LMFDB - Embedded newform 381.2.q.a.61.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [381,2,Mod(25,381)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(381, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 16]))

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

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

chi := DirichletCharacter("381.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 381 = 3 \cdot 127 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	381.q (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:	$3.04230031701$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$10$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			61.5
Character	$\chi$	$=$	381.61
Dual form			381.2.q.a.25.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0597923 - 0.261967i) q^{2} +(-0.365341 + 0.930874i) q^{3} +(1.73689 + 0.836440i) q^{4} +(3.54884 - 1.70903i) q^{5} +(0.222014 + 0.151366i) q^{6} +(3.49359 + 2.38189i) q^{7} +(0.658041 - 0.825157i) q^{8} +(-0.733052 - 0.680173i) q^{9} +O(q^{10})$	\(q+(0.0597923 - 0.261967i) q^{2} +(-0.365341 + 0.930874i) q^{3} +(1.73689 + 0.836440i) q^{4} +(3.54884 - 1.70903i) q^{5} +(0.222014 + 0.151366i) q^{6} +(3.49359 + 2.38189i) q^{7} +(0.658041 - 0.825157i) q^{8} +(-0.733052 - 0.680173i) q^{9} +(-0.235517 - 1.03187i) q^{10} +(-5.18101 - 1.59813i) q^{11} +(-1.41318 + 1.31124i) q^{12} +(-2.94966 - 2.01104i) q^{13} +(0.832866 - 0.772787i) q^{14} +(0.294356 + 3.92790i) q^{15} +(2.22711 + 2.79270i) q^{16} +(0.222779 - 2.97278i) q^{17} +(-0.222014 + 0.151366i) q^{18} -5.88663 q^{19} +7.59344 q^{20} +(-3.49359 + 2.38189i) q^{21} +(-0.728442 + 1.26170i) q^{22} +(-6.19750 + 1.91168i) q^{23} +(0.527708 + 0.914017i) q^{24} +(6.55604 - 8.22101i) q^{25} +(-0.703193 + 0.652468i) q^{26} +(0.900969 - 0.433884i) q^{27} +(4.07566 + 7.05925i) q^{28} +(2.53326 - 0.381827i) q^{29} +(1.04658 + 0.157747i) q^{30} +(0.369947 + 4.93660i) q^{31} +(2.76655 - 1.33230i) q^{32} +(3.38049 - 4.23900i) q^{33} +(-0.765451 - 0.236110i) q^{34} +(16.4689 + 2.48229i) q^{35} +(-0.704304 - 1.79454i) q^{36} +(0.603280 - 1.04491i) q^{37} +(-0.351975 + 1.54210i) q^{38} +(2.94966 - 2.01104i) q^{39} +(0.925063 - 4.05296i) q^{40} +(-0.570464 + 7.61232i) q^{41} +(0.415087 + 1.05762i) q^{42} +(-5.81738 + 0.876830i) q^{43} +(-7.66208 - 7.10937i) q^{44} +(-3.76392 - 1.16102i) q^{45} +(0.130233 + 1.73784i) q^{46} +(-3.81888 - 1.83908i) q^{47} +(-3.41331 + 1.05287i) q^{48} +(3.97438 + 10.1266i) q^{49} +(-1.76163 - 2.20902i) q^{50} +(2.68590 + 1.29346i) q^{51} +(-3.44110 - 5.96016i) q^{52} +(2.47065 + 2.29243i) q^{53} +(-0.0597923 - 0.261967i) q^{54} +(-21.1178 + 3.18300i) q^{55} +(4.26436 - 1.31538i) q^{56} +(2.15063 - 5.47970i) q^{57} +(0.0514431 - 0.686460i) q^{58} +(3.98418 - 6.90080i) q^{59} +(-2.77419 + 7.06853i) q^{60} +(-5.31905 - 6.66988i) q^{61} +(1.31535 + 0.198257i) q^{62} +(-0.940886 - 4.12229i) q^{63} +(1.40609 + 6.16048i) q^{64} +(-13.9048 - 2.09581i) q^{65} +(-0.908352 - 1.13904i) q^{66} +(-1.80784 + 4.60630i) q^{67} +(2.87350 - 4.97705i) q^{68} +(0.484672 - 6.46750i) q^{69} +(1.63499 - 4.16589i) q^{70} +(12.9856 - 4.00553i) q^{71} +(-1.04363 + 0.157302i) q^{72} +(2.51533 + 11.0204i) q^{73} +(-0.237661 - 0.220517i) q^{74} +(5.25753 + 9.10632i) q^{75} +(-10.2244 - 4.92381i) q^{76} +(-14.2937 - 17.9238i) q^{77} +(-0.350460 - 0.892958i) q^{78} +(2.57840 - 0.795332i) q^{79} +(12.6765 + 6.10467i) q^{80} +(0.0747301 + 0.997204i) q^{81} +(1.96007 + 0.604601i) q^{82} +(0.705441 + 0.654553i) q^{83} +(-8.06027 + 1.21489i) q^{84} +(-4.28997 - 10.9307i) q^{85} +(-0.118134 + 1.57639i) q^{86} +(-0.570070 + 2.49764i) q^{87} +(-4.72802 + 3.22351i) q^{88} +(0.0784525 - 0.343723i) q^{89} +(-0.529202 + 0.916604i) q^{90} +(-5.51481 - 14.0515i) q^{91} +(-12.3634 - 1.86348i) q^{92} +(-4.73051 - 1.45917i) q^{93} +(-0.710117 + 0.890458i) q^{94} +(-20.8907 + 10.0604i) q^{95} +(0.229469 + 3.06206i) q^{96} +(9.26643 + 1.39669i) q^{97} +(2.89046 - 0.435667i) q^{98} +(2.71094 + 4.69549i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 3 q^{2} - 10 q^{3} - 15 q^{4} + 2 q^{5} + 2 q^{6} + 11 q^{7} + 20 q^{8} + 10 q^{9}+O(q^{10}) $ 120 * q - 3 * q^2 - 10 * q^3 - 15 * q^4 + 2 * q^5 + 2 * q^6 + 11 * q^7 + 20 * q^8 + 10 * q^9	\( 120 q - 3 q^{2} - 10 q^{3} - 15 q^{4} + 2 q^{5} + 2 q^{6} + 11 q^{7} + 20 q^{8} + 10 q^{9} + 4 q^{10} - 36 q^{11} - 18 q^{12} + q^{13} + 4 q^{14} + q^{15} - 15 q^{16} - 5 q^{17} - 2 q^{18} - 54 q^{19} + 18 q^{20} - 11 q^{21} + 19 q^{22} - 22 q^{23} - 18 q^{24} - 26 q^{25} + 54 q^{26} + 20 q^{27} - 19 q^{28} + 31 q^{29} - 19 q^{30} - 3 q^{31} - q^{32} + 33 q^{33} + 23 q^{34} + 70 q^{35} + 4 q^{36} + 36 q^{37} - 55 q^{38} - q^{39} - 80 q^{40} + 8 q^{41} + 10 q^{42} - 41 q^{43} - 118 q^{44} - q^{45} + 46 q^{46} + 15 q^{47} + 52 q^{48} - 11 q^{49} - 26 q^{50} - 10 q^{51} + 72 q^{52} + 30 q^{53} + 3 q^{54} - 87 q^{55} - 103 q^{56} + 8 q^{57} + 36 q^{58} - 16 q^{59} - 96 q^{60} + 43 q^{61} + 6 q^{63} - 28 q^{64} - 33 q^{65} + 3 q^{66} - 10 q^{67} + 67 q^{68} - 6 q^{69} - 72 q^{70} + 55 q^{71} - 10 q^{72} + 47 q^{73} + 101 q^{74} + 29 q^{75} - 59 q^{76} - 15 q^{77} + 2 q^{78} - 148 q^{79} + 27 q^{80} + 10 q^{81} + 106 q^{82} - 4 q^{83} + 12 q^{84} - 47 q^{85} - 157 q^{86} - 8 q^{87} + 85 q^{88} + 16 q^{89} + 5 q^{90} - 111 q^{91} - 157 q^{92} - 25 q^{93} - 18 q^{94} - 24 q^{95} + 10 q^{96} + 52 q^{97} - 4 q^{98} + 6 q^{99}+O(q^{100}) \) 120 * q - 3 * q^2 - 10 * q^3 - 15 * q^4 + 2 * q^5 + 2 * q^6 + 11 * q^7 + 20 * q^8 + 10 * q^9 + 4 * q^10 - 36 * q^11 - 18 * q^12 + q^13 + 4 * q^14 + q^15 - 15 * q^16 - 5 * q^17 - 2 * q^18 - 54 * q^19 + 18 * q^20 - 11 * q^21 + 19 * q^22 - 22 * q^23 - 18 * q^24 - 26 * q^25 + 54 * q^26 + 20 * q^27 - 19 * q^28 + 31 * q^29 - 19 * q^30 - 3 * q^31 - q^32 + 33 * q^33 + 23 * q^34 + 70 * q^35 + 4 * q^36 + 36 * q^37 - 55 * q^38 - q^39 - 80 * q^40 + 8 * q^41 + 10 * q^42 - 41 * q^43 - 118 * q^44 - q^45 + 46 * q^46 + 15 * q^47 + 52 * q^48 - 11 * q^49 - 26 * q^50 - 10 * q^51 + 72 * q^52 + 30 * q^53 + 3 * q^54 - 87 * q^55 - 103 * q^56 + 8 * q^57 + 36 * q^58 - 16 * q^59 - 96 * q^60 + 43 * q^61 + 6 * q^63 - 28 * q^64 - 33 * q^65 + 3 * q^66 - 10 * q^67 + 67 * q^68 - 6 * q^69 - 72 * q^70 + 55 * q^71 - 10 * q^72 + 47 * q^73 + 101 * q^74 + 29 * q^75 - 59 * q^76 - 15 * q^77 + 2 * q^78 - 148 * q^79 + 27 * q^80 + 10 * q^81 + 106 * q^82 - 4 * q^83 + 12 * q^84 - 47 * q^85 - 157 * q^86 - 8 * q^87 + 85 * q^88 + 16 * q^89 + 5 * q^90 - 111 * q^91 - 157 * q^92 - 25 * q^93 - 18 * q^94 - 24 * q^95 + 10 * q^96 + 52 * q^97 - 4 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/381\mathbb{Z}\right)^\times$.

$n$	$128$	$130$
$\chi(n)$	$1$	$e\left(\frac{13}{21}\right)$

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 $

$2$	0.0597923	−	0.261967i	0.0422795	−	0.185239i	−0.949379	−	0.314134i	$-0.898286\pi$
$2$	0.0597923	−	0.261967i	0.0422795	−	0.185239i	0.991658	+	0.128895i	$0.0411431\pi$
$3$	−0.365341	+	0.930874i	−0.210930	+	0.537440i
$3$	−0.365341	+	0.930874i	−0.210930	+	0.537440i
$4$	1.73689	+	0.836440i	0.868443	+	0.418220i
$5$	3.54884	−	1.70903i	1.58709	−	0.764302i	0.588081	−	0.808802i	$-0.299884\pi$
$5$	3.54884	−	1.70903i	1.58709	−	0.764302i	0.999009	+	0.0444998i	$0.0141694\pi$
$6$	0.222014	+	0.151366i	0.0906367	+	0.0617951i
$7$	3.49359	+	2.38189i	1.32045	+	0.900269i	0.998912	−	0.0466269i	$-0.0148472\pi$
$7$	3.49359	+	2.38189i	1.32045	+	0.900269i	0.321540	+	0.946896i	$0.395800\pi$
$8$	0.658041	−	0.825157i	0.232653	−	0.291737i
$9$	−0.733052	−	0.680173i	−0.244351	−	0.226724i
$10$	−0.235517	−	1.03187i	−0.0744770	−	0.326305i
$11$	−5.18101	−	1.59813i	−1.56213	−	0.481854i	−0.611259	−	0.791431i	$-0.709336\pi$
$11$	−5.18101	−	1.59813i	−1.56213	−	0.481854i	−0.950874	+	0.309577i	$0.899813\pi$
$12$	−1.41318	+	1.31124i	−0.407949	+	0.378521i
$13$	−2.94966	−	2.01104i	−0.818087	−	0.557762i	0.0803997	−	0.996763i	$-0.474380\pi$
$13$	−2.94966	−	2.01104i	−0.818087	−	0.557762i	−0.898487	+	0.439000i	$0.855333\pi$
$14$	0.832866	−	0.772787i	0.222593	−	0.206536i
$15$	0.294356	+	3.92790i	0.0760023	+	1.01418i
$16$	2.22711	+	2.79270i	0.556777	+	0.698176i
$17$	0.222779	−	2.97278i	0.0540319	−	0.721006i	−0.902744	−	0.430179i	$-0.858451\pi$
$17$	0.222779	−	2.97278i	0.0540319	−	0.721006i	0.956776	−	0.290827i	$-0.0939305\pi$
$18$	−0.222014	+	0.151366i	−0.0523291	+	0.0356774i
$19$	−5.88663			−1.35048			−0.675242	−	0.737596i	$-0.735961\pi$
$19$	−5.88663			−1.35048			−0.675242	+	0.737596i	$0.735961\pi$
$20$	7.59344			1.69794
$21$	−3.49359	+	2.38189i	−0.762364	+	0.519771i
$22$	−0.728442	+	1.26170i	−0.155304	+	0.268995i
$23$	−6.19750	+	1.91168i	−1.29227	+	0.398612i	−0.863292	−	0.504704i	$-0.831602\pi$
$23$	−6.19750	+	1.91168i	−1.29227	+	0.398612i	−0.428975	+	0.903316i	$0.641125\pi$
$24$	0.527708	+	0.914017i	0.107718	+	0.186573i
$25$	6.55604	−	8.22101i	1.31121	−	1.64420i
$26$	−0.703193	+	0.652468i	−0.137908	+	0.127960i
$27$	0.900969	−	0.433884i	0.173392	−	0.0835010i
$28$	4.07566	+	7.05925i	0.770227	+	1.33407i
$29$	2.53326	−	0.381827i	0.470414	−	0.0709035i	0.0904424	−	0.995902i	$-0.471172\pi$
$29$	2.53326	−	0.381827i	0.470414	−	0.0709035i	0.379971	+	0.924998i	$0.375934\pi$
$30$	1.04658	+	0.157747i	0.191079	+	0.0288005i
$31$	0.369947	+	4.93660i	0.0664445	+	0.886640i	0.926465	+	0.376381i	$0.122832\pi$
$31$	0.369947	+	4.93660i	0.0664445	+	0.886640i	−0.860021	+	0.510259i	$0.829549\pi$
$32$	2.76655	−	1.33230i	0.489062	−	0.235520i
$33$	3.38049	−	4.23900i	0.588468	−	0.737916i
$34$	−0.765451	−	0.236110i	−0.131274	−	0.0404926i
$35$	16.4689	+	2.48229i	2.78375	+	0.419584i
$36$	−0.704304	−	1.79454i	−0.117384	−	0.299089i
$37$	0.603280	−	1.04491i	0.0991786	−	0.171782i	−0.812166	−	0.583426i	$-0.801712\pi$
$37$	0.603280	−	1.04491i	0.0991786	−	0.171782i	0.911345	+	0.411644i	$0.135045\pi$
$38$	−0.351975	+	1.54210i	−0.0570979	+	0.250162i
$39$	2.94966	−	2.01104i	0.472323	−	0.322024i
$40$	0.925063	−	4.05296i	0.146265	−	0.640830i
$41$	−0.570464	+	7.61232i	−0.0890916	+	1.18884i	0.756128	+	0.654424i	$0.227089\pi$
