LMFDB - Embedded newform 300.2.w.a.163.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(67,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 0, 13]))

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

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

chi := DirichletCharacter("300.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.w (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			163.24
Character	$\chi$	$=$	300.163
Dual form			300.2.w.a.127.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.17502 - 0.786967i) q^{2} +(0.891007 + 0.453990i) q^{3} +(0.761365 - 1.84941i) q^{4} +(-0.0577937 + 2.23532i) q^{5} +(1.40423 - 0.167743i) q^{6} +(0.0211854 + 0.0211854i) q^{7} +(-0.560803 - 2.77227i) q^{8} +(0.587785 + 0.809017i) q^{9} +O(q^{10})$	\(q+(1.17502 - 0.786967i) q^{2} +(0.891007 + 0.453990i) q^{3} +(0.761365 - 1.84941i) q^{4} +(-0.0577937 + 2.23532i) q^{5} +(1.40423 - 0.167743i) q^{6} +(0.0211854 + 0.0211854i) q^{7} +(-0.560803 - 2.77227i) q^{8} +(0.587785 + 0.809017i) q^{9} +(1.69122 + 2.67204i) q^{10} +(1.52583 - 2.10012i) q^{11} +(1.51800 - 1.30219i) q^{12} +(3.59397 + 0.569229i) q^{13} +(0.0415656 + 0.00822116i) q^{14} +(-1.06631 + 1.96545i) q^{15} +(-2.84065 - 2.81616i) q^{16} +(-1.43409 - 2.81456i) q^{17} +(1.32733 + 0.488047i) q^{18} +(-1.41553 + 4.35657i) q^{19} +(4.09003 + 1.80878i) q^{20} +(0.00925837 + 0.0284943i) q^{21} +(0.140158 - 3.66847i) q^{22} +(-5.82595 + 0.922739i) q^{23} +(0.758907 - 2.72471i) q^{24} +(-4.99332 - 0.258375i) q^{25} +(4.67097 - 2.15948i) q^{26} +(0.156434 + 0.987688i) q^{27} +(0.0553104 - 0.0230507i) q^{28} +(-7.62028 + 2.47598i) q^{29} +(0.293804 + 3.14860i) q^{30} +(1.76558 + 0.573671i) q^{31} +(-5.55405 - 1.07356i) q^{32} +(2.31296 - 1.17851i) q^{33} +(-3.90006 - 2.17860i) q^{34} +(-0.0485806 + 0.0461318i) q^{35} +(1.94372 - 0.471099i) q^{36} +(1.30788 - 8.25760i) q^{37} +(1.76519 + 6.23305i) q^{38} +(2.94383 + 2.13882i) q^{39} +(6.22933 - 1.09336i) q^{40} +(-0.210898 + 0.153226i) q^{41} +(0.0333029 + 0.0261955i) q^{42} +(1.26128 - 1.26128i) q^{43} +(-2.72228 - 4.42084i) q^{44} +(-1.84238 + 1.26713i) q^{45} +(-6.11947 + 5.66907i) q^{46} +(-5.36731 + 10.5339i) q^{47} +(-1.25253 - 3.79884i) q^{48} -6.99910i q^{49} +(-6.07061 + 3.62598i) q^{50} -3.15886i q^{51} +(3.78906 - 6.21334i) q^{52} +(-1.61963 + 3.17871i) q^{53} +(0.961093 + 1.03745i) q^{54} +(4.60626 + 3.53209i) q^{55} +(0.0468509 - 0.0706126i) q^{56} +(-3.23909 + 3.23909i) q^{57} +(-7.00551 + 8.90625i) q^{58} +(0.594783 - 0.432135i) q^{59} +(2.82307 + 3.46847i) q^{60} +(3.96742 + 2.88250i) q^{61} +(2.52606 - 0.715375i) q^{62} +(-0.00468689 + 0.0295918i) q^{63} +(-7.37100 + 3.10940i) q^{64} +(-1.48012 + 8.00078i) q^{65} +(1.79033 - 3.20500i) q^{66} +(2.97451 - 1.51559i) q^{67} +(-6.29715 + 0.509314i) q^{68} +(-5.60987 - 1.82276i) q^{69} +(-0.0207792 + 0.0924374i) q^{70} +(10.8065 - 3.51125i) q^{71} +(1.91318 - 2.08320i) q^{72} +(-1.68398 - 10.6322i) q^{73} +(-4.96167 - 10.7321i) q^{74} +(-4.33178 - 2.49713i) q^{75} +(6.97935 + 5.93485i) q^{76} +(0.0768172 - 0.0121667i) q^{77} +(5.14225 + 0.196465i) q^{78} +(4.55633 + 14.0229i) q^{79} +(6.45918 - 6.18700i) q^{80} +(-0.309017 + 0.951057i) q^{81} +(-0.127226 + 0.346014i) q^{82} +(-5.86554 - 11.5118i) q^{83} +(0.0597467 + 0.00457206i) q^{84} +(6.37433 - 3.04299i) q^{85} +(0.489447 - 2.47461i) q^{86} +(-7.91379 - 1.25342i) q^{87} +(-6.67780 - 3.05226i) q^{88} +(-5.58568 + 7.68803i) q^{89} +(-1.16765 + 2.93881i) q^{90} +(0.0640804 + 0.0881991i) q^{91} +(-2.72915 + 11.4771i) q^{92} +(1.31270 + 1.31270i) q^{93} +(1.98314 + 16.6015i) q^{94} +(-9.65652 - 3.41596i) q^{95} +(-4.46131 - 3.47803i) q^{96} +(5.72355 + 2.91630i) q^{97} +(-5.50806 - 8.22412i) q^{98} +2.59589 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 12 q^{8}+O(q^{10}) $ 240 * q + 12 * q^8	$ 240 q + 12 q^{8} + 8 q^{10} + 8 q^{12} + 4 q^{13} + 20 q^{17} - 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} - 8 q^{30} - 20 q^{32} - 8 q^{33} - 4 q^{37} - 76 q^{38} - 92 q^{40} - 20 q^{42} - 140 q^{44} - 4 q^{45} - 16 q^{48} - 164 q^{50} - 172 q^{52} - 4 q^{53} - 120 q^{58} + 20 q^{60} - 44 q^{62} - 60 q^{64} - 20 q^{65} + 16 q^{68} - 44 q^{70} + 12 q^{72} - 44 q^{73} - 48 q^{77} + 24 q^{78} - 4 q^{80} + 60 q^{81} + 24 q^{82} + 80 q^{84} - 64 q^{85} + 60 q^{88} - 260 q^{89} + 48 q^{90} + 144 q^{92} - 64 q^{93} + 40 q^{94} - 20 q^{96} - 180 q^{97} + 256 q^{98}+O(q^{100}) $ 240 * q + 12 * q^8 + 8 * q^10 + 8 * q^12 + 4 * q^13 + 20 * q^17 - 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 - 8 * q^30 - 20 * q^32 - 8 * q^33 - 4 * q^37 - 76 * q^38 - 92 * q^40 - 20 * q^42 - 140 * q^44 - 4 * q^45 - 16 * q^48 - 164 * q^50 - 172 * q^52 - 4 * q^53 - 120 * q^58 + 20 * q^60 - 44 * q^62 - 60 * q^64 - 20 * q^65 + 16 * q^68 - 44 * q^70 + 12 * q^72 - 44 * q^73 - 48 * q^77 + 24 * q^78 - 4 * q^80 + 60 * q^81 + 24 * q^82 + 80 * q^84 - 64 * q^85 + 60 * q^88 - 260 * q^89 + 48 * q^90 + 144 * q^92 - 64 * q^93 + 40 * q^94 - 20 * q^96 - 180 * q^97 + 256 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$-1$	$e\left(\frac{19}{20}\right)$

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 $

$2$	1.17502	−	0.786967i	0.830868	−	0.556470i
$2$	1.17502	−	0.786967i	0.830868	−	0.556470i
$3$	0.891007	+	0.453990i	0.514423	+	0.262112i
$3$	0.891007	+	0.453990i	0.514423	+	0.262112i
$4$	0.761365	−	1.84941i	0.380683	−	0.924706i
$5$	−0.0577937	+	2.23532i	−0.0258461	+	0.999666i
$5$	−0.0577937	+	2.23532i	−0.0258461	+	0.999666i
$6$	1.40423	−	0.167743i	0.573275	−	0.0684808i
$7$	0.0211854	+	0.0211854i	0.00800734	+	0.00800734i	0.711099	−	0.703092i	$-0.248198\pi$
$7$	0.0211854	+	0.0211854i	0.00800734	+	0.00800734i	−0.703092	+	0.711099i	$0.748198\pi$
$8$	−0.560803	−	2.77227i	−0.198274	−	0.980147i
$9$	0.587785	+	0.809017i	0.195928	+	0.269672i
$10$	1.69122	+	2.67204i	0.534809	+	0.844973i
$11$	1.52583	−	2.10012i	0.460054	−	0.633210i	−0.514466	−	0.857511i	$-0.672010\pi$
$11$	1.52583	−	2.10012i	0.460054	−	0.633210i	0.974520	+	0.224301i	$0.0720097\pi$
$12$	1.51800	−	1.30219i	0.438208	−	0.375908i
$13$	3.59397	+	0.569229i	0.996788	+	0.157876i	0.633452	−	0.773782i	$-0.281638\pi$
$13$	3.59397	+	0.569229i	0.996788	+	0.157876i	0.363336	+	0.931658i	$0.381638\pi$
$14$	0.0415656	+	0.00822116i	0.0111089	+	0.00219720i
$15$	−1.06631	+	1.96545i	−0.275320	+	0.507476i
$16$	−2.84065	−	2.81616i	−0.710161	−	0.704039i
$17$	−1.43409	−	2.81456i	−0.347818	−	0.682632i	0.649132	−	0.760676i	$-0.275132\pi$
$17$	−1.43409	−	2.81456i	−0.347818	−	0.682632i	−0.996950	+	0.0780444i	$0.975132\pi$
$18$	1.32733	+	0.488047i	0.312855	+	0.115034i
$19$	−1.41553	+	4.35657i	−0.324746	+	0.999465i	0.646809	+	0.762652i	$0.276103\pi$
$19$	−1.41553	+	4.35657i	−0.324746	+	0.999465i	−0.971555	+	0.236813i	$0.923897\pi$
$20$	4.09003	+	1.80878i	0.914558	+	0.404456i
$21$	0.00925837	+	0.0284943i	0.00202034	+	0.00621797i
$22$	0.140158	−	3.66847i	0.0298818	−	0.782120i
$23$	−5.82595	+	0.922739i	−1.21479	+	0.192404i	−0.730754	−	0.682641i	$-0.760831\pi$
$23$	−5.82595	+	0.922739i	−1.21479	+	0.192404i	−0.484040	+	0.875046i	$0.660831\pi$
$24$	0.758907	−	2.72471i	0.154911	−	0.556180i
$25$	−4.99332	−	0.258375i	−0.998664	−	0.0516749i
$26$	4.67097	−	2.15948i	0.916052	−	0.423509i
$27$	0.156434	+	0.987688i	0.0301058	+	0.190081i
$28$	0.0553104	−	0.0230507i	0.0104527	−	0.00435618i
$29$	−7.62028	+	2.47598i	−1.41505	+	0.459778i	−0.914026	−	0.405655i	$-0.867043\pi$
$29$	−7.62028	+	2.47598i	−1.41505	+	0.459778i	−0.501025	+	0.865433i	$0.667043\pi$
$30$	0.293804	+	3.14860i	0.0536410	+	0.574853i
$31$	1.76558	+	0.573671i	0.317107	+	0.103034i	0.463246	−	0.886230i	$-0.346685\pi$
$31$	1.76558	+	0.573671i	0.317107	+	0.103034i	−0.146139	+	0.989264i	$0.546685\pi$
$32$	−5.55405	−	1.07356i	−0.981827	−	0.189780i
$33$	2.31296	−	1.17851i	0.402634	−	0.205152i
$34$	−3.90006	−	2.17860i	−0.668855	−	0.373626i
$35$	−0.0485806	+	0.0461318i	−0.00821162	+	0.00779770i
$36$	1.94372	−	0.471099i	0.323954	−	0.0785165i
$37$	1.30788	−	8.25760i	0.215013	−	1.35754i	−0.609988	−	0.792410i	$-0.708826\pi$
$37$	1.30788	−	8.25760i	0.215013	−	1.35754i	0.825002	−	0.565130i	$-0.191174\pi$
$38$	1.76519	+	6.23305i	0.286351	+	1.01113i
$39$	2.94383	+	2.13882i	0.471390	+	0.342485i
$40$	6.22933	−	1.09336i	0.984944	−	0.172875i
$41$	−0.210898	+	0.153226i	−0.0329367	+	0.0239299i	−0.604132	−	0.796884i	$-0.706480\pi$
$41$	−0.210898	+	0.153226i	−0.0329367	+	0.0239299i	0.571195	+	0.820814i	$0.306480\pi$
$42$	0.0333029	+	0.0261955i	0.00513875	+	0.00404205i
$43$	1.26128	−	1.26128i	0.192343	−	0.192343i	−0.604365	−	0.796708i	$-0.706573\pi$
$43$	1.26128	−	1.26128i	0.192343	−	0.192343i	0.796708	+	0.604365i	$0.206573\pi$
$44$	−2.72228	−	4.42084i	−0.410399	−	0.666467i
$45$	−1.84238	+	1.26713i	−0.274646	+	0.188893i
$46$	−6.11947	+	5.66907i	−0.902266	+	0.835859i
$47$	−5.36731	+	10.5339i	−0.782903	+	1.53653i	0.0598348	+	0.998208i	$0.480943\pi$
$47$	−5.36731	+	10.5339i	−0.782903	+	1.53653i	−0.842737	+	0.538325i	$0.819057\pi$
$48$	−1.25253	−	3.79884i	−0.180787	−	0.548315i
$49$		−	6.99910i		−	0.999872i
$50$	−6.07061	+	3.62598i	−0.858513	+	0.512791i
$51$		−	3.15886i		−	0.442329i
$52$	3.78906	−	6.21334i	0.525449	−	0.861635i
$53$	−1.61963	+	3.17871i	−0.222474	+	0.436629i	−0.975084	−	0.221837i	$-0.928795\pi$
$53$	−1.61963	+	3.17871i	−0.222474	+	0.436629i	0.752610	+	0.658466i	$0.228795\pi$
$54$	0.961093	+	1.03745i	0.130788	+	0.141179i
$55$	4.60626	+	3.53209i	0.621108	+	0.476267i
$56$	0.0468509	−	0.0706126i	0.00626072	−	0.00943601i
$57$	−3.23909	+	3.23909i	−0.429028	+	0.429028i
$58$	−7.00551	+	8.90625i	−0.919868	+	1.16945i
$59$	0.594783	−	0.432135i	0.0774341	−	0.0562592i	−0.548395	−	0.836220i	$-0.684761\pi$
$59$	0.594783	−	0.432135i	0.0774341	−	0.0562592i	0.625829	+	0.779960i	$0.284761\pi$
$60$	2.82307	+	3.46847i	0.364457	+	0.447777i
