LMFDB - Embedded newform 171.2.x.a.110.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [171,2,Mod(14,171)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(171, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([15, 7]))

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

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

chi := DirichletCharacter("171.14");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	171.x (of order $18$, degree $6$, 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:	$1.36544187456$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$18$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			110.9
Character	$\chi$	$=$	171.110
Dual form			171.2.x.a.14.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.247109 + 0.207349i) q^{2} +(0.668060 + 1.59803i) q^{3} +(-0.329227 + 1.86714i) q^{4} +(-0.0294890 + 0.0810203i) q^{5} +(-0.496432 - 0.256365i) q^{6} +(-0.0754752 - 0.130727i) q^{7} +(-0.628371 - 1.08837i) q^{8} +(-2.10739 + 2.13516i) q^{9} +O(q^{10})$	\(q+(-0.247109 + 0.207349i) q^{2} +(0.668060 + 1.59803i) q^{3} +(-0.329227 + 1.86714i) q^{4} +(-0.0294890 + 0.0810203i) q^{5} +(-0.496432 - 0.256365i) q^{6} +(-0.0754752 - 0.130727i) q^{7} +(-0.628371 - 1.08837i) q^{8} +(-2.10739 + 2.13516i) q^{9} +(-0.00951247 - 0.0261353i) q^{10} -1.72768i q^{11} +(-3.20369 + 0.721248i) q^{12} +(0.805863 + 2.21409i) q^{13} +(0.0457566 + 0.0166540i) q^{14} +(-0.149173 + 0.00700221i) q^{15} +(-3.18226 - 1.15825i) q^{16} +(0.788265 - 2.16574i) q^{17} +(0.0780319 - 0.964581i) q^{18} +(3.17839 + 2.98293i) q^{19} +(-0.141568 - 0.0817341i) q^{20} +(0.158483 - 0.207945i) q^{21} +(0.358233 + 0.426925i) q^{22} +(5.13795 + 0.905959i) q^{23} +(1.31946 - 1.73125i) q^{24} +(3.82453 + 3.20916i) q^{25} +(-0.658225 - 0.380026i) q^{26} +(-4.81991 - 1.94126i) q^{27} +(0.268934 - 0.0978839i) q^{28} +(0.930382 - 5.27646i) q^{29} +(0.0354100 - 0.0326611i) q^{30} -0.157915i q^{31} +(3.38843 - 1.23329i) q^{32} +(2.76089 - 1.15420i) q^{33} +(0.254276 + 0.698619i) q^{34} +(0.0128172 - 0.00226002i) q^{35} +(-3.29283 - 4.63775i) q^{36} +1.03696i q^{37} +(-1.40391 - 0.0780729i) q^{38} +(-2.99982 + 2.76694i) q^{39} +(0.106710 - 0.0188159i) q^{40} +(3.23970 - 2.71843i) q^{41} +(0.00395453 + 0.0842463i) q^{42} +(-0.868665 - 4.92644i) q^{43} +(3.22582 + 0.568800i) q^{44} +(-0.110846 - 0.233705i) q^{45} +(-1.45748 + 0.841477i) q^{46} +(-11.1068 - 1.95842i) q^{47} +(-0.275028 - 5.85912i) q^{48} +(3.48861 - 6.04244i) q^{49} -1.61049 q^{50} +(3.98752 - 0.187175i) q^{51} +(-4.39933 + 0.775721i) q^{52} +(3.60211 + 3.02253i) q^{53} +(1.59356 - 0.519701i) q^{54} +(0.139977 + 0.0509475i) q^{55} +(-0.0948529 + 0.164290i) q^{56} +(-2.64345 + 7.07193i) q^{57} +(0.864161 + 1.49677i) q^{58} +(-0.485489 - 2.75335i) q^{59} +(0.0360377 - 0.280832i) q^{60} +(5.10362 - 1.85757i) q^{61} +(0.0327436 + 0.0390223i) q^{62} +(0.438178 + 0.114341i) q^{63} +(2.80490 - 4.85823i) q^{64} -0.203150 q^{65} +(-0.442917 + 0.857677i) q^{66} +(1.30076 - 1.55018i) q^{67} +(3.78422 + 2.18482i) q^{68} +(1.98471 + 8.81582i) q^{69} +(-0.00269863 + 0.00321610i) q^{70} +(-10.6749 + 8.95732i) q^{71} +(3.64807 + 0.951951i) q^{72} +(-0.405662 - 2.30062i) q^{73} +(-0.215012 - 0.256241i) q^{74} +(-2.57331 + 8.25562i) q^{75} +(-6.61596 + 4.95243i) q^{76} +(-0.225854 + 0.130397i) q^{77} +(0.167559 - 1.30574i) q^{78} +(-1.22472 + 3.36489i) q^{79} +(0.187683 - 0.223672i) q^{80} +(-0.117807 - 8.99923i) q^{81} +(-0.236895 + 1.34350i) q^{82} +(-3.67729 + 2.12308i) q^{83} +(0.336085 + 0.364372i) q^{84} +(0.152224 + 0.127731i) q^{85} +(1.23615 + 1.03725i) q^{86} +(9.05348 - 2.03822i) q^{87} +(-1.88036 + 1.08563i) q^{88} +(-2.82275 + 16.0086i) q^{89} +(0.0758495 + 0.0347666i) q^{90} +(0.228619 - 0.272457i) q^{91} +(-3.38311 + 9.29500i) q^{92} +(0.252353 - 0.105497i) q^{93} +(3.15065 - 1.81903i) q^{94} +(-0.335405 + 0.169550i) q^{95} +(4.23450 + 4.59090i) q^{96} +(1.33420 + 1.59003i) q^{97} +(0.390828 + 2.21650i) q^{98} +(3.68888 + 3.64090i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9}+O(q^{10}) $ 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9	\( 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9} - 12 q^{10} - 9 q^{12} - 6 q^{13} - 9 q^{14} - 36 q^{15} - 9 q^{16} + 27 q^{17} + 36 q^{18} - 15 q^{19} - 18 q^{20} + 3 q^{21} + 30 q^{22} - 45 q^{23} - 21 q^{24} - 3 q^{25} - 72 q^{26} - 36 q^{28} - 9 q^{29} - 21 q^{30} - 9 q^{32} - 6 q^{33} + 33 q^{34} + 45 q^{35} + 18 q^{36} - 9 q^{38} - 18 q^{39} + 15 q^{40} - 9 q^{41} + 15 q^{42} + 9 q^{43} - 63 q^{44} + 33 q^{45} - 18 q^{46} - 9 q^{47} + 3 q^{48} - 15 q^{49} + 126 q^{50} + 39 q^{51} - 39 q^{52} - 51 q^{54} + 3 q^{55} + 63 q^{56} - 78 q^{57} - 6 q^{58} + 36 q^{59} - 75 q^{60} - 24 q^{61} + 18 q^{62} - 9 q^{63} - 18 q^{65} + 159 q^{66} - 63 q^{67} + 54 q^{68} - 9 q^{69} + 39 q^{70} + 141 q^{72} - 45 q^{73} - 117 q^{74} - 3 q^{76} - 18 q^{77} + 27 q^{78} + 3 q^{79} + 126 q^{80} - 60 q^{81} - 3 q^{82} + 27 q^{83} - 117 q^{84} - 3 q^{85} - 171 q^{86} + 15 q^{87} - 9 q^{88} + 54 q^{89} - 21 q^{90} - 9 q^{91} - 27 q^{92} + 42 q^{93} + 99 q^{95} + 207 q^{96} - 57 q^{97} - 27 q^{98} + 39 q^{99}+O(q^{100}) \) 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9 - 12 * q^10 - 9 * q^12 - 6 * q^13 - 9 * q^14 - 36 * q^15 - 9 * q^16 + 27 * q^17 + 36 * q^18 - 15 * q^19 - 18 * q^20 + 3 * q^21 + 30 * q^22 - 45 * q^23 - 21 * q^24 - 3 * q^25 - 72 * q^26 - 36 * q^28 - 9 * q^29 - 21 * q^30 - 9 * q^32 - 6 * q^33 + 33 * q^34 + 45 * q^35 + 18 * q^36 - 9 * q^38 - 18 * q^39 + 15 * q^40 - 9 * q^41 + 15 * q^42 + 9 * q^43 - 63 * q^44 + 33 * q^45 - 18 * q^46 - 9 * q^47 + 3 * q^48 - 15 * q^49 + 126 * q^50 + 39 * q^51 - 39 * q^52 - 51 * q^54 + 3 * q^55 + 63 * q^56 - 78 * q^57 - 6 * q^58 + 36 * q^59 - 75 * q^60 - 24 * q^61 + 18 * q^62 - 9 * q^63 - 18 * q^65 + 159 * q^66 - 63 * q^67 + 54 * q^68 - 9 * q^69 + 39 * q^70 + 141 * q^72 - 45 * q^73 - 117 * q^74 - 3 * q^76 - 18 * q^77 + 27 * q^78 + 3 * q^79 + 126 * q^80 - 60 * q^81 - 3 * q^82 + 27 * q^83 - 117 * q^84 - 3 * q^85 - 171 * q^86 + 15 * q^87 - 9 * q^88 + 54 * q^89 - 21 * q^90 - 9 * q^91 - 27 * q^92 + 42 * q^93 + 99 * q^95 + 207 * q^96 - 57 * q^97 - 27 * q^98 + 39 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{18}\right)$

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 $

$2$	−0.247109	+	0.207349i	−0.174732	+	0.146618i	−0.725960	−	0.687737i	$-0.758604\pi$
$2$	−0.247109	+	0.207349i	−0.174732	+	0.146618i	0.551228	+	0.834355i	$0.314160\pi$
$3$	0.668060	+	1.59803i	0.385705	+	0.922622i
$3$	0.668060	+	1.59803i	0.385705	+	0.922622i
$4$	−0.329227	+	1.86714i	−0.164614	+	0.933570i
$5$	−0.0294890	+	0.0810203i	−0.0131879	+	0.0362334i	−0.946112	−	0.323840i	$-0.895026\pi$
$5$	−0.0294890	+	0.0810203i	−0.0131879	+	0.0362334i	0.932924	+	0.360073i	$0.117248\pi$
$6$	−0.496432	−	0.256365i	−0.202668	−	0.104661i
$7$	−0.0754752	−	0.130727i	−0.0285269	−	0.0494101i	0.851409	−	0.524502i	$-0.175748\pi$
$7$	−0.0754752	−	0.130727i	−0.0285269	−	0.0494101i	−0.879936	+	0.475091i	$0.842415\pi$
$8$	−0.628371	−	1.08837i	−0.222163	−	0.384797i
$9$	−2.10739	+	2.13516i	−0.702464	+	0.711720i
$10$	−0.00951247	−	0.0261353i	−0.00300811	−	0.00826471i
$11$		−	1.72768i		−	0.520916i	−0.965485	−	0.260458i	$-0.916126\pi$
$11$		−	1.72768i		−	0.520916i	0.965485	−	0.260458i	$-0.0838735\pi$
$12$	−3.20369	+	0.721248i	−0.924825	+	0.208206i
$13$	0.805863	+	2.21409i	0.223506	+	0.614078i	0.999869	−	0.0162084i	$-0.00515951\pi$
$13$	0.805863	+	2.21409i	0.223506	+	0.614078i	−0.776362	+	0.630287i	$0.782937\pi$
$14$	0.0457566	+	0.0166540i	0.0122290	+	0.00445098i
$15$	−0.149173	+	0.00700221i	−0.0385163	+	0.00180796i
$16$	−3.18226	−	1.15825i	−0.795565	−	0.289562i
$17$	0.788265	−	2.16574i	0.191182	−	0.525269i	−0.806653	−	0.591025i	$-0.798724\pi$
$17$	0.788265	−	2.16574i	0.191182	−	0.525269i	0.997836	+	0.0657556i	$0.0209458\pi$
$18$	0.0780319	−	0.964581i	0.0183923	−	0.227354i
$19$	3.17839	+	2.98293i	0.729172	+	0.684331i
$19$	3.17839	+	2.98293i	0.729172	+	0.684331i
$20$	−0.141568	−	0.0817341i	−0.0316555	−	0.0182763i
$21$	0.158483	−	0.207945i	0.0345839	−	0.0453773i
$22$	0.358233	+	0.426925i	0.0763754	+	0.0910207i
$23$	5.13795	+	0.905959i	1.07134	+	0.188906i	0.681381	−	0.731928i	$-0.261379\pi$
$23$	5.13795	+	0.905959i	1.07134	+	0.188906i	0.389955	+	0.920834i	$0.372491\pi$
$24$	1.31946	−	1.73125i	0.269333	−	0.353391i
$25$	3.82453	+	3.20916i	0.764906	+	0.641832i
$26$	−0.658225	−	0.380026i	−0.129088	−	0.0745293i
$27$	−4.81991	−	1.94126i	−0.927592	−	0.373595i
$28$	0.268934	−	0.0978839i	0.0508237	−	0.0184983i
$29$	0.930382	−	5.27646i	0.172768	−	0.979814i	−0.767922	−	0.640544i	$-0.778709\pi$
$29$	0.930382	−	5.27646i	0.172768	−	0.979814i	0.940689	−	0.339270i	$-0.110180\pi$
$30$	0.0354100	−	0.0326611i	0.00646496	−	0.00596308i
$31$		−	0.157915i		−	0.0283625i	−0.999899	−	0.0141812i	$-0.995486\pi$
$31$		−	0.157915i		−	0.0283625i	0.999899	−	0.0141812i	$-0.00451418\pi$
$32$	3.38843	−	1.23329i	0.598995	−	0.218016i
$33$	2.76089	−	1.15420i	0.480608	−	0.200920i
$34$	0.254276	+	0.698619i	0.0436080	+	0.119812i
$35$	0.0128172	−	0.00226002i	0.00216650	−	0.000382013i
$36$	−3.29283	−	4.63775i	−0.548805	−	0.772958i
$37$			1.03696i			0.170475i	0.996361	+	0.0852374i	$0.0271649\pi$
$37$			1.03696i			0.170475i	−0.996361	+	0.0852374i	$0.972835\pi$
$38$	−1.40391	−	0.0780729i	−0.227745	−	0.0126651i
$39$	−2.99982	+	2.76694i	−0.480355	+	0.443065i
$40$	0.106710	−	0.0188159i	0.0168724	−	0.00297505i
$41$	3.23970	−	2.71843i	0.505957	−	0.424548i	−0.353747	−	0.935341i	$-0.615093\pi$
$41$	3.23970	−	2.71843i	0.505957	−	0.424548i	0.859704	+	0.510793i	$0.170648\pi$
$42$	0.00395453	+	0.0842463i	0.000610198	+	0.0129995i
$43$	−0.868665	−	4.92644i	−0.132470	−	0.751276i	−0.976588	−	0.215118i	$-0.930986\pi$
$43$	−0.868665	−	4.92644i	−0.132470	−	0.751276i	0.844118	−	0.536158i	$-0.180125\pi$
$44$	3.22582	+	0.568800i	0.486311	+	0.0857498i
$45$	−0.110846	−	0.233705i	−0.0165240	−	0.0348387i
$46$	−1.45748	+	0.841477i	−0.214894	+	0.124069i
$47$	−11.1068	−	1.95842i	−1.62009	−	0.285665i	−0.711290	−	0.702899i	$-0.751889\pi$
