LMFDB - Embedded newform 403.2.bl.b.126.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(16,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([10, 6]))

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

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

chi := DirichletCharacter("403.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.bl (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$280$
Relative dimension:	$35$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			126.13
Character	$\chi$	$=$	403.126
Dual form			403.2.bl.b.16.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.657025 + 0.292526i) q^{2} +(-0.0382007 - 0.363455i) q^{3} +(-0.992151 + 1.10190i) q^{4} -0.138184 q^{5} +(0.131419 + 0.227624i) q^{6} +(-1.74853 + 1.94194i) q^{7} +(0.774026 - 2.38221i) q^{8} +(2.80380 - 0.595967i) q^{9} +O(q^{10})$	\(q+(-0.657025 + 0.292526i) q^{2} +(-0.0382007 - 0.363455i) q^{3} +(-0.992151 + 1.10190i) q^{4} -0.138184 q^{5} +(0.131419 + 0.227624i) q^{6} +(-1.74853 + 1.94194i) q^{7} +(0.774026 - 2.38221i) q^{8} +(2.80380 - 0.595967i) q^{9} +(0.0907902 - 0.0404224i) q^{10} +(-2.01171 - 0.427602i) q^{11} +(0.438391 + 0.318509i) q^{12} +(-2.66374 + 2.42992i) q^{13} +(0.580758 - 1.78739i) q^{14} +(0.00527872 + 0.0502236i) q^{15} +(-0.121675 - 1.15766i) q^{16} +(-4.54556 + 0.966188i) q^{17} +(-1.66783 + 1.21175i) q^{18} +(-0.0199969 + 0.190257i) q^{19} +(0.137099 - 0.152264i) q^{20} +(0.772602 + 0.561328i) q^{21} +(1.44683 - 0.307533i) q^{22} +(-5.22877 - 5.80714i) q^{23} +(-0.895395 - 0.190322i) q^{24} -4.98091 q^{25} +(1.03933 - 2.37573i) q^{26} +(-0.662512 - 2.03900i) q^{27} +(-0.405008 - 3.85339i) q^{28} +(-0.320281 + 0.142598i) q^{29} +(-0.0181600 - 0.0314540i) q^{30} +(-1.53719 + 5.35136i) q^{31} +(2.92339 + 5.06346i) q^{32} +(-0.0785655 + 0.747501i) q^{33} +(2.70391 - 1.96450i) q^{34} +(0.241618 - 0.268344i) q^{35} +(-2.12510 + 3.68079i) q^{36} +(-3.98719 + 6.90601i) q^{37} +(-0.0425168 - 0.130853i) q^{38} +(0.984923 + 0.875326i) q^{39} +(-0.106958 + 0.329183i) q^{40} +(-0.827375 + 0.368371i) q^{41} +(-0.671822 - 0.142800i) q^{42} +(1.06821 - 10.1634i) q^{43} +(2.46709 - 1.79245i) q^{44} +(-0.387440 + 0.0823529i) q^{45} +(5.13417 + 2.28588i) q^{46} +(2.99692 - 2.17739i) q^{47} +(-0.416108 + 0.0884465i) q^{48} +(0.0179304 + 0.170597i) q^{49} +(3.27258 - 1.45705i) q^{50} +(0.524810 + 1.61520i) q^{51} +(-0.0346822 - 5.34601i) q^{52} +(-2.65330 + 8.16603i) q^{53} +(1.03175 + 1.14587i) q^{54} +(0.277986 + 0.0590877i) q^{55} +(3.27269 + 5.66847i) q^{56} +0.0699139 q^{57} +(0.168719 - 0.187381i) q^{58} +(-3.95013 - 1.75871i) q^{59} +(-0.0605785 - 0.0440129i) q^{60} +(-1.43052 - 2.47773i) q^{61} +(-0.555441 - 3.96564i) q^{62} +(-3.74520 + 6.48687i) q^{63} +(-1.51849 - 1.10325i) q^{64} +(0.368086 - 0.335775i) q^{65} +(-0.167044 - 0.514109i) q^{66} +(0.624921 - 1.08239i) q^{67} +(3.44524 - 5.96734i) q^{68} +(-1.91089 + 2.12226i) q^{69} +(-0.0802514 + 0.246988i) q^{70} +(11.2909 - 2.39996i) q^{71} +(0.750501 - 7.14054i) q^{72} +(2.08989 + 6.43203i) q^{73} +(0.599491 - 5.70377i) q^{74} +(0.190274 + 1.81034i) q^{75} +(-0.189804 - 0.210799i) q^{76} +(4.34790 - 3.15894i) q^{77} +(-0.903174 - 0.286995i) q^{78} +(-0.484542 + 1.49127i) q^{79} +(0.0168135 + 0.159969i) q^{80} +(7.14009 - 3.17897i) q^{81} +(0.435848 - 0.484058i) q^{82} +(4.52538 + 3.28788i) q^{83} +(-1.38506 + 0.294404i) q^{84} +(0.628123 - 0.133512i) q^{85} +(2.27121 + 6.99006i) q^{86} +(0.0640631 + 0.110960i) q^{87} +(-2.57575 + 4.46133i) q^{88} +(1.87406 + 0.398343i) q^{89} +(0.230467 - 0.167444i) q^{90} +(-0.0611226 - 9.42159i) q^{91} +11.5866 q^{92} +(2.00370 + 0.354275i) q^{93} +(-1.33211 + 2.30727i) q^{94} +(0.00276324 - 0.0262905i) q^{95} +(1.72867 - 1.25595i) q^{96} +(-8.66381 + 9.62213i) q^{97} +(-0.0616848 - 0.106841i) q^{98} -5.89527 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 280 q + q^{2} + 39 q^{4} - 8 q^{5} - 2 q^{7} + 12 q^{8} + 29 q^{9}+O(q^{10}) $ 280 * q + q^2 + 39 * q^4 - 8 * q^5 - 2 * q^7 + 12 * q^8 + 29 * q^9	\( 280 q + q^{2} + 39 q^{4} - 8 q^{5} - 2 q^{7} + 12 q^{8} + 29 q^{9} - 21 q^{10} - q^{11} - 16 q^{12} - 54 q^{14} - 27 q^{15} + 31 q^{16} + 2 q^{17} - 10 q^{18} + 5 q^{19} - 3 q^{20} + 68 q^{21} - 39 q^{22} - 7 q^{23} + 48 q^{24} + 200 q^{25} + 6 q^{26} - 78 q^{27} + 30 q^{28} - 16 q^{29} - 66 q^{30} - 62 q^{31} - 56 q^{32} - 20 q^{33} - 126 q^{34} - 37 q^{35} - 140 q^{36} - 36 q^{37} + 4 q^{38} + 28 q^{39} - 158 q^{40} - 4 q^{41} + 16 q^{42} - 16 q^{43} + 42 q^{44} - 46 q^{45} - 29 q^{46} + 8 q^{47} - 36 q^{48} + 43 q^{49} - 5 q^{50} - 134 q^{51} - q^{52} + 8 q^{53} + 44 q^{54} - 55 q^{55} - 42 q^{56} + 140 q^{57} + 38 q^{58} - 23 q^{59} + 38 q^{60} + 40 q^{61} + 19 q^{62} - 146 q^{63} - 68 q^{64} + 2 q^{65} + 6 q^{66} + 46 q^{67} + 86 q^{68} - 32 q^{69} - 4 q^{70} + 60 q^{71} + 73 q^{72} - 12 q^{73} - 44 q^{74} + 16 q^{75} - 70 q^{76} + 10 q^{77} - 142 q^{78} + 134 q^{79} - 72 q^{80} - 18 q^{81} + 28 q^{82} - 88 q^{83} + 81 q^{84} - 69 q^{85} + 188 q^{86} - 28 q^{87} + 42 q^{88} + 12 q^{89} + 22 q^{90} + 67 q^{91} - 324 q^{92} - 25 q^{93} - 62 q^{94} + 16 q^{95} + 276 q^{96} + 16 q^{97} + 76 q^{98} - 60 q^{99}+O(q^{100}) \) 280 * q + q^2 + 39 * q^4 - 8 * q^5 - 2 * q^7 + 12 * q^8 + 29 * q^9 - 21 * q^10 - q^11 - 16 * q^12 - 54 * q^14 - 27 * q^15 + 31 * q^16 + 2 * q^17 - 10 * q^18 + 5 * q^19 - 3 * q^20 + 68 * q^21 - 39 * q^22 - 7 * q^23 + 48 * q^24 + 200 * q^25 + 6 * q^26 - 78 * q^27 + 30 * q^28 - 16 * q^29 - 66 * q^30 - 62 * q^31 - 56 * q^32 - 20 * q^33 - 126 * q^34 - 37 * q^35 - 140 * q^36 - 36 * q^37 + 4 * q^38 + 28 * q^39 - 158 * q^40 - 4 * q^41 + 16 * q^42 - 16 * q^43 + 42 * q^44 - 46 * q^45 - 29 * q^46 + 8 * q^47 - 36 * q^48 + 43 * q^49 - 5 * q^50 - 134 * q^51 - q^52 + 8 * q^53 + 44 * q^54 - 55 * q^55 - 42 * q^56 + 140 * q^57 + 38 * q^58 - 23 * q^59 + 38 * q^60 + 40 * q^61 + 19 * q^62 - 146 * q^63 - 68 * q^64 + 2 * q^65 + 6 * q^66 + 46 * q^67 + 86 * q^68 - 32 * q^69 - 4 * q^70 + 60 * q^71 + 73 * q^72 - 12 * q^73 - 44 * q^74 + 16 * q^75 - 70 * q^76 + 10 * q^77 - 142 * q^78 + 134 * q^79 - 72 * q^80 - 18 * q^81 + 28 * q^82 - 88 * q^83 + 81 * q^84 - 69 * q^85 + 188 * q^86 - 28 * q^87 + 42 * q^88 + 12 * q^89 + 22 * q^90 + 67 * q^91 - 324 * q^92 - 25 * q^93 - 62 * q^94 + 16 * q^95 + 276 * q^96 + 16 * q^97 + 76 * q^98 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.657025	+	0.292526i	−0.464587	+	0.206847i	−0.625661	−	0.780095i	$-0.715171\pi$
$2$	−0.657025	+	0.292526i	−0.464587	+	0.206847i	0.161075	+	0.986942i	$0.448504\pi$
$3$	−0.0382007	−	0.363455i	−0.0220552	−	0.209841i	−1.00000		0.000975363i	$-0.999690\pi$
$3$	−0.0382007	−	0.363455i	−0.0220552	−	0.209841i	0.977944	−	0.208866i	$-0.0669771\pi$
$4$	−0.992151	+	1.10190i	−0.496076	+	0.550948i
$5$	−0.138184			−0.0617977			−0.0308988	−	0.999523i	$-0.509837\pi$
$5$	−0.138184			−0.0617977			−0.0308988	+	0.999523i	$0.509837\pi$
$6$	0.131419	+	0.227624i	0.0536516	+	0.0929273i
$7$	−1.74853	+	1.94194i	−0.660881	+	0.733983i	−0.976646	−	0.214855i	$-0.931072\pi$
$7$	−1.74853	+	1.94194i	−0.660881	+	0.733983i	0.315765	+	0.948837i	$0.397739\pi$
$8$	0.774026	−	2.38221i	0.273660	−	0.842238i
$9$	2.80380	−	0.595967i	0.934601	−	0.198656i
$10$	0.0907902	−	0.0404224i	0.0287104	−	0.0127827i
$11$	−2.01171	−	0.427602i	−0.606553	−	0.128927i	−0.105611	−	0.994408i	$-0.533680\pi$
$11$	−2.01171	−	0.427602i	−0.606553	−	0.128927i	−0.500942	+	0.865481i	$0.667013\pi$
$12$	0.438391	+	0.318509i	0.126552	+	0.0919458i
$13$	−2.66374	+	2.42992i	−0.738788	+	0.673938i
$13$	−2.66374	+	2.42992i	−0.738788	+	0.673938i
$14$	0.580758	−	1.78739i	0.155214	−	0.477700i
$15$	0.00527872	+	0.0502236i	0.00136296	+	0.0129677i
$16$	−0.121675	−	1.15766i	−0.0304186	−	0.289414i
$17$	−4.54556	+	0.966188i	−1.10246	+	0.234335i	−0.722983	−	0.690866i	$-0.757229\pi$
$17$	−4.54556	+	0.966188i	−1.10246	+	0.234335i	−0.379477	+	0.925201i	$0.623896\pi$
$18$	−1.66783	+	1.21175i	−0.393112	+	0.285612i
$19$	−0.0199969	+	0.190257i	−0.00458759	+	0.0436480i	−0.996576	−	0.0826793i	$-0.973652\pi$
$19$	−0.0199969	+	0.190257i	−0.00458759	+	0.0436480i	0.991989	+	0.126327i	$0.0403190\pi$
$20$	0.137099	−	0.152264i	0.0306563	−	0.0340473i
$21$	0.772602	+	0.561328i	0.168596	+	0.122492i
$22$	1.44683	−	0.307533i	0.308465	−	0.0655662i
$23$	−5.22877	−	5.80714i	−1.09027	−	1.21087i	−0.976080	−	0.217413i	$-0.930238\pi$
$23$	−5.22877	−	5.80714i	−1.09027	−	1.21087i	−0.114194	−	0.993458i	$-0.536429\pi$
$24$	−0.895395	−	0.190322i	−0.182772	−	0.0388493i
$25$	−4.98091			−0.996181
$26$	1.03933	−	2.37573i	0.203829	−	0.465919i
$27$	−0.662512	−	2.03900i	−0.127500	−	0.392406i
$28$	−0.405008	−	3.85339i	−0.0765392	−	0.728222i
$29$	−0.320281	+	0.142598i	−0.0594747	+	0.0264798i	−0.436258	−	0.899821i	$-0.643697\pi$
$29$	−0.320281	+	0.142598i	−0.0594747	+	0.0264798i	0.376784	+	0.926301i	$0.377030\pi$
$30$	−0.0181600	−	0.0314540i	−0.00331554	−	0.00574269i
$31$	−1.53719	+	5.35136i	−0.276088	+	0.961132i
$31$	−1.53719	+	5.35136i	−0.276088	+	0.961132i
$32$	2.92339	+	5.06346i	0.516787	+	0.895102i
$33$	−0.0785655	+	0.747501i	−0.0136765	+	0.130123i
$34$	2.70391	−	1.96450i	0.463717	−	0.336910i
$35$	0.241618	−	0.268344i	0.0408409	−	0.0453584i
$36$	−2.12510	+	3.68079i	−0.354184	+	0.613465i
$37$	−3.98719	+	6.90601i	−0.655489	+	1.13534i	0.326282	+	0.945273i	$0.394204\pi$
$37$	−3.98719	+	6.90601i	−0.655489	+	1.13534i	−0.981771	+	0.190068i	$0.939129\pi$
$38$	−0.0425168	−	0.130853i	−0.00689714	−	0.0212272i
$39$	0.984923	+	0.875326i	0.157714	+	0.140164i
$40$	−0.106958	+	0.329183i	−0.0169115	+	0.0520483i
$41$	−0.827375	+	0.368371i	−0.129214	+	0.0575299i	−0.470325	−	0.882493i	$-0.655863\pi$
$41$	−0.827375	+	0.368371i	−0.129214	+	0.0575299i	0.341111	+	0.940023i	$0.389197\pi$
$42$	−0.671822	−	0.142800i	−0.103664	−	0.0220345i
$43$	1.06821	−	10.1634i	0.162901	−	1.54990i	−0.541870	−	0.840463i	$-0.682283\pi$
$43$	1.06821	−	10.1634i	0.162901	−	1.54990i	0.704770	−	0.709435i	$-0.251050\pi$
$44$	2.46709	−	1.79245i	0.371928	−	0.270222i
$45$	−0.387440	+	0.0823529i	−0.0577562	+	0.0122764i
$46$	5.13417	+	2.28588i	0.756992	+	0.337035i
