LMFDB - Embedded newform 147.2.m.b.109.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,2,Mod(4,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("147.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	147.m (of order $21$, degree $12$, 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:	$1.17380090971$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$5$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			109.2
Character	$\chi$	$=$	147.109
Dual form			147.2.m.b.58.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.03880 + 0.963867i) q^{2} +(-0.988831 + 0.149042i) q^{3} +(0.000608887 - 0.00812503i) q^{4} +(-0.107830 + 0.274746i) q^{5} +(0.883542 - 1.10793i) q^{6} +(-1.39076 + 2.25073i) q^{7} +(-1.75989 - 2.20683i) q^{8} +(0.955573 - 0.294755i) q^{9} +O(q^{10})$	\(q+(-1.03880 + 0.963867i) q^{2} +(-0.988831 + 0.149042i) q^{3} +(0.000608887 - 0.00812503i) q^{4} +(-0.107830 + 0.274746i) q^{5} +(0.883542 - 1.10793i) q^{6} +(-1.39076 + 2.25073i) q^{7} +(-1.75989 - 2.20683i) q^{8} +(0.955573 - 0.294755i) q^{9} +(-0.152805 - 0.389340i) q^{10} +(-5.11416 - 1.57751i) q^{11} +(0.000608887 + 0.00812503i) q^{12} +(0.514524 + 2.25428i) q^{13} +(-0.724688 - 3.67857i) q^{14} +(0.0656767 - 0.287748i) q^{15} +(3.97137 + 0.598588i) q^{16} +(-4.63769 + 3.16192i) q^{17} +(-0.708546 + 1.22724i) q^{18} +(-3.21076 - 5.56120i) q^{19} +(0.00216666 + 0.00104341i) q^{20} +(1.03977 - 2.43288i) q^{21} +(6.83311 - 3.29065i) q^{22} +(5.80770 + 3.95962i) q^{23} +(2.06914 + 1.91988i) q^{24} +(3.60140 + 3.34161i) q^{25} +(-2.70731 - 1.84581i) q^{26} +(-0.900969 + 0.433884i) q^{27} +(0.0174405 + 0.0126704i) q^{28} +(3.53338 + 1.70159i) q^{29} +(0.209126 + 0.362217i) q^{30} +(-3.27241 + 5.66798i) q^{31} +(-0.0380819 + 0.0259638i) q^{32} +(5.29216 + 0.797665i) q^{33} +(1.76997 - 7.75473i) q^{34} +(-0.468415 - 0.624801i) q^{35} +(-0.00181306 - 0.00794353i) q^{36} +(0.599368 + 7.99800i) q^{37} +(8.69560 + 2.68224i) q^{38} +(-0.844760 - 2.15241i) q^{39} +(0.796085 - 0.245560i) q^{40} +(1.79402 + 2.24963i) q^{41} +(1.26486 + 3.52947i) q^{42} +(4.17158 - 5.23100i) q^{43} +(-0.0159313 + 0.0405922i) q^{44} +(-0.0220565 + 0.294323i) q^{45} +(-9.84960 + 1.48459i) q^{46} +(-4.12309 + 3.82567i) q^{47} -4.01623 q^{48} +(-3.13160 - 6.26044i) q^{49} -6.96201 q^{50} +(4.11463 - 3.81782i) q^{51} +(0.0186294 - 0.00280792i) q^{52} +(0.232676 - 3.10485i) q^{53} +(0.517722 - 1.31913i) q^{54} +(0.984874 - 1.23499i) q^{55} +(7.41455 - 0.891876i) q^{56} +(4.00375 + 5.02055i) q^{57} +(-5.31059 + 1.63810i) q^{58} +(1.07811 + 2.74697i) q^{59} +(-0.00229798 - 0.000708832i) q^{60} +(-0.246792 - 3.29321i) q^{61} +(-2.06379 - 9.04207i) q^{62} +(-0.665553 + 2.56067i) q^{63} +(-1.77286 + 7.76739i) q^{64} +(-0.674835 - 0.101715i) q^{65} +(-6.26635 + 4.27232i) q^{66} +(-1.22841 + 2.12766i) q^{67} +(0.0228669 + 0.0396066i) q^{68} +(-6.33298 - 3.04980i) q^{69} +(1.08881 + 0.197554i) q^{70} +(0.756494 - 0.364308i) q^{71} +(-2.33217 - 1.59005i) q^{72} +(-6.76324 - 6.27537i) q^{73} +(-8.33163 - 7.73063i) q^{74} +(-4.05922 - 2.76753i) q^{75} +(-0.0471399 + 0.0227014i) q^{76} +(10.6631 - 9.31669i) q^{77} +(2.95218 + 1.42169i) q^{78} +(-6.17678 - 10.6985i) q^{79} +(-0.592692 + 1.02657i) q^{80} +(0.826239 - 0.563320i) q^{81} +(-4.03197 - 0.607721i) q^{82} +(-2.83042 + 12.4009i) q^{83} +(-0.0191341 - 0.00992949i) q^{84} +(-0.368644 - 1.61514i) q^{85} +(0.708540 + 9.45481i) q^{86} +(-3.74753 - 1.15596i) q^{87} +(5.51905 + 14.0623i) q^{88} +(-6.03004 + 1.86002i) q^{89} +(-0.260776 - 0.327003i) q^{90} +(-5.78935 - 1.97709i) q^{91} +(0.0357083 - 0.0447768i) q^{92} +(2.39109 - 6.09240i) q^{93} +(0.595637 - 7.94822i) q^{94} +(1.87413 - 0.282480i) q^{95} +(0.0337869 - 0.0313496i) q^{96} +4.63741 q^{97} +(9.28734 + 3.48491i) q^{98} -5.35194 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + q^{2} + 5 q^{3} + 5 q^{4} - 2 q^{5} - 2 q^{6} + 5 q^{7} + 6 q^{8} + 5 q^{9}+O(q^{10}) $ 60 * q + q^2 + 5 * q^3 + 5 * q^4 - 2 * q^5 - 2 * q^6 + 5 * q^7 + 6 * q^8 + 5 * q^9	\( 60 q + q^{2} + 5 q^{3} + 5 q^{4} - 2 q^{5} - 2 q^{6} + 5 q^{7} + 6 q^{8} + 5 q^{9} - 34 q^{10} - 11 q^{11} + 5 q^{12} - 2 q^{13} + 40 q^{14} - 3 q^{15} - 31 q^{16} - 9 q^{17} - 6 q^{18} - 29 q^{19} - 43 q^{20} - 11 q^{21} + 9 q^{22} - 4 q^{23} - 24 q^{24} + 55 q^{25} + 36 q^{26} - 10 q^{27} - 57 q^{28} + 4 q^{29} - 20 q^{30} - 39 q^{31} - 92 q^{32} - 18 q^{33} - 36 q^{34} - 33 q^{35} - 10 q^{36} - 24 q^{37} + 118 q^{38} - 6 q^{39} + 35 q^{41} + 38 q^{42} + 2 q^{43} + 40 q^{44} + 12 q^{45} - 40 q^{46} - 5 q^{47} + 76 q^{48} + 129 q^{49} - 176 q^{50} + 54 q^{51} - 6 q^{52} + 26 q^{53} + q^{54} + 2 q^{55} + 63 q^{56} - 12 q^{57} + 11 q^{58} - 41 q^{59} + 32 q^{60} + 6 q^{61} + 36 q^{62} - q^{63} + 74 q^{64} - 51 q^{65} - 15 q^{66} - 55 q^{67} - 22 q^{68} + 8 q^{69} - 68 q^{70} - 66 q^{71} - 24 q^{72} + 24 q^{73} + 28 q^{74} + 41 q^{75} + 3 q^{76} - 34 q^{77} - 30 q^{78} - 51 q^{79} - 5 q^{80} + 5 q^{81} - 41 q^{82} + 30 q^{83} - 30 q^{84} + 68 q^{85} + 110 q^{86} + 19 q^{87} + 129 q^{88} + 75 q^{89} - 16 q^{90} + 5 q^{91} - 4 q^{93} + 38 q^{94} + 36 q^{95} - 57 q^{96} - 168 q^{97} + 227 q^{98} + 36 q^{99}+O(q^{100}) \) 60 * q + q^2 + 5 * q^3 + 5 * q^4 - 2 * q^5 - 2 * q^6 + 5 * q^7 + 6 * q^8 + 5 * q^9 - 34 * q^10 - 11 * q^11 + 5 * q^12 - 2 * q^13 + 40 * q^14 - 3 * q^15 - 31 * q^16 - 9 * q^17 - 6 * q^18 - 29 * q^19 - 43 * q^20 - 11 * q^21 + 9 * q^22 - 4 * q^23 - 24 * q^24 + 55 * q^25 + 36 * q^26 - 10 * q^27 - 57 * q^28 + 4 * q^29 - 20 * q^30 - 39 * q^31 - 92 * q^32 - 18 * q^33 - 36 * q^34 - 33 * q^35 - 10 * q^36 - 24 * q^37 + 118 * q^38 - 6 * q^39 + 35 * q^41 + 38 * q^42 + 2 * q^43 + 40 * q^44 + 12 * q^45 - 40 * q^46 - 5 * q^47 + 76 * q^48 + 129 * q^49 - 176 * q^50 + 54 * q^51 - 6 * q^52 + 26 * q^53 + q^54 + 2 * q^55 + 63 * q^56 - 12 * q^57 + 11 * q^58 - 41 * q^59 + 32 * q^60 + 6 * q^61 + 36 * q^62 - q^63 + 74 * q^64 - 51 * q^65 - 15 * q^66 - 55 * q^67 - 22 * q^68 + 8 * q^69 - 68 * q^70 - 66 * q^71 - 24 * q^72 + 24 * q^73 + 28 * q^74 + 41 * q^75 + 3 * q^76 - 34 * q^77 - 30 * q^78 - 51 * q^79 - 5 * q^80 + 5 * q^81 - 41 * q^82 + 30 * q^83 - 30 * q^84 + 68 * q^85 + 110 * q^86 + 19 * q^87 + 129 * q^88 + 75 * q^89 - 16 * q^90 + 5 * q^91 - 4 * q^93 + 38 * q^94 + 36 * q^95 - 57 * q^96 - 168 * q^97 + 227 * q^98 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$1$	$e\left(\frac{20}{21}\right)$

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 $

$2$	−1.03880	+	0.963867i	−0.734544	+	0.681557i	−0.955919	−	0.293632i	$-0.905136\pi$
$2$	−1.03880	+	0.963867i	−0.734544	+	0.681557i	0.221375	+	0.975189i	$0.428946\pi$
$3$	−0.988831	+	0.149042i	−0.570902	+	0.0860496i
$3$	−0.988831	+	0.149042i	−0.570902	+	0.0860496i
$4$	0.000608887	−	0.00812503i	0.000304443	−	0.00406252i
$5$	−0.107830	+	0.274746i	−0.0482230	+	0.122870i	−0.952956	−	0.303109i	$-0.901975\pi$
$5$	−0.107830	+	0.274746i	−0.0482230	+	0.122870i	0.904733	+	0.425980i	$0.140070\pi$
$6$	0.883542	−	1.10793i	0.360705	−	0.452309i
$7$	−1.39076	+	2.25073i	−0.525656	+	0.850697i
$7$	−1.39076	+	2.25073i	−0.525656	+	0.850697i
$8$	−1.75989	−	2.20683i	−0.622213	−	0.780231i
$9$	0.955573	−	0.294755i	0.318524	−	0.0982517i
$10$	−0.152805	−	0.389340i	−0.0483211	−	0.123120i
$11$	−5.11416	−	1.57751i	−1.54198	−	0.475637i	−0.596855	−	0.802349i	$-0.703583\pi$
$11$	−5.11416	−	1.57751i	−1.54198	−	0.475637i	−0.945124	+	0.326712i	$0.894059\pi$
$12$	0.000608887		0.00812503i	0.000175771		0.00234549i
$13$	0.514524	+	2.25428i	0.142703	+	0.625224i	0.994801	+	0.101841i	$0.0324732\pi$
$13$	0.514524	+	2.25428i	0.142703	+	0.625224i	−0.852097	+	0.523383i	$0.824670\pi$
$14$	−0.724688	−	3.67857i	−0.193681	−	0.983139i
$15$	0.0656767	−	0.287748i	0.0169577	−	0.0742963i
$16$	3.97137	+	0.598588i	0.992843	+	0.149647i
$17$	−4.63769	+	3.16192i	−1.12481	+	0.766879i	−0.975081	−	0.221849i	$-0.928791\pi$
$17$	−4.63769	+	3.16192i	−1.12481	+	0.766879i	−0.149724	+	0.988728i	$0.547839\pi$
$18$	−0.708546	+	1.22724i	−0.167006	+	0.289263i
$19$	−3.21076	−	5.56120i	−0.736599	−	1.27583i	−0.954018	−	0.299749i	$-0.903097\pi$
$19$	−3.21076	−	5.56120i	−0.736599	−	1.27583i	0.217419	−	0.976078i	$-0.430236\pi$
$20$	0.00216666	+	0.00104341i	0.000484481	+	0.000233314i
$21$	1.03977	−	2.43288i	0.226896	−	0.530897i
$22$	6.83311	−	3.29065i	1.45682	−	0.701570i
$23$	5.80770	+	3.95962i	1.21099	+	0.825638i	0.988783	−	0.149361i	$-0.0477217\pi$
$23$	5.80770	+	3.95962i	1.21099	+	0.825638i	0.222207	+	0.975000i	$0.428674\pi$
$24$	2.06914	+	1.91988i	0.422361	+	0.391894i
$25$	3.60140	+	3.34161i	0.720280	+	0.668322i
$26$	−2.70731	−	1.84581i	−0.530948	−	0.361994i
$27$	−0.900969	+	0.433884i	−0.173392	+	0.0835010i
$28$	0.0174405	+	0.0126704i	0.00329594	+	0.00239448i
$29$	3.53338	+	1.70159i	0.656133	+	0.315977i	0.732164	−	0.681129i	$-0.238511\pi$
$29$	3.53338	+	1.70159i	0.656133	+	0.315977i	−0.0760312	+	0.997105i	$0.524225\pi$
$30$	0.209126	+	0.362217i	0.0381810	+	0.0661315i
$31$	−3.27241	+	5.66798i	−0.587742	+	1.01800i	0.406786	+	0.913524i	$0.366650\pi$
$31$	−3.27241	+	5.66798i	−0.587742	+	1.01800i	−0.994527	+	0.104475i	$0.966684\pi$
$32$	−0.0380819	+	0.0259638i	−0.00673200	+	0.00458980i
$33$	5.29216	+	0.797665i	0.921247	+	0.138856i
$34$	1.76997	−	7.75473i	0.303547	−	1.32992i
$35$	−0.468415	−	0.624801i	−0.0791766	−	0.105611i
$36$	−0.00181306	−	0.00794353i	−0.000302177	−	0.00132392i
$37$	0.599368	+	7.99800i	0.0985354	+	1.31486i	0.799067	+	0.601242i	$0.205327\pi$
$37$	0.599368	+	7.99800i	0.0985354	+	1.31486i	−0.700531	+	0.713622i	$0.747054\pi$
$38$	8.69560	+	2.68224i	1.41061	+	0.435117i
$39$	−0.844760	−	2.15241i	−0.135270	−	0.344662i
$40$	0.796085	−	0.245560i	0.125872	−	0.0388264i
$41$	1.79402	+	2.24963i	0.280178	+	0.351332i	0.901930	−	0.431882i	$-0.142150\pi$
$41$	1.79402	+	2.24963i	0.280178	+	0.351332i	−0.621752	+	0.783214i	$0.713579\pi$
$42$	1.26486	+	3.52947i	0.195172	+	0.544609i
$43$	4.17158	−	5.23100i	0.636160	−	0.797719i	−0.354357	−	0.935110i	$-0.615300\pi$
$43$	4.17158	−	5.23100i	0.636160	−	0.797719i	0.990517	+	0.137391i	$0.0438716\pi$
$44$	−0.0159313	+	0.0405922i	−0.00240173	+	0.00611951i
$45$	−0.0220565	+	0.294323i	−0.00328798	+	0.0438751i
$46$	−9.84960	+	1.48459i	−1.45224	+	0.218891i
