LMFDB - Embedded newform 441.2.bb.d.109.2

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			109.2
Character	$\chi$	$=$	441.109
Dual form			441.2.bb.d.352.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.168237 + 0.156102i) q^{2} +(-0.145524 + 1.94188i) q^{4} +(-0.711168 + 1.81203i) q^{5} +(-2.04196 - 1.68237i) q^{7} +(-0.564834 - 0.708279i) q^{8} +O(q^{10})$	\(q+(-0.168237 + 0.156102i) q^{2} +(-0.145524 + 1.94188i) q^{4} +(-0.711168 + 1.81203i) q^{5} +(-2.04196 - 1.68237i) q^{7} +(-0.564834 - 0.708279i) q^{8} +(-0.163215 - 0.415865i) q^{10} +(1.25783 + 0.387990i) q^{11} +(0.866993 + 3.79854i) q^{13} +(0.606156 - 0.0357152i) q^{14} +(-3.64557 - 0.549481i) q^{16} +(-5.18854 + 3.53749i) q^{17} +(-1.89946 - 3.28997i) q^{19} +(-3.41525 - 1.64470i) q^{20} +(-0.272180 + 0.131075i) q^{22} +(-3.21984 - 2.19525i) q^{23} +(0.887576 + 0.823550i) q^{25} +(-0.738819 - 0.503718i) q^{26} +(3.56413 - 3.72043i) q^{28} +(-5.98313 - 2.88132i) q^{29} +(-0.842691 + 1.45958i) q^{31} +(2.19611 - 1.49728i) q^{32} +(0.320699 - 1.40508i) q^{34} +(4.50069 - 2.50364i) q^{35} +(-0.0956045 - 1.27575i) q^{37} +(0.833130 + 0.256987i) q^{38} +(1.68511 - 0.519788i) q^{40} +(5.27874 + 6.61934i) q^{41} +(-3.86669 + 4.84868i) q^{43} +(-0.936476 + 2.38610i) q^{44} +(0.884379 - 0.133299i) q^{46} +(2.40667 - 2.23306i) q^{47} +(1.33923 + 6.87070i) q^{49} -0.277881 q^{50} +(-7.50250 + 1.13082i) q^{52} +(-0.377467 + 5.03694i) q^{53} +(-1.59758 + 2.00330i) q^{55} +(-0.0382211 + 2.39654i) q^{56} +(1.45637 - 0.449229i) q^{58} +(4.20642 + 10.7178i) q^{59} +(0.0815328 + 1.08798i) q^{61} +(-0.0860711 - 0.377102i) q^{62} +(1.50502 - 6.59391i) q^{64} +(-7.49964 - 1.13039i) q^{65} +(4.35072 - 7.53567i) q^{67} +(-6.11433 - 10.5903i) q^{68} +(-0.366362 + 1.12377i) q^{70} +(13.6653 - 6.58084i) q^{71} +(9.63581 + 8.94072i) q^{73} +(0.215231 + 0.199705i) q^{74} +(6.66516 - 3.20977i) q^{76} +(-1.91570 - 2.90841i) q^{77} +(2.17868 + 3.77359i) q^{79} +(3.58829 - 6.21510i) q^{80} +(-1.92137 - 0.289600i) q^{82} +(-2.19813 + 9.63062i) q^{83} +(-2.72010 - 11.9175i) q^{85} +(-0.106364 - 1.41933i) q^{86} +(-0.435661 - 1.11005i) q^{88} +(4.32484 - 1.33404i) q^{89} +(4.62021 - 9.21509i) q^{91} +(4.73148 - 5.93309i) q^{92} +(-0.0563074 + 0.751370i) q^{94} +(7.31236 - 1.10216i) q^{95} -14.3073 q^{97} +(-1.29783 - 0.946852i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.168237	+	0.156102i	−0.118962	+	0.110380i	−0.737411	−	0.675444i	$-0.763952\pi$
$2$	−0.168237	+	0.156102i	−0.118962	+	0.110380i	0.618449	+	0.785825i	$0.287761\pi$
$3$		0			0
$3$		0			0
$4$	−0.145524	+	1.94188i	−0.0727620	+	0.970942i
$5$	−0.711168	+	1.81203i	−0.318044	+	0.810363i	0.679043	+	0.734098i	$0.262395\pi$
$5$	−0.711168	+	1.81203i	−0.318044	+	0.810363i	−0.997088	+	0.0762653i	$0.975700\pi$
$6$		0			0
$7$	−2.04196	−	1.68237i	−0.771790	−	0.635878i
$7$	−2.04196	−	1.68237i	−0.771790	−	0.635878i
$8$	−0.564834	−	0.708279i	−0.199699	−	0.250414i
$9$		0			0
$10$	−0.163215	−	0.415865i	−0.0516132	−	0.131508i
$11$	1.25783	+	0.387990i	0.379251	+	0.116983i	0.478519	−	0.878077i	$-0.341174\pi$
$11$	1.25783	+	0.387990i	0.379251	+	0.116983i	−0.0992679	+	0.995061i	$0.531650\pi$
$12$		0			0
$13$	0.866993	+	3.79854i	0.240460	+	1.05353i	0.940599	+	0.339519i	$0.110264\pi$
$13$	0.866993	+	3.79854i	0.240460	+	1.05353i	−0.700139	+	0.714007i	$0.746878\pi$
$14$	0.606156	−	0.0357152i	0.162002	−	0.00954528i
$15$		0			0
$16$	−3.64557	−	0.549481i	−0.911392	−	0.137370i
$17$	−5.18854	+	3.53749i	−1.25841	+	0.857966i	−0.994309	−	0.106530i	$-0.966026\pi$
$17$	−5.18854	+	3.53749i	−1.25841	+	0.857966i	−0.264096	+	0.964496i	$0.585074\pi$
$18$		0			0
$19$	−1.89946	−	3.28997i	−0.435767	−	0.754771i	0.561591	−	0.827415i	$-0.310190\pi$
$19$	−1.89946	−	3.28997i	−0.435767	−	0.754771i	−0.997358	+	0.0726443i	$0.976856\pi$
$20$	−3.41525	−	1.64470i	−0.763674	−	0.367766i
$21$		0			0
$22$	−0.272180	+	0.131075i	−0.0580290	+	0.0279453i
$23$	−3.21984	−	2.19525i	−0.671383	−	0.457741i	0.179039	−	0.983842i	$-0.442701\pi$
$23$	−3.21984	−	2.19525i	−0.671383	−	0.457741i	−0.850422	+	0.526101i	$0.823653\pi$
$24$		0			0
$25$	0.887576	+	0.823550i	0.177515	+	0.164710i
$26$	−0.738819	−	0.503718i	−0.144894	−	0.0987873i
$27$		0			0
$28$	3.56413	−	3.72043i	0.673557	−	0.703095i
$29$	−5.98313	−	2.88132i	−1.11104	−	0.535048i	−0.213926	−	0.976850i	$-0.568625\pi$
$29$	−5.98313	−	2.88132i	−1.11104	−	0.535048i	−0.897113	+	0.441801i	$0.854340\pi$
$30$		0			0
$31$	−0.842691	+	1.45958i	−0.151352	+	0.262149i	−0.931725	−	0.363165i	$-0.881696\pi$
$31$	−0.842691	+	1.45958i	−0.151352	+	0.262149i	0.780373	+	0.625314i	$0.215029\pi$
$32$	2.19611	−	1.49728i	0.388222	−	0.264685i
$33$		0			0
$34$	0.320699	−	1.40508i	0.0549995	−	0.240969i
$35$	4.50069	−	2.50364i	0.760755	−	0.423193i
$36$		0			0
$37$	−0.0956045	−	1.27575i	−0.0157173	−	0.209733i	−0.999533	−	0.0305506i	$-0.990274\pi$
$37$	−0.0956045	−	1.27575i	−0.0157173	−	0.209733i	0.983816	−	0.179182i	$-0.0573451\pi$
$38$	0.833130	+	0.256987i	0.135152	+	0.0416887i
$39$		0			0
$40$	1.68511	−	0.519788i	0.266440	−	0.0821858i
$41$	5.27874	+	6.61934i	0.824401	+	1.03377i	0.998794	+	0.0490905i	$0.0156323\pi$
$41$	5.27874	+	6.61934i	0.824401	+	1.03377i	−0.174393	+	0.984676i	$0.555796\pi$
$42$		0			0
$43$	−3.86669	+	4.84868i	−0.589665	+	0.739417i	−0.983728	−	0.179667i	$-0.942498\pi$
$43$	−3.86669	+	4.84868i	−0.589665	+	0.739417i	0.394062	+	0.919084i	$0.371069\pi$
$44$	−0.936476	+	2.38610i	−0.141179	+	0.359718i
$45$		0			0
$46$	0.884379	−	0.133299i	0.130395	−	0.0196538i
$47$	2.40667	−	2.23306i	0.351049	−	0.325726i	−0.484862	−	0.874591i	$-0.661130\pi$
$47$	2.40667	−	2.23306i	0.351049	−	0.325726i	0.835911	+	0.548865i	$0.184940\pi$
$48$		0			0
$49$	1.33923	+	6.87070i	0.191319	+	0.981528i
$50$	−0.277881			−0.0392983
$51$		0			0
$52$	−7.50250	+	1.13082i	−1.04041	+	0.156816i
$53$	−0.377467	+	5.03694i	−0.0518490	+	0.691877i	0.909352	+	0.416028i	$0.136578\pi$
$53$	−0.377467	+	5.03694i	−0.0518490	+	0.691877i	−0.961201	+	0.275849i	$0.911041\pi$
$54$		0			0
$55$	−1.59758	+	2.00330i	−0.215418	+	0.270125i
$56$	−0.0382211	+	2.39654i	−0.00510751	+	0.320251i
$57$		0			0
$58$	1.45637	−	0.449229i	0.191230	−	0.0589867i
$59$	4.20642	+	10.7178i	0.547629	+	1.39534i	0.890082	+	0.455801i	$0.150647\pi$
$59$	4.20642	+	10.7178i	0.547629	+	1.39534i	−0.342453	+	0.939535i	$0.611258\pi$
$60$		0			0
$61$	0.0815328	+	1.08798i	0.0104392	+	0.139302i	0.999988	−	0.00489682i	$-0.00155871\pi$
$61$	0.0815328	+	1.08798i	0.0104392	+	0.139302i	−0.989549	+	0.144198i	$0.953940\pi$
$62$	−0.0860711	−	0.377102i	−0.0109310	−	0.0478920i
$63$		0			0
$64$	1.50502	−	6.59391i	0.188127	−	0.824238i
$65$	−7.49964	−	1.13039i	−0.930216	−	0.140208i
$66$		0			0
$67$	4.35072	−	7.53567i	0.531525	−	0.920629i	−0.467798	−	0.883836i	$-0.654952\pi$
$67$	4.35072	−	7.53567i	0.531525	−	0.920629i	0.999323	−	0.0367931i	$-0.0117142\pi$
$68$	−6.11433	−	10.5903i	−0.741471	−	1.28427i
$69$		0			0
$70$	−0.366362	+	1.12377i	−0.0437886	+	0.134316i
$71$	13.6653	−	6.58084i	1.62177	−	0.781002i	0.621770	−	0.783200i	$-0.286414\pi$
$71$	13.6653	−	6.58084i	1.62177	−	0.781002i	0.999998	+	0.00219731i	$0.000699426\pi$
$72$		0			0
$73$	9.63581	+	8.94072i	1.12779	+	1.04643i	0.998496	+	0.0548258i	$0.0174604\pi$
$73$	9.63581	+	8.94072i	1.12779	+	1.04643i	0.129290	+	0.991607i	$0.458730\pi$
$74$	0.215231	+	0.199705i	0.0250201	+	0.0232153i
$75$		0			0
$76$	6.66516	−	3.20977i	0.764546	−	0.368186i
$77$	−1.91570	−	2.90841i	−0.218315	−	0.331444i
$78$		0			0
$79$	2.17868	+	3.77359i	0.245121	+	0.424562i	0.962166	−	0.272466i	$-0.0878391\pi$
$79$	2.17868	+	3.77359i	0.245121	+	0.424562i	−0.717045	+	0.697027i	$0.754506\pi$
$80$	3.58829	−	6.21510i	0.401183	−	0.694869i
$81$		0			0
$82$	−1.92137	−	0.289600i	−0.212180	−	0.0319810i
