LMFDB - Embedded newform 273.2.bw.b.11.18

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			11.18
Character	$\chi$	$=$	273.11
Dual form			273.2.bw.b.149.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0262469 + 0.0979549i) q^{2} +(-0.748033 - 1.56219i) q^{3} +(1.72314 - 0.994858i) q^{4} +(-2.20563 - 0.590996i) q^{5} +(0.133391 - 0.114276i) q^{6} +(1.71000 - 2.01889i) q^{7} +(0.286094 + 0.286094i) q^{8} +(-1.88089 + 2.33714i) q^{9} +O(q^{10})$	\(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} +(0.133391 - 0.114276i) 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} +(-2.84313 - 1.94770i) q^{12} +(-3.55468 - 0.603532i) q^{13} +(0.242642 + 0.114513i) q^{14} +(0.726632 + 3.88770i) q^{15} +(1.96920 - 3.41076i) q^{16} +(-2.42420 - 4.19884i) q^{17} +(-0.278302 - 0.122900i) q^{18} +(2.56822 + 2.56822i) q^{19} +(-4.38857 + 1.17591i) q^{20} +(-4.43303 - 1.16115i) q^{21} +(0.00712633 - 0.0123432i) q^{22} +(-0.0913731 + 0.158263i) q^{23} +(0.232927 - 0.660943i) 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} +(-0.0809111 + 0.229590i) q^{33} +(0.347669 - 0.347669i) q^{34} +(-4.96477 + 3.44231i) q^{35} +(-0.915925 + 5.89846i) q^{36} +(1.36877 + 5.10833i) q^{37} +(-0.184161 + 0.318977i) q^{38} +(1.71618 + 6.00456i) q^{39} +(-0.461937 - 0.800098i) q^{40} +(8.90385 + 2.38578i) q^{41} +(-0.00261321 - 0.464713i) q^{42} +(-0.414218 - 0.239149i) q^{43} +(-0.270115 - 0.0723770i) q^{44} +(5.52979 - 4.04327i) q^{45} +(-0.0179009 - 0.00479653i) q^{46} +(2.83925 - 10.5962i) q^{47} +(-6.80129 - 0.524913i) q^{48} +(-1.15182 - 6.90459i) q^{49} +(-0.00561860 + 0.0209689i) q^{50} +(-4.74602 + 6.92795i) q^{51} +(-6.72566 + 2.49643i) q^{52} +(8.04797 + 4.64650i) q^{53} +(0.0161861 + 0.526695i) q^{54} +(0.160462 + 0.277928i) q^{55} +(1.06681 - 0.0883724i) q^{56} +(2.09094 - 5.93316i) q^{57} +(0.472126 + 0.472126i) q^{58} +(-3.80035 + 14.1831i) q^{59} +(5.11980 + 5.97617i) q^{60} +5.35525 q^{61} +(-0.0296882 - 0.0514214i) q^{62} +(1.50211 + 7.79382i) q^{63} -7.75424i q^{64} +(7.48361 + 3.43197i) q^{65} +(-0.0246131 - 0.00189961i) q^{66} +(-0.176349 - 0.176349i) q^{67} +(-8.35451 - 4.82348i) q^{68} +(0.315587 + 0.0243566i) q^{69} +(-0.467502 - 0.395973i) q^{70} +(2.26554 + 8.45513i) q^{71} +(-1.20676 + 0.130531i) q^{72} +(1.95176 + 7.28406i) q^{73} +(-0.464460 + 0.268156i) q^{74} +(0.0285310 - 0.369675i) q^{75} +(6.98042 + 1.87040i) q^{76} +(-0.370576 + 0.0306977i) q^{77} +(-0.543131 + 0.325710i) 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} +(-8.79393 + 2.40941i) q^{84} +(2.86539 + 10.6938i) q^{85} +(0.0125539 - 0.0468516i) q^{86} +(-9.40797 - 6.44497i) 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} +(0.659788 + 0.770149i) q^{93} +1.11248 q^{94} +(-4.14672 - 7.18233i) q^{95} +(-0.384597 - 2.05771i) q^{96} +(-14.6793 + 3.93330i) q^{97} +(0.646106 - 0.294051i) q^{98} +(0.419188 - 0.0453421i) 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	0.974584	−	0.224020i	$-0.0719182\pi$
$2$	0.0262469	+	0.0979549i	0.0185594	+	0.0692646i	−0.956025	+	0.293285i	$0.905252\pi$
$3$	−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	−0.270654	−	0.962677i	$-0.587240\pi$
$5$	−2.20563	−	0.590996i	−0.986386	−	0.264301i	−0.715732	+	0.698375i	$0.753907\pi$
$6$	0.133391	−	0.114276i	0.0544566	−	0.0466531i
$7$	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	0.691966	−	0.721930i	$-0.256745\pi$
$11$	−0.0993799	−	0.0993799i	−0.0299642	−	0.0299642i	−0.721930	+	0.691966i	$0.756745\pi$
$12$	−2.84313	−	1.94770i	−0.820741	−	0.562252i
$13$	−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
$15$	0.726632	+	3.88770i	0.187616	+	1.00380i
$16$	1.96920	−	3.41076i	0.492300	−	0.852689i
$17$	−2.42420	−	4.19884i	−0.587956	−	1.01837i	−0.994500	−	0.104738i	$-0.966600\pi$
$17$	−2.42420	−	4.19884i	−0.587956	−	1.01837i	0.406544	−	0.913631i	$-0.366734\pi$
$18$	−0.278302	−	0.122900i	−0.0655965	−	0.0289678i
$19$	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
$21$	−4.43303	−	1.16115i	−0.967366	−	0.253383i
$22$	0.00712633	−	0.0123432i	0.00151934	−	0.00263157i
$23$	−0.0913731	+	0.158263i	−0.0190526	+	0.0330001i	−0.875395	−	0.483409i	$-0.839398\pi$
$23$	−0.0913731	+	0.158263i	−0.0190526	+	0.0330001i	0.856342	+	0.516409i	$0.172732\pi$
$24$	0.232927	−	0.660943i	0.0475459	−	0.134914i
$25$	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	0.133715	−	0.991020i	$-0.457309\pi$
$29$	5.70192	−	3.29201i	1.05882	−	0.611310i	0.925106	+	0.379710i	$0.123976\pi$
$30$	−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
$33$	−0.0809111	+	0.229590i	−0.0140848	+	0.0399665i
$34$	0.347669	−	0.347669i	0.0596248	−	0.0596248i
$35$	−4.96477	+	3.44231i	−0.839199	+	0.581857i
$36$	−0.915925	+	5.89846i	−0.152654	+	0.983076i
$37$	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
$39$	1.71618	+	6.00456i	0.274809	+	0.961499i
$40$	−0.461937	−	0.800098i	−0.0730386	−	0.126507i
$41$	8.90385	+	2.38578i	1.39055	+	0.372596i	0.874941	−	0.484229i	$-0.160900\pi$
$41$	8.90385	+	2.38578i	1.39055	+	0.372596i	0.515607	+	0.856825i	$0.327567\pi$
$42$	−0.00261321	−	0.464713i	−0.000403227	−	0.0717068i
$43$	−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
$45$	5.52979	−	4.04327i	0.824333	−	0.602735i
$46$	−0.0179009	−	0.00479653i	−0.00263934	−	0.000707209i
$47$	2.83925	−	10.5962i	0.414148	−	1.54562i	−0.372388	−	0.928077i	$-0.621461\pi$
$47$	2.83925	−	10.5962i	0.414148	−	1.54562i	0.786536	−	0.617544i	$-0.211872\pi$
$48$	−6.80129	−	0.524913i	−0.981681	−	0.0757647i
$49$	−1.15182	−	6.90459i	−0.164546	−	0.986369i
$50$	−0.00561860	+	0.0209689i	−0.000794590	+	0.00296545i
$51$	−4.74602	+	6.92795i	−0.664576	+	0.970107i
$52$	−6.72566	+	2.49643i	−0.932681	+	0.346192i
$53$	8.04797	+	4.64650i	1.10547	+	0.638245i	0.937653	−	0.347572i	$-0.112994\pi$
$53$	8.04797	+	4.64650i	1.10547	+	0.638245i	0.167820	+	0.985818i	$0.446327\pi$
$54$	0.0161861	+	0.526695i	0.00220265	+	0.0716741i
$55$	0.160462	+	0.277928i	0.0216367	+	0.0374758i
$56$	1.06681	−	0.0883724i	0.142559	−	0.0118093i
$57$	2.09094	−	5.93316i	0.276951	−	0.785866i
$58$	0.472126	+	0.472126i	0.0619932	+	0.0619932i
$59$	−3.80035	+	14.1831i	−0.494763	+	1.84648i	0.0365899	+	0.999330i	$0.488350\pi$
$59$	−3.80035	+	14.1831i	−0.494763	+	1.84648i	−0.531353	+	0.847151i	$0.678316\pi$
$60$	5.11980	+	5.97617i	0.660963	+	0.771520i
$61$	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
$63$	1.50211	+	7.79382i	0.189248	+	0.981929i
$64$		−	7.75424i		−	0.969280i
$65$	7.48361	+	3.43197i	0.928228	+	0.425683i
$66$	−0.0246131	−	0.00189961i	−0.00302967	−	0.000233825i
$67$	−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
$69$	0.315587	+	0.0243566i	0.0379922	+	0.00293218i
$70$	−0.467502	−	0.395973i	−0.0558771	−	0.0473279i
$71$	2.26554	+	8.45513i	0.268871	+	1.00344i	0.959838	+	0.280553i	$0.0905180\pi$
$71$	2.26554	+	8.45513i	0.268871	+	1.00344i	−0.690968	+	0.722886i	$0.742815\pi$
$72$	−1.20676	+	0.130531i	−0.142218	+	0.0153832i
$73$	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
