LMFDB - Embedded newform 128.2.k.a.5.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,2,Mod(5,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("128.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	128.k (of order $32$, degree $16$, 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:	$1.02208514587$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$15$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			5.9
Character	$\chi$	$=$	128.5
Dual form			128.2.k.a.77.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.432421 + 1.34648i) q^{2} +(2.51607 + 0.763243i) q^{3} +(-1.62602 + 1.16449i) q^{4} +(-1.42404 - 0.140256i) q^{5} +(0.0603114 + 3.71789i) q^{6} +(-0.954234 - 1.42811i) q^{7} +(-2.27110 - 1.68586i) q^{8} +(3.25368 + 2.17404i) q^{9} +O(q^{10})$	\(q+(0.432421 + 1.34648i) q^{2} +(2.51607 + 0.763243i) q^{3} +(-1.62602 + 1.16449i) q^{4} +(-1.42404 - 0.140256i) q^{5} +(0.0603114 + 3.71789i) q^{6} +(-0.954234 - 1.42811i) q^{7} +(-2.27110 - 1.68586i) q^{8} +(3.25368 + 2.17404i) q^{9} +(-0.426934 - 1.97810i) q^{10} +(1.73596 - 3.24775i) q^{11} +(-4.97999 + 1.68890i) q^{12} +(-0.0559220 - 0.567786i) q^{13} +(1.51030 - 1.90240i) q^{14} +(-3.47595 - 1.43979i) q^{15} +(1.28791 - 3.78699i) q^{16} +(3.78617 - 1.56828i) q^{17} +(-1.52034 + 5.32112i) q^{18} +(-4.62888 + 5.64030i) q^{19} +(2.47886 - 1.43023i) q^{20} +(-1.31093 - 4.32155i) q^{21} +(5.12370 + 0.933040i) q^{22} +(1.54300 + 7.75719i) q^{23} +(-4.42753 - 5.97515i) q^{24} +(-2.89570 - 0.575990i) q^{25} +(0.740331 - 0.320821i) q^{26} +(1.52317 + 1.85599i) q^{27} +(3.21464 + 1.21095i) q^{28} +(-0.915268 + 0.489221i) q^{29} +(0.435570 - 5.30290i) q^{30} +(-4.02439 - 4.02439i) q^{31} +(5.65603 + 0.0965697i) q^{32} +(6.84662 - 6.84662i) q^{33} +(3.74888 + 4.41985i) q^{34} +(1.15857 + 2.16753i) q^{35} +(-7.82222 + 0.253850i) q^{36} +(5.22039 - 4.28427i) q^{37} +(-9.59619 - 3.79371i) q^{38} +(0.292655 - 1.47127i) q^{39} +(2.99769 + 2.71927i) q^{40} +(4.10656 - 0.816845i) q^{41} +(5.25201 - 3.63387i) q^{42} +(-10.7378 + 3.25728i) q^{43} +(0.959275 + 7.30243i) q^{44} +(-4.32846 - 3.55228i) q^{45} +(-9.77768 + 5.43199i) q^{46} +(-2.19371 - 5.29608i) q^{47} +(6.13087 - 8.54536i) q^{48} +(1.54984 - 3.74165i) q^{49} +(-0.476601 - 4.14807i) q^{50} +(10.7233 - 1.05615i) q^{51} +(0.752114 + 0.858113i) q^{52} +(1.08552 + 0.580223i) q^{53} +(-1.84041 + 2.85349i) q^{54} +(-2.92760 + 4.38146i) q^{55} +(-0.240439 + 4.85209i) q^{56} +(-15.9515 + 10.6585i) q^{57} +(-1.05451 - 1.02084i) q^{58} +(-0.837165 + 8.49988i) q^{59} +(7.32860 - 1.70660i) q^{60} +(-4.25056 + 14.0122i) q^{61} +(3.67854 - 7.15900i) q^{62} -6.72117i q^{63} +(2.31576 + 7.65750i) q^{64} +0.816395i q^{65} +(12.1795 + 6.25823i) q^{66} +(-1.80820 + 5.96082i) q^{67} +(-4.33015 + 6.95904i) q^{68} +(-2.03831 + 20.6954i) q^{69} +(-2.41755 + 2.49728i) q^{70} +(13.2698 - 8.86660i) q^{71} +(-3.72430 - 10.4227i) q^{72} +(3.40436 - 5.09499i) q^{73} +(8.02609 + 5.17656i) q^{74} +(-6.84617 - 3.65935i) q^{75} +(0.958567 - 14.5616i) q^{76} +(-6.29466 + 0.619970i) q^{77} +(2.10759 - 0.242156i) q^{78} +(-2.83531 + 6.84505i) q^{79} +(-2.36519 + 5.21220i) q^{80} +(-2.07667 - 5.01353i) q^{81} +(2.87563 + 5.17618i) q^{82} +(-4.31830 - 3.54394i) q^{83} +(7.16402 + 5.50038i) q^{84} +(-5.61163 + 1.70227i) q^{85} +(-9.02913 - 13.0498i) q^{86} +(-2.67628 + 0.532344i) q^{87} +(-9.41778 + 4.44937i) q^{88} +(0.305791 - 1.53731i) q^{89} +(2.91136 - 7.36428i) q^{90} +(-0.757499 + 0.621664i) q^{91} +(-11.5422 - 10.8166i) q^{92} +(-7.05408 - 13.1973i) q^{93} +(6.18247 - 5.24393i) q^{94} +(7.38281 - 7.38281i) q^{95} +(14.1573 + 4.55990i) q^{96} +(6.12498 + 6.12498i) q^{97} +(5.70825 + 0.468865i) q^{98} +(12.7090 - 6.79310i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9}+O(q^{10}) $ 240 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9	\( 240 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} - 16 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 16 q^{17} - 16 q^{18} - 16 q^{19} - 16 q^{20} - 16 q^{21} - 16 q^{22} - 16 q^{23} - 16 q^{24} - 16 q^{25} - 16 q^{26} - 16 q^{27} - 16 q^{28} - 16 q^{29} - 16 q^{30} - 16 q^{31} - 16 q^{32} - 16 q^{33} - 16 q^{34} - 16 q^{35} - 16 q^{36} - 16 q^{37} - 16 q^{38} - 16 q^{39} - 16 q^{40} - 16 q^{41} - 16 q^{42} - 16 q^{43} - 16 q^{44} - 16 q^{45} - 16 q^{46} - 16 q^{47} - 16 q^{48} - 16 q^{49} + 32 q^{50} - 16 q^{51} + 80 q^{52} - 16 q^{53} + 112 q^{54} - 16 q^{55} + 96 q^{56} - 16 q^{57} + 128 q^{58} - 16 q^{59} + 176 q^{60} - 16 q^{61} + 80 q^{62} + 176 q^{64} + 176 q^{66} - 16 q^{67} + 80 q^{68} - 16 q^{69} + 176 q^{70} - 16 q^{71} + 128 q^{72} - 16 q^{73} + 96 q^{74} - 16 q^{75} + 112 q^{76} - 16 q^{77} + 80 q^{78} - 16 q^{79} + 32 q^{80} - 16 q^{81} - 16 q^{82} - 16 q^{83} - 16 q^{84} - 16 q^{85} - 16 q^{86} - 16 q^{87} - 16 q^{88} - 16 q^{89} - 16 q^{90} - 16 q^{91} - 16 q^{92} - 16 q^{93} - 16 q^{94} - 16 q^{95} - 16 q^{96} - 16 q^{97} - 16 q^{98} - 16 q^{99}+O(q^{100}) \) 240 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9 - 16 * q^10 - 16 * q^11 - 16 * q^12 - 16 * q^13 - 16 * q^14 - 16 * q^15 - 16 * q^16 - 16 * q^17 - 16 * q^18 - 16 * q^19 - 16 * q^20 - 16 * q^21 - 16 * q^22 - 16 * q^23 - 16 * q^24 - 16 * q^25 - 16 * q^26 - 16 * q^27 - 16 * q^28 - 16 * q^29 - 16 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 16 * q^34 - 16 * q^35 - 16 * q^36 - 16 * q^37 - 16 * q^38 - 16 * q^39 - 16 * q^40 - 16 * q^41 - 16 * q^42 - 16 * q^43 - 16 * q^44 - 16 * q^45 - 16 * q^46 - 16 * q^47 - 16 * q^48 - 16 * q^49 + 32 * q^50 - 16 * q^51 + 80 * q^52 - 16 * q^53 + 112 * q^54 - 16 * q^55 + 96 * q^56 - 16 * q^57 + 128 * q^58 - 16 * q^59 + 176 * q^60 - 16 * q^61 + 80 * q^62 + 176 * q^64 + 176 * q^66 - 16 * q^67 + 80 * q^68 - 16 * q^69 + 176 * q^70 - 16 * q^71 + 128 * q^72 - 16 * q^73 + 96 * q^74 - 16 * q^75 + 112 * q^76 - 16 * q^77 + 80 * q^78 - 16 * q^79 + 32 * q^80 - 16 * q^81 - 16 * q^82 - 16 * q^83 - 16 * q^84 - 16 * q^85 - 16 * q^86 - 16 * q^87 - 16 * q^88 - 16 * q^89 - 16 * q^90 - 16 * q^91 - 16 * q^92 - 16 * q^93 - 16 * q^94 - 16 * q^95 - 16 * q^96 - 16 * q^97 - 16 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{1}{32}\right)$	$1$

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 $

$2$	0.432421	+	1.34648i	0.305768	+	0.952106i
$2$	0.432421	+	1.34648i	0.305768	+	0.952106i
$3$	2.51607	+	0.763243i	1.45266	+	0.440658i	0.915326	−	0.402713i	$-0.131933\pi$
$3$	2.51607	+	0.763243i	1.45266	+	0.440658i	0.537330	+	0.843372i	$0.319433\pi$
$4$	−1.62602	+	1.16449i	−0.813012	+	0.582247i
$5$	−1.42404	−	0.140256i	−0.636852	−	0.0627244i	−0.225562	−	0.974229i	$-0.572422\pi$
$5$	−1.42404	−	0.140256i	−0.636852	−	0.0627244i	−0.411290	+	0.911504i	$0.634922\pi$
$6$	0.0603114	+	3.71789i	0.0246220	+	1.51782i
$7$	−0.954234	−	1.42811i	−0.360667	−	0.539776i	0.606116	−	0.795376i	$-0.292727\pi$
$7$	−0.954234	−	1.42811i	−0.360667	−	0.539776i	−0.966782	+	0.255601i	$0.917727\pi$
$8$	−2.27110	−	1.68586i	−0.802954	−	0.596041i
$9$	3.25368	+	2.17404i	1.08456	+	0.724680i
$10$	−0.426934	−	1.97810i	−0.135009	−	0.625530i
$11$	1.73596	−	3.24775i	0.523411	−	0.979233i	−0.471821	−	0.881695i	$-0.656403\pi$
$11$	1.73596	−	3.24775i	0.523411	−	0.979233i	0.995232	−	0.0975389i	$-0.0310970\pi$
$12$	−4.97999	+	1.68890i	−1.43760	+	0.487544i
$13$	−0.0559220	−	0.567786i	−0.0155100	−	0.157475i	0.984310	−	0.176448i	$-0.0564606\pi$
$13$	−0.0559220	−	0.567786i	−0.0155100	−	0.157475i	−0.999820	+	0.0189721i	$0.993961\pi$
$14$	1.51030	−	1.90240i	0.403644	−	0.508439i
$15$	−3.47595	−	1.43979i	−0.897487	−	0.371751i
$16$	1.28791	−	3.78699i	0.321977	−	0.946747i
$17$	3.78617	−	1.56828i	0.918281	−	0.380364i	0.127060	−	0.991895i	$-0.459446\pi$
$17$	3.78617	−	1.56828i	0.918281	−	0.380364i	0.791221	+	0.611531i	$0.209446\pi$
$18$	−1.52034	+	5.32112i	−0.358349	+	1.25420i
$19$	−4.62888	+	5.64030i	−1.06194	+	1.29397i	−0.107941	+	0.994157i	$0.534426\pi$
$19$	−4.62888	+	5.64030i	−1.06194	+	1.29397i	−0.953997	+	0.299817i	$0.903074\pi$
$20$	2.47886	−	1.43023i	0.554289	−	0.319809i
$21$	−1.31093	−	4.32155i	−0.286068	−	0.943039i
$22$	5.12370	+	0.933040i	1.09238	+	0.198925i
$23$	1.54300	+	7.75719i	0.321738	+	1.61749i	0.715734	+	0.698373i	$0.246093\pi$
$23$	1.54300	+	7.75719i	0.321738	+	1.61749i	−0.393996	+	0.919112i	$0.628907\pi$
$24$	−4.42753	−	5.97515i	−0.903765	−	1.21967i
$25$	−2.89570	−	0.575990i	−0.579139	−	0.115198i
$26$	0.740331	−	0.320821i	0.145191	−	0.0629181i
$27$	1.52317	+	1.85599i	0.293135	+	0.357186i
$28$	3.21464	+	1.21095i	0.607509	+	0.228847i
$29$	−0.915268	+	0.489221i	−0.169961	+	0.0908460i	−0.554184	−	0.832394i	$-0.686969\pi$
$29$	−0.915268	+	0.489221i	−0.169961	+	0.0908460i	0.384223	+	0.923240i	$0.374469\pi$
$30$	0.435570	−	5.30290i	0.0795239	−	0.968172i
$31$	−4.02439	−	4.02439i	−0.722802	−	0.722802i	0.246373	−	0.969175i	$-0.420761\pi$
$31$	−4.02439	−	4.02439i	−0.722802	−	0.722802i	−0.969175	+	0.246373i	$0.920761\pi$
$32$	5.65603	+	0.0965697i	0.999854	+	0.0170713i
$33$	6.84662	−	6.84662i	1.19184	−	1.19184i
$34$	3.74888	+	4.41985i	0.642928	+	0.757998i
$35$	1.15857	+	2.16753i	0.195834	+	0.366380i
$36$	−7.82222	+	0.253850i	−1.30370	+	0.0423084i
$37$	5.22039	−	4.28427i	0.858227	−	0.704329i	−0.0985557	−	0.995132i	$-0.531422\pi$
$37$	5.22039	−	4.28427i	0.858227	−	0.704329i	0.956783	+	0.290803i	$0.0939223\pi$
$38$	−9.59619	−	3.79371i	−1.55671	−	0.615421i
$39$	0.292655	−	1.47127i	0.0468622	−	0.235592i
$40$	2.99769	+	2.71927i	0.473976	+	0.429955i
$41$	4.10656	−	0.816845i	0.641337	−	0.127570i	0.136300	−	0.990668i	$-0.456479\pi$
$41$	4.10656	−	0.816845i	0.641337	−	0.127570i	0.505037	+	0.863098i	$0.331479\pi$
$42$	5.25201	−	3.63387i	0.810403	−	0.560718i
$43$	−10.7378	+	3.25728i	−1.63750	+	0.496731i	−0.969017	−	0.246995i	$-0.920557\pi$
$43$	−10.7378	+	3.25728i	−1.63750	+	0.496731i	−0.668485	+	0.743726i	$0.733057\pi$
$44$	0.959275	+	7.30243i	0.144616	+	1.10088i
$45$	−4.32846	−	3.55228i	−0.645249	−	0.529542i
$46$	−9.77768	+	5.43199i	−1.44164	+	0.800904i
