LMFDB - Embedded newform 864.2.bk.a.37.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(37,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("864.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bk (of order $24$, degree $8$, 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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	no (minimal twist has level 288)
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			37.15
Character	$\chi$	$=$	864.37
Dual form			864.2.bk.a.397.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.830777 - 1.14447i) q^{2} +(-0.619620 + 1.90160i) q^{4} +(1.83769 - 1.41011i) q^{5} +(0.454899 - 1.69771i) q^{7} +(2.69109 - 0.870667i) q^{8} +O(q^{10})$	\(q+(-0.830777 - 1.14447i) q^{2} +(-0.619620 + 1.90160i) q^{4} +(1.83769 - 1.41011i) q^{5} +(0.454899 - 1.69771i) q^{7} +(2.69109 - 0.870667i) q^{8} +(-3.14054 - 0.931695i) q^{10} +(4.25482 - 0.560157i) q^{11} +(-0.303048 + 2.30188i) q^{13} +(-2.32089 + 0.889796i) q^{14} +(-3.23214 - 2.35653i) q^{16} -1.85832i q^{17} +(2.22188 - 0.920333i) q^{19} +(1.54279 + 4.36828i) q^{20} +(-4.17588 - 4.40414i) q^{22} +(1.01925 + 3.80389i) q^{23} +(0.0946054 - 0.353072i) q^{25} +(2.88619 - 1.56552i) q^{26} +(2.94649 + 1.91697i) q^{28} +(3.06112 - 3.98933i) q^{29} +(-3.53119 + 6.11620i) q^{31} +(-0.0117927 + 5.65684i) q^{32} +(-2.12679 + 1.54385i) q^{34} +(-1.55799 - 3.76132i) q^{35} +(3.25157 + 1.34684i) q^{37} +(-2.89918 - 1.77828i) q^{38} +(3.71765 - 5.39475i) q^{40} +(-3.20240 - 11.9515i) q^{41} +(-2.39632 + 0.315482i) q^{43} +(-1.57118 + 8.43803i) q^{44} +(3.50667 - 4.32669i) q^{46} +(5.58096 - 3.22217i) q^{47} +(3.38691 + 1.95543i) q^{49} +(-0.482676 + 0.185051i) q^{50} +(-4.18947 - 2.00256i) q^{52} +(3.40394 - 8.21784i) q^{53} +(7.02916 - 7.02916i) q^{55} +(-0.253964 - 4.96473i) q^{56} +(-7.10878 - 0.189116i) q^{58} +(-11.8297 + 9.07722i) q^{59} +(8.00680 - 10.4347i) q^{61} +(9.93343 - 1.03986i) q^{62} +(6.48388 - 4.68608i) q^{64} +(2.68899 + 4.65747i) q^{65} +(-5.13255 - 0.675713i) q^{67} +(3.53377 + 1.15145i) q^{68} +(-3.01037 + 4.90789i) q^{70} +(-0.786895 - 0.786895i) q^{71} +(6.89191 - 6.89191i) q^{73} +(-1.15991 - 4.84024i) q^{74} +(0.373381 + 4.79538i) q^{76} +(0.984528 - 7.47824i) q^{77} +(-7.90822 + 4.56581i) q^{79} +(-9.26266 + 0.227094i) q^{80} +(-11.0177 + 13.5941i) q^{82} +(-2.78023 - 2.13335i) q^{83} +(-2.62043 - 3.41501i) q^{85} +(2.35187 + 2.48042i) q^{86} +(10.9624 - 5.21196i) q^{88} +(-3.68687 - 3.68687i) q^{89} +(3.77005 + 1.56161i) q^{91} +(-7.86502 - 0.418765i) q^{92} +(-8.32420 - 3.71033i) q^{94} +(2.78536 - 4.82439i) q^{95} +(-4.33284 - 7.50470i) q^{97} +(-0.575832 - 5.50074i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 16 q^{8}+O(q^{10}) $ 368 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 16 * q^8	$ 368 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 16 q^{8} - 16 q^{10} + 4 q^{11} - 4 q^{13} + 4 q^{14} - 4 q^{16} - 16 q^{19} + 4 q^{20} - 4 q^{22} + 4 q^{23} - 4 q^{25} + 16 q^{26} - 16 q^{28} + 4 q^{29} - 8 q^{31} + 4 q^{32} + 4 q^{34} + 16 q^{35} - 16 q^{37} + 60 q^{38} - 4 q^{40} + 4 q^{41} - 4 q^{43} + 104 q^{44} - 16 q^{46} - 48 q^{50} - 4 q^{52} + 16 q^{53} - 16 q^{55} + 84 q^{56} - 40 q^{58} + 4 q^{59} - 4 q^{61} + 24 q^{62} - 16 q^{64} + 8 q^{65} - 4 q^{67} - 12 q^{68} - 4 q^{70} + 16 q^{71} - 16 q^{73} + 4 q^{74} + 20 q^{76} + 4 q^{77} - 48 q^{80} - 16 q^{82} - 36 q^{83} + 16 q^{85} - 100 q^{86} - 4 q^{88} + 16 q^{89} - 16 q^{91} + 80 q^{92} - 20 q^{94} + 136 q^{95} - 8 q^{97} - 104 q^{98}+O(q^{100}) $ 368 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 16 * q^8 - 16 * q^10 + 4 * q^11 - 4 * q^13 + 4 * q^14 - 4 * q^16 - 16 * q^19 + 4 * q^20 - 4 * q^22 + 4 * q^23 - 4 * q^25 + 16 * q^26 - 16 * q^28 + 4 * q^29 - 8 * q^31 + 4 * q^32 + 4 * q^34 + 16 * q^35 - 16 * q^37 + 60 * q^38 - 4 * q^40 + 4 * q^41 - 4 * q^43 + 104 * q^44 - 16 * q^46 - 48 * q^50 - 4 * q^52 + 16 * q^53 - 16 * q^55 + 84 * q^56 - 40 * q^58 + 4 * q^59 - 4 * q^61 + 24 * q^62 - 16 * q^64 + 8 * q^65 - 4 * q^67 - 12 * q^68 - 4 * q^70 + 16 * q^71 - 16 * q^73 + 4 * q^74 + 20 * q^76 + 4 * q^77 - 48 * q^80 - 16 * q^82 - 36 * q^83 + 16 * q^85 - 100 * q^86 - 4 * q^88 + 16 * q^89 - 16 * q^91 + 80 * q^92 - 20 * q^94 + 136 * q^95 - 8 * q^97 - 104 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.830777	−	1.14447i	−0.587448	−	0.809262i
$2$	−0.830777	−	1.14447i	−0.587448	−	0.809262i
$3$		0			0
$3$		0			0
$4$	−0.619620	+	1.90160i	−0.309810	+	0.950799i
$5$	1.83769	−	1.41011i	0.821841	−	0.630621i	−0.109819	−	0.993952i	$-0.535027\pi$
$5$	1.83769	−	1.41011i	0.821841	−	0.630621i	0.931660	+	0.363331i	$0.118360\pi$
$6$		0			0
$7$	0.454899	−	1.69771i	0.171936	−	0.641672i	−0.825118	−	0.564961i	$-0.808891\pi$
$7$	0.454899	−	1.69771i	0.171936	−	0.641672i	0.997053	−	0.0767115i	$-0.0244420\pi$
$8$	2.69109	−	0.870667i	0.951442	−	0.307827i
$9$		0			0
$10$	−3.14054	−	0.931695i	−0.993126	−	0.294628i
$11$	4.25482	−	0.560157i	1.28288	−	0.168894i	0.541910	−	0.840437i	$-0.317702\pi$
$11$	4.25482	−	0.560157i	1.28288	−	0.168894i	0.740966	+	0.671543i	$0.234368\pi$
$12$		0			0
$13$	−0.303048	+	2.30188i	−0.0840503	+	0.638425i	0.896626	+	0.442788i	$0.146011\pi$
$13$	−0.303048	+	2.30188i	−0.0840503	+	0.638425i	−0.980676	+	0.195637i	$0.937323\pi$
$14$	−2.32089	+	0.889796i	−0.620284	+	0.237808i
$15$		0			0
$16$	−3.23214	−	2.35653i	−0.808036	−	0.589134i
$17$		−	1.85832i		−	0.450708i	−0.974277	−	0.225354i	$-0.927646\pi$
$17$		−	1.85832i		−	0.450708i	0.974277	−	0.225354i	$-0.0723539\pi$
$18$		0			0
$19$	2.22188	−	0.920333i	0.509734	−	0.211139i	−0.112967	−	0.993599i	$-0.536035\pi$
$19$	2.22188	−	0.920333i	0.509734	−	0.211139i	0.622701	+	0.782460i	$0.286035\pi$
$20$	1.54279	+	4.36828i	0.344979	+	0.976778i
$21$		0			0
$22$	−4.17588	−	4.40414i	−0.890302	−	0.938966i
$23$	1.01925	+	3.80389i	0.212528	+	0.793167i	0.987022	+	0.160585i	$0.0513381\pi$
$23$	1.01925	+	3.80389i	0.212528	+	0.793167i	−0.774494	+	0.632582i	$0.781995\pi$
$24$		0			0
$25$	0.0946054	−	0.353072i	0.0189211	−	0.0706145i
$26$	2.88619	−	1.56552i	0.566029	−	0.307023i
$27$		0			0
$28$	2.94649	+	1.91697i	0.556834	+	0.362272i
$29$	3.06112	−	3.98933i	0.568436	−	0.740800i	−0.417361	−	0.908741i	$-0.637045\pi$
$29$	3.06112	−	3.98933i	0.568436	−	0.740800i	0.985797	+	0.167940i	$0.0537116\pi$
$30$		0			0
$31$	−3.53119	+	6.11620i	−0.634220	+	1.09850i	0.352460	+	0.935827i	$0.385345\pi$
$31$	−3.53119	+	6.11620i	−0.634220	+	1.09850i	−0.986680	+	0.162674i	$0.947988\pi$
$32$	−0.0117927	+	5.65684i	−0.00208468	+	0.999998i
$33$		0			0
$34$	−2.12679	+	1.54385i	−0.364741	+	0.264767i
$35$	−1.55799	−	3.76132i	−0.263348	−	0.635779i
$36$		0			0
$37$	3.25157	+	1.34684i	0.534554	+	0.221420i	0.633597	−	0.773664i	$-0.281578\pi$
$37$	3.25157	+	1.34684i	0.534554	+	0.221420i	−0.0990423	+	0.995083i	$0.531578\pi$
$38$	−2.89918	−	1.77828i	−0.470309	−	0.288476i
$39$		0			0
$40$	3.71765	−	5.39475i	0.587812	−	0.852984i
$41$	−3.20240	−	11.9515i	−0.500131	−	1.86651i	−0.499154	−	0.866513i	$-0.666356\pi$
$41$	−3.20240	−	11.9515i	−0.500131	−	1.86651i	−0.000976646	−	1.00000i	$-0.500311\pi$
$42$		0			0
$43$	−2.39632	+	0.315482i	−0.365435	+	0.0481105i	−0.311008	−	0.950407i	$-0.600667\pi$
$43$	−2.39632	+	0.315482i	−0.365435	+	0.0481105i	−0.0544273	+	0.998518i	$0.517333\pi$
$44$	−1.57118	+	8.43803i	−0.236864	+	1.27208i
$45$		0			0
$46$	3.50667	−	4.32669i	0.517030	−	0.637935i
$47$	5.58096	−	3.22217i	0.814066	−	0.470001i	−0.0342998	−	0.999412i	$-0.510920\pi$
$47$	5.58096	−	3.22217i	0.814066	−	0.470001i	0.848366	+	0.529410i	$0.177587\pi$
$48$		0			0
$49$	3.38691	+	1.95543i	0.483844	+	0.279347i
$50$	−0.482676	+	0.185051i	−0.0682607	+	0.0261702i
$51$		0			0
$52$	−4.18947	−	2.00256i	−0.580974	−	0.277705i
$53$	3.40394	−	8.21784i	0.467567	−	1.12881i	−0.497655	−	0.867375i	$-0.665805\pi$
$53$	3.40394	−	8.21784i	0.467567	−	1.12881i	0.965222	−	0.261432i	$-0.0841948\pi$
$54$		0			0
$55$	7.02916	−	7.02916i	0.947812	−	0.947812i
$56$	−0.253964	−	4.96473i	−0.0339374	−	0.663441i
$57$		0			0
$58$	−7.10878	−	0.189116i	−0.933428	−	0.0248321i
