LMFDB - Embedded newform 135.2.p.a.124.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,2,Mod(4,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([2, 9]))

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

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

chi := DirichletCharacter("135.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	135.p (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.07798042729$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			124.7
Character	$\chi$	$=$	135.124
Dual form			135.2.p.a.49.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.195467 + 0.232949i) q^{2} +(-1.57417 + 0.722492i) q^{3} +(0.331239 + 1.87855i) q^{4} +(-2.07799 - 0.825805i) q^{5} +(0.139394 - 0.507924i) q^{6} +(-3.36181 - 0.592777i) q^{7} +(-1.02906 - 0.594126i) q^{8} +(1.95601 - 2.27465i) q^{9} +O(q^{10})$	\(q+(-0.195467 + 0.232949i) q^{2} +(-1.57417 + 0.722492i) q^{3} +(0.331239 + 1.87855i) q^{4} +(-2.07799 - 0.825805i) q^{5} +(0.139394 - 0.507924i) q^{6} +(-3.36181 - 0.592777i) q^{7} +(-1.02906 - 0.594126i) q^{8} +(1.95601 - 2.27465i) q^{9} +(0.598549 - 0.322648i) q^{10} +(-2.75854 + 1.00403i) q^{11} +(-1.87866 - 2.71783i) q^{12} +(3.53380 + 4.21142i) q^{13} +(0.795210 - 0.667260i) q^{14} +(3.86774 - 0.201377i) q^{15} +(-3.24543 + 1.18124i) q^{16} +(-1.83496 + 1.05942i) q^{17} +(0.147541 + 0.900269i) q^{18} +(-2.20534 + 3.81976i) q^{19} +(0.863003 - 4.17714i) q^{20} +(5.72033 - 1.49575i) q^{21} +(0.305317 - 0.838853i) q^{22} +(4.56507 - 0.804944i) q^{23} +(2.04916 + 0.191769i) q^{24} +(3.63609 + 3.43203i) q^{25} -1.67179 q^{26} +(-1.43567 + 4.99388i) q^{27} -6.51167i q^{28} +(0.308828 + 0.259138i) q^{29} +(-0.709106 + 0.940348i) q^{30} +(-0.573021 - 3.24976i) q^{31} +(1.17202 - 3.22009i) q^{32} +(3.61701 - 3.57353i) q^{33} +(0.111885 - 0.634533i) q^{34} +(6.49629 + 4.00798i) q^{35} +(4.92094 + 2.92101i) q^{36} +(3.52072 - 2.03269i) q^{37} +(-0.458737 - 1.26037i) q^{38} +(-8.60551 - 4.07634i) q^{39} +(1.64774 + 2.08439i) q^{40} +(-3.73852 + 3.13699i) q^{41} +(-0.769703 + 1.62491i) q^{42} +(0.0361245 + 0.0992511i) q^{43} +(-2.79985 - 4.84948i) q^{44} +(-5.94299 + 3.11142i) q^{45} +(-0.704810 + 1.22077i) q^{46} +(-11.3497 - 2.00126i) q^{47} +(4.25542 - 4.20427i) q^{48} +(4.37252 + 1.59147i) q^{49} +(-1.51022 + 0.176174i) q^{50} +(2.12312 - 2.99344i) q^{51} +(-6.74082 + 8.03340i) q^{52} +11.5814i q^{53} +(-0.882691 - 1.31058i) q^{54} +(6.56135 + 0.191657i) q^{55} +(3.10730 + 2.60734i) q^{56} +(0.711828 - 7.60629i) q^{57} +(-0.120732 + 0.0212882i) q^{58} +(5.15923 + 1.87781i) q^{59} +(1.65944 + 7.19904i) q^{60} +(1.18992 - 6.74834i) q^{61} +(0.869034 + 0.501737i) q^{62} +(-7.92409 + 6.48745i) q^{63} +(-2.93269 - 5.07957i) q^{64} +(-3.86539 - 11.6695i) q^{65} +(0.125444 + 1.54108i) q^{66} +(-2.45463 - 2.92531i) q^{67} +(-2.59797 - 3.09614i) q^{68} +(-6.60462 + 4.56534i) q^{69} +(-2.20346 + 0.729873i) q^{70} +(6.75694 + 11.7034i) q^{71} +(-3.36427 + 1.17862i) q^{72} +(-6.69232 - 3.86382i) q^{73} +(-0.214673 + 1.21747i) q^{74} +(-8.20344 - 2.77554i) q^{75} +(-7.90610 - 2.87758i) q^{76} +(9.86885 - 1.74014i) q^{77} +(2.63167 - 1.20785i) q^{78} +(-1.80591 - 1.51534i) q^{79} +(7.71945 + 0.225486i) q^{80} +(-1.34805 - 8.89847i) q^{81} -1.48406i q^{82} +(-4.37992 + 5.21978i) q^{83} +(4.70463 + 10.2505i) q^{84} +(4.68790 - 0.686136i) q^{85} +(-0.0301816 - 0.0109852i) q^{86} +(-0.673373 - 0.184800i) q^{87} +(3.43521 + 0.605720i) q^{88} +(0.870723 - 1.50814i) q^{89} +(0.436858 - 1.99259i) q^{90} +(-9.38352 - 16.2527i) q^{91} +(3.02425 + 8.30907i) q^{92} +(3.24996 + 4.70167i) q^{93} +(2.68468 - 2.25271i) q^{94} +(7.73705 - 6.11625i) q^{95} +(0.481539 + 5.91574i) q^{96} +(-0.152119 - 0.417944i) q^{97} +(-1.22541 + 0.707493i) q^{98} +(-3.11193 + 8.23860i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 12 q^{4} - 9 q^{5} - 6 q^{6} - 18 q^{9}+O(q^{10}) $ 96 * q - 12 * q^4 - 9 * q^5 - 6 * q^6 - 18 * q^9	$ 96 q - 12 q^{4} - 9 q^{5} - 6 q^{6} - 18 q^{9} - 3 q^{10} - 6 q^{11} - 18 q^{14} - 21 q^{15} - 24 q^{16} - 6 q^{19} - 57 q^{20} + 24 q^{21} - 30 q^{24} + 3 q^{25} + 48 q^{26} - 30 q^{29} - 51 q^{30} - 30 q^{31} - 24 q^{34} - 12 q^{35} + 54 q^{36} - 6 q^{39} - 9 q^{40} - 12 q^{41} + 78 q^{44} + 45 q^{45} - 6 q^{46} - 30 q^{49} + 84 q^{50} - 90 q^{51} + 108 q^{54} - 12 q^{55} - 96 q^{56} + 66 q^{59} + 84 q^{60} + 6 q^{61} + 45 q^{65} - 150 q^{66} + 24 q^{69} - 33 q^{70} - 90 q^{71} + 66 q^{74} + 39 q^{75} + 12 q^{76} + 24 q^{79} + 30 q^{80} - 54 q^{81} + 198 q^{84} - 21 q^{85} + 18 q^{86} + 96 q^{89} + 90 q^{90} - 6 q^{91} + 24 q^{94} + 87 q^{95} + 42 q^{96} + 36 q^{99}+O(q^{100}) $ 96 * q - 12 * q^4 - 9 * q^5 - 6 * q^6 - 18 * q^9 - 3 * q^10 - 6 * q^11 - 18 * q^14 - 21 * q^15 - 24 * q^16 - 6 * q^19 - 57 * q^20 + 24 * q^21 - 30 * q^24 + 3 * q^25 + 48 * q^26 - 30 * q^29 - 51 * q^30 - 30 * q^31 - 24 * q^34 - 12 * q^35 + 54 * q^36 - 6 * q^39 - 9 * q^40 - 12 * q^41 + 78 * q^44 + 45 * q^45 - 6 * q^46 - 30 * q^49 + 84 * q^50 - 90 * q^51 + 108 * q^54 - 12 * q^55 - 96 * q^56 + 66 * q^59 + 84 * q^60 + 6 * q^61 + 45 * q^65 - 150 * q^66 + 24 * q^69 - 33 * q^70 - 90 * q^71 + 66 * q^74 + 39 * q^75 + 12 * q^76 + 24 * q^79 + 30 * q^80 - 54 * q^81 + 198 * q^84 - 21 * q^85 + 18 * q^86 + 96 * q^89 + 90 * q^90 - 6 * q^91 + 24 * q^94 + 87 * q^95 + 42 * q^96 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.195467	+	0.232949i	−0.138216	+	0.164720i	−0.830712	−	0.556702i	$-0.812067\pi$
$2$	−0.195467	+	0.232949i	−0.138216	+	0.164720i	0.692496	+	0.721422i	$0.256511\pi$
$3$	−1.57417	+	0.722492i	−0.908846	+	0.417131i
$3$	−1.57417	+	0.722492i	−0.908846	+	0.417131i
$4$	0.331239	+	1.87855i	0.165619	+	0.939274i
$5$	−2.07799	−	0.825805i	−0.929306	−	0.369311i
$5$	−2.07799	−	0.825805i	−0.929306	−	0.369311i
$6$	0.139394	−	0.507924i	0.0569076	−	0.207359i
$7$	−3.36181	−	0.592777i	−1.27064	−	0.224049i	−0.502641	−	0.864495i	$-0.667638\pi$
$7$	−3.36181	−	0.592777i	−1.27064	−	0.224049i	−0.768003	+	0.640446i	$0.778749\pi$
$8$	−1.02906	−	0.594126i	−0.363826	−	0.210055i
$9$	1.95601	−	2.27465i	0.652003	−	0.758216i
$10$	0.598549	−	0.322648i	0.189278	−	0.102030i
$11$	−2.75854	+	1.00403i	−0.831732	+	0.302726i	−0.722569	−	0.691298i	$-0.757039\pi$
$11$	−2.75854	+	1.00403i	−0.831732	+	0.302726i	−0.109162	+	0.994024i	$0.534817\pi$
$12$	−1.87866	−	2.71783i	−0.542323	−	0.784571i
$13$	3.53380	+	4.21142i	0.980100	+	1.16804i	0.985778	+	0.168053i	$0.0537481\pi$
$13$	3.53380	+	4.21142i	0.980100	+	1.16804i	−0.00567819	+	0.999984i	$0.501807\pi$
$14$	0.795210	−	0.667260i	0.212529	−	0.178333i
$15$	3.86774	−	0.201377i	0.998647	−	0.0519954i
$16$	−3.24543	+	1.18124i	−0.811358	+	0.295310i
$17$	−1.83496	+	1.05942i	−0.445044	+	0.256946i	−0.705735	−	0.708476i	$-0.749383\pi$
$17$	−1.83496	+	1.05942i	−0.445044	+	0.256946i	0.260691	+	0.965422i	$0.416050\pi$
$18$	0.147541	+	0.900269i	0.0347757	+	0.212195i
$19$	−2.20534	+	3.81976i	−0.505940	+	0.876313i	0.494037	+	0.869441i	$0.335521\pi$
$19$	−2.20534	+	3.81976i	−0.505940	+	0.876313i	−0.999976	+	0.00687212i	$0.997813\pi$
$20$	0.863003	−	4.17714i	0.192973	−	0.934038i
$21$	5.72033	−	1.49575i	1.24828	−	0.326399i
$22$	0.305317	−	0.838853i	0.0650939	−	0.178844i
$23$	4.56507	−	0.804944i	0.951882	−	0.167843i	0.323918	−	0.946085i	$-0.395000\pi$
$23$	4.56507	−	0.804944i	0.951882	−	0.167843i	0.627964	+	0.778243i	$0.283889\pi$
$24$	2.04916	+	0.191769i	0.418283	+	0.0391446i
$25$	3.63609	+	3.43203i	0.727219	+	0.686406i
