LMFDB - Embedded newform 507.2.m.a.40.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(40,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(26))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("507.40");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.m (of order $13$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$180$
Relative dimension:	$15$ over $\Q(\zeta_{13})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{13}]$

Embedding invariants

Embedding label			40.4
Character	$\chi$	$=$	507.40
Dual form			507.2.m.a.469.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.73397 - 0.427384i) q^{2} +(-0.120537 + 0.992709i) q^{3} +(1.05307 + 0.552694i) q^{4} +(0.457873 - 0.663343i) q^{5} +(0.633275 - 1.66981i) q^{6} +(-0.852902 - 0.755605i) q^{7} +(1.08370 + 0.960071i) q^{8} +(-0.970942 - 0.239316i) q^{9} +O(q^{10})$	\(q+(-1.73397 - 0.427384i) q^{2} +(-0.120537 + 0.992709i) q^{3} +(1.05307 + 0.552694i) q^{4} +(0.457873 - 0.663343i) q^{5} +(0.633275 - 1.66981i) q^{6} +(-0.852902 - 0.755605i) q^{7} +(1.08370 + 0.960071i) q^{8} +(-0.970942 - 0.239316i) q^{9} +(-1.07744 + 0.954527i) q^{10} +(-3.01609 + 0.743398i) q^{11} +(-0.675597 + 0.978772i) q^{12} +(2.28746 - 2.78703i) q^{13} +(1.15597 + 1.67471i) q^{14} +(0.603316 + 0.534492i) q^{15} +(-2.81997 - 4.08543i) q^{16} +(-0.450342 - 0.398968i) q^{17} +(1.58130 + 0.829931i) q^{18} +1.30918 q^{19} +(0.848798 - 0.445483i) q^{20} +(0.852902 - 0.755605i) q^{21} +5.54751 q^{22} -6.64668 q^{23} +(-1.08370 + 0.960071i) q^{24} +(1.54265 + 4.06763i) q^{25} +(-5.15751 + 3.85499i) q^{26} +(0.354605 - 0.935016i) q^{27} +(-0.480547 - 1.26710i) q^{28} +(-0.672147 - 0.165669i) q^{29} +(-0.817697 - 1.18464i) q^{30} +(2.17770 - 5.74211i) q^{31} +(2.11689 + 5.58177i) q^{32} +(-0.374429 - 3.08370i) q^{33} +(0.610364 + 0.884266i) q^{34} +(-0.891746 + 0.219796i) q^{35} +(-0.890201 - 0.788650i) q^{36} +(3.51137 - 9.25872i) q^{37} +(-2.27008 - 0.559525i) q^{38} +(2.49098 + 2.60672i) q^{39} +(1.13305 - 0.279272i) q^{40} +(1.10627 - 9.11099i) q^{41} +(-1.80184 + 0.945677i) q^{42} +(-4.12983 - 10.8895i) q^{43} +(-3.58702 - 0.884121i) q^{44} +(-0.603316 + 0.534492i) q^{45} +(11.5251 + 2.84069i) q^{46} +(-7.85747 + 4.12392i) q^{47} +(4.39555 - 2.30696i) q^{48} +(-0.687254 - 5.66005i) q^{49} +(-0.936459 - 7.71243i) q^{50} +(0.450342 - 0.398968i) q^{51} +(3.94923 - 1.67067i) q^{52} +(-3.86911 - 3.42773i) q^{53} +(-1.01448 + 1.46973i) q^{54} +(-0.887855 + 2.34108i) q^{55} +(-0.198852 - 1.63769i) q^{56} +(-0.157805 + 1.29964i) q^{57} +(1.09468 + 0.574530i) q^{58} +(3.07179 - 4.45026i) q^{59} +(0.339924 + 0.896306i) q^{60} +(-10.4963 + 9.29895i) q^{61} +(-6.23014 + 9.02592i) q^{62} +(0.647290 + 0.937761i) q^{63} +(-0.0883196 - 0.727377i) q^{64} +(-0.801389 - 2.79348i) q^{65} +(-0.668678 + 5.50706i) q^{66} +(-7.54969 + 3.96238i) q^{67} +(-0.253734 - 0.669042i) q^{68} +(0.801169 - 6.59822i) q^{69} +1.64020 q^{70} +(1.71956 - 14.1618i) q^{71} +(-0.822446 - 1.19152i) q^{72} +(11.0269 - 2.71789i) q^{73} +(-10.0456 + 14.5536i) q^{74} +(-4.22392 + 1.04110i) q^{75} +(1.37866 + 0.723578i) q^{76} +(3.13414 + 1.64492i) q^{77} +(-3.20521 - 5.58458i) q^{78} +(1.73507 - 0.910637i) q^{79} -4.00123 q^{80} +(0.885456 + 0.464723i) q^{81} +(-5.81214 + 15.3253i) q^{82} +(0.185566 + 1.52827i) q^{83} +(1.31578 - 0.324311i) q^{84} +(-0.470852 + 0.116055i) q^{85} +(2.50700 + 20.6470i) q^{86} +(0.245480 - 0.647277i) q^{87} +(-3.98224 - 2.09004i) q^{88} +5.56869 q^{89} +(1.27456 - 0.668943i) q^{90} +(-4.05687 + 0.648643i) q^{91} +(-6.99942 - 3.67358i) q^{92} +(5.43776 + 2.85395i) q^{93} +(15.3871 - 3.79257i) q^{94} +(0.599440 - 0.868439i) q^{95} +(-5.79623 + 1.42864i) q^{96} +(7.16835 + 10.3851i) q^{97} +(-1.22734 + 10.1081i) q^{98} +3.10635 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 180 q - q^{2} + 15 q^{3} - 15 q^{4} - 2 q^{5} + q^{6} + 4 q^{7} + 3 q^{8} - 15 q^{9}+O(q^{10}) $ 180 * q - q^2 + 15 * q^3 - 15 * q^4 - 2 * q^5 + q^6 + 4 * q^7 + 3 * q^8 - 15 * q^9	\( 180 q - q^{2} + 15 q^{3} - 15 q^{4} - 2 q^{5} + q^{6} + 4 q^{7} + 3 q^{8} - 15 q^{9} - 2 q^{10} - 4 q^{11} + 15 q^{12} - 14 q^{13} + 6 q^{14} + 2 q^{15} - 15 q^{16} - 2 q^{17} - q^{18} + 2 q^{20} - 4 q^{21} - 28 q^{22} - 52 q^{23} - 3 q^{24} - 67 q^{25} - 40 q^{26} + 15 q^{27} - 4 q^{28} - 27 q^{29} + 2 q^{30} + 22 q^{31} - 5 q^{32} - 9 q^{33} + 63 q^{34} - 31 q^{35} - 15 q^{36} + 2 q^{37} + 65 q^{38} + q^{39} + 45 q^{40} - 6 q^{41} + 59 q^{42} - 60 q^{43} - 35 q^{44} - 2 q^{45} - 156 q^{46} + 15 q^{48} + 59 q^{49} - 51 q^{50} + 2 q^{51} + 66 q^{52} + 50 q^{53} + q^{54} + 55 q^{55} - 14 q^{56} - 13 q^{57} + 36 q^{58} + 92 q^{59} - 15 q^{60} + 6 q^{61} + 61 q^{62} + 4 q^{63} - 203 q^{64} - 54 q^{65} + 54 q^{66} + 86 q^{67} + 32 q^{68} + 112 q^{70} + 39 q^{71} + 3 q^{72} - 158 q^{73} - 80 q^{74} + 15 q^{75} + 130 q^{76} - 64 q^{77} + 66 q^{78} - 10 q^{79} - 310 q^{80} - 15 q^{81} + 59 q^{82} - 82 q^{83} + 4 q^{84} + 22 q^{85} - q^{86} + 40 q^{87} + 10 q^{88} + 2 q^{89} - 2 q^{90} - 100 q^{91} - 54 q^{92} + 43 q^{93} + 65 q^{94} + 58 q^{95} - 60 q^{96} + 16 q^{97} - 113 q^{98} - 30 q^{99}+O(q^{100}) \) 180 * q - q^2 + 15 * q^3 - 15 * q^4 - 2 * q^5 + q^6 + 4 * q^7 + 3 * q^8 - 15 * q^9 - 2 * q^10 - 4 * q^11 + 15 * q^12 - 14 * q^13 + 6 * q^14 + 2 * q^15 - 15 * q^16 - 2 * q^17 - q^18 + 2 * q^20 - 4 * q^21 - 28 * q^22 - 52 * q^23 - 3 * q^24 - 67 * q^25 - 40 * q^26 + 15 * q^27 - 4 * q^28 - 27 * q^29 + 2 * q^30 + 22 * q^31 - 5 * q^32 - 9 * q^33 + 63 * q^34 - 31 * q^35 - 15 * q^36 + 2 * q^37 + 65 * q^38 + q^39 + 45 * q^40 - 6 * q^41 + 59 * q^42 - 60 * q^43 - 35 * q^44 - 2 * q^45 - 156 * q^46 + 15 * q^48 + 59 * q^49 - 51 * q^50 + 2 * q^51 + 66 * q^52 + 50 * q^53 + q^54 + 55 * q^55 - 14 * q^56 - 13 * q^57 + 36 * q^58 + 92 * q^59 - 15 * q^60 + 6 * q^61 + 61 * q^62 + 4 * q^63 - 203 * q^64 - 54 * q^65 + 54 * q^66 + 86 * q^67 + 32 * q^68 + 112 * q^70 + 39 * q^71 + 3 * q^72 - 158 * q^73 - 80 * q^74 + 15 * q^75 + 130 * q^76 - 64 * q^77 + 66 * q^78 - 10 * q^79 - 310 * q^80 - 15 * q^81 + 59 * q^82 - 82 * q^83 + 4 * q^84 + 22 * q^85 - q^86 + 40 * q^87 + 10 * q^88 + 2 * q^89 - 2 * q^90 - 100 * q^91 - 54 * q^92 + 43 * q^93 + 65 * q^94 + 58 * q^95 - 60 * q^96 + 16 * q^97 - 113 * q^98 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{1}{13}\right)$

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 $

$2$	−1.73397	−	0.427384i	−1.22610	−	0.302206i	−0.427470	−	0.904030i	$-0.640595\pi$
$2$	−1.73397	−	0.427384i	−1.22610	−	0.302206i	−0.798629	+	0.601823i	$0.794441\pi$
$3$	−0.120537	+	0.992709i	−0.0695919	+	0.573141i
$3$	−0.120537	+	0.992709i	−0.0695919	+	0.573141i
$4$	1.05307	+	0.552694i	0.526535	+	0.276347i
$5$	0.457873	−	0.663343i	0.204767	−	0.296656i	−0.707123	−	0.707090i	$-0.750007\pi$
$5$	0.457873	−	0.663343i	0.204767	−	0.296656i	0.911890	+	0.410434i	$0.134623\pi$
$6$	0.633275	−	1.66981i	0.258533	−	0.681696i
$7$	−0.852902	−	0.755605i	−0.322367	−	0.285592i	0.486382	−	0.873746i	$-0.338316\pi$
$7$	−0.852902	−	0.755605i	−0.322367	−	0.285592i	−0.808749	+	0.588154i	$0.799855\pi$
$8$	1.08370	+	0.960071i	0.383144	+	0.339436i
$9$	−0.970942	−	0.239316i	−0.323647	−	0.0797719i
$10$	−1.07744	+	0.954527i	−0.340716	+	0.301848i
$11$	−3.01609	+	0.743398i	−0.909384	+	0.224143i	−0.666144	−	0.745823i	$-0.732056\pi$
$11$	−3.01609	+	0.743398i	−0.909384	+	0.224143i	−0.243240	+	0.969966i	$0.578210\pi$
$12$	−0.675597	+	0.978772i	−0.195028	+	0.282547i
$13$	2.28746	−	2.78703i	0.634428	−	0.772982i
$13$	2.28746	−	2.78703i	0.634428	−	0.772982i
$14$	1.15597	+	1.67471i	0.308946	+	0.447585i
$15$	0.603316	+	0.534492i	0.155776	+	0.138005i
$16$	−2.81997	−	4.08543i	−0.704992	−	1.02136i
$17$	−0.450342	−	0.398968i	−0.109224	−	0.0967639i	0.606743	−	0.794898i	$-0.292476\pi$
$17$	−0.450342	−	0.398968i	−0.109224	−	0.0967639i	−0.715967	+	0.698134i	$0.754014\pi$
$18$	1.58130	+	0.829931i	0.372716	+	0.195617i
$19$	1.30918			0.300348			0.150174	−	0.988660i	$-0.452017\pi$
$19$	1.30918			0.300348			0.150174	+	0.988660i	$0.452017\pi$
$20$	0.848798	−	0.445483i	0.189797	−	0.0996131i
$21$	0.852902	−	0.755605i	0.186118	−	0.164887i
$22$	5.54751			1.18273
$23$	−6.64668			−1.38593			−0.692964	−	0.720972i	$-0.743696\pi$
$23$	−6.64668			−1.38593			−0.692964	+	0.720972i	$0.743696\pi$
$24$	−1.08370	+	0.960071i	−0.221209	+	0.195974i
$25$	1.54265	+	4.06763i	0.308530	+	0.813525i
$26$	−5.15751	+	3.85499i	−1.01147	+	0.756025i
$27$	0.354605	−	0.935016i	0.0682437	−	0.179944i
$28$	−0.480547	−	1.26710i	−0.0908149	−	0.239459i
$29$	−0.672147	−	0.165669i	−0.124815	−	0.0307640i	0.176414	−	0.984316i	$-0.443550\pi$
$29$	−0.672147	−	0.165669i	−0.124815	−	0.0307640i	−0.301228	+	0.953552i	$0.597397\pi$
$30$	−0.817697	−	1.18464i	−0.149290	−	0.216284i
$31$	2.17770	−	5.74211i	0.391126	−	1.03131i	−0.584407	−	0.811461i	$-0.698673\pi$
$31$	2.17770	−	5.74211i	0.391126	−	1.03131i	0.975533	−	0.219854i	$-0.0705580\pi$
$32$	2.11689	+	5.58177i	0.374216	+	0.986727i
$33$	−0.374429	−	3.08370i	−0.0651798	−	0.536804i
$34$	0.610364	+	0.884266i	0.104677	+	0.151650i
$35$	−0.891746	+	0.219796i	−0.150733	+	0.0371523i
$36$	−0.890201	−	0.788650i	−0.148367	−	0.131442i
$37$	3.51137	−	9.25872i	0.577265	−	1.52212i	−0.254543	−	0.967061i	$-0.581925\pi$
$37$	3.51137	−	9.25872i	0.577265	−	1.52212i	0.831809	−	0.555062i	$-0.187306\pi$
$38$	−2.27008	−	0.559525i	−0.368256	−	0.0907670i
$39$	2.49098	+	2.60672i	0.398877	+	0.417410i
$40$	1.13305	−	0.279272i	0.179151	−	0.0441568i
$41$	1.10627	−	9.11099i	0.172771	−	1.42290i	−0.605938	−	0.795512i	$-0.707202\pi$
$41$	1.10627	−	9.11099i	0.172771	−	1.42290i	0.778709	−	0.627386i	$-0.215875\pi$
$42$	−1.80184	+	0.945677i	−0.278029	+	0.145921i
$43$	−4.12983	−	10.8895i	−0.629794	−	1.66063i	−0.744818	−	0.667267i	$-0.767464\pi$
$43$	−4.12983	−	10.8895i	−0.629794	−	1.66063i	0.115025	−	0.993363i	$-0.463305\pi$
$44$	−3.58702	−	0.884121i	−0.540764	−	0.133286i
$45$	−0.603316	+	0.534492i	−0.0899371	+	0.0796773i
