LMFDB - Embedded newform 225.2.q.a.211.3

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			211.3
Character	$\chi$	$=$	225.211
Dual form			225.2.q.a.16.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.13701 - 0.951457i) q^{2} +(-0.620400 - 1.61713i) q^{3} +(2.32327 + 2.58025i) q^{4} +(-1.69271 - 1.46108i) q^{5} +(-0.212829 + 4.04610i) q^{6} +(-0.915602 - 1.58587i) q^{7} +(-1.06411 - 3.27499i) q^{8} +(-2.23021 + 2.00653i) q^{9} +O(q^{10})$	\(q+(-2.13701 - 0.951457i) q^{2} +(-0.620400 - 1.61713i) q^{3} +(2.32327 + 2.58025i) q^{4} +(-1.69271 - 1.46108i) q^{5} +(-0.212829 + 4.04610i) q^{6} +(-0.915602 - 1.58587i) q^{7} +(-1.06411 - 3.27499i) q^{8} +(-2.23021 + 2.00653i) q^{9} +(2.22718 + 4.73287i) q^{10} +(-1.75350 - 0.780708i) q^{11} +(2.73124 - 5.35781i) q^{12} +(-0.319779 + 0.142375i) q^{13} +(0.447762 + 4.26017i) q^{14} +(-1.31259 + 3.64378i) q^{15} +(-0.116144 + 1.10504i) q^{16} +(-0.815069 - 2.50853i) q^{17} +(6.67510 - 2.16603i) q^{18} +(1.57929 + 4.86056i) q^{19} +(-0.162673 - 7.76208i) q^{20} +(-1.99652 + 2.46452i) q^{21} +(3.00443 + 3.33676i) q^{22} +(0.789361 + 7.51027i) q^{23} +(-4.63591 + 3.75261i) q^{24} +(0.730517 + 4.94635i) q^{25} +0.818832 q^{26} +(4.62844 + 2.36168i) q^{27} +(1.96475 - 6.04688i) q^{28} +(7.09948 - 1.50904i) q^{29} +(6.27191 - 6.53790i) q^{30} +(-6.88248 - 1.46292i) q^{31} +(-2.14393 + 3.71340i) q^{32} +(-0.174634 + 3.31998i) q^{33} +(-0.644945 + 6.13624i) q^{34} +(-0.767228 + 4.02218i) q^{35} +(-10.3587 - 1.09278i) q^{36} +(-4.22488 - 3.06955i) q^{37} +(1.24966 - 11.8897i) q^{38} +(0.428629 + 0.428794i) q^{39} +(-2.98378 + 7.09835i) q^{40} +(-2.49525 + 1.11096i) q^{41} +(6.61145 - 3.36710i) q^{42} +(-3.95848 - 6.85628i) q^{43} +(-2.05942 - 6.33826i) q^{44} +(6.70678 - 0.137972i) q^{45} +(5.45883 - 16.8005i) q^{46} +(-10.9951 + 2.33709i) q^{47} +(1.85904 - 0.497745i) q^{48} +(1.82334 - 3.15813i) q^{49} +(3.14511 - 11.2654i) q^{50} +(-3.55094 + 2.87436i) q^{51} +(-1.11029 - 0.494334i) q^{52} +(0.727074 - 2.23770i) q^{53} +(-7.64398 - 9.45069i) q^{54} +(1.82749 + 3.88350i) q^{55} +(-4.21941 + 4.68613i) q^{56} +(6.88036 - 5.56941i) q^{57} +(-16.6074 - 3.53002i) q^{58} +(-5.30179 + 2.36051i) q^{59} +(-12.4514 + 5.07866i) q^{60} +(-7.48156 - 3.33100i) q^{61} +(13.3160 + 9.67464i) q^{62} +(5.22408 + 1.69963i) q^{63} +(9.91258 - 7.20191i) q^{64} +(0.749312 + 0.226222i) q^{65} +(3.53201 - 6.92867i) q^{66} +(4.64929 + 0.988236i) q^{67} +(4.57900 - 7.93106i) q^{68} +(11.6553 - 5.93587i) q^{69} +(5.46650 - 7.86544i) q^{70} +(4.20239 - 12.9336i) q^{71} +(8.94456 + 5.16874i) q^{72} +(-10.4569 + 7.59738i) q^{73} +(6.10804 + 10.5794i) q^{74} +(7.54566 - 4.25005i) q^{75} +(-8.87235 + 15.3674i) q^{76} +(0.367406 + 3.49564i) q^{77} +(-0.508004 - 1.32416i) q^{78} +(-6.36493 + 1.35291i) q^{79} +(1.81114 - 1.70081i) q^{80} +(0.947652 - 8.94997i) q^{81} +6.38940 q^{82} +(-6.26629 + 6.95942i) q^{83} +(-10.9975 + 0.574231i) q^{84} +(-2.28547 + 5.43708i) q^{85} +(1.93584 + 18.4182i) q^{86} +(-6.84483 - 10.5446i) q^{87} +(-0.690898 + 6.57345i) q^{88} +(-8.55403 + 6.21487i) q^{89} +(-14.4637 - 6.08637i) q^{90} +(0.518578 + 0.376769i) q^{91} +(-17.5445 + 19.4851i) q^{92} +(1.90417 + 12.0374i) q^{93} +(25.7203 + 5.46703i) q^{94} +(4.42837 - 10.5350i) q^{95} +(7.33515 + 1.16322i) q^{96} +(13.4736 - 2.86389i) q^{97} +(-6.90132 + 5.01410i) q^{98} +(5.47718 - 1.77731i) 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 $

$2$	−2.13701	−	0.951457i	−1.51109	−	0.672782i	−0.526907	−	0.849923i	$-0.676648\pi$
$2$	−2.13701	−	0.951457i	−1.51109	−	0.672782i	−0.984185	+	0.177142i	$0.943315\pi$
$3$	−0.620400	−	1.61713i	−0.358188	−	0.933649i
$3$	−0.620400	−	1.61713i	−0.358188	−	0.933649i
$4$	2.32327	+	2.58025i	1.16163	+	1.29012i
$5$	−1.69271	−	1.46108i	−0.757002	−	0.653413i
$5$	−1.69271	−	1.46108i	−0.757002	−	0.653413i
$6$	−0.212829	+	4.04610i	−0.0868869	+	1.65181i
$7$	−0.915602	−	1.58587i	−0.346065	−	0.599402i	0.639482	−	0.768806i	$-0.279149\pi$
$7$	−0.915602	−	1.58587i	−0.346065	−	0.599402i	−0.985547	+	0.169404i	$0.945816\pi$
$8$	−1.06411	−	3.27499i	−0.376219	−	1.15788i
$9$	−2.23021	+	2.00653i	−0.743403	+	0.668844i
$10$	2.22718	+	4.73287i	0.704295	+	1.49666i
$11$	−1.75350	−	0.780708i	−0.528700	−	0.235392i	0.124986	−	0.992159i	$-0.460111\pi$
$11$	−1.75350	−	0.780708i	−0.528700	−	0.235392i	−0.653686	+	0.756766i	$0.726778\pi$
$12$	2.73124	−	5.35781i	0.788441	−	1.54667i
$13$	−0.319779	+	0.142375i	−0.0886906	+	0.0394876i	−0.450602	−	0.892725i	$-0.648791\pi$
$13$	−0.319779	+	0.142375i	−0.0886906	+	0.0394876i	0.361912	+	0.932212i	$0.382124\pi$
$14$	0.447762	+	4.26017i	0.119669	+	1.13858i
$15$	−1.31259	+	3.64378i	−0.338909	+	0.940819i
$16$	−0.116144	+	1.10504i	−0.0290360	+	0.276259i
$17$	−0.815069	−	2.50853i	−0.197683	−	0.608407i	−0.999935	−	0.0114205i	$-0.996365\pi$
$17$	−0.815069	−	2.50853i	−0.197683	−	0.608407i	0.802251	−	0.596986i	$-0.203635\pi$
$18$	6.67510	−	2.16603i	1.57334	−	0.510538i
$19$	1.57929	+	4.86056i	0.362315	+	1.11509i	0.951646	+	0.307198i	$0.0993914\pi$
$19$	1.57929	+	4.86056i	0.362315	+	1.11509i	−0.589331	+	0.807892i	$0.700609\pi$
$20$	−0.162673	−	7.76208i	−0.0363747	−	1.73565i
$21$	−1.99652	+	2.46452i	−0.435675	+	0.537802i
$22$	3.00443	+	3.33676i	0.640546	+	0.711399i
$23$	0.789361	+	7.51027i	0.164593	+	1.56600i	0.695473	+	0.718552i	$0.255195\pi$
$23$	0.789361	+	7.51027i	0.164593	+	1.56600i	−0.530880	+	0.847447i	$0.678138\pi$
$24$	−4.63591	+	3.75261i	−0.946301	+	0.765998i
$25$	0.730517	+	4.94635i	0.146103	+	0.989269i
$26$	0.818832			0.160586
$27$	4.62844	+	2.36168i	0.890744	+	0.454505i
$28$	1.96475	−	6.04688i	0.371303	−	1.14275i
$29$	7.09948	−	1.50904i	1.31834	−	0.280222i	0.505560	−	0.862792i	$-0.331286\pi$
$29$	7.09948	−	1.50904i	1.31834	−	0.280222i	0.812781	+	0.582570i	$0.197953\pi$
$30$	6.27191	−	6.53790i	1.14509	−	1.19365i
$31$	−6.88248	−	1.46292i	−1.23613	−	0.262747i	−0.456918	−	0.889509i	$-0.651047\pi$
$31$	−6.88248	−	1.46292i	−1.23613	−	0.262747i	−0.779211	+	0.626761i	$0.784380\pi$
$32$	−2.14393	+	3.71340i	−0.378998	+	0.656443i
$33$	−0.174634	+	3.31998i	−0.0303999	+	0.577935i
$34$	−0.644945	+	6.13624i	−0.110607	+	1.05236i
$35$	−0.767228	+	4.02218i	−0.129685	+	0.679872i
$36$	−10.3587	−	1.09278i	−1.72645	−	0.182130i
$37$	−4.22488	−	3.06955i	−0.694565	−	0.504631i	0.183592	−	0.983002i	$-0.441227\pi$
$37$	−4.22488	−	3.06955i	−0.694565	−	0.504631i	−0.878158	+	0.478371i	$0.841227\pi$
$38$	1.24966	−	11.8897i	0.202721	−	1.92876i
$39$	0.428629	+	0.428794i	0.0686355	+	0.0686619i
$40$	−2.98378	+	7.09835i	−0.471778	+	1.12235i
$41$	−2.49525	+	1.11096i	−0.389693	+	0.173502i	−0.592224	−	0.805773i	$-0.701750\pi$
$41$	−2.49525	+	1.11096i	−0.389693	+	0.173502i	0.202531	+	0.979276i	$0.435083\pi$
$42$	6.61145	−	3.36710i	1.02017	−	0.519555i
$43$	−3.95848	−	6.85628i	−0.603662	−	1.04557i	−0.992261	−	0.124167i	$-0.960374\pi$
$43$	−3.95848	−	6.85628i	−0.603662	−	1.04557i	0.388599	−	0.921407i	$-0.372959\pi$
$44$	−2.05942	−	6.33826i	−0.310470	−	0.955528i
$45$	6.70678	−	0.137972i	0.999788	−	0.0205676i
$46$	5.45883	−	16.8005i	0.804860	−	2.47710i
$47$	−10.9951	+	2.33709i	−1.60381	+	0.340900i	−0.920959	−	0.389660i	$-0.872592\pi$
$47$	−10.9951	+	2.33709i	−1.60381	+	0.340900i	−0.682848	+	0.730560i	$0.739259\pi$
$48$	1.85904	−	0.497745i	0.268330	−	0.0718433i
$49$	1.82334	−	3.15813i	0.260478	−	0.451161i
$50$	3.14511	−	11.2654i	0.444786	−	1.59317i
$51$	−3.55094	+	2.87436i	−0.497231	+	0.402491i
$52$	−1.11029	−	0.494334i	−0.153970	−	0.0685518i
$53$	0.727074	−	2.23770i	0.0998713	−	0.307372i	−0.888621	−	0.458642i	$-0.848336\pi$
$53$	0.727074	−	2.23770i	0.0998713	−	0.307372i	0.988493	+	0.151269i	$0.0483361\pi$
$54$	−7.64398	−	9.45069i	−1.04021	−	1.28608i
$55$	1.82749	+	3.88350i	0.246418	+	0.523651i
$56$	−4.21941	+	4.68613i	−0.563842	+	0.626210i
$57$	6.88036	−	5.56941i	0.911326	−	0.737687i
$58$	−16.6074	−	3.53002i	−2.18066	−	0.463514i
$59$	−5.30179	+	2.36051i	−0.690235	+	0.307312i	−0.721713	−	0.692192i	$-0.756645\pi$
$59$	−5.30179	+	2.36051i	−0.690235	+	0.307312i	0.0314785	+	0.999504i	$0.489978\pi$
$60$	−12.4514	+	5.07866i	−1.60746	+	0.655652i
$61$	−7.48156	−	3.33100i	−0.957916	−	0.426491i	−0.132604	−	0.991169i	$-0.542334\pi$
$61$	−7.48156	−	3.33100i	−0.957916	−	0.426491i	−0.825312	+	0.564678i	$0.809001\pi$
$62$	13.3160	+	9.67464i	1.69113	+	1.22868i
$63$	5.22408	+	1.69963i	0.658173	+	0.214134i
$64$	9.91258	−	7.20191i	1.23907	−	0.900239i
$65$	0.749312	+	0.226222i	0.0929407	+	0.0280594i
$66$	3.53201	−	6.92867i	0.434761	−	0.852860i
$67$	4.64929	+	0.988236i	0.568001	+	0.120732i	0.482956	−	0.875645i	$-0.339563\pi$
$67$	4.64929	+	0.988236i	0.568001	+	0.120732i	0.0850451	+	0.996377i	$0.472897\pi$
$68$	4.57900	−	7.93106i	0.555285	−	0.961782i
$69$	11.6553	−	5.93587i	1.40314	−	0.714595i
$70$	5.46650	−	7.86544i	0.653372	−	0.940100i
$71$	4.20239	−	12.9336i	0.498732	−	1.53494i	−0.312328	−	0.949974i	$-0.601109\pi$
$71$	4.20239	−	12.9336i	0.498732	−	1.53494i	0.811059	−	0.584964i	$-0.198891\pi$
$72$	8.94456	+	5.16874i	1.05413	+	0.609142i
$73$	−10.4569	+	7.59738i	−1.22389	+	0.889206i	−0.996417	−	0.0845796i	$-0.973045\pi$
$73$	−10.4569	+	7.59738i	−1.22389	+	0.889206i	−0.227470	+	0.973785i	$0.573045\pi$
$74$	6.10804	+	10.5794i	0.710046	+	1.22984i
$75$	7.54566	−	4.25005i	0.871298	−	0.490754i
$76$	−8.87235	+	15.3674i	−1.01773	+	1.76276i