$47$	−11.1068	−	1.95842i	−1.62009	−	0.285665i	−0.908799	+	0.417233i	$0.863000\pi$
$48$	−0.275028	−	5.85912i	−0.0396969	−	0.845692i
$49$	3.48861	−	6.04244i	0.498372	−	0.863206i
$50$	−1.61049			−0.227757
$51$	3.98752	−	0.187175i	0.558365	−	0.0262098i
$52$	−4.39933	+	0.775721i	−0.610078	+	0.107573i
$53$	3.60211	+	3.02253i	0.494788	+	0.415176i	0.855738	−	0.517409i	$-0.173103\pi$
$53$	3.60211	+	3.02253i	0.494788	+	0.415176i	−0.360951	+	0.932585i	$0.617548\pi$
$54$	1.59356	−	0.519701i	0.216856	−	0.0707223i
$55$	0.139977	+	0.0509475i	0.0188745	+	0.00686977i
$56$	−0.0948529	+	0.164290i	−0.0126753	+	0.0219542i
$57$	−2.64345	+	7.07193i	−0.350134	+	0.936700i
$58$	0.864161	+	1.49677i	0.113470	+	0.196536i
$59$	−0.485489	−	2.75335i	−0.0632053	−	0.358455i	−0.999964	−	0.00847925i	$-0.997301\pi$
$59$	−0.485489	−	2.75335i	−0.0632053	−	0.358455i	0.936759	−	0.349976i	$-0.113810\pi$
$60$	0.0360377	−	0.280832i	0.00465245	−	0.0362553i
$61$	5.10362	−	1.85757i	0.653452	−	0.237837i	0.00604535	−	0.999982i	$-0.498076\pi$
$61$	5.10362	−	1.85757i	0.653452	−	0.237837i	0.647407	+	0.762145i	$0.275853\pi$
$62$	0.0327436	+	0.0390223i	0.00415844	+	0.00495583i
$63$	0.438178	+	0.114341i	0.0552053	+	0.0144056i
$64$	2.80490	−	4.85823i	0.350613	−	0.607279i
$65$	−0.203150			−0.0251977
$66$	−0.442917	+	0.857677i	−0.0545193	+	0.105573i
$67$	1.30076	−	1.55018i	0.158913	−	0.189385i	−0.680713	−	0.732550i	$-0.738330\pi$
$67$	1.30076	−	1.55018i	0.158913	−	0.189385i	0.839626	+	0.543165i	$0.182774\pi$
$68$	3.78422	+	2.18482i	0.458904	+	0.264949i
$69$	1.98471	+	8.81582i	0.238931	+	1.06130i
$70$	−0.00269863	+	0.00321610i	−0.000322548	+	0.000384398i
$71$	−10.6749	+	8.95732i	−1.26688	+	1.06304i	−0.271966	+	0.962307i	$0.587674\pi$
$71$	−10.6749	+	8.95732i	−1.26688	+	1.06304i	−0.994914	+	0.100731i	$0.967882\pi$
$72$	3.64807	+	0.951951i	0.429929	+	0.112188i
$73$	−0.405662	−	2.30062i	−0.0474791	−	0.269268i	0.951822	−	0.306652i	$-0.0992086\pi$
$73$	−0.405662	−	2.30062i	−0.0474791	−	0.269268i	−0.999301	+	0.0373840i	$0.988098\pi$
$74$	−0.215012	−	0.256241i	−0.0249946	−	0.0297874i
$75$	−2.57331	+	8.25562i	−0.297141	+	0.953276i
$76$	−6.61596	+	4.95243i	−0.758902	+	0.568083i
$77$	−0.225854	+	0.130397i	−0.0257385	+	0.0148601i
$78$	0.167559	−	1.30574i	0.0189723	−	0.147846i
$79$	−1.22472	+	3.36489i	−0.137792	+	0.378580i	−0.989326	−	0.145719i	$-0.953450\pi$
$79$	−1.22472	+	3.36489i	−0.137792	+	0.378580i	0.851534	+	0.524299i	$0.175673\pi$
$80$	0.187683	−	0.223672i	0.0209836	−	0.0250073i
$81$	−0.117807	−	8.99923i	−0.0130897	−	0.999914i
$82$	−0.236895	+	1.34350i	−0.0261606	+	0.148364i
$83$	−3.67729	+	2.12308i	−0.403635	+	0.233039i	−0.688051	−	0.725662i	$-0.741534\pi$
$83$	−3.67729	+	2.12308i	−0.403635	+	0.233039i	0.284416	+	0.958701i	$0.408200\pi$
$84$	0.336085	+	0.364372i	0.0366699	+	0.0397562i
$85$	0.152224	+	0.127731i	0.0165110	+	0.0138544i
$86$	1.23615	+	1.03725i	0.133297	+	0.111850i
$87$	9.05348	−	2.03822i	0.970635	−	0.218520i
$88$	−1.88036	+	1.08563i	−0.200447	+	0.115728i
$89$	−2.82275	+	16.0086i	−0.299211	+	1.69691i	0.350365	+	0.936613i	$0.386058\pi$
$89$	−2.82275	+	16.0086i	−0.299211	+	1.69691i	−0.649576	+	0.760297i	$0.725054\pi$
$90$	0.0758495	+	0.0347666i	0.00799524	+	0.00366473i
$91$	0.228619	−	0.272457i	0.0239657	−	0.0285612i
$92$	−3.38311	+	9.29500i	−0.352713	+	0.969071i
$93$	0.252353	−	0.105497i	0.0261678	−	0.0109395i
$94$	3.15065	−	1.81903i	0.324965	−	0.187619i
$95$	−0.335405	+	0.169550i	−0.0344118	+	0.0173955i
$96$	4.23450	+	4.59090i	0.432182	+	0.468556i
$97$	1.33420	+	1.59003i	0.135467	+	0.161443i	0.829513	−	0.558487i	$-0.188618\pi$
$97$	1.33420	+	1.59003i	0.135467	+	0.161443i	−0.694046	+	0.719931i	$0.744174\pi$
$98$	0.390828	+	2.21650i	0.0394796	+	0.223900i
$99$	3.68888	+	3.64090i	0.370746	+	0.365924i
$100$	−7.25109	+	6.08439i	−0.725109	+	0.608439i
$101$	8.78539	−	10.4700i	0.874179	−	1.04181i	−0.124591	−	0.992208i	$-0.539762\pi$
$101$	8.78539	−	10.4700i	0.874179	−	1.04181i	0.998769	−	0.0495973i	$-0.0157938\pi$
$102$	−0.946540	+	0.873060i	−0.0937215	+	0.0864458i
$103$	−13.2363	−	7.64196i	−1.30421	−	0.752985i	−0.323085	−	0.946370i	$-0.604720\pi$
$103$	−13.2363	−	7.64196i	−1.30421	−	0.752985i	−0.981123	+	0.193385i	$0.938053\pi$
$104$	1.90337	−	2.26835i	0.186641	−	0.222430i
$105$	0.0121742	+	0.0189724i	0.00118808	+	0.00185152i
$106$	−1.51683			−0.147327
$107$	−7.38383	+	12.7892i	−0.713822	+	1.23638i	0.249590	+	0.968352i	$0.419704\pi$
$107$	−7.38383	+	12.7892i	−0.713822	+	1.23638i	−0.963412	+	0.268025i	$0.913629\pi$
$108$	5.21144	−	8.36033i	0.501471	−	0.804473i
$109$	−6.64212	−	7.91577i	−0.636200	−	0.758193i	0.347565	−	0.937656i	$-0.387009\pi$
$109$	−6.64212	−	7.91577i	−0.636200	−	0.758193i	−0.983765	+	0.179463i	$0.942564\pi$
$110$	−0.0451535	+	0.0164345i	−0.00430521	+	0.00156697i
$111$	−1.65709	+	0.692751i	−0.157284	+	0.0657530i
$112$	0.0887676	+	0.503426i	0.00838775	+	0.0475693i
$113$	−6.25695	−	10.8374i	−0.588605	−	1.01949i	−0.994415	−	0.105536i	$-0.966344\pi$
$113$	−6.25695	−	10.8374i	−0.588605	−	1.01949i	0.405811	−	0.913957i	$-0.366989\pi$
$114$	−0.813135	−	2.29565i	−0.0761571	−	0.215007i
$115$	−0.224914	+	0.389562i	−0.0209733	+	0.0363269i
$116$	9.54558	+	3.47431i	0.886285	+	0.322581i
$117$	−6.42571	−	2.94531i	−0.594057	−	0.272294i
$118$	0.690871	+	0.579709i	0.0635998	+	0.0533666i
$119$	−0.342615	+	0.0604122i	−0.0314075	+	0.00553798i
$120$	0.101357	+	0.157956i	0.00925260	+	0.0144193i
$121$	8.01512			0.728647
$122$	−0.875985	+	1.51725i	−0.0793080	+	0.137365i
$123$	6.50845	+	3.36106i	0.586847	+	0.303057i
$124$	0.294850	+	0.0519901i	0.0264783	+	0.00466885i
$125$	−0.746132	+	0.430779i	−0.0667360	+	0.0385301i
$126$	−0.131986	+	0.0626010i	−0.0117583	+	0.00557694i
$127$	−12.2504	−	2.16007i	−1.08704	−	0.191675i	−0.398716	−	0.917075i	$-0.630544\pi$
$127$	−12.2504	−	2.16007i	−1.08704	−	0.191675i	−0.688328	+	0.725400i	$0.741655\pi$
$128$	1.56655	+	8.88432i	0.138464	+	0.785271i
$129$	7.29228	−	4.67931i	0.642049	−	0.411991i
$130$	0.0502002	−	0.0421230i	0.00440285	−	0.00369443i
$131$	6.56092	−	1.15687i	0.573230	−	0.101076i	0.120484	−	0.992715i	$-0.461555\pi$
$131$	6.56092	−	1.15687i	0.573230	−	0.101076i	0.452747	+	0.891639i	$0.350444\pi$
$132$	1.24609	+	5.53495i	0.108458	+	0.481756i
$133$	0.150060	−	0.640637i	0.0130118	−	0.0555503i
$134$			0.652773i			0.0563910i
$135$	0.299415	−	0.333265i	0.0257696	−	0.0286829i
$136$	−2.85245	+	0.502964i	−0.244596	+	0.0431288i
$137$	−4.28317	−	11.7679i	−0.365936	−	1.00540i	−0.976892	−	0.213735i	$-0.931437\pi$
$137$	−4.28317	−	11.7679i	−0.365936	−	1.00540i	0.610956	−	0.791665i	$-0.290785\pi$
$138$	−2.31839	−	1.76694i	−0.197354	−	0.150412i
$139$	13.5159	−	4.91940i	1.14641	−	0.417258i	0.302184	−	0.953250i	$-0.402284\pi$
$139$	13.5159	−	4.91940i	1.14641	−	0.417258i	0.844223	+	0.535992i	$0.180062\pi$
$140$			0.0246756i			0.00208547i
$141$	−4.29038	−	19.0573i	−0.361315	−	1.60491i
$142$	0.780575	−	4.42686i	0.0655044	−	0.371494i
$143$	3.82525	−	1.39228i	0.319883	−	0.116428i
$144$	9.17931	−	4.35375i	0.764943	−	0.362813i
$145$	0.400064	+	0.230977i	0.0332235	+	0.0191816i
$146$	0.577274	+	0.484390i	0.0477755	+	0.0400884i
$147$	11.9866	+	1.53818i	0.988638	+	0.126867i
$148$	−1.93615	−	0.341395i	−0.159150	−	0.0280625i
$149$	−4.31828	−	5.14633i	−0.353768	−	0.421604i	0.559585	−	0.828773i	$-0.310960\pi$
$149$	−4.31828	−	5.14633i	−0.353768	−	0.421604i	−0.913353	+	0.407169i	$0.866516\pi$
$150$	−1.07590	−	2.57361i	−0.0878471	−	0.210134i
$151$	4.36850	+	2.52215i	0.355503	+	0.205250i	0.667106	−	0.744962i	$-0.267533\pi$
$151$	4.36850	+	2.52215i	0.355503	+	0.205250i	−0.311603	+	0.950212i	$0.600866\pi$
$152$	1.24933	−	5.33365i	0.101334	−	0.432616i
$153$	2.96302	+	6.24713i	0.239546	+	0.505051i
$154$	0.0287729	−	0.0790528i	0.00231858	−	0.00637026i
$155$	0.0127944	+	0.00465676i	0.00102767	+	0.000374040i
$156$	−4.17864	−	6.51203i	−0.334559	−	0.521380i
$157$	−21.6123	−	7.86625i	−1.72485	−	0.627795i	−0.726610	−	0.687050i	$-0.758905\pi$
$157$	−21.6123	−	7.86625i	−1.72485	−	0.627795i	−0.998243	+	0.0592545i	$0.981128\pi$
$158$	−0.395067	−	1.08544i	−0.0314299	−	0.0863529i
$159$	−2.42366	+	7.77550i	−0.192209	+	0.616638i
$160$			0.310900i			0.0245788i
$161$	−0.269354	−	0.740045i	−0.0212281	−	0.0583237i
$162$	1.89509	+	2.19936i	0.148892	+	0.172798i
$163$	−3.90710	−	6.76730i	−0.306028	−	0.530056i	0.671462	−	0.741039i	$-0.265667\pi$
$163$	−3.90710	−	6.76730i	−0.306028	−	0.530056i	−0.977490	+	0.210983i	$0.932333\pi$
$164$	4.00910	+	6.94396i	0.313058	+	0.542232i
$165$	0.0120976	+	0.257724i	0.000941797	+	0.0200638i
$166$	0.468471	−	1.28711i	0.0363604	−	0.0998994i
$167$	−3.55086	+	20.1379i	−0.274774	+	1.55832i	0.464905	+	0.885361i	$0.346089\pi$
$167$	−3.55086	+	20.1379i	−0.274774	+	1.55832i	−0.739679	+	0.672960i	$0.765023\pi$
$168$	−0.325908	−	0.0418220i	−0.0251443	−	0.00322664i
$169$	5.70579	−	4.78773i	0.438907	−	0.368287i
$170$	−0.0641006			−0.00491629
$171$	−13.0671	+	0.500163i	−0.999268	+	0.0382484i
$172$	9.48435			0.723175
$173$	4.17762	−	3.50544i	0.317618	−	0.266513i	−0.470014	−	0.882659i	$-0.655751\pi$
$173$	4.17762	−	3.50544i	0.317618	−	0.266513i	0.787632	+	0.616146i	$0.211307\pi$
$174$	−1.81457	+	2.38089i	−0.137562	+	0.180495i
$175$	0.130866	−	0.742180i	0.00989257	−	0.0561036i
$176$	−2.00108	+	5.49793i	−0.150837	+	0.414422i
$177$	4.07559	−	2.61523i	0.306340	−	0.196572i
$178$	−2.62184	−	4.54116i	−0.196515	−	0.340374i
$179$	−7.16626	−	12.4123i	−0.535632	−	0.927741i	−0.999132	−	0.0416446i	$-0.986740\pi$
$179$	−7.16626	−	12.4123i	−0.535632	−	0.927741i	0.463501	−	0.886096i	$-0.346593\pi$
$180$	0.472854	−	0.130024i	0.0352444	−	0.00969139i
$181$	5.22208	+	14.3475i	0.388154	+	1.06644i	0.967832	+	0.251599i	$0.0809563\pi$
$181$	5.22208	+	14.3475i	0.388154	+	1.06644i	−0.579678	+	0.814846i	$0.696821\pi$
$182$			0.114730i			0.00850437i
$183$	6.37798	+	6.91477i	0.471474	+	0.511155i
$184$	−2.24252	−	6.16127i	−0.165321	−	0.454215i
$185$	−0.0840146	−	0.0305788i	−0.00617688	−	0.00224820i
$186$	−0.0404840	+	0.0783944i	−0.00296843	+	0.00574815i
$187$	−3.74171	−	1.36187i	−0.273621	−	0.0995899i
$188$	7.31330	−	20.0931i	0.533378	−	1.46544i
$189$	0.110009	+	0.776608i	0.00800200	+	0.0564899i
