LMFDB - Embedded newform 225.2.q.a.106.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(16,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

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

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

chi := DirichletCharacter("225.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			106.16
Character	$\chi$	$=$	225.106
Dual form			225.2.q.a.121.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.322170 + 0.0684793i) q^{2} +(-0.519845 - 1.65220i) q^{3} +(-1.72799 - 0.769349i) q^{4} +(-1.71956 + 1.42937i) q^{5} +(-0.0543370 - 0.567887i) q^{6} +(-1.22023 + 2.11349i) q^{7} +(-1.03695 - 0.753387i) q^{8} +(-2.45952 + 1.71778i) q^{9} +O(q^{10})$	\(q+(0.322170 + 0.0684793i) q^{2} +(-0.519845 - 1.65220i) q^{3} +(-1.72799 - 0.769349i) q^{4} +(-1.71956 + 1.42937i) q^{5} +(-0.0543370 - 0.567887i) q^{6} +(-1.22023 + 2.11349i) q^{7} +(-1.03695 - 0.753387i) q^{8} +(-2.45952 + 1.71778i) q^{9} +(-0.651873 + 0.342746i) q^{10} +(-1.65447 - 0.351668i) q^{11} +(-0.372832 + 3.25492i) q^{12} +(2.11839 - 0.450278i) q^{13} +(-0.537850 + 0.597343i) q^{14} +(3.25551 + 2.09801i) q^{15} +(2.24886 + 2.49761i) q^{16} +(-3.09482 - 2.24852i) q^{17} +(-0.910015 + 0.384989i) q^{18} +(-4.15077 - 3.01571i) q^{19} +(4.07107 - 1.14699i) q^{20} +(4.12624 + 0.917366i) q^{21} +(-0.508937 - 0.226593i) q^{22} +(-5.83819 + 6.48397i) q^{23} +(-0.705692 + 2.10489i) q^{24} +(0.913787 - 4.91579i) q^{25} +0.713316 q^{26} +(4.11668 + 3.17064i) q^{27} +(3.73455 - 2.71331i) q^{28} +(-0.606373 - 5.76925i) q^{29} +(0.905158 + 0.898849i) q^{30} +(0.743462 - 7.07356i) q^{31} +(1.83522 + 3.17869i) q^{32} +(0.279041 + 2.91632i) q^{33} +(-0.843080 - 0.936336i) q^{34} +(-0.922715 - 5.37844i) q^{35} +(5.57159 - 1.07606i) q^{36} +(2.56039 - 7.88008i) q^{37} +(-1.13074 - 1.25581i) q^{38} +(-1.84518 - 3.26593i) q^{39} +(2.85997 - 0.186690i) q^{40} +(-4.23841 + 0.900902i) q^{41} +(1.26653 + 0.578109i) q^{42} +(-3.28981 + 5.69811i) q^{43} +(2.58834 + 1.88054i) q^{44} +(1.77396 - 6.46939i) q^{45} +(-2.32491 + 1.68914i) q^{46} +(0.832694 + 7.92255i) q^{47} +(2.95750 - 5.01394i) q^{48} +(0.522100 + 0.904304i) q^{49} +(0.631024 - 1.52114i) q^{50} +(-2.10617 + 6.28214i) q^{51} +(-4.00697 - 0.851708i) q^{52} +(-2.04603 + 1.48652i) q^{53} +(1.10915 + 1.30339i) q^{54} +(3.34762 - 1.76013i) q^{55} +(2.85759 - 1.27228i) q^{56} +(-2.82480 + 8.42560i) q^{57} +(0.199719 - 1.90020i) q^{58} +(0.942892 - 0.200418i) q^{59} +(-4.01139 - 6.12995i) q^{60} +(8.52867 + 1.81282i) q^{61} +(0.723913 - 2.22798i) q^{62} +(-0.629334 - 7.29425i) q^{63} +(-1.70356 - 5.24301i) q^{64} +(-2.99909 + 3.80225i) q^{65} +(-0.109809 + 0.958658i) q^{66} +(-0.353406 + 3.36243i) q^{67} +(3.61791 + 6.26641i) q^{68} +(13.7478 + 6.27520i) q^{69} +(0.0710407 - 1.79596i) q^{70} +(-0.529305 + 0.384563i) q^{71} +(3.84454 + 0.0717278i) q^{72} +(3.37004 + 10.3719i) q^{73} +(1.36450 - 2.36339i) q^{74} +(-8.59689 + 1.04569i) q^{75} +(4.85234 + 8.40450i) q^{76} +(2.76207 - 3.06759i) q^{77} +(-0.370814 - 1.17854i) q^{78} +(-0.658241 - 6.26274i) q^{79} +(-7.43708 - 1.08034i) q^{80} +(3.09850 - 8.44981i) q^{81} -1.42718 q^{82} +(-13.0700 + 5.81913i) q^{83} +(-6.42431 - 4.75972i) q^{84} +(8.53571 - 0.557185i) q^{85} +(-1.45008 + 1.61048i) q^{86} +(-9.21673 + 4.00097i) q^{87} +(1.45065 + 1.61111i) q^{88} +(-2.96245 - 9.11749i) q^{89} +(1.01454 - 1.96276i) q^{90} +(-1.63326 + 5.02664i) q^{91} +(15.0768 - 6.71261i) q^{92} +(-12.0734 + 2.44881i) q^{93} +(-0.274262 + 2.60943i) q^{94} +(11.4481 - 0.747296i) q^{95} +(4.29780 - 4.68457i) q^{96} +(0.161080 + 1.53258i) q^{97} +(0.106279 + 0.327092i) q^{98} +(4.67328 - 1.97707i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) $ 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.322170	+	0.0684793i	0.227808	+	0.0484222i	0.320401	−	0.947282i	$-0.396182\pi$
$2$	0.322170	+	0.0684793i	0.227808	+	0.0484222i	−0.0925930	+	0.995704i	$0.529516\pi$
$3$	−0.519845	−	1.65220i	−0.300133	−	0.953897i
$3$	−0.519845	−	1.65220i	−0.300133	−	0.953897i
$4$	−1.72799	−	0.769349i	−0.863994	−	0.384675i
$5$	−1.71956	+	1.42937i	−0.769012	+	0.639235i
$5$	−1.71956	+	1.42937i	−0.769012	+	0.639235i
$6$	−0.0543370	−	0.567887i	−0.0221830	−	0.231839i
$7$	−1.22023	+	2.11349i	−0.461202	+	0.798825i	−0.999021	−	0.0442351i	$-0.985915\pi$
$7$	−1.22023	+	2.11349i	−0.461202	+	0.798825i	0.537819	+	0.843060i	$0.319248\pi$
$8$	−1.03695	−	0.753387i	−0.366616	−	0.266362i
$9$	−2.45952	+	1.71778i	−0.819841	+	0.572592i
$10$	−0.651873	+	0.342746i	−0.206140	+	0.108386i
$11$	−1.65447	−	0.351668i	−0.498840	−	0.106032i	−0.0483813	−	0.998829i	$-0.515406\pi$
$11$	−1.65447	−	0.351668i	−0.498840	−	0.106032i	−0.450459	+	0.892797i	$0.648740\pi$
$12$	−0.372832	+	3.25492i	−0.107627	+	0.939615i
$13$	2.11839	−	0.450278i	0.587536	−	0.124885i	0.0954545	−	0.995434i	$-0.469570\pi$
$13$	2.11839	−	0.450278i	0.587536	−	0.124885i	0.492081	+	0.870549i	$0.336236\pi$
$14$	−0.537850	+	0.597343i	−0.143746	+	0.159647i
$15$	3.25551	+	2.09801i	0.840570	+	0.541703i
$16$	2.24886	+	2.49761i	0.562216	+	0.624404i
$17$	−3.09482	−	2.24852i	−0.750604	−	0.545346i	0.145410	−	0.989372i	$-0.453550\pi$
$17$	−3.09482	−	2.24852i	−0.750604	−	0.545346i	−0.896014	+	0.444025i	$0.853550\pi$
$18$	−0.910015	+	0.384989i	−0.214493	+	0.0907427i
$19$	−4.15077	−	3.01571i	−0.952252	−	0.691851i	−0.000913382	−	1.00000i	$-0.500291\pi$
$19$	−4.15077	−	3.01571i	−0.952252	−	0.691851i	−0.951338	+	0.308148i	$0.900291\pi$
$20$	4.07107	−	1.14699i	0.910318	−	0.256476i
$21$	4.12624	+	0.917366i	0.900419	+	0.200186i
$22$	−0.508937	−	0.226593i	−0.108506	−	0.0483098i
$23$	−5.83819	+	6.48397i	−1.21735	+	1.35200i	−0.299987	+	0.953943i	$0.596982\pi$
$23$	−5.83819	+	6.48397i	−1.21735	+	1.35200i	−0.917360	+	0.398058i	$0.869684\pi$
$24$	−0.705692	+	2.10489i	−0.144049	+	0.429658i
$25$	0.913787	−	4.91579i	0.182757	−	0.983158i
$26$	0.713316			0.139893
$27$	4.11668	+	3.17064i	0.792255	+	0.610190i
$28$	3.73455	−	2.71331i	0.705763	−	0.512767i
$29$	−0.606373	−	5.76925i	−0.112601	−	1.07132i	−0.894239	−	0.447591i	$-0.852282\pi$
$29$	−0.606373	−	5.76925i	−0.112601	−	1.07132i	0.781638	−	0.623732i	$-0.214384\pi$
$30$	0.905158	+	0.898849i	0.165258	+	0.164107i
$31$	0.743462	−	7.07356i	0.133530	−	1.27045i	−0.698456	−	0.715653i	$-0.746129\pi$
$31$	0.743462	−	7.07356i	0.133530	−	1.27045i	0.831986	−	0.554797i	$-0.187204\pi$
$32$	1.83522	+	3.17869i	0.324424	+	0.561918i
$33$	0.279041	+	2.91632i	0.0485749	+	0.507666i
$34$	−0.843080	−	0.936336i	−0.144587	−	0.160580i
$35$	−0.922715	−	5.37844i	−0.155967	−	0.909122i
$36$	5.57159	−	1.07606i	0.928599	−	0.179344i
$37$	2.56039	−	7.88008i	0.420926	−	1.29548i	−0.485916	−	0.874006i	$-0.661514\pi$
$37$	2.56039	−	7.88008i	0.420926	−	1.29548i	0.906842	−	0.421472i	$-0.138486\pi$
$38$	−1.13074	−	1.25581i	−0.183430	−	0.203720i
$39$	−1.84518	−	3.26593i	−0.295466	−	0.522967i
$40$	2.85997	−	0.186690i	0.452200	−	0.0295183i
$41$	−4.23841	+	0.900902i	−0.661928	+	0.140697i	−0.526613	−	0.850105i	$-0.676538\pi$
$41$	−4.23841	+	0.900902i	−0.661928	+	0.140697i	−0.135316	+	0.990803i	$0.543205\pi$
$42$	1.26653	+	0.578109i	0.195430	+	0.0892042i
$43$	−3.28981	+	5.69811i	−0.501691	+	0.868954i	0.498307	+	0.867001i	$0.333955\pi$
$43$	−3.28981	+	5.69811i	−0.501691	+	0.868954i	−0.999998	+	0.00195353i	$0.999378\pi$
$44$	2.58834	+	1.88054i	0.390207	+	0.283502i
$45$	1.77396	−	6.46939i	0.264446	−	0.964400i
$46$	−2.32491	+	1.68914i	−0.342789	+	0.249051i
$47$	0.832694	+	7.92255i	0.121461	+	1.15562i	0.870179	+	0.492735i	$0.164003\pi$
$47$	0.832694	+	7.92255i	0.121461	+	1.15562i	−0.748718	+	0.662888i	$0.769330\pi$
$48$	2.95750	−	5.01394i	0.426878	−	0.723700i
$49$	0.522100	+	0.904304i	0.0745857	+	0.129186i
$50$	0.631024	−	1.52114i	0.0892403	−	0.215122i
$51$	−2.10617	+	6.28214i	−0.294923	+	0.879676i
$52$	−4.00697	−	0.851708i	−0.555667	−	0.118111i
$53$	−2.04603	+	1.48652i	−0.281043	+	0.204190i	−0.719372	−	0.694625i	$-0.755570\pi$
$53$	−2.04603	+	1.48652i	−0.281043	+	0.204190i	0.438329	+	0.898815i	$0.355570\pi$
$54$	1.10915	+	1.30339i	0.150936	+	0.177369i
$55$	3.34762	−	1.76013i	0.451393	−	0.237336i
$56$	2.85759	−	1.27228i	0.381861	−	0.170015i
$57$	−2.82480	+	8.42560i	−0.374153	+	1.11600i
$58$	0.199719	−	1.90020i	0.0262244	−	0.249509i
$59$	0.942892	−	0.200418i	0.122754	−	0.0260922i	−0.146125	−	0.989266i	$-0.546680\pi$
$59$	0.942892	−	0.200418i	0.122754	−	0.0260922i	0.268879	+	0.963174i	$0.413347\pi$
$60$	−4.01139	−	6.12995i	−0.517868	−	0.791374i
$61$	8.52867	+	1.81282i	1.09198	+	0.232108i	0.718499	−	0.695528i	$-0.244829\pi$
$61$	8.52867	+	1.81282i	1.09198	+	0.232108i	0.373485	+	0.927636i	$0.378163\pi$
$62$	0.723913	−	2.22798i	0.0919371	−	0.282953i
$63$	−0.629334	−	7.29425i	−0.0792886	−	0.918990i
$64$	−1.70356	−	5.24301i	−0.212945	−	0.655376i
$65$	−2.99909	+	3.80225i	−0.371991	+	0.471611i
$66$	−0.109809	+	0.958658i	−0.0135165	+	0.118003i
$67$	−0.353406	+	3.36243i	−0.0431754	+	0.410787i	0.951494	+	0.307668i	$0.0995487\pi$
$67$	−0.353406	+	3.36243i	−0.0431754	+	0.410787i	−0.994669	+	0.103118i	$0.967118\pi$
$68$	3.61791	+	6.26641i	0.438737	+	0.759914i
$69$	13.7478	+	6.27520i	1.65504	+	0.755445i
$70$	0.0710407	−	1.79596i	0.00849099	−	0.214658i
$71$	−0.529305	+	0.384563i	−0.0628170	+	0.0456392i	−0.618751	−	0.785587i	$-0.712361\pi$
$71$	−0.529305	+	0.384563i	−0.0628170	+	0.0456392i	0.555934	+	0.831227i	$0.312361\pi$
$72$	3.84454	+	0.0717278i	0.453084	+	0.00845320i
