LMFDB - Embedded newform 600.2.bk.a.59.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [600,2,Mod(59,600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(600, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 5, 5, 7]))

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

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

chi := DirichletCharacter("600.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.bk (of order $10$, 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:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$464$
Relative dimension:	$116$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			59.1
Character	$\chi$	$=$	600.59
Dual form			600.2.bk.a.539.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41378 + 0.0350741i) q^{2} +(1.68189 - 0.413828i) q^{3} +(1.99754 - 0.0991741i) q^{4} +(-0.0280397 + 2.23589i) q^{5} +(-2.36330 + 0.644051i) q^{6} -3.19488 q^{7} +(-2.82060 + 0.210272i) q^{8} +(2.65749 - 1.39202i) q^{9} +O(q^{10})$	\(q+(-1.41378 + 0.0350741i) q^{2} +(1.68189 - 0.413828i) q^{3} +(1.99754 - 0.0991741i) q^{4} +(-0.0280397 + 2.23589i) q^{5} +(-2.36330 + 0.644051i) q^{6} -3.19488 q^{7} +(-2.82060 + 0.210272i) q^{8} +(2.65749 - 1.39202i) q^{9} +(-0.0387801 - 3.16204i) q^{10} +(-1.85977 + 2.55976i) q^{11} +(3.31860 - 0.993437i) q^{12} +(-3.44432 + 2.50244i) q^{13} +(4.51686 - 0.112058i) q^{14} +(0.878114 + 3.77212i) q^{15} +(3.98033 - 0.396208i) q^{16} +(0.844018 - 2.59762i) q^{17} +(-3.70828 + 2.06122i) q^{18} +(-2.41687 + 7.43835i) q^{19} +(0.165732 + 4.46906i) q^{20} +(-5.37344 + 1.32213i) q^{21} +(2.53953 - 3.68416i) q^{22} +(-3.46187 + 4.76486i) q^{23} +(-4.65692 + 1.52090i) q^{24} +(-4.99843 - 0.125387i) q^{25} +(4.78173 - 3.65871i) q^{26} +(3.89355 - 3.44097i) q^{27} +(-6.38191 + 0.316850i) q^{28} +(-1.57294 - 4.84102i) q^{29} +(-1.37376 - 5.30215i) q^{30} +(8.97422 + 2.91590i) q^{31} +(-5.61341 + 0.699757i) q^{32} +(-2.06863 + 5.07485i) q^{33} +(-1.10214 + 3.70206i) q^{34} +(0.0895836 - 7.14342i) q^{35} +(5.17040 - 3.04418i) q^{36} +(0.452412 - 0.328697i) q^{37} +(3.15602 - 10.6009i) q^{38} +(-4.75737 + 5.63418i) q^{39} +(-0.391057 - 6.31245i) q^{40} +(-2.31106 - 3.18090i) q^{41} +(7.55048 - 2.05767i) q^{42} +0.561175i q^{43} +(-3.46111 + 5.29766i) q^{44} +(3.03790 + 5.98090i) q^{45} +(4.72720 - 6.85787i) q^{46} +(5.09154 - 1.65434i) q^{47} +(6.53051 - 2.31355i) q^{48} +3.20729 q^{49} +(7.07107 + 0.00195455i) q^{50} +(0.344577 - 4.71818i) q^{51} +(-6.63198 + 5.34031i) q^{52} +(1.35978 - 0.441818i) q^{53} +(-5.38393 + 5.00133i) q^{54} +(-5.67120 - 4.23003i) q^{55} +(9.01149 - 0.671795i) q^{56} +(-0.986704 + 13.5106i) q^{57} +(2.39359 + 6.78897i) q^{58} +(4.66344 + 6.41867i) q^{59} +(2.12816 + 7.44788i) q^{60} +(-4.11132 + 5.65874i) q^{61} +(-12.7898 - 3.80768i) q^{62} +(-8.49039 + 4.44735i) q^{63} +(7.91157 - 1.18619i) q^{64} +(-5.49861 - 7.77129i) q^{65} +(2.74659 - 7.24727i) q^{66} +(0.0188877 + 0.00613698i) q^{67} +(1.42834 - 5.27255i) q^{68} +(-3.85065 + 9.44657i) q^{69} +(0.123898 + 10.1024i) q^{70} +(-0.183719 - 0.565428i) q^{71} +(-7.20302 + 4.48514i) q^{72} +(1.95452 - 2.69016i) q^{73} +(-0.628082 + 0.480572i) q^{74} +(-8.45868 + 1.85760i) q^{75} +(-4.09009 + 15.0981i) q^{76} +(5.94176 - 8.17813i) q^{77} +(6.52826 - 8.13234i) q^{78} +(3.13606 - 1.01897i) q^{79} +(0.774272 + 8.91070i) q^{80} +(5.12454 - 7.39858i) q^{81} +(3.37889 + 4.41603i) q^{82} +(-5.34513 + 16.4506i) q^{83} +(-10.6025 + 3.17392i) q^{84} +(5.78433 + 1.95997i) q^{85} +(-0.0196827 - 0.793377i) q^{86} +(-4.64886 - 7.49113i) q^{87} +(4.70743 - 7.61111i) q^{88} +(-0.409412 + 0.563507i) q^{89} +(-4.50469 - 8.34912i) q^{90} +(11.0042 - 7.99501i) q^{91} +(-6.44267 + 9.86132i) q^{92} +(16.3003 + 1.19044i) q^{93} +(-7.14029 + 2.51745i) q^{94} +(-16.5636 - 5.61242i) q^{95} +(-9.15154 + 3.49990i) q^{96} +(-10.8821 + 3.53580i) q^{97} +(-4.53440 + 0.112493i) q^{98} +(-1.37909 + 9.39139i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 464 q - 10 q^{3} - 6 q^{4} + q^{6} - 6 q^{9}+O(q^{10}) $ 464 * q - 10 * q^3 - 6 * q^4 + q^6 - 6 * q^9	$ 464 q - 10 q^{3} - 6 q^{4} + q^{6} - 6 q^{9} - 16 q^{10} - 5 q^{12} - 18 q^{16} - 12 q^{19} - 10 q^{22} + 12 q^{24} - 16 q^{25} - 10 q^{27} - 50 q^{28} - 21 q^{30} - 10 q^{33} - 14 q^{34} - 25 q^{36} - 32 q^{40} + 15 q^{42} - 34 q^{46} - 70 q^{48} + 336 q^{49} - 4 q^{51} - 60 q^{52} + 40 q^{54} - 70 q^{58} - 50 q^{60} - 30 q^{64} + 28 q^{66} - 20 q^{67} - 16 q^{70} - 5 q^{72} - 20 q^{73} - 42 q^{75} - 48 q^{76} + 75 q^{78} - 6 q^{81} - 76 q^{84} - 70 q^{88} + 66 q^{90} - 96 q^{91} - 108 q^{94} - 50 q^{96} - 60 q^{97} - 52 q^{99}+O(q^{100}) $ 464 * q - 10 * q^3 - 6 * q^4 + q^6 - 6 * q^9 - 16 * q^10 - 5 * q^12 - 18 * q^16 - 12 * q^19 - 10 * q^22 + 12 * q^24 - 16 * q^25 - 10 * q^27 - 50 * q^28 - 21 * q^30 - 10 * q^33 - 14 * q^34 - 25 * q^36 - 32 * q^40 + 15 * q^42 - 34 * q^46 - 70 * q^48 + 336 * q^49 - 4 * q^51 - 60 * q^52 + 40 * q^54 - 70 * q^58 - 50 * q^60 - 30 * q^64 + 28 * q^66 - 20 * q^67 - 16 * q^70 - 5 * q^72 - 20 * q^73 - 42 * q^75 - 48 * q^76 + 75 * q^78 - 6 * q^81 - 76 * q^84 - 70 * q^88 + 66 * q^90 - 96 * q^91 - 108 * q^94 - 50 * q^96 - 60 * q^97 - 52 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$-1$	$-1$	$-1$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−1.41378	+	0.0350741i	−0.999692	+	0.0248012i
$2$	−1.41378	+	0.0350741i	−0.999692	+	0.0248012i
$3$	1.68189	−	0.413828i	0.971038	−	0.238923i
$3$	1.68189	−	0.413828i	0.971038	−	0.238923i
$4$	1.99754	−	0.0991741i	0.998770	−	0.0495870i
$5$	−0.0280397	+	2.23589i	−0.0125397	+	0.999921i
$5$	−0.0280397	+	2.23589i	−0.0125397	+	0.999921i
$6$	−2.36330	+	0.644051i	−0.964814	+	0.262933i
$7$	−3.19488			−1.20755			−0.603776	−	0.797154i	$-0.706338\pi$
$7$	−3.19488			−1.20755			−0.603776	+	0.797154i	$0.706338\pi$
$8$	−2.82060	+	0.210272i	−0.997233	+	0.0743424i
$9$	2.65749	−	1.39202i	0.885831	−	0.464008i
$10$	−0.0387801	−	3.16204i	−0.0122633	−	0.999925i
$11$	−1.85977	+	2.55976i	−0.560743	+	0.771796i	−0.991421	−	0.130710i	$-0.958274\pi$
$11$	−1.85977	+	2.55976i	−0.560743	+	0.771796i	0.430678	+	0.902506i	$0.358274\pi$
$12$	3.31860	−	0.993437i	0.957996	−	0.286780i
$13$	−3.44432	+	2.50244i	−0.955281	+	0.694053i	−0.952050	−	0.305942i	$-0.901029\pi$
$13$	−3.44432	+	2.50244i	−0.955281	+	0.694053i	−0.00323125	+	0.999995i	$0.501029\pi$
$14$	4.51686	−	0.112058i	1.20718	−	0.0299487i
$15$	0.878114	+	3.77212i	0.226728	+	0.973958i
$16$	3.98033	−	0.396208i	0.995082	−	0.0990521i
$17$	0.844018	−	2.59762i	0.204704	−	0.630015i	−0.795021	−	0.606582i	$-0.792540\pi$
$17$	0.844018	−	2.59762i	0.204704	−	0.630015i	0.999725	−	0.0234333i	$-0.00745975\pi$
$18$	−3.70828	+	2.06122i	−0.874051	+	0.485835i
$19$	−2.41687	+	7.43835i	−0.554467	+	1.70647i	0.142880	+	0.989740i	$0.454364\pi$
$19$	−2.41687	+	7.43835i	−0.554467	+	1.70647i	−0.697347	+	0.716734i	$0.745636\pi$
$20$	0.165732	+	4.46906i	0.0370588	+	0.999313i
$21$	−5.37344	+	1.32213i	−1.17258	+	0.288513i
$22$	2.53953	−	3.68416i	0.541429	−	0.785466i
$23$	−3.46187	+	4.76486i	−0.721850	+	0.993541i	0.277610	+	0.960694i	$0.410458\pi$
$23$	−3.46187	+	4.76486i	−0.721850	+	0.993541i	−0.999460	+	0.0328474i	$0.989542\pi$
$24$	−4.65692	+	1.52090i	−0.950589	+	0.310452i
$25$	−4.99843	−	0.125387i	−0.999686	−	0.0250775i
$26$	4.78173	−	3.65871i	0.937774	−	0.717531i
$27$	3.89355	−	3.44097i	0.749314	−	0.662215i
$28$	−6.38191	+	0.316850i	−1.20607	+	0.0598790i
$29$	−1.57294	−	4.84102i	−0.292088	−	0.898956i	−0.984184	−	0.177150i	$-0.943312\pi$
$29$	−1.57294	−	4.84102i	−0.292088	−	0.898956i	0.692096	−	0.721806i	$-0.256688\pi$
$30$	−1.37376	−	5.30215i	−0.250814	−	0.968035i
$31$	8.97422	+	2.91590i	1.61182	+	0.523711i	0.969992	−	0.243138i	$-0.0781769\pi$
$31$	8.97422	+	2.91590i	1.61182	+	0.523711i	0.641827	+	0.766850i	$0.278177\pi$
$32$	−5.61341	+	0.699757i	−0.992320	+	0.123701i
$33$	−2.06863	+	5.07485i	−0.360103	+	0.883418i
$34$	−1.10214	+	3.70206i	−0.189016	+	0.634898i
$35$	0.0895836	−	7.14342i	0.0151424	−	1.20746i
$36$	5.17040	−	3.04418i	0.861733	−	0.507363i
$37$	0.452412	−	0.328697i	0.0743761	−	0.0540374i	−0.549976	−	0.835181i	$-0.685363\pi$
$37$	0.452412	−	0.328697i	0.0743761	−	0.0540374i	0.624352	+	0.781143i	$0.285363\pi$
$38$	3.15602	−	10.6009i	0.511974	−	1.71970i
$39$	−4.75737	+	5.63418i	−0.761789	+	0.902191i
$40$	−0.391057	−	6.31245i	−0.0618316	−	0.998087i
$41$	−2.31106	−	3.18090i	−0.360927	−	0.496773i	0.589480	−	0.807783i	$-0.299333\pi$
$41$	−2.31106	−	3.18090i	−0.360927	−	0.496773i	−0.950407	+	0.311010i	$0.899333\pi$
$42$	7.55048	−	2.05767i	1.16506	−	0.317505i
$43$			0.561175i			0.0855784i	0.999084	+	0.0427892i	$0.0136244\pi$
$43$			0.561175i			0.0855784i	−0.999084	+	0.0427892i	$0.986376\pi$
$44$	−3.46111	+	5.29766i	−0.521782	+	0.798652i
$45$	3.03790	+	5.98090i	0.452863	+	0.891580i
$46$	4.72720	−	6.85787i	0.696987	−	1.01114i
$47$	5.09154	−	1.65434i	0.742677	−	0.241311i	0.0868500	−	0.996221i	$-0.472320\pi$
$47$	5.09154	−	1.65434i	0.742677	−	0.241311i	0.655827	+	0.754911i	$0.272320\pi$
$48$	6.53051	−	2.31355i	0.942597	−	0.333932i
$49$	3.20729			0.458184
$50$	7.07107	+	0.00195455i	1.00000	+	0.000276415i
$51$	0.344577	−	4.71818i	0.0482504	−	0.660678i
$52$	−6.63198	+	5.34031i	−0.919690	+	0.740568i
$53$	1.35978	−	0.441818i	0.186780	−	0.0606884i	−0.214134	−	0.976804i	$-0.568693\pi$
$53$	1.35978	−	0.441818i	0.186780	−	0.0606884i	0.400913	+	0.916116i	$0.368693\pi$
$54$	−5.38393	+	5.00133i	−0.732660	+	0.680595i
$55$	−5.67120	−	4.23003i	−0.764704	−	0.570377i
$56$	9.01149	−	0.671795i	1.20421	−	0.0897724i
$57$	−0.986704	+	13.5106i	−0.130692	+	1.78953i
$58$	2.39359	+	6.78897i	0.314294	+	0.891435i