$61$	3.96742	+	2.88250i	0.507976	+	0.369066i	0.812055	−	0.583581i	$-0.198349\pi$
$61$	3.96742	+	2.88250i	0.507976	+	0.369066i	−0.304079	+	0.952647i	$0.598349\pi$
$62$	2.52606	−	0.715375i	0.320810	−	0.0908527i
$63$	−0.00468689	+	0.0295918i	−0.000590492	+	0.00372822i
$64$	−7.37100	+	3.10940i	−0.921375	+	0.388675i
$65$	−1.48012	+	8.00078i	−0.183586	+	0.992375i
$66$	1.79033	−	3.20500i	0.220375	−	0.394508i
$67$	2.97451	−	1.51559i	0.363394	−	0.185158i	−0.262754	−	0.964863i	$-0.584631\pi$
$67$	2.97451	−	1.51559i	0.363394	−	0.185158i	0.626148	+	0.779705i	$0.284631\pi$
$68$	−6.29715	+	0.509314i	−0.763642	+	0.0617634i
$69$	−5.60987	−	1.82276i	−0.675349	−	0.219434i
$70$	−0.0207792	+	0.0924374i	−0.00248358	+	0.0110484i
$71$	10.8065	−	3.51125i	1.28250	−	0.416709i	0.413038	−	0.910714i	$-0.364468\pi$
$71$	10.8065	−	3.51125i	1.28250	−	0.416709i	0.869459	+	0.494005i	$0.164468\pi$
$72$	1.91318	−	2.08320i	0.225471	−	0.245508i
$73$	−1.68398	−	10.6322i	−0.197094	−	1.24441i	−0.865614	−	0.500711i	$-0.833072\pi$
$73$	−1.68398	−	10.6322i	−0.197094	−	1.24441i	0.668520	−	0.743694i	$-0.266928\pi$
$74$	−4.96167	−	10.7321i	−0.576783	−	1.24759i
$75$	−4.33178	−	2.49713i	−0.500191	−	0.288344i
$76$	6.97935	+	5.93485i	0.800586	+	0.680774i
$77$	0.0768172	−	0.0121667i	0.00875414	−	0.00138652i
$78$	5.14225	+	0.196465i	0.582245	+	0.0222453i
$79$	4.55633	+	14.0229i	0.512627	+	1.57770i	0.787558	+	0.616240i	$0.211345\pi$
$79$	4.55633	+	14.0229i	0.512627	+	1.57770i	−0.274931	+	0.961464i	$0.588655\pi$
$80$	6.45918	−	6.18700i	0.722159	−	0.691727i
$81$	−0.309017	+	0.951057i	−0.0343352	+	0.105673i
$82$	−0.127226	+	0.346014i	−0.0140498	+	0.0382108i
$83$	−5.86554	−	11.5118i	−0.643826	−	1.26358i	−0.950192	−	0.311666i	$-0.899113\pi$
$83$	−5.86554	−	11.5118i	−0.643826	−	1.26358i	0.306366	−	0.951914i	$-0.400887\pi$
$84$	0.0597467	+	0.00457206i	0.00651890	+	0.000498853i
$85$	6.37433	−	3.04299i	0.691393	−	0.330059i
$86$	0.489447	−	2.47461i	0.0527784	−	0.266844i
$87$	−7.91379	−	1.25342i	−0.848448	−	0.134381i
$88$	−6.67780	−	3.05226i	−0.711856	−	0.325372i
$89$	−5.58568	+	7.68803i	−0.592081	+	0.814930i	−0.994955	−	0.100326i	$-0.968011\pi$
$89$	−5.58568	+	7.68803i	−0.592081	+	0.814930i	0.402874	+	0.915256i	$0.368011\pi$
$90$	−1.16765	+	2.93881i	−0.123081	+	0.309777i
$91$	0.0640804	+	0.0881991i	0.00671745	+	0.00924578i
$92$	−2.72915	+	11.4771i	−0.284534	+	1.19657i
$93$	1.31270	+	1.31270i	0.136121	+	0.136121i
$94$	1.98314	+	16.6015i	0.204546	+	1.71232i
$95$	−9.65652	−	3.41596i	−0.990738	−	0.350470i
$96$	−4.46131	−	3.47803i	−0.455331	−	0.354975i
$97$	5.72355	+	2.91630i	0.581139	+	0.296105i	0.719740	−	0.694243i	$-0.244261\pi$
$97$	5.72355	+	2.91630i	0.581139	+	0.296105i	−0.138602	+	0.990348i	$0.544261\pi$
$98$	−5.50806	−	8.22412i	−0.556398	−	0.830761i
$99$	2.59589			0.260897
$100$	−4.27958	+	9.03799i	−0.427958	+	0.903799i
$101$	15.7080			1.56301			0.781505	−	0.623900i	$-0.214453\pi$
$101$	15.7080			1.56301			0.781505	+	0.623900i	$0.214453\pi$
$102$	−2.48592	−	3.71174i	−0.246142	−	0.367517i
$103$	−2.92604	−	1.49089i	−0.288311	−	0.146902i	0.303854	−	0.952719i	$-0.401727\pi$
$103$	−2.92604	−	1.49089i	−0.288311	−	0.146902i	−0.592165	+	0.805817i	$0.701727\pi$
$104$	−0.437451	−	10.2827i	−0.0428956	−	1.00830i
$105$	−0.0642290	+	0.0190486i	−0.00626811	+	0.00185896i
$106$	0.598431	+	5.00966i	0.0581247	+	0.486581i
$107$	−8.49218	−	8.49218i	−0.820970	−	0.820970i	0.165277	−	0.986247i	$-0.447148\pi$
$107$	−8.49218	−	8.49218i	−0.820970	−	0.820970i	−0.986247	+	0.165277i	$0.947148\pi$
$108$	1.94575	+	0.462680i	0.187229	+	0.0445214i
$109$	5.49608	+	7.56470i	0.526429	+	0.724567i	0.986581	−	0.163273i	$-0.0522051\pi$
$109$	5.49608	+	7.56470i	0.526429	+	0.724567i	−0.460152	+	0.887840i	$0.652205\pi$
$110$	8.19211	+	0.525313i	0.781087	+	0.0500866i
$111$	4.91420	−	6.76381i	0.466435	−	0.641993i
$112$	−0.000518830	−	0.119842i	−4.90248e−5	−	0.0113240i
$113$	1.12540	+	0.178245i	0.105868	+	0.0167679i	0.209144	−	0.977885i	$-0.432932\pi$
$113$	1.12540	+	0.178245i	0.105868	+	0.0167679i	−0.103276	+	0.994653i	$0.532932\pi$
$114$	−1.25695	+	6.35507i	−0.117724	+	0.595207i
$115$	−1.72592	−	13.0762i	−0.160942	−	1.21936i
$116$	−1.22271	+	15.9782i	−0.113526	+	1.48354i
$117$	1.65197	+	3.24217i	0.152724	+	0.299738i
$118$	0.358808	−	0.975844i	0.0330310	−	0.0898337i
$119$	0.0292459	−	0.0900095i	0.00268096	−	0.00825116i
$120$	6.04675	+	1.85387i	0.551990	+	0.169234i
$121$	1.31683	+	4.05278i	0.119712	+	0.368434i
$122$	6.93025	+	0.264778i	0.627435	+	0.0239719i
$123$	−0.257474	+	0.0407799i	−0.0232157	+	0.00367700i
$124$	2.40520	−	2.82851i	0.215994	−	0.254008i
$125$	0.866133	−	11.1467i	0.0774693	−	0.996995i
$126$	0.0177806	+	0.0384596i	0.00158402	+	0.00342625i
$127$	1.77224	+	11.1895i	0.157261	+	0.992904i	0.932482	+	0.361215i	$0.117638\pi$
$127$	1.77224	+	11.1895i	0.157261	+	0.992904i	−0.775222	+	0.631689i	$0.782362\pi$
$128$	−6.21411	+	9.45436i	−0.549255	+	0.835655i
$129$	1.69641	−	0.551197i	0.149361	−	0.0485302i
$130$	4.55718	+	10.5659i	0.399691	+	0.926692i
$131$	9.16360	+	2.97743i	0.800628	+	0.260140i	0.680623	−	0.732634i	$-0.261709\pi$
$131$	9.16360	+	2.97743i	0.800628	+	0.260140i	0.120004	+	0.992773i	$0.461709\pi$
$132$	−0.418545	−	5.17489i	−0.0364297	−	0.450416i
$133$	−0.122284	+	0.0623070i	−0.0106034	+	0.00540270i
$134$	2.30240	−	4.12169i	0.198897	−	0.356060i
$135$	−2.21684	+	0.292599i	−0.190795	+	0.0251829i
$136$	−6.99849	+	5.55411i	−0.600116	+	0.476261i
$137$	0.0445855	−	0.281502i	0.00380919	−	0.0240503i	−0.985711	−	0.168448i	$-0.946124\pi$
$137$	0.0445855	−	0.281502i	0.00380919	−	0.0240503i	0.989520	+	0.144398i	$0.0461245\pi$
$138$	−8.02619	+	2.27300i	−0.683234	+	0.193491i
$139$	5.57303	+	4.04904i	0.472698	+	0.343435i	0.798492	−	0.602006i	$-0.205632\pi$
$139$	5.57303	+	4.04904i	0.472698	+	0.343435i	−0.325794	+	0.945441i	$0.605632\pi$
$140$	0.0483292	+	0.124969i	0.00408456	+	0.0105618i
$141$	−9.56462	+	6.94910i	−0.805486	+	0.585220i
$142$	9.93468	−	12.6302i	0.833700	−	1.05990i
$143$	6.67923	−	6.67923i	0.558545	−	0.558545i
$144$	0.608628	−	3.95343i	0.0507190	−	0.329452i
$145$	−5.09421	−	17.1769i	−0.423051	−	1.42646i
$146$	−10.3459	−	11.1679i	−0.856233	−	0.924259i
$147$	3.17753	−	6.23625i	0.262078	−	0.514357i
$148$	−14.2759	−	8.70585i	−1.17347	−	0.715616i
$149$			8.23987i			0.675036i	0.941319	+	0.337518i	$0.109587\pi$
$149$			8.23987i			0.675036i	−0.941319	+	0.337518i	$0.890413\pi$
$150$	−7.05511	+	0.474776i	−0.576047	+	0.0387653i
$151$		−	22.2516i		−	1.81081i	−0.424548	−	0.905406i	$-0.639567\pi$
$151$		−	22.2516i		−	1.81081i	0.424548	−	0.905406i	$-0.360433\pi$
$152$	12.8714	+	1.48107i	1.04401	+	0.120131i
$153$	1.43409	−	2.81456i	0.115939	−	0.227544i
$154$	0.0806874	−	0.0747488i	0.00650198	−	0.00602343i
$155$	−1.38438	+	3.91348i	−0.111196	+	0.314338i
$156$	6.19688	−	3.81593i	0.496147	−	0.305519i
$157$	5.82859	−	5.82859i	0.465172	−	0.465172i	−0.435174	−	0.900346i	$-0.643313\pi$
$157$	5.82859	−	5.82859i	0.465172	−	0.465172i	0.900346	+	0.435174i	$0.143313\pi$
$158$	16.3894	+	12.8916i	1.30387	+	1.02560i
$159$	−2.88621	+	2.09695i	−0.228891	+	0.166299i
$160$	2.72073	−	12.3530i	0.215093	−	0.976594i
$161$	−0.142974	−	0.103877i	−0.0112679	−	0.00818662i
$162$	0.385348	+	1.36070i	0.0302758	+	0.106907i
$163$	3.20813	−	20.2553i	0.251280	−	1.58652i	−0.462805	−	0.886460i	$-0.653157\pi$
$163$	3.20813	−	20.2553i	0.251280	−	1.58652i	0.714085	−	0.700059i	$-0.246843\pi$
$164$	0.122808	+	0.506697i	0.00958969	+	0.0395664i
$165$	2.50068	+	5.23831i	0.194677	+	0.407802i
$166$	−15.9515	−	8.91062i	−1.23808	−	0.691598i
$167$	10.1310	−	5.16198i	0.783957	−	0.399446i	−0.0157198	−	0.999876i	$-0.505004\pi$
$167$	10.1310	−	5.16198i	0.783957	−	0.399446i	0.799677	+	0.600430i	$0.205004\pi$
$168$	0.0738019	−	0.0416464i	0.00569394	−	0.00321309i
$169$	0.228867	+	0.0743633i	0.0176051	+	0.00572025i
$170$	5.09526	−	8.59198i	0.390789	−	0.658975i
$171$	−4.35657	+	1.41553i	−0.333155	+	0.108249i
$172$	−1.37233	−	3.29291i	−0.104639	−	0.251082i
$173$	−3.10093	−	19.5785i	−0.235759	−	1.48852i	−0.767188	−	0.641422i	$-0.778345\pi$
$173$	−3.10093	−	19.5785i	−0.235759	−	1.48852i	0.531429	−	0.847103i	$-0.321655\pi$
$174$	−10.2853	+	4.75509i	−0.779727	+	0.360483i
$175$	−0.100312	−	0.111259i	−0.00758286	−	0.00841042i
$176$	−10.2486	+	1.66873i	−0.772518	+	0.125785i
$177$	0.726141	−	0.115009i	0.0545801	−	0.00864463i
$178$	−0.513085	+	13.4294i	−0.0384573	+	1.00657i
$179$	−4.56995	−	14.0649i	−0.341574	−	1.05126i	−0.963392	−	0.268095i	$-0.913606\pi$
$179$	−4.56995	−	14.0649i	−0.341574	−	1.05126i	0.621818	−	0.783162i	$-0.286394\pi$
$180$	0.940723	+	4.37208i	0.0701174	+	0.325875i
$181$	−4.73402	+	14.5698i	−0.351877	+	1.08297i	0.605921	+	0.795525i	$0.292805\pi$
$181$	−4.73402	+	14.5698i	−0.351877	+	1.08297i	−0.957798	+	0.287442i	$0.907195\pi$
$182$	0.144706	+	0.0532070i	0.0107263	+	0.00394396i
$183$	2.22637	+	4.36950i	0.164578	+	0.323002i
$184$	5.82530	+	15.6336i	0.429446	+	1.15253i
$185$	18.3828	+	3.40076i	1.35153	+	0.250029i
$186$	2.57551	+	0.509403i	0.188845	+	0.0373513i
$187$	−8.09910	−	1.28277i	−0.592265	−	0.0938055i
$188$	15.3951	+	17.9465i	1.12280	+	1.30889i
$189$	−0.0176105	+	0.0242387i	−0.00128097	+	0.00176311i
$190$	−14.0349	+	3.58553i	−1.01820	+	0.260122i
$191$	13.5147	+	18.6014i	0.977888	+	1.34595i	0.937959	+	0.346745i	$0.112713\pi$
$191$	13.5147	+	18.6014i	0.977888	+	1.34595i	0.0399290	+	0.999203i	$0.487287\pi$
$192$	−7.97925	−	0.575869i	−0.575853	−	0.0415598i
$193$	8.41078	+	8.41078i	0.605421	+	0.605421i	0.941746	−	0.336325i	$-0.109184\pi$
$193$	8.41078	+	8.41078i	0.605421	+	0.605421i	−0.336325	+	0.941746i	$0.609184\pi$
$194$	9.02034	−	1.07753i	0.647623	−	0.0773621i
$195$	−4.95107	+	6.45679i	−0.354554	+	0.462380i
$196$	−12.9442	−	5.32887i	−0.924587	−	0.380634i
$197$	−13.3126	−	6.78313i	−0.948486	−	0.483278i	−0.0899021	−	0.995951i	$-0.528655\pi$