$41$	−0.570464	+	7.61232i	−0.0890916	+	1.18884i	−0.845219	+	0.534420i	$0.820530\pi$
$42$	0.415087	+	1.05762i	0.0640493	+	0.163195i
$43$	−5.81738	+	0.876830i	−0.887143	+	0.133715i	−0.576777	−	0.816902i	$-0.695690\pi$
$43$	−5.81738	+	0.876830i	−0.887143	+	0.133715i	−0.310366	+	0.950617i	$0.600452\pi$
$44$	−7.66208	−	7.10937i	−1.15510	−	1.07178i
$45$	−3.76392	−	1.16102i	−0.561092	−	0.173074i
$46$	0.130233	+	1.73784i	0.0192019	+	0.256231i
$47$	−3.81888	−	1.83908i	−0.557041	−	0.268257i	0.134111	−	0.990966i	$-0.457182\pi$
$47$	−3.81888	−	1.83908i	−0.557041	−	0.268257i	−0.691152	+	0.722710i	$0.742896\pi$
$48$	−3.41331	+	1.05287i	−0.492669	+	0.151968i
$49$	3.97438	+	10.1266i	0.567769	+	1.44665i
$50$	−1.76163	−	2.20902i	−0.249133	−	0.312403i
$51$	2.68590	+	1.29346i	0.376101	+	0.181121i
$52$	−3.44110	−	5.96016i	−0.477195	−	0.826525i
$53$	2.47065	+	2.29243i	0.339370	+	0.314889i	0.831384	−	0.555698i	$-0.187549\pi$
$53$	2.47065	+	2.29243i	0.339370	+	0.314889i	−0.492015	+	0.870587i	$0.663739\pi$
$54$	−0.0597923	−	0.261967i	−0.00813670	−	0.0356492i
$55$	−21.1178	+	3.18300i	−2.84753	+	0.429196i
$56$	4.26436	−	1.31538i	0.569848	−	0.175775i
$57$	2.15063	−	5.47970i	0.284857	−	0.725805i
$58$	0.0514431	−	0.686460i	0.00675481	−	0.0901366i
$59$	3.98418	−	6.90080i	0.518696	−	0.898408i	−0.481068	−	0.876683i	$-0.659751\pi$
$59$	3.98418	−	6.90080i	0.518696	−	0.898408i	0.999764	−	0.0217247i	$-0.00691574\pi$
$60$	−2.77419	+	7.06853i	−0.358147	+	0.912543i
$61$	−5.31905	−	6.66988i	−0.681035	−	0.853991i	0.314414	−	0.949286i	$-0.398192\pi$
$61$	−5.31905	−	6.66988i	−0.681035	−	0.853991i	−0.995449	+	0.0952953i	$0.969620\pi$
$62$	1.31535	+	0.198257i	0.167049	+	0.0251786i
$63$	−0.940886	−	4.12229i	−0.118541	−	0.519360i
$64$	1.40609	+	6.16048i	0.175761	+	0.770060i
$65$	−13.9048	−	2.09581i	−1.72468	−	0.259953i
$66$	−0.908352	−	1.13904i	−0.111810	−	0.140206i
$67$	−1.80784	+	4.60630i	−0.220863	+	0.562749i	−0.997761	−	0.0668768i	$-0.978697\pi$
$67$	−1.80784	+	4.60630i	−0.220863	+	0.562749i	0.776899	+	0.629626i	$0.216792\pi$
$68$	2.87350	−	4.97705i	0.348463	−	0.603555i
$69$	0.484672	−	6.46750i	0.0583477	−	0.778596i
$70$	1.63499	−	4.16589i	0.195419	−	0.497919i
$71$	12.9856	−	4.00553i	1.54111	−	0.475369i	0.596235	−	0.802810i	$-0.296662\pi$
$71$	12.9856	−	4.00553i	1.54111	−	0.475369i	0.944872	+	0.327441i	$0.106186\pi$
$72$	−1.04363	+	0.157302i	−0.122993	+	0.0185382i
$73$	2.51533	+	11.0204i	0.294397	+	1.28984i	0.878338	+	0.478040i	$0.158653\pi$
$73$	2.51533	+	11.0204i	0.294397	+	1.28984i	−0.583941	+	0.811796i	$0.698490\pi$
$74$	−0.237661	−	0.220517i	−0.0276275	−	0.0256346i
$75$	5.25753	+	9.10632i	0.607088	+	1.05151i
$76$	−10.2244	−	4.92381i	−1.17282	−	0.564800i
$77$	−14.2937	−	17.9238i	−1.62892	−	2.04261i
$78$	−0.350460	−	0.892958i	−0.0396818	−	0.101108i
$79$	2.57840	−	0.795332i	0.290093	−	0.0894819i	−0.146293	−	0.989241i	$-0.546734\pi$
$79$	2.57840	−	0.795332i	0.290093	−	0.0894819i	0.436386	+	0.899759i	$0.356258\pi$
$80$	12.6765	+	6.10467i	1.41727	+	0.682522i
$81$	0.0747301	+	0.997204i	0.00830334	+	0.110800i
$82$	1.96007	+	0.604601i	0.216453	+	0.0667670i
$83$	0.705441	+	0.654553i	0.0774322	+	0.0718466i	0.717940	−	0.696105i	$-0.245085\pi$
$83$	0.705441	+	0.654553i	0.0774322	+	0.0718466i	−0.640507	+	0.767952i	$0.721276\pi$
$84$	−8.06027	+	1.21489i	−0.879448	+	0.132555i
$85$	−4.28997	−	10.9307i	−0.465313	−	1.18560i
$86$	−0.118134	+	1.57639i	−0.0127387	+	0.169987i
$87$	−0.570070	+	2.49764i	−0.0611179	+	0.267775i
$88$	−4.72802	+	3.22351i	−0.504009	+	0.343627i
$89$	0.0784525	−	0.343723i	0.00831595	−	0.0364346i	−0.970600	−	0.240699i	$-0.922623\pi$
$89$	0.0784525	−	0.343723i	0.00831595	−	0.0364346i	0.978916	+	0.204265i	$0.0654804\pi$
$90$	−0.529202	+	0.916604i	−0.0557827	+	0.0966185i
$91$	−5.51481	−	14.0515i	−0.578109	−	1.47300i
$92$	−12.3634	−	1.86348i	−1.28897	−	0.194281i
$93$	−4.73051	−	1.45917i	−0.490531	−	0.151309i
$94$	−0.710117	+	0.890458i	−0.0732429	+	0.0918437i
$95$	−20.8907	+	10.0604i	−2.14334	+	1.03218i
$96$	0.229469	+	3.06206i	0.0234201	+	0.312520i
$97$	9.26643	+	1.39669i	0.940864	+	0.141812i	0.601527	−	0.798853i	$-0.294559\pi$
$97$	9.26643	+	1.39669i	0.940864	+	0.141812i	0.339337	+	0.940665i	$0.389797\pi$
$98$	2.89046	−	0.435667i	0.291981	−	0.0440090i
$99$	2.71094	+	4.69549i	0.272460	+	0.471915i
$100$	18.2635	−	8.79523i	1.82635	−	0.879523i
$101$	−8.40798	+	7.80146i	−0.836625	+	0.776274i	−0.976868	−	0.213843i	$-0.931402\pi$
$101$	−8.40798	+	7.80146i	−0.836625	+	0.776274i	0.140243	+	0.990117i	$0.455212\pi$
$102$	0.499440	−	0.626278i	0.0494519	−	0.0620107i
$103$	−0.605001	−	1.04789i	−0.0596125	−	0.103252i	0.834679	−	0.550737i	$-0.185653\pi$
$103$	−0.605001	−	1.04789i	−0.0596125	−	0.103252i	−0.894291	+	0.447485i	$0.852320\pi$
$104$	−3.60042	+	1.11058i	−0.353050	+	0.108902i
$105$	−8.32747	+	14.4236i	−0.812678	+	1.40760i
$106$	0.748266	−	0.510159i	0.0726781	−	0.0495511i
$107$	−2.89918			−0.280274			−0.140137	−	0.990132i	$-0.544754\pi$
$107$	−2.89918			−0.280274			−0.140137	+	0.990132i	$0.544754\pi$
$108$	1.92780			0.185502
$109$	16.0620	−	10.9509i	1.53846	−	1.04891i	0.563615	−	0.826038i	$-0.309410\pi$
$109$	16.0620	−	10.9509i	1.53846	−	1.04891i	0.974849	−	0.222868i	$-0.0715420\pi$
$110$	−0.428842	+	5.72250i	−0.0408885	+	0.545619i
$111$	0.752278	+	0.943327i	0.0714031	+	0.0895366i
$112$	1.12869	+	15.0613i	0.106651	+	1.42316i
$113$	−3.18543	+	2.95564i	−0.299660	+	0.278044i	−0.815644	−	0.578555i	$-0.803617\pi$
$113$	−3.18543	+	2.95564i	−0.299660	+	0.278044i	0.515984	+	0.856598i	$0.327426\pi$
$114$	−1.30691	−	0.891037i	−0.122403	−	0.0834533i
$115$	−18.7268	+	17.3760i	−1.74629	+	1.62032i
$116$	4.71935	+	1.45573i	0.438181	+	0.135161i
$117$	0.794395	+	3.48047i	0.0734419	+	0.321770i
$118$	−1.56956	−	1.45634i	−0.144490	−	0.134067i
$119$	7.85914	−	9.85505i	0.720446	−	0.903411i
$120$	3.43483	+	2.34183i	0.313556	+	0.213779i
$121$	15.2002	+	10.3633i	1.38184	+	0.942121i
$122$	−2.06533	+	0.994609i	−0.186986	+	0.0900477i
$123$	−6.87769	−	3.31212i	−0.620141	−	0.298644i
$124$	−3.48662	+	8.88376i	−0.313108	+	0.797785i
$125$	4.83391	−	21.1787i	0.432358	−	1.89428i
$126$	−1.13616			−0.101217
$127$	5.96018	+	9.56432i	0.528880	+	0.848697i
$127$	5.96018	+	9.56432i	0.528880	+	0.848697i
$128$	7.83920			0.692894
$129$	1.30911	−	5.73559i	0.115261	−	0.504991i
$130$	−1.38043	+	3.51729i	−0.121072	+	0.308486i
$131$	−3.08540	−	1.48585i	−0.269573	−	0.129819i	0.294215	−	0.955739i	$-0.404942\pi$
$131$	−3.08540	−	1.48585i	−0.269573	−	0.129819i	−0.563787	+	0.825920i	$0.690656\pi$
$132$	9.41720	−	4.53509i	0.819662	−	0.394729i
$133$	−20.5654	−	14.0213i	−1.78325	−	1.21580i
$134$	1.09860	+	0.749016i	0.0949049	+	0.0647051i
$135$	2.45587	−	3.07957i	0.211368	−	0.265047i
$136$	−2.30642	−	2.14004i	−0.197773	−	0.183507i
$137$	−0.825971	−	3.61882i	−0.0705675	−	0.309176i	0.927310	−	0.374294i	$-0.122115\pi$
$137$	−0.825971	−	3.61882i	−0.0705675	−	0.309176i	−0.997878	+	0.0651176i	$0.979258\pi$
$138$	−1.66529	−	0.513675i	−0.141759	−	0.0437269i
$139$	7.47159	−	6.93263i	0.633732	−	0.588018i	−0.296480	−	0.955039i	$-0.595813\pi$
$139$	7.47159	−	6.93263i	0.633732	−	0.588018i	0.930213	+	0.367021i	$0.119622\pi$
$140$	26.5283	+	18.0867i	2.24205	+	1.52861i
$141$	3.10714	−	2.88300i	0.261668	−	0.242793i
$142$	−0.272878	−	3.64130i	−0.0228994	−	0.305571i
$143$	12.0683	+	15.1332i	1.00920	+	1.26550i
$144$	0.266936	−	3.56201i	0.0222447	−	0.296834i
$145$	8.33757	−	5.68446i	0.692398	−	0.472069i
$146$	3.03737			0.251375
$147$	−10.8786			−0.897248
$148$	1.92183	−	1.31028i	0.157974	−	0.107705i
$149$	−1.23793	+	2.14416i	−0.101415	+	0.175656i	−0.912268	−	0.409594i	$-0.865670\pi$
$149$	−1.23793	+	2.14416i	−0.101415	+	0.175656i	0.810853	+	0.585250i	$0.199004\pi$
$150$	2.69992	−	0.832814i	0.220447	−	0.0679989i
$151$	−4.42619	−	7.66638i	−0.360198	−	0.623881i	0.627795	−	0.778379i	$-0.283958\pi$
$151$	−4.42619	−	7.66638i	−0.360198	−	0.623881i	−0.987993	+	0.154497i	$0.950624\pi$
$152$	−3.87364	+	4.85739i	−0.314194	+	0.393986i
$153$	−2.18532	+	2.02768i	−0.176672	+	0.163928i
$154$	−5.55010	+	2.67279i	−0.447240	+	0.215379i
$155$	9.74970	+	16.8870i	0.783115	+	1.35639i
$156$	6.80533	−	1.02574i	0.544863	−	0.0821248i
$157$	−5.08764	−	0.766838i	−0.406038	−	0.0612004i	−0.0571518	−	0.998366i	$-0.518202\pi$
$157$	−5.08764	−	0.766838i	−0.406038	−	0.0612004i	−0.348886	+	0.937165i	$0.613440\pi$
$158$	−0.0541822	−	0.723012i	−0.00431051	−	0.0575197i
$159$	−3.03659	+	1.46234i	−0.240817	+	0.115971i
$160$	7.54111	−	9.45626i	0.596177	−	0.747583i
$161$	−26.2049	−	8.08314i	−2.06524	−	0.637041i
$162$	0.265703	+	0.0400483i	0.0208756	+	0.00314649i
$163$	0.967501	+	2.46515i	0.0757806	+	0.193086i	0.963744	−	0.266828i	$-0.0859756\pi$
$163$	0.967501	+	2.46515i	0.0757806	+	0.193086i	−0.887964	+	0.459914i	$0.847880\pi$
$164$	−7.35808	+	12.7446i	−0.574570	+	0.995184i
$165$	4.75224	−	20.8209i	0.369961	−	1.62091i
$166$	0.213651	−	0.145665i	0.0165826	−	0.0113058i
$167$	2.54917	−	11.1686i	0.197261	−	0.864255i	−0.775298	−	0.631596i	$-0.782400\pi$
$167$	2.54917	−	11.1686i	0.197261	−	0.864255i	0.972558	−	0.232659i	$-0.0747427\pi$
$168$	−0.333492	+	4.45014i	−0.0257295	+	0.343336i
$169$	−0.0932520	−	0.237602i	−0.00717323	−	0.0182771i
$170$	−3.11999	+	0.470262i	−0.239292	+	0.0360675i
$171$	4.31520	+	4.00392i	0.329992	+	0.306188i
$172$	−10.8375	−	3.34294i	−0.826355	−	0.254897i
$173$	−0.980423	−	13.0828i	−0.0745402	−	0.994669i	−0.901604	−	0.432562i	$-0.857610\pi$
$173$	−0.980423	−	13.0828i	−0.0745402	−	0.994669i	0.827064	−	0.562108i	$-0.190009\pi$
$174$	0.620213	+	0.298679i	0.0470183	+	0.0226428i
$175$	42.4856	−	13.1051i	3.21161	−	0.990651i
$176$	−7.07556	−	18.0282i	−0.533340	−	1.35893i
$177$	4.96819	+	6.22992i	0.373432	+	0.468269i
$178$	−0.0853533	−	0.0411040i	−0.00639750	−	0.00308087i
$179$	8.04166	+	13.9286i	0.601062	+	1.04107i	0.992661	+	0.120933i	$0.0385888\pi$
$179$	8.04166	+	13.9286i	0.601062	+	1.04107i	−0.391599	+	0.920136i	$0.628078\pi$
$180$	−5.56638	−	5.16485i	−0.414894	−	0.384965i
$181$	−4.62818	−	20.2774i	−0.344010	−	1.50721i	−0.790525	−	0.612430i	$-0.790192\pi$
