LMFDB - Embedded newform 603.2.z.c.73.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [603,2,Mod(10,603)]

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([0, 16]))

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

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

chi := DirichletCharacter("603.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 603 = 3^{2} \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	603.z (of order $33$, 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:	$100$
Relative dimension:	$5$ over $\Q(\zeta_{33})$
Twist minimal:	no (minimal twist has level 67)
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			73.4
Character	$\chi$	$=$	603.73
Dual form			603.2.z.c.190.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.679423 - 1.96306i) q^{2} +(-1.81990 - 1.43118i) q^{4} +(-2.54249 - 0.746543i) q^{5} +(-3.22458 + 0.621487i) q^{7} +(-0.550889 + 0.354035i) q^{8} +O(q^{10})$	\(q+(0.679423 - 1.96306i) q^{2} +(-1.81990 - 1.43118i) q^{4} +(-2.54249 - 0.746543i) q^{5} +(-3.22458 + 0.621487i) q^{7} +(-0.550889 + 0.354035i) q^{8} +(-3.19294 + 4.48386i) q^{10} +(-0.175586 + 0.167421i) q^{11} +(-0.236977 + 4.97475i) q^{13} +(-0.970836 + 6.75231i) q^{14} +(-0.770969 - 3.17798i) q^{16} +(-2.13858 + 1.68180i) q^{17} +(-3.92536 - 0.756551i) q^{19} +(3.55864 + 4.99741i) q^{20} +(0.209361 + 0.458437i) q^{22} +(2.00300 - 0.191263i) q^{23} +(1.70067 + 1.09296i) q^{25} +(9.60475 + 3.84516i) q^{26} +(6.75787 + 3.48392i) q^{28} +(-1.22669 + 2.12469i) q^{29} +(-0.117746 - 2.47179i) q^{31} +(-8.06614 - 0.770223i) q^{32} +(1.84848 + 5.34083i) q^{34} +(8.66244 + 0.827163i) q^{35} +(2.34289 + 4.05800i) q^{37} +(-4.15214 + 7.19171i) q^{38} +(1.66493 - 0.488868i) q^{40} +(-6.14863 - 2.46154i) q^{41} +(-0.527043 - 3.66566i) q^{43} +(0.559160 - 0.0533933i) q^{44} +(0.985422 - 4.06197i) q^{46} +(-5.36335 - 7.53177i) q^{47} +(3.51310 - 1.40643i) q^{49} +(3.30102 - 2.59595i) q^{50} +(7.55106 - 8.71439i) q^{52} +(0.132001 - 0.918084i) q^{53} +(0.571415 - 0.294585i) q^{55} +(1.55636 - 1.48398i) q^{56} +(3.33747 + 3.85164i) q^{58} +(-9.49898 + 6.10462i) q^{59} +(-4.59799 - 4.38418i) q^{61} +(-4.93228 - 1.44825i) q^{62} +(-4.27537 + 9.36176i) q^{64} +(4.31638 - 12.4714i) q^{65} +(2.77883 + 7.69923i) q^{67} +6.29897 q^{68} +(7.50924 - 16.4429i) q^{70} +(6.87694 + 5.40808i) q^{71} +(-12.1228 - 11.5591i) q^{73} +(9.55793 - 1.84214i) q^{74} +(6.06099 + 6.99476i) q^{76} +(0.462143 - 0.648989i) q^{77} +(14.0293 - 7.23262i) q^{79} +(-0.412314 + 8.65554i) q^{80} +(-9.00969 + 10.3977i) q^{82} +(-1.44626 - 5.96158i) q^{83} +(6.69287 - 2.67942i) q^{85} +(-7.55402 - 1.45592i) q^{86} +(0.0374556 - 0.154394i) q^{88} +(-0.203900 - 0.446478i) q^{89} +(-2.32759 - 16.1888i) q^{91} +(-3.91899 - 2.51858i) q^{92} +(-18.4293 + 5.41134i) q^{94} +(9.41540 + 4.85398i) q^{95} +(-1.49771 - 2.59411i) q^{97} +(-0.374037 - 7.85201i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q + 24 q^{2} - 18 q^{4} + 16 q^{5} - 24 q^{7} - 23 q^{8}+O(q^{10}) $ 100 * q + 24 * q^2 - 18 * q^4 + 16 * q^5 - 24 * q^7 - 23 * q^8	$ 100 q + 24 q^{2} - 18 q^{4} + 16 q^{5} - 24 q^{7} - 23 q^{8} + 8 q^{10} + 24 q^{11} - 22 q^{13} + 32 q^{14} - 28 q^{16} - 17 q^{17} + 15 q^{20} + 49 q^{22} + 13 q^{23} - 34 q^{25} + 27 q^{26} + 22 q^{28} - 8 q^{29} + 10 q^{31} - 34 q^{32} - 50 q^{34} + q^{35} + 7 q^{37} - 50 q^{38} + 43 q^{40} + 5 q^{41} + 2 q^{43} + 19 q^{44} + 52 q^{46} + 6 q^{47} - 27 q^{49} - 134 q^{50} + 120 q^{52} + 52 q^{53} - 64 q^{55} + 124 q^{56} - 56 q^{58} - 27 q^{59} - 16 q^{61} + 74 q^{62} - 197 q^{64} + 92 q^{65} - 56 q^{67} - 16 q^{68} - 22 q^{70} + 113 q^{71} + q^{73} + 24 q^{74} - 144 q^{76} - 85 q^{77} + 36 q^{79} + 13 q^{80} - 20 q^{82} + 61 q^{83} - 6 q^{85} - 189 q^{86} + 129 q^{88} - 95 q^{89} + 42 q^{91} - 4 q^{92} + 70 q^{94} + 20 q^{95} + 53 q^{97} - q^{98}+O(q^{100}) $ 100 * q + 24 * q^2 - 18 * q^4 + 16 * q^5 - 24 * q^7 - 23 * q^8 + 8 * q^10 + 24 * q^11 - 22 * q^13 + 32 * q^14 - 28 * q^16 - 17 * q^17 + 15 * q^20 + 49 * q^22 + 13 * q^23 - 34 * q^25 + 27 * q^26 + 22 * q^28 - 8 * q^29 + 10 * q^31 - 34 * q^32 - 50 * q^34 + q^35 + 7 * q^37 - 50 * q^38 + 43 * q^40 + 5 * q^41 + 2 * q^43 + 19 * q^44 + 52 * q^46 + 6 * q^47 - 27 * q^49 - 134 * q^50 + 120 * q^52 + 52 * q^53 - 64 * q^55 + 124 * q^56 - 56 * q^58 - 27 * q^59 - 16 * q^61 + 74 * q^62 - 197 * q^64 + 92 * q^65 - 56 * q^67 - 16 * q^68 - 22 * q^70 + 113 * q^71 + q^73 + 24 * q^74 - 144 * q^76 - 85 * q^77 + 36 * q^79 + 13 * q^80 - 20 * q^82 + 61 * q^83 - 6 * q^85 - 189 * q^86 + 129 * q^88 - 95 * q^89 + 42 * q^91 - 4 * q^92 + 70 * q^94 + 20 * q^95 + 53 * q^97 - q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$136$	$470$
$\chi(n)$	$e\left(\frac{20}{33}\right)$	$1$

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 $

$2$	0.679423	−	1.96306i	0.480425	−	1.38810i	−0.401133	−	0.916020i	$-0.631384\pi$
$2$	0.679423	−	1.96306i	0.480425	−	1.38810i	0.881558	−	0.472076i	$-0.156495\pi$
$3$		0			0
$3$		0			0
$4$	−1.81990	−	1.43118i	−0.909949	−	0.715592i
$5$	−2.54249	−	0.746543i	−1.13704	−	0.333864i	−0.341567	−	0.939857i	$-0.610958\pi$
$5$	−2.54249	−	0.746543i	−1.13704	−	0.333864i	−0.795470	+	0.605993i	$0.792776\pi$
$6$		0			0
$7$	−3.22458	+	0.621487i	−1.21878	+	0.234900i	−0.757785	−	0.652504i	$-0.773718\pi$
$7$	−3.22458	+	0.621487i	−1.21878	+	0.234900i	−0.460992	+	0.887404i	$0.652506\pi$
$8$	−0.550889	+	0.354035i	−0.194769	+	0.125170i
$9$		0			0
$10$	−3.19294	+	4.48386i	−1.00970	+	1.41792i
$11$	−0.175586	+	0.167421i	−0.0529413	+	0.0504794i	−0.716088	−	0.698010i	$-0.754069\pi$
$11$	−0.175586	+	0.167421i	−0.0529413	+	0.0504794i	0.663147	+	0.748490i	$0.269221\pi$
$12$		0			0
$13$	−0.236977	+	4.97475i	−0.0657255	+	1.37975i	0.689501	+	0.724285i	$0.257830\pi$
$13$	−0.236977	+	4.97475i	−0.0657255	+	1.37975i	−0.755227	+	0.655464i	$0.772473\pi$
$14$	−0.970836	+	6.75231i	−0.259467	+	1.80463i
$15$		0			0
$16$	−0.770969	−	3.17798i	−0.192742	−	0.794494i
$17$	−2.13858	+	1.68180i	−0.518683	+	0.407897i	−0.842887	−	0.538090i	$-0.819146\pi$
$17$	−2.13858	+	1.68180i	−0.518683	+	0.407897i	0.324204	+	0.945987i	$0.394903\pi$
$18$		0			0
$19$	−3.92536	−	0.756551i	−0.900539	−	0.173565i	−0.282089	−	0.959388i	$-0.591027\pi$
$19$	−3.92536	−	0.756551i	−0.900539	−	0.173565i	−0.618451	+	0.785824i	$0.712239\pi$
$20$	3.55864	+	4.99741i	0.795735	+	1.11745i
$21$		0			0
$22$	0.209361	+	0.458437i	0.0446360	+	0.0977392i
$23$	2.00300	−	0.191263i	0.417654	−	0.0398812i	0.115886	−	0.993262i	$-0.463029\pi$
$23$	2.00300	−	0.191263i	0.417654	−	0.0398812i	0.301768	+	0.953381i	$0.402423\pi$
$24$		0			0
$25$	1.70067	+	1.09296i	0.340135	+	0.218591i
$26$	9.60475	+	3.84516i	1.88365	+	0.754098i
$27$		0			0
$28$	6.75787	+	3.48392i	1.27712	+	0.658400i
$29$	−1.22669	+	2.12469i	−0.227791	+	0.394546i	−0.957153	−	0.289582i	$-0.906484\pi$
$29$	−1.22669	+	2.12469i	−0.227791	+	0.394546i	0.729362	+	0.684128i	$0.239817\pi$
$30$		0			0
$31$	−0.117746	−	2.47179i	−0.0211478	−	0.443947i	−0.984465	−	0.175581i	$-0.943820\pi$
$31$	−0.117746	−	2.47179i	−0.0211478	−	0.443947i	0.963317	−	0.268365i	$-0.0864835\pi$
$32$	−8.06614	−	0.770223i	−1.42591	−	0.136157i
$33$		0			0
$34$	1.84848	+	5.34083i	0.317012	+	0.915945i
$35$	8.66244	+	0.827163i	1.46422	+	0.139816i
$36$		0			0
$37$	2.34289	+	4.05800i	0.385168	+	0.667131i	0.991793	−	0.127857i	$-0.0408100\pi$
$37$	2.34289	+	4.05800i	0.385168	+	0.667131i	−0.606624	+	0.794989i	$0.707477\pi$
$38$	−4.15214	+	7.19171i	−0.673566	+	1.16665i
$39$		0			0
$40$	1.66493	−	0.488868i	0.263249	−	0.0772969i
$41$	−6.14863	−	2.46154i	−0.960255	−	0.384428i	−0.162029	−	0.986786i	$-0.551804\pi$
$41$	−6.14863	−	2.46154i	−0.960255	−	0.384428i	−0.798226	+	0.602358i	$0.794228\pi$
$42$		0			0
$43$	−0.527043	−	3.66566i	−0.0803733	−	0.559009i	−0.989725	−	0.142981i	$-0.954331\pi$
$43$	−0.527043	−	3.66566i	−0.0803733	−	0.559009i	0.909352	−	0.416027i	$-0.136578\pi$
$44$	0.559160	−	0.0533933i	0.0842966	−	0.00804935i
$45$		0			0
$46$	0.985422	−	4.06197i	0.145293	−	0.598904i
$47$	−5.36335	−	7.53177i	−0.782325	−	1.09862i	−0.992654	−	0.120991i	$-0.961393\pi$
$47$	−5.36335	−	7.53177i	−0.782325	−	1.09862i	0.210329	−	0.977631i	$-0.432546\pi$
$48$		0			0
