LMFDB - Embedded newform 115.2.g.c.6.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,2,Mod(6,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("115.6");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	115.g (of order $11$, degree $10$, 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:	$0.918279623245$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$5$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			6.1
Character	$\chi$	$=$	115.6
Dual form			115.2.g.c.96.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.02998 + 2.25535i) q^{2} +(2.16804 + 0.636595i) q^{3} +(-2.71600 - 3.13443i) q^{4} +(0.841254 - 0.540641i) q^{5} +(-3.66879 + 4.23400i) q^{6} +(-0.617798 + 4.29688i) q^{7} +(5.10871 - 1.50005i) q^{8} +(1.77140 + 1.13841i) q^{9} +O(q^{10})$	\(q+(-1.02998 + 2.25535i) q^{2} +(2.16804 + 0.636595i) q^{3} +(-2.71600 - 3.13443i) q^{4} +(0.841254 - 0.540641i) q^{5} +(-3.66879 + 4.23400i) q^{6} +(-0.617798 + 4.29688i) q^{7} +(5.10871 - 1.50005i) q^{8} +(1.77140 + 1.13841i) q^{9} +(0.352856 + 2.45417i) q^{10} +(-1.51892 - 3.32596i) q^{11} +(-3.89304 - 8.52457i) q^{12} +(-0.268762 - 1.86928i) q^{13} +(-9.05463 - 5.81905i) q^{14} +(2.16804 - 0.636595i) q^{15} +(-0.698255 + 4.85647i) q^{16} +(3.37557 - 3.89562i) q^{17} +(-4.39201 + 2.82257i) q^{18} +(3.25094 + 3.75178i) q^{19} +(-3.97944 - 1.16847i) q^{20} +(-4.07478 + 8.92253i) q^{21} +9.06565 q^{22} +(-4.69919 + 0.957943i) q^{23} +12.0308 q^{24} +(0.415415 - 0.909632i) q^{25} +(4.49269 + 1.31917i) q^{26} +(-1.32335 - 1.52723i) q^{27} +(15.1462 - 9.73387i) q^{28} +(3.85727 - 4.45153i) q^{29} +(-0.797303 + 5.54537i) q^{30} +(-1.82753 + 0.536611i) q^{31} +(-1.27552 - 0.819726i) q^{32} +(-1.17578 - 8.17776i) q^{33} +(5.30919 + 11.6255i) q^{34} +(1.80334 + 3.94877i) q^{35} +(-1.24285 - 8.64423i) q^{36} +(4.20088 + 2.69974i) q^{37} +(-11.8100 + 3.46772i) q^{38} +(0.607287 - 4.22377i) q^{39} +(3.48673 - 4.02390i) q^{40} +(-2.74736 + 1.76562i) q^{41} +(-15.9264 - 18.3801i) q^{42} +(0.333417 + 0.0979000i) q^{43} +(-6.29962 + 13.7942i) q^{44} +2.10566 q^{45} +(2.67958 - 11.5850i) q^{46} -1.89188 q^{47} +(-4.60545 + 10.0845i) q^{48} +(-11.3650 - 3.33708i) q^{49} +(1.62366 + 1.87381i) q^{50} +(9.79832 - 6.29700i) q^{51} +(-5.12917 + 5.91938i) q^{52} +(-0.408046 + 2.83802i) q^{53} +(4.80747 - 1.41160i) q^{54} +(-3.07594 - 1.97679i) q^{55} +(3.28939 + 22.8782i) q^{56} +(4.65981 + 10.2036i) q^{57} +(6.06681 + 13.2845i) q^{58} +(-2.01869 - 14.0403i) q^{59} +(-7.88376 - 5.06659i) q^{60} +(-2.79510 + 0.820714i) q^{61} +(0.672078 - 4.67441i) q^{62} +(-5.98596 + 6.90817i) q^{63} +(-5.09255 + 3.27278i) q^{64} +(-1.23671 - 1.42723i) q^{65} +(19.6547 + 5.77115i) q^{66} +(-2.01422 + 4.41052i) q^{67} -21.3786 q^{68} +(-10.7979 - 0.914617i) q^{69} -10.7633 q^{70} +(-3.32266 + 7.27561i) q^{71} +(10.7572 + 3.15861i) q^{72} +(-5.80660 - 6.70118i) q^{73} +(-10.4157 + 6.69375i) q^{74} +(1.47970 - 1.70767i) q^{75} +(2.93016 - 20.3797i) q^{76} +(15.2296 - 4.47182i) q^{77} +(8.90057 + 5.72005i) q^{78} +(0.523690 + 3.64234i) q^{79} +(2.03820 + 4.46303i) q^{80} +(-4.52103 - 9.89968i) q^{81} +(-1.15235 - 8.01480i) q^{82} +(12.4356 + 7.99184i) q^{83} +(39.0342 - 11.4615i) q^{84} +(0.733582 - 5.10218i) q^{85} +(-0.564211 + 0.651135i) q^{86} +(11.1965 - 7.19558i) q^{87} +(-12.7488 - 14.7129i) q^{88} +(-4.64976 - 1.36529i) q^{89} +(-2.16879 + 4.74900i) q^{90} +8.19811 q^{91} +(15.7656 + 12.1275i) q^{92} -4.30376 q^{93} +(1.94860 - 4.26684i) q^{94} +(4.76323 + 1.39861i) q^{95} +(-2.24355 - 2.58919i) q^{96} +(-11.3339 + 7.28385i) q^{97} +(19.2320 - 22.1950i) q^{98} +(1.09570 - 7.62074i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - 5 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 11 q^{6} - 5 q^{7} - 2 q^{8} + 3 q^{9}+O(q^{10}) $ 50 * q - 5 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 11 * q^6 - 5 * q^7 - 2 * q^8 + 3 * q^9	\( 50 q - 5 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 11 q^{6} - 5 q^{7} - 2 q^{8} + 3 q^{9} - 5 q^{10} - 16 q^{11} - 9 q^{12} - 14 q^{13} - 12 q^{14} - 2 q^{15} + 27 q^{16} + 38 q^{17} - 42 q^{18} - 5 q^{19} - 11 q^{20} - 9 q^{21} + 6 q^{22} - 8 q^{23} + 102 q^{24} - 5 q^{25} - 19 q^{26} + 7 q^{27} - 34 q^{28} - 38 q^{29} - 11 q^{30} + 2 q^{31} + 49 q^{32} - 2 q^{33} - 31 q^{34} + 6 q^{35} - 59 q^{36} - 35 q^{37} + 30 q^{38} + 32 q^{39} + 42 q^{40} - 11 q^{41} - 102 q^{42} + 6 q^{43} - 55 q^{44} + 58 q^{45} + 153 q^{46} - 10 q^{47} + 84 q^{48} + 6 q^{50} - 20 q^{51} - 97 q^{52} - 29 q^{53} + 19 q^{54} + 17 q^{55} + 77 q^{56} - 49 q^{57} - 12 q^{58} - 50 q^{59} + 2 q^{60} + 4 q^{61} + 126 q^{62} + 74 q^{63} - 44 q^{64} - 14 q^{65} - 144 q^{66} - 43 q^{67} + 54 q^{68} - 50 q^{69} - 12 q^{70} - 25 q^{71} - 14 q^{72} - 20 q^{73} - 47 q^{74} - 2 q^{75} - 26 q^{76} + 150 q^{77} + 174 q^{78} + 72 q^{79} - 28 q^{80} - 71 q^{81} - 11 q^{82} + 36 q^{83} + 100 q^{84} - 6 q^{85} - 20 q^{86} + 85 q^{87} - 45 q^{88} - 24 q^{89} - 42 q^{90} + 38 q^{91} + 74 q^{92} + 100 q^{93} + 150 q^{94} - 5 q^{95} - 169 q^{96} - 14 q^{97} - 44 q^{98} + 36 q^{99}+O(q^{100}) \) 50 * q - 5 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 11 * q^6 - 5 * q^7 - 2 * q^8 + 3 * q^9 - 5 * q^10 - 16 * q^11 - 9 * q^12 - 14 * q^13 - 12 * q^14 - 2 * q^15 + 27 * q^16 + 38 * q^17 - 42 * q^18 - 5 * q^19 - 11 * q^20 - 9 * q^21 + 6 * q^22 - 8 * q^23 + 102 * q^24 - 5 * q^25 - 19 * q^26 + 7 * q^27 - 34 * q^28 - 38 * q^29 - 11 * q^30 + 2 * q^31 + 49 * q^32 - 2 * q^33 - 31 * q^34 + 6 * q^35 - 59 * q^36 - 35 * q^37 + 30 * q^38 + 32 * q^39 + 42 * q^40 - 11 * q^41 - 102 * q^42 + 6 * q^43 - 55 * q^44 + 58 * q^45 + 153 * q^46 - 10 * q^47 + 84 * q^48 + 6 * q^50 - 20 * q^51 - 97 * q^52 - 29 * q^53 + 19 * q^54 + 17 * q^55 + 77 * q^56 - 49 * q^57 - 12 * q^58 - 50 * q^59 + 2 * q^60 + 4 * q^61 + 126 * q^62 + 74 * q^63 - 44 * q^64 - 14 * q^65 - 144 * q^66 - 43 * q^67 + 54 * q^68 - 50 * q^69 - 12 * q^70 - 25 * q^71 - 14 * q^72 - 20 * q^73 - 47 * q^74 - 2 * q^75 - 26 * q^76 + 150 * q^77 + 174 * q^78 + 72 * q^79 - 28 * q^80 - 71 * q^81 - 11 * q^82 + 36 * q^83 + 100 * q^84 - 6 * q^85 - 20 * q^86 + 85 * q^87 - 45 * q^88 - 24 * q^89 - 42 * q^90 + 38 * q^91 + 74 * q^92 + 100 * q^93 + 150 * q^94 - 5 * q^95 - 169 * q^96 - 14 * q^97 - 44 * q^98 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{9}{11}\right)$

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 $

$2$	−1.02998	+	2.25535i	−0.728307	+	1.59477i	0.0735764	+	0.997290i	$0.476559\pi$
$2$	−1.02998	+	2.25535i	−0.728307	+	1.59477i	−0.801883	+	0.597480i	$0.796169\pi$
$3$	2.16804	+	0.636595i	1.25172	+	0.367538i	0.839407	−	0.543504i	$-0.182903\pi$
$3$	2.16804	+	0.636595i	1.25172	+	0.367538i	0.412313	+	0.911042i	$0.364721\pi$
$4$	−2.71600	−	3.13443i	−1.35800	−	1.56722i
$5$	0.841254	−	0.540641i	0.376220	−	0.241782i
$5$	0.841254	−	0.540641i	0.376220	−	0.241782i
$6$	−3.66879	+	4.23400i	−1.49778	+	1.72853i
$7$	−0.617798	+	4.29688i	−0.233506	+	1.62407i	0.449240	+	0.893411i	$0.351695\pi$
$7$	−0.617798	+	4.29688i	−0.233506	+	1.62407i	−0.682746	+	0.730656i	$0.739214\pi$
$8$	5.10871	−	1.50005i	1.80620	−	0.530349i
$9$	1.77140	+	1.13841i	0.590465	+	0.379469i
$10$	0.352856	+	2.45417i	0.111583	+	0.776076i
$11$	−1.51892	−	3.32596i	−0.457970	−	1.00282i	−0.987946	−	0.154802i	$-0.950526\pi$
$11$	−1.51892	−	3.32596i	−0.457970	−	1.00282i	0.529975	−	0.848013i	$-0.322201\pi$
$12$	−3.89304	−	8.52457i	−1.12382	−	2.46083i
$13$	−0.268762	−	1.86928i	−0.0745411	−	0.518445i	−0.992545	−	0.121875i	$-0.961109\pi$
$13$	−0.268762	−	1.86928i	−0.0745411	−	0.518445i	0.918004	−	0.396570i	$-0.129800\pi$
$14$	−9.05463	−	5.81905i	−2.41995	−	1.55521i
$15$	2.16804	−	0.636595i	0.559786	−	0.164368i
$16$	−0.698255	+	4.85647i	−0.174564	+	1.21412i
$17$	3.37557	−	3.89562i	0.818697	−	0.944827i	−0.180552	−	0.983565i	$-0.557789\pi$
$17$	3.37557	−	3.89562i	0.818697	−	0.944827i	0.999249	+	0.0387386i	$0.0123340\pi$
$18$	−4.39201	+	2.82257i	−1.03521	+	0.665287i
$19$	3.25094	+	3.75178i	0.745817	+	0.860718i	0.994156	−	0.107955i	$-0.0344302\pi$
$19$	3.25094	+	3.75178i	0.745817	+	0.860718i	−0.248339	+	0.968673i	$0.579885\pi$
$20$	−3.97944	−	1.16847i	−0.889831	−	0.261278i
$21$	−4.07478	+	8.92253i	−0.889191	+	1.94706i
$22$	9.06565			1.93280
$23$	−4.69919	+	0.957943i	−0.979848	+	0.199745i
$23$	−4.69919	+	0.957943i	−0.979848	+	0.199745i
$24$	12.0308			2.45578
$25$	0.415415	−	0.909632i	0.0830830	−	0.181926i
$26$	4.49269	+	1.31917i	0.881089	+	0.258711i
$27$	−1.32335	−	1.52723i	−0.254680	−	0.293916i
$28$	15.1462	−	9.73387i	2.86236	−	1.83953i
$29$	3.85727	−	4.45153i	0.716277	−	0.826628i	−0.274577	−	0.961565i	$-0.588538\pi$
$29$	3.85727	−	4.45153i	0.716277	−	0.826628i	0.990854	+	0.134938i	$0.0430834\pi$
$30$	−0.797303	+	5.54537i	−0.145567	+	1.01244i
$31$	−1.82753	+	0.536611i	−0.328234	+	0.0963781i	−0.441698	−	0.897164i	$-0.645624\pi$
$31$	−1.82753	+	0.536611i	−0.328234	+	0.0963781i	0.113464	+	0.993542i	$0.463805\pi$
$32$	−1.27552	−	0.819726i	−0.225482	−	0.144908i
$33$	−1.17578	−	8.17776i	−0.204678	−	1.42357i
$34$	5.30919	+	11.6255i	0.910519	+	1.99376i
$35$	1.80334	+	3.94877i	0.304821	+	0.667464i
$36$	−1.24285	−	8.64423i	−0.207142	−	1.44071i
$37$	4.20088	+	2.69974i	0.690620	+	0.443835i	0.838306	−	0.545200i	$-0.183546\pi$
$37$	4.20088	+	2.69974i	0.690620	+	0.443835i	−0.147686	+	0.989034i	$0.547182\pi$
$38$	−11.8100	+	3.46772i	−1.91583	+	0.562539i
$39$	0.607287	−	4.22377i	0.0972437	−	0.676345i
$40$	3.48673	−	4.02390i	0.551301	−	0.636235i
$41$	−2.74736	+	1.76562i	−0.429066	+	0.275744i	−0.737298	−	0.675567i	$-0.763899\pi$
$41$	−2.74736	+	1.76562i	−0.429066	+	0.275744i	0.308233	+	0.951311i	$0.400262\pi$
$42$	−15.9264	−	18.3801i	−2.45750	−	2.83611i
$43$	0.333417	+	0.0979000i	0.0508456	+	0.0149296i	0.307056	−	0.951691i	$-0.400656\pi$
$43$	0.333417	+	0.0979000i	0.0508456	+	0.0149296i	−0.256211	+	0.966621i	$0.582474\pi$