$59$	4.66344	+	6.41867i	0.607128	+	0.835639i	0.996337	−	0.0855097i	$-0.0272519\pi$
$59$	4.66344	+	6.41867i	0.607128	+	0.835639i	−0.389210	+	0.921149i	$0.627252\pi$
$60$	2.12816	+	7.44788i	0.274745	+	0.961517i
$61$	−4.11132	+	5.65874i	−0.526400	+	0.724528i	−0.986577	−	0.163300i	$-0.947786\pi$
$61$	−4.11132	+	5.65874i	−0.526400	+	0.724528i	0.460176	+	0.887828i	$0.347786\pi$
$62$	−12.7898	−	3.80768i	−1.62431	−	0.483575i
$63$	−8.49039	+	4.44735i	−1.06969	+	0.560314i
$64$	7.91157	−	1.18619i	0.988946	−	0.148273i
$65$	−5.49861	−	7.77129i	−0.682019	−	0.963909i
$66$	2.74659	−	7.24727i	0.338082	−	0.892078i
$67$	0.0188877	+	0.00613698i	0.00230750	+	0.000749751i	0.310171	−	0.950681i	$-0.399614\pi$
$67$	0.0188877	+	0.00613698i	0.00230750	+	0.000749751i	−0.307863	+	0.951431i	$0.599614\pi$
$68$	1.42834	−	5.27255i	0.173212	−	0.639391i
$69$	−3.85065	+	9.44657i	−0.463564	+	1.13723i
$70$	0.123898	+	10.1024i	0.0148086	+	1.20746i
$71$	−0.183719	−	0.565428i	−0.0218034	−	0.0671039i	0.939563	−	0.342377i	$-0.111232\pi$
$71$	−0.183719	−	0.565428i	−0.0218034	−	0.0671039i	−0.961366	+	0.275273i	$0.911232\pi$
$72$	−7.20302	+	4.48514i	−0.848884	+	0.528579i
$73$	1.95452	−	2.69016i	0.228759	−	0.314859i	−0.679172	−	0.733979i	$-0.737661\pi$
$73$	1.95452	−	2.69016i	0.228759	−	0.314859i	0.907931	+	0.419119i	$0.137661\pi$
$74$	−0.628082	+	0.480572i	−0.0730130	+	0.0558654i
$75$	−8.45868	+	1.85760i	−0.976725	+	0.214497i
$76$	−4.09009	+	15.0981i	−0.469166	+	1.73187i
$77$	5.94176	−	8.17813i	0.677127	−	0.931985i
$78$	6.52826	−	8.13234i	0.739180	−	0.920806i
$79$	3.13606	−	1.01897i	0.352835	−	0.114643i	−0.127237	−	0.991872i	$-0.540611\pi$
$79$	3.13606	−	1.01897i	0.352835	−	0.114643i	0.480071	+	0.877229i	$0.340611\pi$
$80$	0.774272	+	8.91070i	0.0865662	+	0.996246i
$81$	5.12454	−	7.39858i	0.569394	−	0.822065i
$82$	3.37889	+	4.41603i	0.373136	+	0.487669i
$83$	−5.34513	+	16.4506i	−0.586705	+	1.80569i	0.00560930	+	0.999984i	$0.498214\pi$
$83$	−5.34513	+	16.4506i	−0.586705	+	1.80569i	−0.592314	+	0.805707i	$0.701786\pi$
$84$	−10.6025	+	3.17392i	−1.15683	+	0.346303i
$85$	5.78433	+	1.95997i	0.627399	+	0.212588i
$86$	−0.0196827	−	0.793377i	−0.00212244	−	0.0855521i
$87$	−4.64886	−	7.49113i	−0.498411	−	0.803134i
$88$	4.70743	−	7.61111i	0.501814	−	0.811347i
$89$	−0.409412	+	0.563507i	−0.0433975	+	0.0597316i	−0.830164	−	0.557519i	$-0.811753\pi$
$89$	−0.409412	+	0.563507i	−0.0433975	+	0.0597316i	0.786767	+	0.617250i	$0.211753\pi$
$90$	−4.50469	−	8.34912i	−0.474836	−	0.880074i
$91$	11.0042	−	7.99501i	1.15355	−	0.838105i
$92$	−6.44267	+	9.86132i	−0.671695	+	1.02811i
$93$	16.3003	+	1.19044i	1.69026	+	0.123443i
$94$	−7.14029	+	2.51745i	−0.736464	+	0.259656i
$95$	−16.5636	−	5.61242i	−1.69939	−	0.575822i
$96$	−9.15154	+	3.49990i	−0.934025	+	0.357207i
$97$	−10.8821	+	3.53580i	−1.10491	+	0.359006i	−0.803989	−	0.594644i	$-0.797293\pi$
$97$	−10.8821	+	3.53580i	−1.10491	+	0.359006i	−0.300918	+	0.953650i	$0.597293\pi$
$98$	−4.53440	+	0.112493i	−0.458043	+	0.0113635i
$99$	−1.37909	+	9.39139i	−0.138604	+	0.943870i
$100$	−9.99699	+	0.245248i	−0.999699	+	0.0245248i
$101$	6.45132			0.641930			0.320965	−	0.947091i	$-0.395993\pi$
$101$	6.45132			0.641930			0.320965	+	0.947091i	$0.395993\pi$
$102$	−0.321669	+	6.68255i	−0.0318500	+	0.661671i
$103$	1.07778	+	3.31707i	0.106197	+	0.326841i	0.990010	−	0.141000i	$-0.0450319\pi$
$103$	1.07778	+	3.31707i	0.106197	+	0.326841i	−0.883812	+	0.467841i	$0.845032\pi$
$104$	9.18884	−	7.78263i	0.901040	−	0.763150i
$105$	−2.80547	−	12.0515i	−0.273786	−	1.17611i
$106$	−1.90693	+	0.672326i	−0.185217	+	0.0653020i
$107$	14.2162			1.37433			0.687165	−	0.726502i	$-0.258855\pi$
$107$	14.2162			1.37433			0.687165	+	0.726502i	$0.258855\pi$
$108$	7.43626	−	7.25961i	0.715555	−	0.698557i
$109$	−4.15648	−	5.72091i	−0.398119	−	0.547964i	0.562152	−	0.827034i	$-0.309974\pi$
$109$	−4.15648	−	5.72091i	−0.398119	−	0.547964i	−0.960271	+	0.279070i	$0.909974\pi$
$110$	8.16618	+	5.78141i	0.778615	+	0.551236i
$111$	0.624883	−	0.740051i	0.0593112	−	0.0702426i
$112$	−12.7167	+	1.26584i	−1.20161	+	0.119611i
$113$	−3.06774	+	2.22884i	−0.288589	+	0.209672i	−0.722655	−	0.691209i	$-0.757078\pi$
$113$	−3.06774	+	2.22884i	−0.288589	+	0.209672i	0.434066	+	0.900881i	$0.357078\pi$
$114$	0.921107	−	19.1356i	0.0862696	−	1.79222i
$115$	−10.5566	−	7.87397i	−0.984411	−	0.734252i
$116$	−3.62212	−	9.51414i	−0.336306	−	0.883366i
$117$	−5.66979	+	11.4448i	−0.524172	+	1.05807i
$118$	−6.81819	−	8.91101i	−0.627666	−	0.820325i
$119$	−2.69654	+	8.29909i	−0.247191	+	0.760777i
$120$	−3.26998	−	10.4550i	−0.298507	−	0.954407i
$121$	0.305581	+	0.940482i	0.0277801	+	0.0854984i
$122$	5.61402	−	8.14441i	0.508269	−	0.737360i
$123$	−5.20329	−	4.39354i	−0.469165	−	0.396152i
$124$	18.2155	+	4.93462i	1.63580	+	0.443142i
$125$	0.420507	−	11.1724i	0.0376113	−	0.999292i
$126$	11.8475	−	6.58537i	1.05546	−	0.586671i
$127$	−7.06143	−	5.13043i	−0.626600	−	0.455252i	0.228621	−	0.973516i	$-0.426578\pi$
$127$	−7.06143	−	5.13043i	−0.626600	−	0.455252i	−0.855221	+	0.518264i	$0.826578\pi$
$128$	−11.1436	+	1.95450i	−0.984965	+	0.172755i
$129$	0.232230	+	0.943834i	0.0204467	+	0.0830999i
$130$	8.04639	+	10.7940i	0.705715	+	0.946698i
$131$	15.5747	+	5.06054i	1.36077	+	0.442141i	0.896300	−	0.443447i	$-0.146245\pi$
$131$	15.5747	+	5.06054i	1.36077	+	0.442141i	0.464470	+	0.885589i	$0.346245\pi$
$132$	−3.62888	+	10.3424i	−0.315853	+	0.900188i
$133$	7.72161	−	23.7647i	0.669548	−	2.06066i
$134$	−0.0269182	−	0.00801386i	−0.00232538	−	0.000692292i
$135$	7.58447	+	8.80204i	0.652767	+	0.757559i
$136$	−1.83443	+	7.50432i	−0.157301	+	0.643490i
$137$	17.6740	−	12.8409i	1.50999	−	1.09707i	0.543812	−	0.839207i	$-0.316981\pi$
$137$	17.6740	−	12.8409i	1.50999	−	1.09707i	0.966181	−	0.257866i	$-0.0830194\pi$
$138$	5.11264	−	13.4904i	0.435216	−	1.14838i
$139$	14.5851	+	10.5967i	1.23709	+	0.898802i	0.997401	−	0.0720467i	$-0.0229531\pi$
$139$	14.5851	+	10.5967i	1.23709	+	0.898802i	0.239693	+	0.970849i	$0.422953\pi$
$140$	−0.529495	−	14.2781i	−0.0447505	−	1.20672i
$141$	7.87879	−	4.88944i	0.663514	−	0.411765i
$142$	0.279569	+	0.792946i	0.0234609	+	0.0665426i
$143$		−	13.4706i		−	1.12647i
$144$	10.0262	−	6.59363i	0.835514	−	0.549469i
$145$	10.8681	−	3.38119i	0.902548	−	0.280793i
$146$	−2.66890	+	3.87184i	−0.220880	+	0.320436i
$147$	5.39430	−	1.32726i	0.444914	−	0.109471i
$148$	0.871113	−	0.701452i	0.0716050	−	0.0576590i
$149$	19.0091			1.55728			0.778641	−	0.627469i	$-0.215909\pi$
$149$	19.0091			1.55728			0.778641	+	0.627469i	$0.215909\pi$
$150$	11.8936	−	2.92292i	0.971104	−	0.238655i
$151$		−	9.95254i		−	0.809926i	−0.914333	−	0.404963i	$-0.867284\pi$
$151$		−	9.95254i		−	0.809926i	0.914333	−	0.404963i	$-0.132716\pi$
$152$	5.25293	−	21.4888i	0.426069	−	1.74297i
$153$	−1.37297	−	8.07805i	−0.110998	−	0.653071i
$154$	−8.11349	+	11.7705i	−0.653804	+	0.948492i
$155$	−6.77128	+	19.9836i	−0.543882	+	1.60512i
$156$	−8.94428	+	11.7263i	−0.716115	+	0.938856i
$157$	3.66973			0.292877			0.146438	−	0.989220i	$-0.453219\pi$
$157$	3.66973			0.292877			0.146438	+	0.989220i	$0.453219\pi$
$158$	−4.39796	+	1.55059i	−0.349883	+	0.123358i
$159$	2.10415	−	1.30580i	0.166870	−	0.103557i
$160$	−1.40718	−	12.5706i	−0.111248	−	0.993793i
$161$	11.0603	−	15.2232i	0.871672	−	1.19975i
$162$	−6.98547	+	10.6397i	−0.548830	+	0.835934i
$163$	−13.2590	−	18.2494i	−1.03852	−	1.42941i	−0.898350	−	0.439280i	$-0.855234\pi$
$163$	−13.2590	−	18.2494i	−1.03852	−	1.42941i	−0.140174	−	0.990127i	$-0.544766\pi$
$164$	−4.93190	−	6.12478i	−0.385116	−	0.478265i
$165$	−11.2888	−	4.76753i	−0.878833	−	0.371152i
$166$	6.97984	−	23.4450i	0.541741	−	1.81969i
$167$	−18.4790	−	6.00418i	−1.42995	−	0.464617i	−0.511198	−	0.859463i	$-0.670798\pi$
$167$	−18.4790	−	6.00418i	−1.42995	−	0.464617i	−0.918747	+	0.394846i	$0.870798\pi$
$168$	14.8783	−	4.85909i	1.14789	−	0.374887i
$169$	1.58387	−	4.87467i	0.121837	−	0.374974i
$170$	−8.24651	−	2.56808i	−0.632478	−	0.196963i
$171$	3.93155	+	23.1317i	0.300653	+	1.76892i
$172$	0.0556540	+	1.12097i	0.00424358	+	0.0854731i
$173$	8.62645	−	11.8733i	0.655857	−	0.902709i	−0.343479	−	0.939160i	$-0.611605\pi$
$173$	8.62645	−	11.8733i	0.655857	−	0.902709i	0.999335	+	0.0364511i	$0.0116053\pi$
$174$	6.83521	+	10.4277i	0.518176	+	0.790525i
$175$	15.9694	+	0.400598i	1.20717	+	0.0302824i
$176$	−6.38831	+	10.9255i	−0.481537	+	0.823543i
$177$	10.4996	+	8.86562i	0.789198	+	0.666381i
$178$	0.559053	−	0.811034i	0.0419028	−	0.0607895i
$179$	−18.5370	+	6.02305i	−1.38552	+	0.450184i	−0.904481	−	0.426514i	$-0.859742\pi$
$179$	−18.5370	+	6.02305i	−1.38552	+	0.450184i	−0.481042	+	0.876697i	$0.659742\pi$
$180$	6.66147	+	11.6458i	0.496517	+	0.868027i
$181$	−6.56520	−	2.13316i	−0.487987	−	0.158557i	0.0546808	−	0.998504i	$-0.482586\pi$
$181$	−6.56520	−	2.13316i	−0.487987	−	0.158557i	−0.542668	+	0.839947i	$0.682586\pi$
$182$	−15.2771	+	11.6891i	−1.13241	+	0.866457i
$183$	−4.57303	+	11.2187i	−0.338048	+	0.829314i
$184$	8.76264	−	14.1677i	0.645990	−	1.04446i
$185$	0.722245	+	1.02076i	0.0531005	+	0.0750479i
$186$	−23.0868	−	1.11130i	−1.69281	−	0.0814843i
$187$	5.07960	+	6.99146i	0.371457	+	0.511266i
$188$	10.0065	−	3.80956i	0.729798	−	0.277841i
$189$	−12.4394	+	10.9935i	−0.904836	+	0.799660i
$190$	23.6141	+	7.35377i	1.71315	+	0.533498i
$191$	−10.3328	+	7.50722i	−0.747655	+	0.543203i	−0.895099	−	0.445867i	$-0.852895\pi$
$191$	−10.3328	+	7.50722i	−0.747655	+	0.543203i	0.147444	+	0.989070i	$0.452895\pi$
$192$	12.8155	−	5.26906i	0.924879	−	0.380262i
$193$			9.11958i			0.656442i	0.944601	+	0.328221i	$0.106449\pi$
$193$			9.11958i			0.656442i	−0.944601	+	0.328221i	$0.893551\pi$
$194$	15.2608	−	5.38052i	1.09566	−	0.386299i
$195$	−12.4640	−	10.7950i	−0.892567	−	0.773043i
