LMFDB - Embedded newform 441.2.u.c.190.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(64,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("441.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.u (of order $7$, degree $6$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{7})$
Twist minimal:	no (minimal twist has level 147)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			190.4
Character	$\chi$	$=$	441.190
Dual form			441.2.u.c.253.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.65876 - 2.08002i) q^{2} +(-1.12995 - 4.95062i) q^{4} +(-2.59504 - 1.24971i) q^{5} +(-1.31683 + 2.29477i) q^{7} +(-7.37774 - 3.55293i) q^{8} +O(q^{10})$	\(q+(1.65876 - 2.08002i) q^{2} +(-1.12995 - 4.95062i) q^{4} +(-2.59504 - 1.24971i) q^{5} +(-1.31683 + 2.29477i) q^{7} +(-7.37774 - 3.55293i) q^{8} +(-6.90396 + 3.32477i) q^{10} +(2.50706 - 3.14376i) q^{11} +(2.30745 - 2.89345i) q^{13} +(2.58885 + 6.54549i) q^{14} +(-10.4779 + 5.04589i) q^{16} +(-0.667699 + 2.92538i) q^{17} -3.46493 q^{19} +(-3.25457 + 14.2592i) q^{20} +(-2.38046 - 10.4295i) q^{22} +(-0.254612 - 1.11553i) q^{23} +(2.05504 + 2.57694i) q^{25} +(-2.19092 - 9.59906i) q^{26} +(12.8485 + 3.92616i) q^{28} +(0.836382 - 3.66443i) q^{29} +7.66612 q^{31} +(-3.24046 + 14.1974i) q^{32} +(4.97729 + 6.24132i) q^{34} +(6.28502 - 4.30937i) q^{35} +(1.88592 - 8.26276i) q^{37} +(-5.74748 + 7.20712i) q^{38} +(14.7054 + 18.4400i) q^{40} +(1.93192 + 0.930364i) q^{41} +(6.76663 - 3.25864i) q^{43} +(-18.3964 - 8.85925i) q^{44} +(-2.74266 - 1.32080i) q^{46} +(-0.562355 + 0.705171i) q^{47} +(-3.53192 - 6.04364i) q^{49} +8.76888 q^{50} +(-16.9317 - 8.15387i) q^{52} +(0.409047 + 1.79215i) q^{53} +(-10.4347 + 5.02510i) q^{55} +(17.8684 - 12.2516i) q^{56} +(-6.23472 - 7.81809i) q^{58} +(-3.66438 + 1.76467i) q^{59} +(-0.415738 + 1.82147i) q^{61} +(12.7162 - 15.9457i) q^{62} +(9.65375 + 12.1054i) q^{64} +(-9.60390 + 4.62499i) q^{65} +14.1346 q^{67} +15.2369 q^{68} +(1.46176 - 20.2211i) q^{70} +(3.15081 + 13.8046i) q^{71} +(3.63187 + 4.55422i) q^{73} +(-14.0584 - 17.6287i) q^{74} +(3.91519 + 17.1536i) q^{76} +(3.91282 + 9.89292i) q^{77} -15.8711 q^{79} +33.4965 q^{80} +(5.13976 - 2.47518i) q^{82} +(1.57731 + 1.97788i) q^{83} +(5.38858 - 6.75706i) q^{85} +(4.44618 - 19.4800i) q^{86} +(-29.6660 + 14.2864i) q^{88} +(-3.41131 - 4.27764i) q^{89} +(3.60128 + 9.10524i) q^{91} +(-5.23487 + 2.52098i) q^{92} +(0.533956 + 2.33942i) q^{94} +(8.99166 + 4.33015i) q^{95} -2.32328 q^{97} +(-18.4295 - 2.67848i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - q^{2} - 3 q^{4} - 3 q^{8}+O(q^{10}) $ 24 * q - q^2 - 3 * q^4 - 3 * q^8	$ 24 q - q^{2} - 3 q^{4} - 3 q^{8} - 30 q^{10} - 9 q^{11} + 21 q^{14} - 29 q^{16} - 5 q^{17} + 26 q^{19} + 13 q^{20} + 11 q^{22} - 4 q^{23} - 28 q^{25} + 22 q^{26} - 7 q^{28} - 6 q^{29} + 36 q^{31} - 14 q^{32} + 46 q^{34} + 7 q^{35} - 22 q^{37} + 45 q^{38} + 35 q^{40} + 11 q^{41} + 6 q^{43} - 82 q^{44} - 16 q^{46} - 29 q^{47} - 42 q^{49} + 48 q^{50} - 50 q^{52} - 28 q^{53} + 23 q^{55} - 21 q^{56} + 39 q^{58} + 15 q^{59} - 32 q^{61} + 8 q^{62} + 29 q^{64} + 21 q^{65} - 34 q^{67} + 22 q^{68} - 24 q^{71} - 15 q^{73} - 6 q^{74} + 7 q^{76} + 21 q^{77} - 34 q^{79} - 8 q^{80} + 14 q^{82} - 14 q^{83} + 20 q^{85} + 100 q^{86} - 108 q^{88} - 10 q^{89} + 84 q^{91} + 21 q^{92} + 99 q^{94} - 18 q^{95} - 64 q^{97} - 91 q^{98}+O(q^{100}) $ 24 * q - q^2 - 3 * q^4 - 3 * q^8 - 30 * q^10 - 9 * q^11 + 21 * q^14 - 29 * q^16 - 5 * q^17 + 26 * q^19 + 13 * q^20 + 11 * q^22 - 4 * q^23 - 28 * q^25 + 22 * q^26 - 7 * q^28 - 6 * q^29 + 36 * q^31 - 14 * q^32 + 46 * q^34 + 7 * q^35 - 22 * q^37 + 45 * q^38 + 35 * q^40 + 11 * q^41 + 6 * q^43 - 82 * q^44 - 16 * q^46 - 29 * q^47 - 42 * q^49 + 48 * q^50 - 50 * q^52 - 28 * q^53 + 23 * q^55 - 21 * q^56 + 39 * q^58 + 15 * q^59 - 32 * q^61 + 8 * q^62 + 29 * q^64 + 21 * q^65 - 34 * q^67 + 22 * q^68 - 24 * q^71 - 15 * q^73 - 6 * q^74 + 7 * q^76 + 21 * q^77 - 34 * q^79 - 8 * q^80 + 14 * q^82 - 14 * q^83 + 20 * q^85 + 100 * q^86 - 108 * q^88 - 10 * q^89 + 84 * q^91 + 21 * q^92 + 99 * q^94 - 18 * q^95 - 64 * q^97 - 91 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{1}{7}\right)$	$1$

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 $

$2$	1.65876	−	2.08002i	1.17292	−	1.47079i	0.321030	−	0.947069i	$-0.395971\pi$
$2$	1.65876	−	2.08002i	1.17292	−	1.47079i	0.851888	−	0.523724i	$-0.175458\pi$
$3$		0			0
$3$		0			0
$4$	−1.12995	−	4.95062i	−0.564974	−	2.47531i
$5$	−2.59504	−	1.24971i	−1.16054	−	0.558886i	−0.248356	−	0.968669i	$-0.579890\pi$
$5$	−2.59504	−	1.24971i	−1.16054	−	0.558886i	−0.912183	+	0.409783i	$0.865605\pi$
$6$		0			0
$7$	−1.31683	+	2.29477i	−0.497715	+	0.867341i
$7$	−1.31683	+	2.29477i	−0.497715	+	0.867341i
$8$	−7.37774	−	3.55293i	−2.60842	−	1.25615i
$9$		0			0
$10$	−6.90396	+	3.32477i	−2.18322	+	1.05139i
$11$	2.50706	−	3.14376i	0.755908	−	0.947879i	−0.243851	−	0.969813i	$-0.578411\pi$
$11$	2.50706	−	3.14376i	0.755908	−	0.947879i	0.999759	+	0.0219339i	$0.00698232\pi$
$12$		0			0
$13$	2.30745	−	2.89345i	0.639971	−	0.802498i	−0.351028	−	0.936365i	$-0.614168\pi$
$13$	2.30745	−	2.89345i	0.639971	−	0.802498i	0.990999	+	0.133866i	$0.0427393\pi$
$14$	2.58885	+	6.54549i	0.691900	+	1.74936i
$15$		0			0
$16$	−10.4779	+	5.04589i	−2.61947	+	1.26147i
$17$	−0.667699	+	2.92538i	−0.161941	+	0.709509i	0.827123	+	0.562021i	$0.189976\pi$
$17$	−0.667699	+	2.92538i	−0.161941	+	0.709509i	−0.989064	+	0.147488i	$0.952881\pi$
$18$		0			0
$19$	−3.46493			−0.794910			−0.397455	−	0.917622i	$-0.630107\pi$
$19$	−3.46493			−0.794910			−0.397455	+	0.917622i	$0.630107\pi$
$20$	−3.25457	+	14.2592i	−0.727744	+	3.18845i
$21$		0			0
$22$	−2.38046	−	10.4295i	−0.507515	−	2.22357i
$23$	−0.254612	−	1.11553i	−0.0530904	−	0.232604i	0.941421	−	0.337234i	$-0.109491\pi$
$23$	−0.254612	−	1.11553i	−0.0530904	−	0.232604i	−0.994511	+	0.104630i	$0.966634\pi$
$24$		0			0
$25$	2.05504	+	2.57694i	0.411008	+	0.515387i
$26$	−2.19092	−	9.59906i	−0.429675	−	1.88253i
$27$		0			0
$28$	12.8485	+	3.92616i	2.42814	+	0.741975i
$29$	0.836382	−	3.66443i	0.155312	−	0.680468i	−0.835977	−	0.548765i	$-0.815098\pi$
$29$	0.836382	−	3.66443i	0.155312	−	0.680468i	0.991289	−	0.131703i	$-0.0420445\pi$
$30$		0			0
$31$	7.66612			1.37688			0.688438	−	0.725295i	$-0.258297\pi$
$31$	7.66612			1.37688			0.688438	+	0.725295i	$0.258297\pi$
$32$	−3.24046	+	14.1974i	−0.572837	+	2.50976i
$33$		0			0
$34$	4.97729	+	6.24132i	0.853597	+	1.07038i
$35$	6.28502	−	4.30937i	1.06236	−	0.728417i
$36$		0			0
$37$	1.88592	−	8.26276i	0.310044	−	1.35839i	−0.544391	−	0.838831i	$-0.683239\pi$
$37$	1.88592	−	8.26276i	0.310044	−	1.35839i	0.854435	−	0.519558i	$-0.173904\pi$
$38$	−5.74748	+	7.20712i	−0.932365	+	1.16915i
$39$		0			0
$40$	14.7054	+	18.4400i	2.32513	+	2.91563i
$41$	1.93192	+	0.930364i	0.301715	+	0.145298i	0.578616	−	0.815600i	$-0.303593\pi$
$41$	1.93192	+	0.930364i	0.301715	+	0.145298i	−0.276901	+	0.960899i	$0.589307\pi$
$42$		0			0
$43$	6.76663	−	3.25864i	1.03190	−	0.496938i	0.160257	−	0.987075i	$-0.448768\pi$
$43$	6.76663	−	3.25864i	1.03190	−	0.496938i	0.871645	+	0.490138i	$0.163054\pi$
$44$	−18.3964	−	8.85925i	−2.77336	−	1.33558i
$45$		0			0
$46$	−2.74266	−	1.32080i	−0.404383	−	0.194741i
$47$	−0.562355	+	0.705171i	−0.0820279	+	0.102860i	−0.821152	−	0.570709i	$-0.806668\pi$
$47$	−0.562355	+	0.705171i	−0.0820279	+	0.102860i	0.739124	+	0.673569i	$0.235240\pi$
$48$		0			0
$49$	−3.53192	−	6.04364i	−0.504560	−	0.863377i
$50$	8.76888			1.24011
$51$		0			0
$52$	−16.9317	−	8.15387i	−2.34800	−	1.13074i
$53$	0.409047	+	1.79215i	0.0561870	+	0.246171i	0.995220	−	0.0976548i	$-0.0311341\pi$
$53$	0.409047	+	1.79215i	0.0561870	+	0.246171i	−0.939033	+	0.343826i	$0.888277\pi$
$54$		0			0
$55$	−10.4347	+	5.02510i	−1.40702	+	0.677584i
$56$	17.8684	−	12.2516i	2.38776	−	1.63719i