$75$	0.0285310	−	0.369675i	0.00329448	−	0.0426864i
$76$	6.98042	+	1.87040i	0.800709	+	0.214549i
$77$	−0.370576	+	0.0306977i	−0.0422311	+	0.00349833i
$78$	−0.543131	+	0.325710i	−0.0614975	+	0.0368794i
$79$	−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	−0.601081	−	0.799188i	$-0.705263\pi$
$83$	1.80484	−	1.80484i	0.198107	−	0.198107i	0.799188	+	0.601081i	$0.205263\pi$
$84$	−8.79393	+	2.40941i	−0.959496	+	0.262888i
$85$	2.86539	+	10.6938i	0.310795	+	1.15990i
$86$	0.0125539	−	0.0468516i	0.00135372	−	0.00505214i
$87$	−9.40797	−	6.44497i	−1.00864	−	0.690974i
$88$		−	0.0568640i		−	0.00606173i
$89$	10.5564	−	2.82858i	1.11898	−	0.299829i	0.348507	−	0.937306i	$-0.386689\pi$
$89$	10.5564	−	2.82858i	1.11898	−	0.299829i	0.770469	+	0.637478i	$0.220022\pi$
$90$	0.541198	+	0.435547i	0.0570473	+	0.0459107i
$91$	−7.29695	+	6.14447i	−0.764929	+	0.644115i
$92$			0.363613i			0.0379093i
$93$	0.659788	+	0.770149i	0.0684169	+	0.0798607i
$94$	1.11248			0.114743
$95$	−4.14672	−	7.18233i	−0.425445	−	0.736892i
$96$	−0.384597	−	2.05771i	−0.0392528	−	0.210014i
$97$	−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
$99$	0.419188	−	0.0453421i	0.0421300	−	0.00455706i
$100$	0.425932			0.0425932
$101$	−10.8586			−1.08047			−0.540233	−	0.841515i	$-0.681664\pi$
$101$	−10.8586			−1.08047			−0.540233	+	0.841515i	$0.681664\pi$
$102$	−0.803195	−	0.283059i	−0.0795282	−	0.0280270i
$103$	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
$105$	9.09137	+	5.18096i	0.887227	+	0.505610i
$106$	−0.243913	+	0.910294i	−0.0236909	+	0.0884156i
$107$	−13.8616	−	8.00300i	−1.34005	−	0.773679i	−0.353237	−	0.935534i	$-0.614919\pi$
$107$	−13.8616	−	8.00300i	−1.34005	−	0.773679i	−0.986815	+	0.161854i	$0.948253\pi$
$108$	9.89967	−	2.98139i	0.952596	−	0.286884i
$109$	−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
$111$	6.95631	−	5.95949i	0.660264	−	0.565650i
$112$	−3.51861	−	9.80798i	−0.332477	−	0.926767i
$113$	4.43949	+	2.56314i	0.417632	+	0.241120i	0.694064	−	0.719914i	$-0.255819\pi$
$113$	4.43949	+	2.56314i	0.417632	+	0.241120i	−0.276432	+	0.961034i	$0.589152\pi$
$114$	0.636063	+	0.0490904i	0.0595727	+	0.00459774i
$115$	0.295068	−	0.295068i	0.0275152	−	0.0275152i
$116$	6.55016	−	11.3452i	0.608167	−	1.05338i
$117$	8.09651	−	7.17262i	0.748523	−	0.663109i
$118$	−1.48905			−0.137078
$119$	−12.6224	−	2.28581i	−1.15709	−	0.209540i
$120$	−0.904364	+	1.32013i	−0.0825567	+	0.120511i
$121$		−	10.9802i		−	0.998204i
$122$	0.140559	+	0.524573i	0.0127256	+	0.0474926i
$123$	−2.93333	−	15.6942i	−0.264489	−	1.41510i
$124$	−0.823772	+	0.823772i	−0.0739769	+	0.0739769i
$125$	7.72752	+	7.72752i	0.691170	+	0.691170i
$126$	−0.724017	+	0.351703i	−0.0645006	+	0.0313322i
$127$	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
$129$	−0.0637479	+	0.825980i	−0.00561269	+	0.0727235i
$130$	−0.139756	+	0.823135i	−0.0122574	+	0.0721937i
$131$	1.61992	−	0.935259i	0.141533	−	0.0817140i	−0.427562	−	0.903986i	$-0.640627\pi$
$131$	1.61992	−	0.935259i	0.141533	−	0.0817140i	0.569094	+	0.822272i	$0.307294\pi$
$132$	0.0889879	+	0.476112i	0.00774540	+	0.0414402i
$133$	9.57658	−	0.793303i	0.830395	−	0.0687881i
$134$	0.0126456	−	0.0219029i	0.00109242	−	0.00189212i
$135$	−10.4528	−	5.61410i	−0.899636	−	0.483185i
$136$	0.507715	−	1.89482i	0.0435362	−	0.162479i
$137$	3.17505	−	11.8494i	0.271263	−	1.01237i	−0.687042	−	0.726618i	$-0.741091\pi$
$137$	3.17505	−	11.8494i	0.271263	−	1.01237i	0.958305	−	0.285749i	$-0.0922422\pi$
$138$	0.00589735	+	0.0315526i	0.000502016	+	0.00268593i
$139$	−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
$141$	−18.6772	+	3.49088i	−1.57291	+	0.293985i
$142$	−0.768757	+	0.443842i	−0.0645127	+	0.0372464i
$143$	0.293285	+	0.413243i	0.0245257	+	0.0345571i
$144$	4.26757	+	11.0176i	0.355631	+	0.918131i
$145$	−14.5219	+	3.89112i	−1.20598	+	0.323140i
$146$	−0.662282	+	0.382369i	−0.0548108	+	0.0316451i
$147$	−9.92469	+	6.96423i	−0.818575	+	0.574400i
$148$	7.44066	+	7.44066i	0.611619	+	0.611619i
$149$	−3.96245	+	3.96245i	−0.324616	+	0.324616i	−0.850535	−	0.525919i	$-0.823722\pi$
$149$	−3.96245	+	3.96245i	−0.324616	+	0.324616i	0.525919	+	0.850535i	$0.323722\pi$
$150$	0.0369604	−	0.00690809i	0.00301780	−	0.000564043i
$151$	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
$153$	14.3730	+	2.23186i	1.16199	+	0.180436i
$154$	−0.0127335	−	0.0354940i	−0.00102609	−	0.00286019i
$155$	1.33696			0.107387
$156$	8.93092	+	8.63936i	0.715045	+	0.691703i
$157$	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
$159$	1.23858	−	16.0482i	0.0982256	−	1.27271i
$160$	−2.39000	−	1.37987i	−0.188946	−	0.109088i
$161$	0.163267	+	0.455101i	0.0128673	+	0.0358670i
$162$	0.810692	−	0.419271i	0.0636939	−	0.0329411i
$163$	−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
$165$	0.314146	−	0.458572i	0.0244563	−	0.0356998i
$166$	0.224165	+	0.129422i	0.0173986	+	0.0100451i
$167$	0.867439	−	3.23732i	0.0671244	−	0.250512i	−0.924208	−	0.381890i	$-0.875273\pi$
$167$	0.867439	−	3.23732i	0.0671244	−	0.250512i	0.991332	+	0.131378i	$0.0419401\pi$
$168$	−0.936066	−	1.60046i	−0.0722191	−	0.123478i
$169$	12.2715	+	4.29073i	0.943961	+	0.330056i
$170$	−0.972300	+	0.561358i	−0.0745720	+	0.0430542i
$171$	−10.8328	+	1.17175i	−0.828407	+	0.0896060i
$172$	−0.951677			−0.0725647
$173$	−11.6730			−0.887479			−0.443739	−	0.896156i	$-0.646348\pi$
$173$	−11.6730			−0.887479			−0.443739	+	0.896156i	$0.646348\pi$
$174$	0.384386	−	1.09072i	0.0291402	−	0.0826871i
$175$	0.533100	−	0.191250i	0.0402986	−	0.0144571i
$176$	−0.534659	+	0.143262i	−0.0403015	+	0.0107987i
$177$	24.9995	−	4.67254i	1.87908	−	0.351210i
$178$	0.554146	+	0.959809i	0.0415350	+	0.0719407i
$179$	−19.1698			−1.43282			−0.716409	−	0.697680i	$-0.754216\pi$
$179$	−19.1698			−1.43282			−0.716409	+	0.697680i	$0.754216\pi$
$180$	5.50615	−	12.4685i	0.410404	−	0.929346i
$181$			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
$186$	−0.0581224	+	0.0848436i	−0.00426174	+	0.00622103i
$187$	−0.176364	+	0.658198i	−0.0128970	+	0.0481322i
$188$	−5.64931	−	21.0835i	−0.412018	−	1.53767i
$189$	11.0518	−	8.17663i	0.803902	−	0.594762i
$190$	0.594706	−	0.594706i	0.0431445	−	0.0431445i
$191$			10.4621i			0.757015i	0.925598	+	0.378507i	$0.123562\pi$
$191$			10.4621i			0.757015i	−0.925598	+	0.378507i	$0.876438\pi$
$192$	−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
$195$	−0.236592	−	14.2581i	−0.0169427	−	1.02104i
$196$	−8.85384	−	10.7517i	−0.632417	−	0.767978i
$197$	−12.6332	−	3.38506i	−0.900079	−	0.241175i	−0.221029	−	0.975267i	$-0.570941\pi$
$197$	−12.6332	−	3.38506i	−0.900079	−	0.241175i	−0.679050	+	0.734092i	$0.737608\pi$
$198$	0.0154439	+	0.0398714i	0.00109755	+	0.00283354i
$199$	−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
$201$	−0.143576	+	0.407406i	−0.0101271	+	0.0287362i
$202$	−0.285004	−	1.06365i	−0.0200528	−	0.0748380i
$203$	3.10407	−	17.1409i	0.217863	−	1.20305i
$204$	−1.28575	+	16.6595i	−0.0900208	+	1.16640i
$205$	−18.2286	−	10.5243i	−1.27314	−	0.735048i
$206$	1.25099	+	1.25099i	0.0871603	+	0.0871603i
