LMFDB - Embedded newform 441.2.u.e.64.2

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:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			64.2
Character	$\chi$	$=$	441.64
Dual form			441.2.u.e.379.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.458811 + 2.01018i) q^{2} +(-2.02838 - 0.976818i) q^{4} +(-2.04151 + 2.55997i) q^{5} +(2.15910 + 1.52915i) q^{7} +(0.323108 - 0.405164i) q^{8} +O(q^{10})$	\(q+(-0.458811 + 2.01018i) q^{2} +(-2.02838 - 0.976818i) q^{4} +(-2.04151 + 2.55997i) q^{5} +(2.15910 + 1.52915i) q^{7} +(0.323108 - 0.405164i) q^{8} +(-4.20934 - 5.27834i) q^{10} +(0.0128085 - 0.0561176i) q^{11} +(-0.441405 + 1.93392i) q^{13} +(-4.06448 + 3.63859i) q^{14} +(-2.14116 - 2.68493i) q^{16} +(-0.338314 + 0.162923i) q^{17} +0.444193 q^{19} +(6.64159 - 3.19842i) q^{20} +(0.106930 + 0.0514947i) q^{22} +(-4.37481 - 2.10680i) q^{23} +(-1.27309 - 5.57775i) q^{25} +(-3.68502 - 1.77461i) q^{26} +(-2.88578 - 5.21075i) q^{28} +(7.57289 - 3.64691i) q^{29} -6.88972 q^{31} +(7.31340 - 3.52195i) q^{32} +(-0.172284 - 0.754824i) q^{34} +(-8.32239 + 2.40545i) q^{35} +(-8.09529 + 3.89849i) q^{37} +(-0.203801 + 0.892909i) q^{38} +(0.377581 + 1.65429i) q^{40} +(3.40304 - 4.26728i) q^{41} +(2.32695 + 2.91790i) q^{43} +(-0.0807972 + 0.101317i) q^{44} +(6.24225 - 7.82754i) q^{46} +(-2.22645 + 9.75472i) q^{47} +(2.32341 + 6.60316i) q^{49} +11.7964 q^{50} +(2.78443 - 3.49157i) q^{52} +(-3.35260 - 1.61453i) q^{53} +(0.117511 + 0.147354i) q^{55} +(1.31718 - 0.380709i) q^{56} +(3.85643 + 16.8961i) q^{58} +(4.50630 + 5.65072i) q^{59} +(11.5744 - 5.57393i) q^{61} +(3.16108 - 13.8496i) q^{62} +(2.19594 + 9.62105i) q^{64} +(-4.04965 - 5.07810i) q^{65} +14.0871 q^{67} +0.845378 q^{68} +(-1.01700 - 17.8332i) q^{70} +(-9.52248 - 4.58578i) q^{71} +(3.17316 + 13.9025i) q^{73} +(-4.12246 - 18.0617i) q^{74} +(-0.900995 - 0.433896i) q^{76} +(0.113467 - 0.101577i) q^{77} -4.03334 q^{79} +11.2445 q^{80} +(7.01665 + 8.79860i) q^{82} +(2.70809 + 11.8649i) q^{83} +(0.273592 - 1.19868i) q^{85} +(-6.93314 + 3.33883i) q^{86} +(-0.0185983 - 0.0233216i) q^{88} +(2.26247 + 9.91252i) q^{89} +(-3.91030 + 3.50056i) q^{91} +(6.81583 + 8.54678i) q^{92} +(-18.5872 - 8.95114i) q^{94} +(-0.906824 + 1.13712i) q^{95} -11.3016 q^{97} +(-14.3396 + 1.64086i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 12 q^{4} - 2 q^{7}+O(q^{10}) $ 60 * q - 12 * q^4 - 2 * q^7	$ 60 q - 12 q^{4} - 2 q^{7} + 12 q^{10} - 4 q^{13} - 48 q^{19} + 6 q^{22} - 22 q^{25} + 40 q^{28} - 76 q^{31} - 12 q^{34} + 34 q^{37} + 86 q^{40} + 4 q^{43} + 8 q^{46} + 26 q^{49} + 66 q^{52} + 10 q^{55} + 42 q^{58} + 62 q^{61} - 128 q^{64} + 8 q^{67} + 96 q^{70} - 70 q^{73} + 50 q^{76} - 24 q^{79} - 36 q^{82} + 72 q^{85} - 216 q^{88} + 52 q^{91} - 38 q^{94} - 252 q^{97}+O(q^{100}) $ 60 * q - 12 * q^4 - 2 * q^7 + 12 * q^10 - 4 * q^13 - 48 * q^19 + 6 * q^22 - 22 * q^25 + 40 * q^28 - 76 * q^31 - 12 * q^34 + 34 * q^37 + 86 * q^40 + 4 * q^43 + 8 * q^46 + 26 * q^49 + 66 * q^52 + 10 * q^55 + 42 * q^58 + 62 * q^61 - 128 * q^64 + 8 * q^67 + 96 * q^70 - 70 * q^73 + 50 * q^76 - 24 * q^79 - 36 * q^82 + 72 * q^85 - 216 * q^88 + 52 * q^91 - 38 * q^94 - 252 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{5}{7}\right)$	$1$

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 $

$2$	−0.458811	+	2.01018i	−0.324428	+	1.42141i	0.505154	+	0.863029i	$0.331436\pi$
$2$	−0.458811	+	2.01018i	−0.324428	+	1.42141i	−0.829583	+	0.558384i	$0.811422\pi$
$3$		0			0
$3$		0			0
$4$	−2.02838	−	0.976818i	−1.01419	−	0.488409i
$5$	−2.04151	+	2.55997i	−0.912990	+	1.14485i	0.0760352	+	0.997105i	$0.475774\pi$
$5$	−2.04151	+	2.55997i	−0.912990	+	1.14485i	−0.989025	+	0.147748i	$0.952798\pi$
$6$		0			0
$7$	2.15910	+	1.52915i	0.816062	+	0.577964i
$7$	2.15910	+	1.52915i	0.816062	+	0.577964i
$8$	0.323108	−	0.405164i	0.114236	−	0.143247i
$9$		0			0
$10$	−4.20934	−	5.27834i	−1.33111	−	1.66916i
$11$	0.0128085	−	0.0561176i	0.00386190	−	0.0169201i	−0.972960	−	0.230973i	$-0.925809\pi$
$11$	0.0128085	−	0.0561176i	0.00386190	−	0.0169201i	0.976822	+	0.214053i	$0.0686664\pi$
$12$		0			0
$13$	−0.441405	+	1.93392i	−0.122424	+	0.536374i	0.876103	+	0.482123i	$0.160134\pi$
$13$	−0.441405	+	1.93392i	−0.122424	+	0.536374i	−0.998527	+	0.0542509i	$0.982723\pi$
$14$	−4.06448	+	3.63859i	−1.08628	+	0.972453i
$15$		0			0
$16$	−2.14116	−	2.68493i	−0.535291	−	0.671233i
$17$	−0.338314	+	0.162923i	−0.0820532	+	0.0395147i	−0.474460	−	0.880277i	$-0.657357\pi$
$17$	−0.338314	+	0.162923i	−0.0820532	+	0.0395147i	0.392407	+	0.919792i	$0.371642\pi$
$18$		0			0
$19$	0.444193			0.101905			0.0509525	−	0.998701i	$-0.483774\pi$
$19$	0.444193			0.101905			0.0509525	+	0.998701i	$0.483774\pi$
$20$	6.64159	−	3.19842i	1.48510	−	0.715188i
$21$		0			0
$22$	0.106930	+	0.0514947i	0.0227975	+	0.0109787i
$23$	−4.37481	−	2.10680i	−0.912210	−	0.439297i	−0.0819267	−	0.996638i	$-0.526107\pi$
$23$	−4.37481	−	2.10680i	−0.912210	−	0.439297i	−0.830284	+	0.557341i	$0.811822\pi$
$24$		0			0
$25$	−1.27309	−	5.57775i	−0.254617	−	1.11555i
$26$	−3.68502	−	1.77461i	−0.722691	−	0.348030i
$27$		0			0
$28$	−2.88578	−	5.21075i	−0.545361	−	0.984739i
$29$	7.57289	−	3.64691i	1.40625	−	0.677215i	0.431832	−	0.901954i	$-0.357867\pi$
$29$	7.57289	−	3.64691i	1.40625	−	0.677215i	0.974419	+	0.224739i	$0.0721531\pi$
$30$		0			0
$31$	−6.88972			−1.23743			−0.618715	−	0.785615i	$-0.712346\pi$
$31$	−6.88972			−1.23743			−0.618715	+	0.785615i	$0.712346\pi$
$32$	7.31340	−	3.52195i	1.29284	−	0.622598i
$33$		0			0
$34$	−0.172284	−	0.754824i	−0.0295464	−	0.129451i
$35$	−8.32239	+	2.40545i	−1.40674	+	0.406596i
$36$		0			0
$37$	−8.09529	+	3.89849i	−1.33086	+	0.640908i	−0.957943	−	0.286958i	$-0.907356\pi$
$37$	−8.09529	+	3.89849i	−1.33086	+	0.640908i	−0.372915	+	0.927865i	$0.621642\pi$
$38$	−0.203801	+	0.892909i	−0.0330608	+	0.144849i
$39$		0			0
$40$	0.377581	+	1.65429i	0.0597008	+	0.261566i
$41$	3.40304	−	4.26728i	0.531466	−	0.666437i	−0.441534	−	0.897245i	$-0.645565\pi$
$41$	3.40304	−	4.26728i	0.531466	−	0.666437i	0.972999	+	0.230808i	$0.0741369\pi$
$42$		0			0
$43$	2.32695	+	2.91790i	0.354857	+	0.444976i	0.926934	−	0.375223i	$-0.122434\pi$
$43$	2.32695	+	2.91790i	0.354857	+	0.444976i	−0.572078	+	0.820199i	$0.693863\pi$
$44$	−0.0807972	+	0.101317i	−0.0121806	+	0.0152740i
$45$		0			0
$46$	6.24225	−	7.82754i	0.920370	−	1.15411i
$47$	−2.22645	+	9.75472i	−0.324761	+	1.42287i	0.504210	+	0.863581i	$0.331784\pi$
$47$	−2.22645	+	9.75472i	−0.324761	+	1.42287i	−0.828971	+	0.559291i	$0.811073\pi$
$48$		0			0
$49$	2.32341	+	6.60316i	0.331915	+	0.943309i
$50$	11.7964			1.66826
$51$		0			0
$52$	2.78443	−	3.49157i	0.386131	−	0.484193i
$53$	−3.35260	−	1.61453i	−0.460515	−	0.221772i	0.189217	−	0.981935i	$-0.439405\pi$
$53$	−3.35260	−	1.61453i	−0.460515	−	0.221772i	−0.649733	+	0.760163i	$0.725119\pi$
$54$		0			0
$55$	0.117511	+	0.147354i	0.0158451	+	0.0198692i
$56$	1.31718	−	0.380709i	0.176015	−	0.0508744i
$57$		0			0
$58$	3.85643	+	16.8961i	0.506374	+	2.21857i
$59$	4.50630	+	5.65072i	0.586670	+	0.735661i	0.983234	−	0.182346i	$-0.0583690\pi$
$59$	4.50630	+	5.65072i	0.586670	+	0.735661i	−0.396564	+	0.918007i	$0.629798\pi$
$60$		0			0
$61$	11.5744	−	5.57393i	1.48195	−	0.713668i	0.494145	−	0.869379i	$-0.335481\pi$
$61$	11.5744	−	5.57393i	1.48195	−	0.713668i	0.987803	+	0.155711i	$0.0497668\pi$
$62$	3.16108	−	13.8496i	0.401457	−	1.75890i
$63$		0			0
$64$	2.19594	+	9.62105i	0.274493	+	1.20263i
$65$	−4.04965	−	5.07810i	−0.502298	−	0.629861i
$66$		0			0
$67$	14.0871			1.72101			0.860507	−	0.509439i	$-0.170147\pi$
$67$	14.0871			1.72101			0.860507	+	0.509439i	$0.170147\pi$
$68$	0.845378			0.102517
$69$		0			0