$47$	−2.19371	−	5.29608i	−0.319985	−	0.772513i	−0.999254	−	0.0386232i	$-0.987703\pi$
$47$	−2.19371	−	5.29608i	−0.319985	−	0.772513i	0.679268	−	0.733890i	$-0.262297\pi$
$48$	6.13087	−	8.54536i	0.884914	−	1.23342i
$49$	1.54984	−	3.74165i	0.221406	−	0.534521i
$50$	−0.476601	−	4.14807i	−0.0674015	−	0.586626i
$51$	10.7233	−	1.05615i	1.50156	−	0.147891i
$52$	0.752114	+	0.858113i	0.104299	+	0.118999i
$53$	1.08552	+	0.580223i	0.149108	+	0.0796997i	0.544263	−	0.838915i	$-0.316809\pi$
$53$	1.08552	+	0.580223i	0.149108	+	0.0796997i	−0.395155	+	0.918614i	$0.629309\pi$
$54$	−1.84041	+	2.85349i	−0.250447	+	0.388311i
$55$	−2.92760	+	4.38146i	−0.394757	+	0.590796i
$56$	−0.240439	+	4.85209i	−0.0321300	+	0.648387i
$57$	−15.9515	+	10.6585i	−2.11283	+	1.41175i
$58$	−1.05451	−	1.02084i	−0.138464	−	0.134043i
$59$	−0.837165	+	8.49988i	−0.108990	+	1.10659i	0.772704	+	0.634767i	$0.218904\pi$
$59$	−0.837165	+	8.49988i	−0.108990	+	1.10659i	−0.881693	+	0.471823i	$0.843596\pi$
$60$	7.32860	−	1.70660i	0.946118	−	0.220321i
$61$	−4.25056	+	14.0122i	−0.544229	+	1.79408i	0.0611316	+	0.998130i	$0.480529\pi$
$61$	−4.25056	+	14.0122i	−0.544229	+	1.79408i	−0.605360	+	0.795952i	$0.706971\pi$
$62$	3.67854	−	7.15900i	0.467175	−	0.909194i
$63$		−	6.72117i		−	0.846788i
$64$	2.31576	+	7.65750i	0.289470	+	0.957187i
$65$			0.816395i			0.101261i
$66$	12.1795	+	6.25823i	1.49919	+	0.770334i
$67$	−1.80820	+	5.96082i	−0.220906	+	0.728231i	0.774507	+	0.632565i	$0.217998\pi$
$67$	−1.80820	+	5.96082i	−0.220906	+	0.728231i	−0.995414	+	0.0956655i	$0.969502\pi$
$68$	−4.33015	+	6.95904i	−0.525107	+	0.843907i
$69$	−2.03831	+	20.6954i	−0.245384	+	2.49143i
$70$	−2.41755	+	2.49728i	−0.288953	+	0.298482i
$71$	13.2698	−	8.86660i	1.57484	−	1.05227i	0.608983	−	0.793183i	$-0.291578\pi$
$71$	13.2698	−	8.86660i	1.57484	−	1.05227i	0.965853	−	0.259089i	$-0.0834224\pi$
$72$	−3.72430	−	10.4227i	−0.438913	−	1.22833i
$73$	3.40436	−	5.09499i	0.398451	−	0.596324i	−0.576945	−	0.816783i	$-0.695756\pi$
$73$	3.40436	−	5.09499i	0.398451	−	0.596324i	0.975396	+	0.220459i	$0.0707555\pi$
$74$	8.02609	+	5.17656i	0.933014	+	0.601762i
$75$	−6.84617	−	3.65935i	−0.790528	−	0.422546i
$76$	0.958567	−	14.5616i	0.109955	−	1.67033i
$77$	−6.29466	+	0.619970i	−0.717343	+	0.0706522i
$78$	2.10759	−	0.242156i	0.238638	−	0.0274188i
$79$	−2.83531	+	6.84505i	−0.318997	+	0.770128i	0.680310	+	0.732924i	$0.261845\pi$
$79$	−2.83531	+	6.84505i	−0.318997	+	0.770128i	−0.999308	+	0.0372037i	$0.988155\pi$
$80$	−2.36519	+	5.21220i	−0.264436	+	0.582742i
$81$	−2.07667	−	5.01353i	−0.230741	−	0.557059i
$82$	2.87563	+	5.17618i	0.317560	+	0.571614i
$83$	−4.31830	−	3.54394i	−0.473995	−	0.388998i	0.366844	−	0.930282i	$-0.380438\pi$
$83$	−4.31830	−	3.54394i	−0.473995	−	0.388998i	−0.840840	+	0.541284i	$0.817938\pi$
$84$	7.16402	+	5.50038i	0.781658	+	0.600140i
$85$	−5.61163	+	1.70227i	−0.608667	+	0.184637i
$86$	−9.02913	−	13.0498i	−0.973636	−	1.40719i
$87$	−2.67628	+	0.532344i	−0.286927	+	0.0570733i
$88$	−9.41778	+	4.44937i	−1.00394	+	0.474305i
$89$	0.305791	−	1.53731i	0.0324138	−	0.162955i	−0.961188	−	0.275894i	$-0.911026\pi$
$89$	0.305791	−	1.53731i	0.0324138	−	0.162955i	0.993602	+	0.112938i	$0.0360263\pi$
$90$	2.91136	−	7.36428i	0.306884	−	0.776263i
$91$	−0.757499	+	0.621664i	−0.0794075	+	0.0651681i
$92$	−11.5422	−	10.8166i	−1.20335	−	1.12770i
$93$	−7.05408	−	13.1973i	−0.731474	−	1.36849i
$94$	6.18247	−	5.24393i	0.637673	−	0.540870i
$95$	7.38281	−	7.38281i	0.757461	−	0.757461i
$96$	14.1573	+	4.55990i	1.44492	+	0.465393i
$97$	6.12498	+	6.12498i	0.621898	+	0.621898i	0.946016	−	0.324119i	$-0.105068\pi$
$97$	6.12498	+	6.12498i	0.621898	+	0.621898i	−0.324119	+	0.946016i	$0.605068\pi$
$98$	5.70825	+	0.468865i	0.576620	+	0.0473625i
$99$	12.7090	−	6.79310i	1.27730	−	0.682732i
$100$	5.37921	−	2.43545i	0.537921	−	0.243545i
$101$	4.49222	+	5.47378i	0.446993	+	0.544662i	0.946947	−	0.321390i	$-0.104150\pi$
$101$	4.49222	+	5.47378i	0.446993	+	0.544662i	−0.499955	+	0.866052i	$0.666650\pi$
$102$	6.05905	+	13.9820i	0.599936	+	1.38442i
$103$	3.24356	+	0.645185i	0.319598	+	0.0635720i	0.352282	−	0.935894i	$-0.385406\pi$
$103$	3.24356	+	0.645185i	0.319598	+	0.0635720i	−0.0326846	+	0.999466i	$0.510406\pi$
$104$	−0.830203	+	1.38377i	−0.0814081	+	0.135690i
$105$	1.26069	+	6.33794i	0.123031	+	0.618520i
$106$	−0.311857	+	1.71253i	−0.0302903	+	0.166336i
$107$	0.326101	+	1.07501i	0.0315253	+	0.103925i	0.971291	−	0.237894i	$-0.0764570\pi$
$107$	0.326101	+	1.07501i	0.0315253	+	0.103925i	−0.939766	+	0.341819i	$0.888957\pi$
$108$	−4.63801	−	1.24416i	−0.446292	−	0.119719i
$109$	3.09131	−	3.76677i	0.296094	−	0.360791i	−0.603620	−	0.797272i	$-0.706275\pi$
$109$	3.09131	−	3.76677i	0.296094	−	0.360791i	0.899713	+	0.436481i	$0.143775\pi$
$110$	−7.16551	−	2.04732i	−0.683204	−	0.195204i
$111$	16.4048	−	6.79510i	1.55708	−	0.644963i
$112$	−6.63721	+	1.77440i	−0.627158	+	0.167665i
$113$	5.81623	+	2.40916i	0.547145	+	0.226635i	0.639094	−	0.769129i	$-0.279310\pi$
$113$	5.81623	+	2.40916i	0.547145	+	0.226635i	−0.0919485	+	0.995764i	$0.529310\pi$
$114$	−21.2492	−	16.8695i	−1.99017	−	1.57997i
$115$	−1.10931	−	11.2630i	−0.103443	−	1.05028i
$116$	0.918553	−	1.86131i	0.0852855	−	0.172818i
$117$	1.05244	−	1.96897i	0.0972979	−	0.182031i
$118$	−11.8069	+	2.54830i	−1.08692	+	0.234590i
$119$	−5.85258	−	3.91057i	−0.536505	−	0.358481i
$120$	5.46694	+	9.12986i	0.499061	+	0.833438i
$121$	−1.42306	−	2.12975i	−0.129369	−	0.193614i
$122$	−20.7052	+	0.335879i	−1.87456	+	0.0304091i
$123$	10.9559	+	1.07906i	0.987857	+	0.0972954i
$124$	11.2301	+	1.85738i	1.00850	+	0.166798i
$125$	10.8894	+	3.30327i	0.973978	+	0.295453i
$126$	9.04993	−	2.90638i	0.806232	−	0.258920i
$127$	−2.21742			−0.196765			−0.0983823	−	0.995149i	$-0.531367\pi$
$127$	−2.21742			−0.196765			−0.0983823	+	0.995149i	$0.531367\pi$
$128$	−9.30930	+	6.42939i	−0.822833	+	0.568283i
$129$	−29.5032			−2.59762
$130$	−1.09926	+	0.353027i	−0.0964116	+	0.0309625i
$131$	1.87048	+	0.567404i	0.163425	+	0.0495743i	0.370937	−	0.928658i	$-0.379037\pi$
$131$	1.87048	+	0.567404i	0.163425	+	0.0495743i	−0.207512	+	0.978232i	$0.566537\pi$
$132$	−3.15992	+	19.1056i	−0.275036	+	1.66293i
$133$	12.4720	+	1.22839i	1.08146	+	0.106515i
$134$	−8.80804	+	0.142884i	−0.760899	+	0.0123433i
$135$	−1.90875	−	2.85665i	−0.164279	−	0.245861i
$136$	−11.2427	−	2.82123i	−0.964050	−	0.241918i
$137$	−5.25000	−	3.50794i	−0.448538	−	0.299703i	0.310710	−	0.950505i	$-0.399433\pi$
$137$	−5.25000	−	3.50794i	−0.448538	−	0.299703i	−0.759248	+	0.650801i	$0.774433\pi$
$138$	−28.7473	+	6.20455i	−2.44713	+	0.528167i
$139$	2.87905	−	5.38632i	0.244198	−	0.456862i	−0.729725	−	0.683740i	$-0.760352\pi$
$139$	2.87905	−	5.38632i	0.244198	−	0.456862i	0.973923	+	0.226879i	$0.0728520\pi$
$140$	−4.40794	−	2.17531i	−0.372539	−	0.183847i
$141$	−1.47734	−	14.9997i	−0.124414	−	1.26320i
$142$	17.6769	+	14.0334i	1.48341	+	1.17766i
$143$	−1.94110	−	0.804032i	−0.162323	−	0.0672365i
$144$	12.4235	−	9.52170i	1.03529	−	0.793475i
$145$	1.37200	−	0.568300i	0.113938	−	0.0471947i
$146$	8.33243	+	2.38073i	0.689597	+	0.197031i
$147$	6.75530	−	8.23136i	0.557168	−	0.678911i
$148$	−3.49948	+	13.0454i	−0.287656	+	1.07233i
$149$	−2.07014	−	6.82434i	−0.169593	−	0.559072i	−0.999998	−	0.00191236i	$-0.999391\pi$
$149$	−2.07014	−	6.82434i	−0.169593	−	0.559072i	0.830406	−	0.557159i	$-0.188109\pi$
$150$	1.96682	−	10.8006i	0.160590	−	0.881867i
$151$	−0.724979	−	3.64472i	−0.0589980	−	0.296603i	0.940009	−	0.341149i	$-0.110816\pi$
$151$	−0.724979	−	3.64472i	−0.0589980	−	0.296603i	−0.999007	+	0.0445458i	$0.985816\pi$
$152$	20.0214	−	5.00604i	1.62395	−	0.406043i
$153$	15.7285	+	3.12859i	1.27157	+	0.252932i
$154$	−3.55672	−	8.20756i	−0.286609	−	0.661384i
$155$	5.16647	+	6.29536i	0.414981	+	0.505655i
$156$	1.23743	+	2.73312i	0.0990734	+	0.218825i
$157$	1.16006	−	0.620065i	0.0925829	−	0.0494866i	−0.424455	−	0.905449i	$-0.639534\pi$
$157$	1.16006	−	0.620065i	0.0925829	−	0.0494866i	0.517038	+	0.855962i	$0.327034\pi$
$158$	−10.4428	−	0.857751i	−0.830783	−	0.0682390i
$159$	2.28840	+	2.28840i	0.181482	+	0.181482i
$160$	−8.04089	−	0.930812i	−0.635688	−	0.0735871i
$161$	9.60575	−	9.60575i	0.757039	−	0.757039i
$162$	5.85263	−	4.96416i	0.459826	−	0.390021i
$163$	−0.552697	−	1.03402i	−0.0432906	−	0.0809909i	0.859346	−	0.511395i	$-0.170871\pi$
$163$	−0.552697	−	1.03402i	−0.0432906	−	0.0809909i	−0.902636	+	0.430404i	$0.858371\pi$
$164$	−5.72615	+	6.11027i	−0.447137	+	0.477132i
$165$	−10.7102	+	8.78961i	−0.833786	+	0.684270i
$166$	2.90452	−	7.34699i	0.225435	−	0.570237i
$167$	−4.20793	+	21.1547i	−0.325619	+	1.63700i	0.377560	+	0.925985i	$0.376763\pi$
$167$	−4.20793	+	21.1547i	−0.325619	+	1.63700i	−0.703179	+	0.711013i	$0.748237\pi$
$168$	−4.30828	+	12.0247i	−0.332391	+	0.927725i
$169$	12.4310	−	2.47267i	0.956227	−	0.190205i
$170$	−4.71866	−	6.81986i	−0.361905	−	0.523060i
$171$	−27.3232	+	8.28839i	−2.08945	+	0.633829i
$172$	13.6669	−	17.8005i	1.04209	−	1.35728i
$173$	−13.5915	−	11.1542i	−1.03334	−	0.848042i	−0.0448009	−	0.998996i	$-0.514265\pi$
$173$	−13.5915	−	11.1542i	−1.03334	−	0.848042i	−0.988541	+	0.150954i	$0.951765\pi$
$174$	−1.87407	−	3.37336i	−0.142073	−	0.255734i
$175$	1.94060	+	4.68501i	0.146695	+	0.354154i
$176$	−10.0634	−	10.7569i	−0.758560	−	0.810829i
$177$	−8.59384	+	20.7474i	−0.645953	+	1.55947i
$178$	2.20220	−	0.253026i	0.165062	−	0.0189651i
$179$	11.6039	−	1.14289i	0.867319	−	0.0854235i	0.345438	−	0.938442i	$-0.387730\pi$
$179$	11.6039	−	1.14289i	0.867319	−	0.0854235i	0.521881	+	0.853018i	$0.325230\pi$
$180$	11.1748	+	0.735620i	0.832920	+	0.0548299i
$181$	16.3226	+	8.72463i	1.21325	+	0.648497i	0.948793	−	0.315900i	$-0.102306\pi$
$181$	16.3226	+	8.72463i	1.21325	+	0.648497i	0.264460	+	0.964397i	$0.414806\pi$
$182$	−1.16462	−	0.751138i	−0.0863272	−	0.0556781i
$183$	−21.3895	+	32.0116i	−1.58115	+	2.36636i
$184$	9.57323	−	20.2186i	0.705748	−	1.49054i
$185$	−8.03496	+	5.36879i	−0.590742	+	0.394721i
$186$	14.7195	−	15.2050i	1.07929	−	1.11488i
$187$	1.47924	−	15.0190i	0.108173	−	1.09830i