$59$	−11.8297	+	9.07722i	−1.54009	+	1.18175i	−0.623569	+	0.781768i	$0.714318\pi$
$59$	−11.8297	+	9.07722i	−1.54009	+	1.18175i	−0.916522	+	0.399985i	$0.869015\pi$
$60$		0			0
$61$	8.00680	−	10.4347i	1.02517	−	1.33602i	0.0845990	−	0.996415i	$-0.473039\pi$
$61$	8.00680	−	10.4347i	1.02517	−	1.33602i	0.940567	−	0.339608i	$-0.110294\pi$
$62$	9.93343	−	1.03986i	1.26155	−	0.132062i
$63$		0			0
$64$	6.48388	−	4.68608i	0.810485	−	0.585760i
$65$	2.68899	+	4.65747i	0.333528	+	0.577688i
$66$		0			0
$67$	−5.13255	−	0.675713i	−0.627041	−	0.0825515i	−0.189692	−	0.981844i	$-0.560749\pi$
$67$	−5.13255	−	0.675713i	−0.627041	−	0.0825515i	−0.437348	+	0.899292i	$0.644082\pi$
$68$	3.53377	+	1.15145i	0.428533	+	0.139634i
$69$		0			0
$70$	−3.01037	+	4.90789i	−0.359808	+	0.586605i
$71$	−0.786895	−	0.786895i	−0.0933873	−	0.0933873i	0.658870	−	0.752257i	$-0.271035\pi$
$71$	−0.786895	−	0.786895i	−0.0933873	−	0.0933873i	−0.752257	+	0.658870i	$0.771035\pi$
$72$		0			0
$73$	6.89191	−	6.89191i	0.806637	−	0.806637i	−0.177486	−	0.984123i	$-0.556797\pi$
$73$	6.89191	−	6.89191i	0.806637	−	0.806637i	0.984123	+	0.177486i	$0.0567966\pi$
$74$	−1.15991	−	4.84024i	−0.134836	−	0.562667i
$75$		0			0
$76$	0.373381	+	4.79538i	0.0428298	+	0.550068i
$77$	0.984528	−	7.47824i	0.112197	−	0.852224i
$78$		0			0
$79$	−7.90822	+	4.56581i	−0.889745	+	0.513694i	−0.873859	−	0.486180i	$-0.838390\pi$
$79$	−7.90822	+	4.56581i	−0.889745	+	0.513694i	−0.0158857	+	0.999874i	$0.505057\pi$
$80$	−9.26266	+	0.227094i	−1.03560	+	0.0253898i
$81$		0			0
$82$	−11.0177	+	13.5941i	−1.21670	+	1.50122i
$83$	−2.78023	−	2.13335i	−0.305170	−	0.234165i	0.444811	−	0.895624i	$-0.353271\pi$
$83$	−2.78023	−	2.13335i	−0.305170	−	0.234165i	−0.749981	+	0.661459i	$0.769938\pi$
$84$		0			0
$85$	−2.62043	−	3.41501i	−0.284226	−	0.370410i
$86$	2.35187	+	2.48042i	0.253608	+	0.267471i
$87$		0			0
$88$	10.9624	−	5.21196i	1.16859	−	0.555596i
$89$	−3.68687	−	3.68687i	−0.390808	−	0.390808i	0.484168	−	0.874975i	$-0.339123\pi$
$89$	−3.68687	−	3.68687i	−0.390808	−	0.390808i	−0.874975	+	0.484168i	$0.839123\pi$
$90$		0			0
$91$	3.77005	+	1.56161i	0.395209	+	0.163701i
$92$	−7.86502	−	0.418765i	−0.819985	−	0.0436593i
$93$		0			0
$94$	−8.32420	−	3.71033i	−0.858576	−	0.382692i
$95$	2.78536	−	4.82439i	0.285772	−	0.494972i
$96$		0			0
$97$	−4.33284	−	7.50470i	−0.439933	−	0.761987i	0.557750	−	0.830009i	$-0.311665\pi$
$97$	−4.33284	−	7.50470i	−0.439933	−	0.761987i	−0.997684	+	0.0680218i	$0.978331\pi$
$98$	−0.575832	−	5.50074i	−0.0581679	−	0.555659i
$99$		0			0
$100$	0.612782	+	0.398672i	0.0612782	+	0.0398672i
$101$	1.11753	+	8.48846i	0.111198	+	0.844633i	0.952600	+	0.304224i	$0.0983972\pi$
$101$	1.11753	+	8.48846i	0.111198	+	0.844633i	−0.841402	+	0.540409i	$0.818269\pi$
$102$		0			0
$103$	5.15005	−	1.37995i	0.507449	−	0.135971i	0.00399421	−	0.999992i	$-0.498729\pi$
$103$	5.15005	−	1.37995i	0.507449	−	0.135971i	0.503455	+	0.864021i	$0.332062\pi$
$104$	1.18864	+	6.45840i	0.116556	+	0.633298i
$105$		0			0
$106$	−12.2330	+	2.93149i	−1.18817	+	0.284731i
$107$	2.80668	−	6.77594i	0.271332	−	0.655055i	−0.728208	−	0.685356i	$-0.759647\pi$
$107$	2.80668	−	6.77594i	0.271332	−	0.655055i	0.999541	+	0.0303013i	$0.00964668\pi$
$108$		0			0
$109$	−16.4296	+	6.80536i	−1.57367	+	0.651835i	−0.987395	−	0.158277i	$-0.949406\pi$
$109$	−16.4296	+	6.80536i	−1.57367	+	0.651835i	−0.586275	+	0.810112i	$0.699406\pi$
$110$	−13.8843	−	2.20499i	−1.32382	−	0.210238i
$111$		0			0
$112$	−5.47100	+	4.41524i	−0.516961	+	0.417201i
$113$	7.30520	+	4.21766i	0.687216	+	0.396764i	0.802568	−	0.596561i	$-0.203466\pi$
$113$	7.30520	+	4.21766i	0.687216	+	0.396764i	−0.115353	+	0.993325i	$0.536800\pi$
$114$		0			0
$115$	7.23698	+	5.55313i	0.674852	+	0.517832i
$116$	5.68937	+	8.29289i	0.528245	+	0.769975i
$117$		0			0
$118$	20.2164	+	5.99754i	1.86107	+	0.552119i
$119$	−3.15487	−	0.845346i	−0.289207	−	0.0774927i
$120$		0			0
$121$	7.16449	−	1.91972i	0.651318	−	0.174520i
$122$	−18.5940	−	0.494660i	−1.68342	−	0.0447844i
$123$		0			0
$124$	−9.44255	−	10.5046i	−0.847966	−	0.943342i
$125$	4.10815	+	9.91795i	0.367444	+	0.887088i
$126$		0			0
$127$	−6.45329			−0.572637			−0.286318	−	0.958135i	$-0.592431\pi$
$127$	−6.45329			−0.572637			−0.286318	+	0.958135i	$0.592431\pi$
$128$	−10.7497	−	3.52752i	−0.950151	−	0.311791i
$129$		0			0
$130$	3.09638	−	6.94679i	0.271570	−	0.609274i
$131$	−13.9681	−	1.83894i	−1.22040	−	0.160669i	−0.507324	−	0.861755i	$-0.669365\pi$
$131$	−13.9681	−	1.83894i	−1.22040	−	0.160669i	−0.713076	+	0.701087i	$0.752699\pi$
$132$		0			0
$133$	−0.551723	−	4.19076i	−0.0478405	−	0.363385i
$134$	3.49067	+	6.43541i	0.301548	+	0.555935i
$135$		0			0
$136$	−1.61797	−	5.00089i	−0.138740	−	0.428823i
$137$	−15.6302	−	4.18811i	−1.33538	−	0.357814i	−0.480662	−	0.876906i	$-0.659604\pi$
$137$	−15.6302	−	4.18811i	−1.33538	−	0.357814i	−0.854718	+	0.519092i	$0.826270\pi$
$138$		0			0
$139$	13.4223	+	17.4923i	1.13846	+	1.48367i	0.850456	+	0.526046i	$0.176326\pi$
$139$	13.4223	+	17.4923i	1.13846	+	1.48367i	0.288007	+	0.957628i	$0.407007\pi$
$140$	8.11787	−	0.632080i	0.686085	−	0.0534205i
$141$		0			0
$142$	−0.246843	+	1.55431i	−0.0207146	+	0.130435i
$143$			9.96381i			0.833216i
$144$		0			0
$145$		−	11.6477i		−	0.967288i
$146$	−13.6132	−	2.16194i	−1.12664	−	0.178923i
$147$		0			0
$148$	−4.57589	+	5.34864i	−0.376136	+	0.439655i
$149$	6.93266	+	9.03482i	0.567946	+	0.740161i	0.985721	−	0.168389i	$-0.0538566\pi$
$149$	6.93266	+	9.03482i	0.567946	+	0.740161i	−0.417775	+	0.908551i	$0.637190\pi$
$150$		0			0
$151$	14.1741	+	3.79793i	1.15347	+	0.309071i	0.784355	−	0.620313i	$-0.212994\pi$
$151$	14.1741	+	3.79793i	1.15347	+	0.309071i	0.369115	+	0.929384i	$0.379661\pi$
$152$	5.17797	−	4.41121i	0.419989	−	0.357797i
$153$		0			0
$154$	−9.37654	+	5.08598i	−0.755583	+	0.409840i
$155$	2.13528	+	16.2191i	0.171510	+	1.30275i
$156$		0			0
$157$	−1.68402	−	0.221706i	−0.134400	−	0.0176941i	0.0630262	−	0.998012i	$-0.479925\pi$
$157$	−1.68402	−	0.221706i	−0.134400	−	0.0176941i	−0.197426	+	0.980318i	$0.563258\pi$
$158$	11.7954	+	5.25755i	0.938392	+	0.418268i
$159$		0			0
$160$	7.95510	+	10.4122i	0.628906	+	0.823154i
$161$	6.92155			0.545494
$162$		0			0
$163$	−3.09378	−	7.46904i	−0.242323	−	0.585020i	0.755189	−	0.655507i	$-0.227545\pi$
$163$	−3.09378	−	7.46904i	−0.242323	−	0.585020i	−0.997513	+	0.0704864i	$0.977545\pi$
$164$	24.7112	+	1.31572i	1.92962	+	0.102741i
$165$		0			0
$166$	−0.131798	+	4.95423i	−0.0102295	+	0.384523i
$167$	20.5475	−	5.50569i	1.59001	−	0.426043i	0.648007	−	0.761634i	$-0.275603\pi$
$167$	20.5475	−	5.50569i	1.59001	−	0.426043i	0.942008	+	0.335591i	$0.108936\pi$
$168$		0			0
$169$	7.35024	+	1.96949i	0.565403	+	0.151499i
$170$	−1.73138	+	5.83612i	−0.132791	+	0.447610i
$171$		0			0
$172$	0.884889	−	4.75231i	0.0674721	−	0.362361i
$173$	4.37183	+	3.35462i	0.332384	+	0.255047i	0.761447	−	0.648227i	$-0.224489\pi$
$173$	4.37183	+	3.35462i	0.332384	+	0.255047i	−0.429063	+	0.903275i	$0.641156\pi$
$174$		0			0
$175$	−0.556377	−	0.321224i	−0.0420581	−	0.0242823i
$176$	−15.0722	−	8.21611i	−1.13611	−	0.619313i
$177$		0			0
$178$	−1.15654	+	7.28248i	−0.0866867	+	0.545845i
$179$	−20.4046	+	8.45184i	−1.52511	+	0.631721i	−0.978607	−	0.205738i	$-0.934041\pi$
$179$	−20.4046	+	8.45184i	−1.52511	+	0.631721i	−0.546501	+	0.837458i	$0.684041\pi$
$180$		0			0
$181$	−7.15352	+	17.2701i	−0.531717	+	1.28368i	0.398669	+	0.917095i	$0.369472\pi$
$181$	−7.15352	+	17.2701i	−0.531717	+	1.28368i	−0.930385	+	0.366583i	$0.880528\pi$
$182$	−1.34486	−	5.61205i	−0.0996877	−	0.415993i
$183$		0			0
$184$	6.05481	+	9.34918i	0.446367	+	0.689230i
$185$	7.87458	−	2.10999i	0.578951	−	0.155129i
$186$		0			0
$187$	−1.04095	−	7.90679i	−0.0761218	−	0.578202i
$188$	2.66919	+	12.6092i	0.194671	+	0.919624i
$189$		0			0
$190$	−7.83538	+	0.820228i	−0.568438	+	0.0595056i
$191$	7.49890	+	12.9885i	0.542601	+	0.939813i	0.998754	+	0.0499114i	$0.0158939\pi$
$191$	7.49890	+	12.9885i	0.542601	+	0.939813i	−0.456152	+	0.889902i	$0.650773\pi$
$192$		0			0
$193$	−0.624997	+	1.08253i	−0.0449883	+	0.0779220i	−0.887643	−	0.460533i	$-0.847658\pi$