$49$	3.51310	−	1.40643i	0.501872	−	0.200919i
$50$	3.30102	−	2.59595i	0.466835	−	0.367123i
$51$		0			0
$52$	7.55106	−	8.71439i	1.04714	−	1.20847i
$53$	0.132001	−	0.918084i	0.0181317	−	0.126109i	−0.978745	−	0.205080i	$-0.934255\pi$
$53$	0.132001	−	0.918084i	0.0181317	−	0.126109i	0.996877	+	0.0789715i	$0.0251636\pi$
$54$		0			0
$55$	0.571415	−	0.294585i	0.0770495	−	0.0397218i
$56$	1.55636	−	1.48398i	0.207977	−	0.198306i
$57$		0			0
$58$	3.33747	+	3.85164i	0.438231	+	0.505745i
$59$	−9.49898	+	6.10462i	−1.23666	+	0.794754i	−0.984915	−	0.173039i	$-0.944641\pi$
$59$	−9.49898	+	6.10462i	−1.23666	+	0.794754i	−0.251746	+	0.967793i	$0.581005\pi$
$60$		0			0
$61$	−4.59799	−	4.38418i	−0.588713	−	0.561336i	0.336068	−	0.941838i	$-0.390903\pi$
$61$	−4.59799	−	4.38418i	−0.588713	−	0.561336i	−0.924780	+	0.380502i	$0.875751\pi$
$62$	−4.93228	−	1.44825i	−0.626400	−	0.183928i
$63$		0			0
$64$	−4.27537	+	9.36176i	−0.534421	+	1.17022i
$65$	4.31638	−	12.4714i	0.535381	−	1.54688i
$66$		0			0
$67$	2.77883	+	7.69923i	0.339488	+	0.940610i
$67$	2.77883	+	7.69923i	0.339488	+	0.940610i
$68$	6.29897			0.763862
$69$		0			0
$70$	7.50924	−	16.4429i	0.897525	−	1.96531i
$71$	6.87694	+	5.40808i	0.816143	+	0.641822i	0.936405	−	0.350921i	$-0.114131\pi$
$71$	6.87694	+	5.40808i	0.816143	+	0.641822i	−0.120263	+	0.992742i	$0.538374\pi$
$72$		0			0
$73$	−12.1228	−	11.5591i	−1.41887	−	1.35289i	−0.845933	−	0.533290i	$-0.820956\pi$
$73$	−12.1228	−	11.5591i	−1.41887	−	1.35289i	−0.572937	−	0.819600i	$-0.694196\pi$
$74$	9.55793	−	1.84214i	1.11109	−	0.214144i
$75$		0			0
$76$	6.06099	+	6.99476i	0.695243	+	0.802353i
$77$	0.462143	−	0.648989i	0.0526660	−	0.0739591i
$78$		0			0
$79$	14.0293	−	7.23262i	1.57842	−	0.813733i	0.578425	−	0.815736i	$-0.303668\pi$
$79$	14.0293	−	7.23262i	1.57842	−	0.813733i	0.999998	+	0.00200242i	$0.000637389\pi$
$80$	−0.412314	+	8.65554i	−0.0460981	+	0.967719i
$81$		0			0
$82$	−9.00969	+	10.3977i	−0.994954	+	1.14824i
$83$	−1.44626	−	5.96158i	−0.158748	−	0.654369i	−0.994452	−	0.105189i	$-0.966455\pi$
$83$	−1.44626	−	5.96158i	−0.158748	−	0.654369i	0.835704	−	0.549180i	$-0.185060\pi$
$84$		0			0
$85$	6.69287	−	2.67942i	0.725944	−	0.290624i
$86$	−7.55402	−	1.45592i	−0.814571	−	0.156996i
$87$		0			0
$88$	0.0374556	−	0.154394i	0.00399278	−	0.0164585i
$89$	−0.203900	−	0.446478i	−0.0216133	−	0.0473265i	0.898517	−	0.438938i	$-0.144645\pi$
$89$	−0.203900	−	0.446478i	−0.0216133	−	0.0473265i	−0.920131	+	0.391611i	$0.871918\pi$
$90$		0			0
$91$	−2.32759	−	16.1888i	−0.243998	−	1.69704i
$92$	−3.91899	−	2.51858i	−0.408583	−	0.262580i
$93$		0			0
$94$	−18.4293	+	5.41134i	−1.90084	+	0.558137i
$95$	9.41540	+	4.85398i	0.966000	+	0.498007i
$96$		0			0
$97$	−1.49771	−	2.59411i	−0.152069	−	0.263391i	0.779919	−	0.625881i	$-0.215260\pi$
$97$	−1.49771	−	2.59411i	−0.152069	−	0.263391i	−0.931988	+	0.362489i	$0.881927\pi$
$98$	−0.374037	−	7.85201i	−0.0377835	−	0.793173i
$99$		0			0
$100$	−1.53083	−	4.42305i	−0.153083	−	0.442305i
$101$	−4.15581	−	12.0074i	−0.413518	−	1.19478i	−0.938982	−	0.343967i	$-0.888229\pi$
$101$	−4.15581	−	12.0074i	−0.413518	−	1.19478i	0.525463	−	0.850816i	$-0.323892\pi$
$102$		0			0
$103$	0.220926	+	4.63781i	0.0217685	+	0.456977i	0.983267	+	0.182168i	$0.0583115\pi$
$103$	0.220926	+	4.63781i	0.0217685	+	0.456977i	−0.961499	+	0.274809i	$0.911385\pi$
$104$	−1.63069	−	2.82443i	−0.159902	−	0.276958i
$105$		0			0
$106$	−1.71257	−	0.882893i	−0.166340	−	0.0857541i
$107$	7.47261	−	2.19416i	0.722404	−	0.212117i	0.100195	−	0.994968i	$-0.468053\pi$
$107$	7.47261	−	2.19416i	0.722404	−	0.212117i	0.622209	+	0.782851i	$0.286235\pi$
$108$		0			0
$109$	−3.25550	−	2.09218i	−0.311820	−	0.200395i	0.375365	−	0.926877i	$-0.377517\pi$
$109$	−3.25550	−	2.09218i	−0.311820	−	0.200395i	−0.687185	+	0.726483i	$0.741154\pi$
$110$	−0.190056	−	1.32187i	−0.0181212	−	0.126035i
$111$		0			0
$112$	4.46112	+	9.76849i	0.421536	+	0.923036i
$113$	0.280384	−	1.15576i	0.0263764	−	0.108725i	−0.957102	−	0.289752i	$-0.906427\pi$
$113$	0.280384	−	1.15576i	0.0263764	−	0.108725i	0.983478	+	0.181027i	$0.0579423\pi$
$114$		0			0
$115$	−5.23540	−	1.00904i	−0.488203	−	0.0940935i
$116$	5.27328	−	2.11110i	0.489612	−	0.196011i
$117$		0			0
$118$	5.52994	+	22.7947i	0.509072	+	2.09842i
$119$	5.85082	−	6.75221i	0.536344	−	0.618974i
$120$		0			0
$121$	−0.520600	+	10.9287i	−0.0473273	+	0.993522i
$122$	−11.7304	+	6.04744i	−1.06202	+	0.547510i
$123$		0			0
$124$	−3.32330	+	4.66692i	−0.298441	+	0.419102i
$125$	5.16833	+	5.96458i	0.462270	+	0.533488i
$126$		0			0
$127$	−6.14854	+	1.18503i	−0.545594	+	0.105155i	−0.454598	−	0.890697i	$-0.650217\pi$
$127$	−6.14854	+	1.18503i	−0.545594	+	0.105155i	−0.0909961	+	0.995851i	$0.529005\pi$
$128$	3.74436	+	3.57024i	0.330958	+	0.315567i
$129$		0			0
$130$	−21.5494	−	16.9467i	−1.89001	−	1.48632i
$131$	4.61701	−	10.1098i	0.403390	−	0.883301i	−0.593525	−	0.804816i	$-0.702264\pi$
$131$	4.61701	−	10.1098i	0.403390	−	0.883301i	0.996915	−	0.0784858i	$-0.0250085\pi$
$132$		0			0
$133$	13.1278			1.13833
$134$	17.0021	−	0.223984i	1.46876	−	0.0193493i
$135$		0			0
$136$	0.582706	−	1.68362i	0.0499666	−	0.144369i
$137$	−1.38040	+	3.02265i	−0.117935	+	0.258242i	−0.959389	−	0.282088i	$-0.908973\pi$
$137$	−1.38040	+	3.02265i	−0.117935	+	0.258242i	0.841454	+	0.540330i	$0.181700\pi$
$138$		0			0
$139$	−0.482138	−	0.141569i	−0.0408944	−	0.0120077i	0.261221	−	0.965279i	$-0.415875\pi$
$139$	−0.482138	−	0.141569i	−0.0408944	−	0.0120077i	−0.302116	+	0.953271i	$0.597693\pi$
$140$	−14.5809	−	13.9029i	−1.23231	−	1.17501i
$141$		0			0
$142$	15.2888	−	9.82549i	1.28300	−	0.824537i
$143$	−0.791270	−	0.913174i	−0.0661693	−	0.0763635i
$144$		0			0
$145$	4.70503	−	4.48624i	0.390732	−	0.372562i
$146$	−30.9278	+	15.9444i	−2.55960	+	1.31957i
$147$		0			0
$148$	1.54393	−	10.7383i	0.126910	−	0.882679i
$149$	−5.31591	+	6.13489i	−0.435496	+	0.502590i	−0.930495	−	0.366304i	$-0.880623\pi$
$149$	−5.31591	+	6.13489i	−0.435496	+	0.502590i	0.494999	+	0.868894i	$0.335168\pi$
$150$		0			0
$151$	−8.72343	+	6.86018i	−0.709903	+	0.558274i	−0.906498	−	0.422211i	$-0.861254\pi$
$151$	−8.72343	+	6.86018i	−0.709903	+	0.558274i	0.196595	+	0.980485i	$0.437012\pi$
$152$	2.43028	−	0.972938i	0.197122	−	0.0789157i
$153$		0			0
$154$	−0.960016	−	1.34815i	−0.0773603	−	0.108637i
$155$	−1.54593	+	6.37241i	−0.124172	+	0.511844i
$156$		0			0
$157$	3.56173	−	0.340104i	0.284257	−	0.0271433i	0.0480465	−	0.998845i	$-0.484700\pi$
$157$	3.56173	−	0.340104i	0.284257	−	0.0271433i	0.236211	+	0.971702i	$0.424094\pi$
$158$	−4.66625	−	32.4545i	−0.371227	−	2.58194i
$159$		0			0
$160$	19.9331	+	7.98001i	1.57585	+	0.630875i
$161$	−6.33997	+	1.86158i	−0.499660	+	0.146713i
$162$		0			0
$163$	−6.66560	+	11.5452i	−0.522090	+	0.904286i	0.477580	+	0.878588i	$0.341514\pi$
$163$	−6.66560	+	11.5452i	−0.522090	+	0.904286i	−0.999670	+	0.0256979i	$0.991819\pi$
$164$	7.66697	+	13.2796i	0.598690	+	1.03696i
$165$		0			0
$166$	−12.6856	−	1.21133i	−0.984593	−	0.0940172i
$167$	3.63369	+	10.4988i	0.281183	+	0.812425i	0.993831	+	0.110904i	$0.0353745\pi$
$167$	3.63369	+	10.4988i	0.281183	+	0.812425i	−0.712648	+	0.701522i	$0.752504\pi$
$168$		0			0
$169$	−11.7509	−	1.12207i	−0.903914	−	0.0863133i
$170$	−0.712585	−	14.9590i	−0.0546528	−	1.14730i
$171$		0			0
$172$	−4.28707	+	7.42543i	−0.326886	+	0.566184i
$173$	18.9716	+	9.78055i	1.44239	+	0.743601i	0.989028	−	0.147728i	$-0.0471960\pi$
$173$	18.9716	+	9.78055i	1.44239	+	0.743601i	0.453357	+	0.891329i	$0.350226\pi$
$174$		0			0
$175$	−6.16322	−	2.46738i	−0.465896	−	0.186516i
$176$	0.667433	+	0.428933i	0.0503096	+	0.0323320i
$177$		0			0
$178$	−1.01500	+	0.0969206i	−0.0760773	+	0.00726451i
$179$	0.337591	+	0.739222i	0.0252328	+	0.0552521i	0.921829	−	0.387597i	$-0.126695\pi$
$179$	0.337591	+	0.739222i	0.0252328	+	0.0552521i	−0.896596	+	0.442849i	$0.853968\pi$
$180$		0			0
$181$	−11.6561	−	16.3686i	−0.866388	−	1.21667i	−0.974915	−	0.222579i	$-0.928553\pi$
$181$	−11.6561	−	16.3686i	−0.866388	−	1.21667i	0.108526	−	0.994094i	$-0.465387\pi$
$182$	−33.3610	−	6.42981i	−2.47288	−	0.476609i
$183$		0			0
$184$	−1.03572	+	0.814496i	−0.0763540	+	0.0600454i
$185$	−2.92730	−	12.0665i	−0.215220	−	0.887147i
$186$		0			0
$187$	0.0939370	−	0.653346i	0.00686935	−	0.0477774i
