LMFDB - Embedded newform 441.2.bb.d.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(37,441)]

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([0, 32]))

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

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

chi := DirichletCharacter("441.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.bb (of order $21$, 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:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 49)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			109.1
Character	$\chi$	$=$	441.109
Dual form			441.2.bb.d.352.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.51353 + 1.40435i) q^{2} +(0.169112 - 2.25665i) q^{4} +(0.0830372 - 0.211575i) q^{5} +(1.07894 + 2.41576i) q^{7} +(0.338532 + 0.424506i) q^{8} +O(q^{10})$	\(q+(-1.51353 + 1.40435i) q^{2} +(0.169112 - 2.25665i) q^{4} +(0.0830372 - 0.211575i) q^{5} +(1.07894 + 2.41576i) q^{7} +(0.338532 + 0.424506i) q^{8} +(0.171447 + 0.436839i) q^{10} +(4.81478 + 1.48516i) q^{11} +(-1.11960 - 4.90527i) q^{13} +(-5.02558 - 2.14111i) q^{14} +(3.36686 + 0.507473i) q^{16} +(-2.03464 + 1.38719i) q^{17} +(1.49378 + 2.58730i) q^{19} +(-0.463408 - 0.223166i) q^{20} +(-9.37300 + 4.51380i) q^{22} +(3.79491 + 2.58732i) q^{23} +(3.62739 + 3.36573i) q^{25} +(8.58326 + 5.85197i) q^{26} +(5.63398 - 2.02625i) q^{28} +(-0.637668 - 0.307085i) q^{29} +(-4.05198 + 7.01823i) q^{31} +(-6.70576 + 4.57191i) q^{32} +(1.13138 - 4.95690i) q^{34} +(0.600707 - 0.0276793i) q^{35} +(-0.200105 - 2.67021i) q^{37} +(-5.89435 - 1.81816i) q^{38} +(0.117926 - 0.0363752i) q^{40} +(1.10568 + 1.38648i) q^{41} +(-0.910094 + 1.14122i) q^{43} +(4.16573 - 10.6141i) q^{44} +(-9.37722 + 1.41339i) q^{46} +(-4.11267 + 3.81600i) q^{47} +(-4.67178 + 5.21292i) q^{49} -10.2168 q^{50} +(-11.2588 + 1.69699i) q^{52} +(0.329416 - 4.39576i) q^{53} +(0.714029 - 0.895364i) q^{55} +(-0.660247 + 1.27583i) q^{56} +(1.39638 - 0.430727i) q^{58} +(2.06545 + 5.26268i) q^{59} +(0.642677 + 8.57593i) q^{61} +(-3.72327 - 16.3127i) q^{62} +(2.21348 - 9.69790i) q^{64} +(-1.13080 - 0.170441i) q^{65} +(5.97762 - 10.3535i) q^{67} +(2.78632 + 4.82605i) q^{68} +(-0.870316 + 0.885497i) q^{70} +(-2.34135 + 1.12753i) q^{71} +(-2.04449 - 1.89701i) q^{73} +(4.05278 + 3.76043i) q^{74} +(6.09123 - 2.93338i) q^{76} +(1.60706 + 13.2337i) q^{77} +(2.40092 + 4.15851i) q^{79} +(0.386944 - 0.670206i) q^{80} +(-3.62058 - 0.545714i) q^{82} +(1.53769 - 6.73708i) q^{83} +(0.124545 + 0.545667i) q^{85} +(-0.225221 - 3.00536i) q^{86} +(0.999497 + 2.54668i) q^{88} +(9.81790 - 3.02842i) q^{89} +(10.6420 - 7.99717i) q^{91} +(6.48044 - 8.12622i) q^{92} +(0.865647 - 11.5513i) q^{94} +(0.671447 - 0.101204i) q^{95} +0.497851 q^{97} +(-0.249890 - 14.4507i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 13 q^{2} - 9 q^{4} + 14 q^{5} - 14 q^{7} + 20 q^{8}+O(q^{10}) $ 48 * q + 13 * q^2 - 9 * q^4 + 14 * q^5 - 14 * q^7 + 20 * q^8	$ 48 q + 13 q^{2} - 9 q^{4} + 14 q^{5} - 14 q^{7} + 20 q^{8} - 14 q^{10} + 3 q^{11} - 14 q^{13} - 21 q^{14} - 3 q^{16} + 7 q^{17} + 21 q^{19} - 14 q^{20} - 20 q^{22} - 15 q^{23} - 4 q^{25} + 28 q^{28} - 12 q^{29} + 35 q^{31} - 45 q^{32} + 70 q^{34} + 15 q^{37} + 28 q^{38} - 42 q^{40} + 42 q^{41} - 30 q^{43} + 50 q^{44} - 78 q^{46} - 21 q^{47} - 70 q^{49} - 40 q^{50} - 70 q^{52} - 11 q^{53} - 7 q^{55} + 28 q^{56} + 16 q^{58} + 28 q^{59} + 7 q^{61} + 28 q^{62} - 32 q^{64} - 14 q^{65} + 11 q^{67} - 77 q^{68} + 70 q^{70} - 19 q^{71} + 7 q^{73} - 34 q^{74} + 119 q^{76} - 7 q^{77} + 15 q^{79} - 70 q^{80} - 14 q^{82} - 26 q^{85} + 33 q^{86} - 77 q^{88} + 14 q^{89} + 84 q^{91} + 38 q^{92} + 14 q^{94} + 61 q^{95} + 161 q^{98}+O(q^{100}) $ 48 * q + 13 * q^2 - 9 * q^4 + 14 * q^5 - 14 * q^7 + 20 * q^8 - 14 * q^10 + 3 * q^11 - 14 * q^13 - 21 * q^14 - 3 * q^16 + 7 * q^17 + 21 * q^19 - 14 * q^20 - 20 * q^22 - 15 * q^23 - 4 * q^25 + 28 * q^28 - 12 * q^29 + 35 * q^31 - 45 * q^32 + 70 * q^34 + 15 * q^37 + 28 * q^38 - 42 * q^40 + 42 * q^41 - 30 * q^43 + 50 * q^44 - 78 * q^46 - 21 * q^47 - 70 * q^49 - 40 * q^50 - 70 * q^52 - 11 * q^53 - 7 * q^55 + 28 * q^56 + 16 * q^58 + 28 * q^59 + 7 * q^61 + 28 * q^62 - 32 * q^64 - 14 * q^65 + 11 * q^67 - 77 * q^68 + 70 * q^70 - 19 * q^71 + 7 * q^73 - 34 * q^74 + 119 * q^76 - 7 * q^77 + 15 * q^79 - 70 * q^80 - 14 * q^82 - 26 * q^85 + 33 * q^86 - 77 * q^88 + 14 * q^89 + 84 * q^91 + 38 * q^92 + 14 * q^94 + 61 * q^95 + 161 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{20}{21}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.51353	+	1.40435i	−1.07023	+	0.993026i	−0.999990	−	0.00450433i	$-0.998566\pi$
$2$	−1.51353	+	1.40435i	−1.07023	+	0.993026i	−0.0702376	+	0.997530i	$0.522376\pi$
$3$		0			0
$3$		0			0
$4$	0.169112	−	2.25665i	0.0845562	−	1.12832i
$5$	0.0830372	−	0.211575i	0.0371353	−	0.0946193i	−0.911103	−	0.412179i	$-0.864768\pi$
$5$	0.0830372	−	0.211575i	0.0371353	−	0.0946193i	0.948238	+	0.317559i	$0.102863\pi$
$6$		0			0
$7$	1.07894	+	2.41576i	0.407801	+	0.913071i
$7$	1.07894	+	2.41576i	0.407801	+	0.913071i
$8$	0.338532	+	0.424506i	0.119689	+	0.150085i
$9$		0			0
$10$	0.171447	+	0.436839i	0.0542162	+	0.138141i
$11$	4.81478	+	1.48516i	1.45171	+	0.447793i	0.917560	−	0.397597i	$-0.130156\pi$
$11$	4.81478	+	1.48516i	1.45171	+	0.447793i	0.534150	+	0.845390i	$0.320632\pi$
$12$		0			0
$13$	−1.11960	−	4.90527i	−0.310520	−	1.36048i	−0.853658	−	0.520834i	$-0.825621\pi$
$13$	−1.11960	−	4.90527i	−0.310520	−	1.36048i	0.543138	−	0.839643i	$-0.317236\pi$
$14$	−5.02558	−	2.14111i	−1.34314	−	0.572236i
$15$		0			0
$16$	3.36686	+	0.507473i	0.841716	+	0.126868i
$17$	−2.03464	+	1.38719i	−0.493472	+	0.336443i	−0.784352	−	0.620316i	$-0.787004\pi$
$17$	−2.03464	+	1.38719i	−0.493472	+	0.336443i	0.290880	+	0.956760i	$0.406052\pi$
$18$		0			0
$19$	1.49378	+	2.58730i	0.342696	+	0.593566i	0.984932	−	0.172940i	$-0.0553267\pi$
$19$	1.49378	+	2.58730i	0.342696	+	0.593566i	−0.642237	+	0.766506i	$0.721993\pi$
$20$	−0.463408	−	0.223166i	−0.103621	−	0.0499013i
$21$		0			0
$22$	−9.37300	+	4.51380i	−1.99833	+	0.962345i
$23$	3.79491	+	2.58732i	0.791293	+	0.539494i	0.890183	−	0.455604i	$-0.150577\pi$
$23$	3.79491	+	2.58732i	0.791293	+	0.539494i	−0.0988896	+	0.995098i	$0.531529\pi$
$24$		0			0
$25$	3.62739	+	3.36573i	0.725478	+	0.673145i
$26$	8.58326	+	5.85197i	1.68332	+	1.14767i
$27$		0			0
$28$	5.63398	−	2.02625i	1.06472	−	0.382926i
$29$	−0.637668	−	0.307085i	−0.118412	−	0.0570242i	0.373740	−	0.927534i	$-0.378075\pi$
$29$	−0.637668	−	0.307085i	−0.118412	−	0.0570242i	−0.492152	+	0.870509i	$0.663790\pi$
$30$		0			0
$31$	−4.05198	+	7.01823i	−0.727756	+	1.26051i	0.230073	+	0.973173i	$0.426103\pi$
$31$	−4.05198	+	7.01823i	−0.727756	+	1.26051i	−0.957829	+	0.287337i	$0.907230\pi$
$32$	−6.70576	+	4.57191i	−1.18542	+	0.808207i
$33$		0			0
$34$	1.13138	−	4.95690i	0.194030	−	0.850101i
$35$	0.600707	−	0.0276793i	0.101538	−	0.00467866i
$36$		0			0
$37$	−0.200105	−	2.67021i	−0.0328970	−	0.438980i	−0.989197	−	0.146593i	$-0.953169\pi$
$37$	−0.200105	−	2.67021i	−0.0328970	−	0.438980i	0.956300	−	0.292387i	$-0.0944497\pi$
$38$	−5.89435	−	1.81816i	−0.956189	−	0.294945i
$39$		0			0
$40$	0.117926	−	0.0363752i	0.0186457	−	0.00575143i
$41$	1.10568	+	1.38648i	0.172678	+	0.216531i	0.860638	−	0.509217i	$-0.170065\pi$
$41$	1.10568	+	1.38648i	0.172678	+	0.216531i	−0.687960	+	0.725749i	$0.741494\pi$
$42$		0			0
$43$	−0.910094	+	1.14122i	−0.138788	+	0.174035i	−0.846368	−	0.532599i	$-0.821216\pi$
$43$	−0.910094	+	1.14122i	−0.138788	+	0.174035i	0.707580	+	0.706633i	$0.249787\pi$
$44$	4.16573	−	10.6141i	0.628007	−	1.60014i
$45$		0			0
$46$	−9.37722	+	1.41339i	−1.38260	+	0.208393i
$47$	−4.11267	+	3.81600i	−0.599894	+	0.556620i	−0.920574	−	0.390567i	$-0.872279\pi$
$47$	−4.11267	+	3.81600i	−0.599894	+	0.556620i	0.320680	+	0.947187i	$0.396088\pi$
$48$		0			0
$49$	−4.67178	+	5.21292i	−0.667397	+	0.744702i
$50$	−10.2168			−1.44488
$51$		0			0
$52$	−11.2588	+	1.69699i	−1.56131	+	0.235330i
$53$	0.329416	−	4.39576i	0.0452488	−	0.603804i	−0.927781	−	0.373125i	$-0.878286\pi$
$53$	0.329416	−	4.39576i	0.0452488	−	0.603804i	0.973030	−	0.230679i	$-0.0740946\pi$
$54$		0			0
$55$	0.714029	−	0.895364i	0.0962797	−	0.120731i
$56$	−0.660247	+	1.27583i	−0.0882293	+	0.170490i
