LMFDB - Embedded newform 441.2.bg.a.17.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(17,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 25]))

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

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

chi := DirichletCharacter("441.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.bg (of order $42$, degree $12$, 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:	$216$
Relative dimension:	$18$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			17.3
Character	$\chi$	$=$	441.17
Dual form			441.2.bg.a.26.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.05710 + 0.154158i) q^{2} +(2.23024 - 0.336155i) q^{4} +(-1.16105 + 1.07730i) q^{5} +(1.82087 + 1.91949i) q^{7} +(-0.513717 + 0.117252i) q^{8} +O(q^{10})$	\(q+(-2.05710 + 0.154158i) q^{2} +(2.23024 - 0.336155i) q^{4} +(-1.16105 + 1.07730i) q^{5} +(1.82087 + 1.91949i) q^{7} +(-0.513717 + 0.117252i) q^{8} +(2.22233 - 2.39510i) q^{10} +(-0.0139650 - 0.0204828i) q^{11} +(1.10822 - 2.30125i) q^{13} +(-4.04162 - 3.66788i) q^{14} +(-3.27177 + 1.00921i) q^{16} +(0.633525 + 1.61419i) q^{17} +(-0.930215 + 0.537060i) q^{19} +(-2.22729 + 2.79293i) q^{20} +(0.0318849 + 0.0399825i) q^{22} +(-1.77453 - 0.696453i) q^{23} +(-0.186182 + 2.48442i) q^{25} +(-1.92497 + 4.90474i) q^{26} +(4.70623 + 3.66883i) q^{28} +(4.80927 + 3.83527i) q^{29} +(2.94216 + 1.69866i) q^{31} +(7.55580 - 2.96543i) q^{32} +(-1.55207 - 3.22290i) q^{34} +(-4.18199 - 0.267001i) q^{35} +(-8.39478 - 1.26531i) q^{37} +(1.83076 - 1.24819i) q^{38} +(0.470136 - 0.689562i) q^{40} +(1.28868 + 5.64609i) q^{41} +(-1.80900 + 7.92573i) q^{43} +(-0.0380307 - 0.0409873i) q^{44} +(3.75776 + 1.15912i) q^{46} +(0.940891 + 12.5553i) q^{47} +(-0.368854 + 6.99028i) q^{49} -5.13941i q^{50} +(1.69803 - 5.50487i) q^{52} +(-0.948540 - 6.29315i) q^{53} +(0.0382802 + 0.00873720i) q^{55} +(-1.16048 - 0.772570i) q^{56} +(-10.4844 - 7.14815i) q^{58} +(-2.72354 - 2.52708i) q^{59} +(-2.00844 + 13.3251i) q^{61} +(-6.31419 - 3.04075i) q^{62} +(-8.91627 + 4.29385i) q^{64} +(1.19243 + 3.86575i) q^{65} +(-0.628525 + 1.08864i) q^{67} +(1.95553 + 3.38708i) q^{68} +(8.64393 - 0.0954412i) q^{70} +(3.64976 - 2.91058i) q^{71} +(2.37199 + 0.177756i) q^{73} +(17.4640 + 1.30874i) q^{74} +(-1.89407 + 1.51047i) q^{76} +(0.0138881 - 0.0641021i) q^{77} +(-3.37733 - 5.84971i) q^{79} +(2.71148 - 4.69642i) q^{80} +(-3.52135 - 11.4159i) q^{82} +(-8.13058 + 3.91548i) q^{83} +(-2.47452 - 1.19167i) q^{85} +(2.49947 - 16.5829i) q^{86} +(0.00957569 + 0.00888495i) q^{88} +(7.34185 + 5.00559i) q^{89} +(6.43514 - 2.06306i) q^{91} +(-4.19176 - 0.956742i) q^{92} +(-3.87102 - 25.6825i) q^{94} +(0.501454 - 1.62567i) q^{95} -15.6871i q^{97} +(-0.318839 - 14.4366i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 16 q^{4} + 2 q^{7}+O(q^{10}) $ 216 * q - 16 * q^4 + 2 * q^7	$ 216 q - 16 q^{4} + 2 q^{7} + 12 q^{10} + 12 q^{16} - 6 q^{19} + 44 q^{22} + 26 q^{25} + 84 q^{28} - 6 q^{31} - 112 q^{34} + 60 q^{37} - 304 q^{40} + 20 q^{43} - 20 q^{46} - 86 q^{49} - 168 q^{52} - 84 q^{55} - 120 q^{58} - 2 q^{61} + 32 q^{64} + 22 q^{67} - 136 q^{70} - 6 q^{73} + 84 q^{76} + 2 q^{79} - 104 q^{82} + 96 q^{85} - 12 q^{88} + 58 q^{91} + 52 q^{94}+O(q^{100}) $ 216 * q - 16 * q^4 + 2 * q^7 + 12 * q^10 + 12 * q^16 - 6 * q^19 + 44 * q^22 + 26 * q^25 + 84 * q^28 - 6 * q^31 - 112 * q^34 + 60 * q^37 - 304 * q^40 + 20 * q^43 - 20 * q^46 - 86 * q^49 - 168 * q^52 - 84 * q^55 - 120 * q^58 - 2 * q^61 + 32 * q^64 + 22 * q^67 - 136 * q^70 - 6 * q^73 + 84 * q^76 + 2 * q^79 - 104 * q^82 + 96 * q^85 - 12 * q^88 + 58 * q^91 + 52 * q^94

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{25}{42}\right)$	$-1$

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 $

$2$	−2.05710	+	0.154158i	−1.45459	+	0.109007i	−0.778423	−	0.627741i	$-0.783980\pi$
$2$	−2.05710	+	0.154158i	−1.45459	+	0.109007i	−0.676168	+	0.736747i	$0.736361\pi$
$3$		0			0
$3$		0			0
$4$	2.23024	−	0.336155i	1.11512	−	0.168078i
$5$	−1.16105	+	1.07730i	−0.519238	+	0.481783i	−0.895706	−	0.444647i	$-0.853329\pi$
$5$	−1.16105	+	1.07730i	−0.519238	+	0.481783i	0.376468	+	0.926430i	$0.377139\pi$
$6$		0			0
$7$	1.82087	+	1.91949i	0.688225	+	0.725498i
$7$	1.82087	+	1.91949i	0.688225	+	0.725498i
$8$	−0.513717	+	0.117252i	−0.181626	+	0.0414550i
$9$		0			0
$10$	2.22233	−	2.39510i	0.702762	−	0.757397i
$11$	−0.0139650	−	0.0204828i	−0.00421059	−	0.00617581i	0.824128	−	0.566404i	$-0.191666\pi$
$11$	−0.0139650	−	0.0204828i	−0.00421059	−	0.00617581i	−0.828338	+	0.560228i	$0.810713\pi$
$12$		0			0
$13$	1.10822	−	2.30125i	0.307365	−	0.638251i	−0.688875	−	0.724880i	$-0.741895\pi$
$13$	1.10822	−	2.30125i	0.307365	−	0.638251i	0.996241	+	0.0866291i	$0.0276095\pi$
$14$	−4.04162	−	3.66788i	−1.08017	−	0.980281i
$15$		0			0
$16$	−3.27177	+	1.00921i	−0.817943	+	0.252302i
$17$	0.633525	+	1.61419i	0.153652	+	0.391500i	0.986885	−	0.161422i	$-0.0516081\pi$
$17$	0.633525	+	1.61419i	0.153652	+	0.391500i	−0.833233	+	0.552922i	$0.813513\pi$
$18$		0			0
$19$	−0.930215	+	0.537060i	−0.213406	+	0.123210i	−0.602893	−	0.797822i	$-0.705986\pi$
$19$	−0.930215	+	0.537060i	−0.213406	+	0.123210i	0.389487	+	0.921032i	$0.372652\pi$
$20$	−2.22729	+	2.79293i	−0.498037	+	0.624518i
$21$		0			0
$22$	0.0318849	+	0.0399825i	0.00679789	+	0.00852429i
$23$	−1.77453	−	0.696453i	−0.370016	−	0.145221i	0.173045	−	0.984914i	$-0.444639\pi$
$23$	−1.77453	−	0.696453i	−0.370016	−	0.145221i	−0.543061	+	0.839693i	$0.682735\pi$
$24$		0			0
$25$	−0.186182	+	2.48442i	−0.0372363	+	0.496884i
$26$	−1.92497	+	4.90474i	−0.377517	+	0.961899i
$27$		0			0
$28$	4.70623	+	3.66883i	0.889394	+	0.693343i
$29$	4.80927	+	3.83527i	0.893060	+	0.712191i	0.958326	−	0.285677i	$-0.0922183\pi$
$29$	4.80927	+	3.83527i	0.893060	+	0.712191i	−0.0652665	+	0.997868i	$0.520790\pi$
$30$		0			0
$31$	2.94216	+	1.69866i	0.528428	+	0.305088i	0.740376	−	0.672193i	$-0.234647\pi$
$31$	2.94216	+	1.69866i	0.528428	+	0.305088i	−0.211948	+	0.977281i	$0.567981\pi$
$32$	7.55580	−	2.96543i	1.33569	−	0.524219i
$33$		0			0
$34$	−1.55207	−	3.22290i	−0.266177	−	0.552723i
$35$	−4.18199	−	0.267001i	−0.706885	−	0.0451313i
$36$		0			0
$37$	−8.39478	−	1.26531i	−1.38009	−	0.208016i	−0.583294	−	0.812261i	$-0.698237\pi$
$37$	−8.39478	−	1.26531i	−1.38009	−	0.208016i	−0.796798	+	0.604245i	$0.793475\pi$
$38$	1.83076	−	1.24819i	0.296988	−	0.202483i
$39$		0			0
$40$	0.470136	−	0.689562i	0.0743350	−	0.109029i
$41$	1.28868	+	5.64609i	0.201259	+	0.881772i	0.970172	+	0.242418i	$0.0779407\pi$
$41$	1.28868	+	5.64609i	0.201259	+	0.881772i	−0.768913	+	0.639353i	$0.779202\pi$
$42$		0			0
$43$	−1.80900	+	7.92573i	−0.275869	+	1.20866i	0.627093	+	0.778944i	$0.284245\pi$
$43$	−1.80900	+	7.92573i	−0.275869	+	1.20866i	−0.902963	+	0.429719i	$0.858613\pi$
$44$	−0.0380307	−	0.0409873i	−0.00573334	−	0.00617907i
$45$		0			0
$46$	3.75776	+	1.15912i	0.554052	+	0.170902i
$47$	0.940891	+	12.5553i	0.137243	+	1.83138i	0.463496	+	0.886099i	$0.346595\pi$
$47$	0.940891	+	12.5553i	0.137243	+	1.83138i	−0.326253	+	0.945283i	$0.605786\pi$
$48$		0			0
$49$	−0.368854	+	6.99028i	−0.0526935	+	0.998611i
$50$		−	5.13941i		−	0.726822i
$51$		0			0
$52$	1.69803	−	5.50487i	0.235474	−	0.763388i
$53$	−0.948540	−	6.29315i	−0.130292	−	0.864431i	−0.954514	−	0.298165i	$-0.903626\pi$
$53$	−0.948540	−	6.29315i	−0.130292	−	0.864431i	0.824223	−	0.566266i	$-0.191613\pi$
$54$		0			0
$55$	0.0382802	+	0.00873720i	0.00516170	+	0.00117812i
$56$	−1.16048	−	0.772570i	−0.155075	−	0.103239i
$57$		0			0
$58$	−10.4844	−	7.14815i	−1.37667	−	0.938598i
$59$	−2.72354	−	2.52708i	−0.354575	−	0.328998i	0.482694	−	0.875789i	$-0.339658\pi$
$59$	−2.72354	−	2.52708i	−0.354575	−	0.328998i	−0.837269	+	0.546792i	$0.815849\pi$
$60$		0			0
$61$	−2.00844	+	13.3251i	−0.257154	+	1.70610i	0.371512	+	0.928428i	$0.378839\pi$
$61$	−2.00844	+	13.3251i	−0.257154	+	1.70610i	−0.628666	+	0.777676i	$0.716399\pi$
$62$	−6.31419	−	3.04075i	−0.801903	−	0.386176i