$188$	9.73428	+	6.05700i	0.709945	+	0.441752i
$189$	1.19710	−	3.94631i	0.0870763	−	0.287052i
$190$	13.1333	+	6.74834i	0.952790	+	0.489576i
$191$		−	4.44984i		−	0.321979i	−0.986956	−	0.160990i	$-0.948531\pi$
$191$		−	4.44984i		−	0.321979i	0.986956	−	0.160990i	$-0.0514685\pi$
$192$	−0.0179120	+	21.0343i	−0.00129269	+	1.51802i
$193$		−	16.0454i		−	1.15497i	−0.816400	−	0.577487i	$-0.804033\pi$
$193$		−	16.0454i		−	1.15497i	0.816400	−	0.577487i	$-0.195967\pi$
$194$	−5.59860	+	10.8957i	−0.401956	+	0.782269i
$195$	−0.623108	+	2.05411i	−0.0446217	+	0.147098i
$196$	1.83705	+	7.88879i	0.131218	+	0.563485i
$197$	0.197232	−	2.00253i	0.0140522	−	0.142674i	−0.985599	−	0.169102i	$-0.945913\pi$
$197$	0.197232	−	2.00253i	0.0140522	−	0.142674i	0.999651	+	0.0264279i	$0.00841323\pi$
$198$	14.6424	+	14.1750i	1.04059	+	1.00737i
$199$	5.05804	−	3.37968i	0.358555	−	0.239579i	−0.363225	−	0.931702i	$-0.618324\pi$
$199$	5.05804	−	3.37968i	0.358555	−	0.239579i	0.721780	+	0.692123i	$0.243324\pi$
$200$	5.60537	+	6.18987i	0.396360	+	0.437690i
$201$	−9.09911	+	13.6178i	−0.641802	+	0.960524i
$202$	−5.42782	+	8.41567i	−0.381900	+	0.592124i
$203$	1.57204	+	0.840274i	0.110336	+	0.0589757i
$204$	−16.2064	+	14.2045i	−1.13468	+	0.994514i
$205$	−5.96249	+	0.587254i	−0.416438	+	0.0410156i
$206$	0.533856	+	4.64639i	0.0371955	+	0.323729i
$207$	−11.8440	+	28.5940i	−0.823216	+	1.98742i
$208$	−2.22222	−	0.519480i	−0.154083	−	0.0360194i
$209$	10.2828	+	24.8248i	0.711273	+	1.71717i
$210$	−7.98877	+	4.43816i	−0.551277	+	0.306262i
$211$	−7.96325	−	6.53527i	−0.548213	−	0.449906i	0.319064	−	0.947733i	$-0.396632\pi$
$211$	−7.96325	−	6.53527i	−0.548213	−	0.449906i	−0.867277	+	0.497827i	$0.834132\pi$
$212$	−2.44075	+	0.320626i	−0.167631	+	0.0220207i
$213$	40.1552	−	12.1809i	2.75139	−	0.834625i
$214$	−1.30647	+	0.903945i	−0.0893083	+	0.0617924i
$215$	15.7480	−	3.13247i	1.07400	−	0.213632i
$216$	−0.330332	−	6.78299i	−0.0224762	−	0.461524i
$217$	−1.90707	+	9.58750i	−0.129460	+	0.650842i
$218$	6.40863	+	2.53356i	0.434047	+	0.171594i
$219$	12.4544	−	10.2210i	0.841587	−	0.690673i
$220$	−0.341839	−	10.5335i	−0.0230468	−	0.710170i
$221$	−1.10218	−	2.06203i	−0.0741406	−	0.138707i
$222$	16.2433	+	19.1505i	1.09018	+	1.28529i
$223$	−9.54241	+	9.54241i	−0.639007	+	0.639007i	−0.950311	−	0.311304i	$-0.899234\pi$
$223$	−9.54241	+	9.54241i	−0.639007	+	0.639007i	0.311304	+	0.950311i	$0.399234\pi$
$224$	−5.25926	−	8.16960i	−0.351399	−	0.545854i
$225$	−8.16945	−	8.16945i	−0.544630	−	0.544630i
$226$	−0.728831	+	8.87322i	−0.0484811	+	0.590238i
$227$	−7.39709	+	3.95383i	−0.490962	+	0.262425i	−0.698248	−	0.715856i	$-0.746037\pi$
$227$	−7.39709	+	3.95383i	−0.490962	+	0.262425i	0.207286	+	0.978280i	$0.433537\pi$
$228$	13.5258	−	35.9064i	0.895771	−	2.37796i
$229$	−16.4298	−	20.0198i	−1.08571	−	1.32295i	−0.942856	−	0.333202i	$-0.891871\pi$
$229$	−16.4298	−	20.0198i	−1.08571	−	1.32295i	−0.142857	−	0.989743i	$-0.545629\pi$
$230$	14.6857	−	6.36402i	0.968348	−	0.419631i
$231$	−16.3110	−	3.24447i	−1.07319	−	0.213470i
$232$	2.90342	+	0.431945i	0.190619	+	0.0283586i
$233$	−1.52793	−	7.68144i	−0.100098	−	0.503228i	−0.998010	−	0.0630527i	$-0.979916\pi$
$233$	−1.52793	−	7.68144i	−0.100098	−	0.503228i	0.897912	−	0.440175i	$-0.145084\pi$
$234$	3.10628	+	0.565662i	0.203064	+	0.0369785i
$235$	2.38113	+	7.84954i	0.155328	+	0.512047i
$236$	−8.53681	−	14.7959i	−0.555699	−	0.963130i
$237$	−12.3583	+	15.0586i	−0.802757	+	0.978162i
$238$	2.73473	−	9.57140i	0.177266	−	0.620422i
$239$	25.5288	−	10.5744i	1.65132	−	0.684000i	0.653955	−	0.756533i	$-0.273109\pi$
$239$	25.5288	−	10.5744i	1.65132	−	0.684000i	0.997366	+	0.0725339i	$0.0231086\pi$
$240$	−9.92916	+	11.3091i	−0.640925	+	0.729998i
$241$	−19.7411	−	8.17702i	−1.27163	−	0.526728i	−0.358174	−	0.933655i	$-0.616600\pi$
$241$	−19.7411	−	8.17702i	−1.27163	−	0.526728i	−0.913461	+	0.406927i	$0.866600\pi$
$242$	2.25231	−	2.83707i	0.144784	−	0.182374i
$243$	−2.10454	−	21.3677i	−0.135006	−	1.37074i
$244$	−9.40563	−	27.7340i	−0.602134	−	1.77549i
$245$	−2.73183	+	5.11090i	−0.174530	+	0.326523i
$246$	3.28461	+	15.2185i	0.209419	+	0.970294i
$247$	3.46134	+	2.31279i	0.220240	+	0.147160i
$248$	2.35522	+	15.9243i	0.149557	+	1.01120i
$249$	−8.16029	−	12.2127i	−0.517137	−	0.773950i
$250$	0.261024	+	16.0908i	0.0165086	+	1.01767i
$251$	−23.9016	−	2.35411i	−1.50866	−	0.148590i	−0.690394	−	0.723433i	$-0.742563\pi$
$251$	−23.9016	−	2.35411i	−1.50866	−	0.148590i	−0.818263	+	0.574843i	$0.805063\pi$
$252$	7.82676	+	10.9288i	0.493040	+	0.688449i
$253$	27.8720	+	8.45488i	1.75230	+	0.531554i
$254$	−0.958861	−	2.98572i	−0.0601643	−	0.187341i
$255$	−15.4185			−0.965546
$256$	−12.6826	−	9.75459i	−0.792662	−	0.609662i
$257$	3.96749			0.247485			0.123742	−	0.992314i	$-0.460510\pi$
$257$	3.96749			0.247485			0.123742	+	0.992314i	$0.460510\pi$
$258$	−12.7578	−	39.7256i	−0.794267	−	2.47321i
$259$	−11.0999	−	3.36712i	−0.689714	−	0.209222i
$260$	−0.950687	−	1.32748i	−0.0589591	−	0.0823267i
$261$	−4.04158	−	0.398060i	−0.250167	−	0.0246393i
$262$	0.0448363	+	2.76393i	0.00277000	+	0.170756i
$263$	8.48740	+	12.7023i	0.523356	+	0.783257i	0.995141	−	0.0984563i	$-0.0313905\pi$
$263$	8.48740	+	12.7023i	0.523356	+	0.783257i	−0.471786	+	0.881713i	$0.656390\pi$
$264$	−27.0918	+	4.00690i	−1.66738	+	0.246608i
$265$	−1.46445	−	0.978514i	−0.0899604	−	0.0601096i
$266$	3.73917	+	17.3245i	0.229263	+	1.06223i
$267$	1.94274	−	3.63461i	0.118894	−	0.222434i
$268$	−4.00117	−	11.7981i	−0.244411	−	0.720682i
$269$	0.622166	+	6.31696i	0.0379341	+	0.385152i	0.995342	+	0.0964113i	$0.0307364\pi$
$269$	0.622166	+	6.31696i	0.0379341	+	0.385152i	−0.957407	+	0.288740i	$0.906764\pi$
$270$	3.02104	−	3.80537i	0.183854	−	0.231588i
$271$	1.76595	+	0.731482i	0.107274	+	0.0444344i	0.435675	−	0.900104i	$-0.356510\pi$
$271$	1.76595	+	0.731482i	0.107274	+	0.0444344i	−0.328401	+	0.944538i	$0.606510\pi$
$272$	−1.06283	−	16.3580i	−0.0644437	−	0.991849i
$273$	−2.38041	+	0.985996i	−0.144069	+	0.0596752i
$274$	2.45316	−	8.58594i	0.148201	−	0.518695i
$275$	−6.89748	+	8.40461i	−0.415934	+	0.506817i
$276$	−20.7853	−	36.0247i	−1.25113	−	2.16843i
$277$	−6.27232	−	20.6771i	−0.376867	−	1.24236i	−0.916354	−	0.400370i	$-0.868882\pi$
$277$	−6.27232	−	20.6771i	−0.376867	−	1.24236i	0.539487	−	0.841994i	$-0.318618\pi$
$278$	8.49754	+	1.54743i	0.509649	+	0.0928085i
$279$	−4.34490	−	21.8433i	−0.260122	−	1.30772i
$280$	1.02293	−	6.87586i	0.0611317	−	0.410911i
$281$	−4.60748	−	0.916484i	−0.274859	−	0.0546729i	0.0557361	−	0.998446i	$-0.482249\pi$
$281$	−4.60748	−	0.916484i	−0.274859	−	0.0546729i	−0.330595	+	0.943773i	$0.607249\pi$
$282$	19.5579	−	8.47538i	1.16466	−	0.504702i
$283$	−12.3729	−	15.0764i	−0.735491	−	0.896198i	0.262137	−	0.965031i	$-0.415573\pi$
$283$	−12.3729	−	15.0764i	−0.735491	−	0.896198i	−0.997628	+	0.0688324i	$0.978073\pi$
$284$	−11.2519	+	29.8699i	−0.667679	+	1.77245i
$285$	24.2106	−	12.9408i	1.43411	−	0.766548i
$286$	0.243239	−	2.96134i	0.0143830	−	0.175108i
$287$	−5.08517	−	5.08517i	−0.300168	−	0.300168i
$288$	18.1930	+	12.6106i	1.07203	+	0.743090i
$289$	−0.145244	+	0.145244i	−0.00854375	+	0.00854375i
$290$	1.35849	+	1.60162i	0.0797730	+	0.0940506i
$291$	10.7361	+	20.0858i	0.629359	+	1.17745i
$292$	0.397508	+	12.2489i	0.0232624	+	0.716815i
$293$	−13.9550	+	11.4526i	−0.815261	+	0.669067i	−0.946650	−	0.322264i	$-0.895556\pi$
$293$	−13.9550	+	11.4526i	−0.815261	+	0.669067i	0.131389	+	0.991331i	$0.458056\pi$
$294$	14.0045	+	5.53648i	0.816760	+	0.322894i
$295$	2.38432	−	11.9868i	0.138820	−	0.697897i
$296$	−19.0787	+	0.929133i	−1.10893	+	0.0540048i
$297$	8.67196	−	1.72496i	0.503198	−	0.100092i
$298$	8.29367	−	5.73839i	0.480440	−	0.332416i
$299$	4.31813	−	1.30989i	0.249724	−	0.0757530i
$300$	15.3933	−	2.02213i	0.888734	−	0.116747i
$301$	14.8982	+	12.2266i	0.858715	+	0.704729i
$302$	4.59405	−	2.55222i	0.264358	−	0.146864i
$303$	7.12493	+	17.2011i	0.409317	+	0.988178i
$304$	15.3982	+	24.7937i	0.883148	+	1.42202i
$305$	8.01829	−	19.3579i	0.459126	−	1.10843i
$306$	2.58874	+	22.5310i	0.147989	+	1.28801i
$307$	−12.0480	+	1.18662i	−0.687614	+	0.0677240i	−0.435789	−	0.900049i	$-0.643531\pi$
$307$	−12.0480	+	1.18662i	−0.687614	+	0.0677240i	−0.251825	+	0.967773i	$0.581031\pi$
$308$	9.51332	−	8.33818i	0.542072	−	0.475112i
$309$	7.66862	+	4.09896i	0.436252	+	0.233182i
$310$	−6.24249	+	9.67880i	−0.354550	+	0.549719i
$311$	12.5241	−	18.7436i	0.710176	−	1.06285i	−0.284386	−	0.958710i	$-0.591790\pi$
$311$	12.5241	−	18.7436i	0.710176	−	1.06285i	0.994562	−	0.104144i	$-0.0332102\pi$
$312$	−3.14501	+	2.84803i	−0.178051	+	0.161238i
$313$	−5.30536	+	3.54493i	−0.299877	+	0.200371i	−0.696401	−	0.717653i	$-0.745216\pi$
$313$	−5.30536	+	3.54493i	−0.299877	+	0.200371i	0.396524	+	0.918024i	$0.370216\pi$
$314$	1.33654	+	1.29387i	0.0754254	+	0.0730174i
$315$	−0.942685	+	9.57124i	−0.0531143	+	0.539278i
$316$	−3.36073	−	14.4319i	−0.189056	−	0.811858i
$317$	−4.28081	+	14.1119i	−0.240434	+	0.792605i	0.750805	+	0.660524i	$0.229666\pi$
$317$	−4.28081	+	14.1119i	−0.240434	+	0.792605i	−0.991239	+	0.132081i	$0.957834\pi$
$318$	−2.09174	+	4.07084i	−0.117299	+	0.228281i
$319$			3.82183i			0.213981i
$320$	−2.22373	−	11.2294i	−0.124310	−	0.627743i
$321$			2.95370i			0.164859i
$322$	17.0877	+	8.78024i	0.952260	+	0.489304i
$323$	−8.68013	+	28.6145i	−0.482975	+	1.59216i
$324$	9.21495	+	5.73385i	0.511942	+	0.318547i
$325$	−0.165106	+	1.67635i	−0.00915842	+	0.0929870i
$326$	1.15330	−	1.19133i	0.0638751	−	0.0659816i
$327$	10.6529	−	7.11805i	0.589108	−	0.393629i
$328$	−10.7035	−	5.06795i	−0.591001	−	0.279831i
$329$	−5.47009	+	8.18657i	−0.301576	+	0.451340i
$330$	−16.4664	−	10.6202i	−0.906443	−	0.584625i
$331$	18.6549	+	9.97125i	1.02537	+	0.548070i	0.896245	−	0.443559i	$-0.146284\pi$
$331$	18.6549	+	9.97125i	1.02537	+	0.548070i	0.129121	+	0.991629i	$0.458784\pi$
$332$	11.1486	+	0.733894i	0.611857	+	0.0402776i
$333$	26.2997	−	2.59029i	1.44121	−	0.141947i
$334$	−30.3040	+	3.48183i	−1.65816	+	0.190517i