$77$	0.367406	+	3.49564i	0.0418698	+	0.398365i
$78$	−0.508004	−	1.32416i	−0.0575201	−	0.149931i
$79$	−6.36493	+	1.35291i	−0.716111	+	0.152214i	−0.551537	−	0.834151i	$-0.685958\pi$
$79$	−6.36493	+	1.35291i	−0.716111	+	0.152214i	−0.164574	+	0.986365i	$0.552625\pi$
$80$	1.81114	−	1.70081i	0.202492	−	0.190156i
$81$	0.947652	−	8.94997i	0.105295	−	0.994441i
$82$	6.38940			0.705591
$83$	−6.26629	+	6.95942i	−0.687815	+	0.763896i	−0.981387	−	0.192041i	$-0.938489\pi$
$83$	−6.26629	+	6.95942i	−0.687815	+	0.763896i	0.293572	+	0.955937i	$0.405156\pi$
$84$	−10.9975	+	0.574231i	−1.19993	+	0.0626538i
$85$	−2.28547	+	5.43708i	−0.247894	+	0.589734i
$86$	1.93584	+	18.4182i	0.208747	+	1.98609i
$87$	−6.84483	−	10.5446i	−0.733843	−	1.13050i
$88$	−0.690898	+	6.57345i	−0.0736499	+	0.700732i
$89$	−8.55403	+	6.21487i	−0.906726	+	0.658775i	−0.940185	−	0.340665i	$-0.889348\pi$
$89$	−8.55403	+	6.21487i	−0.906726	+	0.658775i	0.0334588	+	0.999440i	$0.489348\pi$
$90$	−14.4637	−	6.08637i	−1.52461	−	0.641560i
$91$	0.518578	+	0.376769i	0.0543617	+	0.0394961i
$92$	−17.5445	+	19.4851i	−1.82914	+	2.03146i
$93$	1.90417	+	12.0374i	0.197453	+	1.24822i
$94$	25.7203	+	5.46703i	2.65285	+	0.563881i
$95$	4.42837	−	10.5350i	0.454341	−	1.08087i
$96$	7.33515	+	1.16322i	0.748640	+	0.118721i
$97$	13.4736	−	2.86389i	1.36803	−	0.290784i	0.535395	−	0.844602i	$-0.320163\pi$
$97$	13.4736	−	2.86389i	1.36803	−	0.290784i	0.832638	+	0.553817i	$0.186829\pi$
$98$	−6.90132	+	5.01410i	−0.697139	+	0.506501i
$99$	5.47718	−	1.77731i	0.550477	−	0.178627i
$100$	−11.0656	+	13.3766i	−1.10656	+	1.33766i
$101$	3.06658	+	5.31147i	0.305136	+	0.528511i	0.977292	−	0.211899i	$-0.0679647\pi$
$101$	3.06658	+	5.31147i	0.305136	+	0.528511i	−0.672155	+	0.740410i	$0.734631\pi$
$102$	10.3232	−	2.76396i	1.02215	−	0.273673i
$103$	−5.33351	−	5.92347i	−0.525527	−	0.583657i	0.420684	−	0.907207i	$-0.361790\pi$
$103$	−5.33351	−	5.92347i	−0.525527	−	0.583657i	−0.946211	+	0.323551i	$0.895123\pi$
$104$	0.806555	+	0.895770i	0.0790892	+	0.0878375i
$105$	6.98037	−	1.25465i	0.681214	−	0.122442i
$106$	−3.68284	+	4.09021i	−0.357709	+	0.397276i
$107$	−12.9593			−1.25282			−0.626412	−	0.779492i	$-0.715477\pi$
$107$	−12.9593			−1.25282			−0.626412	+	0.779492i	$0.715477\pi$
$108$	4.65939	+	17.4293i	0.448350	+	1.67714i
$109$	4.11285	+	2.98816i	0.393939	+	0.286214i	0.767068	−	0.641566i	$-0.221715\pi$
$109$	4.11285	+	2.98816i	0.393939	+	0.286214i	−0.373129	+	0.927780i	$0.621715\pi$
$110$	−0.210367	−	10.0378i	−0.0200577	−	0.957071i
$111$	−2.34275	+	8.73652i	−0.222364	+	0.829234i
$112$	1.85879	−	0.827585i	0.175639	−	0.0781995i
$113$	12.2106	−	5.43653i	1.14868	−	0.511426i	0.258041	−	0.966134i	$-0.416923\pi$
$113$	12.2106	−	5.43653i	1.14868	−	0.511426i	0.890640	+	0.454708i	$0.150256\pi$
$114$	−20.0024	+	5.35551i	−1.87340	+	0.501589i
$115$	9.63691	−	13.8660i	0.898647	−	1.29301i
$116$	20.3877	+	14.8125i	1.89295	+	1.37531i
$117$	0.427493	−	0.959171i	0.0395218	−	0.0886754i
$118$	13.5759			1.24976
$119$	−3.23192	+	3.58941i	−0.296269	+	0.329040i
$120$	13.3301	+	0.421347i	1.21686	+	0.0384635i
$121$	−4.89518	−	5.43665i	−0.445017	−	0.494241i
$122$	12.8188	+	14.2368i	1.16056	+	1.28894i
$123$	3.34461	+	3.34590i	0.301574	+	0.301690i
$124$	−12.2151	−	21.1573i	−1.09695	−	1.89998i
$125$	5.99043	−	9.44006i	0.535801	−	0.844345i
$126$	−9.54678	−	8.60262i	−0.850494	−	0.766382i
$127$	−9.17993	+	6.66961i	−0.814587	+	0.591832i	−0.915157	−	0.403098i	$-0.867933\pi$
$127$	−9.17993	+	6.66961i	−0.814587	+	0.591832i	0.100570	+	0.994930i	$0.467933\pi$
$128$	−19.6472	+	4.17615i	−1.73659	+	0.369123i
$129$	−8.63165	+	10.6550i	−0.759975	+	0.938121i
$130$	−1.38604	−	1.19638i	−0.121564	−	0.104929i
$131$	4.59865	+	0.977473i	0.401786	+	0.0854022i	0.404372	−	0.914594i	$-0.367490\pi$
$131$	4.59865	+	0.977473i	0.401786	+	0.0854022i	−0.00258661	+	0.999997i	$0.500823\pi$
$132$	−8.97211	+	7.26261i	−0.780922	+	0.632129i
$133$	6.26222	−	6.95489i	0.543003	−	0.603066i
$134$	−8.99529	−	6.53546i	−0.777075	−	0.564578i
$135$	−4.38401	−	10.7601i	−0.377315	−	0.926085i
$136$	−7.34808	+	5.33869i	−0.630092	+	0.457789i
$137$	1.03584	−	9.85536i	0.0884978	−	0.842000i	−0.856769	−	0.515701i	$-0.827532\pi$
$137$	1.03584	−	9.85536i	0.0884978	−	0.842000i	0.945267	−	0.326299i	$-0.105802\pi$
$138$	−30.5553	+	1.59543i	−2.60104	+	0.135812i
$139$	−0.971177	−	9.24013i	−0.0823742	−	0.783738i	−0.955251	−	0.295797i	$-0.904415\pi$
$139$	−0.971177	−	9.24013i	−0.0823742	−	0.783738i	0.872877	−	0.487941i	$-0.162252\pi$
$140$	−12.1607	+	7.36495i	−1.02777	+	0.622452i
$141$	10.6008	+	16.3306i	0.892746	+	1.37529i
$142$	−21.2863	+	23.6408i	−1.78631	+	1.98390i
$143$	0.671884			0.0561858
$144$	−1.95827	−	2.69751i	−0.163189	−	0.224792i
$145$	−14.2222	−	7.81851i	−1.18109	−	0.649292i
$146$	29.5750	−	6.28636i	2.44765	−	0.520263i
$147$	−6.23830	−	0.989281i	−0.514526	−	0.0815945i
$148$	−1.89531	−	18.0326i	−0.155793	−	1.48227i
$149$	6.77464	−	11.7340i	0.555000	−	0.961288i	−0.442903	−	0.896569i	$-0.646052\pi$
$149$	6.77464	−	11.7340i	0.555000	−	0.961288i	0.997904	−	0.0647191i	$-0.0206151\pi$
$150$	−20.1689	+	1.90302i	−1.64678	+	0.155381i
$151$	−0.919523	−	1.59266i	−0.0748297	−	0.129609i	0.826182	−	0.563403i	$-0.190508\pi$
$151$	−0.919523	−	1.59266i	−0.0748297	−	0.129609i	−0.901012	+	0.433794i	$0.857175\pi$
$152$	14.2378	−	10.3443i	1.15484	−	0.839037i
$153$	6.85121	+	3.95907i	0.553888	+	0.320072i
$154$	2.54080	−	7.81977i	0.204743	−	0.630135i
$155$	9.51259	+	12.5321i	0.764070	+	1.00660i
$156$	−0.110576	+	2.10217i	−0.00885318	+	0.168308i
$157$	0.169592	−	0.293742i	0.0135349	−	0.0234432i	−0.859179	−	0.511676i	$-0.829025\pi$
$157$	0.169592	−	0.293742i	0.0135349	−	0.0234432i	0.872714	+	0.488233i	$0.162358\pi$
$158$	14.8891	+	3.16478i	1.18452	+	0.251777i
$159$	−4.06973	+	0.212500i	−0.322751	+	0.0168523i
$160$	9.05461	−	3.15326i	0.715830	−	0.249287i
$161$	11.1876	−	8.12824i	0.881704	−	0.640595i
$162$	−10.5406	+	18.2245i	−0.828152	+	1.43185i
$163$	14.9764	+	10.8810i	1.17304	+	0.852264i	0.991370	−	0.131095i	$-0.0418493\pi$
$163$	14.9764	+	10.8810i	1.17304	+	0.852264i	0.181671	+	0.983359i	$0.441849\pi$
$164$	−8.66368	−	3.85732i	−0.676520	−	0.301206i
$165$	5.14635	−	5.36461i	0.400643	−	0.417634i
$166$	20.0127	−	8.91022i	1.55329	−	0.691568i
$167$	−9.71158	−	2.06426i	−0.751504	−	0.159737i	−0.183793	−	0.982965i	$-0.558838\pi$
$167$	−9.71158	−	2.06426i	−0.751504	−	0.159737i	−0.567711	+	0.823228i	$0.692171\pi$
$168$	10.1958	+	3.91605i	0.786623	+	0.302130i
$169$	−8.61671	+	9.56983i	−0.662824	+	0.736140i
$170$	10.0572	−	9.44455i	0.771353	−	0.724364i
$171$	−13.2750	−	7.67116i	−1.01517	−	0.586628i
$172$	8.49433	−	26.1428i	0.647686	−	1.99337i
$173$	8.63521	+	3.84464i	0.656523	+	0.292303i	0.707833	−	0.706380i	$-0.249673\pi$
$173$	8.63521	+	3.84464i	0.656523	+	0.292303i	−0.0513101	+	0.998683i	$0.516340\pi$
$174$	4.59476	+	29.0464i	0.348328	+	2.20200i
$175$	7.17540	−	5.68739i	0.542409	−	0.429926i
$176$	1.06637	−	1.84701i	0.0803806	−	0.139223i
$177$	7.10648	+	7.10922i	0.534156	+	0.534362i
$178$	24.1932	−	5.14243i	1.81336	−	0.385441i
$179$	−2.63484	+	8.10919i	−0.196937	+	0.606109i	0.803012	+	0.595963i	$0.203230\pi$
$179$	−2.63484	+	8.10919i	−0.196937	+	0.606109i	−0.999949	+	0.0101460i	$0.996770\pi$
$180$	15.9377	+	16.9846i	1.18792	+	1.26596i
$181$	0.994944	+	3.06212i	0.0739536	+	0.227606i	0.981200	−	0.192994i	$-0.0618197\pi$
$181$	0.994944	+	3.06212i	0.0739536	+	0.227606i	−0.907246	+	0.420600i	$0.861820\pi$
$182$	−0.749725	−	1.29856i	−0.0555733	−	0.0962558i
$183$	−0.745102	+	14.1652i	−0.0550796	+	1.04712i
$184$	23.7561	−	10.5769i	1.75132	−	0.779739i
$185$	2.66663	+	11.3687i	0.196055	+	0.835845i
$186$	7.38389	−	27.5358i	0.541413	−	2.01902i
$187$	−0.529203	+	5.03503i	−0.0386991	+	0.368198i
$188$	−31.5749	−	22.9405i	−2.30284	−	1.67311i
$189$	−0.492497	−	9.50246i	−0.0358239	−	0.691203i
$190$	−19.4870	+	18.2999i	−1.41374	+	1.32762i
$191$	0.939890	−	8.94245i	0.0680080	−	0.647053i	−0.906424	−	0.422370i	$-0.861198\pi$
$191$	0.939890	−	8.94245i	0.0680080	−	0.647053i	0.974432	−	0.224684i	$-0.0721349\pi$
$192$	−17.7962	−	11.5618i	−1.28433	−	0.834405i
$193$	0.925754	−	1.60345i	0.0666372	−	0.115419i	−0.830782	−	0.556598i	$-0.812106\pi$
$193$	0.925754	−	1.60345i	0.0666372	−	0.115419i	0.897419	+	0.441179i	$0.145440\pi$
$194$	−31.5180	−	6.69935i	−2.26286	−	0.480986i
$195$	−0.0990428	−	1.35208i	−0.00709260	−	0.0968245i
$196$	12.3849	−	2.63249i	0.884634	−	0.188035i
$197$	5.40845	−	16.6455i	0.385336	−	1.18594i	−0.550900	−	0.834571i	$-0.685715\pi$
$197$	5.40845	−	16.6455i	0.385336	−	1.18594i	0.936236	−	0.351371i	$-0.114285\pi$
$198$	−13.3958	−	1.41317i	−0.951999	−	0.100430i
$199$	−20.1811			−1.43060			−0.715300	−	0.698817i	$-0.753710\pi$
$199$	−20.1811			−1.43060			−0.715300	+	0.698817i	$0.753710\pi$
$200$	15.4219	−	7.65589i	1.09049	−	0.541353i
$201$	−1.28631	−	8.13159i	−0.0907295	−	0.573558i
$202$	−1.49967	−	14.2684i	−0.105516	−	1.00392i
$203$	−8.89344	−	9.87717i	−0.624197	−	0.693241i
$204$	−15.6663	−	2.48440i	−1.09686	−	0.173943i
$205$	5.84692	+	1.76522i	0.408367	+	0.123289i
$206$	5.76183	+	17.7331i	0.401446	+	1.23552i
$207$	−16.8300	−	15.1656i	−1.16977	−	1.05408i
$208$	−0.120189	−	0.369903i	−0.00833360	−	0.0256482i
$209$	1.02539	−	9.75595i	0.0709279	−	0.674833i
$210$	−16.1108	−	3.96032i	−1.11175	−	0.273288i