$63$		0			0
$64$	−8.91627	+	4.29385i	−1.11453	+	0.536731i
$65$	1.19243	+	3.86575i	0.147902	+	0.479488i
$66$		0			0
$67$	−0.628525	+	1.08864i	−0.0767865	+	0.132998i	−0.901862	−	0.432025i	$-0.857799\pi$
$67$	−0.628525	+	1.08864i	−0.0767865	+	0.132998i	0.825075	+	0.565023i	$0.191133\pi$
$68$	1.95553	+	3.38708i	0.237143	+	0.410744i
$69$		0			0
$70$	8.64393	−	0.0954412i	1.03315	−	0.0114074i
$71$	3.64976	−	2.91058i	0.433146	−	0.345423i	−0.382518	−	0.923948i	$-0.624943\pi$
$71$	3.64976	−	2.91058i	0.433146	−	0.345423i	0.815664	+	0.578525i	$0.196372\pi$
$72$		0			0
$73$	2.37199	+	0.177756i	0.277620	+	0.0208047i	0.212813	−	0.977093i	$-0.431738\pi$
$73$	2.37199	+	0.177756i	0.277620	+	0.0208047i	0.0648075	+	0.997898i	$0.479357\pi$
$74$	17.4640	+	1.30874i	2.03015	+	0.152138i
$75$		0			0
$76$	−1.89407	+	1.51047i	−0.217265	+	0.173263i
$77$	0.0138881	−	0.0641021i	0.00158270	−	0.00730512i
$78$		0			0
$79$	−3.37733	−	5.84971i	−0.379979	−	0.658143i	0.611080	−	0.791569i	$-0.290736\pi$
$79$	−3.37733	−	5.84971i	−0.379979	−	0.658143i	−0.991059	+	0.133426i	$0.957402\pi$
$80$	2.71148	−	4.69642i	0.303152	−	0.525075i
$81$		0			0
$82$	−3.52135	−	11.4159i	−0.388868	−	1.26068i
$83$	−8.13058	+	3.91548i	−0.892447	+	0.429780i	−0.823155	−	0.567817i	$-0.807788\pi$
$83$	−8.13058	+	3.91548i	−0.892447	+	0.429780i	−0.0692918	+	0.997596i	$0.522074\pi$
$84$		0			0
$85$	−2.47452	−	1.19167i	−0.268400	−	0.129255i
$86$	2.49947	−	16.5829i	0.269525	−	1.78818i
$87$		0			0
$88$	0.00957569	+	0.00888495i	0.00102077	+	0.000947138i
$89$	7.34185	+	5.00559i	0.778234	+	0.530591i	0.886056	−	0.463579i	$-0.153435\pi$
$89$	7.34185	+	5.00559i	0.778234	+	0.530591i	−0.107821	+	0.994170i	$0.534387\pi$
$90$		0			0
$91$	6.43514	−	2.06306i	0.674586	−	0.216267i
$92$	−4.19176	−	0.956742i	−0.437021	−	0.0997472i
$93$		0			0
$94$	−3.87102	−	25.6825i	−0.399265	−	2.64895i
$95$	0.501454	−	1.62567i	0.0514481	−	0.166791i
$96$		0			0
$97$		−	15.6871i		−	1.59279i	−0.604780	−	0.796393i	$-0.706739\pi$
$97$		−	15.6871i		−	1.59279i	0.604780	−	0.796393i	$-0.293261\pi$
$98$	−0.318839	−	14.4366i	−0.0322076	−	1.45831i
$99$		0			0
$100$	0.419920	+	5.60345i	0.0419920	+	0.560345i
$101$	3.71303	+	1.14532i	0.369461	+	0.113964i	0.473925	−	0.880565i	$-0.342837\pi$
$101$	3.71303	+	1.14532i	0.369461	+	0.113964i	−0.104465	+	0.994529i	$0.533313\pi$
$102$		0			0
$103$	−0.412699	−	0.444784i	−0.0406645	−	0.0438259i	0.712392	−	0.701782i	$-0.247612\pi$
$103$	−0.412699	−	0.444784i	−0.0406645	−	0.0438259i	−0.753057	+	0.657956i	$0.771421\pi$
$104$	−0.299485	+	1.31213i	−0.0293669	+	0.128665i
$105$		0			0
$106$	2.92139	+	12.7994i	0.283750	+	1.24319i
$107$	1.06170	−	1.55723i	0.102639	−	0.150543i	−0.771484	−	0.636249i	$-0.780485\pi$
$107$	1.06170	−	1.55723i	0.102639	−	0.150543i	0.874122	+	0.485706i	$0.161437\pi$
$108$		0			0
$109$	6.61784	−	4.51197i	0.633874	−	0.432168i	−0.203291	−	0.979118i	$-0.565164\pi$
$109$	6.61784	−	4.51197i	0.633874	−	0.432168i	0.837165	+	0.546950i	$0.184211\pi$
$110$	−0.0800931	−	0.0120721i	−0.00763658	−	0.00115103i
$111$		0			0
$112$	−7.89463	−	4.44248i	−0.745973	−	0.419775i
$113$	−4.97596	−	10.3327i	−0.468099	−	0.972018i	−0.992693	−	0.120665i	$-0.961497\pi$
$113$	−4.97596	−	10.3327i	−0.468099	−	0.972018i	0.524594	−	0.851353i	$-0.324217\pi$
$114$		0			0
$115$	2.81061	−	1.10308i	0.262091	−	0.102863i
$116$	12.0151	+	6.93692i	1.11557	+	0.644076i
$117$		0			0
$118$	5.99218	+	4.77860i	0.551625	+	0.439906i
$119$	−1.94486	+	4.15528i	−0.178285	+	0.380914i
$120$		0			0
$121$	4.01853	−	10.2390i	0.365321	−	0.930822i
$122$	2.07738	−	27.7207i	0.188077	−	2.50971i
$123$		0			0
$124$	7.13275	+	2.79940i	0.640540	+	0.251393i
$125$	−7.39790	−	9.27667i	−0.661688	−	0.829731i
$126$		0			0
$127$	−3.33645	+	4.18378i	−0.296062	+	0.371250i	−0.907507	−	0.420037i	$-0.862017\pi$
$127$	−3.33645	+	4.18378i	−0.296062	+	0.371250i	0.611445	+	0.791287i	$0.290589\pi$
$128$	3.62089	−	2.09052i	0.320044	−	0.184778i
$129$		0			0
$130$	−3.04888	−	7.76842i	−0.267405	−	0.681336i
$131$	10.6218	−	3.27638i	0.928029	−	0.286259i	0.206343	−	0.978480i	$-0.433844\pi$
$131$	10.6218	−	3.27638i	0.928029	−	0.286259i	0.721686	+	0.692221i	$0.243368\pi$
$132$		0			0
$133$	−2.72468	−	0.807618i	−0.236260	−	0.0700294i
$134$	1.12512	−	2.33633i	0.0971953	−	0.201828i
$135$		0			0
$136$	−0.514720	−	0.754956i	−0.0441369	−	0.0647370i
$137$	−7.75901	+	8.36222i	−0.662897	+	0.714433i	−0.971575	−	0.236734i	$-0.923923\pi$
$137$	−7.75901	+	8.36222i	−0.662897	+	0.714433i	0.308678	+	0.951167i	$0.400113\pi$
$138$		0			0
$139$	19.5310	−	4.45782i	1.65660	−	0.378108i	0.710936	−	0.703257i	$-0.248272\pi$
$139$	19.5310	−	4.45782i	1.65660	−	0.378108i	0.945663	+	0.325149i	$0.105415\pi$
$140$	−9.41660	+	0.810319i	−0.795848	+	0.0684845i
$141$		0			0
$142$	−7.05923	+	6.55001i	−0.592398	+	0.549665i
$143$	−0.0626123	+	0.00943729i	−0.00523590	+	0.000789186i
$144$		0			0
$145$	−9.71554	+	0.728079i	−0.806832	+	0.0604637i
$146$	−4.90682			−0.406091
$147$		0			0
$148$	−19.1477			−1.57393
$149$	−13.7959	+	1.03386i	−1.13020	+	0.0846971i	−0.626675	−	0.779281i	$-0.715585\pi$
$149$	−13.7959	+	1.03386i	−1.13020	+	0.0846971i	−0.503530	+	0.863978i	$0.667966\pi$
$150$		0			0
$151$	22.2806	−	3.35826i	1.81317	−	0.273291i	0.847073	−	0.531476i	$-0.178363\pi$
$151$	22.2806	−	3.35826i	1.81317	−	0.273291i	0.966095	+	0.258185i	$0.0831245\pi$
$152$	0.414895	−	0.384967i	0.0336525	−	0.0312249i
$153$		0			0
$154$	−0.0186874	+	0.134006i	−0.00150587	+	0.0107985i
$155$	−5.24596	+	1.19736i	−0.421366	+	0.0961740i
$156$		0			0
$157$	−1.20823	+	1.30217i	−0.0964275	+	0.103924i	−0.779422	−	0.626500i	$-0.784487\pi$
$157$	−1.20823	+	1.30217i	−0.0964275	+	0.103924i	0.682994	+	0.730424i	$0.260677\pi$
$158$	7.84929	+	11.5128i	0.624456	+	0.915909i
$159$		0			0
$160$	−5.57802	+	11.5829i	−0.440981	+	0.915706i
$161$	−1.89437	−	4.67435i	−0.149297	−	0.368390i
$162$		0			0
$163$	7.29866	−	2.25134i	0.571675	−	0.176338i	0.00457818	−	0.999990i	$-0.498543\pi$
$163$	7.29866	−	2.25134i	0.571675	−	0.176338i	0.567097	+	0.823651i	$0.308067\pi$
$164$	4.77204	+	12.1590i	0.372634	+	0.949456i
$165$		0			0
$166$	16.1218	−	9.30794i	1.25130	−	0.722436i
$167$	−14.4408	+	18.1081i	−1.11746	+	1.40125i	−0.211765	+	0.977321i	$0.567921\pi$
$167$	−14.4408	+	18.1081i	−1.11746	+	1.40125i	−0.905695	+	0.423930i	$0.860650\pi$
$168$		0			0
$169$	4.03779	+	5.06323i	0.310599	+	0.389479i
$170$	5.27406	+	2.06991i	0.404502	+	0.158755i
$171$		0			0
$172$	−1.37023	+	18.2844i	−0.104479	+	1.39417i
$173$	5.56652	−	14.1833i	0.423215	−	1.07833i	−0.547224	−	0.836986i	$-0.684315\pi$
$173$	5.56652	−	14.1833i	0.423215	−	1.07833i	0.970439	−	0.241348i	$-0.0775895\pi$
$174$		0			0
$175$	−5.10782	+	4.16644i	−0.386115	+	0.314953i
$176$	0.0663616	+	0.0529216i	0.00500219	+	0.00398912i
$177$		0			0
$178$	−15.8746	−	9.16520i	−1.18985	−	0.686961i
$179$	−13.6127	+	5.34259i	−1.01746	+	0.399324i	−0.814687	−	0.579902i	$-0.803091\pi$
$179$	−13.6127	+	5.34259i	−1.01746	+	0.399324i	−0.202774	+	0.979226i	$0.564996\pi$
$180$		0			0
$181$	8.68741	+	18.0396i	0.645730	+	1.34087i	0.924746	+	0.380585i	$0.124277\pi$
$181$	8.68741	+	18.0396i	0.645730	+	1.34087i	−0.279016	+	0.960286i	$0.590008\pi$
$182$	−12.9197	+	5.23595i	−0.957672	+	0.388115i
$183$		0			0
$184$	0.993269	+	0.149711i	0.0732247	+	0.0110369i
$185$	11.1099	−	7.57459i	0.816815	−	0.556895i
$186$		0			0
$187$	0.0242161	−	0.0355185i	0.00177086	−	0.00259737i
$188$	6.31895	+	27.6851i	0.460857	+	2.01915i
$189$		0			0
$190$	−0.780931	+	3.42148i	−0.0566547	+	0.248220i
$191$	17.6093	+	18.9783i	1.27417	+	1.37322i	0.893849	+	0.448368i	$0.147995\pi$
$191$	17.6093	+	18.9783i	1.27417	+	1.37322i	0.380317	+	0.924856i	$0.375815\pi$
$192$		0			0
$193$	−13.7765	−	4.24949i	−0.991655	−	0.305885i	−0.243857	−	0.969811i	$-0.578413\pi$
$193$	−13.7765	−	4.24949i	−0.991655	−	0.305885i	−0.747798	+	0.663926i	$0.768889\pi$
$194$	2.41830	+	32.2700i	0.173624	+	2.31685i
$195$		0			0
$196$	1.52718	+	15.7140i	0.109084	+	1.12243i