$46$	11.5251	+	2.84069i	1.69929	+	0.418836i
$47$	−7.85747	+	4.12392i	−1.14613	+	0.601535i	−0.927334	−	0.374236i	$-0.877905\pi$
$47$	−7.85747	+	4.12392i	−1.14613	+	0.601535i	−0.218796	+	0.975771i	$0.570213\pi$
$48$	4.39555	−	2.30696i	0.634443	−	0.332981i
$49$	−0.687254	−	5.66005i	−0.0981792	−	0.808578i
$50$	−0.936459	−	7.71243i	−0.132435	−	1.09070i
$51$	0.450342	−	0.398968i	0.0630604	−	0.0558667i
$52$	3.94923	−	1.67067i	0.547660	−	0.231680i
$53$	−3.86911	−	3.42773i	−0.531463	−	0.470835i	0.354196	−	0.935171i	$-0.384755\pi$
$53$	−3.86911	−	3.42773i	−0.531463	−	0.470835i	−0.885659	+	0.464336i	$0.846293\pi$
$54$	−1.01448	+	1.46973i	−0.138054	+	0.200005i
$55$	−0.887855	+	2.34108i	−0.119718	+	0.315671i
$56$	−0.198852	−	1.63769i	−0.0265727	−	0.218846i
$57$	−0.157805	+	1.29964i	−0.0209018	+	0.172141i
$58$	1.09468	+	0.574530i	0.143738	+	0.0754395i
$59$	3.07179	−	4.45026i	0.399914	−	0.579375i	−0.570357	−	0.821397i	$-0.693195\pi$
$59$	3.07179	−	4.45026i	0.399914	−	0.579375i	0.970271	+	0.242022i	$0.0778106\pi$
$60$	0.339924	+	0.896306i	0.0438840	+	0.115713i
$61$	−10.4963	+	9.29895i	−1.34392	+	1.19061i	−0.379822	+	0.925060i	$0.624015\pi$
$61$	−10.4963	+	9.29895i	−1.34392	+	1.19061i	−0.964097	+	0.265549i	$0.914447\pi$
$62$	−6.23014	+	9.02592i	−0.791229	+	1.14629i
$63$	0.647290	+	0.937761i	0.0815509	+	0.118147i
$64$	−0.0883196	−	0.727377i	−0.0110400	−	0.0909222i
$65$	−0.801389	−	2.79348i	−0.0994001	−	0.346488i
$66$	−0.668678	+	5.50706i	−0.0823086	+	0.677872i
$67$	−7.54969	+	3.96238i	−0.922342	+	0.484082i	−0.857887	−	0.513838i	$-0.828223\pi$
$67$	−7.54969	+	3.96238i	−0.922342	+	0.484082i	−0.0644548	+	0.997921i	$0.520531\pi$
$68$	−0.253734	−	0.669042i	−0.0307698	−	0.0811332i
$69$	0.801169	−	6.59822i	0.0964494	−	0.794332i
$70$	1.64020			0.196041
$71$	1.71956	−	14.1618i	0.204074	−	1.68070i	−0.426433	−	0.904519i	$-0.640230\pi$
$71$	1.71956	−	14.1618i	0.204074	−	1.68070i	0.630508	−	0.776183i	$-0.282847\pi$
$72$	−0.822446	−	1.19152i	−0.0969262	−	0.140422i
$73$	11.0269	−	2.71789i	1.29060	−	0.318105i	0.466487	−	0.884528i	$-0.345519\pi$
$73$	11.0269	−	2.71789i	1.29060	−	0.318105i	0.824114	+	0.566424i	$0.191673\pi$
$74$	−10.0456	+	14.5536i	−1.16778	+	1.69182i
$75$	−4.22392	+	1.04110i	−0.487736	+	0.120216i
$76$	1.37866	+	0.723578i	0.158144	+	0.0830001i
$77$	3.13414	+	1.64492i	0.357168	+	0.187456i
$78$	−3.20521	−	5.58458i	−0.362918	−	0.632329i
$79$	1.73507	−	0.910637i	0.195211	−	0.102455i	−0.364286	−	0.931287i	$-0.618687\pi$
$79$	1.73507	−	0.910637i	0.195211	−	0.102455i	0.559497	+	0.828833i	$0.310994\pi$
$80$	−4.00123			−0.447351
$81$	0.885456	+	0.464723i	0.0983840	+	0.0516359i
$82$	−5.81214	+	15.3253i	−0.641843	+	1.69240i
$83$	0.185566	+	1.52827i	0.0203685	+	0.167750i	0.999343	−	0.0362308i	$-0.0115351\pi$
$83$	0.185566	+	1.52827i	0.0203685	+	0.167750i	−0.978975	+	0.203981i	$0.934612\pi$
$84$	1.31578	−	0.324311i	0.143564	−	0.0353853i
$85$	−0.470852	+	0.116055i	−0.0510710	+	0.0125879i
$86$	2.50700	+	20.6470i	0.270337	+	2.22642i
$87$	0.245480	−	0.647277i	0.0263182	−	0.0693954i
$88$	−3.98224	−	2.09004i	−0.424508	−	0.222799i
$89$	5.56869			0.590280			0.295140	−	0.955454i	$-0.404634\pi$
$89$	5.56869			0.590280			0.295140	+	0.955454i	$0.404634\pi$
$90$	1.27456	−	0.668943i	0.134351	−	0.0705127i
$91$	−4.05687	+	0.648643i	−0.425276	+	0.0679962i
$92$	−6.99942	−	3.67358i	−0.729740	−	0.382997i
$93$	5.43776	+	2.85395i	0.563869	+	0.295941i
$94$	15.3871	−	3.79257i	1.58706	−	0.391174i
$95$	0.599440	−	0.868439i	0.0615013	−	0.0891000i
$96$	−5.79623	+	1.42864i	−0.591576	+	0.145810i
$97$	7.16835	+	10.3851i	0.727836	+	1.05445i	0.995848	+	0.0910365i	$0.0290180\pi$
$97$	7.16835	+	10.3851i	0.727836	+	1.05445i	−0.268012	+	0.963416i	$0.586367\pi$
$98$	−1.22734	+	10.1081i	−0.123980	+	1.02107i
$99$	3.10635			0.312200
$100$	−0.623636	+	5.13611i	−0.0623636	+	0.513611i
$101$	0.288460	+	0.760606i	0.0287028	+	0.0756831i	0.948602	−	0.316473i	$-0.102499\pi$
$101$	0.288460	+	0.760606i	0.0287028	+	0.0756831i	−0.919899	+	0.392156i	$0.871729\pi$
$102$	−0.951390	+	0.499328i	−0.0942016	+	0.0494408i
$103$	1.20491	−	9.92333i	0.118723	−	0.977774i	−0.804618	−	0.593793i	$-0.797630\pi$
$103$	1.20491	−	9.92333i	0.118723	−	0.977774i	0.923341	−	0.383981i	$-0.125447\pi$
$104$	5.15466	−	0.824165i	0.505456	−	0.0808160i
$105$	−0.110705	−	0.911738i	−0.0108037	−	0.0889765i
$106$	5.24395	+	7.59717i	0.509337	+	0.737903i
$107$	−5.95523	+	8.62764i	−0.575714	+	0.834065i	−0.997354	−	0.0726980i	$-0.976839\pi$
$107$	−5.95523	+	8.62764i	−0.575714	+	0.834065i	0.421640	+	0.906763i	$0.361454\pi$
$108$	0.890201	−	0.788650i	0.0856597	−	0.0758878i
$109$	−4.43675	−	11.6988i	−0.424964	−	1.12054i	−0.961050	−	0.276374i	$-0.910867\pi$
$109$	−4.43675	−	11.6988i	−0.424964	−	1.12054i	0.536086	−	0.844163i	$-0.319902\pi$
$110$	2.54005	−	3.67990i	0.242185	−	0.350865i
$111$	8.76796	+	4.60178i	0.832218	+	0.436782i
$112$	−0.681815	+	5.61525i	−0.0644255	+	0.530591i
$113$	1.04486	+	8.60521i	0.0982924	+	0.809510i	0.955592	+	0.294693i	$0.0952173\pi$
$113$	1.04486	+	8.60521i	0.0982924	+	0.809510i	−0.857300	+	0.514818i	$0.827860\pi$
$114$	0.829074	−	2.18609i	0.0776499	−	0.204746i
$115$	−3.04333	+	4.40903i	−0.283792	+	0.411144i
$116$	−0.616254	−	0.545953i	−0.0572177	−	0.0506905i
$117$	−2.88797	+	2.15862i	−0.266993	+	0.199564i
$118$	−7.22836	+	6.40377i	−0.665424	+	0.589515i
$119$	0.0826350	+	0.680561i	0.00757514	+	0.0623869i
$120$	0.140662	+	1.15845i	0.0128406	+	0.105752i
$121$	−1.19589	+	0.627649i	−0.108717	+	0.0570590i
$122$	22.1745	−	11.6381i	2.00759	−	1.05366i
$123$	8.91122	+	2.19642i	0.803497	+	0.198044i
$124$	5.46690	−	4.84325i	0.490942	−	0.434937i
$125$	7.31757	+	1.80362i	0.654504	+	0.161321i
$126$	−0.721594	−	1.90269i	−0.0642847	−	0.169505i
$127$	−15.8520	+	8.31980i	−1.40664	+	0.738262i	−0.985650	−	0.168802i	$-0.946010\pi$
$127$	−15.8520	+	8.31980i	−1.40664	+	0.738262i	−0.420992	+	0.907065i	$0.638318\pi$
$128$	1.28141	−	10.5534i	0.113262	−	0.932794i
$129$	11.3079	−	2.78714i	0.995603	−	0.245394i
$130$	0.195694	+	5.18630i	0.0171635	+	0.454868i
$131$	14.3630	+	3.54016i	1.25490	+	0.309305i	0.810083	−	0.586315i	$-0.199422\pi$
$131$	14.3630	+	3.54016i	1.25490	+	0.309305i	0.444818	+	0.895621i	$0.353268\pi$
$132$	1.31004	−	3.45430i	0.114025	−	0.300658i
$133$	−1.11661	−	0.989227i	−0.0968220	−	0.0857768i
$134$	14.7844	−	3.64402i	1.27718	−	0.314795i
$135$	−0.457873	−	0.663343i	−0.0394074	−	0.0570915i
$136$	−0.104996	−	0.864720i	−0.00900333	−	0.0741491i
$137$	2.78071	+	7.33212i	0.237572	+	0.626426i	0.999781	−	0.0209047i	$-0.00665465\pi$
$137$	2.78071	+	7.33212i	0.237572	+	0.626426i	−0.762210	+	0.647330i	$0.775885\pi$
$138$	−4.20917	+	11.0987i	−0.358309	+	0.944782i
$139$	9.06258	+	13.1294i	0.768678	+	1.11362i	0.990362	+	0.138504i	$0.0442293\pi$
$139$	9.06258	+	13.1294i	0.768678	+	1.11362i	−0.221684	+	0.975119i	$0.571155\pi$
$140$	−1.06055	−	0.261402i	−0.0896329	−	0.0220925i
$141$	−3.14674	−	8.29726i	−0.265003	−	0.698755i
$142$	−9.03421	+	23.8213i	−0.758134	+	1.99904i
$143$	−4.82731	+	10.1064i	−0.403680	+	0.845140i
$144$	1.76032	+	4.64158i	0.146693	+	0.386798i
$145$	−0.417654	+	0.370009i	−0.0346843	+	0.0307276i
$146$	−20.2819			−1.67854
$147$	5.70162			0.470262
$148$	8.81495	−	7.80936i	0.724584	−	0.641926i
$149$	6.25818	−	3.28455i	0.512690	−	0.269080i	−0.188477	−	0.982078i	$-0.560355\pi$
$149$	6.25818	−	3.28455i	0.512690	−	0.269080i	0.701167	+	0.712997i	$0.252663\pi$
$150$	7.76908			0.634343
$151$	8.25065	+	4.33027i	0.671428	+	0.352393i	0.765740	−	0.643150i	$-0.222373\pi$
$151$	8.25065	+	4.33027i	0.671428	+	0.352393i	−0.0943119	+	0.995543i	$0.530065\pi$
$152$	1.41876	+	1.25691i	0.115077	+	0.101949i
$153$	0.341776	+	0.495148i	0.0276310	+	0.0400304i
$154$	−4.73148	−	4.19172i	−0.381273	−	0.337779i
$155$	−2.81189	−	4.07372i	−0.225856	−	0.327209i
$156$	1.18246	+	4.12181i	0.0946726	+	0.330009i
$157$	−6.17282	+	8.94287i	−0.492644	+	0.713719i	−0.987911	−	0.155022i	$-0.950455\pi$
$157$	−6.17282	+	8.94287i	−0.492644	+	0.713719i	0.495267	+	0.868741i	$0.335070\pi$
$158$	−3.39775	+	0.837471i	−0.270311	+	0.0666256i
$159$	3.86911	−	3.42773i	0.306841	−	0.271837i
$160$	4.67189	+	1.15152i	0.369346	+	0.0910355i
$161$	5.66896	+	5.02226i	0.446777	+	0.395810i
$162$	−1.33674	−	1.18424i	−0.105024	−	0.0930430i
$163$	−5.25170	+	13.8476i	−0.411345	+	1.08463i	0.556005	+	0.831179i	$0.312334\pi$
$163$	−5.25170	+	13.8476i	−0.411345	+	1.08463i	−0.967349	+	0.253447i	$0.918436\pi$
$164$	6.20057	−	8.98308i	0.484183	−	0.701461i
$165$	−2.21699	−	1.16357i	−0.172593	−	0.0905837i
$166$	0.331395	−	2.72928i	0.0257212	−	0.211833i
$167$	−5.54554	−	1.36685i	−0.429127	−	0.105770i	0.0188357	−	0.999823i	$-0.494004\pi$
$167$	−5.54554	−	1.36685i	−0.429127	−	0.105770i	−0.447963	+	0.894052i	$0.647850\pi$
$168$	1.64972			0.127279
$169$	−2.53504	−	12.7504i	−0.195003	−	0.980803i
$170$	0.866041			0.0664223
$171$	−1.27114	−	0.313308i	−0.0972067	−	0.0239593i
$172$	1.66954	−	13.7499i	0.127301	−	1.04842i
$173$	−12.3926	−	6.50415i	−0.942194	−	0.494502i	−0.0776067	−	0.996984i	$-0.524728\pi$
$173$	−12.3926	−	6.50415i	−0.942194	−	0.494502i	−0.864587	+	0.502482i	$0.832420\pi$
$174$	−0.702290	+	1.01744i	−0.0532405	+	0.0771321i
$175$	1.75779	−	4.63492i	0.132877	−	0.350367i
$176$	11.5424	+	10.2256i	0.870039	+	0.770787i
$177$	4.04755	+	3.58582i	0.304233	+	0.269527i
$178$	−9.65591	−	2.37997i	−0.723741	−	0.178386i
$179$	5.42982	−	4.81040i	0.405844	−	0.359547i	−0.435367	−	0.900253i	$-0.643381\pi$
$179$	5.42982	−	4.81040i	0.405844	−	0.359547i	0.841211	+	0.540706i	$0.181843\pi$
$180$	−0.930745	+	0.229408i	−0.0693736	+	0.0170991i
$181$	9.44254	−	13.6799i	0.701859	−	1.01682i	−0.296236	−	0.955115i	$-0.595731\pi$
$181$	9.44254	−	13.6799i	0.701859	−	1.01682i	0.998095	−	0.0617029i	$-0.0196531\pi$
$182$	7.31170	+	0.609119i	0.541979	+	0.0451509i
$183$	−7.96596	−	11.5407i	−0.588860	−	0.853112i
$184$	−7.20298	−	6.38128i	−0.531011	−	0.470434i
$185$	−4.53395	−	6.56856i	−0.333343	−	0.482930i
