LMFDB - Embedded newform 225.2.q.a.211.13

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			211.13
Character	$\chi$	$=$	225.211
Dual form			225.2.q.a.16.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.217479 - 0.0968278i) q^{2} +(-1.50542 - 0.856567i) q^{3} +(-1.30034 - 1.44417i) q^{4} +(1.93124 + 1.12708i) q^{5} +(0.244458 + 0.332052i) q^{6} +(-1.58050 - 2.73751i) q^{7} +(0.290090 + 0.892804i) q^{8} +(1.53259 + 2.57899i) q^{9} +O(q^{10})$	\(q+(-0.217479 - 0.0968278i) q^{2} +(-1.50542 - 0.856567i) q^{3} +(-1.30034 - 1.44417i) q^{4} +(1.93124 + 1.12708i) q^{5} +(0.244458 + 0.332052i) q^{6} +(-1.58050 - 2.73751i) q^{7} +(0.290090 + 0.892804i) q^{8} +(1.53259 + 2.57899i) q^{9} +(-0.310871 - 0.432114i) q^{10} +(-3.55139 - 1.58118i) q^{11} +(0.720527 + 3.28792i) q^{12} +(-5.89635 + 2.62522i) q^{13} +(0.0786587 + 0.748387i) q^{14} +(-1.94191 - 3.35097i) q^{15} +(-0.382906 + 3.64311i) q^{16} +(-2.22145 - 6.83693i) q^{17} +(-0.0835871 - 0.709272i) q^{18} +(-0.490230 - 1.50877i) q^{19} +(-0.883563 - 4.25464i) q^{20} +(0.0344602 + 5.47491i) q^{21} +(0.619250 + 0.687747i) q^{22} +(0.172818 + 1.64425i) q^{23} +(0.328039 - 1.59253i) q^{24} +(2.45937 + 4.35333i) q^{25} +1.53653 q^{26} +(-0.0981099 - 5.19523i) q^{27} +(-1.89825 + 5.84221i) q^{28} +(2.56366 - 0.544923i) q^{29} +(0.0978562 + 0.916796i) q^{30} +(1.69775 + 0.360869i) q^{31} +(1.37478 - 2.38118i) q^{32} +(3.99195 + 5.42235i) q^{33} +(-0.178886 + 1.70199i) q^{34} +(0.0330743 - 7.06814i) q^{35} +(1.73163 - 5.56688i) q^{36} +(-0.974207 - 0.707803i) q^{37} +(-0.0394766 + 0.375594i) q^{38} +(11.1252 + 1.09855i) q^{39} +(-0.446032 + 2.05117i) q^{40} +(5.00852 - 2.22994i) q^{41} +(0.522629 - 1.19401i) q^{42} +(-5.96998 - 10.3403i) q^{43} +(2.33451 + 7.18490i) q^{44} +(0.0530542 + 6.70799i) q^{45} +(0.121625 - 0.374323i) q^{46} +(6.01847 - 1.27926i) q^{47} +(3.69700 - 5.15643i) q^{48} +(-1.49598 + 2.59111i) q^{49} +(-0.113337 - 1.18489i) q^{50} +(-2.51207 + 12.1953i) q^{51} +(11.4585 + 5.10167i) q^{52} +(0.201993 - 0.621671i) q^{53} +(-0.481706 + 1.13935i) q^{54} +(-5.07646 - 7.05635i) q^{55} +(1.98557 - 2.20520i) q^{56} +(-0.554363 + 2.69126i) q^{57} +(-0.610306 - 0.129724i) q^{58} +(0.228332 - 0.101660i) q^{59} +(-2.31425 + 7.16185i) q^{60} +(-0.279455 - 0.124421i) q^{61} +(-0.334283 - 0.242871i) q^{62} +(4.63775 - 8.27157i) q^{63} +(5.39759 - 3.92158i) q^{64} +(-14.3461 - 1.57574i) q^{65} +(-0.343131 - 1.56578i) q^{66} +(-3.64909 - 0.775638i) q^{67} +(-6.98507 + 12.0985i) q^{68} +(1.14825 - 2.62332i) q^{69} +(-0.691586 + 1.53397i) q^{70} +(0.0407718 - 0.125483i) q^{71} +(-1.85794 + 2.11644i) q^{72} +(-1.55794 + 1.13191i) q^{73} +(0.143334 + 0.248263i) q^{74} +(0.0265392 - 8.66021i) q^{75} +(-1.54147 + 2.66990i) q^{76} +(1.28448 + 12.2210i) q^{77} +(-2.31312 - 1.31614i) q^{78} +(-2.79800 + 0.594732i) q^{79} +(-4.84557 + 6.60415i) q^{80} +(-4.30236 + 7.90504i) q^{81} -1.30517 q^{82} +(0.0920635 - 0.102247i) q^{83} +(7.86191 - 7.16901i) q^{84} +(3.41563 - 15.7075i) q^{85} +(0.297115 + 2.82686i) q^{86} +(-4.32615 - 1.37561i) q^{87} +(0.381463 - 3.62938i) q^{88} +(11.1238 - 8.08188i) q^{89} +(0.637982 - 1.46398i) q^{90} +(16.5058 + 11.9921i) q^{91} +(2.14986 - 2.38766i) q^{92} +(-2.24673 - 1.99750i) q^{93} +(-1.43276 - 0.304542i) q^{94} +(0.753762 - 3.46633i) q^{95} +(-4.10926 + 2.40710i) q^{96} +(-7.27218 + 1.54575i) q^{97} +(0.576234 - 0.418659i) q^{98} +(-1.36496 - 11.5823i) 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 $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.217479	−	0.0968278i	−0.153781	−	0.0684676i	0.328403	−	0.944538i	$-0.393490\pi$
$2$	−0.217479	−	0.0968278i	−0.153781	−	0.0684676i	−0.482184	+	0.876070i	$0.660156\pi$
$3$	−1.50542	−	0.856567i	−0.869155	−	0.494539i
$3$	−1.50542	−	0.856567i	−0.869155	−	0.494539i
$4$	−1.30034	−	1.44417i	−0.650170	−	0.722087i
$5$	1.93124	+	1.12708i	0.863676	+	0.504047i
$5$	1.93124	+	1.12708i	0.863676	+	0.504047i
$6$	0.244458	+	0.332052i	0.0997994	+	0.135560i
$7$	−1.58050	−	2.73751i	−0.597374	−	1.03468i	−0.993207	−	0.116359i	$-0.962878\pi$
$7$	−1.58050	−	2.73751i	−0.597374	−	1.03468i	0.395833	−	0.918322i	$-0.370456\pi$
$8$	0.290090	+	0.892804i	0.102562	+	0.315654i
$9$	1.53259	+	2.57899i	0.510862	+	0.859663i
$10$	−0.310871	−	0.432114i	−0.0983059	−	0.136647i
$11$	−3.55139	−	1.58118i	−1.07078	−	0.476744i	−0.205826	−	0.978589i	$-0.565988\pi$
$11$	−3.55139	−	1.58118i	−1.07078	−	0.476744i	−0.864958	+	0.501845i	$0.832655\pi$
$12$	0.720527	+	3.28792i	0.207998	+	0.949140i
$13$	−5.89635	+	2.62522i	−1.63535	+	0.728106i	−0.999060	−	0.0433424i	$-0.986199\pi$
$13$	−5.89635	+	2.62522i	−1.63535	+	0.728106i	−0.636292	+	0.771448i	$0.719533\pi$
$14$	0.0786587	+	0.748387i	0.0210224	+	0.200015i
$15$	−1.94191	−	3.35097i	−0.501398	−	0.865217i
$16$	−0.382906	+	3.64311i	−0.0957265	+	0.910777i
$17$	−2.22145	−	6.83693i	−0.538782	−	1.65820i	−0.735333	−	0.677706i	$-0.762974\pi$
$17$	−2.22145	−	6.83693i	−0.538782	−	1.65820i	0.196551	−	0.980494i	$-0.437026\pi$
$18$	−0.0835871	−	0.709272i	−0.0197017	−	0.167177i
$19$	−0.490230	−	1.50877i	−0.112467	−	0.346137i	0.878944	−	0.476926i	$-0.158249\pi$
$19$	−0.490230	−	1.50877i	−0.112467	−	0.346137i	−0.991410	+	0.130789i	$0.958249\pi$
$20$	−0.883563	−	4.25464i	−0.197571	−	0.951365i
$21$	0.0344602	+	5.47491i	0.00751984	+	1.19472i
$22$	0.619250	+	0.687747i	0.132025	+	0.146628i
$23$	0.172818	+	1.64425i	0.0360350	+	0.342850i	0.997654	+	0.0684609i	$0.0218088\pi$
$23$	0.172818	+	1.64425i	0.0360350	+	0.342850i	−0.961619	+	0.274389i	$0.911524\pi$
$24$	0.328039	−	1.59253i	0.0669608	−	0.325073i
$25$	2.45937	+	4.35333i	0.491873	+	0.870667i
$26$	1.53653			0.301337
$27$	−0.0981099	−	5.19523i	−0.0188813	−	0.999822i
$28$	−1.89825	+	5.84221i	−0.358736	+	1.10407i
$29$	2.56366	−	0.544923i	0.476060	−	0.101190i	0.0363682	−	0.999338i	$-0.488421\pi$
$29$	2.56366	−	0.544923i	0.476060	−	0.101190i	0.439692	+	0.898149i	$0.355088\pi$
$30$	0.0978562	+	0.916796i	0.0178660	+	0.167383i
$31$	1.69775	+	0.360869i	0.304926	+	0.0648139i	0.357833	−	0.933785i	$-0.383516\pi$
$31$	1.69775	+	0.360869i	0.304926	+	0.0648139i	−0.0529078	+	0.998599i	$0.516849\pi$
$32$	1.37478	−	2.38118i	0.243029	−	0.420938i
$33$	3.99195	+	5.42235i	0.694909	+	0.943909i
$34$	−0.178886	+	1.70199i	−0.0306787	+	0.291888i
$35$	0.0330743	−	7.06814i	0.00559057	−	1.19473i
$36$	1.73163	−	5.56688i	0.288604	−	0.927813i
$37$	−0.974207	−	0.707803i	−0.160159	−	0.116362i	0.504819	−	0.863225i	$-0.331559\pi$
$37$	−0.974207	−	0.707803i	−0.160159	−	0.116362i	−0.664978	+	0.746863i	$0.731559\pi$
$38$	−0.0394766	+	0.375594i	−0.00640394	+	0.0609295i
$39$	11.1252	+	1.09855i	1.78145	+	0.175909i
$40$	−0.446032	+	2.05117i	−0.0705238	+	0.324319i
$41$	5.00852	−	2.22994i	0.782199	−	0.348258i	0.0235212	−	0.999723i	$-0.492512\pi$
$41$	5.00852	−	2.22994i	0.782199	−	0.348258i	0.758678	+	0.651466i	$0.225846\pi$
$42$	0.522629	−	1.19401i	0.0806435	−	0.184240i
$43$	−5.96998	−	10.3403i	−0.910413	−	1.57688i	−0.813482	−	0.581591i	$-0.802431\pi$
$43$	−5.96998	−	10.3403i	−0.910413	−	1.57688i	−0.0969314	−	0.995291i	$-0.530903\pi$
$44$	2.33451	+	7.18490i	0.351941	+	1.08316i
$45$	0.0530542	+	6.70799i	0.00790886	+	0.999969i
$46$	0.121625	−	0.374323i	0.0179326	−	0.0551909i
$47$	6.01847	−	1.27926i	0.877883	−	0.186600i	0.253140	−	0.967430i	$-0.418537\pi$
$47$	6.01847	−	1.27926i	0.877883	−	0.186600i	0.624744	+	0.780830i	$0.285203\pi$
$48$	3.69700	−	5.15643i	0.533616	−	0.744266i
$49$	−1.49598	+	2.59111i	−0.213711	+	0.370158i
$50$	−0.113337	−	1.18489i	−0.0160282	−	0.167569i
$51$	−2.51207	+	12.1953i	−0.351760	+	1.70768i
$52$	11.4585	+	5.10167i	1.58901	+	0.707474i
$53$	0.201993	−	0.621671i	0.0277459	−	0.0853931i	−0.936225	−	0.351402i	$-0.885705\pi$
$53$	0.201993	−	0.621671i	0.0277459	−	0.0853931i	0.963971	+	0.266009i	$0.0857050\pi$
$54$	−0.481706	+	1.13935i	−0.0655518	+	0.155046i
$55$	−5.07646	−	7.05635i	−0.684510	−	0.951478i
$56$	1.98557	−	2.20520i	0.265333	−	0.294682i
$57$	−0.554363	+	2.69126i	−0.0734272	+	0.356466i
$58$	−0.610306	−	0.129724i	−0.0801370	−	0.0170337i
$59$	0.228332	−	0.101660i	0.0297263	−	0.0132350i	−0.391820	−	0.920042i	$-0.628154\pi$
$59$	0.228332	−	0.101660i	0.0297263	−	0.0132350i	0.421546	+	0.906807i	$0.361488\pi$
$60$	−2.31425	+	7.16185i	−0.298768	+	0.924591i
$61$	−0.279455	−	0.124421i	−0.0357805	−	0.0159305i	0.388768	−	0.921336i	$-0.372901\pi$
$61$	−0.279455	−	0.124421i	−0.0357805	−	0.0159305i	−0.424549	+	0.905405i	$0.639567\pi$
$62$	−0.334283	−	0.242871i	−0.0424540	−	0.0308447i
$63$	4.63775	−	8.27157i	0.584302	−	1.04212i
$64$	5.39759	−	3.92158i	0.674699	−	0.490198i
$65$	−14.3461	−	1.57574i	−1.77941	−	0.195447i
$66$	−0.343131	−	1.56578i	−0.0422365	−	0.192734i
$67$	−3.64909	−	0.775638i	−0.445807	−	0.0947592i	−0.0204623	−	0.999791i	$-0.506514\pi$
$67$	−3.64909	−	0.775638i	−0.445807	−	0.0947592i	−0.425345	+	0.905031i	$0.639847\pi$
$68$	−6.98507	+	12.0985i	−0.847065	+	1.46716i
$69$	1.14825	−	2.62332i	0.138233	−	0.315810i
$70$	−0.691586	+	1.53397i	−0.0826603	+	0.183344i
$71$	0.0407718	−	0.125483i	0.00483872	−	0.0148920i	−0.948608	−	0.316454i	$-0.897508\pi$
$71$	0.0407718	−	0.125483i	0.00483872	−	0.0148920i	0.953447	+	0.301562i	$0.0975079\pi$
$72$	−1.85794	+	2.11644i	−0.218961	+	0.249424i
$73$	−1.55794	+	1.13191i	−0.182343	+	0.132480i	−0.675212	−	0.737623i	$-0.735948\pi$
$73$	−1.55794	+	1.13191i	−0.182343	+	0.132480i	0.492869	+	0.870103i	$0.335948\pi$
$74$	0.143334	+	0.248263i	0.0166623	+	0.0288599i
