LMFDB - Embedded newform 603.2.bj.a.503.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [603,2,Mod(44,603)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(603, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([33, 61]))

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

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

chi := DirichletCharacter("603.44");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 603 = 3^{2} \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	603.bj (of order $66$, degree $20$, 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:	$4.81497924188$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$22$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			503.7
Character	$\chi$	$=$	603.503
Dual form			603.2.bj.a.404.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0581060 - 1.21980i) q^{2} +(0.506420 - 0.0483572i) q^{4} +(0.949437 + 1.09571i) q^{5} +(1.57167 - 3.04861i) q^{7} +(-0.435996 - 3.03242i) q^{8} +O(q^{10})$	\(q+(-0.0581060 - 1.21980i) q^{2} +(0.506420 - 0.0483572i) q^{4} +(0.949437 + 1.09571i) q^{5} +(1.57167 - 3.04861i) q^{7} +(-0.435996 - 3.03242i) q^{8} +(1.28137 - 1.22179i) q^{10} +(-0.207518 + 0.599583i) q^{11} +(-0.662085 + 0.841910i) q^{13} +(-3.81001 - 1.73997i) q^{14} +(-2.67453 + 0.515474i) q^{16} +(-0.229427 + 2.40267i) q^{17} +(5.75797 - 2.96844i) q^{19} +(0.533799 + 0.508977i) q^{20} +(0.743426 + 0.218290i) q^{22} +(-1.93917 - 0.470437i) q^{23} +(0.412427 - 2.86849i) q^{25} +(1.06543 + 0.758688i) q^{26} +(0.648502 - 1.61988i) q^{28} +(-5.18957 + 2.99620i) q^{29} +(3.17788 + 4.04100i) q^{31} +(-0.660363 - 2.72205i) q^{32} +(2.94410 + 0.140245i) q^{34} +(4.83259 - 1.17237i) q^{35} +(0.645189 - 1.11750i) q^{37} +(-3.95546 - 6.85106i) q^{38} +(2.90870 - 3.35681i) q^{40} +(4.34251 - 6.09821i) q^{41} +(-0.287488 + 0.131291i) q^{43} +(-0.0760969 + 0.313676i) q^{44} +(-0.461159 + 2.39272i) q^{46} +(4.56577 - 4.78844i) q^{47} +(-2.76349 - 3.88078i) q^{49} +(-3.52294 - 0.336400i) q^{50} +(-0.294580 + 0.458376i) q^{52} +(-1.60686 + 3.51853i) q^{53} +(-0.853993 + 0.341887i) q^{55} +(-9.92990 - 3.43677i) q^{56} +(3.95630 + 6.15612i) q^{58} +(-1.38438 + 0.199044i) q^{59} +(-12.6197 + 4.36774i) q^{61} +(4.74454 - 4.11117i) q^{62} +(-8.50882 + 2.49842i) q^{64} +(-1.55110 + 0.0738878i) q^{65} +(-4.94655 + 6.52163i) q^{67} +1.22786i q^{68} +(-1.71086 - 5.82665i) q^{70} +(1.18234 + 12.3821i) q^{71} +(-0.711796 - 2.05660i) q^{73} +(-1.40061 - 0.722065i) q^{74} +(2.77241 - 1.78172i) q^{76} +(1.50175 + 1.57499i) q^{77} +(2.83885 + 7.09112i) q^{79} +(-3.10411 - 2.44110i) q^{80} +(-7.69089 - 4.94263i) q^{82} +(-1.98415 - 10.2948i) q^{83} +(-2.85046 + 2.02980i) q^{85} +(0.176853 + 0.343048i) q^{86} +(1.90866 + 0.367864i) q^{88} +(-0.0633517 + 0.215756i) q^{89} +(1.52608 + 3.34164i) q^{91} +(-1.00478 - 0.144466i) q^{92} +(-6.10622 - 5.29107i) q^{94} +(8.71938 + 3.49071i) q^{95} +(-2.46197 - 1.42142i) q^{97} +(-4.57319 + 3.59639i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q + 20 q^{4}+O(q^{10}) $ 440 * q + 20 * q^4	$ 440 q + 20 q^{4} + 18 q^{13} + 8 q^{16} + 36 q^{19} - 12 q^{22} - 44 q^{25} - 128 q^{28} + 82 q^{31} + 24 q^{34} - 8 q^{37} - 32 q^{40} - 44 q^{43} + 80 q^{46} - 10 q^{49} + 132 q^{52} - 64 q^{55} - 176 q^{58} - 86 q^{61} - 136 q^{64} - 78 q^{67} - 352 q^{70} + 180 q^{73} - 256 q^{76} + 104 q^{79} + 88 q^{82} - 84 q^{85} - 268 q^{88} - 328 q^{91} + 88 q^{94} - 6 q^{97}+O(q^{100}) $ 440 * q + 20 * q^4 + 18 * q^13 + 8 * q^16 + 36 * q^19 - 12 * q^22 - 44 * q^25 - 128 * q^28 + 82 * q^31 + 24 * q^34 - 8 * q^37 - 32 * q^40 - 44 * q^43 + 80 * q^46 - 10 * q^49 + 132 * q^52 - 64 * q^55 - 176 * q^58 - 86 * q^61 - 136 * q^64 - 78 * q^67 - 352 * q^70 + 180 * q^73 - 256 * q^76 + 104 * q^79 + 88 * q^82 - 84 * q^85 - 268 * q^88 - 328 * q^91 + 88 * q^94 - 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/603\mathbb{Z}\right)^\times$.

$n$	$136$	$470$
$\chi(n)$	$e\left(\frac{65}{66}\right)$	$-1$

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 $

$2$	−0.0581060	−	1.21980i	−0.0410872	−	0.862526i	−0.921514	−	0.388344i	$-0.873047\pi$
$2$	−0.0581060	−	1.21980i	−0.0410872	−	0.862526i	0.880427	−	0.474181i	$-0.157256\pi$
$3$		0			0
$3$		0			0
$4$	0.506420	−	0.0483572i	0.253210	−	0.0241786i
$5$	0.949437	+	1.09571i	0.424601	+	0.490016i	0.927233	−	0.374485i	$-0.122180\pi$
$5$	0.949437	+	1.09571i	0.424601	+	0.490016i	−0.502632	+	0.864501i	$0.667635\pi$
$6$		0			0
$7$	1.57167	−	3.04861i	0.594035	−	1.15227i	−0.379812	−	0.925064i	$-0.624011\pi$
$7$	1.57167	−	3.04861i	0.594035	−	1.15227i	0.973847	−	0.227203i	$-0.0729583\pi$
$8$	−0.435996	−	3.03242i	−0.154148	−	1.07212i
$9$		0			0
$10$	1.28137	−	1.22179i	0.405206	−	0.386363i
$11$	−0.207518	+	0.599583i	−0.0625689	+	0.180781i	−0.971952	−	0.235178i	$-0.924433\pi$
$11$	−0.207518	+	0.599583i	−0.0625689	+	0.180781i	0.909383	+	0.415959i	$0.136554\pi$
$12$		0			0
$13$	−0.662085	+	0.841910i	−0.183629	+	0.233504i	−0.869149	−	0.494551i	$-0.835333\pi$
$13$	−0.662085	+	0.841910i	−0.183629	+	0.233504i	0.685520	+	0.728054i	$0.259575\pi$
$14$	−3.81001	−	1.73997i	−1.01827	−	0.465027i
$15$		0			0
$16$	−2.67453	+	0.515474i	−0.668633	+	0.128868i
$17$	−0.229427	+	2.40267i	−0.0556443	+	0.582734i	0.924055	+	0.382260i	$0.124854\pi$
$17$	−0.229427	+	2.40267i	−0.0556443	+	0.582734i	−0.979699	+	0.200474i	$0.935752\pi$
$18$		0			0
$19$	5.75797	−	2.96844i	1.32097	−	0.681007i	0.353844	−	0.935305i	$-0.384875\pi$
$19$	5.75797	−	2.96844i	1.32097	−	0.681007i	0.967126	+	0.254298i	$0.0818442\pi$
$20$	0.533799	+	0.508977i	0.119361	+	0.113811i
$21$		0			0
$22$	0.743426	+	0.218290i	0.158499	+	0.0465395i
$23$	−1.93917	−	0.470437i	−0.404344	−	0.0980928i	0.0284287	−	0.999596i	$-0.490950\pi$
$23$	−1.93917	−	0.470437i	−0.404344	−	0.0980928i	−0.432773	+	0.901503i	$0.642465\pi$
$24$		0			0
$25$	0.412427	−	2.86849i	0.0824854	−	0.573699i
$26$	1.06543	+	0.758688i	0.208948	+	0.148791i
$27$		0			0
$28$	0.648502	−	1.61988i	0.122555	−	0.306128i
$29$	−5.18957	+	2.99620i	−0.963680	+	0.556381i	−0.897304	−	0.441414i	$-0.854477\pi$
$29$	−5.18957	+	2.99620i	−0.963680	+	0.556381i	−0.0663761	+	0.997795i	$0.521144\pi$
$30$		0			0
$31$	3.17788	+	4.04100i	0.570764	+	0.725786i	0.982654	−	0.185448i	$-0.0593736\pi$
$31$	3.17788	+	4.04100i	0.570764	+	0.725786i	−0.411890	+	0.911234i	$0.635131\pi$
$32$	−0.660363	−	2.72205i	−0.116737	−	0.481195i
$33$		0			0
$34$	2.94410	+	0.140245i	0.504909	+	0.0240518i
$35$	4.83259	−	1.17237i	0.816857	−	0.198167i
$36$		0			0
$37$	0.645189	−	1.11750i	0.106068	−	0.183716i	−0.808106	−	0.589037i	$-0.799507\pi$
$37$	0.645189	−	1.11750i	0.106068	−	0.183716i	0.914174	+	0.405321i	$0.132840\pi$
$38$	−3.95546	−	6.85106i	−0.641661	−	1.11139i
$39$		0			0
$40$	2.90870	−	3.35681i	0.459905	−	0.530759i
$41$	4.34251	−	6.09821i	0.678187	−	0.952380i	−0.321798	−	0.946808i	$-0.604287\pi$
$41$	4.34251	−	6.09821i	0.678187	−	0.952380i	0.999984	−	0.00557138i	$-0.00177343\pi$
$42$		0			0
$43$	−0.287488	+	0.131291i	−0.0438415	+	0.0200217i	−0.437215	−	0.899357i	$-0.644035\pi$
$43$	−0.287488	+	0.131291i	−0.0438415	+	0.0200217i	0.393374	+	0.919379i	$0.371308\pi$
$44$	−0.0760969	+	0.313676i	−0.0114720	+	0.0472884i
$45$		0			0
$46$	−0.461159	+	2.39272i	−0.0679942	+	0.352788i
$47$	4.56577	−	4.78844i	0.665986	−	0.698466i	−0.300905	−	0.953654i	$-0.597289\pi$
$47$	4.56577	−	4.78844i	0.665986	−	0.698466i	0.966892	+	0.255188i	$0.0821373\pi$
$48$		0			0
$49$	−2.76349	−	3.88078i	−0.394785	−	0.554398i
$50$	−3.52294	−	0.336400i	−0.498219	−	0.0475741i
$51$		0			0
$52$	−0.294580	+	0.458376i	−0.0408510	+	0.0635653i
$53$	−1.60686	+	3.51853i	−0.220719	+	0.483307i	−0.987305	−	0.158834i	$-0.949226\pi$
$53$	−1.60686	+	3.51853i	−0.220719	+	0.483307i	0.766586	+	0.642141i	$0.221954\pi$
$54$		0			0
$55$	−0.853993	+	0.341887i	−0.115152	+	0.0461001i
$56$	−9.92990	−	3.43677i	−1.32694	−	0.459258i
$57$		0			0
$58$	3.95630	+	6.15612i	0.519487	+	0.808338i
$59$	−1.38438	+	0.199044i	−0.180231	+	0.0259134i	−0.231840	−	0.972754i	$-0.574474\pi$