$57$		0			0
$58$	−6.23472	−	7.81809i	−0.818659	−	1.02657i
$59$	−3.66438	+	1.76467i	−0.477061	+	0.229740i	−0.656932	−	0.753950i	$-0.728146\pi$
$59$	−3.66438	+	1.76467i	−0.477061	+	0.229740i	0.179871	+	0.983690i	$0.442432\pi$
$60$		0			0
$61$	−0.415738	+	1.82147i	−0.0532298	+	0.233215i	−0.994544	−	0.104316i	$-0.966735\pi$
$61$	−0.415738	+	1.82147i	−0.0532298	+	0.233215i	0.941314	+	0.337531i	$0.109592\pi$
$62$	12.7162	−	15.9457i	1.61496	−	2.02510i
$63$		0			0
$64$	9.65375	+	12.1054i	1.20672	+	1.51318i
$65$	−9.60390	+	4.62499i	−1.19122	+	0.573660i
$66$		0			0
$67$	14.1346			1.72682			0.863410	−	0.504503i	$-0.168324\pi$
$67$	14.1346			1.72682			0.863410	+	0.504503i	$0.168324\pi$
$68$	15.2369			1.84775
$69$		0			0
$70$	1.46176	−	20.2211i	0.174714	−	2.41689i
$71$	3.15081	+	13.8046i	0.373932	+	1.63830i	0.715621	+	0.698489i	$0.246144\pi$
$71$	3.15081	+	13.8046i	0.373932	+	1.63830i	−0.341689	+	0.939813i	$0.610999\pi$
$72$		0			0
$73$	3.63187	+	4.55422i	0.425078	+	0.533031i	0.947542	−	0.319630i	$-0.103559\pi$
$73$	3.63187	+	4.55422i	0.425078	+	0.533031i	−0.522465	+	0.852661i	$0.674987\pi$
$74$	−14.0584	−	17.6287i	−1.63425	−	2.04929i
$75$		0			0
$76$	3.91519	+	17.1536i	0.449104	+	1.96765i
$77$	3.91282	+	9.89292i	0.445907	+	1.12740i
$78$		0			0
$79$	−15.8711			−1.78564			−0.892818	−	0.450417i	$-0.851275\pi$
$79$	−15.8711			−1.78564			−0.892818	+	0.450417i	$0.851275\pi$
$80$	33.4965			3.74502
$81$		0			0
$82$	5.13976	−	2.47518i	0.567592	−	0.273338i
$83$	1.57731	+	1.97788i	0.173132	+	0.217101i	0.860825	−	0.508901i	$-0.169948\pi$
$83$	1.57731	+	1.97788i	0.173132	+	0.217101i	−0.687693	+	0.726001i	$0.741377\pi$
$84$		0			0
$85$	5.38858	−	6.75706i	0.584473	−	0.732906i
$86$	4.44618	−	19.4800i	0.479444	−	2.10058i
$87$		0			0
$88$	−29.6660	+	14.2864i	−3.16241	+	1.52294i
$89$	−3.41131	−	4.27764i	−0.361598	−	0.453429i	0.567440	−	0.823415i	$-0.307934\pi$
$89$	−3.41131	−	4.27764i	−0.361598	−	0.453429i	−0.929037	+	0.369986i	$0.879363\pi$
$90$		0			0
$91$	3.60128	+	9.10524i	0.377516	+	0.954488i
$92$	−5.23487	+	2.52098i	−0.545773	+	0.262830i
$93$		0			0
$94$	0.533956	+	2.33942i	0.0550734	+	0.241292i
$95$	8.99166	+	4.33015i	0.922525	+	0.444264i
$96$		0			0
$97$	−2.32328			−0.235893			−0.117946	−	0.993020i	$-0.537631\pi$
$97$	−2.32328			−0.235893			−0.117946	+	0.993020i	$0.537631\pi$
$98$	−18.4295	−	2.67848i	−1.86166	−	0.270568i
$99$		0			0
$100$	10.4354	−	13.0855i	1.04354	−	1.30855i
$101$	−0.908725	−	0.437619i	−0.0904215	−	0.0435447i	0.388126	−	0.921606i	$-0.373122\pi$
$101$	−0.908725	−	0.437619i	−0.0904215	−	0.0435447i	−0.478548	+	0.878061i	$0.658837\pi$
$102$		0			0
$103$	0.207124	+	0.0997454i	0.0204085	+	0.00982821i	0.444060	−	0.895997i	$-0.353538\pi$
$103$	0.207124	+	0.0997454i	0.0204085	+	0.00982821i	−0.423652	+	0.905825i	$0.639252\pi$
$104$	−27.3040	+	13.1489i	−2.67738	+	1.28936i
$105$		0			0
$106$	4.40622	+	2.12192i	0.427969	+	0.206099i
$107$	4.52805	+	5.67799i	0.437743	+	0.548912i	0.950947	−	0.309355i	$-0.100113\pi$
$107$	4.52805	+	5.67799i	0.437743	+	0.548912i	−0.513204	+	0.858267i	$0.671542\pi$
$108$		0			0
$109$	−2.28381	+	2.86381i	−0.218750	+	0.274303i	−0.879082	−	0.476670i	$-0.841844\pi$
$109$	−2.28381	+	2.86381i	−0.218750	+	0.274303i	0.660333	+	0.750973i	$0.270415\pi$
$110$	−6.85639	+	30.0398i	−0.653731	+	2.86418i
$111$		0			0
$112$	2.21847	−	30.6889i	0.209625	−	2.89983i
$113$	6.10535	+	7.65587i	0.574343	+	0.720204i	0.981136	−	0.193317i	$-0.0619245\pi$
$113$	6.10535	+	7.65587i	0.574343	+	0.720204i	−0.406793	+	0.913520i	$0.633353\pi$
$114$		0			0
$115$	−0.733356	+	3.21304i	−0.0683858	+	0.299618i
$116$	−19.0863			−1.77212
$117$		0			0
$118$	−2.40777	+	10.5491i	−0.221653	+	0.971125i
$119$	−5.83382	−	5.38444i	−0.534786	−	0.493591i
$120$		0			0
$121$	−1.15012	−	5.03900i	−0.104556	−	0.458091i
$122$	3.09907	+	3.88611i	0.280577	+	0.351832i
$123$		0			0
$124$	−8.66232	−	37.9521i	−0.777899	−	3.40820i
$125$	1.09212	+	4.78487i	0.0976819	+	0.427972i
$126$		0			0
$127$	−1.73721	+	7.61121i	−0.154152	+	0.675386i	0.837499	+	0.546439i	$0.184017\pi$
$127$	−1.73721	+	7.61121i	−0.154152	+	0.675386i	−0.991651	+	0.128947i	$0.958840\pi$
$128$	12.0677			1.06665
$129$		0			0
$130$	−6.31047	+	27.6480i	−0.553465	+	2.42489i
$131$	18.2999	−	8.81275i	1.59887	−	0.769974i	0.599333	−	0.800500i	$-0.295433\pi$
$131$	18.2999	−	8.81275i	1.59887	−	0.769974i	0.999534	+	0.0305261i	$0.00971826\pi$
$132$		0			0
$133$	4.56273	−	7.95122i	0.395639	−	0.689458i
$134$	23.4459	−	29.4003i	2.02542	−	2.53979i
$135$		0			0
$136$	15.3198	−	19.2104i	1.31366	−	1.64728i
$137$	−0.798532	+	0.384553i	−0.0682232	+	0.0328546i	−0.467684	−	0.883896i	$-0.654912\pi$
$137$	−0.798532	+	0.384553i	−0.0682232	+	0.0328546i	0.399461	+	0.916750i	$0.369197\pi$
$138$		0			0
$139$	0.124193	+	0.0598082i	0.0105339	+	0.00507286i	0.439143	−	0.898417i	$-0.355282\pi$
$139$	0.124193	+	0.0598082i	0.0105339	+	0.00507286i	−0.428609	+	0.903490i	$0.640996\pi$
$140$	−28.4358	−	26.2454i	−2.40327	−	2.21814i
$141$		0			0
$142$	33.9402	+	16.3447i	2.84820	+	1.37162i
$143$	−3.31138	−	14.5081i	−0.276912	−	1.21323i
$144$		0			0
$145$	−6.74992	+	8.46413i	−0.560550	+	0.702908i
$146$	15.4972			1.28256
$147$		0			0
$148$	−43.0368			−3.53761
$149$	−1.83947	+	2.30662i	−0.150695	+	0.188966i	−0.851449	−	0.524437i	$-0.824276\pi$
$149$	−1.83947	+	2.30662i	−0.150695	+	0.188966i	0.700754	+	0.713403i	$0.252847\pi$
$150$		0			0
$151$	−0.775385	−	3.39718i	−0.0630999	−	0.276459i	0.933529	−	0.358502i	$-0.116712\pi$
$151$	−0.775385	−	3.39718i	−0.0630999	−	0.276459i	−0.996629	+	0.0820435i	$0.973855\pi$
$152$	25.5634	+	12.3107i	2.07346	+	0.998527i
$153$		0			0
$154$	27.0678	+	8.27123i	2.18119	+	0.666515i
$155$	−19.8939	−	9.58041i	−1.59792	−	0.769517i
$156$		0			0
$157$	−18.5079	+	8.91293i	−1.47709	+	0.711329i	−0.987056	−	0.160374i	$-0.948730\pi$
$157$	−18.5079	+	8.91293i	−1.47709	+	0.711329i	−0.490034	+	0.871703i	$0.663016\pi$
$158$	−26.3263	+	33.0121i	−2.09441	+	2.62630i
$159$		0			0
$160$	26.1517	−	32.7932i	2.06747	−	2.59253i
$161$	2.89516	+	0.884687i	0.228171	+	0.0697231i
$162$		0			0
$163$	−0.982255	+	0.473029i	−0.0769361	+	0.0370505i	−0.471956	−	0.881622i	$-0.656452\pi$
$163$	−0.982255	+	0.473029i	−0.0769361	+	0.0370505i	0.395020	+	0.918673i	$0.370738\pi$
$164$	2.42291	−	10.6155i	0.189198	−	0.828930i
$165$		0			0
$166$	6.73039			0.522380
$167$	5.59553	−	24.5156i	0.432995	−	1.89707i	−0.00880696	−	0.999961i	$-0.502803\pi$
$167$	5.59553	−	24.5156i	0.432995	−	1.89707i	0.441802	−	0.897113i	$-0.354339\pi$
$168$		0			0
$169$	−0.154956	−	0.678907i	−0.0119197	−	0.0522236i
$170$	−5.11645	−	22.4167i	−0.392414	−	1.71928i
$171$		0			0
$172$	−23.7782	−	29.8170i	−1.81307	−	2.27352i
$173$	−1.20176	−	5.26526i	−0.0913683	−	0.400311i	0.908476	−	0.417936i	$-0.137246\pi$
$173$	−1.20176	−	5.26526i	−0.0913683	−	0.400311i	−0.999845	+	0.0176256i	$0.994389\pi$
$174$		0			0
$175$	−8.61961	+	1.32245i	−0.651581	+	0.0999677i
$176$	−10.4057	+	45.5903i	−0.784359	+	3.43650i
$177$		0			0
$178$	−14.5561			−1.09102
$179$	1.62485	−	7.11895i	0.121447	−	0.532095i	−0.877201	−	0.480123i	$-0.840592\pi$
$179$	1.62485	−	7.11895i	0.121447	−	0.532095i	0.998649	−	0.0519722i	$-0.0165507\pi$
$180$		0			0
$181$	−5.62035	−	7.04770i	−0.417758	−	0.523851i	0.527773	−	0.849386i	$-0.323027\pi$
$181$	−5.62035	−	7.04770i	−0.417758	−	0.523851i	−0.945530	+	0.325534i	$0.894456\pi$
$182$	24.9127	+	7.61267i	1.84665	+	0.564289i
$183$		0			0
$184$	−2.08494	+	9.13471i	−0.153704	+	0.673420i
$185$	−15.2201	+	19.0854i	−1.11900	+	1.40319i
$186$		0			0
$187$	7.52272	+	9.43320i	0.550116	+	0.689824i
$188$	4.12647	+	1.98720i	0.300954	+	0.144932i
$189$		0			0
$190$	23.9218	−	11.5201i	1.73547	−	0.835757i
$191$	14.3148	+	6.89366i	1.03579	+	0.498808i	0.872932	−	0.487842i	$-0.162216\pi$