$83$	−2.19813	+	9.63062i	−0.241276	+	1.05710i	0.698582	+	0.715530i	$0.253815\pi$
$83$	−2.19813	+	9.63062i	−0.241276	+	1.05710i	−0.939857	+	0.341567i	$0.889042\pi$
$84$		0			0
$85$	−2.72010	−	11.9175i	−0.295036	−	1.29264i
$86$	−0.106364	−	1.41933i	−0.0114695	−	0.153050i
$87$		0			0
$88$	−0.435661	−	1.11005i	−0.0464416	−	0.118331i
$89$	4.32484	−	1.33404i	0.458432	−	0.141408i	−0.0569335	−	0.998378i	$-0.518132\pi$
$89$	4.32484	−	1.33404i	0.458432	−	0.141408i	0.515366	+	0.856970i	$0.327656\pi$
$90$		0			0
$91$	4.62021	−	9.21509i	0.484329	−	0.966004i
$92$	4.73148	−	5.93309i	0.493291	−	0.618567i
$93$		0			0
$94$	−0.0563074	+	0.751370i	−0.00580766	+	0.0774979i
$95$	7.31236	−	1.10216i	0.750232	−	0.113079i
$96$		0			0
$97$	−14.3073			−1.45268			−0.726341	−	0.687335i	$-0.758781\pi$
$97$	−14.3073			−1.45268			−0.726341	+	0.687335i	$0.758781\pi$
$98$	−1.29783	−	0.946852i	−0.131101	−	0.0956465i
$99$		0			0
$100$	−1.72840	+	1.60372i	−0.172840	+	0.160372i
$101$	13.3675	−	2.01483i	1.33012	−	0.200483i	0.554764	−	0.832008i	$-0.312809\pi$
$101$	13.3675	−	2.01483i	1.33012	−	0.200483i	0.775356	+	0.631525i	$0.217571\pi$
$102$		0			0
$103$	−1.99420	+	5.08114i	−0.196495	+	0.500660i	−0.994830	−	0.101553i	$-0.967619\pi$
$103$	−1.99420	+	5.08114i	−0.196495	+	0.500660i	0.798336	+	0.602213i	$0.205714\pi$
$104$	2.20072	−	2.75962i	0.215798	−	0.270603i
$105$		0			0
$106$	−0.722770	−	0.906325i	−0.0702016	−	0.0880301i
$107$	−10.8967	+	3.36120i	−1.05343	+	0.324940i	−0.772649	−	0.634833i	$-0.781069\pi$
$107$	−10.8967	+	3.36120i	−1.05343	+	0.324940i	−0.280779	+	0.959773i	$0.590593\pi$
$108$		0			0
$109$	1.97231	+	0.608377i	0.188913	+	0.0582720i	0.387768	−	0.921757i	$-0.373246\pi$
$109$	1.97231	+	0.608377i	0.188913	+	0.0582720i	−0.198855	+	0.980029i	$0.563722\pi$
$110$	−0.0439457	−	0.586415i	−0.00419006	−	0.0559125i
$111$		0			0
$112$	6.51968	+	7.25523i	0.616052	+	0.685555i
$113$	−0.00426021	+	0.0186652i	−0.000400767	+	0.00175587i	−0.975128	−	0.221643i	$-0.928858\pi$
$113$	−0.00426021	+	0.0186652i	−0.000400767	+	0.00175587i	0.974727	+	0.223399i	$0.0717152\pi$
$114$		0			0
$115$	6.26770	−	4.27324i	0.584466	−	0.398482i
$116$	6.46588	−	11.1992i	0.600342	−	1.03982i
$117$		0			0
$118$	−2.38074	−	1.14650i	−0.219165	−	0.105544i
$119$	16.5462	+	1.50565i	1.51679	+	0.138023i
$120$		0			0
$121$	−7.65702	−	5.22047i	−0.696093	−	0.474588i
$122$	−0.183552	−	0.170312i	−0.0166180	−	0.0154193i
$123$		0			0
$124$	−2.71171	−	1.84881i	−0.243519	−	0.166028i
$125$	−10.8926	+	5.24559i	−0.974263	+	0.469180i
$126$		0			0
$127$	15.3988	+	7.41569i	1.36643	+	0.658036i	0.966060	−	0.258319i	$-0.0831687\pi$
$127$	15.3988	+	7.41569i	1.36643	+	0.658036i	0.400366	+	0.916355i	$0.368883\pi$
$128$	3.43408	+	5.94801i	0.303533	+	0.525734i
$129$		0			0
$130$	1.43818	−	0.980532i	0.126136	−	0.0859983i
$131$	−14.9770	−	2.25742i	−1.30854	−	0.197231i	−0.542520	−	0.840043i	$-0.682530\pi$
$131$	−14.9770	−	2.25742i	−1.30854	−	0.197231i	−0.766024	+	0.642811i	$0.777768\pi$
$132$		0			0
$133$	−1.65632	+	9.91361i	−0.143622	+	0.859619i
$134$	0.444375	+	1.94694i	0.0383882	+	0.168190i
$135$		0			0
$136$	5.43619	+	1.67684i	0.466149	+	0.143788i
$137$	−1.24597	−	3.17467i	−0.106450	−	0.271231i	0.867717	−	0.497059i	$-0.165587\pi$
$137$	−1.24597	−	3.17467i	−0.106450	−	0.271231i	−0.974167	+	0.225828i	$0.927491\pi$
$138$		0			0
$139$	3.54216	+	4.44173i	0.300442	+	0.376743i	0.909021	−	0.416751i	$-0.136831\pi$
$139$	3.54216	+	4.44173i	0.300442	+	0.376743i	−0.608578	+	0.793494i	$0.708260\pi$
$140$	4.20682	+	9.10415i	0.355541	+	0.769442i
$141$		0			0
$142$	−1.27173	+	3.24031i	−0.106721	+	0.271921i
$143$	−0.383265	+	5.11431i	−0.0320502	+	0.427680i
$144$		0			0
$145$	9.47605	−	8.79249i	0.786943	−	0.730177i
$146$	−3.01676			−0.249669
$147$		0			0
$148$	2.49128			0.204782
$149$	4.62518	−	4.29154i	0.378910	−	0.351577i	−0.467609	−	0.883935i	$-0.654885\pi$
$149$	4.62518	−	4.29154i	0.378910	−	0.351577i	0.846519	+	0.532358i	$0.178694\pi$
$150$		0			0
$151$	−0.503039	+	6.71259i	−0.0409367	+	0.546263i	0.938601	+	0.345004i	$0.112122\pi$
$151$	−0.503039	+	6.71259i	−0.0409367	+	0.546263i	−0.979538	+	0.201259i	$0.935497\pi$
$152$	−1.25733	+	3.20364i	−0.101983	+	0.259849i
$153$		0			0
$154$	0.776300	+	0.190259i	0.0625560	+	0.0153315i
$155$	−2.04551	−	2.56499i	−0.164299	−	0.206025i
$156$		0			0
$157$	−4.18388	−	10.6603i	−0.333910	−	0.850788i	−0.994944	−	0.100432i	$-0.967977\pi$
$157$	−4.18388	−	10.6603i	−0.333910	−	0.850788i	0.661034	−	0.750356i	$-0.270118\pi$
$158$	−0.955598	−	0.294763i	−0.0760233	−	0.0234501i
$159$		0			0
$160$	1.15131	+	5.04424i	0.0910194	+	0.398782i
$161$	2.88156	+	9.89959i	0.227099	+	0.780197i
$162$		0			0
$163$	−5.01630	−	0.756086i	−0.392907	−	0.0592212i	−0.0503824	−	0.998730i	$-0.516044\pi$
$163$	−5.01630	−	0.756086i	−0.392907	−	0.0592212i	−0.342525	+	0.939509i	$0.611282\pi$
$164$	−13.6222	+	9.28743i	−1.06371	+	0.725227i
$165$		0			0
$166$	−1.13355	−	1.96336i	−0.0879803	−	0.152386i
$167$	−14.7880	−	7.12153i	−1.14433	−	0.551080i	−0.237004	−	0.971509i	$-0.576166\pi$
$167$	−14.7880	−	7.12153i	−1.14433	−	0.551080i	−0.907326	+	0.420428i	$0.861880\pi$
$168$		0			0
$169$	−1.96466	+	0.946128i	−0.151127	+	0.0727791i
$170$	2.31797	+	1.58036i	0.177780	+	0.121208i
$171$		0			0
$172$	−8.85288	−	8.21427i	−0.675026	−	0.626332i
$173$	5.63684	+	3.84313i	0.428561	+	0.292188i	0.758327	−	0.651875i	$-0.226017\pi$
$173$	5.63684	+	3.84313i	0.428561	+	0.292188i	−0.329765	+	0.944063i	$0.606970\pi$
$174$		0			0
$175$	−0.426877	−	3.17489i	−0.0322689	−	0.239999i
$176$	−4.37232	−	2.10560i	−0.329576	−	0.158715i
$177$		0			0
$178$	−0.519355	+	0.899549i	−0.0389273	+	0.0674241i
$179$	13.9861	−	9.53556i	1.04537	−	0.712721i	0.0864092	−	0.996260i	$-0.472461\pi$
$179$	13.9861	−	9.53556i	1.04537	−	0.712721i	0.958961	+	0.283538i	$0.0915084\pi$
$180$		0			0
$181$	−1.35044	+	5.91666i	−0.100377	+	0.439782i	0.899618	+	0.436678i	$0.143845\pi$
$181$	−1.35044	+	5.91666i	−0.100377	+	0.439782i	−0.999995	+	0.00310385i	$0.999012\pi$
$182$	0.661198	+	2.27154i	0.0490113	+	0.168378i
$183$		0			0
$184$	0.263825	+	3.52049i	0.0194494	+	0.259534i
$185$	2.37969	+	0.734038i	0.174958	+	0.0539675i
$186$		0			0
$187$	−7.89882	+	2.43646i	−0.577619	+	0.178172i
$188$	3.98612	+	4.99844i	0.290718	+	0.364548i
$189$		0			0
$190$	−1.05816	+	1.32689i	−0.0767672	+	0.0962630i
$191$	4.16507	−	10.6124i	0.301374	−	0.767888i	−0.697318	−	0.716762i	$-0.745624\pi$
$191$	4.16507	−	10.6124i	0.301374	−	0.767888i	0.998692	−	0.0511266i	$-0.0162812\pi$
$192$		0			0
$193$	−4.78868	+	0.721778i	−0.344697	+	0.0519547i	−0.319109	−	0.947718i	$-0.603384\pi$
$193$	−4.78868	+	0.721778i	−0.344697	+	0.0519547i	−0.0255875	+	0.999673i	$0.508146\pi$
$194$	2.40702	−	2.23338i	0.172814	−	0.160348i
$195$		0			0
$196$	−13.5370	+	1.60078i	−0.966927	+	0.114341i
$197$	−11.7220			−0.835157			−0.417579	−	0.908641i	$-0.637121\pi$
$197$	−11.7220			−0.835157			−0.417579	+	0.908641i	$0.637121\pi$
$198$		0			0
$199$	10.5322	−	1.58747i	0.746607	−	0.112533i	0.235290	−	0.971925i	$-0.424396\pi$
$199$	10.5322	−	1.58747i	0.746607	−	0.112533i	0.511317	+	0.859392i	$0.329158\pi$
$200$	0.0819705	−	1.09382i	0.00579619	−	0.0773447i
$201$		0			0
$202$	−1.93440	+	2.42566i	−0.136104	+	0.170669i
$203$	7.36987	+	15.9494i	0.517263	+	1.11943i
$204$		0			0
$205$	−15.7485	+	4.85777i	−1.09992	+	0.339281i
$206$	−0.457675	−	1.16614i	−0.0318877	−	0.0812486i
$207$		0			0
$208$	−1.07345	−	14.3242i	−0.0744306	−	0.993207i
$209$	−1.11273	−	4.87520i	−0.0769694	−	0.337225i
$210$		0			0
$211$	2.67928	−	11.7387i	0.184449	−	0.808124i	−0.795029	−	0.606572i	$-0.792544\pi$
$211$	2.67928	−	11.7387i	0.184449	−	0.808124i	0.979478	−	0.201552i	$-0.0645985\pi$
$212$	−9.72622	−	1.46599i	−0.668000	−	0.100685i
$213$		0			0
$214$	1.30855	−	2.26648i	0.0894508	−	0.154933i
$215$	−6.03607	−	10.4548i	−0.411657	−	0.713011i