$59$	−1.38438	+	0.199044i	−0.180231	+	0.0259134i	0.0516081	+	0.998667i	$0.483565\pi$
$60$		0			0
$61$	−12.6197	+	4.36774i	−1.61579	+	0.559231i	−0.977568	−	0.210618i	$-0.932452\pi$
$61$	−12.6197	+	4.36774i	−1.61579	+	0.559231i	−0.638225	+	0.769850i	$0.720331\pi$
$62$	4.74454	−	4.11117i	0.602557	−	0.522119i
$63$		0			0
$64$	−8.50882	+	2.49842i	−1.06360	+	0.312302i
$65$	−1.55110	+	0.0738878i	−0.192390	+	0.00916466i
$66$		0			0
$67$	−4.94655	+	6.52163i	−0.604317	+	0.796744i
$67$	−4.94655	+	6.52163i	−0.604317	+	0.796744i
$68$			1.22786i			0.148899i
$69$		0			0
$70$	−1.71086	−	5.82665i	−0.204487	−	0.696418i
$71$	1.18234	+	12.3821i	0.140318	+	1.46948i	0.741814	+	0.670606i	$0.233966\pi$
$71$	1.18234	+	12.3821i	0.140318	+	1.46948i	−0.601496	+	0.798876i	$0.705428\pi$
$72$		0			0
$73$	−0.711796	−	2.05660i	−0.0833094	−	0.240707i	0.895651	−	0.444758i	$-0.146710\pi$
$73$	−0.711796	−	2.05660i	−0.0833094	−	0.240707i	−0.978960	+	0.204051i	$0.934589\pi$
$74$	−1.40061	−	0.722065i	−0.162818	−	0.0839383i
$75$		0			0
$76$	2.77241	−	1.78172i	0.318017	−	0.204377i
$77$	1.50175	+	1.57499i	0.171140	+	0.179486i
$78$		0			0
$79$	2.83885	+	7.09112i	0.319396	+	0.797813i	0.997994	+	0.0633033i	$0.0201635\pi$
$79$	2.83885	+	7.09112i	0.319396	+	0.797813i	−0.678598	+	0.734510i	$0.737412\pi$
$80$	−3.10411	−	2.44110i	−0.347050	−	0.272923i
$81$		0			0
$82$	−7.69089	−	4.94263i	−0.849317	−	0.545823i
$83$	−1.98415	−	10.2948i	−0.217789	−	1.13000i	−0.911989	−	0.410215i	$-0.865454\pi$
$83$	−1.98415	−	10.2948i	−0.217789	−	1.13000i	0.694200	−	0.719782i	$-0.255758\pi$
$84$		0			0
$85$	−2.85046	+	2.02980i	−0.309176	+	0.220163i
$86$	0.176853	+	0.343048i	0.0190706	+	0.0369918i
$87$		0			0
$88$	1.90866	+	0.367864i	0.203464	+	0.0392145i
$89$	−0.0633517	+	0.215756i	−0.00671527	+	0.0228701i	−0.962782	−	0.270277i	$-0.912885\pi$
$89$	−0.0633517	+	0.215756i	−0.00671527	+	0.0228701i	0.956067	+	0.293148i	$0.0947027\pi$
$90$		0			0
$91$	1.52608	+	3.34164i	0.159976	+	0.350299i
$92$	−1.00478	−	0.144466i	−0.104756	−	0.0150616i
$93$		0			0
$94$	−6.10622	−	5.29107i	−0.629808	−	0.545732i
$95$	8.71938	+	3.49071i	0.894590	+	0.358140i
$96$		0			0
$97$	−2.46197	−	1.42142i	−0.249975	−	0.144323i	0.369778	−	0.929120i	$-0.379434\pi$
$97$	−2.46197	−	1.42142i	−0.249975	−	0.144323i	−0.619753	+	0.784797i	$0.712767\pi$
$98$	−4.57319	+	3.59639i	−0.461962	+	0.363291i
$99$		0			0
$100$	0.0701488	−	1.47260i	0.00701488	−	0.147260i
$101$	−0.160914	+	3.37801i	−0.0160116	+	0.336124i	0.976622	+	0.214966i	$0.0689640\pi$
$101$	−0.160914	+	3.37801i	−0.0160116	+	0.336124i	−0.992633	+	0.121159i	$0.961339\pi$
$102$		0			0
$103$	−1.43647	+	1.12965i	−0.141540	+	0.111308i	−0.686418	−	0.727207i	$-0.740818\pi$
$103$	−1.43647	+	1.12965i	−0.141540	+	0.111308i	0.544879	+	0.838515i	$0.316576\pi$
$104$	2.84169	+	1.64065i	0.278650	+	0.160879i
$105$		0			0
$106$	4.38525	+	1.75559i	0.425933	+	0.170518i
$107$	9.84579	+	8.53143i	0.951829	+	0.824764i	0.984622	−	0.174698i	$-0.0558948\pi$
$107$	9.84579	+	8.53143i	0.951829	+	0.824764i	−0.0327932	+	0.999462i	$0.510440\pi$
$108$		0			0
$109$	14.6480	+	2.10606i	1.40302	+	0.201724i	0.801912	−	0.597442i	$-0.203816\pi$
$109$	14.6480	+	2.10606i	1.40302	+	0.201724i	0.601110	+	0.799166i	$0.294725\pi$
$110$	0.466655	+	1.02183i	0.0444938	+	0.0974278i
$111$		0			0
$112$	−2.63200	+	8.96377i	−0.248701	+	0.846996i
$113$	3.09189	+	0.595913i	0.290861	+	0.0560588i	0.332594	−	0.943070i	$-0.392076\pi$
$113$	3.09189	+	0.595913i	0.290861	+	0.0560588i	−0.0417337	+	0.999129i	$0.513288\pi$
$114$		0			0
$115$	−1.32566	−	2.57141i	−0.123618	−	0.239786i
$116$	−2.48321	+	1.76829i	−0.230561	+	0.164182i
$117$		0			0
$118$	0.323234	+	1.67710i	0.0297561	+	0.154390i
$119$	6.96423	+	4.47564i	0.638410	+	0.410281i
$120$		0			0
$121$	8.33015	+	6.55090i	0.757286	+	0.595536i
$122$	6.06103	+	15.1397i	0.548740	+	1.37069i
$123$		0			0
$124$	1.80475	+	1.89277i	0.162072	+	0.169976i
$125$	9.63298	−	6.19074i	0.861600	−	0.553717i
$126$		0			0
$127$	−2.35837	−	1.21582i	−0.209271	−	0.107887i	0.350405	−	0.936598i	$-0.386044\pi$
$127$	−2.35837	−	1.21582i	−0.209271	−	0.107887i	−0.559676	+	0.828712i	$0.689074\pi$
$128$	1.70973	+	4.93994i	0.151120	+	0.436633i
$129$		0			0
$130$	0.180256	+	1.88773i	0.0158095	+	0.165565i
$131$	4.70487	+	16.0233i	0.411067	+	1.39996i	0.861774	+	0.507293i	$0.169354\pi$
$131$	4.70487	+	16.0233i	0.411067	+	1.39996i	−0.450707	+	0.892672i	$0.648828\pi$
$132$		0			0
$133$		−	22.2192i		−	1.92665i
$134$	8.24248	+	5.65483i	0.712042	+	0.488503i
$135$		0			0
$136$	7.38593	−	0.351835i	0.633339	−	0.0301696i
$137$	−11.6588	+	3.42332i	−0.996076	+	0.292474i	−0.738845	−	0.673876i	$-0.764628\pi$
$137$	−11.6588	+	3.42332i	−0.996076	+	0.292474i	−0.257231	+	0.966350i	$0.582810\pi$
$138$		0			0
$139$	−16.4905	+	14.2891i	−1.39870	+	1.21198i	−0.451125	+	0.892461i	$0.648977\pi$
$139$	−16.4905	+	14.2891i	−1.39870	+	1.21198i	−0.947579	+	0.319523i	$0.896477\pi$
$140$	2.39063	−	0.827404i	0.202045	−	0.0699284i
$141$		0			0
$142$	15.0349	−	2.16169i	1.26170	−	0.181405i
$143$	−0.367400	−	0.571686i	−0.0307236	−	0.0478068i
$144$		0			0
$145$	−8.21014	−	2.84156i	−0.681815	−	0.235979i
$146$	−2.46727	+	0.987746i	−0.204193	+	0.0817465i
$147$		0			0
$148$	0.272697	−	0.597123i	0.0224156	−	0.0490832i
$149$	4.38844	−	6.82854i	0.359515	−	0.559416i	−0.613635	−	0.789590i	$-0.710293\pi$
$149$	4.38844	−	6.82854i	0.359515	−	0.559416i	0.973149	+	0.230174i	$0.0739296\pi$
$150$		0			0
$151$	4.66511	+	0.445464i	0.379641	+	0.0362513i	0.283133	−	0.959081i	$-0.408626\pi$
$151$	4.66511	+	0.445464i	0.379641	+	0.0362513i	0.0965087	+	0.995332i	$0.469232\pi$
$152$	−11.5120	−	16.1663i	−0.933746	−	1.31126i
$153$		0			0
$154$	1.83390	−	1.92334i	0.147780	−	0.154987i
$155$	−1.41057	+	7.31871i	−0.113299	+	0.587853i
$156$		0			0
$157$	−5.13673	+	21.1739i	−0.409956	+	1.68986i	0.275138	+	0.961405i	$0.411277\pi$
$157$	−5.13673	+	21.1739i	−0.409956	+	1.68986i	−0.685093	+	0.728455i	$0.740239\pi$
$158$	8.48476	−	3.87486i	0.675011	−	0.308267i
$159$		0			0
$160$	2.35560	−	3.30798i	0.186227	−	0.261519i
$161$	−4.48191	+	5.17240i	−0.353224	+	0.407642i
$162$		0			0
$163$	−8.58253	−	14.8654i	−0.672236	−	1.16435i	−0.977269	−	0.212005i	$-0.932001\pi$
$163$	−8.58253	−	14.8654i	−0.672236	−	1.16435i	0.305033	−	0.952342i	$-0.401333\pi$
$164$	1.90424	−	3.29824i	0.148696	−	0.257550i
$165$		0			0
$166$	−12.4422	+	3.01845i	−0.965703	+	0.234277i
$167$	20.8727	+	0.994289i	1.61518	+	0.0769404i	0.835591	−	0.549353i	$-0.185126\pi$
$167$	20.8727	+	0.994289i	1.61518	+	0.0769404i	0.779588	+	0.626293i	$0.215429\pi$
$168$		0			0
$169$	2.79441	+	11.5187i	0.214955	+	0.886055i
$170$	2.64157	+	3.35903i	0.202599	+	0.257626i
$171$		0			0
$172$	−0.139241	+	0.0803907i	−0.0106170	+	0.00612973i
$173$	−1.59300	+	3.97913i	−0.121114	+	0.302528i	−0.976519	−	0.215432i	$-0.930884\pi$
$173$	−1.59300	+	3.97913i	−0.121114	+	0.302528i	0.855405	+	0.517960i	$0.173308\pi$
$174$		0			0
$175$	−8.09672	−	5.76565i	−0.612055	−	0.435842i
$176$	0.245943	−	1.71057i	0.0185387	−	0.128939i
$177$		0			0
$178$	0.266859	+	0.0647394i	0.0200020	+	0.00485242i
$179$	−5.76967	−	1.69413i	−0.431245	−	0.126625i	0.0589037	−	0.998264i	$-0.481239\pi$
$179$	−5.76967	−	1.69413i	−0.431245	−	0.126625i	−0.490149	+	0.871639i	$0.663058\pi$
$180$		0			0
$181$	−15.7106	−	14.9800i	−1.16776	−	1.11346i	−0.991633	−	0.129091i	$-0.958794\pi$
$181$	−15.7106	−	14.9800i	−1.16776	−	1.11346i	−0.176129	−	0.984367i	$-0.556357\pi$
$182$	3.98745	−	2.05567i	0.295569	−	0.152377i
$183$		0			0
$184$	−0.581092	+	6.08547i	−0.0428387	+	0.448627i
$185$	1.83702	−	0.354057i	0.135060	−	0.0260308i
$186$		0			0
$187$	−1.39299	−	0.636158i	−0.101866	−	0.0465205i
$188$	2.08064	−	2.64575i	0.151746	−	0.192961i
$189$		0			0
$190$	3.75131	−	10.8387i	0.272149	−	0.786321i
$191$	−14.7638	+	14.0772i	−1.06827	+	1.01859i	−0.0684896	+	0.997652i	$0.521818\pi$
$191$	−14.7638	+	14.0772i	−1.06827	+	1.01859i	−0.999781	+	0.0209418i	$0.993334\pi$
$192$		0			0
$193$	0.430128	+	2.99161i	0.0309613	+	0.215341i	0.999429	−	0.0338000i	$-0.0107609\pi$