$186$	−8.20915	−	7.27267i	−0.601924	−	0.533258i
$187$	1.65486	+	0.868538i	0.121015	+	0.0635138i
$188$	−10.5537			−0.769709
$189$	−1.00895	+	0.529536i	−0.0733900	+	0.0385181i
$190$	−1.41057	+	1.24965i	−0.102333	+	0.0906594i
$191$	−11.1111			−0.803970			−0.401985	−	0.915646i	$-0.631680\pi$
$191$	−11.1111			−0.803970			−0.401985	+	0.915646i	$0.631680\pi$
$192$	0.732720			0.0528795
$193$	−12.0907	+	10.7114i	−0.870306	+	0.771024i	−0.974701	−	0.223512i	$-0.928248\pi$
$193$	−12.0907	+	10.7114i	−0.870306	+	0.771024i	0.104395	+	0.994536i	$0.466709\pi$
$194$	−7.99123	−	21.0711i	−0.573737	−	1.51282i
$195$	2.86971	−	0.458830i	0.205504	−	0.0328575i
$196$	2.40455	−	6.34027i	0.171753	−	0.452876i
$197$	2.22160	+	5.85787i	0.158282	+	0.417356i	0.990573	−	0.136983i	$-0.0437405\pi$
$197$	2.22160	+	5.85787i	0.158282	+	0.417356i	−0.832291	+	0.554339i	$0.812971\pi$
$198$	−5.38631	−	1.32761i	−0.382788	−	0.0943488i
$199$	−4.18142	−	6.05783i	−0.296413	−	0.429428i	0.646275	−	0.763105i	$-0.276326\pi$
$199$	−4.18142	−	6.05783i	−0.296413	−	0.429428i	−0.942688	+	0.333677i	$0.891711\pi$
$200$	−2.23345	+	5.88912i	−0.157929	+	0.416424i
$201$	−3.02348	−	7.97226i	−0.213260	−	0.562320i
$202$	−0.175108	−	1.44215i	−0.0123206	−	0.101469i
$203$	0.448095	+	0.649178i	0.0314501	+	0.0455633i
$204$	0.694748	−	0.171240i	0.0486421	−	0.0119892i
$205$	−5.53718	−	4.90552i	−0.386734	−	0.342616i
$206$	−6.33035	+	16.6918i	−0.441056	+	1.16297i
$207$	6.45354	+	1.59065i	0.448552	+	0.110558i
$208$	−17.8368	−	1.48593i	−1.23676	−	0.103031i
$209$	−3.94861	+	0.973246i	−0.273131	+	0.0673208i
$210$	−0.197704	+	1.62824i	−0.0136429	+	0.112359i
$211$	8.71108	−	4.57193i	0.599695	−	0.314744i	−0.137418	−	0.990513i	$-0.543880\pi$
$211$	8.71108	−	4.57193i	0.599695	−	0.314744i	0.737114	+	0.675769i	$0.236188\pi$
$212$	−2.17996	−	5.74808i	−0.149720	−	0.394780i
$213$	13.8513	+	3.41404i	0.949077	+	0.233926i
$214$	14.0135	−	12.4149i	0.957942	−	0.848662i
$215$	−9.11440	−	2.24650i	−0.621597	−	0.153210i
$216$	1.28197	−	0.672828i	0.0872267	−	0.0457801i
$217$	−6.19613	+	3.25198i	−0.420621	+	0.220759i
$218$	2.69331	+	22.1814i	0.182414	+	1.50232i
$219$	1.36892	+	11.2741i	0.0925033	+	0.761834i
$220$	−2.22888	+	1.97461i	−0.150271	+	0.133128i
$221$	−2.14207	+	0.342491i	−0.144091	+	0.0230384i
$222$	−13.2366	−	11.7266i	−0.888384	−	0.787039i
$223$	−4.90204	+	7.10183i	−0.328265	+	0.475574i	−0.952016	−	0.306050i	$-0.900993\pi$
$223$	−4.90204	+	7.10183i	−0.328265	+	0.475574i	0.623751	+	0.781623i	$0.285608\pi$
$224$	2.41212	−	6.36023i	0.161166	−	0.424961i
$225$	−0.524374	−	4.31861i	−0.0349583	−	0.287907i
$226$	1.86598	−	15.3677i	0.124123	−	1.02224i
$227$	−0.0727818	−	0.0381989i	−0.00483070	−	0.00253535i	0.462306	−	0.886720i	$-0.347022\pi$
$227$	−0.0727818	−	0.0381989i	−0.00483070	−	0.00253535i	−0.467137	+	0.884185i	$0.654714\pi$
$228$	−0.884482	+	1.28139i	−0.0585763	+	0.0848624i
$229$	1.99017	+	5.24766i	0.131514	+	0.346775i	0.984556	−	0.175067i	$-0.0560143\pi$
$229$	1.99017	+	5.24766i	0.131514	+	0.346775i	−0.853042	+	0.521842i	$0.825245\pi$
$230$	7.16139	−	6.34444i	0.472208	−	0.418340i
$231$	−2.01071	+	2.91302i	−0.132295	+	0.191662i
$232$	−0.569349	−	0.824844i	−0.0373796	−	0.0541537i
$233$	−2.10884	−	17.3679i	−0.138155	−	1.13781i	−0.882600	−	0.470124i	$-0.844209\pi$
$233$	−2.10884	−	17.3679i	−0.138155	−	1.13781i	0.744445	−	0.667683i	$-0.232714\pi$
$234$	5.93020	−	2.50869i	0.387670	−	0.163998i
$235$	−0.862148	+	7.10043i	−0.0562403	+	0.463181i
$236$	5.69445	−	2.98868i	0.370677	−	0.194546i
$237$	0.694857	+	1.83219i	0.0451358	+	0.119013i
$238$	0.147575	−	1.21539i	0.00956584	−	0.0787818i
$239$	−5.93867			−0.384141			−0.192070	−	0.981381i	$-0.561520\pi$
$239$	−5.93867			−0.384141			−0.192070	+	0.981381i	$0.561520\pi$
$240$	0.482295	−	3.97206i	0.0311320	−	0.256395i
$241$	−0.285663	−	0.413854i	−0.0184012	−	0.0266587i	0.813675	−	0.581320i	$-0.197463\pi$
$241$	−0.285663	−	0.413854i	−0.0184012	−	0.0266587i	−0.832077	+	0.554661i	$0.812848\pi$
$242$	2.34187	−	0.577220i	0.150541	−	0.0371051i
$243$	−0.568065	+	0.822984i	−0.0364414	+	0.0527944i
$244$	−16.1929	+	3.99118i	−1.03664	+	0.255509i
$245$	−4.06923	−	2.13570i	−0.259974	−	0.136445i
$246$	−14.5130	−	7.61703i	−0.925317	−	0.485644i
$247$	2.99471	−	3.64873i	0.190549	−	0.232163i
$248$	7.87280	−	4.13196i	0.499923	−	0.262380i
$249$	−1.53950			−0.0975617
$250$	−11.9176	−	6.25483i	−0.753734	−	0.395590i
$251$	8.28982	−	21.8585i	0.523249	−	1.37969i	−0.369538	−	0.929216i	$-0.620484\pi$
$251$	8.28982	−	21.8585i	0.523249	−	1.37969i	0.892787	−	0.450479i	$-0.148747\pi$
$252$	0.163347	+	1.34528i	0.0102899	+	0.0847448i
$253$	20.0470	−	4.94113i	1.26034	−	0.310646i
$254$	31.0427	−	7.65133i	1.94779	−	0.480087i
$255$	−0.0584535	−	0.481408i	−0.00366050	−	0.0301469i
$256$	−7.25191	+	19.1217i	−0.453245	+	1.19511i
$257$	16.0877	+	8.44345i	1.00352	+	0.526688i	0.884667	−	0.466224i	$-0.154386\pi$
$257$	16.0877	+	8.44345i	1.00352	+	0.526688i	0.118853	+	0.992912i	$0.462078\pi$
$258$	−20.7987			−1.29487
$259$	−9.99079	+	5.24357i	−0.620797	+	0.325820i
$260$	0.700018	−	3.38465i	0.0434133	−	0.209907i
$261$	0.612969	+	0.321711i	0.0379418	+	0.0199134i
$262$	−23.3920	−	12.2770i	−1.44516	−	0.758478i
$263$	−11.3897	+	2.80732i	−0.702321	+	0.173107i	−0.574276	−	0.818662i	$-0.694716\pi$
$263$	−11.3897	+	2.80732i	−0.702321	+	0.173107i	−0.128045	+	0.991768i	$0.540870\pi$
$264$	2.55480	−	3.70127i	0.157237	−	0.227798i
$265$	−4.04533	+	0.997083i	−0.248502	+	0.0612503i
$266$	1.51338	+	2.19251i	0.0927911	+	0.134431i
$267$	−0.671231	+	5.52808i	−0.0410787	+	0.338313i
$268$	−10.1403			−0.619420
$269$	−0.316865	+	2.60962i	−0.0193196	+	0.159111i	−0.999176	−	0.0405934i	$-0.987075\pi$
$269$	−0.316865	+	2.60962i	−0.0193196	+	0.159111i	0.979856	+	0.199705i	$0.0639982\pi$
$270$	0.510434	+	1.34590i	0.0310640	+	0.0819090i
$271$	−5.97921	+	3.13813i	−0.363211	+	0.190628i	−0.636449	−	0.771319i	$-0.719598\pi$
$271$	−5.97921	+	3.13813i	−0.363211	+	0.190628i	0.273238	+	0.961946i	$0.411905\pi$
$272$	−0.360006	+	2.96491i	−0.0218286	+	0.179774i
$273$	−0.154912	−	4.10548i	−0.00937568	−	0.248475i
$274$	−1.68802	−	13.9021i	−0.101977	−	0.839856i
$275$	−7.67662	−	11.1215i	−0.462918	−	0.670652i
$276$	4.49048	−	6.50558i	0.270295	−	0.391590i
$277$	−1.95181	+	1.72916i	−0.117273	+	0.103895i	−0.719721	−	0.694263i	$-0.755730\pi$
$277$	−1.95181	+	1.72916i	−0.117273	+	0.103895i	0.602448	+	0.798158i	$0.294192\pi$
$278$	−10.1029	−	26.6392i	−0.605932	−	1.59771i
$279$	−3.48859	+	5.05410i	−0.208857	+	0.302581i
$280$	−1.17740	−	0.617948i	−0.0703632	−	0.0369295i
$281$	0.473935	−	3.90321i	0.0282726	−	0.232846i	−0.971722	−	0.236128i	$-0.924122\pi$
$281$	0.473935	−	3.90321i	0.0282726	−	0.232846i	0.999995	+	0.00328188i	$0.00104466\pi$
$282$	1.91021	+	15.7320i	0.113752	+	0.936829i
$283$	0.892307	−	2.35282i	0.0530421	−	0.139861i	−0.905876	−	0.423542i	$-0.860787\pi$
$283$	0.892307	−	2.35282i	0.0530421	−	0.139861i	0.958919	+	0.283681i	$0.0915558\pi$
$284$	9.63798	−	13.9630i	0.571909	−	0.828553i
$285$	0.789853	+	0.699748i	0.0467868	+	0.0414495i
$286$	12.6897	−	15.4611i	0.750358	−	0.914231i
$287$	−7.82786	+	6.93487i	−0.462064	+	0.409353i
$288$	−0.719568	−	5.92618i	−0.0424010	−	0.349203i
$289$	−2.00549	−	16.5167i	−0.117970	−	0.971571i
$290$	0.882333	−	0.463084i	0.0518124	−	0.0271932i
$291$	−11.1735	+	5.86429i	−0.655001	+	0.343771i
$292$	13.1143	+	3.23237i	0.767454	+	0.189160i
$293$	12.9222	−	11.4481i	0.754922	−	0.668803i	−0.195171	−	0.980769i	$-0.562526\pi$
$293$	12.9222	−	11.4481i	0.754922	−	0.668803i	0.950093	+	0.311967i	$0.100988\pi$
$294$	−9.88642	−	2.43678i	−0.576588	−	0.142116i
$295$	−1.54556	−	4.07531i	−0.0899860	−	0.237274i
$296$	12.6943	−	6.66247i	0.737840	−	0.387248i
$297$	−0.374429	+	3.08370i	−0.0217266	+	0.178935i
$298$	−12.2552	+	3.02064i	−0.709927	+	0.174981i
$299$	−15.2040	+	18.5245i	−0.879271	+	1.07130i
$300$	−5.02349	−	1.23818i	−0.290031	−	0.0714863i
$301$	−4.70580	+	12.4082i	−0.271238	+	0.715196i
$302$	−12.4557	−	11.0347i	−0.716743	−	0.634978i
$303$	−0.789830	+	0.194676i	−0.0453745	+	0.0111838i
$304$	−3.69186	−	5.34858i	−0.211743	−	0.306762i
$305$	1.36241	+	11.2204i	0.0780111	+	0.642479i
$306$	−0.381010	−	1.00464i	−0.0217809	−	0.0574315i
$307$	1.37147	−	3.61628i	0.0782742	−	0.206392i	−0.890167	−	0.455635i	$-0.849412\pi$
$307$	1.37147	−	3.61628i	0.0782742	−	0.206392i	0.968441	+	0.249242i	$0.0801816\pi$
$308$	2.39133	+	3.46444i	0.136259	+	0.197405i
$309$	9.70574	+	2.39225i	0.552140	+	0.136090i
$310$	3.13467	+	8.26545i	0.178037	+	0.469446i
$311$	−4.96781	+	13.0990i	−0.281699	+	0.742778i	0.717245	+	0.696821i	$0.245403\pi$
$311$	−4.96781	+	13.0990i	−0.281699	+	0.742778i	−0.998943	+	0.0459569i	$0.985366\pi$
$312$	0.196830	+	5.21642i	0.0111433	+	0.295321i
$313$	6.78868	+	17.9003i	0.383719	+	1.01178i	0.978198	+	0.207673i	$0.0665889\pi$
$313$	6.78868	+	17.9003i	0.383719	+	1.01178i	−0.594479	+	0.804111i	$0.702642\pi$
$314$	14.5255	−	12.8685i	0.819721	−	0.726210i
$315$	0.918434			0.0517479
$316$	2.33046			0.131098
$317$	17.0670	−	15.1200i	0.958577	−	0.849225i	−0.0300597	−	0.999548i	$-0.509570\pi$
$317$	17.0670	−	15.1200i	0.958577	−	0.849225i	0.988637	+	0.150323i	$0.0480313\pi$
$318$	−8.17387	+	4.28998i	−0.458368	+	0.240570i
$319$	2.15041			0.120400
$320$	−0.522940	−	0.274460i	−0.0292332	−	0.0153428i
$321$	−7.84691	−	6.95175i	−0.437972	−	0.388009i
$322$	−7.68336	−	11.1313i	−0.428177	−	0.620321i
$323$	−0.589580	−	0.522323i	−0.0328051	−	0.0290628i
$324$	0.675597	+	0.978772i	0.0375332	+	0.0543762i
$325$	14.8653	+	5.00514i	0.824580	+	0.277635i
$326$	15.0245	−	21.7668i	0.832130	−	1.20555i
$327$	12.1482	−	2.99427i	0.671800	−	0.165584i
$328$	9.94606	−	8.81144i	0.549179	−	0.486531i
$329$	9.81770	+	2.41985i	0.541267	+	0.133410i
$330$	3.34690	+	2.96510i	0.184241	+	0.163223i
$331$	25.4122	+	22.5133i	1.39678	+	1.23744i	0.936963	+	0.349427i	$0.113624\pi$
$331$	25.4122	+	22.5133i	1.39678	+	1.23744i	0.459818	+	0.888013i	$0.347915\pi$