$207$	−0.198020	−	0.511227i	−0.0137633	−	0.0355328i
$208$	−9.05838	+	10.9357i	−0.628086	+	0.758252i
$209$		−	0.510458i		−	0.0353091i
$210$	−0.268880	+	1.02653i	−0.0185545	+	0.0708372i
$211$	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
$213$	11.5138	−	9.86393i	0.788915	−	0.675865i
$214$	0.420109	−	1.56787i	0.0287180	−	0.107177i
$215$	0.772275	+	0.772275i	0.0526687	+	0.0526687i
$216$	1.10661	+	1.78755i	0.0752951	+	0.121627i
$217$	−0.661154	+	1.40093i	−0.0448821	+	0.0951010i
$218$	−0.121485	−	0.210418i	−0.00822798	−	0.0142513i
$219$	9.91913	−	8.49774i	0.670273	−	0.574224i
$220$	0.552998	+	0.319273i	0.0372831	+	0.0215254i
$221$	6.08313	+	16.3886i	0.409196	+	1.10242i
$222$	0.766343	+	0.524987i	0.0514336	+	0.0352348i
$223$	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
$225$	−0.598846	+	0.231958i	−0.0399231	+	0.0154639i
$226$	−0.134549	+	0.502144i	−0.00895008	+	0.0334022i
$227$	3.06928	+	0.822412i	0.203716	+	0.0545854i	0.359234	−	0.933248i	$-0.383038\pi$
$227$	3.06928	+	0.822412i	0.203716	+	0.0545854i	−0.155518	+	0.987833i	$0.549705\pi$
$228$	−2.29966	−	12.3039i	−0.152299	−	0.814844i
$229$	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
$231$	0.325159	+	0.555949i	0.0213939	+	0.0365787i
$232$	2.57311	+	0.689463i	0.168933	+	0.0452655i
$233$	8.04672	+	13.9373i	0.527158	+	0.913065i	0.999499	+	0.0316488i	$0.0100758\pi$
$233$	8.04672	+	13.9373i	0.527158	+	0.913065i	−0.472341	+	0.881416i	$0.656591\pi$
$234$	0.915102	+	0.604834i	0.0598221	+	0.0395392i
$235$	−12.5247	+	21.6934i	−0.817020	+	1.41512i
$236$	7.56161	+	28.2203i	0.492219	+	1.83699i
$237$	−3.33254	+	4.86464i	−0.216472	+	0.315992i
$238$	−0.107393	−	1.29642i	−0.00696122	−	0.0840344i
$239$	−7.82407	+	7.82407i	−0.506097	+	0.506097i	−0.913326	−	0.407229i	$-0.866495\pi$
$239$	−7.82407	+	7.82407i	−0.506097	+	0.506097i	0.407229	+	0.913326i	$0.366495\pi$
$240$	14.6909	+	5.17730i	0.948292	+	0.334193i
$241$	−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
$249$	−4.16960	−	1.46943i	−0.264238	−	0.0931214i
$250$	−0.554124	+	0.959772i	−0.0350459	+	0.0607013i
$251$	−13.2053	+	22.8723i	−0.833513	+	1.44369i	0.0617231	+	0.998093i	$0.480340\pi$
$251$	−13.2053	+	22.8723i	−0.833513	+	1.44369i	−0.895236	+	0.445593i	$0.852993\pi$
$252$	10.3421	+	11.9355i	0.651491	+	0.751865i
$253$	0.0248088	−	0.00664749i	0.00155971	−	0.000417924i
$254$	0.303383	+	0.303383i	0.0190360	+	0.0190360i
$255$	14.5623	−	12.4756i	0.911929	−	0.781252i
$256$	−7.59180	−	13.1494i	−0.474488	−	0.821837i
$257$	10.6569	−	18.4584i	0.664761	−	1.15140i	−0.314589	−	0.949228i	$-0.601867\pi$
$257$	10.6569	−	18.4584i	0.664761	−	1.15140i	0.979350	−	0.202172i	$-0.0648001\pi$
$258$	−0.0825820	+	0.0154350i	−0.00514133	+	0.000960943i
$259$	12.6538	+	5.97183i	0.786266	+	0.371071i
$260$	16.3097	−	1.53135i	1.01148	−	0.0949705i
$261$	−3.03081	+	19.5181i	−0.187603	+	1.20814i
$262$	0.134131	+	0.134131i	0.00828664	+	0.00828664i
$263$			16.0738i			0.991156i	0.868563	+	0.495578i	$0.165044\pi$
$263$			16.0738i			0.991156i	−0.868563	+	0.495578i	$0.834956\pi$
$264$	−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
$267$	−12.3153	−	14.3752i	−0.753685	−	0.879751i
$268$	−0.479317	−	0.128433i	−0.0292790	−	0.00784527i
$269$	15.7901	−	9.11639i	0.962737	−	0.555836i	0.0657224	−	0.997838i	$-0.479065\pi$
$269$	15.7901	−	9.11639i	0.962737	−	0.555836i	0.897014	+	0.442002i	$0.145731\pi$
$270$	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
$273$	15.0572	+	6.80299i	0.911303	+	0.411736i
$274$	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
$279$	0.709578	−	1.60681i	0.0424813	−	0.0961974i
$280$	−2.40522	−	0.435566i	−0.143739	−	0.0260300i
$281$	4.03859	+	4.03859i	0.240922	+	0.240922i	0.817232	−	0.576310i	$-0.195508\pi$
$281$	4.03859	+	4.03859i	0.240922	+	0.240922i	−0.576310	+	0.817232i	$0.695508\pi$
$282$	−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
$285$	−8.11830	+	11.8506i	−0.480887	+	0.701969i
$286$	−0.0327813	+	0.0395750i	−0.00193840	+	0.00234012i
$287$	20.0422	−	13.8962i	1.18305	−	0.820267i
$288$	−2.92685	+	2.14005i	−0.172466	+	0.126104i
$289$	−3.25353	+	5.63528i	−0.191384	+	0.331487i
$290$	−0.762309	−	1.32036i	−0.0447644	−	0.0775341i
$291$	17.1251	+	19.9896i	1.00389	+	1.17181i
$292$	10.6098	+	10.6098i	0.620890	+	0.620890i
$293$	9.98973	−	2.67674i	0.583606	−	0.156377i	0.0450769	−	0.998984i	$-0.485647\pi$
$293$	9.98973	−	2.67674i	0.583606	−	0.156377i	0.538529	+	0.842607i	$0.318980\pi$
$294$	−0.942673	−	0.789382i	−0.0549778	−	0.0460377i
$295$	16.7643	−	29.0366i	0.976055	−	1.69058i
$296$	−1.06987	+	1.85306i	−0.0621848	+	0.107707i
$297$	−0.384400	−	0.620935i	−0.0223051	−	0.0360303i
$298$	−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
$306$	0.158624	+	1.46648i	0.00906795	+	0.0838332i
$307$	−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
$309$	−24.9282	−	17.0771i	−1.41811	−	0.971485i
$310$	0.0350912	+	0.130962i	0.00199304	+	0.00743814i
$311$	1.13541	−	1.96659i	0.0643833	−	0.111515i	−0.832037	−	0.554720i	$-0.812825\pi$
$311$	1.13541	−	1.96659i	0.0643833	−	0.111515i	0.896420	+	0.443205i	$0.146159\pi$
$312$	−1.22688	+	2.20886i	−0.0694584	+	0.125052i
$313$	−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
$315$	1.29302	−	18.0780i	0.0728532	−	1.01858i
$316$	−5.86633	−	3.38693i	−0.330007	−	0.190530i
$317$	−18.9068	−	5.06606i	−1.06191	−	0.284538i	−0.314746	−	0.949176i	$-0.601919\pi$
$317$	−18.9068	−	5.06606i	−1.06191	−	0.284538i	−0.747166	+	0.664638i	$0.768586\pi$
$318$	1.60451	−	0.299892i	0.0899764	−	0.0168171i
$319$	−0.893815	−	0.239497i	−0.0500441	−	0.0134093i
$320$	−4.58272	+	17.1030i	−0.256182	+	0.956084i
$321$	−2.13329	+	27.6410i	−0.119069	+	1.54277i
$322$	−0.0402941	+	0.0279378i	−0.00224550	+	0.00155692i
$323$	4.55766	−	17.0094i	0.253595	−	0.946429i
$324$	−12.0628	−	13.2350i	−0.670155	−	0.735279i
$325$	−0.594394	−	0.492357i	−0.0329711	−	0.0273110i
$326$	−1.09631	−	0.632954i	−0.0607189	−	0.0350561i
$327$	2.69987	+	3.15147i	0.149303	+	0.174277i
$328$	1.86478	+	3.22990i	0.102965	+	0.178341i
$329$	−16.5375	−	23.8517i	−0.911743	−	1.31499i
$330$	0.0531647	+	0.0187361i	0.00292662	+	0.00103139i
$331$	−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
$333$	−14.5134	−	6.40921i	−0.795331	−	0.351222i
$334$	0.339879			0.0185974
$335$	0.284739	+	0.493182i	0.0155569	+	0.0269454i
$336$	−12.6899	+	12.8334i	−0.692292	+	0.700122i
$337$		−	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
$339$	0.683235	−	8.85265i	0.0371082	−	0.480810i
$340$	15.5763	+	15.5763i	0.844742	+	0.844742i
$341$	0.0712648	+	0.0411447i	0.00385920	+	0.00222811i
$342$	−0.399107	−	1.03037i	−0.0215812	−	0.0557162i
$343$	−15.9092	−	9.48141i	−0.859016	−	0.511948i
$344$	−0.0500863	−	0.186925i	−0.00270047	−	0.0100783i
$345$	−0.681673	−	0.240232i	−0.0367000	−	0.0129337i
$346$	−0.306379	−	1.14342i	−0.0164711	−	0.0614708i
$347$	−29.5306	+	17.0495i	−1.58528	+	0.915264i	−0.591214	+	0.806515i	$0.701351\pi$
$347$	−29.5306	+	17.0495i	−1.58528	+	0.915264i	−0.994069	+	0.108749i	$0.965315\pi$