$190$	0.0477254	−	0.111443i	0.00346237	−	0.00808493i
$191$	−1.47331	−	0.850617i	−0.106605	−	0.0615485i	0.445750	−	0.895158i	$-0.352937\pi$
$191$	−1.47331	−	0.850617i	−0.106605	−	0.0615485i	−0.552355	+	0.833609i	$0.686271\pi$
$192$	9.63744	+	1.23672i	0.695522	+	0.0892527i
$193$	10.6727	+	12.7192i	0.768237	+	0.915549i	0.998339	−	0.0576178i	$-0.0183505\pi$
$193$	10.6727	+	12.7192i	0.768237	+	0.915549i	−0.230102	+	0.973166i	$0.573906\pi$
$194$	−0.659382	−	0.116267i	−0.0473409	−	0.00834748i
$195$	−0.135717	−	0.324640i	−0.00971887	−	0.0232480i
$196$	10.1335	+	8.50306i	0.723825	+	0.607361i
$197$	−19.5986	−	11.3153i	−1.39634	−	0.806179i	−0.402335	−	0.915492i	$-0.631801\pi$
$197$	−19.5986	−	11.3153i	−1.39634	−	0.806179i	−0.994007	+	0.109313i	$0.965135\pi$
$198$	−1.66649	−	0.134814i	−0.118432	−	0.00958083i
$199$	18.8242	−	6.85144i	1.33441	−	0.485686i	0.426363	−	0.904552i	$-0.359795\pi$
$199$	18.8242	−	6.85144i	1.33441	−	0.485686i	0.908048	+	0.418866i	$0.137572\pi$
$200$	1.08953	−	6.17905i	0.0770416	−	0.436925i
$201$	3.34622	+	1.04303i	0.236024	+	0.0735698i
$202$			4.40887i			0.310207i
$203$	−0.759995	+	0.276616i	−0.0533412	+	0.0194146i
$204$	−0.963319	+	7.50689i	−0.0674458	+	0.525587i
$205$	0.124713	+	0.342645i	0.00871031	+	0.0239314i
$206$	4.85534	−	0.856128i	0.338288	−	0.0596493i
$207$	−12.7620	+	9.06113i	−0.887023	+	0.629792i
$208$		−	7.97921i		−	0.553258i
$209$	5.15355	−	5.49124i	0.356479	−	0.379837i
$210$	−0.00694227	−	0.00216394i	−0.000479062	−	0.000149326i
$211$	−4.16483	+	0.734372i	−0.286719	+	0.0505563i	−0.315158	−	0.949039i	$-0.602057\pi$
$211$	−4.16483	+	0.734372i	−0.286719	+	0.0505563i	0.0284390	+	0.999596i	$0.490946\pi$
$212$	−6.82940	+	5.73054i	−0.469045	+	0.393575i
$213$	−21.4455	−	11.0748i	−1.46942	−	0.758832i
$214$	−0.827210	−	4.69134i	−0.0565469	−	0.320694i
$215$	0.424758	+	0.0748963i	0.0289682	+	0.00510788i
$216$	0.915886	+	6.46568i	0.0623182	+	0.439934i
$217$	−0.0206438	+	0.0119187i	−0.00140139	+	0.000809094i
$218$	3.28265	+	0.578819i	0.222329	+	0.0392026i
$219$	3.40546	−	2.18521i	0.230119	−	0.147663i
$220$	−0.141211	+	0.244584i	−0.00952041	+	0.0164898i
$221$	5.43038			0.365287
$222$	0.265840	−	0.514780i	0.0178420	−	0.0345498i
$223$	−3.70129	+	0.652637i	−0.247857	+	0.0437038i	−0.296196	−	0.955127i	$-0.595718\pi$
$223$	−3.70129	+	0.652637i	−0.247857	+	0.0437038i	0.0483394	+	0.998831i	$0.484607\pi$
$224$	−0.416966	−	0.349876i	−0.0278597	−	0.0233771i
$225$	−14.9118	+	1.40302i	−0.994123	+	0.0935347i
$226$	3.79326	+	1.38063i	0.252324	+	0.0918383i
$227$	−9.58934	+	16.6092i	−0.636467	+	1.10239i	0.349736	+	0.936848i	$0.386271\pi$
$227$	−9.58934	+	16.6092i	−0.636467	+	1.10239i	−0.986202	+	0.165544i	$0.947062\pi$
$228$	−12.3340	−	7.26397i	−0.816838	−	0.481068i
$229$	5.98108	+	10.3595i	0.395241	+	0.684577i	0.993132	−	0.117000i	$-0.0373278\pi$
$229$	5.98108	+	10.3595i	0.395241	+	0.684577i	−0.597891	+	0.801577i	$0.703994\pi$
$230$	−0.0251971	−	0.142900i	−0.00166145	−	0.00942253i
$231$	−0.359263	−	0.273809i	−0.0236377	−	0.0180153i
$232$	−6.32737	+	2.30297i	−0.415412	+	0.151198i
$233$	10.9340	+	13.0306i	0.716309	+	0.853664i	0.994267	−	0.106929i	$-0.0341019\pi$
$233$	10.9340	+	13.0306i	0.716309	+	0.853664i	−0.277957	+	0.960593i	$0.589657\pi$
$234$	2.19855	−	0.604550i	0.143724	−	0.0395207i
$235$	0.486199	−	0.842122i	0.0317161	−	0.0549340i
$236$	5.30072			0.345047
$237$	−6.19539	+	0.290813i	−0.402434	+	0.0188903i
$238$	0.0721366	−	0.0859691i	0.00467592	−	0.00557255i
$239$	−11.7291	−	6.77179i	−0.758692	−	0.438031i	0.0701341	−	0.997538i	$-0.477657\pi$
$239$	−11.7291	−	6.77179i	−0.758692	−	0.438031i	−0.828826	+	0.559507i	$0.810991\pi$
$240$	0.482818	+	0.150497i	0.0311658	+	0.00971451i
$241$	−9.44271	+	11.2534i	−0.608259	+	0.724894i	−0.979004	−	0.203840i	$-0.934658\pi$
$241$	−9.44271	+	11.2534i	−0.608259	+	0.724894i	0.370746	+	0.928734i	$0.379102\pi$
$242$	−1.98060	+	1.66192i	−0.127318	+	0.106832i
$243$	14.3023	−	6.20029i	0.917494	−	0.397749i
$244$	1.78809	+	10.1407i	0.114471	+	0.649195i
$245$	0.386685	+	0.460833i	0.0247044	+	0.0294416i
$246$	−2.30521	+	0.518972i	−0.146975	+	0.0330884i
$247$	−4.04313	+	9.44107i	−0.257258	+	0.600721i
$248$	−0.171871	+	0.0992296i	−0.0109138	+	0.00630108i
$249$	−5.84940	−	4.45807i	−0.370691	−	0.282518i
$250$	0.0950540	−	0.261159i	0.00601174	−	0.0165171i
$251$	13.8093	−	16.4573i	0.871638	−	1.03878i	−0.127261	−	0.991869i	$-0.540619\pi$
$251$	13.8093	−	16.4573i	0.871638	−	1.03878i	0.998899	−	0.0469085i	$-0.0149369\pi$
$252$	−0.357751	+	0.780496i	−0.0225362	+	0.0491666i
$253$	1.56521	−	8.87674i	0.0984038	−	0.558076i
$254$	3.47506	−	2.00632i	0.218044	−	0.125888i
$255$	−0.102423	+	0.328590i	−0.00641397	+	0.0205771i
$256$	6.36546	+	5.34125i	0.397841	+	0.333828i
$257$	19.0745	+	16.0054i	1.18984	+	0.998391i	0.999862	+	0.0166022i	$0.00528490\pi$
$257$	19.0745	+	16.0054i	1.18984	+	0.998391i	0.189974	+	0.981789i	$0.439160\pi$
$258$	−0.831735	+	2.66834i	−0.0517815	+	0.166124i
$259$	0.135558	−	0.0782646i	0.00842318	−	0.00486313i
$260$	0.0668826	−	0.379310i	0.00414788	−	0.0235238i
$261$	9.30540	+	13.1061i	0.575990	+	0.811246i
$262$	−1.38138	+	1.64627i	−0.0853422	+	0.101707i
$263$	−4.24298	+	11.6575i	−0.261633	+	0.718832i	0.737424	+	0.675430i	$0.236042\pi$
$263$	−4.24298	+	11.6575i	−0.261633	+	0.718832i	−0.999058	+	0.0434019i	$0.986180\pi$
$264$	−2.99105	−	2.27960i	−0.184087	−	0.140300i
$265$	−0.351108	+	0.202713i	−0.0215684	+	0.0124525i
$266$	0.0957543	+	0.189422i	0.00587107	+	0.0116142i
$267$	−27.4680	+	6.18388i	−1.68101	+	0.378448i
$268$	2.46616	+	2.93906i	0.150645	+	0.179532i
$269$	−3.68997	−	20.9268i	−0.224981	−	1.27593i	−0.862721	−	0.505680i	$-0.831242\pi$
$269$	−3.68997	−	20.9268i	−0.224981	−	1.27593i	0.637740	−	0.770252i	$-0.279869\pi$
$270$	−0.00488606	+	0.144436i	−0.000297356	+	0.00879009i
$271$	−16.4641	+	13.8150i	−1.00012	+	0.839204i	−0.987002	−	0.160710i	$-0.948622\pi$
$271$	−16.4641	+	13.8150i	−1.00012	+	0.839204i	−0.0131225	+	0.999914i	$0.504177\pi$
$272$	−5.01693	+	5.97894i	−0.304196	+	0.362527i
$273$	0.588125	+	0.183321i	0.0355949	+	0.0110951i
$274$	3.49847	+	2.01984i	0.211350	+	0.122023i
$275$	5.54441	−	6.60757i	0.334340	−	0.398451i
$276$	−17.1138	+	0.803325i	−1.03013	+	0.0483545i
$277$	11.3297			0.680735			0.340367	−	0.940293i	$-0.389449\pi$
$277$	11.3297			0.680735			0.340367	+	0.940293i	$0.389449\pi$
$278$	−2.31987	+	4.01814i	−0.139137	+	0.240992i
$279$	0.337175	+	0.332790i	0.0201861	+	0.0199236i
$280$	−0.0105137	−	0.0125297i	−0.000628314	−	0.000748796i
$281$	28.1095	−	10.2310i	1.67687	−	0.610332i	0.683997	−	0.729485i	$-0.260240\pi$
$281$	28.1095	−	10.2310i	1.67687	−	0.610332i	0.992876	+	0.119154i	$0.0380181\pi$
$282$	5.01169	+	3.81961i	0.298442	+	0.227455i
$283$	4.84259	+	27.4637i	0.287862	+	1.63255i	0.694878	+	0.719127i	$0.255458\pi$
$283$	4.84259	+	27.4637i	0.287862	+	1.63255i	−0.407016	+	0.913421i	$0.633431\pi$
$284$	−13.2101	−	22.8806i	−0.783875	−	1.35771i
$285$	−0.495017	−	0.422717i	−0.0293223	−	0.0250396i
$286$	−0.656564	+	1.13720i	−0.0388235	+	0.0672442i
$287$	−0.599889	−	0.218342i	−0.0354104	−	0.0128883i
$288$	−4.50748	+	9.83385i	−0.265606	+	0.579465i
$289$	8.95369	+	7.51304i	0.526687	+	0.441943i
$290$	−0.146752	+	0.0258763i	−0.00861757	+	0.00151951i
$291$	−1.64959	+	3.19432i	−0.0967009	+	0.187254i
$292$	4.42914			0.259196
$293$	0.816749	−	1.41465i	0.0477150	−	0.0826448i	−0.841182	−	0.540753i	$-0.818139\pi$
$293$	0.816749	−	1.41465i	0.0477150	−	0.0826448i	0.888896	+	0.458108i	$0.151473\pi$
$294$	−3.28093	+	2.10531i	−0.191348	+	0.122784i
$295$	0.237393	+	0.0418588i	0.0138216	+	0.00243712i
$296$	1.12860	−	0.651595i	0.0655983	−	0.0378732i
$297$	−3.35387	+	8.32727i	−0.194611	+	0.483197i
$298$	2.13417	+	0.376312i	0.123629	+	0.0217991i
$299$	2.13461	+	12.1060i	0.123448	+	0.700106i
$300$	−14.5672	−	7.52271i	−0.841037	−	0.434324i
$301$	−0.578456	+	0.485382i	−0.0333416	+	0.0279770i
$302$	−1.60246	+	0.282557i	−0.0922111	+	0.0162593i
$303$	22.6006	+	7.04470i	1.29837	+	0.404707i
$304$	−6.65948	−	13.1738i	−0.381947	−	0.755570i
$305$			0.468275i			0.0268133i
$306$	−2.02752	−	0.929342i	−0.115906	−	0.0531269i
$307$	25.4595	−	4.48919i	1.45305	−	0.256212i	0.609296	−	0.792943i	$-0.291452\pi$
$307$	25.4595	−	4.48919i	1.45305	−	0.256212i	0.843753	+	0.536731i	$0.180341\pi$
$308$	−0.169112	−	0.464632i	−0.00963607	−	0.0264749i
$309$	3.36945	−	26.2572i	0.191681	−	1.49372i
$310$	−0.00412717	+	0.00150217i	−0.000234407	+	8.53173e-5i
$311$			15.5145i			0.879746i	0.898060	+	0.439873i	$0.144977\pi$
$311$			15.5145i			0.879746i	−0.898060	+	0.439873i	$0.855023\pi$
$312$	4.89646	+	1.52625i	0.277207	+	0.0864068i
$313$	−1.21737	+	6.90405i	−0.0688098	+	0.390240i	0.930880	+	0.365326i	$0.119042\pi$
$313$	−1.21737	+	6.90405i	−0.0688098	+	0.390240i	−0.999690	+	0.0249142i	$0.992069\pi$
$314$	6.97165	−	2.53747i	0.393433	−	0.143198i
$315$	−0.0221854	+	0.0321295i	−0.00125000	+	0.00181029i
$316$	−5.87952	−	3.39454i	−0.330749	−	0.190958i
$317$	−7.73472	−	6.49020i	−0.434425	−	0.364526i	0.399193	−	0.916867i	$-0.369290\pi$
$317$	−7.73472	−	6.49020i	−0.434425	−	0.364526i	−0.833618	+	0.552341i	$0.813735\pi$
$318$	−1.01333	−	2.42394i	−0.0568249	−	0.135928i
$319$	−9.11604	−	1.60740i	−0.510400	−	0.0899973i
$320$	0.310902	+	0.370518i	0.0173799	+	0.0207126i
$321$	−25.3703	−	3.25564i	−1.41603	−	0.181712i
$322$	0.220007	+	0.127021i	0.0122605	+	0.00707861i
$323$	8.96566	−	4.53222i	0.498863	−	0.252179i
$324$	16.8416	+	2.74283i	0.935645	+	0.152379i
$325$	−4.02333	+	11.0540i	−0.223174	+	0.613165i
$326$	2.36867	+	0.862125i	0.131188	+	0.0477487i
$327$	8.21229	−	15.9025i	0.454141	−	0.879411i
$328$	−4.99440	−	1.81781i	−0.275770	−	0.100372i
$329$	0.582267	+	1.59977i	0.0321014	+	0.0881979i
$330$	−0.0564281	−	0.0611773i	−0.00310626	−	0.00336770i
$331$		−	9.42992i		−	0.518316i	−0.965835	−	0.259158i	$-0.916555\pi$
$331$		−	9.42992i		−	0.518316i	0.965835	−	0.259158i	$-0.0834450\pi$
$332$	−2.75343	−	7.56499i	−0.151114	−	0.415183i
$333$	−2.21407	−	2.18528i	−0.121330	−	0.119752i
$334$	−3.29813	−	5.71252i	−0.180465	−	0.312575i
$335$	0.0872382	+	0.151101i	0.00476633	+	0.00825553i
$336$	−0.745187	+	0.478172i	−0.0406533	+	0.0260864i
