LMFDB - Embedded newform 441.2.bb.c.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 32]))

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

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

chi := DirichletCharacter("441.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.bb (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 147)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			37.1
Character	$\chi$	$=$	441.37
Dual form			441.2.bb.c.298.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.65175 + 1.12614i) q^{2} +(0.729391 - 1.85846i) q^{4} +(0.400180 + 0.123439i) q^{5} +(-1.90889 + 1.83197i) q^{7} +(-0.00157168 - 0.00688598i) q^{8} +O(q^{10})$	\(q+(-1.65175 + 1.12614i) q^{2} +(0.729391 - 1.85846i) q^{4} +(0.400180 + 0.123439i) q^{5} +(-1.90889 + 1.83197i) q^{7} +(-0.00157168 - 0.00688598i) q^{8} +(-0.800006 + 0.246769i) q^{10} +(-0.0436333 - 0.582246i) q^{11} +(-3.22770 - 1.55438i) q^{13} +(1.08994 - 5.17564i) q^{14} +(2.93738 + 2.72549i) q^{16} +(0.518106 + 0.0780919i) q^{17} +(-0.603015 + 1.04445i) q^{19} +(0.521294 - 0.653682i) q^{20} +(0.727763 + 0.912586i) q^{22} +(-8.89988 + 1.34144i) q^{23} +(-3.98629 - 2.71780i) q^{25} +(7.08179 - 1.06741i) q^{26} +(2.01232 + 4.88382i) q^{28} +(2.11419 - 2.65111i) q^{29} +(-3.57740 - 6.19624i) q^{31} +(-7.90713 - 1.19181i) q^{32} +(-0.943723 + 0.454473i) q^{34} +(-0.990037 + 0.497487i) q^{35} +(1.29416 + 3.29747i) q^{37} +(-0.180174 - 2.40425i) q^{38} +(0.000221045 - 0.00294963i) q^{40} +(-0.789835 - 3.46050i) q^{41} +(1.23768 - 5.42262i) q^{43} +(-1.11391 - 0.343595i) q^{44} +(13.1897 - 12.2383i) q^{46} +(4.74838 - 3.23739i) q^{47} +(0.287736 - 6.99408i) q^{49} +9.64498 q^{50} +(-5.24300 + 4.86480i) q^{52} +(1.18402 - 3.01682i) q^{53} +(0.0544107 - 0.238389i) q^{55} +(0.0156151 + 0.0102653i) q^{56} +(-0.506580 + 6.75984i) q^{58} +(-8.24358 + 2.54281i) q^{59} +(2.07940 + 5.29823i) q^{61} +(12.8868 + 6.20597i) q^{62} +(7.18226 - 3.45880i) q^{64} +(-1.09979 - 1.02045i) q^{65} +(-3.72619 - 6.45396i) q^{67} +(0.523033 - 0.905919i) q^{68} +(1.07505 - 1.93665i) q^{70} +(5.36805 + 6.73132i) q^{71} +(-10.4454 - 7.12155i) q^{73} +(-5.85105 - 3.98918i) q^{74} +(1.50124 + 1.88249i) q^{76} +(1.14995 + 1.03151i) q^{77} +(-4.12595 + 7.14636i) q^{79} +(0.839047 + 1.45327i) q^{80} +(5.20162 + 4.82640i) q^{82} +(-15.5836 + 7.50467i) q^{83} +(0.197696 + 0.0952053i) q^{85} +(4.06231 + 10.3506i) q^{86} +(-0.00394076 + 0.00121556i) q^{88} +(0.281727 - 3.75938i) q^{89} +(9.00891 - 2.94592i) q^{91} +(-3.99848 + 17.5185i) q^{92} +(-4.19736 + 10.6947i) q^{94} +(-0.370241 + 0.343533i) q^{95} -5.47393 q^{97} +(7.40107 + 11.8765i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + q^{2} + 3 q^{4} - 6 q^{8}+O(q^{10}) $ 48 * q + q^2 + 3 * q^4 - 6 * q^8	$ 48 q + q^{2} + 3 q^{4} - 6 q^{8} + 30 q^{10} + 9 q^{11} + 42 q^{14} + 29 q^{16} + 5 q^{17} - 26 q^{19} + 5 q^{20} + q^{22} + 4 q^{23} - 56 q^{25} + 62 q^{26} + 7 q^{28} - 12 q^{29} - 36 q^{31} + 14 q^{32} - 76 q^{34} - 7 q^{35} - 20 q^{37} + 60 q^{38} + 28 q^{40} - 41 q^{41} + 12 q^{43} - 44 q^{44} + 16 q^{46} - 13 q^{47} - 84 q^{49} + 12 q^{50} + 92 q^{52} - 14 q^{53} - 38 q^{55} - 105 q^{56} + 3 q^{58} - 57 q^{59} + 11 q^{61} + 16 q^{62} - 110 q^{64} - 21 q^{65} + 34 q^{67} - 22 q^{68} - 6 q^{71} - 69 q^{73} + 90 q^{74} - 49 q^{76} + 34 q^{79} - 55 q^{80} + 91 q^{82} - 28 q^{83} - 44 q^{85} + 26 q^{86} + 45 q^{88} - 11 q^{89} - 84 q^{92} + 90 q^{94} - 150 q^{95} + 124 q^{97} - 119 q^{98}+O(q^{100}) $ 48 * q + q^2 + 3 * q^4 - 6 * q^8 + 30 * q^10 + 9 * q^11 + 42 * q^14 + 29 * q^16 + 5 * q^17 - 26 * q^19 + 5 * q^20 + q^22 + 4 * q^23 - 56 * q^25 + 62 * q^26 + 7 * q^28 - 12 * q^29 - 36 * q^31 + 14 * q^32 - 76 * q^34 - 7 * q^35 - 20 * q^37 + 60 * q^38 + 28 * q^40 - 41 * q^41 + 12 * q^43 - 44 * q^44 + 16 * q^46 - 13 * q^47 - 84 * q^49 + 12 * q^50 + 92 * q^52 - 14 * q^53 - 38 * q^55 - 105 * q^56 + 3 * q^58 - 57 * q^59 + 11 * q^61 + 16 * q^62 - 110 * q^64 - 21 * q^65 + 34 * q^67 - 22 * q^68 - 6 * q^71 - 69 * q^73 + 90 * q^74 - 49 * q^76 + 34 * q^79 - 55 * q^80 + 91 * q^82 - 28 * q^83 - 44 * q^85 + 26 * q^86 + 45 * q^88 - 11 * q^89 - 84 * q^92 + 90 * q^94 - 150 * q^95 + 124 * q^97 - 119 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{16}{21}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.65175	+	1.12614i	−1.16796	+	0.796303i	−0.982484	−	0.186346i	$-0.940336\pi$
$2$	−1.65175	+	1.12614i	−1.16796	+	0.796303i	−0.185478	+	0.982648i	$0.559383\pi$
$3$		0			0
$3$		0			0
$4$	0.729391	−	1.85846i	0.364696	−	0.929229i
$5$	0.400180	+	0.123439i	0.178966	+	0.0552036i	0.382943	−	0.923772i	$-0.374911\pi$
$5$	0.400180	+	0.123439i	0.178966	+	0.0552036i	−0.203977	+	0.978976i	$0.565387\pi$
$6$		0			0
$7$	−1.90889	+	1.83197i	−0.721493	+	0.692421i
$7$	−1.90889	+	1.83197i	−0.721493	+	0.692421i
$8$	−0.00157168	−	0.00688598i	−0.000555673	−	0.00243456i
$9$		0			0
$10$	−0.800006	+	0.246769i	−0.252984	+	0.0780352i
$11$	−0.0436333	−	0.582246i	−0.0131559	−	0.175554i	−0.999911	−	0.0133369i	$-0.995755\pi$
$11$	−0.0436333	−	0.582246i	−0.0131559	−	0.175554i	0.986755	−	0.162217i	$-0.0518644\pi$
$12$		0			0
$13$	−3.22770	−	1.55438i	−0.895203	−	0.431107i	−0.0710488	−	0.997473i	$-0.522635\pi$
$13$	−3.22770	−	1.55438i	−0.895203	−	0.431107i	−0.824154	+	0.566366i	$0.808349\pi$
$14$	1.08994	−	5.17564i	0.291299	−	1.38325i
$15$		0			0
$16$	2.93738	+	2.72549i	0.734345	+	0.681372i
$17$	0.518106	+	0.0780919i	0.125659	+	0.0189401i	0.211571	−	0.977363i	$-0.432142\pi$
$17$	0.518106	+	0.0780919i	0.125659	+	0.0189401i	−0.0859115	+	0.996303i	$0.527380\pi$
$18$		0			0
$19$	−0.603015	+	1.04445i	−0.138341	+	0.239614i	−0.926869	−	0.375385i	$-0.877510\pi$
$19$	−0.603015	+	1.04445i	−0.138341	+	0.239614i	0.788528	+	0.614999i	$0.210844\pi$
$20$	0.521294	−	0.653682i	0.116565	−	0.146168i
$21$		0			0
$22$	0.727763	+	0.912586i	0.155160	+	0.194564i
$23$	−8.89988	+	1.34144i	−1.85575	+	0.279710i	−0.979395	−	0.201952i	$-0.935271\pi$
$23$	−8.89988	+	1.34144i	−1.85575	+	0.279710i	−0.876357	+	0.481662i	$0.840033\pi$
$24$		0			0
$25$	−3.98629	−	2.71780i	−0.797257	−	0.543561i
$26$	7.08179	−	1.06741i	1.38885	−	0.209336i
$27$		0			0
$28$	2.01232	+	4.88382i	0.380293	+	0.922956i
$29$	2.11419	−	2.65111i	0.392595	−	0.492299i	−0.545775	−	0.837932i	$-0.683765\pi$
$29$	2.11419	−	2.65111i	0.392595	−	0.492299i	0.938370	+	0.345633i	$0.112336\pi$
$30$		0			0
$31$	−3.57740	−	6.19624i	−0.642521	−	1.11288i	−0.984868	−	0.173305i	$-0.944555\pi$
$31$	−3.57740	−	6.19624i	−0.642521	−	1.11288i	0.342348	−	0.939573i	$-0.388778\pi$
$32$	−7.90713	−	1.19181i	−1.39780	−	0.210684i
$33$		0			0
$34$	−0.943723	+	0.454473i	−0.161847	+	0.0779415i
$35$	−0.990037	+	0.497487i	−0.167347	+	0.0840907i
$36$		0			0
$37$	1.29416	+	3.29747i	0.212759	+	0.542100i	0.996917	−	0.0784602i	$-0.0250003\pi$
$37$	1.29416	+	3.29747i	0.212759	+	0.542100i	−0.784159	+	0.620561i	$0.786905\pi$
$38$	−0.180174	−	2.40425i	−0.0292281	−	0.390022i
$39$		0			0
$40$	0.000221045	−	0.00294963i	3.49502e−5	−	0.000466378i
$41$	−0.789835	−	3.46050i	−0.123352	−	0.540439i	−0.998407	−	0.0564164i	$-0.982033\pi$
$41$	−0.789835	−	3.46050i	−0.123352	−	0.540439i	0.875056	−	0.484022i	$-0.160825\pi$
$42$		0			0
$43$	1.23768	−	5.42262i	0.188744	−	0.826941i	−0.788536	−	0.614989i	$-0.789161\pi$
$43$	1.23768	−	5.42262i	0.188744	−	0.826941i	0.977280	−	0.211953i	$-0.0679823\pi$
$44$	−1.11391	−	0.343595i	−0.167928	−	0.0517988i
$45$		0			0
$46$	13.1897	−	12.2383i	1.94471	−	1.80443i
$47$	4.74838	−	3.23739i	0.692623	−	0.472222i	−0.165139	−	0.986270i	$-0.552807\pi$
$47$	4.74838	−	3.23739i	0.692623	−	0.472222i	0.857761	+	0.514048i	$0.171855\pi$
$48$		0			0
$49$	0.287736	−	6.99408i	0.0411051	−	0.999155i
$50$	9.64498			1.36401
$51$		0			0
$52$	−5.24300	+	4.86480i	−0.727074	+	0.674626i
$53$	1.18402	−	3.01682i	0.162637	−	0.414392i	−0.826203	−	0.563372i	$-0.809504\pi$
$53$	1.18402	−	3.01682i	0.162637	−	0.414392i	0.988840	+	0.148980i	$0.0475990\pi$
$54$		0			0
$55$	0.0544107	−	0.238389i	0.00733674	−	0.0321444i
$56$	0.0156151	+	0.0102653i	0.00208666	+	0.00137176i
$57$		0			0
$58$	−0.506580	+	6.75984i	−0.0665172	+	0.887611i