$57$		0			0
$58$	1.39638	−	0.430727i	0.183354	−	0.0565573i
$59$	2.06545	+	5.26268i	0.268899	+	0.685143i	0.999996	+	0.00286948i	$0.000913384\pi$
$59$	2.06545	+	5.26268i	0.268899	+	0.685143i	−0.731097	+	0.682273i	$0.760991\pi$
$60$		0			0
$61$	0.642677	+	8.57593i	0.0822864	+	1.09804i	0.873606	+	0.486633i	$0.161775\pi$
$61$	0.642677	+	8.57593i	0.0822864	+	1.09804i	−0.791320	+	0.611402i	$0.790606\pi$
$62$	−3.72327	−	16.3127i	−0.472855	−	2.07171i
$63$		0			0
$64$	2.21348	−	9.69790i	0.276685	−	1.21224i
$65$	−1.13080	−	0.170441i	−0.140259	−	0.0211406i
$66$		0			0
$67$	5.97762	−	10.3535i	0.730283	−	1.26489i	−0.226479	−	0.974016i	$-0.572722\pi$
$67$	5.97762	−	10.3535i	0.730283	−	1.26489i	0.956762	−	0.290871i	$-0.0939451\pi$
$68$	2.78632	+	4.82605i	0.337891	+	0.585244i
$69$		0			0
$70$	−0.870316	+	0.885497i	−0.104023	+	0.105837i
$71$	−2.34135	+	1.12753i	−0.277867	+	0.133814i	−0.567627	−	0.823286i	$-0.692139\pi$
$71$	−2.34135	+	1.12753i	−0.277867	+	0.133814i	0.289761	+	0.957099i	$0.406424\pi$
$72$		0			0
$73$	−2.04449	−	1.89701i	−0.239289	−	0.222028i	0.551407	−	0.834236i	$-0.314091\pi$
$73$	−2.04449	−	1.89701i	−0.239289	−	0.222028i	−0.790697	+	0.612208i	$0.790281\pi$
$74$	4.05278	+	3.76043i	0.471126	+	0.437141i
$75$		0			0
$76$	6.09123	−	2.93338i	0.698712	−	0.336482i
$77$	1.60706	+	13.2337i	0.183142	+	1.50812i
$78$		0			0
$79$	2.40092	+	4.15851i	0.270124	+	0.467869i	0.968893	−	0.247478i	$-0.0796019\pi$
$79$	2.40092	+	4.15851i	0.270124	+	0.467869i	−0.698769	+	0.715347i	$0.746269\pi$
$80$	0.386944	−	0.670206i	0.0432616	−	0.0749313i
$81$		0			0
$82$	−3.62058	−	0.545714i	−0.399826	−	0.0602640i
$83$	1.53769	−	6.73708i	0.168784	−	0.739490i	−0.817702	−	0.575642i	$-0.804752\pi$
$83$	1.53769	−	6.73708i	0.168784	−	0.739490i	0.986486	−	0.163848i	$-0.0523907\pi$
$84$		0			0
$85$	0.124545	+	0.545667i	0.0135088	+	0.0591859i
$86$	−0.225221	−	3.00536i	−0.0242862	−	0.324077i
$87$		0			0
$88$	0.999497	+	2.54668i	0.106547	+	0.271477i
$89$	9.81790	−	3.02842i	1.04070	−	0.321012i	0.273126	−	0.961978i	$-0.411942\pi$
$89$	9.81790	−	3.02842i	1.04070	−	0.321012i	0.767569	+	0.640966i	$0.221466\pi$
$90$		0			0
$91$	10.6420	−	7.99717i	1.11558	−	0.838331i
$92$	6.48044	−	8.12622i	0.675633	−	0.847217i
$93$		0			0
$94$	0.865647	−	11.5513i	0.0892847	−	1.19142i
$95$	0.671447	−	0.101204i	0.0688890	−	0.0103833i
$96$		0			0
$97$	0.497851			0.0505491			0.0252746	−	0.999681i	$-0.491954\pi$
$97$	0.497851			0.0505491			0.0252746	+	0.999681i	$0.491954\pi$
$98$	−0.249890	−	14.4507i	−0.0252427	−	1.45974i
$99$		0			0
$100$	8.20869	−	7.61655i	0.820869	−	0.761655i
$101$	0.351055	−	0.0529130i	0.0349313	−	0.00526505i	−0.131553	−	0.991309i	$-0.541996\pi$
$101$	0.351055	−	0.0529130i	0.0349313	−	0.00526505i	0.166485	+	0.986044i	$0.446758\pi$
$102$		0			0
$103$	2.93087	−	7.46774i	0.288788	−	0.735819i	−0.710690	−	0.703505i	$-0.751617\pi$
$103$	2.93087	−	7.46774i	0.288788	−	0.735819i	0.999478	−	0.0323136i	$-0.0102875\pi$
$104$	1.70330	−	2.13587i	0.167022	−	0.209439i
$105$		0			0
$106$	5.67460	+	7.11573i	0.551166	+	0.691140i
$107$	19.6890	−	6.07324i	1.90340	−	0.587123i	0.925200	−	0.379479i	$-0.123897\pi$
$107$	19.6890	−	6.07324i	1.90340	−	0.587123i	0.978205	−	0.207643i	$-0.0665794\pi$
$108$		0			0
$109$	−1.96161	−	0.605076i	−0.187888	−	0.0579558i	0.199383	−	0.979922i	$-0.436106\pi$
$109$	−1.96161	−	0.605076i	−0.187888	−	0.0579558i	−0.387271	+	0.921966i	$0.626582\pi$
$110$	0.176701	+	2.35791i	0.0168478	+	0.224818i
$111$		0			0
$112$	2.40671	+	8.68107i	0.227413	+	0.820284i
$113$	−1.78611	+	7.82546i	−0.168023	+	0.736157i	0.818763	+	0.574131i	$0.194660\pi$
$113$	−1.78611	+	7.82546i	−0.168023	+	0.736157i	−0.986786	+	0.162026i	$0.948197\pi$
$114$		0			0
$115$	0.862532	−	0.588064i	0.0804315	−	0.0548373i
$116$	−0.800819	+	1.38706i	−0.0743542	+	0.128785i
$117$		0			0
$118$	−10.5168	−	5.06461i	−0.968148	−	0.466235i
$119$	−5.54637	−	3.41849i	−0.508435	−	0.313373i
$120$		0			0
$121$	11.8878	+	8.10493i	1.08070	+	0.736812i
$122$	−13.0163	−	12.0774i	−1.17844	−	1.09344i
$123$		0			0
$124$	15.1524	+	10.3307i	1.36073	+	0.927728i
$125$	2.03720	−	0.981066i	0.182213	−	0.0877492i
$126$		0			0
$127$	4.74925	+	2.28712i	0.421427	+	0.202949i	0.632564	−	0.774508i	$-0.282002\pi$
$127$	4.74925	+	2.28712i	0.421427	+	0.202949i	−0.211137	+	0.977456i	$0.567717\pi$
$128$	2.15308	+	3.72924i	0.190307	+	0.329621i
$129$		0			0
$130$	1.95086	−	1.33007i	0.171102	−	0.116655i
$131$	1.61551	+	0.243498i	0.141147	+	0.0212745i	0.219236	−	0.975672i	$-0.429644\pi$
$131$	1.61551	+	0.243498i	0.141147	+	0.0212745i	−0.0780885	+	0.996946i	$0.524882\pi$
$132$		0			0
$133$	−4.63859	+	6.40014i	−0.402216	+	0.554962i
$134$	5.49270	+	24.0651i	0.474497	+	2.07891i
$135$		0			0
$136$	−1.27766	−	0.394106i	−0.109559	−	0.0337943i
$137$	−1.24531	−	3.17299i	−0.106394	−	0.271087i	0.867756	−	0.496991i	$-0.165562\pi$
$137$	−1.24531	−	3.17299i	−0.106394	−	0.271087i	−0.974150	+	0.225904i	$0.927466\pi$
$138$		0			0
$139$	−9.49516	−	11.9065i	−0.805369	−	1.00990i	−0.999581	−	0.0289408i	$-0.990787\pi$
$139$	−9.49516	−	11.9065i	−0.805369	−	1.00990i	0.194213	−	0.980959i	$-0.437785\pi$
$140$	0.0391245	−	1.36026i	0.00330662	−	0.114963i
$141$		0			0
$142$	1.96025	−	4.99463i	0.164500	−	0.419140i
$143$	1.89452	−	25.2806i	0.158427	−	2.11407i
$144$		0			0
$145$	−0.117922	+	0.109415i	−0.00979286	+	0.00908644i
$146$	5.75846			0.476573
$147$		0			0
$148$	−6.05957			−0.498093
$149$	7.92270	−	7.35119i	0.649053	−	0.602233i	−0.285362	−	0.958420i	$-0.592114\pi$
$149$	7.92270	−	7.35119i	0.649053	−	0.602233i	0.934415	+	0.356187i	$0.115923\pi$
$150$		0			0
$151$	1.31752	−	17.5811i	0.107218	−	1.43073i	−0.641134	−	0.767429i	$-0.721536\pi$
$151$	1.31752	−	17.5811i	0.107218	−	1.43073i	0.748353	−	0.663301i	$-0.230845\pi$
$152$	−0.592631	+	1.51000i	−0.0480687	+	0.122477i
$153$		0			0
$154$	−21.0172	−	17.7728i	−1.69361	−	1.43217i
$155$	1.14842	+	1.44007i	0.0922432	+	0.115669i
$156$		0			0
$157$	−0.510341	−	1.30033i	−0.0407296	−	0.103777i	0.909062	−	0.416662i	$-0.136800\pi$
$157$	−0.510341	−	1.30033i	−0.0407296	−	0.103777i	−0.949791	+	0.312884i	$0.898705\pi$
$158$	−9.47386	−	2.92230i	−0.753700	−	0.232486i
$159$		0			0
$160$	0.410475	+	1.79841i	0.0324509	+	0.142177i
$161$	−2.15587	+	11.9591i	−0.169906	+	0.942513i
$162$		0			0
$163$	−1.92379	−	0.289964i	−0.150683	−	0.0227118i	0.0732677	−	0.997312i	$-0.476657\pi$
$163$	−1.92379	−	0.289964i	−0.150683	−	0.0227118i	−0.223950	+	0.974601i	$0.571895\pi$
$164$	3.31577	−	2.26066i	0.258918	−	0.176528i
$165$		0			0
$166$	7.13388	+	12.3562i	0.553696	+	0.959030i
$167$	−20.7503	−	9.99282i	−1.60571	−	0.773267i	−0.605953	−	0.795500i	$-0.707208\pi$
$167$	−20.7503	−	9.99282i	−1.60571	−	0.773267i	−0.999753	+	0.0222327i	$0.992923\pi$
$168$		0			0
$169$	−11.0956	+	5.34335i	−0.853507	+	0.411027i
$170$	−0.954811	−	0.650979i	−0.0732307	−	0.0499278i
$171$		0			0
$172$	2.42143	+	2.24676i	0.184632	+	0.171313i
$173$	−19.0337	−	12.9769i	−1.44710	−	0.986618i	−0.995536	−	0.0943809i	$-0.969913\pi$
$173$	−19.0337	−	12.9769i	−1.44710	−	0.986618i	−0.451567	−	0.892237i	$-0.649135\pi$
$174$		0			0
$175$	−4.21704	+	12.3943i	−0.318779	+	0.936922i
$176$	15.4570	+	7.44371i	1.16512	+	0.561091i
$177$		0			0
$178$	−10.6067	+	18.3714i	−0.795008	+	1.37699i
$179$	−13.4982	+	9.20295i	−1.00891	+	0.687861i	−0.950594	−	0.310438i	$-0.899524\pi$
$179$	−13.4982	+	9.20295i	−1.00891	+	0.687861i	−0.0583126	+	0.998298i	$0.518572\pi$
$180$		0			0
$181$	−2.23430	+	9.78911i	−0.166074	+	0.727619i	0.821467	+	0.570256i	$0.193156\pi$
$181$	−2.23430	+	9.78911i	−0.166074	+	0.727619i	−0.987541	+	0.157362i	$0.949701\pi$
$182$	−4.87612	+	27.0490i	−0.361442	+	2.00501i
$183$		0			0
$184$	0.186364	+	2.48685i	0.0137389	+	0.183333i
$185$	−0.581567	−	0.179390i	−0.0427576	−	0.0131890i
$186$		0			0
$187$	−11.8565	+	3.65726i	−0.867035	+	0.267445i
$188$	7.91586	+	9.92617i	0.577323	+	0.723940i
$189$		0			0
$190$	−0.874128	+	1.09612i	−0.0634159	+	0.0795211i
$191$	−0.613387	+	1.56288i	−0.0443831	+	0.113086i	−0.951346	−	0.308123i	$-0.900299\pi$
$191$	−0.613387	+	1.56288i	−0.0443831	+	0.113086i	0.906963	+	0.421210i	$0.138394\pi$
$192$		0			0
$193$	3.81096	−	0.574410i	0.274319	−	0.0413469i	−0.0104421	−	0.999945i	$-0.503324\pi$