$196$	6.40669	−	0.318080i	0.457621	−	0.0227200i
$197$	−2.24879	+	0.730676i	−0.160220	+	0.0520585i	−0.388029	−	0.921647i	$-0.626844\pi$
$197$	−2.24879	+	0.730676i	−0.160220	+	0.0520585i	0.227809	+	0.973706i	$0.426844\pi$
$198$	1.62034	−	13.3257i	0.115152	−	0.947017i
$199$			1.88910i			0.133915i	0.997756	+	0.0669573i	$0.0213291\pi$
$199$			1.88910i			0.133915i	−0.997756	+	0.0669573i	$0.978671\pi$
$200$	14.1249	−	0.697362i	0.998783	−	0.0493110i
$201$	0.0343066	+	0.00250547i	0.00241980	+	0.000176722i
$202$	−9.12073	+	0.226274i	−0.641732	+	0.0159206i
$203$	5.02537	+	15.4665i	0.352712	+	1.08554i
$204$	0.220384	−	9.45893i	0.0154300	−	0.662257i
$205$	7.17695	−	5.07809i	0.501260	−	0.354669i
$206$	−1.64009	−	4.65180i	−0.114270	−	0.324107i
$207$	−2.56711	+	17.4816i	−0.178426	+	1.21505i
$208$	−12.7180	+	11.3252i	−0.881836	+	0.785262i
$209$	−14.5455	−	20.0202i	−1.00614	−	1.38483i
$210$	4.38901	+	16.9398i	0.302871	+	1.16895i
$211$	−8.11770	−	5.89785i	−0.558846	−	0.406025i	0.272191	−	0.962243i	$-0.412252\pi$
$211$	−8.11770	−	5.89785i	−0.558846	−	0.406025i	−0.831036	+	0.556218i	$0.812252\pi$
$212$	2.67239	−	1.01740i	0.183540	−	0.0698755i
$213$	−0.542984	−	0.874959i	−0.0372046	−	0.0599512i
$214$	−20.0985	+	0.498620i	−1.37391	+	0.0340849i
$215$	−1.25473	−	0.0157352i	−0.0855717	−	0.00107313i
$216$	−10.2586	+	10.5243i	−0.698010	+	0.716088i
$217$	−28.6716	−	9.31597i	−1.94636	−	0.632409i
$218$	6.07700	+	7.94231i	0.411587	+	0.537921i
$219$	2.17401	−	5.33338i	0.146906	−	0.360396i
$220$	−11.7479	−	7.88721i	−0.792046	−	0.531756i
$221$	3.59333	+	11.0591i	0.241713	+	0.743917i
$222$	−0.857489	+	1.06819i	−0.0575509	+	0.0716920i
$223$	3.17447	+	2.30639i	0.212578	+	0.154447i	0.688980	−	0.724781i	$-0.258059\pi$
$223$	3.17447	+	2.30639i	0.212578	+	0.154447i	−0.476401	+	0.879228i	$0.658059\pi$
$224$	17.9342	−	2.23564i	1.19828	−	0.149375i
$225$	−13.4578	+	6.62471i	−0.897189	+	0.441647i
$226$	4.25893	−	3.25869i	0.283300	−	0.216765i
$227$	6.55338	+	4.76131i	0.434963	+	0.316019i	0.783630	−	0.621227i	$-0.213366\pi$
$227$	6.55338	+	4.76131i	0.434963	+	0.316019i	−0.348667	+	0.937247i	$0.613366\pi$
$228$	−0.631075	+	27.0859i	−0.0417940	+	1.79381i
$229$	−7.33700	+	2.38394i	−0.484843	+	0.157535i	−0.541231	−	0.840874i	$-0.682042\pi$
$229$	−7.33700	+	2.38394i	−0.484843	+	0.157535i	0.0563882	+	0.998409i	$0.482042\pi$
$230$	15.2009	+	10.7618i	1.00232	+	0.709612i
$231$	6.60904	−	16.2136i	0.434843	−	1.06677i
$232$	5.45458	+	13.3238i	0.358111	+	0.874753i
$233$	−1.17690	+	3.62212i	−0.0771011	+	0.237293i	−0.982177	−	0.187957i	$-0.939814\pi$
$233$	−1.17690	+	3.62212i	−0.0771011	+	0.237293i	0.905076	+	0.425249i	$0.139814\pi$
$234$	7.61441	−	16.3793i	0.497770	−	1.07075i
$235$	3.55616	+	11.4305i	0.231979	+	0.745645i
$236$	9.95196	+	12.3591i	0.647818	+	0.804506i
$237$	4.85283	−	3.01158i	0.315225	−	0.195623i
$238$	3.52123	−	11.8277i	0.228247	−	0.766673i
$239$	−7.95106	−	5.77678i	−0.514311	−	0.373669i	0.300145	−	0.953893i	$-0.402965\pi$
$239$	−7.95106	−	5.77678i	−0.514311	−	0.373669i	−0.814457	+	0.580225i	$0.802965\pi$
$240$	4.98973	+	14.6664i	0.322086	+	0.946711i
$241$	14.2231	−	10.3337i	0.916192	−	0.665652i	−0.0263815	−	0.999652i	$-0.508398\pi$
$241$	14.2231	−	10.3337i	0.916192	−	0.665652i	0.942573	+	0.334000i	$0.108398\pi$
$242$	−0.465011	−	1.31892i	−0.0298920	−	0.0847831i
$243$	5.55717	−	14.5643i	0.356493	−	0.934298i
$244$	−7.65132	+	11.7113i	−0.489826	+	0.749739i
$245$	−0.0899314	+	7.17115i	−0.00574550	+	0.458148i
$246$	7.51039	+	6.02899i	0.478845	+	0.384394i
$247$	−10.2896	−	31.6681i	−0.654711	−	2.01499i
$248$	−25.9258	−	6.33756i	−1.64629	−	0.402436i
$249$	−2.18219	+	29.8801i	−0.138291	+	1.89357i
$250$	−0.202641	+	15.8101i	−0.0128161	+	0.999918i
$251$		−	16.4679i		−	1.03945i	−0.854335	−	0.519723i	$-0.826035\pi$
$251$		−	16.4679i		−	1.03945i	0.854335	−	0.519723i	$-0.173965\pi$
$252$	−16.5188	+	9.72579i	−1.04059	+	0.612667i
$253$	−5.75859	−	17.7231i	−0.362039	−	1.11424i
$254$	10.1632	+	7.00561i	0.637698	+	0.439571i
$255$	10.5397	+	0.902732i	0.660021	+	0.0565313i
$256$	15.6860	−	3.15408i	0.980377	−	0.197130i
$257$	−12.2483			−0.764029			−0.382015	−	0.924156i	$-0.624770\pi$
$257$	−12.2483			−0.764029			−0.382015	+	0.924156i	$0.624770\pi$
$258$	−0.361426	−	1.32623i	−0.0225014	−	0.0825673i
$259$	−1.44540	+	1.05015i	−0.0898131	+	0.0652530i
$260$	−11.7544	−	14.9781i	−0.728977	−	0.928904i
$261$	−10.9189	−	10.6754i	−0.675863	−	0.660792i
$262$	−22.1967	−	6.60821i	−1.37132	−	0.408257i
$263$	16.9970	+	23.3944i	1.04808	+	1.44256i	0.890462	+	0.455058i	$0.150382\pi$
$263$	16.9970	+	23.3944i	1.04808	+	1.44256i	0.157618	+	0.987500i	$0.449618\pi$
$264$	4.76768	−	14.7491i	0.293431	−	0.907745i
$265$	0.949729	+	3.05270i	0.0583414	+	0.187526i
$266$	−10.0831	+	33.8688i	−0.618236	+	2.07663i
$267$	−0.455390	+	1.11718i	−0.0278694	+	0.0683704i
$268$	0.0383375	+	0.0103857i	0.00234184	+	0.000634407i
$269$	−2.01171	+	6.19140i	−0.122656	+	0.377496i	−0.993467	−	0.114122i	$-0.963594\pi$
$269$	−2.01171	+	6.19140i	−0.122656	+	0.377496i	0.870811	+	0.491618i	$0.163594\pi$
$270$	−11.0315	−	12.1781i	−0.671354	−	0.741136i
$271$	16.9043	−	5.49254i	1.02686	−	0.333648i	0.253313	−	0.967384i	$-0.418480\pi$
$271$	16.9043	−	5.49254i	1.02686	−	0.333648i	0.773549	+	0.633737i	$0.218480\pi$
$272$	2.33027	−	10.6738i	0.141293	−	0.647193i
$273$	15.1993	−	18.0006i	0.919901	−	1.08944i
$274$	−24.5367	+	18.7741i	−1.48232	+	1.13419i
$275$	9.61690	−	12.5616i	0.579921	−	0.757491i
$276$	−6.75497	+	19.2518i	−0.406601	+	1.15882i
$277$	23.5912	+	17.1400i	1.41746	+	1.02984i	0.992185	+	0.124775i	$0.0398209\pi$
$277$	23.5912	+	17.1400i	1.41746	+	1.02984i	0.425270	+	0.905066i	$0.360179\pi$
$278$	−20.9918	−	14.4699i	−1.25901	−	0.867844i
$279$	27.9079	−	4.74334i	1.67080	−	0.283976i
$280$	1.24938	+	20.1676i	0.0746649	+	1.20524i
$281$	−27.1580	−	8.82416i	−1.62011	−	0.526405i	−0.648142	−	0.761520i	$-0.724454\pi$
$281$	−27.1580	−	8.82416i	−1.62011	−	0.526405i	−0.971968	+	0.235114i	$0.924454\pi$
$282$	−10.9674	+	7.18892i	−0.653097	+	0.428094i
$283$	−5.53278	−	1.79771i	−0.328889	−	0.106863i	0.139918	−	0.990163i	$-0.455316\pi$
$283$	−5.53278	−	1.79771i	−0.328889	−	0.106863i	−0.468807	+	0.883300i	$0.655316\pi$
$284$	−0.423061	−	1.11124i	−0.0251041	−	0.0659402i
$285$	−30.1806	−	2.58500i	−1.78775	−	0.153122i
$286$	0.472469	+	19.0444i	0.0279377	+	1.12612i
$287$	7.38357	+	10.1626i	0.435838	+	0.599880i
$288$	−13.9435	+	9.67359i	−0.821629	+	0.570022i
$289$	7.71803	+	5.60748i	0.454002	+	0.329852i
$290$	−15.2465	+	5.16145i	−0.895306	+	0.303091i
$291$	−16.8392	+	10.4501i	−0.987132	+	0.612597i
$292$	3.63743	−	5.56754i	0.212864	−	0.325816i
$293$			23.2229i			1.35670i	0.734740	+	0.678349i	$0.237304\pi$
$293$			23.2229i			1.35670i	−0.734740	+	0.678349i	$0.762696\pi$
$294$	−7.57979	+	2.06566i	−0.442063	+	0.120472i
$295$	−14.4822	+	10.2470i	−0.843187	+	0.596601i
$296$	−1.20696	+	1.02225i	−0.0701530	+	0.0594172i
$297$	1.56694	+	16.3660i	0.0909229	+	0.949650i
$298$	−26.8746	+	0.666726i	−1.55680	+	0.0386224i
$299$		−	25.0748i		−	1.45011i
$300$	−16.7123	+	4.54951i	−0.964887	+	0.262666i
$301$		−	1.79289i		−	0.103340i
$302$	0.349077	+	14.0707i	0.0200871	+	0.809677i
$303$	10.8504	−	2.66973i	0.623339	−	0.153372i
$304$	−6.67278	+	30.5647i	−0.382710	+	1.75300i
$305$	−12.5371	−	9.35113i	−0.717870	−	0.535444i
$306$	2.22441	+	11.3724i	0.127161	+	0.650118i
$307$		−	1.60932i		−	0.0918485i	−0.998945	−	0.0459243i	$-0.985377\pi$
$307$		−	1.60932i		−	0.0918485i	0.998945	−	0.0459243i	$-0.0146233\pi$
$308$	11.0578	−	16.9254i	0.630079	−	0.964415i
$309$	3.18541	+	5.13293i	0.181211	+	0.292002i
$310$	8.87218	−	28.4899i	0.503906	−	1.61812i
$311$	−9.57804	−	6.95885i	−0.543121	−	0.394600i	0.282122	−	0.959379i	$-0.408962\pi$
$311$	−9.57804	−	6.95885i	−0.543121	−	0.394600i	−0.825243	+	0.564778i	$0.808962\pi$
$312$	12.2339	−	16.8921i	0.692610	−	0.956327i
$313$	5.30240	+	7.29813i	0.299709	+	0.412515i	0.932138	−	0.362104i	$-0.117942\pi$
$313$	5.30240	+	7.29813i	0.299709	+	0.412515i	−0.632428	+	0.774619i	$0.717942\pi$
$314$	−5.18819	+	0.128713i	−0.292787	+	0.00726368i
$315$	−9.70574	−	19.1083i	−0.546856	−	1.07663i
$316$	6.16336	−	2.34645i	0.346716	−	0.131998i
$317$	17.0337	+	5.53458i	0.956707	+	0.310853i	0.745438	−	0.666575i	$-0.232240\pi$
$317$	17.0337	+	5.53458i	0.956707	+	0.310853i	0.211269	+	0.977428i	$0.432240\pi$
$318$	−2.92901	+	1.91991i	−0.164251	+	0.107663i
$319$	15.3172	+	4.97685i	0.857597	+	0.278650i
$320$	2.43035	+	17.7227i	0.135861	+	0.990728i
$321$	23.9100	−	5.88304i	1.33453	−	0.328359i
$322$	−15.1028	+	21.9101i	−0.841649	+	1.22100i
$323$	17.2821	+	12.5562i	0.961603	+	0.698645i
$324$	9.50273	−	15.2872i	0.527929	−	0.849288i
$325$	17.5299	−	12.0764i	0.972386	−	0.669878i
$326$	19.3854	+	25.3356i	1.07366	+	1.40321i
$327$	−9.35821	−	7.90186i	−0.517510	−	0.436974i
$328$	7.18743	+	8.48610i	0.396859	+	0.468566i
$329$	−16.2669	+	5.28543i	−0.896822	+	0.291395i
$330$	16.1271	+	6.34429i	0.887768	+	0.349242i
$331$	−2.15044	+	6.61837i	−0.118199	+	0.363779i	−0.992601	−	0.121424i	$-0.961254\pi$
$331$	−2.15044	+	6.61837i	−0.118199	+	0.363779i	0.874402	+	0.485202i	$0.161254\pi$
$332$	−9.04564	+	33.3909i	−0.496444	+	1.83256i
$333$	0.744729	−	1.50328i	0.0408109	−	0.0823791i
$334$	26.3358	+	7.84045i	1.44103	+	0.429010i
$335$	−0.0142512	+	0.0420587i	−0.000778627	+	0.00229791i
$336$	−20.8642	+	7.39152i	−1.13824	+	0.403240i
$337$	3.37443	+	4.64451i	0.183817	+	0.253003i	0.890974	−	0.454054i	$-0.150023\pi$
$337$	3.37443	+	4.64451i	0.183817	+	0.253003i	−0.707157	+	0.707056i	$0.750023\pi$
$338$	−2.06827	+	6.94725i	−0.112499	+	0.377881i
$339$	−4.23724	+	5.01818i	−0.230135	+	0.272550i
$340$	11.7488	+	3.34146i	0.637169	+	0.181216i
