LMFDB - Embedded newform 507.2.m.a.40.3

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			40.3
Character	$\chi$	$=$	507.40
Dual form			507.2.m.a.469.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.76615 - 0.435317i) q^{2} +(-0.120537 + 0.992709i) q^{3} +(1.15887 + 0.608224i) q^{4} +(1.67811 - 2.43117i) q^{5} +(0.645029 - 1.70080i) q^{6} +(3.62124 + 3.20814i) q^{7} +(0.941117 + 0.833757i) q^{8} +(-0.970942 - 0.239316i) q^{9} +O(q^{10})$	\(q+(-1.76615 - 0.435317i) q^{2} +(-0.120537 + 0.992709i) q^{3} +(1.15887 + 0.608224i) q^{4} +(1.67811 - 2.43117i) q^{5} +(0.645029 - 1.70080i) q^{6} +(3.62124 + 3.20814i) q^{7} +(0.941117 + 0.833757i) q^{8} +(-0.970942 - 0.239316i) q^{9} +(-4.02213 + 3.56330i) q^{10} +(-0.787223 + 0.194033i) q^{11} +(-0.743477 + 1.07711i) q^{12} +(1.80938 + 3.11867i) q^{13} +(-4.99909 - 7.24244i) q^{14} +(2.21117 + 1.95892i) q^{15} +(-2.78616 - 4.03645i) q^{16} +(-0.881705 - 0.781123i) q^{17} +(1.61065 + 0.845335i) q^{18} -3.99516 q^{19} +(3.42342 - 1.79675i) q^{20} +(-3.62124 + 3.20814i) q^{21} +1.47482 q^{22} +3.68355 q^{23} +(-0.941117 + 0.833757i) q^{24} +(-1.32149 - 3.48447i) q^{25} +(-1.83803 - 6.29570i) q^{26} +(0.354605 - 0.935016i) q^{27} +(2.24529 + 5.92035i) q^{28} +(1.98754 + 0.489884i) q^{29} +(-3.05250 - 4.42231i) q^{30} +(1.33419 - 3.51796i) q^{31} +(2.27194 + 5.99061i) q^{32} +(-0.0977291 - 0.804872i) q^{33} +(1.21719 + 1.76340i) q^{34} +(13.8764 - 3.42022i) q^{35} +(-0.979642 - 0.867887i) q^{36} +(-2.20264 + 5.80788i) q^{37} +(7.05605 + 1.73916i) q^{38} +(-3.31403 + 1.42028i) q^{39} +(3.60630 - 0.888874i) q^{40} +(-0.895286 + 7.37334i) q^{41} +(7.79221 - 4.08967i) q^{42} +(4.25806 + 11.2276i) q^{43} +(-1.03031 - 0.253948i) q^{44} +(-2.21117 + 1.95892i) q^{45} +(-6.50571 - 1.60351i) q^{46} +(5.93926 - 3.11716i) q^{47} +(4.34285 - 2.27930i) q^{48} +(1.97746 + 16.2859i) q^{49} +(0.817093 + 6.72937i) q^{50} +(0.881705 - 0.781123i) q^{51} +(0.199996 + 4.71466i) q^{52} +(-7.18256 - 6.36320i) q^{53} +(-1.03331 + 1.49701i) q^{54} +(-0.849323 + 2.23948i) q^{55} +(0.733202 + 6.03846i) q^{56} +(0.481563 - 3.96603i) q^{57} +(-3.29703 - 1.73042i) q^{58} +(2.47716 - 3.58878i) q^{59} +(1.37100 + 3.61503i) q^{60} +(4.36238 - 3.86473i) q^{61} +(-3.88780 + 5.63245i) q^{62} +(-2.74825 - 3.98153i) q^{63} +(-0.222391 - 1.83155i) q^{64} +(10.6184 + 0.834575i) q^{65} +(-0.177770 + 1.46407i) q^{66} +(9.30463 - 4.88345i) q^{67} +(-0.546688 - 1.44150i) q^{68} +(-0.444003 + 3.65670i) q^{69} -25.9966 q^{70} +(1.74447 - 14.3670i) q^{71} +(-0.714239 - 1.03475i) q^{72} +(0.210667 - 0.0519247i) q^{73} +(6.41846 - 9.29874i) q^{74} +(3.61835 - 0.891844i) q^{75} +(-4.62989 - 2.42995i) q^{76} +(-3.47321 - 1.82288i) q^{77} +(6.47135 - 1.06577i) q^{78} +(8.38273 - 4.39960i) q^{79} -14.4888 q^{80} +(0.885456 + 0.464723i) q^{81} +(4.79095 - 12.6327i) q^{82} +(0.678007 + 5.58389i) q^{83} +(-6.14783 + 1.51530i) q^{84} +(-3.37864 + 0.832761i) q^{85} +(-2.63282 - 21.6832i) q^{86} +(-0.725883 + 1.91400i) q^{87} +(-0.902645 - 0.473745i) q^{88} -6.15514 q^{89} +(4.75801 - 2.49719i) q^{90} +(-3.45292 + 17.0982i) q^{91} +(4.26878 + 2.24043i) q^{92} +(3.33149 + 1.74850i) q^{93} +(-11.8466 + 2.91992i) q^{94} +(-6.70433 + 9.71290i) q^{95} +(-6.22078 + 1.53329i) q^{96} +(-7.58144 - 10.9836i) q^{97} +(3.59702 - 29.6242i) q^{98} +0.810783 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 $

$2$	−1.76615	−	0.435317i	−1.24886	−	0.307816i	−0.441168	−	0.897424i	$-0.645436\pi$
$2$	−1.76615	−	0.435317i	−1.24886	−	0.307816i	−0.807689	+	0.589609i	$0.799282\pi$
$3$	−0.120537	+	0.992709i	−0.0695919	+	0.573141i
$3$	−0.120537	+	0.992709i	−0.0695919	+	0.573141i
$4$	1.15887	+	0.608224i	0.579437	+	0.304112i
$5$	1.67811	−	2.43117i	0.750475	−	1.08725i	−0.242641	−	0.970116i	$-0.578014\pi$
$5$	1.67811	−	2.43117i	0.750475	−	1.08725i	0.993116	−	0.117135i	$-0.0373710\pi$
$6$	0.645029	−	1.70080i	0.263332	−	0.694349i
$7$	3.62124	+	3.20814i	1.36870	+	1.21256i	0.952967	+	0.303075i	$0.0980132\pi$
$7$	3.62124	+	3.20814i	1.36870	+	1.21256i	0.415732	+	0.909487i	$0.363525\pi$
$8$	0.941117	+	0.833757i	0.332735	+	0.294778i
$9$	−0.970942	−	0.239316i	−0.323647	−	0.0797719i
$10$	−4.02213	+	3.56330i	−1.27191	+	1.12681i
$11$	−0.787223	+	0.194033i	−0.237357	+	0.0585032i	−0.356200	−	0.934410i	$-0.615928\pi$
$11$	−0.787223	+	0.194033i	−0.237357	+	0.0585032i	0.118843	+	0.992913i	$0.462082\pi$
$12$	−0.743477	+	1.07711i	−0.214623	+	0.310935i
$13$	1.80938	+	3.11867i	0.501833	+	0.864965i
$13$	1.80938	+	3.11867i	0.501833	+	0.864965i
$14$	−4.99909	−	7.24244i	−1.33606	−	1.93562i
$15$	2.21117	+	1.95892i	0.570921	+	0.505792i
$16$	−2.78616	−	4.03645i	−0.696540	−	1.00911i
$17$	−0.881705	−	0.781123i	−0.213845	−	0.189450i	0.549400	−	0.835560i	$-0.314856\pi$
$17$	−0.881705	−	0.781123i	−0.213845	−	0.189450i	−0.763245	+	0.646110i	$0.776395\pi$
$18$	1.61065	+	0.845335i	0.379634	+	0.199247i
$19$	−3.99516			−0.916552			−0.458276	−	0.888810i	$-0.651533\pi$
$19$	−3.99516			−0.916552			−0.458276	+	0.888810i	$0.651533\pi$
$20$	3.42342	−	1.79675i	0.765500	−	0.401765i
$21$	−3.62124	+	3.20814i	−0.790219	+	0.700073i
$22$	1.47482			0.314433
$23$	3.68355			0.768074			0.384037	−	0.923318i	$-0.374534\pi$
$23$	3.68355			0.768074			0.384037	+	0.923318i	$0.374534\pi$
$24$	−0.941117	+	0.833757i	−0.192105	+	0.170190i
$25$	−1.32149	−	3.48447i	−0.264297	−	0.696894i
$26$	−1.83803	−	6.29570i	−0.360468	−	1.23469i
$27$	0.354605	−	0.935016i	0.0682437	−	0.179944i
$28$	2.24529	+	5.92035i	0.424321	+	1.11884i
$29$	1.98754	+	0.489884i	0.369076	+	0.0909691i	0.419492	−	0.907759i	$-0.362208\pi$
$29$	1.98754	+	0.489884i	0.369076	+	0.0909691i	−0.0504154	+	0.998728i	$0.516055\pi$
$30$	−3.05250	−	4.42231i	−0.557308	−	0.807400i
$31$	1.33419	−	3.51796i	0.239627	−	0.631844i	−0.760214	−	0.649673i	$-0.774906\pi$
$31$	1.33419	−	3.51796i	0.239627	−	0.631844i	0.999841	+	0.0178284i	$0.00567526\pi$
$32$	2.27194	+	5.99061i	0.401626	+	1.05900i
$33$	−0.0977291	−	0.804872i	−0.0170125	−	0.140110i
$34$	1.21719	+	1.76340i	0.208746	+	0.302421i
$35$	13.8764	−	3.42022i	2.34553	−	0.578122i
$36$	−0.979642	−	0.867887i	−0.163274	−	0.144648i
$37$	−2.20264	+	5.80788i	−0.362112	+	0.954810i	0.622897	+	0.782304i	$0.285956\pi$
$37$	−2.20264	+	5.80788i	−0.362112	+	0.954810i	−0.985009	+	0.172506i	$0.944814\pi$
$38$	7.05605	+	1.73916i	1.14464	+	0.282129i
$39$	−3.31403	+	1.42028i	−0.530670	+	0.227426i
$40$	3.60630	−	0.888874i	0.570207	−	0.140543i
$41$	−0.895286	+	7.37334i	−0.139820	+	1.15152i	0.738774	+	0.673953i	$0.235405\pi$
$41$	−0.895286	+	7.37334i	−0.139820	+	1.15152i	−0.878594	+	0.477569i	$0.841518\pi$
$42$	7.79221	−	4.08967i	1.20236	−	0.631049i
$43$	4.25806	+	11.2276i	0.649348	+	1.71219i	0.700649	+	0.713506i	$0.252894\pi$
$43$	4.25806	+	11.2276i	0.649348	+	1.71219i	−0.0513018	+	0.998683i	$0.516337\pi$
$44$	−1.03031	−	0.253948i	−0.155325	−	0.0382841i
$45$	−2.21117	+	1.95892i	−0.329621	+	0.292019i
$46$	−6.50571	−	1.60351i	−0.959214	−	0.236425i
$47$	5.93926	−	3.11716i	0.866330	−	0.454685i	0.0278466	−	0.999612i	$-0.491135\pi$
$47$	5.93926	−	3.11716i	0.866330	−	0.454685i	0.838483	+	0.544927i	$0.183443\pi$
$48$	4.34285	−	2.27930i	0.626837	−	0.328989i
$49$	1.97746	+	16.2859i	0.282495	+	2.32656i
$50$	0.817093	+	6.72937i	0.115554	+	0.951676i
$51$	0.881705	−	0.781123i	0.123463	−	0.109379i
$52$	0.199996	+	4.71466i	0.0277344	+	0.653806i
$53$	−7.18256	−	6.36320i	−0.986601	−	0.874052i	0.00543781	−	0.999985i	$-0.498269\pi$
$53$	−7.18256	−	6.36320i	−0.986601	−	0.874052i	−0.992039	+	0.125933i	$0.959808\pi$
$54$	−1.03331	+	1.49701i	−0.140616	+	0.203718i
$55$	−0.849323	+	2.23948i	−0.114523	+	0.301972i
$56$	0.733202	+	6.03846i	0.0979783	+	0.806924i
$57$	0.481563	−	3.96603i	0.0637846	−	0.525313i
$58$	−3.29703	−	1.73042i	−0.432922	−	0.227215i
$59$	2.47716	−	3.58878i	0.322498	−	0.467220i	−0.627883	−	0.778308i	$-0.716078\pi$
$59$	2.47716	−	3.58878i	0.322498	−	0.467220i	0.950381	+	0.311089i	$0.100694\pi$
$60$	1.37100	+	3.61503i	0.176995	+	0.466699i
$61$	4.36238	−	3.86473i	0.558546	−	0.494829i	−0.335965	−	0.941874i	$-0.609062\pi$
$61$	4.36238	−	3.86473i	0.558546	−	0.494829i	0.894511	+	0.447046i	$0.147524\pi$
$62$	−3.88780	+	5.63245i	−0.493751	+	0.715322i
$63$	−2.74825	−	3.98153i	−0.346247	−	0.501626i
$64$	−0.222391	−	1.83155i	−0.0277988	−	0.228944i
$65$	10.6184	+	0.834575i	1.31705	+	0.103516i
$66$	−0.177770	+	1.46407i	−0.0218820	+	0.180214i
$67$	9.30463	−	4.88345i	1.13674	−	0.596608i	0.212025	−	0.977264i	$-0.431994\pi$
$67$	9.30463	−	4.88345i	1.13674	−	0.596608i	0.924717	+	0.380656i	$0.124302\pi$
$68$	−0.546688	−	1.44150i	−0.0662957	−	0.174807i
$69$	−0.444003	+	3.65670i	−0.0534517	+	0.440214i
$70$	−25.9966			−3.10719
$71$	1.74447	−	14.3670i	0.207030	−	1.70505i	−0.405087	−	0.914278i	$-0.632759\pi$
$71$	1.74447	−	14.3670i	0.207030	−	1.70505i	0.612117	−	0.790768i	$-0.290318\pi$
$72$	−0.714239	−	1.03475i	−0.0841738	−	0.121947i
$73$	0.210667	−	0.0519247i	0.0246567	−	0.00607733i	−0.226968	−	0.973902i	$-0.572881\pi$
$73$	0.210667	−	0.0519247i	0.0246567	−	0.00607733i	0.251625	+	0.967825i	$0.419035\pi$
$74$	6.41846	−	9.29874i	0.746131	−	1.08096i
$75$	3.61835	−	0.891844i	0.417811	−	0.102981i
