LMFDB - Embedded newform 273.2.bw.b.11.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(11,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 8, 7]))

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

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

chi := DirichletCharacter("273.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bw (of order $12$, degree $4$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			11.15
Character	$\chi$	$=$	273.11
Dual form			273.2.bw.b.149.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0262469 - 0.0979549i) q^{2} +(-0.748033 + 1.56219i) q^{3} +(1.72314 - 0.994858i) q^{4} +(2.20563 + 0.590996i) q^{5} +(0.172658 + 0.0322707i) q^{6} +(1.71000 - 2.01889i) q^{7} +(-0.286094 - 0.286094i) q^{8} +(-1.88089 - 2.33714i) q^{9} +O(q^{10})$	\(q+(-0.0262469 - 0.0979549i) q^{2} +(-0.748033 + 1.56219i) q^{3} +(1.72314 - 0.994858i) q^{4} +(2.20563 + 0.590996i) q^{5} +(0.172658 + 0.0322707i) q^{6} +(1.71000 - 2.01889i) q^{7} +(-0.286094 - 0.286094i) q^{8} +(-1.88089 - 2.33714i) q^{9} -0.231564i q^{10} +(0.0993799 + 0.0993799i) q^{11} +(0.265191 + 3.43607i) q^{12} +(-3.55468 - 0.603532i) q^{13} +(-0.242642 - 0.114513i) q^{14} +(-2.57313 + 3.00353i) q^{15} +(1.96920 - 3.41076i) q^{16} +(2.42420 + 4.19884i) q^{17} +(-0.179567 + 0.245586i) q^{18} +(2.56822 + 2.56822i) q^{19} +(4.38857 - 1.17591i) q^{20} +(1.87476 + 4.18154i) q^{21} +(0.00712633 - 0.0123432i) q^{22} +(0.0913731 - 0.158263i) q^{23} +(0.660943 - 0.232927i) q^{24} +(0.185387 + 0.107033i) q^{25} +(0.0341805 + 0.364039i) q^{26} +(5.05804 - 1.19006i) q^{27} +(0.938063 - 5.18004i) q^{28} +(-5.70192 + 3.29201i) q^{29} +(0.361747 + 0.173217i) q^{30} +(-0.565555 + 0.151540i) q^{31} +(-1.16741 - 0.312807i) q^{32} +(-0.229590 + 0.0809111i) q^{33} +(0.347669 - 0.347669i) q^{34} +(4.96477 - 3.44231i) q^{35} +(-5.56618 - 2.15602i) q^{36} +(1.36877 + 5.10833i) q^{37} +(0.184161 - 0.318977i) q^{38} +(3.60185 - 5.10163i) q^{39} +(-0.461937 - 0.800098i) q^{40} +(-8.90385 - 2.38578i) q^{41} +(0.360396 - 0.293395i) q^{42} +(-0.414218 - 0.239149i) q^{43} +(0.270115 + 0.0723770i) q^{44} +(-2.76731 - 6.26647i) q^{45} +(-0.0179009 - 0.00479653i) q^{46} +(-2.83925 + 10.5962i) q^{47} +(3.85523 + 5.62763i) q^{48} +(-1.15182 - 6.90459i) q^{49} +(0.00561860 - 0.0209689i) q^{50} +(-8.37279 + 0.646200i) q^{51} +(-6.72566 + 2.49643i) q^{52} +(-8.04797 - 4.64650i) q^{53} +(-0.249330 - 0.464224i) q^{54} +(0.160462 + 0.277928i) q^{55} +(-1.06681 + 0.0883724i) q^{56} +(-5.93316 + 2.09094i) q^{57} +(0.472126 + 0.472126i) q^{58} +(3.80035 - 14.1831i) q^{59} +(-1.44579 + 7.73542i) q^{60} +5.35525 q^{61} +(0.0296882 + 0.0514214i) q^{62} +(-7.93475 - 0.199193i) q^{63} -7.75424i q^{64} +(-7.48361 - 3.43197i) q^{65} +(0.0139517 + 0.0203658i) q^{66} +(-0.176349 - 0.176349i) q^{67} +(8.35451 + 4.82348i) q^{68} +(0.178887 + 0.261128i) q^{69} +(-0.467502 - 0.395973i) q^{70} +(-2.26554 - 8.45513i) q^{71} +(-0.130531 + 1.20676i) q^{72} +(1.95176 + 7.28406i) q^{73} +(0.464460 - 0.268156i) q^{74} +(-0.305883 + 0.209546i) q^{75} +(6.98042 + 1.87040i) q^{76} +(0.370576 - 0.0306977i) q^{77} +(-0.594268 - 0.218917i) q^{78} +(-1.70222 - 2.94833i) q^{79} +(6.35907 - 6.35907i) q^{80} +(-1.92448 + 8.79184i) q^{81} +0.934795i q^{82} +(-1.80484 + 1.80484i) q^{83} +(7.39052 + 5.34028i) q^{84} +(2.86539 + 10.6938i) q^{85} +(-0.0125539 + 0.0468516i) q^{86} +(-0.877522 - 11.3700i) q^{87} -0.0568640i q^{88} +(-10.5564 + 2.82858i) q^{89} +(-0.541198 + 0.435547i) q^{90} +(-7.29695 + 6.14447i) q^{91} -0.363613i q^{92} +(0.186319 - 0.996863i) q^{93} +1.11248 q^{94} +(4.14672 + 7.18233i) q^{95} +(1.36193 - 1.58973i) q^{96} +(-14.6793 + 3.93330i) q^{97} +(-0.646106 + 0.294051i) q^{98} +(0.0453421 - 0.419188i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 4 q^{3} - 12 q^{4} - 4 q^{6} - 16 q^{7} - 16 q^{9}+O(q^{10}) $ 128 * q - 4 * q^3 - 12 * q^4 - 4 * q^6 - 16 * q^7 - 16 * q^9	$ 128 q - 4 q^{3} - 12 q^{4} - 4 q^{6} - 16 q^{7} - 16 q^{9} - 48 q^{12} - 16 q^{13} - 6 q^{15} + 32 q^{16} + 22 q^{18} - 16 q^{19} - 18 q^{21} - 8 q^{22} - 4 q^{24} - 40 q^{27} - 76 q^{28} - 4 q^{31} + 50 q^{33} - 48 q^{34} - 60 q^{36} + 28 q^{37} + 40 q^{39} + 44 q^{40} + 44 q^{42} - 144 q^{43} + 58 q^{45} + 48 q^{46} - 64 q^{48} + 24 q^{49} + 36 q^{51} - 22 q^{54} - 16 q^{55} + 40 q^{57} - 28 q^{58} - 4 q^{60} - 40 q^{61} + 20 q^{63} - 34 q^{66} + 96 q^{67} - 54 q^{69} + 64 q^{70} - 98 q^{72} + 48 q^{73} - 12 q^{75} + 144 q^{76} + 82 q^{78} - 24 q^{79} - 48 q^{81} + 4 q^{84} + 56 q^{85} - 2 q^{87} - 24 q^{91} + 10 q^{93} + 32 q^{94} - 54 q^{96} + 52 q^{97} - 10 q^{99}+O(q^{100}) $ 128 * q - 4 * q^3 - 12 * q^4 - 4 * q^6 - 16 * q^7 - 16 * q^9 - 48 * q^12 - 16 * q^13 - 6 * q^15 + 32 * q^16 + 22 * q^18 - 16 * q^19 - 18 * q^21 - 8 * q^22 - 4 * q^24 - 40 * q^27 - 76 * q^28 - 4 * q^31 + 50 * q^33 - 48 * q^34 - 60 * q^36 + 28 * q^37 + 40 * q^39 + 44 * q^40 + 44 * q^42 - 144 * q^43 + 58 * q^45 + 48 * q^46 - 64 * q^48 + 24 * q^49 + 36 * q^51 - 22 * q^54 - 16 * q^55 + 40 * q^57 - 28 * q^58 - 4 * q^60 - 40 * q^61 + 20 * q^63 - 34 * q^66 + 96 * q^67 - 54 * q^69 + 64 * q^70 - 98 * q^72 + 48 * q^73 - 12 * q^75 + 144 * q^76 + 82 * q^78 - 24 * q^79 - 48 * q^81 + 4 * q^84 + 56 * q^85 - 2 * q^87 - 24 * q^91 + 10 * q^93 + 32 * q^94 - 54 * q^96 + 52 * q^97 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.0262469	−	0.0979549i	−0.0185594	−	0.0692646i	0.956025	−	0.293285i	$-0.0947485\pi$
$2$	−0.0262469	−	0.0979549i	−0.0185594	−	0.0692646i	−0.974584	+	0.224020i	$0.928082\pi$
$3$	−0.748033	+	1.56219i	−0.431877	+	0.901932i
$3$	−0.748033	+	1.56219i	−0.431877	+	0.901932i
$4$	1.72314	−	0.994858i	0.861572	−	0.497429i
$5$	2.20563	+	0.590996i	0.986386	+	0.264301i	0.715732	−	0.698375i	$-0.246093\pi$
$5$	2.20563	+	0.590996i	0.986386	+	0.264301i	0.270654	+	0.962677i	$0.412760\pi$
$6$	0.172658	+	0.0322707i	0.0704873	+	0.0131745i
$7$	1.71000	−	2.01889i	0.646318	−	0.763068i
$7$	1.71000	−	2.01889i	0.646318	−	0.763068i
$8$	−0.286094	−	0.286094i	−0.101150	−	0.101150i
$9$	−1.88089	−	2.33714i	−0.626964	−	0.779048i
$10$		−	0.231564i		−	0.0732269i
$11$	0.0993799	+	0.0993799i	0.0299642	+	0.0299642i	0.721930	−	0.691966i	$-0.243255\pi$
$11$	0.0993799	+	0.0993799i	0.0299642	+	0.0299642i	−0.691966	+	0.721930i	$0.743255\pi$
$12$	0.265191	+	3.43607i	0.0765540	+	0.991908i
$13$	−3.55468	−	0.603532i	−0.985891	−	0.167390i
$13$	−3.55468	−	0.603532i	−0.985891	−	0.167390i
$14$	−0.242642	−	0.114513i	−0.0648489	−	0.0306049i
$15$	−2.57313	+	3.00353i	−0.664380	+	0.775508i
$16$	1.96920	−	3.41076i	0.492300	−	0.852689i
$17$	2.42420	+	4.19884i	0.587956	+	1.01837i	0.994500	+	0.104738i	$0.0334005\pi$
$17$	2.42420	+	4.19884i	0.587956	+	1.01837i	−0.406544	+	0.913631i	$0.633266\pi$
$18$	−0.179567	+	0.245586i	−0.0423243	+	0.0578851i
$19$	2.56822	+	2.56822i	0.589189	+	0.589189i	0.937412	−	0.348223i	$-0.113215\pi$
$19$	2.56822	+	2.56822i	0.589189	+	0.589189i	−0.348223	+	0.937412i	$0.613215\pi$
$20$	4.38857	−	1.17591i	0.981314	−	0.262942i
$21$	1.87476	+	4.18154i	0.409106	+	0.912487i
$22$	0.00712633	−	0.0123432i	0.00151934	−	0.00263157i
$23$	0.0913731	−	0.158263i	0.0190526	−	0.0330001i	−0.856342	−	0.516409i	$-0.827268\pi$
$23$	0.0913731	−	0.158263i	0.0190526	−	0.0330001i	0.875395	+	0.483409i	$0.160602\pi$
$24$	0.660943	−	0.232927i	0.134914	−	0.0475459i
$25$	0.185387	+	0.107033i	0.0370775	+	0.0214067i
$26$	0.0341805	+	0.364039i	0.00670335	+	0.0713940i
$27$	5.05804	−	1.19006i	0.973420	−	0.229027i
$28$	0.938063	−	5.18004i	0.177277	−	0.978936i
$29$	−5.70192	+	3.29201i	−1.05882	+	0.611310i	−0.925106	−	0.379710i	$-0.876024\pi$
$29$	−5.70192	+	3.29201i	−1.05882	+	0.611310i	−0.133715	+	0.991020i	$0.542691\pi$
$30$	0.361747	+	0.173217i	0.0660457	+	0.0316250i
$31$	−0.565555	+	0.151540i	−0.101577	+	0.0272174i	−0.309249	−	0.950981i	$-0.600078\pi$
$31$	−0.565555	+	0.151540i	−0.101577	+	0.0272174i	0.207673	+	0.978198i	$0.433411\pi$
$32$	−1.16741	−	0.312807i	−0.206371	−	0.0552969i
$33$	−0.229590	+	0.0809111i	−0.0399665	+	0.0140848i
$34$	0.347669	−	0.347669i	0.0596248	−	0.0596248i
$35$	4.96477	−	3.44231i	0.839199	−	0.581857i
$36$	−5.56618	−	2.15602i	−0.927696	−	0.359336i
$37$	1.36877	+	5.10833i	0.225025	+	0.839805i	0.982394	+	0.186818i	$0.0598176\pi$
$37$	1.36877	+	5.10833i	0.225025	+	0.839805i	−0.757369	+	0.652987i	$0.773516\pi$
$38$	0.184161	−	0.318977i	0.0298749	−	0.0517449i
$39$	3.60185	−	5.10163i	0.576758	−	0.816915i
$40$	−0.461937	−	0.800098i	−0.0730386	−	0.126507i
$41$	−8.90385	−	2.38578i	−1.39055	−	0.372596i	−0.515607	−	0.856825i	$-0.672433\pi$
$41$	−8.90385	−	2.38578i	−1.39055	−	0.372596i	−0.874941	+	0.484229i	$0.839100\pi$
$42$	0.360396	−	0.293395i	0.0556102	−	0.0452718i
$43$	−0.414218	−	0.239149i	−0.0631677	−	0.0364699i	0.468084	−	0.883684i	$-0.344945\pi$
$43$	−0.414218	−	0.239149i	−0.0631677	−	0.0364699i	−0.531251	+	0.847214i	$0.678278\pi$
$44$	0.270115	+	0.0723770i	0.0407213	+	0.0109112i
$45$	−2.76731	−	6.26647i	−0.412526	−	0.934150i
$46$	−0.0179009	−	0.00479653i	−0.00263934	−	0.000707209i
$47$	−2.83925	+	10.5962i	−0.414148	+	1.54562i	0.372388	+	0.928077i	$0.378539\pi$
$47$	−2.83925	+	10.5962i	−0.414148	+	1.54562i	−0.786536	+	0.617544i	$0.788128\pi$
$48$	3.85523	+	5.62763i	0.556455	+	0.812278i
$49$	−1.15182	−	6.90459i	−0.164546	−	0.986369i
$50$	0.00561860	−	0.0209689i	0.000794590	−	0.00296545i
$51$	−8.37279	+	0.646200i	−1.17243	+	0.0904861i
$52$	−6.72566	+	2.49643i	−0.932681	+	0.346192i
$53$	−8.04797	−	4.64650i	−1.10547	−	0.638245i	−0.167820	−	0.985818i	$-0.553673\pi$
$53$	−8.04797	−	4.64650i	−1.10547	−	0.638245i	−0.937653	+	0.347572i	$0.887006\pi$
$54$	−0.249330	−	0.464224i	−0.0339295	−	0.0631729i
$55$	0.160462	+	0.277928i	0.0216367	+	0.0374758i
$56$	−1.06681	+	0.0883724i	−0.142559	+	0.0118093i
$57$	−5.93316	+	2.09094i	−0.785866	+	0.276951i