$216$		0			0
$217$	4.17631	−	1.56269i	0.283507	−	0.106083i
$218$	−0.426785	+	0.205529i	−0.0289055	+	0.0139202i
$219$		0			0
$220$	−3.65769	−	3.39384i	−0.246601	−	0.228813i
$221$	−17.9357	−	16.6419i	−1.20649	−	1.11946i
$222$		0			0
$223$	1.47211	−	0.708933i	0.0985801	−	0.0474737i	−0.383944	−	0.923356i	$-0.625434\pi$
$223$	1.47211	−	0.708933i	0.0985801	−	0.0474737i	0.482524	+	0.875883i	$0.339720\pi$
$224$	−7.00338	−	0.637285i	−0.467933	−	0.0425804i
$225$		0			0
$226$	−0.00219694	−	0.00380521i	−0.000146138	−	0.000253119i
$227$	−4.74247	+	8.21419i	−0.314769	+	0.545195i	−0.979388	−	0.201987i	$-0.935260\pi$
$227$	−4.74247	+	8.21419i	−0.314769	+	0.545195i	0.664620	+	0.747182i	$0.268594\pi$
$228$		0			0
$229$	−9.75976	−	1.47105i	−0.644943	−	0.0972095i	−0.181577	−	0.983377i	$-0.558120\pi$
$229$	−9.75976	−	1.47105i	−0.644943	−	0.0972095i	−0.463366	+	0.886167i	$0.653358\pi$
$230$	−0.387401	+	1.69732i	−0.0255445	+	0.111918i
$231$		0			0
$232$	1.33869	+	5.86519i	0.0878894	+	0.385069i
$233$	0.943100	+	12.5848i	0.0617845	+	0.824457i	0.938903	+	0.344183i	$0.111844\pi$
$233$	0.943100	+	12.5848i	0.0617845	+	0.824457i	−0.877118	+	0.480275i	$0.840537\pi$
$234$		0			0
$235$	2.33483	+	5.94904i	0.152307	+	0.388072i
$236$	−21.4248	+	6.60868i	−1.39464	+	0.430188i
$237$		0			0
$238$	−3.01872	+	2.32958i	−0.195675	+	0.151004i
$239$	2.61540	−	3.27961i	0.169176	−	0.212140i	−0.690015	−	0.723795i	$-0.742396\pi$
$239$	2.61540	−	3.27961i	0.169176	−	0.212140i	0.859191	+	0.511655i	$0.170967\pi$
$240$		0			0
$241$	−1.94139	+	25.9060i	−0.125056	+	1.66875i	0.483577	+	0.875302i	$0.339337\pi$
$241$	−1.94139	+	25.9060i	−0.125056	+	1.66875i	−0.608633	+	0.793452i	$0.708282\pi$
$242$	2.10312	−	0.316994i	0.135194	−	0.0203772i
$243$		0			0
$244$	−2.12459			−0.136013
$245$	−13.4023	−	2.45950i	−0.856242	−	0.157132i
$246$		0			0
$247$	10.8503	−	10.0676i	0.690386	−	0.640585i
$248$	1.50977	−	0.227562i	0.0958707	−	0.0144502i
$249$		0			0
$250$	1.01370	−	2.58285i	0.0641117	−	0.163354i
$251$	−18.6534	+	23.3906i	−1.17739	+	1.47640i	−0.331166	+	0.943572i	$0.607442\pi$
$251$	−18.6534	+	23.3906i	−1.17739	+	1.47640i	−0.846224	+	0.532828i	$0.821129\pi$
$252$		0			0
$253$	−3.19828	−	4.01052i	−0.201074	−	0.252139i
$254$	−3.74826	+	1.15619i	−0.235187	+	0.0725455i
$255$		0			0
$256$	11.4198	+	3.52253i	0.713735	+	0.220158i
$257$	−0.637170	−	8.50244i	−0.0397456	−	0.530368i	−0.981170	−	0.193145i	$-0.938131\pi$
$257$	−0.637170	−	8.50244i	−0.0397456	−	0.530368i	0.941425	−	0.337223i	$-0.109488\pi$
$258$		0			0
$259$	−1.95107	+	2.76588i	−0.121234	+	0.171864i
$260$	3.28646	−	14.3989i	0.203818	−	0.892984i
$261$		0			0
$262$	2.87207	−	1.95815i	0.177437	−	0.120975i
$263$	−3.33908	+	5.78346i	−0.205897	+	0.356623i	−0.950418	−	0.310975i	$-0.899344\pi$
$263$	−3.33908	+	5.78346i	−0.205897	+	0.356623i	0.744521	+	0.667599i	$0.232678\pi$
$264$		0			0
$265$	−8.85864	−	4.26609i	−0.544182	−	0.262064i
$266$	−1.26887	−	1.92639i	−0.0777996	−	0.118115i
$267$		0			0
$268$	14.0003	+	9.54521i	0.855202	+	0.583067i
$269$	7.44514	+	6.90808i	0.453938	+	0.421193i	0.873718	−	0.486433i	$-0.161702\pi$
$269$	7.44514	+	6.90808i	0.453938	+	0.421193i	−0.419780	+	0.907626i	$0.637893\pi$
$270$		0			0
$271$	17.2798	+	11.7812i	1.04967	+	0.715656i	0.959910	−	0.280307i	$-0.0904362\pi$
$271$	17.2798	+	11.7812i	1.04967	+	0.715656i	0.0897645	+	0.995963i	$0.471389\pi$
$272$	20.8589	−	10.0451i	1.26476	−	0.609076i
$273$		0			0
$274$	0.705190	+	0.339602i	0.0426021	+	0.0205161i
$275$	0.796892	+	1.38026i	0.0480544	+	0.0832327i
$276$		0			0
$277$	5.47510	−	3.73286i	0.328967	−	0.224286i	−0.387561	−	0.921844i	$-0.626682\pi$
$277$	5.47510	−	3.73286i	0.328967	−	0.224286i	0.716528	+	0.697558i	$0.245730\pi$
$278$	−1.28929	−	0.194328i	−0.0773262	−	0.0116550i
$279$		0			0
$280$	−4.31542	−	1.77360i	−0.257896	−	0.105993i
$281$	2.52879	+	11.0793i	0.150855	+	0.660939i	0.992638	+	0.121122i	$0.0386492\pi$
$281$	2.52879	+	11.0793i	0.150855	+	0.660939i	−0.841783	+	0.539816i	$0.818494\pi$
$282$		0			0
$283$	−22.7664	−	7.02250i	−1.35332	−	0.417445i	−0.468537	−	0.883444i	$-0.655219\pi$
$283$	−22.7664	−	7.02250i	−1.35332	−	0.417445i	−0.884785	+	0.465999i	$0.845695\pi$
$284$	10.7906	+	27.4940i	0.640305	+	1.63147i
$285$		0			0
$286$	−0.733873	−	0.920247i	−0.0433948	−	0.0544154i
$287$	0.357202	−	22.3973i	0.0210849	−	1.32207i
$288$		0			0
$289$	8.19633	−	20.8839i	0.482137	−	1.22847i
$290$	−0.221705	+	2.95845i	−0.0130190	+	0.173726i
$291$		0			0
$292$	−18.7641	+	17.4105i	−1.09809	+	1.01887i
$293$	−2.59574			−0.151645			−0.0758224	−	0.997121i	$-0.524158\pi$
$293$	−2.59574			−0.151645			−0.0758224	+	0.997121i	$0.524158\pi$
$294$		0			0
$295$	−22.4124			−1.30490
$296$	−0.849589	+	0.788303i	−0.0493813	+	0.0458192i
$297$		0			0
$298$	−0.108213	+	1.44400i	−0.00626858	+	0.0836484i
$299$	5.54717	−	14.1340i	0.320801	−	0.817388i
$300$		0			0
$301$	16.0529	−	3.39560i	0.925277	−	0.195719i
$302$	−0.963215	−	1.20783i	−0.0554268	−	0.0695030i
$303$		0			0
$304$	5.11685	+	13.0375i	0.293472	+	0.747753i
$305$	−2.02943	−	0.625997i	−0.116205	−	0.0358445i
$306$		0			0
$307$	−0.00518329	−	0.0227095i	−0.000295826	−	0.00129610i	0.974780	−	0.223169i	$-0.0716402\pi$
$307$	−0.00518329	−	0.0227095i	−0.000295826	−	0.00129610i	−0.975076	+	0.221873i	$0.928783\pi$
$308$	5.92657	−	3.29683i	0.337698	−	0.187854i
$309$		0			0
$310$	0.744530	+	0.112220i	0.0422865	+	0.00637366i
$311$	16.5378	−	11.2753i	0.937775	−	0.639364i	0.00506329	−	0.999987i	$-0.498388\pi$
$311$	16.5378	−	11.2753i	0.937775	−	0.639364i	0.932712	+	0.360623i	$0.117436\pi$
$312$		0			0
$313$	−7.23514	−	12.5316i	−0.408954	−	0.708330i	0.585818	−	0.810442i	$-0.300773\pi$
$313$	−7.23514	−	12.5316i	−0.408954	−	0.708330i	−0.994773	+	0.102113i	$0.967440\pi$
$314$	2.36798	+	1.14036i	0.133633	+	0.0643542i
$315$		0			0
$316$	−7.64491	+	3.68160i	−0.430060	+	0.207106i
$317$	−12.7939	−	8.72272i	−0.718576	−	0.489916i	0.147984	−	0.988990i	$-0.452721\pi$
$317$	−12.7939	−	8.72272i	−0.718576	−	0.489916i	−0.866560	+	0.499073i	$0.833674\pi$
$318$		0			0
$319$	−6.40785	−	5.94562i	−0.358771	−	0.332891i
$320$	10.8780	+	7.41651i	0.608100	+	0.414595i
$321$		0			0
$322$	−2.03013	−	1.21567i	−0.113135	−	0.0677464i
$323$	21.4937	+	10.3508i	1.19594	+	0.575934i
$324$		0			0
$325$	−2.35877	+	4.08551i	−0.130841	+	0.226623i
$326$	0.961956	−	0.655851i	0.0532778	−	0.0363242i
$327$		0			0
$328$	1.70672	−	7.47765i	0.0942381	−	0.412884i
$329$	−8.67118	+	0.510913i	−0.478058	+	0.0281675i
$330$		0			0
$331$	1.02847	+	13.7240i	0.0565298	+	0.754338i	0.951389	+	0.307990i	$0.0996564\pi$
$331$	1.02847	+	13.7240i	0.0565298	+	0.754338i	−0.894860	+	0.446348i	$0.852725\pi$
$332$	−18.3817	−	5.66999i	−1.00882	−	0.311181i
$333$		0			0
$334$	3.59958	−	1.11032i	0.196960	−	0.0607541i
$335$	10.5607	+	13.2428i	0.576995	+	0.723529i
$336$		0			0
$337$	5.89602	−	7.39337i	0.321177	−	0.402743i	−0.594865	−	0.803825i	$-0.702795\pi$
$337$	5.89602	−	7.39337i	0.321177	−	0.402743i	0.916042	+	0.401083i	$0.131366\pi$
$338$	0.182836	−	0.465860i	0.00994499	−	0.0253394i
$339$		0			0
$340$	23.5383	−	3.54783i	1.27654	−	0.192408i
$341$	−1.62627	+	1.50896i	−0.0880674	+	0.0817146i
$342$		0			0
$343$	8.82443	−	16.2828i	0.476474	−	0.879188i
$344$	5.61826			0.302916
$345$		0			0
$346$	−1.54825	+	0.233361i	−0.0832343	+	0.0125455i
$347$	−1.19348	+	15.9259i	−0.0640696	+	0.854949i	0.868899	+	0.494990i	$0.164828\pi$
$347$	−1.19348	+	15.9259i	−0.0640696	+	0.854949i	−0.932968	+	0.359959i	$0.882791\pi$
$348$		0			0
$349$	3.48773	−	4.37347i	0.186694	−	0.234107i	−0.679673	−	0.733516i	$-0.737878\pi$
$349$	3.48773	−	4.37347i	0.186694	−	0.234107i	0.866366	+	0.499409i	$0.166450\pi$
$350$	0.567422	+	0.467500i	0.0303300	+	0.0249889i
$351$		0			0
$352$	3.34327	−	1.03126i	0.178197	−	0.0549665i