$193$	0.430128	+	2.99161i	0.0309613	+	0.215341i	−0.968467	+	0.249141i	$0.919852\pi$
$194$	−1.59078	+	3.08569i	−0.114212	+	0.221540i
$195$		0			0
$196$	−1.58715	−	1.83167i	−0.113368	−	0.130834i
$197$	3.16011	−	0.301754i	0.225148	−	0.0214991i	0.0181279	−	0.999836i	$-0.494229\pi$
$197$	3.16011	−	0.301754i	0.225148	−	0.0214991i	0.207020	+	0.978337i	$0.433623\pi$
$198$		0			0
$199$	0.642519	+	13.4881i	0.0455470	+	0.956149i	0.899803	+	0.436296i	$0.143710\pi$
$199$	0.642519	+	13.4881i	0.0455470	+	0.956149i	−0.854256	+	0.519852i	$0.825987\pi$
$200$	−8.87828			−0.627789
$201$		0			0
$202$	4.12983			0.290574
$203$	0.977966	+	20.5300i	0.0686398	+	1.44093i
$204$		0			0
$205$	10.8048	−	1.03173i	0.754640	−	0.0720594i
$206$	1.46141	+	1.68656i	0.101821	+	0.117508i
$207$		0			0
$208$	1.33679	−	2.59300i	0.0926894	−	0.179792i
$209$	0.584946	+	4.06839i	0.0404615	+	0.281416i
$210$		0			0
$211$	−3.39725	+	3.23927i	−0.233876	+	0.223001i	−0.797950	−	0.602724i	$-0.794082\pi$
$211$	−3.39725	+	3.23927i	−0.233876	+	0.223001i	0.564073	+	0.825725i	$0.309234\pi$
$212$	−0.643598	+	1.85956i	−0.0442025	+	0.127715i
$213$		0			0
$214$	9.83450	−	12.5056i	0.672272	−	0.854864i
$215$	−0.416809	−	0.190350i	−0.0284261	−	0.0129818i
$216$		0			0
$217$	17.3140	−	3.33700i	1.17535	−	0.226531i
$218$	1.71783	−	17.9899i	0.116346	−	1.21843i
$219$		0			0
$220$	−0.415946	+	0.214435i	−0.0280431	+	0.0144572i
$221$	−1.87093	−	1.78393i	−0.125853	−	0.120000i
$222$		0			0
$223$	−6.84304	−	2.00930i	−0.458244	−	0.134553i	0.0444600	−	0.999011i	$-0.485843\pi$
$223$	−6.84304	−	2.00930i	−0.458244	−	0.134553i	−0.502704	+	0.864459i	$0.667661\pi$
$224$	−9.33635	−	2.26497i	−0.623811	−	0.151335i
$225$		0			0
$226$	0.547235	−	3.80610i	0.0364015	−	0.253178i
$227$	8.71469	+	6.20570i	0.578414	+	0.411887i	0.831474	−	0.555564i	$-0.187498\pi$
$227$	8.71469	+	6.20570i	0.578414	+	0.411887i	−0.253060	+	0.967451i	$0.581437\pi$
$228$		0			0
$229$	−1.56150	+	3.90045i	−0.103187	+	0.257749i	−0.970973	−	0.239190i	$-0.923118\pi$
$229$	−1.56150	+	3.90045i	−0.103187	+	0.257749i	0.867786	+	0.496938i	$0.165543\pi$
$230$	−3.05957	+	1.76644i	−0.201742	+	0.116476i
$231$		0			0
$232$	11.3484	+	14.4306i	0.745056	+	0.947416i
$233$	−4.47847	−	18.4605i	−0.293394	−	1.20939i	−0.907462	−	0.420135i	$-0.861983\pi$
$233$	−4.47847	−	18.4605i	−0.293394	−	1.20939i	0.614067	−	0.789254i	$-0.289532\pi$
$234$		0			0
$235$	9.58166	+	0.456431i	0.625038	+	0.0297742i
$236$	−0.691454	+	0.167745i	−0.0450098	+	0.0109193i
$237$		0			0
$238$	5.05470	−	8.75500i	0.327648	−	0.567502i
$239$	−4.84006	−	8.38323i	−0.313077	−	0.542266i	0.665950	−	0.745997i	$-0.268027\pi$
$239$	−4.84006	−	8.38323i	−0.313077	−	0.542266i	−0.979027	+	0.203731i	$0.934693\pi$
$240$		0			0
$241$	6.24670	−	7.20908i	0.402385	−	0.464377i	−0.518005	−	0.855377i	$-0.673325\pi$
$241$	6.24670	−	7.20908i	0.402385	−	0.464377i	0.920391	+	0.391000i	$0.127871\pi$
$242$	7.50673	−	10.5417i	0.482551	−	0.677648i
$243$		0			0
$244$	−6.17968	+	2.82216i	−0.395613	+	0.180671i
$245$	1.62845	−	6.71255i	0.104038	−	0.428849i
$246$		0			0
$247$	−1.31311	+	6.81305i	−0.0835511	+	0.433504i
$248$	10.8685	−	11.3985i	0.690148	−	0.723806i
$249$		0			0
$250$	−8.11117	−	11.3905i	−0.512996	−	0.720402i
$251$	−17.6591	−	1.68624i	−1.11463	−	0.106434i	−0.478553	−	0.878059i	$-0.658839\pi$
$251$	−17.6591	−	1.68624i	−1.11463	−	0.106434i	−0.636079	+	0.771624i	$0.719445\pi$
$252$		0			0
$253$	0.684477	−	1.06507i	0.0430327	−	0.0669602i
$254$	−1.34602	+	2.94737i	−0.0844568	+	0.184935i
$255$		0			0
$256$	−10.5392	+	4.21927i	−0.658702	+	0.263705i
$257$	−11.9125	−	4.12296i	−0.743083	−	0.257183i	−0.0708129	−	0.997490i	$-0.522559\pi$
$257$	−11.9125	−	4.12296i	−0.743083	−	0.257183i	−0.672270	+	0.740306i	$0.734681\pi$
$258$		0			0
$259$	−2.39280	−	3.72327i	−0.148681	−	0.231353i
$260$	−0.781933	+	0.112425i	−0.0484934	+	0.00697230i
$261$		0			0
$262$	19.2718	−	6.67003i	1.19062	−	0.412076i
$263$	23.3397	−	20.2240i	1.43919	−	1.24706i	0.519467	−	0.854491i	$-0.326131\pi$
$263$	23.3397	−	20.2240i	1.43919	−	1.24706i	0.919721	−	0.392573i	$-0.128415\pi$
$264$		0			0
$265$	−5.38090	+	1.57997i	−0.330546	+	0.0970570i
$266$	−27.1029	+	1.29107i	−1.66179	+	0.0791606i
$267$		0			0
$268$	−2.18966	+	3.54188i	−0.133755	+	0.216355i
$269$		−	7.61219i		−	0.464123i	−0.972701	−	0.232062i	$-0.925453\pi$
$269$		−	7.61219i		−	0.464123i	0.972701	−	0.232062i	$-0.0745471\pi$
$270$		0			0
$271$	3.74233	+	12.7452i	0.227330	+	0.774216i	0.991603	+	0.129322i	$0.0412802\pi$
$271$	3.74233	+	12.7452i	0.227330	+	0.774216i	−0.764272	+	0.644894i	$0.776902\pi$
$272$	−0.624904	−	6.54429i	−0.0378904	−	0.396806i
$273$		0			0
$274$	4.85320	+	14.0224i	0.293192	+	0.847124i
$275$	1.63431	+	0.842547i	0.0985528	+	0.0508075i
$276$		0			0
$277$	−17.5700	+	11.2916i	−1.05568	+	0.678445i	−0.948816	−	0.315829i	$-0.897717\pi$
$277$	−17.5700	+	11.2916i	−1.05568	+	0.678445i	−0.106864	+	0.994274i	$0.534081\pi$
$278$	18.3879	+	19.2847i	1.10284	+	1.15662i
$279$		0			0
$280$	−5.66212	−	14.1433i	−0.338376	−	0.845223i
$281$	−12.8652	−	10.1173i	−0.767471	−	0.603546i	0.155758	−	0.987795i	$-0.450218\pi$
$281$	−12.8652	−	10.1173i	−0.767471	−	0.603546i	−0.923230	+	0.384249i	$0.874460\pi$
$282$		0			0
$283$	8.50429	+	5.46538i	0.505528	+	0.324883i	0.768424	−	0.639941i	$-0.221041\pi$
$283$	8.50429	+	5.46538i	0.505528	+	0.324883i	−0.262896	+	0.964824i	$0.584678\pi$
$284$	1.19753	+	6.21335i	0.0710600	+	0.368694i
$285$		0			0
$286$	−0.675992	+	0.481371i	−0.0399722	+	0.0284641i
$287$	−11.7661	−	22.8230i	−0.694529	−	1.34720i
$288$		0			0
$289$	10.9726	+	2.11479i	0.645446	+	0.124400i
$290$	−2.98906	+	10.1798i	−0.175524	+	0.597779i
$291$		0			0
$292$	−0.459919	−	1.00708i	−0.0269147	−	0.0589350i
$293$	−26.9826	−	3.87951i	−1.57634	−	0.226643i	−0.702077	−	0.712101i	$-0.747744\pi$
$293$	−26.9826	−	3.87951i	−1.57634	−	0.226643i	−0.874260	+	0.485458i	$0.838653\pi$
$294$		0			0
$295$	−1.53248	−	1.32790i	−0.0892245	−	0.0773135i
$296$	−3.67002	−	1.46926i	−0.213316	−	0.0853988i
$297$		0			0
$298$	−8.58442	−	4.95622i	−0.497282	−	0.287106i
$299$	1.67996	−	1.32113i	0.0971545	−	0.0764031i
$300$		0			0
$301$	−0.0515795	+	1.08279i	−0.00297299	+	0.0624108i
$302$	0.272304	−	5.71636i	0.0156693	−	0.328940i
$303$		0			0
$304$	−13.8697	+	10.9073i	−0.795484	+	0.625575i
$305$	−16.7674	−	9.68068i	−0.960100	−	0.554314i
$306$		0			0
$307$	−8.29211	−	3.31966i	−0.473256	−	0.189463i	0.122759	−	0.992437i	$-0.460826\pi$
$307$	−8.29211	−	3.31966i	−0.473256	−	0.189463i	−0.596015	+	0.802974i	$0.703250\pi$
$308$	0.836676	+	0.724984i	0.0476740	+	0.0413098i
$309$		0			0
$310$	9.00929	+	1.29534i	0.511693	+	0.0735704i
$311$	−6.22872	−	13.6390i	−0.353198	−	0.773396i	−0.999943	−	0.0106894i	$-0.996597\pi$
$311$	−6.22872	−	13.6390i	−0.353198	−	0.773396i	0.646745	−	0.762706i	$-0.276130\pi$
$312$		0			0
$313$	3.63713	−	12.3869i	0.205583	−	0.700151i	−0.790558	−	0.612387i	$-0.790210\pi$
$313$	3.63713	−	12.3869i	0.205583	−	0.700151i	0.996141	−	0.0877644i	$-0.0279722\pi$
$314$	26.1263	+	5.03543i	1.47439	+	0.284166i
$315$		0			0
$316$	1.78056	+	3.45380i	0.100164	+	0.194292i
$317$	16.6599	−	11.8635i	0.935713	−	0.666318i	−0.00698129	−	0.999976i	$-0.502222\pi$
$317$	16.6599	−	11.8635i	0.935713	−	0.666318i	0.942694	+	0.333657i	$0.108283\pi$
$318$		0			0
$319$	−0.719543	−	3.73334i	−0.0402867	−	0.209027i
$320$	−10.8161	−	6.95110i	−0.604640	−	0.388579i
$321$		0			0
$322$	6.56969	+	5.16646i	0.366115	+	0.287916i
$323$	5.81116	+	14.5156i	0.323341	+	0.807668i
$324$		0			0
$325$	2.14195	+	2.24641i	0.118814	+	0.124609i
$326$	−17.6340	+	11.3327i	−0.976659	+	0.627660i
$327$		0			0
$328$	−20.3856	−	10.5095i	−1.12561	−	0.580291i
$329$	−7.42223	−	21.4451i	−0.409201	−	1.18231i
$330$		0			0
$331$	−0.120172	−	1.25850i	−0.00660526	−	0.0691734i	0.991568	−	0.129585i	$-0.0413646\pi$
$331$	−0.120172	−	1.25850i	−0.00660526	−	0.0691734i	−0.998174	+	0.0604119i	$0.980759\pi$
$332$	−1.50264	−	5.11752i	−0.0824681	−	0.280860i
$333$		0			0
$334$		−	25.5182i		−	1.39629i