$58$	0.472126	+	0.472126i	0.0619932	+	0.0619932i
$59$	3.80035	−	14.1831i	0.494763	−	1.84648i	−0.0365899	−	0.999330i	$-0.511650\pi$
$59$	3.80035	−	14.1831i	0.494763	−	1.84648i	0.531353	−	0.847151i	$-0.321684\pi$
$60$	−1.44579	+	7.73542i	−0.186651	+	0.998638i
$61$	5.35525			0.685670			0.342835	−	0.939396i	$-0.388613\pi$
$61$	5.35525			0.685670			0.342835	+	0.939396i	$0.388613\pi$
$62$	0.0296882	+	0.0514214i	0.00377040	+	0.00653053i
$63$	−7.93475	−	0.199193i	−0.999685	−	0.0250960i
$64$		−	7.75424i		−	0.969280i
$65$	−7.48361	−	3.43197i	−0.928228	−	0.425683i
$66$	0.0139517	+	0.0203658i	0.00171733	+	0.00250686i
$67$	−0.176349	−	0.176349i	−0.0215445	−	0.0215445i	0.696252	−	0.717797i	$-0.254849\pi$
$67$	−0.176349	−	0.176349i	−0.0215445	−	0.0215445i	−0.717797	+	0.696252i	$0.754849\pi$
$68$	8.35451	+	4.82348i	1.01313	+	0.584933i
$69$	0.178887	+	0.261128i	0.0215355	+	0.0314361i
$70$	−0.467502	−	0.395973i	−0.0558771	−	0.0473279i
$71$	−2.26554	−	8.45513i	−0.268871	−	1.00344i	−0.959838	−	0.280553i	$-0.909482\pi$
$71$	−2.26554	−	8.45513i	−0.268871	−	1.00344i	0.690968	−	0.722886i	$-0.257185\pi$
$72$	−0.130531	+	1.20676i	−0.0153832	+	0.142218i
$73$	1.95176	+	7.28406i	0.228436	+	0.852535i	0.980999	+	0.194014i	$0.0621509\pi$
$73$	1.95176	+	7.28406i	0.228436	+	0.852535i	−0.752563	+	0.658521i	$0.771182\pi$
$74$	0.464460	−	0.268156i	0.0539924	−	0.0311725i
$75$	−0.305883	+	0.209546i	−0.0353203	+	0.0241963i
$76$	6.98042	+	1.87040i	0.800709	+	0.214549i
$77$	0.370576	−	0.0306977i	0.0422311	−	0.00349833i
$78$	−0.594268	−	0.218917i	−0.0672875	−	0.0247874i
$79$	−1.70222	−	2.94833i	−0.191514	−	0.331713i	0.754238	−	0.656601i	$-0.228007\pi$
$79$	−1.70222	−	2.94833i	−0.191514	−	0.331713i	−0.945752	+	0.324889i	$0.894673\pi$
$80$	6.35907	−	6.35907i	0.710965	−	0.710965i
$81$	−1.92448	+	8.79184i	−0.213831	+	0.976871i
$82$			0.934795i			0.103231i
$83$	−1.80484	+	1.80484i	−0.198107	+	0.198107i	−0.799188	−	0.601081i	$-0.794737\pi$
$83$	−1.80484	+	1.80484i	−0.198107	+	0.198107i	0.601081	+	0.799188i	$0.294737\pi$
$84$	7.39052	+	5.34028i	0.806372	+	0.582672i
$85$	2.86539	+	10.6938i	0.310795	+	1.15990i
$86$	−0.0125539	+	0.0468516i	−0.00135372	+	0.00505214i
$87$	−0.877522	−	11.3700i	−0.0940803	−	1.21900i
$88$		−	0.0568640i		−	0.00606173i
$89$	−10.5564	+	2.82858i	−1.11898	+	0.299829i	−0.770469	−	0.637478i	$-0.779978\pi$
$89$	−10.5564	+	2.82858i	−1.11898	+	0.299829i	−0.348507	+	0.937306i	$0.613311\pi$
$90$	−0.541198	+	0.435547i	−0.0570473	+	0.0459107i
$91$	−7.29695	+	6.14447i	−0.764929	+	0.644115i
$92$		−	0.363613i		−	0.0379093i
$93$	0.186319	−	0.996863i	0.0193204	−	0.103370i
$94$	1.11248			0.114743
$95$	4.14672	+	7.18233i	0.425445	+	0.736892i
$96$	1.36193	−	1.58973i	0.139001	−	0.162251i
$97$	−14.6793	+	3.93330i	−1.49045	+	0.399366i	−0.909890	−	0.414850i	$-0.863834\pi$
$97$	−14.6793	+	3.93330i	−1.49045	+	0.399366i	−0.580563	+	0.814215i	$0.697167\pi$
$98$	−0.646106	+	0.294051i	−0.0652666	+	0.0297036i
$99$	0.0453421	−	0.419188i	0.00455706	−	0.0421300i
$100$	0.425932			0.0425932
$101$	10.8586			1.08047			0.540233	−	0.841515i	$-0.318336\pi$
$101$	10.8586			1.08047			0.540233	+	0.841515i	$0.318336\pi$
$102$	0.283059	+	0.803195i	0.0280270	+	0.0795282i
$103$	15.1083	−	8.72278i	1.48866	−	0.859481i	0.488749	−	0.872425i	$-0.337454\pi$
$103$	15.1083	−	8.72278i	1.48866	−	0.859481i	0.999916	+	0.0129436i	$0.00412018\pi$
$104$	0.844307	+	1.18964i	0.0827911	+	0.116654i
$105$	1.66375	+	10.3309i	0.162365	+	1.00819i
$106$	−0.243913	+	0.910294i	−0.0236909	+	0.0884156i
$107$	13.8616	+	8.00300i	1.34005	+	0.773679i	0.986815	−	0.161854i	$-0.0517474\pi$
$107$	13.8616	+	8.00300i	1.34005	+	0.773679i	0.353237	+	0.935534i	$0.385081\pi$
$108$	7.53180	−	7.08267i	0.724747	−	0.681530i
$109$	−2.31426	+	0.620105i	−0.221666	+	0.0593953i	−0.367943	−	0.929848i	$-0.619938\pi$
$109$	−2.31426	+	0.620105i	−0.221666	+	0.0593953i	0.146276	+	0.989244i	$0.453271\pi$
$110$	0.0230128	−	0.0230128i	0.00219418	−	0.00219418i
$111$	−9.00409	−	1.68291i	−0.854630	−	0.159735i
$112$	−3.51861	−	9.80798i	−0.332477	−	0.926767i
$113$	−4.43949	−	2.56314i	−0.417632	−	0.241120i	0.276432	−	0.961034i	$-0.410848\pi$
$113$	−4.43949	−	2.56314i	−0.417632	−	0.241120i	−0.694064	+	0.719914i	$0.744181\pi$
$114$	0.360545	+	0.526301i	0.0337681	+	0.0492926i
$115$	0.295068	−	0.295068i	0.0275152	−	0.0275152i
$116$	−6.55016	+	11.3452i	−0.608167	+	1.05338i
$117$	5.27543	+	9.44298i	0.487714	+	0.873004i
$118$	−1.48905			−0.137078
$119$	12.6224	+	2.28581i	1.15709	+	0.209540i
$120$	1.59545	−	0.123135i	0.145644	−	0.0112406i
$121$		−	10.9802i		−	0.998204i
$122$	−0.140559	−	0.524573i	−0.0127256	−	0.0474926i
$123$	10.3874	−	12.1249i	0.936602	−	1.09326i
$124$	−0.823772	+	0.823772i	−0.0739769	+	0.0739769i
$125$	−7.72752	−	7.72752i	−0.691170	−	0.691170i
$126$	0.188751	+	0.782476i	0.0168153	+	0.0697085i
$127$	3.66400	−	2.11541i	0.325127	−	0.187712i	−0.328548	−	0.944487i	$-0.606559\pi$
$127$	3.66400	−	2.11541i	0.325127	−	0.187712i	0.653676	+	0.756775i	$0.273226\pi$
$128$	−3.09439	+	0.829138i	−0.273508	+	0.0732862i
$129$	0.683446	−	0.468197i	0.0601740	−	0.0412225i
$130$	−0.139756	+	0.823135i	−0.0122574	+	0.0721937i
$131$	−1.61992	+	0.935259i	−0.141533	+	0.0817140i	−0.569094	−	0.822272i	$-0.692706\pi$
$131$	−1.61992	+	0.935259i	−0.141533	+	0.0817140i	0.427562	+	0.903986i	$0.359373\pi$
$132$	−0.315122	+	0.367831i	−0.0274278	+	0.0320156i
$133$	9.57658	−	0.793303i	0.830395	−	0.0687881i
$134$	−0.0126456	+	0.0219029i	−0.00109242	+	0.00189212i
$135$	11.8595	+	0.364459i	1.02070	+	0.0313676i
$136$	0.507715	−	1.89482i	0.0435362	−	0.162479i
$137$	−3.17505	+	11.8494i	−0.271263	+	1.01237i	0.687042	+	0.726618i	$0.258909\pi$
$137$	−3.17505	+	11.8494i	−0.271263	+	1.01237i	−0.958305	+	0.285749i	$0.907758\pi$
$138$	0.0208835	−	0.0243767i	0.00177773	−	0.00207508i
$139$	−0.989015	+	1.71302i	−0.0838871	+	0.145297i	−0.904916	−	0.425589i	$-0.860067\pi$
$139$	−0.989015	+	1.71302i	−0.0838871	+	0.145297i	0.821029	+	0.570886i	$0.193400\pi$
$140$	5.13040	−	10.8708i	0.433598	−	0.918754i
$141$	−14.4295	−	12.3618i	−1.21518	−	1.04105i
$142$	−0.768757	+	0.443842i	−0.0645127	+	0.0372464i
$143$	−0.293285	−	0.413243i	−0.0245257	−	0.0345571i
$144$	−11.6753	+	1.81296i	−0.972940	+	0.151080i
$145$	−14.5219	+	3.89112i	−1.20598	+	0.323140i
$146$	0.662282	−	0.382369i	0.0548108	−	0.0316451i
$147$	11.6479	+	3.36549i	0.960702	+	0.277581i
$148$	7.44066	+	7.44066i	0.611619	+	0.611619i
$149$	3.96245	−	3.96245i	0.324616	−	0.324616i	−0.525919	−	0.850535i	$-0.676278\pi$
$149$	3.96245	−	3.96245i	0.324616	−	0.324616i	0.850535	+	0.525919i	$0.176278\pi$
$150$	0.0285546	+	0.0244628i	0.00233147	+	0.00199738i
$151$	1.30750	+	4.87965i	0.106403	+	0.397100i	0.998501	−	0.0547421i	$-0.0174337\pi$
$151$	1.30750	+	4.87965i	0.106403	+	0.397100i	−0.892098	+	0.451842i	$0.850767\pi$
$152$		−	1.46950i		−	0.119193i
$153$	5.25363	−	13.5633i	0.424731	−	1.09653i
$154$	−0.0127335	−	0.0354940i	−0.00102609	−	0.00286019i
$155$	−1.33696			−0.107387
$156$	1.13111	−	12.3742i	0.0905614	−	0.990728i
$157$	1.24722	−	2.16024i	0.0995386	−	0.172406i	−0.811955	−	0.583720i	$-0.801597\pi$
$157$	1.24722	−	2.16024i	0.0995386	−	0.172406i	0.911494	+	0.411314i	$0.134930\pi$
$158$	−0.244125	+	0.244125i	−0.0194215	+	0.0194215i
$159$	13.2789	−	9.09674i	1.05308	−	0.721419i
$160$	−2.39000	−	1.37987i	−0.188946	−	0.109088i
$161$	−0.163267	−	0.455101i	−0.0128673	−	0.0358670i
$162$	0.911715	−	0.0422463i	0.0716311	−	0.00331918i
$163$	−8.82683	+	8.82683i	−0.691371	+	0.691371i	−0.962534	−	0.271163i	$-0.912592\pi$
$163$	−8.82683	+	8.82683i	−0.691371	+	0.691371i	0.271163	+	0.962534i	$0.412592\pi$
$164$	−17.7161	+	4.74702i	−1.38340	+	0.370680i
$165$	−0.554208	+	0.0427730i	−0.0431450	+	0.00332987i
$166$	0.224165	+	0.129422i	0.0173986	+	0.0100451i
$167$	−0.867439	+	3.23732i	−0.0671244	+	0.250512i	−0.991332	−	0.131378i	$-0.958060\pi$
$167$	−0.867439	+	3.23732i	−0.0671244	+	0.250512i	0.924208	+	0.381890i	$0.124727\pi$
$168$	0.659957	−	1.73267i	0.0509168	−	0.133679i
$169$	12.2715	+	4.29073i	0.943961	+	0.330056i
$170$	0.972300	−	0.561358i	0.0745720	−	0.0430542i
$171$	1.17175	−	10.8328i	0.0896060	−	0.828407i
$172$	−0.951677			−0.0725647
$173$	11.6730			0.887479			0.443739	−	0.896156i	$-0.353652\pi$
$173$	11.6730			0.887479			0.443739	+	0.896156i	$0.353652\pi$
$174$	−1.09072	+	0.384386i	−0.0826871	+	0.0291402i
$175$	0.533100	−	0.191250i	0.0402986	−	0.0144571i
$176$	0.534659	−	0.143262i	0.0403015	−	0.0107987i
$177$	19.3139	+	16.5463i	1.45172	+	1.24370i
$178$	0.554146	+	0.959809i	0.0415350	+	0.0719407i
$179$	19.1698			1.43282			0.716409	−	0.697680i	$-0.245784\pi$
$179$	19.1698			1.43282			0.716409	+	0.697680i	$0.245784\pi$
$180$	−11.0027	−	8.04495i	−0.820094	−	0.599635i
$181$			13.4896i			1.00268i	0.865252	+	0.501338i	$0.167159\pi$
$181$			13.4896i			1.00268i	−0.865252	+	0.501338i	$0.832841\pi$
$182$	0.793403	+	0.553499i	0.0588110	+	0.0410281i
$183$	−4.00591	+	8.36594i	−0.296125	+	0.618428i
$184$	−0.0714194	+	0.0191368i	−0.00526511	+	0.00141078i
$185$			12.0760i			0.887847i
$186$	−0.102538	+	0.00791373i	−0.00751844	+	0.000580263i
$187$	−0.176364	+	0.658198i	−0.0128970	+	0.0481322i
$188$	5.64931	+	21.0835i	0.412018	+	1.53767i
$189$	6.24664	−	12.2466i	0.454376	−	0.890810i
$190$	0.594706	−	0.594706i	0.0431445	−	0.0431445i
$191$		−	10.4621i		−	0.757015i	−0.925598	−	0.378507i	$-0.876438\pi$
$191$		−	10.4621i		−	0.757015i	0.925598	−	0.378507i	$-0.123562\pi$
$192$	12.1136	+	5.80043i	0.874225	+	0.418610i
$193$	−4.61507	+	4.61507i	−0.332200	+	0.332200i	−0.853421	−	0.521222i	$-0.825477\pi$
$193$	−4.61507	+	4.61507i	−0.332200	+	0.332200i	0.521222	+	0.853421i	$0.325477\pi$
$194$	0.770571	+	1.33467i	0.0553238	+	0.0958236i
$195$	10.9594	−	9.12362i	0.784818	−	0.653356i
$196$	−8.85384	−	10.7517i	−0.632417	−	0.767978i
$197$	12.6332	+	3.38506i	0.900079	+	0.241175i	0.679050	−	0.734092i	$-0.262392\pi$