$75$	0.0265392	−	8.66021i	0.00306449	−	0.999995i
$76$	−1.54147	+	2.66990i	−0.176818	+	0.306258i
$77$	1.28448	+	12.2210i	0.146380	+	1.39272i
$78$	−2.31312	−	1.31614i	−0.261909	−	0.149023i
$79$	−2.79800	+	0.594732i	−0.314799	+	0.0669126i	−0.362602	−	0.931944i	$-0.618111\pi$
$79$	−2.79800	+	0.594732i	−0.314799	+	0.0669126i	0.0478026	+	0.998857i	$0.484778\pi$
$80$	−4.84557	+	6.60415i	−0.541751	+	0.738366i
$81$	−4.30236	+	7.90504i	−0.478040	+	0.878338i
$82$	−1.30517			−0.144132
$83$	0.0920635	−	0.102247i	0.0101053	−	0.0112231i	−0.738071	−	0.674723i	$-0.764263\pi$
$83$	0.0920635	−	0.102247i	0.0101053	−	0.0112231i	0.748176	+	0.663500i	$0.230930\pi$
$84$	7.86191	−	7.16901i	0.857805	−	0.782203i
$85$	3.41563	−	15.7075i	0.370478	−	1.70372i
$86$	0.297115	+	2.82686i	0.0320387	+	0.304828i
$87$	−4.32615	−	1.37561i	−0.463812	−	0.147481i
$88$	0.381463	−	3.62938i	0.0406641	−	0.386893i
$89$	11.1238	−	8.08188i	1.17912	−	0.856678i	0.187044	−	0.982352i	$-0.440109\pi$
$89$	11.1238	−	8.08188i	1.17912	−	0.856678i	0.992072	+	0.125674i	$0.0401093\pi$
$90$	0.637982	−	1.46398i	0.0672492	−	0.154317i
$91$	16.5058	+	11.9921i	1.73027	+	1.25712i
$92$	2.14986	−	2.38766i	0.224138	−	0.248931i
$93$	−2.24673	−	1.99750i	−0.232975	−	0.207131i
$94$	−1.43276	−	0.304542i	−0.147778	−	0.0314111i
$95$	0.753762	−	3.46633i	0.0773343	−	0.355638i
$96$	−4.10926	+	2.40710i	−0.419400	+	0.245673i
$97$	−7.27218	+	1.54575i	−0.738378	+	0.156947i	−0.561722	−	0.827326i	$-0.689861\pi$
$97$	−7.27218	+	1.54575i	−0.738378	+	0.156947i	−0.176655	+	0.984273i	$0.556528\pi$
$98$	0.576234	−	0.418659i	0.0582084	−	0.0422909i
$99$	−1.36496	−	11.5823i	−0.137184	−	1.16406i
$100$	3.08896	−	9.21257i	0.308896	−	0.921257i
$101$	−4.13170	−	7.15632i	−0.411120	−	0.712080i	0.583893	−	0.811831i	$-0.301529\pi$
$101$	−4.13170	−	7.15632i	−0.411120	−	0.712080i	−0.995012	+	0.0997505i	$0.968196\pi$
$102$	1.72716	−	2.40898i	0.171015	−	0.238524i
$103$	7.34507	+	8.15753i	0.723732	+	0.803785i	0.986963	−	0.160947i	$-0.0514550\pi$
$103$	7.34507	+	8.15753i	0.723732	+	0.803785i	−0.263231	+	0.964733i	$0.584788\pi$
$104$	−4.05428	−	4.50273i	−0.397555	−	0.441529i
$105$	−6.10413	+	10.6122i	−0.595702	+	1.03564i
$106$	−0.104124	+	0.115642i	−0.0101135	+	0.0112321i
$107$	13.7957			1.33368			0.666842	−	0.745199i	$-0.267646\pi$
$107$	13.7957			1.33368			0.666842	+	0.745199i	$0.267646\pi$
$108$	−7.37523	+	6.89725i	−0.709682	+	0.663688i
$109$	−11.6911	−	8.49409i	−1.11981	−	0.813586i	−0.135626	−	0.990760i	$-0.543304\pi$
$109$	−11.6911	−	8.49409i	−1.11981	−	0.813586i	−0.984180	+	0.177174i	$0.943304\pi$
$110$	0.420772	+	2.02615i	0.0401190	+	0.193186i
$111$	0.860312	+	1.90002i	0.0816572	+	0.180342i
$112$	10.5782	−	4.70973i	0.999549	−	0.445028i
$113$	3.56300	−	1.58635i	0.335179	−	0.149231i	−0.232245	−	0.972657i	$-0.574607\pi$
$113$	3.56300	−	1.58635i	0.335179	−	0.149231i	0.567423	+	0.823426i	$0.307940\pi$
$114$	0.381151	−	0.531613i	0.0356980	−	0.0497902i
$115$	−1.51945	+	3.37022i	−0.141690	+	0.314274i
$116$	−4.12059	−	2.99379i	−0.382587	−	0.277966i
$117$	−15.8071	−	11.1832i	−1.46136	−	1.03389i
$118$	−0.0595009			−0.00547750
$119$	−15.2052	+	16.8870i	−1.39386	+	1.54803i
$120$	2.42843	−	2.70582i	0.221685	−	0.247007i
$121$	2.75180	+	3.05618i	0.250164	+	0.277835i
$122$	0.0487280	+	0.0541180i	0.00441163	+	0.00489961i
$123$	−9.45002	−	0.933139i	−0.852080	−	0.0841383i
$124$	−1.68650	−	2.92110i	−0.151452	−	0.262323i
$125$	−0.156944	+	11.1792i	−0.0140375	+	0.999901i
$126$	−1.80953	+	1.34983i	−0.161206	+	0.120252i
$127$	−13.6713	+	9.93278i	−1.21313	+	0.881391i	−0.995511	−	0.0946423i	$-0.969829\pi$
$127$	−13.6713	+	9.93278i	−1.21313	+	0.881391i	−0.217620	+	0.976034i	$0.569829\pi$
$128$	−6.93252	+	1.47355i	−0.612754	+	0.130245i
$129$	0.130165	+	20.6802i	0.0114604	+	1.82079i
$130$	2.96740	+	1.73179i	0.260258	+	0.151888i
$131$	−15.9546	−	3.39126i	−1.39396	−	0.296296i	−0.551106	−	0.834435i	$-0.685794\pi$
$131$	−15.9546	−	3.39126i	−1.39396	−	0.296296i	−0.842856	+	0.538140i	$0.819127\pi$
$132$	2.63992	−	12.8160i	0.229775	−	1.11549i
$133$	−3.35547	+	3.72663i	−0.290957	+	0.323140i
$134$	0.718496	+	0.522018i	0.0620686	+	0.0450955i
$135$	5.66598	−	10.1438i	0.487650	−	0.873039i
$136$	5.45962	−	3.96665i	0.468159	−	0.340137i
$137$	0.594954	−	5.66061i	0.0508303	−	0.483618i	−0.939262	−	0.343201i	$-0.888489\pi$
$137$	0.594954	−	5.66061i	0.0508303	−	0.483618i	0.990092	−	0.140418i	$-0.0448445\pi$
$138$	−0.503729	+	0.459334i	−0.0428803	+	0.0391011i
$139$	0.755820	+	7.19114i	0.0641078	+	0.609945i	0.978661	+	0.205480i	$0.0658755\pi$
$139$	0.755820	+	7.19114i	0.0641078	+	0.609945i	−0.914554	+	0.404465i	$0.867458\pi$
$140$	−10.2506	+	9.14322i	−0.866337	+	0.772743i
$141$	−10.1561	−	3.22939i	−0.855298	−	0.271964i
$142$	−0.0210172	+	0.0233420i	−0.00176372	+	0.00195881i
$143$	25.0912			2.09823
$144$	−9.98237	+	4.59586i	−0.831864	+	0.382989i
$145$	5.56521	+	1.83708i	0.462166	+	0.152561i
$146$	0.448419	−	0.0953144i	0.0371114	−	0.00788828i
$147$	4.47153	−	2.61930i	0.368805	−	0.216036i
$148$	0.244610	+	2.32731i	0.0201068	+	0.191304i
$149$	−7.43364	+	12.8754i	−0.608988	+	1.05480i	0.382420	+	0.923989i	$0.375091\pi$
$149$	−7.43364	+	12.8754i	−0.608988	+	1.05480i	−0.991408	+	0.130809i	$0.958243\pi$
$150$	−0.844321	+	1.88084i	−0.0689385	+	0.153570i
$151$	−6.50424	−	11.2657i	−0.529308	−	0.916788i	−0.999416	−	0.0341791i	$-0.989118\pi$
$151$	−6.50424	−	11.2657i	−0.529308	−	0.916788i	0.470108	−	0.882609i	$-0.344215\pi$
$152$	1.20483	−	0.875359i	0.0977245	−	0.0710010i
$153$	14.2278	−	16.2073i	1.15025	−	1.31028i
$154$	0.903988	−	2.78219i	0.0728454	−	0.224195i
$155$	2.87204	+	2.61043i	0.230688	+	0.209675i
$156$	−12.8800	−	17.4952i	−1.03123	−	1.40073i
$157$	9.19914	−	15.9334i	0.734172	−	1.27162i	−0.220914	−	0.975293i	$-0.570904\pi$
$157$	9.19914	−	15.9334i	0.734172	−	1.27162i	0.955086	−	0.296329i	$-0.0957626\pi$
$158$	0.666091	+	0.141582i	0.0529914	+	0.0112637i
$159$	−0.836588	+	0.762857i	−0.0663458	+	0.0604985i
$160$	5.33882	−	3.04915i	0.422071	−	0.241056i
$161$	4.22801	−	3.07183i	0.333214	−	0.242094i
$162$	1.70110	−	1.30259i	0.133651	−	0.102341i
$163$	5.72788	+	4.16155i	0.448642	+	0.325958i	0.789059	−	0.614317i	$-0.210568\pi$
$163$	5.72788	+	4.16155i	0.448642	+	0.325958i	−0.340417	+	0.940274i	$0.610568\pi$
$164$	−9.73319	−	4.33350i	−0.760035	−	0.338389i
$165$	1.59797	+	14.9711i	0.124402	+	1.16550i
$166$	−0.0299222	+	0.0133222i	−0.00232241	+	0.00103401i
$167$	3.52725	+	0.749739i	0.272947	+	0.0580166i	0.342351	−	0.939572i	$-0.388777\pi$
$167$	3.52725	+	0.749739i	0.272947	+	0.0580166i	−0.0694048	+	0.997589i	$0.522110\pi$
$168$	−4.87803	+	1.61898i	−0.376348	+	0.124907i
$169$	19.1764	−	21.2976i	1.47511	−	1.63827i
$170$	−2.26375	+	3.08532i	−0.173622	+	0.236634i
$171$	3.13979	−	3.57662i	0.240106	−	0.273511i
$172$	−7.17020	+	22.0676i	−0.546722	+	1.68264i
$173$	17.3194	+	7.71110i	1.31677	+	0.586264i	0.940358	−	0.340188i	$-0.110491\pi$
$173$	17.3194	+	7.71110i	1.31677	+	0.586264i	0.376413	+	0.926452i	$0.377157\pi$
$174$	0.807649	+	0.718058i	0.0612277	+	0.0544358i
$175$	8.03026	−	13.6130i	0.607031	−	1.02905i
$176$	7.12026	−	12.3327i	0.536710	−	0.929609i
$177$	−0.430814	−	0.0425406i	−0.0323820	−	0.00319755i
$178$	−3.20173	+	0.680549i	−0.239980	+	0.0510093i
$179$	−1.72359	+	5.30468i	−0.128827	+	0.396490i	−0.994579	−	0.103984i	$-0.966841\pi$
$179$	−1.72359	+	5.30468i	−0.128827	+	0.396490i	0.865752	+	0.500474i	$0.166841\pi$
$180$	9.61852	−	8.79929i	0.716922	−	0.655860i
$181$	5.22413	+	16.0782i	0.388307	+	1.19509i	0.934053	+	0.357135i	$0.116246\pi$
$181$	5.22413	+	16.0782i	0.388307	+	1.19509i	−0.545746	+	0.837951i	$0.683754\pi$
$182$	−2.42848	−	4.20625i	−0.180011	−	0.311788i
$183$	0.314122	+	0.426678i	0.0232206	+	0.0315410i
$184$	−1.41786	+	0.631272i	−0.104526	+	0.0465380i
$185$	−1.08367	−	2.46495i	−0.0796733	−	0.181227i
$186$	0.295202	+	0.651959i	0.0216452	+	0.0478040i
$187$	−2.92118	+	27.7931i	−0.213618	+	2.03244i
$188$	−9.67353	−	7.02823i	−0.705515	−	0.512586i
$189$	−14.0669	+	8.47964i	−1.02322	+	0.616803i
$190$	−0.499565	+	0.680869i	−0.0362422	+	0.0493954i
$191$	0.392239	−	3.73191i	0.0283814	−	0.270031i	−0.971124	−	0.238576i	$-0.923319\pi$
$191$	0.392239	−	3.73191i	0.0283814	−	0.270031i	0.999505	−	0.0314549i	$-0.0100140\pi$
$192$	−11.4847	+	1.28023i	−0.828840	+	0.0923926i
$193$	−8.37215	+	14.5010i	−0.602640	+	1.04380i	0.389779	+	0.920908i	$0.372551\pi$
$193$	−8.37215	+	14.5010i	−0.602640	+	1.04380i	−0.992420	+	0.122896i	$0.960782\pi$
$194$	1.73122	+	0.367981i	0.124294	+	0.0264195i
$195$	20.2472	+	14.6606i	1.44993	+	1.04986i
$196$	5.68728	−	1.20887i	0.406234	−	0.0863478i
$197$	−3.50778	+	10.7958i	−0.249919	+	0.769171i	0.744870	+	0.667210i	$0.232512\pi$
$197$	−3.50778	+	10.7958i	−0.249919	+	0.769171i	−0.994788	+	0.101961i	$0.967488\pi$
$198$	−0.824637	+	2.65107i	−0.0586044	+	0.188403i
$199$	5.25300			0.372375			0.186188	−	0.982514i	$-0.440387\pi$
$199$	5.25300			0.372375			0.186188	+	0.982514i	$0.440387\pi$
$200$	−3.17324	+	3.45859i	−0.224382	+	0.244559i
$201$	4.82903	+	4.29335i	0.340613	+	0.302830i
$202$	0.205627	+	1.95641i	0.0144679	+	0.137653i
$203$	−5.54360	−	6.15679i	−0.389085	−	0.432122i
$204$	20.8787	−	12.2302i	1.46180	−	0.856282i
$205$	12.1860	+	1.33848i	0.851105	+	0.0934833i
$206$	−0.807522	−	2.48530i	−0.0562627	−	0.173159i
$207$	−3.97564	+	2.96565i	−0.276326	+	0.206127i
$208$	−7.30622	−	22.4862i	−0.506596	−	1.55914i
$209$	−0.644645	+	6.13339i	−0.0445910	+	0.424255i