$193$	3.81096	−	0.574410i	0.274319	−	0.0413469i	0.284761	+	0.958599i	$0.408086\pi$
$194$	−0.753513	+	0.699158i	−0.0540991	+	0.0501966i
$195$		0			0
$196$	10.9737	+	11.4241i	0.783833	+	0.816008i
$197$	1.66391			0.118549			0.0592744	−	0.998242i	$-0.481121\pi$
$197$	1.66391			0.118549			0.0592744	+	0.998242i	$0.481121\pi$
$198$		0			0
$199$	26.2162	−	3.95146i	1.85842	−	0.280112i	0.878239	−	0.478221i	$-0.158718\pi$
$199$	26.2162	−	3.95146i	1.85842	−	0.280112i	0.980180	+	0.198110i	$0.0634802\pi$
$200$	−0.200782	+	2.67925i	−0.0141975	+	0.189452i
$201$		0			0
$202$	−0.457024	+	0.573090i	−0.0321561	+	0.0403225i
$203$	0.0538368	−	1.87178i	0.00377860	−	0.131373i
$204$		0			0
$205$	0.385156	−	0.118805i	0.0269005	−	0.00829770i
$206$	6.05137	+	15.4186i	0.421619	+	1.07427i
$207$		0			0
$208$	−1.28023	−	17.0835i	−0.0887683	−	1.18453i
$209$	3.34965	+	14.6758i	0.231700	+	1.01514i
$210$		0			0
$211$	1.85114	−	8.11037i	0.127438	−	0.558341i	−0.870384	−	0.492373i	$-0.836129\pi$
$211$	1.85114	−	8.11037i	0.127438	−	0.558341i	0.997822	−	0.0659675i	$-0.0210134\pi$
$212$	−9.86396	−	1.48675i	−0.677460	−	0.102111i
$213$		0			0
$214$	−21.2709	+	36.8423i	−1.45405	+	2.51849i
$215$	0.165883	+	0.287317i	0.0113131	+	0.0195949i
$216$		0			0
$217$	−21.3262	−	2.21635i	−1.44772	−	0.150455i
$218$	3.81869	−	1.83899i	0.258635	−	0.124552i
$219$		0			0
$220$	−1.89977	−	1.76273i	−0.128082	−	0.118843i
$221$	9.08252	+	8.42735i	0.610957	+	0.566885i
$222$		0			0
$223$	−13.6100	+	6.55421i	−0.911390	+	0.438902i	−0.829989	−	0.557779i	$-0.811654\pi$
$223$	−13.6100	+	6.55421i	−0.911390	+	0.438902i	−0.0814005	+	0.996681i	$0.525939\pi$
$224$	−18.2797	−	11.2667i	−1.22137	−	0.752786i
$225$		0			0
$226$	−8.28636	−	14.3524i	−0.551200	−	0.954707i
$227$	−8.07507	+	13.9864i	−0.535961	+	0.928312i	0.463155	+	0.886277i	$0.346717\pi$
$227$	−8.07507	+	13.9864i	−0.535961	+	0.928312i	−0.999116	+	0.0420345i	$0.986616\pi$
$228$		0			0
$229$	−4.87264	−	0.734432i	−0.321993	−	0.0485327i	−0.0139430	−	0.999903i	$-0.504438\pi$
$229$	−4.87264	−	0.734432i	−0.321993	−	0.0485327i	−0.308050	+	0.951370i	$0.599676\pi$
$230$	−0.479620	+	2.10135i	−0.0316252	+	0.138559i
$231$		0			0
$232$	−0.0855118	−	0.374652i	−0.00561412	−	0.0245971i
$233$	1.24102	+	16.5602i	0.0813019	+	1.08490i	0.877409	+	0.479743i	$0.159270\pi$
$233$	1.24102	+	16.5602i	0.0813019	+	1.08490i	−0.796107	+	0.605155i	$0.793111\pi$
$234$		0			0
$235$	0.465866	+	1.18701i	0.0303898	+	0.0774319i
$236$	12.2253	−	3.77101i	0.795800	−	0.245472i
$237$		0			0
$238$	13.1954	−	2.61506i	0.855329	−	0.169509i
$239$	−2.55561	+	3.20463i	−0.165309	+	0.207290i	−0.857585	−	0.514342i	$-0.828036\pi$
$239$	−2.55561	+	3.20463i	−0.165309	+	0.207290i	0.692277	+	0.721632i	$0.256608\pi$
$240$		0			0
$241$	2.15116	−	28.7052i	0.138568	−	1.84907i	−0.304419	−	0.952538i	$-0.598462\pi$
$241$	2.15116	−	28.7052i	0.138568	−	1.84907i	0.442988	−	0.896528i	$-0.353919\pi$
$242$	−29.3746	+	4.42752i	−1.88827	+	0.284611i
$243$		0			0
$244$	19.4615			1.24590
$245$	0.714993	+	1.42130i	0.0456792	+	0.0908034i
$246$		0			0
$247$	11.0190	−	10.2241i	0.701120	−	0.650544i
$248$	−4.35100	+	0.655808i	−0.276289	+	0.0416438i
$249$		0			0
$250$	−1.70561	+	4.34582i	−0.107872	+	0.274854i
$251$	10.4444	−	13.0968i	0.659242	−	0.826663i	−0.334019	−	0.942566i	$-0.608405\pi$
$251$	10.4444	−	13.0968i	0.659242	−	0.826663i	0.993260	+	0.115903i	$0.0369763\pi$
$252$		0			0
$253$	14.4290	+	18.0934i	0.907146	+	1.13753i
$254$	−10.4000	+	3.20799i	−0.652557	+	0.201287i
$255$		0			0
$256$	10.5148	+	3.24339i	0.657177	+	0.202712i
$257$	0.968617	+	12.9253i	0.0604207	+	0.806258i	0.942297	+	0.334778i	$0.108661\pi$
$257$	0.968617	+	12.9253i	0.0604207	+	0.806258i	−0.881876	+	0.471481i	$0.843720\pi$
$258$		0			0
$259$	6.23469	−	3.36440i	0.387405	−	0.209054i
$260$	−0.575858	+	2.52300i	−0.0357132	+	0.156470i
$261$		0			0
$262$	−2.78707	+	1.90019i	−0.172186	+	0.117394i
$263$	3.11106	−	5.38852i	0.191836	−	0.332270i	−0.754023	−	0.656849i	$-0.771889\pi$
$263$	3.11106	−	5.38852i	0.191836	−	0.332270i	0.945859	+	0.324578i	$0.105222\pi$
$264$		0			0
$265$	−0.902679	−	0.434708i	−0.0554512	−	0.0267039i
$266$	−1.96740	−	16.2010i	−0.120629	−	0.993347i
$267$		0			0
$268$	−22.3534	−	15.2403i	−1.36545	−	0.930949i
$269$	−15.5032	−	14.3849i	−0.945247	−	0.877061i	0.0473051	−	0.998880i	$-0.484937\pi$
$269$	−15.5032	−	14.3849i	−0.945247	−	0.877061i	−0.992552	+	0.121819i	$0.961127\pi$
$270$		0			0
$271$	−12.2823	−	8.37393i	−0.746096	−	0.508680i	0.129586	−	0.991568i	$-0.458635\pi$
$271$	−12.2823	−	8.37393i	−0.746096	−	0.508680i	−0.875682	+	0.482888i	$0.839588\pi$
$272$	−7.55431	+	3.63796i	−0.458047	+	0.220584i
$273$		0			0
$274$	6.34080	+	3.05357i	0.383062	+	0.184473i
$275$	12.4664	+	21.5925i	0.751754	+	1.30208i
$276$		0			0
$277$	−17.6286	+	12.0190i	−1.05920	+	0.722151i	−0.961982	−	0.273112i	$-0.911947\pi$
$277$	−17.6286	+	12.0190i	−1.05920	+	0.722151i	−0.0972190	+	0.995263i	$0.530995\pi$
$278$	31.0922	+	4.68639i	1.86478	+	0.281071i
$279$		0			0
$280$	0.215109	+	0.245633i	0.0128552	+	0.0146794i
$281$	−5.58838	−	24.4843i	−0.333375	−	1.46061i	−0.812550	−	0.582891i	$-0.801921\pi$
$281$	−5.58838	−	24.4843i	−0.333375	−	1.46061i	0.479176	−	0.877719i	$-0.340936\pi$
$282$		0			0
$283$	−13.7387	−	4.23782i	−0.816680	−	0.251912i	−0.141853	−	0.989888i	$-0.545306\pi$
$283$	−13.7387	−	4.23782i	−0.816680	−	0.251912i	−0.674828	+	0.737975i	$0.735782\pi$
$284$	2.14849	+	5.47427i	0.127490	+	0.324838i
$285$		0			0
$286$	32.6354	+	40.9235i	1.92977	+	2.41986i
$287$	−2.15643	+	4.16698i	−0.127290	+	0.245969i
$288$		0			0
$289$	−3.99535	+	10.1800i	−0.235021	+	0.598823i
$290$	0.0248205	−	0.331207i	0.00145751	−	0.0194491i
$291$		0			0
$292$	−4.62662	+	4.29288i	−0.270753	+	0.251222i
$293$	15.0206			0.877512			0.438756	−	0.898606i	$-0.355419\pi$
$293$	15.0206			0.877512			0.438756	+	0.898606i	$0.355419\pi$
$294$		0			0
$295$	1.28496			0.0748134
$296$	1.06578	−	0.988898i	0.0619471	−	0.0574785i
$297$		0			0
$298$	−1.66759	+	22.2525i	−0.0966012	+	1.28905i
$299$	8.44276	−	21.5118i	0.488257	−	1.24406i
$300$		0			0
$301$	−3.73885	−	0.967257i	−0.215504	−	0.0557518i
$302$	22.6959	+	28.4598i	1.30600	+	1.63768i
$303$		0			0
$304$	3.71636	+	9.46913i	0.213148	+	0.543092i
$305$	1.86782	+	0.576146i	0.106951	+	0.0329901i
$306$		0			0
$307$	−1.54569	−	6.77213i	−0.0882174	−	0.386506i	0.911474	−	0.411358i	$-0.134946\pi$
$307$	−1.54569	−	6.77213i	−0.0882174	−	0.386506i	−0.999691	+	0.0248526i	$0.992088\pi$
$308$	30.1357	−	1.38859i	1.71714	−	0.0791222i
$309$		0			0
$310$	−3.76053	−	0.566809i	−0.213584	−	0.0321926i
$311$	8.92284	−	6.08349i	0.505968	−	0.344963i	−0.283281	−	0.959037i	$-0.591423\pi$
$311$	8.92284	−	6.08349i	0.505968	−	0.344963i	0.789248	+	0.614074i	$0.210470\pi$
$312$		0			0
$313$	−5.85713	−	10.1448i	−0.331065	−	0.573421i	0.651656	−	0.758514i	$-0.274074\pi$
$313$	−5.85713	−	10.1448i	−0.331065	−	0.573421i	−0.982721	+	0.185094i	$0.940741\pi$
$314$	2.59853	+	1.25139i	0.146644	+	0.0706199i
$315$		0			0
$316$	9.79031	−	4.71476i	0.550748	−	0.265226i
$317$	−18.6699	−	12.7289i	−1.04861	−	0.714927i	−0.0889305	−	0.996038i	$-0.528345\pi$
$317$	−18.6699	−	12.7289i	−1.04861	−	0.714927i	−0.959675	+	0.281110i	$0.909297\pi$
$318$		0			0
$319$	−2.61416	−	2.42558i	−0.146365	−	0.135807i
$320$	−1.86803	−	1.27360i	−0.104426	−	0.0711966i
$321$		0			0
$322$	−13.5319	−	21.1281i	−0.754101	−	1.17742i
$323$	−6.62837	−	3.19205i	−0.368812	−	0.177611i
$324$		0			0
$325$	12.4486	−	21.5616i	0.690523	−	1.19602i
$326$	3.31892	−	2.26280i	0.183818	−	0.125325i
$327$		0			0
$328$	−0.214260	+	0.938734i	−0.0118305	+	0.0518329i
$329$	−13.6558	−	5.81798i	−0.752871	−	0.320755i
$330$		0			0
$331$	1.01634	+	13.5622i	0.0558632	+	0.745443i	0.952861	+	0.303408i	$0.0981244\pi$
$331$	1.01634	+	13.5622i	0.0558632	+	0.745443i	−0.896998	+	0.442035i	$0.854257\pi$
$332$	−14.9432	−	4.60936i	−0.820113	−	0.252971i
$333$		0			0
$334$	45.4396	−	14.0163i	2.48635	−	0.766936i
$335$	−1.69419	−	2.12445i	−0.0925635	−	0.116071i
$336$		0			0
$337$	5.06821	−	6.35533i	0.276083	−	0.346197i	−0.624387	−	0.781115i	$-0.714651\pi$
$337$	5.06821	−	6.35533i	0.276083	−	0.346197i	0.900470	+	0.434918i	$0.143223\pi$
$338$	9.28956	−	23.6694i	0.505286	−	1.28745i
$339$		0			0