$44$	−6.29962	+	13.7942i	−0.949704	+	2.07956i
$45$	2.10566			0.313894
$46$	2.67958	−	11.5850i	0.395083	−	1.70811i
$47$	−1.89188			−0.275959			−0.137980	−	0.990435i	$-0.544061\pi$
$47$	−1.89188			−0.275959			−0.137980	+	0.990435i	$0.544061\pi$
$48$	−4.60545	+	10.0845i	−0.664740	+	1.45558i
$49$	−11.3650	−	3.33708i	−1.62358	−	0.476725i
$50$	1.62366	+	1.87381i	0.229621	+	0.264997i
$51$	9.79832	−	6.29700i	1.37204	−	0.881756i
$52$	−5.12917	+	5.91938i	−0.711288	+	0.820870i
$53$	−0.408046	+	2.83802i	−0.0560494	+	0.389832i	0.942415	+	0.334444i	$0.108549\pi$
$53$	−0.408046	+	2.83802i	−0.0560494	+	0.389832i	−0.998465	+	0.0553879i	$0.982360\pi$
$54$	4.80747	−	1.41160i	0.654214	−	0.192094i
$55$	−3.07594	−	1.97679i	−0.414760	−	0.266550i
$56$	3.28939	+	22.8782i	0.439564	+	3.05723i
$57$	4.65981	+	10.2036i	0.617207	+	1.35149i
$58$	6.06681	+	13.2845i	0.796611	+	1.74434i
$59$	−2.01869	−	14.0403i	−0.262811	−	1.82789i	−0.511472	−	0.859300i	$-0.670900\pi$
$59$	−2.01869	−	14.0403i	−0.262811	−	1.82789i	0.248661	−	0.968590i	$-0.420009\pi$
$60$	−7.88376	−	5.06659i	−1.01779	−	0.654094i
$61$	−2.79510	+	0.820714i	−0.357875	+	0.105082i	−0.455728	−	0.890119i	$-0.650621\pi$
$61$	−2.79510	+	0.820714i	−0.357875	+	0.105082i	0.0978523	+	0.995201i	$0.468803\pi$
$62$	0.672078	−	4.67441i	0.0853540	−	0.593650i
$63$	−5.98596	+	6.90817i	−0.754160	+	0.870348i
$64$	−5.09255	+	3.27278i	−0.636569	+	0.409098i
$65$	−1.23671	−	1.42723i	−0.153395	−	0.177027i
$66$	19.6547	+	5.77115i	2.41933	+	0.710379i
$67$	−2.01422	+	4.41052i	−0.246076	+	0.538831i	−0.991856	−	0.127361i	$-0.959349\pi$
$67$	−2.01422	+	4.41052i	−0.246076	+	0.538831i	0.745781	+	0.666192i	$0.232077\pi$
$68$	−21.3786			−2.59254
$69$	−10.7979	−	0.914617i	−1.29991	−	0.110107i
$70$	−10.7633			−1.28645
$71$	−3.32266	+	7.27561i	−0.394327	+	0.863456i	0.603487	+	0.797373i	$0.293777\pi$
$71$	−3.32266	+	7.27561i	−0.394327	+	0.863456i	−0.997814	+	0.0660829i	$0.978950\pi$
$72$	10.7572	+	3.15861i	1.26775	+	0.372245i
$73$	−5.80660	−	6.70118i	−0.679612	−	0.784314i	0.306236	−	0.951955i	$-0.400930\pi$
$73$	−5.80660	−	6.70118i	−0.679612	−	0.784314i	−0.985848	+	0.167642i	$0.946385\pi$
$74$	−10.4157	+	6.69375i	−1.21080	+	0.778133i
$75$	1.47970	−	1.70767i	0.170862	−	0.197185i
$76$	2.93016	−	20.3797i	0.336112	−	2.33771i
$77$	15.2296	−	4.47182i	1.73558	−	0.509612i
$78$	8.90057	+	5.72005i	1.00779	+	0.647668i
$79$	0.523690	+	3.64234i	0.0589197	+	0.409796i	0.997842	+	0.0656656i	$0.0209171\pi$
$79$	0.523690	+	3.64234i	0.0589197	+	0.409796i	−0.938922	+	0.344130i	$0.888174\pi$
$80$	2.03820	+	4.46303i	0.227877	+	0.498982i
$81$	−4.52103	−	9.89968i	−0.502337	−	1.09996i
$82$	−1.15235	−	8.01480i	−0.127256	−	0.885087i
$83$	12.4356	+	7.99184i	1.36498	+	0.877219i	0.998582	−	0.0532396i	$-0.0169547\pi$
$83$	12.4356	+	7.99184i	1.36498	+	0.877219i	0.366397	+	0.930458i	$0.380591\pi$
$84$	39.0342	−	11.4615i	4.25898	−	1.25055i
$85$	0.733582	−	5.10218i	0.0795682	−	0.553409i
$86$	−0.564211	+	0.651135i	−0.0608405	+	0.0702137i
$87$	11.1965	−	7.19558i	1.20040	−	0.771447i
$88$	−12.7488	−	14.7129i	−1.35903	−	1.56840i
$89$	−4.64976	−	1.36529i	−0.492873	−	0.144721i	0.0258450	−	0.999666i	$-0.491772\pi$
$89$	−4.64976	−	1.36529i	−0.492873	−	0.144721i	−0.518718	+	0.854945i	$0.673591\pi$
$90$	−2.16879	+	4.74900i	−0.228611	+	0.500588i
$91$	8.19811			0.859395
$92$	15.7656	+	12.1275i	1.64368	+	1.26438i
$93$	−4.30376			−0.446279
$94$	1.94860	−	4.26684i	0.200983	−	0.440091i
$95$	4.76323	+	1.39861i	0.488697	+	0.143494i
$96$	−2.24355	−	2.58919i	−0.228981	−	0.264258i
$97$	−11.3339	+	7.28385i	−1.15078	+	0.739563i	−0.969795	−	0.243922i	$-0.921566\pi$
$97$	−11.3339	+	7.28385i	−1.15078	+	0.739563i	−0.180988	+	0.983485i	$0.557929\pi$
$98$	19.2320	−	22.1950i	1.94273	−	2.24203i
$99$	1.09570	−	7.62074i	0.110122	−	0.765913i
$100$	−3.97944	+	1.16847i	−0.397944	+	0.116847i
$101$	−8.58522	−	5.51738i	−0.854261	−	0.549000i	0.0386399	−	0.999253i	$-0.487697\pi$
$101$	−8.58522	−	5.51738i	−0.854261	−	0.549000i	−0.892901	+	0.450253i	$0.851334\pi$
$102$	4.10982	+	28.5844i	0.406932	+	2.83028i
$103$	0.743468	+	1.62797i	0.0732560	+	0.160408i	0.942717	−	0.333593i	$-0.108261\pi$
$103$	0.743468	+	1.62797i	0.0732560	+	0.160408i	−0.869461	+	0.494001i	$0.835534\pi$
$104$	−4.17705	−	9.14645i	−0.409593	−	0.896884i
$105$	1.39596	+	9.70910i	0.136232	+	0.947512i
$106$	−5.98044	−	3.84340i	−0.580872	−	0.373304i
$107$	−16.2650	+	4.77585i	−1.57240	+	0.461699i	−0.947699	−	0.319165i	$-0.896598\pi$
$107$	−16.2650	+	4.77585i	−1.57240	+	0.461699i	−0.624702	+	0.780863i	$0.714779\pi$
$108$	−1.19277	+	8.29593i	−0.114775	+	0.798276i
$109$	−1.20295	+	1.38827i	−0.115221	+	0.132972i	−0.810430	−	0.585835i	$-0.800766\pi$
$109$	−1.20295	+	1.38827i	−0.115221	+	0.132972i	0.695209	+	0.718808i	$0.255312\pi$
$110$	7.62651	−	4.90126i	0.727159	−	0.467317i
$111$	7.38905	+	8.52741i	0.701337	+	0.809386i
$112$	−20.4363	−	6.00064i	−1.93105	−	0.567007i
$113$	0.743006	−	1.62696i	0.0698961	−	0.153051i	−0.871459	−	0.490468i	$-0.836826\pi$
$113$	0.743006	−	1.62696i	0.0698961	−	0.153051i	0.941355	+	0.337417i	$0.109553\pi$
$114$	−27.8121			−2.60484
$115$	−3.43530	+	3.34644i	−0.320344	+	0.312058i
$116$	−24.4293			−2.26821
$117$	1.65192	−	3.61720i	0.152720	−	0.334410i
$118$	33.7449	+	9.90840i	3.10647	+	0.912142i
$119$	14.6536	+	16.9111i	1.34329	+	1.55024i
$120$	10.1210	−	6.50436i	0.923915	−	0.593764i
$121$	−1.55145	+	1.79047i	−0.141041	+	0.162770i
$122$	1.02790	−	7.14923i	0.0930620	−	0.647261i
$123$	−7.08038	+	2.07899i	−0.638416	+	0.187456i
$124$	6.64553	+	4.27083i	0.596787	+	0.383531i
$125$	−0.142315	−	0.989821i	−0.0127290	−	0.0885323i
$126$	−9.41488	−	20.6157i	−0.838744	−	1.83659i
$127$	5.36979	+	11.7582i	0.476492	+	1.04337i	0.983413	+	0.181379i	$0.0580562\pi$
$127$	5.36979	+	11.7582i	0.476492	+	1.04337i	−0.506921	+	0.861992i	$0.669217\pi$
$128$	−2.56758	−	17.8579i	−0.226944	−	1.57843i
$129$	0.660539	+	0.424503i	0.0581572	+	0.0373754i
$130$	4.49269	−	1.31917i	0.394035	−	0.115699i
$131$	−0.619691	+	4.31004i	−0.0541426	+	0.376570i	0.944677	+	0.328002i	$0.106375\pi$
$131$	−0.619691	+	4.31004i	−0.0541426	+	0.376570i	−0.998820	+	0.0485688i	$0.984534\pi$
$132$	−22.4392	+	25.8962i	−1.95308	+	2.25398i
$133$	−18.1294	+	11.6510i	−1.57202	+	1.01027i
$134$	−7.87264	−	9.08551i	−0.680093	−	0.784869i
$135$	−1.93896	−	0.569330i	−0.166879	−	0.0490002i
$136$	11.4012	−	24.9651i	0.977645	−	2.14074i
$137$	4.56418			0.389945			0.194972	−	0.980809i	$-0.437538\pi$
$137$	4.56418			0.389945			0.194972	+	0.980809i	$0.437538\pi$
$138$	13.1844	−	23.4109i	1.12233	−	1.99286i
$139$	16.6490			1.41215			0.706073	−	0.708139i	$-0.250465\pi$
$139$	16.6490			1.41215			0.706073	+	0.708139i	$0.250465\pi$
$140$	7.47927	−	16.3773i	0.632114	−	1.38414i
$141$	−4.10168	−	1.20436i	−0.345424	−	0.101426i
$142$	−12.9867	−	14.9875i	−1.08982	−	1.25772i
$143$	−5.80893	+	3.73317i	−0.485767	+	0.312183i
$144$	−6.76553	+	7.80784i	−0.563794	+	0.650653i
$145$	0.838265	−	5.83026i	0.0696141	−	0.484177i
$146$	21.0942	−	6.19381i	1.74577	−	0.512603i
$147$	−22.5155	−	14.4699i	−1.85705	−	1.19345i
$148$	−2.94743	−	20.4999i	−0.242278	−	1.68508i
$149$	0.944034	+	2.06715i	0.0773383	+	0.169347i	0.944352	−	0.328938i	$-0.106691\pi$
$149$	0.944034	+	2.06715i	0.0773383	+	0.169347i	−0.867013	+	0.498285i	$0.833963\pi$
$150$	2.32732	+	5.09611i	0.190025	+	0.416096i
$151$	1.30835	+	9.09979i	0.106472	+	0.740531i	0.971196	+	0.238283i	$0.0765845\pi$
$151$	1.30835	+	9.09979i	0.106472	+	0.740531i	−0.864724	+	0.502248i	$0.832506\pi$
$152$	22.2360	+	14.2902i	1.80358	+	1.15909i
$153$	10.4143	−	3.05791i	0.841945	−	0.247217i
$154$	−5.60074	+	38.9540i	−0.451320	+	3.13900i
$155$	−1.24730	+	1.43946i	−0.100186	+	0.115620i
$156$	−14.8885	+	9.56826i	−1.19203	+	0.766074i
$157$	−0.509640	−	0.588156i	−0.0406737	−	0.0469400i	0.735048	−	0.678015i	$-0.237160\pi$
$157$	−0.509640	−	0.588156i	−0.0406737	−	0.0469400i	−0.775722	+	0.631075i	$0.782614\pi$
$158$	−8.75414	−	2.57045i	−0.696442	−	0.204494i
$159$	−2.69133	+	5.89319i	−0.213436	+	0.467361i
$160$	−1.51621			−0.119867
$161$	−1.21302	−	20.7836i	−0.0955990	−	1.63798i
$162$	26.9838			2.12005
$163$	5.07395	−	11.1104i	0.397423	−	0.870234i	−0.600103	−	0.799923i	$-0.704874\pi$
$163$	5.07395	−	11.1104i	0.397423	−	0.870234i	0.997525	−	0.0703109i	$-0.0223991\pi$
$164$	12.9960	+	3.81598i	1.01482	+	0.297978i
$165$	−5.41036	−	6.24389i	−0.421196	−	0.486086i
$166$	−30.8328	+	19.8150i	−2.39309	+	1.53794i
$167$	0.698926	−	0.806604i	0.0540845	−	0.0624169i	−0.728063	−	0.685511i	$-0.759579\pi$
$167$	0.698926	−	0.806604i	0.0540845	−	0.0624169i	0.782147	+	0.623094i	$0.214124\pi$
$168$	−7.43262	+	51.6950i	−0.573439	+	3.98836i
$169$	9.05143	−	2.65774i	0.696264	−	0.204442i
$170$	10.7516	+	6.90963i	0.824610	+	0.529945i
$171$	1.48764	+	10.3468i	0.113763	+	0.791239i
$172$	−0.598699	−	1.31097i	−0.0456504	−	0.0999604i
$173$	4.43802	+	9.71790i	0.337416	+	0.738839i	0.999948	−	0.0101953i	$-0.00324531\pi$
$173$	4.43802	+	9.71790i	0.337416	+	0.738839i	−0.662532	+	0.749034i	$0.730518\pi$
$174$	4.69629	+	32.6634i	0.356025	+	2.47621i
$175$	3.65194	+	2.34696i	0.276060	+	0.177413i
$176$	17.2130	−	5.05420i	1.29748	−	0.380975i
$177$	4.56137	−	31.7250i	0.342854	−	2.38460i
$178$	7.86837	−	9.08058i	0.589759	−	0.680618i
$179$	−1.26996	+	0.816152i	−0.0949211	+	0.0610021i	−0.587240	−	0.809413i	$-0.699786\pi$
$179$	−1.26996	+	0.816152i	−0.0949211	+	0.0610021i	0.492319	+	0.870415i	$0.336149\pi$
$180$	−5.71898	−	6.60005i	−0.426268	−	0.491939i
$181$	−2.95065	−	0.866390i	−0.219320	−	0.0643982i	0.170226	−	0.985405i	$-0.445550\pi$
$181$	−2.95065	−	0.866390i	−0.219320	−	0.0643982i	−0.389547	+	0.921007i	$0.627368\pi$
$182$	−8.44390	+	18.4896i	−0.625904	+	1.37054i
$183$	−6.58235			−0.486581
$184$	−22.5698	+	11.9429i	−1.66387	+	0.880441i
$185$	4.99360			0.367136
$186$	4.43280	−	9.70647i	0.325028	−	0.711713i