$76$	−4.62989	−	2.42995i	−0.531084	−	0.278735i
$77$	−3.47321	−	1.82288i	−0.395809	−	0.207736i
$78$	6.47135	−	1.06577i	0.732736	−	0.120674i
$79$	8.38273	−	4.39960i	0.943131	−	0.494993i	0.0782297	−	0.996935i	$-0.475073\pi$
$79$	8.38273	−	4.39960i	0.943131	−	0.494993i	0.864901	+	0.501942i	$0.167381\pi$
$80$	−14.4888			−1.61989
$81$	0.885456	+	0.464723i	0.0983840	+	0.0516359i
$82$	4.79095	−	12.6327i	0.529072	−	1.39505i
$83$	0.678007	+	5.58389i	0.0744209	+	0.612912i	0.981433	+	0.191806i	$0.0614346\pi$
$83$	0.678007	+	5.58389i	0.0744209	+	0.612912i	−0.907012	+	0.421105i	$0.861642\pi$
$84$	−6.14783	+	1.51530i	−0.670783	+	0.165333i
$85$	−3.37864	+	0.832761i	−0.366465	+	0.0903256i
$86$	−2.63282	−	21.6832i	−0.283904	−	2.33816i
$87$	−0.725883	+	1.91400i	−0.0778228	+	0.205202i
$88$	−0.902645	−	0.473745i	−0.0962223	−	0.0505014i
$89$	−6.15514			−0.652443			−0.326222	−	0.945293i	$-0.605776\pi$
$89$	−6.15514			−0.652443			−0.326222	+	0.945293i	$0.605776\pi$
$90$	4.75801	−	2.49719i	0.501538	−	0.263227i
$91$	−3.45292	+	17.0982i	−0.361965	+	1.79238i
$92$	4.26878	+	2.24043i	0.445051	+	0.233581i
$93$	3.33149	+	1.74850i	0.345460	+	0.181311i
$94$	−11.8466	+	2.91992i	−1.22188	+	0.301167i
$95$	−6.70433	+	9.71290i	−0.687850	+	0.996522i
$96$	−6.22078	+	1.53329i	−0.634906	+	0.156490i
$97$	−7.58144	−	10.9836i	−0.769778	−	1.11522i	−0.990179	−	0.139807i	$-0.955352\pi$
$97$	−7.58144	−	10.9836i	−0.769778	−	1.11522i	0.220400	−	0.975410i	$-0.429264\pi$
$98$	3.59702	−	29.6242i	0.363354	−	2.99249i
$99$	0.810783			0.0814868
$100$	0.587904	−	4.84182i	0.0587904	−	0.484182i
$101$	2.25637	+	5.94957i	0.224518	+	0.592004i	0.999185	−	0.0403646i	$-0.0128519\pi$
$101$	2.25637	+	5.94957i	0.224518	+	0.592004i	−0.774667	+	0.632369i	$0.782083\pi$
$102$	−1.89726	+	0.995759i	−0.187857	+	0.0985949i
$103$	1.87571	−	15.4479i	0.184819	−	1.52212i	−0.544973	−	0.838454i	$-0.683460\pi$
$103$	1.87571	−	15.4479i	0.184819	−	1.52212i	0.729792	−	0.683669i	$-0.239617\pi$
$104$	−0.897374	+	4.44362i	−0.0879948	+	0.435733i
$105$	1.72267	+	14.1875i	0.168115	+	1.38455i
$106$	9.91548	+	14.3651i	0.963077	+	1.39526i
$107$	−10.3550	+	15.0017i	−1.00105	+	1.45027i	−0.111323	+	0.993784i	$0.535509\pi$
$107$	−10.3550	+	15.0017i	−1.00105	+	1.45027i	−0.889729	+	0.456489i	$0.849107\pi$
$108$	0.979642	−	0.867887i	0.0942661	−	0.0835125i
$109$	−0.507419	−	1.33795i	−0.0486020	−	0.128153i	0.908517	−	0.417848i	$-0.137215\pi$
$109$	−0.507419	−	1.33795i	−0.0486020	−	0.128153i	−0.957119	+	0.289695i	$0.906446\pi$
$110$	2.47492	−	3.58554i	0.235974	−	0.341867i
$111$	−5.50004	−	2.88664i	−0.522040	−	0.273988i
$112$	2.86013	−	23.5553i	0.270257	−	2.22577i
$113$	1.11918	+	9.21725i	0.105283	+	0.867086i	0.945677	+	0.325109i	$0.105401\pi$
$113$	1.11918	+	9.21725i	0.105283	+	0.867086i	−0.840393	+	0.541977i	$0.817676\pi$
$114$	−2.57699	+	6.79497i	−0.241357	+	0.636407i
$115$	6.18142	−	8.95533i	0.576420	−	0.835089i
$116$	2.00535	+	1.77658i	0.186192	+	0.164951i
$117$	−1.01046	−	3.46107i	−0.0934170	−	0.319976i
$118$	−5.93729	+	5.25998i	−0.546572	+	0.484220i
$119$	−0.686916	−	5.65726i	−0.0629695	−	0.518600i
$120$	0.447701	+	3.68715i	0.0408693	+	0.336589i
$121$	−9.15794	+	4.80646i	−0.832540	+	0.436951i
$122$	−9.38701	+	4.92668i	−0.849860	+	0.446041i
$123$	−7.21167	−	1.77752i	−0.650254	−	0.160273i
$124$	3.68586	−	3.26539i	0.331000	−	0.293241i
$125$	3.65231	+	0.900213i	0.326672	+	0.0805175i
$126$	3.12060	+	8.22835i	0.278005	+	0.733040i
$127$	10.1311	−	5.31719i	0.898986	−	0.471824i	0.0491020	−	0.998794i	$-0.484364\pi$
$127$	10.1311	−	5.31719i	0.898986	−	0.471824i	0.849884	+	0.526969i	$0.176672\pi$
$128$	1.14002	−	9.38888i	0.100764	−	0.829868i
$129$	−11.6590	+	2.87368i	−1.02651	+	0.253013i
$130$	−18.3903	−	6.09634i	−1.61294	−	0.534685i
$131$	2.28770	+	0.563866i	0.199877	+	0.0492652i	0.337983	−	0.941152i	$-0.390255\pi$
$131$	2.28770	+	0.563866i	0.199877	+	0.0492652i	−0.138106	+	0.990417i	$0.544102\pi$
$132$	0.376287	−	0.992186i	0.0327516	−	0.0863587i
$133$	−14.4674	−	12.8170i	−1.25448	−	1.11138i
$134$	−18.5592	+	4.57444i	−1.60327	+	0.395171i
$135$	−1.67811	−	2.43117i	−0.144429	−	0.209242i
$136$	−0.178521	−	1.47026i	−0.0153081	−	0.126073i
$137$	−3.79957	−	10.0187i	−0.324619	−	0.855951i	−0.993629	−	0.112698i	$-0.964051\pi$
$137$	−3.79957	−	10.0187i	−0.324619	−	0.855951i	0.669010	−	0.743253i	$-0.266718\pi$
$138$	2.37600	−	6.26499i	0.202258	−	0.533312i
$139$	8.40701	+	12.1797i	0.713073	+	1.03307i	0.997237	+	0.0742892i	$0.0236688\pi$
$139$	8.40701	+	12.1797i	0.713073	+	1.03307i	−0.284163	+	0.958776i	$0.591716\pi$
$140$	18.1612	+	4.47634i	1.53490	+	0.378320i
$141$	2.37854	+	6.27169i	0.200309	+	0.528171i
$142$	−9.33518	+	24.6148i	−0.783391	+	2.06563i
$143$	−2.02952	−	2.10401i	−0.169717	−	0.175946i
$144$	1.73921	+	4.58593i	0.144934	+	0.382161i
$145$	4.52630	−	4.00995i	0.375889	−	0.333008i
$146$	−0.394673			−0.0326634
$147$	−16.4055			−1.35310
$148$	−6.08508	+	5.39091i	−0.500190	+	0.443130i
$149$	−15.5045	+	8.13738i	−1.27018	+	0.666640i	−0.958917	−	0.283685i	$-0.908443\pi$
$149$	−15.5045	+	8.13738i	−1.27018	+	0.666640i	−0.311259	+	0.950325i	$0.600751\pi$
$150$	−6.77879			−0.553486
$151$	−6.56874	−	3.44754i	−0.534556	−	0.280557i	0.175768	−	0.984432i	$-0.443759\pi$
$151$	−6.56874	−	3.44754i	−0.534556	−	0.280557i	−0.710324	+	0.703875i	$0.751452\pi$
$152$	−3.75991	−	3.33099i	−0.304969	−	0.270179i
$153$	0.669150	+	0.969431i	0.0540976	+	0.0783738i
$154$	5.34068	+	4.73143i	0.430364	+	0.381269i
$155$	−6.31383	−	9.14717i	−0.507139	−	0.734718i
$156$	−4.70440	−	0.369753i	−0.376653	−	0.0296039i
$157$	0.534576	−	0.774468i	0.0426638	−	0.0618092i	−0.801071	−	0.598569i	$-0.795736\pi$
$157$	0.534576	−	0.774468i	0.0426638	−	0.0618092i	0.843735	+	0.536759i	$0.180352\pi$
$158$	−16.7204	+	4.12120i	−1.33020	+	0.327865i
$159$	7.18256	−	6.36320i	0.569614	−	0.504634i
$160$	18.3767	+	4.52946i	1.45281	+	0.358085i
$161$	13.3390	+	11.8173i	1.05126	+	0.931337i
$162$	−1.36155	−	1.20623i	−0.106973	−	0.0947700i
$163$	−4.79812	+	12.6516i	−0.375818	+	0.990951i	0.605035	+	0.796199i	$0.293159\pi$
$163$	−4.79812	+	12.6516i	−0.375818	+	0.990951i	−0.980853	+	0.194752i	$0.937610\pi$
$164$	−5.52217	+	8.00024i	−0.431209	+	0.624714i
$165$	−2.12078	−	1.11307i	−0.165102	−	0.0866524i
$166$	1.23330	−	10.1571i	0.0957226	−	0.788347i
$167$	−21.6354	−	5.33266i	−1.67420	−	0.412653i	−0.715852	−	0.698252i	$-0.753961\pi$
$167$	−21.6354	−	5.33266i	−1.67420	−	0.412653i	−0.958349	+	0.285599i	$0.907807\pi$
$168$	−6.08281			−0.469299
$169$	−6.45226	+	11.2858i	−0.496328	+	0.868135i
$170$	6.32971			0.485466
$171$	3.87906	+	0.956104i	0.296639	+	0.0731151i
$172$	−1.89433	+	15.6012i	−0.144441	+	1.18958i
$173$	−3.24072	−	1.70086i	−0.246387	−	0.129314i	0.337010	−	0.941501i	$-0.390585\pi$
$173$	−3.24072	−	1.70086i	−0.246387	−	0.129314i	−0.583397	+	0.812187i	$0.698277\pi$
$174$	2.11521	−	3.06442i	0.160354	−	0.232313i
$175$	6.39325	−	16.8576i	0.483284	−	1.27432i
$176$	2.97653	+	2.63698i	0.224365	+	0.198770i
$177$	3.26403	+	2.89168i	0.245339	+	0.217352i
$178$	10.8709	+	2.67944i	0.814808	+	0.200832i
$179$	5.73857	−	5.08393i	0.428921	−	0.379991i	−0.420861	−	0.907125i	$-0.638272\pi$
$179$	5.73857	−	5.08393i	0.428921	−	0.379991i	0.849782	+	0.527134i	$0.176734\pi$
$180$	−3.75393	+	0.925261i	−0.279801	+	0.0689649i
$181$	8.38108	−	12.1421i	0.622961	−	0.902514i	−0.376756	−	0.926312i	$-0.622961\pi$
$181$	8.38108	−	12.1421i	0.622961	−	0.902514i	0.999717	+	0.0237983i	$0.00757595\pi$
$182$	13.5415	−	28.6949i	1.00376	−	2.12701i
$183$	3.31073	+	4.79642i	0.244736	+	0.354561i
$184$	3.46665	+	3.07119i	0.255565	+	0.226411i
$185$	10.4237	+	15.1013i	0.766362	+	1.11027i
$186$	−5.12276	−	4.53837i	−0.375619	−	0.332770i
$187$	0.845663	+	0.443838i	0.0618410	+	0.0324567i
$188$	8.77879			0.640259
$189$	4.28377	−	2.24830i	0.311598	−	0.163539i
$190$	16.0690	−	14.2359i	1.16577	−	1.03278i
$191$	3.15797			0.228503			0.114251	−	0.993452i	$-0.463553\pi$
$191$	3.15797			0.228503			0.114251	+	0.993452i	$0.463553\pi$
$192$	1.84500			0.133152
$193$	−2.25915	+	2.00144i	−0.162617	+	0.144067i	−0.740507	−	0.672048i	$-0.765415\pi$
$193$	−2.25915	+	2.00144i	−0.162617	+	0.144067i	0.577890	+	0.816115i	$0.303876\pi$
$194$	8.60861	+	22.6990i	0.618062	+	1.62970i
$195$	−2.10839	+	10.4404i	−0.150985	+	0.747649i
$196$	−7.61384	+	20.0760i	−0.543846	+	1.43400i
$197$	−5.22847	−	13.7864i	−0.372513	−	0.982237i	−0.981906	−	0.189368i	$-0.939356\pi$
$197$	−5.22847	−	13.7864i	−0.372513	−	0.982237i	0.609393	−	0.792869i	$-0.291413\pi$
$198$	−1.43197	−	0.352948i	−0.101765	−	0.0250829i
$199$	−9.03844	−	13.0944i	−0.640718	−	0.928240i	0.359269	−	0.933234i	$-0.383026\pi$
$199$	−9.03844	−	13.0944i	−0.640718	−	0.928240i	−0.999988	+	0.00499347i	$0.998411\pi$
$200$	1.66153	−	4.38109i	0.117488	−	0.309790i
$201$	3.72629	+	9.82542i	0.262832	+	0.693032i
$202$	−1.39515	−	11.4901i	−0.0981622	−	0.808439i
$203$	5.62573	+	8.15027i	0.394849	+	0.572037i
$204$	1.49688	−	0.368949i	0.104803	−	0.0258316i
$205$	16.4234	+	14.5499i	1.14706	+	1.01621i
$206$	−10.0375	+	26.4667i	−0.699346	+	1.84402i
$207$	−3.57652	−	0.881532i	−0.248585	−	0.0612707i
$208$	7.54713	−	15.9926i	0.523300	−	1.10889i
$209$	3.14508	−	0.775193i	0.217550	−	0.0536212i