$197$	−13.3126	−	6.78313i	−0.948486	−	0.483278i	−0.858584	+	0.512673i	$0.828655\pi$
$198$	3.05024	−	2.04288i	0.216771	−	0.145181i
$199$	17.0769			1.21055			0.605276	−	0.796016i	$-0.293063\pi$
$199$	17.0769			1.21055			0.605276	+	0.796016i	$0.293063\pi$
$200$	2.08398	+	13.9877i	0.147360	+	0.989083i
$201$	3.33837			0.235470
$202$	18.4573	−	12.3617i	1.29865	−	0.869767i
$203$	−0.213894	−	0.108984i	−0.0150124	−	0.00764919i
$204$	−5.84203	−	2.40504i	−0.409024	−	0.168387i
$205$	−0.330321	−	0.480279i	−0.0230706	−	0.0335442i
$206$	−4.61145	+	0.550863i	−0.321295	+	0.0383805i
$207$	−4.17092	−	4.17092i	−0.289899	−	0.289899i
$208$	−8.60616	−	11.7382i	−0.596730	−	0.813895i
$209$	6.98946	+	9.62017i	0.483471	+	0.665441i
$210$	−0.0604801	+	0.0729288i	−0.00417352	+	0.00503256i
$211$	−5.30779	+	7.30555i	−0.365404	+	0.502935i	−0.951644	−	0.307202i	$-0.900607\pi$
$211$	−5.30779	+	7.30555i	−0.365404	+	0.502935i	0.586241	+	0.810137i	$0.300607\pi$
$212$	4.64561	+	5.41552i	0.319061	+	0.371940i
$213$	11.2227	+	1.77751i	0.768970	+	0.121793i
$214$	−16.6616	−	3.29545i	−1.13896	−	0.225272i
$215$	2.74646	+	2.89225i	0.187307	+	0.197250i
$216$	2.65041	−	0.987578i	0.180338	−	0.0671962i
$217$	0.0252511	+	0.0495580i	0.00171415	+	0.00336422i
$218$	12.4112	+	4.56348i	0.840593	+	0.309078i
$219$	3.32649	−	10.2379i	0.224783	−	0.691811i
$220$	10.0393	−	5.82966i	0.676852	−	0.393036i
$221$	−3.55195	−	10.9318i	−0.238930	−	0.735351i
$222$	0.451404	−	11.8150i	0.0302963	−	0.792968i
$223$	−9.74743	+	1.54384i	−0.652736	+	0.103383i	−0.474015	−	0.880517i	$-0.657196\pi$
$223$	−9.74743	+	1.54384i	−0.652736	+	0.103383i	−0.178721	+	0.983900i	$0.557196\pi$
$224$	−0.0949211	−	0.140409i	−0.00634218	−	0.00938145i
$225$	−2.72597	−	4.19155i	−0.181731	−	0.279437i
$226$	1.46264	−	0.676207i	0.0972934	−	0.0449806i
$227$	3.93830	+	24.8654i	0.261394	+	1.65038i	0.673461	+	0.739223i	$0.264807\pi$
$227$	3.93830	+	24.8654i	0.261394	+	1.65038i	−0.412067	+	0.911154i	$0.635193\pi$
$228$	3.52428	+	8.45654i	0.233401	+	0.560048i
$229$	9.35273	−	3.03889i	0.618046	−	0.200815i	0.0167733	−	0.999859i	$-0.494661\pi$
$229$	9.35273	−	3.03889i	0.618046	−	0.200815i	0.601272	+	0.799044i	$0.294661\pi$
$230$	−12.3185	−	14.0066i	−0.812260	−	0.923568i
$231$	0.0739682	+	0.0240337i	0.00486675	+	0.00158130i
$232$	11.1376	+	19.7370i	0.731218	+	1.29580i
$233$	−10.0980	+	5.14520i	−0.661543	+	0.337073i	−0.752320	−	0.658798i	$-0.771065\pi$
$233$	−10.0980	+	5.14520i	−0.661543	+	0.337073i	0.0907764	+	0.995871i	$0.471065\pi$
$234$	4.49258	+	2.50958i	0.293689	+	0.164057i
$235$	−23.2365	−	12.6065i	−1.51578	−	0.822355i
$236$	−0.346348	−	1.42901i	−0.0225454	−	0.0930207i
$237$	−2.30656	+	14.5631i	−0.149827	+	0.945973i
$238$	−0.0364699	−	0.128779i	−0.00236399	−	0.00834750i
$239$	16.1051	+	11.7010i	1.04175	+	0.756877i	0.970627	−	0.240590i	$-0.0773410\pi$
$239$	16.1051	+	11.7010i	1.04175	+	0.756877i	0.0711251	+	0.997467i	$0.477341\pi$
$240$	8.56401	−	2.58025i	0.552805	−	0.166554i
$241$	−14.9844	+	10.8868i	−0.965232	+	0.701282i	−0.954360	−	0.298659i	$-0.903461\pi$
$241$	−14.9844	+	10.8868i	−0.965232	+	0.701282i	−0.0108717	+	0.999941i	$0.503461\pi$
$242$	4.73671	+	3.72581i	0.304487	+	0.239504i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	8.35158	−	5.14276i	0.534655	−	0.329231i
$245$	15.6452	+	0.404504i	0.999538	+	0.0258428i
$246$	−0.270446	+	0.250541i	−0.0172430	+	0.0159739i
$247$	−7.56727	+	14.8516i	−0.481494	+	0.944985i
$248$	0.600232	−	5.21638i	0.0381147	−	0.331241i
$249$		−	12.9200i		−	0.818769i
$250$	−7.75439	−	13.7793i	−0.490431	−	0.871480i
$251$		−	11.5425i		−	0.728554i	−0.931291	−	0.364277i	$-0.881316\pi$
$251$		−	11.5425i		−	0.728554i	0.931291	−	0.364277i	$-0.118684\pi$
$252$	0.0511591	+	0.0311982i	0.00322272	+	0.00196530i
$253$	−6.95153	+	13.6431i	−0.437039	+	0.857737i
$254$	10.8882	+	11.7532i	0.683184	+	0.737461i
$255$	7.06106	+	0.182562i	0.442181	+	0.0114325i
$256$	0.138535	+	15.9994i	0.00865842	+	0.999963i
$257$	7.29636	−	7.29636i	0.455134	−	0.455134i	−0.441920	−	0.897054i	$-0.645703\pi$
$257$	7.29636	−	7.29636i	0.455134	−	0.455134i	0.897054	+	0.441920i	$0.145703\pi$
$258$	1.55955	−	1.98269i	0.0970934	−	0.123437i
$259$	0.202649	−	0.147233i	0.0125920	−	0.00914860i
$260$	13.6698	+	8.82886i	0.847766	+	0.547543i
$261$	−6.48220	−	4.70959i	−0.401238	−	0.291517i
$262$	13.1106	−	3.71289i	0.809976	−	0.229383i
$263$	−1.98412	+	12.5273i	−0.122346	+	0.772464i	0.847866	+	0.530210i	$0.177887\pi$
$263$	−1.98412	+	12.5273i	−0.122346	+	0.772464i	−0.970213	+	0.242254i	$0.922113\pi$
$264$	−4.56427	−	5.75124i	−0.280911	−	0.353964i
$265$	−7.01183	−	3.80411i	−0.430733	−	0.233684i
$266$	−0.0946536	+	0.169446i	−0.00580359	+	0.0103894i
$267$	−8.46717	+	4.31424i	−0.518183	+	0.264027i
$268$	−0.538257	−	6.65500i	−0.0328793	−	0.406519i
$269$	−18.1138	−	5.88553i	−1.10442	−	0.358847i	−0.300617	−	0.953745i	$-0.597192\pi$
$269$	−18.1138	−	5.88553i	−1.10442	−	0.358847i	−0.803801	+	0.594898i	$0.797192\pi$
$270$	−2.37458	+	2.08839i	−0.144512	+	0.127096i
$271$	−17.6810	+	5.74491i	−1.07404	+	0.348978i	−0.792062	−	0.610441i	$-0.790992\pi$
$271$	−17.6810	+	5.74491i	−1.07404	+	0.348978i	−0.281983	+	0.959419i	$0.590992\pi$
$272$	−3.85250	+	12.0338i	−0.233592	+	0.729656i
$273$	0.0170545	+	0.107678i	0.00103219	+	0.00651696i
$274$	−0.169143	−	0.365859i	−0.0102183	−	0.0221023i
$275$	−8.16156	+	10.0923i	−0.492161	+	0.608591i
$276$	−7.64219	+	8.98718i	−0.460006	+	0.540964i
$277$	−27.8230	+	4.40673i	−1.67172	+	0.264774i	−0.919199	−	0.393793i	$-0.871163\pi$
$277$	−27.8230	+	4.40673i	−1.67172	+	0.264774i	−0.752521	+	0.658568i	$0.771163\pi$
$278$	9.73491	+	0.371934i	0.583861	+	0.0223071i
$279$	0.573671	+	1.76558i	0.0343448	+	0.105702i
$280$	0.155134	+	0.108808i	0.00927104	+	0.00650251i
$281$	4.15266	−	12.7806i	0.247727	−	0.762425i	−0.747449	−	0.664319i	$-0.768722\pi$
$281$	4.15266	−	12.7806i	0.247727	−	0.762425i	0.995176	−	0.0981057i	$-0.0312783\pi$
$282$	−5.76995	+	15.6924i	−0.343595	+	0.934469i
$283$	−4.92195	−	9.65986i	−0.292579	−	0.574219i	0.697192	−	0.716885i	$-0.254433\pi$
$283$	−4.92195	−	9.65986i	−0.292579	−	0.574219i	−0.989771	+	0.142666i	$0.954433\pi$
$284$	1.73396	−	22.6590i	0.102892	−	1.34457i
$285$	−7.05321	−	7.42761i	−0.417796	−	0.439973i
$286$	2.59192	−	13.1046i	0.153264	−	0.774891i
$287$	−0.00771411	−	0.00122180i	−0.000455350	−	7.21203e-5i
$288$	−2.39606	−	5.12434i	−0.141189	−	0.301955i
$289$	4.12720	−	5.68061i	0.242777	−	0.334153i
$290$	−19.5035	−	16.1743i	−1.14528	−	0.949786i
$291$	3.77575	+	5.19688i	0.221339	+	0.304646i
$292$	−20.9454	−	4.98063i	−1.22574	−	0.291469i
$293$	0.921753	+	0.921753i	0.0538494	+	0.0538494i	0.733519	−	0.679669i	$-0.237877\pi$
$293$	0.921753	+	0.921753i	0.0538494	+	0.0538494i	−0.679669	+	0.733519i	$0.737877\pi$
$294$	−1.17405	−	9.82835i	−0.0684720	−	0.573201i
$295$	0.931586	+	1.35451i	0.0542390	+	0.0788623i
$296$	−23.6258	+	1.00510i	−1.37322	+	0.0584202i
$297$	2.31296	+	1.17851i	0.134211	+	0.0683841i
$298$	6.48451	+	9.68205i	0.375637	+	0.560866i
$299$	−21.4635			−1.24127
$300$	−7.91629	+	6.11001i	−0.457047	+	0.352762i
$301$	0.0534413			0.00308030
$302$	−17.5113	−	26.1462i	−1.00766	−	1.50454i
$303$	13.9960	+	7.13130i	0.804048	+	0.409683i
$304$	16.2898	−	8.38910i	0.934284	−	0.481148i
$305$	−6.67260	+	8.70187i	−0.382072	+	0.498267i
$306$	−0.529876	−	4.43576i	−0.0302910	−	0.253576i
$307$	15.8559	+	15.8559i	0.904945	+	0.904945i	0.995859	−	0.0909141i	$-0.0289789\pi$
$307$	15.8559	+	15.8559i	0.904945	+	0.904945i	−0.0909141	+	0.995859i	$0.528979\pi$
$308$	0.0359848	−	0.151330i	0.00205043	−	0.00862283i
$309$	−1.93027	−	2.65679i	−0.109809	−	0.151140i
$310$	1.45310	+	5.68790i	0.0825306	+	0.323051i
$311$	−10.3201	+	14.2044i	−0.585200	+	0.805458i	−0.994253	−	0.107052i	$-0.965859\pi$
$311$	−10.3201	+	14.2044i	−0.585200	+	0.805458i	0.409054	+	0.912510i	$0.365859\pi$
$312$	4.27847	−	9.36055i	0.242221	−	0.529937i
$313$	−12.9632	−	2.05317i	−0.732722	−	0.116052i	−0.221086	−	0.975254i	$-0.570960\pi$
$313$	−12.9632	−	2.05317i	−0.732722	−	0.116052i	−0.511636	+	0.859202i	$0.670960\pi$
$314$	2.26183	−	11.4356i	0.127642	−	0.645351i
$315$	−0.0658764	−	0.0121869i	−0.00371171	−	0.000686655i
$316$	29.4032	+	2.25005i	1.65406	+	0.126575i
$317$	−3.09677	−	6.07775i	−0.173932	−	0.341360i	0.787540	−	0.616263i	$-0.211354\pi$
$317$	−3.09677	−	6.07775i	−0.173932	−	0.341360i	−0.961472	+	0.274903i	$0.911354\pi$
$318$	−1.74113	+	4.73532i	−0.0976378	+	0.265543i
$319$	−6.42738	+	19.7814i	−0.359864	+	1.10755i
$320$	−6.52451	−	16.6563i	−0.364731	−	0.931113i
$321$	−3.71122	−	11.4220i	−0.207140	−	0.637511i
$322$	−0.249745	−	0.00954180i	−0.0139177	−	0.000531744i
$323$	14.2918	−	2.26360i	0.795219	−	0.125950i
$324$	1.52362	+	1.29560i	0.0846456	+	0.0719778i
$325$	−17.7988	−	3.77093i	−0.987298	−	0.209174i
$326$	−12.1706	−	26.3252i	−0.674069	−	1.45802i
$327$	1.46274	+	9.23537i	0.0808896	+	0.510717i
$328$	0.543057	+	0.498736i	0.0299853	+	0.0275381i
$329$	−0.336875	+	0.109457i	−0.0185725	+	0.00603457i
$330$	7.06073	+	4.18720i	0.388681	+	0.230498i
$331$	−6.17995	−	2.00799i	−0.339681	−	0.110369i	0.134209	−	0.990953i	$-0.457151\pi$
$331$	−6.17995	−	2.00799i	−0.339681	−	0.110369i	−0.473890	+	0.880584i	$0.657151\pi$
$332$	−25.7558	+	2.08313i	−1.41353	+	0.114327i
$333$	7.44929	−	3.79560i	0.408218	−	0.207998i
$334$	7.84182	−	14.0382i	0.429085	−	0.768136i
$335$	3.21591	+	6.73657i	0.175704	+	0.368058i
$336$	0.0539447	−	0.107015i	0.00294293	−	0.00583816i
$337$	−4.19864	+	26.5091i	−0.228714	+	1.44405i	0.559595	+	0.828766i	$0.310957\pi$
$337$	−4.19864	+	26.5091i	−0.228714	+	1.44405i	−0.788309	+	0.615279i	$0.789043\pi$
$338$	0.327445	−	0.0927319i	0.0178107	−	0.00504395i
$339$	0.921813	+	0.669736i	0.0500660	+	0.0363751i
$340$	−0.774546	−	14.1056i	−0.0420056	−	0.764983i
$341$	3.89875	−	2.83261i	0.211129	−	0.153394i