$59$	−8.24358	+	2.54281i	−1.07322	+	0.331045i	−0.780503	−	0.625153i	$-0.785037\pi$
$59$	−8.24358	+	2.54281i	−1.07322	+	0.331045i	−0.292721	+	0.956198i	$0.594561\pi$
$60$		0			0
$61$	2.07940	+	5.29823i	0.266240	+	0.678368i	0.999999	−	0.00104096i	$-0.000331349\pi$
$61$	2.07940	+	5.29823i	0.266240	+	0.678368i	−0.733760	+	0.679409i	$0.762236\pi$
$62$	12.8868	+	6.20597i	1.63663	+	0.788159i
$63$		0			0
$64$	7.18226	−	3.45880i	0.897783	−	0.432349i
$65$	−1.09979	−	1.02045i	−0.136412	−	0.126572i
$66$		0			0
$67$	−3.72619	−	6.45396i	−0.455227	−	0.788476i	0.543474	−	0.839426i	$-0.317109\pi$
$67$	−3.72619	−	6.45396i	−0.455227	−	0.788476i	−0.998701	+	0.0509495i	$0.983775\pi$
$68$	0.523033	−	0.905919i	0.0634270	−	0.109859i
$69$		0			0
$70$	1.07505	−	1.93665i	0.128493	−	0.231473i
$71$	5.36805	+	6.73132i	0.637070	+	0.798860i	0.990633	−	0.136550i	$-0.0436015\pi$
$71$	5.36805	+	6.73132i	0.637070	+	0.798860i	−0.353563	+	0.935411i	$0.615030\pi$
$72$		0			0
$73$	−10.4454	−	7.12155i	−1.22254	−	0.833515i	−0.232269	−	0.972652i	$-0.574615\pi$
$73$	−10.4454	−	7.12155i	−1.22254	−	0.833515i	−0.990273	+	0.139137i	$0.955567\pi$
$74$	−5.85105	−	3.98918i	−0.680170	−	0.463732i
$75$		0			0
$76$	1.50124	+	1.88249i	0.172204	+	0.215937i
$77$	1.14995	+	1.03151i	0.131049	+	0.117551i
$78$		0			0
$79$	−4.12595	+	7.14636i	−0.464206	+	0.804028i	−0.999165	−	0.0408494i	$-0.986994\pi$
$79$	−4.12595	+	7.14636i	−0.464206	+	0.804028i	0.534959	+	0.844878i	$0.320327\pi$
$80$	0.839047	+	1.45327i	0.0938083	+	0.162481i
$81$		0			0
$82$	5.20162	+	4.82640i	0.574423	+	0.532986i
$83$	−15.5836	+	7.50467i	−1.71052	+	0.823745i	−0.718821	+	0.695196i	$0.755318\pi$
$83$	−15.5836	+	7.50467i	−1.71052	+	0.823745i	−0.991703	+	0.128549i	$0.958968\pi$
$84$		0			0
$85$	0.197696	+	0.0952053i	0.0214431	+	0.0103265i
$86$	4.06231	+	10.3506i	0.438050	+	1.11613i
$87$		0			0
$88$	−0.00394076	+	0.00121556i	−0.000420086	+	0.000129579i
$89$	0.281727	−	3.75938i	0.0298630	−	0.398494i	−0.962164	−	0.272470i	$-0.912159\pi$
$89$	0.281727	−	3.75938i	0.0298630	−	0.398494i	0.992027	−	0.126024i	$-0.0402216\pi$
$90$		0			0
$91$	9.00891	−	2.94592i	0.944390	−	0.308817i
$92$	−3.99848	+	17.5185i	−0.416870	+	1.82643i
$93$		0			0
$94$	−4.19736	+	10.6947i	−0.432925	+	1.10307i
$95$	−0.370241	+	0.343533i	−0.0379859	+	0.0352458i
$96$		0			0
$97$	−5.47393			−0.555793			−0.277896	−	0.960611i	$-0.589637\pi$
$97$	−5.47393			−0.555793			−0.277896	+	0.960611i	$0.589637\pi$
$98$	7.40107	+	11.8765i	0.747621	+	1.19971i
$99$		0			0
$100$	−7.95849	+	5.42601i	−0.795849	+	0.542601i
$101$	3.44967	−	3.20082i	0.343255	−	0.318494i	−0.489641	−	0.871924i	$-0.662872\pi$
$101$	3.44967	−	3.20082i	0.343255	−	0.318494i	0.832895	+	0.553431i	$0.186682\pi$
$102$		0			0
$103$	16.5324	+	5.09958i	1.62899	+	0.502477i	0.968637	−	0.248479i	$-0.0799306\pi$
$103$	16.5324	+	5.09958i	1.62899	+	0.502477i	0.660353	+	0.750956i	$0.270407\pi$
$104$	−0.00563050	+	0.0246689i	−0.000552116	+	0.00241898i
$105$		0			0
$106$	1.44168	+	6.31640i	0.140028	+	0.613503i
$107$	−1.20419	+	16.0688i	−0.116414	+	1.55343i	0.567194	+	0.823584i	$0.308029\pi$
$107$	−1.20419	+	16.0688i	−0.116414	+	1.55343i	−0.683608	+	0.729850i	$0.739590\pi$
$108$		0			0
$109$	1.22963	+	16.4083i	0.117777	+	1.57163i	0.672821	+	0.739805i	$0.265082\pi$
$109$	1.22963	+	16.4083i	0.117777	+	1.57163i	−0.555044	+	0.831821i	$0.687298\pi$
$110$	0.178587	+	0.455033i	0.0170276	+	0.0433857i
$111$		0			0
$112$	−10.6002	+	0.178540i	−1.00162	+	0.0168705i
$113$	−12.4836	+	6.01178i	−1.17436	+	0.565541i	−0.916262	−	0.400579i	$-0.868809\pi$
$113$	−12.4836	+	6.01178i	−1.17436	+	0.565541i	−0.258095	+	0.966120i	$0.583095\pi$
$114$		0			0
$115$	−3.72713	−	0.561775i	−0.347557	−	0.0523858i
$116$	−3.38491	−	5.86283i	−0.314281	−	0.544350i
$117$		0			0
$118$	10.7528	−	13.4835i	0.989871	−	1.24126i
$119$	−1.13207	+	0.800088i	−0.103777	+	0.0733440i
$120$		0			0
$121$	10.5400	−	1.58865i	0.958185	−	0.144423i
$122$	−9.40120	−	6.40963i	−0.851145	−	0.580301i
$123$		0			0
$124$	−14.1248	+	2.12897i	−1.26844	+	0.191187i
$125$	−2.56529	−	3.21677i	−0.229446	−	0.287717i
$126$		0			0
$127$	−10.1131	+	12.6814i	−0.897391	+	1.12529i	0.0941573	+	0.995557i	$0.469984\pi$
$127$	−10.1131	+	12.6814i	−0.897391	+	1.12529i	−0.991549	+	0.129736i	$0.958587\pi$
$128$	0.0282522	−	0.0489343i	0.00249717	−	0.00432522i
$129$		0			0
$130$	2.96575	+	0.447015i	0.260113	+	0.0392058i
$131$	−13.6159	−	12.6337i	−1.18962	−	1.10381i	−0.992350	−	0.123460i	$-0.960601\pi$
$131$	−13.6159	−	12.6337i	−1.18962	−	1.10381i	−0.197273	−	0.980349i	$-0.563209\pi$
$132$		0			0
$133$	−0.762321	−	3.09846i	−0.0661016	−	0.268670i
$134$	13.4228	+	6.46408i	1.15955	+	0.558412i
$135$		0			0
$136$	−0.000276557	−	0.00369040i	−2.37146e−5	−	0.000316449i
$137$	17.4439	−	5.38073i	1.49033	−	0.459707i	0.560645	−	0.828056i	$-0.310553\pi$
$137$	17.4439	−	5.38073i	1.49033	−	0.459707i	0.929687	+	0.368350i	$0.120077\pi$
$138$		0			0
$139$	4.63783	+	20.3197i	0.393376	+	1.72349i	0.652624	+	0.757682i	$0.273668\pi$
$139$	4.63783	+	20.3197i	0.393376	+	1.72349i	−0.259249	+	0.965811i	$0.583475\pi$
$140$	0.202435	+	2.20281i	0.0171089	+	0.186171i
$141$		0			0
$142$	−16.4471	−	5.07325i	−1.38021	−	0.425738i
$143$	−0.764195	+	1.94714i	−0.0639052	+	0.162828i
$144$		0			0
$145$	1.17331	−	0.799946i	0.0974377	−	0.0664319i
$146$	25.2730			2.09161
$147$		0			0
$148$	7.07216			0.581328
$149$	8.21075	−	5.59799i	0.672651	−	0.458606i	−0.178213	−	0.983992i	$-0.557032\pi$
$149$	8.21075	−	5.59799i	0.672651	−	0.458606i	0.850864	+	0.525386i	$0.176079\pi$
$150$		0			0
$151$	−3.37853	+	8.60837i	−0.274941	+	0.700539i	0.724989	+	0.688760i	$0.241845\pi$
$151$	−3.37853	+	8.60837i	−0.274941	+	0.700539i	−0.999931	+	0.0117789i	$0.996251\pi$
$152$	0.00813983	+	0.00251081i	0.000660227	+	0.000203653i
$153$		0			0
$154$	−3.06106	−	0.408784i	−0.246667	−	0.0329408i
$155$	−0.666745	−	2.92120i	−0.0535543	−	0.234637i
$156$		0			0
$157$	−12.2928	+	3.79182i	−0.981070	+	0.302620i	−0.743489	−	0.668748i	$-0.766831\pi$
$157$	−12.2928	+	3.79182i	−0.981070	+	0.302620i	−0.237581	+	0.971368i	$0.576354\pi$
$158$	−1.23279	−	16.4504i	−0.0980753	−	1.30872i
$159$		0			0
$160$	−3.01716	−	1.45299i	−0.238527	−	0.114869i
$161$	14.5314	−	18.8650i	1.14524	−	1.48677i
$162$		0			0
$163$	0.383636	+	0.355962i	0.0300487	+	0.0278811i	0.695054	−	0.718957i	$-0.255380\pi$
$163$	0.383636	+	0.355962i	0.0300487	+	0.0278811i	−0.665006	+	0.746838i	$0.731571\pi$
$164$	−7.00729	−	1.05618i	−0.547177	−	0.0824737i
$165$		0			0
$166$	17.2889	−	29.9452i	1.34188	−	2.32420i
$167$	−1.29705	+	1.62644i	−0.100368	+	0.125858i	−0.829479	−	0.558538i	$-0.811363\pi$
$167$	−1.29705	+	1.62644i	−0.100368	+	0.125858i	0.729111	+	0.684396i	$0.239934\pi$
$168$		0			0
$169$	−0.103417	−	0.129681i	−0.00795518	−	0.00997548i
$170$	−0.433758	+	0.0653786i	−0.0332677	+	0.00501431i
$171$		0			0
$172$	−9.17496	−	6.25538i	−0.699584	−	0.476968i
$173$	−3.69219	+	0.556508i	−0.280712	+	0.0423105i	−0.287889	−	0.957664i	$-0.592953\pi$
$173$	−3.69219	+	0.556508i	−0.280712	+	0.0423105i	0.00717723	+	0.999974i	$0.497715\pi$
$174$		0			0
$175$	12.5883	−	2.11478i	0.951589	−	0.159863i
$176$	1.45874	−	1.82920i	0.109956	−	0.137881i
$177$		0			0
$178$	3.76826	+	6.52682i	0.282443	+	0.489206i
$179$	1.37222	+	0.206829i	0.102565	+	0.0154591i	0.200124	−	0.979771i	$-0.435865\pi$
$179$	1.37222	+	0.206829i	0.102565	+	0.0154591i	−0.0975594	+	0.995230i	$0.531104\pi$
$180$		0			0
$181$	5.74938	−	2.76876i	0.427348	−	0.205800i	−0.207831	−	0.978165i	$-0.566640\pi$
$181$	5.74938	−	2.76876i	0.427348	−	0.205800i	0.635179	+	0.772365i	$0.280926\pi$
$182$	−11.5629	+	15.0112i	−0.857100	+	1.11271i
$183$		0			0
$184$	0.0232249	+	0.0591761i	0.00171216	+	0.00436252i
$185$	0.110860	+	1.47933i	0.00815062	+	0.108762i
$186$		0			0
$187$	0.0228620	−	0.305073i	0.00167184	−	0.0223091i
$188$	−2.55313	−	11.1860i	−0.186206	−	0.815822i
$189$		0			0
$190$	0.224677	−	0.984374i	0.0162998	−	0.0714140i
$191$	−4.10943	−	1.26759i	−0.297348	−	0.0917198i	0.142492	−	0.989796i	$-0.454489\pi$
$191$	−4.10943	−	1.26759i	−0.297348	−	0.0917198i	−0.439840	+	0.898076i	$0.644965\pi$
$192$		0			0