$353$	−5.94999	−	15.1603i	−0.316686	−	0.806903i	−0.997243	−	0.0742075i	$-0.976357\pi$
$353$	−5.94999	−	15.1603i	−0.316686	−	0.806903i	0.680557	−	0.732695i	$-0.261738\pi$
$354$		0			0
$355$	2.20637	+	29.4419i	0.117102	+	1.56261i
$356$	1.96118	+	8.59247i	0.103942	+	0.455400i
$357$		0			0
$358$	−0.864470	+	3.78749i	−0.0456886	+	0.200175i
$359$	−13.8398	−	2.08601i	−0.730435	−	0.110095i	−0.226713	−	0.973962i	$-0.572798\pi$
$359$	−13.8398	−	2.08601i	−0.730435	−	0.110095i	−0.503721	+	0.863866i	$0.668036\pi$
$360$		0			0
$361$	2.28407	−	3.95612i	0.120214	−	0.208217i
$362$	−0.696405	−	1.20621i	−0.0366023	−	0.0633970i
$363$		0			0
$364$	17.2223	+	10.3129i	0.902693	+	0.540544i
$365$	−23.0535	+	11.1020i	−1.20668	+	0.581105i
$366$		0			0
$367$	−8.30654	−	7.70735i	−0.433598	−	0.402320i	0.432947	−	0.901420i	$-0.357474\pi$
$367$	−8.30654	−	7.70735i	−0.433598	−	0.402320i	−0.866545	+	0.499099i	$0.833664\pi$
$368$	10.5319	+	9.77217i	0.549013	+	0.509409i
$369$		0			0
$370$	−0.514938	+	0.247981i	−0.0267703	+	0.0128919i
$371$	9.24480	−	9.65021i	0.479966	−	0.501014i
$372$		0			0
$373$	1.76713	+	3.06075i	0.0914983	+	0.158480i	0.908142	−	0.418663i	$-0.137501\pi$
$373$	1.76713	+	3.06075i	0.0914983	+	0.158480i	−0.816643	+	0.577143i	$0.804168\pi$
$374$	0.948542	−	1.64292i	0.0490479	−	0.0849535i
$375$		0			0
$376$	−2.94100	−	0.443284i	−0.151670	−	0.0228606i
$377$	5.75750	−	25.2253i	0.296526	−	1.29917i
$378$		0			0
$379$	5.25920	+	23.0421i	0.270147	+	1.18359i	0.909840	+	0.414960i	$0.136204\pi$
$379$	5.25920	+	23.0421i	0.270147	+	1.18359i	−0.639693	+	0.768631i	$0.720938\pi$
$380$	1.07614	+	14.3601i	0.0552050	+	0.736659i
$381$		0			0
$382$	0.955895	+	2.43558i	0.0489079	+	0.124615i
$383$	22.9217	−	7.07042i	1.17125	−	0.361282i	0.352708	−	0.935733i	$-0.385261\pi$
$383$	22.9217	−	7.07042i	1.17125	−	0.361282i	0.818539	+	0.574452i	$0.194785\pi$
$384$		0			0
$385$	6.63250	−	1.40294i	0.338024	−	0.0715005i
$386$	0.692965	−	0.868951i	0.0352710	−	0.0442284i
$387$		0			0
$388$	2.08205	−	27.7830i	0.105700	−	1.41047i
$389$	4.65716	−	0.701954i	0.236127	−	0.0355905i	−0.0299124	−	0.999553i	$-0.509523\pi$
$389$	4.65716	−	0.701954i	0.236127	−	0.0355905i	0.266040	+	0.963962i	$0.414285\pi$
$390$		0			0
$391$	24.4719			1.23760
$392$	4.10993	−	4.82935i	0.207583	−	0.243919i
$393$		0			0
$394$	1.97208	−	1.82982i	0.0993518	−	0.0921850i
$395$	−8.38725	+	1.26417i	−0.422008	+	0.0636075i
$396$		0			0
$397$	7.90786	−	20.1489i	0.396884	−	1.01124i	−0.583141	−	0.812371i	$-0.698176\pi$
$397$	7.90786	−	20.1489i	0.396884	−	1.01124i	0.980025	−	0.198873i	$-0.0637283\pi$
$398$	−1.52410	+	1.91116i	−0.0763963	+	0.0957980i
$399$		0			0
$400$	−2.78319	−	3.49001i	−0.139160	−	0.174501i
$401$	3.51903	−	1.08548i	0.175732	−	0.0542061i	−0.205641	−	0.978628i	$-0.565928\pi$
$401$	3.51903	−	1.08548i	0.175732	−	0.0542061i	0.381372	+	0.924422i	$0.375452\pi$
$402$		0			0
$403$	−6.27490	−	1.93555i	−0.312575	−	0.0964166i
$404$	1.96727	+	26.2514i	0.0978754	+	1.30606i
$405$		0			0
$406$	−3.72962	−	1.53284i	−0.185098	−	0.0760737i
$407$	0.374725	−	1.64178i	0.0185744	−	0.0813799i
$408$		0			0
$409$	−25.6939	+	17.5178i	−1.27048	+	0.866200i	−0.995455	−	0.0952366i	$-0.969639\pi$
$409$	−25.6939	+	17.5178i	−1.27048	+	0.866200i	−0.275027	+	0.961436i	$0.588687\pi$
$410$	1.89118	−	3.27562i	0.0933988	−	0.161771i
$411$		0			0
$412$	−9.57678	−	4.61194i	−0.471814	−	0.227214i
$413$	9.44197	−	28.9621i	0.464609	−	1.42513i
$414$		0			0
$415$	−15.8877	−	10.8321i	−0.779897	−	0.531725i
$416$	7.59151	+	7.04389i	0.372204	+	0.345355i
$417$		0			0
$418$	0.948230	+	0.646492i	0.0463795	+	0.0316210i
$419$	29.2143	−	14.0689i	1.42721	−	0.687309i	0.448736	−	0.893665i	$-0.351875\pi$
$419$	29.2143	−	14.0689i	1.42721	−	0.687309i	0.978477	+	0.206355i	$0.0661602\pi$
$420$		0			0
$421$	−23.6529	−	11.3906i	−1.15277	−	0.555144i	−0.242905	−	0.970050i	$-0.578100\pi$
$421$	−23.6529	−	11.3906i	−1.15277	−	0.555144i	−0.909864	+	0.414906i	$0.863815\pi$
$422$	1.38167	+	2.39312i	0.0672587	+	0.116495i
$423$		0			0
$424$	3.78077	−	2.57768i	0.183610	−	0.125183i
$425$	−7.51852	−	1.13323i	−0.364702	−	0.0549699i
$426$		0			0
$427$	1.66390	−	2.35878i	0.0805219	−	0.114150i
$428$	−4.94132	−	21.6493i	−0.238848	−	1.04646i
$429$		0			0
$430$	2.64750	+	0.816646i	0.127674	+	0.0393822i
$431$	−10.2055	−	26.0032i	−0.491582	−	1.25253i	−0.934498	−	0.355968i	$-0.884151\pi$
$431$	−10.2055	−	26.0032i	−0.491582	−	1.25253i	0.442916	−	0.896563i	$-0.353944\pi$
$432$		0			0
$433$	15.9326	+	19.9788i	0.765670	+	0.960119i	0.999927	−	0.0120552i	$-0.00383737\pi$
$433$	15.9326	+	19.9788i	0.765670	+	0.960119i	−0.234258	+	0.972175i	$0.575266\pi$
$434$	−0.458673	+	0.914832i	−0.0220170	+	0.0439134i
$435$		0			0
$436$	−1.46842	+	3.74146i	−0.0703244	+	0.179184i
$437$	−1.10633	+	14.7630i	−0.0529230	+	0.706208i
$438$		0			0
$439$	12.0745	−	11.2035i	0.576286	−	0.534715i	−0.337281	−	0.941404i	$-0.609507\pi$
$439$	12.0745	−	11.2035i	0.576286	−	0.534715i	0.913567	+	0.406689i	$0.133317\pi$
$440$	2.32126			0.110662
$441$		0			0
$442$	5.61529			0.267092
$443$	21.0708	−	19.5508i	1.00110	−	0.928889i	0.00363528	−	0.999993i	$-0.498843\pi$
$443$	21.0708	−	19.5508i	1.00110	−	0.928889i	0.997469	+	0.0711045i	$0.0226524\pi$
$444$		0			0
$445$	−0.658379	+	8.78546i	−0.0312102	+	0.416471i
$446$	−0.136999	+	0.349068i	−0.00648710	+	0.0165289i
$447$		0			0
$448$	−14.1666	+	10.9325i	−0.669309	+	0.516513i
$449$	−4.18327	−	5.24565i	−0.197421	−	0.247558i	0.673261	−	0.739405i	$-0.264893\pi$
$449$	−4.18327	−	5.24565i	−0.197421	−	0.247558i	−0.870681	+	0.491848i	$0.836322\pi$
$450$		0			0
$451$	4.07154	+	10.3741i	0.191721	+	0.488498i
$452$	−0.0356257	−	0.0109891i	−0.00167569	−	0.000516882i
$453$		0			0
$454$	−0.484388	−	2.12224i	−0.0227334	−	0.0996017i
$455$	13.4123	+	14.9254i	0.628776	+	0.699715i
$456$		0			0
$457$	−5.03828	−	0.759399i	−0.235681	−	0.0355232i	0.0301397	−	0.999546i	$-0.490405\pi$
$457$	−5.03828	−	0.759399i	−0.235681	−	0.0355232i	−0.265821	+	0.964023i	$0.585643\pi$
$458$	1.87159	−	1.27603i	0.0874536	−	0.0596249i
$459$		0			0
$460$	7.38604	+	12.7930i	0.344376	+	0.596477i
$461$	−5.02225	−	2.41859i	−0.233910	−	0.112645i	0.313258	−	0.949668i	$-0.398580\pi$
$461$	−5.02225	−	2.41859i	−0.233910	−	0.112645i	−0.547167	+	0.837023i	$0.684294\pi$
$462$		0			0
$463$	31.1411	−	14.9967i	1.44725	−	0.696958i	0.465133	−	0.885241i	$-0.346007\pi$
$463$	31.1411	−	14.9967i	1.44725	−	0.696958i	0.982115	+	0.188283i	$0.0602922\pi$
$464$	20.2287	+	13.7917i	0.939092	+	0.640262i
$465$		0			0
$466$	−2.12317	−	1.97001i	−0.0983540	−	0.0912591i
$467$	28.0974	+	19.1565i	1.30019	+	0.886458i	0.997772	−	0.0667161i	$-0.0212522\pi$
$467$	28.0974	+	19.1565i	1.30019	+	0.886458i	0.302423	+	0.953174i	$0.402205\pi$
$468$		0			0
$469$	−21.5618	+	8.06802i	−0.995633	+	0.372547i
$470$	−1.32146	−	0.636381i	−0.0609543	−	0.0293541i
$471$		0			0
$472$	5.21525	−	9.03308i	0.240051	−	0.415781i
$473$	−6.74489	+	4.59859i	−0.310131	+	0.211443i
$474$		0			0
$475$	1.02354	−	4.48440i	0.0469630	−	0.205758i
$476$	−5.33167	+	31.9117i	−0.244376	+	1.46267i
$477$		0			0
$478$	0.0719437	+	0.960021i	0.00329063	+	0.0439104i
$479$	−2.34533	−	0.723439i	−0.107161	−	0.0330548i	0.240711	−	0.970597i	$-0.422619\pi$
$479$	−2.34533	−	0.723439i	−0.107161	−	0.0330548i	−0.347872	+	0.937542i	$0.613096\pi$
$480$		0			0
$481$	4.76312	−	1.46923i	0.217179	−	0.0669910i
$482$	−3.71736	−	4.66142i	−0.169321	−	0.212322i
$483$		0			0
$484$	11.2518	−	14.1093i	0.511446	−	0.641333i
$485$	10.1749	−	25.9251i	0.462017	−	1.17720i
$486$		0			0
$487$	−29.4789	+	4.44323i	−1.33582	+	0.201342i	−0.777813	−	0.628496i	$-0.783671\pi$
$487$	−29.4789	+	4.44323i	−1.33582	+	0.201342i	−0.558004	+	0.829838i	$0.688433\pi$
$488$	0.724541	−	0.672275i	0.0327984	−	0.0304325i
$489$		0			0
$490$	2.63870	−	1.67834i	0.119204	−	0.0758197i