$337$	6.09916	−	16.7573i	0.332242	−	0.912828i	−0.655285	−	0.755382i	$-0.727452\pi$
$337$	6.09916	−	16.7573i	0.332242	−	0.912828i	0.987527	−	0.157447i	$-0.0503262\pi$
$338$	−0.417221	+	2.36618i	−0.0226938	+	0.128703i
$339$	13.1384	−	17.2388i	0.713579	−	0.936283i
$340$	−0.288608	+	0.242171i	−0.0156519	+	0.0131335i
$341$	−0.272828			−0.0147744
$342$	3.12529	−	2.83305i	0.168996	−	0.153194i
$343$	−2.10987			−0.113922
$344$	−4.81596	+	4.04107i	−0.259659	+	0.217880i
$345$	−0.772787	−	0.0991677i	−0.0416055	−	0.00533901i
$346$	−0.305477	+	1.73245i	−0.0164225	+	0.0931369i
$347$	−2.73316	+	7.50929i	−0.146724	+	0.403120i	−0.991183	−	0.132500i	$-0.957700\pi$
$347$	−2.73316	+	7.50929i	−0.146724	+	0.403120i	0.844459	+	0.535620i	$0.179922\pi$
$348$	0.824981	+	17.5752i	0.0442236	+	0.942127i
$349$	5.01110	+	8.67948i	0.268238	+	0.464602i	0.968407	−	0.249375i	$-0.0802253\pi$
$349$	5.01110	+	8.67948i	0.268238	+	0.464602i	−0.700169	+	0.713977i	$0.746892\pi$
$350$	0.121552	+	0.210534i	0.00649722	+	0.0112535i
$351$	0.413930	−	12.2361i	0.0220939	−	0.653115i
$352$	−2.13073	−	5.85413i	−0.113568	−	0.312026i
$353$		−	5.84678i		−	0.311193i	−0.987821	−	0.155596i	$-0.950270\pi$
$353$		−	5.84678i		−	0.311193i	0.987821	−	0.155596i	$-0.0497299\pi$
$354$	−0.464849	+	1.49131i	−0.0247064	+	0.0792624i
$355$	−0.410932	−	1.12903i	−0.0218100	−	0.0599225i
$356$	−28.9610	−	10.5409i	−1.53493	−	0.558669i
$357$	−0.325428	−	0.507149i	−0.0172235	−	0.0268412i
$358$	4.34452	+	1.58128i	0.229615	+	0.0835731i
$359$	9.59683	−	26.3671i	0.506501	−	1.39160i	−0.378322	−	0.925674i	$-0.623499\pi$
$359$	9.59683	−	26.3671i	0.506501	−	1.39160i	0.884824	−	0.465926i	$-0.154279\pi$
$360$	−0.184705	+	0.267496i	−0.00973481	+	0.0140983i
$361$	1.20427	+	18.9618i	0.0633829	+	0.997989i
$362$	−4.26536	−	2.46261i	−0.224183	−	0.129432i
$363$	5.35458	+	12.8084i	0.281043	+	0.672266i
$364$	0.433448	+	0.516563i	0.0227188	+	0.0270753i
$365$	0.198360	+	0.0349762i	0.0103826	+	0.00183074i
$366$	−3.00982	−	0.386234i	−0.157326	−	0.0201888i
$367$	−21.7260	−	18.2303i	−1.13409	−	0.951615i	−0.134861	−	0.990865i	$-0.543059\pi$
$367$	−21.7260	−	18.2303i	−1.13409	−	0.951615i	−0.999229	+	0.0392499i	$0.987503\pi$
$368$	−15.3010	−	8.83402i	−0.797618	−	0.460505i
$369$	−1.02303	+	12.6461i	−0.0532570	+	0.658329i
$370$	0.0271012	−	0.00986403i	0.00140892	−	0.000512807i
$371$	0.123256	−	0.699018i	0.00639912	−	0.0362912i
$372$	0.113896	+	0.505912i	0.00590524	+	0.0262303i
$373$		−	27.1009i		−	1.40323i	−0.712556	−	0.701615i	$-0.752463\pi$
$373$		−	27.1009i		−	1.40323i	0.712556	−	0.701615i	$-0.247537\pi$
$374$	1.20699	−	0.439309i	0.0624120	−	0.0227161i
$375$	−1.18686	−	0.904553i	−0.0612891	−	0.0467109i
$376$	4.84769	+	13.3189i	0.250000	+	0.686870i
$377$	12.4323	−	2.19215i	0.640297	−	0.112902i
$378$	−0.188213	−	0.169096i	−0.00968063	−	0.00869737i
$379$		−	33.2252i		−	1.70666i	−0.521369	−	0.853331i	$-0.674578\pi$
$379$		−	33.2252i		−	1.70666i	0.521369	−	0.853331i	$-0.325422\pi$
$380$	−0.206150	−	0.682069i	−0.0105752	−	0.0349894i
$381$	−4.73213	−	21.0195i	−0.242434	−	1.07686i
$382$	0.540442	−	0.0952945i	0.0276514	−	0.00487569i
$383$	6.34489	−	5.32400i	0.324209	−	0.272044i	−0.466126	−	0.884718i	$-0.654351\pi$
$383$	6.34489	−	5.32400i	0.324209	−	0.272044i	0.790335	+	0.612675i	$0.209906\pi$
$384$	−13.1509	+	8.43865i	−0.671102	+	0.430633i
$385$	−0.00390460	−	0.0221441i	−0.000198997	−	0.00112857i
$386$	−5.27462	−	0.930058i	−0.268471	−	0.0473387i
$387$	12.3494	+	8.52721i	0.627753	+	0.433462i
$388$	−3.40807	+	1.96765i	−0.173018	+	0.0998922i
$389$	−13.4798	−	2.37684i	−0.683451	−	0.120511i	−0.178867	−	0.983873i	$-0.557243\pi$
$389$	−13.4798	−	2.37684i	−0.683451	−	0.120511i	−0.504584	+	0.863363i	$0.668354\pi$
$390$	0.100850	+	0.0520807i	0.00510676	+	0.00263721i
$391$	6.01214	−	10.4133i	0.304047	−	0.526625i
$392$	−8.76856			−0.442879
$393$	6.23180	+	9.71168i	0.314353	+	0.489890i
$394$	7.18919	−	1.26765i	0.362186	−	0.0638632i
$395$	−0.236509	−	0.198455i	−0.0119001	−	0.00998533i
$396$	−8.01255	+	5.68896i	−0.402646	+	0.285881i
$397$	10.1988	+	3.71207i	0.511864	+	0.186303i	0.585023	−	0.811017i	$-0.301086\pi$
$397$	10.1988	+	3.71207i	0.511864	+	0.186303i	−0.0731584	+	0.997320i	$0.523308\pi$
$398$	−3.23098	+	5.59622i	−0.161954	+	0.280513i
$399$	1.12401	−	0.188185i	0.0562707	−	0.00942103i
$400$	−8.45364	−	14.6421i	−0.422682	−	0.732107i
$401$	1.36403	+	7.73580i	0.0681164	+	0.386307i	0.999738	+	0.0228782i	$0.00728299\pi$
$401$	1.36403	+	7.73580i	0.0681164	+	0.386307i	−0.931622	+	0.363429i	$0.881606\pi$
$402$	−1.04315	+	0.436092i	−0.0520276	+	0.0217503i
$403$	0.349639	−	0.127258i	0.0174168	−	0.00633919i
$404$	16.6566	+	19.8506i	0.828697	+	0.987602i
$405$	0.732594	+	0.255833i	0.0364029	+	0.0127125i
$406$	0.130445	−	0.225938i	0.00647390	−	0.0112131i
$407$	1.79153			0.0888030
$408$	−2.70936	−	4.22229i	−0.134133	−	0.209035i
$409$	−16.1350	+	19.2289i	−0.797822	+	0.950808i	−0.999590	−	0.0286256i	$-0.990887\pi$
$409$	−16.1350	+	19.2289i	−0.797822	+	0.950808i	0.201768	+	0.979433i	$0.435331\pi$
$410$	−0.101865	−	0.0588116i	−0.00503074	−	0.00290450i
$411$	15.9440	−	14.7063i	0.786461	−	0.725408i
$412$	18.6264	−	22.1980i	0.917655	−	1.09362i
$413$	−0.323294	+	0.271276i	−0.0159082	+	0.0133486i
$414$	1.27479	−	4.88527i	0.0626527	−	0.240098i
$415$	−0.0635734	−	0.360543i	−0.00312069	−	0.0176983i
$416$	5.46122	+	6.50843i	0.267758	+	0.319102i
$417$	16.8908	+	18.3124i	0.827146	+	0.896762i
$418$	−0.134885	+	2.42551i	−0.00659745	+	0.118636i
$419$	12.1917	−	7.03889i	0.595605	−	0.343872i	−0.171706	−	0.985148i	$-0.554928\pi$
$419$	12.1917	−	7.03889i	0.595605	−	0.343872i	0.767310	+	0.641276i	$0.221595\pi$
$420$	−0.0394323	+	0.0164848i	−0.00192410	+	0.000804375i
$421$	0.887017	−	2.43706i	0.0432306	−	0.118775i	−0.916199	−	0.400724i	$-0.868759\pi$
$421$	0.887017	−	2.43706i	0.0432306	−	0.118775i	0.959429	+	0.281949i	$0.0909809\pi$
$422$	0.876894	−	1.04504i	0.0426866	−	0.0508719i
$423$	27.5879	−	19.5876i	1.34137	−	0.952380i
$424$	1.02617	−	5.81970i	0.0498352	−	0.282630i
$425$	9.96495	−	5.75326i	0.483371	−	0.279074i
$426$	7.59572	−	1.71003i	0.368014	−	0.0828511i
$427$	−0.628031	−	0.526981i	−0.0303925	−	0.0255024i
$428$	−21.4482	−	17.9972i	−1.03674	−	0.869927i
$429$	4.78039	+	5.18273i	0.230799	+	0.250224i
$430$	−0.120491	+	0.0695655i	−0.00581059	+	0.00335474i
$431$	−4.59656	+	26.0684i	−0.221409	+	1.25567i	0.648024	+	0.761620i	$0.275596\pi$
$431$	−4.59656	+	26.0684i	−0.221409	+	1.25567i	−0.869433	+	0.494051i	$0.835516\pi$
$432$	13.0898	+	11.7602i	0.629781	+	0.565815i
$433$	−21.4572	+	25.5717i	−1.03117	+	1.22890i	−0.0581179	+	0.998310i	$0.518510\pi$
$433$	−21.4572	+	25.5717i	−1.03117	+	1.22890i	−0.973051	+	0.230590i	$0.925935\pi$
$434$	0.00262993	−	0.00722567i	0.000126241	−	0.000346843i
$435$	−0.101841	+	0.793620i	−0.00488291	+	0.0380512i
$436$	16.9666	−	9.79568i	0.812554	−	0.469128i
$437$	13.6280	+	18.2056i	0.651914	+	0.870893i
$438$	−0.388416	+	1.24610i	−0.0185592	+	0.0595410i
$439$	−9.82602	−	11.7102i	−0.468970	−	0.558897i	0.478770	−	0.877940i	$-0.341083\pi$
$439$	−9.82602	−	11.7102i	−0.468970	−	0.558897i	−0.947740	+	0.319043i	$0.896638\pi$
$440$	−0.0325079	−	0.184361i	−0.00154975	−	0.00878907i
$441$	5.54972	+	20.1825i	0.264272	+	0.961073i
$442$	−1.34189	+	1.12598i	−0.0638274	+	0.0535575i
$443$	−20.5463	+	24.4861i	−0.976183	+	1.16337i	0.0103733	+	0.999946i	$0.496698\pi$
$443$	−20.5463	+	24.4861i	−0.976183	+	1.16337i	−0.986556	+	0.163423i	$0.947746\pi$
$444$	−0.747904	−	3.32209i	−0.0354939	−	0.157659i
$445$	−1.21378	−	0.700778i	−0.0575388	−	0.0332200i
$446$	0.779297	−	0.928730i	0.0369008	−	0.0439766i
$447$	5.33911	−	10.3388i	0.252531	−	0.489008i
$448$	−0.846802			−0.0400076
$449$	−5.22655	+	9.05266i	−0.246656	+	0.427221i	−0.962596	−	0.270941i	$-0.912665\pi$
$449$	−5.22655	+	9.05266i	−0.246656	+	0.427221i	0.715940	+	0.698162i	$0.245999\pi$
$450$	3.39393	−	3.43865i	0.159991	−	0.162099i
$451$	−4.69659	−	5.59718i	−0.221154	−	0.263561i
$452$	22.2948	−	8.11465i	1.04866	−	0.381681i
$453$	−1.11205	+	8.66593i	−0.0522488	+	0.407161i
$454$	−1.07429	−	6.09262i	−0.0504190	−	0.285941i
$455$	0.0153328	+	0.0265572i	0.000718813	+	0.00124502i
$456$	9.35795	−	1.56674i	0.438226	−	0.0733694i
$457$	−10.6919	+	18.5189i	−0.500146	+	0.866278i	0.499854	+	0.866109i	$0.333387\pi$
$457$	−10.6919	+	18.5189i	−0.500146	+	0.866278i	−1.00000		0.000168214i	$0.999946\pi$
$458$	−3.62601	−	1.31976i	−0.169432	−	0.0616683i
$459$	−8.00362	+	8.90845i	−0.373577	+	0.415811i
$460$	−0.653319	−	0.548200i	−0.0304612	−	0.0255600i
$461$	29.0219	−	5.11734i	1.35168	−	0.238338i	0.549538	−	0.835468i	$-0.314804\pi$
$461$	29.0219	−	5.11734i	1.35168	−	0.238338i	0.802144	+	0.597130i	$0.203692\pi$
$462$	0.145551	−	0.00683218i	0.00677163	−	0.000317862i
$463$	11.3288			0.526493			0.263246	−	0.964729i	$-0.415207\pi$
$463$	11.3288			0.526493			0.263246	+	0.964729i	$0.415207\pi$
$464$	−9.07217	+	15.7135i	−0.421165	+	0.729479i
$465$	0.00110576	+	0.0235567i	5.12783e−5	+	0.00109242i
$466$	−5.40376	−	0.952829i	−0.250324	−	0.0441389i
$467$	−25.8398	+	14.9186i	−1.19572	+	0.690352i	−0.959599	−	0.281370i	$-0.909211\pi$
$467$	−25.8398	+	14.9186i	−1.19572	+	0.690352i	−0.236126	+	0.971723i	$0.575878\pi$
$468$	7.61482	−	11.0280i	0.351995	−	0.509770i
$469$	−0.300825	−	0.0530436i	−0.0138908	−	0.00244933i
$470$	0.0544689	+	0.308908i	0.00251246	+	0.0142489i
$471$	−1.86786	−	39.7923i	−0.0860663	−	1.83353i
$472$	−2.69159	+	2.25852i	−0.123891	+	0.103957i
$473$	−8.51133	+	1.50078i	−0.391351	+	0.0690058i
$474$	1.47063	−	1.35647i	0.0675484	−	0.0623046i
$475$	2.58313	+	21.6082i	0.118522	+	0.991454i
$476$		−	0.659599i		−	0.0302327i
$477$	−14.0446	+	1.32143i	−0.643059	+	0.0605040i
$478$	4.30248	−	0.758643i	0.196791	−	0.0346995i
$479$	9.82162	+	26.9847i	0.448761	+	1.23296i	0.933587	+	0.358350i	$0.116661\pi$
$479$	9.82162	+	26.9847i	0.448761	+	1.23296i	−0.484826	+	0.874611i	$0.661117\pi$
$480$	−0.496827	+	0.207700i	−0.0226769	+	0.00948016i
$481$	−2.29592	+	0.835647i	−0.104685	+	0.0381022i
$482$		−	4.73874i		−	0.215844i
$483$	1.00267	−	0.924831i	0.0456230	−	0.0420813i
$484$	−2.63879	+	14.9653i	−0.119945	+	0.680243i