$193$	−0.668928	+	0.620675i	−0.0481505	+	0.0446772i	−0.703881	−	0.710318i	$-0.748551\pi$
$193$	−0.668928	+	0.620675i	−0.0481505	+	0.0446772i	0.655731	+	0.754995i	$0.272361\pi$
$194$	9.04154	−	6.16442i	0.649145	−	0.442580i
$195$		0			0
$196$	−12.7883	−	5.63617i	−0.913453	−	0.402584i
$197$	1.21408			0.0864996			0.0432498	−	0.999064i	$-0.486229\pi$
$197$	1.21408			0.0864996			0.0432498	+	0.999064i	$0.486229\pi$
$198$		0			0
$199$	19.7202	−	18.2976i	1.39793	−	1.29709i	0.493957	−	0.869486i	$-0.335550\pi$
$199$	19.7202	−	18.2976i	1.39793	−	1.29709i	0.903969	−	0.427599i	$-0.140640\pi$
$200$	−0.0124496	+	0.0317210i	−0.000880318	+	0.00224301i
$201$		0			0
$202$	−2.09340	+	9.17176i	−0.147291	+	0.645323i
$203$	0.821007	+	8.93382i	0.0576234	+	0.627031i
$204$		0			0
$205$	0.111084	−	1.48232i	0.00775846	−	0.103529i
$206$	−33.0503	+	10.1947i	−2.30272	+	0.710296i
$207$		0			0
$208$	−5.24453	−	13.3629i	−0.363643	−	0.926547i
$209$	0.634440	+	0.305530i	0.0438852	+	0.0211340i
$210$		0			0
$211$	7.35971	−	3.54425i	0.506663	−	0.243996i	−0.163048	−	0.986618i	$-0.552132\pi$
$211$	7.35971	−	3.54425i	0.506663	−	0.243996i	0.669711	+	0.742622i	$0.266418\pi$
$212$	−4.74303	−	4.40089i	−0.325753	−	0.302254i
$213$		0			0
$214$	−16.1068	−	27.8978i	−1.10104	−	1.90705i
$215$	1.16466	−	2.01724i	0.0794289	−	0.137575i
$216$		0			0
$217$	18.1802	+	5.27425i	1.23416	+	0.358039i
$218$	−20.5091	−	25.7176i	−1.38905	−	1.74181i
$219$		0			0
$220$	−0.403349	−	0.274999i	−0.0271938	−	0.0185404i
$221$	−1.55091	−	1.05739i	−0.104325	−	0.0711277i
$222$		0			0
$223$	−0.739572	−	0.927394i	−0.0495254	−	0.0621029i	0.756452	−	0.654049i	$-0.226931\pi$
$223$	−0.739572	−	0.927394i	−0.0495254	−	0.0621029i	−0.805977	+	0.591946i	$0.798360\pi$
$224$	17.2772	−	12.2106i	1.15438	−	0.815857i
$225$		0			0
$226$	13.8496	−	23.9882i	0.921263	−	1.59567i
$227$	−6.74190	−	11.6773i	−0.447475	−	0.775050i	0.550746	−	0.834673i	$-0.314343\pi$
$227$	−6.74190	−	11.6773i	−0.447475	−	0.775050i	−0.998221	+	0.0596230i	$0.981010\pi$
$228$		0			0
$229$	−15.9196	−	14.7712i	−1.05200	−	0.976110i	−0.0522496	−	0.998634i	$-0.516639\pi$
$229$	−15.9196	−	14.7712i	−1.05200	−	0.976110i	−0.999746	+	0.0225245i	$0.992830\pi$
$230$	6.78893	−	3.26937i	0.447648	−	0.215576i
$231$		0			0
$232$	−0.0215783	−	0.0103916i	−0.00141669	−	0.000682240i
$233$	6.91890	+	17.6291i	0.453272	+	1.15492i	0.956750	+	0.290911i	$0.0939584\pi$
$233$	6.91890	+	17.6291i	0.453272	+	1.15492i	−0.503478	+	0.864008i	$0.667946\pi$
$234$		0			0
$235$	2.29983	−	0.709402i	0.150024	−	0.0462763i
$236$	−1.28709	+	17.1751i	−0.0837826	+	1.11800i
$237$		0			0
$238$	0.968882	−	2.59642i	0.0628033	−	0.168301i
$239$	−4.80624	+	21.0575i	−0.310890	+	1.36210i	0.542163	+	0.840273i	$0.317605\pi$
$239$	−4.80624	+	21.0575i	−0.310890	+	1.36210i	−0.853053	+	0.521824i	$0.825252\pi$
$240$		0			0
$241$	3.93690	−	10.0311i	0.253598	−	0.646157i	−0.746211	−	0.665710i	$-0.768129\pi$
$241$	3.93690	−	10.0311i	0.253598	−	0.646157i	0.999809	+	0.0195526i	$0.00622417\pi$
$242$	−15.6204	+	14.4936i	−1.00412	+	0.931686i
$243$		0			0
$244$	11.3632			0.727456
$245$	0.978489	−	2.76337i	0.0625134	−	0.176545i
$246$		0			0
$247$	3.56983	−	2.43387i	0.227143	−	0.154863i
$248$	−0.0370447	+	0.0343724i	−0.00235234	+	0.00218265i
$249$		0			0
$250$	7.85975	+	2.42441i	0.497094	+	0.153333i
$251$	5.60284	−	24.5476i	0.353648	−	1.54943i	−0.415037	−	0.909805i	$-0.636231\pi$
$251$	5.60284	−	24.5476i	0.353648	−	1.54943i	0.768685	−	0.639628i	$-0.220912\pi$
$252$		0			0
$253$	1.16938	+	5.12339i	0.0735183	+	0.322105i
$254$	2.42319	−	32.3353i	0.152045	−	2.02889i
$255$		0			0
$256$	1.19989	+	16.0115i	0.0749934	+	1.00072i
$257$	1.38263	+	3.52288i	0.0862459	+	0.219751i	0.967489	−	0.252912i	$-0.0813882\pi$
$257$	1.38263	+	3.52288i	0.0862459	+	0.219751i	−0.881243	+	0.472663i	$0.843293\pi$
$258$		0			0
$259$	−8.51129	−	3.92364i	−0.528866	−	0.243803i
$260$	−2.69865	+	1.29960i	−0.167363	+	0.0805978i
$261$		0			0
$262$	36.7173	+	5.53424i	2.26840	+	0.341906i
$263$	8.93985	+	15.4843i	0.551255	+	0.954801i	0.998184	+	0.0602322i	$0.0191841\pi$
$263$	8.93985	+	15.4843i	0.551255	+	0.954801i	−0.446930	+	0.894569i	$0.647483\pi$
$264$		0			0
$265$	0.846212	−	1.06112i	0.0519824	−	0.0651839i
$266$	4.74847	+	4.25939i	0.291147	+	0.261160i
$267$		0			0
$268$	−14.7123	+	2.21752i	−0.898695	+	0.135456i
$269$	−12.0568	−	8.22018i	−0.735115	−	0.501193i	0.136953	−	0.990578i	$-0.456269\pi$
$269$	−12.0568	−	8.22018i	−0.735115	−	0.501193i	−0.872068	+	0.489384i	$0.837221\pi$
$270$		0			0
$271$	−27.9620	+	4.21460i	−1.69857	+	0.256018i	−0.925622	−	0.378449i	$-0.876457\pi$
$271$	−27.9620	+	4.21460i	−1.69857	+	0.256018i	−0.772949	+	0.634468i	$0.781219\pi$
$272$	1.30903	+	1.64148i	0.0793719	+	0.0995292i
$273$		0			0
$274$	−22.7534	+	28.5319i	−1.37459	+	1.72368i
$275$	−1.40850	+	2.43959i	−0.0849355	+	0.147113i
$276$		0			0
$277$	−8.02685	−	1.20985i	−0.482287	−	0.0726930i	−0.0966008	−	0.995323i	$-0.530797\pi$
$277$	−8.02685	−	1.20985i	−0.482287	−	0.0726930i	−0.385686	+	0.922630i	$0.626035\pi$
$278$	−30.5434	−	28.3401i	−1.83187	−	1.69973i
$279$		0			0
$280$	0.00498171	+	0.00603548i	0.000297714	+	0.000360689i
$281$	−11.4061	−	5.49288i	−0.680430	−	0.327678i	0.0615458	−	0.998104i	$-0.480397\pi$
$281$	−11.4061	−	5.49288i	−0.680430	−	0.327678i	−0.741976	+	0.670426i	$0.766111\pi$
$282$		0			0
$283$	−0.399686	−	5.33344i	−0.0237589	−	0.317040i	−0.996403	−	0.0847402i	$-0.972994\pi$
$283$	−0.399686	−	5.33344i	−0.0237589	−	0.317040i	0.972644	−	0.232300i	$-0.0746251\pi$
$284$	16.4253	−	5.06653i	0.974661	−	0.300643i
$285$		0			0
$286$	−0.930497	−	4.07677i	−0.0550214	−	0.241065i
$287$	7.84725	+	5.15875i	0.463209	+	0.304512i
$288$		0			0
$289$	−15.9824	−	4.92992i	−0.940141	−	0.289995i
$290$	−1.03715	+	2.64262i	−0.0609036	+	0.155180i
$291$		0			0
$292$	−20.8539	+	14.2179i	−1.22038	+	0.832042i
$293$	14.1680			0.827701			0.413850	−	0.910345i	$-0.364184\pi$
$293$	14.1680			0.827701			0.413850	+	0.910345i	$0.364184\pi$
$294$		0			0
$295$	−3.61280			−0.210345
$296$	0.0206723	−	0.0140941i	0.00120155	−	0.000819205i
$297$		0			0
$298$	−7.25795	+	18.4929i	−0.420442	+	1.07127i
$299$	30.8112	+	9.50401i	1.78186	+	0.549631i
$300$		0			0
$301$	7.57151	+	12.6186i	0.436414	+	0.727323i
$302$	−4.11376	−	18.0236i	−0.236720	−	1.03714i
$303$		0			0
$304$	−4.61793	+	1.42444i	−0.264856	+	0.0816974i
$305$	0.178126	+	2.37692i	0.0101994	+	0.136102i
$306$		0			0
$307$	−11.8233	−	5.69379i	−0.674789	−	0.324961i	0.0649175	−	0.997891i	$-0.479322\pi$
$307$	−11.8233	−	5.69379i	−0.674789	−	0.324961i	−0.739707	+	0.672929i	$0.765036\pi$
$308$	2.75578	−	1.38476i	0.157025	−	0.0789042i
$309$		0			0
$310$	4.39098	+	4.07424i	0.249391	+	0.231401i
$311$	27.9145	+	4.20743i	1.58289	+	0.238582i	0.880792	−	0.473503i	$-0.157011\pi$
$311$	27.9145	+	4.20743i	1.58289	+	0.238582i	0.702093	+	0.712085i	$0.252249\pi$
$312$		0			0
$313$	11.7846	−	20.4115i	0.666104	−	1.15373i	−0.312880	−	0.949793i	$-0.601294\pi$
$313$	11.7846	−	20.4115i	0.666104	−	1.15373i	0.978985	−	0.203934i	$-0.0653728\pi$
$314$	16.0344	−	20.1065i	0.904875	−	1.13468i
$315$		0			0
$316$	10.2718	+	12.8804i	0.577833	+	0.724580i
$317$	−18.4215	+	2.77660i	−1.03466	+	0.155949i	−0.644346	−	0.764734i	$-0.722870\pi$
$317$	−18.4215	+	2.77660i	−1.03466	+	0.155949i	−0.390310	+	0.920684i	$0.627632\pi$
$318$		0			0
$319$	−1.63585	−	1.11530i	−0.0915898	−	0.0624449i
$320$	3.30115	−	0.497568i	0.184540	−	0.0278149i
$321$		0			0
$322$	−2.75754	+	47.5247i	−0.153672	+	2.64845i
$323$	−0.393989	+	0.494047i	−0.0219221	+	0.0274895i
$324$		0			0
$325$	8.64204	+	14.9685i	0.479374	+	0.830300i
$326$	−1.03453	−	0.155931i	−0.0572976	−	0.00863622i
$327$		0			0
$328$	−0.0225875	+	0.0108776i	−0.00124719	+	0.000600614i
$329$	−3.13333	+	14.8787i	−0.172746	+	0.820292i
$330$		0			0
$331$	0.833154	+	2.12284i	0.0457943	+	0.116682i	0.951941	−	0.306282i	$-0.0990850\pi$
$331$	0.833154	+	2.12284i	0.0457943	+	0.116682i	−0.906147	+	0.422964i	$0.860990\pi$
$332$	2.58057	+	34.4353i	0.141627	+	1.88988i
$333$		0			0
$334$	0.310785	−	4.14714i	0.0170054	−	0.226921i
$335$	−0.694476	−	3.04270i	−0.0379433	−	0.166240i
$336$		0			0
$337$	1.46979	−	6.43956i	0.0800644	−	0.350785i	−0.918989	−	0.394283i	$-0.870993\pi$