$491$	12.3685			0.558182			0.279091	−	0.960265i	$-0.409967\pi$
$491$	12.3685			0.558182			0.279091	+	0.960265i	$0.409967\pi$
$492$		0			0
$493$	41.2363	−	6.21538i	1.85719	−	0.279927i
$494$	−0.253857	+	3.38749i	−0.0114216	+	0.152410i
$495$		0			0
$496$	3.87410	−	4.85797i	0.173952	−	0.218129i
$497$	−38.9754	−	9.55225i	−1.74829	−	0.428477i
$498$		0			0
$499$	21.3040	−	6.57140i	0.953697	−	0.294176i	0.221416	−	0.975179i	$-0.428932\pi$
$499$	21.3040	−	6.57140i	0.953697	−	0.294176i	0.732281	+	0.681003i	$0.238456\pi$
$500$	−8.60120	−	21.9155i	−0.384657	−	0.980091i
$501$		0			0
$502$	−0.513111	−	6.84699i	−0.0229013	−	0.305596i
$503$	−3.12017	−	13.6704i	−0.139121	−	0.609531i	−0.995629	−	0.0933964i	$-0.970228\pi$
$503$	−3.12017	−	13.6704i	−0.139121	−	0.609531i	0.856508	−	0.516134i	$-0.172630\pi$
$504$		0			0
$505$	−5.85564	+	25.6552i	−0.260572	+	1.14164i
$506$	1.16412	+	0.175463i	0.0517514	+	0.00780027i
$507$		0			0
$508$	−16.6413	+	28.8236i	−0.738338	+	1.27884i
$509$	7.06031	+	12.2288i	0.312943	+	0.542033i	0.978998	−	0.203870i	$-0.0653519\pi$
$509$	7.06031	+	12.2288i	0.312943	+	0.542033i	−0.666055	+	0.745902i	$0.732019\pi$
$510$		0			0
$511$	−4.63432	−	34.4677i	−0.205010	−	1.52476i
$512$	−14.8471	+	7.14999i	−0.656156	+	0.315988i
$513$		0			0
$514$	1.43444	+	1.33097i	0.0632704	+	0.0587064i
$515$	−7.78896	−	7.22710i	−0.343222	−	0.318464i
$516$		0			0
$517$	3.89359	−	1.87506i	0.171240	−	0.0824649i
$518$	−0.103515	−	0.769891i	−0.00454819	−	0.0338271i
$519$		0			0
$520$	3.43542	+	5.95032i	0.150653	+	0.260939i
$521$	−7.72210	+	13.3751i	−0.338311	+	0.585973i	−0.984115	−	0.177531i	$-0.943189\pi$
$521$	−7.72210	+	13.3751i	−0.338311	+	0.585973i	0.645804	+	0.763503i	$0.276522\pi$
$522$		0			0
$523$	5.61984	+	0.847055i	0.245739	+	0.0370391i	0.270756	−	0.962648i	$-0.412726\pi$
$523$	5.61984	+	0.847055i	0.245739	+	0.0370391i	−0.0250179	+	0.999687i	$0.507964\pi$
$524$	6.56315	−	28.7550i	0.286712	−	1.25617i
$525$		0			0
$526$	−0.341048	−	1.49423i	−0.0148704	−	0.0651515i
$527$	−0.790922	−	10.5541i	−0.0344531	−	0.459745i
$528$		0			0
$529$	−2.85460	−	7.27341i	−0.124113	−	0.316235i
$530$	2.15630	−	0.665130i	0.0936636	−	0.0288914i
$531$		0			0
$532$	−19.0100	−	4.65906i	−0.824190	−	0.201996i
$533$	−20.5672	+	25.7905i	−0.890864	+	1.11711i
$534$		0			0
$535$	1.65883	−	22.1356i	0.0717176	−	0.957005i
$536$	−7.79479	+	1.17488i	−0.336684	+	0.0507469i
$537$		0			0
$538$	−2.33091			−0.100493
$539$	−0.981235	+	9.16179i	−0.0422648	+	0.394626i
$540$		0			0
$541$	−16.1455	+	14.9809i	−0.694151	+	0.644078i	−0.946180	−	0.323642i	$-0.895093\pi$
$541$	−16.1455	+	14.9809i	−0.694151	+	0.644078i	0.252029	+	0.967720i	$0.418902\pi$
$542$	−4.74618	+	0.715371i	−0.203866	+	0.0307278i
$543$		0			0
$544$	−6.09799	+	15.5374i	−0.261449	+	0.666162i
$545$	−2.50504	+	3.14122i	−0.107304	+	0.134555i
$546$		0			0
$547$	12.6910	+	15.9140i	0.542628	+	0.680434i	0.975241	−	0.221146i	$-0.0709797\pi$
$547$	12.6910	+	15.9140i	0.542628	+	0.680434i	−0.432613	+	0.901580i	$0.642408\pi$
$548$	6.34617	−	1.95753i	0.271095	−	0.0836217i
$549$		0			0
$550$	−0.349527	−	0.107815i	−0.0149039	−	0.00459725i
$551$	1.88528	+	25.1573i	0.0803156	+	1.07174i
$552$		0			0
$553$	1.89980	−	11.3709i	0.0807877	−	0.483539i
$554$	−0.338412	+	1.48268i	−0.0143777	+	0.0629930i
$555$		0			0
$556$	−9.14079	+	6.23209i	−0.387656	+	0.264299i
$557$	−15.6299	+	27.0718i	−0.662261	+	1.14707i	0.317759	+	0.948172i	$0.397070\pi$
$557$	−15.6299	+	27.0718i	−0.662261	+	1.14707i	−0.980020	+	0.198898i	$0.936264\pi$
$558$		0			0
$559$	−21.7703	−	10.4840i	−0.920786	−	0.443427i
$560$	−17.7833	+	6.65415i	−0.751480	+	0.281189i
$561$		0			0
$562$	−2.15494	−	1.46921i	−0.0909007	−	0.0619750i
$563$	0.775527	+	0.719583i	0.0326845	+	0.0303268i	0.696346	−	0.717706i	$-0.254808\pi$
$563$	0.775527	+	0.719583i	0.0326845	+	0.0303268i	−0.663661	+	0.748033i	$0.730998\pi$
$564$		0			0
$565$	−0.0307921	−	0.0209937i	−0.00129543	−	0.000883212i
$566$	4.92638	−	2.37242i	0.207071	−	0.0997203i
$567$		0			0
$568$	−12.3797	−	5.96173i	−0.519439	−	0.250149i
$569$	20.4609	+	35.4393i	0.857764	+	1.48569i	0.874057	+	0.485824i	$0.161480\pi$
$569$	20.4609	+	35.4393i	0.857764	+	1.48569i	−0.0162921	+	0.999867i	$0.505186\pi$
$570$		0			0
$571$	−15.7607	+	10.7455i	−0.659566	+	0.449684i	−0.846286	−	0.532729i	$-0.821167\pi$
$571$	−15.7607	+	10.7455i	−0.659566	+	0.449684i	0.186720	+	0.982413i	$0.440214\pi$
$572$	−9.87563	−	1.48851i	−0.412921	−	0.0622378i
$573$		0			0
$574$	3.43615	+	3.82382i	0.143422	+	0.159603i
$575$	−1.04995	−	4.60015i	−0.0437861	−	0.191839i
$576$		0			0
$577$	5.70648	+	1.76021i	0.237564	+	0.0732787i	0.411251	−	0.911522i	$-0.365092\pi$
$577$	5.70648	+	1.76021i	0.237564	+	0.0732787i	−0.173687	+	0.984801i	$0.555568\pi$
$578$	1.88108	+	4.79292i	0.0782426	+	0.199359i
$579$		0			0
$580$	15.6950	+	19.6809i	0.651699	+	0.817205i
$581$	20.6908	−	15.9673i	0.858399	−	0.662435i
$582$		0			0
$583$	−2.42907	+	6.18918i	−0.100602	+	0.256329i
$584$	0.889898	−	11.8749i	0.0368242	−	0.491385i
$585$		0			0
$586$	0.436701	−	0.405199i	0.0180399	−	0.0167386i
$587$	−9.35768			−0.386233			−0.193116	−	0.981176i	$-0.561860\pi$
$587$	−9.35768			−0.386233			−0.193116	+	0.981176i	$0.561860\pi$
$588$		0			0
$589$	6.40265			0.263817
$590$	3.77060	−	3.49861i	0.155233	−	0.144035i
$591$		0			0
$592$	−0.352469	+	4.70338i	−0.0144864	+	0.193308i
$593$	3.08065	−	7.84937i	0.126507	−	0.322335i	−0.853562	−	0.520991i	$-0.825562\pi$
$593$	3.08065	−	7.84937i	0.126507	−	0.322335i	0.980069	+	0.198656i	$0.0636577\pi$
$594$		0			0
$595$	−14.4954	+	28.9114i	−0.594254	+	1.18525i
$596$	7.66060	+	9.60609i	0.313790	+	0.393481i
$597$		0			0
$598$	1.27309	+	3.24378i	0.0520605	+	0.132648i
$599$	−14.3551	−	4.42797i	−0.586534	−	0.180922i	−0.0127364	−	0.999919i	$-0.504054\pi$
$599$	−14.3551	−	4.42797i	−0.586534	−	0.180922i	−0.573798	+	0.818997i	$0.694530\pi$
$600$		0			0
$601$	−10.5469	−	46.2088i	−0.430215	−	1.88490i	−0.464659	−	0.885490i	$-0.653823\pi$
$601$	−10.5469	−	46.2088i	−0.430215	−	1.88490i	0.0344440	−	0.999407i	$-0.489034\pi$
$602$	−2.17065	+	3.07716i	−0.0884690	+	0.125416i
$603$		0			0
$604$	−12.9619	−	1.95369i	−0.527410	−	0.0794943i
$605$	14.9051	−	10.1621i	0.605977	−	0.413148i
$606$		0			0
$607$	−2.78915	−	4.83095i	−0.113208	−	0.196082i	0.803854	−	0.594827i	$-0.202779\pi$
$607$	−2.78915	−	4.83095i	−0.113208	−	0.196082i	−0.917062	+	0.398745i	$0.869446\pi$
$608$	−9.09746	−	4.38111i	−0.368951	−	0.177677i
$609$		0			0
$610$	0.439146	−	0.211481i	0.0177805	−	0.00856263i
$611$	10.5690	+	7.20579i	0.427574	+	0.291515i
$612$		0			0
$613$	16.1714	+	15.0048i	0.653156	+	0.606040i	0.935523	−	0.353267i	$-0.114929\pi$
$613$	16.1714	+	15.0048i	0.653156	+	0.606040i	−0.282367	+	0.959306i	$0.591120\pi$
$614$	0.00441700	+	0.00301146i	0.000178256	+	0.000121533i
$615$		0			0
$616$	−0.977910	+	2.99962i	−0.0394011	+	0.120858i
$617$	10.5623	+	5.08655i	0.425223	+	0.204777i	0.634242	−	0.773135i	$-0.281312\pi$
$617$	10.5623	+	5.08655i	0.425223	+	0.204777i	−0.209018	+	0.977912i	$0.567027\pi$
$618$		0			0
$619$	13.6878	−	23.7079i	0.550157	−	0.952901i	−0.448105	−	0.893981i	$-0.647901\pi$
$619$	13.6878	−	23.7079i	0.550157	−	0.952901i	0.998263	−	0.0589198i	$-0.0187656\pi$
$620$	5.27858	−	3.59888i	0.211993	−	0.144534i
$621$		0			0
$622$	−1.02219	+	4.47851i	−0.0409861	+	0.179572i
$623$	−11.0755	−	4.55195i	−0.443731	−	0.182370i
$624$		0			0
$625$	−1.30628	−	17.4311i	−0.0522513	−	0.697245i
$626$	3.17343	+	0.978873i	0.126836	+	0.0391236i
$627$		0			0
$628$	21.3100	−	6.57327i	0.850362	−	0.262302i
$629$	5.00901	+	6.28110i	0.199722	+	0.250444i
$630$		0			0
$631$	−4.54775	+	5.70270i	−0.181043	+	0.227021i	−0.864069	−	0.503373i	$-0.832092\pi$
$631$	−4.54775	+	5.70270i	−0.181043	+	0.227021i	0.683026	+	0.730394i	$0.260664\pi$
$632$	1.44216	−	3.67456i	0.0573660	−	0.146166i
$633$		0			0