$211$	0.0863484	+	0.821550i	0.00594447	+	0.0565578i	0.997092	−	0.0762073i	$-0.0242811\pi$
$211$	0.0863484	+	0.821550i	0.00594447	+	0.0565578i	−0.991148	+	0.132765i	$0.957614\pi$
$212$	7.46302	−	3.32275i	0.512563	−	0.228208i
$213$	−23.5225	+	1.22822i	−1.61173	+	0.0841561i
$214$	27.6941	+	12.3302i	1.89313	+	0.842877i
$215$	−3.31700	+	17.3893i	−0.226218	+	1.18594i
$216$	2.80931	−	17.6712i	0.191149	−	1.20237i
$217$	3.98162	+	12.2542i	0.270290	+	0.831867i
$218$	−5.94608	−	10.2989i	−0.402719	−	0.697530i
$219$	18.7734	+	12.1967i	1.26859	+	0.824178i
$220$	−5.77467	+	13.7378i	−0.389328	+	0.926202i
$221$	0.617792	+	0.686127i	0.0415572	+	0.0461539i
$222$	13.3189	−	16.4410i	0.893905	−	1.10345i
$223$	−4.47037	−	1.99034i	−0.299358	−	0.133283i	0.251561	−	0.967841i	$-0.419056\pi$
$223$	−4.47037	−	1.99034i	−0.299358	−	0.133283i	−0.550919	+	0.834559i	$0.685723\pi$
$224$	7.85196			0.524631
$225$	−11.5542	−	9.56557i	−0.770281	−	0.637705i
$226$	−31.2669			−2.07984
$227$	−15.2860	−	6.80578i	−1.01457	−	0.451716i	−0.169021	−	0.985613i	$-0.554060\pi$
$227$	−15.2860	−	6.80578i	−1.01457	−	0.451716i	−0.845550	+	0.533897i	$0.820727\pi$
$228$	30.3554	+	4.81382i	2.01033	+	0.318803i
$229$	2.47511	+	2.74889i	0.163560	+	0.181652i	0.819354	−	0.573289i	$-0.194333\pi$
$229$	2.47511	+	2.74889i	0.163560	+	0.181652i	−0.655794	+	0.754940i	$0.727666\pi$
$230$	−33.7870	+	20.4626i	−2.22785	+	1.34927i
$231$	5.42496	−	2.76284i	0.356936	−	0.181781i
$232$	−12.4967	−	21.6450i	−0.820450	−	1.42106i
$233$	0.0866930	+	0.266814i	0.00567945	+	0.0174795i	0.953856	−	0.300264i	$-0.0970748\pi$
$233$	0.0866930	+	0.266814i	0.00567945	+	0.0174795i	−0.948177	+	0.317744i	$0.897075\pi$
$234$	−1.82617	+	1.64301i	−0.119380	+	0.107407i
$235$	22.0262	+	12.1087i	1.43683	+	0.789886i
$236$	−18.4082	−	8.19586i	−1.19827	−	0.533505i
$237$	6.13663	+	9.45356i	0.398617	+	0.614075i
$238$	10.3218	−	4.59556i	0.669062	−	0.297886i
$239$	−1.97184	−	18.7608i	−0.127548	−	1.21354i	−0.851750	−	0.523949i	$-0.824458\pi$
$239$	−1.97184	−	18.7608i	−0.127548	−	1.21354i	0.724202	−	0.689588i	$-0.242208\pi$
$240$	−3.87406	−	1.87366i	−0.250069	−	0.120945i
$241$	−1.59183	+	15.1453i	−0.102539	+	0.975592i	0.815408	+	0.578887i	$0.196513\pi$
$241$	−1.59183	+	15.1453i	−0.102539	+	0.975592i	−0.917946	+	0.396704i	$0.870154\pi$
$242$	5.28830	+	16.2757i	0.339945	+	1.04624i
$243$	−15.0612	+	4.02009i	−0.966175	+	0.257889i
$244$	−8.78684	−	27.0431i	−0.562520	−	1.73126i
$245$	−7.70065	+	2.68174i	−0.491976	+	0.171330i
$246$	−3.96398	−	10.3325i	−0.252734	−	0.658774i
$247$	−1.19704	−	1.32945i	−0.0761661	−	0.0845910i
$248$	2.53267	+	24.0968i	0.160825	+	1.53015i
$249$	15.1419	+	5.81577i	0.959578	+	0.368559i
$250$	−21.7834	+	14.4738i	−1.37770	+	0.915406i
$251$	8.19742			0.517417			0.258708	−	0.965956i	$-0.416703\pi$
$251$	8.19742			0.517417			0.258708	+	0.965956i	$0.416703\pi$
$252$	7.75147	+	17.4281i	0.488296	+	1.09787i
$253$	4.47918	−	13.7855i	0.281604	−	0.866687i
$254$	25.9634	−	5.51870i	1.62909	−	0.346274i
$255$	10.2104	+	0.322737i	0.639397	+	0.0202105i
$256$	21.9899	+	4.67410i	1.37437	+	0.292132i
$257$	8.09787	−	14.0259i	0.505131	−	0.874913i	−0.494851	−	0.868978i	$-0.664777\pi$
$257$	8.09787	−	14.0259i	0.505131	−	0.874913i	0.999982	−	0.00593500i	$-0.00188918\pi$
$258$	28.5837	−	14.5572i	1.77954	−	0.906290i
$259$	−0.999604	+	9.51059i	−0.0621123	+	0.590959i
$260$	1.15714	+	2.45899i	0.0717629	+	0.152500i
$261$	−12.8054	+	17.6108i	−0.792633	+	1.09008i
$262$	−8.89732	−	6.46428i	−0.549678	−	0.399365i
$263$	−1.80260	+	17.1506i	−0.111153	+	1.05755i	0.786724	+	0.617305i	$0.211776\pi$
$263$	−1.80260	+	17.1506i	−0.111153	+	1.05755i	−0.897877	+	0.440247i	$0.854891\pi$
$264$	11.0587	−	2.96090i	0.680619	−	0.182231i
$265$	−4.50018	+	2.72547i	−0.276444	+	0.167424i
$266$	−19.9997	+	8.90443i	−1.22626	+	0.545966i
$267$	15.3572	+	9.97727i	0.939843	+	0.610599i
$268$	8.25164	+	14.2923i	0.504049	+	0.873039i
$269$	−5.23420	−	16.1092i	−0.319135	−	0.982196i	−0.974019	−	0.226467i	$-0.927283\pi$
$269$	−5.23420	−	16.1092i	−0.319135	−	0.982196i	0.654884	−	0.755729i	$-0.272717\pi$
$270$	−0.869148	+	27.1657i	−0.0528947	+	1.65325i
$271$	−4.11591	+	12.6675i	−0.250024	+	0.769494i	0.744746	+	0.667349i	$0.232571\pi$
$271$	−4.11591	+	12.6675i	−0.250024	+	0.769494i	−0.994769	+	0.102146i	$0.967429\pi$
$272$	2.86668	−	0.609332i	0.173818	−	0.0369462i
$273$	0.287558	−	1.07235i	0.0174038	−	0.0649018i
$274$	−11.5905	+	20.0754i	−0.700210	+	1.21280i
$275$	2.58069	−	9.24373i	0.155621	−	0.557418i
$276$	42.3945	+	16.2831i	2.55185	+	0.980127i
$277$	17.7559	+	7.90542i	1.06685	+	0.474991i	0.863621	−	0.504141i	$-0.168191\pi$
$277$	17.7559	+	7.90542i	1.06685	+	0.474991i	0.203225	+	0.979132i	$0.434858\pi$
$278$	−6.71617	+	20.6703i	−0.402809	+	1.23972i
$279$	18.2847	−	10.5473i	1.09468	−	0.631451i
$280$	13.9890	−	1.76737i	0.836003	−	0.105621i
$281$	−10.1495	+	11.2721i	−0.605466	+	0.672438i	−0.965471	−	0.260512i	$-0.916109\pi$
$281$	−10.1495	+	11.2721i	−0.605466	+	0.672438i	0.360004	+	0.932951i	$0.382775\pi$
$282$	−7.11602	−	44.9848i	−0.423753	−	2.67881i
$283$	19.8178	+	4.21241i	1.17805	+	0.250402i	0.755012	−	0.655711i	$-0.227631\pi$
$283$	19.8178	+	4.21241i	1.17805	+	0.250402i	0.423036	+	0.906113i	$0.360964\pi$
$284$	43.1352	−	19.2050i	2.55961	−	1.13961i
$285$	−19.7838	−	0.625340i	−1.17189	−	0.0370419i
$286$	−1.43582	−	0.639269i	−0.0849019	−	0.0378007i
$287$	4.04649	+	2.93995i	0.238857	+	0.173540i
$288$	−2.66965	−	12.5835i	−0.157310	−	0.741492i
$289$	8.12493	−	5.90310i	0.477937	−	0.347241i
$290$	22.9539	+	30.2400i	1.34790	+	1.77575i
$291$	−12.9903	−	20.0117i	−0.761504	−	1.17311i
$292$	−43.8973	−	9.33065i	−2.56889	−	0.546035i
$293$	−8.88207	+	15.3842i	−0.518896	+	0.898754i	0.480863	+	0.876796i	$0.340323\pi$
$293$	−8.88207	+	15.3842i	−0.518896	+	0.898754i	−0.999759	+	0.0219583i	$0.993010\pi$
$294$	12.3900	+	8.04957i	0.722601	+	0.469460i
$295$	12.4233	+	3.75067i	0.723311	+	0.218372i
$296$	−5.55703	+	17.1028i	−0.322996	+	0.994079i
$297$	−6.27218	−	7.75466i	−0.363949	−	0.449971i
$298$	−25.6419	+	18.6299i	−1.48539	+	1.07920i
$299$	−1.32169	−	2.28924i	−0.0764354	−	0.132390i
$300$	28.4968	+	9.59569i	1.64526	+	0.554007i
$301$	−7.24878	+	12.5553i	−0.417813	+	0.723673i
$302$	0.449680	+	4.27841i	0.0258761	+	0.246195i
$303$	6.68683	−	8.25429i	0.384148	−	0.474197i
$304$	−5.55453	+	1.18065i	−0.318574	+	0.0677150i
$305$	7.79724	+	16.5695i	0.446469	+	0.948769i
$306$	−10.8742	−	14.9792i	−0.621637	−	0.856303i
$307$	8.60655			0.491202			0.245601	−	0.969371i	$-0.421015\pi$
$307$	8.60655			0.491202			0.245601	+	0.969371i	$0.421015\pi$
$308$	−8.16604	+	9.06930i	−0.465303	+	0.516771i
$309$	−6.27009	+	12.2999i	−0.356693	+	0.699717i
$310$	−8.40471	−	35.8320i	−0.477356	−	2.03512i
$311$	−1.67359	−	15.9231i	−0.0949005	−	0.902918i	−0.933598	−	0.358321i	$-0.883349\pi$
$311$	−1.67359	−	15.9231i	−0.0949005	−	0.902918i	0.838698	−	0.544597i	$-0.183317\pi$
$312$	0.948188	−	1.86004i	0.0536806	−	0.105304i
$313$	−0.888904	+	8.45736i	−0.0502438	+	0.478038i	0.940250	+	0.340484i	$0.110591\pi$
$313$	−0.888904	+	8.45736i	−0.0502438	+	0.478038i	−0.990494	+	0.137554i	$0.956076\pi$
$314$	−0.641902	+	0.466369i	−0.0362246	+	0.0263187i
$315$	−6.35955	−	10.5098i	−0.358320	−	0.592158i
$316$	−18.2783	−	13.2799i	−1.02823	−	0.747055i
$317$	12.6616	−	14.0621i	0.711146	−	0.789807i	−0.273963	−	0.961740i	$-0.588335\pi$
$317$	12.6616	−	14.0621i	0.711146	−	0.789807i	0.985109	+	0.171933i	$0.0550013\pi$
$318$	8.89923	+	3.41806i	0.499044	+	0.191675i
$319$	−13.6270	−	2.89652i	−0.762968	−	0.162174i
$320$	−27.3016	−	2.29230i	−1.52621	−	0.128143i
$321$	8.03996	+	20.9569i	0.448747	+	1.16970i
$322$	−31.6416	+	6.72563i	−1.76332	+	0.374804i
$323$	10.9056	−	7.92339i	0.606805	−	0.440869i
$324$	25.2948	−	18.3480i	1.40527	−	1.01933i
$325$	−0.937838	−	1.47773i	−0.0520219	−	0.0819696i
$326$	−21.6519	−	37.5021i	−1.19919	−	2.07705i
$327$	2.28062	−	8.50485i	0.126119	−	0.470319i
$328$	6.29360	+	6.98975i	0.347506	+	0.385944i
$329$	13.7735	+	15.2970i	0.759358	+	0.843352i
$330$	−16.1020	+	6.56767i	−0.886385	+	0.361538i
$331$	−3.12999	+	3.47621i	−0.172040	+	0.191070i	−0.822998	−	0.568044i	$-0.807701\pi$
$331$	−3.12999	+	3.47621i	−0.172040	+	0.191070i	0.650959	+	0.759113i	$0.274367\pi$
$332$	−32.5153			−1.78451
$333$	15.5815	−	1.63161i	0.853861	−	0.0894119i
$334$	18.7897	+	13.6515i	1.02812	+	0.746976i
$335$	−6.42599	−	8.46575i	−0.351090	−	0.462534i
$336$	−2.49150	−	2.49246i	−0.135923	−	0.135975i
$337$	−22.7914	+	10.1474i	−1.24153	+	0.552764i	−0.919173	−	0.393854i	$-0.871142\pi$
$337$	−22.7914	+	10.1474i	−1.24153	+	0.552764i	−0.322356	+	0.946618i	$0.604475\pi$
$338$	27.5192	−	12.2524i	1.49685	−	0.666440i
$339$	−16.3671	−	16.3734i	−0.888936	−	0.889279i
$340$	−19.3388	+	6.73470i	−1.04879	+	0.365240i
$341$	10.9263	+	7.93842i	0.591692	+	0.429890i
$342$	21.0700	+	29.0239i	1.13934	+	1.56944i
$343$	−19.4963			−1.05270
$344$	−18.2420	+	20.2598i	−0.983544	+	1.09234i
$345$	−28.4018	−	6.98165i	−1.52910	−	0.375880i
$346$	−14.7955	−	16.4321i	−0.795410	−	0.883393i
$347$	22.2680	+	24.7312i	1.19541	+	1.32764i	0.931784	+	0.363013i	$0.118252\pi$
$347$	22.2680	+	24.7312i	1.19541	+	1.32764i	0.263626	+	0.964625i	$0.415081\pi$
$348$	11.3052	−	42.1592i	0.606024	−	2.25997i
$349$	−5.88580	−	10.1945i	−0.315060	−	0.545700i	0.664390	−	0.747386i	$-0.268691\pi$