$47$	2.99692	−	2.17739i	0.437145	−	0.317605i	−0.347354	−	0.937734i	$-0.612920\pi$
$47$	2.99692	−	2.17739i	0.437145	−	0.317605i	0.784500	+	0.620129i	$0.212920\pi$
$48$	−0.416108	+	0.0884465i	−0.0600600	+	0.0127662i
$49$	0.0179304	+	0.170597i	0.00256149	+	0.0243710i
$50$	3.27258	−	1.45705i	0.462812	−	0.206057i
$51$	0.524810	+	1.61520i	0.0734881	+	0.226173i
$52$	−0.0346822	−	5.34601i	−0.00480956	−	0.741358i
$53$	−2.65330	+	8.16603i	−0.364459	+	1.12169i	0.585860	+	0.810413i	$0.300757\pi$
$53$	−2.65330	+	8.16603i	−0.364459	+	1.12169i	−0.950319	+	0.311278i	$0.899243\pi$
$54$	1.03175	+	1.14587i	0.140403	+	0.155933i
$55$	0.277986	+	0.0590877i	0.0374836	+	0.00796738i
$56$	3.27269	+	5.66847i	0.437332	+	0.757481i
$57$	0.0699139			0.00926033
$58$	0.168719	−	0.187381i	0.0221539	−	0.0246044i
$59$	−3.95013	−	1.75871i	−0.514263	−	0.228965i	0.133161	−	0.991094i	$-0.457487\pi$
$59$	−3.95013	−	1.75871i	−0.514263	−	0.228965i	−0.647424	+	0.762130i	$0.724154\pi$
$60$	−0.0605785	−	0.0440129i	−0.00782065	−	0.00568203i
$61$	−1.43052	−	2.47773i	−0.183159	−	0.317240i	0.759796	−	0.650162i	$-0.225299\pi$
$61$	−1.43052	−	2.47773i	−0.183159	−	0.317240i	−0.942955	+	0.332922i	$0.891966\pi$
$62$	−0.555441	−	3.96564i	−0.0705410	−	0.503637i
$63$	−3.74520	+	6.48687i	−0.471850	+	0.817269i
$64$	−1.51849	−	1.10325i	−0.189811	−	0.137906i
$65$	0.368086	−	0.335775i	0.0456554	−	0.0416478i
$66$	−0.167044	−	0.514109i	−0.0205617	−	0.0632824i
$67$	0.624921	−	1.08239i	0.0763462	−	0.132236i	−0.825325	−	0.564658i	$-0.809008\pi$
$67$	0.624921	−	1.08239i	0.0763462	−	0.132236i	0.901671	+	0.432423i	$0.142341\pi$
$68$	3.44524	−	5.96734i	0.417797	−	0.723646i
$69$	−1.91089	+	2.12226i	−0.230044	+	0.255490i
$70$	−0.0802514	+	0.246988i	−0.00959187	+	0.0295208i
$71$	11.2909	−	2.39996i	1.33998	−	0.284822i	0.518512	−	0.855071i	$-0.326486\pi$
$71$	11.2909	−	2.39996i	1.33998	−	0.284822i	0.821472	+	0.570248i	$0.193153\pi$
$72$	0.750501	−	7.14054i	0.0884473	−	0.841520i
$73$	2.08989	+	6.43203i	0.244603	+	0.752812i	0.995701	+	0.0926213i	$0.0295246\pi$
$73$	2.08989	+	6.43203i	0.244603	+	0.752812i	−0.751098	+	0.660191i	$0.770475\pi$
$74$	0.599491	−	5.70377i	0.0696894	−	0.663050i
$75$	0.190274	+	1.81034i	0.0219710	+	0.209040i
$76$	−0.189804	−	0.210799i	−0.0217720	−	0.0241803i
$77$	4.34790	−	3.15894i	0.495490	−	0.359994i
$78$	−0.903174	−	0.286995i	−0.102264	−	0.0324958i
$79$	−0.484542	+	1.49127i	−0.0545152	+	0.167780i	−0.974607	−	0.223922i	$-0.928114\pi$
$79$	−0.484542	+	1.49127i	−0.0545152	+	0.167780i	0.920092	+	0.391703i	$0.128114\pi$
$80$	0.0168135	+	0.159969i	0.00187980	+	0.0178851i
$81$	7.14009	−	3.17897i	0.793344	−	0.353219i
$82$	0.435848	−	0.484058i	0.0481313	−	0.0534552i
$83$	4.52538	+	3.28788i	0.496725	+	0.360892i	0.807765	−	0.589505i	$-0.200677\pi$
$83$	4.52538	+	3.28788i	0.496725	+	0.360892i	−0.311039	+	0.950397i	$0.600677\pi$
$84$	−1.38506	+	0.294404i	−0.151123	+	0.0321221i
$85$	0.628123	−	0.133512i	0.0681295	−	0.0144814i
$86$	2.27121	+	6.99006i	0.244911	+	0.753757i
$87$	0.0640631	+	0.110960i	0.00686828	+	0.0118962i
$88$	−2.57575	+	4.46133i	−0.274576	+	0.475580i
$89$	1.87406	+	0.398343i	0.198650	+	0.0422243i	0.306162	−	0.951979i	$-0.400955\pi$
$89$	1.87406	+	0.398343i	0.198650	+	0.0422243i	−0.107512	+	0.994204i	$0.534288\pi$
$90$	0.230467	−	0.167444i	0.0242934	−	0.0176502i
$91$	−0.0611226	−	9.42159i	−0.00640739	−	0.987651i
$92$	11.5866			1.20799
$93$	2.00370	+	0.354275i	0.207774	+	0.0367366i
$94$	−1.33211	+	2.30727i	−0.137396	+	0.237977i
$95$	0.00276324	−	0.0262905i	0.000283503	−	0.00269735i
$96$	1.72867	−	1.25595i	0.176431	−	0.128185i
$97$	−8.66381	+	9.62213i	−0.879677	+	0.976980i	−0.999876	−	0.0157701i	$-0.994980\pi$
$97$	−8.66381	+	9.62213i	−0.879677	+	0.976980i	0.120199	+	0.992750i	$0.461647\pi$
$98$	−0.0616848	−	0.106841i	−0.00623110	−	0.0107926i
$99$	−5.89527			−0.592497
$100$	4.94181	−	5.48844i	0.494181	−	0.548844i
$101$	11.7445	+	13.0436i	1.16862	+	1.29789i	0.946440	+	0.322880i	$0.104651\pi$
$101$	11.7445	+	13.0436i	1.16862	+	1.29789i	0.222182	+	0.975005i	$0.428682\pi$
$102$	−0.817301	−	0.907705i	−0.0809248	−	0.0898761i
$103$	−9.22179	−	6.70002i	−0.908650	−	0.660173i	0.0320234	−	0.999487i	$-0.489805\pi$
$103$	−9.22179	−	6.70002i	−0.908650	−	0.660173i	−0.940673	+	0.339315i	$0.889805\pi$
$104$	3.72676	+	8.22640i	0.365439	+	0.806665i
$105$	−0.106761	−	0.0775665i	−0.0104188	−	0.00756971i
$106$	−0.645492	−	6.14144i	−0.0626957	−	0.596510i
$107$	11.4163	+	12.6791i	1.10366	+	1.22574i	0.972135	+	0.234422i	$0.0753197\pi$
$107$	11.4163	+	12.6791i	1.10366	+	1.22574i	0.131522	+	0.991313i	$0.458014\pi$
$108$	2.90408	+	1.29298i	0.279445	+	0.124417i
$109$	4.50263	−	3.27135i	0.431274	−	0.313339i	−0.350884	−	0.936419i	$-0.614119\pi$
$109$	4.50263	−	3.27135i	0.431274	−	0.313339i	0.782158	+	0.623080i	$0.214119\pi$
$110$	−0.199928	+	0.0424960i	−0.0190624	+	0.00405184i
$111$	2.66234	+	1.18535i	0.252698	+	0.112508i
$112$	2.46085	+	1.78791i	0.232528	+	0.168942i
$113$	4.91394	−	5.45748i	0.462264	−	0.513397i	−0.466270	−	0.884642i	$-0.654403\pi$
$113$	4.91394	−	5.45748i	0.462264	−	0.513397i	0.928535	+	0.371246i	$0.121069\pi$
$114$	−0.0459352	+	0.0204517i	−0.00430222	+	0.00191547i
$115$	0.722531	+	0.802452i	0.0673764	+	0.0748291i
$116$	0.160639	−	0.494395i	0.0149149	−	0.0459035i
$117$	−6.02045	+	8.40051i	−0.556591	+	0.776627i
$118$	3.10980			0.286281
$119$	6.07176	−	10.5166i	0.556597	−	0.964055i
$120$	0.123729	+	0.0262994i	0.0112949	+	0.00240080i
$121$	−6.18487	−	2.75368i	−0.562261	−	0.250335i
$122$	1.66468	+	1.20946i	0.150713	+	0.109500i
$123$	0.165493	+	0.286642i	0.0149220	+	0.0258456i
$124$	−4.37151	−	7.00318i	−0.392574	−	0.628904i
$125$	1.37920			0.123359
$126$	0.563107	−	5.35760i	0.0501655	−	0.477293i
$127$	0.384266	+	3.65605i	0.0340981	+	0.324422i	0.998253	+	0.0590823i	$0.0188175\pi$
$127$	0.384266	+	3.65605i	0.0340981	+	0.324422i	−0.964155	+	0.265340i	$0.914516\pi$
$128$	−10.1176	−	2.15057i	−0.894279	−	0.190085i
$129$	−3.73473			−0.328825
$130$	−0.143618	+	0.328287i	−0.0125962	+	0.0287927i
$131$	−1.30563	−	4.01833i	−0.114074	−	0.351083i	0.877679	−	0.479249i	$-0.159091\pi$
$131$	−1.30563	−	4.01833i	−0.114074	−	0.351083i	−0.991753	+	0.128166i	$0.959091\pi$
$132$	−0.745719	−	0.828205i	−0.0649065	−	0.0720860i
$133$	−0.334503	−	0.371503i	−0.0290051	−	0.0322134i
$134$	−0.0939596	+	0.893966i	−0.00811687	+	0.0772269i
$135$	0.0915484	+	0.281757i	0.00787923	+	0.0242498i
$136$	−1.21672	+	11.5763i	−0.104333	+	0.992662i
$137$	1.85012	+	0.823727i	0.158066	+	0.0703757i	0.484245	−	0.874932i	$-0.339094\pi$
$137$	1.85012	+	0.823727i	0.158066	+	0.0703757i	−0.326178	+	0.945308i	$0.605761\pi$
$138$	0.634686	−	1.95336i	0.0540281	−	0.166281i
$139$	−10.5385	−	4.69205i	−0.893865	−	0.397974i	−0.0921948	−	0.995741i	$-0.529388\pi$
$139$	−10.5385	−	4.69205i	−0.893865	−	0.397974i	−0.801670	+	0.597767i	$0.796055\pi$
$140$	0.0559655	+	0.532476i	0.00472995	+	0.0450024i
$141$	−0.905867	−	1.00607i	−0.0762878	−	0.0847262i
$142$	−6.71635	+	4.87972i	−0.563624	+	0.409497i
$143$	6.39770	−	3.74926i	0.535003	−	0.313529i
$144$	−1.03108	−	3.17333i	−0.0859230	−	0.264444i
$145$	0.0442576	−	0.0197048i	0.00367540	−	0.00163639i
$146$	−3.25465	−	3.61465i	−0.269357	−	0.299151i
$147$	0.0613193	−	0.0130338i	0.00505753	−	0.00107501i
$148$	−3.65381	−	11.2453i	−0.300341	−	0.924355i
$149$	0.748108	+	1.29576i	0.0612874	+	0.106153i	0.895041	−	0.445984i	$-0.147146\pi$
$149$	0.748108	+	1.29576i	0.0612874	+	0.106153i	−0.833754	+	0.552136i	$0.813813\pi$
$150$	−0.654586	−	1.13378i	−0.0534467	−	0.0925724i
$151$	6.87502	+	21.1591i	0.559481	+	1.72191i	0.683805	+	0.729664i	$0.260324\pi$
$151$	6.87502	+	21.1591i	0.559481	+	1.72191i	−0.124324	+	0.992242i	$0.539676\pi$
$152$	0.437755	+	0.194901i	0.0355066	+	0.0158086i
$153$	−12.1690	+	5.41800i	−0.983808	+	0.438020i
$154$	−1.93261	+	3.34737i	−0.155734	+	0.269739i
$155$	0.212415	−	0.739471i	0.0170616	−	0.0593958i
$156$	−1.94171	+	0.216827i	−0.155461	+	0.0173600i
$157$	−5.85289	−	4.25237i	−0.467111	−	0.339376i	0.329203	−	0.944259i	$-0.393220\pi$
$157$	−5.85289	−	4.25237i	−0.467111	−	0.339376i	−0.796314	+	0.604883i	$0.793220\pi$
$158$	−0.117879	−	1.12154i	−0.00937791	−	0.0892249i
$159$	3.06934	+	0.652409i	0.243415	+	0.0517394i
$160$	−0.403965	−	0.699688i	−0.0319362	−	0.0553152i
$161$	20.4197			1.60930
$162$	−3.76128	+	4.17733i	−0.295514	+	0.328202i
$163$	3.58468	−	0.761947i	0.280774	−	0.0596803i	−0.0653723	−	0.997861i	$-0.520823\pi$
$163$	3.58468	−	0.761947i	0.280774	−	0.0596803i	0.346146	+	0.938181i	$0.387490\pi$
$164$	0.414975	−	1.27716i	0.0324041	−	0.0997295i
$165$	0.0108565	−	0.103293i	0.000845176	−	0.00804131i
$166$	−3.93508	−	0.836427i	−0.305421	−	0.0649193i
$167$	−18.9454	+	8.43505i	−1.46604	+	0.652724i	−0.975761	−	0.218840i	$-0.929773\pi$
$167$	−18.9454	+	8.43505i	−1.46604	+	0.652724i	−0.490281	+	0.871564i	$0.663106\pi$
$168$	1.93521	−	1.40602i	0.149305	−	0.108476i
$169$	1.19101	−	12.9453i	0.0916163	−	0.995794i
$170$	−0.373636	+	0.271463i	−0.0286566	+	0.0208202i
$171$	0.0573198	+	0.545362i	0.00438336	+	0.0417048i
$172$	10.1391	+	11.2607i	0.773102	+	0.858617i
$173$	19.5426	+	8.70091i	1.48579	+	0.661518i	0.979610	−	0.200909i	$-0.0643894\pi$
$173$	19.5426	+	8.70091i	1.48579	+	0.661518i	0.506183	+	0.862426i	$0.331056\pi$
$174$	−0.0745498	−	0.0541636i	−0.00565161	−	0.00410613i
$175$	8.70925	−	9.67260i	0.658357	−	0.731180i
$176$	−0.250242	+	2.38090i	−0.0188627	+	0.179467i
$177$	−0.488315	+	1.50288i	−0.0367040	+	0.112963i
$178$	−1.34783	+	0.286490i	−0.101024	+	0.0214733i
$179$	−21.3988	−	4.54846i	−1.59942	−	0.339968i	−0.679992	−	0.733219i	$-0.738017\pi$
$179$	−21.3988	−	4.54846i	−1.59942	−	0.339968i	−0.919431	+	0.393252i	$0.871350\pi$
$180$	0.293655	−	0.508625i	0.0218877	−	0.0379107i
$181$	12.3749			0.919818			0.459909	−	0.887966i	$-0.347882\pi$
$181$	12.3749			0.919818			0.459909	+	0.887966i	$0.347882\pi$
$182$	2.79622	+	6.17233i	0.207270	+	0.457524i
$183$	−0.845896	+	0.614579i	−0.0625304	+	0.0454310i
$184$	−17.8810	+	7.96114i	−1.31821	+	0.586903i
$185$	0.550964	−	0.954298i	0.0405077	−	0.0701614i
$186$	−1.42012	+	0.353368i	−0.104128	+	0.0259102i
$187$	9.55749			0.698913
$188$	−0.574141	+	5.46259i	−0.0418735	+	0.398400i
