LMFDB - Embedded newform 225.2.q.a.196.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [225,2,Mod(16,225)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("225.16"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(225, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([20, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.q (of order $15$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			196.19
Character	$\chi$	$=$	225.196
Dual form			225.2.q.a.31.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.721003 + 0.800755i) q^{2} +(0.776008 + 1.54849i) q^{3} +(0.0876938 - 0.834351i) q^{4} +(2.23594 - 0.0235208i) q^{5} +(-0.680454 + 1.73786i) q^{6} +(0.316483 - 0.548165i) q^{7} +(2.47480 - 1.79805i) q^{8} +(-1.79562 + 2.40328i) q^{9} +(1.63096 + 1.77348i) q^{10} +(-3.49321 - 3.87960i) q^{11} +(1.36003 - 0.511670i) q^{12} +(-2.54696 + 2.82868i) q^{13} +(0.667131 - 0.141803i) q^{14} +(1.77153 + 3.44408i) q^{15} +(1.58291 + 0.336458i) q^{16} +(-0.365368 + 0.265455i) q^{17} +(-3.21908 + 0.294915i) q^{18} +(-3.97313 + 2.88665i) q^{19} +(0.176454 - 1.86763i) q^{20} +(1.09442 + 0.0646897i) q^{21} +(0.587996 - 5.59441i) q^{22} +(0.100362 - 0.0213327i) q^{23} +(4.70473 + 2.43690i) q^{24} +(4.99889 - 0.105182i) q^{25} -4.10144 q^{26} +(-5.11486 - 0.915539i) q^{27} +(-0.429608 - 0.312129i) q^{28} +(-9.17597 + 4.08540i) q^{29} +(-1.48058 + 3.90175i) q^{30} +(3.69032 + 1.64304i) q^{31} +(-2.18716 - 3.78828i) q^{32} +(3.29675 - 8.41979i) q^{33} +(-0.475995 - 0.101176i) q^{34} +(0.694745 - 1.23311i) q^{35} +(1.84771 + 1.70893i) q^{36} +(0.0800637 + 0.246411i) q^{37} +(-5.17614 - 1.10022i) q^{38} +(-6.35664 - 1.74885i) q^{39} +(5.49123 - 4.07855i) q^{40} +(5.23896 - 5.81846i) q^{41} +(0.737279 + 0.923003i) q^{42} +(3.68846 - 6.38860i) q^{43} +(-3.54328 + 2.57435i) q^{44} +(-3.95839 + 5.41583i) q^{45} +(0.0894437 + 0.0649846i) q^{46} +(9.67748 - 4.30869i) q^{47} +(0.707350 + 2.71221i) q^{48} +(3.29968 + 5.71521i) q^{49} +(3.68844 + 3.92705i) q^{50} +(-0.694582 - 0.359772i) q^{51} +(2.13676 + 2.37311i) q^{52} +(-4.56626 - 3.31758i) q^{53} +(-2.95471 - 4.75585i) q^{54} +(-7.90187 - 8.59241i) q^{55} +(-0.202394 - 1.92565i) q^{56} +(-7.55312 - 3.91228i) q^{57} +(-9.88730 - 4.40211i) q^{58} +(4.79365 - 5.32388i) q^{59} +(3.02892 - 1.17606i) q^{60} +(3.08519 + 3.42646i) q^{61} +(1.34506 + 4.13967i) q^{62} +(0.749107 + 1.74489i) q^{63} +(2.45668 - 7.56088i) q^{64} +(-5.62832 + 6.38468i) q^{65} +(9.11915 - 3.43080i) q^{66} +(3.18608 + 1.41853i) q^{67} +(0.189442 + 0.328124i) q^{68} +(0.110915 + 0.138855i) q^{69} +(1.48833 - 0.332755i) q^{70} +(-3.47832 - 2.52715i) q^{71} +(-0.122605 + 9.17626i) q^{72} +(-4.75735 + 14.6416i) q^{73} +(-0.139588 + 0.241774i) q^{74} +(4.04205 + 7.65910i) q^{75} +(2.06006 + 3.56813i) q^{76} +(-3.23220 + 0.687026i) q^{77} +(-3.18275 - 6.35103i) q^{78} +(1.24677 - 0.555098i) q^{79} +(3.54721 + 0.715070i) q^{80} +(-2.55147 - 8.63076i) q^{81} +8.43646 q^{82} +(-0.223611 - 2.12752i) q^{83} +(0.149948 - 0.907457i) q^{84} +(-0.810698 + 0.602136i) q^{85} +(7.77509 - 1.65265i) q^{86} +(-13.4468 - 11.0386i) q^{87} +(-15.6207 - 3.32029i) q^{88} +(-5.42929 + 16.7096i) q^{89} +(-7.19076 + 0.735128i) q^{90} +(0.744515 + 2.29138i) q^{91} +(-0.00899778 - 0.0856081i) q^{92} +(0.319497 + 6.98942i) q^{93} +(10.4277 + 4.64271i) q^{94} +(-8.81581 + 6.54784i) q^{95} +(4.16885 - 6.32653i) q^{96} +(-5.56983 + 2.47985i) q^{97} +(-2.19740 + 6.76291i) q^{98} +(15.5962 - 1.42884i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20}+ \cdots - 20 q^{99}+O(q^{100}) $ 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	0.721003	+	0.800755i	0.509826	+	0.566219i	0.942018	−	0.335563i	$-0.108926\pi$
$2$	0.721003	+	0.800755i	0.509826	+	0.566219i	−0.432192	+	0.901782i	$0.642260\pi$
$3$	0.776008	+	1.54849i	0.448028	+	0.894019i
$3$	0.776008	+	1.54849i	0.448028	+	0.894019i
$4$	0.0876938	−	0.834351i	0.0438469	−	0.417176i
$5$	2.23594	−	0.0235208i	0.999945	−	0.0105188i
$5$	2.23594	−	0.0235208i	0.999945	−	0.0105188i
$6$	−0.680454	+	1.73786i	−0.277794	+	0.709476i
$7$	0.316483	−	0.548165i	0.119619	−	0.207187i	−0.799998	−	0.600003i	$-0.795166\pi$
$7$	0.316483	−	0.548165i	0.119619	−	0.207187i	0.919617	+	0.392817i	$0.128499\pi$
$8$	2.47480	−	1.79805i	0.874976	−	0.635707i
$9$	−1.79562	+	2.40328i	−0.598541	+	0.801092i
$10$	1.63096	+	1.77348i	0.515754	+	0.560825i
$11$	−3.49321	−	3.87960i	−1.05324	−	1.16974i	−0.985085	−	0.172069i	$-0.944955\pi$
$11$	−3.49321	−	3.87960i	−1.05324	−	1.16974i	−0.0681573	−	0.997675i	$-0.521712\pi$
$12$	1.36003	−	0.511670i	0.392608	−	0.147706i
$13$	−2.54696	+	2.82868i	−0.706399	+	0.784535i	−0.984381	−	0.176051i	$-0.943668\pi$
$13$	−2.54696	+	2.82868i	−0.706399	+	0.784535i	0.277982	+	0.960586i	$0.410334\pi$
$14$	0.667131	−	0.141803i	0.178298	−	0.0378984i
$15$	1.77153	+	3.44408i	0.457408	+	0.889257i
$16$	1.58291	+	0.336458i	0.395728	+	0.0841145i
$17$	−0.365368	+	0.265455i	−0.0886146	+	0.0643823i	−0.631210	−	0.775612i	$-0.717442\pi$
$17$	−0.365368	+	0.265455i	−0.0886146	+	0.0643823i	0.542596	+	0.839994i	$0.317442\pi$
$18$	−3.21908	+	0.294915i	−0.758745	+	0.0695120i
$19$	−3.97313	+	2.88665i	−0.911499	+	0.662243i	−0.941394	−	0.337310i	$-0.890483\pi$
$19$	−3.97313	+	2.88665i	−0.911499	+	0.662243i	0.0298945	+	0.999553i	$0.490483\pi$
$20$	0.176454	−	1.86763i	0.0394563	−	0.417614i
$21$	1.09442	+	0.0646897i	0.238822	+	0.0141165i
$22$	0.587996	−	5.59441i	0.125361	−	1.19273i
$23$	0.100362	−	0.0213327i	0.0209270	−	0.00444817i	−0.197436	−	0.980316i	$-0.563262\pi$
$23$	0.100362	−	0.0213327i	0.0209270	−	0.00444817i	0.218363	+	0.975868i	$0.429928\pi$
$24$	4.70473	+	2.43690i	0.960348	+	0.497430i
$25$	4.99889	−	0.105182i	0.999779	−	0.0210365i
$26$	−4.10144			−0.804359
$27$	−5.11486	−	0.915539i	−0.984355	−	0.176195i
$28$	−0.429608	−	0.312129i	−0.0811883	−	0.0589868i
$29$	−9.17597	+	4.08540i	−1.70393	+	0.758640i	−0.705165	+	0.709044i	$0.749127\pi$
$29$	−9.17597	+	4.08540i	−1.70393	+	0.758640i	−0.998769	+	0.0495967i	$0.984206\pi$
$30$	−1.48058	+	3.90175i	−0.270316	+	0.712359i
$31$	3.69032	+	1.64304i	0.662801	+	0.295098i	0.710431	−	0.703767i	$-0.248500\pi$
$31$	3.69032	+	1.64304i	0.662801	+	0.295098i	−0.0476300	+	0.998865i	$0.515167\pi$
$32$	−2.18716	−	3.78828i	−0.386640	−	0.669680i
$33$	3.29675	−	8.41979i	0.573891	−	1.46570i
$34$	−0.475995	−	0.101176i	−0.0816325	−	0.0173515i
$35$	0.694745	−	1.23311i	0.117433	−	0.208434i
$36$	1.84771	+	1.70893i	0.307952	+	0.284822i
$37$	0.0800637	+	0.246411i	0.0131624	+	0.0405097i	0.957422	−	0.288692i	$-0.0932204\pi$
$37$	0.0800637	+	0.246411i	0.0131624	+	0.0405097i	−0.944260	+	0.329202i	$0.893220\pi$
$38$	−5.17614	−	1.10022i	−0.839680	−	0.178480i
$39$	−6.35664	−	1.74885i	−1.01788	−	0.280040i
$40$	5.49123	−	4.07855i	0.868240	−	0.644876i
$41$	5.23896	−	5.81846i	0.818188	−	0.908690i	−0.178983	−	0.983852i	$-0.557281\pi$
$41$	5.23896	−	5.81846i	0.818188	−	0.908690i	0.997171	+	0.0751620i	$0.0239474\pi$
$42$	0.737279	+	0.923003i	0.113765	+	0.142422i
$43$	3.68846	−	6.38860i	0.562485	−	0.974253i	−0.434794	−	0.900530i	$-0.643179\pi$
$43$	3.68846	−	6.38860i	0.562485	−	0.974253i	0.997279	−	0.0737227i	$-0.0234880\pi$
$44$	−3.54328	+	2.57435i	−0.534170	+	0.388097i
$45$	−3.95839	+	5.41583i	−0.590082	+	0.807344i
$46$	0.0894437	+	0.0649846i	0.0131878	+	0.00958146i
$47$	9.67748	−	4.30869i	1.41161	−	0.628487i	0.447567	−	0.894250i	$-0.352291\pi$
$47$	9.67748	−	4.30869i	1.41161	−	0.628487i	0.964038	+	0.265763i	$0.0856239\pi$
$48$	0.707350	+	2.71221i	0.102097	+	0.391474i
$49$	3.29968	+	5.71521i	0.471382	+	0.816458i
$50$	3.68844	+	3.92705i	0.521624	+	0.555369i
$51$	−0.694582	−	0.359772i	−0.0972609	−	0.0503781i
$52$	2.13676	+	2.37311i	0.296316	+	0.329092i
$53$	−4.56626	−	3.31758i	−0.627224	−	0.455705i	0.228213	−	0.973611i	$-0.426712\pi$
$53$	−4.56626	−	3.31758i	−0.627224	−	0.455705i	−0.855437	+	0.517906i	$0.826712\pi$
$54$	−2.95471	−	4.75585i	−0.402085	−	0.647190i
$55$	−7.90187	−	8.59241i	−1.06549	−	1.15860i
$56$	−0.202394	−	1.92565i	−0.0270461	−	0.257326i
$57$	−7.55312	−	3.91228i	−1.00044	−	0.518194i
$58$	−9.88730	−	4.40211i	−1.29827	−	0.578025i
$59$	4.79365	−	5.32388i	0.624079	−	0.693110i	−0.345352	−	0.938473i	$-0.612240\pi$
$59$	4.79365	−	5.32388i	0.624079	−	0.693110i	0.969431	+	0.245363i	$0.0789071\pi$
$60$	3.02892	−	1.17606i	0.391032	−	0.151828i
$61$	3.08519	+	3.42646i	0.395019	+	0.438713i	0.907542	−	0.419960i	$-0.137956\pi$
$61$	3.08519	+	3.42646i	0.395019	+	0.438713i	−0.512524	+	0.858673i	$0.671289\pi$
$62$	1.34506	+	4.13967i	0.170823	+	0.525739i
$63$	0.749107	+	1.74489i	0.0943786	+	0.219836i
$64$	2.45668	−	7.56088i	0.307085	−	0.945110i
$65$	−5.62832	+	6.38468i	−0.698107	+	0.791922i
$66$	9.11915	−	3.43080i	1.12249	−	0.422302i
$67$	3.18608	+	1.41853i	0.389241	+	0.173301i	0.592020	−	0.805923i	$-0.298331\pi$
$67$	3.18608	+	1.41853i	0.389241	+	0.173301i	−0.202779	+	0.979225i	$0.564997\pi$
$68$	0.189442	+	0.328124i	0.0229732	+	0.0397908i
$69$	0.110915	+	0.138855i	0.0133526	+	0.0167162i
$70$	1.48833	−	0.332755i	0.177890	−	0.0397718i
$71$	−3.47832	−	2.52715i	−0.412801	−	0.299917i	0.361934	−	0.932204i	$-0.382117\pi$
$71$	−3.47832	−	2.52715i	−0.412801	−	0.299917i	−0.774735	+	0.632286i	$0.782117\pi$
$72$	−0.122605	+	9.17626i	−0.0144492	+	1.08143i
$73$	−4.75735	+	14.6416i	−0.556806	+	1.71367i	0.134320	+	0.990938i	$0.457115\pi$
$73$	−4.75735	+	14.6416i	−0.556806	+	1.71367i	−0.691126	+	0.722734i	$0.742885\pi$