$210$	3.13355	−	25.8071i	0.216235	−	1.78086i
$211$	15.0158	−	7.88090i	1.03373	−	0.542543i	0.139533	−	0.990217i	$-0.455440\pi$
$211$	15.0158	−	7.88090i	1.03373	−	0.542543i	0.894197	+	0.447674i	$0.147748\pi$
$212$	−4.45344	−	11.7428i	−0.305864	−	0.806496i
$213$	14.0519	+	3.46349i	0.962824	+	0.237315i
$214$	24.8189	−	21.9877i	1.69659	−	1.50305i
$215$	34.4416	+	8.48910i	2.34890	+	0.578952i
$216$	1.11330	−	0.584305i	0.0757505	−	0.0397569i
$217$	16.1175	−	8.45912i	1.09413	−	0.574242i
$218$	0.313744	+	2.58392i	0.0212495	+	0.175005i
$219$	0.0261531	+	0.215390i	0.00176726	+	0.0145547i
$220$	−2.34637	+	2.07870i	−0.158192	+	0.140146i
$221$	0.840724	−	4.16310i	0.0565532	−	0.280041i
$222$	8.45729	+	7.49250i	0.567616	+	0.502864i
$223$	9.77027	−	14.1547i	0.654266	−	0.947868i	−0.345689	−	0.938349i	$-0.612355\pi$
$223$	9.77027	−	14.1547i	0.654266	−	0.947868i	0.999955	−	0.00951865i	$-0.00302993\pi$
$224$	−10.9915	+	28.9821i	−0.734398	+	1.93645i
$225$	0.449197	+	3.69947i	0.0299465	+	0.246631i
$226$	2.03579	−	16.7662i	0.135419	−	1.11527i
$227$	−20.7262	−	10.8780i	−1.37565	−	0.721995i	−0.395166	−	0.918610i	$-0.629313\pi$
$227$	−20.7262	−	10.8780i	−1.37565	−	0.721995i	−0.980481	+	0.196615i	$0.937005\pi$
$228$	2.97031	−	4.30323i	0.196713	−	0.284988i
$229$	3.78071	+	9.96891i	0.249836	+	0.658764i	0.999997	−	0.00249136i	$-0.000793026\pi$
$229$	3.78071	+	9.96891i	0.249836	+	0.658764i	−0.750161	+	0.661256i	$0.770024\pi$
$230$	−14.8157	+	13.1256i	−0.976920	+	0.865476i
$231$	2.22824	−	3.22816i	0.146607	−	0.212397i
$232$	1.46206	+	2.11816i	0.0959889	+	0.139064i
$233$	0.993826	+	8.18490i	0.0651077	+	0.536210i	0.988373	+	0.152048i	$0.0485867\pi$
$233$	0.993826	+	8.18490i	0.0651077	+	0.536210i	−0.923265	+	0.384163i	$0.874490\pi$
$234$	0.277962	+	6.55263i	0.0181709	+	0.428359i
$235$	2.38841	−	19.6703i	0.155802	−	1.28315i
$236$	5.05350	−	2.65228i	0.328955	−	0.172649i
$237$	3.35709	+	8.85192i	0.218067	+	0.574994i
$238$	−1.24951	+	10.2906i	−0.0809934	+	0.667041i
$239$	−24.4910			−1.58419			−0.792096	−	0.610396i	$-0.791010\pi$
$239$	−24.4910			−1.58419			−0.792096	+	0.610396i	$0.791010\pi$
$240$	1.74643	−	14.3831i	0.112731	−	0.928427i
$241$	−10.2453	−	14.8428i	−0.659955	−	0.956109i	−0.999877	−	0.0156559i	$-0.995016\pi$
$241$	−10.2453	−	14.8428i	−0.659955	−	0.956109i	0.339923	−	0.940453i	$-0.389599\pi$
$242$	18.2666	−	4.50232i	1.17422	−	0.289420i
$243$	−0.568065	+	0.822984i	−0.0364414	+	0.0527944i
$244$	7.40608	−	1.82543i	0.474126	−	0.116861i
$245$	42.9121	+	22.5220i	2.74156	+	1.43888i
$246$	11.9631	+	6.27872i	0.762740	+	0.400317i
$247$	−7.22877	−	12.4596i	−0.459956	−	0.792785i
$248$	4.18875	−	2.19842i	0.265986	−	0.139600i
$249$	−5.62490			−0.356464
$250$	−6.05864	−	3.17982i	−0.383182	−	0.201110i
$251$	6.56679	−	17.3152i	0.414492	−	1.09293i	−0.551459	−	0.834202i	$-0.685929\pi$
$251$	6.56679	−	17.3152i	0.414492	−	1.09293i	0.965951	−	0.258724i	$-0.0833020\pi$
$252$	−0.763216	−	6.28565i	−0.0480781	−	0.395959i
$253$	−2.89978	+	0.714731i	−0.182308	+	0.0449348i
$254$	−20.2076	+	4.98074i	−1.26794	+	0.312519i
$255$	−0.419439	−	3.45439i	−0.0262663	−	0.216322i
$256$	−7.40907	+	19.5361i	−0.463067	+	1.22101i
$257$	−11.5176	−	6.04490i	−0.718448	−	0.377070i	0.0655375	−	0.997850i	$-0.479124\pi$
$257$	−11.5176	−	6.04490i	−0.718448	−	0.377070i	−0.783985	+	0.620780i	$0.786816\pi$
$258$	21.8424			1.35985
$259$	−26.6087	+	13.9653i	−1.65339	+	0.867765i
$260$	11.7978	+	7.42552i	0.731666	+	0.460511i
$261$	−1.81255	−	0.951297i	−0.112194	−	0.0588838i
$262$	−3.79495	−	1.99175i	−0.234453	−	0.123050i
$263$	15.0991	−	3.72159i	0.931049	−	0.229483i	0.255509	−	0.966807i	$-0.417757\pi$
$263$	15.0991	−	3.72159i	0.931049	−	0.229483i	0.675539	+	0.737324i	$0.263911\pi$
$264$	0.579093	−	0.838960i	0.0356407	−	0.0516344i
$265$	−27.5232	+	6.78385i	−1.69073	+	0.416728i
$266$	19.9722	+	28.9347i	1.22457	+	1.77410i
$267$	0.741920	−	6.11026i	0.0454047	−	0.373942i
$268$	13.7531			0.840106
$269$	−2.59002	+	21.3308i	−0.157916	+	1.30056i	0.671113	+	0.741355i	$0.265816\pi$
$269$	−2.59002	+	21.3308i	−0.157916	+	1.30056i	−0.829030	+	0.559204i	$0.811107\pi$
$270$	1.90547	+	5.02432i	0.115963	+	0.305770i
$271$	−16.4316	+	8.62396i	−0.998147	+	0.523868i	−0.882946	−	0.469474i	$-0.844443\pi$
$271$	−16.4316	+	8.62396i	−0.998147	+	0.523868i	−0.115201	+	0.993342i	$0.536751\pi$
$272$	−0.696390	+	5.73529i	−0.0422249	+	0.347753i
$273$	−16.5573	−	5.48871i	−1.00210	−	0.332192i
$274$	2.34933	+	19.3485i	0.141928	+	1.16888i
$275$	1.71641	+	2.48664i	0.103503	+	0.149950i
$276$	−2.73864	+	3.96760i	−0.164846	+	0.238821i
$277$	11.8455	−	10.4942i	0.711726	−	0.630535i	−0.227522	−	0.973773i	$-0.573062\pi$
$277$	11.8455	−	10.4942i	0.711726	−	0.630535i	0.939248	+	0.343238i	$0.111524\pi$
$278$	−9.54603	−	25.1708i	−0.572533	−	1.50965i
$279$	−2.13732	+	3.09644i	−0.127958	+	0.185379i
$280$	15.9109	+	8.35069i	0.950859	+	0.499049i
$281$	1.97101	−	16.2327i	0.117580	−	0.968362i	−0.807835	−	0.589408i	$-0.799361\pi$
$281$	1.97101	−	16.2327i	0.117580	−	0.968362i	0.925416	−	0.378954i	$-0.123716\pi$
$282$	−1.47068	−	12.1122i	−0.0875779	−	0.721269i
$283$	−6.39345	+	16.8581i	−0.380051	+	1.00211i	0.599403	+	0.800447i	$0.295405\pi$
$283$	−6.39345	+	16.8581i	−0.380051	+	1.00211i	−0.979454	+	0.201665i	$0.935365\pi$
$284$	10.7600	−	15.5885i	0.638486	−	0.925007i
$285$	−8.83396	−	7.82621i	−0.523279	−	0.463584i
$286$	2.66852	+	4.59949i	0.157793	+	0.271973i
$287$	−26.8967	+	23.8284i	−1.58766	+	1.40655i
$288$	−0.772273	−	6.36024i	−0.0455066	−	0.374781i
$289$	−1.88187	−	15.4986i	−0.110698	−	0.911683i
$290$	−9.73973	+	5.11180i	−0.571937	+	0.300176i
$291$	11.8174	−	6.20223i	0.692746	−	0.363581i
$292$	0.275718	+	0.0679585i	0.0161352	+	0.00397697i
$293$	−12.0742	+	10.6968i	−0.705380	+	0.624912i	−0.937585	−	0.347755i	$-0.886944\pi$
$293$	−12.0742	+	10.6968i	−0.705380	+	0.624912i	0.232206	+	0.972667i	$0.425406\pi$
$294$	28.9746	+	7.14159i	1.68983	+	0.416506i
$295$	−4.56798	−	12.0448i	−0.265958	−	0.701274i
$296$	−6.91530	+	3.62943i	−0.401944	+	0.210956i
$297$	−0.0977291	+	0.804872i	−0.00567082	+	0.0467034i
$298$	30.9256	−	7.62247i	1.79147	−	0.441558i
$299$	6.66496	+	11.4878i	0.385445	+	0.664357i
$300$	4.73566	+	1.16723i	0.273413	+	0.0673903i
$301$	−20.6002	+	54.3181i	−1.18737	+	3.13085i
$302$	10.1006	+	8.94836i	0.581225	+	0.514920i
$303$	−6.17817	+	1.52278i	−0.354926	+	0.0874815i
$304$	11.1311	+	16.1262i	0.638415	+	0.924903i
$305$	−2.07524	−	17.0911i	−0.118828	−	0.978636i
$306$	−0.759809	−	2.00345i	−0.0434354	−	0.114530i
$307$	1.78039	−	4.69451i	0.101612	−	0.267930i	−0.874563	−	0.484911i	$-0.838852\pi$
$307$	1.78039	−	4.69451i	0.101612	−	0.267930i	0.976176	+	0.216981i	$0.0696211\pi$
$308$	−2.91629	−	4.22498i	−0.166171	−	0.240740i
$309$	15.1091	+	3.72407i	0.859529	+	0.211855i
$310$	7.16926	+	18.9038i	0.407187	+	1.07366i
$311$	−1.97606	+	5.21045i	−0.112052	+	0.295457i	−0.979298	−	0.202422i	$-0.935119\pi$
$311$	−1.97606	+	5.21045i	−0.112052	+	0.295457i	0.867246	+	0.497880i	$0.165888\pi$
$312$	−4.30306	−	1.42645i	−0.243613	−	0.0807569i
$313$	−2.99078	−	7.88603i	−0.169049	−	0.445745i	0.823541	−	0.567256i	$-0.191995\pi$
$313$	−2.99078	−	7.88603i	−0.169049	−	0.445745i	−0.992590	+	0.121511i	$0.961226\pi$
$314$	−1.28128	+	1.13512i	−0.0723069	+	0.0640583i
$315$	−14.2917			−0.805244
$316$	12.3905			0.697019
$317$	20.0098	−	17.7272i	1.12387	−	0.995658i	0.123871	−	0.992298i	$-0.460469\pi$
$317$	20.0098	−	17.7272i	1.12387	−	0.995658i	0.999994	−	0.00335924i	$-0.00106928\pi$
$318$	−15.4555	+	8.11167i	−0.866701	+	0.454880i
$319$	−1.65969			−0.0929247
$320$	−4.82600	−	2.53288i	−0.269782	−	0.141592i
$321$	−13.6442	−	12.0877i	−0.761546	−	0.674671i
$322$	−18.4144	−	26.6779i	−1.02620	−	1.48670i
$323$	3.52255	+	3.12071i	0.196000	+	0.173641i
$324$	0.743477	+	1.07711i	0.0413043	+	0.0598395i
$325$	8.47586	−	10.4260i	0.470156	−	0.578332i
$326$	13.9817	−	20.2559i	0.774373	−	1.12187i
$327$	1.38936	−	0.342447i	0.0768319	−	0.0189374i
$328$	−6.99014	+	6.19272i	−0.385966	+	0.341936i
$329$	31.5078	+	7.76596i	1.73708	+	0.428151i
$330$	3.26108	+	2.88906i	0.179516	+	0.159038i
$331$	−7.28365	−	6.45275i	−0.400346	−	0.354675i	0.438797	−	0.898586i	$-0.355405\pi$
$331$	−7.28365	−	6.45275i	−0.400346	−	0.354675i	−0.839143	+	0.543911i	$0.816943\pi$
$332$	−2.61053	+	6.88341i	−0.143272	+	0.377776i
$333$	3.52855	−	5.11199i	0.193363	−	0.280135i
$334$	35.8900	+	18.8366i	1.96382	+	1.03069i
$335$	3.74175	−	30.8161i	0.204434	−	1.68366i
$336$	23.0388	+	5.67856i	1.25687	+	0.309791i
$337$	12.0624			0.657083			0.328541	−	0.944490i	$-0.393443\pi$
$337$	12.0624			0.657083			0.328541	+	0.944490i	$0.393443\pi$
$338$	16.3085	−	17.1236i	0.887068	−	0.931399i
$339$	−9.28495			−0.504289
$340$	−4.42193	−	1.08991i	−0.239813	−	0.0591085i
$341$	−0.367702	+	3.02830i	−0.0199122	+	0.163991i
$342$	−6.43480	−	3.37725i	−0.347954	−	0.182621i
$343$	−25.8487	+	37.4483i	−1.39570	+	2.02202i
$344$	−5.35374	+	14.1166i	−0.288654	+	0.761118i
$345$	8.14495	+	7.21580i	0.438509	+	0.388485i
$346$	4.98319	+	4.41472i	0.267898	+	0.237337i
$347$	−19.4060	−	4.78315i	−1.04177	−	0.256773i	−0.318922	−	0.947781i	$-0.603321\pi$
$347$	−19.4060	−	4.78315i	−1.04177	−	0.256773i	−0.722847	+	0.691008i	$0.757167\pi$