$73$	3.37004	+	10.3719i	0.394434	+	1.21394i	0.929402	+	0.369070i	$0.120324\pi$
$73$	3.37004	+	10.3719i	0.394434	+	1.21394i	−0.534968	+	0.844872i	$0.679676\pi$
$74$	1.36450	−	2.36339i	0.158620	−	0.274738i
$75$	−8.59689	+	1.04569i	−0.992683	+	0.120746i
$76$	4.85234	+	8.40450i	0.556602	+	0.964062i
$77$	2.76207	−	3.06759i	0.314767	−	0.349584i
$78$	−0.370814	−	1.17854i	−0.0419864	−	0.133443i
$79$	−0.658241	−	6.26274i	−0.0740579	−	0.704613i	−0.967058	−	0.254557i	$-0.918070\pi$
$79$	−0.658241	−	6.26274i	−0.0740579	−	0.704613i	0.893000	−	0.450057i	$-0.148596\pi$
$80$	−7.43708	−	1.08034i	−0.831491	−	0.120786i
$81$	3.09850	−	8.44981i	0.344277	−	0.938868i
$82$	−1.42718			−0.157606
$83$	−13.0700	+	5.81913i	−1.43462	+	0.638732i	−0.969181	−	0.246350i	$-0.920769\pi$
$83$	−13.0700	+	5.81913i	−1.43462	+	0.638732i	−0.465435	+	0.885082i	$0.654102\pi$
$84$	−6.42431	−	4.75972i	−0.700950	−	0.519328i
$85$	8.53571	−	0.557185i	0.925828	−	0.0604352i
$86$	−1.45008	+	1.61048i	−0.156366	+	0.173662i
$87$	−9.21673	+	4.00097i	−0.988137	+	0.428949i
$88$	1.45065	+	1.61111i	0.154640	+	0.171745i
$89$	−2.96245	−	9.11749i	−0.314019	−	0.966452i	−0.976156	−	0.217069i	$-0.930350\pi$
$89$	−2.96245	−	9.11749i	−0.314019	−	0.966452i	0.662137	−	0.749383i	$-0.269650\pi$
$90$	1.01454	−	1.96276i	0.106941	−	0.206893i
$91$	−1.63326	+	5.02664i	−0.171212	+	0.526935i
$92$	15.0768	−	6.71261i	1.57186	−	0.699838i
$93$	−12.0734	+	2.44881i	−1.25196	+	0.253930i
$94$	−0.274262	+	2.60943i	−0.0282880	+	0.269142i
$95$	11.4481	−	0.747296i	1.17455	−	0.0766709i
$96$	4.29780	−	4.68457i	0.438642	−	0.478117i
$97$	0.161080	+	1.53258i	0.0163552	+	0.155609i	0.999651	−	0.0264034i	$-0.00840543\pi$
$97$	0.161080	+	1.53258i	0.0163552	+	0.155609i	−0.983296	+	0.182013i	$0.941739\pi$
$98$	0.106279	+	0.327092i	0.0107358	+	0.0330413i
$99$	4.67328	−	1.97707i	0.469682	−	0.198703i
$100$	−5.36097	+	7.79140i	−0.536097	+	0.779140i
$101$	4.44731	−	7.70297i	0.442524	−	0.766474i	−0.555352	−	0.831616i	$-0.687416\pi$
$101$	4.44731	−	7.70297i	0.442524	−	0.766474i	0.997876	+	0.0651410i	$0.0207497\pi$
$102$	−1.10874	+	1.87969i	−0.109782	+	0.186117i
$103$	−9.05359	−	4.03092i	−0.892076	−	0.397178i	−0.0910775	−	0.995844i	$-0.529031\pi$
$103$	−9.05359	−	4.03092i	−0.892076	−	0.397178i	−0.800999	+	0.598666i	$0.795698\pi$
$104$	−2.53589	−	1.12905i	−0.248665	−	0.110713i
$105$	−8.40658	+	4.32046i	−0.820398	+	0.421634i
$106$	−0.760964	+	0.338803i	−0.0739113	+	0.0329074i
$107$	0.789838			0.0763565			0.0381783	−	0.999271i	$-0.487845\pi$
$107$	0.789838			0.0763565			0.0381783	+	0.999271i	$0.487845\pi$
$108$	−4.67423	−	8.64599i	−0.449778	−	0.831961i
$109$	−5.37002	+	16.5272i	−0.514354	+	1.58302i	0.270100	+	0.962832i	$0.412943\pi$
$109$	−5.37002	+	16.5272i	−0.514354	+	1.58302i	−0.784454	+	0.620187i	$0.787057\pi$
$110$	1.19903	−	0.337819i	0.114323	−	0.0322098i
$111$	−14.3505	−	0.133857i	−1.36209	−	0.0127051i
$112$	−8.02281	+	1.70530i	−0.758084	+	0.161136i
$113$	−2.12606	+	0.451907i	−0.200003	+	0.0425119i	−0.306824	−	0.951766i	$-0.599266\pi$
$113$	−2.12606	+	0.451907i	−0.200003	+	0.0425119i	0.106821	+	0.994278i	$0.465933\pi$
$114$	−1.48704	+	2.52103i	−0.139274	+	0.236116i
$115$	0.771124	−	19.4945i	0.0719077	−	1.81788i
$116$	−3.39077	+	10.4357i	−0.314825	+	0.968931i
$117$	−4.43675	+	4.74639i	−0.410178	+	0.438804i
$118$	0.317496			0.0292279
$119$	8.52861	−	3.79718i	0.781816	−	0.348087i
$120$	−1.79519	−	4.62818i	−0.163878	−	0.422493i
$121$	−7.43541	−	3.31046i	−0.675947	−	0.300951i
$122$	2.62354	+	1.16807i	0.237524	+	0.105752i
$123$	3.69179	+	6.53437i	0.332877	+	0.589184i
$124$	−6.72673	+	11.6510i	−0.604079	+	1.04629i
$125$	5.45518	+	9.75915i	0.487926	+	0.872885i
$126$	0.296753	−	2.39308i	0.0264369	−	0.213193i
$127$	−4.55776	−	14.0274i	−0.404436	−	1.24473i	−0.921365	−	0.388698i	$-0.872925\pi$
$127$	−4.55776	−	14.0274i	−0.404436	−	1.24473i	0.516929	−	0.856028i	$-0.327075\pi$
$128$	−0.957127	−	9.10645i	−0.0845989	−	0.804904i
$129$	11.1246	+	2.47328i	0.979467	+	0.217760i
$130$	−1.22659	+	1.01959i	−0.107579	+	0.0894243i
$131$	0.220445	−	2.09740i	0.0192604	−	0.183250i	−0.980662	−	0.195709i	$-0.937299\pi$
$131$	0.220445	−	2.09740i	0.0192604	−	0.183250i	0.999922	+	0.0124587i	$0.00396583\pi$
$132$	1.76149	−	5.25404i	0.153318	−	0.457306i
$133$	11.4386	−	5.09277i	0.991848	−	0.441599i
$134$	−0.344114	+	1.05907i	−0.0297269	+	0.0914900i
$135$	−11.6109	+	0.432150i	−0.999308	+	0.0371936i
$136$	1.51516	+	4.66319i	0.129924	+	0.399866i
$137$	3.08638	+	3.42777i	0.263687	+	0.292854i	0.860420	−	0.509586i	$-0.170201\pi$
$137$	3.08638	+	3.42777i	0.263687	+	0.292854i	−0.596733	+	0.802440i	$0.703535\pi$
$138$	3.99939	+	2.96311i	0.340451	+	0.252237i
$139$	−2.67827	+	2.97452i	−0.227168	+	0.252295i	−0.845944	−	0.533272i	$-0.820962\pi$
$139$	−2.67827	+	2.97452i	−0.227168	+	0.252295i	0.618776	+	0.785567i	$0.287629\pi$
$140$	−2.54346	+	10.0038i	−0.214961	+	0.845472i
$141$	12.6568	−	5.49428i	1.06589	−	0.462702i
$142$	−0.196861	+	0.0876480i	−0.0165202	+	0.00735525i
$143$	−3.66315			−0.306328
$144$	−9.82147	−	2.27990i	−0.818456	−	0.189992i
$145$	9.28911	+	9.05385i	0.771418	+	0.751882i
$146$	0.375464	+	3.57230i	0.0310736	+	0.295645i
$147$	1.22268	−	1.33271i	0.100845	−	0.109920i
$148$	−10.4869	+	11.6468i	−0.862015	+	0.957364i
$149$	−6.88364	−	11.9228i	−0.563929	−	0.976755i	−0.997148	−	0.0754658i	$-0.975956\pi$
$149$	−6.88364	−	11.9228i	−0.563929	−	0.976755i	0.433219	−	0.901289i	$-0.357378\pi$
$150$	−2.84127	−	0.251819i	−0.231988	−	0.0205609i
$151$	−10.1492	+	17.5789i	−0.825931	+	1.43055i	0.0752750	+	0.997163i	$0.476017\pi$
$151$	−10.1492	+	17.5789i	−0.825931	+	1.43055i	−0.901206	+	0.433391i	$0.857317\pi$
$152$	2.03213	+	6.25427i	0.164828	+	0.507288i
$153$	11.4742	+	0.214075i	0.927637	+	0.0173069i
$154$	1.09992	−	0.799139i	0.0886341	−	0.0643965i
$155$	8.83233	+	13.2261i	0.709430	+	1.06235i
$156$	0.675814	+	7.06307i	0.0541084	+	0.565498i
$157$	−4.22601	−	7.31966i	−0.337272	−	0.584172i	0.646647	−	0.762790i	$-0.276171\pi$
$157$	−4.22601	−	7.31966i	−0.337272	−	0.584172i	−0.983919	+	0.178618i	$0.942838\pi$
$158$	0.216803	−	2.06274i	0.0172479	−	0.164103i
$159$	3.51965	+	2.60768i	0.279127	+	0.206802i
$160$	−7.69931	−	2.84275i	−0.608684	−	0.224739i
$161$	−6.57991	−	20.2509i	−0.518570	−	1.59599i
$162$	1.57688	−	2.51009i	0.123891	−	0.197211i
$163$	2.21761	−	6.82510i	0.173696	−	0.534583i	−0.825875	−	0.563853i	$-0.809318\pi$
$163$	2.21761	−	6.82510i	0.173696	−	0.534583i	0.999572	+	0.0292704i	$0.00931840\pi$
$164$	8.01702	+	1.70407i	0.626024	+	0.133066i
$165$	−4.64834	−	4.61594i	−0.361872	−	0.359350i
$166$	−4.60924	+	0.979724i	−0.357746	+	0.0760413i
$167$	0.633238	−	6.02486i	0.0490014	−	0.466217i	−0.942316	−	0.334725i	$-0.891357\pi$
$167$	0.633238	−	6.02486i	0.0490014	−	0.466217i	0.991317	−	0.131492i	$-0.0419768\pi$
$168$	−3.58756	−	4.05991i	−0.276786	−	0.313229i
$169$	−7.59126	+	3.37985i	−0.583943	+	0.259988i
$170$	2.78810	+	0.405011i	0.213838	+	0.0310629i
$171$	15.3892	+	0.287117i	1.17684	+	0.0219564i
$172$	10.0686	−	7.31525i	0.767722	−	0.557783i
$173$	19.0929	+	4.05833i	1.45161	+	0.308549i	0.865184	−	0.501454i	$-0.167201\pi$
$173$	19.0929	+	4.05833i	1.45161	+	0.308549i	0.586426	+	0.810003i	$0.300535\pi$
$174$	−3.24333	+	0.657835i	−0.245876	+	0.0498703i
$175$	9.27446	+	7.92965i	0.701083	+	0.599425i
$176$	−2.84234	−	4.92307i	−0.214249	−	0.371090i
$177$	−0.821288	−	1.45366i	−0.0617318	−	0.109264i
$178$	−0.330053	−	3.14024i	−0.0247385	−	0.235371i
$179$	−3.88878	+	2.82536i	−0.290661	+	0.211178i	−0.723554	−	0.690268i	$-0.757493\pi$
$179$	−3.88878	+	2.82536i	−0.290661	+	0.211178i	0.432893	+	0.901445i	$0.357493\pi$
$180$	−8.04260	+	9.81424i	−0.599460	+	0.731510i
$181$	4.50290	+	3.27155i	0.334698	+	0.243172i	0.742421	−	0.669933i	$-0.233677\pi$
$181$	4.50290	+	3.27155i	0.334698	+	0.243172i	−0.407724	+	0.913105i	$0.633677\pi$
$182$	−0.870406	+	1.50759i	−0.0645188	+	0.111750i
$183$	−1.43844	−	15.0334i	−0.106333	−	1.11130i
$184$	10.9388	−	2.32512i	0.806422	−	0.171410i
$185$	6.86082	+	17.2100i	0.504417	+	1.26531i
$186$	−4.05738	−	0.0378461i	−0.297502	−	0.00277501i
$187$	4.32954	+	4.80845i	0.316608	+	0.351628i
$188$	4.65633	−	14.3307i	0.339598	−	1.04517i
$189$	−11.7244	+	4.83167i	−0.852825	+	0.351452i
$190$	3.73940	+	0.543200i	0.271284	+	0.0394079i
$191$	−15.8456	−	17.5983i	−1.14655	−	1.27337i	−0.956545	−	0.291583i	$-0.905818\pi$
$191$	−15.8456	−	17.5983i	−1.14655	−	1.27337i	−0.190000	−	0.981784i	$-0.560849\pi$
$192$	−7.77690	+	5.54017i	−0.561250	+	0.399827i
$193$	−0.637107	−	1.10350i	−0.0458600	−	0.0794318i	0.842184	−	0.539190i	$-0.181269\pi$
$193$	−0.637107	−	1.10350i	−0.0458600	−	0.0794318i	−0.888044	+	0.459758i	$0.847936\pi$
$194$	−0.0530545	+	0.504780i	−0.00380909	+	0.0362411i
$195$	7.84114	+	2.97851i	0.561515	+	0.213296i
$196$	−0.206457	−	1.96430i	−0.0147469	−	0.140307i
$197$	−7.96236	+	5.78499i	−0.567295	+	0.412164i	−0.834122	−	0.551581i	$-0.814025\pi$
$197$	−7.96236	+	5.78499i	−0.567295	+	0.412164i	0.266827	+	0.963745i	$0.414025\pi$
$198$	1.64098	−	0.316928i	0.116619	−	0.0225231i
$199$	−18.5853			−1.31747			−0.658737	−	0.752373i	$-0.728909\pi$
$199$	−18.5853			−1.31747			−0.658737	+	0.752373i	$0.728909\pi$
$200$	−4.65104	+	4.40898i	−0.328878	+	0.311762i
$201$	5.73913	−	1.16405i	0.404807	−	0.0821056i
$202$	1.96028	−	2.17712i	0.137925	−	0.153181i
$203$	12.9332	+	5.75822i	0.907731	+	0.404148i
$204$	8.47260	−	9.23508i	0.593201	−	0.646585i
$205$	6.00048	−	7.60742i	0.419092	−	0.531325i