$348$	−22.6231	−	1.74602i	−1.21273	−	0.0935965i
$349$	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
$351$	−17.2615	−	7.28296i	−0.921349	−	0.388736i
$352$	−0.0849304	−	0.147104i	−0.00452680	−	0.00784066i
$353$	6.42719	−	6.42719i	0.342085	−	0.342085i	−0.515066	−	0.857151i	$-0.672233\pi$
$353$	6.42719	−	6.42719i	0.342085	−	0.342085i	0.857151	+	0.515066i	$0.172233\pi$
$354$	1.11386	+	2.32618i	0.0592009	+	0.123635i
$355$		−	19.9878i		−	1.06084i
$356$	15.3762	−	15.3762i	0.814935	−	0.814935i
$357$	5.87108	+	21.4285i	0.310731	+	1.13411i
$358$	−0.503149	−	1.87778i	−0.0265922	−	0.0992436i
$359$	6.49014	−	24.2215i	0.342536	−	1.27836i	−0.552928	−	0.833229i	$-0.686489\pi$
$359$	6.49014	−	24.2215i	0.342536	−	1.27836i	0.895464	−	0.445134i	$-0.146844\pi$
$360$	2.73880	+	0.425286i	0.144347	+	0.0224146i
$361$		−	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
$366$	0.714342	−	0.611978i	0.0373392	−	0.0319886i
$367$	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
$369$	−22.3231	+	16.3222i	−1.16209	+	0.849699i
$370$	1.18291	−	0.316958i	0.0614963	−	0.0164779i
$371$	23.1428	−	8.30246i	1.20151	−	0.431042i
$372$	1.90310	+	0.670682i	0.0986711	+	0.0347732i
$373$	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
$375$	6.29143	−	17.8523i	0.324888	−	0.921889i
$376$	3.84382	−	2.21923i	0.198230	−	0.114448i
$377$	−22.2553	+	8.26073i	−1.14621	+	0.425449i
$378$	1.09102	+	0.867969i	0.0561159	+	0.0446435i
$379$	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
$381$	−6.04547	−	4.14147i	−0.309719	−	0.212174i
$382$	−1.02482	+	0.274599i	−0.0524343	+	0.0140497i
$383$	−9.28218	+	9.28218i	−0.474297	+	0.474297i	−0.903302	−	0.429005i	$-0.858864\pi$
$383$	−9.28218	+	9.28218i	−0.474297	+	0.474297i	0.429005	+	0.903302i	$0.358864\pi$
$384$	−3.60998	−	4.21380i	−0.184221	−	0.215035i
$385$	0.835495	+	0.151301i	0.0425808	+	0.00771103i
$386$	−0.573200	−	0.330937i	−0.0291751	−	0.0168443i
$387$	1.33803	−	0.518274i	0.0680157	−	0.0263453i
$388$	−21.3814	+	21.3814i	−1.08548	+	1.08548i
$389$	6.54242	−	11.3318i	0.331714	−	0.574545i	−0.651134	−	0.758963i	$-0.725707\pi$
$389$	6.54242	−	11.3318i	0.331714	−	0.574545i	0.982848	+	0.184418i	$0.0590399\pi$
$390$	1.39044	−	0.397406i	0.0704076	−	0.0201234i
$391$	0.886028			0.0448084
$392$	1.64583	−	2.30489i	0.0831271	−	0.116415i
$393$	−2.67281	−	1.83102i	−0.134825	−	0.0923626i
$394$		−	1.32633i		−	0.0668196i
$395$	2.01201	+	7.50891i	0.101235	+	0.377814i
$396$	0.677212	−	0.495164i	0.0340312	−	0.0248829i
$397$	−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
$399$	−8.40289	−	14.3670i	−0.420671	−	0.719252i
$400$	0.730130	−	0.421541i	0.0365065	−	0.0210770i
$401$	−14.5662	+	3.90300i	−0.727401	+	0.194907i	−0.603472	−	0.797384i	$-0.706216\pi$
$401$	−14.5662	+	3.90300i	−0.727401	+	0.194907i	−0.123930	+	0.992291i	$0.539550\pi$
$402$	−0.0436759	−	0.00337084i	−0.00217835	−	0.000168122i
$403$	2.10183	−	0.197345i	0.104699	−	0.00983047i
$404$	−18.7109	+	10.8027i	−0.930900	+	0.537455i
$405$	−0.951249	+	20.5289i	−0.0472680	+	1.02009i
$406$	1.76050	−	0.145836i	0.0873723	−	0.00723773i
$407$	0.371637	−	0.643694i	0.0184214	−	0.0319067i
$408$	−3.33986	+	0.624238i	−0.165348	+	0.0309044i
$409$	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
$411$	−20.8862	+	3.90374i	−1.03024	+	0.192557i
$412$	17.3559	−	30.0612i	0.855062	−	1.48101i
$413$	22.1355	+	31.9255i	1.08922	+	1.57095i
$414$	0.0448798	−	0.0328152i	0.00220572	−	0.00161278i
$415$	−5.04747	+	2.91416i	−0.247770	+	0.143050i
$416$	−3.96098	−	1.81650i	−0.194203	−	0.0890611i
$417$	3.41589	+	0.263633i	0.167277	+	0.0129102i
$418$	0.0500018	−	0.0133980i	0.00244567	−	0.000655315i
$419$	8.90455	−	5.14105i	0.435016	−	0.251157i	−0.266465	−	0.963845i	$-0.585856\pi$
$419$	8.90455	−	5.14105i	0.435016	−	0.251157i	0.701481	+	0.712688i	$0.252522\pi$
$420$	20.8201	−	0.117077i	1.01592	−	0.00571277i
$421$	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
$423$	19.4246	+	26.5661i	0.944457	+	1.29169i
$424$	0.973142	+	3.63181i	0.0472599	+	0.176377i
$425$		−	1.03788i		−	0.0503447i
$426$	1.26842	+	0.868939i	0.0614553	+	0.0421002i
$427$	9.15746	−	10.8117i	0.443161	−	0.523213i
$428$	−31.8474			−1.53940
$429$	0.426178	−	0.767286i	0.0205761	−	0.0370449i
$430$	−0.0553783	+	0.0959180i	−0.00267058	+	0.00462557i
$431$	17.6837	−	17.6837i	0.851794	−	0.851794i	−0.138560	−	0.990354i	$-0.544247\pi$
$431$	17.6837	−	17.6837i	0.851794	−	0.851794i	0.990354	+	0.138560i	$0.0442474\pi$
$432$	14.0193	−	14.9083i	0.674503	−	0.717275i
$433$	−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
$435$	16.9415	+	19.7753i	0.812284	+	0.948152i
$436$	−3.37089	+	3.37089i	−0.161437	+	0.161437i
$437$	−0.641119	+	0.171787i	−0.0306689	+	0.00821770i
$438$	1.09274	+	0.748588i	0.0522133	+	0.0357689i
$439$	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
$441$	18.3035	+	10.2948i	0.871594	+	0.490229i
$442$	−1.44568	+	1.02602i	−0.0687641	+	0.0488030i
$443$	−15.3702	+	8.87401i	−0.730262	+	0.421617i	−0.818518	−	0.574481i	$-0.805204\pi$
$443$	−15.3702	+	8.87401i	−0.730262	+	0.421617i	0.0882559	+	0.996098i	$0.471871\pi$
$444$	6.05789	−	17.1896i	0.287495	−	0.815783i
$445$	−24.9551			−1.18299
$446$	0.504646			0.0238957
$447$	9.15415	+	3.22607i	0.432976	+	0.152588i
$448$	−15.6549	−	13.2597i	−0.739627	−	0.626463i
$449$	−26.9065	+	7.20957i	−1.26980	+	0.340241i	−0.829953	−	0.557834i	$-0.811633\pi$
$449$	−26.9065	+	7.20957i	−1.26980	+	0.340241i	−0.439843	+	0.898075i	$0.644966\pi$
$450$	−0.0384393	−	0.0525717i	−0.00181205	−	0.00247826i
$451$	−0.647765	−	1.12196i	−0.0305021	−	0.0528311i
$452$	10.1998			0.479760
$453$	6.64490	−	5.69270i	0.312205	−	0.267466i
$454$			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
$459$	−7.26486	−	24.1229i	−0.339094	−	1.12596i
$460$	0.214894	−	0.801994i	0.0100195	−	0.0373932i
$461$	3.03989	+	11.3450i	0.141582	+	0.528390i	0.999884	+	0.0152454i	$0.00485295\pi$
$461$	3.03989	+	11.3450i	0.141582	+	0.528390i	−0.858302	+	0.513145i	$0.828480\pi$
$462$	−0.0459235	+	0.0464429i	−0.00213655	+	0.00216072i
$463$	−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	$0.0377343\pi$
$467$	12.9426	+	22.4173i	0.598914	+	1.03735i	−0.394068	+	0.919081i	$0.628932\pi$
$468$	6.81573	−	20.4143i	0.315057	−	0.943653i
$469$	−0.657586	+	0.0544729i	−0.0303645	+	0.00251533i
$470$	−2.45371	−	0.657469i	−0.113181	−	0.0303268i
$471$	−4.30767	−	0.332460i	−0.198487	−	0.0153189i
$472$	−5.14496	+	2.97044i	−0.236816	+	0.136726i
$473$	0.0173984	+	0.0649316i	0.000799977	+	0.00298556i
$474$	−0.563984	−	0.198757i	−0.0259046	−	0.00912920i
$475$	0.201230	+	0.751000i	0.00923305	+	0.0344582i
$476$	−24.0242	+	8.61869i	−1.10115	+	0.395037i
$477$	−25.9969	+	10.0697i	−1.19032	+	0.461060i
$478$	−0.971764	−	0.561048i	−0.0444475	−	0.0256618i
$479$	−9.60829	−	9.60829i	−0.439014	−	0.439014i	0.452666	−	0.891680i	$-0.350473\pi$
$479$	−9.60829	−	9.60829i	−0.439014	−	0.439014i	−0.891680	+	0.452666i	$0.850473\pi$
$480$	−0.367820	+	4.76584i	−0.0167886	+	0.217530i
$481$	−1.78251	−	18.9846i	−0.0812754	−	0.865623i
$482$		−	0.204746i		−	0.00932592i