$210$	2.35508	−	1.71688i	0.162516	−	0.118476i
$211$	−1.59702	−	15.1947i	−0.109944	−	1.04604i	−0.900857	−	0.434116i	$-0.857061\pi$
$211$	−1.59702	−	15.1947i	−0.109944	−	1.04604i	0.790913	−	0.611928i	$-0.209606\pi$
$212$	−1.16046	+	0.516671i	−0.0797008	+	0.0354851i
$213$	−0.168863	+	0.153980i	−0.0115703	+	0.0105506i
$214$	−3.00028	−	1.33581i	−0.205095	−	0.0913141i
$215$	0.124930	−	26.6983i	0.00852018	−	1.82081i
$216$	4.60986	−	1.59467i	0.313661	−	0.108504i
$217$	−1.69542	−	5.21797i	−0.115093	−	0.354219i
$218$	1.72010	+	2.97931i	0.116500	+	0.201784i
$219$	3.31491	−	0.369520i	0.224001	−	0.0249699i
$220$	−3.58947	+	16.5069i	−0.242002	+	1.11290i
$221$	31.0469	+	34.4811i	2.08844	+	2.31945i
$222$	−0.00312517	−	0.496515i	−0.000209748	−	0.0333239i
$223$	−2.18024	−	0.970703i	−0.145999	−	0.0650031i	0.332436	−	0.943126i	$-0.392129\pi$
$223$	−2.18024	−	0.970703i	−0.145999	−	0.0650031i	−0.478436	+	0.878123i	$0.658796\pi$
$224$	−8.69136			−0.580716
$225$	−7.45801	+	13.0145i	−0.497200	+	0.867636i
$226$	−0.928479			−0.0617615
$227$	3.82540	+	1.70318i	0.253901	+	0.113044i	0.529741	−	0.848160i	$-0.322289\pi$
$227$	3.82540	+	1.70318i	0.253901	+	0.113044i	−0.275840	+	0.961204i	$0.588956\pi$
$228$	4.60750	−	2.69895i	0.305139	−	0.178742i
$229$	−10.9507	−	12.1620i	−0.723646	−	0.803690i	0.263305	−	0.964713i	$-0.415187\pi$
$229$	−10.9507	−	12.1620i	−0.723646	−	0.803690i	−0.986951	+	0.161023i	$0.948521\pi$
$230$	0.656780	−	0.585826i	0.0433068	−	0.0386282i
$231$	8.53444	−	19.4980i	0.561525	−	1.28288i
$232$	1.23020	+	2.13077i	0.0807666	+	0.139892i
$233$	0.488148	+	1.50237i	0.0319797	+	0.0984233i	0.965772	−	0.259391i	$-0.0835220\pi$
$233$	0.488148	+	1.50237i	0.0319797	+	0.0984233i	−0.933793	+	0.357815i	$0.883522\pi$
$234$	2.35486	+	3.96268i	0.153942	+	0.259049i
$235$	13.0649	+	4.31275i	0.852262	+	0.281333i
$236$	−0.443724	−	0.197559i	−0.0288840	−	0.0128600i
$237$	4.72159	+	1.50135i	0.306700	+	0.0975231i
$238$	4.94194	−	2.20029i	0.320338	−	0.142624i
$239$	0.353687	+	3.36511i	0.0228781	+	0.217671i	0.999988	+	0.00493466i	$0.00157076\pi$
$239$	0.353687	+	3.36511i	0.0228781	+	0.217671i	−0.977110	+	0.212736i	$0.931763\pi$
$240$	12.9515	−	5.79146i	0.836017	−	0.373837i
$241$	1.90906	−	18.1635i	0.122974	−	1.17002i	−0.742777	−	0.669539i	$-0.766492\pi$
$241$	1.90906	−	18.1635i	0.122974	−	1.17002i	0.865750	−	0.500476i	$-0.166842\pi$
$242$	−0.302535	−	0.931106i	−0.0194477	−	0.0598538i
$243$	13.2481	−	8.21515i	0.849864	−	0.527002i
$244$	0.183700	+	0.565371i	0.0117602	+	0.0361942i
$245$	−5.80948	+	3.31795i	−0.371154	+	0.211976i
$246$	1.96483	+	1.11796i	0.125273	+	0.0712787i
$247$	6.85144	+	7.60929i	0.435947	+	0.484168i
$248$	0.170316	+	1.62044i	0.0108151	+	0.102898i
$249$	−0.226176	+	0.0750660i	−0.0143333	+	0.00475712i
$250$	1.11659	−	2.41605i	0.0706195	−	0.152804i
$251$	−25.5610			−1.61339			−0.806697	−	0.590965i	$-0.798747\pi$
$251$	−25.5610			−1.61339			−0.806697	+	0.590965i	$0.798747\pi$
$252$	−17.9762	+	4.05813i	−1.13240	+	0.255638i
$253$	1.98611	−	6.11263i	0.124866	−	0.384297i
$254$	3.93499	−	0.836407i	0.246903	−	0.0524808i
$255$	−18.5965	+	20.7207i	−1.16456	+	1.29758i
$256$	−11.4016	−	2.42349i	−0.712602	−	0.151468i
$257$	6.52191	−	11.2963i	0.406825	−	0.704642i	−0.587707	−	0.809074i	$-0.699969\pi$
$257$	6.52191	−	11.2963i	0.406825	−	0.704642i	0.994532	+	0.104432i	$0.0333024\pi$
$258$	1.97411	−	4.51011i	0.122903	−	0.280787i
$259$	−0.397881	+	3.78559i	−0.0247231	+	0.235225i
$260$	16.3792	+	22.7673i	1.01579	+	1.41197i
$261$	5.33438	+	5.77651i	0.330190	+	0.357557i
$262$	3.14142	+	2.28238i	0.194078	+	0.141006i
$263$	−2.58003	+	24.5473i	−0.159091	+	1.51365i	0.565657	+	0.824641i	$0.308623\pi$
$263$	−2.58003	+	24.5473i	−0.159091	+	1.51365i	−0.724749	+	0.689013i	$0.758044\pi$
$264$	−3.68307	+	5.13699i	−0.226677	+	0.316160i
$265$	1.09077	−	0.972933i	0.0670056	−	0.0597668i
$266$	1.09059	−	0.485560i	0.0668681	−	0.0297716i
$267$	−23.6686	+	2.63839i	−1.44850	+	0.161467i
$268$	3.62490	+	6.27851i	0.221426	+	0.383521i
$269$	−0.768419	−	2.36495i	−0.0468513	−	0.144193i	0.924894	−	0.380225i	$-0.124153\pi$
$269$	−0.768419	−	2.36495i	−0.0468513	−	0.144193i	−0.971746	+	0.236031i	$0.924153\pi$
$270$	−2.21443	+	1.65744i	−0.134766	+	0.100868i
$271$	6.79309	−	20.9070i	0.412651	−	1.27001i	−0.501685	−	0.865050i	$-0.667286\pi$
$271$	6.79309	−	20.9070i	0.412651	−	1.27001i	0.914336	−	0.404958i	$-0.132714\pi$
$272$	25.7583	−	5.47510i	1.56183	−	0.331976i
$273$	−14.5761	−	32.1915i	−0.882183	−	1.94832i
$274$	−0.677494	+	1.17345i	−0.0409289	+	0.0708910i
$275$	−1.85076	−	19.3491i	−0.111605	−	1.16679i
$276$	−5.28164	+	1.75294i	−0.317917	+	0.105514i
$277$	−7.12911	−	3.17409i	−0.428347	−	0.190712i	0.181228	−	0.983441i	$-0.441993\pi$
$277$	−7.12911	−	3.17409i	−0.428347	−	0.190712i	−0.609574	+	0.792729i	$0.708660\pi$
$278$	0.531928	−	1.63711i	0.0319029	−	0.0981871i
$279$	1.67128	+	4.93155i	0.100057	+	0.295244i
$280$	6.32006	−	2.02087i	0.377696	−	0.120770i
$281$	8.97416	−	9.96681i	0.535354	−	0.594570i	−0.413415	−	0.910543i	$-0.635664\pi$
$281$	8.97416	−	9.96681i	0.535354	−	0.594570i	0.948768	+	0.315972i	$0.102331\pi$
$282$	1.89604	+	1.68572i	0.112908	+	0.100383i
$283$	−0.532717	−	0.113232i	−0.0316667	−	0.00673097i	0.192051	−	0.981385i	$-0.438486\pi$
$283$	−0.532717	−	0.113232i	−0.0316667	−	0.00673097i	−0.223718	+	0.974654i	$0.571819\pi$
$284$	−0.234236	+	0.104288i	−0.0138993	+	0.00618838i
$285$	−4.10388	+	4.57264i	−0.243093	+	0.270860i
$286$	−5.45680	−	2.42952i	−0.322667	−	0.143661i
$287$	−14.0204	−	10.1865i	−0.827601	−	0.601287i
$288$	8.24801	−	0.103834i	0.486019	−	0.00611845i
$289$	−28.0555	+	20.3835i	−1.65032	+	1.19903i
$290$	−1.03244	−	0.938394i	−0.0606267	−	0.0551044i
$291$	12.2717	+	3.90210i	0.719381	+	0.228745i
$292$	3.66052	+	0.778068i	0.214216	+	0.0455330i
$293$	10.5504	−	18.2739i	0.616363	−	1.06757i	−0.373781	−	0.927517i	$-0.621939\pi$
$293$	10.5504	−	18.2739i	0.616363	−	1.06757i	0.990144	−	0.140055i	$-0.0447278\pi$
$294$	−1.22608	+	0.136674i	−0.0715067	+	0.00797101i
$295$	0.555543	+	0.0610195i	0.0323450	+	0.00355269i
$296$	0.349322	−	1.07510i	0.0203039	−	0.0624890i
$297$	−7.86616	+	18.6054i	−0.456441	+	1.07959i
$298$	2.86336	−	2.08035i	0.165870	−	0.120512i
$299$	−5.33551	−	9.24138i	−0.308561	−	0.534443i
$300$	−12.5414	+	11.2229i	−0.724076	+	0.647954i
$301$	−18.8711	+	32.6858i	−1.08771	+	1.88398i
$302$	0.323704	+	3.07984i	0.0186271	+	0.177225i
$303$	0.0900849	+	14.3124i	0.00517524	+	0.822223i
$304$	5.68434	−	1.20824i	0.326019	−	0.0692975i
$305$	−0.399461	−	0.555256i	−0.0228731	−	0.0317939i
$306$	−4.66356	+	2.14710i	−0.266598	+	0.122741i
$307$	0.469136			0.0267750			0.0133875	−	0.999910i	$-0.495738\pi$
$307$	0.469136			0.0267750			0.0133875	+	0.999910i	$0.495738\pi$
$308$	15.9790	−	17.7465i	0.910489	−	1.01120i
$309$	−4.06996	−	18.5721i	−0.231532	−	1.05653i
$310$	−0.371845	−	0.845807i	−0.0211194	−	0.0480386i
$311$	−2.63914	−	25.1098i	−0.149652	−	1.42384i	−0.769262	−	0.638934i	$-0.779376\pi$
$311$	−2.63914	−	25.1098i	−0.149652	−	1.42384i	0.619610	−	0.784910i	$-0.287291\pi$
$312$	2.24650	+	10.2513i	0.127183	+	0.580364i
$313$	−0.357603	+	3.40236i	−0.0202129	+	0.192313i	−0.999969	−	0.00788231i	$-0.997491\pi$
$313$	−0.357603	+	3.40236i	−0.0202129	+	0.192313i	0.979756	+	0.200195i	$0.0641576\pi$
$314$	−3.54341	+	2.57444i	−0.199966	+	0.145284i
$315$	18.2794	−	10.7472i	1.02992	−	0.605538i
$316$	4.49724	+	3.26744i	0.252990	+	0.183808i
$317$	−18.2621	+	20.2821i	−1.02570	+	1.13916i	−0.0355182	+	0.999369i	$0.511308\pi$
$317$	−18.2621	+	20.2821i	−1.02570	+	1.13916i	−0.990182	+	0.139786i	$0.955358\pi$
$318$	0.255806	−	0.0849001i	0.0143449	−	0.00476096i
$319$	−9.96618	−	2.11838i	−0.557999	−	0.118606i
$320$	14.8440	−	1.48997i	0.829804	−	0.0832920i
$321$	−20.7684	−	11.8170i	−1.15918	−	0.659559i
$322$	−1.21694	+	0.258669i	−0.0678175	+	0.0144151i
$323$	−9.22636	+	6.70335i	−0.513369	+	0.372984i
$324$	17.0108	−	4.06588i	0.945044	−	0.225882i
$325$	−25.9298	−	19.2124i	−1.43832	−	1.06571i
$326$	−0.842739	−	1.45967i	−0.0466750	−	0.0808435i
$327$	10.3243	+	22.8014i	0.570934	+	1.26092i
$328$	3.44381	+	3.82474i	0.190153	+	0.211186i
$329$	−13.0142	−	14.4537i	−0.717496	−	0.796860i
$330$	1.10209	−	3.41063i	0.0606683	−	0.187749i
$331$	−8.77034	+	9.74045i	−0.482061	+	0.535383i	−0.934288	−	0.356520i	$-0.883963\pi$
$331$	−8.77034	+	9.74045i	−0.482061	+	0.535383i	0.452226	+	0.891903i	$0.350630\pi$
$332$	−0.267376			−0.0146742
$333$	0.332360	−	3.59724i	0.0182132	−	0.197127i
$334$	−0.694506	−	0.504588i	−0.0380017	−	0.0276098i
$335$	−6.17305	−	5.61077i	−0.337270	−	0.306549i
$336$	−19.9589	−	1.97084i	−1.08885	−	0.107518i
$337$	−6.32944	+	2.81805i	−0.344786	+	0.153509i	−0.571822	−	0.820378i	$-0.693763\pi$
$337$	−6.32944	+	2.81805i	−0.344786	+	0.153509i	0.227036	+	0.973886i	$0.427097\pi$
$338$	−6.23266	+	2.77496i	−0.339012	+	0.150938i
$339$	−6.72263	−	0.663824i	−0.365123	−	0.0360539i
$340$	−27.1259	+	15.4923i	−1.47111	+	0.840190i
$341$	−5.45879	−	3.96604i	−0.295610	−	0.214773i
$342$	−1.02915	+	0.473821i	−0.0556503	+	0.0256213i
$343$	−12.6695			−0.684087
$344$	7.50003	−	8.32963i	0.404375	−	0.449104i
$345$	5.17424	−	3.77208i	0.278571	−	0.203082i
$346$	−3.01996	−	3.35400i	−0.162354	−	0.180312i
$347$	−3.53309	−	3.92390i	−0.189666	−	0.210646i	0.640810	−	0.767699i	$-0.278599\pi$
$347$	−3.53309	−	3.92390i	−0.189666	−	0.210646i	−0.830477	+	0.557053i	$0.811932\pi$
$348$	3.63885	+	8.03647i	0.195063	+	0.430800i
$349$	7.40744	+	12.8301i	0.396511	+	0.686777i	0.993293	−	0.115626i	$-0.0368875\pi$