$47$	−4.12309	+	3.82567i	−0.601414	+	0.558031i	−0.921018	−	0.389520i	$-0.872641\pi$
$47$	−4.12309	+	3.82567i	−0.601414	+	0.558031i	0.319603	+	0.947551i	$0.396450\pi$
$48$	−4.01623			−0.579693
$49$	−3.13160	−	6.26044i	−0.447371	−	0.894348i
$50$	−6.96201			−0.984577
$51$	4.11463	−	3.81782i	0.576164	−	0.534602i
$52$	0.0186294	−	0.00280792i	0.00258343	−	0.000389389i
$53$	0.232676	−	3.10485i	0.0319605	−	0.426483i	−0.958157	−	0.286243i	$-0.907593\pi$
$53$	0.232676	−	3.10485i	0.0319605	−	0.426483i	0.990118	−	0.140240i	$-0.0447875\pi$
$54$	0.517722	−	1.31913i	0.0704530	−	0.179511i
$55$	0.984874	−	1.23499i	0.132800	−	0.166526i
$56$	7.41455	−	0.891876i	0.990810	−	0.119182i
$57$	4.00375	+	5.02055i	0.530310	+	0.664988i
$58$	−5.31059	+	1.63810i	−0.697314	+	0.215093i
$59$	1.07811	+	2.74697i	0.140357	+	0.357625i	0.983717	−	0.179725i	$-0.0575208\pi$
$59$	1.07811	+	2.74697i	0.140357	+	0.357625i	−0.843360	+	0.537350i	$0.819426\pi$
$60$	−0.00229798		0.000708832i	−0.000296667		9.15098e-5i
$61$	−0.246792	−	3.29321i	−0.0315985	−	0.421652i	−0.990462	−	0.137785i	$-0.956002\pi$
$61$	−0.246792	−	3.29321i	−0.0315985	−	0.421652i	0.958864	−	0.283867i	$-0.0916174\pi$
$62$	−2.06379	−	9.04207i	−0.262102	−	1.14834i
$63$	−0.665553	+	2.56067i	−0.0838518	+	0.322614i
$64$	−1.77286	+	7.76739i	−0.221607	+	0.970924i
$65$	−0.674835	−	0.101715i	−0.0837029	−	0.0126162i
$66$	−6.26635	+	4.27232i	−0.771334	+	0.525886i
$67$	−1.22841	+	2.12766i	−0.150074	+	0.259935i	−0.931254	−	0.364370i	$-0.881284\pi$
$67$	−1.22841	+	2.12766i	−0.150074	+	0.259935i	0.781181	+	0.624305i	$0.214618\pi$
$68$	0.0228669	+	0.0396066i	0.00277302	+	0.00480301i
$69$	−6.33298	−	3.04980i	−0.762402	−	0.367153i
$70$	1.08881	+	0.197554i	0.130138	+	0.0236122i
$71$	0.756494	−	0.364308i	0.0897793	−	0.0432354i	−0.388455	−	0.921468i	$-0.626991\pi$
$71$	0.756494	−	0.364308i	0.0897793	−	0.0432354i	0.478235	+	0.878232i	$0.341277\pi$
$72$	−2.33217	−	1.59005i	−0.274849	−	0.187389i
$73$	−6.76324	−	6.27537i	−0.791578	−	0.734477i	0.176724	−	0.984260i	$-0.443450\pi$
$73$	−6.76324	−	6.27537i	−0.791578	−	0.734477i	−0.968302	+	0.249784i	$0.919640\pi$
$74$	−8.33163	−	7.73063i	−0.968533	−	0.898667i
$75$	−4.05922	−	2.76753i	−0.468718	−	0.319567i
$76$	−0.0471399	+	0.0227014i	−0.00540732	+	0.00260403i
$77$	10.6631	−	9.31669i	1.21517	−	1.06174i
$78$	2.95218	+	1.42169i	0.334268	+	0.160975i
$79$	−6.17678	−	10.6985i	−0.694943	−	1.20368i	−0.970200	−	0.242305i	$-0.922096\pi$
$79$	−6.17678	−	10.6985i	−0.694943	−	1.20368i	0.275258	−	0.961371i	$-0.411237\pi$
$80$	−0.592692	+	1.02657i	−0.0662650	+	0.114774i
$81$	0.826239	−	0.563320i	0.0918043	−	0.0625911i
$82$	−4.03197	−	0.607721i	−0.445256	−	0.0671116i
$83$	−2.83042	+	12.4009i	−0.310679	+	1.36117i	0.542721	+	0.839913i	$0.317394\pi$
$83$	−2.83042	+	12.4009i	−0.310679	+	1.36117i	−0.853399	+	0.521258i	$0.825463\pi$
$84$	−0.0191341	−	0.00992949i	−0.00208770	−	0.00108340i
$85$	−0.368644	−	1.61514i	−0.0399851	−	0.175186i
$86$	0.708540	+	9.45481i	0.0764039	+	1.01954i
$87$	−3.74753	−	1.15596i	−0.401777	−	0.123932i
$88$	5.51905	+	14.0623i	0.588333	+	1.49905i
$89$	−6.03004	+	1.86002i	−0.639183	+	0.197162i	−0.597373	−	0.801964i	$-0.703789\pi$
$89$	−6.03004	+	1.86002i	−0.639183	+	0.197162i	−0.0418100	+	0.999126i	$0.513312\pi$
$90$	−0.260776	−	0.327003i	−0.0274882	−	0.0344691i
$91$	−5.78935	−	1.97709i	−0.606889	−	0.207256i
$92$	0.0357083	−	0.0447768i	0.00372285	−	0.00466830i
$93$	2.39109	−	6.09240i	0.247945	−	0.631752i
$94$	0.595637	−	7.94822i	0.0614352	−	0.819796i
$95$	1.87413	−	0.282480i	0.192282	−	0.0289819i
$96$	0.0337869	−	0.0313496i	0.00344836	−	0.00319961i
$97$	4.63741			0.470858			0.235429	−	0.971892i	$-0.424351\pi$
$97$	4.63741			0.470858			0.235429	+	0.971892i	$0.424351\pi$
$98$	9.28734	+	3.48491i	0.938163	+	0.352029i
$99$	−5.35194			−0.537890
$100$	0.0293436	−	0.0272268i	0.00293436	−	0.00272268i
$101$	14.5667	−	2.19557i	1.44944	−	0.218468i	0.623321	−	0.781966i	$-0.285783\pi$
$101$	14.5667	−	2.19557i	1.44944	−	0.218468i	0.826117	+	0.563498i	$0.190545\pi$
$102$	−0.594415	+	7.93191i	−0.0588558	+	0.785376i
$103$	−3.28034	+	8.35816i	−0.323221	+	0.823554i	0.673234	+	0.739429i	$0.264905\pi$
$103$	−3.28034	+	8.35816i	−0.323221	+	0.823554i	−0.996455	+	0.0841245i	$0.973191\pi$
$104$	4.06929	−	5.10273i	0.399027	−	0.500364i
$105$	0.556305	+	0.548008i	0.0542898	+	0.0534801i
$106$	2.75095	+	3.44959i	0.267196	+	0.335053i
$107$	0.641470	−	0.197867i	0.0620132	−	0.0191285i	−0.263593	−	0.964634i	$-0.584908\pi$
$107$	0.641470	−	0.197867i	0.0620132	−	0.0191285i	0.325607	+	0.945505i	$0.394432\pi$
$108$	0.00297673	+	0.00758459i	0.000286436	+	0.000729827i
$109$	8.64048	+	2.66524i	0.827608	+	0.255283i	0.679489	−	0.733686i	$-0.262202\pi$
$109$	8.64048	+	2.66524i	0.827608	+	0.255283i	0.148120	+	0.988969i	$0.452678\pi$
$110$	0.167280	+	2.23220i	0.0159495	+	0.212832i
$111$	−1.78471	−	7.81934i	−0.169398	−	0.742179i
$112$	−6.87047	+	8.10601i	−0.649198	+	0.765946i
$113$	−2.01162	+	8.81349i	−0.189237	+	0.829103i	0.787782	+	0.615954i	$0.211229\pi$
$113$	−2.01162	+	8.81349i	−0.189237	+	0.829103i	−0.977020	+	0.213149i	$0.931628\pi$
$114$	−8.99825	−	1.35627i	−0.842763	−	0.127026i
$115$	−1.71413	+	1.16868i	−0.159844	+	0.108980i
$116$	0.0159769	−	0.0276728i	0.00148342	−	0.00256935i
$117$	1.15613	+	2.00247i	0.106884	+	0.185128i
$118$	−3.76765	−	1.81440i	−0.346840	−	0.167029i
$119$	−0.666753	−	14.8357i	−0.0611212	−	1.35998i
$120$	−0.750594	+	0.361467i	−0.0685196	+	0.0329973i
$121$	14.5775	+	9.93878i	1.32523	+	0.903525i
$122$	3.43058	+	3.18312i	0.310590	+	0.288186i
$123$	−2.10927	−	1.95711i	−0.190186	−	0.176467i
$124$	0.0440600	+	0.0300396i	0.00395670	+	0.00269763i
$125$	−2.63603	+	1.26945i	−0.235774	+	0.113543i
$126$	−1.77677	−	3.30153i	−0.158287	−	0.294124i
$127$	3.24779	+	1.56405i	0.288195	+	0.138787i	0.572396	−	0.819977i	$-0.306014\pi$
$127$	3.24779	+	1.56405i	0.288195	+	0.138787i	−0.284201	+	0.958765i	$0.591728\pi$
$128$	−5.69118	−	9.85741i	−0.503034	−	0.871280i
$129$	−3.34535	+	5.79431i	−0.294541	+	0.510161i
$130$	0.799059	−	0.544789i	0.0700821	−	0.0477812i
$131$	11.0848	+	1.67077i	0.968486	+	0.145976i	0.614190	−	0.789158i	$-0.289483\pi$
$131$	11.0848	+	1.67077i	0.968486	+	0.145976i	0.354295	+	0.935134i	$0.384721\pi$
$132$	0.00970338	−	0.0425133i	0.000844571	−	0.00370031i
$133$	16.9822	+	0.507705i	1.47254	+	0.0440236i
$134$	−0.774713	−	3.39424i	−0.0669250	−	0.293218i
$135$	−0.0220565	−	0.294323i	−0.00189832	−	0.0253313i
$136$	15.1396	+	4.66995i	1.29821	+	0.400445i
$137$	−1.59837	−	4.07259i	−0.136558	−	0.347945i	0.846193	−	0.532876i	$-0.178889\pi$
$137$	−1.59837	−	4.07259i	−0.136558	−	0.347945i	−0.982751	+	0.184932i	$0.940794\pi$
$138$	9.51832	−	2.93601i	0.810253	−	0.249930i
$139$	−5.95696	−	7.46979i	−0.505262	−	0.633579i	0.462145	−	0.886804i	$-0.347080\pi$
$139$	−5.95696	−	7.46979i	−0.505262	−	0.633579i	−0.967407	+	0.253225i	$0.918509\pi$
$140$	−0.00536174	+	0.00342545i	−0.000453149	+	0.000289504i
$141$	3.50685	−	4.39745i	0.295330	−	0.370332i
$142$	−0.434702	+	1.10760i	−0.0364794	+	0.0929480i
$143$	0.924786	−	12.3404i	0.0773345	−	1.03196i
$144$	3.97137	−	0.598588i	0.330948	−	0.0498823i
$145$	−0.848508	+	0.787301i	−0.0704648	+	0.0653818i
$146$	13.0743			1.08204
$147$	4.02969	+	5.72377i	0.332363	+	0.472089i
$148$	0.0653490			0.00537165
$149$	−3.49201	+	3.24011i	−0.286077	+	0.265441i	−0.810137	−	0.586241i	$-0.800607\pi$
$149$	−3.49201	+	3.24011i	−0.286077	+	0.265441i	0.524060	+	0.851681i	$0.324417\pi$
$150$	6.88425	−	1.03763i	0.562097	−	0.0847224i
$151$	0.572964	−	7.64567i	0.0466271	−	0.622196i	−0.924122	−	0.382098i	$-0.875202\pi$
$151$	0.572964	−	7.64567i	0.0466271	−	0.622196i	0.970749	−	0.240098i	$-0.0771794\pi$
$152$	−6.62204	+	16.8727i	−0.537118	+	1.36855i
$153$	−3.49966	+	4.38843i	−0.282931	+	0.354784i
$154$	−2.09681	+	19.9560i	−0.168965	+	1.60810i
$155$	−1.20439	−	1.51026i	−0.0967390	−	0.121307i
$156$	−0.0180028	+	0.00555313i	−0.00144138	+	0.000444606i
$157$	−5.32378	−	13.5648i	−0.424884	−	1.08259i	−0.969758	−	0.244068i	$-0.921518\pi$
$157$	−5.32378	−	13.5648i	−0.424884	−	1.08259i	0.544874	−	0.838518i	$-0.316577\pi$
$158$	16.7284	+	5.16002i	1.33084	+	0.410509i
$159$	0.232676	+	3.10485i	0.0184524	+	0.246230i
$160$	−0.00302709	−	0.0132625i	−0.000239312	−	0.00104850i
$161$	−16.9891	+	7.56472i	−1.33893	+	0.596183i
$162$	−0.315332	+	1.38156i	−0.0247749	+	0.108546i
$163$	−14.7771	−	2.22728i	−1.15743	−	0.174454i	−0.457863	−	0.889023i	$-0.651385\pi$
$163$	−14.7771	−	2.22728i	−1.15743	−	0.174454i	−0.699566	+	0.714568i	$0.746623\pi$
$164$	0.0193706	−	0.0132067i	0.00151259	−	0.00103127i
$165$	−0.789808	+	1.36799i	−0.0614864	+	0.106498i
$166$	−9.01254	−	15.6102i	−0.699509	−	1.21158i
$167$	8.45408	+	4.07127i	0.654196	+	0.315044i	0.731378	−	0.681973i	$-0.238878\pi$
$167$	8.45408	+	4.07127i	0.654196	+	0.315044i	−0.0771813	+	0.997017i	$0.524592\pi$
$168$	−7.19880	+	1.98700i	−0.555400	+	0.153300i
$169$	6.89556	−	3.32073i	0.530428	−	0.255441i
$170$	1.93972	+	1.32248i	0.148770	+	0.101430i
$171$	−4.70731	−	4.36775i	−0.359977	−	0.334010i
$172$	−0.0399620	−	0.0370793i	−0.00304707	−	0.00282727i
$173$	−10.6087	−	7.23291i	−0.806567	−	0.549908i	0.0883771	−	0.996087i	$-0.471832\pi$
$173$	−10.6087	−	7.23291i	−0.806567	−	0.549908i	−0.894944	+	0.446179i	$0.852784\pi$
$174$	5.00713	−	2.41130i	0.379589	−	0.182801i
$175$	−12.5297	+	3.45843i	−0.947160	+	0.261433i
$176$	−19.3660	−	9.32616i	−1.45976	−	0.702986i
$177$	−1.47548	−	2.55560i	−0.110904	−	0.192091i
$178$	4.47120	−	7.74434i	0.335131	−	0.580463i
$179$	9.10511	−	6.20776i	0.680548	−	0.463990i	−0.173056	−	0.984912i	$-0.555364\pi$
$179$	9.10511	−	6.20776i	0.680548	−	0.463990i	0.853604	+	0.520922i	$0.174412\pi$
$180$	0.00237796		0.000358419i	0.000177242		2.67150e-5i
$181$	−1.06259	+	4.65552i	−0.0789818	+	0.346042i	−0.998943	−	0.0459677i	$-0.985363\pi$
$181$	−1.06259	+	4.65552i	−0.0789818	+	0.346042i	0.919961	+	0.392010i	$0.128220\pi$
$182$	7.91964	−	3.52636i	0.587043	−	0.261391i
$183$	0.734863	+	3.21964i	0.0543226	+	0.238003i
$184$	−1.48269	−	19.7851i	−0.109305	−	1.45857i
$185$	−2.26205	−	0.697750i	−0.166309	−	0.0512996i
$186$	3.38839	+	8.63348i	0.248449	+	0.633038i
$187$	28.7059	−	8.85459i	2.09918	−	0.647512i