$340$	1.25244	−	0.188775i	0.0679231	−	0.0102378i
$341$	−29.9326	+	27.7734i	−1.62094	+	1.50401i
$342$		0			0
$343$	−17.6337	−	5.66146i	−0.952131	−	0.305690i
$344$	−0.792551			−0.0427315
$345$		0			0
$346$	47.0322	−	7.08896i	2.52847	−	0.381105i
$347$	0.895690	−	11.9522i	0.0480832	−	0.641625i	−0.920148	−	0.391570i	$-0.871932\pi$
$347$	0.895690	−	11.9522i	0.0480832	−	0.641625i	0.968232	−	0.250055i	$-0.0804488\pi$
$348$		0			0
$349$	10.8397	−	13.5925i	0.580235	−	0.727592i	−0.401918	−	0.915676i	$-0.631656\pi$
$349$	10.8397	−	13.5925i	0.580235	−	0.727592i	0.982153	+	0.188084i	$0.0602277\pi$
$350$	−11.0233	−	24.6814i	−0.589223	−	1.31928i
$351$		0			0
$352$	−39.0768	+	12.0536i	−2.08280	+	0.642458i
$353$	8.01626	+	20.4251i	0.426663	+	1.08712i	0.969022	+	0.246973i	$0.0794357\pi$
$353$	8.01626	+	20.4251i	0.426663	+	1.08712i	−0.542360	+	0.840146i	$0.682469\pi$
$354$		0			0
$355$	0.0441393	+	0.588998i	0.00234267	+	0.0312608i
$356$	−5.17375	−	22.6677i	−0.274208	−	1.20138i
$357$		0			0
$358$	7.50584	−	32.8852i	0.396696	−	1.73804i
$359$	−3.85236	−	0.580650i	−0.203320	−	0.0306455i	0.0465926	−	0.998914i	$-0.485164\pi$
$359$	−3.85236	−	0.580650i	−0.203320	−	0.0306455i	−0.249912	+	0.968268i	$0.580402\pi$
$360$		0			0
$361$	5.03727	−	8.72480i	0.265119	−	0.459200i
$362$	−10.3657	−	17.9538i	−0.544807	−	0.943633i
$363$		0			0
$364$	−16.2471	−	25.3676i	−0.851579	−	1.32962i
$365$	−0.571128	+	0.275041i	−0.0298942	+	0.0143963i
$366$		0			0
$367$	9.47776	+	8.79407i	0.494735	+	0.459047i	0.887644	−	0.460530i	$-0.152341\pi$
$367$	9.47776	+	8.79407i	0.494735	+	0.459047i	−0.392909	+	0.919577i	$0.628531\pi$
$368$	11.4639	+	10.6370i	0.597599	+	0.554491i
$369$		0			0
$370$	1.13214	−	0.545212i	0.0588574	−	0.0283442i
$371$	10.9745	−	3.94697i	0.569768	−	0.204916i
$372$		0			0
$373$	10.8513	+	18.7949i	0.561857	+	0.973164i	0.997335	+	0.0729647i	$0.0232460\pi$
$373$	10.8513	+	18.7949i	0.561857	+	0.973164i	−0.435478	+	0.900199i	$0.643421\pi$
$374$	12.8091	−	22.1861i	0.662345	−	1.14722i
$375$		0			0
$376$	−3.01218	−	0.454013i	−0.155341	−	0.0234140i
$377$	−0.792403	+	3.47174i	−0.0408108	+	0.178804i
$378$		0			0
$379$	4.05550	+	17.7683i	0.208317	+	0.912697i	0.965687	+	0.259710i	$0.0836271\pi$
$379$	4.05550	+	17.7683i	0.208317	+	0.912697i	−0.757369	+	0.652987i	$0.773516\pi$
$380$	−0.114832	−	1.53233i	−0.00589078	−	0.0786070i
$381$		0			0
$382$	−1.26646	−	3.22688i	−0.0647976	−	0.165102i
$383$	18.0705	−	5.57400i	0.923357	−	0.284818i	0.203608	−	0.979052i	$-0.434733\pi$
$383$	18.0705	−	5.57400i	0.923357	−	0.284818i	0.719749	+	0.694235i	$0.244257\pi$
$384$		0			0
$385$	2.93338	+	0.758877i	0.149499	+	0.0386760i
$386$	−4.96133	+	6.22131i	−0.252525	+	0.316656i
$387$		0			0
$388$	0.0841928	−	1.12347i	0.00427424	−	0.0570358i
$389$	24.2559	−	3.65598i	1.22982	−	0.185366i	0.498191	−	0.867067i	$-0.333998\pi$
$389$	24.2559	−	3.65598i	1.22982	−	0.185366i	0.731630	+	0.681702i	$0.238760\pi$
$390$		0			0
$391$	−11.3104			−0.571990
$392$	−3.79446	−	0.218456i	−0.191649	−	0.0110337i
$393$		0			0
$394$	−2.51838	+	2.33672i	−0.126874	+	0.117722i
$395$	1.07920	−	0.162664i	0.0543006	−	0.00818449i
$396$		0			0
$397$	10.3814	−	26.4514i	0.521028	−	1.32756i	−0.392115	−	0.919916i	$-0.628256\pi$
$397$	10.3814	−	26.4514i	0.521028	−	1.32756i	0.913142	−	0.407641i	$-0.133648\pi$
$398$	−34.1298	+	42.7974i	−1.71077	+	2.14524i
$399$		0			0
$400$	10.5049	+	13.1727i	0.525246	+	0.658637i
$401$	−21.7793	+	6.71804i	−1.08761	+	0.335483i	−0.786175	−	0.618004i	$-0.787941\pi$
$401$	−21.7793	+	6.71804i	−1.08761	+	0.335483i	−0.301434	+	0.953487i	$0.597465\pi$
$402$		0			0
$403$	38.9629	+	12.0185i	1.94088	+	0.598682i
$404$	−0.0600383	−	0.801156i	−0.00298702	−	0.0398590i
$405$		0			0
$406$	2.54715	+	2.90860i	0.126413	+	0.144351i
$407$	3.00224	−	13.1537i	0.148815	−	0.652003i
$408$		0			0
$409$	−25.4353	+	17.3415i	−1.25769	+	0.857481i	−0.994238	−	0.107191i	$-0.965814\pi$
$409$	−25.4353	+	17.3415i	−1.25769	+	0.857481i	−0.263455	+	0.964672i	$0.584862\pi$
$410$	−0.416102	+	0.720710i	−0.0205498	+	0.0355933i
$411$		0			0
$412$	−16.3564	−	7.87684i	−0.805823	−	0.388064i
$413$	−10.4849	+	10.6677i	−0.515927	+	0.524926i
$414$		0			0
$415$	−1.29771	−	0.884766i	−0.0637022	−	0.0434315i
$416$	29.9342	+	27.7749i	1.46764	+	1.36177i
$417$		0			0
$418$	−25.6797	−	17.5081i	−1.25604	−	0.856350i
$419$	30.9123	−	14.8866i	1.51016	−	0.727256i	0.518376	−	0.855153i	$-0.326537\pi$
$419$	30.9123	−	14.8866i	1.51016	−	0.727256i	0.991787	+	0.127897i	$0.0408226\pi$
$420$		0			0
$421$	2.45681	+	1.18314i	0.119738	+	0.0576626i	0.492794	−	0.870146i	$-0.335976\pi$
$421$	2.45681	+	1.18314i	0.119738	+	0.0576626i	−0.373056	+	0.927809i	$0.621690\pi$
$422$	8.58805	+	14.8749i	0.418060	+	0.724101i
$423$		0			0
$424$	1.97754	−	1.34827i	0.0960379	−	0.0654775i
$425$	−12.0493	−	1.81614i	−0.584478	−	0.0880959i
$426$		0			0
$427$	−20.0240	+	10.8055i	−0.969028	+	0.522913i
$428$	−10.3755	−	45.4581i	−0.501520	−	2.19730i
$429$		0			0
$430$	−0.654562	−	0.201906i	−0.0315658	−	0.00973676i
$431$	−6.26362	−	15.9594i	−0.301708	−	0.768740i	−0.998666	−	0.0516280i	$-0.983559\pi$
$431$	−6.26362	−	15.9594i	−0.301708	−	0.768740i	0.696958	−	0.717112i	$-0.254536\pi$
$432$		0			0
$433$	18.6888	+	23.4351i	0.898128	+	1.12622i	0.991438	+	0.130580i	$0.0416839\pi$
$433$	18.6888	+	23.4351i	0.898128	+	1.12622i	−0.0933098	+	0.995637i	$0.529745\pi$
$434$	35.3903	−	26.5949i	1.69879	−	1.27660i
$435$		0			0
$436$	−1.69718	+	4.32433i	−0.0812800	+	0.207098i
$437$	−1.02543	+	13.6834i	−0.0490530	+	0.654567i
$438$		0			0
$439$	−0.156532	+	0.145240i	−0.00747085	+	0.00693194i	−0.683899	−	0.729576i	$-0.739717\pi$
$439$	−0.156532	+	0.145240i	−0.00747085	+	0.00693194i	0.676428	+	0.736508i	$0.263527\pi$
$440$	0.621809			0.0296436
$441$		0			0
$442$	−25.5816			−1.21679
$443$	−7.42830	+	6.89245i	−0.352929	+	0.327470i	−0.836636	−	0.547760i	$-0.815481\pi$
$443$	−7.42830	+	6.89245i	−0.352929	+	0.327470i	0.483706	+	0.875230i	$0.339290\pi$
$444$		0			0
$445$	0.174512	−	2.32870i	0.00827265	−	0.110391i
$446$	11.3947	−	29.0331i	0.539553	−	1.37476i
$447$		0			0
$448$	25.8160	−	5.11622i	1.21969	−	0.241718i
$449$	4.44189	+	5.56996i	0.209626	+	0.262862i	0.875518	−	0.483186i	$-0.160520\pi$
$449$	4.44189	+	5.56996i	0.209626	+	0.262862i	−0.665892	+	0.746048i	$0.731949\pi$
$450$		0			0
$451$	3.26445	+	8.31769i	0.153717	+	0.391665i
$452$	17.3572	+	5.35400i	0.816416	+	0.251831i
$453$		0			0
$454$	−7.41999	−	32.5091i	−0.348237	−	1.52573i
$455$	−0.808323	−	2.91564i	−0.0378948	−	0.136687i
$456$		0			0
$457$	−8.56621	−	1.29115i	−0.400711	−	0.0603974i	−0.0544045	−	0.998519i	$-0.517326\pi$
$457$	−8.56621	−	1.29115i	−0.400711	−	0.0603974i	−0.346306	+	0.938122i	$0.612564\pi$
$458$	8.40629	−	5.73131i	0.392800	−	0.267807i
$459$		0			0
$460$	−1.18119	−	2.04588i	−0.0550732	−	0.0953896i
$461$	−8.95670	−	4.31332i	−0.417155	−	0.200891i	0.213519	−	0.976939i	$-0.431507\pi$
$461$	−8.95670	−	4.31332i	−0.417155	−	0.200891i	−0.630674	+	0.776048i	$0.717222\pi$
$462$		0			0
$463$	−19.2129	+	9.25247i	−0.892901	+	0.429999i	−0.823320	−	0.567578i	$-0.807881\pi$
$463$	−19.2129	+	9.25247i	−0.892901	+	0.429999i	−0.0695815	+	0.997576i	$0.522166\pi$
$464$	−1.99110	−	1.35751i	−0.0924347	−	0.0630209i
$465$		0			0
$466$	−25.1347	−	23.3216i	−1.16434	−	1.08035i
$467$	−0.0962343	−	0.0656115i	−0.00445319	−	0.00303614i	0.561091	−	0.827754i	$-0.310382\pi$
$467$	−0.0962343	−	0.0656115i	−0.00445319	−	0.00303614i	−0.565545	+	0.824718i	$0.691334\pi$
$468$		0			0
$469$	31.4612	+	3.26964i	1.45274	+	0.150978i
$470$	−2.37208	−	1.14233i	−0.109416	−	0.0526919i
$471$		0			0
$472$	−1.53482	+	2.65838i	−0.0706457	+	0.122362i
$473$	−6.07680	+	4.14309i	−0.279412	+	0.190500i
$474$		0			0
$475$	−3.28962	+	14.4128i	−0.150938	+	0.661303i
$476$	−8.65229	+	11.9381i	−0.396577	+	0.547182i
$477$		0			0
$478$	−0.632436	−	8.43928i	−0.0289270	−	0.386003i
$479$	−7.92658	−	2.44503i	−0.362175	−	0.111716i	0.108327	−	0.994115i	$-0.465451\pi$
$479$	−7.92658	−	2.44503i	−0.362175	−	0.111716i	−0.470501	+	0.882399i	$0.655927\pi$
$480$		0			0
$481$	−12.8741	+	3.97113i	−0.587007	+	0.181068i
$482$	37.0564	+	46.4672i	1.68787	+	2.11652i
$483$		0			0
$484$	20.3003	−	25.4558i	0.922743	−	1.15708i
$485$	0.0413402	−	0.105333i	0.00187716	−	0.00478293i