$348$	−2.00535	+	1.77658i	−0.107498	+	0.0952348i
$349$	9.30688	−	2.29394i	0.498186	−	0.122792i	0.0177869	−	0.999842i	$-0.494338\pi$
$349$	9.30688	−	2.29394i	0.498186	−	0.122792i	0.480399	+	0.877050i	$0.340492\pi$
$350$	−18.6298	+	26.9900i	−0.995807	+	1.44268i
$351$	3.55763	−	0.585906i	0.189892	−	0.0312734i
$352$	−2.95090	−	4.27512i	−0.157283	−	0.227864i
$353$	−5.94498	−	5.26679i	−0.316419	−	0.280323i	0.489931	−	0.871761i	$-0.337022\pi$
$353$	−5.94498	−	5.26679i	−0.316419	−	0.280323i	−0.806350	+	0.591438i	$0.798560\pi$
$354$	−4.50597	−	6.52802i	−0.239489	−	0.346960i
$355$	−32.0011	−	28.3505i	−1.69844	−	1.50469i
$356$	−7.13303	−	3.74370i	−0.378050	−	0.198416i
$357$	5.69881			0.301613
$358$	−12.3483	+	6.48089i	−0.652628	+	0.342526i
$359$	2.62457	−	2.32516i	0.138519	−	0.122717i	−0.591018	−	0.806658i	$-0.701274\pi$
$359$	2.62457	−	2.32516i	0.138519	−	0.122717i	0.729537	+	0.683941i	$0.239735\pi$
$360$	−3.71423			−0.195757
$361$	−3.03872			−0.159933
$362$	−20.0879	+	17.7963i	−1.05580	+	0.935354i
$363$	−3.66755	−	9.67053i	−0.192496	−	0.507571i
$364$	−14.4011	+	17.7145i	−0.754820	+	0.928494i
$365$	0.227285	−	0.599302i	0.0118967	−	0.0313689i
$366$	−3.75928	−	9.91241i	−0.196501	−	0.518130i
$367$	−6.64367	−	1.63752i	−0.346797	−	0.0854777i	0.0620701	−	0.998072i	$-0.480230\pi$
$367$	−6.64367	−	1.63752i	−0.346797	−	0.0854777i	−0.408867	+	0.912594i	$0.634076\pi$
$368$	−10.2630	−	14.8685i	−0.534994	−	0.775072i
$369$	2.63383	−	6.94483i	0.137112	−	0.361533i
$370$	−11.8359	−	31.2087i	−0.615319	−	1.62246i
$371$	−5.59577	−	46.0853i	−0.290518	−	2.39263i
$372$	2.79730	+	4.05259i	0.145033	+	0.210117i
$373$	22.1999	−	5.47178i	1.14947	−	0.283318i	0.381848	−	0.924225i	$-0.375288\pi$
$373$	22.1999	−	5.47178i	1.14947	−	0.283318i	0.767618	+	0.640907i	$0.221442\pi$
$374$	−1.30036	−	1.15202i	−0.0672399	−	0.0595693i
$375$	−1.33389	+	3.51717i	−0.0688816	+	0.181626i
$376$	8.18849	+	2.01828i	0.422289	+	0.104085i
$377$	2.06843	+	7.08487i	0.106529	+	0.364889i
$378$	−8.54450	+	2.10603i	−0.439482	+	0.108323i
$379$	−3.13329	+	25.8050i	−0.160946	+	1.32551i	0.658597	+	0.752496i	$0.271150\pi$
$379$	−3.13329	+	25.8050i	−0.160946	+	1.32551i	−0.819543	+	0.573017i	$0.805773\pi$
$380$	−13.6771	+	7.17829i	−0.701620	+	0.368239i
$381$	4.05726	+	10.6981i	0.207860	+	0.548081i
$382$	−5.57745	−	1.37472i	−0.285367	−	0.0703367i
$383$	−4.04913	+	3.58722i	−0.206901	+	0.183298i	−0.760209	−	0.649678i	$-0.774904\pi$
$383$	−4.04913	+	3.58722i	−0.206901	+	0.183298i	0.553308	+	0.832977i	$0.313365\pi$
$384$	9.18301	+	2.26341i	0.468619	+	0.115504i
$385$	−10.2602	+	5.38495i	−0.522906	+	0.274442i
$386$	4.86127	−	2.55139i	0.247432	−	0.129862i
$387$	−1.44739	−	11.9203i	−0.0735750	−	0.605945i
$388$	−2.10544	−	17.3398i	−0.106887	−	0.880297i
$389$	−3.44421	+	3.05131i	−0.174628	+	0.154707i	−0.745910	−	0.666047i	$-0.767985\pi$
$389$	−3.44421	+	3.05131i	−0.174628	+	0.154707i	0.571281	+	0.820754i	$0.306447\pi$
$390$	8.26860	−	17.5214i	0.418697	−	0.887232i
$391$	−3.24781	−	2.87731i	−0.164249	−	0.145512i
$392$	−11.7174	+	16.9756i	−0.591820	+	0.857400i
$393$	−0.835506	+	2.20305i	−0.0421457	+	0.111129i
$394$	3.23284	+	26.6248i	0.162868	+	1.34134i
$395$	3.37102	−	27.7628i	0.169614	−	1.39690i
$396$	0.939596	+	0.493138i	0.0472165	+	0.0247811i
$397$	9.82964	−	14.2407i	0.493335	−	0.714720i	−0.494680	−	0.869075i	$-0.664715\pi$
$397$	9.82964	−	14.2407i	0.493335	−	0.714720i	0.988015	+	0.154355i	$0.0493301\pi$
$398$	10.2630	+	27.0613i	0.514438	+	1.35646i
$399$	14.4674	−	12.8170i	0.724277	−	0.641653i
$400$	−10.3830	+	15.0424i	−0.519151	+	0.752120i
$401$	−9.72098	−	14.0833i	−0.485443	−	0.703285i	0.501355	−	0.865242i	$-0.332835\pi$
$401$	−9.72098	−	14.0833i	−0.485443	−	0.703285i	−0.986798	+	0.161956i	$0.948220\pi$
$402$	−2.30402	−	18.9753i	−0.114914	−	0.946401i
$403$	13.3854	−	2.20445i	0.666775	−	0.109811i
$404$	−1.00382	+	8.26719i	−0.0499418	+	0.411308i
$405$	2.61572	−	1.37283i	0.129976	−	0.0682167i
$406$	−6.38793	−	16.8436i	−0.317028	−	0.835933i
$407$	0.607047	−	4.99948i	0.0300902	−	0.247815i
$408$	1.48105			0.0733231
$409$	−1.04989	+	8.64659i	−0.0519135	+	0.427546i	0.943462	+	0.331482i	$0.107549\pi$
$409$	−1.04989	+	8.64659i	−0.0519135	+	0.427546i	−0.995375	+	0.0960644i	$0.969375\pi$
$410$	−22.6724	−	32.8467i	−1.11971	−	1.62218i
$411$	10.4036	−	2.56425i	0.513171	−	0.126485i
$412$	11.5695	−	16.7613i	0.569987	−	0.825769i
$413$	20.4837	−	5.04877i	1.00794	−	0.248434i
$414$	5.93292	+	3.11384i	0.291587	+	0.153037i
$415$	14.7131	+	7.72205i	0.722240	+	0.379061i
$416$	−14.5719	+	17.9247i	−0.714449	+	0.878833i
$417$	−13.1042	+	6.87762i	−0.641716	+	0.336798i
$418$	−5.89214			−0.288194
$419$	17.6493	+	9.26305i	0.862224	+	0.452530i	0.837033	−	0.547153i	$-0.184288\pi$
$419$	17.6493	+	9.26305i	0.862224	+	0.452530i	0.0251908	+	0.999683i	$0.491981\pi$
$420$	−6.63280	+	17.4893i	−0.323647	+	0.853388i
$421$	−0.551000	−	4.53789i	−0.0268541	−	0.221163i	0.973104	−	0.230368i	$-0.0739930\pi$
$421$	−0.551000	−	4.53789i	−0.0268541	−	0.221163i	−0.999958	+	0.00920489i	$0.997070\pi$
$422$	−29.9508	+	7.38222i	−1.45798	+	0.359361i
$423$	−6.51266	+	1.60523i	−0.316656	+	0.0780488i
$424$	−1.45427	−	11.9770i	−0.0706258	−	0.581656i
$425$	−1.55664	+	4.10452i	−0.0755081	+	0.199098i
$426$	−23.3101	−	12.2341i	−1.12938	−	0.592744i
$427$	28.1958			1.36449
$428$	−21.1245	+	11.0870i	−1.02109	+	0.535911i
$429$	2.33330	−	1.76111i	0.112653	−	0.0850270i
$430$	−57.1336	−	29.9860i	−2.75523	−	1.44606i
$431$	8.22411	+	4.31635i	0.396141	+	0.207911i	0.651018	−	0.759063i	$-0.274342\pi$
$431$	8.22411	+	4.31635i	0.396141	+	0.207911i	−0.254876	+	0.966974i	$0.582035\pi$
$432$	−4.76213	+	1.17376i	−0.229118	+	0.0564725i
$433$	−23.1282	+	33.5069i	−1.11147	+	1.61024i	−0.385192	+	0.922836i	$0.625865\pi$
$433$	−23.1282	+	33.5069i	−1.11147	+	1.61024i	−0.726276	+	0.687403i	$0.758750\pi$
$434$	−32.1483	+	7.92385i	−1.54317	+	0.380357i
$435$	3.43513	+	4.97665i	0.164702	+	0.238612i
$436$	0.225741	−	1.85915i	0.0108110	−	0.0890370i
$437$	−14.7164			−0.703979
$438$	0.0475726	−	0.391796i	0.00227311	−	0.0187207i
$439$	−12.1007	−	31.9070i	−0.577536	−	1.52284i	−0.831444	−	0.555608i	$-0.812485\pi$
$439$	−12.1007	−	31.9070i	−0.577536	−	1.52284i	0.253908	−	0.967228i	$-0.418284\pi$
$440$	−2.66650	+	1.39948i	−0.127120	+	0.0667178i
$441$	1.97746	−	16.2859i	0.0941650	−	0.775519i
$442$	−3.29712	+	6.98669i	−0.156828	+	0.332323i
$443$	3.65631	+	30.1124i	0.173716	+	1.43068i	0.775159	+	0.631767i	$0.217670\pi$
$443$	3.65631	+	30.1124i	0.173716	+	1.43068i	−0.601442	+	0.798916i	$0.705407\pi$
$444$	−4.61813	−	6.69051i	−0.219167	−	0.317518i
$445$	−10.3290	+	14.9642i	−0.489642	+	0.709370i
$446$	−23.4176	+	20.7461i	−1.10885	+	0.982358i
$447$	−6.20919	−	16.3723i	−0.293685	−	0.774382i
$448$	5.07054	−	7.34594i	0.239560	−	0.347063i
$449$	−5.21308	−	2.73603i	−0.246020	−	0.129121i	0.337207	−	0.941431i	$-0.390518\pi$
$449$	−5.21308	−	2.73603i	−0.246020	−	0.129121i	−0.583227	+	0.812309i	$0.698210\pi$
$450$	0.817093	−	6.72937i	0.0385181	−	0.317225i
$451$	−0.725882	−	5.97818i	−0.0341805	−	0.281501i
$452$	−4.30917	+	11.3623i	−0.202686	+	0.534440i
$453$	4.21418	−	6.10529i	0.197999	−	0.286852i
$454$	31.8702	+	28.2346i	1.49574	+	1.32511i
$455$	35.7742	+	37.0874i	1.67712	+	1.73868i
$456$	3.75991	−	3.33099i	0.176074	−	0.155988i
$457$	−1.82154	−	15.0017i	−0.0852081	−	0.701752i	−0.971236	−	0.238120i	$-0.923469\pi$
$457$	−1.82154	−	15.0017i	−0.0852081	−	0.701752i	0.886028	−	0.463632i	$-0.153454\pi$
$458$	−2.33767	−	19.2524i	−0.109232	−	0.899606i
$459$	−1.04302	+	0.547419i	−0.0486840	+	0.0255513i
$460$	12.6103	−	6.61842i	0.587960	−	0.308585i
$461$	−8.22240	−	2.02664i	−0.382955	−	0.0943900i	0.0431382	−	0.999069i	$-0.486264\pi$
$461$	−8.22240	−	2.02664i	−0.382955	−	0.0943900i	−0.426094	+	0.904679i	$0.640111\pi$
$462$	−5.34068	+	4.73143i	−0.248471	+	0.220126i
$463$	−15.2358	−	3.75528i	−0.708066	−	0.174523i	−0.131193	−	0.991357i	$-0.541881\pi$
$463$	−15.2358	−	3.75528i	−0.708066	−	0.174523i	−0.576873	+	0.816834i	$0.695727\pi$
$464$	−3.56020	−	9.38748i	−0.165278	−	0.435803i
$465$	9.84152	−	5.16523i	0.456390	−	0.239532i
$466$	1.80778	−	14.8884i	0.0837437	−	0.689691i
$467$	4.83620	−	1.19202i	0.223792	−	0.0551599i	−0.125825	−	0.992052i	$-0.540158\pi$
$467$	4.83620	−	1.19202i	0.223792	−	0.0551599i	0.349617	+	0.936893i	$0.386312\pi$
$468$	0.934109	−	4.62553i	0.0431792	−	0.213815i
$469$	49.3610	+	12.1664i	2.27928	+	0.561792i
$470$	−12.7811	+	33.7010i	−0.589548	+	1.55451i
$471$	0.704385	+	0.624031i	0.0324563	+	0.0287538i
$472$	5.32347	−	1.31212i	0.245032	−	0.0603951i
$473$	−5.53056	−	8.01240i	−0.254296	−	0.368411i
$474$	−2.07574	−	17.0952i	−0.0953417	−	0.785210i
$475$	5.27954	+	13.9210i	0.242242	+	0.638740i
$476$	2.64484	−	6.97386i	0.121226	−	0.319646i
$477$	5.45104	+	7.89719i	0.249586	+	0.361588i
$478$	43.2548	+	10.6614i	1.97843	+	0.487639i
$479$	3.82516	+	10.0861i	0.174776	+	0.460847i	0.993567	−	0.113245i	$-0.0361245\pi$
$479$	3.82516	+	10.0861i	0.174776	+	0.460847i	−0.818791	+	0.574092i	$0.805355\pi$
$480$	−6.71151	+	17.6968i	−0.306337	+	0.807744i
$481$	−22.0983	+	3.63937i	−1.00760	+	0.165941i
$482$	11.6333	+	30.6746i	0.529884	+	1.39719i