$188$	0.0285732	+	0.0358296i	0.00208391	+	0.00261314i
$189$	0.276471	−	2.63127i	0.0201103	−	0.191396i
$190$	−1.67458	+	2.09986i	−0.121487	+	0.152340i
$191$	−7.10267	+	18.0973i	−0.513931	+	1.30948i	0.404732	+	0.914435i	$0.367365\pi$
$191$	−7.10267	+	18.0973i	−0.513931	+	1.30948i	−0.918664	+	0.395041i	$0.870731\pi$
$192$	0.595385	−	7.94487i	0.0429682	−	0.573371i
$193$	8.89187	−	1.34023i	0.640051	−	0.0964721i	0.179005	−	0.983848i	$-0.442712\pi$
$193$	8.89187	−	1.34023i	0.640051	−	0.0964721i	0.461046	+	0.887376i	$0.347474\pi$
$194$	−4.81735	+	4.46984i	−0.345865	+	0.320916i
$195$	0.682457			0.0488718
$196$	−0.0527731	+	0.0216324i	−0.00376950	+	0.00154517i
$197$	−18.2654			−1.30136			−0.650680	−	0.759352i	$-0.725516\pi$
$197$	−18.2654			−1.30136			−0.650680	+	0.759352i	$0.725516\pi$
$198$	5.55960	−	5.15855i	0.395103	−	0.366602i
$199$	−21.8087	+	3.28713i	−1.54598	+	0.233019i	−0.865936	−	0.500154i	$-0.833277\pi$
$199$	−21.8087	+	3.28713i	−1.54598	+	0.233019i	−0.680042	+	0.733173i	$0.738039\pi$
$200$	1.03630	−	13.8285i	0.0732778	−	0.977824i
$201$	0.897575	−	2.28698i	0.0633101	−	0.161311i
$202$	−13.0156	+	16.3211i	−0.915778	+	1.14835i
$203$	−8.74389	+	5.58621i	−0.613701	+	0.392075i
$204$	−0.0285146	−	0.0357561i	−0.00199642	−	0.00250343i
$205$	−0.811524	+	0.250322i	−0.0566793	+	0.0174832i
$206$	−4.64853	−	11.8443i	−0.323879	−	0.825230i
$207$	6.71680	+	2.07186i	0.466850	+	0.144004i
$208$	0.693983	+	9.26056i	0.0481191	+	0.642104i
$209$	7.64751	+	33.5059i	0.528989	+	2.31765i
$210$	−1.10610	−	0.0330683i	−0.0763280	−	0.00228193i
$211$	−3.91907	+	17.1706i	−0.269800	+	1.18207i	0.640447	+	0.768003i	$0.278749\pi$
$211$	−3.91907	+	17.1706i	−0.269800	+	1.18207i	−0.910246	+	0.414067i	$0.864108\pi$
$212$	−0.0250853	−	0.00378100i	−0.00172287	−	0.000259680i
$213$	−0.693747	+	0.472989i	−0.0475348	+	0.0324087i
$214$	−0.475642	+	0.823836i	−0.0325142	+	0.0563163i
$215$	0.987374	+	1.71018i	0.0673384	+	0.116633i
$216$	2.54311	+	1.22470i	0.173037	+	0.0833300i
$217$	−8.20599	−	15.2481i	−0.557059	−	1.03511i
$218$	−11.5447	+	5.55962i	−0.781904	+	0.376545i
$219$	7.62300	+	5.19727i	0.515114	+	0.351199i
$220$	−0.00943468	−	0.00875411i	−0.000636086	−	0.000590202i
$221$	−9.51406	−	8.82776i	−0.639985	−	0.593819i
$222$	9.39077	+	6.40252i	0.630267	+	0.429709i
$223$	4.21292	−	2.02884i	0.282118	−	0.135861i	−0.287474	−	0.957788i	$-0.592815\pi$
$223$	4.21292	−	2.02884i	0.282118	−	0.135861i	0.569592	+	0.821928i	$0.307101\pi$
$224$	−0.00547498	−	0.121822i	−0.000365812	−	0.00813955i
$225$	4.42636	+	2.13162i	0.295091	+	0.142108i
$226$	−6.40535	−	11.0944i	−0.426078	−	0.737988i
$227$	1.07960	−	1.86992i	0.0716555	−	0.124111i	−0.827971	−	0.560770i	$-0.810505\pi$
$227$	1.07960	−	1.86992i	0.0716555	−	0.124111i	0.899627	+	0.436659i	$0.143838\pi$
$228$	0.0432300	−	0.0294737i	0.00286297	−	0.00195194i
$229$	9.32059	+	1.40485i	0.615922	+	0.0928353i	0.449591	−	0.893235i	$-0.351570\pi$
$229$	9.32059	+	1.40485i	0.615922	+	0.0928353i	0.166331	+	0.986070i	$0.446808\pi$
$230$	0.654196	−	2.86622i	0.0431364	−	0.188993i
$231$	−9.15543	+	10.8019i	−0.602383	+	0.710712i
$232$	−2.46324	−	10.7922i	−0.161720	−	0.708540i
$233$	0.747043	+	9.96860i	0.0489404	+	0.653065i	0.966697	+	0.255922i	$0.0823791\pi$
$233$	0.747043	+	9.96860i	0.0489404	+	0.653065i	−0.917757	+	0.397143i	$0.870002\pi$
$234$	−3.13110	−	0.965815i	−0.204686	−	0.0631373i
$235$	−0.606495	−	1.54532i	−0.0395633	−	0.100806i
$236$	0.0229756	−	0.00708705i	0.00149559	−	0.000461328i
$237$	7.70232	+	9.65841i	0.500320	+	0.627381i
$238$	14.9922	+	14.7687i	0.971802	+	0.957309i
$239$	12.4260	−	15.5817i	0.803772	−	1.00790i	−0.195856	−	0.980633i	$-0.562749\pi$
$239$	12.4260	−	15.5817i	0.803772	−	1.00790i	0.999628	−	0.0272656i	$-0.00868000\pi$
$240$	0.433069	−	1.10344i	0.0279545	−	0.0712269i
$241$	−1.88583	+	25.1647i	−0.121477	+	1.62100i	0.520213	+	0.854037i	$0.325853\pi$
$241$	−1.88583	+	25.1647i	−0.121477	+	1.62100i	−0.641690	+	0.766964i	$0.721767\pi$
$242$	−24.7228	+	3.72636i	−1.58924	+	0.239540i
$243$	−0.733052	+	0.680173i	−0.0470253	+	0.0436331i
$244$	−0.0269077			−0.00172259
$245$	2.05771	−	0.185332i	0.131462	−	0.0118404i
$246$	4.07751			0.259972
$247$	10.8845	−	10.0993i	0.692563	−	0.642604i
$248$	18.2673	−	2.75335i	1.15997	−	0.174838i
$249$	0.950550	−	12.6842i	0.0602386	−	0.803829i
$250$	1.51474	−	3.85948i	0.0958003	−	0.244095i
$251$	7.53070	−	9.44320i	0.475334	−	0.596050i	−0.485134	−	0.874440i	$-0.661229\pi$
$251$	7.53070	−	9.44320i	0.475334	−	0.596050i	0.960468	+	0.278390i	$0.0898008\pi$
$252$	0.0204003	+	0.00696680i	0.00128510	+	0.000438867i
$253$	−23.4552	−	29.4119i	−1.47461	−	1.84911i
$254$	−4.88135	+	1.50570i	−0.306283	+	0.0944758i
$255$	0.605250	+	1.54215i	0.0379023	+	0.0965734i
$256$	0.186857	+	0.0576377i	0.0116786	+	0.00360236i
$257$	−0.937302	−	12.5074i	−0.0584673	−	0.780192i	−0.946970	−	0.321321i	$-0.895873\pi$
$257$	−0.937302	−	12.5074i	−0.0584673	−	0.780192i	0.888503	−	0.458871i	$-0.151746\pi$
$258$	−2.10979	−	9.24361i	−0.131350	−	0.575482i
$259$	−18.8349	−	9.77425i	−1.17035	−	0.607342i
$260$	−0.00123734	+	0.00542112i	−7.67363e−5	+	0.000336204i
$261$	3.87796	+	0.584508i	0.240039	+	0.0361801i
$262$	−13.1253	+	8.94870i	−0.810886	+	0.552852i
$263$	−4.85395	+	8.40729i	−0.299307	+	0.518416i	−0.975978	−	0.217870i	$-0.930089\pi$
$263$	−4.85395	+	8.40729i	−0.299307	+	0.518416i	0.676670	+	0.736286i	$0.263422\pi$
$264$	−7.55328	−	13.0827i	−0.464873	−	0.805183i
$265$	0.827954	+	0.398722i	0.0508608	+	0.0244933i
$266$	−18.1305	+	15.8411i	−1.11165	+	0.971283i
$267$	5.68546	−	2.73798i	0.347945	−	0.167561i
$268$	0.0165394	+	0.0112764i	0.00101030	+	0.000688813i
$269$	−1.31561	−	1.22070i	−0.0802139	−	0.0744277i	0.639047	−	0.769168i	$-0.279329\pi$
$269$	−1.31561	−	1.22070i	−0.0802139	−	0.0744277i	−0.719261	+	0.694740i	$0.755519\pi$
$270$	0.306601	+	0.284484i	0.0186591	+	0.0173131i
$271$	26.7728	+	18.2534i	1.62633	+	1.10881i	0.912981	+	0.408002i	$0.133774\pi$
$271$	26.7728	+	18.2534i	1.62633	+	1.10881i	0.713348	+	0.700810i	$0.247178\pi$
$272$	−20.3107	+	9.78111i	−1.23152	+	0.593067i
$273$	6.01936	+	1.09215i	0.364308	+	0.0661000i
$274$	5.58582	+	2.68999i	0.337452	+	0.162508i
$275$	−13.1467	−	22.7708i	−0.792778	−	1.37313i
$276$	−0.0286358	+	0.0495987i	−0.00172367	+	0.00298549i
$277$	12.3319	−	8.40774i	0.740951	−	0.505172i	−0.133042	−	0.991110i	$-0.542474\pi$
$277$	12.3319	−	8.40774i	0.740951	−	0.505172i	0.873993	+	0.485938i	$0.161522\pi$
$278$	13.3880	+	2.01791i	0.802957	+	0.121026i
$279$	−1.45636	+	6.38072i	−0.0871899	+	0.382004i
$280$	−0.554470	+	2.13329i	−0.0331359	+	0.127488i
$281$	−2.94605	−	12.9075i	−0.175746	−	0.769995i	−0.983564	−	0.180562i	$-0.942208\pi$
$281$	−2.94605	−	12.9075i	−0.175746	−	0.769995i	0.807817	−	0.589433i	$-0.200649\pi$
$282$	0.595637	+	7.94822i	0.0354696	+	0.473309i
$283$	25.3155	+	7.80880i	1.50485	+	0.464185i	0.934122	−	0.356954i	$-0.116185\pi$
$283$	25.3155	+	7.80880i	1.50485	+	0.464185i	0.570729	+	0.821139i	$0.306661\pi$
$284$	−0.00249940	−	0.00636836i	−0.000148312	−	0.000377893i
$285$	−1.81110	+	0.558650i	−0.107280	+	0.0330916i
$286$	10.9338	+	13.7106i	0.646532	+	0.810725i
$287$	−7.55834	+	0.909173i	−0.446155	+	0.0536668i
$288$	−0.0287371	+	0.0360352i	−0.00169335	+	0.00212339i
$289$	5.29961	−	13.5032i	0.311742	−	0.794306i
$290$	0.122579	−	1.63570i	0.00719806	−	0.0960515i
$291$	−4.58561	+	0.691170i	−0.268813	+	0.0405171i
$292$	−0.0551056	+	0.0511306i	−0.00322481	+	0.00299219i
$293$	−15.5543			−0.908691			−0.454345	−	0.890826i	$-0.650127\pi$
$293$	−15.5543			−0.908691			−0.454345	+	0.890826i	$0.650127\pi$
$294$	−9.70301	−	2.06178i	−0.565891	−	0.120245i
$295$	−0.870970			−0.0507098
$296$	16.5954	−	15.3983i	0.964587	−	0.895006i
$297$	5.29216	−	0.797665i	0.307082	−	0.0462852i
$298$	0.504469	−	6.73167i	0.0292231	−	0.389955i
$299$	−5.93789	+	15.1295i	−0.343397	+	0.874961i
$300$	−0.0249579	+	0.0312962i	−0.00144094	+	0.00180688i
$301$	5.97193	+	16.6641i	0.344216	+	0.960506i
$302$	6.77422	+	8.49460i	0.389812	+	0.488809i
$303$	−14.0767	+	4.34210i	−0.808688	+	0.249447i
$304$	−9.42226	−	24.0075i	−0.540404	−	1.37693i
$305$	0.931407	+	0.287301i	0.0533322	+	0.0164508i
$306$	−0.594415	−	7.93191i	−0.0339804	−	0.453437i
$307$	−0.295880	−	1.29633i	−0.0168868	−	0.0739857i	0.965782	−	0.259354i	$-0.0835095\pi$
$307$	−0.295880	−	1.29633i	−0.0168868	−	0.0739857i	−0.982669	+	0.185368i	$0.940652\pi$
$308$	−0.0692058	−	0.0923109i	−0.00394336	−	0.00525990i
$309$	1.99798	−	8.75371i	0.113661	−	0.497981i
$310$	2.70681	+	0.407986i	0.153737	+	0.0231720i
$311$	−5.77642	+	3.93830i	−0.327551	+	0.223320i	−0.715918	−	0.698184i	$-0.753992\pi$
$311$	−5.77642	+	3.93830i	−0.327551	+	0.223320i	0.388367	+	0.921505i	$0.373039\pi$
$312$	−3.26332	+	5.65224i	−0.184749	+	0.319995i
$313$	10.9959	+	19.0454i	0.621524	+	1.07651i	0.989202	+	0.146558i	$0.0468195\pi$
$313$	10.9959	+	19.0454i	0.621524	+	1.07651i	−0.367678	+	0.929953i	$0.619847\pi$
$314$	18.6050	+	8.95968i	1.04994	+	0.505624i
$315$	−0.631768	−	0.458975i	−0.0355961	−	0.0258603i
$316$	−0.0906867	+	0.0436724i	−0.00510152	+	0.00245676i
$317$	13.7261	+	9.35828i	0.770933	+	0.525613i	0.883726	−	0.468005i	$-0.155027\pi$
$317$	13.7261	+	9.35828i	0.770933	+	0.525613i	−0.112792	+	0.993619i	$0.535980\pi$
$318$	−3.23436	−	3.00105i	−0.181374	−	0.168290i
$319$	−15.3860	−	14.2761i	−0.861452	−	0.799311i
$320$	−1.94289	−	1.32464i	−0.108611	−	0.0740497i
$321$	−0.604815	+	0.291263i	−0.0337575	+	0.0162567i
$322$	10.3570	−	24.2335i	0.577171	−	1.35048i
$323$	32.4746	+	15.6390i	1.80694	+	0.870175i
$324$	−0.00407391	−	0.00705621i	−0.000226328	−	0.000392012i
$325$	−5.67991	+	9.83790i	−0.315065	+	0.545708i
$326$	17.4972	−	11.9294i	0.969082	−	0.660709i
$327$	−8.94121	−	1.34767i	−0.494450	−	0.0745263i
$328$	1.80727	−	7.91816i	0.0997897	−	0.437207i
$329$	−2.87635	−	14.6005i	−0.158578	−	0.804954i
$330$	−0.498104	−	2.18234i	−0.0274197	−	0.120134i
$331$	1.58846	+	21.1965i	0.0873095	+	1.16506i	0.853020	+	0.521879i	$0.174769\pi$
$331$	1.58846	+	21.1965i	0.0873095	+	1.16506i	−0.765710	+	0.643186i	$0.777612\pi$
$332$	0.0990340	+	0.0305479i	0.00543520	+	0.00167654i
$333$	2.93019	+	7.46601i	0.160574	+	0.409135i
$334$	−12.7063	+	3.91937i	−0.695256	+	0.214458i
$335$	−0.452108	−	0.566925i	−0.0247013	−	0.0309744i