$70$	−1.01700	−	17.8332i	−0.121554	−	2.13147i
$71$	−9.52248	−	4.58578i	−1.13011	−	0.544232i	−0.227109	−	0.973869i	$-0.572927\pi$
$71$	−9.52248	−	4.58578i	−1.13011	−	0.544232i	−0.903002	+	0.429637i	$0.858642\pi$
$72$		0			0
$73$	3.17316	+	13.9025i	0.371390	+	1.62717i	0.722879	+	0.690975i	$0.242818\pi$
$73$	3.17316	+	13.9025i	0.371390	+	1.62717i	−0.351489	+	0.936192i	$0.614324\pi$
$74$	−4.12246	−	18.0617i	−0.479226	−	2.09963i
$75$		0			0
$76$	−0.900995	−	0.433896i	−0.103351	−	0.0497713i
$77$	0.113467	−	0.101577i	0.0129308	−	0.0115758i
$78$		0			0
$79$	−4.03334			−0.453786			−0.226893	−	0.973920i	$-0.572857\pi$
$79$	−4.03334			−0.453786			−0.226893	+	0.973920i	$0.572857\pi$
$80$	11.2445			1.25718
$81$		0			0
$82$	7.01665	+	8.79860i	0.774859	+	0.971643i
$83$	2.70809	+	11.8649i	0.297251	+	1.30234i	0.874202	+	0.485563i	$0.161385\pi$
$83$	2.70809	+	11.8649i	0.297251	+	1.30234i	−0.576951	+	0.816779i	$0.695758\pi$
$84$		0			0
$85$	0.273592	−	1.19868i	0.0296752	−	0.130015i
$86$	−6.93314	+	3.33883i	−0.747620	+	0.360035i
$87$		0			0
$88$	−0.0185983	−	0.0233216i	−0.00198259	−	0.00248609i
$89$	2.26247	+	9.91252i	0.239821	+	1.05072i	0.941177	+	0.337914i	$0.109721\pi$
$89$	2.26247	+	9.91252i	0.239821	+	1.05072i	−0.701356	+	0.712811i	$0.747422\pi$
$90$		0			0
$91$	−3.91030	+	3.50056i	−0.409910	+	0.366958i
$92$	6.81583	+	8.54678i	0.710600	+	0.891064i
$93$		0			0
$94$	−18.5872	−	8.95114i	−1.91713	−	0.923240i
$95$	−0.906824	+	1.13712i	−0.0930382	+	0.116666i
$96$		0			0
$97$	−11.3016			−1.14750			−0.573750	−	0.819030i	$-0.694512\pi$
$97$	−11.3016			−1.14750			−0.573750	+	0.819030i	$0.694512\pi$
$98$	−14.3396	+	1.64086i	−1.44851	+	0.165752i
$99$		0			0
$100$	−2.86614	+	12.5574i	−0.286614	+	1.25574i
$101$	−4.30496	+	5.39825i	−0.428359	+	0.537146i	−0.948434	−	0.316975i	$-0.897333\pi$
$101$	−4.30496	+	5.39825i	−0.428359	+	0.537146i	0.520074	+	0.854121i	$0.325904\pi$
$102$		0			0
$103$	−5.59281	+	7.01316i	−0.551076	+	0.691027i	−0.976880	−	0.213788i	$-0.931420\pi$
$103$	−5.59281	+	7.01316i	−0.551076	+	0.691027i	0.425804	+	0.904815i	$0.359991\pi$
$104$	0.640935	+	0.803707i	0.0628489	+	0.0788100i
$105$		0			0
$106$	4.78370	−	5.99858i	0.464634	−	0.582633i
$107$	−3.15842	−	13.8379i	−0.305336	−	1.33776i	−0.861951	−	0.506992i	$-0.830757\pi$
$107$	−3.15842	−	13.8379i	−0.305336	−	1.33776i	0.556615	−	0.830771i	$-0.312100\pi$
$108$		0			0
$109$	−2.65521	+	11.6333i	−0.254323	+	1.11426i	0.672894	+	0.739739i	$0.265051\pi$
$109$	−2.65521	+	11.6333i	−0.254323	+	1.11426i	−0.927217	+	0.374524i	$0.877806\pi$
$110$	−0.350123	+	0.168610i	−0.0333829	+	0.0160764i
$111$		0			0
$112$	−0.517316	−	9.07119i	−0.0488818	−	0.857147i
$113$	0.735211	+	3.22117i	0.0691628	+	0.303022i	0.997664	−	0.0683063i	$-0.0217595\pi$
$113$	0.735211	+	3.22117i	0.0691628	+	0.303022i	−0.928502	+	0.371329i	$0.878902\pi$
$114$		0			0
$115$	14.3245	−	6.89833i	1.33577	−	0.643273i
$116$	−18.9231			−1.75697
$117$		0			0
$118$	−13.4265	+	6.46587i	−1.23601	+	0.595231i
$119$	−0.979587	−	0.165565i	−0.0897986	−	0.0151773i
$120$		0			0
$121$	9.90767	+	4.77128i	0.900697	+	0.433753i
$122$	5.89416	+	25.8240i	0.533632	+	2.33799i
$123$		0			0
$124$	13.9750	+	6.73000i	1.25499	+	0.604372i
$125$	2.12757	+	1.02458i	0.190296	+	0.0916416i
$126$		0			0
$127$	15.2555	−	7.34667i	1.35371	−	0.651912i	0.390484	−	0.920610i	$-0.372308\pi$
$127$	15.2555	−	7.34667i	1.35371	−	0.651912i	0.963225	+	0.268698i	$0.0865933\pi$
$128$	−4.11306			−0.363547
$129$		0			0
$130$	12.0659	−	5.81065i	1.05825	−	0.509628i
$131$	0.888123	+	1.11367i	0.0775956	+	0.0973018i	0.819114	−	0.573631i	$-0.194465\pi$
$131$	0.888123	+	1.11367i	0.0775956	+	0.0973018i	−0.741519	+	0.670932i	$0.765894\pi$
$132$		0			0
$133$	0.959057	+	0.679238i	0.0831608	+	0.0588974i
$134$	−6.46332	+	28.3176i	−0.558345	+	2.44627i
$135$		0			0
$136$	−0.0433011	+	0.189715i	−0.00371304	+	0.0162679i
$137$	6.71614	+	8.42177i	0.573798	+	0.719520i	0.981041	−	0.193800i	$-0.0620811\pi$
$137$	6.71614	+	8.42177i	0.573798	+	0.719520i	−0.407243	+	0.913320i	$0.633510\pi$
$138$		0			0
$139$	−0.772553	+	0.968750i	−0.0655271	+	0.0821683i	−0.813515	−	0.581544i	$-0.802449\pi$
$139$	−0.772553	+	0.968750i	−0.0655271	+	0.0821683i	0.747988	+	0.663713i	$0.231020\pi$
$140$	19.2307	+	3.25028i	1.62529	+	0.274698i
$141$		0			0
$142$	13.5873	−	17.0379i	1.14022	−	1.42979i
$143$	0.102873	+	0.0495412i	0.00860271	+	0.00414285i
$144$		0			0
$145$	−6.12413	+	26.8316i	−0.508581	+	2.22824i
$146$	−29.4025			−2.43337
$147$		0			0
$148$	20.2285			1.66277
$149$	2.18273	−	9.56316i	0.178816	−	0.783444i	−0.803362	−	0.595491i	$-0.796957\pi$
$149$	2.18273	−	9.56316i	0.178816	−	0.783444i	0.982178	−	0.187953i	$-0.0601854\pi$
$150$		0			0
$151$	−9.39088	−	4.52241i	−0.764219	−	0.368029i	0.0108202	−	0.999941i	$-0.496556\pi$
$151$	−9.39088	−	4.52241i	−0.764219	−	0.368029i	−0.775039	+	0.631913i	$0.782270\pi$
$152$	0.143522	−	0.179971i	0.0116412	−	0.0145976i
$153$		0			0
$154$	0.152129	+	0.274694i	0.0122589	+	0.0221355i
$155$	14.0654	−	17.6375i	1.12976	−	1.41668i
$156$		0			0
$157$	−6.75526	−	8.47083i	−0.539129	−	0.676046i	0.435419	−	0.900228i	$-0.356600\pi$
$157$	−6.75526	−	8.47083i	−0.539129	−	0.676046i	−0.974547	+	0.224182i	$0.928029\pi$
$158$	1.85054	−	8.10775i	0.147221	−	0.645018i
$159$		0			0
$160$	−5.91428	+	25.9122i	−0.467565	+	2.04854i
$161$	−6.22403	−	11.2385i	−0.490522	−	0.885719i
$162$		0			0
$163$	−5.71975	−	7.17233i	−0.448005	−	0.561781i	0.505628	−	0.862751i	$-0.331261\pi$
$163$	−5.71975	−	7.17233i	−0.448005	−	0.561781i	−0.953633	+	0.300971i	$0.902689\pi$
$164$	−11.0710	+	5.33152i	−0.864502	+	0.416322i
$165$		0			0
$166$	−25.0931			−1.94760
$167$	−3.56354	+	1.71611i	−0.275755	+	0.132797i	−0.566651	−	0.823958i	$-0.691761\pi$
$167$	−3.56354	+	1.71611i	−0.275755	+	0.132797i	0.290896	+	0.956755i	$0.406047\pi$
$168$		0			0
$169$	8.16737	+	3.93320i	0.628259	+	0.302554i
$170$	2.28404	+	1.09994i	0.175178	+	0.0843614i
$171$		0			0
$172$	−1.86969	−	8.19163i	−0.142562	−	0.624606i
$173$	20.9449	+	10.0865i	1.59241	+	0.766866i	0.999269	−	0.0382300i	$-0.0121720\pi$
$173$	20.9449	+	10.0865i	1.59241	+	0.766866i	0.593145	+	0.805096i	$0.297886\pi$
$174$		0			0
$175$	5.78050	−	13.9897i	0.436965	−	1.05752i
$176$	−0.178097	+	0.0857670i	−0.0134246	+	0.00646493i
$177$		0			0
$178$	−20.9640			−1.57132
$179$	7.18382	−	3.45955i	0.536944	−	0.258579i	−0.145701	−	0.989329i	$-0.546544\pi$
$179$	7.18382	−	3.45955i	0.536944	−	0.258579i	0.682645	+	0.730750i	$0.260829\pi$
$180$		0			0
$181$	−2.04966	−	8.98016i	−0.152350	−	0.667490i	−0.992198	−	0.124669i	$-0.960213\pi$
$181$	−2.04966	−	8.98016i	−0.152350	−	0.667490i	0.839848	−	0.542822i	$-0.182644\pi$
$182$	−5.24267	−	9.46650i	−0.388612	−	0.701703i
$183$		0			0
$184$	−2.26713	+	1.09179i	−0.167135	+	0.0804881i
$185$	6.54659	−	28.6825i	0.481315	−	2.10878i
$186$		0			0
$187$	0.00480959	+	0.0210722i	0.000351712	+	0.00154095i
$188$	14.0447	−	17.6115i	1.02431	−	1.28445i
$189$		0			0
$190$	−1.86976	−	2.34460i	−0.135647	−	0.170095i
$191$	0.106644	−	0.133727i	0.00771648	−	0.00967617i	−0.777958	−	0.628316i	$-0.783745\pi$
$191$	0.106644	−	0.133727i	0.00771648	−	0.00967617i	0.785675	+	0.618640i	$0.212316\pi$
$192$		0			0
$193$	−8.05961	+	10.1064i	−0.580143	+	0.727476i	−0.982137	−	0.188166i	$-0.939746\pi$
$193$	−8.05961	+	10.1064i	−0.580143	+	0.727476i	0.401994	+	0.915642i	$0.368317\pi$
$194$	5.18528	−	22.7182i	0.372281	−	1.63107i
$195$		0			0
$196$	1.73733	−	15.6633i	0.124095	−	1.11881i
$197$	−3.15471			−0.224763			−0.112382	−	0.993665i	$-0.535848\pi$
$197$	−3.15471			−0.224763			−0.112382	+	0.993665i	$0.535848\pi$
$198$		0			0
$199$	0.677428	−	0.849467i	0.0480216	−	0.0602172i	−0.757241	−	0.653136i	$-0.773453\pi$