$483$	−13.3390	+	11.8173i	−0.606946	+	0.537708i
$484$	−13.5363			−0.615287
$485$	−39.4255			−1.79022
$486$	1.36155	−	1.20623i	0.0617610	−	0.0547155i
$487$	7.14267	−	3.74876i	0.323665	−	0.169873i	−0.295063	−	0.955478i	$-0.595341\pi$
$487$	7.14267	−	3.74876i	0.323665	−	0.169873i	0.618728	+	0.785605i	$0.287648\pi$
$488$	7.32776			0.331712
$489$	−11.9810	−	6.28812i	−0.541800	−	0.284359i
$490$	−65.9851	−	58.4577i	−2.98090	−	2.64085i
$491$	−15.8593	−	22.9762i	−0.715721	−	1.03690i	−0.997010	−	0.0772781i	$-0.975377\pi$
$491$	−15.8593	−	22.9762i	−0.715721	−	1.03690i	0.281288	−	0.959623i	$-0.409238\pi$
$492$	−7.27629	−	6.44623i	−0.328040	−	0.290618i
$493$	−1.36976	−	1.98444i	−0.0616910	−	0.0893748i
$494$	7.34323	+	25.1523i	0.330387	+	1.13166i
$495$	1.36059	−	1.97115i	0.0611538	−	0.0885966i
$496$	−17.9173	+	4.41622i	−0.804511	+	0.198294i
$497$	52.4083	−	46.4297i	2.35084	−	2.08266i
$498$	9.93442	+	2.44862i	0.445172	+	0.109725i
$499$	12.6275	+	11.1870i	0.565284	+	0.500798i	0.896671	−	0.442697i	$-0.145978\pi$
$499$	12.6275	+	11.1870i	0.565284	+	0.500798i	−0.331387	+	0.943495i	$0.607517\pi$
$500$	3.68503	+	3.26466i	0.164800	+	0.146000i
$501$	7.90164	−	20.8349i	0.353019	−	0.930835i
$502$	−19.1355	+	27.7226i	−0.854061	+	1.23732i
$503$	22.6810	+	11.9039i	1.01130	+	0.530770i	0.887144	−	0.461493i	$-0.152686\pi$
$503$	22.6810	+	11.9039i	1.01130	+	0.530770i	0.124154	+	0.992263i	$0.460378\pi$
$504$	0.733202	−	6.03846i	0.0326594	−	0.268975i
$505$	18.2509	+	4.49843i	0.812152	+	0.200178i
$506$	5.43258			0.241508
$507$	−10.4257	−	7.76556i	−0.463023	−	0.344881i
$508$	14.9747			0.664394
$509$	−0.119611	−	0.0294814i	−0.00530166	−	0.00130674i	0.236664	−	0.971592i	$-0.423946\pi$
$509$	−0.119611	−	0.0294814i	−0.00530166	−	0.00130674i	−0.241966	+	0.970285i	$0.577792\pi$
$510$	−0.762962	+	6.28356i	−0.0337845	+	0.278241i
$511$	0.929457	+	0.487817i	0.0411167	+	0.0215797i
$512$	10.8446	−	15.7111i	0.479269	−	0.694341i
$513$	−1.41670	+	3.73554i	−0.0625489	+	0.164928i
$514$	17.7104	+	15.6900i	0.781170	+	0.692056i
$515$	−34.4087	−	30.4834i	−1.51623	−	1.34326i
$516$	−15.2591	−	3.76103i	−0.671745	−	0.165570i
$517$	−4.07069	+	3.60632i	−0.179029	+	0.158606i
$518$	53.0744	−	13.0817i	2.33196	−	0.574775i
$519$	2.07909	−	3.01208i	0.0912617	−	0.132215i
$520$	9.29730	+	9.63857i	0.407713	+	0.422679i
$521$	−17.8991	−	25.9313i	−0.784173	−	1.13607i	−0.987602	−	0.156980i	$-0.949824\pi$
$521$	−17.8991	−	25.9313i	−0.784173	−	1.13607i	0.203429	−	0.979090i	$-0.434791\pi$
$522$	2.78711	+	2.46917i	0.121989	+	0.108072i
$523$	−24.2089	−	35.0726i	−1.05858	−	1.53362i	−0.828130	−	0.560536i	$-0.810595\pi$
$523$	−24.2089	−	35.0726i	−1.05858	−	1.53362i	−0.230451	−	0.973084i	$-0.574020\pi$
$524$	2.30819	+	2.04488i	0.100834	+	0.0893311i
$525$	15.9641	+	8.37859i	0.696729	+	0.365672i
$526$	−28.2873			−1.23338
$527$	−3.92432	+	2.05964i	−0.170946	+	0.0897194i
$528$	−2.97653	+	2.63698i	−0.129537	+	0.114760i
$529$	−9.43144			−0.410063
$530$	51.5632			2.23976
$531$	−3.26403	+	2.89168i	−0.141647	+	0.125488i
$532$	−8.97030	−	23.6527i	−0.388912	−	1.02548i
$533$	−24.6150	+	10.5491i	−1.06619	+	0.456932i
$534$	−3.97024	+	10.4687i	−0.171809	+	0.453023i
$535$	19.0950	+	50.3493i	0.825547	+	2.17679i
$536$	12.8283	+	3.16190i	0.554100	+	0.136573i
$537$	4.35515	+	6.30953i	0.187939	+	0.272276i
$538$	13.8600	−	36.5458i	0.597548	−	1.57560i
$539$	−4.71671	−	12.4369i	−0.203163	−	0.535697i
$540$	−0.466028	−	3.83809i	−0.0200547	−	0.165165i
$541$	−16.5288	−	23.9461i	−0.710628	−	1.02952i	−0.997438	−	0.0715352i	$-0.977210\pi$
$541$	−16.5288	−	23.9461i	−0.710628	−	1.02952i	0.286810	−	0.957988i	$-0.407405\pi$
$542$	32.7748	−	8.07826i	1.40780	−	0.346991i
$543$	11.0433	+	9.78354i	0.473915	+	0.419852i
$544$	2.67622	−	7.05662i	0.114742	−	0.302550i
$545$	−4.10430	−	1.01162i	−0.175809	−	0.0433330i
$546$	26.8534	+	16.9016i	1.14922	+	0.723321i
$547$	4.54611	−	1.12052i	0.194378	−	0.0479098i	−0.140925	−	0.990020i	$-0.545008\pi$
$547$	4.54611	−	1.12052i	0.194378	−	0.0479098i	0.335303	+	0.942110i	$0.391161\pi$
$548$	1.69036	−	13.9214i	0.0722085	−	0.594691i
$549$	−5.16051	+	2.70845i	−0.220245	+	0.115594i
$550$	−1.94895	−	5.13897i	−0.0831037	−	0.219126i
$551$	−7.94052	−	1.95716i	−0.338277	−	0.0833779i
$552$	−3.46665	+	3.07119i	−0.147551	+	0.130718i
$553$	44.4704	+	10.9610i	1.89107	+	0.466108i
$554$	−25.4892	+	13.3778i	−1.08293	+	0.568367i
$555$	−16.2476	+	8.52740i	−0.689672	+	0.361968i
$556$	2.33471	+	19.2280i	0.0990136	+	0.815451i
$557$	−1.94268	−	15.9994i	−0.0823140	−	0.677917i	−0.974205	−	0.225666i	$-0.927544\pi$
$557$	−1.94268	−	15.9994i	−0.0823140	−	0.677917i	0.891891	−	0.452251i	$-0.149379\pi$
$558$	5.12276	−	4.53837i	0.216864	−	0.192125i
$559$	−27.3107	+	33.5945i	−1.15512	+	1.42090i
$560$	−52.4673	−	46.4820i	−2.21715	−	1.96422i
$561$	−0.542535	+	0.785998i	−0.0229059	+	0.0331849i
$562$	−10.5475	+	27.8114i	−0.444918	+	1.17315i
$563$	−3.95320	−	32.5575i	−0.166608	−	1.37214i	−0.800786	−	0.598950i	$-0.795585\pi$
$563$	−3.95320	−	32.5575i	−0.166608	−	1.37214i	0.634178	−	0.773187i	$-0.281338\pi$
$564$	−1.05817	+	8.71478i	−0.0445568	+	0.366959i
$565$	24.2868	+	12.7467i	1.02175	+	0.536257i
$566$	18.6304	−	26.9908i	0.783095	−	1.13451i
$567$	1.71555	+	4.52354i	0.0720464	+	0.189971i
$568$	13.6203	−	12.0665i	0.571495	−	0.506301i
$569$	−8.57025	+	12.4162i	−0.359284	+	0.520512i	−0.960391	−	0.278656i	$-0.910111\pi$
$569$	−8.57025	+	12.4162i	−0.359284	+	0.520512i	0.601107	+	0.799168i	$0.294726\pi$
$570$	12.1952	+	17.6678i	0.510802	+	0.740024i
$571$	2.05096	+	16.8912i	0.0858302	+	0.706875i	0.970575	+	0.240799i	$0.0774096\pi$
$571$	2.05096	+	16.8912i	0.0858302	+	0.706875i	−0.884745	+	0.466076i	$0.845667\pi$
$572$	−1.07224	−	3.67269i	−0.0448327	−	0.153563i
$573$	−0.380651	+	3.13494i	−0.0159019	+	0.130964i
$574$	57.8766	−	30.3760i	2.41572	−	1.26787i
$575$	−4.86776	−	12.8352i	−0.203000	−	0.535266i
$576$	−0.222391	+	1.83155i	−0.00926627	+	0.0763146i
$577$	17.7050			0.737069			0.368535	−	0.929614i	$-0.379860\pi$
$577$	17.7050			0.737069			0.368535	+	0.929614i	$0.379860\pi$
$578$	−3.42314	+	28.1921i	−0.142384	+	1.17264i
$579$	−1.71453	−	2.48393i	−0.0712535	−	0.103229i
$580$	7.68437	−	1.89403i	0.319076	−	0.0786452i
$581$	−15.4587	+	22.3957i	−0.641333	+	0.929132i
$582$	−23.5712	+	5.80978i	−0.977057	+	0.240823i
$583$	6.88895	+	3.61560i	0.285311	+	0.149743i
$584$	0.241555	+	0.126778i	0.00999561	+	0.00524610i
$585$	−10.1101	−	3.35147i	−0.418001	−	0.138566i
$586$	25.9813	−	13.6360i	1.07328	−	0.563299i
$587$	39.7305			1.63985			0.819926	−	0.572469i	$-0.194014\pi$
$587$	39.7305			1.63985			0.819926	+	0.572469i	$0.194014\pi$
$588$	−19.0119	−	9.97823i	−0.784038	−	0.411495i
$589$	−5.33028	+	14.0548i	−0.219630	+	0.579118i
$590$	2.82444	+	23.2614i	0.116281	+	0.957656i
$591$	14.3161	−	3.52859i	0.588884	−	0.145147i
$592$	29.5801	−	7.29084i	1.21573	−	0.299652i
$593$	3.55111	+	29.2460i	0.145827	+	1.20099i	0.863405	+	0.504512i	$0.168327\pi$
$593$	3.55111	+	29.2460i	0.145827	+	1.20099i	−0.717578	+	0.696478i	$0.754749\pi$
$594$	0.522979	−	1.37898i	0.0214581	−	0.0565803i
$595$	−14.9065	−	7.82352i	−0.611106	−	0.320733i
$596$	−22.9171			−0.938721
$597$	14.0884	−	7.39418i	0.576601	−	0.302624i
$598$	−6.77049	−	23.1906i	−0.276866	−	0.948332i
$599$	16.1399	+	8.47087i	0.659458	+	0.346110i	0.761029	−	0.648718i	$-0.224695\pi$
$599$	16.1399	+	8.47087i	0.659458	+	0.346110i	−0.101571	+	0.994828i	$0.532387\pi$
$600$	4.14887	+	2.17750i	0.169377	+	0.0888959i
$601$	−18.2016	+	4.48630i	−0.742461	+	0.183000i	−0.592363	−	0.805671i	$-0.701805\pi$
$601$	−18.2016	+	4.48630i	−0.742461	+	0.183000i	−0.150097	+	0.988671i	$0.547959\pi$
$602$	60.0286	−	86.9664i	2.44658	−	3.54449i
$603$	−10.2029	+	2.51480i	−0.415496	+	0.102411i
$604$	−5.51547	−	7.99053i	−0.224421	−	0.325130i
$605$	−3.68276	+	30.3303i	−0.149726	+	1.23310i
$606$	11.5745			0.470180
$607$	−0.0341122	+	0.280939i	−0.00138457	+	0.0114030i	−0.993385	−	0.114833i	$-0.963367\pi$
$607$	−0.0341122	+	0.280939i	−0.00138457	+	0.0114030i	0.992000	+	0.126236i	$0.0402897\pi$
$608$	−9.07675	−	23.9334i	−0.368111	−	0.970628i
$609$	−8.76895	+	4.60230i	−0.355336	+	0.186495i
$610$	−3.77488	+	31.0889i	−0.152840	+	1.25875i
$611$	20.4678	+	12.8825i	0.828039	+	0.521169i
$612$	0.185829	+	1.53044i	0.00751170	+	0.0618644i
$613$	−23.9323	−	34.6719i	−0.966617	−	1.40039i	−0.915780	−	0.401680i	$-0.868426\pi$
$613$	−23.9323	−	34.6719i	−0.966617	−	1.40039i	−0.0508370	−	0.998707i	$-0.516189\pi$
$614$	−5.18804	+	7.51618i	−0.209372	+	0.303328i
$615$	−16.4234	+	14.5499i	−0.662257	+	0.586708i
$616$	−1.74886	−	4.61135i	−0.0704634	−	0.185797i
$617$	1.15710	−	1.67634i	0.0465830	−	0.0674871i	−0.799000	−	0.601331i	$-0.794637\pi$
$617$	1.15710	−	1.67634i	0.0465830	−	0.0674871i	0.845583	+	0.533844i	$0.179253\pi$
$618$	−25.0639	−	13.1545i	−1.00822	−	0.529153i
$619$	−4.20624	+	34.6415i	−0.169063	+	1.39236i	0.623144	+	0.782107i	$0.285855\pi$
$619$	−4.20624	+	34.6415i	−0.169063	+	1.39236i	−0.792207	+	0.610252i	$0.791068\pi$
$620$	−1.75341	−	14.4406i	−0.0704187	−	0.579950i
$621$	1.30621	−	3.44418i	0.0524162	−	0.138210i
$622$	5.75822	−	8.34222i	0.230884	−	0.334493i
$623$	−22.2892	−	19.7465i	−0.892998	−	0.791127i