$74$	−0.139588	+	0.241774i	−0.0162268	+	0.0281057i
$75$	4.04205	+	7.65910i	0.466736	+	0.884397i
$76$	2.06006	+	3.56813i	0.236305	+	0.409292i
$77$	−3.23220	+	0.687026i	−0.368344	+	0.0782938i
$78$	−3.18275	−	6.35103i	−0.360376	−	0.719113i
$79$	1.24677	−	0.555098i	0.140273	−	0.0624534i	−0.335400	−	0.942076i	$-0.608871\pi$
$79$	1.24677	−	0.555098i	0.140273	−	0.0624534i	0.475673	+	0.879622i	$0.342205\pi$
$80$	3.54721	+	0.715070i	0.396591	+	0.0799473i
$81$	−2.55147	−	8.63076i	−0.283497	−	0.958973i
$82$	8.43646			0.931651
$83$	−0.223611	−	2.12752i	−0.0245445	−	0.233525i	−0.999916	−	0.0129571i	$-0.995876\pi$
$83$	−0.223611	−	2.12752i	−0.0245445	−	0.233525i	0.975372	−	0.220568i	$-0.0707911\pi$
$84$	0.149948	−	0.907457i	0.0163606	−	0.0990117i
$85$	−0.810698	+	0.602136i	−0.0879325	+	0.0653109i
$86$	7.77509	−	1.65265i	0.838410	−	0.178210i
$87$	−13.4468	−	11.0386i	−1.44165	−	1.18346i
$88$	−15.6207	−	3.32029i	−1.66518	−	0.353944i
$89$	−5.42929	+	16.7096i	−0.575504	+	1.77122i	0.0589537	+	0.998261i	$0.481224\pi$
$89$	−5.42929	+	16.7096i	−0.575504	+	1.77122i	−0.634457	+	0.772958i	$0.718776\pi$
$90$	−7.19076	+	0.735128i	−0.757972	+	0.0774893i
$91$	0.744515	+	2.29138i	0.0780464	+	0.240202i
$92$	−0.00899778	−	0.0856081i	−0.000938083	−	0.00892526i
$93$	0.319497	+	6.98942i	0.0331303	+	0.724769i
$94$	10.4277	+	4.64271i	1.07553	+	0.478859i
$95$	−8.81581	+	6.54784i	−0.904483	+	0.671794i
$96$	4.16885	−	6.32653i	0.425481	−	0.645699i
$97$	−5.56983	+	2.47985i	−0.565531	+	0.251791i	−0.669528	−	0.742787i	$-0.733503\pi$
$97$	−5.56983	+	2.47985i	−0.565531	+	0.251791i	0.103997	+	0.994578i	$0.466837\pi$
$98$	−2.19740	+	6.76291i	−0.221971	+	0.683157i
$99$	15.5962	−	1.42884i	1.56748	−	0.143604i
$100$	0.350613	−	4.18006i	0.0350613	−	0.418006i
$101$	1.98334	−	3.43524i	0.197350	−	0.341820i	−0.750319	−	0.661076i	$-0.770100\pi$
$101$	1.98334	−	3.43524i	0.197350	−	0.341820i	0.947668	+	0.319257i	$0.103433\pi$
$102$	−0.212707	−	0.815586i	−0.0210611	−	0.0807550i
$103$	−0.119994	+	1.14167i	−0.0118234	+	0.112492i	−0.998842	−	0.0481151i	$-0.984679\pi$
$103$	−0.119994	+	1.14167i	−0.0118234	+	0.112492i	0.987018	+	0.160607i	$0.0513452\pi$
$104$	−1.21711	+	11.5800i	−0.119347	+	1.13551i
$105$	2.44858	+	0.118901i	0.238957	+	0.0116036i
$106$	−0.635717	−	6.04844i	−0.0617462	−	0.587476i
$107$	4.10301			0.396653			0.198326	−	0.980136i	$-0.436449\pi$
$107$	4.10301			0.396653			0.198326	+	0.980136i	$0.436449\pi$
$108$	−1.21242	+	4.18730i	−0.116665	+	0.402923i
$109$	0.0306236	+	0.0942499i	0.00293321	+	0.00902750i	0.952512	−	0.304500i	$-0.0984893\pi$
$109$	0.0306236	+	0.0942499i	0.00293321	+	0.00902750i	−0.949579	+	0.313527i	$0.898489\pi$
$110$	1.18314	−	12.5226i	0.112808	−	1.19398i
$111$	−0.319434	+	0.315194i	−0.0303193	+	0.0299169i
$112$	0.685399	−	0.761212i	0.0647641	−	0.0719278i
$113$	8.89638	−	9.88043i	0.836901	−	0.929473i	−0.161450	−	0.986881i	$-0.551617\pi$
$113$	8.89638	−	9.88043i	0.836901	−	0.929473i	0.998351	+	0.0574080i	$0.0182836\pi$
$114$	−2.31304	−	8.86896i	−0.216636	−	0.830654i
$115$	0.223903	−	0.0500592i	0.0208790	−	0.00466805i
$116$	2.60399	+	8.01424i	0.241774	+	0.744104i
$117$	−2.22473	−	11.2003i	−0.205676	−	1.03547i
$118$	7.71936			0.710624
$119$	0.0298805	+	0.284294i	0.00273914	+	0.0260612i
$120$	10.5768	+	5.33812i	0.965527	+	0.487301i
$121$	−1.69899	+	16.1648i	−0.154453	+	1.46953i
$122$	−0.519317	+	4.94097i	−0.0470167	+	0.447334i
$123$	13.0753	+	3.59730i	1.17896	+	0.324357i
$124$	1.69449	−	2.93494i	0.152169	−	0.263565i
$125$	11.1748	−	0.352760i	0.999502	−	0.0315518i
$126$	−0.857124	+	1.85792i	−0.0763586	+	0.165517i
$127$	1.73383	−	5.33620i	0.153853	−	0.473511i	−0.844190	−	0.536044i	$-0.819918\pi$
$127$	1.73383	−	5.33620i	0.153853	−	0.473511i	0.998043	+	0.0625335i	$0.0199180\pi$
$128$	−0.166613	+	0.0741808i	−0.0147266	+	0.00655672i
$129$	12.7549	+	0.753929i	1.12301	+	0.0663797i
$130$	−9.17060	+	0.0964691i	−0.804315	+	0.00846090i
$131$	−5.01793	−	2.23413i	−0.438418	−	0.195196i	0.175644	−	0.984454i	$-0.443799\pi$
$131$	−5.01793	−	2.23413i	−0.438418	−	0.195196i	−0.614063	+	0.789257i	$0.710466\pi$
$132$	−6.73596	−	3.48902i	−0.586290	−	0.303680i
$133$	0.324930	+	3.09151i	0.0281750	+	0.268068i
$134$	1.16127	+	3.57403i	0.100319	+	0.308749i
$135$	−11.4581	−	1.92679i	−0.986154	−	0.165831i
$136$	−0.426912	+	1.31390i	−0.0366074	+	0.112666i
$137$	9.73009	+	2.06819i	0.831298	+	0.176698i	0.603856	−	0.797094i	$-0.293630\pi$
$137$	9.73009	+	2.06819i	0.831298	+	0.176698i	0.227442	+	0.973792i	$0.426964\pi$
$138$	−0.0312189	+	0.188931i	−0.00265753	+	0.0160829i
$139$	−4.21294	+	0.895488i	−0.357337	+	0.0759543i	−0.383082	−	0.923714i	$-0.625137\pi$
$139$	−4.21294	+	0.895488i	−0.357337	+	0.0759543i	0.0257454	+	0.999669i	$0.491804\pi$
$140$	−0.967922	−	0.687798i	−0.0818043	−	0.0581295i
$141$	14.1818	+	11.6419i	1.19432	+	0.980423i
$142$	−0.484253	−	4.60736i	−0.0406376	−	0.386641i
$143$	19.8712			1.66171
$144$	−3.65091	+	3.20002i	−0.304243	+	0.266668i
$145$	−20.4209	+	9.35056i	−1.69586	+	0.776522i
$146$	−15.1544	+	6.74718i	−1.25419	+	0.558400i
$147$	−6.28935	+	9.54455i	−0.518737	+	0.787221i
$148$	0.212614	−	0.0451925i	0.0174768	−	0.00371480i
$149$	−0.0389321	−	0.0674323i	−0.00318944	−	0.00552427i	0.864426	−	0.502760i	$-0.167682\pi$
$149$	−0.0389321	−	0.0674323i	−0.00318944	−	0.00552427i	−0.867616	+	0.497235i	$0.834349\pi$
$150$	−3.21873	+	8.75892i	−0.262808	+	0.715163i
$151$	−8.59717	+	14.8907i	−0.699628	+	1.21179i	0.268968	+	0.963149i	$0.413318\pi$
$151$	−8.59717	+	14.8907i	−0.699628	+	1.21179i	−0.968595	+	0.248642i	$0.920016\pi$
$152$	−4.64238	+	14.2878i	−0.376547	+	1.15889i
$153$	0.0181008	−	1.35474i	0.00146336	−	0.109524i
$154$	−2.88057	−	2.09285i	−0.232123	−	0.168647i
$155$	8.28999	+	3.58694i	0.665868	+	0.288110i
$156$	−2.01659	+	5.15030i	−0.161457	+	0.412354i
$157$	−5.71800	−	9.90387i	−0.456346	−	0.790415i	0.542418	−	0.840109i	$-0.317509\pi$
$157$	−5.71800	−	9.90387i	−0.456346	−	0.790415i	−0.998765	+	0.0496936i	$0.984176\pi$
$158$	1.34342	+	0.598130i	0.106877	+	0.0475847i
$159$	1.59378	−	9.64526i	0.126395	−	0.764919i
$160$	−4.97948	−	8.41894i	−0.393663	−	0.665576i
$161$	0.0200691	−	0.0617665i	0.00158167	−	0.00486788i
$162$	5.07150	−	8.26590i	0.398455	−	0.649431i
$163$	1.40825	+	4.33413i	0.110302	+	0.339476i	0.990938	−	0.134318i	$-0.0428843\pi$
$163$	1.40825	+	4.33413i	0.110302	+	0.339476i	−0.880636	+	0.473793i	$0.842884\pi$
$164$	−4.39521	−	4.88138i	−0.343208	−	0.381171i
$165$	7.17332	−	18.9037i	0.558442	−	1.47165i
$166$	1.54239	−	1.71300i	0.119713	−	0.132955i
$167$	13.6779	+	6.08979i	1.05843	+	0.471242i	0.860751	−	0.509025i	$-0.169994\pi$
$167$	13.6779	+	6.08979i	1.05843	+	0.471242i	0.197675	+	0.980268i	$0.436661\pi$
$168$	2.82479	−	1.80773i	0.217937	−	0.139469i
$169$	−0.155583	−	1.48028i	−0.0119679	−	0.113867i
$170$	−1.06668	−	0.215028i	−0.0818105	−	0.0164919i
$171$	0.196834	−	14.7319i	0.0150523	−	1.12657i
$172$	−5.00688	−	3.63771i	−0.381771	−	0.277373i
$173$	2.39115	+	2.65564i	0.181796	+	0.201905i	0.827154	−	0.561975i	$-0.189958\pi$
$173$	2.39115	+	2.65564i	0.181796	+	0.201905i	−0.645358	+	0.763880i	$0.723292\pi$
$174$	−0.856013	−	18.7264i	−0.0648942	−	1.41965i
$175$	1.52441	−	2.77351i	0.115234	−	0.209657i
$176$	−4.22411	−	7.31638i	−0.318405	−	0.551493i
$177$	11.9639	+	3.29152i	0.899259	+	0.247406i
$178$	−17.2949	+	7.70017i	−1.29630	+	0.577152i
$179$	−17.6257	−	12.8058i	−1.31741	−	0.957151i	−0.999961	−	0.00887412i	$-0.997175\pi$
$179$	−17.6257	−	12.8058i	−1.31741	−	0.957151i	−0.317445	−	0.948277i	$-0.602825\pi$
$180$	4.17157	+	3.77762i	0.310931	+	0.281567i
$181$	14.5760	−	10.5901i	1.08343	−	0.787155i	0.105148	−	0.994457i	$-0.466468\pi$
$181$	14.5760	−	10.5901i	1.08343	−	0.787155i	0.978277	+	0.207302i	$0.0664682\pi$
$182$	−1.29804	+	2.24827i	−0.0962169	+	0.166653i
$183$	−2.91169	+	7.43634i	−0.215238	+	0.549710i
$184$	0.210020	−	0.233251i	0.0154829	−	0.0171955i
$185$	0.184814	+	0.549078i	0.0135878	+	0.0403690i
$186$	−5.36645	+	5.29523i	−0.393487	+	0.388265i
$187$	2.30617	+	0.490191i	0.168643	+	0.0358463i
$188$	−2.74631	−	8.45226i	−0.200295	−	0.616445i
$189$	−2.12063	+	2.51403i	−0.154253	+	0.182869i
$190$	−11.5994	−	2.33829i	−0.841511	−	0.169637i
$191$	−9.98949	−	2.12333i	−0.722814	−	0.153639i	−0.168207	−	0.985752i	$-0.553798\pi$
$191$	−9.98949	−	2.12333i	−0.722814	−	0.153639i	−0.554606	+	0.832113i	$0.687131\pi$
$192$	13.6143	−	2.06317i	0.982530	−	0.148896i
$193$	−6.35646	−	11.0097i	−0.457548	−	0.792496i	0.541283	−	0.840841i	$-0.317939\pi$
$193$	−6.35646	−	11.0097i	−0.457548	−	0.792496i	−0.998831	+	0.0483444i	$0.984605\pi$
$194$	−6.00162	−	2.67209i	−0.430891	−	0.191845i
$195$	−14.2542	−	3.76082i	−1.02077	−	0.269318i
$196$	5.05785	−	2.25190i	0.361275	−	0.160850i
$197$	5.47291	+	3.97630i	0.389929	+	0.283300i	0.765426	−	0.643524i	$-0.222528\pi$
$197$	5.47291	+	3.97630i	0.389929	+	0.283300i	−0.375498	+	0.926823i	$0.622528\pi$
$198$	12.3891	+	11.4586i	0.880454	+	0.814325i
$199$	7.09600			0.503022			0.251511	−	0.967854i	$-0.419073\pi$
$199$	7.09600			0.503022			0.251511	+	0.967854i	$0.419073\pi$
$200$	12.1822	−	9.24857i	0.861409	−	0.653973i
$201$	0.275841	+	6.03439i	0.0194563	+	0.425633i
$202$	4.18078	−	0.888652i	0.294159	−	0.0625254i
$203$	−0.664564	+	6.32290i	−0.0466432	+	0.443781i
$204$	−0.361086	+	0.547975i	−0.0252811	+	0.0383660i
$205$	11.5772	−	13.1330i	0.808585	−	0.917246i
$206$	−1.00071	+	0.727061i	−0.0697230	+	0.0506567i