$342$	−4.00509	+	5.09176i	−0.216571	+	0.275331i
$343$	0.296577	−	0.296577i	0.0160136	−	0.0160136i
$344$	−4.20393	−	2.78927i	−0.226661	−	0.150387i
$345$	4.39866	−	12.4345i	0.236816	−	0.669452i
$346$	−19.0513	−	20.5649i	−1.02420	−	1.10557i
$347$	5.17054	−	10.1478i	0.277569	−	0.544760i	−0.709568	−	0.704637i	$-0.751110\pi$
$347$	5.17054	−	10.1478i	0.277569	−	0.544760i	0.987137	+	0.159877i	$0.0511098\pi$
$348$	−8.34338	+	13.6816i	−0.447252	+	0.733408i
$349$		−	3.75104i		−	0.200789i	−0.994948	−	0.100394i	$-0.967990\pi$
$349$		−	3.75104i		−	0.200789i	0.994948	−	0.100394i	$-0.0320104\pi$
$350$	−0.205426	−	0.0517904i	−0.0109805	−	0.00276831i
$351$			3.63877i			0.194223i
$352$	−10.7291	+	10.0261i	−0.571864	+	0.534394i
$353$	−13.7908	+	27.0659i	−0.734008	+	1.44057i	0.157478	+	0.987522i	$0.449664\pi$
$353$	−13.7908	+	27.0659i	−0.734008	+	1.44057i	−0.891486	+	0.453049i	$0.850336\pi$
$354$	0.762724	−	0.706588i	0.0405383	−	0.0375547i
$355$	7.22422	+	24.3590i	0.383422	+	1.29284i
$356$	9.96559	+	16.1836i	0.528175	+	0.857730i
$357$	0.0669217	−	0.0669217i	0.00354187	−	0.00354187i
$358$	−16.4384	−	12.9302i	−0.868796	−	0.683380i
$359$	−1.82816	+	1.32824i	−0.0964867	+	0.0701017i	−0.634983	−	0.772526i	$-0.718993\pi$
$359$	−1.82816	+	1.32824i	−0.0964867	+	0.0701017i	0.538496	+	0.842628i	$0.318993\pi$
$360$	4.54605	+	4.39698i	0.239598	+	0.231741i
$361$	−1.60462	−	1.16583i	−0.0844538	−	0.0613593i
$362$	5.90338	+	20.8454i	0.310275	+	1.09561i
$363$	−0.666621	+	4.20888i	−0.0349885	+	0.220909i
$364$	0.211905	−	0.0513593i	0.0111068	−	0.00269196i
$365$	23.8637	−	3.14975i	1.24908	−	0.164866i
$366$	6.05469	+	3.38219i	0.316484	+	0.176790i
$367$	22.5340	−	11.4816i	1.17627	−	0.599337i	0.247096	−	0.968991i	$-0.420524\pi$
$367$	22.5340	−	11.4816i	1.17627	−	0.599337i	0.929169	+	0.369654i	$0.120524\pi$
$368$	19.1480	+	13.7856i	0.998160	+	0.718624i
$369$	−0.247925	−	0.0805557i	−0.0129065	−	0.00419356i
$370$	24.2765	−	10.4707i	1.26208	−	0.544345i
$371$	−0.101655	+	0.0330297i	−0.00527766	+	0.00171481i
$372$	3.42717	−	1.42828i	0.177690	−	0.0740528i
$373$	2.74365	+	17.3227i	0.142061	+	0.896935i	0.951033	+	0.309089i	$0.100024\pi$
$373$	2.74365	+	17.3227i	0.142061	+	0.896935i	−0.808973	+	0.587846i	$0.799976\pi$
$374$	−10.5261	+	4.86644i	−0.544294	+	0.251637i
$375$	5.83224	−	9.53860i	0.301176	−	0.492571i
$376$	32.2130	+	8.97219i	1.66126	+	0.462705i
$377$	−28.7965	+	4.56091i	−1.48309	+	0.234899i
$378$	−0.00161765	+	0.0423400i	−8.32028e−5	+	0.00217773i
$379$	−7.30173	−	22.4724i	−0.375065	−	1.15433i	−0.943435	−	0.331557i	$-0.892426\pi$
$379$	−7.30173	−	22.4724i	−0.375065	−	1.15433i	0.568371	−	0.822773i	$-0.307574\pi$
$380$	−13.6696	+	15.2581i	−0.701238	+	0.782723i
$381$	−3.50084	+	10.7745i	−0.179353	+	0.551993i
$382$	30.5188	+	11.2215i	1.56148	+	0.574139i
$383$	2.62572	+	5.15327i	0.134168	+	0.263320i	0.948310	−	0.317347i	$-0.102792\pi$
$383$	2.62572	+	5.15327i	0.134168	+	0.263320i	−0.814141	+	0.580667i	$0.802792\pi$
$384$	−9.82900	+	5.60274i	−0.501584	+	0.285914i
$385$	0.0227568	+	0.172414i	0.00115980	+	0.00878705i
$386$	16.5019	+	3.26387i	0.839924	+	0.166126i
$387$	1.76175	+	0.279034i	0.0895549	+	0.0141841i
$388$	9.75115	−	8.36484i	0.495039	−	0.424660i
$389$	12.5726	−	17.3047i	0.637456	−	0.877382i	−0.361021	−	0.932558i	$-0.617572\pi$
$389$	12.5726	−	17.3047i	0.637456	−	0.877382i	0.998477	+	0.0551754i	$0.0175718\pi$
$390$	−0.736353	+	11.4832i	−0.0372867	+	0.581475i
$391$	10.9520	+	15.0742i	0.553869	+	0.762335i
$392$	−19.4034	+	3.92512i	−0.980021	+	0.198248i
$393$	6.81310	+	6.81310i	0.343676	+	0.343676i
$394$	−20.9808	+	2.50627i	−1.05700	+	0.126264i
$395$	−31.6091	+	9.37442i	−1.59043	+	0.471678i
$396$	1.97642	−	4.80087i	0.0993190	−	0.241253i
$397$	6.27013	+	3.19479i	0.314689	+	0.160342i	0.604200	−	0.796833i	$-0.293493\pi$
$397$	6.27013	+	3.19479i	0.314689	+	0.160342i	−0.289511	+	0.957175i	$0.593493\pi$
$398$	20.0658	−	13.4390i	1.00581	−	0.673636i
$399$	−0.137243			−0.00687074
$400$	13.4566	+	14.7959i	0.672831	+	0.739796i
$401$	30.8073			1.53844			0.769221	−	0.638983i	$-0.220645\pi$
$401$	30.8073			1.53844			0.769221	+	0.638983i	$0.220645\pi$
$402$	3.92266	−	2.62718i	0.195645	−	0.131032i
$403$	6.01889	+	3.06678i	0.299822	+	0.152767i
$404$	11.9596	−	29.0506i	0.595010	−	1.44532i
$405$	−2.10806	−	0.745717i	−0.104750	−	0.0370550i
$406$	−0.337097	+	0.0402681i	−0.0167299	+	0.00199847i
$407$	−15.3464	−	15.3464i	−0.760691	−	0.760691i
$408$	−8.75722	+	1.77150i	−0.433547	+	0.0877022i
$409$	−0.908588	−	1.25056i	−0.0449268	−	0.0618364i	0.785963	−	0.618274i	$-0.212168\pi$
$409$	−0.908588	−	1.25056i	−0.0449268	−	0.0618364i	−0.830889	+	0.556438i	$0.812168\pi$
$410$	−0.766099	−	0.304388i	−0.0378349	−	0.0150327i
$411$	0.167525	−	0.230578i	0.00826340	−	0.0113736i
$412$	−4.98506	+	4.27634i	−0.245596	+	0.210680i
$413$	0.0217557	+	0.00344576i	0.00107053	+	0.000169555i
$414$	−8.18331	−	1.61856i	−0.402188	−	0.0795477i
$415$	26.0715	−	12.4460i	1.27980	−	0.610952i
$416$	−19.3500	−	7.01986i	−0.948711	−	0.344177i
$417$	3.12738	+	6.13783i	0.153148	+	0.300571i
$418$	15.7835	+	5.80346i	0.771998	+	0.283856i
$419$	4.92418	−	15.1551i	0.240562	−	0.740373i	−0.755773	−	0.654834i	$-0.772739\pi$
$419$	4.92418	−	15.1551i	0.240562	−	0.740373i	0.996335	−	0.0855393i	$-0.0272613\pi$
$420$	−0.0136730	+	0.133289i	−0.000667174	+	0.00650383i
$421$	0.995697	+	3.06444i	0.0485273	+	0.149352i	0.972384	−	0.233387i	$-0.0749809\pi$
$421$	0.995697	+	3.06444i	0.0485273	+	0.149352i	−0.923857	+	0.382739i	$0.874981\pi$
$422$	−0.487559	+	12.7613i	−0.0237340	+	0.621209i
$423$	−11.6770	+	1.84945i	−0.567753	+	0.0899233i
$424$	9.72054	+	2.70743i	0.472071	+	0.131485i
$425$	6.43366	+	14.4245i	0.312079	+	0.699693i
$426$	14.5858	−	6.74332i	0.706686	−	0.326715i
$427$	0.0229845	+	0.145118i	0.00111230	+	0.00702277i
$428$	−22.1712	+	9.23988i	−1.07168	+	0.446626i
$429$	8.98354	−	2.91893i	0.433730	−	0.140927i
$430$	5.50326	+	1.23709i	0.265391	+	0.0596577i
$431$	−29.8166	−	9.68800i	−1.43621	−	0.466654i	−0.515499	−	0.856890i	$-0.672394\pi$
$431$	−29.8166	−	9.68800i	−1.43621	−	0.466654i	−0.920715	+	0.390235i	$0.872394\pi$
$432$	2.33711	−	3.24622i	0.112444	−	0.156184i
$433$	25.0873	−	12.7826i	1.20562	−	0.614293i	0.268491	−	0.963282i	$-0.413475\pi$
$433$	25.0873	−	12.7826i	1.20562	−	0.614293i	0.937127	+	0.348990i	$0.113475\pi$
$434$	0.0686711	+	0.0383601i	0.00329632	+	0.00184134i
$435$	3.25917	−	17.6174i	0.156265	−	0.844691i
$436$	18.1748	−	4.40501i	0.870414	−	0.210962i
$437$	4.22685	−	26.6873i	0.202198	−	1.27663i
$438$	−4.14817	−	14.6476i	−0.198207	−	0.699889i
$439$	−25.3167	−	18.3936i	−1.20830	−	0.877881i	−0.213224	−	0.977003i	$-0.568396\pi$
$439$	−25.3167	−	18.3936i	−1.20830	−	0.877881i	−0.995075	+	0.0991225i	$0.968396\pi$
$440$	7.20871	−	14.7506i	0.343662	−	0.703208i
$441$	5.66239	−	4.11397i	0.269638	−	0.195903i
$442$	−12.7766	−	10.0498i	−0.607720	−	0.478022i
$443$	27.6411	−	27.6411i	1.31327	−	1.31327i	0.394278	−	0.918991i	$-0.370995\pi$
$443$	27.6411	−	27.6411i	1.31327	−	1.31327i	0.918991	−	0.394278i	$-0.129005\pi$
$444$	−8.76757	−	14.2381i	−0.416090	−	0.675710i
$445$	−16.8624	−	12.9301i	−0.799354	−	0.612946i
$446$	−10.2385	+	9.48496i	−0.484808	+	0.449126i
$447$	−3.74082	+	7.34178i	−0.176935	+	0.347254i
$448$	−0.222032	−	0.0902838i	−0.0104900	−	0.00426551i
$449$			32.7243i			1.54436i	0.635406	+	0.772178i	$0.280833\pi$
$449$			32.7243i			1.54436i	−0.635406	+	0.772178i	$0.719167\pi$
$450$	−6.50169	−	2.77992i	−0.306493	−	0.131047i
$451$			0.676707i			0.0318649i
$452$	1.18649	−	1.94561i	0.0558076	−	0.0915137i
$453$	10.1020	−	19.8263i	0.474634	−	0.931523i
$454$	24.1959	+	26.1182i	1.13557	+	1.22579i
$455$	−0.200857	+	0.138143i	−0.00941631	+	0.00647624i
$456$	10.7961	+	7.16315i	0.505576	+	0.335445i
$457$	7.11038	−	7.11038i	0.332610	−	0.332610i	−0.520967	−	0.853577i	$-0.674429\pi$
$457$	7.11038	−	7.11038i	0.332610	−	0.332610i	0.853577	+	0.520967i	$0.174429\pi$
$458$	8.59818	−	10.9311i	0.401767	−	0.510775i
$459$	2.55557	−	1.85673i	0.119284	−	0.0866647i
$460$	−25.4973	−	6.76383i	−1.18882	−	0.315365i
$461$	−20.0752	−	14.5855i	−0.934994	−	0.679313i	0.0122168	−	0.999925i	$-0.496111\pi$
$461$	−20.0752	−	14.5855i	−0.934994	−	0.679313i	−0.947210	+	0.320613i	$0.896111\pi$
$462$	0.105828	−	0.0299703i	0.00492357	−	0.00139435i
$463$	−4.64024	+	29.2973i	−0.215650	+	1.36156i	0.607763	+	0.794119i	$0.292067\pi$
$463$	−4.64024	+	29.2973i	−0.215650	+	1.36156i	−0.823413	+	0.567443i	$0.807933\pi$
$464$	28.6193	+	14.4265i	1.32862	+	0.669735i
$465$	−3.01017	+	2.85844i	−0.139593	+	0.132557i
$466$	−7.81632	+	13.9925i	−0.362084	+	0.648192i
$467$	35.6038	−	18.1410i	1.64755	−	0.839468i	0.650768	−	0.759276i	$-0.274447\pi$
$467$	35.6038	−	18.1410i	1.64755	−	0.839468i	0.996779	−	0.0801913i	$-0.0255531\pi$
$468$	7.25385	−	0.586692i	0.335309	−	0.0271199i
$469$	0.0951245	+	0.0309078i	0.00439244	+	0.00142719i
$470$	−37.2244	+	3.47350i	−1.71703	+	0.160221i
$471$	7.83943	−	2.54719i	0.361222	−	0.117368i
$472$	−1.53155	−	1.40656i	−0.0704954	−	0.0647421i
$473$	−0.724343	−	4.57332i	−0.0333053	−	0.210281i
$474$	8.75039	+	18.9271i	0.401919	+	0.869353i
$475$	8.19384	−	21.3880i	0.375959	−	0.981349i
$476$	−0.144198	−	0.122618i	−0.00660930	−	0.00562018i
$477$	−3.52362	+	0.558087i	−0.161336	+	0.0255531i
$478$	28.1322	+	1.07482i	1.28674	+	0.0491613i
$479$	1.67227	+	5.14672i	0.0764080	+	0.235160i	0.981964	−	0.189067i	$-0.0605462\pi$
$479$	1.67227	+	5.14672i	0.0764080	+	0.235160i	−0.905556	+	0.424226i	$0.860546\pi$
$480$	8.03235	−	9.77145i	0.366625	−	0.446004i
$481$	9.40093	−	28.9331i	0.428645	−	1.31923i
$482$	−9.03949	+	24.5845i	−0.411738	+	1.11979i
$483$	−0.0802316	−	0.157463i	−0.00365066	−	0.00716483i
$484$	8.49784	+	0.650289i	0.386265	+	0.0295586i
$485$	−6.84964	+	12.6254i	−0.311026	+	0.573291i
$486$	−0.274398	+	1.38734i	−0.0124469	+	0.0629309i