$483$	0.588826	−	0.595486i	0.0267925	−	0.0270955i
$484$	−10.9238	−	18.9206i	−0.496536	−	0.860025i
$485$	34.7015			1.57572
$486$	−1.26141	−	0.952828i	−0.0572186	−	0.0432212i
$487$	−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
$489$	20.3920	+	7.18645i	0.922157	+	0.324983i
$490$	−1.59885	+	0.266721i	−0.0722288	+	0.0120492i
$491$	4.53840	+	7.86073i	0.204815	+	0.354750i	0.950074	−	0.312025i	$-0.101007\pi$
$491$	4.53840	+	7.86073i	0.204815	+	0.354750i	−0.745259	+	0.666775i	$0.767674\pi$
$492$	−20.6680	−	24.1251i	−0.931786	−	1.08764i
$493$	−27.6452	−	15.9610i	−1.24508	−	0.718847i
$494$	0.847148	−	1.02271i	0.0381150	−	0.0460141i
$495$	−0.951369	−	0.147731i	−0.0427609	−	0.00664000i
$496$	−0.596825	+	2.22738i	−0.0267982	+	0.100012i
$497$	20.9440	+	9.88435i	0.939468	+	0.443374i
$498$	0.0344989	−	0.447001i	0.00154593	−	0.0200306i
$499$	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
$501$	−5.70620	+	1.06652i	−0.254934	+	0.0476486i
$502$	−2.58705	−	0.693199i	−0.115466	−	0.0309390i
$503$	−6.12042	−	3.53362i	−0.272896	−	0.157557i	0.357307	−	0.933987i	$-0.383695\pi$
$503$	−6.12042	−	3.53362i	−0.272896	−	0.157557i	−0.630203	+	0.776430i	$0.717028\pi$
$504$	−1.80002	+	2.65951i	−0.0801794	+	0.118464i
$505$	23.9499	+	6.41736i	1.06576	+	0.285569i
$506$	0.00130231	+	0.00225567i	5.78947e−5	+	0.000100277i
$507$	−2.47654	−	22.3801i	−0.109987	−	0.993933i
$508$	4.20906	−	7.29031i	0.186747	−	0.323455i
$509$	0.325714	+	1.21558i	0.0144370	+	0.0538796i	0.972769	−	0.231779i	$-0.0744545\pi$
$509$	0.325714	+	1.21558i	0.0144370	+	0.0538796i	−0.958332	+	0.285658i	$0.907788\pi$
$510$	1.60426	+	1.09901i	0.0710379	+	0.0486648i
$511$	18.0432	+	8.51534i	0.798185	+	0.376696i
$512$	5.61928	−	5.61928i	0.248339	−	0.248339i
$513$	9.93381	+	16.0465i	0.438589	+	0.708468i
$514$	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	0.141006	−	0.990009i	$-0.454966\pi$
$521$	−14.7421	−	8.51137i	−0.645864	−	0.372890i	−0.786870	+	0.617119i	$0.788300\pi$
$522$	−1.99145	+	0.215408i	−0.0871632	+	0.00942815i
$523$	−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
$525$	−0.697546	−	0.689744i	−0.0304434	−	0.0301029i
$526$	−1.57451	+	0.421889i	−0.0686520	+	0.0183952i
$527$	2.00731	+	2.00731i	0.0874399	+	0.0874399i
$528$	0.623745	+	0.728077i	0.0271450	+	0.0316855i
$529$	11.4833	+	19.8897i	0.499274	+	0.864768i
$530$	1.07596	−	1.86362i	0.0467367	−	0.0809504i
$531$	−25.9999	−	35.5588i	−1.12830	−	1.54312i
$532$	15.7126	−	10.8943i	0.681228	−	0.472328i
$533$	−30.2104	−	13.8544i	−1.30856	−	0.600103i
$534$	1.08489	−	1.58365i	0.0469477	−	0.0685313i
$535$	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
$540$	−23.5970	+	0.725170i	−1.01545	+	0.0312064i
$541$	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
$546$	−0.271180	+	1.65348i	−0.0116055	+	0.0707626i
$547$	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
$552$	0.0833194	+	0.0972560i	0.00354631	+	0.00413949i
$553$	−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	0.616031	−	0.787722i	$-0.288740\pi$
$557$	−4.05205	−	4.05205i	−0.171691	−	0.171691i	−0.787722	+	0.616031i	$0.788740\pi$
$558$	0.176019	+	0.0273327i	0.00745150	+	0.00115708i
$559$	1.32808	+	1.10009i	0.0561718	+	0.0465289i
$560$	1.96427	+	23.7122i	0.0830055	+	1.00202i
$561$	1.16016	−	0.216840i	0.0489819	−	0.00915498i
$562$	−0.289599	+	0.501600i	−0.0122160	+	0.0211587i
$563$	12.7027	+	22.0017i	0.535355	+	0.927262i	0.999146	+	0.0413171i	$0.0131554\pi$
$563$	12.7027	+	22.0017i	0.535355	+	0.927262i	−0.463791	+	0.885944i	$0.653511\pi$
$564$	−28.7106	+	24.5965i	−1.20894	+	1.03570i
$565$	−8.27705	−	8.27705i	−0.348218	−	0.348218i
$566$	−2.24065	+	0.600381i	−0.0941816	+	0.0252359i
$567$	−21.0406	−	11.1487i	−0.883622	−	0.468201i
$568$	−1.77080	+	3.06712i	−0.0743013	+	0.128694i
$569$	19.6875	−	34.0997i	0.825342	−	1.42953i	−0.0763150	−	0.997084i	$-0.524315\pi$
$569$	19.6875	−	34.0997i	0.825342	−	1.42953i	0.901657	−	0.432451i	$-0.142351\pi$
$570$	−1.37390	−	0.484185i	−0.0575465	−	0.0202803i
$571$	−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
$579$	10.6618	+	3.75740i	0.443091	+	0.156152i
$580$	−21.1522	+	21.1522i	−0.878296	+	0.878296i
$581$	−0.557503	−	6.73006i	−0.0231291	−	0.279210i
$582$	−1.50860	+	2.20216i	−0.0625333	+	0.0912823i
$583$	−0.338038	−	1.26157i	−0.0140001	−	0.0522491i
$584$	−1.52554	+	2.64232i	−0.0631274	+	0.109340i
$585$	−22.0969	+	11.0351i	−0.913594	+	0.456246i
$586$	0.524400	+	0.908287i	0.0216628	+	0.0375210i
$587$	26.0005	+	6.96680i	1.07315	+	0.287551i	0.751788	−	0.659405i	$-0.229192\pi$
$587$	26.0005	+	6.96680i	1.07315	+	0.287551i	0.321365	+	0.946955i	$0.395858\pi$
$588$	−10.1733	+	21.8740i	−0.419538	+	0.902070i
$589$	−1.84165	−	1.06328i	−0.0758840	−	0.0438117i
$590$	3.28429	+	0.880023i	0.135212	+	0.0362300i
$591$	4.16194	+	22.2676i	0.171199	+	0.915968i
$592$	20.1187	+	5.39078i	0.826872	+	0.221560i
$593$	−6.69834	+	24.9985i	−0.275068	+	1.02657i	0.680728	+	0.732536i	$0.261663\pi$
$593$	−6.69834	+	24.9985i	−0.275068	+	1.02657i	−0.955796	+	0.294031i	$0.905003\pi$
$594$	0.0507343	−	0.0539515i	0.00208165	−	0.00221366i
$595$	26.4894	+	12.5014i	1.08596	+	0.512508i
$596$	−2.88580	+	10.7699i	−0.118207	+	0.441154i
$597$	35.8924	+	24.5882i	1.46898	+	1.00633i
$598$	0.0607370	+	0.0278539i	0.00248372	+	0.00113903i
$599$	12.3777	+	7.14624i	0.505737	+	0.291988i	0.731080	−	0.682292i	$-0.239017\pi$
$599$	12.3777	+	7.14624i	0.505737	+	0.291988i	−0.225342	+	0.974280i	$0.572350\pi$
$600$	0.113925	−	0.0975995i	0.00465095	−	0.00398448i
$601$	−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
$603$	0.743847	−	0.0804594i	0.0302918	−	0.00327656i
$604$	7.10757	+	7.10757i	0.289203	+	0.289203i
$605$	−6.48928	+	24.2183i	−0.263827	+	0.984615i
$606$	−1.44843	+	1.24087i	−0.0588385	+	0.0504071i
$607$	−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
$609$	−29.0993	+	7.97278i	−1.17916	+	0.323073i
$610$		−	1.24008i		−	0.0502095i
$611$	−16.4878	+	35.9527i	−0.667026	+	1.45449i
$612$	26.9871	−	10.4532i	1.09089	−	0.422547i
$613$	−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
$615$	−2.80537	+	36.3491i	−0.113123	+	1.46574i
$616$	−0.114802	−	0.0972373i	−0.00462551	−	0.00391780i
$617$	−2.23580	−	8.34413i	−0.0900101	−	0.335922i	0.906206	−	0.422837i	$-0.138966\pi$
$617$	−2.23580	−	8.34413i	−0.0900101	−	0.335922i	−0.996216	+	0.0869150i	$0.972299\pi$
$618$	1.01850	−	2.89006i	0.0409702	−	0.116255i
$619$	−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
$621$	−0.650510	+	0.691760i	−0.0261041	+	0.0277594i
$622$	0.222438	+	0.0596022i	0.00891896	+	0.00238983i
$623$	12.3408	−	26.1490i	0.494424	−	1.04764i
$624$	23.8596	+	5.97070i	0.955148	+	0.239019i
$625$	−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
$630$	1.80477	−	0.347835i	0.0719036	−	0.0138581i
$631$	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
$633$	13.7341	−	20.0482i	0.545882	−	0.796845i
$634$		−	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
$639$	−24.0221	−	10.6083i	−0.950299	−	0.419657i
$640$	−7.31508			−0.289154