$187$	−18.0839	−	5.30991i	−1.32243	−	0.388299i
$188$	5.13835	+	5.92997i	0.374752	+	0.432487i
$189$	7.37990	−	4.74277i	0.536809	−	0.344986i
$190$	−8.06039	+	9.30219i	−0.584762	+	0.674852i
$191$	−0.0481716	+	0.335041i	−0.00348557	+	0.0242427i	−0.991490	−	0.130183i	$-0.958444\pi$
$191$	−0.0481716	+	0.335041i	−0.00348557	+	0.0242427i	0.988004	+	0.154426i	$0.0493527\pi$
$192$	−13.1243	+	3.85364i	−0.947165	+	0.278113i
$193$	2.35491	+	1.51341i	0.169510	+	0.108937i	0.622645	−	0.782504i	$-0.286058\pi$
$193$	2.35491	+	1.51341i	0.169510	+	0.108937i	−0.453135	+	0.891442i	$0.649694\pi$
$194$	−4.75390	−	33.0641i	−0.341310	−	2.37386i
$195$	−1.77266	−	3.88159i	−0.126943	−	0.277966i
$196$	20.4076	+	44.6864i	1.45769	+	3.19189i
$197$	2.37167	+	16.4953i	0.168974	+	1.17524i	0.881009	+	0.473099i	$0.156865\pi$
$197$	2.37167	+	16.4953i	0.168974	+	1.17524i	−0.712035	+	0.702144i	$0.752226\pi$
$198$	16.0589	+	10.3204i	1.14125	+	0.733439i
$199$	11.2365	−	3.29934i	0.796536	−	0.233884i	0.141952	−	0.989873i	$-0.454662\pi$
$199$	11.2365	−	3.29934i	0.796536	−	0.233884i	0.654584	+	0.755989i	$0.272844\pi$
$200$	0.757739	−	5.27019i	0.0535802	−	0.372659i
$201$	−7.17462	+	8.27996i	−0.506059	+	0.584023i
$202$	21.2862	−	13.6798i	1.49769	−	0.962509i
$203$	16.7447	+	19.3244i	1.17524	+	1.35630i
$204$	−46.3497	−	13.6095i	−3.24513	−	0.952856i
$205$	−1.35666	+	2.97067i	−0.0947532	+	0.207481i
$206$	−4.43739			−0.309167
$207$	−9.41465	−	3.65269i	−0.654363	−	0.253880i
$208$	9.26577			0.642466
$209$	7.54039	−	16.5111i	0.521579	−	1.14210i
$210$	−23.3352	−	6.85183i	−1.61028	−	0.472821i
$211$	−14.7746	−	17.0508i	−1.01712	−	1.17382i	−0.984684	−	0.174349i	$-0.944218\pi$
$211$	−14.7746	−	17.0508i	−1.01712	−	1.17382i	−0.0324397	−	0.999474i	$-0.510328\pi$
$212$	10.0038	−	6.42907i	0.687066	−	0.441551i
$213$	−11.8353	+	13.6586i	−0.810940	+	0.935874i
$214$	5.98151	−	41.6023i	0.408888	−	2.84388i
$215$	0.333417	−	0.0979000i	0.0227388	−	0.00667672i
$216$	−9.05157	−	5.81709i	−0.615881	−	0.395803i
$217$	−1.17671	−	8.18418i	−0.0798801	−	0.555579i
$218$	−1.89202	−	4.14295i	−0.128144	−	0.280596i
$219$	−8.32303	−	18.2249i	−0.562418	−	1.23152i
$220$	2.15815	+	15.0103i	0.145503	+	1.01199i
$221$	−8.18923	−	5.26290i	−0.550867	−	0.354021i
$222$	−26.8428	+	7.88177i	−1.80157	+	0.528990i
$223$	2.65623	−	18.4745i	0.177875	−	1.23715i	−0.683794	−	0.729675i	$-0.739672\pi$
$223$	2.65623	−	18.4745i	0.177875	−	1.23715i	0.861669	−	0.507471i	$-0.169419\pi$
$224$	4.31027	−	4.97432i	0.287992	−	0.332361i
$225$	1.77140	−	1.13841i	0.118093	−	0.0758938i
$226$	2.90406	+	3.35147i	0.193176	+	0.222936i
$227$	21.4357	+	6.29408i	1.42274	+	0.417753i	0.900428	−	0.435004i	$-0.143253\pi$
$227$	21.4357	+	6.29408i	1.42274	+	0.417753i	0.522307	+	0.852757i	$0.325071\pi$
$228$	19.3263	−	42.3187i	1.27992	−	2.80262i
$229$	9.55700			0.631545			0.315772	−	0.948835i	$-0.397736\pi$
$229$	9.55700			0.631545			0.315772	+	0.948835i	$0.397736\pi$
$230$	−4.00909	−	11.1946i	−0.264351	−	0.738148i
$231$	35.8652			2.35976
$232$	13.0281	−	28.5277i	0.855340	−	1.87293i
$233$	−24.9170	−	7.31628i	−1.63236	−	0.479305i	−0.668061	−	0.744107i	$-0.732875\pi$
$233$	−24.9170	−	7.31628i	−1.63236	−	0.479305i	−0.964303	+	0.264801i	$0.914694\pi$
$234$	6.45658	+	7.45129i	0.422080	+	0.487106i
$235$	−1.59155	+	1.02283i	−0.103821	+	0.0667219i
$236$	−38.5256	+	44.4609i	−2.50780	+	2.89416i
$237$	−1.18332	+	8.23014i	−0.0768646	+	0.534605i
$238$	−53.2334	+	15.6307i	−3.45061	+	1.01319i
$239$	10.7713	+	6.92229i	0.696737	+	0.447766i	0.840475	−	0.541850i	$-0.182276\pi$
$239$	10.7713	+	6.92229i	0.696737	+	0.447766i	−0.143738	+	0.989616i	$0.545912\pi$
$240$	1.57776	+	10.9735i	0.101844	+	0.708340i
$241$	7.93056	+	17.3655i	0.510852	+	1.11861i	0.972788	+	0.231697i	$0.0744279\pi$
$241$	7.93056	+	17.3655i	0.510852	+	1.11861i	−0.461935	+	0.886914i	$0.652845\pi$
$242$	−2.44016	−	5.34320i	−0.156859	−	0.343474i
$243$	−2.63693	−	18.3403i	−0.169159	−	1.17653i
$244$	10.1639	+	6.53197i	0.650680	+	0.418167i
$245$	−11.3650	+	3.33708i	−0.726086	+	0.213198i
$246$	2.60383	−	18.1100i	0.166014	−	1.15465i
$247$	6.13941	−	7.08525i	0.390641	−	0.450824i
$248$	−8.53137	+	5.48278i	−0.541742	+	0.348157i
$249$	21.8732	+	25.2431i	1.38616	+	1.59971i
$250$	2.37897	+	0.698529i	0.150459	+	0.0441788i
$251$	8.59035	−	18.8102i	0.542218	−	1.18729i	−0.418104	−	0.908399i	$-0.637305\pi$
$251$	8.59035	−	18.8102i	0.542218	−	1.18729i	0.960322	−	0.278893i	$-0.0899674\pi$
$252$	37.9110			2.38817
$253$	10.3237	+	14.1743i	0.649048	+	0.891129i
$254$	−32.0496			−2.01097
$255$	4.83846	−	10.5947i	0.302996	−	0.663469i
$256$	31.3037	+	9.19160i	1.95648	+	0.574475i
$257$	−0.201803	−	0.232893i	−0.0125881	−	0.0145274i	0.749421	−	0.662094i	$-0.230332\pi$
$257$	−0.201803	−	0.232893i	−0.0125881	−	0.0145274i	−0.762009	+	0.647567i	$0.775787\pi$
$258$	−1.63774	+	1.05251i	−0.101961	+	0.0655267i
$259$	−14.1958	+	16.3828i	−0.882081	+	1.01798i
$260$	−1.11468	+	7.75274i	−0.0691292	+	0.480804i
$261$	11.9004	−	3.49427i	0.736616	−	0.216290i
$262$	−9.08237	−	5.83688i	−0.561111	−	0.360604i
$263$	1.03397	+	7.19140i	0.0637571	+	0.443441i	0.996548	+	0.0830218i	$0.0264571\pi$
$263$	1.03397	+	7.19140i	0.0637571	+	0.443441i	−0.932791	+	0.360419i	$0.882634\pi$
$264$	−18.2738	−	40.0141i	−1.12468	−	2.46270i
$265$	1.19108	+	2.60810i	0.0731675	+	0.160214i
$266$	−7.60420	−	52.8884i	−0.466244	−	3.24280i
$267$	−9.21173	−	5.92002i	−0.563749	−	0.362299i
$268$	19.2951	−	5.66555i	1.17863	−	0.346078i
$269$	−2.02227	+	14.0652i	−0.123300	+	0.857572i	0.830476	+	0.557054i	$0.188068\pi$
$269$	−2.02227	+	14.0652i	−0.123300	+	0.857572i	−0.953776	+	0.300517i	$0.902841\pi$
$270$	3.28113	−	3.78663i	0.199683	−	0.230447i
$271$	10.3783	−	6.66973i	0.630437	−	0.405158i	−0.186034	−	0.982543i	$-0.559563\pi$
$271$	10.3783	−	6.66973i	0.630437	−	0.405158i	0.816471	+	0.577386i	$0.195927\pi$
$272$	16.5620	+	19.1135i	1.00422	+	1.15893i
$273$	17.7739	+	5.21887i	1.07572	+	0.315861i
$274$	−4.70103	+	10.2938i	−0.283999	+	0.621872i
$275$	−3.65638			−0.220488
$276$	26.4602	+	36.3292i	1.59272	+	2.18676i
$277$	−2.41565			−0.145143			−0.0725713	−	0.997363i	$-0.523120\pi$
$277$	−2.41565			−0.145143			−0.0725713	+	0.997363i	$0.523120\pi$
$278$	−17.1481	+	37.5491i	−1.02848	+	2.25205i
$279$	−3.84816	−	1.12992i	−0.230383	−	0.0676466i
$280$	15.1361	+	17.4680i	0.904556	+	1.04391i
$281$	16.8878	−	10.8531i	1.00744	−	0.647444i	0.0707124	−	0.997497i	$-0.477473\pi$
$281$	16.8878	−	10.8531i	1.00744	−	0.647444i	0.936730	+	0.350053i	$0.113836\pi$
$282$	6.94090	−	8.01023i	0.413325	−	0.477002i
$283$	−0.296705	+	2.06363i	−0.0176373	+	0.122670i	−0.996738	−	0.0807065i	$-0.974282\pi$
$283$	−0.296705	+	2.06363i	−0.0176373	+	0.122670i	0.979101	+	0.203376i	$0.0651915\pi$
$284$	31.8292	−	9.34590i	1.88872	−	0.554577i
$285$	9.43654	+	6.06450i	0.558972	+	0.359230i
$286$	−2.43650	−	16.9462i	−0.144073	−	1.00205i
$287$	−5.88935	−	12.8959i	−0.347637	−	0.761219i
$288$	−1.32627	−	2.90412i	−0.0781510	−	0.171127i
$289$	−1.36200	−	9.47295i	−0.0801179	−	0.557232i
$290$	12.2858	+	7.89564i	0.721450	+	0.463648i
$291$	−29.2092	+	8.57660i	−1.71228	+	0.502769i
$292$	−5.23364	+	36.4008i	−0.306276	+	2.13019i
$293$	−0.421702	+	0.486670i	−0.0246361	+	0.0284316i	−0.767934	−	0.640529i	$-0.778715\pi$
$293$	−0.421702	+	0.486670i	−0.0246361	+	0.0284316i	0.743298	+	0.668961i	$0.233261\pi$
$294$	55.8251	−	35.8766i	3.25579	−	2.09237i
$295$	−9.28898	−	10.7201i	−0.540826	−	0.624146i
$296$	25.5108	+	7.49066i	1.48279	+	0.435386i
$297$	−3.06945	+	6.72117i	−0.178108	+	0.390002i
$298$	−5.63447			−0.326396
$299$	3.05362	+	8.52664i	0.176596	+	0.493108i
$300$	−9.37145			−0.541061
$301$	−0.626649	+	1.37217i	−0.0361194	+	0.0790905i
$302$	−21.8708	−	6.42183i	−1.25852	−	0.369535i
$303$	−15.1008	−	17.4272i	−0.867517	−	1.00117i
$304$	−20.4904	+	13.1684i	−1.17521	+	0.755259i
$305$	−1.90767	+	2.20157i	−0.109233	+	0.126062i
$306$	−3.82988	+	26.6374i	−0.218940	+	1.52276i
$307$	−27.7034	+	8.13444i	−1.58111	+	0.464257i	−0.950212	−	0.311605i	$-0.899133\pi$
$307$	−27.7034	+	8.13444i	−1.58111	+	0.464257i	−0.630902	+	0.775862i	$0.717315\pi$
$308$	−55.3803	−	35.5908i	−3.15559	−	2.02797i
$309$	0.575514	+	4.00279i	0.0327399	+	0.227711i
$310$	−1.96179	−	4.29571i	−0.111422	−	0.243980i
$311$	0.700892	+	1.53474i	0.0397439	+	0.0870271i	0.928463	−	0.371426i	$-0.121131\pi$
$311$	0.700892	+	1.53474i	0.0397439	+	0.0870271i	−0.888719	+	0.458453i	$0.848404\pi$
$312$	−3.23343	−	22.4890i	−0.183057	−	1.27319i
$313$	−8.51751	−	5.47387i	−0.481438	−	0.309402i	0.277316	−	0.960779i	$-0.410555\pi$
$313$	−8.51751	−	5.47387i	−0.481438	−	0.309402i	−0.758754	+	0.651377i	$0.774192\pi$
$314$	1.85142	−	0.543625i	0.104481	−	0.0306785i
$315$	−1.30087	+	9.04778i	−0.0732960	+	0.509785i
$316$	9.99433	−	11.5341i	0.562225	−	0.648842i
$317$	9.71999	−	6.24666i	0.545929	−	0.350847i	−0.238425	−	0.971161i	$-0.576631\pi$
$317$	9.71999	−	6.24666i	0.545929	−	0.350847i	0.784354	+	0.620314i	$0.212995\pi$
$318$	−10.5192	−	12.1398i	−0.589885	−	0.680764i
$319$	−20.6645	−	6.06764i	−1.15699	−	0.339722i
$320$	−2.51473	+	5.50648i	−0.140577	+	0.307822i
$321$	−38.3036			−2.13790
$322$	48.1237	+	18.6710i	2.68183	+	1.04049i
$323$	25.5893			1.42383
$324$	−18.7507	+	41.0584i	−1.04171	+	2.28102i
$325$	−1.81200	−	0.532053i	−0.100512	−	0.0295130i
$326$	19.8317	+	22.8870i	1.09838	+	1.26760i
$327$	−3.49181	+	2.24405i	−0.193097	+	0.124096i
$328$	−11.3869	+	13.1412i	−0.628739	+	0.725603i
$329$	1.16880	−	8.12918i	0.0644380	−	0.448176i
$330$	19.6547	−	5.77115i	1.08196	−	0.317691i
$331$	28.3822	+	18.2401i	1.56003	+	1.00257i	0.982514	+	0.186188i	$0.0596132\pi$
$331$	28.3822	+	18.2401i	1.56003	+	1.00257i	0.577513	+	0.816381i	$0.304023\pi$
$332$	−8.72507	−	60.6842i	−0.478851	−	3.33048i
$333$	4.36802	+	9.56462i	0.239366	+	0.524138i
$334$	1.09929	+	2.40711i	0.0601504	+	0.131711i
$335$	0.690040	+	4.79933i	0.0377009	+	0.262216i