$191$	14.3148	+	6.89366i	1.03579	+	0.498808i	0.162854	+	0.986650i	$0.447930\pi$
$192$		0			0
$193$	20.1002	+	9.67977i	1.44685	+	0.696765i	0.982044	−	0.188650i	$-0.0604110\pi$
$193$	20.1002	+	9.67977i	1.44685	+	0.696765i	0.464803	+	0.885414i	$0.346125\pi$
$194$	−3.85375	+	4.83245i	−0.276683	+	0.346950i
$195$		0			0
$196$	−25.9289	+	24.3142i	−1.85206	+	1.73673i
$197$	−6.84526			−0.487705			−0.243852	−	0.969812i	$-0.578411\pi$
$197$	−6.84526			−0.487705			−0.243852	+	0.969812i	$0.578411\pi$
$198$		0			0
$199$	5.08353	+	2.44810i	0.360362	+	0.173541i	0.605300	−	0.795998i	$-0.293053\pi$
$199$	5.08353	+	2.44810i	0.360362	+	0.173541i	−0.244938	+	0.969539i	$0.578768\pi$
$200$	−6.00586	−	26.3134i	−0.424678	−	1.86064i
$201$		0			0
$202$	−2.41761	+	1.16426i	−0.170102	+	0.0819169i
$203$	7.30764	+	6.74474i	0.512896	+	0.473388i
$204$		0			0
$205$	−3.85074	−	4.82867i	−0.268947	−	0.337249i
$206$	0.551040	−	0.265367i	0.0383928	−	0.0184890i
$207$		0			0
$208$	−9.57719	+	41.9604i	−0.664058	+	2.90943i
$209$	−8.68681	+	10.8929i	−0.600879	+	0.753479i
$210$		0			0
$211$	−5.68743	−	7.13181i	−0.391539	−	0.490974i	0.546522	−	0.837445i	$-0.315951\pi$
$211$	−5.68743	−	7.13181i	−0.391539	−	0.490974i	−0.938061	+	0.346471i	$0.887380\pi$
$212$	8.41007	−	4.05008i	0.577606	−	0.278161i
$213$		0			0
$214$	19.3212			1.32077
$215$	−21.6321			−1.47529
$216$		0			0
$217$	−10.0950	+	17.5920i	−0.685292	+	1.19422i
$218$	2.16848	+	9.50074i	0.146868	+	0.643471i
$219$		0			0
$220$	36.6681	+	45.9803i	2.47216	+	3.09999i
$221$	6.92376	+	8.68212i	0.465742	+	0.584022i
$222$		0			0
$223$	−2.15088	−	9.42362i	−0.144034	−	0.631053i	−0.994474	−	0.104981i	$-0.966522\pi$
$223$	−2.15088	−	9.42362i	−0.144034	−	0.631053i	0.850441	−	0.526071i	$-0.176335\pi$
$224$	−28.3125	−	26.1316i	−1.89171	−	1.74599i
$225$		0			0
$226$	26.0516			1.73293
$227$	21.7006			1.44032			0.720159	−	0.693809i	$-0.244069\pi$
$227$	21.7006			1.44032			0.720159	+	0.693809i	$0.244069\pi$
$228$		0			0
$229$	−11.2613	+	5.42316i	−0.744168	+	0.358372i	−0.767239	−	0.641362i	$-0.778370\pi$
$229$	−11.2613	+	5.42316i	−0.744168	+	0.358372i	0.0230711	+	0.999734i	$0.492656\pi$
$230$	5.46672	+	6.85505i	0.360465	+	0.452008i
$231$		0			0
$232$	−19.1901	+	24.0636i	−1.25989	+	1.57985i
$233$	−5.51258	+	24.1522i	−0.361141	+	1.58226i	0.389163	+	0.921169i	$0.372764\pi$
$233$	−5.51258	+	24.1522i	−0.361141	+	1.58226i	−0.750304	+	0.661093i	$0.770093\pi$
$234$		0			0
$235$	2.34059	−	1.12717i	0.152684	−	0.0735285i
$236$	12.8768	+	16.1470i	0.838206	+	1.05108i
$237$		0			0
$238$	−20.8766	+	3.20296i	−1.35323	+	0.207617i
$239$	10.7308	−	5.16768i	0.694118	−	0.334270i	−0.0533421	−	0.998576i	$-0.516987\pi$
$239$	10.7308	−	5.16768i	0.694118	−	0.334270i	0.747460	+	0.664307i	$0.231273\pi$
$240$		0			0
$241$	4.09789	+	17.9540i	0.263968	+	1.15652i	0.916904	+	0.399108i	$0.130680\pi$
$241$	4.09789	+	17.9540i	0.263968	+	1.15652i	−0.652935	+	0.757414i	$0.726463\pi$
$242$	−12.3890	−	5.96621i	−0.796392	−	0.383522i
$243$		0			0
$244$	9.48716			0.607353
$245$	1.61270	+	20.0974i	0.103032	+	1.28397i
$246$		0			0
$247$	−7.99516	+	10.0256i	−0.508720	+	0.637914i
$248$	−56.5587	−	27.2372i	−3.59148	−	1.72956i
$249$		0			0
$250$	11.7642	+	5.66533i	0.744031	+	0.358307i
$251$	−24.6974	+	11.8936i	−1.55888	+	0.750718i	−0.997066	−	0.0765432i	$-0.975612\pi$
$251$	−24.6974	+	11.8936i	−1.55888	+	0.750718i	−0.561817	+	0.827262i	$0.689897\pi$
$252$		0			0
$253$	−4.14529	−	1.99626i	−0.260612	−	0.125504i
$254$	12.9498	+	16.2386i	0.812545	+	1.01890i
$255$		0			0
$256$	0.709936	−	0.890232i	0.0443710	−	0.0556395i
$257$	5.69646	−	24.9578i	0.355335	−	1.55683i	−0.409323	−	0.912389i	$-0.634235\pi$
$257$	5.69646	−	24.9578i	0.355335	−	1.55683i	0.764659	−	0.644436i	$-0.222908\pi$
$258$		0			0
$259$	16.4777	+	15.2084i	1.02387	+	0.945004i
$260$	33.7485	+	42.3193i	2.09299	+	2.62453i
$261$		0			0
$262$	12.0244	−	52.6822i	0.742868	−	3.25472i
$263$	1.53540			0.0946767			0.0473383	−	0.998879i	$-0.484926\pi$
$263$	1.53540			0.0946767			0.0473383	+	0.998879i	$0.484926\pi$
$264$		0			0
$265$	1.17817	−	5.16191i	0.0723745	−	0.317093i
$266$	−8.97020	−	22.6797i	−0.549998	−	1.39058i
$267$		0			0
$268$	−15.9714	−	69.9753i	−0.975608	−	4.27442i
$269$	−3.23330	−	4.05443i	−0.197138	−	0.247203i	0.673430	−	0.739251i	$-0.264820\pi$
$269$	−3.23330	−	4.05443i	−0.197138	−	0.247203i	−0.870568	+	0.492047i	$0.836249\pi$
$270$		0			0
$271$	−6.77944	−	29.7027i	−0.411822	−	1.80431i	−0.575509	−	0.817796i	$-0.695196\pi$
$271$	−6.77944	−	29.7027i	−0.411822	−	1.80431i	0.163687	−	0.986512i	$-0.447661\pi$
$272$	−7.76506	−	34.0210i	−0.470826	−	2.06282i
$273$		0			0
$274$	−0.524695	+	2.29884i	−0.0316980	+	0.138878i
$275$	13.2534			0.799209
$276$		0			0
$277$	5.13940	−	22.5172i	0.308797	−	1.35293i	−0.547657	−	0.836703i	$-0.684480\pi$
$277$	5.13940	−	22.5172i	0.308797	−	1.35293i	0.856454	−	0.516224i	$-0.172663\pi$
$278$	0.330408	−	0.159116i	0.0198165	−	0.00954315i
$279$		0			0
$280$	−61.6801	+	9.46317i	−3.68609	+	0.565533i
$281$	−14.4045	+	18.0626i	−0.859298	+	1.07753i	0.136915	+	0.990583i	$0.456281\pi$
$281$	−14.4045	+	18.0626i	−0.859298	+	1.07753i	−0.996213	+	0.0869428i	$0.972290\pi$
$282$		0			0
$283$	7.64664	−	9.58859i	0.454546	−	0.569982i	−0.500766	−	0.865583i	$-0.666948\pi$
$283$	7.64664	−	9.58859i	0.454546	−	0.569982i	0.955312	+	0.295600i	$0.0955197\pi$
$284$	64.7811	−	31.1969i	3.84405	−	1.85120i
$285$		0			0
$286$	−35.6699	−	17.1777i	−2.10921	−	1.01574i
$287$	−4.67898	+	3.20818i	−0.276192	+	0.189373i
$288$		0			0
$289$	7.20444	+	3.46948i	0.423791	+	0.204087i
$290$	6.40905	+	28.0799i	0.376352	+	1.64891i
$291$		0			0
$292$	18.4424	−	23.1260i	1.07926	−	1.35335i
$293$	−4.50322			−0.263081			−0.131540	−	0.991311i	$-0.541992\pi$
$293$	−4.50322			−0.263081			−0.131540	+	0.991311i	$0.541992\pi$
$294$		0			0
$295$	11.7145			0.682047
$296$	−43.2709	+	54.2600i	−2.51507	+	3.15380i
$297$		0			0
$298$	1.74658	+	7.65225i	0.101176	+	0.443283i
$299$	−3.81523	−	1.83732i	−0.220641	−	0.106255i
$300$		0			0
$301$	−1.43269	+	19.8189i	−0.0825787	+	1.14234i
$302$	−8.35237	−	4.02229i	−0.480625	−	0.231457i
$303$		0			0
$304$	36.3052	−	17.4837i	2.08225	−	1.00276i
$305$	3.35516	−	4.20724i	0.192116	−	0.240906i
$306$		0			0
$307$	−2.89816	+	3.63418i	−0.165407	+	0.207413i	−0.857626	−	0.514274i	$-0.828062\pi$
$307$	−2.89816	+	3.63418i	−0.165407	+	0.207413i	0.692219	+	0.721687i	$0.256633\pi$
$308$	44.5549	−	30.5494i	2.53875	−	1.74071i
$309$		0			0
$310$	−52.9266	+	25.4881i	−3.00603	+	1.44763i
$311$	6.78041	−	29.7069i	0.384482	−	1.68453i	−0.298756	−	0.954330i	$-0.596572\pi$
$311$	6.78041	−	29.7069i	0.384482	−	1.68453i	0.683238	−	0.730196i	$-0.260571\pi$
$312$		0			0
$313$	17.7660			1.00419			0.502096	−	0.864812i	$-0.332562\pi$
$313$	17.7660			1.00419			0.502096	+	0.864812i	$0.332562\pi$
$314$	−12.1611	+	53.2811i	−0.686288	+	3.00683i
$315$		0			0
$316$	17.9335	+	78.5718i	1.00884	+	4.42001i
$317$	−5.26916	−	23.0857i	−0.295945	−	1.29662i	−0.876106	−	0.482119i	$-0.839867\pi$
$317$	−5.26916	−	23.0857i	−0.295945	−	1.29662i	0.580160	−	0.814502i	$-0.302990\pi$
$318$		0			0
$319$	−9.42322	−	11.8163i	−0.527599	−	0.661588i
$320$	−9.92368	−	43.4785i	−0.554750	−	2.43052i
$321$		0			0
$322$	6.64253	−	4.55450i	0.370174	−	0.253813i
$323$	2.31353	−	10.1362i	0.128728	−	0.563996i
$324$		0			0
$325$	12.1981			0.676631
$326$	−0.645414	+	2.82774i	−0.0357462	+	0.156614i
$327$		0			0
$328$	−10.9477	−	13.7280i	−0.604485	−	0.758000i
$329$	−0.877678	−	2.21907i	−0.0483879	−	0.122341i
$330$		0			0
$331$	−4.81818	+	21.1098i	−0.264831	+	1.16030i	0.651108	+	0.758985i	$0.274304\pi$
$331$	−4.81818	+	21.1098i	−0.264831	+	1.16030i	−0.915940	+	0.401316i	$0.868553\pi$
$332$	8.00947	−	10.0436i	0.439577	−	0.551212i
$333$		0			0
$334$	−41.7112	−	52.3042i	−2.28234	−	2.86196i
$335$	−36.6800	−	17.6642i	−2.00404	−	0.965096i