$207$	−0.128945	+	0.279504i	−0.00896227	+	0.0194268i
$208$	−4.98334	+	3.62061i	−0.345532	+	0.251044i
$209$	25.0780	+	5.33050i	1.73468	+	0.368718i
$210$	1.67022	+	2.04644i	0.115256	+	0.141218i
$211$	−25.9163	+	5.50868i	−1.78415	+	0.379233i	−0.977357	−	0.211598i	$-0.932133\pi$
$211$	−25.9163	+	5.50868i	−1.78415	+	0.379233i	−0.806795	+	0.590831i	$0.798800\pi$
$212$	−3.16846	+	3.51893i	−0.217611	+	0.241681i
$213$	1.21405	−	7.34722i	0.0831855	−	0.503423i
$214$	2.95828	+	3.28550i	0.202224	+	0.224592i
$215$	8.09693	−	14.3713i	0.552206	−	0.980116i
$216$	−14.3045	+	6.93100i	−0.973296	+	0.471595i
$217$	2.06858	−	1.50291i	0.140424	−	0.102024i
$218$	−0.0533913	+	0.0924764i	−0.00361611	+	0.00626329i
$219$	−26.3641	+	3.99532i	−1.78152	+	0.269979i
$220$	−7.86203	+	5.83943i	−0.530058	+	0.393695i
$221$	0.179687	−	1.70961i	0.0120871	−	0.115001i
$222$	−0.482706	−	0.0285321i	−0.0323971	−	0.00191495i
$223$	2.63479	+	2.92623i	0.176438	+	0.195955i	0.824877	−	0.565312i	$-0.191244\pi$
$223$	2.63479	+	2.92623i	0.176438	+	0.195955i	−0.648439	+	0.761267i	$0.724578\pi$
$224$	−2.76880			−0.184998
$225$	−8.72335	+	12.2026i	−0.581557	+	0.813506i
$226$	14.3261			0.952959
$227$	−16.1638	−	17.9518i	−1.07283	−	1.19150i	−0.980652	−	0.195759i	$-0.937283\pi$
$227$	−16.1638	−	17.9518i	−1.07283	−	1.19150i	−0.0921803	−	0.995742i	$-0.529384\pi$
$228$	−3.92658	+	5.95887i	−0.260044	+	0.394636i
$229$	1.58289	−	15.0602i	0.104601	−	0.995208i	−0.808783	−	0.588107i	$-0.799873\pi$
$229$	1.58289	−	15.0602i	0.104601	−	0.995208i	0.913383	−	0.407100i	$-0.133460\pi$
$230$	0.201520	+	0.143198i	0.0132878	+	0.00944221i
$231$	−3.57206	−	4.47188i	−0.235025	−	0.294228i
$232$	−15.3630	+	26.6094i	−1.00863	+	1.74699i
$233$	10.3302	−	7.50529i	0.676751	−	0.491688i	−0.195527	−	0.980698i	$-0.562642\pi$
$233$	10.3302	−	7.50529i	0.676751	−	0.491688i	0.872278	+	0.489010i	$0.162642\pi$
$234$	7.36465	−	9.85690i	0.481442	−	0.644366i
$235$	21.5370	−	9.86162i	1.40492	−	0.643301i
$236$	−4.02161	−	4.46646i	−0.261785	−	0.290742i
$237$	1.82707	+	1.49985i	0.118681	+	0.0974256i
$238$	−0.206106	+	0.228903i	−0.0133598	+	0.0148376i
$239$	12.5453	−	2.66658i	0.811485	−	0.172487i	0.216562	−	0.976269i	$-0.430516\pi$
$239$	12.5453	−	2.66658i	0.811485	−	0.172487i	0.594923	+	0.803782i	$0.297182\pi$
$240$	1.64539	+	6.04771i	0.106209	+	0.390378i
$241$	−27.0379	−	5.74709i	−1.74167	−	0.370203i	−0.776151	−	0.630548i	$-0.782830\pi$
$241$	−27.0379	−	5.74709i	−1.74167	−	0.370203i	−0.965516	+	0.260345i	$0.916164\pi$
$242$	−14.1690	+	10.2944i	−0.910817	+	0.661748i
$243$	11.3847	−	10.6485i	0.730326	−	0.683099i
$244$	3.12942	−	2.27366i	0.200341	−	0.145556i
$245$	7.51232	+	12.7013i	0.479945	+	0.811455i
$246$	6.54676	+	13.0637i	0.417406	+	0.832914i
$247$	1.95398	−	18.5909i	0.124329	−	1.18291i
$248$	12.0871	−	2.56919i	0.767530	−	0.163144i
$249$	3.12091	−	1.99723i	0.197779	−	0.126569i
$250$	8.33952	+	8.69391i	0.527437	+	0.549851i
$251$	−2.88989			−0.182408			−0.0912042	−	0.995832i	$-0.529072\pi$
$251$	−2.88989			−0.182408			−0.0912042	+	0.995832i	$0.529072\pi$
$252$	1.52155	−	0.472002i	0.0958484	−	0.0297333i
$253$	−0.433349	−	0.314846i	−0.0272444	−	0.0197942i
$254$	5.52308	−	2.45903i	0.346549	−	0.154294i
$255$	−1.56151	−	0.788092i	−0.0977854	−	0.0493523i
$256$	−14.7049	−	6.54703i	−0.919054	−	0.409189i
$257$	3.00243	+	5.20037i	0.187287	+	0.324390i	0.944345	−	0.328958i	$-0.106697\pi$
$257$	3.00243	+	5.20037i	0.187287	+	0.324390i	−0.757058	+	0.653348i	$0.773364\pi$
$258$	8.59264	+	10.7572i	0.534954	+	0.669712i
$259$	0.160412	+	0.0340967i	0.00996755	+	0.00211867i
$260$	4.83350	+	5.25589i	0.299761	+	0.325957i
$261$	6.65823	−	29.3882i	0.412134	−	1.81909i
$262$	−1.82895	−	5.62894i	−0.112993	−	0.347757i
$263$	−13.4022	−	2.84872i	−0.826413	−	0.175660i	−0.224757	−	0.974415i	$-0.572159\pi$
$263$	−13.4022	−	2.84872i	−0.826413	−	0.175660i	−0.601656	+	0.798755i	$0.705492\pi$
$264$	−6.98039	−	26.7651i	−0.429613	−	1.64728i
$265$	−10.2879	−	7.31053i	−0.631983	−	0.449082i
$266$	−2.24126	+	2.48917i	−0.137421	+	0.152621i
$267$	−30.0878	+	4.55963i	−1.84135	+	0.279045i
$268$	1.46295	−	2.53391i	0.0893641	−	0.154783i
$269$	−13.3513	+	9.70027i	−0.814041	+	0.591436i	−0.915000	−	0.403455i	$-0.867809\pi$
$269$	−13.3513	+	9.70027i	−0.814041	+	0.591436i	0.100958	+	0.994891i	$0.467809\pi$
$270$	−6.71842	−	10.5643i	−0.408870	−	0.642924i
$271$	−4.70284	−	3.41681i	−0.285677	−	0.207557i	0.435713	−	0.900086i	$-0.356496\pi$
$271$	−4.70284	−	3.41681i	−0.285677	−	0.207557i	−0.721390	+	0.692529i	$0.756496\pi$
$272$	−0.667659	+	0.297261i	−0.0404828	+	0.0180241i
$273$	−2.97042	+	2.93100i	−0.179778	+	0.177392i
$274$	5.35931	+	9.28259i	0.323768	+	0.560782i
$275$	−17.8702	−	19.0263i	−1.07762	−	1.14733i
$276$	0.125581	−	0.0803655i	0.00755907	−	0.00483743i
$277$	15.0212	+	16.6827i	0.902537	+	1.00237i	0.999975	+	0.00712721i	$0.00226868\pi$
$277$	15.0212	+	16.6827i	0.902537	+	1.00237i	−0.0974376	+	0.995242i	$0.531065\pi$
$278$	−3.75461	−	2.72788i	−0.225186	−	0.163607i
$279$	−10.5751	+	5.91858i	−0.633114	+	0.354336i
$280$	−0.497835	−	4.30089i	−0.0297513	−	0.257027i
$281$	2.41825	+	23.0081i	0.144261	+	1.37255i	0.791923	+	0.610621i	$0.209080\pi$
$281$	2.41825	+	23.0081i	0.144261	+	1.37255i	−0.647662	+	0.761928i	$0.724253\pi$
$282$	0.902799	+	19.7499i	0.0537609	+	1.17609i
$283$	17.1116	+	7.61859i	1.01718	+	0.452878i	0.846466	−	0.532443i	$-0.178726\pi$
$283$	17.1116	+	7.61859i	1.01718	+	0.452878i	0.170714	+	0.985321i	$0.445392\pi$
$284$	−2.41356	+	2.68053i	−0.143218	+	0.159060i
$285$	−16.9804	−	8.56999i	−1.00583	−	0.507642i
$286$	14.3272	+	15.9120i	0.847185	+	0.940894i
$287$	−1.53143	−	4.71326i	−0.0903974	−	0.278215i
$288$	13.0316	+	1.54596i	0.767895	+	0.0910969i
$289$	−5.19026	+	15.9740i	−0.305310	+	0.939646i
$290$	−22.2110	−	9.61032i	−1.30427	−	0.564337i
$291$	−8.16225	−	6.70043i	−0.478479	−	0.392786i
$292$	11.7991	+	5.25328i	0.690488	+	0.307425i
$293$	−7.31930	−	12.6774i	−0.427598	−	0.740622i	0.569061	−	0.822295i	$-0.307307\pi$
$293$	−7.31930	−	12.6774i	−0.427598	−	0.740622i	−0.996659	+	0.0816737i	$0.973973\pi$
$294$	−12.1775	+	1.84542i	−0.710205	+	0.107627i
$295$	10.5931	−	12.0167i	0.616754	−	0.699637i
$296$	0.641201	+	0.465860i	0.0372691	+	0.0270776i
$297$	14.3153	+	23.0418i	0.830661	+	1.33702i
$298$	0.0259266	−	0.0797939i	0.00150189	−	0.00462234i
$299$	−0.195275	+	0.338226i	−0.0112930	+	0.0195601i
$300$	6.74484	−	2.70084i	0.389414	−	0.155933i
$301$	−2.33467	−	4.04377i	−0.134568	−	0.233079i
$302$	−18.1224	+	3.85204i	−1.04283	+	0.221660i
$303$	6.85852	+	0.405398i	0.394012	+	0.0232895i
$304$	−7.26035	+	3.23252i	−0.416410	+	0.185397i
$305$	6.97892	+	7.58880i	0.399612	+	0.434533i
$306$	1.09786	−	0.962274i	0.0627606	−	0.0550096i
$307$	33.9350			1.93677			0.968386	−	0.249455i	$-0.0802515\pi$
$307$	33.9350			1.93677			0.968386	+	0.249455i	$0.0802515\pi$
$308$	0.289777	+	2.75704i	0.0165115	+	0.157097i
$309$	−1.86098	+	0.700135i	−0.105867	+	0.0398293i
$310$	3.10485	+	9.22444i	0.176344	+	0.523913i
$311$	−8.92071	+	1.89616i	−0.505847	+	0.107521i	−0.453764	−	0.891122i	$-0.649919\pi$
$311$	−8.92071	+	1.89616i	−0.505847	+	0.107521i	−0.0520826	+	0.998643i	$0.516586\pi$
$312$	−18.8760	+	7.10149i	−1.06864	+	0.402043i
$313$	23.1828	+	4.92767i	1.31037	+	0.278528i	0.809565	−	0.587031i	$-0.199703\pi$
$313$	23.1828	+	4.92767i	1.31037	+	0.278528i	0.500807	+	0.865559i	$0.333037\pi$
$314$	3.80788	−	11.7194i	0.214891	−	0.661366i
$315$	1.71600	+	3.88387i	0.0966858	+	0.218831i
$316$	−0.353813	−	1.08892i	−0.0199035	−	0.0612567i
$317$	3.01881	+	28.7221i	0.169554	+	1.61319i	0.666563	+	0.745449i	$0.267765\pi$
$317$	3.01881	+	28.7221i	0.169554	+	1.61319i	−0.497009	+	0.867745i	$0.665568\pi$
$318$	8.87261	−	5.67803i	0.497551	−	0.318408i
$319$	47.9033	+	21.3279i	2.68207	+	1.19413i
$320$	5.31516	−	16.9635i	0.297127	−	0.948288i
$321$	3.18397	+	6.35346i	0.177712	+	0.354615i
$322$	0.0639297	−	0.0284633i	0.00356266	−	0.00158620i
$323$	0.685378	−	2.10938i	0.0381354	−	0.117369i
$324$	−7.42483	+	1.37196i	−0.412491	+	0.0762200i
$325$	−12.4344	+	14.4082i	−0.689739	+	0.799222i
$326$	−2.45523	+	4.25258i	−0.135983	+	0.235529i
$327$	−0.122181	+	0.120559i	−0.00675660	+	0.00666692i
$328$	2.50353	−	23.8195i	0.138234	−	1.31521i
$329$	0.700886	−	6.66848i	0.0386411	−	0.367645i
$330$	20.3092	−	7.88557i	1.11799	−	0.434086i
$331$	2.55027	+	24.2642i	0.140176	+	1.33368i	0.807921	+	0.589291i	$0.200593\pi$
$331$	2.55027	+	24.2642i	0.140176	+	1.33368i	−0.667745	+	0.744390i	$0.732740\pi$
$332$	−1.79470			−0.0984972
$333$	−0.735957	−	0.250046i	−0.0403302	−	0.0137024i
$334$	4.98537	+	15.3434i	0.272787	+	0.839553i
$335$	7.15725	+	3.09682i	0.391043	+	0.169197i
$336$	1.71060	+	0.470624i	0.0933210	+	0.0256747i
$337$	−0.868681	+	0.964768i	−0.0473201	+	0.0525543i	−0.766340	−	0.642435i	$-0.777924\pi$
$337$	−0.868681	+	0.964768i	−0.0473201	+	0.0525543i	0.719020	+	0.694989i	$0.244591\pi$
$338$	1.07316	−	1.19187i	0.0583723	−	0.0648290i
$339$	22.2034	+	6.10864i	1.20592	+	0.331776i
$340$	0.431300	+	0.729210i	0.0233905	+	0.0395470i
$341$	−6.51673	−	20.0564i	−0.352901	−	1.08612i
$342$	11.9385	−	10.4641i	0.645562	−	0.565834i
$343$	8.60793			0.464784
$344$	−2.35881	−	22.4426i	−0.127179	−	1.21002i
$345$	0.251266	+	0.307864i	0.0135277	+	0.0165748i
$346$	−0.402491	+	3.82945i	−0.0216381	+	0.205873i
$347$	−1.80712	+	17.1936i	−0.0970113	+	0.923000i	0.832455	+	0.554093i	$0.186935\pi$
$347$	−1.80712	+	17.1936i	−0.0970113	+	0.923000i	−0.929466	+	0.368908i	$0.879732\pi$