$189$	5.11803	+	2.27869i	0.372282	+	0.165751i
$190$	0.00587514	+	0.0180818i	0.000426227	+	0.00131179i
$191$	−9.23303	−	15.9921i	−0.668078	−	1.15715i	−0.978441	−	0.206527i	$-0.933784\pi$
$191$	−9.23303	−	15.9921i	−0.668078	−	1.15715i	0.310362	−	0.950618i	$-0.399550\pi$
$192$	−0.342974	+	0.594048i	−0.0247520	+	0.0428717i
$193$	−25.9582	−	5.51758i	−1.86851	−	0.397164i	−0.872672	−	0.488306i	$-0.837615\pi$
$193$	−25.9582	−	5.51758i	−1.86851	−	0.397164i	−0.995838	+	0.0911424i	$0.970948\pi$
$194$	2.87761	−	8.85637i	0.206600	−	0.635850i
$195$	−0.136100	−	0.120956i	−0.00974635	−	0.00866183i
$196$	−0.205770	−	0.149500i	−0.0146978	−	0.0106786i
$197$	−14.5822	−	3.09953i	−1.03894	−	0.220833i	−0.343299	−	0.939226i	$-0.611544\pi$
$197$	−14.5822	−	3.09953i	−1.03894	−	0.220833i	−0.695637	+	0.718394i	$0.744878\pi$
$198$	3.87334	−	1.72452i	0.275266	−	0.122556i
$199$	−14.2441	−	6.34188i	−1.00974	−	0.449564i	−0.165888	−	0.986145i	$-0.553049\pi$
$199$	−14.2441	−	6.34188i	−1.00974	−	0.449564i	−0.843849	+	0.536581i	$0.819716\pi$
$200$	−3.85535	+	11.8656i	−0.272615	+	0.839021i
$201$	−0.417274	−	0.185783i	−0.0294323	−	0.0131041i
$202$	−11.5320	−	5.13439i	−0.811390	−	0.361254i
$203$	0.283103	−	0.871302i	0.0198700	−	0.0611534i
$204$	−2.30047	−	1.02424i	−0.161065	−	0.0717108i
$205$	0.114330	−	0.0509029i	0.00798514	−	0.00355521i
$206$	8.01887	+	1.70446i	0.558701	+	0.118756i
$207$	−18.1213	−	13.1659i	−1.25952	−	0.915093i
$208$	3.13712	+	2.78803i	0.217520	+	0.193315i
$209$	0.121582	−	0.374192i	0.00841002	−	0.0258834i
$210$	0.0928349	+	0.0197327i	0.00640621	+	0.00136168i
$211$	−0.225876	+	0.391229i	−0.0155500	+	0.0269333i	−0.873696	−	0.486473i	$-0.838283\pi$
$211$	−0.225876	+	0.391229i	−0.0155500	+	0.0269333i	0.858146	+	0.513406i	$0.171617\pi$
$212$	−6.36563	−	11.0256i	−0.437194	−	0.757242i
$213$	−1.30360	−	4.01206i	−0.0893210	−	0.274902i
$214$	−11.2098	−	4.99091i	−0.766284	−	0.341172i
$215$	−0.147610	+	1.40441i	−0.0100669	+	0.0957801i
$216$	−5.37013			−0.365391
$217$	−7.70418	−	12.3421i	−0.522994	−	0.837838i
$218$	−2.00138	+	3.46650i	−0.135551	+	0.234781i
$219$	2.25792	−	1.00529i	0.152576	−	0.0679312i
$220$	−0.340912	+	0.247687i	−0.0229843	+	0.0166991i
$221$	9.76043	−	13.6190i	0.656557	−	0.916113i
$222$	−2.09597			−0.140672
$223$	−10.6858	+	18.5083i	−0.715571	+	1.23941i	0.247168	+	0.968973i	$0.420500\pi$
$223$	−10.6858	+	18.5083i	−0.715571	+	1.23941i	−0.962739	+	0.270433i	$0.912833\pi$
$224$	−14.9445	−	3.17656i	−0.998524	−	0.212243i
$225$	−13.9655	+	2.96845i	−0.931032	+	0.197897i
$226$	−1.63212	+	5.02316i	−0.108567	+	0.334135i
$227$	0.226502	−	2.15502i	0.0150334	−	0.143034i	−0.984430	−	0.175775i	$-0.943757\pi$
$227$	0.226502	−	2.15502i	0.0150334	−	0.143034i	0.999464	+	0.0327410i	$0.0104237\pi$
$228$	−0.0693652	+	0.0770379i	−0.00459382	+	0.00510196i
$229$	12.6954	+	9.22378i	0.838939	+	0.609525i	0.922074	−	0.387013i	$-0.126493\pi$
$229$	12.6954	+	9.22378i	0.838939	+	0.609525i	−0.0831351	+	0.996538i	$0.526493\pi$
$230$	−0.709459	−	0.315872i	−0.0467804	−	0.0208280i
$231$	−1.31422	−	1.45959i	−0.0864697	−	0.0960343i
$232$	0.0917929	+	0.873351i	0.00602650	+	0.0573383i
$233$	5.42545	−	3.94182i	0.355433	−	0.258237i	−0.395712	−	0.918375i	$-0.629502\pi$
$233$	5.42545	−	3.94182i	0.355433	−	0.258237i	0.751145	+	0.660138i	$0.229502\pi$
$234$	1.49822	−	7.28048i	0.0979414	−	0.475940i
$235$	−0.414125	+	0.300880i	−0.0270146	+	0.0196272i
$236$	5.85704	−	2.60772i	0.381261	−	0.169748i
$237$	0.560518	+	0.119142i	0.0364096	+	0.00773909i
$238$	−0.912915	+	8.68581i	−0.0591755	+	0.563017i
$239$	−5.05541	+	15.5589i	−0.327007	+	1.00642i	0.643519	+	0.765430i	$0.277474\pi$
$239$	−5.05541	+	15.5589i	−0.327007	+	1.00642i	−0.970526	+	0.240995i	$0.922526\pi$
$240$	0.0574994	−	0.0122219i	0.00371157	−	0.000788919i
$241$	2.21303	−	2.45782i	0.142554	−	0.158322i	−0.667640	−	0.744484i	$-0.732695\pi$
$241$	2.21303	−	2.45782i	0.142554	−	0.158322i	0.810193	+	0.586163i	$0.199362\pi$
$242$	4.86914			0.313000
$243$	−4.64407	−	8.04377i	−0.297917	−	0.516008i
$244$	4.14948	+	0.882000i	0.265643	+	0.0564643i
$245$	−0.00247770	−	0.0235737i	−0.000158294	−	0.00150607i
$246$	−0.192583	−	0.139920i	−0.0122786	−	0.00892096i
$247$	−0.409043	−	0.555387i	−0.0260268	−	0.0353384i
$248$	11.5582	+	7.80400i	0.733948	+	0.495555i
$249$	1.02213	−	1.77037i	0.0647746	−	0.112193i
$250$	−0.906168	+	0.403452i	−0.0573111	+	0.0255165i
$251$	9.34388	+	4.16016i	0.589781	+	0.262587i	0.679854	−	0.733348i	$-0.262043\pi$
$251$	9.34388	+	4.16016i	0.589781	+	0.262587i	−0.0900729	+	0.995935i	$0.528710\pi$
$252$	−3.43205	−	10.5628i	−0.216199	−	0.665392i
$253$	8.03562	+	13.9181i	0.505195	+	0.875023i
$254$	−1.32196	−	2.28971i	−0.0829474	−	0.143669i
$255$	−0.0725202	−	0.223194i	−0.00454139	−	0.0139770i
$256$	10.9485	−	2.32718i	0.684281	−	0.145448i
$257$	−20.0821	−	22.3034i	−1.25268	−	1.39125i	−0.887823	−	0.460185i	$-0.847783\pi$
$257$	−20.0821	−	22.3034i	−1.25268	−	1.39125i	−0.364861	−	0.931062i	$-0.618884\pi$
$258$	2.45381	−	1.09251i	0.152768	−	0.0680165i
$259$	−6.43932	−	19.8182i	−0.400120	−	1.23144i
$260$	0.00479252	+	0.738732i	0.000297220	+	0.0458142i
$261$	−0.813021	+	0.590694i	−0.0503247	+	0.0365631i
$262$	2.03330	+	2.25821i	0.125618	+	0.139513i
$263$	−1.80541	−	17.1773i	−0.111326	−	1.05920i	−0.897446	−	0.441124i	$-0.854580\pi$
$263$	−1.80541	−	17.1773i	−0.111326	−	1.05920i	0.786120	−	0.618074i	$-0.212087\pi$
$264$	1.71989	+	0.765745i	0.105852	+	0.0471283i
$265$	0.366644	−	1.12841i	0.0225227	−	0.0693179i
$266$	0.328451	+	0.146236i	0.0201386	+	0.00896629i
$267$	0.0731896	−	0.696353i	0.00447913	−	0.0426161i
$268$	0.572670	+	1.76250i	0.0349814	+	0.107662i
$269$	−0.447174	+	4.25458i	−0.0272647	+	0.259406i	0.972395	+	0.233339i	$0.0749651\pi$
$269$	−0.447174	+	4.25458i	−0.0272647	+	0.259406i	−0.999660	+	0.0260675i	$0.991702\pi$
$270$	−0.142571	−	0.158341i	−0.00867659	−	0.00963633i
$271$	2.86424	+	3.18106i	0.173990	+	0.193236i	0.823832	−	0.566833i	$-0.191832\pi$
$271$	2.86424	+	3.18106i	0.173990	+	0.193236i	−0.649842	+	0.760069i	$0.725165\pi$
$272$	1.67159	+	5.14463i	0.101355	+	0.311939i
$273$	−3.42199	+	0.382126i	−0.207108	+	0.0231273i
$274$	−1.45654			−0.0879926
$275$	10.0201	+	2.12984i	0.604237	+	0.128434i
$276$	−0.442616	−	4.21121i	−0.0266423	−	0.253485i
$277$	−3.17747	+	30.2316i	−0.190916	+	1.81644i	0.309768	+	0.950812i	$0.399749\pi$
$277$	−3.17747	+	30.2316i	−0.190916	+	1.81644i	−0.500684	+	0.865630i	$0.666918\pi$
$278$	8.29661			0.497598
$279$	−1.12075	+	15.9203i	−0.0670974	+	0.953121i
$280$	−0.452233	−	0.783290i	−0.0270261	−	0.0468105i
$281$	11.2692	+	8.18753i	0.672262	+	0.488427i	0.870782	−	0.491670i	$-0.163613\pi$
$281$	11.2692	+	8.18753i	0.672262	+	0.488427i	−0.198520	+	0.980097i	$0.563613\pi$
$282$	0.889478	+	0.396021i	0.0529677	+	0.0235827i
$283$	3.97013	+	0.843876i	0.235999	+	0.0501632i	0.324393	−	0.945922i	$-0.394840\pi$
$283$	3.97013	+	0.843876i	0.235999	+	0.0501632i	−0.0883935	+	0.996086i	$0.528173\pi$
$284$	−8.55779	+	14.8225i	−0.507811	+	0.879555i
$285$	−0.00966097			−0.000572267
$286$	−3.10669	+	4.33486i	−0.183702	+	0.256325i
$287$	0.731335	−	2.25082i	0.0431693	−	0.132862i
$288$	11.2143	+	12.4547i	0.660807	+	0.733900i
$289$	4.19832	−	1.86921i	0.246960	−	0.109954i
$290$	−0.0233142	+	0.0258930i	−0.00136906	+	0.00152049i
$291$	3.82818	+	2.78133i	0.224412	+	0.163045i
$292$	−9.16092	−	4.07870i	−0.536102	−	0.238688i
$293$	−8.39556	+	1.78453i	−0.490474	+	0.104253i	−0.446508	−	0.894780i	$-0.647333\pi$
$293$	−8.39556	+	1.78453i	−0.490474	+	0.104253i	−0.0439658	+	0.999033i	$0.513999\pi$
$294$	−0.0364756	+	0.0265011i	−0.00212730	+	0.00154557i
$295$	0.545844	+	0.243025i	0.0317803	+	0.0141495i
$296$	13.3654	+	14.8437i	0.776846	+	0.862775i
$297$	0.460900	+	4.38517i	0.0267441	+	0.254453i
$298$	−0.870569	−	0.632505i	−0.0504307	−	0.0366401i
$299$	28.0389	+	2.76322i	1.62153	+	0.159801i
$300$	−2.18358	−	1.58647i	−0.126069	−	0.0915946i
$301$	17.8688	+	19.8453i	1.02994	+	1.14386i
$302$	−10.7067	−	11.8909i	−0.616099	−	0.684247i
$303$	4.29211	−	4.76687i	0.246575	−	0.273850i
$304$	0.222686			0.0127719
$305$	0.197674	+	0.342382i	0.0113188	+	0.0196047i
$306$	6.41045	−	7.11952i	0.366461	−	0.406996i
$307$	22.3972	−	16.2725i	1.27828	−	0.928722i	0.278777	−	0.960356i	$-0.410071\pi$
$307$	22.3972	−	16.2725i	1.27828	−	0.928722i	0.999500	+	0.0316339i	$0.0100711\pi$
$308$	−0.832959	+	7.92508i	−0.0474623	+	0.451573i
$309$	−2.08288	+	3.60765i	−0.118491	+	0.205232i
$310$	0.0767529	+	0.547988i	0.00435927	+	0.0311236i
$311$	10.5681			0.599259			0.299630	−	0.954056i	$-0.403137\pi$
$311$	10.5681			0.599259			0.299630	+	0.954056i	$0.403137\pi$
$312$	2.84756	−	1.66877i	0.161212	−	0.0944753i
$313$	−5.52363	+	4.01315i	−0.312214	+	0.226837i	−0.732846	−	0.680395i	$-0.761808\pi$
$313$	−5.52363	+	4.01315i	−0.312214	+	0.226837i	0.420632	+	0.907231i	$0.361808\pi$
$314$	5.08942	+	1.08179i	0.287213	+	0.0610489i
$315$	0.517525	−	0.896380i	0.0291593	−	0.0505053i
$316$	−1.16248	−	2.01348i	−0.0653946	−	0.113267i
$317$	−0.773075	−	2.37928i	−0.0434202	−	0.133634i	0.926996	−	0.375070i	$-0.122381\pi$
$317$	−0.773075	−	2.37928i	−0.0434202	−	0.133634i	−0.970417	+	0.241437i	$0.922381\pi$
$318$	−2.20748	+	0.469215i	−0.123789	+	0.0263123i
$319$	0.705287	−	0.149913i	0.0394885	−	0.00839354i
$320$	0.209831	+	0.152451i	0.0117299	+	0.00852226i
$321$	4.17218	−	4.63367i	0.232868	−	0.258626i
$322$	−13.4163	+	5.97331i	−0.747659	+	0.332879i
$323$	−0.0929276	−	0.884147i	−0.00517063	−	0.0491953i
$324$	−3.58116	+	11.0217i	−0.198953	+	0.612315i
$325$	13.2678	−	12.1032i	0.735967	−	0.671364i
$326$	−2.13233	+	1.54923i	−0.118099	+	0.0858040i
$327$	−1.36099	−	1.51154i	−0.0752631	−	0.0835882i
$328$	0.237127	+	2.25611i	0.0130931	+	0.124573i
$329$	−1.01184	+	9.62704i	−0.0557847	+	0.530756i
$330$	0.0230828	+	0.0710415i	0.00127067	+	0.00391071i
$331$	1.77162	−	16.8558i	0.0973770	−	0.926480i	−0.831358	−	0.555737i	$-0.812436\pi$
$331$	1.77162	−	16.8558i	0.0973770	−	0.926480i	0.928735	−	0.370743i	$-0.120897\pi$
$332$	−8.11277	+	1.72442i	−0.445246	+	0.0946400i
$333$	−7.06353	+	21.7393i	−0.387079	+	1.19131i
$334$	9.98015	−	11.0841i	0.546089	−	0.606494i