$486$		0			0
$487$	−22.3900	+	3.37475i	−1.01459	+	0.152924i	−0.635228	−	0.772325i	$-0.719094\pi$
$487$	−22.3900	+	3.37475i	−1.01459	+	0.152924i	−0.379360	+	0.925249i	$0.623856\pi$
$488$	−3.42297	+	3.17605i	−0.154950	+	0.143773i
$489$		0			0
$490$	−3.07816	−	1.14708i	−0.139057	−	0.0518196i
$491$	−23.0338			−1.03950			−0.519751	−	0.854318i	$-0.673975\pi$
$491$	−23.0338			−1.03950			−0.519751	+	0.854318i	$0.673975\pi$
$492$		0			0
$493$	1.72341	−	0.259762i	0.0776184	−	0.0116991i
$494$	−2.31930	+	30.9490i	−0.104350	+	1.39246i
$495$		0			0
$496$	−17.2040	+	21.5732i	−0.772483	+	0.968663i
$497$	−5.25002	−	4.43959i	−0.235496	−	0.199143i
$498$		0			0
$499$	−8.02980	+	2.47686i	−0.359463	+	0.110880i	−0.469226	−	0.883078i	$-0.655467\pi$
$499$	−8.02980	+	2.47686i	−0.359463	+	0.110880i	0.109763	+	0.993958i	$0.464991\pi$
$500$	−1.86940	−	4.76316i	−0.0836022	−	0.213015i
$501$		0			0
$502$	2.58466	+	34.4899i	0.115359	+	1.53936i
$503$	−5.84482	−	25.6078i	−0.260607	−	1.14180i	−0.920595	−	0.390519i	$-0.872296\pi$
$503$	−5.84482	−	25.6078i	−0.260607	−	1.14180i	0.659987	−	0.751277i	$-0.270562\pi$
$504$		0			0
$505$	0.0179555	−	0.0786683i	0.000799011	−	0.00350069i
$506$	−47.2483	−	7.12154i	−2.10044	−	0.316591i
$507$		0			0
$508$	5.96437	−	10.3306i	0.264626	−	0.458346i
$509$	−0.971128	−	1.68204i	−0.0430445	−	0.0745553i	0.843700	−	0.536814i	$-0.180372\pi$
$509$	−0.971128	−	1.68204i	−0.0430445	−	0.0745553i	−0.886745	+	0.462259i	$0.847039\pi$
$510$		0			0
$511$	2.37683	−	6.98575i	0.105145	−	0.309031i
$512$	−28.2288	+	13.5943i	−1.24755	+	0.600788i
$513$		0			0
$514$	−19.6177	−	18.2026i	−0.865299	−	0.802880i
$515$	−1.33662	−	1.24020i	−0.0588984	−	0.0546498i
$516$		0			0
$517$	−25.4690	+	12.2652i	−1.12012	+	0.539423i
$518$	−4.71158	+	13.8478i	−0.207015	+	0.608438i
$519$		0			0
$520$	−0.310459	−	0.537732i	−0.0136145	−	0.0235811i
$521$	1.14420	−	1.98182i	0.0501284	−	0.0868249i	−0.839872	−	0.542784i	$-0.817370\pi$
$521$	1.14420	−	1.98182i	0.0501284	−	0.0868249i	0.890001	+	0.455959i	$0.150704\pi$
$522$		0			0
$523$	21.9439	+	3.30751i	0.959541	+	0.144627i	0.610094	−	0.792329i	$-0.291132\pi$
$523$	21.9439	+	3.30751i	0.959541	+	0.144627i	0.349446	+	0.936956i	$0.386370\pi$
$524$	0.822691	−	3.60445i	0.0359394	−	0.157461i
$525$		0			0
$526$	2.85868	+	12.5247i	0.124644	+	0.546103i
$527$	−1.49133	−	19.9004i	−0.0649633	−	0.866876i
$528$		0			0
$529$	−0.695767	−	1.77279i	−0.0302507	−	0.0770776i
$530$	1.97671	−	0.609736i	0.0858630	−	0.0264852i
$531$		0			0
$532$	13.6584	+	11.5500i	0.592167	+	0.500756i
$533$	5.56313	−	6.97594i	0.240966	−	0.302162i
$534$		0			0
$535$	0.349968	−	4.67000i	0.0151305	−	0.201902i
$536$	6.41876	−	0.967472i	0.277248	−	0.0417884i
$537$		0			0
$538$	43.6660			1.88257
$539$	−30.2356	+	18.1607i	−1.30234	+	0.782236i
$540$		0			0
$541$	6.23981	−	5.78969i	0.268270	−	0.248918i	−0.534554	−	0.845134i	$-0.679520\pi$
$541$	6.23981	−	5.78969i	0.268270	−	0.248918i	0.802824	+	0.596216i	$0.203330\pi$
$542$	30.3496	−	4.57446i	1.30362	−	0.196490i
$543$		0			0
$544$	7.30167	−	18.6043i	0.313056	−	0.797655i
$545$	−0.290906	+	0.364784i	−0.0124610	+	0.0156256i
$546$		0			0
$547$	5.86827	+	7.35858i	0.250909	+	0.314630i	0.891296	−	0.453423i	$-0.149797\pi$
$547$	5.86827	+	7.35858i	0.250909	+	0.314630i	−0.640386	+	0.768053i	$0.721226\pi$
$548$	−7.37091	+	2.27363i	−0.314870	+	0.0971245i
$549$		0			0
$550$	−49.1917	−	15.1736i	−2.09754	−	0.647006i
$551$	−0.158014	−	2.10855i	−0.00673162	−	0.0898273i
$552$		0			0
$553$	−7.45550	+	10.2868i	−0.317040	+	0.437440i
$554$	9.80257	−	42.9479i	0.416471	−	1.82468i
$555$		0			0
$556$	−28.4746	+	19.4137i	−1.20759	+	0.823323i
$557$	−15.0441	+	26.0572i	−0.637440	+	1.10408i	0.348552	+	0.937289i	$0.386673\pi$
$557$	−15.0441	+	26.0572i	−0.637440	+	1.10408i	−0.985993	+	0.166789i	$0.946660\pi$
$558$		0			0
$559$	6.61694	+	3.18655i	0.279867	+	0.134777i
$560$	2.03655	+	0.211650i	0.0860597	+	0.00894385i
$561$		0			0
$562$	42.8427	+	29.2097i	1.80721	+	1.23214i
$563$	19.8632	+	18.4303i	0.837133	+	0.776746i	0.976958	−	0.213430i	$-0.0684636\pi$
$563$	19.8632	+	18.4303i	0.837133	+	0.776746i	−0.139825	+	0.990176i	$0.544654\pi$
$564$		0			0
$565$	1.50736	+	1.02770i	0.0634151	+	0.0432357i
$566$	26.7453	−	12.8799i	1.12419	−	0.541381i
$567$		0			0
$568$	−1.27127	−	0.612209i	−0.0533411	−	0.0256877i
$569$	−1.16041	−	2.00989i	−0.0486469	−	0.0842589i	0.840677	−	0.541537i	$-0.182158\pi$
$569$	−1.16041	−	2.00989i	−0.0486469	−	0.0842589i	−0.889324	+	0.457279i	$0.848824\pi$
$570$		0			0
$571$	23.0695	−	15.7285i	0.965426	−	0.658217i	0.0255292	−	0.999674i	$-0.491873\pi$
$571$	23.0695	−	15.7285i	0.965426	−	0.658217i	0.939897	+	0.341457i	$0.110921\pi$
$572$	−56.7289	−	8.55051i	−2.37196	−	0.357515i
$573$		0			0
$574$	−2.58807	−	9.33523i	−0.108024	−	0.389645i
$575$	5.05739	+	22.1579i	0.210908	+	0.924046i
$576$		0			0
$577$	−13.7493	−	4.24111i	−0.572392	−	0.176560i	−0.00497163	−	0.999988i	$-0.501583\pi$
$577$	−13.7493	−	4.24111i	−0.572392	−	0.176560i	−0.567421	+	0.823428i	$0.692059\pi$
$578$	−8.24919	−	21.0186i	−0.343121	−	0.874258i
$579$		0			0
$580$	0.226970	+	0.284611i	0.00942440	+	0.0118178i
$581$	17.9342	−	3.55421i	0.744037	−	0.147453i
$582$		0			0
$583$	8.11448	−	20.6754i	0.336067	−	0.856286i
$584$	0.113166	−	1.51009i	0.00468284	−	0.0624882i
$585$		0			0
$586$	−22.7341	+	21.0942i	−0.939137	+	0.871392i
$587$	−28.9239			−1.19382			−0.596908	−	0.802309i	$-0.703604\pi$
$587$	−28.9239			−1.19382			−0.596908	+	0.802309i	$0.703604\pi$
$588$		0			0
$589$	−24.2110			−0.997596
$590$	−1.94483	+	1.80454i	−0.0800674	+	0.0742917i
$591$		0			0
$592$	0.681336	−	9.09179i	0.0280027	−	0.373670i
$593$	−8.11219	+	20.6695i	−0.333128	+	0.848795i	0.661936	+	0.749560i	$0.269735\pi$
$593$	−8.11219	+	20.6695i	−0.333128	+	0.848795i	−0.995064	+	0.0992352i	$0.968360\pi$
$594$		0			0
$595$	−1.18382	+	0.889613i	−0.0485320	+	0.0364706i
$596$	−15.2492	−	19.1219i	−0.624632	−	0.783264i
$597$		0			0
$598$	17.4317	+	44.4154i	0.712837	+	1.81628i
$599$	18.4562	+	5.69298i	0.754099	+	0.232609i	0.647889	−	0.761735i	$-0.275652\pi$
$599$	18.4562	+	5.69298i	0.754099	+	0.232609i	0.106210	+	0.994344i	$0.466128\pi$
$600$		0			0
$601$	−7.61197	−	33.3502i	−0.310499	−	1.36038i	−0.853693	−	0.520777i	$-0.825642\pi$
$601$	−7.61197	−	33.3502i	−0.310499	−	1.36038i	0.543194	−	0.839607i	$-0.317215\pi$
$602$	7.01723	−	3.78669i	0.286001	−	0.154334i
$603$		0			0
$604$	−39.4515	−	5.94636i	−1.60526	−	0.241954i
$605$	2.70193	−	1.84214i	0.109849	−	0.0748938i
$606$		0			0
$607$	−14.9939	−	25.9701i	−0.608582	−	1.05410i	−0.991474	−	0.130302i	$-0.958405\pi$
$607$	−14.9939	−	25.9701i	−0.608582	−	1.05410i	0.382892	−	0.923793i	$-0.374928\pi$
$608$	−21.8458	−	10.5204i	−0.885963	−	0.426657i
$609$		0			0
$610$	−3.63612	+	1.75106i	−0.147222	+	0.0708984i
$611$	23.3230	+	15.9014i	0.943549	+	0.643301i
$612$		0			0
$613$	11.7343	+	10.8878i	0.473943	+	0.439755i	0.880624	−	0.473815i	$-0.157124\pi$
$613$	11.7343	+	10.8878i	0.473943	+	0.439755i	−0.406681	+	0.913570i	$0.633314\pi$
$614$	11.8499	+	8.07912i	0.478223	+	0.326047i
$615$		0			0
$616$	−5.07376	+	5.16225i	−0.204427	+	0.207993i
$617$	17.2284	+	8.29675i	0.693588	+	0.334015i	0.747248	−	0.664545i	$-0.231374\pi$
$617$	17.2284	+	8.29675i	0.693588	+	0.334015i	−0.0536602	+	0.998559i	$0.517089\pi$
$618$		0			0
$619$	−19.1806	+	33.2218i	−0.770934	+	1.33530i	0.166117	+	0.986106i	$0.446877\pi$
$619$	−19.1806	+	33.2218i	−0.770934	+	1.33530i	−0.937051	+	0.349191i	$0.886456\pi$
$620$	3.44394	−	2.34804i	0.138312	−	0.0942996i
$621$		0			0
$622$	−4.96163	+	21.7383i	−0.198943	+	0.871628i
$623$	17.9089	+	20.4502i	0.717503	+	0.819320i
$624$		0			0
$625$	1.81054	+	24.1600i	0.0724218	+	0.966401i
$626$	23.1119	+	7.12907i	0.923736	+	0.284935i
$627$		0			0
$628$	−3.02069	+	0.931758i	−0.120538	+	0.0371812i
$629$	4.11124	+	5.15533i	0.163926	+	0.205556i
$630$		0			0
$631$	22.2301	−	27.8757i	0.884968	−	1.10971i	−0.108328	−	0.994115i	$-0.534550\pi$
$631$	22.2301	−	27.8757i	0.884968	−	1.10971i	0.993296	−	0.115599i	$-0.0368788\pi$
$632$	−0.952523	+	2.42699i	−0.0378894	+	0.0965405i
$633$		0			0
$634$	46.1333	−	6.95348i	1.83219	−	0.276158i
$635$	0.878261	−	0.814907i	0.0348527	−	0.0323386i
$636$		0			0
$637$	30.8013	+	17.0800i	1.22039	+	0.676733i