$348$	−10.3892	+	10.2514i	−0.556922	+	0.549530i
$349$	14.5339	−	25.1734i	0.777980	−	1.34750i	−0.155124	−	0.987895i	$-0.549578\pi$
$349$	14.5339	−	25.1734i	0.777980	−	1.34750i	0.933104	−	0.359606i	$-0.117089\pi$
$350$	3.32000	−	0.779028i	0.177461	−	0.0416408i
$351$	15.6171	−	12.1365i	0.833579	−	0.647797i
$352$	−7.05679	+	21.7186i	−0.376128	+	1.15760i
$353$	−17.0643	+	7.59750i	−0.908239	+	0.404374i	−0.807043	−	0.590493i	$-0.798934\pi$
$353$	−17.0643	+	7.59750i	−0.908239	+	0.404374i	−0.101196	+	0.994867i	$0.532267\pi$
$354$	5.99028	+	11.9533i	0.318380	+	0.635312i
$355$	−7.83677	−	5.56875i	−0.415933	−	0.295559i
$356$	13.4656	+	5.99527i	0.713675	+	0.317749i
$357$	−0.417037	+	0.266884i	−0.0220720	+	0.0141250i
$358$	−2.45385	−	23.3469i	−0.129690	−	1.23392i
$359$	1.18928	+	3.66023i	0.0627679	+	0.193180i	0.977523	−	0.210829i	$-0.0676164\pi$
$359$	1.18928	+	3.66023i	0.0627679	+	0.193180i	−0.914755	+	0.404009i	$0.867616\pi$
$360$	−0.0583054	+	20.5205i	−0.00307297	+	1.08152i
$361$	1.58171	−	4.86800i	0.0832479	−	0.256211i
$362$	18.9894	+	4.03632i	0.998060	+	0.212144i
$363$	−26.3494	+	9.91314i	−1.38298	+	0.520305i
$364$	1.97711	−	0.420247i	0.103629	−	0.0220269i
$365$	−10.2928	+	32.8497i	−0.538749	+	1.71943i
$366$	−8.05402	+	3.03008i	−0.420990	+	0.158385i
$367$	−2.42108	−	23.0350i	−0.126379	−	1.20242i	−0.855416	−	0.517942i	$-0.826698\pi$
$367$	−2.42108	−	23.0350i	−0.126379	−	1.20242i	0.729037	−	0.684475i	$-0.239968\pi$
$368$	0.166042			0.00865554
$369$	4.57615	+	23.0384i	0.238225	+	1.19933i
$370$	−0.306425	+	0.543877i	−0.0159303	+	0.0282748i
$371$	−3.26372	+	1.45310i	−0.169444	+	0.0754414i
$372$	5.85965	+	0.346356i	0.303809	+	0.0179577i
$373$	16.1831	−	3.43982i	0.837929	−	0.178107i	0.231090	−	0.972932i	$-0.425771\pi$
$373$	16.1831	−	3.43982i	0.837929	−	0.178107i	0.606839	+	0.794825i	$0.292437\pi$
$374$	1.27023	+	2.20010i	0.0656820	+	0.113765i
$375$	9.21796	+	17.0302i	0.476013	+	0.879438i
$376$	16.2026	−	28.0638i	0.835587	−	1.44728i
$377$	11.8145	−	36.3612i	0.608477	−	1.87270i
$378$	−3.54211	+	0.114519i	−0.182186	+	0.00589020i
$379$	−18.9711	−	13.7833i	−0.974478	−	0.708000i	−0.0180106	−	0.999838i	$-0.505733\pi$
$379$	−18.9711	−	13.7833i	−0.974478	−	0.708000i	−0.956468	+	0.291838i	$0.905733\pi$
$380$	4.69010	+	7.92968i	0.240597	+	0.406784i
$381$	9.60850	−	1.45611i	0.492258	−	0.0745987i
$382$	−5.50218	−	9.53006i	−0.281516	−	0.487600i
$383$	−19.8926	−	8.85675i	−1.01646	−	0.452559i	−0.170249	−	0.985401i	$-0.554457\pi$
$383$	−19.8926	−	8.85675i	−1.01646	−	0.452559i	−0.846215	+	0.532842i	$0.821124\pi$
$384$	−0.244161	−	0.200433i	−0.0124598	−	0.0102283i
$385$	−7.21086	+	1.61218i	−0.367500	+	0.0821641i
$386$	4.23305	−	13.0280i	0.215457	−	0.663107i
$387$	8.73049	+	20.3359i	0.443796	+	1.03373i
$388$	1.58063	+	4.86466i	0.0802441	+	0.246966i
$389$	−0.729663	−	0.810373i	−0.0369954	−	0.0410875i	0.724363	−	0.689419i	$-0.242134\pi$
$389$	−0.729663	−	0.810373i	−0.0369954	−	0.0410875i	−0.761359	+	0.648331i	$0.775467\pi$
$390$	−7.26584	−	14.1257i	−0.367920	−	0.715282i
$391$	−0.0310062	+	0.0344359i	−0.00156805	+	0.00174150i
$392$	18.4423	+	8.21104i	0.931476	+	0.414720i
$393$	−0.434437	−	9.50389i	−0.0219145	−	0.479408i
$394$	0.761941	+	7.24938i	0.0383860	+	0.365219i
$395$	2.77465	−	1.27049i	0.139608	−	0.0639255i
$396$	0.175539	−	13.1380i	0.00882117	−	0.660212i
$397$	−15.4671	−	11.2375i	−0.776274	−	0.563996i	0.127585	−	0.991828i	$-0.459278\pi$
$397$	−15.4671	−	11.2375i	−0.776274	−	0.563996i	−0.903858	+	0.427832i	$0.859278\pi$
$398$	5.11623	+	5.68215i	0.256454	+	0.284821i
$399$	−4.53501	+	2.90218i	−0.227034	+	0.145291i
$400$	7.94819	+	1.51542i	0.397410	+	0.0757712i
$401$	0.466700	+	0.808348i	0.0233059	+	0.0403670i	0.877443	−	0.479681i	$-0.159248\pi$
$401$	0.466700	+	0.808348i	0.0233059	+	0.0403670i	−0.854137	+	0.520048i	$0.825914\pi$
$402$	−4.63318	+	4.57169i	−0.231082	+	0.228015i
$403$	−14.0467	+	6.25400i	−0.699716	+	0.311534i
$404$	−2.69227	−	1.95605i	−0.133946	−	0.0973172i
$405$	−5.90795	−	19.2379i	−0.293568	−	0.955938i
$406$	−5.54224	+	4.02668i	−0.275057	+	0.199841i
$407$	0.676296	−	1.17138i	0.0335228	−	0.0580631i
$408$	−2.36584	+	0.358529i	−0.117127	+	0.0177498i
$409$	−15.2857	+	16.9765i	−0.755829	+	0.839433i	−0.991186	−	0.132476i	$-0.957707\pi$
$409$	−15.2857	+	16.9765i	−0.755829	+	0.839433i	0.235357	+	0.971909i	$0.424374\pi$
$410$	18.8635	−	0.198432i	0.931600	−	0.00979987i
$411$	4.34806	+	16.6719i	0.214474	+	0.822362i
$412$	0.942031	+	0.200235i	0.0464105	+	0.00986486i
$413$	−1.40126	−	4.31263i	−0.0689514	−	0.212210i
$414$	−0.316783	+	0.0982699i	−0.0155690	+	0.00482970i
$415$	−0.550022	−	4.75175i	−0.0269995	−	0.233254i
$416$	16.2865	+	3.46179i	0.798509	+	0.169728i
$417$	−4.65592	−	5.82877i	−0.228002	−	0.285436i
$418$	13.8129	+	23.9247i	0.675611	+	1.17019i
$419$	−9.69838	−	4.31800i	−0.473797	−	0.210948i	0.155924	−	0.987769i	$-0.450164\pi$
$419$	−9.69838	−	4.31800i	−0.473797	−	0.210948i	−0.629722	+	0.776821i	$0.716831\pi$
$420$	0.313931	−	2.03255i	0.0153183	−	0.0991783i
$421$	16.7951	−	7.47766i	0.818544	−	0.364439i	0.0456363	−	0.998958i	$-0.485468\pi$
$421$	16.7951	−	7.47766i	0.818544	−	0.364439i	0.772907	+	0.634519i	$0.218802\pi$
$422$	−23.0968	−	16.7808i	−1.12434	−	0.816878i
$423$	−7.02214	+	30.9944i	−0.341428	+	1.50700i
$424$	−17.2658			−0.838500
$425$	−1.79851	+	1.36541i	−0.0872407	+	0.0662322i
$426$	6.75866	−	4.32521i	0.327458	−	0.209557i
$427$	2.85467	−	0.606780i	0.138147	−	0.0293641i
$428$	0.359809	−	3.42335i	0.0173920	−	0.165474i
$429$	15.4202	+	30.7703i	0.744495	+	1.48560i
$430$	17.3458	−	3.87810i	0.836489	−	0.187019i
$431$	−5.96554	+	4.33422i	−0.287350	+	0.208772i	−0.722117	−	0.691771i	$-0.756831\pi$
$431$	−5.96554	+	4.33422i	−0.287350	+	0.208772i	0.434767	+	0.900543i	$0.356831\pi$
$432$	−7.78833	−	3.17015i	−0.374716	−	0.152524i
$433$	4.26267	−	3.09701i	0.204851	−	0.148833i	−0.480630	−	0.876923i	$-0.659592\pi$
$433$	4.26267	−	3.09701i	0.204851	−	0.148833i	0.685481	+	0.728091i	$0.259592\pi$
$434$	2.69491	+	0.572821i	0.129360	+	0.0274963i
$435$	−30.3260	−	24.3653i	−1.45402	−	1.16823i
$436$	0.0813230	−	0.0172857i	0.00389467	−	0.000827837i
$437$	−0.337173	+	0.374468i	−0.0161292	+	0.0179132i
$438$	−22.2079	−	18.2305i	−1.06113	−	0.871089i
$439$	−22.6157	−	25.1173i	−1.07939	−	1.19878i	−0.979006	−	0.203833i	$-0.934660\pi$
$439$	−22.6157	−	25.1173i	−1.07939	−	1.19878i	−0.100382	−	0.994949i	$-0.532007\pi$
$440$	−35.0052	−	7.05657i	−1.66881	−	0.336409i
$441$	−19.6602	−	2.33233i	−0.936200	−	0.111063i
$442$	1.49853	−	1.08875i	0.0712780	−	0.0517865i
$443$	11.5704	−	20.0405i	0.549726	−	0.952153i	−0.448567	−	0.893749i	$-0.648065\pi$
$443$	11.5704	−	20.0405i	0.549726	−	0.952153i	0.998293	−	0.0584042i	$-0.0186012\pi$
$444$	0.234970	+	0.294161i	0.0111512	+	0.0139602i
$445$	−11.7466	+	37.4895i	−0.556841	+	1.77717i
$446$	−0.443502	+	4.21964i	−0.0210004	+	0.199806i
$447$	0.0742065	−	0.112614i	0.00350985	−	0.00532645i
$448$	−3.36711	−	3.73956i	−0.159081	−	0.176677i
$449$	19.7430			0.931731			0.465866	−	0.884856i	$-0.345743\pi$
$449$	19.7430			0.931731			0.465866	+	0.884856i	$0.345743\pi$
$450$	−16.0608	+	1.81284i	−0.757115	+	0.0854580i
$451$	−40.8741			−1.92469
$452$	−7.46359	−	8.28916i	−0.351058	−	0.389889i
$453$	−29.7296	−	1.75728i	−1.39682	−	0.0825641i
$454$	2.72079	−	25.8866i	0.127693	−	1.21492i
$455$	1.71859	+	5.10589i	0.0805687	+	0.239368i
$456$	−25.7270	+	3.89876i	−1.20478	+	0.182576i
$457$	−0.754881	+	1.30749i	−0.0353119	+	0.0611619i	−0.883141	−	0.469107i	$-0.844576\pi$
$457$	−0.754881	+	1.30749i	−0.0353119	+	0.0611619i	0.847829	+	0.530269i	$0.177909\pi$
$458$	13.2008	−	9.59095i	0.616834	−	0.448156i
$459$	2.11184	−	1.02326i	0.0985722	−	0.0477616i
$460$	−0.0221321	−	0.191203i	−0.00103191	−	0.00891490i
$461$	0.664833	+	0.738372i	0.0309643	+	0.0343894i	0.758428	−	0.651757i	$-0.225968\pi$
$461$	0.664833	+	0.738372i	0.0309643	+	0.0343894i	−0.727464	+	0.686146i	$0.759301\pi$
$462$	1.00541	−	6.08459i	0.0467761	−	0.283081i
$463$	12.7970	−	14.2125i	0.594726	−	0.660510i	−0.368367	−	0.929681i	$-0.620083\pi$
$463$	12.7970	−	14.2125i	0.594726	−	0.660510i	0.963092	+	0.269171i	$0.0867496\pi$
$464$	−15.8993	+	3.37950i	−0.738106	+	0.156889i
$465$	0.878774	+	15.6204i	0.0407522	+	0.724380i
$466$	13.4580	+	2.86058i	0.623428	+	0.132514i
$467$	−7.86342	+	5.71311i	−0.363875	+	0.264371i	−0.754667	−	0.656108i	$-0.772201\pi$
$467$	−7.86342	+	5.71311i	−0.363875	+	0.264371i	0.390791	+	0.920479i	$0.372201\pi$
$468$	−9.54007	+	0.874008i	−0.440990	+	0.0404010i
$469$	1.78593	−	1.29755i	0.0824665	−	0.0599154i
$470$	23.4249	+	10.1356i	1.08051	+	0.467519i
$471$	10.8988	−	16.5397i	0.502190	−	0.762111i
$472$	2.29072	−	21.7948i	0.105439	−	1.00319i
$473$	−37.6698	+	8.00696i	−1.73206	+	0.368161i
$474$	0.116310	+	2.54443i	0.00534228	+	0.116869i
$475$	−19.5576	+	14.8480i	−0.897366	+	0.681271i
$476$	0.239821			0.0109922
$477$	16.1723	−	5.01685i	0.740481	−	0.229706i
$478$	11.1804	+	8.12306i	0.511381	+	0.371540i
$479$	−14.1221	+	6.28758i	−0.645256	+	0.287287i	−0.703156	−	0.711036i	$-0.748226\pi$
$479$	−14.1221	+	6.28758i	−0.645256	+	0.287287i	0.0578994	+	0.998322i	$0.481560\pi$
$480$	9.17250	−	14.2438i	0.418665	−	0.650139i
$481$	−0.900936	−	0.401123i	−0.0410792	−	0.0182896i
$482$	−14.8924	−	25.7944i	−0.678331	−	1.17490i
$483$	0.111218	−	0.0168545i	0.00506061	−	0.000766904i
$484$	13.3381	+	2.83510i	0.606278	+	0.128868i