$197$		−	17.3897i		−	1.23897i	−0.785010	−	0.619483i	$-0.787342\pi$
$197$		−	17.3897i		−	1.23897i	0.785010	−	0.619483i	$-0.212658\pi$
$198$		0			0
$199$	−5.77828	+	18.7327i	−0.409611	+	1.32793i	0.482415	+	0.875943i	$0.339760\pi$
$199$	−5.77828	+	18.7327i	−0.409611	+	1.32793i	−0.892026	+	0.451984i	$0.850716\pi$
$200$	−0.195660	−	1.29812i	−0.0138352	−	0.0917908i
$201$		0			0
$202$	−7.81465	−	1.78364i	−0.549837	−	0.125497i
$203$	1.39533	+	16.2149i	0.0979326	+	1.13806i
$204$		0			0
$205$	−7.57876	−	5.16711i	−0.529323	−	0.360887i
$206$	0.917532	+	0.851345i	0.0639275	+	0.0593160i
$207$		0			0
$208$	−1.30341	+	8.64758i	−0.0903754	+	0.599602i
$209$	0.0239909	+	0.0115534i	0.00165949	+	0.000799167i
$210$		0			0
$211$	4.58913	−	2.21001i	0.315929	−	0.152143i	−0.269198	−	0.963085i	$-0.586759\pi$
$211$	4.58913	−	2.21001i	0.315929	−	0.152143i	0.585127	+	0.810941i	$0.301044\pi$
$212$	−4.23095	−	13.7164i	−0.290583	−	0.942046i
$213$		0			0
$214$	−1.94397	+	3.36706i	−0.132887	+	0.230167i
$215$	−6.43804	−	11.1510i	−0.439071	−	0.760493i
$216$		0			0
$217$	2.09675	+	8.74047i	0.142336	+	0.593342i
$218$	−12.9180	+	10.3018i	−0.874919	+	0.697724i
$219$		0			0
$220$	0.0883111	+	0.00661800i	0.00595393	+	0.000446186i
$221$	4.41674	+	0.330989i	0.297102	+	0.0222647i
$222$		0			0
$223$	3.06932	−	2.44770i	0.205537	−	0.163910i	−0.515312	−	0.857003i	$-0.672324\pi$
$223$	3.06932	−	2.44770i	0.205537	−	0.163910i	0.720848	+	0.693093i	$0.243752\pi$
$224$	19.4502	+	9.10358i	1.29957	+	0.608258i
$225$		0			0
$226$	11.8289	+	20.4883i	0.786849	+	1.36286i
$227$	−2.75156	+	4.76584i	−0.182627	+	0.316320i	−0.942774	−	0.333431i	$-0.891794\pi$
$227$	−2.75156	+	4.76584i	−0.182627	+	0.316320i	0.760147	+	0.649751i	$0.225127\pi$
$228$		0			0
$229$	−7.26405	−	23.5495i	−0.480022	−	1.55619i	−0.794705	−	0.606996i	$-0.792374\pi$
$229$	−7.26405	−	23.5495i	−0.480022	−	1.55619i	0.314683	−	0.949197i	$-0.398102\pi$
$230$	−5.61167	+	2.70244i	−0.370023	+	0.178194i
$231$		0			0
$232$	−2.92030	−	1.40634i	−0.191727	−	0.0923308i
$233$	2.13224	−	14.1465i	0.139688	−	0.926766i	−0.803691	−	0.595047i	$-0.797133\pi$
$233$	2.13224	−	14.1465i	0.139688	−	0.926766i	0.943378	−	0.331719i	$-0.107629\pi$
$234$		0			0
$235$	−14.6183	−	13.5638i	−0.953590	−	0.884802i
$236$	−6.92365	−	4.72047i	−0.450691	−	0.307276i
$237$		0			0
$238$	3.36020	−	8.84766i	0.217809	−	0.573508i
$239$	−14.5649	−	3.32434i	−0.942125	−	0.215034i	−0.276240	−	0.961089i	$-0.589089\pi$
$239$	−14.5649	−	3.32434i	−0.942125	−	0.215034i	−0.665885	+	0.746055i	$0.731946\pi$
$240$		0			0
$241$	−1.26529	−	8.39465i	−0.0815045	−	0.540747i	−0.991901	−	0.127011i	$-0.959462\pi$
$241$	−1.26529	−	8.39465i	−0.0815045	−	0.540747i	0.910397	−	0.413736i	$-0.135776\pi$
$242$	−6.68809	+	21.6822i	−0.429926	+	1.39379i
$243$		0			0
$244$			30.3933i			1.94573i
$245$	−7.10235	−	8.51344i	−0.453753	−	0.543904i
$246$		0			0
$247$	0.205023	+	2.73584i	0.0130453	+	0.174077i
$248$	−1.71061	−	0.527653i	−0.108624	−	0.0335060i
$249$		0			0
$250$	16.6483	+	17.9426i	1.05293	+	1.13479i
$251$	4.71772	−	20.6697i	0.297780	−	1.30466i	−0.575644	−	0.817700i	$-0.695249\pi$
$251$	4.71772	−	20.6697i	0.297780	−	1.30466i	0.873424	−	0.486960i	$-0.161894\pi$
$252$		0			0
$253$	0.0105160	+	0.0460734i	0.000661133	+	0.00289661i
$254$	6.21845	−	9.12080i	0.390181	−	0.572290i
$255$		0			0
$256$	9.22717	−	6.29098i	0.576698	−	0.393186i
$257$	17.6453	+	2.65960i	1.10068	+	0.165901i	0.674167	−	0.738579i	$-0.264503\pi$
$257$	17.6453	+	2.65960i	1.10068	+	0.165901i	0.426515	+	0.904480i	$0.359741\pi$
$258$		0			0
$259$	−12.8571	−	18.4176i	−0.798899	−	1.14442i
$260$	3.95889	+	8.22073i	0.245520	+	0.509828i
$261$		0			0
$262$	−21.3450	+	8.37729i	−1.31870	+	0.517551i
$263$	2.98981	+	1.72617i	0.184359	+	0.106440i	0.589339	−	0.807886i	$-0.299388\pi$
$263$	2.98981	+	1.72617i	0.184359	+	0.106440i	−0.404980	+	0.914326i	$0.632721\pi$
$264$		0			0
$265$	7.88091	+	6.28481i	0.484120	+	0.386073i
$266$	5.72945	+	1.24132i	0.351295	+	0.0761102i
$267$		0			0
$268$	−1.03581	+	2.63921i	−0.0632723	+	0.161215i
$269$	−0.304849	+	4.06793i	−0.0185870	+	0.248026i	0.980169	+	0.198163i	$0.0634975\pi$
$269$	−0.304849	+	4.06793i	−0.0185870	+	0.248026i	−0.998756	+	0.0498630i	$0.984122\pi$
$270$		0			0
$271$	14.9522	+	5.86831i	0.908282	+	0.356474i	0.773054	−	0.634340i	$-0.218728\pi$
$271$	14.9522	+	5.86831i	0.908282	+	0.356474i	0.135228	+	0.990815i	$0.456823\pi$
$272$	−3.70181	−	4.64192i	−0.224455	−	0.281458i
$273$		0			0
$274$	14.6720	−	18.3981i	0.886366	−	1.11147i
$275$	0.0534880	−	0.0308813i	0.00322545	−	0.00186221i
$276$		0			0
$277$	−9.56252	−	24.3649i	−0.574556	−	1.46395i	−0.862380	−	0.506262i	$-0.831027\pi$
$277$	−9.56252	−	24.3649i	−0.574556	−	1.46395i	0.287823	−	0.957684i	$-0.407068\pi$
$278$	−39.4901	+	12.1811i	−2.36846	+	0.730572i
$279$		0			0
$280$	2.17966	−	0.353186i	0.130260	−	0.0211069i
$281$	9.93035	−	20.6206i	0.592395	−	1.23012i	−0.362168	−	0.932113i	$-0.617963\pi$
$281$	9.93035	−	20.6206i	0.592395	−	1.23012i	0.954563	−	0.298008i	$-0.0963224\pi$
$282$		0			0
$283$	15.3722	+	22.5469i	0.913782	+	1.34027i	0.940201	+	0.340621i	$0.110637\pi$
$283$	15.3722	+	22.5469i	0.913782	+	1.34027i	−0.0264192	+	0.999651i	$0.508410\pi$
$284$	7.16144	−	7.71819i	0.424953	−	0.457991i
$285$		0			0
$286$	0.127345	−	0.0290657i	0.00753007	−	0.00171869i
$287$	−8.49107	+	12.7544i	−0.501212	+	0.752870i
$288$		0			0
$289$	10.2576	−	9.51767i	0.603389	−	0.559863i
$290$	19.8736	−	2.99547i	1.16702	−	0.175900i
$291$		0			0
$292$	5.34986	−	0.400917i	0.313077	−	0.0234619i
$293$	24.2102			1.41438			0.707188	−	0.707025i	$-0.249963\pi$
$293$	24.2102			1.41438			0.707188	+	0.707025i	$0.249963\pi$
$294$		0			0
$295$	5.88459			0.342614
$296$	4.46090	−	0.334298i	0.259284	−	0.0194307i
$297$		0			0
$298$	28.2202	−	4.25351i	1.63475	−	0.246399i
$299$	−3.56929	+	3.31182i	−0.206417	+	0.191527i
$300$		0			0
$301$	−18.5073	+	10.9594i	−1.06674	+	0.631689i
$302$	−45.3157	+	10.3430i	−2.60763	+	0.595174i
$303$		0			0
$304$	2.50145	−	2.69592i	0.143468	−	0.154622i
$305$	−12.0232	−	17.6348i	−0.688447	−	1.00977i
$306$		0			0
$307$	1.71898	−	3.56949i	0.0981071	−	0.203721i	−0.846139	−	0.532963i	$-0.821079\pi$
$307$	1.71898	−	3.56949i	0.0981071	−	0.203721i	0.944246	+	0.329241i	$0.106793\pi$
$308$	0.00942562	−	0.147632i	0.000537074	−	0.00841211i
$309$		0			0
$310$	10.6069	−	3.27179i	0.602431	−	0.185825i
$311$	8.97248	+	22.8615i	0.508783	+	1.29636i	0.922516	+	0.385959i	$0.126129\pi$
$311$	8.97248	+	22.8615i	0.508783	+	1.29636i	−0.413733	+	0.910398i	$0.635775\pi$
$312$		0			0
$313$	4.67698	−	2.70025i	0.264358	−	0.152627i	−0.361963	−	0.932193i	$-0.617893\pi$
$313$	4.67698	−	2.70025i	0.264358	−	0.152627i	0.626321	+	0.779565i	$0.284560\pi$
$314$	2.28472	−	2.86495i	0.128934	−	0.161678i
$315$		0			0
$316$	−9.49867	−	11.9110i	−0.534342	−	0.670044i
$317$	−10.1831	−	3.99658i	−0.571940	−	0.224470i	0.0617040	−	0.998094i	$-0.480347\pi$
$317$	−10.1831	−	3.99658i	−0.571940	−	0.224470i	−0.633644	+	0.773624i	$0.718442\pi$
$318$		0			0
$319$	0.0113958	−	0.152067i	0.000638044	−	0.00851411i
$320$	5.72649	−	14.5909i	0.320121	−	0.815654i
$321$		0			0
$322$	4.61749	+	9.32357i	0.257323	+	0.519583i
$323$	−1.45623	−	1.16131i	−0.0810270	−	0.0646169i
$324$		0			0
$325$	5.51093	+	3.18174i	0.305692	+	0.176491i
$326$	−14.6670	+	5.75638i	−0.812331	+	0.318817i
$327$		0			0
$328$	−1.32404	−	2.74939i	−0.0731077	−	0.151810i
$329$	−22.3865	+	24.6677i	−1.23421	+	1.35997i
$330$		0			0
$331$	−9.66964	−	1.45746i	−0.531491	−	0.0801094i	−0.122187	−	0.992507i	$-0.538991\pi$
$331$	−9.66964	−	1.45746i	−0.531491	−	0.0801094i	−0.409305	+	0.912398i	$0.634229\pi$
$332$	−16.8170	+	11.4656i	−0.922950	+	0.629257i
$333$		0			0
$334$	26.9146	−	39.4765i	1.47270	−	2.16006i
$335$	−0.443037	−	1.94107i	−0.0242057	−	0.106052i
$336$		0			0
$337$	4.67155	−	20.4674i	0.254475	−	1.11493i	−0.672586	−	0.740019i	$-0.734816\pi$
$337$	4.67155	−	20.4674i	0.254475	−	1.11493i	0.927061	−	0.374910i	$-0.122326\pi$