$193$	−0.624997	+	1.08253i	−0.0449883	+	0.0779220i	0.842654	+	0.538455i	$0.180992\pi$
$194$	−4.98928	+	11.1935i	−0.358209	+	0.803649i
$195$		0			0
$196$	−5.81704	+	5.22891i	−0.415503	+	0.373494i
$197$	−0.313242	−	0.129749i	−0.0223176	−	0.00924423i	0.371497	−	0.928434i	$-0.378845\pi$
$197$	−0.313242	−	0.129749i	−0.0223176	−	0.00924423i	−0.393814	+	0.919190i	$0.628845\pi$
$198$		0			0
$199$	4.29098	+	4.29098i	0.304179	+	0.304179i	0.842646	−	0.538467i	$-0.180996\pi$
$199$	4.29098	+	4.29098i	0.304179	+	0.304179i	−0.538467	+	0.842646i	$0.680996\pi$
$200$	−0.0528170	−	1.03252i	−0.00373473	−	0.0730100i
$201$		0			0
$202$	8.78637	−	8.33099i	0.618207	−	0.586167i
$203$	−5.38021	−	7.01162i	−0.377617	−	0.492120i
$204$		0			0
$205$	−22.7380	−	17.4475i	−1.58809	−	1.21858i
$206$	−5.85785	−	4.74764i	−0.408136	−	0.330784i
$207$		0			0
$208$	6.40394	−	6.72585i	0.444034	−	0.466354i
$209$	8.93816	−	5.16045i	0.618265	−	0.356956i
$210$		0			0
$211$	−1.02001	+	7.74778i	−0.0702207	+	0.533379i	0.919793	+	0.392405i	$0.128357\pi$
$211$	−1.02001	+	7.74778i	−0.0702207	+	0.533379i	−0.990013	+	0.140974i	$0.954977\pi$
$212$	13.5179	+	11.5649i	0.928411	+	0.794278i
$213$		0			0
$214$	−10.0866	+	2.41713i	−0.689504	+	0.165231i
$215$	−3.95884	+	3.95884i	−0.269990	+	0.269990i
$216$		0			0
$217$	8.77716	+	8.77716i	0.595833	+	0.595833i
$218$	21.4378	+	13.1494i	1.45195	+	0.890592i
$219$		0			0
$220$	9.01122	+	17.7220i	0.607536	+	1.19482i
$221$	4.27761	+	0.563159i	0.287743	+	0.0378821i
$222$		0			0
$223$	8.01763	+	13.8869i	0.536900	+	0.929938i	0.999069	+	0.0431461i	$0.0137381\pi$
$223$	8.01763	+	13.8869i	0.536900	+	0.929938i	−0.462169	+	0.886792i	$0.652929\pi$
$224$	9.59828	+	2.59331i	0.641312	+	0.173273i
$225$		0			0
$226$	−1.24201	−	11.8645i	−0.0826172	−	0.789216i
$227$	14.3169	−	18.6581i	0.950243	−	1.23838i	−0.0208752	−	0.999782i	$-0.506645\pi$
$227$	14.3169	−	18.6581i	0.950243	−	1.23838i	0.971118	−	0.238599i	$-0.0766881\pi$
$228$		0			0
$229$	−5.90651	+	4.53223i	−0.390313	+	0.299498i	−0.785212	−	0.619227i	$-0.787446\pi$
$229$	−5.90651	+	4.53223i	−0.390313	+	0.299498i	0.394899	+	0.918725i	$0.370780\pi$
$230$	0.343072	−	12.8959i	0.0226215	−	0.850332i
$231$		0			0
$232$	4.76436	−	13.4008i	0.312796	−	0.879809i
$233$	−5.74620	+	5.74620i	−0.376446	+	0.376446i	−0.869818	−	0.493372i	$-0.835764\pi$
$233$	−5.74620	+	5.74620i	−0.376446	+	0.376446i	0.493372	+	0.869818i	$0.335764\pi$
$234$		0			0
$235$	5.71247	−	13.7911i	0.372640	−	0.899633i
$236$	−9.93132	−	28.1197i	−0.646474	−	1.83044i
$237$		0			0
$238$	1.65352	+	4.31295i	0.107182	+	0.279567i
$239$	−6.52718	−	3.76847i	−0.422208	−	0.243762i	0.273814	−	0.961783i	$-0.411715\pi$
$239$	−6.52718	−	3.76847i	−0.422208	−	0.243762i	−0.696021	+	0.718021i	$0.745048\pi$
$240$		0			0
$241$	13.4698	−	7.77681i	0.867668	−	0.500948i	0.00109546	−	0.999999i	$-0.499651\pi$
$241$	13.4698	−	7.77681i	0.867668	−	0.500948i	0.866573	+	0.499051i	$0.166318\pi$
$242$	−8.14916	−	6.60468i	−0.523848	−	0.424565i
$243$		0			0
$244$	14.8814	+	21.6912i	0.952682	+	1.38864i
$245$	8.98147	−	1.18243i	0.573805	−	0.0755429i
$246$		0			0
$247$	1.44516	+	5.39340i	0.0919531	+	0.343174i
$248$	−4.17756	+	19.5337i	−0.265275	+	1.24039i
$249$		0			0
$250$	7.93783	−	12.9413i	0.502033	−	0.818477i
$251$	−4.10085	−	1.69863i	−0.258843	−	0.107216i	0.249488	−	0.968378i	$-0.419738\pi$
$251$	−4.10085	−	1.69863i	−0.258843	−	0.107216i	−0.508332	+	0.861161i	$0.669738\pi$
$252$		0			0
$253$	6.46750	+	15.6139i	0.406608	+	0.981639i
$254$	5.36124	+	7.38559i	0.336394	+	0.463413i
$255$		0			0
$256$	4.89349	+	15.2333i	0.305843	+	0.952082i
$257$	10.8708	−	18.8289i	0.678105	−	1.17451i	−0.297446	−	0.954738i	$-0.596135\pi$
$257$	10.8708	−	18.8289i	0.678105	−	1.17451i	0.975551	−	0.219773i	$-0.0705317\pi$
$258$		0			0
$259$	3.76568	−	4.90752i	0.233988	−	0.304939i
$260$	−10.5228	+	2.22752i	−0.652595	+	0.138145i
$261$		0			0
$262$	9.49978	+	17.5138i	0.586898	+	1.08201i
$263$	−5.44235	+	20.3111i	−0.335590	+	1.25244i	0.567638	+	0.823278i	$0.307857\pi$
$263$	−5.44235	+	20.3111i	−0.335590	+	1.25244i	−0.903228	+	0.429160i	$0.858810\pi$
$264$		0			0
$265$	−5.33267	−	19.9018i	−0.327583	−	1.22256i
$266$	−4.33783	+	4.11301i	−0.265970	+	0.252185i
$267$		0			0
$268$	4.46516	−	9.34135i	0.272753	−	0.570614i
$269$	−25.8978	+	10.7272i	−1.57902	+	0.654051i	−0.988258	−	0.152796i	$-0.951172\pi$
$269$	−25.8978	+	10.7272i	−1.57902	+	0.654051i	−0.590761	+	0.806847i	$0.701172\pi$
$270$		0			0
$271$			23.6586i			1.43716i	0.695446	+	0.718578i	$0.255207\pi$
$271$			23.6586i			1.43716i	−0.695446	+	0.718578i	$0.744793\pi$
$272$	−4.37919	+	6.00634i	−0.265527	+	0.364188i
$273$		0			0
$274$	8.19207	+	21.3677i	0.494901	+	1.29087i
$275$	0.204753	−	1.55525i	0.0123471	−	0.0937852i
$276$		0			0
$277$	−4.03808	+	0.531624i	−0.242625	+	0.0319422i	−0.250858	−	0.968024i	$-0.580713\pi$
$277$	−4.03808	+	0.531624i	−0.242625	+	0.0319422i	0.00823300	+	0.999966i	$0.497379\pi$
$278$	8.86843	−	29.8936i	0.531893	−	1.79290i
$279$		0			0
$280$	−7.46753	−	8.76554i	−0.446271	−	0.523841i
$281$	−3.88392	+	14.4950i	−0.231695	+	0.864699i	0.747915	+	0.663794i	$0.231055\pi$
$281$	−3.88392	+	14.4950i	−0.231695	+	0.864699i	−0.979611	+	0.200905i	$0.935612\pi$
$282$		0			0
$283$	−6.90282	+	5.29672i	−0.410330	+	0.314857i	−0.793218	−	0.608937i	$-0.791596\pi$
$283$	−6.90282	+	5.29672i	−0.410330	+	0.314857i	0.382888	+	0.923795i	$0.374929\pi$
$284$	1.98393	−	1.00878i	0.117725	−	0.0598602i
$285$		0			0
$286$	11.4033	−	8.27770i	0.674290	−	0.489471i
$287$	−21.7469			−1.28368
$288$		0			0
$289$	13.5467			0.796862
$290$	−13.3304	+	9.67663i	−0.782789	+	0.568231i
$291$		0			0
$292$	8.83527	+	17.3760i	0.517045	+	1.01685i
$293$	−7.03681	+	5.39954i	−0.411095	+	0.315444i	−0.793522	−	0.608541i	$-0.791755\pi$
$293$	−7.03681	+	5.39954i	−0.411095	+	0.315444i	0.382427	+	0.923986i	$0.375088\pi$
$294$		0			0
$295$	−8.93940	+	33.3623i	−0.520472	+	1.94243i
$296$	9.92289	+	0.793439i	0.576757	+	0.0461177i
$297$		0			0
$298$	4.58058	−	15.4401i	0.265346	−	0.894423i
$299$	−9.06497	+	1.19343i	−0.524241	+	0.0690176i
$300$		0			0
$301$	−0.554488	+	4.21176i	−0.0319602	+	0.242762i
$302$	−7.42887	−	19.3770i	−0.427483	−	1.11502i
$303$		0			0
$304$	−9.35023	−	2.26129i	−0.536272	−	0.129694i
$305$		−	30.4662i		−	1.74449i
$306$		0			0
$307$	−21.6584	+	8.97121i	−1.23611	+	0.512014i	−0.902497	−	0.430696i	$-0.858268\pi$
$307$	−21.6584	+	8.97121i	−1.23611	+	0.512014i	−0.333614	+	0.942710i	$0.608268\pi$
$308$	13.6106	+	6.50584i	0.775534	+	0.370705i
$309$		0			0
$310$	16.7883	−	15.9182i	0.953510	−	0.904092i
$311$	2.12062	+	7.91425i	0.120249	+	0.448776i	0.999626	−	0.0273506i	$-0.00870704\pi$
$311$	2.12062	+	7.91425i	0.120249	+	0.448776i	−0.879377	+	0.476127i	$0.842040\pi$
$312$		0			0
$313$	−3.00966	+	11.2322i	−0.170116	+	0.634882i	0.827216	+	0.561884i	$0.189923\pi$
$313$	−3.00966	+	11.2322i	−0.170116	+	0.634882i	−0.997332	+	0.0729977i	$0.976743\pi$
$314$	1.14531	+	2.11150i	0.0646337	+	0.119159i
$315$		0			0
$316$	−3.78225	−	17.8673i	−0.212768	−	1.00512i
$317$	2.53499	−	3.30366i	0.142379	−	0.185552i	−0.716720	−	0.697361i	$-0.754358\pi$
$317$	2.53499	−	3.30366i	0.142379	−	0.185552i	0.859100	+	0.511808i	$0.171024\pi$
$318$		0			0
$319$	10.7899	−	18.6886i	0.604116	−	1.04636i
$320$	5.30749	−	17.7546i	0.296698	−	0.992510i
$321$		0			0
$322$	−5.75026	−	7.92150i	−0.320449	−	0.441448i
$323$	−1.71027	−	4.12896i	−0.0951620	−	0.229741i
$324$		0			0
$325$	0.784059	+	0.324768i	0.0434917	+	0.0180149i
$326$	−5.97785	+	9.74584i	−0.331082	+	0.539772i
$327$		0			0
$328$	−19.0237	−	29.3743i	−1.05041	−	1.62193i
$329$	−2.93152	−	10.9406i	−0.161620	−	0.603174i
$330$		0			0
$331$	−18.8304	+	2.47907i	−1.03501	+	0.136262i	−0.628840	−	0.777534i	$-0.716470\pi$
$331$	−18.8304	+	2.47907i	−1.03501	+	0.136262i	−0.406173	+	0.913796i	$0.633137\pi$
$332$	5.77946	−	3.96502i	0.317189	−	0.217609i
$333$		0			0
$334$	−23.3715	−	18.9420i	−1.27883	−	1.03646i
$335$	−10.3849	+	5.99571i	−0.567386	+	0.327581i
$336$		0			0
$337$	−25.9301	−	14.9707i	−1.41250	−	0.815508i	−0.416878	−	0.908963i	$-0.636876\pi$
$337$	−25.9301	−	14.9707i	−1.41250	−	0.815508i	−0.995624	+	0.0934545i	$0.970209\pi$