$485$	−12.3955	+	5.67581i	−0.562851	+	0.257725i
$486$	16.7352	+	1.43875i	0.759123	+	0.0652630i
$487$	4.43743	+	13.6570i	0.201079	+	0.618858i	0.999852	+	0.0172246i	$0.00548302\pi$
$487$	4.43743	+	13.6570i	0.201079	+	0.618858i	−0.798773	+	0.601633i	$0.794517\pi$
$488$	13.7962	+	2.93247i	0.624525	+	0.132747i
$489$	−5.61854	+	5.54397i	−0.254079	+	0.250707i
$490$	−4.75420	+	15.1732i	−0.214773	+	0.685454i
$491$	−2.51084	+	2.78857i	−0.113313	+	0.125846i	−0.797132	−	0.603805i	$-0.793651\pi$
$491$	−2.51084	+	2.78857i	−0.113313	+	0.125846i	0.683820	+	0.729651i	$0.260317\pi$
$492$	4.14803	−	10.5939i	0.187008	−	0.477611i
$493$	2.26811	−	3.92848i	0.102150	−	0.176930i
$494$	16.2956	−	11.8394i	0.733173	−	0.532681i
$495$	34.8387	−	3.56165i	1.56588	−	0.160084i
$496$	5.28863	+	3.84242i	0.237467	+	0.172530i
$497$	−2.48612	+	1.10689i	−0.111518	+	0.0496510i
$498$	3.84947	+	1.05907i	0.172499	+	0.0474582i
$499$	−1.24260	−	2.15224i	−0.0556263	−	0.0963476i	0.836871	−	0.547400i	$-0.184382\pi$
$499$	−1.24260	−	2.15224i	−0.0556263	−	0.0963476i	−0.892498	+	0.451052i	$0.851049\pi$
$500$	0.685633	−	9.35462i	0.0306625	−	0.418351i
$501$	1.18419	+	25.9058i	0.0529058	+	1.15738i
$502$	−2.08362	−	2.31409i	−0.0929965	−	0.103283i
$503$	−2.61295	−	1.89842i	−0.116506	−	0.0846463i	0.528007	−	0.849240i	$-0.322940\pi$
$503$	−2.61295	−	1.89842i	−0.116506	−	0.0846463i	−0.644512	+	0.764594i	$0.722940\pi$
$504$	4.99130	+	2.97134i	0.222330	+	0.132354i
$505$	4.35384	−	7.72766i	0.193743	−	0.343877i
$506$	−0.0603310	−	0.574011i	−0.00268204	−	0.0255179i
$507$	2.17145	−	1.38962i	0.0964376	−	0.0617154i
$508$	−4.30021	−	1.91458i	−0.190791	−	0.0849457i
$509$	8.30576	−	9.22448i	0.368146	−	0.408868i	−0.530399	−	0.847748i	$-0.677958\pi$
$509$	8.30576	−	9.22448i	0.368146	−	0.408868i	0.898546	+	0.438880i	$0.144625\pi$
$510$	−0.494783	−	1.81860i	−0.0219094	−	0.0805290i
$511$	6.52040	+	7.24164i	0.288445	+	0.320351i
$512$	−5.24697	−	16.1485i	−0.231885	−	0.713670i
$513$	22.9649	−	11.1273i	1.01392	−	0.491280i
$514$	−1.99946	+	6.15369i	−0.0881922	+	0.271428i
$515$	−0.241448	+	2.55553i	−0.0106395	+	0.112610i
$516$	1.74757	−	10.5760i	0.0769325	−	0.465582i
$517$	−50.5215	−	22.4936i	−2.22193	−	0.989268i
$518$	0.0883547	+	0.153035i	0.00388208	+	0.00672397i
$519$	−2.25668	+	5.76346i	−0.0990570	+	0.252988i
$520$	−2.44901	+	25.9208i	−0.107396	+	1.13670i
$521$	18.5974	+	13.5118i	0.814765	+	0.591962i	0.915208	−	0.402981i	$-0.132026\pi$
$521$	18.5974	+	13.5118i	0.814765	+	0.591962i	−0.100443	+	0.994943i	$0.532026\pi$
$522$	28.3334	−	15.8574i	1.24012	−	0.694059i
$523$	−6.02620	+	18.5468i	−0.263508	+	0.810993i	0.728526	+	0.685018i	$0.240206\pi$
$523$	−6.02620	+	18.5468i	−0.263508	+	0.810993i	−0.992033	+	0.125975i	$0.959794\pi$
$524$	−2.30409	+	3.99080i	−0.100654	+	0.174339i
$525$	5.47769	+	0.208264i	0.239066	+	0.00908937i
$526$	−7.38188	−	12.7858i	−0.321865	−	0.557487i
$527$	−1.78447	+	0.379302i	−0.0777329	+	0.0165226i
$528$	8.05137	−	12.2186i	0.350391	−	0.531744i
$529$	−21.0019	+	9.35066i	−0.913127	+	0.406550i
$530$	−1.56369	−	13.5090i	−0.0679224	−	0.586794i
$531$	4.18718	+	21.0801i	0.181708	+	0.914800i
$532$	2.60790			0.113067
$533$	3.11515	+	29.6387i	0.134932	+	1.28380i
$534$	−25.3446	−	20.8055i	−1.09677	−	0.900341i
$535$	9.17410	−	0.0965060i	0.396631	−	0.00417232i
$536$	10.4355	−	2.21814i	0.450745	−	0.0958089i
$537$	6.15196	−	37.2305i	0.265477	−	1.60662i
$538$	−17.3938	−	3.69717i	−0.749902	−	0.159397i
$539$	10.6463	−	32.7658i	0.458567	−	1.41132i
$540$	−2.61242	+	9.39109i	−0.112421	+	0.404128i
$541$	−4.92323	−	15.1521i	−0.211666	−	0.651442i	−0.999374	−	0.0353920i	$-0.988732\pi$
$541$	−4.92323	−	15.1521i	−0.211666	−	0.651442i	0.787707	−	0.616050i	$-0.211268\pi$
$542$	−0.654731	−	6.22935i	−0.0281231	−	0.267574i
$543$	27.7097	+	14.3528i	1.18914	+	0.615936i
$544$	1.80474	+	0.803521i	0.0773775	+	0.0344507i
$545$	0.0706896	+	0.210017i	0.00302801	+	0.00899615i
$546$	−4.48870	−	0.265321i	−0.192099	−	0.0113547i
$547$	−13.2926	+	5.91824i	−0.568350	+	0.253046i	−0.670733	−	0.741699i	$-0.734020\pi$
$547$	−13.2926	+	5.91824i	−0.568350	+	0.253046i	0.102382	+	0.994745i	$0.467354\pi$
$548$	2.57887	−	7.93695i	0.110164	−	0.339050i
$549$	−13.7746	+	1.26195i	−0.587884	+	0.0538587i
$550$	2.35090	−	28.0277i	0.100243	−	1.19510i
$551$	24.6642	−	42.7196i	1.05073	−	1.81992i
$552$	0.524163	+	0.144209i	0.0223098	+	0.00613793i
$553$	0.0902966	−	0.859115i	0.00383980	−	0.0365333i
$554$	−2.52845	+	24.0566i	−0.107424	+	1.02207i
$555$	−0.706822	+	0.712270i	−0.0300029	+	0.0302342i
$556$	0.377702	+	3.59360i	0.0160182	+	0.152403i
$557$	31.2370			1.32355			0.661776	−	0.749701i	$-0.269803\pi$
$557$	31.2370			1.32355			0.661776	+	0.749701i	$0.269803\pi$
$558$	−12.3640	−	4.20074i	−0.523410	−	0.177832i
$559$	8.67697	+	26.7050i	0.366997	+	1.12950i
$560$	1.51461	−	1.71815i	0.0640039	−	0.0726051i
$561$	1.03055	+	3.95146i	0.0435098	+	0.166831i
$562$	−16.6803	+	18.5253i	−0.703616	+	0.781444i
$563$	−26.8720	+	29.8443i	−1.13252	+	1.25779i	−0.170335	+	0.985386i	$0.554485\pi$
$563$	−26.8720	+	29.8443i	−1.13252	+	1.25779i	−0.962183	+	0.272402i	$0.912182\pi$
$564$	10.9571	−	10.8116i	0.461376	−	0.455252i
$565$	19.6594	−	22.3013i	0.827078	−	0.938225i
$566$	6.23691	+	19.1952i	0.262157	+	0.806836i
$567$	−5.53857	−	1.33286i	−0.232598	−	0.0559749i
$568$	−13.1521			−0.551850
$569$	−3.32079	−	31.5952i	−0.139215	−	1.32454i	−0.811546	−	0.584288i	$-0.801374\pi$
$569$	−3.32079	−	31.5952i	−0.139215	−	1.32454i	0.672331	−	0.740250i	$-0.265293\pi$
$570$	−5.38044	−	19.7761i	−0.225362	−	0.828330i
$571$	2.01441	−	19.1658i	0.0843005	−	0.802066i	−0.867930	−	0.496686i	$-0.834550\pi$
$571$	2.01441	−	19.1658i	0.0843005	−	0.802066i	0.952231	−	0.305379i	$-0.0987833\pi$
$572$	1.74258	−	16.5796i	0.0728611	−	0.693227i
$573$	−4.46397	−	17.1163i	−0.186485	−	0.715044i
$574$	2.67000	−	4.62457i	0.111444	−	0.193026i
$575$	0.499456	−	0.117196i	0.0208288	−	0.00488741i
$576$	13.7596	+	19.4806i	0.573317	+	0.811691i
$577$	9.95121	−	30.6267i	0.414274	−	1.27500i	−0.498624	−	0.866818i	$-0.666161\pi$
$577$	9.95121	−	30.6267i	0.414274	−	1.27500i	0.912898	−	0.408187i	$-0.133839\pi$
$578$	−16.5334	+	7.36116i	−0.687700	+	0.306184i
$579$	12.1157	−	18.3865i	0.503512	−	0.764117i
$580$	6.01087	+	17.8582i	0.249588	+	0.741519i
$581$	−1.23700	−	0.550747i	−0.0513193	−	0.0228488i
$582$	−0.519602	−	11.3670i	−0.0215382	−	0.471177i
$583$	3.08000	+	29.3043i	0.127561	+	1.21366i
$584$	14.5529	+	44.7891i	0.602202	+	1.85339i
$585$	−5.23781	−	24.9909i	−0.216557	−	1.03325i
$586$	4.87425	−	15.0014i	0.201353	−	0.619702i
$587$	11.3286	+	2.40796i	0.467580	+	0.0993871i	0.435675	−	0.900104i	$-0.356510\pi$
$587$	11.3286	+	2.40796i	0.467580	+	0.0993871i	0.0319041	+	0.999491i	$0.489843\pi$
$588$	7.41197	+	6.08453i	0.305665	+	0.250922i
$589$	−19.4050	+	4.12466i	−0.799569	+	0.169954i
$590$	17.2600	−	0.181565i	0.710585	−	0.00747492i
$591$	−1.91023	+	11.5604i	−0.0785764	+	0.475530i
$592$	0.0438268	+	0.416984i	0.00180127	+	0.0171379i
$593$	−22.3537			−0.917955			−0.458977	−	0.888448i	$-0.651784\pi$
$593$	−22.3537			−0.917955			−0.458977	+	0.888448i	$0.651784\pi$
$594$	−8.12941	+	28.0763i	−0.333554	+	1.15198i
$595$	0.0734979	+	0.634962i	0.00301312	+	0.0260309i
$596$	−0.0596763	+	0.0265696i	−0.00244444	+	0.00108833i
$597$	5.50655	+	10.9881i	0.225368	+	0.449711i
$598$	−0.411630	+	0.0874947i	−0.0168328	+	0.00357792i
$599$	−2.18765	−	3.78911i	−0.0893848	−	0.154819i	0.817866	−	0.575408i	$-0.195157\pi$
$599$	−2.18765	−	3.78911i	−0.0893848	−	0.154819i	−0.907251	+	0.420589i	$0.861823\pi$
$600$	23.7747	+	11.6870i	0.970600	+	0.477118i
$601$	−7.07808	+	12.2596i	−0.288721	+	0.500079i	−0.973505	−	0.228667i	$-0.926563\pi$
$601$	−7.07808	+	12.2596i	−0.288721	+	0.500079i	0.684784	+	0.728746i	$0.259897\pi$
$602$	1.55476	−	4.78507i	0.0633674	−	0.195025i
$603$	−9.13012	+	5.10987i	−0.371807	+	0.208090i
$604$	11.6702	+	8.47889i	0.474853	+	0.345001i
$605$	−3.41863	+	36.1835i	−0.138987	+	1.47107i
$606$	4.62039	+	5.78428i	0.187690	+	0.234970i
$607$	17.2199	+	29.8257i	0.698933	+	1.21059i	0.968837	+	0.247700i	$0.0796748\pi$
$607$	17.2199	+	29.8257i	0.698933	+	1.21059i	−0.269904	+	0.962887i	$0.586992\pi$
$608$	19.6253	+	8.73776i	0.795912	+	0.354363i
$609$	−10.3066	+	3.87755i	−0.417646	+	0.157126i
$610$	−1.04495	+	11.0599i	−0.0423087	+	0.447804i
$611$	−12.4602	+	38.3486i	−0.504086	+	1.55142i
$612$	−1.12874	−	0.133904i	−0.0456266	−	0.00541277i
$613$	−2.88297	−	8.87288i	−0.116442	−	0.358372i	0.875803	−	0.482669i	$-0.160333\pi$
$613$	−2.88297	−	8.87288i	−0.116442	−	0.358372i	−0.992245	+	0.124297i	$0.960333\pi$
$614$	24.4672	+	27.1736i	0.987417	+	1.09664i
$615$	29.3202	+	7.73581i	1.18230	+	0.311938i
$616$	−6.76376	+	7.51192i	−0.272520	+	0.302664i
$617$	−19.7638	−	8.79942i	−0.795661	−	0.354251i	−0.0316870	−	0.999498i	$-0.510088\pi$
$617$	−19.7638	−	8.79942i	−0.795661	−	0.354251i	−0.763974	+	0.645247i	$0.776755\pi$
$618$	−1.90241	−	0.985387i	−0.0765260	−	0.0396381i
$619$	−1.68039	−	15.9879i	−0.0675406	−	0.642606i	−0.974960	−	0.222380i	$-0.928617\pi$
$619$	−1.68039	−	15.9879i	−0.0675406	−	0.642606i	0.907419	−	0.420226i	$-0.138049\pi$
$620$	3.71975	−	6.60221i	0.149389	−	0.265151i
$621$	−0.532870	+	0.0172280i	−0.0213833	+	0.000691337i
$622$	−7.95021	−	5.77617i	−0.318774	−	0.231603i
$623$	7.44136	+	8.26446i	0.298132	+	0.331109i
$624$	−9.47357	−	4.90701i	−0.379246	−	0.196438i
$625$	24.9779	−	1.05159i	0.999115	−	0.0420636i
$626$	12.7690	+	22.1166i	0.510354	+	0.883958i