$336$	5.58559	−	9.03946i	0.304719	−	0.493143i
$337$	−17.5050	+	21.9505i	−0.953556	+	1.19572i	0.0270311	+	0.999635i	$0.491395\pi$
$337$	−17.5050	+	21.9505i	−0.953556	+	1.19572i	−0.980587	+	0.196086i	$0.937177\pi$
$338$	−3.96238	+	10.0960i	−0.215525	+	0.549149i
$339$	0.675571	−	9.01486i	0.0366920	−	0.489620i
$340$	−0.0133475	+	0.00201181i	−0.000723870	+	0.000109106i
$341$	25.6769	−	23.8247i	1.39048	−	1.29018i
$342$	9.09989			0.492065
$343$	18.4459	+	1.65835i	0.995983	+	0.0895423i
$344$	−18.8854			−1.01823
$345$	1.52081	−	1.41110i	0.0818774	−	0.0759712i
$346$	17.9919	−	2.71185i	0.967252	−	0.145790i
$347$	0.225676	−	3.01144i	0.0121149	−	0.161663i	−0.987865	−	0.155315i	$-0.950361\pi$
$347$	0.225676	−	3.01144i	0.0121149	−	0.161663i	0.999980	−	0.00634709i	$-0.00202035\pi$
$348$	−0.0116740	+	0.0297449i	−0.000625793	+	0.00159450i
$349$	−0.611775	+	0.767142i	−0.0327476	+	0.0410642i	−0.797936	−	0.602743i	$-0.794075\pi$
$349$	−0.611775	+	0.767142i	−0.0327476	+	0.0410642i	0.765188	+	0.643807i	$0.222646\pi$
$350$	9.68245	−	15.6696i	0.517549	−	0.837577i
$351$	−1.44166	−	1.80779i	−0.0769504	−	0.0964927i
$352$	0.235715	−	0.0727086i	0.0125637	−	0.00387538i
$353$	−4.19772	−	10.6956i	−0.223422	−	0.569271i	0.774578	−	0.632478i	$-0.217962\pi$
$353$	−4.19772	−	10.6956i	−0.223422	−	0.569271i	−0.998000	+	0.0632075i	$0.979867\pi$
$354$	3.99599	+	1.23260i	0.212384	+	0.0655119i
$355$	0.0185196	+	0.247127i	0.000982919	+	0.0131161i
$356$	0.0114411	+	0.0501268i	0.000606378	+	0.00265671i
$357$	2.87045	+	14.5706i	0.151920	+	0.771157i
$358$	−3.47495	+	15.2247i	−0.183657	+	0.804653i
$359$	9.35161	+	1.40953i	0.493559	+	0.0743921i	0.391106	−	0.920346i	$-0.372093\pi$
$359$	9.35161	+	1.40953i	0.493559	+	0.0743921i	0.102453	+	0.994738i	$0.467331\pi$
$360$	0.688337	−	0.469300i	0.0362785	−	0.0247343i
$361$	−11.1180	+	19.2569i	−0.585157	+	1.01352i
$362$	−3.38348	−	5.86036i	−0.177832	−	0.308014i
$363$	−15.8960	−	7.65510i	−0.834323	−	0.401789i
$364$	−0.0195890	+	0.0458349i	−0.00102674	+	0.00240240i
$365$	2.45341	−	1.18150i	0.128417	−	0.0618426i
$366$	−3.86669	−	2.63626i	−0.202115	−	0.137800i
$367$	18.8774	+	17.5157i	0.985394	+	0.914312i	0.996327	−	0.0856283i	$-0.0272898\pi$
$367$	18.8774	+	17.5157i	0.985394	+	0.914312i	−0.0109333	+	0.999940i	$0.503480\pi$
$368$	20.6944	+	19.2016i	1.07877	+	1.00095i
$369$	2.37740	+	1.62089i	0.123763	+	0.0843799i
$370$	3.02236	−	1.45549i	0.157125	−	0.0756674i
$371$	6.66458	+	4.84177i	0.346008	+	0.251372i
$372$	−0.0480450	−	0.0231373i	−0.00249102	−	0.00119961i
$373$	3.35239	+	5.80651i	0.173580	+	0.300650i	0.939669	−	0.342085i	$-0.111133\pi$
$373$	3.35239	+	5.80651i	0.173580	+	0.300650i	−0.766089	+	0.642735i	$0.777800\pi$
$374$	−21.2851	+	36.8668i	−1.10062	+	1.90634i
$375$	2.41739	−	1.64815i	0.124833	−	0.0851099i
$376$	15.6987	+	2.36621i	0.809601	+	0.122028i
$377$	−2.01784	+	8.84073i	−0.103924	+	0.455321i
$378$	2.24899	+	2.99984i	0.115676	+	0.154295i
$379$	3.75095	+	16.4340i	0.192673	+	0.844157i	0.975162	+	0.221493i	$0.0710928\pi$
$379$	3.75095	+	16.4340i	0.192673	+	0.844157i	−0.782489	+	0.622665i	$0.786050\pi$
$380$	−0.00115403	−	0.0153994i	−5.92002e−5	−	0.000789972i
$381$	−3.44463	−	1.06253i	−0.176474	−	0.0544349i
$382$	−10.0651	−	25.6455i	−0.514977	−	1.31214i
$383$	2.27723	−	0.702434i	0.116361	−	0.0358927i	−0.236028	−	0.971746i	$-0.575846\pi$
$383$	2.27723	−	0.702434i	0.116361	−	0.0358927i	0.352389	+	0.935854i	$0.385369\pi$
$384$	7.09678	+	8.89908i	0.362156	+	0.454129i
$385$	1.40992	+	3.93426i	0.0718562	+	0.200509i
$386$	−7.94508	+	9.96281i	−0.404394	+	0.507094i
$387$	2.44439	−	6.22819i	0.124255	−	0.316597i
$388$	0.00282366	−	0.0376791i	0.000143350	−	0.00191287i
$389$	9.47962	−	1.42882i	0.480636	−	0.0724442i	0.0957441	−	0.995406i	$-0.469477\pi$
$389$	9.47962	−	1.42882i	0.480636	−	0.0724442i	0.384892	+	0.922962i	$0.374239\pi$
$390$	−0.708937	+	0.657798i	−0.0358984	+	0.0333089i
$391$	−39.4543			−1.99529
$392$	−8.30444	+	17.9285i	−0.419438	+	0.905528i
$393$	−11.2100			−0.565471
$394$	18.9742	−	17.6055i	0.955905	−	0.886950i
$395$	3.60541	−	0.543428i	0.181408	−	0.0273429i
$396$	−0.00325872	+	0.0434847i	−0.000163757	+	0.00218519i
$397$	7.39215	−	18.8349i	0.371001	−	0.945296i	−0.616453	−	0.787392i	$-0.711431\pi$
$397$	7.39215	−	18.8349i	0.371001	−	0.945296i	0.987454	−	0.157904i	$-0.0504738\pi$
$398$	19.4866	−	24.4354i	0.976773	−	1.22483i
$399$	−16.8682	+	2.02903i	−0.844464	+	0.101578i
$400$	12.3023	+	15.4265i	0.615113	+	0.771327i
$401$	−13.2509	+	4.08737i	−0.661720	+	0.204114i	−0.607383	−	0.794409i	$-0.707781\pi$
$401$	−13.2509	+	4.08737i	−0.661720	+	0.204114i	−0.0543371	+	0.998523i	$0.517305\pi$
$402$	1.27195	+	3.24086i	0.0634389	+	0.161640i
$403$	−14.4609	−	4.46061i	−0.720350	−	0.222199i
$404$	−0.00896965	−	0.119692i	−0.000446257	−	0.00595488i
$405$	0.0656767	+	0.287748i	0.00326350	+	0.0142983i
$406$	3.69880	−	14.2309i	0.183569	−	0.706268i
$407$	9.55167	−	41.8486i	0.473459	−	2.07436i
$408$	−15.6665	−	2.36135i	−0.775609	−	0.116904i
$409$	−8.02904	+	5.47411i	−0.397011	+	0.270677i	−0.745326	−	0.666700i	$-0.767706\pi$
$409$	−8.02904	+	5.47411i	−0.397011	+	0.270677i	0.348315	+	0.937377i	$0.386754\pi$
$410$	0.601735	−	1.04224i	0.0297176	−	0.0514724i
$411$	2.18751	+	3.78888i	0.107902	+	0.186891i
$412$	0.0659130	+	0.0317420i	0.00324730	+	0.00156382i
$413$	−7.68207	−	1.39383i	−0.378010	−	0.0685860i
$414$	−8.97442	+	4.32185i	−0.441069	+	0.212407i
$415$	−3.10188	−	2.11483i	−0.152265	−	0.103813i
$416$	−0.0781237	−	0.0724882i	−0.00383033	−	0.00355403i
$417$	7.00374	+	6.49852i	0.342974	+	0.318234i
$418$	−40.2395	−	27.4348i	−1.96818	−	1.34188i
$419$	17.2662	−	8.31495i	0.843508	−	0.406212i	0.0383440	−	0.999265i	$-0.487792\pi$
$419$	17.2662	−	8.31495i	0.843508	−	0.406212i	0.805164	+	0.593053i	$0.202077\pi$
$420$	0.00479131	−	0.00418632i	0.000233792	−	0.000204271i
$421$	−22.9543	−	11.0542i	−1.11872	−	0.538748i	−0.219225	−	0.975674i	$-0.570353\pi$
$421$	−22.9543	−	11.0542i	−1.11872	−	0.538748i	−0.899497	+	0.436926i	$0.856067\pi$
$422$	−12.4790	−	21.6143i	−0.607468	−	1.05217i
$423$	−2.81228	+	4.87101i	−0.136738	+	0.236836i
$424$	−7.26134	+	4.95070i	−0.352642	+	0.240427i
$425$	−27.2681	−	4.11001i	−1.32270	−	0.199365i
$426$	0.264767	−	1.16002i	0.0128280	−	0.0562032i
$427$	7.75536	+	4.02459i	0.375308	+	0.194763i
$428$	−0.00121710	−	0.00533244i	−5.88305e−5	−	0.000257753i
$429$	0.924786	+	12.3404i	0.0446491	+	0.595801i
$430$	−2.67407	−	0.824842i	−0.128955	−	0.0397774i
$431$	8.64196	+	22.0193i	0.416268	+	1.06063i	0.973176	+	0.230060i	$0.0738923\pi$
$431$	8.64196	+	22.0193i	0.416268	+	1.06063i	−0.556908	+	0.830574i	$0.688012\pi$
$432$	−3.83780	+	1.18380i	−0.184646	+	0.0569558i
$433$	−13.6957	−	17.1738i	−0.658172	−	0.825322i	0.334971	−	0.942229i	$-0.391274\pi$
$433$	−13.6957	−	17.1738i	−0.658172	−	0.825322i	−0.993143	+	0.116907i	$0.962702\pi$
$434$	23.2215	+	7.93026i	1.11467	+	0.380665i
$435$	0.721690	−	0.904971i	0.0346024	−	0.0433900i
$436$	0.0269162	−	0.0685814i	0.00128905	−	0.00328445i
$437$	3.37312	−	45.0112i	0.161358	−	2.15318i
$438$	−12.9283	+	1.94862i	−0.617736	+	0.0931087i
$439$	−26.1375	+	24.2520i	−1.24747	+	1.15749i	−0.266397	+	0.963863i	$0.585833\pi$
$439$	−26.1375	+	24.2520i	−1.24747	+	1.15749i	−0.981076	+	0.193623i	$0.937976\pi$
$440$	−4.45868			−0.212559
$441$	−4.83777	−	5.05925i	−0.230370	−	0.240917i
$442$	18.3920			0.874818
$443$	−25.1744	+	23.3584i	−1.19607	+	1.10979i	−0.204683	+	0.978828i	$0.565616\pi$
$443$	−25.1744	+	23.3584i	−1.19607	+	1.10979i	−0.991387	+	0.130962i	$0.958193\pi$
$444$	−0.0646191	+	0.00973976i	−0.00306669	+	0.000462229i
$445$	0.139185	−	1.85729i	0.00659800	−	0.0880442i
$446$	−2.42086	+	6.16825i	−0.114631	+	0.292075i
$447$	2.97010	−	3.72438i	0.140481	−	0.176157i
$448$	−15.0167	−	14.7928i	−0.709473	−	0.698893i
$449$	18.4950	+	23.1920i	0.872832	+	1.09450i	0.994788	+	0.101961i	$0.0325118\pi$
$449$	18.4950	+	23.1920i	0.872832	+	1.09450i	−0.121956	+	0.992535i	$0.538917\pi$
$450$	−6.65271	+	2.05209i	−0.313612	+	0.0967364i
$451$	−5.62609	−	14.3350i	−0.264922	−	0.675010i
$452$	0.0703850	+	0.0217109i	0.00331063	+	0.00102119i
$453$	0.572964	+	7.64567i	0.0269202	+	0.359225i
$454$	0.680865	+	2.98307i	0.0319546	+	0.140002i
$455$	1.16746	−	1.37741i	0.0547315	−	0.0645741i
$456$	4.03333	−	17.6712i	0.188878	−	0.827529i
$457$	−23.9192	−	3.60524i	−1.11889	−	0.168646i	−0.436551	−	0.899679i	$-0.643800\pi$
$457$	−23.9192	−	3.60524i	−1.11889	−	0.168646i	−0.682342	+	0.731034i	$0.739038\pi$
$458$	−11.0363	+	7.52444i	−0.515694	+	0.351594i
$459$	2.80651	−	4.86101i	0.130997	−	0.226893i
$460$	0.00845182	+	0.0146390i	0.000394068	+	0.000682546i
$461$	−14.0557	−	6.76889i	−0.654641	−	0.315259i	0.0769170	−	0.997038i	$-0.475492\pi$
$461$	−14.0557	−	6.76889i	−0.654641	−	0.315259i	−0.731558	+	0.681779i	$0.761207\pi$
$462$	−0.900902	−	20.0456i	−0.0419138	−	0.932607i
$463$	9.50079	−	4.57534i	0.441539	−	0.212634i	−0.199887	−	0.979819i	$-0.564057\pi$
$463$	9.50079	−	4.57534i	0.441539	−	0.212634i	0.641426	+	0.767185i	$0.278343\pi$
$464$	13.0138	+	8.87267i	0.604152	+	0.411904i
$465$	1.41603	+	1.31388i	0.0656669	+	0.0609299i
$466$	−10.3844	−	9.63535i	−0.481050	−	0.446349i
$467$	4.97635	+	3.39282i	0.230278	+	0.157001i	0.672963	−	0.739676i	$-0.265021\pi$
$467$	4.97635	+	3.39282i	0.230278	+	0.157001i	−0.442684	+	0.896677i	$0.645974\pi$
$468$	0.0169741	−	0.00817428i	0.000784626	−	0.000377856i
$469$	−3.08039	−	5.72388i	−0.142239	−	0.264304i
$470$	2.11951	+	1.02070i	0.0977659	+	0.0470816i
$471$	7.28604	+	12.6198i	0.335723	+	0.581489i
$472$	4.16474	−	7.21354i	0.191698	−	0.332030i
$473$	−29.5861	+	20.1715i	−1.36037	+	0.927485i
$474$	−17.3106	−	2.60915i	−0.795102	−	0.119842i
$475$	7.02014	−	30.7572i	0.322106	−	1.41124i
$476$	−0.120946	−	0.00361585i	−0.00554356	−	0.000165732i
$477$	−0.692830	−	3.03549i	−0.0317225	−	0.138985i
$478$	2.11055	+	28.1633i	0.0965344	+	1.28816i
$479$	37.3458	+	11.5196i	1.70637	+	0.526346i	0.985929	−	0.167167i	$-0.0534619\pi$
$479$	37.3458	+	11.5196i	1.70637	+	0.526346i	0.720444	+	0.693513i	$0.243938\pi$
$480$	0.00496995	+	0.0126632i	0.000226846	+	0.000577995i
$481$	−17.7213	+	5.46631i	−0.808023	+	0.249242i
$482$	−22.2964	−	27.9588i	−1.01557	−	1.27349i
$483$	15.6719	−	10.0123i	0.713097	−	0.455577i