$197$	12.6332	+	3.38506i	0.900079	+	0.241175i	0.221029	+	0.975267i	$0.429059\pi$
$198$	−0.0422516	+	0.00656092i	−0.00300269	+	0.000466264i
$199$	−21.7534	+	12.5593i	−1.54206	+	0.890309i	−0.543351	+	0.839506i	$0.682845\pi$
$199$	−21.7534	+	12.5593i	−1.54206	+	0.890309i	−0.998709	+	0.0508031i	$0.983822\pi$
$200$	−0.0224166	−	0.0836599i	−0.00158509	−	0.00591565i
$201$	0.407406	−	0.143576i	0.0287362	−	0.0101271i
$202$	−0.285004	−	1.06365i	−0.0200528	−	0.0748380i
$203$	−3.10407	+	17.1409i	−0.217863	+	1.20305i
$204$	−13.7846	+	9.44323i	−0.965119	+	0.661158i
$205$	−18.2286	−	10.5243i	−1.27314	−	0.735048i
$206$	−1.25099	−	1.25099i	−0.0871603	−	0.0871603i
$207$	−0.541746	+	0.0841234i	−0.0376539	+	0.00584698i
$208$	−9.05838	+	10.9357i	−0.628086	+	0.758252i
$209$			0.510458i			0.0353091i
$210$	0.968293	−	0.434127i	0.0668186	−	0.0299576i
$211$	7.01520	+	12.1507i	0.482946	+	0.836488i	0.999808	−	0.0195811i	$-0.00623326\pi$
$211$	7.01520	+	12.1507i	0.482946	+	0.836488i	−0.516862	+	0.856069i	$0.672900\pi$
$212$	−18.4904			−1.26993
$213$	14.9032	+	2.78550i	1.02115	+	0.190859i
$214$	0.420109	−	1.56787i	0.0287180	−	0.107177i
$215$	−0.772275	−	0.772275i	−0.0526687	−	0.0526687i
$216$	−1.78755	−	1.10661i	−0.121627	−	0.0752951i
$217$	−0.661154	+	1.40093i	−0.0448821	+	0.0951010i
$218$	0.121485	+	0.210418i	0.00822798	+	0.0142513i
$219$	−12.8391	−	2.39970i	−0.867585	−	0.162156i
$220$	0.552998	+	0.319273i	0.0372831	+	0.0215254i
$221$	−6.08313	−	16.3886i	−0.409196	−	1.10242i
$222$	0.0714802	+	0.926166i	0.00479743	+	0.0621602i
$223$	1.28795	−	4.80671i	0.0862478	−	0.321881i	−0.909300	−	0.416142i	$-0.863382\pi$
$223$	1.28795	−	4.80671i	0.0862478	−	0.321881i	0.995548	+	0.0942606i	$0.0300487\pi$
$224$	−2.62779	+	1.82197i	−0.175577	+	0.121736i
$225$	−0.0985413	−	0.634595i	−0.00656942	−	0.0423064i
$226$	−0.134549	+	0.502144i	−0.00895008	+	0.0334022i
$227$	−3.06928	−	0.822412i	−0.203716	−	0.0545854i	0.155518	−	0.987833i	$-0.450295\pi$
$227$	−3.06928	−	0.822412i	−0.203716	−	0.0545854i	−0.359234	+	0.933248i	$0.616962\pi$
$228$	−8.14350	+	9.50564i	−0.539317	+	0.629526i
$229$	5.86430	+	1.57134i	0.387524	+	0.103837i	0.447320	−	0.894374i	$-0.352378\pi$
$229$	5.86430	+	1.57134i	0.387524	+	0.103837i	−0.0597962	+	0.998211i	$0.519045\pi$
$230$	−0.0366479	−	0.0211587i	−0.00241649	−	0.00139516i
$231$	−0.229247	+	0.601874i	−0.0150834	+	0.0396004i
$232$	2.57311	+	0.689463i	0.168933	+	0.0452655i
$233$	−8.04672	−	13.9373i	−0.527158	−	0.913065i	−0.999499	−	0.0316488i	$-0.989924\pi$
$233$	−8.04672	−	13.9373i	−0.527158	−	0.913065i	0.472341	−	0.881416i	$-0.343409\pi$
$234$	0.786522	−	0.764604i	0.0514166	−	0.0499837i
$235$	−12.5247	+	21.6934i	−0.817020	+	1.41512i
$236$	−7.56161	−	28.2203i	−0.492219	−	1.83699i
$237$	5.87917	−	0.453746i	0.381893	−	0.0294740i
$238$	−0.107393	−	1.29642i	−0.00696122	−	0.0840344i
$239$	7.82407	−	7.82407i	0.506097	−	0.506097i	−0.407229	−	0.913326i	$-0.633505\pi$
$239$	7.82407	−	7.82407i	0.506097	−	0.506097i	0.913326	+	0.407229i	$0.133505\pi$
$240$	5.17730	+	14.6909i	0.334193	+	0.948292i
$241$	−1.95019	−	0.522551i	−0.125623	−	0.0336605i	0.195460	−	0.980712i	$-0.437380\pi$
$241$	−1.95019	−	0.522551i	−0.125623	−	0.0336605i	−0.321083	+	0.947051i	$0.604047\pi$
$242$	−1.07557	+	0.288198i	−0.0691402	+	0.0185261i
$243$	−12.2950	−	9.58300i	−0.788722	−	0.614749i
$244$	9.22787	−	5.32771i	0.590754	−	0.341072i
$245$	1.54009	−	15.9097i	0.0983925	−	1.01643i
$246$	−1.46033	−	0.699258i	−0.0931073	−	0.0445830i
$247$	−7.57918	−	10.6792i	−0.482252	−	0.679500i
$248$	0.205157	+	0.118447i	0.0130275	+	0.00752141i
$249$	−1.46943	−	4.16960i	−0.0931214	−	0.264238i
$250$	−0.554124	+	0.959772i	−0.0350459	+	0.0607013i
$251$	13.2053	−	22.8723i	0.833513	−	1.44369i	−0.0617231	−	0.998093i	$-0.519660\pi$
$251$	13.2053	−	22.8723i	0.833513	−	1.44369i	0.895236	−	0.445593i	$-0.147007\pi$
$252$	−13.8709	+	7.55071i	−0.873784	+	0.475650i
$253$	0.0248088	−	0.00664749i	0.00155971	−	0.000417924i
$254$	−0.303383	−	0.303383i	−0.0190360	−	0.0190360i
$255$	−18.8492	−	3.52301i	−1.18038	−	0.220619i
$256$	−7.59180	−	13.1494i	−0.474488	−	0.821837i
$257$	−10.6569	+	18.4584i	−0.664761	+	1.15140i	0.314589	+	0.949228i	$0.398133\pi$
$257$	−10.6569	+	18.4584i	−0.664761	+	1.15140i	−0.979350	+	0.202172i	$0.935200\pi$
$258$	−0.0638006	−	0.0546581i	−0.00397205	−	0.00340287i
$259$	12.6538	+	5.97183i	0.786266	+	0.371071i
$260$	−16.3097	+	1.53135i	−1.01148	+	0.0949705i
$261$	18.4186	+	7.13430i	1.14008	+	0.441602i
$262$	0.134131	+	0.134131i	0.00828664	+	0.00828664i
$263$		−	16.0738i		−	0.991156i	−0.868563	−	0.495578i	$-0.834956\pi$
$263$		−	16.0738i		−	0.991156i	0.868563	−	0.495578i	$-0.165044\pi$
$264$	0.0888326	+	0.0425362i	0.00546727	+	0.00261792i
$265$	−15.0048	−	15.0048i	−0.921735	−	0.921735i
$266$	−0.329064	−	0.917251i	−0.0201762	−	0.0562403i
$267$	3.47775	−	18.6070i	0.212835	−	1.13873i
$268$	−0.479317	−	0.128433i	−0.0292790	−	0.00784527i
$269$	−15.7901	+	9.11639i	−0.962737	+	0.555836i	−0.897014	−	0.442002i	$-0.854269\pi$
$269$	−15.7901	+	9.11639i	−0.962737	+	0.555836i	−0.0657224	+	0.997838i	$0.520935\pi$
$270$	−0.275574	−	1.17126i	−0.0167709	−	0.0712805i
$271$	6.34764	+	23.6897i	0.385592	+	1.43905i	0.837232	+	0.546848i	$0.184172\pi$
$271$	6.34764	+	23.6897i	0.385592	+	1.43905i	−0.451640	+	0.892200i	$0.649161\pi$
$272$	19.0950			1.15780
$273$	−4.14048	−	15.9955i	−0.250593	−	0.968093i
$274$	1.24405			0.0751556
$275$	0.00778680	+	0.0290607i	0.000469562	+	0.00175243i
$276$	0.568034	+	0.271994i	0.0341916	+	0.0163721i
$277$	24.0917	−	13.9093i	1.44753	−	0.835730i	0.449194	−	0.893434i	$-0.351711\pi$
$277$	24.0917	−	13.9093i	1.44753	−	0.835730i	0.998334	+	0.0577042i	$0.0183780\pi$
$278$	0.193758	+	0.0519172i	0.0116208	+	0.00311379i
$279$	1.41792	+	1.03675i	0.0848886	+	0.0620688i
$280$	−2.40522	−	0.435566i	−0.143739	−	0.0260300i
$281$	−4.03859	−	4.03859i	−0.240922	−	0.240922i	0.576310	−	0.817232i	$-0.304492\pi$
$281$	−4.03859	−	4.03859i	−0.240922	−	0.240922i	−0.817232	+	0.576310i	$0.804492\pi$
$282$	−0.832169	+	1.73790i	−0.0495549	+	0.103491i
$283$			22.8743i			1.35974i	0.733334	+	0.679869i	$0.237963\pi$
$283$			22.8743i			1.35974i	−0.733334	+	0.679869i	$0.762037\pi$
$284$	−12.3155	−	12.3155i	−0.730791	−	0.730791i
$285$	−14.3221	+	1.10536i	−0.848366	+	0.0654757i
$286$	−0.0327813	+	0.0395750i	−0.00193840	+	0.00234012i
$287$	−20.0422	+	13.8962i	−1.18305	+	0.820267i
$288$	1.46470	+	3.31676i	0.0863083	+	0.195442i
$289$	−3.25353	+	5.63528i	−0.191384	+	0.331487i
$290$	0.762309	+	1.32036i	0.0447644	+	0.0775341i
$291$	4.83600	−	25.8741i	0.283492	−	1.51676i
$292$	10.6098	+	10.6098i	0.620890	+	0.620890i
$293$	−9.98973	+	2.67674i	−0.583606	+	0.156377i	−0.538529	−	0.842607i	$-0.681020\pi$
$293$	−9.98973	+	2.67674i	−0.583606	+	0.156377i	−0.0450769	+	0.998984i	$0.514353\pi$
$294$	0.0239442	−	1.22930i	0.00139645	−	0.0716944i
$295$	16.7643	−	29.0366i	0.976055	−	1.69058i
$296$	1.06987	−	1.85306i	0.0621848	−	0.107707i
$297$	0.620935	+	0.384400i	0.0360303	+	0.0223051i
$298$	−0.492143	−	0.284139i	−0.0285091	−	0.0164597i
$299$	−0.420319	+	0.507427i	−0.0243077	+	0.0293453i
$300$	−0.318611	+	0.665388i	−0.0183950	+	0.0384162i
$301$	−1.19113	+	0.427317i	−0.0686554	+	0.0246301i
$302$	0.443668	−	0.256152i	0.0255302	−	0.0147399i
$303$	−8.12256	+	16.9632i	−0.466629	+	0.974508i
$304$	13.8169	−	3.70222i	0.792453	−	0.212337i
$305$	11.8117	+	3.16493i	0.676335	+	0.181223i
$306$	−1.46648	−	0.158624i	−0.0838332	−	0.00906795i
$307$	−7.38343	+	7.38343i	−0.421395	+	0.421395i	−0.885684	−	0.464289i	$-0.846310\pi$
$307$	−7.38343	+	7.38343i	−0.421395	+	0.421395i	0.464289	+	0.885684i	$0.346310\pi$
$308$	0.608016	−	0.421567i	0.0346449	−	0.0240210i
$309$	2.32516	+	30.1270i	0.132274	+	1.71387i
$310$	0.0350912	+	0.130962i	0.00199304	+	0.00743814i
$311$	−1.13541	+	1.96659i	−0.0643833	+	0.111515i	−0.896420	−	0.443205i	$-0.853841\pi$
$311$	−1.13541	+	1.96659i	−0.0643833	+	0.111515i	0.832037	+	0.554720i	$0.187175\pi$
$312$	−2.49002	+	0.429079i	−0.140970	+	0.0242918i
$313$	−6.85454	−	11.8724i	−0.387442	−	0.671069i	0.604663	−	0.796481i	$-0.293308\pi$
$313$	−6.85454	−	11.8724i	−0.387442	−	0.671069i	−0.992105	+	0.125413i	$0.959975\pi$
$314$	−0.244342	−	0.0654712i	−0.0137890	−	0.00369475i
$315$	−17.3834	−	5.12875i	−0.979443	−	0.288973i
$316$	−5.86633	−	3.38693i	−0.330007	−	0.190530i
$317$	18.9068	+	5.06606i	1.06191	+	0.284538i	0.747166	−	0.664638i	$-0.231414\pi$
$317$	18.9068	+	5.06606i	1.06191	+	0.284538i	0.314746	+	0.949176i	$0.398081\pi$
$318$	−1.23960	−	1.06197i	−0.0695133	−	0.0595522i
$319$	−0.893815	−	0.239497i	−0.0500441	−	0.0134093i
$320$	4.58272	−	17.1030i	0.256182	−	0.956084i
$321$	−22.8712	+	15.6680i	−1.27654	+	0.874502i
$322$	−0.0402941	+	0.0279378i	−0.00224550	+	0.00155692i
$323$	−4.55766	+	17.0094i	−0.253595	+	0.946429i
$324$	5.43047	+	17.0642i	0.301693	+	0.948011i
$325$	−0.594394	−	0.492357i	−0.0329711	−	0.0273110i
$326$	1.09631	+	0.632954i	0.0607189	+	0.0350561i
$327$	0.762422	−	4.07919i	0.0421620	−	0.225579i
$328$	1.86478	+	3.22990i	0.102965	+	0.178341i
$329$	16.5375	+	23.8517i	0.911743	+	1.31499i
$330$	0.0187361	+	0.0531647i	0.00103139	+	0.00292662i
$331$	−19.4713	−	19.4713i	−1.07024	−	1.07024i	−0.997339	−	0.0728994i	$-0.976775\pi$
$331$	−19.4713	−	19.4713i	−1.07024	−	1.07024i	−0.0728994	−	0.997339i	$-0.523225\pi$
$332$	−1.31444	+	4.90557i	−0.0721395	+	0.269228i
$333$	9.36439	−	12.8073i	0.513166	−	0.701833i
$334$	0.339879			0.0185974
$335$	−0.284739	−	0.493182i	−0.0155569	−	0.0269454i
$336$	17.9540	+	1.83994i	0.979470	+	0.100377i
$337$		−	9.32250i		−	0.507829i	−0.967227	−	0.253914i	$-0.918282\pi$
$337$		−	9.32250i		−	0.507829i	0.967227	−	0.253914i	$-0.0817182\pi$
$338$	0.0982087	−	1.31467i	0.00534185	−	0.0715087i
$339$	7.32501	−	5.01803i	0.397840	−	0.272542i
$340$	15.5763	+	15.5763i	0.844742	+	0.844742i