$335$	−0.0863539	+	0.149569i	−0.00471802	+	0.00817185i
$336$	0.555819	−	0.962707i	0.0303224	−	0.0525200i
$337$	4.05033	+	12.4656i	0.220635	+	0.679046i	0.998705	+	0.0508683i	$0.0161989\pi$
$337$	4.05033	+	12.4656i	0.220635	+	0.679046i	−0.778070	+	0.628178i	$0.783801\pi$
$338$	3.00432	+	8.85380i	0.163414	+	0.481583i
$339$	−2.17127	−	1.57752i	−0.117927	−	0.0856790i
$340$	−0.476077	+	0.824589i	−0.0258189	+	0.0447196i
$341$	5.38063	−	10.1081i	0.291378	−	0.547383i
$342$	−0.197193	−	0.341548i	−0.0106630	−	0.0184688i
$343$	−15.1611	−	11.0152i	−0.818624	−	0.594765i
$344$	−23.3844	−	10.4114i	−1.26080	−	0.561346i
$345$	0.264054	−	0.293262i	0.0142162	−	0.0157887i
$346$	−15.3852			−0.827112
$347$	−1.16754	−	2.02224i	−0.0626768	−	0.108559i	0.832984	−	0.553297i	$-0.186630\pi$
$347$	−1.16754	−	2.02224i	−0.0626768	−	0.108559i	−0.895661	+	0.444737i	$0.853297\pi$
$348$	−0.185827	−	0.0394988i	−0.00996138	−	0.00211736i
$349$	18.4695	+	20.5125i	0.988651	+	1.09801i	0.995183	+	0.0980300i	$0.0312541\pi$
$349$	18.4695	+	20.5125i	0.988651	+	1.09801i	−0.00653199	+	0.999979i	$0.502079\pi$
$350$	−2.89270	+	8.90282i	−0.154621	+	0.475876i
$351$	6.71936	+	3.82152i	0.358653	+	0.203978i
$352$	−3.71586	−	11.4363i	−0.198056	−	0.609554i
$353$	6.74233	−	3.00188i	0.358858	−	0.159774i	−0.219385	−	0.975638i	$-0.570405\pi$
$353$	6.74233	−	3.00188i	0.358858	−	0.159774i	0.578243	+	0.815865i	$0.303739\pi$
$354$	−0.118797	−	1.13027i	−0.00631397	−	0.0600734i
$355$	−1.56022	+	0.331635i	−0.0828079	+	0.0176014i
$356$	−2.29828	+	1.66980i	−0.121809	+	0.0884992i
$357$	−4.05426	−	1.80507i	−0.214574	−	0.0955345i
$358$	15.3901	−	3.27127i	0.813392	−	0.172892i
$359$	20.0244	−	14.5486i	1.05685	−	0.767843i	0.0833435	−	0.996521i	$-0.473440\pi$
$359$	20.0244	−	14.5486i	1.05685	−	0.767843i	0.973502	+	0.228678i	$0.0734401\pi$
$360$	−0.103707	+	0.986706i	−0.00546584	+	0.0520040i
$361$	18.5490	+	3.94271i	0.976263	+	0.207511i
$362$	−8.13060	+	3.61998i	−0.427335	+	0.190262i
$363$	−0.764574	+	2.35312i	−0.0401297	+	0.123507i
$364$	10.4422	+	9.28029i	0.547323	+	0.486419i
$365$	−0.288789	−	0.888802i	−0.0151159	−	0.0465220i
$366$	0.375994	−	0.651240i	0.0196535	−	0.0340409i
$367$	16.0392	−	27.7807i	0.837239	−	1.45014i	−0.0549552	−	0.998489i	$-0.517502\pi$
$367$	16.0392	−	27.7807i	0.837239	−	1.45014i	0.892194	−	0.451652i	$-0.149165\pi$
$368$	−6.08646	+	6.75970i	−0.317279	+	0.352374i
$369$	−2.10026	+	1.52593i	−0.109335	+	0.0794366i
$370$	−0.0828399	+	0.788169i	−0.00430664	+	0.0409750i
$371$	−11.2185	−	19.4311i	−0.582437	−	1.00881i
$372$	−2.37835	+	1.85638i	−0.123312	+	0.0962486i
$373$	−14.7786	−	25.5973i	−0.765207	−	1.32538i	−0.940137	−	0.340797i	$-0.889303\pi$
$373$	−14.7786	−	25.5973i	−0.765207	−	1.32538i	0.174930	−	0.984581i	$-0.444030\pi$
$374$	−6.27950	+	2.79582i	−0.324705	+	0.144568i
$375$	−0.0526864	−	0.501277i	−0.00272071	−	0.0258858i
$376$	−2.86730	−	8.82463i	−0.147870	−	0.455096i
$377$	0.506643	−	1.15810i	0.0260934	−	0.0596452i
$378$	−4.02925			−0.207242
$379$	−11.5448	−	2.45393i	−0.593018	−	0.126050i	−0.0983801	−	0.995149i	$-0.531366\pi$
$379$	−11.5448	−	2.45393i	−0.593018	−	0.126050i	−0.494638	+	0.869099i	$0.664699\pi$
$380$	0.0262278	+	0.0291290i	0.00134546	+	0.00149428i
$381$	1.31413	−	0.279327i	0.0673250	−	0.0143104i
$382$	10.7444	+	7.80628i	0.549733	+	0.399404i
$383$	8.71876	−	9.68317i	0.445508	−	0.494787i	−0.478003	−	0.878358i	$-0.658639\pi$
$383$	8.71876	−	9.68317i	0.445508	−	0.494787i	0.923511	+	0.383571i	$0.125306\pi$
$384$	−0.395134	+	3.75945i	−0.0201641	+	0.191849i
$385$	−0.600810	+	0.436514i	−0.0306201	+	0.0222468i
$386$	18.6692	−	3.96826i	0.950237	−	0.201979i
$387$	−3.06197	−	29.1327i	−0.155649	−	1.48090i
$388$	−2.00678	−	19.0932i	−0.101879	−	0.969312i
$389$	0.775557	−	2.38692i	0.0393223	−	0.121022i	−0.929468	−	0.368902i	$-0.879734\pi$
$389$	0.775557	−	2.38692i	0.0393223	−	0.121022i	0.968791	+	0.247880i	$0.0797339\pi$
$390$	0.124804	+	0.0396580i	0.00631970	+	0.00200816i
$391$	29.3785	+	21.3447i	1.48573	+	1.07945i
$392$	0.420276	+	0.0893324i	0.0212271	+	0.00451197i
$393$	−1.41061	+	0.628042i	−0.0711557	+	0.0316805i
$394$	10.4875	−	2.22919i	0.528354	−	0.112305i
$395$	0.0669558	−	0.206069i	0.00336891	−	0.0103684i
$396$	5.84900	−	6.49597i	0.293923	−	0.326435i
$397$	8.19003	+	14.1855i	0.411046	+	0.711952i	0.995004	−	0.0998312i	$-0.0318303\pi$
$397$	8.19003	+	14.1855i	0.411046	+	0.711952i	−0.583959	+	0.811783i	$0.698497\pi$
$398$	11.2139			0.562101
$399$	−0.122246	+	0.135768i	−0.00611998	+	0.00679692i
$400$	0.606049	+	5.76618i	0.0303025	+	0.288309i
$401$	−22.4412	+	9.99147i	−1.12066	+	0.498950i	−0.881573	−	0.472048i	$-0.843515\pi$
$401$	−22.4412	+	9.99147i	−1.12066	+	0.498950i	−0.239088	+	0.970998i	$0.576848\pi$
$402$	0.328506			0.0163844
$403$	−8.90868	−	17.9899i	−0.443773	−	0.896139i
$404$	−26.0250			−1.29479
$405$	−0.986645	+	0.439283i	−0.0490268	+	0.0218281i
$406$	0.0688729	+	0.655282i	0.00341811	+	0.0325211i
$407$	10.9741	−	12.1879i	0.543965	−	0.604134i
$408$	4.25396			0.210602
$409$	7.18540	+	12.4455i	0.355295	+	0.615390i	0.987168	−	0.159682i	$-0.0510470\pi$
$409$	7.18540	+	12.4455i	0.355295	+	0.615390i	−0.631873	+	0.775072i	$0.717714\pi$
$410$	−0.0602271	+	0.0668890i	−0.00297440	+	0.00330341i
$411$	0.228712	−	0.703903i	0.0112815	−	0.0347210i
$412$	16.5321	−	3.51401i	0.814480	−	0.173123i
$413$	10.3222	−	4.59575i	0.507923	−	0.226142i
$414$	15.7575	+	3.34936i	0.774439	+	0.164612i
$415$	−0.625335	−	0.454332i	−0.0306965	−	0.0223023i
$416$	−20.0909	−	6.38414i	−0.985039	−	0.313008i
$417$	−1.30277	+	4.00952i	−0.0637970	+	0.196347i
$418$	0.0295783	+	0.281419i	0.00144672	+	0.0137647i
$419$	1.34450	+	12.7921i	0.0656833	+	0.624935i	0.977001	+	0.213232i	$0.0683992\pi$
$419$	1.34450	+	12.7921i	0.0656833	+	0.624935i	−0.911318	+	0.411703i	$0.864934\pi$
$420$	0.191393	−	0.0406819i	0.00933904	−	0.00198507i
$421$	−22.7432	+	16.5239i	−1.10843	+	0.805324i	−0.982416	−	0.186704i	$-0.940220\pi$
$421$	−22.7432	+	16.5239i	−1.10843	+	0.805324i	−0.126017	+	0.992028i	$0.540220\pi$
$422$	0.0339615	−	0.323122i	0.00165322	−	0.0157293i
$423$	7.10511	−	7.89103i	0.345462	−	0.383675i
$424$	17.3995	+	12.6414i	0.844992	+	0.613923i
$425$	22.6410	−	4.81249i	1.09825	−	0.233440i
$426$	2.03013	+	2.25469i	0.0983600	+	0.109240i
$427$	7.31288	+	1.55440i	0.353895	+	0.0752227i
$428$	−25.2978			−1.22281
$429$	−1.60709	−	2.18205i	−0.0775909	−	0.105351i
$430$	−0.313844	−	0.965913i	−0.0151349	−	0.0465805i
$431$	2.41519	+	22.9790i	0.116336	+	1.10686i	0.884479	+	0.466581i	$0.154514\pi$
$431$	2.41519	+	22.9790i	0.116336	+	1.10686i	−0.768143	+	0.640278i	$0.778819\pi$
$432$	−2.27985	+	1.01506i	−0.109689	+	0.0488369i
$433$	10.7840	+	18.6784i	0.518246	+	0.897629i	0.999775	+	0.0211985i	$0.00674821\pi$
$433$	10.7840	+	18.6784i	0.518246	+	0.897629i	−0.481529	+	0.876430i	$0.659918\pi$
$434$	8.67223	+	5.85541i	0.416280	+	0.281068i
$435$	−0.00885248	−	0.0153329i	−0.000424444	−	0.000735158i
$436$	−0.862602	+	8.20711i	−0.0413111	+	0.393049i
$437$	1.20941	−	0.878688i	0.0578539	−	0.0420333i
$438$	−1.18944	+	1.32100i	−0.0568334	+	0.0631199i
$439$	−9.44178	+	16.3536i	−0.450632	+	0.780517i	−0.998425	−	0.0560967i	$-0.982135\pi$
$439$	−9.44178	+	16.3536i	−0.450632	+	0.780517i	0.547794	+	0.836613i	$0.315468\pi$
$440$	0.355927	−	0.616484i	0.0169682	−	0.0293897i
$441$	0.151943	+	0.467634i	0.00723540	+	0.0222683i
$442$	−2.42893	+	11.8032i	−0.115532	+	0.561421i
$443$	−0.766876	+	2.36020i	−0.0364354	+	0.112137i	−0.967620	−	0.252411i	$-0.918776\pi$
$443$	−0.766876	+	2.36020i	−0.0364354	+	0.112137i	0.931185	+	0.364548i	$0.118776\pi$
$444$	−3.94757	+	1.75757i	−0.187344	+	0.0834107i
$445$	−0.258964	−	0.0550446i	−0.0122761	−	0.00260936i
$446$	1.60665	−	15.2862i	0.0760771	−	0.723825i
$447$	0.442373	−	0.321403i	0.0209235	−	0.0152018i
$448$	4.79756	−	1.01975i	0.226663	−	0.0481787i
$449$	−4.65303	−	2.07166i	−0.219590	−	0.0977678i	0.293993	−	0.955807i	$-0.405016\pi$
$449$	−4.65303	−	2.07166i	−0.219590	−	0.0977678i	−0.513583	+	0.858040i	$0.671682\pi$
$450$	8.30731	−	6.03561i	0.391610	−	0.284522i
$451$	1.82195	−	0.387268i	0.0857925	−	0.0182358i
$452$	1.13820	+	10.8293i	0.0535367	+	0.509367i
$453$	7.42777	−	3.30706i	0.348987	−	0.155379i
$454$	0.481582	+	1.48216i	0.0226018	+	0.0695611i
$455$	0.00844615	+	1.30191i	0.000395962	+	0.0610345i
$456$	0.0541152	−	0.166550i	0.00253418	−	0.00779940i
$457$	−23.6727	−	26.2912i	−1.10736	−	1.22985i	−0.970971	−	0.239195i	$-0.923116\pi$
$457$	−23.6727	−	26.2912i	−1.10736	−	1.22985i	−0.136391	−	0.990655i	$-0.543550\pi$
$458$	−11.0394	−	2.34650i	−0.515838	−	0.109645i
$459$	4.98155	+	8.62829i	0.232519	+	0.402734i
$460$	−1.60108			−0.0746507
$461$	11.1663	−	12.4015i	0.520068	−	0.577594i	−0.424700	−	0.905334i	$-0.639620\pi$
$461$	11.1663	−	12.4015i	0.520068	−	0.577594i	0.944768	+	0.327740i	$0.106287\pi$
$462$	1.29045	+	0.574544i	0.0600371	+	0.0267302i
$463$	−24.9170	−	18.1033i	−1.15799	−	0.841331i	−0.168470	−	0.985707i	$-0.553883\pi$
$463$	−24.9170	−	18.1033i	−1.15799	−	0.841331i	−0.989523	+	0.144376i	$0.953883\pi$
$464$	0.204050	+	0.353425i	0.00947278	+	0.0164073i
$465$	−0.276879	−	0.0489550i	−0.0128400	−	0.00227023i
$466$	−2.41157	+	4.17696i	−0.111714	+	0.193494i
$467$	−15.7875	−	11.4703i	−0.730557	−	0.530781i	0.159182	−	0.987249i	$-0.449114\pi$
$467$	−15.7875	−	11.4703i	−0.730557	−	0.530781i	−0.889740	+	0.456468i	$0.849114\pi$
$468$	−3.28328	−	14.9685i	−0.151770	−	0.691918i
$469$	1.00925	+	3.10615i	0.0466028	+	0.143429i
$470$	0.184075	−	0.318828i	0.00849076	−	0.0147064i
$471$	−1.32196	+	2.28971i	−0.0609128	+	0.105504i
$472$	−7.24712	+	8.04875i	−0.333576	+	0.370474i
$473$	−6.49480	+	19.9890i	−0.298631	+	0.919093i
$474$	−0.403126	+	0.0856871i	−0.0185162	+	0.00393574i
$475$	0.0996025	−	0.947654i	0.00457007	−	0.0434813i
$476$	5.56409	+	17.1245i	0.255029	+	0.784900i
$477$	−2.57266	+	24.4772i	−0.117794	+	1.12073i
$478$	−1.22987	−	11.7015i	−0.0562530	−	0.535212i
$479$	−17.5746	−	19.5186i	−0.803004	−	0.891826i	0.192995	−	0.981200i	$-0.438180\pi$
$479$	−17.5746	−	19.5186i	−0.803004	−	0.891826i	−0.995998	+	0.0893740i	$0.971513\pi$
$480$	−0.238874	+	0.173552i	−0.0109030	+	0.00792152i
$481$	−6.16020	−	28.0843i	−0.280881	−	1.28054i