$336$		0			0
$337$	13.9038	−	6.69571i	0.757387	−	0.364739i	−0.0150023	−	0.999887i	$-0.504776\pi$
$337$	13.9038	−	6.69571i	0.757387	−	0.364739i	0.772390	+	0.635149i	$0.219061\pi$
$338$	−1.66917	−	0.803831i	−0.0907910	−	0.0437226i
$339$		0			0
$340$	−39.5405	−	19.0417i	−2.14438	−	1.03268i
$341$	19.2195	−	24.1004i	1.04079	−	1.30511i
$342$		0			0
$343$	18.5197	−	0.146486i	0.999969	−	0.00790951i
$344$	−61.5002			−3.31587
$345$		0			0
$346$	−12.9453	−	6.23411i	−0.695942	−	0.335148i
$347$	3.44808	+	15.1070i	0.185103	+	0.810988i	0.979151	+	0.203133i	$0.0651125\pi$
$347$	3.44808	+	15.1070i	0.185103	+	0.810988i	−0.794048	+	0.607855i	$0.792030\pi$
$348$		0			0
$349$	−27.3427	+	13.1676i	−1.46362	+	0.704844i	−0.984900	−	0.173123i	$-0.944614\pi$
$349$	−27.3427	+	13.1676i	−1.46362	+	0.704844i	−0.478722	+	0.877966i	$0.658900\pi$
$350$	−11.5471	+	20.1225i	−0.617220	+	1.07559i
$351$		0			0
$352$	36.5091	+	45.7809i	1.94594	+	2.44013i
$353$	−13.5855	+	6.54244i	−0.723084	+	0.348219i	−0.758960	−	0.651137i	$-0.774292\pi$
$353$	−13.5855	+	6.54244i	−0.723084	+	0.348219i	0.0358761	+	0.999356i	$0.488578\pi$
$354$		0			0
$355$	9.07521	−	39.7611i	0.481662	−	2.11030i
$356$	−17.3224	+	21.7216i	−0.918086	+	1.15124i
$357$		0			0
$358$	−12.1123	−	15.1883i	−0.640154	−	0.802728i
$359$	−1.09889	+	0.529198i	−0.0579973	+	0.0279300i	−0.462658	−	0.886537i	$-0.653104\pi$
$359$	−1.09889	+	0.529198i	−0.0579973	+	0.0279300i	0.404660	+	0.914467i	$0.367390\pi$
$360$		0			0
$361$	−6.99423			−0.368118
$362$	−23.9821			−1.26047
$363$		0			0
$364$	41.0074	−	28.1170i	2.14937	−	1.47373i
$365$	−3.73342	−	16.3572i	−0.195416	−	0.856173i
$366$		0			0
$367$	−5.62908	−	7.05865i	−0.293836	−	0.368458i	0.612898	−	0.790162i	$-0.290004\pi$
$367$	−5.62908	−	7.05865i	−0.293836	−	0.368458i	−0.906734	+	0.421704i	$0.861432\pi$
$368$	8.29664	+	10.4037i	0.432492	+	0.542328i
$369$		0			0
$370$	14.4515	+	63.3160i	0.751296	+	3.29164i
$371$	−4.65122	−	1.42129i	−0.241479	−	0.0737898i
$372$		0			0
$373$	−19.9112			−1.03096			−0.515482	−	0.856901i	$-0.672387\pi$
$373$	−19.9112			−1.03096			−0.515482	+	0.856901i	$0.672387\pi$
$374$	32.0996			1.65983
$375$		0			0
$376$	6.65434	−	3.20456i	0.343171	−	0.165263i
$377$	−8.67293	−	10.8755i	−0.446679	−	0.560118i
$378$		0			0
$379$	9.70166	−	12.1655i	0.498341	−	0.624899i	−0.467513	−	0.883986i	$-0.654850\pi$
$379$	9.70166	−	12.1655i	0.498341	−	0.624899i	0.965854	+	0.259087i	$0.0834215\pi$
$380$	11.2769	−	49.4072i	0.578491	−	2.53453i
$381$		0			0
$382$	38.0838	−	18.3402i	1.94854	−	0.938365i
$383$	7.99290	+	10.0228i	0.408418	+	0.512140i	0.942916	−	0.333029i	$-0.108071\pi$
$383$	7.99290	+	10.0228i	0.408418	+	0.512140i	−0.534498	+	0.845170i	$0.679499\pi$
$384$		0			0
$385$	2.20932	−	30.5625i	0.112598	−	1.55761i
$386$	53.4755	−	25.7524i	2.72183	−	1.31076i
$387$		0			0
$388$	2.62518	+	11.5017i	0.133273	+	0.583909i
$389$	20.4686	+	9.85717i	1.03780	+	0.499778i	0.873598	−	0.486648i	$-0.161781\pi$
$389$	20.4686	+	9.85717i	1.03780	+	0.499778i	0.164202	+	0.986427i	$0.447495\pi$
$390$		0			0
$391$	3.43335			0.173632
$392$	4.58493	+	57.1370i	0.231574	+	2.88586i
$393$		0			0
$394$	−11.3546	+	14.2382i	−0.572038	+	0.717313i
$395$	41.1862	+	19.8342i	2.07230	+	0.997967i
$396$		0			0
$397$	−14.3541	−	6.91255i	−0.720410	−	0.346931i	0.0374944	−	0.999297i	$-0.488062\pi$
$397$	−14.3541	−	6.91255i	−0.720410	−	0.346931i	−0.757904	+	0.652366i	$0.773777\pi$
$398$	13.5244	−	6.51302i	0.677919	−	0.326468i
$399$		0			0
$400$	−34.5354	−	16.6314i	−1.72677	−	0.831569i
$401$	−16.6231	−	20.8447i	−0.830116	−	1.04093i	−0.998475	−	0.0552072i	$-0.982418\pi$
$401$	−16.6231	−	20.8447i	−0.830116	−	1.04093i	0.168359	−	0.985726i	$-0.446153\pi$
$402$		0			0
$403$	17.6892	−	22.1815i	0.881161	−	1.10494i
$404$	−1.13968	+	4.99324i	−0.0567010	+	0.248423i
$405$		0			0
$406$	26.1508	−	4.01214i	1.29784	−	0.199119i
$407$	−21.2480	−	26.6442i	−1.05322	−	1.32070i
$408$		0			0
$409$	−8.11310	+	35.5458i	−0.401167	+	1.75763i	0.221520	+	0.975156i	$0.428898\pi$
$409$	−8.11310	+	35.5458i	−0.401167	+	1.75763i	−0.622687	+	0.782471i	$0.713959\pi$
$410$	−16.4312			−0.811477
$411$		0			0
$412$	0.259763	−	1.13810i	0.0127976	−	0.0560701i
$413$	0.775851	−	10.7327i	0.0381771	−	0.528120i
$414$		0			0
$415$	−1.62141	−	7.10386i	−0.0795919	−	0.348715i
$416$	33.6022	+	42.1358i	1.64748	+	2.06588i
$417$		0			0
$418$	8.24812	+	36.1374i	0.403429	+	1.76754i
$419$	1.17677	+	5.15575i	0.0574888	+	0.251875i	0.995504	−	0.0947191i	$-0.0301953\pi$
$419$	1.17677	+	5.15575i	0.0574888	+	0.251875i	−0.938015	+	0.346594i	$0.887338\pi$
$420$		0			0
$421$	−5.03840	+	22.0747i	−0.245557	+	1.07585i	0.690314	+	0.723510i	$0.257472\pi$
$421$	−5.03840	+	22.0747i	−0.245557	+	1.07585i	−0.935871	+	0.352344i	$0.885385\pi$
$422$	−24.2683			−1.18136
$423$		0			0
$424$	3.34955	−	14.6754i	0.162669	−	0.712698i
$425$	−8.91067	+	4.29115i	−0.432231	+	0.208151i
$426$		0			0
$427$	−3.63239	−	3.35259i	−0.175784	−	0.162243i
$428$	22.9932	−	28.8325i	1.11142	−	1.39367i
$429$		0			0
$430$	−35.8823	+	44.9950i	−1.73040	+	2.16985i
$431$	−3.53059	+	1.70024i	−0.170062	+	0.0818977i	−0.516978	−	0.855999i	$-0.672943\pi$
$431$	−3.53059	+	1.70024i	−0.170062	+	0.0818977i	0.346916	+	0.937896i	$0.387229\pi$
$432$		0			0
$433$	17.2301	+	8.29756i	0.828023	+	0.398755i	0.799374	−	0.600834i	$-0.205165\pi$
$433$	17.2301	+	8.29756i	0.828023	+	0.398755i	0.0286500	+	0.999590i	$0.490879\pi$
$434$	19.8465	+	50.1785i	0.952660	+	2.40865i
$435$		0			0
$436$	16.7582	+	8.07035i	0.802575	+	0.386500i
$437$	0.882215	+	3.86524i	0.0422021	+	0.184899i
$438$		0			0
$439$	8.27084	−	10.3713i	0.394746	−	0.494995i	−0.544251	−	0.838923i	$-0.683186\pi$
$439$	8.27084	−	10.3713i	0.394746	−	0.494995i	0.938996	+	0.343927i	$0.111757\pi$
$440$	94.8385			4.52125
$441$		0			0
$442$	29.5438			1.40525
$443$	11.5596	−	14.4952i	0.549212	−	0.688689i	−0.427311	−	0.904105i	$-0.640539\pi$
$443$	11.5596	−	14.4952i	0.549212	−	0.688689i	0.976523	+	0.215415i	$0.0691105\pi$
$444$		0			0
$445$	3.50669	+	15.3638i	0.166233	+	0.728314i
$446$	−23.1691	−	11.1576i	−1.09709	−	0.528329i
$447$		0			0
$448$	−40.4915	+	6.21233i	−1.91304	+	0.293505i
$449$	−5.88855	−	2.83577i	−0.277898	−	0.133828i	0.289744	−	0.957104i	$-0.406430\pi$
$449$	−5.88855	−	2.83577i	−0.277898	−	0.133828i	−0.567642	+	0.823276i	$0.692144\pi$
$450$		0			0
$451$	7.76829	−	3.74101i	0.365794	−	0.176157i
$452$	31.0026	−	38.8760i	1.45824	−	1.82857i
$453$		0			0
$454$	35.9960	−	45.1375i	1.68937	−	2.11841i
$455$	2.03342	−	28.1290i	0.0953280	−	1.31871i
$456$		0			0
$457$	−4.55672	+	2.19440i	−0.213155	+	0.102650i	−0.537415	−	0.843318i	$-0.680599\pi$
$457$	−4.55672	+	2.19440i	−0.213155	+	0.102650i	0.324260	+	0.945968i	$0.394885\pi$
$458$	−7.39951	+	32.4194i	−0.345756	+	1.51486i
$459$		0			0
$460$	16.7352			0.780283
$461$	−2.70399	+	11.8470i	−0.125937	+	0.551768i	0.872110	+	0.489309i	$0.162751\pi$
$461$	−2.70399	+	11.8470i	−0.125937	+	0.551768i	−0.998048	+	0.0624582i	$0.980106\pi$
$462$		0			0
$463$	−1.69480	−	7.42539i	−0.0787639	−	0.345087i	0.920156	−	0.391552i	$-0.128062\pi$
$463$	−1.69480	−	7.42539i	−0.0787639	−	0.345087i	−0.998920	+	0.0464647i	$0.985205\pi$
$464$	9.72678	+	42.6158i	0.451555	+	1.97839i
$465$		0			0
$466$	41.0929	+	51.5289i	1.90359	+	2.38703i
$467$	3.39195	+	14.8611i	0.156961	+	0.687689i	0.990761	+	0.135623i	$0.0433035\pi$
$467$	3.39195	+	14.8611i	0.156961	+	0.687689i	−0.833800	+	0.552067i	$0.813839\pi$
$468$		0			0
$469$	−18.6129	+	32.4357i	−0.859464	+	1.49774i
$470$	1.53794	−	6.73818i	0.0709401	−	0.310809i
$471$		0			0
$472$	33.3046			1.53297
$473$	6.72000	−	29.4423i	0.308986	−	1.35376i
$474$		0			0
$475$	−7.12057	−	8.92891i	−0.326714	−	0.409687i
$476$	−20.0644	+	34.9652i	−0.919652	+	1.60263i
$477$		0			0
$478$	7.05094	−	30.8922i	0.322502	−	1.41298i