$336$	−40.4868	−	26.0193i	−2.20874	−	1.41947i
$337$	33.7615	−	9.91328i	1.83911	−	0.540011i	0.839115	−	0.543954i	$-0.183073\pi$
$337$	33.7615	−	9.91328i	1.83911	−	0.540011i	0.999992	+	0.00394293i	$0.00125508\pi$
$338$	−3.32869	+	23.1515i	−0.181057	+	1.25928i
$339$	2.64658	−	3.05432i	0.143742	−	0.165888i
$340$	−17.9848	+	11.5581i	−0.975364	+	0.626829i
$341$	4.56061	+	5.26322i	0.246971	+	0.285019i
$342$	−24.8678	−	7.30185i	−1.34470	−	0.394839i
$343$	8.73691	−	19.1312i	0.471749	−	1.03299i
$344$	1.85018			0.0997553
$345$	−9.57821	+	5.06834i	−0.515674	+	0.272870i
$346$	−26.4883			−1.42402
$347$	−6.08520	+	13.3247i	−0.326671	+	0.715309i	−0.999705	−	0.0243027i	$-0.992263\pi$
$347$	−6.08520	+	13.3247i	−0.326671	+	0.715309i	0.673034	+	0.739611i	$0.264991\pi$
$348$	−52.9638	−	15.5516i	−2.83916	−	0.833653i
$349$	11.4217	+	13.1813i	0.611389	+	0.705581i	0.974048	−	0.226341i	$-0.0726764\pi$
$349$	11.4217	+	13.1813i	0.611389	+	0.705581i	−0.362659	+	0.931922i	$0.618131\pi$
$350$	−9.05463	+	5.81905i	−0.483990	+	0.311042i
$351$	−2.49916	+	2.88418i	−0.133395	+	0.153946i
$352$	−0.788972	+	5.48742i	−0.0420523	+	0.292480i
$353$	11.2046	−	3.28997i	0.596360	−	0.175107i	0.0303975	−	0.999538i	$-0.490323\pi$
$353$	11.2046	−	3.28997i	0.596360	−	0.175107i	0.565963	+	0.824431i	$0.308505\pi$
$354$	66.8528	+	42.9637i	3.55319	+	2.28349i
$355$	1.13829	+	7.91699i	0.0604143	+	0.420190i
$356$	8.34932	+	18.2825i	0.442513	+	0.968969i
$357$	21.0041	+	45.9925i	1.11165	+	2.43418i
$358$	−0.532672	−	3.70481i	−0.0281526	−	0.195806i
$359$	−22.2237	−	14.2823i	−1.17292	−	0.753790i	−0.198848	−	0.980030i	$-0.563720\pi$
$359$	−22.2237	−	14.2823i	−1.17292	−	0.753790i	−0.974072	+	0.226240i	$0.927357\pi$
$360$	10.7572	−	3.15861i	0.566955	−	0.166473i
$361$	−0.803294	+	5.58703i	−0.0422786	+	0.294054i
$362$	4.99313	−	5.76237i	0.262433	−	0.302864i
$363$	−4.50341	+	2.89417i	−0.236368	+	0.151904i
$364$	−22.2661	−	25.6964i	−1.16706	−	1.34686i
$365$	−8.50776	−	2.49810i	−0.445316	−	0.130757i
$366$	6.77970	−	14.8455i	0.354381	−	0.775985i
$367$	−34.5897			−1.80557			−0.902783	−	0.430096i	$-0.858480\pi$
$367$	−34.5897			−1.80557			−0.902783	+	0.430096i	$0.858480\pi$
$368$	−1.37099	−	23.4904i	−0.0714678	−	1.22452i
$369$	−6.87666			−0.357985
$370$	−5.14331	+	11.2623i	−0.267388	+	0.585498i
$371$	−11.9425	−	3.50665i	−0.620026	−	0.182056i
$372$	11.6890	+	13.4898i	0.606047	+	0.699416i
$373$	26.0693	−	16.7537i	1.34982	−	0.867476i	0.352165	−	0.935938i	$-0.385446\pi$
$373$	26.0693	−	16.7537i	1.34982	−	0.867476i	0.997654	+	0.0684619i	$0.0218091\pi$
$374$	30.6018	−	35.3163i	1.58238	−	1.82616i
$375$	0.321571	−	2.23657i	0.0166058	−	0.115496i
$376$	−9.66507	+	2.83792i	−0.498438	+	0.146355i
$377$	−9.35783	−	6.01392i	−0.481953	−	0.309732i
$378$	3.09543	+	21.5292i	0.159212	+	1.10734i
$379$	−3.06505	−	6.71153i	−0.157441	−	0.344748i	0.814430	−	0.580262i	$-0.197050\pi$
$379$	−3.06505	−	6.71153i	−0.157441	−	0.344748i	−0.971871	+	0.235514i	$0.924323\pi$
$380$	−8.55308	−	18.7286i	−0.438764	−	0.960759i
$381$	4.15673	+	28.9107i	0.212956	+	1.48114i
$382$	−0.706017	−	0.453729i	−0.0361230	−	0.0232148i
$383$	−5.86253	+	1.72140i	−0.299561	+	0.0879592i	−0.428059	−	0.903751i	$-0.640803\pi$
$383$	−5.86253	+	1.72140i	−0.299561	+	0.0879592i	0.128498	+	0.991710i	$0.458984\pi$
$384$	5.80163	−	40.3513i	0.296063	−	2.05917i
$385$	10.3943	−	11.9957i	0.529744	−	0.611358i
$386$	−5.83877	+	3.75235i	−0.297185	+	0.190990i
$387$	0.479163	+	0.552984i	0.0243572	+	0.0281097i
$388$	53.6136	+	15.7424i	2.72182	+	0.799197i
$389$	−7.08372	+	15.5112i	−0.359159	+	0.786448i	0.640668	+	0.767818i	$0.278658\pi$
$389$	−7.08372	+	15.5112i	−0.359159	+	0.786448i	−0.999826	+	0.0186297i	$0.994070\pi$
$390$	10.5801			0.535746
$391$	−12.1307	+	21.5399i	−0.613474	+	1.08932i
$392$	−63.0665			−3.18534
$393$	−4.08727	+	8.94987i	−0.206175	+	0.451461i
$394$	−39.6454	−	11.6409i	−1.99731	−	0.586462i
$395$	2.40976	+	2.78101i	0.121248	+	0.139928i
$396$	−26.8626	+	17.2635i	−1.34990	+	0.867526i
$397$	6.59884	−	7.61547i	0.331186	−	0.382209i	−0.565595	−	0.824683i	$-0.691354\pi$
$397$	6.59884	−	7.61547i	0.331186	−	0.382209i	0.896782	+	0.442474i	$0.145899\pi$
$398$	−4.13226	+	28.7405i	−0.207132	+	1.44063i
$399$	−46.7223	+	13.7189i	−2.33904	+	0.686804i
$400$	4.12754	+	2.65261i	0.206377	+	0.132630i
$401$	−2.52352	−	17.5515i	−0.126019	−	0.876480i	−0.950530	−	0.310634i	$-0.899459\pi$
$401$	−2.52352	−	17.5515i	−0.126019	−	0.876480i	0.824511	−	0.565846i	$-0.191450\pi$
$402$	−11.2844	−	24.7095i	−0.562816	−	1.23240i
$403$	1.49425	+	3.27194i	0.0744337	+	0.162987i
$404$	6.02359	+	41.8950i	0.299685	+	2.08435i
$405$	−9.15551	−	5.88389i	−0.454941	−	0.292373i
$406$	−60.8298	+	17.8612i	−3.01893	+	0.886438i
$407$	2.59845	−	18.0726i	0.128801	−	0.895828i
$408$	40.6110	−	46.8675i	2.01054	−	2.32029i
$409$	−15.2334	+	9.78992i	−0.753244	+	0.484080i	−0.860057	−	0.510199i	$-0.829572\pi$
$409$	−15.2334	+	9.78992i	−0.753244	+	0.484080i	0.106813	+	0.994279i	$0.465935\pi$
$410$	−5.30255	−	6.11947i	−0.261874	−	0.302219i
$411$	9.89535	+	2.90554i	0.488101	+	0.143320i
$412$	3.08349	−	6.75190i	0.151913	−	0.332642i
$413$	61.5766			3.02998
$414$	17.9350	−	17.4711i	0.881457	−	0.858657i
$415$	14.7822			0.725628
$416$	−1.18949	+	2.60461i	−0.0583194	+	0.127702i
$417$	36.0957	+	10.5986i	1.76761	+	0.519018i
$418$	29.4719	+	34.0124i	1.44152	+	1.66360i
$419$	6.96522	−	4.47628i	0.340273	−	0.218680i	−0.359332	−	0.933210i	$-0.616995\pi$
$419$	6.96522	−	4.47628i	0.340273	−	0.218680i	0.699605	+	0.714529i	$0.253359\pi$
$420$	26.6411	−	30.7455i	1.29995	−	1.50022i
$421$	1.57614	−	10.9623i	0.0768163	−	0.534269i	−0.914684	−	0.404169i	$-0.867561\pi$
$421$	1.57614	−	10.9623i	0.0768163	−	0.534269i	0.991501	−	0.130101i	$-0.0415300\pi$
$422$	53.6729	−	15.7598i	2.61276	−	0.767174i
$423$	−3.35127	−	2.15373i	−0.162944	−	0.104718i
$424$	2.17259	+	15.1107i	0.105510	+	0.733842i
$425$	−2.14132	−	4.68883i	−0.103869	−	0.227442i
$426$	−18.6148	−	40.7608i	−0.901891	−	1.97487i
$427$	−1.79970	−	12.5172i	−0.0870938	−	0.605751i
$428$	59.1454	+	38.0104i	2.85890	+	1.83730i
$429$	−14.9705	+	4.39574i	−0.722784	+	0.212228i
$430$	−0.122615	+	0.852805i	−0.00591301	+	0.0411259i
$431$	0.109783	−	0.126696i	0.00528807	−	0.00610275i	−0.753099	−	0.657907i	$-0.771442\pi$
$431$	0.109783	−	0.126696i	0.00528807	−	0.00610275i	0.758387	+	0.651804i	$0.225988\pi$
$432$	8.34100	−	5.36044i	0.401307	−	0.257904i
$433$	0.885340	+	1.02174i	0.0425467	+	0.0491015i	0.776624	−	0.629964i	$-0.216931\pi$
$433$	0.885340	+	1.02174i	0.0425467	+	0.0491015i	−0.734077	+	0.679066i	$0.762385\pi$
$434$	19.6701	+	5.77568i	0.944197	+	0.277241i
$435$	5.52891	−	12.1066i	0.265091	−	0.580468i
$436$	7.61864			0.364867
$437$	−18.8708	−	14.5161i	−0.902711	−	0.694400i
$438$	49.6760			2.37361
$439$	8.64989	−	18.9406i	0.412837	−	0.903987i	−0.582969	−	0.812494i	$-0.698109\pi$
$439$	8.64989	−	18.9406i	0.412837	−	0.903987i	0.995806	−	0.0914922i	$-0.0291637\pi$
$440$	−18.6794	−	5.48477i	−0.890505	−	0.261476i
$441$	−16.3330	−	18.8493i	−0.777764	−	0.897587i
$442$	20.3044	−	13.0489i	0.965783	−	0.620671i
$443$	5.20038	−	6.00156i	0.247078	−	0.285143i	−0.618641	−	0.785674i	$-0.712316\pi$
$443$	5.20038	−	6.00156i	0.247078	−	0.285143i	0.865719	+	0.500531i	$0.166862\pi$
$444$	6.65994	−	46.3209i	0.316067	−	2.19829i
$445$	−4.64976	+	1.36529i	−0.220420	+	0.0647210i
$446$	38.9305	+	25.0191i	1.84341	+	1.18469i
$447$	0.730772	+	5.08263i	0.0345643	+	0.240400i
$448$	−10.9166	−	23.9040i	−0.515760	−	1.12936i
$449$	14.5664	+	31.8961i	0.687433	+	1.50527i	0.854571	+	0.519335i	$0.173820\pi$
$449$	14.5664	+	31.8961i	0.687433	+	1.50527i	−0.167138	+	0.985934i	$0.553452\pi$
$450$	0.742996	+	5.16765i	0.0350252	+	0.243605i
$451$	10.0454	+	6.45578i	0.473019	+	0.303991i
$452$	−7.11758	+	2.08991i	−0.334783	+	0.0983011i
$453$	−2.95632	+	20.5616i	−0.138900	+	0.966070i
$454$	−36.2737	+	41.8621i	−1.70241	+	1.96468i
$455$	6.89669	−	4.43223i	0.323322	−	0.207786i
$456$	39.1115	+	45.1371i	1.83156	+	2.11374i
$457$	0.642571	+	0.188676i	0.0300582	+	0.00882589i	0.296727	−	0.954962i	$-0.404105\pi$
$457$	0.642571	+	0.188676i	0.0300582	+	0.00882589i	−0.266669	+	0.963788i	$0.585923\pi$
$458$	−9.84354	+	21.5543i	−0.459958	+	1.00717i
$459$	−10.4166			−0.486205
$460$	19.8195	+	1.67878i	0.924088	+	0.0782735i
$461$	−15.8552			−0.738453			−0.369226	−	0.929340i	$-0.620377\pi$
$461$	−15.8552			−0.738453			−0.369226	+	0.929340i	$0.620377\pi$
$462$	−36.9406	+	80.8885i	−1.71863	+	3.76327i
$463$	−25.6570	−	7.53357i	−1.19238	−	0.350115i	−0.375446	−	0.926844i	$-0.622510\pi$
$463$	−25.6570	−	7.53357i	−1.19238	−	0.350115i	−0.816935	+	0.576730i	$0.804329\pi$
$464$	18.9254	+	21.8410i	0.878588	+	1.01394i
$465$	−3.62056	+	2.32679i	−0.167899	+	0.107902i
$466$	42.1647	−	48.6607i	1.95324	−	2.25416i
$467$	−5.53940	+	38.5274i	−0.256333	+	1.78283i	0.302092	+	0.953279i	$0.402315\pi$
$467$	−5.53940	+	38.5274i	−0.256333	+	1.78283i	−0.558425	+	0.829555i	$0.688594\pi$
$468$	−15.8245	+	4.64648i	−0.731486	+	0.214784i
$469$	−17.7071	−	11.3797i	−0.817638	−	0.525464i
$470$	−0.667561	−	4.64299i	−0.0307923	−	0.214165i
$471$	−0.730505	−	1.59958i	−0.0336599	−	0.0737049i
$472$	−31.3741	−	68.6996i	−1.44411	−	3.16216i
$473$	−0.180820	−	1.25763i	−0.00831413	−	0.0578260i
$474$	−17.3430	−	11.1457i	−0.796591	−	0.511938i
$475$	4.76323	−	1.39861i	0.218552	−	0.0641727i
$476$	13.2077	−	91.8613i	0.605372	−	4.21046i
$477$	−3.95364	+	4.56274i	−0.181025	+	0.208913i
$478$	−26.7064	+	17.1632i	−1.22152	+	0.785024i
$479$	−5.99204	−	6.91518i	−0.273783	−	0.315963i	0.602161	−	0.798374i	$-0.294306\pi$
$479$	−5.99204	−	6.91518i	−0.273783	−	0.315963i	−0.875945	+	0.482412i	$0.839761\pi$
$480$	−3.28721	−	0.965212i	−0.150040	−	0.0440557i
$481$	3.91754	−	8.57821i	0.178624	−	0.391133i
$482$	−47.3336			−2.15598
$483$	10.6009	−	45.8320i	0.482357	−	2.08543i
$484$	9.82583			0.446629
$485$	−5.59673	+	12.2551i	−0.254134	+	0.556477i