$641$	6.61429	+	11.4563i	0.261249	+	0.452496i	0.966574	−	0.256388i	$-0.0825324\pi$
$641$	6.61429	+	11.4563i	0.261249	+	0.452496i	−0.705325	+	0.708884i	$0.749199\pi$
$642$	−2.76357	+	0.516525i	−0.109069	+	0.0203856i
$643$	−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
$645$	0.628755	−	1.78413i	0.0247572	−	0.0702500i
$646$	1.78578			0.0702606
$647$	8.96491			0.352447			0.176223	−	0.984350i	$-0.443612\pi$
$647$	8.96491			0.352447			0.176223	+	0.984350i	$0.443612\pi$
$648$	1.96471	−	3.06588i	0.0771811	−	0.120439i
$649$	1.78719	−	1.03184i	0.0701534	−	0.0405031i
$650$	0.0326277	−	0.0711467i	0.00127976	−	0.00279060i
$651$	2.68308	−	0.0150877i	0.105158	−	0.000591333i
$652$	−6.42846	+	23.9914i	−0.251758	+	0.939574i
$653$	38.5553	+	22.2599i	1.50878	+	0.871097i	0.999948	+	0.0102334i	$0.00325743\pi$
$653$	38.5553	+	22.2599i	1.50878	+	0.871097i	0.508836	+	0.860863i	$0.330076\pi$
$654$	−0.237838	+	0.347182i	−0.00930022	+	0.0135759i
$655$	−4.12567	+	1.10547i	−0.161203	+	0.0431942i
$656$	25.6708	−	25.6708i	1.00228	−	1.00228i
$657$	−20.6950	−	9.13900i	−0.807387	−	0.356546i
$658$	1.90233	−	2.24596i	0.0741605	−	0.0875568i
$659$	1.89755	+	1.09555i	0.0739179	+	0.0426765i	0.536503	−	0.843898i	$-0.319745\pi$
$659$	1.89755	+	1.09555i	0.0739179	+	0.0426765i	−0.462586	+	0.886575i	$0.653078\pi$
$660$	0.0851060	−	1.10272i	0.00331275	−	0.0429232i
$661$	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
$663$	21.0518	−	21.7623i	0.817585	−	0.845176i
$664$	1.03271			0.0400770
$665$	−21.5912	−	3.90999i	−0.837271	−	0.151623i
$666$	0.246880	−	1.58988i	0.00956642	−	0.0616067i
$667$			1.20320i			0.0465882i
$668$	−1.72596	−	6.44136i	−0.0667793	−	0.249224i
$669$	−8.47244	+	1.58355i	−0.327564	+	0.0612234i
$670$	−0.0408361	+	0.0408361i	−0.00157763	+	0.00157763i
$671$	−0.532204	−	0.532204i	−0.0205455	−	0.0205455i
$672$	−4.81195	−	2.74222i	−0.185625	−	0.105783i
$673$	−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
$675$	0.810321	+	0.762001i	0.0311893	+	0.0293294i
$676$	25.4142	−	4.81485i	0.977470	−	0.185187i
$677$	34.2771	−	19.7899i	1.31738	−	0.760587i	0.334070	−	0.942548i	$-0.391578\pi$
$677$	34.2771	−	19.7899i	1.31738	−	0.760587i	0.983306	+	0.181961i	$0.0582445\pi$
$678$	0.885094	−	0.165429i	0.0339918	−	0.00635326i
$679$	−17.1606	+	36.3617i	−0.658563	+	1.39543i
$680$	−2.23966	+	3.87920i	−0.0858870	+	0.148761i
$681$	−1.01116	−	5.41001i	−0.0387477	−	0.207312i
$682$	−0.00215985	+	0.00806066i	−8.27048e−5	+	0.000308659i
$683$	6.38384	−	23.8248i	0.244271	−	0.911631i	−0.729478	−	0.684005i	$-0.760237\pi$
$683$	6.38384	−	23.8248i	0.244271	−	0.911631i	0.973748	−	0.227627i	$-0.0730966\pi$
$684$	−17.5008	+	12.7962i	−0.669160	+	0.489276i
$685$	−14.0060	+	24.2590i	−0.535140	+	0.926889i
$686$	0.511183	−	1.80724i	0.0195170	−	0.0690008i
$687$	−1.93196	−	10.3366i	−0.0737090	−	0.394365i
$688$	−1.63136	+	0.941865i	−0.0621949	+	0.0359083i
$689$	−25.8036	−	21.3740i	−0.983040	−	0.814285i
$690$	0.00564010	−	0.0730786i	0.000214715	−	0.00278205i
$691$	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
$693$	0.625269	−	0.923829i	0.0237520	−	0.0350934i
$694$	−2.44517	−	2.44517i	−0.0928172	−	0.0928172i
$695$	3.19379	−	3.19379i	0.121147	−	0.121147i
$696$	−0.847698	−	4.53544i	−0.0321319	−	0.171915i
$697$	−11.5672	−	43.1695i	−0.438140	−	1.63516i
$698$			2.93479i			0.111083i
$699$	15.7536	−	22.9961i	0.595855	−	0.869793i
$700$	0.728343	−	0.859910i	0.0275288	−	0.0325015i
$701$	29.3612			1.10896			0.554479	−	0.832198i	$-0.312918\pi$
$701$	29.3612			1.10896			0.554479	+	0.832198i	$0.312918\pi$
$702$	0.260341	−	1.88200i	0.00982594	−	0.0710316i
$703$	−9.60399	+	16.6346i	−0.362222	+	0.627386i
$704$	−0.770615	+	0.770615i	−0.0290437	+	0.0290437i
$705$	43.2581	+	3.33860i	1.62919	+	0.125739i
$706$	0.798269	+	0.460881i	0.0300432	+	0.0173455i
$707$	−18.5681	+	21.9222i	−0.698325	+	0.824470i
$708$	38.4292	−	32.9224i	1.44426	−	1.23730i
$709$	−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
$711$	10.0924	+	1.56716i	0.378493	+	0.0587731i
$712$	3.82936	+	2.21088i	0.143511	+	0.0828564i
$713$	0.0276933	−	0.103353i	0.00103712	−	0.00387060i
$714$	−1.94492	+	1.13753i	−0.0727870	+	0.0425711i
$715$	−0.402652	−	1.08479i	−0.0150583	−	0.0405688i
$716$	−33.0323	+	19.0712i	−1.23448	+	0.712725i
$717$	18.0754	+	6.37005i	0.675037	+	0.237894i
$718$	2.54296			0.0949025
$719$	−18.1615			−0.677310			−0.338655	−	0.940911i	$-0.609972\pi$
$719$	−18.1615			−0.677310			−0.338655	+	0.940911i	$0.609972\pi$
$720$	−2.90133	−	26.8228i	−0.108126	−	0.999626i
$721$	8.22481	−	45.4179i	0.306308	−	1.69145i
$722$	0.568975	−	0.152456i	0.0211751	−	0.00567384i
$723$	0.642479	+	3.43746i	0.0238941	+	0.127840i
$724$	13.4203	+	23.2446i	0.498760	+	0.863877i
$725$	1.40942			0.0523445
$726$	−1.25478	−	1.46466i	−0.0465693	−	0.0543588i
$727$		−	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
$732$	−15.2257	−	10.4304i	−0.562757	−	0.385519i
$733$	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
$735$	26.0060	−	9.49504i	0.959246	−	0.350230i
$736$	−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
$741$	−11.0135	+	19.8285i	−0.404590	+	0.728419i
$742$	1.42069	+	2.04903i	0.0521553	+	0.0752223i
$743$	4.71832	+	1.26427i	0.173098	+	0.0463816i	0.344327	−	0.938850i	$-0.388107\pi$
$743$	4.71832	+	1.26427i	0.173098	+	0.0463816i	−0.171229	+	0.985231i	$0.554774\pi$
$744$	−0.0315735	+	0.409097i	−0.00115754	+	0.0149982i
$745$	11.0815	−	6.39789i	0.405994	−	0.234401i
$746$	0.891147	+	3.32581i	0.0326272	+	0.121766i
$747$	0.823461	+	7.61290i	0.0301289	+	0.278541i
$748$	0.350913	+	1.30963i	0.0128307	+	0.0478847i
$749$	−39.8605	+	14.2999i	−1.45647	+	0.522508i
$750$	1.91385	+	0.147708i	0.0698840	+	0.00539354i
$751$	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
$753$	45.6089	+	3.52003i	1.66208	+	0.128277i
$754$	−1.39331	−	1.96320i	−0.0507415	−	0.0714955i
$755$		−	11.5354i		−	0.419817i
$756$	10.9093	−	25.0845i	0.396768	−	0.912315i
$757$	−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
$759$	−0.0289425	−	0.0337836i	−0.00105054	−	0.00122627i
$760$	0.868471	−	3.24118i	0.0315028	−	0.117570i
$761$	−26.5493	−	26.5493i	−0.962412	−	0.962412i	0.0369072	−	0.999319i	$-0.488249\pi$
$761$	−26.5493	−	26.5493i	−0.962412	−	0.962412i	−0.999319	+	0.0369072i	$0.988249\pi$
$762$	0.247003	−	0.700884i	0.00894796	−	0.0253904i
$763$	−2.70546	+	5.73262i	−0.0979442	+	0.207535i
$764$	10.4084	+	18.0278i	0.376561	+	0.652223i
$765$	−30.3824	−	13.4170i	−1.09848	−	0.485094i
$766$	−1.15286	−	0.665606i	−0.0416546	−	0.0240493i
$767$	22.0690	−	48.1227i	0.796864	−	1.73761i
$768$	−14.8630	+	21.6960i	−0.536321	+	0.782888i
$769$	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
$771$	−36.8072	−	2.84073i	−1.32558	−	0.102306i
$772$	−3.36109	+	12.5438i	−0.120968	+	0.451460i
$773$	−0.917027	−	0.245717i	−0.0329832	−	0.00883782i	0.242290	−	0.970204i	$-0.422102\pi$
$773$	−0.917027	−	0.245717i	−0.0329832	−	0.00883782i	−0.275273	+	0.961366i	$0.588768\pi$
$774$	0.0858865	+	0.117463i	0.00308713	+	0.00422212i