$479$	−15.4807	+	19.4121i	−0.707329	+	0.886963i	−0.997547	−	0.0699980i	$-0.977701\pi$
$479$	−15.4807	+	19.4121i	−0.707329	+	0.886963i	0.290218	+	0.956961i	$0.406272\pi$
$480$		0			0
$481$	−19.5562	−	24.5227i	−0.891687	−	1.11814i
$482$	44.1421	+	21.2577i	2.01062	+	0.968262i
$483$		0			0
$484$	−23.6466	+	11.3876i	−1.07485	+	0.517618i
$485$	6.02901	+	2.90342i	0.273763	+	0.131837i
$486$		0			0
$487$	−12.5173	−	6.02804i	−0.567215	−	0.273156i	0.128219	−	0.991746i	$-0.459074\pi$
$487$	−12.5173	−	6.02804i	−0.567215	−	0.273156i	−0.695435	+	0.718589i	$0.744788\pi$
$488$	9.53876	−	11.9612i	0.431799	−	0.541459i
$489$		0			0
$490$	44.4779	+	29.9822i	2.00931	+	1.35446i
$491$	31.8031			1.43526			0.717628	−	0.696427i	$-0.245228\pi$
$491$	31.8031			1.43526			0.717628	+	0.696427i	$0.245228\pi$
$492$		0			0
$493$	10.1614	+	4.89347i	0.457646	+	0.220391i
$494$	7.59140	+	33.2601i	0.341553	+	1.49644i
$495$		0			0
$496$	−80.3249	+	38.6824i	−3.60669	+	1.73689i
$497$	−35.8274	−	10.9479i	−1.60708	−	0.491081i
$498$		0			0
$499$	4.58315	+	5.74709i	0.205170	+	0.257275i	0.873761	−	0.486355i	$-0.161674\pi$
$499$	4.58315	+	5.74709i	0.205170	+	0.257275i	−0.668591	+	0.743630i	$0.733102\pi$
$500$	22.4541	−	10.8133i	1.00418	−	0.483586i
$501$		0			0
$502$	−16.2280	+	71.0995i	−0.724291	+	3.17333i
$503$	2.34236	−	2.93723i	0.104441	−	0.130965i	−0.726864	−	0.686781i	$-0.759023\pi$
$503$	2.34236	−	2.93723i	0.104441	−	0.130965i	0.831305	+	0.555817i	$0.187594\pi$
$504$		0			0
$505$	1.81129	+	2.27128i	0.0806012	+	0.101071i
$506$	−11.0283	+	5.31094i	−0.490267	+	0.236100i
$507$		0			0
$508$	39.6432			1.75888
$509$	10.8158			0.479403			0.239701	−	0.970847i	$-0.422950\pi$
$509$	10.8158			0.479403			0.239701	+	0.970847i	$0.422950\pi$
$510$		0			0
$511$	−15.2334	+	2.33716i	−0.673887	+	0.103390i
$512$	4.69656	+	20.5770i	0.207561	+	0.909383i
$513$		0			0
$514$	−42.4636	−	53.2477i	−1.87299	−	2.34865i
$515$	−0.412842	−	0.517688i	−0.0181920	−	0.0228120i
$516$		0			0
$517$	0.807027	+	3.53582i	0.0354930	+	0.155505i
$518$	58.9662	−	9.04679i	2.59083	−	0.397493i
$519$		0			0
$520$	87.2873			3.82780
$521$	9.23743			0.404699			0.202350	−	0.979313i	$-0.435142\pi$
$521$	9.23743			0.404699			0.202350	+	0.979313i	$0.435142\pi$
$522$		0			0
$523$	−3.10970	+	1.49755i	−0.135978	+	0.0654834i	−0.500635	−	0.865658i	$-0.666900\pi$
$523$	−3.10970	+	1.49755i	−0.135978	+	0.0654834i	0.364658	+	0.931142i	$0.381186\pi$
$524$	−64.3065	−	80.6378i	−2.80924	−	3.52268i
$525$		0			0
$526$	2.54685	−	3.19365i	0.111048	−	0.139250i
$527$	−5.11866	+	22.4263i	−0.222972	+	0.976906i
$528$		0			0
$529$	19.5427	−	9.41127i	0.849683	−	0.409186i
$530$	−8.78254	−	11.0130i	−0.381489	−	0.478373i
$531$		0			0
$532$	−44.5191	−	13.6039i	−1.93015	−	0.589804i
$533$	7.14977	−	3.44315i	0.309691	−	0.149139i
$534$		0			0
$535$	−4.65466	−	20.3934i	−0.201238	−	0.881683i
$536$	−104.282	−	50.2194i	−4.50428	−	2.16915i
$537$		0			0
$538$	−13.7965			−0.594811
$539$	−27.8545	−	4.04829i	−1.19978	−	0.174372i
$540$		0			0
$541$	7.39016	−	9.26696i	0.317728	−	0.398418i	−0.597163	−	0.802120i	$-0.703705\pi$
$541$	7.39016	−	9.26696i	0.317728	−	0.398418i	0.914890	+	0.403702i	$0.132277\pi$
$542$	−73.0274	−	35.1682i	−3.13680	−	1.51060i
$543$		0			0
$544$	−39.3690	−	18.9591i	−1.68793	−	0.812866i
$545$	9.50553	−	4.57762i	0.407172	−	0.196084i
$546$		0			0
$547$	7.53073	+	3.62661i	0.321991	+	0.155063i	0.587896	−	0.808937i	$-0.299956\pi$
$547$	7.53073	+	3.62661i	0.321991	+	0.155063i	−0.265905	+	0.963999i	$0.585671\pi$
$548$	2.80608	+	3.51871i	0.119870	+	0.150312i
$549$		0			0
$550$	21.9841	−	27.5672i	0.937407	−	1.17547i
$551$	−2.89801	+	12.6970i	−0.123459	+	0.540911i
$552$		0			0
$553$	20.8995	−	36.4204i	0.888738	−	1.54875i
$554$	−38.3111	−	48.0406i	−1.62768	−	2.04105i
$555$		0			0
$556$	0.155756	−	0.682413i	0.00660554	−	0.0289408i
$557$	13.8920			0.588621			0.294310	−	0.955710i	$-0.404910\pi$
$557$	13.8920			0.588621			0.294310	+	0.955710i	$0.404910\pi$
$558$		0			0
$559$	6.18495	−	27.0980i	0.261596	−	1.14613i
$560$	−44.1092	+	76.8667i	−1.86395	+	3.24821i
$561$		0			0
$562$	13.6770	+	59.9230i	0.576931	+	2.52770i
$563$	22.3004	+	27.9639i	0.939851	+	1.17854i	0.983758	+	0.179500i	$0.0574480\pi$
$563$	22.3004	+	27.9639i	0.939851	+	1.17854i	−0.0439070	+	0.999036i	$0.513981\pi$
$564$		0			0
$565$	−6.27606	−	27.4972i	−0.264036	−	1.15682i
$566$	−7.26049	−	31.8103i	−0.305181	−	1.33709i
$567$		0			0
$568$	25.8009	−	113.041i	1.08258	−	4.74310i
$569$	4.37693			0.183491			0.0917453	−	0.995783i	$-0.470755\pi$
$569$	4.37693			0.183491			0.0917453	+	0.995783i	$0.470755\pi$
$570$		0			0
$571$	1.11652	−	4.89180i	0.0467250	−	0.204716i	−0.946177	−	0.323649i	$-0.895090\pi$
$571$	1.11652	−	4.89180i	0.0467250	−	0.204716i	0.992902	+	0.118933i	$0.0379475\pi$
$572$	−68.0826	+	32.7868i	−2.84668	+	1.37089i
$573$		0			0
$574$	−1.08823	+	15.0539i	−0.0454219	+	0.628339i
$575$	2.35141	−	2.94858i	0.0980606	−	0.122964i
$576$		0			0
$577$	−11.4792	+	14.3945i	−0.477886	+	0.599250i	−0.961082	−	0.276262i	$-0.910904\pi$
$577$	−11.4792	+	14.3945i	−0.477886	+	0.599250i	0.483196	+	0.875512i	$0.339476\pi$
$578$	19.1670	−	9.23034i	0.797242	−	0.383931i
$579$		0			0
$580$	49.5298	+	23.8523i	2.05661	+	0.990412i
$581$	−6.61582	+	1.01502i	−0.274470	+	0.0421102i
$582$		0			0
$583$	6.65960	+	3.20710i	0.275813	+	0.132824i
$584$	−10.6141	−	46.5036i	−0.439216	−	1.92433i
$585$		0			0
$586$	−7.46974	+	9.36676i	−0.308572	+	0.386937i
$587$	9.09184			0.375261			0.187630	−	0.982240i	$-0.439919\pi$
$587$	9.09184			0.375261			0.187630	+	0.982240i	$0.439919\pi$
$588$		0			0
$589$	−26.5626			−1.09449
$590$	19.4316	−	24.3664i	0.799985	−	1.00315i
$591$		0			0
$592$	21.9325	+	96.0925i	0.901420	+	3.94938i
$593$	−38.8507	−	18.7095i	−1.59541	−	0.768308i	−0.596009	−	0.802978i	$-0.703248\pi$
$593$	−38.8507	−	18.7095i	−1.59541	−	0.768308i	−0.999399	+	0.0346695i	$0.988962\pi$
$594$		0			0
$595$	8.41005	+	21.2634i	0.344778	+	0.871716i
$596$	13.4977	+	6.50016i	0.552888	+	0.266257i
$597$		0			0
$598$	−10.1502	+	4.88808i	−0.415073	+	0.199888i
$599$	5.51558	−	6.91631i	0.225360	−	0.282593i	−0.656277	−	0.754520i	$-0.727870\pi$
$599$	5.51558	−	6.91631i	0.225360	−	0.282593i	0.881638	+	0.471927i	$0.156441\pi$
$600$		0			0
$601$	−14.3313	+	17.9708i	−0.584584	+	0.733045i	−0.982887	−	0.184209i	$-0.941028\pi$
$601$	−14.3313	+	17.9708i	−0.584584	+	0.733045i	0.398303	+	0.917254i	$0.369599\pi$
$602$	38.8472	+	35.8548i	1.58329	+	1.46133i
$603$		0			0
$604$	−15.9420	+	7.67728i	−0.648672	+	0.312384i
$605$	−3.31266	+	14.5137i	−0.134679	+	0.590067i
$606$		0			0
$607$	46.5010			1.88742			0.943709	−	0.330777i	$-0.107311\pi$
$607$	46.5010			1.88742			0.943709	+	0.330777i	$0.107311\pi$
$608$	11.2280	−	49.1929i	0.455354	−	1.99504i
$609$		0			0
$610$	−3.18572	−	13.9576i	−0.128986	−	0.565126i
$611$	0.742771	+	3.25429i	0.0300493	+	0.131655i
$612$		0			0
$613$	3.06401	+	3.84214i	0.123754	+	0.155183i	0.839849	−	0.542820i	$-0.182644\pi$
$613$	3.06401	+	3.84214i	0.123754	+	0.155183i	−0.716095	+	0.698003i	$0.754072\pi$
$614$	2.75180	+	12.0564i	0.111054	+	0.486558i
$615$		0			0
$616$	6.28113	−	86.8894i	0.253074	−	3.50087i
$617$	−4.92328	+	21.5703i	−0.198204	+	0.868387i	0.773802	+	0.633428i	$0.218353\pi$
$617$	−4.92328	+	21.5703i	−0.198204	+	0.868387i	−0.972005	+	0.234959i	$0.924504\pi$
$618$		0			0
$619$	−33.6017			−1.35057			−0.675283	−	0.737559i	$-0.735978\pi$
$619$	−33.6017			−1.35057			−0.675283	+	0.737559i	$0.735978\pi$
$620$	−24.9499	+	109.313i	−1.00201	+	4.39011i
$621$		0			0
$622$	−50.5438	−	63.3800i	−2.02662	−	2.54130i
$623$	14.3083	−	2.19523i	0.573250	−	0.0879499i
$624$		0			0
$625$	6.81278	−	29.8487i	0.272511	−	1.19395i
$626$	29.4694	−	36.9535i	1.17784	−	1.47696i
$627$		0			0
$628$	65.0375	+	81.5545i	2.59528	+	3.25438i
$629$	22.9125	+	11.0341i	0.913581	+	0.439957i
$630$		0			0