$181$	−4.62818	−	20.2774i	−0.344010	−	1.50721i	0.446515	−	0.894776i	$-0.352665\pi$
$182$	−4.01077	+	0.604527i	−0.297298	+	0.0448105i
$183$	8.15208	−	2.51458i	0.602619	−	0.185883i
$184$	−2.50077	+	6.37187i	−0.184360	+	0.469740i
$185$	0.355158	−	4.73925i	0.0261117	−	0.348437i
$186$	−0.665103	+	1.15199i	−0.0487677	+	0.0844681i
$187$	−5.90512	+	15.0460i	−0.431825	+	1.10027i
$188$	−5.09468	−	6.38853i	−0.371568	−	0.465931i
$189$	4.18108	+	0.630196i	0.304129	+	0.0458400i
$190$	1.38640	+	6.07421i	0.100580	+	0.440670i
$191$	−1.09401	−	4.79315i	−0.0791594	−	0.346820i	0.919802	−	0.392383i	$-0.128349\pi$
$191$	−1.09401	−	4.79315i	−0.0791594	−	0.346820i	−0.998961	+	0.0455626i	$0.985492\pi$
$192$	−6.24833	−	0.941785i	−0.450935	−	0.0679674i
$193$	−9.37405	−	11.7547i	−0.674759	−	0.846121i	0.320101	−	0.947384i	$-0.396283\pi$
$193$	−9.37405	−	11.7547i	−0.674759	−	0.846121i	−0.994860	+	0.101262i	$0.967712\pi$
$194$	0.919948	−	2.34399i	0.0660484	−	0.168289i
$195$	7.03093	−	12.1779i	0.503495	−	0.872079i
$196$	−1.56721	+	20.9130i	−0.111944	+	1.49379i
$197$	−5.13159	+	13.0751i	−0.365611	+	0.931561i	0.623157	+	0.782097i	$0.285850\pi$
$197$	−5.13159	+	13.0751i	−0.365611	+	0.931561i	−0.988767	+	0.149464i	$0.952245\pi$
$198$	1.39216	−	0.429424i	0.0989364	−	0.0305178i
$199$	10.3496	−	1.55995i	0.733661	−	0.110582i	0.228423	−	0.973562i	$-0.426643\pi$
$199$	10.3496	−	1.55995i	0.733661	−	0.110582i	0.505238	+	0.862980i	$0.331405\pi$
$200$	−2.46948	−	10.8195i	−0.174619	−	0.765056i
$201$	−3.62740	−	3.36574i	−0.255857	−	0.237401i
$202$	1.54099	+	2.66908i	0.108424	+	0.187796i
$203$	9.75962	+	4.69999i	0.684991	+	0.329874i
$204$	3.58319	+	4.49318i	0.250874	+	0.314586i
$205$	10.9852	+	27.9899i	0.767240	+	1.95490i
$206$	−0.310688	+	0.0958344i	−0.0216466	+	0.00667710i
$207$	5.84336	+	2.81401i	0.406141	+	0.195587i
$208$	−0.952956	−	12.7163i	−0.0660756	−	0.881718i
$209$	30.4987	+	9.40759i	2.10964	+	0.650737i
$210$	3.28059	+	3.04394i	0.226382	+	0.210052i
$211$	9.77533	−	1.47339i	0.672961	−	0.101433i	0.196333	−	0.980537i	$-0.437097\pi$
$211$	9.77533	−	1.47339i	0.672961	−	0.101433i	0.476629	+	0.879105i	$0.341859\pi$
$212$	2.37376	+	6.04824i	0.163030	+	0.415395i
$213$	−1.01553	+	13.5513i	−0.0695831	+	0.928522i
$214$	−0.173348	+	0.759489i	−0.0118499	+	0.0519176i
$215$	−19.1464	+	13.0538i	−1.30578	+	0.890264i
$216$	0.234852	−	1.02895i	0.0159797	−	0.0700115i
$217$	−10.4660	+	18.1276i	−0.710478	+	1.23058i
$218$	−1.90839	−	4.86250i	−0.129253	−	0.329330i
$219$	−11.1775	−	1.68474i	−0.755307	−	0.113844i
$220$	−39.3417	−	12.1353i	−2.65241	−	0.818161i
$221$	−6.63551	+	8.32067i	−0.446353	+	0.559709i
$222$	0.292101	−	0.140668i	0.0196045	−	0.00944105i
$223$	1.23623	+	16.4964i	0.0827842	+	1.10468i	0.871655	+	0.490120i	$0.163047\pi$
$223$	1.23623	+	16.4964i	0.0827842	+	1.10468i	−0.788871	+	0.614559i	$0.789334\pi$
$224$	12.8386	+	1.93511i	0.857815	+	0.129295i
$225$	−10.3976	+	1.56719i	−0.693175	+	0.104479i
$226$	0.583817	+	1.01120i	0.0388350	+	0.0672641i
$227$	−8.45559	+	4.07200i	−0.561217	+	0.270268i	−0.692912	−	0.721022i	$-0.743672\pi$
$227$	−8.45559	+	4.07200i	−0.561217	+	0.270268i	0.131694	+	0.991290i	$0.457958\pi$
$228$	8.31884	−	7.71875i	0.550928	−	0.511187i
$229$	15.8563	−	19.8831i	1.04781	−	1.31391i	0.100033	−	0.994984i	$-0.468105\pi$
$229$	15.8563	−	19.8831i	1.04781	−	1.31391i	0.947778	−	0.318930i	$-0.103323\pi$
$230$	3.43221	+	5.94476i	0.226313	+	0.391986i
$231$	21.9069	−	6.75738i	1.44137	−	0.444603i
$232$	1.35192	−	2.34159i	0.0887578	−	0.153733i
$233$	−15.1405	+	10.3226i	−0.991887	+	0.676257i	−0.946497	−	0.322712i	$-0.895405\pi$
$233$	−15.1405	+	10.3226i	−0.991887	+	0.676257i	−0.0453902	+	0.998969i	$0.514453\pi$
$234$	0.959268			0.0627093
$235$	−16.6956			−1.08910
$236$	12.6922	−	8.65338i	0.826190	−	0.563287i
$237$	−0.201643	+	2.69074i	−0.0130981	+	0.174782i
$238$	−2.11178	−	2.64809i	−0.136887	−	0.171650i
$239$	−1.70384	−	22.7361i	−0.110212	−	1.47068i	−0.728672	−	0.684863i	$-0.759862\pi$
$239$	−1.70384	−	22.7361i	−0.110212	−	1.47068i	0.618460	−	0.785816i	$-0.287757\pi$
$240$	−10.3139	+	9.56991i	−0.665760	+	0.617735i
$241$	5.31301	+	3.62235i	0.342241	+	0.233336i	0.722227	−	0.691656i	$-0.243119\pi$
$241$	5.31301	+	3.62235i	0.342241	+	0.233336i	−0.379986	+	0.924992i	$0.624071\pi$
$242$	3.62371	−	3.36231i	0.232941	−	0.216137i
$243$	−0.955573	−	0.294755i	−0.0613000	−	0.0189086i
$244$	−3.65963	−	16.0339i	−0.234284	−	1.02646i
$245$	31.4111	+	29.1452i	2.00678	+	1.86202i
$246$	−1.27890	+	1.60369i	−0.0815397	+	0.102248i
$247$	17.3635	+	11.8382i	1.10481	+	0.753249i
$248$	4.31691	+	2.94322i	0.274124	+	0.186895i
$249$	−0.867033	+	0.417541i	−0.0549460	+	0.0264606i
$250$	−5.25910	−	2.53265i	−0.332615	−	0.160179i
$251$	6.77658	−	17.2664i	0.427734	−	1.08985i	−0.540841	−	0.841125i	$-0.681894\pi$
$251$	6.77658	−	17.2664i	0.427734	−	1.08985i	0.968575	−	0.248723i	$-0.0800109\pi$
$252$	1.81384	−	7.94695i	0.114261	−	0.500611i
$253$	35.1644			2.21077
$254$	2.86191	−	0.989497i	0.179572	−	0.0620866i
$255$	11.7424			0.735337
$256$	−2.34346	+	10.2673i	−0.146466	+	0.641709i
$257$	−0.262789	+	0.669577i	−0.0163924	+	0.0417670i	−0.938836	−	0.344366i	$-0.888094\pi$
$257$	−0.262789	+	0.669577i	−0.0163924	+	0.0417670i	0.922443	+	0.386133i	$0.126189\pi$
$258$	−1.42426	−	0.685888i	−0.0886707	−	0.0427015i
$259$	4.59647	−	2.21355i	0.285611	−	0.137543i
$260$	−22.3980	−	15.2707i	−1.38907	−	0.947049i
$261$	−2.11672	−	1.44315i	−0.131021	−	0.0893289i
$262$	−0.573727	+	0.719431i	−0.0354450	+	0.0444466i
$263$	0.861042	+	0.798930i	0.0530941	+	0.0492641i	0.706274	−	0.707939i	$-0.250375\pi$
$263$	0.861042	+	0.798930i	0.0530941	+	0.0492641i	−0.653180	+	0.757203i	$0.726565\pi$
$264$	−1.27334	−	5.57887i	−0.0783687	−	0.343356i
$265$	12.6858	+	3.91304i	0.779281	+	0.240376i
$266$	−4.90277	+	4.54911i	−0.300608	+	0.278924i
$267$	0.291301	+	0.198606i	0.0178273	+	0.0121545i
$268$	−6.99290	+	6.48847i	−0.427160	+	0.396346i
$269$	1.74142	+	23.2377i	0.106177	+	1.41683i	0.754918	+	0.655819i	$0.227677\pi$
$269$	1.74142	+	23.2377i	0.106177	+	1.41683i	−0.648742	+	0.761009i	$0.724704\pi$
$270$	−0.659904	−	0.827493i	−0.0401605	−	0.0503596i
$271$	2.36392	−	31.5443i	0.143598	−	1.91618i	−0.204753	−	0.978814i	$-0.565639\pi$
$271$	2.36392	−	31.5443i	0.143598	−	1.91618i	0.348351	−	0.937364i	$-0.386742\pi$
$272$	8.79826	−	5.99855i	0.533473	−	0.363716i
$273$	15.0950			0.913588
$274$	−0.997397			−0.0602550
$275$	−47.1051	+	32.1157i	−2.84055	+	1.93665i
$276$	6.25150	−	10.8279i	0.376296	−	0.651764i
$277$	−16.0244	+	4.94286i	−0.962811	+	0.296988i	−0.736023	−	0.676956i	$-0.763299\pi$
$277$	−16.0244	+	4.94286i	−0.962811	+	0.296988i	−0.226788	+	0.973944i	$0.572822\pi$
$278$	−1.36938	−	2.37183i	−0.0821297	−	0.142253i
$279$	3.08655	−	3.87041i	0.184787	−	0.231716i
$280$	12.8855	−	11.9560i	0.770056	−	0.714507i
$281$	−20.3419	+	9.79613i	−1.21349	+	0.584388i	−0.927493	−	0.373841i	$-0.878041\pi$
$281$	−20.3419	+	9.79613i	−1.21349	+	0.584388i	−0.286002	+	0.958229i	$0.592326\pi$
$282$	−0.569469	−	0.986350i	−0.0339114	−	0.0587363i
$283$	12.5805	−	1.89620i	0.747830	−	0.112717i	0.235940	−	0.971768i	$-0.424183\pi$
$283$	12.5805	−	1.89620i	0.747830	−	0.112717i	0.511891	+	0.859050i	$0.328945\pi$
$284$	25.9049	+	3.90453i	1.53717	+	0.231691i
$285$	−1.73276	−	23.1221i	−0.102640	−	1.36963i
$286$	4.68598	−	2.25665i	0.277088	−	0.133438i
$287$	−20.1247	+	25.2355i	−1.18792	+	1.48961i
$288$	−2.93422	−	0.905088i	−0.172901	−	0.0533328i
$289$	8.02231	+	1.20917i	0.471901	+	0.0711276i
$290$	−0.990619	−	2.52406i	−0.0581712	−	0.148218i
$291$	−4.68555	+	8.11561i	−0.274672	+	0.475745i
$292$	−4.84904	+	21.2450i	−0.283769	+	1.24327i
$293$	−6.90680	+	4.70897i	−0.403499	+	0.275101i	−0.748018	−	0.663678i	$-0.768994\pi$
$293$	−6.90680	+	4.70897i	−0.403499	+	0.275101i	0.344519	+	0.938779i	$0.388042\pi$
$294$	−0.650454	+	2.84982i	−0.0379352	+	0.166205i
$295$	2.34553	−	31.2990i	0.136562	−	1.82230i
$296$	−0.465233	−	1.18540i	−0.0270411	−	0.0688997i
$297$	−5.36133	+	0.808090i	−0.311096	+	0.0468902i
$298$	0.487681	+	0.452501i	0.0282506	+	0.0262127i
$299$	22.1249	+	6.82464i	1.27952	+	0.394679i
$300$	1.51485	+	20.2142i	0.0874598	+	1.16707i
$301$	−22.4121	−	10.7931i	−1.29181	−	0.622103i
$302$	−2.27299	+	0.701125i	−0.130796	+	0.0403452i
$303$	−4.19040	−	10.6770i	−0.240732	−	0.613375i
$304$	−13.1101	−	16.4396i	−0.751918	−	0.942876i
$305$	−30.2755	−	14.5799i	−1.73357	−	0.834844i
$306$	0.400520	+	0.693720i	0.0228962	+	0.0396573i
$307$	8.46095	+	7.85061i	0.482892	+	0.448058i	0.883665	−	0.468119i	$-0.155068\pi$
$307$	8.46095	+	7.85061i	0.482892	+	0.448058i	−0.400774	+	0.916177i	$0.631259\pi$
$308$	−9.83443	−	43.0874i	−0.560369	−	2.45514i
$309$	1.19649	−	0.180341i	0.0680657	−	0.0102593i
$310$	5.00679	−	1.54439i	0.284367	−	0.0877155i
$311$	−3.35205	+	8.54087i	−0.190077	+	0.484309i	−0.993864	−	0.110609i	$-0.964720\pi$
$311$	−3.35205	+	8.54087i	−0.190077	+	0.484309i	0.803787	+	0.594917i	$0.202815\pi$
$312$	0.281569	−	3.75728i	0.0159407	−	0.212714i
$313$	1.22505	−	2.12186i	0.0692441	−	0.119934i	−0.829325	−	0.558767i	$-0.811275\pi$
$313$	1.22505	−	2.12186i	0.0692441	−	0.119934i	0.898569	+	0.438833i	$0.144608\pi$
$314$	−0.505088	+	1.28694i	−0.0285038	+	0.0726264i
$315$	−10.3842	−	13.0214i	−0.585082	−	0.733670i
$316$	5.14364	+	0.775279i	0.289352	+	0.0436129i
$317$	−0.308831	−	1.35308i	−0.0173457	−	0.0759963i	0.965514	−	0.260350i	$-0.0838380\pi$
$317$	−0.308831	−	1.35308i	−0.0173457	−	0.0759963i	−0.982860	+	0.184354i	$0.940981\pi$
$318$	0.201522	+	0.882924i	0.0113008	+	0.0495119i
$319$	−13.7350	−	2.07022i	−0.769014	−	0.115910i
$320$	15.5184	+	19.4595i	0.867508	+	1.08782i
$321$	1.05919	−	2.69877i	0.0591181	−	0.150631i
$322$	−3.68437	+	6.38151i	−0.205322	+	0.355628i
$323$	−1.31142	+	17.4997i	−0.0729693	+	0.973707i
$324$	−0.704304	+	1.79454i	−0.0391280	+	0.0996965i
$325$	−35.8708	+	11.0647i	−1.98976	+	0.613759i
$326$	0.703638	−	0.106056i	0.0389709	−	0.00587392i
$327$	4.32579	+	18.9525i	0.239217	+	1.04808i
$328$	5.90597	+	5.47994i	0.326103	+	0.302579i
$329$	−8.96112	−	15.5211i	−0.494042	−	0.855707i
$330$	−5.17025	−	2.48986i	−0.284613	−	0.137062i