$335$	3.41099	−	8.23486i	0.186362	−	0.449919i
$336$	−18.0540	−	0.601288i	−0.984928	−	0.0328029i
$337$	6.62848	+	16.0026i	0.361076	+	0.871716i	0.995143	+	0.0984373i	$0.0313844\pi$
$337$	6.62848	+	16.0026i	0.361076	+	0.871716i	−0.634067	+	0.773278i	$0.718616\pi$
$338$	8.70481	+	15.6688i	0.473479	+	0.852271i
$339$	12.7953	+	10.5008i	0.694945	+	0.570327i
$340$	7.14237	−	9.30264i	0.387349	−	0.504507i
$341$	−20.0564	+	6.08404i	−1.08612	+	0.329469i
$342$	−22.9753	−	33.2060i	−1.24236	−	1.79558i
$343$	−18.6144	+	3.70264i	−1.00508	+	0.199924i
$344$	29.8779	+	10.7048i	1.61091	+	0.577167i
$345$	5.80530	−	29.1852i	0.312547	−	1.57128i
$346$	9.14174	−	23.1240i	0.491463	−	1.24315i
$347$	4.94779	−	4.06054i	0.265611	−	0.217981i	−0.492155	−	0.870508i	$-0.663791\pi$
$347$	4.94779	−	4.06054i	0.265611	−	0.217981i	0.757766	+	0.652526i	$0.226291\pi$
$348$	3.73178	−	3.98211i	0.200044	−	0.213464i
$349$	1.07231	+	2.00616i	0.0573997	+	0.107387i	0.908985	−	0.416829i	$-0.136858\pi$
$349$	1.07231	+	2.00616i	0.0573997	+	0.107387i	−0.851585	+	0.524216i	$0.824358\pi$
$350$	−5.46913	+	4.63887i	−0.292337	+	0.247958i
$351$	0.968627	−	0.968627i	0.0517015	−	0.0517015i
$352$	10.1323	−	18.2017i	0.540052	−	0.970156i
$353$	−10.1367	−	10.1367i	−0.539520	−	0.539520i	0.383868	−	0.923388i	$-0.374592\pi$
$353$	−10.1367	−	10.1367i	−0.539520	−	0.539520i	−0.923388	+	0.383868i	$0.874592\pi$
$354$	−31.6521	−	2.59985i	−1.68229	−	0.138180i
$355$	−20.1404	+	10.7653i	−1.06894	+	0.571361i
$356$	1.29297	+	2.85580i	0.0685273	+	0.151357i
$357$	−11.7408	−	14.3062i	−0.621389	−	0.757165i
$358$	6.55667	+	15.1303i	0.346531	+	0.799660i
$359$	−2.83075	−	0.563071i	−0.149401	−	0.0297177i	0.119823	−	0.992795i	$-0.461767\pi$
$359$	−2.83075	−	0.563071i	−0.149401	−	0.0297177i	−0.269224	+	0.963078i	$0.586767\pi$
$360$	3.84172	+	15.3647i	0.202476	+	0.809793i
$361$	−6.67980	−	33.5816i	−0.351569	−	1.76745i
$362$	−4.68930	+	25.7508i	−0.246464	+	1.35343i
$363$	−1.95500	−	6.44476i	−0.102611	−	0.338262i
$364$	0.507789	−	1.89294i	0.0266154	−	0.0992172i
$365$	−5.56257	+	6.77801i	−0.291158	+	0.354777i
$366$	−52.3523	−	14.9580i	−2.73650	−	0.781868i
$367$	−19.5260	+	8.08793i	−1.01925	+	0.422186i	−0.828820	−	0.559515i	$-0.810987\pi$
$367$	−19.5260	+	8.08793i	−1.01925	+	0.422186i	−0.190428	+	0.981701i	$0.560987\pi$
$368$	31.3636	+	4.14722i	1.63494	+	0.216189i
$369$	15.1373	+	6.27007i	0.788016	+	0.326407i
$370$	−10.7035	−	8.49735i	−0.556447	−	0.441756i
$371$	−0.207217	−	2.10391i	−0.0107582	−	0.109230i
$372$	26.8382	+	13.2446i	1.39150	+	0.686702i
$373$	0.703378	−	1.31593i	0.0364195	−	0.0681362i	−0.863053	−	0.505113i	$-0.831451\pi$
$373$	0.703378	−	1.31593i	0.0364195	−	0.0681362i	0.899473	+	0.436977i	$0.143951\pi$
$374$	20.8625	−	4.50276i	1.07877	−	0.232832i
$375$	24.8774	+	16.6225i	1.28466	+	0.858383i
$376$	−3.94633	+	15.7262i	−0.203516	+	0.811017i
$377$	0.328956	+	0.492318i	0.0169421	+	0.0253557i
$378$	5.83129	−	0.0945949i	0.299929	−	0.00486544i
$379$	33.1444	+	3.26444i	1.70251	+	0.167683i	0.902030	−	0.431673i	$-0.142076\pi$
$379$	33.1444	+	3.26444i	1.70251	+	0.167683i	0.800483	+	0.599356i	$0.204576\pi$
$380$	−3.40739	+	20.6019i	−0.174795	+	1.05685i
$381$	−5.57920	−	1.69243i	−0.285831	−	0.0867060i
$382$	5.99163	−	1.92420i	0.306558	−	0.0984509i
$383$	−28.8712			−1.47525			−0.737625	−	0.675211i	$-0.764053\pi$
$383$	−28.8712			−1.47525			−0.737625	+	0.675211i	$0.764053\pi$
$384$	−28.3301	+	9.07157i	−1.44571	+	0.462931i
$385$	9.05083			0.461273
$386$	21.6048	−	6.93837i	1.09966	−	0.353154i
$387$	−42.0189	−	12.7463i	−2.13594	−	0.647931i
$388$	−17.0919	−	2.82686i	−0.867709	−	0.143512i
$389$	10.9069	+	1.07424i	0.553002	+	0.0544659i	0.370659	−	0.928769i	$-0.379132\pi$
$389$	10.9069	+	1.07424i	0.553002	+	0.0544659i	0.182343	+	0.983235i	$0.441632\pi$
$390$	−3.03527	+	0.0492380i	−0.153697	+	0.00249326i
$391$	18.0075	+	26.9502i	0.910680	+	1.36293i
$392$	−9.82773	+	5.88483i	−0.496376	+	0.297229i
$393$	4.27320	+	2.85526i	0.215555	+	0.144029i
$394$	2.78165	−	0.600367i	0.140138	−	0.0302460i
$395$	4.99767	−	9.34998i	0.251460	−	0.470448i
$396$	−12.7546	+	25.8453i	−0.640943	+	1.29878i
$397$	2.15058	+	21.8352i	0.107935	+	1.09588i	0.884723	+	0.466117i	$0.154347\pi$
$397$	2.15058	+	21.8352i	0.107935	+	1.09588i	−0.776788	+	0.629762i	$0.783153\pi$
$398$	6.73788	+	5.34912i	0.337739	+	0.268127i
$399$	30.4430	+	12.6099i	1.52406	+	0.631284i
$400$	−5.91066	+	10.2242i	−0.295533	+	0.511208i
$401$	14.5533	−	6.02818i	0.726758	−	0.301033i	0.0115389	−	0.999933i	$-0.496327\pi$
$401$	14.5533	−	6.02818i	0.726758	−	0.301033i	0.715219	+	0.698900i	$0.246327\pi$
$402$	−22.2707	−	6.36317i	−1.11076	−	0.317366i
$403$	−2.05994	+	2.51005i	−0.102613	+	0.125034i
$404$	−13.6786	−	3.66934i	−0.680538	−	0.182557i
$405$	2.25409	+	7.43076i	0.112007	+	0.369237i
$406$	−0.451629	+	2.48008i	−0.0224140	+	0.123084i
$407$	−4.85184	−	24.3918i	−0.240497	−	1.20906i
$408$	−26.1341	−	15.6793i	−1.29383	−	0.776241i
$409$	9.23659	+	1.83727i	0.456720	+	0.0908472i	0.418088	−	0.908406i	$-0.362700\pi$
$409$	9.23659	+	1.83727i	0.456720	+	0.0908472i	0.0386314	+	0.999254i	$0.487700\pi$
$410$	−3.36903	−	7.77444i	−0.166385	−	0.383952i
$411$	−10.5320	−	12.8333i	−0.519505	−	0.633018i
$412$	−6.02543	+	2.72802i	−0.296851	+	0.134400i
$413$	12.9376	−	6.91531i	0.636619	−	0.340280i
$414$	−43.6229	−	3.58310i	−2.14395	−	0.176100i
$415$	5.65239	+	5.65239i	0.277465	+	0.277465i
$416$	−0.261466	−	3.21681i	−0.0128194	−	0.157717i
$417$	11.3550	−	11.3550i	0.556055	−	0.556055i
$418$	−28.9796	+	24.5803i	−1.41744	+	1.20226i
$419$	2.60804	+	4.87931i	0.127411	+	0.238370i	0.937536	−	0.347887i	$-0.113101\pi$
$419$	2.60804	+	4.87931i	0.127411	+	0.238370i	−0.810125	+	0.586257i	$0.800601\pi$
$420$	−9.43041	−	8.83757i	−0.460157	−	0.431229i
$421$	20.7144	−	16.9999i	1.00956	−	0.828523i	0.0243190	−	0.999704i	$-0.492258\pi$
$421$	20.7144	−	16.9999i	1.00956	−	0.828523i	0.985240	+	0.171181i	$0.0547583\pi$
$422$	5.35614	−	13.5484i	0.260733	−	0.659524i
$423$	4.37627	−	22.0010i	0.212781	−	1.06972i
$424$	−1.48715	−	3.14778i	−0.0722223	−	0.152870i
$425$	−11.8669	+	2.36048i	−0.575630	+	0.114500i
$426$	33.7654	+	48.8009i	1.63594	+	2.36441i
$427$	24.0671	−	7.30066i	1.16469	−	0.353304i
$428$	−1.78209	−	1.36825i	−0.0861406	−	0.0661368i
$429$	−4.27029	−	3.50454i	−0.206172	−	0.169201i
$430$	11.0276	+	19.8498i	0.531796	+	0.957243i
$431$	−2.91703	−	7.04234i	−0.140509	−	0.339218i	0.837923	−	0.545788i	$-0.183770\pi$
$431$	−2.91703	−	7.04234i	−0.140509	−	0.339218i	−0.978432	+	0.206571i	$0.933770\pi$
$432$	8.99033	−	3.37789i	0.432547	−	0.162519i
$433$	−9.00923	+	21.7502i	−0.432956	+	1.04525i	0.545373	+	0.838193i	$0.316388\pi$
$433$	−9.00923	+	21.7502i	−0.432956	+	1.04525i	−0.978329	+	0.207055i	$0.933612\pi$
$434$	−13.7340	+	1.57800i	−0.659255	+	0.0757464i
$435$	3.88580	−	0.382718i	0.186310	−	0.0183499i
$436$	−0.640161	+	9.72467i	−0.0306581	+	0.465727i
$437$	−50.8953	−	27.2041i	−2.43465	−	1.30135i
$438$	19.1479	+	12.3498i	0.914924	+	0.590095i
$439$	4.58148	−	6.85666i	0.218662	−	0.327251i	−0.705880	−	0.708332i	$-0.749448\pi$
$439$	4.58148	−	6.85666i	0.218662	−	0.327251i	0.924542	+	0.381081i	$0.124448\pi$
$440$	14.0354	−	5.01520i	0.669111	−	0.239090i
$441$	13.1772	−	8.80472i	0.627485	−	0.419272i
$442$	2.29988	−	2.37573i	0.109394	−	0.113002i
$443$	−2.17797	+	22.1133i	−0.103478	+	1.05063i	0.793504	+	0.608565i	$0.208255\pi$
$443$	−2.17797	+	22.1133i	−0.103478	+	1.05063i	−0.896982	+	0.442067i	$0.854245\pi$
$444$	−18.7618	+	30.1523i	−0.890395	+	1.43097i
$445$	−0.651077	+	2.14631i	−0.0308640	+	0.101745i
$446$	−16.9750	−	8.72234i	−0.803790	−	0.413015i
$447$		−	18.7506i		−	0.886871i
$448$	8.72599	−	10.6142i	0.412264	−	0.501474i
$449$			33.9842i			1.60381i	0.597449	+	0.801907i	$0.296181\pi$
$449$			33.9842i			1.60381i	−0.597449	+	0.801907i	$0.703819\pi$
$450$	7.46737	−	14.5327i	0.352015	−	0.685076i
$451$	4.47591	−	14.7551i	0.210762	−	0.694790i
$452$	−12.2628	+	2.85561i	−0.576793	+	0.134317i
$453$	0.957702	−	9.72372i	0.0449968	−	0.456860i
$454$	−8.52242	−	8.25033i	−0.399977	−	0.387207i
$455$	1.16590	−	0.779032i	0.0546584	−	0.0365216i
$456$	54.1961	+	2.68562i	2.53797	+	0.125766i
$457$	−3.62647	+	5.42740i	−0.169639	+	0.253883i	−0.906542	−	0.422116i	$-0.861288\pi$
$457$	−3.62647	+	5.42740i	−0.169639	+	0.253883i	0.736903	+	0.675999i	$0.236288\pi$
$458$	19.8517	−	30.7794i	0.927608	−	1.43823i
$459$	8.67771	+	4.63833i	0.405041	+	0.216499i
$460$	14.9194	+	17.0221i	0.695623	+	0.793660i
$461$	−8.71415	+	0.858269i	−0.405858	+	0.0399736i	−0.298887	−	0.954289i	$-0.596615\pi$
$461$	−8.71415	+	0.858269i	−0.405858	+	0.0399736i	−0.106971	+	0.994262i	$0.534115\pi$
$462$	−2.68462	−	23.3655i	−0.124900	−	1.08706i
$463$	5.17452	−	12.4924i	0.240481	−	0.580571i	−0.756850	−	0.653588i	$-0.773263\pi$
$463$	5.17452	−	12.4924i	0.240481	−	0.580571i	0.997331	+	0.0730171i	$0.0232628\pi$
$464$	0.673894	+	4.09618i	0.0312847	+	0.190160i
$465$	8.19433	+	19.7829i	0.380003	+	0.917408i
$466$	9.68220	−	5.37895i	0.448519	−	0.249175i
$467$	20.4106	+	16.7506i	0.944491	+	0.775124i	0.974491	−	0.224426i	$-0.0720508\pi$
$467$	20.4106	+	16.7506i	0.944491	+	0.775124i	−0.0300002	+	0.999550i	$0.509551\pi$
$468$	0.581567	+	4.42715i	0.0268830	+	0.204645i
$469$	10.2382	−	3.10571i	0.472755	−	0.143409i
$470$	−9.53960	+	6.60045i	−0.440029	+	0.304456i
$471$	3.39206	−	0.674723i	0.156298	−	0.0310896i
$472$	16.2309	−	17.8927i	0.747087	−	0.823578i
$473$	−8.06157	+	40.5282i	−0.370671	+	1.86349i
$474$	−25.6201	−	10.1285i	−1.17677	−	0.465219i
$475$	16.6526	−	13.6664i	0.764073	−	0.627059i
$476$	14.0703	−	0.456615i	0.644909	−	0.0209289i
$477$	2.27051	+	4.24783i	0.103960	+	0.194495i
$478$	25.2774	+	29.8015i	1.15616	+	1.36309i
$479$	5.08752	−	5.08752i	0.232455	−	0.232455i	−0.581262	−	0.813717i	$-0.697441\pi$
$479$	5.08752	−	5.08752i	0.232455	−	0.232455i	0.813717	+	0.581262i	$0.197441\pi$
$480$	−19.5210	−	8.47914i	−0.891010	−	0.387018i
$481$	−2.72448	−	2.72448i	−0.124226	−	0.124226i
$482$	2.47375	−	30.1169i	0.112676	−	1.37179i