$188$	−1.01860	+	21.3830i	−0.0742888	+	1.55951i
$189$		0			0
$190$	15.9257	−	15.1851i	1.15537	−	1.10164i
$191$	5.04744	−	7.08814i	0.365220	−	0.512880i	−0.590548	−	0.807003i	$-0.701088\pi$
$191$	5.04744	−	7.08814i	0.365220	−	0.512880i	0.955767	+	0.294123i	$0.0950276\pi$
$192$		0			0
$193$	−3.71593	+	2.38809i	−0.267479	+	0.171898i	−0.667505	−	0.744606i	$-0.732638\pi$
$193$	−3.71593	+	2.38809i	−0.267479	+	0.171898i	0.400026	+	0.916504i	$0.369001\pi$
$194$	−6.10997	+	1.17760i	−0.438670	+	0.0845468i
$195$		0			0
$196$	−8.40635	−	2.46833i	−0.600454	−	0.176309i
$197$	−10.4678	−	8.23201i	−0.745803	−	0.586506i	0.171270	−	0.985224i	$-0.445213\pi$
$197$	−10.4678	−	8.23201i	−0.745803	−	0.586506i	−0.917074	+	0.398718i	$0.869455\pi$
$198$		0			0
$199$	−3.81406	+	11.0200i	−0.270372	+	0.781187i	0.725316	+	0.688416i	$0.241694\pi$
$199$	−3.81406	+	11.0200i	−0.270372	+	0.781187i	−0.995687	+	0.0927712i	$0.970427\pi$
$200$	−1.32383			−0.0936087
$201$		0			0
$202$	−26.3949			−1.85714
$203$	2.63510	−	7.61362i	0.184948	−	0.534372i
$204$		0			0
$205$	13.7952	+	10.8487i	0.963499	+	0.757704i
$206$	9.25442	+	2.71734i	0.644786	+	0.189326i
$207$		0			0
$208$	15.9923	−	3.08227i	1.10887	−	0.213717i
$209$	0.815903	−	0.524349i	0.0564372	−	0.0362700i
$210$		0			0
$211$	15.9062	−	22.3371i	1.09503	−	1.53775i	0.278502	−	0.960436i	$-0.410162\pi$
$211$	15.9062	−	22.3371i	1.09503	−	1.53775i	0.816523	−	0.577312i	$-0.195899\pi$
$212$	−1.55417	+	1.48190i	−0.106741	+	0.101777i
$213$		0			0
$214$	0.769794	−	16.1600i	0.0526220	−	1.10467i
$215$	−1.39657	+	9.71339i	−0.0952456	+	0.662447i
$216$		0			0
$217$	1.91587	+	7.89731i	0.130057	+	0.536104i
$218$	−6.31894	+	4.96927i	−0.427973	+	0.336562i
$219$		0			0
$220$	−1.46152	−	0.281685i	−0.0985357	−	0.0189912i
$221$	−7.85975	−	11.0375i	−0.528704	−	0.742461i
$222$		0			0
$223$	2.49232	+	5.45742i	0.166898	+	0.365456i	0.974539	−	0.224219i	$-0.0719831\pi$
$223$	2.49232	+	5.45742i	0.166898	+	0.365456i	−0.807641	+	0.589675i	$0.799256\pi$
$224$	26.4886	−	2.52935i	1.76984	−	0.169000i
$225$		0			0
$226$	−2.07833	−	1.33566i	−0.138249	−	0.0888470i
$227$	11.5650	+	4.62993i	0.767597	+	0.307300i	0.722214	−	0.691670i	$-0.243125\pi$
$227$	11.5650	+	4.62993i	0.767597	+	0.307300i	0.0453836	+	0.998970i	$0.485549\pi$
$228$		0			0
$229$	22.9003	+	11.8059i	1.51329	+	0.780156i	0.997084	−	0.0763077i	$-0.0243131\pi$
$229$	22.9003	+	11.8059i	1.51329	+	0.780156i	0.516207	+	0.856464i	$0.327343\pi$
$230$	−5.53786	+	9.59186i	−0.365156	+	0.632468i
$231$		0			0
$232$	−0.0764442	−	1.60476i	−0.00501881	−	0.105358i
$233$	−19.9872	−	1.90855i	−1.30941	−	0.125033i	−0.583099	−	0.812401i	$-0.698160\pi$
$233$	−19.9872	−	1.90855i	−1.30941	−	0.125033i	−0.726309	+	0.687368i	$0.758766\pi$
$234$		0			0
$235$	8.01348	+	23.1534i	0.522742	+	1.51036i
$236$	26.0240	+	2.48499i	1.69402	+	0.161759i
$237$		0			0
$238$	−9.27983	−	16.0731i	−0.601522	−	1.04187i
$239$	−5.19027	+	8.98981i	−0.335731	+	0.581502i	−0.983625	−	0.180228i	$-0.942316\pi$
$239$	−5.19027	+	8.98981i	−0.335731	+	0.581502i	0.647894	+	0.761730i	$0.275650\pi$
$240$		0			0
$241$	−13.5836	+	3.98851i	−0.874997	+	0.256922i	−0.688239	−	0.725484i	$-0.741616\pi$
$241$	−13.5836	+	3.98851i	−0.874997	+	0.256922i	−0.186758	+	0.982406i	$0.559798\pi$
$242$	21.1001	+	8.44721i	1.35637	+	0.543007i
$243$		0			0
$244$	2.09331	+	14.5593i	0.134011	+	0.932065i
$245$	−9.98200	+	0.953166i	−0.637727	+	0.0608955i
$246$		0			0
$247$	4.69387	−	19.3484i	0.298664	−	1.23111i
$248$	0.939964	+	1.31999i	0.0596878	+	0.0838197i
$249$		0			0
$250$	15.2203	−	6.09330i	0.962618	−	0.385374i
$251$	6.61204	−	5.19976i	0.417348	−	0.328206i	−0.387305	−	0.921952i	$-0.626594\pi$
$251$	6.61204	−	5.19976i	0.417348	−	0.328206i	0.804653	+	0.593746i	$0.202351\pi$
$252$		0			0
$253$	−0.319678	+	0.368928i	−0.0200980	+	0.0231943i
$254$	−1.85116	+	12.8751i	−0.116152	+	0.807856i
$255$		0			0
$256$	−8.74284	+	4.50725i	−0.546427	+	0.281703i
$257$	−0.839239	+	0.800213i	−0.0523503	+	0.0499159i	−0.715803	−	0.698303i	$-0.753939\pi$
$257$	−0.839239	+	0.800213i	−0.0523503	+	0.0499159i	0.663452	+	0.748218i	$0.269091\pi$
$258$		0			0
$259$	−10.0768	−	11.6293i	−0.626144	−	0.722608i
$260$	−25.7042	+	16.5191i	−1.59411	+	1.02447i
$261$		0			0
$262$	−16.7094	−	15.9324i	−1.03231	−	0.984304i
$263$	7.05728	+	2.07221i	0.435171	+	0.127778i	0.491978	−	0.870607i	$-0.336274\pi$
$263$	7.05728	+	2.07221i	0.435171	+	0.127778i	−0.0568075	+	0.998385i	$0.518092\pi$
$264$		0			0
$265$	−1.02100	+	2.23568i	−0.0627195	+	0.137337i
$266$	8.91935	−	25.7708i	0.546880	−	1.58011i
$267$		0			0
$268$	5.96182	−	17.9888i	0.364176	−	1.09884i
$269$	−18.9613			−1.15609			−0.578045	−	0.816005i	$-0.696184\pi$
$269$	−18.9613			−1.15609			−0.578045	+	0.816005i	$0.696184\pi$
$270$		0			0
$271$	−5.22255	+	11.4358i	−0.317247	+	0.694674i	−0.999330	−	0.0366005i	$-0.988347\pi$
$271$	−5.22255	+	11.4358i	−0.317247	+	0.694674i	0.682083	+	0.731275i	$0.261074\pi$
$272$	6.99351	+	5.49975i	0.424044	+	0.333472i
$273$		0			0
$274$	4.99577	+	4.76346i	0.301806	+	0.287771i
$275$	−0.481600	+	0.0928207i	−0.0290416	+	0.00559730i
$276$		0			0
$277$	12.4085	+	14.3201i	0.745552	+	0.860413i	0.994129	−	0.108199i	$-0.0345084\pi$
$277$	12.4085	+	14.3201i	0.745552	+	0.860413i	−0.248577	+	0.968612i	$0.579963\pi$
$278$	−0.605484	+	0.850284i	−0.0363145	+	0.0509966i
$279$		0			0
$280$	−5.06488	+	2.61113i	−0.302685	+	0.156045i
$281$	0.922917	−	19.3744i	0.0550566	−	1.15578i	−0.787198	−	0.616701i	$-0.788469\pi$
$281$	0.922917	−	19.3744i	0.0550566	−	1.15578i	0.842254	−	0.539080i	$-0.181228\pi$
$282$		0			0
$283$	9.80753	−	11.3185i	0.582997	−	0.672814i	−0.385249	−	0.922813i	$-0.625885\pi$
$283$	9.80753	−	11.3185i	0.582997	−	0.672814i	0.968246	+	0.249998i	$0.0804300\pi$
$284$	−4.77537	−	19.6843i	−0.283366	−	1.16805i
$285$		0			0
$286$	−2.33023	+	0.932882i	−0.137789	+	0.0551625i
$287$	21.3566	+	4.11614i	1.26064	+	0.242968i
$288$		0			0
$289$	−2.26281	+	9.32745i	−0.133107	+	0.548673i
$290$	−5.61007	−	12.2843i	−0.329435	−	0.721361i
$291$		0			0
$292$	5.51912	+	38.3864i	0.322982	+	2.24639i
$293$	27.3509	+	17.5773i	1.59786	+	1.02688i	0.968257	+	0.249959i	$0.0804170\pi$
$293$	27.3509	+	17.5773i	1.59786	+	1.02688i	0.629599	+	0.776921i	$0.283219\pi$
$294$		0			0
$295$	28.7084	−	8.42956i	1.67147	−	0.490788i
$296$	−2.72734	−	1.40604i	−0.158524	−	0.0817246i
$297$		0			0
$298$	8.43142	+	14.6037i	0.488419	+	0.845967i
$299$	0.476823	+	10.0098i	0.0275754	+	0.578879i
$300$		0			0
$301$	3.97766	+	11.4927i	0.229268	+	0.662427i
$302$	7.54008	+	21.7856i	0.433883	+	1.25362i
$303$		0			0
$304$	0.622028	+	13.0580i	0.0356758	+	0.748926i
$305$	8.41738	+	14.5793i	0.481978	+	0.834810i
$306$		0			0
$307$	29.5832	+	15.2512i	1.68840	+	0.870432i	0.987584	+	0.157094i	$0.0502125\pi$
$307$	29.5832	+	15.2512i	1.68840	+	0.870432i	0.700820	+	0.713339i	$0.252818\pi$
$308$	−1.76987	+	0.519682i	−0.100848	+	0.0296116i
$309$		0			0
$310$	11.4591	+	7.36432i	0.650834	+	0.418265i
$311$	−2.46548	−	17.1478i	−0.139805	−	0.972363i	−0.932094	−	0.362217i	$-0.882020\pi$
$311$	−2.46548	−	17.1478i	−0.139805	−	0.972363i	0.792289	−	0.610146i	$-0.208889\pi$
$312$		0			0
$313$	−0.562147	−	1.23093i	−0.0317744	−	0.0695763i	0.893079	−	0.449899i	$-0.148540\pi$
$313$	−0.562147	−	1.23093i	−0.0317744	−	0.0695763i	−0.924854	+	0.380323i	$0.875813\pi$
$314$	1.75228	−	7.22299i	0.0988867	−	0.407617i
$315$		0			0
$316$	−35.8831	−	6.91591i	−2.01858	−	0.389050i
$317$	4.08685	−	1.63613i	0.229540	−	0.0918940i	−0.254041	−	0.967193i	$-0.581760\pi$
$317$	4.08685	−	1.63613i	0.229540	−	0.0918940i	0.483582	+	0.875299i	$0.339336\pi$
$318$		0			0
$319$	−0.140329	−	0.578442i	−0.00785689	−	0.0323865i
$320$	17.8591	−	20.6105i	0.998352	−	1.15216i
$321$		0			0
$322$	−0.653115	+	13.7106i	−0.0363967	+	0.764060i
$323$	9.66708	−	4.98373i	0.537891	−	0.277302i
$324$		0			0
$325$	−5.84021	+	8.20143i	−0.323957	+	0.454933i
$326$	18.1351	+	20.9290i	1.00441	+	1.15915i
$327$		0			0
$328$	4.25868	−	0.820794i	0.235146	−	0.0453208i
$329$	21.9754	+	20.9535i	1.21155	+	1.15521i
$330$		0			0
$331$	−14.0690	−	11.0640i	−0.773305	−	0.608134i	0.151552	−	0.988449i	$-0.451573\pi$
$331$	−14.0690	−	11.0640i	−0.773305	−	0.608134i	−0.924857	+	0.380316i	$0.875815\pi$