$332$	−0.649253	+	1.71194i	−0.0356324	+	0.0939549i
$333$	−5.62509	+	8.14935i	−0.308253	+	0.446582i
$334$	9.03161	+	4.74015i	0.494188	+	0.259370i
$335$	−0.828378	+	6.82231i	−0.0452591	+	0.372742i
$336$	−5.49213	−	1.35369i	−0.299620	−	0.0738497i
$337$	−2.54969			−0.138890			−0.0694451	−	0.997586i	$-0.522123\pi$
$337$	−2.54969			−0.138890			−0.0694451	+	0.997586i	$0.522123\pi$
$338$	−1.05366	+	23.1923i	−0.0573117	+	1.26149i
$339$	−8.66842			−0.470804
$340$	−0.559982	−	0.138023i	−0.0303693	−	0.00748536i
$341$	−2.29944	+	18.9376i	−0.124522	+	1.02553i
$342$	2.07021	+	1.08653i	0.111944	+	0.0587530i
$343$	−8.22163	+	11.9111i	−0.443926	+	0.643138i
$344$	5.97919	−	15.7658i	0.322376	−	0.850036i
$345$	−4.01005	−	3.55259i	−0.215894	−	0.191265i
$346$	18.7086	+	16.5744i	1.00578	+	0.891045i
$347$	−29.7091	−	7.32262i	−1.59487	−	0.393099i	−0.660903	−	0.750471i	$-0.729827\pi$
$347$	−29.7091	−	7.32262i	−1.59487	−	0.393099i	−0.933962	+	0.357372i	$0.883673\pi$
$348$	0.616254	−	0.545953i	0.0330347	−	0.0292662i
$349$	5.32463	−	1.31240i	0.285021	−	0.0702514i	−0.0942133	−	0.995552i	$-0.530034\pi$
$349$	5.32463	−	1.31240i	0.285021	−	0.0702514i	0.379234	+	0.925301i	$0.376187\pi$
$350$	−5.02885	+	7.28554i	−0.268803	+	0.389429i
$351$	−1.79477	−	3.12711i	−0.0957978	−	0.166913i
$352$	−10.5342	−	15.2614i	−0.561474	−	0.813435i
$353$	−10.0395	−	8.89420i	−0.534347	−	0.473390i	0.352267	−	0.935899i	$-0.385411\pi$
$353$	−10.0395	−	8.89420i	−0.534347	−	0.473390i	−0.886615	+	0.462509i	$0.846949\pi$
$354$	−5.48579	−	7.94755i	−0.291567	−	0.422407i
$355$	−8.60683	−	7.62498i	−0.456803	−	0.404692i
$356$	5.86422	+	3.07778i	0.310803	+	0.163122i
$357$	−0.685559			−0.0362836
$358$	−11.4710	+	6.02046i	−0.606262	+	0.318191i
$359$	−1.25973	+	1.11602i	−0.0664859	+	0.0589014i	−0.695711	−	0.718321i	$-0.744911\pi$
$359$	−1.25973	+	1.11602i	−0.0664859	+	0.0589014i	0.629225	+	0.777223i	$0.283372\pi$
$360$	−1.16696			−0.0615043
$361$	−17.2860			−0.909791
$362$	−22.2196	+	19.6849i	−1.16784	+	1.03461i
$363$	−0.478925	−	1.26282i	−0.0251370	−	0.0662809i
$364$	−4.63067	−	1.55914i	−0.242713	−	0.0817212i
$365$	3.24603	−	8.55907i	0.169905	−	0.448002i
$366$	8.88039	+	23.4157i	0.464186	+	1.22396i
$367$	25.9923	+	6.40654i	1.35679	+	0.334418i	0.849605	−	0.527419i	$-0.176840\pi$
$367$	25.9923	+	6.40654i	1.35679	+	0.334418i	0.507184	+	0.861838i	$0.330686\pi$
$368$	18.7434	+	27.1545i	0.977068	+	1.41553i
$369$	−3.25453	+	8.58149i	−0.169424	+	0.446735i
$370$	5.05442	+	13.3274i	0.262767	+	0.692858i
$371$	0.709959	+	5.84704i	0.0368593	+	0.303563i
$372$	4.14897	+	6.01083i	0.215114	+	0.311647i
$373$	16.8794	−	4.16039i	0.873981	−	0.215417i	0.223283	−	0.974754i	$-0.428323\pi$
$373$	16.8794	−	4.16039i	0.873981	−	0.215417i	0.650698	+	0.759337i	$0.274476\pi$
$374$	−2.49827	−	2.21328i	−0.129183	−	0.114446i
$375$	−2.67251	+	7.04682i	−0.138008	+	0.363896i
$376$	−12.4744	−	3.07465i	−0.643316	−	0.158563i
$377$	−1.99924	+	1.49433i	−0.102966	+	0.0769619i
$378$	1.97579	−	0.486989i	0.101624	−	0.0250480i
$379$	2.32280	−	19.1299i	0.119314	−	0.982640i	−0.802941	−	0.596058i	$-0.796733\pi$
$379$	2.32280	−	19.1299i	0.119314	−	0.982640i	0.922255	−	0.386581i	$-0.126344\pi$
$380$	1.11123	−	0.583220i	0.0570051	−	0.0299186i
$381$	−6.34838	−	16.7393i	−0.325237	−	0.857581i
$382$	19.2662	+	4.74870i	0.985747	+	0.242965i
$383$	23.5710	−	20.8821i	1.20442	−	1.06703i	0.208391	−	0.978046i	$-0.433177\pi$
$383$	23.5710	−	20.8821i	1.20442	−	1.06703i	0.996033	−	0.0889813i	$-0.0283611\pi$
$384$	10.3220	+	2.54413i	0.526740	+	0.129830i
$385$	2.52619	−	1.32585i	0.128746	−	0.0675713i
$386$	25.5427	−	13.4059i	1.30009	−	0.682340i
$387$	1.40381	+	11.5614i	0.0713595	+	0.587698i
$388$	1.80897	+	14.8982i	0.0918364	+	0.756341i
$389$	13.4204	−	11.8894i	0.680441	−	0.602819i	−0.250443	−	0.968131i	$-0.580576\pi$
$389$	13.4204	−	11.8894i	0.680441	−	0.602819i	0.930885	+	0.365313i	$0.119038\pi$
$390$	−5.17207	−	0.430872i	−0.261898	−	0.0218180i
$391$	2.99328	+	2.65181i	0.151376	+	0.134108i
$392$	4.68927	−	6.79358i	0.236844	−	0.343128i
$393$	−5.24562	+	13.8316i	−0.264606	+	0.697710i
$394$	−1.34861	−	11.1068i	−0.0679421	−	0.559553i
$395$	0.190378	−	1.56791i	0.00957897	−	0.0788899i
$396$	3.27120	+	1.71686i	0.164384	+	0.0862755i
$397$	−13.7659	+	19.9433i	−0.690889	+	1.00092i	0.307885	+	0.951423i	$0.400379\pi$
$397$	−13.7659	+	19.9433i	−0.690889	+	1.00092i	−0.998774	+	0.0495015i	$0.984237\pi$
$398$	4.66142	+	12.2911i	0.233656	+	0.616100i
$399$	1.11661	−	0.989227i	0.0559002	−	0.0495233i
$400$	12.2678	−	17.7730i	0.613389	−	0.888648i
$401$	−1.70260	−	2.46664i	−0.0850239	−	0.123178i	0.778164	−	0.628061i	$-0.216151\pi$
$401$	−1.70260	−	2.46664i	−0.0850239	−	0.123178i	−0.863188	+	0.504883i	$0.831536\pi$
$402$	1.83539	+	15.1158i	0.0915411	+	0.753909i
$403$	−11.0220	−	19.2042i	−0.549046	−	0.956628i
$404$	−0.116614	+	0.960401i	−0.00580175	+	0.0477817i
$405$	0.713697	−	0.374577i	0.0354639	−	0.0186129i
$406$	−0.499533	−	1.31716i	−0.0247914	−	0.0653696i
$407$	−3.70767	+	30.5354i	−0.183782	+	1.51359i
$408$	0.871071			0.0431244
$409$	1.19816	−	9.86776i	0.0592453	−	0.487929i	−0.932641	−	0.360805i	$-0.882502\pi$
$409$	1.19816	−	9.86776i	0.0592453	−	0.487929i	0.991887	−	0.127125i	$-0.0405748\pi$
$410$	7.50475	+	10.8725i	0.370633	+	0.536955i
$411$	−7.61384	+	1.87664i	−0.375563	+	0.0925680i
$412$	6.75341	−	9.78401i	0.332717	−	0.482024i
$413$	−5.98258	+	1.47457i	−0.294383	+	0.0725590i
$414$	−10.5104	−	5.51628i	−0.516558	−	0.271110i
$415$	1.09874	+	0.576661i	0.0539348	+	0.0283072i
$416$	20.3988	+	6.86826i	1.00014	+	0.336744i
$417$	−14.1261	+	7.41393i	−0.691756	+	0.363062i
$418$	7.26271			0.355231
$419$	27.7826	+	14.5814i	1.35727	+	0.712349i	0.977142	−	0.212586i	$-0.0681886\pi$
$419$	27.7826	+	14.5814i	1.35727	+	0.712349i	0.380125	+	0.924935i	$0.375881\pi$
$420$	0.387332	−	1.02131i	0.0188998	−	0.0498348i
$421$	0.0366478	+	0.301822i	0.00178610	+	0.0147099i	0.993575	−	0.113178i	$-0.0361032\pi$
$421$	0.0366478	+	0.301822i	0.00178610	+	0.0147099i	−0.991789	+	0.127888i	$0.959180\pi$
$422$	−17.0587	+	4.20459i	−0.830404	+	0.204676i
$423$	8.61606	−	2.12367i	0.418927	−	0.103256i
$424$	−0.902073	−	7.42924i	−0.0438086	−	0.360796i
$425$	0.928134	−	2.44729i	0.0450211	−	0.118711i
$426$	−22.5586	−	11.8397i	−1.09297	−	0.573634i
$427$	15.9787			0.773263
$428$	−11.0397	+	5.79409i	−0.533625	+	0.280068i
$429$	−9.45085	−	6.01031i	−0.456291	−	0.290180i
$430$	14.8439	+	7.79071i	0.715839	+	0.375701i
$431$	−15.7058	−	8.24303i	−0.756521	−	0.397053i	0.0419238	−	0.999121i	$-0.486651\pi$
$431$	−15.7058	−	8.24303i	−0.756521	−	0.397053i	−0.798445	+	0.602068i	$0.794344\pi$
$432$	−4.81992	+	1.18800i	−0.231898	+	0.0571578i
$433$	−0.0954302	+	0.138254i	−0.00458608	+	0.00664409i	−0.825270	−	0.564738i	$-0.808977\pi$
$433$	−0.0954302	+	0.138254i	−0.00458608	+	0.00664409i	0.820684	+	0.571382i	$0.193593\pi$
$434$	12.1337	−	2.99070i	0.582438	−	0.143558i
$435$	−0.316969	−	0.459208i	−0.0151975	−	0.0220173i
$436$	1.79362	−	14.7718i	0.0858987	−	0.707439i
$437$	−8.70173			−0.416260
$438$	2.44471	−	20.1340i	0.116813	−	0.962039i
$439$	9.61990	+	25.3656i	0.459133	+	1.21063i	0.942200	+	0.335051i	$0.108753\pi$
$439$	9.61990	+	25.3656i	0.459133	+	1.21063i	−0.483067	+	0.875583i	$0.660477\pi$
$440$	−3.20977	+	1.68462i	−0.153020	+	0.0803110i
$441$	−0.687254	+	5.66005i	−0.0327264	+	0.269526i
$442$	3.86066	+	0.321621i	0.183633	+	0.0152980i
$443$	2.17926	+	17.9478i	0.103540	+	0.852725i	0.948255	+	0.317509i	$0.102847\pi$
$443$	2.17926	+	17.9478i	0.103540	+	0.852725i	−0.844716	+	0.535216i	$0.820230\pi$
$444$	6.68990	+	9.69199i	0.317489	+	0.459962i
$445$	2.54975	−	3.69395i	0.120870	−	0.175110i
$446$	11.5352	−	10.2193i	0.546207	−	0.483897i
$447$	2.50626	+	6.60846i	0.118542	+	0.312569i
$448$	−0.474282	+	0.687116i	−0.0224077	+	0.0324632i
$449$	31.9183	+	16.7520i	1.50632	+	0.790577i	0.997525	−	0.0703116i	$-0.0223994\pi$
$449$	31.9183	+	16.7520i	1.50632	+	0.790577i	0.508794	+	0.860889i	$0.330092\pi$
$450$	−0.936459	+	7.71243i	−0.0441451	+	0.363568i
$451$	3.43648	+	28.3019i	0.161817	+	1.33269i
$452$	−3.65573	+	9.63938i	−0.171951	+	0.453398i
$453$	−5.29321	+	7.66854i	−0.248697	+	0.360299i
$454$	0.109876	+	0.0973413i	0.00515672	+	0.00456846i
$455$	−1.42726	+	2.98810i	−0.0669109	+	0.140084i
$456$	−1.41876	+	1.25691i	−0.0664395	+	0.0588602i
$457$	−4.00471	−	32.9817i	−0.187332	−	1.54282i	−0.718484	−	0.695544i	$-0.755164\pi$
$457$	−4.00471	−	32.9817i	−0.187332	−	1.54282i	0.531151	−	0.847277i	$-0.321760\pi$
$458$	−1.20813	−	9.94983i	−0.0564521	−	0.464925i
$459$	−0.532735	+	0.279601i	−0.0248659	+	0.0130506i
$460$	−5.64169	+	2.96099i	−0.263045	+	0.138057i
$461$	−37.8905	−	9.33916i	−1.76474	−	0.434968i	−0.782504	−	0.622645i	$-0.786058\pi$
$461$	−37.8905	−	9.33916i	−1.76474	−	0.434968i	−0.982231	+	0.187677i	$0.939904\pi$
$462$	4.73148	−	4.19172i	0.220128	−	0.195017i
$463$	26.9805	+	6.65009i	1.25389	+	0.309056i	0.809682	−	0.586869i	$-0.199640\pi$
$463$	26.9805	+	6.65009i	1.25389	+	0.309056i	0.444206	+	0.895924i	$0.353486\pi$
$464$	1.21860	+	3.21319i	0.0565722	+	0.149169i
$465$	4.38295	−	2.30035i	0.203255	−	0.106676i
$466$	−3.76610	+	31.0166i	−0.174461	+	1.43682i
$467$	−15.1947	+	3.74515i	−0.703126	+	0.173305i	−0.574640	−	0.818406i	$-0.694858\pi$
$467$	−15.1947	+	3.74515i	−0.703126	+	0.173305i	−0.128486	+	0.991711i	$0.541012\pi$
$468$	−4.23429	+	0.677010i	−0.195730	+	0.0312948i
$469$	9.43315	+	2.32506i	0.435582	+	0.107361i
$470$	4.52955	−	11.9434i	0.208932	−	0.550910i
$471$	−8.13361	−	7.20575i	−0.374777	−	0.332024i
$472$	7.60146	−	1.87359i	0.349885	−	0.0862390i
$473$	20.5512	+	29.7735i	0.944943	+	1.36899i
$474$	−0.421811	−	3.47392i	−0.0193744	−	0.159563i
$475$	2.01961	+	5.32528i	0.0926661	+	0.244340i
$476$	−0.289121	+	0.762350i	−0.0132518	+	0.0349422i
$477$	2.93637	+	4.25407i	0.134447	+	0.194780i
$478$	10.2975	+	2.53809i	0.470995	+	0.116090i
$479$	−1.05425	−	2.77984i	−0.0481700	−	0.127014i	0.908772	−	0.417293i	$-0.137021\pi$