$634$	3.51404	−	0.529656i	0.139560	−	0.0210353i
$635$	−24.3886	+	22.6293i	−0.967832	+	0.898017i
$636$		0			0
$637$	−24.9375	+	11.0440i	−0.988061	+	0.437578i
$638$	2.00616			0.0794246
$639$		0			0
$640$	−13.2202	+	1.99262i	−0.522573	+	0.0787652i
$641$	−0.514161	+	6.86100i	−0.0203081	+	0.270993i	0.977801	+	0.209534i	$0.0671946\pi$
$641$	−0.514161	+	6.86100i	−0.0203081	+	0.270993i	−0.998110	+	0.0614595i	$0.980424\pi$
$642$		0			0
$643$	−10.5608	+	13.2428i	−0.416476	+	0.522244i	−0.945175	−	0.326565i	$-0.894109\pi$
$643$	−10.5608	+	13.2428i	−0.416476	+	0.522244i	0.528699	+	0.848810i	$0.322680\pi$
$644$	−19.6432	+	4.15503i	−0.774050	+	0.163731i
$645$		0			0
$646$	−5.23182	+	1.61380i	−0.205843	+	0.0634942i
$647$	−8.99173	−	22.9106i	−0.353502	−	0.900707i	−0.991433	−	0.130614i	$-0.958305\pi$
$647$	−8.99173	−	22.9106i	−0.353502	−	0.900707i	0.637932	−	0.770093i	$-0.279790\pi$
$648$		0			0
$649$	1.13258	+	15.1132i	0.0444576	+	0.593246i
$650$	−0.240921	−	1.05554i	−0.00944968	−	0.0414018i
$651$		0			0
$652$	2.19822	−	9.63105i	0.0860891	−	0.377181i
$653$	−33.0979	−	4.98871i	−1.29522	−	0.195223i	−0.534981	−	0.844864i	$-0.679681\pi$
$653$	−33.0979	−	4.98871i	−1.29522	−	0.195223i	−0.760241	+	0.649641i	$0.774919\pi$
$654$		0			0
$655$	14.7417	−	25.5333i	0.576004	−	0.997668i
$656$	−15.6068	−	27.0318i	−0.609344	−	1.05541i
$657$		0			0
$658$	1.37906	−	1.43954i	0.0537615	−	0.0561191i
$659$	−4.23634	+	2.04012i	−0.165024	+	0.0794716i	−0.514573	−	0.857447i	$-0.672049\pi$
$659$	−4.23634	+	2.04012i	−0.165024	+	0.0794716i	0.349548	+	0.936918i	$0.386335\pi$
$660$		0			0
$661$	−12.1210	−	11.2466i	−0.471452	−	0.437443i	0.408321	−	0.912839i	$-0.366115\pi$
$661$	−12.1210	−	11.2466i	−0.471452	−	0.437443i	−0.879772	+	0.475395i	$0.842305\pi$
$662$	−2.31536	−	2.14834i	−0.0899890	−	0.0834976i
$663$		0			0
$664$	8.06274	−	3.88281i	0.312895	−	0.150682i
$665$	−16.7858	−	10.0516i	−0.650926	−	0.389782i
$666$		0			0
$667$	12.9395	+	22.4119i	0.501019	+	0.867790i
$668$	15.9812	−	27.6802i	0.618331	−	1.07098i
$669$		0			0
$670$	−3.84393	−	0.579379i	−0.148504	−	0.0223834i
$671$	−0.319571	+	1.40013i	−0.0123369	+	0.0540514i
$672$		0			0
$673$	8.54457	+	37.4362i	0.329369	+	1.44306i	0.820336	+	0.571882i	$0.193786\pi$
$673$	8.54457	+	37.4362i	0.329369	+	1.44306i	−0.490967	+	0.871178i	$0.663356\pi$
$674$	0.162186	+	2.16422i	0.00624716	+	0.0833626i
$675$		0			0
$676$	−1.55137	−	3.95282i	−0.0596679	−	0.152031i
$677$	33.0099	−	10.1822i	1.26867	−	0.391334i	0.413894	−	0.910325i	$-0.364168\pi$
$677$	33.0099	−	10.1822i	1.26867	−	0.391334i	0.854780	+	0.518991i	$0.173692\pi$
$678$		0			0
$679$	29.2149	+	24.0702i	1.12116	+	0.923728i
$680$	−6.90453	+	8.65801i	−0.264777	+	0.332019i
$681$		0			0
$682$	0.0380488	−	0.507726i	0.00145696	−	0.0194418i
$683$	−34.7063	+	5.23114i	−1.32800	+	0.200164i	−0.774441	−	0.632646i	$-0.781969\pi$
$683$	−34.7063	+	5.23114i	−1.32800	+	0.200164i	−0.553559	+	0.832810i	$0.686731\pi$
$684$		0			0
$685$	6.63869			0.253651
$686$	1.05717	+	4.11688i	0.0403629	+	0.157183i
$687$		0			0
$688$	16.7606	−	15.5515i	0.638990	−	0.592896i
$689$	−19.4603	+	2.93317i	−0.741378	+	0.111745i
$690$		0			0
$691$	2.29662	−	5.85170i	0.0873677	−	0.222609i	−0.880512	−	0.474025i	$-0.842801\pi$
$691$	2.29662	−	5.85170i	0.0873677	−	0.222609i	0.967879	+	0.251415i	$0.0808960\pi$
$692$	−8.28321	+	10.3868i	−0.314881	+	0.394848i
$693$		0			0
$694$	−2.28527	−	2.86564i	−0.0867478	−	0.108778i
$695$	−10.5676	+	3.25968i	−0.400852	+	0.123647i
$696$		0			0
$697$	−50.8048	−	15.6712i	−1.92437	−	0.593589i
$698$	0.0959393	+	1.28022i	0.00363136	+	0.0484571i
$699$		0			0
$700$	6.22739	−	0.366923i	0.235373	−	0.0138684i
$701$	−8.89681	+	38.9795i	−0.336028	+	1.47223i	0.471216	+	0.882018i	$0.343815\pi$
$701$	−8.89681	+	38.9795i	−0.336028	+	1.47223i	−0.807244	+	0.590217i	$0.799042\pi$
$702$		0			0
$703$	−4.01559	+	2.73779i	−0.151451	+	0.103258i
$704$	4.45143	−	7.71010i	0.167769	−	0.290585i
$705$		0			0
$706$	3.36756	+	1.62173i	0.126740	+	0.0610347i
$707$	−30.6857	−	18.3750i	−1.15406	−	0.691063i
$708$		0			0
$709$	36.5806	+	24.9402i	1.37381	+	0.936650i	0.999958	+	0.00916229i	$0.00291649\pi$
$709$	36.5806	+	24.9402i	1.37381	+	0.936650i	0.373855	+	0.927487i	$0.378036\pi$
$710$	−4.96712	−	4.60881i	−0.186413	−	0.172966i
$711$		0			0
$712$	−3.38769	−	2.30968i	−0.126959	−	0.0865591i
$713$	5.91748	−	2.84971i	0.221611	−	0.106722i
$714$		0			0
$715$	−8.99471	−	4.33163i	−0.336383	−	0.161994i
$716$	16.4816	+	28.5470i	0.615948	+	1.06685i
$717$		0			0
$718$	2.65400	−	1.80946i	0.0990462	−	0.0675286i
$719$	7.79571	+	1.17501i	0.290731	+	0.0438206i	0.292788	−	0.956177i	$-0.405417\pi$
$719$	7.79571	+	1.17501i	0.290731	+	0.0438206i	−0.00205753	+	0.999998i	$0.500655\pi$
$720$		0			0
$721$	12.6205	−	7.02051i	0.470011	−	0.261458i
$722$	0.233291	+	1.02211i	0.00868218	+	0.0380391i
$723$		0			0
$724$	−11.2929	−	3.48341i	−0.419699	−	0.129460i
$725$	−2.93757	−	7.48480i	−0.109098	−	0.277978i
$726$		0			0
$727$	−15.1433	−	18.9891i	−0.561634	−	0.704266i	0.417225	−	0.908803i	$-0.363003\pi$
$727$	−15.1433	−	18.9891i	−0.561634	−	0.704266i	−0.978859	+	0.204537i	$0.934431\pi$
$728$	−9.13650	+	1.93260i	−0.338621	+	0.0716269i
$729$		0			0
$730$	2.14543	−	5.46646i	0.0794058	−	0.202323i
$731$	2.91035	−	38.8359i	0.107643	−	1.43640i
$732$		0			0
$733$	−24.9499	+	23.1501i	−0.921545	+	0.855069i	−0.989780	−	0.142601i	$-0.954454\pi$
$733$	−24.9499	+	23.1501i	−0.921545	+	0.855069i	0.0682355	+	0.997669i	$0.478263\pi$
$734$	2.60060			0.0959899
$735$		0			0
$736$	−10.3580			−0.381802
$737$	8.39624	−	7.79057i	0.309280	−	0.286970i
$738$		0			0
$739$	1.40800	−	18.7885i	0.0517941	−	0.691144i	−0.909515	−	0.415672i	$-0.863547\pi$
$739$	1.40800	−	18.7885i	0.0517941	−	0.691144i	0.961309	−	0.275473i	$-0.0888344\pi$
$740$	−1.77172	+	4.51426i	−0.0651296	+	0.165948i
$741$		0			0
$742$	−0.0489084	+	3.06665i	−0.00179548	+	0.112580i
$743$	22.6601	+	28.4149i	0.831318	+	1.04244i	0.998403	+	0.0564973i	$0.0179932\pi$
$743$	22.6601	+	28.4149i	0.831318	+	1.04244i	−0.167085	+	0.985943i	$0.553435\pi$
$744$		0			0
$745$	4.48711	+	11.4330i	0.164395	+	0.418871i
$746$	−0.775085	−	0.239082i	−0.0283779	−	0.00875342i
$747$		0			0
$748$	−3.58186	−	15.6932i	−0.130966	−	0.573799i
$749$	27.9056	+	11.4690i	1.01965	+	0.419067i
$750$		0			0
$751$	−10.2130	−	1.53937i	−0.372679	−	0.0561724i	−0.0399677	−	0.999201i	$-0.512725\pi$
$751$	−10.2130	−	1.53937i	−0.372679	−	0.0561724i	−0.332712	+	0.943029i	$0.607964\pi$
$752$	−10.0007	+	6.81836i	−0.364688	+	0.248640i
$753$		0			0
$754$	2.96907	+	5.14259i	0.108127	+	0.187282i
$755$	−11.8056	−	5.68530i	−0.429651	−	0.206909i
$756$		0			0
$757$	−29.4089	+	14.1626i	−1.06889	+	0.514748i	−0.883747	−	0.467964i	$-0.844988\pi$
$757$	−29.4089	+	14.1626i	−1.06889	+	0.514748i	−0.185138	+	0.982712i	$0.559273\pi$
$758$	−4.48169	−	3.05557i	−0.162782	−	0.110983i
$759$		0			0
$760$	−4.91090	−	4.55665i	−0.178137	−	0.165287i
$761$	−2.91858	−	1.98986i	−0.105799	−	0.0721323i	0.509265	−	0.860610i	$-0.329917\pi$
$761$	−2.91858	−	1.98986i	−0.105799	−	0.0721323i	−0.615064	+	0.788477i	$0.710870\pi$
$762$		0			0
$763$	−3.00387	−	4.56045i	−0.108747	−	0.165099i
$764$	20.0020	+	9.63244i	0.723646	+	0.348490i
$765$		0			0
$766$	−2.75259	+	4.76763i	−0.0994552	+	0.172261i
$767$	−37.0650	+	25.2705i	−1.33834	+	0.912465i
$768$		0			0
$769$	−1.05987	+	4.64361i	−0.0382200	+	0.167453i	−0.990436	−	0.137972i	$-0.955941\pi$
$769$	−1.05987	+	4.64361i	−0.0382200	+	0.167453i	0.952216	+	0.305425i	$0.0987986\pi$
$770$	−0.896834	+	1.27137i	−0.0323197	+	0.0458170i
$771$		0			0
$772$	−0.704740	−	9.40410i	−0.0253641	−	0.338461i
$773$	26.9194	+	8.30353i	0.968223	+	0.298657i	0.738241	−	0.674538i	$-0.235657\pi$
$773$	26.9194	+	8.30353i	0.968223	+	0.298657i	0.229982	+	0.973195i	$0.426133\pi$
$774$		0			0