$624$	14.9663	+	9.41980i	0.599131	+	0.377094i
$625$	22.2647	−	19.7248i	0.890589	−	0.788993i
$626$	1.84924	+	15.2299i	0.0739105	+	0.608707i
$627$	0.390443	+	3.21559i	0.0155928	+	0.128418i
$628$	1.09056	−	0.572369i	0.0435180	−	0.0228400i
$629$	6.47875	−	3.40031i	0.258325	−	0.135579i
$630$	25.2412	+	6.22140i	1.00563	+	0.247867i
$631$	−13.7770	+	12.2053i	−0.548453	+	0.485887i	−0.891244	−	0.453525i	$-0.850166\pi$
$631$	−13.7770	+	12.2053i	−0.548453	+	0.485887i	0.342790	+	0.939412i	$0.388628\pi$
$632$	11.5573	+	2.84862i	0.459726	+	0.113312i
$633$	6.01348	+	15.8562i	0.239014	+	0.630229i
$634$	−43.0573	+	22.5982i	−1.71003	+	0.897491i
$635$	4.07409	−	33.5532i	0.161675	−	1.33152i
$636$	12.1939	−	3.00554i	0.483521	−	0.119177i
$637$	−47.2124	+	35.6345i	−1.87062	+	1.41189i
$638$	2.93126	+	0.722491i	0.116050	+	0.0286037i
$639$	−5.13202	+	13.5320i	−0.203019	+	0.535318i
$640$	−20.9129	−	18.5272i	−0.826654	−	0.732351i
$641$	24.2794	−	5.98433i	0.958978	−	0.236367i	0.271391	−	0.962469i	$-0.412516\pi$
$641$	24.2794	−	5.98433i	0.958978	−	0.236367i	0.687587	+	0.726102i	$0.258670\pi$
$642$	18.8357	+	27.2883i	0.743388	+	1.07698i
$643$	4.66764	+	38.4415i	0.184074	+	1.51598i	0.733067	+	0.680157i	$0.238088\pi$
$643$	4.66764	+	38.4415i	0.184074	+	1.51598i	−0.548993	+	0.835827i	$0.684989\pi$
$644$	8.27066	+	21.8079i	0.325910	+	0.859353i
$645$	−12.5787	+	33.1673i	−0.495285	+	1.30596i
$646$	−4.86286	−	7.04507i	−0.191327	−	0.277184i
$647$	37.4725	+	9.23615i	1.47320	+	0.363110i	0.892514	−	0.451019i	$-0.148939\pi$
$647$	37.4725	+	9.23615i	1.47320	+	0.363110i	0.580683	+	0.814130i	$0.302786\pi$
$648$	0.445851	+	1.17561i	0.0175147	+	0.0461825i
$649$	−1.25373	+	3.30582i	−0.0492133	+	0.129765i
$650$	−19.5083	+	14.7243i	−0.765177	+	0.577533i
$651$	6.45469	+	17.0196i	0.252979	+	0.667051i
$652$	−13.2554	+	11.7433i	−0.519123	+	0.459903i
$653$	−38.9507			−1.52426			−0.762129	−	0.647425i	$-0.775846\pi$
$653$	−38.9507			−1.52426			−0.762129	+	0.647425i	$0.775846\pi$
$654$	−2.60290			−0.101781
$655$	5.20987	−	4.61554i	0.203566	−	0.180344i
$656$	32.2565	−	16.9295i	1.25941	−	0.660987i
$657$	−0.216972			−0.00846487
$658$	−52.2668	−	27.4317i	−2.03757	−	1.06940i
$659$	30.5469	+	27.0622i	1.18994	+	1.05419i	0.997338	+	0.0729159i	$0.0232305\pi$
$659$	30.5469	+	27.0622i	1.18994	+	1.05419i	0.192600	+	0.981277i	$0.438308\pi$
$660$	−1.78072	−	2.57982i	−0.0693144	−	0.100419i
$661$	−5.04784	−	4.47200i	−0.196338	−	0.173941i	0.559226	−	0.829016i	$-0.311099\pi$
$661$	−5.04784	−	4.47200i	−0.196338	−	0.173941i	−0.755564	+	0.655075i	$0.772637\pi$
$662$	10.0550	+	14.5672i	0.390800	+	0.566172i
$663$	4.03141	+	1.33640i	0.156567	+	0.0519015i
$664$	−4.01752	+	5.82039i	−0.155910	+	0.225875i
$665$	−55.4383	+	13.6643i	−2.14980	+	0.529879i
$666$	−8.45729	+	7.49250i	−0.327713	+	0.290329i
$667$	7.32119	+	1.80451i	0.283478	+	0.0698710i
$668$	−21.8293	−	19.3391i	−0.844601	−	0.748252i
$669$	12.8738	+	11.4052i	0.497730	+	0.440950i
$670$	−20.0233	+	52.7970i	−0.773566	+	2.03973i
$671$	−2.68428	+	3.88886i	−0.103626	+	0.150128i
$672$	−27.4459	−	14.4047i	−1.05875	−	0.555675i
$673$	−2.35716	+	19.4130i	−0.0908619	+	0.748315i	0.874067	+	0.485805i	$0.161473\pi$
$673$	−2.35716	+	19.4130i	−0.0908619	+	0.748315i	−0.964929	+	0.262510i	$0.915450\pi$
$674$	−21.3041	−	5.25098i	−0.820603	−	0.202260i
$675$	−3.72664			−0.143439
$676$	−14.3416	+	9.15436i	−0.551601	+	0.352091i
$677$	−19.7307			−0.758313			−0.379156	−	0.925333i	$-0.623786\pi$
$677$	−19.7307			−0.758313			−0.379156	+	0.925333i	$0.623786\pi$
$678$	16.3986	+	4.04190i	0.629785	+	0.155228i
$679$	7.78273	−	64.0966i	0.298674	−	2.45980i
$680$	−3.87402	−	2.03324i	−0.148562	−	0.0779712i
$681$	13.2969	−	19.2639i	0.509539	−	0.738194i
$682$	1.96768	−	5.18836i	0.0753465	−	0.198673i
$683$	21.2085	+	18.7891i	0.811521	+	0.718945i	0.962996	−	0.269516i	$-0.0868638\pi$
$683$	21.2085	+	18.7891i	0.811521	+	0.718945i	−0.151475	+	0.988461i	$0.548402\pi$
$684$	3.91382	+	3.46735i	0.149649	+	0.132577i
$685$	−30.7331	−	7.57504i	−1.17425	−	0.289427i
$686$	61.9546	−	54.8870i	2.36544	−	2.09560i
$687$	−10.3519	+	2.55153i	−0.394951	+	0.0973468i
$688$	33.4559	−	48.4692i	1.27549	−	1.84787i
$689$	6.84872	−	33.9135i	0.260915	−	1.29200i
$690$	−11.2441	−	16.2898i	−0.428054	−	0.620143i
$691$	−34.2580	−	30.3500i	−1.30324	−	1.15457i	−0.977924	−	0.208961i	$-0.932992\pi$
$691$	−34.2580	−	30.3500i	−1.30324	−	1.15457i	−0.325313	−	0.945606i	$-0.605470\pi$
$692$	−2.72108	−	3.94217i	−0.103440	−	0.149859i
$693$	2.93604	+	2.60110i	0.111531	+	0.0988077i
$694$	32.1918	+	16.8955i	1.22198	+	0.641346i
$695$	43.7187			1.65835
$696$	−2.27895	+	1.19608i	−0.0863833	+	0.0453374i
$697$	6.54886	−	5.80179i	0.248056	−	0.219758i
$698$	−17.4359			−0.659960
$699$	−8.24501			−0.311855
$700$	17.6622	−	15.6473i	0.667567	−	0.591413i
$701$	13.5301	+	35.6759i	0.511024	+	1.34746i	0.903851	+	0.427847i	$0.140728\pi$
$701$	13.5301	+	35.6759i	0.511024	+	1.34746i	−0.392828	+	0.919612i	$0.628503\pi$
$702$	−6.53836	−	0.513897i	−0.246775	−	0.0193958i
$703$	8.79988	−	23.2034i	0.331894	−	0.875132i
$704$	0.530453	+	1.39869i	0.0199922	+	0.0527151i
$705$	19.2390	+	4.74198i	0.724582	+	0.178593i
$706$	8.20701	+	11.8899i	0.308875	+	0.447482i
$707$	−10.9162	+	28.7836i	−0.410545	+	1.08252i
$708$	2.02381	+	5.33635i	0.0760595	+	0.200552i
$709$	−2.00774	−	16.5352i	−0.0754023	−	0.620994i	−0.980602	−	0.196008i	$-0.937202\pi$
$709$	−2.00774	−	16.5352i	−0.0754023	−	0.620994i	0.905200	−	0.424986i	$-0.139721\pi$
$710$	44.1773	+	64.0019i	1.65794	+	2.40195i
$711$	−9.19204	+	2.26563i	−0.344728	+	0.0849679i
$712$	−5.79270	−	5.13189i	−0.217091	−	0.192326i
$713$	4.91454	−	12.9586i	0.184051	−	0.485303i
$714$	−10.0650	−	2.48079i	−0.376672	−	0.0928413i
$715$	−8.52096	+	1.40332i	−0.318666	+	0.0524812i
$716$	9.74245	−	2.40130i	0.364093	−	0.0897407i
$717$	2.95207	−	24.3125i	0.110247	−	0.907965i
$718$	−5.64756	+	2.96407i	−0.210765	+	0.110618i
$719$	−10.7852	−	28.4383i	−0.402222	−	1.06057i	−0.971210	−	0.238226i	$-0.923434\pi$
$719$	−10.7852	−	28.4383i	−0.402222	−	1.06057i	0.568988	−	0.822346i	$-0.307335\pi$
$720$	14.0678	+	3.46739i	0.524274	+	0.129222i
$721$	56.3512	−	49.9229i	2.09863	−	1.85922i
$722$	5.36684	+	1.32281i	0.199733	+	0.0492298i
$723$	15.9695	−	8.38145i	0.593913	−	0.311709i
$724$	17.0977	−	8.97358i	0.635432	−	0.333500i
$725$	−0.919515	−	7.57289i	−0.0341499	−	0.281250i
$726$	2.26770	+	18.6762i	0.0841621	+	0.693137i
$727$	7.67079	−	6.79573i	0.284494	−	0.252040i	−0.508791	−	0.860890i	$-0.669907\pi$
$727$	7.67079	−	6.79573i	0.284494	−	0.252040i	0.793285	+	0.608850i	$0.208369\pi$
$728$	−17.5054	+	13.2125i	−0.648792	+	0.489688i
$729$	−0.748511	−	0.663123i	−0.0277226	−	0.0245601i
$730$	−0.662307	+	0.959517i	−0.0245131	+	0.0355133i
$731$	5.01576	−	13.2255i	0.185515	−	0.489162i
$732$	0.919421	+	7.57211i	0.0339828	+	0.279873i
$733$	2.79518	−	23.0204i	0.103242	−	0.850278i	−0.845445	−	0.534063i	$-0.820665\pi$
$733$	2.79518	−	23.0204i	0.103242	−	0.850278i	0.948687	−	0.316216i	$-0.102412\pi$
$734$	11.0209	+	5.78420i	0.406788	+	0.213499i
$735$	−27.5303	+	39.8845i	−1.01547	+	1.47116i
$736$	8.36880	+	22.0667i	0.308478	+	0.813390i
$737$	−6.37727	+	5.64977i	−0.234910	+	0.208112i
$738$	−7.67493	+	11.1191i	−0.282518	+	0.409298i
$739$	−15.2210	−	22.0514i	−0.559913	−	0.811175i	0.436145	−	0.899876i	$-0.356344\pi$
$739$	−15.2210	−	22.0514i	−0.559913	−	0.811175i	−0.996058	+	0.0887019i	$0.971728\pi$
$740$	2.89475	+	23.8404i	0.106413	+	0.876390i
$741$	13.2401	−	5.67423i	0.486387	−	0.208448i
$742$	−10.1787	+	83.8295i	−0.373673	+	3.07748i
$743$	25.0663	−	13.1558i	0.919593	−	0.482639i	0.0626409	−	0.998036i	$-0.480048\pi$
$743$	25.0663	−	13.1558i	0.919593	−	0.482639i	0.856952	+	0.515397i	$0.172355\pi$
$744$	1.67750	+	4.42320i	0.0615000	+	0.162162i
$745$	−6.23495	+	51.3494i	−0.228431	+	1.88130i
$746$	−41.5903			−1.52273
$747$	0.678007	−	5.58389i	0.0248070	−	0.204304i
$748$	0.710064	+	1.02871i	0.0259625	+	0.0376132i
$749$	−85.6254	+	21.1048i	−3.12868	+	0.771152i
$750$	3.88693	−	5.63119i	0.141930	−	0.205622i
$751$	−1.29677	+	0.319625i	−0.0473198	+	0.0116633i	−0.262904	−	0.964822i	$-0.584680\pi$
$751$	−1.29677	+	0.319625i	−0.0473198	+	0.0116633i	0.215585	+	0.976485i	$0.430834\pi$
$752$	−29.1300	−	15.2886i	−1.06226	−	0.557518i
$753$	16.3974	+	8.60603i	0.597555	+	0.313621i
$754$	−0.568993	−	13.4134i	−0.0207215	−	0.488486i
$755$	−19.4046	+	10.1843i	−0.706207	+	0.370646i
$756$	6.33182			0.230286
$757$	42.3931	+	22.2496i	1.54080	+	0.808677i	0.999483	−	0.0321389i	$-0.0102319\pi$
$757$	42.3931	+	22.2496i	1.54080	+	0.808677i	0.541321	+	0.840816i	$0.317924\pi$
$758$	16.7672	−	44.2115i	0.609013	−	1.60583i
$759$	−0.359990	−	2.96479i	−0.0130668	−	0.107615i
$760$	−14.4077	+	3.55119i	−0.522624	+	0.128815i
$761$	−2.18403	+	0.538314i	−0.0791709	+	0.0195139i	−0.278702	−	0.960378i	$-0.589904\pi$
$761$	−2.18403	+	0.538314i	−0.0791709	+	0.0195139i	0.199531	+	0.979891i	$0.436058\pi$
$762$	−2.50866	−	20.6607i	−0.0908791	−	0.748457i
$763$	2.45486	−	6.47292i	0.0888718	−	0.234336i
$764$	3.65969	+	1.92075i	0.132403	+	0.0694904i
$765$	3.47976			0.125811
$766$	8.71295	−	4.57291i	0.314812	−	0.165226i
$767$	15.6744	+	1.23196i	0.565969	+	0.0444836i