$332$	−5.90007	+	12.9193i	−0.323808	+	0.709041i
$333$		0			0
$334$	23.0787			1.26281
$335$	−1.31734	−	21.6497i	−0.0719742	−	1.18285i
$336$		0			0
$337$	4.18936	−	12.1044i	0.228209	−	0.659367i	−0.771522	−	0.636202i	$-0.780504\pi$
$337$	4.18936	−	12.1044i	0.228209	−	0.659367i	0.999732	−	0.0231651i	$-0.00737435\pi$
$338$	−10.1865	+	22.3054i	−0.554074	+	1.21325i
$339$		0			0
$340$	−16.0151	−	4.70245i	−0.868540	−	0.255026i
$341$	0.434505	+	0.414300i	0.0235298	+	0.0224356i
$342$		0			0
$343$	8.88410	−	5.70946i	0.479696	−	0.308282i
$344$	1.58811	+	1.83278i	0.0856254	+	0.0988169i
$345$		0			0
$346$	32.0896	−	30.5974i	1.72515	−	1.64492i
$347$	−1.92617	+	0.993010i	−0.103402	+	0.0533076i	−0.509152	−	0.860677i	$-0.670041\pi$
$347$	−1.92617	+	0.993010i	−0.103402	+	0.0533076i	0.405750	+	0.913984i	$0.367011\pi$
$348$		0			0
$349$	−0.435801	+	3.03106i	−0.0233279	+	0.162249i	−0.998155	−	0.0607115i	$-0.980663\pi$
$349$	−0.435801	+	3.03106i	−0.0233279	+	0.162249i	0.974827	+	0.222961i	$0.0715721\pi$
$350$	−9.03106	+	10.4224i	−0.482730	+	0.557101i
$351$		0			0
$352$	1.54526	−	1.21520i	0.0823624	−	0.0647705i
$353$	−25.2273	+	10.0995i	−1.34271	+	0.537541i	−0.928057	−	0.372438i	$-0.878522\pi$
$353$	−25.2273	+	10.0995i	−1.34271	+	0.537541i	−0.414655	+	0.909979i	$0.636098\pi$
$354$		0			0
$355$	−13.4472	−	18.8839i	−0.713703	−	1.00226i
$356$	−0.267915	+	1.10436i	−0.0141995	+	0.0585310i
$357$		0			0
$358$	1.68051	−	0.160469i	0.0888176	−	0.00848105i
$359$	−1.75628	−	12.2152i	−0.0926929	−	0.644693i	−0.982209	−	0.187790i	$-0.939868\pi$
$359$	−1.75628	−	12.2152i	−0.0926929	−	0.644693i	0.889516	−	0.456903i	$-0.151041\pi$
$360$		0			0
$361$	−2.80291	−	1.12212i	−0.147522	−	0.0590587i
$362$	−40.0521	+	11.7604i	−2.10509	+	0.618111i
$363$		0			0
$364$	−18.9331	+	32.7931i	−0.992365	+	1.71883i
$365$	22.1928	+	38.4391i	1.16163	+	2.01200i
$366$		0			0
$367$	−3.69129	−	0.352475i	−0.192684	−	0.0183991i	−0.00173199	−	0.999999i	$-0.500551\pi$
$367$	−3.69129	−	0.352475i	−0.192684	−	0.0183991i	−0.190952	+	0.981599i	$0.561157\pi$
$368$	−2.15208	−	6.21803i	−0.112185	−	0.324137i
$369$		0			0
$370$	−25.6762	−	2.45178i	−1.33484	−	0.127462i
$371$	0.144931	+	3.04247i	0.00752444	+	0.157957i
$372$		0			0
$373$	13.4857	−	23.3580i	0.698265	−	1.20943i	−0.270802	−	0.962635i	$-0.587289\pi$
$373$	13.4857	−	23.3580i	0.698265	−	1.20943i	0.969067	−	0.246796i	$-0.0793778\pi$
$374$	−1.21874	−	0.628303i	−0.0630194	−	0.0324888i
$375$		0			0
$376$	5.62111	+	2.25035i	0.289887	+	0.116053i
$377$	−10.2791	−	6.60600i	−0.529402	−	0.340226i
$378$		0			0
$379$	−19.9621	+	1.90615i	−1.02538	+	0.0979123i	−0.594172	−	0.804338i	$-0.702520\pi$
$379$	−19.9621	+	1.90615i	−1.02538	+	0.0979123i	−0.431213	+	0.902250i	$0.641914\pi$
$380$	−10.1881	−	22.3089i	−0.522640	−	1.14442i
$381$		0			0
$382$	−10.4851	−	14.7243i	−0.536465	−	0.753360i
$383$	31.7193	+	6.11339i	1.62078	+	0.312380i	0.917258	−	0.398294i	$-0.130398\pi$
$383$	31.7193	+	6.11339i	1.62078	+	0.312380i	0.703522	+	0.710674i	$0.251610\pi$
$384$		0			0
$385$	−1.65949	+	1.30504i	−0.0845756	+	0.0665109i
$386$	2.16327	+	8.91714i	0.110108	+	0.453870i
$387$		0			0
$388$	−0.986966	+	6.86450i	−0.0501056	+	0.348492i
$389$	−1.52075	+	31.9245i	−0.0771053	+	1.61864i	0.546886	+	0.837207i	$0.315813\pi$
$389$	−1.52075	+	31.9245i	−0.0771053	+	1.61864i	−0.623991	+	0.781431i	$0.714490\pi$
$390$		0			0
$391$	−3.96192	+	3.77768i	−0.200363	+	0.191046i
$392$	−1.43740	+	2.01855i	−0.0725998	+	0.101952i
$393$		0			0
$394$	−23.2721	+	14.9560i	−1.17243	+	0.753474i
$395$	−41.0689	+	7.91539i	−2.06640	+	0.398266i
$396$		0			0
$397$	−17.4696	−	5.12955i	−0.876776	−	0.257445i	−0.187781	−	0.982211i	$-0.560130\pi$
$397$	−17.4696	−	5.12955i	−0.876776	−	0.257445i	−0.688995	+	0.724766i	$0.741948\pi$
$398$	19.0416	+	14.9745i	0.954470	+	0.750603i
$399$		0			0
$400$	2.16222	−	6.24734i	0.108111	−	0.312367i
$401$	−18.0673			−0.902235			−0.451118	−	0.892464i	$-0.648975\pi$
$401$	−18.0673			−0.902235			−0.451118	+	0.892464i	$0.648975\pi$
$402$		0			0
$403$	12.3244			0.613925
$404$	−9.62167	+	27.8000i	−0.478696	+	1.38310i
$405$		0			0
$406$	−13.1557	−	10.3457i	−0.652905	−	0.513450i
$407$	−1.09078	−	0.320281i	−0.0540677	−	0.0158757i
$408$		0			0
$409$	−18.2395	+	3.51537i	−0.901883	+	0.173824i	−0.619056	−	0.785347i	$-0.712484\pi$
$409$	−18.2395	+	3.51537i	−0.901883	+	0.173824i	−0.282827	+	0.959171i	$0.591272\pi$
$410$	30.6694	−	19.7100i	1.51465	−	0.973409i
$411$		0			0
$412$	6.23549	−	8.75653i	0.307201	−	0.431403i
$413$	26.8363	−	25.5883i	1.32053	−	1.25912i
$414$		0			0
$415$	−0.773463	+	16.2370i	−0.0379678	+	0.797042i
$416$	5.74316	−	39.9445i	0.281581	−	1.95844i
$417$		0			0
$418$	−0.474987	−	1.95792i	−0.0232324	−	0.0957652i
$419$	−22.4460	+	17.6517i	−1.09656	+	0.862343i	−0.991237	−	0.132095i	$-0.957830\pi$
$419$	−22.4460	+	17.6517i	−1.09656	+	0.862343i	−0.105321	+	0.994438i	$0.533587\pi$
$420$		0			0
$421$	2.62828	+	0.506559i	0.128094	+	0.0246882i	0.252895	−	0.967494i	$-0.418617\pi$
$421$	2.62828	+	0.506559i	0.128094	+	0.0246882i	−0.124801	+	0.992182i	$0.539829\pi$
$422$	−33.0421	−	46.4011i	−1.60846	−	2.25877i
$423$		0			0
$424$	0.252316	+	0.552495i	0.0122535	+	0.0268315i
$425$	−5.47517	+	0.522815i	−0.265585	+	0.0253603i
$426$		0			0
$427$	17.5513	+	11.2795i	0.849367	+	0.545855i
$428$	−16.7396	−	6.70153i	−0.809140	−	0.323931i
$429$		0			0
$430$	18.1191	+	9.34106i	0.873782	+	0.450466i
$431$	8.59072	−	14.8796i	0.413800	−	0.716723i	−0.581501	−	0.813545i	$-0.697535\pi$
$431$	8.59072	−	14.8796i	0.413800	−	0.716723i	0.995302	+	0.0968223i	$0.0308678\pi$
$432$		0			0
$433$	−0.244940	−	5.14192i	−0.0117711	−	0.247105i	−0.997082	−	0.0763360i	$-0.975678\pi$
$433$	−0.244940	−	5.14192i	−0.0117711	−	0.247105i	0.985311	−	0.170769i	$-0.0546252\pi$
$434$	16.8046	+	1.60465i	0.806647	+	0.0770254i
$435$		0			0
$436$	2.93038	+	8.46677i	0.140340	+	0.405485i
$437$	−8.00720	−	0.764594i	−0.383036	−	0.0365755i
$438$		0			0
$439$	−10.0396	−	17.3891i	−0.479164	−	0.829937i	0.520550	−	0.853831i	$-0.325727\pi$
$439$	−10.0396	−	17.3891i	−0.479164	−	0.829937i	−0.999714	+	0.0238942i	$0.992394\pi$
$440$	−0.210493	+	0.364584i	−0.0100348	+	0.0173809i
$441$		0			0
$442$	−27.0074	+	7.93008i	−1.28461	+	0.377195i
$443$	−17.2121	−	6.89070i	−0.817773	−	0.327387i	−0.0752138	−	0.997167i	$-0.523964\pi$
$443$	−17.2121	−	6.89070i	−0.817773	−	0.327387i	−0.742559	+	0.669781i	$0.766388\pi$
$444$		0			0
$445$	0.185098	+	1.28739i	0.00877450	+	0.0610280i
$446$	12.4066	−	1.18469i	0.587470	−	0.0560965i
$447$		0			0
$448$	7.96807	−	32.8448i	0.376456	−	1.55177i
$449$	−22.7323	−	31.9231i	−1.07281	−	1.50655i	−0.846426	−	0.532506i	$-0.821250\pi$
$449$	−22.7323	−	31.9231i	−1.07281	−	1.50655i	−0.226380	−	0.974039i	$-0.572689\pi$
$450$		0			0
$451$	1.49173	−	0.597199i	0.0702429	−	0.0281210i
$452$	−2.16438	+	1.70208i	−0.101804	+	0.0800593i
$453$		0			0
$454$	16.9464	−	19.5572i	0.795334	−	0.917864i
$455$	−6.16773	+	42.8975i	−0.289148	+	2.01107i
$456$		0			0
$457$	1.06158	−	0.547284i	0.0496588	−	0.0256009i	−0.433218	−	0.901289i	$-0.642622\pi$
$457$	1.06158	−	0.547284i	0.0496588	−	0.0256009i	0.482877	+	0.875688i	$0.339592\pi$
$458$	38.7347	−	36.9335i	1.80995	−	1.72579i
$459$		0			0
$460$	8.08377	+	9.32917i	0.376908	+	0.434975i
$461$	−34.2420	+	22.0060i	−1.59481	+	1.02492i	−0.625133	+	0.780518i	$0.714955\pi$
$461$	−34.2420	+	22.0060i	−1.59481	+	1.02492i	−0.969674	+	0.244402i	$0.921408\pi$
$462$		0			0
$463$	23.8181	+	22.7105i	1.10692	+	1.05545i	0.998114	+	0.0613833i	$0.0195512\pi$
$463$	23.8181	+	22.7105i	1.10692	+	1.05545i	0.108806	+	0.994063i	$0.465297\pi$
$464$	7.69797	+	2.26033i	0.357369	+	0.104933i
$465$		0			0
$466$	−17.3264	+	37.9395i	−0.802630	+	1.75751i
$467$	−5.94779	+	17.1850i	−0.275231	+	0.795227i	0.719665	+	0.694321i	$0.244295\pi$
$467$	−5.94779	+	17.1850i	−0.275231	+	0.795227i	−0.994896	+	0.100906i	$0.967826\pi$
$468$		0			0
$469$	−13.7455	−	23.0998i	−0.634710	−	1.06665i
$470$	50.8962			2.34767
$471$		0			0
$472$	3.07163	−	6.72593i	0.141383	−	0.309586i
$473$	0.706252	+	0.555403i	0.0324735	+	0.0255375i
$474$		0			0
$475$	−5.84888	−	5.57690i	−0.268365	−	0.255886i
$476$	−20.3115	+	3.91473i	−0.930978	+	0.179431i
$477$		0			0