$331$	12.2568	+	15.3695i	0.673695	+	0.844787i	0.994757	−	0.102272i	$-0.0326111\pi$
$331$	12.2568	+	15.3695i	0.673695	+	0.844787i	−0.321062	+	0.947058i	$0.604040\pi$
$332$	0.677776	+	1.72694i	0.0371978	+	0.0947784i
$333$	−1.15296	+	0.355640i	−0.0631816	+	0.0194889i
$334$	−2.77340	−	1.33560i	−0.151753	−	0.0730806i
$335$	1.45658	+	19.4367i	0.0795813	+	1.06194i
$336$	−14.4325	−	4.45184i	−0.787358	−	0.242868i
$337$	12.8488	+	11.9220i	0.699921	+	0.649432i	0.947618	−	0.319405i	$-0.103483\pi$
$337$	12.8488	+	11.9220i	0.699921	+	0.649432i	−0.247697	+	0.968838i	$0.579674\pi$
$338$	−0.0678197	+	0.0102222i	−0.00368891	+	0.000556013i
$339$	−1.58756	−	4.04505i	−0.0862246	−	0.219697i
$340$	1.69166	−	22.5736i	0.0917432	−	1.22423i
$341$	5.97263	−	26.1678i	0.323436	−	1.41707i
$342$	1.30691	−	0.891037i	0.0706697	−	0.0481818i
$343$	−3.64928	+	15.9885i	−0.197042	+	0.863299i
$344$	−3.10455	+	5.37725i	−0.167386	+	0.289922i
$345$	−9.33314	−	23.7805i	−0.502480	−	1.28030i
$346$	−3.48589	−	0.525414i	−0.187403	−	0.0282464i
$347$	−31.7673	−	9.79891i	−1.70536	−	0.526033i	−0.719627	−	0.694361i	$-0.755687\pi$
$347$	−31.7673	−	9.79891i	−1.70536	−	0.526033i	−0.985731	+	0.168328i	$0.946163\pi$
$348$	−3.07927	+	3.86128i	−0.165066	+	0.206987i
$349$	−14.9071	+	7.17886i	−0.797957	+	0.384276i	−0.788000	−	0.615675i	$-0.788884\pi$
$349$	−14.9071	+	7.17886i	−0.797957	+	0.384276i	−0.00995647	+	0.999950i	$0.503169\pi$
$350$	−0.892787	−	11.9134i	−0.0477215	−	0.636799i
$351$	−3.53011	−	0.532078i	−0.188423	−	0.0284002i
$352$	−16.4627	+	2.48136i	−0.877466	+	0.132257i
$353$	4.38580	+	7.59642i	0.233432	+	0.404317i	0.958816	−	0.284028i	$-0.0916709\pi$
$353$	4.38580	+	7.59642i	0.233432	+	0.404317i	−0.725384	+	0.688345i	$0.758338\pi$
$354$	1.92909	−	0.929002i	0.102530	−	0.0493759i
$355$	39.2383	−	36.4078i	2.08255	−	1.93232i
$356$	0.423767	−	0.531387i	0.0224596	−	0.0281634i
$357$	6.30254	+	10.9163i	0.333566	+	0.577753i
$358$	4.12965	−	1.27383i	0.218259	−	0.0673240i
$359$	2.90352	−	5.02905i	0.153242	−	0.265423i	−0.779175	−	0.626806i	$-0.784362\pi$
$359$	2.90352	−	5.02905i	0.153242	−	0.265423i	0.932418	+	0.361383i	$0.117695\pi$
$360$	−3.43483	+	2.34183i	−0.181032	+	0.123425i
$361$	15.6524			0.823808
$362$	−5.58874			−0.293738
$363$	−15.2002	+	10.3633i	−0.797804	+	0.543934i
$364$	2.17465	−	29.0187i	0.113983	−	1.52099i
$365$	27.7607	+	34.8108i	1.45306	+	1.82208i
$366$	−0.171307	−	2.28593i	−0.00895435	−	0.119488i
$367$	−12.0506	+	11.1814i	−0.629038	+	0.583662i	−0.928905	−	0.370319i	$-0.879248\pi$
$367$	−12.0506	+	11.1814i	−0.629038	+	0.583662i	0.299867	+	0.953981i	$0.403058\pi$
$368$	−19.1412	−	13.0503i	−0.997806	−	0.680292i
$369$	5.59587	−	5.19221i	0.291309	−	0.270296i
$370$	−1.22029	−	0.376410i	−0.0634400	−	0.0195686i
$371$	3.17113	+	13.8936i	0.164637	+	0.721320i
$372$	−6.99585	−	6.49120i	−0.362718	−	0.336553i
$373$	4.30748	−	5.40141i	0.223033	−	0.279675i	−0.657708	−	0.753273i	$-0.728474\pi$
$373$	4.30748	−	5.40141i	0.223033	−	0.279675i	0.880741	+	0.473599i	$0.157045\pi$
$374$	3.58847	+	2.44658i	0.185556	+	0.126510i
$375$	17.9487	+	12.2372i	0.926867	+	0.631927i
$376$	−4.03050	+	1.94099i	−0.207857	+	0.100099i
$377$	−8.24010	−	3.96822i	−0.424387	−	0.204374i
$378$	0.415087	−	1.05762i	0.0213498	−	0.0543983i
$379$	−5.99062	+	26.2466i	−0.307717	+	1.34820i	0.550467	+	0.834857i	$0.314450\pi$
$379$	−5.99062	+	26.2466i	−0.307717	+	1.34820i	−0.858184	+	0.513341i	$0.828407\pi$
$380$	−44.6997			−2.29305
$381$	−11.0807	+	2.05393i	−0.567680	+	0.105226i
$382$	−1.32106			−0.0675913
$383$	2.52148	−	11.0473i	0.128842	−	0.564492i	−0.868758	−	0.495238i	$-0.835081\pi$
$383$	2.52148	−	11.0473i	0.128842	−	0.564492i	0.997599	−	0.0692540i	$-0.0220619\pi$
$384$	−2.86398	+	7.29731i	−0.146152	+	0.372389i
$385$	−81.3586	−	39.1802i	−4.14642	−	1.99681i
$386$	−3.63984	+	1.75285i	−0.185263	+	0.0892179i
$387$	4.86084	+	3.31406i	0.247090	+	0.168463i
$388$	14.9265	+	10.1767i	0.757778	+	0.516644i
$389$	−4.36693	+	5.47596i	−0.221412	+	0.277642i	−0.880114	−	0.474762i	$-0.842534\pi$
$389$	−4.36693	+	5.47596i	−0.221412	+	0.277642i	0.658702	+	0.752404i	$0.271106\pi$
$390$	−2.76982	−	2.57002i	−0.140255	−	0.130138i
$391$	4.30232	+	18.8497i	0.217578	+	0.953270i
$392$	10.9713	+	3.38420i	0.554135	+	0.170928i
$393$	2.51036	−	2.32928i	0.126631	−	0.117496i
$394$	3.11841	+	2.12610i	0.157103	+	0.107111i
$395$	7.79110	−	7.22908i	0.392013	−	0.363735i
$396$	0.781102	+	10.4231i	0.0392518	+	0.523779i
$397$	9.11052	+	11.4242i	0.457244	+	0.573366i	0.955996	−	0.293379i	$-0.0947798\pi$
$397$	9.11052	+	11.4242i	0.457244	+	0.573366i	−0.498752	+	0.866744i	$0.666208\pi$
$398$	0.210170	−	2.80452i	0.0105348	−	0.140578i
$399$	20.5654	−	14.0213i	1.02956	−	0.701942i
$400$	37.5598			1.87799
$401$	25.8595			1.29136			0.645681	−	0.763607i	$-0.276574\pi$
$401$	25.8595			1.29136			0.645681	+	0.763607i	$0.276574\pi$
$402$	−1.09860	+	0.749016i	−0.0547934	+	0.0373575i
$403$	8.83650	−	15.3053i	0.440177	−	0.762409i
$404$	−21.1292	+	6.51748i	−1.05121	+	0.324257i
$405$	1.96946	+	3.41120i	0.0978632	+	0.169504i
$406$	1.81479	−	2.27568i	0.0900666	−	0.112940i
$407$	−4.79550	+	4.44958i	−0.237704	+	0.220557i
$408$	2.83474	−	1.36514i	0.140340	−	0.0675843i
$409$	4.91528	+	8.51351i	0.243045	+	0.420966i	0.961580	−	0.274524i	$-0.0885204\pi$
$409$	4.91528	+	8.51351i	0.243045	+	0.420966i	−0.718535	+	0.695491i	$0.755187\pi$
$410$	7.98925	−	1.20419i	0.394561	−	0.0594705i
$411$	3.67042	+	0.553227i	0.181049	+	0.0272887i
$412$	−0.174318	−	2.32612i	−0.00858804	−	0.114599i
$413$	30.3560	−	14.6187i	1.49372	−	0.719339i
$414$	1.08657	−	1.36251i	0.0534018	−	0.0669638i
$415$	3.62215	+	1.11729i	0.177804	+	0.0548454i
$416$	−10.8397	−	1.63382i	−0.531460	−	0.0801047i
$417$	3.72372	+	9.48788i	0.182351	+	0.464624i
$418$	4.28806	−	7.42714i	0.209736	−	0.363274i
$419$	5.99265	−	26.2555i	0.292760	−	1.28267i	−0.587906	−	0.808929i	$-0.700048\pi$
$419$	5.99265	−	26.2555i	0.292760	−	1.28267i	0.880666	−	0.473737i	$-0.157095\pi$
$420$	−26.5283	+	18.0867i	−1.29445	+	0.882541i
$421$	−4.90112	+	21.4732i	−0.238866	+	1.04654i	0.703169	+	0.711023i	$0.251768\pi$
$421$	−4.90112	+	21.4732i	−0.238866	+	1.04654i	−0.942034	+	0.335516i	$0.891089\pi$
$422$	0.198509	−	2.64891i	0.00966325	−	0.128947i
$423$	1.54855	+	3.94563i	0.0752930	+	0.191843i
$424$	3.51740	−	0.530163i	0.170820	−	0.0257470i
$425$	−22.9787	−	21.3212i	−1.11463	−	1.03423i
$426$	3.48928	+	1.07630i	0.169056	+	0.0521470i
$427$	−2.69567	−	35.9712i	−0.130453	−	1.74077i
$428$	−5.03554	−	2.42499i	−0.243402	−	0.117216i
$429$	−18.4961	+	5.70529i	−0.893000	+	0.275454i
$430$	2.27486	+	5.79626i	0.109704	+	0.279520i
$431$	18.3652	+	23.0292i	0.884619	+	1.10928i	0.993342	+	0.115205i	$0.0367524\pi$
$431$	18.3652	+	23.0292i	0.884619	+	1.10928i	−0.108723	+	0.994072i	$0.534676\pi$
$432$	3.21826	+	1.54983i	0.154839	+	0.0745664i
$433$	−3.66544	−	6.34873i	−0.176150	−	0.305101i	0.764409	−	0.644732i	$-0.223031\pi$
$433$	−3.66544	−	6.34873i	−0.176150	−	0.305101i	−0.940559	+	0.339631i	$0.889698\pi$
$434$	4.12306	+	3.82564i	0.197913	+	0.183637i
$435$	2.24546	+	9.83799i	0.107661	+	0.471696i
$436$	37.0577	−	5.58555i	1.77474	−	0.267499i
$437$	36.4823	−	11.2533i	1.74519	−	0.538319i
$438$	−1.10968	+	2.82741i	−0.0530224	+	0.135099i
$439$	2.97935	−	39.7567i	0.142197	−	1.89748i	−0.235990	−	0.971755i	$-0.575833\pi$
$439$	2.97935	−	39.7567i	0.142197	−	1.89748i	0.378187	−	0.925729i	$-0.376548\pi$
$440$	−11.2699	+	19.5201i	−0.537272	+	0.930583i
$441$	3.97438	−	10.1266i	0.189256	−	0.482217i
$442$	1.78299	+	2.23580i	0.0848082	+	0.106346i
$443$	−1.43748	−	0.216666i	−0.0682968	−	0.0102941i	0.114805	−	0.993388i	$-0.463376\pi$
$443$	−1.43748	−	0.216666i	−0.0682968	−	0.0102941i	−0.183102	+	0.983094i	$0.558614\pi$
$444$	0.517585	+	2.26769i	0.0245635	+	0.107620i
$445$	−0.309018	−	1.35390i	−0.0146489	−	0.0641809i
$446$	4.39542	+	0.662503i	0.208129	+	0.0313704i
$447$	−1.54367	−	1.93571i	−0.0730133	−	0.0915558i
$448$	−9.76128	+	24.8713i	−0.461177	+	1.17506i
$449$	−2.70191	+	4.67984i	−0.127511	+	0.220855i	−0.922712	−	0.385491i	$-0.874032\pi$
$449$	−2.70191	+	4.67984i	−0.127511	+	0.220855i	0.795201	+	0.606346i	$0.207365\pi$
$450$	−0.211146	+	2.81754i	−0.00995350	+	0.132820i
$451$	15.1211	−	38.5278i	0.712022	−	1.81420i
$452$	−8.00494	+	2.46920i	−0.376521	+	0.116141i
$453$	8.75350	−	1.31938i	0.411275	−	0.0619898i
$454$	0.561151	+	2.45856i	0.0263361	+	0.115386i
$455$	−43.5856	−	40.4416i	−2.04333	−	1.89593i
$456$	−3.10642	−	5.38047i	−0.145471	−	0.251964i
$457$	−19.6193	−	9.44816i	−0.917753	−	0.441966i	−0.0854843	−	0.996340i	$-0.527244\pi$
$457$	−19.6193	−	9.44816i	−0.917753	−	0.441966i	−0.832268	+	0.554373i	$0.812958\pi$
$458$	−4.26064	−	5.34268i	−0.199087	−	0.249647i
$459$	−1.08913	−	2.77505i	−0.0508360	−	0.129528i
$460$	−47.0603	+	14.5162i	−2.19420	+	0.676821i
$461$	−21.8758	−	10.5348i	−1.01886	−	0.490656i	−0.151562	−	0.988448i	$-0.548430\pi$
$461$	−21.8758	−	10.5348i	−1.01886	−	0.490656i	−0.867297	+	0.497792i	$0.834144\pi$
$462$	−0.460348	−	6.14292i	−0.0214173	−	0.285795i
$463$	−8.11106	−	2.50193i	−0.376953	−	0.116275i	0.100488	−	0.994938i	$-0.467959\pi$
$463$	−8.11106	−	2.50193i	−0.376953	−	0.116275i	−0.477441	+	0.878664i	$0.658436\pi$
$464$	6.70816	+	6.22426i	0.311419	+	0.288954i
$465$	−19.2816	+	2.90623i	−0.894163	+	0.134773i
$466$	1.79890	+	4.58353i	0.0833325	+	0.212328i
$467$	3.00859	−	40.1468i	0.139221	−	1.85777i	−0.293136	−	0.956071i	$-0.594699\pi$
$467$	3.00859	−	40.1468i	0.139221	−	1.85777i	0.432357	−	0.901703i	$-0.357682\pi$
$468$	−1.53143	+	6.70965i	−0.0707905	+	0.310154i
$469$	−17.2875	+	11.7864i	−0.798264	+	0.544247i
$470$	−0.998270	+	4.37371i	−0.0460468	+	0.201744i
$471$	2.57255	−	4.45579i	0.118537	−	0.205312i
$472$	−3.07249	−	7.82858i	−0.141423	−	0.360340i
$473$	31.5412	+	4.75407i	1.45027	+	0.218592i
$474$	0.692828	+	0.213709i	0.0318226	+	0.00981598i
$475$	−38.5929	+	48.3940i	−1.77077	+	2.22047i
$476$	21.8936	−	10.5434i	1.00349	−	0.483256i
$477$	−0.251867	−	3.36094i	−0.0115322	−	0.153887i
$478$	−6.05800	−	0.913096i	−0.277086	−	0.0417641i