$26$	−1.67179			−0.327864
$27$	−1.43567	+	4.99388i	−0.276295	+	0.961073i
$28$		−	6.51167i		−	1.23059i
$29$	0.308828	+	0.259138i	0.0573480	+	0.0481207i	0.671011	−	0.741447i	$-0.265860\pi$
$29$	0.308828	+	0.259138i	0.0573480	+	0.0481207i	−0.613663	+	0.789568i	$0.710305\pi$
$30$	−0.709106	+	0.940348i	−0.129465	+	0.171683i
$31$	−0.573021	−	3.24976i	−0.102918	−	0.583674i	−0.992032	−	0.125989i	$-0.959790\pi$
$31$	−0.573021	−	3.24976i	−0.102918	−	0.583674i	0.889114	−	0.457686i	$-0.151321\pi$
$32$	1.17202	−	3.22009i	0.207186	−	0.569238i
$33$	3.61701	−	3.57353i	0.629640	−	0.622072i
$34$	0.111885	−	0.634533i	0.0191882	−	0.108821i
$35$	6.49629	+	4.00798i	1.09807	+	0.677473i
$36$	4.92094	+	2.92101i	0.820157	+	0.486834i
$37$	3.52072	−	2.03269i	0.578803	−	0.334172i	−0.181854	−	0.983325i	$-0.558210\pi$
$37$	3.52072	−	2.03269i	0.578803	−	0.334172i	0.760658	+	0.649153i	$0.224877\pi$
$38$	−0.458737	−	1.26037i	−0.0744169	−	0.204459i
$39$	−8.60551	−	4.07634i	−1.37798	−	0.652736i
$40$	1.64774	+	2.08439i	0.260530	+	0.329570i
$41$	−3.73852	+	3.13699i	−0.583859	+	0.489916i	−0.886212	−	0.463280i	$-0.846672\pi$
$41$	−3.73852	+	3.13699i	−0.583859	+	0.489916i	0.302353	+	0.953196i	$0.402228\pi$
$42$	−0.769703	+	1.62491i	−0.118768	+	0.250729i
$43$	0.0361245	+	0.0992511i	0.00550893	+	0.0151357i	0.942417	−	0.334441i	$-0.108548\pi$
$43$	0.0361245	+	0.0992511i	0.00550893	+	0.0151357i	−0.936908	+	0.349577i	$0.886325\pi$
$44$	−2.79985	−	4.84948i	−0.422093	−	0.731087i
$45$	−5.94299	+	3.11142i	−0.885928	+	0.463823i
$46$	−0.704810	+	1.22077i	−0.103919	+	0.179992i
$47$	−11.3497	−	2.00126i	−1.65552	−	0.291913i	−0.733684	−	0.679490i	$-0.762201\pi$
$47$	−11.3497	−	2.00126i	−1.65552	−	0.291913i	−0.921837	+	0.387577i	$0.873312\pi$
$48$	4.25542	−	4.20427i	0.614217	−	0.606834i
$49$	4.37252	+	1.59147i	0.624646	+	0.227352i
$50$	−1.51022	+	0.176174i	−0.213578	+	0.0249148i
$51$	2.12312	−	2.99344i	0.297296	−	0.419166i
$52$	−6.74082	+	8.03340i	−0.934784	+	1.11403i
$53$			11.5814i			1.59083i	0.606068	+	0.795413i	$0.292746\pi$
$53$			11.5814i			1.59083i	−0.606068	+	0.795413i	$0.707254\pi$
$54$	−0.882691	−	1.31058i	−0.120119	−	0.178347i
$55$	6.56135	+	0.191657i	0.884733	+	0.0258431i
$56$	3.10730	+	2.60734i	0.415231	+	0.348420i
$57$	0.711828	−	7.60629i	0.0942839	−	1.00748i
$58$	−0.120732	+	0.0212882i	−0.0158528	+	0.00279528i
$59$	5.15923	+	1.87781i	0.671674	+	0.244469i	0.655269	−	0.755396i	$-0.272555\pi$
$59$	5.15923	+	1.87781i	0.671674	+	0.244469i	0.0164056	+	0.999865i	$0.494778\pi$
$60$	1.65944	+	7.19904i	0.214233	+	0.929392i
$61$	1.18992	−	6.74834i	0.152353	−	0.864037i	−0.808813	−	0.588066i	$-0.799890\pi$
$61$	1.18992	−	6.74834i	0.152353	−	0.864037i	0.961166	−	0.275971i	$-0.0889993\pi$
$62$	0.869034	+	0.501737i	0.110367	+	0.0637207i
$63$	−7.92409	+	6.48745i	−0.998341	+	0.817342i
$64$	−2.93269	−	5.07957i	−0.366586	−	0.634946i
$65$	−3.86539	−	11.6695i	−0.479443	−	1.44743i
$66$	0.125444	+	1.54108i	0.0154411	+	0.189694i
$67$	−2.45463	−	2.92531i	−0.299881	−	0.357384i	0.594971	−	0.803747i	$-0.297163\pi$
$67$	−2.45463	−	2.92531i	−0.299881	−	0.357384i	−0.894852	+	0.446363i	$0.852719\pi$
$68$	−2.59797	−	3.09614i	−0.315051	−	0.375463i
$69$	−6.60462	+	4.56534i	−0.795102	+	0.549603i
$70$	−2.20346	+	0.729873i	−0.263364	+	0.0872365i
$71$	6.75694	+	11.7034i	0.801901	+	1.38893i	0.918363	+	0.395738i	$0.129511\pi$
$71$	6.75694	+	11.7034i	0.801901	+	1.38893i	−0.116462	+	0.993195i	$0.537155\pi$
$72$	−3.36427	+	1.17862i	−0.396483	+	0.138902i
$73$	−6.69232	−	3.86382i	−0.783277	−	0.452225i	0.0543132	−	0.998524i	$-0.482703\pi$
$73$	−6.69232	−	3.86382i	−0.783277	−	0.452225i	−0.837591	+	0.546299i	$0.816036\pi$
$74$	−0.214673	+	1.21747i	−0.0249552	+	0.141528i
$75$	−8.20344	−	2.77554i	−0.947251	−	0.320492i
$76$	−7.90610	−	2.87758i	−0.906891	−	0.330082i
$77$	9.86885	−	1.74014i	1.12466	−	0.198308i
$78$	2.63167	−	1.20785i	0.297978	−	0.136762i
$79$	−1.80591	−	1.51534i	−0.203181	−	0.170489i	0.535520	−	0.844523i	$-0.320116\pi$
$79$	−1.80591	−	1.51534i	−0.203181	−	0.170489i	−0.738701	+	0.674034i	$0.764560\pi$
$80$	7.71945	+	0.225486i	0.863061	+	0.0252100i
$81$	−1.34805	−	8.89847i	−0.149784	−	0.988719i
$82$		−	1.48406i		−	0.163887i
$83$	−4.37992	+	5.21978i	−0.480758	+	0.572946i	−0.950842	−	0.309676i	$-0.899779\pi$
$83$	−4.37992	+	5.21978i	−0.480758	+	0.572946i	0.470084	+	0.882622i	$0.344224\pi$
$84$	4.70463	+	10.2505i	0.513317	+	1.11842i
$85$	4.68790	−	0.686136i	0.508475	−	0.0744219i
$86$	−0.0301816	−	0.0109852i	−0.00325456	−	0.00118456i
$87$	−0.673373	−	0.184800i	−0.0721931	−	0.0198127i
$88$	3.43521	+	0.605720i	0.366195	+	0.0645700i
$89$	0.870723	−	1.50814i	0.0922964	−	0.159862i	−0.816181	−	0.577797i	$-0.803913\pi$
$89$	0.870723	−	1.50814i	0.0922964	−	0.159862i	0.908477	+	0.417935i	$0.137246\pi$
$90$	0.436858	−	1.99259i	0.0460489	−	0.210037i
$91$	−9.38352	−	16.2527i	−0.983660	−	1.70375i
$92$	3.02425	+	8.30907i	0.315300	+	0.866280i
$93$	3.24996	+	4.70167i	0.337005	+	0.487540i
$94$	2.68468	−	2.25271i	0.276904	−	0.232350i
$95$	7.73705	−	6.11625i	0.793805	−	0.627514i
$96$	0.481539	+	5.91574i	0.0491469	+	0.603773i
$97$	−0.152119	−	0.417944i	−0.0154454	−	0.0424358i	0.931730	−	0.363151i	$-0.118299\pi$
$97$	−0.152119	−	0.417944i	−0.0154454	−	0.0424358i	−0.947176	+	0.320715i	$0.896077\pi$
$98$	−1.22541	+	0.707493i	−0.123785	+	0.0714676i
$99$	−3.11193	+	8.23860i	−0.312760	+	0.828010i
$100$	−5.24282	+	7.96740i	−0.524282	+	0.796740i
$101$	−1.10822	+	6.28500i	−0.110272	+	0.625381i	0.878712	+	0.477353i	$0.158404\pi$
$101$	−1.10822	+	6.28500i	−0.110272	+	0.625381i	−0.988983	+	0.148028i	$0.952707\pi$
$102$	0.282319	+	1.07970i	0.0279537	+	0.106906i
$103$	−4.17454	+	11.4695i	−0.411330	+	1.13012i	0.545155	+	0.838335i	$0.316471\pi$
$103$	−4.17454	+	11.4695i	−0.411330	+	1.13012i	−0.956484	+	0.291783i	$0.905751\pi$
$104$	−1.13437	−	6.43330i	−0.111234	−	0.630837i
$105$	−13.1220	−	1.61572i	−1.28057	−	0.157678i
$106$	−2.69787	−	2.26378i	−0.262040	−	0.219878i
$107$		−	1.69143i		−	0.163517i	−0.996652	−	0.0817585i	$-0.973946\pi$
$107$		−	1.69143i		−	0.163517i	0.996652	−	0.0817585i	$-0.0260536\pi$
$108$	−9.85679	−	1.04281i	−0.948471	−	0.100345i
$109$	15.3531			1.47056			0.735279	−	0.677765i	$-0.237051\pi$
$109$	15.3531			1.47056			0.735279	+	0.677765i	$0.237051\pi$
$110$	−1.32718	+	1.49100i	−0.126541	+	0.142161i
$111$	−4.07361	+	5.74349i	−0.386650	+	0.545148i
$112$	11.6107	−	2.04729i	1.09711	−	0.193450i
$113$	5.36085	−	14.7288i	0.504307	−	1.38557i	−0.382725	−	0.923862i	$-0.625014\pi$
$113$	5.36085	−	14.7288i	0.504307	−	1.38557i	0.887031	−	0.461709i	$-0.152764\pi$
$114$	1.63273	+	1.65260i	0.152920	+	0.154780i
$115$	−10.1509	−	2.09719i	−0.946576	−	0.195564i
$116$	−0.384507	+	0.665985i	−0.0357005	+	0.0618352i
$117$	16.4916	+	0.199423i	1.52465	+	0.0184366i
$118$	−1.44589	+	0.834786i	−0.133105	+	0.0768483i
$119$	6.79679	−	2.47383i	0.623060	−	0.226775i
$120$	−4.09977	−	2.09070i	−0.374256	−	0.190854i
$121$	−1.82501	+	1.53136i	−0.165910	+	0.139215i
$122$	1.33943	+	1.59627i	0.121266	+	0.144519i
$123$	3.61861	−	7.63921i	0.326279	−	0.688804i
$124$	5.91503	−	2.15289i	0.531185	−	0.193336i
$125$	−4.72158	−	10.1344i	−0.422311	−	0.906451i
$126$	0.0376555	−	3.11399i	0.00335462	−	0.277416i
$127$	11.2018	+	6.46736i	0.993998	+	0.573885i	0.906467	−	0.422277i	$-0.138769\pi$
$127$	11.2018	+	6.46736i	0.993998	+	0.573885i	0.0875312	+	0.996162i	$0.472102\pi$
$128$	8.50591	+	1.49982i	0.751823	+	0.132567i
$129$	−0.128574	−	0.130138i	−0.0113203	−	0.0114580i