$338$	−3.85239	−	10.0483i	−0.209542	−	0.546557i
$339$		0			0
$340$	8.11765	−	2.86700i	0.440242	−	0.155485i
$341$	−11.5985	+	28.0013i	−0.628095	+	1.51636i
$342$		0			0
$343$	13.5601	−	13.5601i	0.732176	−	0.732176i
$344$	−6.17402	+	2.93538i	−0.332881	+	0.158265i
$345$		0			0
$346$	0.207248	−	7.79037i	0.0111417	−	0.418813i
$347$	−6.79457	+	5.21366i	−0.364752	+	0.279884i	−0.774834	−	0.632165i	$-0.782167\pi$
$347$	−6.79457	+	5.21366i	−0.364752	+	0.279884i	0.410082	+	0.912048i	$0.365500\pi$
$348$		0			0
$349$	5.31013	−	6.92030i	0.284245	−	0.370435i	−0.629308	−	0.777156i	$-0.716661\pi$
$349$	5.31013	−	6.92030i	0.284245	−	0.370435i	0.913552	+	0.406721i	$0.133328\pi$
$350$	0.0945936	+	0.903622i	0.00505624	+	0.0483006i
$351$		0			0
$352$	3.11854	+	24.0754i	0.166219	+	1.28322i
$353$	−0.687258	−	1.19037i	−0.0365790	−	0.0633567i	0.847156	−	0.531344i	$-0.178313\pi$
$353$	−0.687258	−	1.19037i	−0.0365790	−	0.0633567i	−0.883735	+	0.467987i	$0.844979\pi$
$354$		0			0
$355$	−2.55568	−	0.336462i	−0.135641	−	0.0178575i
$356$	9.29541	−	4.72649i	0.492656	−	0.250503i
$357$		0			0
$358$	26.6245	+	16.3308i	1.40715	+	0.863109i
$359$	−5.66910	−	5.66910i	−0.299204	−	0.299204i	0.541498	−	0.840702i	$-0.317857\pi$
$359$	−5.66910	−	5.66910i	−0.299204	−	0.299204i	−0.840702	+	0.541498i	$0.817857\pi$
$360$		0			0
$361$	−9.34529	+	9.34529i	−0.491857	+	0.491857i
$362$	25.7081	−	6.16063i	1.35119	−	0.323796i
$363$		0			0
$364$	−5.30554	+	6.20151i	−0.278086	+	0.325048i
$365$	2.94685	−	22.3836i	0.154245	−	1.17161i
$366$		0			0
$367$	−30.7867	+	17.7747i	−1.60705	+	0.927832i	−0.617027	+	0.786942i	$0.711663\pi$
$367$	−30.7867	+	17.7747i	−1.60705	+	0.927832i	−0.990025	+	0.140890i	$0.955004\pi$
$368$	5.66965	−	14.6966i	0.295551	−	0.766115i
$369$		0			0
$370$	−8.95683	−	7.25929i	−0.465644	−	0.377392i
$371$	−12.4030	−	9.51717i	−0.643933	−	0.494107i
$372$		0			0
$373$	−14.1600	−	18.4537i	−0.733178	−	0.955496i	0.266788	−	0.963755i	$-0.414038\pi$
$373$	−14.1600	−	18.4537i	−0.733178	−	0.955496i	−0.999966	+	0.00825904i	$0.997371\pi$
$374$	−8.18429	+	7.76012i	−0.423199	+	0.401266i
$375$		0			0
$376$	12.2134	−	13.5303i	0.629858	−	0.697771i
$377$	8.25528	+	8.25528i	0.425169	+	0.425169i
$378$		0			0
$379$	−5.76133	−	2.38642i	−0.295939	−	0.122582i	0.229774	−	0.973244i	$-0.426201\pi$
$379$	−5.76133	−	2.38642i	−0.295939	−	0.122582i	−0.525713	+	0.850662i	$0.676201\pi$
$380$	7.44818	+	8.28592i	0.382083	+	0.425059i
$381$		0			0
$382$	8.63500	−	19.3728i	0.441805	−	0.991198i
$383$	14.3541	−	24.8620i	0.733458	−	1.27039i	−0.221938	−	0.975061i	$-0.571238\pi$
$383$	14.3541	−	24.8620i	0.733458	−	1.27039i	0.955396	−	0.295326i	$-0.0954283\pi$
$384$		0			0
$385$	−8.73588	−	15.1310i	−0.445222	−	0.771147i
$386$	1.75815	−	0.184048i	0.0894876	−	0.00936780i
$387$		0			0
$388$	16.9556	−	3.58926i	0.860792	−	0.182217i
$389$	0.287817	+	2.18619i	0.0145929	+	0.110844i	0.997191	−	0.0749000i	$-0.0238638\pi$
$389$	0.287817	+	2.18619i	0.0145929	+	0.110844i	−0.982598	+	0.185744i	$0.940530\pi$
$390$		0			0
$391$	7.06884	−	1.89409i	0.357487	−	0.0957882i
$392$	10.8170	+	2.31337i	0.546340	+	0.116843i
$393$		0			0
$394$	0.111740	+	0.466288i	0.00562939	+	0.0234913i
$395$	−8.09458	+	19.5420i	−0.407282	+	0.983267i
$396$		0			0
$397$	6.18835	−	2.56330i	0.310584	−	0.128648i	−0.221947	−	0.975059i	$-0.571241\pi$
$397$	6.18835	−	2.56330i	0.310584	−	0.128648i	0.532531	+	0.846411i	$0.321241\pi$
$398$	1.34605	−	8.47573i	0.0674712	−	0.424850i
$399$		0			0
$400$	−1.13781	+	0.918239i	−0.0568903	+	0.0459119i
$401$	2.39063	+	1.38023i	0.119382	+	0.0689254i	0.558502	−	0.829503i	$-0.311376\pi$
$401$	2.39063	+	1.38023i	0.119382	+	0.0689254i	−0.439120	+	0.898429i	$0.644710\pi$
$402$		0			0
$403$	−13.0086	−	9.98185i	−0.648005	−	0.497231i
$404$	−16.8341	−	3.13453i	−0.837526	−	0.155949i
$405$		0			0
$406$	−3.55484	+	11.9826i	−0.176424	+	0.594685i
$407$	14.5893	+	3.90918i	0.723163	+	0.193771i
$408$		0			0
$409$	−12.1909	+	3.26654i	−0.602801	+	0.161520i	−0.547297	−	0.836938i	$-0.684343\pi$
$409$	−12.1909	+	3.26654i	−0.602801	+	0.161520i	−0.0555039	+	0.998458i	$0.517677\pi$
$410$	−1.07790	+	40.5179i	−0.0532338	+	2.00104i
$411$		0			0
$412$	−0.566961	+	10.6484i	−0.0279322	+	0.524607i
$413$	10.0291	+	24.2125i	0.493502	+	1.19142i
$414$		0			0
$415$	−8.11747			−0.398471
$416$	−13.0178	−	1.74144i	−0.638249	−	0.0853810i
$417$		0			0
$418$	−13.3316	−	5.94227i	−0.652069	−	0.290646i
$419$	1.70659	+	0.224677i	0.0833725	+	0.0109762i	0.172097	−	0.985080i	$-0.444946\pi$
$419$	1.70659	+	0.224677i	0.0833725	+	0.0109762i	−0.0887245	+	0.996056i	$0.528279\pi$
$420$		0			0
$421$	4.47164	+	33.9655i	0.217934	+	1.65537i	0.654766	+	0.755832i	$0.272767\pi$
$421$	4.47164	+	33.9655i	0.217934	+	1.65537i	−0.436832	+	0.899543i	$0.643899\pi$
$422$	9.71450	−	5.26930i	0.472895	−	0.256506i
$423$		0			0
$424$	2.00530	−	25.0786i	0.0973858	−	1.21793i
$425$	−0.656120	−	0.175807i	−0.0318265	−	0.00852789i
$426$		0			0
$427$	−14.0727	−	18.3399i	−0.681026	−	0.887530i
$428$	11.1460	+	9.53569i	0.538763	+	0.460925i
$429$		0			0
$430$	7.81967	+	1.24186i	0.377098	+	0.0598877i
$431$		−	6.06871i		−	0.292319i	−0.989261	−	0.146160i	$-0.953309\pi$
$431$		−	6.06871i		−	0.292319i	0.989261	−	0.146160i	$-0.0466913\pi$
$432$		0			0
$433$		−	22.3463i		−	1.07390i	−0.843615	−	0.536948i	$-0.819577\pi$
$433$		−	22.3463i		−	1.07390i	0.843615	−	0.536948i	$-0.180423\pi$
$434$	2.75333	−	17.3371i	0.132164	−	0.832205i
$435$		0			0
$436$	−2.76095	−	35.4592i	−0.132226	−	1.69819i
$437$	5.76550	+	7.51375i	0.275801	+	0.359431i
$438$		0			0
$439$	3.99922	+	1.07159i	0.190872	+	0.0511440i	0.352989	−	0.935628i	$-0.385165\pi$
$439$	3.99922	+	1.07159i	0.190872	+	0.0511440i	−0.162117	+	0.986772i	$0.551832\pi$
$440$	12.7960	−	25.0361i	0.610026	−	1.19355i
$441$		0			0
$442$	−2.90922	−	5.36346i	−0.138378	−	0.255114i
$443$	2.96177	+	22.4968i	0.140718	+	1.06886i	0.905433	+	0.424489i	$0.139546\pi$
$443$	2.96177	+	22.4968i	0.140718	+	1.06886i	−0.764715	+	0.644368i	$0.777120\pi$
$444$		0			0
$445$	−11.9742	−	1.57644i	−0.567633	−	0.0747304i
$446$	9.23231	−	20.7129i	0.437163	−	0.980783i
$447$		0			0
$448$	−5.00607	−	13.1394i	−0.236514	−	0.620779i
$449$	30.9160			1.45901			0.729507	−	0.683973i	$-0.239749\pi$
$449$	30.9160			1.45901			0.729507	+	0.683973i	$0.239749\pi$
$450$		0			0
$451$	−20.3203	−	49.0576i	−0.956847	−	2.31003i
$452$	−12.5467	+	11.2782i	−0.590149	+	0.530482i
$453$		0			0
$454$	−33.2477	−	0.884494i	−1.56039	−	0.0415114i
$455$	9.13023	−	2.44644i	0.428032	−	0.114691i
$456$		0			0
$457$	14.5332	+	3.89417i	0.679836	+	0.182161i	0.582181	−	0.813059i	$-0.302199\pi$
$457$	14.5332	+	3.89417i	0.679836	+	0.182161i	0.0976544	+	0.995220i	$0.468866\pi$
$458$	10.0940	+	2.99455i	0.471661	+	0.139926i
$459$		0			0
$460$	−15.0440	+	10.3210i	−0.701430	+	0.481219i
$461$	−4.99081	−	3.82958i	−0.232445	−	0.178361i	0.485971	−	0.873975i	$-0.338466\pi$
$461$	−4.99081	−	3.82958i	−0.232445	−	0.178361i	−0.718416	+	0.695614i	$0.755133\pi$
$462$		0			0
$463$	34.3974	+	19.8593i	1.59858	+	0.922941i	0.991761	+	0.128101i	$0.0408882\pi$
$463$	34.3974	+	19.8593i	1.59858	+	0.922941i	0.606819	+	0.794840i	$0.292445\pi$
$464$	−19.2950	+	5.68045i	−0.895747	+	0.263708i
$465$		0			0
$466$	11.3502	+	1.80254i	0.525786	+	0.0835011i
$467$	25.1605	−	10.4218i	1.16429	−	0.482265i	0.284989	−	0.958531i	$-0.408010\pi$
$467$	25.1605	−	10.4218i	1.16429	−	0.482265i	0.879301	+	0.476266i	$0.158010\pi$
$468$		0			0
$469$	−3.48195	+	8.40617i	−0.160782	+	0.388161i
$470$	−20.5293	+	4.91960i	−0.946946	+	0.226924i
$471$		0			0
$472$	−23.9314	+	34.7273i	−1.10153	+	1.59845i
$473$	−10.0192	+	2.68463i	−0.460682	+	0.123439i
$474$		0			0
$475$	−0.114742	−	0.871553i	−0.00526473	−	0.0399896i
$476$	3.56233	−	5.47551i	0.163279	−	0.250969i
$477$		0			0
$478$	1.10973	+	10.6009i	0.0507579	+	0.484874i
$479$	−5.20509	−	9.01548i	−0.237827	−	0.411928i	0.722264	−	0.691618i	$-0.243102\pi$
$479$	−5.20509	−	9.01548i	−0.237827	−	0.411928i	−0.960090	+	0.279690i	$0.909768\pi$
$480$		0			0
$481$	−4.08564	+	7.07654i	−0.186289	+	0.322663i
$482$	−20.0907	−	8.95501i	−0.915108	−	0.407890i