$483$	31.5003	−	16.8373i	1.43331	−	0.766122i
$484$	4.79401	+	1.80589i	0.217909	+	0.0820859i
$485$	−7.86318	−	9.58131i	−0.357049	−	0.435065i
$486$	27.8612	−	12.0736i	1.26381	−	0.547668i
$487$	−11.0870	−	2.20534i	−0.502400	−	0.0999336i	−0.0626169	−	0.998038i	$-0.519945\pi$
$487$	−11.0870	−	2.20534i	−0.502400	−	0.0999336i	−0.439783	+	0.898104i	$0.644945\pi$
$488$	33.2761	−	24.6573i	1.50634	−	1.11618i
$489$	−0.601416	−	3.02352i	−0.0271970	−	0.136728i
$490$	−8.06303	−	1.46830i	−0.364251	−	0.0663311i
$491$	−3.49795	−	11.5312i	−0.157860	−	0.520395i	0.841956	−	0.539546i	$-0.181404\pi$
$491$	−3.49795	−	11.5312i	−0.157860	−	0.520395i	−0.999817	+	0.0191502i	$0.993904\pi$
$492$	−19.0710	+	11.0035i	−0.859789	+	0.496074i
$493$	−2.69812	+	3.28767i	−0.121517	+	0.148069i
$494$	−1.61738	+	5.66073i	−0.0727693	+	0.254688i
$495$	−19.0509	+	7.89116i	−0.856276	+	0.354681i
$496$	−20.4234	+	10.0573i	−0.917037	+	0.451586i
$497$	−25.3250	−	10.4900i	−1.13598	−	0.470539i
$498$	12.9155	−	16.2687i	0.578759	−	0.729019i
$499$	−3.61767	−	36.7309i	−0.161949	−	1.64430i	−0.641745	−	0.766918i	$-0.721789\pi$
$499$	−3.61767	−	36.7309i	−0.161949	−	1.64430i	0.479795	−	0.877380i	$-0.340711\pi$
$500$	−21.5531	+	7.30946i	−0.963883	+	0.326889i
$501$	−26.7336	+	50.0151i	−1.19437	+	2.23451i
$502$	−7.16581	−	33.2011i	−0.319826	−	1.48184i
$503$	−10.8462	−	7.24719i	−0.483608	−	0.323136i	0.289754	−	0.957101i	$-0.406426\pi$
$503$	−10.8462	−	7.24719i	−0.483608	−	0.323136i	−0.773362	+	0.633965i	$0.781426\pi$
$504$	−11.3309	+	15.2644i	−0.504720	+	0.679931i
$505$	−5.62939	−	8.42497i	−0.250504	−	0.374906i
$506$	0.668104	+	41.1852i	0.0297009	+	1.83091i
$507$	33.1645	+	3.26641i	1.47289	+	0.145067i
$508$	3.60558	−	2.58218i	0.159972	−	0.114566i
$509$	−29.7143	−	9.01372i	−1.31706	−	0.399526i	−0.447913	−	0.894077i	$-0.647833\pi$
$509$	−29.7143	−	9.01372i	−1.31706	−	0.399526i	−0.869149	+	0.494551i	$0.835333\pi$
$510$	−6.66730	−	20.7608i	−0.295233	−	0.919302i
$511$	−10.5248			−0.465589
$512$	7.65015	−	21.2950i	0.338092	−	0.941113i
$513$	−17.5189			−0.773480
$514$	1.71562	+	5.34215i	0.0756730	+	0.235632i
$515$	−4.52849	−	1.37370i	−0.199549	−	0.0605325i
$516$	47.9730	−	34.3563i	2.11189	−	1.51245i
$517$	−21.0085	−	2.06916i	−0.923955	−	0.0910016i
$518$	−0.266069	−	16.4018i	−0.0116904	−	0.720654i
$519$	−25.6838	−	38.4385i	−1.12739	−	1.68726i
$520$	1.37633	−	1.85411i	0.0603560	−	0.0813082i
$521$	34.3587	+	22.9577i	1.50528	+	1.00580i	0.988758	+	0.149522i	$0.0477733\pi$
$521$	34.3587	+	22.9577i	1.50528	+	1.00580i	0.516521	+	0.856274i	$0.327227\pi$
$522$	−1.21168	−	5.61404i	−0.0530339	−	0.245720i
$523$	2.60539	−	4.87435i	0.113926	−	0.213140i	−0.818496	−	0.574513i	$-0.805192\pi$
$523$	2.60539	−	4.87435i	0.113926	−	0.213140i	0.932422	+	0.361372i	$0.117692\pi$
$524$	−3.70219	+	1.25555i	−0.161731	+	0.0548490i
$525$	1.30688	+	13.2690i	0.0570369	+	0.579106i
$526$	−13.4333	+	16.9209i	−0.585718	+	0.737785i
$527$	−21.5484	−	8.92565i	−0.938664	−	0.388807i
$528$	−17.1103	−	34.7459i	−0.744629	−	1.51212i
$529$	−36.5439	+	15.1370i	−1.58887	+	0.658130i
$530$	0.684292	−	2.39498i	0.0297237	−	0.104031i
$531$	−21.2030	+	25.8359i	−0.920130	+	1.12118i
$532$	−21.7103	+	12.5262i	−0.941259	+	0.543080i
$533$	−0.693440	−	2.28597i	−0.0300362	−	0.0990162i
$534$	5.73401	+	1.04418i	0.248135	+	0.0451861i
$535$	−0.313605	−	1.57660i	−0.0135583	−	0.0681623i
$536$	14.1557	−	10.4892i	0.611433	−	0.453066i
$537$	30.0687	+	5.98103i	1.29756	+	0.258101i
$538$	−8.23663	+	3.56932i	−0.355106	+	0.153884i
$539$	−9.46148	−	11.5288i	−0.407535	−	0.496583i
$540$	6.43022	+	2.42225i	0.276713	+	0.104237i
$541$	−28.0163	+	14.9750i	−1.20452	+	0.643827i	−0.946622	−	0.322346i	$-0.895529\pi$
$541$	−28.0163	+	14.9750i	−1.20452	+	0.643827i	−0.257894	+	0.966173i	$0.583029\pi$
$542$	−0.221291	+	2.69413i	−0.00950528	+	0.115723i
$543$	34.4100	+	34.4100i	1.47667	+	1.47667i
$544$	21.5661	−	8.50463i	0.924641	−	0.364633i
$545$	−4.93047	+	4.93047i	−0.211198	+	0.211198i
$546$	−2.35696	−	2.77881i	−0.100869	−	0.118922i
$547$	9.66434	+	18.0807i	0.413217	+	0.773075i	0.999309	−	0.0371695i	$-0.0118341\pi$
$547$	9.66434	+	18.0807i	0.413217	+	0.773075i	−0.586092	+	0.810245i	$0.699334\pi$
$548$	12.6216	−	0.409602i	0.539168	−	0.0174973i
$549$	−44.2931	+	36.3504i	−1.89038	+	1.55140i
$550$	−14.2993	−	5.65300i	−0.609723	−	0.241045i
$551$	1.47731	−	7.42693i	0.0629355	−	0.316398i
$552$	39.5187	−	43.5648i	1.68203	−	1.85424i
$553$	12.4810	−	2.48263i	0.530748	−	0.105572i
$554$	25.1290	−	17.3868i	1.06763	−	0.738692i
$555$	−24.3143	+	7.37565i	−1.03208	+	0.313079i
$556$	1.59094	+	12.1109i	0.0674707	+	0.513618i
$557$	−27.9940	−	22.9741i	−1.18615	−	0.973445i	−0.186187	−	0.982514i	$-0.559613\pi$
$557$	−27.9940	−	22.9741i	−1.18615	−	0.973445i	−0.999959	+	0.00906977i	$0.997113\pi$
$558$	27.5328	−	15.2958i	1.16555	−	0.647524i
$559$	2.44992	+	5.91463i	0.103621	+	0.250162i
$560$	9.70055	−	1.59591i	0.409923	−	0.0674396i
$561$	15.1850	−	36.6599i	0.641113	−	1.54778i
$562$	−0.758342	−	6.60019i	−0.0319887	−	0.278412i
$563$	−9.51779	+	0.937420i	−0.401127	+	0.0395076i	−0.296569	−	0.955011i	$-0.595843\pi$
$563$	−9.51779	+	0.937420i	−0.401127	+	0.0395076i	−0.104557	+	0.994519i	$0.533343\pi$
$564$	19.8692	+	22.6695i	0.836645	+	0.954557i
$565$	−7.94467	−	4.24652i	−0.334235	−	0.178652i
$566$	14.9498	−	23.1792i	0.628386	−	0.974294i
$567$	−5.17826	+	7.74981i	−0.217466	+	0.325461i
$568$	−45.0849	−	2.23412i	−1.89172	−	0.0937416i
$569$	23.0755	−	15.4186i	0.967375	−	0.646379i	0.0317952	−	0.999494i	$-0.489878\pi$
$569$	23.0755	−	15.4186i	0.967375	−	0.646379i	0.935580	+	0.353115i	$0.114878\pi$
$570$	27.8937	+	27.0032i	1.16834	+	1.13104i
$571$	−4.46632	+	45.3473i	−0.186909	+	1.89772i	0.206635	+	0.978418i	$0.433749\pi$
$571$	−4.46632	+	45.3473i	−0.186909	+	1.89772i	−0.393544	+	0.919306i	$0.628751\pi$
$572$	4.09257	−	0.953030i	0.171119	−	0.0398482i
$573$	3.39631	−	11.1961i	0.141883	−	0.467725i
$574$	4.64815	−	9.04601i	0.194010	−	0.377573i
$575$		−	23.3512i		−	0.973813i
$576$	−9.11297	+	29.9496i	−0.379707	+	1.24790i
$577$			14.9558i			0.622618i	0.950309	+	0.311309i	$0.100767\pi$
$577$			14.9558i			0.622618i	−0.950309	+	0.311309i	$0.899233\pi$
$578$	−0.258375	−	0.132762i	−0.0107470	−	0.00552215i
$579$	12.2465	−	40.3714i	0.508949	−	1.67778i
$580$	−1.56912	+	2.52175i	−0.0651541	+	0.104710i
$581$	−0.940472	+	9.54877i	−0.0390173	+	0.396150i
$582$	−22.4026	+	23.1414i	−0.928618	+	0.959243i
$583$	3.76884	−	2.51826i	0.156089	−	0.104296i
$584$	−16.3211	+	5.83194i	−0.675371	+	0.241327i
$585$	−1.77488	+	2.65629i	−0.0733821	+	0.109824i
$586$	−21.4551	−	13.8378i	−0.886304	−	0.571635i
$587$	5.92221	+	3.16549i	0.244436	+	0.130654i	0.589066	−	0.808085i	$-0.299496\pi$
$587$	5.92221	+	3.16549i	0.244436	+	0.130654i	−0.344630	+	0.938738i	$0.611996\pi$
$588$	−1.39892	+	21.2509i	−0.0576903	+	0.876372i
$589$	41.3272	−	4.07038i	1.70286	−	0.167717i
$590$	17.1710	−	1.97290i	0.706919	−	0.0812228i
$591$	2.02467	−	4.88798i	0.0832836	−	0.201064i
$592$	−9.50109	−	25.2873i	−0.390492	−	1.03930i
$593$	−1.01446	−	2.44913i	−0.0416590	−	0.100574i	0.901680	−	0.432403i	$-0.142334\pi$
$593$	−1.01446	−	2.44913i	−0.0416590	−	0.100574i	−0.943339	+	0.331829i	$0.892334\pi$
$594$	6.07256	+	10.9307i	0.249160	+	0.448493i
$595$	7.78585	+	6.38968i	0.319189	+	0.261951i
$596$	11.3130	+	8.68587i	0.463399	+	0.355787i
$597$	15.3059	−	4.64300i	0.626430	−	0.190026i
$598$	3.63100	+	5.24786i	0.148483	+	0.214601i
$599$	−23.9088	+	4.75575i	−0.976886	+	0.194315i	−0.657619	−	0.753350i	$-0.728437\pi$
$599$	−23.9088	+	4.75575i	−0.976886	+	0.194315i	−0.319266	+	0.947665i	$0.603437\pi$
$600$	9.37916	+	19.8524i	0.382902	+	0.810472i
$601$	1.13409	−	5.70145i	0.0462604	−	0.232567i	−0.950737	−	0.309998i	$-0.899672\pi$
$601$	1.13409	−	5.70145i	0.0462604	−	0.232567i	0.996998	+	0.0774308i	$0.0246717\pi$
$602$	−10.0206	+	25.3471i	−0.408410	+	1.03307i
$603$	−18.8424	+	15.4635i	−0.767321	+	0.629724i
$604$	5.42309	+	5.08216i	0.220662	+	0.206790i
$605$	1.72778	+	3.23245i	0.0702444	+	0.131418i
$606$	−20.0800	+	17.0317i	−0.815694	+	0.691866i
$607$	−11.3092	+	11.3092i	−0.459027	+	0.459027i	−0.898336	−	0.439309i	$-0.855223\pi$
$607$	−11.3092	+	11.3092i	−0.459027	+	0.459027i	0.439309	+	0.898336i	$0.355223\pi$
$608$	−26.7258	+	31.4547i	−1.08387	+	1.27566i
$609$	3.31404	+	3.31404i	0.134292	+	0.134292i
$610$	29.5323	+	2.42573i	1.19573	+	0.0982148i
$611$	−2.88436	+	1.54172i	−0.116689	+	0.0623715i
$612$	−29.2182	+	13.2286i	−1.18107	+	0.534734i
$613$	13.4546	+	16.3945i	0.543426	+	0.662166i	0.970232	−	0.242177i	$-0.0778614\pi$
$613$	13.4546	+	16.3945i	0.543426	+	0.662166i	−0.426806	+	0.904343i	$0.640361\pi$
$614$	−6.80756	−	15.7092i	−0.274731	−	0.633973i
$615$	−15.4503	−	3.07325i	−0.623015	−	0.123925i
$616$	15.3410	+	9.20390i	0.618105	+	0.370836i
$617$	−7.43392	−	37.3728i	−0.299278	−	1.50457i	−0.778928	−	0.627113i	$-0.784236\pi$
$617$	−7.43392	−	37.3728i	−0.299278	−	1.50457i	0.479650	−	0.877460i	$-0.340764\pi$
$618$	−2.20310	+	12.0981i	−0.0886218	+	0.486658i
$619$	4.57625	+	15.0859i	0.183935	+	0.606353i	0.999612	+	0.0278454i	$0.00886462\pi$
$619$	4.57625	+	15.0859i	0.183935	+	0.606353i	−0.815677	+	0.578507i	$0.803635\pi$
$620$	−15.7317	−	4.22008i	−0.631800	−	0.169483i
$621$	−12.0470	+	14.6793i	−0.483430	+	0.589061i
$622$	30.6536	+	8.75832i	1.22910	+	0.351176i
$623$	−2.48725	+	1.03025i	−0.0996498	+	0.0412763i
$624$	−5.19479	−	3.00314i	−0.207958	−	0.120222i
$625$	−1.40525	−	0.582075i	−0.0562101	−	0.0232830i
$626$	−7.06733	−	5.61066i	−0.282467	−	0.224247i
$627$	6.92485	+	70.3092i	0.276552	+	2.80788i
$628$	−1.16422	+	2.35912i	−0.0464576	+	0.0941393i
$629$	13.0464	−	24.4080i	0.520192	−	0.973211i
$630$	−13.2951	+	2.86950i	−0.529691	+	0.114324i
$631$	−20.4497	−	13.6641i	−0.814091	−	0.543958i	0.0773983	−	0.997000i	$-0.475339\pi$
$631$	−20.4497	−	13.6641i	−0.814091	−	0.543958i	−0.891489	+	0.453042i	$0.850339\pi$
$632$	17.9790	−	10.7658i	0.715168	−	0.428242i
$633$	−15.0481	−	22.5211i	−0.598109	−	0.895134i
$634$	−20.8526	+	0.338270i	−0.828161	+	0.0134344i