$130$	3.47396	+	1.38057i	0.304686	+	0.121084i
$131$	1.99841	+	11.3335i	0.174602	+	0.990215i	0.938603	+	0.345000i	$0.112121\pi$
$131$	1.99841	+	11.3335i	0.174602	+	0.990215i	−0.764001	+	0.645215i	$0.776768\pi$
$132$	7.91114	+	5.61103i	0.688577	+	0.488377i
$133$	9.67820	−	11.5340i	0.839206	−	1.00013i
$134$	1.16125			0.100316
$135$	7.10728	−	9.19166i	0.611698	−	0.791092i
$136$	2.51770			0.215891
$137$	7.83825	−	9.34126i	0.669667	−	0.798078i	−0.319072	−	0.947731i	$-0.603371\pi$
$137$	7.83825	−	9.34126i	0.669667	−	0.798078i	0.988739	+	0.149653i	$0.0478155\pi$
$138$	0.227495	−	2.43091i	0.0193656	−	0.206933i
$139$	−0.0420242	−	0.238331i	−0.00356445	−	0.0202150i	0.982974	−	0.183747i	$-0.0588226\pi$
$139$	−0.0420242	−	0.238331i	−0.00356445	−	0.0202150i	−0.986538	+	0.163532i	$0.947711\pi$
$140$	−5.37737	+	13.5312i	−0.454470	+	1.14359i
$141$	19.3122	−	5.04975i	1.62638	−	0.425265i
$142$	−4.04704	−	0.713602i	−0.339620	−	0.0598842i
$143$	−13.9765	−	8.06934i	−1.16877	−	0.674792i
$144$	−3.66119	+	9.69273i	−0.305099	+	0.807728i
$145$	−0.427745	−	0.793518i	−0.0355223	−	0.0658980i
$146$	2.20820	−	0.803719i	0.182752	−	0.0665163i
$147$	−8.03290	+	0.653875i	−0.662543	+	0.0539307i
$148$	4.98470	+	5.94054i	0.409740	+	0.488309i
$149$	−9.73479	+	8.16846i	−0.797505	+	0.669186i	−0.947591	−	0.319487i	$-0.896489\pi$
$149$	−9.73479	+	8.16846i	−0.797505	+	0.669186i	0.150086	+	0.988673i	$0.452045\pi$
$150$	2.25006	−	1.36845i	0.183717	−	0.111734i
$151$	4.13101	−	1.50356i	0.336177	−	0.122358i	−0.168416	−	0.985716i	$-0.553865\pi$
$151$	4.13101	−	1.50356i	0.336177	−	0.122358i	0.504592	+	0.863358i	$0.331643\pi$
$152$	4.53883	−	2.62050i	0.368148	−	0.212550i
$153$	−1.17940	+	6.24612i	−0.0953492	+	0.504969i
$154$	−1.52367	+	2.63908i	−0.122781	+	0.212663i
$155$	−1.49294	+	7.22618i	−0.119916	+	0.580421i
$156$	4.80712	−	17.5161i	0.384877	−	1.40241i
$157$	1.69008	−	4.64345i	0.134883	−	0.370587i	−0.853802	−	0.520599i	$-0.825709\pi$
$157$	1.69008	−	4.64345i	0.134883	−	0.370587i	0.988684	+	0.150011i	$0.0479310\pi$
$158$	0.705992	−	0.124486i	0.0561657	−	0.00990353i
$159$	−8.36746	−	18.2310i	−0.663583	−	1.44582i
$160$	−5.09461	+	5.72347i	−0.402765	+	0.452480i
$161$	−15.8240			−1.24711
$162$	2.33639	+	1.42533i	0.183564	+	0.111985i
$163$			0.134430i			0.0105294i	0.999986	+	0.00526468i	$0.00167581\pi$
$163$			0.134430i			0.0105294i	−0.999986	+	0.00526468i	$0.998324\pi$
$164$	−7.13134	−	5.98390i	−0.556864	−	0.467264i
$165$	−10.4671	+	4.43883i	−0.814866	+	0.345562i
$166$	−0.359811	−	2.04059i	−0.0279268	−	0.158381i
$167$	−5.22746	+	14.3623i	−0.404513	+	1.11139i	0.555520	+	0.831503i	$0.312519\pi$
$167$	−5.22746	+	14.3623i	−0.404513	+	1.11139i	−0.960033	+	0.279887i	$0.909703\pi$
$168$	−6.77520	−	1.85938i	−0.522718	−	0.143455i
$169$	−2.99088	+	16.9621i	−0.230068	+	1.30478i
$170$	−0.756497	+	1.22616i	−0.0580206	+	0.0940420i
$171$	4.37495	+	12.4879i	0.334561	+	0.954971i
$172$	−0.174482	+	0.100737i	−0.0133041	+	0.00768115i
$173$	5.17275	+	14.2120i	0.393277	+	1.08052i	0.965496	+	0.260419i	$0.0838607\pi$
$173$	5.17275	+	14.2120i	0.393277	+	1.08052i	−0.572218	+	0.820101i	$0.693917\pi$
$174$	0.174671	−	0.120739i	0.0132418	−	0.00915319i
$175$	−10.1894	−	13.6932i	−0.770248	−	1.03511i
$176$	7.76666	−	6.51700i	0.585434	−	0.491238i
$177$	−9.47819	+	0.771521i	−0.712424	+	0.0579911i
$178$	0.181121	+	0.497625i	0.0135756	+	0.0372985i
$179$	0.794987	+	1.37696i	0.0594201	+	0.102919i	0.894205	−	0.447657i	$-0.147742\pi$
$179$	0.794987	+	1.37696i	0.0594201	+	0.102919i	−0.834785	+	0.550576i	$0.814408\pi$
$180$	−7.81349	−	10.1336i	−0.582383	−	0.755311i
$181$	−10.8756	+	18.8371i	−0.808375	+	1.40015i	0.105613	+	0.994407i	$0.466319\pi$
$181$	−10.8756	+	18.8371i	−0.808375	+	1.40015i	−0.913989	+	0.405740i	$0.867014\pi$
$182$	5.62022	+	0.990997i	0.416599	+	0.0734576i
$183$	3.00250	+	11.4827i	0.221951	+	0.848828i
$184$	−5.17595	−	1.88389i	−0.381576	−	0.138882i
$185$	−8.99463	+	1.31648i	−0.661299	+	0.0967897i
$186$	−1.73051	−	0.161948i	−0.126887	−	0.0118746i
$187$	3.99814	−	4.76479i	0.292373	−	0.348436i
$188$		−	21.9838i		−	1.60333i
$189$	7.78671	−	15.9374i	0.566400	−	1.15928i
$190$	−0.0875677	+	2.99786i	−0.00635283	+	0.217488i
$191$	−6.03626	−	5.06502i	−0.436768	−	0.366492i	0.397730	−	0.917502i	$-0.369798\pi$
$191$	−6.03626	−	5.06502i	−0.436768	−	0.366492i	−0.834498	+	0.551010i	$0.814242\pi$
$192$	8.28650	+	5.87725i	0.598026	+	0.424154i
$193$	−17.5840	+	3.10054i	−1.26573	+	0.223182i	−0.765909	−	0.642950i	$-0.777710\pi$
$193$	−17.5840	+	3.10054i	−1.26573	+	0.223182i	−0.499817	+	0.866131i	$0.666599\pi$
$194$	0.127094	+	0.0462583i	0.00912480	+	0.00332115i
$195$	14.5159	+	15.5771i	1.03951	+	1.11550i
$196$	−1.54130	+	8.74114i	−0.110093	+	0.624367i
$197$	8.23989	+	4.75730i	0.587068	+	0.338944i	0.763937	−	0.645291i	$-0.223264\pi$
$197$	8.23989	+	4.75730i	0.587068	+	0.338944i	−0.176870	+	0.984234i	$0.556597\pi$
$198$	−1.31089	−	2.33529i	−0.0931610	−	0.165962i
$199$	−5.46922	−	9.47297i	−0.387703	−	0.671521i	0.604437	−	0.796653i	$-0.293398\pi$
$199$	−5.46922	−	9.47297i	−0.387703	−	0.671521i	−0.992140	+	0.125132i	$0.960065\pi$
$200$	−1.70269	−	5.69205i	−0.120398	−	0.402488i
$201$	5.97751	+	2.83148i	0.421621	+	0.199717i
$202$	−1.24746	−	1.48667i	−0.0877712	−	0.104602i
$203$	−0.884610	−	1.05424i	−0.0620875	−	0.0739930i
$204$	6.32659	+	2.99684i	0.442950	+	0.209820i
$205$	10.3592	−	3.43135i	0.723515	−	0.239656i
$206$	−1.85581	−	3.21435i	−0.129300	−	0.223955i
$207$	7.09835	−	11.9584i	0.493369	−	0.831166i
$208$	−16.4434	−	9.49360i	−1.14014	−	0.658263i
$209$	2.24838	−	12.7512i	0.155524	−	0.882018i
$210$	2.94130	−	2.74093i	0.202969	−	0.189142i
$211$	9.58727	+	3.48948i	0.660015	+	0.240226i	0.650243	−	0.759727i	$-0.274667\pi$
$211$	9.58727	+	3.48948i	0.660015	+	0.240226i	0.00977203	+	0.999952i	$0.496889\pi$
$212$	−21.7562	+	3.83620i	−1.49422	+	0.263471i
$213$	−19.0921	−	13.5412i	−1.30817	−	0.927829i
$214$	0.394017	+	0.330619i	0.0269344	+	0.0226007i
$215$	0.00689575	−	0.236075i	0.000470286	−	0.0161002i
$216$	4.44438	−	4.28601i	0.302402	−	0.291626i
$217$			11.2647i			0.764701i
$218$	−3.00102	+	3.57648i	−0.203255	+	0.242230i
$219$	13.3264	+	1.24714i	0.900516	+	0.0842740i
$220$	1.81334	+	12.3893i	0.122255	+	0.835287i
$221$	−10.9460	−	3.98403i	−0.736310	−	0.267995i
$222$	−0.541682	−	2.07160i	−0.0363553	−	0.139037i
$223$	22.5991	+	3.98483i	1.51335	+	0.266844i	0.867815	−	0.496888i	$-0.165524\pi$
$223$	22.5991	+	3.98483i	1.51335	+	0.266844i	0.645534	+	0.763732i	$0.276635\pi$
$224$	−5.84890	+	10.1306i	−0.390796	+	0.676879i
$225$	14.9189	−	1.55775i	0.994593	−	0.103850i
$226$	2.38319	+	4.12780i	0.158527	+	0.274577i
$227$	−2.44376	−	6.71417i	−0.162198	−	0.445635i	0.831794	−	0.555084i	$-0.187314\pi$
$227$	−2.44376	−	6.71417i	−0.162198	−	0.445635i	−0.993992	+	0.109448i	$0.965092\pi$
$228$	14.5246	−	1.18229i	0.961912	−	0.0782993i
$229$	−14.3264	+	12.0213i	−0.946713	+	0.794387i	−0.978741	−	0.205100i	$-0.934248\pi$
$229$	−14.3264	+	12.0213i	−0.946713	+	0.794387i	0.0320278	+	0.999487i	$0.489803\pi$
$230$	2.47270	−	1.95471i	0.163045	−	0.128890i
$231$	−14.2780	+	9.86945i	−0.939423	+	0.649362i
$232$	−0.163841	−	0.450150i	−0.0107567	−	0.0295538i
$233$	−21.3371	+	12.3190i	−1.39784	+	0.807043i	−0.994166	−	0.107861i	$-0.965600\pi$
$233$	−21.3371	+	12.3190i	−1.39784	+	0.807043i	−0.403673	+	0.914903i	$0.632267\pi$
$234$	−3.27003	+	3.80273i	−0.213768	+	0.248592i
$235$	21.9319	+	13.5312i	1.43068	+	0.882679i
$236$	−1.81861	+	10.3139i	−0.118382	+	0.671375i