$337$	1.46979	−	6.43956i	0.0800644	−	0.350785i	0.999054	+	0.0434979i	$0.0138502\pi$
$338$	0.316859	+	0.0977380i	0.0172349	+	0.00531625i
$339$		0			0
$340$	0.321133	−	0.297968i	0.0174159	−	0.0161596i
$341$	−3.45165	+	2.35329i	−0.186917	+	0.127438i
$342$		0			0
$343$	12.2637	+	13.8781i	0.662179	+	0.749346i
$344$	−0.0392853			−0.00211812
$345$		0			0
$346$	5.47186	−	5.07714i	0.294169	−	0.272949i
$347$	−7.92772	+	20.1995i	−0.425582	+	1.08437i	0.543888	+	0.839158i	$0.316952\pi$
$347$	−7.92772	+	20.1995i	−0.425582	+	1.08437i	−0.969470	+	0.245208i	$0.921144\pi$
$348$		0			0
$349$	−1.67770	+	7.35046i	−0.0898050	+	0.393461i	−0.999775	−	0.0212128i	$-0.993247\pi$
$349$	−1.67770	+	7.35046i	−0.0898050	+	0.393461i	0.909970	+	0.414674i	$0.136104\pi$
$350$	−18.4112	+	17.6694i	−0.984121	+	0.944467i
$351$		0			0
$352$	−0.348911	+	4.65590i	−0.0185970	+	0.248160i
$353$	31.7205	−	9.78446i	1.68831	−	0.520774i	0.706028	−	0.708184i	$-0.250485\pi$
$353$	31.7205	−	9.78446i	1.68831	−	0.520774i	0.982282	+	0.187410i	$0.0600092\pi$
$354$		0			0
$355$	1.31728	+	3.35636i	0.0699137	+	0.178137i
$356$	−6.78117	−	3.26564i	−0.359401	−	0.173079i
$357$		0			0
$358$	−2.49948	+	1.20369i	−0.132102	+	0.0636168i
$359$	−1.15137	−	1.06832i	−0.0607671	−	0.0563837i	0.649205	−	0.760614i	$-0.275102\pi$
$359$	−1.15137	−	1.06832i	−0.0607671	−	0.0563837i	−0.709972	+	0.704230i	$0.751292\pi$
$360$		0			0
$361$	8.77274	+	15.1948i	0.461723	+	0.799728i
$362$	−6.37852	+	11.0479i	−0.335247	+	0.580666i
$363$		0			0
$364$	1.09614	−	18.8914i	0.0574534	−	0.990179i
$365$	−3.30096	−	4.13927i	−0.172780	−	0.216659i
$366$		0			0
$367$	7.75356	+	5.28629i	0.404733	+	0.275942i	0.748529	−	0.663102i	$-0.230761\pi$
$367$	7.75356	+	5.28629i	0.404733	+	0.275942i	−0.343796	+	0.939044i	$0.611713\pi$
$368$	−29.7984	−	20.3162i	−1.55335	−	1.05905i
$369$		0			0
$370$	−1.84905	−	2.31863i	−0.0961275	−	0.120540i
$371$	3.26658	+	7.92787i	0.169593	+	0.411595i
$372$		0			0
$373$	11.2138	−	19.4229i	0.580630	−	1.00568i	−0.414774	−	0.909924i	$-0.636140\pi$
$373$	11.2138	−	19.4229i	0.580630	−	1.00568i	0.995405	−	0.0957569i	$-0.0305271\pi$
$374$	0.305793	+	0.529649i	0.0158122	+	0.0273875i
$375$		0			0
$376$	−0.0297555	−	0.0276091i	−0.00153453	−	0.00142383i
$377$	−10.9448	+	5.27073i	−0.563685	+	0.271457i
$378$		0			0
$379$	−13.6377	−	6.56755i	−0.700520	−	0.337353i	0.0494944	−	0.998774i	$-0.484239\pi$
$379$	−13.6377	−	6.56755i	−0.700520	−	0.337353i	−0.750014	+	0.661422i	$0.769953\pi$
$380$	0.368392	+	0.938647i	0.0188981	+	0.0481516i
$381$		0			0
$382$	8.21524	−	2.53407i	0.420328	−	0.129654i
$383$	−1.11199	+	14.8385i	−0.0568203	+	0.758214i	0.893920	+	0.448226i	$0.147944\pi$
$383$	−1.11199	+	14.8385i	−0.0568203	+	0.758214i	−0.950740	+	0.309988i	$0.899675\pi$
$384$		0			0
$385$	0.332859	+	0.554738i	0.0169640	+	0.0282721i
$386$	0.405933	−	1.77851i	0.0206614	−	0.0905236i
$387$		0			0
$388$	−3.99263	+	10.1731i	−0.202695	+	0.516459i
$389$	20.9613	−	19.4492i	1.06278	−	0.986116i	0.0628509	−	0.998023i	$-0.479981\pi$
$389$	20.9613	−	19.4492i	1.06278	−	0.986116i	0.999929	+	0.0119072i	$0.00379026\pi$
$390$		0			0
$391$	−4.71584			−0.238490
$392$	−0.0486133	+	0.00901112i	−0.00245534	+	0.000455130i
$393$		0			0
$394$	−2.00535	+	1.36723i	−0.101028	+	0.0688798i
$395$	−2.53326	+	2.35052i	−0.127462	+	0.118268i
$396$		0			0
$397$	24.6672	+	7.60883i	1.23801	+	0.381876i	0.843557	−	0.537039i	$-0.180457\pi$
$397$	24.6672	+	7.60883i	1.23801	+	0.381876i	0.394455	+	0.918915i	$0.370934\pi$
$398$	−11.9670	+	52.4308i	−0.599851	+	2.62812i
$399$		0			0
$400$	−4.30189	−	18.8478i	−0.215094	−	0.942390i
$401$	−0.825390	+	11.0141i	−0.0412180	+	0.550016i	0.937924	+	0.346840i	$0.112745\pi$
$401$	−0.825390	+	11.0141i	−0.0412180	+	0.550016i	−0.979142	+	0.203176i	$0.934874\pi$
$402$		0			0
$403$	1.91548	+	25.5603i	0.0954167	+	1.27325i
$404$	−3.43244	−	8.74571i	−0.170770	−	0.435115i
$405$		0			0
$406$	−11.4169	−	13.8318i	−0.566609	−	0.686463i
$407$	1.86347	−	0.897400i	0.0923687	−	0.0444824i
$408$		0			0
$409$	−12.6415	−	1.90540i	−0.625083	−	0.0942161i	−0.171140	−	0.985247i	$-0.554745\pi$
$409$	−12.6415	−	1.90540i	−0.625083	−	0.0942161i	−0.453943	+	0.891031i	$0.649983\pi$
$410$	1.48582	+	2.57351i	0.0733792	+	0.127097i
$411$		0			0
$412$	21.5360	−	27.0053i	1.06100	−	1.33045i
$413$	11.0777	−	19.9560i	0.545100	−	0.981970i
$414$		0			0
$415$	−7.16261	+	1.07959i	−0.351599	+	0.0529950i
$416$	23.6693	+	16.1375i	1.16048	+	0.791204i
$417$		0			0
$418$	−1.39201	+	0.209811i	−0.0680853	+	0.0102622i
$419$	−11.3849	−	14.2763i	−0.556191	−	0.697442i	0.421657	−	0.906755i	$-0.361448\pi$
$419$	−11.3849	−	14.2763i	−0.556191	−	0.697442i	−0.977849	+	0.209314i	$0.932877\pi$
$420$		0			0
$421$	0.239758	−	0.300647i	0.0116851	−	0.0146526i	−0.775955	−	0.630789i	$-0.782731\pi$
$421$	0.239758	−	0.300647i	0.0116851	−	0.0146526i	0.787640	+	0.616136i	$0.211303\pi$
$422$	−8.16505	+	14.1423i	−0.397468	+	0.688436i
$423$		0			0
$424$	−0.0226347	−	0.00341163i	−0.00109924	−	0.000165683i
$425$	−1.85308	−	1.71941i	−0.0898876	−	0.0834035i
$426$		0			0
$427$	−13.6756	−	6.30433i	−0.661807	−	0.305088i
$428$	28.9850	+	13.9584i	1.40104	+	0.674706i
$429$		0			0
$430$	0.347985	+	4.64354i	0.0167814	+	0.223932i
$431$	−28.4440	+	8.77380i	−1.37010	+	0.422619i	−0.890546	−	0.454894i	$-0.849677\pi$
$431$	−28.4440	+	8.77380i	−1.37010	+	0.422619i	−0.479552	+	0.877513i	$0.659201\pi$
$432$		0			0
$433$	−3.85588	−	16.8937i	−0.185302	−	0.811861i	−0.979051	−	0.203615i	$-0.934731\pi$
$433$	−3.85588	−	16.8937i	−0.185302	−	0.811861i	0.793749	−	0.608245i	$-0.208126\pi$
$434$	−35.9687	+	11.7618i	−1.72655	+	0.564585i
$435$		0			0
$436$	31.3910	+	9.68283i	1.50335	+	0.463723i
$437$	3.96569	−	10.1044i	0.189705	−	0.483360i
$438$		0			0
$439$	−14.8937	+	10.1544i	−0.710837	+	0.484641i	−0.863956	−	0.503567i	$-0.832021\pi$
$439$	−14.8937	+	10.1544i	−0.710837	+	0.484641i	0.153119	+	0.988208i	$0.451068\pi$
$440$	−0.00172706			−8.23343e−5
$441$		0			0
$442$	3.75248			0.178487
$443$	20.1455	−	13.7349i	0.957140	−	0.652567i	0.0193657	−	0.999812i	$-0.493835\pi$
$443$	20.1455	−	13.7349i	0.957140	−	0.652567i	0.937774	+	0.347246i	$0.112883\pi$
$444$		0			0
$445$	0.576796	−	1.46965i	0.0273428	−	0.0696682i
$446$	2.26596	+	0.698958i	0.107297	+	0.0330966i
$447$		0			0
$448$	−7.37374	+	19.7602i	−0.348376	+	0.933581i
$449$	2.64558	+	11.5910i	0.124853	+	0.547015i	0.998203	+	0.0599225i	$0.0190854\pi$
$449$	2.64558	+	11.5910i	0.124853	+	0.547015i	−0.873350	+	0.487092i	$0.838057\pi$
$450$		0			0
$451$	−1.98040	+	0.610872i	−0.0932532	+	0.0287648i
$452$	2.06722	+	27.5852i	0.0972340	+	1.29750i
$453$		0			0
$454$	24.2862	+	11.6956i	1.13981	+	0.548903i
$455$	3.96882	−	0.0668475i	0.186061	−	0.00313386i
$456$		0			0
$457$	−8.41461	−	7.80762i	−0.393619	−	0.365225i	0.458391	−	0.888751i	$-0.348426\pi$
$457$	−8.41461	−	7.80762i	−0.393619	−	0.365225i	−0.852010	+	0.523526i	$0.824616\pi$
$458$	42.9296	+	6.47060i	2.00597	+	0.302351i
$459$		0			0
$460$	−3.76258	+	6.51697i	−0.175431	+	0.303855i
$461$	4.37468	−	5.48567i	0.203749	−	0.255493i	−0.669450	−	0.742857i	$-0.733470\pi$
$461$	4.37468	−	5.48567i	0.203749	−	0.255493i	0.873199	+	0.487364i	$0.162042\pi$
$462$		0			0
$463$	−18.1164	−	22.7172i	−0.841938	−	1.05576i	−0.997688	−	0.0679609i	$-0.978351\pi$
$463$	−18.1164	−	22.7172i	−0.841938	−	1.05576i	0.155749	−	0.987797i	$-0.450221\pi$
$464$	13.4357	−	2.02511i	0.623739	−	0.0940135i
$465$		0			0
$466$	−31.2811	−	21.3271i	−1.44907	−	0.987960i
$467$	−5.31401	+	0.800959i	−0.245903	+	0.0370639i	−0.270837	−	0.962625i	$-0.587301\pi$
$467$	−5.31401	+	0.800959i	−0.245903	+	0.0370639i	0.0249341	+	0.999689i	$0.492062\pi$
$468$		0			0
$469$	18.9364	+	5.49361i	0.874401	+	0.253671i
$470$	−2.99984	+	3.76168i	−0.138372	+	0.173514i
$471$		0			0
$472$	0.0304660	+	0.0527687i	0.00140231	+	0.00242887i
$473$	−3.21130	−	0.484026i	−0.147656	−	0.0222555i
$474$		0			0
$475$	5.24241	−	2.52461i	0.240538	−	0.115837i
$476$	0.661208	+	2.68748i	0.0303064	+	0.123181i
$477$		0			0
$478$	−15.7751	−	40.1942i	−0.721535	−	1.83844i
$479$	−1.85770	−	24.7893i	−0.0848805	−	1.13265i	−0.863227	−	0.504816i	$-0.831560\pi$