$338$	−9.08668	−	9.79312i	−0.494250	−	0.532675i
$339$		0			0
$340$	−5.91938	−	1.82589i	−0.321023	−	0.0990225i
$341$	−0.00629384	−	0.0839855i	−0.000340831	−	0.00454807i
$342$		0			0
$343$	−14.0894	+	12.0204i	−0.760755	+	0.649040i
$344$		−	4.28369i		−	0.230961i
$345$		0			0
$346$	−9.26444	+	30.0346i	−0.498059	+	1.61467i
$347$	−3.54695	−	23.5325i	−0.190410	−	1.26329i	−0.856001	−	0.516973i	$-0.827059\pi$
$347$	−3.54695	−	23.5325i	−0.190410	−	1.26329i	0.665591	−	0.746317i	$-0.268180\pi$
$348$		0			0
$349$	−18.1974	−	4.15345i	−0.974086	−	0.222329i	−0.294279	−	0.955720i	$-0.595079\pi$
$349$	−18.1974	−	4.15345i	−0.974086	−	0.222329i	−0.679807	+	0.733391i	$0.737937\pi$
$350$	9.86502	−	9.35820i	0.527308	−	0.500217i
$351$		0			0
$352$	−0.166257	−	0.113352i	−0.00886152	−	0.00604168i
$353$	4.90415	+	4.55038i	0.261021	+	0.242192i	0.799817	−	0.600244i	$-0.204930\pi$
$353$	4.90415	+	4.55038i	0.261021	+	0.242192i	−0.538795	+	0.842437i	$0.681120\pi$
$354$		0			0
$355$	−1.10199	+	7.31122i	−0.0584875	+	0.388039i
$356$	18.0568	+	8.69568i	0.957006	+	0.460870i
$357$		0			0
$358$	27.1791	−	13.0888i	1.43646	−	0.691763i
$359$	3.05783	+	9.91324i	0.161386	+	0.523201i	0.999760	−	0.0218943i	$-0.00696971\pi$
$359$	3.05783	+	9.91324i	0.161386	+	0.523201i	−0.838374	+	0.545095i	$0.816494\pi$
$360$		0			0
$361$	−8.92313	+	15.4553i	−0.469639	+	0.813438i
$362$	−20.6518	−	35.7700i	−1.08544	−	1.88003i
$363$		0			0
$364$	13.6584	−	6.76432i	0.715896	−	0.354547i
$365$	−2.94550	+	2.34895i	−0.154174	+	0.122950i
$366$		0			0
$367$	12.9015	+	0.966830i	0.673450	+	0.0504681i	0.407066	−	0.913399i	$-0.366552\pi$
$367$	12.9015	+	0.966830i	0.673450	+	0.0504681i	0.266384	+	0.963867i	$0.414171\pi$
$368$	6.50874	+	0.487762i	0.339291	+	0.0254264i
$369$		0			0
$370$	−21.6865	+	17.2944i	−1.12743	+	0.899093i
$371$	10.3524	−	13.2797i	0.537472	−	0.689449i
$372$		0			0
$373$	3.66077	+	6.34064i	0.189548	+	0.328306i	0.945099	−	0.326783i	$-0.105965\pi$
$373$	3.66077	+	6.34064i	0.189548	+	0.328306i	−0.755552	+	0.655089i	$0.772631\pi$
$374$	−0.0443396	+	0.0767984i	−0.00229274	+	0.00397115i
$375$		0			0
$376$	−1.95549	−	6.33956i	−0.100847	−	0.326938i
$377$	14.1556	−	6.81699i	0.729052	−	0.351093i
$378$		0			0
$379$	−12.4480	−	5.99463i	−0.639410	−	0.307924i	0.0859438	−	0.996300i	$-0.472609\pi$
$379$	−12.4480	−	5.99463i	−0.639410	−	0.307924i	−0.725354	+	0.688376i	$0.758324\pi$
$380$	0.571886	−	3.79421i	0.0293371	−	0.194639i
$381$		0			0
$382$	−39.1499	−	36.3258i	−2.00308	−	1.85859i
$383$	11.2151	+	7.64631i	0.573063	+	0.390708i	0.814894	−	0.579611i	$-0.196795\pi$
$383$	11.2151	+	7.64631i	0.573063	+	0.390708i	−0.241830	+	0.970319i	$0.577748\pi$
$384$		0			0
$385$	0.0529323	+	0.0893876i	0.00269768	+	0.00455561i
$386$	28.9948	+	6.61787i	1.47580	+	0.336841i
$387$		0			0
$388$	−5.27330	−	34.9861i	−0.267711	−	1.77615i
$389$	5.54465	−	17.9753i	0.281125	−	0.911384i	−0.699357	−	0.714773i	$-0.746530\pi$
$389$	5.54465	−	17.9753i	0.281125	−	0.911384i	0.980482	−	0.196611i	$-0.0629937\pi$
$390$		0			0
$391$		−	3.30566i		−	0.167175i
$392$	−0.630140	−	3.63427i	−0.0318269	−	0.183558i
$393$		0			0
$394$	2.68077	+	35.7724i	0.135055	+	1.80219i
$395$	10.2231	+	3.15342i	0.514382	+	0.158666i
$396$		0			0
$397$	5.43344	+	5.85585i	0.272696	+	0.293897i	0.854520	−	0.519418i	$-0.173851\pi$
$397$	5.43344	+	5.85585i	0.272696	+	0.293897i	−0.581824	+	0.813315i	$0.697661\pi$
$398$	8.99870	−	39.4259i	0.451064	−	1.97624i
$399$		0			0
$400$	−1.89815	−	8.31635i	−0.0949076	−	0.415818i
$401$	17.6387	−	25.8712i	0.880834	−	1.29195i	−0.0747422	−	0.997203i	$-0.523813\pi$
$401$	17.6387	−	25.8712i	0.880834	−	1.29195i	0.955576	−	0.294744i	$-0.0952342\pi$
$402$		0			0
$403$	7.16960	−	4.88815i	0.357143	−	0.243496i
$404$	8.66597	+	1.30619i	0.431148	+	0.0649851i
$405$		0			0
$406$	−5.36999	−	33.1405i	−0.266508	−	1.64474i
$407$	0.0913156	+	0.189619i	0.00452635	+	0.00939905i
$408$		0			0
$409$	−17.0742	+	6.70113i	−0.844265	+	0.331350i	−0.747749	−	0.663982i	$-0.768865\pi$
$409$	−17.0742	+	6.70113i	−0.844265	+	0.331350i	−0.0965163	+	0.995331i	$0.530770\pi$
$410$	16.3868	+	9.46094i	0.809288	+	0.467243i
$411$		0			0
$412$	−1.06994	−	0.853245i	−0.0527120	−	0.0420364i
$413$	−0.108529	−	9.82929i	−0.00534037	−	0.483668i
$414$		0			0
$415$	5.22188	−	13.3051i	0.256332	−	0.653123i
$416$	1.54931	−	20.6741i	0.0759612	−	1.01363i
$417$		0			0
$418$	−0.0511328	−	0.0200682i	−0.00250099	−	0.000981566i
$419$	18.7981	+	23.5720i	0.918346	+	1.15157i	0.988070	+	0.154004i	$0.0492167\pi$
$419$	18.7981	+	23.5720i	0.918346	+	1.15157i	−0.0697240	+	0.997566i	$0.522212\pi$
$420$		0			0
$421$	11.2650	−	14.1259i	0.549023	−	0.688454i	−0.427463	−	0.904033i	$-0.640593\pi$
$421$	11.2650	−	14.1259i	0.549023	−	0.688454i	0.976486	+	0.215579i	$0.0691640\pi$
$422$	−9.09962	+	5.25367i	−0.442963	+	0.255745i
$423$		0			0
$424$	1.22517	+	3.12168i	0.0594994	+	0.151602i
$425$	−4.12829	+	1.27341i	−0.200251	+	0.0617694i
$426$		0			0
$427$	−29.2344	+	20.4081i	−1.41475	+	0.987618i
$428$	1.84438	−	3.82990i	0.0891517	−	0.185125i
$429$		0			0
$430$	14.9627	+	21.9463i	0.721567	+	1.05834i
$431$	−25.6720	+	27.6678i	−1.23658	+	1.33271i	−0.312781	+	0.949825i	$0.601261\pi$
$431$	−25.6720	+	27.6678i	−1.23658	+	1.33271i	−0.923795	+	0.382887i	$0.874930\pi$
$432$		0			0
$433$	17.1321	−	3.91028i	0.823315	−	0.187916i	0.209946	−	0.977713i	$-0.432671\pi$
$433$	17.1321	−	3.91028i	0.823315	−	0.187916i	0.613369	+	0.789797i	$0.289814\pi$
$434$	−5.66064	−	17.6568i	−0.271720	−	0.847554i
$435$		0			0
$436$	13.2427	−	12.2874i	0.634209	−	0.588460i
$437$	2.02474	−	0.305180i	0.0968563	−	0.0145987i
$438$		0			0
$439$	−33.5692	+	2.51566i	−1.60217	+	0.120066i	−0.845589	−	0.533835i	$-0.820750\pi$
$439$	−33.5692	+	2.51566i	−1.60217	+	0.120066i	−0.756580	+	0.653901i	$0.773131\pi$
$440$	−0.0206896			−0.000986339
$441$		0			0
$442$	−9.13672			−0.434589
$443$	2.93923	−	0.220264i	0.139647	−	0.0104651i	−0.00472328	−	0.999989i	$-0.501503\pi$
$443$	2.93923	−	0.220264i	0.139647	−	0.0104651i	0.144370	+	0.989524i	$0.453884\pi$
$444$		0			0
$445$	−13.9168	+	2.09762i	−0.659719	+	0.0994366i
$446$	−5.93657	+	5.50834i	−0.281105	+	0.260827i
$447$		0			0
$448$	−24.4774	−	9.29611i	−1.15645	−	0.439200i
$449$	26.6555	−	6.08394i	1.25795	−	0.287119i	0.458956	−	0.888459i	$-0.348224\pi$
$449$	26.6555	−	6.08394i	1.25795	−	0.287119i	0.798993	+	0.601340i	$0.205366\pi$
$450$		0			0
$451$	0.0976516	−	0.105243i	0.00459823	−	0.00495572i
$452$	−14.5710	−	21.3717i	−0.685362	−	1.00524i
$453$		0			0
$454$	4.92554	−	10.2280i	0.231167	−	0.480024i
$455$	−5.24900	+	9.32788i	−0.246077	+	0.437298i
$456$		0			0
$457$	−33.1314	+	10.2197i	−1.54982	+	0.478057i	−0.947381	−	0.320107i	$-0.896281\pi$
$457$	−33.1314	+	10.2197i	−1.54982	+	0.478057i	−0.602441	+	0.798164i	$0.705805\pi$
$458$	18.5732	+	47.3239i	0.867871	+	2.21130i
$459$		0			0
$460$	5.89755	−	3.40495i	0.274974	−	0.158757i
$461$	12.6975	−	15.9222i	0.591381	−	0.741569i	−0.392626	−	0.919698i	$-0.628433\pi$
$461$	12.6975	−	15.9222i	0.591381	−	0.741569i	0.984007	+	0.178130i	$0.0570046\pi$
$462$		0			0
$463$	10.2185	+	12.8136i	0.474894	+	0.595499i	0.960362	−	0.278756i	$-0.0899221\pi$
$463$	10.2185	+	12.8136i	0.474894	+	0.595499i	−0.485468	+	0.874255i	$0.661351\pi$
$464$	−19.6054	−	7.69456i	−0.910159	−	0.357211i
$465$		0			0
$466$	−2.20543	+	29.4294i	−0.102165	+	1.36329i
$467$	13.7256	−	34.9724i	0.635147	−	1.61833i	−0.142622	−	0.989777i	$-0.545553\pi$
$467$	13.7256	−	34.9724i	0.635147	−	1.61833i	0.777769	−	0.628550i	$-0.216351\pi$
$468$		0			0
$469$	−3.23409	+	0.775823i	−0.149336	+	0.0358242i
$470$	32.1622	+	25.6485i	1.48353	+	1.18308i
$471$		0			0
$472$	1.69544	+	0.978860i	0.0780388	+	0.0450557i
$473$	0.187604	−	0.0736292i	0.00862604	−	0.00338547i
$474$		0			0
$475$	−1.16109	−	2.41104i	−0.0532746	−	0.110626i
$476$	−2.94068	+	9.92106i	−0.134786	+	0.454731i
$477$		0			0
$478$	30.4740	+	4.59321i	1.39385	+	0.210089i