$635$	3.15771	+	0.311007i	0.125310	+	0.0123419i
$636$	−6.38582	−	1.05617i	−0.253214	−	0.0418797i
$637$	−2.21113	−	0.670738i	−0.0876080	−	0.0265756i
$638$	−5.14602	+	1.65264i	−0.203733	+	0.0654286i
$639$	62.4521			2.47057
$640$	14.1586	−	7.85004i	0.559668	−	0.310300i
$641$	42.6690			1.68532			0.842662	−	0.538443i	$-0.180987\pi$
$641$	42.6690			1.68532			0.842662	+	0.538443i	$0.180987\pi$
$642$	−3.97710	+	1.27724i	−0.156964	+	0.0504087i
$643$	9.35940	+	2.83914i	0.369099	+	0.111965i	0.469385	−	0.882994i	$-0.344476\pi$
$643$	9.35940	+	2.83914i	0.369099	+	0.111965i	−0.100286	+	0.994959i	$0.531976\pi$
$644$	−4.43334	+	26.8050i	−0.174698	+	1.05627i
$645$	42.0139	+	4.13801i	1.65430	+	0.162934i
$646$	−42.2824	+	0.685904i	−1.66358	+	0.0269865i
$647$	−1.84175	−	2.75638i	−0.0724067	−	0.108364i	0.793499	−	0.608572i	$-0.208257\pi$
$647$	−1.84175	−	2.75638i	−0.0724067	−	0.108364i	−0.865906	+	0.500207i	$0.833257\pi$
$648$	−3.73578	+	14.8872i	−0.146755	+	0.584824i
$649$	26.1522	+	17.4743i	1.02656	+	0.685928i
$650$	−2.32856	+	0.502576i	−0.0913338	+	0.0197126i
$651$	−12.1159	+	22.6673i	−0.474861	+	0.888402i
$652$	2.10281	+	1.03773i	0.0823525	+	0.0406408i
$653$	−3.03489	−	30.8138i	−0.118765	−	1.20584i	−0.851141	−	0.524937i	$-0.824089\pi$
$653$	−3.03489	−	30.8138i	−0.118765	−	1.20584i	0.732376	−	0.680900i	$-0.238411\pi$
$654$	14.1909	+	11.2660i	0.554907	+	0.440534i
$655$	−2.58407	−	1.07036i	−0.100968	−	0.0418222i
$656$	2.19548	−	16.6035i	0.0857193	−	0.648259i
$657$	22.1534	−	9.17626i	0.864288	−	0.358000i
$658$	−13.3884	−	3.82533i	−0.521936	−	0.149127i
$659$	5.03586	−	6.13621i	0.196169	−	0.239033i	−0.665631	−	0.746281i	$-0.731837\pi$
$659$	5.03586	−	6.13621i	0.196169	−	0.239033i	0.861800	+	0.507248i	$0.169337\pi$
$660$	7.17955	−	26.7640i	0.279464	−	1.04179i
$661$	0.108742	+	0.358475i	0.00422958	+	0.0139430i	0.959030	−	0.283305i	$-0.0914310\pi$
$661$	0.108742	+	0.358475i	0.00422958	+	0.0139430i	−0.954800	+	0.297248i	$0.903931\pi$
$662$	−5.35933	+	29.4303i	−0.208296	+	1.14384i
$663$	−1.19933	−	6.02946i	−0.0465783	−	0.234165i
$664$	3.83270	+	15.3287i	0.148738	+	0.594868i
$665$	−17.5884	−	3.49855i	−0.682050	−	0.135668i
$666$	14.8603	+	34.2919i	0.575825	+	1.32878i
$667$	−5.20724	−	6.34504i	−0.201625	−	0.245681i
$668$	−17.7923	−	39.2981i	−0.688405	−	1.52049i
$669$	−31.2926	+	16.7262i	−1.20984	+	0.646674i
$670$	12.5631	+	1.03191i	0.485354	+	0.0398661i
$671$	38.1294	+	38.1294i	1.47197	+	1.47197i
$672$	−6.99732	−	24.5694i	−0.269927	−	0.947786i
$673$	−24.8167	+	24.8167i	−0.956613	+	0.956613i	−0.999097	−	0.0424843i	$-0.986473\pi$
$673$	−24.8167	+	24.8167i	−0.956613	+	0.956613i	0.0424843	+	0.999097i	$0.486473\pi$
$674$	−18.6809	+	15.8450i	−0.719560	+	0.610326i
$675$	−3.34161	−	6.25172i	−0.128619	−	0.240629i
$676$	−17.3336	+	18.4964i	−0.666678	+	0.711400i
$677$	23.4167	−	19.2176i	0.899977	−	0.738592i	−0.0658365	−	0.997830i	$-0.520972\pi$
$677$	23.4167	−	19.2176i	0.899977	−	0.738592i	0.965813	+	0.259238i	$0.0834716\pi$
$678$	−8.60622	+	21.7694i	−0.330520	+	0.836049i
$679$	2.90250	−	14.5918i	0.111388	−	0.559983i
$680$	15.6143	+	5.59440i	0.598783	+	0.214536i
$681$	−21.6294	+	4.30235i	−0.828839	+	0.164866i
$682$	−16.8649	−	24.3747i	−0.645789	−	0.933356i
$683$	20.0925	−	6.09498i	0.768817	−	0.233218i	0.118575	−	0.992945i	$-0.462167\pi$
$683$	20.0925	−	6.09498i	0.768817	−	0.233218i	0.650242	+	0.759727i	$0.274667\pi$
$684$	34.7763	−	45.2948i	1.32971	−	1.73189i
$685$	6.98422	+	5.73180i	0.266853	+	0.219001i
$686$	−13.0348	−	23.4629i	−0.497671	−	0.895817i
$687$	−26.0587	−	62.9112i	−0.994201	−	2.40021i
$688$	−1.49403	+	44.8591i	−0.0569593	+	1.71024i
$689$	0.268738	−	0.648791i	0.0102381	−	0.0247169i
$690$	41.8077	−	4.80357i	1.59159	−	0.182869i
$691$	−33.5621	+	3.30558i	−1.27676	+	0.125750i	−0.713575	−	0.700579i	$-0.752925\pi$
$691$	−33.5621	+	3.30558i	−1.27676	+	0.125750i	−0.563187	+	0.826329i	$0.690425\pi$
$692$	35.0891	+	2.30987i	1.33389	+	0.0878079i
$693$	−21.8287	−	11.6677i	−0.829203	−	0.443218i
$694$	7.60697	+	4.90624i	0.288757	+	0.186238i
$695$	−4.85536	+	7.26655i	−0.184174	+	0.275636i
$696$	6.97554	+	3.30282i	0.264407	+	0.125193i
$697$	14.2671	−	9.53296i	0.540404	−	0.361087i
$698$	−2.23756	+	2.31136i	−0.0846930	+	0.0874861i
$699$	2.01841	−	20.4933i	0.0763433	−	0.775126i
$700$	−8.61112	−	5.35813i	−0.325470	−	0.202518i
$701$	−2.81161	+	9.26865i	−0.106193	+	0.350072i	−0.993893	−	0.110351i	$-0.964802\pi$
$701$	−2.81161	+	9.26865i	−0.106193	+	0.350072i	0.887699	+	0.460423i	$0.152302\pi$
$702$	1.72309	+	0.885383i	0.0650339	+	0.0334166i
$703$			49.2760i			1.85848i
$704$	28.8897	+	5.77210i	1.08882	+	0.217544i
$705$			21.5674i			0.812275i
$706$	9.26551	−	18.0321i	0.348712	−	0.678648i
$707$	3.53055	−	11.6387i	0.132780	−	0.437717i
$708$	−10.1864	−	43.7432i	−0.382828	−	1.64397i
$709$	3.62722	−	36.8278i	0.136223	−	1.38310i	−0.647537	−	0.762034i	$-0.724201\pi$
$709$	3.62722	−	36.8278i	0.136223	−	1.38310i	0.783760	−	0.621064i	$-0.213299\pi$
$710$	−23.2043	−	22.4635i	−0.870844	−	0.843041i
$711$	−24.1066	+	16.1075i	−0.904069	+	0.604079i
$712$	−3.28618	+	2.97587i	−0.123155	+	0.111525i
$713$	25.0083	−	37.4276i	0.936570	−	1.40168i
$714$	14.1861	−	21.9951i	0.530901	−	0.823146i
$715$	2.65145	+	1.41723i	0.0991585	+	0.0530013i
$716$	−17.5374	+	15.3711i	−0.655403	+	0.574444i
$717$	72.3032	−	7.12124i	2.70021	−	0.265948i
$718$	−0.465911	−	4.05503i	−0.0173876	−	0.151333i
$719$	−7.24873	+	17.5000i	−0.270332	+	0.652640i	−0.999497	−	0.0316980i	$-0.989909\pi$
$719$	−7.24873	+	17.5000i	−0.270332	+	0.652640i	0.729165	+	0.684338i	$0.239909\pi$
$720$	−19.0271	+	11.8168i	−0.709098	+	0.440388i
$721$	−2.17372	−	5.24783i	−0.0809537	−	0.195439i
$722$	42.3286	−	23.5156i	1.57531	−	0.875162i
$723$	−43.4290	−	35.6412i	−1.61514	−	1.32551i
$724$	−36.7008	+	4.82115i	−1.36397	+	0.179177i
$725$	2.93212	−	0.889450i	0.108896	−	0.0330334i
$726$	7.83236	−	5.41921i	0.290686	−	0.201126i
$727$	5.95606	−	1.18473i	0.220898	−	0.0439393i	−0.0834004	−	0.996516i	$-0.526578\pi$
$727$	5.95606	−	1.18473i	0.220898	−	0.0439393i	0.304298	+	0.952577i	$0.401578\pi$
$728$	2.76839	−	0.134821i	0.102603	−	0.00499679i
$729$	7.83755	−	39.4020i	0.290280	−	1.45933i
$730$	−11.5318	−	4.55894i	−0.426812	−	0.168734i
$731$	−35.5469	+	29.1726i	−1.31475	+	1.07899i
$732$	−2.49752	−	76.9595i	−0.0923112	−	2.84451i
$733$	12.3622	+	23.1281i	0.456608	+	0.854254i	0.999892	+	0.0147048i	$0.00468087\pi$
$733$	12.3622	+	23.1281i	0.456608	+	0.854254i	−0.543284	+	0.839549i	$0.682819\pi$
$734$	−19.3337	−	22.7940i	−0.713619	−	0.841341i
$735$	−10.7743	+	10.7743i	−0.397418	+	0.397418i
$736$	7.97815	+	44.0239i	0.294079	+	1.62274i
$737$	16.2203	+	16.2203i	0.597483	+	0.597483i
$738$	−1.89685	+	23.0934i	−0.0698240	+	0.850080i
$739$	15.2974	−	8.17664i	0.562724	−	0.300782i	−0.165401	−	0.986226i	$-0.552892\pi$
$739$	15.2974	−	8.17664i	0.562724	−	0.300782i	0.728125	+	0.685444i	$0.240392\pi$
$740$	6.81312	−	18.0864i	0.250455	−	0.664871i
$741$	6.94377	+	8.46101i	0.255086	+	0.310823i
$742$	2.74328	−	1.18879i	0.100709	−	0.0436419i
$743$	−13.3068	−	2.64689i	−0.488180	−	0.0971051i	−0.0551382	−	0.998479i	$-0.517560\pi$
$743$	−13.3068	−	2.64689i	−0.488180	−	0.0971051i	−0.433042	+	0.901374i	$0.642560\pi$
$744$	−6.22822	+	41.8644i	−0.228338	+	1.53483i
$745$	1.99082	+	10.0085i	0.0729379	+	0.366683i
$746$	2.07603	+	0.378051i	0.0760088	+	0.0138414i
$747$	−6.34572	−	20.9190i	−0.232178	−	0.765387i
$748$	15.0843	+	26.1438i	0.551535	+	0.955913i
$749$	1.22406	−	1.49152i	0.0447261	−	0.0544989i
$750$	−11.6244	+	40.6848i	−0.424464	+	1.48560i
$751$	30.0522	−	12.4480i	1.09662	−	0.454235i	0.240310	−	0.970696i	$-0.422751\pi$
$751$	30.0522	−	12.4480i	1.09662	−	0.454235i	0.856311	+	0.516461i	$0.172751\pi$
$752$	−22.8815	+	1.48669i	−0.834403	+	0.0542139i
$753$	−58.3415	−	24.1659i	−2.12608	−	0.880653i
$754$	−0.520649	+	0.655822i	−0.0189609	+	0.0238836i
$755$	0.521209	+	5.29192i	0.0189687	+	0.192593i
$756$	2.64894	+	7.81081i	0.0963411	+	0.284077i
$757$	−12.5698	+	23.5164i	−0.456856	+	0.854717i	0.543032	+	0.839712i	$0.317276\pi$
$757$	−12.5698	+	23.5164i	−0.456856	+	0.854717i	−0.999887	+	0.0150046i	$0.995224\pi$
$758$	9.93683	+	46.0399i	0.360922	+	1.67225i
$759$	63.6749	+	42.5462i	2.31125	+	1.54433i
$760$	−29.2135	+	4.32070i	−1.05968	+	0.156728i
$761$	13.7090	+	20.5170i	0.496952	+	0.743741i	0.992152	−	0.125038i	$-0.0399052\pi$
$761$	13.7090	+	20.5170i	0.496952	+	0.743741i	−0.495200	+	0.868779i	$0.664905\pi$
$762$	−0.133736	−	8.24414i	−0.00484475	−	0.298654i
$763$	−8.32920	−	0.820355i	−0.301537	−	0.0296988i
$764$	5.18181	+	7.23555i	0.187471	+	0.261773i
$765$	−21.9593	−	6.66127i	−0.793939	−	0.240839i
$766$	−12.4845	−	38.8745i	−0.451084	−	1.40459i
$767$	4.87293			0.175951
$768$	−24.4652	−	34.2232i	−0.882812	−	1.23492i
$769$	−26.0000			−0.937584			−0.468792	−	0.883309i	$-0.655311\pi$
$769$	−26.0000			−0.937584			−0.468792	+	0.883309i	$0.655311\pi$
$770$	3.91377	+	12.1868i	0.141042	+	0.439181i
$771$	9.98249	+	3.02816i	0.359511	+	0.109056i
$772$	18.6848	+	26.0902i	0.672480	+	0.939008i
$773$	31.1453	+	3.06754i	1.12022	+	0.110332i	0.641128	−	0.767434i	$-0.278467\pi$
$773$	31.1453	+	3.06754i	1.12022	+	0.110332i	0.479090	+	0.877766i	$0.340967\pi$
$774$	−1.00721	−	62.0894i	−0.0362035	−	2.23176i
$775$	9.33541	+	13.9714i	0.335338	+	0.501869i
$776$	−3.58457	−	24.2363i	−0.128678	−	0.870032i
$777$	−25.3582	−	16.9438i	−0.909721	−	0.607856i
$778$	3.26993	+	15.1505i	0.117233	+	0.543170i
$779$	−14.4015	+	26.9433i	−0.515987	+	0.965345i
$780$	−1.37881	−	4.06564i	−0.0493694	−	0.145573i
$781$	−5.76067	−	58.4891i	−0.206133	−	2.09290i
$782$	−28.5011	+	35.9006i	−1.01920	+	1.28380i
$783$	−2.30210	−	0.953561i	−0.0822703	−	0.0340775i
$784$	−12.1735	−	10.6881i	−0.434769	−	0.381719i
$785$	−1.73895	+	0.720295i	−0.0620656	+	0.0257084i
$786$	−1.99674	+	6.98846i	−0.0712212	+	0.249270i
$787$	−16.8606	+	20.5446i	−0.601014	+	0.732338i	−0.981290	−	0.192535i	$-0.938329\pi$
$787$	−16.8606	+	20.5446i	−0.601014	+	0.732338i	0.380276	+	0.924873i	$0.375829\pi$