$341$	−0.0712648	−	0.0411447i	−0.00385920	−	0.00222811i
$342$	−1.09188	+	0.169550i	−0.0590423	+	0.00916821i
$343$	−15.9092	−	9.48141i	−0.859016	−	0.511948i
$344$	0.0500863	+	0.186925i	0.00270047	+	0.0100783i
$345$	0.240232	+	0.681673i	0.0129337	+	0.0367000i
$346$	−0.306379	−	1.14342i	−0.0164711	−	0.0614708i
$347$	29.5306	−	17.0495i	1.58528	−	0.915264i	0.591214	−	0.806515i	$-0.298649\pi$
$347$	29.5306	−	17.0495i	1.58528	−	0.915264i	0.994069	−	0.108749i	$-0.0346846\pi$
$348$	−12.8237	−	18.7192i	−0.687421	−	1.00345i
$349$	27.9536	+	7.49016i	1.49632	+	0.400939i	0.911867	−	0.410486i	$-0.134641\pi$
$349$	27.9536	+	7.49016i	1.49632	+	0.400939i	0.584457	+	0.811425i	$0.301307\pi$
$350$	−0.0327261	−	0.0472001i	−0.00174928	−	0.00252295i
$351$	−18.6979	+	1.17758i	−0.998023	+	0.0628546i
$352$	−0.0849304	−	0.147104i	−0.00452680	−	0.00784066i
$353$	−6.42719	+	6.42719i	−0.342085	+	0.342085i	−0.857151	−	0.515066i	$-0.827767\pi$
$353$	−6.42719	+	6.42719i	−0.342085	+	0.342085i	0.515066	+	0.857151i	$0.327767\pi$
$354$	1.11386	−	2.32618i	0.0592009	−	0.123635i
$355$		−	19.9878i		−	1.06084i
$356$	−15.3762	+	15.3762i	−0.814935	+	0.814935i
$357$	−13.0128	+	18.0087i	−0.688712	+	0.953123i
$358$	−0.503149	−	1.87778i	−0.0265922	−	0.0992436i
$359$	−6.49014	+	24.2215i	−0.342536	+	1.27836i	0.552928	+	0.833229i	$0.313511\pi$
$359$	−6.49014	+	24.2215i	−0.342536	+	1.27836i	−0.895464	+	0.445134i	$0.853156\pi$
$360$	−1.00109	+	2.58451i	−0.0527621	+	0.136216i
$361$		−	5.80854i		−	0.305713i
$362$	1.32137	−	0.354061i	0.0694499	−	0.0186090i
$363$	17.1533	+	8.21359i	0.900313	+	0.431102i
$364$	−6.46084	+	17.8472i	−0.338640	+	0.935449i
$365$			17.2194i			0.901305i
$366$	0.924627	+	0.172818i	0.0483310	+	0.00903333i
$367$	24.8514			1.29723			0.648617	−	0.761115i	$-0.275348\pi$
$367$	24.8514			1.29723			0.648617	+	0.761115i	$0.275348\pi$
$368$	−0.359864	−	0.623302i	−0.0187592	−	0.0324919i
$369$	11.1713	+	25.2970i	0.581554	+	1.31691i
$370$	1.18291	−	0.316958i	0.0614963	−	0.0164779i
$371$	−23.1428	+	8.30246i	−1.20151	+	0.431042i
$372$	−0.670682	−	1.90310i	−0.0347732	−	0.0986711i
$373$	33.9524			1.75799			0.878995	−	0.476831i	$-0.158215\pi$
$373$	33.9524			1.75799			0.878995	+	0.476831i	$0.158215\pi$
$374$	0.0691027			0.00357322
$375$	17.8523	−	6.29143i	0.921889	−	0.324888i
$376$	3.84382	−	2.21923i	0.198230	−	0.114448i
$377$	22.2553	−	8.26073i	1.14621	−	0.425449i
$378$	−1.36357	−	0.290453i	−0.0701345	−	0.0149393i
$379$	8.90954	−	33.2509i	0.457653	−	1.70798i	−0.222518	−	0.974929i	$-0.571428\pi$
$379$	8.90954	−	33.2509i	0.457653	−	1.70798i	0.680171	−	0.733054i	$-0.261906\pi$
$380$	14.2908	+	8.25080i	0.733102	+	0.423257i
$381$	0.563887	+	7.30626i	0.0288888	+	0.374311i
$382$	−1.02482	+	0.274599i	−0.0524343	+	0.0140497i
$383$	9.28218	−	9.28218i	0.474297	−	0.474297i	−0.429005	−	0.903302i	$-0.641136\pi$
$383$	9.28218	−	9.28218i	0.474297	−	0.474297i	0.903302	+	0.429005i	$0.141136\pi$
$384$	1.01943	−	5.45425i	0.0520225	−	0.278336i
$385$	0.835495	+	0.151301i	0.0425808	+	0.00771103i
$386$	0.573200	+	0.330937i	0.0291751	+	0.0168443i
$387$	0.220175	+	1.41790i	0.0111921	+	0.0720760i
$388$	−21.3814	+	21.3814i	−1.08548	+	1.08548i
$389$	−6.54242	+	11.3318i	−0.331714	+	0.574545i	−0.982848	−	0.184418i	$-0.940960\pi$
$389$	−6.54242	+	11.3318i	−0.331714	+	0.574545i	0.651134	+	0.758963i	$0.274293\pi$
$390$	−1.18135	−	0.834059i	−0.0598202	−	0.0422342i
$391$	0.886028			0.0448084
$392$	−1.64583	+	2.30489i	−0.0831271	+	0.116415i
$393$	−0.249304	−	3.23023i	−0.0125757	−	0.162943i
$394$		−	1.32633i		−	0.0668196i
$395$	−2.01201	−	7.50891i	−0.101235	−	0.377814i
$396$	−0.338901	−	0.767430i	−0.0170304	−	0.0385648i
$397$	−6.56991	+	6.56991i	−0.329734	+	0.329734i	−0.852485	−	0.522751i	$-0.824906\pi$
$397$	−6.56991	+	6.56991i	−0.329734	+	0.329734i	0.522751	+	0.852485i	$0.324906\pi$
$398$	1.80121	+	1.80121i	0.0902865	+	0.0902865i
$399$	−5.92431	+	15.5539i	−0.296586	+	0.778668i
$400$	0.730130	−	0.421541i	0.0365065	−	0.0210770i
$401$	14.5662	−	3.90300i	0.727401	−	0.194907i	0.123930	−	0.992291i	$-0.460450\pi$
$401$	14.5662	−	3.90300i	0.727401	−	0.194907i	0.603472	+	0.797384i	$0.293784\pi$
$402$	−0.0247572	−	0.0361390i	−0.00123478	−	0.00180245i
$403$	2.10183	−	0.197345i	0.104699	−	0.00983047i
$404$	18.7109	−	10.8027i	0.930900	−	0.537455i
$405$	−9.44063	+	18.2541i	−0.469109	+	0.907056i
$406$	1.76050	−	0.145836i	0.0873723	−	0.00723773i
$407$	−0.371637	+	0.643694i	−0.0184214	+	0.0319067i
$408$	2.58028	+	2.21053i	0.127743	+	0.109438i
$409$	2.62405	−	9.79307i	0.129751	−	0.484236i	−0.870214	−	0.492674i	$-0.836019\pi$
$409$	2.62405	−	9.79307i	0.129751	−	0.484236i	0.999964	+	0.00843825i	$0.00268601\pi$
$410$	−0.552460	+	2.06181i	−0.0272841	+	0.101826i
$411$	−16.1361	−	13.8238i	−0.795934	−	0.681879i
$412$	17.3559	−	30.0612i	0.855062	−	1.48101i
$413$	−22.1355	−	31.9255i	−1.08922	−	1.57095i
$414$	0.0224595	+	0.0508587i	0.00110382	+	0.00249957i
$415$	−5.04747	+	2.91416i	−0.247770	+	0.143050i
$416$	3.96098	+	1.81650i	0.194203	+	0.0890611i
$417$	−1.93626	−	2.82643i	−0.0948189	−	0.138411i
$418$	0.0500018	−	0.0133980i	0.00244567	−	0.000655315i
$419$	−8.90455	+	5.14105i	−0.435016	+	0.251157i	−0.701481	−	0.712688i	$-0.747478\pi$
$419$	−8.90455	+	5.14105i	−0.435016	+	0.251157i	0.266465	+	0.963845i	$0.414144\pi$
$420$	13.1446	+	16.1464i	0.641393	+	0.787865i
$421$	7.97769	+	7.97769i	0.388809	+	0.388809i	0.874262	−	0.485454i	$-0.161346\pi$
$421$	7.97769	+	7.97769i	0.388809	+	0.388809i	−0.485454	+	0.874262i	$0.661346\pi$
$422$	1.00609	−	1.00609i	0.0489758	−	0.0489758i
$423$	30.1053	−	13.2947i	1.46377	−	0.646408i
$424$	0.973142	+	3.63181i	0.0472599	+	0.176377i
$425$			1.03788i			0.0503447i
$426$	−0.118311	−	1.53296i	−0.00573220	−	0.0742720i
$427$	9.15746	−	10.8117i	0.443161	−	0.523213i
$428$	31.8474			1.53940
$429$	0.864951	−	0.149048i	0.0417602	−	0.00719611i
$430$	−0.0553783	+	0.0959180i	−0.00267058	+	0.00462557i
$431$	−17.6837	+	17.6837i	−0.851794	+	0.851794i	−0.990354	−	0.138560i	$-0.955753\pi$
$431$	−17.6837	+	17.6837i	−0.851794	+	0.851794i	0.138560	+	0.990354i	$0.455753\pi$
$432$	5.90130	−	19.5952i	0.283926	−	0.942774i
$433$	−20.7642	−	11.9882i	−0.997863	−	0.576116i	−0.0902476	−	0.995919i	$-0.528766\pi$
$433$	−20.7642	−	11.9882i	−0.997863	−	0.576116i	−0.907615	+	0.419803i	$0.862099\pi$
$434$	0.154581	+	0.0279933i	0.00742011	+	0.00134372i
$435$	4.78416	−	25.5967i	0.229383	−	1.22727i
$436$	−3.37089	+	3.37089i	−0.161437	+	0.161437i
$437$	0.641119	−	0.171787i	0.0306689	−	0.00821770i
$438$	0.101925	+	1.32064i	0.00487016	+	0.0631025i
$439$	13.2516	+	7.65080i	0.632463	+	0.365153i	0.781705	−	0.623648i	$-0.214350\pi$
$439$	13.2516	+	7.65080i	0.632463	+	0.365153i	−0.149242	+	0.988801i	$0.547683\pi$
$440$	0.0336064	−	0.125421i	0.00160212	−	0.00597921i
$441$	−13.9705	+	15.6788i	−0.665264	+	0.746608i
$442$	−1.44568	+	1.02602i	−0.0687641	+	0.0488030i
$443$	15.3702	−	8.87401i	0.730262	−	0.421617i	−0.0882559	−	0.996098i	$-0.528129\pi$
$443$	15.3702	−	8.87401i	0.730262	−	0.421617i	0.818518	+	0.574481i	$0.194796\pi$
$444$	−17.1896	+	6.05789i	−0.815783	+	0.287495i
$445$	−24.9551			−1.18299
$446$	−0.504646			−0.0238957
$447$	3.22607	+	9.15415i	0.152588	+	0.432976i
$448$	−15.6549	−	13.2597i	−0.739627	−	0.626463i
$449$	26.9065	−	7.20957i	1.26980	−	0.340241i	0.439843	−	0.898075i	$-0.355034\pi$
$449$	26.9065	−	7.20957i	1.26980	−	0.340241i	0.829953	+	0.557834i	$0.188367\pi$
$450$	−0.0595753	+	0.0263088i	−0.00280841	+	0.00124021i
$451$	−0.647765	−	1.12196i	−0.0305021	−	0.0528311i
$452$	−10.1998			−0.479760
$453$	−8.60100	−	1.60757i	−0.404110	−	0.0755304i
$454$			0.322237i			0.0151233i
$455$	−19.7257	+	9.23993i	−0.924756	+	0.433175i
$456$	2.29565	+	1.09924i	0.107504	+	0.0514765i
$457$	7.40899	−	1.98523i	0.346578	−	0.0928653i	−0.0813309	−	0.996687i	$-0.525917\pi$
$457$	7.40899	−	1.98523i	0.346578	−	0.0928653i	0.427909	+	0.903822i	$0.359250\pi$
$458$		−	0.615680i		−	0.0287688i
$459$	17.2586	+	18.3530i	0.805562	+	0.856644i
$460$	0.214894	−	0.801994i	0.0100195	−	0.0373932i
$461$	−3.03989	−	11.3450i	−0.141582	−	0.528390i	−0.999884	−	0.0152454i	$-0.995147\pi$
$461$	−3.03989	−	11.3450i	−0.141582	−	0.528390i	0.858302	−	0.513145i	$-0.171520\pi$
$462$	0.0649736	+	0.00665856i	0.00302284	+	0.000309784i
$463$	−3.08392	+	3.08392i	−0.143322	+	0.143322i	−0.775127	−	0.631805i	$-0.782314\pi$
$463$	−3.08392	+	3.08392i	−0.143322	+	0.143322i	0.631805	+	0.775127i	$0.282314\pi$
$464$			25.9305i			1.20379i
$465$	1.00009	−	2.08859i	0.0463782	−	0.0968562i
$466$	−1.15403	+	1.15403i	−0.0534593	+	0.0534593i
$467$	−12.9426	−	22.4173i	−0.598914	−	1.03735i	−0.992982	−	0.118268i	$-0.962266\pi$
$467$	−12.9426	−	22.4173i	−0.598914	−	1.03735i	0.394068	−	0.919081i	$-0.371068\pi$
$468$	18.4848	+	11.0233i	0.854458	+	0.509553i
$469$	−0.657586	+	0.0544729i	−0.0303645	+	0.00251533i
$470$	2.45371	+	0.657469i	0.113181	+	0.0303268i
$471$	2.44175	+	3.56432i	0.112510	+	0.164235i
$472$	−5.14496	+	2.97044i	−0.236816	+	0.136726i
$473$	−0.0173984	−	0.0649316i	−0.000799977	−	0.00298556i
$474$	−0.198757	−	0.563984i	−0.00912920	−	0.0259046i
$475$	0.201230	+	0.751000i	0.00923305	+	0.0344582i
$476$	24.0242	−	8.61869i	1.10115	−	0.395037i
$477$	4.27784	+	27.5488i	0.195869	+	1.26137i
$478$	−0.971764	−	0.561048i	−0.0444475	−	0.0256618i
$479$	9.60829	+	9.60829i	0.439014	+	0.439014i	0.891680	−	0.452666i	$-0.149527\pi$
$479$	9.60829	+	9.60829i	0.439014	+	0.439014i	−0.452666	+	0.891680i	$0.649527\pi$
$480$	3.94342	−	2.70146i	0.179992	−	0.123304i
$481$	−1.78251	−	18.9846i	−0.0812754	−	0.865623i
$482$			0.204746i			0.00932592i
$483$	0.833085	+	0.0853754i	0.0379067	+	0.00388471i
$484$	−10.9238	−	18.9206i	−0.496536	−	0.860025i
$485$	−34.7015			−1.57572
$486$	−0.615996	+	1.45588i	−0.0279422	+	0.0660399i
$487$	−2.61585	+	9.76249i	−0.118536	+	0.442381i	−0.999527	−	0.0307513i	$-0.990210\pi$