$478$	14.1212	+	16.2967i	0.645888	+	0.745394i
$479$	16.7672	−	23.5463i	0.766115	−	1.07586i	−0.228634	−	0.973513i	$-0.573426\pi$
$479$	16.7672	−	23.5463i	0.766115	−	1.07586i	0.994749	−	0.102346i	$-0.0326348\pi$
$480$		0			0
$481$	−20.7428	+	10.6936i	−0.945789	+	0.487588i
$482$	−1.39932	+	29.3754i	−0.0637373	+	1.33801i
$483$		0			0
$484$	16.5885	−	19.1441i	0.754022	−	0.870188i
$485$	1.87130	+	7.71360i	0.0849713	+	0.350256i
$486$		0			0
$487$	−6.95324	+	2.78366i	−0.315081	+	0.126140i	−0.523813	−	0.851833i	$-0.675491\pi$
$487$	−6.95324	+	2.78366i	−0.315081	+	0.126140i	0.208731	+	0.977973i	$0.433067\pi$
$488$	4.08513	+	0.787345i	0.184925	+	0.0356414i
$489$		0			0
$490$	−4.91088	+	20.2429i	−0.221851	+	0.914481i
$491$	−9.53714	−	20.8834i	−0.430405	−	0.942456i	−0.993261	−	0.115901i	$-0.963025\pi$
$491$	−9.53714	−	20.8834i	−0.430405	−	0.942456i	0.562856	−	0.826555i	$-0.309703\pi$
$492$		0			0
$493$	−0.949928	−	6.60689i	−0.0427826	−	0.297559i
$494$	−34.7930	−	22.3601i	−1.56541	−	1.00603i
$495$		0			0
$496$	−7.76451	+	2.27987i	−0.348637	+	0.102369i
$497$	−25.5363	−	13.1649i	−1.14546	−	0.590526i
$498$		0			0
$499$	−11.6255	−	20.1359i	−0.520427	−	0.901406i	−0.999718	−	0.0237499i	$-0.992439\pi$
$499$	−11.6255	−	20.1359i	−0.520427	−	0.901406i	0.479291	−	0.877656i	$-0.340894\pi$
$500$	−0.869438	−	18.2518i	−0.0388825	−	0.816243i
$501$		0			0
$502$	−5.71510	−	16.5127i	−0.255077	−	0.736997i
$503$	−7.27804	−	21.0285i	−0.324512	−	0.937615i	−0.982772	−	0.184824i	$-0.940828\pi$
$503$	−7.27804	−	21.0285i	−0.324512	−	0.937615i	0.658260	−	0.752791i	$-0.271293\pi$
$504$		0			0
$505$	1.60205	+	33.6313i	0.0712905	+	1.49657i
$506$	0.507033	+	0.878207i	0.0225404	+	0.0390411i
$507$		0			0
$508$	12.8857	+	6.64304i	0.571711	+	0.294737i
$509$	−19.7869	+	5.80995i	−0.877038	+	0.257521i	−0.689106	−	0.724661i	$-0.741997\pi$
$509$	−19.7869	+	5.80995i	−0.877038	+	0.257521i	−0.187932	+	0.982182i	$0.560178\pi$
$510$		0			0
$511$	46.2749	+	29.7390i	2.04708	+	1.31558i
$512$	4.38051	+	30.4671i	0.193593	+	1.34647i
$513$		0			0
$514$	1.00067	+	2.19116i	0.0441377	+	0.0966480i
$515$	2.90062	−	11.9565i	0.127817	−	0.526868i
$516$		0			0
$517$	2.20271	+	0.424538i	0.0968751	+	0.0186711i
$518$	−29.6755	+	11.8803i	−1.30386	+	0.521989i
$519$		0			0
$520$	2.03745	+	8.39848i	0.0893480	+	0.368298i
$521$	−24.1806	+	27.9059i	−1.05937	+	1.22258i	−0.0852941	+	0.996356i	$0.527183\pi$
$521$	−24.1806	+	27.9059i	−1.05937	+	1.22258i	−0.974076	+	0.226222i	$0.927362\pi$
$522$		0			0
$523$	0.680689	−	14.2894i	0.0297645	−	0.624833i	−0.933871	−	0.357611i	$-0.883591\pi$
$523$	0.680689	−	14.2894i	0.0297645	−	0.624833i	0.963635	−	0.267222i	$-0.0861057\pi$
$524$	−22.8715	+	11.7911i	−0.999148	+	0.515096i
$525$		0			0
$526$	8.86275	−	12.4460i	0.386434	−	0.542671i
$527$	4.40887	+	5.08811i	0.192053	+	0.221641i
$528$		0			0
$529$	−18.6089	+	3.58658i	−0.809084	+	0.155938i
$530$	3.69509	+	3.52326i	0.160504	+	0.153041i
$531$		0			0
$532$	−23.8913	−	18.7883i	−1.03582	−	0.814577i
$533$	13.7026	−	30.0046i	0.593528	−	1.29964i
$534$		0			0
$535$	−20.6371			−0.892219
$536$	−4.25662	−	3.25762i	−0.183858	−	0.140708i
$537$		0			0
$538$	−12.8827	+	37.2222i	−0.555415	+	1.60476i
$539$	−0.381386	+	0.835119i	−0.0164275	+	0.0359711i
$540$		0			0
$541$	4.29594	+	1.26140i	0.184697	+	0.0542319i	0.372773	−	0.927923i	$-0.378407\pi$
$541$	4.29594	+	1.26140i	0.184697	+	0.0542319i	−0.188076	+	0.982154i	$0.560225\pi$
$542$	18.9009	+	18.0219i	0.811861	+	0.774108i
$543$		0			0
$544$	18.5455	−	11.9185i	0.795131	−	0.511000i
$545$	6.71517	+	7.74972i	0.287646	+	0.331962i
$546$		0			0
$547$	21.4684	−	20.4701i	0.917922	−	0.875237i	−0.0746113	−	0.997213i	$-0.523772\pi$
$547$	21.4684	−	20.4701i	0.917922	−	0.875237i	0.992533	+	0.121976i	$0.0389231\pi$
$548$	6.83814	−	3.52531i	0.292111	−	0.150594i
$549$		0			0
$550$	−0.144997	+	1.00848i	−0.00618269	+	0.0430015i
$551$	6.42265	−	7.41213i	0.273614	−	0.315767i
$552$		0			0
$553$	−40.7437	+	32.0412i	−1.73260	+	1.36253i
$554$	36.5419	−	14.6292i	1.55252	−	0.621534i
$555$		0			0
$556$	0.674832	+	0.947669i	0.0286193	+	0.0401901i
$557$	−0.870299	+	3.58742i	−0.0368757	+	0.152004i	−0.987273	−	0.159035i	$-0.949162\pi$
$557$	−0.870299	+	3.58742i	−0.0368757	+	0.152004i	0.950397	+	0.311039i	$0.100677\pi$
$558$		0			0
$559$	18.3607	−	1.75323i	0.776574	−	0.0741538i
$560$	−4.04977	−	28.1667i	−0.171134	−	1.19026i
$561$		0			0
$562$	−37.4062	−	14.9752i	−1.57788	−	0.631690i
$563$	14.8995	−	4.37487i	0.627937	−	0.184379i	0.0477462	−	0.998859i	$-0.484796\pi$
$563$	14.8995	−	4.37487i	0.627937	−	0.184379i	0.580191	+	0.814481i	$0.302978\pi$
$564$		0			0
$565$	−1.57570	+	2.72919i	−0.0662902	+	0.114818i
$566$	−15.5555	−	26.9428i	−0.653845	−	1.13249i
$567$		0			0
$568$	−5.70308	−	0.544578i	−0.239296	−	0.0228500i
$569$	7.90678	+	22.8452i	0.331470	+	0.957719i	0.980425	+	0.196892i	$0.0630849\pi$
$569$	7.90678	+	22.8452i	0.331470	+	0.957719i	−0.648956	+	0.760826i	$0.724794\pi$
$570$		0			0
$571$	−27.3680	−	2.61333i	−1.14532	−	0.109364i	−0.494905	−	0.868947i	$-0.664797\pi$
$571$	−27.3680	−	2.61333i	−1.14532	−	0.109364i	−0.650411	+	0.759583i	$0.725403\pi$
$572$	0.133111	+	2.79434i	0.00556564	+	0.116837i
$573$		0			0
$574$	22.5904	−	39.1277i	0.942906	−	1.63316i
$575$	3.61549	+	1.86392i	0.150776	+	0.0777307i
$576$		0			0
$577$	−31.2943	−	12.5284i	−1.30280	−	0.521562i	−0.386586	−	0.922253i	$-0.626346\pi$
$577$	−31.2943	−	12.5284i	−1.30280	−	0.521562i	−0.916213	+	0.400691i	$0.868770\pi$
$578$	16.7730	+	10.7793i	0.697664	+	0.448361i
$579$		0			0
$580$	−14.9833	+	1.43073i	−0.622148	+	0.0594079i
$581$	8.36864	+	18.3248i	0.347190	+	0.760240i
$582$		0			0
$583$	0.130529	+	0.183303i	0.00540597	+	0.00759163i
$584$	10.7706	+	2.07587i	0.445692	+	0.0859002i
$585$		0			0
$586$	53.0883	−	41.7491i	2.19306	−	1.72464i
$587$	4.18910	+	17.2677i	0.172903	+	0.712715i	0.990568	+	0.137021i	$0.0437528\pi$
$587$	4.18910	+	17.2677i	0.172903	+	0.712715i	−0.817665	+	0.575694i	$0.804732\pi$
$588$		0			0
$589$	−1.40784	+	9.79174i	−0.0580091	+	0.403462i
$590$	2.95741	−	62.0837i	0.121755	−	2.55595i
$591$		0			0
$592$	11.0899	−	10.5742i	0.455794	−	0.434598i
$593$	−15.3128	+	21.5039i	−0.628823	+	0.883058i	−0.998945	−	0.0459248i	$-0.985377\pi$
$593$	−15.3128	+	21.5039i	−0.628823	+	0.883058i	0.370122	+	0.928983i	$0.379316\pi$
$594$		0			0
$595$	−19.9165	+	12.7995i	−0.816496	+	0.524730i
$596$	18.4546	−	3.55683i	0.755928	−	0.145693i
$597$		0			0
$598$	19.9738	+	5.86482i	0.816788	+	0.239830i
$599$	−26.1620	−	20.5741i	−1.06895	−	0.840633i	−0.0812050	−	0.996697i	$-0.525877\pi$
$599$	−26.1620	−	20.5741i	−1.06895	−	0.840633i	−0.987747	+	0.156064i	$0.950119\pi$
$600$		0			0
$601$	10.7397	−	31.0303i	0.438081	−	1.26575i	−0.482740	−	0.875764i	$-0.660358\pi$
$601$	10.7397	−	31.0303i	0.438081	−	1.26575i	0.920820	−	0.389987i	$-0.127521\pi$
$602$	25.2634			1.02966
$603$		0			0
$604$	25.6939			1.04547
$605$	9.48240	−	27.3976i	0.385515	−	1.11387i
$606$		0			0
$607$	13.6186	+	10.7098i	0.552762	+	0.434697i	0.855069	−	0.518514i	$-0.173515\pi$
$607$	13.6186	+	10.7098i	0.552762	+	0.434697i	−0.302308	+	0.953210i	$0.597757\pi$
$608$	31.0798	+	9.12585i	1.26045	+	0.370102i
$609$		0			0
$610$	34.3391	−	6.61832i	1.39035	−	0.267968i
$611$	38.7397	−	24.8965i	1.56724	−	1.00720i
$612$		0			0
$613$	−17.7671	+	24.9504i	−0.717606	+	1.00774i	0.281237	+	0.959638i	$0.409255\pi$
$613$	−17.7671	+	24.9504i	−0.717606	+	1.00774i	−0.998843	+	0.0480977i	$0.984684\pi$
$614$	50.0386	−	47.7117i	2.01939	−	1.92549i
$615$		0			0
$616$	−0.0248247	+	0.521135i	−0.00100022	+	0.0209971i
$617$	0.576863	−	4.01217i	0.0232236	−	0.161524i	−0.974909	−	0.222602i	$-0.928545\pi$
$617$	0.576863	−	4.01217i	0.0232236	−	0.161524i	0.998133	+	0.0610784i	$0.0194540\pi$
$618$		0			0
$619$	−7.69763	−	31.7301i	−0.309394	−	1.27534i	−0.888042	−	0.459762i	$-0.847935\pi$
$619$	−7.69763	−	31.7301i	−0.309394	−	1.27534i	0.578648	−	0.815577i	$-0.303580\pi$
$620$	11.9335	−	9.38462i	0.479262	−	0.376896i
$621$		0			0
$622$	−35.3374	−	6.81072i	−1.41690	−	0.273085i
$623$	0.934971	+	1.31298i	0.0374588	+	0.0526035i
$624$		0			0
$625$	−12.8866	−	28.2178i	−0.515466	−	1.12871i
$626$	−2.79833	+	0.267208i	−0.111844	+	0.0106798i
$627$		0			0