$788$	2.01123	+	3.48583i	0.0716471	+	0.124178i
$789$	11.6600	+	38.4379i	0.415107	+	1.36842i
$790$	14.7507	+	2.68614i	0.524805	+	0.0955685i
$791$	−2.10949	−	10.6051i	−0.0750050	−	0.377075i
$792$	−40.3156	−	5.99780i	−1.43255	−	0.213122i
$793$	8.19364	+	1.62982i	0.290965	+	0.0578765i
$794$	−28.4708	+	12.3377i	−1.01039	+	0.437850i
$795$	−2.93782	−	3.57974i	−0.104194	−	0.126960i
$796$	−4.28889	+	11.3855i	−0.152016	+	0.403548i
$797$	11.5426	−	6.16966i	0.408861	−	0.218541i	−0.254127	−	0.967171i	$-0.581788\pi$
$797$	11.5426	−	6.16966i	0.408861	−	0.218541i	0.662988	+	0.748630i	$0.269288\pi$
$798$	−3.81480	+	46.4437i	−0.135043	+	1.64409i
$799$	−16.6115	−	16.6115i	−0.587673	−	0.587673i
$800$	−16.3225	−	3.53745i	−0.577089	−	0.125068i
$801$	4.33713	−	4.33713i	0.153245	−	0.153245i
$802$	14.4100	+	16.9891i	0.508835	+	0.599904i
$803$	−10.6374	−	19.9012i	−0.375387	−	0.702299i
$804$	−1.06245	−	32.7387i	−0.0374698	−	1.15461i
$805$	−15.0263	+	12.3317i	−0.529607	+	0.434637i
$806$	−4.27049	−	1.68828i	−0.150422	−	0.0594670i
$807$	−3.25596	+	16.3688i	−0.114615	+	0.576209i
$808$	−0.974232	−	20.0047i	−0.0342734	−	0.703764i
$809$	−1.20506	+	0.239702i	−0.0423678	+	0.00842748i	−0.216229	−	0.976343i	$-0.569376\pi$
$809$	−1.20506	+	0.239702i	−0.0423678	+	0.00842748i	0.173861	+	0.984770i	$0.444376\pi$
$810$	−9.03066	+	6.24831i	−0.317305	+	0.219543i
$811$	26.3126	−	7.98184i	0.923961	−	0.280280i	0.207764	−	0.978179i	$-0.433381\pi$
$811$	26.3126	−	7.98184i	0.923961	−	0.280280i	0.716197	+	0.697899i	$0.245881\pi$
$812$	−3.53467	+	0.464328i	−0.124043	+	0.0162947i
$813$	3.88498	+	3.18832i	0.136252	+	0.111819i
$814$	30.7451	−	17.0805i	1.07762	−	0.598670i
$815$	0.642037	+	1.55001i	0.0224896	+	0.0542946i
$816$	9.81095	−	41.9691i	0.343452	−	1.46921i
$817$	31.3320	−	75.6421i	1.09617	−	2.64638i
$818$	1.52024	+	13.2314i	0.0531541	+	0.462624i
$819$	−3.81618	+	0.375861i	−0.133348	+	0.0131337i
$820$	9.01129	−	7.89817i	0.314688	−	0.275816i
$821$	48.1667	+	25.7456i	1.68103	+	0.898529i	0.983261	+	0.182205i	$0.0583235\pi$
$821$	48.1667	+	25.7456i	1.68103	+	0.898529i	0.697768	+	0.716323i	$0.254176\pi$
$822$	12.7255	−	19.7305i	0.443853	−	0.688180i
$823$	25.4024	−	38.0174i	0.885473	−	1.32520i	−0.0595586	−	0.998225i	$-0.518969\pi$
$823$	25.4024	−	38.0174i	0.885473	−	1.32520i	0.945032	−	0.326979i	$-0.106031\pi$
$824$	−6.27875	−	6.93347i	−0.218731	−	0.241539i
$825$	−23.7693	+	15.8822i	−0.827542	+	0.552946i
$826$	14.9058	+	14.4300i	0.518640	+	0.502082i
$827$	0.206054	−	2.09211i	0.00716522	−	0.0727497i	−0.990937	−	0.134326i	$-0.957113\pi$
$827$	0.206054	−	2.09211i	0.00716522	−	0.0727497i	0.998102	+	0.0615768i	$0.0196129\pi$
$828$	−14.0389	−	60.2868i	−0.487884	−	2.09511i
$829$	5.96194	−	19.6539i	0.207067	−	0.682608i	−0.790472	−	0.612498i	$-0.790165\pi$
$829$	5.96194	−	19.6539i	0.207067	−	0.682608i	0.997539	−	0.0701102i	$-0.0223351\pi$
$830$	−5.16663	+	10.0551i	−0.179336	+	0.349016i
$831$		−	56.8123i		−	1.97080i
$832$	4.21832	−	1.74308i	0.146244	−	0.0604303i
$833$		−	16.5971i		−	0.575056i
$834$	20.1994	+	10.3791i	0.699448	+	0.359400i
$835$	8.95934	−	29.5350i	0.310051	−	1.02210i
$836$	−45.6283	−	28.3915i	−1.57809	−	0.981940i
$837$	1.33939	−	13.5991i	0.0462962	−	0.470053i
$838$	−5.44212	+	5.62160i	−0.187995	+	0.194195i
$839$	−32.9148	+	21.9930i	−1.13635	+	0.759281i	−0.973797	−	0.227419i	$-0.926971\pi$
$839$	−32.9148	+	21.9930i	−1.13635	+	0.759281i	−0.162548	+	0.986701i	$0.551971\pi$
$840$	7.82172	−	16.5194i	0.269875	−	0.569975i
$841$	−15.5132	+	23.2171i	−0.534937	+	0.800589i
$842$	31.8474	+	20.5405i	1.09753	+	0.707871i
$843$	−10.8933	−	5.82257i	−0.375184	−	0.200540i
$844$	20.5587	+	1.35335i	0.707660	+	0.0465842i
$845$	−18.0490	+	1.77767i	−0.620906	+	0.0611539i
$846$	31.5163	−	3.62113i	1.08355	−	0.124497i
$847$	−1.68360	+	4.06457i	−0.0578491	+	0.139660i
$848$	3.59535	−	3.36358i	0.123465	−	0.115506i
$849$	−19.6241	−	47.3768i	−0.673498	−	1.62597i
$850$	−8.30984	−	14.9579i	−0.285025	−	0.513050i
$851$	41.2889	+	33.8850i	1.41537	+	1.16156i
$852$	−51.1087	+	66.5670i	−1.75095	+	2.28055i
$853$	−46.6519	+	14.1517i	−1.59733	+	0.484545i	−0.958570	−	0.284859i	$-0.908053\pi$
$853$	−46.6519	+	14.1517i	−1.59733	+	0.484545i	−0.638763	+	0.769404i	$0.720553\pi$
$854$	20.2373	+	29.2489i	0.692507	+	1.00088i
$855$	40.0719	−	7.97079i	1.37043	−	0.272595i
$856$	1.07171	−	2.99121i	0.0366303	−	0.102237i
$857$	−9.95539	+	50.0491i	−0.340070	+	1.70965i	0.310817	+	0.950470i	$0.399398\pi$
$857$	−9.95539	+	50.0491i	−0.340070	+	1.70965i	−0.650886	+	0.759175i	$0.725602\pi$
$858$	2.87223	−	7.26531i	0.0980564	−	0.248033i
$859$	6.69785	−	5.49678i	0.228528	−	0.187548i	−0.513161	−	0.858293i	$-0.671525\pi$
$859$	6.69785	−	5.49678i	0.228528	−	0.187548i	0.741688	+	0.670745i	$0.234025\pi$
$860$	−21.9588	+	23.4319i	−0.748790	+	0.799021i
$861$	−8.91344	−	16.6759i	−0.303769	−	0.568312i
$862$	8.22099	−	6.97299i	0.280008	−	0.237501i
$863$	25.1702	−	25.1702i	0.856803	−	0.856803i	−0.134157	−	0.990960i	$-0.542833\pi$
$863$	25.1702	−	25.1702i	0.856803	−	0.856803i	0.990960	+	0.134157i	$0.0428328\pi$
$864$	8.43588	+	10.6446i	0.286994	+	0.362138i
$865$	17.7904	+	17.7904i	0.604893	+	0.604893i
$866$	−33.1820	−	2.72551i	−1.12757	−	0.0926167i
$867$	−0.476301	+	0.254588i	−0.0161760	+	0.00864626i
$868$	−8.06364	−	17.8103i	−0.273698	−	0.604520i
$869$	17.3090	+	21.0911i	0.587168	+	0.715467i
$870$	2.19562	+	5.06666i	0.0744386	+	0.171776i
$871$	3.48559	+	0.693327i	0.118105	+	0.0234925i
$872$	−13.3709	+	3.34319i	−0.452796	+	0.113215i
$873$	6.61279	+	33.2447i	0.223809	+	1.12516i
$874$	14.6216	−	80.2932i	0.494583	−	2.71596i
$875$	−5.67361	−	18.7034i	−0.191803	−	0.632290i
$876$	−8.34876	+	31.1226i	−0.282078	+	1.05154i
$877$	−2.12383	+	2.58789i	−0.0717166	+	0.0873869i	−0.807633	−	0.589686i	$-0.799252\pi$
$877$	−2.12383	+	2.58789i	−0.0717166	+	0.0873869i	0.735916	+	0.677072i	$0.236752\pi$
$878$	11.2135	+	3.20391i	0.378437	+	0.108127i
$879$	−43.8530	+	18.1645i	−1.47912	+	0.612673i
$880$	12.8221	+	16.7297i	0.432232	+	0.563958i
$881$	51.3227	+	21.2586i	1.72911	+	0.716219i	0.999476	+	0.0323778i	$0.0103080\pi$
$881$	51.3227	+	21.2586i	1.72911	+	0.716219i	0.729631	+	0.683841i	$0.239692\pi$
$882$	17.5535	+	13.9355i	0.591057	+	0.469233i
$883$	−3.50066	−	35.5428i	−0.117806	−	1.19611i	−0.854342	−	0.519711i	$-0.826040\pi$
$883$	−3.50066	−	35.5428i	−0.117806	−	1.19611i	0.736536	−	0.676398i	$-0.236460\pi$
$884$	4.19339	+	2.06943i	0.141039	+	0.0696026i
$885$	15.1479	−	28.3398i	0.509193	−	0.952633i
$886$	−30.7169	+	6.62965i	−1.03195	+	0.222727i
$887$	−0.972215	−	0.649613i	−0.0326438	−	0.0218119i	0.539141	−	0.842215i	$-0.318749\pi$
$887$	−0.972215	−	0.649613i	−0.0326438	−	0.0218119i	−0.571785	+	0.820403i	$0.693749\pi$
$888$	−48.7125	−	12.2239i	−1.63469	−	0.410207i
$889$	2.11594	+	3.16673i	0.0709664	+	0.106209i
$890$	−3.17151	+	0.0514481i	−0.106309	+	0.00172455i
$891$	−19.8877	−	1.95877i	−0.666264	−	0.0656212i
$892$	4.40411	−	26.6283i	0.147460	−	0.891580i
$893$	40.0259	+	12.1417i	1.33942	+	0.406308i
$894$	25.2473	−	8.10814i	0.844396	−	0.271177i
$895$	−16.6848			−0.557712
$896$	18.0651	+	7.15958i	0.603514	+	0.239185i
$897$	11.8645			0.396145
$898$	−45.7591	+	14.6955i	−1.52700	+	0.490395i
$899$	5.65221	+	1.71458i	0.188512	+	0.0571844i
$900$	22.7970	+	3.77045i	0.759900	+	0.125682i
$901$	5.01992	+	0.494419i	0.167238	+	0.0164715i
$902$	21.8029	−	0.353686i	0.725958	−	0.0117765i
$903$	28.1530	+	42.1339i	0.936873	+	1.40213i
$904$	−9.14772	−	15.2768i	−0.304249	−	0.508099i
$905$	−22.0205	−	14.7136i	−0.731985	−	0.489097i
$906$	13.5069	−	2.91521i	0.448738	−	0.0968514i
$907$	13.4101	−	25.0885i	0.445275	−	0.833050i	−0.554725	−	0.832034i	$-0.687176\pi$
$907$	13.4101	−	25.0885i	0.445275	−	0.833050i	0.999999	−	0.00101644i	$-0.000323544\pi$
$908$	7.42364	−	15.0429i	0.246362	−	0.499216i
$909$	2.71602	+	27.5762i	0.0900847	+	0.914646i
$910$	1.55311	+	1.23300i	0.0514852	+	0.0408735i
$911$	−51.2146	−	21.2138i	−1.69682	−	0.702844i	−0.696919	−	0.717150i	$-0.745446\pi$
$911$	−51.2146	−	21.2138i	−1.69682	−	0.702844i	−0.999898	+	0.0143056i	$0.995446\pi$
$912$	19.8194	+	74.1354i	0.656286	+	2.45487i
$913$	−19.0062	+	7.87264i	−0.629014	+	0.260546i
$914$	−8.87606	−	2.53606i	−0.293594	−	0.0838853i
$915$	34.9493	−	42.5859i	1.15539	−	1.40785i
$916$	50.0282	+	13.4202i	1.65298	+	0.443417i
$917$	−0.974560	−	3.21269i	−0.0321828	−	0.106093i
$918$	−2.49300	+	13.6901i	−0.0822814	+	0.451840i
$919$	6.83966	+	34.3853i	0.225620	+	1.13427i	0.912997	+	0.407966i	$0.133762\pi$
$919$	6.83966	+	34.3853i	0.225620	+	1.13427i	−0.687377	+	0.726300i	$0.741238\pi$
$920$	−16.4685	+	27.4495i	−0.542950	+	0.904982i
$921$	−31.2193	−	6.20990i	−1.02871	−	0.204623i
$922$	−4.92382	−	11.3623i	−0.162158	−	0.374198i
$923$	−5.77641	−	7.03857i	−0.190133	−	0.231677i
$924$	30.3003	−	13.7185i	0.996806	−	0.451306i
$925$	−17.5844	+	9.39904i	−0.578171	+	0.309039i
$926$	19.0584	+	1.56542i	0.626297	+	0.0514429i
$927$	9.15087	+	9.15087i	0.300554	+	0.300554i
$928$	−5.22402	+	2.67866i	−0.171487	+	0.0879313i
$929$	−2.82110	+	2.82110i	−0.0925572	+	0.0925572i	−0.751869	−	0.659312i	$-0.770848\pi$
$929$	−2.82110	+	2.82110i	−0.0925572	+	0.0925572i	0.659312	+	0.751869i	$0.270848\pi$
$930$	−23.0938	+	19.5880i	−0.757277	+	0.642317i
$931$	13.9300	+	26.0612i	0.456538	+	0.854122i
$932$	11.4294	+	10.7109i	0.374384	+	0.350848i
$933$	45.8175	−	37.6014i	1.50000	−	1.23102i
$934$	−13.7283	+	34.7258i	−0.449205	+	1.13626i
$935$	−4.21301	+	21.1803i	−0.137780	+	0.692668i
$936$	−5.70960	+	2.69746i	−0.186624	+	0.0881693i
$937$	2.48040	−	0.493382i	0.0810310	−	0.0161181i	−0.154408	−	0.988007i	$-0.549347\pi$
$937$	2.48040	−	0.493382i	0.0810310	−	0.0161181i	0.235439	+	0.971889i	$0.424347\pi$
$938$	8.60899	+	12.4425i	0.281093	+	0.406263i
$939$	−16.0543	+	4.87002i	−0.523913	+	0.158927i
$940$	−13.0125	−	9.99072i	−0.424421	−	0.325861i
$941$	8.03823	+	6.59680i	0.262039	+	0.215050i	0.756234	−	0.654301i	$-0.227037\pi$
$941$	8.03823	+	6.59680i	0.262039	+	0.215050i	−0.494195	+	0.869351i	$0.664537\pi$