$479$	−20.8694	+	3.14556i	−0.953547	+	0.143724i	−0.607347	−	0.794437i	$-0.707766\pi$
$479$	−20.8694	+	3.14556i	−0.953547	+	0.143724i	−0.346200	+	0.938161i	$0.612528\pi$
$480$	6.04750	+	10.4746i	0.276029	+	0.478097i
$481$	−3.88083	+	1.86891i	−0.176951	+	0.0852149i
$482$	1.26661	−	1.17525i	0.0576927	−	0.0535310i
$483$	17.0981	−	21.4404i	0.777991	−	0.975570i
$484$	17.7327	+	30.7140i	0.806033	+	1.39609i
$485$	35.2721	−	10.8800i	1.60162	−	0.494035i
$486$	−0.134352	+	0.232705i	−0.00609433	+	0.0105557i
$487$	−29.8345	+	20.3408i	−1.35193	+	0.921729i	−0.999898	−	0.0142591i	$-0.995461\pi$
$487$	−29.8345	+	20.3408i	−1.35193	+	0.921729i	−0.352030	+	0.935989i	$0.614509\pi$
$488$	−9.00385			−0.407585
$489$	−2.64821			−0.119756
$490$	9.51323	−	6.48601i	0.429764	−	0.293008i
$491$	−1.44391	+	19.2676i	−0.0651627	+	0.869535i	0.864855	+	0.502021i	$0.167410\pi$
$491$	−1.44391	+	19.2676i	−0.0651627	+	0.869535i	−0.930018	+	0.367514i	$0.880209\pi$
$492$	−9.17538	−	11.5056i	−0.413658	−	0.518711i
$493$	−0.570732	−	7.61589i	−0.0257045	−	0.343002i
$494$	4.13944	−	3.84083i	0.186242	−	0.172807i
$495$	17.6455	+	12.0305i	0.793104	+	0.540729i
$496$	−12.9626	+	12.0275i	−0.582036	+	0.540051i
$497$	54.9071	+	16.9366i	2.46292	+	0.759710i
$498$	0.0575402	+	0.252100i	0.00257844	+	0.0112969i
$499$	31.4001	+	29.1350i	1.40566	+	1.30426i	0.896116	+	0.443820i	$0.146377\pi$
$499$	31.4001	+	29.1350i	1.40566	+	1.30426i	0.509546	+	0.860443i	$0.329813\pi$
$500$	26.1107	−	32.7418i	1.16771	−	1.46426i
$501$	9.46528	+	6.45332i	0.422877	+	0.288313i
$502$	−4.11805	−	2.80764i	−0.183798	−	0.125311i
$503$	9.25065	−	4.45488i	0.412466	−	0.198633i	−0.216131	−	0.976364i	$-0.569344\pi$
$503$	9.25065	−	4.45488i	0.412466	−	0.198633i	0.628597	+	0.777731i	$0.283629\pi$
$504$	−4.02068	−	1.93626i	−0.179095	−	0.0862477i
$505$	−16.5056	+	42.0557i	−0.734491	+	1.87145i
$506$	2.10256	−	9.21192i	0.0934702	−	0.409520i
$507$	0.255246			0.0113359
$508$	2.35216	+	21.5975i	0.104360	+	0.958233i
$509$	−15.3573			−0.680700			−0.340350	−	0.940299i	$-0.610545\pi$
$509$	−15.3573			−0.680700			−0.340350	+	0.940299i	$0.610545\pi$
$510$	0.702104	−	3.07612i	0.0310897	−	0.136213i
$511$	−17.4618	+	44.4918i	−0.772463	+	1.96820i
$512$	16.6753	+	8.03042i	0.736953	+	0.354898i
$513$	−5.30367	+	2.55411i	−0.234163	+	0.112767i
$514$	0.159694	+	0.108878i	0.00704381	+	0.00480239i
$515$	−3.93793	−	2.68484i	−0.173526	−	0.118308i
$516$	7.07126	−	8.86708i	0.311295	−	0.390351i
$517$	16.8466	+	15.6313i	0.740911	+	0.687465i
$518$	−0.305042	−	1.33648i	−0.0134028	−	0.0587215i
$519$	12.5367	+	3.86705i	0.550298	+	0.169744i
$520$	−10.8793	+	10.0945i	−0.477089	+	0.442674i
$521$	2.07703	+	1.41610i	0.0909965	+	0.0620404i	0.607964	−	0.793965i	$-0.291987\pi$
$521$	2.07703	+	1.41610i	0.0909965	+	0.0620404i	−0.516967	+	0.856005i	$0.672939\pi$
$522$	−0.504622	+	0.468221i	−0.0220867	+	0.0204935i
$523$	1.99581	+	26.6322i	0.0872705	+	1.16454i	0.853187	+	0.521605i	$0.174666\pi$
$523$	1.99581	+	26.6322i	0.0872705	+	1.16454i	−0.765917	+	0.642940i	$0.777715\pi$
$524$	−4.11616	−	5.16151i	−0.179815	−	0.225481i
$525$	−3.32257	+	44.3366i	−0.145009	+	1.93501i
$526$	0.260777	−	0.177795i	0.0113704	−	0.00775222i
$527$	14.7579			0.642863
$528$	19.3670			0.842840
$529$	15.7510	−	10.7388i	0.684826	−	0.466906i
$530$	1.78360	−	3.08929i	0.0774746	−	0.134190i
$531$	−7.61435	+	2.34872i	−0.330435	+	0.101926i
$532$	−23.9919	−	41.5551i	−1.04018	−	1.80164i
$533$	16.9914	−	21.3065i	0.735977	−	0.922886i
$534$	0.0694457	−	0.0644362i	0.00300521	−	0.00278843i
$535$	−10.2887	+	4.95479i	−0.444820	+	0.214214i
$536$	2.61129	+	4.52288i	0.112790	+	0.195359i
$537$	−15.9037	+	2.39709i	−0.686294	+	0.103442i
$538$	6.19164	+	0.933239i	0.266940	+	0.0402348i
$539$	−4.40775	−	58.8174i	−0.189855	−	2.53344i
$540$	6.84145	−	3.29467i	0.294409	−	0.141780i
$541$	2.81344	−	3.52794i	0.120959	−	0.151678i	−0.717665	−	0.696389i	$-0.754789\pi$
$541$	2.81344	−	3.52794i	0.120959	−	0.151678i	0.838624	+	0.544711i	$0.183360\pi$
$542$	−8.12222	−	2.50537i	−0.348879	−	0.107615i
$543$	20.5666	+	3.09991i	0.882595	+	0.133030i
$544$	−3.34431	−	8.52117i	−0.143386	−	0.365342i
$545$	38.2861	−	66.3135i	1.64000	−	2.84056i
$546$	0.902562	−	3.95438i	0.0386261	−	0.169232i
$547$	18.2226	−	12.4239i	0.779141	−	0.531209i	−0.107203	−	0.994237i	$-0.534189\pi$
$547$	18.2226	−	12.4239i	0.779141	−	0.531209i	0.886344	+	0.463028i	$0.153237\pi$
$548$	1.59231	−	6.97635i	0.0680199	−	0.298015i
$549$	−0.637530	+	8.50724i	−0.0272091	+	0.363080i
$550$	5.59674	+	14.2603i	0.238646	+	0.608060i
$551$	−14.9123	+	2.24767i	−0.635287	+	0.0957540i
$552$	−5.01777	−	4.65581i	−0.213570	−	0.198164i
$553$	10.9023	+	3.36291i	0.463612	+	0.143005i
$554$	0.336734	+	4.49340i	0.0143065	+	0.190906i
$555$	4.28189	+	2.06205i	0.181756	+	0.0875291i
$556$	18.7760	−	5.79164i	0.796281	−	0.245620i
$557$	−4.76086	−	12.1305i	−0.201724	−	0.513984i	0.793834	−	0.608134i	$-0.208082\pi$
$557$	−4.76086	−	12.1305i	−0.201724	−	0.513984i	−0.995558	+	0.0941502i	$0.969987\pi$
$558$	−0.829369	−	1.04000i	−0.0351100	−	0.0440266i
$559$	18.9226	+	9.11265i	0.800342	+	0.385424i
$560$	29.7457	+	51.5211i	1.25699	+	2.17716i
$561$	−11.8485	−	10.9938i	−0.500246	−	0.464160i
$562$	1.34998	+	5.91464i	0.0569454	+	0.249494i
$563$	−4.55866	+	0.687107i	−0.192124	+	0.0289581i	−0.244400	−	0.969675i	$-0.578591\pi$
$563$	−4.55866	+	0.687107i	−0.192124	+	0.0289581i	0.0522751	+	0.998633i	$0.483353\pi$
$564$	7.80821	−	2.40851i	0.328785	−	0.101417i
$565$	−6.25328	+	15.9331i	−0.263078	+	0.670311i
$566$	0.255473	−	3.40904i	0.0107383	−	0.143293i
$567$	−2.11415	+	3.66182i	−0.0887860	+	0.153782i
$568$	5.23986	−	13.3510i	0.219860	−	0.560194i
$569$	1.20195	+	1.50720i	0.0503884	+	0.0631851i	0.806387	−	0.591388i	$-0.201420\pi$
$569$	1.20195	+	1.50720i	0.0503884	+	0.0631851i	−0.755999	+	0.654573i	$0.772848\pi$
$570$	−6.16083	−	0.928596i	−0.258049	−	0.0388946i
$571$	1.53263	+	6.71491i	0.0641388	+	0.281010i	0.996819	−	0.0796928i	$-0.0253939\pi$
$571$	1.53263	+	6.71491i	0.0641388	+	0.281010i	−0.932681	+	0.360703i	$0.882537\pi$
$572$	8.30326	+	36.3790i	0.347177	+	1.52108i
$573$	4.86150	+	0.732754i	0.203092	+	0.0306112i
$574$	5.40758	+	6.78089i	0.225708	+	0.283029i
$575$	−24.9151	+	63.4827i	−1.03903	+	2.64741i
$576$	3.15945	−	5.47234i	0.131644	−	0.228014i
$577$	1.09270	−	14.5810i	0.0454895	−	0.607015i	−0.927149	−	0.374692i	$-0.877748\pi$
$577$	1.09270	−	14.5810i	0.0454895	−	0.607015i	0.972639	−	0.232323i	$-0.0746326\pi$
$578$	0.796435	−	2.02928i	0.0331273	−	0.0844070i
$579$	14.3669	−	4.43159i	0.597066	−	0.184171i
$580$	19.2361	−	2.89938i	0.798736	−	0.120390i
$581$	0.905447	+	3.96702i	0.0375643	+	0.164580i
$582$	1.84586	+	1.71271i	0.0765135	+	0.0709941i
$583$	−9.13686	−	15.8255i	−0.378410	−	0.655425i
$584$	10.7487	+	5.17631i	0.444785	+	0.214197i
$585$	8.76742	+	10.9940i	0.362488	+	0.454546i
$586$	0.820623	+	2.09091i	0.0338996	+	0.0863749i
$587$	−21.3592	+	6.58844i	−0.881589	+	0.271934i	−0.702316	−	0.711865i	$-0.747851\pi$
$587$	−21.3592	+	6.58844i	−0.881589	+	0.271934i	−0.179273	+	0.983799i	$0.557374\pi$
$588$	−18.8948	−	9.09926i	−0.779209	−	0.375247i
$589$	−2.17774	−	29.0599i	−0.0897323	−	1.19739i
$590$	−8.05905	−	2.48589i	−0.331786	−	0.102342i
$591$	−10.2965	−	9.55372i	−0.423540	−	0.392988i
$592$	4.26170	−	0.642348i	0.175155	−	0.0264003i
$593$	−7.43540	−	18.9451i	−0.305335	−	0.777982i	−0.998370	−	0.0570774i	$-0.981822\pi$
$593$	−7.43540	−	18.9451i	−0.305335	−	0.777982i	0.693034	−	0.720905i	$-0.256273\pi$
$594$	−0.108873	+	1.45281i	−0.00446712	+	0.0596095i
$595$	11.0482	−	48.4055i	0.452934	−	1.98443i
$596$	−3.94361	+	2.68871i	−0.161536	+	0.110134i
$597$	−2.32901	+	10.2040i	−0.0953199	+	0.417624i
$598$	3.11073	−	5.38795i	0.127207	−	0.220330i
$599$	12.3978	+	31.5892i	0.506562	+	1.29070i	0.924139	+	0.382057i	$0.124784\pi$
$599$	12.3978	+	31.5892i	0.506562	+	1.29070i	−0.417576	+	0.908642i	$0.637120\pi$
$600$	10.9738	+	1.65404i	0.448004	+	0.0675257i
$601$	33.4490	+	10.3177i	1.36442	+	0.420866i	0.888602	−	0.458680i	$-0.151678\pi$
$601$	33.4490	+	10.3177i	1.36442	+	0.420866i	0.475813	+	0.879546i	$0.342154\pi$
$602$	−4.16750	+	5.22588i	−0.169855	+	0.212991i
$603$	4.45832	−	2.14701i	0.181557	−	0.0874331i
$604$	−1.27531	−	17.0179i	−0.0518918	−	0.692447i
$605$	71.6544	+	10.8002i	2.91317	+	0.439089i
$606$	−3.04757	+	0.459347i	−0.123799	+	0.0186597i
$607$	−8.29437	−	14.3663i	−0.336658	−	0.583109i	0.647144	−	0.762368i	$-0.275963\pi$
$607$	−8.29437	−	14.3663i	−0.336658	−	0.583109i	−0.983802	+	0.179259i	$0.942630\pi$
$608$	−16.2857	+	7.84276i	−0.660471	+	0.318066i
$609$	−7.94069	+	7.36788i	−0.321773	+	0.298562i
$610$	−5.62970	+	7.05942i	−0.227940	+	0.285828i
$611$	7.56592	+	13.1046i	0.306084	+	0.530154i
$612$	−5.49167	+	1.69396i	−0.221988	+	0.0684742i
$613$	−7.83882	+	13.5772i	−0.316607	+	0.548379i	−0.979778	−	0.200089i	$-0.935877\pi$
$613$	−7.83882	+	13.5772i	−0.316607	+	0.548379i	0.663171	+	0.748468i	$0.269210\pi$
$614$	2.56250	−	1.74708i	0.103414	−	0.0705066i
$615$	−30.0684			−1.21247
$616$	−24.1958			−0.974877
$617$	−17.6082	+	12.0051i	−0.708880	+	0.483306i	−0.863295	−	0.504700i	$-0.831603\pi$
$617$	−17.6082	+	12.0051i	−0.708880	+	0.483306i	0.154415	+	0.988006i	$0.450651\pi$
$618$	0.0242972	−	0.324223i	0.000977375	−	0.0130422i
$619$	2.45011	+	3.07234i	0.0984783	+	0.123488i	0.828629	−	0.559799i	$-0.189121\pi$
$619$	2.45011	+	3.07234i	0.0984783	+	0.123488i	−0.730150	+	0.683286i	$0.760550\pi$
$620$	2.80917	+	37.4858i	0.112819	+	1.50547i
$621$	−4.75431	+	4.41135i	−0.190784	+	0.177022i
$622$	2.03700	+	1.38880i	0.0816763	+	0.0556860i
$623$	1.09279	−	1.01396i	0.0437817	−	0.0406235i
$624$	12.1854	+	3.75871i	0.487808	+	0.150469i
$625$	−7.34126	−	32.1641i	−0.293650	−	1.28657i
$626$	−0.482608	−	0.447794i	−0.0192889	−	0.0178975i
$627$	−19.8997	+	24.9534i	−0.794717	+	0.996544i
$628$	−8.19524	−	5.58742i	−0.327025	−	0.222962i
$629$	−2.97190	−	2.02621i	−0.118497	−	0.0807901i
$630$	−4.03206	+	1.94174i	−0.160641	+	0.0773607i
$631$	−15.3881	−	7.41053i	−0.612592	−	0.295009i	0.101745	−	0.994810i	$-0.467557\pi$