$487$	−33.8274	−	5.35774i	−1.53287	−	0.242782i	−0.667763	−	0.744374i	$-0.732748\pi$
$487$	−33.8274	−	5.35774i	−1.53287	−	0.242782i	−0.865105	+	0.501591i	$0.832748\pi$
$488$	5.76613	−	12.6153i	0.261021	−	0.571067i
$489$	12.0542	−	16.5912i	0.545109	−	0.750278i
$490$	18.7019	−	11.8370i	0.844864	−	0.534741i
$491$	8.94325	+	12.3093i	0.403603	+	0.555512i	0.961644	−	0.274302i	$-0.0884467\pi$
$491$	8.94325	+	12.3093i	0.403603	+	0.555512i	−0.558041	+	0.829814i	$0.688447\pi$
$492$	−0.120613	+	0.507224i	−0.00543766	+	0.0228674i
$493$	17.8970	+	17.8970i	0.806040	+	0.806040i
$494$	2.79600	+	23.4062i	0.125798	+	1.05309i
$495$	−0.150026	+	5.80265i	−0.00674317	+	0.260810i
$496$	−3.39984	−	6.60174i	−0.152657	−	0.296427i
$497$	0.303328	+	0.154553i	0.0136061	+	0.00693266i
$498$	−10.1676	−	15.1813i	−0.455620	−	0.680289i
$499$	−2.90097			−0.129865			−0.0649327	−	0.997890i	$-0.520683\pi$
$499$	−2.90097			−0.129865			−0.0649327	+	0.997890i	$0.520683\pi$
$500$	−19.9555	−	10.0886i	−0.892436	−	0.451175i
$501$	11.3702			0.507985
$502$	−9.08354	−	13.5627i	−0.405418	−	0.605332i
$503$	−7.33460	−	3.73716i	−0.327034	−	0.166632i	0.282763	−	0.959190i	$-0.408749\pi$
$503$	−7.33460	−	3.73716i	−0.327034	−	0.166632i	−0.609797	+	0.792558i	$0.708749\pi$
$504$	0.0846651	−	0.00360186i	0.00377128	−	0.000160440i
$505$	−0.907825	+	35.1125i	−0.0403977	+	1.56249i
$506$	2.56849	+	21.5016i	0.114183	+	0.955865i
$507$	0.170161	+	0.170161i	0.00755714	+	0.00755714i
$508$	22.0432	+	5.24167i	0.978011	+	0.232562i
$509$	3.84108	+	5.28680i	0.170253	+	0.234333i	0.885614	−	0.464422i	$-0.153738\pi$
$509$	3.84108	+	5.28680i	0.170253	+	0.234333i	−0.715361	+	0.698755i	$0.753738\pi$
$510$	8.44059	−	5.34231i	0.373756	−	0.236561i
$511$	0.189572	−	0.260923i	0.00838617	−	0.0115426i
$512$	12.7538	+	18.6907i	0.563643	+	0.826019i
$513$	−4.52437	−	0.716590i	−0.199756	−	0.0316382i
$514$	2.83141	−	14.3154i	0.124888	−	0.631425i
$515$	3.50173	−	6.45448i	0.154305	−	0.284418i
$516$	0.272198	−	3.55703i	0.0119828	−	0.156589i
$517$	13.9330	+	27.3450i	0.612771	+	1.20263i
$518$	0.122250	−	0.332480i	0.00537134	−	0.0146083i
$519$	6.12550	−	18.8523i	0.268880	−	0.827526i
$520$	23.0104	−	0.383570i	1.00907	−	0.0168207i
$521$	−5.29421	−	16.2939i	−0.231944	−	0.713849i	−0.997512	−	0.0704945i	$-0.977542\pi$
$521$	−5.29421	−	16.2939i	−0.231944	−	0.713849i	0.765569	−	0.643354i	$-0.222458\pi$
$522$	−11.3230	−	0.432610i	−0.495596	−	0.0189348i
$523$	6.28174	−	0.994930i	0.274681	−	0.0435053i	−0.0175740	−	0.999846i	$-0.505594\pi$
$523$	6.28174	−	0.994930i	0.274681	−	0.0435053i	0.292255	+	0.956340i	$0.405594\pi$
$524$	12.4833	−	14.6804i	0.545338	−	0.641314i
$525$	−0.0388678	−	0.144673i	−0.00169633	−	0.00631407i
$526$	7.52715	+	16.2813i	0.328199	+	0.709898i
$527$	−0.917367	−	5.79203i	−0.0399611	−	0.252305i
$528$	−9.88916	−	3.16592i	−0.430370	−	0.137779i
$529$	11.2159	−	3.64427i	0.487648	−	0.158447i
$530$	−11.2328	+	1.04816i	−0.487921	+	0.0455291i
$531$	0.699209	+	0.227187i	0.0303431	+	0.00985907i
$532$	0.0221282	+	0.273593i	0.000959379	+	0.0118617i
$533$	−0.845180	+	0.430641i	−0.0366088	+	0.0186531i
$534$	−6.55397	+	11.7327i	−0.283618	+	0.507725i
$535$	19.4735	−	18.4919i	0.841914	−	0.799477i
$536$	−5.86973	−	7.39620i	−0.253534	−	0.319467i
$537$	2.31346	−	14.6066i	0.0998331	−	0.630321i
$538$	−25.9159	+	7.33932i	−1.11731	+	0.316421i
$539$	−14.6990	−	10.6794i	−0.633129	−	0.459995i
$540$	−1.14669	+	4.32263i	−0.0493457	+	0.186016i
$541$	−22.6575	+	16.4616i	−0.974122	+	0.707741i	−0.956387	−	0.292102i	$-0.905645\pi$
$541$	−22.6575	+	16.4616i	−0.974122	+	0.707741i	−0.0177348	+	0.999843i	$0.505645\pi$
$542$	−16.2546	+	20.6648i	−0.698193	+	0.887628i
$543$	−10.8326	+	10.8326i	−0.464872	+	0.464872i
$544$	4.94342	+	17.1718i	0.211947	+	0.736235i
$545$	−17.2272	+	11.8483i	−0.737931	+	0.507526i
$546$	0.104778	+	0.113103i	0.00448410	+	0.00484035i
$547$	1.24110	−	2.43580i	0.0530657	−	0.104147i	−0.862951	−	0.505288i	$-0.831386\pi$
$547$	1.24110	−	2.43580i	0.0530657	−	0.104147i	0.916016	+	0.401141i	$0.131386\pi$
$548$	−0.486666	−	0.296782i	−0.0207894	−	0.0126779i
$549$			4.90400i			0.209298i
$550$	−1.64769	+	18.2816i	−0.0702579	+	0.779531i
$551$		−	36.7031i		−	1.56361i
$552$	−1.90715	+	16.5743i	−0.0811737	+	0.705449i
$553$	−0.200554	+	0.393610i	−0.00852843	+	0.0167380i
$554$	−29.2247	+	27.0738i	−1.24164	+	1.15025i
$555$	14.8353	+	11.3757i	0.629723	+	0.482872i
$556$	11.7315	−	7.22402i	0.497525	−	0.306367i
$557$	14.0130	−	14.0130i	0.593751	−	0.593751i	−0.344891	−	0.938643i	$-0.612084\pi$
$557$	14.0130	−	14.0130i	0.593751	−	0.593751i	0.938643	+	0.344891i	$0.112084\pi$
$558$	2.06353	+	1.62314i	0.0873562	+	0.0687129i
$559$	5.25094	−	3.81503i	0.222091	−	0.161359i
$560$	0.267915	+	0.00576634i	0.0113215	+	0.000243672i
$561$	−6.63398	−	4.81987i	−0.280087	−	0.203495i
$562$	−5.17841	−	18.2855i	−0.218438	−	0.771327i
$563$	−2.73526	+	17.2697i	−0.115277	+	0.727832i	0.860562	+	0.509345i	$0.170112\pi$
$563$	−2.73526	+	17.2697i	−0.115277	+	0.727832i	−0.975840	+	0.218487i	$0.929888\pi$
$564$	5.56958	+	22.9797i	0.234522	+	0.967621i
$565$	−0.463476	+	2.50532i	−0.0194986	+	0.105400i
$566$	−13.3854	−	7.47717i	−0.562630	−	0.314289i
$567$	−0.0266952	+	0.0136019i	−0.00112109	+	0.000571225i
$568$	−15.7945	−	27.9895i	−0.662721	−	1.17441i
$569$	27.6880	+	8.99636i	1.16074	+	0.377147i	0.825179	−	0.564871i	$-0.191074\pi$
$569$	27.6880	+	8.99636i	1.16074	+	0.377147i	0.335561	+	0.942019i	$0.391074\pi$
$570$	−14.1330	−	3.17698i	−0.591965	−	0.133069i
$571$	−1.78586	+	0.580261i	−0.0747358	+	0.0242831i	−0.346146	−	0.938181i	$-0.612510\pi$
$571$	−1.78586	+	0.580261i	−0.0747358	+	0.0242831i	0.271410	+	0.962464i	$0.412510\pi$
$572$	−7.26731	−	17.4380i	−0.303861	−	0.729118i
$573$	3.59683	+	22.7095i	0.150260	+	0.948702i
$574$	−0.0100258	+	0.00463511i	−0.000418468	+	0.000193466i
$575$	29.3292	−	3.10226i	1.22311	−	0.129373i
$576$	−6.84812	−	4.13561i	−0.285338	−	0.172317i
$577$	25.2103	−	3.99292i	1.04952	−	0.166227i	0.392231	−	0.919867i	$-0.371703\pi$
$577$	25.2103	−	3.99292i	1.04952	−	0.166227i	0.657288	+	0.753639i	$0.271703\pi$
$578$	0.379113	−	9.92283i	0.0157690	−	0.412735i
$579$	3.67565	+	11.3125i	0.152755	+	0.470130i
$580$	−35.6457	−	3.65659i	−1.48011	−	0.151832i
$581$	0.119618	−	0.368145i	0.00496258	−	0.0152732i
$582$	8.52637	+	3.13507i	0.353430	+	0.129953i
$583$	4.20439	+	8.25158i	0.174128	+	0.341746i
$584$	−28.5310	+	10.6310i	−1.18062	+	0.439914i
$585$	−7.34276	+	3.50530i	−0.303586	+	0.144926i
$586$	1.80847	+	0.357693i	0.0747073	+	0.0147762i
$587$	13.7586	+	2.17915i	0.567879	+	0.0899432i	0.433771	−	0.901023i	$-0.357183\pi$
$587$	13.7586	+	2.17915i	0.567879	+	0.0899432i	0.134109	+	0.990967i	$0.457183\pi$
$588$	−9.11413	−	10.6246i	−0.375860	−	0.438152i
$589$	−4.99848	+	6.87981i	−0.205959	+	0.283478i
$590$	2.16059	+	0.858449i	0.0889500	+	0.0353418i
$591$	−8.78217	−	12.0876i	−0.361250	−	0.497218i
$592$	−26.9699	+	19.7737i	−1.10846	+	0.812695i
$593$	−30.4927	−	30.4927i	−1.25219	−	1.25219i	−0.954738	−	0.297448i	$-0.903864\pi$
$593$	−30.4927	−	30.4927i	−1.25219	−	1.25219i	−0.297448	−	0.954738i	$-0.596136\pi$
$594$	3.64523	−	0.435443i	0.149566	−	0.0178664i
$595$	0.199510	+	0.0705759i	0.00817911	+	0.00289333i
$596$	15.2389	+	6.27355i	0.624210	+	0.256975i
$597$	15.2157	+	7.75277i	0.622736	+	0.317300i
$598$	−25.2202	+	16.8911i	−1.03133	+	0.690728i
$599$	−20.9517			−0.856063			−0.428032	−	0.903764i	$-0.640793\pi$
$599$	−20.9517			−0.856063			−0.428032	+	0.903764i	$0.640793\pi$
$600$	−4.49346	+	13.4093i	−0.183445	+	0.547432i
$601$	−34.4158			−1.40385			−0.701925	−	0.712251i	$-0.747676\pi$
$601$	−34.4158			−1.40385			−0.701925	+	0.712251i	$0.747676\pi$
$602$	0.0627948	−	0.0420565i	0.00255933	−	0.00171410i
$603$	2.97451	+	1.51559i	0.121131	+	0.0617194i
$604$	−41.1524	−	16.9416i	−1.67447	−	0.689344i
$605$	−9.13536	+	2.70931i	−0.371405	+	0.110149i
$606$	22.0577	−	2.63491i	0.896033	−	0.107036i
$607$	−30.1682	−	30.1682i	−1.22449	−	1.22449i	−0.966020	−	0.258469i	$-0.916782\pi$
$607$	−30.1682	−	30.1682i	−1.22449	−	1.22449i	−0.258469	−	0.966020i	$-0.583218\pi$
$608$	12.5390	−	22.6769i	0.508523	−	0.919671i
$609$	−0.141103	−	0.194211i	−0.00571777	−	0.00786984i
$610$	−0.992389	+	15.4760i	−0.0401806	+	0.626606i
$611$	−25.2862	+	34.8034i	−1.02297	+	1.40800i
$612$	−4.11342	−	4.79514i	−0.166275	−	0.193832i
$613$	−32.0453	−	5.07547i	−1.29430	−	0.204996i	−0.528971	−	0.848640i	$-0.677422\pi$
$613$	−32.0453	−	5.07547i	−1.29430	−	0.204996i	−0.765326	+	0.643643i	$0.777422\pi$
$614$	31.1092	+	6.15300i	1.25546	+	0.248315i
$615$	−0.0762758	−	0.577895i	−0.00307574	−	0.0233030i
$616$	−0.0768087	−	0.206135i	−0.00309471	−	0.00830543i
$617$	5.54357	+	10.8799i	0.223176	+	0.438007i	0.975260	−	0.221060i	$-0.0709516\pi$
$617$	5.54357	+	10.8799i	0.223176	+	0.438007i	−0.752085	+	0.659067i	$0.770952\pi$
$618$	−4.35892	−	1.60273i	−0.175342	−	0.0644714i
$619$	2.03053	−	6.24934i	0.0816140	−	0.251182i	−0.901921	−	0.431902i	$-0.857843\pi$
$619$	2.03053	−	6.24934i	0.0816140	−	0.251182i	0.983535	+	0.180720i	$0.0578427\pi$
$620$	6.18362	+	5.53987i	0.248340	+	0.222487i
$621$	−1.82276	−	5.60987i	−0.0731448	−	0.225116i
$622$	−0.947976	+	24.8121i	−0.0380104	+	0.994876i
$623$	−0.281209	+	0.0445392i	−0.0112664	+	0.00178442i
$624$	−2.33913	−	14.3659i	−0.0936402	−	0.575096i
$625$	24.8665	+	2.58030i	0.994659	+	0.103212i
$626$	−16.8478	+	7.78908i	−0.673375	+	0.311314i
$627$	1.86019	+	11.7448i	0.0742888	+	0.469041i
$628$	−6.34177	−	15.2171i	−0.253064	−	0.607230i
$629$	−25.1171	+	8.16105i	−1.00149	+	0.325402i
$630$	−0.0869971	+	0.0375226i	−0.00346605	+	0.00149494i
$631$	−12.7502	−	4.14278i	−0.507576	−	0.164921i	0.0440238	−	0.999030i	$-0.485982\pi$
$631$	−12.7502	−	4.14278i	−0.507576	−	0.164921i	−0.551599	+	0.834109i	$0.685982\pi$
$632$	36.3202	−	20.4955i	1.44474	−	0.815267i
$633$	−8.04593	+	4.09961i	−0.319797	+	0.162945i