$768$	−18.5006	−	9.70987i	−0.667584	−	0.350375i
$769$	−32.0665	−	16.8298i	−1.15635	−	0.606899i	−0.226200	−	0.974081i	$-0.572630\pi$
$769$	−32.0665	−	16.8298i	−1.15635	−	0.606899i	−0.930149	+	0.367182i	$0.880323\pi$
$770$	20.4652	−	5.04421i	0.737513	−	0.181781i
$771$	7.38912	−	10.7050i	0.266112	−	0.385531i
$772$	−3.83540	+	0.945341i	−0.138039	+	0.0340236i
$773$	26.4118	+	38.2641i	0.949966	+	1.37626i	0.926400	+	0.376541i	$0.122887\pi$
$773$	26.4118	+	38.2641i	0.949966	+	1.37626i	0.0235659	+	0.999722i	$0.492498\pi$
$774$	−2.63282	+	21.6832i	−0.0946346	+	0.779386i
$775$	−14.0213			−0.503661
$776$	2.02264	−	16.6579i	0.0726085	−	0.597985i
$777$	−10.6562	−	28.0981i	−0.382289	−	1.00801i
$778$	7.41128	−	3.88974i	0.265707	−	0.139454i
$779$	3.57681	−	29.4576i	0.128152	−	1.05543i
$780$	−8.79344	+	10.8167i	−0.314856	+	0.387300i
$781$	1.41438	+	11.6485i	0.0506106	+	0.416816i
$782$	4.48358	+	6.49558i	0.160332	+	0.232282i
$783$	1.16284	−	1.68466i	0.0415565	−	0.0602050i
$784$	60.2276	−	53.3570i	2.15099	−	1.90561i
$785$	−0.985781	−	2.59929i	−0.0351840	−	0.0927726i
$786$	2.43465	−	3.52721i	0.0868412	−	0.125811i
$787$	25.0589	+	13.1519i	0.893253	+	0.468815i	0.847900	−	0.530156i	$-0.177867\pi$
$787$	25.0589	+	13.1519i	0.893253	+	0.468815i	0.0453525	+	0.998971i	$0.485559\pi$
$788$	2.32605	−	19.1567i	0.0828621	−	0.682431i
$789$	1.87446	+	15.4376i	0.0667325	+	0.549592i
$790$	−18.0394	+	47.5659i	−0.641812	+	1.69232i
$791$	−25.5174	+	36.9683i	−0.907294	+	1.31444i
$792$	0.763042	+	0.675996i	0.0271135	+	0.0240205i
$793$	19.9461	+	6.61206i	0.708306	+	0.234801i
$794$	−23.5598	+	20.8722i	−0.836107	+	0.740726i
$795$	−3.41684	−	28.1402i	−0.121183	−	0.998029i
$796$	−2.51006	−	20.6722i	−0.0889668	−	0.732707i
$797$	−33.0862	+	17.3650i	−1.17197	+	0.615098i	−0.934384	−	0.356267i	$-0.884049\pi$
$797$	−33.0862	+	17.3650i	−1.17197	+	0.615098i	−0.237588	+	0.971366i	$0.576357\pi$
$798$	−31.1311	+	16.3389i	−1.10203	+	0.578389i
$799$	−7.67157	−	1.89087i	−0.271400	−	0.0668942i
$800$	17.8718	−	15.8330i	0.631862	−	0.559781i
$801$	5.97628	+	1.47302i	0.211161	+	0.0520466i
$802$	11.0380	+	29.1049i	0.389766	+	1.02773i
$803$	−0.155767	+	0.0817527i	−0.00549689	+	0.00288499i
$804$	−1.65776	+	13.6529i	−0.0584646	+	0.481499i
$805$	51.1143	−	12.5986i	1.80154	−	0.444041i
$806$	−24.6003	−	1.93352i	−0.866509	−	0.0681052i
$807$	−20.8630	−	5.14228i	−0.734414	−	0.181017i
$808$	−2.83698	+	7.48051i	−0.0998047	+	0.263163i
$809$	−7.26771	−	6.43862i	−0.255519	−	0.226370i	0.525632	−	0.850712i	$-0.323829\pi$
$809$	−7.26771	−	6.43862i	−0.255519	−	0.226370i	−0.781151	+	0.624342i	$0.785367\pi$
$810$	−5.21737	+	1.28597i	−0.183320	+	0.0451842i
$811$	19.1224	+	27.7036i	0.671478	+	0.972804i	0.999603	+	0.0281695i	$0.00896781\pi$
$811$	19.1224	+	27.7036i	0.671478	+	0.972804i	−0.328125	+	0.944634i	$0.606417\pi$
$812$	1.56232	+	12.8668i	0.0548266	+	0.451538i
$813$	−6.58047	−	17.3513i	−0.230787	−	0.608536i
$814$	−3.24850	+	8.56558i	−0.113860	+	0.300223i
$815$	22.7064	+	32.8959i	0.795370	+	1.15229i
$816$	−5.60953	−	1.38263i	−0.196373	−	0.0484016i
$817$	−17.0116	−	44.8559i	−0.595161	−	1.56931i
$818$	5.61826	−	14.8141i	0.196438	−	0.517964i
$819$	7.44446	−	15.7750i	0.260130	−	0.551224i
$820$	10.1831	+	26.8506i	0.355609	+	0.937665i
$821$	−0.867748	+	0.768758i	−0.0302846	+	0.0268298i	−0.678129	−	0.734943i	$-0.737209\pi$
$821$	−0.867748	+	0.768758i	−0.0302846	+	0.0268298i	0.647845	+	0.761772i	$0.275671\pi$
$822$	−19.4906			−0.679812
$823$	35.9699			1.25383			0.626916	−	0.779087i	$-0.284317\pi$
$823$	35.9699			1.25383			0.626916	+	0.779087i	$0.284317\pi$
$824$	14.6450	−	12.9744i	0.510184	−	0.451983i
$825$	−2.67540	+	1.40416i	−0.0931456	+	0.0488866i
$826$	−38.3751			−1.33524
$827$	−19.5022	−	10.2356i	−0.678159	−	0.355925i	0.0902187	−	0.995922i	$-0.471243\pi$
$827$	−19.5022	−	10.2356i	−0.678159	−	0.355925i	−0.768378	+	0.639997i	$0.778936\pi$
$828$	−3.60856	−	3.19691i	−0.125406	−	0.111100i
$829$	16.6713	+	24.1525i	0.579017	+	0.838851i	0.997594	−	0.0693303i	$-0.0220862\pi$
$829$	16.6713	+	24.1525i	0.579017	+	0.838851i	−0.418577	+	0.908181i	$0.637471\pi$
$830$	−22.6241	−	20.0432i	−0.785294	−	0.695709i
$831$	8.98986	+	13.0241i	0.311855	+	0.451800i
$832$	5.30962	−	4.00754i	0.184078	−	0.138937i
$833$	10.9777	−	15.9040i	0.380356	−	0.551041i
$834$	26.1379	−	6.44242i	0.905083	−	0.223083i
$835$	−49.2713	+	43.6506i	−1.70510	+	1.51059i
$836$	4.11624	+	1.01456i	0.142363	+	0.0350894i
$837$	−2.81624	−	2.49497i	−0.0973435	−	0.0862388i
$838$	−27.1389	−	24.0430i	−0.937498	−	0.830551i
$839$	14.8979	−	39.2825i	0.514332	−	1.35618i	−0.386610	−	0.922243i	$-0.626354\pi$
$839$	14.8979	−	39.2825i	0.514332	−	1.35618i	0.900942	−	0.433939i	$-0.142877\pi$
$840$	−10.2077	+	14.7883i	−0.352198	+	0.510246i
$841$	−21.9679	−	11.5296i	−0.757514	−	0.397574i
$842$	−1.00227	+	8.25446i	−0.0345406	+	0.284467i
$843$	15.8768	+	3.91327i	0.546825	+	0.134780i
$844$	22.1948			0.763976
$845$	16.6099	+	34.6253i	0.571400	+	1.19115i
$846$	12.2011			0.419483
$847$	−48.5829	−	11.9746i	−1.66933	−	0.411452i
$848$	−5.67295	+	46.7209i	−0.194810	+	1.60440i
$849$	−15.9646	−	8.37886i	−0.547903	−	0.287562i
$850$	4.53603	−	6.57157i	0.155584	−	0.225403i
$851$	−8.11353	+	21.3936i	−0.278128	+	0.733364i
$852$	14.1779	+	12.5605i	0.485726	+	0.430315i
$853$	3.53638	+	3.13296i	0.121083	+	0.107271i	0.721492	−	0.692423i	$-0.243457\pi$
$853$	3.53638	+	3.13296i	0.121083	+	0.107271i	−0.600408	+	0.799694i	$0.704995\pi$
$854$	−49.7981	−	12.2741i	−1.70405	−	0.420012i
$855$	8.83396	−	7.82621i	0.302115	−	0.267651i
$856$	−22.2530	+	5.48488i	−0.760593	+	0.187469i
$857$	−9.48044	+	13.7348i	−0.323846	+	0.469171i	−0.950765	−	0.309913i	$-0.899700\pi$
$857$	−9.48044	+	13.7348i	−0.323846	+	0.469171i	0.626919	+	0.779084i	$0.284316\pi$
$858$	−4.88760	+	2.09465i	−0.166860	+	0.0715103i
$859$	−24.1167	−	34.9390i	−0.822850	−	1.19210i	−0.978897	−	0.204354i	$-0.934491\pi$
$859$	−24.1167	−	34.9390i	−0.822850	−	1.19210i	0.156047	−	0.987750i	$-0.450125\pi$
$860$	34.7502	+	30.7860i	1.18497	+	1.04979i
$861$	−20.4126	−	29.5728i	−0.695661	−	1.00784i
$862$	−12.6460	−	11.2034i	−0.430726	−	0.381590i
$863$	−12.1543	−	6.37905i	−0.413736	−	0.217146i	0.244994	−	0.969525i	$-0.421214\pi$
$863$	−12.1543	−	6.37905i	−0.413736	−	0.217146i	−0.658730	+	0.752379i	$0.728906\pi$
$864$	6.40696			0.217969
$865$	−9.57337	+	5.02449i	−0.325505	+	0.170838i
$866$	55.4339	−	49.1102i	1.88372	−	1.66883i
$867$	15.6124			0.530226
$868$	23.8232			0.808612
$869$	−5.74541	+	5.08999i	−0.194900	+	0.172666i
$870$	−3.90054	−	10.2849i	−0.132241	−	0.348690i
$871$	32.0655	+	20.1821i	1.08650	+	0.683844i
$872$	0.637988	−	1.68224i	0.0216050	−	0.0569677i
$873$	4.73259	+	12.4788i	0.160174	+	0.422343i
$874$	25.9913	+	6.40629i	0.879170	+	0.216696i
$875$	10.3379	+	14.9770i	0.349484	+	0.506314i
$876$	−0.100697	+	0.265517i	−0.00340224	+	0.00897098i
$877$	−0.622157	−	1.64049i	−0.0210088	−	0.0553955i	0.924102	−	0.382147i	$-0.124815\pi$
$877$	−0.622157	−	1.64049i	−0.0210088	−	0.0553955i	−0.945110	+	0.326752i	$0.894046\pi$
$878$	7.48204	+	61.6202i	0.252507	+	2.07958i
$879$	−9.16340	−	13.2755i	−0.309074	−	0.447771i
$880$	11.4059	−	2.81130i	0.384493	−	0.0947690i
$881$	−0.633659	−	0.561373i	−0.0213485	−	0.0189131i	0.652381	−	0.757891i	$-0.273770\pi$
$881$	−0.633659	−	0.561373i	−0.0213485	−	0.0189131i	−0.673729	+	0.738978i	$0.735309\pi$
$882$	−10.5820	+	27.9025i	−0.356315	+	0.939526i
$883$	−48.3082	−	11.9069i	−1.62570	−	0.400699i	−0.681961	−	0.731389i	$-0.738873\pi$
$883$	−48.3082	−	11.9069i	−1.62570	−	0.400699i	−0.943740	+	0.330689i	$0.892719\pi$
$884$	3.50639	−	4.31317i	0.117933	−	0.145067i
$885$	12.5076	−	3.08284i	0.420437	−	0.103628i
$886$	6.65085	−	54.7747i	0.223440	−	1.84019i
$887$	42.1625	−	22.1286i	1.41568	−	0.743004i	0.428636	−	0.903477i	$-0.358994\pi$
$887$	42.1625	−	22.1286i	1.41568	−	0.743004i	0.987040	+	0.160473i	$0.0513019\pi$
$888$	−2.76942	−	7.30236i	−0.0929356	−	0.245051i
$889$	53.7453	+	13.2470i	1.80256	+	0.444291i
$890$	24.7568	−	21.9326i	0.829848	−	0.735182i
$891$	−0.787223	−	0.194033i	−0.0263730	−	0.00650035i
$892$	19.9317	−	10.4610i	0.667364	−	0.350260i
$893$	−23.7283	+	12.4536i	−0.794036	+	0.416742i
$894$	3.83923	+	31.6189i	0.128403	+	1.05749i
$895$	−2.72991	−	22.4828i	−0.0912508	−	0.751518i
$896$	34.2491	−	30.3420i	1.14418	−	1.01366i
$897$	−12.2074	+	5.23166i	−0.407594	+	0.174680i
$898$	8.01603	+	7.10159i	0.267499	+	0.236983i
$899$	4.37513	−	6.33848i	0.145919	−	0.211400i
$900$	−1.72955	+	4.56044i	−0.0576515	+	0.152015i
$901$	1.36247	+	11.2209i	0.0453904	+	0.373823i
$902$	−1.32039	+	10.8744i	−0.0439640	+	0.362076i
$903$	−51.4390	−	26.9973i	−1.71178	−	0.898413i
$904$	−6.63167	+	9.60763i	−0.220566	+	0.319545i
$905$	−15.4550	−	40.7516i	−0.513743	−	1.35463i
$906$	−10.1006	+	8.94836i	−0.335570	+	0.297289i
$907$	−13.4936	+	19.5488i	−0.448047	+	0.649108i	−0.980309	−	0.197472i	$-0.936727\pi$
$907$	−13.4936	+	19.5488i	−0.448047	+	0.649108i	0.532261	+	0.846580i	$0.321342\pi$
$908$	−17.4028	−	25.2124i	−0.577533	−	0.836702i
$909$	−0.766983	−	6.31667i	−0.0254392	−	0.209511i
$910$	−47.0379	−	81.0750i	−1.55929	−	2.68761i
$911$	0.238904	−	1.96755i	0.00791525	−	0.0651879i	−0.988216	−	0.153066i	$-0.951085\pi$