$483$		0			0
$484$	−0.788728	+	14.8135i	−0.0358513	+	0.673340i
$485$	−18.5449	−	7.68155i	−0.842080	−	0.348801i
$486$		0			0
$487$	−2.62552	−	2.62552i	−0.118974	−	0.118974i	0.645113	−	0.764087i	$-0.276810\pi$
$487$	−2.62552	−	2.62552i	−0.118974	−	0.118974i	−0.764087	+	0.645113i	$0.776810\pi$
$488$	12.4619	−	35.0518i	0.564122	−	1.58672i
$489$		0			0
$490$	−8.81486	−	9.29668i	−0.398215	−	0.419981i
$491$	10.7896	+	14.0613i	0.486928	+	0.634577i	0.970607	−	0.240668i	$-0.0773666\pi$
$491$	10.7896	+	14.0613i	0.486928	+	0.634577i	−0.483680	+	0.875245i	$0.660700\pi$
$492$		0			0
$493$	−7.41344	−	5.68853i	−0.333885	−	0.256199i
$494$	4.97197	−	6.13465i	0.223700	−	0.276011i
$495$		0			0
$496$	25.8263	−	11.4470i	1.15964	−	0.513988i
$497$	−1.69387	+	0.977958i	−0.0759806	+	0.0438674i
$498$		0			0
$499$	2.87974	−	21.8738i	0.128915	−	0.979206i	−0.797663	−	0.603103i	$-0.793931\pi$
$499$	2.87974	−	21.8738i	0.128915	−	0.979206i	0.926578	−	0.376102i	$-0.122736\pi$
$500$	−21.4054	+	1.66669i	−0.957280	+	0.0745364i
$501$		0			0
$502$	1.46286	+	6.10447i	0.0652908	+	0.272456i
$503$	11.3945	−	11.3945i	0.508054	−	0.508054i	−0.405875	−	0.913929i	$-0.633033\pi$
$503$	11.3945	−	11.3945i	0.508054	−	0.508054i	0.913929	+	0.405875i	$0.133033\pi$
$504$		0			0
$505$	14.0233	+	14.0233i	0.624031	+	0.624031i
$506$	12.4966	−	20.3735i	0.555542	−	0.905714i
$507$		0			0
$508$	3.99859	−	12.2716i	0.177409	−	0.544462i
$509$	−35.6378	−	4.69180i	−1.57962	−	0.207960i	−0.710908	−	0.703285i	$-0.751716\pi$
$509$	−35.6378	−	4.69180i	−1.57962	−	0.207960i	−0.868708	+	0.495325i	$0.835049\pi$
$510$		0			0
$511$	−8.56531	−	14.8355i	−0.378907	−	0.656286i
$512$	13.3687	−	18.2559i	0.590817	−	0.806806i
$513$		0			0
$514$	−30.5803	+	3.20123i	−1.34884	+	0.141200i
$515$	7.51832	−	9.79807i	0.331297	−	0.431754i
$516$		0			0
$517$	21.9410	−	16.8359i	0.964965	−	0.740444i
$518$	−8.74495	−	0.232643i	−0.384231	−	0.0102218i
$519$		0			0
$520$	11.2914	+	10.1924i	0.495161	+	0.446968i
$521$	8.86700	−	8.86700i	0.388470	−	0.388470i	−0.485671	−	0.874142i	$-0.661425\pi$
$521$	8.86700	−	8.86700i	0.388470	−	0.388470i	0.874142	+	0.485671i	$0.161425\pi$
$522$		0			0
$523$	6.58354	−	15.8941i	0.287878	−	0.695000i	−0.712097	−	0.702081i	$-0.752254\pi$
$523$	6.58354	−	15.8941i	0.287878	−	0.695000i	0.999975	+	0.00708176i	$0.00225421\pi$
$524$	12.1518	−	25.4223i	0.530856	−	1.11058i
$525$		0			0
$526$	27.7669	−	10.6454i	1.21069	−	0.464162i
$527$	11.3658	+	6.56206i	0.495103	+	0.285848i
$528$		0			0
$529$	6.48785	−	3.74576i	0.282080	−	0.162859i
$530$	−18.3467	+	22.6370i	−0.796932	+	0.983290i
$531$		0			0
$532$	8.31099	+	1.54752i	0.360327	+	0.0670935i
$533$	28.4814	−	3.74964i	1.23367	−	0.162415i
$534$		0			0
$535$	−4.39700	−	16.4098i	−0.190099	−	0.709459i
$536$	−14.4004	+	2.65034i	−0.622005	+	0.114477i
$537$		0			0
$538$	33.7923	+	20.7273i	1.45689	+	0.893619i
$539$	15.5060	+	6.42280i	0.667891	+	0.276650i
$540$		0			0
$541$	−7.03001	−	16.9719i	−0.302244	−	0.729681i	−0.999912	−	0.0132601i	$-0.995779\pi$
$541$	−7.03001	−	16.9719i	−0.302244	−	0.729681i	0.697668	−	0.716421i	$-0.254221\pi$
$542$	27.0765	−	19.6550i	1.16304	−	0.844254i
$543$		0			0
$544$	10.5122	+	0.0219146i	0.450707	+	0.000939581i
$545$	−20.5962	+	35.6737i	−0.882245	+	1.52809i
$546$		0			0
$547$	−0.688805	+	0.897668i	−0.0294512	+	0.0383815i	−0.807847	−	0.589393i	$-0.799367\pi$
$547$	−0.688805	+	0.897668i	−0.0294512	+	0.0383815i	0.778396	+	0.627774i	$0.216034\pi$
$548$	17.6489	−	27.1274i	0.753923	−	1.15882i
$549$		0			0
$550$	−1.95004	+	1.05773i	−0.0831500	+	0.0451019i
$551$	3.12993	−	11.6811i	0.133340	−	0.497630i
$552$		0			0
$553$	4.15397	+	15.5028i	0.176645	+	0.659247i
$554$	3.96317	+	4.17980i	0.168379	+	0.177583i
$555$		0			0
$556$	−41.5799	+	14.6852i	−1.76338	+	0.622792i
$557$	−22.7424	+	9.42021i	−0.963626	+	0.399147i	−0.808336	−	0.588722i	$-0.799631\pi$
$557$	−22.7424	+	9.42021i	−0.963626	+	0.399147i	−0.155290	+	0.987869i	$0.549631\pi$
$558$		0			0
$559$		−	5.61164i		−	0.237347i
$560$	−3.82803	+	15.8286i	−0.161764	+	0.668879i
$561$		0			0
$562$	19.8157	−	7.59707i	0.835877	−	0.320463i
$563$	−1.37291	+	10.4283i	−0.0578615	+	0.439501i	0.937854	+	0.347030i	$0.112810\pi$
$563$	−1.37291	+	10.4283i	−0.0578615	+	0.439501i	−0.995715	+	0.0924711i	$0.970523\pi$
$564$		0			0
$565$	19.3721	−	2.55038i	0.814990	−	0.107295i
$566$	11.7966	+	3.49967i	0.495850	+	0.147102i
$567$		0			0
$568$	−2.80273	−	1.43248i	−0.117600	−	0.0601055i
$569$	−6.74726	+	25.1811i	−0.282860	+	1.05565i	0.667529	+	0.744584i	$0.267352\pi$
$569$	−6.74726	+	25.1811i	−0.282860	+	1.05565i	−0.950389	+	0.311064i	$0.899315\pi$
$570$		0			0
$571$	−1.21106	+	0.929276i	−0.0506811	+	0.0388890i	−0.633791	−	0.773504i	$-0.718502\pi$
$571$	−1.21106	+	0.929276i	−0.0506811	+	0.0388890i	0.583110	+	0.812393i	$0.301836\pi$
$572$	−18.9472	−	6.17377i	−0.792220	−	0.258138i
$573$		0			0
$574$	18.0668	+	24.8887i	0.754095	+	1.03883i
$575$	1.43948			0.0600303
$576$		0			0
$577$	−7.93730			−0.330434			−0.165217	−	0.986257i	$-0.552832\pi$
$577$	−7.93730			−0.330434			−0.165217	+	0.986257i	$0.552832\pi$
$578$	−11.2542	−	15.5037i	−0.468115	−	0.644870i
$579$		0			0
$580$	22.1492	+	7.21714i	0.919696	+	0.299675i
$581$	−4.88652	+	3.74956i	−0.202727	+	0.155558i
$582$		0			0
$583$	9.87986	−	36.8721i	0.409182	−	1.52709i
$584$	12.5462	−	24.5473i	0.519164	−	1.01577i
$585$		0			0
$586$	12.0256	+	3.56761i	0.496774	+	0.147377i
$587$	−35.8443	+	4.71899i	−1.47945	+	0.194774i	−0.826633	−	0.562741i	$-0.809747\pi$
$587$	−35.8443	+	4.71899i	−1.47945	+	0.194774i	−0.652819	+	0.757514i	$0.726414\pi$
$588$		0			0
$589$	−2.21694	+	16.8393i	−0.0913474	+	0.693852i
$590$	45.6087	−	17.4857i	1.87768	−	0.719877i
$591$		0			0
$592$	−7.33564	−	12.0156i	−0.301493	−	0.493839i
$593$		−	3.46481i		−	0.142283i	−0.997466	−	0.0711414i	$-0.977336\pi$
$593$		−	3.46481i		−	0.142283i	0.997466	−	0.0711414i	$-0.0226641\pi$
$594$		0			0
$595$	−6.98972	+	2.89524i	−0.286551	+	0.118693i
$596$	−21.4762	+	7.58497i	−0.879699	+	0.310693i
$597$		0			0
$598$	8.89681	+	9.38311i	0.363818	+	0.383704i
$599$	3.63671	+	13.5724i	0.148592	+	0.554552i	0.999569	+	0.0293500i	$0.00934372\pi$
$599$	3.63671	+	13.5724i	0.148592	+	0.554552i	−0.850977	+	0.525202i	$0.823990\pi$
$600$		0			0
$601$	4.39361	−	16.3972i	0.179219	−	0.668854i	−0.816576	−	0.577239i	$-0.804130\pi$
$601$	4.39361	−	16.3972i	0.179219	−	0.668854i	0.995794	−	0.0916156i	$-0.0292031\pi$
$602$	5.28088	−	2.86443i	0.215233	−	0.116746i
$603$		0			0
$604$	−16.0047	+	24.6001i	−0.651221	+	1.00096i
$605$	10.4591	−	13.6306i	0.425224	−	0.554162i
$606$		0			0
$607$	11.5502	−	20.0056i	0.468809	−	0.812001i	−0.530555	−	0.847650i	$-0.678017\pi$
$607$	11.5502	−	20.0056i	0.468809	−	0.812001i	0.999364	+	0.0356492i	$0.0113499\pi$
$608$	5.17998	+	12.5797i	0.210076	+	0.510173i
$609$		0			0
$610$	−34.8676	+	25.3106i	−1.41175	+	1.02480i
$611$	5.72573	+	13.8231i	0.231638	+	0.559224i
$612$		0			0
$613$	31.7359	+	13.1454i	1.28180	+	0.530940i	0.916532	−	0.399962i	$-0.130977\pi$
$613$	31.7359	+	13.1454i	1.28180	+	0.530940i	0.365270	+	0.930902i	$0.380977\pi$
$614$	28.2606	+	17.3343i	1.14050	+	0.699556i
$615$		0			0
$616$	−3.86160	−	20.9818i	−0.155588	−	0.845379i
$617$	−2.69022	−	10.0400i	−0.108304	−	0.404196i	0.890395	−	0.455189i	$-0.150428\pi$
$617$	−2.69022	−	10.0400i	−0.108304	−	0.404196i	−0.998699	+	0.0509925i	$0.983762\pi$
$618$		0			0
$619$	−14.1656	+	1.86494i	−0.569364	+	0.0749582i	−0.409712	−	0.912215i	$-0.634371\pi$
$619$	−14.1656	+	1.86494i	−0.569364	+	0.0749582i	−0.159653	+	0.987173i	$0.551037\pi$
$620$	−32.1652	−	5.98921i	−1.29178	−	0.240532i
$621$		0			0
$622$	7.29586	−	9.00196i	0.292537	−	0.360946i
$623$	−7.93638	+	4.58207i	−0.317964	+	0.183577i
$624$		0			0
$625$	23.1177	+	13.3470i	0.924708	+	0.533881i
$626$	15.3553	−	5.88699i	0.613720	−	0.235291i
$627$		0			0
$628$	1.46505	−	3.06496i	0.0584618	−	0.122305i
$629$	2.50286	−	6.04244i	0.0997956	−	0.240928i
$630$		0			0
$631$	−13.2206	+	13.2206i	−0.526306	+	0.526306i	−0.919469	−	0.393163i	$-0.871381\pi$
$631$	−13.2206	+	13.2206i	−0.526306	+	0.526306i	0.393163	+	0.919469i	$0.371381\pi$