$479$	−1.05425	−	2.77984i	−0.0481700	−	0.127014i	−0.956942	+	0.290279i	$0.906252\pi$
$480$	−1.70626	+	4.49903i	−0.0778796	+	0.205352i
$481$	−17.7722	−	30.9652i	−0.810341	−	1.41189i
$482$	0.318455	+	0.839697i	0.0145052	+	0.0382472i
$483$	−5.66896	+	5.02226i	−0.257947	+	0.228521i
$484$	−1.60625			−0.0730113
$485$	10.1711			0.461846
$486$	1.33674	−	1.18424i	0.0606356	−	0.0537184i
$487$	−26.5940	+	13.9576i	−1.20509	+	0.632479i	−0.943073	−	0.332585i	$-0.892079\pi$
$487$	−26.5940	+	13.9576i	−1.20509	+	0.632479i	−0.262015	+	0.965064i	$0.584387\pi$
$488$	−20.3025			−0.919051
$489$	−13.1136	−	6.88255i	−0.593017	−	0.311240i
$490$	6.14315	+	5.44235i	0.277519	+	0.245860i
$491$	20.3679	+	29.5081i	0.919192	+	1.33168i	0.943290	+	0.331970i	$0.107713\pi$
$491$	20.3679	+	29.5081i	0.919192	+	1.33168i	−0.0240974	+	0.999710i	$0.507671\pi$
$492$	8.17019	+	7.23815i	0.368340	+	0.326321i
$493$	0.236599	+	0.342773i	0.0106559	+	0.0154377i
$494$	−6.75214	+	5.04689i	−0.303793	+	0.227070i
$495$	1.42231	−	2.06058i	0.0639282	−	0.0926161i
$496$	−29.6000	+	7.29575i	−1.32908	+	0.327589i
$497$	−12.1674	+	10.7794i	−0.545782	+	0.483520i
$498$	2.66944	+	0.657957i	0.119620	+	0.0294838i
$499$	−16.5675	−	14.6775i	−0.741663	−	0.657056i	0.205190	−	0.978722i	$-0.434219\pi$
$499$	−16.5675	−	14.6775i	−0.741663	−	0.657056i	−0.946853	+	0.321666i	$0.895757\pi$
$500$	6.70907	+	5.94372i	0.300039	+	0.265811i
$501$	2.02533	−	5.34035i	0.0904850	−	0.238589i
$502$	−23.7162	+	34.3589i	−1.05851	+	1.53351i
$503$	−21.0508	−	11.0483i	−0.938608	−	0.492620i	−0.0752241	−	0.997167i	$-0.523967\pi$
$503$	−21.0508	−	11.0483i	−0.938608	−	0.492620i	−0.863384	+	0.504547i	$0.831660\pi$
$504$	−0.198852	+	1.63769i	−0.00885757	+	0.0729486i
$505$	0.636621	+	0.156913i	0.0283292	+	0.00698253i
$506$	−36.8725			−1.63918
$507$	12.9630	−	0.979661i	0.575709	−	0.0435083i
$508$	−21.2916			−0.944662
$509$	25.8637	+	6.37482i	1.14639	+	0.282559i	0.766357	−	0.642415i	$-0.222068\pi$
$509$	25.8637	+	6.37482i	1.14639	+	0.282559i	0.380030	+	0.924974i	$0.375914\pi$
$510$	−0.104390	+	0.859727i	−0.00462245	+	0.0380693i
$511$	−11.4585	−	6.01389i	−0.506895	−	0.266039i
$512$	8.66885	−	12.5590i	0.383113	−	0.555035i
$513$	0.464243	−	1.22411i	0.0204968	−	0.0540457i
$514$	−24.2868	−	21.5163i	−1.07125	−	0.949042i
$515$	−6.03088	−	5.34289i	−0.265752	−	0.235436i
$516$	13.4484	+	3.31474i	0.592034	+	0.145923i
$517$	20.6331	−	18.2793i	0.907442	−	0.803923i
$518$	19.5647	−	4.82227i	0.859624	−	0.211878i
$519$	7.95050	−	11.5183i	0.348988	−	0.505597i
$520$	1.81347	−	3.79667i	0.0795261	−	0.166495i
$521$	−16.0736	−	23.2866i	−0.704195	−	1.02020i	−0.997930	−	0.0643161i	$-0.979513\pi$
$521$	−16.0736	−	23.2866i	−0.704195	−	1.02020i	0.293734	−	0.955887i	$-0.405102\pi$
$522$	−0.925373	−	0.819809i	−0.0405025	−	0.0358821i
$523$	9.69012	+	14.0386i	0.423719	+	0.613863i	0.975466	−	0.220148i	$-0.0706541\pi$
$523$	9.69012	+	14.0386i	0.423719	+	0.613863i	−0.551747	+	0.834011i	$0.686039\pi$
$524$	13.1686	+	11.6664i	0.575274	+	0.509648i
$525$	4.38925	+	2.30365i	0.191562	+	0.100540i
$526$	20.9492			0.913429
$527$	−3.27163	+	1.71708i	−0.142514	+	0.0747973i
$528$	−11.5424	+	10.2256i	−0.502317	+	0.445014i
$529$	21.1783			0.920797
$530$	7.44060			0.323199
$531$	−4.04755	+	3.58582i	−0.175649	+	0.155611i
$532$	−0.629125	−	1.65887i	−0.0272760	−	0.0719210i
$533$	−22.8620	−	23.9243i	−0.990264	−	1.03627i
$534$	3.52651	−	9.29864i	0.152607	−	0.402391i
$535$	2.99635	+	7.90072i	0.129543	+	0.341578i
$536$	−11.9857	−	2.95422i	−0.517705	−	0.127603i
$537$	4.12084	+	5.97006i	0.177827	+	0.257627i
$538$	1.66474	−	4.38957i	0.0717722	−	0.189248i
$539$	6.28049	+	16.5603i	0.270520	+	0.713302i
$540$	−0.115546	−	0.951610i	−0.00497233	−	0.0409508i
$541$	−12.8988	−	18.6871i	−0.554562	−	0.803422i	0.441002	−	0.897506i	$-0.354623\pi$
$541$	−12.8988	−	18.6871i	−0.554562	−	0.803422i	−0.995564	+	0.0940844i	$0.970008\pi$
$542$	11.7089	−	2.88599i	0.502942	−	0.123964i
$543$	12.4420	+	11.0226i	0.533936	+	0.473026i
$544$	1.27362	−	3.35827i	0.0546062	−	0.143985i
$545$	−9.79176	−	2.41345i	−0.419433	−	0.103381i
$546$	−1.48601	+	7.18497i	−0.0635952	+	0.307488i
$547$	22.0166	−	5.42661i	0.941363	−	0.232025i	0.261366	−	0.965240i	$-0.415827\pi$
$547$	22.0166	−	5.42661i	0.941363	−	0.232025i	0.679997	+	0.733215i	$0.261981\pi$
$548$	−1.12414	+	9.25812i	−0.0480208	+	0.395487i
$549$	12.4167	−	6.51680i	0.529933	−	0.278130i
$550$	8.55785	+	22.5652i	0.364908	+	0.962183i
$551$	−0.879965	−	0.216892i	−0.0374878	−	0.00923990i
$552$	7.20298	−	6.38128i	0.306579	−	0.271605i
$553$	−2.16793	−	0.534347i	−0.0921898	−	0.0227227i
$554$	4.12339	−	2.16412i	0.175186	−	0.0919448i
$555$	7.06717	−	3.70914i	0.299985	−	0.157444i
$556$	2.28699	+	18.8350i	0.0969898	+	0.798783i
$557$	−3.47110	−	28.5871i	−0.147075	−	1.21127i	−0.860097	−	0.510131i	$-0.829597\pi$
$557$	−3.47110	−	28.5871i	−0.147075	−	1.21127i	0.713021	−	0.701142i	$-0.247326\pi$
$558$	8.20915	−	7.27267i	0.347521	−	0.307877i
$559$	−39.7961	−	13.3993i	−1.68320	−	0.566730i
$560$	3.41266	+	3.02335i	0.144211	+	0.127760i
$561$	−1.06168	+	1.53810i	−0.0448240	+	0.0649388i
$562$	−2.48996	+	6.56548i	−0.105033	+	0.276948i
$563$	−3.11066	−	25.6186i	−0.131099	−	1.07970i	−0.898637	−	0.438693i	$-0.855442\pi$
$563$	−3.11066	−	25.6186i	−0.131099	−	1.07970i	0.767538	−	0.641003i	$-0.221481\pi$
$564$	1.27211	−	10.4768i	0.0535655	−	0.441152i
$565$	6.18663	+	3.24699i	0.260273	+	0.136602i
$566$	−2.55279	+	3.69835i	−0.107302	+	0.155453i
$567$	−0.404060	−	1.06542i	−0.0169689	−	0.0447434i
$568$	15.4599	−	13.6962i	0.648681	−	0.574681i
$569$	−22.5804	+	32.7134i	−0.946620	+	1.37142i	−0.0182203	+	0.999834i	$0.505800\pi$
$569$	−22.5804	+	32.7134i	−0.946620	+	1.37142i	−0.928400	+	0.371582i	$0.878815\pi$
$570$	−1.07052	−	1.55091i	−0.0448390	−	0.0649605i
$571$	4.99857	+	41.1670i	0.209184	+	1.72278i	0.598024	+	0.801479i	$0.295953\pi$
$571$	4.99857	+	41.1670i	0.209184	+	1.72278i	−0.388840	+	0.921305i	$0.627124\pi$
$572$	−10.6692	+	7.97473i	−0.446103	+	0.333440i
$573$	1.33929	−	11.0301i	0.0559498	−	0.460788i
$574$	16.5371	−	8.67934i	0.690245	−	0.362269i
$575$	−10.2535	−	27.0362i	−0.427600	−	1.12749i
$576$	−0.0883196	+	0.727377i	−0.00367998	+	0.0303074i
$577$	−40.9148			−1.70331			−0.851654	−	0.524105i	$-0.824400\pi$
$577$	−40.9148			−1.70331			−0.851654	+	0.524105i	$0.824400\pi$
$578$	−3.58153	+	29.4965i	−0.148972	+	1.22689i
$579$	−9.17594	−	13.2936i	−0.381339	−	0.552465i
$580$	−0.644320	+	0.158811i	−0.0267539	+	0.00659425i
$581$	0.996502	−	1.44368i	0.0413418	−	0.0598940i
$582$	21.8807	−	5.39312i	0.906986	−	0.223552i
$583$	14.2177	+	7.46205i	0.588839	+	0.309046i
$584$	14.5592	+	7.64124i	0.602463	+	0.316197i
$585$	0.109580	+	2.90409i	0.00453056	+	0.120069i
$586$	−27.2994	+	14.3278i	−1.12773	+	0.591876i
$587$	−15.3070			−0.631789			−0.315895	−	0.948794i	$-0.602305\pi$
$587$	−15.3070			−0.631789			−0.315895	+	0.948794i	$0.602305\pi$
$588$	6.00420	+	3.15125i	0.247609	+	0.129955i
$589$	2.85101	−	7.51749i	0.117474	−	0.309753i
$590$	0.938227	+	7.72700i	0.0386262	+	0.318115i
$591$	−6.08294	+	1.49931i	−0.250219	+	0.0616734i
$592$	−47.7278	+	11.7638i	−1.96160	+	0.483491i
$593$	−3.79064	−	31.2187i	−0.155663	−	1.28200i	−0.835849	−	0.548960i	$-0.815024\pi$
$593$	−3.79064	−	31.2187i	−0.155663	−	1.28200i	0.680186	−	0.733040i	$-0.261899\pi$
$594$	1.96717	−	5.18701i	0.0807141	−	0.212826i
$595$	0.489282	+	0.256795i	0.0200586	+	0.0105276i
$596$	8.40565			0.344309
$597$	6.51768	−	3.42074i	0.266751	−	0.140002i
$598$	34.2803	−	25.6229i	1.40183	−	1.04780i
$599$	−14.2935	−	7.50183i	−0.584019	−	0.306517i	0.146716	−	0.989179i	$-0.453130\pi$
$599$	−14.2935	−	7.50183i	−0.584019	−	0.306517i	−0.730734	+	0.682662i	$0.760822\pi$
$600$	−5.57697	−	2.92702i	−0.227679	−	0.119495i
$601$	34.4504	−	8.49127i	1.40526	−	0.346366i	0.537466	−	0.843285i	$-0.319382\pi$
$601$	34.4504	−	8.49127i	1.40526	−	0.346366i	0.867797	+	0.496919i	$0.165535\pi$
$602$	13.4628	−	19.5042i	0.548701	−	0.794931i
$603$	8.27857	−	2.04049i	0.337130	−	0.0830950i
$604$	6.29519	+	9.12016i	0.256148	+	0.371094i
$605$	−0.131217	+	1.08067i	−0.00533471	+	0.0439353i
$606$	1.45274			0.0590135
$607$	−1.17983	+	9.71678i	−0.0478878	+	0.394392i	0.948982	+	0.315331i	$0.102115\pi$
$607$	−1.17983	+	9.71678i	−0.0478878	+	0.394392i	−0.996870	+	0.0790613i	$0.974808\pi$
$608$	2.77139	+	7.30757i	0.112395	+	0.296361i
$609$	−0.698456	+	0.366578i	−0.0283029	+	0.0148545i
$610$	2.43307	−	20.0381i	0.0985119	−	0.811319i
$611$	−6.48019	+	31.3323i	−0.262160	+	1.26757i
$612$	0.0862489	+	0.710323i	0.00348640	+	0.0287131i
$613$	0.262751	+	0.380661i	0.0106124	+	0.0153747i	0.828254	−	0.560353i	$-0.189334\pi$
$613$	0.262751	+	0.380661i	0.0106124	+	0.0153747i	−0.817642	+	0.575727i	$0.804719\pi$
$614$	−3.92363	+	5.68436i	−0.158345	+	0.229402i
$615$	5.53718	−	4.90552i	0.223281	−	0.197810i
$616$	1.81721	+	4.79159i	0.0732176	+	0.193059i
$617$	−7.69168	+	11.1433i	−0.309655	+	0.448613i	−0.946654	−	0.322252i	$-0.895560\pi$
$617$	−7.69168	+	11.1433i	−0.309655	+	0.448613i	0.636999	+	0.770865i	$0.280176\pi$
$618$	−15.8070	−	8.29616i	−0.635851	−	0.333721i
$619$	5.24623	−	43.2066i	0.210864	−	1.73662i	−0.375722	−	0.926732i	$-0.622605\pi$
$619$	5.24623	−	43.2066i	0.210864	−	1.73662i	0.586586	−	0.809887i	$-0.300472\pi$
$620$	−0.709593	−	5.84402i	−0.0284979	−	0.234702i
$621$	−2.35694	+	6.21475i	−0.0945809	+	0.249389i
$622$	14.2123	−	20.5901i	0.569863	−	0.825589i
$623$	−4.74954	−	4.20773i	−0.190286	−	0.168579i
$624$	3.62509	−	17.5276i	0.145120	−	0.701666i
$625$	−11.7344	+	10.3958i	−0.469376	+	0.415831i
$626$	−4.12105	−	33.9399i	−0.164710	−	1.35651i
$627$	−0.490197	−	4.03714i	−0.0195766	−	0.161228i
$628$	−11.4431	+	6.00579i	−0.456628	+	0.239657i
$629$	−5.27524	+	2.76866i	−0.210338	+	0.110394i
$630$	−1.59253	−	0.392524i	−0.0634481	−	0.0156385i
$631$	9.59051	−	8.49645i	0.381792	−	0.338238i	−0.450298	−	0.892878i	$-0.648682\pi$
$631$	9.59051	−	8.49645i	0.381792	−	0.338238i	0.832091	+	0.554640i	$0.187144\pi$