$237$	3.93763	+	1.08064i	0.255776	+	0.0701952i
$238$	−0.752273	+	2.06685i	−0.0487626	+	0.133974i
$239$	−3.02299	−	17.1443i	−0.195541	−	1.10897i	−0.911646	−	0.410977i	$-0.865188\pi$
$239$	−3.02299	−	17.1443i	−0.195541	−	1.10897i	0.716105	−	0.697993i	$-0.245923\pi$
$240$	−12.3146	+	5.22229i	−0.794906	+	0.337098i
$241$	−5.58320	−	4.68486i	−0.359646	−	0.301778i	0.445004	−	0.895529i	$-0.353202\pi$
$241$	−5.58320	−	4.68486i	−0.359646	−	0.301778i	−0.804649	+	0.593750i	$0.797647\pi$
$242$		−	0.724464i		−	0.0465703i
$243$	8.55114	+	13.0337i	0.548556	+	0.836114i
$244$	13.0712			0.836800
$245$	−7.77181	−	6.91790i	−0.496523	−	0.441968i
$246$	1.07222	+	2.33616i	0.0683625	+	0.148948i
$247$	−23.8798	+	4.21066i	−1.51944	+	0.267918i
$248$	−1.34110	+	3.68463i	−0.0851597	+	0.233974i
$249$	3.12347	−	11.3813i	0.197942	−	0.721259i
$250$	3.28372	+	0.881061i	0.207680	+	0.0557232i
$251$	11.4223	−	19.7840i	0.720971	−	1.24876i	−0.239641	−	0.970862i	$-0.577030\pi$
$251$	11.4223	−	19.7840i	0.720971	−	1.24876i	0.960611	−	0.277896i	$-0.0896371\pi$
$252$	−14.8118	−	12.7369i	−0.933053	−	0.802348i
$253$	−11.7847	+	6.80392i	−0.740900	+	0.427759i
$254$	−3.69614	+	1.34529i	−0.231917	+	0.0844108i
$255$	−6.88382	+	4.46707i	−0.431082	+	0.279739i
$256$	6.97428	−	5.85212i	0.435892	−	0.365757i
$257$	0.945818	+	1.12718i	0.0589985	+	0.0703117i	0.794737	−	0.606955i	$-0.207609\pi$
$257$	0.945818	+	1.12718i	0.0589985	+	0.0703117i	−0.735738	+	0.677266i	$0.763165\pi$
$258$	0.0554476	−	0.00451341i	0.00345201	−	0.000280993i
$259$	−13.0409	+	4.74651i	−0.810324	+	0.294934i
$260$	20.6414	−	11.1267i	1.28012	−	0.690050i
$261$	1.19352	−	0.195600i	0.0738769	−	0.0121073i
$262$	−3.03075	−	1.74981i	−0.187241	−	0.108103i
$263$	21.2787	+	3.75201i	1.31210	+	0.231359i	0.785557	−	0.618790i	$-0.212377\pi$
$263$	21.2787	+	3.75201i	1.31210	+	0.231359i	0.526543	+	0.850148i	$0.323488\pi$
$264$	−5.84523	+	1.52841i	−0.359749	+	0.0940670i
$265$	9.56396	−	24.0660i	0.587510	−	1.47836i
$266$	0.795066	+	4.50905i	0.0487486	+	0.276467i
$267$	−0.281047	+	3.00315i	−0.0171998	+	0.183790i
$268$	4.68227	−	5.58012i	0.286015	−	0.340860i
$269$	13.3362			0.813125			0.406562	−	0.913623i	$-0.366727\pi$
$269$	13.3362			0.813125			0.406562	+	0.913623i	$0.366727\pi$
$270$	0.751943	+	3.45230i	0.0457618	+	0.210100i
$271$	19.7312			1.19859			0.599293	−	0.800530i	$-0.295448\pi$
$271$	19.7312			1.19859			0.599293	+	0.800530i	$0.295448\pi$
$272$	4.70382	−	5.60579i	0.285211	−	0.339901i
$273$	26.5137	+	18.8050i	1.60468	+	1.13813i
$274$	0.643914	+	3.65182i	0.0389003	+	0.220614i
$275$	−13.4762	−	5.81666i	−0.812643	−	0.350758i
$276$	−10.7639	−	10.8949i	−0.647912	−	0.655794i
$277$	26.1115	+	4.60416i	1.56889	+	0.276637i	0.889428	−	0.457075i	$-0.151103\pi$
$277$	26.1115	+	4.60416i	1.56889	+	0.276637i	0.679460	+	0.733712i	$0.262214\pi$
$278$	0.0637333	+	0.0367964i	0.00382247	+	0.00220690i
$279$	−8.51290	−	5.05314i	−0.509654	−	0.302524i
$280$	−4.30380	−	7.98405i	−0.257201	−	0.477138i
$281$	−6.13842	+	2.23420i	−0.366188	+	0.133281i	−0.518559	−	0.855042i	$-0.673531\pi$
$281$	−6.13842	+	2.23420i	−0.366188	+	0.133281i	0.152371	+	0.988323i	$0.451309\pi$
$282$	−2.59857	+	5.48581i	−0.154742	+	0.326675i
$283$	−4.12955	−	4.92140i	−0.245476	−	0.292547i	0.629212	−	0.777234i	$-0.283378\pi$
$283$	−4.12955	−	4.92140i	−0.245476	−	0.292547i	−0.874688	+	0.484687i	$0.838933\pi$
$284$	−19.7472	+	16.5698i	−1.17178	+	0.983239i
$285$	−7.76048	+	15.2180i	−0.459691	+	0.901434i
$286$	4.61169	−	1.67852i	0.272695	−	0.0992529i
$287$	14.4277	−	8.32986i	0.851642	−	0.491696i
$288$	−5.03210	−	8.96447i	−0.296520	−	0.528236i
$289$	−6.25528	+	10.8345i	−0.367957	+	0.637321i
$290$	0.268459	+	0.0554639i	0.0157645	+	0.00325695i
$291$	0.541422	+	0.548009i	0.0317387	+	0.0321248i
$292$	5.04161	−	13.8517i	0.295038	−	0.810609i
$293$	13.7780	−	2.42943i	0.804919	−	0.141929i	0.243974	−	0.969782i	$-0.421549\pi$
$293$	13.7780	−	2.42943i	0.804919	−	0.141929i	0.560945	+	0.827853i	$0.310438\pi$
$294$	1.41785	−	1.99906i	0.0826906	−	0.116588i
$295$	−9.17013	−	8.16258i	−0.533905	−	0.475244i
$296$	−4.83069			−0.280778
$297$	−1.05363	−	15.2173i	−0.0611379	−	0.882996i
$298$		−	3.86437i		−	0.223857i
$299$	19.5220	+	16.3809i	1.12899	+	0.947332i
$300$	2.49669	−	16.3299i	0.144147	−	0.942808i
$301$	−0.0626096	−	0.355077i	−0.00360876	−	0.0204663i
$302$	−0.457223	+	1.25621i	−0.0263102	+	0.0722868i
$303$	−2.79635	−	10.6943i	−0.160646	−	0.614373i
$304$	2.64522	−	15.0018i	0.151714	−	0.860413i
$305$	−8.04545	+	13.0404i	−0.460681	+	0.746689i
$306$	−1.22449	−	1.49565i	−0.0699995	−	0.0855007i
$307$	−13.7290	+	7.92646i	−0.783557	+	0.452387i	−0.837689	−	0.546147i	$-0.816094\pi$
$307$	−13.7290	+	7.92646i	−0.783557	+	0.452387i	0.0541324	+	0.998534i	$0.482761\pi$
$308$	6.53789	+	17.9627i	0.372531	+	1.02352i
$309$	−1.71517	−	21.0709i	−0.0975723	−	1.19868i
$310$	−1.39151	−	1.76026i	−0.0790324	−	0.0999759i
$311$	11.9922	−	10.0626i	0.680015	−	0.570600i	−0.235996	−	0.971754i	$-0.575835\pi$
$311$	11.9922	−	10.0626i	0.680015	−	0.570600i	0.916011	+	0.401154i	$0.131391\pi$
$312$	6.43369	+	9.30753i	0.364236	+	0.526935i
$313$	0.347220	+	0.953980i	0.0196261	+	0.0539221i	0.949119	−	0.314918i	$-0.101977\pi$
$313$	0.347220	+	0.953980i	0.0196261	+	0.0539221i	−0.929493	+	0.368840i	$0.879755\pi$
$314$	0.751330	+	1.30134i	0.0424000	+	0.0734390i
$315$	21.8236	−	6.93712i	1.22962	−	0.390862i
$316$	2.24845	−	3.89443i	0.126485	−	0.219079i
$317$	−11.3695	−	2.00474i	−0.638573	−	0.112598i	−0.155018	−	0.987912i	$-0.549544\pi$
$317$	−11.3695	−	2.00474i	−0.638573	−	0.112598i	−0.483555	+	0.875314i	$0.660655\pi$
$318$	5.88246	+	1.61438i	0.329872	+	0.0905300i
$319$	−1.11210	−	0.404770i	−0.0622655	−	0.0226628i
$320$	1.89937	+	12.9771i	0.106178	+	0.725444i
$321$	1.22205	+	2.66260i	0.0682080	+	0.148612i
$322$	3.09308	−	3.68619i	0.172370	−	0.205423i
$323$		−	9.34549i		−	0.519997i
$324$	16.2697	−	5.47990i	0.903871	−	0.304439i
$325$	−1.60449	+	27.4412i	−0.0890009	+	1.52216i
$326$	−0.0313152	−	0.0262766i	−0.00173439	−	0.00145533i
$327$	−24.1683	+	11.0925i	−1.33651	+	0.613415i
$328$	5.71092	−	1.00699i	0.315333	−	0.0556017i
$329$	36.9692	+	13.4557i	2.03818	+	0.741835i
$330$	1.01196	−	3.30595i	0.0557068	−	0.181987i
$331$	−0.601404	+	3.41073i	−0.0330562	+	0.187471i	−0.996865	−	0.0791244i	$-0.974788\pi$
$331$	−0.601404	+	3.41073i	−0.0330562	+	0.187471i	0.963809	+	0.266595i	$0.0858987\pi$
$332$	−11.2564	−	6.49889i	−0.617776	−	0.356673i
$333$	2.26291	−	11.9844i	0.124007	−	0.656739i
$334$	−2.32389	−	4.02509i	−0.127157	−	0.220243i
$335$	2.68496	+	8.10582i	0.146695	+	0.442868i
$336$	−16.7981	+	11.6114i	−0.916411	+	0.633456i
$337$	0.0975969	+	0.116311i	0.00531644	+	0.00633589i	0.768696	−	0.639614i	$-0.220906\pi$
$337$	0.0975969	+	0.116311i	0.00531644	+	0.00633589i	−0.763380	+	0.645950i	$0.776461\pi$
$338$	−3.36668	−	4.01226i	−0.183123	−	0.218238i
$339$	2.20258	+	27.0588i	0.119628	+	1.46963i
$340$	2.84176	+	8.57918i	0.154116	+	0.465271i
$341$	4.84355	+	8.38927i	0.262293	+	0.454305i
$342$	−3.76419	−	1.42183i	−0.203544	−	0.0768837i
$343$	6.93809	+	4.00571i	0.374622	+	0.216288i
$344$	0.0217936	−	0.123597i	0.00117503	−	0.00666392i
$345$	17.4944	−	4.03262i	0.941868	−	0.217109i
$346$	−4.32178	−	1.57300i	−0.232340	−	0.0845649i
$347$	−20.4648	+	3.60850i	−1.09861	+	0.193714i	−0.693430	−	0.720524i	$-0.743901\pi$
$347$	−20.4648	+	3.60850i	−1.09861	+	0.193714i	−0.405178	+	0.914238i	$0.632790\pi$
$348$	0.124109	−	1.32618i	0.00665294	−	0.0710905i