$479$	−4.18996	+	2.85667i	−0.191444	+	0.130524i	−0.655249	−	0.755413i	$-0.727436\pi$
$479$	−4.18996	+	2.85667i	−0.191444	+	0.130524i	0.463805	+	0.885937i	$0.346484\pi$
$480$		0			0
$481$	−12.2151	+	17.9162i	−0.556959	+	0.816909i
$482$	3.89694	+	17.0736i	0.177501	+	0.777681i
$483$		0			0
$484$	5.52039	−	24.1864i	0.250927	−	1.09938i
$485$	16.8997	+	18.2136i	0.767376	+	0.827035i
$486$		0			0
$487$	−9.15556	−	2.82411i	−0.414878	−	0.127973i	0.0802873	−	0.996772i	$-0.474416\pi$
$487$	−9.15556	−	2.82411i	−0.414878	−	0.127973i	−0.495165	+	0.868799i	$0.664892\pi$
$488$	−0.530634	−	7.08082i	−0.0240207	−	0.320534i
$489$		0			0
$490$	15.9227	+	16.4181i	0.719314	+	0.741695i
$491$		−	16.5564i		−	0.747180i	−0.927594	−	0.373590i	$-0.878127\pi$
$491$		−	16.5564i		−	0.747180i	0.927594	−	0.373590i	$-0.121873\pi$
$492$		0			0
$493$	−3.14407	+	10.1928i	−0.141602	+	0.459062i
$494$	−0.843505	−	5.59629i	−0.0379511	−	0.251789i
$495$		0			0
$496$	−11.3404	−	2.58837i	−0.509198	−	0.116221i
$497$	12.2326	+	1.70586i	0.548705	+	0.0765182i
$498$		0			0
$499$	9.03976	+	6.16320i	0.404675	+	0.275903i	0.748505	−	0.663129i	$-0.230772\pi$
$499$	9.03976	+	6.16320i	0.404675	+	0.275903i	−0.343830	+	0.939032i	$0.611724\pi$
$500$	−19.6175	−	18.2024i	−0.877322	−	0.814036i
$501$		0			0
$502$	−6.51843	+	43.2470i	−0.290932	+	1.93021i
$503$	8.08470	+	3.89339i	0.360479	+	0.173598i	0.605353	−	0.795957i	$-0.293032\pi$
$503$	8.08470	+	3.89339i	0.360479	+	0.173598i	−0.244874	+	0.969555i	$0.578746\pi$
$504$		0			0
$505$	−5.54487	+	2.67027i	−0.246744	+	0.118825i
$506$	−0.0287350	−	0.0931566i	−0.00127743	−	0.00414132i
$507$		0			0
$508$	−6.03470	+	10.4524i	−0.267746	+	0.463750i
$509$	4.15844	+	7.20262i	0.184319	+	0.319251i	0.943347	−	0.331808i	$-0.107659\pi$
$509$	4.15844	+	7.20262i	0.184319	+	0.319251i	−0.759028	+	0.651059i	$0.774325\pi$
$510$		0			0
$511$	3.97788	+	4.87667i	0.175971	+	0.215731i
$512$	−24.5492	+	19.5773i	−1.08493	+	0.865203i
$513$		0			0
$514$	−36.7081	−	2.75089i	−1.61913	−	0.121337i
$515$	0.958330	+	0.0718169i	0.0422291	+	0.00316463i
$516$		0			0
$517$	0.244029	−	0.194607i	0.0107324	−	0.00855879i
$518$	29.2875	+	35.9049i	1.28682	+	1.57757i
$519$		0			0
$520$	−1.06584	−	1.84609i	−0.0467401	−	0.0809562i
$521$	−16.4443	+	28.4824i	−0.720439	+	1.24784i	0.240385	+	0.970678i	$0.422726\pi$
$521$	−16.4443	+	28.4824i	−0.720439	+	1.24784i	−0.960824	+	0.277160i	$0.910607\pi$
$522$		0			0
$523$	−9.16933	−	29.7262i	−0.400947	−	1.29984i	−0.900991	−	0.433838i	$-0.857159\pi$
$523$	−9.16933	−	29.7262i	−0.400947	−	1.29984i	0.500044	−	0.866000i	$-0.333317\pi$
$524$	22.5878	−	10.8777i	0.986751	−	0.475194i
$525$		0			0
$526$	−6.41644	−	3.09000i	−0.279770	−	0.134730i
$527$	−0.878032	+	5.82536i	−0.0382477	+	0.253757i
$528$		0			0
$529$	−14.1963	−	13.1722i	−0.617229	−	0.572705i
$530$	−17.1807	−	11.7136i	−0.746281	−	0.508806i
$531$		0			0
$532$	−6.34819	−	0.885269i	−0.275229	−	0.0383813i
$533$	14.4212	+	3.29154i	0.624652	+	0.142573i
$534$		0			0
$535$	0.444912	+	2.95180i	0.0192352	+	0.127617i
$536$	0.195238	−	0.632947i	0.00843301	−	0.0273391i
$537$		0			0
$538$		−	8.41514i		−	0.362802i
$539$	0.148332	−	0.0900637i	0.00638910	−	0.00387932i
$540$		0			0
$541$	−1.70890	−	22.8037i	−0.0734713	−	0.980407i	−0.905134	−	0.425126i	$-0.860230\pi$
$541$	−1.70890	−	22.8037i	−0.0734713	−	0.980407i	0.831663	−	0.555281i	$-0.187389\pi$
$542$	−31.6629	−	9.76670i	−1.36004	−	0.419516i
$543$		0			0
$544$	9.57357	+	10.3179i	0.410463	+	0.442374i
$545$	−2.82292	+	12.3680i	−0.120921	+	0.529788i
$546$		0			0
$547$	3.70261	+	16.2222i	0.158312	+	0.693611i	0.990315	+	0.138839i	$0.0443372\pi$
$547$	3.70261	+	16.2222i	0.158312	+	0.693611i	−0.832003	+	0.554771i	$0.812806\pi$
$548$	−14.4935	+	21.2580i	−0.619130	+	0.908097i
$549$		0			0
$550$	−0.105270	+	0.0717716i	−0.00448871	+	0.00306035i
$551$	−6.53343	−	0.984756i	−0.278333	−	0.0419520i
$552$		0			0
$553$	5.07875	−	17.1343i	0.215970	−	0.728625i
$554$	23.4271	+	48.6470i	0.995324	+	2.06681i
$555$		0			0
$556$	42.0604	−	16.5075i	1.78376	−	0.700073i
$557$	−13.7460	−	7.93624i	−0.582436	−	0.336269i	0.179665	−	0.983728i	$-0.442499\pi$
$557$	−13.7460	−	7.93624i	−0.582436	−	0.336269i	−0.762101	+	0.647458i	$0.775832\pi$
$558$		0			0
$559$	16.2343	+	12.9464i	0.686638	+	0.547575i
$560$	13.9520	−	3.34693i	0.589578	−	0.141434i
$561$		0			0
$562$	−17.2489	+	43.9495i	−0.727601	+	1.85390i
$563$	2.94422	−	39.2878i	0.124084	−	1.65578i	−0.493845	−	0.869550i	$-0.664409\pi$
$563$	2.94422	−	39.2878i	0.124084	−	1.65578i	0.617929	−	0.786234i	$-0.287972\pi$
$564$		0			0
$565$	16.9087	+	6.63619i	0.711356	+	0.279187i
$566$	−35.0979	−	44.0114i	−1.47528	−	1.84994i
$567$		0			0
$568$	−1.53367	+	1.92316i	−0.0643513	+	0.0806939i
$569$	−9.17204	+	5.29548i	−0.384512	+	0.221998i	−0.679780	−	0.733417i	$-0.737925\pi$
$569$	−9.17204	+	5.29548i	−0.384512	+	0.221998i	0.295268	+	0.955415i	$0.404591\pi$
$570$		0			0
$571$	9.93798	+	25.3216i	0.415891	+	1.05967i	0.973321	+	0.229450i	$0.0736926\pi$
$571$	9.93798	+	25.3216i	0.415891	+	1.05967i	−0.557429	+	0.830225i	$0.688212\pi$
$572$	−0.136468	+	0.0420949i	−0.00570603	+	0.00176008i
$573$		0			0
$574$	15.5008	−	27.5461i	0.646991	−	1.14975i
$575$	2.06067	−	4.27902i	0.0859358	−	0.178448i
$576$		0			0
$577$	3.79455	+	5.56558i	0.157969	+	0.231698i	0.897061	−	0.441906i	$-0.145698\pi$
$577$	3.79455	+	5.56558i	0.157969	+	0.231698i	−0.739092	+	0.673604i	$0.764745\pi$
$578$	−19.6337	+	21.1601i	−0.816655	+	0.880145i
$579$		0			0
$580$	−21.4233	+	4.88972i	−0.889553	+	0.203035i
$581$	−22.3204	−	8.47695i	−0.926008	−	0.351683i
$582$		0			0
$583$	−0.115655	+	0.107312i	−0.00478995	+	0.00444442i
$584$	−1.23937	+	0.186805i	−0.0512855	+	0.00773005i
$585$		0			0
$586$	−49.8029	+	3.73221i	−2.05734	+	0.154176i
$587$	−31.5688			−1.30298			−0.651491	−	0.758656i	$-0.725856\pi$
$587$	−31.5688			−1.30298			−0.651491	+	0.758656i	$0.725856\pi$
$588$		0			0
$589$	−3.64912			−0.150360
$590$	−12.1052	+	0.907160i	−0.498364	+	0.0373472i
$591$		0			0
$592$	28.7427	−	4.33227i	1.18132	−	0.178055i
$593$	−3.39846	+	3.15331i	−0.139558	+	0.129491i	−0.746863	−	0.664978i	$-0.768441\pi$
$593$	−3.39846	+	3.15331i	−0.139558	+	0.129491i	0.607305	+	0.794469i	$0.292251\pi$
$594$		0			0
$595$	−2.21840	−	6.91969i	−0.0909455	−	0.283680i
$596$	−30.4207	+	6.94332i	−1.24608	+	0.284410i
$597$		0			0
$598$	6.83185	−	7.36298i	0.279375	−	0.301095i
$599$	−0.460460	−	0.675370i	−0.0188139	−	0.0275949i	0.816717	−	0.577039i	$-0.195792\pi$
$599$	−0.460460	−	0.675370i	−0.0188139	−	0.0275949i	−0.835530	+	0.549444i	$0.814840\pi$
$600$		0			0
$601$	6.33656	−	13.1580i	0.258474	−	0.536726i	−0.730837	−	0.682552i	$-0.760870\pi$
$601$	6.33656	−	13.1580i	0.258474	−	0.536726i	0.989310	+	0.145827i	$0.0465841\pi$
$602$	36.3819	−	25.3977i	1.48282	−	1.03513i
$603$		0			0
$604$	48.5622	−	14.9795i	1.97597	−	0.609506i
$605$	6.36478	+	16.2172i	0.258765	+	0.659323i
$606$		0			0
$607$	23.4430	−	13.5348i	0.951521	−	0.549361i	0.0579680	−	0.998318i	$-0.481538\pi$
$607$	23.4430	−	13.5348i	0.951521	−	0.549361i	0.893553	+	0.448957i	$0.148205\pi$
$608$	−5.43590	+	6.81641i	−0.220455	+	0.276442i
$609$		0			0
$610$	27.4515	+	34.4231i	1.11148	+	1.39375i
$611$	29.9356	+	11.7489i	1.21106	+	0.475308i
$612$		0			0
$613$	−2.82091	+	37.6424i	−0.113935	+	1.52036i	0.588432	+	0.808547i	$0.299746\pi$
$613$	−2.82091	+	37.6424i	−0.113935	+	1.52036i	−0.702367	+	0.711815i	$0.747873\pi$
$614$	−2.98584	+	7.60780i	−0.120499	+	0.307026i
$615$		0			0
$616$	0.000381577		0.0345588i	1.53742e−5		0.00139241i
$617$	−5.92929	−	4.72845i	−0.238704	−	0.190360i	0.496830	−	0.867848i	$-0.334497\pi$
$617$	−5.92929	−	4.72845i	−0.238704	−	0.190360i	−0.735534	+	0.677488i	$0.763069\pi$
$618$		0			0
$619$	−10.3354	−	5.96714i	−0.415415	−	0.239840i	0.277699	−	0.960668i	$-0.410428\pi$
$619$	−10.3354	−	5.96714i	−0.415415	−	0.239840i	−0.693114	+	0.720828i	$0.743762\pi$
$620$	−11.2973	+	4.43385i	−0.453709	+	0.178068i
$621$		0			0
$622$	−21.9816	−	45.6453i	−0.881382	−	1.83021i