$341$	−24.1540	+	17.5489i	−1.30801	+	0.950328i
$342$	−6.36966	−	32.5652i	−0.344432	−	1.76092i
$343$	12.1173			0.654271
$344$	−0.118000	−	1.58285i	−0.00636211	−	0.0853416i
$345$	−21.0135	−	8.87452i	−1.13133	−	0.477788i
$346$	−11.7794	+	17.0888i	−0.633267	+	0.918698i
$347$	1.98745	+	6.11674i	0.106692	+	0.328364i	0.990124	−	0.140196i	$-0.0447732\pi$
$347$	1.98745	+	6.11674i	0.106692	+	0.328364i	−0.883432	+	0.468559i	$0.844773\pi$
$348$	−10.0292	−	14.5028i	−0.537622	−	0.777431i
$349$		−	20.3022i		−	1.08675i	−0.839490	−	0.543376i	$-0.817146\pi$
$349$		−	20.3022i		−	1.08675i	0.839490	−	0.543376i	$-0.182854\pi$
$350$	−22.5912	−	0.00624457i	−1.20755	−	0.000333786i
$351$	−4.79978	+	21.5952i	−0.256193	+	1.15266i
$352$	8.64845	−	15.6704i	0.460964	−	0.835233i
$353$	9.40254	+	28.9381i	0.500447	+	1.54022i	0.808293	+	0.588781i	$0.200392\pi$
$353$	9.40254	+	28.9381i	0.500447	+	1.54022i	−0.307846	+	0.951436i	$0.599608\pi$
$354$	−15.1551	−	12.1658i	−0.805482	−	0.646603i
$355$	1.26939	−	0.394921i	0.0673721	−	0.0209602i
$356$	−0.761931	+	1.16623i	−0.0403822	+	0.0618101i
$357$	−1.10088	+	15.0740i	−0.0582649	+	0.797803i
$358$	25.9960	−	9.16543i	1.37393	−	0.484408i
$359$	14.3236	−	10.4067i	0.755972	−	0.549246i	−0.141700	−	0.989910i	$-0.545257\pi$
$359$	14.3236	−	10.4067i	0.755972	−	0.549246i	0.897672	+	0.440664i	$0.145257\pi$
$360$	−9.82631	−	16.2309i	−0.517892	−	0.855446i
$361$	−34.1165	−	24.7871i	−1.79560	−	1.30458i
$362$	9.35656	+	2.78555i	0.491770	+	0.146405i
$363$	0.903151	+	1.45533i	0.0474031	+	0.0763849i
$364$	21.1884	−	17.0617i	1.11057	−	0.894275i
$365$	5.96010	+	4.44552i	0.311966	+	0.232689i
$366$	6.07177	−	16.0212i	0.317376	−	0.837443i
$367$	4.29018	−	13.2038i	0.223946	−	0.689234i	−0.774451	−	0.632634i	$-0.781974\pi$
$367$	4.29018	−	13.2038i	0.223946	−	0.689234i	0.998397	−	0.0566004i	$-0.0180261\pi$
$368$	−11.8915	+	20.3373i	−0.619888	+	1.06016i
$369$	−10.5695	−	5.23617i	−0.550227	−	0.272584i
$370$	−1.05690	−	1.41780i	−0.0549454	−	0.0737078i
$371$	−4.34433	+	1.41156i	−0.225546	+	0.0732844i
$372$	32.6786	+	0.761380i	1.69431	+	0.0394757i
$373$	15.1901	+	11.0363i	0.786514	+	0.571436i	0.906927	−	0.421288i	$-0.138422\pi$
$373$	15.1901	+	11.0363i	0.786514	+	0.571436i	−0.120413	+	0.992724i	$0.538422\pi$
$374$	−7.42664	−	9.70622i	−0.384023	−	0.501897i
$375$	−3.91621	−	18.9648i	−0.202232	−	0.979338i
$376$	−14.0133	+	5.73685i	−0.722683	+	0.295855i
$377$	17.5321	+	12.7378i	0.902949	+	0.656031i
$378$	17.2010	−	15.9787i	0.884725	−	0.821855i
$379$	−0.658091	−	2.02539i	−0.0338038	−	0.104038i	0.932731	−	0.360573i	$-0.117419\pi$
$379$	−0.658091	−	2.02539i	−0.0338038	−	0.104038i	−0.966535	+	0.256536i	$0.917419\pi$
$380$	−33.6430	−	9.56835i	−1.72585	−	0.490846i
$381$	−13.9996	−	5.70659i	−0.717223	−	0.292357i
$382$	14.3450	−	10.9760i	0.733953	−	0.561579i
$383$	−0.741958	−	0.241077i	−0.0379123	−	0.0123184i	0.289999	−	0.957027i	$-0.406345\pi$
$383$	−0.741958	−	0.241077i	−0.0379123	−	0.0123184i	−0.327912	+	0.944708i	$0.606345\pi$
$384$	−17.9335	+	7.89878i	−0.915164	+	0.403083i
$385$	18.1188	+	13.5144i	0.923420	+	0.688760i
$386$	−0.319861	−	12.8931i	−0.0162805	−	0.656240i
$387$	0.781169	+	1.49132i	0.0397090	+	0.0758080i
$388$	−21.3867	+	8.14212i	−1.08575	+	0.413354i
$389$	8.54566	+	6.20878i	0.433282	+	0.314798i	0.782960	−	0.622072i	$-0.213709\pi$
$389$	8.54566	+	6.20878i	0.433282	+	0.314798i	−0.349678	+	0.936870i	$0.613709\pi$
$390$	18.0000	+	14.8245i	0.911465	+	0.750668i
$391$	9.45540	+	13.0142i	0.478180	+	0.658159i
$392$	−9.04648	+	0.674404i	−0.456916	+	0.0340625i
$393$	28.2891	+	2.06600i	1.42700	+	0.104216i
$394$	3.15366	−	1.11189i	0.158879	−	0.0560161i
$395$	2.19037	+	7.04047i	0.110209	+	0.354245i
$396$	−1.82341	+	18.8964i	−0.0916298	+	0.949582i
$397$	6.38052	+	19.6372i	0.320229	+	0.985564i	0.973548	+	0.228482i	$0.0733761\pi$
$397$	6.38052	+	19.6372i	0.320229	+	0.985564i	−0.653319	+	0.757083i	$0.726624\pi$
$398$	−0.0662585	−	2.67077i	−0.00332124	−	0.133873i
$399$	3.15240	−	43.1649i	0.157818	−	2.16095i
$400$	−19.9451	+	1.48134i	−0.997253	+	0.0740668i
$401$			17.4022i			0.869023i	0.900666	+	0.434511i	$0.143079\pi$
$401$			17.4022i			0.869023i	−0.900666	+	0.434511i	$0.856921\pi$
$402$	−0.0485898	−	0.00233890i	−0.00242344	−	0.000116654i
$403$	−38.2069	+	12.4142i	−1.90322	+	0.618395i
$404$	12.8868	−	0.639803i	0.641140	−	0.0318314i
$405$	16.3987	+	11.6654i	0.814860	+	0.579657i
$406$	−7.64724	−	21.6900i	−0.379526	−	1.07645i
$407$			1.76937i			0.0877043i
$408$	0.0201896	+	13.3806i	0.000999535	+	0.662436i
$409$	−14.5065	+	10.5396i	−0.717299	+	0.521149i	−0.885520	−	0.464601i	$-0.846198\pi$
$409$	−14.5065	+	10.5396i	−0.717299	+	0.521149i	0.168221	+	0.985749i	$0.446198\pi$
$410$	−9.96851	+	7.43102i	−0.492310	+	0.366992i
$411$	24.4118	−	28.9110i	1.20414	−	1.42607i
$412$	2.48188	+	6.51910i	0.122273	+	0.321173i
$413$	−14.8991	−	20.5069i	−0.733139	−	1.00908i
$414$	3.01617	−	24.8051i	0.148237	−	1.21911i
$415$	−36.6320	−	12.4124i	−1.79819	−	0.609301i
$416$	17.5832	−	16.4574i	0.862089	−	0.806891i
$417$	28.9158	+	11.7868i	1.41601	+	0.577200i
$418$	21.2664	+	27.7940i	1.04017	+	1.35945i
$419$	−23.8145	−	7.73780i	−1.16341	−	0.378016i	−0.337234	−	0.941421i	$-0.609491\pi$
$419$	−23.8145	−	7.73780i	−1.16341	−	0.378016i	−0.826181	+	0.563405i	$0.809491\pi$
$420$	−6.79924	−	23.7951i	−0.331769	−	1.16108i
$421$	7.89845	−	2.56636i	0.384947	−	0.125077i	−0.110149	−	0.993915i	$-0.535133\pi$
$421$	7.89845	−	2.56636i	0.384947	−	0.125077i	0.495096	+	0.868838i	$0.335133\pi$
$422$	11.6835	+	8.05354i	0.568744	+	0.392040i
$423$	11.2279	−	11.4839i	0.545917	−	0.558368i
$424$	−3.74248	+	1.53211i	−0.181751	+	0.0744061i
$425$	−4.54447	+	12.8782i	−0.220439	+	0.624684i
$426$	0.798347	+	1.21795i	0.0386801	+	0.0590100i
$427$	13.1352	−	18.0790i	0.635656	−	0.874906i
$428$	28.3974	−	1.40988i	1.37264	−	0.0681489i
$429$	−5.57450	−	22.6560i	−0.269139	−	1.09384i
$430$	1.77446	−	0.0217624i	0.0855720	−	0.00104948i
$431$	−6.42852	+	19.7849i	−0.309651	+	0.953007i	0.668250	+	0.743937i	$0.267044\pi$
$431$	−6.42852	+	19.7849i	−0.309651	+	0.953007i	−0.977901	+	0.209070i	$0.932956\pi$
$432$	14.1343	−	15.2389i	0.680035	−	0.733180i
$433$	36.0331	+	11.7079i	1.73164	+	0.562645i	0.993685	−	0.112203i	$-0.0357906\pi$
$433$	36.0331	+	11.7079i	1.73164	+	0.562645i	0.737957	+	0.674847i	$0.235791\pi$
$434$	40.8621	+	12.1651i	1.96144	+	0.583943i
$435$	16.8797	−	10.1843i	0.809320	−	0.488300i
$436$	−8.87011	−	11.0155i	−0.424801	−	0.527548i
$437$	−27.0758	−	37.2666i	−1.29521	−	1.78270i
$438$	−2.88651	+	7.61647i	−0.137923	+	0.363929i
$439$	−11.4335	+	15.7369i	−0.545693	+	0.751083i	−0.989420	−	0.145080i	$-0.953656\pi$
$439$	−11.4335	+	15.7369i	−0.545693	+	0.751083i	0.443727	+	0.896162i	$0.353656\pi$
$440$	16.8856	+	10.7387i	0.804991	+	0.511948i
$441$	8.52335	−	4.46462i	0.405874	−	0.212601i
$442$	−5.46806	−	15.5091i	−0.260089	−	0.737694i
$443$	−22.9487			−1.09032			−0.545162	−	0.838331i	$-0.683532\pi$
$443$	−22.9487			−1.09032			−0.545162	+	0.838331i	$0.683532\pi$
$444$	1.17483	−	1.54025i	0.0557552	−	0.0730972i
$445$	−1.24846	−	0.931201i	−0.0591827	−	0.0441432i
$446$	−4.56890	−	3.14938i	−0.216343	−	0.149128i
$447$	31.9711	−	7.86647i	1.51218	−	0.372071i
$448$	−25.2766	+	3.78973i	−1.19421	+	0.179048i
$449$			0.409419i			0.0193217i	0.999953	+	0.00966084i	$0.00307519\pi$
$449$			0.409419i			0.0193217i	−0.999953	+	0.00966084i	$0.996925\pi$
$450$	18.7940	−	9.83790i	0.885959	−	0.463763i
$451$	12.4404			0.585795
$452$	−5.90689	+	4.75644i	−0.277837	+	0.223724i
$453$	−4.11864	−	16.7391i	−0.193510	−	0.786469i
$454$	−9.43202	−	6.50158i	−0.442667	−	0.305134i
$455$	17.5674	+	24.8284i	0.823574	+	1.16397i
$456$	−0.0578135	−	38.3156i	−0.00270736	−	1.79429i
$457$		−	9.58380i		−	0.448311i	−0.974553	−	0.224156i	$-0.928038\pi$
$457$		−	9.58380i		−	0.448311i	0.974553	−	0.224156i	$-0.0719624\pi$
$458$	10.2893	−	3.62770i	0.480787	−	0.169511i
$459$	−5.65211	−	13.0182i	−0.263818	−	0.607637i
$460$	−21.8682	−	14.6816i	−1.01961	−	0.684535i
$461$	−8.79648	−	6.39102i	−0.409693	−	0.297659i	0.363785	−	0.931483i	$-0.381484\pi$
$461$	−8.79648	−	6.39102i	−0.409693	−	0.297659i	−0.773477	+	0.633824i	$0.781484\pi$
$462$	−8.77504	+	23.1542i	−0.408252	+	1.07723i
$463$	−28.2505	+	20.5252i	−1.31291	+	0.953888i	−0.312922	+	0.949779i	$0.601308\pi$
$463$	−28.2505	+	20.5252i	−1.31291	+	0.953888i	−0.999992	+	0.00410901i	$0.998692\pi$
$464$	−8.17889	−	18.6457i	−0.379695	−	0.865603i
$465$	−3.11875	+	36.4124i	−0.144629	+	1.68858i
$466$	1.53683	−	5.16215i	0.0711923	−	0.239132i
$467$	2.57983	−	7.93990i	0.119380	−	0.367415i	−0.873455	−	0.486905i	$-0.838126\pi$
$467$	2.57983	−	7.93990i	0.119380	−	0.367415i	0.992835	+	0.119490i	$0.0381259\pi$
$468$	−10.1906	+	23.4237i	−0.471061	+	1.08276i
$469$	−0.0603439	−	0.0196069i	−0.00278642	−	0.000905364i
$470$	−5.42854	−	16.0355i	−0.250400	−	0.739662i
$471$	6.17208	−	1.51864i	0.284394	−	0.0699751i
$472$	−14.5034	−	17.1239i	−0.667571	−	0.788192i
$473$	−1.43647	−	1.04366i	−0.0660491	−	0.0479875i
$474$	−6.75520	+	4.42792i	−0.310277	+	0.203381i
$475$	13.0132	−	36.8770i	0.597087	−	1.69203i
$476$	−4.56339	+	16.8452i	−0.209163	+	0.772098i
$477$	2.99857	−	3.06697i	0.137295	−	0.140427i
$478$	11.4437	+	7.88821i	0.523420	+	0.360799i
$479$	10.0161	+	30.8264i	0.457647	+	1.40849i	0.868000	+	0.496565i	$0.165406\pi$
$479$	10.0161	+	30.8264i	0.457647	+	1.40849i	−0.410353	+	0.911927i	$0.634594\pi$
$480$	−7.56878	−	20.5600i	−0.345466	−	0.938431i
$481$	−0.735706	+	2.26427i	−0.0335453	+	0.103242i
$482$	−19.7459	+	15.1084i	−0.899401	+	0.688170i
$483$	12.3024	−	30.1807i	0.559778	−	1.37327i
$484$	0.703682	+	1.84834i	0.0319855	+	0.0840157i
$485$	−7.60054	−	24.4303i	−0.345123	−	1.10932i