$631$	−29.6016	+	14.2554i	−1.17842	+	0.567497i	−0.917450	−	0.397850i	$-0.869756\pi$
$631$	−29.6016	+	14.2554i	−1.17842	+	0.567497i	−0.260969	+	0.965347i	$0.584042\pi$
$632$	117.093	+	56.3889i	4.65770	+	2.24303i
$633$		0			0
$634$	−56.7589	−	27.3336i	−2.25418	−	1.08556i
$635$	14.0199	−	17.5804i	0.556364	−	0.697658i
$636$		0			0
$637$	−25.6367	−	3.72596i	−1.01576	−	0.147628i
$638$	−40.2090			−1.59189
$639$		0			0
$640$	−31.3163	−	15.0811i	−1.23789	−	0.596134i
$641$	−1.82854	−	8.01136i	−0.0722230	−	0.316430i	0.925893	−	0.377786i	$-0.123315\pi$
$641$	−1.82854	−	8.01136i	−0.0722230	−	0.316430i	−0.998116	+	0.0613564i	$0.980457\pi$
$642$		0			0
$643$	28.4108	−	13.6819i	1.12041	−	0.539563i	0.220393	−	0.975411i	$-0.429266\pi$
$643$	28.4108	−	13.6819i	1.12041	−	0.539563i	0.900020	+	0.435848i	$0.143552\pi$
$644$	1.10837	−	15.3325i	0.0436759	−	0.604186i
$645$		0			0
$646$	−17.2460	−	21.6258i	−0.678533	−	0.850854i
$647$	−0.0428392	+	0.0206303i	−0.00168418	+	0.000811060i	−0.434726	−	0.900563i	$-0.643155\pi$
$647$	−0.0428392	+	0.0206303i	−0.00168418	+	0.000811060i	0.433041	+	0.901374i	$0.357440\pi$
$648$		0			0
$649$	−3.63913	+	15.9440i	−0.142848	+	0.625859i
$650$	20.2337	−	25.3723i	0.793632	−	0.995184i
$651$		0			0
$652$	3.45169	+	4.32828i	0.135178	+	0.169508i
$653$	−33.3337	+	16.0527i	−1.30445	+	0.628190i	−0.951557	−	0.307473i	$-0.900516\pi$
$653$	−33.3337	+	16.0527i	−1.30445	+	0.628190i	−0.352894	+	0.935663i	$0.614802\pi$
$654$		0			0
$655$	−58.5023			−2.28588
$656$	−24.9370			−0.973626
$657$		0			0
$658$	−6.07154	−	1.85531i	−0.236693	−	0.0723274i
$659$	2.37752	+	10.4166i	0.0926150	+	0.405773i	0.999891	−	0.0147627i	$-0.00469929\pi$
$659$	2.37752	+	10.4166i	0.0926150	+	0.405773i	−0.907276	+	0.420536i	$0.861842\pi$
$660$		0			0
$661$	−15.9542	−	20.0060i	−0.620548	−	0.778143i	0.367873	−	0.929876i	$-0.380086\pi$
$661$	−15.9542	−	20.0060i	−0.620548	−	0.778143i	−0.988422	+	0.151733i	$0.951515\pi$
$662$	35.9166	+	45.0380i	1.39594	+	1.75045i
$663$		0			0
$664$	−4.60968	−	20.1963i	−0.178890	−	0.783770i
$665$	−21.7772	+	14.9317i	−0.844483	+	0.579026i
$666$		0			0
$667$	−4.30074			−0.166525
$668$	−127.690			−4.94048
$669$		0			0
$670$	−97.5849	+	46.9944i	−3.77003	+	1.81555i
$671$	4.68397	+	5.87351i	0.180823	+	0.226744i
$672$		0			0
$673$	23.2427	−	29.1454i	0.895939	−	1.12347i	−0.0958258	−	0.995398i	$-0.530549\pi$
$673$	23.2427	−	29.1454i	0.895939	−	1.12347i	0.991765	−	0.128074i	$-0.0408794\pi$
$674$	9.13582	−	40.0266i	0.351899	−	1.54177i
$675$		0			0
$676$	−3.18592	+	1.53426i	−0.122535	+	0.0590100i
$677$	9.99929	+	12.5387i	0.384304	+	0.481902i	0.935928	−	0.352191i	$-0.114563\pi$
$677$	9.99929	+	12.5387i	0.384304	+	0.481902i	−0.551624	+	0.834093i	$0.685992\pi$
$678$		0			0
$679$	3.05936	−	5.33138i	0.117407	−	0.204600i
$680$	−63.7629	+	30.7066i	−2.44520	+	1.17754i
$681$		0			0
$682$	−18.2489	−	79.9536i	−0.698786	−	3.06158i
$683$	−8.97562	−	4.32243i	−0.343443	−	0.165393i	0.254209	−	0.967149i	$-0.418185\pi$
$683$	−8.97562	−	4.32243i	−0.343443	−	0.165393i	−0.597651	+	0.801756i	$0.703899\pi$
$684$		0			0
$685$	2.55281			0.0975377
$686$	30.4150	−	38.7642i	1.16125	−	1.48002i
$687$		0			0
$688$	−54.4573	+	68.2873i	−2.07617	+	2.60343i
$689$	6.12936	+	2.95174i	0.233510	+	0.112452i
$690$		0			0
$691$	15.4908	+	7.45999i	0.589299	+	0.283791i	0.704675	−	0.709531i	$-0.251093\pi$
$691$	15.4908	+	7.45999i	0.589299	+	0.283791i	−0.115376	+	0.993322i	$0.536807\pi$
$692$	−24.7084	+	11.8989i	−0.939273	+	0.452330i
$693$		0			0
$694$	37.1424	+	17.8868i	1.40991	+	0.678975i
$695$	−0.247544	−	0.310410i	−0.00938986	−	0.0117745i
$696$		0			0
$697$	−4.01161	+	5.03040i	−0.151951	+	0.190540i
$698$	−17.9662	+	78.7151i	−0.680031	+	2.97941i
$699$		0			0
$700$	16.2867	+	41.1781i	0.615578	+	1.55639i
$701$	26.6892	+	33.4672i	1.00804	+	1.26404i	0.964249	+	0.264997i	$0.0853710\pi$
$701$	26.6892	+	33.4672i	1.00804	+	1.26404i	0.0437875	+	0.999041i	$0.486058\pi$
$702$		0			0
$703$	−6.53459	+	28.6299i	−0.246457	+	1.07980i
$704$	62.2591			2.34648
$705$		0			0
$706$	−8.92669	+	39.1104i	−0.335960	+	1.47194i
$707$	2.20087	−	1.50904i	0.0827722	−	0.0567534i
$708$		0			0
$709$	−0.0799121	−	0.350118i	−0.00300116	−	0.0131490i	0.973405	−	0.229090i	$-0.0735751\pi$
$709$	−0.0799121	−	0.350118i	−0.00300116	−	0.0131490i	−0.976406	+	0.215941i	$0.930718\pi$
$710$	−67.6501	−	84.8306i	−2.53886	−	3.18363i
$711$		0			0
$712$	9.96955	+	43.6795i	0.373625	+	1.63696i
$713$	−1.95189	−	8.55179i	−0.0730989	−	0.320267i
$714$		0			0
$715$	−9.53772	+	41.7875i	−0.356691	+	1.56276i
$716$	−37.0792			−1.38572
$717$		0			0
$718$	−0.722053	+	3.16352i	−0.0269468	+	0.118062i
$719$	−16.0616	+	7.73486i	−0.598997	+	0.288462i	−0.708708	−	0.705502i	$-0.750722\pi$
$719$	−16.0616	+	7.73486i	−0.598997	+	0.288462i	0.109711	+	0.993964i	$0.465007\pi$
$720$		0			0
$721$	−0.501639	+	0.343953i	−0.0186820	+	0.0128095i
$722$	−11.6017	+	14.5481i	−0.431772	+	0.541425i
$723$		0			0
$724$	−28.5398	+	35.7878i	−1.06067	+	1.33004i
$725$	11.1618	−	5.37524i	0.414539	−	0.199631i
$726$		0			0
$727$	34.6810	+	16.7015i	1.28625	+	0.619424i	0.946988	−	0.321269i	$-0.104109\pi$
$727$	34.6810	+	16.7015i	1.28625	+	0.619424i	0.339259	+	0.940693i	$0.389824\pi$
$728$	5.78102	−	79.9712i	0.214259	−	2.96393i
$729$		0			0
$730$	−40.2160	−	19.3670i	−1.48846	−	0.716805i
$731$	5.01468	+	21.9708i	0.185475	+	0.812618i
$732$		0			0
$733$	3.92979	−	4.92780i	0.145150	−	0.182013i	−0.703942	−	0.710258i	$-0.748578\pi$
$733$	3.92979	−	4.92780i	0.145150	−	0.182013i	0.849092	+	0.528245i	$0.177150\pi$
$734$	−24.0194			−0.886571
$735$		0			0
$736$	16.6626			0.614193
$737$	35.4364	−	44.4359i	1.30532	−	1.63682i
$738$		0			0
$739$	4.19271	+	18.3694i	0.154231	+	0.675731i	0.991627	+	0.129134i	$0.0412198\pi$
$739$	4.19271	+	18.3694i	0.154231	+	0.675731i	−0.837396	+	0.546597i	$0.815923\pi$
$740$	111.683	+	53.7835i	4.10553	+	1.97712i
$741$		0			0
$742$	−10.6716	+	7.31703i	−0.391765	+	0.268617i
$743$	−31.8810	−	15.3531i	−1.16960	−	0.563250i	−0.254736	−	0.967011i	$-0.581989\pi$
$743$	−31.8810	−	15.3531i	−1.16960	−	0.563250i	−0.914865	+	0.403760i	$0.867703\pi$
$744$		0			0
$745$	7.65611	−	3.68699i	0.280498	−	0.135081i
$746$	−33.0279	+	41.4156i	−1.20924	+	1.51633i
$747$		0			0
$748$	38.1999	−	47.9012i	1.39673	−	1.75144i
$749$	−18.9923	+	2.91387i	−0.693965	+	0.106470i
$750$		0			0
$751$	42.7761	−	20.5999i	1.56092	−	0.751700i	0.563685	−	0.825990i	$-0.309383\pi$
$751$	42.7761	−	20.5999i	1.56092	−	0.751700i	0.997237	+	0.0742892i	$0.0236688\pi$
$752$	2.33408	−	10.2263i	0.0851153	−	0.372915i
$753$		0			0
$754$	−37.0075			−1.34773
$755$	−2.23333	+	9.78484i	−0.0812791	+	0.356107i
$756$		0			0
$757$	−1.15024	−	5.03954i	−0.0418063	−	0.183165i	0.949714	−	0.313120i	$-0.101374\pi$
$757$	−1.15024	−	5.03954i	−0.0418063	−	0.183165i	−0.991520	+	0.129954i	$0.958517\pi$
$758$	−9.21172	−	40.3592i	−0.334585	−	1.46591i
$759$		0			0
$760$	−50.9534	−	63.8935i	−1.84827	−	2.31766i
$761$	3.19660	+	14.0052i	0.115877	+	0.507689i	0.999239	+	0.0389988i	$0.0124168\pi$
$761$	3.19660	+	14.0052i	0.115877	+	0.507689i	−0.883363	+	0.468690i	$0.844726\pi$
$762$		0			0
$763$	−3.56439	−	9.01198i	−0.129040	−	0.326255i
$764$	17.9529	−	78.6569i	0.649514	−	2.84571i
$765$		0			0
$766$	34.1058			1.23229
$767$	−3.34937	+	14.6746i	−0.120939	+	0.529868i
$768$		0			0
$769$	−16.7649	−	21.0225i	−0.604558	−	0.758092i	0.381523	−	0.924359i	$-0.375400\pi$
$769$	−16.7649	−	21.0225i	−0.604558	−	0.758092i	−0.986081	+	0.166268i	$0.946828\pi$
$770$	−59.9057	−	55.2911i	−2.15885	−	1.99255i
$771$		0			0
$772$	25.2087	−	110.446i	0.907280	−	3.97505i
$773$	34.0966	−	42.7558i	1.22637	−	1.53782i	0.471627	−	0.881798i	$-0.343667\pi$
$773$	34.0966	−	42.7558i	1.22637	−	1.53782i	0.754742	−	0.656021i	$-0.227762\pi$
$774$		0			0
$775$	15.7542	+	19.7551i	0.565907	+	0.709625i