$623$	3.76041	+	23.2071i	0.150658	+	0.929773i
$624$		0			0
$625$	6.26529	+	0.944341i	0.250612	+	0.0377736i
$626$	−9.20475	+	6.27569i	−0.367896	+	0.250827i
$627$		0			0
$628$	−2.25692	+	3.31030i	−0.0900611	+	0.132095i
$629$	−3.27584	−	14.3524i	−0.130616	−	0.572268i
$630$		0			0
$631$	−1.78464	+	7.81900i	−0.0710452	+	0.311270i	−0.997948	−	0.0640325i	$-0.979604\pi$
$631$	−1.78464	+	7.81900i	−0.0710452	+	0.311270i	0.926903	+	0.375302i	$0.122461\pi$
$632$	2.42088	+	2.60909i	0.0962976	+	0.103784i
$633$		0			0
$634$	21.5638	+	6.65155i	0.856408	+	0.264167i
$635$	−0.633385	−	8.45193i	−0.0251351	−	0.335405i
$636$		0			0
$637$	15.6776	+	8.59560i	0.621168	+	0.340570i
$638$			0.314574i			0.0124541i
$639$		0			0
$640$	−1.95192	+	6.32798i	−0.0771566	+	0.250135i
$641$	−2.81239	−	18.6590i	−0.111083	−	0.736985i	−0.973147	−	0.230186i	$-0.926067\pi$
$641$	−2.81239	−	18.6590i	−0.111083	−	0.736985i	0.862064	−	0.506799i	$-0.169171\pi$
$642$		0			0
$643$	5.92739	+	1.35289i	0.233754	+	0.0533527i	0.337793	−	0.941220i	$-0.390320\pi$
$643$	5.92739	+	1.35289i	0.233754	+	0.0533527i	−0.104039	+	0.994573i	$0.533177\pi$
$644$	−5.79620	−	9.78813i	−0.228402	−	0.385706i
$645$		0			0
$646$	3.17465	+	2.16444i	0.124905	+	0.0851587i
$647$	−35.2612	−	32.7176i	−1.38626	−	1.28626i	−0.914530	−	0.404519i	$-0.867439\pi$
$647$	−35.2612	−	32.7176i	−1.38626	−	1.28626i	−0.471730	−	0.881743i	$-0.656370\pi$
$648$		0			0
$649$	−0.0137276	+	0.0910764i	−0.000538854	+	0.00357506i
$650$	−11.8270	−	5.69560i	−0.463895	−	0.223400i
$651$		0			0
$652$	15.5210	−	7.47451i	0.607849	−	0.292724i
$653$	3.10106	+	10.0534i	0.121354	+	0.393420i	0.995784	−	0.0917323i	$-0.0292404\pi$
$653$	3.10106	+	10.0534i	0.121354	+	0.393420i	−0.874430	+	0.485152i	$0.838764\pi$
$654$		0			0
$655$	−8.80279	+	15.2469i	−0.343953	+	0.595745i
$656$	−9.91436	−	17.1722i	−0.387091	−	0.670461i
$657$		0			0
$658$	42.2486	−	54.1950i	1.64702	−	2.11274i
$659$	8.42794	−	6.72106i	0.328306	−	0.261815i	−0.445439	−	0.895312i	$-0.646952\pi$
$659$	8.42794	−	6.72106i	0.328306	−	0.261815i	0.773745	+	0.633497i	$0.218381\pi$
$660$		0			0
$661$	38.9257	+	2.91708i	1.51404	+	0.113461i	0.805662	−	0.592376i	$-0.201810\pi$
$661$	38.9257	+	2.91708i	1.51404	+	0.113461i	0.708374	+	0.705837i	$0.249429\pi$
$662$	20.1161	+	1.50749i	0.781835	+	0.0585904i
$663$		0			0
$664$	3.71771	−	2.96478i	0.144275	−	0.115056i
$665$	4.03354	−	1.99761i	0.156414	−	0.0774640i
$666$		0			0
$667$	−5.86313	−	10.1552i	−0.227021	−	0.393213i
$668$	−26.1193	+	45.2399i	−1.01058	+	1.75038i
$669$		0			0
$670$	1.21061	+	3.92469i	0.0467698	+	0.151624i
$671$	0.300983	−	0.144946i	0.0116193	−	0.00559558i
$672$		0			0
$673$	−18.6393	−	8.97621i	−0.718492	−	0.346007i	0.0386545	−	0.999253i	$-0.487693\pi$
$673$	−18.6393	−	8.97621i	−0.718492	−	0.346007i	−0.757146	+	0.653245i	$0.773407\pi$
$674$	−6.45463	+	42.8237i	−0.248623	+	1.64951i
$675$		0			0
$676$	10.7073	+	9.93490i	0.411818	+	0.382112i
$677$	10.6247	+	7.24382i	0.408341	+	0.278402i	0.750021	−	0.661414i	$-0.230043\pi$
$677$	10.6247	+	7.24382i	0.408341	+	0.278402i	−0.341680	+	0.939817i	$0.610996\pi$
$678$		0			0
$679$	30.1112	−	28.5642i	1.15556	−	1.09619i
$680$	1.41093	+	0.322036i	0.0541067	+	0.0123495i
$681$		0			0
$682$	0.0258941	+	0.171796i	0.000991538	+	0.00657843i
$683$	0.271537	−	0.880302i	0.0103901	−	0.0336838i	−0.950229	−	0.311551i	$-0.899151\pi$
$683$	0.271537	−	0.880302i	0.0103901	−	0.0336838i	0.960619	+	0.277867i	$0.0896276\pi$
$684$		0			0
$685$		−	18.0677i		−	0.690333i
$686$	27.1302	−	26.8991i	1.03584	−	1.02701i
$687$		0			0
$688$	−2.08009	−	27.7568i	−0.0793026	−	1.05822i
$689$	−15.5333	−	4.79138i	−0.591771	−	0.182537i
$690$		0			0
$691$	−14.2028	−	15.3070i	−0.540301	−	0.582307i	0.402601	−	0.915376i	$-0.368106\pi$
$691$	−14.2028	−	15.3070i	−0.540301	−	0.582307i	−0.942902	+	0.333069i	$0.891916\pi$
$692$	7.64692	−	33.5034i	0.290692	−	1.27361i
$693$		0			0
$694$	10.9242	+	47.8619i	0.414676	+	1.81681i
$695$	−17.8741	+	26.2165i	−0.678003	+	0.994448i
$696$		0			0
$697$	−8.29748	+	5.65713i	−0.314289	+	0.214279i
$698$	38.0743	+	5.73877i	1.44113	+	0.217216i
$699$		0			0
$700$	−9.99112	+	11.0092i	−0.377629	+	0.416108i
$701$	3.27599	+	6.80266i	0.123732	+	0.256933i	0.953629	−	0.300984i	$-0.0973151\pi$
$701$	3.27599	+	6.80266i	0.123732	+	0.256933i	−0.829897	+	0.557917i	$0.811601\pi$
$702$		0			0
$703$	8.48850	−	3.33149i	0.320150	−	0.125649i
$704$	0.212466	+	0.122667i	0.00800760	+	0.00462319i
$705$		0			0
$706$	−10.7898	−	8.60458i	−0.406080	−	0.323838i
$707$	4.56253	+	9.21260i	0.171592	+	0.346475i
$708$		0			0
$709$	8.10828	−	20.6596i	0.304513	−	0.775886i	−0.693927	−	0.720046i	$-0.744121\pi$
$709$	8.10828	−	20.6596i	0.304513	−	0.775886i	0.998440	−	0.0558406i	$-0.0177839\pi$
$710$	1.13982	−	15.2098i	0.0427766	−	0.570814i
$711$		0			0
$712$	−4.35855	−	1.71060i	−0.163343	−	0.0641076i
$713$	−4.03793	−	5.06340i	−0.151222	−	0.189626i
$714$		0			0
$715$	0.0625294	−	0.0784093i	0.00233847	−	0.00293234i
$716$	−28.5637	+	16.4913i	−1.06748	+	0.616307i
$717$		0			0
$718$	−7.81848	−	19.9212i	−0.291783	−	0.743451i
$719$	−0.460322	+	0.141990i	−0.0171671	+	0.00529535i	−0.303327	−	0.952887i	$-0.598097\pi$
$719$	−0.460322	+	0.141990i	−0.0171671	+	0.00529535i	0.286160	+	0.958182i	$0.407621\pi$
$720$		0			0
$721$	0.102284	−	1.60206i	0.00380927	−	0.0596640i
$722$	15.9732	−	33.1687i	0.594462	−	1.23441i
$723$		0			0
$724$	25.4391	+	37.3123i	0.945438	+	1.38670i
$725$	−10.4238	+	11.2342i	−0.387131	+	0.417228i
$726$		0			0
$727$	20.3795	−	4.65149i	0.755834	−	0.172514i	0.172795	−	0.984958i	$-0.444720\pi$
$727$	20.3795	−	4.65149i	0.755834	−	0.172514i	0.583040	+	0.812444i	$0.301863\pi$
$728$	−3.06394	+	1.81436i	−0.113557	+	0.0672448i
$729$		0			0
$730$	5.69707	−	5.28611i	0.210858	−	0.195648i
$731$	−13.9397	+	2.10107i	−0.515579	+	0.0777111i
$732$		0			0
$733$	−47.5504	+	3.56341i	−1.75632	+	0.131618i	−0.913567	−	0.406689i	$-0.866683\pi$
$733$	−47.5504	+	3.56341i	−1.75632	+	0.131618i	−0.842749	+	0.538307i	$0.819064\pi$
$734$	−26.6887			−0.985096
$735$		0			0
$736$	−15.4733			−0.570354
$737$	0.0310757	−	0.00232880i	0.00114469	−	8.57825e-5i
$738$		0			0
$739$	28.0545	−	4.22854i	1.03200	−	0.155549i	0.388861	−	0.921296i	$-0.372869\pi$
$739$	28.0545	−	4.22854i	1.03200	−	0.155549i	0.643142	+	0.765747i	$0.277631\pi$
$740$	22.2315	−	20.6278i	0.817246	−	0.758294i
$741$		0			0
$742$	−19.2489	+	28.9137i	−0.706648	+	1.06145i
$743$	−24.1000	+	5.50068i	−0.884145	+	0.201800i	−0.640402	−	0.768040i	$-0.721232\pi$
$743$	−24.1000	+	5.50068i	−0.884145	+	0.201800i	−0.243743	+	0.969840i	$0.578375\pi$
$744$		0			0
$745$	14.9040	−	16.0627i	0.546040	−	0.588491i
$746$	−8.50805	−	12.4790i	−0.311502	−	0.456889i
$747$		0			0
$748$	0.0420681	−	0.0873553i	0.00153816	−	0.00319403i
$749$	4.92231	−	0.797596i	0.179857	−	0.0291435i
$750$		0			0
$751$	0.349930	−	0.107939i	0.0127691	−	0.00393875i	−0.288364	−	0.957521i	$-0.593111\pi$
$751$	0.349930	−	0.107939i	0.0127691	−	0.00393875i	0.301133	+	0.953582i	$0.402635\pi$
$752$	−15.7493	−	40.1286i	−0.574318	−	1.46334i
$753$		0			0
$754$	−28.0687	+	16.2055i	−1.02220	+	0.590168i
$755$	−22.2511	+	27.9020i	−0.809799	+	1.01546i
$756$		0			0
$757$	6.69035	+	8.38944i	0.243165	+	0.304919i	0.888405	−	0.459061i	$-0.151814\pi$
$757$	6.69035	+	8.38944i	0.243165	+	0.304919i	−0.645240	+	0.763980i	$0.723243\pi$
$758$	26.5309	+	10.4126i	0.963645	+	0.378203i
$759$		0			0
$760$	−0.0669910	+	0.893933i	−0.00243002	+	0.0324263i
$761$	−1.33468	+	3.40070i	−0.0483820	+	0.123275i	−0.953022	−	0.302902i	$-0.902045\pi$
$761$	−1.33468	+	3.40070i	−0.0483820	+	0.123275i	0.904640	+	0.426177i	$0.140140\pi$
$762$		0			0
$763$	20.7109	+	4.48714i	0.749785	+	0.162445i
$764$	45.6527	+	36.4068i	1.65166	+	1.31715i
$765$		0			0
$766$	−24.2493	−	14.0003i	−0.876163	−	0.505853i
$767$	−8.83372	+	3.46698i	−0.318967	+	0.125185i
$768$		0			0
$769$	2.46410	+	5.11675i	0.0888577	+	0.184515i	0.940662	−	0.339346i	$-0.110206\pi$