$631$	−15.3881	−	7.41053i	−0.612592	−	0.295009i	−0.714337	+	0.699802i	$0.753272\pi$
$632$	1.04042	−	2.65095i	0.0413857	−	0.105449i
$633$	−2.19979	+	9.63789i	−0.0874336	+	0.383072i
$634$	−0.372927			−0.0148108
$635$	37.4975	+	23.7561i	1.48804	+	0.942734i
$636$	−6.49738			−0.257638
$637$	8.64187	−	37.8625i	0.342403	−	1.50017i
$638$	−1.36358	+	3.47434i	−0.0539846	+	0.137551i
$639$	−12.2436	−	5.89619i	−0.484348	−	0.233250i
$640$	27.8201	−	13.3974i	1.09969	−	0.529581i
$641$	15.1649	+	10.3393i	0.598978	+	0.408376i	0.824500	−	0.565862i	$-0.191456\pi$
$641$	15.1649	+	10.3393i	0.598978	+	0.408376i	−0.225522	+	0.974238i	$0.572409\pi$
$642$	−0.643657	−	0.438838i	−0.0254031	−	0.0173196i
$643$	28.8293	−	36.1507i	1.13691	−	1.42565i	0.247298	−	0.968940i	$-0.420457\pi$
$643$	28.8293	−	36.1507i	1.13691	−	1.42565i	0.889617	−	0.456707i	$-0.150971\pi$
$644$	−38.7539	−	35.9583i	−1.52712	−	1.41696i
$645$	−5.15648	−	22.5920i	−0.203036	−	0.889560i
$646$	4.50592	+	1.38989i	0.177283	+	0.0546846i
$647$	−9.15558	+	8.49513i	−0.359943	+	0.333978i	−0.839327	−	0.543627i	$-0.817051\pi$
$647$	−9.15558	+	8.49513i	−0.359943	+	0.333978i	0.479384	+	0.877605i	$0.340860\pi$
$648$	0.872025	+	0.594537i	0.0342564	+	0.0233556i
$649$	−31.6705	+	29.3859i	−1.24317	+	1.15350i
$650$	0.753785	+	10.0586i	0.0295659	+	0.394529i
$651$	−13.0509	−	16.3653i	−0.511504	−	0.641406i
$652$	−0.381514	+	5.09095i	−0.0149412	+	0.199377i
$653$	19.1453	−	13.0531i	0.749215	−	0.510806i	−0.127487	−	0.991840i	$-0.540691\pi$
$653$	19.1453	−	13.0531i	0.749215	−	0.510806i	0.876702	+	0.481034i	$0.159739\pi$
$654$	5.22359			0.204259
$655$	−13.4890			−0.527057
$656$	−22.5294	+	15.3603i	−0.879626	+	0.599719i
$657$	5.65189	−	9.78935i	0.220501	−	0.381919i
$658$	−4.60183	+	1.41948i	−0.179398	+	0.0553369i
$659$	−8.99261	−	15.5757i	−0.350302	−	0.606741i	0.636000	−	0.771689i	$-0.280588\pi$
$659$	−8.99261	−	15.5757i	−0.350302	−	0.606741i	−0.986302	+	0.164948i	$0.947255\pi$
$660$	25.6696	−	32.1886i	0.999186	−	1.25294i
$661$	−22.0311	+	20.4419i	−0.856911	+	0.795097i	−0.980352	−	0.197255i	$-0.936797\pi$
$661$	−22.0311	+	20.4419i	−0.856911	+	0.795097i	0.123441	+	0.992352i	$0.460607\pi$
$662$	4.75918	−	2.29190i	0.184971	−	0.0890772i
$663$	−5.32127	−	9.21671i	−0.206661	−	0.357947i
$664$	1.00432	−	0.151377i	0.0389751	−	0.00587455i
$665$	−96.9463	−	14.6123i	−3.75942	−	0.566641i
$666$	0.0242281	+	0.323301i	0.000938819	+	0.0125277i
$667$	−14.9699	+	7.20913i	−0.579638	+	0.279139i
$668$	13.7695	−	17.2664i	0.532759	−	0.668058i
$669$	−15.8077	−	4.87602i	−0.611160	−	0.188518i
$670$	5.17886	+	0.780588i	0.200077	+	0.0301567i
$671$	16.8987	+	43.0572i	0.652368	+	1.66221i
$672$	−6.49180	+	11.2441i	−0.250427	+	0.433752i
$673$	3.40931	−	14.9372i	0.131419	−	0.575786i	−0.865742	−	0.500491i	$-0.833153\pi$
$673$	3.40931	−	14.9372i	0.131419	−	0.575786i	0.997161	−	0.0752950i	$-0.0239899\pi$
$674$	3.89143	−	2.65313i	0.149892	−	0.102195i
$675$	2.33982	−	10.2514i	0.0900598	−	0.394578i
$676$	0.0367720	−	0.490688i	0.00141431	−	0.0188726i
$677$	2.30166	+	5.86453i	0.0884599	+	0.225392i	0.968257	−	0.249958i	$-0.0804167\pi$
$677$	2.30166	+	5.86453i	0.0884599	+	0.225392i	−0.879797	+	0.475350i	$0.842321\pi$
$678$	−1.15459	+	0.174027i	−0.0443419	+	0.00668347i
$679$	29.0463	+	26.9511i	1.11470	+	1.03429i
$680$	−11.8425	−	3.65293i	−0.454139	−	0.140083i
$681$	−0.701342	−	9.35876i	−0.0268755	−	0.358628i
$682$	−6.49799	−	3.12927i	−0.248821	−	0.119826i
$683$	−1.61526	+	0.498243i	−0.0618063	+	0.0190647i	−0.325504	−	0.945541i	$-0.605534\pi$
$683$	−1.61526	+	0.498243i	−0.0618063	+	0.0190647i	0.263698	+	0.964605i	$0.415058\pi$
$684$	4.14597	+	10.5638i	0.158525	+	0.403916i
$685$	−9.11591	−	11.4310i	−0.348301	−	0.436756i
$686$	3.97027	+	1.91198i	0.151586	+	0.0729998i
$687$	12.7157	+	22.0243i	0.485136	+	0.840279i
$688$	−15.4047	−	14.2934i	−0.587297	−	0.544932i
$689$	−2.67740	−	11.7304i	−0.102001	−	0.446894i
$690$	−6.78775	+	1.02309i	−0.258405	+	0.0389483i
$691$	−11.7483	+	3.62388i	−0.446927	+	0.137859i	−0.510046	−	0.860147i	$-0.670372\pi$
$691$	−11.7483	+	3.62388i	−0.446927	+	0.137859i	0.0631186	+	0.998006i	$0.479895\pi$
$692$	9.24013	−	23.5435i	0.351257	−	0.894988i
$693$	−1.71322	+	22.8613i	−0.0650797	+	0.868428i
$694$	−4.46643	+	7.73609i	−0.169543	+	0.293658i
$695$	14.6674	−	37.3720i	0.556367	−	1.41760i
$696$	1.68581	+	2.11395i	0.0639007	+	0.0801289i
$697$	22.5027	+	3.39173i	0.852350	+	0.128471i
$698$	0.989299	+	4.33440i	0.0374455	+	0.164060i
$699$	−4.07761	−	17.8652i	−0.154229	−	0.675723i
$700$	84.7543	+	12.7747i	3.20341	+	0.482837i
$701$	18.0883	+	22.6820i	0.683186	+	0.856688i	0.995643	−	0.0932439i	$-0.0297236\pi$
$701$	18.0883	+	22.6820i	0.683186	+	0.856688i	−0.312458	+	0.949932i	$0.601152\pi$
$702$	−0.350460	+	0.892958i	−0.0132273	+	0.0337025i
$703$	−3.55128	+	6.15100i	−0.133939	+	0.231989i
$704$	2.56028	−	34.1646i	0.0964943	−	1.28763i
$705$	6.09960	−	15.5415i	0.229724	−	0.585328i
$706$	2.25225	−	0.694727i	0.0847645	−	0.0261464i
$707$	−47.9562	+	7.22824i	−1.80358	+	0.271846i
$708$	3.41823	+	14.9763i	0.128465	+	0.562842i
$709$	−25.8506	−	23.9858i	−0.970839	−	0.900807i	0.0242585	−	0.999706i	$-0.492278\pi$
$709$	−25.8506	−	23.9858i	−0.970839	−	0.900807i	−0.995097	+	0.0988988i	$0.968468\pi$
$710$	−7.19150	−	12.4560i	−0.269892	−	0.467467i
$711$	−2.43107	−	1.17074i	−0.0911721	−	0.0439062i
$712$	−0.232001	−	0.290919i	−0.00869459	−	0.0109027i
$713$	−11.7299	−	29.8874i	−0.439289	−	1.11929i
$714$	3.23656	−	0.998346i	0.121125	−	0.0373622i
$715$	68.6915	+	33.0801i	2.56892	+	1.23712i
$716$	2.31704	+	30.9187i	0.0865917	+	1.15549i
$717$	21.7870	+	6.72039i	0.813649	+	0.250977i
$718$	−1.14384	−	1.06133i	−0.0426876	−	0.0396083i
$719$	41.7506	−	6.29289i	1.55704	−	0.234685i	0.686625	−	0.727012i	$-0.259092\pi$
$719$	41.7506	−	6.29289i	1.55704	−	0.234685i	0.870411	+	0.492327i	$0.163853\pi$
$720$	−5.14028	−	13.0972i	−0.191567	−	0.488105i
$721$	0.382338	−	5.10195i	0.0142390	−	0.190006i
$722$	0.935890	−	4.10040i	0.0348302	−	0.152601i
$723$	−5.31301	+	3.62235i	−0.197593	+	0.134717i
$724$	8.92220	−	39.0907i	0.331591	−	1.45279i
$725$	13.4691	−	23.3292i	0.500231	−	0.866425i
$726$	1.80600	+	4.60160i	0.0670268	+	0.170781i
$727$	−44.9983	−	6.78240i	−1.66889	−	0.251545i	−0.754479	−	0.656324i	$-0.772111\pi$
$727$	−44.9983	−	6.78240i	−1.66889	−	0.251545i	−0.914415	+	0.404778i	$0.867349\pi$
$728$	−15.2237	−	4.69588i	−0.564226	−	0.174041i
$729$	0.623490	−	0.781831i	0.0230922	−	0.0289567i
$730$	10.7791	−	5.19096i	0.398954	−	0.192126i
$731$	1.31063	+	17.4892i	0.0484755	+	0.646860i
$732$	16.2625	+	2.45118i	0.601081	+	0.0905983i
$733$	10.1272	−	1.52644i	0.374058	−	0.0563802i	0.0406771	−	0.999172i	$-0.487049\pi$
$733$	10.1272	−	1.52644i	0.374058	−	0.0563802i	0.333381	+	0.942792i	$0.391810\pi$
$734$	2.20861	+	3.82543i	0.0815213	+	0.141199i
$735$	−38.6063	+	18.5918i	−1.42401	+	0.685769i
$736$	−14.5988	+	13.5457i	−0.538118	+	0.499301i
$737$	16.7279	−	20.9761i	0.616180	−	0.772665i
$738$	−1.02560	−	1.77639i	−0.0377528	−	0.0653898i
$739$	−10.5928	+	3.26743i	−0.389661	+	0.120194i	−0.483394	−	0.875403i	$-0.660596\pi$
$739$	−10.5928	+	3.26743i	−0.389661	+	0.120194i	0.0937332	+	0.995597i	$0.470120\pi$
$740$	4.58097	−	7.93447i	0.168400	−	0.291677i
$741$	−17.3635	+	11.8382i	−0.637865	+	0.434889i
$742$	3.82928			0.140577
$743$	22.3864			0.821276			0.410638	−	0.911799i	$-0.365306\pi$
$743$	22.3864			0.821276			0.410638	+	0.911799i	$0.365306\pi$
$744$	−4.31691	+	2.94322i	−0.158266	+	0.107904i
$745$	−0.728784	+	9.72495i	−0.0267006	+	0.356294i
$746$	−1.15744	−	1.45138i	−0.0423768	−	0.0531389i
$747$	−0.0719153	−	0.959643i	−0.00263124	−	0.0351115i
$748$	−22.8416	+	21.1939i	−0.835171	+	0.774925i
$749$	−10.1285	−	6.90552i	−0.370089	−	0.252322i
$750$	4.27894	−	3.97028i	0.156245	−	0.144974i
$751$	19.1887	+	5.91893i	0.700206	+	0.215985i	0.624362	−	0.781135i	$-0.285359\pi$
$751$	19.1887	+	5.91893i	0.700206	+	0.215985i	0.0758434	+	0.997120i	$0.475835\pi$
$752$	−3.36906	−	14.7608i	−0.122857	−	0.538271i
$753$	13.5971	+	12.6163i	0.495506	+	0.459763i
$754$	−1.53224	+	1.92137i	−0.0558008	+	0.0699721i
$755$	−28.8099	−	19.6423i	−1.04850	−	0.714856i
$756$	6.73493	+	4.59180i	0.244947	+	0.167002i
$757$	0.719044	−	0.346274i	0.0261341	−	0.0125855i	−0.420771	−	0.907167i	$-0.638240\pi$
$757$	0.719044	−	0.346274i	0.0261341	−	0.0125855i	0.446905	+	0.894581i	$0.352526\pi$
$758$	6.51756	+	3.13869i	0.236728	+	0.114002i
$759$	−12.8470	+	32.7336i	−0.466316	+	1.18815i
$760$	−5.44550	+	23.8583i	−0.197529	+	0.865431i
$761$	−7.58561			−0.274978			−0.137489	−	0.990503i	$-0.543903\pi$
$761$	−7.58561			−0.274978			−0.137489	+	0.990503i	$0.543903\pi$
$762$	−0.124476	+	3.02558i	−0.00450931	+	0.109605i
$763$	82.1979			2.97577
$764$	2.10902	−	9.24023i	0.0763017	−	0.334300i
$765$	−4.28997	+	10.9307i	−0.155104	+	0.395199i
$766$	−2.74327	−	1.32109i	−0.0991184	−	0.0477329i
$767$	−25.6298	+	12.3426i	−0.925437	+	0.445667i
$768$	−8.70145	−	5.93254i	−0.313986	−	0.214072i
$769$	−19.4390	−	13.2533i	−0.700989	−	0.477926i	0.159629	−	0.987177i	$-0.448970\pi$
$769$	−19.4390	−	13.2533i	−0.700989	−	0.477926i	−0.860618	+	0.509251i	$0.829923\pi$
$770$	−15.1285	+	18.9706i	−0.545195	+	0.683653i
$771$	−0.527284	−	0.489248i	−0.0189897	−	0.0176198i
$772$	−6.44957	−	28.2574i	−0.232125	−	1.01701i
$773$	−2.44245	−	0.753395i	−0.0878487	−	0.0270977i	0.250519	−	0.968112i	$-0.419399\pi$
$773$	−2.44245	−	0.753395i	−0.0878487	−	0.0270977i	−0.338368	+	0.941014i	$0.609875\pi$
$774$	1.15882	−	1.07522i	0.0416528	−	0.0386482i
$775$	43.0093	+	29.3232i	1.54494	+	1.05332i
$776$	7.25018	−	6.72718i	0.260266	−	0.241492i
$777$	0.381251	+	5.08744i	0.0136773	+	0.182511i
$778$	1.17341	+	1.47141i	0.0420689	+	0.0527527i
$779$	3.35811	−	44.8109i	0.120317	−	1.60552i
$780$	22.3980	−	15.2707i	0.801978	−	0.546779i
$781$	−73.6799			−2.63647
$782$	5.19525			0.185782
$783$	2.11672	−	1.44315i	0.0756453	−	0.0515741i
$784$	−19.4291	+	33.6522i	−0.693897	+	1.20186i
$785$	−19.3658	+	5.97355i	−0.691194	+	0.213205i
$786$	−0.460093	−	0.796905i	−0.0164110	−	0.0284247i
$787$	−31.2017	+	39.1257i	−1.11222	+	1.39468i	−0.202587	+	0.979264i	$0.564935\pi$