$349$	7.40744	+	12.8301i	0.396511	+	0.686777i	−0.596782	+	0.802404i	$0.703554\pi$
$350$	−3.06453	+	2.18299i	−0.163806	+	0.116686i
$351$	14.2171	+	30.3753i	0.758854	+	1.62131i
$352$	−8.64745	+	6.28274i	−0.460911	+	0.334871i
$353$	16.0891	−	3.41985i	0.856338	−	0.182020i	0.241235	−	0.970467i	$-0.422448\pi$
$353$	16.0891	−	3.41985i	0.856338	−	0.182020i	0.615103	+	0.788446i	$0.289114\pi$
$354$	0.0895739	+	0.0509665i	0.00476080	+	0.00270884i
$355$	0.220169	−	0.196384i	0.0116854	−	0.0104230i
$356$	−26.1363	−	5.55544i	−1.38522	−	0.294438i
$357$	37.3551	−	12.3979i	1.97704	−	0.656165i
$358$	0.888485	−	0.986763i	0.0469579	−	0.0521520i
$359$	−4.52740	−	3.28935i	−0.238947	−	0.173605i	0.461867	−	0.886949i	$-0.347180\pi$
$359$	−4.52740	−	3.28935i	−0.238947	−	0.173605i	−0.700814	+	0.713344i	$0.747180\pi$
$360$	−5.97353	+	1.99329i	−0.314833	+	0.105055i
$361$	13.3352	−	9.68863i	0.701855	−	0.509928i
$362$	0.420681	−	4.00252i	0.0221105	−	0.210368i
$363$	−1.52479	−	6.95794i	−0.0800308	−	0.365197i
$364$	−4.14437	−	39.4310i	−0.217224	−	2.06675i
$365$	−4.28451	+	0.430060i	−0.224261	+	0.0225104i
$366$	−0.0270005	−	0.123209i	−0.00141134	−	0.00644025i
$367$	−1.21156	+	1.34557i	−0.0632427	+	0.0702382i	−0.773936	−	0.633264i	$-0.781715\pi$
$367$	−1.21156	+	1.34557i	−0.0632427	+	0.0702382i	0.710693	+	0.703502i	$0.248381\pi$
$368$	−6.05635			−0.315709
$369$	13.4270	+	9.49934i	0.698980	+	0.494516i
$370$	−0.00299948	+	0.641004i	−0.000155935	+	0.0333242i
$371$	−2.02108	+	0.429594i	−0.104929	+	0.0223034i
$372$	0.0367713	+	5.84209i	0.00190650	+	0.302898i
$373$	−0.685263	−	6.51984i	−0.0354816	−	0.337585i	−0.997834	−	0.0657804i	$-0.979046\pi$
$373$	−0.685263	−	6.51984i	−0.0354816	−	0.337585i	0.962353	−	0.271804i	$-0.0876203\pi$
$374$	3.32644	−	5.76157i	0.172006	−	0.297924i
$375$	9.81203	−	16.6950i	0.506691	−	0.862128i
$376$	2.88803	+	5.00221i	0.148939	+	0.257969i
$377$	−13.6857	+	9.94323i	−0.704849	+	0.512103i
$378$	3.88032	−	0.482074i	0.199582	−	0.0247952i
$379$	−5.74831	+	17.6915i	−0.295271	+	0.908750i	0.687860	+	0.725844i	$0.258550\pi$
$379$	−5.74831	+	17.6915i	−0.295271	+	0.908750i	−0.983130	+	0.182906i	$0.941450\pi$
$380$	−5.98613	+	3.41885i	−0.307082	+	0.175383i
$381$	29.0891	−	3.24263i	1.49028	−	0.166125i
$382$	−0.446656	+	0.773631i	−0.0228529	+	0.0395824i
$383$	16.1666	+	3.43632i	0.826075	+	0.175588i	0.601504	−	0.798870i	$-0.294568\pi$
$383$	16.1666	+	3.43632i	0.826075	+	0.175588i	0.224571	+	0.974458i	$0.427902\pi$
$384$	11.6986	+	3.71985i	0.596990	+	0.189828i
$385$	−11.2935	+	25.0494i	−0.575569	+	1.27664i
$386$	3.22486	−	2.34300i	0.164141	−	0.119256i
$387$	17.5180	−	31.2439i	0.890491	−	1.58822i
$388$	11.6886	+	8.49229i	0.593400	+	0.431131i
$389$	−3.63182	−	1.61699i	−0.184141	−	0.0819847i	0.312595	−	0.949886i	$-0.398802\pi$
$389$	−3.63182	−	1.61699i	−0.184141	−	0.0819847i	−0.496736	+	0.867902i	$0.665468\pi$
$390$	−2.98379	−	5.14885i	−0.151090	−	0.260722i
$391$	10.8577	−	4.83417i	0.549098	−	0.244474i
$392$	−2.74732	−	0.583960i	−0.138760	−	0.0294944i
$393$	21.1136	+	18.7715i	1.06504	+	0.946896i
$394$	1.80820	−	2.00821i	0.0910960	−	0.101172i
$395$	−6.07391	−	2.00500i	−0.305612	−	0.100883i
$396$	−14.9519	+	17.0322i	−0.751362	+	0.855898i
$397$	5.77168	−	17.7634i	0.289672	−	0.891520i	−0.695287	−	0.718732i	$-0.744723\pi$
$397$	5.77168	−	17.7634i	0.289672	−	0.891520i	0.984959	−	0.172787i	$-0.0552773\pi$
$398$	−1.14242	−	0.508637i	−0.0572642	−	0.0254957i
$399$	8.24351	−	2.73596i	0.412692	−	0.136969i
$400$	−16.8014	+	7.29282i	−0.840069	+	0.364641i
$401$	7.28121	−	12.6114i	0.363606	−	0.629785i	−0.624945	−	0.780669i	$-0.714879\pi$
$401$	7.28121	−	12.6114i	0.363606	−	0.629785i	0.988551	+	0.150884i	$0.0482120\pi$
$402$	−0.634496	−	1.40130i	−0.0316458	−	0.0698903i
$403$	−10.9579	+	2.32917i	−0.545852	+	0.116024i
$404$	−4.96235	+	15.2725i	−0.246886	+	0.759837i
$405$	−17.2185	+	10.4174i	−0.855596	+	0.517645i
$406$	0.609467	+	1.87575i	0.0302474	+	0.0930918i
$407$	2.34063	+	4.05408i	0.116021	+	0.200953i
$408$	−11.6167	+	1.29494i	−0.575114	+	0.0641092i
$409$	−5.24999	+	2.33744i	−0.259595	+	0.115579i	−0.532408	−	0.846488i	$-0.678713\pi$
$409$	−5.24999	+	2.33744i	−0.259595	+	0.115579i	0.272813	+	0.962067i	$0.412046\pi$
$410$	−2.52059	−	1.47103i	−0.124483	−	0.0726491i
$411$	−5.74435	+	8.01198i	−0.283348	+	0.395202i
$412$	2.22980	−	21.2151i	0.109854	−	1.04519i
$413$	−0.639175	−	0.464388i	−0.0314517	−	0.0228510i
$414$	1.15178	−	0.260013i	0.0566067	−	0.0127789i
$415$	0.293037	−	0.0936999i	0.0143846	−	0.00459955i
$416$	−1.85503	+	17.6494i	−0.0909501	+	0.865332i
$417$	5.02187	−	11.4731i	0.245922	−	0.561841i
$418$	0.734079	−	1.27146i	0.0359050	−	0.0621893i
$419$	14.5102	+	3.08423i	0.708868	+	0.150675i	0.548216	−	0.836337i	$-0.315307\pi$
$419$	14.5102	+	3.08423i	0.708868	+	0.150675i	0.160652	+	0.987011i	$0.448640\pi$
$420$	23.2633	−	4.98405i	1.13513	−	0.243197i
$421$	11.6112	−	2.46804i	0.565897	−	0.120285i	0.0839255	−	0.996472i	$-0.473254\pi$
$421$	11.6112	−	2.46804i	0.565897	−	0.120285i	0.481971	+	0.876187i	$0.339921\pi$
$422$	−1.12395	+	3.45915i	−0.0547129	+	0.168389i
$423$	12.5230	+	13.5610i	0.608890	+	0.659357i
$424$	0.613627			0.0298003
$425$	24.3001	−	26.4853i	1.17873	−	1.28472i
$426$	0.0516337	−	0.0171368i	0.00250166	−	0.000830283i
$427$	0.101074	+	0.961658i	0.00489133	+	0.0465379i
$428$	−17.9391	−	19.9234i	−0.867121	−	0.963035i
$429$	−37.7728	−	21.4923i	−1.82369	−	1.03766i
$430$	−2.61230	+	5.79421i	−0.125976	+	0.279422i
$431$	−0.657311	−	2.02300i	−0.0316616	−	0.0974443i	0.933977	−	0.357333i	$-0.116314\pi$
$431$	−0.657311	−	2.02300i	−0.0316616	−	0.0974443i	−0.965638	+	0.259889i	$0.916314\pi$
$432$	18.9643	+	1.63186i	0.912422	+	0.0785129i
$433$	−4.80484	−	14.7878i	−0.230906	−	0.710655i	−0.997638	−	0.0686884i	$-0.978119\pi$
$433$	−4.80484	−	14.7878i	−0.230906	−	0.710655i	0.766732	−	0.641967i	$-0.221881\pi$
$434$	−0.136526	+	1.29896i	−0.00655348	+	0.0623522i
$435$	−6.80441	−	7.53256i	−0.326246	−	0.361159i
$436$	2.93548	+	27.9292i	0.140584	+	1.33757i
$437$	2.39608	−	1.06680i	0.114620	−	0.0510321i
$438$	−0.756703	−	0.240613i	−0.0361567	−	0.0114969i
$439$	18.0157	+	8.02110i	0.859842	+	0.382826i	0.788802	−	0.614647i	$-0.210702\pi$
$439$	18.0157	+	8.02110i	0.859842	+	0.382826i	0.0710398	+	0.997473i	$0.477368\pi$
$440$	4.82731	−	6.57925i	0.230133	−	0.313654i
$441$	−8.97514	+	0.112987i	−0.427388	+	0.00538035i
$442$	−3.41332	−	10.5051i	−0.162355	−	0.499678i
$443$	−18.9074	−	32.7486i	−0.898320	−	1.55594i	−0.829642	−	0.558296i	$-0.811455\pi$
$443$	−18.9074	−	32.7486i	−0.898320	−	1.55594i	−0.0686778	−	0.997639i	$-0.521878\pi$
$444$	1.62526	−	3.71311i	0.0771312	−	0.176216i
$445$	30.5916	−	3.07065i	1.45018	−	0.145563i
$446$	0.380164	+	0.422215i	0.0180013	+	0.0199925i
$447$	22.2194	−	13.0156i	1.05094	−	0.615614i
$448$	−19.2663	−	8.57790i	−0.910246	−	0.405268i
$449$	5.81005			0.274193			0.137096	−	0.990558i	$-0.456223\pi$
$449$	5.81005			0.274193			0.137096	+	0.990558i	$0.456223\pi$
$450$	2.88213	−	2.10824i	0.135865	−	0.0993835i
$451$	−21.3131			−1.00360
$452$	−6.92407	−	3.08279i	−0.325681	−	0.145002i
$453$	0.141814	+	22.5309i	0.00666302	+	1.05859i
$454$	−0.667029	−	0.740810i	−0.0313052	−	0.0347680i
$455$	18.3604	+	41.7631i	0.860751	+	1.95788i
$456$	−2.56358	+	0.285768i	−0.120051	+	0.0133823i
$457$	6.14909	+	10.6505i	0.287642	+	0.498211i	0.973247	−	0.229763i	$-0.0737952\pi$
$457$	6.14909	+	10.6505i	0.287642	+	0.498211i	−0.685604	+	0.727974i	$0.740462\pi$
$458$	1.20393	+	3.70532i	0.0562561	+	0.173138i
$459$	−35.3015	+	12.2117i	−1.64773	+	0.569995i
$460$	6.84299	−	2.18807i	0.319056	−	0.102019i
$461$	10.4194	+	4.63904i	0.485282	+	0.216062i	0.634769	−	0.772702i	$-0.281095\pi$
$461$	10.4194	+	4.63904i	0.485282	+	0.216062i	−0.149487	+	0.988764i	$0.547762\pi$
$462$	−3.74401	+	3.41404i	−0.174187	+	0.158835i
$463$	−7.79120	+	3.46887i	−0.362088	+	0.161212i	−0.579713	−	0.814820i	$-0.696835\pi$
$463$	−7.79120	+	3.46887i	−0.362088	+	0.161212i	0.217626	+	0.976032i	$0.430169\pi$
$464$	1.00357	+	9.54835i	0.0465896	+	0.443271i
$465$	−2.08762	−	6.38989i	−0.0968109	−	0.296324i
$466$	0.0393089	−	0.373999i	0.00182095	−	0.0173252i
$467$	−4.57078	−	14.0674i	−0.211510	−	0.650962i	−0.999383	−	0.0351238i	$-0.988817\pi$
$467$	−4.57078	−	14.0674i	−0.211510	−	0.650962i	0.787873	−	0.615838i	$-0.211183\pi$
$468$	4.40404	+	37.3702i	0.203577	+	1.72744i
$469$	3.64408	+	11.2153i	0.168268	+	0.517875i
$470$	−2.42375	−	2.20298i	−0.111799	−	0.101616i
$471$	−27.4966	+	16.1068i	−1.26698	+	0.742161i
$472$	0.156999	+	0.174365i	0.00722647	+	0.00802581i
$473$	4.85183	+	46.1621i	0.223087	+	2.12253i
$474$	−0.881474	−	0.783693i	−0.0404874	−	0.0359962i
$475$	5.36254	−	5.84477i	0.246050	−	0.268176i
$476$	44.1597			2.02406
$477$	1.91286	−	0.431826i	0.0875836	−	0.0197720i
$478$	0.248916	−	0.766086i	0.0113852	−	0.0350400i
$479$	37.6768	−	8.00845i	1.72150	−	0.365915i	0.761987	−	0.647592i	$-0.224224\pi$
$479$	37.6768	−	8.00845i	1.72150	−	0.365915i	0.959509	+	0.281676i	$0.0908904\pi$
$480$	−10.6490	+	0.0171962i	−0.486057	+	0.000784893i
$481$	7.60241	+	1.61594i	0.346640	+	0.0736806i
$482$	−2.17391	+	3.76533i	−0.0990191	+	0.171506i
$483$	−8.99616	+	1.00282i	−0.409340	+	0.0456300i
$484$	0.835385	−	7.94815i	0.0379720	−	0.361280i
$485$	−15.7865	−	5.21114i	−0.716828	−	0.236626i
$486$	−3.67663	+	0.503840i	−0.166775	+	0.0228547i
$487$	−17.5649	−	12.7617i	−0.795944	−	0.578287i	0.113778	−	0.993506i	$-0.463705\pi$