$486$	44.0796	+	12.9429i	1.99949	+	0.587104i
$487$	−17.4973	−	20.1929i	−0.792876	−	0.915028i	0.205092	−	0.978743i	$-0.434251\pi$
$487$	−17.4973	−	20.1929i	−0.792876	−	0.915028i	−0.997968	+	0.0637148i	$0.979705\pi$
$488$	−13.0482	+	8.38558i	−0.590665	+	0.379597i
$489$	18.0734	−	20.8578i	0.817306	−	0.943221i
$490$	4.17952	−	29.0692i	0.188812	−	1.31321i
$491$	−18.0280	+	5.29349i	−0.813591	+	0.238892i	−0.661954	−	0.749544i	$-0.730273\pi$
$491$	−18.0280	+	5.29349i	−0.813591	+	0.238892i	−0.151637	+	0.988436i	$0.548455\pi$
$492$	25.7467	+	16.5464i	1.16075	+	0.745971i
$493$	−4.32096	−	30.0529i	−0.194606	−	1.35352i
$494$	9.65622	+	21.1442i	0.434454	+	0.951321i
$495$	−3.19832	−	7.00335i	−0.143754	−	0.314777i
$496$	−1.32995	−	9.25003i	−0.0597167	−	0.415339i
$497$	−29.2097	−	18.7719i	−1.31023	−	0.842035i
$498$	−79.4609	+	23.3318i	−3.56073	+	1.04552i
$499$	3.73255	−	25.9605i	0.167092	−	1.16215i	−0.717765	−	0.696286i	$-0.754835\pi$
$499$	3.73255	−	25.9605i	0.167092	−	1.16215i	0.884856	−	0.465864i	$-0.154256\pi$
$500$	−2.71600	+	3.13443i	−0.121463	+	0.140176i
$501$	2.02878	−	1.30382i	0.0906393	−	0.0582503i
$502$	33.5757	+	38.7484i	1.49856	+	1.72943i
$503$	−26.3062	−	7.72419i	−1.17293	−	0.344405i	−0.363489	−	0.931599i	$-0.618414\pi$
$503$	−26.3062	−	7.72419i	−1.17293	−	0.344405i	−0.809446	+	0.587194i	$0.800233\pi$
$504$	−20.2179	+	44.2711i	−0.900578	+	1.97199i
$505$	−10.2053			−0.454129
$506$	−42.6012	+	8.68437i	−1.89385	+	0.386067i
$507$	21.3158			0.946668
$508$	22.2709	−	48.7665i	0.988112	−	2.16366i
$509$	−27.8063	−	8.16467i	−1.23249	−	0.361893i	−0.400303	−	0.916383i	$-0.631095\pi$
$509$	−27.8063	−	8.16467i	−1.23249	−	0.361893i	−0.832190	+	0.554490i	$0.812913\pi$
$510$	18.9113	+	21.8248i	0.837406	+	0.966418i
$511$	32.3815	−	20.8103i	1.43247	−	0.920593i
$512$	−29.3431	+	33.8637i	−1.29679	+	1.49658i
$513$	1.42770	−	9.92988i	0.0630346	−	0.438415i
$514$	0.733106	−	0.215259i	0.0323359	−	0.00949468i
$515$	1.50559	+	0.967584i	0.0663442	+	0.0426368i
$516$	−0.463450	−	3.22336i	−0.0204022	−	0.141901i
$517$	2.87361	+	6.29232i	0.126381	+	0.276736i
$518$	−22.3274	−	48.8903i	−0.981012	−	2.14812i
$519$	3.43545	+	23.8941i	0.150799	+	1.04883i
$520$	−8.45890	−	5.43621i	−0.370947	−	0.238393i
$521$	1.12889	−	0.331473i	0.0494577	−	0.0145221i	−0.256910	−	0.966435i	$-0.582704\pi$
$521$	1.12889	−	0.331473i	0.0494577	−	0.0145221i	0.306368	+	0.951913i	$0.400886\pi$
$522$	−4.37640	+	30.4386i	−0.191550	+	1.33226i
$523$	−23.7077	+	27.3602i	−1.03667	+	1.19638i	−0.0564587	+	0.998405i	$0.517981\pi$
$523$	−23.7077	+	27.3602i	−1.03667	+	1.19638i	−0.980208	+	0.197972i	$0.936565\pi$
$524$	15.1926	−	9.76370i	0.663692	−	0.426529i
$525$	6.42349	+	7.41311i	0.280344	+	0.323534i
$526$	−17.2841	−	5.07506i	−0.753620	−	0.221283i
$527$	−4.07853	+	8.93073i	−0.177663	+	0.389029i
$528$	40.5361			1.76411
$529$	21.1647	−	9.00310i	0.920204	−	0.391439i
$530$	−7.10896			−0.308794
$531$	12.4077	−	27.1690i	0.538447	−	1.17903i
$532$	85.7588	+	25.1811i	3.71811	+	1.09174i
$533$	4.03883	+	4.66105i	0.174941	+	0.201893i
$534$	22.8396	−	14.6781i	0.988366	−	0.635185i
$535$	−11.1010	+	12.8112i	−0.479938	+	0.553878i
$536$	−3.67404	+	25.5535i	−0.158694	+	1.10374i
$537$	−3.27288	+	0.961004i	−0.141235	+	0.0414704i
$538$	−29.6390	−	19.0478i	−1.27783	−	0.821211i
$539$	6.16355	+	42.8684i	0.265483	+	1.84647i
$540$	3.48169	+	7.62384i	0.149828	+	0.328078i
$541$	0.986468	+	2.16006i	0.0424116	+	0.0928684i	0.929652	−	0.368439i	$-0.120108\pi$
$541$	0.986468	+	2.16006i	0.0424116	+	0.0928684i	−0.887240	+	0.461308i	$0.847380\pi$
$542$	4.35309	+	30.2764i	0.186981	+	1.30048i
$543$	−5.84560	−	3.75674i	−0.250859	−	0.161217i
$544$	−7.49895	+	2.20189i	−0.321515	+	0.0944052i
$545$	−0.261425	+	1.81825i	−0.0111982	+	0.0778853i
$546$	−30.0771	+	34.7108i	−1.28718	+	1.48549i
$547$	11.3183	−	7.27380i	0.483934	−	0.311005i	−0.275828	−	0.961207i	$-0.588952\pi$
$547$	11.3183	−	7.27380i	0.483934	−	0.311005i	0.759762	+	0.650202i	$0.225316\pi$
$548$	−12.3963	−	14.3061i	−0.529545	−	0.611127i
$549$	−5.88553	−	1.72815i	−0.251188	−	0.0737555i
$550$	3.76601	−	8.24640i	0.160583	−	0.351628i
$551$	29.2409			1.24570
$552$	−56.5351	+	11.5248i	−2.40629	+	0.490530i
$553$	−15.9742			−0.679294
$554$	2.48808	−	5.44813i	0.105708	−	0.231469i
$555$	10.8263	+	3.17890i	0.459552	+	0.134937i
$556$	−45.2186	−	52.1850i	−1.91769	−	2.21314i
$557$	−31.1934	+	20.0468i	−1.32171	+	0.849410i	−0.995396	−	0.0958528i	$-0.969442\pi$
$557$	−31.1934	+	20.0468i	−1.32171	+	0.849410i	−0.326311	+	0.945262i	$0.605806\pi$
$558$	6.51190	−	7.51513i	0.275671	−	0.318141i
$559$	0.0933928	−	0.649561i	0.00395009	−	0.0274735i
$560$	−20.4363	+	6.00064i	−0.863591	+	0.253573i
$561$	−35.8264	−	23.0242i	−1.51259	−	0.972084i
$562$	7.08344	+	49.2664i	0.298797	+	2.07818i
$563$	19.3845	+	42.4462i	0.816961	+	1.78890i	0.573991	+	0.818862i	$0.305395\pi$
$563$	19.3845	+	42.4462i	0.816961	+	1.78890i	0.242971	+	0.970034i	$0.421878\pi$
$564$	7.36517	+	16.1275i	0.310130	+	0.679089i
$565$	−0.254542	−	1.77038i	−0.0107087	−	0.0744805i
$566$	−4.34859	−	2.79467i	−0.182785	−	0.117469i
$567$	45.3308	−	13.3103i	1.90372	−	0.558981i
$568$	−6.06070	+	42.1531i	−0.254302	+	1.76871i
$569$	18.1507	−	20.9470i	0.760915	−	0.878143i	−0.234663	−	0.972077i	$-0.575399\pi$
$569$	18.1507	−	20.9470i	0.760915	−	0.878143i	0.995578	+	0.0939339i	$0.0299442\pi$
$570$	−23.3970	+	15.0363i	−0.979993	+	0.629803i
$571$	−18.3192	−	21.1415i	−0.766635	−	0.884744i	0.229434	−	0.973324i	$-0.426312\pi$
$571$	−18.3192	−	21.1415i	−0.766635	−	0.884744i	−0.996069	+	0.0885802i	$0.971767\pi$
$572$	27.4784	+	8.06839i	1.14893	+	0.337356i
$573$	−0.317723	+	0.695717i	−0.0132731	+	0.0290640i
$574$	35.1506			1.46716
$575$	−1.08074	+	4.67247i	−0.0450699	+	0.194856i
$576$	−12.7467			−0.531112
$577$	2.28763	−	5.00921i	0.0952353	−	0.208536i	−0.856019	−	0.516945i	$-0.827069\pi$
$577$	2.28763	−	5.00921i	0.0952353	−	0.208536i	0.951254	+	0.308409i	$0.0997964\pi$
$578$	22.7676	+	6.68518i	0.947008	+	0.278067i
$579$	4.14211	+	4.78025i	0.172140	+	0.198661i
$580$	−20.5513	+	13.2075i	−0.853345	+	0.548411i
$581$	−42.0226	+	48.4967i	−1.74339	+	2.01198i
$582$	10.7418	−	74.7106i	0.445261	−	3.09686i
$583$	10.0589	−	2.95357i	0.416599	−	0.122324i
$584$	−39.7164	−	25.5242i	−1.64348	−	1.05620i
$585$	−0.565922	−	3.93607i	−0.0233980	−	0.162737i
$586$	−0.663264	−	1.45235i	−0.0273992	−	0.0599958i
$587$	−7.94258	−	17.3918i	−0.327826	−	0.717838i	0.671915	−	0.740629i	$-0.265472\pi$
$587$	−7.94258	−	17.3918i	−0.327826	−	0.717838i	−0.999740	+	0.0227907i	$0.992745\pi$
$588$	15.7974	+	109.873i	0.651475	+	4.53111i
$589$	−7.95443	−	5.11200i	−0.327757	−	0.210636i
$590$	33.7449	−	9.90840i	1.38926	−	0.407922i
$591$	−5.35896	+	37.2724i	−0.220438	+	1.53318i
$592$	−16.0445	+	18.5164i	−0.659425	+	0.761017i
$593$	12.5762	−	8.08220i	0.516441	−	0.331896i	−0.256322	−	0.966592i	$-0.582511\pi$
$593$	12.5762	−	8.08220i	0.516441	−	0.331896i	0.772763	+	0.634695i	$0.218874\pi$
$594$	−11.9971	−	13.8454i	−0.492246	−	0.568082i
$595$	21.4702	+	6.30423i	0.880194	+	0.258448i
$596$	3.91533	−	8.57338i	0.160378	−	0.351179i
$597$	26.4616			1.08300
$598$	−22.3757	−	1.89530i	−0.915010	−	0.0775046i
$599$	−15.7792			−0.644720			−0.322360	−	0.946617i	$-0.604476\pi$
$599$	−15.7792			−0.644720			−0.322360	+	0.946617i	$0.604476\pi$
$600$	4.99779	−	10.9436i	0.204034	−	0.446772i
$601$	36.0826	+	10.5948i	1.47184	+	0.432171i	0.916696	−	0.399585i	$-0.130846\pi$
$601$	36.0826	+	10.5948i	1.47184	+	0.432171i	0.555142	+	0.831756i	$0.312664\pi$
$602$	−2.44928	−	2.82662i	−0.0998251	−	0.115204i
$603$	−8.58895	+	5.51978i	−0.349769	+	0.224783i
$604$	24.9692	−	28.8160i	1.01598	−	1.17251i
$605$	−0.337162	+	2.34501i	−0.0137076	+	0.0953383i
$606$	54.8580	−	16.1078i	2.22845	−	0.654333i
$607$	38.7920	+	24.9301i	1.57452	+	1.01188i	0.977828	+	0.209408i	$0.0671538\pi$
$607$	38.7920	+	24.9301i	1.57452	+	1.01188i	0.596689	+	0.802473i	$0.296483\pi$
$608$	−1.07120	−	7.45035i	−0.0434428	−	0.302152i
$609$	24.0013	+	52.5556i	0.972583	+	2.12966i
$610$	−3.00044	−	6.57004i	−0.121484	−	0.266013i
$611$	0.508465	+	3.53645i	0.0205703	+	0.143070i
$612$	−37.8700	−	24.3376i	−1.53080	−	0.983788i
$613$	−27.0855	+	7.95303i	−1.09397	+	0.321220i	−0.778455	−	0.627700i	$-0.783997\pi$
$613$	−27.0855	+	7.95303i	−1.09397	+	0.321220i	−0.315518	+	0.948920i	$0.602178\pi$
$614$	10.1880	−	70.8590i	0.411153	−	2.85963i
$615$	−4.83241	+	5.57690i	−0.194862	+	0.224882i
$616$	71.0958	−	45.6905i	2.86453	−	1.84092i
$617$	9.18818	+	10.6037i	0.369902	+	0.426890i	0.909933	−	0.414755i	$-0.136133\pi$
$617$	9.18818	+	10.6037i	0.369902	+	0.426890i	−0.540031	+	0.841645i	$0.681587\pi$
$618$	−9.62044	−	2.82482i	−0.386991	−	0.113631i
$619$	−11.4645	+	25.1037i	−0.460796	+	1.00900i	0.526510	+	0.850169i	$0.323500\pi$
$619$	−11.4645	+	25.1037i	−0.460796	+	1.00900i	−0.987306	+	0.158833i	$0.949227\pi$
$620$	7.89956			0.317254
$621$	7.68169	+	5.90905i	0.308256	+	0.237122i
$622$	−4.18327			−0.167734
$623$	8.73910	−	19.1360i	0.350125	−	0.766666i
$624$	20.0886	+	5.89854i	0.804187	+	0.236131i
$625$	−0.654861	−	0.755750i	−0.0261944	−	0.0302300i
$626$	21.1184	−	13.5719i	0.844059	−	0.542444i
$627$	26.8588	−	30.9967i	1.07264	−	1.23789i
$628$	−0.459352	+	3.19486i	−0.0183301	+	0.127489i
$629$	24.6976	−	7.25186i	0.984756	−	0.289150i
$630$	−19.0660	−	12.2530i	−0.759607	−	0.488170i
$631$	−5.83468	−	40.5811i	−0.232275	−	1.61551i	−0.688222	−	0.725500i	$-0.741609\pi$
$631$	−5.83468	−	40.5811i	−0.232275	−	1.61551i	0.455948	−	0.890007i	$-0.349300\pi$
$632$	8.13909	+	17.8221i	0.323756	+	0.708926i
$633$	−21.1775	−	46.3722i	−0.841729	−	1.84313i
$634$	4.07696	+	28.3559i	0.161917	+	1.12616i
$635$	10.8743	+	6.98850i	0.431534	+	0.277330i
$636$	25.7815	−	7.57012i	1.02230	−	0.300175i
$637$	−3.18344	+	22.1413i	−0.126133	+	0.877271i
$638$	34.9686	−	40.3560i	1.38442	−	1.59771i