$632$	−17.3064	+	19.1724i	−0.688412	+	0.762638i
$633$		0			0
$634$	−5.88696	−	0.156612i	−0.233801	−	0.00621984i
$635$	−11.8592	+	9.09985i	−0.470616	+	0.361117i
$636$		0			0
$637$	−5.52756	+	7.20365i	−0.219010	+	0.285419i
$638$	−30.3525	+	3.17738i	−1.20167	+	0.125794i
$639$		0			0
$640$	−24.7289	+	8.67582i	−0.977495	+	0.342942i
$641$	−24.8380	−	43.0207i	−0.981042	−	1.69921i	−0.658354	−	0.752708i	$-0.728747\pi$
$641$	−24.8380	−	43.0207i	−0.981042	−	1.69921i	−0.322687	−	0.946506i	$-0.604586\pi$
$642$		0			0
$643$	12.8341	+	1.68965i	0.506129	+	0.0666331i	0.379267	−	0.925287i	$-0.376176\pi$
$643$	12.8341	+	1.68965i	0.506129	+	0.0666331i	0.126862	+	0.991920i	$0.459510\pi$
$644$	−4.28873	+	13.1620i	−0.169000	+	0.518655i
$645$		0			0
$646$	−3.30461	+	5.38759i	−0.130018	+	0.211972i
$647$	2.03731	+	2.03731i	0.0800948	+	0.0800948i	0.746019	−	0.665924i	$-0.231963\pi$
$647$	2.03731	+	2.03731i	0.0800948	+	0.0800948i	−0.665924	+	0.746019i	$0.731963\pi$
$648$		0			0
$649$	−45.2484	+	45.2484i	−1.77615	+	1.77615i
$650$	−0.279691	−	1.16714i	−0.0109704	−	0.0457790i
$651$		0			0
$652$	16.1201	−	1.25515i	0.631311	−	0.0491556i
$653$	−3.71856	+	28.2453i	−0.145519	+	1.10532i	0.750362	+	0.661027i	$0.229879\pi$
$653$	−3.71856	+	28.2453i	−0.145519	+	1.10532i	−0.895880	+	0.444295i	$0.853454\pi$
$654$		0			0
$655$	−28.2622	+	16.3172i	−1.10430	+	0.637566i
$656$	−17.8135	+	46.1756i	−0.695502	+	1.80285i
$657$		0			0
$658$	−10.0857	+	12.4442i	−0.393182	+	0.485126i
$659$	−4.14294	−	3.17899i	−0.161386	−	0.123836i	0.524911	−	0.851157i	$-0.324098\pi$
$659$	−4.14294	−	3.17899i	−0.161386	−	0.123836i	−0.686297	+	0.727321i	$0.740765\pi$
$660$		0			0
$661$	11.2302	+	14.6355i	0.436806	+	0.569256i	0.958941	−	0.283607i	$-0.0915310\pi$
$661$	11.2302	+	14.6355i	0.436806	+	0.569256i	−0.522135	+	0.852863i	$0.674864\pi$
$662$	18.4811	+	19.4913i	0.718288	+	0.757550i
$663$		0			0
$664$	−9.33928	−	3.32037i	−0.362434	−	0.128855i
$665$	−6.92333	−	6.92333i	−0.268475	−	0.268475i
$666$		0			0
$667$	18.2950	+	7.57806i	0.708387	+	0.293423i
$668$	−2.26205	+	42.4845i	−0.0875212	+	1.64378i
$669$		0			0
$670$	15.4894	+	6.90407i	0.598409	+	0.266728i
$671$	28.2224	−	48.8827i	1.08951	−	1.88709i
$672$		0			0
$673$	25.3190	+	43.8538i	0.975976	+	1.69044i	0.676677	+	0.736280i	$0.263419\pi$
$673$	25.3190	+	43.8538i	0.975976	+	1.69044i	0.299299	+	0.954159i	$0.403247\pi$
$674$	4.40856	+	42.1135i	0.169811	+	1.62215i
$675$		0			0
$676$	−8.29954	+	12.7569i	−0.319213	+	0.490649i
$677$	4.63871	+	35.2345i	0.178280	+	1.35417i	0.813375	+	0.581739i	$0.197628\pi$
$677$	4.63871	+	35.2345i	0.178280	+	1.35417i	−0.635095	+	0.772434i	$0.719039\pi$
$678$		0			0
$679$	−14.7118	+	3.94201i	−0.564586	+	0.151280i
$680$	−10.0251	−	6.90857i	−0.384447	−	0.264932i
$681$		0			0
$682$	41.6824	−	9.98868i	1.59610	−	0.382486i
$683$	8.93273	−	21.5655i	0.341801	−	0.825182i	−0.655732	−	0.754993i	$-0.727640\pi$
$683$	8.93273	−	21.5655i	0.341801	−	0.825182i	0.997534	−	0.0701882i	$-0.0223600\pi$
$684$		0			0
$685$	−34.6292	+	14.3439i	−1.32312	+	0.548052i
$686$	−26.7845	−	4.25370i	−1.02264	−	0.162407i
$687$		0			0
$688$	8.48869	+	4.62733i	0.323628	+	0.176415i
$689$	17.8849	+	10.3258i	0.681360	+	0.393383i
$690$		0			0
$691$	18.4151	+	14.1304i	0.700545	+	0.537547i	0.896488	−	0.443068i	$-0.146110\pi$
$691$	18.4151	+	14.1304i	0.700545	+	0.537547i	−0.195943	+	0.980615i	$0.562777\pi$
$692$	−9.08802	+	6.23487i	−0.345475	+	0.237014i
$693$		0			0
$694$	11.6116	+	3.44479i	0.440772	+	0.130762i
$695$	49.3321	+	13.2185i	1.87127	+	0.501406i
$696$		0			0
$697$	−22.2097	+	5.95107i	−0.841252	+	0.225413i
$698$	−12.3316	−	0.328059i	−0.466758	−	0.0124172i
$699$		0			0
$700$	0.955581	−	0.858967i	0.0361176	−	0.0324659i
$701$	−7.72776	−	18.6565i	−0.291873	−	0.704645i	0.708126	−	0.706087i	$-0.249541\pi$
$701$	−7.72776	−	18.6565i	−0.291873	−	0.704645i	−0.999999	+	0.00144185i	$0.999541\pi$
$702$		0			0
$703$	8.46414			0.319231
$704$	24.9628	−	23.5704i	0.940820	−	0.888342i
$705$		0			0
$706$	−0.791379	+	1.77547i	−0.0297839	+	0.0668208i
$707$	14.9193	+	1.96416i	0.561097	+	0.0738698i
$708$		0			0
$709$	−0.363175	−	2.75859i	−0.0136393	−	0.103601i	0.983271	−	0.182148i	$-0.0583051\pi$
$709$	−0.363175	−	2.75859i	−0.0136393	−	0.103601i	−0.996910	+	0.0785475i	$0.974972\pi$
$710$	1.73813	+	3.20442i	0.0652309	+	0.120260i
$711$		0			0
$712$	−13.1317	−	6.71165i	−0.492132	−	0.251530i
$713$	−26.8645	−	7.19833i	−1.00608	−	0.269579i
$714$		0			0
$715$	14.0501	+	18.3104i	0.525443	+	0.684771i
$716$	−3.42893	−	44.0382i	−0.128145	−	1.64578i
$717$		0			0
$718$	−1.77835	+	11.1979i	−0.0663676	+	0.417901i
$719$			21.4415i			0.799633i	0.916595	+	0.399816i	$0.130926\pi$
$719$			21.4415i			0.799633i	−0.916595	+	0.399816i	$0.869074\pi$
$720$		0			0
$721$		−	9.37100i		−	0.348994i
$722$	18.4592	+	2.93155i	0.686982	+	0.109101i
$723$		0			0
$724$	−28.4083	−	24.3040i	−1.05579	−	0.903252i
$725$	−1.11892	−	1.45821i	−0.0415558	−	0.0541566i
$726$		0			0
$727$	8.94901	+	2.39788i	0.331900	+	0.0889325i	0.420921	−	0.907097i	$-0.361707\pi$
$727$	8.94901	+	2.39788i	0.331900	+	0.0889325i	−0.0890205	+	0.996030i	$0.528374\pi$
$728$	11.5052	+	0.919957i	0.426410	+	0.0340959i
$729$		0			0
$730$	−28.0655	+	15.2232i	−1.03875	+	0.563435i
$731$	0.586265	+	4.45312i	0.0216838	+	0.164705i
$732$		0			0
$733$	−19.0409	−	2.50679i	−0.703293	−	0.0925902i	−0.229606	−	0.973284i	$-0.573744\pi$
$733$	−19.0409	−	2.50679i	−0.703293	−	0.0925902i	−0.473687	+	0.880693i	$0.657077\pi$
$734$	45.9195	+	20.4676i	1.69492	+	0.755473i
$735$		0			0
$736$	−21.5300	+	5.72088i	−0.793608	+	0.210874i
$737$	−22.2166			−0.818357
$738$		0			0
$739$	1.58086	+	3.81654i	0.0581529	+	0.140394i	0.950285	−	0.311380i	$-0.100791\pi$
$739$	1.58086	+	3.81654i	0.0581529	+	0.140394i	−0.892132	+	0.451774i	$0.850791\pi$
$740$	−0.866901	+	16.2817i	−0.0318679	+	0.598526i
$741$		0			0
$742$	−0.587970	+	22.1015i	−0.0215851	+	0.811373i
$743$	−1.95375	+	0.523506i	−0.0716762	+	0.0192056i	−0.294479	−	0.955658i	$-0.595146\pi$
$743$	−1.95375	+	0.523506i	−0.0716762	+	0.0192056i	0.222803	+	0.974864i	$0.428479\pi$
$744$		0			0
$745$	25.4802	+	6.82740i	0.933522	+	0.250136i
$746$	−9.35587	+	31.5366i	−0.342543	+	1.15464i
$747$		0			0
$748$	15.6805	+	2.91974i	0.573337	+	0.106756i
$749$	−10.2268	−	7.84729i	−0.373679	−	0.286734i
$750$		0			0
$751$	13.0403	+	7.52882i	0.475847	+	0.274730i	0.718684	−	0.695337i	$-0.244745\pi$
$751$	13.0403	+	7.52882i	0.475847	+	0.274730i	−0.242837	+	0.970067i	$0.578078\pi$
$752$	−25.6316	−	2.73722i	−0.934688	−	0.0998160i
$753$		0			0
$754$	2.58962	−	16.3062i	0.0943084	−	0.593837i
$755$	31.4031	−	13.0076i	1.14287	−	0.473394i
$756$		0			0
$757$	10.9898	−	26.5317i	0.399430	−	0.964310i	−0.588371	−	0.808591i	$-0.700231\pi$
$757$	10.9898	−	26.5317i	0.399430	−	0.964310i	0.987801	−	0.155719i	$-0.0497694\pi$
$758$	2.05519	+	8.57624i	0.0746479	+	0.311503i
$759$		0			0
$760$	3.29521	−	15.4080i	0.119530	−	0.558905i
$761$	−23.6362	+	6.33331i	−0.856813	+	0.229582i	−0.660377	−	0.750934i	$-0.729603\pi$
$761$	−23.6362	+	6.33331i	−0.856813	+	0.229582i	−0.196436	+	0.980517i	$0.562937\pi$
$762$		0			0
$763$	4.07969	+	30.9883i	0.147695	+	1.12185i
$764$	−29.3453	+	6.21197i	−1.06168	+	0.224741i
$765$		0			0
$766$	−40.3788	+	4.22696i	−1.45894	+	0.152726i
$767$	−17.3097	−	29.9812i	−0.625016	−	1.08256i
$768$		0			0
$769$	−1.81707	+	3.14725i	−0.0655252	+	0.113493i	−0.896927	−	0.442179i	$-0.854206\pi$
$769$	−1.81707	+	3.14725i	−0.0655252	+	0.113493i	0.831402	+	0.555672i	$0.187539\pi$
$770$	−10.0594	+	22.5684i	−0.362515	+	0.813310i
$771$		0			0
$772$	−1.67127	−	1.85925i	−0.0601503	−	0.0669158i
$773$	3.52157	+	1.45868i	0.126662	+	0.0524652i	0.445114	−	0.895474i	$-0.353163\pi$
$773$	3.52157	+	1.45868i	0.126662	+	0.0524652i	−0.318452	+	0.947939i	$0.603163\pi$
$774$		0			0
$775$	1.82539	+	1.82539i	0.0655699	+	0.0655699i
$776$	−18.1941	−	16.4233i	−0.653131	−	0.589563i
$777$		0			0
$778$	2.26291	−	2.14563i	0.0811294	−	0.0769247i
$779$	−18.1147	−	23.6076i	−0.649027	−	0.845829i
$780$		0			0
$781$	−3.78888	−	2.90731i	−0.135577	−	0.104032i
$782$	−8.04036	−	6.51650i	−0.287523	−	0.233030i