$482$	−0.735038	+	2.26222i	−0.0334801	+	0.103041i
$483$	−0.780048	−	7.42166i	−0.0354934	−	0.337697i
$484$	9.17060	−	4.08301i	0.416845	−	0.185592i
$485$	1.19720	−	1.32962i	0.0543620	−	0.0603751i
$486$	5.40428	+	3.92644i	0.245143	+	0.178107i
$487$	10.1673	−	2.16113i	0.460726	−	0.0979302i	0.0282992	−	0.999599i	$-0.490991\pi$
$487$	10.1673	−	2.16113i	0.460726	−	0.0979302i	0.432426	+	0.901669i	$0.357658\pi$
$488$	−7.00972	+	1.48996i	−0.317315	+	0.0674474i
$489$	−0.413871	−	1.27376i	−0.0187159	−	0.0576016i
$490$	0.00852384	+	0.0147637i	0.000385068	+	0.000666957i
$491$	10.6345	−	18.4196i	0.479930	−	0.831263i	−0.519805	−	0.854285i	$-0.673995\pi$
$491$	10.6345	−	18.4196i	0.479930	−	0.831263i	0.999735	+	0.0230221i	$0.00732882\pi$
$492$	−0.480043	−	0.102036i	−0.0216420	−	0.00460015i
$493$	1.31808	−	0.957641i	0.0593633	−	0.0431300i
$494$	0.431217	+	0.245247i	0.0194014	+	0.0110342i
$495$	0.814631			0.0366149
$496$	6.38207	+	1.12841i	0.286563	+	0.0506673i
$497$	−15.0819	+	26.1226i	−0.676515	+	1.17176i
$498$	−0.153681	+	1.46218i	−0.00688661	+	0.0655218i
$499$	−5.51847	+	4.00941i	−0.247041	+	0.179486i	−0.704414	−	0.709789i	$-0.748790\pi$
$499$	−5.51847	+	4.00941i	−0.247041	+	0.179486i	0.457373	+	0.889275i	$0.348790\pi$
$500$	−1.36837	+	1.51973i	−0.0611956	+	0.0679646i
$501$	3.78949	+	6.56360i	0.169302	+	0.293240i
$502$	−7.35612			−0.328320
$503$	−18.0261	+	20.0200i	−0.803744	+	0.892648i	−0.996060	−	0.0886849i	$-0.971734\pi$
$503$	−18.0261	+	20.0200i	−0.803744	+	0.892648i	0.192316	+	0.981333i	$0.438400\pi$
$504$	12.5542	+	13.9428i	0.559208	+	0.621064i
$505$	−1.62290	−	1.80241i	−0.0722181	−	0.0802063i
$506$	−9.35101	−	6.79391i	−0.415703	−	0.302026i
$507$	−4.75054	+	0.0616409i	−0.210979	+	0.00273757i
$508$	−4.40984	−	3.20393i	−0.195655	−	0.142152i
$509$	−3.31532	−	31.5431i	−0.146949	−	1.39813i	−0.780854	−	0.624714i	$-0.785216\pi$
$509$	−3.31532	−	31.5431i	−0.146949	−	1.39813i	0.633905	−	0.773411i	$-0.281451\pi$
$510$	0.112938	+	0.125430i	0.00500097	+	0.00555414i
$511$	−16.1448	−	7.18814i	−0.714205	−	0.317985i
$512$	10.2237	−	7.42795i	0.451828	−	0.328272i
$513$	0.401183	−	0.0852742i	0.0177127	−	0.00376495i
$514$	19.7187	+	8.77934i	0.869756	+	0.387240i
$515$	1.27430	+	0.925834i	0.0561524	+	0.0407971i
$516$	3.70542	−	4.11529i	0.163122	−	0.181165i
$517$	−6.95998	+	3.09878i	−0.306099	+	0.136284i
$518$	10.0281	+	11.1374i	0.440611	+	0.489348i
$519$	2.41585	−	7.43522i	0.106044	−	0.326370i
$520$	−0.514978	−	1.13676i	−0.0225833	−	0.0498500i
$521$	−10.5077			−0.460350			−0.230175	−	0.973149i	$-0.573930\pi$
$521$	−10.5077			−0.460350			−0.230175	+	0.973149i	$0.573930\pi$
$522$	0.361381	−	0.625931i	0.0158172	−	0.0273962i
$523$	28.6129	+	6.08185i	1.25115	+	0.265941i	0.785408	−	0.618978i	$-0.212453\pi$
$523$	28.6129	+	6.08185i	1.25115	+	0.265941i	0.465745	+	0.884919i	$0.345786\pi$
$524$	5.72316	+	2.54812i	0.250018	+	0.111315i
$525$	−3.84826	−	2.79592i	−0.167952	−	0.122024i
$526$	6.21101	+	10.7578i	0.270813	+	0.469061i
$527$	1.81697	−	25.8101i	0.0791485	−	1.12431i
$528$	0.874908			0.0380755
$529$	−3.97865	+	37.8544i	−0.172985	+	1.64584i
$530$	0.0891965	+	0.848648i	0.00387445	+	0.0368629i
$531$	−12.1235	−	2.57693i	−0.526116	−	0.111829i
$532$	0.741235			0.0321366
$533$	1.30880	−	2.99170i	0.0566904	−	0.129585i
$534$	0.155614	+	0.478931i	0.00673408	+	0.0207254i
$535$	−1.57755	−	1.75205i	−0.0682034	−	0.0757476i
$536$	−2.09478	−	2.32649i	−0.0904809	−	0.100489i
$537$	−0.835712	+	7.95127i	−0.0360636	+	0.343123i
$538$	−0.950772	−	2.92617i	−0.0409907	−	0.126156i
$539$	0.0368767	−	0.350858i	0.00158839	−	0.0151125i
$540$	−0.401297	−	0.178669i	−0.0172691	−	0.00768868i
$541$	−2.87062	+	8.83487i	−0.123418	+	0.379841i	−0.993609	−	0.112873i	$-0.963995\pi$
$541$	−2.87062	+	8.83487i	−0.123418	+	0.379841i	0.870192	+	0.492713i	$0.163995\pi$
$542$	−2.81242	−	1.25217i	−0.120804	−	0.0537853i
$543$	−0.472729	−	4.49772i	−0.0202867	−	0.193016i
$544$	−18.1807	−	20.1917i	−0.779491	−	0.865713i
$545$	−0.622191	+	0.452048i	−0.0266517	+	0.0193636i
$546$	2.13655	−	1.25209i	0.0914359	−	0.0535844i
$547$	0.499860	+	1.53841i	0.0213725	+	0.0657777i	0.961174	−	0.275943i	$-0.0889902\pi$
$547$	0.499860	+	1.53841i	0.0213725	+	0.0657777i	−0.939801	+	0.341721i	$0.888990\pi$
$548$	−2.74326	+	1.22138i	−0.117186	+	0.0521747i
$549$	−5.48752	−	6.09451i	−0.234202	−	0.260108i
$550$	−7.20651	+	1.53179i	−0.307287	+	0.0653158i
$551$	−0.0207258	−	0.0637873i	−0.000882947	−	0.00271743i
$552$	3.57659	+	6.19483i	0.152230	+	0.263669i
$553$	−2.04871	−	3.54847i	−0.0871199	−	0.150896i
$554$	−6.75587	−	20.7924i	−0.287029	−	0.883385i
$555$	−0.367892	−	0.163796i	−0.0156161	−	0.00695276i
$556$	15.6259	−	6.95712i	0.662688	−	0.295048i
$557$	10.5463	−	18.2668i	0.446863	−	0.773989i	−0.551317	−	0.834296i	$-0.685875\pi$
$557$	10.5463	−	18.2668i	0.446863	−	0.773989i	0.998180	+	0.0603069i	$0.0192079\pi$
$558$	−3.92074	−	10.7879i	−0.165978	−	0.456686i
$559$	21.8507	+	29.6682i	0.924185	+	1.25483i
$560$	−0.340049	−	0.247060i	−0.0143697	−	0.0104402i
$561$	−0.365103	−	3.47372i	−0.0154146	−	0.146661i
$562$	−9.79919	−	2.08288i	−0.413354	−	0.0878610i
$563$	23.4235	+	40.5707i	0.987184	+	1.70985i	0.631797	+	0.775134i	$0.282318\pi$
$563$	23.4235	+	40.5707i	0.987184	+	1.70985i	0.355387	+	0.934719i	$0.384349\pi$
$564$	2.00734			0.0845242
$565$	−0.679027	+	0.754136i	−0.0285669	+	0.0317267i
$566$	−2.85533	+	0.606918i	−0.120018	+	0.0255107i
$567$	−6.31128	+	19.4241i	−0.265049	+	0.815737i
$568$	3.02226	−	28.7549i	0.126811	−	1.20653i
$569$	−27.3210	−	5.80726i	−1.14536	−	0.243453i	−0.404126	−	0.914703i	$-0.632424\pi$
$569$	−27.3210	−	5.80726i	−1.14536	−	0.243453i	−0.741231	+	0.671250i	$0.765758\pi$
$570$	0.00634750	−	0.00282609i	0.000265867	−	0.000118372i
$571$	2.25620	−	1.63922i	0.0944189	−	0.0685994i	−0.539574	−	0.841938i	$-0.681415\pi$
$571$	2.25620	−	1.63922i	0.0944189	−	0.0685994i	0.633993	+	0.773339i	$0.281415\pi$
$572$	−2.21619	+	10.7694i	−0.0926637	+	0.450293i
$573$	−5.45970	+	3.96670i	−0.228082	+	0.165711i
$574$	0.177918	+	1.69278i	0.00742615	+	0.0706551i
$575$	26.0440	+	28.9248i	1.08611	+	1.20625i
$576$	−4.91504	−	2.18832i	−0.204793	−	0.0911799i
$577$	−20.2879	−	14.7400i	−0.844596	−	0.613635i	0.0790551	−	0.996870i	$-0.474810\pi$
$577$	−20.2879	−	14.7400i	−0.844596	−	0.613635i	−0.923651	+	0.383236i	$0.874810\pi$
$578$	−2.21160	+	2.45624i	−0.0919906	+	0.102166i
$579$	−1.01377	+	9.64541i	−0.0421310	+	0.400850i
$580$	−0.0221977	+	0.0683174i	−0.000921708	+	0.00283673i
$581$	−14.2976	+	3.03905i	−0.593165	+	0.126081i
$582$	−3.32882	−	0.707563i	−0.137984	−	0.0293294i
$583$	8.82948	−	15.2931i	0.365680	−	0.633376i
$584$	16.9401			0.700985
$585$	0.831929	−	1.16081i	0.0343960	−	0.0479937i
$586$	4.99407	−	3.62840i	0.206303	−	0.149888i
$587$	−32.0871	+	14.2861i	−1.32438	+	0.589651i	−0.942390	−	0.334517i	$-0.891427\pi$
$587$	−32.0871	+	14.2861i	−1.32438	+	0.589651i	−0.381987	+	0.924168i	$0.624760\pi$
$588$	−0.0464762	+	0.0804991i	−0.00191664	+	0.00331973i
$589$	−0.987397	−	0.399472i	−0.0406850	−	0.0164600i
$590$	−0.429724			−0.0176915
$591$	−0.569493	+	5.41837i	−0.0234258	+	0.222882i
$592$	8.47992	+	3.77550i	0.348523	+	0.155172i
$593$	6.67652	+	20.5482i	0.274172	+	0.843814i	0.989437	+	0.144961i	$0.0463057\pi$
$593$	6.67652	+	20.5482i	0.274172	+	0.843814i	−0.715266	+	0.698853i	$0.753694\pi$
$594$	−1.58560	−	2.74634i	−0.0650579	−	0.112684i
$595$	−0.839019	+	1.45322i	−0.0343964	+	0.0595763i
$596$	−2.17003	−	0.461254i	−0.0888879	−	0.0188937i
$597$	−1.76085	+	5.41935i	−0.0720670	+	0.221799i
$598$	−19.2306	+	6.38662i	−0.786397	+	0.261168i
$599$	−9.48801	−	6.89344i	−0.387669	−	0.281658i	0.376830	−	0.926282i	$-0.377014\pi$
$599$	−9.48801	−	6.89344i	−0.387669	−	0.281658i	−0.764500	+	0.644624i	$0.777014\pi$
$600$	4.45988	+	0.947976i	0.182074	+	0.0387009i
$601$	−5.99881	+	2.67084i	−0.244696	+	0.108946i	−0.525421	−	0.850843i	$-0.676092\pi$
$601$	−5.99881	+	2.67084i	−0.244696	+	0.108946i	0.280724	+	0.959788i	$0.409425\pi$
$602$	−17.5455	−	7.81177i	−0.715102	−	0.318384i
$603$	1.10708	−	3.40725i	0.0450839	−	0.138754i
$604$	−30.1362	−	13.4175i	−1.22623	−	0.545951i
$605$	0.854649	+	0.380514i	0.0347464	+	0.0154701i
$606$	−1.42559	+	4.38751i	−0.0579106	+	0.178230i
$607$	6.79308	+	3.02447i	0.275723	+	0.122760i	0.539940	−	0.841704i	$-0.318447\pi$
$607$	6.79308	+	3.02447i	0.275723	+	0.122760i	−0.264217	+	0.964463i	$0.585114\pi$
$608$	−1.02182	+	0.454943i	−0.0414402	+	0.0184504i
$609$	−0.327494	−	0.0696110i	−0.0132707	−	0.00282078i
$610$	−0.230032	−	0.167128i	−0.00931374	−	0.00676683i
$611$	−2.69213	+	13.0822i	−0.108912	+	0.529251i
$612$	6.10345	−	18.7845i	0.246717	−	0.759318i
$613$	−23.1670	−	4.92431i	−0.935708	−	0.198891i	−0.285267	−	0.958448i	$-0.592082\pi$
$613$	−23.1670	−	4.92431i	−0.935708	−	0.198891i	−0.650441	+	0.759557i	$0.725416\pi$
$614$	−9.95538	+	17.2432i	−0.401766	+	0.695880i
$615$	−0.0228684	−	0.0396093i	−0.000922144	−	0.00159720i
$616$	−4.15985	−	12.8027i	−0.167605	−	0.515836i
$617$	−17.6159	−	7.84309i	−0.709188	−	0.315751i	0.0202528	−	0.999795i	$-0.493553\pi$
$617$	−17.6159	−	7.84309i	−0.709188	−	0.315751i	−0.729441	+	0.684044i	$0.760220\pi$
$618$	0.313170	−	2.97961i	0.0125975	−	0.119858i
$619$	−3.77307			−0.151652			−0.0758262	−	0.997121i	$-0.524159\pi$
$619$	−3.77307			−0.151652			−0.0758262	+	0.997121i	$0.524159\pi$
$620$	0.604072	+	0.967726i	0.0242601	+	0.0388648i
$621$	−8.37664	+	14.5088i	−0.336143	+	0.582217i
$622$	−6.94347	+	3.09143i	−0.278408	+	0.123955i
$623$	−4.05040	+	2.94279i	−0.162276	+	0.117900i
$624$	0.893486	−	1.24671i	0.0357681	−	0.0499082i
$625$	24.7139			0.988558
$626$	2.45521	−	4.25255i	0.0981299	−	0.169966i
$627$	−0.140646	−	0.0298953i	−0.00561688	−	0.00119390i
$628$	10.4926	−	2.23028i	0.418701	−	0.0889977i
$629$	11.4515	−	35.2440i	0.456601	−	1.40527i
$630$	−0.0778122	+	0.740334i	−0.00310011	+	0.0294956i
$631$	14.7629	−	16.3958i	0.587700	−	0.652707i	−0.373801	−	0.927509i	$-0.621946\pi$
$631$	14.7629	−	16.3958i	0.587700	−	0.652707i	0.961501	+	0.274802i	$0.0886123\pi$
$632$	3.17746	+	2.30856i	0.126392	+	0.0918295i
$633$	0.150823	+	0.0671507i	0.00599467	+	0.00266900i
$634$	1.20393	+	1.33710i	0.0478142	+	0.0531030i