$206$	−2.64076	−	1.91862i	−0.183990	−	0.133677i
$207$	3.22116	−	25.9762i	0.223886	−	1.80547i
$208$	5.88859	+	4.27831i	0.408300	+	0.296647i
$209$	5.80678	+	6.44908i	0.401663	+	0.446092i
$210$	−3.00421	+	0.816246i	−0.207310	+	0.0563263i
$211$	1.47743	−	1.64086i	0.101711	−	0.112961i	−0.690140	−	0.723676i	$-0.742451\pi$
$211$	1.47743	−	1.64086i	0.101711	−	0.112961i	0.791851	+	0.610715i	$0.209118\pi$
$212$	4.67916	−	0.994587i	0.321366	−	0.0683085i
$213$	0.910531	+	0.674604i	0.0623885	+	0.0462231i
$214$	0.254462	+	0.0540875i	0.0173946	+	0.00369735i
$215$	−2.48770	−	14.5006i	−0.169660	−	0.988934i
$216$	−1.88006	−	6.38924i	−0.127922	−	0.434733i
$217$	14.0427	+	10.2026i	0.953283	+	0.692600i
$218$	−2.86183	+	4.95683i	−0.193827	+	0.335719i
$219$	15.3846	−	10.9598i	1.03959	−	0.740593i
$220$	−7.13880	+	0.465999i	−0.481298	+	0.0314177i
$221$	−7.56850	−	3.36971i	−0.509112	−	0.226671i
$222$	−4.61412	−	1.02583i	−0.309679	−	0.0688495i
$223$	25.6468	+	5.45140i	1.71744	+	0.365053i	0.958275	−	0.285849i	$-0.0922755\pi$
$223$	25.6468	+	5.45140i	1.71744	+	0.365053i	0.759162	+	0.650901i	$0.225609\pi$
$224$	−8.95752			−0.598499
$225$	6.19674	+	13.6602i	0.413116	+	0.910678i
$226$	−0.715897			−0.0476208
$227$	7.25153	+	1.54136i	0.481301	+	0.102304i	0.442171	−	0.896931i	$-0.354208\pi$
$227$	7.25153	+	1.54136i	0.481301	+	0.102304i	0.0391292	+	0.999234i	$0.487542\pi$
$228$	11.3634	−	12.3861i	0.752562	−	0.820288i
$229$	18.6311	+	8.29511i	1.23118	+	0.548156i	0.916116	−	0.400914i	$-0.131307\pi$
$229$	18.6311	+	8.29511i	1.23118	+	0.548156i	0.315064	+	0.949071i	$0.397974\pi$
$230$	1.58341	−	6.22774i	0.104407	−	0.410645i
$231$	−6.50411	−	2.96881i	−0.427939	−	0.195334i
$232$	−3.71770	+	6.43924i	−0.244079	+	0.422757i
$233$	6.14372	+	4.46367i	0.402488	+	0.292425i	0.770554	−	0.637375i	$-0.219980\pi$
$233$	6.14372	+	4.46367i	0.402488	+	0.292425i	−0.368065	+	0.929800i	$0.619980\pi$
$234$	−1.75442	+	1.22532i	−0.114690	+	0.0801014i
$235$	−12.7562	−	12.4331i	−0.832120	−	0.811045i
$236$	−1.78350	−	0.379094i	−0.116096	−	0.0246769i
$237$	−10.0051	+	4.34320i	−0.649902	+	0.282121i
$238$	3.00769	−	0.639304i	0.194959	−	0.0414399i
$239$	10.8522	−	12.0526i	0.701969	−	0.779615i	−0.281719	−	0.959497i	$-0.590905\pi$
$239$	10.8522	−	12.0526i	0.701969	−	0.779615i	0.983688	+	0.179881i	$0.0575714\pi$
$240$	2.08119	+	12.8491i	0.134340	+	0.829409i
$241$	−9.82298	−	10.9095i	−0.632754	−	0.702744i	0.338453	−	0.940983i	$-0.390097\pi$
$241$	−9.82298	−	10.9095i	−0.632754	−	0.702744i	−0.971207	+	0.238239i	$0.923430\pi$
$242$	−2.16877	−	1.57570i	−0.139414	−	0.101290i
$243$	−15.5715	−	0.726738i	−0.998913	−	0.0466203i
$244$	−13.3427	−	9.69406i	−0.854181	−	0.620599i
$245$	−2.19037	−	0.808731i	−0.139938	−	0.0516679i
$246$	0.741913	+	2.35798i	0.0473026	+	0.150340i
$247$	−10.1509	−	4.51945i	−0.645884	−	0.287566i
$248$	−6.10006	+	6.77480i	−0.387354	+	0.430200i
$249$	16.4087	+	18.5691i	1.03986	+	1.17677i
$250$	1.08920	+	3.51767i	0.0688867	+	0.222477i
$251$	17.7351			1.11943			0.559716	−	0.828685i	$-0.310910\pi$
$251$	17.7351			1.11943			0.559716	+	0.828685i	$0.310910\pi$
$252$	−4.52435	+	13.0886i	−0.285007	+	0.824501i
$253$	11.9393	−	8.67440i	0.750617	−	0.545355i
$254$	−0.507790	−	4.83130i	−0.0318616	−	0.303143i
$255$	−5.35783	−	13.8130i	−0.335520	−	0.865006i
$256$	−0.837248	+	7.96588i	−0.0523280	+	0.497868i
$257$	−3.02034	−	5.23139i	−0.188404	−	0.326325i	0.756314	−	0.654208i	$-0.226998\pi$
$257$	−3.02034	−	5.23139i	−0.188404	−	0.326325i	−0.944718	+	0.327883i	$0.893665\pi$
$258$	3.41464	+	1.55862i	0.212586	+	0.0970355i
$259$	13.5302	+	15.0268i	0.840728	+	0.933723i
$260$	8.10765	−	4.26289i	0.502815	−	0.264373i
$261$	11.4017	+	13.1480i	0.705745	+	0.813840i
$262$	0.214649	−	0.660622i	0.0132611	−	0.0408133i
$263$	−6.77522	−	7.52465i	−0.417778	−	0.463990i	0.497116	−	0.867684i	$-0.334392\pi$
$263$	−6.77522	−	7.52465i	−0.417778	−	0.463990i	−0.914894	+	0.403695i	$0.867726\pi$
$264$	1.90776	−	3.23430i	0.117415	−	0.199057i
$265$	1.39347	−	5.48071i	0.0856002	−	0.336677i
$266$	4.03390	−	0.857433i	0.247335	−	0.0525726i
$267$	−13.5239	+	9.63424i	−0.827648	+	0.589606i
$268$	3.19757	−	5.53835i	0.195323	−	0.338309i
$269$	21.9237	+	15.9285i	1.33671	+	0.971177i	0.999558	+	0.0297274i	$0.00946393\pi$
$269$	21.9237	+	15.9285i	1.33671	+	0.971177i	0.337153	+	0.941450i	$0.390536\pi$
$270$	−3.77028	−	0.655881i	−0.229452	−	0.0399156i
$271$	−8.50805	+	6.18146i	−0.516827	+	0.375497i	−0.815407	−	0.578888i	$-0.803487\pi$
$271$	−8.50805	+	6.18146i	−0.516827	+	0.375497i	0.298580	+	0.954385i	$0.403487\pi$
$272$	−1.34389	−	12.7863i	−0.0814855	−	0.775282i
$273$	9.15405	+	0.0853863i	0.554029	+	0.00516781i
$274$	0.759606	+	1.31568i	0.0458895	+	0.0794829i
$275$	−3.24055	+	7.81166i	−0.195413	+	0.471061i
$276$	−18.9281	−	21.4203i	−1.13934	−	1.28935i
$277$	−15.9055	−	3.38081i	−0.955668	−	0.203133i	−0.296419	−	0.955058i	$-0.595792\pi$
$277$	−15.9055	−	3.38081i	−0.955668	−	0.203133i	−0.659249	+	0.751925i	$0.729126\pi$
$278$	−1.06655	+	0.774893i	−0.0639674	+	0.0464750i
$279$	10.3222	+	18.6747i	0.617976	+	1.11802i
$280$	−3.09524	+	6.27232i	−0.184976	+	0.374843i
$281$	−13.8705	+	6.17553i	−0.827443	+	0.368401i	−0.776357	−	0.630293i	$-0.782935\pi$
$281$	−13.8705	+	6.17553i	−0.827443	+	0.368401i	−0.0510856	+	0.998694i	$0.516268\pi$
$282$	4.45387	−	0.903364i	0.265224	−	0.0537945i
$283$	0.197779	−	1.88174i	0.0117568	−	0.111858i	−0.987070	−	0.160292i	$-0.948756\pi$
$283$	0.197779	−	1.88174i	0.0117568	−	0.111858i	0.998826	+	0.0484340i	$0.0154231\pi$
$284$	1.21050	−	0.257299i	0.0718297	−	0.0152679i
$285$	−7.18591	−	18.5260i	−0.425657	−	1.09739i
$286$	−1.18016	−	0.250850i	−0.0697841	−	0.0148331i
$287$	3.26777	−	10.0571i	0.192890	−	0.593655i
$288$	−9.97404	−	4.66557i	−0.587726	−	0.274921i
$289$	−0.731209	−	2.25043i	−0.0430123	−	0.132378i
$290$	2.37267	+	3.55299i	0.139328	+	0.208639i
$291$	2.44838	−	1.06284i	0.143527	−	0.0623047i
$292$	2.15624	−	20.5153i	0.126185	−	1.20057i
$293$	−3.67099	−	6.35834i	−0.214462	−	0.371458i	0.738644	−	0.674095i	$-0.235466\pi$
$293$	−3.67099	−	6.35834i	−0.214462	−	0.371458i	−0.953106	+	0.302637i	$0.902133\pi$
$294$	0.485173	−	0.345631i	0.0282959	−	0.0201576i
$295$	−1.33489	+	1.69238i	−0.0777203	+	0.0985339i
$296$	−8.59174	+	6.24227i	−0.499385	+	0.362824i
$297$	−5.69589	−	6.69342i	−0.330509	−	0.388392i
$298$	−1.40123	−	4.31255i	−0.0811713	−	0.249820i
$299$	−9.44799	+	16.3644i	−0.546391	+	0.946377i
$300$	15.6598	+	4.80707i	0.904120	+	0.277536i
$301$	−8.02861	−	13.9060i	−0.462761	−	0.801526i
$302$	−4.47356	+	4.96839i	−0.257424	+	0.285899i
$303$	−15.0388	−	3.34349i	−0.863954	−	0.192079i
$304$	−1.80243	−	17.1489i	−0.103376	−	0.983559i
$305$	−17.2568	+	9.07338i	−0.988120	+	0.519540i
$306$	3.68199	+	0.854716i	0.210485	+	0.0488608i
$307$	4.38216			0.250103			0.125051	−	0.992150i	$-0.460090\pi$
$307$	4.38216			0.250103			0.125051	+	0.992150i	$0.460090\pi$
$308$	−7.13286	+	3.17576i	−0.406433	+	0.180955i
$309$	−1.95341	+	17.0538i	−0.111126	+	0.970156i
$310$	1.93979	+	4.86588i	0.110173	+	0.276364i
$311$	−11.9357	+	13.2559i	−0.676810	+	0.751674i	−0.979506	−	0.201413i	$-0.935447\pi$
$311$	−11.9357	+	13.2559i	−0.676810	+	0.751674i	0.302696	+	0.953087i	$0.402113\pi$
$312$	−0.547147	+	4.77673i	−0.0309761	+	0.270429i
$313$	10.9079	+	12.1145i	0.616554	+	0.684752i	0.967855	−	0.251510i	$-0.0809273\pi$
$313$	10.9079	+	12.1145i	0.616554	+	0.684752i	−0.351301	+	0.936263i	$0.614261\pi$
$314$	−0.860246	−	2.64756i	−0.0485465	−	0.149411i
$315$	11.5084	+	11.6434i	0.648424	+	0.656030i
$316$	−3.68081	+	11.3284i	−0.207061	+	0.637270i
$317$	−19.2520	+	8.57156i	−1.08130	+	0.481427i	−0.868510	−	0.495671i	$-0.834922\pi$
$317$	−19.2520	+	8.57156i	−1.08130	+	0.481427i	−0.212792	+	0.977098i	$0.568256\pi$
$318$	0.955353	+	1.08114i	0.0535735	+	0.0606272i
$319$	−1.02564	+	9.75827i	−0.0574246	+	0.546358i
$320$	10.4236	+	6.58066i	0.582696	+	0.367870i
$321$	−0.410593	−	1.30497i	−0.0229171	−	0.0728363i
$322$	−0.733082	−	6.97481i	−0.0408530	−	0.388691i
$323$	6.06501	+	18.6662i	0.337466	+	1.03861i
$324$	−11.8550	+	12.2173i	−0.658612	+	0.678741i
$325$	−0.277714	−	10.8250i	−0.0154048	−	0.600464i
$326$	1.18182	−	2.04698i	0.0654551	−	0.113372i
$327$	30.0978	+	0.280743i	1.66441	+	0.0155251i
$328$	5.07374	+	2.25897i	0.280150	+	0.124731i
$329$	−17.7603	−	7.90741i	−0.979159	−	0.435950i
$330$	−1.18146	−	1.80543i	−0.0650371	−	0.0993856i
$331$	−16.5483	+	7.36780i	−0.909580	+	0.404971i	−0.807542	−	0.589810i	$-0.799203\pi$
$331$	−16.5483	+	7.36780i	−0.909580	+	0.404971i	−0.102037	+	0.994781i	$0.532536\pi$
$332$	27.0617			1.48520
$333$	7.23886	+	23.7794i	0.396687	+	1.30310i
$334$	0.616588	−	1.89766i	0.0337382	−	0.103835i
$335$	−4.19847	−	6.28706i	−0.229387	−	0.343499i
$336$	6.98811	+	12.3688i	0.381233	+	0.674772i
$337$	3.61975	−	0.769402i	0.197180	−	0.0419120i	−0.108263	−	0.994122i	$-0.534529\pi$
$337$	3.61975	−	0.769402i	0.197180	−	0.0419120i	0.305443	+	0.952210i	$0.401195\pi$
$338$	−2.67712	+	0.569040i	−0.145616	+	0.0309517i
$339$	1.85186	+	3.27775i	0.100579	+	0.178023i
$340$	−15.1783	−	5.60413i	−0.823157	−	0.303927i
$341$	−3.71757	+	11.4415i	−0.201318	+	0.619593i
$342$	4.93828	+	1.14634i	0.267031	+	0.0619871i
$343$	−19.6315			−1.06000
$344$	7.70424	−	3.43015i	0.415385	−	0.184941i
$345$	−32.6097	+	8.86009i	−1.75565	+	0.477011i
$346$	5.87326	+	2.61494i	0.315748	+	0.140580i
$347$	−23.5571	−	10.4883i	−1.26461	−	0.563041i	−0.338739	−	0.940880i	$-0.610000\pi$