$199$	0.677428	−	0.849467i	0.0480216	−	0.0602172i	0.805262	+	0.592919i	$0.202024\pi$
$200$	−2.67125	−	1.28641i	−0.188886	−	0.0909627i
$201$		0			0
$202$	−8.87629	−	11.1305i	−0.624534	−	0.783141i
$203$	21.9273	+	3.70604i	1.53899	+	0.260113i
$204$		0			0
$205$	3.97677	+	17.4234i	0.277749	+	1.21690i
$206$	−11.5317	−	14.4603i	−0.803451	−	1.00750i
$207$		0			0
$208$	6.13758	−	2.95570i	0.425564	−	0.204941i
$209$	0.00568944	−	0.0249271i	0.000393547	−	0.00172424i
$210$		0			0
$211$	−4.47309	−	19.5979i	−0.307940	−	1.34917i	−0.857829	−	0.513936i	$-0.828187\pi$
$211$	−4.47309	−	19.5979i	−0.307940	−	1.34917i	0.549889	−	0.835238i	$-0.314670\pi$
$212$	5.22326	+	6.54977i	0.358735	+	0.449840i
$213$		0			0
$214$	29.2659			2.00057
$215$	−12.2202			−0.833413
$216$		0			0
$217$	−14.8756	−	10.5354i	−1.00982	−	0.715190i
$218$	−22.1667	−	10.6749i	−1.50132	−	0.722997i
$219$		0			0
$220$	−0.0944190	−	0.413677i	−0.00636573	−	0.0278901i
$221$	−0.165748	−	0.726189i	−0.0111494	−	0.0488488i
$222$		0			0
$223$	−0.337180	−	0.162377i	−0.0225792	−	0.0108736i	0.422560	−	0.906335i	$-0.361132\pi$
$223$	−0.337180	−	0.162377i	−0.0225792	−	0.0108736i	−0.445139	+	0.895461i	$0.646846\pi$
$224$	21.1759	+	3.57905i	1.41488	+	0.239135i
$225$		0			0
$226$	−6.81246			−0.453158
$227$	28.9672			1.92262			0.961310	−	0.275469i	$-0.0888333\pi$
$227$	28.9672			1.92262			0.961310	+	0.275469i	$0.0888333\pi$
$228$		0			0
$229$	−2.16605	−	2.71614i	−0.143137	−	0.179488i	0.705095	−	0.709112i	$-0.250904\pi$
$229$	−2.16605	−	2.71614i	−0.143137	−	0.179488i	−0.848232	+	0.529625i	$0.822333\pi$
$230$	7.29465	+	31.9599i	0.480995	+	2.10738i
$231$		0			0
$232$	0.969261	−	4.24661i	0.0636351	−	0.278804i
$233$	14.6370	−	7.04879i	0.958899	−	0.461781i	0.112102	−	0.993697i	$-0.464242\pi$
$233$	14.6370	−	7.04879i	0.958899	−	0.461781i	0.846798	+	0.531915i	$0.178528\pi$
$234$		0			0
$235$	−20.4265	−	25.6140i	−1.33248	−	1.67087i
$236$	−3.62078	−	15.8637i	−0.235693	−	1.03264i
$237$		0			0
$238$	0.782261	−	1.89319i	0.0507065	−	0.122717i
$239$	−16.0742	−	20.1564i	−1.03975	−	1.30381i	−0.951480	−	0.307710i	$-0.900437\pi$
$239$	−16.0742	−	20.1564i	−1.03975	−	1.30381i	−0.0882706	−	0.996097i	$-0.528134\pi$
$240$		0			0
$241$	13.7829	+	6.63747i	0.887832	+	0.427557i	0.821479	−	0.570239i	$-0.193149\pi$
$241$	13.7829	+	6.63747i	0.887832	+	0.427557i	0.0663528	+	0.997796i	$0.478864\pi$
$242$	−14.1369	+	17.7271i	−0.908754	+	1.13954i
$243$		0			0
$244$	−28.9220			−1.85154
$245$	−21.6471	−	7.53256i	−1.38299	−	0.481238i
$246$		0			0
$247$	−0.196069	+	0.859036i	−0.0124756	+	0.0546592i
$248$	−2.22612	+	2.79147i	−0.141359	+	0.177258i
$249$		0			0
$250$	−3.03575	+	3.80671i	−0.191998	+	0.240758i
$251$	0.0288724	+	0.0362048i	0.00182241	+	0.00228523i	0.782742	−	0.622347i	$-0.213821\pi$
$251$	0.0288724	+	0.0362048i	0.00182241	+	0.00228523i	−0.780919	+	0.624632i	$0.785249\pi$
$252$		0			0
$253$	−0.174263	+	0.218519i	−0.0109558	+	0.0137382i
$254$	7.76875	+	34.0371i	0.487454	+	2.13568i
$255$		0			0
$256$	−2.50477	+	10.9741i	−0.156548	+	0.685882i
$257$	−5.78625	+	2.78651i	−0.360937	+	0.173818i	−0.605559	−	0.795801i	$-0.707050\pi$
$257$	−5.78625	+	2.78651i	−0.360937	+	0.173818i	0.244622	+	0.969618i	$0.421336\pi$
$258$		0			0
$259$	−23.4399	−	3.96170i	−1.45648	−	0.246168i
$260$	3.25387	+	14.2561i	0.201796	+	0.884127i
$261$		0			0
$262$	−2.64616	+	1.27432i	−0.163480	+	0.0787280i
$263$	19.8392			1.22334			0.611669	−	0.791114i	$-0.290498\pi$
$263$	19.8392			1.22334			0.611669	+	0.791114i	$0.290498\pi$
$264$		0			0
$265$	10.9775	−	5.28649i	0.674343	−	0.324746i
$266$	−1.80542	+	1.61624i	−0.110697	+	0.0990978i
$267$		0			0
$268$	−28.5741	−	13.7605i	−1.74544	−	0.840559i
$269$	−0.598505	−	2.62222i	−0.0364915	−	0.159880i	0.953399	−	0.301712i	$-0.0975579\pi$
$269$	−0.598505	−	2.62222i	−0.0364915	−	0.159880i	−0.989891	+	0.141832i	$0.954701\pi$
$270$		0			0
$271$	19.7473	+	9.50982i	1.19957	+	0.577680i	0.923552	−	0.383473i	$-0.125272\pi$
$271$	19.7473	+	9.50982i	1.19957	+	0.577680i	0.276014	+	0.961154i	$0.410987\pi$
$272$	1.16182	+	0.559505i	0.0704459	+	0.0339250i
$273$		0			0
$274$	−20.0107	+	9.63666i	−1.20889	+	0.582172i
$275$	−0.329316			−0.0198585
$276$		0			0
$277$	16.0682	−	7.73803i	0.965443	−	0.464933i	0.116369	−	0.993206i	$-0.462875\pi$
$277$	16.0682	−	7.73803i	0.965443	−	0.464933i	0.849074	+	0.528273i	$0.177160\pi$
$278$	−1.59291	−	1.99744i	−0.0955363	−	0.119799i
$279$		0			0
$280$	−1.71442	+	4.14916i	−0.102456	+	0.247959i
$281$	−3.31077	+	14.5054i	−0.197504	+	0.865321i	0.774912	+	0.632069i	$0.217794\pi$
$281$	−3.31077	+	14.5054i	−0.197504	+	0.865321i	−0.972416	+	0.233252i	$0.925063\pi$
$282$		0			0
$283$	3.30486	−	14.4795i	0.196453	−	0.860718i	−0.776574	−	0.630027i	$-0.783044\pi$
$283$	3.30486	−	14.4795i	0.196453	−	0.860718i	0.973027	−	0.230692i	$-0.0740989\pi$
$284$	14.8358	+	18.6035i	0.880341	+	1.10391i
$285$		0			0
$286$	−0.146786	+	0.184064i	−0.00867966	+	0.0108839i
$287$	13.8728	−	4.00971i	0.818885	−	0.236686i
$288$		0			0
$289$	−10.5114	+	13.1809i	−0.618318	+	0.775347i
$290$	−51.1265	−	24.6212i	−3.00225	−	1.44581i
$291$		0			0
$292$	7.14385	−	31.2993i	0.418062	−	1.83165i
$293$	−25.0235			−1.46189			−0.730945	−	0.682436i	$-0.760921\pi$
$293$	−25.0235			−1.46189			−0.730945	+	0.682436i	$0.760921\pi$
$294$		0			0
$295$	−23.6653			−1.37785
$296$	−1.03612	+	4.53956i	−0.0602235	+	0.263856i
$297$		0			0
$298$	18.2222	+	8.77536i	1.05559	+	0.508343i
$299$	6.00545	−	7.53059i	0.347304	−	0.435505i
$300$		0			0
$301$	0.562203	+	9.85829i	0.0324049	+	0.568222i
$302$	13.3995	−	16.8024i	0.771055	−	0.966872i
$303$		0			0
$304$	−0.951090	−	1.19263i	−0.0545488	−	0.0684020i
$305$	−9.36010	+	41.0093i	−0.535958	+	2.34818i
$306$		0			0
$307$	4.18396	−	18.3311i	0.238791	−	1.04621i	−0.703309	−	0.710884i	$-0.748295\pi$
$307$	4.18396	−	18.3311i	0.238791	−	1.04621i	0.942101	−	0.335330i	$-0.108848\pi$
$308$	−0.329377	+	0.0952012i	−0.0187680	+	0.00542459i
$309$		0			0
$310$	29.0011	+	36.3663i	1.64715	+	2.06547i
$311$	−22.5178	+	10.8440i	−1.27687	+	0.614908i	−0.944584	−	0.328271i	$-0.893534\pi$
$311$	−22.5178	+	10.8440i	−1.27687	+	0.614908i	−0.332286	+	0.943179i	$0.607820\pi$
$312$		0			0
$313$	−3.25648			−0.184067			−0.0920335	−	0.995756i	$-0.529337\pi$
$313$	−3.25648			−0.184067			−0.0920335	+	0.995756i	$0.529337\pi$
$314$	20.1273	−	9.69280i	1.13585	−	0.546996i
$315$		0			0
$316$	8.18117	+	3.93984i	0.460227	+	0.221633i
$317$	27.9209	+	13.4460i	1.56819	+	0.755202i	0.997808	−	0.0661755i	$-0.0210797\pi$
$317$	27.9209	+	13.4460i	1.56819	+	0.755202i	0.570385	+	0.821377i	$0.306794\pi$
$318$		0			0
$319$	−0.107659	−	0.471684i	−0.00602774	−	0.0264092i
$320$	−29.1126	−	14.0199i	−1.62745	−	0.783736i
$321$		0			0
$322$	25.4471	−	7.35508i	1.41811	−	0.409883i
$323$	−0.150277	+	0.0723695i	−0.00836163	+	0.00402675i
$324$		0			0
$325$	11.3489			0.629523
$326$	17.0420	−	8.20698i	0.943868	−	0.454543i
$327$		0			0
$328$	−0.629400	−	2.75758i	−0.0347528	−	0.152262i
$329$	−19.7236	+	17.6568i	−1.08739	+	0.973452i
$330$		0			0
$331$	17.6284	−	8.48937i	0.968942	−	0.466618i	0.118654	−	0.992936i	$-0.462142\pi$
$331$	17.6284	−	8.48937i	0.968942	−	0.466618i	0.850288	+	0.526318i	$0.176428\pi$
$332$	6.09681	−	26.7119i	0.334606	−	1.46600i
$333$		0			0
$334$	−1.81470	−	7.95074i	−0.0992962	−	0.435045i
$335$	−28.7589	+	36.0626i	−1.57127	+	1.97031i
$336$		0			0
$337$	14.4460	+	18.1147i	0.786924	+	0.986772i	0.999953	+	0.00972588i	$0.00309589\pi$
$337$	14.4460	+	18.1147i	0.786924	+	0.986772i	−0.213028	+	0.977046i	$0.568333\pi$
$338$	−11.6537	+	14.6133i	−0.633879	+	0.794859i
$339$		0			0
$340$	−1.72584	+	2.16414i	−0.0935971	+	0.117367i