$635$	−0.0530994	−	0.505207i	−0.00210719	−	0.0200485i
$636$	−3.76414	+	2.73481i	−0.149258	+	0.108442i
$637$	−0.462298	−	0.410856i	−0.0183169	−	0.0162787i
$638$	−0.419538	+	0.304812i	−0.0166097	+	0.0120676i
$639$	30.2272	−	13.4580i	1.19577	−	0.532390i
$640$	1.39809	+	0.297173i	0.0552644	+	0.0117468i
$641$	2.07134	−	19.7075i	0.0818131	−	0.778400i	−0.874297	−	0.485392i	$-0.838677\pi$
$641$	2.07134	−	19.7075i	0.0818131	−	0.778400i	0.956110	−	0.293008i	$-0.0946563\pi$
$642$	−1.38575	+	4.26491i	−0.0546913	+	0.168322i
$643$	−43.3664	+	9.21782i	−1.71021	+	0.363515i	−0.956055	−	0.293186i	$-0.905284\pi$
$643$	−43.3664	+	9.21782i	−1.71021	+	0.363515i	−0.754150	+	0.656702i	$0.771951\pi$
$644$	−20.2595	+	22.5004i	−0.798335	+	0.886641i
$645$	0.516080			0.0203206
$646$	0.319692	+	0.553723i	0.0125781	+	0.0217859i
$647$	9.14998	+	1.94489i	0.359723	+	0.0764614i	0.384228	−	0.923238i	$-0.374468\pi$
$647$	9.14998	+	1.94489i	0.359723	+	0.0764614i	−0.0245052	+	0.999700i	$0.507801\pi$
$648$	−2.04636	−	19.4698i	−0.0803886	−	0.764846i
$649$	7.19448	+	5.22710i	0.282408	+	0.205182i
$650$	−5.17679	+	11.8333i	−0.203051	+	0.464139i
$651$	−4.19151	+	3.27160i	−0.164278	+	0.128224i
$652$	−2.71696	+	4.70591i	−0.106404	+	0.184298i
$653$	−20.9383	+	9.32233i	−0.819378	+	0.364811i	−0.773231	−	0.634124i	$-0.781361\pi$
$653$	−20.9383	+	9.32233i	−0.819378	+	0.364811i	−0.0461470	+	0.998935i	$0.514694\pi$
$654$	1.33637	+	0.594991i	0.0522562	+	0.0232660i
$655$	0.180417	+	0.555268i	0.00704949	+	0.0216961i
$656$	0.527118	+	0.912995i	0.0205805	+	0.0356464i
$657$	9.69292	+	16.7886i	0.378157	+	0.654987i
$658$	−2.15136	−	6.62119i	−0.0838686	−	0.258121i
$659$	−10.0745	+	2.14140i	−0.392447	+	0.0834172i	−0.399909	−	0.916555i	$-0.630958\pi$
$659$	−10.0745	+	2.14140i	−0.392447	+	0.0834172i	0.00746161	+	0.999972i	$0.497625\pi$
$660$	0.103046	+	0.114445i	0.00401107	+	0.00445475i
$661$	27.2520	−	12.1334i	1.05998	−	0.471933i	0.198697	−	0.980061i	$-0.436329\pi$
$661$	27.2520	−	12.1334i	1.05998	−	0.471933i	0.861282	+	0.508128i	$0.169662\pi$
$662$	3.76677	+	11.5929i	0.146400	+	0.450572i
$663$	−5.32275	−	3.02722i	−0.206719	−	0.117568i
$664$	11.3352	−	8.23550i	0.439891	−	0.319599i
$665$	0.0462228	+	0.0513357i	0.00179245	+	0.00199071i
$666$	−1.71840	−	16.3495i	−0.0665868	−	0.633531i
$667$	2.50276	+	1.11430i	0.0969074	+	0.0431459i
$668$	9.50220	−	29.2448i	0.367651	−	1.13151i
$669$	7.13513	+	3.17676i	0.275860	+	0.122821i
$670$	0.0129837	−	0.123532i	0.000501604	−	0.00477244i
$671$	1.81830	+	5.59615i	0.0701947	+	0.216037i
$672$	−0.583646	+	5.55302i	−0.0225146	+	0.214212i
$673$	−5.71342	−	6.34540i	−0.220236	−	0.244597i	0.622894	−	0.782306i	$-0.285957\pi$
$673$	−5.71342	−	6.34540i	−0.220236	−	0.244597i	−0.843131	+	0.537709i	$0.819290\pi$
$674$	−6.30769	−	7.00540i	−0.242963	−	0.269838i
$675$	3.29991	+	10.1561i	0.127014	+	0.390908i
$676$	13.0827	+	14.1561i	0.503182	+	0.544465i
$677$	−0.547972			−0.0210603			−0.0105301	−	0.999945i	$-0.503352\pi$
$677$	−0.547972			−0.0210603			−0.0105301	+	0.999945i	$0.503352\pi$
$678$	1.88804	+	0.401315i	0.0725098	+	0.0154124i
$679$	−3.53667	−	33.6491i	−0.135725	−	1.29134i
$680$	0.168131	−	1.59966i	0.00644753	−	0.0613442i
$681$	−0.791905			−0.0303459
$682$	−0.578332	+	8.21523i	−0.0221455	+	0.314577i
$683$	−0.589129	−	1.02040i	−0.0225424	−	0.0390446i	0.854534	−	0.519395i	$-0.173843\pi$
$683$	−0.589129	−	1.02040i	−0.0225424	−	0.0390446i	−0.877077	+	0.480351i	$0.840509\pi$
$684$	−0.657802	−	0.477921i	−0.0251517	−	0.0182738i
$685$	−0.255657	−	0.113826i	−0.00976814	−	0.00434906i
$686$	13.1835	+	2.80223i	0.503347	+	0.106990i
$687$	2.86746	−	4.96658i	0.109400	−	0.189487i
$688$	−11.8957			−0.453517
$689$	−12.7751	−	28.1995i	−0.486691	−	1.07431i
$690$	−0.0877034	+	0.269923i	−0.00333881	+	0.0102758i
$691$	11.7790	+	13.0819i	0.448094	+	0.497659i	0.924296	−	0.381677i	$-0.124653\pi$
$691$	11.7790	+	13.0819i	0.448094	+	0.497659i	−0.476201	+	0.879336i	$0.657987\pi$
$692$	−28.9767	+	12.9012i	−1.10153	+	0.490432i
$693$	10.3080	−	11.4482i	0.391570	−	0.434883i
$694$	1.35866	+	0.987124i	0.0515740	+	0.0374707i
$695$	1.45625	+	0.648365i	0.0552388	+	0.0245939i
$696$	0.313917	−	0.0667252i	0.0118990	−	0.00252921i
$697$	3.40497	−	2.47385i	0.128972	−	0.0937039i
$698$	−18.1354	−	8.07439i	−0.686434	−	0.305620i
$699$	−1.63993	−	1.82133i	−0.0620279	−	0.0688889i
$700$	2.01730	+	19.1934i	0.0762469	+	0.725441i
$701$	−25.8504	−	18.7814i	−0.976356	−	0.709364i	−0.0194644	−	0.999811i	$-0.506196\pi$
$701$	−25.8504	−	18.7814i	−0.976356	−	0.709364i	−0.956891	+	0.290447i	$0.906196\pi$
$702$	−5.53268	−	0.545243i	−0.208818	−	0.0205789i
$703$	−1.23419	−	0.896690i	−0.0465483	−	0.0338193i
$704$	2.58301	+	2.86872i	0.0973508	+	0.108119i
$705$	0.125176	+	0.139022i	0.00471441	+	0.00523588i
$706$	−3.55175	+	3.94461i	−0.133672	+	0.148457i
$707$	−45.8654			−1.72495
$708$	−1.17153	−	2.02916i	−0.0440290	−	0.0762604i
$709$	19.1606	−	21.2800i	0.719593	−	0.799189i	−0.266772	−	0.963760i	$-0.585957\pi$
$709$	19.1606	−	21.2800i	0.719593	−	0.799189i	0.986365	+	0.164571i	$0.0526239\pi$
$710$	0.928091	−	0.674298i	0.0348306	−	0.0253059i
$711$	−0.469814	+	4.46998i	−0.0176194	+	0.167637i
$712$	2.39951	−	4.15607i	0.0899253	−	0.155755i
$713$	39.1137	−	19.0543i	1.46482	−	0.713591i
$714$	3.19178			0.119449
$715$	−0.884059	+	0.518088i	−0.0330619	+	0.0193754i
$716$	26.2428	−	19.0665i	0.980740	−	0.712549i
$717$	5.84810	+	1.24305i	0.218401	+	0.0464226i
$718$	−8.90067	+	15.4164i	−0.332170	+	0.575335i
$719$	−14.2805	−	24.7345i	−0.532573	−	0.922443i	−0.999277	−	0.0380292i	$-0.987892\pi$
$719$	−14.2805	−	24.7345i	−0.532573	−	0.922443i	0.466704	−	0.884414i	$-0.345441\pi$
$720$	0.142478	+	0.438502i	0.00530984	+	0.0163420i
$721$	29.1356	−	6.19295i	1.08506	−	0.230638i
$722$	−13.3405	+	2.83561i	−0.496482	+	0.105531i
$723$	−0.977846	−	0.710447i	−0.0363665	−	0.0264218i
$724$	−12.2778	+	13.6358i	−0.456299	+	0.506772i
$725$	1.59529	−	0.710269i	0.0592476	−	0.0263787i
$726$	−0.186004	−	1.76971i	−0.00690327	−	0.0656802i
$727$	−11.2814	+	34.7206i	−0.418404	+	1.28771i	0.490767	+	0.871291i	$0.336717\pi$
$727$	−11.2814	+	34.7206i	−0.418404	+	1.28771i	−0.909171	+	0.416423i	$0.863283\pi$
$728$	−22.4915	−	7.14695i	−0.833590	−	0.264884i
$729$	16.2232	−	11.7869i	0.600860	−	0.436550i
$730$	0.449740	+	0.499487i	0.0166456	+	0.0184868i
$731$	4.96410	+	47.2303i	0.183604	+	1.74687i
$732$	0.162054	−	1.54184i	0.00598970	−	0.0569882i
$733$	12.4152	+	38.2102i	0.458567	+	1.41133i	0.866895	+	0.498490i	$0.166112\pi$
$733$	12.4152	+	38.2102i	0.458567	+	1.41133i	−0.408328	+	0.912835i	$0.633888\pi$
$734$	−2.41156	+	22.9445i	−0.0890124	+	0.846896i
$735$	−0.00847334	+	0.00180106i	−0.000312544	+	6.64332e-5i
$736$	14.1185	−	43.4522i	0.520414	−	1.60167i
$737$	−1.71999	+	1.91025i	−0.0633567	+	0.0703648i
$738$	0.933548	−	1.61695i	0.0343644	−	0.0595209i
$739$	−2.34170	+	4.05595i	−0.0861409	+	0.149200i	−0.905877	−	0.423541i	$-0.860787\pi$
$739$	−2.34170	+	4.05595i	−0.0861409	+	0.149200i	0.819736	+	0.572742i	$0.194120\pi$
$740$	0.504897	+	1.55391i	0.0185604	+	0.0571230i
$741$	−0.186233	+	0.169885i	−0.00684142	+	0.00624088i
$742$	13.0550	+	9.48498i	0.479262	+	0.348205i
$743$	−9.00953	+	15.6050i	−0.330528	+	0.572491i	−0.982615	−	0.185653i	$-0.940560\pi$
$743$	−9.00953	+	15.6050i	−0.330528	+	0.572491i	0.652088	+	0.758143i	$0.273893\pi$
$744$	2.39487	−	4.49902i	0.0878003	−	0.164942i
$745$	−0.103376	−	0.179053i	−0.00378742	−	0.00656000i
$746$	17.1978	+	12.4949i	0.629656	+	0.457472i
$747$	14.6477	+	6.52160i	0.535933	+	0.238613i
$748$	−9.48247	+	10.5314i	−0.346714	+	0.385064i
$749$	−44.5837			−1.62905
$750$	0.181253	+	0.313939i	0.00661842	+	0.0114634i
$751$	−7.94379	−	1.68850i	−0.289873	−	0.0616144i	0.0606801	−	0.998157i	$-0.480673\pi$
$751$	−7.94379	−	1.68850i	−0.289873	−	0.0616144i	−0.350553	+	0.936543i	$0.614006\pi$
$752$	−2.88531	−	3.20447i	−0.105217	−	0.116855i
$753$	1.15509	−	3.55500i	0.0420939	−	0.129552i
$754$	0.00589784	+	0.909107i	0.000214786	+	0.0331077i
$755$	−0.950016	−	2.92385i	−0.0345746	−	0.106410i
$756$	−7.58875	+	3.37873i	−0.276000	+	0.122883i
$757$	3.87124	+	36.8324i	0.140703	+	1.33870i	0.805910	+	0.592038i	$0.201677\pi$
$757$	3.87124	+	36.8324i	0.140703	+	1.33870i	−0.665207	+	0.746659i	$0.731657\pi$
$758$	8.30308	−	1.76487i	0.301581	−	0.0641031i
$759$	4.75164	−	3.45227i	0.172474	−	0.125309i
$760$	−0.0604906	−	0.0269322i	−0.00219422	−	0.000976932i
$761$	−31.6434	+	6.72601i	−1.14707	+	0.243818i	−0.741957	−	0.670448i	$-0.766102\pi$
$761$	−31.6434	+	6.72601i	−1.14707	+	0.243818i	−0.405116	+	0.914265i	$0.632769\pi$
$762$	−0.781706	+	0.567943i	−0.0283182	+	0.0205744i
$763$	−1.52021	+	14.4639i	−0.0550354	+	0.523627i
$764$	26.7822	+	5.69272i	0.968945	+	0.205956i
$765$	1.68156	−	0.748680i	0.0607971	−	0.0270686i
$766$	−2.89586	+	8.91255i	−0.104632	+	0.322023i
$767$	14.7956	−	4.91374i	0.534240	−	0.177425i
$768$	−1.26406	−	3.89039i	−0.0456130	−	0.140382i
$769$	12.4892	−	21.6319i	0.450372	−	0.780067i	−0.548037	−	0.836454i	$-0.684625\pi$
$769$	12.4892	−	21.6319i	0.450372	−	0.780067i	0.998409	+	0.0563870i	$0.0179581\pi$
$770$	0.267055	−	0.462553i	0.00962400	−	0.0166693i
$771$	−7.33913	+	8.15093i	−0.264312	+	0.293549i
$772$	31.8342	−	23.1289i	1.14574	−	0.832428i
$773$	5.48668	−	52.2023i	0.197342	−	1.87759i	−0.229570	−	0.973292i	$-0.573732\pi$
$773$	5.48668	−	52.2023i	0.197342	−	1.87759i	0.426912	−	0.904293i	$-0.359601\pi$
$774$	10.5339	+	18.2452i	0.378632	+	0.655809i
$775$	7.65660	−	26.6546i	0.275033	−	0.957462i
$776$	16.2159	+	28.0868i	0.582117	+	1.00826i
$777$	−6.95704	+	3.09748i	−0.249583	+	0.111121i
$778$	0.188676	+	1.79514i	0.00676437	+	0.0643587i
$779$	−0.0535404	−	0.164780i	−0.00191828	−	0.00590387i
$780$	0.268313	−	0.0299619i	0.00960714	−	0.00107281i
$781$	−23.7402			−0.849493
$782$	−25.5463	−	5.43003i	−0.913533	−	0.194177i
$783$	0.502948	+	0.558581i	0.0179739	+	0.0199620i
$784$	0.195311	−	0.0415146i	0.00697538	−	0.00148266i
$785$	0.808774	+	0.587609i	0.0288664	+	0.0209727i
$786$	0.743084	−	0.825278i	0.0265049	−	0.0294367i
$787$	−0.922217	+	8.77431i	−0.0328735	+	0.312770i	0.965713	+	0.259613i	$0.0835951\pi$