$639$	−14.1683	+	9.10544i	−0.560491	+	0.360206i
$640$	−11.8147	−	13.6349i	−0.467017	−	0.538967i
$641$	−5.88425	−	1.72777i	−0.232414	−	0.0682429i	0.163452	−	0.986551i	$-0.447737\pi$
$641$	−5.88425	−	1.72777i	−0.232414	−	0.0682429i	−0.395866	+	0.918308i	$0.629555\pi$
$642$	39.4520	−	86.3878i	1.55705	−	3.40946i
$643$	−11.4517			−0.451611			−0.225806	−	0.974172i	$-0.572501\pi$
$643$	−11.4517			−0.451611			−0.225806	+	0.974172i	$0.572501\pi$
$644$	−61.8503	+	60.2505i	−2.43724	+	2.37420i
$645$	0.785184			0.0309166
$646$	−26.3565	+	57.7127i	−1.03698	+	2.27068i
$647$	19.5034	+	5.72671i	0.766757	+	0.225140i	0.641644	−	0.767002i	$-0.278253\pi$
$647$	19.5034	+	5.72671i	0.766757	+	0.225140i	0.125113	+	0.992143i	$0.460071\pi$
$648$	−37.9467	−	43.7928i	−1.49069	−	1.72034i
$649$	−43.6313	+	28.0401i	−1.71268	+	1.10067i
$650$	3.06629	−	3.53869i	0.120270	−	0.138799i
$651$	2.65886	−	18.4927i	0.104209	−	0.724788i
$652$	−48.6056	+	14.2719i	−1.90354	+	0.558931i
$653$	−35.9838	−	23.1254i	−1.40816	−	0.904967i	−0.408188	−	0.912898i	$-0.633839\pi$
$653$	−35.9838	−	23.1254i	−1.40816	−	0.904967i	−0.999969	+	0.00793066i	$0.997476\pi$
$654$	−1.46461	−	10.1866i	−0.0572706	−	0.398326i
$655$	1.80887	+	3.96087i	0.0706784	+	0.154764i
$656$	−6.65633	−	14.5753i	−0.259886	−	0.569071i
$657$	−2.65713	−	18.4807i	−0.103664	−	0.721002i
$658$	17.1303	+	11.0090i	0.667807	+	0.429174i
$659$	10.7208	−	3.14791i	0.417623	−	0.122625i	−0.0661687	−	0.997808i	$-0.521078\pi$
$659$	10.7208	−	3.14791i	0.417623	−	0.122625i	0.483791	+	0.875183i	$0.339259\pi$
$660$	−4.87650	+	33.9168i	−0.189818	+	1.32021i
$661$	−6.64621	+	7.67013i	−0.258507	+	0.298334i	−0.870136	−	0.492811i	$-0.835969\pi$
$661$	−6.64621	+	7.67013i	−0.258507	+	0.298334i	0.611629	+	0.791145i	$0.290515\pi$
$662$	−70.3710	+	45.2247i	−2.73505	+	1.75771i
$663$	−14.4043	−	16.6234i	−0.559416	−	0.645600i
$664$	75.5178	+	22.1740i	2.93066	+	0.860519i
$665$	−8.95238	+	19.6030i	−0.347158	+	0.760171i
$666$	−26.0705			−1.01021
$667$	−13.8617	+	24.6136i	−0.536728	+	0.953042i
$668$	−4.42653			−0.171267
$669$	17.5196	−	38.3626i	0.677347	−	1.48318i
$670$	−11.5349	−	3.38695i	−0.445631	−	0.130849i
$671$	6.97518	+	8.04979i	0.269274	+	0.310759i
$672$	12.5115	−	8.04065i	0.482641	−	0.310175i
$673$	−8.00289	+	9.23582i	−0.308489	+	0.356015i	−0.888731	−	0.458429i	$-0.848412\pi$
$673$	−8.00289	+	9.23582i	−0.308489	+	0.356015i	0.580242	+	0.814444i	$0.302958\pi$
$674$	−12.4159	+	86.3544i	−0.478242	+	3.32625i
$675$	−1.93896	+	0.569330i	−0.0746306	+	0.0219135i
$676$	−32.9142	−	21.1527i	−1.26593	−	0.813564i
$677$	−3.16767	−	22.0316i	−0.121743	−	0.846743i	−0.955580	−	0.294732i	$-0.904770\pi$
$677$	−3.16767	−	22.0316i	−0.121743	−	0.846743i	0.833837	−	0.552011i	$-0.186139\pi$
$678$	4.16261	+	9.11484i	0.159864	+	0.350053i
$679$	−24.2958	−	53.2003i	−0.932386	−	2.04164i
$680$	−3.90588	−	27.1660i	−0.149784	−	1.04177i
$681$	42.4667	+	27.2917i	1.62733	+	1.04582i
$682$	−16.5677	+	4.86472i	−0.634411	+	0.186280i
$683$	−6.60778	+	45.9581i	−0.252840	+	1.75854i	0.328149	+	0.944626i	$0.393575\pi$
$683$	−6.60778	+	45.9581i	−0.252840	+	1.75854i	−0.580988	+	0.813912i	$0.697334\pi$
$684$	28.3908	−	32.7648i	1.08555	−	1.25279i
$685$	3.83964	−	2.46758i	0.146705	−	0.0942815i
$686$	34.1485	+	39.4095i	1.30380	+	1.50466i
$687$	20.7200	+	6.08394i	0.790517	+	0.232117i
$688$	−0.708259	+	1.55087i	−0.0270021	+	0.0591264i
$689$	5.41473			0.206285
$690$	−1.56547	−	26.8225i	−0.0595963	−	1.02111i
$691$	25.6092			0.974222			0.487111	−	0.873340i	$-0.338051\pi$
$691$	25.6092			0.974222			0.487111	+	0.873340i	$0.338051\pi$
$692$	18.4064	−	40.3045i	0.699708	−	1.53215i
$693$	32.0685	+	9.41616i	1.21818	+	0.357690i
$694$	−23.7842	−	27.4484i	−0.902836	−	1.04193i
$695$	14.0060	−	9.00111i	0.531278	−	0.341431i
$696$	46.4061	−	53.5555i	1.75902	−	2.03002i
$697$	−2.39573	+	16.6627i	−0.0907447	+	0.631143i
$698$	−41.4926	+	12.1833i	−1.57052	+	0.461146i
$699$	−49.3635	−	31.7240i	−1.86710	−	1.19991i
$700$	−2.56228	−	17.8211i	−0.0968452	−	0.673573i
$701$	−12.0572	−	26.4017i	−0.455396	−	0.997177i	−0.988513	−	0.151136i	$-0.951707\pi$
$701$	−12.0572	−	26.4017i	−0.455396	−	0.997177i	0.533117	−	0.846041i	$-0.321020\pi$
$702$	−3.93074	−	8.60712i	−0.148356	−	0.324855i
$703$	3.52796	+	24.5375i	0.133059	+	0.925449i
$704$	18.6203	+	11.9665i	0.701779	+	0.451006i
$705$	−4.10168	+	1.20436i	−0.154478	+	0.0453589i
$706$	−4.12052	+	28.6588i	−0.155078	+	1.07859i
$707$	29.0115	−	33.4810i	1.09109	−	1.25918i
$708$	−111.829	+	71.8679i	−4.20278	+	2.70096i
$709$	4.15842	+	4.79907i	0.156173	+	0.180233i	0.828444	−	0.560072i	$-0.189227\pi$
$709$	4.15842	+	4.79907i	0.156173	+	0.180233i	−0.672271	+	0.740305i	$0.734681\pi$
$710$	−19.0280	−	5.58712i	−0.714107	−	0.209681i
$711$	−3.21881	+	7.04821i	−0.120715	+	0.264328i
$712$	−25.8023			−0.966981
$713$	8.07385	−	4.27230i	0.302368	−	0.159999i
$714$	−125.363			−4.69158
$715$	−2.86848	+	6.28109i	−0.107275	+	0.234899i
$716$	6.00738	+	1.76392i	0.224506	+	0.0659210i
$717$	18.9459	+	21.8648i	0.707549	+	0.816555i
$718$	55.1014	−	35.4115i	2.05637	−	1.32155i
$719$	1.56147	−	1.80204i	0.0582332	−	0.0672047i	−0.725886	−	0.687815i	$-0.758570\pi$
$719$	1.56147	−	1.80204i	0.0582332	−	0.0672047i	0.784119	+	0.620611i	$0.213115\pi$
$720$	−1.47029	+	10.2261i	−0.0547945	+	0.381104i
$721$	−7.45449	+	2.18884i	−0.277620	+	0.0815165i
$722$	−11.7733	−	7.56625i	−0.438157	−	0.281587i
$723$	6.13901	+	42.6977i	0.228312	+	1.58795i
$724$	5.29833	+	11.6017i	0.196911	+	0.431175i
$725$	−2.44688	−	5.35793i	−0.0908749	−	0.198988i
$726$	−1.88891	−	13.1377i	−0.0701042	−	0.487585i
$727$	8.59578	+	5.52417i	0.318800	+	0.204880i	0.690247	−	0.723574i	$-0.257502\pi$
$727$	8.59578	+	5.52417i	0.318800	+	0.204880i	−0.371447	+	0.928454i	$0.621138\pi$
$728$	41.8818	−	12.2976i	1.55224	−	0.455779i
$729$	1.31182	−	9.12392i	0.0485860	−	0.337923i
$730$	14.3969	−	16.6149i	0.532854	−	0.614946i
$731$	1.50685	−	0.968396i	0.0557330	−	0.0358174i
$732$	17.8777	+	20.6319i	0.660777	+	0.762578i
$733$	43.9363	+	12.9009i	1.62283	+	0.476504i	0.961776	−	0.273838i	$-0.0882932\pi$
$733$	43.9363	+	12.9009i	1.62283	+	0.476504i	0.661049	+	0.750342i	$0.270111\pi$
$734$	35.6267	−	78.0117i	1.31501	−	2.87946i
$735$	−26.7643			−0.987215
$736$	6.77915	+	2.63017i	0.249883	+	0.0969494i
$737$	17.7286			0.653043
$738$	7.08283	−	15.5092i	0.260723	−	0.570903i
$739$	13.8662	+	4.07149i	0.510077	+	0.149772i	0.526636	−	0.850091i	$-0.323453\pi$
$739$	13.8662	+	4.07149i	0.510077	+	0.149772i	−0.0165592	+	0.999863i	$0.505271\pi$
$740$	−13.5626	−	15.6521i	−0.498571	−	0.575382i
$741$	17.8209	−	11.4528i	0.654668	−	0.420730i
$742$	20.2093	−	23.3228i	0.741907	−	0.856206i
$743$	−2.44968	+	17.0379i	−0.0898701	+	0.625060i	0.894252	+	0.447565i	$0.147709\pi$
$743$	−2.44968	+	17.0379i	−0.0898701	+	0.625060i	−0.984122	+	0.177496i	$0.943200\pi$
$744$	−21.9867	+	6.45587i	−0.806071	+	0.236684i
$745$	1.91176	+	1.22861i	0.0700413	+	0.0450128i
$746$	10.9345	+	76.0514i	0.400342	+	2.78444i
$747$	12.9303	+	28.3134i	0.473096	+	1.03593i
$748$	32.4723	+	71.1044i	1.18731	+	2.59984i
$749$	−10.4727	−	72.8394i	−0.382665	−	2.66149i
$750$	4.71303	+	3.02888i	0.172096	+	0.110599i
$751$	28.2286	−	8.28865i	1.03007	−	0.302457i	0.277334	−	0.960774i	$-0.410549\pi$
$751$	28.2286	−	8.28865i	1.03007	−	0.302457i	0.752741	+	0.658316i	$0.228731\pi$
$752$	1.32102	−	9.18787i	0.0481725	−	0.335047i
$753$	30.5987	−	35.3128i	1.11508	−	1.28687i
$754$	23.2019	−	14.9109i	0.844962	−	0.543024i
$755$	6.02038	+	6.94789i	0.219104	+	0.252859i
$756$	−34.9097	−	10.2504i	−1.26965	−	0.372804i
$757$	3.00422	−	6.57832i	0.109190	−	0.239093i	−0.847147	−	0.531358i	$-0.821682\pi$
$757$	3.00422	−	6.57832i	0.109190	−	0.239093i	0.956337	+	0.292265i	$0.0944090\pi$
$758$	18.2938			0.664460
$759$	13.3591	+	37.3025i	0.484903	+	1.35399i
$760$	26.4320			0.958788
$761$	15.5339	−	34.0145i	0.563104	−	1.23302i	−0.387285	−	0.921960i	$-0.626587\pi$
$761$	15.5339	−	34.0145i	0.563104	−	1.23302i	0.950389	−	0.311065i	$-0.100686\pi$
$762$	−69.4849	−	20.4026i	−2.51717	−	0.739108i
$763$	−5.22206	−	6.02658i	−0.189051	−	0.218177i
$764$	1.18100	−	0.758980i	0.0427269	−	0.0274589i
$765$	7.10782	−	8.20286i	0.256984	−	0.296575i
$766$	2.15596	−	14.9950i	0.0778981	−	0.541793i
$767$	−25.7027	+	7.54699i	−0.928070	+	0.272506i
$768$	62.0165	+	39.8556i	2.23783	+	1.43816i
$769$	6.08301	+	42.3083i	0.219359	+	1.52568i	0.740414	+	0.672152i	$0.234630\pi$
$769$	6.08301	+	42.3083i	0.219359	+	1.52568i	−0.521055	+	0.853523i	$0.674461\pi$
$770$	16.3485	+	35.7982i	0.589158	+	1.29008i
$771$	−0.289258	−	0.633388i	−0.0104174	−	0.0228109i
$772$	−1.65226	−	11.4917i	−0.0594661	−	0.413596i
$773$	−6.82067	−	4.38338i	−0.245322	−	0.157659i	0.412202	−	0.911093i	$-0.364760\pi$
$773$	−6.82067	−	4.38338i	−0.245322	−	0.157659i	−0.657524	+	0.753433i	$0.728396\pi$
$774$	−1.74070	+	0.511115i	−0.0625681	+	0.0183717i
$775$	−0.271064	+	1.88529i	−0.00973692	+	0.0677218i
$776$	−46.9754	+	54.2125i	−1.68632	+	1.94612i
$777$	−41.2062	+	26.4816i	−1.47826	+	0.950023i
$778$	−27.6870	−	31.9525i	−0.992626	−	1.14555i
$779$	−15.5557	−	4.56757i	−0.557342	−	0.163650i
$780$	−7.35202	+	16.0987i	−0.263244	+	0.576425i
$781$	29.2452			1.04648
$782$	−36.0854	−	49.5445i	−1.29041	−	1.77171i
$783$	−11.9030			−0.425380
$784$	24.1421	−	52.8639i	0.862219	−	1.88800i
$785$	−0.746718	−	0.219256i	−0.0266515	−	0.00782559i
$786$	−15.9752	−	18.4364i	−0.569818	−	0.657605i
$787$	−11.3159	+	7.27230i	−0.403369	+	0.259229i	−0.726558	−	0.687105i	$-0.758881\pi$
$787$	−11.3159	+	7.27230i	−0.403369	+	0.259229i	0.323189	+	0.946334i	$0.395245\pi$
$788$	45.2620	−	52.2351i	1.61239	−	1.86080i
$789$	−2.33632	+	16.2495i	−0.0831753	+	0.578497i
$790$	−8.75414	+	2.57045i	−0.311458	+	0.0914524i
$791$	6.53180	+	4.19774i	0.232244	+	0.149254i
$792$	−5.83391	−	40.5758i	−0.207299	−	1.44180i
$793$	2.28536	+	5.00424i	0.0811555	+	0.177706i
$794$	10.3788	+	22.7265i	0.368331	+	0.806532i
