	yes	576	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 639 = 3^{2} \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	639.z (of order \(70\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(0.101824 + 0.271308i) q^{2} +(1.44290 - 1.26063i) q^{4} +(0.133137 + 0.183248i) q^{5} +(-1.23575 + 0.815710i) q^{7} +(0.999308 + 0.537751i) q^{8} +O(q^{10})\)	\(q+(0.101824 + 0.271308i) q^{2} +(1.44290 - 1.26063i) q^{4} +(0.133137 + 0.183248i) q^{5} +(-1.23575 + 0.815710i) q^{7} +(0.999308 + 0.537751i) q^{8} +(-0.0361601 + 0.0547802i) q^{10} +(0.0814888 - 0.0852306i) q^{11} +(2.93071 - 2.80205i) q^{13} +(-0.347137 - 0.252210i) q^{14} +(0.470245 - 3.47149i) q^{16} +(2.00647 + 6.17527i) q^{17} +(7.01242 + 0.631129i) q^{19} +(0.423112 + 0.0965725i) q^{20} +(0.0314212 + 0.0134301i) q^{22} +(3.06602 - 3.84467i) q^{23} +(1.52923 - 4.70649i) q^{25} +(1.05863 + 0.509810i) q^{26} +(-0.754758 + 2.73481i) q^{28} +(-7.84698 + 3.35396i) q^{29} +(-4.48459 + 0.607479i) q^{31} +(3.20244 - 0.730936i) q^{32} +(-1.47109 + 1.17316i) q^{34} +(-0.314001 - 0.117847i) q^{35} +(-5.76969 - 7.23496i) q^{37} +(0.542799 + 1.96679i) q^{38} +(0.0345036 + 0.254716i) q^{40} +(10.3412 - 4.98004i) q^{41} +(6.36882 + 1.75768i) q^{43} +(0.0101365 - 0.225706i) q^{44} +(1.35528 + 0.440358i) q^{46} +(1.62906 - 0.973316i) q^{47} +(-1.88949 + 4.42067i) q^{49} +(1.43262 - 0.0643390i) q^{50} +(0.696397 - 7.73761i) q^{52} +(-2.03207 - 1.77536i) q^{53} +(0.0264675 + 0.00358527i) q^{55} +(-1.67354 + 0.150621i) q^{56} +(-1.70896 - 1.78743i) q^{58} +(-12.6331 + 2.29256i) q^{59} +(4.83129 + 3.18911i) q^{61} +(-0.621451 - 1.15485i) q^{62} +(-3.33541 - 5.05293i) q^{64} +(0.903656 + 0.163989i) q^{65} +(4.43218 + 5.07304i) q^{67} +(10.6798 + 6.38091i) q^{68} -0.0971906i q^{70} +(-5.19473 + 6.63436i) q^{71} +(-1.59463 + 0.598476i) q^{73} +(1.37541 - 2.30205i) q^{74} +(10.9139 - 7.92938i) q^{76} +(-0.0311761 + 0.171795i) q^{77} +(-7.66558 + 14.2450i) q^{79} +(0.698751 - 0.376014i) q^{80} +(2.40410 + 2.29855i) q^{82} +(2.67721 + 14.7526i) q^{83} +(-0.864469 + 1.18984i) q^{85} +(0.171623 + 1.90688i) q^{86} +(0.127265 - 0.0413510i) q^{88} +(-0.278916 + 0.319245i) q^{89} +(-1.33596 + 5.85323i) q^{91} +(-0.422720 - 9.41259i) q^{92} +(0.429944 + 0.342869i) q^{94} +(0.817962 + 1.36904i) q^{95} +(-0.454465 + 0.943705i) q^{97} +(-1.39176 - 0.0625039i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 576 q - 24 q^{4}+O(q^{10}) \) 576 * q - 24 * q^4	\( 576 q - 24 q^{4} - 16 q^{10} + 76 q^{16} - 8 q^{19} + 20 q^{22} + 168 q^{25} - 20 q^{28} - 28 q^{31} + 40 q^{37} + 32 q^{40} + 52 q^{43} - 20 q^{46} - 208 q^{52} - 92 q^{55} + 56 q^{58} + 56 q^{61} - 144 q^{64} - 16 q^{67} - 44 q^{73} - 336 q^{76} + 88 q^{79} - 124 q^{82} + 60 q^{85} - 260 q^{88} + 80 q^{91} + 56 q^{94} - 56 q^{97}+O(q^{100}) \) 576 * q - 24 * q^4 - 16 * q^10 + 76 * q^16 - 8 * q^19 + 20 * q^22 + 168 * q^25 - 20 * q^28 - 28 * q^31 + 40 * q^37 + 32 * q^40 + 52 * q^43 - 20 * q^46 - 208 * q^52 - 92 * q^55 + 56 * q^58 + 56 * q^61 - 144 * q^64 - 16 * q^67 - 44 * q^73 - 336 * q^76 + 88 * q^79 - 124 * q^82 + 60 * q^85 - 260 * q^88 + 80 * q^91 + 56 * q^94 - 56 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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