$484$	0.0896289	−	0.112391i	0.00407404	−	0.00510869i
$485$	−0.500051	+	1.27411i	−0.0227061	+	0.0578543i
$486$	0.105899	−	1.41313i	0.00480369	−	0.0641008i
$487$	−0.465905	+	0.0702239i	−0.0211122	+	0.00318215i	−0.159590	−	0.987183i	$-0.551017\pi$
$487$	−0.465905	+	0.0702239i	−0.0211122	+	0.00318215i	0.138478	+	0.990366i	$0.455779\pi$
$488$	−6.83322	+	6.34030i	−0.309325	+	0.287012i
$489$	14.9440			0.675790
$490$	−1.95892	+	2.17588i	−0.0884948	+	0.0982963i
$491$	37.0047			1.67000			0.834999	−	0.550252i	$-0.185468\pi$
$491$	37.0047			1.67000			0.834999	+	0.550252i	$0.185468\pi$
$492$	−0.0171859	+	0.0159462i	−0.000774801	+	0.000718911i
$493$	−21.7670	+	3.28085i	−0.980337	+	0.147762i
$494$	−1.57241	+	20.9824i	−0.0707462	+	0.944042i
$495$	0.577098	−	1.47042i	0.0259386	−	0.0660906i
$496$	−16.3887	+	20.5508i	−0.735876	+	0.922759i
$497$	−0.232137	+	2.20933i	−0.0104128	+	0.0991020i
$498$	11.2385	+	14.0926i	0.503607	+	0.631503i
$499$	−10.3963	+	3.20683i	−0.465402	+	0.143558i	−0.518583	−	0.855027i	$-0.673540\pi$
$499$	−10.3963	+	3.20683i	−0.465402	+	0.143558i	0.0531807	+	0.998585i	$0.483064\pi$
$500$	0.00870924	+	0.0221908i	0.000389489	+	0.000992402i
$501$	−8.96645	−	2.76578i	−0.400591	−	0.123566i
$502$	1.27908	+	17.0682i	0.0570884	+	0.761791i
$503$	−8.26162	−	36.1965i	−0.368367	−	1.61392i	−0.731265	−	0.682094i	$-0.761070\pi$
$503$	−8.26162	−	36.1965i	−0.368367	−	1.61392i	0.362897	−	0.931829i	$-0.381788\pi$
$504$	6.82225	−	3.03773i	0.303887	−	0.135311i
$505$	−0.967498	+	4.23888i	−0.0430531	+	0.188628i
$506$	52.7144	+	7.94542i	2.34344	+	0.353217i
$507$	−6.32362	+	4.31137i	−0.280842	+	0.191475i
$508$	0.0146855	−	0.0254361i	0.000651565	−	0.00112854i
$509$	3.47500	+	6.01888i	0.154027	+	0.266782i	0.932704	−	0.360642i	$-0.117443\pi$
$509$	3.47500	+	6.01888i	0.154027	+	0.266782i	−0.778678	+	0.627424i	$0.784109\pi$
$510$	−2.11517	−	1.01861i	−0.0936611	−	0.0451048i
$511$	23.5302	−	6.49475i	1.04091	−	0.287311i
$512$	20.2606	−	9.75700i	0.895402	−	0.431203i
$513$	5.30571	+	3.61737i	0.234253	+	0.159711i
$514$	13.0292	+	12.0893i	0.574692	+	0.533236i
$515$	−1.94265	−	1.80252i	−0.0856035	−	0.0794284i
$516$	0.0450420	+	0.0307091i	0.00198286	+	0.00135189i
$517$	27.1212	−	13.0609i	1.19279	−	0.574417i
$518$	28.9868	−	8.00087i	1.27361	−	0.351538i
$519$	11.5682	+	5.57097i	0.507790	+	0.244539i
$520$	0.963164	+	1.66825i	0.0422375	+	0.0731576i
$521$	−2.50142	+	4.33258i	−0.109589	+	0.189814i	−0.915604	−	0.402082i	$-0.868287\pi$
$521$	−2.50142	+	4.33258i	−0.109589	+	0.189814i	0.806015	+	0.591895i	$0.201620\pi$
$522$	−4.59181	+	3.13065i	−0.200978	+	0.137025i
$523$	−25.5103	−	3.84506i	−1.11549	−	0.168133i	−0.434673	−	0.900589i	$-0.643136\pi$
$523$	−25.5103	−	3.84506i	−1.11549	−	0.168133i	−0.680814	+	0.732456i	$0.738374\pi$
$524$	0.0203245	−	0.0890472i	0.000887878	−	0.00389005i
$525$	11.8743	−	5.28726i	0.518239	−	0.230755i
$526$	−3.06122	−	13.4121i	−0.133475	−	0.584794i
$527$	−2.74530	−	36.6334i	−0.119587	−	1.59578i
$528$	20.5397	+	6.33564i	0.893874	+	0.275724i
$529$	9.64792	+	24.5825i	0.419475	+	1.06880i
$530$	−1.24439	+	0.383845i	−0.0540531	+	0.0166732i
$531$	1.83989	+	2.30715i	0.0798445	+	0.100122i
$532$	0.0144653	−	0.137672i	0.000627152	−	0.00596882i
$533$	−4.14821	+	5.20170i	−0.179679	+	0.225310i
$534$	−3.26702	+	8.32424i	−0.141378	+	0.360225i
$535$	−0.0148064	+	0.197577i	−0.000640135	+	0.00854201i
$536$	6.85724	−	1.03356i	0.296188	−	0.0446431i
$537$	−8.07820	+	7.49547i	−0.348600	+	0.323454i
$538$	2.54325			0.109647
$539$	6.13960	+	36.9570i	0.264451	+	1.59185i
$540$	−0.00240481			−0.000103487
$541$	13.5725	−	12.5934i	0.583526	−	0.541433i	−0.332214	−	0.943204i	$-0.607796\pi$
$541$	13.5725	−	12.5934i	0.583526	−	0.541433i	0.915740	+	0.401771i	$0.131605\pi$
$542$	−45.4054	+	6.84376i	−1.95033	+	0.293965i
$543$	0.356854	−	4.76189i	0.0153141	−	0.204352i
$544$	0.0945166	−	0.240824i	0.00405237	−	0.0103253i
$545$	−1.66396	+	2.08655i	−0.0712764	+	0.0893778i
$546$	−7.30561	+	4.66734i	−0.312651	+	0.199744i
$547$	−22.3923	−	28.0790i	−0.957424	−	1.20057i	−0.979629	−	0.200818i	$-0.935640\pi$
$547$	−22.3923	−	28.0790i	−0.957424	−	1.20057i	0.0222047	−	0.999753i	$-0.492931\pi$
$548$	−0.0340631	+	0.0105071i	−0.00145510	+	0.000448840i
$549$	−1.20652	−	3.07416i	−0.0514929	−	0.131202i
$550$	35.6049	+	10.9826i	1.51820	+	0.468302i
$551$	−1.88198	−	25.1132i	−0.0801749	−	1.06986i
$552$	4.41494	+	19.3431i	0.187912	+	0.823297i
$553$	32.6699	+	0.976710i	1.38926	+	0.0415339i
$554$	−4.70644	+	20.6203i	−0.199958	+	0.876071i
$555$	2.34078	+	0.352815i	0.0993605	+	0.0149762i
$556$	−0.0643194	+	0.0438522i	−0.00272775	+	0.00185975i
$557$	−9.47566	+	16.4123i	−0.401496	+	0.695412i	−0.993907	−	0.110224i	$-0.964843\pi$
$557$	−9.47566	+	16.4123i	−0.401496	+	0.695412i	0.592410	+	0.805636i	$0.298176\pi$
$558$	−4.63730	−	8.03204i	−0.196313	−	0.340023i
$559$	13.9385	+	6.71243i	0.589536	+	0.283905i
$560$	−1.48625	−	2.76170i	−0.0628056	−	0.116703i
$561$	−27.0656	+	13.0341i	−1.14271	+	0.550299i
$562$	15.5014	+	10.5687i	0.653889	+	0.445814i
$563$	−2.19141	−	2.03333i	−0.0923570	−	0.0856948i	0.632643	−	0.774443i	$-0.281970\pi$
$563$	−2.19141	−	2.03333i	−0.0923570	−	0.0856948i	−0.725000	+	0.688749i	$0.758160\pi$
$564$	−0.0335942	−	0.0311708i	−0.00141457	−	0.00131253i
$565$	−2.20456	−	1.50304i	−0.0927464	−	0.0632334i
$566$	−33.8244	+	16.2890i	−1.42175	+	0.684677i
$567$	0.118787	+	2.64308i	0.00498859	+	0.110999i
$568$	−2.13531	−	1.02831i	−0.0895955	−	0.0431469i
$569$	−11.6579	−	20.1920i	−0.488723	−	0.846492i	0.511193	−	0.859466i	$-0.329204\pi$
$569$	−11.6579	−	20.1920i	−0.488723	−	0.846492i	−0.999916	+	0.0129734i	$0.995870\pi$
$570$	1.34291	−	2.32599i	0.0562482	−	0.0974248i
$571$	19.9538	−	13.6043i	0.835042	−	0.569322i	−0.0685835	−	0.997645i	$-0.521848\pi$
$571$	19.9538	−	13.6043i	0.835042	−	0.569322i	0.903626	+	0.428323i	$0.140896\pi$
$572$	−0.0997032	−	0.0150278i	−0.00416880	−	0.000628345i
$573$	4.32608	−	18.9538i	0.180724	−	0.791806i
$574$	6.97530	−	8.22969i	0.291143	−	0.343501i
$575$	7.68434	+	33.6673i	0.320459	+	1.40402i
$576$	0.595385	+	7.94487i	0.0248077	+	0.331036i
$577$	31.5073	+	9.71870i	1.31166	+	0.404595i	0.870207	−	0.492687i	$-0.163985\pi$
$577$	31.5073	+	9.71870i	1.31166	+	0.404595i	0.441458	+	0.897282i	$0.354461\pi$
$578$	7.51004	+	19.1353i	0.312376	+	0.795922i
$579$	−8.59280	+	2.65053i	−0.357105	+	0.110152i
$580$	0.00588020	+	0.00737353i	0.000244162	+	0.000306169i
$581$	−23.9746	−	23.6171i	−0.994635	−	0.979801i
$582$	4.09735	−	5.13791i	0.169840	−	0.212973i
$583$	−6.08787	+	15.5116i	−0.252134	+	0.642427i
$584$	−1.94612	+	25.9692i	−0.0805312	+	1.07461i
$585$	−0.674835	+	0.101715i	−0.0279010	+	0.00420540i
$586$	16.1578	−	14.9923i	0.667473	−	0.619324i
$587$	46.8141			1.93223			0.966113	−	0.258120i	$-0.0831030\pi$
$587$	46.8141			1.93223			0.966113	+	0.258120i	$0.0831030\pi$
$588$	0.0489595	−	0.0292562i	0.00201905	−	0.00120651i
$589$	42.0277			1.73172
$590$	0.904765	−	0.839499i	0.0372486	−	0.0345616i
$591$	18.0614	−	2.72232i	0.742948	−	0.111981i
$592$	−2.40720	+	32.1218i	−0.0989352	+	1.32020i
$593$	14.4406	−	36.7939i	0.593002	−	1.51095i	−0.247362	−	0.968923i	$-0.579564\pi$
$593$	14.4406	−	36.7939i	0.593002	−	1.51095i	0.840364	−	0.542022i	$-0.182341\pi$
$594$	−4.72866	+	5.92955i	−0.194019	+	0.243292i
$595$	4.14794	+	1.41654i	0.170049	+	0.0580725i
$596$	0.0241998	+	0.0303456i	0.000991262	+	0.00124300i
$597$	21.0752	−	6.50084i	0.862551	−	0.266062i
$598$	−8.41453	−	21.4399i	−0.344096	−	0.876741i
$599$	−2.71357	−	0.837027i	−0.110874	−	0.0342000i	0.238822	−	0.971063i	$-0.423239\pi$
$599$	−2.71357	−	0.837027i	−0.110874	−	0.0342000i	−0.349696	+	0.936863i	$0.613715\pi$
$600$	1.03630	+	13.8285i	0.0423069	+	0.564547i
$601$	1.44133	+	6.31487i	0.0587930	+	0.257589i	0.995780	−	0.0917761i	$-0.0292544\pi$
$601$	1.44133	+	6.31487i	0.0587930	+	0.257589i	−0.936987	+	0.349365i	$0.886397\pi$
$602$	−22.2657	−	11.5546i	−0.907481	−	0.470930i
$603$	−0.546693	+	2.39522i	−0.0222630	+	0.0975408i
$604$	−0.0617725	−	0.00931070i	−0.00251349	−	0.000378847i
$605$	−4.30253	+	2.93341i	−0.174923	+	0.119260i
$606$	10.4377	−	18.0787i	0.424004	−	0.734397i
$607$	5.24760	+	9.08911i	0.212994	+	0.368916i	0.952650	−	0.304069i	$-0.0983453\pi$
$607$	5.24760	+	9.08911i	0.212994	+	0.368916i	−0.739656	+	0.672985i	$0.765012\pi$
$608$	0.266662	+	0.128418i	0.0108146	+	0.00520803i
$609$	7.81365	−	6.82702i	0.316625	−	0.276645i
$610$	−1.24447	+	0.599304i	−0.0503870	+	0.0242651i
$611$	−10.7455	−	7.32619i	−0.434718	−	0.296386i
$612$	0.0335253	+	0.0311069i	0.00135518	+	0.00125742i
$613$	−8.39112	−	7.78582i	−0.338914	−	0.314466i	0.492293	−	0.870430i	$-0.336159\pi$
$613$	−8.39112	−	7.78582i	−0.338914	−	0.314466i	−0.831207	+	0.555963i	$0.812349\pi$
$614$	1.55685	+	1.06144i	0.0628295	+	0.0428364i
$615$	0.765151	−	0.368477i	0.0308539	−	0.0148584i
$616$	−39.3262	−	7.13532i	−1.58450	−	0.287490i
$617$	2.49873	+	1.20333i	0.100595	+	0.0484441i	0.483505	−	0.875342i	$-0.339364\pi$
$617$	2.49873	+	1.20333i	0.100595	+	0.0484441i	−0.382909	+	0.923786i	$0.625078\pi$
$618$	6.36191	+	11.0192i	0.255914	+	0.443255i
$619$	−11.0641	+	19.1636i	−0.444705	+	0.770251i	−0.998032	−	0.0627129i	$-0.980025\pi$
$619$	−11.0641	+	19.1636i	−0.444705	+	0.770251i	0.553327	+	0.832964i	$0.313358\pi$
$620$	−0.0130042	+	0.00886614i	−0.000522263	+	0.000356073i
$621$	−6.95057	−	1.04763i	−0.278917	−	0.0420400i
$622$	2.20456	−	9.65881i	0.0883949	−	0.387283i
$623$	4.19990	−	16.1588i	0.168265	−	0.647390i
$624$	−2.06645	−	9.05370i	−0.0827241	−	0.362438i
$625$	1.77117	+	23.6346i	0.0708468	+	0.945385i
$626$	−29.7798	−	9.18585i	−1.19024	−	0.367140i
$627$	−12.5559	−	31.9919i	−0.501434	−	1.27763i
$628$	−0.113456	+	0.0349965i	−0.00452738	+	0.00139651i
$629$	−28.0688	−	35.1971i	−1.11917	−	1.40340i
$630$	1.09867	−	0.132156i	0.0437721	−	0.00526523i
$631$	11.0002	−	13.7938i	0.437911	−	0.549123i	−0.513080	−	0.858341i	$-0.671496\pi$
$631$	11.0002	−	13.7938i	0.437911	−	0.549123i	0.950991	+	0.309218i	$0.100067\pi$
$632$	−12.7393	+	32.4592i	−0.506742	+	1.29116i
$633$	1.31616	−	17.5629i	0.0523125	−	0.698062i
$634$	−23.2788	+	3.50872i	−0.924519	+	0.139349i
$635$	−0.779926	+	0.723666i	−0.0309504	+	0.0287178i
$636$	0.0253686			0.00100593