$487$	−17.5649	−	12.7617i	−0.795944	−	0.578287i	−0.909721	+	0.415219i	$0.863705\pi$
$488$	0.0300169	−	0.285591i	0.00135880	−	0.0129281i
$489$	−5.05823	−	11.1712i	−0.228741	−	0.505179i
$490$	1.58471	−	0.159066i	0.0715898	−	0.00718587i
$491$	−21.9371	+	9.76704i	−0.990009	+	0.440780i	−0.836857	−	0.547422i	$-0.815609\pi$
$491$	−21.9371	+	9.76704i	−0.990009	+	0.440780i	−0.153152	+	0.988203i	$0.548943\pi$
$492$	10.9406	+	14.8609i	0.493241	+	0.669980i
$493$	−9.42066	−	16.3171i	−0.424285	−	0.734883i
$494$	−0.753251	−	2.31827i	−0.0338904	−	0.104304i
$495$	10.4181	−	23.9066i	0.468260	−	1.07452i
$496$	−1.96476	+	6.04692i	−0.0882205	+	0.271515i
$497$	−0.407950	+	0.0867124i	−0.0182990	+	0.00388958i
$498$	0.0564569	+	0.00557482i	0.00252989	+	0.000249814i
$499$	−8.41774	+	14.5800i	−0.376830	+	0.652688i	−0.990599	−	0.136797i	$-0.956319\pi$
$499$	−8.41774	+	14.5800i	−0.376830	+	0.652688i	0.613769	+	0.789485i	$0.289653\pi$
$500$	16.3488	−	14.3102i	0.731142	−	0.639970i
$501$	−4.66779	−	4.15000i	−0.208541	−	0.185408i
$502$	5.55897	+	2.47501i	0.248109	+	0.110465i
$503$	0.184791	−	0.568727i	0.00823941	−	0.0253583i	−0.946852	−	0.321669i	$-0.895756\pi$
$503$	0.184791	−	0.568727i	0.00823941	−	0.0253583i	0.955092	+	0.296310i	$0.0957563\pi$
$504$	8.73025	+	1.74111i	0.388876	+	0.0775551i
$505$	0.0864618	−	18.4773i	0.00384750	−	0.822231i
$506$	−1.02381	+	1.13706i	−0.0455139	+	0.0505483i
$507$	−47.1114	+	15.6359i	−2.09229	+	0.694416i
$508$	32.1220	+	6.82774i	1.42518	+	0.302932i
$509$	11.2050	−	4.98877i	0.496651	−	0.221123i	−0.143096	−	0.989709i	$-0.545706\pi$
$509$	11.2050	−	4.98877i	0.496651	−	0.221123i	0.639747	+	0.768586i	$0.279039\pi$
$510$	6.05069	−	2.70566i	0.267929	−	0.119808i
$511$	5.56094	+	2.47589i	0.246001	+	0.109527i
$512$	13.7126	+	9.96279i	0.606017	+	0.440297i
$513$	−7.79033	+	2.69488i	−0.343951	+	0.118982i
$514$	−2.51217	+	1.82520i	−0.110807	+	0.0805060i
$515$	4.99088	+	24.0326i	0.219924	+	1.05900i
$516$	29.6965	−	27.0793i	1.30732	−	1.19210i
$517$	−23.3967	−	4.97311i	−1.02898	−	0.218717i
$518$	0.453081	−	0.784759i	0.0199072	−	0.0344803i
$519$	−19.4679	−	26.4437i	−0.854548	−	1.16075i
$520$	−2.75483	−	13.2654i	−0.120807	−	0.581724i
$521$	−8.73777	+	26.8921i	−0.382809	+	1.17816i	0.555249	+	0.831684i	$0.312623\pi$
$521$	−8.73777	+	26.8921i	−0.382809	+	1.17816i	−0.938058	+	0.346479i	$0.887377\pi$
$522$	−0.600788	−	1.77278i	−0.0262958	−	0.0775927i
$523$	23.4654	−	17.0486i	1.02607	−	0.745484i	0.0585521	−	0.998284i	$-0.481352\pi$
$523$	23.4654	−	17.0486i	1.02607	−	0.745484i	0.967518	+	0.252800i	$0.0813516\pi$
$524$	15.8489	+	27.4510i	0.692361	+	1.19920i
$525$	−23.7494	+	13.6148i	−1.03651	+	0.594200i
$526$	2.93797	−	5.08871i	0.128101	−	0.221878i
$527$	−1.30425	−	12.4091i	−0.0568139	−	0.540548i
$528$	−21.2827	+	12.4669i	−0.926212	+	0.542550i
$529$	19.8237	−	4.21366i	0.861900	−	0.183203i
$530$	−0.331427	+	0.105975i	−0.0143963	+	0.00460327i
$531$	0.612118	+	0.433063i	0.0265637	+	0.0187933i
$532$	9.74516			0.422506
$533$	−23.6779	+	26.2970i	−1.02560	+	1.13905i
$534$	5.40289	+	1.71799i	0.233806	+	0.0743445i
$535$	26.6428	+	15.5489i	1.15187	+	0.672239i
$536$	−0.366070	−	3.48292i	−0.0158118	−	0.150439i
$537$	7.13855	−	6.50940i	0.308051	−	0.280901i
$538$	−0.0618781	+	0.588731i	−0.00266775	+	0.0253820i
$539$	9.40980	−	6.83662i	0.405309	−	0.294474i
$540$	−22.0171	+	5.00773i	−0.947465	+	0.215498i
$541$	27.2419	+	19.7924i	1.17122	+	0.850941i	0.991154	−	0.132714i	$-0.0423690\pi$
$541$	27.2419	+	19.7924i	1.17122	+	0.850941i	0.180065	+	0.983655i	$0.442369\pi$
$542$	−3.50173	+	3.88906i	−0.150412	+	0.167050i
$543$	5.90756	−	28.6793i	0.253518	−	1.23075i
$544$	−19.3340	−	4.10957i	−0.828939	−	0.176196i
$545$	−13.0048	−	29.5810i	−0.557064	−	1.26711i
$546$	0.0529490	+	8.41234i	0.00226601	+	0.360015i
$547$	29.2637	−	6.22019i	1.25123	−	0.265956i	0.465788	−	0.884897i	$-0.345771\pi$
$547$	29.2637	−	6.22019i	1.25123	−	0.265956i	0.785438	+	0.618940i	$0.212438\pi$
$548$	−8.94854	+	6.50150i	−0.382263	+	0.277730i
$549$	−0.107407	−	0.911397i	−0.00458403	−	0.0388975i
$550$	−1.47103	+	4.38722i	−0.0627248	+	0.187072i
$551$	−2.07895	−	3.60085i	−0.0885662	−	0.153401i
$552$	2.67520	+	0.264162i	0.113864	+	0.0112435i
$553$	6.05032	+	6.71957i	0.257286	+	0.285745i
$554$	1.24309	+	1.38059i	0.0528139	+	0.0586558i
$555$	−0.480009	+	4.63903i	−0.0203752	+	0.196916i
$556$	9.40244	−	10.4425i	0.398752	−	0.442859i
$557$	11.2275			0.475724			0.237862	−	0.971299i	$-0.423553\pi$
$557$	11.2275			0.475724			0.237862	+	0.971299i	$0.423553\pi$
$558$	0.114044	−	1.23433i	0.00482786	−	0.0522535i
$559$	62.3467	+	45.2975i	2.63698	+	1.91588i
$560$	25.7374	+	2.82693i	1.08760	+	0.119460i
$561$	28.2043	−	39.3382i	1.19079	−	1.66086i
$562$	−2.91675	+	1.29862i	−0.123036	+	0.0547791i
$563$	−5.27419	+	2.34822i	−0.222281	+	0.0989658i	−0.514856	−	0.857277i	$-0.672155\pi$
$563$	−5.27419	+	2.34822i	−0.222281	+	0.0989658i	0.292575	+	0.956243i	$0.405488\pi$
$564$	8.54259	+	18.8665i	0.359708	+	0.794422i
$565$	8.66895	+	0.952176i	0.364705	+	0.0400584i
$566$	0.104891	+	0.0762074i	0.00440888	+	0.00320324i
$567$	28.4400	−	0.716172i	1.19437	−	0.0300764i
$568$	0.123859			0.00519700
$569$	16.5397	−	18.3692i	0.693380	−	0.770076i	−0.288928	−	0.957351i	$-0.593299\pi$
$569$	16.5397	−	18.3692i	0.693380	−	0.770076i	0.982308	+	0.187275i	$0.0599655\pi$
$570$	1.33527	−	0.597084i	0.0559281	−	0.0250091i
$571$	−16.5015	−	18.3268i	−0.690568	−	0.766954i	0.291277	−	0.956639i	$-0.405920\pi$
$571$	−16.5015	−	18.3268i	−0.690568	−	0.766954i	−0.981845	+	0.189685i	$0.939253\pi$
$572$	−32.6271	−	36.2360i	−1.36421	−	1.51510i
$573$	−3.78711	+	5.28211i	−0.158209	+	0.220663i
$574$	2.06282	+	3.57291i	0.0861004	+	0.149130i
$575$	−6.73294	+	4.79614i	−0.280783	+	0.200013i
$576$	18.3860	+	7.91017i	0.766083	+	0.329591i
$577$	16.1544	−	11.7369i	0.672518	−	0.488613i	−0.198349	−	0.980131i	$-0.563558\pi$
$577$	16.1544	−	11.7369i	0.672518	−	0.488613i	0.870867	+	0.491518i	$0.163558\pi$
$578$	8.07517	−	1.71643i	0.335883	−	0.0713941i
$579$	25.0247	−	14.6588i	1.03999	−	0.609198i
$580$	−4.58360	−	10.4260i	−0.190324	−	0.432915i
$581$	−0.425408	−	0.0904234i	−0.0176489	−	0.00375139i
$582$	−2.29101	−	2.03687i	−0.0949653	−	0.0844310i
$583$	−1.70033	+	1.88841i	−0.0704206	+	0.0782099i
$584$	−1.46251	−	1.06258i	−0.0605193	−	0.0439698i
$585$	−17.9228	−	39.4134i	−0.741017	−	1.62954i
$586$	−4.06392	+	2.95261i	−0.167879	+	0.121971i
$587$	−2.10300	+	20.0087i	−0.0868001	+	0.825848i	0.861347	+	0.508017i	$0.169621\pi$
$587$	−2.10300	+	20.0087i	−0.0868001	+	0.825848i	−0.948147	+	0.317831i	$0.897046\pi$
$588$	−9.59723	−	3.05168i	−0.395783	−	0.125849i
$589$	−0.287821	−	2.73844i	−0.0118595	−	0.112835i
$590$	−0.114910	−	0.0670625i	−0.00473079	−	0.00276092i
$591$	14.5280	−	13.2476i	0.597603	−	0.544934i
$592$	2.95163	−	3.27812i	0.121311	−	0.134730i
$593$	−26.2817			−1.07926			−0.539630	−	0.841902i	$-0.681436\pi$
$593$	−26.2817			−1.07926			−0.539630	+	0.841902i	$0.681436\pi$
$594$	3.51224	−	3.28462i	0.144109	−	0.134769i
$595$	−48.3979	+	15.4754i	−1.98412	+	0.634431i
$596$	28.2606	−	6.00698i	1.15760	−	0.246056i
$597$	−7.90798	−	4.49955i	−0.323652	−	0.184154i
$598$	0.265539	+	2.52643i	0.0108587	+	0.103313i
$599$	10.6072	−	18.3722i	0.433397	−	0.750666i	−0.563766	−	0.825935i	$-0.690648\pi$
$599$	10.6072	−	18.3722i	0.433397	−	0.750666i	0.997163	+	0.0752684i	$0.0239814\pi$
$600$	7.73957	−	2.48854i	0.315967	−	0.101594i
$601$	−19.6890	−	34.1024i	−0.803132	−	1.39107i	−0.917545	−	0.397633i	$-0.869832\pi$
$601$	−19.6890	−	34.1024i	−0.803132	−	1.39107i	0.114412	−	0.993433i	$-0.463501\pi$
$602$	7.26896	−	5.28121i	0.296261	−	0.215246i
$603$	−3.59218	−	10.5997i	−0.146285	−	0.431653i
$604$	−7.81187	+	24.0425i	−0.317861	+	0.978274i
$605$	1.86981	+	9.00373i	0.0760186	+	0.366054i
$606$	1.36624	−	3.12136i	0.0554998	−	0.126796i
$607$	20.2987	−	35.1584i	0.823898	−	1.42703i	−0.0788598	−	0.996886i	$-0.525128\pi$
$607$	20.2987	−	35.1584i	0.823898	−	1.42703i	0.902758	−	0.430148i	$-0.141539\pi$
$608$	−4.26663	−	0.906900i	−0.173035	−	0.0367796i
$609$	3.07175	+	14.0170i	0.124474	+	0.567999i
$610$	0.0331100	+	0.159435i	0.00134059	+	0.00645535i
$611$	−32.1286	+	23.3428i	−1.29978	+	0.944349i
$612$	−41.9071	+	0.527565i	−1.69400	+	0.0213256i
$613$	16.2372	+	11.7970i	0.655814	+	0.476477i	0.865247	−	0.501346i	$-0.167162\pi$
$613$	16.2372	+	11.7970i	0.655814	+	0.476477i	−0.209432	+	0.977823i	$0.567162\pi$
$614$	−0.102027	−	0.0454255i	−0.00411748	−	0.00183322i
$615$	−17.1985	−	12.4531i	−0.693511	−	0.502156i
$616$	−10.5384	+	4.69198i	−0.424603	+	0.189045i
$617$	4.71104	+	1.00136i	0.189659	+	0.0403134i	0.301762	−	0.953383i	$-0.402425\pi$
$617$	4.71104	+	1.00136i	0.189659	+	0.0403134i	−0.112103	+	0.993697i	$0.535759\pi$
$618$	−0.913163	+	4.43312i	−0.0367328	+	0.178326i
$619$	−13.9520	+	15.4953i	−0.560778	+	0.622807i	−0.955142	−	0.296147i	$-0.904298\pi$
$619$	−13.9520	+	15.4953i	−0.560778	+	0.622807i	0.394364	+	0.918954i	$0.370965\pi$
$620$	0.0352924	−	7.54217i	0.00141738	−	0.302901i
$621$	8.52529	−	1.05914i	0.342108	−	0.0425020i
$622$	−1.85737	+	5.71638i	−0.0744736	+	0.229206i
$623$	−39.7054	−	17.6780i	−1.59076	−	0.708253i
$624$	−8.26203	+	40.1095i	−0.330746	+	1.60567i
$625$	−12.9030	+	21.4129i	−0.516121	+	0.856516i
$626$	0.407214	−	0.705316i	0.0162756	−	0.0281901i
$627$	6.22412	−	8.68115i	0.248567	−	0.346692i
$628$	−34.9726	+	7.43365i	−1.39556	+	0.296635i
$629$	−2.67505	+	8.23294i	−0.106661	+	0.328269i