$487$	−2.61585	+	9.76249i	−0.118536	+	0.442381i	0.880991	+	0.473132i	$0.156877\pi$
$488$	−1.53211	−	1.53211i	−0.0693552	−	0.0693552i
$489$	−7.18645	−	20.3920i	−0.324983	−	0.922157i
$490$	−1.59885	+	0.266721i	−0.0722288	+	0.0120492i
$491$	−4.53840	−	7.86073i	−0.204815	−	0.354750i	0.745259	−	0.666775i	$-0.232326\pi$
$491$	−4.53840	−	7.86073i	−0.204815	−	0.354750i	−0.950074	+	0.312025i	$0.898993\pi$
$492$	5.83649	−	31.2269i	0.263129	−	1.40782i
$493$	−27.6452	−	15.9610i	−1.24508	−	0.718847i
$494$	−0.847148	+	1.02271i	−0.0381150	+	0.0460141i
$495$	0.347746	−	0.897775i	0.0156300	−	0.0403520i
$496$	−0.596825	+	2.22738i	−0.0267982	+	0.100012i
$497$	−20.9440	−	9.88435i	−0.939468	−	0.443374i
$498$	−0.369864	+	0.253377i	−0.0165740	+	0.0113541i
$499$	5.54150	−	20.6812i	0.248072	−	0.925816i	−0.723743	−	0.690069i	$-0.757580\pi$
$499$	5.54150	−	20.6812i	0.248072	−	0.925816i	0.971815	−	0.235746i	$-0.0757534\pi$
$500$	−21.0034	−	5.62785i	−0.939301	−	0.251685i
$501$	−4.40845	−	3.77673i	−0.196955	−	0.168732i
$502$	−2.58705	−	0.693199i	−0.115466	−	0.0309390i
$503$	6.12042	+	3.53362i	0.272896	+	0.157557i	0.630203	−	0.776430i	$-0.282972\pi$
$503$	6.12042	+	3.53362i	0.272896	+	0.157557i	−0.357307	+	0.933987i	$0.616305\pi$
$504$	2.21310	+	2.32708i	0.0985793	+	0.103656i
$505$	23.9499	+	6.41736i	1.06576	+	0.285569i
$506$	−0.00130231	−	0.00225567i	−5.78947e−5	−	0.000100277i
$507$	−15.8824	+	15.9608i	−0.705364	+	0.708846i
$508$	4.20906	−	7.29031i	0.186747	−	0.323455i
$509$	−0.325714	−	1.21558i	−0.0144370	−	0.0538796i	0.958332	−	0.285658i	$-0.0922122\pi$
$509$	−0.325714	−	1.21558i	−0.0144370	−	0.0538796i	−0.972769	+	0.231779i	$0.925546\pi$
$510$	0.149636	+	1.93884i	0.00662601	+	0.0858531i
$511$	18.0432	+	8.51534i	0.798185	+	0.376696i
$512$	−5.61928	+	5.61928i	−0.248339	+	0.248339i
$513$	16.0465	+	9.93381i	0.708468	+	0.438589i
$514$	2.08780	+	0.559424i	0.0920888	+	0.0246751i
$515$	38.4784	−	10.3103i	1.69556	−	0.454324i
$516$	0.711886	−	1.48670i	0.0313390	−	0.0654485i
$517$	−1.33522	+	0.770888i	−0.0587228	+	0.0339036i
$518$	0.252848	−	1.39624i	0.0111095	−	0.0613472i
$519$	−8.73176	+	18.2354i	−0.383282	+	0.800446i
$520$	1.15915	+	3.12289i	0.0508322	+	0.136948i
$521$	14.7421	+	8.51137i	0.645864	+	0.372890i	0.786870	−	0.617119i	$-0.211700\pi$
$521$	14.7421	+	8.51137i	0.645864	+	0.372890i	−0.141006	+	0.990009i	$0.545034\pi$
$522$	0.215408	−	1.99145i	0.00942815	−	0.0871632i
$523$	−17.8502	+	30.9175i	−0.780535	+	1.35193i	0.151096	+	0.988519i	$0.451720\pi$
$523$	−17.8502	+	30.9175i	−0.780535	+	1.35193i	−0.931631	+	0.363407i	$0.881613\pi$
$524$	−1.86090	+	3.22317i	−0.0812938	+	0.140805i
$525$	−0.100008	+	0.975867i	−0.00436470	+	0.0425903i
$526$	−1.57451	+	0.421889i	−0.0686520	+	0.0183952i
$527$	−2.00731	−	2.00731i	−0.0874399	−	0.0874399i
$528$	−0.176141	+	0.942405i	−0.00766554	+	0.0410129i
$529$	11.4833	+	19.8897i	0.499274	+	0.864768i
$530$	−1.07596	+	1.86362i	−0.0467367	+	0.0809504i
$531$	−40.2960	+	17.7949i	−1.74870	+	0.772234i
$532$	15.7126	−	10.8943i	0.681228	−	0.472328i
$533$	30.2104	+	13.8544i	1.30856	+	0.600103i
$534$	−1.91393	+	0.147714i	−0.0828237	+	0.00639221i
$535$	25.8438	+	25.8438i	1.11732	+	1.11732i
$536$			0.100905i			0.00435843i
$537$	−14.3396	+	29.9469i	−0.618801	+	1.29231i
$538$	1.30744	+	1.30744i	0.0563676	+	0.0563676i
$539$	0.571709	−	0.800645i	0.0246252	−	0.0344862i
$540$	20.7982	−	11.1705i	0.895010	−	0.480700i
$541$	25.7456	+	6.89851i	1.10689	+	0.296590i	0.765567	−	0.643356i	$-0.222459\pi$
$541$	25.7456	+	6.89851i	1.10689	+	0.296590i	0.341322	+	0.939946i	$0.389125\pi$
$542$	2.15392	−	1.24357i	0.0925187	−	0.0534157i
$543$	−21.0734	−	10.0907i	−0.904345	−	0.433032i
$544$	−1.51661	−	5.66008i	−0.0650243	−	0.242674i
$545$	−5.47088			−0.234347
$546$	−1.45816	+	0.825413i	−0.0624037	+	0.0353244i
$547$	19.5045			0.833953			0.416977	−	0.908917i	$-0.363090\pi$
$547$	19.5045			0.833953			0.416977	+	0.908917i	$0.363090\pi$
$548$	6.31745	+	23.5770i	0.269868	+	1.00716i
$549$	−10.0727	−	12.5160i	−0.429890	−	0.534170i
$550$	0.00264226	−	0.00152551i	0.000112666	−	6.50480e-5i
$551$	−23.0983	−	6.18918i	−0.984022	−	0.263668i
$552$	0.0235288	−	0.125886i	0.00100145	−	0.00535806i
$553$	−8.86313	−	1.60504i	−0.376899	−	0.0682533i
$554$	−1.99482	−	1.99482i	−0.0847517	−	0.0847517i
$555$	−18.8651	−	9.03326i	−0.800778	−	0.383441i
$556$			3.93572i			0.166912i
$557$	4.05205	+	4.05205i	0.171691	+	0.171691i	0.787722	−	0.616031i	$-0.211260\pi$
$557$	4.05205	+	4.05205i	0.171691	+	0.171691i	−0.616031	+	0.787722i	$0.711260\pi$
$558$	0.0643390	−	0.166104i	0.00272369	−	0.00703173i
$559$	1.32808	+	1.10009i	0.0561718	+	0.0465289i
$560$	−1.96427	−	23.7122i	−0.0830055	−	1.00202i
$561$	−0.896306	−	0.767868i	−0.0378421	−	0.0324194i
$562$	−0.289599	+	0.501600i	−0.0122160	+	0.0211587i
$563$	−12.7027	−	22.0017i	−0.535355	−	0.927262i	−0.999146	−	0.0413171i	$-0.986845\pi$
$563$	−12.7027	−	22.0017i	−0.535355	−	0.927262i	0.463791	−	0.885944i	$-0.346489\pi$
$564$	−37.1624	−	6.94585i	−1.56482	−	0.292473i
$565$	−8.27705	−	8.27705i	−0.348218	−	0.348218i
$566$	2.24065	−	0.600381i	0.0941816	−	0.0252359i
$567$	14.4589	+	18.9193i	0.607216	+	0.794537i
$568$	−1.77080	+	3.06712i	−0.0743013	+	0.128694i
$569$	−19.6875	+	34.0997i	−0.825342	+	1.42953i	0.0763150	+	0.997084i	$0.475685\pi$
$569$	−19.6875	+	34.0997i	−0.825342	+	1.42953i	−0.901657	+	0.432451i	$0.857649\pi$
$570$	0.484185	+	1.37390i	0.0202803	+	0.0575465i
$571$	−29.1505	−	16.8300i	−1.21991	−	0.704316i	−0.255012	−	0.966938i	$-0.582079\pi$
$571$	−29.1505	−	16.8300i	−1.21991	−	0.704316i	−0.964899	+	0.262622i	$0.915413\pi$
$572$	−0.916490	−	0.420300i	−0.0383204	−	0.0175736i
$573$	16.3439	+	7.82603i	0.682776	+	0.326937i
$574$	1.88725	+	1.59850i	0.0787722	+	0.0667199i
$575$	0.0338788	−	0.0195599i	0.00141284	−	0.000815706i
$576$	−18.1228	+	14.5849i	−0.755115	+	0.607704i
$577$	−8.32931	+	2.23183i	−0.346754	+	0.0929124i	−0.427993	−	0.903782i	$-0.640779\pi$
$577$	−8.32931	+	2.23183i	−0.346754	+	0.0929124i	0.0812387	+	0.996695i	$0.474112\pi$
$578$	0.637398	+	0.170790i	0.0265123	+	0.00710394i
$579$	−3.75740	−	10.6618i	−0.156152	−	0.443091i
$580$	−21.1522	+	21.1522i	−0.878296	+	0.878296i
$581$	0.557503	+	6.73006i	0.0231291	+	0.279210i
$582$	−2.66142	+	0.205405i	−0.110319	+	0.00851430i
$583$	−0.338038	−	1.26157i	−0.0140001	−	0.0522491i
$584$	1.52554	−	2.64232i	0.0631274	−	0.109340i
$585$	6.05487	+	23.9454i	0.250338	+	0.990022i
$586$	0.524400	+	0.908287i	0.0216628	+	0.0375210i
$587$	−26.0005	−	6.96680i	−1.07315	−	0.287551i	−0.321365	−	0.946955i	$-0.604142\pi$
$587$	−26.0005	−	6.96680i	−1.07315	−	0.287551i	−0.751788	+	0.659405i	$0.770808\pi$
$588$	23.4192	−	5.78879i	0.965791	−	0.238725i
$589$	−1.84165	−	1.06328i	−0.0758840	−	0.0438117i
$590$	−3.28429	−	0.880023i	−0.135212	−	0.0362300i
$591$	−14.7382	+	17.2034i	−0.606247	+	0.707652i
$592$	20.1187	+	5.39078i	0.826872	+	0.221560i
$593$	6.69834	−	24.9985i	0.275068	−	1.02657i	−0.680728	−	0.732536i	$-0.738337\pi$
$593$	6.69834	−	24.9985i	0.275068	−	1.02657i	0.955796	−	0.294031i	$-0.0949968\pi$
$594$	0.0213562	−	0.0709129i	0.000876255	−	0.00290959i
$595$	26.4894	+	12.5014i	1.08596	+	0.512508i
$596$	2.88580	−	10.7699i	0.118207	−	0.441154i
$597$	−3.34784	−	43.3779i	−0.137018	−	1.77534i
$598$	0.0607370	+	0.0278539i	0.00248372	+	0.00113903i
$599$	−12.3777	−	7.14624i	−0.505737	−	0.291988i	0.225342	−	0.974280i	$-0.427650\pi$
$599$	−12.3777	−	7.14624i	−0.505737	−	0.291988i	−0.731080	+	0.682292i	$0.760983\pi$
$600$	0.147461	+	0.0275613i	0.00602008	+	0.00112519i
$601$	−6.08576	−	10.5408i	−0.248243	−	0.429970i	0.714795	−	0.699334i	$-0.246520\pi$
$601$	−6.08576	−	10.5408i	−0.248243	−	0.429970i	−0.963039	+	0.269364i	$0.913187\pi$
$602$	0.0731212	+	0.105461i	0.00298020	+	0.00429827i
$603$	−0.0804594	+	0.743847i	−0.00327656	+	0.0302918i
$604$	7.10757	+	7.10757i	0.289203	+	0.289203i
$605$	6.48928	−	24.2183i	0.263827	−	0.984615i
$606$	1.87482	+	0.350413i	0.0761592	+	0.0142346i
$607$	−0.243995			−0.00990345			−0.00495172	−	0.999988i	$-0.501576\pi$
$607$	−0.243995			−0.00990345			−0.00495172	+	0.999988i	$0.501576\pi$
$608$	−2.19481	−	3.80152i	−0.0890111	−	0.154172i
$609$	−24.4554	−	17.6711i	−0.990982	−	0.716069i
$610$		−	1.24008i		−	0.0502095i
$611$	16.4878	−	35.9527i	0.667026	−	1.45449i
$612$	−4.44078	−	28.5981i	−0.179508	−	1.15601i
$613$	−23.2218	−	23.2218i	−0.937919	−	0.937919i	0.0602635	−	0.998183i	$-0.480806\pi$
$613$	−23.2218	−	23.2218i	−0.937919	−	0.937919i	−0.998183	+	0.0602635i	$0.980806\pi$
$614$	0.917036	+	0.529451i	0.0370086	+	0.0213669i
$615$	30.0765	−	20.6041i	1.21280	−	0.830836i
$616$	−0.114802	−	0.0972373i	−0.00462551	−	0.00391780i
$617$	2.23580	+	8.34413i	0.0900101	+	0.335922i	0.996216	−	0.0869150i	$-0.0277009\pi$
$617$	2.23580	+	8.34413i	0.0900101	+	0.335922i	−0.906206	+	0.422837i	$0.861034\pi$
$618$	2.89006	−	1.01850i	0.116255	−	0.0409702i
$619$	−3.90559	−	14.5759i	−0.156979	−	0.585853i	−0.998928	−	0.0462959i	$-0.985258\pi$
$619$	−3.90559	−	14.5759i	−0.156979	−	0.585853i	0.841949	−	0.539557i	$-0.181408\pi$
$620$	−2.30378	+	1.33009i	−0.0925220	+	0.0534176i
$621$	0.273827	−	0.909239i	0.0109883	−	0.0364865i
$622$	0.222438	+	0.0596022i	0.00891896	+	0.00238983i
$623$	−12.3408	+	26.1490i	−0.494424	+	1.04764i
$624$	−10.3077	−	22.3312i	−0.412636	−	0.893963i
$625$	−13.0123	−	22.5379i	−0.520490	−	0.901515i
$626$	−0.983051	+	0.983051i	−0.0392906	+	0.0392906i
$627$	−0.797434	−	0.381839i	−0.0318464	−	0.0152492i
$628$		−	4.96321i		−	0.198054i
$629$	−18.1309	+	18.1309i	−0.722927	+	0.722927i
$630$	−0.0461259	+	1.83740i	−0.00183770	+	0.0732038i
$631$	8.63210	+	32.2154i	0.343638	+	1.28248i	0.894195	+	0.447678i	$0.147749\pi$
$631$	8.63210	+	32.2154i	0.343638	+	1.28248i	−0.550556	+	0.834798i	$0.685584\pi$
$632$	−0.356505	+	1.33049i	−0.0141810	+	0.0529242i
$633$	−24.2293	+	1.86998i	−0.963029	+	0.0743252i