$486$	−7.34578	+	20.7856i	−0.333211	+	0.942852i
$487$	26.2779	−	19.0920i	1.19077	−	0.865142i	0.197421	−	0.980319i	$-0.436743\pi$
$487$	26.2779	−	19.0920i	1.19077	−	0.865142i	0.993345	+	0.115177i	$0.0367434\pi$
$488$	10.4065	−	16.8255i	0.471080	−	0.761657i
$489$	−29.8523	−	25.2066i	−1.34997	−	1.13988i
$490$	−0.124379	−	10.1416i	−0.00561887	−	0.458150i
$491$	−19.0928	−	26.2790i	−0.861646	−	1.18595i	−0.981175	−	0.193123i	$-0.938138\pi$
$491$	−19.0928	−	26.2790i	−0.861646	−	1.18595i	0.119529	−	0.992831i	$-0.461862\pi$
$492$	−10.8295	−	8.26023i	−0.488231	−	0.372400i
$493$	−13.9027			−0.626147
$494$	15.6579	+	44.4108i	0.704483	+	1.99813i
$495$	−20.9595	−	3.34683i	−0.942058	−	0.150429i
$496$	36.8757	+	8.05059i	1.65577	+	0.361482i
$497$	0.586960	+	1.80648i	0.0263288	+	0.0810316i
$498$	2.03712	−	42.3204i	0.0912854	−	1.89642i
$499$	2.40671			0.107739			0.0538695	−	0.998548i	$-0.482845\pi$
$499$	2.40671			0.107739			0.0538695	+	0.998548i	$0.482845\pi$
$500$	−0.268036	−	22.3591i	−0.0119869	−	0.999928i
$501$	−33.5642	−	2.45125i	−1.49954	−	0.109514i
$502$	0.577598	+	23.2820i	0.0257795	+	1.03913i
$503$	−18.2205	+	5.92020i	−0.812412	+	0.263969i	−0.685619	−	0.727961i	$-0.740468\pi$
$503$	−18.2205	+	5.92020i	−0.812412	+	0.263969i	−0.126793	+	0.991929i	$0.540468\pi$
$504$	23.0128	−	14.3295i	1.02507	−	0.638287i
$505$	−0.180893	+	14.4244i	−0.00804963	+	0.641879i
$506$	8.76299	+	24.8546i	0.389562	+	1.10492i
$507$	0.646629	−	8.85409i	0.0287178	−	0.393224i
$508$	−14.6143	−	9.54792i	−0.648404	−	0.423620i
$509$	−17.7600	+	12.9034i	−0.787197	+	0.571932i	−0.907130	−	0.420850i	$-0.861732\pi$
$509$	−17.7600	+	12.9034i	−0.787197	+	0.571932i	0.119933	+	0.992782i	$0.461732\pi$
$510$	−14.9324	−	0.906593i	−0.661220	−	0.0401446i
$511$	−6.24445	+	8.59475i	−0.276238	+	0.380209i
$512$	−22.0660	+	5.00934i	−0.975187	+	0.221384i
$513$	16.1850	+	37.2779i	0.714583	+	1.64586i
$514$	17.3164	−	0.429599i	0.763794	−	0.0189488i
$515$	−7.44684	+	2.31680i	−0.328147	+	0.102090i
$516$	0.557492	+	1.86231i	0.0245422	+	0.0819838i
$517$	−5.23440	+	16.1098i	−0.230208	+	0.708509i
$518$	2.00665	−	1.53537i	0.0881671	−	0.0674604i
$519$	9.59523	−	23.5394i	0.421184	−	1.03327i
$520$	17.1435	+	20.7635i	0.751791	+	0.910539i
$521$	17.3417	−	5.63465i	0.759752	−	0.246858i	0.0965798	−	0.995325i	$-0.469210\pi$
$521$	17.3417	−	5.63465i	0.759752	−	0.246858i	0.663172	+	0.748467i	$0.269210\pi$
$522$	15.8113	+	14.7097i	0.692044	+	0.643826i
$523$	−7.59643	+	10.4556i	−0.332169	+	0.457191i	−0.942134	−	0.335237i	$-0.891183\pi$
$523$	−7.59643	+	10.4556i	−0.332169	+	0.457191i	0.609965	+	0.792428i	$0.291183\pi$
$524$	31.6130	+	8.56401i	1.38102	+	0.374121i
$525$	27.0245	−	5.93482i	1.17945	−	0.259017i
$526$	−24.8505	−	32.4783i	−1.08353	−	1.41612i
$527$	15.1488	−	20.8505i	0.659892	−	0.908264i
$528$	−6.22313	+	21.0192i	−0.270827	+	0.914743i
$529$	−3.61191	−	11.1163i	−0.157040	−	0.483319i
$530$	−1.44978	−	4.28253i	−0.0629743	−	0.186021i
$531$	21.3280	+	10.5660i	0.925556	+	0.458524i
$532$	13.0674	−	48.2366i	0.566543	−	2.09132i
$533$	15.9200	+	5.17273i	0.689573	+	0.224056i
$534$	0.604636	−	1.59542i	0.0261652	−	0.0690405i
$535$	−0.398617	+	31.7858i	−0.0172337	+	1.37422i
$536$	−0.0545650	−	0.0133384i	−0.00235685	−	0.000576131i
$537$	−28.6847	+	17.8012i	−1.23784	+	0.768180i
$538$	2.62695	−	8.82382i	0.113256	−	0.380422i
$539$	−5.96483	+	8.20989i	−0.256923	+	0.353625i
$540$	16.0232	+	16.8302i	0.689529	+	0.724258i
$541$	−16.0842	−	22.1380i	−0.691514	−	0.951788i	−1.00000		0.000558616i	$-0.999822\pi$
$541$	−16.0842	−	22.1380i	−0.691514	−	0.951788i	0.308486	−	0.951229i	$-0.400178\pi$
$542$	−23.7063	+	8.35813i	−1.01827	+	0.359012i
$543$	−11.9247	−	0.870880i	−0.511737	−	0.0373730i
$544$	−2.92011	+	15.1721i	−0.125199	+	0.650498i
$545$	12.9079	−	9.13304i	0.552913	−	0.391216i
$546$	−20.8570	+	25.9819i	−0.892599	+	1.11192i
$547$	12.1139	−	3.93606i	0.517955	−	0.168294i	−0.0383622	−	0.999264i	$-0.512214\pi$
$547$	12.1139	−	3.93606i	0.517955	−	0.168294i	0.556317	+	0.830970i	$0.312214\pi$
$548$	34.0310	−	27.4030i	1.45373	−	1.17060i
$549$	−3.04870	+	20.7611i	−0.130115	+	0.886063i
$550$	−13.1556	+	18.0966i	−0.560956	+	0.771641i
$551$	39.8108			1.69600
$552$	8.87479	−	27.4547i	0.377736	−	1.16855i
$553$	−10.0194	+	3.25549i	−0.426067	+	0.138437i
$554$	−33.9538	−	23.4047i	−1.44256	−	0.994370i
$555$	1.63715	+	1.41792i	0.0694933	+	0.0601874i
$556$	30.1853	+	19.7209i	1.28014	+	0.836352i
$557$			37.6614i			1.59576i	0.602815	+	0.797881i	$0.294046\pi$
$557$			37.6614i			1.59576i	−0.602815	+	0.797881i	$0.705954\pi$
$558$	−39.2893	+	7.68487i	−1.66325	+	0.325327i
$559$	−1.40431	−	1.93286i	−0.0593959	−	0.0817515i
$560$	−2.47371	−	28.4686i	−0.104533	−	1.20302i
$561$	11.4366	+	9.65678i	0.482852	+	0.407710i
$562$	38.7049	+	11.5229i	1.63267	+	0.486063i
$563$	22.3918	−	16.2686i	0.943702	−	0.685639i	−0.00560711	−	0.999984i	$-0.501785\pi$
$563$	22.3918	−	16.2686i	0.943702	−	0.685639i	0.949309	+	0.314345i	$0.101785\pi$
$564$	15.2533	−	10.5482i	0.642279	−	0.444160i
$565$	−4.89744	−	6.92163i	−0.206037	−	0.291195i
$566$	7.88518	+	2.34750i	0.331439	+	0.0986730i
$567$	−16.3723	+	23.6376i	−0.687573	+	0.992687i
$568$	0.637091	+	1.55622i	0.0267317	+	0.0652973i
$569$	−9.49824	−	3.08617i	−0.398187	−	0.129379i	0.103077	−	0.994673i	$-0.467131\pi$
$569$	−9.49824	−	3.08617i	−0.398187	−	0.129379i	−0.501264	+	0.865295i	$0.667131\pi$
$570$	42.7594	+	2.59605i	1.79100	+	0.108737i
$571$	2.97063	+	9.14267i	0.124317	+	0.382609i	0.993776	−	0.111397i	$-0.0355324\pi$
$571$	2.97063	+	9.14267i	0.124317	+	0.382609i	−0.869459	+	0.494005i	$0.835532\pi$
$572$	−1.33593	−	26.9080i	−0.0558582	−	1.12508i
$573$	−14.2719	+	16.9023i	−0.596218	+	0.706104i
$574$	−10.7952	−	14.1087i	−0.450582	−	0.588886i
$575$	17.9014	−	23.3827i	0.746538	−	0.975127i
$576$	19.3737	−	14.1654i	0.807240	−	0.590224i
$577$	1.98269	−	2.72893i	0.0825403	−	0.113607i	−0.765750	−	0.643138i	$-0.777632\pi$
$577$	1.98269	−	2.72893i	0.0825403	−	0.113607i	0.848290	+	0.529531i	$0.177632\pi$
$578$	−11.1083	−	7.65703i	−0.462043	−	0.318490i
$579$	3.77394	+	15.3381i	0.156839	+	0.637430i
$580$	21.3742	−	7.83190i	0.887514	−	0.325202i
$581$	17.0771	−	52.5579i	0.708477	−	2.18047i
$582$	23.4404	−	15.3648i	0.971636	−	0.636891i
$583$	−1.39793	+	4.30238i	−0.0578962	+	0.178186i
$584$	−4.94724	+	7.99885i	−0.204718	+	0.330995i
$585$	−25.4303	−	12.9979i	−1.05142	−	0.537399i
$586$	−0.814524	−	32.8321i	−0.0336477	−	1.35628i
$587$	23.3983	−	16.9999i	0.965753	−	0.701660i	0.0112731	−	0.999936i	$-0.496412\pi$
$587$	23.3983	−	16.9999i	0.965753	−	0.701660i	0.954480	+	0.298276i	$0.0964116\pi$
$588$	10.6437	−	3.18624i	0.438939	−	0.131398i
$589$	−43.3790	+	59.7061i	−1.78740	+	2.46014i
$590$	20.1152	−	14.9949i	0.828131	−	0.617330i
$591$	−3.47984	+	2.15953i	−0.143141	+	0.0888310i
$592$	1.67052	−	1.48757i	0.0686578	−	0.0611388i
$593$	23.8052			0.977564			0.488782	−	0.872406i	$-0.337441\pi$
$593$	23.8052			0.977564			0.488782	+	0.872406i	$0.337441\pi$
$594$	−2.78932	−	23.0829i	−0.114447	−	0.947103i
$595$	−18.4803	−	6.26187i	−0.757617	−	0.256712i
$596$	37.9713	−	1.88521i	1.55537	−	0.0772211i
$597$	0.781761	+	3.17725i	0.0319954	+	0.130036i
$598$	0.879477	+	35.4502i	0.0359645	+	1.44967i
$599$	−20.0311			−0.818450			−0.409225	−	0.912434i	$-0.634201\pi$
$599$	−20.0311			−0.818450			−0.409225	+	0.912434i	$0.634201\pi$
$600$	23.4680	−	7.01817i	0.958076	−	0.286516i
$601$	4.88539			0.199279			0.0996397	−	0.995024i	$-0.468231\pi$
$601$	4.88539			0.199279			0.0996397	+	0.995024i	$0.468231\pi$
$602$	0.0628841	+	2.53475i	0.00256296	+	0.103309i
$603$	0.0587367	−	0.00998310i	0.00239194	−	0.000406543i
$604$	−0.987034	−	19.8806i	−0.0401618	−	0.808930i
$605$	−2.11138	+	0.656876i	−0.0858400	+	0.0267058i
$606$	−15.2464	+	4.15498i	−0.619343	+	0.168784i
$607$	−30.1854			−1.22519			−0.612594	−	0.790398i	$-0.709874\pi$
$607$	−30.1854			−1.22519			−0.612594	+	0.790398i	$0.709874\pi$
$608$	8.36181	−	43.4457i	0.339116	−	1.76196i
$609$	14.8526	+	23.9333i	0.601857	+	0.969826i
$610$	18.0526	+	12.7807i	0.730929	+	0.517476i
$611$	−13.3970	+	18.4394i	−0.541984	+	0.745977i
$612$	−3.54370	−	16.0001i	−0.143246	−	0.646764i
$613$	−31.0095	+	22.5297i	−1.25246	+	0.909967i	−0.998362	−	0.0572108i	$-0.981779\pi$
$613$	−31.0095	+	22.5297i	−1.25246	+	0.909967i	−0.254100	+	0.967178i	$0.581779\pi$
$614$	0.0564454	+	2.27522i	0.00227795	+	0.0918203i
$615$	9.96937	−	11.5108i	0.402004	−	0.464160i
$616$	−15.0397	+	24.3166i	−0.605967	+	0.979745i
$617$	7.06625	−	21.7477i	0.284476	−	0.875528i	−0.702079	−	0.712099i	$-0.747745\pi$
$617$	7.06625	−	21.7477i	0.284476	−	0.875528i	0.986555	−	0.163429i	$-0.0522554\pi$
$618$	−4.68349	−	7.14510i	−0.188398	−	0.287418i
$619$	−7.65157	+	23.5491i	−0.307542	+	0.946518i	0.671174	+	0.741300i	$0.265790\pi$
$619$	−7.65157	+	23.5491i	−0.307542	+	0.946518i	−0.978716	+	0.205218i	$0.934210\pi$
$620$	−11.5440	+	40.5896i	−0.463620	+	1.63012i
$621$	2.91677	+	30.4644i	0.117046	+	1.22249i
$622$	13.7853	+	9.50233i	0.552740	+	0.381009i
$623$	1.30802	−	1.80034i	0.0524048	−	0.0721291i
$624$	−16.7036	+	24.3108i	−0.668679	+	0.973211i
$625$	24.9686	+	1.25348i	0.998742	+	0.0501392i
$626$	−7.75239	−	10.1320i	−0.309848	−	0.404955i
$627$	−32.7489	−	27.6524i	−1.30787	−	1.10433i
$628$	7.33044	−	0.363942i	0.292516	−	0.0145229i
$629$	−0.471985	−	1.45262i	−0.0188193	−	0.0579198i
$630$	14.3920	+	26.6745i	0.573390	+	1.06274i
$631$	−9.69802	−	3.15108i	−0.386072	−	0.125442i	0.109549	−	0.993981i	$-0.465059\pi$
$631$	−9.69802	−	3.15108i	−0.386072	−	0.125442i	−0.495621	+	0.868539i	$0.665059\pi$
$632$	−8.63132	+	3.53353i	−0.343335	+	0.140556i
$633$	−16.0938	−	6.56020i	−0.639669	−	0.260745i
$634$	−24.2760	−	7.22722i	−0.964122	−	0.287030i