$630$	−5.01600	+	0.567347i	−0.199842	+	0.0226036i
$631$	5.06778	+	15.5970i	0.201745	+	0.620908i	0.999831	+	0.0183646i	$0.00584598\pi$
$631$	5.06778	+	15.5970i	0.201745	+	0.620908i	−0.798086	+	0.602543i	$0.794154\pi$
$632$	−1.34265	−	2.32554i	−0.0534077	−	0.0925048i
$633$	−10.6111	+	24.2423i	−0.421752	+	0.963546i
$634$	5.93548	−	2.64265i	0.235728	−	0.104953i
$635$	−37.5976	+	3.77388i	−1.49202	+	0.149762i
$636$	2.18955	+	0.216206i	0.0868212	+	0.00857313i
$637$	2.01856	−	19.2053i	0.0799783	−	0.760943i
$638$	1.96231	+	1.42571i	0.0776888	+	0.0564442i
$639$	0.386104	−	0.0871629i	0.0152741	−	0.00344811i
$640$	−15.0492	−	4.96775i	−0.594871	−	0.196367i
$641$	−3.43163	+	32.6498i	−0.135541	+	1.28959i	0.689405	+	0.724376i	$0.257872\pi$
$641$	−3.43163	+	32.6498i	−0.135541	+	1.28959i	−0.824946	+	0.565212i	$0.808794\pi$
$642$	3.37247	+	4.58090i	0.133101	+	0.180794i
$643$	−8.85367	+	15.3350i	−0.349155	+	0.604754i	−0.986100	−	0.166156i	$-0.946865\pi$
$643$	−8.85367	+	15.3350i	−0.349155	+	0.604754i	0.636945	+	0.770909i	$0.280198\pi$
$644$	−9.93411	−	2.11156i	−0.391459	−	0.0832071i
$645$	−23.0569	+	40.0851i	−0.907865	+	1.57835i
$646$	2.65561	−	0.564467i	0.104484	−	0.0222087i
$647$	−9.85870	+	30.3419i	−0.387585	+	1.19287i	0.547002	+	0.837131i	$0.315769\pi$
$647$	−9.85870	+	30.3419i	−0.387585	+	1.19287i	−0.934587	+	0.355734i	$0.884231\pi$
$648$	−8.30572	−	1.54800i	−0.326279	−	0.0608110i
$649$	−0.971639			−0.0381402
$650$	3.77888	+	6.68901i	0.148220	+	0.262364i
$651$	−1.91722	+	9.30749i	−0.0751417	+	0.364789i
$652$	−1.43819	−	13.6835i	−0.0563239	−	0.535887i
$653$	−17.4627	−	19.3943i	−0.683368	−	0.758957i	0.297269	−	0.954794i	$-0.403924\pi$
$653$	−17.4627	−	19.3943i	−0.683368	−	0.758957i	−0.980636	+	0.195837i	$0.937258\pi$
$654$	−0.0375040	−	5.95850i	−0.00146652	−	0.232996i
$655$	−26.9900	−	24.5315i	−1.05458	−	0.958526i
$656$	6.20611	+	19.1004i	0.242308	+	0.745747i
$657$	−5.30686	−	2.28316i	−0.207040	−	0.0890745i
$658$	1.43079	+	4.40352i	0.0557780	+	0.171667i
$659$	−3.27906	+	31.1982i	−0.127734	+	1.21531i	0.723426	+	0.690402i	$0.242566\pi$
$659$	−3.27906	+	31.1982i	−0.127734	+	1.21531i	−0.851160	+	0.524906i	$0.824100\pi$
$660$	19.5430	−	21.7753i	0.760709	−	0.847601i
$661$	−2.52351	−	24.0096i	−0.0981531	−	0.933864i	−0.927170	−	0.374641i	$-0.877766\pi$
$661$	−2.52351	−	24.0096i	−0.0981531	−	0.933864i	0.829017	−	0.559223i	$-0.188901\pi$
$662$	2.85051	−	1.26913i	0.110788	−	0.0493261i
$663$	−17.2033	−	78.5024i	−0.668122	−	3.04878i
$664$	0.117993	+	0.0525339i	0.00457902	+	0.00203871i
$665$	−10.6804	+	3.41512i	−0.414170	+	0.132433i
$666$	−0.420594	+	0.750142i	−0.0162977	+	0.0290674i
$667$	1.33903	+	4.12112i	0.0518476	+	0.159571i
$668$	−3.50387	−	6.06887i	−0.135569	−	0.234812i
$669$	2.45070	+	3.32884i	0.0947495	+	0.128700i
$670$	0.799230	+	1.81795i	0.0308769	+	0.0702334i
$671$	0.795720	+	0.883737i	0.0307184	+	0.0341163i
$672$	13.0842	+	7.44473i	0.504732	+	0.287187i
$673$	24.1911	+	10.7706i	0.932499	+	0.415175i	0.816024	−	0.578018i	$-0.196174\pi$
$673$	24.1911	+	10.7706i	0.932499	+	0.415175i	0.116475	+	0.993194i	$0.462840\pi$
$674$	1.64938			0.0635319
$675$	22.3753	−	13.2041i	0.861224	−	0.508225i
$676$	−55.6932			−2.14205
$677$	−9.54246	−	4.24858i	−0.366747	−	0.163286i	0.215085	−	0.976595i	$-0.430997\pi$
$677$	−9.54246	−	4.24858i	−0.366747	−	0.163286i	−0.581832	+	0.813309i	$0.697664\pi$
$678$	1.39775	+	0.795305i	0.0536803	+	0.0305435i
$679$	15.7252	+	17.4646i	0.603478	+	0.670230i
$680$	15.0146	−	1.50710i	0.575782	−	0.0577945i
$681$	−4.29995	−	5.84071i	−0.164775	−	0.223817i
$682$	0.803147	+	1.39109i	0.0307541	+	0.0532677i
$683$	8.03768	+	24.7374i	0.307553	+	0.946552i	0.978712	+	0.205238i	$0.0657969\pi$
$683$	8.03768	+	24.7374i	0.307553	+	0.946552i	−0.671159	+	0.741314i	$0.734203\pi$
$684$	−9.24806	+	0.116423i	−0.353608	+	0.00445155i
$685$	7.52897	−	10.2614i	0.287667	−	0.392069i
$686$	2.75534	+	1.22676i	0.105199	+	0.0468378i
$687$	6.06789	+	27.6890i	0.231504	+	1.05640i
$688$	39.9568	−	17.7899i	1.52334	−	0.678234i
$689$	0.441004	+	4.19587i	0.0168009	+	0.159850i
$690$	−1.49053	+	0.319338i	−0.0567435	+	0.0121570i
$691$	−0.421945	+	4.01454i	−0.0160515	+	0.152720i	−0.999612	−	0.0278597i	$-0.991131\pi$
$691$	−0.421945	+	4.01454i	−0.0160515	+	0.152720i	0.983560	+	0.180580i	$0.0577975\pi$
$692$	−11.3850	−	35.0393i	−0.432791	−	1.33199i
$693$	−29.5493	+	22.0424i	−1.12249	+	0.837323i
$694$	0.388430	+	1.19547i	0.0147446	+	0.0453793i
$695$	−6.64535	+	14.7397i	−0.252072	+	0.559108i
$696$	−0.0268225	−	4.26145i	−0.00101670	−	0.161530i
$697$	−26.3721	−	29.2892i	−0.998915	−	1.10941i
$698$	−0.368654	−	3.50751i	−0.0139538	−	0.132761i
$699$	0.552008	−	2.67982i	0.0208789	−	0.101360i
$700$	−30.1016	+	6.10443i	−1.13773	+	0.230726i
$701$	47.5351			1.79538			0.897688	−	0.440631i	$-0.145245\pi$
$701$	47.5351			1.79538			0.897688	+	0.440631i	$0.145245\pi$
$702$	−0.150748	−	7.98260i	−0.00568963	−	0.301284i
$703$	−0.590329	+	1.81685i	−0.0222647	+	0.0685236i
$704$	−25.3697	+	5.39249i	−0.956156	+	0.203237i
$705$	−15.9741	−	17.6835i	−0.601618	−	0.665999i
$706$	−3.83018	−	0.814131i	−0.144151	−	0.0306402i
$707$	−13.0603	+	22.6212i	−0.491184	+	0.850756i
$708$	0.498769	+	0.677488i	0.0187449	+	0.0254616i
$709$	3.30725	−	31.4664i	0.124206	−	1.18174i	−0.737862	−	0.674952i	$-0.764164\pi$
$709$	3.30725	−	31.4664i	0.124206	−	1.18174i	0.862068	−	0.506792i	$-0.169169\pi$
$710$	−0.0668976	+	0.0213908i	−0.00251062	+	0.000802782i
$711$	−5.82198	−	6.30452i	−0.218341	−	0.236438i
$712$	10.4424	+	7.58686i	0.391346	+	0.284330i
$713$	−0.299956	+	2.85389i	−0.0112335	+	0.106879i
$714$	−9.32439	−	0.920735i	−0.348957	−	0.0344576i
$715$	48.4571	+	28.2798i	1.81219	+	1.05761i
$716$	9.90213	−	4.40871i	0.370060	−	0.164761i
$717$	2.34999	−	5.36886i	0.0877621	−	0.200504i
$718$	0.666113	+	1.15374i	0.0248591	+	0.0430573i
$719$	−16.1827	−	49.8053i	−0.603514	−	1.85742i	−0.506702	−	0.862121i	$-0.669135\pi$
$719$	−16.1827	−	49.8053i	−0.603514	−	1.85742i	−0.0968119	−	0.995303i	$-0.530865\pi$
$720$	−24.4583	−	2.37525i	−0.911506	−	0.0885203i
$721$	10.7224	−	33.0002i	0.399324	−	1.22899i
$722$	−3.83826	+	0.815848i	−0.142845	+	0.0303627i
$723$	−18.4322	+	25.7085i	−0.685501	+	0.956110i
$724$	16.4266	−	28.4517i	0.610490	−	1.05740i
$725$	8.67721	+	9.82030i	0.322264	+	0.364717i
$726$	−0.342113	+	1.66085i	−0.0126970	+	0.0616398i
$727$	33.6167	+	14.9671i	1.24678	+	0.555100i	0.920710	−	0.390247i	$-0.127610\pi$
$727$	33.6167	+	14.9671i	1.24678	+	0.555100i	0.326065	+	0.945347i	$0.394277\pi$
$728$	−5.91848	+	18.2152i	−0.219353	+	0.675100i
$729$	−26.9807	+	1.01941i	−0.999287	+	0.0377558i
$730$	0.973432	+	0.321331i	0.0360283	+	0.0118930i
$731$	−57.4339	+	63.7869i	−2.12427	+	2.35924i
$732$	0.207732	−	1.00847i	0.00767800	−	0.0372742i
$733$	−21.2694	−	4.52096i	−0.785604	−	0.166985i	−0.202391	−	0.979305i	$-0.564871\pi$
$733$	−21.2694	−	4.52096i	−0.785604	−	0.166985i	−0.583213	+	0.812319i	$0.698205\pi$
$734$	0.393776	−	0.175321i	0.0145346	−	0.00647120i
$735$	11.5878	−	0.0187121i	0.427421	−	0.000690207i
$736$	4.15285	+	1.84897i	0.153076	+	0.0681538i
$737$	11.7329	+	8.52446i	0.432187	+	0.314002i
$738$	−2.00028	−	3.36601i	−0.0736313	−	0.123905i
$739$	29.1586	−	21.1850i	1.07262	−	0.779302i	0.0962360	−	0.995359i	$-0.469320\pi$
$739$	29.1586	−	21.1850i	1.07262	−	0.779302i	0.976381	+	0.216057i	$0.0693196\pi$
$740$	−2.15067	+	4.77029i	−0.0790602	+	0.175359i
$741$	−3.79643	−	17.3239i	−0.139465	−	0.636410i
$742$	0.481139	+	0.102269i	0.0176632	+	0.00375443i
$743$	21.5435	−	37.3144i	0.790353	−	1.36893i	−0.135395	−	0.990792i	$-0.543230\pi$
$743$	21.5435	−	37.3144i	0.790353	−	1.36893i	0.925748	−	0.378140i	$-0.123436\pi$
$744$	1.13162	−	2.58534i	0.0414873	−	0.0947831i
$745$	−28.8678	+	16.4872i	−1.05764	+	0.604045i
$746$	−0.482272	+	1.48428i	−0.0176572	+	0.0543434i
$747$	0.404789	+	0.0807286i	0.0148104	+	0.00295371i
$748$	43.9366	−	31.9218i	1.60648	−	1.16718i
$749$	−21.8042	−	37.7659i	−0.796707	−	1.37994i
$750$	−3.75045	+	2.68074i	−0.136947	+	0.0978867i
$751$	−6.79013	+	11.7609i	−0.247775	+	0.429160i	−0.962908	−	0.269829i	$-0.913033\pi$
$751$	−6.79013	+	11.7609i	−0.247775	+	0.429160i	0.715133	+	0.698989i	$0.246366\pi$
$752$	2.35599	+	22.4158i	0.0859142	+	0.817419i
$753$	38.4800	+	21.8947i	1.40229	+	0.797887i
$754$	3.93913	−	0.837288i	0.143455	−	0.0304922i
$755$	0.136111	−	29.0875i	0.00495357	−	1.05860i
$756$	30.5379	+	9.28866i	1.11065	+	0.337825i
$757$	−38.0734			−1.38380			−0.691901	−	0.721993i	$-0.743226\pi$
$757$	−38.0734			−1.38380			−0.691901	+	0.721993i	$0.743226\pi$
$758$	2.96316	−	3.29092i	0.107627	−	0.119532i
$759$	−8.22581	+	7.50084i	−0.298578	+	0.272263i
$760$	3.31341	−	0.332586i	0.120190	−	0.0120642i
$761$	4.27495	+	40.6734i	0.154967	+	1.47441i	0.745018	+	0.667044i	$0.232441\pi$
$761$	4.27495	+	40.6734i	0.154967	+	1.47441i	−0.590051	+	0.807366i	$0.700892\pi$
$762$	−6.64025	−	2.11143i	−0.240551	−	0.0764892i
$763$	−4.77483	+	45.4295i	−0.172860	+	1.64466i
$764$	−5.89956	+	4.28628i	−0.213439	+	0.155072i
$765$	45.7443	−	15.2642i	1.65389	−	0.551879i
$766$	−3.18316	−	2.31270i	−0.115012	−	0.0835614i
$767$	−1.07944	+	1.19885i	−0.0389765	+	0.0432878i
$768$	15.0884	+	13.4146i	0.544455	+	0.484059i
$769$	37.9648	+	8.06966i	1.36904	+	0.290999i	0.833038	−	0.553215i	$-0.186599\pi$
$769$	37.9648	+	8.06966i	1.36904	+	0.290999i	0.536006	+	0.844214i	$0.319933\pi$
$770$	4.88157	−	4.35420i	0.175920	−	0.156914i
$771$	−19.4942	+	11.4192i	−0.702068	+	0.411252i
$772$	31.8286	−	6.76537i	1.14554	−	0.243491i