$349$	−5.88580	−	10.1945i	−0.315060	−	0.545700i	−0.979450	+	0.201686i	$0.935358\pi$
$350$	−20.7452	+	5.32691i	−1.10888	+	0.284736i
$351$	−1.81632	−	0.0962417i	−0.0969480	−	0.00513700i
$352$	6.65847	−	4.83766i	0.354898	−	0.257848i
$353$	−8.12194	+	1.72637i	−0.432287	+	0.0918855i	−0.418916	−	0.908025i	$-0.637590\pi$
$353$	−8.12194	+	1.72637i	−0.432287	+	0.0918855i	−0.0133714	+	0.999911i	$0.504256\pi$
$354$	−8.42249	−	21.9540i	−0.447650	−	1.16684i
$355$	−26.0104	+	15.7528i	−1.38049	+	0.836073i
$356$	−35.9092	−	7.63274i	−1.90319	−	0.404535i
$357$	7.80961	+	2.99955i	0.413328	+	0.158753i
$358$	13.3462	−	14.8225i	0.705369	−	0.783392i
$359$	−18.6157	−	13.5251i	−0.982499	−	0.713828i	−0.0242336	−	0.999706i	$-0.507715\pi$
$359$	−18.6157	−	13.5251i	−0.982499	−	0.713828i	−0.958266	+	0.285879i	$0.907715\pi$
$360$	−7.58861	−	21.8178i	−0.399955	−	1.14990i
$361$	−5.75958	+	4.18458i	−0.303136	+	0.220241i
$362$	0.787276	−	7.49043i	0.0413783	−	0.393688i
$363$	−5.75479	+	11.2890i	−0.302048	+	0.592521i
$364$	0.232637	+	2.21339i	0.0121935	+	0.116013i
$365$	28.8008	+	2.41817i	1.50750	+	0.126573i
$366$	15.0699	−	29.5622i	0.787714	−	1.54524i
$367$	23.6129	−	26.2247i	1.23258	−	1.36892i	0.326845	−	0.945078i	$-0.394014\pi$
$367$	23.6129	−	26.2247i	1.23258	−	1.36892i	0.905736	−	0.423842i	$-0.139319\pi$
$368$	−8.39081			−0.437401
$369$	3.33576	−	7.48447i	0.173652	−	0.389626i
$370$	5.11823	−	26.8322i	0.266084	−	1.39494i
$371$	−4.21442	+	0.895802i	−0.218802	+	0.0465077i
$372$	−26.6357	+	32.8794i	−1.38100	+	1.70472i
$373$	−2.06339	−	19.6318i	−0.106838	−	1.01650i	−0.908262	−	0.418401i	$-0.862591\pi$
$373$	−2.06339	−	19.6318i	−0.106838	−	1.01650i	0.801424	−	0.598096i	$-0.204076\pi$
$374$	5.92152	−	10.2564i	0.306195	−	0.530344i
$375$	−18.9823	−	3.83069i	−0.980239	−	0.197816i
$376$	19.3540	+	33.5221i	0.998106	+	1.72877i
$377$	−2.05541	+	1.49334i	−0.105859	+	0.0769112i
$378$	−7.98871	+	20.7754i	−0.410895	+	1.06857i
$379$	−3.23744	+	9.96380i	−0.166296	+	0.511806i	−0.999129	−	0.0417174i	$-0.986717\pi$
$379$	−3.23744	+	9.96380i	−0.166296	+	0.511806i	0.832834	+	0.553524i	$0.186717\pi$
$380$	37.4712	−	13.0493i	1.92223	−	0.669413i
$381$	16.4808	+	10.7073i	0.844339	+	0.548552i
$382$	−10.5169	+	18.2158i	−0.538092	+	0.932003i
$383$	−12.3836	−	2.63221i	−0.632770	−	0.134500i	−0.119650	−	0.992816i	$-0.538177\pi$
$383$	−12.3836	−	2.63221i	−0.632770	−	0.134500i	−0.513120	+	0.858317i	$0.671511\pi$
$384$	18.9425	+	29.1812i	0.966656	+	1.48915i
$385$	4.48548	−	6.45390i	0.228601	−	0.328921i
$386$	−3.50396	+	2.54578i	−0.178347	+	0.129577i
$387$	22.5856	+	7.34812i	1.14809	+	0.373526i
$388$	38.6923	+	28.1116i	1.96430	+	1.42715i
$389$	1.65129	+	0.735200i	0.0837236	+	0.0372761i	0.448171	−	0.893948i	$-0.352076\pi$
$389$	1.65129	+	0.735200i	0.0837236	+	0.0372761i	−0.364448	+	0.931224i	$0.618742\pi$
$390$	−1.07479	+	2.98364i	−0.0544242	+	0.151083i
$391$	18.1963	−	8.10152i	0.920227	−	0.409712i
$392$	−12.2831	−	2.61085i	−0.620389	−	0.131868i
$393$	−1.27230	−	8.04303i	−0.0641792	−	0.405717i
$394$	−27.3954	+	30.4256i	−1.38016	+	1.53282i
$395$	12.7507	+	7.00957i	0.641556	+	0.352690i
$396$	17.3109	+	10.0033i	0.869904	+	0.502686i
$397$	8.63713	−	26.5824i	0.433485	−	1.33413i	−0.461146	−	0.887324i	$-0.652561\pi$
$397$	8.63713	−	26.5824i	0.433485	−	1.33413i	0.894631	−	0.446806i	$-0.147439\pi$
$398$	43.1272	+	19.2015i	2.16177	+	0.962482i
$399$	−15.1320	−	5.81199i	−0.757549	−	0.290963i
$400$	−5.55074	+	0.232760i	−0.277537	+	0.0116380i
$401$	9.31544	−	16.1348i	0.465191	−	0.805734i	−0.534019	−	0.845472i	$-0.679319\pi$
$401$	9.31544	−	16.1348i	0.465191	−	0.805734i	0.999210	+	0.0397380i	$0.0126523\pi$
$402$	−4.98800	+	18.6011i	−0.248779	+	0.927741i
$403$	2.40915	−	0.512081i	0.120008	−	0.0255086i
$404$	−6.58044	+	20.2525i	−0.327389	+	1.00760i
$405$	−14.6807	+	13.7651i	−0.729489	+	0.683993i
$406$	9.60765	+	29.5693i	0.476820	+	1.46750i
$407$	5.01189	+	8.68085i	0.248430	+	0.430294i
$408$	13.1921	+	8.57066i	0.653106	+	0.424311i
$409$	−32.3359	+	14.3969i	−1.59891	+	0.711879i	−0.996283	−	0.0861459i	$-0.972545\pi$
$409$	−32.3359	+	14.3969i	−1.59891	+	0.711879i	−0.602624	+	0.798025i	$0.705878\pi$
$410$	−10.8154	−	9.33539i	−0.534133	−	0.461042i
$411$	−16.5800	+	4.43918i	−0.817832	+	0.218969i
$412$	2.89285	−	27.5236i	0.142520	−	1.35599i
$413$	8.59780	+	6.24667i	0.423070	+	0.307378i
$414$	21.5365	+	48.4220i	1.05846	+	2.37981i
$415$	20.7752	−	2.62474i	1.01982	−	0.128843i
$416$	0.156890	−	1.49271i	0.00769216	−	0.0731860i
$417$	−14.3400	+	7.30310i	−0.702231	+	0.357634i
$418$	−11.4736	+	19.8729i	−0.561194	+	0.972017i
$419$	−2.54495	−	0.540947i	−0.124329	−	0.0264270i	0.145327	−	0.989384i	$-0.453577\pi$
$419$	−2.54495	−	0.540947i	−0.124329	−	0.0264270i	−0.269656	+	0.962957i	$0.586910\pi$
$420$	19.4546	+	15.0962i	0.949286	+	0.736619i
$421$	6.57273	−	1.39708i	0.320335	−	0.0680893i	−0.0449378	−	0.998990i	$-0.514309\pi$
$421$	6.57273	−	1.39708i	0.320335	−	0.0680893i	0.365273	+	0.930900i	$0.380976\pi$
$422$	0.597142	−	1.83781i	0.0290684	−	0.0894634i
$423$	19.8320	−	27.2743i	0.964265	−	1.32612i
$424$	−8.10215			−0.393475
$425$	11.8126	−	5.86414i	0.572996	−	0.284452i
$426$	51.4363	+	19.7559i	2.49210	+	0.957177i
$427$	1.56759	+	14.9147i	0.0758612	+	0.721771i
$428$	−30.1079	−	33.4383i	−1.45532	−	1.61630i
$429$	−0.416837	−	1.08652i	−0.0201251	−	0.0524578i
$430$	23.6336	−	34.0051i	1.13972	−	1.63987i
$431$	−8.85920	−	27.2658i	−0.426732	−	1.31335i	−0.901326	−	0.433142i	$-0.857405\pi$
$431$	−8.85920	−	27.2658i	−0.426732	−	1.31335i	0.474593	−	0.880205i	$-0.342595\pi$
$432$	−3.14731	+	4.84031i	−0.151425	+	0.232879i
$433$	−5.20231	−	16.0111i	−0.250007	−	0.769443i	−0.994772	−	0.102116i	$-0.967439\pi$
$433$	−5.20231	−	16.0111i	−0.250007	−	0.769443i	0.744765	−	0.667327i	$-0.232561\pi$
$434$	3.15056	−	29.9756i	0.151232	−	1.43887i
$435$	−3.82010	+	27.8497i	−0.183160	+	1.33529i
$436$	1.84505	+	17.5545i	0.0883618	+	0.840706i
$437$	−35.2575	+	15.6976i	−1.68659	+	0.750920i
$438$	−28.5142	−	43.9265i	−1.36246	−	2.09889i
$439$	7.10691	+	3.16420i	0.339194	+	0.151019i	0.569263	−	0.822155i	$-0.307229\pi$
$439$	7.10691	+	3.16420i	0.339194	+	0.151019i	−0.230069	+	0.973174i	$0.573895\pi$
$440$	10.7738	−	10.1175i	0.513621	−	0.482332i
$441$	2.27045	+	10.7019i	0.108116	+	0.509613i
$442$	−0.667405	−	2.05406i	−0.0317452	−	0.0977017i
$443$	6.75591	+	11.7016i	0.320983	+	0.555959i	0.980691	−	0.195563i	$-0.0626534\pi$
$443$	6.75591	+	11.7016i	0.320983	+	0.555959i	−0.659708	+	0.751522i	$0.729320\pi$
$444$	−27.9852	+	14.2524i	−1.32812	+	0.676389i
$445$	23.5599	+	1.97813i	1.11685	+	0.0937725i
$446$	7.65950	+	8.50673i	0.362688	+	0.402806i
$447$	−23.1784	−	3.67568i	−1.09630	−	0.173853i
$448$	−20.4973	−	9.12598i	−0.968405	−	0.431162i
$449$	−32.5272			−1.53506			−0.767528	−	0.641016i	$-0.778513\pi$
$449$	−32.5272			−1.53506			−0.767528	+	0.641016i	$0.778513\pi$
$450$	15.5902	+	31.4350i	0.734929	+	1.48186i
$451$	5.24275			0.246872
$452$	42.3962	+	18.8760i	1.99415	+	0.887853i
$453$	−2.00507	+	2.47507i	−0.0942062	+	0.116289i
$454$	26.1910	+	29.0880i	1.22920	+	1.36517i
$455$	−0.327313	−	1.39544i	−0.0153447	−	0.0654192i
$456$	−25.5612	−	16.6067i	−1.19701	−	0.777678i
$457$	−1.62771	−	2.81927i	−0.0761410	−	0.131880i	0.825441	−	0.564489i	$-0.190927\pi$
$457$	−1.62771	−	2.81927i	−0.0761410	−	0.131880i	−0.901582	+	0.432608i	$0.857593\pi$
$458$	−2.67388	−	8.22935i	−0.124942	−	0.384532i
$459$	2.15183	−	13.5355i	0.100439	−	0.631783i
$460$	58.1669	−	7.34880i	2.71204	−	0.342639i
$461$	−23.3371	−	10.3904i	−1.08692	−	0.483927i	−0.216521	−	0.976278i	$-0.569471\pi$
$461$	−23.3371	−	10.3904i	−1.08692	−	0.483927i	−0.870397	+	0.492351i	$0.836138\pi$
$462$	−14.2219	+	0.742591i	−0.661662	+	0.0345485i
$463$	30.0355	−	13.3727i	1.39587	−	0.621481i	0.435494	−	0.900192i	$-0.356574\pi$
$463$	30.0355	−	13.3727i	1.39587	−	0.621481i	0.960375	+	0.278711i	$0.0899072\pi$
$464$	0.842984	+	8.02046i	0.0391346	+	0.372340i
$465$	14.3644	−	23.1580i	0.666134	−	1.07393i
$466$	0.0685981	−	0.652668i	0.00317775	−	0.0302342i
$467$	−3.22065	−	9.91215i	−0.149034	−	0.458680i	0.848474	−	0.529238i	$-0.177522\pi$
$467$	−3.22065	−	9.91215i	−0.149034	−	0.458680i	−0.997508	+	0.0705580i	$0.977522\pi$
$468$	3.46808	−	1.12537i	0.160312	−	0.0520203i
$469$	−2.68968	−	8.27799i	−0.124198	−	0.382242i
$470$	−35.5493	−	46.8334i	−1.63977	−	2.16027i
$471$	−0.580233	−	0.0920145i	−0.0267357	−	0.00423980i
$472$	13.3723	+	14.8515i	0.615512	+	0.683595i
$473$	1.58843	+	15.1129i	0.0730361	+	0.694892i
$474$	−4.11936	−	26.0411i	−0.189208	−	1.19611i
$475$	−22.8883	+	11.3625i	−1.05019	+	0.521345i
$476$	−16.7702			−0.768659
$477$	2.86850	+	6.44944i	0.131340	+	0.295300i
$478$	−13.6363	+	41.9682i	−0.623709	+	1.91958i
$479$	25.2389	−	5.36469i	1.15319	−	0.245119i	0.408650	−	0.912691i	$-0.366000\pi$
$479$	25.2389	−	5.36469i	1.15319	−	0.245119i	0.744545	+	0.667572i	$0.232666\pi$
$480$	−10.7167	−	12.6862i	−0.489148	−	0.579043i
$481$	1.78805	+	0.380062i	0.0815281	+	0.0173293i
$482$	17.8118	−	30.8510i	0.811306	−	1.40522i
$483$	−20.0852	−	13.0490i	−0.913907	−	0.593749i
$484$	2.65510	−	25.2616i	0.120686	−	1.14825i
$485$	−26.9912	−	14.8382i	−1.22561	−	0.673766i
$486$	36.0108	+	5.73910i	1.63348	+	0.260331i
$487$	−2.52369	−	1.83357i	−0.114359	−	0.0830868i	0.529136	−	0.848537i	$-0.322516\pi$
$487$	−2.52369	−	1.83357i	−0.114359	−	0.0830868i	−0.643495	+	0.765450i	$0.722516\pi$