$479$	−1.85770	−	24.7893i	−0.0848805	−	1.13265i	0.778346	−	0.627835i	$-0.216059\pi$
$480$		0			0
$481$	0.948350	−	12.6548i	0.0432410	−	0.577011i
$482$	4.79363	+	21.0023i	0.218344	+	0.956628i
$483$		0			0
$484$	4.73536	−	20.7470i	0.215244	−	0.943044i
$485$	−2.19055	−	0.675696i	−0.0994679	−	0.0306818i
$486$		0			0
$487$	−9.15953	+	8.49880i	−0.415058	+	0.385117i	−0.859876	−	0.510504i	$-0.829459\pi$
$487$	−9.15953	+	8.49880i	−0.415058	+	0.385117i	0.444818	+	0.895621i	$0.353268\pi$
$488$	0.0332153	−	0.0226458i	0.00150359	−	0.00102513i
$489$		0			0
$490$	1.49573	+	5.66631i	0.0675703	+	0.255978i
$491$	19.7440			0.891034			0.445517	−	0.895273i	$-0.353020\pi$
$491$	19.7440			0.891034			0.445517	+	0.895273i	$0.353020\pi$
$492$		0			0
$493$	1.30240	−	1.20845i	0.0586573	−	0.0544261i
$494$	−3.15557	+	8.04027i	−0.141976	+	0.361749i
$495$		0			0
$496$	6.37961	−	27.9509i	0.286453	−	1.25503i
$497$	−22.5786	−	3.01523i	−1.01279	−	0.135252i
$498$		0			0
$499$	−1.24138	+	16.5650i	−0.0555716	+	0.741552i	0.897925	+	0.440148i	$0.145074\pi$
$499$	−1.24138	+	16.5650i	−0.0555716	+	0.741552i	−0.953497	+	0.301403i	$0.902545\pi$
$500$	−7.84933	+	2.42120i	−0.351033	+	0.108279i
$501$		0			0
$502$	18.3897	+	46.8561i	0.820770	+	2.09129i
$503$	−22.0010	−	10.5951i	−0.980976	−	0.472413i	−0.126535	−	0.991962i	$-0.540386\pi$
$503$	−22.0010	−	10.5951i	−0.980976	−	0.472413i	−0.854441	+	0.519549i	$0.826100\pi$
$504$		0			0
$505$	1.77559	−	0.855080i	0.0790128	−	0.0380506i
$506$	−7.70118	−	7.14565i	−0.342359	−	0.317663i
$507$		0			0
$508$	16.1915	+	28.0445i	0.718381	+	1.24427i
$509$	0.896731	−	1.55318i	0.0397469	−	0.0688437i	−0.845468	−	0.534027i	$-0.820678\pi$
$509$	0.896731	−	1.55318i	0.0397469	−	0.0688437i	0.885215	+	0.465183i	$0.154012\pi$
$510$		0			0
$511$	32.9856	−	5.54144i	1.45920	−	0.245139i
$512$	−19.9427	−	25.0073i	−0.881350	−	1.10518i
$513$		0			0
$514$	−6.25101	−	4.26187i	−0.275720	−	0.187983i
$515$	5.98646	+	4.08150i	0.263795	+	0.179852i
$516$		0			0
$517$	−2.09215	−	2.62347i	−0.0920125	−	0.115380i
$518$	18.4771	−	3.10406i	0.811836	−	0.136385i
$519$		0			0
$520$	−0.00529831	+	0.00917695i	−0.000232346	+	0.000402436i
$521$	−11.9197	−	20.6456i	−0.522212	−	0.904498i	−0.999666	−	0.0258413i	$-0.991774\pi$
$521$	−11.9197	−	20.6456i	−0.522212	−	0.904498i	0.477454	−	0.878657i	$-0.341560\pi$
$522$		0			0
$523$	−8.39745	−	7.79169i	−0.367195	−	0.340707i	0.474897	−	0.880041i	$-0.342485\pi$
$523$	−8.39745	−	7.79169i	−0.367195	−	0.340707i	−0.842092	+	0.539335i	$0.818676\pi$
$524$	−33.4104	+	16.0896i	−1.45954	+	0.702878i
$525$		0			0
$526$	−32.2039	−	15.5086i	−1.40416	−	0.676206i
$527$	−1.36960	−	3.48968i	−0.0596606	−	0.152013i
$528$		0			0
$529$	55.4302	−	17.0979i	2.41001	−	0.743389i
$530$	−0.202761	+	2.70565i	−0.00880736	+	0.117526i
$531$		0			0
$532$	−6.31439	−	0.843246i	−0.273763	−	0.0365593i
$533$	−2.82957	+	12.3971i	−0.122562	+	0.536980i
$534$		0			0
$535$	−2.46542	+	6.28178i	−0.106589	+	0.271585i
$536$	−0.0385854	+	0.0358021i	−0.00166664	+	0.00154641i
$537$		0			0
$538$	29.1719			1.25769
$539$	−4.08483	+	0.137642i	−0.175946	+	0.00592866i
$540$		0			0
$541$	−7.83545	+	5.34212i	−0.336872	+	0.229676i	−0.719927	−	0.694050i	$-0.755825\pi$
$541$	−7.83545	+	5.34212i	−0.336872	+	0.229676i	0.383054	+	0.923726i	$0.374872\pi$
$542$	41.4400	−	38.4507i	1.78000	−	1.65160i
$543$		0			0
$544$	−4.00366	−	1.23497i	−0.171656	−	0.0529487i
$545$	−1.53335	+	6.71804i	−0.0656814	+	0.287769i
$546$		0			0
$547$	−2.12726	−	9.32014i	−0.0909552	−	0.398501i	0.908872	−	0.417074i	$-0.136945\pi$
$547$	−2.12726	−	9.32014i	−0.0909552	−	0.398501i	−0.999827	+	0.0185738i	$0.994087\pi$
$548$	2.72356	−	36.3434i	0.116345	−	1.55251i
$549$		0			0
$550$	−0.420842	−	5.61575i	−0.0179448	−	0.239456i
$551$	1.49407	+	3.80683i	0.0636496	+	0.162176i
$552$		0			0
$553$	−5.21596	−	21.2003i	−0.221805	−	0.901527i
$554$	14.6208	−	7.04100i	0.621178	−	0.299144i
$555$		0			0
$556$	41.1461	+	6.20177i	1.74498	+	0.263014i
$557$	−3.74059	−	6.47889i	−0.158494	−	0.274520i	0.775832	−	0.630940i	$-0.217330\pi$
$557$	−3.74059	−	6.47889i	−0.158494	−	0.274520i	−0.934326	+	0.356420i	$0.883997\pi$
$558$		0			0
$559$	−12.4236	+	15.5788i	−0.525464	+	0.658911i
$560$	−4.26401	−	1.23703i	−0.180187	−	0.0522739i
$561$		0			0
$562$	25.0258	−	3.77203i	1.05565	−	0.159113i
$563$	−6.86277	−	4.67896i	−0.289231	−	0.197195i	0.410009	−	0.912082i	$-0.365526\pi$
$563$	−6.86277	−	4.67896i	−0.289231	−	0.197195i	−0.699240	+	0.714887i	$0.746478\pi$
$564$		0			0
$565$	−5.73777	+	0.864829i	−0.241390	+	0.0363836i
$566$	6.66639	+	8.35939i	0.280209	+	0.351372i
$567$		0			0
$568$	0.0379149	−	0.0475437i	0.00159087	−	0.00199489i
$569$	15.4397	−	26.7424i	0.647267	−	1.12110i	−0.336506	−	0.941681i	$-0.609245\pi$
$569$	15.4397	−	26.7424i	0.647267	−	1.12110i	0.983773	−	0.179418i	$-0.0574216\pi$
$570$		0			0
$571$	−11.7144	−	1.76566i	−0.490231	−	0.0738905i	−0.100725	−	0.994914i	$-0.532116\pi$
$571$	−11.7144	−	1.76566i	−0.490231	−	0.0738905i	−0.389506	+	0.921024i	$0.627354\pi$
$572$	3.06128	+	2.84045i	0.127998	+	0.118765i
$573$		0			0
$574$	−18.7712	+	0.316165i	−0.783493	+	0.0131965i
$575$	39.1232	+	18.8408i	1.63155	+	0.785714i
$576$		0			0
$577$	−0.594509	−	7.93317i	−0.0247497	−	0.330262i	−0.995811	−	0.0914328i	$-0.970855\pi$
$577$	−0.594509	−	7.93317i	−0.0247497	−	0.330262i	0.971062	−	0.238829i	$-0.0767637\pi$
$578$	31.9507	−	9.85548i	1.32897	−	0.409934i
$579$		0			0
$580$	−0.630868	−	2.76401i	−0.0261954	−	0.114769i
$581$	15.9991	−	42.8744i	0.663753	−	1.77873i
$582$		0			0
$583$	−1.80820	−	0.557754i	−0.0748878	−	0.0230998i
$584$	−0.0326220	+	0.0831196i	−0.00134991	+	0.00343951i
$585$		0			0
$586$	−23.4019	+	15.9551i	−0.966723	+	0.659101i
$587$	−21.9680			−0.906715			−0.453358	−	0.891329i	$-0.649774\pi$
$587$	−21.9680			−0.906715			−0.453358	+	0.891329i	$0.649774\pi$
$588$		0			0
$589$	8.62892			0.355548
$590$	5.96743	−	4.06852i	0.245675	−	0.167498i
$591$		0			0
$592$	−5.18577	+	13.2131i	−0.213134	+	0.543056i
$593$	−19.8840	−	6.13341i	−0.816539	−	0.251869i	−0.141772	−	0.989899i	$-0.545280\pi$
$593$	−19.8840	−	6.13341i	−0.816539	−	0.251869i	−0.674768	+	0.738030i	$0.735756\pi$
$594$		0			0
$595$	−0.551794	+	0.180437i	−0.0226213	+	0.00739720i
$596$	−4.41479	−	19.3425i	−0.180837	−	0.792298i
$597$		0			0
$598$	−61.5952	+	18.9996i	−2.51882	+	0.776952i
$599$	2.73232	+	36.4602i	0.111639	+	1.48972i	0.718840	+	0.695176i	$0.244673\pi$
$599$	2.73232	+	36.4602i	0.111639	+	1.48972i	−0.607201	+	0.794549i	$0.707708\pi$
$600$		0			0
$601$	−22.2689	−	10.7242i	−0.908369	−	0.437448i	−0.0794648	−	0.996838i	$-0.525321\pi$
$601$	−22.2689	−	10.7242i	−0.908369	−	0.437448i	−0.828905	+	0.559390i	$0.811035\pi$
$602$	−26.7165	−	12.3161i	−1.08888	−	0.501967i
$603$		0			0
$604$	13.5340	+	12.5577i	0.550691	+	0.510967i
$605$	4.41401	+	0.665305i	0.179455	+	0.0270485i
$606$		0			0
$607$	4.14928	−	7.18677i	0.168414	−	0.291702i	−0.769448	−	0.638709i	$-0.779469\pi$
$607$	4.14928	−	7.18677i	0.168414	−	0.291702i	0.937862	+	0.347007i	$0.112802\pi$
$608$	6.01291	−	7.53995i	0.243856	−	0.305785i
$609$		0			0
$610$	−2.97097	−	3.72548i	−0.120291	−	0.150840i
$611$	−20.3585	+	3.06855i	−0.823616	+	0.124140i
$612$		0			0
$613$	7.70363	+	5.25224i	0.311147	+	0.212136i	0.708817	−	0.705392i	$-0.249229\pi$
$613$	7.70363	+	5.25224i	0.311147	+	0.212136i	−0.397671	+	0.917528i	$0.630181\pi$
$614$	25.9411	−	3.90999i	1.04690	−	0.157794i
$615$		0			0
$616$	0.00529560	−	0.00953975i	0.000213366	−	0.000384367i
$617$	−12.6094	+	15.8117i	−0.507635	+	0.636554i	−0.967932	−	0.251211i	$-0.919171\pi$
$617$	−12.6094	+	15.8117i	−0.507635	+	0.636554i	0.460298	+	0.887765i	$0.347743\pi$
$618$		0			0
$619$	5.14840	+	8.91730i	0.206932	+	0.358416i	0.950747	−	0.309969i	$-0.100319\pi$
$619$	5.14840	+	8.91730i	0.206932	+	0.358416i	−0.743815	+	0.668386i	$0.766985\pi$
$620$	−5.91525	−	0.891581i	−0.237562	−	0.0358067i
$621$		0			0
$622$	−50.8459	+	24.4861i	−2.03873	+	0.981802i
$623$	6.34931	+	7.69237i	0.254380	+	0.308188i
$624$		0			0
$625$	8.18366	+	20.8516i	0.327346	+	0.834065i
$626$	3.52110	+	46.9858i	0.140731	+	1.87793i
$627$		0			0
$628$	−1.91930	+	25.6113i	−0.0765885	+	1.02200i