$347$	−23.5571	−	10.4883i	−1.26461	−	0.563041i	−0.925871	+	0.377840i	$0.876667\pi$
$348$	19.0045	+	0.177269i	1.01875	+	0.00950260i
$349$	15.6853	−	27.1678i	0.839616	−	1.45426i	−0.0506002	−	0.998719i	$-0.516113\pi$
$349$	15.6853	−	27.1678i	0.839616	−	1.45426i	0.890216	−	0.455538i	$-0.150553\pi$
$350$	2.44493	+	3.18980i	0.130687	+	0.170502i
$351$	10.1484	+	4.86301i	0.541681	+	0.259568i
$352$	−1.91846	−	5.90442i	−0.102254	−	0.314707i
$353$	0.0104724	+	0.0996384i	0.000557391	+	0.00530322i	0.994797	−	0.101876i	$-0.0324846\pi$
$353$	0.0104724	+	0.0996384i	0.000557391	+	0.00530322i	−0.994240	+	0.107180i	$0.965818\pi$
$354$	−0.165049	−	0.524566i	−0.00877224	−	0.0278804i
$355$	0.360489	−	1.41785i	0.0191328	−	0.0752519i
$356$	−1.89546	+	18.0341i	−0.100459	+	0.955803i
$357$	−10.7073	−	12.1170i	−0.566688	−	0.641300i
$358$	−1.44633	+	0.643946i	−0.0764407	+	0.0340336i
$359$	4.79343	−	14.7527i	0.252988	−	0.778616i	−0.741232	−	0.671249i	$-0.765758\pi$
$359$	4.79343	−	14.7527i	0.252988	−	0.778616i	0.994219	−	0.107367i	$-0.0342419\pi$
$360$	−6.71346	+	5.37195i	−0.353830	+	0.283126i
$361$	2.26305	+	6.96496i	0.119108	+	0.366577i
$362$	1.22666	+	1.36235i	0.0644720	+	0.0716034i
$363$	−1.60427	+	14.0057i	−0.0842025	+	0.735109i
$364$	6.68949	−	7.42943i	0.350624	−	0.389408i
$365$	−20.6203	−	13.0181i	−1.07932	−	0.681400i
$366$	0.566057	−	4.94182i	0.0295883	−	0.258313i
$367$	−11.7943	+	5.25116i	−0.615657	+	0.274108i	−0.690779	−	0.723066i	$-0.742732\pi$
$367$	−11.7943	+	5.25116i	−0.615657	+	0.274108i	0.0751217	+	0.997174i	$0.476065\pi$
$368$	−29.3238			−1.52861
$369$	8.87691	−	9.49642i	0.462114	−	0.494364i
$370$	1.03182	+	6.01438i	0.0536416	+	0.312673i
$371$	−0.645146	−	6.13816i	−0.0334943	−	0.318677i
$372$	22.7467	+	5.05716i	1.17936	+	0.262202i
$373$	−0.154958	+	0.172099i	−0.00802344	+	0.00891094i	−0.747143	−	0.664663i	$-0.768575\pi$
$373$	−0.154958	+	0.172099i	−0.00802344	+	0.00891094i	0.739120	+	0.673574i	$0.235242\pi$
$374$	1.06557	+	1.84562i	0.0550993	+	0.0954347i
$375$	13.2882	−	14.0863i	0.686200	−	0.727413i
$376$	5.10529	−	8.84261i	0.263285	−	0.456023i
$377$	−3.88230	−	11.9485i	−0.199949	−	0.615379i
$378$	−4.10812	+	0.753738i	−0.211299	+	0.0387681i
$379$	4.51376	−	3.27944i	0.231856	−	0.168453i	−0.465791	−	0.884895i	$-0.654230\pi$
$379$	4.51376	−	3.27944i	0.231856	−	0.168453i	0.697647	+	0.716441i	$0.254230\pi$
$380$	−20.3571	−	7.51626i	−1.04430	−	0.385576i
$381$	−20.8066	+	14.8224i	−1.06596	+	0.759374i
$382$	−3.89984	−	6.75473i	−0.199533	−	0.345602i
$383$	1.40274	−	13.3462i	0.0716768	−	0.681960i	−0.898403	−	0.439173i	$-0.855272\pi$
$383$	1.40274	−	13.3462i	0.0716768	−	0.681960i	0.970080	−	0.242787i	$-0.0780616\pi$
$384$	−14.5481	+	6.31531i	−0.742405	+	0.322277i
$385$	−0.364821	+	9.22293i	−0.0185930	+	0.470044i
$386$	−0.129690	−	0.399143i	−0.00660102	−	0.0203159i
$387$	−1.69672	−	19.6658i	−0.0862494	−	0.999668i
$388$	0.900742	−	2.77220i	0.0457282	−	0.140737i
$389$	−33.2854	−	7.07503i	−1.68764	−	0.358718i	−0.738663	−	0.674075i	$-0.764543\pi$
$389$	−33.2854	−	7.07503i	−1.68764	−	0.358718i	−0.948973	+	0.315356i	$0.897876\pi$
$390$	2.32221	+	1.49654i	0.117590	+	0.0757803i
$391$	32.6475	−	6.93944i	1.65105	−	0.350943i
$392$	0.139900	−	1.33106i	0.00706601	−	0.0672286i
$393$	−3.57991	+	0.726102i	−0.180583	+	0.0366270i
$394$	−2.96138	+	1.31849i	−0.149192	+	0.0664247i
$395$	10.0837	+	9.82830i	0.507365	+	0.494515i
$396$	−9.59642	−	0.179041i	−0.482238	−	0.00899714i
$397$	22.7816	−	16.5518i	1.14338	−	0.830711i	0.155790	−	0.987790i	$-0.450208\pi$
$397$	22.7816	−	16.5518i	1.14338	−	0.830711i	0.987586	+	0.157079i	$0.0502078\pi$
$398$	−5.98761	−	1.27271i	−0.300132	−	0.0637950i
$399$	−14.3606	−	16.2513i	−0.718927	−	0.813583i
$400$	14.3327	−	8.77265i	0.716637	−	0.438632i
$401$	−6.50887	−	11.2737i	−0.325037	−	0.562981i	0.656483	−	0.754341i	$-0.272044\pi$
$401$	−6.50887	−	11.2737i	−0.325037	−	0.562981i	−0.981520	+	0.191360i	$0.938710\pi$
$402$	1.92869	+	0.0179902i	0.0961941	+	0.000897270i
$403$	−1.61013	−	15.3193i	−0.0802061	−	0.763110i
$404$	−13.6112	+	9.88910i	−0.677181	+	0.492001i
$405$	6.74987	+	18.9589i	0.335404	+	0.942074i
$406$	3.77236	+	2.74078i	0.187219	+	0.136023i
$407$	−7.00725	+	12.1369i	−0.347337	+	0.601605i
$408$	6.91687	−	4.92749i	0.342436	−	0.243947i
$409$	−32.6846	+	6.94732i	−1.61615	+	0.343523i	−0.925229	−	0.379408i	$-0.876128\pi$
$409$	−32.6846	+	6.94732i	−1.61615	+	0.343523i	−0.690920	+	0.722931i	$0.742794\pi$
$410$	2.45412	−	2.03997i	0.121201	−	0.100747i
$411$	4.05892	−	6.88122i	0.200212	−	0.339425i
$412$	12.5433	+	13.9307i	0.617964	+	0.686318i
$413$	−0.726959	+	2.23735i	−0.0357713	+	0.110093i
$414$	2.81659	−	8.14815i	0.138428	−	0.400460i
$415$	14.1569	−	28.6882i	0.694936	−	1.40825i
$416$	5.31900	+	5.90735i	0.260786	+	0.289632i
$417$	6.30678	+	2.87874i	0.308844	+	0.140973i
$418$	1.42914	+	2.47534i	0.0699015	+	0.121073i
$419$	−4.12688	+	39.2646i	−0.201611	+	1.91820i	0.162249	+	0.986750i	$0.448125\pi$
$419$	−4.12688	+	39.2646i	−0.201611	+	1.91820i	−0.363860	+	0.931454i	$0.618541\pi$
$420$	17.8504	−	0.998109i	0.871011	−	0.0487027i
$421$	−0.275383	−	2.62010i	−0.0134214	−	0.127696i	0.985760	−	0.168161i	$-0.0537827\pi$
$421$	−0.275383	−	2.62010i	−0.0134214	−	0.127696i	−0.999181	+	0.0404650i	$0.987116\pi$
$422$	0.588349	−	0.427460i	0.0286404	−	0.0208084i
$423$	−15.6572	−	18.0553i	−0.761279	−	0.877879i
$424$	3.24155			0.157424
$425$	−13.8813	+	13.1588i	−0.673340	+	0.638297i
$426$	0.247149	+	0.279689i	0.0119744	+	0.0135510i
$427$	−14.2383	+	15.8132i	−0.689039	+	0.765255i
$428$	−1.36483	−	0.607661i	−0.0659715	−	0.0293724i
$429$	1.90427	+	6.05226i	0.0919391	+	0.292206i
$430$	0.191530	−	4.84201i	0.00923641	−	0.233503i
$431$	27.7928	+	20.1926i	1.33873	+	0.972644i	0.999490	+	0.0319446i	$0.0101700\pi$
$431$	27.7928	+	20.1926i	1.33873	+	0.972644i	0.339240	+	0.940700i	$0.389830\pi$
$432$	1.33880	+	17.4122i	0.0644129	+	0.837745i
$433$	−22.0022	−	15.9856i	−1.05736	−	0.768217i	−0.0837621	−	0.996486i	$-0.526694\pi$
$433$	−22.0022	−	15.9856i	−1.05736	−	0.768217i	−0.973598	+	0.228269i	$0.926694\pi$
$434$	3.82547	+	4.24862i	0.183629	+	0.203940i
$435$	10.1299	−	20.0541i	0.485690	−	0.961518i
$436$	21.9945	−	24.4274i	1.05335	−	1.16986i
$437$	43.7868	−	9.30717i	2.09461	−	0.445222i
$438$	5.70696	−	2.47738i	0.272689	−	0.118374i
$439$	14.6868	+	3.12178i	0.700965	+	0.148995i	0.544589	−	0.838703i	$-0.316686\pi$
$439$	14.6868	+	3.12178i	0.700965	+	0.148995i	0.156376	+	0.987698i	$0.450019\pi$
$440$	−4.79737	−	0.696885i	−0.228706	−	0.0332227i
$441$	−2.83751	−	1.32730i	−0.135119	−	0.0632050i
$442$	−2.20759	−	1.60390i	−0.105004	−	0.0762900i
$443$	5.24719	−	9.08840i	0.249301	−	0.431803i	−0.714031	−	0.700114i	$-0.753132\pi$
$443$	5.24719	−	9.08840i	0.249301	−	0.431803i	0.963332	+	0.268312i	$0.0864657\pi$
$444$	24.6944	+	11.2718i	1.17195	+	0.534937i
$445$	18.1264	+	11.4436i	0.859274	+	0.542480i
$446$	7.88931	+	3.51255i	0.373570	+	0.166324i
$447$	−16.1204	+	17.5712i	−0.762470	+	0.831087i
$448$	13.1598	+	2.79720i	0.621741	+	0.132155i
$449$	19.5039			0.920444			0.460222	−	0.887804i	$-0.347770\pi$
$449$	19.5039			0.920444			0.460222	+	0.887804i	$0.347770\pi$
$450$	1.06096	+	4.82524i	0.0500143	+	0.227464i
$451$	7.32912			0.345115
$452$	4.02147	+	0.854791i	0.189154	+	0.0402060i
$453$	34.3199	+	7.63018i	1.61249	+	0.358497i
$454$	2.23067	+	0.993158i	0.104691	+	0.0466112i
$455$	−4.37646	−	10.9782i	−0.205172	−	0.514664i
$456$	9.27690	−	6.60874i	0.434431	−	0.309483i
$457$	−6.38012	+	11.0507i	−0.298449	+	0.516929i	−0.975781	−	0.218748i	$-0.929803\pi$
$457$	−6.38012	+	11.0507i	−0.298449	+	0.516929i	0.677332	+	0.735677i	$0.263136\pi$
$458$	5.43434	+	3.94828i	0.253930	+	0.184491i
$459$	−5.61113	−	19.0690i	−0.261905	−	0.890065i
$460$	−16.3306	+	33.0931i	−0.761419	+	1.54297i
$461$	13.7821	+	2.92948i	0.641898	+	0.136440i	0.517350	−	0.855774i	$-0.326919\pi$
$461$	13.7821	+	2.92948i	0.641898	+	0.136440i	0.124548	+	0.992214i	$0.460252\pi$
$462$	−1.89212	−	1.40186i	−0.0880296	−	0.0652204i
$463$	−29.6100	+	6.29379i	−1.37609	+	0.292497i	−0.835825	−	0.548996i	$-0.815010\pi$
$463$	−29.6100	+	6.29379i	−1.37609	+	0.292497i	−0.540267	+	0.841494i	$0.681677\pi$
$464$	13.0457	−	14.4887i	0.605632	−	0.672623i
$465$	17.2607	−	21.4683i	0.800447	−	0.995569i
$466$	1.67365	+	1.85878i	0.0775304	+	0.0861062i
$467$	−0.459190	−	0.333621i	−0.0212488	−	0.0154382i	0.577110	−	0.816666i	$-0.304180\pi$
$467$	−0.459190	−	0.333621i	−0.0212488	−	0.0154382i	−0.598359	+	0.801228i	$0.704180\pi$
$468$	11.3183	−	4.78828i	0.523188	−	0.221338i
$469$	−6.67524	−	4.84985i	−0.308234	−	0.223945i
$470$	−3.25824	−	4.87910i	−0.150291	−	0.225056i
$471$	−9.89666	+	10.7873i	−0.456014	+	0.497052i
$472$	−1.12872	−	0.502539i	−0.0519536	−	0.0231313i
$473$	7.44671	−	8.27041i	0.342400	−	0.380274i
$474$	−3.52076	+	0.714105i	−0.161714	+	0.0327999i
$475$	−18.6175	+	17.6486i	−0.854230	+	0.809773i
$476$	−17.6587			−0.809384
$477$	2.47873	−	7.17075i	0.113493	−	0.328326i
$478$	4.32159	−	3.13982i	0.197665	−	0.143612i
$479$	−0.950144	−	9.04001i	−0.0434132	−	0.413049i	−0.994549	−	0.104275i	$-0.966748\pi$
$479$	−0.950144	−	9.04001i	−0.0434132	−	0.413049i	0.951135	−	0.308774i	$-0.0999187\pi$
$480$	−0.694334	+	14.1986i	−0.0316919	+	0.648073i
$481$	1.87569	−	17.8460i	0.0855240	−	0.813707i
$482$	−2.41759	−	4.18739i	−0.110118	−	0.190730i
$483$	−30.0379	+	21.3986i	−1.36677	+	0.973672i
$484$	10.3014	+	11.4409i	0.468245	+	0.520039i
$485$	−2.46761	−	2.40511i	−0.112048	−	0.109211i