$488$	−2.94782	+	28.0466i	−0.133441	+	1.26961i
$489$	8.30459	−	30.9693i	0.375547	−	1.40048i
$490$	19.0079	+	1.59594i	0.858689	+	0.0720972i
$491$	−3.78904	+	1.68699i	−0.170997	+	0.0761328i	−0.490450	−	0.871469i	$-0.663168\pi$
$491$	−3.78904	+	1.68699i	−0.170997	+	0.0761328i	0.319453	+	0.947602i	$0.396501\pi$
$492$	−0.862832	+	16.4034i	−0.0388995	+	0.739521i
$493$	−9.57204	−	16.5793i	−0.431103	−	0.746692i
$494$	1.29318	+	3.97999i	0.0581827	+	0.179068i
$495$	−11.8681	−	4.99411i	−0.533429	−	0.224468i
$496$	2.41594	−	7.43548i	0.108479	−	0.333863i
$497$	−24.3588	+	5.17761i	−1.09264	+	0.232248i
$498$	−26.8248	−	26.8352i	−1.20205	−	1.20251i
$499$	−5.49337	+	9.51479i	−0.245917	+	0.425941i	−0.962389	−	0.271675i	$-0.912422\pi$
$499$	−5.49337	+	9.51479i	−0.245917	+	0.425941i	0.716472	+	0.697616i	$0.245756\pi$
$500$	38.2751	−	6.47497i	1.71171	−	0.289569i
$501$	2.68689	+	16.9855i	0.120041	+	0.758858i
$502$	−17.5179	−	7.79949i	−0.781864	−	0.348108i
$503$	−0.0760290	+	0.233993i	−0.00338996	+	0.0104332i	−0.952737	−	0.303796i	$-0.901746\pi$
$503$	−0.0760290	+	0.233993i	−0.00338996	+	0.0104332i	0.949347	+	0.314229i	$0.101746\pi$
$504$	0.00728756	−	18.9174i	0.000324614	−	0.842649i
$505$	2.56964	−	13.4713i	0.114347	−	0.599464i
$506$	−22.6884	+	25.1980i	−1.00862	+	1.12019i
$507$	20.8214	+	7.99721i	0.924713	+	0.355168i
$508$	−38.5367	−	8.19123i	−1.70979	−	0.363427i
$509$	14.0356	−	6.24904i	0.622115	−	0.276984i	−0.0713749	−	0.997450i	$-0.522739\pi$
$509$	14.0356	−	6.24904i	0.622115	−	0.276984i	0.693490	+	0.720466i	$0.256072\pi$
$510$	−21.5125	−	10.4044i	−0.952591	−	0.460715i
$511$	21.6228	+	9.62709i	0.956536	+	0.425877i
$512$	−10.0453	−	7.29837i	−0.443946	−	0.322546i
$513$	−4.16942	+	26.2266i	−0.184085	+	1.15793i
$514$	−30.6503	+	22.2687i	−1.35192	+	0.982231i
$515$	0.373447	+	17.8194i	0.0164560	+	0.785215i
$516$	−47.5462	+	2.48261i	−2.09311	+	0.109291i
$517$	21.1046	+	4.48591i	0.928177	+	0.197290i
$518$	11.1851	−	19.3731i	0.491444	−	0.851206i
$519$	0.859996	−	16.3495i	0.0377497	−	0.717661i
$520$	−0.0564741	−	2.69471i	−0.00247655	−	0.118171i
$521$	−3.21801	+	9.90401i	−0.140983	+	0.433902i	−0.996473	−	0.0839183i	$-0.973257\pi$
$521$	−3.21801	+	9.90401i	−0.140983	+	0.433902i	0.855489	+	0.517821i	$0.173257\pi$
$522$	44.1211	−	25.4507i	1.93113	−	1.11395i
$523$	8.70698	−	6.32599i	0.380730	−	0.276616i	−0.380916	−	0.924609i	$-0.624391\pi$
$523$	8.70698	−	6.32599i	0.380730	−	0.276616i	0.761646	+	0.647993i	$0.224391\pi$
$524$	8.16176	+	14.1366i	0.356548	+	0.617560i
$525$	−13.6489	−	8.07508i	−0.595685	−	0.352425i
$526$	20.1702	−	34.9359i	0.879464	−	1.52328i
$527$	1.93993	+	18.4572i	0.0845049	+	0.804010i
$528$	−3.64842	−	0.578574i	−0.158777	−	0.0251792i
$529$	−33.2836	+	7.07466i	−1.44712	+	0.307594i
$530$	12.2101	−	1.54262i	0.530372	−	0.0670071i
$531$	7.08766	−	15.9027i	0.307578	−	0.690116i
$532$	32.4942			1.40880
$533$	0.639756	−	0.710521i	0.0277109	−	0.0307761i
$534$	−23.3254	−	35.9332i	−1.00939	−	1.55498i
$535$	21.9363	+	18.9345i	0.948390	+	0.818611i
$536$	−1.71088	−	16.2780i	−0.0738989	−	0.703101i
$537$	14.7483	−	0.770075i	0.636434	−	0.0332312i
$538$	−4.14170	+	39.4056i	−0.178561	+	1.69890i
$539$	−5.66281	+	4.11427i	−0.243914	+	0.177214i
$540$	17.5786	−	36.3105i	0.756463	−	1.56256i
$541$	−18.6252	−	13.5320i	−0.800760	−	0.581786i	0.110377	−	0.993890i	$-0.464794\pi$
$541$	−18.6252	−	13.5320i	−0.800760	−	0.581786i	−0.911137	+	0.412104i	$0.864794\pi$
$542$	20.8483	−	23.1544i	0.895511	−	0.994566i
$543$	4.33458	−	3.50869i	0.186015	−	0.150572i
$544$	11.0626	+	2.35143i	0.474306	+	0.100817i
$545$	−2.59592	−	11.0673i	−0.111197	−	0.474069i
$546$	−1.63481	+	2.01803i	−0.0699634	+	0.0863636i
$547$	−19.2259	+	4.08660i	−0.822041	+	0.174730i	−0.599686	−	0.800235i	$-0.704708\pi$
$547$	−19.2259	+	4.08660i	−0.822041	+	0.174730i	−0.222355	+	0.974966i	$0.571374\pi$
$548$	27.8358	−	20.2239i	1.18909	−	0.863922i
$549$	23.3692	−	7.58316i	0.997373	−	0.323641i
$550$	−14.3100	+	17.2985i	−0.610179	+	0.737611i
$551$	18.5469	+	32.1243i	0.790126	+	1.36854i
$552$	−31.8425	−	31.8548i	−1.35531	−	1.35583i
$553$	7.97328	+	8.85522i	0.339058	+	0.376562i
$554$	−30.4227	−	33.7879i	−1.29254	−	1.43551i
$555$	16.7303	−	11.3654i	0.710161	−	0.482436i
$556$	21.5855	−	23.9732i	0.915431	−	1.01669i
$557$	31.2358			1.32350			0.661751	−	0.749724i	$-0.269814\pi$
$557$	31.2358			1.32350			0.661751	+	0.749724i	$0.269814\pi$
$558$	−49.1099	+	5.14253i	−2.07899	+	0.217701i
$559$	2.24200	+	1.62891i	0.0948264	+	0.0688954i
$560$	−4.35555	−	1.31497i	−0.184055	−	0.0555675i
$561$	8.47060	−	2.26794i	0.357629	−	0.0957526i
$562$	32.4144	−	14.4318i	1.36732	−	0.608770i
$563$	−15.3024	+	6.81308i	−0.644921	+	0.287137i	−0.703016	−	0.711174i	$-0.748164\pi$
$563$	−15.3024	+	6.81308i	−0.644921	+	0.287137i	0.0580954	+	0.998311i	$0.481497\pi$
$564$	−17.5087	+	65.2931i	−0.737249	+	2.74933i
$565$	−28.6122	−	8.63822i	−1.20373	−	0.363413i
$566$	−38.3429	−	27.8578i	−1.61167	−	1.17095i
$567$	−15.0612	+	6.69176i	−0.632509	+	0.281028i
$568$	−46.8293			−1.96491
$569$	13.1713	−	14.6283i	0.552171	−	0.613249i	−0.400853	−	0.916142i	$-0.631286\pi$
$569$	13.1713	−	14.6283i	0.552171	−	0.613249i	0.953024	+	0.302894i	$0.0979528\pi$
$570$	41.6831	+	20.1598i	1.74591	+	0.844399i
$571$	0.969716	+	1.07698i	0.0405813	+	0.0450701i	0.763094	−	0.646288i	$-0.223679\pi$
$571$	0.969716	+	1.07698i	0.0405813	+	0.0450701i	−0.722512	+	0.691358i	$0.757013\pi$
$572$	1.56097	+	1.73363i	0.0652673	+	0.0724867i
$573$	−15.0442	+	4.02798i	−0.628481	+	0.168271i
$574$	−5.85015	−	10.1328i	−0.244180	−	0.422933i
$575$	−36.5717	+	9.39083i	−1.52515	+	0.391625i
$576$	−7.65624	+	35.9517i	−0.319010	+	1.49799i
$577$	31.9709	−	23.2282i	1.33097	−	0.967004i	0.331243	−	0.943546i	$-0.392532\pi$
$577$	31.9709	−	23.2282i	1.33097	−	0.967004i	0.999725	−	0.0234587i	$-0.00746783\pi$
$578$	−22.9796	+	4.88446i	−0.955824	+	0.203167i
$579$	−3.16733	−	0.502281i	−0.131630	−	0.0208741i
$580$	−12.8682	−	54.8612i	−0.534322	−	2.27799i
$581$	16.7742	+	3.56546i	0.695910	+	0.147920i
$582$	8.72004	+	55.1249i	0.361457	+	2.28500i
$583$	−3.02192	+	3.35618i	−0.125155	+	0.138999i
$584$	36.0086	+	26.1618i	1.49005	+	1.08258i
$585$	−2.12504	+	0.998996i	−0.0878597	+	0.0413034i
$586$	33.6184	−	24.4252i	1.38876	−	1.00900i
$587$	−1.25291	+	11.9206i	−0.0517130	+	0.492016i	0.937758	+	0.347288i	$0.112897\pi$
$587$	−1.25291	+	11.9206i	−0.0517130	+	0.492016i	−0.989471	+	0.144728i	$0.953769\pi$
$588$	−11.9406	−	18.3947i	−0.492424	−	0.758586i
$589$	−3.75885	−	35.7631i	−0.154881	−	1.47359i
$590$	−22.9800	−	19.8354i	−0.946072	−	0.816611i
$591$	−30.2733	+	1.58071i	−1.24528	+	0.0650217i
$592$	3.88266	−	4.31214i	0.159577	−	0.177228i
$593$	−23.8651			−0.980022			−0.490011	−	0.871716i	$-0.663007\pi$
$593$	−23.8651			−0.980022			−0.490011	+	0.871716i	$0.663007\pi$
$594$	6.02548	+	22.5395i	0.247228	+	0.924806i
$595$	10.7151	−	1.35374i	0.439275	−	0.0554980i
$596$	46.0160	−	9.78100i	1.88489	−	0.400646i
$597$	12.5204	+	32.6354i	0.512424	+	1.33568i
$598$	0.646354	+	6.14965i	0.0264314	+	0.251478i
$599$	−20.3323	+	35.2166i	−0.830757	+	1.43891i	0.0666825	+	0.997774i	$0.478759\pi$
$599$	−20.3323	+	35.2166i	−0.830757	+	1.43891i	−0.897439	+	0.441138i	$0.854575\pi$
$600$	−21.9483	−	20.1895i	−0.896036	−	0.824231i
$601$	10.9275	+	18.9269i	0.445741	+	0.772046i	0.998104	−	0.0615580i	$-0.0196069\pi$
$601$	10.9275	+	18.9269i	0.445741	+	0.772046i	−0.552363	+	0.833604i	$0.686274\pi$
$602$	27.4365	−	19.9338i	1.11823	−	0.812440i
$603$	−12.3518	+	7.12497i	−0.503004	+	0.290151i
$604$	1.97317	−	6.07278i	0.0802870	−	0.247098i
$605$	0.342755	+	16.3549i	0.0139350	+	0.664921i
$606$	−22.1434	+	11.2773i	−0.899514	+	0.458107i
$607$	−12.4376	+	21.5426i	−0.504827	+	0.874385i	0.495158	+	0.868803i	$0.335110\pi$
$607$	−12.4376	+	21.5426i	−0.504827	+	0.874385i	−0.999984	+	0.00558229i	$0.998223\pi$
$608$	−21.4351	−	4.55618i	−0.869309	−	0.184777i
$609$	−10.4552	+	20.5096i	−0.423664	+	0.831092i
$610$	−0.897560	−	42.8280i	−0.0363412	−	1.73405i
$611$	3.18327	−	2.31278i	0.128781	−	0.0935651i
$612$	5.70181	+	26.8758i	0.230482	+	1.08639i
$613$	−6.49407	−	4.71822i	−0.262293	−	0.190567i	0.448864	−	0.893600i	$-0.351829\pi$
$613$	−6.49407	−	4.71822i	−0.262293	−	0.190567i	−0.711157	+	0.703033i	$0.751829\pi$
$614$	−18.3923	−	8.18876i	−0.742251	−	0.330472i
$615$	−0.772837	−	10.5504i	−0.0311638	−	0.425432i
$616$	11.0572	−	4.92299i	0.445508	−	0.198353i
$617$	7.88641	+	1.67631i	0.317495	+	0.0674857i	0.363903	−	0.931437i	$-0.381444\pi$
$617$	7.88641	+	1.67631i	0.317495	+	0.0674857i	−0.0464078	+	0.998923i	$0.514777\pi$
$618$	25.1021	−	20.3192i	1.00975	−	0.817360i
$619$	23.9530	−	26.6025i	0.962751	−	1.06924i	−0.0348064	−	0.999394i	$-0.511081\pi$
$619$	23.9530	−	26.6025i	0.962751	−	1.06924i	0.997558	−	0.0698494i	$-0.0222519\pi$
$620$	−10.2357	+	53.6603i	−0.411075	+	2.15505i
$621$	−14.0833	+	36.6251i	−0.565145	+	1.46971i
$622$	−11.5737	+	35.6202i	−0.464063	+	1.42824i
$623$	17.6881	+	7.87524i	0.708658	+	0.315515i
$624$	−0.523616	+	0.423849i	−0.0209614	+	0.0169675i
$625$	−23.9327	+	7.22678i	−0.957308	+	0.289071i
$626$	9.94640	−	17.2277i	0.397538	−	0.688556i
$627$	−16.4128	+	4.39440i	−0.655463	+	0.175496i
$628$	1.15194	−	0.244851i	0.0459672	−	0.00977063i
$629$	−4.25648	+	13.1001i	−0.169717	+	0.522336i
$630$	3.59083	+	28.5103i	0.143062	+	1.13588i