$349$	4.76037	+	3.99442i	0.254817	+	0.213816i	0.761243	−	0.648467i	$-0.224589\pi$
$349$	4.76037	+	3.99442i	0.254817	+	0.213816i	−0.506427	+	0.862283i	$0.669034\pi$
$350$	5.18151	+	0.302963i	0.276963	+	0.0161940i
$351$	−26.1047	+	11.6012i	−1.39337	+	0.619224i
$352$			10.0595i			0.536173i
$353$	3.85011	−	4.58839i	0.204921	−	0.244215i	−0.653789	−	0.756677i	$-0.726822\pi$
$353$	3.85011	−	4.58839i	0.204921	−	0.244215i	0.858710	+	0.512461i	$0.171266\pi$
$354$	1.67295	−	2.35874i	0.0889163	−	0.125366i
$355$	−4.37617	−	29.8994i	−0.232263	−	1.58689i
$356$	3.12152	+	1.13614i	0.165440	+	0.0602154i
$357$	−8.91196	+	8.80485i	−0.471671	+	0.466002i
$358$	−0.476154	−	0.0839588i	−0.0251655	−	0.00443736i
$359$	−0.255829	+	0.443109i	−0.0135022	+	0.0233864i	−0.872698	−	0.488261i	$-0.837631\pi$
$359$	−0.255829	+	0.443109i	−0.0135022	+	0.0233864i	0.859195	+	0.511648i	$0.170965\pi$
$360$	7.96424	+	0.329058i	0.419752	+	0.0173429i
$361$	−0.227046	−	0.393256i	−0.0119498	−	0.0206977i
$362$	−2.26225	−	6.21548i	−0.118901	−	0.326678i
$363$	1.76647	−	3.72918i	0.0927157	−	0.195731i
$364$	27.4234	−	23.0109i	1.43737	−	1.20610i
$365$	10.7158	+	13.5555i	0.560892	+	0.709529i
$366$	−3.26178	−	1.54507i	−0.170496	−	0.0807620i
$367$	−7.02326	−	19.2963i	−0.366611	−	1.00726i	−0.976641	−	0.214878i	$-0.931065\pi$
$367$	−7.02326	−	19.2963i	−0.366611	−	1.00726i	0.610030	−	0.792378i	$-0.291157\pi$
$368$	−13.8648	+	8.00483i	−0.722752	+	0.417281i
$369$	−0.177030	+	14.6398i	−0.00921581	+	0.762118i
$370$	1.45148	−	2.35262i	0.0754590	−	0.122307i
$371$	6.86518	−	38.9344i	0.356423	−	2.02137i
$372$	−7.75580	+	7.66258i	−0.402119	+	0.397286i
$373$	−4.29128	+	11.7902i	−0.222194	+	0.610472i	−0.999834	−	0.0182375i	$-0.994195\pi$
$373$	−4.29128	+	11.7902i	−0.222194	+	0.610472i	0.777640	+	0.628710i	$0.216417\pi$
$374$	0.328448	+	1.86272i	0.0169836	+	0.0963190i
$375$	14.7546	+	12.5420i	0.761925	+	0.647665i
$376$	10.4905	+	8.80254i	0.541004	+	0.453956i
$377$			2.21635i			0.114148i
$378$	2.19056	+	4.92915i	0.112670	+	0.253528i
$379$	−29.8914			−1.53542			−0.767710	−	0.640798i	$-0.778604\pi$
$379$	−29.8914			−1.53542			−0.767710	+	0.640798i	$0.778604\pi$
$380$	14.0525	+	12.5085i	0.720877	+	0.641672i
$381$	−22.3061	−	2.08750i	−1.14278	−	0.106946i
$382$	2.35978	−	0.416093i	0.120737	−	0.0212892i
$383$	7.45556	−	20.4840i	0.380961	−	1.04668i	−0.589991	−	0.807410i	$-0.700869\pi$
$383$	7.45556	−	20.4840i	0.380961	−	1.04668i	0.970952	−	0.239273i	$-0.0769089\pi$
$384$	−14.4733	+	3.78448i	−0.738589	+	0.193126i
$385$	−21.9444	−	4.53374i	−1.11839	−	0.231061i
$386$	2.71483	−	4.70223i	0.138181	−	0.239337i
$387$	0.296421	+	0.111966i	0.0150679	+	0.00569154i
$388$	0.734740	−	0.424202i	0.0373008	−	0.0215356i
$389$	−9.78677	+	3.56209i	−0.496209	+	0.180605i	−0.577988	−	0.816045i	$-0.696162\pi$
$389$	−9.78677	+	3.56209i	−0.496209	+	0.180605i	0.0817791	+	0.996650i	$0.473940\pi$
$390$	−6.46604	+	0.336660i	−0.327421	+	0.0170474i
$391$	−7.52395	+	6.31335i	−0.380503	+	0.319280i
$392$	−3.55403	−	4.23553i	−0.179506	−	0.213927i
$393$	−11.3342	−	16.3971i	−0.571736	−	0.827122i
$394$	−2.71883	+	0.989574i	−0.136973	+	0.0498540i
$395$	2.50129	+	4.64019i	0.125854	+	0.233473i
$396$	−16.5074	−	3.11696i	−0.829528	−	0.156633i
$397$	−18.9260	−	10.9269i	−0.949866	−	0.548406i	−0.0568270	−	0.998384i	$-0.518098\pi$
$397$	−18.9260	−	10.9269i	−0.949866	−	0.548406i	−0.893039	+	0.449978i	$0.851432\pi$
$398$	3.27577	+	0.577606i	0.164199	+	0.0289528i
$399$	−6.90186	+	25.1489i	−0.345525	+	1.25902i
$400$	−15.8547	−	6.84332i	−0.792737	−	0.342166i
$401$	−3.50040	−	19.8518i	−0.174802	−	0.991351i	−0.938372	−	0.345626i	$-0.887667\pi$
$401$	−3.50040	−	19.8518i	−0.174802	−	0.991351i	0.763570	−	0.645725i	$-0.223445\pi$
$402$	−1.82800	+	0.838992i	−0.0911722	+	0.0418451i
$403$	11.6612	−	13.8972i	0.580884	−	0.692271i
$404$	−12.1738			−0.605667
$405$	−4.54716	+	19.6042i	−0.225950	+	0.974139i
$406$	0.418495			0.0207696
$407$	−7.67118	+	9.14216i	−0.380246	+	0.453160i
$408$	−3.96329	+	1.81902i	−0.196212	+	0.0900550i
$409$	−2.34346	−	13.2904i	−0.115876	−	0.657168i	−0.986313	−	0.164887i	$-0.947274\pi$
$409$	−2.34346	−	13.2904i	−0.115876	−	0.657168i	0.870436	−	0.492282i	$-0.163837\pi$
$410$	−1.22555	+	3.08387i	−0.0605254	+	0.152301i
$411$	−5.58973	+	20.3678i	−0.275721	+	1.00467i
$412$	−22.9287	−	4.04295i	−1.12962	−	0.199182i
$413$	−16.2312	−	9.37109i	−0.798686	−	0.461121i
$414$	1.39820	+	3.99102i	0.0687178	+	0.196148i
$415$	13.4120	−	7.22970i	0.658367	−	0.354892i
$416$	17.7028	−	6.44331i	0.867953	−	0.315909i
$417$	0.238346	+	0.344811i	0.0116718	+	0.0168855i
$418$	2.53089	+	3.01619i	0.123790	+	0.147527i
$419$	1.56378	−	1.31217i	0.0763959	−	0.0641037i	−0.603790	−	0.797143i	$-0.706343\pi$
$419$	1.56378	−	1.31217i	0.0763959	−	0.0641037i	0.680186	+	0.733040i	$0.261899\pi$
$420$	−1.31130	−	25.1855i	−0.0639850	−	1.22892i
$421$	−2.58533	+	0.940984i	−0.126001	+	0.0458608i	−0.404251	−	0.914648i	$-0.632468\pi$
$421$	−2.58533	+	0.940984i	−0.126001	+	0.0458608i	0.278250	+	0.960509i	$0.410246\pi$
$422$	−2.68687	+	1.55126i	−0.130795	+	0.0755143i
$423$	−26.7522	+	21.9021i	−1.30074	+	1.06491i
$424$	6.88080	−	11.9179i	0.334161	−	0.578784i
$425$	−10.3080	−	2.44551i	−0.500013	−	0.118625i
$426$	6.88629	−	1.80063i	0.333642	−	0.0872406i
$427$	−8.00053	+	21.9813i	−0.387173	+	1.06375i
$428$	3.17744	−	0.560268i	0.153587	−	0.0270816i
$429$	27.8314	+	2.60458i	1.34371	+	0.125750i
$430$	0.0536454	+	0.0477512i	0.00258701	+	0.00230277i
$431$	20.0948			0.967932			0.483966	−	0.875087i	$-0.339196\pi$
$431$	20.0948			0.967932			0.483966	+	0.875087i	$0.339196\pi$
$432$	−1.23960	−	17.9032i	−0.0596403	−	0.861367i
$433$		−	11.8614i		−	0.570023i	−0.958524	−	0.285011i	$-0.908003\pi$
$433$		−	11.8614i		−	0.570023i	0.958524	−	0.285011i	$-0.0919974\pi$
$434$	−2.62411	−	2.20189i	−0.125961	−	0.105694i
$435$	1.24665	+	0.940087i	0.0597724	+	0.0450737i
$436$	5.08553	+	28.8415i	0.243553	+	1.38126i
$437$	−6.99283	+	19.2126i	−0.334512	+	0.919065i
$438$	−2.89540	+	2.86060i	−0.138347	+	0.136685i
$439$	6.50324	−	36.8817i	0.310383	−	1.76027i	−0.286636	−	0.958040i	$-0.592537\pi$
$439$	6.50324	−	36.8817i	0.310383	−	1.76027i	0.597018	−	0.802228i	$-0.296352\pi$
$440$	−6.63813	−	4.09549i	−0.316460	−	0.195245i
$441$	12.1727	−	6.83302i	0.579653	−	0.325382i
$442$	3.06766	−	1.77112i	0.145914	−	0.0842434i
$443$	5.07737	+	13.9500i	0.241233	+	0.662783i	0.999936	+	0.0113453i	$0.00361141\pi$
$443$	5.07737	+	13.9500i	0.241233	+	0.662783i	−0.758702	+	0.651437i	$0.774166\pi$
$444$	−12.1388	−	5.75000i	−0.576080	−	0.272883i
$445$	−3.05478	+	2.41485i	−0.144810	+	0.114475i
$446$	−5.34565	+	4.48553i	−0.253124	+	0.212396i
$447$	9.42255	−	19.8918i	0.445671	−	0.940852i
$448$	6.84809	+	18.8150i	0.323542	+	0.888924i
$449$	−8.86789	−	15.3596i	−0.418502	−	0.724866i	0.577287	−	0.816541i	$-0.304111\pi$
$449$	−8.86789	−	15.3596i	−0.418502	−	0.724866i	−0.995789	+	0.0916751i	$0.970778\pi$
$450$	−2.55328	+	3.77983i	−0.120363	+	0.178183i
$451$	7.16325	−	12.4071i	0.337304	−	0.584228i
$452$	29.4445	+	5.19186i	1.38495	+	0.244205i
$453$	−5.41659	+	5.35149i	−0.254494	+	0.251435i
$454$	2.04173	+	0.743130i	0.0958232	+	0.0348768i
$455$	6.07729	+	41.5220i	0.284908	+	1.94658i
$456$	−5.25160	+	7.40438i	−0.245929	+	0.346742i
$457$	−9.44358	+	11.2544i	−0.441752	+	0.526460i	−0.940275	−	0.340417i	$-0.889432\pi$
$457$	−9.44358	+	11.2544i	−0.441752	+	0.526460i	0.498522	+	0.866877i	$0.333876\pi$
$458$		−	5.68707i		−	0.265739i