$632$	2.75457	+	0.678940i	0.109571	+	0.0270068i
$633$	3.48859	+	9.19865i	0.138659	+	0.365614i
$634$	−36.0556	+	18.9235i	−1.43195	+	0.751547i
$635$	−1.73934	+	14.3248i	−0.0690236	+	0.568461i
$636$	5.96893	−	1.47121i	0.236684	−	0.0583373i
$637$	−17.3468	−	11.0317i	−0.687304	−	0.437094i
$638$	−3.72874	−	0.919052i	−0.147622	−	0.0363856i
$639$	−5.05874	+	13.3388i	−0.200121	+	0.527675i
$640$	−6.41378	−	5.68211i	−0.253527	−	0.224605i
$641$	12.2809	−	3.02697i	0.485066	−	0.119558i	0.0108037	−	0.999942i	$-0.496561\pi$
$641$	12.2809	−	3.02697i	0.485066	−	0.119558i	0.474262	+	0.880384i	$0.342715\pi$
$642$	10.6352	+	15.4078i	0.419738	+	0.608095i
$643$	2.15456	+	17.7444i	0.0849676	+	0.699771i	0.971489	+	0.237084i	$0.0761916\pi$
$643$	2.15456	+	17.7444i	0.0849676	+	0.699771i	−0.886522	+	0.462687i	$0.846885\pi$
$644$	3.19404	+	8.42200i	0.125863	+	0.331873i
$645$	3.32874	−	8.77716i	0.131069	−	0.345600i
$646$	0.799080	+	1.15767i	0.0314394	+	0.0455478i
$647$	7.44566	+	1.83519i	0.292719	+	0.0721488i	0.382941	−	0.923773i	$-0.374911\pi$
$647$	7.44566	+	1.83519i	0.292719	+	0.0721488i	−0.0902216	+	0.995922i	$0.528758\pi$
$648$	0.513398	+	1.35372i	0.0201682	+	0.0531791i
$649$	−5.95648	+	15.7059i	−0.233812	+	0.616512i
$650$	−23.6369	−	15.0320i	−0.927114	−	0.589602i
$651$	−2.48141	−	6.54294i	−0.0972541	−	0.256438i
$652$	−13.1839	+	11.6799i	−0.516320	+	0.457420i
$653$	35.9320			1.40613			0.703064	−	0.711127i	$-0.251815\pi$
$653$	35.9320			1.40613			0.703064	+	0.711127i	$0.251815\pi$
$654$	−22.3444			−0.873733
$655$	8.92477	−	7.90666i	0.348720	−	0.308939i
$656$	−40.3420	+	21.1731i	−1.57509	+	0.826671i
$657$	−11.3569			−0.443075
$658$	−15.9894	−	8.39186i	−0.623330	−	0.327149i
$659$	−23.9431	−	21.2117i	−0.932691	−	0.826292i	0.0523474	−	0.998629i	$-0.483330\pi$
$659$	−23.9431	−	21.2117i	−0.932691	−	0.826292i	−0.985038	+	0.172337i	$0.944868\pi$
$660$	−1.69155	−	2.45064i	−0.0658436	−	0.0953909i
$661$	15.5068	+	13.7379i	0.603146	+	0.534341i	0.908493	−	0.417901i	$-0.137234\pi$
$661$	15.5068	+	13.7379i	0.603146	+	0.534341i	−0.305347	+	0.952241i	$0.598772\pi$
$662$	−34.4421	−	49.8980i	−1.33863	−	1.93934i
$663$	−0.0817950	−	2.16774i	−0.00317666	−	0.0841879i
$664$	−1.26615	+	1.83434i	−0.0491363	+	0.0711862i
$665$	−1.16746	+	0.287753i	−0.0452722	+	0.0111586i
$666$	13.2366	−	11.7266i	0.512909	−	0.454397i
$667$	4.46755	+	1.10115i	0.172984	+	0.0426368i
$668$	−5.08439	−	4.50438i	−0.196721	−	0.174280i
$669$	−6.45918	−	5.72233i	−0.249726	−	0.221238i
$670$	4.35213	−	11.4756i	0.168137	−	0.443342i
$671$	24.7450	−	35.8494i	0.955272	−	1.38395i
$672$	6.02311	+	3.16117i	0.232346	+	0.121945i
$673$	2.55646	−	21.0543i	0.0985441	−	0.811584i	−0.856710	−	0.515798i	$-0.827495\pi$
$673$	2.55646	−	21.0543i	0.0985441	−	0.811584i	0.955254	−	0.295786i	$-0.0955815\pi$
$674$	4.42107	+	1.08970i	0.170293	+	0.0419735i
$675$	4.35033			0.167444
$676$	4.37751	−	14.8282i	0.168366	−	0.570315i
$677$	7.49368			0.288005			0.144003	−	0.989577i	$-0.454003\pi$
$677$	7.49368			0.288005			0.144003	+	0.989577i	$0.454003\pi$
$678$	15.0307	+	3.70475i	0.577252	+	0.142280i
$679$	1.73317	−	14.2740i	0.0665130	−	0.547784i
$680$	−0.621681	−	0.326283i	−0.0238404	−	0.0125124i
$681$	0.0466932	−	0.0676468i	0.00178929	−	0.00259223i
$682$	12.0808	−	31.8544i	0.462597	−	1.21977i
$683$	26.6925	+	23.6475i	1.02136	+	0.904845i	0.995494	−	0.0948200i	$-0.0302276\pi$
$683$	26.6925	+	23.6475i	1.02136	+	0.904845i	0.0258649	+	0.999665i	$0.491766\pi$
$684$	−1.16544	−	1.03249i	−0.0445616	−	0.0394782i
$685$	6.13693	+	1.51262i	0.234480	+	0.0577941i
$686$	19.3466	−	17.1396i	0.738658	−	0.654394i
$687$	−5.44928	+	1.34313i	−0.207903	+	0.0512435i
$688$	−32.8422	+	47.5801i	−1.25210	+	1.81398i
$689$	−18.4036	+	2.94251i	−0.701123	+	0.112101i
$690$	5.43497	+	7.87391i	0.206906	+	0.299755i
$691$	4.24932	+	3.76457i	0.161652	+	0.143211i	0.740071	−	0.672529i	$-0.234792\pi$
$691$	4.24932	+	3.76457i	0.161652	+	0.143211i	−0.578419	+	0.815740i	$0.696330\pi$
$692$	−9.45550	−	13.6987i	−0.359444	−	0.520745i
$693$	−2.64941	−	2.34717i	−0.100643	−	0.0891618i
$694$	48.3849	+	25.3944i	1.83667	+	0.963957i
$695$	12.8588			0.487763
$696$	0.887458	−	0.465774i	0.0336390	−	0.0176551i
$697$	−4.13319	+	3.66169i	−0.156556	+	0.138696i
$698$	−9.79364			−0.370695
$699$	17.4954			0.661738
$700$	4.41277	−	3.90937i	0.166787	−	0.147760i
$701$	15.5296	+	40.9482i	0.586545	+	1.54659i	0.818885	+	0.573958i	$0.194593\pi$
$701$	15.5296	+	40.9482i	0.586545	+	1.54659i	−0.232340	+	0.972635i	$0.574638\pi$
$702$	1.77559	+	6.18936i	0.0670155	+	0.233602i
$703$	4.59703	−	12.1214i	0.173380	−	0.457166i
$704$	0.807111	+	2.12818i	0.0304191	+	0.0802086i
$705$	−6.94474	−	1.71172i	−0.261554	−	0.0644673i
$706$	13.6069	+	19.7130i	0.512101	+	0.741907i
$707$	0.328690	−	0.866684i	0.0123616	−	0.0325950i
$708$	2.28050	+	6.01317i	0.0857063	+	0.225989i
$709$	−2.15297	−	17.7313i	−0.0808565	−	0.665913i	−0.975635	−	0.219402i	$-0.929589\pi$
$709$	−2.15297	−	17.7313i	−0.0808565	−	0.665913i	0.894778	−	0.446511i	$-0.147334\pi$
$710$	11.6652	+	16.8999i	0.437785	+	0.634242i
$711$	−1.90259	+	0.468945i	−0.0713525	+	0.0175868i
$712$	6.03476	+	5.34633i	0.226162	+	0.200362i
$713$	−14.4745	+	38.1660i	−0.542072	+	1.42933i
$714$	1.18874	+	0.292997i	0.0444873	+	0.0109651i
$715$	4.49372	+	7.82961i	0.168056	+	0.292811i
$716$	8.37666	−	2.06466i	0.313051	−	0.0771601i
$717$	0.715828	−	5.89537i	0.0267331	−	0.220167i
$718$	2.66130	−	1.39676i	0.0993188	−	0.0521265i
$719$	−7.43693	−	19.6096i	−0.277351	−	0.731314i	−0.999228	−	0.0392924i	$-0.987490\pi$
$719$	−7.43693	−	19.6096i	−0.277351	−	0.731314i	0.721877	−	0.692021i	$-0.243280\pi$
$720$	3.88496	+	0.957557i	0.144784	+	0.0356860i
$721$	−8.52579	+	7.55319i	−0.317517	+	0.281295i
$722$	29.9734	+	7.38778i	1.11549	+	0.274945i
$723$	0.445270	−	0.233696i	0.0165598	−	0.00869123i
$724$	17.5044	−	9.18704i	0.650547	−	0.341434i
$725$	−0.363005	−	2.98961i	−0.0134817	−	0.111031i
$726$	0.290730	+	2.39437i	0.0107900	+	0.0888635i
$727$	2.07293	−	1.83646i	0.0768807	−	0.0681104i	−0.623807	−	0.781578i	$-0.714415\pi$
$727$	2.07293	−	1.83646i	0.0768807	−	0.0681104i	0.700688	+	0.713468i	$0.252877\pi$
$728$	−5.01916	−	3.19195i	−0.186022	−	0.118302i
$729$	−0.748511	−	0.663123i	−0.0277226	−	0.0245601i
$730$	−9.28651	+	13.4538i	−0.343709	+	0.497949i
$731$	−2.48471	+	6.55165i	−0.0919005	+	0.242322i
$732$	−2.01025	−	16.5559i	−0.0743009	−	0.611923i
$733$	−0.0753858	+	0.620858i	−0.00278444	+	0.0229319i	−0.994035	−	0.109063i	$-0.965215\pi$
$733$	−0.0753858	+	0.620858i	−0.00278444	+	0.0229319i	0.991250	+	0.131995i	$0.0421382\pi$
$734$	−42.3318	−	22.2174i	−1.56249	−	0.820061i
$735$	2.61062	−	3.78213i	0.0962941	−	0.139506i
$736$	−14.0703	−	37.1002i	−0.518637	−	1.36753i
$737$	19.8249	−	17.5633i	0.730259	−	0.646953i
$738$	9.31084	−	13.4891i	0.342737	−	0.496540i
$739$	−10.9081	−	15.8031i	−0.401259	−	0.581325i	0.569317	−	0.822118i	$-0.307208\pi$
$739$	−10.9081	−	15.8031i	−0.401259	−	0.581325i	−0.970576	+	0.240793i	$0.922592\pi$
$740$	−1.14416	−	9.42304i	−0.0420603	−	0.346398i
$741$	3.26116	+	3.41268i	0.119802	+	0.125368i
$742$	1.26789	−	10.4420i	0.0465456	−	0.383338i
$743$	24.2527	−	12.7288i	0.889744	−	0.466974i	0.0430616	−	0.999072i	$-0.486289\pi$
$743$	24.2527	−	12.7288i	0.889744	−	0.466974i	0.846682	+	0.532099i	$0.178597\pi$
$744$	3.15288	+	8.31345i	0.115590	+	0.304786i
$745$	0.686669	−	5.65523i	0.0251576	−	0.207191i
$746$	−31.0464			−1.13669
$747$	0.185566	−	1.52827i	0.00678950	−	0.0559166i
$748$	1.26265	+	1.82926i	0.0461670	+	0.0668844i
$749$	11.5983	−	2.85873i	0.423793	−	0.104456i
$750$	7.64573	−	11.0768i	0.279183	−	0.404466i
$751$	19.5135	−	4.80966i	0.712059	−	0.175507i	0.133383	−	0.991065i	$-0.457416\pi$
$751$	19.5135	−	4.80966i	0.712059	−	0.175507i	0.578676	+	0.815558i	$0.303570\pi$
$752$	39.0058	+	20.4718i	1.42239	+	0.746530i
$753$	20.6999	+	10.8641i	0.754345	+	0.395911i
$754$	4.10526	−	1.73668i	0.149505	−	0.0632460i
$755$	6.65021	−	3.49030i	0.242026	−	0.127025i
$756$	−1.35516			−0.0492868
$757$	14.6068	+	7.66625i	0.530894	+	0.278635i	0.708796	−	0.705414i	$-0.249239\pi$
$757$	14.6068	+	7.66625i	0.530894	+	0.278635i	−0.177902	+	0.984048i	$0.556931\pi$
$758$	−12.2035	+	32.1780i	−0.443251	+	1.16876i
$759$	2.48871	+	20.4964i	0.0903345	+	0.743971i
$760$	1.48337	−	0.365619i	0.0538076	−	0.0132624i
$761$	−46.8753	+	11.5537i	−1.69923	+	0.418822i	−0.965454	−	0.260572i	$-0.916089\pi$
$761$	−46.8753	+	11.5537i	−1.69923	+	0.418822i	−0.733773	+	0.679394i	$0.762243\pi$
$762$	3.85376	+	31.7386i	0.139607	+	1.14977i
$763$	−5.05552	+	13.3303i	−0.183022	+	0.482590i
$764$	−11.7007	−	6.14102i	−0.423318	−	0.222174i
$765$	0.484943			0.0175332
$766$	−49.7961	+	26.1350i	−1.79921	+	0.944296i
$767$	−5.37639	−	18.7410i	−0.194130	−	0.676697i
$768$	−18.1082	−	9.50391i	−0.653423	−	0.342943i
$769$	1.32120	+	0.693419i	0.0476437	+	0.0250053i	0.488377	−	0.872633i	$-0.337589\pi$
$769$	1.32120	+	0.693419i	0.0476437	+	0.0250053i	−0.440733	+	0.897638i	$0.645281\pi$
$770$	−4.94697	+	1.21932i	−0.178276	+	0.0439412i
$771$	−10.3210	+	14.9526i	−0.371703	+	0.538505i
$772$	−18.6525	+	4.59742i	−0.671317	+	0.165465i
$773$	−8.51278	−	12.3329i	−0.306184	−	0.443583i	0.639443	−	0.768839i	$-0.279165\pi$
$773$	−8.51278	−	12.3329i	−0.306184	−	0.443583i	−0.945626	+	0.325255i	$0.894550\pi$
$774$	2.50700	−	20.6470i	0.0901123	−	0.742142i
$775$	26.7162			0.959674
$776$	−2.20217	+	18.1365i	−0.0790532	+	0.651061i
$777$	−4.00108	−	10.5500i	−0.143538	−	0.378479i
$778$	−28.3519	+	14.8802i	−1.01646	+	0.533482i
$779$	1.44832	−	11.9280i	0.0518914	−	0.427364i
$780$	3.27559	+	1.10289i	0.117285	+	0.0394897i
$781$	5.34155	+	43.9917i	0.191136	+	1.57415i
$782$	−4.05690	−	5.87743i	−0.145074	−	0.210176i
$783$	−0.393250	+	0.569721i	−0.0140536	+	0.0203602i
$784$	−21.1857	+	18.7689i	−0.756632	+	0.670317i
$785$	3.10583	+	8.18939i	0.110852	+	0.292292i
$786$	15.0071	−	21.7416i	0.535286	−	0.775496i