$631$	−5.23845	−	16.1223i	−0.208539	−	0.641818i	−0.999549	−	0.0300148i	$-0.990445\pi$
$631$	−5.23845	−	16.1223i	−0.208539	−	0.641818i	0.791010	−	0.611803i	$-0.209555\pi$
$632$	11.2037	+	19.4054i	0.445661	+	0.771907i
$633$	1.27498	−	0.649326i	0.0506760	−	0.0258084i
$634$	−40.4374	+	18.0039i	−1.60597	+	0.715026i
$635$	25.2837	+	2.12287i	1.00335	+	0.0842436i
$636$	−10.0034	−	10.0072i	−0.396660	−	0.396813i
$637$	−0.133430	+	1.26950i	−0.00528668	+	0.0502994i
$638$	26.3652	+	19.1554i	1.04381	+	0.758371i
$639$	16.5795	+	37.2769i	0.655876	+	1.47465i
$640$	39.3587	+	21.6371i	1.55579	+	0.855281i
$641$	1.42670	−	13.5742i	0.0563514	−	0.536148i	−0.929535	−	0.368733i	$-0.879792\pi$
$641$	1.42670	−	13.5742i	0.0563514	−	0.536148i	0.985887	−	0.167415i	$-0.0535418\pi$
$642$	2.75811	−	52.4346i	0.108854	−	2.06943i
$643$	7.28773	−	12.6227i	0.287400	−	0.497792i	−0.685788	−	0.727801i	$-0.740542\pi$
$643$	7.28773	−	12.6227i	0.287400	−	0.497792i	0.973188	+	0.230009i	$0.0738757\pi$
$644$	46.9646	+	9.98264i	1.85066	+	0.393371i
$645$	30.1786	−	5.42431i	1.18828	−	0.213582i
$646$	−30.8441	+	6.55612i	−1.21355	+	0.257947i
$647$	5.64337	−	17.3685i	0.221864	−	0.682826i	−0.776731	−	0.629832i	$-0.783124\pi$
$647$	5.64337	−	17.3685i	0.221864	−	0.682826i	0.998595	−	0.0529938i	$-0.0168763\pi$
$648$	−30.3195	+	6.42019i	−1.19106	+	0.252209i
$649$	11.1396			0.437266
$650$	0.598171	+	4.05023i	0.0234622	+	0.158863i
$651$	17.3464	−	14.0413i	0.679857	−	0.550321i
$652$	6.71850	+	63.9223i	0.263117	+	2.50339i
$653$	−2.34266	−	2.60179i	−0.0916755	−	0.101816i	0.695561	−	0.718467i	$-0.255156\pi$
$653$	−2.34266	−	2.60179i	−0.0916755	−	0.101816i	−0.787237	+	0.616651i	$0.788489\pi$
$654$	−12.9657	+	16.0050i	−0.506999	+	0.625846i
$655$	−6.35600	−	8.37355i	−0.248350	−	0.327182i
$656$	−0.937841	−	2.88638i	−0.0366165	−	0.112694i
$657$	8.07665	−	37.9258i	0.315100	−	1.47963i
$658$	−14.8796	−	45.7947i	−0.580068	−	1.78527i
$659$	−3.96337	+	37.7090i	−0.154391	+	1.46893i	0.593351	+	0.804944i	$0.297804\pi$
$659$	−3.96337	+	37.7090i	−0.154391	+	1.46893i	−0.747742	+	0.663989i	$0.768862\pi$
$660$	25.7984	+	0.815454i	1.00420	+	0.0317415i
$661$	−4.01695	−	38.2188i	−0.156241	−	1.48654i	−0.738897	−	0.673818i	$-0.764653\pi$
$661$	−4.01695	−	38.2188i	−0.156241	−	1.48654i	0.582656	−	0.812719i	$-0.302014\pi$
$662$	9.99628	−	4.45063i	0.388516	−	0.172979i
$663$	0.726278	−	1.42472i	0.0282063	−	0.0553316i
$664$	29.4601	+	13.1165i	1.14327	+	0.509017i
$665$	−20.7617	+	2.62303i	−0.805105	+	0.101717i
$666$	−34.8502	−	11.3384i	−1.35042	−	0.439353i
$667$	16.9374	+	52.1278i	0.655817	+	2.01840i
$668$	−17.2363	−	29.8541i	−0.666892	−	1.15509i
$669$	−0.445213	+	8.46397i	−0.0172129	+	0.327236i
$670$	5.67760	+	24.2054i	0.219345	+	0.935137i
$671$	10.5184	+	11.6818i	0.406057	+	0.450972i
$672$	−4.87136	−	12.6976i	−0.187917	−	0.489822i
$673$	−3.09220	−	1.37674i	−0.119196	−	0.0530693i	0.346272	−	0.938134i	$-0.387447\pi$
$673$	−3.09220	−	1.37674i	−0.119196	−	0.0530693i	−0.465468	+	0.885065i	$0.654114\pi$
$674$	58.3603			2.24795
$675$	−8.30052	+	24.6191i	−0.319487	+	0.947591i
$676$	−44.7115			−1.71967
$677$	−37.2359	−	16.5785i	−1.43109	−	0.637162i	−0.462680	−	0.886525i	$-0.653112\pi$
$677$	−37.2359	−	16.5785i	−1.43109	−	0.637162i	−0.968410	+	0.249363i	$0.919779\pi$
$678$	19.3980	+	50.5625i	0.744974	+	1.94184i
$679$	−16.8782	−	18.7451i	−0.647726	−	0.719372i
$680$	20.2384	+	1.69925i	0.776106	+	0.0651634i
$681$	−1.52237	+	28.9418i	−0.0583372	+	1.10905i
$682$	−15.7965	−	27.3604i	−0.604880	−	1.04768i
$683$	8.88733	+	27.3524i	0.340064	+	1.04661i	0.964173	+	0.265273i	$0.0854622\pi$
$683$	8.88733	+	27.3524i	0.340064	+	1.04661i	−0.624109	+	0.781337i	$0.714538\pi$
$684$	−11.0479	−	52.0751i	−0.422428	−	1.99114i
$685$	−16.1528	+	15.1688i	−0.617167	+	0.579570i
$686$	41.6637	+	18.5499i	1.59073	+	0.708237i
$687$	2.90974	−	5.70798i	0.111014	−	0.217773i
$688$	8.03620	−	3.57795i	0.306377	−	0.136408i
$689$	0.0860895	+	0.819087i	0.00327975	+	0.0312047i
$690$	54.0522	+	41.9430i	2.05773	+	1.59674i
$691$	0.128443	−	1.22205i	0.00488620	−	0.0464891i	−0.991807	−	0.127744i	$-0.959226\pi$
$691$	0.128443	−	1.22205i	0.00488620	−	0.0464891i	0.996693	+	0.0812554i	$0.0258929\pi$
$692$	10.1418	+	31.2131i	0.385532	+	1.18655i
$693$	−7.83351	−	7.05879i	−0.297570	−	0.268141i
$694$	−24.0563	−	74.0377i	−0.913165	−	2.81043i
$695$	−11.8566	+	17.0598i	−0.449747	+	0.647115i
$696$	−27.2497	+	33.6373i	−1.03290	+	1.27502i
$697$	4.82067	+	5.35389i	0.182596	+	0.202793i
$698$	2.87837	+	27.3858i	0.108948	+	1.03657i
$699$	0.377688	−	0.305725i	0.0142855	−	0.0115636i
$700$	31.3453	+	5.30099i	1.18474	+	0.200359i
$701$	1.48967			0.0562639			0.0281319	−	0.999604i	$-0.491044\pi$
$701$	1.48967			0.0562639			0.0281319	+	0.999604i	$0.491044\pi$
$702$	3.78992	+	1.93382i	0.143041	+	0.0729873i
$703$	8.24744	−	25.3830i	0.311058	−	0.957338i
$704$	−23.0043	+	4.88971i	−0.867007	+	0.184288i
$705$	5.91629	−	43.1315i	0.222820	−	1.62443i
$706$	18.9992	+	4.03841i	0.715045	+	0.151987i
$707$	5.61554	−	9.72640i	0.211194	−	0.365799i
$708$	−1.83331	+	34.8531i	−0.0688999	+	1.30986i
$709$	0.602510	−	5.73250i	0.0226277	−	0.215289i	−0.977365	−	0.211559i	$-0.932146\pi$
$709$	0.602510	−	5.73250i	0.0226277	−	0.215289i	0.999993	−	0.00372988i	$-0.00118726\pi$
$710$	70.5726	−	8.91613i	2.64854	−	0.334616i
$711$	11.4805	−	15.7887i	0.430551	−	0.592123i
$712$	29.4561	+	21.4011i	1.10391	+	0.802040i
$713$	5.55413	−	52.8440i	0.208004	−	1.97902i
$714$	−13.8352	−	13.8406i	−0.517771	−	0.517971i
$715$	−1.13730	−	0.981673i	−0.0425327	−	0.0367125i
$716$	−27.0452	+	12.0413i	−1.01073	+	0.450004i
$717$	−29.1153	+	14.8279i	−1.08733	+	0.553760i
$718$	26.9133	+	46.6153i	1.00440	+	1.73967i
$719$	13.2328	+	40.7262i	0.493498	+	1.51883i	0.819284	+	0.573388i	$0.194371\pi$
$719$	13.2328	+	40.7262i	0.493498	+	1.51883i	−0.325786	+	0.945444i	$0.605629\pi$
$720$	−0.626490	+	7.42727i	−0.0233479	+	0.276798i
$721$	−4.51047	+	13.8818i	−0.167979	+	0.516985i
$722$	16.2897	−	3.46249i	0.606240	−	0.128860i
$723$	25.4794	−	6.82192i	0.947589	−	0.253710i
$724$	−5.58952	+	9.68134i	−0.207733	+	0.359804i
$725$	12.6505	+	34.0141i	0.469829	+	1.26325i
$726$	23.0391	−	18.6493i	0.855060	−	0.692141i
$727$	−4.04978	−	1.80308i	−0.150198	−	0.0668726i	0.330261	−	0.943890i	$-0.392863\pi$
$727$	−4.04978	−	1.80308i	−0.150198	−	0.0668726i	−0.480459	+	0.877017i	$0.659530\pi$
$728$	0.682091	−	2.09926i	0.0252800	−	0.0778038i
$729$	15.8449	+	21.8618i	0.586850	+	0.809696i
$730$	−59.2467	−	32.5704i	−2.19282	−	1.20548i
$731$	−13.9727	+	15.5183i	−0.516800	+	0.573965i
$732$	−38.2808	+	30.9870i	−1.41490	+	1.14531i
$733$	−10.5947	−	2.25196i	−0.391323	−	0.0831782i	0.00804825	−	0.999968i	$-0.497438\pi$
$733$	−10.5947	−	2.25196i	−0.391323	−	0.0831782i	−0.399371	+	0.916789i	$0.630771\pi$
$734$	−75.4126	+	33.5758i	−2.78353	+	1.23931i
$735$	9.11420	+	10.7892i	0.336182	+	0.397965i
$736$	−29.5810	−	13.1703i	−1.09037	−	0.485464i
$737$	−7.38099	−	5.36261i	−0.271882	−	0.197534i
$738$	−14.2497	+	12.8205i	−0.524538	+	0.471930i
$739$	−5.09046	+	3.69843i	−0.187256	+	0.136049i	−0.677463	−	0.735556i	$-0.736921\pi$
$739$	−5.09046	+	3.69843i	−0.187256	+	0.136049i	0.490208	+	0.871605i	$0.336921\pi$
$740$	−23.1388	+	33.2931i	−0.850600	+	1.22388i
$741$	−1.40725	+	2.76057i	−0.0516966	+	0.101412i
$742$	9.85856	+	2.09550i	0.361919	+	0.0769283i
$743$	2.22447	−	3.85289i	0.0816077	−	0.141349i	−0.822333	−	0.569007i	$-0.807328\pi$
$743$	2.22447	−	3.85289i	0.0816077	−	0.141349i	0.903941	+	0.427658i	$0.140661\pi$
$744$	37.3963	−	19.0453i	1.37101	−	0.698234i
$745$	−28.6118	+	9.96401i	−1.04825	+	0.365053i
$746$	−14.2694	+	43.9166i	−0.522438	+	1.60790i
$747$	0.0108228	−	28.0945i	0.000395987	−	1.02792i
$748$	−14.2211	+	10.3322i	−0.519975	+	0.377784i
$749$	11.8656	+	20.5518i	0.433559	+	0.750946i
$750$	36.9205	+	26.2470i	1.34814	+	0.958405i
$751$	−7.46181	+	12.9242i	−0.272285	+	0.471612i	−0.969447	−	0.245302i	$-0.921113\pi$
$751$	−7.46181	+	12.9242i	−0.272285	+	0.471612i	0.697161	+	0.716914i	$0.254446\pi$
$752$	−1.30555	−	12.4215i	−0.0476085	−	0.452965i
$753$	−5.08568	−	13.2563i	−0.185332	−	0.483086i
$754$	5.81328	−	1.23565i	0.211707	−	0.0449998i
$755$	−0.770514	+	4.03940i	−0.0280419	+	0.147009i
$756$	23.3745	−	23.3475i	0.850123	−	0.849142i
$757$	−7.36085			−0.267535			−0.133767	−	0.991013i	$-0.542707\pi$
$757$	−7.36085			−0.267535			−0.133767	+	0.991013i	$0.542707\pi$
$758$	16.3985	−	18.2124i	0.595622	−	0.661505i
$759$	−25.0718	+	1.30912i	−0.910049	+	0.0475179i
$760$	−39.2142	−	3.29250i	−1.42245	−	0.119432i
$761$	4.50351	+	42.8480i	0.163252	+	1.55324i	0.702863	+	0.711325i	$0.251905\pi$
$761$	4.50351	+	42.8480i	0.163252	+	1.55324i	−0.539611	+	0.841914i	$0.681429\pi$
$762$	−25.0322	−	38.5624i	−0.906819	−	1.39697i
$763$	0.973097	−	9.25840i	0.0352285	−	0.335177i
$764$	25.2574	−	18.3506i	0.913780	−	0.663900i
$765$	−5.81260	−	16.7117i	−0.210155	−	0.604212i
$766$	23.9593	+	17.4075i	0.865686	+	0.628957i
$767$	1.35932	−	1.50968i	0.0490823	−	0.0545114i
$768$	−6.08393	−	38.4604i	−0.219535	−	1.38782i
$769$	24.6957	+	5.24924i	0.890550	+	0.189292i	0.630395	−	0.776274i	$-0.282893\pi$
$769$	24.6957	+	5.24924i	0.890550	+	0.189292i	0.260155	+	0.965567i	$0.416226\pi$
$770$	−15.7261	+	9.52429i	−0.566730	+	0.343232i
$771$	−27.7056	−	4.39361i	−0.997794	−	0.158232i
$772$	6.28809	−	1.33657i	0.226313	−	0.0481043i