$773$	38.3733	−	27.8798i	1.38019	−	1.00277i	0.383329	−	0.923612i	$-0.374778\pi$
$773$	38.3733	−	27.8798i	1.38019	−	1.00277i	0.996862	−	0.0791554i	$-0.0252223\pi$
$774$	−6.83508	+	5.09866i	−0.245682	+	0.183267i
$775$	2.60442	+	8.27840i	0.0935534	+	0.297369i
$776$	−3.48963	−	6.04422i	−0.125270	−	0.216975i
$777$	3.84159	−	5.35809i	0.137816	−	0.192220i
$778$	0.633274	+	0.703322i	0.0227040	+	0.0252153i
$779$	−5.81980	−	6.46354i	−0.208516	−	0.231580i
$780$	−5.15585	−	48.3042i	−0.184609	−	1.72957i
$781$	−0.343207	+	0.381170i	−0.0122809	+	0.0136393i
$782$	−2.82941			−0.101179
$783$	−3.08252	−	13.2653i	−0.110160	−	0.474064i
$784$	−8.86686	−	6.44215i	−0.316674	−	0.230077i
$785$	35.7240	−	20.4030i	1.27504	−	0.728213i
$786$	−2.77416	−	6.12678i	−0.0989509	−	0.218535i
$787$	9.06338	−	4.03528i	0.323075	−	0.143842i	−0.238790	−	0.971071i	$-0.576751\pi$
$787$	9.06338	−	4.03528i	0.323075	−	0.143842i	0.561865	+	0.827229i	$0.310084\pi$
$788$	20.1523	−	8.97240i	0.717898	−	0.319629i
$789$	24.9105	−	34.7441i	0.886837	−	1.23692i
$790$	1.12681	+	1.02417i	0.0400900	+	0.0364383i
$791$	−9.97397	−	7.24651i	−0.354634	−	0.257656i
$792$	9.94475	−	4.57854i	0.353371	−	0.162691i
$793$	1.97440			0.0701128
$794$	−2.97521	+	3.30431i	−0.105586	+	0.117265i
$795$	−2.47545	+	0.530354i	−0.0877953	+	0.0188097i
$796$	−6.83069	−	7.58625i	−0.242107	−	0.268887i
$797$	26.3912	+	29.3104i	0.934826	+	1.03823i	0.999188	+	0.0403024i	$0.0128321\pi$
$797$	26.3912	+	29.3104i	0.934826	+	1.03823i	−0.0643619	+	0.997927i	$0.520501\pi$
$798$	−2.05771	−	0.203188i	−0.0728420	−	0.00719276i
$799$	−22.1160	−	38.3060i	−0.782408	−	1.35517i
$800$	13.7472	+	0.128658i	0.486036	+	0.00454876i
$801$	37.8912	+	16.3019i	1.33882	+	0.575998i
$802$	−2.80465	+	2.03770i	−0.0990355	+	0.0719535i
$803$	7.32260	−	1.55647i	0.258409	−	0.0549265i
$804$	−0.0790349	−	12.5568i	−0.00278735	−	0.442843i
$805$	11.6275	−	1.16712i	0.409816	−	0.0411355i
$806$	2.60864	+	0.554484i	0.0918855	+	0.0195309i
$807$	−0.868944	+	4.21845i	−0.0305883	+	0.148496i
$808$	5.19062	−	5.76477i	0.182606	−	0.202804i
$809$	9.94398	+	7.22472i	0.349612	+	0.254008i	0.748706	−	0.662902i	$-0.230675\pi$
$809$	9.94398	+	7.22472i	0.349612	+	0.254008i	−0.399094	+	0.916910i	$0.630675\pi$
$810$	4.75336	−	0.598332i	0.167016	−	0.0210232i
$811$	−35.0096	+	25.4360i	−1.22935	+	0.893177i	−0.996842	−	0.0794163i	$-0.974694\pi$
$811$	−35.0096	+	25.4360i	−1.22935	+	0.893177i	−0.232512	+	0.972594i	$0.574694\pi$
$812$	−1.68291	+	16.0119i	−0.0590587	+	0.561906i
$813$	−28.1347	+	25.6551i	−0.986726	+	0.899762i
$814$	−0.116489	−	1.10831i	−0.00408292	−	0.0388464i
$815$	6.37149	+	14.4927i	0.223184	+	0.507659i
$816$	−43.4669	−	13.8214i	−1.52165	−	0.483845i
$817$	−12.6745	+	14.0765i	−0.443425	+	0.492474i
$818$	1.36809			0.0478342
$819$	−5.63110	+	60.9472i	−0.196766	+	2.12967i
$820$	−13.9129	−	19.3391i	−0.485860	−	0.675352i
$821$	3.24959	−	0.690722i	0.113412	−	0.0241064i	−0.150856	−	0.988556i	$-0.548203\pi$
$821$	3.24959	−	0.690722i	0.113412	−	0.0241064i	0.264268	+	0.964449i	$0.414870\pi$
$822$	2.02506	−	1.18622i	0.0706319	−	0.0413743i
$823$	1.44219	+	13.7215i	0.0502715	+	0.478301i	0.990475	+	0.137689i	$0.0439676\pi$
$823$	1.44219	+	13.7215i	0.0502715	+	0.478301i	−0.940204	+	0.340612i	$0.889366\pi$
$824$	−5.15234	+	8.92412i	−0.179490	+	0.310887i
$825$	−13.7876	+	30.7138i	−0.480023	+	1.06932i
$826$	0.0940413	+	0.162884i	0.00327212	+	0.00566747i
$827$	−11.8606	+	8.61719i	−0.412432	+	0.299649i	−0.774586	−	0.632469i	$-0.782042\pi$
$827$	−11.8606	+	8.61719i	−0.412432	+	0.299649i	0.362154	+	0.932118i	$0.382042\pi$
$828$	9.45259	+	1.88517i	0.328500	+	0.0655141i
$829$	7.55408	−	23.2491i	0.262364	−	0.807474i	−0.729925	−	0.683528i	$-0.760445\pi$
$829$	7.55408	−	23.2491i	0.262364	−	0.807474i	0.992289	−	0.123946i	$-0.0395551\pi$
$830$	−0.0728022	−	0.00799642i	−0.00252700	−	0.000277560i
$831$	8.01350	+	10.8849i	0.277985	+	0.377593i
$832$	−21.5311	+	37.2929i	−0.746455	+	1.29290i
$833$	21.0385	+	4.47186i	0.728939	+	0.154941i
$834$	−2.20307	+	2.00890i	−0.0762860	+	0.0695626i
$835$	5.96694	+	5.42343i	0.206494	+	0.187685i
$836$	9.69593	−	7.04451i	0.335341	−	0.243639i
$837$	1.70823	−	8.85562i	0.0590450	−	0.306095i
$838$	−2.85701	−	2.07574i	−0.0986939	−	0.0717053i
$839$	8.39033	+	3.73562i	0.289666	+	0.128968i	0.546426	−	0.837508i	$-0.315988\pi$
$839$	8.39033	+	3.73562i	0.289666	+	0.128968i	−0.256759	+	0.966475i	$0.582655\pi$
$840$	−11.2454	−	2.37130i	−0.388002	−	0.0818177i
$841$	−20.2174	+	9.00137i	−0.697152	+	0.310392i
$842$	−2.76417	−	0.587543i	−0.0952597	−	0.0202481i
$843$	−22.0471	+	7.31728i	−0.759344	+	0.252021i
$844$	−19.8671	+	22.0646i	−0.683852	+	0.759495i
$845$	61.0384	−	19.5173i	2.09978	−	0.671415i
$846$	−1.41041	−	4.16180i	−0.0484910	−	0.143086i
$847$	4.01711	−	12.3634i	0.138029	−	0.424811i
$848$	2.18747	+	0.973925i	0.0751181	+	0.0334447i
$849$	0.704972	+	0.626770i	0.0241946	+	0.0215107i
$850$	−7.84926	+	3.40706i	−0.269228	+	0.116861i
$851$	0.995445	−	1.72416i	0.0341234	−	0.0591035i
$852$	0.441954	+	0.0436406i	0.0151411	+	0.00149510i
$853$	17.3167	−	3.68078i	0.592913	−	0.126028i	0.0983238	−	0.995154i	$-0.468652\pi$
$853$	17.3167	−	3.68078i	0.592913	−	0.126028i	0.494589	+	0.869127i	$0.335319\pi$
$854$	0.0711337	−	0.218927i	0.00243415	−	0.00749153i
$855$	10.0948	−	3.36851i	0.345236	−	0.115201i
$856$	4.00200	+	12.3169i	0.136785	+	0.420982i
$857$	−22.6850	−	39.2915i	−0.774904	−	1.34217i	−0.934849	−	0.355047i	$-0.884465\pi$
$857$	−22.6850	−	39.2915i	−0.774904	−	1.34217i	0.159945	−	0.987126i	$-0.448868\pi$
$858$	6.13373	+	8.33157i	0.209402	+	0.284435i
$859$	−26.6886	+	11.8825i	−0.910602	+	0.405426i	−0.807923	−	0.589288i	$-0.799408\pi$
$859$	−26.6886	+	11.8825i	−0.910602	+	0.405426i	−0.102679	+	0.994714i	$0.532742\pi$
$860$	−38.7194	+	34.5364i	−1.32032	+	1.17768i
$861$	12.3813	+	27.3444i	0.421954	+	0.931893i
$862$	−0.0529310	+	0.503605i	−0.00180284	+	0.0171528i
$863$	−44.0416	−	31.9981i	−1.49919	−	1.08923i	−0.970702	−	0.240287i	$-0.922758\pi$
$863$	−44.0416	−	31.9981i	−1.49919	−	1.08923i	−0.528490	−	0.848939i	$-0.677242\pi$
$864$	−12.5057	−	6.90866i	−0.425452	−	0.235037i
$865$	24.7569	+	34.4124i	0.841759	+	1.17006i
$866$	−0.386917	+	3.68127i	−0.0131480	+	0.125095i
$867$	59.6952	−	6.65436i	2.02736	−	0.225994i
$868$	−5.33103	+	9.23362i	−0.180947	+	0.313409i
$869$	10.8772	+	2.31201i	0.368982	+	0.0784296i
$870$	0.750453	+	2.29703i	0.0254427	+	0.0778766i
$871$	23.5525	−	5.00624i	0.798046	−	0.169630i
$872$	4.19209	−	12.9019i	0.141962	−	0.436914i
$873$	−15.1317	−	16.3859i	−0.512130	−	0.554578i
$874$	−0.624393			−0.0211204
$875$	30.8513	−	17.2392i	1.04297	−	0.582791i
$876$	−4.84416	−	4.30680i	−0.163669	−	0.145513i
$877$	−2.85940	−	27.2054i	−0.0965550	−	0.918660i	−0.930372	−	0.366618i	$-0.880516\pi$
$877$	−2.85940	−	27.2054i	−0.0965550	−	0.918660i	0.833816	−	0.552042i	$-0.186151\pi$
$878$	−3.14137	−	3.48884i	−0.106016	−	0.117743i
$879$	−31.5356	+	18.4727i	−1.06367	+	0.623070i
$880$	27.6509	−	15.7922i	0.932110	−	0.532354i
$881$	−17.3071	−	53.2658i	−0.583091	−	1.79457i	−0.606803	−	0.794852i	$-0.707548\pi$
$881$	−17.3071	−	53.2658i	−0.583091	−	1.79457i	0.0237119	−	0.999719i	$-0.492452\pi$
$882$	1.96284	+	0.844471i	0.0660924	+	0.0284348i
$883$	−1.49760	−	4.60915i	−0.0503984	−	0.155110i	0.922690	−	0.385543i	$-0.125986\pi$
$883$	−1.49760	−	4.60915i	−0.0503984	−	0.155110i	−0.973088	+	0.230433i	$0.925986\pi$
$884$	9.42515	−	89.6744i	0.317002	−	3.01607i
$885$	−0.784059	−	0.567720i	−0.0263558	−	0.0190837i
$886$	0.940988	+	8.95290i	0.0316131	+	0.300779i
$887$	14.0804	−	6.26899i	0.472773	−	0.210492i	−0.156498	−	0.987678i	$-0.550020\pi$
$887$	14.0804	−	6.26899i	0.472773	−	0.210492i	0.629271	+	0.777186i	$0.283354\pi$
$888$	−1.44677	+	1.31926i	−0.0485505	+	0.0442716i
$889$	48.7986	+	21.7265i	1.63665	+	0.728684i
$890$	−6.95034	−	2.29432i	−0.232976	−	0.0769056i
$891$	27.7787	−	21.2711i	0.930620	−	0.712608i
$892$	1.43318	+	4.41088i	0.0479865	+	0.147687i
$893$	−4.88056	−	8.45337i	−0.163322	−	0.282881i
$894$	−6.09253	+	0.679147i	−0.203765	+	0.0227141i
$895$	−9.30748	+	8.30196i	−0.311115	+	0.277504i
$896$	14.9907	+	16.6489i	0.500805	+	0.556201i
$897$	0.116332	+	18.4824i	0.00388421	+	0.617109i
$898$	−1.26356	−	0.562574i	−0.0421656	−	0.0187733i
$899$	4.54911			0.151721
$900$	28.4932	−	6.15266i	0.949773	−	0.205089i
$901$	−4.69905			−0.156548
$902$	4.63516	+	2.06370i	0.154334	+	0.0687138i
$903$	56.4065	−	33.0414i	1.87709	−	1.09955i
$904$	2.44989	+	2.72087i	0.0814820	+	0.0904949i
$905$	−8.03245	+	36.9389i	−0.267008	+	1.22789i
$906$	2.15078	−	4.91373i	0.0714548	−	0.163248i
$907$	9.54540	+	16.5331i	0.316950	+	0.548973i	0.979850	−	0.199735i	$-0.0640080\pi$
$907$	9.54540	+	16.5331i	0.316950	+	0.548973i	−0.662900	+	0.748708i	$0.730675\pi$
$908$	−2.51464	−	7.73925i	−0.0834511	−	0.256836i
$909$	12.1239	−	21.6233i	0.402124	−	0.717199i
$910$	0.0508194	−	10.8604i	0.00168465	−	0.360018i
$911$	45.2104	+	20.1290i	1.49789	+	0.666903i	0.981849	−	0.189662i	$-0.0607393\pi$
$911$	45.2104	+	20.1290i	1.49789	+	0.666903i	0.516039	+	0.856565i	$0.327406\pi$
$912$	−9.59227	−	3.05010i	−0.317632	−	0.100999i
$913$	−0.488624	+	0.217549i	−0.0161711	+	0.00719984i
$914$	−0.306029	−	2.91167i	−0.0101225	−	0.0963095i
$915$	0.125743	+	1.17806i	0.00415692	+	0.0389454i
$916$	−3.32440	+	31.6296i	−0.109841	+	1.04507i
$917$	15.9327	+	49.0358i	0.526144	+	1.61931i
$918$	8.85976	+	0.762372i	0.292416	+	0.0251620i