$335$	−11.8422	+	0.771901i	−0.647011	+	0.0421735i
$336$		0			0
$337$	22.0007	−	1.04802i	1.19845	−	0.0570894i	0.561158	−	0.827709i	$-0.310356\pi$
$337$	22.0007	−	1.04802i	1.19845	−	0.0570894i	0.637296	+	0.770619i	$0.280053\pi$
$338$	13.8881	−	4.07792i	0.755413	−	0.221809i
$339$		0			0
$340$	−1.34537	+	1.16577i	−0.0729631	+	0.0632229i
$341$	−3.08238	+	1.06682i	−0.166920	+	0.0577717i
$342$		0			0
$343$	7.59058	−	1.09136i	0.409853	−	0.0589279i
$344$	0.523474	+	0.814541i	0.0282238	+	0.0439171i
$345$		0			0
$346$	4.94629	+	1.71193i	0.265914	+	0.0920338i
$347$	−7.51993	+	3.01052i	−0.403691	+	0.161613i	−0.564617	−	0.825353i	$-0.690976\pi$
$347$	−7.51993	+	3.01052i	−0.403691	+	0.161613i	0.160926	+	0.986966i	$0.448552\pi$
$348$		0			0
$349$	3.99540	−	8.74871i	0.213869	−	0.468308i	−0.772043	−	0.635570i	$-0.780765\pi$
$349$	3.99540	−	8.74871i	0.213869	−	0.468308i	0.985913	+	0.167262i	$0.0534925\pi$
$350$	−6.56244	+	10.2114i	−0.350777	+	0.545820i
$351$		0			0
$352$	1.76913	+	0.168932i	0.0942951	+	0.00900409i
$353$	1.41444	+	1.98631i	0.0752831	+	0.105720i	0.850501	−	0.525974i	$-0.176299\pi$
$353$	1.41444	+	1.98631i	0.0752831	+	0.105720i	−0.775217	+	0.631694i	$0.782360\pi$
$354$		0			0
$355$	−12.4446	+	13.0515i	−0.660490	+	0.692702i
$356$	−0.0216492	+	0.112327i	−0.00114740	+	0.00595330i
$357$		0			0
$358$	−1.73124	+	7.13625i	−0.0914987	+	0.377163i
$359$	−12.9579	+	5.91768i	−0.683892	+	0.312323i	−0.726892	−	0.686752i	$-0.759036\pi$
$359$	−12.9579	+	5.91768i	−0.683892	+	0.312323i	0.0429996	+	0.999075i	$0.486309\pi$
$360$		0			0
$361$	13.3215	−	18.7075i	0.701133	−	0.984603i
$362$	−17.3597	+	20.0342i	−0.912406	+	1.05297i
$363$		0			0
$364$	0.934428	+	1.61848i	0.0489773	+	0.0848312i
$365$	1.57763	−	2.73253i	0.0825769	−	0.143027i
$366$		0			0
$367$	−11.8180	+	2.86701i	−0.616894	+	0.149657i	−0.532016	−	0.846734i	$-0.678565\pi$
$367$	−11.8180	+	2.86701i	−0.616894	+	0.149657i	−0.0848784	+	0.996391i	$0.527050\pi$
$368$	5.42886	+	0.258609i	0.282999	+	0.0134809i
$369$		0			0
$370$	−0.538619	−	2.22022i	−0.0280015	−	0.115424i
$371$	8.20118	+	10.4286i	0.425784	+	0.541429i
$372$		0			0
$373$	−7.69298	+	4.44155i	−0.398328	+	0.229975i	−0.685762	−	0.727826i	$-0.740531\pi$
$373$	−7.69298	+	4.44155i	−0.398328	+	0.229975i	0.287435	+	0.957800i	$0.407198\pi$
$374$	−0.695041	+	1.73613i	−0.0359397	+	0.0897731i
$375$		0			0
$376$	−16.5112	−	11.7576i	−0.851501	−	0.606351i
$377$	0.913408	−	6.35289i	0.0470429	−	0.327191i
$378$		0			0
$379$	−22.2104	−	5.38818i	−1.14087	−	0.276772i	−0.379564	−	0.925165i	$-0.623926\pi$
$379$	−22.2104	−	5.38818i	−1.14087	−	0.276772i	−0.761306	+	0.648393i	$0.775441\pi$
$380$	4.58447	+	1.34612i	0.235178	+	0.0690546i
$381$		0			0
$382$	18.0292	+	17.1908i	0.922455	+	0.879559i
$383$	21.8083	−	11.2429i	1.11435	−	0.574487i	0.200156	−	0.979764i	$-0.435855\pi$
$383$	21.8083	−	11.2429i	1.11435	−	0.574487i	0.914194	+	0.405277i	$0.132825\pi$
$384$		0			0
$385$	−0.299913	+	3.14083i	−0.0152850	+	0.160071i
$386$	3.62416	−	0.698499i	0.184465	−	0.0355527i
$387$		0			0
$388$	−1.31552	−	0.600780i	−0.0667856	−	0.0305000i
$389$	18.7533	−	23.8467i	0.950828	−	1.20908i	−0.0269939	−	0.999636i	$-0.508593\pi$
$389$	18.7533	−	23.8467i	0.950828	−	1.20908i	0.977821	−	0.209440i	$-0.0671641\pi$
$390$		0			0
$391$	1.57520	−	4.55125i	0.0796615	−	0.230167i
$392$	−10.5633	+	10.0721i	−0.533526	+	0.508716i
$393$		0			0
$394$	−0.551699	−	3.83715i	−0.0277942	−	0.193313i
$395$	−5.07449	+	9.84313i	−0.255325	+	0.495262i
$396$		0			0
$397$	−2.64024	−	3.04700i	−0.132510	−	0.152925i	0.685617	−	0.727963i	$-0.259533\pi$
$397$	−2.64024	−	3.04700i	−0.132510	−	0.152925i	−0.818127	+	0.575038i	$0.804987\pi$
$398$	16.4154	−	1.56748i	0.822831	−	0.0785709i
$399$		0			0
$400$	0.375584	+	7.88447i	0.0187792	+	0.394224i
$401$	−11.7767			−0.588099			−0.294050	−	0.955790i	$-0.595003\pi$
$401$	−11.7767			−0.588099			−0.294050	+	0.955790i	$0.595003\pi$
$402$		0			0
$403$	−5.50619			−0.274283
$404$	0.0818609	+	1.71847i	0.00407273	+	0.0854971i
$405$		0			0
$406$	24.9856	−	2.38584i	1.24002	−	0.118407i
$407$	0.536146	+	0.618745i	0.0265758	+	0.0306701i
$408$		0			0
$409$	16.1502	−	31.3270i	0.798577	−	1.54902i	−0.0367859	−	0.999323i	$-0.511712\pi$
$409$	16.1502	−	31.3270i	0.798577	−	1.54902i	0.835363	−	0.549699i	$-0.185258\pi$
$410$	−1.88633	−	13.1197i	−0.0931591	−	0.647936i
$411$		0			0
$412$	−0.672830	+	0.641542i	−0.0331479	+	0.0316065i
$413$	−1.56898	+	4.53328i	−0.0772047	+	0.223068i
$414$		0			0
$415$	9.39624	−	11.9483i	0.461243	−	0.586518i
$416$	2.72894	+	1.24626i	0.133797	+	0.0611031i
$417$		0			0
$418$	4.92861	−	0.949911i	0.241066	−	0.0464617i
$419$	0.507135	−	5.31095i	0.0247751	−	0.259457i	−0.974595	−	0.223974i	$-0.928097\pi$
$419$	0.507135	−	5.31095i	0.0247751	−	0.259457i	0.999370	−	0.0354831i	$-0.0112970\pi$
$420$		0			0
$421$	33.3206	−	17.1780i	1.62395	−	0.837202i	0.625573	−	0.780165i	$-0.284865\pi$
$421$	33.3206	−	17.1780i	1.62395	−	0.837202i	0.998372	−	0.0570369i	$-0.0181653\pi$
$422$	4.14865	+	3.95573i	0.201953	+	0.192562i
$423$		0			0
$424$	11.3702	+	3.33860i	0.552187	+	0.162137i
$425$	6.79743	+	1.64904i	0.329724	+	0.0799901i
$426$		0			0
$427$	−6.51853	+	45.3374i	−0.315454	+	2.19403i
$428$	5.39866	+	3.84437i	0.260954	+	0.185825i
$429$		0			0
$430$	−0.207969	+	0.519482i	−0.0100292	+	0.0250517i
$431$	32.9263	−	19.0100i	1.58600	−	0.915680i	0.592048	−	0.805903i	$-0.298320\pi$
$431$	32.9263	−	19.0100i	1.58600	−	0.915680i	0.993956	−	0.109777i	$-0.0350137\pi$
$432$		0			0
$433$	2.49476	+	3.17234i	0.119890	+	0.152453i	0.842294	−	0.539019i	$-0.181205\pi$
$433$	2.49476	+	3.17234i	0.119890	+	0.152453i	−0.722403	+	0.691472i	$0.756963\pi$
$434$	−5.07651	−	20.9257i	−0.243680	−	1.00446i
$435$		0			0
$436$	7.51987	+	0.358216i	0.360137	+	0.0171554i
$437$	−12.5621	+	3.04754i	−0.600928	+	0.145784i
$438$		0			0
$439$	10.2887	−	17.8206i	0.491055	−	0.850532i	−0.508892	−	0.860830i	$-0.669945\pi$
$439$	10.2887	−	17.8206i	0.491055	−	0.850532i	0.999947	+	0.0102981i	$0.00327803\pi$
$440$	1.40908	+	2.44060i	0.0671754	+	0.116351i
$441$		0			0
$442$	−2.06732	+	2.38581i	−0.0983323	+	0.113482i
$443$	2.03617	−	2.85940i	0.0967414	−	0.135854i	−0.763368	−	0.645964i	$-0.776456\pi$
$443$	2.03617	−	2.85940i	0.0967414	−	0.135854i	0.860110	+	0.510109i	$0.170395\pi$
$444$		0			0
$445$	−0.296555	+	0.135432i	−0.0140580	+	0.00642009i
$446$	−2.05331	+	8.46386i	−0.0972271	+	0.400776i
$447$		0			0
$448$	−5.75635	+	29.8668i	−0.271962	+	1.41107i
$449$	−22.1133	+	23.1917i	−1.04359	+	1.09448i	−0.0481735	+	0.998839i	$0.515340\pi$
$449$	−22.1133	+	23.1917i	−1.04359	+	1.09448i	−0.995415	+	0.0956456i	$0.969508\pi$
$450$		0			0
$451$	2.75523	+	3.86918i	0.129739	+	0.182193i
$452$	1.59461	+	0.152267i	0.0750042	+	0.00716204i
$453$		0			0
$454$	7.06331	−	10.9907i	0.331498	−	0.515820i
$455$	−2.21255	+	4.84482i	−0.103726	+	0.227129i
$456$		0			0
$457$	26.5378	−	10.6241i	1.24139	−	0.496976i	0.344311	−	0.938855i	$-0.388112\pi$
$457$	26.5378	−	10.6241i	1.24139	−	0.496976i	0.897074	+	0.441880i	$0.145688\pi$
$458$	4.84848	+	1.67808i	0.226555	+	0.0784113i
$459$		0			0
$460$	−0.795684	−	1.23811i	−0.0370990	−	0.0577271i
$461$	−25.0290	+	3.59862i	−1.16571	+	0.167604i	−0.697882	−	0.716213i	$-0.745874\pi$
$461$	−25.0290	+	3.59862i	−1.16571	+	0.167604i	−0.467832	+	0.883817i	$0.654965\pi$
$462$		0			0
$463$	−0.677013	+	0.234316i	−0.0314635	+	0.0108896i	−0.342754	−	0.939425i	$-0.611360\pi$
$463$	−0.677013	+	0.234316i	−0.0314635	+	0.0108896i	0.311291	+	0.950315i	$0.399239\pi$
$464$	12.3352	−	10.6885i	0.572648	−	0.496203i
$465$		0			0
$466$	−22.2578	+	6.53548i	−1.03107	+	0.302750i
$467$	6.31633	−	0.300884i	0.292285	−	0.0139232i	0.0990725	−	0.995080i	$-0.468412\pi$
$467$	6.31633	−	0.300884i	0.292285	−	0.0139232i	0.193212	+	0.981157i	$0.438109\pi$
$468$		0			0
$469$	12.1076	+	25.3299i	0.559076	+	1.16963i
$470$		−	11.7142i		−	0.540335i
$471$		0			0
$472$	1.20717	+	4.11125i	0.0555645	+	0.189235i
$473$	−0.0190612	−	0.199618i	−0.000876436	−	0.00917845i
$474$		0			0