$635$	11.6691	−	15.6447i	0.463073	−	0.620842i
$636$	4.07363	−	2.81707i	0.161530	−	0.111704i
$637$	−11.0469	+	8.02606i	−0.437695	+	0.318004i
$638$	−21.8296	−	6.49893i	−0.864244	−	0.257295i
$639$	−1.27532	−	1.24688i	−0.0504509	−	0.0493258i
$640$	−4.05758	−	24.9707i	−0.160390	−	0.987054i
$641$	−9.76636	−	13.4422i	−0.385748	−	0.530936i	0.571348	−	0.820708i	$-0.306421\pi$
$641$	−9.76636	−	13.4422i	−0.385748	−	0.530936i	−0.957096	+	0.289772i	$0.906421\pi$
$642$	−33.5971	+	9.15594i	−1.32597	+	0.361356i
$643$			45.8989i			1.81007i	0.425332	+	0.905037i	$0.360157\pi$
$643$			45.8989i			1.81007i	−0.425332	+	0.905037i	$0.639843\pi$
$644$	20.5836	−	31.5058i	0.811107	−	1.24150i
$645$	−2.11682	+	0.492776i	−0.0833498	+	0.0194030i
$646$	−24.8735	−	17.1455i	−0.978634	−	0.674581i
$647$	−7.72499	+	2.51000i	−0.303701	+	0.0986783i	−0.456903	−	0.889517i	$-0.651041\pi$
$647$	−7.72499	+	2.51000i	−0.303701	+	0.0986783i	0.153202	+	0.988195i	$0.451041\pi$
$648$	−12.8986	+	21.9460i	−0.506704	+	0.862120i
$649$	−25.1032			−0.985386
$650$	−24.3599	+	17.6882i	−0.955473	+	0.693788i
$651$	−52.0776	−	3.80332i	−2.04108	−	0.149064i
$652$	−28.2952	−	35.1390i	−1.10813	−	1.37615i
$653$	−5.01671	+	1.63003i	−0.196319	+	0.0637879i	−0.405526	−	0.914083i	$-0.632912\pi$
$653$	−5.01671	+	1.63003i	−0.196319	+	0.0637879i	0.209207	+	0.977871i	$0.432912\pi$
$654$	13.5076	+	10.8432i	0.528188	+	0.424005i
$655$	−11.7515	+	34.6815i	−0.459170	+	1.35512i
$656$	−10.4591	−	11.7454i	−0.408358	−	0.458580i
$657$	1.44935	−	9.86981i	0.0565444	−	0.385058i
$658$	22.8124	−	8.04298i	0.889320	−	0.313548i
$659$	17.4110	+	23.9642i	0.678236	+	0.933512i	0.999911	−	0.0133385i	$-0.00424590\pi$
$659$	17.4110	+	23.9642i	0.678236	+	0.933512i	−0.321675	+	0.946850i	$0.604246\pi$
$660$	−23.0227	−	8.40378i	−0.896156	−	0.327117i
$661$	−11.5853	+	15.9458i	−0.450617	+	0.620221i	−0.972530	−	0.232778i	$-0.925218\pi$
$661$	−11.5853	+	15.9458i	−0.450617	+	0.620221i	0.521913	+	0.852999i	$0.325218\pi$
$662$	2.80811	−	9.43234i	0.109140	−	0.366598i
$663$	10.6201	+	17.1132i	0.412452	+	0.664621i
$664$	11.6174	−	47.5246i	0.450842	−	1.84431i
$665$	52.9187	+	17.9310i	2.05210	+	0.695336i
$666$	−1.00016	+	2.15142i	−0.0387552	+	0.0833659i
$667$	28.5121	+	9.26415i	1.10399	+	0.358709i
$668$	−37.5079	−	10.1610i	−1.45122	−	0.393139i
$669$	6.29355	+	2.56540i	0.243323	+	0.0991842i
$670$	0.0186729	−	0.0599616i	0.000721397	−	0.00231652i
$671$	−6.83890	−	21.0480i	−0.264013	−	0.812547i
$672$	29.2381	−	11.1818i	1.12789	−	0.431346i
$673$	0.882766	−	1.21502i	0.0340281	−	0.0468357i	−0.791664	−	0.610957i	$-0.790785\pi$
$673$	0.882766	−	1.21502i	0.0340281	−	0.0468357i	0.825692	+	0.564121i	$0.190785\pi$
$674$	−4.93360	−	6.44795i	−0.190035	−	0.248366i
$675$	−19.8931	+	16.7112i	−0.765685	+	0.643216i
$676$	2.68041	−	9.89442i	0.103093	−	0.380554i
$677$	3.31461	−	4.56217i	0.127391	−	0.175338i	−0.740557	−	0.671993i	$-0.765438\pi$
$677$	3.31461	−	4.56217i	0.127391	−	0.175338i	0.867948	+	0.496655i	$0.165438\pi$
$678$	5.81451	−	7.24321i	0.223305	−	0.278174i
$679$	34.7670	−	11.2965i	1.33423	−	0.433519i
$680$	−16.7274	−	4.31200i	−0.641467	−	0.165358i
$681$	12.9924	+	5.29602i	0.497870	+	0.202944i
$682$	33.5329	−	25.6575i	1.28404	−	0.982476i
$683$	−6.27079	+	19.2995i	−0.239945	+	0.738475i	0.756482	+	0.654015i	$0.226917\pi$
$683$	−6.27079	+	19.2995i	−0.239945	+	0.738475i	−0.996427	+	0.0844605i	$0.973083\pi$
$684$	10.1475	+	45.8166i	0.387999	+	1.75184i
$685$	28.2153	+	39.8772i	1.07805	+	1.52363i
$686$	−17.1311	+	0.425003i	−0.654070	+	0.0162267i
$687$	−11.3535	+	7.04577i	−0.433162	+	0.268813i
$688$	0.222342	+	2.23366i	0.00847672	+	0.0851576i
$689$	−3.57787	+	4.92452i	−0.136306	+	0.187609i
$690$	30.0198	+	11.8096i	1.14283	+	0.449583i
$691$	−14.6649	+	10.6547i	−0.557878	+	0.405322i	−0.830682	−	0.556747i	$-0.812049\pi$
$691$	−14.6649	+	10.6547i	−0.557878	+	0.405322i	0.272804	+	0.962070i	$0.412049\pi$
$692$	16.0542	−	24.5729i	0.610287	−	0.934121i
$693$	4.40604	−	30.0044i	0.167372	−	1.13977i
$694$	−3.02435	−	8.57800i	−0.114803	−	0.325617i
$695$	−24.1021	+	32.3137i	−0.914244	+	1.22573i
$696$	14.6878	+	20.1520i	0.556738	+	0.763858i
$697$	−10.2133	+	3.31852i	−0.386858	+	0.125698i
$698$	0.712082	+	28.7028i	0.0269527	+	1.08642i
$699$	−0.480477	+	6.57903i	−0.0181733	+	0.248842i
$700$	31.9392	−	0.783540i	1.20719	−	0.0296150i
$701$	33.5569			1.26743			0.633713	−	0.773568i	$-0.281530\pi$
$701$	33.5569			1.26743			0.633713	+	0.773568i	$0.281530\pi$
$702$	6.02840	−	30.6991i	0.227527	−	1.15866i
$703$	1.35154	+	4.15961i	0.0509743	+	0.156883i
$704$	−11.6774	+	22.4577i	−0.440108	+	0.846408i
$705$	10.7113	+	17.7532i	0.403412	+	0.668625i
$706$	−14.3081	−	40.5822i	−0.538492	−	1.52733i
$707$	−20.6112			−0.775164
$708$	21.8526	+	16.6681i	0.821271	+	0.626427i
$709$	−18.5443	−	25.5241i	−0.696447	−	0.958577i	−0.999983	−	0.00575711i	$-0.998167\pi$
$709$	−18.5443	−	25.5241i	−0.696447	−	0.958577i	0.303537	−	0.952820i	$-0.401833\pi$
$710$	−1.78078	+	0.602853i	−0.0668315	+	0.0226247i
$711$	6.91564	−	7.07338i	0.259357	−	0.265272i
$712$	1.03630	−	1.67552i	0.0388369	−	0.0627926i
$713$	−44.9615	+	32.6664i	−1.68382	+	1.22337i
$714$	1.02769	−	21.3500i	0.0384605	−	0.799003i
$715$	30.1188	+	0.377711i	1.12638	+	0.0141256i
$716$	−36.4311	+	13.8697i	−1.36150	+	0.518334i
$717$	−15.7634	−	6.42553i	−0.588694	−	0.239966i
$718$	−19.8854	+	15.2152i	−0.742118	+	0.567826i
$719$	4.60668	−	14.1779i	0.171800	−	0.528746i	−0.827673	−	0.561211i	$-0.810336\pi$
$719$	4.60668	−	14.1779i	0.171800	−	0.528746i	0.999473	+	0.0324647i	$0.0103356\pi$
$720$	14.4615	+	22.6023i	0.538949	+	0.842338i
$721$	−3.44339	−	10.5977i	−0.128239	−	0.394678i
$722$	49.1025	+	33.8468i	1.82741	+	1.25965i
$723$	19.6453	−	23.2660i	0.730617	−	0.865274i
$724$	−13.3258	−	3.60998i	−0.495249	−	0.134164i
$725$	7.25524	+	24.3947i	0.269453	+	0.905998i
$726$	−1.32790	−	2.02583i	−0.0492830	−	0.0751857i
$727$	30.4643	+	22.1336i	1.12986	+	0.820891i	0.985674	−	0.168660i	$-0.0539438\pi$
$727$	30.4643	+	22.1336i	1.12986	+	0.820891i	0.144185	+	0.989551i	$0.453944\pi$
$728$	−29.3573	+	24.8646i	−1.08805	+	0.921544i
$729$	3.31944	−	26.7952i	0.122942	−	0.992414i
$730$	−8.58219	−	6.07593i	−0.317641	−	0.224880i
$731$	1.45772	+	0.473642i	0.0539157	+	0.0175183i
$732$	−8.02220	+	22.8634i	−0.296509	+	0.845056i
$733$	0.474196	−	1.45942i	0.0175148	−	0.0539051i	−0.941917	−	0.335845i	$-0.890978\pi$
$733$	0.474196	−	1.45942i	0.0175148	−	0.0539051i	0.959432	+	0.281940i	$0.0909780\pi$
$734$	−5.60226	+	18.8178i	−0.206783	+	0.694576i
$735$	2.81637	+	12.0983i	0.103883	+	0.446252i
$736$	16.0986	−	29.1695i	0.593404	−	1.07520i
$737$	−0.0508360	+	0.0369345i	−0.00187257	+	0.00136050i
$738$	15.1266	+	7.03207i	0.556818	+	0.258854i
$739$	7.48359	+	5.43714i	0.275288	+	0.200009i	0.716860	−	0.697217i	$-0.245579\pi$
$739$	7.48359	+	5.43714i	0.275288	+	0.200009i	−0.441571	+	0.897226i	$0.645579\pi$
$740$	1.54395	+	1.96738i	0.0567566	+	0.0723224i
$741$	−30.4111	−	49.0041i	−1.11718	−	1.80021i
$742$	6.09241	−	2.14800i	0.223659	−	0.0788557i
$743$		−	25.3269i		−	0.929155i	−0.885532	−	0.464577i	$-0.846206\pi$
$743$		−	25.3269i		−	0.929155i	0.885532	−	0.464577i	$-0.153794\pi$
$744$	−46.2270	+	0.0697509i	−1.69476	+	0.00255719i
$745$	−0.533008	+	42.5022i	−0.0195279	+	1.55716i
$746$	−21.8625	−	15.0701i	−0.800444	−	0.551754i
$747$	8.69500	+	51.1580i	0.318133	+	1.87177i
$748$	10.8401	+	13.4620i	0.396352	+	0.492218i
$749$	−45.4190			−1.65958
$750$	6.20183	+	26.6747i	0.226459	+	0.974021i
$751$			9.81189i			0.358041i	0.983845	+	0.179020i	$0.0572928\pi$
$751$			9.81189i			0.358041i	−0.983845	+	0.179020i	$0.942707\pi$
$752$	19.6105	−	8.60213i	0.715123	−	0.313688i
$753$	−6.81488	−	27.6972i	−0.248348	−	1.00934i
$754$	−25.2333	−	17.3935i	−0.918941	−	0.633435i
$755$	22.2528	+	0.279066i	0.809862	+	0.0101563i
$756$	−23.7580	+	23.1936i	−0.864070	+	0.843544i
$757$	−36.1841			−1.31513			−0.657567	−	0.753396i	$-0.728415\pi$
$757$	−36.1841			−1.31513			−0.657567	+	0.753396i	$0.728415\pi$
$758$	1.00143	+	2.84038i	0.0363737	+	0.103167i
$759$	−17.0196	−	27.4252i	−0.617772	−	0.995472i
$760$	47.8994	+	12.3475i	1.73749	+	0.447892i
$761$	−4.73241	+	6.51361i	−0.171550	+	0.236118i	−0.886131	−	0.463434i	$-0.846617\pi$
$761$	−4.73241	+	6.51361i	−0.171550	+	0.236118i	0.714582	+	0.699552i	$0.246617\pi$
$762$	19.9925	+	7.57683i	0.724253	+	0.274480i
$763$	13.2795	+	18.2776i	0.480750	+	0.661695i
$764$	−19.8957	+	16.0207i	−0.719800	+	0.579609i
$765$	18.1001	−	2.84332i	0.654412	−	0.102800i
$766$	1.05742	+	0.314806i	0.0382061	+	0.0113744i
$767$	−32.1247	−	10.4379i	−1.15996	−	0.376892i
$768$	25.0769	−	11.7961i	0.904885	−	0.425656i
$769$	9.37546	−	28.8547i	0.338088	−	1.04053i	−0.627093	−	0.778944i	$-0.715755\pi$
$769$	9.37546	−	28.8547i	0.338088	−	1.04053i	0.965181	−	0.261583i	$-0.0842445\pi$
$770$	−26.0900	−	18.4709i	−0.940218	−	0.665646i
$771$	−20.6003	+	5.06869i	−0.741902	+	0.182544i
$772$	0.904427	+	18.2167i	0.0325510	+	0.655635i
$773$	8.11992	−	11.1761i	0.292053	−	0.401977i	−0.637626	−	0.770346i	$-0.720084\pi$
$773$	8.11992	−	11.1761i	0.292053	−	0.401977i	0.929680	+	0.368369i	$0.120084\pi$
$774$	−1.15671	−	2.08100i	−0.0415770	−	0.0747999i
$775$	−44.4914	−	15.7002i	−1.59818	−	0.563967i
$776$	29.9505	−	12.2613i	1.07516	−	0.440154i
$777$	−1.99643	+	2.36438i	−0.0716215	+	0.0848216i
$778$	−12.2994	−	8.47811i	−0.440956	−	0.303955i
$779$	29.2462	−	9.50265i	1.04785	−	0.340468i
$780$	−25.9680	−	20.3272i	−0.929802	−	0.727832i
$781$	1.78903	+	0.581292i	0.0640167	+	0.0208003i
$782$	−13.8243	−	18.0676i	−0.494356	−	0.646097i
$783$	−22.7822	−	13.4363i	−0.814168	−	0.480174i
$784$	12.7661	−	1.27075i	0.455931	−	0.0453841i
$785$	−0.102898	+	8.20513i	−0.00367259	+	0.292854i