$638$	7.36298			0.291503
$639$		0			0
$640$	0.967801	−	0.145872i	0.0382557	−	0.00576612i
$641$	3.04018	−	40.5684i	0.120080	−	1.60235i	−0.533703	−	0.845672i	$-0.679200\pi$
$641$	3.04018	−	40.5684i	0.120080	−	1.60235i	0.653783	−	0.756682i	$-0.273181\pi$
$642$		0			0
$643$	17.3801	−	21.7940i	0.685404	−	0.859470i	−0.310435	−	0.950595i	$-0.600475\pi$
$643$	17.3801	−	21.7940i	0.685404	−	0.859470i	0.995839	+	0.0911247i	$0.0290462\pi$
$644$	26.6230	+	6.88748i	1.04909	+	0.271405i
$645$		0			0
$646$	14.5150	−	4.47728i	0.571085	−	0.176156i
$647$	−12.8622	−	32.7722i	−0.505664	−	1.28841i	−0.924789	−	0.380481i	$-0.875758\pi$
$647$	−12.8622	−	32.7722i	−0.505664	−	1.28841i	0.419125	−	0.907929i	$-0.362337\pi$
$648$		0			0
$649$	2.12875	+	28.4062i	0.0835607	+	1.11504i
$650$	11.4387	+	50.1163i	0.448663	+	1.96572i
$651$		0			0
$652$	−0.979683	+	4.29227i	−0.0383674	+	0.168098i
$653$	20.3537	+	3.06782i	0.796501	+	0.120053i	0.534670	−	0.845061i	$-0.320436\pi$
$653$	20.3537	+	3.06782i	0.796501	+	0.120053i	0.261830	+	0.965114i	$0.415674\pi$
$654$		0			0
$655$	0.185665	−	0.321582i	0.00725454	−	0.0125652i
$656$	3.01907	+	5.22918i	0.117875	+	0.204165i
$657$		0			0
$658$	28.8390	−	10.3719i	1.12426	−	0.404339i
$659$	14.0715	−	6.77647i	0.548147	−	0.263974i	−0.139248	−	0.990258i	$-0.544469\pi$
$659$	14.0715	−	6.77647i	0.548147	−	0.263974i	0.687395	+	0.726284i	$0.258754\pi$
$660$		0			0
$661$	14.5172	+	13.4700i	0.564655	+	0.523923i	0.910030	−	0.414541i	$-0.136058\pi$
$661$	14.5172	+	13.4700i	0.564655	+	0.523923i	−0.345376	+	0.938465i	$0.612248\pi$
$662$	−20.5843	−	19.0994i	−0.800031	−	0.742320i
$663$		0			0
$664$	3.38049	−	1.62796i	0.131188	−	0.0631770i
$665$	0.968936	+	1.51286i	0.0375737	+	0.0586662i
$666$		0			0
$667$	−1.62536	−	2.81521i	−0.0629343	−	0.109005i
$668$	−26.0594	+	45.1362i	−1.00827	+	1.74637i
$669$		0			0
$670$	5.54767	+	0.836177i	0.214325	+	0.0323044i
$671$	−9.64230	+	42.2457i	−0.372237	+	1.63088i
$672$		0			0
$673$	−10.2014	−	44.6953i	−0.393236	−	1.72288i	−0.653134	−	0.757242i	$-0.726546\pi$
$673$	−10.2014	−	44.6953i	−0.393236	−	1.72288i	0.259898	−	0.965636i	$-0.416311\pi$
$674$	1.25423	+	16.7365i	0.0483111	+	0.644667i
$675$		0			0
$676$	10.1817	+	25.9425i	0.391602	+	0.997787i
$677$	−33.3348	+	10.2824i	−1.28116	+	0.395186i	−0.859299	−	0.511474i	$-0.829100\pi$
$677$	−33.3348	+	10.2824i	−1.28116	+	0.395186i	−0.421863	+	0.906660i	$0.638624\pi$
$678$		0			0
$679$	0.537152	+	1.20269i	0.0206140	+	0.0461549i
$680$	−0.189476	+	0.237596i	−0.00726609	+	0.00911139i
$681$		0			0
$682$	6.30030	−	84.0716i	0.241251	−	3.21927i
$683$	49.3621	−	7.44014i	1.88879	−	0.284689i	0.900217	−	0.435442i	$-0.143408\pi$
$683$	49.3621	−	7.44014i	1.88879	−	0.284689i	0.988571	+	0.150753i	$0.0481698\pi$
$684$		0			0
$685$	−0.774733			−0.0296010
$686$	34.6398	−	16.1951i	1.32255	−	0.618333i
$687$		0			0
$688$	−3.64330	+	3.38049i	−0.138900	+	0.128880i
$689$	−21.9312	+	3.30559i	−0.835512	+	0.125933i
$690$		0			0
$691$	−1.95357	+	4.97761i	−0.0743172	+	0.189357i	−0.963205	−	0.268768i	$-0.913384\pi$
$691$	−1.95357	+	4.97761i	−0.0743172	+	0.189357i	0.888888	+	0.458125i	$0.151479\pi$
$692$	−32.5032	+	40.7577i	−1.23559	+	1.54938i
$693$		0			0
$694$	15.4294	+	19.3478i	0.585691	+	0.734433i
$695$	−3.30758	+	1.02025i	−0.125464	+	0.0387004i
$696$		0			0
$697$	−4.17296	−	1.28719i	−0.158062	−	0.0487557i
$698$	2.68250	+	35.7954i	0.101534	+	1.35488i
$699$		0			0
$700$	27.2564	+	11.6124i	1.03020	+	0.438908i
$701$	7.20895	−	31.5845i	0.272278	−	1.19293i	−0.635038	−	0.772481i	$-0.719016\pi$
$701$	7.20895	−	31.5845i	0.272278	−	1.19293i	0.907316	−	0.420448i	$-0.138127\pi$
$702$		0			0
$703$	6.60972	−	4.50643i	0.249290	−	0.169963i
$704$	25.0604	−	43.4059i	0.944499	−	1.63592i
$705$		0			0
$706$	−40.8169	−	19.6564i	−1.53616	−	0.739777i
$707$	0.506593	+	0.790974i	0.0190524	+	0.0297477i
$708$		0			0
$709$	−16.5882	−	11.3097i	−0.622984	−	0.424743i	0.210262	−	0.977645i	$-0.432568\pi$
$709$	−16.5882	−	11.3097i	−0.622984	−	0.424743i	−0.833247	+	0.552902i	$0.813521\pi$
$710$	−0.893966	−	0.829480i	−0.0335500	−	0.0311298i
$711$		0			0
$712$	4.60926	+	3.14254i	0.172739	+	0.117772i
$713$	−33.5353	+	16.1497i	−1.25591	+	0.604813i
$714$		0			0
$715$	−5.19143	−	2.50006i	−0.194148	−	0.0934969i
$716$	18.4851	+	32.0171i	0.690820	+	1.19654i
$717$		0			0
$718$	6.64610	−	4.53123i	0.248030	−	0.169104i
$719$	−24.3253	−	3.66645i	−0.907182	−	0.136736i	−0.321154	−	0.947027i	$-0.604071\pi$
$719$	−24.3253	−	3.66645i	−0.907182	−	0.136736i	−0.586027	+	0.810291i	$0.699309\pi$
$720$		0			0
$721$	21.2025	−	0.976967i	0.789622	−	0.0363842i
$722$	4.62863	+	20.2793i	0.172260	+	0.754719i
$723$		0			0
$724$	21.7127	+	6.69748i	0.806947	+	0.248910i
$725$	−1.27951	−	3.26013i	−0.0475197	−	0.121078i
$726$		0			0
$727$	7.17815	+	9.00112i	0.266223	+	0.333833i	0.896917	−	0.442198i	$-0.145801\pi$
$727$	7.17815	+	9.00112i	0.266223	+	0.333833i	−0.630694	+	0.776031i	$0.717230\pi$
$728$	6.99749	+	1.81028i	0.259344	+	0.0670935i
$729$		0			0
$730$	0.478166	−	1.21835i	0.0176977	−	0.0450931i
$731$	0.268617	−	3.58445i	0.00993516	−	0.132576i
$732$		0			0
$733$	−14.0937	+	13.0770i	−0.520562	+	0.483011i	−0.896135	−	0.443782i	$-0.853637\pi$
$733$	−14.0937	+	13.0770i	−0.520562	+	0.483011i	0.375573	+	0.926793i	$0.377446\pi$
$734$	−26.6948			−0.985324
$735$		0			0
$736$	−37.2767			−1.37404
$737$	44.1576	−	40.9723i	1.62657	−	1.50923i
$738$		0			0
$739$	0.649629	−	8.66869i	0.0238970	−	0.318883i	−0.972426	−	0.233210i	$-0.925077\pi$
$739$	0.649629	−	8.66869i	0.0238970	−	0.318883i	0.996323	−	0.0856728i	$-0.0273040\pi$
$740$	−0.503169	+	1.28205i	−0.0184969	+	0.0471292i
$741$		0			0
$742$	−11.0673	+	21.3859i	−0.406294	+	0.785101i
$743$	−9.51278	−	11.9286i	−0.348990	−	0.437619i	0.576093	−	0.817384i	$-0.304576\pi$
$743$	−9.51278	−	11.9286i	−0.348990	−	0.437619i	−0.925083	+	0.379764i	$0.876005\pi$
$744$		0			0
$745$	−0.897452	−	2.28667i	−0.0328801	−	0.0837771i
$746$	−42.8184	−	13.2077i	−1.56769	−	0.483569i
$747$		0			0
$748$	6.24805	+	27.3745i	0.228451	+	1.00091i
$749$	35.9147	+	41.0111i	1.31230	+	1.49851i
$750$		0			0
$751$	6.85033	+	1.03252i	0.249972	+	0.0376772i	0.272833	−	0.962061i	$-0.412039\pi$
$751$	6.85033	+	1.03252i	0.249972	+	0.0376772i	−0.0228609	+	0.999739i	$0.507277\pi$
$752$	−15.7833	+	10.7609i	−0.575558	+	0.392409i
$753$		0			0
$754$	−3.67622	−	6.36740i	−0.133880	−	0.231887i
$755$	−3.61032	−	1.73864i	−0.131393	−	0.0632756i
$756$		0			0
$757$	4.41120	−	2.12432i	0.160328	−	0.0772099i	−0.351999	−	0.936000i	$-0.614498\pi$
$757$	4.41120	−	2.12432i	0.160328	−	0.0772099i	0.512327	+	0.858791i	$0.328784\pi$
$758$	−31.0911	−	21.1975i	−1.12928	−	0.769929i
$759$		0			0
$760$	0.270268	+	0.250772i	0.00980365	+	0.00909646i
$761$	20.8755	+	14.2327i	0.756736	+	0.515934i	0.879150	−	0.476546i	$-0.158111\pi$
$761$	20.8755	+	14.2327i	0.756736	+	0.515934i	−0.122414	+	0.992479i	$0.539064\pi$
$762$		0			0
$763$	−0.654741	−	5.39161i	−0.0237032	−	0.195190i
$764$	3.42315	+	1.64850i	0.123845	+	0.0596406i
$765$		0			0
$766$	−19.5223	+	33.8137i	−0.705370	+	1.22174i
$767$	23.5024	−	16.0237i	0.848623	−	0.578581i
$768$		0			0
$769$	0.789269	−	3.45801i	0.0284618	−	0.124699i	−0.958701	−	0.284415i	$-0.908201\pi$
$769$	0.789269	−	3.45801i	0.0284618	−	0.124699i	0.987163	+	0.159716i	$0.0510578\pi$
$770$	−5.50549	+	2.97091i	−0.198404	+	0.107064i
$771$		0			0
$772$	−0.651760	−	8.69713i	−0.0234574	−	0.313017i
$773$	−43.1188	−	13.3004i	−1.55087	−	0.478381i	−0.603192	−	0.797596i	$-0.706105\pi$
$773$	−43.1188	−	13.3004i	−1.55087	−	0.478381i	−0.947682	+	0.319215i	$0.896581\pi$
$774$		0			0
$775$	−38.3195	+	11.8200i	−1.37648	+	0.424587i
$776$	0.168539	+	0.211341i	0.00605018	+	0.00758669i
$777$		0			0
$778$	−31.5777	+	39.5972i	−1.13212	+	1.41963i
$779$	−1.93559	+	4.93180i	−0.0693497	+	0.176700i
$780$		0			0
$781$	−12.9476	+	1.95154i	−0.463303	+	0.0698317i
$782$	17.1186	−	15.8837i	0.612160	−	0.568001i
$783$		0			0
$784$	−18.3747	+	15.1804i	−0.656238	+	0.542157i
$785$	−0.317494			−0.0113319
$786$		0			0
$787$	23.6601	−	3.56618i	0.843391	−	0.127121i	0.286886	−	0.957965i	$-0.407380\pi$
$787$	23.6601	−	3.56618i	0.843391	−	0.127121i	0.556505	+	0.830844i	$0.312142\pi$
$788$	0.281388	−	3.75486i	0.0100240	−	0.133761i