$629$	0.413007	+	1.80950i	0.0164677	+	0.0721495i
$630$		0			0
$631$	−4.58464	+	20.0866i	−0.182512	+	0.799636i	0.797918	+	0.602766i	$0.205935\pi$
$631$	−4.58464	+	20.0866i	−0.182512	+	0.799636i	−0.980430	+	0.196870i	$0.936922\pi$
$632$	0.0556944	+	0.0171794i	0.00221540	+	0.000683361i
$633$		0			0
$634$	27.3008	−	25.3315i	1.08426	−	1.00604i
$635$	−5.61243	+	3.82649i	−0.222723	+	0.151850i
$636$		0			0
$637$	−11.8002	+	22.1275i	−0.467540	+	0.876725i
$638$	3.95799			0.156699
$639$		0			0
$640$	0.0173464	−	0.0160951i	0.000685675	−	0.000636213i
$641$	−2.22102	+	5.65906i	−0.0877250	+	0.223520i	−0.968003	−	0.250939i	$-0.919261\pi$
$641$	−2.22102	+	5.65906i	−0.0877250	+	0.223520i	0.880278	+	0.474458i	$0.157356\pi$
$642$		0			0
$643$	−5.15467	+	22.5841i	−0.203280	+	0.890630i	0.765642	+	0.643266i	$0.222421\pi$
$643$	−5.15467	+	22.5841i	−0.203280	+	0.890630i	−0.968923	+	0.247363i	$0.920436\pi$
$644$	−24.4608	−	40.7660i	−0.963889	−	1.60641i
$645$		0			0
$646$	0.0944036	−	1.25973i	0.00371426	−	0.0495634i
$647$	−26.1560	+	8.06806i	−1.02830	+	0.317188i	−0.762602	−	0.646868i	$-0.776078\pi$
$647$	−26.1560	+	8.06806i	−1.02830	+	0.317188i	−0.265697	+	0.964057i	$0.585602\pi$
$648$		0			0
$649$	1.84024	+	4.68884i	0.0722356	+	0.184053i
$650$	−31.1311	−	14.9919i	−1.22106	−	0.588032i
$651$		0			0
$652$	0.941362	−	0.453336i	0.0368666	−	0.0177540i
$653$	3.07136	+	2.84980i	0.120192	+	0.111521i	0.737979	−	0.674824i	$-0.235780\pi$
$653$	3.07136	+	2.84980i	0.120192	+	0.111521i	−0.617787	+	0.786345i	$0.711971\pi$
$654$		0			0
$655$	−3.88930	−	6.73646i	−0.151967	−	0.263215i
$656$	7.11150	−	12.3175i	0.277657	−	0.480916i
$657$		0			0
$658$	−11.5801	−	28.1045i	−0.451440	−	1.09563i
$659$	−19.4640	−	24.4070i	−0.758208	−	0.950763i	0.241600	−	0.970376i	$-0.422328\pi$
$659$	−19.4640	−	24.4070i	−0.758208	−	0.950763i	−0.999808	+	0.0196131i	$0.993757\pi$
$660$		0			0
$661$	−32.8524	−	22.3984i	−1.27781	−	0.871196i	−0.281716	−	0.959498i	$-0.590904\pi$
$661$	−32.8524	−	22.3984i	−1.27781	−	0.871196i	−0.996094	+	0.0883017i	$0.971856\pi$
$662$	−3.76678	−	2.56815i	−0.146400	−	0.0998140i
$663$		0			0
$664$	0.0761695	+	0.0955135i	0.00295595	+	0.00370664i
$665$	0.0774053	−	1.33404i	0.00300165	−	0.0517318i
$666$		0			0
$667$	−15.2597	+	26.4306i	−0.590859	+	1.02340i
$668$	2.07663	+	3.59682i	0.0803471	+	0.139165i
$669$		0			0
$670$	4.57361	+	4.24369i	0.176694	+	0.163948i
$671$	2.99414	−	1.44190i	0.115588	−	0.0556640i
$672$		0			0
$673$	20.0630	+	9.66181i	0.773370	+	0.372435i	0.778575	−	0.627551i	$-0.215943\pi$
$673$	20.0630	+	9.66181i	0.773370	+	0.372435i	−0.00520530	+	0.999986i	$0.501657\pi$
$674$	4.82414	+	12.2917i	0.185819	+	0.473459i
$675$		0			0
$676$	−0.316439	+	0.0976085i	−0.0121707	+	0.00375417i
$677$	−3.36420	+	44.8921i	−0.129297	+	1.72534i	0.435564	+	0.900158i	$0.356549\pi$
$677$	−3.36420	+	44.8921i	−0.129297	+	1.72534i	−0.564861	+	0.825186i	$0.691070\pi$
$678$		0			0
$679$	10.4491	−	10.0281i	0.401001	−	0.384843i
$680$	0.000344867	−	0.00151096i	1.32251e−5	−	5.79427e-5i
$681$		0			0
$682$	3.05111	−	7.77409i	0.116833	−	0.297685i
$683$	31.0767	−	28.8349i	1.18912	−	1.10334i	0.196693	−	0.980465i	$-0.436980\pi$
$683$	31.0767	−	28.8349i	1.18912	−	1.10334i	0.992422	−	0.122873i	$-0.0392108\pi$
$684$		0			0
$685$	7.64488			0.292096
$686$	−35.8853	−	9.11237i	−1.37011	−	0.347912i
$687$		0			0
$688$	18.4148	−	12.5550i	0.702058	−	0.478655i
$689$	−8.51093	+	7.89699i	−0.324240	+	0.300851i
$690$		0			0
$691$	13.4189	+	4.13920i	0.510481	+	0.157462i	0.539286	−	0.842123i	$-0.318694\pi$
$691$	13.4189	+	4.13920i	0.510481	+	0.157462i	−0.0288054	+	0.999585i	$0.509170\pi$
$692$	−1.65880	+	7.26769i	−0.0630583	+	0.276276i
$693$		0			0
$694$	−9.65293	−	42.2922i	−0.366420	−	1.60539i
$695$	−0.652275	+	8.70401i	−0.0247422	+	0.330162i
$696$		0			0
$697$	−0.138982	−	1.85458i	−0.00526431	−	0.0702474i
$698$	−5.50654	−	14.0304i	−0.208426	−	0.531060i
$699$		0			0
$700$	5.25159	−	24.9374i	0.198491	−	0.942546i
$701$	7.27902	−	3.50539i	0.274925	−	0.132397i	−0.291342	−	0.956619i	$-0.594102\pi$
$701$	7.27902	−	3.50539i	0.274925	−	0.132397i	0.566266	+	0.824222i	$0.308387\pi$
$702$		0			0
$703$	−4.22445	−	0.636733i	−0.159328	−	0.0240149i
$704$	−2.32726	−	4.03093i	−0.0877118	−	0.151921i
$705$		0			0
$706$	−41.3755	+	51.8832i	−1.55719	+	1.95265i
$707$	−0.721213	+	12.4297i	−0.0271240	+	0.467468i
$708$		0			0
$709$	28.3890	−	4.27895i	1.06617	−	0.160699i	0.407556	−	0.913180i	$-0.366381\pi$
$709$	28.3890	−	4.27895i	1.06617	−	0.160699i	0.658614	+	0.752481i	$0.271143\pi$
$710$	−5.95555	−	4.06042i	−0.223508	−	0.152385i
$711$		0			0
$712$	−0.0263298	+	0.00396858i	−0.000986752	+	0.000148729i
$713$	40.1503	+	50.3469i	1.50364	+	1.88551i
$714$		0			0
$715$	−0.546168	+	0.684873i	−0.0204255	+	0.0256128i
$716$	1.38527	−	2.39936i	0.0517699	−	0.0896682i
$717$		0			0
$718$	3.10486	+	0.467982i	0.115872	+	0.0174649i
$719$	14.1561	+	13.1349i	0.527934	+	0.489851i	0.898511	−	0.438951i	$-0.144650\pi$
$719$	14.1561	+	13.1349i	0.527934	+	0.489851i	−0.370577	+	0.928802i	$0.620840\pi$
$720$		0			0
$721$	−40.9010	+	20.5525i	−1.52323	+	0.765414i
$722$	−31.6019	−	15.2187i	−1.17610	−	0.566381i
$723$		0			0
$724$	−0.952071	−	12.7045i	−0.0353834	−	0.472159i
$725$	−15.6330	+	4.82213i	−0.580594	+	0.179089i
$726$		0			0
$727$	−9.30383	−	40.7627i	−0.345060	−	1.51181i	−0.788237	−	0.615372i	$-0.789006\pi$
$727$	−9.30383	−	40.7627i	−0.345060	−	1.51181i	0.443177	−	0.896434i	$-0.353851\pi$
$728$	−0.0344447	−	0.0574051i	−0.00127661	−	0.00212758i
$729$		0			0
$730$	10.1138	+	3.11968i	0.374327	+	0.115465i
$731$	1.06471	−	2.71284i	0.0393797	−	0.100338i
$732$		0			0
$733$	8.80597	−	6.00381i	0.325256	−	0.221756i	−0.389672	−	0.920954i	$-0.627412\pi$
$733$	8.80597	−	6.00381i	0.325256	−	0.221756i	0.714928	+	0.699198i	$0.246459\pi$
$734$	−18.7600			−0.692446
$735$		0			0
$736$	71.9712			2.65289
$737$	−3.59521	+	2.45117i	−0.132431	+	0.0902900i
$738$		0			0
$739$	10.2628	−	26.1492i	0.377524	−	0.961915i	−0.608236	−	0.793756i	$-0.708123\pi$
$739$	10.2628	−	26.1492i	0.377524	−	0.961915i	0.985760	−	0.168159i	$-0.0537821\pi$
$740$	2.83013	+	0.872980i	0.104038	+	0.0320914i
$741$		0			0
$742$	−14.3235	−	9.41621i	−0.525832	−	0.345680i
$743$	−7.96345	−	34.8902i	−0.292151	−	1.28000i	−0.881525	−	0.472136i	$-0.843483\pi$
$743$	−7.96345	−	34.8902i	−0.292151	−	1.28000i	0.589375	−	0.807860i	$-0.299374\pi$
$744$		0			0
$745$	3.97679	−	1.22668i	0.145698	−	0.0449419i
$746$	3.35056	+	44.7101i	0.122673	+	1.63695i
$747$		0			0
$748$	−0.550290	−	0.265005i	−0.0201206	−	0.00968956i
$749$	−27.1391	−	32.8797i	−0.991639	−	1.20140i
$750$		0			0
$751$	15.3056	+	14.2016i	0.558511	+	0.518222i	0.908140	−	0.418666i	$-0.137502\pi$
$751$	15.3056	+	14.2016i	0.558511	+	0.518222i	−0.349630	+	0.936888i	$0.613693\pi$
$752$	22.7713	+	3.43222i	0.830383	+	0.125160i
$753$		0			0
$754$	12.1424	−	21.0313i	0.442201	−	0.765915i
$755$	−2.41463	+	3.02785i	−0.0878773	+	0.110195i
$756$		0			0
$757$	17.4038	+	21.8237i	0.632554	+	0.793197i	0.990050	−	0.140718i	$-0.0449409\pi$
$757$	17.4038	+	21.8237i	0.632554	+	0.793197i	−0.357496	+	0.933915i	$0.616370\pi$
$758$	29.9220	−	4.51001i	1.08682	−	0.163811i
$759$		0			0
$760$	0.00294746	+	0.00200955i	0.000106916	+	7.28939e-5i
$761$	−30.4402	+	4.58812i	−1.10346	+	0.166319i	−0.675414	−	0.737439i	$-0.736035\pi$
$761$	−30.4402	+	4.58812i	−1.10346	+	0.166319i	−0.428043	+	0.903758i	$0.640797\pi$
$762$		0			0
$763$	−32.4068	−	29.0690i	−1.17320	−	1.05237i
$764$	−5.35315	+	6.71264i	−0.193670	+	0.242855i
$765$		0			0
$766$	−14.8736	−	25.7618i	−0.537404	−	0.930811i
$767$	30.5603	+	4.60622i	1.10347	+	0.166321i
$768$		0			0
$769$	−8.80823	+	4.24182i	−0.317633	+	0.152964i	−0.585906	−	0.810379i	$-0.699261\pi$
$769$	−8.80823	+	4.24182i	−0.317633	+	0.152964i	0.268273	+	0.963343i	$0.413547\pi$
$770$	−1.17451	−	0.541441i	−0.0423265	−	0.0195122i
$771$		0			0
$772$	0.665588	+	1.69589i	0.0239550	+	0.0610364i
$773$	0.354596	+	4.73176i	0.0127539	+	0.170190i	0.999943	+	0.0106373i	$0.00338601\pi$
$773$	0.354596	+	4.73176i	0.0127539	+	0.170190i	−0.987189	+	0.159552i	$0.948995\pi$
$774$		0			0
$775$	−2.57962	+	34.4227i	−0.0926629	+	1.23650i