$485$	−0.168169	+	0.0612085i	−0.00763616	+	0.00277933i
$486$	−2.24860	+	4.49771i	−0.101999	+	0.204020i
$487$	−27.4668	−	15.8580i	−1.24464	−	0.718592i	−0.274604	−	0.961558i	$-0.588547\pi$
$487$	−27.4668	−	15.8580i	−1.24464	−	0.718592i	−0.970035	+	0.242965i	$0.921880\pi$
$488$	−5.22870	−	4.38740i	−0.236692	−	0.198608i
$489$	8.20416	−	10.7646i	0.371005	−	0.486793i
$490$	−0.191106	−	0.0336972i	−0.00863330	−	0.00152228i
$491$	−23.4935	−	27.9984i	−1.06025	−	1.26355i	−0.963347	−	0.268257i	$-0.913552\pi$
$491$	−23.4935	−	27.9984i	−1.06025	−	1.26355i	−0.0968982	−	0.995294i	$-0.530892\pi$
$492$	−8.41833	+	11.0456i	−0.379528	+	0.497976i
$493$	−10.6940	−	6.17421i	−0.481636	−	0.278073i
$494$	−0.958501	−	3.17131i	−0.0431250	−	0.142684i
$495$	−0.403768	+	0.191507i	−0.0181480	+	0.00860761i
$496$	−0.182905	+	0.502528i	−0.00821269	+	0.0225642i
$497$	1.97665	+	0.719443i	0.0886650	+	0.0322714i
$498$	2.36981	−	0.111239i	0.106194	−	0.00498475i
$499$	−15.2044	−	5.53395i	−0.680643	−	0.247734i	−0.0215192	−	0.999768i	$-0.506850\pi$
$499$	−15.2044	−	5.53395i	−0.680643	−	0.247734i	−0.659123	+	0.752035i	$0.729073\pi$
$500$	−0.558679	−	1.53496i	−0.0249849	−	0.0686454i
$501$	−34.5532	+	7.77898i	−1.54372	+	0.347539i
$502$			6.93010i			0.309305i
$503$	9.45909	+	25.9886i	0.421760	+	1.15878i	0.950699	+	0.310116i	$0.100368\pi$
$503$	9.45909	+	25.9886i	0.421760	+	1.15878i	−0.528939	+	0.848660i	$0.677410\pi$
$504$	−0.150893	−	0.548749i	−0.00672132	−	0.0244432i
$505$	0.589211	+	1.02054i	0.0262196	+	0.0454136i
$506$	1.45380	+	2.51806i	0.0646295	+	0.111942i
$507$	11.4627	+	5.91953i	0.509078	+	0.262895i
$508$	8.06630	−	22.1620i	0.357884	−	0.983279i
$509$	−6.22984	+	35.3312i	−0.276133	+	1.56603i	0.459207	+	0.888329i	$0.348134\pi$
$509$	−6.22984	+	35.3312i	−0.276133	+	1.56603i	−0.735340	+	0.677698i	$0.762978\pi$
$510$	−0.0428231	−	0.102435i	−0.00189624	−	0.00453588i
$511$	−0.270136	+	0.226671i	−0.0119501	+	0.0100273i
$512$	−20.7232			−0.915845
$513$	−9.52890	−	20.5475i	−0.420711	−	0.907195i
$514$	−8.03218			−0.354284
$515$	1.00948	−	0.847052i	0.0444829	−	0.0373256i
$516$	6.33612	+	15.1563i	0.278932	+	0.667217i
$517$	−3.38353	+	19.1890i	−0.148808	+	0.843930i
$518$	−0.0172695	+	0.0474477i	−0.000758780	+	0.00208473i
$519$	8.39269	+	4.33411i	0.368398	+	0.190246i
$520$	0.127654	+	0.221103i	0.00559799	+	0.00969601i
$521$	11.5657	+	20.0324i	0.506704	+	0.877637i	0.999970	+	0.00775847i	$0.00246962\pi$
$521$	11.5657	+	20.0324i	0.506704	+	0.877637i	−0.493266	+	0.869879i	$0.664197\pi$
$522$	−5.01697	−	1.30916i	−0.219587	−	0.0573004i
$523$	−1.11987	−	3.07682i	−0.0489685	−	0.134540i	0.912797	−	0.408413i	$-0.133918\pi$
$523$	−1.11987	−	3.07682i	−0.0489685	−	0.134540i	−0.961766	+	0.273873i	$0.911695\pi$
$524$			12.6310i			0.551789i
$525$	1.27345	−	0.286693i	0.0555780	−	0.0125123i
$526$	−1.36869	−	3.76044i	−0.0596777	−	0.163963i
$527$	−0.342004	−	0.124479i	−0.0148979	−	0.00542240i
$528$	−10.1227	+	0.475161i	−0.440534	+	0.0206787i
$529$	3.96483	+	1.44308i	0.172384	+	0.0627425i
$530$	0.0447297	−	0.122894i	0.00194293	−	0.00533817i
$531$	6.90194	+	4.76578i	0.299519	+	0.206817i
$532$	1.14676	+	0.491098i	0.0497182	+	0.0212918i
$533$	8.62962	+	4.98231i	0.373790	+	0.215808i
$534$	5.50535	−	7.22354i	0.238240	−	0.312593i
$535$	−0.818441	−	0.975380i	−0.0353843	−	0.0421693i
$536$	−2.50453	−	0.441617i	−0.108179	−	0.0190749i
$537$	15.0478	−	19.7441i	0.649359	−	0.852020i
$538$	5.25097	+	4.40609i	0.226385	+	0.189960i
$539$	−10.4394	−	6.02720i	−0.449658	−	0.259610i
$540$	0.523676	+	0.668770i	0.0225354	+	0.0287793i
$541$	−37.3818	+	13.6059i	−1.60717	+	0.584962i	−0.980877	−	0.194626i	$-0.937651\pi$
$541$	−37.3818	+	13.6059i	−1.60717	+	0.584962i	−0.626292	+	0.779588i	$0.715428\pi$
$542$	1.20389	−	6.82763i	0.0517117	−	0.293272i
$543$	−19.4391	+	17.9301i	−0.834213	+	0.769452i
$544$		−	8.31061i		−	0.356315i
$545$	0.837207	−	0.304718i	0.0358620	−	0.0130527i
$546$	−0.183342	+	0.0766467i	−0.00784632	+	0.00328017i
$547$	−12.2992	−	33.7919i	−0.525878	−	1.44484i	−0.863883	−	0.503693i	$-0.831974\pi$
$547$	−12.2992	−	33.7919i	−0.525878	−	1.44484i	0.338005	−	0.941144i	$-0.390248\pi$
$548$	23.3825	−	4.12296i	0.998849	−	0.176124i
$549$	−6.78913	+	14.8117i	−0.289753	+	0.632147i
$550$			2.78241i			0.118642i
$551$	18.6964	−	13.9954i	0.796494	−	0.596222i
$552$	8.34775	−	7.69971i	0.355304	−	0.327722i
$553$	0.532318	−	0.0938621i	0.0226365	−	0.00399142i
$554$	−2.79966	+	2.34919i	−0.118946	+	0.0998077i
$555$	−0.00726100	−	0.154686i	−0.000308212	−	0.00656607i
$556$	4.73539	+	26.8558i	0.200825	+	1.13894i
$557$	−39.1010	−	6.89456i	−1.65676	−	0.292132i	−0.734475	−	0.678636i	$-0.762571\pi$
$557$	−39.1010	−	6.89456i	−1.65676	−	0.292132i	−0.922288	+	0.386504i	$0.873683\pi$
$558$	−0.152322	−	0.0123224i	−0.00644831	−	0.000521650i
$559$	10.2076	−	5.89334i	0.431734	−	0.249262i
$560$	−0.0434054	−	0.00765354i	−0.00183421	−	0.000323421i
$561$	−0.323379	−	6.88917i	−0.0136531	−	0.290861i
$562$	−4.82471	+	8.35664i	−0.203518	+	0.352504i
$563$	7.45419			0.314157			0.157078	−	0.987586i	$-0.449793\pi$
$563$	7.45419			0.314157			0.157078	+	0.987586i	$0.449793\pi$
$564$	36.9951	−	1.73656i	1.55778	−	0.0731223i
$565$	1.06256	−	0.187357i	0.0447021	−	0.00788219i
$566$	−6.89121	−	5.78241i	−0.289659	−	0.243053i
$567$	−1.16755	+	0.694619i	−0.0490325	+	0.0291713i
$568$	16.4567	+	5.98975i	0.690508	+	0.251324i
$569$	−15.4418	+	26.7460i	−0.647354	+	1.12125i	0.336398	+	0.941720i	$0.390791\pi$
$569$	−15.4418	+	26.7460i	−0.647354	+	1.12125i	−0.983752	+	0.179530i	$0.942542\pi$
$570$	0.209973	+	0.00181589i	0.00879479	+	7.60593e-5i
$571$	3.96444	+	6.86661i	0.165907	+	0.287359i	0.936977	−	0.349391i	$-0.113612\pi$
$571$	3.96444	+	6.86661i	0.165907	+	0.287359i	−0.771070	+	0.636750i	$0.780278\pi$
$572$	1.34020	+	7.60065i	0.0560365	+	0.317799i
$573$	0.375049	−	2.92266i	0.0156679	−	0.122096i
$574$	0.193511	−	0.0704321i	0.00807698	−	0.00293978i
$575$	16.7429	+	19.9534i	0.698226	+	0.832113i
$576$	4.46207	+	16.2271i	0.185920	+	0.676129i
$577$	17.4276	−	30.1855i	0.725520	−	1.25664i	−0.233240	−	0.972419i	$-0.574933\pi$
$577$	17.4276	−	30.1855i	0.725520	−	1.25664i	0.958760	−	0.284218i	$-0.0917340\pi$
$578$	−3.77035			−0.156826
$579$	−13.1957	+	25.5525i	−0.548393	+	1.06192i
$580$	−0.562979	+	0.670932i	−0.0233764	+	0.0278589i
$581$	0.555088	+	0.320480i	0.0230289	+	0.0132958i
$582$	−0.254709	−	1.13138i	−0.0105580	−	0.0468974i
$583$	5.22197	−	6.22330i	0.216272	−	0.257743i
$584$	−2.24903	+	1.88716i	−0.0930654	+	0.0780911i
$585$	0.428117	−	0.433758i	0.0177005	−	0.0179337i
$586$	0.0915003	+	0.518924i	0.00377984	+	0.0214366i
$587$	−9.18377	−	10.9448i	−0.379055	−	0.451740i	0.542461	−	0.840081i	$-0.317493\pi$
$587$	−9.18377	−	10.9448i	−0.379055	−	0.451740i	−0.921516	+	0.388341i	$0.873048\pi$
$588$	−6.81831	+	21.8743i	−0.281182	+	0.902079i
$589$	0.471050	−	0.501916i	0.0194093	−	0.0206811i
$590$	−0.0673413	+	0.0388795i	−0.00277240	+	0.00160064i
$591$	4.98906	−	38.8784i	0.205222	−	1.59924i
$592$	1.20105	−	3.29987i	0.0493631	−	0.135624i
$593$	9.60631	−	11.4483i	0.394484	−	0.470127i	−0.531846	−	0.846841i	$-0.678502\pi$
$593$	9.60631	−	11.4483i	0.394484	−	0.470127i	0.926330	+	0.376714i	$0.122946\pi$
$594$	−0.897878	−	2.75316i	−0.0368404	−	0.112964i
$595$	0.00520874	−	0.0295402i	0.000213538	−	0.00121103i
$596$	11.0306	−	6.36853i	0.451832	−	0.260865i
$597$	23.5245	+	25.5044i	0.962793	+	1.04383i
$598$	−3.03764	−	2.54888i	−0.124218	−	0.104231i
$599$	16.0294	+	13.4503i	0.654944	+	0.549563i	0.908567	−	0.417740i	$-0.137178\pi$
$599$	16.0294	+	13.4503i	0.654944	+	0.549563i	−0.253623	+	0.967303i	$0.581622\pi$
$600$	10.6022	−	2.38687i	0.432832	−	0.0974437i
$601$	19.9148	−	11.4978i	0.812341	−	0.469005i	−0.0354270	−	0.999372i	$-0.511279\pi$
$601$	19.9148	−	11.4978i	0.812341	−	0.469005i	0.847768	+	0.530367i	$0.177946\pi$
$602$	0.0422980	−	0.239884i	0.00172394	−	0.00977695i
$603$	0.568681	+	6.04416i	0.0231585	+	0.246137i
$604$	−6.14744	+	7.32624i	−0.250136	+	0.298100i
$605$	−0.236357	+	0.649387i	−0.00960930	+	0.0264013i
$606$	−7.04550	+	2.94539i	−0.286204	+	0.119648i
$607$	12.7334	−	7.35163i	0.516833	−	0.298394i	−0.218805	−	0.975769i	$-0.570216\pi$
$607$	12.7334	−	7.35163i	0.516833	−	0.298394i	0.735638	+	0.677375i	$0.236883\pi$
$608$	14.4485	+	6.18758i	0.585966	+	0.250939i
$609$	−0.949763	−	1.02970i	−0.0384863	−	0.0417255i
$610$	−0.0970961	−	0.115715i	−0.00393131	−	0.00468515i
$611$	−4.61441	−	26.1696i	−0.186679	−	1.05871i
$612$	−12.6398	+	3.47564i	−0.510933	+	0.140495i
$613$	1.14891	−	0.964051i	0.0464041	−	0.0389376i	−0.619291	−	0.785162i	$-0.712580\pi$
$613$	1.14891	−	0.964051i	0.0464041	−	0.0389376i	0.665695	+	0.746224i	$0.268135\pi$
$614$	−5.36042	+	6.38830i	−0.216329	+	0.257811i
$615$	−0.464241	+	0.428202i	−0.0187200	+	0.0172668i
$616$	0.283841	+	0.163876i	0.0114363	+	0.00660274i
$617$	8.72507	−	10.3981i	0.351258	−	0.418613i	−0.561266	−	0.827635i	$-0.689686\pi$
$617$	8.72507	−	10.3981i	0.351258	−	0.418613i	0.912524	+	0.409022i	$0.134130\pi$
$618$	4.61178	+	7.18703i	0.185513	+	0.289105i
$619$	−25.4951			−1.02474			−0.512368	−	0.858766i	$-0.671232\pi$
$619$	−25.4951			−1.02474			−0.512368	+	0.858766i	$0.671232\pi$
$620$	−0.0129071	+	0.0223557i	−0.000518361	+	0.000897827i
$621$	−23.0057	−	14.3407i	−0.923189	−	0.575473i
$622$	−3.21691	−	3.83376i	−0.128986	−	0.153720i
$623$	2.30580	−	0.839244i	0.0923801	−	0.0336236i
$624$	12.7510	−	5.33059i	0.510449	−	0.213394i
$625$	4.32185	+	24.5104i	0.172874	+	0.980417i
$626$	−1.13072	−	1.95847i	−0.0451928	−	0.0782762i
$627$	12.2180	+	4.56704i	0.487942	+	0.182390i
$628$	21.8028	−	37.7635i	0.870025	−	1.50693i
$629$	2.24578	+	0.817398i	0.0895452	+	0.0325918i
$630$	−0.00117982	−	0.0125396i	−4.70052e−5	−	0.000499589i
$631$	16.7276	+	14.0361i	0.665915	+	0.558769i	0.911853	−	0.410516i	$-0.134652\pi$
$631$	16.7276	+	14.0361i	0.665915	+	0.558769i	−0.245938	+	0.969286i	$0.579096\pi$
$632$	4.43183	−	0.781452i	0.176289	−	0.0310845i
$633$	−3.95591	−	6.16492i	−0.157233	−	0.245033i
$634$	3.25705			0.129354
$635$	0.536260	−	0.928829i	0.0212808	−	0.0368595i
$636$	−13.7200	−	7.08522i	−0.544034	−	0.280947i