$919$	5.17126	+	15.9155i	0.170584	+	0.525004i	0.999404	−	0.0345111i	$-0.0109874\pi$
$919$	5.17126	+	15.9155i	0.170584	+	0.525004i	−0.828820	+	0.559515i	$0.810987\pi$
$920$	−3.44972	−	0.378909i	−0.113734	−	0.0124923i
$921$	−0.706248	−	0.401847i	−0.0232717	−	0.0132413i
$922$	−1.81682	−	2.01778i	−0.0598338	−	0.0664522i
$923$	0.0890153	+	0.846924i	0.00292997	+	0.0278768i
$924$	−39.2562	+	13.0289i	−1.29143	+	0.428618i
$925$	0.685369	−	5.98180i	0.0225348	−	0.196680i
$926$	2.03030			0.0667199
$927$	−9.78122	+	31.4450i	−0.321258	+	1.03279i
$928$	2.22690	−	6.85370i	0.0731016	−	0.224984i
$929$	2.10950	−	0.448388i	0.0692105	−	0.0147111i	−0.173176	−	0.984891i	$-0.555403\pi$
$929$	2.10950	−	0.448388i	0.0692105	−	0.0147111i	0.242387	+	0.970180i	$0.422070\pi$
$930$	−0.164707	+	1.59181i	−0.00540096	+	0.0521974i
$931$	4.64277	+	0.986850i	0.152160	+	0.0323427i
$932$	1.53492	−	2.65856i	0.0502779	−	0.0870839i
$933$	−17.5352	+	40.0614i	−0.574076	+	1.31155i
$934$	−0.368069	+	3.50194i	−0.0120436	+	0.114587i
$935$	−36.9667	+	50.3828i	−1.20894	+	1.64769i
$936$	5.39896	−	17.3568i	0.176471	−	0.567323i
$937$	−20.6023	−	14.9684i	−0.673048	−	0.488998i	0.197996	−	0.980203i	$-0.436557\pi$
$937$	−20.6023	−	14.9684i	−0.673048	−	0.488998i	−0.871044	+	0.491205i	$0.836557\pi$
$938$	0.293445	−	2.79194i	0.00958131	−	0.0911601i
$939$	3.45269	−	4.81568i	0.112674	−	0.157154i
$940$	−10.7605	−	24.4761i	−0.350969	−	0.798321i
$941$	−23.7260	+	10.5635i	−0.773447	+	0.344361i	−0.755219	−	0.655473i	$-0.772469\pi$
$941$	−23.7260	+	10.5635i	−0.773447	+	0.344361i	−0.0182285	+	0.999834i	$0.505803\pi$
$942$	7.53951	−	0.840446i	0.245651	−	0.0273832i
$943$	4.53213	+	7.84988i	0.147586	+	0.255627i
$944$	0.282929	+	0.870765i	0.00920854	+	0.0283410i
$945$	−36.7239	+	0.521626i	−1.19463	+	0.0169685i
$946$	3.41460	−	10.5091i	0.111018	−	0.341679i
$947$	−36.1299	+	7.67964i	−1.17406	+	0.249555i	−0.753338	−	0.657634i	$-0.771557\pi$
$947$	−36.1299	+	7.67964i	−1.17406	+	0.249555i	−0.420725	+	0.907188i	$0.638224\pi$
$948$	−3.97146	−	8.77106i	−0.128987	−	0.284871i
$949$	6.21464	−	10.7641i	0.201736	−	0.349416i
$950$	−1.73217	+	0.751870i	−0.0561992	+	0.0243939i
$951$	44.8651	−	14.8904i	1.45485	−	0.482854i
$952$	−19.4877	−	8.67647i	−0.631599	−	0.281206i
$953$	−9.21306	+	28.3549i	−0.298440	+	0.918505i	0.683604	+	0.729853i	$0.260412\pi$
$953$	−9.21306	+	28.3549i	−0.298440	+	0.918505i	−0.982044	+	0.188652i	$0.939588\pi$
$954$	−0.457818	−	0.0913046i	−0.0148224	−	0.00295609i
$955$	4.96367	−	6.76511i	0.160621	−	0.218914i
$956$	4.39988	−	4.88657i	0.142302	−	0.158043i
$957$	13.1888	+	11.7257i	0.426332	+	0.379040i
$958$	−8.96935	−	1.90649i	−0.289786	−	0.0615960i
$959$	−16.4363	+	7.31791i	−0.530756	+	0.236308i
$960$	−23.6227	−	10.4718i	−0.762420	−	0.337977i
$961$	−25.5678	−	11.3835i	−0.824767	−	0.367210i
$962$	−1.49689	−	1.08756i	−0.0482618	−	0.0350643i
$963$	21.1431	+	35.5790i	0.681328	+	1.14652i
$964$	−28.7137	+	20.8617i	−0.924806	+	0.671911i
$965$	−32.5124	+	18.5688i	−1.04661	+	0.597750i
$966$	2.05358	+	0.652986i	0.0660727	+	0.0210095i
$967$	23.1383	+	4.91820i	0.744078	+	0.158159i	0.564325	−	0.825553i	$-0.309137\pi$
$967$	23.1383	+	4.91820i	0.744078	+	0.158159i	0.179754	+	0.983712i	$0.442470\pi$
$968$	−1.93030	+	3.34338i	−0.0620423	+	0.107460i
$969$	19.6314	−	2.18836i	0.630652	−	0.0703002i
$970$	2.92865	+	2.66188i	0.0940331	+	0.0854679i
$971$	6.29152	−	19.3633i	0.201904	−	0.621398i	−0.797922	−	0.602761i	$-0.794067\pi$
$971$	6.29152	−	19.3633i	0.201904	−	0.621398i	0.999826	−	0.0186371i	$-0.00593273\pi$
$972$	−29.0911	−	8.45002i	−0.933097	−	0.271034i
$973$	18.4913	−	13.4347i	0.592802	−	0.430696i
$974$	2.58432	+	4.47617i	0.0828069	+	0.143426i
$975$	22.5785	+	51.1333i	0.723091	+	1.63758i
$976$	0.560285	−	0.970442i	0.0179343	−	0.0310631i
$977$	−5.96896	−	56.7909i	−0.190964	−	1.81690i	−0.500194	−	0.865914i	$-0.666738\pi$
$977$	−5.96896	−	56.7909i	−0.190964	−	1.81690i	0.309230	−	0.950987i	$-0.399929\pi$
$978$	0.0183745	+	2.91928i	0.000587553	+	0.0933482i
$979$	−52.2837	+	11.1132i	−1.67099	+	0.355181i
$980$	12.3460	+	4.07542i	0.394378	+	0.130185i
$981$	3.98853	−	43.1692i	0.127344	−	1.37829i
$982$	5.71658			0.182423
$983$	26.5534	−	29.4905i	0.846921	−	0.940601i	−0.151937	−	0.988390i	$-0.548551\pi$
$983$	26.5534	−	29.4905i	0.846921	−	0.940601i	0.998857	+	0.0477896i	$0.0152177\pi$
$984$	−1.90824	−	8.70771i	−0.0608325	−	0.277592i
$985$	−18.9421	+	16.8958i	−0.603547	+	0.538344i
$986$	0.468849	+	4.46080i	0.0149312	+	0.142061i
$987$	7.21126	+	32.9065i	0.229537	+	1.04743i
$988$	2.07994	−	19.7893i	0.0661718	−	0.629582i
$989$	15.9703	−	11.6031i	0.507827	−	0.368958i
$990$	−4.58055	+	4.19041i	−0.145579	+	0.133180i
$991$	−30.6573	−	22.2738i	−0.973860	−	0.707551i	−0.0175320	−	0.999846i	$-0.505581\pi$
$991$	−30.6573	−	22.2738i	−0.973860	−	0.707551i	−0.956328	+	0.292296i	$0.905581\pi$
$992$	3.19333	−	3.54655i	0.101388	−	0.112603i
$993$	21.5464	−	7.15109i	0.683754	−	0.226933i
$994$	0.0971166	+	0.0206428i	0.00308035	+	0.000654749i
$995$	10.1448	+	5.92057i	0.321612	+	0.187695i
$996$	0.402514	+	0.229026i	0.0127541	+	0.00725695i
$997$	−48.4198	+	10.2920i	−1.53347	+	0.325949i	−0.895835	−	0.444388i	$-0.853421\pi$
$997$	−48.4198	+	10.2920i	−1.53347	+	0.325949i	−0.637637	+	0.770337i	$0.720088\pi$
$998$	3.24243	−	2.35576i	0.102637	−	0.0745703i
$999$	−3.58162	+	5.13067i	−0.113317	+	0.162327i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.211.13	yes	224
3.2	odd	2		675.2.r.a.361.16		224
9.2	odd	6		675.2.r.a.586.13		224
9.7	even	3	inner	225.2.q.a.61.16	yes	224
25.16	even	5	inner	225.2.q.a.166.16	yes	224
75.41	odd	10		675.2.r.a.91.13		224
225.16	even	15	inner	225.2.q.a.16.13	✓	224
225.191	odd	30		675.2.r.a.316.16		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.16.13	✓	224	225.16	even	15	inner
225.2.q.a.61.16	yes	224	9.7	even	3	inner
225.2.q.a.166.16	yes	224	25.16	even	5	inner
225.2.q.a.211.13	yes	224	1.1	even	1	trivial
675.2.r.a.91.13		224	75.41	odd	10
675.2.r.a.316.16		224	225.191	odd	30
675.2.r.a.361.16		224	3.2	odd	2
675.2.r.a.586.13		224	9.2	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)

\(f(q)\)	\(=\)	\(q+(-0.217479 - 0.0968278i) q^{2} +(-1.50542 - 0.856567i) q^{3} +(-1.30034 - 1.44417i) q^{4} +(1.93124 + 1.12708i) q^{5} +(0.244458 + 0.332052i) q^{6} +(-1.58050 - 2.73751i) q^{7} +(0.290090 + 0.892804i) q^{8} +(1.53259 + 2.57899i) q^{9} +O(q^{10})\)	\(q+(-0.217479 - 0.0968278i) q^{2} +(-1.50542 - 0.856567i) q^{3} +(-1.30034 - 1.44417i) q^{4} +(1.93124 + 1.12708i) q^{5} +(0.244458 + 0.332052i) q^{6} +(-1.58050 - 2.73751i) q^{7} +(0.290090 + 0.892804i) q^{8} +(1.53259 + 2.57899i) q^{9} +(-0.310871 - 0.432114i) q^{10} +(-3.55139 - 1.58118i) q^{11} +(0.720527 + 3.28792i) q^{12} +(-5.89635 + 2.62522i) q^{13} +(0.0786587 + 0.748387i) q^{14} +(-1.94191 - 3.35097i) q^{15} +(-0.382906 + 3.64311i) q^{16} +(-2.22145 - 6.83693i) q^{17} +(-0.0835871 - 0.709272i) q^{18} +(-0.490230 - 1.50877i) q^{19} +(-0.883563 - 4.25464i) q^{20} +(0.0344602 + 5.47491i) q^{21} +(0.619250 + 0.687747i) q^{22} +(0.172818 + 1.64425i) q^{23} +(0.328039 - 1.59253i) q^{24} +(2.45937 + 4.35333i) q^{25} +1.53653 q^{26} +(-0.0981099 - 5.19523i) q^{27} +(-1.89825 + 5.84221i) q^{28} +(2.56366 - 0.544923i) q^{29} +(0.0978562 + 0.916796i) q^{30} +(1.69775 + 0.360869i) q^{31} +(1.37478 - 2.38118i) q^{32} +(3.99195 + 5.42235i) q^{33} +(-0.178886 + 1.70199i) q^{34} +(0.0330743 - 7.06814i) q^{35} +(1.73163 - 5.56688i) q^{36} +(-0.974207 - 0.707803i) q^{37} +(-0.0394766 + 0.375594i) q^{38} +(11.1252 + 1.09855i) q^{39} +(-0.446032 + 2.05117i) q^{40} +(5.00852 - 2.22994i) q^{41} +(0.522629 - 1.19401i) q^{42} +(-5.96998 - 10.3403i) q^{43} +(2.33451 + 7.18490i) q^{44} +(0.0530542 + 6.70799i) q^{45} +(0.121625 - 0.374323i) q^{46} +(6.01847 - 1.27926i) q^{47} +(3.69700 - 5.15643i) q^{48} +(-1.49598 + 2.59111i) q^{49} +(-0.113337 - 1.18489i) q^{50} +(-2.51207 + 12.1953i) q^{51} +(11.4585 + 5.10167i) q^{52} +(0.201993 - 0.621671i) q^{53} +(-0.481706 + 1.13935i) q^{54} +(-5.07646 - 7.05635i) q^{55} +(1.98557 - 2.20520i) q^{56} +(-0.554363 + 2.69126i) q^{57} +(-0.610306 - 0.129724i) q^{58} +(0.228332 - 0.101660i) q^{59} +(-2.31425 + 7.16185i) q^{60} +(-0.279455 - 0.124421i) q^{61} +(-0.334283 - 0.242871i) q^{62} +(4.63775 - 8.27157i) q^{63} +(5.39759 - 3.92158i) q^{64} +(-14.3461 - 1.57574i) q^{65} +(-0.343131 - 1.56578i) q^{66} +(-3.64909 - 0.775638i) q^{67} +(-6.98507 + 12.0985i) q^{68} +(1.14825 - 2.62332i) q^{69} +(-0.691586 + 1.53397i) q^{70} +(0.0407718 - 0.125483i) q^{71} +(-1.85794 + 2.11644i) q^{72} +(-1.55794 + 1.13191i) q^{73} +(0.143334 + 0.248263i) q^{74} +(0.0265392 - 8.66021i) q^{75} +(-1.54147 + 2.66990i) q^{76} +(1.28448 + 12.2210i) q^{77} +(-2.31312 - 1.31614i) q^{78} +(-2.79800 + 0.594732i) q^{79} +(-4.84557 + 6.60415i) q^{80} +(-4.30236 + 7.90504i) q^{81} -1.30517 q^{82} +(0.0920635 - 0.102247i) q^{83} +(7.86191 - 7.16901i) q^{84} +(3.41563 - 15.7075i) q^{85} +(0.297115 + 2.82686i) q^{86} +(-4.32615 - 1.37561i) q^{87} +(0.381463 - 3.62938i) q^{88} +(11.1238 - 8.08188i) q^{89} +(0.637982 - 1.46398i) q^{90} +(16.5058 + 11.9921i) q^{91} +(2.14986 - 2.38766i) q^{92} +(-2.24673 - 1.99750i) q^{93} +(-1.43276 - 0.304542i) q^{94} +(0.753762 - 3.46633i) q^{95} +(-4.10926 + 2.40710i) q^{96} +(-7.27218 + 1.54575i) q^{97} +(0.576234 - 0.418659i) q^{98} +(-1.36496 - 11.5823i) 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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