$776$	17.1405	+	8.25444i	0.615309	+	0.296317i
$777$		0			0
$778$	54.4555	−	26.2244i	1.95233	−	0.940190i
$779$	−6.69398	−	3.22365i	−0.239837	−	0.115499i
$780$		0			0
$781$	51.2975	+	24.7036i	1.83557	+	0.883964i
$782$	5.69510	−	7.14143i	0.203656	−	0.255377i
$783$		0			0
$784$	67.5026	+	45.5030i	2.41081	+	1.62511i
$785$	59.1674			2.11177
$786$		0			0
$787$	21.9115	+	10.5520i	0.781062	+	0.376140i	0.781536	−	0.623860i	$-0.214437\pi$
$787$	21.9115	+	10.5520i	0.781062	+	0.376140i	−0.000474064		1.00000i	$0.500151\pi$
$788$	7.73479	+	33.8883i	0.275540	+	1.20722i
$789$		0			0
$790$	109.573	−	52.7677i	3.89844	−	1.87739i
$791$	−25.6081	+	3.92889i	−0.910521	+	0.139695i
$792$		0			0
$793$	4.31103	+	5.40586i	0.153089	+	0.191968i
$794$	−38.1881	+	18.3904i	−1.35525	+	0.652652i
$795$		0			0
$796$	6.37550	−	27.9329i	0.225974	−	0.990055i
$797$	13.7646	−	17.2602i	0.487565	−	0.611388i	−0.475809	−	0.879549i	$-0.657845\pi$
$797$	13.7646	−	17.2602i	0.487565	−	0.611388i	0.963374	+	0.268161i	$0.0864159\pi$
$798$		0			0
$799$	−1.68741	−	2.11594i	−0.0596963	−	0.0748567i
$800$	−43.2450	+	20.8257i	−1.52894	+	0.736299i
$801$		0			0
$802$	−70.9309			−2.50466
$803$	23.4227			0.826568
$804$		0			0
$805$	−6.40748	−	5.91391i	−0.225834	−	0.208438i
$806$	−16.7959	−	73.5876i	−0.591610	−	2.59201i
$807$		0			0
$808$	5.14950	+	6.45727i	0.181159	+	0.227166i
$809$	−13.5317	−	16.9682i	−0.475748	−	0.596569i	0.484820	−	0.874614i	$-0.338885\pi$
$809$	−13.5317	−	16.9682i	−0.475748	−	0.596569i	−0.960568	+	0.278045i	$0.910314\pi$
$810$		0			0
$811$	6.96638	+	30.5217i	0.244623	+	1.07176i	0.936754	+	0.349990i	$0.113815\pi$
$811$	6.96638	+	30.5217i	0.244623	+	1.07176i	−0.692131	+	0.721772i	$0.743328\pi$
$812$	25.1334	−	43.7986i	0.882009	−	1.53703i
$813$		0			0
$814$	−90.6655			−3.17783
$815$	3.14014			0.109994
$816$		0			0
$817$	−23.4459	+	11.2910i	−0.820269	+	0.395021i
$818$	60.4782	+	75.8372i	2.11457	+	2.65159i
$819$		0			0
$820$	−19.5538	+	24.5197i	−0.682849	+	0.856265i
$821$	−8.88353	+	38.9213i	−0.310037	+	1.35836i	0.544408	+	0.838821i	$0.316754\pi$
$821$	−8.88353	+	38.9213i	−0.310037	+	1.35836i	−0.854445	+	0.519542i	$0.826103\pi$
$822$		0			0
$823$	−42.9231	+	20.6707i	−1.49620	+	0.720534i	−0.989893	−	0.141817i	$-0.954706\pi$
$823$	−42.9231	+	20.6707i	−1.49620	+	0.720534i	−0.506311	+	0.862351i	$0.668991\pi$
$824$	−1.17371	−	1.47179i	−0.0408883	−	0.0512723i
$825$		0			0
$826$	−21.0372	−	19.4167i	−0.731976	−	0.675592i
$827$	−30.2708	+	14.5776i	−1.05262	+	0.506914i	−0.878466	−	0.477805i	$-0.841433\pi$
$827$	−30.2708	+	14.5776i	−1.05262	+	0.506914i	−0.174152	+	0.984719i	$0.555718\pi$
$828$		0			0
$829$	10.0234	+	43.9153i	0.348126	+	1.52524i	0.781430	+	0.623993i	$0.214491\pi$
$829$	10.0234	+	43.9153i	0.348126	+	1.52524i	−0.433304	+	0.901248i	$0.642652\pi$
$830$	−17.4657	−	8.41102i	−0.606242	−	0.291951i
$831$		0			0
$832$	57.3019			1.98659
$833$	20.0382	−	6.29687i	0.694282	−	0.218174i
$834$		0			0
$835$	−45.1580	+	56.6263i	−1.56276	+	1.95963i
$836$	63.7424	+	30.6967i	2.20458	+	1.06167i
$837$		0			0
$838$	12.6760	+	6.10445i	0.437886	+	0.210875i
$839$	8.90705	−	4.28941i	0.307505	−	0.148087i	−0.273767	−	0.961796i	$-0.588270\pi$
$839$	8.90705	−	4.28941i	0.307505	−	0.148087i	0.581272	+	0.813709i	$0.302555\pi$
$840$		0			0
$841$	13.3996	+	6.45290i	0.462054	+	0.222514i
$842$	37.5582	+	47.0965i	1.29434	+	1.62305i
$843$		0			0
$844$	−28.8804	+	36.2149i	−0.994105	+	1.24657i
$845$	−0.446317	+	1.95544i	−0.0153538	+	0.0672693i
$846$		0			0
$847$	13.0778	+	3.99625i	0.449360	+	0.137313i
$848$	−13.3290	−	16.7140i	−0.457718	−	0.573961i
$849$		0			0
$850$	−5.85497	+	25.6523i	−0.200824	+	0.879867i
$851$	−9.69754			−0.332427
$852$		0			0
$853$	−9.69756	+	42.4878i	−0.332038	+	1.45475i	0.483140	+	0.875543i	$0.339496\pi$
$853$	−9.69756	+	42.4878i	−0.332038	+	1.45475i	−0.815178	+	0.579210i	$0.803361\pi$
$854$	−12.9987	+	1.99430i	−0.444806	+	0.0682435i
$855$		0			0
$856$	−13.2332	−	57.9786i	−0.452303	−	1.98167i
$857$	−12.9404	−	16.2267i	−0.442035	−	0.554294i	0.510043	−	0.860149i	$-0.329629\pi$
$857$	−12.9404	−	16.2267i	−0.442035	−	0.554294i	−0.952078	+	0.305854i	$0.901058\pi$
$858$		0			0
$859$	3.94969	+	17.3047i	0.134762	+	0.590429i	0.996538	+	0.0831404i	$0.0264950\pi$
$859$	3.94969	+	17.3047i	0.134762	+	0.590429i	−0.861776	+	0.507288i	$0.830648\pi$
$860$	24.4431	+	107.092i	0.833503	+	3.65181i
$861$		0			0
$862$	−2.31986	+	10.1640i	−0.0790147	+	0.346186i
$863$	19.3023			0.657059			0.328529	−	0.944494i	$-0.393447\pi$
$863$	19.3023			0.657059			0.328529	+	0.944494i	$0.393447\pi$
$864$		0			0
$865$	−3.46141	+	15.1654i	−0.117692	+	0.515641i
$866$	45.8395	−	22.0751i	1.55769	−	0.750144i
$867$		0			0
$868$	98.4981	+	30.0985i	3.34324	+	1.02161i
$869$	−39.7898	+	49.8948i	−1.34978	+	1.69257i
$870$		0			0
$871$	32.6149	−	40.8978i	1.10511	−	1.38577i
$872$	27.0243	−	13.0142i	0.915159	−	0.440717i
$873$		0			0
$874$	9.50313	+	4.57647i	0.321448	+	0.154801i
$875$	−12.4183	−	3.79471i	−0.419815	−	0.128285i
$876$		0			0
$877$	23.7677	+	11.4459i	0.802578	+	0.386501i	0.789759	−	0.613417i	$-0.210205\pi$
$877$	23.7677	+	11.4459i	0.802578	+	0.386501i	0.0128185	+	0.999918i	$0.495920\pi$
$878$	−7.85316	−	34.4069i	−0.265031	−	1.16118i
$879$		0			0
$880$	83.9779	−	105.305i	2.83089	−	3.54983i
$881$	−19.7835			−0.666525			−0.333262	−	0.942834i	$-0.608149\pi$
$881$	−19.7835			−0.666525			−0.333262	+	0.942834i	$0.608149\pi$
$882$		0			0
$883$	−17.9768			−0.604969			−0.302484	−	0.953154i	$-0.597816\pi$
$883$	−17.9768			−0.604969			−0.302484	+	0.953154i	$0.597816\pi$
$884$	35.1584	−	44.0873i	1.18251	−	1.48282i
$885$		0			0
$886$	−10.9758	−	48.0881i	−0.368739	−	1.61555i
$887$	−35.3522	−	17.0247i	−1.18701	−	0.571635i	−0.267065	−	0.963678i	$-0.586054\pi$
$887$	−35.3522	−	17.0247i	−1.18701	−	0.571635i	−0.919947	+	0.392044i	$0.871768\pi$
$888$		0			0
$889$	−15.1784	−	14.0092i	−0.509066	−	0.469852i
$890$	37.7737	+	18.1909i	1.26618	+	0.609759i
$891$		0			0
$892$	−44.2224	+	21.2964i	−1.48068	+	0.713056i
$893$	1.94852	−	2.44337i	0.0652049	−	0.0817643i
$894$		0			0
$895$	−13.1132	+	16.4434i	−0.438325	+	0.549642i
$896$	−15.8912	+	27.6926i	−0.530886	+	0.925146i
$897$		0			0
$898$	−15.6661	+	7.54441i	−0.522785	+	0.251760i
$899$	6.41181	−	28.0920i	0.213846	−	0.936920i
$900$		0			0
$901$	−5.51585			−0.183760
$902$	5.10434	−	22.3636i	0.169956	−	0.744626i
$903$		0			0
$904$	−17.8429	−	78.1749i	−0.593446	−	2.60006i
$905$	5.77750	+	25.3129i	0.192051	+	0.841429i
$906$		0			0
$907$	−5.33742	−	6.69291i	−0.177226	−	0.222234i	0.685282	−	0.728278i	$-0.259679\pi$
$907$	−5.33742	−	6.69291i	−0.177226	−	0.222234i	−0.862508	+	0.506043i	$0.831108\pi$
$908$	−24.5205	−	107.431i	−0.813742	−	3.56524i
$909$		0			0
$910$	−55.1359	−	50.8888i	−1.82774	−	1.68695i
$911$	−7.86910	+	34.4768i	−0.260715	+	1.14227i	0.659764	+	0.751473i	$0.270656\pi$
$911$	−7.86910	+	34.4768i	−0.260715	+	1.14227i	−0.920479	+	0.390793i	$0.872201\pi$
$912$		0			0
$913$	10.1724			0.336657
$914$	−2.99411	+	13.1180i	−0.0990363	+	0.433906i
$915$		0			0
$916$	39.5727	+	49.6226i	1.30752	+	1.63958i
$917$	−3.87460	+	53.5988i	−0.127950	+	1.76999i
$918$		0			0
$919$	−5.33300	+	23.3654i	−0.175919	+	0.770753i	0.807568	+	0.589775i	$0.200783\pi$
$919$	−5.33300	+	23.3654i	−0.175919	+	0.770753i	−0.983487	+	0.180978i	$0.942074\pi$
$920$	16.8262	−	21.0994i	0.554744	−	0.695627i
$921$		0			0
$922$	20.1566	+	25.2756i	0.663822	+	0.832406i
$923$	47.2132	+	22.7367i	1.55404	+	0.748387i
$924$		0			0
$925$	25.1683	−	12.1204i	0.827527	−	0.398516i
$926$	−18.2562	−	8.79172i	−0.599935	−	0.288914i
$927$		0			0
$928$	49.3150	+	23.7489i	1.61884	+	0.779594i
$929$	2.79400	−	3.50356i	0.0916681	−	0.114948i	−0.733882	−	0.679277i	$-0.762294\pi$
$929$	2.79400	−	3.50356i	0.0916681	−	0.114948i	0.825550	+	0.564329i	$0.190865\pi$
$930$		0			0