$475$	−6.14021	−	17.7410i	−0.281732	−	0.814011i
$476$	3.74325	+	1.92978i	0.171572	+	0.0884514i
$477$		0			0
$478$	−9.94459	+	6.39100i	−0.454855	+	0.292317i
$479$	2.70253	+	2.83433i	0.123482	+	0.129504i	0.782572	−	0.622560i	$-0.213907\pi$
$479$	2.70253	+	2.83433i	0.123482	+	0.129504i	−0.659091	+	0.752063i	$0.729059\pi$
$480$		0			0
$481$	0.513664	+	1.28307i	0.0234211	+	0.0585030i
$482$	−9.15657	−	7.20080i	−0.417070	−	0.327988i
$483$		0			0
$484$	4.53533	+	2.91468i	0.206152	+	0.132486i
$485$	−0.780024	−	4.04715i	−0.0354191	−	0.183772i
$486$		0			0
$487$	9.72072	−	6.92209i	0.440488	−	0.313670i	−0.338208	−	0.941071i	$-0.609821\pi$
$487$	9.72072	−	6.92209i	0.440488	−	0.313670i	0.778696	+	0.627401i	$0.215881\pi$
$488$	18.7470	+	36.3640i	0.848635	+	1.64612i
$489$		0			0
$490$	−8.28256	−	1.59633i	−0.374168	−	0.0721149i
$491$	−10.6824	+	36.3808i	−0.482088	+	1.64184i	0.255660	+	0.966767i	$0.417707\pi$
$491$	−10.6824	+	36.3808i	−0.482088	+	1.64184i	−0.737748	+	0.675076i	$0.764111\pi$
$492$		0			0
$493$	−6.00826	−	13.1563i	−0.270599	−	0.592528i
$494$	8.38683	+	1.20584i	0.377341	+	0.0542535i
$495$		0			0
$496$	−10.5824	−	9.16968i	−0.475163	−	0.411731i
$497$	39.6064	+	15.8560i	1.77659	+	0.711239i
$498$		0			0
$499$	−23.9049	−	13.8015i	−1.07013	−	0.617841i	−0.141915	−	0.989879i	$-0.545326\pi$
$499$	−23.9049	−	13.8015i	−1.07013	−	0.617841i	−0.928218	+	0.372038i	$0.878659\pi$
$500$	4.57897	−	3.60094i	0.204778	−	0.161039i
$501$		0			0
$502$	−1.03077	+	21.6385i	−0.0460054	+	0.965772i
$503$	−1.18234	+	24.8204i	−0.0527179	+	1.10669i	0.805234	+	0.592957i	$0.202039\pi$
$503$	−1.18234	+	24.8204i	−0.0527179	+	1.10669i	−0.857952	+	0.513729i	$0.828264\pi$
$504$		0			0
$505$	−3.85409	+	3.03089i	−0.171505	+	0.134873i
$506$	−1.33894	−	0.773035i	−0.0595230	−	0.0343656i
$507$		0			0
$508$	−1.25312	−	0.501672i	−0.0555981	−	0.0222581i
$509$	9.88487	+	8.56529i	0.438139	+	0.379650i	0.845814	−	0.533477i	$-0.179115\pi$
$509$	9.88487	+	8.56529i	0.438139	+	0.379650i	−0.407675	+	0.913127i	$0.633660\pi$
$510$		0			0
$511$	−7.38848	−	1.06230i	−0.326847	−	0.0469935i
$512$	10.1022	+	22.1206i	0.446457	+	0.977604i
$513$		0			0
$514$	−4.33698	+	14.7704i	−0.191296	+	0.651495i
$515$	−2.60161	−	0.501419i	−0.114641	−	0.0220952i
$516$		0			0
$517$	1.92359	+	3.73125i	0.0845994	+	0.164100i
$518$	−4.40259	+	3.13507i	−0.193439	+	0.137747i
$519$		0			0
$520$	0.900330	+	4.67135i	0.0394821	+	0.204852i
$521$	−36.8683	−	23.6938i	−1.61523	−	1.03804i	−0.958969	−	0.283510i	$-0.908501\pi$
$521$	−36.8683	−	23.6938i	−1.61523	−	1.03804i	−0.656260	−	0.754535i	$-0.727862\pi$
$522$		0			0
$523$	−15.9742	−	12.5622i	−0.698503	−	0.549309i	0.204541	−	0.978858i	$-0.434430\pi$
$523$	−15.9742	−	12.5622i	−0.698503	−	0.549309i	−0.903043	+	0.429549i	$0.858672\pi$
$524$	3.15748	+	7.88701i	0.137935	+	0.344546i
$525$		0			0
$526$	−26.0253	−	27.2945i	−1.13476	−	1.19010i
$527$	−10.4383	+	6.70829i	−0.454700	+	0.292218i
$528$		0			0
$529$	−16.9042	−	8.71470i	−0.734963	−	0.378900i
$530$	2.23991	+	6.47179i	0.0972953	+	0.281116i
$531$		0			0
$532$	−1.07446	−	11.2523i	−0.0465838	−	0.487847i
$533$	2.25903	+	7.69353i	0.0978492	+	0.333244i
$534$		0			0
$535$			18.8882i			0.816607i
$536$	21.9330	+	12.1566i	0.947360	+	0.525085i
$537$		0			0
$538$	−9.28531	+	0.442314i	−0.400318	+	0.0190695i
$539$	2.90033	−	0.851613i	0.124926	−	0.0366815i
$540$		0			0
$541$	−16.3301	+	14.1501i	−0.702087	+	0.608362i	−0.930972	−	0.365092i	$-0.881038\pi$
$541$	−16.3301	+	14.1501i	−0.702087	+	0.608362i	0.228885	+	0.973454i	$0.426492\pi$
$542$	15.3291	−	5.30545i	0.658441	−	0.227889i
$543$		0			0
$544$	6.69170	−	0.962122i	0.286904	−	0.0412506i
$545$	11.5997	+	18.0495i	0.496877	+	0.773156i
$546$		0			0
$547$	18.5837	+	6.43188i	0.794582	+	0.275007i	0.694050	−	0.719926i	$-0.255824\pi$
$547$	18.5837	+	6.43188i	0.794582	+	0.275007i	0.100532	+	0.994934i	$0.467946\pi$
$548$	−5.73869	+	2.29742i	−0.245145	+	0.0981411i
$549$		0			0
$550$	0.932771	−	2.04248i	0.0397735	−	0.0870918i
$551$	−20.9874	+	32.6570i	−0.894092	+	1.39123i
$552$		0			0
$553$	26.0798	+	2.49032i	1.10903	+	0.105899i
$554$	14.7943	+	20.7757i	0.628551	+	0.882676i
$555$		0			0
$556$	−7.66012	+	8.03370i	−0.324861	+	0.340705i
$557$	3.86363	−	20.0464i	0.163707	−	0.849395i	−0.803480	−	0.595332i	$-0.797021\pi$
$557$	3.86363	−	20.0464i	0.163707	−	0.849395i	0.967188	−	0.254063i	$-0.0817672\pi$
$558$		0			0
$559$	0.0798060	−	0.328965i	0.00337544	−	0.0139137i
$560$	−12.3206	+	5.62663i	−0.520640	+	0.237768i
$561$		0			0
$562$	−11.5935	+	16.2807i	−0.489041	+	0.686762i
$563$	25.2526	−	29.1431i	1.06427	−	1.22824i	0.0916629	−	0.995790i	$-0.470782\pi$
$563$	25.2526	−	29.1431i	1.06427	−	1.22824i	0.972609	−	0.232446i	$-0.0746728\pi$
$564$		0			0
$565$	2.28261	+	3.95360i	0.0960301	+	0.166329i
$566$	6.17249	−	10.6911i	0.259449	−	0.449379i
$567$		0			0
$568$	37.0321	−	8.98389i	1.55383	−	0.376956i
$569$	11.4132	+	0.543678i	0.478466	+	0.0227922i	0.285430	−	0.958400i	$-0.407864\pi$
$569$	11.4132	+	0.543678i	0.478466	+	0.0227922i	0.193036	+	0.981192i	$0.438167\pi$
$570$		0			0
$571$	−1.95541	−	8.06030i	−0.0818312	−	0.337313i	0.916149	−	0.400838i	$-0.131281\pi$
$571$	−1.95541	−	8.06030i	−0.0818312	−	0.337313i	−0.997980	+	0.0635249i	$0.979766\pi$
$572$	−0.213704	−	0.271747i	−0.00893541	−	0.0113623i
$573$		0			0
$574$	−27.1557	+	15.6784i	−1.13346	+	0.654402i
$575$	−2.14921	+	5.36847i	−0.0896282	+	0.223880i
$576$		0			0
$577$	−33.9072	−	24.1452i	−1.41158	−	1.00518i	−0.995391	−	0.0958982i	$-0.969428\pi$
$577$	−33.9072	−	24.1452i	−1.41158	−	1.00518i	−0.416184	−	0.909280i	$-0.636633\pi$
$578$	1.94204	−	13.5072i	0.0807783	−	0.561825i
$579$		0			0
$580$	−4.29519	−	1.04200i	−0.178348	−	0.0432667i
$581$	−34.5032	−	10.1310i	−1.43143	−	0.420306i
$582$		0			0
$583$	−1.77620	−	1.69360i	−0.0735626	−	0.0701418i
$584$	−5.92613	+	3.05513i	−0.245225	+	0.126422i
$585$		0			0
$586$	−3.16435	+	33.1386i	−0.130718	+	1.36894i
$587$	29.7975	−	5.74299i	1.22987	−	0.237039i	0.467392	−	0.884050i	$-0.345194\pi$
$587$	29.7975	−	5.74299i	1.22987	−	0.237039i	0.762480	+	0.647011i	$0.223981\pi$
$588$		0			0
$589$	30.2936	+	13.8346i	1.24823	+	0.570046i
$590$	−1.53072	+	1.94647i	−0.0630188	+	0.0801350i
$591$		0			0
$592$	−1.14954	+	3.32137i	−0.0472457	+	0.136507i
$593$	−7.11439	+	6.78356i	−0.292153	+	0.278567i	−0.821953	−	0.569555i	$-0.807115\pi$
$593$	−7.11439	+	6.78356i	−0.292153	+	0.278567i	0.529800	+	0.848123i	$0.322267\pi$
$594$		0			0
$595$	1.70810	+	11.8801i	0.0700254	+	0.487037i
$596$	1.89218	−	3.67032i	0.0775068	−	0.150342i
$597$		0			0
$598$	−1.70913	−	1.97244i	−0.0698915	−	0.0806591i
$599$	22.1994	−	2.11979i	0.907045	−	0.0866123i	0.368904	−	0.929467i	$-0.379733\pi$
$599$	22.1994	−	2.11979i	0.907045	−	0.0866123i	0.538141	+	0.842855i	$0.319127\pi$
$600$		0			0
$601$	−1.57828	−	33.1321i	−0.0643792	−	1.35149i	−0.767790	−	0.640702i	$-0.778643\pi$
$601$	−1.57828	−	33.1321i	−0.0643792	−	1.35149i	0.703410	−	0.710784i	$-0.251660\pi$
$602$	1.32377			0.0539530
$603$		0			0
$604$	2.38404			0.0970054
$605$	0.731072	+	15.3471i	0.0297223	+	0.623948i
$606$		0			0
$607$	6.17221	−	0.589375i	0.250522	−	0.0239220i	0.0309607	−	0.999521i	$-0.490143\pi$
$607$	6.17221	−	0.589375i	0.250522	−	0.0239220i	0.219562	+	0.975599i	$0.429537\pi$
$608$	−11.8826	−	13.7133i	−0.481903	−	0.556146i
$609$		0			0
$610$	−10.8342	+	21.0153i	−0.438662	+	0.850886i
$611$	1.00851	+	7.01432i	0.0407998	+	0.283769i
$612$		0			0
$613$	−28.6039	+	27.2738i	−1.15530	+	1.10158i	−0.161909	+	0.986806i	$0.551765\pi$
$613$	−28.6039	+	27.2738i	−1.15530	+	1.10158i	−0.993392	+	0.114771i	$0.963387\pi$
$614$	−3.56748	+	10.3076i	−0.143972	+	0.415980i
$615$		0			0
$616$	4.12126	−	5.24061i	0.166050	−	0.211150i
$617$	−12.1038	−	5.52764i	−0.487283	−	0.222535i	0.156595	−	0.987663i	$-0.449948\pi$
$617$	−12.1038	−	5.52764i	−0.487283	−	0.222535i	−0.643878	+	0.765128i	$0.722675\pi$
$618$		0			0
$619$	19.6488	−	3.78700i	0.789753	−	0.152212i	0.221603	−	0.975137i	$-0.428871\pi$
$619$	19.6488	−	3.78700i	0.789753	−	0.152212i	0.568151	+	0.822925i	$0.307659\pi$