$634$		−	1.98498i		−	0.0788337i
$635$	9.33161	−	2.50040i	0.370314	−	0.0992252i
$636$	13.8314	−	28.8856i	0.548452	−	1.14539i
$637$	−0.0727726	+	25.2388i	−0.00288336	+	0.999996i
$638$			0.0938397i			0.00371515i
$639$	−15.4996	+	21.1981i	−0.613155	+	0.838584i
$640$	−7.31508			−0.289154
$641$	−6.61429	−	11.4563i	−0.261249	−	0.452496i	0.705325	−	0.708884i	$-0.250801\pi$
$641$	−6.61429	−	11.4563i	−0.261249	−	0.452496i	−0.966574	+	0.256388i	$0.917468\pi$
$642$	2.13505	+	1.82911i	0.0842639	+	0.0721891i
$643$	−17.9921	+	4.82096i	−0.709538	+	0.190120i	−0.595499	−	0.803356i	$-0.703046\pi$
$643$	−17.9921	+	4.82096i	−0.709538	+	0.190120i	−0.114039	+	0.993476i	$0.536379\pi$
$644$	−0.734094	−	0.621777i	−0.0289274	−	0.0245014i
$645$	1.78413	−	0.628755i	0.0702500	−	0.0247572i
$646$	1.78578			0.0702606
$647$	−8.96491			−0.352447			−0.176223	−	0.984350i	$-0.556388\pi$
$647$	−8.96491			−0.352447			−0.176223	+	0.984350i	$0.556388\pi$
$648$	3.06588	−	1.96471i	0.120439	−	0.0771811i
$649$	1.78719	−	1.03184i	0.0701534	−	0.0405031i
$650$	−0.0326277	+	0.0711467i	−0.00127976	+	0.00279060i
$651$	−1.69395	−	2.08079i	−0.0663911	−	0.0815526i
$652$	−6.42846	+	23.9914i	−0.251758	+	0.939574i
$653$	−38.5553	−	22.2599i	−1.50878	−	0.871097i	−0.999948	−	0.0102334i	$-0.996743\pi$
$653$	−38.5553	−	22.2599i	−1.50878	−	0.871097i	−0.508836	−	0.860863i	$-0.669924\pi$
$654$	−0.419587	+	0.0323832i	−0.0164072	+	0.00126628i
$655$	−4.12567	+	1.10547i	−0.161203	+	0.0431942i
$656$	−25.6708	+	25.6708i	−1.00228	+	1.00228i
$657$	13.3529	−	18.2621i	0.520944	−	0.712472i
$658$	1.90233	−	2.24596i	0.0741605	−	0.0875568i
$659$	−1.89755	−	1.09555i	−0.0739179	−	0.0426765i	0.462586	−	0.886575i	$-0.346922\pi$
$659$	−1.89755	−	1.09555i	−0.0739179	−	0.0426765i	−0.536503	+	0.843898i	$0.680255\pi$
$660$	−0.912427	+	0.625062i	−0.0355162	+	0.0243305i
$661$	18.4861	−	18.4861i	0.719027	−	0.719027i	−0.249379	−	0.968406i	$-0.580227\pi$
$661$	18.4861	−	18.4861i	0.719027	−	0.719027i	0.968406	+	0.249379i	$0.0802266\pi$
$662$	−1.39625	+	2.41837i	−0.0542667	+	0.0939926i
$663$	30.1526	+	2.75622i	1.17103	+	0.107043i
$664$	1.03271			0.0400770
$665$	21.5912	+	3.90999i	0.837271	+	0.151623i
$666$	−1.50032	−	0.581137i	−0.0581362	−	0.0225186i
$667$			1.20320i			0.0465882i
$668$	1.72596	+	6.44136i	0.0667793	+	0.249224i
$669$	6.54558	+	5.60761i	0.253067	+	0.216803i
$670$	−0.0408361	+	0.0408361i	−0.00157763	+	0.00157763i
$671$	0.532204	+	0.532204i	0.0205455	+	0.0205455i
$672$	−0.880601	−	5.46801i	−0.0339699	−	0.210933i
$673$	−15.2773	+	8.82036i	−0.588897	+	0.340000i	−0.764661	−	0.644432i	$-0.777094\pi$
$673$	−15.2773	+	8.82036i	−0.588897	+	0.340000i	0.175764	+	0.984432i	$0.443760\pi$
$674$	−0.913185	+	0.244687i	−0.0351746	+	0.00942499i
$675$	1.06507	+	0.320758i	0.0409947	+	0.0123460i
$676$	25.4142	−	4.81485i	0.977470	−	0.185187i
$677$	−34.2771	+	19.7899i	−1.31738	+	0.760587i	−0.983306	−	0.181961i	$-0.941756\pi$
$677$	−34.2771	+	19.7899i	−1.31738	+	0.760587i	−0.334070	+	0.942548i	$0.608422\pi$
$678$	−0.683799	−	0.585812i	−0.0262612	−	0.0224980i
$679$	−17.1606	+	36.3617i	−0.658563	+	1.39543i
$680$	2.23966	−	3.87920i	0.0858870	−	0.148761i
$681$	3.58069	−	4.17962i	0.137212	−	0.160163i
$682$	−0.00215985	+	0.00806066i	−8.27048e−5	+	0.000308659i
$683$	−6.38384	+	23.8248i	−0.244271	+	0.911631i	0.729478	+	0.684005i	$0.239763\pi$
$683$	−6.38384	+	23.8248i	−0.244271	+	0.911631i	−0.973748	+	0.227627i	$0.926903\pi$
$684$	−8.75803	−	19.8323i	−0.334872	−	0.758305i
$685$	−14.0060	+	24.2590i	−0.535140	+	0.926889i
$686$	−0.511183	+	1.80724i	−0.0195170	+	0.0690008i
$687$	−6.84142	+	7.98576i	−0.261017	+	0.304676i
$688$	−1.63136	+	0.941865i	−0.0621949	+	0.0359083i
$689$	25.8036	+	21.3740i	0.983040	+	0.814285i
$690$	0.0604678	−	0.0414237i	0.00230197	−	0.00157697i
$691$	4.29321	−	1.15036i	0.163321	−	0.0437618i	−0.176232	−	0.984349i	$-0.556391\pi$
$691$	4.29321	−	1.15036i	0.163321	−	0.0437618i	0.339553	+	0.940587i	$0.389724\pi$
$692$	20.1142	−	11.6129i	0.764627	−	0.441458i
$693$	−0.768759	−	0.808351i	−0.0292027	−	0.0307067i
$694$	−2.44517	−	2.44517i	−0.0928172	−	0.0928172i
$695$	−3.19379	+	3.19379i	−0.121147	+	0.121147i
$696$	−3.00185	+	3.50396i	−0.113785	+	0.132817i
$697$	−11.5672	−	43.1695i	−0.438140	−	1.63516i
$698$		−	2.93479i		−	0.111083i
$699$	27.7920	−	2.14495i	1.05119	−	0.0811293i
$700$	0.728343	−	0.859910i	0.0275288	−	0.0325015i
$701$	−29.3612			−1.10896			−0.554479	−	0.832198i	$-0.687082\pi$
$701$	−29.3612			−1.10896			−0.554479	+	0.832198i	$0.687082\pi$
$702$	0.606114	+	1.80065i	0.0228763	+	0.0679611i
$703$	−9.60399	+	16.6346i	−0.362222	+	0.627386i
$704$	0.770615	−	0.770615i	0.0290437	−	0.0290437i
$705$	−24.5204	−	35.7933i	−0.923490	−	1.34805i
$706$	0.798269	+	0.460881i	0.0300432	+	0.0173455i
$707$	18.5681	−	21.9222i	0.698325	−	0.824470i
$708$	49.7419	+	9.29704i	1.86942	+	0.349404i
$709$	−34.8585	+	34.8585i	−1.30914	+	1.30914i	−0.387101	+	0.922037i	$0.626524\pi$
$709$	−34.8585	+	34.8585i	−1.30914	+	1.30914i	−0.922037	+	0.387101i	$0.873476\pi$
$710$	−1.95790	+	0.524618i	−0.0734787	+	0.0196886i
$711$	−3.68897	+	9.52381i	−0.138347	+	0.357171i
$712$	3.82936	+	2.21088i	0.143511	+	0.0828564i
$713$	−0.0276933	+	0.103353i	−0.00103712	+	0.00387060i
$714$	2.10559	+	0.801997i	0.0787997	+	0.0300140i
$715$	−0.402652	−	1.08479i	−0.0150583	−	0.0405688i
$716$	33.0323	−	19.0712i	1.23448	−	0.712725i
$717$	6.37005	+	18.0754i	0.237894	+	0.675037i
$718$	2.54296			0.0949025
$719$	18.1615			0.677310			0.338655	−	0.940911i	$-0.390028\pi$
$719$	18.1615			0.677310			0.338655	+	0.940911i	$0.390028\pi$
$720$	−26.8228	−	2.90133i	−0.999626	−	0.108126i
$721$	8.22481	−	45.4179i	0.306308	−	1.69145i
$722$	−0.568975	+	0.152456i	−0.0211751	+	0.00567384i
$723$	2.27513	−	2.65568i	0.0846130	−	0.0987660i
$724$	13.4203	+	23.2446i	0.498760	+	0.863877i
$725$	−1.40942			−0.0523445
$726$	0.354341	−	1.89583i	0.0131508	−	0.0703608i
$727$		−	28.2928i		−	1.04932i	−0.851312	−	0.524660i	$-0.824192\pi$
$727$		−	28.2928i		−	1.04932i	0.851312	−	0.524660i	$-0.175808\pi$
$728$	3.84551	+	0.329721i	0.142524	+	0.0122203i
$729$	24.1675	−	12.0387i	0.895094	−	0.445878i
$730$	1.68673	−	0.451957i	0.0624285	−	0.0167277i
$731$		−	2.31898i		−	0.0857707i
$732$	1.42016	+	18.4010i	0.0524908	+	0.680121i
$733$	5.85862	−	21.8647i	0.216393	−	0.807590i	−0.769278	−	0.638914i	$-0.779384\pi$
$733$	5.85862	−	21.8647i	0.216393	−	0.807590i	0.985671	−	0.168677i	$-0.0539493\pi$
$734$	−0.652274	−	2.43432i	−0.0240759	−	0.0898523i
$735$	23.7019	+	14.3069i	0.874259	+	0.527717i
$736$	−0.156176	+	0.156176i	−0.00575671	+	0.00575671i
$737$		−	0.0350511i		−	0.00129112i
$738$	2.18475	−	1.75825i	0.0804218	−	0.0647221i
$739$	−15.9702	+	15.9702i	−0.587473	+	0.587473i	−0.936946	−	0.349473i	$-0.886360\pi$
$739$	−15.9702	+	15.9702i	−0.587473	+	0.587473i	0.349473	+	0.936946i	$0.386360\pi$
$740$	12.0139	+	20.8087i	0.441641	+	0.764944i
$741$	22.3524	−	3.85176i	0.821137	−	0.141498i
$742$	1.42069	+	2.04903i	0.0521553	+	0.0752223i
$743$	−4.71832	−	1.26427i	−0.173098	−	0.0463816i	0.171229	−	0.985231i	$-0.445226\pi$
$743$	−4.71832	−	1.26427i	−0.173098	−	0.0463816i	−0.344327	+	0.938850i	$0.611893\pi$
$744$	−0.338502	+	0.231892i	−0.0124101	+	0.00850157i
$745$	11.0815	−	6.39789i	0.405994	−	0.234401i
$746$	−0.891147	−	3.32581i	−0.0326272	−	0.121766i
$747$	7.61290	+	0.823461i	0.278541	+	0.0301289i
$748$	0.350913	+	1.30963i	0.0128307	+	0.0478847i
$749$	39.8605	−	14.2999i	1.45647	−	0.522508i
$750$	−1.08485	−	1.58359i	−0.0396129	−	0.0578245i
$751$	29.2296	+	16.8757i	1.06660	+	0.615805i	0.927252	−	0.374438i	$-0.122164\pi$
$751$	29.2296	+	16.8757i	1.06660	+	0.615805i	0.139353	+	0.990243i	$0.455498\pi$
$752$	30.5501	+	30.5501i	1.11405	+	1.11405i
$753$	25.8529	+	37.7385i	0.942132	+	1.37527i
$754$	−1.39331	−	1.96320i	−0.0507415	−	0.0714955i
$755$			11.5354i			0.419817i
$756$	−1.41978	−	27.3172i	−0.0516370	−	0.993517i
$757$	−0.0746351	−	0.129272i	−0.00271266	−	0.00469846i	0.864666	−	0.502347i	$-0.167530\pi$
$757$	−0.0746351	−	0.129272i	−0.00271266	−	0.00469846i	−0.867379	+	0.497649i	$0.834197\pi$
$758$	−3.49093			−0.126796
$759$	−0.00817312	+	0.0437286i	−0.000296666	+	0.00158725i
$760$	0.868471	−	3.24118i	0.0315028	−	0.117570i
$761$	26.5493	+	26.5493i	0.962412	+	0.962412i	0.999319	−	0.0369072i	$-0.0117506\pi$
$761$	26.5493	+	26.5493i	0.962412	+	0.962412i	−0.0369072	+	0.999319i	$0.511751\pi$
$762$	0.700884	−	0.247003i	0.0253904	−	0.00894796i
$763$	−2.70546	+	5.73262i	−0.0979442	+	0.207535i
$764$	−10.4084	−	18.0278i	−0.376561	−	0.652223i
$765$	19.6034	−	26.8107i	0.708763	−	0.969342i
$766$	−1.15286	−	0.665606i	−0.0416546	−	0.0240493i
$767$	−22.0690	+	48.1227i	−0.796864	+	1.73761i
$768$	26.2208	−	2.02368i	0.946162	−	0.0730234i
$769$	2.09223	−	7.80831i	0.0754477	−	0.281575i	−0.917887	−	0.396842i	$-0.870106\pi$
$769$	2.09223	−	7.80831i	0.0754477	−	0.281575i	0.993334	+	0.115268i	$0.0367726\pi$
$770$	−0.00710848	−	0.0858120i	−0.000256172	−	0.00309245i
$771$	−20.8638	−	30.4556i	−0.751390	−	1.09683i
$772$	−3.36109	+	12.5438i	−0.120968	+	0.451460i
$773$	0.917027	+	0.245717i	0.0329832	+	0.00883782i	0.275273	−	0.961366i	$-0.411232\pi$
$773$	0.917027	+	0.245717i	0.0329832	+	0.00883782i	−0.242290	+	0.970204i	$0.577898\pi$
$774$	0.133111	−	0.0587827i	0.00478459	−	0.00211290i
$775$	−0.121067	−	0.0324397i	−0.00434884	−	0.00116527i
$776$	5.32495	+	3.07436i	0.191154	+	0.110363i
$777$	−18.7946	+	15.3005i	−0.674252	+	0.548902i
$778$	1.28172	+	0.343437i	0.0459520	+	0.0123128i
$779$	−16.7398	−	28.9942i	−0.599766	−	1.03882i
$780$	9.80790	−	26.6243i	0.351179	−	0.953305i
$781$	0.615120	−	1.06542i	0.0220107	−	0.0381237i
$782$	−0.0232555	−	0.0867908i	−0.000831616	−	0.00310363i
$783$	−24.9229	+	23.4367i	−0.890671	+	0.837560i
$784$	−25.8180	−	9.66792i	−0.922072	−	0.345283i
$785$	4.02759	−	4.02759i	0.143751	−	0.143751i