$628$	−6.96874	−	4.47854i	−0.278083	−	0.178713i
$629$	−11.8352	−	4.73811i	−0.471901	−	0.188921i
$630$		0			0
$631$	19.6430	+	10.1266i	0.781974	+	0.403135i	0.802499	−	0.596654i	$-0.203503\pi$
$631$	19.6430	+	10.1266i	0.781974	+	0.403135i	−0.0205251	+	0.999789i	$0.506534\pi$
$632$	−5.16800	+	8.95124i	−0.205572	+	0.356061i
$633$		0			0
$634$	−0.435123	−	9.13436i	−0.0172810	−	0.362772i
$635$	16.5173	+	1.57721i	0.655469	+	0.0625897i
$636$		0			0
$637$	6.16414	+	17.8101i	0.244232	+	0.705662i
$638$	−1.23086	−	0.117533i	−0.0487303	−	0.00465318i
$639$		0			0
$640$	−6.85467	−	11.8726i	−0.270954	−	0.469307i
$641$	3.77712	−	6.54217i	0.149187	−	0.258400i	−0.781740	−	0.623604i	$-0.785668\pi$
$641$	3.77712	−	6.54217i	0.149187	−	0.258400i	0.930927	+	0.365204i	$0.119001\pi$
$642$		0			0
$643$	30.1455	−	8.85152i	1.18882	−	0.349070i	0.373254	−	0.927729i	$-0.378242\pi$
$643$	30.1455	−	8.85152i	1.18882	−	0.349070i	0.815569	+	0.578659i	$0.196424\pi$
$644$	14.2024	+	5.68577i	0.559651	+	0.224051i
$645$		0			0
$646$	−3.21534	−	22.3632i	−0.126506	−	0.879867i
$647$	−10.1498	+	0.969191i	−0.399031	+	0.0381028i	−0.292643	−	0.956222i	$-0.594535\pi$
$647$	−10.1498	+	0.969191i	−0.399031	+	0.0381028i	−0.106388	+	0.994325i	$0.533929\pi$
$648$		0			0
$649$	0.645848	−	2.66222i	0.0253517	−	0.104501i
$650$	12.1320	+	17.0369i	0.475854	+	0.668244i
$651$		0			0
$652$	28.6539	−	11.4713i	1.12217	−	0.449251i
$653$	13.3573	−	10.5043i	0.522712	−	0.411065i	−0.321634	−	0.946864i	$-0.604232\pi$
$653$	13.3573	−	10.5043i	0.522712	−	0.411065i	0.844346	+	0.535799i	$0.179989\pi$
$654$		0			0
$655$	−19.2862	+	22.2574i	−0.753572	+	0.869669i
$656$	−3.08232	+	21.4380i	−0.120344	+	0.837013i
$657$		0			0
$658$	56.0638	−	28.9029i	2.18559	−	1.12675i
$659$	−11.0837	+	10.5683i	−0.431760	+	0.411683i	−0.874544	−	0.484946i	$-0.838839\pi$
$659$	−11.0837	+	10.5683i	−0.431760	+	0.411683i	0.442784	+	0.896628i	$0.353991\pi$
$660$		0			0
$661$	5.16931	+	5.96571i	0.201063	+	0.232039i	0.847323	−	0.531079i	$-0.178213\pi$
$661$	5.16931	+	5.96571i	0.201063	+	0.232039i	−0.646260	+	0.763118i	$0.723668\pi$
$662$	−31.2782	+	20.1013i	−1.21566	+	0.781259i
$663$		0			0
$664$	2.90734	+	2.77214i	0.112827	+	0.107580i
$665$	−33.3774	−	9.80049i	−1.29432	−	0.380047i
$666$		0			0
$667$	−2.05069	+	4.49038i	−0.0794030	+	0.173868i
$668$	8.41284	−	24.3073i	0.325503	−	0.940478i
$669$		0			0
$670$	−43.3949	−	12.1233i	−1.67649	−	0.468364i
$671$	1.54135			0.0595032
$672$		0			0
$673$	0.179080	−	0.392131i	0.00690303	−	0.0151155i	−0.906149	−	0.422958i	$-0.860992\pi$
$673$	0.179080	−	0.392131i	0.00690303	−	0.0151155i	0.913052	+	0.407843i	$0.133719\pi$
$674$	−20.9153	−	16.4480i	−0.805628	−	0.633552i
$675$		0			0
$676$	19.7795	+	18.8597i	0.760750	+	0.725374i
$677$	14.9889	−	2.88888i	0.576072	−	0.111029i	0.107110	−	0.994247i	$-0.465840\pi$
$677$	14.9889	−	2.88888i	0.576072	−	0.111029i	0.468962	+	0.883218i	$0.344628\pi$
$678$		0			0
$679$	6.44168	+	7.43410i	0.247209	+	0.285294i
$680$	−2.73842	+	3.84557i	−0.105014	+	0.147471i
$681$		0			0
$682$	1.10851	−	0.571476i	0.0424470	−	0.0218830i
$683$	−1.64287	+	34.4880i	−0.0628625	+	1.31965i	0.718482	+	0.695546i	$0.244837\pi$
$683$	−1.64287	+	34.4880i	−0.0628625	+	1.31965i	−0.781344	+	0.624100i	$0.785466\pi$
$684$		0			0
$685$	5.76618	−	6.65453i	0.220314	−	0.254256i
$686$	−5.17198	−	21.3192i	−0.197467	−	0.813970i
$687$		0			0
$688$	−11.2431	+	4.50104i	−0.428638	+	0.171601i
$689$	4.53596	+	0.874235i	0.172806	+	0.0333057i
$690$		0			0
$691$	−5.09411	+	20.9982i	−0.193789	+	0.798810i	0.789048	+	0.614332i	$0.210574\pi$
$691$	−5.09411	+	20.9982i	−0.193789	+	0.798810i	−0.982837	+	0.184478i	$0.940941\pi$
$692$	−20.5286	−	44.9515i	−0.780382	−	1.70880i
$693$		0			0
$694$	0.640658	+	4.45587i	0.0243190	+	0.169143i
$695$	1.12015	+	0.719874i	0.0424896	+	0.0273064i
$696$		0			0
$697$	17.2892	−	5.07657i	0.654875	−	0.192289i
$698$	5.65408	+	2.91488i	0.214010	+	0.110330i
$699$		0			0
$700$	7.68516	+	13.3111i	0.290472	+	0.503112i
$701$	−1.31126	−	27.5268i	−0.0495258	−	1.03967i	−0.877702	−	0.479206i	$-0.840925\pi$
$701$	−1.31126	−	27.5268i	−0.0495258	−	1.03967i	0.828177	−	0.560467i	$-0.189378\pi$
$702$		0			0
$703$	−6.12659	−	17.7016i	−0.231069	−	0.667630i
$704$	−0.816661	−	2.35959i	−0.0307791	−	0.0889303i
$705$		0			0
$706$	2.68593	+	56.3846i	0.101086	+	2.12206i
$707$	20.8632	+	36.1361i	0.784641	+	1.35904i
$708$		0			0
$709$	−37.1992	−	19.1775i	−1.39705	−	0.720227i	−0.415169	−	0.909745i	$-0.636277\pi$
$709$	−37.1992	−	19.1775i	−1.39705	−	0.720227i	−0.981877	+	0.189517i	$0.939308\pi$
$710$	−46.2067	+	13.5675i	−1.73411	+	0.509180i
$711$		0			0
$712$	0.270395	+	0.173772i	0.0101335	+	0.00651238i
$713$	−0.708608	−	4.92847i	−0.0265376	−	0.184573i
$714$		0			0
$715$	1.33007	+	2.91246i	0.0497420	+	0.108920i
$716$	0.443581	−	1.82846i	0.0165774	−	0.0683329i
$717$		0			0
$718$	−25.1725	−	4.85159i	−0.939428	−	0.181060i
$719$	−5.98260	+	2.39507i	−0.223113	+	0.0893210i	−0.480526	−	0.876980i	$-0.659554\pi$
$719$	−5.98260	+	2.39507i	−0.223113	+	0.0893210i	0.257413	+	0.966302i	$0.417130\pi$
$720$		0			0
$721$	−3.59473	−	14.8177i	−0.133875	−	0.551840i
$722$	−4.10715	+	4.73990i	−0.152852	+	0.176401i
$723$		0			0
$724$	−2.21370	+	46.4712i	−0.0822714	+	1.72709i
$725$	−4.40840	+	2.27269i	−0.163724	+	0.0844056i
$726$		0			0
$727$	−9.05092	+	12.7102i	−0.335680	+	0.471397i	−0.947571	−	0.319545i	$-0.896470\pi$
$727$	−9.05092	+	12.7102i	−0.335680	+	0.471397i	0.611891	+	0.790942i	$0.290409\pi$
$728$	7.01363	+	8.09416i	0.259943	+	0.299990i
$729$		0			0
$730$	90.5368	−	17.4495i	3.35092	−	0.645836i
$731$	7.29205	+	6.95295i	0.269706	+	0.257164i
$732$		0			0
$733$	−10.3547	−	8.14300i	−0.382459	−	0.300769i	0.408358	−	0.912822i	$-0.366101\pi$
$733$	−10.3547	−	8.14300i	−0.382459	−	0.300769i	−0.790817	+	0.612053i	$0.790344\pi$
$734$	−3.19988	+	7.00675i	−0.118110	+	0.258624i
$735$		0			0
$736$	−16.3038			−0.600966
$737$	−1.77694	−	0.886645i	−0.0654544	−	0.0326600i
$738$		0			0
$739$	2.23339	−	6.45296i	0.0821566	−	0.237376i	−0.896440	−	0.443166i	$-0.853855\pi$
$739$	2.23339	−	6.45296i	0.0821566	−	0.237376i	0.978596	+	0.205790i	$0.0659764\pi$
$740$	−11.9420	+	26.1493i	−0.438996	+	0.961268i
$741$		0			0
$742$	6.07104	+	1.78262i	0.222875	+	0.0654420i
$743$	−12.0126	−	11.4540i	−0.440699	−	0.420206i	0.436967	−	0.899477i	$-0.356053\pi$
$743$	−12.0126	−	11.4540i	−0.440699	−	0.420206i	−0.877667	+	0.479271i	$0.840901\pi$
$744$		0			0
$745$	18.0956	−	11.6293i	0.662972	−	0.426066i
$746$	−36.6907	−	42.3433i	−1.34334	−	1.55030i
$747$		0			0
$748$	−1.10601	+	1.05458i	−0.0404399	+	0.0385593i
$749$	−22.7324	+	11.7194i	−0.830623	+	0.428216i
$750$		0			0
$751$	−5.73623	+	39.8963i	−0.209318	+	1.45584i	0.566072	+	0.824356i	$0.308462\pi$
$751$	−5.73623	+	39.8963i	−0.209318	+	1.45584i	−0.775390	+	0.631483i	$0.782447\pi$
$752$	−19.8008	+	22.8513i	−0.722061	+	0.833303i
$753$		0			0
$754$	−19.9519	+	15.6903i	−0.726604	+	0.571408i
$755$	27.3007	−	10.9295i	0.993574	−	0.397767i
$756$		0			0
$757$	1.38257	+	1.94155i	0.0502505	+	0.0705669i	0.838937	−	0.544229i	$-0.183178\pi$
$757$	1.38257	+	1.94155i	0.0502505	+	0.0705669i	−0.788686	+	0.614796i	$0.789238\pi$
$758$	−9.82082	+	40.4820i	−0.356708	+	1.47037i
$759$		0			0
$760$	−6.90531	+	0.659377i	−0.250482	+	0.0239181i
$761$	3.93507	+	27.3690i	0.142646	+	0.992125i	0.927867	+	0.372910i	$0.121640\pi$
$761$	3.93507	+	27.3690i	0.142646	+	0.992125i	−0.785221	+	0.619215i	$0.787451\pi$
$762$		0			0
$763$	11.7979	+	4.72316i	0.427112	+	0.170990i
$764$	−19.3302	+	5.67587i	−0.699344	+	0.205346i
$765$		0			0
$766$	33.5518	−	58.1134i	1.21228	−	2.09972i
$767$	−28.1179	−	48.7017i	−1.01528	−	1.75852i
$768$		0			0
$769$	−44.3303	−	4.23303i	−1.59859	−	0.152647i	−0.742635	−	0.669696i	$-0.766424\pi$
$769$	−44.3303	−	4.23303i	−1.59859	−	0.152647i	−0.855956	+	0.517049i	$0.827030\pi$
$770$	1.43438	+	4.14436i	0.0516914	+	0.149352i
$771$		0			0
$772$	10.1804	+	0.972111i	0.366401	+	0.0349870i
$773$	0.391595	+	8.22058i	0.0140847	+	0.295674i	0.994909	+	0.100779i	$0.0321335\pi$
$773$	0.391595	+	8.22058i	0.0140847	+	0.295674i	−0.980824	+	0.194895i	$0.937563\pi$
$774$		0			0
$775$	2.50131	−	4.33240i	0.0898498	−	0.155624i
$776$	1.74347	+	0.898823i	0.0625870	+	0.0322659i