$786$	−40.0671	−	1.92865i	−1.42914	−	0.0687928i
$787$	−25.0832	−	34.5241i	−0.894119	−	1.23065i	−0.972306	−	0.233711i	$-0.924913\pi$
$787$	−25.0832	−	34.5241i	−0.894119	−	1.23065i	0.0781866	−	0.996939i	$-0.475087\pi$
$788$	−4.41958	+	1.68258i	−0.157441	+	0.0599393i
$789$	38.2683	+	32.3129i	1.36239	+	1.15037i
$790$	−3.34364	−	9.87684i	−0.118961	−	0.351402i
$791$	9.80108	−	7.12090i	0.348486	−	0.253190i
$792$	1.91512	−	26.7793i	0.0680509	−	0.951562i
$793$		−	29.7788i		−	1.05748i
$794$	−9.70941	−	27.5389i	−0.344574	−	0.977319i
$795$	2.86063	+	4.74127i	0.101456	+	0.168156i
$796$	0.187350	+	3.77355i	0.00664043	+	0.133750i
$797$	36.7782	−	11.9500i	1.30275	−	0.423290i	0.426214	−	0.904622i	$-0.359847\pi$
$797$	36.7782	−	11.9500i	1.30275	−	0.423290i	0.876538	+	0.481333i	$0.159847\pi$
$798$	−2.94283	+	61.1362i	−0.104175	+	2.16420i
$799$		−	14.6222i		−	0.517295i
$800$	28.1459	−	2.79384i	0.995110	−	0.0987770i
$801$	−0.303594	+	2.06743i	−0.0107270	+	0.0730489i
$802$	−0.610366	−	24.6028i	−0.0215528	−	0.868756i
$803$	3.25120	+	10.0062i	0.114732	+	0.353110i
$804$	0.0687773	+	0.00160244i	0.00242559	+	5.65138e-5i
$805$	33.7272	+	25.1564i	1.18873	+	0.886648i
$806$	53.5807	−	18.8910i	1.88730	−	0.665407i
$807$	−0.821294	+	11.2457i	−0.0289109	+	0.395869i
$808$	−18.1966	+	1.35653i	−0.640154	+	0.0477226i
$809$	−13.9702	−	19.2283i	−0.491166	−	0.676032i	0.489436	−	0.872039i	$-0.337203\pi$
$809$	−13.9702	−	19.2283i	−0.491166	−	0.676032i	−0.980603	+	0.196007i	$0.937203\pi$
$810$	−23.5934	−	15.9171i	−0.828986	−	0.559270i
$811$	−8.11960	−	5.89923i	−0.285118	−	0.207150i	0.436029	−	0.899933i	$-0.356385\pi$
$811$	−8.11960	−	5.89923i	−0.285118	−	0.207150i	−0.721147	+	0.692783i	$0.756385\pi$
$812$	11.5723	+	30.3966i	0.406107	+	1.06671i
$813$	26.1581	−	16.2333i	0.917406	−	0.569326i
$814$	−0.0620590	−	2.50149i	−0.00217517	−	0.0876773i
$815$	41.1756	−	29.1340i	1.44232	−	1.02052i
$816$	−0.497855	−	18.9164i	−0.0174284	−	0.662208i
$817$	−4.17422	−	1.35628i	−0.146037	−	0.0474504i
$818$	20.1393	−	15.4094i	0.704154	−	0.538778i
$819$	18.1143	−	36.5648i	0.632966	−	1.27768i
$820$	13.8326	−	10.8554i	0.483056	−	0.379089i
$821$	6.61691	+	20.3648i	0.230932	+	0.710735i	0.997635	+	0.0687335i	$0.0218958\pi$
$821$	6.61691	+	20.3648i	0.230932	+	0.710735i	−0.766703	+	0.642002i	$0.778104\pi$
$822$	−33.4988	+	41.7299i	−1.16841	+	1.45550i
$823$	36.4456	+	26.4793i	1.27041	+	0.923009i	0.999219	−	0.0395161i	$-0.0125816\pi$
$823$	36.4456	+	26.4793i	1.27041	+	0.923009i	0.271194	+	0.962525i	$0.412582\pi$
$824$	−3.73748	−	9.12951i	−0.130201	−	0.318042i
$825$	10.9762	−	25.1069i	0.382143	−	0.874110i
$826$	21.7833	+	28.4697i	0.757940	+	0.990586i
$827$	6.61032	+	4.80268i	0.229864	+	0.167006i	0.696755	−	0.717309i	$-0.254626\pi$
$827$	6.61032	+	4.80268i	0.229864	+	0.167006i	−0.466892	+	0.884314i	$0.654626\pi$
$828$	−3.39418	+	35.1747i	−0.117956	+	1.22241i
$829$	19.2697	−	6.26109i	0.669263	−	0.217457i	0.0453742	−	0.998970i	$-0.485552\pi$
$829$	19.2697	−	6.26109i	0.669263	−	0.217457i	0.623888	+	0.781513i	$0.285552\pi$
$830$	52.2248	+	16.2636i	1.81275	+	0.564517i
$831$	46.7707	+	19.0648i	1.62246	+	0.661352i
$832$	−24.2816	+	23.8839i	−0.841812	+	0.828024i
$833$	2.70701	−	8.33132i	0.0937923	−	0.288663i
$834$	−41.2939	−	15.6497i	−1.42989	−	0.541904i
$835$	13.9428	−	41.1486i	0.482512	−	1.42401i
$836$	−31.0408	−	38.5487i	−1.07357	−	1.33323i
$837$	44.9751	−	19.5268i	1.55457	−	0.674946i
$838$	33.9398	+	10.1043i	1.17243	+	0.349046i
$839$	4.25685	+	3.09278i	0.146963	+	0.106775i	0.658837	−	0.752286i	$-0.271049\pi$
$839$	4.25685	+	3.09278i	0.146963	+	0.106775i	−0.511874	+	0.859060i	$0.671049\pi$
$840$	10.4472	+	33.4026i	0.360463	+	1.15250i
$841$	2.50014	−	1.81645i	0.0862116	−	0.0626364i
$842$	−11.0766	+	3.90530i	−0.381727	+	0.134586i
$843$	−49.3284	−	3.60253i	−1.69896	−	0.124078i
$844$	−16.8003	−	10.9761i	−0.578292	−	0.377814i
$845$	10.8548	+	3.67806i	0.373417	+	0.126529i
$846$	−15.4709	+	16.6296i	−0.531901	+	0.571736i
$847$	−0.976297	−	3.00473i	−0.0335459	−	0.103244i
$848$	5.23730	−	2.29733i	0.179850	−	0.0788908i
$849$	−10.0495	−	0.733928i	−0.344896	−	0.0251883i
$850$	5.97318	−	18.3663i	0.204878	−	0.629959i
$851$			3.29358i			0.112903i
$852$	−1.17141	−	1.69391i	−0.0401317	−	0.0580325i
$853$	−10.9357	−	33.6567i	−0.374433	−	1.15238i	−0.943861	−	0.330344i	$-0.892835\pi$
$853$	−10.9357	−	33.6567i	−0.374433	−	1.15238i	0.569428	−	0.822041i	$-0.307165\pi$
$854$	−17.9361	+	26.0205i	−0.613762	+	0.890402i
$855$	−51.8302	+	8.14191i	−1.77256	+	0.278447i
$856$	−40.0981	+	2.98927i	−1.37053	+	0.102171i
$857$	−5.45153			−0.186221			−0.0931104	−	0.995656i	$-0.529681\pi$
$857$	−5.45153			−0.186221			−0.0931104	+	0.995656i	$0.529681\pi$
$858$	8.67575	+	31.8351i	0.296185	+	1.08683i
$859$	6.76204	−	4.91291i	0.230718	−	0.167626i	−0.466420	−	0.884563i	$-0.654457\pi$
$859$	6.76204	−	4.91291i	0.230718	−	0.167626i	0.697138	+	0.716937i	$0.254457\pi$
$860$	−2.50793	+	0.0930048i	−0.0855196	+	0.00317144i
$861$	16.6239	+	14.0368i	0.566541	+	0.478374i
$862$	8.39456	−	28.1970i	0.285920	−	0.960394i
$863$	−17.3042	−	23.8172i	−0.589042	−	0.810747i	0.405608	−	0.914047i	$-0.367060\pi$
$863$	−17.3042	−	23.8172i	−0.589042	−	0.810747i	−0.994650	+	0.103300i	$0.967060\pi$
$864$	−19.4482	+	22.0401i	−0.661642	+	0.749820i
$865$	26.3055	+	19.6207i	0.894414	+	0.667125i
$866$	−51.3535	−	15.2885i	−1.74506	−	0.519525i
$867$	15.3014	+	6.23721i	0.519662	+	0.211827i
$868$	−58.1966	−	15.7655i	−1.97532	−	0.535117i
$869$	−3.22405	+	9.92262i	−0.109369	+	0.336602i
$870$	−23.5070	+	14.9904i	−0.796961	+	0.508222i
$871$	−0.0804125	+	0.0261276i	−0.00272467	+	0.000885300i
$872$	12.9267	+	15.2624i	0.437754	+	0.516850i
$873$	−23.9971	+	24.5445i	−0.812180	+	0.830704i
$874$	39.5863	+	51.7371i	1.33902	+	1.75003i
$875$	−1.34347	+	35.6946i	−0.0454176	+	1.20670i
$876$	3.81375	−	10.8692i	0.128855	−	0.367238i
$877$	15.0758	+	10.9532i	0.509074	+	0.369864i	0.812472	−	0.583000i	$-0.198121\pi$
$877$	15.0758	+	10.9532i	0.509074	+	0.369864i	−0.303398	+	0.952864i	$0.598121\pi$
$878$	15.6125	−	22.6496i	0.526898	−	0.764385i
$879$	9.61029	+	39.0584i	0.324147	+	1.31741i
$880$	−24.2492	−	14.5899i	−0.817440	−	0.491826i
$881$	−24.4991	−	7.96023i	−0.825395	−	0.268187i	−0.134291	−	0.990942i	$-0.542876\pi$
$881$	−24.4991	−	7.96023i	−0.825395	−	0.268187i	−0.691104	+	0.722755i	$0.742876\pi$
$882$	−11.8935	+	6.61093i	−0.400476	+	0.222602i
$883$	37.8036	+	12.2831i	1.27219	+	0.413361i	0.865824	−	0.500348i	$-0.166795\pi$
$883$	37.8036	+	12.2831i	1.27219	+	0.413361i	0.406369	+	0.913709i	$0.366795\pi$
$884$	8.27459	+	21.7347i	0.278305	+	0.731016i
$885$	−20.1170	+	23.2274i	−0.676225	+	0.780780i
$886$	32.4443	−	0.804905i	1.08999	−	0.0270413i
$887$	6.23892	+	8.58714i	0.209483	+	0.288328i	0.900810	−	0.434214i	$-0.142974\pi$
$887$	6.23892	+	8.58714i	0.209483	+	0.288328i	−0.691327	+	0.722542i	$0.742974\pi$
$888$	−1.60693	+	2.21878i	−0.0539251	+	0.0744575i
$889$	22.5604	+	16.3911i	0.756653	+	0.549741i
$890$	1.79771	+	1.27272i	0.0602593	+	0.0426618i
$891$	9.40810	+	26.8773i	0.315183	+	0.900423i
$892$	6.56987	+	4.29228i	0.219975	+	0.143716i
$893$			41.8710i			1.40116i
$894$	−44.9242	+	12.2428i	−1.50249	+	0.409461i
$895$	−12.9471	−	41.6157i	−0.432774	−	1.39106i
$896$	35.6025	−	6.24440i	1.18940	−	0.208611i
$897$	−10.3766	−	42.1730i	−0.346466	−	1.40812i
$898$	−0.0143600	−	0.578828i	−0.000479200	−	0.0193157i
$899$		−	48.0310i		−	1.60192i
$900$	−26.2256	+	14.5678i	−0.874185	+	0.485593i
$901$		−	3.90508i		−	0.130097i
$902$	−17.5879	+	0.436336i	−0.585614	+	0.0145284i
$903$	−0.741947	−	3.01544i	−0.0246905	−	0.100348i
$904$	8.18421	−	6.93174i	0.272203	−	0.230546i
$905$	4.95361	−	14.6193i	0.164663	−	0.485961i
$906$	6.40995	+	23.5209i	0.212956	+	0.781428i
$907$			2.90593i			0.0964899i	0.998836	+	0.0482449i	$0.0153628\pi$
$907$			2.90593i			0.0964899i	−0.998836	+	0.0482449i	$0.984637\pi$
$908$	13.5628	+	8.86097i	0.450098	+	0.294062i
$909$	17.1443	−	8.98038i	0.568642	−	0.297860i
$910$	−25.7073	−	34.4856i	−0.852189	−	1.14319i
$911$	−10.2839	−	7.47167i	−0.340720	−	0.247547i	0.404246	−	0.914650i	$-0.367534\pi$
$911$	−10.2839	−	7.47167i	−0.340720	−	0.247547i	−0.744965	+	0.667103i	$0.767534\pi$
$912$	1.42562	+	54.1677i	0.0472070	+	1.79367i
$913$	−32.1689	−	44.2767i	−1.06464	−	1.46534i
$914$	0.336144	+	13.5494i	0.0111186	+	0.448174i
$915$	−24.9557	−	10.5394i	−0.825010	−	0.348421i
$916$	−14.4195	+	5.48965i	−0.476435	+	0.181383i
$917$	−49.7595	−	16.1678i	−1.64320	−	0.533909i
$918$	8.44743	+	18.2066i	0.278807	+	0.600907i
$919$	12.8021	+	4.15967i	0.422303	+	0.137215i	0.512456	−	0.858713i	$-0.328736\pi$
$919$	12.8021	+	4.15967i	0.422303	+	0.137215i	−0.0901530	+	0.995928i	$0.528736\pi$
$920$	31.4317	+	19.9896i	1.03627	+	0.659037i
$921$	−0.665979	−	2.70669i	−0.0219448	−	0.0891884i
$922$	12.6604	+	8.72695i	0.416949	+	0.287407i
$923$	2.04774	+	1.48777i	0.0674020	+	0.0489704i
$924$	11.5939	−	33.0427i	0.381410	−	1.08702i
$925$	−2.30256	+	1.58624i	−0.0757078	+	0.0521552i
$926$	39.2201	−	30.0090i	1.28885	−	0.986156i
$927$	7.48164	+	7.31480i	0.245729	+	0.240250i
$928$	12.2171	+	26.0740i	0.401047	+	0.855920i
$929$	30.2502	−	9.82890i	0.992478	−	0.322476i	0.232622	−	0.972567i	$-0.425269\pi$
$929$	30.2502	−	9.82890i	0.992478	−	0.322476i	0.759856	+	0.650091i	$0.225269\pi$
$930$	3.13209	−	51.5884i	0.102705	−	1.69165i
$931$	−7.75159	+	23.8569i	−0.254048	+	0.781879i
$932$	−1.99168	+	7.35204i	−0.0652396	+	0.240824i
$933$	−18.9890	−	7.74035i	−0.621670	−	0.253408i
$934$	−3.36882	+	11.3157i	−0.110231	+	0.370262i
$935$	−15.7746	+	11.1614i	−0.515884	+	0.365016i
$936$	13.5857	−	33.4734i	0.444062	−	1.09411i
$937$	−25.8757	−	35.6148i	−0.845321	−	1.16348i	−0.984874	−	0.173270i	$-0.944567\pi$