$773$	12.5696	−	9.13238i	0.452099	−	0.328469i	−0.338325	−	0.941029i	$-0.609860\pi$
$773$	12.5696	−	9.13238i	0.452099	−	0.328469i	0.790424	+	0.612560i	$0.209860\pi$
$774$	−41.2741	−	37.1922i	−1.48357	−	1.33685i
$775$	2.20832	−	35.1118i	0.0793252	−	1.26125i
$776$	−23.7166	−	41.0783i	−0.851376	−	1.47463i
$777$	16.0000	−	4.28388i	0.573997	−	0.153684i
$778$	−2.82930	−	3.14226i	−0.101435	−	0.112655i
$779$	−9.34061	−	10.3738i	−0.334662	−	0.371680i
$780$	3.25860	−	3.39680i	0.116677	−	0.121625i
$781$	−17.4663	+	19.3982i	−0.624992	+	0.694124i
$782$	−46.5939			−1.66619
$783$	36.4234	+	9.78218i	1.30167	+	0.349587i
$784$	3.27808	+	2.38166i	0.117074	+	0.0850593i
$785$	−0.716249	+	0.249432i	−0.0255640	+	0.00890263i
$786$	−4.93367	+	18.3985i	−0.175978	+	0.656254i
$787$	20.1517	−	8.97212i	0.718331	−	0.319822i	−0.0148173	−	0.999890i	$-0.504717\pi$
$787$	20.1517	−	8.97212i	0.718331	−	0.319822i	0.733149	+	0.680069i	$0.238050\pi$
$788$	55.5148	−	24.7168i	1.97763	−	0.880499i
$789$	28.8531	−	7.72520i	1.02720	−	0.275025i
$790$	−20.5790	−	27.1112i	−0.732166	−	0.964573i
$791$	−19.8017	−	14.3868i	−0.704068	−	0.511536i
$792$	−11.6490	−	16.0465i	−0.413929	−	0.570186i
$793$	2.86669			0.101799
$794$	−43.7496	+	48.5888i	−1.55261	+	1.72435i
$795$	7.19934	+	5.58649i	0.255334	+	0.198132i
$796$	−46.8861	−	52.0723i	−1.66183	−	1.84565i
$797$	−15.4348	−	17.1421i	−0.546730	−	0.607205i	0.404934	−	0.914346i	$-0.367294\pi$
$797$	−15.4348	−	17.1421i	−0.546730	−	0.607205i	−0.951664	+	0.307141i	$0.900628\pi$
$798$	26.8074	+	26.8177i	0.948972	+	0.949338i
$799$	14.8245	+	25.6767i	0.524452	+	0.908377i
$800$	−19.9340	−	7.89194i	−0.704772	−	0.279022i
$801$	6.60693	−	31.0244i	0.233444	−	1.09619i
$802$	−35.2587	+	25.6170i	−1.24503	+	0.904567i
$803$	24.2675	−	5.15821i	0.856380	−	0.182029i
$804$	17.9931	−	22.2109i	0.634568	−	0.783317i
$805$	−30.8133	−	2.58714i	−1.08602	−	0.0911847i
$806$	−5.63559	−	1.19788i	−0.198505	−	0.0421936i
$807$	−22.8034	+	18.4585i	−0.802717	+	0.649771i
$808$	14.1319	−	15.6950i	0.497157	−	0.552149i
$809$	37.9002	+	27.5361i	1.33250	+	0.968117i	0.999684	+	0.0251253i	$0.00799846\pi$
$809$	37.9002	+	27.5361i	1.33250	+	0.968117i	0.332815	+	0.942992i	$0.392002\pi$
$810$	44.4696	−	15.4481i	1.56250	−	0.542790i
$811$	2.78560	−	2.02385i	0.0978155	−	0.0710671i	−0.537802	−	0.843071i	$-0.680745\pi$
$811$	2.78560	−	2.02385i	0.0978155	−	0.0710671i	0.635618	+	0.772004i	$0.280745\pi$
$812$	4.82372	−	45.8946i	0.169279	−	1.61059i
$813$	23.0384	−	1.20294i	0.807994	−	0.0421891i
$814$	−2.45099	−	23.3196i	−0.0859072	−	0.817353i
$815$	−9.45271	−	40.3000i	−0.331114	−	1.41165i
$816$	−2.76386	−	4.25776i	−0.0967543	−	0.149051i
$817$	27.0738	−	30.0685i	0.947193	−	1.05196i
$818$	82.8000			2.89503
$819$	−1.91253	+	0.200271i	−0.0668294	+	0.00699802i
$820$	9.02924	+	19.1876i	0.315315	+	0.670060i
$821$	20.9987	−	4.46341i	0.732860	−	0.155774i	0.173658	−	0.984806i	$-0.444441\pi$
$821$	20.9987	−	4.46341i	0.732860	−	0.155774i	0.559202	+	0.829032i	$0.311108\pi$
$822$	39.6553	+	6.28861i	1.38314	+	0.219340i
$823$	1.07907	+	10.2667i	0.0376141	+	0.357875i	0.997099	+	0.0761147i	$0.0242515\pi$
$823$	1.07907	+	10.2667i	0.0376141	+	0.357875i	−0.959485	+	0.281760i	$0.909082\pi$
$824$	−13.7239	+	23.7704i	−0.478094	+	0.828082i
$825$	−16.5494	+	1.56150i	−0.576175	+	0.0543646i
$826$	−12.4301	−	21.5296i	−0.432499	−	0.749111i
$827$	−26.2851	+	19.0973i	−0.914024	+	0.664077i	−0.942029	−	0.335531i	$-0.891084\pi$
$827$	−26.2851	+	19.0973i	−0.914024	+	0.664077i	0.0280054	+	0.999608i	$0.491084\pi$
$828$	0.0303020	−	78.6594i	0.00105307	−	2.73360i
$829$	−12.1262	+	37.3205i	−0.421160	+	1.29620i	0.485464	+	0.874257i	$0.338651\pi$
$829$	−12.1262	+	37.3205i	−0.421160	+	1.29620i	−0.906624	+	0.421940i	$0.861349\pi$
$830$	−46.8941	−	14.1576i	−1.62772	−	0.491419i
$831$	1.76834	−	33.6180i	0.0613430	−	1.16620i
$832$	−2.14446	+	3.71432i	−0.0743458	+	0.128771i
$833$	−9.40839	−	1.99982i	−0.325981	−	0.0692895i
$834$	37.5932	−	1.96291i	1.30175	−	0.0679702i
$835$	13.4228	+	17.6835i	0.464516	+	0.611964i
$836$	27.5551	−	20.0199i	0.953012	−	0.692404i
$837$	−28.4002	−	23.0252i	−0.981655	−	0.795868i
$838$	4.92390	+	3.57742i	0.170093	+	0.123580i
$839$	−15.6689	−	6.97622i	−0.540949	−	0.240846i	0.118026	−	0.993010i	$-0.462343\pi$
$839$	−15.6689	−	6.97622i	−0.540949	−	0.240846i	−0.658975	+	0.752164i	$0.729010\pi$
$840$	−11.5368	−	21.5256i	−0.398059	−	0.742702i
$841$	21.6326	−	9.63146i	0.745952	−	0.332119i
$842$	−15.3752	−	3.26810i	−0.529865	−	0.112626i
$843$	24.5252	+	9.41976i	0.844693	+	0.324434i
$844$	−1.91919	+	2.13148i	−0.0660614	+	0.0733686i
$845$	28.5678	−	3.60925i	0.982762	−	0.124162i
$846$	−68.3315	+	39.4161i	−2.34929	+	1.35515i
$847$	−4.13978	+	12.7409i	−0.142245	+	0.437784i
$848$	2.38830	+	1.06334i	0.0820146	+	0.0365153i
$849$	−5.48298	−	34.6614i	−0.188175	−	1.18957i
$850$	−30.8231	+	1.29251i	−1.05722	+	0.0443327i
$851$	19.7182	−	34.1529i	0.675931	−	1.17075i
$852$	−57.8181	−	57.8404i	−1.98082	−	1.98158i
$853$	4.46538	−	0.949146i	0.152892	−	0.0324982i	−0.130830	−	0.991405i	$-0.541764\pi$
$853$	4.46538	−	0.949146i	0.152892	−	0.0324982i	0.283722	+	0.958907i	$0.408431\pi$
$854$	10.8407	−	33.3642i	0.370961	−	1.14170i
$855$	11.2626	+	32.3809i	0.385173	+	1.10740i
$856$	13.7901	+	42.4416i	0.471337	+	1.45062i
$857$	−1.28768	−	2.23032i	−0.0439863	−	0.0761864i	0.843194	−	0.537609i	$-0.180672\pi$
$857$	−1.28768	−	2.23032i	−0.0439863	−	0.0761864i	−0.887180	+	0.461423i	$0.847339\pi$
$858$	−0.142996	+	2.71851i	−0.00488181	+	0.0928084i
$859$	33.4553	−	14.8952i	1.14148	−	0.508219i	0.253150	−	0.967427i	$-0.418533\pi$
$859$	33.4553	−	14.8952i	1.14148	−	0.508219i	0.888329	+	0.459208i	$0.151867\pi$
$860$	−52.5751	+	31.8413i	−1.79280	+	1.08578i
$861$	2.24383	−	8.36764i	0.0764695	−	0.285168i
$862$	−7.01007	+	66.6963i	−0.238764	+	2.27169i
$863$	−1.15071	−	0.836039i	−0.0391706	−	0.0284591i	0.568028	−	0.823009i	$-0.307707\pi$
$863$	−1.15071	−	0.836039i	−0.0391706	−	0.0284591i	−0.607198	+	0.794550i	$0.707707\pi$
$864$	−18.6929	+	12.1240i	−0.635947	+	0.412466i
$865$	−8.99957	−	19.1245i	−0.305995	−	0.650254i
$866$	−4.11646	+	39.1655i	−0.139883	+	1.33090i
$867$	−14.5868	−	9.47676i	−0.495393	−	0.321848i
$868$	−22.3684	+	38.7433i	−0.759234	+	1.31503i
$869$	12.2171	+	2.59683i	0.414437	+	0.0880914i
$870$	34.6613	−	55.8803i	1.17513	−	1.89452i
$871$	−1.62744	+	0.345923i	−0.0551438	+	0.0117212i
$872$	5.40967	−	16.6493i	0.183195	−	0.563815i
$873$	−24.3024	+	33.4222i	−0.822510	+	1.13117i
$874$	90.2812			3.05381
$875$	−20.4556	−	0.856707i	−0.691524	−	0.0289620i
$876$	12.1450	+	76.7763i	0.410342	+	2.59403i
$877$	−4.24444	−	40.3832i	−0.143325	−	1.36364i	−0.795674	−	0.605725i	$-0.792883\pi$
$877$	−4.24444	−	40.3832i	−0.143325	−	1.36364i	0.652350	−	0.757918i	$-0.273783\pi$
$878$	−12.1769	−	13.5238i	−0.410951	−	0.456407i
$879$	30.3886	+	4.81909i	1.02498	+	0.162544i
$880$	−4.50367	+	1.56840i	−0.151819	+	0.0528706i
$881$	−5.17310	−	15.9212i	−0.174286	−	0.536398i	0.825314	−	0.564674i	$-0.190998\pi$
$881$	−5.17310	−	15.9212i	−0.174286	−	0.536398i	−0.999600	+	0.0282762i	$0.990998\pi$
$882$	5.33042	−	25.0302i	0.179484	−	0.842811i
$883$	−8.19206	−	25.2126i	−0.275685	−	0.848470i	−0.989037	−	0.147665i	$-0.952824\pi$
$883$	−8.19206	−	25.2126i	−0.275685	−	0.848470i	0.713353	−	0.700805i	$-0.247176\pi$
$884$	−0.335084	+	3.18812i	−0.0112701	+	0.107228i
$885$	−1.64209	−	22.4169i	−0.0551982	−	0.753537i
$886$	−3.30388	−	31.4343i	−0.110996	−	1.05606i
$887$	−9.70153	+	4.31940i	−0.325745	+	0.145031i	−0.563093	−	0.826394i	$-0.690389\pi$
$887$	−9.70153	+	4.31940i	−0.325745	+	0.145031i	0.237347	+	0.971425i	$0.423722\pi$
$888$	31.1050	−	1.62413i	1.04381	−	0.0545024i
$889$	18.9823	+	8.45147i	0.636646	+	0.283453i
$890$	−48.4655	−	26.6435i	−1.62457	−	0.893092i
$891$	−8.64902	+	14.9539i	−0.289753	+	0.500975i
$892$	−5.25030	−	16.1588i	−0.175793	−	0.541036i
$893$	−28.7241	−	49.7517i	−0.961216	−	1.66488i
$894$	46.0352	+	29.9082i	1.53965	+	1.00028i
$895$	16.3081	−	9.87679i	0.545121	−	0.330145i
$896$	24.6119	+	27.3343i	0.822225	+	0.913173i
$897$	−2.88201	+	3.55759i	−0.0962276	+	0.118784i
$898$	69.5110	+	30.9483i	2.31961	+	1.03276i
$899$	−51.0696			−1.70327
$900$	−2.16196	−	52.0361i	−0.0720652	−	1.73454i
$901$	−6.20595			−0.206750
$902$	−11.2038	−	4.98825i	−0.373046	−	0.166091i
$903$	24.8006	+	3.93293i	0.825313	+	0.130880i
$904$	−30.7981	−	34.2047i	−1.02433	−	1.13763i
$905$	2.78984	−	6.63697i	0.0927376	−	0.220620i
$906$	6.63976	−	3.38152i	0.220591	−	0.112343i
$907$	−14.7362	−	25.5239i	−0.489309	−	0.847508i	0.510615	−	0.859809i	$-0.329418\pi$
$907$	−14.7362	−	25.5239i	−0.489309	−	0.847508i	−0.999924	+	0.0123013i	$0.996084\pi$
$908$	−17.9529	−	55.2535i	−0.595789	−	1.83365i
$909$	−17.4968	−	5.69249i	−0.580331	−	0.188808i
$910$	−0.628231	+	3.29349i	−0.0208257	+	0.109178i
$911$	1.95117	+	0.868718i	0.0646452	+	0.0287819i	0.438805	−	0.898583i	$-0.355402\pi$
$911$	1.95117	+	0.868718i	0.0646452	+	0.0287819i	−0.374159	+	0.927364i	$0.622069\pi$
$912$	5.35529	+	8.24991i	0.177332	+	0.273182i
$913$	16.4212	−	7.31119i	0.543462	−	0.241965i
$914$	0.796007	+	7.57350i	0.0263296	+	0.250509i
$915$	21.9577	−	22.8889i	0.725898	−	0.756683i
$916$	−1.34248	+	12.7728i	−0.0443566	+	0.422025i
$917$	−2.66039	−	8.18783i	−0.0878538	−	0.270386i
$918$	−17.4769	+	26.8781i	−0.576824	+	0.887109i