$620$	−0.360426	+	3.77455i	−0.0144751	+	0.151590i
$621$		0			0
$622$	−16.2748	+	8.39026i	−0.652562	+	0.336419i
$623$	0.558189	+	0.532232i	0.0223634	+	0.0213234i
$624$		0			0
$625$	2.02616	+	0.594935i	0.0810466	+	0.0237974i
$626$	−15.3209	−	3.71680i	−0.612345	−	0.148553i
$627$		0			0
$628$	−1.57743	+	10.9713i	−0.0629463	+	0.437801i
$629$	2.53696	+	1.80656i	0.101155	+	0.0720324i
$630$		0			0
$631$	−10.1594	+	25.3769i	−0.404438	+	1.01024i	0.576705	+	0.816952i	$0.304338\pi$
$631$	−10.1594	+	25.3769i	−0.404438	+	1.01024i	−0.981143	+	0.193284i	$0.938086\pi$
$632$	20.2655	−	11.7003i	0.806118	−	0.465412i
$633$		0			0
$634$	−15.4390	−	19.6323i	−0.613162	−	0.779699i
$635$	−0.906934	−	3.73843i	−0.0359906	−	0.148355i
$636$		0			0
$637$	5.09694	+	0.242797i	0.201948	+	0.00961997i
$638$	−4.51211	+	1.09463i	−0.178636	+	0.0433366i
$639$		0			0
$640$	−3.78945	+	6.56353i	−0.149791	+	0.259446i
$641$	−7.91720	−	13.7130i	−0.312711	−	0.541631i	0.666237	−	0.745740i	$-0.267904\pi$
$641$	−7.91720	−	13.7130i	−0.312711	−	0.541631i	−0.978948	+	0.204109i	$0.934570\pi$
$642$		0			0
$643$	−24.1886	+	27.9151i	−0.953904	+	1.10086i	0.0409108	+	0.999163i	$0.486974\pi$
$643$	−24.1886	+	27.9151i	−0.953904	+	1.10086i	−0.994815	+	0.101701i	$0.967571\pi$
$644$	−2.01960	+	2.83614i	−0.0795835	+	0.111759i
$645$		0			0
$646$	17.3684	−	7.93186i	0.683349	−	0.312075i
$647$	8.10668	−	33.4162i	0.318707	−	1.31373i	−0.556851	−	0.830612i	$-0.687991\pi$
$647$	8.10668	−	33.4162i	0.318707	−	1.31373i	0.875558	−	0.483114i	$-0.160494\pi$
$648$		0			0
$649$	0.167941	−	0.871358i	0.00659224	−	0.0342038i
$650$	2.61570	−	2.74327i	0.102596	−	0.107600i
$651$		0			0
$652$	−5.06521	−	7.11310i	−0.198369	−	0.278570i
$653$	16.0221	+	1.52993i	0.626993	+	0.0598706i	0.403716	−	0.914884i	$-0.367718\pi$
$653$	16.0221	+	1.52993i	0.626993	+	0.0598706i	0.223277	+	0.974755i	$0.428324\pi$
$654$		0			0
$655$	−13.0899	+	20.3683i	−0.511466	+	0.795856i
$656$	−8.47073	+	18.5483i	−0.330726	+	0.724190i
$657$		0			0
$658$	−25.7274	+	10.2997i	−1.00296	+	0.401524i
$659$	11.8533	+	4.10246i	0.461738	+	0.159809i	0.548026	−	0.836461i	$-0.315379\pi$
$659$	11.8533	+	4.10246i	0.461738	+	0.159809i	−0.0862883	+	0.996270i	$0.527501\pi$
$660$		0			0
$661$	−25.5227	−	39.7142i	−0.992719	−	1.54470i	−0.829799	−	0.558062i	$-0.811545\pi$
$661$	−25.5227	−	39.7142i	−0.992719	−	1.54470i	−0.162920	−	0.986639i	$-0.552091\pi$
$662$	−1.52813	+	0.219712i	−0.0593924	+	0.00853934i
$663$		0			0
$664$	−30.3529	+	10.5052i	−1.17792	+	0.407683i
$665$	24.3458	−	21.0958i	0.944090	−	0.818059i
$666$		0			0
$667$	11.4730	−	3.36877i	0.444235	−	0.130439i
$668$	10.6184	−	0.505818i	0.410839	−	0.0195707i
$669$		0			0
$670$	1.62967	+	14.4003i	0.0629595	+	0.556331i
$671$		−	8.47297i		−	0.327095i
$672$		0			0
$673$	−6.29325	−	21.4328i	−0.242587	−	0.826175i	−0.987310	−	0.158802i	$-0.949237\pi$
$673$	−6.29325	−	21.4328i	−0.242587	−	0.826175i	0.744724	−	0.667373i	$-0.232581\pi$
$674$	−2.55675	−	26.7754i	−0.0984821	−	1.03135i
$675$		0			0
$676$	1.97216	+	5.69818i	0.0758522	+	0.219161i
$677$	6.16591	+	3.17875i	0.236975	+	0.122169i	0.572624	−	0.819818i	$-0.305925\pi$
$677$	6.16591	+	3.17875i	0.236975	+	0.122169i	−0.335649	+	0.941987i	$0.608956\pi$
$678$		0			0
$679$	−8.20275	+	5.27159i	−0.314793	+	0.202305i
$680$	7.39799	+	7.75879i	0.283700	+	0.297536i
$681$		0			0
$682$	1.48041	+	3.69789i	0.0566878	+	0.141599i
$683$	−15.0873	−	11.8648i	−0.577300	−	0.453994i	0.286322	−	0.958133i	$-0.407567\pi$
$683$	−15.0873	−	11.8648i	−0.577300	−	0.453994i	−0.863622	+	0.504140i	$0.831810\pi$
$684$		0			0
$685$	−14.8202	−	9.52439i	−0.566252	−	0.363908i
$686$	−1.77229	−	9.19554i	−0.0676665	−	0.351087i
$687$		0			0
$688$	0.701219	−	0.499336i	0.0267337	−	0.0190370i
$689$	−1.89841	−	3.68239i	−0.0723235	−	0.140288i
$690$		0			0
$691$	24.3349	+	4.69016i	0.925743	+	0.178422i	0.629777	−	0.776776i	$-0.283146\pi$
$691$	24.3349	+	4.69016i	0.925743	+	0.178422i	0.295966	+	0.955199i	$0.404359\pi$
$692$	−0.614309	+	2.09214i	−0.0233525	+	0.0795314i
$693$		0			0
$694$	4.10918	+	8.99784i	0.155982	+	0.341553i
$695$	−31.3133	−	4.50218i	−1.18778	−	0.170777i
$696$		0			0
$697$	13.6557	+	11.8327i	0.517247	+	0.448197i
$698$	−10.9038	−	4.36522i	−0.412715	−	0.165226i
$699$		0			0
$700$	−4.37915	−	2.52830i	−0.165516	−	0.0955609i
$701$	−27.7840	+	21.8496i	−1.04939	+	0.825248i	−0.984979	−	0.172676i	$-0.944759\pi$
$701$	−27.7840	+	21.8496i	−1.04939	+	0.825248i	−0.0644093	+	0.997924i	$0.520516\pi$
$702$		0			0
$703$	0.397747	−	8.34974i	0.0150013	−	0.314916i
$704$	0.267724	−	5.62021i	0.0100902	−	0.211820i
$705$		0			0
$706$	2.34070	−	1.84075i	0.0880934	−	0.0692774i
$707$	10.0453	+	5.79967i	0.377794	+	0.218119i
$708$		0			0
$709$	41.0593	+	16.4377i	1.54201	+	0.617329i	0.978031	−	0.208458i	$-0.0668445\pi$
$709$	41.0593	+	16.4377i	1.54201	+	0.617329i	0.563982	+	0.825787i	$0.309269\pi$
$710$	16.6433	+	14.4215i	0.624611	+	0.541228i
$711$		0			0
$712$	0.681883	+	0.0980400i	0.0255547	+	0.00367421i
$713$	−4.26140	−	9.33117i	−0.159591	−	0.349455i
$714$		0			0
$715$	0.277578	−	0.945344i	0.0103808	−	0.0353539i
$716$	−3.00380	−	0.578934i	−0.112257	−	0.0216358i
$717$		0			0
$718$	7.97129	+	15.4621i	0.297486	+	0.577042i
$719$	−19.7016	+	14.0294i	−0.734746	+	0.523210i	−0.885088	−	0.465424i	$-0.845902\pi$
$719$	−19.7016	+	14.0294i	−0.734746	+	0.523210i	0.150342	+	0.988634i	$0.451963\pi$
$720$		0			0
$721$	1.18622	+	6.15468i	0.0441770	+	0.229212i
$722$	−23.5933	−	15.1625i	−0.878053	−	0.564290i
$723$		0			0
$724$	−8.68056	−	6.82647i	−0.322611	−	0.253704i
$725$	6.45426	+	16.1220i	0.239705	+	0.598755i
$726$		0			0
$727$	−7.70704	−	8.08291i	−0.285838	−	0.299778i	0.565123	−	0.825006i	$-0.308829\pi$
$727$	−7.70704	−	8.08291i	−0.285838	−	0.299778i	−0.850962	+	0.525228i	$0.823980\pi$
$728$	9.46789	−	6.08464i	0.350903	−	0.225512i
$729$		0			0
$730$	−3.42480	−	1.76561i	−0.126758	−	0.0653481i
$731$	−0.249493	−	0.720862i	−0.00922782	−	0.0266620i
$732$		0			0
$733$	−2.94318	−	30.8224i	−0.108709	−	1.13845i	−0.871023	−	0.491243i	$-0.836543\pi$
$733$	−2.94318	−	30.8224i	−0.108709	−	1.13845i	0.762314	−	0.647208i	$-0.224063\pi$
$734$	4.18387	+	14.2489i	0.154429	+	0.525938i
$735$		0			0
$736$			5.58917i			0.206020i
$737$	−2.88376	−	4.31922i	−0.106225	−	0.159100i
$738$		0			0
$739$	33.8090	−	1.61052i	1.24368	−	0.0592440i	0.584605	−	0.811318i	$-0.301249\pi$
$739$	33.8090	−	1.61052i	1.24368	−	0.0592440i	0.659079	+	0.752074i	$0.270946\pi$
$740$	0.913183	−	0.268135i	0.0335693	−	0.00985682i
$741$		0			0
$742$	12.2443	−	10.6097i	0.449502	−	0.389495i
$743$	−17.8752	+	6.18666i	−0.655777	+	0.226967i	−0.634637	−	0.772810i	$-0.718851\pi$
$743$	−17.8752	+	6.18666i	−0.655777	+	0.226967i	−0.0211393	+	0.999777i	$0.506729\pi$
$744$		0			0
$745$	11.6486	−	1.67482i	0.426773	−	0.0613607i
$746$	5.86478	+	9.12578i	0.214725	+	0.334119i
$747$		0			0
$748$	−0.736201	−	0.254802i	−0.0269182	−	0.00931647i
$749$	41.4833	−	16.6074i	1.51577	−	0.606822i
$750$		0			0
$751$	−5.65464	+	12.3819i	−0.206341	+	0.451823i	−0.984303	−	0.176488i	$-0.943526\pi$
$751$	−5.65464	+	12.3819i	−0.206341	+	0.451823i	0.777962	+	0.628311i	$0.216254\pi$
$752$	−9.74299	+	15.1604i	−0.355290	+	0.552842i
$753$		0			0
$754$	−7.80230	−	0.745030i	−0.284143	−	0.0271324i
$755$	3.94113	+	5.53454i	0.143432	+	0.201423i
$756$		0			0
$757$	−17.4805	+	18.3330i	−0.635339	+	0.666324i	−0.960160	−	0.279451i	$-0.909847\pi$
$757$	−17.4805	+	18.3330i	−0.635339	+	0.666324i	0.324821	+	0.945776i	$0.394696\pi$
$758$	−5.28192	+	27.4052i	−0.191848	+	0.995401i
$759$		0			0
$760$	6.78368	−	27.9627i	0.246070	−	1.01431i
$761$	−38.7102	+	17.6783i	−1.40324	+	0.640839i	−0.966009	−	0.258509i	$-0.916769\pi$
$761$	−38.7102	+	17.6783i	−1.40324	+	0.640839i	−0.437233	+	0.899348i	$0.644042\pi$
$762$		0			0
$763$	29.4424	−	41.3460i	1.06588	−	1.49683i
$764$	−6.79594	+	7.84293i	−0.245868	+	0.283747i
$765$		0			0
$766$	−14.9813	−	25.9483i	−0.541295	−	0.937551i
$767$	0.749003	−	1.29731i	0.0270449	−	0.0468432i
$768$		0			0