$911$	0.238904	−	1.96755i	0.00791525	−	0.0651879i	0.996131	+	0.0878777i	$0.0280085\pi$
$912$	−17.3504	+	9.10618i	−0.574528	+	0.301536i
$913$	−1.61720	−	4.26421i	−0.0535216	−	0.141125i
$914$	−3.31340	+	27.2883i	−0.109597	+	0.902616i
$915$	17.2167			0.569166
$916$	−1.68197	+	13.8522i	−0.0555737	+	0.457691i
$917$	6.47533	+	9.38113i	0.213834	+	0.309792i
$918$	2.08043	−	0.512780i	0.0686644	−	0.0169243i
$919$	23.7360	−	34.3875i	0.782978	−	1.13434i	−0.204851	−	0.978793i	$-0.565671\pi$
$919$	23.7360	−	34.3875i	0.782978	−	1.13434i	0.987829	−	0.155546i	$-0.0497137\pi$
$920$	13.2840	−	3.27421i	0.437961	−	0.107948i
$921$	4.44568	+	2.33327i	0.146490	+	0.0768839i
$922$	13.6398	+	7.15870i	0.449202	+	0.235759i
$923$	47.9623	−	20.5549i	1.57870	−	0.676574i
$924$	4.54569	−	2.38576i	0.149542	−	0.0784859i
$925$	23.1481			0.761106
$926$	25.2739	+	13.2648i	0.830552	+	0.435908i
$927$	−5.51812	+	14.5501i	−0.181239	+	0.477888i
$928$	1.58086	+	13.0195i	0.0518942	+	0.427387i
$929$	−3.49471	+	0.861368i	−0.114658	+	0.0282606i	−0.296227	−	0.955118i	$-0.595728\pi$
$929$	−3.49471	+	0.861368i	−0.114658	+	0.0282606i	0.181569	+	0.983378i	$0.441882\pi$
$930$	−19.6301	+	4.83839i	−0.643697	+	0.158657i
$931$	−7.90028	−	65.0647i	−0.258921	−	2.13241i
$932$	−3.82653	+	10.0897i	−0.125342	+	0.330500i
$933$	−4.93427	−	2.58970i	−0.161541	−	0.0847831i
$934$	−9.06035			−0.296464
$935$	2.49816	−	1.31114i	0.0816987	−	0.0428788i
$936$	1.93473	−	4.09974i	0.0632385	−	0.134004i
$937$	52.5074	+	27.5580i	1.71534	+	0.900282i	0.973174	+	0.230069i	$0.0738950\pi$
$937$	52.5074	+	27.5580i	1.71534	+	0.900282i	0.742169	+	0.670213i	$0.233797\pi$
$938$	−81.8828	−	42.9754i	−2.67357	−	1.40320i
$939$	8.18903	−	2.01842i	0.267239	−	0.0658685i
$940$	14.7318	−	21.3427i	0.480499	−	0.696123i
$941$	36.9478	−	9.10682i	1.20446	−	0.296874i	0.414513	−	0.910043i	$-0.363952\pi$
$941$	36.9478	−	9.10682i	1.20446	−	0.296874i	0.789951	+	0.613170i	$0.210106\pi$
$942$	−0.972399	−	1.40876i	−0.0316825	−	0.0459000i
$943$	−3.29783	+	27.1601i	−0.107392	+	0.884454i
$944$	−21.3877			−0.696110
$945$	1.72267	−	14.1875i	0.0560384	−	0.461518i
$946$	6.27987	+	16.5587i	0.204176	+	0.538368i
$947$	40.8483	−	21.4388i	1.32739	−	0.696669i	0.356075	−	0.934458i	$-0.384115\pi$
$947$	40.8483	−	21.4388i	1.32739	−	0.696669i	0.971317	+	0.237789i	$0.0764226\pi$
$948$	−1.49351	+	12.3001i	−0.0485068	+	0.399490i
$949$	0.543114	+	0.563050i	0.0176302	+	0.0182774i
$950$	−3.26441	−	26.8849i	−0.105912	−	0.872260i
$951$	15.1860	+	22.0007i	0.492440	+	0.713423i
$952$	4.07031	−	5.89687i	0.131920	−	0.191119i
$953$	−11.0733	+	9.81009i	−0.358699	+	0.317780i	−0.823155	−	0.567816i	$-0.807788\pi$
$953$	−11.0733	+	9.81009i	−0.358699	+	0.317780i	0.464456	+	0.885596i	$0.346250\pi$
$954$	−6.18957	−	16.3206i	−0.200395	−	0.528398i
$955$	5.29943	−	7.67755i	0.171486	−	0.248440i
$956$	−28.3820	−	14.8960i	−0.917940	−	0.481772i
$957$	0.200053	−	1.64759i	0.00646681	−	0.0532589i
$958$	−2.36515	−	19.4788i	−0.0764146	−	0.629331i
$959$	18.3820	−	48.4695i	0.593587	−	1.56516i
$960$	3.09613	−	4.48551i	0.0999270	−	0.144769i
$961$	12.6078	+	11.1696i	0.406705	+	0.360309i
$962$	40.6132	+	3.19209i	1.30942	+	0.102917i
$963$	13.6442	−	12.0877i	0.439679	−	0.389521i
$964$	−2.84520	−	23.4324i	−0.0916378	−	0.754706i
$965$	1.07471	+	8.85102i	0.0345961	+	0.284924i
$966$	28.7030	−	15.0645i	0.923504	−	0.484692i
$967$	−22.0630	+	11.5796i	−0.709498	+	0.372373i	−0.780545	−	0.625100i	$-0.785058\pi$
$967$	−22.0630	+	11.5796i	−0.709498	+	0.372373i	0.0710469	+	0.997473i	$0.477366\pi$
$968$	−12.6261	−	3.11206i	−0.405819	−	0.100025i
$969$	−3.52255	+	3.12071i	−0.113161	+	0.100252i
$970$	69.6314	+	17.1626i	2.23573	+	0.551058i
$971$	9.95814	+	26.2575i	0.319572	+	0.842642i	0.994498	+	0.104756i	$0.0334063\pi$
$971$	9.95814	+	26.2575i	0.319572	+	0.842642i	−0.674926	+	0.737885i	$0.735824\pi$
$972$	−1.15887	+	0.608224i	−0.0371709	+	0.0195088i
$973$	−8.63022	+	71.0763i	−0.276672	+	2.27860i
$974$	−14.2469	+	3.51155i	−0.456501	+	0.112517i
$975$	9.32836	+	9.67078i	0.298747	+	0.309713i
$976$	−27.7541	−	6.84077i	−0.888387	−	0.218968i
$977$	−5.55746	+	14.6538i	−0.177799	+	0.468817i	−0.994056	−	0.108872i	$-0.965276\pi$
$977$	−5.55746	+	14.6538i	−0.177799	+	0.468817i	0.816257	+	0.577689i	$0.196045\pi$
$978$	18.4230	+	16.3213i	0.589101	+	0.521898i
$979$	4.84547	−	1.19430i	0.154862	−	0.0381700i
$980$	36.0313	+	52.2004i	1.15098	+	1.66748i
$981$	0.172481	+	1.42051i	0.00550690	+	0.0453534i
$982$	18.0080	+	47.4833i	0.574659	+	1.51525i
$983$	12.1883	−	32.1379i	0.388746	−	1.02504i	−0.587662	−	0.809107i	$-0.699952\pi$
$983$	12.1883	−	32.1379i	0.388746	−	1.02504i	0.976408	−	0.215933i	$-0.0692793\pi$
$984$	−5.30500	−	7.68562i	−0.169117	−	0.245009i
$985$	−42.2909	−	10.4238i	−1.34750	−	0.332129i
$986$	1.55534	+	4.10111i	0.0495323	+	0.130606i
$987$	−11.5072	+	30.3419i	−0.366278	+	0.965795i
$988$	−0.799014	−	18.8358i	−0.0254200	−	0.599247i
$989$	15.6848	+	41.3574i	0.498747	+	1.31509i
$990$	−3.26108	+	2.88906i	−0.103644	+	0.0918204i
$991$	12.4565			0.395693			0.197846	−	0.980233i	$-0.436605\pi$
$991$	12.4565			0.395693			0.197846	+	0.980233i	$0.436605\pi$
$992$	24.1059			0.765363
$993$	7.28365	−	6.45275i	0.231140	−	0.204772i
$994$	−112.773	+	59.1877i	−3.57693	+	1.87732i
$995$	−47.0023			−1.49007
$996$	−6.51856	−	3.42120i	−0.206548	−	0.108405i
$997$	12.5451	+	11.1140i	0.397306	+	0.351983i	0.837996	−	0.545677i	$-0.183727\pi$
$997$	12.5451	+	11.1140i	0.397306	+	0.351983i	−0.440689	+	0.897660i	$0.645266\pi$
$998$	−17.4322	−	25.2548i	−0.551805	−	0.799428i
$999$	4.64940	+	4.11901i	0.147100	+	0.130320i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.m.a.40.3	✓	180
169.131	even	13	inner	507.2.m.a.469.3	yes	180

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.m.a.40.3	✓	180	1.1	even	1	trivial
507.2.m.a.469.3	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)

\(f(q)\)	\(=\)	\(q+(-1.76615 - 0.435317i) q^{2} +(-0.120537 + 0.992709i) q^{3} +(1.15887 + 0.608224i) q^{4} +(1.67811 - 2.43117i) q^{5} +(0.645029 - 1.70080i) q^{6} +(3.62124 + 3.20814i) q^{7} +(0.941117 + 0.833757i) q^{8} +(-0.970942 - 0.239316i) q^{9} +O(q^{10})\)	\(q+(-1.76615 - 0.435317i) q^{2} +(-0.120537 + 0.992709i) q^{3} +(1.15887 + 0.608224i) q^{4} +(1.67811 - 2.43117i) q^{5} +(0.645029 - 1.70080i) q^{6} +(3.62124 + 3.20814i) q^{7} +(0.941117 + 0.833757i) q^{8} +(-0.970942 - 0.239316i) q^{9} +(-4.02213 + 3.56330i) q^{10} +(-0.787223 + 0.194033i) q^{11} +(-0.743477 + 1.07711i) q^{12} +(1.80938 + 3.11867i) q^{13} +(-4.99909 - 7.24244i) q^{14} +(2.21117 + 1.95892i) q^{15} +(-2.78616 - 4.03645i) q^{16} +(-0.881705 - 0.781123i) q^{17} +(1.61065 + 0.845335i) q^{18} -3.99516 q^{19} +(3.42342 - 1.79675i) q^{20} +(-3.62124 + 3.20814i) q^{21} +1.47482 q^{22} +3.68355 q^{23} +(-0.941117 + 0.833757i) q^{24} +(-1.32149 - 3.48447i) q^{25} +(-1.83803 - 6.29570i) q^{26} +(0.354605 - 0.935016i) q^{27} +(2.24529 + 5.92035i) q^{28} +(1.98754 + 0.489884i) q^{29} +(-3.05250 - 4.42231i) q^{30} +(1.33419 - 3.51796i) q^{31} +(2.27194 + 5.99061i) q^{32} +(-0.0977291 - 0.804872i) q^{33} +(1.21719 + 1.76340i) q^{34} +(13.8764 - 3.42022i) q^{35} +(-0.979642 - 0.867887i) q^{36} +(-2.20264 + 5.80788i) q^{37} +(7.05605 + 1.73916i) q^{38} +(-3.31403 + 1.42028i) q^{39} +(3.60630 - 0.888874i) q^{40} +(-0.895286 + 7.37334i) q^{41} +(7.79221 - 4.08967i) q^{42} +(4.25806 + 11.2276i) q^{43} +(-1.03031 - 0.253948i) q^{44} +(-2.21117 + 1.95892i) q^{45} +(-6.50571 - 1.60351i) q^{46} +(5.93926 - 3.11716i) q^{47} +(4.34285 - 2.27930i) q^{48} +(1.97746 + 16.2859i) q^{49} +(0.817093 + 6.72937i) q^{50} +(0.881705 - 0.781123i) q^{51} +(0.199996 + 4.71466i) q^{52} +(-7.18256 - 6.36320i) q^{53} +(-1.03331 + 1.49701i) q^{54} +(-0.849323 + 2.23948i) q^{55} +(0.733202 + 6.03846i) q^{56} +(0.481563 - 3.96603i) q^{57} +(-3.29703 - 1.73042i) q^{58} +(2.47716 - 3.58878i) q^{59} +(1.37100 + 3.61503i) q^{60} +(4.36238 - 3.86473i) q^{61} +(-3.88780 + 5.63245i) q^{62} +(-2.74825 - 3.98153i) q^{63} +(-0.222391 - 1.83155i) q^{64} +(10.6184 + 0.834575i) q^{65} +(-0.177770 + 1.46407i) q^{66} +(9.30463 - 4.88345i) q^{67} +(-0.546688 - 1.44150i) q^{68} +(-0.444003 + 3.65670i) q^{69} -25.9966 q^{70} +(1.74447 - 14.3670i) q^{71} +(-0.714239 - 1.03475i) q^{72} +(0.210667 - 0.0519247i) q^{73} +(6.41846 - 9.29874i) q^{74} +(3.61835 - 0.891844i) q^{75} +(-4.62989 - 2.42995i) q^{76} +(-3.47321 - 1.82288i) q^{77} +(6.47135 - 1.06577i) q^{78} +(8.38273 - 4.39960i) q^{79} -14.4888 q^{80} +(0.885456 + 0.464723i) q^{81} +(4.79095 - 12.6327i) q^{82} +(0.678007 + 5.58389i) q^{83} +(-6.14783 + 1.51530i) q^{84} +(-3.37864 + 0.832761i) q^{85} +(-2.63282 - 21.6832i) q^{86} +(-0.725883 + 1.91400i) q^{87} +(-0.902645 - 0.473745i) q^{88} -6.15514 q^{89} +(4.75801 - 2.49719i) q^{90} +(-3.45292 + 17.0982i) q^{91} +(4.26878 + 2.24043i) q^{92} +(3.33149 + 1.74850i) q^{93} +(-11.8466 + 2.91992i) q^{94} +(-6.70433 + 9.71290i) q^{95} +(-6.22078 + 1.53329i) q^{96} +(-7.58144 - 10.9836i) q^{97} +(3.59702 - 29.6242i) q^{98} +0.810783 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

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