$937$	−25.8757	−	35.6148i	−0.845321	−	1.16348i	0.139553	−	0.990215i	$-0.455433\pi$
$938$	0.0860007	+	0.0256034i	0.00280802	+	0.000835979i
$939$	11.9382	+	10.0804i	0.389589	+	0.328960i
$940$	8.23719	+	22.4802i	0.268668	+	0.733225i
$941$	−21.4140	+	15.5582i	−0.698078	+	0.507183i	−0.879306	−	0.476258i	$-0.841993\pi$
$941$	−21.4140	+	15.5582i	−0.698078	+	0.507183i	0.181228	+	0.983441i	$0.441993\pi$
$942$	−8.67269	+	2.36350i	−0.282571	+	0.0770069i
$943$	23.1571			0.754100
$944$	21.1051	+	23.7007i	0.686914	+	0.771393i
$945$	−24.2315	−	28.1215i	−0.788251	−	0.914792i
$946$	2.06746	+	1.42512i	0.0672189	+	0.0463346i
$947$	−10.4715	−	32.2281i	−0.340280	−	1.04727i	−0.964063	−	0.265675i	$-0.914405\pi$
$947$	−10.4715	−	32.2281i	−0.340280	−	1.04727i	0.623783	−	0.781598i	$-0.285595\pi$
$948$	9.39505	−	6.49703i	0.305137	−	0.211014i
$949$			14.1568i			0.459550i
$950$	−17.1044	+	52.5923i	−0.554939	+	1.70632i
$951$	30.9391	+	2.25953i	1.00327	+	0.0732704i
$952$	5.86079	−	23.9754i	0.189949	−	0.777048i
$953$	−13.4099	−	41.2714i	−0.434389	−	1.33691i	−0.893712	−	0.448642i	$-0.851908\pi$
$953$	−13.4099	−	41.2714i	−0.434389	−	1.33691i	0.459323	−	0.888269i	$-0.348092\pi$
$954$	−4.13175	+	4.44118i	−0.133770	+	0.143789i
$955$	−16.4956	−	23.3135i	−0.533785	−	0.754408i
$956$	−16.4555	−	10.7508i	−0.532208	−	0.347706i
$957$	27.8213	+	2.03184i	0.899336	+	0.0656799i
$958$	−15.2417	−	43.2303i	−0.492438	−	1.39671i
$959$	−56.4664	+	41.0253i	−1.82340	+	1.32477i
$960$	11.4217	+	28.8018i	0.368634	+	0.929575i
$961$	46.9547	+	34.1146i	1.51467	+	1.10047i
$962$	0.960708	−	3.22698i	0.0309745	−	0.104042i
$963$	37.7794	−	19.7892i	1.21742	−	0.637699i
$964$	27.3864	−	22.0525i	0.882057	−	0.710265i
$965$	−20.3904	−	0.255710i	−0.656390	−	0.00823160i
$966$	−16.3343	+	43.1003i	−0.525547	+	1.38673i
$967$	−4.49384	+	13.8306i	−0.144512	+	0.444763i	−0.996948	−	0.0780690i	$-0.975125\pi$
$967$	−4.49384	+	13.8306i	−0.144512	+	0.444763i	0.852436	+	0.522832i	$0.175125\pi$
$968$	−1.05968	−	2.58847i	−0.0340594	−	0.0831965i
$969$	34.2627	+	13.9663i	1.10068	+	0.448662i
$970$	11.6024	+	34.2724i	0.372529	+	1.10042i
$971$	−47.2880	+	15.3648i	−1.51754	+	0.493080i	−0.945077	−	0.326848i	$-0.894013\pi$
$971$	−47.2880	+	15.3648i	−1.51754	+	0.493080i	−0.572467	+	0.819928i	$0.694013\pi$
$972$	9.65627	−	29.6438i	0.309725	−	0.950826i
$973$	−46.5978	−	33.8553i	−1.49386	−	1.08535i
$974$	−36.4815	+	27.9136i	−1.16894	+	0.894408i
$975$	24.4858	−	27.5655i	0.784175	−	0.882803i
$976$	−14.1224	+	24.1526i	−0.452046	+	0.773106i
$977$	−8.71527	−	6.33202i	−0.278826	−	0.202579i	0.439579	−	0.898204i	$-0.355128\pi$
$977$	−8.71527	−	6.33202i	−0.278826	−	0.202579i	−0.718405	+	0.695625i	$0.755128\pi$
$978$	43.0886	+	34.5895i	1.37782	+	1.10605i
$979$	−0.681028	−	2.09599i	−0.0217658	−	0.0669881i
$980$	0.531551	+	14.3336i	0.0169798	+	0.457869i
$981$	−19.0095	−	9.41736i	−0.606926	−	0.300673i
$982$	27.9147	+	36.4830i	0.890794	+	1.16422i
$983$	44.4292	+	14.4359i	1.41707	+	0.460435i	0.914671	−	0.404200i	$-0.132450\pi$
$983$	44.4292	+	14.4359i	1.41707	+	0.460435i	0.502401	+	0.864635i	$0.332450\pi$
$984$	15.6002	+	11.2983i	0.497317	+	0.360177i
$985$	−1.57066	−	5.04854i	−0.0500453	−	0.160860i
$986$	19.6554	−	0.487626i	0.625955	−	0.0155292i
$987$	−25.1718	+	15.6212i	−0.801228	+	0.497228i
$988$	−23.6945	−	62.2378i	−0.753823	−	1.98005i
$989$	−2.67392	−	1.94272i	−0.0850257	−	0.0617748i
$990$	29.7494	+	3.99655i	0.945499	+	0.127019i
$991$	−10.3708	−	14.2742i	−0.329439	−	0.453434i	0.611881	−	0.790950i	$-0.290413\pi$
$991$	−10.3708	−	14.2742i	−0.329439	−	0.453434i	−0.941320	+	0.337516i	$0.890413\pi$
$992$	−52.4164	−	10.0884i	−1.66422	−	0.320306i
$993$	−0.877933	+	12.0213i	−0.0278604	+	0.381484i
$994$	−0.893192	−	2.53337i	−0.0283303	−	0.0803537i
$995$	−4.22382	−	0.0529697i	−0.133904	−	0.00167925i
$996$	−1.39568	+	59.9031i	−0.0442239	+	1.89810i
$997$	−12.4602	−	38.3486i	−0.394619	−	1.21451i	−0.929258	−	0.369433i	$-0.879552\pi$
$997$	−12.4602	−	38.3486i	−0.394619	−	1.21451i	0.534638	−	0.845081i	$-0.320448\pi$
$998$	−3.40255	+	0.0844131i	−0.107706	+	0.00267205i
$999$	0.630453	−	2.83653i	0.0199466	−	0.0897439i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.bk.a.59.1	✓	464
3.2	odd	2	inner	600.2.bk.a.59.116	yes	464
8.3	odd	2	inner	600.2.bk.a.59.48	yes	464
24.11	even	2	inner	600.2.bk.a.59.69	yes	464
25.14	even	10	inner	600.2.bk.a.539.69	yes	464
75.14	odd	10	inner	600.2.bk.a.539.48	yes	464
200.139	odd	10	inner	600.2.bk.a.539.116	yes	464
600.539	even	10	inner	600.2.bk.a.539.1	yes	464

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
600.2.bk.a.59.1	✓	464	1.1	even	1	trivial
600.2.bk.a.59.48	yes	464	8.3	odd	2	inner
600.2.bk.a.59.69	yes	464	24.11	even	2	inner
600.2.bk.a.59.116	yes	464	3.2	odd	2	inner
600.2.bk.a.539.1	yes	464	600.539	even	10	inner
600.2.bk.a.539.48	yes	464	75.14	odd	10	inner
600.2.bk.a.539.69	yes	464	25.14	even	10	inner
600.2.bk.a.539.116	yes	464	200.139	odd	10	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:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.bk (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41378 + 0.0350741i) q^{2} +(1.68189 - 0.413828i) q^{3} +(1.99754 - 0.0991741i) q^{4} +(-0.0280397 + 2.23589i) q^{5} +(-2.36330 + 0.644051i) q^{6} -3.19488 q^{7} +(-2.82060 + 0.210272i) q^{8} +(2.65749 - 1.39202i) q^{9} +O(q^{10})\)	\(q+(-1.41378 + 0.0350741i) q^{2} +(1.68189 - 0.413828i) q^{3} +(1.99754 - 0.0991741i) q^{4} +(-0.0280397 + 2.23589i) q^{5} +(-2.36330 + 0.644051i) q^{6} -3.19488 q^{7} +(-2.82060 + 0.210272i) q^{8} +(2.65749 - 1.39202i) q^{9} +(-0.0387801 - 3.16204i) q^{10} +(-1.85977 + 2.55976i) q^{11} +(3.31860 - 0.993437i) q^{12} +(-3.44432 + 2.50244i) q^{13} +(4.51686 - 0.112058i) q^{14} +(0.878114 + 3.77212i) q^{15} +(3.98033 - 0.396208i) q^{16} +(0.844018 - 2.59762i) q^{17} +(-3.70828 + 2.06122i) q^{18} +(-2.41687 + 7.43835i) q^{19} +(0.165732 + 4.46906i) q^{20} +(-5.37344 + 1.32213i) q^{21} +(2.53953 - 3.68416i) q^{22} +(-3.46187 + 4.76486i) q^{23} +(-4.65692 + 1.52090i) q^{24} +(-4.99843 - 0.125387i) q^{25} +(4.78173 - 3.65871i) q^{26} +(3.89355 - 3.44097i) q^{27} +(-6.38191 + 0.316850i) q^{28} +(-1.57294 - 4.84102i) q^{29} +(-1.37376 - 5.30215i) q^{30} +(8.97422 + 2.91590i) q^{31} +(-5.61341 + 0.699757i) q^{32} +(-2.06863 + 5.07485i) q^{33} +(-1.10214 + 3.70206i) q^{34} +(0.0895836 - 7.14342i) q^{35} +(5.17040 - 3.04418i) q^{36} +(0.452412 - 0.328697i) q^{37} +(3.15602 - 10.6009i) q^{38} +(-4.75737 + 5.63418i) q^{39} +(-0.391057 - 6.31245i) q^{40} +(-2.31106 - 3.18090i) q^{41} +(7.55048 - 2.05767i) q^{42} +0.561175i q^{43} +(-3.46111 + 5.29766i) q^{44} +(3.03790 + 5.98090i) q^{45} +(4.72720 - 6.85787i) q^{46} +(5.09154 - 1.65434i) q^{47} +(6.53051 - 2.31355i) q^{48} +3.20729 q^{49} +(7.07107 + 0.00195455i) q^{50} +(0.344577 - 4.71818i) q^{51} +(-6.63198 + 5.34031i) q^{52} +(1.35978 - 0.441818i) q^{53} +(-5.38393 + 5.00133i) q^{54} +(-5.67120 - 4.23003i) q^{55} +(9.01149 - 0.671795i) q^{56} +(-0.986704 + 13.5106i) q^{57} +(2.39359 + 6.78897i) q^{58} +(4.66344 + 6.41867i) q^{59} +(2.12816 + 7.44788i) q^{60} +(-4.11132 + 5.65874i) q^{61} +(-12.7898 - 3.80768i) q^{62} +(-8.49039 + 4.44735i) q^{63} +(7.91157 - 1.18619i) q^{64} +(-5.49861 - 7.77129i) q^{65} +(2.74659 - 7.24727i) q^{66} +(0.0188877 + 0.00613698i) q^{67} +(1.42834 - 5.27255i) q^{68} +(-3.85065 + 9.44657i) q^{69} +(0.123898 + 10.1024i) q^{70} +(-0.183719 - 0.565428i) q^{71} +(-7.20302 + 4.48514i) q^{72} +(1.95452 - 2.69016i) q^{73} +(-0.628082 + 0.480572i) q^{74} +(-8.45868 + 1.85760i) q^{75} +(-4.09009 + 15.0981i) q^{76} +(5.94176 - 8.17813i) q^{77} +(6.52826 - 8.13234i) q^{78} +(3.13606 - 1.01897i) q^{79} +(0.774272 + 8.91070i) q^{80} +(5.12454 - 7.39858i) q^{81} +(3.37889 + 4.41603i) q^{82} +(-5.34513 + 16.4506i) q^{83} +(-10.6025 + 3.17392i) q^{84} +(5.78433 + 1.95997i) q^{85} +(-0.0196827 - 0.793377i) q^{86} +(-4.64886 - 7.49113i) q^{87} +(4.70743 - 7.61111i) q^{88} +(-0.409412 + 0.563507i) q^{89} +(-4.50469 - 8.34912i) q^{90} +(11.0042 - 7.99501i) q^{91} +(-6.44267 + 9.86132i) q^{92} +(16.3003 + 1.19044i) q^{93} +(-7.14029 + 2.51745i) q^{94} +(-16.5636 - 5.61242i) q^{95} +(-9.15154 + 3.49990i) q^{96} +(-10.8821 + 3.53580i) q^{97} +(-4.53440 + 0.112493i) q^{98} +(-1.37909 + 9.39139i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 464 q - 10 q^{3} - 6 q^{4} + q^{6} - 6 q^{9}+O(q^{10}) \) 464 * q - 10 * q^3 - 6 * q^4 + q^6 - 6 * q^9	\( 464 q - 10 q^{3} - 6 q^{4} + q^{6} - 6 q^{9} - 16 q^{10} - 5 q^{12} - 18 q^{16} - 12 q^{19} - 10 q^{22} + 12 q^{24} - 16 q^{25} - 10 q^{27} - 50 q^{28} - 21 q^{30} - 10 q^{33} - 14 q^{34} - 25 q^{36} - 32 q^{40} + 15 q^{42} - 34 q^{46} - 70 q^{48} + 336 q^{49} - 4 q^{51} - 60 q^{52} + 40 q^{54} - 70 q^{58} - 50 q^{60} - 30 q^{64} + 28 q^{66} - 20 q^{67} - 16 q^{70} - 5 q^{72} - 20 q^{73} - 42 q^{75} - 48 q^{76} + 75 q^{78} - 6 q^{81} - 76 q^{84} - 70 q^{88} + 66 q^{90} - 96 q^{91} - 108 q^{94} - 50 q^{96} - 60 q^{97} - 52 q^{99}+O(q^{100}) \) 464 * q - 10 * q^3 - 6 * q^4 + q^6 - 6 * q^9 - 16 * q^10 - 5 * q^12 - 18 * q^16 - 12 * q^19 - 10 * q^22 + 12 * q^24 - 16 * q^25 - 10 * q^27 - 50 * q^28 - 21 * q^30 - 10 * q^33 - 14 * q^34 - 25 * q^36 - 32 * q^40 + 15 * q^42 - 34 * q^46 - 70 * q^48 + 336 * q^49 - 4 * q^51 - 60 * q^52 + 40 * q^54 - 70 * q^58 - 50 * q^60 - 30 * q^64 + 28 * q^66 - 20 * q^67 - 16 * q^70 - 5 * q^72 - 20 * q^73 - 42 * q^75 - 48 * q^76 + 75 * q^78 - 6 * q^81 - 76 * q^84 - 70 * q^88 + 66 * q^90 - 96 * q^91 - 108 * q^94 - 50 * q^96 - 60 * q^97 - 52 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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