$486$	−4.96690	−	1.30046i	−0.225303	−	0.0589900i
$487$	−9.84622	+	30.3036i	−0.446175	+	1.37319i	0.435015	+	0.900423i	$0.356743\pi$
$487$	−9.84622	+	30.3036i	−0.446175	+	1.37319i	−0.881190	+	0.472762i	$0.843257\pi$
$488$	−7.47803	−	8.30519i	−0.338514	−	0.375958i
$489$	−12.4292	−	0.115936i	−0.562069	−	0.00524281i
$490$	−0.650290	−	0.410544i	−0.0293771	−	0.0185465i
$491$	41.2802	−	8.77439i	1.86295	−	0.395982i	0.868019	−	0.496531i	$-0.165393\pi$
$491$	41.2802	−	8.77439i	1.86295	−	0.395982i	0.994932	+	0.100549i	$0.0320598\pi$
$492$	−1.35215	−	14.1316i	−0.0609595	−	0.637100i
$493$	−11.0957	+	19.2182i	−0.499723	+	0.865546i
$494$	−2.96081	−	2.15115i	−0.133213	−	0.0967850i
$495$	−5.21003	+	10.0795i	−0.234173	+	0.453042i
$496$	19.3390	−	14.0506i	0.868346	−	0.630890i
$497$	−0.166899	−	1.58794i	−0.00748643	−	0.0712286i
$498$	4.01479	+	7.10607i	0.179907	+	0.318431i
$499$	9.50928	+	16.4706i	0.425694	+	0.737323i	0.996485	−	0.0837721i	$-0.0266968\pi$
$499$	9.50928	+	16.4706i	0.425694	+	0.737323i	−0.570791	+	0.821095i	$0.693363\pi$
$500$	−1.91829	−	21.0606i	−0.0857886	−	0.941860i
$501$	−10.2834	+	2.08576i	−0.459430	+	0.0931848i
$502$	5.71372	+	1.21449i	0.255016	+	0.0542053i
$503$	8.48894	−	6.16758i	0.378503	−	0.274999i	−0.382225	−	0.924069i	$-0.624842\pi$
$503$	8.48894	−	6.16758i	0.378503	−	0.274999i	0.760728	+	0.649071i	$0.224842\pi$
$504$	−4.84281	+	8.03789i	−0.215716	+	0.358036i
$505$	3.36299	+	19.6026i	0.149651	+	0.872305i
$506$	4.44049	−	1.97704i	0.197404	−	0.0878900i
$507$	9.53046	+	10.7853i	0.423263	+	0.478991i
$508$	−2.91618	+	27.7456i	−0.129385	+	1.23101i
$509$	26.9653	−	5.73166i	1.19522	−	0.254051i	0.433013	−	0.901388i	$-0.357450\pi$
$509$	26.9653	−	5.73166i	1.19522	−	0.254051i	0.762204	+	0.647336i	$0.224117\pi$
$510$	−0.780223	−	4.81704i	−0.0345488	−	0.213302i
$511$	−26.0332	−	5.53353i	−1.15164	−	0.244789i
$512$	−6.47433	+	19.9259i	−0.286128	+	0.880611i
$513$	−7.52564	−	25.5753i	−0.332265	−	1.12918i
$514$	−0.614821	−	1.89222i	−0.0271186	−	0.0834624i
$515$	21.3299	−	6.00954i	0.939907	−	0.264812i
$516$	−17.3204	−	12.8325i	−0.762486	−	0.564919i
$517$	1.40844	−	13.4004i	0.0619432	−	0.589350i
$518$	3.33000	+	5.76773i	0.146312	+	0.253420i
$519$	−3.22021	−	33.6551i	−0.141351	−	1.47729i
$520$	5.97446	−	1.68326i	0.261998	−	0.0738159i
$521$	24.6933	−	17.9407i	1.08183	−	0.785998i	0.103831	−	0.994595i	$-0.466890\pi$
$521$	24.6933	−	17.9407i	1.08183	−	0.785998i	0.978002	+	0.208597i	$0.0668898\pi$
$522$	2.77291	+	5.01666i	0.121367	+	0.219573i
$523$	−4.73750	−	14.5805i	−0.207156	−	0.637562i	−0.999618	−	0.0276401i	$-0.991201\pi$
$523$	−4.73750	−	14.5805i	−0.207156	−	0.637562i	0.792461	−	0.609922i	$-0.208799\pi$
$524$	−1.99456	+	3.45467i	−0.0871326	+	0.150918i
$525$	8.28008	−	19.4454i	0.361372	−	0.848669i
$526$	−1.66749	−	2.88818i	−0.0727060	−	0.125930i
$527$	−18.2059	+	20.2197i	−0.793063	+	0.880785i
$528$	−6.65632	+	7.25534i	−0.289679	+	0.315748i
$529$	−5.55322	−	52.8353i	−0.241444	−	2.29719i
$530$	0.824249	−	1.67029i	0.0358031	−	0.0725529i
$531$	−1.97479	+	2.11261i	−0.0856986	+	0.0916794i
$532$	−23.6838			−1.02682
$533$	−8.57295	+	3.81692i	−0.371336	+	0.165329i
$534$	−5.01673	+	2.17775i	−0.217095	+	0.0942406i
$535$	−1.35818	+	1.12897i	−0.0587190	+	0.0488098i
$536$	2.89968	−	3.22042i	0.125247	−	0.139101i
$537$	6.68963	+	4.95629i	0.288679	+	0.213879i
$538$	5.97238	+	6.63299i	0.257487	+	0.285969i
$539$	−0.545782	−	1.67975i	−0.0235085	−	0.0723518i
$540$	20.3960	+	8.18610i	0.877703	+	0.352274i
$541$	0.320574	−	0.986626i	0.0137826	−	0.0424184i	−0.943929	−	0.330149i	$-0.892901\pi$
$541$	0.320574	−	0.986626i	0.0137826	−	0.0424184i	0.957711	+	0.287731i	$0.0929009\pi$
$542$	−3.16434	+	1.40885i	−0.135920	+	0.0605154i
$543$	3.06444	−	9.14038i	0.131508	−	0.392251i
$544$	1.46768	−	13.9640i	0.0629261	−	0.598702i
$545$	−14.3895	−	36.0953i	−0.616377	−	1.54615i
$546$	2.94331	+	0.654372i	0.125962	+	0.0280045i
$547$	2.97140	+	28.2710i	0.127048	+	1.20878i	0.853325	+	0.521379i	$0.174582\pi$
$547$	2.97140	+	28.2710i	0.127048	+	1.20878i	−0.726277	+	0.687402i	$0.758751\pi$
$548$	−2.69607	−	8.29764i	−0.115170	−	0.354458i
$549$	−24.0905	+	10.1917i	−1.02816	+	0.434969i
$550$	−1.57894	+	2.29477i	−0.0673264	+	0.0978492i
$551$	−14.8815	+	25.7755i	−0.633972	+	1.09807i
$552$	−9.52806	−	16.8644i	−0.405541	−	0.717798i
$553$	14.0395	+	6.25077i	0.597018	+	0.265810i
$554$	−4.89275	−	2.17839i	−0.207873	−	0.0925510i
$555$	24.8679	−	20.2820i	1.05558	−	0.860923i
$556$	6.91645	−	3.07940i	0.293323	−	0.130596i
$557$	23.9335			1.01409			0.507047	−	0.861919i	$-0.330737\pi$
$557$	23.9335			1.01409			0.507047	+	0.861919i	$0.330737\pi$
$558$	2.04668	+	6.72328i	0.0866429	+	0.284619i
$559$	−4.40336	+	13.5522i	−0.186242	+	0.573195i
$560$	11.3582	−	14.4000i	0.479972	−	0.608509i
$561$	5.69382	−	9.65292i	0.240393	−	0.407546i
$562$	−4.89154	+	1.03973i	−0.206337	+	0.0438583i
$563$	−3.45562	+	0.734514i	−0.145637	+	0.0309561i	−0.280153	−	0.959955i	$-0.590385\pi$
$563$	−3.45562	+	0.734514i	−0.145637	+	0.0309561i	0.134516	+	0.990911i	$0.457052\pi$
$564$	−26.0977	−	0.243432i	−1.09891	−	0.0102503i
$565$	3.00994	−	3.81601i	0.126629	−	0.160541i
$566$	0.192579	−	0.592697i	0.00809470	−	0.0249129i
$567$	14.0777	+	16.8593i	0.591210	+	0.708025i
$568$	0.838586			0.0351863
$569$	−16.8695	+	7.51077i	−0.707205	+	0.314868i	−0.728635	−	0.684902i	$-0.759845\pi$
$569$	−16.8695	+	7.51077i	−0.707205	+	0.314868i	0.0214298	+	0.999770i	$0.493178\pi$
$570$	−1.04643	−	6.46061i	−0.0438303	−	0.270605i
$571$	−24.6819	−	10.9891i	−1.03291	−	0.459879i	−0.180949	−	0.983492i	$-0.557917\pi$
$571$	−24.6819	−	10.9891i	−1.03291	−	0.459879i	−0.851956	+	0.523613i	$0.824584\pi$
$572$	6.32988	+	2.81824i	0.264666	+	0.117837i
$573$	−20.8386	+	35.3284i	−0.870546	+	1.47587i
$574$	1.74148	−	3.01633i	0.0726880	−	0.125899i
$575$	26.5390	+	34.6243i	1.10675	+	1.44393i
$576$	13.1962	+	9.96896i	0.549843	+	0.415374i
$577$	4.52246	+	13.9187i	0.188273	+	0.579444i	0.999989	−	0.00460768i	$-0.00146668\pi$
$577$	4.52246	+	13.9187i	0.188273	+	0.579444i	−0.811717	+	0.584051i	$0.801467\pi$
$578$	−0.0814655	−	0.775093i	−0.00338852	−	0.0322396i
$579$	−1.49201	+	1.62628i	−0.0620057	+	0.0675858i
$580$	−9.08588	−	22.7915i	−0.377271	−	0.946366i
$581$	3.64963	−	34.7239i	0.151412	−	1.44059i
$582$	0.861577	−	0.174751i	0.0357135	−	0.00724365i
$583$	3.90784	−	1.73988i	0.161846	−	0.0720586i
$584$	4.31951	−	13.2941i	0.178743	−	0.550113i
$585$	0.844914	−	14.5035i	0.0349329	−	0.599645i
$586$	−0.747267	−	2.29985i	−0.0308693	−	0.0950060i
$587$	−19.9388	−	22.1443i	−0.822964	−	0.913994i	0.174537	−	0.984651i	$-0.444157\pi$
$587$	−19.9388	−	22.1443i	−0.822964	−	0.913994i	−0.997501	+	0.0706567i	$0.977491\pi$
$588$	−3.13809	+	1.36224i	−0.129413	+	0.0561779i
$589$	−24.4178	+	27.1187i	−1.00612	+	1.11741i
$590$	−0.545954	+	0.453820i	−0.0224766	+	0.0186835i
$591$	13.6972	+	10.1481i	0.563426	+	0.417437i
$592$	25.4394	−	11.3263i	1.04555	−	0.465510i
$593$	15.3217			0.629186			0.314593	−	0.949227i	$-0.398132\pi$
$593$	15.3217			0.629186			0.314593	+	0.949227i	$0.398132\pi$
$594$	−1.37668	−	2.54647i	−0.0564859	−	0.104483i
$595$	−9.23788	+	18.7200i	−0.378716	+	0.767447i
$596$	2.72203	+	25.8984i	0.111499	+	1.06084i
$597$	9.66146	+	30.7066i	0.395417	+	1.25674i
$598$	−4.16448	+	4.62512i	−0.170298	+	0.189135i
$599$	−14.5795	−	25.2524i	−0.595702	−	1.03179i	−0.993447	−	0.114290i	$-0.963541\pi$
$599$	−14.5795	−	25.2524i	−0.595702	−	1.03179i	0.397745	−	0.917496i	$-0.369793\pi$
$600$	9.70234	+	5.39245i	0.396096	+	0.220146i
$601$	−5.97136	+	10.3427i	−0.243577	+	0.421888i	−0.961731	−	0.273997i	$-0.911654\pi$
$601$	−5.97136	+	10.3427i	−0.243577	+	0.421888i	0.718154	+	0.695885i	$0.244987\pi$
$602$	−1.63430	−	5.02987i	−0.0666093	−	0.205002i
$603$	−4.90670	−	8.87705i	−0.199816	−	0.361501i
$604$	31.0621	−	22.5679i	1.26390	−	0.918275i
$605$	17.5175	−	4.93544i	0.712189	−	0.200654i
$606$	−4.61607	−	2.10701i	−0.187515	−	0.0855916i
$607$	11.8537	+	20.5312i	0.481127	+	0.833336i	0.999765	−	0.0216578i	$-0.00689442\pi$
$607$	11.8537	+	20.5312i	0.481127	+	0.833336i	−0.518639	+	0.854993i	$0.673561\pi$
$608$	1.96844	−	18.7285i	0.0798310	−	0.759541i
$609$	2.79048	−	24.3616i	0.113076	−	0.987181i
$610$	−6.18095	+	1.74144i	−0.250259	+	0.0705087i
$611$	5.33132	+	16.4081i	0.215682	+	0.663801i
$612$	−19.6626	−	9.19761i	−0.794815	−	0.371791i
$613$	10.4855	−	32.2710i	0.423505	−	1.30341i	−0.480914	−	0.876768i	$-0.659695\pi$
$613$	10.4855	−	32.2710i	0.423505	−	1.30341i	0.904419	−	0.426646i	$-0.140305\pi$
$614$	1.41180	+	0.300087i	0.0569755	+	0.0121105i
$615$	−15.6883	−	5.95931i	−0.632613	−	0.240303i
$616$	−5.17520	+	1.10002i	−0.208515	+	0.0443212i
$617$	−1.06496	+	10.1324i	−0.0428737	+	0.407916i	0.951946	+	0.306265i	$0.0990793\pi$
$617$	−1.06496	+	10.1324i	−0.0428737	+	0.407916i	−0.994820	+	0.101651i	$0.967587\pi$
$618$	−1.79716	+	5.36044i	−0.0722924	+	0.215629i
$619$	−6.04802	+	2.69275i	−0.243091	+	0.108231i	−0.524666	−	0.851308i	$-0.675810\pi$
$619$	−6.04802	+	2.69275i	−0.243091	+	0.108231i	0.281575	+	0.959539i	$0.409143\pi$
$620$	−5.08665	−	29.6497i	−0.204285	−	1.19076i
$621$	−44.5923	+	8.18159i	−1.78943	+	0.328316i
$622$	−4.75307	+	3.45330i	−0.190581	+	0.138465i
$623$	22.8846	+	4.86427i	0.916852	+	0.194883i
$624$	4.00747	−	11.9532i	0.160427	−	0.478510i
$625$	−23.3300	−	8.98397i	−0.933199	−	0.359359i
$626$	2.68462	+	4.64989i	0.107299	+	0.185847i
$627$	7.63654	−	12.9465i	0.304974	−	0.517032i
$628$	1.67111	+	15.8995i	0.0666845	+	0.634461i