$637$	12.5015	−	10.2806i	0.495327	−	0.407334i
$638$	29.7433			1.17755
$639$	0.615503	−	0.571104i	0.0243489	−	0.0225925i
$640$	3.32196	−	0.500705i	0.131312	−	0.0197921i
$641$	1.16854	−	15.5931i	0.0461545	−	0.615888i	−0.925388	−	0.379022i	$-0.876261\pi$
$641$	1.16854	−	15.5931i	0.0461545	−	0.615888i	0.971542	−	0.236867i	$-0.0761204\pi$
$642$	0.347543	−	0.885526i	0.0137164	−	0.0349489i
$643$	−6.97587	+	8.74747i	−0.275102	+	0.344966i	−0.900119	−	0.435645i	$-0.856520\pi$
$643$	−6.97587	+	8.74747i	−0.275102	+	0.344966i	0.625017	+	0.780611i	$0.285092\pi$
$644$	0.0511191	+	0.142643i	0.00201437	+	0.00562094i
$645$	−1.23124	−	1.54392i	−0.0484798	−	0.0607918i
$646$	−48.8086	+	15.0554i	−1.92035	+	0.592349i
$647$	−1.06904	−	2.72387i	−0.0420283	−	0.107086i	0.908318	−	0.418279i	$-0.137367\pi$
$647$	−1.06904	−	2.72387i	−0.0420283	−	0.107086i	−0.950347	+	0.311193i	$0.899271\pi$
$648$	−2.69723	−	0.831987i	−0.105957	−	0.0326835i
$649$	−1.18024	−	15.7492i	−0.0463284	−	0.618209i
$650$	−3.58212	−	15.6943i	−0.140502	−	0.615581i
$651$	10.3869	+	13.8547i	0.407096	+	0.543010i
$652$	−0.0270943	+	0.118708i	−0.00106110	+	0.00464896i
$653$	30.6786	+	4.62405i	1.20055	+	0.180953i	0.718711	−	0.695309i	$-0.244733\pi$
$653$	30.6786	+	4.62405i	1.20055	+	0.180953i	0.481835	+	0.876262i	$0.339971\pi$
$654$	10.5871	−	7.21817i	0.413989	−	0.282253i
$655$	−1.65431	+	2.86535i	−0.0646393	+	0.111959i
$656$	5.77811	+	10.0080i	0.225597	+	0.390746i
$657$	−8.31247	−	4.00307i	−0.324300	−	0.156175i
$658$	17.0609	+	12.3946i	0.665104	+	0.483194i
$659$	−38.9163	+	18.7411i	−1.51597	+	0.730050i	−0.992528	−	0.122014i	$-0.961065\pi$
$659$	−38.9163	+	18.7411i	−1.51597	+	0.730050i	−0.523437	+	0.852064i	$0.675350\pi$
$660$	0.0106340	+	0.00725016i	0.000413929	+	0.000282212i
$661$	−12.6084	−	11.6989i	−0.490409	−	0.455033i	0.395788	−	0.918342i	$-0.370472\pi$
$661$	−12.6084	−	11.6989i	−0.490409	−	0.455033i	−0.886197	+	0.463309i	$0.846662\pi$
$662$	−22.0807	−	20.4879i	−0.858190	−	0.796284i
$663$	10.7235	+	7.31116i	0.416466	+	0.283942i
$664$	32.3478	−	15.5779i	1.25534	−	0.604538i
$665$	−1.97067	+	4.61104i	−0.0764195	+	0.178808i
$666$	−10.2401	−	4.93138i	−0.396797	−	0.191087i
$667$	13.7832	+	23.8732i	0.533687	+	0.924373i
$668$	0.0382268	−	0.0662107i	0.00147904	−	0.00256177i
$669$	−3.86348	+	2.63408i	−0.149371	+	0.101839i
$670$	1.01609	+	0.153151i	0.0392550	+	0.00591674i
$671$	−3.93294	+	17.2313i	−0.151829	+	0.665208i
$672$	0.0235704	+	0.119645i	0.000909248	+	0.00461540i
$673$	0.471605	+	2.06623i	0.0181790	+	0.0796475i	0.983204	−	0.182511i	$-0.0584227\pi$
$673$	0.471605	+	2.06623i	0.0181790	+	0.0796475i	−0.965025	+	0.262159i	$0.915566\pi$
$674$	−2.97321	−	39.6747i	−0.114524	−	1.52821i
$675$	−4.69462	−	1.44810i	−0.180696	−	0.0557374i
$676$	−0.0227824	−	0.0580486i	−0.000876246	−	0.00223264i
$677$	−35.2324	+	10.8677i	−1.35409	+	0.417681i	−0.885050	−	0.465496i	$-0.845876\pi$
$677$	−35.2324	+	10.8677i	−1.35409	+	0.417681i	−0.469040	+	0.883177i	$0.655400\pi$
$678$	7.98735	+	10.0158i	0.306752	+	0.384655i
$679$	−6.44950	+	10.4376i	−0.247509	+	0.400557i
$680$	−2.91555	+	3.65599i	−0.111806	+	0.140201i
$681$	−0.788843	+	2.00994i	−0.0302285	+	0.0770211i
$682$	−3.70938	+	49.4983i	−0.142040	+	1.89539i
$683$	−24.1571	+	3.64110i	−0.924347	+	0.139323i	−0.593934	−	0.804514i	$-0.702426\pi$
$683$	−24.1571	+	3.64110i	−0.924347	+	0.139323i	−0.330413	+	0.943837i	$0.607188\pi$
$684$	−0.0383543	+	0.0355876i	−0.00146651	+	0.00136073i
$685$	1.29128			0.0493372
$686$	−20.7600	+	16.0567i	−0.792621	+	0.613046i
$687$	−9.42587			−0.359619
$688$	19.6981	−	18.2772i	0.750983	−	0.696811i
$689$	7.11890	−	1.07300i	0.271209	−	0.0408781i
$690$	−0.219701	+	2.93171i	−0.00836388	+	0.111608i
$691$	9.41992	−	24.0016i	0.358350	−	0.913062i	−0.632062	−	0.774918i	$-0.717791\pi$
$691$	9.41992	−	24.0016i	0.358350	−	0.913062i	0.990412	−	0.138144i	$-0.0441137\pi$
$692$	−0.0652271	+	0.0817922i	−0.00247956	+	0.00310927i
$693$	7.44323	−	12.0458i	0.282745	−	0.457581i
$694$	2.66819	+	3.34581i	0.101283	+	0.127005i
$695$	2.69463	−	0.831184i	0.102213	−	0.0315286i
$696$	4.04421	+	10.3045i	0.153296	+	0.390591i
$697$	−15.4332	−	4.76052i	−0.584576	−	0.180318i
$698$	−0.103910	−	1.38658i	−0.00393304	−	0.0524828i
$699$	−2.22444	−	9.74592i	−0.0841362	−	0.368625i
$700$	0.0204706	+	0.103910i	0.000773717	+	0.00392744i
$701$	5.54248	−	24.2832i	0.209336	−	0.917163i	−0.755673	−	0.654949i	$-0.772690\pi$
$701$	5.54248	−	24.2832i	0.209336	−	0.917163i	0.965010	−	0.262214i	$-0.0844527\pi$
$702$	3.24007	+	0.488362i	0.122289	+	0.0184320i
$703$	42.5541	−	29.0129i	1.60496	−	1.09424i
$704$	21.3198	−	36.9270i	0.803521	−	1.39174i
$705$	0.830039	+	1.43767i	0.0312611	+	0.0541458i
$706$	14.6698	+	7.06458i	0.552104	+	0.265879i
$707$	−15.3170	+	35.8392i	−0.576057	+	1.34787i
$708$	−0.0216628	+	0.0104322i	−0.000814136	+	0.000392067i
$709$	−14.5679	−	9.93224i	−0.547110	−	0.373013i	0.257995	−	0.966146i	$-0.416938\pi$
$709$	−14.5679	−	9.93224i	−0.547110	−	0.373013i	−0.805104	+	0.593133i	$0.797891\pi$
$710$	−0.257436	−	0.238865i	−0.00966139	−	0.00896446i
$711$	−9.05581	−	8.40256i	−0.339619	−	0.315121i
$712$	14.7169	+	10.0338i	0.551540	+	0.376033i
$713$	−41.4482	+	19.9604i	−1.55225	+	0.747523i
$714$	−17.0259	−	12.3692i	−0.637180	−	0.462906i
$715$	3.29076	+	1.58475i	0.123067	+	0.0592661i
$716$	−0.0448943	−	0.0777592i	−0.00167778	−	0.00290600i
$717$	−9.96489	+	17.2597i	−0.372146	+	0.644575i
$718$	−11.0731	+	7.54949i	−0.413243	+	0.281744i
$719$	44.1084	+	6.64827i	1.64497	+	0.247939i	0.905219	−	0.424946i	$-0.139707\pi$
$719$	44.1084	+	6.64827i	1.64497	+	0.247939i	0.739747	+	0.672885i	$0.234945\pi$
$720$	−0.263773	+	1.15566i	−0.00983023	+	0.0430690i
$721$	−14.2498	−	19.0073i	−0.530692	−	0.707869i
$722$	−7.01172	−	30.7204i	−0.260949	−	1.14329i
$723$	−1.88583	−	25.1647i	−0.0701349	−	0.935885i
$724$	0.0371792	+	0.0114683i	0.00138176	+	0.000426215i
$725$	7.03908	+	17.9353i	0.261425	+	0.666100i
$726$	23.8913	−	7.36948i	0.886688	−	0.273507i
$727$	10.4756	+	13.1360i	0.388519	+	0.487187i	0.937174	−	0.348861i	$-0.113432\pi$
$727$	10.4756	+	13.1360i	0.388519	+	0.487187i	−0.548656	+	0.836049i	$0.684860\pi$
$728$	5.82550	+	16.2556i	0.215907	+	0.602471i
$729$	0.623490	−	0.781831i	0.0230922	−	0.0289567i
$730$	−1.40980	+	3.59211i	−0.0521790	+	0.132950i
$731$	−2.80649	+	37.4500i	−0.103802	+	1.38514i
$732$	0.0266072	−	0.00401038i	0.000983429	−	0.000148228i
$733$	1.24123	−	1.15169i	0.0458458	−	0.0425387i	−0.656917	−	0.753963i	$-0.728140\pi$
$733$	1.24123	−	1.15169i	0.0458458	−	0.0425387i	0.702763	+	0.711424i	$0.251949\pi$
$734$	−36.4927			−1.34697
$735$	−2.00710	+	0.489948i	−0.0740332	+	0.0180720i
$736$	−0.323975			−0.0119419
$737$	9.63869	−	8.94339i	0.355046	−	0.329434i
$738$	−4.03197	+	0.607721i	−0.148419	+	0.0223705i
$739$	1.98367	−	26.4702i	0.0729704	−	0.973722i	−0.833792	−	0.552079i	$-0.813835\pi$
$739$	1.98367	−	26.4702i	0.0729704	−	0.973722i	0.906762	−	0.421643i	$-0.138546\pi$
$740$	−0.00704657	+	0.0179544i	−0.000259037	+	0.000660016i
$741$	−9.25768	+	11.6088i	−0.340090	+	0.426459i
$742$	−11.5900	+	1.39413i	−0.425482	+	0.0511802i
$743$	−11.2973	−	14.1664i	−0.414458	−	0.519714i	0.530155	−	0.847901i	$-0.322134\pi$
$743$	−11.2973	−	14.1664i	−0.414458	−	0.519714i	−0.944613	+	0.328187i	$0.893562\pi$
$744$	−17.6529	+	5.44520i	−0.647187	+	0.199631i
$745$	−0.513665	−	1.30880i	−0.0188192	−	0.0479506i
$746$	−9.07917	−	2.80055i	−0.332412	−	0.102536i
$747$	0.950550	+	12.6842i	0.0347788	+	0.464091i
$748$	−0.0544652	−	0.238628i	−0.00199145	−	0.00872509i
$749$	−0.446781	+	1.71896i	−0.0163250	+	0.0628095i
$750$	−0.922591	+	4.04214i	−0.0336883	+	0.147598i
$751$	24.6711	+	3.71857i	0.900260	+	0.135692i	0.582835	−	0.812591i	$-0.301944\pi$
$751$	24.6711	+	3.71857i	0.900260	+	0.135692i	0.317425	+	0.948283i	$0.397182\pi$
$752$	−18.6643	+	12.7251i	−0.680618	+	0.464037i
$753$	−6.03915	+	10.4601i	−0.220079	+	0.381188i
$754$	−6.42515	−	11.1287i	−0.233990	−	0.405283i
$755$	2.03883	+	0.981851i	0.0742008	+	0.0357332i
$756$	−0.0212108	−	0.00384848i	−0.000771429	−	0.000139968i
$757$	−13.1042	+	6.31063i	−0.476279	+	0.229364i	−0.656593	−	0.754245i	$-0.728003\pi$
$757$	−13.1042	+	6.31063i	−0.476279	+	0.229364i	0.180314	+	0.983609i	$0.442289\pi$
$758$	−19.7367	−	13.4562i	−0.716868	−	0.488752i
$759$	27.5768	+	25.5876i	1.00098	+	0.928769i
$760$	−3.92164	−	3.63875i	−0.142253	−	0.131992i
$761$	−10.4488	−	7.12388i	−0.378769	−	0.258240i	0.358938	−	0.933361i	$-0.383139\pi$
$761$	−10.4488	−	7.12388i	−0.378769	−	0.258240i	−0.737707	+	0.675121i	$0.764091\pi$
$762$	4.60242	−	2.21641i	0.166728	−	0.0802919i
$763$	−18.0155	+	15.7407i	−0.652206	+	0.569853i
$764$	0.142717	+	0.0687287i	0.00516330	+	0.00248652i
$765$	−0.828336	−	1.43472i	−0.0299486	−	0.0518724i
$766$	−1.68854	+	2.92464i	−0.0610095	+	0.105672i
$767$	−5.63772	+	3.84373i	−0.203566	+	0.138789i
$768$	−0.193360	−	0.0291444i	−0.00697729	−	0.00105166i
$769$	−12.0564	+	52.8226i	−0.434766	+	1.90483i	−0.00908592	+	0.999959i	$0.502892\pi$
$769$	−12.0564	+	52.8226i	−0.434766	+	1.90483i	−0.425680	+	0.904874i	$0.639965\pi$
$770$	−5.25673	−	2.72794i	−0.189440	−	0.0983082i
$771$	2.79097	+	12.2280i	0.100514	+	0.440382i
$772$	−0.00547530	−	0.0730628i	−0.000197060	−	0.00262959i
$773$	−33.7278	−	10.4037i	−1.21311	−	0.374194i	−0.378792	−	0.925482i	$-0.623660\pi$
$773$	−33.7278	−	10.4037i	−1.21311	−	0.374194i	−0.834315	+	0.551288i	$0.814136\pi$
$774$	3.46392	+	8.82592i	0.124508	+	0.317241i
$775$	−30.7254	+	9.47754i	−1.10369	+	0.340443i
$776$	−8.16131	−	10.2340i	−0.292974	−	0.367378i
$777$	20.0814	+	6.85788i	0.720414	+	0.246025i
$778$	−8.47024	+	10.6213i	−0.303673	+	0.380794i
$779$	6.75046	−	17.1999i	0.241860	−	0.616250i
$780$	0.000415539	−	0.00554499i	1.48787e−5	−	0.000198542i
$781$	−4.44354	+	0.669755i	−0.159002	+	0.0239657i
$782$	40.9852	−	38.0287i	1.46563	−	1.35990i
$783$	−3.92176			−0.140152
$784$	−8.68932	−	26.7371i	−0.310333	−	0.954895i
$785$	4.30093			0.153507
$786$	11.6450	−	10.8050i	0.415363	−	0.385401i
$787$	−0.229411	+	0.0345782i	−0.00817762	+	0.00123258i	−0.153130	−	0.988206i	$-0.548935\pi$
$787$	−0.229411	+	0.0345782i	−0.00817762	+	0.00123258i	0.144952	+	0.989439i	$0.453697\pi$
$788$	−0.0111216	+	0.148407i	−0.000396190	+	0.00528679i