$769$	2.46410	+	5.11675i	0.0888577	+	0.184515i	−0.851804	+	0.523860i	$0.824491\pi$
$770$	−0.122667	−	0.175719i	−0.00442061	−	0.00633249i
$771$		0			0
$772$	−32.1534	−	4.84635i	−1.15723	−	0.174424i
$773$	−24.6065	+	16.7764i	−0.885034	+	0.603406i	−0.918232	−	0.396043i	$-0.870383\pi$
$773$	−24.6065	+	16.7764i	−0.885034	+	0.603406i	0.0331979	+	0.999449i	$0.489431\pi$
$774$		0			0
$775$	−4.76796	+	6.99331i	−0.171270	+	0.251207i
$776$	1.83935	+	8.05873i	0.0660289	+	0.289292i
$777$		0			0
$778$	−8.63486	+	37.8318i	−0.309575	+	1.35634i
$779$	−4.23105	−	4.55998i	−0.151593	−	0.163378i
$780$		0			0
$781$	−0.110586	−	0.0341112i	−0.00395707	−	0.00122059i
$782$	0.509596	+	6.80009i	0.0182231	+	0.243171i
$783$		0			0
$784$	−5.84783	−	23.2428i	−0.208851	−	0.830101i
$785$		−	2.81351i		−	0.100418i
$786$		0			0
$787$	0.466224	−	1.51146i	0.0166191	−	0.0538777i	−0.946883	−	0.321577i	$-0.895787\pi$
$787$	0.466224	−	1.51146i	0.0166191	−	0.0538777i	0.963503	+	0.267699i	$0.0862633\pi$
$788$	−5.84564	−	38.7833i	−0.208242	−	1.38160i
$789$		0			0
$790$	−21.5162	−	4.91092i	−0.765511	−	0.174723i
$791$	10.7729	−	28.3658i	0.383039	−	1.00857i
$792$		0			0
$793$	28.4385	+	19.3891i	1.00988	+	0.688526i
$794$	−12.0799	−	11.2085i	−0.428698	−	0.397774i
$795$		0			0
$796$	−6.58986	+	43.7209i	−0.233572	+	1.54965i
$797$	31.2650	+	15.0564i	1.10746	+	0.533326i	0.895998	−	0.444059i	$-0.146462\pi$
$797$	31.2650	+	15.0564i	1.10746	+	0.533326i	0.211466	+	0.977385i	$0.432176\pi$
$798$		0			0
$799$	−19.6707	+	9.47289i	−0.695898	+	0.335127i
$800$	5.96063	+	19.3239i	0.210740	+	0.683202i
$801$		0			0
$802$	−32.2963	+	55.9389i	−1.14042	+	1.97527i
$803$	−0.0294837	−	0.0510674i	−0.00104046	−	0.00180213i
$804$		0			0
$805$	7.23512	+	3.38636i	0.255005	+	0.119353i
$806$	−13.9950	+	11.1607i	−0.492954	+	0.393118i
$807$		0			0
$808$	−2.04174	−	0.153007i	−0.0718281	−	0.00538277i
$809$	8.70298	+	0.652198i	0.305981	+	0.0229301i	0.226836	−	0.973933i	$-0.427162\pi$
$809$	8.70298	+	0.652198i	0.305981	+	0.0229301i	0.0791449	+	0.996863i	$0.474781\pi$
$810$		0			0
$811$	−20.3767	+	16.2499i	−0.715523	+	0.570610i	−0.912144	−	0.409869i	$-0.865574\pi$
$811$	−20.3767	+	16.2499i	−0.715523	+	0.570610i	0.196622	+	0.980479i	$0.437003\pi$
$812$	8.56262	+	35.6940i	0.300489	+	1.25262i
$813$		0			0
$814$	−0.217077	−	0.375988i	−0.00760854	−	0.0131784i
$815$	−6.04876	+	10.4768i	−0.211879	+	0.366985i
$816$		0			0
$817$	−2.57384	−	8.34418i	−0.0900472	−	0.291926i
$818$	34.0903	−	16.4170i	1.19194	−	0.574009i
$819$		0			0
$820$	−18.6394	−	8.97627i	−0.650917	−	0.313465i
$821$	−5.96585	+	39.5808i	−0.208210	+	1.38138i	0.603520	+	0.797348i	$0.293764\pi$
$821$	−5.96585	+	39.5808i	−0.208210	+	1.38138i	−0.811730	+	0.584033i	$0.801474\pi$
$822$		0			0
$823$	38.7480	+	35.9529i	1.35067	+	1.25324i	0.939879	+	0.341509i	$0.110938\pi$
$823$	38.7480	+	35.9529i	1.35067	+	1.25324i	0.410791	+	0.911730i	$0.365253\pi$
$824$	0.264162	+	0.180103i	0.00920254	+	0.00627418i
$825$		0			0
$826$	1.73852	+	20.2031i	0.0604910	+	0.702957i
$827$	−10.4739	−	2.39060i	−0.364213	−	0.0831292i	0.0364981	−	0.999334i	$-0.488380\pi$
$827$	−10.4739	−	2.39060i	−0.364213	−	0.0831292i	−0.400711	+	0.916204i	$0.631237\pi$
$828$		0			0
$829$	−3.01579	−	20.0085i	−0.104743	−	0.694924i	−0.978145	−	0.207924i	$-0.933329\pi$
$829$	−3.01579	−	20.0085i	−0.104743	−	0.694924i	0.873402	−	0.487000i	$-0.161909\pi$
$830$	−8.69084	+	28.1750i	−0.301664	+	0.977969i
$831$		0			0
$832$			25.2771i			0.876325i
$833$	−11.5173	+	3.83311i	−0.399052	+	0.132809i
$834$		0			0
$835$	−2.74140	−	36.5815i	−0.0948702	−	1.26596i
$836$	0.0573893	+	0.0177023i	0.00198485	+	0.000612246i
$837$		0			0
$838$	−42.3034	−	45.5922i	−1.46135	−	1.57496i
$839$	−11.1673	+	48.9273i	−0.385539	+	1.68916i	0.294234	+	0.955733i	$0.404936\pi$
$839$	−11.1673	+	48.9273i	−0.385539	+	1.68916i	−0.679773	+	0.733423i	$0.737922\pi$
$840$		0			0
$841$	1.96672	+	8.61678i	0.0678181	+	0.297130i
$842$	−20.9957	+	30.7950i	−0.723558	+	1.06127i
$843$		0			0
$844$	9.49198	−	6.47152i	0.326727	−	0.222759i
$845$	−10.1427	−	1.52876i	−0.348919	−	0.0525911i
$846$		0			0
$847$	26.9709	−	10.9305i	0.926732	−	0.375575i
$848$	9.45450	+	19.6325i	0.324669	+	0.674182i
$849$		0			0
$850$	8.29600	−	3.25594i	0.284551	−	0.111678i
$851$	14.0156	+	8.09190i	0.480448	+	0.277387i
$852$		0			0
$853$	−17.8925	−	14.2688i	−0.612628	−	0.488555i	0.267330	−	0.963605i	$-0.413858\pi$
$853$	−17.8925	−	14.2688i	−0.612628	−	0.488555i	−0.879959	+	0.475050i	$0.842430\pi$
$854$	56.9921	−	46.4883i	1.95023	−	1.59080i
$855$		0			0
$856$	−0.362825	+	0.924464i	−0.0124011	+	0.0315975i
$857$	1.35420	−	18.0706i	0.0462587	−	0.617280i	−0.925109	−	0.379701i	$-0.876027\pi$
$857$	1.35420	−	18.0706i	0.0462587	−	0.617280i	0.971368	−	0.237579i	$-0.0763540\pi$
$858$		0			0
$859$	−9.76029	−	3.83063i	−0.333017	−	0.130699i	0.192941	−	0.981210i	$-0.438198\pi$
$859$	−9.76029	−	3.83063i	−0.333017	−	0.130699i	−0.525957	+	0.850511i	$0.676293\pi$
$860$	−18.1069	−	22.7053i	−0.617439	−	0.774244i
$861$		0			0
$862$	48.5447	−	60.8731i	1.65344	−	2.07335i
$863$	23.0418	−	13.3032i	0.784353	−	0.452847i	−0.0536175	−	0.998562i	$-0.517075\pi$
$863$	23.0418	−	13.3032i	0.784353	−	0.452847i	0.837971	+	0.545715i	$0.183742\pi$
$864$		0			0
$865$	8.81660	+	22.4643i	0.299773	+	0.763810i
$866$	−34.6396	+	10.6849i	−1.17710	+	0.363088i
$867$		0			0
$868$	7.61441	+	18.7885i	0.258450	+	0.637725i
$869$	−0.0726543	+	0.150868i	−0.00246463	+	0.00511785i
$870$		0			0
$871$	1.80868	+	2.65284i	0.0612847	+	0.0898881i
$872$	−2.87066	+	3.09383i	−0.0972127	+	0.104770i
$873$		0			0
$874$	−4.11804	+	0.939916i	−0.139295	+	0.0317931i
$875$	4.33582	−	31.0918i	0.146578	−	1.05109i
$876$		0			0
$877$	−33.2797	+	30.8791i	−1.12378	+	1.04271i	−0.125055	+	0.992150i	$0.539911\pi$
$877$	−33.2797	+	30.8791i	−1.12378	+	1.04271i	−0.998721	+	0.0505624i	$0.983899\pi$
$878$	68.6674	−	10.3499i	2.31741	−	0.349294i
$879$		0			0
$880$	−0.134062	+	0.0100465i	−0.00451921	+	0.000338668i
$881$	−32.1178			−1.08208			−0.541039	−	0.840998i	$-0.681969\pi$
$881$	−32.1178			−1.08208			−0.541039	+	0.840998i	$0.681969\pi$
$882$		0			0
$883$	−24.3974			−0.821038			−0.410519	−	0.911852i	$-0.634652\pi$
$883$	−24.3974			−0.821038			−0.410519	+	0.911852i	$0.634652\pi$
$884$	9.96168	−	0.746525i	0.335047	−	0.0251083i
$885$		0			0
$886$	−6.01233	+	0.906213i	−0.201988	+	0.0304448i
$887$	37.8972	−	35.1635i	1.27246	−	1.18067i	0.298389	−	0.954444i	$-0.403551\pi$
$887$	37.8972	−	35.1635i	1.27246	−	1.18067i	0.974074	−	0.226229i	$-0.0726399\pi$
$888$		0			0
$889$	−14.1059	+	1.21385i	−0.473098	+	0.0407112i
$890$	28.3049	−	6.46040i	0.948782	−	0.216553i
$891$		0			0
$892$	6.02252	−	6.49074i	0.201649	−	0.217326i
$893$	−7.61819	−	11.1738i	−0.254933	−	0.373918i
$894$		0			0
$895$	10.0495	−	20.8680i	0.335917	−	0.697539i
$896$	10.6059	+	3.14368i	0.354318	+	0.105023i
$897$		0			0
$898$	−53.8951	+	16.6244i	−1.79850	+	0.554765i
$899$	7.63485	+	19.4533i	0.254637	+	0.648803i
$900$		0			0
$901$	9.55744	−	5.51799i	0.318405	−	0.183831i
$902$	−0.184655	+	0.231550i	−0.00614834	+	0.00770978i
$903$		0			0
$904$	3.76777	+	4.72463i	0.125314	+	0.157139i
$905$	−29.5205	−	11.5860i	−0.981296	−	0.385130i
$906$		0			0
$907$	−1.15713	+	15.4409i	−0.0384220	+	0.512705i	0.944479	+	0.328571i	$0.106567\pi$
$907$	−1.15713	+	15.4409i	−0.0384220	+	0.512705i	−0.982901	+	0.184134i	$0.941052\pi$
$908$	−4.53458	+	11.5539i	−0.150485	+	0.383431i
$909$		0			0
$910$	9.35976	−	19.9976i	0.310273	−	0.662914i
$911$	42.0096	+	33.5015i	1.39184	+	1.10995i	0.980067	+	0.198668i	$0.0636616\pi$
$911$	42.0096	+	33.5015i	1.39184	+	1.10995i	0.411773	+	0.911287i	$0.364910\pi$
$912$		0			0
$913$	0.193743	+	0.111858i	0.00641197	+	0.00370195i
$914$	66.5792	−	26.1304i	2.20225	−	0.864318i
$915$		0			0
$916$	−24.1169	−	50.0792i	−0.796844	−	1.65466i
$917$	25.6299	+	14.4225i	0.846372	+	0.476272i
$918$		0			0
$919$	12.6029	+	1.89958i	0.415732	+	0.0626615i	0.353578	−	0.935405i	$-0.384965\pi$