$341$	−0.0882468	+	0.386635i	−0.00477883	+	0.0209374i
$342$		0			0
$343$	−5.08077	+	17.8097i	−0.274336	+	0.961634i
$344$	1.93409			0.104279
$345$		0			0
$346$	−29.8855	+	37.4753i	−1.60666	+	2.01468i
$347$	12.6239	+	6.07937i	0.677689	+	0.326358i	0.740874	−	0.671644i	$-0.234412\pi$
$347$	12.6239	+	6.07937i	0.677689	+	0.326358i	−0.0631853	+	0.998002i	$0.520126\pi$
$348$		0			0
$349$	−3.05210	−	3.82722i	−0.163375	−	0.204866i	0.693405	−	0.720548i	$-0.256110\pi$
$349$	−3.05210	−	3.82722i	−0.163375	−	0.204866i	−0.856780	+	0.515682i	$0.827538\pi$
$350$	25.4696	+	18.0385i	1.36141	+	0.964196i
$351$		0			0
$352$	−0.103970	−	0.455521i	−0.00554161	−	0.0242794i
$353$	−7.98067	−	10.0074i	−0.424768	−	0.532642i	0.522690	−	0.852523i	$-0.324929\pi$
$353$	−7.98067	−	10.0074i	−0.424768	−	0.532642i	−0.947458	+	0.319881i	$0.896357\pi$
$354$		0			0
$355$	31.1797	−	15.0153i	1.65485	−	0.796932i
$356$	5.09358	−	22.3164i	0.269959	−	1.18277i
$357$		0			0
$358$	3.65830	+	16.0281i	0.193347	+	0.847110i
$359$	3.43488	+	4.30721i	0.181286	+	0.227326i	0.864168	−	0.503203i	$-0.167845\pi$
$359$	3.43488	+	4.30721i	0.181286	+	0.227326i	−0.682882	+	0.730529i	$0.739274\pi$
$360$		0			0
$361$	−18.8027			−0.989615
$362$	18.9922			0.998206
$363$		0			0
$364$	11.3510	−	3.28082i	0.594953	−	0.171962i
$365$	−42.0681	−	20.2589i	−2.20194	−	1.06040i
$366$		0			0
$367$	−5.99499	−	26.2658i	−0.312936	−	1.37106i	−0.849672	−	0.527312i	$-0.823200\pi$
$367$	−5.99499	−	26.2658i	−0.312936	−	1.37106i	0.536736	−	0.843750i	$-0.319657\pi$
$368$	3.71057	+	16.2571i	0.193427	+	0.847458i
$369$		0			0
$370$	54.6534	+	26.3197i	2.84129	+	1.36829i
$371$	−4.76974	−	8.61255i	−0.247633	−	0.447141i
$372$		0			0
$373$	−26.8298			−1.38920			−0.694598	−	0.719398i	$-0.744418\pi$
$373$	−26.8298			−1.38920			−0.694598	+	0.719398i	$0.744418\pi$
$374$	−0.0445656			−0.00230443
$375$		0			0
$376$	3.23288	+	4.05391i	0.166723	+	0.209064i
$377$	3.71014	+	16.2552i	0.191082	+	0.837184i
$378$		0			0
$379$	0.386441	−	1.69311i	0.0198501	−	0.0869691i	−0.964033	−	0.265784i	$-0.914369\pi$
$379$	0.386441	−	1.69311i	0.0198501	−	0.0869691i	0.983883	+	0.178815i	$0.0572263\pi$
$380$	2.95015	−	1.42072i	0.151339	−	0.0728812i
$381$		0			0
$382$	0.219887	+	0.275729i	0.0112504	+	0.0141075i
$383$	−4.66936	−	20.4578i	−0.238593	−	1.04535i	−0.942278	−	0.334833i	$-0.891320\pi$
$383$	−4.66936	−	20.4578i	−0.238593	−	1.04535i	0.703684	−	0.710513i	$-0.251537\pi$
$384$		0			0
$385$	0.0283912	+	0.497843i	0.00144695	+	0.0253724i
$386$	−16.6179	−	20.8382i	−0.845830	−	1.06064i
$387$		0			0
$388$	22.9239	+	11.0396i	1.16379	+	0.560450i
$389$	0.913732	−	1.14578i	0.0463280	−	0.0580935i	−0.758128	−	0.652106i	$-0.773886\pi$
$389$	0.913732	−	1.14578i	0.0463280	−	0.0580935i	0.804456	+	0.594013i	$0.202457\pi$
$390$		0			0
$391$	1.82331			0.0922085
$392$	3.42608	+	1.19217i	0.173043	+	0.0602138i
$393$		0			0
$394$	1.44741	−	6.34153i	0.0729196	−	0.319482i
$395$	8.23410	−	10.3252i	0.414302	−	0.519519i
$396$		0			0
$397$	−12.9325	+	16.2169i	−0.649065	+	0.813902i	−0.992104	−	0.125420i	$-0.959972\pi$
$397$	−12.9325	+	16.2169i	−0.649065	+	0.813902i	0.343039	+	0.939321i	$0.388544\pi$
$398$	1.39677	+	1.75150i	0.0700139	+	0.0877946i
$399$		0			0
$400$	−12.2500	+	15.3610i	−0.612500	+	0.768051i
$401$	−1.67507	−	7.33898i	−0.0836492	−	0.366491i	0.915727	−	0.401800i	$-0.131615\pi$
$401$	−1.67507	−	7.33898i	−0.0836492	−	0.366491i	−0.999376	+	0.0353094i	$0.988758\pi$
$402$		0			0
$403$	3.04116	−	13.3242i	0.151491	−	0.663725i
$404$	14.0052	−	6.74455i	0.696785	−	0.335554i
$405$		0			0
$406$	−17.5103	+	42.3775i	−0.869021	+	2.10316i
$407$	0.115085	+	0.504222i	0.00570457	+	0.0249934i
$408$		0			0
$409$	−16.4113	+	7.90328i	−0.811488	+	0.390792i	−0.793140	−	0.609040i	$-0.791555\pi$
$409$	−16.4113	+	7.90328i	−0.811488	+	0.390792i	−0.0183482	+	0.999832i	$0.505841\pi$
$410$	−36.8487			−1.81983
$411$		0			0
$412$	18.1950	−	8.76223i	0.896401	−	0.431684i
$413$	1.08875	+	19.0913i	0.0535737	+	0.939420i
$414$		0			0
$415$	−35.9023	−	17.2897i	−1.76238	−	0.848716i
$416$	3.58300	+	15.6982i	0.175671	+	0.769666i
$417$		0			0
$418$	0.0474976	+	0.0228736i	0.00232318	+	0.00111879i
$419$	2.62750	+	1.26534i	0.128362	+	0.0618157i	0.496962	−	0.867772i	$-0.334449\pi$
$419$	2.62750	+	1.26534i	0.128362	+	0.0618157i	−0.368601	+	0.929588i	$0.620163\pi$
$420$		0			0
$421$	6.95105	−	3.34745i	0.338774	−	0.163145i	−0.256760	−	0.966475i	$-0.582655\pi$
$421$	6.95105	−	3.34745i	0.338774	−	0.163145i	0.595534	+	0.803330i	$0.296941\pi$
$422$	41.4476			2.01764
$423$		0			0
$424$	−1.73740	+	0.836688i	−0.0843756	+	0.0406332i
$425$	1.33945	+	1.67962i	0.0649729	+	0.0814734i
$426$		0			0
$427$	33.5136	+	5.66430i	1.62184	+	0.274115i
$428$	−7.11066	+	31.1538i	−0.343707	+	1.50588i
$429$		0			0
$430$	5.60677	−	24.5649i	0.270383	−	1.18462i
$431$	6.46318	+	8.10458i	0.311321	+	0.390384i	0.912734	−	0.408554i	$-0.133967\pi$
$431$	6.46318	+	8.10458i	0.311321	+	0.390384i	−0.601413	+	0.798938i	$0.705396\pi$
$432$		0			0
$433$	17.8668	−	22.4043i	0.858626	−	1.07668i	−0.137652	−	0.990481i	$-0.543956\pi$
$433$	17.8668	−	22.4043i	0.858626	−	1.07668i	0.996278	−	0.0862021i	$-0.0274731\pi$
$434$	28.0032	−	25.0688i	1.34419	−	1.20334i
$435$		0			0
$436$	16.7494	−	21.0030i	0.802149	−	1.00586i
$437$	−1.94326	−	0.935825i	−0.0929588	−	0.0447666i
$438$		0			0
$439$	−1.45936	+	6.39387i	−0.0696514	+	0.305163i	−0.997740	−	0.0671976i	$-0.978594\pi$
$439$	−1.45936	+	6.39387i	−0.0696514	+	0.305163i	0.928088	+	0.372360i	$0.121451\pi$
$440$	0.0976712			0.00465629
$441$		0			0
$442$	1.53582			0.0730514
$443$	−8.28874	+	36.3153i	−0.393810	+	1.72539i	0.257231	+	0.966350i	$0.417190\pi$
$443$	−8.28874	+	36.3153i	−0.393810	+	1.72539i	−0.651040	+	0.759043i	$0.725667\pi$
$444$		0			0
$445$	−29.9946	−	14.4446i	−1.42188	−	0.684741i
$446$	0.481109	−	0.603292i	0.0227812	−	0.0285667i
$447$		0			0
$448$	−9.97077	+	24.1307i	−0.471075	+	1.14007i
$449$	−14.3386	+	17.9801i	−0.676682	+	0.848532i	−0.995044	−	0.0994368i	$-0.968296\pi$
$449$	−14.3386	+	17.9801i	−0.676682	+	0.848532i	0.318362	+	0.947969i	$0.396867\pi$
$450$		0			0
$451$	−0.195882	−	0.245628i	−0.00922371	−	0.0115662i
$452$	1.65521	−	7.25194i	0.0778544	−	0.341102i
$453$		0			0
$454$	−13.2905	+	58.2293i	−0.623752	+	2.73284i
$455$	−0.978417	−	17.1566i	−0.0458689	−	0.804316i
$456$		0			0
$457$	2.52795	+	3.16995i	0.118253	+	0.148284i	0.837434	−	0.546538i	$-0.184055\pi$
$457$	2.52795	+	3.16995i	0.118253	+	0.148284i	−0.719182	+	0.694822i	$0.755483\pi$
$458$	6.45374	−	3.10796i	0.301563	−	0.145225i
$459$		0			0
$460$	−35.7941			−1.66891
$461$	9.36148	−	4.50825i	0.436008	−	0.209970i	−0.202987	−	0.979181i	$-0.565065\pi$
$461$	9.36148	−	4.50825i	0.436008	−	0.209970i	0.638995	+	0.769211i	$0.279351\pi$
$462$		0			0
$463$	9.70762	+	4.67494i	0.451151	+	0.217263i	0.645640	−	0.763642i	$-0.276591\pi$
$463$	9.70762	+	4.67494i	0.451151	+	0.217263i	−0.194489	+	0.980905i	$0.562305\pi$
$464$	−26.0065	−	12.5241i	−1.20732	−	0.581415i
$465$		0			0
$466$	7.45375	+	32.6570i	0.345288	+	1.51281i
$467$	−7.86449	−	3.78734i	−0.363925	−	0.175257i	0.242980	−	0.970031i	$-0.421875\pi$
$467$	−7.86449	−	3.78734i	−0.363925	−	0.175257i	−0.606905	+	0.794774i	$0.707589\pi$
$468$		0			0
$469$	30.4154	+	21.5413i	1.40445	+	0.994684i
$470$	60.8606	−	29.3089i	2.80729	−	1.35192i
$471$		0			0
$472$	3.74549			0.172400
$473$	0.193550	−	0.0932090i	0.00889946	−	0.00428575i
$474$		0			0
$475$	−0.565496	−	2.47760i	−0.0259467	−	0.113680i
$476$	1.82525	+	1.29271i	0.0836603	+	0.0592512i
$477$		0			0
$478$	47.8929	−	23.0640i	2.19057	−	1.05492i
$479$	5.10814	−	22.3802i	0.233397	−	1.02258i	−0.713403	−	0.700754i	$-0.752847\pi$