$789$	3.54670	−	9.03683i	0.126266	−	0.321720i
$790$	−3.22151	+	4.03965i	−0.114616	+	0.143724i
$791$	−17.0391	−	16.7850i	−0.605842	−	0.596807i
$792$	9.41879	+	11.8108i	0.334682	+	0.419678i
$793$	7.29683	−	2.25077i	0.259118	−	0.0799273i
$794$	10.4754	+	26.6908i	0.371756	+	0.947220i
$795$	−0.878133	−	0.270868i	−0.0311442	−	0.00960670i
$796$	0.0134290	+	0.179198i	0.000475979	+	0.00635150i
$797$	11.0103	+	48.2392i	0.390004	+	1.70872i	0.664634	+	0.747169i	$0.268587\pi$
$797$	11.0103	+	48.2392i	0.390004	+	1.70872i	−0.274630	+	0.961550i	$0.588555\pi$
$798$	15.5670	−	18.3664i	0.551064	−	0.650164i
$799$	7.02514	−	30.7792i	0.248532	−	1.08889i
$800$	−0.223909	−	0.0337489i	−0.00791639	−	0.00119320i
$801$	−5.21389	+	3.55477i	−0.184224	+	0.125602i
$802$	9.82541	−	17.0181i	0.346947	−	0.600930i
$803$	24.6889	+	42.7624i	0.871251	+	1.50905i
$804$	−0.0180353	−	0.00868534i	−0.000636056	−	0.000306308i
$805$	−0.246438	−	5.48340i	−0.00868581	−	0.193264i
$806$	19.3215	−	9.30473i	0.680570	−	0.327745i
$807$	1.48285	+	1.01099i	0.0521987	+	0.0355885i
$808$	−30.4809	−	28.2822i	−1.07232	−	0.994963i
$809$	24.2324	+	22.4843i	0.851964	+	0.790507i	0.979525	−	0.201324i	$-0.0645243\pi$
$809$	24.2324	+	22.4843i	0.851964	+	0.790507i	−0.127561	+	0.991831i	$0.540715\pi$
$810$	−0.345576	−	0.235610i	−0.0121423	−	0.00827849i
$811$	40.6811	−	19.5910i	1.42851	−	0.687933i	0.449788	−	0.893135i	$-0.351499\pi$
$811$	40.6811	−	19.5910i	1.42851	−	0.687933i	0.978720	+	0.205202i	$0.0657851\pi$
$812$	0.0400641	+	0.0744458i	0.00140597	+	0.00261253i
$813$	−29.1942	−	14.0592i	−1.02389	−	0.493078i
$814$	30.4142	+	52.6789i	1.06602	+	1.84640i
$815$	2.20535	−	3.81977i	0.0772499	−	0.133801i
$816$	18.6260	−	12.6990i	0.652041	−	0.444554i
$817$	−42.4846	−	6.40352i	−1.48635	−	0.224031i
$818$	3.06427	−	13.4254i	0.107140	−	0.469410i
$819$	−6.11491	−	0.182813i	−0.213672	−	0.00638802i
$820$	0.00153975	+	0.00674608i	5.37703e−5	+	0.000235583i
$821$	0.778090	+	10.3829i	0.0271555	+	0.362365i	0.994184	+	0.107696i	$0.0343475\pi$
$821$	0.778090	+	10.3829i	0.0271555	+	0.362365i	−0.967028	+	0.254669i	$0.918033\pi$
$822$	−5.92436	−	1.82742i	−0.206636	−	0.0637387i
$823$	1.95131	+	4.97186i	0.0680184	+	0.173308i	0.960841	−	0.277101i	$-0.0893735\pi$
$823$	1.95131	+	4.97186i	0.0680184	+	0.173308i	−0.892822	+	0.450409i	$0.851278\pi$
$824$	24.2180	−	7.47027i	0.843674	−	0.260239i
$825$	16.3937	+	20.5571i	0.570755	+	0.715705i
$826$	9.32362	−	5.95658i	0.324410	−	0.207256i
$827$	2.88791	−	3.62132i	0.100422	−	0.125926i	−0.729081	−	0.684428i	$-0.760052\pi$
$827$	2.88791	−	3.62132i	0.100422	−	0.125926i	0.829503	+	0.558502i	$0.188624\pi$
$828$	0.0209237	−	0.0533127i	0.000727148	−	0.00185274i
$829$	1.58100	−	21.0970i	0.0549104	−	0.732729i	−0.900010	−	0.435868i	$-0.856441\pi$
$829$	1.58100	−	21.0970i	0.0549104	−	0.732729i	0.954921	−	0.296860i	$-0.0959396\pi$
$830$	5.26065	−	0.792916i	0.182600	−	0.0275225i
$831$	−10.9410	+	10.1518i	−0.379541	+	0.352162i
$832$	−18.4220			−0.638669
$833$	34.3184	+	19.1321i	1.18906	+	0.662888i
$834$	−13.5392			−0.468824
$835$	−2.03017	+	1.88372i	−0.0702568	+	0.0651888i
$836$	0.276893	−	0.0417349i	0.00957655	−	0.00144343i
$837$	0.489095	−	6.52652i	0.0169056	−	0.225589i
$838$	−9.92162	+	25.2799i	−0.342737	+	0.873279i
$839$	19.7857	−	24.8104i	0.683077	−	0.856551i	−0.312557	−	0.949899i	$-0.601186\pi$
$839$	19.7857	−	24.8104i	0.683077	−	0.856551i	0.995634	+	0.0933481i	$0.0297570\pi$
$840$	0.230327	−	2.19210i	0.00794704	−	0.0756346i
$841$	−8.49181	−	10.6484i	−0.292821	−	0.367186i
$842$	34.4997	−	10.6417i	1.18894	−	0.366739i
$843$	4.83690	+	12.3242i	0.166592	+	0.424469i
$844$	0.137125	+	0.0422975i	0.00472004	+	0.00145594i
$845$	0.168809	+	2.25260i	0.00580721	+	0.0774918i
$846$	−1.77360	−	7.77067i	−0.0609778	−	0.267161i
$847$	−42.6433	+	18.9877i	−1.46524	+	0.652424i
$848$	2.78257	−	12.1912i	0.0955537	−	0.418648i
$849$	−26.1966	−	3.94850i	−0.899065	−	0.135512i
$850$	32.2877	−	22.0133i	1.10746	−	0.755052i
$851$	−28.1881	+	48.8233i	−0.966277	+	1.67364i
$852$	0.00342064	+	0.00592472i	0.000117189	+	0.000202977i
$853$	−12.5985	−	6.06711i	−0.431364	−	0.207734i	0.205586	−	0.978639i	$-0.434090\pi$
$853$	−12.5985	−	6.06711i	−0.431364	−	0.207734i	−0.636950	+	0.770905i	$0.719804\pi$
$854$	−11.9354	+	3.29439i	−0.408423	+	0.112732i
$855$	1.70761	−	0.822341i	0.0583990	−	0.0281235i
$856$	−1.56557	−	1.06739i	−0.0535101	−	0.0364826i
$857$	−1.29576	−	1.20229i	−0.0442622	−	0.0410693i	0.657732	−	0.753252i	$-0.271516\pi$
$857$	−1.29576	−	1.20229i	−0.0442622	−	0.0410693i	−0.701994	+	0.712183i	$0.747707\pi$
$858$	−12.8552	−	11.9279i	−0.438869	−	0.407211i
$859$	−5.36135	−	3.65531i	−0.182927	−	0.124717i	0.468394	−	0.883519i	$-0.344833\pi$
$859$	−5.36135	−	3.65531i	−0.182927	−	0.124717i	−0.651321	+	0.758802i	$0.725785\pi$
$860$	0.0144965	−	0.00698114i	0.000494326	−	0.000238055i
$861$	7.33842	−	2.02553i	0.250093	−	0.0690299i
$862$	−30.2010	−	14.5440i	−1.02865	−	0.495372i
$863$	−16.8325	−	29.1548i	−0.572985	−	0.992439i	−0.996257	−	0.0864368i	$-0.972452\pi$
$863$	−16.8325	−	29.1548i	−0.572985	−	0.992439i	0.423272	−	0.906003i	$-0.360881\pi$
$864$	0.0230454	−	0.0399157i	0.000784019	−	0.00135796i
$865$	3.13115	−	2.13478i	0.106462	−	0.0725847i
$866$	30.7804	+	4.63940i	1.04596	+	0.157653i
$867$	−3.22788	+	14.1422i	−0.109624	+	0.480296i
$868$	−0.128888	+	0.0573895i	−0.00437473	+	0.00194793i
$869$	14.7121	+	64.4579i	0.499073	+	2.18658i
$870$	0.122579	+	1.63570i	0.00415580	+	0.0554554i
$871$	−5.42839	−	1.67444i	−0.183934	−	0.0567361i
$872$	−9.32454	−	23.7586i	−0.315769	−	0.804566i
$873$	4.43138	−	1.36690i	0.149980	−	0.0462626i
$874$	39.8808	+	50.0089i	1.34899	+	1.69158i
$875$	0.808891	−	7.69849i	0.0273455	−	0.260256i
$876$	0.0468695	−	0.0587726i	0.00158358	−	0.00198574i
$877$	8.39419	−	21.3881i	0.283452	−	0.722223i	−0.716251	−	0.697843i	$-0.754143\pi$
$877$	8.39419	−	21.3881i	0.283452	−	0.722223i	0.999703	−	0.0243806i	$-0.00776136\pi$
$878$	3.77592	−	50.3861i	0.127431	−	1.70045i
$879$	15.3806	−	2.31825i	0.518773	−	0.0781925i
$880$	4.65055	−	4.31508i	0.156770	−	0.145461i
$881$	4.10439			0.138280			0.0691402	−	0.997607i	$-0.477974\pi$
$881$	4.10439			0.138280			0.0691402	+	0.997607i	$0.477974\pi$
$882$	9.90192	+	0.592592i	0.333415	+	0.0199536i
$883$	−12.7735			−0.429861			−0.214931	−	0.976629i	$-0.568953\pi$
$883$	−12.7735			−0.429861			−0.214931	+	0.976629i	$0.568953\pi$
$884$	−0.0775188	+	0.0719269i	−0.00260724	+	0.00241916i
$885$	0.861242	−	0.129811i	0.0289503	−	0.00436356i
$886$	3.63678	−	48.5295i	0.122180	−	1.63038i
$887$	12.1219	−	30.8862i	0.407015	−	1.03706i	−0.569574	−	0.821940i	$-0.692892\pi$
$887$	12.1219	−	30.8862i	0.407015	−	1.03706i	0.976588	−	0.215116i	$-0.0690130\pi$
$888$	−14.1150	+	17.6997i	−0.473670	+	0.593963i
$889$	−8.03715	+	5.13469i	−0.269557	+	0.172212i
$890$	1.64560	+	2.06351i	0.0551606	+	0.0691692i
$891$	−5.11416	+	1.57751i	−0.171331	+	0.0528486i
$892$	−0.0139192	−	0.0354654i	−0.000466048	−	0.00118747i
$893$	34.5136	+	10.6460i	1.15495	+	0.356256i
$894$	0.504469	+	6.73167i	0.0168720	+	0.225141i
$895$	0.723754	+	3.17098i	0.0241924	+	0.105994i
$896$	30.1014	+	0.899923i	1.00562	+	0.0300643i
$897$	3.61663	−	15.8455i	0.120756	−	0.529066i
$898$	−41.5666	−	6.26515i	−1.38709	−	0.209071i
$899$	−21.2072	+	14.4588i	−0.707301	+	0.482229i
$900$	0.0200146	−	0.0346664i	0.000667155	−	0.00115555i
$901$	8.73821	+	15.1350i	0.291112	+	0.504221i
$902$	19.6614	+	9.46845i	0.654655	+	0.315265i
$903$	−8.38889	−	15.5880i	−0.279165	−	0.518735i
$904$	22.9901	−	11.0714i	0.764638	−	0.368230i
$905$	−1.16451	−	0.793947i	−0.0387095	−	0.0263917i
$906$	−7.96461	−	7.39008i	−0.264606	−	0.245519i
$907$	36.3948	+	33.7695i	1.20847	+	1.12130i	0.989344	+	0.145600i	$0.0465112\pi$
$907$	36.3948	+	33.7695i	1.20847	+	1.12130i	0.219126	+	0.975696i	$0.429679\pi$
$908$	−0.0145358	−	0.00991034i	−0.000482388	−	0.000328886i
$909$	13.2724	−	6.39163i	0.440217	−	0.211997i
$910$	0.114879	+	2.55614i	0.00380822	+	0.0847351i
$911$	−0.925275	−	0.445589i	−0.0306557	−	0.0147630i	0.418493	−	0.908220i	$-0.362558\pi$
$911$	−0.925275	−	0.445589i	−0.0306557	−	0.0147630i	−0.449149	+	0.893457i	$0.648273\pi$
$912$	12.8952	+	22.3351i	0.427001	+	0.739588i
$913$	34.0377	−	58.9550i	1.12648	−	1.95113i
$914$	28.3223	−	19.3098i	0.936817	−	0.638711i
$915$	−0.963824	−	0.145273i	−0.0318631	−	0.00480258i
$916$	0.0170897	−	0.0748747i	0.000564658	−	0.00247393i
$917$	−19.1767	+	22.6253i	−0.633271	+	0.747155i
$918$	1.76997	+	7.75473i	0.0584176	+	0.255944i
$919$	−2.67570	−	35.7047i	−0.0882631	−	1.17779i	−0.848879	−	0.528587i	$-0.822722\pi$
$919$	−2.67570	−	35.7047i	−0.0882631	−	1.17779i	0.760616	−	0.649202i	$-0.224897\pi$
$920$	5.59574	+	1.72606i	0.184486	+	0.0569065i
$921$	0.485784	+	1.23776i	0.0160071	+	0.0407855i
$922$	21.1254	−	6.51634i	0.695729	−	0.214604i
$923$	1.21049	+	1.51790i	0.0398437	+	0.0499624i
$924$	0.0821910	+	0.0809653i	0.00270389	+	0.00266356i
$925$	−24.5677	+	30.8069i	−0.807780	+	1.01292i
$926$	−5.45942	+	13.9104i	−0.179408	+	0.457123i
$927$	−0.670989	+	8.95372i	−0.0220382	+	0.294079i
$928$	−0.178738	+	0.0269404i	−0.00586735	+	0.000884361i
$929$	29.0716	−	26.9745i	0.953808	−	0.885005i	−0.0396485	−	0.999214i	$-0.512624\pi$
$929$	29.0716	−	26.9745i	0.953808	−	0.885005i	0.993457	+	0.114209i	$0.0364333\pi$
$930$	−2.73738			−0.0897624
$931$	−24.7608	+	37.5162i	−0.811501	+	1.22954i
$932$	0.0814501			0.00266799
$933$	5.12493	−	4.75524i	0.167783	−	0.155680i
$934$	−8.43967	+	1.27208i	−0.276155	+	0.0416236i
$935$	−0.662587	+	8.84161i	−0.0216689	+	0.289152i
$936$	2.38445	−	6.07548i	0.0779382	−	0.198583i
$937$	6.70641	−	8.40957i	0.219089	−	0.274729i	−0.660125	−	0.751155i	$-0.729497\pi$
$937$	6.70641	−	8.40957i	0.219089	−	0.274729i	0.879214	+	0.476427i	$0.158068\pi$
$938$	8.71697	+	2.97689i	0.284619	+	0.0971988i
$939$	−13.7116	−	17.1939i	−0.447462	−	0.561100i
$940$	−0.0129251	+	0.00398686i	−0.000421570	+	0.000130037i
$941$	9.09685	+	23.1784i	0.296549	+	0.755595i	0.999036	+	0.0438980i	$0.0139776\pi$
$941$	9.09685	+	23.1784i	0.296549	+	0.755595i	−0.702487	+	0.711697i	$0.747927\pi$
$942$	−19.7325	−	6.08668i	−0.642921	−	0.198315i
$943$	1.51144	+	20.1688i	0.0492193	+	0.656786i
$944$	2.63726	+	11.5546i	0.0858353	+	0.376069i