$637$	16.1899	+	2.85471i	0.641466	+	0.113108i
$638$	2.58594	−	1.49300i	0.102379	−	0.0591083i
$639$	3.37092	−	41.6692i	0.133352	−	1.64841i
$640$	−0.766006	−	0.135068i	−0.0302790	−	0.00533901i
$641$	−5.13023	−	29.0950i	−0.202632	−	1.14918i	−0.901123	−	0.433564i	$-0.857256\pi$
$641$	−5.13023	−	29.0950i	−0.202632	−	1.14918i	0.698491	−	0.715619i	$-0.253855\pi$
$642$	6.94427	−	4.45600i	0.274069	−	0.175864i
$643$	17.0820	−	14.3335i	0.673649	−	0.565258i	−0.240494	−	0.970651i	$-0.577309\pi$
$643$	17.0820	−	14.3335i	0.673649	−	0.565258i	0.914143	+	0.405392i	$0.132865\pi$
$644$	1.47045	−	0.259280i	0.0579437	−	0.0102170i
$645$	0.164077	+	0.728810i	0.00646054	+	0.0286969i
$646$	−1.27574	+	2.97897i	−0.0501933	+	0.117206i
$647$		−	18.5156i		−	0.727923i	−0.931414	−	0.363962i	$-0.881424\pi$
$647$		−	18.5156i		−	0.727923i	0.931414	−	0.363962i	$-0.118576\pi$
$648$	−9.72048	+	5.78308i	−0.381856	+	0.227181i
$649$	−4.75690	+	0.838771i	−0.186725	+	0.0329246i
$650$	−1.29783	−	3.56577i	−0.0509052	−	0.139861i
$651$	−0.0328377	−	0.0250270i	−0.00128701	−	0.000980884i
$652$	13.9218	−	5.06713i	0.545221	−	0.198444i
$653$		−	1.37543i		−	0.0538247i	−0.999638	−	0.0269123i	$-0.991432\pi$
$653$		−	1.37543i		−	0.0538247i	0.999638	−	0.0269123i	$-0.00856750\pi$
$654$	1.26804	+	5.63245i	0.0495842	+	0.220246i
$655$	−0.0997451	+	0.565683i	−0.00389736	+	0.0221030i
$656$	−13.4582	+	4.89838i	−0.525454	+	0.191250i
$657$	5.76708	+	3.98216i	0.224995	+	0.155359i
$658$	−0.475592	−	0.274583i	−0.0185405	−	0.0107044i
$659$	−27.1471	−	22.7791i	−1.05750	−	0.887348i	−0.0636378	−	0.997973i	$-0.520270\pi$
$659$	−27.1471	−	22.7791i	−1.05750	−	0.887348i	−0.993862	+	0.110625i	$0.964715\pi$
$660$	−0.485189	−	0.0622617i	−0.0188860	−	0.00242353i
$661$	−35.1372	−	6.19563i	−1.36668	−	0.240982i	−0.558296	−	0.829642i	$-0.688545\pi$
$661$	−35.1372	−	6.19563i	−1.36668	−	0.240982i	−0.808381	+	0.588660i	$0.799656\pi$
$662$	1.95528	+	2.33021i	0.0759942	+	0.0905664i
$663$	3.62782	+	8.67790i	0.140893	+	0.337022i
$664$	4.62141	+	2.66817i	0.179345	+	0.103545i
$665$	0.0474795	+	0.0310496i	0.00184118	+	0.00120405i
$666$	1.00023	+	0.0809158i	0.0387581	+	0.00313542i
$667$	9.56051	−	26.2673i	0.370184	−	1.01707i
$668$	−36.4313	−	13.2599i	−1.40957	−	0.513042i
$669$	−3.51562	−	5.47877i	−0.135922	−	0.211821i
$670$	−0.0528879	−	0.0192496i	−0.00204324	−	0.000743677i
$671$	−3.20929	−	8.81744i	−0.123893	−	0.340394i
$672$	0.280553	−	0.900062i	0.0108226	−	0.0347206i
$673$			27.1473i			1.04645i	0.852194	+	0.523227i	$0.175272\pi$
$673$			27.1473i			1.04645i	−0.852194	+	0.523227i	$0.824728\pi$
$674$	1.96745	+	5.40552i	0.0757833	+	0.208213i
$675$	−12.2041	−	22.8922i	−0.469735	−	0.881123i
$676$	7.06086	+	12.2298i	0.271571	+	0.470376i
$677$	−8.93252	−	15.4716i	−0.343305	−	0.594621i	0.641740	−	0.766923i	$-0.278213\pi$
$677$	−8.93252	−	15.4716i	−0.343305	−	0.594621i	−0.985044	+	0.172301i	$0.944880\pi$
$678$	0.327834	+	6.98408i	0.0125904	+	0.268222i
$679$	0.107161	−	0.294423i	0.00411247	−	0.0112989i
$680$	0.0433656	−	0.245938i	0.00166299	−	0.00943131i
$681$	−32.9483	−	4.22808i	−1.26258	−	0.162020i
$682$	0.0674180	−	0.0565704i	0.00258157	−	0.00216619i
$683$	0.0434208			0.00166145			0.000830726	−	1.00000i	$-0.499736\pi$
$683$	0.0434208			0.00166145			0.000830726		1.00000i	$0.499736\pi$
$684$	3.36818	−	24.5628i	0.128786	−	0.939183i
$685$	1.07974			0.0412549
$686$	0.521366	−	0.437478i	0.0199058	−	0.0167030i
$687$	−12.5591	+	16.4787i	−0.479160	+	0.628703i
$688$	−2.94173	+	16.6834i	−0.112152	+	0.636047i
$689$	−3.78935	+	10.4111i	−0.144363	+	0.396633i
$690$	0.211525	−	0.135731i	0.00805261	−	0.00516720i
$691$	8.84893	+	15.3268i	0.336629	+	0.583059i	0.983796	−	0.179289i	$-0.0573798\pi$
$691$	8.84893	+	15.3268i	0.336629	+	0.583059i	−0.647167	+	0.762348i	$0.724046\pi$
$692$	5.16976	+	8.95428i	0.196525	+	0.340391i
$693$	0.197545	−	0.757033i	0.00750411	−	0.0287573i
$694$	−0.881655	−	2.42233i	−0.0334672	−	0.0919503i
$695$			1.24013i			0.0470409i
$696$	−7.90728	−	8.57279i	−0.299725	−	0.324951i
$697$	−3.33368	−	9.15920i	−0.126272	−	0.346929i
$698$	−3.03796	−	1.10573i	−0.114989	−	0.0418524i
$699$	−13.5187	+	26.1781i	−0.511326	+	0.990145i
$700$	1.34267	+	0.488692i	0.0507482	+	0.0184708i
$701$	7.25275	−	19.9268i	0.273932	−	0.752623i	−0.724087	−	0.689709i	$-0.757738\pi$
$701$	7.25275	−	19.9268i	0.273932	−	0.752623i	0.998019	−	0.0629140i	$-0.0200394\pi$
$702$	2.43485	+	3.10947i	0.0918977	+	0.117360i
$703$	−3.09317	+	3.29585i	−0.116661	+	0.124305i
$704$	−8.39348	−	4.84598i	−0.316341	−	0.182640i
$705$	1.67055	+	0.214372i	0.0629164	+	0.00807372i
$706$	1.21232	+	1.44479i	0.0456264	+	0.0543754i
$707$	−2.03179	−	0.358260i	−0.0764134	−	0.0134737i
$708$	3.54120	+	8.47070i	0.133086	+	0.318348i
$709$	−31.5002	−	26.4318i	−1.18301	−	0.992666i	−0.999954	−	0.00956419i	$-0.996956\pi$
$709$	−31.5002	−	26.4318i	−1.18301	−	0.992666i	−0.183059	−	0.983102i	$-0.558600\pi$
$710$	0.335647	+	0.193786i	0.0125966	+	0.00727265i
$711$	−4.60362	−	9.70612i	−0.172649	−	0.364008i
$712$	19.1971	−	6.98716i	0.719440	−	0.261855i
$713$	0.143065	−	0.811361i	0.00535782	−	0.0303857i
$714$	0.185573	+	0.0578439i	0.00694488	+	0.00216475i
$715$			0.350979i			0.0131259i
$716$	25.5349	−	9.29394i	0.954284	−	0.347331i
$717$	2.98578	−	23.2674i	0.111506	−	0.868936i
$718$	3.09572	+	8.50541i	0.115531	+	0.317419i
$719$	37.2325	−	6.56510i	1.38854	−	0.244837i	0.571113	−	0.820871i	$-0.306512\pi$
$719$	37.2325	−	6.56510i	1.38854	−	0.244837i	0.817425	+	0.576034i	$0.195401\pi$
$720$	0.0820537	+	0.872098i	0.00305796	+	0.0325012i
$721$			2.30711i			0.0859214i
$722$	−4.22929	−	4.43592i	−0.157398	−	0.165088i
$723$	−24.2915	−	7.57178i	−0.903412	−	0.281598i
$724$	−28.5081	+	5.02675i	−1.05950	+	0.186818i
$725$	20.4913	−	17.1942i	0.761027	−	0.638577i
$726$	−3.97896	−	2.05480i	−0.147673	−	0.0762606i
$727$	−1.30263	−	7.38756i	−0.0483117	−	0.273989i	0.951077	−	0.308954i	$-0.0999791\pi$
$727$	−1.30263	−	7.38756i	−0.0483117	−	0.273989i	−0.999389	+	0.0349652i	$0.988868\pi$
$728$	−0.440192	−	0.0776177i	−0.0163146	−	0.00287670i
$729$	19.4631	+	18.7134i	0.720854	+	0.693087i
$730$	−0.0562686	+	0.0324867i	−0.00208260	+	0.00120239i
$731$	−11.3541	−	2.00204i	−0.419948	−	0.0740481i
$732$	−15.0107	+	9.63204i	−0.554810	+	0.356011i
$733$	−0.165796	+	0.287166i	−0.00612380	+	0.0106067i	−0.869071	−	0.494687i	$-0.835283\pi$
$733$	−0.165796	+	0.287166i	−0.00612380	+	0.0106067i	0.862947	+	0.505294i	$0.168616\pi$
$734$	9.14872			0.337685
$735$	−0.478096	+	0.925798i	−0.0176348	+	0.0341486i
$736$	18.5269	−	3.26679i	0.682910	−	0.120415i
$737$	−2.67822	−	2.24729i	−0.0986535	−	0.0827802i
$738$	−2.36935	−	3.33708i	−0.0872169	−	0.122840i
$739$	27.8907	+	10.1514i	1.02597	+	0.373424i	0.799547	−	0.600604i	$-0.205073\pi$
$739$	27.8907	+	10.1514i	1.02597	+	0.373424i	0.226428	+	0.974028i	$0.427295\pi$
$740$	0.0847548	−	0.146800i	0.00311565	−	0.00539646i
$741$	−17.7882	−	0.153836i	−0.653464	−	0.00565130i
$742$	0.114483	+	0.198290i	0.00420280	+	0.00727946i
$743$	−8.14656	−	46.2014i	−0.298868	−	1.69497i	−0.651050	−	0.759035i	$-0.725671\pi$
$743$	−8.14656	−	46.2014i	−0.298868	−	1.69497i	0.352182	−	0.935931i	$-0.385440\pi$
$744$	−0.273392	−	0.208363i	−0.0100230	−	0.00763895i
$745$	0.544299	−	0.198109i	0.0199416	−	0.00725814i
$746$	5.61933	+	6.69686i	0.205738	+	0.245189i
$747$	3.21636	−	12.3258i	0.117681	−	0.450976i
$748$	3.77468	−	6.53793i	0.138016	−	0.239050i
$749$	2.22918			0.0814526
$750$	0.480841	−	0.0225708i	0.0175578	−	0.000824167i
$751$	−16.4991	+	19.6629i	−0.602061	+	0.717509i	−0.977876	−	0.209186i	$-0.932918\pi$
$751$	−16.4991	+	19.6629i	−0.602061	+	0.717509i	0.375815	+	0.926695i	$0.377363\pi$
$752$	33.0763	+	19.0966i	1.20617	+	0.696382i
$753$	35.5248	+	11.0732i	1.29459	+	0.403531i
$754$	−2.61759	+	3.11952i	−0.0953271	+	0.113606i
$755$	−0.333168	+	0.279561i	−0.0121252	+	0.0101743i
$756$	−1.48625	−	0.0502778i	−0.0540546	−	0.00182859i
$757$	2.62865	+	14.9078i	0.0955399	+	0.541834i	0.994581	+	0.103969i	$0.0331542\pi$
$757$	2.62865	+	14.9078i	0.0955399	+	0.541834i	−0.899041	+	0.437865i	$0.855735\pi$
$758$	6.88920	+	8.21022i	0.250227	+	0.298209i
$759$	15.2309	−	3.42895i	0.552848	−	0.124463i
$760$	0.395292	+	0.258505i	0.0143388	+	0.00937695i
$761$	11.9493	−	6.89891i	0.433161	−	0.250085i	−0.267532	−	0.963549i	$-0.586208\pi$
$761$	11.9493	−	6.89891i	0.433161	−	0.250085i	0.700692	+	0.713464i	$0.252875\pi$
$762$	5.52771	+	4.21289i	0.200248	+	0.152617i
$763$	−0.533488	+	1.46575i	−0.0193136	+	0.0530636i
$764$	2.07328	−	2.47083i	0.0750085	−	0.0893916i
$765$	−0.593521	+	0.0558430i	−0.0214588	+	0.00201901i
$766$	−0.463953	+	2.63121i	−0.0167633	+	0.0950695i
$767$	5.70492	−	3.29374i	0.205993	−	0.118930i
$768$	−4.28297	+	13.7405i	−0.154548	+	0.495816i
$769$	13.7525	+	11.5397i	0.495928	+	0.416133i	0.856145	−	0.516736i	$-0.172853\pi$
$769$	13.7525	+	11.5397i	0.495928	+	0.416133i	−0.360217	+	0.932868i	$0.617297\pi$
$770$	0.00555640	+	0.00466237i	0.000200239	+	0.000168020i
$771$	−12.8342	+	41.1742i	−0.462212	+	1.48285i
$772$	−27.2623	+	15.7399i	−0.981191	+	0.566491i
$773$	−4.90434	+	27.8139i	−0.176397	+	1.00040i	0.760122	+	0.649780i	$0.225139\pi$
$773$	−4.90434	+	27.8139i	−0.176397	+	1.00040i	−0.936519	+	0.350616i	$0.885972\pi$
$774$	−4.81974	+	0.453478i	−0.173242	+	0.0162999i
$775$	0.506776	−	0.603952i	0.0182039	−	0.0216946i
$776$	0.892175	−	2.45123i	0.0320272	−	0.0879941i
$777$	0.215630	+	0.164341i	0.00773569	+	0.00589568i
$778$	3.82380	−	2.20767i	0.137090	−	0.0791488i
$779$	18.4059	+	1.02357i	0.659460	+	0.0366732i
$780$	0.650830	−	0.146522i	0.0233035	−	0.00524632i
$781$	15.4754	+	18.4429i	0.553753	+	0.659937i
$782$	0.673539	+	3.81983i	0.0240857	+	0.136597i
$783$	−14.7273	+	23.6259i	−0.526311	+	0.844322i
$784$	−18.1003	+	15.1880i	−0.646440	+	0.542427i
$785$	1.27465	−	1.51907i	0.0454943	−	0.0542180i
$786$	−3.55364	−	1.10768i	−0.126754	−	0.0395098i
$787$	36.1084	+	20.8472i	1.28713	+	0.743122i	0.978141	−	0.207945i	$-0.0666775\pi$
$787$	36.1084	+	20.8472i	1.28713	+	0.743122i	0.308985	+	0.951067i	$0.400011\pi$
$788$	27.5796	−	32.8681i	0.982482	−	1.17088i
$789$	−21.4636	+	1.00750i	−0.764123	+	0.0358681i
$790$	0.0995926			0.00354335