$479$	5.10814	−	22.3802i	0.233397	−	1.02258i	0.946800	−	0.321824i	$-0.104296\pi$
$480$		0			0
$481$	−3.96607	−	17.3765i	−0.180837	−	0.792300i
$482$	−19.6662	+	24.6607i	−0.895773	+	1.12326i
$483$		0			0
$484$	−15.4359	−	19.3560i	−0.701631	−	0.879818i
$485$	23.0722	−	28.9317i	1.04766	−	1.31372i
$486$		0			0
$487$	−1.82197	+	2.28468i	−0.0825615	+	0.103529i	−0.821397	−	0.570357i	$-0.806805\pi$
$487$	−1.82197	+	2.28468i	−0.0825615	+	0.103529i	0.738835	+	0.673886i	$0.235376\pi$
$488$	1.48142	−	6.49051i	0.0670605	−	0.293811i
$489$		0			0
$490$	25.0738	−	40.0587i	1.13272	−	1.80967i
$491$	−4.51822			−0.203904			−0.101952	−	0.994789i	$-0.532509\pi$
$491$	−4.51822			−0.203904			−0.101952	+	0.994789i	$0.532509\pi$
$492$		0			0
$493$	−1.96785	+	2.46760i	−0.0886274	+	0.111135i
$494$	−1.63686	−	0.788270i	−0.0736458	−	0.0354660i
$495$		0			0
$496$	14.7520	+	18.4984i	0.662385	+	0.830604i
$497$	−13.5476	−	24.4624i	−0.607693	−	1.09729i
$498$		0			0
$499$	−0.215918	−	0.945999i	−0.00966583	−	0.0423488i	0.969865	−	0.243643i	$-0.0783425\pi$
$499$	−0.215918	−	0.945999i	−0.00966583	−	0.0423488i	−0.979531	+	0.201294i	$0.935485\pi$
$500$	−3.31470	−	4.15650i	−0.148238	−	0.185884i
$501$		0			0
$502$	−0.0860253	+	0.0414276i	−0.00383950	+	0.00184900i
$503$	2.23455	−	9.79021i	0.0996338	−	0.436524i	−0.900365	−	0.435135i	$-0.856701\pi$
$503$	2.23455	−	9.79021i	0.0996338	−	0.436524i	0.999999	−	0.00138914i	$-0.000442178\pi$
$504$		0			0
$505$	−5.03074	−	22.0411i	−0.223865	−	0.980817i
$506$	−0.359309	−	0.450559i	−0.0159732	−	0.0200298i
$507$		0			0
$508$	−38.1204			−1.69132
$509$	9.76741			0.432933			0.216467	−	0.976290i	$-0.430547\pi$
$509$	9.76741			0.432933			0.216467	+	0.976290i	$0.430547\pi$
$510$		0			0
$511$	−14.4079	+	34.8691i	−0.637367	+	1.54252i
$512$	−28.3222	−	13.6393i	−1.25168	−	0.602776i
$513$		0			0
$514$	−2.94660	−	12.9099i	−0.129969	−	0.569431i
$515$	−6.53572	−	28.6348i	−0.287998	−	1.26180i
$516$		0			0
$517$	0.518894	+	0.249886i	0.0228209	+	0.0109900i
$518$	18.7182	−	45.3008i	0.822431	−	1.99040i
$519$		0			0
$520$	−3.36594			−0.147606
$521$	45.1777			1.97927			0.989635	−	0.143605i	$-0.0458695\pi$
$521$	45.1777			1.97927			0.989635	+	0.143605i	$0.0458695\pi$
$522$		0			0
$523$	−4.13527	−	5.18546i	−0.180823	−	0.226744i	0.683157	−	0.730272i	$-0.260607\pi$
$523$	−4.13527	−	5.18546i	−0.180823	−	0.226744i	−0.863979	+	0.503528i	$0.832035\pi$
$524$	−0.713600	−	3.12649i	−0.0311738	−	0.136581i
$525$		0			0
$526$	−9.10244	+	39.8804i	−0.396885	+	1.73887i
$527$	2.33089	−	1.12250i	0.101535	−	0.0488967i
$528$		0			0
$529$	0.360085	+	0.451533i	0.0156559	+	0.0196319i
$530$	5.59020	+	24.4923i	0.242823	+	1.06388i
$531$		0			0
$532$	−1.28184	−	2.31458i	−0.0555750	−	0.100350i
$533$	6.75047	+	8.46482i	0.292395	+	0.366652i
$534$		0			0
$535$	41.8726	+	20.1648i	1.81031	+	0.871799i
$536$	4.55165	−	5.70759i	0.196601	−	0.246530i
$537$		0			0
$538$	5.54574			0.239094
$539$	0.400313	−	0.0458075i	0.0172427	−	0.00197307i
$540$		0			0
$541$	2.17044	−	9.50931i	0.0933144	−	0.408837i	−0.906599	−	0.421993i	$-0.861331\pi$
$541$	2.17044	−	9.50931i	0.0933144	−	0.408837i	0.999913	+	0.0131559i	$0.00418777\pi$
$542$	−28.1767	+	35.3325i	−1.21030	+	1.51766i
$543$		0			0
$544$	−1.90042	+	2.38305i	−0.0814797	+	0.102172i
$545$	−24.3601	−	30.5466i	−1.04347	−	1.30847i
$546$		0			0
$547$	10.5633	−	13.2459i	0.451653	−	0.566355i	−0.502920	−	0.864333i	$-0.667741\pi$
$547$	10.5633	−	13.2459i	0.451653	−	0.566355i	0.954573	+	0.297978i	$0.0963123\pi$
$548$	−5.39637	−	23.6430i	−0.230521	−	1.00998i
$549$		0			0
$550$	0.151094	−	0.661986i	0.00644267	−	0.0282272i
$551$	3.36383	−	1.61993i	0.143304	−	0.0690115i
$552$		0			0
$553$	−8.70838	−	6.16758i	−0.370318	−	0.262272i
$554$	8.18258	+	35.8502i	0.347645	+	1.52313i
$555$		0			0
$556$	2.51333	−	1.21035i	0.106589	−	0.0513304i
$557$	29.8992			1.26687			0.633435	−	0.773796i	$-0.281644\pi$
$557$	29.8992			1.26687			0.633435	+	0.773796i	$0.281644\pi$
$558$		0			0
$559$	−6.67013	+	3.21217i	−0.282116	+	0.135860i
$560$	24.2781	+	17.1946i	1.02594	+	0.726604i
$561$		0			0
$562$	−27.6395	−	13.3105i	−1.16590	−	0.561469i
$563$	4.18806	+	18.3491i	0.176506	+	0.773322i	0.983226	+	0.182389i	$0.0583830\pi$
$563$	4.18806	+	18.3491i	0.176506	+	0.773322i	−0.806721	+	0.590933i	$0.798760\pi$
$564$		0			0
$565$	−9.74704	−	4.69393i	−0.410061	−	0.197475i
$566$	27.5902	+	13.2867i	1.15970	+	0.558483i
$567$		0			0
$568$	−4.93478	+	2.37647i	−0.207059	+	0.0997143i
$569$	−37.6936			−1.58020			−0.790100	−	0.612978i	$-0.789971\pi$
$569$	−37.6936			−1.58020			−0.790100	+	0.612978i	$0.789971\pi$
$570$		0			0
$571$	1.92787	−	0.928414i	0.0806789	−	0.0388529i	−0.393109	−	0.919492i	$-0.628601\pi$
$571$	1.92787	−	0.928414i	0.0806789	−	0.0388529i	0.473788	+	0.880639i	$0.342886\pi$
$572$	−0.160274	−	0.200977i	−0.00670140	−	0.00840328i
$573$		0			0
$574$	1.69526	+	29.7265i	0.0707587	+	1.24076i
$575$	−6.18168	+	27.0837i	−0.257794	+	1.12947i
$576$		0			0
$577$	−1.90752	+	8.35741i	−0.0794113	+	0.347924i	−0.998988	−	0.0449881i	$-0.985675\pi$
$577$	−1.90752	+	8.35741i	−0.0794113	+	0.347924i	0.919576	+	0.392912i	$0.128532\pi$
$578$	−21.6732	−	27.1774i	−0.901488	−	1.13043i
$579$		0			0
$580$	38.6317	−	48.4426i	1.60409	−	2.01147i
$581$	−12.2962	+	29.7585i	−0.510131	+	1.23459i
$582$		0			0
$583$	−0.133545	+	0.167460i	−0.00553088	+	0.00693550i
$584$	6.65808	+	3.20636i	0.275513	+	0.132680i
$585$		0			0
$586$	11.4811	−	50.3018i	0.474279	−	2.07795i
$587$	−38.8083			−1.60179			−0.800894	−	0.598806i	$-0.795642\pi$
$587$	−38.8083			−1.60179			−0.800894	+	0.598806i	$0.795642\pi$
$588$		0			0
$589$	−3.06037			−0.126100
$590$	10.8579	−	47.5716i	0.447013	−	1.95849i
$591$		0			0
$592$	27.8005	+	13.3880i	1.14259	+	0.550244i
$593$	17.4209	−	21.8451i	0.715391	−	0.897072i	−0.282676	−	0.959215i	$-0.591222\pi$
$593$	17.4209	−	21.8451i	0.715391	−	0.897072i	0.998067	+	0.0621437i	$0.0197937\pi$
$594$		0			0
$595$	2.42368	−	2.16971i	0.0993610	−	0.0889495i
$596$	−13.7689	+	17.2656i	−0.563995	+	0.707228i
$597$		0			0
$598$	12.3825	+	15.5272i	0.506358	+	0.634953i
$599$	4.44883	−	19.4916i	0.181774	−	0.796405i	−0.799011	−	0.601316i	$-0.794643\pi$
$599$	4.44883	−	19.4916i	0.181774	−	0.796405i	0.980786	−	0.195089i	$-0.0624996\pi$
$600$		0			0
$601$	−1.18134	+	5.17577i	−0.0481877	+	0.211124i	−0.993290	−	0.115651i	$-0.963105\pi$
$601$	−1.18134	+	5.17577i	−0.0481877	+	0.211124i	0.945102	+	0.326775i	$0.105962\pi$
$602$	−20.0749	−	3.39296i	−0.818192	−	0.138287i
$603$		0			0
$604$	14.6307	+	18.3464i	0.595316	+	0.746503i
$605$	−32.4409	+	15.6227i	−1.31891	+	0.635154i
$606$		0			0
$607$	9.18955			0.372992			0.186496	−	0.982456i	$-0.440287\pi$
$607$	9.18955			0.372992			0.186496	+	0.982456i	$0.440287\pi$
$608$	3.24856	−	1.56443i	0.131747	−	0.0634458i
$609$		0			0
$610$	−78.1416	−	37.6310i	−3.16386	−	1.52363i
$611$	−17.8821	−	8.61158i	−0.723433	−	0.348387i
$612$		0			0
$613$	2.43997	+	10.6902i	0.0985494	+	0.431773i	0.999999	−	0.00111008i	$-0.000353349\pi$
$613$	2.43997	+	10.6902i	0.0985494	+	0.431773i	−0.901450	+	0.432883i	$0.857496\pi$
$614$	34.9293	+	16.8211i	1.40963	+	0.678842i
$615$		0			0
$616$	−0.00449345	−	0.0787932i	−0.000181046	−	0.00317467i
$617$	35.5963	−	17.1423i	1.43305	−	0.690121i	0.453489	−	0.891262i	$-0.350179\pi$
$617$	35.5963	−	17.1423i	1.43305	−	0.690121i	0.979562	+	0.201140i	$0.0644647\pi$
$618$		0			0
$619$	18.0910			0.727138			0.363569	−	0.931567i	$-0.381558\pi$
$619$	18.0910			0.727138			0.363569	+	0.931567i	$0.381558\pi$
$620$	−45.7587	+	22.0362i	−1.83771	+	0.884995i
$621$		0			0
$622$	−11.4670	−	50.2403i	−0.459786	−	2.01445i
$623$	−10.2728	+	24.8617i	−0.411572	+	0.996065i
$624$		0			0
$625$	18.8067	−	9.05685i	0.752269	−	0.362274i