$789$		0			0
$790$	−1.40497	+	1.76177i	−0.0499865	+	0.0626811i
$791$	−20.8315	+	4.12839i	−0.740683	+	0.146789i
$792$		0			0
$793$	41.3477	−	12.7541i	1.46830	−	0.452911i
$794$	21.4345	+	54.6141i	0.760680	+	1.93818i
$795$		0			0
$796$	−4.48357	−	59.8290i	−0.158916	−	2.12058i
$797$	−10.0446	−	44.0085i	−0.355800	−	1.55886i	−0.763539	−	0.645762i	$-0.776540\pi$
$797$	−10.0446	−	44.0085i	−0.355800	−	1.55886i	0.407739	−	0.913098i	$-0.366317\pi$
$798$		0			0
$799$	3.07426	−	13.4692i	0.108760	−	0.476507i
$800$	−39.7122	−	5.98565i	−1.40404	−	0.211625i
$801$		0			0
$802$	23.5292	−	40.7538i	0.830845	−	1.43907i
$803$	−7.02639	−	12.1701i	−0.247956	−	0.429472i
$804$		0			0
$805$	2.35124	+	1.44918i	0.0828704	+	0.0510770i
$806$	−75.8496	+	36.5273i	−2.67169	+	1.28662i
$807$		0			0
$808$	0.141305	+	0.131112i	0.00497110	+	0.00461251i
$809$	−13.0517	−	12.1102i	−0.458873	−	0.425772i	0.416562	−	0.909107i	$-0.363235\pi$
$809$	−13.0517	−	12.1102i	−0.458873	−	0.425772i	−0.875435	+	0.483335i	$0.839425\pi$
$810$		0			0
$811$	32.2066	−	15.5099i	1.13093	−	0.544625i	0.227674	−	0.973737i	$-0.426888\pi$
$811$	32.2066	−	15.5099i	1.13093	−	0.544625i	0.903251	+	0.429112i	$0.141174\pi$
$812$	−4.21483	−	0.438031i	−0.147912	−	0.0153719i
$813$		0			0
$814$	13.9284	+	24.1247i	0.488190	+	0.845569i
$815$	−0.221095	+	0.382948i	−0.00774462	+	0.0134141i
$816$		0			0
$817$	−4.31215	−	0.649953i	−0.150863	−	0.0227390i
$818$	14.1435	−	61.9669i	0.494517	−	2.16662i
$819$		0			0
$820$	−0.202966	−	0.889254i	−0.00708789	−	0.0310541i
$821$	2.78133	+	37.1143i	0.0970691	+	1.29530i	0.806800	+	0.590824i	$0.201197\pi$
$821$	2.78133	+	37.1143i	0.0970691	+	1.29530i	−0.709731	+	0.704473i	$0.751184\pi$
$822$		0			0
$823$	−12.7743	−	32.5484i	−0.445284	−	1.13457i	−0.960691	−	0.277620i	$-0.910454\pi$
$823$	−12.7743	−	32.5484i	−0.445284	−	1.13457i	0.515407	−	0.856946i	$-0.327641\pi$
$824$	4.16230	−	1.28390i	0.145000	−	0.0447267i
$825$		0			0
$826$	0.887907	−	30.8704i	0.0308942	−	1.07412i
$827$	2.57533	−	3.22936i	0.0895529	−	0.112296i	−0.735036	−	0.678028i	$-0.762835\pi$
$827$	2.57533	−	3.22936i	0.0895529	−	0.112296i	0.824589	+	0.565732i	$0.191406\pi$
$828$		0			0
$829$	−3.06105	+	40.8469i	−0.106315	+	1.41867i	0.647740	+	0.761861i	$0.275714\pi$
$829$	−3.06105	+	40.8469i	−0.106315	+	1.41867i	−0.754055	+	0.656811i	$0.771905\pi$
$830$	3.20665	−	0.483325i	0.111304	−	0.0167764i
$831$		0			0
$832$	−50.0490			−1.73514
$833$	2.27405	−	17.0870i	0.0787912	−	0.592031i
$834$		0			0
$835$	−3.83728	+	3.56047i	−0.132795	+	0.123215i
$836$	33.6845	−	5.07712i	1.16500	−	0.175596i
$837$		0			0
$838$	−25.8807	+	65.9429i	−0.894034	+	2.27796i
$839$	1.07588	−	1.34911i	0.0371434	−	0.0465763i	−0.762913	−	0.646501i	$-0.776231\pi$
$839$	1.07588	−	1.34911i	0.0371434	−	0.0465763i	0.800056	+	0.599925i	$0.204803\pi$
$840$		0			0
$841$	−17.7689	−	22.2815i	−0.612720	−	0.768327i
$842$	−5.37999	+	1.65951i	−0.185407	+	0.0571904i
$843$		0			0
$844$	−17.9892	−	5.54893i	−0.619213	−	0.191002i
$845$	0.209175	+	2.79125i	0.00719584	+	0.0960219i
$846$		0			0
$847$	−6.75338	+	37.4627i	−0.232049	+	1.28723i
$848$	3.33983	−	14.6327i	0.114690	−	0.502491i
$849$		0			0
$850$	20.7875	−	14.1727i	0.713006	−	0.486120i
$851$	6.14932	−	10.6509i	0.210796	−	0.365110i
$852$		0			0
$853$	−42.8819	−	20.6508i	−1.46825	−	0.707071i	−0.482593	−	0.875845i	$-0.660305\pi$
$853$	−42.8819	−	20.6508i	−1.46825	−	0.707071i	−0.985655	+	0.168773i	$0.946019\pi$
$854$	15.1322	−	44.4751i	0.517814	−	1.52191i
$855$		0			0
$856$	9.24348	+	6.30209i	0.315935	+	0.215401i
$857$	15.7900	+	14.6510i	0.539377	+	0.500469i	0.902158	−	0.431406i	$-0.141982\pi$
$857$	15.7900	+	14.6510i	0.539377	+	0.500469i	−0.362781	+	0.931874i	$0.618173\pi$
$858$		0			0
$859$	24.6735	+	16.8221i	0.841849	+	0.573963i	0.905663	−	0.423999i	$-0.139374\pi$
$859$	24.6735	+	16.8221i	0.841849	+	0.573963i	−0.0638134	+	0.997962i	$0.520326\pi$
$860$	0.676426	−	0.325750i	0.0230659	−	0.0111080i
$861$		0			0
$862$	31.8928	+	15.3588i	1.08627	+	0.523122i
$863$	25.9789	+	44.9968i	0.884332	+	1.53171i	0.846477	+	0.532425i	$0.178719\pi$
$863$	25.9789	+	44.9968i	0.884332	+	1.53171i	0.0378545	+	0.999283i	$0.487948\pi$
$864$		0			0
$865$	−4.32610	+	2.94949i	−0.147092	+	0.100286i
$866$	−61.1972	−	9.22399i	−2.07956	−	0.313444i
$867$		0			0
$868$	−8.60803	+	47.7508i	−0.292176	+	1.62077i
$869$	5.38382	+	23.5880i	0.182633	+	0.800169i
$870$		0			0
$871$	−57.4795	−	17.7301i	−1.94762	−	0.600761i
$872$	−0.407209	−	1.03755i	−0.0137898	−	0.0351359i
$873$		0			0
$874$	−17.6643	−	22.1504i	−0.597504	−	0.749247i
$875$	4.56804	+	3.86288i	0.154428	+	0.130589i
$876$		0			0
$877$	11.2821	−	28.7463i	0.380970	−	0.970695i	−0.603847	−	0.797100i	$-0.706366\pi$
$877$	11.2821	−	28.7463i	0.380970	−	0.970695i	0.984817	−	0.173595i	$-0.0555384\pi$
$878$	0.0329473	−	0.439651i	0.00111192	−	0.0148375i
$879$		0			0
$880$	2.85841	−	2.65222i	0.0963571	−	0.0894063i
$881$	57.6244			1.94141			0.970707	−	0.240266i	$-0.0772347\pi$
$881$	57.6244			1.94141			0.970707	+	0.240266i	$0.0772347\pi$
$882$		0			0
$883$	−45.7898			−1.54095			−0.770475	−	0.637471i	$-0.779981\pi$
$883$	−45.7898			−1.54095			−0.770475	+	0.637471i	$0.779981\pi$
$884$	20.5535	−	19.0709i	0.691290	−	0.641423i
$885$		0			0
$886$	1.56353	−	20.8639i	0.0525279	−	0.700936i
$887$	−0.950713	+	2.42238i	−0.0319218	+	0.0813355i	−0.945946	−	0.324324i	$-0.894863\pi$
$887$	−0.950713	+	2.42238i	−0.0319218	+	0.0813355i	0.914024	+	0.405660i	$0.132958\pi$
$888$		0			0
$889$	−0.400968	+	13.9407i	−0.0134480	+	0.467556i
$890$	3.00618	+	3.76963i	0.100767	+	0.126358i
$891$		0			0
$892$	12.4889	+	31.8213i	0.418160	+	1.06545i
$893$	−16.0165	−	4.94044i	−0.535972	−	0.165326i
$894$		0			0
$895$	0.826260	+	3.62008i	0.0276188	+	0.121006i
$896$	−6.68590	+	9.22495i	−0.223360	+	0.308184i
$897$		0			0
$898$	−14.5451	−	2.19232i	−0.485377	−	0.0731587i
$899$	4.73900	−	3.23100i	0.158055	−	0.107760i
$900$		0			0
$901$	5.42752	+	9.40073i	0.180817	+	0.313184i
$902$	−16.6218	−	8.00464i	−0.553445	−	0.266525i
$903$		0			0
$904$	−3.92661	+	1.89095i	−0.130597	+	0.0628922i
$905$	1.88560	+	1.28558i	0.0626796	+	0.0427342i
$906$		0			0
$907$	7.68999	+	7.13526i	0.255342	+	0.236923i	0.797448	−	0.603387i	$-0.206183\pi$
$907$	7.68999	+	7.13526i	0.255342	+	0.236923i	−0.542107	+	0.840310i	$0.682373\pi$
$908$	30.1968	+	20.5879i	1.00212	+	0.683232i
$909$		0			0
$910$	5.31800	+	3.27774i	0.176290	+	0.108656i
$911$	−45.0044	−	21.6730i	−1.49106	−	0.718057i	−0.501904	−	0.864923i	$-0.667367\pi$
$911$	−45.0044	−	21.6730i	−1.49106	−	0.718057i	−0.989156	+	0.146866i	$0.953081\pi$
$912$		0			0
$913$	17.4093	−	30.1538i	0.576164	−	0.997946i
$914$	14.7784	−	10.0758i	0.488828	−	0.333277i
$915$		0			0
$916$	−2.48138	+	10.8716i	−0.0819870	+	0.359209i
$917$	1.15480	+	4.16539i	0.0381349	+	0.137553i
$918$		0			0
$919$	2.71205	+	36.1898i	0.0894623	+	1.19379i	0.843562	+	0.537032i	$0.180454\pi$
$919$	2.71205	+	36.1898i	0.0894623	+	1.19379i	−0.754100	+	0.656760i	$0.771927\pi$
$920$	0.541631	+	0.167071i	0.0178571	+	0.00550817i
$921$		0			0
$922$	19.6136	−	6.05001i	0.645941	−	0.199246i
$923$	8.15222	+	10.2226i	0.268334	+	0.336480i
$924$		0			0
$925$	8.26135	−	10.3594i	0.271631	−	0.340615i
$926$	16.0857	−	40.9856i	0.528608	−	1.34687i
$927$		0			0
$928$	5.68001	−	0.856123i	0.186455	−	0.0281036i
$929$	18.3924	−	17.0656i	0.603434	−	0.559904i	−0.318172	−	0.948033i	$-0.603069\pi$
$929$	18.3924	−	17.0656i	0.603434	−	0.559904i	0.921605	+	0.388129i	$0.126878\pi$
$930$		0			0
$931$	−20.4659	−	4.30034i	−0.670744	−	0.140938i
$932$	37.5805			1.23099
$933$		0			0
$934$	0.237795	−	0.0358418i	0.00778089	−	0.00117278i
$935$	−0.210748	+	2.81224i	−0.00689220	+	0.0919700i
$936$		0			0
$937$	−9.74381	+	12.2183i	−0.318316	+	0.399156i	−0.915087	−	0.403255i	$-0.867879\pi$
$937$	−9.74381	+	12.2183i	−0.318316	+	0.399156i	0.596771	+	0.802412i	$0.296450\pi$
$938$	−52.2091	+	39.2338i	−1.70469	+	1.28103i
$939$		0			0
$940$	2.75744	−	0.850558i	0.0899378	−	0.0277422i
$941$	−9.00338	−	22.9402i	−0.293502	−	0.747830i	−0.999226	−	0.0393435i	$-0.987473\pi$
$941$	−9.00338	−	22.9402i	−0.293502	−	0.747830i	0.705724	−	0.708487i	$-0.250622\pi$
$942$		0			0
$943$	0.608682	+	8.12230i	0.0198214	+	0.264498i
$944$	4.28342	+	18.7669i	0.139414	+	0.610811i