$919$	12.6029	+	1.89958i	0.415732	+	0.0626615i	0.0621539	+	0.998067i	$0.480203\pi$
$920$	−1.31452	+	0.896225i	−0.0433384	+	0.0295476i
$921$		0			0
$922$	−23.6655	+	34.7109i	−0.779382	+	1.14314i
$923$	−2.65323	−	11.6246i	−0.0873321	−	0.382627i
$924$		0			0
$925$	4.70651	−	20.6206i	0.154749	−	0.678000i
$926$	−22.9958	−	24.7836i	−0.755690	−	0.814440i
$927$		0			0
$928$	47.7111	+	14.7169i	1.56619	+	0.483107i
$929$	1.18280	+	15.7834i	0.0388064	+	0.517835i	0.982407	+	0.186751i	$0.0597956\pi$
$929$	1.18280	+	15.7834i	0.0388064	+	0.517835i	−0.943601	+	0.331085i	$0.892585\pi$
$930$		0			0
$931$	−3.41108	−	6.70056i	−0.111794	−	0.219602i
$932$		−	32.2668i		−	1.05694i
$933$		0			0
$934$	−22.8438	+	74.0576i	−0.747471	+	2.42324i
$935$	0.0101479	+	0.0673269i	0.000331872	+	0.00220182i
$936$		0			0
$937$	−18.7284	−	4.27463i	−0.611829	−	0.139646i	−0.0946320	−	0.995512i	$-0.530167\pi$
$937$	−18.7284	−	4.27463i	−0.611829	−	0.139646i	−0.517197	+	0.855866i	$0.673025\pi$
$938$	6.53324	−	2.09451i	0.213318	−	0.0683881i
$939$		0			0
$940$	−37.1618	−	25.3365i	−1.21208	−	0.826385i
$941$	4.54898	+	4.22084i	0.148293	+	0.137595i	0.750831	−	0.660495i	$-0.229653\pi$
$941$	4.54898	+	4.22084i	0.148293	+	0.137595i	−0.602538	+	0.798090i	$0.705844\pi$
$942$		0			0
$943$	1.64543	−	10.9167i	0.0535825	−	0.355497i
$944$	11.4612	+	5.51940i	0.373029	+	0.179641i
$945$		0			0
$946$	−0.374570	+	0.180383i	−0.0121783	+	0.00586477i
$947$	4.09810	+	13.2857i	0.133170	+	0.431728i	0.997457	−	0.0712719i	$-0.0227058\pi$
$947$	4.09810	+	13.2857i	0.133170	+	0.431728i	−0.864286	+	0.503000i	$0.832230\pi$
$948$		0			0
$949$	3.03775	−	5.26153i	0.0986094	−	0.170797i
$950$	2.76017	+	4.78076i	0.0895518	+	0.155108i
$951$		0			0
$952$	0.511888	−	2.36268i	0.0165904	−	0.0765748i
$953$	7.46197	−	5.95072i	0.241717	−	0.192763i	−0.495137	−	0.868815i	$-0.664882\pi$
$953$	7.46197	−	5.95072i	0.241717	−	0.192763i	0.736854	+	0.676052i	$0.236311\pi$
$954$		0			0
$955$	−40.8907	−	3.06433i	−1.32319	−	0.0991595i
$956$	−33.6008	−	2.51803i	−1.08673	−	0.0814389i
$957$		0			0
$958$	8.17880	−	6.52237i	0.264245	−	0.210728i
$959$	−30.1793	+	0.333222i	−0.974541	+	0.0107603i
$960$		0			0
$961$	−9.72913	−	16.8513i	−0.313843	−	0.543592i
$962$	22.3657	−	38.7385i	0.721099	−	1.24898i
$963$		0			0
$964$	−5.64381	−	18.2968i	−0.181775	−	0.589299i
$965$	20.5732	−	9.90754i	0.662275	−	0.318935i
$966$		0			0
$967$	18.9182	+	9.11053i	0.608369	+	0.292975i	0.712592	−	0.701579i	$-0.247521\pi$
$967$	18.9182	+	9.11053i	0.608369	+	0.292975i	−0.104223	+	0.994554i	$0.533236\pi$
$968$	−0.863831	+	5.73115i	−0.0277646	+	0.184206i
$969$		0			0
$970$	−37.5722	−	34.8619i	−1.20637	−	1.11935i
$971$	−31.1107	−	21.2109i	−0.998389	−	0.680690i	−0.0503130	−	0.998734i	$-0.516022\pi$
$971$	−31.1107	−	21.2109i	−0.998389	−	0.680690i	−0.948076	+	0.318043i	$0.896974\pi$
$972$		0			0
$973$	44.1202	+	29.3724i	1.41443	+	0.941635i
$974$	19.2693	+	4.39809i	0.617427	+	0.140924i
$975$		0			0
$976$	−6.87665	−	45.6236i	−0.220116	−	1.46038i
$977$	9.66156	−	31.3220i	0.309101	−	1.00208i	−0.659132	−	0.752028i	$-0.729076\pi$
$977$	9.66156	−	31.3220i	0.309101	−	1.00208i	0.968232	−	0.250052i	$-0.0804478\pi$
$978$		0			0
$979$		−	0.220285i		−	0.00704033i
$980$	−18.7018	−	16.5995i	−0.597407	−	0.530253i
$981$		0			0
$982$	2.55231	+	34.0582i	0.0814475	+	1.08684i
$983$	−18.4478	−	5.69040i	−0.588394	−	0.181496i	−0.0137593	−	0.999905i	$-0.504380\pi$
$983$	−18.4478	−	5.69040i	−0.588394	−	0.181496i	−0.574635	+	0.818410i	$0.694856\pi$
$984$		0			0
$985$	18.7339	+	20.1903i	0.596912	+	0.643318i
$986$	4.89637	−	21.4524i	0.155932	−	0.683183i
$987$		0			0
$988$	1.37692	+	6.03266i	0.0438055	+	0.191924i
$989$	8.73003	−	12.8046i	0.277599	−	0.407163i
$990$		0			0
$991$	28.0093	−	19.0964i	0.889744	−	0.606617i	−0.0298209	−	0.999555i	$-0.509494\pi$
$991$	28.0093	−	19.0964i	0.889744	−	0.606617i	0.919565	+	0.392938i	$0.128541\pi$
$992$	27.2676	+	4.10993i	0.865748	+	0.130490i
$993$		0			0
$994$	−25.4266	−	1.62337i	−0.806483	−	0.0514902i
$995$	−13.4718	−	27.9746i	−0.427086	−	0.886854i
$996$		0			0
$997$	55.6984	−	21.8600i	1.76398	−	0.692313i	0.765160	−	0.643840i	$-0.222660\pi$
$997$	55.6984	−	21.8600i	1.76398	−	0.692313i	0.998825	−	0.0484727i	$-0.0154354\pi$
$998$	−19.5458	−	11.2848i	−0.618712	−	0.357214i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bg.a.17.3	✓	216
3.2	odd	2	inner	441.2.bg.a.17.16	yes	216
49.26	odd	42	inner	441.2.bg.a.26.16	yes	216
147.26	even	42	inner	441.2.bg.a.26.3	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.bg.a.17.3	✓	216	1.1	even	1	trivial
441.2.bg.a.17.16	yes	216	3.2	odd	2	inner
441.2.bg.a.26.3	yes	216	147.26	even	42	inner
441.2.bg.a.26.16	yes	216	49.26	odd	42	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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.bg (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.05710 + 0.154158i) q^{2} +(2.23024 - 0.336155i) q^{4} +(-1.16105 + 1.07730i) q^{5} +(1.82087 + 1.91949i) q^{7} +(-0.513717 + 0.117252i) q^{8} +O(q^{10})\)	\(q+(-2.05710 + 0.154158i) q^{2} +(2.23024 - 0.336155i) q^{4} +(-1.16105 + 1.07730i) q^{5} +(1.82087 + 1.91949i) q^{7} +(-0.513717 + 0.117252i) q^{8} +(2.22233 - 2.39510i) q^{10} +(-0.0139650 - 0.0204828i) q^{11} +(1.10822 - 2.30125i) q^{13} +(-4.04162 - 3.66788i) q^{14} +(-3.27177 + 1.00921i) q^{16} +(0.633525 + 1.61419i) q^{17} +(-0.930215 + 0.537060i) q^{19} +(-2.22729 + 2.79293i) q^{20} +(0.0318849 + 0.0399825i) q^{22} +(-1.77453 - 0.696453i) q^{23} +(-0.186182 + 2.48442i) q^{25} +(-1.92497 + 4.90474i) q^{26} +(4.70623 + 3.66883i) q^{28} +(4.80927 + 3.83527i) q^{29} +(2.94216 + 1.69866i) q^{31} +(7.55580 - 2.96543i) q^{32} +(-1.55207 - 3.22290i) q^{34} +(-4.18199 - 0.267001i) q^{35} +(-8.39478 - 1.26531i) q^{37} +(1.83076 - 1.24819i) q^{38} +(0.470136 - 0.689562i) q^{40} +(1.28868 + 5.64609i) q^{41} +(-1.80900 + 7.92573i) q^{43} +(-0.0380307 - 0.0409873i) q^{44} +(3.75776 + 1.15912i) q^{46} +(0.940891 + 12.5553i) q^{47} +(-0.368854 + 6.99028i) q^{49} -5.13941i q^{50} +(1.69803 - 5.50487i) q^{52} +(-0.948540 - 6.29315i) q^{53} +(0.0382802 + 0.00873720i) q^{55} +(-1.16048 - 0.772570i) q^{56} +(-10.4844 - 7.14815i) q^{58} +(-2.72354 - 2.52708i) q^{59} +(-2.00844 + 13.3251i) q^{61} +(-6.31419 - 3.04075i) q^{62} +(-8.91627 + 4.29385i) q^{64} +(1.19243 + 3.86575i) q^{65} +(-0.628525 + 1.08864i) q^{67} +(1.95553 + 3.38708i) q^{68} +(8.64393 - 0.0954412i) q^{70} +(3.64976 - 2.91058i) q^{71} +(2.37199 + 0.177756i) q^{73} +(17.4640 + 1.30874i) q^{74} +(-1.89407 + 1.51047i) q^{76} +(0.0138881 - 0.0641021i) q^{77} +(-3.37733 - 5.84971i) q^{79} +(2.71148 - 4.69642i) q^{80} +(-3.52135 - 11.4159i) q^{82} +(-8.13058 + 3.91548i) q^{83} +(-2.47452 - 1.19167i) q^{85} +(2.49947 - 16.5829i) q^{86} +(0.00957569 + 0.00888495i) q^{88} +(7.34185 + 5.00559i) q^{89} +(6.43514 - 2.06306i) q^{91} +(-4.19176 - 0.956742i) q^{92} +(-3.87102 - 25.6825i) q^{94} +(0.501454 - 1.62567i) q^{95} -15.6871i q^{97} +(-0.318839 - 14.4366i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 16 q^{4} + 2 q^{7}+O(q^{10}) \) 216 * q - 16 * q^4 + 2 * q^7	\( 216 q - 16 q^{4} + 2 q^{7} + 12 q^{10} + 12 q^{16} - 6 q^{19} + 44 q^{22} + 26 q^{25} + 84 q^{28} - 6 q^{31} - 112 q^{34} + 60 q^{37} - 304 q^{40} + 20 q^{43} - 20 q^{46} - 86 q^{49} - 168 q^{52} - 84 q^{55} - 120 q^{58} - 2 q^{61} + 32 q^{64} + 22 q^{67} - 136 q^{70} - 6 q^{73} + 84 q^{76} + 2 q^{79} - 104 q^{82} + 96 q^{85} - 12 q^{88} + 58 q^{91} + 52 q^{94}+O(q^{100}) \) 216 * q - 16 * q^4 + 2 * q^7 + 12 * q^10 + 12 * q^16 - 6 * q^19 + 44 * q^22 + 26 * q^25 + 84 * q^28 - 6 * q^31 - 112 * q^34 + 60 * q^37 - 304 * q^40 + 20 * q^43 - 20 * q^46 - 86 * q^49 - 168 * q^52 - 84 * q^55 - 120 * q^58 - 2 * q^61 + 32 * q^64 + 22 * q^67 - 136 * q^70 - 6 * q^73 + 84 * q^76 + 2 * q^79 - 104 * q^82 + 96 * q^85 - 12 * q^88 + 58 * q^91 + 52 * q^94

Introduction

L-functions

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