$626$	1.49411	−	6.54611i	0.0597165	−	0.261635i
$627$		0			0
$628$	5.42780	+	23.7808i	0.216593	+	0.948956i
$629$	2.10360	−	2.63783i	0.0838759	−	0.105177i
$630$		0			0
$631$	−21.4724	−	26.9255i	−0.854801	−	1.07189i	−0.996633	−	0.0819961i	$-0.973870\pi$
$631$	−21.4724	−	26.9255i	−0.854801	−	1.07189i	0.141831	−	0.989891i	$-0.454701\pi$
$632$	−1.30320	+	1.63417i	−0.0518387	+	0.0650036i
$633$		0			0
$634$	−39.8393	+	49.9569i	−1.58222	+	1.98404i
$635$	−12.3370	+	54.0520i	−0.489579	+	2.14499i
$636$		0			0
$637$	−13.7956	+	1.57862i	−0.546601	+	0.0625470i
$638$	0.997566			0.0394940
$639$		0			0
$640$	8.39684	−	10.5293i	0.331914	−	0.416207i
$641$	−15.0836	−	7.26386i	−0.595765	−	0.286905i	0.111601	−	0.993753i	$-0.464402\pi$
$641$	−15.0836	−	7.26386i	−0.595765	−	0.286905i	−0.707366	+	0.706848i	$0.750117\pi$
$642$		0			0
$643$	−26.4441	−	33.1599i	−1.04286	−	1.30770i	−0.950078	−	0.312012i	$-0.898997\pi$
$643$	−26.4441	−	33.1599i	−1.04286	−	1.30770i	−0.0927769	−	0.995687i	$-0.529574\pi$
$644$	1.64674	+	28.8758i	0.0648907	+	1.13786i
$645$		0			0
$646$	−0.0765272	−	0.335288i	−0.00301092	−	0.0131917i
$647$	29.8588	+	37.4418i	1.17387	+	1.47199i	0.850703	+	0.525646i	$0.176177\pi$
$647$	29.8588	+	37.4418i	1.17387	+	1.47199i	0.323168	+	0.946342i	$0.395252\pi$
$648$		0			0
$649$	0.374824	−	0.180506i	0.0147131	−	0.00708547i
$650$	−5.20700	+	22.8133i	−0.204235	+	0.894813i
$651$		0			0
$652$	4.59577	+	20.1354i	0.179984	+	0.788563i
$653$	12.9217	+	16.2033i	0.505664	+	0.634083i	0.967496	−	0.252884i	$-0.0813793\pi$
$653$	12.9217	+	16.2033i	0.505664	+	0.634083i	−0.461832	+	0.886967i	$0.652808\pi$
$654$		0			0
$655$	−4.66407			−0.182240
$656$	−18.7438			−0.731823
$657$		0			0
$658$	−26.4440	−	47.7491i	−1.03090	−	1.86145i
$659$	5.08619	+	2.44938i	0.198130	+	0.0954142i	0.530318	−	0.847799i	$-0.322073\pi$
$659$	5.08619	+	2.44938i	0.198130	+	0.0954142i	−0.332188	+	0.943213i	$0.607787\pi$
$660$		0			0
$661$	9.87715	+	43.2746i	0.384177	+	1.68319i	0.684231	+	0.729265i	$0.260138\pi$
$661$	9.87715	+	43.2746i	0.384177	+	1.68319i	−0.300054	+	0.953922i	$0.597005\pi$
$662$	8.97709	+	39.3312i	0.348904	+	1.52865i
$663$		0			0
$664$	5.68224	+	2.73642i	0.220514	+	0.106194i
$665$	−3.69675	+	1.06849i	−0.143354	+	0.0414341i
$666$		0			0
$667$	−40.8132			−1.58030
$668$	8.90456			0.344528
$669$		0			0
$670$	−59.2974	−	74.3566i	−2.29086	−	2.87264i
$671$	−0.164545	−	0.720920i	−0.00635220	−	0.0278308i
$672$		0			0
$673$	5.71159	−	25.0241i	0.220166	−	0.964609i	−0.737187	−	0.675689i	$-0.763846\pi$
$673$	5.71159	−	25.0241i	0.220166	−	0.964609i	0.957353	−	0.288921i	$-0.0932964\pi$
$674$	−43.0419	+	20.7279i	−1.65791	+	0.798408i
$675$		0			0
$676$	−12.7245	−	15.9561i	−0.489406	−	0.613695i
$677$	5.79464	+	25.3880i	0.222706	+	0.975739i	0.955431	+	0.295214i	$0.0953910\pi$
$677$	5.79464	+	25.3880i	0.222706	+	0.975739i	−0.732725	+	0.680525i	$0.761752\pi$
$678$		0			0
$679$	−24.4012	−	17.2818i	−0.936432	−	0.663214i
$680$	−0.397264	−	0.498153i	−0.0152344	−	0.0191033i
$681$		0			0
$682$	−0.736717	−	0.354784i	−0.0282104	−	0.0135854i
$683$	1.34176	−	1.68251i	0.0513410	−	0.0643796i	−0.755498	−	0.655151i	$-0.772605\pi$
$683$	1.34176	−	1.68251i	0.0513410	−	0.0643796i	0.806839	+	0.590771i	$0.201176\pi$
$684$		0			0
$685$	−35.2705			−1.34762
$686$	−33.4696	−	18.3845i	−1.27788	−	0.701925i
$687$		0			0
$688$	2.85199	−	12.4954i	0.108731	−	0.476383i
$689$	4.60223	−	5.77102i	0.175331	−	0.219858i
$690$		0			0
$691$	−4.56794	+	5.72802i	−0.173773	+	0.217904i	−0.861089	−	0.508454i	$-0.830217\pi$
$691$	−4.56794	+	5.72802i	−0.173773	+	0.217904i	0.687316	+	0.726358i	$0.258789\pi$
$692$	−32.6316	−	40.9188i	−1.24047	−	1.55550i
$693$		0			0
$694$	−18.0126	+	22.5871i	−0.683750	+	0.857396i
$695$	−0.902799	−	3.95542i	−0.0342451	−	0.150038i
$696$		0			0
$697$	−0.456057	+	1.99812i	−0.0172744	+	0.0756840i
$698$	9.09374	−	4.37931i	0.344203	−	0.165759i
$699$		0			0
$700$	−25.3904	+	22.7299i	−0.959668	+	0.859109i
$701$	8.60396	+	37.6964i	0.324967	+	1.42377i	0.828593	+	0.559851i	$0.189142\pi$
$701$	8.60396	+	37.6964i	0.324967	+	1.42377i	−0.503626	+	0.863922i	$0.668001\pi$
$702$		0			0
$703$	−3.59588	+	1.73168i	−0.135621	+	0.0653117i
$704$	0.568037			0.0214087
$705$		0			0
$706$	23.7784	−	11.4511i	0.894911	−	0.430967i
$707$	−17.5495	+	5.07242i	−0.660019	+	0.190768i
$708$		0			0
$709$	4.15323	+	2.00009i	0.155978	+	0.0751151i	0.510244	−	0.860030i	$-0.329555\pi$
$709$	4.15323	+	2.00009i	0.155978	+	0.0751151i	−0.354266	+	0.935145i	$0.615269\pi$
$710$	15.8780	+	69.5660i	0.595890	+	2.61077i
$711$		0			0
$712$	4.74722	+	2.28614i	0.177910	+	0.0856767i
$713$	30.1412	+	14.5152i	1.12880	+	0.543600i
$714$		0			0
$715$	−0.336841	+	0.162214i	−0.0125971	+	0.00606646i
$716$	−17.9509			−0.670857
$717$		0			0
$718$	−10.2342	+	4.92854i	−0.381938	+	0.183932i
$719$	−29.0137	−	36.3820i	−1.08203	−	1.35682i	−0.929628	−	0.368500i	$-0.879872\pi$
$719$	−29.0137	−	36.3820i	−1.08203	−	1.35682i	−0.152399	−	0.988319i	$-0.548700\pi$
$720$		0			0
$721$	−22.7996	+	6.58986i	−0.849101	+	0.245419i
$722$	8.62688	−	37.7968i	0.321059	−	1.40665i
$723$		0			0
$724$	−4.61448	+	20.2174i	−0.171496	+	0.751373i
$725$	−29.9825	−	37.5969i	−1.11352	−	1.39631i
$726$		0			0
$727$	−4.74974	+	5.95598i	−0.176158	+	0.220895i	−0.862070	−	0.506789i	$-0.830832\pi$
$727$	−4.74974	+	5.95598i	−0.176158	+	0.220895i	0.685912	+	0.727685i	$0.259404\pi$
$728$	0.154853	+	2.71537i	0.00573925	+	0.100638i
$729$		0			0
$730$	60.0254	−	75.2694i	2.22164	−	2.78585i
$731$	−1.26263	−	0.608053i	−0.0467002	−	0.0224896i
$732$		0			0
$733$	1.75402	−	7.68486i	0.0647862	−	0.283847i	−0.932149	−	0.362074i	$-0.882069\pi$
$733$	1.75402	−	7.68486i	0.0647862	−	0.283847i	0.996936	+	0.0782271i	$0.0249259\pi$
$734$	55.5495			2.05037
$735$		0			0
$736$	−39.4147			−1.45285
$737$	0.180434	−	0.790535i	0.00664639	−	0.0291197i
$738$		0			0
$739$	43.8632	+	21.1234i	1.61353	+	0.777037i	0.999921	−	0.0125696i	$-0.00400113\pi$
$739$	43.8632	+	21.1234i	1.61353	+	0.777037i	0.613613	+	0.789607i	$0.289715\pi$
$740$	−41.2966	+	51.7843i	−1.51809	+	1.90363i
$741$		0			0
$742$	19.5012	−	5.63651i	0.715912	−	0.206923i
$743$	7.89544	−	9.90057i	0.289656	−	0.363217i	−0.615619	−	0.788044i	$-0.711094\pi$
$743$	7.89544	−	9.90057i	0.289656	−	0.363217i	0.905274	+	0.424828i	$0.139665\pi$
$744$		0			0
$745$	20.0253	+	25.1110i	0.733672	+	0.919995i
$746$	12.3098	−	53.9328i	0.450694	−	1.97462i
$747$		0			0
$748$	0.0108280	−	0.0474406i	0.000395911	−	0.00173460i
$749$	14.3409	−	34.7071i	0.524006	−	1.26817i
$750$		0			0
$751$	−3.54159	−	4.44102i	−0.129235	−	0.162055i	0.713004	−	0.701160i	$-0.247334\pi$
$751$	−3.54159	−	4.44102i	−0.129235	−	0.162055i	−0.842239	+	0.539105i	$0.818763\pi$
$752$	30.9580	−	14.9086i	1.12892	−	0.543660i
$753$		0			0
$754$	−34.3781			−1.25198
$755$	30.7488	−	14.8078i	1.11906	−	0.538912i
$756$		0			0
$757$	27.6536	+	13.3173i	1.00509	+	0.484025i	0.862662	−	0.505781i	$-0.168796\pi$
$757$	27.6536	+	13.3173i	1.00509	+	0.484025i	0.142426	+	0.989806i	$0.454510\pi$
$758$	3.22615	+	1.55363i	0.117179	+	0.0564305i
$759$		0			0
$760$	0.167719	+	0.734826i	0.00608381	+	0.0266549i
$761$	3.40008	+	1.63739i	0.123253	+	0.0593555i	0.494494	−	0.869181i	$-0.335353\pi$
$761$	3.40008	+	1.63739i	0.123253	+	0.0593555i	−0.371241	+	0.928537i	$0.621068\pi$
$762$		0			0
$763$	−23.5218	+	21.0571i	−0.851548	+	0.762319i
$764$	−0.346942	+	0.167079i	−0.0125519	+	0.00604469i
$765$		0			0
$766$	43.2663			1.56327
$767$	−12.9172	+	6.22058i	−0.466412	+	0.224612i
$768$		0			0
$769$	−3.83657	−	16.8091i	−0.138350	−	0.606152i	−0.995798	−	0.0915803i	$-0.970808\pi$
$769$	−3.83657	−	16.8091i	−0.138350	−	0.606152i	0.857448	−	0.514571i	$-0.172049\pi$