$777$		0			0
$778$	61.6367	+	24.6756i	2.20978	+	0.884663i
$779$	22.2733	+	14.3142i	0.798024	+	0.512859i
$780$		0			0
$781$	−2.11293	+	0.201760i	−0.0756065	+	0.00721954i
$782$	4.72401	+	10.3441i	0.168930	+	0.369906i
$783$		0			0
$784$	−7.17811	−	10.0802i	−0.256361	−	0.360009i
$785$	−9.30959	−	1.79428i	−0.332273	−	0.0640404i
$786$		0			0
$787$	−5.51789	+	4.33932i	−0.196692	+	0.154680i	−0.711648	−	0.702537i	$-0.752051\pi$
$787$	−5.51789	+	4.33932i	−0.196692	+	0.154680i	0.514956	+	0.857217i	$0.327808\pi$
$788$	7.26890	+	29.9628i	0.258944	+	1.06738i
$789$		0			0
$790$	−12.3648	+	85.9988i	−0.439919	+	3.05970i
$791$	−0.185832	+	3.90110i	−0.00660743	+	0.138707i
$792$		0			0
$793$	22.8998	−	21.8349i	0.813196	−	0.775381i
$794$	−21.9389	+	30.8089i	−0.778582	+	1.09337i
$795$		0			0
$796$	22.7128	−	14.5967i	0.805036	−	0.517365i
$797$	35.4220	−	6.82703i	1.25471	−	0.241826i	0.481767	−	0.876299i	$-0.339995\pi$
$797$	35.4220	−	6.82703i	1.25471	−	0.241826i	0.772945	+	0.634473i	$0.218783\pi$
$798$		0			0
$799$	24.1369	+	7.08724i	0.853902	+	0.250728i
$800$	−12.8761	−	10.1258i	−0.455237	−	0.358002i
$801$		0			0
$802$	−12.2753	+	35.4672i	−0.433456	+	1.25239i
$803$	4.06384			0.143410
$804$		0			0
$805$	17.5091			0.617114
$806$	8.37351	−	24.1937i	0.294944	−	0.852186i
$807$		0			0
$808$	6.54043	+	5.14345i	0.230092	+	0.180946i
$809$	−9.25390	−	2.71719i	−0.325350	−	0.0955313i	0.114979	−	0.993368i	$-0.463320\pi$
$809$	−9.25390	−	2.71719i	−0.325350	−	0.0955313i	−0.440329	+	0.897837i	$0.645138\pi$
$810$		0			0
$811$	21.4517	−	4.13447i	0.753270	−	0.145181i	0.201859	−	0.979415i	$-0.435302\pi$
$811$	21.4517	−	4.13447i	0.753270	−	0.145181i	0.551411	+	0.834234i	$0.314090\pi$
$812$	−15.6921	+	10.0847i	−0.550685	+	0.353904i
$813$		0			0
$814$	−1.36983	+	1.92366i	−0.0480125	+	0.0674241i
$815$	25.5662	−	24.3773i	0.895545	−	0.853900i
$816$		0			0
$817$	−0.704429	+	14.7878i	−0.0246449	+	0.517359i
$818$	−5.49142	+	38.1936i	−0.192003	+	1.33541i
$819$		0			0
$820$	−9.57943	−	39.4870i	−0.334528	−	1.37894i
$821$	0.464380	−	0.365193i	0.0162070	−	0.0127453i	−0.610023	−	0.792384i	$-0.708840\pi$
$821$	0.464380	−	0.365193i	0.0162070	−	0.0127453i	0.626230	+	0.779639i	$0.284597\pi$
$822$		0			0
$823$	−9.30601	−	1.79359i	−0.324387	−	0.0625205i	0.0244581	−	0.999701i	$-0.492214\pi$
$823$	−9.30601	−	1.79359i	−0.324387	−	0.0625205i	−0.348845	+	0.937180i	$0.613426\pi$
$824$	−1.76365	−	2.47670i	−0.0614397	−	0.0862800i
$825$		0			0
$826$	−31.9984	−	70.0666i	−1.11337	−	2.43793i
$827$	−2.08088	+	0.198700i	−0.0723594	+	0.00690949i	−0.131173	−	0.991359i	$-0.541874\pi$
$827$	−2.08088	+	0.198700i	−0.0723594	+	0.00690949i	0.0588135	+	0.998269i	$0.481268\pi$
$828$		0			0
$829$	11.4074	+	7.33110i	0.396196	+	0.254620i	0.723536	−	0.690287i	$-0.242516\pi$
$829$	11.4074	+	7.33110i	0.396196	+	0.254620i	−0.327340	+	0.944907i	$0.606152\pi$
$830$	31.3487	+	12.5501i	1.08813	+	0.435621i
$831$		0			0
$832$	−45.5593	−	23.4874i	−1.57948	−	0.814281i
$833$	−5.14772	+	8.91612i	−0.178358	+	0.308925i
$834$		0			0
$835$	−1.40078	−	29.4060i	−0.0484759	−	1.01763i
$836$	−2.23530	−	0.213445i	−0.0773094	−	0.00738216i
$837$		0			0
$838$	19.4011	+	56.0559i	0.670201	+	1.93642i
$839$	7.57228	+	0.723065i	0.261424	+	0.0249630i	0.224945	−	0.974371i	$-0.427780\pi$
$839$	7.57228	+	0.723065i	0.261424	+	0.0249630i	0.0364790	+	0.999334i	$0.488386\pi$
$840$		0			0
$841$	11.4904	+	19.9020i	0.396222	+	0.686277i
$842$	2.78012	−	4.81531i	0.0958093	−	0.165947i
$843$		0			0
$844$	−60.9161	+	17.8866i	−2.09682	+	0.615681i
$845$	29.0389	+	11.6254i	0.998967	+	0.399926i
$846$		0			0
$847$	−5.11336	−	35.5642i	−0.175697	−	1.22200i
$848$	−3.01942	+	0.288319i	−0.103687	+	0.00990093i
$849$		0			0
$850$	−2.69364	+	11.1033i	−0.0923910	+	0.380841i
$851$	5.46895	+	7.68007i	0.187473	+	0.263269i
$852$		0			0
$853$	−32.6856	+	13.0854i	−1.11913	+	0.448034i	−0.856130	−	0.516761i	$-0.827138\pi$
$853$	−32.6856	+	13.0854i	−1.11913	+	0.448034i	−0.263005	+	0.964795i	$0.584713\pi$
$854$	34.0672	−	26.7908i	1.16576	−	0.916761i
$855$		0			0
$856$	−3.33977	+	3.85430i	−0.114151	+	0.131737i
$857$	−1.09737	+	7.63238i	−0.0374855	+	0.260717i	−0.999943	−	0.0107167i	$-0.996589\pi$
$857$	−1.09737	+	7.63238i	−0.0374855	+	0.260717i	0.962457	+	0.271434i	$0.0874978\pi$
$858$		0			0
$859$	10.3648	−	5.34344i	0.353644	−	0.182316i	−0.272246	−	0.962228i	$-0.587766\pi$
$859$	10.3648	−	5.34344i	0.353644	−	0.182316i	0.625889	+	0.779912i	$0.284736\pi$
$860$	16.4433	−	15.6786i	0.560710	−	0.534636i
$861$		0			0
$862$	−23.3728	−	26.9736i	−0.796080	−	0.918726i
$863$	−6.09898	+	3.91958i	−0.207612	+	0.133424i	−0.640315	−	0.768112i	$-0.721196\pi$
$863$	−6.09898	+	3.91958i	−0.207612	+	0.133424i	0.432703	+	0.901536i	$0.357560\pi$
$864$		0			0
$865$	−40.9336	−	39.0301i	−1.39178	−	1.32706i
$866$	−10.2603	−	3.01271i	−0.348661	−	0.102376i
$867$		0			0
$868$	7.81582	−	17.1143i	0.265286	−	0.580896i
$869$	−1.25246	+	3.61876i	−0.0424870	+	0.122758i
$870$		0			0
$871$	−38.9603	+	11.9994i	−1.32012	+	0.406586i
$872$	2.53412			0.0858162
$873$		0			0
$874$	−6.94122	+	15.1992i	−0.234790	+	0.514119i
$875$	−20.3726	−	16.0212i	−0.688720	−	0.541616i
$876$		0			0
$877$	9.60341	+	9.15683i	0.324284	+	0.309204i	0.834680	−	0.550735i	$-0.185653\pi$
$877$	9.60341	+	9.15683i	0.324284	+	0.309204i	−0.510396	+	0.859940i	$0.670501\pi$
$878$	−40.9571	+	7.89383i	−1.38223	+	0.266404i
$879$		0			0
$880$	−1.37673	−	1.58883i	−0.0464094	−	0.0535593i
$881$	−2.68708	+	3.77348i	−0.0905300	+	0.127132i	−0.857357	−	0.514722i	$-0.827895\pi$
$881$	−2.68708	+	3.77348i	−0.0905300	+	0.127132i	0.766827	+	0.641854i	$0.221834\pi$
$882$		0			0
$883$	−39.5378	+	20.3831i	−1.33055	+	0.685947i	−0.969152	−	0.246464i	$-0.920731\pi$
$883$	−39.5378	+	20.3831i	−1.33055	+	0.685947i	−0.361400	+	0.932411i	$0.617701\pi$
$884$	−1.49271	+	31.3358i	−0.0502053	+	1.05394i
$885$		0			0
$886$	−25.2212	+	29.1068i	−0.847322	+	0.977862i
$887$	1.08626	+	4.47763i	0.0364731	+	0.150344i	0.987136	−	0.159880i	$-0.0511109\pi$
$887$	1.08626	+	4.47763i	0.0364731	+	0.150344i	−0.950663	+	0.310225i	$0.899596\pi$
$888$		0			0
$889$	19.0900	−	7.64247i	0.640257	−	0.256320i
$890$	2.65298	+	0.511320i	0.0889281	+	0.0171395i
$891$		0			0
$892$	3.27480	−	13.4989i	0.109648	−	0.451977i
$893$	15.3549	+	33.6225i	0.513832	+	1.12514i
$894$		0			0
$895$	−0.306463	−	2.13149i	−0.0102439	−	0.0712480i
$896$	−14.2928	−	9.18545i	−0.477490	−	0.306864i
$897$		0			0
$898$	−78.1120	+	22.9358i	−2.60663	+	0.765376i
$899$	5.39624	+	2.78195i	0.179975	+	0.0927833i
$900$		0			0
$901$	1.26174	+	2.18540i	0.0420347	+	0.0728062i
$902$	−0.158823	−	3.33412i	−0.00528824	−	0.111014i
$903$		0			0
$904$	0.254719	+	0.735961i	0.00847181	+	0.0244777i
$905$	17.4155	+	50.3189i	0.578912	+	1.67266i
$906$		0			0
$907$	1.25225	+	26.2879i	0.0415801	+	0.872874i	0.919266	+	0.393637i	$0.128783\pi$
$907$	1.25225	+	26.2879i	0.0415801	+	0.872874i	−0.877686	+	0.479237i	$0.840914\pi$
$908$	−14.4209	−	24.9777i	−0.478573	−	0.828913i
$909$		0			0
$910$	80.0200	+	41.2532i	2.65264	+	1.36753i
$911$	−43.5074	+	12.7749i	−1.44146	+	0.423252i	−0.906710	−	0.421755i	$-0.861414\pi$
$911$	−43.5074	+	12.7749i	−1.44146	+	0.423252i	−0.534755	+	0.845007i	$0.679596\pi$
$912$		0			0
$913$	1.25204	+	0.804638i	0.0414365	+	0.0266296i
$914$	−0.353090	−	2.45579i	−0.0116792	−	0.0812304i
$915$		0			0
$916$	−24.7797	−	54.2600i	−0.818745	−	1.79280i
$917$	−8.60479	+	35.4694i	−0.284155	+	1.17130i
$918$		0			0
$919$	7.44212	+	1.43435i	0.245493	+	0.0473149i	0.310513	−	0.950569i	$-0.399499\pi$
$919$	7.44212	+	1.43435i	0.245493	+	0.0473149i	−0.0650203	+	0.997884i	$0.520711\pi$
$920$	3.24136	−	1.29764i	0.106864	−	0.0427820i
$921$		0			0
$922$	19.9344	+	82.1705i	0.656503	+	2.70614i
$923$	−28.5336	+	32.9295i	−0.939194	+	1.08389i
$924$		0			0
$925$	−0.450731	+	9.46201i	−0.0148200	+	0.311109i
$926$	60.7647	−	31.3264i	1.99685	−	1.02945i
$927$		0			0
$928$	11.5312	−	16.1932i	0.378529	−	0.531569i
$929$	−32.8784	−	37.9437i	−1.07871	−	1.24489i	−0.967976	−	0.251043i	$-0.919226\pi$
$929$	−32.8784	−	37.9437i	−1.07871	−	1.24489i	−0.110731	−	0.993850i	$-0.535319\pi$
$930$		0			0
$931$	−14.8542	+	2.86292i	−0.486828	+	0.0938284i
$932$	33.6433	+	32.0788i	1.10202	+	1.05078i
$933$		0			0