$786$	−0.309873	+	0.109204i	−0.0110528	+	0.00389518i
$787$	19.4813	+	5.22001i	0.694435	+	0.186073i	0.588737	−	0.808325i	$-0.299626\pi$
$787$	19.4813	+	5.22001i	0.694435	+	0.186073i	0.105698	+	0.994398i	$0.466292\pi$
$788$	25.1365	−	6.73530i	0.895451	−	0.239935i
$789$	25.1105	+	12.0238i	0.893956	+	0.428058i
$790$	−0.682726	+	0.394172i	−0.0242903	+	0.0140240i
$791$	−12.7662	+	4.57988i	−0.453914	+	0.162842i
$792$	−0.132899	+	0.106955i	−0.00472238	+	0.00380049i
$793$	−19.0362	−	3.23207i	−0.675995	−	0.114774i
$794$	0.815995	+	0.471115i	0.0289586	+	0.0167192i
$795$	34.6644	−	12.2163i	1.22942	−	0.433266i
$796$	−24.9895	+	43.2831i	−0.885731	+	1.53413i
$797$	22.7805	−	39.4570i	0.806927	−	1.39764i	−0.108055	−	0.994145i	$-0.534462\pi$
$797$	22.7805	−	39.4570i	0.806927	−	1.39764i	0.914982	−	0.403494i	$-0.132204\pi$
$798$	1.67907	+	0.172073i	0.0594386	+	0.00609132i
$799$	−51.3749	+	13.7659i	−1.81751	+	0.487001i
$800$	−0.182942	−	0.182942i	−0.00646799	−	0.00646799i
$801$	26.4662	+	19.3516i	0.935138	+	0.683754i
$802$	−0.764636	−	1.32439i	−0.0270002	−	0.0467658i
$803$	−0.529924	+	0.917855i	−0.0187006	+	0.0323904i
$804$	0.559182	−	0.652714i	0.0197208	−	0.0230195i
$805$	−0.0911442	−	1.10027i	−0.00321241	−	0.0387795i
$806$	−0.0744974	−	0.200704i	−0.00262406	−	0.00706951i
$807$	−2.43008	−	31.4865i	−0.0855429	−	1.10838i
$808$	−3.10657	−	3.10657i	−0.109289	−	0.109289i
$809$		−	42.7852i		−	1.50425i	−0.659021	−	0.752124i	$-0.729029\pi$
$809$		−	42.7852i		−	1.50425i	0.659021	−	0.752124i	$-0.270971\pi$
$810$	2.03587	+	0.445640i	0.0715332	+	0.0156582i
$811$	32.9310	+	32.9310i	1.15636	+	1.15636i	0.985252	+	0.171110i	$0.0547354\pi$
$811$	32.9310	+	32.9310i	1.15636	+	1.15636i	0.171110	+	0.985252i	$0.445265\pi$
$812$	11.7040	+	32.6243i	0.410729	+	1.14489i
$813$	−41.7562	−	7.80446i	−1.46445	−	0.273714i
$814$	0.0728073	+	0.0195087i	0.00255190	+	0.000683778i
$815$	−24.6853	+	14.2521i	−0.864689	+	0.499229i
$816$	−14.2837	+	29.8300i	−0.500029	+	1.04426i
$817$	−0.449615	−	1.67799i	−0.0157301	−	0.0587054i
$818$	−1.02815			−0.0359485
$819$	28.0853	+	5.49695i	0.981379	+	0.192079i
$820$	−41.8806			−1.46254
$821$	6.81177	+	25.4219i	0.237732	+	0.887229i	0.976898	+	0.213706i	$0.0685534\pi$
$821$	6.81177	+	25.4219i	0.237732	+	0.887229i	−0.739166	+	0.673524i	$0.764780\pi$
$822$	−0.930588	+	1.94344i	−0.0324580	+	0.0677853i
$823$	−14.4139	+	8.32184i	−0.502435	+	0.290081i	−0.729719	−	0.683747i	$-0.760349\pi$
$823$	−14.4139	+	8.32184i	−0.502435	+	0.290081i	0.227283	+	0.973829i	$0.427016\pi$
$824$	−6.81794	−	1.82686i	−0.237514	−	0.0636417i
$825$	−0.0512233	−	0.00957391i	−0.00178337	−	0.000333321i
$826$	−2.54627	+	3.00623i	−0.0885961	+	0.104600i
$827$	−11.2719	−	11.2719i	−0.391964	−	0.391964i	0.483423	−	0.875387i	$-0.339393\pi$
$827$	−11.2719	−	11.2719i	−0.391964	−	0.391964i	−0.875387	+	0.483423i	$0.839393\pi$
$828$	−0.849816	+	0.683917i	−0.0295331	+	0.0237678i
$829$		−	37.5182i		−	1.30306i	−0.758622	−	0.651531i	$-0.774127\pi$
$829$		−	37.5182i		−	1.30306i	0.758622	−	0.651531i	$-0.225873\pi$
$830$	0.417937	+	0.417937i	0.0145068	+	0.0145068i
$831$	3.70769	+	48.0404i	0.128618	+	1.66650i
$832$	−4.67993	+	27.5638i	−0.162248	+	0.955604i
$833$	26.1990	−	21.5745i	0.907742	−	0.747511i
$834$	−0.226042	+	0.263851i	−0.00782719	+	0.00913641i
$835$	−3.82649	+	6.62768i	−0.132421	+	0.229360i
$836$	0.507833	+	0.879593i	0.0175638	+	0.0304213i
$837$	−2.68026	+	1.43954i	−0.0926433	+	0.0497577i
$838$	0.737308	+	0.737308i	0.0254699	+	0.0254699i
$839$	13.7295	−	3.67881i	0.473996	−	0.127007i	−0.0139098	−	0.999903i	$-0.504428\pi$
$839$	13.7295	−	3.67881i	0.473996	−	0.127007i	0.487905	+	0.872897i	$0.337761\pi$
$840$	2.47962	−	3.43160i	0.0855551	−	0.118401i
$841$	7.17461	−	12.4268i	0.247400	−	0.428510i
$842$	0.572064	−	0.990844i	0.0197146	−	0.0341467i
$843$	9.33005	−	3.28806i	0.321344	−	0.113247i
$844$	24.1764	+	13.9583i	0.832186	+	0.480463i
$845$	24.5305	+	16.7162i	0.843876	+	0.575053i
$846$	−2.09245	−	2.60002i	−0.0719398	−	0.0893904i
$847$	−22.1679	−	18.7762i	−0.761698	−	0.645157i
$848$	−31.6961	+	18.2998i	−1.08845	+	0.628417i
$849$	−35.7341	−	17.1107i	−1.22639	−	0.587239i
$850$	0.101666	−	0.0272413i	0.00348711	−	0.000934368i
$851$	0.933528	+	0.250138i	0.0320009	+	0.00857463i
$852$	28.4516	−	10.0268i	0.974736	−	0.343512i
$853$	−16.1848	+	16.1848i	−0.554157	+	0.554157i	−0.927638	−	0.373481i	$-0.878164\pi$
$853$	−16.1848	+	16.1848i	−0.554157	+	0.554157i	0.373481	+	0.927638i	$0.378164\pi$
$854$	−1.29941	−	0.613245i	−0.0444649	−	0.0209848i
$855$	8.98660	−	23.2007i	0.307335	−	0.793446i
$856$	−1.67611	−	6.25534i	−0.0572884	−	0.213803i
$857$	23.1221	−	40.0487i	0.789837	−	1.36804i	−0.136230	−	0.990677i	$-0.543499\pi$
$857$	23.1221	−	40.0487i	0.789837	−	1.36804i	0.926067	−	0.377360i	$-0.123168\pi$
$858$	−0.0373023	−	0.0808142i	−0.00127348	−	0.00275895i
$859$	−12.5798	−	21.7888i	−0.429216	−	0.743424i	0.567588	−	0.823313i	$-0.307877\pi$
$859$	−12.5798	−	21.7888i	−0.429216	−	0.743424i	−0.996804	+	0.0798889i	$0.974543\pi$
$860$	−2.09904	−	0.562437i	−0.0715768	−	0.0191790i
$861$	−6.71635	−	41.7046i	−0.228893	−	1.42129i
$862$	2.19635	+	1.26806i	0.0748079	+	0.0431904i
$863$	56.2453	+	15.0709i	1.91461	+	0.513018i	0.991806	+	0.127750i	$0.0407754\pi$
$863$	56.2453	+	15.0709i	1.91461	+	0.513018i	0.922804	+	0.385269i	$0.125891\pi$
$864$	−6.27706	−	0.192904i	−0.213550	−	0.00656271i
$865$	25.7462	+	6.89867i	0.875397	+	0.234562i
$866$	−0.629307	+	2.34861i	−0.0213847	+	0.0798089i
$867$	−6.36964	−	9.29802i	−0.216324	−	0.315777i
$868$	0.254457	+	3.07175i	0.00863683	+	0.104262i
$869$	0.123838	−	0.462170i	0.00420092	−	0.0156781i
$870$	−2.63289	+	0.203202i	−0.0892632	+	0.00688921i
$871$	0.520432	+	0.733297i	0.0176342	+	0.0248468i
$872$	0.839507	+	0.484689i	0.0284293	+	0.0164137i
$873$	36.8028	+	26.9094i	1.24559	+	0.910746i
$874$	−0.0336548	−	0.0582918i	−0.00113839	−	0.00197175i
$875$	−28.8150	+	2.38697i	−0.974126	+	0.0806944i
$876$	−24.5110	+	8.63805i	−0.828149	+	0.291853i
$877$	19.2407	+	19.2407i	0.649714	+	0.649714i	0.952924	−	0.303210i	$-0.0980584\pi$
$877$	19.2407	+	19.2407i	0.649714	+	0.649714i	−0.303210	+	0.952924i	$0.598058\pi$
$878$	0.401620	−	1.49887i	0.0135540	−	0.0505843i
$879$	3.29106	−	17.6082i	0.111005	−	0.593909i
$880$	1.26393			0.0426069
$881$	14.1689	+	24.5413i	0.477364	+	0.826818i	0.999663	−	0.0259440i	$-0.00825917\pi$
$881$	14.1689	+	24.5413i	0.477364	+	0.826818i	−0.522300	+	0.852762i	$0.674926\pi$
$882$	1.90250	+	0.956964i	0.0640604	+	0.0322227i
$883$			13.0830i			0.440279i	0.975468	+	0.220140i	$0.0706513\pi$
$883$			13.0830i			0.440279i	−0.975468	+	0.220140i	$0.929349\pi$
$884$	−26.7865	−	22.1881i	−0.900927	−	0.746268i
$885$	32.8205	+	47.9094i	1.10325	+	1.61046i
$886$	−1.27267	−	1.27267i	−0.0427563	−	0.0427563i
$887$	−2.79106	−	1.61142i	−0.0937146	−	0.0541062i	0.452410	−	0.891810i	$-0.350564\pi$
$887$	−2.79106	−	1.61142i	−0.0937146	−	0.0541062i	−0.546125	+	0.837704i	$0.683898\pi$
$888$	2.09455	+	3.05749i	0.0702884	+	0.102603i
$889$	1.99464	−	11.0145i	0.0668982	−	0.369416i
$890$	0.654996	+	2.44448i	0.0219555	+	0.0819391i
$891$	−1.06499	+	0.682477i	−0.0356784	+	0.0228638i
$892$	−2.56266	−	9.56399i	−0.0858043	−	0.320226i
$893$	−34.5053	+	19.9216i	−1.15467	+	0.666651i
$894$	0.812019	−	0.556277i	0.0271580	−	0.0186047i
$895$	42.2814	+	11.3293i	1.41331	+	0.378696i
$896$	−3.61745	+	7.66504i	−0.120851	+	0.256071i
$897$	−0.478286	−	1.03619i	−0.0159695	−	0.0345974i
$898$	−1.41243	−	2.44639i	−0.0471333	−	0.0816372i
$899$	2.72588	−	2.72588i	0.0909132	−	0.0909132i
$900$	−0.801133	−	0.995465i	−0.0267044	−	0.0331822i
$901$		−	45.0562i		−	1.50104i
$902$	−0.0928998	+	0.0928998i	−0.00309323	+	0.00309323i
$903$	0.223451	−	2.18042i	0.00743599	−	0.0725597i
$904$	0.536813	+	2.00341i	0.0178541	+	0.0666325i
$905$	−7.97231	+	29.7531i	−0.265009	+	0.989025i
$906$	0.0682802	+	0.884704i	0.00226846	+	0.0293923i
$907$			1.58126i			0.0525049i	0.999655	+	0.0262524i	$0.00835737\pi$
$907$			1.58126i			0.0525049i	−0.999655	+	0.0262524i	$0.991643\pi$
$908$	−6.10700	+	1.63637i	−0.202668	+	0.0543047i
$909$	−20.4238	−	25.3780i	−0.677414	−	0.841735i
$910$	1.42284	+	1.68971i	0.0471665	+	0.0560134i
$911$		−	12.0071i		−	0.397812i	−0.980019	−	0.198906i	$-0.936261\pi$
$911$		−	12.0071i		−	0.397812i	0.980019	−	0.198906i	$-0.0637389\pi$
$912$	−4.55190	+	24.3540i	−0.150728	+	0.806442i
$913$	−0.358730			−0.0118722
$914$	−0.388927	−	0.673641i	−0.0128645	−	0.0222821i
$915$	−13.7798	+	16.0847i	−0.455545	+	0.531742i
$916$	11.6683	−	3.12651i	0.385531	−	0.103303i
$917$	−0.881867	+	4.86972i	−0.0291218	+	0.160812i
$918$	1.34478	−	2.17227i	0.0443843	−	0.0716957i
$919$	26.1485			0.862559			0.431280	−	0.902218i	$-0.358062\pi$
$919$	26.1485			0.862559			0.431280	+	0.902218i	$0.358062\pi$
$920$	−0.168834			−0.00556630
$921$	−6.01130	−	17.0574i	−0.198079	−	0.562060i
$922$	−1.03151	+	0.595544i	−0.0339711	+	0.0196132i
$923$	2.95034	+	31.4226i	0.0971117	+	1.03429i
$924$	0.203753	+	1.26519i	0.00670298	+	0.0416215i
$925$	−0.293009	+	1.09352i	−0.00963408	+	0.0359549i
$926$	0.383029	+	0.221142i	0.0125871	+	0.00726716i
$927$	−48.8035	−	18.9036i	−1.60292	−	0.620877i
$928$	7.68624	−	2.05952i	0.252313	−	0.0676071i
$929$	29.8793	−	29.8793i	0.980309	−	0.980309i	−0.0195013	−	0.999810i	$-0.506208\pi$
$929$	29.8793	−	29.8793i	0.980309	−	0.980309i	0.999810	+	0.0195013i	$0.00620785\pi$
$930$	−0.230837	−	0.0431448i	−0.00756945	−	0.00141477i
$931$	14.7743	−	20.6906i	0.484209	−	0.678107i
$932$	−27.7313	−	16.0107i	−0.908370	−	0.524448i
$933$	−2.22287	−	3.24481i	−0.0727734	−	0.106230i
$934$	−1.85618	+	1.85618i	−0.0607361	+	0.0607361i
$935$	−0.777984	+	1.34751i	−0.0254428	+	0.0440682i
$936$	1.19231	−	4.21085i	0.0389719	−	0.137636i
$937$	2.63265			0.0860050			0.0430025	−	0.999075i	$-0.486308\pi$
$937$	2.63265			0.0860050			0.0430025	+	0.999075i	$0.486308\pi$