$629$	−25.6425	+	18.6303i	−1.02243	+	0.742841i
$630$	2.91032	+	4.53923i	0.115950	+	0.180847i
$631$	18.8353	+	13.6847i	0.749823	+	0.544778i	0.895772	−	0.444514i	$-0.146623\pi$
$631$	18.8353	+	13.6847i	0.749823	+	0.544778i	−0.145949	+	0.989292i	$0.546623\pi$
$632$	−4.03570	+	6.99004i	−0.160532	+	0.278049i
$633$	−3.47906	−	1.58802i	−0.138280	−	0.0631182i
$634$	−6.78939	+	1.44313i	−0.269641	+	0.0573140i
$635$	27.8877	+	17.6062i	1.10669	+	0.698679i
$636$	−4.07570	−	7.21388i	−0.161612	−	0.286049i
$637$	1.51320	+	1.68058i	0.0599552	+	0.0665870i
$638$	−0.998668	+	3.07358i	−0.0395376	+	0.121684i
$639$	0.641245	−	1.85507i	0.0253673	−	0.0733853i
$640$	14.6624	+	14.2910i	0.579581	+	0.564902i
$641$	16.7041	+	18.5518i	0.659773	+	0.732752i	0.976441	−	0.215784i	$-0.0692308\pi$
$641$	16.7041	+	18.5518i	0.659773	+	0.732752i	−0.316668	+	0.948536i	$0.602564\pi$
$642$	−0.0429174	−	0.448539i	−0.00169381	−	0.0177024i
$643$	4.76373	+	8.25102i	0.187863	+	0.325388i	0.944538	−	0.328403i	$-0.106511\pi$
$643$	4.76373	+	8.25102i	0.187863	+	0.325388i	−0.756674	+	0.653792i	$0.773177\pi$
$644$	−4.21000	+	40.0555i	−0.165897	+	1.57841i
$645$	−22.6647	+	11.6483i	−0.892421	+	0.458649i
$646$	0.675715	+	6.42900i	0.0265857	+	0.252946i
$647$	−38.6632	+	28.0905i	−1.52001	+	1.10435i	−0.558525	+	0.829487i	$0.688633\pi$
$647$	−38.6632	+	28.0905i	−1.52001	+	1.10435i	−0.961483	+	0.274863i	$0.911367\pi$
$648$	−9.57895	+	6.42765i	−0.376297	+	0.252502i
$649$	−1.63046			−0.0640013
$650$	0.651819	−	3.50651i	0.0255664	−	0.137537i
$651$	9.55675	−	28.5052i	0.374558	−	1.11721i
$652$	−9.08288	+	10.0876i	−0.355713	+	0.395059i
$653$	−12.4685	−	5.55135i	−0.487932	−	0.217241i	0.147999	−	0.988988i	$-0.452717\pi$
$653$	−12.4685	−	5.55135i	−0.487932	−	0.217241i	−0.635931	+	0.771746i	$0.719384\pi$
$654$	9.67738	+	2.15152i	0.378415	+	0.0841312i
$655$	2.61889	+	3.92170i	0.102329	+	0.153234i
$656$	−11.7817	−	8.55991i	−0.459998	−	0.334208i
$657$	−26.1053	−	19.7210i	−1.01847	−	0.769390i
$658$	−5.18035	−	3.76374i	−0.201951	−	0.146726i
$659$	−4.87000	−	5.40868i	−0.189708	−	0.210692i	0.640786	−	0.767720i	$-0.278609\pi$
$659$	−4.87000	−	5.40868i	−0.189708	−	0.210692i	−0.830494	+	0.557027i	$0.811942\pi$
$660$	4.48100	+	11.5525i	0.174423	+	0.449679i
$661$	−14.5946	+	16.2089i	−0.567663	+	0.630454i	−0.956807	−	0.290723i	$-0.906104\pi$
$661$	−14.5946	+	16.2089i	−0.567663	+	0.630454i	0.389144	+	0.921177i	$0.372771\pi$
$662$	−5.83592	+	1.24046i	−0.226819	+	0.0482119i
$663$	−1.63299	+	14.2564i	−0.0634200	+	0.553672i
$664$	17.9369	+	3.81261i	0.696088	+	0.147958i
$665$	−12.3898	+	25.1073i	−0.480457	+	0.973619i
$666$	0.703745	+	8.15672i	0.0272696	+	0.316066i
$667$	40.9478	+	29.7503i	1.58550	+	1.15194i
$668$	−5.72945	+	9.92369i	−0.221679	+	0.383959i
$669$	−4.32558	−	45.2075i	−0.167236	−	1.74782i
$670$	−0.922085	−	2.31301i	−0.0356233	−	0.0893593i
$671$	−13.4729	−	5.99851i	−0.520115	−	0.231570i
$672$	4.65652	+	14.7996i	0.179629	+	0.570907i
$673$	−47.4181	−	10.0790i	−1.82783	−	0.388518i	−0.839817	−	0.542870i	$-0.817338\pi$
$673$	−47.4181	−	10.0790i	−1.82783	−	0.388518i	−0.988016	+	0.154352i	$0.950671\pi$
$674$	1.21886			0.0469488
$675$	19.3480	−	17.3394i	0.744704	−	0.667395i
$676$	15.7179			0.604534
$677$	9.67370	+	2.05621i	0.371790	+	0.0790265i	0.390018	−	0.920807i	$-0.372469\pi$
$677$	9.67370	+	2.05621i	0.371790	+	0.0790265i	−0.0182272	+	0.999834i	$0.505802\pi$
$678$	0.372156	+	1.18280i	0.0142926	+	0.0454254i
$679$	−3.43564	−	1.52965i	−0.131848	−	0.0587024i
$680$	−9.27086	−	5.85292i	−0.355521	−	0.224449i
$681$	−1.22304	−	12.7822i	−0.0468669	−	0.489816i
$682$	−1.98120	+	3.43153i	−0.0758639	+	0.131400i
$683$	22.0510	+	16.0210i	0.843757	+	0.613026i	0.923418	−	0.383796i	$-0.125384\pi$
$683$	22.0510	+	16.0210i	0.843757	+	0.613026i	−0.0796603	+	0.996822i	$0.525384\pi$
$684$	−26.3715	−	12.3358i	−1.00834	−	0.471672i
$685$	−10.2068	−	1.48268i	−0.389981	−	0.0566502i
$686$	−6.32466	−	1.34435i	−0.241477	−	0.0513275i
$687$	4.01987	−	35.0945i	0.153368	−	1.33894i
$688$	−21.6300	+	4.59760i	−0.824637	+	0.175282i
$689$	−3.66493	+	4.07032i	−0.139623	+	0.155067i
$690$	−11.1126	+	0.621363i	−0.423049	+	0.0236549i
$691$	−0.499317	−	0.554547i	−0.0189949	−	0.0210960i	0.733573	−	0.679611i	$-0.237851\pi$
$691$	−0.499317	−	0.554547i	−0.0189949	−	0.0210960i	−0.752567	+	0.658515i	$0.771185\pi$
$692$	−29.8701	−	21.7019i	−1.13549	−	0.824982i
$693$	−1.52394	+	12.2894i	−0.0578897	+	0.466836i
$694$	−6.87115	−	4.99218i	−0.260825	−	0.189501i
$695$	0.353753	−	8.94311i	0.0134186	−	0.339231i
$696$	12.5715	+	2.79497i	0.476523	+	0.105943i
$697$	15.1428	+	6.74202i	0.573575	+	0.255372i
$698$	6.91376	−	7.67851i	0.261690	−	0.290636i
$699$	4.18109	−	12.4711i	0.158143	−	0.471699i
$700$	−9.92547	−	20.8376i	−0.375148	−	0.787589i
$701$	−14.0062			−0.529006			−0.264503	−	0.964385i	$-0.585208\pi$
$701$	−14.0062			−0.529006			−0.264503	+	0.964385i	$0.585208\pi$
$702$	2.93649	+	2.26167i	0.110831	+	0.0853612i
$703$	−34.3916	+	24.9870i	−1.29711	+	0.942402i
$704$	0.974680	+	9.27346i	0.0367346	+	0.349507i
$705$	−13.9107	+	27.5390i	−0.523908	+	1.03718i
$706$	−0.00344927	+	0.0328176i	−0.000129815	+	0.00123511i
$707$	10.8534	+	18.7987i	0.408186	+	0.706999i
$708$	0.300804	+	3.14376i	0.0113049	+	0.118150i
$709$	16.5678	+	18.4004i	0.622216	+	0.691041i	0.969044	−	0.246888i	$-0.0794079\pi$
$709$	16.5678	+	18.4004i	0.622216	+	0.691041i	−0.346828	+	0.937929i	$0.612741\pi$
$710$	0.213232	−	0.432103i	0.00800247	−	0.0162165i
$711$	12.3769	+	14.2726i	0.464171	+	0.535266i
$712$	−3.79708	+	11.6862i	−0.142302	+	0.437960i
$713$	41.5243	+	46.1174i	1.55510	+	1.72711i
$714$	−2.61979	−	4.63696i	−0.0980431	−	0.173534i
$715$	6.29902	−	5.23601i	0.235570	−	0.195816i
$716$	8.89345	−	1.89036i	0.332364	−	0.0706461i
$717$	−25.5547	−	11.6645i	−0.954357	−	0.435618i
$718$	2.55455	−	4.42461i	0.0953349	−	0.165125i
$719$	7.88850	+	5.73133i	0.294192	+	0.213743i	0.725084	−	0.688661i	$-0.241801\pi$
$719$	7.88850	+	5.73133i	0.294192	+	0.213743i	−0.430892	+	0.902403i	$0.641801\pi$
$720$	20.1474	−	10.1181i	0.750851	−	0.377080i
$721$	19.5667	−	14.2161i	0.728703	−	0.529434i
$722$	0.252132	+	2.39887i	0.00938336	+	0.0892767i
$723$	−12.9183	+	21.9008i	−0.480436	+	0.814499i
$724$	−5.26399	−	9.11749i	−0.195634	−	0.338849i
$725$	−28.9145	−	2.29107i	−1.07386	−	0.0850880i
$726$	−1.47595	+	4.40235i	−0.0547776	+	0.163387i
$727$	2.19463	+	0.466484i	0.0813944	+	0.0173009i	0.248429	−	0.968650i	$-0.420086\pi$
$727$	2.19463	+	0.466484i	0.0813944	+	0.0173009i	−0.167034	+	0.985951i	$0.553419\pi$
$728$	5.48061	−	3.98189i	0.203125	−	0.147579i
$729$	6.89406	+	26.1050i	0.255335	+	0.966853i
$730$	−5.75178	−	5.60611i	−0.212883	−	0.207491i
$731$	22.9937	−	10.2374i	0.850452	−	0.378646i
$732$	−9.08036	+	27.0843i	−0.335620	+	1.00106i
$733$	−0.749981	+	7.13559i	−0.0277012	+	0.263559i	0.971902	+	0.235386i	$0.0756355\pi$
$733$	−0.749981	+	7.13559i	−0.0277012	+	0.263559i	−0.999603	+	0.0281727i	$0.991031\pi$
$734$	−4.15936	+	0.884099i	−0.153525	+	0.0326327i
$735$	−0.197531	+	4.03934i	−0.00728602	+	0.148993i
$736$	−31.3249	−	6.65831i	−1.15465	−	0.245429i
$737$	1.76716	−	5.43875i	0.0650941	−	0.200339i
$738$	3.51018	−	2.45157i	0.129212	−	0.0902437i
$739$	3.95764	+	12.1804i	0.145584	+	0.448062i	0.997086	−	0.0762903i	$-0.0243076\pi$
$739$	3.95764	+	12.1804i	0.145584	+	0.448062i	−0.851502	+	0.524352i	$0.824308\pi$
$740$	1.38513	−	35.0171i	0.0509185	−	1.28725i
$741$	−2.19016	+	19.1207i	−0.0804576	+	0.702415i
$742$	0.212490	−	2.02171i	0.00780075	−	0.0742192i
$743$	−1.45630	−	2.52238i	−0.0534264	−	0.0925372i	0.838075	−	0.545554i	$-0.183681\pi$
$743$	−1.45630	−	2.52238i	−0.0534264	−	0.0925372i	−0.891502	+	0.453017i	$0.850348\pi$
$744$	14.3644	+	6.55666i	0.526625	+	0.240379i
$745$	28.8790	+	10.6627i	1.05804	+	0.390652i
$746$	−0.0617081	+	0.0448336i	−0.00225929	+	0.00164147i
$747$	22.1499	−	36.7635i	0.810424	−	1.34511i
$748$	−3.78202	−	11.6399i	−0.138284	−	0.425596i
$749$	−0.963780	+	1.66932i	−0.0352158	+	0.0609955i
$750$	5.24567	−	3.62821i	0.191545	−	0.132483i
$751$	−17.2581	−	29.8919i	−0.629757	−	1.09077i	−0.987600	−	0.156989i	$-0.949821\pi$
$751$	−17.2581	−	29.8919i	−0.629757	−	1.09077i	0.357843	−	0.933782i	$-0.383512\pi$
$752$	−17.9149	+	19.8965i	−0.653288	+	0.725550i
$753$	−9.21952	−	29.3020i	−0.335978	−	1.06782i
$754$	−0.432535	−	4.11530i	−0.0157520	−	0.149870i
$755$	−7.67467	−	44.7351i	−0.279310	−	1.62808i
$756$	23.9769	+	0.671103i	0.872030	+	0.0244078i
$757$	4.55628			0.165601			0.0828005	−	0.996566i	$-0.473614\pi$
$757$	4.55628			0.165601			0.0828005	+	0.996566i	$0.473614\pi$
$758$	1.67877	−	0.747436i	0.0609756	−	0.0271481i
$759$	−20.5384	−	15.2167i	−0.745498	−	0.552333i
$760$	−12.4341	−	7.84992i	−0.451031	−	0.284747i
$761$	17.2773	−	19.1884i	0.626301	−	0.695577i	−0.343590	−	0.939120i	$-0.611643\pi$
$761$	17.2773	−	19.1884i	0.626301	−	0.695577i	0.969890	+	0.243543i	$0.0783096\pi$
$762$	−7.71829	+	3.35050i	−0.279604	+	0.121376i
$763$	−28.3775	−	31.5164i	−1.02733	−	1.14097i
$764$	13.8417	+	42.6004i	0.500775	+	1.54123i
$765$	−20.0366	+	16.0328i	−0.724426	+	0.579669i
$766$	1.36586	−	4.20369i	0.0493505	−	0.151885i
$767$	1.90717	−	0.849127i	0.0688639	−	0.0306602i
$768$	13.5965	−	2.75773i	0.490620	−	0.0995108i
$769$	−3.43575	+	32.6890i	−0.123896	+	1.17879i	0.739104	+	0.673591i	$0.235249\pi$
$769$	−3.43575	+	32.6890i	−0.123896	+	1.17879i	−0.863000	+	0.505203i	$0.831418\pi$
$770$	−0.749114	+	2.94637i	−0.0269962	+	0.106180i