$627$	11.2065	+	42.9695i	0.447546	+	1.71604i
$628$	−8.76474	+	3.90231i	−0.349751	+	0.155719i
$629$	−0.0946637	−	0.0687772i	−0.00377449	−	0.00274233i
$630$	−1.87278	+	4.17437i	−0.0746134	+	0.166311i
$631$	36.4652	−	26.4935i	1.45165	−	1.05469i	0.466214	−	0.884672i	$-0.345618\pi$
$631$	36.4652	−	26.4935i	1.45165	−	1.05469i	0.985441	−	0.170017i	$-0.0543823\pi$
$632$	2.08742	−	3.61552i	0.0830331	−	0.143818i
$633$	−28.6414	−	35.8563i	−1.13839	−	1.42516i
$634$	−20.8228	+	23.1260i	−0.826978	+	0.918453i
$635$	3.75125	−	11.9722i	0.148864	−	0.475103i
$636$	−7.90777	−	2.17560i	−0.313564	−	0.0862682i
$637$	−24.5706	−	5.22265i	−0.973524	−	0.206929i
$638$	17.4600	+	53.7363i	0.691247	+	2.12744i
$639$	12.3192	−	3.82156i	0.487340	−	0.151179i
$640$	−0.370792	+	0.169783i	−0.0146568	+	0.00671126i
$641$	32.0511	+	6.81267i	1.26594	+	0.269084i	0.791482	−	0.611192i	$-0.209310\pi$
$641$	32.0511	+	6.81267i	1.26594	+	0.269084i	0.474461	+	0.880277i	$0.342643\pi$
$642$	−2.79191	+	7.13044i	−0.110188	+	0.281416i
$643$	−1.00181	−	1.73519i	−0.0395077	−	0.0684294i	0.845595	−	0.533824i	$-0.179246\pi$
$643$	−1.00181	−	1.73519i	−0.0395077	−	0.0684294i	−0.885103	+	0.465395i	$0.845912\pi$
$644$	−0.0497750	−	0.0221613i	−0.00196141	−	0.000873276i
$645$	28.5371	+	1.38574i	1.12365	+	0.0545633i
$646$	2.18325	−	0.972046i	0.0858989	−	0.0382447i
$647$	8.36159	+	6.07505i	0.328728	+	0.238835i	0.739891	−	0.672727i	$-0.234877\pi$
$647$	8.36159	+	6.07505i	0.328728	+	0.238835i	−0.411163	+	0.911562i	$0.634877\pi$
$648$	−21.8329	−	16.7718i	−0.857679	−	0.658857i
$649$	−37.3997			−1.46807
$650$	−20.5027	+	0.431399i	−0.804181	+	0.0169209i
$651$	3.93247	+	2.03690i	0.154126	+	0.0798322i
$652$	3.73968	−	0.794894i	0.146457	−	0.0311305i
$653$	−1.34281	+	12.7760i	−0.0525481	+	0.499962i	0.936318	+	0.351153i	$0.114210\pi$
$653$	−1.34281	+	12.7760i	−0.0525481	+	0.499962i	−0.988866	+	0.148808i	$0.952456\pi$
$654$	−0.184631	−	0.0109133i	−0.00721963	−	0.000426743i
$655$	−11.2724	−	4.87735i	−0.440447	−	0.190574i
$656$	10.2505	−	7.44740i	0.400214	−	0.290772i
$657$	−26.6454	−	37.7241i	−1.03954	−	1.47176i
$658$	5.84516	−	4.24676i	0.227868	−	0.165556i
$659$	−4.63980	−	0.986219i	−0.180741	−	0.0384176i	0.116652	−	0.993173i	$-0.462784\pi$
$659$	−4.63980	−	0.986219i	−0.180741	−	0.0384176i	−0.297393	+	0.954755i	$0.596117\pi$
$660$	−15.1433	−	7.64281i	−0.589452	−	0.297496i
$661$	−3.96345	+	0.842458i	−0.154160	+	0.0327678i	−0.284345	−	0.958722i	$-0.591776\pi$
$661$	−3.96345	+	0.842458i	−0.154160	+	0.0327678i	0.130185	+	0.991490i	$0.458443\pi$
$662$	−17.5909	+	19.5367i	−0.683691	+	0.759315i
$663$	2.78675	−	1.04843i	0.108228	−	0.0407176i
$664$	−4.37878	−	4.86312i	−0.169929	−	0.188726i
$665$	0.799241	+	6.90479i	0.0309932	+	0.267756i
$666$	−0.330402	−	0.769605i	−0.0128028	−	0.0298216i
$667$	−0.833768	+	0.605768i	−0.0322836	+	0.0234554i
$668$	6.28049	−	10.8781i	0.242999	−	0.420887i
$669$	−2.48661	+	6.35071i	−0.0961379	+	0.245533i
$670$	2.68061	+	7.96402i	0.103561	+	0.307677i
$671$	2.51605	−	23.9387i	0.0971312	−	0.924141i
$672$	−2.14861	−	4.28745i	−0.0828845	−	0.165392i
$673$	−33.7504	−	37.4836i	−1.30098	−	1.44489i	−0.824673	−	0.565610i	$-0.808641\pi$
$673$	−33.7504	−	37.4836i	−1.30098	−	1.44489i	−0.476309	−	0.879278i	$-0.658026\pi$
$674$	−1.39886			−0.0538822
$675$	−25.6649	−	4.03869i	−0.987844	−	0.155449i
$676$	−1.24871			−0.0480274
$677$	−23.2519	−	25.8238i	−0.893642	−	0.992490i	0.106357	−	0.994328i	$-0.466081\pi$
$677$	−23.2519	−	25.8238i	−0.893642	−	0.992490i	−0.999998	+	0.00183848i	$0.999415\pi$
$678$	11.1172	+	22.1838i	0.426953	+	0.851964i
$679$	−0.403392	+	3.83802i	−0.0154808	+	0.147290i
$680$	−0.923647	+	2.94785i	−0.0354202	+	0.113045i
$681$	15.2548	−	38.9602i	0.584566	−	1.49296i
$682$	11.3617	−	19.6790i	0.435062	−	0.753549i
$683$	−33.1970	+	24.1191i	−1.27025	+	0.922890i	−0.999213	−	0.0396784i	$-0.987367\pi$
$683$	−33.1970	+	24.1191i	−1.27025	+	0.922890i	−0.271037	+	0.962569i	$0.587367\pi$
$684$	−12.2743	−	1.45612i	−0.469319	−	0.0556763i
$685$	21.8046	+	4.39551i	0.833111	+	0.167944i
$686$	6.20634	+	6.89284i	0.236959	+	0.263170i
$687$	24.5489	−	9.23576i	0.936599	−	0.352366i
$688$	7.98800	−	8.87158i	0.304540	−	0.338226i
$689$	21.0144	−	4.46676i	0.800587	−	0.170170i
$690$	−0.0653598	+	0.423173i	−0.00248821	+	0.0161099i
$691$	21.5694	+	4.58473i	0.820540	+	0.174411i	0.599009	−	0.800742i	$-0.295561\pi$
$691$	21.5694	+	4.58473i	0.820540	+	0.174411i	0.221531	+	0.975153i	$0.428895\pi$
$692$	2.42543	−	1.76218i	0.0922009	−	0.0669879i
$693$	4.15271	−	9.00151i	0.157748	−	0.341939i
$694$	−15.0708	+	10.9496i	−0.572079	+	0.415640i
$695$	−9.39883	+	2.10135i	−0.356518	+	0.0797088i
$696$	−53.1261	−	3.14022i	−2.01374	−	0.119030i
$697$	−0.369608	+	3.51658i	−0.0139999	+	0.133200i
$698$	30.6367	−	6.51203i	1.15962	−	0.246484i
$699$	19.6381	+	10.1719i	0.742782	+	0.384738i
$700$	−2.18040	−	1.51511i	−0.0824112	−	0.0572658i
$701$	0.897737			0.0339071			0.0169535	−	0.999856i	$-0.494603\pi$
$701$	0.897737			0.0339071			0.0169535	+	0.999856i	$0.494603\pi$
$702$	20.9783	+	3.75503i	0.791775	+	0.141724i
$703$	−1.02941	−	0.747907i	−0.0388247	−	0.0282078i
$704$	−37.9149	+	16.8808i	−1.42897	+	0.636219i
$705$	31.9834	+	25.6970i	1.20457	+	0.967805i
$706$	−18.3871	−	8.18647i	−0.692008	−	0.308102i
$707$	−1.25539	−	2.17439i	−0.0472137	−	0.0817765i
$708$	3.79544	−	9.69342i	0.142642	−	0.364301i
$709$	−40.6065	−	8.63118i	−1.52501	−	0.324151i	−0.632279	−	0.774741i	$-0.717880\pi$
$709$	−40.6065	−	8.63118i	−1.52501	−	0.324151i	−0.892731	+	0.450590i	$0.851214\pi$
$710$	−1.19113	−	10.2904i	−0.0447024	−	0.386193i
$711$	−0.904677	+	3.99308i	−0.0339280	+	0.149752i
$712$	16.6083	+	51.1152i	0.622424	+	1.91562i
$713$	0.405419	+	0.0861745i	0.0151831	+	0.00322726i
$714$	−0.514393	−	0.141521i	−0.0192507	−	0.00529629i
$715$	44.4309	−	0.467386i	1.66162	−	0.0174793i
$716$	−12.2302	+	13.5830i	−0.457064	+	0.507621i
$717$	13.8644	+	17.3569i	0.517775	+	0.648205i
$718$	−2.07347	+	3.59136i	−0.0773813	+	0.134028i
$719$	34.2388	−	24.8759i	1.27689	−	0.927716i	0.277437	−	0.960744i	$-0.410515\pi$
$719$	34.2388	−	24.8759i	1.27689	−	0.927716i	0.999454	+	0.0330279i	$0.0105150\pi$
$720$	−8.08797	+	7.24094i	−0.301421	+	0.269854i
$721$	0.587847	+	0.427096i	0.0218926	+	0.0159059i
$722$	5.03849	−	2.24328i	0.187513	−	0.0834863i
$723$	−12.0824	−	46.3277i	−0.449348	−	1.72294i
$724$	−7.55762	−	13.0902i	−0.280877	−	0.486493i
$725$	−45.4400	+	21.3876i	−1.68760	+	0.794317i
$726$	−26.9360	−	13.9520i	−0.999687	−	0.517807i
$727$	7.32228	+	8.13221i	0.271568	+	0.301607i	0.863467	−	0.504405i	$-0.168288\pi$
$727$	7.32228	+	8.13221i	0.271568	+	0.301607i	−0.591899	+	0.806012i	$0.701622\pi$
$728$	5.96255	+	4.33205i	0.220987	+	0.160556i
$729$	25.3236	+	9.36570i	0.937910	+	0.346878i
$730$	−33.7257	+	15.4428i	−1.24824	+	0.571562i
$731$	0.348243	+	3.31331i	0.0128802	+	0.122547i
$732$	5.94918	+	3.08149i	0.219888	+	0.113895i
$733$	1.16076	+	0.516802i	0.0428735	+	0.0190885i	0.428061	−	0.903750i	$-0.359197\pi$
$733$	1.16076	+	0.516802i	0.0428735	+	0.0190885i	−0.385188	+	0.922838i	$0.625863\pi$
$734$	16.6998	−	18.5470i	0.616400	−	0.684582i
$735$	−13.8381	+	21.4890i	−0.510428	+	0.792634i
$736$	−0.300323	−	0.333542i	−0.0110700	−	0.0122945i
$737$	−5.62629	−	17.3159i	−0.207247	−	0.637841i
$738$	−15.1487	+	20.2751i	−0.557632	+	0.746338i
$739$	5.82472	−	17.9267i	0.214266	−	0.659443i	−0.784939	−	0.619573i	$-0.787306\pi$
$739$	5.82472	−	17.9267i	0.214266	−	0.659443i	0.999205	−	0.0398696i	$-0.0126943\pi$
$740$	0.474331	−	0.106049i	0.0174367	−	0.00389843i
$741$	30.3041	−	11.4010i	1.11325	−	0.418825i
$742$	−3.51673	−	1.56575i	−0.129103	−	0.0574805i
$743$	0.560250	+	0.970382i	0.0205536	+	0.0355999i	0.876119	−	0.482094i	$-0.160124\pi$
$743$	0.560250	+	0.970382i	0.0205536	+	0.0355999i	−0.855566	+	0.517694i	$0.826790\pi$
$744$	13.3580	+	16.7230i	0.489729	+	0.613094i
$745$	−0.0886360	−	0.149859i	−0.00324737	−	0.00549042i
$746$	14.4225	+	10.4786i	0.528046	+	0.383648i
$747$	5.51453	+	3.28282i	0.201766	+	0.120112i
$748$	0.611228	−	1.88116i	0.0223487	−	0.0687822i
$749$	1.29853	−	2.24913i	0.0474474	−	0.0821813i
$750$	−6.99088	+	19.6602i	−0.255271	+	0.717888i
$751$	6.69286	+	11.5924i	0.244226	+	0.423012i	0.961914	−	0.273353i	$-0.0881328\pi$
$751$	6.69286	+	11.5924i	0.244226	+	0.423012i	−0.717688	+	0.696365i	$0.754799\pi$
$752$	16.7683	−	3.56421i	0.611476	−	0.129973i
$753$	−2.24258	−	4.47496i	−0.0817241	−	0.163077i
$754$	37.6347	−	16.7560i	1.37057	−	0.610219i
$755$	−18.8726	+	33.4971i	−0.686843	+	1.21908i
$756$	1.91162	+	1.98982i	0.0695249	+	0.0723690i
$757$	14.0336			0.510062			0.255031	−	0.966933i	$-0.417914\pi$
$757$	14.0336			0.510062			0.255031	+	0.966933i	$0.417914\pi$
$758$	−2.64116	−	25.1290i	−0.0959313	−	0.912725i
$759$	0.151253	−	0.915358i	0.00549015	−	0.0332254i
$760$	−10.0441	+	32.0559i	−0.364336	+	1.16279i
$761$	−12.9526	+	2.75317i	−0.469533	+	0.0998023i	−0.436601	−	0.899655i	$-0.643818\pi$
$761$	−12.9526	+	2.75317i	−0.469533	+	0.0998023i	−0.0329319	+	0.999458i	$0.510484\pi$
$762$	8.09374	+	6.64419i	0.293205	+	0.240694i
$763$	0.0613563	+	0.0130417i	0.00222125	+	0.000472141i
$764$	−2.64762	+	8.14854i	−0.0957875	+	0.294804i
$765$	0.00860791	−	3.02954i	0.000311220	−	0.109533i
$766$	−7.25052	−	22.3148i	−0.261972	−	0.806267i
$767$	2.85036	+	27.1194i	0.102921	+	0.979225i
$768$	−1.27310	−	27.8508i	−0.0459392	−	1.00498i
$769$	10.4551	+	4.65492i	0.377021	+	0.167861i	0.586493	−	0.809954i	$-0.300508\pi$