$938$	0.0225955	+	0.0629840i	0.000737769	+	0.00205650i
$939$	23.6744	−	1.82716i	0.772586	−	0.0596271i
$940$			49.8411i			1.62564i
$941$	−1.34528	−	5.02066i	−0.0438549	−	0.163669i	0.940526	−	0.339723i	$-0.110333\pi$
$941$	−1.34528	−	5.02066i	−0.0438549	−	0.163669i	−0.984380	+	0.176054i	$0.943667\pi$
$942$	0.285054	−	0.332734i	0.00928757	−	0.0108411i
$943$	−1.19115	+	1.19115i	−0.0387893	+	0.0387893i
$944$	−40.8914	−	40.8914i	−1.33090	−	1.33090i
$945$	21.0154	−	23.3197i	0.683633	−	0.758591i
$946$	−0.00590371	+	0.00340851i	−0.000191946	+	0.000110820i
$947$	47.8503	−	12.8215i	1.55493	−	0.416641i	0.623873	−	0.781525i	$-0.285558\pi$
$947$	47.8503	−	12.8215i	1.55493	−	0.416641i	0.931053	+	0.364884i	$0.118891\pi$
$948$	9.67925	−	6.63081i	0.314367	−	0.215359i
$949$	−2.54171	−	27.0705i	−0.0825074	−	0.878744i
$950$	0.0682824	−	0.0394229i	0.00221537	−	0.00127905i
$951$	−22.0571	+	25.7465i	−0.715250	+	0.834887i
$952$	−2.95723	−	4.26515i	−0.0958445	−	0.138234i
$953$	−10.3964	+	18.0070i	−0.336772	+	0.583305i	−0.983824	−	0.179140i	$-0.942668\pi$
$953$	−10.3964	+	18.0070i	−0.336772	+	0.583305i	0.647052	+	0.762446i	$0.276002\pi$
$954$	2.58626	−	1.14211i	0.0837333	−	0.0369771i
$955$	6.18309	−	23.0756i	0.200080	−	0.746709i
$956$	5.69817	−	21.2658i	0.184292	−	0.687787i
$957$	1.04274	−	1.21716i	0.0337071	−	0.0393452i
$958$	0.688991	−	1.19337i	0.0222603	−	0.0385559i
$959$	18.4934	+	26.6726i	0.597183	+	0.861303i
$960$	23.2901	+	19.9527i	0.751684	+	0.643970i
$961$	−26.5499	+	15.3286i	−0.856448	+	0.494471i
$962$	−1.81285	+	0.672893i	−0.0584486	+	0.0216949i
$963$	−7.36803	−	47.4494i	−0.237432	−	1.52903i
$964$	−3.88032	+	1.03973i	−0.124977	+	0.0334874i
$965$	−12.9066	+	7.45163i	−0.415478	+	0.239876i
$966$	−0.0135030	−	0.0838456i	−0.000434452	−	0.00269769i
$967$	−4.93987	−	4.93987i	−0.158856	−	0.158856i	0.623204	−	0.782059i	$-0.285831\pi$
$967$	−4.93987	−	4.93987i	−0.158856	−	0.158856i	−0.782059	+	0.623204i	$0.785831\pi$
$968$	−3.14139	+	3.14139i	−0.100968	+	0.100968i
$969$	−23.1627	−	19.8435i	−0.744093	−	0.637467i
$970$	0.910809	+	3.39918i	0.0292443	+	0.109141i
$971$			33.9510i			1.08954i	0.838586	+	0.544770i	$0.183383\pi$
$971$			33.9510i			1.08954i	−0.838586	+	0.544770i	$0.816617\pi$
$972$	−30.7197	−	4.28114i	−0.985336	−	0.137318i
$973$	1.76719	+	4.92597i	0.0566536	+	0.157919i
$974$	1.02494			0.0328413
$975$	1.21378	−	0.560260i	0.0388722	−	0.0179427i
$976$	10.5456	−	18.2655i	0.337555	−	0.584663i
$977$	14.0341	−	14.0341i	0.448991	−	0.448991i	−0.446028	−	0.895019i	$-0.647162\pi$
$977$	14.0341	−	14.0341i	0.448991	−	0.448991i	0.895019	+	0.446028i	$0.147162\pi$
$978$	−1.80887	+	1.23918i	−0.0578413	+	0.0396245i
$979$	−1.33020	−	0.767989i	−0.0425133	−	0.0245450i
$980$	−13.1741	−	28.9468i	−0.420830	−	0.924672i
$981$	5.80216	+	4.24242i	0.185249	+	0.135450i
$982$	−0.650878	+	0.650878i	−0.0207704	+	0.0207704i
$983$	−21.2065	+	5.68227i	−0.676383	+	0.181236i	−0.580628	−	0.814169i	$-0.697193\pi$
$983$	−21.2065	+	5.68227i	−0.676383	+	0.181236i	−0.0957545	+	0.995405i	$0.530526\pi$
$984$	−6.44065	+	0.497080i	−0.205320	+	0.0158463i
$985$	25.8636	+	14.9323i	0.824082	+	0.475784i
$986$	−0.837854	+	3.12691i	−0.0266827	+	0.0995812i
$987$	−49.6315	+	7.99296i	−1.57979	+	0.254419i
$988$	−23.6843	−	10.8616i	−0.753498	−	0.345553i
$989$	−0.0756968	+	0.0437036i	−0.00240702	+	0.00138969i
$990$	−0.0970688	−	0.0104996i	−0.00308505	−	0.000333699i
$991$	32.9495			1.04668			0.523338	−	0.852125i	$-0.324686\pi$
$991$	32.9495			1.04668			0.523338	+	0.852125i	$0.324686\pi$
$992$	0.707637			0.0224675
$993$	44.9831	−	15.8527i	1.42749	−	0.503071i
$994$	−0.418504	+	2.31100i	−0.0132741	+	0.0733006i
$995$	−55.4025	+	14.8450i	−1.75638	+	0.470620i
$996$	−6.68020	−	5.72294i	−0.211670	−	0.181338i
$997$	−9.92556	−	17.1916i	−0.314346	−	0.544462i	0.664953	−	0.746886i	$-0.268452\pi$
$997$	−9.92556	−	17.1916i	−0.314346	−	0.544462i	−0.979298	+	0.202423i	$0.935118\pi$
$998$	−2.17127			−0.0687303
$999$	13.0025	+	24.2092i	0.411382	+	0.765946i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bw.b.11.15	yes	128
3.2	odd	2	inner	273.2.bw.b.11.18	yes	128
7.2	even	3		273.2.bv.b.128.15	yes	128
13.6	odd	12		273.2.bv.b.32.18	yes	128
21.2	odd	6		273.2.bv.b.128.18	yes	128
39.32	even	12		273.2.bv.b.32.15	✓	128
91.58	odd	12	inner	273.2.bw.b.149.18	yes	128
273.149	even	12	inner	273.2.bw.b.149.15	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bv.b.32.15	✓	128	39.32	even	12
273.2.bv.b.32.18	yes	128	13.6	odd	12
273.2.bv.b.128.15	yes	128	7.2	even	3
273.2.bv.b.128.18	yes	128	21.2	odd	6
273.2.bw.b.11.15	yes	128	1.1	even	1	trivial
273.2.bw.b.11.18	yes	128	3.2	odd	2	inner
273.2.bw.b.149.15	yes	128	273.149	even	12	inner
273.2.bw.b.149.18	yes	128	91.58	odd	12	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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.bw (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0262469 - 0.0979549i) q^{2} +(-0.748033 + 1.56219i) q^{3} +(1.72314 - 0.994858i) q^{4} +(2.20563 + 0.590996i) q^{5} +(0.172658 + 0.0322707i) q^{6} +(1.71000 - 2.01889i) q^{7} +(-0.286094 - 0.286094i) q^{8} +(-1.88089 - 2.33714i) q^{9} +O(q^{10})\)	\(q+(-0.0262469 - 0.0979549i) q^{2} +(-0.748033 + 1.56219i) q^{3} +(1.72314 - 0.994858i) q^{4} +(2.20563 + 0.590996i) q^{5} +(0.172658 + 0.0322707i) q^{6} +(1.71000 - 2.01889i) q^{7} +(-0.286094 - 0.286094i) q^{8} +(-1.88089 - 2.33714i) q^{9} -0.231564i q^{10} +(0.0993799 + 0.0993799i) q^{11} +(0.265191 + 3.43607i) q^{12} +(-3.55468 - 0.603532i) q^{13} +(-0.242642 - 0.114513i) q^{14} +(-2.57313 + 3.00353i) q^{15} +(1.96920 - 3.41076i) q^{16} +(2.42420 + 4.19884i) q^{17} +(-0.179567 + 0.245586i) q^{18} +(2.56822 + 2.56822i) q^{19} +(4.38857 - 1.17591i) q^{20} +(1.87476 + 4.18154i) q^{21} +(0.00712633 - 0.0123432i) q^{22} +(0.0913731 - 0.158263i) q^{23} +(0.660943 - 0.232927i) q^{24} +(0.185387 + 0.107033i) q^{25} +(0.0341805 + 0.364039i) q^{26} +(5.05804 - 1.19006i) q^{27} +(0.938063 - 5.18004i) q^{28} +(-5.70192 + 3.29201i) q^{29} +(0.361747 + 0.173217i) q^{30} +(-0.565555 + 0.151540i) q^{31} +(-1.16741 - 0.312807i) q^{32} +(-0.229590 + 0.0809111i) q^{33} +(0.347669 - 0.347669i) q^{34} +(4.96477 - 3.44231i) q^{35} +(-5.56618 - 2.15602i) q^{36} +(1.36877 + 5.10833i) q^{37} +(0.184161 - 0.318977i) q^{38} +(3.60185 - 5.10163i) q^{39} +(-0.461937 - 0.800098i) q^{40} +(-8.90385 - 2.38578i) q^{41} +(0.360396 - 0.293395i) q^{42} +(-0.414218 - 0.239149i) q^{43} +(0.270115 + 0.0723770i) q^{44} +(-2.76731 - 6.26647i) q^{45} +(-0.0179009 - 0.00479653i) q^{46} +(-2.83925 + 10.5962i) q^{47} +(3.85523 + 5.62763i) q^{48} +(-1.15182 - 6.90459i) q^{49} +(0.00561860 - 0.0209689i) q^{50} +(-8.37279 + 0.646200i) q^{51} +(-6.72566 + 2.49643i) q^{52} +(-8.04797 - 4.64650i) q^{53} +(-0.249330 - 0.464224i) q^{54} +(0.160462 + 0.277928i) q^{55} +(-1.06681 + 0.0883724i) q^{56} +(-5.93316 + 2.09094i) q^{57} +(0.472126 + 0.472126i) q^{58} +(3.80035 - 14.1831i) q^{59} +(-1.44579 + 7.73542i) q^{60} +5.35525 q^{61} +(0.0296882 + 0.0514214i) q^{62} +(-7.93475 - 0.199193i) q^{63} -7.75424i q^{64} +(-7.48361 - 3.43197i) q^{65} +(0.0139517 + 0.0203658i) q^{66} +(-0.176349 - 0.176349i) q^{67} +(8.35451 + 4.82348i) q^{68} +(0.178887 + 0.261128i) q^{69} +(-0.467502 - 0.395973i) q^{70} +(-2.26554 - 8.45513i) q^{71} +(-0.130531 + 1.20676i) q^{72} +(1.95176 + 7.28406i) q^{73} +(0.464460 - 0.268156i) q^{74} +(-0.305883 + 0.209546i) q^{75} +(6.98042 + 1.87040i) q^{76} +(0.370576 - 0.0306977i) q^{77} +(-0.594268 - 0.218917i) q^{78} +(-1.70222 - 2.94833i) q^{79} +(6.35907 - 6.35907i) q^{80} +(-1.92448 + 8.79184i) q^{81} +0.934795i q^{82} +(-1.80484 + 1.80484i) q^{83} +(7.39052 + 5.34028i) q^{84} +(2.86539 + 10.6938i) q^{85} +(-0.0125539 + 0.0468516i) q^{86} +(-0.877522 - 11.3700i) q^{87} -0.0568640i q^{88} +(-10.5564 + 2.82858i) q^{89} +(-0.541198 + 0.435547i) q^{90} +(-7.29695 + 6.14447i) q^{91} -0.363613i q^{92} +(0.186319 - 0.996863i) q^{93} +1.11248 q^{94} +(4.14672 + 7.18233i) q^{95} +(1.36193 - 1.58973i) q^{96} +(-14.6793 + 3.93330i) q^{97} +(-0.646106 + 0.294051i) q^{98} +(0.0453421 - 0.419188i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 4 q^{3} - 12 q^{4} - 4 q^{6} - 16 q^{7} - 16 q^{9}+O(q^{10}) \) 128 * q - 4 * q^3 - 12 * q^4 - 4 * q^6 - 16 * q^7 - 16 * q^9	\( 128 q - 4 q^{3} - 12 q^{4} - 4 q^{6} - 16 q^{7} - 16 q^{9} - 48 q^{12} - 16 q^{13} - 6 q^{15} + 32 q^{16} + 22 q^{18} - 16 q^{19} - 18 q^{21} - 8 q^{22} - 4 q^{24} - 40 q^{27} - 76 q^{28} - 4 q^{31} + 50 q^{33} - 48 q^{34} - 60 q^{36} + 28 q^{37} + 40 q^{39} + 44 q^{40} + 44 q^{42} - 144 q^{43} + 58 q^{45} + 48 q^{46} - 64 q^{48} + 24 q^{49} + 36 q^{51} - 22 q^{54} - 16 q^{55} + 40 q^{57} - 28 q^{58} - 4 q^{60} - 40 q^{61} + 20 q^{63} - 34 q^{66} + 96 q^{67} - 54 q^{69} + 64 q^{70} - 98 q^{72} + 48 q^{73} - 12 q^{75} + 144 q^{76} + 82 q^{78} - 24 q^{79} - 48 q^{81} + 4 q^{84} + 56 q^{85} - 2 q^{87} - 24 q^{91} + 10 q^{93} + 32 q^{94} - 54 q^{96} + 52 q^{97} - 10 q^{99}+O(q^{100}) \) 128 * q - 4 * q^3 - 12 * q^4 - 4 * q^6 - 16 * q^7 - 16 * q^9 - 48 * q^12 - 16 * q^13 - 6 * q^15 + 32 * q^16 + 22 * q^18 - 16 * q^19 - 18 * q^21 - 8 * q^22 - 4 * q^24 - 40 * q^27 - 76 * q^28 - 4 * q^31 + 50 * q^33 - 48 * q^34 - 60 * q^36 + 28 * q^37 + 40 * q^39 + 44 * q^40 + 44 * q^42 - 144 * q^43 + 58 * q^45 + 48 * q^46 - 64 * q^48 + 24 * q^49 + 36 * q^51 - 22 * q^54 - 16 * q^55 + 40 * q^57 - 28 * q^58 - 4 * q^60 - 40 * q^61 + 20 * q^63 - 34 * q^66 + 96 * q^67 - 54 * q^69 + 64 * q^70 - 98 * q^72 + 48 * q^73 - 12 * q^75 + 144 * q^76 + 82 * q^78 - 24 * q^79 - 48 * q^81 + 4 * q^84 + 56 * q^85 - 2 * q^87 - 24 * q^91 + 10 * q^93 + 32 * q^94 - 54 * q^96 + 52 * q^97 - 10 * q^99

Introduction

L-functions

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Database

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