$791$	−0.944489	+	1.63590i	−0.0335822	+	0.0581660i
$792$	1.64467	−	6.30270i	0.0584407	−	0.223957i
$793$	8.22565	+	9.80295i	0.292101	+	0.348113i
$794$	−3.28991	+	1.19743i	−0.116754	+	0.0424951i
$795$	−0.558502	−	0.425657i	−0.0198080	−	0.0150965i
$796$	6.59517	+	37.4031i	0.233760	+	1.32572i
$797$	1.75112	+	3.03303i	0.0620279	+	0.107435i	0.895372	−	0.445319i	$-0.146910\pi$
$797$	1.75112	+	3.03303i	0.0620279	+	0.107435i	−0.833344	+	0.552755i	$0.813577\pi$
$798$	−0.238732	+	0.279563i	−0.00845100	+	0.00989643i
$799$	−12.9965	+	22.5106i	−0.459784	+	0.796369i
$800$	16.9170	+	6.15727i	0.598105	+	0.217692i
$801$	−28.2323	−	39.7634i	−0.997539	−	1.40497i
$802$	−1.94107	−	1.62875i	−0.0685416	−	0.0575132i
$803$	−3.97475	+	0.700855i	−0.140266	+	0.0247326i
$804$	−3.04915	+	5.90447i	−0.107535	+	0.208234i
$805$	0.0679016			0.00239322
$806$	−0.0600120	+	0.103944i	−0.00211383	+	0.00366127i
$807$	30.9766	−	19.8771i	1.09043	−	0.699706i
$808$	−16.9157	−	2.98270i	−0.595094	−	0.104931i
$809$	−37.8642	+	21.8609i	−1.33123	+	0.768588i	−0.985489	−	0.169741i	$-0.945707\pi$
$809$	−37.8642	+	21.8609i	−1.33123	+	0.768588i	−0.345744	+	0.938329i	$0.612374\pi$
$810$	−0.234077	+	0.0886838i	−0.00822462	+	0.00311603i
$811$	−18.9917	−	3.34875i	−0.666889	−	0.117590i	−0.170053	−	0.985435i	$-0.554394\pi$
$811$	−18.9917	−	3.34875i	−0.666889	−	0.117590i	−0.496836	+	0.867844i	$0.665505\pi$
$812$	−0.266269	−	1.51009i	−0.00934422	−	0.0529937i
$813$	−33.0759	−	17.0809i	−1.16002	−	0.599052i
$814$	−0.442703	+	0.371472i	−0.0155167	+	0.0130201i
$815$	0.663505	−	0.116994i	0.0232416	−	0.00409811i
$816$	−12.9061	−	4.02290i	−0.451805	−	0.140830i
$817$	11.9343	−	18.2493i	0.417528	−	0.638462i
$818$		−	8.09719i		−	0.283111i
$819$	0.0999503	+	1.06231i	0.00349255	+	0.0371201i
$820$	−0.680826	+	0.120048i	−0.0237755	+	0.00419226i
$821$	−0.918034	−	2.52228i	−0.0320396	−	0.0880281i	0.922641	−	0.385659i	$-0.126026\pi$
$821$	−0.918034	−	2.52228i	−0.0320396	−	0.0880281i	−0.954681	+	0.297631i	$0.903804\pi$
$822$	−0.890576	+	6.94002i	−0.0310624	+	0.242061i
$823$	−28.7551	+	10.4660i	−1.00234	+	0.364822i	−0.790487	−	0.612479i	$-0.790172\pi$
$823$	−28.7551	+	10.4660i	−1.00234	+	0.364822i	−0.211854	+	0.977301i	$0.567950\pi$
$824$			19.2080i			0.669141i
$825$	14.2631	+	4.44587i	0.496577	+	0.154785i
$826$	0.0236400	−	0.134069i	0.000822540	−	0.00466486i
$827$	1.32511	−	0.482299i	0.0460785	−	0.0167712i	−0.318878	−	0.947796i	$-0.603306\pi$
$827$	1.32511	−	0.482299i	0.0460785	−	0.0167712i	0.364957	+	0.931025i	$0.381084\pi$
$828$	−12.7168	−	26.8117i	−0.441939	−	0.931770i
$829$	19.8435	+	11.4567i	0.689194	+	0.397906i	0.803310	−	0.595561i	$-0.203070\pi$
$829$	19.8435	+	11.4567i	0.689194	+	0.397906i	−0.114116	+	0.993467i	$0.536404\pi$
$830$	0.0904675	+	0.0759113i	0.00314017	+	0.00263492i
$831$	7.56891	+	18.1052i	0.262563	+	0.628061i
$832$	13.0169	+	2.29524i	0.451281	+	0.0795730i
$833$	−10.3364	−	12.3185i	−0.358136	−	0.426809i
$834$	−7.97091	−	1.02286i	−0.276010	−	0.0354189i
$835$	−1.52687	−	0.881539i	−0.0528395	−	0.0305069i
$836$	8.55623	+	11.4303i	0.295923	+	0.395324i
$837$	−0.306554	+	0.761138i	−0.0105961	+	0.0263088i
$838$	−1.55317	+	4.26731i	−0.0536535	+	0.147412i
$839$	−12.5629	−	4.57253i	−0.433721	−	0.157861i	0.115928	−	0.993258i	$-0.463016\pi$
$839$	−12.5629	−	4.57253i	−0.433721	−	0.157861i	−0.549648	+	0.835396i	$0.685238\pi$
$840$	0.0129991	−	0.0251718i	0.000448512	−	0.000868511i
$841$	0.275689	+	0.100343i	0.00950652	+	0.00346009i
$842$	0.286132	+	0.786140i	0.00986074	+	0.0270922i
$843$	35.1283	+	38.0849i	1.20988	+	1.31171i
$844$		−	8.01810i		−	0.275994i
$845$	0.219645	+	0.603470i	0.00755602	+	0.0207600i
$846$	−2.75574	+	10.5606i	−0.0947443	+	0.363079i
$847$	−0.604942	−	1.04779i	−0.0207861	−	0.0360025i
$848$	−7.96201	−	13.7906i	−0.273417	−	0.473571i
$849$	−40.6527	+	26.0860i	−1.39520	+	0.895270i
$850$	−1.26949	+	3.48790i	−0.0435432	+	0.119634i
$851$	−0.939442	+	5.32784i	−0.0322036	+	0.182636i
$852$	27.7386	−	36.3957i	0.950310	−	1.24690i
$853$	−6.10631	+	5.12381i	−0.209076	+	0.175436i	−0.741312	−	0.671160i	$-0.765796\pi$
$853$	−6.10631	+	5.12381i	−0.209076	+	0.175436i	0.532236	+	0.846596i	$0.321352\pi$
$854$	0.264461			0.00904965
$855$	0.344813	−	1.07345i	0.0117923	−	0.0367113i
$856$	18.5592			0.634339
$857$	−15.7059	+	13.1788i	−0.536504	+	0.450180i	−0.870340	−	0.492451i	$-0.836101\pi$
$857$	−15.7059	+	13.1788i	−0.536504	+	0.450180i	0.333836	+	0.942631i	$0.391657\pi$
$858$	−2.25591	−	0.289489i	−0.0770154	−	0.00988298i
$859$	0.516265	−	2.92788i	0.0176147	−	0.0998980i	−0.974733	−	0.223374i	$-0.928293\pi$
$859$	0.516265	−	2.92788i	0.0176147	−	0.0998980i	0.992348	+	0.123476i	$0.0394041\pi$
$860$	−0.279684	+	0.768425i	−0.00953713	+	0.0262031i
$861$	−0.0518457	−	1.10451i	−0.00176690	−	0.0376415i
$862$	−4.26940	−	7.39482i	−0.145416	−	0.251868i
$863$	18.0449	+	31.2546i	0.614255	+	1.06392i	0.990515	+	0.137406i	$0.0438766\pi$
$863$	18.0449	+	31.2546i	0.614255	+	1.06392i	−0.376260	+	0.926514i	$0.622790\pi$
$864$	−18.7260	−	0.633475i	−0.637073	−	0.0215513i
$865$	0.160818	+	0.441843i	0.00546797	+	0.0150231i
$866$		−	10.7681i		−	0.365916i
$867$	−6.02444	+	19.3274i	−0.204601	+	0.656393i
$868$	−0.0154574	−	0.0424688i	−0.000524658	−	0.00144149i
$869$	5.81347	+	2.11593i	0.197208	+	0.0717780i
$870$	−0.139390	−	0.217227i	−0.00472577	−	0.00736468i
$871$	4.48048	+	1.63076i	0.151815	+	0.0552562i
$872$	−4.44158	+	12.2031i	−0.150411	+	0.413250i
$873$	−6.20664	−	0.502100i	−0.210063	−	0.0169935i
$874$	−7.14250	−	1.67302i	−0.241599	−	0.0565908i
$875$	0.112629	+	0.0650263i	0.00380755	+	0.00219829i
$876$	2.95893	+	7.07789i	0.0999731	+	0.239140i
$877$	−2.02868	−	2.41769i	−0.0685037	−	0.0816396i	0.730704	−	0.682694i	$-0.239192\pi$
$877$	−2.02868	−	2.41769i	−0.0685037	−	0.0816396i	−0.799208	+	0.601055i	$0.794747\pi$
$878$	4.85619	+	0.856277i	0.163888	+	0.0288979i
$879$	2.80629	+	0.360116i	0.0946538	+	0.0121464i
$880$	−0.386434	−	0.324257i	−0.0130267	−	0.0109307i
$881$	−10.9414	−	6.31703i	−0.368626	−	0.212826i	0.304232	−	0.952598i	$-0.401600\pi$
$881$	−10.9414	−	6.31703i	−0.368626	−	0.212826i	−0.672858	+	0.739772i	$0.734933\pi$
$882$	−5.55620	−	3.83655i	−0.187087	−	0.129183i
$883$	11.9266	−	4.34093i	0.401362	−	0.146084i	−0.133449	−	0.991056i	$-0.542605\pi$
$883$	11.9266	−	4.34093i	0.401362	−	0.146084i	0.534811	+	0.844972i	$0.320383\pi$
$884$	−1.78783	+	10.1393i	−0.0601312	+	0.341021i
$885$	0.0917014	+	0.407326i	0.00308251	+	0.0136921i
$886$		−	10.3110i		−	0.346404i
$887$	19.0350	−	6.92817i	0.639133	−	0.232625i	−0.00206875	−	0.999998i	$-0.500659\pi$
$887$	19.0350	−	6.92817i	0.639133	−	0.232625i	0.641201	+	0.767373i	$0.278436\pi$
$888$	1.79524	+	1.36822i	0.0602442	+	0.0459146i
$889$	0.642219	+	1.76448i	0.0215393	+	0.0591788i
$890$	0.445241	−	0.0785080i	0.0149245	−	0.00263160i
$891$	−15.5478	+	0.203534i	−0.520871	+	0.00681864i
$892$		−	7.12569i		−	0.238586i
$893$	−29.4598	−	39.3553i	−0.985834	−	1.31698i
$894$	0.824397	+	3.66186i	0.0275720	+	0.122471i
$895$	1.21698	−	0.214586i	0.0406790	−	0.00717281i
$896$	1.04318	−	0.875335i	0.0348503	−	0.0292429i
$897$	−17.9196	+	11.4987i	−0.598319	+	0.383930i
$898$	−0.585530	−	3.32071i	−0.0195394	−	0.110813i
$899$	−0.833234	−	0.146922i	−0.0277899	−	0.00490011i
$900$	2.28975	−	28.3044i	0.0763249	−	0.943480i
$901$	9.38543	−	5.41868i	0.312674	−	0.180522i
$902$	2.32113	+	0.409279i	0.0772853	+	0.0136275i
$903$	−1.16210	−	0.600125i	−0.0386722	−	0.0199709i
$904$	−7.86338	+	13.6198i	−0.261532	+	0.452987i
$905$	−1.31644			−0.0437598
$906$	−1.52207	−	2.37201i	−0.0505675	−	0.0788047i
$907$	3.84498	−	0.677975i	0.127671	−	0.0225118i	−0.109448	−	0.993993i	$-0.534908\pi$
$907$	3.84498	−	0.677975i	0.127671	−	0.0225118i	0.237118	+	0.971481i	$0.423797\pi$
$908$	−27.8547	−	23.3728i	−0.924390	−	0.775655i
$909$	3.84090	+	40.8226i	0.127395	+	1.35400i
$910$	−0.00929547	−	0.00338327i	−0.000308142	−	0.000112154i
$911$	−0.852452	+	1.47649i	−0.0282430	+	0.0489183i	−0.879801	−	0.475341i	$-0.842325\pi$
$911$	−0.852452	+	1.47649i	−0.0282430	+	0.0489183i	0.851558	+	0.524260i	$0.175658\pi$
$912$	16.6032	−	19.4429i	0.549787	−	0.643820i
$913$	3.66801	+	6.35319i	0.121394	+	0.210260i
$914$	−1.19781	−	6.79313i	−0.0396201	−	0.224697i
$915$	−0.748316	+	0.312836i	−0.0247386	+	0.0103420i
$916$	−21.3118	+	7.75687i	−0.704163	+	0.256294i
$917$	−0.646420	−	0.770374i	−0.0213467	−	0.0254400i
$918$	0.130608	−	3.86089i	0.00431072	−	0.127428i
$919$	−13.7650	+	23.8417i	−0.454067	+	0.786467i	−0.998634	−	0.0522506i	$-0.983361\pi$
$919$	−13.7650	+	23.8417i	−0.454067	+	0.786467i	0.544567	+	0.838717i	$0.316694\pi$
$920$	0.565318			0.0186380
$921$	24.1823	+	37.6859i	0.796834	+	1.24179i
$922$	−6.11048	+	7.28218i	−0.201238	+	0.239826i
$923$	−28.4348	−	16.4169i	−0.935944	−	0.540368i
$924$	0.629518	−	0.580649i	0.0207096	−	0.0191019i
$925$	−3.32776	+	3.96587i	−0.109416	+	0.130397i
$926$	−2.79944	+	2.34900i	−0.0919951	+	0.0771931i
$927$	44.2108	−	12.1569i	1.45207	−	0.399286i
$928$	−3.35486	−	19.0263i	−0.110129	−	0.624570i
$929$	−0.584452	−	0.696523i	−0.0191753	−	0.0228522i	0.756372	−	0.654142i	$-0.226970\pi$
$929$	−0.584452	−	0.696523i	−0.0191753	−	0.0228522i	−0.775547	+	0.631290i	$0.782526\pi$
$930$	−0.00515770	−	0.00559179i	−0.000169128	−	0.000183362i
$931$	29.1123	−	8.79896i	0.954118	−	0.288374i
$932$	−27.9298	+	16.1252i	−0.914869	+	0.528200i
$933$	−24.7926	+	10.3646i	−0.811674	+	0.339322i
$934$	3.29188	−	9.04438i	0.107714	−	0.295941i
$935$	0.220678	−	0.262994i	0.00721695	−	0.00860083i
$936$	0.832140	+	8.84430i	0.0271993	+	0.289085i
$937$	3.40850	−	19.3306i	0.111351	−	0.631503i	−0.877141	−	0.480232i	$-0.840552\pi$
$937$	3.40850	−	19.3306i	0.111351	−	0.631503i	0.988492	−	0.151271i	$-0.0483365\pi$
$938$	0.0853350	−	0.0492682i	0.00278629	−	0.00160866i
$939$	−11.8461	+	2.66693i	−0.386584	+	0.0870319i
$940$	1.41229	+	1.18505i	0.0460638	+	0.0386521i
$941$	18.9832	+	15.9288i	0.618836	+	0.519265i	0.897437	−	0.441142i	$-0.145426\pi$
$941$	18.9832	+	15.9288i	0.618836	+	0.519265i	−0.278601	+	0.960407i	$0.589871\pi$
$942$	8.71244	+	9.44571i	0.283867	+	0.307758i
$943$	19.1082	−	11.0321i	0.622249	−	0.359256i