$459$	−2.65619	−	10.6846i	−0.123980	−	0.498712i
$460$	0.577296	−	19.7636i	0.0269166	−	0.921483i
$461$	11.0104	+	9.23885i	0.512807	+	0.430296i	0.862116	−	0.506711i	$-0.169139\pi$
$461$	11.0104	+	9.23885i	0.512807	+	0.430296i	−0.349308	+	0.937008i	$0.613583\pi$
$462$	0.491802	−	5.25519i	0.0228807	−	0.244494i
$463$	8.00949	−	1.41229i	0.372232	−	0.0656346i	0.0155973	−	0.999878i	$-0.495035\pi$
$463$	8.00949	−	1.41229i	0.372232	−	0.0656346i	0.356635	+	0.934244i	$0.383924\pi$
$464$	−1.30838	−	0.476213i	−0.0607402	−	0.0221076i
$465$	−2.87073	−	12.4539i	−0.133127	−	0.577534i
$466$	1.30101	−	7.37840i	0.0602681	−	0.341798i
$467$	18.6732	+	10.7810i	0.864091	+	0.498883i	0.865380	−	0.501116i	$-0.167077\pi$
$467$	18.6732	+	10.7810i	0.864091	+	0.498883i	−0.00128884	+	0.999999i	$0.500410\pi$
$468$	5.08804	+	31.0464i	0.235195	+	1.43512i
$469$	6.51793	+	11.2894i	0.300970	+	0.521296i
$470$	−7.43904	+	2.46410i	−0.343137	+	0.113660i
$471$	0.694390	+	8.53063i	0.0319958	+	0.393071i
$472$	−4.19348	−	4.99759i	−0.193021	−	0.230033i
$473$	−0.199302	−	0.237518i	−0.00916390	−	0.0109211i
$474$	−1.02141	+	0.706035i	−0.0469149	+	0.0324293i
$475$	−21.1284	+	6.32021i	−0.969435	+	0.289991i
$476$	6.89856	+	11.9487i	0.316195	+	0.547666i
$477$	26.3436	+	22.6533i	1.20619	+	1.03722i
$478$	4.58463	+	2.64694i	0.209696	+	0.121068i
$479$	−6.11802	+	34.6970i	−0.279540	+	1.58535i	0.444622	+	0.895718i	$0.353338\pi$
$479$	−6.11802	+	34.6970i	−0.279540	+	1.58535i	−0.724162	+	0.689630i	$0.757773\pi$
$480$	3.88461	−	12.6905i	0.177308	−	0.579240i
$481$	21.0020	+	7.64412i	0.957610	+	0.348542i
$482$	2.18266	−	0.384863i	0.0994176	−	0.0175300i
$483$	24.9097	−	11.4327i	1.13343	−	0.520208i
$484$	−3.48125	−	2.92112i	−0.158239	−	0.132778i
$485$	−0.0290378	+	0.994104i	−0.00131854	+	0.0451399i
$486$	−4.70766	−	0.555690i	−0.213544	−	0.0252066i
$487$		−	21.9486i		−	0.994588i	−0.867582	−	0.497294i	$-0.834327\pi$
$487$		−	21.9486i		−	0.994588i	0.867582	−	0.497294i	$-0.165673\pi$
$488$	−5.23385	+	6.23746i	−0.236925	+	0.282357i
$489$	−0.0971245	−	0.211615i	−0.00439212	−	0.00956956i
$490$	3.13065	−	0.458212i	0.141428	−	0.0206999i
$491$	−19.2925	−	7.02190i	−0.870659	−	0.316894i	−0.132225	−	0.991220i	$-0.542212\pi$
$491$	−19.2925	−	7.02190i	−0.870659	−	0.316894i	−0.738434	+	0.674326i	$0.764434\pi$
$492$	15.5492	+	4.26733i	0.701014	+	0.192386i
$493$	−0.841223	−	0.148330i	−0.0378868	−	0.00668046i
$494$	3.68686	−	6.38582i	0.165879	−	0.287312i
$495$	13.2700	−	14.5499i	0.596443	−	0.653969i
$496$	5.69845	+	9.87000i	0.255868	+	0.443176i
$497$	−15.7780	−	43.3498i	−0.707742	−	1.94450i
$498$	2.04072	+	2.95227i	0.0914466	+	0.132295i
$499$	−19.5778	+	16.4277i	−0.876422	+	0.735405i	−0.965440	−	0.260625i	$-0.916071\pi$
$499$	−19.5778	+	16.4277i	−0.876422	+	0.735405i	0.0890184	+	0.996030i	$0.471627\pi$
$500$	17.4740	−	12.2266i	0.781463	−	0.546792i
$501$	−2.14777	−	26.3855i	−0.0959553	−	1.17882i
$502$	2.37598	+	6.52794i	0.106045	+	0.291356i
$503$	9.72392	−	5.61411i	0.433568	−	0.250321i	−0.267297	−	0.963614i	$-0.586131\pi$
$503$	9.72392	−	5.61411i	0.433568	−	0.250321i	0.700866	+	0.713293i	$0.252797\pi$
$504$	12.0087	−	1.96805i	0.534910	−	0.0876638i
$505$	7.49305	−	12.1450i	0.333436	−	0.540446i
$506$	0.718565	−	4.07518i	0.0319441	−	0.181164i
$507$	−7.54685	−	28.8621i	−0.335168	−	1.28181i
$508$	−8.43877	+	23.1853i	−0.374410	+	1.02868i
$509$	−5.09372	−	28.8879i	−0.225775	−	1.28043i	−0.861198	−	0.508269i	$-0.830285\pi$
$509$	−5.09372	−	28.8879i	−0.225775	−	1.28043i	0.635423	−	0.772164i	$-0.280826\pi$
$510$	0.304963	−	2.47674i	0.0135040	−	0.109672i
$511$	20.2079	+	16.9565i	0.893946	+	0.750110i
$512$			20.0428i			0.885775i
$513$	−15.9093	−	16.4971i	−0.702412	−	0.728366i
$514$	−0.447452			−0.0197362
$515$	18.1462	−	20.3861i	0.799616	−	0.898317i
$516$	0.201882	−	0.284639i	0.00888737	−	0.0125306i
$517$	33.3179	−	5.87484i	1.46532	−	0.258375i
$518$	1.44338	−	3.96565i	0.0634184	−	0.174241i
$519$	−18.4109	−	18.6348i	−0.808147	−	0.817979i
$520$	−2.95545	+	14.3051i	−0.129605	+	0.627321i
$521$	−4.09744	+	7.09698i	−0.179512	+	0.310924i	−0.941714	−	0.336416i	$-0.890785\pi$
$521$	−4.09744	+	7.09698i	−0.179512	+	0.310924i	0.762201	+	0.647340i	$0.224119\pi$
$522$	−0.187729	+	0.316262i	−0.00821667	+	0.0138424i
$523$	8.30466	−	4.79470i	0.363137	−	0.209657i	−0.307319	−	0.951607i	$-0.599432\pi$
$523$	8.30466	−	4.79470i	0.363137	−	0.209657i	0.670456	+	0.741949i	$0.266098\pi$
$524$	−20.6286	+	7.50821i	−0.901166	+	0.327998i
$525$	25.9331	+	14.1936i	1.13181	+	0.619462i
$526$	−5.03331	+	4.22345i	−0.219463	+	0.184151i
$527$	4.49432	+	5.35612i	0.195776	+	0.233316i
$528$	−7.51754	+	15.8702i	−0.327159	+	0.690662i
$529$	−1.42103	+	0.517213i	−0.0617840	+	0.0224875i
$530$	3.73671	+	6.93203i	0.162312	+	0.301108i
$531$	14.3628	−	8.06242i	0.623294	−	0.349879i
$532$	24.8730	+	14.3604i	1.07838	+	0.622604i
$533$	−26.4224	−	4.65898i	−1.14448	−	0.201803i
$534$	−0.644644	−	0.652487i	−0.0278965	−	0.0282359i
$535$	−1.39679	+	3.51478i	−0.0603886	+	0.151957i
$536$	0.787947	+	4.46867i	0.0340341	+	0.193017i
$537$	−2.24628	−	1.59319i	−0.0969343	−	0.0687513i
$538$	−2.60680	+	3.10666i	−0.112387	+	0.133938i
$539$	−13.6596			−0.588363
$540$	19.6212	+	10.3067i	0.844361	+	0.443531i
$541$	−5.81809			−0.250139			−0.125070	−	0.992148i	$-0.539915\pi$
$541$	−5.81809			−0.250139			−0.125070	+	0.992148i	$0.539915\pi$
$542$	−3.85681	+	4.59636i	−0.165664	+	0.197431i
$543$	3.51036	−	37.5102i	0.150644	−	1.60972i
$544$	1.26081	+	7.15041i	0.0540568	+	0.306571i
$545$	−31.9035	−	12.6786i	−1.36660	−	0.543093i
$546$	−9.56316	+	2.50057i	−0.409266	+	0.107015i
$547$	0.590106	+	0.104052i	0.0252311	+	0.00444893i	0.186249	−	0.982502i	$-0.440367\pi$
$547$	0.590106	+	0.104052i	0.0252311	+	0.00444893i	−0.161018	+	0.986951i	$0.551478\pi$
$548$	20.1443	+	11.6303i	0.860524	+	0.496824i
$549$	−13.0226	−	15.9065i	−0.555792	−	0.678871i
$550$	3.98913	−	2.00229i	0.170097	−	0.0853779i
$551$	−1.67091	+	0.608163i	−0.0711834	+	0.0259086i
$552$	9.50890	−	0.774022i	0.404726	−	0.0329445i
$553$	5.17287	+	6.16478i	0.219973	+	0.262153i
$554$	−6.17648	+	5.18268i	−0.262413	+	0.220191i
$555$	13.2079	−	8.57092i	0.560645	−	0.363815i
$556$	0.433796	−	0.157889i	0.0183971	−	0.00669598i
$557$	3.15552	−	1.82184i	0.133704	−	0.0771940i	−0.431656	−	0.902038i	$-0.642071\pi$
$557$	3.15552	−	1.82184i	0.133704	−	0.0771940i	0.565360	+	0.824844i	$0.308737\pi$
$558$	2.84111	−	0.995345i	0.120274	−	0.0421363i
$559$	−0.290331	+	0.502869i	−0.0122797	+	0.0212691i
$560$	−25.8177	−	5.33396i	−1.09099	−	0.225401i
$561$	−2.85121	+	10.3892i	−0.120378	+	0.438633i
$562$	0.679405	−	1.86665i	0.0286590	−	0.0787399i
$563$	0.769406	−	0.135667i	0.0324266	−	0.00571768i	−0.157411	−	0.987533i	$-0.550315\pi$
$563$	0.769406	−	0.135667i	0.0324266	−	0.00571768i	0.189838	+	0.981815i	$0.439204\pi$
$564$	15.8831	+	34.6062i	0.668801	+	1.45718i
$565$	−23.3029	+	26.1794i	−0.980362	+	1.10137i
$566$	1.95362			0.0821169
$567$	−0.742919	+	30.7140i	−0.0311997	+	1.28987i
$568$		−	16.0579i		−	0.673774i
$569$	−26.6979	−	22.4022i	−1.11923	−	0.939149i	−0.120669	−	0.992693i	$-0.538504\pi$
$569$	−26.6979	−	22.4022i	−1.11923	−	0.939149i	−0.998566	+	0.0535433i	$0.982948\pi$
$570$	−2.02809	−	4.78240i	−0.0849471	−	0.200313i
$571$	−2.28374	−	12.9518i	−0.0955717	−	0.542014i	−0.994571	−	0.104063i	$-0.966816\pi$
$571$	−2.28374	−	12.9518i	−0.0955717	−	0.542014i	0.898999	−	0.437951i	$-0.144296\pi$
$572$	10.5291	−	28.9284i	0.440243	−	1.20956i
$573$	13.1615	+	3.61204i	0.549830	+	0.150895i