$787$	−0.922217	+	8.77431i	−0.0328735	+	0.312770i	−0.998586	+	0.0531571i	$0.983072\pi$
$788$	17.8831	−	12.9928i	0.637058	−	0.462850i
$789$	−6.17421	+	1.31237i	−0.219808	+	0.0467216i
$790$	0.0162889	+	0.154979i	0.000579533	+	0.00551389i
$791$	2.00593	+	19.0851i	0.0713225	+	0.678588i
$792$	−4.56309	+	14.0438i	−0.162143	+	0.499023i
$793$	9.83119	+	3.12398i	0.349116	+	0.110936i
$794$	−9.53070	−	6.92446i	−0.338232	−	0.245740i
$795$	−0.424134	−	0.0901524i	−0.0150425	−	0.00319738i
$796$	21.1204	−	9.40340i	0.748592	−	0.333295i
$797$	40.3619	−	8.57919i	1.42969	−	0.303890i	0.572931	−	0.819604i	$-0.305806\pi$
$797$	40.3619	−	8.57919i	1.42969	−	0.303890i	0.856761	+	0.515713i	$0.172473\pi$
$798$	0.0406031	−	0.124963i	0.00143733	−	0.00442366i
$799$	−11.5189	+	12.7930i	−0.407509	+	0.452585i
$800$	−14.5611	−	25.2206i	−0.514814	−	0.891683i
$801$	5.49188			0.194046
$802$	11.8217	−	13.1293i	0.417437	−	0.463611i
$803$	−1.45391	−	13.8330i	−0.0513073	−	0.488156i
$804$	0.618712	−	0.275469i	0.0218203	−	0.00971503i
$805$	−2.82168			−0.0994510
$806$	11.1157	+	9.21376i	0.391535	+	0.324541i
$807$	1.56343			0.0550354
$808$	40.1631	−	17.8818i	1.41293	−	0.629078i
$809$	0.917283	+	8.72736i	0.0322500	+	0.306838i	0.998742	+	0.0501417i	$0.0159673\pi$
$809$	0.917283	+	8.72736i	0.0322500	+	0.306838i	−0.966492	+	0.256696i	$0.917366\pi$
$810$	0.519749	−	0.577239i	0.0182621	−	0.0202821i
$811$	4.73828			0.166384			0.0831918	−	0.996534i	$-0.473489\pi$
$811$	4.73828			0.166384			0.0831918	+	0.996534i	$0.473489\pi$
$812$	0.679203	+	1.17641i	0.0238354	+	0.0412840i
$813$	1.04676	−	1.16254i	0.0367114	−	0.0407721i
$814$	−3.64495	+	11.2180i	−0.127755	+	0.393190i
$815$	−0.495345	+	0.105289i	−0.0173512	+	0.00368810i
$816$	1.80599	−	0.804078i	0.0632222	−	0.0281484i
$817$	1.91229	+	0.406471i	0.0669027	+	0.0142206i
$818$	−8.36162	−	6.07507i	−0.292357	−	0.212410i
$819$	−5.78633	−	26.3798i	−0.202191	−	0.921786i
$820$	−0.0573428	+	0.176483i	−0.00200250	+	0.00616305i
$821$	3.19507	+	30.3991i	0.111509	+	1.06093i	0.896991	+	0.442050i	$0.145749\pi$
$821$	3.19507	+	30.3991i	0.111509	+	1.06093i	−0.785482	+	0.618885i	$0.787585\pi$
$822$	0.0556407	+	0.529386i	0.00194069	+	0.0184645i
$823$	−53.6123	+	11.3957i	−1.86881	+	0.397227i	−0.995885	−	0.0906297i	$-0.971112\pi$
$823$	−53.6123	+	11.3957i	−1.86881	+	0.397227i	−0.872924	+	0.487857i	$0.837779\pi$
$824$	−23.0987	+	16.7822i	−0.804683	+	0.584636i
$825$	0.391327	−	3.72323i	0.0136243	−	0.129626i
$826$	−5.43757	+	6.03904i	−0.189197	+	0.210125i
$827$	−19.6257	−	14.2589i	−0.682452	−	0.495830i	0.191718	−	0.981450i	$-0.438594\pi$
$827$	−19.6257	−	14.2589i	−0.682452	−	0.495830i	−0.874170	+	0.485620i	$0.838594\pi$
$828$	32.4865	−	6.90522i	1.12898	−	0.239973i
$829$	35.2685	+	39.1697i	1.22493	+	1.36042i	0.911762	+	0.410719i	$0.134722\pi$
$829$	35.2685	+	39.1697i	1.22493	+	1.36042i	0.313164	+	0.949699i	$0.398611\pi$
$830$	0.543764	+	0.115581i	0.0188743	+	0.00401186i
$831$	11.1092			0.385375
$832$	6.72566	−	0.751040i	0.233170	−	0.0260376i
$833$	−0.246333	−	0.758134i	−0.00853492	−	0.0262678i
$834$	−0.316936	−	3.01545i	−0.0109746	−	0.104416i
$835$	2.61795	−	1.16559i	0.0905980	−	0.0403368i
$836$	0.291692	+	0.505226i	0.0100884	+	0.0174736i
$837$	11.9298	−	0.411004i	0.412356	−	0.0142064i
$838$	−4.62540	−	8.01143i	−0.159782	−	0.276750i
$839$	−2.15669	+	20.5195i	−0.0744572	+	0.708413i	0.892079	+	0.451880i	$0.149247\pi$
$839$	−2.15669	+	20.5195i	−0.0744572	+	0.708413i	−0.966536	+	0.256532i	$0.917420\pi$
$840$	−0.267415	+	0.194289i	−0.00922671	+	0.00670359i
$841$	−19.3225	+	21.4599i	−0.666295	+	0.739995i
$842$	10.1091	−	17.5096i	0.348384	−	0.603419i
$843$	2.54531	−	4.40861i	0.0876652	−	0.151840i
$844$	−0.206990	−	0.637051i	−0.00712490	−	0.0219282i
$845$	−0.164579	+	1.78883i	−0.00566167	+	0.0615378i
$846$	−2.35990	+	7.26303i	−0.0811351	+	0.249708i
$847$	16.1619	−	7.19574i	0.555329	−	0.247248i
$848$	9.77629	+	2.07802i	0.335719	+	0.0713594i
$849$	0.155050	−	1.47520i	0.00532129	−	0.0506287i
$850$	−13.4679	+	9.78501i	−0.461946	+	0.335623i
$851$	60.9522	−	12.9558i	2.08941	−	0.444119i
$852$	5.71424	+	2.54414i	0.195767	+	0.0871609i
$853$	−30.5394	+	22.1882i	−1.04565	+	0.759710i	−0.971381	−	0.237529i	$-0.923663\pi$
$853$	−30.5394	+	22.1882i	−1.04565	+	0.759710i	−0.0742699	+	0.997238i	$0.523663\pi$
$854$	−5.25945	+	1.11793i	−0.179975	+	0.0382548i
$855$	−0.00792067	−	0.0753601i	−0.000270881	−	0.00257726i
$856$	39.0408	−	17.3821i	1.33439	−	0.594107i
$857$	11.2725	+	34.6933i	0.385063	+	1.18510i	0.936435	+	0.350842i	$0.114105\pi$
$857$	11.2725	+	34.6933i	0.385063	+	1.18510i	−0.551372	+	0.834260i	$0.685895\pi$
$858$	1.69420	+	0.963549i	0.0578392	+	0.0328950i
$859$	−8.40285	+	25.8613i	−0.286701	+	0.882376i	0.699182	+	0.714944i	$0.253548\pi$
$859$	−8.40285	+	25.8613i	−0.286701	+	0.882376i	−0.985884	+	0.167433i	$0.946452\pi$
$860$	−1.40106	−	1.55604i	−0.0477759	−	0.0530605i
$861$	−0.846009	−	0.179825i	−0.0288319	−	0.00612841i
$862$	−8.30879	−	14.3913i	−0.282999	−	0.490168i
$863$	−44.6541			−1.52004			−0.760022	−	0.649897i	$-0.774812\pi$
$863$	−44.6541			−1.52004			−0.760022	+	0.649897i	$0.774812\pi$
$864$	8.38762	−	9.31540i	0.285353	−	0.316916i
$865$	−2.70046	−	1.20232i	−0.0918185	−	0.0408802i
$866$	−12.5493	−	9.11759i	−0.426442	−	0.309828i
$867$	−0.839753	−	1.45450i	−0.0285195	−	0.0493973i
$868$	21.2434	+	3.75605i	0.721050	+	0.127489i
$869$	1.61242	−	2.79280i	0.0546977	−	0.0947393i
$870$	0.0103016	+	0.00748454i	0.000349256	+	0.000253750i
$871$	0.965503	+	4.40172i	0.0327148	+	0.149147i
$872$	−4.30789	−	13.2583i	−0.145884	−	0.448983i
$873$	−18.5571	+	32.1419i	−0.628064	+	1.08784i
$874$	−0.537573	+	0.931103i	−0.0181837	+	0.0314950i
$875$	−2.41157	+	2.67832i	−0.0815259	+	0.0905436i
$876$	−1.13247	+	3.48539i	−0.0382627	+	0.117761i
$877$	44.5694	−	9.47352i	1.50500	−	0.319898i	0.619671	−	0.784861i	$-0.287266\pi$
$877$	44.5694	−	9.47352i	1.50500	−	0.319898i	0.885330	+	0.464963i	$0.153933\pi$
$878$	1.41961	−	13.5067i	0.0479096	−	0.455829i
$879$	0.969313	+	2.98324i	0.0326941	+	0.100622i
$880$	0.0345794	−	0.329001i	0.00116567	−	0.0110906i
$881$	−3.90501	−	37.1537i	−0.131563	−	1.25174i	−0.838673	−	0.544635i	$-0.816668\pi$
$881$	−3.90501	−	37.1537i	−0.131563	−	1.25174i	0.707110	−	0.707103i	$-0.249998\pi$
$882$	−0.236626	−	0.262799i	−0.00796760	−	0.00884892i
$883$	16.6075	−	12.0661i	0.558887	−	0.406056i	−0.272164	−	0.962251i	$-0.587739\pi$
$883$	16.6075	−	12.0661i	0.558887	−	0.406056i	0.831052	+	0.556195i	$0.187739\pi$
$884$	5.32290	+	24.2671i	0.179029	+	0.816190i
$885$	0.0674773	−	0.207674i	0.00226822	−	0.00698087i
$886$	−0.186564	−	1.77504i	−0.00626775	−	0.0596337i
$887$	4.65205	−	2.07122i	0.156200	−	0.0695449i	−0.327147	−	0.944973i	$-0.606087\pi$
$887$	4.65205	−	2.07122i	0.156200	−	0.0695449i	0.483348	+	0.875428i	$0.339421\pi$
$888$	4.88447	−	5.42475i	0.163912	−	0.182043i
$889$	−7.77172	−	5.64648i	−0.260655	−	0.189377i
$890$	0.186248	−	0.0395882i	0.00624304	−	0.00132700i
$891$	−15.7231	+	3.34205i	−0.526745	+	0.111963i
$892$	−9.79230	−	30.1376i	−0.327870	−	1.00908i
$893$	0.354335	+	0.613726i	0.0118574	+	0.0205376i
$894$	−0.196631	+	0.340575i	−0.00657633	+	0.0113905i
$895$	2.95697	+	0.628524i	0.0988406	+	0.0210092i
$896$	21.8672	−	15.8874i	0.730531	−	0.530762i
$897$	−0.0667983	−	10.2965i	−0.00223033	−	0.343789i
$898$	3.66317			0.122242
$899$	−0.270762	−	1.93314i	−0.00903041	−	0.0644738i
$900$	10.5849	−	18.3337i	0.352831	−	0.611122i
$901$	4.17083	−	39.6828i	0.138950	−	1.32202i
$902$	−1.08378	+	0.787414i	−0.0360860	+	0.0262180i
$903$	6.53028	−	7.25261i	0.217314	−	0.241352i
$904$	−9.19734	−	15.9303i	−0.305899	−	0.529833i
$905$	−1.71001			−0.0568426
$906$	−3.91283	+	4.34563i	−0.129995	+	0.144374i
$907$	−26.0883	−	28.9740i	−0.866248	−	0.962066i	0.133332	−	0.991071i	$-0.457432\pi$
$907$	−26.0883	−	28.9740i	−0.866248	−	0.962066i	−0.999579	+	0.0290060i	$0.990766\pi$
$908$	2.14988	+	2.38769i	0.0713463	+	0.0792381i
$909$	40.7028	+	29.5723i	1.35003	+	0.980852i
$910$	−0.386392	−	0.852917i	−0.0128088	−	0.0282739i
$911$	−16.6253	−	12.0790i	−0.550821	−	0.400195i	0.277267	−	0.960793i	$-0.410571\pi$
$911$	−16.6253	−	12.0790i	−0.550821	−	0.400195i	−0.828088	+	0.560598i	$0.810571\pi$
$912$	−0.00850675	−	0.0809363i	−0.000281687	−	0.00268007i
$913$	−7.69785	−	8.54933i	−0.254762	−	0.282941i
$914$	23.2444	+	10.3491i	0.768857	+	0.342317i
$915$	0.116889	−	0.0849249i	0.00386423	−	0.00280753i
$916$	−22.7595	+	4.83767i	−0.751994	+	0.159841i
$917$	10.0863	+	4.49070i	0.333078	+	0.148296i
$918$	−5.79700	−	4.21177i	−0.191330	−	0.139009i
$919$	−1.24336	+	1.38089i	−0.0410146	+	0.0455513i	−0.763303	−	0.646041i	$-0.776424\pi$
$919$	−1.24336	+	1.38089i	−0.0410146	+	0.0455513i	0.722288	+	0.691592i	$0.243090\pi$
$920$	2.47087	−	1.10010i	0.0814621	−	0.0362693i
$921$	−6.76992	−	7.51876i	−0.223077	−	0.247752i
$922$	−3.70880	+	11.4145i	−0.122143	+	0.375917i
$923$	−24.2443	+	33.8288i	−0.798012	+	1.11349i
$924$	2.91223			0.0958054
$925$	19.8598	−	34.3982i	0.652986	−	1.13100i
$926$	21.6668	+	4.60542i	0.712015	+	0.151343i
$927$	−29.8491	−	13.2897i	−0.980372	−	0.436490i
$928$	−1.65835	−	1.20486i	−0.0544379	−	0.0395515i
$929$	−4.10939	−	7.11766i	−0.134825	−	0.233523i	0.790706	−	0.612196i	$-0.209714\pi$
$929$	−4.10939	−	7.11766i	−0.134825	−	0.233523i	−0.925530	+	0.378673i	$0.876380\pi$
$930$	0.196237	−	0.0488298i	0.00643486	−	0.00160119i
$931$	−0.0328158			−0.00107550
$932$	−1.03939	+	9.88916i	−0.0340464	+	0.323930i
$933$	−0.403707	−	3.84101i	−0.0132168	−	0.125749i
$934$	13.7281	+	2.91800i	0.449198	+	0.0954799i
$935$	−1.32069			−0.0431912
$936$	15.3518	+	20.8442i	0.501788	+	0.681313i
$937$	−7.63678	−	23.5036i	−0.249483	−	0.767829i	−0.994867	−	0.101194i	$-0.967734\pi$
$937$	−7.63678	−	23.5036i	−0.249483	−	0.767829i	0.745384	−	0.666636i	$-0.232266\pi$
$938$	−1.57173	−	1.74559i	−0.0513189	−	0.0569954i
$939$	1.66961	+	1.85429i	0.0544856	+	0.0605124i
$940$	0.0793370	−	0.754841i	0.00258769	−	0.0246202i
$941$	13.2504	+	40.7805i	0.431951	+	1.32941i	0.896179	+	0.443692i	$0.146332\pi$
$941$	13.2504	+	40.7805i	0.431951	+	1.32941i	−0.464229	+	0.885715i	$0.653668\pi$
$942$	0.198763	−	1.89110i	0.00647604	−	0.0616154i