$634$	−8.42177	−	4.70445i	−0.334471	−	0.186838i
$635$	−25.1145	+	3.31484i	−0.996637	+	0.131545i
$636$	1.68067	+	6.93433i	0.0666428	+	0.274964i
$637$	3.98409	−	25.1546i	0.157855	−	0.996660i
$638$	8.01501	+	28.3018i	0.317317	+	1.12048i
$639$	9.19257	+	6.67879i	0.363652	+	0.264209i
$640$	−20.7744	−	14.4369i	−0.821180	−	0.570670i
$641$	−5.26652	+	3.82635i	−0.208015	+	0.151132i	−0.686915	−	0.726738i	$-0.741036\pi$
$641$	−5.26652	+	3.82635i	−0.208015	+	0.151132i	0.478900	+	0.877869i	$0.341036\pi$
$642$	−13.3495	−	10.5005i	−0.526862	−	0.414420i
$643$	−24.1498	+	24.1498i	−0.952377	+	0.952377i	−0.998916	−	0.0465397i	$-0.985181\pi$
$643$	−24.1498	+	24.1498i	−0.952377	+	0.952377i	0.0465397	+	0.998916i	$0.485181\pi$
$644$	−0.300966	+	0.185329i	−0.0118597	+	0.00730300i
$645$	1.13406	+	3.82388i	0.0446536	+	0.150565i
$646$	15.0119	−	13.9070i	0.590634	−	0.547164i
$647$	16.9157	−	33.1990i	0.665026	−	1.30519i	−0.274129	−	0.961693i	$-0.588389\pi$
$647$	16.9157	−	33.1990i	0.665026	−	1.30519i	0.939155	−	0.343494i	$-0.111611\pi$
$648$	2.80989	+	0.323324i	0.110383	+	0.0127014i
$649$		−	1.90848i		−	0.0749144i
$650$	−23.8816	+	9.57611i	−0.936713	+	0.375606i
$651$			0.0556202i			0.00217993i
$652$	−35.0179	−	21.3548i	−1.37141	−	0.836320i
$653$	1.60583	−	3.15162i	0.0628409	−	0.123332i	−0.857450	−	0.514568i	$-0.827952\pi$
$653$	1.60583	−	3.15162i	0.0628409	−	0.123332i	0.920290	+	0.391236i	$0.127952\pi$
$654$	8.98668	+	9.70066i	0.351407	+	0.379326i
$655$	−7.18512	+	20.3115i	−0.280746	+	0.793636i
$656$	1.03059	+	0.158660i	0.0402379	+	0.00619461i
$657$	7.61182	−	7.61182i	0.296965	−	0.296965i
$658$	−0.309697	+	0.393724i	−0.0120732	+	0.0153490i
$659$	−0.360535	+	0.261944i	−0.0140445	+	0.0102039i	−0.594785	−	0.803885i	$-0.702763\pi$
$659$	−0.360535	+	0.261944i	−0.0140445	+	0.0102039i	0.580741	+	0.814088i	$0.302763\pi$
$660$	11.5917	−	0.636508i	0.451207	−	0.0247760i
$661$	12.6735	+	9.20784i	0.492942	+	0.358144i	0.806315	−	0.591487i	$-0.201459\pi$
$661$	12.6735	+	9.20784i	0.492942	+	0.358144i	−0.313372	+	0.949630i	$0.601459\pi$
$662$	−8.84181	+	2.50398i	−0.343647	+	0.0973200i
$663$	1.79811	−	11.3528i	0.0698329	−	0.440908i
$664$	−28.6243	+	22.7167i	−1.11084	+	0.881579i
$665$	−0.132209	−	0.276946i	−0.00512684	−	0.0107395i
$666$	5.76608	−	10.3223i	0.223431	−	0.399980i
$667$	42.1107	−	21.4565i	1.63053	−	0.830798i
$668$	−1.83327	−	22.6665i	−0.0709312	−	0.876992i
$669$	−9.38591	−	3.04967i	−0.362880	−	0.117907i
$670$	9.08023	+	5.38481i	0.350800	+	0.208033i
$671$	12.1072	−	3.93387i	0.467393	−	0.151865i
$672$	−0.0208312	−	0.168198i	−0.000803579	−	0.00648839i
$673$	−5.14603	−	32.4907i	−0.198365	−	1.25243i	−0.862979	−	0.505240i	$-0.831404\pi$
$673$	−5.14603	−	32.4907i	−0.198365	−	1.25243i	0.664614	−	0.747187i	$-0.268596\pi$
$674$	15.9283	+	34.4531i	0.613536	+	1.32708i
$675$	−0.525934	−	4.97226i	−0.0202432	−	0.191382i
$676$	0.311779	−	0.366651i	0.0119915	−	0.0141020i
$677$	9.54108	−	1.51116i	0.366693	−	0.0580785i	0.0296312	−	0.999561i	$-0.490567\pi$
$677$	9.54108	−	1.51116i	0.366693	−	0.0580785i	0.337062	+	0.941482i	$0.390567\pi$
$678$	1.61021	+	0.0615201i	0.0618399	+	0.00236266i
$679$	0.0594729	+	0.183039i	0.00228236	+	0.00702439i
$680$	−12.0107	−	15.9649i	−0.460591	−	0.612225i
$681$	−7.77962	+	23.9432i	−0.298116	+	0.917506i
$682$	2.35196	−	6.39657i	0.0900611	−	0.244937i
$683$	0.657454	+	1.29033i	0.0251568	+	0.0493729i	0.903243	−	0.429130i	$-0.141180\pi$
$683$	0.657454	+	1.29033i	0.0251568	+	0.0493729i	−0.878086	+	0.478503i	$0.841180\pi$
$684$	−0.699034	+	9.13483i	−0.0267282	+	0.349279i
$685$	0.626670	+	0.115932i	0.0239438	+	0.00442953i
$686$	0.115089	−	0.581881i	0.00439411	−	0.0222163i
$687$	9.71297	+	1.53838i	0.370573	+	0.0586930i
$688$	−7.13478	+	0.0308885i	−0.272011	+	0.00117761i
$689$	−7.63032	+	10.5022i	−0.290692	+	0.400103i
$690$	−4.61702	−	18.0725i	−0.175767	−	0.688007i
$691$	8.30255	+	11.4275i	0.315844	+	0.434722i	0.937193	−	0.348812i	$-0.113415\pi$
$691$	8.30255	+	11.4275i	0.315844	+	0.434722i	−0.621349	+	0.783534i	$0.713415\pi$
$692$	−38.5696	−	9.17149i	−1.46620	−	0.348648i
$693$	0.0549951	+	0.0549951i	0.00208909	+	0.00208909i
$694$	−1.91044	−	15.9929i	−0.0725193	−	0.607082i
$695$	−9.37299	+	12.2235i	−0.355538	+	0.463664i
$696$	0.963252	+	22.6421i	0.0365120	+	0.858248i
$697$	0.733711	+	0.373844i	0.0277913	+	0.0141604i
$698$	−2.95195	−	4.40756i	−0.111733	−	0.166829i
$699$	−11.3333			−0.428664
$700$	−0.282138	+	0.100809i	−0.0106638	+	0.00381021i
$701$	21.3510			0.806416			0.403208	−	0.915108i	$-0.367895\pi$
$701$	21.3510			0.806416			0.403208	+	0.915108i	$0.367895\pi$
$702$	2.86359	+	4.27564i	0.108079	+	0.161374i
$703$	34.1234	+	17.3868i	1.28699	+	0.655754i
$704$	−4.71676	+	20.2244i	−0.177770	+	0.762236i
$705$	−14.9807	−	21.7816i	−0.564206	−	0.820343i
$706$	5.09548	+	42.6559i	0.191771	+	1.60538i
$707$	0.332782	+	0.332782i	0.0125155	+	0.0125155i
$708$	0.340159	−	1.43050i	0.0127839	−	0.0537614i
$709$	−12.7559	−	17.5570i	−0.479057	−	0.659366i	0.499266	−	0.866449i	$-0.333603\pi$
$709$	−12.7559	−	17.5570i	−0.479057	−	0.659366i	−0.978323	+	0.207083i	$0.933603\pi$
$710$	27.6583	+	22.9371i	1.03800	+	0.860816i
$711$	−8.66666	+	11.9286i	−0.325025	+	0.447358i
$712$	24.4458	+	11.1736i	0.916145	+	0.418747i
$713$	−10.8155	−	1.71301i	−0.405044	−	0.0641527i
$714$	0.0259695	−	0.131300i	0.000971883	−	0.00491377i
$715$	14.5442	+	15.3162i	0.543922	+	0.572795i
$716$	−29.4911	−	2.25678i	−1.10213	−	0.0843398i
$717$	9.03758	+	17.7373i	0.337515	+	0.662410i
$718$	−1.10286	+	2.99941i	−0.0411582	+	0.111937i
$719$	−6.74838	+	20.7694i	−0.251672	+	0.774567i	0.742795	+	0.669519i	$0.233500\pi$
$719$	−6.74838	+	20.7694i	−0.251672	+	0.774567i	−0.994467	+	0.105048i	$0.966500\pi$
$720$	8.80200	+	1.58896i	0.328031	+	0.0592171i
$721$	−0.0304042	−	0.0935746i	−0.00113231	−	0.00348490i
$722$	−2.80294	−	0.107089i	−0.104315	−	0.00398546i
$723$	−18.2937	+	2.89744i	−0.680351	+	0.107757i
$724$	23.3413	+	19.8481i	0.867472	+	0.737650i
$725$	38.6902	−	10.3945i	1.43692	−	0.386041i
$726$	2.52895	+	5.47014i	0.0938582	+	0.203016i
$727$	−1.62027	−	10.2300i	−0.0600925	−	0.379409i	−0.999345	−	0.0361826i	$-0.988480\pi$
$727$	−1.62027	−	10.2300i	−0.0600925	−	0.379409i	0.939253	−	0.343226i	$-0.111520\pi$
$728$	0.208576	−	0.227111i	0.00773033	−	0.00841729i
$729$	−0.951057	+	0.309017i	−0.0352243	+	0.0114451i
$730$	25.5617	−	22.4810i	0.946081	−	0.832059i
$731$	−5.35872	−	1.74115i	−0.198199	−	0.0643989i
$732$	9.77608	−	0.790690i	0.361334	−	0.0292248i
$733$	7.04429	−	3.58925i	0.260187	−	0.132572i	−0.319032	−	0.947744i	$-0.603358\pi$
$733$	7.04429	−	3.58925i	0.260187	−	0.132572i	0.579219	+	0.815172i	$0.303358\pi$
$734$	17.4423	−	31.2247i	0.643808	−	1.15253i
$735$	13.7564	+	7.46321i	0.507411	+	0.275284i
$736$	33.3482	+	1.12955i	1.22923	+	0.0416356i
$737$	1.35567	−	8.55935i	0.0499366	−	0.315288i
$738$	−0.354713	+	0.100454i	−0.0130572	+	0.00369776i
$739$	−39.2364	−	28.5069i	−1.44334	−	1.04864i	−0.987332	−	0.158666i	$-0.949281\pi$
$739$	−39.2364	−	28.5069i	−1.44334	−	1.04864i	−0.456003	−	0.889978i	$-0.650719\pi$
$740$	20.2854	−	31.4081i	0.745707	−	1.15459i
$741$	−13.4850	+	9.79741i	−0.495383	+	0.359917i
$742$	−0.0934537	+	0.118810i	−0.00343079	+	0.00436164i
$743$	−22.8092	+	22.8092i	−0.836787	+	0.836787i	−0.988435	−	0.151648i	$-0.951542\pi$
$743$	−22.8092	+	22.8092i	−0.836787	+	0.836787i	0.151648	+	0.988435i	$0.451542\pi$
$744$	2.90300	−	4.37533i	0.106429	−	0.160407i
$745$	−18.4188	−	0.476212i	−0.674811	−	0.0174471i
$746$	16.8562	+	18.1954i	0.617151	+	0.666182i
$747$	5.86554	−	11.5118i	0.214609	−	0.421193i
$748$	−8.53874	+	14.0019i	−0.312207	+	0.511960i
$749$		−	0.359821i		−	0.0131476i
$750$	−0.653537	−	15.7979i	−0.0238638	−	0.576857i
$751$		−	46.1937i		−	1.68563i	−0.538201	−	0.842816i	$-0.680896\pi$
$751$		−	46.1937i		−	1.68563i	0.538201	−	0.842816i	$-0.319104\pi$
$752$	44.9118	−	14.8080i	1.63777	−	0.539993i
$753$	5.24017	−	10.2844i	0.190962	−	0.374785i
$754$	−30.2473	+	28.0211i	−1.10154	+	1.02047i
$755$	49.7395	+	1.28600i	1.81021	+	0.0468024i
$756$	0.0314194	+	0.0510235i	0.00114271	+	0.00185571i
$757$	−8.32615	+	8.32615i	−0.302619	+	0.302619i	−0.842038	−	0.539419i	$-0.818644\pi$
$757$	−8.32615	+	8.32615i	−0.302619	+	0.302619i	0.539419	+	0.842038i	$0.318644\pi$
$758$	−26.2648	−	20.6594i	−0.953979	−	0.750383i
$759$	−12.3877	+	9.00020i	−0.449645	+	0.326686i
$760$	−4.05456	+	28.6862i	−0.147074	+	1.04056i
$761$	29.2453	+	21.2480i	1.06014	+	0.770239i	0.974115	−	0.226054i	$-0.0725825\pi$
$761$	29.2453	+	21.2480i	1.06014	+	0.770239i	0.0860281	+	0.996293i	$0.472583\pi$
$762$	4.36558	+	15.4153i	0.158148	+	0.558437i
$763$	−0.0438247	+	0.276698i	−0.00158656	+	0.0100171i
$764$	44.6912	−	10.8318i	1.61687	−	0.391880i
$765$	6.20857	+	3.36832i	0.224471	+	0.121782i
$766$	7.14075	+	3.98887i	0.258006	+	0.144124i
$767$	2.38362	−	1.21451i	0.0860674	−	0.0438535i
$768$	−7.14014	+	14.3185i	−0.257648	+	0.516673i
$769$	−16.5650	−	5.38228i	−0.597348	−	0.194090i	−0.00529061	−	0.999986i	$-0.501684\pi$
$769$	−16.5650	−	5.38228i	−0.597348	−	0.194090i	−0.592057	+	0.805896i	$0.701684\pi$
$770$	0.162424	+	0.184682i	0.00585336	+	0.00665549i
$771$	9.81358	−	3.18863i	0.353427	−	0.114836i
$772$	21.9587	−	9.15132i	0.790310	−	0.329363i
$773$	0.778227	+	4.91353i	0.0279909	+	0.176728i	0.997723	−	0.0674434i	$-0.0214842\pi$
$773$	0.778227	+	4.91353i	0.0279909	+	0.176728i	−0.969732	+	0.244171i	$0.921484\pi$
$774$	2.28969	−	1.05857i	0.0823013	−	0.0380495i
$775$	−8.66788	−	3.32071i	−0.311359	−	0.119283i
$776$	4.87498	−	17.5027i	0.175002	−	0.628311i
$777$	0.247403	−	0.0391849i	0.00887555	−	0.00140575i
$778$	1.15488	−	30.2276i	0.0414045	−	1.08371i
$779$	−0.369007	−	1.13569i	−0.0132210	−	0.0406902i
$780$	8.17168	+	14.0725i	0.292593	+	0.503878i
$781$	9.11482	−	28.0525i	0.326154	−	1.00380i