$787$	−21.6443	−	11.3598i	−0.771534	−	0.404933i	0.0325329	−	0.999471i	$-0.489643\pi$
$787$	−21.6443	−	11.3598i	−0.771534	−	0.404933i	−0.804067	+	0.594538i	$0.797335\pi$
$788$	−0.898110	+	7.39660i	−0.0319939	+	0.263493i
$789$	−1.41397	−	11.6451i	−0.0503386	−	0.414575i
$790$	−1.00021	+	2.63733i	−0.0355858	+	0.0938320i
$791$	5.61098	−	8.12891i	0.199503	−	0.289031i
$792$	3.36634	+	2.98232i	0.119618	+	0.105972i
$793$	1.90644	+	50.5246i	0.0676996	+	1.79418i
$794$	32.3930	−	28.6977i	1.14958	−	1.01844i
$795$	−0.502203	−	4.13602i	−0.0178113	−	0.146689i
$796$	−1.05520	−	8.69036i	−0.0374006	−	0.308022i
$797$	26.9259	−	14.1318i	0.953764	−	0.500574i	0.0853157	−	0.996354i	$-0.472810\pi$
$797$	26.9259	−	14.1318i	0.953764	−	0.500574i	0.868448	+	0.495780i	$0.165118\pi$
$798$	−2.35894	+	1.23807i	−0.0835055	+	0.0438271i
$799$	5.18385	+	1.27771i	0.183392	+	0.0452020i
$800$	−19.4389	+	17.2214i	−0.687271	+	0.608869i
$801$	−5.40687	−	1.33267i	−0.191042	−	0.0470877i
$802$	1.89805	+	5.00474i	0.0670224	+	0.176724i
$803$	−31.2376	+	16.3948i	−1.10235	+	0.578559i
$804$	1.22228	−	10.0664i	0.0431066	−	0.355015i
$805$	5.92715	−	1.46091i	0.208905	−	0.0514904i
$806$	10.9043	+	38.0100i	0.384087	+	1.33885i
$807$	−2.55240	−	0.629109i	−0.0898486	−	0.0221457i
$808$	−0.417633	+	1.10121i	−0.0146923	+	0.0387403i
$809$	22.8561	+	20.2488i	0.803579	+	0.711909i	0.961279	−	0.275578i	$-0.0888693\pi$
$809$	22.8561	+	20.2488i	0.803579	+	0.711909i	−0.157700	+	0.987487i	$0.550408\pi$
$810$	−1.39762	+	0.344481i	−0.0491072	+	0.0121038i
$811$	5.28685	+	7.65933i	0.185646	+	0.268955i	0.904746	−	0.425952i	$-0.140061\pi$
$811$	5.28685	+	7.65933i	0.185646	+	0.268955i	−0.719099	+	0.694907i	$0.755445\pi$
$812$	0.113079	+	0.931289i	0.00396829	+	0.0326818i
$813$	−2.39454	−	6.31387i	−0.0839800	−	0.221437i
$814$	19.4793	−	51.3628i	0.682751	−	1.80027i
$815$	6.78109	+	9.82411i	0.237531	+	0.344124i
$816$	−2.89990	−	0.714762i	−0.101517	−	0.0250217i
$817$	−5.40672	−	14.2563i	−0.189157	−	0.498766i
$818$	−6.29490	+	16.5983i	−0.220096	+	0.580345i
$819$	4.09422	+	0.341079i	0.143064	+	0.0119183i
$820$	−3.11979	−	8.22622i	−0.108948	−	0.287272i
$821$	29.5102	−	26.1437i	1.02991	−	0.912423i	0.0337046	−	0.999432i	$-0.489269\pi$
$821$	29.5102	−	26.1437i	1.02991	−	0.912423i	0.996207	+	0.0870093i	$0.0277310\pi$
$822$	14.0042			0.488452
$823$	2.57528			0.0897687			0.0448843	−	0.998992i	$-0.485708\pi$
$823$	2.57528			0.0897687			0.0448843	+	0.998992i	$0.485708\pi$
$824$	10.8329	−	9.59707i	0.377380	−	0.334330i
$825$	11.9657	−	6.28010i	0.416593	−	0.218645i
$826$	11.0038			0.382871
$827$	−14.2249	−	7.46582i	−0.494649	−	0.259612i	0.198902	−	0.980019i	$-0.436263\pi$
$827$	−14.2249	−	7.46582i	−0.494649	−	0.259612i	−0.693551	+	0.720407i	$0.743955\pi$
$828$	5.91688	+	5.24190i	0.205626	+	0.182169i
$829$	−8.56700	−	12.4114i	−0.297544	−	0.431067i	0.645487	−	0.763771i	$-0.276654\pi$
$829$	−8.56700	−	12.4114i	−0.297544	−	0.431067i	−0.943031	+	0.332704i	$0.892039\pi$
$830$	−1.65871	−	1.46949i	−0.0575748	−	0.0510068i
$831$	−1.48128	−	2.14601i	−0.0513852	−	0.0744443i
$832$	−2.22925	−	1.41770i	−0.0772853	−	0.0491499i
$833$	−1.94868	+	2.82315i	−0.0675177	+	0.0978162i
$834$	27.6627	−	6.81824i	0.957881	−	0.236096i
$835$	−3.44585	+	3.05275i	−0.119248	+	0.105645i
$836$	−4.69607	−	1.15748i	−0.162417	−	0.0400322i
$837$	−4.59675	−	4.07236i	−0.158887	−	0.140761i
$838$	−41.9422	−	37.1575i	−1.44887	−	1.28359i
$839$	11.2924	−	29.7757i	0.389858	−	1.02797i	−0.586143	−	0.810207i	$-0.699354\pi$
$839$	11.2924	−	29.7757i	0.389858	−	1.02797i	0.976001	−	0.217764i	$-0.0698763\pi$
$840$	0.755362	−	1.09433i	0.0260625	−	0.0377580i
$841$	−25.2539	−	13.2543i	−0.870824	−	0.457044i
$842$	0.0654478	−	0.539011i	0.00225548	−	0.0185756i
$843$	3.81762	+	0.940960i	0.131486	+	0.0324084i
$844$	11.7003			0.402739
$845$	−9.61864	−	4.15648i	−0.330891	−	0.142987i
$846$	−15.8476			−0.544851
$847$	1.49423	+	0.368294i	0.0513423	+	0.0126547i
$848$	−3.09299	+	25.4731i	−0.106214	+	0.874749i
$849$	2.22811	+	1.16940i	0.0764685	+	0.0401338i
$850$	−2.65529	+	3.84685i	−0.0910755	+	0.131946i
$851$	−23.3389	+	61.5397i	−0.800048	+	2.10955i
$852$	12.6995	+	11.2508i	0.435077	+	0.385445i
$853$	2.05415	+	1.81981i	0.0703326	+	0.0623093i	0.697557	−	0.716530i	$-0.254271\pi$
$853$	2.05415	+	1.81981i	0.0703326	+	0.0623093i	−0.627224	+	0.778839i	$0.715809\pi$
$854$	−27.7065	−	6.82904i	−0.948097	−	0.233685i
$855$	−0.789853	+	0.699748i	−0.0270124	+	0.0239309i
$856$	−14.7368	+	3.63229i	−0.503693	+	0.124149i
$857$	5.60840	−	8.12517i	0.191579	−	0.277551i	−0.715409	−	0.698706i	$-0.753760\pi$
$857$	5.60840	−	8.12517i	0.191579	−	0.277551i	0.906989	+	0.421155i	$0.138375\pi$
$858$	13.8187	+	14.4608i	0.471764	+	0.493684i
$859$	−0.661454	−	0.958281i	−0.0225685	−	0.0326961i	0.811537	−	0.584301i	$-0.198631\pi$
$859$	−0.661454	−	0.958281i	−0.0225685	−	0.0326961i	−0.834106	+	0.551605i	$0.814016\pi$
$860$	−8.35648	−	7.40319i	−0.284954	−	0.252447i
$861$	−5.94077	−	8.60669i	−0.202461	−	0.293315i
$862$	23.7104	+	21.0055i	0.807578	+	0.715452i
$863$	19.9325	+	10.4614i	0.678511	+	0.356110i	0.768515	−	0.639831i	$-0.220996\pi$
$863$	19.9325	+	10.4614i	0.678511	+	0.356110i	−0.0900045	+	0.995941i	$0.528688\pi$
$864$	5.96970			0.203093
$865$	−9.98874	+	5.24249i	−0.339627	+	0.178250i
$866$	0.224561	−	0.198943i	0.00763088	−	0.00676037i
$867$	16.6380			0.565057
$868$	−8.32231			−0.282478
$869$	−4.55617	+	4.03641i	−0.154557	+	0.136926i
$870$	0.353354	+	0.931719i	0.0119798	+	0.0315882i
$871$	−6.22636	+	30.1050i	−0.210972	+	1.02007i
$872$	6.42354	−	16.9375i	0.217529	−	0.573576i
$873$	−4.47472	−	11.7989i	−0.151446	−	0.399331i
$874$	15.0885	+	3.71898i	0.510376	+	0.125796i
$875$	−4.87835	−	7.06751i	−0.164918	−	0.238925i
$876$	−4.78956	+	12.6290i	−0.161824	+	0.426695i
$877$	−9.86093	−	26.0011i	−0.332980	−	0.877996i	−0.992042	−	0.125907i	$-0.959816\pi$
$877$	−9.86093	−	26.0011i	−0.332980	−	0.877996i	0.659062	−	0.752088i	$-0.270953\pi$
$878$	−5.83973	−	48.0945i	−0.197081	−	1.62311i
$879$	9.80699	+	14.2079i	0.330782	+	0.479220i
$880$	12.0681	−	2.97451i	0.406814	−	0.100271i
$881$	5.90323	+	5.22981i	0.198885	+	0.176197i	0.756687	−	0.653777i	$-0.226817\pi$
$881$	5.90323	+	5.22981i	0.198885	+	0.176197i	−0.557802	+	0.829974i	$0.688355\pi$
$882$	3.61069	−	9.52061i	0.121578	−	0.320576i
$883$	19.8947	+	4.90361i	0.669511	+	0.165020i	0.559398	−	0.828899i	$-0.311032\pi$
$883$	19.8947	+	4.90361i	0.669511	+	0.165020i	0.110113	+	0.993919i	$0.464879\pi$
$884$	−2.44504	−	0.823244i	−0.0822358	−	0.0276887i
$885$	4.23189	−	1.04307i	0.142253	−	0.0350623i
$886$	3.89185	−	32.0522i	0.130749	−	1.07682i
$887$	−41.8857	+	21.9833i	−1.40638	+	0.738127i	−0.985609	−	0.169039i	$-0.945934\pi$
$887$	−41.8857	+	21.9833i	−1.40638	+	0.738127i	−0.420774	+	0.907166i	$0.638241\pi$
$888$	5.08377	+	13.4048i	0.170600	+	0.449836i
$889$	19.8067	+	4.88192i	0.664296	+	0.163734i
$890$	−5.99992	+	5.31546i	−0.201118	+	0.178175i
$891$	−3.01609	−	0.743398i	−0.101043	−	0.0249048i
$892$	−9.08733	+	4.76940i	−0.304266	+	0.159691i
$893$	−10.2869	+	5.39897i	−0.344237	+	0.180670i
$894$	−1.52141	−	12.5300i	−0.0508837	−	0.419065i
$895$	−0.704781	−	5.80439i	−0.0235582	−	0.194019i
$896$	−9.06709	+	8.03274i	−0.302910	+	0.268355i
$897$	−16.5568	−	17.3260i	−0.552814	−	0.578500i
$898$	−48.1857	−	42.6888i	−1.60798	−	1.42454i
$899$	−2.41503	+	3.49877i	−0.0805456	+	0.116690i
$900$	1.83467	−	4.83762i	0.0611555	−	0.161254i
$901$	0.374866	+	3.08730i	0.0124886	+	0.102853i
$902$	6.13707	−	50.5433i	0.204342	−	1.68291i
$903$	−11.7505	−	6.16713i	−0.391032	−	0.205229i
$904$	−7.12930	+	10.3286i	−0.237117	+	0.343523i
$905$	−4.75098	−	12.5273i	−0.157928	−	0.416421i
$906$	12.4557	−	11.0347i	0.413811	−	0.366605i
$907$	22.2785	−	32.2761i	0.739747	−	1.07171i	−0.254756	−	0.967005i	$-0.581995\pi$
$907$	22.2785	−	32.2761i	0.739747	−	1.07171i	0.994503	−	0.104703i	$-0.0333893\pi$
$908$	−0.0555321	−	0.0804521i	−0.00184290	−	0.00266990i
$909$	−0.0980527	−	0.807537i	−0.00325220	−	0.0267843i
$910$	3.75188	−	4.57127i	0.124374	−	0.151536i
$911$	4.23688	−	34.8939i	0.140374	−	1.15608i	−0.736868	−	0.676037i	$-0.763696\pi$
$911$	4.23688	−	34.8939i	0.140374	−	1.15608i	0.877242	−	0.480048i	$-0.159381\pi$
$912$	5.75459	−	3.02024i	0.190554	−	0.100010i
$913$	−1.69580	−	4.47145i	−0.0561227	−	0.147984i
$914$	−7.15185	+	58.9008i	−0.236562	+	1.94826i
$915$	−11.3028			−0.373660
$916$	−0.804555	+	6.62610i	−0.0265832	+	0.218933i
$917$	−9.57527	−	13.8722i	−0.316203	−	0.458099i
$918$	1.04324	−	0.257136i	0.0344321	−	0.00848675i
$919$	−25.3604	+	36.7410i	−0.836564	+	1.21197i	0.138569	+	0.990353i	$0.455750\pi$
$919$	−25.3604	+	36.7410i	−0.836564	+	1.21197i	−0.975133	+	0.221619i	$0.928866\pi$
$920$	−7.53103	+	1.85623i	−0.248291	+	0.0611982i
$921$	3.42460	+	1.79737i	0.112844	+	0.0592253i
$922$	61.7094	+	32.3876i	2.03229	+	1.06663i
$923$	−35.5360	−	37.1871i	−1.16968	−	1.22403i
$924$	−3.72742	+	1.95630i	−0.122623	+	0.0643576i
$925$	43.0778			1.41639
$926$	−43.9411	−	23.0621i	−1.44399	−	0.757866i
$927$	−3.54470	+	9.34662i	−0.116423	+	0.306983i
$928$	−0.498130	−	4.10247i	−0.0163519	−	0.134670i
$929$	−14.8031	+	3.64863i	−0.485673	+	0.119708i	−0.474547	−	0.880230i	$-0.657388\pi$
$929$	−14.8031	+	3.64863i	−0.485673	+	0.119708i	−0.0111268	+	0.999938i	$0.503542\pi$
$930$	−8.58303	+	2.11553i	−0.281449	+	0.0693708i
$931$	−0.899743	−	7.41005i	−0.0294879	−	0.242855i
$932$	7.37836	−	19.4551i	0.241686	−	0.637274i
$933$	−12.4047	−	6.51050i	−0.406112	−	0.213144i
$934$	27.9477			0.914477
$935$	1.33385	−	0.700061i	0.0436217	−	0.0228944i
$936$	−5.20211	−	0.433374i	−0.170036	−	0.0141653i
$937$	−42.3736	−	22.2394i	−1.38429	−	0.726529i	−0.402304	−	0.915506i	$-0.631790\pi$
$937$	−42.3736	−	22.2394i	−1.38429	−	0.726529i	−0.981981	+	0.188977i	$0.939483\pi$
$938$	−15.3631	−	8.06316i	−0.501622	−	0.263271i
$939$	−18.5881	+	4.58154i	−0.606598	+	0.149513i
$940$	−4.83226	+	7.00074i	−0.157611	+	0.228339i
$941$	−28.8636	+	7.11425i	−0.940927	+	0.231918i	−0.679809	−	0.733389i	$-0.737937\pi$