$769$	10.4551	+	4.65492i	0.377021	+	0.167861i	−0.209472	+	0.977815i	$0.567175\pi$
$770$	−6.49001	−	4.61175i	−0.233884	−	0.166196i
$771$	−5.72279	+	8.68476i	−0.206101	+	0.312774i
$772$	−9.74339	+	4.33803i	−0.350672	+	0.156129i
$773$	−9.74410	+	29.9892i	−0.350471	+	1.07864i	0.608119	+	0.793846i	$0.291925\pi$
$773$	−9.74410	+	29.9892i	−0.350471	+	1.07864i	−0.958589	+	0.284792i	$0.908075\pi$
$774$	−9.98938	+	21.6532i	−0.359061	+	0.778309i
$775$	18.6203	+	7.82520i	0.668862	+	0.281090i
$776$	−9.32535	+	16.1520i	−0.334761	+	0.579823i
$777$	0.0716830	+	0.274856i	0.00257161	+	0.00986040i
$778$	0.122821	−	1.16856i	0.00440334	−	0.0418950i
$779$	−4.01924	+	38.2405i	−0.144004	+	1.37011i
$780$	−4.38785	+	11.5632i	−0.157110	+	0.414030i
$781$	2.34617	+	22.3224i	0.0839527	+	0.798757i
$782$	−0.0499303			−0.00178550
$783$	50.6741	−	12.4953i	1.81095	−	0.446546i
$784$	3.30017	+	10.1569i	0.117863	+	0.362745i
$785$	−13.0181	−	22.0100i	−0.464635	−	0.785571i
$786$	7.29706	−	7.20021i	0.260277	−	0.256823i
$787$	−22.8901	+	25.4220i	−0.815944	+	0.906197i	−0.997010	−	0.0772737i	$-0.975378\pi$
$787$	−22.8901	+	25.4220i	−0.815944	+	0.906197i	0.181066	+	0.983471i	$0.442045\pi$
$788$	3.79757	−	4.21763i	0.135283	−	0.150247i
$789$	−5.98899	−	22.9637i	−0.213214	−	0.817530i
$790$	3.01789	+	1.30579i	0.107372	+	0.0464578i
$791$	−2.60055	−	8.00367i	−0.0924649	−	0.284578i
$792$	36.0285	−	31.5789i	1.28022	−	1.12211i
$793$	−17.5502			−0.623226
$794$	−2.15334	−	20.4877i	−0.0764192	−	0.727081i
$795$	3.33674	−	21.6038i	0.118342	−	0.766206i
$796$	0.622275	−	5.92055i	0.0220560	−	0.209848i
$797$	3.91915	−	37.2882i	0.138823	−	1.32082i	−0.674185	−	0.738563i	$-0.735505\pi$
$797$	3.91915	−	37.2882i	0.138823	−	1.32082i	0.813008	−	0.582253i	$-0.197829\pi$
$798$	−5.59369	−	1.53895i	−0.198014	−	0.0544781i
$799$	−2.39207	+	4.14319i	−0.0846255	+	0.146576i
$800$	−11.3319	−	18.7072i	−0.400642	−	0.661398i
$801$	−30.4089	−	43.0523i	−1.07445	−	1.52118i
$802$	−0.310796	+	0.956533i	−0.0109746	+	0.0337764i
$803$	73.4221	−	32.6896i	2.59101	−	1.15359i
$804$	5.05899	+	0.299031i	0.178417	+	0.0105460i
$805$	0.0434207	−	0.138578i	0.00153038	−	0.00488425i
$806$	−15.1356	−	6.73882i	−0.533130	−	0.237365i
$807$	−25.3814	−	13.1468i	−0.893469	−	0.462789i
$808$	−1.26837	−	12.0677i	−0.0446210	−	0.424540i
$809$	−2.07744	−	6.39370i	−0.0730388	−	0.224790i	0.907872	−	0.419247i	$-0.137706\pi$
$809$	−2.07744	−	6.39370i	−0.0730388	−	0.224790i	−0.980911	+	0.194456i	$0.937706\pi$
$810$	11.1452	−	18.6014i	0.391602	−	0.653586i
$811$	−0.0417238	+	0.128413i	−0.00146512	+	0.00450918i	−0.951786	−	0.306762i	$-0.900755\pi$
$811$	−0.0417238	+	0.128413i	−0.00146512	+	0.00450918i	0.950321	+	0.311271i	$0.100755\pi$
$812$	5.21724	+	1.10896i	0.183089	+	0.0389168i
$813$	1.64145	−	9.93376i	0.0575682	−	0.348392i
$814$	1.42560	−	0.303020i	0.0499672	−	0.0106209i
$815$	3.25070	+	9.65776i	0.113867	+	0.338297i
$816$	−0.978413	−	0.803184i	−0.0342513	−	0.0281171i
$817$	3.78691	+	36.0301i	0.132487	+	1.26053i
$818$	−24.6150			−0.860644
$819$	−6.84369	−	2.32518i	−0.239138	−	0.0812485i
$820$	−9.94226	−	10.8111i	−0.347199	−	0.377540i
$821$	2.05660	−	0.915657i	0.0717758	−	0.0319566i	−0.370535	−	0.928819i	$-0.620826\pi$
$821$	2.05660	−	0.915657i	0.0717758	−	0.0319566i	0.442311	+	0.896862i	$0.354159\pi$
$822$	−10.2151	+	15.5022i	−0.356293	+	0.540701i
$823$	54.7025	−	11.6274i	1.90681	−	0.405305i	0.906936	−	0.421269i	$-0.138415\pi$
$823$	54.7025	−	11.6274i	1.90681	−	0.405305i	0.999873	+	0.0159639i	$0.00508169\pi$
$824$	1.75582	+	3.04117i	0.0611668	+	0.105944i
$825$	15.5945	−	42.4364i	0.542931	−	1.47745i
$826$	2.44304	−	4.23148i	0.0850044	−	0.147232i
$827$	−9.90533	+	30.4855i	−0.344442	+	1.06008i	0.617440	+	0.786618i	$0.288170\pi$
$827$	−9.90533	+	30.4855i	−0.344442	+	1.06008i	−0.961882	+	0.273466i	$0.911830\pi$
$828$	0.221897	+	0.132096i	0.00771144	+	0.00459065i
$829$	−27.9759	−	20.3257i	−0.971642	−	0.705939i	−0.0158167	−	0.999875i	$-0.505035\pi$
$829$	−27.9759	−	20.3257i	−0.971642	−	0.705939i	−0.955825	+	0.293936i	$0.905035\pi$
$830$	3.40842	−	3.86646i	0.118308	−	0.134207i
$831$	−14.1764	+	36.2061i	−0.491775	+	1.25598i
$832$	15.1303	+	26.2064i	0.524548	+	0.908544i
$833$	−2.72273	−	1.21224i	−0.0943369	−	0.0420015i
$834$	1.31048	−	7.93082i	0.0453784	−	0.274622i
$835$	30.7262	+	13.2947i	1.06333	+	0.460083i
$836$	6.64670	−	20.4564i	0.229881	−	0.707500i
$837$	−17.3712	−	11.7825i	−0.600436	−	0.407264i
$838$	−3.53490	−	10.8793i	−0.122111	−	0.375820i
$839$	20.4800	+	22.7454i	0.707049	+	0.785258i	0.984482	−	0.175487i	$-0.0561501\pi$
$839$	20.4800	+	22.7454i	0.707049	+	0.785258i	−0.277432	+	0.960745i	$0.589483\pi$
$840$	6.27355	−	4.10842i	0.216458	−	0.141754i
$841$	48.1030	−	53.4238i	1.65873	−	1.84220i
$842$	18.0971	+	8.05735i	0.623667	+	0.277674i
$843$	−33.7512	+	21.5991i	−1.16245	+	0.743913i
$844$	2.32347	+	22.1064i	0.0799773	+	0.760933i
$845$	−0.382693	−	3.30615i	−0.0131650	−	0.113735i
$846$	−29.8819	+	16.7241i	−1.02736	+	0.574985i
$847$	8.32326	+	6.04720i	0.285991	+	0.207784i
$848$	−6.11175	−	6.78779i	−0.209878	−	0.233094i
$849$	1.48147	+	32.4092i	0.0508441	+	1.11228i
$850$	−2.39009	−	0.455701i	−0.0819795	−	0.0156304i
$851$	0.0132920	+	0.0230224i	0.000455643	+	0.000789197i
$852$	−6.02370	−	1.65725i	−0.206369	−	0.0567765i
$853$	24.4106	−	10.8683i	0.835804	−	0.372124i	0.0562178	−	0.998419i	$-0.482096\pi$
$853$	24.4106	−	10.8683i	0.835804	−	0.372124i	0.779587	+	0.626294i	$0.215429\pi$
$854$	2.54411	+	1.84840i	0.0870576	+	0.0632511i
$855$	0.0936054	−	32.9443i	0.00320124	−	1.12667i
$856$	10.1541	−	7.37742i	0.347062	−	0.252155i
$857$	−14.7634	+	25.5710i	−0.504309	+	0.873488i	0.495679	+	0.868506i	$0.334919\pi$
$857$	−14.7634	+	25.5710i	−0.504309	+	0.873488i	−0.999988	+	0.00498242i	$0.998414\pi$
$858$	−13.5215	+	34.5333i	−0.461615	+	1.17895i
$859$	3.57379	−	3.96909i	0.121936	−	0.135424i	−0.679086	−	0.734059i	$-0.737623\pi$
$859$	3.57379	−	3.96909i	0.121936	−	0.135424i	0.801022	+	0.598635i	$0.204290\pi$
$860$	−11.2807	−	8.01596i	−0.384668	−	0.273342i
$861$	6.11001	−	6.02892i	0.208229	−	0.205465i
$862$	−7.77182	−	1.65195i	−0.264709	−	0.0562657i
$863$	−9.94721	−	30.6144i	−0.338607	−	1.04212i	−0.964918	−	0.262552i	$-0.915436\pi$
$863$	−9.94721	−	30.6144i	−0.338607	−	1.04212i	0.626311	−	0.779573i	$-0.284564\pi$
$864$	7.71872	+	21.3790i	0.262596	+	0.727327i
$865$	5.40894	+	5.88163i	0.183910	+	0.199981i
$866$	5.55334	+	1.18040i	0.188710	+	0.0401116i
$867$	−28.7632	+	4.35888i	−0.976849	+	0.148035i
$868$	−1.07255	−	1.85772i	−0.0364048	−	0.0630550i
$869$	−6.50879	−	2.89790i	−0.220796	−	0.0983046i
$870$	−2.35446	−	41.8511i	−0.0798236	−	1.41889i
$871$	−12.1274	+	5.39946i	−0.410920	+	0.182954i
$872$	0.245254	+	0.178187i	0.00830533	+	0.00603418i
$873$	4.04156	−	17.8387i	0.136786	−	0.603749i
$874$	−0.542959			−0.0183659
$875$	3.34326	−	6.23726i	0.113023	−	0.210858i
$876$	1.02153	+	22.3473i	0.0345142	+	0.755045i
$877$	−31.6963	+	6.73725i	−1.07031	+	0.227501i	−0.709188	−	0.705019i	$-0.750938\pi$
$877$	−31.6963	+	6.73725i	−1.07031	+	0.227501i	−0.361119	+	0.932520i	$0.617605\pi$
$878$	3.80680	−	36.2192i	0.128473	−	1.22234i
$879$	13.9510	−	21.1716i	0.470554	−	0.714100i
$880$	−9.61697	−	16.2597i	−0.324188	−	0.548113i
$881$	26.9732	−	19.5972i	0.908750	−	0.660246i	−0.0319481	−	0.999490i	$-0.510171\pi$
$881$	26.9732	−	19.5972i	0.908750	−	0.660246i	0.940699	+	0.339244i	$0.110171\pi$
$882$	−12.3074	−	17.4246i	−0.414413	−	0.586717i
$883$	8.26440	−	6.00444i	0.278119	−	0.202066i	−0.439977	−	0.898009i	$-0.645014\pi$
$883$	8.26440	−	6.00444i	0.278119	−	0.202066i	0.718097	+	0.695943i	$0.245014\pi$
$884$	−1.41066	−	0.299845i	−0.0474456	−	0.0100849i
$885$	26.8280	+	7.07826i	0.901812	+	0.237933i
$886$	24.3898	−	5.18422i	0.819392	−	0.174167i
$887$	24.5274	−	27.2404i	0.823548	−	0.914643i	−0.173992	−	0.984747i	$-0.555667\pi$
$887$	24.5274	−	27.2404i	0.823548	−	0.914643i	0.997540	+	0.0701043i	$0.0223332\pi$
$888$	−0.223801	+	1.35440i	−0.00751026	+	0.0454508i
$889$	−2.37638	−	2.63924i	−0.0797014	−	0.0885173i
$890$	−38.4892	+	17.6239i	−1.29016	+	0.590756i
$891$	−24.5711	+	40.0477i	−0.823162	+	1.34165i
$892$	2.67256	−	1.94173i	0.0894838	−	0.0650138i
$893$	−26.0122	+	45.0545i	−0.870466	+	1.50769i
$894$	0.143679	−	0.0217737i	0.00480535	−	0.000728221i
$895$	−39.7112	−	28.2185i	−1.32740	−	0.943240i
$896$	−0.0120668	+	0.114808i	−0.000403124	+	0.00383547i
$897$	−0.675274	−	0.0399146i	−0.0225467	−	0.00133271i
$898$	14.2348	+	15.8093i	0.475021	+	0.527564i
$899$	−40.5747			−1.35324
$900$	9.41626	+	8.34843i	0.313875	+	0.278281i
$901$	2.54903			0.0849206
$902$	−29.4703	−	32.7301i	−0.981254	−	1.08979i
$903$	4.45000	−	6.75320i	0.148087	−	0.224733i
$904$	4.25129	−	40.4483i	0.141396	−	1.34529i
$905$	32.3420	−	24.0217i	1.07509	−	0.798507i
$906$	−20.0280	−	25.0731i	−0.665385	−	0.832998i
$907$	−10.3737	+	17.9678i	−0.344454	+	0.596612i	−0.985254	−	0.171095i	$-0.945269\pi$
$907$	−10.3737	+	17.9678i	−0.344454	+	0.596612i	0.640800	+	0.767708i	$0.278603\pi$
$908$	−16.3956	+	11.9121i	−0.544106	+	0.395316i
$909$	4.69451	+	10.9349i	0.155707	+	0.362688i
$910$	−2.84946	+	5.05753i	−0.0944586	+	0.167655i
$911$	−37.9975	−	42.2005i	−1.25891	−	1.39816i	−0.881545	−	0.472100i	$-0.843496\pi$
$911$	−37.9975	−	42.2005i	−1.25891	−	1.39816i	−0.377367	−	0.926064i	$-0.623171\pi$
$912$	−10.6396	−	8.73410i	−0.352312	−	0.289215i
$913$	−7.47279	+	8.29938i	−0.247313	+	0.274669i