$795$	0.922009	+	6.41271i	0.0327003	+	0.227435i
$796$	−40.8600	−	26.2591i	−1.44824	−	0.930729i
$797$	8.86486	−	2.60296i	0.314009	−	0.0922014i	−0.120931	−	0.992661i	$-0.538588\pi$
$797$	8.86486	−	2.60296i	0.314009	−	0.0922014i	0.434940	+	0.900460i	$0.356770\pi$
$798$	17.1822	−	119.505i	0.608245	−	4.23043i
$799$	−6.38618	+	7.37005i	−0.225927	+	0.260734i
$800$	−1.27552	+	0.819726i	−0.0450964	+	0.0289817i
$801$	−6.68230	−	7.71179i	−0.236108	−	0.272483i
$802$	42.1839	+	12.3863i	1.48956	+	0.437376i
$803$	−13.4681	+	29.4911i	−0.475280	+	1.04072i
$804$	45.4392			1.60252
$805$	−12.2569	−	16.8285i	−0.432000	−	0.593127i
$806$	−8.91840			−0.314137
$807$	−13.3382	+	29.2066i	−0.469528	+	1.02812i
$808$	−52.1358	−	15.3084i	−1.83413	−	0.538549i
$809$	−13.5975	−	15.6924i	−0.478064	−	0.551716i	0.464573	−	0.885535i	$-0.346208\pi$
$809$	−13.5975	−	15.6924i	−0.478064	−	0.551716i	−0.942637	+	0.333819i	$0.891662\pi$
$810$	22.7002	−	14.5885i	0.797604	−	0.512589i
$811$	−8.10210	+	9.35032i	−0.284503	+	0.328334i	−0.879955	−	0.475057i	$-0.842428\pi$
$811$	−8.10210	+	9.35032i	−0.284503	+	0.328334i	0.595452	+	0.803391i	$0.296973\pi$
$812$	15.0924	−	104.970i	0.529639	−	3.68372i
$813$	26.7465	−	7.85349i	0.938042	−	0.275434i
$814$	38.0837	+	24.4749i	1.33483	+	0.857845i
$815$	−1.73826	−	12.0899i	−0.0608885	−	0.423489i
$816$	23.7395	+	51.9822i	0.831048	+	1.81974i
$817$	0.716618	+	1.56917i	0.0250713	+	0.0548985i
$818$	−6.38952	−	44.4401i	−0.223404	−	1.55381i
$819$	14.5221	+	9.33279i	0.507443	+	0.326114i
$820$	12.9960	−	3.81598i	0.453842	−	0.133260i
$821$	−3.84621	+	26.7510i	−0.134234	+	0.933616i	0.805716	+	0.592302i	$0.201781\pi$
$821$	−3.84621	+	26.7510i	−0.134234	+	0.933616i	−0.939950	+	0.341313i	$0.889128\pi$
$822$	−16.7450	+	19.3248i	−0.584049	+	0.674029i
$823$	48.0036	−	30.8501i	1.67330	−	1.07537i	0.780171	−	0.625566i	$-0.215132\pi$
$823$	48.0036	−	30.8501i	1.67330	−	1.07537i	0.893130	−	0.449799i	$-0.148505\pi$
$824$	6.24020	+	7.20157i	0.217388	+	0.250879i
$825$	−7.92719	−	2.32763i	−0.275989	−	0.0810378i
$826$	−63.4227	+	138.876i	−2.20676	+	4.83213i
$827$	−0.359368			−0.0124965			−0.00624823	−	0.999980i	$-0.501989\pi$
$827$	−0.359368			−0.0124965			−0.00624823	+	0.999980i	$0.501989\pi$
$828$	14.1211	+	39.4303i	0.490741	+	1.37030i
$829$	36.3737			1.26331			0.631655	−	0.775250i	$-0.282376\pi$
$829$	36.3737			1.26331			0.631655	+	0.775250i	$0.282376\pi$
$830$	−15.2254	+	33.3389i	−0.528480	+	1.15721i
$831$	−5.23724	−	1.53779i	−0.181678	−	0.0533454i
$832$	7.48643	+	8.63980i	0.259545	+	0.299531i
$833$	−51.3635	+	33.0093i	−1.77964	+	1.14371i
$834$	−61.0815	+	70.4918i	−2.11508	+	2.44093i
$835$	0.151891	−	1.05643i	0.00525641	−	0.0365591i
$836$	−72.2327	+	21.2094i	−2.49822	+	0.733544i
$837$	3.23800	+	2.08093i	0.111922	+	0.0719276i
$838$	2.92150	+	20.3195i	0.100921	+	0.701924i
$839$	−15.3035	−	33.5101i	−0.528337	−	1.15690i	−0.966186	−	0.257847i	$-0.916987\pi$
$839$	−15.3035	−	33.5101i	−0.528337	−	1.15690i	0.437849	−	0.899048i	$-0.355740\pi$
$840$	21.6957	+	47.5070i	0.748573	+	1.63915i
$841$	−0.810426	−	5.63664i	−0.0279457	−	0.194367i
$842$	23.1003	+	14.8457i	0.796091	+	0.511616i
$843$	43.5225	−	12.7794i	1.49900	−	0.440145i
$844$	−13.3167	+	92.6197i	−0.458380	+	3.18810i
$845$	6.17767	−	7.12941i	0.212518	−	0.245259i
$846$	8.30915	−	5.33997i	0.285675	−	0.183592i
$847$	−6.73494	−	7.77253i	−0.231415	−	0.267067i
$848$	−13.4979	−	3.96333i	−0.463518	−	0.136101i
$849$	−1.95696	+	4.28515i	−0.0671627	+	0.147066i
$850$	12.7804			0.438366
$851$	−22.3269	−	8.66238i	−0.765357	−	0.296943i
$852$	74.9567			2.56797
$853$	−14.7559	+	32.3109i	−0.505232	+	1.10630i	0.469501	+	0.882932i	$0.344434\pi$
$853$	−14.7559	+	32.3109i	−0.505232	+	1.10630i	−0.974733	+	0.223372i	$0.928294\pi$
$854$	30.0843	+	8.83355i	1.02946	+	0.302278i
$855$	6.84538	+	7.89999i	0.234107	+	0.270174i
$856$	−75.9294	+	48.7968i	−2.59521	+	1.66784i
$857$	13.2670	−	15.3109i	0.453191	−	0.523011i	−0.482469	−	0.875913i	$-0.660260\pi$
$857$	13.2670	−	15.3109i	0.453191	−	0.523011i	0.935660	+	0.352903i	$0.114805\pi$
$858$	5.50545	−	38.2912i	0.187953	−	1.30724i
$859$	−10.4413	+	3.06586i	−0.356254	+	0.104606i	−0.454962	−	0.890511i	$-0.650347\pi$
$859$	−10.4413	+	3.06586i	−0.356254	+	0.104606i	0.0987079	+	0.995116i	$0.468529\pi$
$860$	−1.21242	−	0.779175i	−0.0413432	−	0.0265697i
$861$	−4.55891	−	31.7079i	−0.155367	−	1.08060i
$862$	0.172670	+	0.378094i	0.00588115	+	0.0128779i
$863$	−10.9025	−	23.8732i	−0.371127	−	0.812654i	−0.999399	−	0.0346609i	$-0.988965\pi$
$863$	−10.9025	−	23.8732i	−0.371127	−	0.812654i	0.628272	−	0.777994i	$-0.283762\pi$
$864$	0.436051	+	3.03280i	0.0148348	+	0.103178i
$865$	8.98739	+	5.77585i	0.305581	+	0.196385i
$866$	−3.21625	+	0.944377i	−0.109293	+	0.0320913i
$867$	3.07755	−	21.4048i	0.104519	−	0.726945i
$868$	−22.4568	+	25.9165i	−0.762234	+	0.879665i
$869$	11.3189	−	7.27419i	0.383966	−	0.246760i
$870$	21.6099	+	24.9392i	0.732645	+	0.845518i
$871$	8.78584	+	2.57976i	0.297697	+	0.0874117i
$872$	−4.06302	+	8.89677i	−0.137591	+	0.301283i
$873$	−28.3688			−0.960139
$874$	52.1754	−	27.6087i	1.76486	−	0.933880i
$875$	4.34106			0.146755
$876$	−34.5193	+	75.5868i	−1.16630	+	2.55384i
$877$	−40.3742	−	11.8549i	−1.36334	−	0.400313i	−0.483402	−	0.875399i	$-0.660599\pi$
$877$	−40.3742	−	11.8549i	−1.36334	−	0.400313i	−0.879940	+	0.475086i	$0.842417\pi$
$878$	33.8084	+	39.0170i	1.14098	+	1.31676i
$879$	−1.22408	+	0.786669i	−0.0412872	+	0.0265337i
$880$	11.7480	−	13.5579i	0.396026	−	0.457038i
$881$	0.693059	−	4.82033i	0.0233497	−	0.162401i	−0.974810	−	0.223036i	$-0.928403\pi$
$881$	0.693059	−	4.82033i	0.0233497	−	0.162401i	0.998160	+	0.0606347i	$0.0193125\pi$
$882$	59.3345	−	17.4222i	1.99790	−	0.586635i
$883$	25.3793	+	16.3103i	0.854080	+	0.548884i	0.892845	−	0.450364i	$-0.148706\pi$
$883$	25.3793	+	16.3103i	0.854080	+	0.548884i	−0.0387645	+	0.999248i	$0.512342\pi$
$884$	5.74576	+	39.9626i	0.193251	+	1.34409i
$885$	−13.3146	−	29.1549i	−0.447565	−	0.980030i
$886$	8.17929	+	17.9101i	0.274789	+	0.601703i
$887$	−7.17570	−	49.9081i	−0.240936	−	1.67575i	−0.647453	−	0.762105i	$-0.724166\pi$
$887$	−7.17570	−	49.9081i	−0.240936	−	1.67575i	0.406517	−	0.913643i	$-0.366743\pi$
$888$	50.5401	+	32.4801i	1.69601	+	1.08996i
$889$	−53.8410	+	15.8091i	−1.80577	+	0.530222i
$890$	1.70996	−	11.8930i	0.0573180	−	0.398655i
$891$	−26.0589	+	30.0736i	−0.873006	+	1.00750i
$892$	−65.1214	+	41.8510i	−2.18043	+	1.40127i
$893$	−6.15039	−	7.09793i	−0.205815	−	0.237523i
$894$	−12.2158	−	3.58687i	−0.408556	−	0.119963i
$895$	−0.627111	+	1.37318i	−0.0209620	+	0.0459004i
$896$	78.3196			2.61647
$897$	1.19238	+	20.4300i	0.0398123	+	0.682139i
$898$	−86.9398			−2.90122
$899$	−4.66053	+	10.2051i	−0.155437	+	0.340360i
$900$	−8.37937	−	2.46040i	−0.279312	−	0.0820135i
$901$	9.67847	+	11.1695i	0.322436	+	0.372112i
$902$	−24.9066	+	16.0065i	−0.829299	+	0.532958i
$903$	−2.23212	+	2.57600i	−0.0742802	+	0.0857239i
$904$	1.35528	−	9.42619i	0.0450760	−	0.313511i
$905$	−2.95065	+	0.866390i	−0.0980830	+	0.0287998i
$906$	−43.3286	−	27.8456i	−1.43950	−	0.925109i
$907$	−6.03257	−	41.9575i	−0.200308	−	1.39317i	−0.803370	−	0.595480i	$-0.796962\pi$
$907$	−6.03257	−	41.9575i	−0.200308	−	1.39317i	0.603062	−	0.797694i	$-0.293947\pi$
$908$	−38.4909	−	84.2834i	−1.27737	−	2.79704i
$909$	−8.92679	−	19.5470i	−0.296083	−	0.648331i
$910$	2.89275	+	20.1195i	0.0958938	+	0.666956i
$911$	−15.2309	−	9.78832i	−0.504623	−	0.324301i	0.263440	−	0.964676i	$-0.415143\pi$
$911$	−15.2309	−	9.78832i	−0.504623	−	0.324301i	−0.768063	+	0.640374i	$0.778779\pi$
$912$	−52.8071	+	15.5055i	−1.74862	+	0.513440i
$913$	7.69201	−	53.4991i	0.254568	−	1.77056i
$914$	−1.08737	+	1.25489i	−0.0359669	+	0.0415080i
$915$	−5.53742	+	3.55869i	−0.183062	+	0.117647i
$916$	−25.9568	−	29.9558i	−0.857637	−	0.989766i
$917$	−18.1369	−	5.32547i	−0.598933	−	0.175863i
$918$	10.7289	−	23.4930i	0.354107	−	0.775386i
$919$	43.7267			1.44241			0.721205	−	0.692721i	$-0.243588\pi$
$919$	43.7267			1.44241			0.721205	+	0.692721i	$0.243588\pi$
$920$	−12.5301	+	22.2492i	−0.413106	+	0.733533i
$921$	−65.2404			−2.14974
$922$	16.3306	−	35.7591i	0.537820	−	1.17766i
$923$	14.4931	+	4.25557i	0.477048	+	0.140074i
$924$	−97.4100	−	112.417i	−3.20455	−	3.69825i
$925$	4.20088	−	2.69974i	0.138124	−	0.0887670i
$926$	43.4170	−	50.1059i	1.42677	−	1.64658i
$927$	−0.536314	+	3.73014i	−0.0176149	+	0.122514i
$928$	−8.56905	+	2.51610i	−0.281293	+	0.0825950i
$929$	18.3125	+	11.7688i	0.600815	+	0.386120i	0.805403	−	0.592728i	$-0.201949\pi$
$929$	18.3125	+	11.7688i	0.600815	+	0.386120i	−0.204588	+	0.978848i	$0.565585\pi$
$930$	−1.51861	−	10.5622i	−0.0497971	−	0.346347i
$931$	−24.4271	−	53.4878i	−0.800565	−	1.75299i
$932$	44.7421	+	97.9715i	1.46557	+	3.20916i
$933$	0.542557	+	3.77357i	0.0177625	+	0.123541i
$934$	−81.1870	−	52.1757i	−2.65652	−	1.70724i
$935$	−18.0839	+	5.30991i	−0.591407	+	0.173653i
$936$	3.01319	−	20.9572i	0.0984891	−	0.685007i
$937$	−13.0126	+	15.0173i	−0.425102	+	0.490593i	−0.927384	−	0.374110i	$-0.877948\pi$
$937$	−13.0126	+	15.0173i	−0.425102	+	0.490593i	0.502283	+	0.864703i	$0.332494\pi$
$938$	43.9030	−	28.2148i	1.43349	−	0.921245i
$939$	−14.9817	−	17.2898i	−0.488909	−	0.564231i
$940$	7.52863	+	2.21061i	0.245557	+	0.0721020i
$941$	−2.78034	+	6.08810i	−0.0906366	+	0.198467i	−0.949521	−	0.313702i	$-0.898431\pi$
$941$	−2.78034	+	6.08810i	−0.0906366	+	0.198467i	0.858885	+	0.512169i	$0.171158\pi$
$942$	4.36002			0.142057
$943$	11.2190	−	10.9288i	0.365341	−	0.355891i
$944$	69.5959			2.26515
$945$	3.64423	−	7.97975i	0.118547	−	0.259581i
$946$	3.02264	+	0.887527i	0.0982745	+	0.0288560i
$947$	−32.9331	−	38.0068i	−1.07018	−	1.23505i	−0.970771	−	0.240008i	$-0.922850\pi$
$947$	−32.9331	−	38.0068i	−1.07018	−	1.23505i	−0.0994104	−	0.995047i	$-0.531696\pi$
$948$	29.0107	−	18.6440i	0.942223	−	0.605530i
$949$	−10.9658	+	12.6552i	−0.355964	+	0.410805i