$769$	16.7991	−	4.07543i	0.605792	−	0.146964i	0.0788811	−	0.996884i	$-0.474865\pi$
$769$	16.7991	−	4.07543i	0.605792	−	0.146964i	0.526911	+	0.849920i	$0.323350\pi$
$770$	3.84859	+	0.183331i	0.138694	+	0.00660680i
$771$		0			0
$772$	0.362491	+	1.49421i	0.0130463	+	0.0537778i
$773$	4.04510	+	5.14376i	0.145492	+	0.185008i	0.853337	−	0.521359i	$-0.174575\pi$
$773$	4.04510	+	5.14376i	0.145492	+	0.185008i	−0.707845	+	0.706368i	$0.750333\pi$
$774$		0			0
$775$	12.9022	−	7.44911i	0.463462	−	0.267580i
$776$	−3.23692	+	8.08544i	−0.116199	+	0.290250i
$777$		0			0
$778$	−30.1778	−	21.4895i	−1.08193	−	0.770436i
$779$	6.90190	−	48.0038i	0.247286	−	1.71991i
$780$		0			0
$781$	−7.66944	−	1.86058i	−0.274434	−	0.0665770i
$782$	−5.64313	−	1.65697i	−0.201798	−	0.0592532i
$783$		0			0
$784$	9.39150	+	8.95478i	0.335411	+	0.319813i
$785$	−28.0774	+	14.4749i	−1.00213	+	0.516632i
$786$		0			0
$787$	−3.01830	+	31.6091i	−0.107591	+	1.12674i	0.766922	+	0.641741i	$0.221787\pi$
$787$	−3.01830	+	31.6091i	−0.107591	+	1.12674i	−0.874513	+	0.485003i	$0.838819\pi$
$788$	1.58575	−	0.305628i	0.0564900	−	0.0108875i
$789$		0			0
$790$	12.3015	+	5.61789i	0.437666	+	0.199876i
$791$	6.67614	−	8.48940i	0.237376	−	0.301848i
$792$		0			0
$793$	4.67811	−	13.5165i	0.166124	−	0.479985i
$794$	−3.56330	+	3.39760i	−0.126457	+	0.120576i
$795$		0			0
$796$	0.977633	+	6.79959i	0.0346513	+	0.241005i
$797$	7.31232	−	14.1839i	0.259016	−	0.502420i	−0.723089	−	0.690754i	$-0.757279\pi$
$797$	7.31232	−	14.1839i	0.259016	−	0.502420i	0.982105	+	0.188334i	$0.0603088\pi$
$798$		0			0
$799$	10.4576	+	12.0687i	0.369962	+	0.426958i
$800$	−8.08054	+	0.771598i	−0.285690	+	0.0272801i
$801$		0			0
$802$	0.684296	+	14.3651i	0.0241633	+	0.507251i
$803$	1.38081			0.0487278
$804$		0			0
$805$	−9.92273			−0.349730
$806$	0.319942	+	6.71642i	0.0112695	+	0.236576i
$807$		0			0
$808$	10.3137	−	0.984837i	0.362834	−	0.0346464i
$809$	−9.25476	−	10.6806i	−0.325380	−	0.375509i	0.569366	−	0.822084i	$-0.307189\pi$
$809$	−9.25476	−	10.6806i	−0.325380	−	0.375509i	−0.894746	+	0.446576i	$0.852643\pi$
$810$		0			0
$811$	10.5766	−	20.5158i	0.371396	−	0.720407i	−0.626879	−	0.779116i	$-0.715668\pi$
$811$	10.5766	−	20.5158i	0.371396	−	0.720407i	0.998275	+	0.0587090i	$0.0186984\pi$
$812$	1.48804	+	10.3495i	0.0522198	+	0.363197i
$813$		0			0
$814$	0.723589	−	0.689941i	0.0253618	−	0.0241824i
$815$	8.13956	−	23.5177i	0.285116	−	0.823790i
$816$		0			0
$817$	−1.26562	+	1.60936i	−0.0442784	+	0.0563045i
$818$	−39.1510	−	17.8797i	−1.36888	−	0.625148i
$819$		0			0
$820$	5.42187	−	1.04498i	0.189340	−	0.0364923i
$821$	−5.32999	+	55.8181i	−0.186018	+	1.94807i	0.112475	+	0.993655i	$0.464122\pi$
$821$	−5.32999	+	55.8181i	−0.186018	+	1.94807i	−0.298493	+	0.954412i	$0.596484\pi$
$822$		0			0
$823$	34.5972	−	17.8361i	1.20598	−	0.621728i	0.266339	−	0.963879i	$-0.414186\pi$
$823$	34.5972	−	17.8361i	1.20598	−	0.621728i	0.939645	+	0.342151i	$0.111156\pi$
$824$	4.05187	+	3.86345i	0.141154	+	0.134590i
$825$		0			0
$826$	5.62084	+	1.65043i	0.195574	+	0.0574258i
$827$	38.7290	+	9.39555i	1.34674	+	0.326715i	0.843359	−	0.537350i	$-0.180575\pi$
$827$	38.7290	+	9.39555i	1.34674	+	0.326715i	0.503380	+	0.864065i	$0.332090\pi$
$828$		0			0
$829$	−4.42497	+	30.7763i	−0.153686	+	1.06891i	0.756288	+	0.654239i	$0.227011\pi$
$829$	−4.42497	+	30.7763i	−0.153686	+	1.06891i	−0.909973	+	0.414667i	$0.863898\pi$
$830$	−15.1204	−	10.7672i	−0.524838	−	0.373736i
$831$		0			0
$832$	3.53012	−	8.81782i	0.122385	−	0.305703i
$833$	9.95828	−	5.74942i	0.345034	−	0.199205i
$834$		0			0
$835$	18.7279	+	23.8144i	0.648105	+	0.824132i
$836$	0.492964	+	2.03202i	0.0170495	+	0.0702790i
$837$		0			0
$838$	−6.50774	−	0.310002i	−0.224806	−	0.0107088i
$839$	39.3909	−	9.55613i	1.35992	−	0.329914i	0.511524	−	0.859269i	$-0.329081\pi$
$839$	39.3909	−	9.55613i	1.35992	−	0.329914i	0.848401	+	0.529355i	$0.177566\pi$
$840$		0			0
$841$	3.45445	−	5.98329i	0.119119	−	0.206320i
$842$	−22.8897	−	39.6461i	−0.788831	−	1.36630i
$843$		0			0
$844$	−1.56379	+	1.80471i	−0.0538280	+	0.0621208i
$845$	−9.96805	+	13.9982i	−0.342911	+	0.481551i
$846$		0			0
$847$	33.0634	−	15.0995i	1.13607	−	0.518826i
$848$	2.48389	−	10.2387i	0.0852970	−	0.351599i
$849$		0			0
$850$	1.61652	−	8.38729i	0.0554461	−	0.287682i
$851$	−1.77684	+	1.86350i	−0.0609094	+	0.0638799i
$852$		0			0
$853$	−3.62719	−	5.09368i	−0.124193	−	0.174404i	0.747799	−	0.663926i	$-0.231111\pi$
$853$	−3.62719	−	5.09368i	−0.124193	−	0.174404i	−0.871991	+	0.489521i	$0.837171\pi$
$854$	55.6811	+	5.31690i	1.90537	+	0.181940i
$855$		0			0
$856$	21.5781	−	33.5762i	0.737525	−	1.14761i
$857$	7.01196	−	15.3540i	0.239524	−	0.524484i	−0.751249	−	0.660019i	$-0.770548\pi$
$857$	7.01196	−	15.3540i	0.239524	−	0.524484i	0.990773	+	0.135535i	$0.0432754\pi$
$858$		0			0
$859$	−2.01486	+	0.806630i	−0.0687463	+	0.0275218i	−0.405781	−	0.913970i	$-0.633000\pi$
$859$	−2.01486	+	0.806630i	−0.0687463	+	0.0275218i	0.337034	+	0.941492i	$0.390576\pi$
$860$	−0.220285	−	0.0762414i	−0.00751166	−	0.00259981i
$861$		0			0
$862$	−25.1015	−	39.0588i	−0.854962	−	1.33035i
$863$	−28.9450	+	4.16166i	−0.985299	+	0.141665i	−0.616085	−	0.787680i	$-0.711282\pi$
$863$	−28.9450	+	4.16166i	−0.985299	+	0.141665i	−0.369214	+	0.929344i	$0.620373\pi$
$864$		0			0
$865$	−5.87243	+	2.03247i	−0.199669	+	0.0691060i
$866$	3.72465	−	3.22742i	0.126569	−	0.109672i
$867$		0			0
$868$	8.60679	−	2.52718i	0.292134	−	0.0857782i
$869$	−4.84082	+	0.230597i	−0.164214	+	0.00782246i
$870$		0			0
$871$	−2.21559	−	8.48242i	−0.0750723	−	0.287416i
$872$		−	45.3370i		−	1.53531i
$873$		0			0
$874$	4.44731	+	15.1462i	0.150433	+	0.512326i
$875$	−3.73331	−	39.0970i	−0.126209	−	1.32172i
$876$		0			0
$877$	−6.76367	−	19.5423i	−0.228393	−	0.659898i	−0.999725	−	0.0234646i	$-0.992530\pi$
$877$	−6.76367	−	19.5423i	−0.228393	−	0.659898i	0.771332	−	0.636433i	$-0.219591\pi$
$878$	−22.3354	−	11.5147i	−0.753782	−	0.388602i
$879$		0			0
$880$	2.10780	−	1.35460i	0.0710539	−	0.0456636i
$881$	−32.4817	−	34.0658i	−1.09433	−	1.14771i	−0.988171	−	0.153357i	$-0.950992\pi$
$881$	−32.4817	−	34.0658i	−1.09433	−	1.14771i	−0.106164	−	0.994349i	$-0.533857\pi$
$882$		0			0
$883$	−16.1163	−	40.2567i	−0.542358	−	1.35475i	−0.906028	−	0.423217i	$-0.860901\pi$
$883$	−16.1163	−	40.2567i	−0.542358	−	1.35475i	0.363670	−	0.931528i	$-0.381524\pi$
$884$	−1.03374	−	0.812945i	−0.0347685	−	0.0273423i
$885$		0			0
$886$	−3.60620	−	2.31756i	−0.121153	−	0.0778601i
$887$	9.02852	+	46.8444i	0.303148	+	1.57288i	0.739533	+	0.673121i	$0.235047\pi$
$887$	9.02852	+	46.8444i	0.303148	+	1.57288i	−0.436385	+	0.899760i	$0.643741\pi$
$888$		0			0
$889$	−7.41314	+	5.27887i	−0.248629	+	0.177048i
$890$	0.182431	+	0.353866i	0.00611509	+	0.0118616i
$891$		0			0
$892$	−3.56262	−	0.686638i	−0.119285	−	0.0229903i
$893$	12.0754	−	41.1250i	0.404087	−	1.37619i
$894$		0			0
$895$	−3.62167	−	7.93035i	−0.121059	−	0.265082i
$896$	17.7471	+	2.55165i	0.592888	+	0.0852445i
$897$		0			0
$898$	29.5741	+	25.6261i	0.986899	+	0.855153i
$899$	−28.5995	−	11.4495i	−0.953847	−	0.381863i
$900$		0			0
$901$	−8.08522	−	4.66800i	−0.269358	−	0.155514i
$902$	4.55951	−	3.58564i	0.151815	−	0.119389i
$903$		0			0
$904$	0.459006	−	9.63572i	0.0152663	−	0.320479i
$905$	1.49752	−	31.4369i	0.0497794	−	1.04500i
$906$		0			0
$907$	41.5770	−	32.6966i	1.38054	−	1.08567i	0.394552	−	0.918874i	$-0.370900\pi$
$907$	41.5770	−	32.6966i	1.38054	−	1.08567i	0.985991	−	0.166798i	$-0.0533427\pi$
$908$	4.71338	+	2.72127i	0.156419	+	0.0903086i
$909$		0			0
$910$	6.03825	+	2.41735i	0.200166	+	0.0801344i
$911$	4.19205	+	3.63243i	0.138889	+	0.120348i	0.721535	−	0.692378i	$-0.243437\pi$
$911$	4.19205	+	3.63243i	0.138889	+	0.120348i	−0.582646	+	0.812726i	$0.697983\pi$
$912$		0			0
$913$	6.58431	+	0.946681i	0.217909	+	0.0313306i
$914$	−14.5013	−	31.7534i	−0.479659	−	1.05031i
$915$		0			0
$916$	−0.602162	+	2.05077i	−0.0198960	+	0.0677595i
$917$	56.2434	+	10.8400i	1.85732	+	0.357969i
$918$		0			0
$919$	21.7939	+	42.2742i	0.718913	+	1.39450i	0.910703	+	0.413061i	$0.135541\pi$