$776$	0.00860326	+	0.0376933i	0.000308839	+	0.00135311i
$777$		0			0
$778$	−12.7202	+	55.7306i	−0.456040	+	1.99804i
$779$	4.09061	+	1.26179i	0.146561	+	0.0452082i
$780$		0			0
$781$	3.68506	−	3.41923i	0.131862	−	0.122350i
$782$	7.78937	−	5.31070i	0.278547	−	0.189910i
$783$		0			0
$784$	19.9075	−	19.7600i	0.710982	−	0.705716i
$785$	−5.38737			−0.192284
$786$		0			0
$787$	39.4559	−	36.6097i	1.40645	−	1.30499i	0.511178	−	0.859475i	$-0.329209\pi$
$787$	39.4559	−	36.6097i	1.40645	−	1.30499i	0.895272	−	0.445520i	$-0.146981\pi$
$788$	0.885539	−	2.25632i	0.0315460	−	0.0803779i
$789$		0			0
$790$	1.53729	−	6.73529i	0.0546942	−	0.239631i
$791$	12.8164	−	34.3455i	0.455698	−	1.22118i
$792$		0			0
$793$	1.52377	−	20.3333i	0.0541105	−	0.722055i
$794$	−49.3126	+	15.2109i	−1.75004	+	0.539816i
$795$		0			0
$796$	−19.6217	−	49.9953i	−0.695472	−	1.77203i
$797$	0.856018	+	0.412236i	0.0303217	+	0.0146022i	0.448983	−	0.893540i	$-0.351786\pi$
$797$	0.856018	+	0.412236i	0.0303217	+	0.0146022i	−0.418661	+	0.908142i	$0.637501\pi$
$798$		0			0
$799$	2.71298	−	1.30650i	0.0959783	−	0.0462207i
$800$	28.2810	+	26.2409i	0.999884	+	0.927757i
$801$		0			0
$802$	−11.0401	−	19.1220i	−0.389838	−	0.675220i
$803$	−3.69073	+	6.39253i	−0.130243	+	0.225588i
$804$		0			0
$805$	8.14386	−	5.75565i	0.287033	−	0.202860i
$806$	−31.9484	−	40.0620i	−1.12533	−	1.41112i
$807$		0			0
$808$	−0.0274626	−	0.0187237i	−0.000966130	−	0.000658696i
$809$	28.1364	+	19.1831i	0.989224	+	0.674441i	0.945845	−	0.324618i	$-0.105236\pi$
$809$	28.1364	+	19.1831i	0.989224	+	0.674441i	0.0433782	+	0.999059i	$0.486188\pi$
$810$		0			0
$811$	7.81506	+	9.79978i	0.274424	+	0.344117i	0.899876	−	0.436146i	$-0.143657\pi$
$811$	7.81506	+	9.79978i	0.274424	+	0.344117i	−0.625452	+	0.780263i	$0.715085\pi$
$812$	17.2020	+	4.99044i	0.603671	+	0.175130i
$813$		0			0
$814$	−2.06738	+	3.58081i	−0.0724617	+	0.125507i
$815$	0.109584	+	0.189805i	0.00383855	+	0.00664856i
$816$		0			0
$817$	4.91733	+	4.56262i	0.172036	+	0.159626i
$818$	23.0264	−	11.0889i	0.805098	−	0.387715i
$819$		0			0
$820$	−2.67380	−	1.28763i	−0.0933731	−	0.0449661i
$821$	−16.7405	−	42.6541i	−0.584247	−	1.48864i	−0.851155	−	0.524915i	$-0.824097\pi$
$821$	−16.7405	−	42.6541i	−0.584247	−	1.48864i	0.266908	−	0.963722i	$-0.413998\pi$
$822$		0			0
$823$	49.0519	−	15.1305i	1.70984	−	0.527417i	0.723246	−	0.690590i	$-0.242649\pi$
$823$	49.0519	−	15.1305i	1.70984	−	0.527417i	0.986597	+	0.163174i	$0.0521731\pi$
$824$	0.00913192	−	0.121857i	0.000318125	−	0.00424509i
$825$		0			0
$826$	4.17564	+	45.4374i	0.145289	+	1.58097i
$827$	1.76895	−	7.75026i	0.0615123	−	0.269503i	−0.934814	−	0.355137i	$-0.884434\pi$
$827$	1.76895	−	7.75026i	0.0615123	−	0.269503i	0.996327	+	0.0856337i	$0.0272915\pi$
$828$		0			0
$829$	−4.15564	+	10.5884i	−0.144331	+	0.367750i	−0.984698	−	0.174268i	$-0.944244\pi$
$829$	−4.15564	+	10.5884i	−0.144331	+	0.367750i	0.840367	+	0.542018i	$0.182339\pi$
$830$	10.6151	−	9.84933i	0.368454	−	0.341875i
$831$		0			0
$832$	−28.5585			−0.990086
$833$	0.695259	−	3.60121i	0.0240893	−	0.124774i
$834$		0			0
$835$	−0.719818	+	0.490764i	−0.0249103	+	0.0169836i
$836$	1.03057	−	0.956230i	0.0356430	−	0.0330719i
$837$		0			0
$838$	34.8822	+	10.7597i	1.20498	+	0.371689i
$839$	−4.60292	+	20.1667i	−0.158911	+	0.696233i	0.831203	+	0.555968i	$0.187652\pi$
$839$	−4.60292	+	20.1667i	−0.158911	+	0.696233i	−0.990114	+	0.140264i	$0.955205\pi$
$840$		0			0
$841$	3.89452	+	17.0630i	0.134294	+	0.588380i
$842$	−0.0574483	+	0.766594i	−0.00197980	+	0.0264186i
$843$		0			0
$844$	−1.21873	−	16.2629i	−0.0419505	−	0.559791i
$845$	−0.0253778	−	0.0646615i	−0.000873022	−	0.00222442i
$846$		0			0
$847$	−17.2094	+	22.3416i	−0.591322	+	0.767668i
$848$	11.7002	−	5.63453i	0.401787	−	0.193490i
$849$		0			0
$850$	4.99712	+	0.753195i	0.171400	+	0.0258344i
$851$	−15.9412	−	27.6110i	−0.546458	−	0.946493i
$852$		0			0
$853$	−11.7991	+	14.7956i	−0.403992	+	0.506590i	−0.941660	−	0.336567i	$-0.890734\pi$
$853$	−11.7991	+	14.7956i	−0.403992	+	0.506590i	0.537667	+	0.843157i	$0.319306\pi$
$854$	29.6882	−	4.98747i	1.01591	−	0.170668i
$855$		0			0
$856$	0.112542	−	0.0169630i	0.00384662	−	0.000579785i
$857$	13.6992	+	9.33996i	0.467956	+	0.319047i	0.774239	−	0.632894i	$-0.218133\pi$
$857$	13.6992	+	9.33996i	0.467956	+	0.319047i	−0.306283	+	0.951941i	$0.599085\pi$
$858$		0			0
$859$	−19.8862	+	2.99737i	−0.678510	+	0.102269i	−0.479251	−	0.877678i	$-0.659092\pi$
$859$	−19.8862	+	2.99737i	−0.678510	+	0.102269i	−0.199259	+	0.979947i	$0.563854\pi$
$860$	−2.89947	−	3.63582i	−0.0988712	−	0.123981i
$861$		0			0
$862$	37.1017	−	46.5241i	1.26369	−	1.58462i
$863$	−4.91117	+	8.50640i	−0.167178	+	0.289561i	−0.937427	−	0.348183i	$-0.886799\pi$
$863$	−4.91117	+	8.50640i	−0.167178	+	0.289561i	0.770248	+	0.637744i	$0.220132\pi$
$864$		0			0
$865$	−1.54623	−	0.233057i	−0.0525735	−	0.00792418i
$866$	25.3937	+	23.5619i	0.862913	+	0.800666i
$867$		0			0
$868$	23.0625	−	29.9402i	0.782792	−	1.01624i
$869$	4.34097	+	2.09050i	0.147257	+	0.0709154i
$870$		0			0
$871$	1.99514	+	26.6233i	0.0676029	+	0.902098i
$872$	0.111054	−	0.0342557i	0.00376078	−	0.00116005i
$873$		0			0
$874$	4.82869	+	21.1559i	0.163333	+	0.715608i
$875$	10.7899	+	1.44092i	0.364765	+	0.0487120i
$876$		0			0
$877$	−49.1636	−	15.1650i	−1.66014	−	0.512084i	−0.684044	−	0.729441i	$-0.739780\pi$
$877$	−49.1636	−	15.1650i	−1.66014	−	0.512084i	−0.976092	+	0.217356i	$0.930257\pi$
$878$	13.1654	−	33.5448i	0.444310	−	1.13208i
$879$		0			0
$880$	0.809552	−	0.551943i	0.0272900	−	0.0186060i
$881$	−8.84632			−0.298040			−0.149020	−	0.988834i	$-0.547612\pi$
$881$	−8.84632			−0.298040			−0.149020	+	0.988834i	$0.547612\pi$
$882$		0			0
$883$	4.00163			0.134666			0.0673328	−	0.997731i	$-0.478551\pi$
$883$	4.00163			0.134666			0.0673328	+	0.997731i	$0.478551\pi$
$884$	−3.09633	+	2.11104i	−0.104141	+	0.0710021i
$885$		0			0
$886$	−17.8077	+	45.3733i	−0.598262	+	1.52435i
$887$	35.6828	+	11.0067i	1.19811	+	0.369568i	0.828697	−	0.559698i	$-0.189083\pi$
$887$	35.6828	+	11.0067i	1.19811	+	0.369568i	0.369413	+	0.929265i	$0.379559\pi$
$888$		0			0
$889$	−3.92724	−	42.7344i	−0.131715	−	1.43326i
$890$	0.702317	+	3.07705i	0.0235417	+	0.103143i
$891$		0			0
$892$	−2.26296	+	0.698031i	−0.0757696	+	0.0233718i
$893$	0.517957	+	6.91166i	0.0173328	+	0.231290i
$894$		0			0
$895$	0.523604	+	0.252154i	0.0175021	+	0.00842859i
$896$	0.0357159	+	0.145168i	0.00119319	+	0.00484971i
$897$		0			0
$898$	−17.4230	−	16.1662i	−0.581413	−	0.539472i
$899$	−23.9902	−	3.61594i	−0.800119	−	0.120599i
$900$		0			0
$901$	0.849035	−	1.47057i	0.0282855	−	0.0489918i
$902$	2.58319	−	3.23921i	0.0860107	−	0.107854i
$903$		0			0
$904$	0.0610172	+	0.0765131i	0.00202940	+	0.00254479i
$905$	2.64256	−	0.398302i	0.0878416	−	0.0132400i
$906$		0			0
$907$	−43.7240	−	29.8105i	−1.45183	−	0.989842i	−0.994956	−	0.100311i	$-0.968016\pi$
$907$	−43.7240	−	29.8105i	−1.45183	−	0.989842i	−0.456875	−	0.889531i	$-0.651031\pi$
$908$	−26.6193	+	4.01221i	−0.883392	+	0.133150i
$909$		0			0
$910$	−6.48021	+	4.57988i	−0.214817	+	0.151821i
$911$	4.22409	−	5.29685i	0.139950	−	0.175492i	−0.706917	−	0.707297i	$-0.749914\pi$
$911$	4.22409	−	5.29685i	0.139950	−	0.175492i	0.846867	+	0.531804i	$0.178486\pi$
$912$		0			0
$913$	5.04953	+	8.74604i	0.167115	+	0.289452i
$914$	22.6913	+	3.42016i	0.750561	+	0.113129i
$915$		0			0
$916$	−39.0633	+	18.8119i	−1.29069	+	0.621563i
$917$	49.1358	−	0.827600i	1.62261	−	0.0273298i
$918$		0			0
$919$	12.7359	+	32.4505i	0.420119	+	1.07044i	0.971678	+	0.236309i	$0.0759377\pi$
$919$	12.7359	+	32.4505i	0.420119	+	1.07044i	−0.551559	+	0.834136i	$0.685967\pi$
$920$	0.00198949	+	0.0265479i	6.55916e−5	+	0.000875259i
$921$		0			0
$922$	−1.04821	+	13.9875i	−0.0345211	+	0.460652i
$923$	−6.86343	−	30.0706i	−0.225912	−	0.989787i
$924$		0			0
$925$	3.80298	−	16.6619i	0.125041	−	0.547841i
$926$	55.5064	+	17.1215i	1.82405	+	0.562646i
$927$		0			0
$928$	−19.8768	+	18.4429i	−0.652487	+	0.605419i
$929$	−26.2659	+	17.9078i	−0.861758	+	0.587537i	−0.911534	−	0.411224i	$-0.865101\pi$
$929$	−26.2659	+	17.9078i	−0.861758	+	0.587537i	0.0497766	+	0.998760i	$0.484149\pi$
$930$		0			0
$931$	7.13148	+	4.51807i	0.233725	+	0.148074i