$944$	−1.64410	+	9.32418i	−0.0535110	+	0.303476i
$945$	−0.0661651	−	0.0139884i	−0.00215235	−	0.000455042i
$946$	1.79204	−	2.13567i	0.0582642	−	0.0694365i
$947$	−9.90400	+	27.2110i	−0.321837	+	0.884240i	0.668269	+	0.743919i	$0.267035\pi$
$947$	−9.90400	+	27.2110i	−0.321837	+	0.884240i	−0.990106	+	0.140320i	$0.955187\pi$
$948$	1.49670	−	11.6634i	0.0486106	−	0.378810i
$949$	4.76688	−	2.75216i	0.154740	−	0.0893389i
$950$	−5.11875	−	4.80397i	−0.166074	−	0.155861i
$951$	5.20427	−	16.6961i	0.168760	−	0.541410i
$952$	0.281040	+	0.334931i	0.00910857	+	0.0108552i
$953$	1.92175	+	10.8988i	0.0622516	+	0.353046i	0.999984	+	0.00568728i	$0.00181033\pi$
$953$	1.92175	+	10.8988i	0.0622516	+	0.353046i	−0.937732	+	0.347359i	$0.887079\pi$
$954$	3.19655	−	3.23867i	0.103492	−	0.104856i
$955$	0.112364	−	0.0942843i	0.00363600	−	0.00305097i
$956$	16.5054	−	19.6704i	0.533824	−	0.636186i
$957$	−3.52139	−	15.6415i	−0.113830	−	0.505619i
$958$	−8.02224	−	4.63164i	−0.259187	−	0.149642i
$959$	−1.21511	+	1.44811i	−0.0392379	+	0.0467619i
$960$	−0.384398	+	0.744358i	−0.0124064	+	0.0240241i
$961$	30.9751			0.999196
$962$	0.394071	−	0.682551i	0.0127054	−	0.0220063i
$963$	−11.7463	−	42.7174i	−0.378519	−	1.37655i
$964$	−17.9029	−	21.3358i	−0.576612	−	0.687180i
$965$	−1.34524	+	0.489627i	−0.0433048	+	0.0157617i
$966$	−0.0560055	+	0.436436i	−0.00180195	+	0.0140421i
$967$	−6.33572	−	35.9316i	−0.203743	−	1.15548i	−0.899406	−	0.437115i	$-0.856000\pi$
$967$	−6.33572	−	35.9316i	−0.203743	−	1.15548i	0.695663	−	0.718369i	$-0.255111\pi$
$968$	−5.03647	−	8.72342i	−0.161878	−	0.280381i
$969$	13.2322	+	11.2996i	0.425080	+	0.362995i
$970$	0.0288645	−	0.0499947i	0.000926782	−	0.00160523i
$971$	21.2202	+	7.72352i	0.680988	+	0.247860i	0.659272	−	0.751905i	$-0.270865\pi$
$971$	21.2202	+	7.72352i	0.680988	+	0.247860i	0.0217165	+	0.999764i	$0.493087\pi$
$972$	6.86809	+	28.7457i	0.220294	+	0.922020i
$973$	−1.66322	−	1.39560i	−0.0533202	−	0.0447410i
$974$	10.0754	−	1.77656i	0.322837	−	0.0569248i
$975$	−20.3524	+	0.955347i	−0.651799	+	0.0305956i
$976$	−18.3926			−0.588732
$977$	16.8011	−	29.1003i	0.537513	−	0.931000i	−0.461524	−	0.887128i	$-0.652697\pi$
$977$	16.8011	−	29.1003i	0.537513	−	0.931000i	0.999037	−	0.0438726i	$-0.0139696\pi$
$978$	0.204713	+	4.36115i	0.00654601	+	0.139454i
$979$	27.6578	+	4.87682i	0.883947	+	0.155864i
$980$	−0.987748	+	0.570276i	−0.0315524	+	0.0182168i
$981$	30.8990	+	2.49964i	0.986528	+	0.0798074i
$982$	11.6109	+	2.04731i	0.370518	+	0.0653323i
$983$	8.75311	+	49.6413i	0.279181	+	1.58331i	0.725360	+	0.688369i	$0.241673\pi$
$983$	8.75311	+	49.6413i	0.279181	+	1.58331i	−0.446179	+	0.894944i	$0.647216\pi$
$984$	−0.431643	−	9.19561i	−0.0137603	−	0.293145i
$985$	1.49471	−	1.25421i	0.0476254	−	0.0399624i
$986$	3.92281	−	0.691696i	0.124928	−	0.0220281i
$987$	−2.16748	+	1.99922i	−0.0689917	+	0.0636359i
$988$	−16.2967	−	10.6574i	−0.518467	−	0.339056i
$989$		−	26.0988i		−	0.829893i
$990$	0.0600657	−	0.131044i	0.00190901	−	0.00416485i
$991$	−9.82201	+	1.73189i	−0.312007	+	0.0550152i	−0.327459	−	0.944865i	$-0.606192\pi$
$991$	−9.82201	+	1.73189i	−0.312007	+	0.0550152i	0.0154523	+	0.999881i	$0.495081\pi$
$992$	−0.194755	−	0.535085i	−0.00618348	−	0.0169890i
$993$	15.0693	−	6.29976i	0.478209	−	0.199917i
$994$	−0.637623	+	0.232076i	−0.0202242	+	0.00736100i
$995$			1.72718i			0.0547554i
$996$	10.2496	−	9.45393i	0.324771	−	0.299559i
$997$	5.07792	−	28.7983i	0.160819	−	0.912051i	−0.792452	−	0.609935i	$-0.791196\pi$
$997$	5.07792	−	28.7983i	0.160819	−	0.912051i	0.953271	−	0.302117i	$-0.0976932\pi$
$998$	4.90459	−	1.78513i	0.155252	−	0.0565072i
$999$	2.01300	−	4.99804i	0.0636885	−	0.158131i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.2.x.a.110.9	yes	108
3.2	odd	2		513.2.bo.a.224.10		108
9.4	even	3		513.2.cd.a.395.9		108
9.5	odd	6		171.2.bd.a.167.10	yes	108
19.14	odd	18		171.2.bd.a.128.10	yes	108
57.14	even	18		513.2.cd.a.413.9		108
171.14	even	18	inner	171.2.x.a.14.9	✓	108
171.166	odd	18		513.2.bo.a.71.10		108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.x.a.14.9	✓	108	171.14	even	18	inner
171.2.x.a.110.9	yes	108	1.1	even	1	trivial
171.2.bd.a.128.10	yes	108	19.14	odd	18
171.2.bd.a.167.10	yes	108	9.5	odd	6
513.2.bo.a.71.10		108	171.166	odd	18
513.2.bo.a.224.10		108	3.2	odd	2
513.2.cd.a.395.9		108	9.4	even	3
513.2.cd.a.413.9		108	57.14	even	18

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:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	171.x (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.247109 + 0.207349i) q^{2} +(0.668060 + 1.59803i) q^{3} +(-0.329227 + 1.86714i) q^{4} +(-0.0294890 + 0.0810203i) q^{5} +(-0.496432 - 0.256365i) q^{6} +(-0.0754752 - 0.130727i) q^{7} +(-0.628371 - 1.08837i) q^{8} +(-2.10739 + 2.13516i) q^{9} +O(q^{10})\)	\(q+(-0.247109 + 0.207349i) q^{2} +(0.668060 + 1.59803i) q^{3} +(-0.329227 + 1.86714i) q^{4} +(-0.0294890 + 0.0810203i) q^{5} +(-0.496432 - 0.256365i) q^{6} +(-0.0754752 - 0.130727i) q^{7} +(-0.628371 - 1.08837i) q^{8} +(-2.10739 + 2.13516i) q^{9} +(-0.00951247 - 0.0261353i) q^{10} -1.72768i q^{11} +(-3.20369 + 0.721248i) q^{12} +(0.805863 + 2.21409i) q^{13} +(0.0457566 + 0.0166540i) q^{14} +(-0.149173 + 0.00700221i) q^{15} +(-3.18226 - 1.15825i) q^{16} +(0.788265 - 2.16574i) q^{17} +(0.0780319 - 0.964581i) q^{18} +(3.17839 + 2.98293i) q^{19} +(-0.141568 - 0.0817341i) q^{20} +(0.158483 - 0.207945i) q^{21} +(0.358233 + 0.426925i) q^{22} +(5.13795 + 0.905959i) q^{23} +(1.31946 - 1.73125i) q^{24} +(3.82453 + 3.20916i) q^{25} +(-0.658225 - 0.380026i) q^{26} +(-4.81991 - 1.94126i) q^{27} +(0.268934 - 0.0978839i) q^{28} +(0.930382 - 5.27646i) q^{29} +(0.0354100 - 0.0326611i) q^{30} -0.157915i q^{31} +(3.38843 - 1.23329i) q^{32} +(2.76089 - 1.15420i) q^{33} +(0.254276 + 0.698619i) q^{34} +(0.0128172 - 0.00226002i) q^{35} +(-3.29283 - 4.63775i) q^{36} +1.03696i q^{37} +(-1.40391 - 0.0780729i) q^{38} +(-2.99982 + 2.76694i) q^{39} +(0.106710 - 0.0188159i) q^{40} +(3.23970 - 2.71843i) q^{41} +(0.00395453 + 0.0842463i) q^{42} +(-0.868665 - 4.92644i) q^{43} +(3.22582 + 0.568800i) q^{44} +(-0.110846 - 0.233705i) q^{45} +(-1.45748 + 0.841477i) q^{46} +(-11.1068 - 1.95842i) q^{47} +(-0.275028 - 5.85912i) q^{48} +(3.48861 - 6.04244i) q^{49} -1.61049 q^{50} +(3.98752 - 0.187175i) q^{51} +(-4.39933 + 0.775721i) q^{52} +(3.60211 + 3.02253i) q^{53} +(1.59356 - 0.519701i) q^{54} +(0.139977 + 0.0509475i) q^{55} +(-0.0948529 + 0.164290i) q^{56} +(-2.64345 + 7.07193i) q^{57} +(0.864161 + 1.49677i) q^{58} +(-0.485489 - 2.75335i) q^{59} +(0.0360377 - 0.280832i) q^{60} +(5.10362 - 1.85757i) q^{61} +(0.0327436 + 0.0390223i) q^{62} +(0.438178 + 0.114341i) q^{63} +(2.80490 - 4.85823i) q^{64} -0.203150 q^{65} +(-0.442917 + 0.857677i) q^{66} +(1.30076 - 1.55018i) q^{67} +(3.78422 + 2.18482i) q^{68} +(1.98471 + 8.81582i) q^{69} +(-0.00269863 + 0.00321610i) q^{70} +(-10.6749 + 8.95732i) q^{71} +(3.64807 + 0.951951i) q^{72} +(-0.405662 - 2.30062i) q^{73} +(-0.215012 - 0.256241i) q^{74} +(-2.57331 + 8.25562i) q^{75} +(-6.61596 + 4.95243i) q^{76} +(-0.225854 + 0.130397i) q^{77} +(0.167559 - 1.30574i) q^{78} +(-1.22472 + 3.36489i) q^{79} +(0.187683 - 0.223672i) q^{80} +(-0.117807 - 8.99923i) q^{81} +(-0.236895 + 1.34350i) q^{82} +(-3.67729 + 2.12308i) q^{83} +(0.336085 + 0.364372i) q^{84} +(0.152224 + 0.127731i) q^{85} +(1.23615 + 1.03725i) q^{86} +(9.05348 - 2.03822i) q^{87} +(-1.88036 + 1.08563i) q^{88} +(-2.82275 + 16.0086i) q^{89} +(0.0758495 + 0.0347666i) q^{90} +(0.228619 - 0.272457i) q^{91} +(-3.38311 + 9.29500i) q^{92} +(0.252353 - 0.105497i) q^{93} +(3.15065 - 1.81903i) q^{94} +(-0.335405 + 0.169550i) q^{95} +(4.23450 + 4.59090i) q^{96} +(1.33420 + 1.59003i) q^{97} +(0.390828 + 2.21650i) q^{98} +(3.68888 + 3.64090i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9}+O(q^{10}) \) 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9	\( 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9} - 12 q^{10} - 9 q^{12} - 6 q^{13} - 9 q^{14} - 36 q^{15} - 9 q^{16} + 27 q^{17} + 36 q^{18} - 15 q^{19} - 18 q^{20} + 3 q^{21} + 30 q^{22} - 45 q^{23} - 21 q^{24} - 3 q^{25} - 72 q^{26} - 36 q^{28} - 9 q^{29} - 21 q^{30} - 9 q^{32} - 6 q^{33} + 33 q^{34} + 45 q^{35} + 18 q^{36} - 9 q^{38} - 18 q^{39} + 15 q^{40} - 9 q^{41} + 15 q^{42} + 9 q^{43} - 63 q^{44} + 33 q^{45} - 18 q^{46} - 9 q^{47} + 3 q^{48} - 15 q^{49} + 126 q^{50} + 39 q^{51} - 39 q^{52} - 51 q^{54} + 3 q^{55} + 63 q^{56} - 78 q^{57} - 6 q^{58} + 36 q^{59} - 75 q^{60} - 24 q^{61} + 18 q^{62} - 9 q^{63} - 18 q^{65} + 159 q^{66} - 63 q^{67} + 54 q^{68} - 9 q^{69} + 39 q^{70} + 141 q^{72} - 45 q^{73} - 117 q^{74} - 3 q^{76} - 18 q^{77} + 27 q^{78} + 3 q^{79} + 126 q^{80} - 60 q^{81} - 3 q^{82} + 27 q^{83} - 117 q^{84} - 3 q^{85} - 171 q^{86} + 15 q^{87} - 9 q^{88} + 54 q^{89} - 21 q^{90} - 9 q^{91} - 27 q^{92} + 42 q^{93} + 99 q^{95} + 207 q^{96} - 57 q^{97} - 27 q^{98} + 39 q^{99}+O(q^{100}) \) 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9 - 12 * q^10 - 9 * q^12 - 6 * q^13 - 9 * q^14 - 36 * q^15 - 9 * q^16 + 27 * q^17 + 36 * q^18 - 15 * q^19 - 18 * q^20 + 3 * q^21 + 30 * q^22 - 45 * q^23 - 21 * q^24 - 3 * q^25 - 72 * q^26 - 36 * q^28 - 9 * q^29 - 21 * q^30 - 9 * q^32 - 6 * q^33 + 33 * q^34 + 45 * q^35 + 18 * q^36 - 9 * q^38 - 18 * q^39 + 15 * q^40 - 9 * q^41 + 15 * q^42 + 9 * q^43 - 63 * q^44 + 33 * q^45 - 18 * q^46 - 9 * q^47 + 3 * q^48 - 15 * q^49 + 126 * q^50 + 39 * q^51 - 39 * q^52 - 51 * q^54 + 3 * q^55 + 63 * q^56 - 78 * q^57 - 6 * q^58 + 36 * q^59 - 75 * q^60 - 24 * q^61 + 18 * q^62 - 9 * q^63 - 18 * q^65 + 159 * q^66 - 63 * q^67 + 54 * q^68 - 9 * q^69 + 39 * q^70 + 141 * q^72 - 45 * q^73 - 117 * q^74 - 3 * q^76 - 18 * q^77 + 27 * q^78 + 3 * q^79 + 126 * q^80 - 60 * q^81 - 3 * q^82 + 27 * q^83 - 117 * q^84 - 3 * q^85 - 171 * q^86 + 15 * q^87 - 9 * q^88 + 54 * q^89 - 21 * q^90 - 9 * q^91 - 27 * q^92 + 42 * q^93 + 99 * q^95 + 207 * q^96 - 57 * q^97 - 27 * q^98 + 39 * q^99

Introduction

L-functions

Modular forms

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Database

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