$787$	−31.2017	+	39.1257i	−1.11222	+	1.39468i	−0.909632	+	0.415415i	$0.863636\pi$
$788$	−19.8495	+	18.4176i	−0.707109	+	0.656102i
$789$	−1.05828	+	0.509639i	−0.0376757	+	0.0181436i
$790$	−1.42793	−	2.47325i	−0.0508036	−	0.0879945i
$791$	−18.1686	+	2.73847i	−0.646000	+	0.0973689i
$792$	5.65843	+	0.852871i	0.201064	+	0.0303055i
$793$	2.27597	+	30.3707i	0.0808220	+	1.07849i
$794$	3.53751	−	1.70358i	0.125542	−	0.0604576i
$795$	−8.27718	+	10.3793i	−0.293561	+	0.368114i
$796$	19.2808	+	5.94734i	0.683390	+	0.210798i
$797$	29.9837	+	4.51931i	1.06208	+	0.160082i	0.656764	−	0.754096i	$-0.271925\pi$
$797$	29.9837	+	4.51931i	1.06208	+	0.160082i	0.405312	+	0.914178i	$0.367163\pi$
$798$	−2.44346	−	6.22584i	−0.0864976	−	0.220392i
$799$	−6.31794	+	10.9430i	−0.223513	+	0.387135i
$800$	7.18476	−	31.4785i	0.254020	−	1.11293i
$801$	−0.291301	+	0.198606i	−0.0102926	+	0.00701738i
$802$	1.54620	−	6.77434i	0.0545982	−	0.239210i
$803$	4.58004	−	61.1164i	0.161626	−	2.15675i
$804$	−3.48515	−	8.88001i	−0.122912	−	0.313174i
$805$	−106.811	+	16.0992i	−3.76461	+	0.567423i
$806$	−3.48112	−	3.23001i	−0.122617	−	0.113772i
$807$	−22.2676	−	6.86864i	−0.783856	−	0.241788i
$808$	0.904640	+	12.0716i	0.0318251	+	0.424677i
$809$	35.0074	+	16.8587i	1.23079	+	0.592719i	0.932298	−	0.361692i	$-0.117801\pi$
$809$	35.0074	+	16.8587i	1.23079	+	0.592719i	0.298496	+	0.954411i	$0.403515\pi$
$810$	1.01138	−	0.311970i	0.0355363	−	0.0109615i
$811$	−13.7059	−	34.9221i	−0.481280	−	1.22628i	−0.941057	−	0.338247i	$-0.890166\pi$
$811$	−13.7059	−	34.9221i	−0.481280	−	1.22628i	0.459777	−	0.888034i	$-0.347929\pi$
$812$	13.0201	+	16.3267i	0.456916	+	0.572954i
$813$	28.5001	+	13.7249i	0.999542	+	0.481354i
$814$	0.878909	+	1.52231i	0.0308057	+	0.0533571i
$815$	7.64654	+	7.09495i	0.267846	+	0.248525i
$816$	2.36953	+	10.3816i	0.0829501	+	0.363428i
$817$	34.2448	−	5.16157i	1.19807	−	0.180580i
$818$	2.52416	−	0.778599i	0.0882551	−	0.0272231i
$819$	−5.51481	+	14.0515i	−0.192703	+	0.490999i
$820$	−4.33179	+	57.8037i	−0.151272	+	2.01859i
$821$	−20.6269	+	35.7269i	−0.719884	+	1.24688i	0.241161	+	0.970485i	$0.422472\pi$
$821$	−20.6269	+	35.7269i	−0.719884	+	1.24688i	−0.961045	+	0.276391i	$0.910862\pi$
$822$	0.364390	−	0.928451i	0.0127096	−	0.0323835i
$823$	0.313336	+	0.392911i	0.0109222	+	0.0136960i	0.787263	−	0.616618i	$-0.211498\pi$
$823$	0.313336	+	0.392911i	0.0109222	+	0.0136960i	−0.776340	+	0.630314i	$0.782926\pi$
$824$	−1.26279	−	0.190335i	−0.0439914	−	0.00663063i
$825$	−12.6863	−	55.5821i	−0.441679	−	1.93512i
$826$	−2.01456	−	8.82637i	−0.0700955	−	0.307109i
$827$	−35.1413	−	5.29670i	−1.22198	−	0.184184i	−0.493806	−	0.869572i	$-0.664395\pi$
$827$	−35.1413	−	5.29670i	−1.22198	−	0.184184i	−0.728178	+	0.685388i	$0.759633\pi$
$828$	7.79549	+	9.77524i	0.270912	+	0.339713i
$829$	18.5703	−	47.3163i	0.644973	−	1.64336i	−0.114967	−	0.993369i	$-0.536676\pi$
$829$	18.5703	−	47.3163i	0.644973	−	1.64336i	0.759939	−	0.649994i	$-0.225229\pi$
$830$	0.509269	−	0.882079i	0.0176770	−	0.0306174i
$831$	1.25318	−	16.7225i	0.0434723	−	0.580097i
$832$	8.24150	−	20.9990i	0.285723	−	0.728009i
$833$	30.9895	−	9.55899i	1.07372	−	0.331199i
$834$	2.70816	−	0.408190i	0.0937760	−	0.0141345i
$835$	−10.0410	−	43.9923i	−0.347482	−	1.52242i
$836$	45.1038	+	41.8502i	1.55995	+	1.44742i
$837$	2.47522	+	4.28721i	0.0855562	+	0.148188i
$838$	−6.51977	−	3.13975i	−0.225222	−	0.108461i
$839$	−23.2330	−	29.1333i	−0.802092	−	1.00579i	−0.999675	−	0.0255056i	$-0.991880\pi$
$839$	−23.2330	−	29.1333i	−0.802092	−	1.00579i	0.197582	−	0.980286i	$-0.436691\pi$
$840$	6.42192	+	16.3628i	0.221577	+	0.564570i
$841$	−21.4400	+	6.61337i	−0.739311	+	0.228047i
$842$	5.33222	+	2.56786i	0.183761	+	0.0884944i
$843$	−1.68724	−	22.5147i	−0.0581116	−	0.775446i
$844$	18.2110	+	5.61736i	0.626850	+	0.193358i
$845$	−0.737007	−	0.683842i	−0.0253538	−	0.0235249i
$846$	1.12622	−	0.169750i	0.0387202	−	0.00583613i
$847$	28.4190	+	72.4104i	0.976488	+	2.48805i
$848$	−0.899671	+	12.0053i	−0.0308948	+	0.412263i
$849$	−2.83104	+	12.4036i	−0.0971609	+	0.425690i
$850$	−6.95939	+	4.74483i	−0.238705	+	0.162746i
$851$	−1.74130	+	7.62911i	−0.0596908	+	0.261523i
$852$	−13.0987	+	22.6877i	−0.448756	+	0.777268i
$853$	−7.08897	−	18.0624i	−0.242722	−	0.618445i	0.756653	−	0.653817i	$-0.226833\pi$
$853$	−7.08897	−	18.0624i	−0.242722	−	0.618445i	−0.999374	+	0.0353726i	$0.988738\pi$
$854$	−9.58445	−	1.44462i	−0.327973	−	0.0494340i
$855$	22.1568	+	6.83447i	0.757747	+	0.233734i
$856$	−1.90778	+	2.39228i	−0.0652065	+	0.0817663i
$857$	−30.4554	+	14.6666i	−1.04034	+	0.501000i	−0.874435	−	0.485142i	$-0.838768\pi$
$857$	−30.4554	+	14.6666i	−1.04034	+	0.501000i	−0.165902	+	0.986142i	$0.553054\pi$
$858$	0.388675	+	5.18650i	0.0132691	+	0.177064i
$859$	−41.4669	−	6.25013i	−1.41483	−	0.213252i	−0.603279	−	0.797531i	$-0.706139\pi$
$859$	−41.4669	−	6.25013i	−1.41483	−	0.213252i	−0.811553	+	0.584279i	$0.801377\pi$
$860$	−44.1739	+	6.65815i	−1.50632	+	0.227041i
$861$	−16.1387	−	27.9531i	−0.550006	−	0.952639i
$862$	7.13099	−	3.43410i	0.242882	−	0.116966i
$863$	−32.7021	+	30.3431i	−1.11319	+	1.03289i	−0.113970	+	0.993484i	$0.536357\pi$
$863$	−32.7021	+	30.3431i	−1.11319	+	1.03289i	−0.999223	+	0.0394084i	$0.987453\pi$
$864$	1.91451	−	2.40072i	0.0651331	−	0.0816743i
$865$	−25.8383	−	44.7533i	−0.878530	−	1.52166i
$866$	−1.88232	+	0.580620i	−0.0639640	+	0.0197303i
$867$	−4.05646	+	7.02600i	−0.137765	+	0.238615i
$868$	−33.3409	+	22.7315i	−1.13166	+	0.771556i
$869$	−14.6298			−0.496281
$870$	2.71149			0.0919282
$871$	14.5960	−	9.95136i	0.494565	−	0.337189i
$872$	1.53325	−	20.4598i	0.0519225	−	0.692857i
$873$	−5.84278	−	7.32662i	−0.197748	−	0.247969i
$874$	−0.766635	−	10.2300i	−0.0259318	−	0.346036i
$875$	67.3331	−	62.4760i	2.27627	−	2.11207i
$876$	−18.0049	−	12.2755i	−0.608329	−	0.414752i
$877$	−13.7536	+	12.7615i	−0.464426	+	0.430925i	−0.877357	−	0.479838i	$-0.840696\pi$
$877$	−13.7536	+	12.7615i	−0.464426	+	0.430925i	0.412931	+	0.910762i	$0.364505\pi$
$878$	−10.2368	−	3.15764i	−0.345476	−	0.106565i
$879$	−1.86012	−	8.14974i	−0.0627404	−	0.274884i
$880$	−55.9208	−	51.8870i	−1.88509	−	1.74911i
$881$	1.33229	−	1.67064i	0.0448861	−	0.0562854i	−0.758882	−	0.651228i	$-0.774254\pi$
$881$	1.33229	−	1.67064i	0.0448861	−	0.0562854i	0.803768	+	0.594943i	$0.202825\pi$
$882$	−2.41519	−	1.64665i	−0.0813236	−	0.0554455i
$883$	5.97487	+	4.07360i	0.201070	+	0.137087i	0.659670	−	0.751556i	$-0.270696\pi$
$883$	5.97487	+	4.07360i	0.201070	+	0.137087i	−0.458599	+	0.888643i	$0.651649\pi$
$884$	−18.4849	+	8.90185i	−0.621714	+	0.299401i
$885$	28.2785	+	13.6182i	0.950570	+	0.457770i
$886$	−0.142710	+	0.363618i	−0.00479442	+	0.0122160i
$887$	−5.93127	+	25.9866i	−0.199153	+	0.872544i	0.772290	+	0.635270i	$0.219111\pi$
$887$	−5.93127	+	25.9866i	−0.199153	+	0.872544i	−0.971443	+	0.237274i	$0.923746\pi$
$888$	1.27342			0.0427332
$889$	−1.95875	+	47.6103i	−0.0656944	+	1.59680i
$890$	−0.373153			−0.0125081
$891$	1.20648	−	5.28595i	0.0404187	−	0.177086i
$892$	−11.6510	+	29.6863i	−0.390105	+	0.993972i
$893$	22.4803	+	10.8259i	0.752275	+	0.362276i
$894$	−0.599391	+	0.288652i	−0.0200466	+	0.00965396i
$895$	52.3429	+	35.6868i	1.74963	+	1.19288i
$896$	27.3869	+	18.6721i	0.914934	+	0.623791i
$897$	−14.4360	+	18.1022i	−0.482005	+	0.604415i
$898$	1.06441	+	0.987630i	0.0355199	+	0.0329576i
$899$	2.82210	+	12.3644i	0.0941223	+	0.412377i
$900$	−19.3703	−	5.97496i	−0.645678	−	0.199165i
$901$	7.36530	−	6.83400i	0.245374	−	0.227674i
$902$	−9.18890	−	6.26488i	−0.305957	−	0.208598i
$903$	18.2350	−	16.9196i	0.606824	−	0.563050i
$904$	0.342730	+	4.57341i	0.0113990	+	0.152109i
$905$	−51.0794	−	64.0515i	−1.69794	−	2.12914i
$906$	0.177758	−	2.37202i	0.00590562	−	0.0788050i
$907$	−23.2665	+	15.8628i	−0.772550	+	0.526716i	−0.884243	−	0.467027i	$-0.845325\pi$
$907$	−23.2665	+	15.8628i	−0.772550	+	0.526716i	0.111693	+	0.993743i	$0.464373\pi$
$908$	−18.0924			−0.600417
$909$	11.4698			0.380430
$910$	−13.2004	+	8.99991i	−0.437591	+	0.298344i
$911$	10.4379	−	18.0790i	0.345824	−	0.598984i	−0.639679	−	0.768642i	$-0.720933\pi$
$911$	10.4379	−	18.0790i	0.345824	−	0.598984i	0.985503	+	0.169658i	$0.0542662\pi$
$912$	20.0929	−	6.19783i	0.665341	−	0.205231i
$913$	−2.60883	−	4.51863i	−0.0863398	−	0.149545i
$914$	−3.64819	+	4.57469i	−0.120671	+	0.151317i
$915$	24.6329	−	22.8560i	0.814340	−	0.755597i
$916$	44.1716	−	21.2719i	1.45947	−	0.702843i
$917$	−7.23999	−	12.5400i	−0.239086	−	0.414108i
$918$	−0.792092	+	0.119389i	−0.0261429	+	0.00394041i
$919$	−25.8190	−	3.89158i	−0.851690	−	0.128372i	−0.291332	−	0.956622i	$-0.594098\pi$
$919$	−25.8190	−	3.89158i	−0.851690	−	0.128372i	−0.560358	+	0.828251i	$0.689336\pi$
$920$	2.01488	+	26.8867i	0.0664285	+	0.886427i
$921$	−10.3991	+	5.00792i	−0.342661	+	0.165017i
$922$	−4.06779	+	5.10084i	−0.133965	+	0.167987i
$923$	−46.3583	−	14.2996i	−1.52590	−	0.470679i
$924$	43.7019	+	6.58700i	1.43769	+	0.216696i
$925$	−4.63510	−	11.8101i	−0.152401	−	0.388312i
$926$	−1.14040	+	1.97524i	−0.0374760	+	0.0649103i
$927$	−0.269251	+	1.17966i	−0.00884335	+	0.0387452i
$928$	6.49968	−	4.43141i	0.213362	−	0.145468i
$929$	−8.76170	+	38.3875i	−0.287462	+	1.25945i	0.600533	+	0.799600i	$0.294955\pi$
$929$	−8.76170	+	38.3875i	−0.287462	+	1.25945i	−0.887995	+	0.459853i	$0.847902\pi$
$930$	−0.391553	+	5.22492i	−0.0128395	+	0.171332i
$931$	−23.3957	−	59.6113i	−0.766763	−	1.95368i
$932$	−34.9316	+	5.26509i	−1.14422	+	0.172464i
$933$	−6.72584	−	6.24066i	−0.220194	−	0.204310i
$934$	−10.3373	−	3.18862i	−0.338245	−	0.104335i
$935$	4.75776	+	63.4879i	0.155595	+	2.07628i
$936$	3.39468	+	1.63479i	0.110959	+	0.0534349i
$937$	6.57183	−	2.02714i	0.214692	−	0.0662238i	−0.185543	−	0.982636i	$-0.559404\pi$
$937$	6.57183	−	2.02714i	0.214692	−	0.0662238i	0.400236	+	0.916412i	$0.368928\pi$
$938$	2.05400	+	5.23350i	0.0670654	+	0.170880i
$939$	1.52762	+	1.91557i	0.0498519	+	0.0625123i
$940$	−28.9984	−	13.9649i	−0.945824	−	0.455485i
$941$	−21.3044	−	36.9004i	−0.694505	−	1.20292i	−0.970347	−	0.241715i	$-0.922290\pi$