$945$		0			0
$946$	3.37906	−	14.8047i	0.109863	−	0.481341i
$947$	−18.5320	−	2.79324i	−0.602208	−	0.0907682i	−0.159140	−	0.987256i	$-0.550872\pi$
$947$	−18.5320	−	2.79324i	−0.602208	−	0.0907682i	−0.443068	+	0.896488i	$0.646110\pi$
$948$		0			0
$949$	−7.01634	+	12.1526i	−0.227760	+	0.394492i
$950$	−15.2616	−	26.4339i	−0.495153	−	0.857631i
$951$		0			0
$952$	−0.426454	−	3.51174i	−0.0138215	−	0.113816i
$953$	26.3793	−	12.7036i	0.854510	−	0.411510i	0.0452602	−	0.998975i	$-0.485588\pi$
$953$	26.3793	−	12.7036i	0.854510	−	0.411510i	0.809250	+	0.587465i	$0.199874\pi$
$954$		0			0
$955$	0.279734	+	0.259555i	0.00905197	+	0.00839900i
$956$	6.79954	+	6.30905i	0.219913	+	0.204049i
$957$		0			0
$958$	15.4308	−	7.43108i	0.498546	−	0.240087i
$959$	6.32156	−	6.43183i	0.204134	−	0.207694i
$960$		0			0
$961$	−17.3370	−	30.0286i	−0.559258	−	0.968664i
$962$	13.9084	−	24.0901i	0.448426	−	0.776697i
$963$		0			0
$964$	−64.4138	−	9.70881i	−2.07463	−	0.312700i
$965$	0.194920	−	0.854002i	0.00627471	−	0.0274913i
$966$		0			0
$967$	7.26505	+	31.8303i	0.233628	+	1.02359i	0.946603	+	0.322403i	$0.104490\pi$
$967$	7.26505	+	31.8303i	0.233628	+	1.02359i	−0.712974	+	0.701190i	$0.752652\pi$
$968$	0.583795	+	7.79020i	0.0187639	+	0.250386i
$969$		0			0
$970$	0.0853549	+	0.217481i	0.00274058	+	0.00698289i
$971$	−14.8612	+	4.58409i	−0.476920	+	0.147110i	−0.523890	−	0.851786i	$-0.675520\pi$
$971$	−14.8612	+	4.58409i	−0.476920	+	0.147110i	0.0469700	+	0.998896i	$0.485043\pi$
$972$		0			0
$973$	18.5186	−	35.7845i	0.593680	−	1.14720i
$974$	29.1486	−	36.5512i	0.933982	−	1.17118i
$975$		0			0
$976$	−2.18825	+	29.2001i	−0.0700441	+	0.934674i
$977$	−32.5572	+	4.90720i	−1.04160	+	0.156995i	−0.647493	−	0.762071i	$-0.724183\pi$
$977$	−32.5572	+	4.90720i	−1.04160	+	0.156995i	−0.394103	+	0.919066i	$0.628945\pi$
$978$		0			0
$979$	51.7687			1.65454
$980$	3.32828	−	1.37313i	0.106318	−	0.0438630i
$981$		0			0
$982$	34.8624	−	32.3476i	1.11250	−	1.03225i
$983$	7.42196	−	1.11868i	0.236724	−	0.0356804i	−0.0296088	−	0.999562i	$-0.509426\pi$
$983$	7.42196	−	1.11868i	0.236724	−	0.0356804i	0.266333	+	0.963881i	$0.414188\pi$
$984$		0			0
$985$	0.138167	−	0.352043i	0.00440235	−	0.0112170i
$986$	−2.24363	+	2.81343i	−0.0714518	+	0.0895977i
$987$		0			0
$988$	−21.2087	−	26.5949i	−0.674740	−	0.846097i
$989$	−6.40643	+	1.97612i	−0.203713	+	0.0628370i
$990$		0			0
$991$	36.3170	+	11.2023i	1.15365	+	0.355853i	0.811819	−	0.583909i	$-0.198477\pi$
$991$	36.3170	+	11.2023i	1.15365	+	0.355853i	0.341829	+	0.939762i	$0.388954\pi$
$992$	−4.91512	−	65.5878i	−0.156055	−	2.08241i
$993$		0			0
$994$	14.1808	−	0.653422i	0.449788	−	0.0207253i
$995$	1.34089	−	5.87482i	0.0425091	−	0.186244i
$996$		0			0
$997$	−20.0677	+	13.6819i	−0.635550	+	0.433311i	−0.837765	−	0.546030i	$-0.816138\pi$
$997$	−20.0677	+	13.6819i	−0.635550	+	0.433311i	0.202215	+	0.979341i	$0.435186\pi$
$998$	8.67495	−	15.0255i	0.274601	−	0.475623i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bb.d.109.1		48
3.2	odd	2		49.2.g.a.11.4	yes	48
12.11	even	2		784.2.bg.c.305.4		48
21.2	odd	6		343.2.g.i.128.1		48
21.5	even	6		343.2.g.h.128.1		48
21.11	odd	6		343.2.e.d.246.7		48
21.17	even	6		343.2.e.c.246.7		48
21.20	even	2		343.2.g.g.312.4		48
49.9	even	21	inner	441.2.bb.d.352.1		48
147.74	odd	42		343.2.e.d.99.7		48
147.83	even	14		343.2.g.h.67.1		48
147.89	even	42		343.2.g.g.177.4		48
147.95	odd	42		2401.2.a.h.1.4		24
147.101	even	42		2401.2.a.i.1.4		24
147.107	odd	42		49.2.g.a.9.4	✓	48
147.113	odd	14		343.2.g.i.67.1		48
147.122	even	42		343.2.e.c.99.7		48
588.107	even	42		784.2.bg.c.401.4		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.2.g.a.9.4	✓	48	147.107	odd	42
49.2.g.a.11.4	yes	48	3.2	odd	2
343.2.e.c.99.7		48	147.122	even	42
343.2.e.c.246.7		48	21.17	even	6
343.2.e.d.99.7		48	147.74	odd	42
343.2.e.d.246.7		48	21.11	odd	6
343.2.g.g.177.4		48	147.89	even	42
343.2.g.g.312.4		48	21.20	even	2
343.2.g.h.67.1		48	147.83	even	14
343.2.g.h.128.1		48	21.5	even	6
343.2.g.i.67.1		48	147.113	odd	14
343.2.g.i.128.1		48	21.2	odd	6
441.2.bb.d.109.1		48	1.1	even	1	trivial
441.2.bb.d.352.1		48	49.9	even	21	inner
784.2.bg.c.305.4		48	12.11	even	2
784.2.bg.c.401.4		48	588.107	even	42
2401.2.a.h.1.4		24	147.95	odd	42
2401.2.a.i.1.4		24	147.101	even	42

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.bb (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.51353 + 1.40435i) q^{2} +(0.169112 - 2.25665i) q^{4} +(0.0830372 - 0.211575i) q^{5} +(1.07894 + 2.41576i) q^{7} +(0.338532 + 0.424506i) q^{8} +O(q^{10})\)	\(q+(-1.51353 + 1.40435i) q^{2} +(0.169112 - 2.25665i) q^{4} +(0.0830372 - 0.211575i) q^{5} +(1.07894 + 2.41576i) q^{7} +(0.338532 + 0.424506i) q^{8} +(0.171447 + 0.436839i) q^{10} +(4.81478 + 1.48516i) q^{11} +(-1.11960 - 4.90527i) q^{13} +(-5.02558 - 2.14111i) q^{14} +(3.36686 + 0.507473i) q^{16} +(-2.03464 + 1.38719i) q^{17} +(1.49378 + 2.58730i) q^{19} +(-0.463408 - 0.223166i) q^{20} +(-9.37300 + 4.51380i) q^{22} +(3.79491 + 2.58732i) q^{23} +(3.62739 + 3.36573i) q^{25} +(8.58326 + 5.85197i) q^{26} +(5.63398 - 2.02625i) q^{28} +(-0.637668 - 0.307085i) q^{29} +(-4.05198 + 7.01823i) q^{31} +(-6.70576 + 4.57191i) q^{32} +(1.13138 - 4.95690i) q^{34} +(0.600707 - 0.0276793i) q^{35} +(-0.200105 - 2.67021i) q^{37} +(-5.89435 - 1.81816i) q^{38} +(0.117926 - 0.0363752i) q^{40} +(1.10568 + 1.38648i) q^{41} +(-0.910094 + 1.14122i) q^{43} +(4.16573 - 10.6141i) q^{44} +(-9.37722 + 1.41339i) q^{46} +(-4.11267 + 3.81600i) q^{47} +(-4.67178 + 5.21292i) q^{49} -10.2168 q^{50} +(-11.2588 + 1.69699i) q^{52} +(0.329416 - 4.39576i) q^{53} +(0.714029 - 0.895364i) q^{55} +(-0.660247 + 1.27583i) q^{56} +(1.39638 - 0.430727i) q^{58} +(2.06545 + 5.26268i) q^{59} +(0.642677 + 8.57593i) q^{61} +(-3.72327 - 16.3127i) q^{62} +(2.21348 - 9.69790i) q^{64} +(-1.13080 - 0.170441i) q^{65} +(5.97762 - 10.3535i) q^{67} +(2.78632 + 4.82605i) q^{68} +(-0.870316 + 0.885497i) q^{70} +(-2.34135 + 1.12753i) q^{71} +(-2.04449 - 1.89701i) q^{73} +(4.05278 + 3.76043i) q^{74} +(6.09123 - 2.93338i) q^{76} +(1.60706 + 13.2337i) q^{77} +(2.40092 + 4.15851i) q^{79} +(0.386944 - 0.670206i) q^{80} +(-3.62058 - 0.545714i) q^{82} +(1.53769 - 6.73708i) q^{83} +(0.124545 + 0.545667i) q^{85} +(-0.225221 - 3.00536i) q^{86} +(0.999497 + 2.54668i) q^{88} +(9.81790 - 3.02842i) q^{89} +(10.6420 - 7.99717i) q^{91} +(6.48044 - 8.12622i) q^{92} +(0.865647 - 11.5513i) q^{94} +(0.671447 - 0.101204i) q^{95} +0.497851 q^{97} +(-0.249890 - 14.4507i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 13 q^{2} - 9 q^{4} + 14 q^{5} - 14 q^{7} + 20 q^{8}+O(q^{10}) \) 48 * q + 13 * q^2 - 9 * q^4 + 14 * q^5 - 14 * q^7 + 20 * q^8	\( 48 q + 13 q^{2} - 9 q^{4} + 14 q^{5} - 14 q^{7} + 20 q^{8} - 14 q^{10} + 3 q^{11} - 14 q^{13} - 21 q^{14} - 3 q^{16} + 7 q^{17} + 21 q^{19} - 14 q^{20} - 20 q^{22} - 15 q^{23} - 4 q^{25} + 28 q^{28} - 12 q^{29} + 35 q^{31} - 45 q^{32} + 70 q^{34} + 15 q^{37} + 28 q^{38} - 42 q^{40} + 42 q^{41} - 30 q^{43} + 50 q^{44} - 78 q^{46} - 21 q^{47} - 70 q^{49} - 40 q^{50} - 70 q^{52} - 11 q^{53} - 7 q^{55} + 28 q^{56} + 16 q^{58} + 28 q^{59} + 7 q^{61} + 28 q^{62} - 32 q^{64} - 14 q^{65} + 11 q^{67} - 77 q^{68} + 70 q^{70} - 19 q^{71} + 7 q^{73} - 34 q^{74} + 119 q^{76} - 7 q^{77} + 15 q^{79} - 70 q^{80} - 14 q^{82} - 26 q^{85} + 33 q^{86} - 77 q^{88} + 14 q^{89} + 84 q^{91} + 38 q^{92} + 14 q^{94} + 61 q^{95} + 161 q^{98}+O(q^{100}) \) 48 * q + 13 * q^2 - 9 * q^4 + 14 * q^5 - 14 * q^7 + 20 * q^8 - 14 * q^10 + 3 * q^11 - 14 * q^13 - 21 * q^14 - 3 * q^16 + 7 * q^17 + 21 * q^19 - 14 * q^20 - 20 * q^22 - 15 * q^23 - 4 * q^25 + 28 * q^28 - 12 * q^29 + 35 * q^31 - 45 * q^32 + 70 * q^34 + 15 * q^37 + 28 * q^38 - 42 * q^40 + 42 * q^41 - 30 * q^43 + 50 * q^44 - 78 * q^46 - 21 * q^47 - 70 * q^49 - 40 * q^50 - 70 * q^52 - 11 * q^53 - 7 * q^55 + 28 * q^56 + 16 * q^58 + 28 * q^59 + 7 * q^61 + 28 * q^62 - 32 * q^64 - 14 * q^65 + 11 * q^67 - 77 * q^68 + 70 * q^70 - 19 * q^71 + 7 * q^73 - 34 * q^74 + 119 * q^76 - 7 * q^77 + 15 * q^79 - 70 * q^80 - 14 * q^82 - 26 * q^85 + 33 * q^86 - 77 * q^88 + 14 * q^89 + 84 * q^91 + 38 * q^92 + 14 * q^94 + 61 * q^95 + 161 * q^98

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