$775$	−0.121067	−	0.0324397i	−0.00434884	−	0.00116527i
$776$	−5.32495	−	3.07436i	−0.191154	−	0.110363i
$777$	−0.136279	−	24.2347i	−0.00488896	−	0.869416i
$778$	1.28172	+	0.343437i	0.0459520	+	0.0123128i
$779$	16.7398	+	28.9942i	0.599766	+	1.03882i
$780$	−14.5924	−	24.3333i	−0.522493	−	0.871273i
$781$	0.615120	−	1.06542i	0.0220107	−	0.0381237i
$782$	0.0232555	+	0.0867908i	0.000831616	+	0.00310363i
$783$	32.7582	−	9.86548i	1.17068	−	0.352564i
$784$	−25.8180	−	9.66792i	−0.922072	−	0.345283i
$785$	−4.02759	+	4.02759i	−0.143751	+	0.143751i
$786$	0.109204	−	0.309873i	0.00389518	−	0.0110528i
$787$	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
$795$	−12.2163	+	34.6644i	−0.433266	+	1.22942i
$796$	−24.9895	+	43.2831i	−0.885731	+	1.53413i
$797$	−22.7805	+	39.4570i	−0.806927	+	1.39764i	0.108055	+	0.994145i	$0.465538\pi$
$797$	−22.7805	+	39.4570i	−0.806927	+	1.39764i	−0.914982	+	0.403494i	$0.867796\pi$
$798$	1.18677	−	1.20020i	0.0420113	−	0.0424865i
$799$	−51.3749	+	13.7659i	−1.81751	+	0.487001i
$800$	0.182942	+	0.182942i	0.00646799	+	0.00646799i
$801$	−13.2447	+	29.9921i	−0.467977	+	1.05972i
$802$	−0.764636	−	1.32439i	−0.0270002	−	0.0467658i
$803$	0.529924	−	0.917855i	0.0187006	−	0.0323904i
$804$	0.157909	+	0.844858i	0.00556901	+	0.0297958i
$805$	−0.0911442	−	1.10027i	−0.00321241	−	0.0387795i
$806$	0.0744974	+	0.200704i	0.00262406	+	0.00706951i
$807$	−26.0530	−	17.8477i	−0.917111	−	0.628270i
$808$	−3.10657	−	3.10657i	−0.109289	−	0.109289i
$809$			42.7852i			1.50425i	0.659021	+	0.752124i	$0.270971\pi$
$809$			42.7852i			1.50425i	−0.659021	+	0.752124i	$0.729029\pi$
$810$	−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
$813$	32.2597	−	27.6369i	1.13140	−	0.969270i
$814$	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
$819$	−0.635708	−	28.6111i	−0.0222134	−	0.999753i
$820$	−41.8806			−1.46254
$821$	−6.81177	−	25.4219i	−0.237732	−	0.887229i	−0.976898	−	0.213706i	$-0.931447\pi$
$821$	−6.81177	−	25.4219i	−0.237732	−	0.887229i	0.739166	−	0.673524i	$-0.235220\pi$
$822$	−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
$825$	−0.0395737	+	0.0339029i	−0.00137778	+	0.00118035i
$826$	−2.54627	+	3.00623i	−0.0885961	+	0.104600i
$827$	11.2719	+	11.2719i	0.391964	+	0.391964i	0.875387	−	0.483423i	$-0.160607\pi$
$827$	11.2719	+	11.2719i	0.391964	+	0.391964i	−0.483423	+	0.875387i	$0.660607\pi$
$828$	−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
$831$	−39.7504	−	27.2312i	−1.37893	−	0.944639i
$832$	−4.67993	+	27.5638i	−0.162248	+	0.955604i
$833$	−26.1990	+	21.5745i	−0.907742	+	0.747511i
$834$	0.0638324	+	0.341523i	0.00221034	+	0.0118260i
$835$	−3.82649	+	6.62768i	−0.132421	+	0.229360i
$836$	−0.507833	−	0.879593i	−0.0175638	−	0.0304213i
$837$	−3.04094	+	0.0934526i	−0.105110	+	0.00323020i
$838$	0.737308	+	0.737308i	0.0254699	+	0.0254699i
$839$	−13.7295	+	3.67881i	−0.473996	+	0.127007i	−0.487905	−	0.872897i	$-0.662239\pi$
$839$	−13.7295	+	3.67881i	−0.473996	+	0.127007i	0.0139098	+	0.999903i	$0.495572\pi$
$840$	1.11875	+	4.08323i	0.0386004	+	0.140885i
$841$	7.17461	−	12.4268i	0.247400	−	0.428510i
$842$	−0.572064	+	0.990844i	−0.0197146	+	0.0341467i
$843$	3.28806	−	9.33005i	0.113247	−	0.321344i
$844$	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
$852$	10.0268	−	28.4516i	0.343512	−	0.974736i
$853$	−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
$855$	24.5857	+	3.81771i	0.840812	+	0.130563i
$856$	−1.67611	−	6.25534i	−0.0572884	−	0.213803i
$857$	−23.1221	+	40.0487i	−0.789837	+	1.36804i	0.136230	+	0.990677i	$0.456501\pi$
$857$	−23.1221	+	40.0487i	−0.789837	+	1.36804i	−0.926067	+	0.377360i	$0.876832\pi$
$858$	0.0863453	+	0.0216073i	0.00294778	+	0.000737661i
$859$	−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
$861$	−36.7008	−	20.9149i	−1.25076	−	0.712778i
$862$	2.19635	+	1.26806i	0.0748079	+	0.0431904i
$863$	−56.2453	−	15.0709i	−1.91461	−	0.513018i	−0.991806	−	0.127750i	$-0.959225\pi$
$863$	−56.2453	−	15.0709i	−1.91461	−	0.513018i	−0.922804	−	0.385269i	$-0.874109\pi$
$864$	5.53255	+	2.97147i	0.188221	+	0.101092i
$865$	25.7462	+	6.89867i	0.875397	+	0.234562i
$866$	0.629307	−	2.34861i	0.0213847	−	0.0798089i
$867$	11.2371	+	0.867266i	0.381633	+	0.0294539i
$868$	0.254457	+	3.07175i	0.00863683	+	0.104262i
$869$	−0.123838	+	0.462170i	−0.00420092	+	0.0156781i
$870$	−1.49242	+	2.17855i	−0.0505979	+	0.0738596i
$871$	0.520432	+	0.733297i	0.0176342	+	0.0248468i
$872$	−0.839507	−	0.484689i	−0.0284293	−	0.0164137i
$873$	18.4174	−	41.7056i	0.623336	−	1.41152i
$874$	−0.0336548	−	0.0582918i	−0.00113839	−	0.00197175i
$875$	28.8150	−	2.38697i	0.974126	−	0.0806944i
$876$	8.63805	−	24.5110i	0.291853	−	0.828149i
$877$	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
$879$	−11.6542	−	13.6036i	−0.393088	−	0.458838i
$880$	1.26393			0.0426069
$881$	−14.1689	−	24.5413i	−0.477364	−	0.826818i	0.522300	−	0.852762i	$-0.325074\pi$
$881$	−14.1689	−	24.5413i	−0.477364	−	0.826818i	−0.999663	+	0.0259440i	$0.991741\pi$
$882$	−0.528017	+	2.06312i	−0.0177793	+	0.0694689i
$883$			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
$885$	−57.9010	−	4.46872i	−1.94632	−	0.150214i
$886$	−1.27267	−	1.27267i	−0.0427563	−	0.0427563i
$887$	2.79106	+	1.61142i	0.0937146	+	0.0541062i	0.546125	−	0.837704i	$-0.316102\pi$
$887$	2.79106	+	1.61142i	0.0937146	+	0.0541062i	−0.452410	+	0.891810i	$0.649436\pi$
$888$	3.69514	+	0.285186i	0.124001	+	0.00957020i
$889$	1.99464	−	11.0145i	0.0668982	−	0.369416i
$890$	−0.654996	−	2.44448i	−0.0219555	−	0.0819391i
$891$	−0.682477	+	1.06499i	−0.0228638	+	0.0356784i
$892$	−2.56266	−	9.56399i	−0.0858043	−	0.320226i
$893$	34.5053	−	19.9216i	1.15467	−	0.666651i
$894$	−0.0757406	+	0.981368i	−0.00253314	+	0.0328219i
$895$	42.2814	+	11.3293i	1.41331	+	0.378696i
$896$	3.61745	−	7.66504i	0.120851	−	0.256071i
$897$	−1.10711	−	0.277047i	−0.0369654	−	0.00925032i
$898$	−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
$903$	1.55855	+	1.54112i	0.0518654	+	0.0512854i
$904$	0.536813	+	2.00341i	0.0178541	+	0.0666325i
$905$	7.97231	−	29.7531i	0.265009	−	0.989025i
$906$	0.732036	+	0.501485i	0.0243203	+	0.0166607i
$907$			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	$0.0637389\pi$
$911$			12.0071i			0.397812i	−0.980019	+	0.198906i	$0.936261\pi$
$912$	−16.1191	−	18.8153i	−0.533756	−	0.623035i
$913$	−0.358730			−0.0118722
$914$	0.388927	+	0.673641i	0.0128645	+	0.0222821i
$915$	3.89130	+	20.8196i	0.128642	+	0.688275i
$916$	11.6683	−	3.12651i	0.385531	−	0.103303i
$917$	0.881867	−	4.86972i	0.0291218	−	0.160812i
$918$	2.17227	−	1.34478i	0.0716957	−	0.0443843i
$919$	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
$921$	17.0574	+	6.01130i	0.562060	+	0.198079i
$922$	−1.03151	+	0.595544i	−0.0339711	+	0.0196132i
$923$	−2.95034	−	31.4226i	−0.0971117	−	1.03429i
$924$	1.11339	+	0.634493i	0.0366277	+	0.0208733i
$925$	−0.293009	+	1.09352i	−0.00963408	+	0.0359549i
$926$	−0.383029	−	0.221142i	−0.0125871	−	0.00726716i
$927$	−8.03070	+	51.7169i	−0.263763	+	1.69861i
$928$	7.68624	−	2.05952i	0.252313	−	0.0676071i