$919$	21.7939	+	42.2742i	0.718913	+	1.39450i	−0.191790	+	0.981436i	$0.561429\pi$
$920$	−7.21961	+	5.14106i	−0.238024	+	0.169496i
$921$		0			0
$922$	5.84391	+	30.3211i	0.192459	+	0.998572i
$923$	−11.2074	−	7.20256i	−0.368896	−	0.237075i
$924$		0			0
$925$	−2.93945	−	2.31161i	−0.0966484	−	0.0760052i
$926$	0.325157	+	0.812202i	0.0106853	+	0.0266906i
$927$		0			0
$928$	11.5828	+	12.1477i	0.380225	+	0.398768i
$929$	−40.8510	+	26.2533i	−1.34028	+	0.861344i	−0.996963	−	0.0778763i	$-0.975186\pi$
$929$	−40.8510	+	26.2533i	−1.34028	+	0.861344i	−0.343315	+	0.939220i	$0.611550\pi$
$930$		0			0
$931$	−27.4320	−	14.1422i	−0.899048	−	0.463491i
$932$	−3.16068	−	9.13220i	−0.103532	−	0.299135i
$933$		0			0
$934$	−0.734033	−	7.68715i	−0.0240183	−	0.251531i
$935$	−0.625514	−	2.13031i	−0.0204565	−	0.0696684i
$936$		0			0
$937$			42.4403i			1.38646i	0.720715	+	0.693231i	$0.243814\pi$
$937$			42.4403i			1.38646i	−0.720715	+	0.693231i	$0.756186\pi$
$938$	30.1938	−	16.2406i	0.985863	−	0.530274i
$939$		0			0
$940$	4.87441	−	0.232197i	0.158986	−	0.00757342i
$941$	−8.80008	+	2.58394i	−0.286875	+	0.0842340i	−0.422004	−	0.906594i	$-0.638673\pi$
$941$	−8.80008	+	2.58394i	−0.286875	+	0.0842340i	0.135129	+	0.990828i	$0.456855\pi$
$942$		0			0
$943$	−11.2897	+	9.78256i	−0.367642	+	0.318564i
$944$	3.59998	−	1.24596i	0.117169	−	0.0405527i
$945$		0			0
$946$	−0.242386	+	0.0348498i	−0.00788064	+	0.00113307i
$947$	13.2748	+	20.6560i	0.431374	+	0.671231i	0.987095	−	0.160138i	$-0.0511940\pi$
$947$	13.2748	+	20.6560i	0.431374	+	0.671231i	−0.555721	+	0.831369i	$0.687558\pi$
$948$		0			0
$949$	2.20274	+	0.762376i	0.0715040	+	0.0247478i
$950$	−21.2836	+	8.52065i	−0.690530	+	0.276447i
$951$		0			0
$952$	10.5356	−	23.0698i	0.341462	−	0.747697i
$953$	−29.0435	+	45.1925i	−0.940810	+	1.46393i	−0.0557535	+	0.998445i	$0.517756\pi$
$953$	−29.0435	+	45.1925i	−0.940810	+	1.46393i	−0.885056	+	0.465484i	$0.845880\pi$
$954$		0			0
$955$	−29.4419	−	2.81136i	−0.952716	−	0.0909734i
$956$	−2.85649	−	4.01138i	−0.0923855	−	0.129737i
$957$		0			0
$958$	3.30027	−	3.46122i	0.106627	−	0.111827i
$959$	−7.88734	+	40.9234i	−0.254695	+	1.32148i
$960$		0			0
$961$	1.07774	−	4.44252i	0.0347659	−	0.143307i
$962$	1.53524	−	0.701119i	0.0494980	−	0.0226050i
$963$		0			0
$964$	2.81484	−	3.95289i	0.0906599	−	0.127314i
$965$	−2.86955	+	3.31164i	−0.0923742	+	0.106605i
$966$		0			0
$967$	−13.1396	−	22.7584i	−0.422539	−	0.731860i	0.573648	−	0.819102i	$-0.305528\pi$
$967$	−13.1396	−	22.7584i	−0.422539	−	0.731860i	−0.996187	+	0.0872423i	$0.972195\pi$
$968$	16.2331	−	28.1166i	0.521753	−	0.903703i
$969$		0			0
$970$	−4.89137	+	1.18663i	−0.157052	+	0.0381005i
$971$	−9.71691	−	0.462873i	−0.311830	−	0.0148543i	−0.108916	−	0.994051i	$-0.534738\pi$
$971$	−9.71691	−	0.462873i	−0.311830	−	0.0148543i	−0.202914	+	0.979197i	$0.565041\pi$
$972$		0			0
$973$	17.6443	+	72.7307i	0.565650	+	2.33164i
$974$	−9.00837	−	11.4551i	−0.288647	−	0.367044i
$975$		0			0
$976$	31.5005	−	18.1868i	1.00831	−	0.582146i
$977$	17.2213	−	43.0168i	0.550959	−	1.37623i	−0.347710	−	0.937602i	$-0.613041\pi$
$977$	17.2213	−	43.0168i	0.550959	−	1.37623i	0.898669	−	0.438627i	$-0.144535\pi$
$978$		0			0
$979$	−0.116217	−	0.0827578i	−0.00371431	−	0.00264495i
$980$	0.500077	−	3.47811i	0.0159744	−	0.111104i
$981$		0			0
$982$	44.9978	+	10.9164i	1.43594	+	0.348355i
$983$	12.1070	+	3.55493i	0.386153	+	0.113385i	0.469046	−	0.883174i	$-0.344598\pi$
$983$	12.1070	+	3.55493i	0.386153	+	0.113385i	−0.0828933	+	0.996558i	$0.526416\pi$
$984$		0			0
$985$	3.33096	+	3.17606i	0.106133	+	0.101198i
$986$	−15.6988	+	8.09331i	−0.499953	+	0.257743i
$987$		0			0
$988$	−0.335524	+	3.51376i	−0.0106744	+	0.111788i
$989$	0.619252	−	0.119351i	0.0196911	−	0.00379514i
$990$		0			0
$991$	−53.9313	−	24.6296i	−1.71318	−	0.782385i	−0.996371	−	0.0851200i	$-0.972873\pi$
$991$	−53.9313	−	24.6296i	−1.71318	−	0.782385i	−0.716813	−	0.697265i	$-0.754400\pi$
$992$	8.90126	−	11.3189i	0.282615	−	0.359375i
$993$		0			0
$994$	17.0397	−	49.2330i	0.540467	−	1.56158i
$995$	−14.1690	+	13.5102i	−0.449189	+	0.428301i
$996$		0			0
$997$	−2.37157	−	16.4946i	−0.0751084	−	0.522390i	−0.992292	−	0.123925i	$-0.960452\pi$
$997$	−2.37157	−	16.4946i	−0.0751084	−	0.522390i	0.917183	−	0.398466i	$-0.130457\pi$
$998$	−15.4460	+	29.9611i	−0.488935	+	0.948402i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	603.2.bj.a.503.7	yes	440
3.2	odd	2	inner	603.2.bj.a.503.16	yes	440
67.2	odd	66	inner	603.2.bj.a.404.16	yes	440
201.2	even	66	inner	603.2.bj.a.404.7	✓	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
603.2.bj.a.404.7	✓	440	201.2	even	66	inner
603.2.bj.a.404.16	yes	440	67.2	odd	66	inner
603.2.bj.a.503.7	yes	440	1.1	even	1	trivial
603.2.bj.a.503.16	yes	440	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 603 = 3^{2} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	603.bj (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0581060 - 1.21980i) q^{2} +(0.506420 - 0.0483572i) q^{4} +(0.949437 + 1.09571i) q^{5} +(1.57167 - 3.04861i) q^{7} +(-0.435996 - 3.03242i) q^{8} +O(q^{10})\)	\(q+(-0.0581060 - 1.21980i) q^{2} +(0.506420 - 0.0483572i) q^{4} +(0.949437 + 1.09571i) q^{5} +(1.57167 - 3.04861i) q^{7} +(-0.435996 - 3.03242i) q^{8} +(1.28137 - 1.22179i) q^{10} +(-0.207518 + 0.599583i) q^{11} +(-0.662085 + 0.841910i) q^{13} +(-3.81001 - 1.73997i) q^{14} +(-2.67453 + 0.515474i) q^{16} +(-0.229427 + 2.40267i) q^{17} +(5.75797 - 2.96844i) q^{19} +(0.533799 + 0.508977i) q^{20} +(0.743426 + 0.218290i) q^{22} +(-1.93917 - 0.470437i) q^{23} +(0.412427 - 2.86849i) q^{25} +(1.06543 + 0.758688i) q^{26} +(0.648502 - 1.61988i) q^{28} +(-5.18957 + 2.99620i) q^{29} +(3.17788 + 4.04100i) q^{31} +(-0.660363 - 2.72205i) q^{32} +(2.94410 + 0.140245i) q^{34} +(4.83259 - 1.17237i) q^{35} +(0.645189 - 1.11750i) q^{37} +(-3.95546 - 6.85106i) q^{38} +(2.90870 - 3.35681i) q^{40} +(4.34251 - 6.09821i) q^{41} +(-0.287488 + 0.131291i) q^{43} +(-0.0760969 + 0.313676i) q^{44} +(-0.461159 + 2.39272i) q^{46} +(4.56577 - 4.78844i) q^{47} +(-2.76349 - 3.88078i) q^{49} +(-3.52294 - 0.336400i) q^{50} +(-0.294580 + 0.458376i) q^{52} +(-1.60686 + 3.51853i) q^{53} +(-0.853993 + 0.341887i) q^{55} +(-9.92990 - 3.43677i) q^{56} +(3.95630 + 6.15612i) q^{58} +(-1.38438 + 0.199044i) q^{59} +(-12.6197 + 4.36774i) q^{61} +(4.74454 - 4.11117i) q^{62} +(-8.50882 + 2.49842i) q^{64} +(-1.55110 + 0.0738878i) q^{65} +(-4.94655 + 6.52163i) q^{67} +1.22786i q^{68} +(-1.71086 - 5.82665i) q^{70} +(1.18234 + 12.3821i) q^{71} +(-0.711796 - 2.05660i) q^{73} +(-1.40061 - 0.722065i) q^{74} +(2.77241 - 1.78172i) q^{76} +(1.50175 + 1.57499i) q^{77} +(2.83885 + 7.09112i) q^{79} +(-3.10411 - 2.44110i) q^{80} +(-7.69089 - 4.94263i) q^{82} +(-1.98415 - 10.2948i) q^{83} +(-2.85046 + 2.02980i) q^{85} +(0.176853 + 0.343048i) q^{86} +(1.90866 + 0.367864i) q^{88} +(-0.0633517 + 0.215756i) q^{89} +(1.52608 + 3.34164i) q^{91} +(-1.00478 - 0.144466i) q^{92} +(-6.10622 - 5.29107i) q^{94} +(8.71938 + 3.49071i) q^{95} +(-2.46197 - 1.42142i) q^{97} +(-4.57319 + 3.59639i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q + 20 q^{4}+O(q^{10}) \) 440 * q + 20 * q^4	\( 440 q + 20 q^{4} + 18 q^{13} + 8 q^{16} + 36 q^{19} - 12 q^{22} - 44 q^{25} - 128 q^{28} + 82 q^{31} + 24 q^{34} - 8 q^{37} - 32 q^{40} - 44 q^{43} + 80 q^{46} - 10 q^{49} + 132 q^{52} - 64 q^{55} - 176 q^{58} - 86 q^{61} - 136 q^{64} - 78 q^{67} - 352 q^{70} + 180 q^{73} - 256 q^{76} + 104 q^{79} + 88 q^{82} - 84 q^{85} - 268 q^{88} - 328 q^{91} + 88 q^{94} - 6 q^{97}+O(q^{100}) \) 440 * q + 20 * q^4 + 18 * q^13 + 8 * q^16 + 36 * q^19 - 12 * q^22 - 44 * q^25 - 128 * q^28 + 82 * q^31 + 24 * q^34 - 8 * q^37 - 32 * q^40 - 44 * q^43 + 80 * q^46 - 10 * q^49 + 132 * q^52 - 64 * q^55 - 176 * q^58 - 86 * q^61 - 136 * q^64 - 78 * q^67 - 352 * q^70 + 180 * q^73 - 256 * q^76 + 104 * q^79 + 88 * q^82 - 84 * q^85 - 268 * q^88 - 328 * q^91 + 88 * q^94 - 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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