$919$	−18.3755	−	56.5541i	−0.606153	−	1.86555i	−0.488664	−	0.872472i	$-0.662516\pi$
$919$	−18.3755	−	56.5541i	−0.606153	−	1.86555i	−0.117488	−	0.993074i	$-0.537484\pi$
$920$	−55.6658	−	16.8059i	−1.83525	−	0.554073i
$921$	−5.33951	−	13.9179i	−0.175943	−	0.458610i
$922$	39.9856	+	44.4085i	1.31686	+	1.46252i
$923$	0.497585	+	4.73421i	0.0163782	+	0.155828i
$924$	19.7324	+	7.57893i	0.649149	+	0.249329i
$925$	12.0967	−	23.1401i	0.397738	−	0.760841i
$926$	−76.9096			−2.52741
$927$	23.7805	+	2.50869i	0.781053	+	0.0823962i
$928$	−9.61714	+	29.5985i	−0.315698	+	0.971619i
$929$	27.1933	−	5.78011i	0.892182	−	0.189639i	0.261060	−	0.965323i	$-0.415928\pi$
$929$	27.1933	−	5.78011i	0.892182	−	0.189639i	0.631122	+	0.775683i	$0.282595\pi$
$930$	−52.7307	+	35.8217i	−1.72911	+	1.17464i
$931$	18.2299	+	3.87488i	0.597460	+	0.126994i
$932$	−0.487035	+	0.843569i	−0.0159534	+	0.0276320i
$933$	−24.7115	+	12.5851i	−0.809017	+	0.412018i
$934$	−2.54843	+	24.2466i	−0.0833870	+	0.793375i
$935$	8.25234	−	7.74962i	0.269880	−	0.253440i
$936$	−3.59618	−	0.379374i	−0.117545	−	0.0124002i
$937$	5.33825	+	3.87847i	0.174393	+	0.126704i	0.671558	−	0.740952i	$-0.265626\pi$
$937$	5.33825	+	3.87847i	0.174393	+	0.126704i	−0.497165	+	0.867656i	$0.665626\pi$
$938$	−2.12828	+	20.2493i	−0.0694909	+	0.661161i
$939$	14.2281	−	3.80947i	0.464317	−	0.124317i
$940$	19.9293	+	84.9650i	0.650022	+	2.77125i
$941$	−5.11057	+	2.27537i	−0.166600	+	0.0741750i	−0.488342	−	0.872652i	$-0.662398\pi$
$941$	−5.11057	+	2.27537i	−0.166600	+	0.0741750i	0.321742	+	0.946827i	$0.395732\pi$
$942$	1.15241	+	0.748702i	0.0375477	+	0.0243940i
$943$	−10.3132	−	17.8631i	−0.335845	−	0.581701i
$944$	−1.99268	−	6.13284i	−0.0648562	−	0.199607i
$945$	−13.0502	+	16.8045i	−0.424522	+	0.546649i
$946$	10.9848	−	33.8077i	0.357146	−	1.09918i
$947$	4.10820	−	0.873225i	0.133499	−	0.0283760i	−0.140678	−	0.990055i	$-0.544928\pi$
$947$	4.10820	−	0.873225i	0.133499	−	0.0283760i	0.274176	+	0.961679i	$0.411595\pi$
$948$	−10.1355	+	37.7972i	−0.329187	+	1.22760i
$949$	2.26222	−	3.91827i	0.0734346	−	0.127193i
$950$	59.7234	−	2.50439i	1.93768	−	0.0812531i
$951$	−30.5955	−	11.7513i	−0.992127	−	0.381061i
$952$	15.1944	+	6.76498i	0.492453	+	0.219254i
$953$	−9.85039	+	30.3164i	−0.319085	+	0.982044i	0.654955	+	0.755668i	$0.272688\pi$
$953$	−9.85039	+	30.3164i	−0.319085	+	0.982044i	−0.974040	+	0.226376i	$0.927312\pi$
$954$	0.00636083	−	16.5118i	0.000205939	−	0.534588i
$955$	−14.6566	+	13.7637i	−0.474275	+	0.445383i
$956$	43.8265	−	48.6743i	1.41745	−	1.57424i
$957$	3.77018	+	23.8337i	0.121873	+	0.770434i
$958$	−59.0400	−	12.5493i	−1.90750	−	0.405451i
$959$	−16.5777	+	7.38088i	−0.535323	+	0.238341i
$960$	13.2310	+	45.5724i	0.427029	+	1.47084i
$961$	16.9084	+	7.52812i	0.545434	+	0.242843i
$962$	−3.45946	−	2.51345i	−0.111538	−	0.0810368i
$963$	28.9019	−	26.0033i	0.931352	−	0.837944i
$964$	−42.7768	+	31.0792i	−1.37775	+	1.00099i
$965$	−3.90980	+	1.36158i	−0.125861	+	0.0438308i
$966$	30.5066	+	46.9959i	0.981535	+	1.51207i
$967$	6.07669	+	1.29164i	0.195413	+	0.0415364i	0.304578	−	0.952487i	$-0.401484\pi$
$967$	6.07669	+	1.29164i	0.195413	+	0.0415364i	−0.109165	+	0.994024i	$0.534818\pi$
$968$	−12.5960	+	21.8169i	−0.404850	+	0.701221i
$969$	−19.5790	−	12.7201i	−0.628968	−	0.408629i
$970$	43.5625	+	57.3902i	1.39871	+	1.84269i
$971$	16.1639	−	49.7474i	0.518724	−	1.59647i	−0.257678	−	0.966231i	$-0.582957\pi$
$971$	16.1639	−	49.7474i	0.518724	−	1.59647i	0.776402	−	0.630238i	$-0.217043\pi$
$972$	−45.3640	−	29.5219i	−1.45505	−	0.946914i
$973$	−13.7644	+	10.0004i	−0.441268	+	0.320600i
$974$	3.64858	+	6.31952i	0.116908	+	0.202491i
$975$	−1.80784	+	2.43339i	−0.0578973	+	0.0779307i
$976$	4.54982	−	7.88053i	0.145636	−	0.252249i
$977$	−0.0161026	−	0.153206i	−0.000515167	−	0.00490148i	0.994261	−	0.106979i	$-0.0341177\pi$
$977$	−0.0161026	−	0.153206i	−0.000515167	−	0.00490148i	−0.994776	+	0.102077i	$0.967451\pi$
$978$	−47.2129	+	58.2802i	−1.50970	+	1.86359i
$979$	19.8515	−	4.21956i	0.634456	−	0.134858i
$980$	−24.8102	−	13.6392i	−0.792534	−	0.435688i
$981$	−15.1683	+	1.58835i	−0.484288	+	0.0507121i
$982$	9.70230			0.309613
$983$	36.1752	−	40.1766i	1.15381	−	1.28144i	0.200415	−	0.979711i	$-0.435771\pi$
$983$	36.1752	−	40.1766i	1.15381	−	1.28144i	0.953395	−	0.301725i	$-0.0975624\pi$
$984$	7.39877	−	14.5140i	0.235864	−	0.462689i
$985$	−33.4753	+	20.2738i	−1.06661	+	0.645977i
$986$	4.68107	+	44.5374i	0.149076	+	1.41836i
$987$	16.1922	−	31.7638i	0.515403	−	1.01105i
$988$	0.649265	−	6.17735i	0.0206559	−	0.196528i
$989$	48.3679	−	35.1413i	1.53801	−	1.11743i
$990$	20.6104	+	21.9644i	0.655043	+	0.698074i
$991$	37.4071	+	27.1779i	1.18828	+	0.863333i	0.993081	−	0.117431i	$-0.0374659\pi$
$991$	37.4071	+	27.1779i	1.18828	+	0.863333i	0.195195	+	0.980764i	$0.437466\pi$
$992$	20.1880	−	22.4210i	0.640969	−	0.711868i
$993$	7.56332	+	2.90496i	0.240015	+	0.0921861i
$994$	56.9811	+	12.1117i	1.80733	+	0.384160i
$995$	34.1607	+	29.4861i	1.08297	+	0.934773i
$996$	20.1725	+	52.5814i	0.639190	+	1.66611i
$997$	−15.6764	+	3.33213i	−0.496478	+	0.105530i	−0.449344	−	0.893359i	$-0.648342\pi$
$997$	−15.6764	+	3.33213i	−0.496478	+	0.105530i	−0.0471342	+	0.998889i	$0.515009\pi$
$998$	20.7923	−	15.1065i	0.658168	−	0.478187i
$999$	−12.3053	−	24.1850i	−0.389322	−	0.765181i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.211.3	yes	224
3.2	odd	2		675.2.r.a.361.26		224
9.2	odd	6		675.2.r.a.586.3		224
9.7	even	3	inner	225.2.q.a.61.26	yes	224
25.16	even	5	inner	225.2.q.a.166.26	yes	224
75.41	odd	10		675.2.r.a.91.3		224
225.16	even	15	inner	225.2.q.a.16.3	✓	224
225.191	odd	30		675.2.r.a.316.26		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.16.3	✓	224	225.16	even	15	inner
225.2.q.a.61.26	yes	224	9.7	even	3	inner
225.2.q.a.166.26	yes	224	25.16	even	5	inner
225.2.q.a.211.3	yes	224	1.1	even	1	trivial
675.2.r.a.91.3		224	75.41	odd	10
675.2.r.a.316.26		224	225.191	odd	30
675.2.r.a.361.26		224	3.2	odd	2
675.2.r.a.586.3		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)

\(f(q)\)	\(=\)	\(q+(-2.13701 - 0.951457i) q^{2} +(-0.620400 - 1.61713i) q^{3} +(2.32327 + 2.58025i) q^{4} +(-1.69271 - 1.46108i) q^{5} +(-0.212829 + 4.04610i) q^{6} +(-0.915602 - 1.58587i) q^{7} +(-1.06411 - 3.27499i) q^{8} +(-2.23021 + 2.00653i) q^{9} +O(q^{10})\)	\(q+(-2.13701 - 0.951457i) q^{2} +(-0.620400 - 1.61713i) q^{3} +(2.32327 + 2.58025i) q^{4} +(-1.69271 - 1.46108i) q^{5} +(-0.212829 + 4.04610i) q^{6} +(-0.915602 - 1.58587i) q^{7} +(-1.06411 - 3.27499i) q^{8} +(-2.23021 + 2.00653i) q^{9} +(2.22718 + 4.73287i) q^{10} +(-1.75350 - 0.780708i) q^{11} +(2.73124 - 5.35781i) q^{12} +(-0.319779 + 0.142375i) q^{13} +(0.447762 + 4.26017i) q^{14} +(-1.31259 + 3.64378i) q^{15} +(-0.116144 + 1.10504i) q^{16} +(-0.815069 - 2.50853i) q^{17} +(6.67510 - 2.16603i) q^{18} +(1.57929 + 4.86056i) q^{19} +(-0.162673 - 7.76208i) q^{20} +(-1.99652 + 2.46452i) q^{21} +(3.00443 + 3.33676i) q^{22} +(0.789361 + 7.51027i) q^{23} +(-4.63591 + 3.75261i) q^{24} +(0.730517 + 4.94635i) q^{25} +0.818832 q^{26} +(4.62844 + 2.36168i) q^{27} +(1.96475 - 6.04688i) q^{28} +(7.09948 - 1.50904i) q^{29} +(6.27191 - 6.53790i) q^{30} +(-6.88248 - 1.46292i) q^{31} +(-2.14393 + 3.71340i) q^{32} +(-0.174634 + 3.31998i) q^{33} +(-0.644945 + 6.13624i) q^{34} +(-0.767228 + 4.02218i) q^{35} +(-10.3587 - 1.09278i) q^{36} +(-4.22488 - 3.06955i) q^{37} +(1.24966 - 11.8897i) q^{38} +(0.428629 + 0.428794i) q^{39} +(-2.98378 + 7.09835i) q^{40} +(-2.49525 + 1.11096i) q^{41} +(6.61145 - 3.36710i) q^{42} +(-3.95848 - 6.85628i) q^{43} +(-2.05942 - 6.33826i) q^{44} +(6.70678 - 0.137972i) q^{45} +(5.45883 - 16.8005i) q^{46} +(-10.9951 + 2.33709i) q^{47} +(1.85904 - 0.497745i) q^{48} +(1.82334 - 3.15813i) q^{49} +(3.14511 - 11.2654i) q^{50} +(-3.55094 + 2.87436i) q^{51} +(-1.11029 - 0.494334i) q^{52} +(0.727074 - 2.23770i) q^{53} +(-7.64398 - 9.45069i) q^{54} +(1.82749 + 3.88350i) q^{55} +(-4.21941 + 4.68613i) q^{56} +(6.88036 - 5.56941i) q^{57} +(-16.6074 - 3.53002i) q^{58} +(-5.30179 + 2.36051i) q^{59} +(-12.4514 + 5.07866i) q^{60} +(-7.48156 - 3.33100i) q^{61} +(13.3160 + 9.67464i) q^{62} +(5.22408 + 1.69963i) q^{63} +(9.91258 - 7.20191i) q^{64} +(0.749312 + 0.226222i) q^{65} +(3.53201 - 6.92867i) q^{66} +(4.64929 + 0.988236i) q^{67} +(4.57900 - 7.93106i) q^{68} +(11.6553 - 5.93587i) q^{69} +(5.46650 - 7.86544i) q^{70} +(4.20239 - 12.9336i) q^{71} +(8.94456 + 5.16874i) q^{72} +(-10.4569 + 7.59738i) q^{73} +(6.10804 + 10.5794i) q^{74} +(7.54566 - 4.25005i) q^{75} +(-8.87235 + 15.3674i) q^{76} +(0.367406 + 3.49564i) q^{77} +(-0.508004 - 1.32416i) q^{78} +(-6.36493 + 1.35291i) q^{79} +(1.81114 - 1.70081i) q^{80} +(0.947652 - 8.94997i) q^{81} +6.38940 q^{82} +(-6.26629 + 6.95942i) q^{83} +(-10.9975 + 0.574231i) q^{84} +(-2.28547 + 5.43708i) q^{85} +(1.93584 + 18.4182i) q^{86} +(-6.84483 - 10.5446i) q^{87} +(-0.690898 + 6.57345i) q^{88} +(-8.55403 + 6.21487i) q^{89} +(-14.4637 - 6.08637i) q^{90} +(0.518578 + 0.376769i) q^{91} +(-17.5445 + 19.4851i) q^{92} +(1.90417 + 12.0374i) q^{93} +(25.7203 + 5.46703i) q^{94} +(4.42837 - 10.5350i) q^{95} +(7.33515 + 1.16322i) q^{96} +(13.4736 - 2.86389i) q^{97} +(-6.90132 + 5.01410i) q^{98} +(5.47718 - 1.77731i) 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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