$941$	−28.8636	+	7.11425i	−0.940927	+	0.231918i	−0.261118	+	0.965307i	$0.584091\pi$
$942$	11.0238	+	15.9707i	0.359174	+	0.520354i
$943$	−7.35305	+	60.5578i	−0.239448	+	1.97203i
$944$	−26.8436			−0.873684
$945$	−0.110705	+	0.911738i	−0.00360123	+	0.0296588i
$946$	−22.9103	−	60.4095i	−0.744878	−	1.96408i
$947$	7.93335	−	4.16375i	0.257799	−	0.135304i	−0.330873	−	0.943675i	$-0.607343\pi$
$947$	7.93335	−	4.16375i	0.257799	−	0.135304i	0.588672	+	0.808372i	$0.299651\pi$
$948$	−0.280906	+	2.31347i	−0.00912339	+	0.0751379i
$949$	17.6488	−	36.9493i	0.572904	−	1.19943i
$950$	−1.22600	−	10.0970i	−0.0397766	−	0.327590i
$951$	12.9526	+	18.7651i	0.420016	+	0.608499i
$952$	−0.563835	+	0.816856i	−0.0182740	+	0.0264745i
$953$	−14.0291	+	12.4287i	−0.454447	+	0.402605i	−0.859053	−	0.511886i	$-0.828947\pi$
$953$	−14.0291	+	12.4287i	−0.454447	+	0.402605i	0.404606	+	0.914491i	$0.367409\pi$
$954$	−3.27345	−	8.63137i	−0.105982	−	0.279451i
$955$	−5.08746	+	7.37046i	−0.164626	+	0.238503i
$956$	−6.25383	−	3.28227i	−0.202263	−	0.106156i
$957$	−0.259204	+	2.13473i	−0.00837886	+	0.0690061i
$958$	0.639980	+	5.27071i	0.0206768	+	0.170289i
$959$	3.16852	−	8.35470i	0.102317	−	0.269787i
$960$	0.335493	−	0.486045i	0.0108280	−	0.0156870i
$961$	−5.02568	−	4.45237i	−0.162119	−	0.143625i
$962$	17.5823	+	61.2882i	0.566876	+	1.97601i
$963$	7.84691	−	6.95175i	0.252863	−	0.224017i
$964$	−0.0720884	−	0.593702i	−0.00232181	−	0.0191218i
$965$	1.56935	+	12.9247i	0.0505191	+	0.416062i
$966$	11.9762	−	6.28561i	0.385329	−	0.202236i
$967$	−38.6791	+	20.3003i	−1.24383	+	0.652815i	−0.952713	−	0.303871i	$-0.901721\pi$
$967$	−38.6791	+	20.3003i	−1.24383	+	0.652815i	−0.291122	+	0.956686i	$0.594028\pi$
$968$	−1.89856	−	0.467954i	−0.0610221	−	0.0150406i
$969$	0.589580	−	0.522323i	0.0189400	−	0.0167794i
$970$	−17.6364	−	4.34697i	−0.566270	−	0.139573i
$971$	−14.4116	−	38.0004i	−0.462491	−	1.21949i	−0.940095	−	0.340914i	$-0.889264\pi$
$971$	−14.4116	−	38.0004i	−0.462491	−	1.21949i	0.477603	−	0.878576i	$-0.341506\pi$
$972$	−1.05307	+	0.552694i	−0.0337772	+	0.0177277i
$973$	2.19116	−	18.0458i	0.0702454	−	0.578523i
$974$	52.0783	−	12.8362i	1.66870	−	0.411297i
$975$	−6.76047	+	14.1536i	−0.216508	+	0.453279i
$976$	67.5896	+	16.6593i	2.16349	+	0.533252i
$977$	−17.8741	+	47.1302i	−0.571844	+	1.50783i	0.267132	+	0.963660i	$0.413924\pi$
$977$	−17.8741	+	47.1302i	−0.571844	+	1.50783i	−0.838976	+	0.544169i	$0.816845\pi$
$978$	19.7970	+	17.5387i	0.633040	+	0.560824i
$979$	−16.7956	+	4.13975i	−0.536791	+	0.132307i
$980$	−3.10480	−	4.49808i	−0.0991791	−	0.143686i
$981$	1.50813	+	12.4206i	0.0481510	+	0.396559i
$982$	−22.7060	−	59.8709i	−0.724579	−	1.91056i
$983$	15.9612	−	42.0862i	0.509083	−	1.34234i	−0.396447	−	0.918058i	$-0.629757\pi$
$983$	15.9612	−	42.0862i	0.509083	−	1.34234i	0.905530	−	0.424283i	$-0.139474\pi$
$984$	7.54833	+	10.9356i	0.240632	+	0.348616i
$985$	4.90299	+	1.20848i	0.156222	+	0.0385053i
$986$	−0.263759	−	0.695475i	−0.00839980	−	0.0221484i
$987$	−3.58560	+	9.45444i	−0.114131	+	0.300938i
$988$	5.17027	−	2.18721i	0.164488	−	0.0695845i
$989$	27.4497	+	72.3789i	0.872849	+	2.30151i
$990$	−3.34690	+	2.96510i	−0.106372	+	0.0942370i
$991$	19.3544			0.614813			0.307407	−	0.951578i	$-0.400539\pi$
$991$	19.3544			0.614813			0.307407	+	0.951578i	$0.400539\pi$
$992$	36.6611			1.16399
$993$	−25.4122	+	22.5133i	−0.806432	+	0.714437i
$994$	25.7048	−	13.4909i	0.815305	−	0.427905i
$995$	−5.93298			−0.188088
$996$	−1.62120	−	0.850871i	−0.0513697	−	0.0269609i
$997$	−22.9985	−	20.3749i	−0.728369	−	0.645278i	0.215156	−	0.976580i	$-0.430974\pi$
$997$	−22.9985	−	20.3749i	−0.728369	−	0.645278i	−0.943525	+	0.331301i	$0.892512\pi$
$998$	22.4545	+	32.5310i	0.710786	+	1.02975i
$999$	−7.41190	−	6.56637i	−0.234502	−	0.207751i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.m.a.40.4	✓	180
169.131	even	13	inner	507.2.m.a.469.4	yes	180

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.m.a.40.4	✓	180	1.1	even	1	trivial
507.2.m.a.469.4	yes	180	169.131	even	13	inner

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.m (of order \(13\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.73397 - 0.427384i) q^{2} +(-0.120537 + 0.992709i) q^{3} +(1.05307 + 0.552694i) q^{4} +(0.457873 - 0.663343i) q^{5} +(0.633275 - 1.66981i) q^{6} +(-0.852902 - 0.755605i) q^{7} +(1.08370 + 0.960071i) q^{8} +(-0.970942 - 0.239316i) q^{9} +O(q^{10})\)	\(q+(-1.73397 - 0.427384i) q^{2} +(-0.120537 + 0.992709i) q^{3} +(1.05307 + 0.552694i) q^{4} +(0.457873 - 0.663343i) q^{5} +(0.633275 - 1.66981i) q^{6} +(-0.852902 - 0.755605i) q^{7} +(1.08370 + 0.960071i) q^{8} +(-0.970942 - 0.239316i) q^{9} +(-1.07744 + 0.954527i) q^{10} +(-3.01609 + 0.743398i) q^{11} +(-0.675597 + 0.978772i) q^{12} +(2.28746 - 2.78703i) q^{13} +(1.15597 + 1.67471i) q^{14} +(0.603316 + 0.534492i) q^{15} +(-2.81997 - 4.08543i) q^{16} +(-0.450342 - 0.398968i) q^{17} +(1.58130 + 0.829931i) q^{18} +1.30918 q^{19} +(0.848798 - 0.445483i) q^{20} +(0.852902 - 0.755605i) q^{21} +5.54751 q^{22} -6.64668 q^{23} +(-1.08370 + 0.960071i) q^{24} +(1.54265 + 4.06763i) q^{25} +(-5.15751 + 3.85499i) q^{26} +(0.354605 - 0.935016i) q^{27} +(-0.480547 - 1.26710i) q^{28} +(-0.672147 - 0.165669i) q^{29} +(-0.817697 - 1.18464i) q^{30} +(2.17770 - 5.74211i) q^{31} +(2.11689 + 5.58177i) q^{32} +(-0.374429 - 3.08370i) q^{33} +(0.610364 + 0.884266i) q^{34} +(-0.891746 + 0.219796i) q^{35} +(-0.890201 - 0.788650i) q^{36} +(3.51137 - 9.25872i) q^{37} +(-2.27008 - 0.559525i) q^{38} +(2.49098 + 2.60672i) q^{39} +(1.13305 - 0.279272i) q^{40} +(1.10627 - 9.11099i) q^{41} +(-1.80184 + 0.945677i) q^{42} +(-4.12983 - 10.8895i) q^{43} +(-3.58702 - 0.884121i) q^{44} +(-0.603316 + 0.534492i) q^{45} +(11.5251 + 2.84069i) q^{46} +(-7.85747 + 4.12392i) q^{47} +(4.39555 - 2.30696i) q^{48} +(-0.687254 - 5.66005i) q^{49} +(-0.936459 - 7.71243i) q^{50} +(0.450342 - 0.398968i) q^{51} +(3.94923 - 1.67067i) q^{52} +(-3.86911 - 3.42773i) q^{53} +(-1.01448 + 1.46973i) q^{54} +(-0.887855 + 2.34108i) q^{55} +(-0.198852 - 1.63769i) q^{56} +(-0.157805 + 1.29964i) q^{57} +(1.09468 + 0.574530i) q^{58} +(3.07179 - 4.45026i) q^{59} +(0.339924 + 0.896306i) q^{60} +(-10.4963 + 9.29895i) q^{61} +(-6.23014 + 9.02592i) q^{62} +(0.647290 + 0.937761i) q^{63} +(-0.0883196 - 0.727377i) q^{64} +(-0.801389 - 2.79348i) q^{65} +(-0.668678 + 5.50706i) q^{66} +(-7.54969 + 3.96238i) q^{67} +(-0.253734 - 0.669042i) q^{68} +(0.801169 - 6.59822i) q^{69} +1.64020 q^{70} +(1.71956 - 14.1618i) q^{71} +(-0.822446 - 1.19152i) q^{72} +(11.0269 - 2.71789i) q^{73} +(-10.0456 + 14.5536i) q^{74} +(-4.22392 + 1.04110i) q^{75} +(1.37866 + 0.723578i) q^{76} +(3.13414 + 1.64492i) q^{77} +(-3.20521 - 5.58458i) q^{78} +(1.73507 - 0.910637i) q^{79} -4.00123 q^{80} +(0.885456 + 0.464723i) q^{81} +(-5.81214 + 15.3253i) q^{82} +(0.185566 + 1.52827i) q^{83} +(1.31578 - 0.324311i) q^{84} +(-0.470852 + 0.116055i) q^{85} +(2.50700 + 20.6470i) q^{86} +(0.245480 - 0.647277i) q^{87} +(-3.98224 - 2.09004i) q^{88} +5.56869 q^{89} +(1.27456 - 0.668943i) q^{90} +(-4.05687 + 0.648643i) q^{91} +(-6.99942 - 3.67358i) q^{92} +(5.43776 + 2.85395i) q^{93} +(15.3871 - 3.79257i) q^{94} +(0.599440 - 0.868439i) q^{95} +(-5.79623 + 1.42864i) q^{96} +(7.16835 + 10.3851i) q^{97} +(-1.22734 + 10.1081i) q^{98} +3.10635 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 180 q - q^{2} + 15 q^{3} - 15 q^{4} - 2 q^{5} + q^{6} + 4 q^{7} + 3 q^{8} - 15 q^{9}+O(q^{10}) \) 180 * q - q^2 + 15 * q^3 - 15 * q^4 - 2 * q^5 + q^6 + 4 * q^7 + 3 * q^8 - 15 * q^9	\( 180 q - q^{2} + 15 q^{3} - 15 q^{4} - 2 q^{5} + q^{6} + 4 q^{7} + 3 q^{8} - 15 q^{9} - 2 q^{10} - 4 q^{11} + 15 q^{12} - 14 q^{13} + 6 q^{14} + 2 q^{15} - 15 q^{16} - 2 q^{17} - q^{18} + 2 q^{20} - 4 q^{21} - 28 q^{22} - 52 q^{23} - 3 q^{24} - 67 q^{25} - 40 q^{26} + 15 q^{27} - 4 q^{28} - 27 q^{29} + 2 q^{30} + 22 q^{31} - 5 q^{32} - 9 q^{33} + 63 q^{34} - 31 q^{35} - 15 q^{36} + 2 q^{37} + 65 q^{38} + q^{39} + 45 q^{40} - 6 q^{41} + 59 q^{42} - 60 q^{43} - 35 q^{44} - 2 q^{45} - 156 q^{46} + 15 q^{48} + 59 q^{49} - 51 q^{50} + 2 q^{51} + 66 q^{52} + 50 q^{53} + q^{54} + 55 q^{55} - 14 q^{56} - 13 q^{57} + 36 q^{58} + 92 q^{59} - 15 q^{60} + 6 q^{61} + 61 q^{62} + 4 q^{63} - 203 q^{64} - 54 q^{65} + 54 q^{66} + 86 q^{67} + 32 q^{68} + 112 q^{70} + 39 q^{71} + 3 q^{72} - 158 q^{73} - 80 q^{74} + 15 q^{75} + 130 q^{76} - 64 q^{77} + 66 q^{78} - 10 q^{79} - 310 q^{80} - 15 q^{81} + 59 q^{82} - 82 q^{83} + 4 q^{84} + 22 q^{85} - q^{86} + 40 q^{87} + 10 q^{88} + 2 q^{89} - 2 q^{90} - 100 q^{91} - 54 q^{92} + 43 q^{93} + 65 q^{94} + 58 q^{95} - 60 q^{96} + 16 q^{97} - 113 q^{98} - 30 q^{99}+O(q^{100}) \) 180 * q - q^2 + 15 * q^3 - 15 * q^4 - 2 * q^5 + q^6 + 4 * q^7 + 3 * q^8 - 15 * q^9 - 2 * q^10 - 4 * q^11 + 15 * q^12 - 14 * q^13 + 6 * q^14 + 2 * q^15 - 15 * q^16 - 2 * q^17 - q^18 + 2 * q^20 - 4 * q^21 - 28 * q^22 - 52 * q^23 - 3 * q^24 - 67 * q^25 - 40 * q^26 + 15 * q^27 - 4 * q^28 - 27 * q^29 + 2 * q^30 + 22 * q^31 - 5 * q^32 - 9 * q^33 + 63 * q^34 - 31 * q^35 - 15 * q^36 + 2 * q^37 + 65 * q^38 + q^39 + 45 * q^40 - 6 * q^41 + 59 * q^42 - 60 * q^43 - 35 * q^44 - 2 * q^45 - 156 * q^46 + 15 * q^48 + 59 * q^49 - 51 * q^50 + 2 * q^51 + 66 * q^52 + 50 * q^53 + q^54 + 55 * q^55 - 14 * q^56 - 13 * q^57 + 36 * q^58 + 92 * q^59 - 15 * q^60 + 6 * q^61 + 61 * q^62 + 4 * q^63 - 203 * q^64 - 54 * q^65 + 54 * q^66 + 86 * q^67 + 32 * q^68 + 112 * q^70 + 39 * q^71 + 3 * q^72 - 158 * q^73 - 80 * q^74 + 15 * q^75 + 130 * q^76 - 64 * q^77 + 66 * q^78 - 10 * q^79 - 310 * q^80 - 15 * q^81 + 59 * q^82 - 82 * q^83 + 4 * q^84 + 22 * q^85 - q^86 + 40 * q^87 + 10 * q^88 + 2 * q^89 - 2 * q^90 - 100 * q^91 - 54 * q^92 + 43 * q^93 + 65 * q^94 + 58 * q^95 - 60 * q^96 + 16 * q^97 - 113 * q^98 - 30 * q^99

Introduction

L-functions

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