$770$	−1.01378	−	0.171344i	−0.0365341	−	0.00617482i
$771$		0			0
$772$	26.2201	−	12.6269i	0.943683	−	0.454454i
$773$	2.46275	−	10.7900i	0.0885790	−	0.388090i	−0.911132	−	0.412114i	$-0.864791\pi$
$773$	2.46275	−	10.7900i	0.0885790	−	0.388090i	0.999711	+	0.0240238i	$0.00764774\pi$
$774$		0			0
$775$	8.77120	+	38.4292i	0.315071	+	1.38042i
$776$	−3.65162	+	4.57899i	−0.131086	+	0.164376i
$777$		0			0
$778$	1.88400	+	2.36246i	0.0675448	+	0.0846984i
$779$	1.51161	−	1.89550i	0.0541590	−	0.0679132i
$780$		0			0
$781$	−0.379312	+	0.475642i	−0.0135728	+	0.0170198i
$782$	−0.836552	+	3.66518i	−0.0299150	+	0.131066i
$783$		0			0
$784$	12.7543	−	20.3766i	0.455509	−	0.727737i
$785$	35.4760			1.26619
$786$		0			0
$787$	26.7736	−	33.5731i	0.954377	−	1.19675i	−0.0260088	−	0.999662i	$-0.508280\pi$
$787$	26.7736	−	33.5731i	0.954377	−	1.19675i	0.980386	−	0.197089i	$-0.0631488\pi$
$788$	6.39895	+	3.08157i	0.227953	+	0.109777i
$789$		0			0
$790$	16.9777	+	21.2894i	0.604039	+	0.757441i
$791$	−3.33826	+	8.07907i	−0.118695	+	0.287259i
$792$		0			0
$793$	5.67056	+	24.8443i	0.201367	+	0.882248i
$794$	−26.6653	−	33.4372i	−0.946315	−	1.18664i
$795$		0			0
$796$	−2.20386	+	1.06132i	−0.0781137	+	0.0376176i
$797$	9.03541	−	39.5867i	0.320051	−	1.40223i	−0.517411	−	0.855737i	$-0.673104\pi$
$797$	9.03541	−	39.5867i	0.320051	−	1.40223i	0.837461	−	0.546497i	$-0.184039\pi$
$798$		0			0
$799$	−0.836033	−	3.66290i	−0.0295767	−	0.129584i
$800$	−28.9551	−	36.3086i	−1.02372	−	1.28370i
$801$		0			0
$802$	15.5212			0.548073
$803$	0.820820			0.0289661
$804$		0			0
$805$	41.4767	+	7.01018i	1.46186	+	0.247076i
$806$	25.3887	+	12.2266i	0.894280	+	0.430662i
$807$		0			0
$808$	0.796211	+	3.48843i	0.0280106	+	0.122723i
$809$	−2.20304	−	9.65217i	−0.0774549	−	0.339352i	0.921322	−	0.388801i	$-0.127111\pi$
$809$	−2.20304	−	9.65217i	−0.0774549	−	0.339352i	−0.998777	+	0.0494489i	$0.984253\pi$
$810$		0			0
$811$	48.8203	+	23.5106i	1.71431	+	0.825569i	0.990812	+	0.135244i	$0.0431819\pi$
$811$	48.8203	+	23.5106i	1.71431	+	0.825569i	0.723500	+	0.690325i	$0.242532\pi$
$812$	−40.8568	−	28.9362i	−1.43379	−	1.01546i
$813$		0			0
$814$	−1.06638			−0.0373766
$815$	30.0379			1.05218
$816$		0			0
$817$	1.03362	+	1.29611i	0.0361616	+	0.0453453i
$818$	−8.35733	−	36.6159i	−0.292207	−	1.28024i
$819$		0			0
$820$	8.95304	−	39.2258i	0.312654	−	1.36983i
$821$	15.5141	−	7.47117i	0.541444	−	0.260746i	−0.143111	−	0.989707i	$-0.545711\pi$
$821$	15.5141	−	7.47117i	0.541444	−	0.260746i	0.684555	+	0.728961i	$0.259996\pi$
$822$		0			0
$823$	17.7852	+	22.3019i	0.619952	+	0.777396i	0.988338	−	0.152277i	$-0.0486607\pi$
$823$	17.7852	+	22.3019i	0.619952	+	0.777396i	−0.368385	+	0.929673i	$0.620089\pi$
$824$	1.03440	+	4.53201i	0.0360351	+	0.157880i
$825$		0			0
$826$	−38.8764	−	6.57070i	−1.35268	−	0.228624i
$827$	−22.2070	−	27.8467i	−0.772214	−	0.968326i	0.227771	−	0.973715i	$-0.426856\pi$
$827$	−22.2070	−	27.8467i	−0.772214	−	0.968326i	−0.999985	+	0.00538858i	$0.998285\pi$
$828$		0			0
$829$	−12.4911	−	6.01538i	−0.433832	−	0.208923i	0.204205	−	0.978928i	$-0.434539\pi$
$829$	−12.4911	−	6.01538i	−0.433832	−	0.208923i	−0.638037	+	0.770006i	$0.720253\pi$
$830$	51.2277	−	64.2375i	1.77814	−	2.22972i
$831$		0			0
$832$	−19.5757			−0.678665
$833$	−1.86185	−	1.85541i	−0.0645093	−	0.0642860i
$834$		0			0
$835$	2.88180	−	12.6260i	0.0997290	−	0.436941i
$836$	−0.0358896	+	0.0450041i	−0.00124127	+	0.00155650i
$837$		0			0
$838$	−3.74908	+	4.70120i	−0.129510	+	0.162400i
$839$	11.9626	+	15.0006i	0.412994	+	0.517878i	0.944204	−	0.329362i	$-0.106834\pi$
$839$	11.9626	+	15.0006i	0.412994	+	0.517878i	−0.531210	+	0.847240i	$0.678262\pi$
$840$		0			0
$841$	25.9675	−	32.5622i	0.895432	−	1.12284i
$842$	3.53977	+	15.5087i	0.121988	+	0.534466i
$843$		0			0
$844$	−10.0704	+	44.1214i	−0.346638	+	1.51872i
$845$	−26.7426	+	12.8786i	−0.919974	+	0.443036i
$846$		0			0
$847$	14.0956	+	25.4520i	0.484332	+	0.874540i
$848$	2.84357	+	12.4585i	0.0976484	+	0.427826i
$849$		0			0
$850$	−3.99089	+	1.92191i	−0.136886	+	0.0659210i
$851$	43.6287			1.49557
$852$		0			0
$853$	1.27404	−	0.613546i	0.0436223	−	0.0210074i	−0.411945	−	0.911209i	$-0.635151\pi$
$853$	1.27404	−	0.613546i	0.0436223	−	0.0210074i	0.455568	+	0.890201i	$0.349436\pi$
$854$	−26.7627	+	64.7696i	−0.915800	+	2.21637i
$855$		0			0
$856$	−6.62714	−	3.19146i	−0.226511	−	0.109082i
$857$	−0.317281	−	1.39010i	−0.0108381	−	0.0474849i	0.969220	−	0.246197i	$-0.0791811\pi$
$857$	−0.317281	−	1.39010i	−0.0108381	−	0.0474849i	−0.980058	+	0.198712i	$0.936324\pi$
$858$		0			0
$859$	−1.30097	−	0.626513i	−0.0443885	−	0.0213764i	0.411558	−	0.911384i	$-0.364985\pi$
$859$	−1.30097	−	0.626513i	−0.0443885	−	0.0213764i	−0.455946	+	0.890007i	$0.650699\pi$
$860$	24.7873	+	11.9369i	0.845240	+	0.407046i
$861$		0			0
$862$	−19.2570	+	9.27370i	−0.655898	+	0.315864i
$863$	−25.4430			−0.866091			−0.433046	−	0.901372i	$-0.642561\pi$
$863$	−25.4430			−0.866091			−0.433046	+	0.901372i	$0.642561\pi$
$864$		0			0
$865$	−68.5805	+	33.0266i	−2.33181	+	1.12294i
$866$	36.8392	+	46.1949i	1.25185	+	1.56977i
$867$		0			0
$868$	19.8822	+	35.9006i	0.674846	+	1.21855i
$869$	−0.0516610	+	0.226342i	−0.00175248	+	0.00767811i
$870$		0			0
$871$	−6.21813	+	27.2434i	−0.210693	+	0.923107i
$872$	3.85546	+	4.83459i	0.130562	+	0.163720i
$873$		0			0
$874$	2.77277	−	3.47694i	0.0937902	−	0.117609i
$875$	3.02689	+	5.46555i	0.102328	+	0.184769i
$876$		0			0
$877$	6.30152	−	7.90186i	0.212787	−	0.266827i	−0.663971	−	0.747759i	$-0.731130\pi$
$877$	6.30152	−	7.90186i	0.212787	−	0.266827i	0.876758	+	0.480932i	$0.159702\pi$
$878$	−12.1833	−	5.86715i	−0.411165	−	0.198007i
$879$		0			0
$880$	0.144025	−	0.631017i	0.00485510	−	0.0212716i
$881$	41.9874			1.41459			0.707296	−	0.706918i	$-0.249915\pi$
$881$	41.9874			1.41459			0.707296	+	0.706918i	$0.249915\pi$
$882$		0			0
$883$	−2.24352			−0.0755003			−0.0377502	−	0.999287i	$-0.512019\pi$
$883$	−2.24352			−0.0755003			−0.0377502	+	0.999287i	$0.512019\pi$
$884$	−0.373154	+	1.63490i	−0.0125505	+	0.0549875i
$885$		0			0
$886$	−69.1974	−	33.3237i	−2.32473	−	1.11953i
$887$	−0.577861	+	0.724614i	−0.0194027	+	0.0243302i	−0.791438	−	0.611249i	$-0.790667\pi$
$887$	−0.577861	+	0.724614i	−0.0194027	+	0.0243302i	0.772036	+	0.635579i	$0.219239\pi$
$888$		0			0
$889$	44.1723	+	7.46579i	1.48149	+	0.250394i
$890$	42.7982	−	53.6672i	1.43460	−	1.79893i
$891$		0			0
$892$	0.525317	+	0.658726i	0.0175889	+	0.0220558i
$893$	−0.988975	+	4.33298i	−0.0330948	+	0.144998i
$894$		0			0
$895$	−5.80949	+	25.4531i	−0.194190	+	0.850802i
$896$	−8.88050	−	6.28948i	−0.296677	−	0.210117i
$897$		0			0
$898$	−29.5645	−	37.0727i	−0.986580	−	1.23713i
$899$	−52.1751	+	25.1262i	−1.74014	+	0.838006i
$900$		0			0
$901$	1.39728			0.0465500
$902$	0.583629	−	0.281061i	0.0194327	−	0.00935831i
$903$		0			0
$904$	1.54266	+	0.742904i	0.0513080	+	0.0247086i
$905$	27.1734	+	13.0860i	0.903273	+	0.434993i
$906$		0			0
$907$	−4.91102	−	21.5166i	−0.163068	−	0.714446i	−0.988659	−	0.150178i	$-0.952015\pi$
$907$	−4.91102	−	21.5166i	−0.163068	−	0.714446i	0.825591	−	0.564269i	$-0.190842\pi$
$908$	−58.7566	−	28.2957i	−1.94991	−	0.939025i
$909$		0			0
$910$	34.9369	+	5.90486i	1.15815	+	0.195744i
$911$	43.7394	−	21.0638i	1.44915	−	0.697874i	0.466702	−	0.884414i	$-0.345442\pi$
$911$	43.7394	−	21.0638i	1.44915	−	0.697874i	0.982447	+	0.186541i	$0.0597277\pi$
$912$		0			0
$913$	0.700516			0.0231837
$914$	−7.53202	+	3.62723i	−0.249137	+	0.119978i
$915$		0			0
$916$	1.74040	+	7.62521i	0.0575046	+	0.251944i
$917$	0.214575	+	3.76260i	0.00708589	+	0.124252i
$918$		0			0
$919$	−8.45648	+	4.07243i	−0.278954	+	0.134337i	−0.568130	−	0.822939i	$-0.692333\pi$