$783$		0			0
$784$	−6.33893	−	14.3016i	−0.226390	−	0.510772i
$785$	−3.40735	+	1.96723i	−0.121613	+	0.0702135i
$786$		0			0
$787$	2.12471	−	16.1388i	0.0757378	−	0.575286i	−0.910933	−	0.412555i	$-0.864636\pi$
$787$	2.12471	−	16.1388i	0.0757378	−	0.575286i	0.986671	−	0.162731i	$-0.0520302\pi$
$788$	0.440821	−	0.515265i	0.0157036	−	0.0183555i
$789$		0			0
$790$	29.0900	−	6.97108i	1.03498	−	0.248020i
$791$	10.4835	−	10.4835i	0.372749	−	0.372749i
$792$		0			0
$793$	21.5929	+	21.5929i	0.766785	+	0.766785i
$794$	−8.07475	−	4.95285i	−0.286562	−	0.175770i
$795$		0			0
$796$	−10.8185	+	5.50093i	−0.383451	+	0.194975i
$797$	14.9904	+	1.97352i	0.530986	+	0.0699056i	0.391252	−	0.920283i	$-0.372042\pi$
$797$	14.9904	+	1.97352i	0.530986	+	0.0699056i	0.139734	+	0.990189i	$0.455375\pi$
$798$		0			0
$799$	−5.98781	−	10.3712i	−0.211833	−	0.366906i
$800$	1.99616	+	0.539332i	0.0705749	+	0.0190683i
$801$		0			0
$802$	−0.406448	−	3.88266i	−0.0143522	−	0.137102i
$803$	25.4632	−	33.1843i	0.898578	−	1.17105i
$804$		0			0
$805$	12.7197	−	9.76015i	0.448310	−	0.344000i
$806$	−0.616678	+	23.1806i	−0.0217216	+	0.816503i
$807$		0			0
$808$	10.3980	+	21.8702i	0.365800	+	0.769390i
$809$	31.8739	−	31.8739i	1.12063	−	1.12063i	0.128980	−	0.991647i	$-0.458830\pi$
$809$	31.8739	−	31.8739i	1.12063	−	1.12063i	0.991647	−	0.128980i	$-0.0411703\pi$
$810$		0			0
$811$	−7.59731	+	18.3415i	−0.266778	+	0.644058i	−0.999328	−	0.0366546i	$-0.988330\pi$
$811$	−7.59731	+	18.3415i	−0.266778	+	0.644058i	0.732550	+	0.680713i	$0.238330\pi$
$812$	16.6670	−	5.88645i	0.584896	−	0.206574i
$813$		0			0
$814$	−7.64648	−	19.9446i	−0.268009	−	0.699058i
$815$	−16.2176	−	9.36323i	−0.568077	−	0.327980i
$816$		0			0
$817$	−5.03399	+	2.90637i	−0.176117	+	0.101681i
$818$	13.8664	+	11.2383i	0.484826	+	0.392939i
$819$		0			0
$820$	47.2670	−	32.4277i	1.65063	−	1.13242i
$821$	10.9855	−	1.44626i	0.383396	−	0.0504750i	0.0636347	−	0.997973i	$-0.479731\pi$
$821$	10.9855	−	1.44626i	0.383396	−	0.0504750i	0.319761	+	0.947498i	$0.396397\pi$
$822$		0			0
$823$	−4.92417	−	18.3772i	−0.171646	−	0.640590i	−0.997099	−	0.0761196i	$-0.975747\pi$
$823$	−4.92417	−	18.3772i	−0.171646	−	0.640590i	0.825453	−	0.564471i	$-0.190920\pi$
$824$	12.6577	−	8.19754i	0.440953	−	0.285575i
$825$		0			0
$826$	19.3785	−	31.5932i	0.674263	−	1.09927i
$827$	−9.16153	−	3.79483i	−0.318578	−	0.131959i	0.217664	−	0.976024i	$-0.430156\pi$
$827$	−9.16153	−	3.79483i	−0.318578	−	0.131959i	−0.536241	+	0.844065i	$0.680156\pi$
$828$		0			0
$829$	−1.43211	−	3.45742i	−0.0497393	−	0.120081i	0.897057	−	0.441915i	$-0.145701\pi$
$829$	−1.43211	−	3.45742i	−0.0497393	−	0.120081i	−0.946796	+	0.321834i	$0.895701\pi$
$830$	6.74381	+	9.29020i	0.234081	+	0.322468i
$831$		0			0
$832$	8.82184	+	16.3452i	0.305842	+	0.566667i
$833$	3.63381	−	6.29395i	0.125904	−	0.218072i
$834$		0			0
$835$	29.9964	−	39.0921i	1.03807	−	1.35284i
$836$	4.27483	+	20.1943i	0.147848	+	0.698434i
$837$		0			0
$838$	−1.16066	−	2.13980i	−0.0400944	−	0.0739181i
$839$	3.19848	−	11.9369i	0.110424	−	0.412107i	−0.888480	−	0.458915i	$-0.848238\pi$
$839$	3.19848	−	11.9369i	0.110424	−	0.412107i	0.998904	+	0.0468078i	$0.0149048\pi$
$840$		0			0
$841$	0.961452	+	3.58819i	0.0331535	+	0.123731i
$842$	35.1575	−	33.3354i	1.21161	−	1.14881i
$843$		0			0
$844$	−14.1011	−	6.74034i	−0.485381	−	0.232012i
$845$	16.2847	−	6.74534i	0.560210	−	0.232047i
$846$		0			0
$847$		−	13.0365i		−	0.447939i
$848$	−30.3677	+	18.5397i	−1.04283	+	0.636657i
$849$		0			0
$850$	0.343884	+	0.896966i	0.0117951	+	0.0307657i
$851$	−1.80909	+	13.7414i	−0.0620147	+	0.471049i
$852$		0			0
$853$	45.3255	−	5.96722i	1.55192	−	0.204314i	0.694712	−	0.719288i	$-0.255532\pi$
$853$	45.3255	−	5.96722i	1.55192	−	0.204314i	0.857205	+	0.514975i	$0.172199\pi$
$854$	−9.29818	+	31.3422i	−0.318177	+	1.07251i
$855$		0			0
$856$	1.65345	−	20.6783i	0.0565136	−	0.706770i
$857$	−6.43751	+	24.0251i	−0.219901	+	0.820682i	0.764482	+	0.644645i	$0.222995\pi$
$857$	−6.43751	+	24.0251i	−0.219901	+	0.820682i	−0.984383	+	0.176037i	$0.943672\pi$
$858$		0			0
$859$	42.7839	−	32.8292i	1.45977	−	1.12012i	0.491297	−	0.870992i	$-0.336523\pi$
$859$	42.7839	−	32.8292i	1.45977	−	1.12012i	0.968471	−	0.249127i	$-0.0801436\pi$
$860$	−5.07514	−	9.98108i	−0.173061	−	0.340352i
$861$		0			0
$862$	−6.94545	+	5.04174i	−0.236563	+	0.171722i
$863$	−1.48658			−0.0506037			−0.0253019	−	0.999680i	$-0.508055\pi$
$863$	−1.48658			−0.0506037			−0.0253019	+	0.999680i	$0.508055\pi$
$864$		0			0
$865$	12.7645			0.434005
$866$	−25.5747	+	18.5648i	−0.869064	+	0.630858i
$867$		0			0
$868$	−22.1291	+	11.2521i	−0.751112	+	0.381922i
$869$	−31.0905	+	23.8565i	−1.05467	+	0.809278i
$870$		0			0
$871$	3.11081	−	11.6097i	0.105406	−	0.393380i
$872$	−38.2882	+	32.6185i	−1.29660	+	1.10460i
$873$		0			0
$874$	3.80941	−	12.8407i	0.128855	−	0.434343i
$875$	18.7065	−	2.46276i	0.632397	−	0.0832566i
$876$		0			0
$877$	−3.55920	+	27.0348i	−0.120186	+	0.912900i	0.820030	+	0.572320i	$0.193957\pi$
$877$	−3.55920	+	27.0348i	−0.120186	+	0.912900i	−0.940216	+	0.340579i	$0.889377\pi$
$878$	−2.09606	−	5.46723i	−0.0707385	−	0.184510i
$879$		0			0
$880$	−39.2837	+	6.15479i	−1.32425	+	0.207478i
$881$			16.3864i			0.552073i	0.961147	+	0.276036i	$0.0890211\pi$
$881$			16.3864i			0.552073i	−0.961147	+	0.276036i	$0.910979\pi$
$882$		0			0
$883$	−35.6527	+	14.7678i	−1.19981	+	0.496977i	−0.890937	−	0.454127i	$-0.849951\pi$
$883$	−35.6527	+	14.7678i	−1.19981	+	0.496977i	−0.308872	+	0.951104i	$0.599951\pi$
$884$	−3.72140	+	7.78535i	−0.125164	+	0.261850i
$885$		0			0
$886$	23.2864	−	22.0795i	0.782321	−	0.741775i
$887$	0.241937	+	0.902923i	0.00812347	+	0.0303172i	0.969869	−	0.243629i	$-0.0783378\pi$
$887$	0.241937	+	0.902923i	0.00812347	+	0.0303172i	−0.961745	+	0.273946i	$0.911671\pi$
$888$		0			0
$889$	−2.93559	+	10.9558i	−0.0984566	+	0.367445i
$890$	8.14373	+	15.0138i	0.272979	+	0.503264i
$891$		0			0
$892$	−31.3752	+	6.64167i	−1.05052	+	0.222380i
$893$	9.43475	−	12.2956i	0.315722	−	0.411457i
$894$		0			0
$895$	−25.5793	+	44.3046i	−0.855021	+	1.48094i
$896$	−10.8787	+	16.6452i	−0.363433	+	0.556077i
$897$		0			0
$898$	−25.6843	−	35.3824i	−0.857095	−	1.18073i
$899$	13.5901	+	32.8095i	0.453257	+	1.09426i
$900$		0			0
$901$	−15.2714	−	6.32560i	−0.508763	−	0.210736i
$902$	−39.2633	+	64.0119i	−1.30732	+	2.13136i
$903$		0			0
$904$	23.3311	+	4.98969i	0.775981	+	0.165955i
$905$	11.2068	+	41.8244i	0.372527	+	1.39029i
$906$		0			0
$907$	14.1169	−	1.85852i	0.468742	−	0.0617111i	0.107544	−	0.994200i	$-0.465701\pi$
$907$	14.1169	−	1.85852i	0.468742	−	0.0617111i	0.361198	+	0.932489i	$0.382368\pi$
$908$	26.6092	+	38.7858i	0.883056	+	1.28715i
$909$		0			0
$910$	−10.3851	−	8.41682i	−0.344261	−	0.279015i
$911$	−12.0229	+	6.94141i	−0.398336	+	0.229979i	−0.685766	−	0.727822i	$-0.740532\pi$
$911$	−12.0229	+	6.94141i	−0.398336	+	0.229979i	0.287430	+	0.957802i	$0.407199\pi$
$912$		0			0
$913$	−13.0244	−	7.51964i	−0.431044	−	0.248864i
$914$	−7.61712	−	19.8680i	−0.251952	−	0.657176i
$915$		0			0
$916$	−4.95868	−	14.0401i	−0.163839	−	0.463897i
$917$	−9.47605	+	22.8772i	−0.312927	+	0.755472i
$918$		0			0
$919$	26.8207	−	26.8207i	0.884735	−	0.884735i	−0.109277	−	0.994011i	$-0.534853\pi$
$919$	26.8207	−	26.8207i	0.884735	−	0.884735i	0.994011	+	0.109277i	$0.0348534\pi$
$920$	24.3103	+	8.64295i	0.801486	+	0.284950i
$921$		0			0
$922$	−0.236591	+	8.89335i	−0.00779171	+	0.292887i
$923$	2.04980	−	1.57287i	0.0674700	−	0.0517716i
$924$		0			0
$925$	0.783149	−	1.02062i	0.0257498	−	0.0335578i
$926$	−5.84814	−	55.8654i	−0.192182	−	1.83585i
$927$		0			0
$928$	22.5309	+	17.3633i	0.739614	+	0.569979i
$929$	−13.2213	−	22.9000i	−0.433777	−	0.751323i	0.563418	−	0.826172i	$-0.309486\pi$
$929$	−13.2213	−	22.9000i	−0.433777	−	0.751323i	−0.997195	+	0.0748486i	$0.976153\pi$
$930$		0			0
$931$	9.32495	+	1.22765i	0.305613	+	0.0402347i
$932$	−7.36650	−	14.4874i	−0.241298	−	0.474551i
$933$		0			0
$934$	−32.8303	−	20.1372i	−1.07424	−	0.658911i
$935$	−13.0624	−	13.0624i	−0.427186	−	0.427186i
$936$		0			0
$937$	−6.06603	+	6.06603i	−0.198169	+	0.198169i	−0.799215	−	0.601046i	$-0.794751\pi$