$929$	−29.8793	+	29.8793i	−0.980309	+	0.980309i	−0.999810	−	0.0195013i	$-0.993792\pi$
$929$	−29.8793	+	29.8793i	−0.980309	+	0.980309i	0.0195013	+	0.999810i	$0.493792\pi$
$930$	0.178339	−	0.152783i	0.00584795	−	0.00500996i
$931$	14.7743	−	20.6906i	0.484209	−	0.678107i
$932$	27.7313	+	16.0107i	0.908370	+	0.524448i
$933$	−3.92152	−	0.302657i	−0.128385	−	0.00990855i
$934$	−1.85618	+	1.85618i	−0.0607361	+	0.0607361i
$935$	0.777984	−	1.34751i	0.0254428	−	0.0440682i
$936$	4.36841	+	0.264322i	0.142786	+	0.00863963i
$937$	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
$939$	−13.4196	+	19.5891i	−0.437932	+	0.639266i
$940$			49.8411i			1.62564i
$941$	1.34528	+	5.02066i	0.0438549	+	0.163669i	0.984380	−	0.176054i	$-0.0563334\pi$
$941$	1.34528	+	5.02066i	0.0438549	+	0.163669i	−0.940526	+	0.339723i	$0.889667\pi$
$942$	−0.0804971	−	0.430683i	−0.00262274	−	0.0140324i
$943$	−1.19115	+	1.19115i	−0.0387893	+	0.0387893i
$944$	40.8914	+	40.8914i	1.33090	+	1.33090i
$945$	−29.2086	+	11.5030i	−0.950154	+	0.374193i
$946$	−0.00590371	+	0.00340851i	−0.000191946	+	0.000110820i
$947$	−47.8503	+	12.8215i	−1.55493	+	0.416641i	−0.931053	−	0.364884i	$-0.881109\pi$
$947$	−47.8503	+	12.8215i	−1.55493	+	0.416641i	−0.623873	+	0.781525i	$0.714442\pi$
$948$	−0.902825	+	11.6979i	−0.0293224	+	0.379929i
$949$	−2.54171	−	27.0705i	−0.0825074	−	0.878744i
$950$	−0.0682824	+	0.0394229i	−0.00221537	+	0.00127905i
$951$	6.22875	+	33.3256i	0.201981	+	1.08066i
$952$	−2.95723	−	4.26515i	−0.0958445	−	0.138234i
$953$	10.3964	−	18.0070i	0.336772	−	0.583305i	−0.647052	−	0.762446i	$-0.723998\pi$
$953$	10.3964	−	18.0070i	0.336772	−	0.583305i	0.983824	+	0.179140i	$0.0573317\pi$
$954$	−1.66871	−	2.28222i	−0.0540266	−	0.0738897i
$955$	6.18309	−	23.0756i	0.200080	−	0.746709i
$956$	−5.69817	+	21.2658i	−0.184292	+	0.687787i
$957$	0.294463	+	1.57546i	0.00951863	+	0.0509275i
$958$	0.688991	−	1.19337i	0.0222603	−	0.0385559i
$959$	−18.4934	−	26.6726i	−0.597183	−	0.861303i
$960$	30.1461	−	5.63448i	0.972963	−	0.181852i
$961$	−26.5499	+	15.3286i	−0.856448	+	0.494471i
$962$	1.81285	−	0.672893i	0.0584486	−	0.0216949i
$963$	44.7764	−	17.3438i	1.44290	−	0.558895i
$964$	−3.88032	+	1.03973i	−0.124977	+	0.0334874i
$965$	12.9066	−	7.45163i	0.415478	−	0.239876i
$966$	0.0737856	+	0.0420487i	0.00237401	+	0.00135290i
$967$	−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
$969$	−29.9813	+	5.60366i	−0.963137	+	0.180016i
$970$	0.910809	+	3.39918i	0.0292443	+	0.109141i
$971$		−	33.9510i		−	1.08954i	−0.838586	−	0.544770i	$-0.816617\pi$
$971$		−	33.9510i		−	1.08954i	0.838586	−	0.544770i	$-0.183383\pi$
$972$	−11.6523	+	28.7446i	−0.373747	+	0.921984i
$973$	1.76719	+	4.92597i	0.0566536	+	0.157919i
$974$	−1.02494			−0.0328413
$975$	−0.324530	+	1.29686i	−0.0103933	+	0.0415327i
$976$	10.5456	−	18.2655i	0.337555	−	0.584663i
$977$	−14.0341	+	14.0341i	−0.448991	+	0.448991i	−0.895019	−	0.446028i	$-0.852838\pi$
$977$	−14.0341	+	14.0341i	−0.448991	+	0.448991i	0.446028	+	0.895019i	$0.352838\pi$
$978$	−0.168721	+	2.18612i	−0.00539511	+	0.0699043i
$979$	−1.33020	−	0.767989i	−0.0425133	−	0.0245450i
$980$	13.1741	+	28.9468i	0.420830	+	0.924672i
$981$	2.90361	−	6.57512i	0.0927051	−	0.209927i
$982$	−0.650878	+	0.650878i	−0.0207704	+	0.0207704i
$983$	21.2065	−	5.68227i	0.676383	−	0.181236i	0.0957545	−	0.995405i	$-0.469474\pi$
$983$	21.2065	−	5.68227i	0.676383	−	0.181236i	0.580628	+	0.814169i	$0.302807\pi$
$984$	3.65081	−	5.32922i	0.116383	−	0.169889i
$985$	25.8636	+	14.9323i	0.824082	+	0.475784i
$986$	0.837854	−	3.12691i	0.0266827	−	0.0995812i
$987$	−24.8903	+	43.6766i	−0.792267	+	1.39024i
$988$	−23.6843	−	10.8616i	−0.753498	−	0.345553i
$989$	0.0756968	−	0.0437036i	0.00240702	−	0.00138969i
$990$	−0.0104996	−	0.0970688i	−0.000333699	−	0.00308505i
$991$	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
$993$	−15.8527	+	44.9831i	−0.503071	+	1.42749i
$994$	−0.418504	+	2.31100i	−0.0132741	+	0.0733006i
$995$	55.4025	−	14.8450i	1.75638	−	0.470620i
$996$	−8.64670	+	1.61611i	−0.273981	+	0.0512085i
$997$	−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
$999$	0.844104	+	27.4671i	0.0267063	+	0.869020i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(0.0262469 + 0.0979549i) q^{2} +(-0.748033 - 1.56219i) q^{3} +(1.72314 - 0.994858i) q^{4} +(-2.20563 - 0.590996i) q^{5} +(0.133391 - 0.114276i) q^{6} +(1.71000 - 2.01889i) q^{7} +(0.286094 + 0.286094i) q^{8} +(-1.88089 + 2.33714i) q^{9} +O(q^{10})\)	\(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} +(0.133391 - 0.114276i) 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} +(-2.84313 - 1.94770i) q^{12} +(-3.55468 - 0.603532i) q^{13} +(0.242642 + 0.114513i) q^{14} +(0.726632 + 3.88770i) q^{15} +(1.96920 - 3.41076i) q^{16} +(-2.42420 - 4.19884i) q^{17} +(-0.278302 - 0.122900i) q^{18} +(2.56822 + 2.56822i) q^{19} +(-4.38857 + 1.17591i) q^{20} +(-4.43303 - 1.16115i) q^{21} +(0.00712633 - 0.0123432i) q^{22} +(-0.0913731 + 0.158263i) q^{23} +(0.232927 - 0.660943i) 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} +(-0.0809111 + 0.229590i) q^{33} +(0.347669 - 0.347669i) q^{34} +(-4.96477 + 3.44231i) q^{35} +(-0.915925 + 5.89846i) q^{36} +(1.36877 + 5.10833i) q^{37} +(-0.184161 + 0.318977i) q^{38} +(1.71618 + 6.00456i) q^{39} +(-0.461937 - 0.800098i) q^{40} +(8.90385 + 2.38578i) q^{41} +(-0.00261321 - 0.464713i) q^{42} +(-0.414218 - 0.239149i) q^{43} +(-0.270115 - 0.0723770i) q^{44} +(5.52979 - 4.04327i) q^{45} +(-0.0179009 - 0.00479653i) q^{46} +(2.83925 - 10.5962i) q^{47} +(-6.80129 - 0.524913i) q^{48} +(-1.15182 - 6.90459i) q^{49} +(-0.00561860 + 0.0209689i) q^{50} +(-4.74602 + 6.92795i) q^{51} +(-6.72566 + 2.49643i) q^{52} +(8.04797 + 4.64650i) q^{53} +(0.0161861 + 0.526695i) q^{54} +(0.160462 + 0.277928i) q^{55} +(1.06681 - 0.0883724i) q^{56} +(2.09094 - 5.93316i) q^{57} +(0.472126 + 0.472126i) q^{58} +(-3.80035 + 14.1831i) q^{59} +(5.11980 + 5.97617i) q^{60} +5.35525 q^{61} +(-0.0296882 - 0.0514214i) q^{62} +(1.50211 + 7.79382i) q^{63} -7.75424i q^{64} +(7.48361 + 3.43197i) q^{65} +(-0.0246131 - 0.00189961i) q^{66} +(-0.176349 - 0.176349i) q^{67} +(-8.35451 - 4.82348i) q^{68} +(0.315587 + 0.0243566i) q^{69} +(-0.467502 - 0.395973i) q^{70} +(2.26554 + 8.45513i) q^{71} +(-1.20676 + 0.130531i) q^{72} +(1.95176 + 7.28406i) q^{73} +(-0.464460 + 0.268156i) q^{74} +(0.0285310 - 0.369675i) q^{75} +(6.98042 + 1.87040i) q^{76} +(-0.370576 + 0.0306977i) q^{77} +(-0.543131 + 0.325710i) 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} +(-8.79393 + 2.40941i) q^{84} +(2.86539 + 10.6938i) q^{85} +(0.0125539 - 0.0468516i) q^{86} +(-9.40797 - 6.44497i) 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} +(0.659788 + 0.770149i) q^{93} +1.11248 q^{94} +(-4.14672 - 7.18233i) q^{95} +(-0.384597 - 2.05771i) q^{96} +(-14.6793 + 3.93330i) q^{97} +(0.646106 - 0.294051i) q^{98} +(0.419188 - 0.0453421i) 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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