$950$	−1.75169	+	12.1833i	−0.0568324	+	0.395278i
$951$	25.0500	−	7.35533i	0.812301	−	0.238513i
$952$	100.229	+	64.4130i	3.24843	+	2.08764i
$953$	−7.94522	−	55.2602i	−0.257371	−	1.79005i	−0.551383	−	0.834252i	$-0.685900\pi$
$953$	−7.94522	−	55.2602i	−0.257371	−	1.79005i	0.294012	−	0.955802i	$-0.405009\pi$
$954$	−6.21838	−	13.6164i	−0.201327	−	0.440846i
$955$	0.140612	+	0.307898i	0.00455010	+	0.00996334i
$956$	−7.55739	−	52.5628i	−0.244423	−	1.70000i
$957$	−40.9388	−	26.3098i	−1.32336	−	0.850475i
$958$	21.7678	−	6.39160i	0.703286	−	0.206503i
$959$	−2.81974	+	19.6117i	−0.0910543	+	0.633296i
$960$	−8.95743	+	10.3374i	−0.289100	+	0.333639i
$961$	−23.0270	+	14.7985i	−0.742805	+	0.477372i
$962$	15.3118	+	17.6708i	0.493673	+	0.569729i
$963$	−34.2487	−	10.0563i	−1.10365	−	0.324061i
$964$	32.8916	−	72.0225i	1.05937	−	2.31969i
$965$	2.79928			0.0901122
$966$	92.4483	+	71.1148i	2.97448	+	2.28808i
$967$	−43.9121			−1.41212			−0.706059	−	0.708153i	$-0.749529\pi$
$967$	−43.9121			−1.41212			−0.706059	+	0.708153i	$0.749529\pi$
$968$	−5.24011	+	11.4742i	−0.168423	+	0.368796i
$969$	55.4787	+	16.2900i	1.78223	+	0.523311i
$970$	−21.8750	−	25.2451i	−0.702365	−	0.810572i
$971$	−36.9653	+	23.7562i	−1.18627	+	0.762371i	−0.976529	−	0.215385i	$-0.930899\pi$
$971$	−36.9653	+	23.7562i	−1.18627	+	0.762371i	−0.209744	+	0.977756i	$0.567263\pi$
$972$	−50.3243	+	58.0774i	−1.61415	+	1.86283i
$973$	−10.2857	+	71.5385i	−0.329744	+	2.29342i
$974$	63.5638	−	18.6640i	2.03672	−	0.598034i
$975$	−3.58980	−	2.30703i	−0.114966	−	0.0738840i
$976$	−2.03409	−	14.1474i	−0.0651095	−	0.452846i
$977$	7.08667	+	15.5176i	0.226723	+	0.496453i	0.988469	−	0.151422i	$-0.0483852\pi$
$977$	7.08667	+	15.5176i	0.226723	+	0.496453i	−0.761747	+	0.647875i	$0.775658\pi$
$978$	28.4263	+	62.2448i	0.908971	+	1.99037i
$979$	2.52168	+	17.5387i	0.0805932	+	0.560538i
$980$	41.3273	+	26.5594i	1.32015	+	0.848410i
$981$	−3.71131	+	1.08974i	−0.118493	+	0.0347927i
$982$	6.62984	−	46.1115i	0.211567	−	1.47148i
$983$	−15.7512	+	18.1778i	−0.502384	+	0.579782i	−0.949132	−	0.314877i	$-0.898037\pi$
$983$	−15.7512	+	18.1778i	−0.502384	+	0.579782i	0.446748	+	0.894660i	$0.352582\pi$
$984$	−33.0530	+	21.2419i	−1.05369	+	0.677167i
$985$	10.9132	+	12.5945i	0.347724	+	0.401295i
$986$	72.2302	+	21.2087i	2.30028	+	0.675423i
$987$	7.70900	−	16.8804i	0.245380	−	0.537308i
$988$	−38.8829			−1.23703
$989$	−1.66057	−	0.140656i	−0.0528030	−	0.00447261i
$990$	19.0892			0.606695
$991$	−19.5078	+	42.7162i	−0.619687	+	1.35692i	0.296060	+	0.955169i	$0.404327\pi$
$991$	−19.5078	+	42.7162i	−0.619687	+	1.35692i	−0.915747	+	0.401756i	$0.868400\pi$
$992$	2.77092	+	0.813615i	0.0879768	+	0.0258323i
$993$	49.9223	+	57.6134i	1.58424	+	1.82831i
$994$	72.4226	−	46.5432i	2.29710	−	1.47626i
$995$	7.66901	−	8.85051i	0.243124	−	0.280580i
$996$	19.7149	−	137.120i	0.624691	−	4.34482i
$997$	34.6377	−	10.1706i	1.09699	−	0.322105i	0.317333	−	0.948314i	$-0.397213\pi$
$997$	34.6377	−	10.1706i	1.09699	−	0.322105i	0.779655	+	0.626209i	$0.215395\pi$
$998$	54.7053	+	35.1570i	1.73167	+	1.11288i
$999$	−1.43612	−	9.98844i	−0.0454368	−	0.316020i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.2.g.c.6.1	✓	50
5.2	odd	4		575.2.p.d.374.1		100
5.3	odd	4		575.2.p.d.374.10		100
5.4	even	2		575.2.k.d.351.5		50
23.2	even	11		2645.2.a.y.1.2		25
23.4	even	11	inner	115.2.g.c.96.1	yes	50
23.21	odd	22		2645.2.a.x.1.2		25
115.4	even	22		575.2.k.d.326.5		50
115.27	odd	44		575.2.p.d.349.10		100
115.73	odd	44		575.2.p.d.349.1		100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.g.c.6.1	✓	50	1.1	even	1	trivial
115.2.g.c.96.1	yes	50	23.4	even	11	inner
575.2.k.d.326.5		50	115.4	even	22
575.2.k.d.351.5		50	5.4	even	2
575.2.p.d.349.1		100	115.73	odd	44
575.2.p.d.349.10		100	115.27	odd	44
575.2.p.d.374.1		100	5.2	odd	4
575.2.p.d.374.10		100	5.3	odd	4
2645.2.a.x.1.2		25	23.21	odd	22
2645.2.a.y.1.2		25	23.2	even	11

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	115.g (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.02998 + 2.25535i) q^{2} +(2.16804 + 0.636595i) q^{3} +(-2.71600 - 3.13443i) q^{4} +(0.841254 - 0.540641i) q^{5} +(-3.66879 + 4.23400i) q^{6} +(-0.617798 + 4.29688i) q^{7} +(5.10871 - 1.50005i) q^{8} +(1.77140 + 1.13841i) q^{9} +O(q^{10})\)	\(q+(-1.02998 + 2.25535i) q^{2} +(2.16804 + 0.636595i) q^{3} +(-2.71600 - 3.13443i) q^{4} +(0.841254 - 0.540641i) q^{5} +(-3.66879 + 4.23400i) q^{6} +(-0.617798 + 4.29688i) q^{7} +(5.10871 - 1.50005i) q^{8} +(1.77140 + 1.13841i) q^{9} +(0.352856 + 2.45417i) q^{10} +(-1.51892 - 3.32596i) q^{11} +(-3.89304 - 8.52457i) q^{12} +(-0.268762 - 1.86928i) q^{13} +(-9.05463 - 5.81905i) q^{14} +(2.16804 - 0.636595i) q^{15} +(-0.698255 + 4.85647i) q^{16} +(3.37557 - 3.89562i) q^{17} +(-4.39201 + 2.82257i) q^{18} +(3.25094 + 3.75178i) q^{19} +(-3.97944 - 1.16847i) q^{20} +(-4.07478 + 8.92253i) q^{21} +9.06565 q^{22} +(-4.69919 + 0.957943i) q^{23} +12.0308 q^{24} +(0.415415 - 0.909632i) q^{25} +(4.49269 + 1.31917i) q^{26} +(-1.32335 - 1.52723i) q^{27} +(15.1462 - 9.73387i) q^{28} +(3.85727 - 4.45153i) q^{29} +(-0.797303 + 5.54537i) q^{30} +(-1.82753 + 0.536611i) q^{31} +(-1.27552 - 0.819726i) q^{32} +(-1.17578 - 8.17776i) q^{33} +(5.30919 + 11.6255i) q^{34} +(1.80334 + 3.94877i) q^{35} +(-1.24285 - 8.64423i) q^{36} +(4.20088 + 2.69974i) q^{37} +(-11.8100 + 3.46772i) q^{38} +(0.607287 - 4.22377i) q^{39} +(3.48673 - 4.02390i) q^{40} +(-2.74736 + 1.76562i) q^{41} +(-15.9264 - 18.3801i) q^{42} +(0.333417 + 0.0979000i) q^{43} +(-6.29962 + 13.7942i) q^{44} +2.10566 q^{45} +(2.67958 - 11.5850i) q^{46} -1.89188 q^{47} +(-4.60545 + 10.0845i) q^{48} +(-11.3650 - 3.33708i) q^{49} +(1.62366 + 1.87381i) q^{50} +(9.79832 - 6.29700i) q^{51} +(-5.12917 + 5.91938i) q^{52} +(-0.408046 + 2.83802i) q^{53} +(4.80747 - 1.41160i) q^{54} +(-3.07594 - 1.97679i) q^{55} +(3.28939 + 22.8782i) q^{56} +(4.65981 + 10.2036i) q^{57} +(6.06681 + 13.2845i) q^{58} +(-2.01869 - 14.0403i) q^{59} +(-7.88376 - 5.06659i) q^{60} +(-2.79510 + 0.820714i) q^{61} +(0.672078 - 4.67441i) q^{62} +(-5.98596 + 6.90817i) q^{63} +(-5.09255 + 3.27278i) q^{64} +(-1.23671 - 1.42723i) q^{65} +(19.6547 + 5.77115i) q^{66} +(-2.01422 + 4.41052i) q^{67} -21.3786 q^{68} +(-10.7979 - 0.914617i) q^{69} -10.7633 q^{70} +(-3.32266 + 7.27561i) q^{71} +(10.7572 + 3.15861i) q^{72} +(-5.80660 - 6.70118i) q^{73} +(-10.4157 + 6.69375i) q^{74} +(1.47970 - 1.70767i) q^{75} +(2.93016 - 20.3797i) q^{76} +(15.2296 - 4.47182i) q^{77} +(8.90057 + 5.72005i) q^{78} +(0.523690 + 3.64234i) q^{79} +(2.03820 + 4.46303i) q^{80} +(-4.52103 - 9.89968i) q^{81} +(-1.15235 - 8.01480i) q^{82} +(12.4356 + 7.99184i) q^{83} +(39.0342 - 11.4615i) q^{84} +(0.733582 - 5.10218i) q^{85} +(-0.564211 + 0.651135i) q^{86} +(11.1965 - 7.19558i) q^{87} +(-12.7488 - 14.7129i) q^{88} +(-4.64976 - 1.36529i) q^{89} +(-2.16879 + 4.74900i) q^{90} +8.19811 q^{91} +(15.7656 + 12.1275i) q^{92} -4.30376 q^{93} +(1.94860 - 4.26684i) q^{94} +(4.76323 + 1.39861i) q^{95} +(-2.24355 - 2.58919i) q^{96} +(-11.3339 + 7.28385i) q^{97} +(19.2320 - 22.1950i) q^{98} +(1.09570 - 7.62074i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 5 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 11 q^{6} - 5 q^{7} - 2 q^{8} + 3 q^{9}+O(q^{10}) \) 50 * q - 5 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 11 * q^6 - 5 * q^7 - 2 * q^8 + 3 * q^9	\( 50 q - 5 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 11 q^{6} - 5 q^{7} - 2 q^{8} + 3 q^{9} - 5 q^{10} - 16 q^{11} - 9 q^{12} - 14 q^{13} - 12 q^{14} - 2 q^{15} + 27 q^{16} + 38 q^{17} - 42 q^{18} - 5 q^{19} - 11 q^{20} - 9 q^{21} + 6 q^{22} - 8 q^{23} + 102 q^{24} - 5 q^{25} - 19 q^{26} + 7 q^{27} - 34 q^{28} - 38 q^{29} - 11 q^{30} + 2 q^{31} + 49 q^{32} - 2 q^{33} - 31 q^{34} + 6 q^{35} - 59 q^{36} - 35 q^{37} + 30 q^{38} + 32 q^{39} + 42 q^{40} - 11 q^{41} - 102 q^{42} + 6 q^{43} - 55 q^{44} + 58 q^{45} + 153 q^{46} - 10 q^{47} + 84 q^{48} + 6 q^{50} - 20 q^{51} - 97 q^{52} - 29 q^{53} + 19 q^{54} + 17 q^{55} + 77 q^{56} - 49 q^{57} - 12 q^{58} - 50 q^{59} + 2 q^{60} + 4 q^{61} + 126 q^{62} + 74 q^{63} - 44 q^{64} - 14 q^{65} - 144 q^{66} - 43 q^{67} + 54 q^{68} - 50 q^{69} - 12 q^{70} - 25 q^{71} - 14 q^{72} - 20 q^{73} - 47 q^{74} - 2 q^{75} - 26 q^{76} + 150 q^{77} + 174 q^{78} + 72 q^{79} - 28 q^{80} - 71 q^{81} - 11 q^{82} + 36 q^{83} + 100 q^{84} - 6 q^{85} - 20 q^{86} + 85 q^{87} - 45 q^{88} - 24 q^{89} - 42 q^{90} + 38 q^{91} + 74 q^{92} + 100 q^{93} + 150 q^{94} - 5 q^{95} - 169 q^{96} - 14 q^{97} - 44 q^{98} + 36 q^{99}+O(q^{100}) \) 50 * q - 5 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 11 * q^6 - 5 * q^7 - 2 * q^8 + 3 * q^9 - 5 * q^10 - 16 * q^11 - 9 * q^12 - 14 * q^13 - 12 * q^14 - 2 * q^15 + 27 * q^16 + 38 * q^17 - 42 * q^18 - 5 * q^19 - 11 * q^20 - 9 * q^21 + 6 * q^22 - 8 * q^23 + 102 * q^24 - 5 * q^25 - 19 * q^26 + 7 * q^27 - 34 * q^28 - 38 * q^29 - 11 * q^30 + 2 * q^31 + 49 * q^32 - 2 * q^33 - 31 * q^34 + 6 * q^35 - 59 * q^36 - 35 * q^37 + 30 * q^38 + 32 * q^39 + 42 * q^40 - 11 * q^41 - 102 * q^42 + 6 * q^43 - 55 * q^44 + 58 * q^45 + 153 * q^46 - 10 * q^47 + 84 * q^48 + 6 * q^50 - 20 * q^51 - 97 * q^52 - 29 * q^53 + 19 * q^54 + 17 * q^55 + 77 * q^56 - 49 * q^57 - 12 * q^58 - 50 * q^59 + 2 * q^60 + 4 * q^61 + 126 * q^62 + 74 * q^63 - 44 * q^64 - 14 * q^65 - 144 * q^66 - 43 * q^67 + 54 * q^68 - 50 * q^69 - 12 * q^70 - 25 * q^71 - 14 * q^72 - 20 * q^73 - 47 * q^74 - 2 * q^75 - 26 * q^76 + 150 * q^77 + 174 * q^78 + 72 * q^79 - 28 * q^80 - 71 * q^81 - 11 * q^82 + 36 * q^83 + 100 * q^84 - 6 * q^85 - 20 * q^86 + 85 * q^87 - 45 * q^88 - 24 * q^89 - 42 * q^90 + 38 * q^91 + 74 * q^92 + 100 * q^93 + 150 * q^94 - 5 * q^95 - 169 * q^96 - 14 * q^97 - 44 * q^98 + 36 * q^99

Introduction

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