$937$	−6.06603	+	6.06603i	−0.198169	+	0.198169i	0.601046	+	0.799215i	$0.294751\pi$
$938$	12.5133	−	2.99867i	0.408575	−	0.0979100i
$939$		0			0
$940$	22.6856	+	19.4081i	0.739922	+	0.633021i
$941$	1.47034	−	11.1683i	0.0479316	−	0.364077i	−0.950624	−	0.310346i	$-0.899555\pi$
$941$	1.47034	−	11.1683i	0.0479316	−	0.364077i	0.998555	−	0.0537312i	$-0.0171114\pi$
$942$		0			0
$943$	42.1982	−	24.3632i	1.37416	−	0.793374i
$944$	59.6259	−	1.46186i	1.94066	−	0.0475793i
$945$		0			0
$946$	11.3962	+	9.23631i	0.370522	+	0.300298i
$947$	−30.3374	−	23.2787i	−0.985832	−	0.756456i	−0.0159107	−	0.999873i	$-0.505065\pi$
$947$	−30.3374	−	23.2787i	−0.985832	−	0.756456i	−0.969922	+	0.243418i	$0.921731\pi$
$948$		0			0
$949$	13.7757	+	17.9529i	0.447179	+	0.582776i
$950$	−0.902140	+	0.855385i	−0.0292693	+	0.0277523i
$951$		0			0
$952$	−9.22605	+	0.471946i	−0.299018	+	0.0152959i
$953$	−21.1060	−	21.1060i	−0.683689	−	0.683689i	0.277140	−	0.960829i	$-0.410613\pi$
$953$	−21.1060	−	21.1060i	−0.683689	−	0.683689i	−0.960829	+	0.277140i	$0.910613\pi$
$954$		0			0
$955$	32.0959	+	13.2945i	1.03860	+	0.430201i
$956$	11.2105	−	10.0770i	0.362573	−	0.325915i
$957$		0			0
$958$	−5.99367	+	13.4469i	−0.193647	+	0.434450i
$959$	−14.2203	+	24.6303i	−0.459199	+	0.795355i
$960$		0			0
$961$	−9.43857	−	16.3481i	−0.304470	−	0.527357i
$962$	11.4931	−	1.20313i	0.370554	−	0.0387906i
$963$		0			0
$964$	6.44218	+	30.4329i	0.207489	+	0.980176i
$965$	0.377931	+	2.87067i	0.0121660	+	0.0924101i
$966$		0			0
$967$	−22.6691	+	6.07416i	−0.728988	+	0.195332i	−0.604179	−	0.796849i	$-0.706499\pi$
$967$	−22.6691	+	6.07416i	−0.728988	+	0.195332i	−0.124810	+	0.992181i	$0.539832\pi$
$968$	17.6088	−	11.4040i	0.565969	−	0.366539i
$969$		0			0
$970$	6.61537	+	27.6057i	0.212407	+	0.886366i
$971$	−1.72920	+	4.17465i	−0.0554926	+	0.133971i	−0.949194	−	0.314691i	$-0.898099\pi$
$971$	−1.72920	+	4.17465i	−0.0554926	+	0.133971i	0.893702	+	0.448662i	$0.148099\pi$
$972$		0			0
$973$	35.8025	−	14.8299i	1.14777	−	0.475424i
$974$	−0.823607	+	5.18605i	−0.0263901	+	0.166172i
$975$		0			0
$976$	−50.4688	+	14.8580i	−1.61547	+	0.475594i
$977$	17.3350	+	10.0084i	0.554597	+	0.320197i	0.750974	−	0.660332i	$-0.229584\pi$
$977$	17.3350	+	10.0084i	0.554597	+	0.320197i	−0.196377	+	0.980528i	$0.562918\pi$
$978$		0			0
$979$	−17.7522	−	13.6217i	−0.567362	−	0.435353i
$980$	−3.31659	+	17.8118i	−0.105945	+	0.568977i
$981$		0			0
$982$	7.12896	−	24.0302i	0.227494	−	0.766833i
$983$	−36.5166	−	9.78459i	−1.16470	−	0.312080i	−0.375857	−	0.926678i	$-0.622652\pi$
$983$	−36.5166	−	9.78459i	−1.16470	−	0.312080i	−0.788841	+	0.614598i	$0.789318\pi$
$984$		0			0
$985$	−0.758603	+	0.203267i	−0.0241711	+	0.00647662i
$986$	−0.351437	+	13.2104i	−0.0111920	+	0.420704i
$987$		0			0
$988$	−11.1515	−	0.593751i	−0.354777	−	0.0188897i
$989$	−3.64251	−	8.79379i	−0.115825	−	0.279626i
$990$		0			0
$991$	−52.8446			−1.67866			−0.839332	−	0.543619i	$-0.817054\pi$
$991$	−52.8446			−1.67866			−0.839332	+	0.543619i	$0.817054\pi$
$992$	−34.5567	−	20.0475i	−1.09718	−	0.636509i
$993$		0			0
$994$	2.52647	+	1.12612i	0.0801349	+	0.0357184i
$995$	13.9362	+	1.83474i	0.441809	+	0.0581652i
$996$		0			0
$997$	7.96815	+	60.5241i	0.252354	+	1.91682i	0.379981	+	0.924994i	$0.375931\pi$
$997$	7.96815	+	60.5241i	0.252354	+	1.91682i	−0.127627	+	0.991822i	$0.540736\pi$
$998$	−27.4263	+	14.8765i	−0.868165	+	0.470906i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bk.a.37.15		368
3.2	odd	2		288.2.bc.a.229.32	yes	368
9.2	odd	6		288.2.bc.a.133.30	yes	368
9.7	even	3	inner	864.2.bk.a.613.17		368
32.13	even	8	inner	864.2.bk.a.685.17		368
96.77	odd	8		288.2.bc.a.13.30	✓	368
288.173	odd	24		288.2.bc.a.205.32	yes	368
288.205	even	24	inner	864.2.bk.a.397.15		368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bc.a.13.30	✓	368	96.77	odd	8
288.2.bc.a.133.30	yes	368	9.2	odd	6
288.2.bc.a.205.32	yes	368	288.173	odd	24
288.2.bc.a.229.32	yes	368	3.2	odd	2
864.2.bk.a.37.15		368	1.1	even	1	trivial
864.2.bk.a.397.15		368	288.205	even	24	inner
864.2.bk.a.613.17		368	9.7	even	3	inner
864.2.bk.a.685.17		368	32.13	even	8	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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bk (of order \(24\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.830777 - 1.14447i) q^{2} +(-0.619620 + 1.90160i) q^{4} +(1.83769 - 1.41011i) q^{5} +(0.454899 - 1.69771i) q^{7} +(2.69109 - 0.870667i) q^{8} +O(q^{10})\)	\(q+(-0.830777 - 1.14447i) q^{2} +(-0.619620 + 1.90160i) q^{4} +(1.83769 - 1.41011i) q^{5} +(0.454899 - 1.69771i) q^{7} +(2.69109 - 0.870667i) q^{8} +(-3.14054 - 0.931695i) q^{10} +(4.25482 - 0.560157i) q^{11} +(-0.303048 + 2.30188i) q^{13} +(-2.32089 + 0.889796i) q^{14} +(-3.23214 - 2.35653i) q^{16} -1.85832i q^{17} +(2.22188 - 0.920333i) q^{19} +(1.54279 + 4.36828i) q^{20} +(-4.17588 - 4.40414i) q^{22} +(1.01925 + 3.80389i) q^{23} +(0.0946054 - 0.353072i) q^{25} +(2.88619 - 1.56552i) q^{26} +(2.94649 + 1.91697i) q^{28} +(3.06112 - 3.98933i) q^{29} +(-3.53119 + 6.11620i) q^{31} +(-0.0117927 + 5.65684i) q^{32} +(-2.12679 + 1.54385i) q^{34} +(-1.55799 - 3.76132i) q^{35} +(3.25157 + 1.34684i) q^{37} +(-2.89918 - 1.77828i) q^{38} +(3.71765 - 5.39475i) q^{40} +(-3.20240 - 11.9515i) q^{41} +(-2.39632 + 0.315482i) q^{43} +(-1.57118 + 8.43803i) q^{44} +(3.50667 - 4.32669i) q^{46} +(5.58096 - 3.22217i) q^{47} +(3.38691 + 1.95543i) q^{49} +(-0.482676 + 0.185051i) q^{50} +(-4.18947 - 2.00256i) q^{52} +(3.40394 - 8.21784i) q^{53} +(7.02916 - 7.02916i) q^{55} +(-0.253964 - 4.96473i) q^{56} +(-7.10878 - 0.189116i) q^{58} +(-11.8297 + 9.07722i) q^{59} +(8.00680 - 10.4347i) q^{61} +(9.93343 - 1.03986i) q^{62} +(6.48388 - 4.68608i) q^{64} +(2.68899 + 4.65747i) q^{65} +(-5.13255 - 0.675713i) q^{67} +(3.53377 + 1.15145i) q^{68} +(-3.01037 + 4.90789i) q^{70} +(-0.786895 - 0.786895i) q^{71} +(6.89191 - 6.89191i) q^{73} +(-1.15991 - 4.84024i) q^{74} +(0.373381 + 4.79538i) q^{76} +(0.984528 - 7.47824i) q^{77} +(-7.90822 + 4.56581i) q^{79} +(-9.26266 + 0.227094i) q^{80} +(-11.0177 + 13.5941i) q^{82} +(-2.78023 - 2.13335i) q^{83} +(-2.62043 - 3.41501i) q^{85} +(2.35187 + 2.48042i) q^{86} +(10.9624 - 5.21196i) q^{88} +(-3.68687 - 3.68687i) q^{89} +(3.77005 + 1.56161i) q^{91} +(-7.86502 - 0.418765i) q^{92} +(-8.32420 - 3.71033i) q^{94} +(2.78536 - 4.82439i) q^{95} +(-4.33284 - 7.50470i) q^{97} +(-0.575832 - 5.50074i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 16 q^{8}+O(q^{10}) \) 368 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 16 * q^8	\( 368 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 16 q^{8} - 16 q^{10} + 4 q^{11} - 4 q^{13} + 4 q^{14} - 4 q^{16} - 16 q^{19} + 4 q^{20} - 4 q^{22} + 4 q^{23} - 4 q^{25} + 16 q^{26} - 16 q^{28} + 4 q^{29} - 8 q^{31} + 4 q^{32} + 4 q^{34} + 16 q^{35} - 16 q^{37} + 60 q^{38} - 4 q^{40} + 4 q^{41} - 4 q^{43} + 104 q^{44} - 16 q^{46} - 48 q^{50} - 4 q^{52} + 16 q^{53} - 16 q^{55} + 84 q^{56} - 40 q^{58} + 4 q^{59} - 4 q^{61} + 24 q^{62} - 16 q^{64} + 8 q^{65} - 4 q^{67} - 12 q^{68} - 4 q^{70} + 16 q^{71} - 16 q^{73} + 4 q^{74} + 20 q^{76} + 4 q^{77} - 48 q^{80} - 16 q^{82} - 36 q^{83} + 16 q^{85} - 100 q^{86} - 4 q^{88} + 16 q^{89} - 16 q^{91} + 80 q^{92} - 20 q^{94} + 136 q^{95} - 8 q^{97} - 104 q^{98}+O(q^{100}) \) 368 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 16 * q^8 - 16 * q^10 + 4 * q^11 - 4 * q^13 + 4 * q^14 - 4 * q^16 - 16 * q^19 + 4 * q^20 - 4 * q^22 + 4 * q^23 - 4 * q^25 + 16 * q^26 - 16 * q^28 + 4 * q^29 - 8 * q^31 + 4 * q^32 + 4 * q^34 + 16 * q^35 - 16 * q^37 + 60 * q^38 - 4 * q^40 + 4 * q^41 - 4 * q^43 + 104 * q^44 - 16 * q^46 - 48 * q^50 - 4 * q^52 + 16 * q^53 - 16 * q^55 + 84 * q^56 - 40 * q^58 + 4 * q^59 - 4 * q^61 + 24 * q^62 - 16 * q^64 + 8 * q^65 - 4 * q^67 - 12 * q^68 - 4 * q^70 + 16 * q^71 - 16 * q^73 + 4 * q^74 + 20 * q^76 + 4 * q^77 - 48 * q^80 - 16 * q^82 - 36 * q^83 + 16 * q^85 - 100 * q^86 - 4 * q^88 + 16 * q^89 - 16 * q^91 + 80 * q^92 - 20 * q^94 + 136 * q^95 - 8 * q^97 - 104 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more