$934$	29.6942	+	23.3518i	0.971623	+	0.764093i
$935$	−0.726585	+	1.59100i	−0.0237619	+	0.0520313i
$936$		0			0
$937$	−54.4615			−1.77918			−0.889591	−	0.456759i	$-0.849010\pi$
$937$	−54.4615			−1.77918			−0.889591	+	0.456759i	$0.849010\pi$
$938$	−54.6854	+	11.2888i	−1.78554	+	0.368593i
$939$		0			0
$940$	18.5531	−	53.6056i	0.605135	−	1.74842i
$941$	17.8618	−	39.1119i	0.582278	−	1.27501i	−0.357719	−	0.933829i	$-0.616446\pi$
$941$	17.8618	−	39.1119i	0.582278	−	1.27501i	0.939997	−	0.341182i	$-0.110827\pi$
$942$		0			0
$943$	−12.7865	−	3.75446i	−0.416386	−	0.122262i
$944$	26.7237	+	25.4810i	0.869784	+	0.829337i
$945$		0			0
$946$	1.57014	−	1.00906i	0.0510495	−	0.0328075i
$947$	27.7629	+	32.0401i	0.902172	+	1.04116i	0.998948	+	0.0458556i	$0.0146014\pi$
$947$	27.7629	+	32.0401i	0.902172	+	1.04116i	−0.0967763	+	0.995306i	$0.530853\pi$
$948$		0			0
$949$	60.3765	−	57.5688i	1.95990	−	1.86876i
$950$	−14.9217	+	7.69265i	−0.484123	+	0.249583i
$951$		0			0
$952$	−0.832636	+	5.79111i	−0.0269859	+	0.187691i
$953$	−10.4835	+	12.0986i	−0.339594	+	0.391913i	−0.899700	−	0.436508i	$-0.856215\pi$
$953$	−10.4835	+	12.0986i	−0.339594	+	0.391913i	0.560106	+	0.828421i	$0.310760\pi$
$954$		0			0
$955$	−18.1247	+	14.2534i	−0.586501	+	0.461229i
$956$	22.3118	−	8.93231i	0.721616	−	0.288891i
$957$		0			0
$958$	−34.8308	−	48.9131i	−1.12533	−	1.58031i
$959$	2.57266	−	10.6047i	0.0830756	−	0.342442i
$960$		0			0
$961$	24.7637	−	2.36465i	0.798831	−	0.0762791i
$962$	6.89919	+	47.9849i	0.222439	+	1.54709i
$963$		0			0
$964$	30.4291	+	12.1820i	0.980054	+	0.392354i
$965$	11.2305	−	3.29758i	0.361524	−	0.106153i
$966$		0			0
$967$	−0.939641	+	1.62751i	−0.0302168	+	0.0523371i	−0.880738	−	0.473603i	$-0.842953\pi$
$967$	−0.939641	+	1.62751i	−0.0302168	+	0.0523371i	0.850522	+	0.525940i	$0.176286\pi$
$968$	−3.58236	−	6.20483i	−0.115141	−	0.199431i
$969$		0			0
$970$	16.4137	+	1.56732i	0.527012	+	0.0503235i
$971$	7.41881	+	21.4353i	0.238081	+	0.687890i	0.999227	+	0.0393095i	$0.0125158\pi$
$971$	7.41881	+	21.4353i	0.238081	+	0.687890i	−0.761146	+	0.648581i	$0.775363\pi$
$972$		0			0
$973$	1.64268	+	0.156857i	0.0526618	+	0.00502859i
$974$	0.740306	+	15.5409i	0.0237209	+	0.497964i
$975$		0			0
$976$	−10.3879	+	17.9924i	−0.332509	+	0.575922i
$977$	−14.0976	−	7.26781i	−0.451022	−	0.232518i	0.217722	−	0.976011i	$-0.430137\pi$
$977$	−14.0976	−	7.26781i	−0.451022	−	0.232518i	−0.668744	+	0.743493i	$0.733168\pi$
$978$		0			0
$979$	0.110552	+	0.0442583i	0.00353325	+	0.00141450i
$980$	19.5304	+	12.5514i	0.623875	+	0.400940i
$981$		0			0
$982$	−47.4752	+	4.53334i	−1.51500	+	0.144665i
$983$	−6.67492	−	14.6160i	−0.212897	−	0.466179i	0.772812	−	0.634635i	$-0.218849\pi$
$983$	−6.67492	−	14.6160i	−0.212897	−	0.466179i	−0.985709	+	0.168455i	$0.946122\pi$
$984$		0			0
$985$	20.4689	+	28.7445i	0.652193	+	0.915876i
$986$	−13.6152	−	2.62411i	−0.433595	−	0.0835685i
$987$		0			0
$988$	−36.2335	+	28.4943i	−1.15274	+	0.906526i
$989$	−1.75677	−	7.24152i	−0.0558622	−	0.230267i
$990$		0			0
$991$	3.81720	−	26.5492i	0.121257	−	0.843362i	−0.834878	−	0.550436i	$-0.814462\pi$
$991$	3.81720	−	26.5492i	0.121257	−	0.843362i	0.956135	−	0.292927i	$-0.0946292\pi$
$992$	−0.954074	+	20.0285i	−0.0302919	+	0.635905i
$993$		0			0
$994$	−43.1935	+	41.1849i	−1.37001	+	1.30630i
$995$	17.9241	−	25.1709i	0.568233	−	0.797972i
$996$		0			0
$997$	−0.671806	+	0.431743i	−0.0212763	+	0.0136735i	−0.551236	−	0.834350i	$-0.685844\pi$
$997$	−0.671806	+	0.431743i	−0.0212763	+	0.0136735i	0.529959	+	0.848023i	$0.322207\pi$
$998$	−47.4266	+	9.14073i	−1.50126	+	0.289345i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	603.2.z.c.73.4		100
3.2	odd	2		67.2.g.a.6.2	✓	100
67.56	even	33	inner	603.2.z.c.190.4		100
201.56	odd	66		67.2.g.a.56.2	yes	100
201.116	odd	66		4489.2.a.p.1.44		50
201.152	even	66		4489.2.a.q.1.7		50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
67.2.g.a.6.2	✓	100	3.2	odd	2
67.2.g.a.56.2	yes	100	201.56	odd	66
603.2.z.c.73.4		100	1.1	even	1	trivial
603.2.z.c.190.4		100	67.56	even	33	inner
4489.2.a.p.1.44		50	201.116	odd	66
4489.2.a.q.1.7		50	201.152	even	66

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.z (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.679423 - 1.96306i) q^{2} +(-1.81990 - 1.43118i) q^{4} +(-2.54249 - 0.746543i) q^{5} +(-3.22458 + 0.621487i) q^{7} +(-0.550889 + 0.354035i) q^{8} +O(q^{10})\)	\(q+(0.679423 - 1.96306i) q^{2} +(-1.81990 - 1.43118i) q^{4} +(-2.54249 - 0.746543i) q^{5} +(-3.22458 + 0.621487i) q^{7} +(-0.550889 + 0.354035i) q^{8} +(-3.19294 + 4.48386i) q^{10} +(-0.175586 + 0.167421i) q^{11} +(-0.236977 + 4.97475i) q^{13} +(-0.970836 + 6.75231i) q^{14} +(-0.770969 - 3.17798i) q^{16} +(-2.13858 + 1.68180i) q^{17} +(-3.92536 - 0.756551i) q^{19} +(3.55864 + 4.99741i) q^{20} +(0.209361 + 0.458437i) q^{22} +(2.00300 - 0.191263i) q^{23} +(1.70067 + 1.09296i) q^{25} +(9.60475 + 3.84516i) q^{26} +(6.75787 + 3.48392i) q^{28} +(-1.22669 + 2.12469i) q^{29} +(-0.117746 - 2.47179i) q^{31} +(-8.06614 - 0.770223i) q^{32} +(1.84848 + 5.34083i) q^{34} +(8.66244 + 0.827163i) q^{35} +(2.34289 + 4.05800i) q^{37} +(-4.15214 + 7.19171i) q^{38} +(1.66493 - 0.488868i) q^{40} +(-6.14863 - 2.46154i) q^{41} +(-0.527043 - 3.66566i) q^{43} +(0.559160 - 0.0533933i) q^{44} +(0.985422 - 4.06197i) q^{46} +(-5.36335 - 7.53177i) q^{47} +(3.51310 - 1.40643i) q^{49} +(3.30102 - 2.59595i) q^{50} +(7.55106 - 8.71439i) q^{52} +(0.132001 - 0.918084i) q^{53} +(0.571415 - 0.294585i) q^{55} +(1.55636 - 1.48398i) q^{56} +(3.33747 + 3.85164i) q^{58} +(-9.49898 + 6.10462i) q^{59} +(-4.59799 - 4.38418i) q^{61} +(-4.93228 - 1.44825i) q^{62} +(-4.27537 + 9.36176i) q^{64} +(4.31638 - 12.4714i) q^{65} +(2.77883 + 7.69923i) q^{67} +6.29897 q^{68} +(7.50924 - 16.4429i) q^{70} +(6.87694 + 5.40808i) q^{71} +(-12.1228 - 11.5591i) q^{73} +(9.55793 - 1.84214i) q^{74} +(6.06099 + 6.99476i) q^{76} +(0.462143 - 0.648989i) q^{77} +(14.0293 - 7.23262i) q^{79} +(-0.412314 + 8.65554i) q^{80} +(-9.00969 + 10.3977i) q^{82} +(-1.44626 - 5.96158i) q^{83} +(6.69287 - 2.67942i) q^{85} +(-7.55402 - 1.45592i) q^{86} +(0.0374556 - 0.154394i) q^{88} +(-0.203900 - 0.446478i) q^{89} +(-2.32759 - 16.1888i) q^{91} +(-3.91899 - 2.51858i) q^{92} +(-18.4293 + 5.41134i) q^{94} +(9.41540 + 4.85398i) q^{95} +(-1.49771 - 2.59411i) q^{97} +(-0.374037 - 7.85201i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q + 24 q^{2} - 18 q^{4} + 16 q^{5} - 24 q^{7} - 23 q^{8}+O(q^{10}) \) 100 * q + 24 * q^2 - 18 * q^4 + 16 * q^5 - 24 * q^7 - 23 * q^8	\( 100 q + 24 q^{2} - 18 q^{4} + 16 q^{5} - 24 q^{7} - 23 q^{8} + 8 q^{10} + 24 q^{11} - 22 q^{13} + 32 q^{14} - 28 q^{16} - 17 q^{17} + 15 q^{20} + 49 q^{22} + 13 q^{23} - 34 q^{25} + 27 q^{26} + 22 q^{28} - 8 q^{29} + 10 q^{31} - 34 q^{32} - 50 q^{34} + q^{35} + 7 q^{37} - 50 q^{38} + 43 q^{40} + 5 q^{41} + 2 q^{43} + 19 q^{44} + 52 q^{46} + 6 q^{47} - 27 q^{49} - 134 q^{50} + 120 q^{52} + 52 q^{53} - 64 q^{55} + 124 q^{56} - 56 q^{58} - 27 q^{59} - 16 q^{61} + 74 q^{62} - 197 q^{64} + 92 q^{65} - 56 q^{67} - 16 q^{68} - 22 q^{70} + 113 q^{71} + q^{73} + 24 q^{74} - 144 q^{76} - 85 q^{77} + 36 q^{79} + 13 q^{80} - 20 q^{82} + 61 q^{83} - 6 q^{85} - 189 q^{86} + 129 q^{88} - 95 q^{89} + 42 q^{91} - 4 q^{92} + 70 q^{94} + 20 q^{95} + 53 q^{97} - q^{98}+O(q^{100}) \) 100 * q + 24 * q^2 - 18 * q^4 + 16 * q^5 - 24 * q^7 - 23 * q^8 + 8 * q^10 + 24 * q^11 - 22 * q^13 + 32 * q^14 - 28 * q^16 - 17 * q^17 + 15 * q^20 + 49 * q^22 + 13 * q^23 - 34 * q^25 + 27 * q^26 + 22 * q^28 - 8 * q^29 + 10 * q^31 - 34 * q^32 - 50 * q^34 + q^35 + 7 * q^37 - 50 * q^38 + 43 * q^40 + 5 * q^41 + 2 * q^43 + 19 * q^44 + 52 * q^46 + 6 * q^47 - 27 * q^49 - 134 * q^50 + 120 * q^52 + 52 * q^53 - 64 * q^55 + 124 * q^56 - 56 * q^58 - 27 * q^59 - 16 * q^61 + 74 * q^62 - 197 * q^64 + 92 * q^65 - 56 * q^67 - 16 * q^68 - 22 * q^70 + 113 * q^71 + q^73 + 24 * q^74 - 144 * q^76 - 85 * q^77 + 36 * q^79 + 13 * q^80 - 20 * q^82 + 61 * q^83 - 6 * q^85 - 189 * q^86 + 129 * q^88 - 95 * q^89 + 42 * q^91 - 4 * q^92 + 70 * q^94 + 20 * q^95 + 53 * q^97 - q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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