$574$	−0.879719	+	4.98913i	−0.0367188	+	0.208242i
$575$	19.3616	+	12.7406i	0.807435	+	0.531319i
$576$	−17.2906	−	3.26485i	−0.720442	−	0.136035i
$577$	22.3145	−	12.8833i	0.928964	−	0.536338i	0.0424803	−	0.999097i	$-0.486474\pi$
$577$	22.3145	−	12.8833i	0.928964	−	0.536338i	0.886484	+	0.462760i	$0.153141\pi$
$578$	−1.30117	−	3.57494i	−0.0541216	−	0.148698i
$579$	25.4401	−	17.5851i	1.05725	−	0.730811i
$580$	1.34897	−	1.06638i	0.0560131	−	0.0442792i
$581$	17.8186	−	14.9516i	0.739241	−	0.620296i
$582$	−0.233488	+	0.0190058i	−0.00967839	+	0.000787818i
$583$	−11.6280	−	31.9477i	−0.481584	−	1.32314i
$584$	4.59118	+	7.95216i	0.189985	+	0.329063i
$585$	−34.1048	−	14.0333i	−1.41006	−	0.580205i
$586$	−2.12721	+	3.68444i	−0.0878743	+	0.152203i
$587$	−6.55502	−	1.15583i	−0.270555	−	0.0477061i	0.0367248	−	0.999325i	$-0.488308\pi$
$587$	−6.55502	−	1.15583i	−0.270555	−	0.0477061i	−0.307279	+	0.951619i	$0.599419\pi$
$588$	−3.88914	−	14.8736i	−0.160386	−	0.613377i
$589$	13.6770	+	4.97803i	0.563552	+	0.205116i
$590$	3.69392	−	0.540653i	0.152076	−	0.0222584i
$591$	−16.4081	−	1.53554i	−0.674938	−	0.0631635i
$592$	−9.02517	+	10.7558i	−0.370932	+	0.442060i
$593$			46.9838i			1.92939i	0.263360	+	0.964697i	$0.415169\pi$
$593$			46.9838i			1.92939i	−0.263360	+	0.964697i	$0.584831\pi$
$594$	3.75080	+	2.72904i	0.153897	+	0.111974i
$595$	−16.1666	−	0.472226i	−0.662764	−	0.0193594i
$596$	−18.5694	−	15.5816i	−0.760631	−	0.638246i
$597$	15.4536	+	10.9606i	0.632475	+	0.448587i
$598$	−7.63181	+	1.34569i	−0.312088	+	0.0550295i
$599$	30.7181	+	11.1805i	1.25511	+	0.456821i	0.882124	−	0.471018i	$-0.156113\pi$
$599$	30.7181	+	11.1805i	1.25511	+	0.456821i	0.372982	+	0.927839i	$0.378335\pi$
$600$	6.79277	+	7.73006i	0.277314	+	0.315578i
$601$	−4.40564	+	24.9856i	−0.179710	+	1.01918i	0.752856	+	0.658185i	$0.228676\pi$
$601$	−4.40564	+	24.9856i	−0.179710	+	1.01918i	−0.932566	+	0.361000i	$0.882436\pi$
$602$	0.0949528	+	0.0548210i	0.00386999	+	0.00223434i
$603$	−11.4553	−	0.138522i	−0.466497	−	0.00564105i
$604$	4.19287	+	7.26226i	0.170605	+	0.295497i
$605$	5.05696	−	1.67506i	0.205595	−	0.0681008i
$606$	3.03782	+	1.43898i	0.123403	+	0.0584547i
$607$	10.3912	+	12.3838i	0.421766	+	0.502641i	0.934528	−	0.355890i	$-0.115822\pi$
$607$	10.3912	+	12.3838i	0.421766	+	0.502641i	−0.512762	+	0.858531i	$0.671378\pi$
$608$	9.71529	+	11.5782i	0.394007	+	0.469559i
$609$	2.15420	+	1.02042i	0.0872927	+	0.0413496i
$610$	−1.46511	−	4.42314i	−0.0593207	−	0.179088i
$611$	−31.6794	−	54.8703i	−1.28161	−	2.21981i
$612$	−12.1243	−	0.146611i	−0.490096	−	0.00592641i
$613$	−35.6170	−	20.5635i	−1.43856	−	0.830551i	−0.440806	−	0.897602i	$-0.645307\pi$
$613$	−35.6170	−	20.5635i	−1.43856	−	0.830551i	−0.997750	+	0.0670516i	$0.978641\pi$
$614$	0.837116	−	4.74752i	0.0337832	−	0.191594i
$615$	−13.8279	+	12.8859i	−0.557596	+	0.519611i
$616$	−11.1895	−	4.07263i	−0.450836	−	0.164091i
$617$	41.3880	−	7.29783i	1.66622	−	0.293799i	0.740513	−	0.672042i	$-0.234583\pi$
$617$	41.3880	−	7.29783i	1.66622	−	0.293799i	0.925706	+	0.378243i	$0.123472\pi$
$618$	5.24370	+	3.71913i	0.210933	+	0.149605i
$619$	8.65367	+	7.26129i	0.347821	+	0.291856i	0.799914	−	0.600114i	$-0.204878\pi$
$619$	8.65367	+	7.26129i	0.347821	+	0.291856i	−0.452094	+	0.891970i	$0.649323\pi$
$620$	−14.0692	−	0.410963i	−0.565034	−	0.0165047i
$621$	−2.53414	+	23.9530i	−0.101692	+	0.961202i
$622$			4.76048i			0.190878i
$623$	−3.82119	+	4.55392i	−0.153093	+	0.182449i
$624$	32.7437	+	3.06429i	1.31080	+	0.122670i
$625$	1.44235	+	24.9584i	0.0576939	+	0.998334i
$626$	−0.290099	−	0.105587i	−0.0115947	−	0.00422011i
$627$	5.67331	+	21.6969i	0.226570	+	0.866493i
$628$	9.28275	+	1.63680i	0.370422	+	0.0653154i
$629$	−4.30693	+	7.45982i	−0.171728	+	0.297442i
$630$	−2.64979	+	6.43975i	−0.105570	+	0.256566i
$631$	22.9413	+	39.7354i	0.913278	+	1.58184i	0.809404	+	0.587253i	$0.199791\pi$
$631$	22.9413	+	39.7354i	0.913278	+	1.58184i	0.103874	+	0.994590i	$0.466876\pi$
$632$	0.958081	+	2.63231i	0.0381104	+	0.104708i
$633$	−17.6131	+	1.43370i	−0.700058	+	0.0569844i
$634$	2.68936	−	2.25664i	0.106808	−	0.0896227i
$635$	−17.9364	−	22.6896i	−0.711786	−	0.900409i
$636$	31.4763	−	21.7575i	1.24812	−	0.862741i
$637$	8.74927	+	24.0384i	0.346659	+	0.952437i
$638$	0.311669	−	0.179942i	0.0123391	−	0.00712398i
$639$	39.8377	+	7.52223i	1.57595	+	0.297575i
$640$	−16.4366	−	10.1408i	−0.649715	−	0.400852i
$641$	−3.68466	+	20.8967i	−0.145535	+	0.825372i	0.821401	+	0.570352i	$0.193193\pi$
$641$	−3.68466	+	20.8967i	−0.145535	+	0.825372i	−0.966936	+	0.255020i	$0.917918\pi$
$642$	−0.859119	−	0.235776i	−0.0339067	−	0.00930535i
$643$	5.47651	−	15.0466i	0.215972	−	0.593379i	−0.783640	−	0.621215i	$-0.786639\pi$
$643$	5.47651	−	15.0466i	0.215972	−	0.593379i	0.999613	+	0.0278358i	$0.00886157\pi$
$644$	−5.24153	−	29.7262i	−0.206545	−	1.17138i
$645$	0.159707	+	0.376603i	0.00628846	+	0.0148287i
$646$	2.17702	+	1.82674i	0.0856536	+	0.0718719i
$647$		−	14.3391i		−	0.563729i	−0.959454	−	0.281864i	$-0.909047\pi$
$647$		−	14.3391i		−	0.563729i	0.959454	−	0.281864i	$-0.0909528\pi$
$648$	−3.89959	+	9.95793i	−0.153190	+	0.391185i
$649$	−16.1173			−0.632660
$650$	−6.07877	−	5.73762i	−0.238429	−	0.225048i
$651$	−8.13869	−	17.7326i	−0.318981	−	0.694996i
$652$	−0.252533	+	0.0445283i	−0.00988995	+	0.00174386i
$653$	7.51262	−	20.6408i	0.293992	−	0.807735i	−0.701481	−	0.712688i	$-0.747478\pi$
$653$	7.51262	−	20.6408i	0.293992	−	0.807735i	0.995473	−	0.0950471i	$-0.0303002\pi$
$654$	2.14013	−	7.79819i	0.0836858	−	0.304933i
$655$	5.20661	−	25.2013i	0.203439	−	0.984695i
$656$	8.42758	−	14.5970i	0.329042	−	0.569917i
$657$	−21.8791	+	7.66503i	−0.853584	+	0.299041i
$658$	−10.3607	+	5.98177i	−0.403904	+	0.233194i
$659$	41.9142	−	15.2555i	1.63274	−	0.594270i	0.646996	−	0.762494i	$-0.276025\pi$
$659$	41.9142	−	15.2555i	1.63274	−	0.594270i	0.985749	+	0.168223i	$0.0538030\pi$
$660$	−11.8057	−	18.1927i	−0.459535	−	0.708151i
$661$	8.07733	−	6.77768i	0.314172	−	0.263621i	−0.472042	−	0.881576i	$-0.656483\pi$
$661$	8.07733	−	6.77768i	0.314172	−	0.263621i	0.786214	+	0.617955i	$0.212039\pi$
$662$	−0.676971	−	0.806782i	−0.0263112	−	0.0313565i
$663$	20.1093	−	1.63689i	0.780981	−	0.0635716i
$664$	7.60839	−	2.76923i	0.295263	−	0.107467i
$665$	−29.6361	+	15.9753i	−1.14924	+	0.619496i
$666$	2.34942	+	2.86969i	0.0910381	+	0.111198i
$667$	1.61841	+	0.934391i	0.0626652	+	0.0361798i
$668$	−28.7118	−	5.06267i	−1.11089	−	0.195881i
$669$	−38.4538	+	10.0549i	−1.48671	+	0.388744i
$670$	−2.41306	−	0.958963i	−0.0932247	−	0.0370480i
$671$	3.49309	+	19.8103i	0.134849	+	0.764768i
$672$	1.88788	−	20.1730i	0.0728264	−	0.778192i
$673$	−16.9132	+	20.1564i	−0.651957	+	0.776972i	−0.986208	−	0.165513i	$-0.947072\pi$
$673$	−16.9132	+	20.1564i	−0.651957	+	0.776972i	0.334251	+	0.942484i	$0.391517\pi$
$674$	−0.0461716			−0.00177846
$675$	−22.3594	+	13.2309i	−0.860613	+	0.509259i
$676$	−32.8548			−1.26365
$677$	−27.1278	+	32.3296i	−1.04260	+	1.24253i	−0.0731331	+	0.997322i	$0.523300\pi$
$677$	−27.1278	+	32.3296i	−1.04260	+	1.24253i	−0.969471	+	0.245205i	$0.921145\pi$
$678$	−6.73385	−	4.77602i	−0.258612	−	0.183422i
$679$	0.263647	+	1.49522i	0.0101179	+	0.0573812i
$680$	−5.23177	−	2.07913i	−0.200629	−	0.0797311i
$681$	8.69783	+	8.80364i	0.333301	+	0.337356i
$682$	−2.90102	−	0.511529i	−0.111086	−	0.0195875i
$683$	−16.0571	−	9.27055i	−0.614407	−	0.354728i	0.160281	−	0.987071i	$-0.448760\pi$
$683$	−16.0571	−	9.27055i	−0.614407	−	0.354728i	−0.774688	+	0.632343i	$0.782093\pi$