$941$	−21.3044	−	36.9004i	−0.694505	−	1.20292i	0.275843	−	0.961203i	$-0.411043\pi$
$942$	−1.01345	−	0.940346i	−0.0330201	−	0.0306381i
$943$	−11.0168	−	48.2679i	−0.358757	−	1.57182i
$944$	28.1451	−	4.24219i	0.916045	−	0.138072i
$945$	15.9150	−	4.90913i	0.517715	−	0.159694i
$946$	3.13133	−	7.97850i	0.101808	−	0.259404i
$947$	4.13329	−	55.1549i	0.134314	−	1.79229i	−0.370264	−	0.928927i	$-0.620733\pi$
$947$	4.13329	−	55.1549i	0.134314	−	1.79229i	0.504578	−	0.863366i	$-0.331648\pi$
$948$	−2.60087	+	4.50484i	−0.0844723	+	0.146310i
$949$	14.7431	−	37.5647i	0.478580	−	1.21940i
$950$	10.3701	+	13.0037i	0.336450	+	0.421895i
$951$	1.37237	+	0.206852i	0.0445022	+	0.00670763i
$952$	−2.96033	−	12.9700i	−0.0959448	−	0.420362i
$953$	7.97683	+	34.9488i	0.258395	+	1.13210i	0.922967	+	0.384878i	$0.125757\pi$
$953$	7.97683	+	34.9488i	0.258395	+	1.13210i	−0.664573	+	0.747224i	$0.731386\pi$
$954$	−0.895515	−	0.134977i	−0.0289934	−	0.00437005i
$955$	−12.0741	−	15.1404i	−0.390709	−	0.489933i
$956$	16.0581	−	40.9152i	0.519354	−	1.32329i
$957$	6.94509	−	12.0292i	0.224503	−	0.388850i
$958$	−0.423797	+	5.65518i	−0.0136923	+	0.182710i
$959$	5.73401	−	14.6100i	0.185161	−	0.471782i
$960$	−23.7839	+	7.33636i	−0.767621	+	0.236780i
$961$	6.42056	−	0.967743i	0.207115	−	0.0312175i
$962$	0.257549	+	1.12840i	0.00830371	+	0.0363809i
$963$	2.12525	+	1.97194i	0.0684851	+	0.0635449i
$964$	6.19822	+	10.7356i	0.199631	+	0.345771i
$965$	−53.3562	−	25.6950i	−1.71760	−	0.827151i
$966$	−4.59433	−	5.76111i	−0.147820	−	0.185361i
$967$	12.3080	+	31.3602i	0.395798	+	1.00848i	0.980376	+	0.197138i	$0.0631648\pi$
$967$	12.3080	+	31.3602i	0.395798	+	1.00848i	−0.584578	+	0.811337i	$0.698740\pi$
$968$	18.5537	−	5.72307i	0.596339	−	0.183946i
$969$	−15.8109	−	7.61411i	−0.507918	−	0.244600i
$970$	−0.741203	−	9.89067i	−0.0237986	−	0.317570i
$971$	−9.53415	−	2.94090i	−0.305965	−	0.0943778i	0.137971	−	0.990436i	$-0.455942\pi$
$971$	−9.53415	−	2.94090i	−0.305965	−	0.0943778i	−0.443936	+	0.896058i	$0.646418\pi$
$972$	−1.41318	−	1.31124i	−0.0453276	−	0.0420579i
$973$	42.6154	−	6.42324i	1.36619	−	0.205920i
$974$	3.54475	+	9.03187i	0.113581	+	0.289400i
$975$	2.80526	−	37.4336i	0.0898403	−	1.19883i
$976$	6.78090	−	29.7091i	0.217051	−	0.950964i
$977$	4.77421	−	3.25500i	0.152741	−	0.104137i	−0.484538	−	0.874770i	$-0.661012\pi$
$977$	4.77421	−	3.25500i	0.152741	−	0.104137i	0.637279	+	0.770633i	$0.280060\pi$
$978$	−0.158343	+	0.693745i	−0.00506324	+	0.0221835i
$979$	−0.955777	+	1.65545i	−0.0305468	+	0.0529086i
$980$	30.1792	+	76.8954i	0.964040	+	2.45633i
$981$	−19.2228	−	2.89737i	−0.613737	−	0.0925060i
$982$	4.96115	+	1.53031i	0.158317	+	0.0488342i
$983$	−14.5439	+	18.2374i	−0.463877	+	0.581684i	−0.957660	−	0.287902i	$-0.907042\pi$
$983$	−14.5439	+	18.2374i	−0.463877	+	0.581684i	0.493783	+	0.869585i	$0.335614\pi$
$984$	−7.25882	+	3.49567i	−0.231403	+	0.111438i
$985$	4.13453	+	55.1714i	0.131737	+	1.75791i
$986$	−2.02924	−	0.305858i	−0.0646241	−	0.00974051i
$987$	17.7221	−	2.67117i	0.564099	−	0.0850243i
$988$	20.2565	+	35.0852i	0.644444	+	1.11621i
$989$	34.3770	−	16.5551i	1.09313	−	0.526422i
$990$	4.20665	−	3.90320i	0.133696	−	0.124052i
$991$	−1.10391	+	1.38426i	−0.0350668	+	0.0439724i	−0.799056	−	0.601257i	$-0.794667\pi$
$991$	−1.10391	+	1.38426i	−0.0350668	+	0.0439724i	0.763989	+	0.645229i	$0.223238\pi$
$992$	7.60053	+	13.1645i	0.241317	+	0.417973i
$993$	−18.7850	+	5.79441i	−0.596125	+	0.183880i
$994$	7.71985	−	13.3712i	0.244859	−	0.424108i
$995$	34.0630	−	23.2237i	1.07987	−	0.736242i
$996$	−1.85519			−0.0587838
$997$	27.6518			0.875741			0.437871	−	0.899038i	$-0.355733\pi$
$997$	27.6518			0.875741			0.437871	+	0.899038i	$0.355733\pi$
$998$	9.50991	−	6.48375i	0.301031	−	0.205239i
$999$	0.0901663	−	1.20319i	0.00285274	−	0.0380671i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	381.2.q.a.61.5	yes	120
127.25	even	21	inner	381.2.q.a.25.5	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
381.2.q.a.25.5	✓	120	127.25	even	21	inner
381.2.q.a.61.5	yes	120	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 381 = 3 \cdot 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	381.q (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0597923 - 0.261967i) q^{2} +(-0.365341 + 0.930874i) q^{3} +(1.73689 + 0.836440i) q^{4} +(3.54884 - 1.70903i) q^{5} +(0.222014 + 0.151366i) q^{6} +(3.49359 + 2.38189i) q^{7} +(0.658041 - 0.825157i) q^{8} +(-0.733052 - 0.680173i) q^{9} +O(q^{10})\)	\(q+(0.0597923 - 0.261967i) q^{2} +(-0.365341 + 0.930874i) q^{3} +(1.73689 + 0.836440i) q^{4} +(3.54884 - 1.70903i) q^{5} +(0.222014 + 0.151366i) q^{6} +(3.49359 + 2.38189i) q^{7} +(0.658041 - 0.825157i) q^{8} +(-0.733052 - 0.680173i) q^{9} +(-0.235517 - 1.03187i) q^{10} +(-5.18101 - 1.59813i) q^{11} +(-1.41318 + 1.31124i) q^{12} +(-2.94966 - 2.01104i) q^{13} +(0.832866 - 0.772787i) q^{14} +(0.294356 + 3.92790i) q^{15} +(2.22711 + 2.79270i) q^{16} +(0.222779 - 2.97278i) q^{17} +(-0.222014 + 0.151366i) q^{18} -5.88663 q^{19} +7.59344 q^{20} +(-3.49359 + 2.38189i) q^{21} +(-0.728442 + 1.26170i) q^{22} +(-6.19750 + 1.91168i) q^{23} +(0.527708 + 0.914017i) q^{24} +(6.55604 - 8.22101i) q^{25} +(-0.703193 + 0.652468i) q^{26} +(0.900969 - 0.433884i) q^{27} +(4.07566 + 7.05925i) q^{28} +(2.53326 - 0.381827i) q^{29} +(1.04658 + 0.157747i) q^{30} +(0.369947 + 4.93660i) q^{31} +(2.76655 - 1.33230i) q^{32} +(3.38049 - 4.23900i) q^{33} +(-0.765451 - 0.236110i) q^{34} +(16.4689 + 2.48229i) q^{35} +(-0.704304 - 1.79454i) q^{36} +(0.603280 - 1.04491i) q^{37} +(-0.351975 + 1.54210i) q^{38} +(2.94966 - 2.01104i) q^{39} +(0.925063 - 4.05296i) q^{40} +(-0.570464 + 7.61232i) q^{41} +(0.415087 + 1.05762i) q^{42} +(-5.81738 + 0.876830i) q^{43} +(-7.66208 - 7.10937i) q^{44} +(-3.76392 - 1.16102i) q^{45} +(0.130233 + 1.73784i) q^{46} +(-3.81888 - 1.83908i) q^{47} +(-3.41331 + 1.05287i) q^{48} +(3.97438 + 10.1266i) q^{49} +(-1.76163 - 2.20902i) q^{50} +(2.68590 + 1.29346i) q^{51} +(-3.44110 - 5.96016i) q^{52} +(2.47065 + 2.29243i) q^{53} +(-0.0597923 - 0.261967i) q^{54} +(-21.1178 + 3.18300i) q^{55} +(4.26436 - 1.31538i) q^{56} +(2.15063 - 5.47970i) q^{57} +(0.0514431 - 0.686460i) q^{58} +(3.98418 - 6.90080i) q^{59} +(-2.77419 + 7.06853i) q^{60} +(-5.31905 - 6.66988i) q^{61} +(1.31535 + 0.198257i) q^{62} +(-0.940886 - 4.12229i) q^{63} +(1.40609 + 6.16048i) q^{64} +(-13.9048 - 2.09581i) q^{65} +(-0.908352 - 1.13904i) q^{66} +(-1.80784 + 4.60630i) q^{67} +(2.87350 - 4.97705i) q^{68} +(0.484672 - 6.46750i) q^{69} +(1.63499 - 4.16589i) q^{70} +(12.9856 - 4.00553i) q^{71} +(-1.04363 + 0.157302i) q^{72} +(2.51533 + 11.0204i) q^{73} +(-0.237661 - 0.220517i) q^{74} +(5.25753 + 9.10632i) q^{75} +(-10.2244 - 4.92381i) q^{76} +(-14.2937 - 17.9238i) q^{77} +(-0.350460 - 0.892958i) q^{78} +(2.57840 - 0.795332i) q^{79} +(12.6765 + 6.10467i) q^{80} +(0.0747301 + 0.997204i) q^{81} +(1.96007 + 0.604601i) q^{82} +(0.705441 + 0.654553i) q^{83} +(-8.06027 + 1.21489i) q^{84} +(-4.28997 - 10.9307i) q^{85} +(-0.118134 + 1.57639i) q^{86} +(-0.570070 + 2.49764i) q^{87} +(-4.72802 + 3.22351i) q^{88} +(0.0784525 - 0.343723i) q^{89} +(-0.529202 + 0.916604i) q^{90} +(-5.51481 - 14.0515i) q^{91} +(-12.3634 - 1.86348i) q^{92} +(-4.73051 - 1.45917i) q^{93} +(-0.710117 + 0.890458i) q^{94} +(-20.8907 + 10.0604i) q^{95} +(0.229469 + 3.06206i) q^{96} +(9.26643 + 1.39669i) q^{97} +(2.89046 - 0.435667i) q^{98} +(2.71094 + 4.69549i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 3 q^{2} - 10 q^{3} - 15 q^{4} + 2 q^{5} + 2 q^{6} + 11 q^{7} + 20 q^{8} + 10 q^{9}+O(q^{10}) \) 120 * q - 3 * q^2 - 10 * q^3 - 15 * q^4 + 2 * q^5 + 2 * q^6 + 11 * q^7 + 20 * q^8 + 10 * q^9	\( 120 q - 3 q^{2} - 10 q^{3} - 15 q^{4} + 2 q^{5} + 2 q^{6} + 11 q^{7} + 20 q^{8} + 10 q^{9} + 4 q^{10} - 36 q^{11} - 18 q^{12} + q^{13} + 4 q^{14} + q^{15} - 15 q^{16} - 5 q^{17} - 2 q^{18} - 54 q^{19} + 18 q^{20} - 11 q^{21} + 19 q^{22} - 22 q^{23} - 18 q^{24} - 26 q^{25} + 54 q^{26} + 20 q^{27} - 19 q^{28} + 31 q^{29} - 19 q^{30} - 3 q^{31} - q^{32} + 33 q^{33} + 23 q^{34} + 70 q^{35} + 4 q^{36} + 36 q^{37} - 55 q^{38} - q^{39} - 80 q^{40} + 8 q^{41} + 10 q^{42} - 41 q^{43} - 118 q^{44} - q^{45} + 46 q^{46} + 15 q^{47} + 52 q^{48} - 11 q^{49} - 26 q^{50} - 10 q^{51} + 72 q^{52} + 30 q^{53} + 3 q^{54} - 87 q^{55} - 103 q^{56} + 8 q^{57} + 36 q^{58} - 16 q^{59} - 96 q^{60} + 43 q^{61} + 6 q^{63} - 28 q^{64} - 33 q^{65} + 3 q^{66} - 10 q^{67} + 67 q^{68} - 6 q^{69} - 72 q^{70} + 55 q^{71} - 10 q^{72} + 47 q^{73} + 101 q^{74} + 29 q^{75} - 59 q^{76} - 15 q^{77} + 2 q^{78} - 148 q^{79} + 27 q^{80} + 10 q^{81} + 106 q^{82} - 4 q^{83} + 12 q^{84} - 47 q^{85} - 157 q^{86} - 8 q^{87} + 85 q^{88} + 16 q^{89} + 5 q^{90} - 111 q^{91} - 157 q^{92} - 25 q^{93} - 18 q^{94} - 24 q^{95} + 10 q^{96} + 52 q^{97} - 4 q^{98} + 6 q^{99}+O(q^{100}) \) 120 * q - 3 * q^2 - 10 * q^3 - 15 * q^4 + 2 * q^5 + 2 * q^6 + 11 * q^7 + 20 * q^8 + 10 * q^9 + 4 * q^10 - 36 * q^11 - 18 * q^12 + q^13 + 4 * q^14 + q^15 - 15 * q^16 - 5 * q^17 - 2 * q^18 - 54 * q^19 + 18 * q^20 - 11 * q^21 + 19 * q^22 - 22 * q^23 - 18 * q^24 - 26 * q^25 + 54 * q^26 + 20 * q^27 - 19 * q^28 + 31 * q^29 - 19 * q^30 - 3 * q^31 - q^32 + 33 * q^33 + 23 * q^34 + 70 * q^35 + 4 * q^36 + 36 * q^37 - 55 * q^38 - q^39 - 80 * q^40 + 8 * q^41 + 10 * q^42 - 41 * q^43 - 118 * q^44 - q^45 + 46 * q^46 + 15 * q^47 + 52 * q^48 - 11 * q^49 - 26 * q^50 - 10 * q^51 + 72 * q^52 + 30 * q^53 + 3 * q^54 - 87 * q^55 - 103 * q^56 + 8 * q^57 + 36 * q^58 - 16 * q^59 - 96 * q^60 + 43 * q^61 + 6 * q^63 - 28 * q^64 - 33 * q^65 + 3 * q^66 - 10 * q^67 + 67 * q^68 - 6 * q^69 - 72 * q^70 + 55 * q^71 - 10 * q^72 + 47 * q^73 + 101 * q^74 + 29 * q^75 - 59 * q^76 - 15 * q^77 + 2 * q^78 - 148 * q^79 + 27 * q^80 + 10 * q^81 + 106 * q^82 - 4 * q^83 + 12 * q^84 - 47 * q^85 - 157 * q^86 - 8 * q^87 + 85 * q^88 + 16 * q^89 + 5 * q^90 - 111 * q^91 - 157 * q^92 - 25 * q^93 - 18 * q^94 - 24 * q^95 + 10 * q^96 + 52 * q^97 - 4 * q^98 + 6 * q^99

Introduction

L-functions

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