$943$	6.46534	+	2.87855i	0.210540	+	0.0937386i
$944$	−1.55535	+	4.78688i	−0.0506224	+	0.155800i
$945$	−0.707229	−	0.314879i	−0.0230062	−	0.0102430i
$946$	−1.58005	−	15.0331i	−0.0513717	−	0.488769i
$947$	37.1383	+	41.2463i	1.20683	+	1.34032i	0.924581	+	0.380985i	$0.124415\pi$
$947$	37.1383	+	41.2463i	1.20683	+	1.34032i	0.282252	+	0.959340i	$0.408918\pi$
$948$	−0.687401	+	0.499426i	−0.0223257	+	0.0162206i
$949$	−21.1962	−	12.0550i	−0.688059	−	0.391321i
$950$	0.211772	+	0.651768i	0.00687080	+	0.0211462i
$951$	−0.835230	+	0.371868i	−0.0270842	+	0.0120587i
$952$	−20.3530	−	22.6043i	−0.659645	−	0.732610i
$953$	28.5067	−	6.05928i	0.923421	−	0.196279i	0.278419	−	0.960460i	$-0.410190\pi$
$953$	28.5067	−	6.05928i	0.923421	−	0.196279i	0.645002	+	0.764181i	$0.276856\pi$
$954$	−5.46993	−	16.8347i	−0.177095	−	0.545044i
$955$	1.27585	+	2.20985i	0.0412857	+	0.0715089i
$956$	−12.1286	−	21.0074i	−0.392267	−	0.679427i
$957$	−0.0814293	−	0.250614i	−0.00263224	−	0.00810119i
$958$	17.2566	+	7.68315i	0.557536	+	0.248231i
$959$	−4.83461	+	2.15251i	−0.156118	+	0.0695081i
$960$	0.0473934	−	0.0820878i	0.00152962	−	0.00264937i
$961$	−26.2741	−	16.4521i	−0.847551	−	0.530714i
$962$	12.2628	+	16.6501i	0.395369	+	0.536820i
$963$	39.5654	+	28.7460i	1.27498	+	0.926325i
$964$	0.512599	+	4.87705i	0.0165097	+	0.157079i
$965$	3.58700	+	0.762440i	0.115470	+	0.0245438i
$966$	2.68354	+	4.64803i	0.0863415	+	0.149548i
$967$	0.275020			0.00884404			0.00442202	−	0.999990i	$-0.498592\pi$
$967$	0.275020			0.00884404			0.00442202	+	0.999990i	$0.498592\pi$
$968$	−11.3471	+	12.6022i	−0.364710	+	0.405051i
$969$	−0.317798	+	0.0675500i	−0.0102091	+	0.00217002i
$970$	−0.397639	+	1.22381i	−0.0127674	+	0.0392941i
$971$	0.0597782	−	0.568752i	0.00191837	−	0.0182521i	−0.993521	−	0.113650i	$-0.963746\pi$
$971$	0.0597782	−	0.568752i	0.00191837	−	0.0182521i	0.995439	+	0.0953980i	$0.0304124\pi$
$972$	13.4710	+	2.86335i	0.432083	+	0.0918421i
$973$	27.5385	−	12.2609i	0.882845	−	0.393068i
$974$	−6.04800	+	4.39413i	−0.193790	+	0.140797i
$975$	−4.90581	−	4.35991i	−0.157112	−	0.139629i
$976$	−2.69430	+	1.95752i	−0.0862424	+	0.0626587i
$977$	−3.21928	−	30.6294i	−0.102994	−	0.979922i	−0.916952	−	0.398998i	$-0.869358\pi$
$977$	−3.21928	−	30.6294i	−0.102994	−	0.979922i	0.813958	−	0.580924i	$-0.197309\pi$
$978$	0.644533	+	0.715826i	0.0206099	+	0.0228896i
$979$	−3.59972	−	1.60270i	−0.115048	−	0.0512225i
$980$	0.0284340	+	0.0206585i	0.000908292	+	0.000659912i
$981$	10.6749	−	11.8556i	0.340822	−	0.378522i
$982$	−1.59895	+	15.2130i	−0.0510245	+	0.485466i
$983$	3.06678	−	9.43858i	0.0978151	−	0.301044i	−0.890162	−	0.455644i	$-0.849409\pi$
$983$	3.06678	−	9.43858i	0.0978151	−	0.301044i	0.987977	+	0.154600i	$0.0494090\pi$
$984$	0.810936	−	0.172370i	0.0258517	−	0.00549495i
$985$	2.01502	+	0.428305i	0.0642038	+	0.0136469i
$986$	−0.585876	+	1.01477i	−0.0186581	+	0.0323167i
$987$	3.53765			0.112605
$988$	1.01781	+	0.100305i	0.0323809	+	0.00319112i
$989$	−64.6055	+	46.9386i	−2.05433	+	1.49256i
$990$	−0.535233	+	0.238301i	−0.0170108	+	0.00757370i
$991$	−13.8915	+	24.0608i	−0.441279	+	0.764318i	−0.997785	−	0.0665260i	$-0.978808\pi$
$991$	−13.8915	+	24.0608i	−0.441279	+	0.764318i	0.556506	+	0.830844i	$0.312142\pi$
$992$	−31.5902	+	7.86061i	−1.00299	+	0.249574i
$993$	−6.19402			−0.196561
$994$	2.26763	−	21.5750i	0.0719248	−	0.684319i
$995$	1.96830	+	0.876345i	0.0623994	+	0.0277820i
$996$	0.936664	+	2.88275i	0.0296793	+	0.0913436i
$997$	13.9177	+	24.1062i	0.440779	+	0.763451i	0.997747	−	0.0670823i	$-0.0213690\pi$
$997$	13.9177	+	24.1062i	0.440779	+	0.763451i	−0.556969	+	0.830533i	$0.688036\pi$
$998$	2.45292	−	4.24858i	0.0776457	−	0.134486i
$999$	16.7229	+	3.55457i	0.529090	+	0.112462i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.bl.b.126.13	yes	280
13.3	even	3	inner	403.2.bl.b.250.23	yes	280
31.16	even	5	inner	403.2.bl.b.295.23	yes	280
403.16	even	15	inner	403.2.bl.b.16.13	✓	280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.bl.b.16.13	✓	280	403.16	even	15	inner
403.2.bl.b.126.13	yes	280	1.1	even	1	trivial
403.2.bl.b.250.23	yes	280	13.3	even	3	inner
403.2.bl.b.295.23	yes	280	31.16	even	5	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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.bl (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.657025 + 0.292526i) q^{2} +(-0.0382007 - 0.363455i) q^{3} +(-0.992151 + 1.10190i) q^{4} -0.138184 q^{5} +(0.131419 + 0.227624i) q^{6} +(-1.74853 + 1.94194i) q^{7} +(0.774026 - 2.38221i) q^{8} +(2.80380 - 0.595967i) q^{9} +O(q^{10})\)	\(q+(-0.657025 + 0.292526i) q^{2} +(-0.0382007 - 0.363455i) q^{3} +(-0.992151 + 1.10190i) q^{4} -0.138184 q^{5} +(0.131419 + 0.227624i) q^{6} +(-1.74853 + 1.94194i) q^{7} +(0.774026 - 2.38221i) q^{8} +(2.80380 - 0.595967i) q^{9} +(0.0907902 - 0.0404224i) q^{10} +(-2.01171 - 0.427602i) q^{11} +(0.438391 + 0.318509i) q^{12} +(-2.66374 + 2.42992i) q^{13} +(0.580758 - 1.78739i) q^{14} +(0.00527872 + 0.0502236i) q^{15} +(-0.121675 - 1.15766i) q^{16} +(-4.54556 + 0.966188i) q^{17} +(-1.66783 + 1.21175i) q^{18} +(-0.0199969 + 0.190257i) q^{19} +(0.137099 - 0.152264i) q^{20} +(0.772602 + 0.561328i) q^{21} +(1.44683 - 0.307533i) q^{22} +(-5.22877 - 5.80714i) q^{23} +(-0.895395 - 0.190322i) q^{24} -4.98091 q^{25} +(1.03933 - 2.37573i) q^{26} +(-0.662512 - 2.03900i) q^{27} +(-0.405008 - 3.85339i) q^{28} +(-0.320281 + 0.142598i) q^{29} +(-0.0181600 - 0.0314540i) q^{30} +(-1.53719 + 5.35136i) q^{31} +(2.92339 + 5.06346i) q^{32} +(-0.0785655 + 0.747501i) q^{33} +(2.70391 - 1.96450i) q^{34} +(0.241618 - 0.268344i) q^{35} +(-2.12510 + 3.68079i) q^{36} +(-3.98719 + 6.90601i) q^{37} +(-0.0425168 - 0.130853i) q^{38} +(0.984923 + 0.875326i) q^{39} +(-0.106958 + 0.329183i) q^{40} +(-0.827375 + 0.368371i) q^{41} +(-0.671822 - 0.142800i) q^{42} +(1.06821 - 10.1634i) q^{43} +(2.46709 - 1.79245i) q^{44} +(-0.387440 + 0.0823529i) q^{45} +(5.13417 + 2.28588i) q^{46} +(2.99692 - 2.17739i) q^{47} +(-0.416108 + 0.0884465i) q^{48} +(0.0179304 + 0.170597i) q^{49} +(3.27258 - 1.45705i) q^{50} +(0.524810 + 1.61520i) q^{51} +(-0.0346822 - 5.34601i) q^{52} +(-2.65330 + 8.16603i) q^{53} +(1.03175 + 1.14587i) q^{54} +(0.277986 + 0.0590877i) q^{55} +(3.27269 + 5.66847i) q^{56} +0.0699139 q^{57} +(0.168719 - 0.187381i) q^{58} +(-3.95013 - 1.75871i) q^{59} +(-0.0605785 - 0.0440129i) q^{60} +(-1.43052 - 2.47773i) q^{61} +(-0.555441 - 3.96564i) q^{62} +(-3.74520 + 6.48687i) q^{63} +(-1.51849 - 1.10325i) q^{64} +(0.368086 - 0.335775i) q^{65} +(-0.167044 - 0.514109i) q^{66} +(0.624921 - 1.08239i) q^{67} +(3.44524 - 5.96734i) q^{68} +(-1.91089 + 2.12226i) q^{69} +(-0.0802514 + 0.246988i) q^{70} +(11.2909 - 2.39996i) q^{71} +(0.750501 - 7.14054i) q^{72} +(2.08989 + 6.43203i) q^{73} +(0.599491 - 5.70377i) q^{74} +(0.190274 + 1.81034i) q^{75} +(-0.189804 - 0.210799i) q^{76} +(4.34790 - 3.15894i) q^{77} +(-0.903174 - 0.286995i) q^{78} +(-0.484542 + 1.49127i) q^{79} +(0.0168135 + 0.159969i) q^{80} +(7.14009 - 3.17897i) q^{81} +(0.435848 - 0.484058i) q^{82} +(4.52538 + 3.28788i) q^{83} +(-1.38506 + 0.294404i) q^{84} +(0.628123 - 0.133512i) q^{85} +(2.27121 + 6.99006i) q^{86} +(0.0640631 + 0.110960i) q^{87} +(-2.57575 + 4.46133i) q^{88} +(1.87406 + 0.398343i) q^{89} +(0.230467 - 0.167444i) q^{90} +(-0.0611226 - 9.42159i) q^{91} +11.5866 q^{92} +(2.00370 + 0.354275i) q^{93} +(-1.33211 + 2.30727i) q^{94} +(0.00276324 - 0.0262905i) q^{95} +(1.72867 - 1.25595i) q^{96} +(-8.66381 + 9.62213i) q^{97} +(-0.0616848 - 0.106841i) q^{98} -5.89527 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 280 q + q^{2} + 39 q^{4} - 8 q^{5} - 2 q^{7} + 12 q^{8} + 29 q^{9}+O(q^{10}) \) 280 * q + q^2 + 39 * q^4 - 8 * q^5 - 2 * q^7 + 12 * q^8 + 29 * q^9	\( 280 q + q^{2} + 39 q^{4} - 8 q^{5} - 2 q^{7} + 12 q^{8} + 29 q^{9} - 21 q^{10} - q^{11} - 16 q^{12} - 54 q^{14} - 27 q^{15} + 31 q^{16} + 2 q^{17} - 10 q^{18} + 5 q^{19} - 3 q^{20} + 68 q^{21} - 39 q^{22} - 7 q^{23} + 48 q^{24} + 200 q^{25} + 6 q^{26} - 78 q^{27} + 30 q^{28} - 16 q^{29} - 66 q^{30} - 62 q^{31} - 56 q^{32} - 20 q^{33} - 126 q^{34} - 37 q^{35} - 140 q^{36} - 36 q^{37} + 4 q^{38} + 28 q^{39} - 158 q^{40} - 4 q^{41} + 16 q^{42} - 16 q^{43} + 42 q^{44} - 46 q^{45} - 29 q^{46} + 8 q^{47} - 36 q^{48} + 43 q^{49} - 5 q^{50} - 134 q^{51} - q^{52} + 8 q^{53} + 44 q^{54} - 55 q^{55} - 42 q^{56} + 140 q^{57} + 38 q^{58} - 23 q^{59} + 38 q^{60} + 40 q^{61} + 19 q^{62} - 146 q^{63} - 68 q^{64} + 2 q^{65} + 6 q^{66} + 46 q^{67} + 86 q^{68} - 32 q^{69} - 4 q^{70} + 60 q^{71} + 73 q^{72} - 12 q^{73} - 44 q^{74} + 16 q^{75} - 70 q^{76} + 10 q^{77} - 142 q^{78} + 134 q^{79} - 72 q^{80} - 18 q^{81} + 28 q^{82} - 88 q^{83} + 81 q^{84} - 69 q^{85} + 188 q^{86} - 28 q^{87} + 42 q^{88} + 12 q^{89} + 22 q^{90} + 67 q^{91} - 324 q^{92} - 25 q^{93} - 62 q^{94} + 16 q^{95} + 276 q^{96} + 16 q^{97} + 76 q^{98} - 60 q^{99}+O(q^{100}) \) 280 * q + q^2 + 39 * q^4 - 8 * q^5 - 2 * q^7 + 12 * q^8 + 29 * q^9 - 21 * q^10 - q^11 - 16 * q^12 - 54 * q^14 - 27 * q^15 + 31 * q^16 + 2 * q^17 - 10 * q^18 + 5 * q^19 - 3 * q^20 + 68 * q^21 - 39 * q^22 - 7 * q^23 + 48 * q^24 + 200 * q^25 + 6 * q^26 - 78 * q^27 + 30 * q^28 - 16 * q^29 - 66 * q^30 - 62 * q^31 - 56 * q^32 - 20 * q^33 - 126 * q^34 - 37 * q^35 - 140 * q^36 - 36 * q^37 + 4 * q^38 + 28 * q^39 - 158 * q^40 - 4 * q^41 + 16 * q^42 - 16 * q^43 + 42 * q^44 - 46 * q^45 - 29 * q^46 + 8 * q^47 - 36 * q^48 + 43 * q^49 - 5 * q^50 - 134 * q^51 - q^52 + 8 * q^53 + 44 * q^54 - 55 * q^55 - 42 * q^56 + 140 * q^57 + 38 * q^58 - 23 * q^59 + 38 * q^60 + 40 * q^61 + 19 * q^62 - 146 * q^63 - 68 * q^64 + 2 * q^65 + 6 * q^66 + 46 * q^67 + 86 * q^68 - 32 * q^69 - 4 * q^70 + 60 * q^71 + 73 * q^72 - 12 * q^73 - 44 * q^74 + 16 * q^75 - 70 * q^76 + 10 * q^77 - 142 * q^78 + 134 * q^79 - 72 * q^80 - 18 * q^81 + 28 * q^82 - 88 * q^83 + 81 * q^84 - 69 * q^85 + 188 * q^86 - 28 * q^87 + 42 * q^88 + 12 * q^89 + 22 * q^90 + 67 * q^91 - 324 * q^92 - 25 * q^93 - 62 * q^94 + 16 * q^95 + 276 * q^96 + 16 * q^97 + 76 * q^98 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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