$931$	12.2379	+	20.9408i	0.401080	+	0.686307i
$932$	125.797			4.12063
$933$		0			0
$934$	36.5377	+	17.5956i	1.19555	+	0.575747i
$935$	−7.73307	−	33.8808i	−0.252898	−	1.10802i
$936$		0			0
$937$	−18.4946	+	8.90651i	−0.604191	+	0.290963i	−0.710862	−	0.703331i	$-0.751695\pi$
$937$	−18.4946	+	8.90651i	−0.604191	+	0.290963i	0.106671	+	0.994294i	$0.465981\pi$
$938$	36.5925	+	92.5181i	1.19479	+	3.02082i
$939$		0			0
$940$	−8.22495	−	10.3138i	−0.268268	−	0.336398i
$941$	−52.9178	+	25.4839i	−1.72507	+	0.830750i	−0.737161	+	0.675718i	$0.763834\pi$
$941$	−52.9178	+	25.4839i	−1.72507	+	0.830750i	−0.987909	+	0.155032i	$0.950452\pi$
$942$		0			0
$943$	0.545958	−	2.39200i	0.0177788	−	0.0778942i
$944$	29.4906	−	36.9801i	0.959838	−	1.20360i
$945$		0			0
$946$	−50.0935	−	62.8153i	−1.62868	−	2.04230i
$947$	13.8522	−	6.67088i	0.450137	−	0.216774i	−0.195059	−	0.980791i	$-0.562490\pi$
$947$	13.8522	−	6.67088i	0.450137	−	0.216774i	0.645196	+	0.764017i	$0.276776\pi$
$948$		0			0
$949$	21.5577			0.699794
$950$	−30.3836			−0.985773
$951$		0			0
$952$	23.9099	+	60.4522i	0.774923	+	1.95927i
$953$	7.41365	+	32.4813i	0.240152	+	1.05217i	0.940879	+	0.338744i	$0.110002\pi$
$953$	7.41365	+	32.4813i	0.240152	+	1.05217i	−0.700727	+	0.713429i	$0.747141\pi$
$954$		0			0
$955$	−28.5326	−	35.7787i	−0.923293	−	1.15777i
$956$	−37.7085	−	47.2850i	−1.21958	−	1.52931i
$957$		0			0
$958$	14.6989	+	64.4000i	0.474899	+	2.08067i
$959$	0.169072	−	2.33884i	0.00545961	−	0.0755250i
$960$		0			0
$961$	27.7695			0.895789
$962$	−83.4467			−2.69043
$963$		0			0
$964$	84.2533	−	40.5743i	2.71362	−	1.30681i
$965$	−40.0641	−	50.2388i	−1.28971	−	1.61725i
$966$		0			0
$967$	−23.5140	+	29.4856i	−0.756158	+	0.948192i	−0.999765	−	0.0216816i	$-0.993098\pi$
$967$	−23.5140	+	29.4856i	−0.756158	+	0.948192i	0.243607	+	0.969874i	$0.421669\pi$
$968$	−9.41794	+	41.2627i	−0.302704	+	1.32623i
$969$		0			0
$970$	16.0398	−	7.72436i	0.515007	−	0.248014i
$971$	−7.54802	−	9.46491i	−0.242227	−	0.303743i	0.645825	−	0.763485i	$-0.276513\pi$
$971$	−7.54802	−	9.46491i	−0.242227	−	0.303743i	−0.888053	+	0.459742i	$0.847942\pi$
$972$		0			0
$973$	−0.300787	+	0.206237i	−0.00964279	+	0.00661165i
$974$	−33.3016	+	16.0372i	−1.06705	+	0.513866i
$975$		0			0
$976$	−4.83486	−	21.1829i	−0.154760	−	0.678049i
$977$	−19.9009	−	9.58375i	−0.636685	−	0.306611i	0.0875547	−	0.996160i	$-0.472095\pi$
$977$	−19.9009	−	9.58375i	−0.636685	−	0.306611i	−0.724240	+	0.689548i	$0.757809\pi$
$978$		0			0
$979$	−22.0002			−0.703130
$980$	97.6723	−	30.6929i	3.12003	−	0.980448i
$981$		0			0
$982$	52.7537	−	66.1510i	1.68344	−	2.11096i
$983$	41.9322	+	20.1935i	1.33743	+	0.644073i	0.959486	−	0.281756i	$-0.0909167\pi$
$983$	41.9322	+	20.1935i	1.33743	+	0.644073i	0.377944	+	0.925828i	$0.376631\pi$
$984$		0			0
$985$	17.7638	+	8.55458i	0.566000	+	0.272571i
$986$	27.0338	−	13.0188i	0.860931	−	0.414603i
$987$		0			0
$988$	58.6671	+	28.2526i	1.86645	+	0.898835i
$989$	−5.35798	−	6.71869i	−0.170374	−	0.213642i
$990$		0			0
$991$	2.79959	−	3.51057i	0.0889317	−	0.111517i	−0.735375	−	0.677661i	$-0.762994\pi$
$991$	2.79959	−	3.51057i	0.0889317	−	0.111517i	0.824307	+	0.566144i	$0.191565\pi$
$992$	−24.8417	+	108.839i	−0.788726	+	3.45563i
$993$		0			0
$994$	−82.2008	+	56.3616i	−2.60725	+	1.78768i
$995$	−10.1326	−	12.7059i	−0.321225	−	0.402803i
$996$		0			0
$997$	11.9040	−	52.1547i	0.377002	−	1.65175i	−0.329583	−	0.944127i	$-0.606908\pi$
$997$	11.9040	−	52.1547i	0.377002	−	1.65175i	0.706585	−	0.707628i	$-0.250235\pi$
$998$	19.5564			0.619046
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.u.c.190.4		24
3.2	odd	2		147.2.i.a.43.1	✓	24
49.8	even	7	inner	441.2.u.c.253.4		24
147.8	odd	14		147.2.i.a.106.1	yes	24
147.20	even	14		7203.2.a.b.1.1		12
147.29	odd	14		7203.2.a.a.1.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.i.a.43.1	✓	24	3.2	odd	2
147.2.i.a.106.1	yes	24	147.8	odd	14
441.2.u.c.190.4		24	1.1	even	1	trivial
441.2.u.c.253.4		24	49.8	even	7	inner
7203.2.a.a.1.1		12	147.29	odd	14
7203.2.a.b.1.1		12	147.20	even	14

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.u (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.65876 - 2.08002i) q^{2} +(-1.12995 - 4.95062i) q^{4} +(-2.59504 - 1.24971i) q^{5} +(-1.31683 + 2.29477i) q^{7} +(-7.37774 - 3.55293i) q^{8} +O(q^{10})\)	\(q+(1.65876 - 2.08002i) q^{2} +(-1.12995 - 4.95062i) q^{4} +(-2.59504 - 1.24971i) q^{5} +(-1.31683 + 2.29477i) q^{7} +(-7.37774 - 3.55293i) q^{8} +(-6.90396 + 3.32477i) q^{10} +(2.50706 - 3.14376i) q^{11} +(2.30745 - 2.89345i) q^{13} +(2.58885 + 6.54549i) q^{14} +(-10.4779 + 5.04589i) q^{16} +(-0.667699 + 2.92538i) q^{17} -3.46493 q^{19} +(-3.25457 + 14.2592i) q^{20} +(-2.38046 - 10.4295i) q^{22} +(-0.254612 - 1.11553i) q^{23} +(2.05504 + 2.57694i) q^{25} +(-2.19092 - 9.59906i) q^{26} +(12.8485 + 3.92616i) q^{28} +(0.836382 - 3.66443i) q^{29} +7.66612 q^{31} +(-3.24046 + 14.1974i) q^{32} +(4.97729 + 6.24132i) q^{34} +(6.28502 - 4.30937i) q^{35} +(1.88592 - 8.26276i) q^{37} +(-5.74748 + 7.20712i) q^{38} +(14.7054 + 18.4400i) q^{40} +(1.93192 + 0.930364i) q^{41} +(6.76663 - 3.25864i) q^{43} +(-18.3964 - 8.85925i) q^{44} +(-2.74266 - 1.32080i) q^{46} +(-0.562355 + 0.705171i) q^{47} +(-3.53192 - 6.04364i) q^{49} +8.76888 q^{50} +(-16.9317 - 8.15387i) q^{52} +(0.409047 + 1.79215i) q^{53} +(-10.4347 + 5.02510i) q^{55} +(17.8684 - 12.2516i) q^{56} +(-6.23472 - 7.81809i) q^{58} +(-3.66438 + 1.76467i) q^{59} +(-0.415738 + 1.82147i) q^{61} +(12.7162 - 15.9457i) q^{62} +(9.65375 + 12.1054i) q^{64} +(-9.60390 + 4.62499i) q^{65} +14.1346 q^{67} +15.2369 q^{68} +(1.46176 - 20.2211i) q^{70} +(3.15081 + 13.8046i) q^{71} +(3.63187 + 4.55422i) q^{73} +(-14.0584 - 17.6287i) q^{74} +(3.91519 + 17.1536i) q^{76} +(3.91282 + 9.89292i) q^{77} -15.8711 q^{79} +33.4965 q^{80} +(5.13976 - 2.47518i) q^{82} +(1.57731 + 1.97788i) q^{83} +(5.38858 - 6.75706i) q^{85} +(4.44618 - 19.4800i) q^{86} +(-29.6660 + 14.2864i) q^{88} +(-3.41131 - 4.27764i) q^{89} +(3.60128 + 9.10524i) q^{91} +(-5.23487 + 2.52098i) q^{92} +(0.533956 + 2.33942i) q^{94} +(8.99166 + 4.33015i) q^{95} -2.32328 q^{97} +(-18.4295 - 2.67848i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - q^{2} - 3 q^{4} - 3 q^{8}+O(q^{10}) \) 24 * q - q^2 - 3 * q^4 - 3 * q^8	\( 24 q - q^{2} - 3 q^{4} - 3 q^{8} - 30 q^{10} - 9 q^{11} + 21 q^{14} - 29 q^{16} - 5 q^{17} + 26 q^{19} + 13 q^{20} + 11 q^{22} - 4 q^{23} - 28 q^{25} + 22 q^{26} - 7 q^{28} - 6 q^{29} + 36 q^{31} - 14 q^{32} + 46 q^{34} + 7 q^{35} - 22 q^{37} + 45 q^{38} + 35 q^{40} + 11 q^{41} + 6 q^{43} - 82 q^{44} - 16 q^{46} - 29 q^{47} - 42 q^{49} + 48 q^{50} - 50 q^{52} - 28 q^{53} + 23 q^{55} - 21 q^{56} + 39 q^{58} + 15 q^{59} - 32 q^{61} + 8 q^{62} + 29 q^{64} + 21 q^{65} - 34 q^{67} + 22 q^{68} - 24 q^{71} - 15 q^{73} - 6 q^{74} + 7 q^{76} + 21 q^{77} - 34 q^{79} - 8 q^{80} + 14 q^{82} - 14 q^{83} + 20 q^{85} + 100 q^{86} - 108 q^{88} - 10 q^{89} + 84 q^{91} + 21 q^{92} + 99 q^{94} - 18 q^{95} - 64 q^{97} - 91 q^{98}+O(q^{100}) \) 24 * q - q^2 - 3 * q^4 - 3 * q^8 - 30 * q^10 - 9 * q^11 + 21 * q^14 - 29 * q^16 - 5 * q^17 + 26 * q^19 + 13 * q^20 + 11 * q^22 - 4 * q^23 - 28 * q^25 + 22 * q^26 - 7 * q^28 - 6 * q^29 + 36 * q^31 - 14 * q^32 + 46 * q^34 + 7 * q^35 - 22 * q^37 + 45 * q^38 + 35 * q^40 + 11 * q^41 + 6 * q^43 - 82 * q^44 - 16 * q^46 - 29 * q^47 - 42 * q^49 + 48 * q^50 - 50 * q^52 - 28 * q^53 + 23 * q^55 - 21 * q^56 + 39 * q^58 + 15 * q^59 - 32 * q^61 + 8 * q^62 + 29 * q^64 + 21 * q^65 - 34 * q^67 + 22 * q^68 - 24 * q^71 - 15 * q^73 - 6 * q^74 + 7 * q^76 + 21 * q^77 - 34 * q^79 - 8 * q^80 + 14 * q^82 - 14 * q^83 + 20 * q^85 + 100 * q^86 - 108 * q^88 - 10 * q^89 + 84 * q^91 + 21 * q^92 + 99 * q^94 - 18 * q^95 - 64 * q^97 - 91 * q^98

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