$932$	37.8095			1.23849
$933$		0			0
$934$	7.87541	−	7.30732i	0.257691	−	0.239103i
$935$	0.0468068	−	0.119262i	0.00153075	−	0.00390028i
$936$		0			0
$937$	−4.08029	+	17.8769i	−0.133297	+	0.584014i	0.863521	+	0.504312i	$0.168254\pi$
$937$	−4.08029	+	17.8769i	−0.133297	+	0.584014i	−0.996819	+	0.0797017i	$0.974603\pi$
$938$	−37.4647	+	12.2510i	−1.22327	+	0.400010i
$939$		0			0
$940$	0.359078	−	4.79156i	0.0117118	−	0.156284i
$941$	−35.0323	+	10.8060i	−1.14202	+	0.352267i	−0.807353	−	0.590069i	$-0.799101\pi$
$941$	−35.0323	+	10.8060i	−1.14202	+	0.352267i	−0.334669	+	0.942336i	$0.608624\pi$
$942$		0			0
$943$	11.6715	+	29.7385i	0.380076	+	0.968418i
$944$	−31.1449	−	14.9986i	−1.01368	−	0.488163i
$945$		0			0
$946$	5.84934	−	2.81689i	0.190178	−	0.0915851i
$947$	−39.0496	−	36.2327i	−1.26894	−	1.17740i	−0.975153	−	0.221534i	$-0.928894\pi$
$947$	−39.0496	−	36.2327i	−1.26894	−	1.17740i	−0.293787	−	0.955871i	$-0.594916\pi$
$948$		0			0
$949$	22.6450	+	39.2223i	0.735089	+	1.27321i
$950$	−5.81607	+	10.0737i	−0.188698	+	0.326835i
$951$		0			0
$952$	0.00728864	+	0.00653793i	0.000236226	+	0.000211896i
$953$	18.1958	+	22.8168i	0.589418	+	0.739107i	0.983687	−	0.179888i	$-0.0575735\pi$
$953$	18.1958	+	22.8168i	0.589418	+	0.739107i	−0.394269	+	0.918995i	$0.629002\pi$
$954$		0			0
$955$	−1.48804	−	1.01453i	−0.0481519	−	0.0328294i
$956$	35.6289	+	24.2914i	1.15232	+	0.785639i
$957$		0			0
$958$	30.9847	+	38.8536i	1.00107	+	1.25530i
$959$	−23.4411	+	42.2280i	−0.756954	+	1.36361i
$960$		0			0
$961$	−10.0956	+	17.4862i	−0.325666	+	0.564069i
$962$	12.6847	+	21.9706i	0.408972	+	0.708360i
$963$		0			0
$964$	−15.7708	−	14.6331i	−0.507942	−	0.471301i
$965$	−0.344307	+	0.165810i	−0.0110836	+	0.00533760i
$966$		0			0
$967$	16.0872	+	7.74721i	0.517331	+	0.249133i	0.674283	−	0.738473i	$-0.264453\pi$
$967$	16.0872	+	7.74721i	0.517331	+	0.249133i	−0.156952	+	0.987606i	$0.550167\pi$
$968$	−0.0275050	−	0.0700816i	−0.000884044	−	0.00225251i
$969$		0			0
$970$	4.37917	−	1.35080i	0.140607	−	0.0433714i
$971$	−1.09914	+	14.6671i	−0.0352732	+	0.470688i	0.951398	+	0.307963i	$0.0996474\pi$
$971$	−1.09914	+	14.6671i	−0.0352732	+	0.470688i	−0.986671	+	0.162725i	$0.947972\pi$
$972$		0			0
$973$	−46.0783	−	30.2917i	−1.47720	−	0.971106i
$974$	5.55837	−	24.3528i	0.178102	−	0.780314i
$975$		0			0
$976$	−8.33227	+	21.2303i	−0.266709	+	0.679565i
$977$	15.0164	−	13.9332i	0.480419	−	0.445763i	−0.402409	−	0.915460i	$-0.631827\pi$
$977$	15.0164	−	13.9332i	0.480419	−	0.445763i	0.882828	+	0.469696i	$0.155637\pi$
$978$		0			0
$979$	−2.20118			−0.0703500
$980$	−4.42191	−	3.83406i	−0.141253	−	0.122475i
$981$		0			0
$982$	−32.6121	+	22.2346i	−1.04069	+	0.709533i
$983$	14.9220	−	13.8456i	0.475938	−	0.441606i	−0.405367	−	0.914154i	$-0.632856\pi$
$983$	14.9220	−	13.8456i	0.475938	−	0.441606i	0.881305	+	0.472548i	$0.156666\pi$
$984$		0			0
$985$	0.485850	+	0.149865i	0.0154805	+	0.00477509i
$986$	−0.790351	+	3.46275i	−0.0251699	+	0.110277i
$987$		0			0
$988$	−1.91944	−	8.40962i	−0.0610655	−	0.267546i
$989$	−3.74105	+	49.9209i	−0.118959	+	1.58739i
$990$		0			0
$991$	−4.05751	−	54.1437i	−0.128891	−	1.71993i	−0.569296	−	0.822133i	$-0.692784\pi$
$991$	−4.05751	−	54.1437i	−0.128891	−	1.71993i	0.440405	−	0.897799i	$-0.354835\pi$
$992$	20.9023	+	53.2581i	0.663647	+	1.69095i
$993$		0			0
$994$	40.6898	−	20.4463i	1.29060	−	0.648519i
$995$	10.1503	−	4.88810i	0.321785	−	0.154963i
$996$		0			0
$997$	38.5202	+	5.80599i	1.21995	+	0.183877i	0.727280	−	0.686340i	$-0.240784\pi$
$997$	38.5202	+	5.80599i	1.21995	+	0.183877i	0.492667	+	0.870218i	$0.336022\pi$
$998$	−16.6041	−	28.7592i	−0.525594	−	0.910356i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bb.c.37.1		48
3.2	odd	2		147.2.m.a.37.4	yes	48
49.4	even	21	inner	441.2.bb.c.298.1		48
147.2	odd	42		7203.2.a.i.1.22		24
147.47	even	42		7203.2.a.k.1.22		24
147.53	odd	42		147.2.m.a.4.4	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.m.a.4.4	✓	48	147.53	odd	42
147.2.m.a.37.4	yes	48	3.2	odd	2
441.2.bb.c.37.1		48	1.1	even	1	trivial
441.2.bb.c.298.1		48	49.4	even	21	inner
7203.2.a.i.1.22		24	147.2	odd	42
7203.2.a.k.1.22		24	147.47	even	42

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.bb (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.65175 + 1.12614i) q^{2} +(0.729391 - 1.85846i) q^{4} +(0.400180 + 0.123439i) q^{5} +(-1.90889 + 1.83197i) q^{7} +(-0.00157168 - 0.00688598i) q^{8} +O(q^{10})\)	\(q+(-1.65175 + 1.12614i) q^{2} +(0.729391 - 1.85846i) q^{4} +(0.400180 + 0.123439i) q^{5} +(-1.90889 + 1.83197i) q^{7} +(-0.00157168 - 0.00688598i) q^{8} +(-0.800006 + 0.246769i) q^{10} +(-0.0436333 - 0.582246i) q^{11} +(-3.22770 - 1.55438i) q^{13} +(1.08994 - 5.17564i) q^{14} +(2.93738 + 2.72549i) q^{16} +(0.518106 + 0.0780919i) q^{17} +(-0.603015 + 1.04445i) q^{19} +(0.521294 - 0.653682i) q^{20} +(0.727763 + 0.912586i) q^{22} +(-8.89988 + 1.34144i) q^{23} +(-3.98629 - 2.71780i) q^{25} +(7.08179 - 1.06741i) q^{26} +(2.01232 + 4.88382i) q^{28} +(2.11419 - 2.65111i) q^{29} +(-3.57740 - 6.19624i) q^{31} +(-7.90713 - 1.19181i) q^{32} +(-0.943723 + 0.454473i) q^{34} +(-0.990037 + 0.497487i) q^{35} +(1.29416 + 3.29747i) q^{37} +(-0.180174 - 2.40425i) q^{38} +(0.000221045 - 0.00294963i) q^{40} +(-0.789835 - 3.46050i) q^{41} +(1.23768 - 5.42262i) q^{43} +(-1.11391 - 0.343595i) q^{44} +(13.1897 - 12.2383i) q^{46} +(4.74838 - 3.23739i) q^{47} +(0.287736 - 6.99408i) q^{49} +9.64498 q^{50} +(-5.24300 + 4.86480i) q^{52} +(1.18402 - 3.01682i) q^{53} +(0.0544107 - 0.238389i) q^{55} +(0.0156151 + 0.0102653i) q^{56} +(-0.506580 + 6.75984i) q^{58} +(-8.24358 + 2.54281i) q^{59} +(2.07940 + 5.29823i) q^{61} +(12.8868 + 6.20597i) q^{62} +(7.18226 - 3.45880i) q^{64} +(-1.09979 - 1.02045i) q^{65} +(-3.72619 - 6.45396i) q^{67} +(0.523033 - 0.905919i) q^{68} +(1.07505 - 1.93665i) q^{70} +(5.36805 + 6.73132i) q^{71} +(-10.4454 - 7.12155i) q^{73} +(-5.85105 - 3.98918i) q^{74} +(1.50124 + 1.88249i) q^{76} +(1.14995 + 1.03151i) q^{77} +(-4.12595 + 7.14636i) q^{79} +(0.839047 + 1.45327i) q^{80} +(5.20162 + 4.82640i) q^{82} +(-15.5836 + 7.50467i) q^{83} +(0.197696 + 0.0952053i) q^{85} +(4.06231 + 10.3506i) q^{86} +(-0.00394076 + 0.00121556i) q^{88} +(0.281727 - 3.75938i) q^{89} +(9.00891 - 2.94592i) q^{91} +(-3.99848 + 17.5185i) q^{92} +(-4.19736 + 10.6947i) q^{94} +(-0.370241 + 0.343533i) q^{95} -5.47393 q^{97} +(7.40107 + 11.8765i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + q^{2} + 3 q^{4} - 6 q^{8}+O(q^{10}) \) 48 * q + q^2 + 3 * q^4 - 6 * q^8	\( 48 q + q^{2} + 3 q^{4} - 6 q^{8} + 30 q^{10} + 9 q^{11} + 42 q^{14} + 29 q^{16} + 5 q^{17} - 26 q^{19} + 5 q^{20} + q^{22} + 4 q^{23} - 56 q^{25} + 62 q^{26} + 7 q^{28} - 12 q^{29} - 36 q^{31} + 14 q^{32} - 76 q^{34} - 7 q^{35} - 20 q^{37} + 60 q^{38} + 28 q^{40} - 41 q^{41} + 12 q^{43} - 44 q^{44} + 16 q^{46} - 13 q^{47} - 84 q^{49} + 12 q^{50} + 92 q^{52} - 14 q^{53} - 38 q^{55} - 105 q^{56} + 3 q^{58} - 57 q^{59} + 11 q^{61} + 16 q^{62} - 110 q^{64} - 21 q^{65} + 34 q^{67} - 22 q^{68} - 6 q^{71} - 69 q^{73} + 90 q^{74} - 49 q^{76} + 34 q^{79} - 55 q^{80} + 91 q^{82} - 28 q^{83} - 44 q^{85} + 26 q^{86} + 45 q^{88} - 11 q^{89} - 84 q^{92} + 90 q^{94} - 150 q^{95} + 124 q^{97} - 119 q^{98}+O(q^{100}) \) 48 * q + q^2 + 3 * q^4 - 6 * q^8 + 30 * q^10 + 9 * q^11 + 42 * q^14 + 29 * q^16 + 5 * q^17 - 26 * q^19 + 5 * q^20 + q^22 + 4 * q^23 - 56 * q^25 + 62 * q^26 + 7 * q^28 - 12 * q^29 - 36 * q^31 + 14 * q^32 - 76 * q^34 - 7 * q^35 - 20 * q^37 + 60 * q^38 + 28 * q^40 - 41 * q^41 + 12 * q^43 - 44 * q^44 + 16 * q^46 - 13 * q^47 - 84 * q^49 + 12 * q^50 + 92 * q^52 - 14 * q^53 - 38 * q^55 - 105 * q^56 + 3 * q^58 - 57 * q^59 + 11 * q^61 + 16 * q^62 - 110 * q^64 - 21 * q^65 + 34 * q^67 - 22 * q^68 - 6 * q^71 - 69 * q^73 + 90 * q^74 - 49 * q^76 + 34 * q^79 - 55 * q^80 + 91 * q^82 - 28 * q^83 - 44 * q^85 + 26 * q^86 + 45 * q^88 - 11 * q^89 - 84 * q^92 + 90 * q^94 - 150 * q^95 + 124 * q^97 - 119 * q^98

Introduction

L-functions

Modular forms

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Database

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