$771$	−7.07318	+	7.70972i	−0.254734	+	0.277659i
$772$	0.251934	+	2.39699i	0.00906731	+	0.0862697i
$773$	−11.0693	−	34.0677i	−0.398134	−	1.22533i	−0.926494	−	0.376310i	$-0.877193\pi$
$773$	−11.0693	−	34.0677i	−0.398134	−	1.22533i	0.528360	−	0.849020i	$-0.322807\pi$
$774$	0.800065	−	6.45191i	0.0287578	−	0.231909i
$775$	−34.0928	−	10.1184i	−1.22465	−	0.363465i
$776$	0.987590	−	1.71056i	0.0354524	−	0.0614054i
$777$	17.7937	−	30.1663i	0.638346	−	1.08221i
$778$	−10.2391	−	4.55872i	−0.367088	−	0.163438i
$779$	20.3095	+	9.04238i	0.727664	+	0.323977i
$780$	−11.2579	−	11.1794i	−0.403096	−	0.400287i
$781$	1.01096	−	0.450106i	0.0361748	−	0.0161061i
$782$	10.9932			0.393117
$783$	15.7960	−	25.6727i	0.564503	−	0.917469i
$784$	−1.08447	+	3.33766i	−0.0387311	+	0.119202i
$785$	17.7294	+	6.54606i	0.632789	+	0.233639i
$786$	−1.20306	−	0.0112218i	−0.0429118	−	0.000400269i
$787$	2.61715	−	0.556292i	0.0932913	−	0.0198297i	−0.161029	−	0.986950i	$-0.551481\pi$
$787$	2.61715	−	0.556292i	0.0932913	−	0.0198297i	0.254321	+	0.967120i	$0.418148\pi$
$788$	18.2095	−	3.87056i	0.648688	−	0.137883i
$789$	−8.91015	+	15.1057i	−0.317210	+	0.537776i
$790$	2.57562	+	3.85690i	0.0916364	+	0.137222i
$791$	1.63917	−	5.04484i	0.0582820	−	0.179374i
$792$	−6.33544	−	1.47067i	−0.225120	−	0.0522581i
$793$	18.8833			0.670567
$794$	8.47300	−	3.77242i	0.300695	−	0.133878i
$795$	−9.77960	+	0.546828i	−0.346847	+	0.0193940i
$796$	32.1151	+	14.2986i	1.13829	+	0.506799i
$797$	−33.5740	−	14.9481i	−1.18925	−	0.529489i	−0.285846	−	0.958276i	$-0.592274\pi$
$797$	−33.5740	−	14.9481i	−1.18925	−	0.529489i	−0.903406	+	0.428787i	$0.858941\pi$
$798$	−3.51366	−	6.21908i	−0.124382	−	0.220153i
$799$	15.2370	−	26.3912i	0.539045	−	0.933654i
$800$	17.3028	−	6.11690i	0.611746	−	0.216265i
$801$	22.9480	+	17.3358i	0.810828	+	0.612532i
$802$	−1.32495	−	4.07776i	−0.0467854	−	0.143991i
$803$	−1.92815	−	18.3451i	−0.0680430	−	0.647386i
$804$	−10.8127	−	2.40393i	−0.381334	−	0.0847802i
$805$	40.2606	+	25.4175i	1.41900	+	0.895849i
$806$	0.530323	−	5.04568i	0.0186798	−	0.177727i
$807$	14.9201	−	44.5026i	0.525213	−	1.56657i
$808$	−10.4149	+	4.63703i	−0.366397	+	0.163130i
$809$	15.1395	−	46.5946i	0.532276	−	1.63818i	−0.217186	−	0.976130i	$-0.569688\pi$
$809$	15.1395	−	46.5946i	0.532276	−	1.63818i	0.749462	−	0.662048i	$-0.230312\pi$
$810$	0.876314	+	6.57020i	0.0307905	+	0.230853i
$811$	8.75261	+	26.9378i	0.307346	+	0.945913i	0.978791	+	0.204859i	$0.0656736\pi$
$811$	8.75261	+	26.9378i	0.307346	+	0.945913i	−0.671446	+	0.741054i	$0.734326\pi$
$812$	−17.9183	−	19.9003i	−0.628808	−	0.698363i
$813$	14.6359	+	10.8436i	0.513302	+	0.380301i
$814$	−3.08865	+	3.43029i	−0.108257	+	0.120232i
$815$	5.94229	+	14.9060i	0.208149	+	0.522133i
$816$	−20.4269	+	8.86727i	−0.715083	+	0.310416i
$817$	30.8391	−	13.7304i	1.07892	−	0.480367i
$818$	−11.0057			−0.384806
$819$	−4.61762	−	15.1687i	−0.161353	−	0.530037i
$820$	−16.2215	+	8.52906i	−0.566480	+	0.297848i
$821$	−1.08396	−	10.3132i	−0.0378304	−	0.359932i	−0.997018	−	0.0771632i	$-0.975414\pi$
$821$	−1.08396	−	10.3132i	−0.0378304	−	0.359932i	0.959188	−	0.282769i	$-0.0912529\pi$
$822$	1.77888	−	1.93897i	0.0620456	−	0.0676293i
$823$	15.3465	−	17.0440i	0.534945	−	0.594116i	−0.413718	−	0.910405i	$-0.635770\pi$
$823$	15.3465	−	17.0440i	0.534945	−	0.594116i	0.948663	+	0.316289i	$0.102437\pi$
$824$	6.35126	+	11.0007i	0.221257	+	0.383228i
$825$	14.5910	+	1.29319i	0.507993	+	0.0450229i
$826$	−0.387416	+	0.671025i	−0.0134799	+	0.0233479i
$827$	3.87041	+	11.9119i	0.134587	+	0.414218i	0.995526	−	0.0944920i	$-0.0301227\pi$
$827$	3.87041	+	11.9119i	0.134587	+	0.414218i	−0.860938	+	0.508710i	$0.830123\pi$
$828$	−25.5509	+	42.4083i	−0.887954	+	1.47379i
$829$	8.58869	−	6.24005i	0.298297	−	0.216726i	−0.428561	−	0.903513i	$-0.640979\pi$
$829$	8.58869	−	6.24005i	0.298297	−	0.216726i	0.726859	+	0.686787i	$0.240979\pi$
$830$	6.52548	−	8.27301i	0.226503	−	0.287161i
$831$	2.68261	+	28.0365i	0.0930587	+	0.972576i
$832$	−5.96961	−	10.3397i	−0.206959	−	0.358463i
$833$	0.417538	−	3.97261i	0.0144668	−	0.137643i
$834$	1.83472	+	1.35933i	0.0635311	+	0.0470696i
$835$	7.52287	+	11.2652i	0.260340	+	0.389850i
$836$	−5.07244	−	15.6114i	−0.175434	−	0.539930i
$837$	25.4883	−	26.7623i	0.881006	−	0.925041i
$838$	−4.01837	+	12.3673i	−0.138812	+	0.427220i
$839$	6.03383	+	1.28253i	0.208311	+	0.0442778i	0.310885	−	0.950448i	$-0.399375\pi$
$839$	6.03383	+	1.28253i	0.208311	+	0.0442778i	−0.102574	+	0.994725i	$0.532708\pi$
$840$	11.9722	+	1.85331i	0.413079	+	0.0639452i
$841$	−4.55029	+	0.967194i	−0.156907	+	0.0333515i
$842$	0.0907022	−	0.862974i	0.00312580	−	0.0297400i
$843$	17.4137	+	19.7065i	0.599760	+	0.678727i
$844$	−3.81538	+	1.69872i	−0.131331	+	0.0584722i
$845$	8.22258	−	16.6626i	0.282865	−	0.573211i
$846$	−3.80786	−	6.88907i	−0.130917	−	0.236851i
$847$	16.0695	−	11.6752i	0.552155	−	0.401164i
$848$	−8.31400	−	1.76719i	−0.285504	−	0.0606857i
$849$	−3.21183	+	0.651445i	−0.110230	+	0.0223575i
$850$	−5.37323	+	3.28880i	−0.184300	+	0.112805i
$851$	36.1461	+	62.6070i	1.23907	+	2.14614i
$852$	−1.05438	−	1.86622i	−0.0361224	−	0.0639358i
$853$	2.86418	+	27.2508i	0.0980675	+	0.933050i	0.927344	+	0.374211i	$0.122086\pi$
$853$	2.86418	+	27.2508i	0.0980675	+	0.933050i	−0.829276	+	0.558839i	$0.811247\pi$
$854$	−5.67002	+	4.11951i	−0.194024	+	0.140967i
$855$	−26.8731	+	21.5032i	−0.919041	+	0.735394i
$856$	−0.819021	−	0.595053i	−0.0279935	−	0.0203385i
$857$	−16.4638	+	28.5161i	−0.562392	+	0.974092i	0.434895	+	0.900481i	$0.356786\pi$
$857$	−16.4638	+	28.5161i	−0.562392	+	0.974092i	−0.997287	+	0.0736109i	$0.976548\pi$
$858$	0.199045	+	2.08026i	0.00679527	+	0.0710188i
$859$	45.0753	−	9.58106i	1.53795	−	0.326902i	0.640480	−	0.767975i	$-0.278736\pi$
$859$	45.0753	−	9.58106i	1.53795	−	0.326902i	0.897471	+	0.441073i	$0.145402\pi$
$860$	−6.85733	+	26.9708i	−0.233833	+	0.919696i
$861$	−18.3151	−	0.170838i	−0.624178	−	0.00582215i
$862$	7.57121	+	8.40868i	0.257876	+	0.286401i
$863$	1.06714	−	3.28433i	0.0363260	−	0.111800i	−0.931249	−	0.364383i	$-0.881280\pi$
$863$	1.06714	−	3.28433i	0.0363260	−	0.111800i	0.967575	+	0.252583i	$0.0812800\pi$
$864$	−2.52349	+	18.9045i	−0.0858509	+	0.643143i
$865$	−38.6324	+	20.3124i	−1.31354	+	0.690642i
$866$	−5.99377	−	6.65676i	−0.203677	−	0.226206i
$867$	−3.33804	+	2.37798i	−0.113366	+	0.0807604i
$868$	−16.4163	−	28.4338i	−0.557204	−	0.965106i
$869$	−1.11337	+	10.5930i	−0.0377684	+	0.359342i
$870$	4.63682	−	5.76712i	0.157203	−	0.195524i
$871$	0.765377	+	7.28208i	0.0259338	+	0.246744i
$872$	18.0198	−	13.0922i	0.610227	−	0.443356i
$873$	−3.02880	−	3.49270i	−0.102509	−	0.118210i
$874$	14.7441			0.498727
$875$	−27.2824	−	0.378872i	−0.922315	−	0.0128082i
$876$	−35.0163	+	7.10223i	−1.18309	+	0.239962i
$877$	38.2545	−	42.4859i	1.29176	−	1.43465i	0.451688	−	0.892176i	$-0.350822\pi$
$877$	38.2545	−	42.4859i	1.29176	−	1.43465i	0.840074	−	0.542471i	$-0.182511\pi$
$878$	4.51788	+	2.01149i	0.152471	+	0.0678844i
$879$	−8.59690	+	9.37056i	−0.289966	+	0.316061i
$880$	11.9245	+	4.40277i	0.401974	+	0.148417i
$881$	−25.5288	−	18.5478i	−0.860089	−	0.624891i	0.0678204	−	0.997698i	$-0.478396\pi$
$881$	−25.5288	−	18.5478i	−0.860089	−	0.624891i	−0.927909	+	0.372807i	$0.878396\pi$
$882$	−0.823266	−	0.621928i	−0.0277208	−	0.0209414i
$883$	−32.6810	−	23.7441i	−1.09980	−	0.799053i	−0.118775	−	0.992921i	$-0.537897\pi$
$883$	−32.6810	−	23.7441i	−1.09980	−	0.799053i	−0.981028	+	0.193868i	$0.937897\pi$
$884$	10.4858	+	11.6456i	0.352675	+	0.391685i
$885$	3.49008	+	1.32573i	0.117318	+	0.0445639i
$886$	2.31285	−	2.56868i	0.0777018	−	0.0862965i
$887$	11.4156	−	2.42646i	0.383298	−	0.0814726i	−0.0122328	−	0.999925i	$-0.503894\pi$
$887$	11.4156	−	2.42646i	0.383298	−	0.0814726i	0.395531	+	0.918453i	$0.370561\pi$
$888$	14.7798	+	10.9503i	0.495979	+	0.367466i
$889$	35.2082	+	7.48373i	1.18085	+	0.250996i
$890$	5.05612	+	4.92807i	0.169482	+	0.165189i
$891$	−8.09788	+	12.8903i	−0.271289	+	0.431841i
$892$	−40.1233	−	29.1513i	−1.34343	−	0.976058i
$893$	20.4358	−	35.3959i	0.683858	−	1.18448i
$894$	−6.39677	+	4.55698i	−0.213940	+	0.152408i
$895$	2.64850	−	10.4169i	0.0885296	−	0.348199i
$896$	20.4143	+	9.08905i	0.681995	+	0.303644i
$897$	31.9487	+	7.10300i	1.06674	+	0.237162i
$898$	6.28355	+	1.33561i	0.209685	+	0.0445699i
$899$	−41.2600			−1.37610
$900$	−0.198446	−	28.3721i	−0.00661486	−	0.945736i
$901$	9.67456			0.322306
$902$	2.36122	+	0.501893i	0.0786200	+	0.0167112i
$903$	−18.8018	+	20.4938i	−0.625684	+	0.681991i
$904$	2.54507	+	1.13314i	0.0846478	+	0.0376876i
$905$	−12.4193	+	0.810692i	−0.412830	+	0.0269483i
$906$	10.5343	+	4.80842i	0.349980	+	0.159749i
$907$	−15.1100	+	26.1713i	−0.501720	+	0.869005i	0.498278	+	0.867017i	$0.333966\pi$
$907$	−15.1100	+	26.1713i	−0.501720	+	0.869005i	−0.999998	+	0.00198753i	$0.999367\pi$
$908$	−11.3447	−	8.24241i	−0.376487	−	0.273534i
$909$	2.29371	+	26.5851i	0.0760776	+	0.881773i
$910$	−0.658187	−	3.83652i	−0.0218187	−	0.127180i
$911$	54.4117	+	11.5656i	1.80274	+	0.383184i	0.982115	−	0.188282i	$-0.0602920\pi$
$911$	54.4117	+	11.5656i	1.80274	+	0.383184i	0.820625	+	0.571467i	$0.193625\pi$
$912$	−27.3965	+	11.8928i	−0.907188	+	0.393809i
$913$	23.6702	−	5.03126i	0.783370	−	0.166510i
$914$	−2.81222	+	3.12329i	−0.0930201	+	0.103309i
$915$	23.9619	+	23.7949i	0.792156	+	0.786634i
$916$	−25.8125	−	28.6677i	−0.852869	−	0.947207i
$917$	4.16384	+	3.02521i	0.137502	+	0.0999011i
$918$	−0.501905	−	6.52770i	−0.0165653	−	0.215446i