$914$	−1.59125	+	0.338231i	−0.0526340	+	0.0111877i
$915$	−6.33546	+	16.6957i	−0.209444	+	0.551944i
$916$	−12.4267	−	2.64138i	−0.410590	−	0.0872736i
$917$	−2.81276	+	2.04359i	−0.0928854	+	0.0674852i
$918$	2.34202	+	0.953293i	0.0772981	+	0.0314634i
$919$	6.57695	−	4.77844i	0.216954	−	0.157626i	−0.474001	−	0.880524i	$-0.657191\pi$
$919$	6.57695	−	4.77844i	0.216954	−	0.157626i	0.690954	+	0.722898i	$0.257191\pi$
$920$	0.464106	−	0.526475i	0.0153011	−	0.0173574i
$921$	26.3338	+	52.5479i	0.867729	+	1.73151i
$922$	−0.111908	+	1.06474i	−0.00368550	+	0.0350652i
$923$	16.0076	−	3.40253i	0.526898	−	0.111996i
$924$	−4.04437	+	2.58820i	−0.133050	+	0.0851455i
$925$	0.426148	+	1.22336i	0.0140117	+	0.0402238i
$926$	20.6074			0.677200
$927$	−2.52828	−	2.33839i	−0.0830397	−	0.0768027i
$928$	35.5460	+	25.8257i	1.16685	+	0.847769i
$929$	−35.3256	+	15.7280i	−1.15899	+	0.516018i	−0.893927	−	0.448212i	$-0.852061\pi$
$929$	−35.3256	+	15.7280i	−1.15899	+	0.516018i	−0.265068	+	0.964230i	$0.585394\pi$
$930$	−11.8745	+	11.9661i	−0.389381	+	0.392382i
$931$	−29.6079	−	13.1823i	−0.970358	−	0.432031i
$932$	−5.35616	−	9.27714i	−0.175447	−	0.303883i
$933$	−9.85871	−	12.3422i	−0.322760	−	0.404065i
$934$	−10.2443	−	2.17750i	−0.335205	−	0.0712500i
$935$	5.16799	+	1.04180i	0.169011	+	0.0340704i
$936$	−25.6445	−	23.7184i	−0.838215	−	0.775259i
$937$	7.87414	+	24.2341i	0.257237	+	0.791694i	0.993381	+	0.114869i	$0.0366447\pi$
$937$	7.87414	+	24.2341i	0.257237	+	0.791694i	−0.736144	+	0.676825i	$0.763355\pi$
$938$	2.32668	+	0.494551i	0.0759688	+	0.0161477i
$939$	10.3596	+	39.7222i	0.338074	+	1.29629i
$940$	−6.33939	−	18.8342i	−0.206768	−	0.614304i
$941$	7.32250	−	8.13246i	0.238707	−	0.265111i	−0.611874	−	0.790955i	$-0.709584\pi$
$941$	7.32250	−	8.13246i	0.238707	−	0.265111i	0.850581	+	0.525845i	$0.176251\pi$
$942$	21.1023	−	3.19793i	0.687551	−	0.104194i
$943$	0.401671	−	0.695714i	0.0130802	−	0.0226556i
$944$	9.37918	−	6.81437i	0.305266	−	0.221789i
$945$	−4.68248	+	5.67112i	−0.152321	+	0.184481i
$946$	−33.5716	−	24.3912i	−1.09151	−	0.793027i
$947$	−44.9071	+	19.9939i	−1.45928	+	0.649715i	−0.974391	−	0.224859i	$-0.927808\pi$
$947$	−44.9071	+	19.9939i	−1.45928	+	0.649715i	−0.484892	+	0.874574i	$0.661141\pi$
$948$	1.41162	−	1.39289i	0.0458474	−	0.0452389i
$949$	−29.2997	−	50.7486i	−0.951109	−	1.64737i
$950$	−25.9907	−	4.95545i	−0.843249	−	0.160776i
$951$	−42.1332	+	26.9632i	−1.36626	+	0.874341i
$952$	0.585123	+	0.649845i	0.0189639	+	0.0210616i
$953$	13.3275	+	9.68303i	0.431721	+	0.313664i	0.782337	−	0.622856i	$-0.214028\pi$
$953$	13.3275	+	9.68303i	0.431721	+	0.313664i	−0.350615	+	0.936520i	$0.614028\pi$
$954$	15.6776	+	9.33292i	0.507580	+	0.302164i
$955$	−22.3859	−	4.51269i	−0.724390	−	0.146027i
$956$	−1.12472	−	10.7010i	−0.0363760	−	0.346095i
$957$	4.14733	+	90.7283i	0.134064	+	2.93283i
$958$	−15.2169	−	6.77500i	−0.491636	−	0.218890i
$959$	4.21312	−	4.67914i	0.136049	−	0.151097i
$960$	30.3924	−	4.93335i	0.980909	−	0.159223i
$961$	−9.82417	−	10.9108i	−0.316909	−	0.351963i
$962$	−0.328377	−	1.01064i	−0.0105873	−	0.0325843i
$963$	−7.36746	+	9.86067i	−0.237413	+	0.317756i
$964$	−7.16615	+	22.0551i	−0.230806	+	0.710348i
$965$	−14.4716	−	24.4676i	−0.465859	−	0.787639i
$966$	0.0936850	+	0.0769065i	0.00301427	+	0.00247443i
$967$	−36.6655	−	16.3245i	−1.17908	−	0.524962i	−0.278835	−	0.960339i	$-0.589948\pi$
$967$	−36.6655	−	16.3245i	−1.17908	−	0.524962i	−0.900248	+	0.435377i	$0.856615\pi$
$968$	24.8604	+	43.0595i	0.799045	+	1.38399i
$969$	3.79820	−	0.575594i	0.122016	−	0.0184907i
$970$	−13.4821	−	5.83348i	−0.432885	−	0.187302i
$971$	−1.48662	−	1.08010i	−0.0477080	−	0.0346619i	0.563676	−	0.825996i	$-0.309387\pi$
$971$	−1.48662	−	1.08010i	−0.0477080	−	0.0346619i	−0.611384	+	0.791334i	$0.709387\pi$
$972$	−7.88619	−	10.4326i	−0.252950	−	0.334626i
$973$	−0.842449	+	2.59279i	−0.0270077	+	0.0831211i
$974$	−7.73651	+	13.4000i	−0.247894	+	0.429364i
$975$	−31.9601	−	8.07371i	−1.02354	−	0.258566i
$976$	3.73073	+	6.46181i	0.119418	+	0.206838i
$977$	56.7085	−	12.0538i	1.81427	−	0.385634i	0.829358	−	0.558717i	$-0.188706\pi$
$977$	56.7085	−	12.0538i	1.81427	−	0.385634i	0.984907	+	0.173083i	$0.0553729\pi$
$978$	−8.49034	−	0.501854i	−0.271491	−	0.0160475i
$979$	83.7924	−	37.3068i	2.67802	−	1.19233i
$980$	11.2561	−	5.15409i	0.359563	−	0.164641i
$981$	−0.281497	−	0.0956402i	−0.00898751	−	0.00305356i
$982$	−4.04328			−0.129026
$983$	−2.01675	−	19.1881i	−0.0643242	−	0.612004i	−0.978437	−	0.206545i	$-0.933778\pi$
$983$	−2.01675	−	19.1881i	−0.0643242	−	0.612004i	0.914113	−	0.405460i	$-0.132889\pi$
$984$	38.8269	−	14.6074i	1.23776	−	0.465667i
$985$	12.3306	+	8.76206i	0.392887	+	0.279182i
$986$	4.78106	−	1.01625i	0.152260	−	0.0323639i
$987$	10.8699	−	4.08948i	0.345994	−	0.130170i
$988$	−15.3400	−	3.26061i	−0.488030	−	0.103734i
$989$	0.233896	−	0.719859i	0.00743748	−	0.0228902i
$990$	27.9708	+	25.3293i	0.888971	+	0.805018i
$991$	12.9369	+	39.8158i	0.410956	+	1.26479i	0.915819	+	0.401592i	$0.131543\pi$
$991$	12.9369	+	39.8158i	0.410956	+	1.26479i	−0.504863	+	0.863199i	$0.668457\pi$
$992$	−1.84705	−	17.5735i	−0.0586440	−	0.557961i
$993$	−35.5938	+	22.7783i	−1.12953	+	0.722847i
$994$	−2.67885	−	1.19270i	−0.0849680	−	0.0378302i
$995$	15.8663	−	0.166903i	0.502994	−	0.00529119i
$996$	−1.39270	−	2.77908i	−0.0441295	−	0.0880584i
$997$	31.6504	−	14.0917i	1.00238	−	0.446287i	0.161128	−	0.986934i	$-0.448487\pi$
$997$	31.6504	−	14.0917i	1.00238	−	0.446287i	0.841250	+	0.540646i	$0.181820\pi$
$998$	0.827501	−	2.54679i	0.0261941	−	0.0806172i
$999$	−0.183916	−	1.33366i	−0.00581885	−	0.0421951i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.196.19	yes	224
3.2	odd	2		675.2.r.a.46.10		224
9.4	even	3	inner	225.2.q.a.121.10	yes	224
9.5	odd	6		675.2.r.a.496.19		224
25.6	even	5	inner	225.2.q.a.106.10	yes	224
75.56	odd	10		675.2.r.a.181.19		224
225.31	even	15	inner	225.2.q.a.31.19	✓	224
225.131	odd	30		675.2.r.a.631.10		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.19	✓	224	225.31	even	15	inner
225.2.q.a.106.10	yes	224	25.6	even	5	inner
225.2.q.a.121.10	yes	224	9.4	even	3	inner
225.2.q.a.196.19	yes	224	1.1	even	1	trivial
675.2.r.a.46.10		224	3.2	odd	2
675.2.r.a.181.19		224	75.56	odd	10
675.2.r.a.496.19		224	9.5	odd	6
675.2.r.a.631.10		224	225.131	odd	30

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.721003 + 0.800755i) q^{2} +(0.776008 + 1.54849i) q^{3} +(0.0876938 - 0.834351i) q^{4} +(2.23594 - 0.0235208i) q^{5} +(-0.680454 + 1.73786i) q^{6} +(0.316483 - 0.548165i) q^{7} +(2.47480 - 1.79805i) q^{8} +(-1.79562 + 2.40328i) q^{9} +(1.63096 + 1.77348i) q^{10} +(-3.49321 - 3.87960i) q^{11} +(1.36003 - 0.511670i) q^{12} +(-2.54696 + 2.82868i) q^{13} +(0.667131 - 0.141803i) q^{14} +(1.77153 + 3.44408i) q^{15} +(1.58291 + 0.336458i) q^{16} +(-0.365368 + 0.265455i) q^{17} +(-3.21908 + 0.294915i) q^{18} +(-3.97313 + 2.88665i) q^{19} +(0.176454 - 1.86763i) q^{20} +(1.09442 + 0.0646897i) q^{21} +(0.587996 - 5.59441i) q^{22} +(0.100362 - 0.0213327i) q^{23} +(4.70473 + 2.43690i) q^{24} +(4.99889 - 0.105182i) q^{25} -4.10144 q^{26} +(-5.11486 - 0.915539i) q^{27} +(-0.429608 - 0.312129i) q^{28} +(-9.17597 + 4.08540i) q^{29} +(-1.48058 + 3.90175i) q^{30} +(3.69032 + 1.64304i) q^{31} +(-2.18716 - 3.78828i) q^{32} +(3.29675 - 8.41979i) q^{33} +(-0.475995 - 0.101176i) q^{34} +(0.694745 - 1.23311i) q^{35} +(1.84771 + 1.70893i) q^{36} +(0.0800637 + 0.246411i) q^{37} +(-5.17614 - 1.10022i) q^{38} +(-6.35664 - 1.74885i) q^{39} +(5.49123 - 4.07855i) q^{40} +(5.23896 - 5.81846i) q^{41} +(0.737279 + 0.923003i) q^{42} +(3.68846 - 6.38860i) q^{43} +(-3.54328 + 2.57435i) q^{44} +(-3.95839 + 5.41583i) q^{45} +(0.0894437 + 0.0649846i) q^{46} +(9.67748 - 4.30869i) q^{47} +(0.707350 + 2.71221i) q^{48} +(3.29968 + 5.71521i) q^{49} +(3.68844 + 3.92705i) q^{50} +(-0.694582 - 0.359772i) q^{51} +(2.13676 + 2.37311i) q^{52} +(-4.56626 - 3.31758i) q^{53} +(-2.95471 - 4.75585i) q^{54} +(-7.90187 - 8.59241i) q^{55} +(-0.202394 - 1.92565i) q^{56} +(-7.55312 - 3.91228i) q^{57} +(-9.88730 - 4.40211i) q^{58} +(4.79365 - 5.32388i) q^{59} +(3.02892 - 1.17606i) q^{60} +(3.08519 + 3.42646i) q^{61} +(1.34506 + 4.13967i) q^{62} +(0.749107 + 1.74489i) q^{63} +(2.45668 - 7.56088i) q^{64} +(-5.62832 + 6.38468i) q^{65} +(9.11915 - 3.43080i) q^{66} +(3.18608 + 1.41853i) q^{67} +(0.189442 + 0.328124i) q^{68} +(0.110915 + 0.138855i) q^{69} +(1.48833 - 0.332755i) q^{70} +(-3.47832 - 2.52715i) q^{71} +(-0.122605 + 9.17626i) q^{72} +(-4.75735 + 14.6416i) q^{73} +(-0.139588 + 0.241774i) q^{74} +(4.04205 + 7.65910i) q^{75} +(2.06006 + 3.56813i) q^{76} +(-3.23220 + 0.687026i) q^{77} +(-3.18275 - 6.35103i) q^{78} +(1.24677 - 0.555098i) q^{79} +(3.54721 + 0.715070i) q^{80} +(-2.55147 - 8.63076i) q^{81} +8.43646 q^{82} +(-0.223611 - 2.12752i) q^{83} +(0.149948 - 0.907457i) q^{84} +(-0.810698 + 0.602136i) q^{85} +(7.77509 - 1.65265i) q^{86} +(-13.4468 - 11.0386i) q^{87} +(-15.6207 - 3.32029i) q^{88} +(-5.42929 + 16.7096i) q^{89} +(-7.19076 + 0.735128i) q^{90} +(0.744515 + 2.29138i) q^{91} +(-0.00899778 - 0.0856081i) q^{92} +(0.319497 + 6.98942i) q^{93} +(10.4277 + 4.64271i) q^{94} +(-8.81581 + 6.54784i) q^{95} +(4.16885 - 6.32653i) q^{96} +(-5.56983 + 2.47985i) q^{97} +(-2.19740 + 6.76291i) q^{98} +(15.5962 - 1.42884i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20}+ \cdots - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more