$919$	−8.45648	+	4.07243i	−0.278954	+	0.134337i	0.289176	+	0.957276i	$0.406619\pi$
$920$	1.83341	−	8.03269i	0.0604457	−	0.264830i
$921$		0			0
$922$	4.76726	+	20.8867i	0.157001	+	0.687867i
$923$	13.0718	−	16.3916i	0.430265	−	0.539535i
$924$		0			0
$925$	32.0508	+	40.1904i	1.05382	+	1.32145i
$926$	−13.8514	+	17.3692i	−0.455187	+	0.570786i
$927$		0			0
$928$	42.5393	−	53.3426i	1.39642	−	1.75106i
$929$	10.6011	−	46.4464i	0.347810	−	1.52386i	−0.434331	−	0.900754i	$-0.643015\pi$
$929$	10.6011	−	46.4464i	0.347810	−	1.52386i	0.782141	−	0.623102i	$-0.214128\pi$
$930$		0			0
$931$	1.03204	+	2.93308i	0.0338238	+	0.0961279i
$932$	−36.5748			−1.19805
$933$		0			0
$934$	11.2216	−	14.0714i	0.367181	−	0.460430i
$935$	−0.0637630	−	0.0307066i	−0.00208527	−	0.00100421i
$936$		0			0
$937$	−3.92725	−	4.92461i	−0.128298	−	0.160880i	0.713534	−	0.700621i	$-0.247094\pi$
$937$	−3.92725	−	4.92461i	−0.128298	−	0.160880i	−0.841831	+	0.539741i	$0.818522\pi$
$938$	−57.2568	+	51.2572i	−1.86950	+	1.67361i
$939$		0			0
$940$	16.4125	+	71.9080i	0.535317	+	2.34538i
$941$	15.2089	+	19.0713i	0.495794	+	0.621707i	0.965275	−	0.261236i	$-0.0841302\pi$
$941$	15.2089	+	19.0713i	0.495794	+	0.621707i	−0.469480	+	0.882943i	$0.655559\pi$
$942$		0			0
$943$	−23.8779	+	11.4990i	−0.777572	+	0.374459i
$944$	5.52309	−	24.1982i	0.179761	−	0.787585i
$945$		0			0
$946$	0.0985639	+	0.431837i	0.00320459	+	0.0140402i
$947$	−13.4968	−	16.9245i	−0.438587	−	0.549971i	0.512583	−	0.858638i	$-0.328689\pi$
$947$	−13.4968	−	16.9245i	−0.438587	−	0.549971i	−0.951170	+	0.308667i	$0.900117\pi$
$948$		0			0
$949$	−28.2871			−0.918237
$950$	5.23988			0.170004
$951$		0			0
$952$	−0.383593	+	0.343399i	−0.0124323	+	0.0111296i
$953$	27.5456	+	13.2653i	0.892291	+	0.429705i	0.823098	−	0.567899i	$-0.192243\pi$
$953$	27.5456	+	13.2653i	0.892291	+	0.429705i	0.0691924	+	0.997603i	$0.477958\pi$
$954$		0			0
$955$	0.124623	+	0.546010i	0.00403272	+	0.0176685i
$956$	12.9155	+	56.5864i	0.417716	+	1.83013i
$957$		0			0
$958$	42.6446	+	20.5366i	1.37778	+	0.663506i
$959$	1.62265	+	28.4534i	0.0523982	+	0.918808i
$960$		0			0
$961$	16.4682			0.531233
$962$	36.7496			1.18485
$963$		0			0
$964$	−21.4733	−	26.9267i	−0.691609	−	0.867250i
$965$	−9.41839	−	41.2647i	−0.303189	−	1.32836i
$966$		0			0
$967$	−1.61462	+	7.07411i	−0.0519226	+	0.227488i	−0.994231	−	0.107257i	$-0.965793\pi$
$967$	−1.61462	+	7.07411i	−0.0519226	+	0.227488i	0.942309	+	0.334745i	$0.108650\pi$
$968$	5.13440	−	2.47260i	0.165026	−	0.0794723i
$969$		0			0
$970$	47.5721	+	59.6535i	1.52745	+	1.91536i
$971$	−6.25770	−	27.4168i	−0.200819	−	0.879846i	−0.970439	−	0.241345i	$-0.922412\pi$
$971$	−6.25770	−	27.4168i	−0.200819	−	0.879846i	0.769620	−	0.638502i	$-0.220446\pi$
$972$		0			0
$973$	−3.14938	+	0.910278i	−0.100964	+	0.0291822i
$974$	−3.75668	−	4.71073i	−0.120372	−	0.150942i
$975$		0			0
$976$	−39.7483	−	19.1417i	−1.27231	−	0.612712i
$977$	−24.0020	+	30.0976i	−0.767892	+	0.962906i	−0.999952	−	0.00979509i	$-0.996882\pi$
$977$	−24.0020	+	30.0976i	−0.767892	+	0.962906i	0.232060	+	0.972702i	$0.425454\pi$
$978$		0			0
$979$	0.585246			0.0187045
$980$	36.5508	+	36.4243i	1.16757	+	1.16353i
$981$		0			0
$982$	2.07301	−	9.08243i	0.0661523	−	0.289832i
$983$	−1.94115	+	2.43412i	−0.0619130	+	0.0776364i	−0.811824	−	0.583903i	$-0.801525\pi$
$983$	−1.94115	+	2.43412i	−0.0619130	+	0.0776364i	0.749911	+	0.661539i	$0.230096\pi$
$984$		0			0
$985$	6.44035	−	8.07595i	0.205207	−	0.257321i
$986$	−4.05746	−	5.08790i	−0.129216	−	0.162032i
$987$		0			0
$988$	1.23683	−	1.55093i	0.0393487	−	0.0493417i
$989$	−4.03253	−	17.6677i	−0.128227	−	0.561799i
$990$		0			0
$991$	3.63440	−	15.9234i	0.115451	−	0.505822i	−0.883827	−	0.467814i	$-0.845042\pi$
$991$	3.63440	−	15.9234i	0.115451	−	0.505822i	0.999277	−	0.0380081i	$-0.0121013\pi$
$992$	−50.3873	+	24.2652i	−1.59980	+	0.770422i
$993$		0			0
$994$	55.3897	−	16.0095i	1.75686	−	0.507791i
$995$	0.791637	+	3.46839i	0.0250966	+	0.109955i
$996$		0			0
$997$	20.0788	−	9.66946i	0.635903	−	0.306235i	−0.0880165	−	0.996119i	$-0.528053\pi$
$997$	20.0788	−	9.66946i	0.635903	−	0.306235i	0.723920	+	0.689884i	$0.242339\pi$
$998$	2.00070			0.0633309
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.u.e.64.2	✓	60
3.2	odd	2	inner	441.2.u.e.64.9	yes	60
49.36	even	7	inner	441.2.u.e.379.2	yes	60
147.134	odd	14	inner	441.2.u.e.379.9	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.u.e.64.2	✓	60	1.1	even	1	trivial
441.2.u.e.64.9	yes	60	3.2	odd	2	inner
441.2.u.e.379.2	yes	60	49.36	even	7	inner
441.2.u.e.379.9	yes	60	147.134	odd	14	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.u (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.458811 + 2.01018i) q^{2} +(-2.02838 - 0.976818i) q^{4} +(-2.04151 + 2.55997i) q^{5} +(2.15910 + 1.52915i) q^{7} +(0.323108 - 0.405164i) q^{8} +O(q^{10})\)	\(q+(-0.458811 + 2.01018i) q^{2} +(-2.02838 - 0.976818i) q^{4} +(-2.04151 + 2.55997i) q^{5} +(2.15910 + 1.52915i) q^{7} +(0.323108 - 0.405164i) q^{8} +(-4.20934 - 5.27834i) q^{10} +(0.0128085 - 0.0561176i) q^{11} +(-0.441405 + 1.93392i) q^{13} +(-4.06448 + 3.63859i) q^{14} +(-2.14116 - 2.68493i) q^{16} +(-0.338314 + 0.162923i) q^{17} +0.444193 q^{19} +(6.64159 - 3.19842i) q^{20} +(0.106930 + 0.0514947i) q^{22} +(-4.37481 - 2.10680i) q^{23} +(-1.27309 - 5.57775i) q^{25} +(-3.68502 - 1.77461i) q^{26} +(-2.88578 - 5.21075i) q^{28} +(7.57289 - 3.64691i) q^{29} -6.88972 q^{31} +(7.31340 - 3.52195i) q^{32} +(-0.172284 - 0.754824i) q^{34} +(-8.32239 + 2.40545i) q^{35} +(-8.09529 + 3.89849i) q^{37} +(-0.203801 + 0.892909i) q^{38} +(0.377581 + 1.65429i) q^{40} +(3.40304 - 4.26728i) q^{41} +(2.32695 + 2.91790i) q^{43} +(-0.0807972 + 0.101317i) q^{44} +(6.24225 - 7.82754i) q^{46} +(-2.22645 + 9.75472i) q^{47} +(2.32341 + 6.60316i) q^{49} +11.7964 q^{50} +(2.78443 - 3.49157i) q^{52} +(-3.35260 - 1.61453i) q^{53} +(0.117511 + 0.147354i) q^{55} +(1.31718 - 0.380709i) q^{56} +(3.85643 + 16.8961i) q^{58} +(4.50630 + 5.65072i) q^{59} +(11.5744 - 5.57393i) q^{61} +(3.16108 - 13.8496i) q^{62} +(2.19594 + 9.62105i) q^{64} +(-4.04965 - 5.07810i) q^{65} +14.0871 q^{67} +0.845378 q^{68} +(-1.01700 - 17.8332i) q^{70} +(-9.52248 - 4.58578i) q^{71} +(3.17316 + 13.9025i) q^{73} +(-4.12246 - 18.0617i) q^{74} +(-0.900995 - 0.433896i) q^{76} +(0.113467 - 0.101577i) q^{77} -4.03334 q^{79} +11.2445 q^{80} +(7.01665 + 8.79860i) q^{82} +(2.70809 + 11.8649i) q^{83} +(0.273592 - 1.19868i) q^{85} +(-6.93314 + 3.33883i) q^{86} +(-0.0185983 - 0.0233216i) q^{88} +(2.26247 + 9.91252i) q^{89} +(-3.91030 + 3.50056i) q^{91} +(6.81583 + 8.54678i) q^{92} +(-18.5872 - 8.95114i) q^{94} +(-0.906824 + 1.13712i) q^{95} -11.3016 q^{97} +(-14.3396 + 1.64086i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 12 q^{4} - 2 q^{7}+O(q^{10}) \) 60 * q - 12 * q^4 - 2 * q^7	\( 60 q - 12 q^{4} - 2 q^{7} + 12 q^{10} - 4 q^{13} - 48 q^{19} + 6 q^{22} - 22 q^{25} + 40 q^{28} - 76 q^{31} - 12 q^{34} + 34 q^{37} + 86 q^{40} + 4 q^{43} + 8 q^{46} + 26 q^{49} + 66 q^{52} + 10 q^{55} + 42 q^{58} + 62 q^{61} - 128 q^{64} + 8 q^{67} + 96 q^{70} - 70 q^{73} + 50 q^{76} - 24 q^{79} - 36 q^{82} + 72 q^{85} - 216 q^{88} + 52 q^{91} - 38 q^{94} - 252 q^{97}+O(q^{100}) \) 60 * q - 12 * q^4 - 2 * q^7 + 12 * q^10 - 4 * q^13 - 48 * q^19 + 6 * q^22 - 22 * q^25 + 40 * q^28 - 76 * q^31 - 12 * q^34 + 34 * q^37 + 86 * q^40 + 4 * q^43 + 8 * q^46 + 26 * q^49 + 66 * q^52 + 10 * q^55 + 42 * q^58 + 62 * q^61 - 128 * q^64 + 8 * q^67 + 96 * q^70 - 70 * q^73 + 50 * q^76 - 24 * q^79 - 36 * q^82 + 72 * q^85 - 216 * q^88 + 52 * q^91 - 38 * q^94 - 252 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more