$782$	24.7318	+	9.09365i	0.884408	+	0.325188i
$783$	−3.63757	−	7.13914i	−0.129996	−	0.255132i
$784$	−19.7106	+	19.8820i	−0.703949	+	0.710070i
$785$	12.6919	+	13.3656i	0.452994	+	0.477039i
$786$	13.3672	+	2.64387i	0.476794	+	0.0943039i
$787$	−17.8401	−	2.82559i	−0.635930	−	0.100721i	−0.169858	−	0.985468i	$-0.554331\pi$
$787$	−17.8401	−	2.82559i	−0.635930	−	0.100721i	−0.466071	+	0.884747i	$0.654331\pi$
$788$	−22.6806	+	19.4561i	−0.807962	+	0.693095i
$789$	−7.45513	+	10.2611i	−0.265410	+	0.365305i
$790$	−29.7641	+	35.8905i	−1.05896	+	1.27693i
$791$	0.0200658	+	0.0276182i	0.000713457	+	0.000981989i
$792$	−1.45578	−	7.19652i	−0.0517291	−	0.255717i
$793$	12.6180	+	12.6180i	0.448078	+	0.448078i
$794$	9.88176	−	1.18043i	0.350690	−	0.0418919i
$795$	−4.52055	−	6.57279i	−0.160328	−	0.233113i
$796$	13.0018	−	31.5823i	0.460836	−	1.11940i
$797$	11.5754	+	5.89797i	0.410022	+	0.208917i	0.646821	−	0.762642i	$-0.276098\pi$
$797$	11.5754	+	5.89797i	0.410022	+	0.208917i	−0.236799	+	0.971559i	$0.576098\pi$
$798$	−0.161264	+	0.108006i	−0.00570868	+	0.00382336i
$799$	37.3456			1.32119
$800$	27.4558	+	6.79564i	0.970708	+	0.240262i
$801$	−9.50293			−0.335770
$802$	36.1993	−	24.2443i	1.27824	−	0.856097i
$803$	−24.8984	−	12.6864i	−0.878644	−	0.447692i
$804$	2.54172	−	6.17401i	0.0896394	−	0.217741i
$805$	0.240460	−	0.313589i	0.00847511	−	0.0110526i
$806$	9.48579	−	1.13313i	0.334123	−	0.0399128i
$807$	−13.4675	−	13.4675i	−0.474080	−	0.474080i
$808$	−8.80912	−	43.5470i	−0.309904	−	1.53198i
$809$	−21.2576	−	29.2586i	−0.747379	−	1.02868i	−0.998160	−	0.0606351i	$-0.980687\pi$
$809$	−21.2576	−	29.2586i	−0.747379	−	1.02868i	0.250781	−	0.968044i	$-0.419313\pi$
$810$	−3.06387	+	0.782736i	−0.107654	+	0.0275025i
$811$	−30.8598	+	42.4749i	−1.08364	+	1.49150i	−0.228180	+	0.973619i	$0.573277\pi$
$811$	−30.8598	+	42.4749i	−1.08364	+	1.49150i	−0.855455	+	0.517877i	$0.826723\pi$
$812$	−0.364408	+	0.312600i	−0.0127882	+	0.0109701i
$813$	−18.3620	−	2.90826i	−0.643984	−	0.101997i
$814$	−30.1094	−	5.95527i	−1.05534	−	0.208732i
$815$	45.0917	+	8.34182i	1.57949	+	0.292201i
$816$	−8.89583	+	8.97319i	−0.311416	+	0.314125i
$817$	3.70945	+	7.28021i	0.129777	+	0.254702i
$818$	−2.05177	−	0.754415i	−0.0717383	−	0.0263775i
$819$	−0.0336891	+	0.103684i	−0.00117719	+	0.00362302i
$820$	−1.13973	+	0.245231i	−0.0398011	+	0.00856385i
$821$	−2.47595	−	7.62021i	−0.0864114	−	0.265947i	0.898509	−	0.438955i	$-0.144651\pi$
$821$	−2.47595	−	7.62021i	−0.0864114	−	0.265947i	−0.984920	+	0.173008i	$0.944651\pi$
$822$	0.0153884	−	0.402772i	0.000536731	−	0.0140483i
$823$	−33.6993	+	5.33745i	−1.17468	+	0.186052i	−0.713111	−	0.701051i	$-0.752715\pi$
$823$	−33.6993	+	5.33745i	−1.17468	+	0.186052i	−0.461573	+	0.887102i	$0.652715\pi$
$824$	−2.49223	+	8.94789i	−0.0868209	+	0.311714i
$825$	−11.8538	+	5.28707i	−0.412697	+	0.184072i
$826$	0.0282752	−	0.0130722i	0.000983819	−	0.000454839i
$827$	2.27430	+	14.3594i	0.0790852	+	0.499325i	0.995156	+	0.0983080i	$0.0313430\pi$
$827$	2.27430	+	14.3594i	0.0790852	+	0.499325i	−0.916071	+	0.401017i	$0.868657\pi$
$828$	−10.8893	+	4.53815i	−0.378431	+	0.157712i
$829$	−9.98390	+	3.24396i	−0.346755	+	0.112668i	−0.477216	−	0.878786i	$-0.658354\pi$
$829$	−9.98390	+	3.24396i	−0.346755	+	0.112668i	0.130461	+	0.991453i	$0.458354\pi$
$830$	20.8400	−	35.1418i	0.723367	−	1.21979i
$831$	−26.7911	−	8.70494i	−0.929372	−	0.301971i
$832$	−28.2611	+	6.97930i	−0.979778	+	0.241964i
$833$	−19.6994	+	10.0374i	−0.682544	+	0.347774i
$834$	8.50501	+	4.75095i	0.294505	+	0.164512i
$835$	10.9532	+	22.9443i	0.379051	+	0.794020i
$836$	23.1132	−	5.60193i	0.799386	−	0.193747i
$837$	−0.290411	+	1.83358i	−0.0100381	+	0.0633779i
$838$	−6.14050	−	21.6827i	−0.212120	−	0.749017i
$839$	22.2107	+	16.1370i	0.766797	+	0.557111i	0.900988	−	0.433845i	$-0.142843\pi$
$839$	22.2107	+	16.1370i	0.766797	+	0.557111i	−0.134191	+	0.990956i	$0.542843\pi$
$840$	0.0888279	+	0.167378i	0.00306485	+	0.00577509i
$841$	28.4768	−	20.6896i	0.981957	−	0.713434i
$842$	3.58158	+	2.81721i	0.123429	+	0.0970875i
$843$	9.50230	−	9.50230i	0.327277	−	0.327277i
$844$	9.46980	+	15.3785i	0.325964	+	0.529350i
$845$	−0.179453	+	0.507293i	−0.00617337	+	0.0174514i
$846$	−12.2653	+	11.3625i	−0.421688	+	0.390652i
$847$	−0.0579622	+	0.113757i	−0.00199161	+	0.00390875i
$848$	13.5525	−	4.46844i	0.465396	−	0.153447i
$849$		−	10.8415i		−	0.372080i
$850$	18.9114	+	11.8861i	0.648654	+	0.407690i
$851$			49.3152i			1.69050i
$852$	11.8320	−	19.4021i	0.405356	−	0.664706i
$853$	10.4218	−	20.4539i	0.356836	−	0.700329i	−0.640897	−	0.767627i	$-0.721438\pi$
$853$	10.4218	−	20.4539i	0.356836	−	0.700329i	0.997733	+	0.0672973i	$0.0214376\pi$
$854$	0.141211	+	0.152430i	0.00483213	+	0.00521604i
$855$	−2.91239	−	9.82014i	−0.0996017	−	0.335842i
$856$	−18.7802	+	28.3051i	−0.641894	+	0.967447i
$857$	7.96786	−	7.96786i	0.272177	−	0.272177i	−0.557799	−	0.829976i	$-0.688354\pi$
$857$	7.96786	−	7.96786i	0.272177	−	0.272177i	0.829976	+	0.557799i	$0.188354\pi$
$858$	8.25878	−	10.4996i	0.281950	−	0.358449i
$859$	9.67439	−	7.02885i	0.330086	−	0.239821i	−0.410381	−	0.911914i	$-0.634604\pi$
$859$	9.67439	−	7.02885i	0.330086	−	0.239821i	0.740467	+	0.672093i	$0.234604\pi$
$860$	7.44002	−	2.87728i	0.253702	−	0.0981144i
$861$	−0.00631864	−	0.00459076i	−0.000215339	−	0.000156453i
$862$	−42.6594	+	12.0810i	−1.45298	+	0.411482i
$863$	−6.25940	+	39.5203i	−0.213073	+	1.34529i	0.616706	+	0.787194i	$0.288467\pi$
$863$	−6.25940	+	39.5203i	−0.213073	+	1.34529i	−0.829778	+	0.558093i	$0.811533\pi$
$864$	0.191495	−	5.65361i	0.00651479	−	0.192340i
$865$	43.9434	−	5.80005i	1.49412	−	0.197208i
$866$	19.4187	−	34.7627i	0.659873	−	1.18129i
$867$	6.25631	−	3.18775i	0.212475	−	0.108262i
$868$	0.110878	−	0.00896786i	0.00376346	−	0.000304389i
$869$	36.4021	+	11.8277i	1.23486	+	0.401229i
$870$	−10.0347	−	23.2658i	−0.340209	−	0.788784i
$871$	11.5530	−	3.75380i	0.391458	−	0.127193i
$872$	17.8892	−	19.4789i	0.605805	−	0.659640i
$873$	1.00489	+	6.34461i	0.0340103	+	0.214732i
$874$	−16.0354	−	34.6846i	−0.542405	−	1.17323i
$875$	0.254498	−	0.217799i	0.00860359	−	0.00736295i
$876$	−16.4014	−	13.9468i	−0.554151	−	0.471219i
$877$	5.40297	−	0.855747i	0.182445	−	0.0288965i	−0.0645431	−	0.997915i	$-0.520559\pi$
$877$	5.40297	−	0.855747i	0.182445	−	0.0288965i	0.246989	+	0.969018i	$0.420559\pi$
$878$	−44.2229	−	1.68959i	−1.49245	−	0.0570208i
$879$	0.402821	+	1.23976i	0.0135868	+	0.0418159i
$880$	−3.13785	−	23.0054i	−0.105777	−	0.775511i
$881$	−16.7420	+	51.5264i	−0.564051	+	1.73597i	0.106705	+	0.994291i	$0.465970\pi$
$881$	−16.7420	+	51.5264i	−0.564051	+	1.73597i	−0.670755	+	0.741679i	$0.734030\pi$
$882$	3.41589	−	9.29013i	0.115019	−	0.312815i
$883$	20.7386	+	40.7019i	0.697911	+	1.36973i	0.918916	+	0.394454i	$0.129066\pi$
$883$	20.7386	+	40.7019i	0.697911	+	1.36973i	−0.221005	+	0.975273i	$0.570934\pi$
$884$	−22.9217	−	1.75406i	−0.770940	−	0.0589954i
$885$	0.215117	+	1.62980i	0.00723106	+	0.0547853i
$886$	10.7263	−	54.2316i	0.360358	−	1.82195i
$887$	−26.6295	−	4.21771i	−0.894133	−	0.141617i	−0.307575	−	0.951524i	$-0.599517\pi$
$887$	−26.6295	−	4.21771i	−0.894133	−	0.141617i	−0.586558	+	0.809907i	$0.699517\pi$
$888$	−21.5070	−	9.83033i	−0.721729	−	0.329884i
$889$	−0.199508	+	0.274599i	−0.00669128	+	0.00920976i
$890$	−29.9893	−	1.92304i	−1.00524	−	0.0644605i
$891$	1.52583	+	2.10012i	0.0511171	+	0.0703567i
$892$	−4.56616	+	19.2024i	−0.152886	+	0.642945i
$893$	−38.2942	−	38.2942i	−1.28147	−	1.28147i
$894$	1.38218	+	11.5707i	0.0462270	+	0.386981i
$895$	31.7036	−	9.40244i	1.05973	−	0.314289i
$896$	−0.331943	+	0.0686459i	−0.0110894	+	0.00229330i
$897$	−19.1241	−	9.74424i	−0.638537	−	0.325351i
$898$	25.7530	+	38.4519i	0.859388	+	1.28316i
$899$	−14.8746			−0.496096
$900$	−9.82736	+	1.85014i	−0.327579	+	0.0616713i
$901$	11.2694			0.375437
$902$	0.532546	+	0.795147i	0.0177319	+	0.0264755i
$903$	0.0476165	+	0.0242618i	0.00158458	+	0.000807383i
$904$	−0.136981	−	3.21986i	−0.00455592	−	0.107091i
$905$	−32.2946	−	11.4241i	−1.07351	−	0.379750i
$906$	−3.73255	−	31.2464i	−0.124006	−	1.03809i
$907$	−8.52774	−	8.52774i	−0.283159	−	0.283159i	0.551209	−	0.834368i	$-0.314167\pi$
$907$	−8.52774	−	8.52774i	−0.283159	−	0.283159i	−0.834368	+	0.551209i	$0.814167\pi$
$908$	48.9849	+	11.6481i	1.62562	+	0.386557i
$909$	9.23296	+	12.7081i	0.306238	+	0.421500i
$910$	−0.127298	+	0.320389i	−0.00421988	+	0.0106208i
$911$	30.7632	−	42.3419i	1.01923	−	1.40285i	0.106487	−	0.994314i	$-0.466040\pi$
$911$	30.7632	−	42.3419i	1.01923	−	1.40285i	0.912742	−	0.408535i	$-0.133960\pi$
$912$	18.3229	−	0.0793251i	0.606732	−	0.00262672i
$913$	−33.1259	−	5.24663i	−1.09631	−	0.173638i
$914$	2.75924	−	13.9505i	0.0912674	−	0.461442i
$915$	−9.89590	+	4.72412i	−0.327148	+	0.156175i
$916$	1.50069	−	19.6107i	0.0495843	−	0.647957i
$917$	0.131057	+	0.257213i	0.00432787	+	0.00849392i
$918$	1.54167	−	4.19285i	0.0508827	−	0.138385i
$919$	2.30130	−	7.08267i	0.0759129	−	0.233636i	−0.905898	−	0.423495i	$-0.860803\pi$
$919$	2.30130	−	7.08267i	0.0759129	−	0.233636i	0.981811	+	0.189859i	$0.0608031\pi$
$920$	−35.2829	+	12.1179i	−1.16324	+	0.399515i
$921$	6.92929	+	21.3262i	0.228328	+	0.702721i
$922$	−35.0671	−	1.33978i	−1.15487	−	0.0441233i
$923$	40.8370	−	6.46794i	1.34417	−	0.212895i
$924$	0.100765	−	0.118499i	0.00331493	−	0.00389834i
$925$	−8.66419	+	40.8949i	−0.284877	+	1.34462i
$926$	17.6036	+	38.0768i	0.578491	+	1.25128i
$927$	−0.513727	−	3.24354i	−0.0168730	−	0.106532i
$928$	44.9815	−	5.57091i	1.47659	−	0.182874i
$929$	−8.13021	+	2.64167i	−0.266744	+	0.0866703i	−0.439335	−	0.898323i	$-0.644786\pi$
$929$	−8.13021	+	2.64167i	−0.266744	+	0.0866703i	0.172592	+	0.984993i	$0.444786\pi$
$930$	−1.28753	+	5.72765i	−0.0422197	+	0.187817i
$931$	30.4921	+	9.90747i	0.999337	+	0.324704i
$932$	1.82731	+	22.5928i	0.0598554	+	0.740051i
$933$	−15.6440	+	7.97099i	−0.512160	+	0.260959i