$775$	−1.94999	+	0.601493i	−0.0700458	+	0.0216063i
$776$	8.08122	+	10.1335i	0.290099	+	0.363772i
$777$		0			0
$778$	−0.673932	+	0.845084i	−0.0241616	+	0.0302977i
$779$	11.7506	−	29.9401i	0.421010	−	1.07272i
$780$		0			0
$781$	19.7419	−	2.97561i	0.706421	−	0.106476i
$782$	−4.11709	+	3.82010i	−0.147227	+	0.136607i
$783$		0			0
$784$	−1.10694	−	25.7835i	−0.0395334	−	0.920838i
$785$	22.2923			0.795646
$786$		0			0
$787$	−20.7815	+	3.13231i	−0.740781	+	0.111655i	−0.508582	−	0.861014i	$-0.669830\pi$
$787$	−20.7815	+	3.13231i	−0.740781	+	0.111655i	−0.232199	+	0.972668i	$0.574592\pi$
$788$	1.70583	−	22.7627i	0.0607677	−	0.810889i
$789$		0			0
$790$	1.21371	−	1.52194i	0.0431819	−	0.0541483i
$791$	0.0401010	−	0.0309464i	0.00142583	−	0.00110033i
$792$		0			0
$793$	−4.06205	+	1.25298i	−0.144248	+	0.0444945i
$794$	1.81488	+	4.62423i	0.0644075	+	0.164108i
$795$		0			0
$796$	1.55000	+	20.6833i	0.0549383	+	0.733100i
$797$	−3.93142	−	17.2247i	−0.139258	−	0.610130i	−0.995599	−	0.0937182i	$-0.970125\pi$
$797$	−3.93142	−	17.2247i	−0.139258	−	0.610130i	0.856341	−	0.516411i	$-0.172732\pi$
$798$		0			0
$799$	−4.58767	+	20.0999i	−0.162300	+	0.711083i
$800$	3.18230	+	0.479655i	0.112511	+	0.0169584i
$801$		0			0
$802$	−0.422588	+	0.731943i	−0.0149221	+	0.0258458i
$803$	8.65132	+	14.9845i	0.305299	+	0.528793i
$804$		0			0
$805$	−19.9876	−	1.81881i	−0.704471	−	0.0641046i
$806$	1.35782	−	0.653889i	0.0478270	−	0.0230323i
$807$		0			0
$808$	−8.97750	−	8.32990i	−0.315827	−	0.293045i
$809$	18.7991	+	17.4430i	0.660940	+	0.613263i	0.937605	−	0.347704i	$-0.113038\pi$
$809$	18.7991	+	17.4430i	0.660940	+	0.613263i	−0.276664	+	0.960967i	$0.589229\pi$
$810$		0			0
$811$	−23.5526	+	11.3423i	−0.827044	+	0.398283i	−0.799006	−	0.601324i	$-0.794640\pi$
$811$	−23.5526	+	11.3423i	−0.827044	+	0.398283i	−0.0280382	+	0.999607i	$0.508926\pi$
$812$	−32.0444	+	11.9904i	−1.12454	+	0.420780i
$813$		0			0
$814$	0.193241	+	0.334704i	0.00677310	+	0.0117314i
$815$	4.93749	−	8.55198i	0.172953	−	0.299563i
$816$		0			0
$817$	23.2967	+	3.51141i	0.815047	+	0.122849i
$818$	1.58812	−	6.95801i	0.0555273	−	0.243281i
$819$		0			0
$820$	−7.14143	−	31.2887i	−0.249390	−	1.09265i
$821$	1.26427	+	16.8706i	0.0441235	+	0.588787i	0.974820	+	0.222994i	$0.0715831\pi$
$821$	1.26427	+	16.8706i	0.0441235	+	0.588787i	−0.930696	+	0.365793i	$0.880798\pi$
$822$		0			0
$823$	−5.39764	−	13.7530i	−0.188150	−	0.479398i	0.805408	−	0.592720i	$-0.201946\pi$
$823$	−5.39764	−	13.7530i	−0.188150	−	0.479398i	−0.993558	+	0.113322i	$0.963851\pi$
$824$	4.72526	−	1.45755i	0.164612	−	0.0507761i
$825$		0			0
$826$	2.93253	+	6.34641i	0.102036	+	0.220820i
$827$	−9.96056	+	12.4902i	−0.346363	+	0.434325i	−0.924248	−	0.381793i	$-0.875307\pi$
$827$	−9.96056	+	12.4902i	−0.346363	+	0.434325i	0.577885	+	0.816118i	$0.303878\pi$
$828$		0			0
$829$	0.943829	−	12.5945i	0.0327805	−	0.437426i	−0.956533	−	0.291623i	$-0.905805\pi$
$829$	0.943829	−	12.5945i	0.0327805	−	0.437426i	0.989314	−	0.145802i	$-0.0465763\pi$
$830$	4.36381	−	0.657738i	0.151470	−	0.0228304i
$831$		0			0
$832$	26.3521			0.913594
$833$	−31.2536	−	30.9114i	−1.08287	−	1.07102i
$834$		0			0
$835$	23.4212	−	21.7317i	0.810523	−	0.752055i
$836$	9.62901	−	1.45134i	0.333026	−	0.0501956i
$837$		0			0
$838$	−2.71877	+	6.92731i	−0.0939183	+	0.239300i
$839$	−20.1887	+	25.3159i	−0.696992	+	0.874001i	−0.996795	−	0.0800005i	$-0.974508\pi$
$839$	−20.1887	+	25.3159i	−0.696992	+	0.874001i	0.299802	+	0.954001i	$0.403079\pi$
$840$		0			0
$841$	9.41462	+	11.8056i	0.324642	+	0.407088i
$842$	5.75739	−	1.77592i	0.198413	−	0.0612022i
$843$		0			0
$844$	22.4052	+	6.91110i	0.771220	+	0.237890i
$845$	−0.317209	−	4.23287i	−0.0109123	−	0.145615i
$846$		0			0
$847$	6.85257	+	23.5420i	0.235457	+	0.808912i
$848$	4.14378	−	18.1551i	0.142298	−	0.623449i
$849$		0			0
$850$	1.44180	−	0.982999i	0.0494532	−	0.0337166i
$851$	−2.49277	+	4.31760i	−0.0854509	+	0.148005i
$852$		0			0
$853$	12.5065	+	6.02283i	0.428215	+	0.206218i	0.635562	−	0.772050i	$-0.280768\pi$
$853$	12.5065	+	6.02283i	0.428215	+	0.206218i	−0.207347	+	0.978268i	$0.566483\pi$
$854$	0.0882790	+	0.656573i	0.00302084	+	0.0224675i
$855$		0			0
$856$	8.53552	+	5.81942i	0.291738	+	0.198904i
$857$	−4.53851	−	4.21112i	−0.155033	−	0.143849i	0.598843	−	0.800866i	$-0.295627\pi$
$857$	−4.53851	−	4.21112i	−0.155033	−	0.143849i	−0.753875	+	0.657017i	$0.771818\pi$
$858$		0			0
$859$	6.18251	+	4.21516i	0.210945	+	0.143820i	0.664184	−	0.747569i	$-0.268779\pi$
$859$	6.18251	+	4.21516i	0.210945	+	0.143820i	−0.453239	+	0.891389i	$0.649732\pi$
$860$	21.1804	−	10.1999i	0.722245	−	0.347815i
$861$		0			0
$862$	5.77609	+	2.78162i	0.196735	+	0.0947424i
$863$	6.40092	+	11.0867i	0.217890	+	0.377396i	0.954163	−	0.299289i	$-0.0967493\pi$
$863$	6.40092	+	11.0867i	0.217890	+	0.377396i	−0.736273	+	0.676685i	$0.763416\pi$
$864$		0			0
$865$	−10.9726	+	7.48100i	−0.373080	+	0.254362i
$866$	−5.79917	−	0.874084i	−0.197064	−	0.0297026i
$867$		0			0
$868$	2.42682	+	8.33732i	0.0823715	+	0.282987i
$869$	1.27630	+	5.59184i	0.0432956	+	0.189690i
$870$		0			0
$871$	32.3966	+	9.99303i	1.09772	+	0.338601i
$872$	−0.683126	−	1.74058i	−0.0231336	−	0.0589434i
$873$		0			0
$874$	−2.11840	−	2.65638i	−0.0716558	−	0.0898535i
$875$	31.0673	+	7.61410i	1.05027	+	0.257404i
$876$		0			0
$877$	16.0216	−	40.8223i	0.541011	−	1.37847i	−0.355178	−	0.934799i	$-0.615580\pi$
$877$	16.0216	−	40.8223i	0.541011	−	1.37847i	0.896188	−	0.443674i	$-0.146325\pi$
$878$	−0.282500	+	3.76971i	−0.00953393	+	0.127221i
$879$		0			0
$880$	6.92486	−	6.42533i	0.233437	−	0.216598i
$881$	27.5066			0.926721			0.463360	−	0.886170i	$-0.346644\pi$
$881$	27.5066			0.926721			0.463360	+	0.886170i	$0.346644\pi$
$882$		0			0
$883$	25.6139			0.861976			0.430988	−	0.902358i	$-0.358165\pi$
$883$	25.6139			0.861976			0.430988	+	0.902358i	$0.358165\pi$
$884$	34.9267	−	32.4073i	1.17471	−	1.08997i
$885$		0			0
$886$	−0.492981	+	6.57837i	−0.0165620	+	0.221005i
$887$	3.72957	−	9.50279i	0.125227	−	0.319073i	−0.854488	−	0.519472i	$-0.826129\pi$
$887$	3.72957	−	9.50279i	0.125227	−	0.319073i	0.979714	+	0.200399i	$0.0642239\pi$
$888$		0			0
$889$	−18.9679	−	41.0492i	−0.636163	−	1.37675i
$890$	−1.26066	−	1.58082i	−0.0422574	−	0.0529891i
$891$		0			0
$892$	1.16244	+	2.96184i	0.0389213	+	0.0991698i
$893$	−11.9181	−	3.67625i	−0.398824	−	0.123021i
$894$		0			0
$895$	7.33223	+	32.1246i	0.245089	+	1.07381i
$896$	2.99450	−	17.9230i	0.100039	−	0.598766i
$897$		0			0
$898$	1.52264	+	0.229500i	0.0508110	+	0.00765853i
$899$	9.24747	−	6.30481i	0.308420	−	0.210277i
$900$		0			0
$901$	−15.8596	−	27.4697i	−0.528360	−	0.915147i
$902$	−2.30440	−	1.10974i	−0.0767281	−	0.0369503i
$903$		0			0
$904$	0.0156265	−	0.00752531i	0.000519729	−	0.000250288i
$905$	−9.76076	−	6.65478i	−0.324459	−	0.221212i
$906$		0			0
$907$	32.1304	+	29.8126i	1.06687	+	0.989912i	0.999969	−	0.00784726i	$-0.00249789\pi$
$907$	32.1304	+	29.8126i	1.06687	+	0.989912i	0.0669025	+	0.997760i	$0.478688\pi$
$908$	−15.2609	−	10.4047i	−0.506450	−	0.345291i
$909$		0			0
$910$	−4.58632	−	0.417341i	−0.152035	−	0.0138347i
$911$	−36.4318	−	17.5446i	−1.20704	−	0.581280i	−0.281365	−	0.959601i	$-0.590787\pi$
$911$	−36.4318	−	17.5446i	−1.20704	−	0.581280i	−0.925674	+	0.378321i	$0.876502\pi$
$912$		0			0
$913$	−6.50146	+	11.2609i	−0.215167	+	0.372680i
$914$	0.966171	−	0.658724i	0.0319581	−	0.0217887i
$915$		0			0
$916$	4.27688	−	18.7382i	0.141312	−	0.619129i
$917$	26.7846	+	29.8064i	0.884506	+	0.984296i
$918$		0			0
$919$	1.58310	+	21.1249i	0.0522215	+	0.696848i	0.960464	+	0.278404i	$0.0898053\pi$
$919$	1.58310	+	21.1249i	0.0522215	+	0.696848i	−0.908243	+	0.418444i	$0.862576\pi$
$920$	−6.56686	−	2.02561i	−0.216503	−	0.0667823i
$921$		0			0
$922$	1.22248	−	0.377084i	0.0402601	−	0.0124186i
$923$	36.8453	+	46.2025i	1.21278	+	1.52077i