$942$	2.37530	+	4.27558i	0.0773914	+	0.139306i
$943$	12.6728	+	30.5950i	0.412685	+	0.996309i
$944$	31.1108	+	14.1174i	1.01257	+	0.459482i
$945$	−2.25822	+	5.45182i	−0.0734598	+	0.177348i
$946$	−58.0565	+	6.67052i	−1.88758	+	0.216877i
$947$	−2.92477	+	0.288065i	−0.0950424	+	0.00936086i	−0.145427	−	0.989369i	$-0.546455\pi$
$947$	−2.92477	+	0.288065i	−0.0950424	+	0.00936086i	0.0503841	+	0.998730i	$0.483955\pi$
$948$	2.55920	−	38.8768i	0.0831191	−	1.26266i
$949$	−3.08324	−	1.64803i	−0.100086	−	0.0534973i
$950$	25.6025	+	16.5127i	0.830655	+	0.535744i
$951$	−21.5417	+	32.2394i	−0.698536	+	1.04543i
$952$	6.69910	+	18.7479i	0.217119	+	0.607623i
$953$	−21.0622	+	14.0733i	−0.682272	+	0.455880i	−0.847794	−	0.530326i	$-0.822069\pi$
$953$	−21.0622	+	14.0733i	−0.682272	+	0.455880i	0.165521	+	0.986206i	$0.447069\pi$
$954$	−4.73780	+	4.89405i	−0.153392	+	0.158451i
$955$	−0.624117	+	6.33677i	−0.0201960	+	0.205053i
$956$	−29.1966	+	46.9223i	−0.944287	+	1.51758i
$957$	−2.91698	+	9.61600i	−0.0942926	+	0.310841i
$958$	9.05020	+	4.65030i	0.292399	+	0.150244i
$959$			10.8450i			0.350203i
$960$	2.97570	−	29.9513i	0.0960403	−	0.966673i
$961$			1.39148i			0.0448864i
$962$	2.49034	−	4.84659i	0.0802918	−	0.156260i
$963$	−1.27609	+	4.20670i	−0.0411213	+	0.135559i
$964$	41.6216	−	9.69233i	1.34054	−	0.312169i
$965$	−2.25047	+	22.8494i	−0.0724451	+	0.735547i
$966$	36.2925	+	35.1338i	1.16769	+	1.13041i
$967$	29.0245	−	19.3936i	0.933366	−	0.623655i	0.00687640	−	0.999976i	$-0.497811\pi$
$967$	29.0245	−	19.3936i	0.933366	−	0.623655i	0.926489	+	0.376321i	$0.122811\pi$
$968$	−0.358568	+	7.23595i	−0.0115248	+	0.232572i
$969$	−43.6797	+	65.3713i	−1.40319	+	2.10003i
$970$	9.50085	−	14.7308i	0.305054	−	0.472977i
$971$	−22.4191	−	11.9832i	−0.719462	−	0.384560i	0.0706680	−	0.997500i	$-0.477487\pi$
$971$	−22.4191	−	11.9832i	−0.719462	−	0.384560i	−0.790130	+	0.612940i	$0.789987\pi$
$972$	28.3046	+	32.2937i	0.907870	+	1.03582i
$973$	−10.4396	+	1.02821i	−0.334677	+	0.0329628i
$974$	−1.82480	−	15.8821i	−0.0584704	−	0.508894i
$975$	−1.69488	+	4.09180i	−0.0542795	+	0.131042i
$976$	47.5898	+	34.1433i	1.52331	+	1.09290i
$977$	1.12494	+	2.71585i	0.0359901	+	0.0868877i	0.940853	−	0.338816i	$-0.110027\pi$
$977$	1.12494	+	2.71585i	0.0359901	+	0.0868877i	−0.904862	+	0.425704i	$0.860027\pi$
$978$	3.81105	−	2.11723i	0.121864	−	0.0677015i
$979$	−4.46197	−	3.66185i	−0.142605	−	0.117033i
$980$	−1.50959	−	11.4916i	−0.0482219	−	0.367087i
$981$	18.2472	−	5.53524i	0.582590	−	0.176727i
$982$	14.0139	−	9.69625i	0.447203	−	0.309420i
$983$	−33.5615	+	6.67579i	−1.07044	+	0.212925i	−0.698703	−	0.715412i	$-0.746239\pi$
$983$	−33.5615	+	6.67579i	−1.07044	+	0.212925i	−0.371742	+	0.928336i	$0.621239\pi$
$984$	−23.0627	−	20.9207i	−0.735211	−	0.666927i
$985$	−0.561734	+	2.82403i	−0.0178983	+	0.0899809i
$986$	−5.59351	−	2.21131i	−0.178134	−	0.0704225i
$987$	−20.0115	+	16.4230i	−0.636973	+	0.522750i
$988$	−8.32146	+	0.270052i	−0.264741	+	0.00859149i
$989$	−41.8358	−	78.2693i	−1.33030	−	2.48882i
$990$	−18.8633	−	22.2394i	−0.599516	−	0.706816i
$991$	−8.69532	+	8.69532i	−0.276216	+	0.276216i	−0.831596	−	0.555381i	$-0.812573\pi$
$991$	−8.69532	+	8.69532i	−0.276216	+	0.276216i	0.555381	+	0.831596i	$0.312573\pi$
$992$	−22.3735	−	23.1507i	−0.710358	−	0.735036i
$993$	39.3266	+	39.3266i	1.24799	+	1.24799i
$994$	3.17347	−	38.6357i	0.100656	−	1.22545i
$995$	−7.67690	+	4.10339i	−0.243374	+	0.130086i
$996$	27.4905	+	10.3556i	0.871069	+	0.328129i
$997$	−31.1754	−	37.9874i	−0.987336	−	1.20307i	−0.979157	−	0.203106i	$-0.934896\pi$
$997$	−31.1754	−	37.9874i	−0.987336	−	1.20307i	−0.00817911	−	0.999967i	$-0.502604\pi$
$998$	47.8930	−	20.7543i	1.51603	−	0.656967i
$999$	15.9031	+	3.16333i	0.503152	+	0.100083i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.2.k.a.5.9	✓	240
4.3	odd	2		512.2.k.a.113.2		240
128.51	odd	32		512.2.k.a.145.2		240
128.77	even	32	inner	128.2.k.a.77.9	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.2.k.a.5.9	✓	240	1.1	even	1	trivial
128.2.k.a.77.9	yes	240	128.77	even	32	inner
512.2.k.a.113.2		240	4.3	odd	2
512.2.k.a.145.2		240	128.51	odd	32

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:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	128.k (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.432421 + 1.34648i) q^{2} +(2.51607 + 0.763243i) q^{3} +(-1.62602 + 1.16449i) q^{4} +(-1.42404 - 0.140256i) q^{5} +(0.0603114 + 3.71789i) q^{6} +(-0.954234 - 1.42811i) q^{7} +(-2.27110 - 1.68586i) q^{8} +(3.25368 + 2.17404i) q^{9} +O(q^{10})\)	\(q+(0.432421 + 1.34648i) q^{2} +(2.51607 + 0.763243i) q^{3} +(-1.62602 + 1.16449i) q^{4} +(-1.42404 - 0.140256i) q^{5} +(0.0603114 + 3.71789i) q^{6} +(-0.954234 - 1.42811i) q^{7} +(-2.27110 - 1.68586i) q^{8} +(3.25368 + 2.17404i) q^{9} +(-0.426934 - 1.97810i) q^{10} +(1.73596 - 3.24775i) q^{11} +(-4.97999 + 1.68890i) q^{12} +(-0.0559220 - 0.567786i) q^{13} +(1.51030 - 1.90240i) q^{14} +(-3.47595 - 1.43979i) q^{15} +(1.28791 - 3.78699i) q^{16} +(3.78617 - 1.56828i) q^{17} +(-1.52034 + 5.32112i) q^{18} +(-4.62888 + 5.64030i) q^{19} +(2.47886 - 1.43023i) q^{20} +(-1.31093 - 4.32155i) q^{21} +(5.12370 + 0.933040i) q^{22} +(1.54300 + 7.75719i) q^{23} +(-4.42753 - 5.97515i) q^{24} +(-2.89570 - 0.575990i) q^{25} +(0.740331 - 0.320821i) q^{26} +(1.52317 + 1.85599i) q^{27} +(3.21464 + 1.21095i) q^{28} +(-0.915268 + 0.489221i) q^{29} +(0.435570 - 5.30290i) q^{30} +(-4.02439 - 4.02439i) q^{31} +(5.65603 + 0.0965697i) q^{32} +(6.84662 - 6.84662i) q^{33} +(3.74888 + 4.41985i) q^{34} +(1.15857 + 2.16753i) q^{35} +(-7.82222 + 0.253850i) q^{36} +(5.22039 - 4.28427i) q^{37} +(-9.59619 - 3.79371i) q^{38} +(0.292655 - 1.47127i) q^{39} +(2.99769 + 2.71927i) q^{40} +(4.10656 - 0.816845i) q^{41} +(5.25201 - 3.63387i) q^{42} +(-10.7378 + 3.25728i) q^{43} +(0.959275 + 7.30243i) q^{44} +(-4.32846 - 3.55228i) q^{45} +(-9.77768 + 5.43199i) q^{46} +(-2.19371 - 5.29608i) q^{47} +(6.13087 - 8.54536i) q^{48} +(1.54984 - 3.74165i) q^{49} +(-0.476601 - 4.14807i) q^{50} +(10.7233 - 1.05615i) q^{51} +(0.752114 + 0.858113i) q^{52} +(1.08552 + 0.580223i) q^{53} +(-1.84041 + 2.85349i) q^{54} +(-2.92760 + 4.38146i) q^{55} +(-0.240439 + 4.85209i) q^{56} +(-15.9515 + 10.6585i) q^{57} +(-1.05451 - 1.02084i) q^{58} +(-0.837165 + 8.49988i) q^{59} +(7.32860 - 1.70660i) q^{60} +(-4.25056 + 14.0122i) q^{61} +(3.67854 - 7.15900i) q^{62} -6.72117i q^{63} +(2.31576 + 7.65750i) q^{64} +0.816395i q^{65} +(12.1795 + 6.25823i) q^{66} +(-1.80820 + 5.96082i) q^{67} +(-4.33015 + 6.95904i) q^{68} +(-2.03831 + 20.6954i) q^{69} +(-2.41755 + 2.49728i) q^{70} +(13.2698 - 8.86660i) q^{71} +(-3.72430 - 10.4227i) q^{72} +(3.40436 - 5.09499i) q^{73} +(8.02609 + 5.17656i) q^{74} +(-6.84617 - 3.65935i) q^{75} +(0.958567 - 14.5616i) q^{76} +(-6.29466 + 0.619970i) q^{77} +(2.10759 - 0.242156i) q^{78} +(-2.83531 + 6.84505i) q^{79} +(-2.36519 + 5.21220i) q^{80} +(-2.07667 - 5.01353i) q^{81} +(2.87563 + 5.17618i) q^{82} +(-4.31830 - 3.54394i) q^{83} +(7.16402 + 5.50038i) q^{84} +(-5.61163 + 1.70227i) q^{85} +(-9.02913 - 13.0498i) q^{86} +(-2.67628 + 0.532344i) q^{87} +(-9.41778 + 4.44937i) q^{88} +(0.305791 - 1.53731i) q^{89} +(2.91136 - 7.36428i) q^{90} +(-0.757499 + 0.621664i) q^{91} +(-11.5422 - 10.8166i) q^{92} +(-7.05408 - 13.1973i) q^{93} +(6.18247 - 5.24393i) q^{94} +(7.38281 - 7.38281i) q^{95} +(14.1573 + 4.55990i) q^{96} +(6.12498 + 6.12498i) q^{97} +(5.70825 + 0.468865i) q^{98} +(12.7090 - 6.79310i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9}+O(q^{10}) \) 240 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9	\( 240 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} - 16 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 16 q^{17} - 16 q^{18} - 16 q^{19} - 16 q^{20} - 16 q^{21} - 16 q^{22} - 16 q^{23} - 16 q^{24} - 16 q^{25} - 16 q^{26} - 16 q^{27} - 16 q^{28} - 16 q^{29} - 16 q^{30} - 16 q^{31} - 16 q^{32} - 16 q^{33} - 16 q^{34} - 16 q^{35} - 16 q^{36} - 16 q^{37} - 16 q^{38} - 16 q^{39} - 16 q^{40} - 16 q^{41} - 16 q^{42} - 16 q^{43} - 16 q^{44} - 16 q^{45} - 16 q^{46} - 16 q^{47} - 16 q^{48} - 16 q^{49} + 32 q^{50} - 16 q^{51} + 80 q^{52} - 16 q^{53} + 112 q^{54} - 16 q^{55} + 96 q^{56} - 16 q^{57} + 128 q^{58} - 16 q^{59} + 176 q^{60} - 16 q^{61} + 80 q^{62} + 176 q^{64} + 176 q^{66} - 16 q^{67} + 80 q^{68} - 16 q^{69} + 176 q^{70} - 16 q^{71} + 128 q^{72} - 16 q^{73} + 96 q^{74} - 16 q^{75} + 112 q^{76} - 16 q^{77} + 80 q^{78} - 16 q^{79} + 32 q^{80} - 16 q^{81} - 16 q^{82} - 16 q^{83} - 16 q^{84} - 16 q^{85} - 16 q^{86} - 16 q^{87} - 16 q^{88} - 16 q^{89} - 16 q^{90} - 16 q^{91} - 16 q^{92} - 16 q^{93} - 16 q^{94} - 16 q^{95} - 16 q^{96} - 16 q^{97} - 16 q^{98} - 16 q^{99}+O(q^{100}) \) 240 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9 - 16 * q^10 - 16 * q^11 - 16 * q^12 - 16 * q^13 - 16 * q^14 - 16 * q^15 - 16 * q^16 - 16 * q^17 - 16 * q^18 - 16 * q^19 - 16 * q^20 - 16 * q^21 - 16 * q^22 - 16 * q^23 - 16 * q^24 - 16 * q^25 - 16 * q^26 - 16 * q^27 - 16 * q^28 - 16 * q^29 - 16 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 16 * q^34 - 16 * q^35 - 16 * q^36 - 16 * q^37 - 16 * q^38 - 16 * q^39 - 16 * q^40 - 16 * q^41 - 16 * q^42 - 16 * q^43 - 16 * q^44 - 16 * q^45 - 16 * q^46 - 16 * q^47 - 16 * q^48 - 16 * q^49 + 32 * q^50 - 16 * q^51 + 80 * q^52 - 16 * q^53 + 112 * q^54 - 16 * q^55 + 96 * q^56 - 16 * q^57 + 128 * q^58 - 16 * q^59 + 176 * q^60 - 16 * q^61 + 80 * q^62 + 176 * q^64 + 176 * q^66 - 16 * q^67 + 80 * q^68 - 16 * q^69 + 176 * q^70 - 16 * q^71 + 128 * q^72 - 16 * q^73 + 96 * q^74 - 16 * q^75 + 112 * q^76 - 16 * q^77 + 80 * q^78 - 16 * q^79 + 32 * q^80 - 16 * q^81 - 16 * q^82 - 16 * q^83 - 16 * q^84 - 16 * q^85 - 16 * q^86 - 16 * q^87 - 16 * q^88 - 16 * q^89 - 16 * q^90 - 16 * q^91 - 16 * q^92 - 16 * q^93 - 16 * q^94 - 16 * q^95 - 16 * q^96 - 16 * q^97 - 16 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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