$945$	0.693118	+	0.359688i	0.0225471	+	0.0117007i
$946$	11.2915	−	49.4712i	0.367118	−	1.60845i
$947$	−44.6304	−	6.72695i	−1.45029	−	0.218596i	−0.623817	−	0.781570i	$-0.714419\pi$
$947$	−44.6304	−	6.72695i	−1.45029	−	0.218596i	−0.826475	+	0.562974i	$0.809657\pi$
$948$	0.0831647	−	0.0567008i	0.00270106	−	0.00184155i
$949$	10.6666	−	18.4751i	0.346252	−	0.599726i
$950$	22.3534	+	38.7172i	0.725239	+	1.25615i
$951$	−14.9675	−	7.20799i	−0.485356	−	0.233735i
$952$	−31.5663	+	27.5805i	−1.02307	+	0.893888i
$953$	−36.5566	+	17.6047i	−1.18418	+	0.570273i	−0.919128	−	0.393959i	$-0.871105\pi$
$953$	−36.5566	+	17.6047i	−1.18418	+	0.570273i	−0.265057	+	0.964233i	$0.585391\pi$
$954$	3.64552	+	2.48547i	0.118028	+	0.0804702i
$955$	−4.20628	−	3.90286i	−0.136112	−	0.126294i
$956$	−0.119036	−	0.110449i	−0.00384990	−	0.00357218i
$957$	17.3419	+	11.8235i	0.560585	+	0.382200i
$958$	−49.8983	+	24.0297i	−1.61214	+	0.776366i
$959$	11.3893	+	2.06646i	0.367778	+	0.0667296i
$960$	2.11862	+	1.02027i	0.0683781	+	0.0329292i
$961$	−5.91732	−	10.2491i	−0.190881	−	0.330616i
$962$	13.1402	−	22.7594i	0.423656	−	0.733793i
$963$	0.554649	−	0.378153i	0.0178733	−	0.0121858i
$964$	0.203316	+	0.0306449i	0.00654836	+	0.000987006i
$965$	−0.590585	+	2.58752i	−0.0190116	+	0.0832953i
$966$	−6.62947	+	25.5065i	−0.213300	+	0.820657i
$967$	6.57562	+	28.8097i	0.211458	+	0.926457i	0.963577	+	0.267430i	$0.0861745\pi$
$967$	6.57562	+	28.8097i	0.211458	+	0.926457i	−0.752119	+	0.659027i	$0.770968\pi$
$968$	−3.72159	−	49.6611i	−0.119616	−	1.59617i
$969$	−34.4428	−	10.6242i	−1.10646	−	0.341298i
$970$	−0.708618	−	1.80553i	−0.0227524	−	0.0579720i
$971$	−41.6573	+	12.8496i	−1.33685	+	0.412362i	−0.879065	−	0.476702i	$-0.841832\pi$
$971$	−41.6573	+	12.8496i	−1.33685	+	0.412362i	−0.457781	+	0.889065i	$0.651356\pi$
$972$	0.00508008	+	0.00637022i	0.000162944	+	0.000204325i
$973$	25.0972	−	3.01887i	0.804578	−	0.0967806i
$974$	0.416297	−	0.522020i	0.0133390	−	0.0167266i
$975$	4.15021	−	10.5746i	0.132913	−	0.338657i
$976$	0.991173	−	13.2263i	0.0317267	−	0.423363i
$977$	48.8711	−	7.36613i	1.56352	−	0.235663i	0.690497	−	0.723335i	$-0.257392\pi$
$977$	48.8711	−	7.36613i	1.56352	−	0.235663i	0.873027	+	0.487671i	$0.162154\pi$
$978$	−15.5238	+	14.4040i	−0.496397	+	0.460589i
$979$	33.7728			1.07938
$980$	−0.000252916	−	0.0168318i	−8.07909e−6	−	0.000537672i
$981$	9.04220			0.288695
$982$	−38.4405	+	35.6676i	−1.22669	+	1.13820i
$983$	46.1383	−	6.95424i	1.47158	−	0.221806i	0.636223	−	0.771506i	$-0.280496\pi$
$983$	46.1383	−	6.95424i	1.47158	−	0.221806i	0.835362	+	0.549700i	$0.185258\pi$
$984$	−0.606942	+	8.09908i	−0.0193486	+	0.258189i
$985$	1.96956	−	5.01836i	0.0627554	−	0.159898i
$986$	19.4493	−	24.3887i	0.619392	−	0.776693i
$987$	5.02032	+	14.0088i	0.159799	+	0.445904i
$988$	−0.0754299	−	0.0945861i	−0.00239974	−	0.00300918i
$989$	44.9401	−	13.8622i	1.42901	−	0.440791i
$990$	0.817801	+	2.08372i	0.0259914	+	0.0662251i
$991$	−27.9470	−	8.62050i	−0.887765	−	0.273839i	−0.182858	−	0.983139i	$-0.558535\pi$
$991$	−27.9470	−	8.62050i	−0.887765	−	0.273839i	−0.704907	+	0.709300i	$0.749011\pi$
$992$	−0.0225427	−	0.300812i	−0.000715732	−	0.00955078i
$993$	−4.72989	−	20.7230i	−0.150098	−	0.657624i
$994$	−1.88836	−	2.51880i	−0.0598950	−	0.0798916i
$995$	1.44850	−	6.34631i	0.0459206	−	0.201191i
$996$	−0.102481	−	0.0154465i	−0.00324723	−	0.000489441i
$997$	−8.63799	+	5.88928i	−0.273568	+	0.186515i	−0.692331	−	0.721580i	$-0.743416\pi$
$997$	−8.63799	+	5.88928i	−0.273568	+	0.186515i	0.418763	+	0.908095i	$0.362464\pi$
$998$	7.70873	−	13.3519i	0.244016	−	0.422647i
$999$	−4.01022	−	6.94590i	−0.126878	−	0.219758i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.2.m.b.109.2	yes	60
3.2	odd	2		441.2.bb.e.109.4		60
49.3	odd	42		7203.2.a.m.1.22		30
49.9	even	21	inner	147.2.m.b.58.2	✓	60
49.46	even	21		7203.2.a.n.1.22		30
147.107	odd	42		441.2.bb.e.352.4		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.m.b.58.2	✓	60	49.9	even	21	inner
147.2.m.b.109.2	yes	60	1.1	even	1	trivial
441.2.bb.e.109.4		60	3.2	odd	2
441.2.bb.e.352.4		60	147.107	odd	42
7203.2.a.m.1.22		30	49.3	odd	42
7203.2.a.n.1.22		30	49.46	even	21

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:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	147.m (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.03880 + 0.963867i) q^{2} +(-0.988831 + 0.149042i) q^{3} +(0.000608887 - 0.00812503i) q^{4} +(-0.107830 + 0.274746i) q^{5} +(0.883542 - 1.10793i) q^{6} +(-1.39076 + 2.25073i) q^{7} +(-1.75989 - 2.20683i) q^{8} +(0.955573 - 0.294755i) q^{9} +O(q^{10})\)	\(q+(-1.03880 + 0.963867i) q^{2} +(-0.988831 + 0.149042i) q^{3} +(0.000608887 - 0.00812503i) q^{4} +(-0.107830 + 0.274746i) q^{5} +(0.883542 - 1.10793i) q^{6} +(-1.39076 + 2.25073i) q^{7} +(-1.75989 - 2.20683i) q^{8} +(0.955573 - 0.294755i) q^{9} +(-0.152805 - 0.389340i) q^{10} +(-5.11416 - 1.57751i) q^{11} +(0.000608887 + 0.00812503i) q^{12} +(0.514524 + 2.25428i) q^{13} +(-0.724688 - 3.67857i) q^{14} +(0.0656767 - 0.287748i) q^{15} +(3.97137 + 0.598588i) q^{16} +(-4.63769 + 3.16192i) q^{17} +(-0.708546 + 1.22724i) q^{18} +(-3.21076 - 5.56120i) q^{19} +(0.00216666 + 0.00104341i) q^{20} +(1.03977 - 2.43288i) q^{21} +(6.83311 - 3.29065i) q^{22} +(5.80770 + 3.95962i) q^{23} +(2.06914 + 1.91988i) q^{24} +(3.60140 + 3.34161i) q^{25} +(-2.70731 - 1.84581i) q^{26} +(-0.900969 + 0.433884i) q^{27} +(0.0174405 + 0.0126704i) q^{28} +(3.53338 + 1.70159i) q^{29} +(0.209126 + 0.362217i) q^{30} +(-3.27241 + 5.66798i) q^{31} +(-0.0380819 + 0.0259638i) q^{32} +(5.29216 + 0.797665i) q^{33} +(1.76997 - 7.75473i) q^{34} +(-0.468415 - 0.624801i) q^{35} +(-0.00181306 - 0.00794353i) q^{36} +(0.599368 + 7.99800i) q^{37} +(8.69560 + 2.68224i) q^{38} +(-0.844760 - 2.15241i) q^{39} +(0.796085 - 0.245560i) q^{40} +(1.79402 + 2.24963i) q^{41} +(1.26486 + 3.52947i) q^{42} +(4.17158 - 5.23100i) q^{43} +(-0.0159313 + 0.0405922i) q^{44} +(-0.0220565 + 0.294323i) q^{45} +(-9.84960 + 1.48459i) q^{46} +(-4.12309 + 3.82567i) q^{47} -4.01623 q^{48} +(-3.13160 - 6.26044i) q^{49} -6.96201 q^{50} +(4.11463 - 3.81782i) q^{51} +(0.0186294 - 0.00280792i) q^{52} +(0.232676 - 3.10485i) q^{53} +(0.517722 - 1.31913i) q^{54} +(0.984874 - 1.23499i) q^{55} +(7.41455 - 0.891876i) q^{56} +(4.00375 + 5.02055i) q^{57} +(-5.31059 + 1.63810i) q^{58} +(1.07811 + 2.74697i) q^{59} +(-0.00229798 - 0.000708832i) q^{60} +(-0.246792 - 3.29321i) q^{61} +(-2.06379 - 9.04207i) q^{62} +(-0.665553 + 2.56067i) q^{63} +(-1.77286 + 7.76739i) q^{64} +(-0.674835 - 0.101715i) q^{65} +(-6.26635 + 4.27232i) q^{66} +(-1.22841 + 2.12766i) q^{67} +(0.0228669 + 0.0396066i) q^{68} +(-6.33298 - 3.04980i) q^{69} +(1.08881 + 0.197554i) q^{70} +(0.756494 - 0.364308i) q^{71} +(-2.33217 - 1.59005i) q^{72} +(-6.76324 - 6.27537i) q^{73} +(-8.33163 - 7.73063i) q^{74} +(-4.05922 - 2.76753i) q^{75} +(-0.0471399 + 0.0227014i) q^{76} +(10.6631 - 9.31669i) q^{77} +(2.95218 + 1.42169i) q^{78} +(-6.17678 - 10.6985i) q^{79} +(-0.592692 + 1.02657i) q^{80} +(0.826239 - 0.563320i) q^{81} +(-4.03197 - 0.607721i) q^{82} +(-2.83042 + 12.4009i) q^{83} +(-0.0191341 - 0.00992949i) q^{84} +(-0.368644 - 1.61514i) q^{85} +(0.708540 + 9.45481i) q^{86} +(-3.74753 - 1.15596i) q^{87} +(5.51905 + 14.0623i) q^{88} +(-6.03004 + 1.86002i) q^{89} +(-0.260776 - 0.327003i) q^{90} +(-5.78935 - 1.97709i) q^{91} +(0.0357083 - 0.0447768i) q^{92} +(2.39109 - 6.09240i) q^{93} +(0.595637 - 7.94822i) q^{94} +(1.87413 - 0.282480i) q^{95} +(0.0337869 - 0.0313496i) q^{96} +4.63741 q^{97} +(9.28734 + 3.48491i) q^{98} -5.35194 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + q^{2} + 5 q^{3} + 5 q^{4} - 2 q^{5} - 2 q^{6} + 5 q^{7} + 6 q^{8} + 5 q^{9}+O(q^{10}) \) 60 * q + q^2 + 5 * q^3 + 5 * q^4 - 2 * q^5 - 2 * q^6 + 5 * q^7 + 6 * q^8 + 5 * q^9	\( 60 q + q^{2} + 5 q^{3} + 5 q^{4} - 2 q^{5} - 2 q^{6} + 5 q^{7} + 6 q^{8} + 5 q^{9} - 34 q^{10} - 11 q^{11} + 5 q^{12} - 2 q^{13} + 40 q^{14} - 3 q^{15} - 31 q^{16} - 9 q^{17} - 6 q^{18} - 29 q^{19} - 43 q^{20} - 11 q^{21} + 9 q^{22} - 4 q^{23} - 24 q^{24} + 55 q^{25} + 36 q^{26} - 10 q^{27} - 57 q^{28} + 4 q^{29} - 20 q^{30} - 39 q^{31} - 92 q^{32} - 18 q^{33} - 36 q^{34} - 33 q^{35} - 10 q^{36} - 24 q^{37} + 118 q^{38} - 6 q^{39} + 35 q^{41} + 38 q^{42} + 2 q^{43} + 40 q^{44} + 12 q^{45} - 40 q^{46} - 5 q^{47} + 76 q^{48} + 129 q^{49} - 176 q^{50} + 54 q^{51} - 6 q^{52} + 26 q^{53} + q^{54} + 2 q^{55} + 63 q^{56} - 12 q^{57} + 11 q^{58} - 41 q^{59} + 32 q^{60} + 6 q^{61} + 36 q^{62} - q^{63} + 74 q^{64} - 51 q^{65} - 15 q^{66} - 55 q^{67} - 22 q^{68} + 8 q^{69} - 68 q^{70} - 66 q^{71} - 24 q^{72} + 24 q^{73} + 28 q^{74} + 41 q^{75} + 3 q^{76} - 34 q^{77} - 30 q^{78} - 51 q^{79} - 5 q^{80} + 5 q^{81} - 41 q^{82} + 30 q^{83} - 30 q^{84} + 68 q^{85} + 110 q^{86} + 19 q^{87} + 129 q^{88} + 75 q^{89} - 16 q^{90} + 5 q^{91} - 4 q^{93} + 38 q^{94} + 36 q^{95} - 57 q^{96} - 168 q^{97} + 227 q^{98} + 36 q^{99}+O(q^{100}) \) 60 * q + q^2 + 5 * q^3 + 5 * q^4 - 2 * q^5 - 2 * q^6 + 5 * q^7 + 6 * q^8 + 5 * q^9 - 34 * q^10 - 11 * q^11 + 5 * q^12 - 2 * q^13 + 40 * q^14 - 3 * q^15 - 31 * q^16 - 9 * q^17 - 6 * q^18 - 29 * q^19 - 43 * q^20 - 11 * q^21 + 9 * q^22 - 4 * q^23 - 24 * q^24 + 55 * q^25 + 36 * q^26 - 10 * q^27 - 57 * q^28 + 4 * q^29 - 20 * q^30 - 39 * q^31 - 92 * q^32 - 18 * q^33 - 36 * q^34 - 33 * q^35 - 10 * q^36 - 24 * q^37 + 118 * q^38 - 6 * q^39 + 35 * q^41 + 38 * q^42 + 2 * q^43 + 40 * q^44 + 12 * q^45 - 40 * q^46 - 5 * q^47 + 76 * q^48 + 129 * q^49 - 176 * q^50 + 54 * q^51 - 6 * q^52 + 26 * q^53 + q^54 + 2 * q^55 + 63 * q^56 - 12 * q^57 + 11 * q^58 - 41 * q^59 + 32 * q^60 + 6 * q^61 + 36 * q^62 - q^63 + 74 * q^64 - 51 * q^65 - 15 * q^66 - 55 * q^67 - 22 * q^68 + 8 * q^69 - 68 * q^70 - 66 * q^71 - 24 * q^72 + 24 * q^73 + 28 * q^74 + 41 * q^75 + 3 * q^76 - 34 * q^77 - 30 * q^78 - 51 * q^79 - 5 * q^80 + 5 * q^81 - 41 * q^82 + 30 * q^83 - 30 * q^84 + 68 * q^85 + 110 * q^86 + 19 * q^87 + 129 * q^88 + 75 * q^89 - 16 * q^90 + 5 * q^91 - 4 * q^93 + 38 * q^94 + 36 * q^95 - 57 * q^96 - 168 * q^97 + 227 * q^98 + 36 * q^99

Introduction

L-functions

Modular forms

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