$924$		0			0
$925$	0.965790	−	1.21106i	0.0317550	−	0.0398195i
$926$	−2.89808	+	7.38418i	−0.0952367	+	0.242659i
$927$		0			0
$928$	−17.4538	+	2.63074i	−0.572949	+	0.0863581i
$929$	−9.18435	+	8.52183i	−0.301329	+	0.279592i	−0.816316	−	0.577606i	$-0.803987\pi$
$929$	−9.18435	+	8.52183i	−0.301329	+	0.279592i	0.514987	+	0.857198i	$0.327797\pi$
$930$		0			0
$931$	20.0606	−	17.4567i	0.657458	−	0.572119i
$932$	−24.5754			−0.804996
$933$		0			0
$934$	−7.71740	+	1.16321i	−0.252521	+	0.0380614i
$935$	1.20245	−	16.0456i	0.0393244	−	0.524748i
$936$		0			0
$937$	−12.4072	+	15.5582i	−0.405327	+	0.508264i	−0.942040	−	0.335501i	$-0.891094\pi$
$937$	−12.4072	+	15.5582i	−0.405327	+	0.508264i	0.536713	+	0.843765i	$0.319666\pi$
$938$	2.36808	−	4.72318i	0.0773205	−	0.154217i
$939$		0			0
$940$	−11.8921	+	3.66823i	−0.387878	+	0.119644i
$941$	12.6907	+	32.3353i	0.413703	+	1.05410i	0.974149	+	0.225908i	$0.0725348\pi$
$941$	12.6907	+	32.3353i	0.413703	+	1.05410i	−0.560445	+	0.828191i	$0.689370\pi$
$942$		0			0
$943$	−2.46561	−	32.9013i	−0.0802915	−	1.07142i
$944$	−9.44557	−	41.3837i	−0.307427	−	1.34693i
$945$		0			0
$946$	0.416897	−	1.82654i	0.0135545	−	0.0593860i
$947$	15.1991	+	2.29090i	0.493906	+	0.0744443i	0.391272	−	0.920275i	$-0.372035\pi$
$947$	15.1991	+	2.29090i	0.493906	+	0.0744443i	0.102633	+	0.994719i	$0.467273\pi$
$948$		0			0
$949$	−25.6075	+	44.3536i	−0.831256	+	1.43978i
$950$	0.527825	+	0.914219i	0.0171249	+	0.0296612i
$951$		0			0
$952$	−8.27942	−	12.5698i	−0.268338	−	0.407388i
$953$	23.9229	−	11.5207i	0.774940	−	0.373191i	−0.00424060	−	0.999991i	$-0.501350\pi$
$953$	23.9229	−	11.5207i	0.774940	−	0.373191i	0.779180	+	0.626800i	$0.215636\pi$
$954$		0			0
$955$	16.2679	+	15.0944i	0.526418	+	0.488445i
$956$	5.98802	+	5.55607i	0.193666	+	0.179696i
$957$		0			0
$958$	0.507503	−	0.244400i	0.0163967	−	0.00789622i
$959$	−2.79677	+	8.57875i	−0.0903125	+	0.277022i
$960$		0			0
$961$	14.0797	+	24.3868i	0.454185	+	0.786672i
$962$	−0.571986	+	0.990709i	−0.0184416	+	0.0319417i
$963$		0			0
$964$	−50.0240	−	7.53990i	−1.61116	−	0.242844i
$965$	2.09768	−	9.19053i	0.0675267	−	0.295854i
$966$		0			0
$967$	−7.93287	−	34.7562i	−0.255104	−	1.11768i	−0.926414	−	0.376507i	$-0.877125\pi$
$967$	−7.93287	−	34.7562i	−0.255104	−	1.11768i	0.671310	−	0.741177i	$-0.265732\pi$
$968$	0.627395	+	8.37200i	0.0201652	+	0.269086i
$969$		0			0
$970$	2.33516	+	5.94989i	0.0749775	+	0.191040i
$971$	22.7434	−	7.01541i	0.729870	−	0.225135i	0.0925214	−	0.995711i	$-0.470507\pi$
$971$	22.7434	−	7.01541i	0.729870	−	0.225135i	0.637349	+	0.770576i	$0.280031\pi$
$972$		0			0
$973$	0.239691	−	15.0291i	0.00768413	−	0.481811i
$974$	4.26586	−	5.34922i	0.136687	−	0.171400i
$975$		0			0
$976$	0.300591	−	4.01110i	0.00962167	−	0.128392i
$977$	34.3269	−	5.17395i	1.09822	−	0.165529i	0.425158	−	0.905119i	$-0.360219\pi$
$977$	34.3269	−	5.17395i	1.09822	−	0.165529i	0.673058	+	0.739590i	$0.264980\pi$
$978$		0			0
$979$	5.95752			0.190403
$980$	6.72642	−	25.6678i	0.214868	−	0.819928i
$981$		0			0
$982$	−2.08084	+	1.93074i	−0.0664024	+	0.0616124i
$983$	−10.0732	+	1.51829i	−0.321284	+	0.0484258i	−0.307704	−	0.951482i	$-0.599561\pi$
$983$	−10.0732	+	1.51829i	−0.321284	+	0.0484258i	−0.0135797	+	0.999908i	$0.504323\pi$
$984$		0			0
$985$	8.33631	−	21.2406i	0.265617	−	0.676781i
$986$	−5.96727	+	7.48272i	−0.190036	+	0.238298i
$987$		0			0
$988$	17.9711	+	22.5350i	0.571736	+	0.716935i
$989$	23.0942	−	7.12361i	0.734352	−	0.226518i
$990$		0			0
$991$	12.4125	+	3.82874i	0.394295	+	0.121624i	0.485561	−	0.874203i	$-0.338615\pi$
$991$	12.4125	+	3.82874i	0.394295	+	0.121624i	−0.0912662	+	0.995827i	$0.529091\pi$
$992$	0.334767	+	4.46716i	0.0106289	+	0.141832i
$993$		0			0
$994$	8.04824	−	4.47707i	0.255275	−	0.142004i
$995$	−4.61362	+	20.2136i	−0.146262	+	0.640814i
$996$		0			0
$997$	41.5419	−	28.3228i	1.31565	−	0.896992i	0.316970	−	0.948436i	$-0.397335\pi$
$997$	41.5419	−	28.3228i	1.31565	−	0.896992i	0.998676	+	0.0514436i	$0.0163822\pi$
$998$	−2.55832	+	4.43114i	−0.0809822	+	0.140265i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bb.d.109.2		48
3.2	odd	2		49.2.g.a.11.3	yes	48
12.11	even	2		784.2.bg.c.305.2		48
21.2	odd	6		343.2.g.i.128.2		48
21.5	even	6		343.2.g.h.128.2		48
21.11	odd	6		343.2.e.d.246.5		48
21.17	even	6		343.2.e.c.246.5		48
21.20	even	2		343.2.g.g.312.3		48
49.9	even	21	inner	441.2.bb.d.352.2		48
147.74	odd	42		343.2.e.d.99.5		48
147.83	even	14		343.2.g.h.67.2		48
147.89	even	42		343.2.g.g.177.3		48
147.95	odd	42		2401.2.a.h.1.11		24
147.101	even	42		2401.2.a.i.1.11		24
147.107	odd	42		49.2.g.a.9.3	✓	48
147.113	odd	14		343.2.g.i.67.2		48
147.122	even	42		343.2.e.c.99.5		48
588.107	even	42		784.2.bg.c.401.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.2.g.a.9.3	✓	48	147.107	odd	42
49.2.g.a.11.3	yes	48	3.2	odd	2
343.2.e.c.99.5		48	147.122	even	42
343.2.e.c.246.5		48	21.17	even	6
343.2.e.d.99.5		48	147.74	odd	42
343.2.e.d.246.5		48	21.11	odd	6
343.2.g.g.177.3		48	147.89	even	42
343.2.g.g.312.3		48	21.20	even	2
343.2.g.h.67.2		48	147.83	even	14
343.2.g.h.128.2		48	21.5	even	6
343.2.g.i.67.2		48	147.113	odd	14
343.2.g.i.128.2		48	21.2	odd	6
441.2.bb.d.109.2		48	1.1	even	1	trivial
441.2.bb.d.352.2		48	49.9	even	21	inner
784.2.bg.c.305.2		48	12.11	even	2
784.2.bg.c.401.2		48	588.107	even	42
2401.2.a.h.1.11		24	147.95	odd	42
2401.2.a.i.1.11		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)

\(f(q)\)	\(=\)	\(q+(-0.168237 + 0.156102i) q^{2} +(-0.145524 + 1.94188i) q^{4} +(-0.711168 + 1.81203i) q^{5} +(-2.04196 - 1.68237i) q^{7} +(-0.564834 - 0.708279i) q^{8} +O(q^{10})\)	\(q+(-0.168237 + 0.156102i) q^{2} +(-0.145524 + 1.94188i) q^{4} +(-0.711168 + 1.81203i) q^{5} +(-2.04196 - 1.68237i) q^{7} +(-0.564834 - 0.708279i) q^{8} +(-0.163215 - 0.415865i) q^{10} +(1.25783 + 0.387990i) q^{11} +(0.866993 + 3.79854i) q^{13} +(0.606156 - 0.0357152i) q^{14} +(-3.64557 - 0.549481i) q^{16} +(-5.18854 + 3.53749i) q^{17} +(-1.89946 - 3.28997i) q^{19} +(-3.41525 - 1.64470i) q^{20} +(-0.272180 + 0.131075i) q^{22} +(-3.21984 - 2.19525i) q^{23} +(0.887576 + 0.823550i) q^{25} +(-0.738819 - 0.503718i) q^{26} +(3.56413 - 3.72043i) q^{28} +(-5.98313 - 2.88132i) q^{29} +(-0.842691 + 1.45958i) q^{31} +(2.19611 - 1.49728i) q^{32} +(0.320699 - 1.40508i) q^{34} +(4.50069 - 2.50364i) q^{35} +(-0.0956045 - 1.27575i) q^{37} +(0.833130 + 0.256987i) q^{38} +(1.68511 - 0.519788i) q^{40} +(5.27874 + 6.61934i) q^{41} +(-3.86669 + 4.84868i) q^{43} +(-0.936476 + 2.38610i) q^{44} +(0.884379 - 0.133299i) q^{46} +(2.40667 - 2.23306i) q^{47} +(1.33923 + 6.87070i) q^{49} -0.277881 q^{50} +(-7.50250 + 1.13082i) q^{52} +(-0.377467 + 5.03694i) q^{53} +(-1.59758 + 2.00330i) q^{55} +(-0.0382211 + 2.39654i) q^{56} +(1.45637 - 0.449229i) q^{58} +(4.20642 + 10.7178i) q^{59} +(0.0815328 + 1.08798i) q^{61} +(-0.0860711 - 0.377102i) q^{62} +(1.50502 - 6.59391i) q^{64} +(-7.49964 - 1.13039i) q^{65} +(4.35072 - 7.53567i) q^{67} +(-6.11433 - 10.5903i) q^{68} +(-0.366362 + 1.12377i) q^{70} +(13.6653 - 6.58084i) q^{71} +(9.63581 + 8.94072i) q^{73} +(0.215231 + 0.199705i) q^{74} +(6.66516 - 3.20977i) q^{76} +(-1.91570 - 2.90841i) q^{77} +(2.17868 + 3.77359i) q^{79} +(3.58829 - 6.21510i) q^{80} +(-1.92137 - 0.289600i) q^{82} +(-2.19813 + 9.63062i) q^{83} +(-2.72010 - 11.9175i) q^{85} +(-0.106364 - 1.41933i) q^{86} +(-0.435661 - 1.11005i) q^{88} +(4.32484 - 1.33404i) q^{89} +(4.62021 - 9.21509i) q^{91} +(4.73148 - 5.93309i) q^{92} +(-0.0563074 + 0.751370i) q^{94} +(7.31236 - 1.10216i) q^{95} -14.3073 q^{97} +(-1.29783 - 0.946852i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 13 q^{2} - 9 q^{4} + 14 q^{5} - 14 q^{7} + 20 q^{8}+O(q^{10}) \) 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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