$934$	27.5589	−	49.3352i	0.901756	−	1.61430i
$935$	3.33548	−	18.0299i	0.109082	−	0.589642i
$936$	8.06175	−	6.39792i	0.263506	−	0.209123i
$937$	−4.86156	+	30.6947i	−0.158820	+	1.00275i	0.771560	+	0.636156i	$0.219477\pi$
$937$	−4.86156	+	30.6947i	−0.158820	+	1.00275i	−0.930381	+	0.366595i	$0.880523\pi$
$938$	0.136097	−	0.0385424i	0.00444373	−	0.00125845i
$939$	−10.6182	−	7.71455i	−0.346511	−	0.251755i
$940$	−41.0060	+	33.3758i	−1.33747	+	1.08860i
$941$	13.4123	−	9.74458i	0.437227	−	0.317664i	−0.347305	−	0.937752i	$-0.612903\pi$
$941$	13.4123	−	9.74458i	0.437227	−	0.317664i	0.784532	+	0.620088i	$0.212903\pi$
$942$	7.20698	−	9.16238i	0.234816	−	0.298527i
$943$	1.08729	−	1.08729i	0.0354071	−	0.0354071i
$944$	−2.90653	−	0.447459i	−0.0945994	−	0.0145635i
$945$	−0.0531636	−	0.0407659i	−0.00172941	−	0.00132611i
$946$	−4.45017	−	4.80373i	−0.144688	−	0.156183i
$947$	−9.06273	+	17.7866i	−0.294499	+	0.577987i	−0.990087	−	0.140454i	$-0.955144\pi$
$947$	−9.06273	+	17.7866i	−0.294499	+	0.577987i	0.695588	+	0.718441i	$0.255144\pi$
$948$	25.1770	+	15.3536i	0.817710	+	0.498662i
$949$		−	39.1704i		−	1.27152i
$950$	−7.20368	−	31.5797i	−0.233718	−	1.02458i
$951$		−	6.82122i		−	0.221193i
$952$	−0.265932	−	0.0305999i	−0.00861891	−	0.000991749i
$953$	−3.35084	+	6.57639i	−0.108544	+	0.213030i	−0.938889	−	0.344220i	$-0.888143\pi$
$953$	−3.35084	+	6.57639i	−0.108544	+	0.213030i	0.830345	+	0.557250i	$0.188143\pi$
$954$	−3.70115	+	3.42874i	−0.119829	+	0.111010i
$955$	−42.3611	+	29.1346i	−1.37077	+	0.942774i
$956$	33.9019	−	20.8762i	1.09647	−	0.675184i
$957$	−14.7074	+	14.7074i	−0.475423	+	0.475423i
$958$	6.01526	+	4.73150i	0.194344	+	0.152868i
$959$	0.00690829	−	0.00501917i	0.000223080	−	0.000162077i
$960$	1.74840	−	17.8029i	0.0564294	−	0.574586i
$961$	−22.2914	−	16.1956i	−0.719076	−	0.522439i
$962$	−11.7231	−	41.3953i	−0.377967	−	1.33464i
$963$	1.87874	−	11.8619i	0.0605415	−	0.382244i
$964$	8.72559	+	36.0012i	0.281032	+	1.15952i
$965$	−19.2869	+	18.3147i	−0.620867	+	0.589571i
$966$	−0.218193	−	0.121884i	−0.00702023	−	0.00392154i
$967$	−11.2886	+	5.75184i	−0.363018	+	0.184967i	−0.625980	−	0.779839i	$-0.715301\pi$
$967$	−11.2886	+	5.75184i	−0.363018	+	0.184967i	0.262962	+	0.964806i	$0.415301\pi$
$968$	10.4969	−	5.92341i	0.337384	−	0.190386i
$969$	13.7618	+	4.47147i	0.442092	+	0.143644i
$970$	1.88730	+	20.2256i	0.0605977	+	0.649406i
$971$	−22.4953	+	7.30917i	−0.721909	+	0.234563i	−0.646851	−	0.762617i	$-0.723914\pi$
$971$	−22.4953	+	7.30917i	−0.721909	+	0.234563i	−0.0750585	+	0.997179i	$0.523914\pi$
$972$	0.769365	+	1.84610i	0.0246774	+	0.0592136i
$973$	0.0322863	+	0.203848i	0.00103505	+	0.00653505i
$974$	−43.9644	+	20.3256i	−1.40871	+	0.651275i
$975$	−14.1469	−	11.4404i	−0.453062	−	0.366386i
$976$	−3.15247	−	19.3610i	−0.100908	−	0.619731i
$977$	17.2253	−	2.72822i	0.551087	−	0.0872836i	0.125320	−	0.992116i	$-0.460004\pi$
$977$	17.2253	−	2.72822i	0.551087	−	0.0872836i	0.425767	+	0.904833i	$0.360004\pi$
$978$	1.10726	−	28.9813i	0.0354064	−	0.926719i
$979$	7.62301	+	23.4612i	0.243633	+	0.749824i
$980$	12.6598	−	28.6265i	0.404404	−	0.914440i
$981$	−2.88946	+	8.89284i	−0.0922533	+	0.283927i
$982$	20.1956	+	7.42572i	0.644466	+	0.236964i
$983$	−15.5561	−	30.5305i	−0.496162	−	0.973773i	−0.994294	−	0.106672i	$-0.965981\pi$
$983$	−15.5561	−	30.5305i	−0.496162	−	0.973773i	0.498132	−	0.867101i	$-0.334019\pi$
$984$	0.257446	+	0.690920i	0.00820706	+	0.0220257i
$985$	15.9319	−	29.3660i	0.507631	−	0.935679i
$986$	35.1137	+	6.94506i	1.11825	+	0.221176i
$987$	−0.349850	−	0.0554108i	−0.0111359	−	0.00176375i
$988$	21.7053	+	25.3025i	0.690537	+	0.804980i
$989$	−6.18429	+	8.51195i	−0.196649	+	0.270664i
$990$	4.39021	+	6.93633i	0.139530	+	0.220451i
$991$	6.27760	+	8.64037i	0.199414	+	0.274470i	0.897000	−	0.442032i	$-0.145742\pi$
$991$	6.27760	+	8.64037i	0.199414	+	0.274470i	−0.697585	+	0.716502i	$0.745742\pi$
$992$	−9.19024	−	5.08165i	−0.291791	−	0.161343i
$993$	−4.59477	−	4.59477i	−0.145811	−	0.145811i
$994$	0.478046	−	0.0571052i	0.0151627	−	0.00181127i
$995$	−0.986939	+	38.1724i	−0.0312881	+	1.21015i
$996$	−23.8943	−	9.83680i	−0.757120	−	0.311691i
$997$	−8.62027	−	4.39225i	−0.273007	−	0.139104i	0.312128	−	0.950040i	$-0.398958\pi$
$997$	−8.62027	−	4.39225i	−0.273007	−	0.139104i	−0.585135	+	0.810936i	$0.698958\pi$
$998$	−3.40871	+	2.28297i	−0.107901	+	0.0722661i
$999$	8.36053			0.264515

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.w.a.163.24	yes	240
3.2	odd	2		900.2.bj.f.163.7		240
4.3	odd	2	inner	300.2.w.a.163.28	yes	240
12.11	even	2		900.2.bj.f.163.3		240
25.2	odd	20	inner	300.2.w.a.127.28	yes	240
75.2	even	20		900.2.bj.f.127.3		240
100.27	even	20	inner	300.2.w.a.127.24	✓	240
300.227	odd	20		900.2.bj.f.127.7		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.w.a.127.24	✓	240	100.27	even	20	inner
300.2.w.a.127.28	yes	240	25.2	odd	20	inner
300.2.w.a.163.24	yes	240	1.1	even	1	trivial
300.2.w.a.163.28	yes	240	4.3	odd	2	inner
900.2.bj.f.127.3		240	75.2	even	20
900.2.bj.f.127.7		240	300.227	odd	20
900.2.bj.f.163.3		240	12.11	even	2
900.2.bj.f.163.7		240	3.2	odd	2

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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.17502 - 0.786967i) q^{2} +(0.891007 + 0.453990i) q^{3} +(0.761365 - 1.84941i) q^{4} +(-0.0577937 + 2.23532i) q^{5} +(1.40423 - 0.167743i) q^{6} +(0.0211854 + 0.0211854i) q^{7} +(-0.560803 - 2.77227i) q^{8} +(0.587785 + 0.809017i) q^{9} +O(q^{10})\)	\(q+(1.17502 - 0.786967i) q^{2} +(0.891007 + 0.453990i) q^{3} +(0.761365 - 1.84941i) q^{4} +(-0.0577937 + 2.23532i) q^{5} +(1.40423 - 0.167743i) q^{6} +(0.0211854 + 0.0211854i) q^{7} +(-0.560803 - 2.77227i) q^{8} +(0.587785 + 0.809017i) q^{9} +(1.69122 + 2.67204i) q^{10} +(1.52583 - 2.10012i) q^{11} +(1.51800 - 1.30219i) q^{12} +(3.59397 + 0.569229i) q^{13} +(0.0415656 + 0.00822116i) q^{14} +(-1.06631 + 1.96545i) q^{15} +(-2.84065 - 2.81616i) q^{16} +(-1.43409 - 2.81456i) q^{17} +(1.32733 + 0.488047i) q^{18} +(-1.41553 + 4.35657i) q^{19} +(4.09003 + 1.80878i) q^{20} +(0.00925837 + 0.0284943i) q^{21} +(0.140158 - 3.66847i) q^{22} +(-5.82595 + 0.922739i) q^{23} +(0.758907 - 2.72471i) q^{24} +(-4.99332 - 0.258375i) q^{25} +(4.67097 - 2.15948i) q^{26} +(0.156434 + 0.987688i) q^{27} +(0.0553104 - 0.0230507i) q^{28} +(-7.62028 + 2.47598i) q^{29} +(0.293804 + 3.14860i) q^{30} +(1.76558 + 0.573671i) q^{31} +(-5.55405 - 1.07356i) q^{32} +(2.31296 - 1.17851i) q^{33} +(-3.90006 - 2.17860i) q^{34} +(-0.0485806 + 0.0461318i) q^{35} +(1.94372 - 0.471099i) q^{36} +(1.30788 - 8.25760i) q^{37} +(1.76519 + 6.23305i) q^{38} +(2.94383 + 2.13882i) q^{39} +(6.22933 - 1.09336i) q^{40} +(-0.210898 + 0.153226i) q^{41} +(0.0333029 + 0.0261955i) q^{42} +(1.26128 - 1.26128i) q^{43} +(-2.72228 - 4.42084i) q^{44} +(-1.84238 + 1.26713i) q^{45} +(-6.11947 + 5.66907i) q^{46} +(-5.36731 + 10.5339i) q^{47} +(-1.25253 - 3.79884i) q^{48} -6.99910i q^{49} +(-6.07061 + 3.62598i) q^{50} -3.15886i q^{51} +(3.78906 - 6.21334i) q^{52} +(-1.61963 + 3.17871i) q^{53} +(0.961093 + 1.03745i) q^{54} +(4.60626 + 3.53209i) q^{55} +(0.0468509 - 0.0706126i) q^{56} +(-3.23909 + 3.23909i) q^{57} +(-7.00551 + 8.90625i) q^{58} +(0.594783 - 0.432135i) q^{59} +(2.82307 + 3.46847i) q^{60} +(3.96742 + 2.88250i) q^{61} +(2.52606 - 0.715375i) q^{62} +(-0.00468689 + 0.0295918i) q^{63} +(-7.37100 + 3.10940i) q^{64} +(-1.48012 + 8.00078i) q^{65} +(1.79033 - 3.20500i) q^{66} +(2.97451 - 1.51559i) q^{67} +(-6.29715 + 0.509314i) q^{68} +(-5.60987 - 1.82276i) q^{69} +(-0.0207792 + 0.0924374i) q^{70} +(10.8065 - 3.51125i) q^{71} +(1.91318 - 2.08320i) q^{72} +(-1.68398 - 10.6322i) q^{73} +(-4.96167 - 10.7321i) q^{74} +(-4.33178 - 2.49713i) q^{75} +(6.97935 + 5.93485i) q^{76} +(0.0768172 - 0.0121667i) q^{77} +(5.14225 + 0.196465i) q^{78} +(4.55633 + 14.0229i) q^{79} +(6.45918 - 6.18700i) q^{80} +(-0.309017 + 0.951057i) q^{81} +(-0.127226 + 0.346014i) q^{82} +(-5.86554 - 11.5118i) q^{83} +(0.0597467 + 0.00457206i) q^{84} +(6.37433 - 3.04299i) q^{85} +(0.489447 - 2.47461i) q^{86} +(-7.91379 - 1.25342i) q^{87} +(-6.67780 - 3.05226i) q^{88} +(-5.58568 + 7.68803i) q^{89} +(-1.16765 + 2.93881i) q^{90} +(0.0640804 + 0.0881991i) q^{91} +(-2.72915 + 11.4771i) q^{92} +(1.31270 + 1.31270i) q^{93} +(1.98314 + 16.6015i) q^{94} +(-9.65652 - 3.41596i) q^{95} +(-4.46131 - 3.47803i) q^{96} +(5.72355 + 2.91630i) q^{97} +(-5.50806 - 8.22412i) q^{98} +2.59589 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 12 q^{8}+O(q^{10}) \) 240 * q + 12 * q^8	\( 240 q + 12 q^{8} + 8 q^{10} + 8 q^{12} + 4 q^{13} + 20 q^{17} - 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} - 8 q^{30} - 20 q^{32} - 8 q^{33} - 4 q^{37} - 76 q^{38} - 92 q^{40} - 20 q^{42} - 140 q^{44} - 4 q^{45} - 16 q^{48} - 164 q^{50} - 172 q^{52} - 4 q^{53} - 120 q^{58} + 20 q^{60} - 44 q^{62} - 60 q^{64} - 20 q^{65} + 16 q^{68} - 44 q^{70} + 12 q^{72} - 44 q^{73} - 48 q^{77} + 24 q^{78} - 4 q^{80} + 60 q^{81} + 24 q^{82} + 80 q^{84} - 64 q^{85} + 60 q^{88} - 260 q^{89} + 48 q^{90} + 144 q^{92} - 64 q^{93} + 40 q^{94} - 20 q^{96} - 180 q^{97} + 256 q^{98}+O(q^{100}) \) 240 * q + 12 * q^8 + 8 * q^10 + 8 * q^12 + 4 * q^13 + 20 * q^17 - 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 - 8 * q^30 - 20 * q^32 - 8 * q^33 - 4 * q^37 - 76 * q^38 - 92 * q^40 - 20 * q^42 - 140 * q^44 - 4 * q^45 - 16 * q^48 - 164 * q^50 - 172 * q^52 - 4 * q^53 - 120 * q^58 + 20 * q^60 - 44 * q^62 - 60 * q^64 - 20 * q^65 + 16 * q^68 - 44 * q^70 + 12 * q^72 - 44 * q^73 - 48 * q^77 + 24 * q^78 - 4 * q^80 + 60 * q^81 + 24 * q^82 + 80 * q^84 - 64 * q^85 + 60 * q^88 - 260 * q^89 + 48 * q^90 + 144 * q^92 - 64 * q^93 + 40 * q^94 - 20 * q^96 - 180 * q^97 + 256 * q^98

Introduction

L-functions

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