$919$	−45.6386	−	33.1584i	−1.50548	−	1.09379i	−0.968134	−	0.250432i	$-0.919427\pi$
$919$	−45.6386	−	33.1584i	−1.50548	−	1.09379i	−0.537345	−	0.843363i	$-0.680573\pi$
$920$	−15.4865	+	19.6339i	−0.510576	+	0.647309i
$921$	−2.27804	−	7.24019i	−0.0750640	−	0.238572i
$922$	4.23958	+	1.88758i	0.139623	+	0.0621642i
$923$	−0.948115	+	1.05299i	−0.0312076	+	0.0346595i
$924$	8.95496	+	10.1340i	0.294597	+	0.333384i
$925$	−36.3972	−	19.7871i	−1.19673	−	0.650595i
$926$	−9.97042			−0.327648
$927$	29.1917	−	5.63790i	0.958781	−	0.185173i
$928$	17.2258	−	12.5153i	0.565466	−	0.410835i
$929$	1.42087	+	13.5186i	0.0466171	+	0.443532i	0.992790	+	0.119870i	$0.0382476\pi$
$929$	1.42087	+	13.5186i	0.0466171	+	0.443532i	−0.946173	+	0.323663i	$0.895086\pi$
$930$	7.03102	−	5.73443i	0.230556	−	0.188039i
$931$	0.560002	−	5.32806i	0.0183533	−	0.174620i
$932$	−7.18214	−	12.4398i	−0.235259	−	0.407480i
$933$	28.1061	+	12.8291i	0.920152	+	0.420005i
$934$	−0.125091	−	0.138928i	−0.00409310	−	0.00454585i
$935$	−14.3180	−	2.07989i	−0.468248	−	0.0680196i
$936$	8.17654	−	1.57917i	0.267259	−	0.0516166i
$937$	−5.39097	+	16.5917i	−0.176115	+	0.542027i	−0.999683	−	0.0251916i	$-0.991980\pi$
$937$	−5.39097	+	16.5917i	−0.176115	+	0.542027i	0.823567	+	0.567218i	$0.191980\pi$
$938$	−1.81845	−	2.01959i	−0.0593744	−	0.0659419i
$939$	14.3451	−	24.3198i	0.468135	−	0.793645i
$940$	12.4771	+	31.2982i	0.406957	+	1.02083i
$941$	−47.9664	+	10.1956i	−1.56366	+	0.332366i	−0.906772	−	0.421621i	$-0.861461\pi$
$941$	−47.9664	+	10.1956i	−1.56366	+	0.332366i	−0.656889	+	0.753988i	$0.728128\pi$
$942$	−3.92711	+	2.79762i	−0.127952	+	0.0911514i
$943$	18.9032	−	32.7414i	0.615574	−	1.06621i
$944$	2.62100	+	1.90427i	0.0853063	+	0.0619787i
$945$	13.2546	−	25.0669i	0.431172	−	0.815426i
$946$	2.96546	−	2.15453i	0.0964153	−	0.0700498i
$947$	−3.93582	−	37.4468i	−0.127897	−	1.21686i	−0.850643	−	0.525744i	$-0.823787\pi$
$947$	−3.93582	−	37.4468i	−0.127897	−	1.21686i	0.722746	−	0.691114i	$-0.242880\pi$
$948$	20.6301	+	0.192432i	0.670036	+	0.00624990i
$949$	11.8093	+	20.4543i	0.383347	+	0.663976i
$950$	−7.20656	+	4.41093i	−0.233812	+	0.143109i
$951$	24.1700	+	27.3523i	0.783766	+	0.886959i
$952$	−11.7045	−	2.48786i	−0.379344	−	0.0806320i
$953$	−24.9618	+	18.1358i	−0.808594	+	0.587478i	−0.913423	−	0.407013i	$-0.866570\pi$
$953$	−24.9618	+	18.1358i	−0.808594	+	0.587478i	0.104829	+	0.994490i	$0.466570\pi$
$954$	1.28962	−	2.14046i	0.0417530	−	0.0692999i
$955$	52.4020	+	7.61212i	1.69569	+	0.246322i
$956$	−28.0250	+	12.4776i	−0.906395	+	0.403553i
$957$	16.6558	−	3.37824i	0.538405	−	0.109203i
$958$	0.312946	−	2.97748i	0.0101108	−	0.0961981i
$959$	−11.0106	+	2.34038i	−0.355552	+	0.0755749i
$960$	5.45391	−	20.6428i	0.176024	−	0.666242i
$961$	−19.1600	−	4.07258i	−0.618064	−	0.131374i
$962$	1.82637	−	5.62099i	0.0588845	−	0.181228i
$963$	−1.94262	+	1.35676i	−0.0626002	+	0.0437211i
$964$	8.58075	+	26.4088i	0.276367	+	0.850571i
$965$	2.67286	+	0.986876i	0.0860424	+	0.0317687i
$966$	−11.1427	+	4.83702i	−0.358510	+	0.155628i
$967$	−3.01182	+	28.6555i	−0.0968535	+	0.921500i	0.832926	+	0.553384i	$0.186664\pi$
$967$	−3.01182	+	28.6555i	−0.0968535	+	0.921500i	−0.929780	+	0.368116i	$0.880003\pi$
$968$	5.21608	+	9.03451i	0.167651	+	0.290380i
$969$	27.6874	−	19.7241i	0.889446	−	0.633630i
$970$	−0.630288	−	0.943835i	−0.0202373	−	0.0303047i
$971$	0.696107	−	0.505751i	0.0223391	−	0.0162303i	−0.576560	−	0.817055i	$-0.695605\pi$
$971$	0.696107	−	0.505751i	0.0223391	−	0.0162303i	0.598899	+	0.800825i	$0.295605\pi$
$972$	26.3482	+	13.2357i	0.845120	+	0.424536i
$973$	−3.01853	−	9.29008i	−0.0967696	−	0.297826i
$974$	−5.24732	+	9.08862i	−0.168135	+	0.291218i
$975$	−17.7407	+	6.08617i	−0.568158	+	0.194914i
$976$	14.6521	+	25.3781i	0.469001	+	0.812334i
$977$	−33.0380	+	36.6925i	−1.05698	+	1.17390i	−0.0726876	+	0.997355i	$0.523158\pi$
$977$	−33.0380	+	36.6925i	−1.05698	+	1.17390i	−0.984293	+	0.176541i	$0.943509\pi$
$978$	−3.99638	−	0.888495i	−0.127790	−	0.0284110i
$979$	1.69495	+	16.1264i	0.0541708	+	0.515401i
$980$	3.16274	+	3.08264i	0.101030	+	0.0984712i
$981$	−15.1824	−	49.8735i	−0.484735	−	1.59234i
$982$	13.9001			0.443570
$983$	44.0009	−	19.5905i	1.40341	−	0.624839i	0.441267	−	0.897376i	$-0.354529\pi$
$983$	44.0009	−	19.5905i	1.40341	−	0.624839i	0.962145	+	0.272537i	$0.0878627\pi$
$984$	1.09471	−	9.55714i	0.0348982	−	0.304670i
$985$	5.42286	−	21.3288i	0.172787	−	0.679593i
$986$	−4.89074	+	5.43171i	−0.155753	+	0.172981i
$987$	−3.83199	+	33.4542i	−0.121974	+	1.06486i
$988$	14.0635	+	15.6191i	0.447420	+	0.496910i
$989$	−17.7399	−	54.5977i	−0.564095	−	1.73611i
$990$	−2.36875	+	2.89055i	−0.0752839	+	0.0918676i
$991$	6.36275	−	19.5825i	0.202120	−	0.622060i	−0.797700	−	0.603055i	$-0.793950\pi$
$991$	6.36275	−	19.5825i	0.202120	−	0.622060i	0.999819	−	0.0190053i	$-0.00604994\pi$
$992$	23.8491	−	10.6183i	0.757209	−	0.337131i
$993$	20.7757	+	23.5110i	0.659295	+	0.746101i
$994$	0.0549709	−	0.523014i	0.00174357	−	0.0165890i
$995$	31.9585	−	26.5653i	1.01315	−	0.842176i
$996$	−14.0679	−	44.7113i	−0.445758	−	1.41673i
$997$	−5.96957	−	56.7967i	−0.189058	−	1.79877i	−0.519007	−	0.854770i	$-0.673698\pi$
$997$	−5.96957	−	56.7967i	−0.189058	−	1.79877i	0.329949	−	0.943999i	$-0.392969\pi$
$998$	1.93571	+	5.95750i	0.0612738	+	0.188581i
$999$	35.5252	−	24.3217i	1.12397	−	0.769503i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.106.16	yes	224
3.2	odd	2		675.2.r.a.181.13		224
9.4	even	3	inner	225.2.q.a.31.13	✓	224
9.5	odd	6		675.2.r.a.631.16		224
25.21	even	5	inner	225.2.q.a.196.13	yes	224
75.71	odd	10		675.2.r.a.46.16		224
225.121	even	15	inner	225.2.q.a.121.16	yes	224
225.221	odd	30		675.2.r.a.496.13		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.13	✓	224	9.4	even	3	inner
225.2.q.a.106.16	yes	224	1.1	even	1	trivial
225.2.q.a.121.16	yes	224	225.121	even	15	inner
225.2.q.a.196.13	yes	224	25.21	even	5	inner
675.2.r.a.46.16		224	75.71	odd	10
675.2.r.a.181.13		224	3.2	odd	2
675.2.r.a.496.13		224	225.221	odd	30
675.2.r.a.631.16		224	9.5	odd	6

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

\(f(q)\)	\(=\)	\(q+(0.322170 + 0.0684793i) q^{2} +(-0.519845 - 1.65220i) q^{3} +(-1.72799 - 0.769349i) q^{4} +(-1.71956 + 1.42937i) q^{5} +(-0.0543370 - 0.567887i) q^{6} +(-1.22023 + 2.11349i) q^{7} +(-1.03695 - 0.753387i) q^{8} +(-2.45952 + 1.71778i) q^{9} +O(q^{10})\)	\(q+(0.322170 + 0.0684793i) q^{2} +(-0.519845 - 1.65220i) q^{3} +(-1.72799 - 0.769349i) q^{4} +(-1.71956 + 1.42937i) q^{5} +(-0.0543370 - 0.567887i) q^{6} +(-1.22023 + 2.11349i) q^{7} +(-1.03695 - 0.753387i) q^{8} +(-2.45952 + 1.71778i) q^{9} +(-0.651873 + 0.342746i) q^{10} +(-1.65447 - 0.351668i) q^{11} +(-0.372832 + 3.25492i) q^{12} +(2.11839 - 0.450278i) q^{13} +(-0.537850 + 0.597343i) q^{14} +(3.25551 + 2.09801i) q^{15} +(2.24886 + 2.49761i) q^{16} +(-3.09482 - 2.24852i) q^{17} +(-0.910015 + 0.384989i) q^{18} +(-4.15077 - 3.01571i) q^{19} +(4.07107 - 1.14699i) q^{20} +(4.12624 + 0.917366i) q^{21} +(-0.508937 - 0.226593i) q^{22} +(-5.83819 + 6.48397i) q^{23} +(-0.705692 + 2.10489i) q^{24} +(0.913787 - 4.91579i) q^{25} +0.713316 q^{26} +(4.11668 + 3.17064i) q^{27} +(3.73455 - 2.71331i) q^{28} +(-0.606373 - 5.76925i) q^{29} +(0.905158 + 0.898849i) q^{30} +(0.743462 - 7.07356i) q^{31} +(1.83522 + 3.17869i) q^{32} +(0.279041 + 2.91632i) q^{33} +(-0.843080 - 0.936336i) q^{34} +(-0.922715 - 5.37844i) q^{35} +(5.57159 - 1.07606i) q^{36} +(2.56039 - 7.88008i) q^{37} +(-1.13074 - 1.25581i) q^{38} +(-1.84518 - 3.26593i) q^{39} +(2.85997 - 0.186690i) q^{40} +(-4.23841 + 0.900902i) q^{41} +(1.26653 + 0.578109i) q^{42} +(-3.28981 + 5.69811i) q^{43} +(2.58834 + 1.88054i) q^{44} +(1.77396 - 6.46939i) q^{45} +(-2.32491 + 1.68914i) q^{46} +(0.832694 + 7.92255i) q^{47} +(2.95750 - 5.01394i) q^{48} +(0.522100 + 0.904304i) q^{49} +(0.631024 - 1.52114i) q^{50} +(-2.10617 + 6.28214i) q^{51} +(-4.00697 - 0.851708i) q^{52} +(-2.04603 + 1.48652i) q^{53} +(1.10915 + 1.30339i) q^{54} +(3.34762 - 1.76013i) q^{55} +(2.85759 - 1.27228i) q^{56} +(-2.82480 + 8.42560i) q^{57} +(0.199719 - 1.90020i) q^{58} +(0.942892 - 0.200418i) q^{59} +(-4.01139 - 6.12995i) q^{60} +(8.52867 + 1.81282i) q^{61} +(0.723913 - 2.22798i) q^{62} +(-0.629334 - 7.29425i) q^{63} +(-1.70356 - 5.24301i) q^{64} +(-2.99909 + 3.80225i) q^{65} +(-0.109809 + 0.958658i) q^{66} +(-0.353406 + 3.36243i) q^{67} +(3.61791 + 6.26641i) q^{68} +(13.7478 + 6.27520i) q^{69} +(0.0710407 - 1.79596i) q^{70} +(-0.529305 + 0.384563i) q^{71} +(3.84454 + 0.0717278i) q^{72} +(3.37004 + 10.3719i) q^{73} +(1.36450 - 2.36339i) q^{74} +(-8.59689 + 1.04569i) q^{75} +(4.85234 + 8.40450i) q^{76} +(2.76207 - 3.06759i) q^{77} +(-0.370814 - 1.17854i) q^{78} +(-0.658241 - 6.26274i) q^{79} +(-7.43708 - 1.08034i) q^{80} +(3.09850 - 8.44981i) q^{81} -1.42718 q^{82} +(-13.0700 + 5.81913i) q^{83} +(-6.42431 - 4.75972i) q^{84} +(8.53571 - 0.557185i) q^{85} +(-1.45008 + 1.61048i) q^{86} +(-9.21673 + 4.00097i) q^{87} +(1.45065 + 1.61111i) q^{88} +(-2.96245 - 9.11749i) q^{89} +(1.01454 - 1.96276i) q^{90} +(-1.63326 + 5.02664i) q^{91} +(15.0768 - 6.71261i) q^{92} +(-12.0734 + 2.44881i) q^{93} +(-0.274262 + 2.60943i) q^{94} +(11.4481 - 0.747296i) q^{95} +(4.29780 - 4.68457i) q^{96} +(0.161080 + 1.53258i) q^{97} +(0.106279 + 0.327092i) q^{98} +(4.67328 - 1.97707i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Introduction

L-functions

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