$684$	−22.0099	+	12.3550i	−0.841569	+	0.472406i
$685$	−24.0019	+	12.9382i	−0.917064	+	0.494343i
$686$	−2.28929	+	0.833234i	−0.0874056	+	0.0318130i
$687$	13.8669	−	29.2742i	0.529053	−	1.11688i
$688$	−0.234479	−	0.279441i	−0.00893942	−	0.0106536i
$689$	−48.7741	+	40.9263i	−1.85814	+	1.55917i
$690$	−2.48019	+	4.86354i	−0.0944192	+	0.185152i
$691$	−9.82430	+	3.57575i	−0.373734	+	0.136028i	−0.522056	−	0.852911i	$-0.674835\pi$
$691$	−9.82430	+	3.57575i	−0.373734	+	0.136028i	0.148322	+	0.988939i	$0.452613\pi$
$692$	−24.9846	+	14.4248i	−0.949770	+	0.548350i
$693$	15.3454	−	25.8519i	0.582922	−	0.982033i
$694$	3.15960	−	5.47259i	0.119937	−	0.207737i
$695$	−0.109489	+	0.529954i	−0.00415316	+	0.0201023i
$696$	0.583143	+	0.590238i	0.0221040	+	0.0223729i
$697$	3.53667	−	9.71691i	0.133961	−	0.368054i
$698$	−1.86099	+	0.328143i	−0.0704395	+	0.0124204i
$699$	24.6878	−	34.8080i	0.933778	−	1.31656i
$700$	22.3482	−	23.6770i	0.844684	−	0.894908i
$701$	−18.2363			−0.688774			−0.344387	−	0.938828i	$-0.611913\pi$
$701$	−18.2363			−0.688774			−0.344387	+	0.938828i	$0.611913\pi$
$702$	2.40014	−	8.34870i	0.0905873	−	0.315101i
$703$			17.9311i			0.676284i
$704$	13.1900	+	11.0677i	0.497116	+	0.417130i
$705$	−44.3007	−	5.45478i	−1.66846	−	0.205439i
$706$	0.316288	+	1.79376i	0.0119037	+	0.0675090i
$707$	7.45122	−	20.4721i	0.280232	−	0.769931i
$708$	−4.58888	−	17.5497i	−0.172461	−	0.659557i
$709$	−7.63846	+	43.3199i	−0.286869	+	1.62691i	0.411665	+	0.911335i	$0.364947\pi$
$709$	−7.63846	+	43.3199i	−0.286869	+	1.62691i	−0.698534	+	0.715577i	$0.746164\pi$
$710$	7.82042	+	4.82492i	0.293495	+	0.181076i
$711$	−6.97924	+	1.14379i	−0.261742	+	0.0428956i
$712$	−1.79204	+	1.03464i	−0.0671597	+	0.0387747i
$713$	−5.23175	−	14.3741i	−0.195931	−	0.538315i
$714$	−0.309082	−	3.79709i	−0.0115671	−	0.142102i
$715$	22.3794	+	28.3099i	0.836941	+	1.05873i
$716$	−2.32335	+	1.94952i	−0.0868277	+	0.0728571i
$717$	17.1453	+	24.8038i	0.640303	+	0.926316i
$718$	−0.0532155	−	0.146208i	−0.00198598	−	0.00545645i
$719$	21.3751	+	37.0227i	0.797155	+	1.38071i	0.921462	+	0.388469i	$0.126996\pi$
$719$	21.3751	+	37.0227i	0.797155	+	1.38071i	−0.124307	+	0.992244i	$0.539671\pi$
$720$	15.6122	−	17.1180i	0.581833	−	0.637950i
$721$	20.8328	−	36.0835i	0.775855	−	1.34382i
$722$	0.135988	+	0.0239784i	0.00506096	+	0.000892385i
$723$	12.1737	+	3.34094i	0.452744	+	0.124251i
$724$	−38.9887	−	14.1907i	−1.44900	−	0.527394i
$725$	0.233560	+	2.00216i	0.00867421	+	0.0743582i
$726$	0.523420	+	1.14043i	0.0194259	+	0.0423253i
$727$	−6.68922	+	7.97191i	−0.248090	+	0.295662i	−0.875690	−	0.482874i	$-0.839593\pi$
$727$	−6.68922	+	7.97191i	−0.248090	+	0.295662i	0.627600	+	0.778536i	$0.284037\pi$
$728$			22.3000i			0.826492i
$729$	−22.8777	−	14.3391i	−0.847322	−	0.531080i
$730$	−5.25233	−	0.153421i	−0.194398	−	0.00567836i
$731$	−0.171435	−	0.143851i	−0.00634076	−	0.00532053i
$732$	−20.5763	+	9.44387i	−0.760523	+	0.349055i
$733$	32.4643	−	5.72433i	1.19910	−	0.211433i	0.461788	−	0.886990i	$-0.347208\pi$
$733$	32.4643	−	5.72433i	1.19910	−	0.211433i	0.737308	+	0.675557i	$0.236097\pi$
$734$	5.86785	+	2.13572i	0.216586	+	0.0788310i
$735$	17.2323	+	5.27486i	0.635622	+	0.194566i
$736$	2.75835	−	15.6434i	0.101674	−	0.576622i
$737$	9.70829	+	5.60508i	0.357609	+	0.206466i
$738$	−3.37572	−	2.90284i	−0.124262	−	0.106855i
$739$	13.1005	+	22.6907i	0.481909	+	0.834690i	0.999784	−	0.0207656i	$-0.00661038\pi$
$739$	13.1005	+	22.6907i	0.481909	+	0.834690i	−0.517876	+	0.855456i	$0.673277\pi$
$740$	−5.45245	−	16.4608i	−0.200436	−	0.605110i
$741$	34.5487	−	23.8813i	1.26918	−	0.877301i
$742$	7.72780	+	9.20963i	0.283696	+	0.338096i
$743$	−10.4298	−	12.4297i	−0.382631	−	0.456002i	0.540012	−	0.841658i	$-0.318420\pi$
$743$	−10.4298	−	12.4297i	−0.382631	−	0.456002i	−0.922643	+	0.385655i	$0.873975\pi$
$744$	−0.551007	−	6.76916i	−0.0202009	−	0.248169i
$745$	26.9744	−	8.93495i	0.988264	−	0.327351i
$746$	−1.90770	−	3.30424i	−0.0698460	−	0.120977i
$747$	3.30601	+	20.1727i	0.120961	+	0.738081i
$748$	10.2752	+	5.93241i	0.375700	+	0.216910i
$749$	−1.00264	+	5.68627i	−0.0366358	+	0.207772i
$750$	−5.80568	+	0.985521i	−0.211993	+	0.0359861i
$751$	7.02136	+	2.55556i	0.256213	+	0.0932539i	0.466933	−	0.884292i	$-0.345359\pi$
$751$	7.02136	+	2.55556i	0.256213	+	0.0932539i	−0.210720	+	0.977546i	$0.567581\pi$
$752$	39.1986	−	6.91177i	1.42943	−	0.252046i
$753$	−3.68684	+	39.3959i	−0.134356	+	1.43567i
$754$	−0.516295	−	0.433223i	−0.0188023	−	0.0157770i
$755$	−9.82585	−	0.287014i	−0.357599	−	0.0104455i
$756$	32.5185	+	9.34862i	1.18269	+	0.340006i
$757$		−	25.7164i		−	0.934678i	−0.884078	−	0.467339i	$-0.845213\pi$
$757$		−	25.7164i		−	0.934678i	0.884078	−	0.467339i	$-0.154787\pi$
$758$	5.84279	−	6.96317i	0.212220	−	0.252914i
$759$	13.6354	−	19.2249i	0.494933	−	0.697820i
$760$	−11.5957	+	1.69718i	−0.420619	+	0.0615632i
$761$	19.3050	+	7.02645i	0.699807	+	0.254709i	0.667328	−	0.744764i	$-0.267438\pi$
$761$	19.3050	+	7.02645i	0.699807	+	0.254709i	0.0324783	+	0.999472i	$0.489660\pi$
$762$	4.84639	−	4.78814i	0.175566	−	0.173456i
$763$	−51.6141	−	9.10096i	−1.86856	−	0.329477i
$764$	7.51544	−	13.0171i	0.271899	−	0.470943i
$765$	7.60887	−	12.0054i	0.275099	−	0.434057i
$766$	3.31440	+	5.74070i	0.119754	+	0.207420i
$767$	10.3235	+	28.3635i	0.372758	+	1.02414i
$768$	−6.75058	+	14.2511i	−0.243591	+	0.514241i
$769$	−1.56802	+	1.31573i	−0.0565444	+	0.0474464i	−0.670622	−	0.741799i	$-0.733973\pi$
$769$	−1.56802	+	1.31573i	−0.0565444	+	0.0474464i	0.614077	+	0.789246i	$0.289528\pi$
$770$	5.34554	−	4.22572i	0.192640	−	0.152284i
$771$	−2.30326	−	1.09103i	−0.0829497	−	0.0392924i
$772$	−11.6490	−	32.0054i	−0.419257	−	1.15190i
$773$	20.3868	−	11.7703i	0.733262	−	0.423349i	−0.0863523	−	0.996265i	$-0.527521\pi$
$773$	20.3868	−	11.7703i	0.733262	−	0.423349i	0.819614	+	0.572916i	$0.194188\pi$
$774$	−0.0840229	+	0.0471653i	−0.00302014	+	0.00169532i
$775$	9.06972	−	13.7831i	0.325794	−	0.495102i
$776$	−0.0917721	+	0.520465i	−0.00329442	+	0.0186836i
$777$	17.0993	−	16.8938i	0.613434	−	0.606061i
$778$	1.08321	−	2.97609i	0.0388349	−	0.106698i
$779$	−3.73785	−	21.1984i	−0.133922	−	0.759512i
$780$	−24.4540	+	32.4286i	−0.875595	+	1.16113i
$781$	−30.3898	−	25.5001i	−1.08743	−	0.912464i
$782$		−	2.98675i		−	0.106806i
$783$	−1.73748	+	1.17021i	−0.0620924	+	0.0418201i
$784$	−16.0706			−0.573951
$785$	−7.34654	+	8.25337i	−0.262209	+	0.294575i
$786$	6.03514	+	0.564793i	0.215266	+	0.0201455i
$787$	−23.3076	+	4.10976i	−0.830826	+	0.146497i	−0.572856	−	0.819656i	$-0.694165\pi$
$787$	−23.3076	+	4.10976i	−0.830826	+	0.146497i	−0.257970	+	0.966153i	$0.583053\pi$
$788$	−6.20745	+	17.0548i	−0.221131	+	0.607553i
$789$	−36.2070	+	9.46740i	−1.28900	+	0.337048i
$790$	−1.56985	−	0.324332i	−0.0558526	−	0.0115392i
$791$	−26.7531	+	46.3377i	−0.951230	+	1.64758i
$792$	8.09711	−	6.62910i	0.287718	−	0.235555i
$793$	32.6250	−	18.8361i	1.15855	−	0.668888i
$794$	6.24481	−	2.27292i	0.221620	−	0.0806631i
$795$	2.33223	+	44.7938i	0.0827156	+	1.58867i
$796$	15.9838	−	13.4120i	0.566531	−	0.475376i
$797$	18.5974	+	22.1635i	0.658755	+	0.785073i	0.987206	−	0.159448i	$-0.0509713\pi$
$797$	18.5974	+	22.1635i	0.658755	+	0.785073i	−0.328452	+	0.944521i	$0.606527\pi$
$798$	−4.50932	−	6.52357i	−0.159628	−	0.230932i
$799$	22.9464	−	8.35181i	0.811785	−	0.295466i
$800$	15.3130	−	7.68616i	0.541397	−	0.271747i
$801$	−1.72734	−	4.93052i	−0.0610325	−	0.174211i
$802$	5.30866	+	3.06496i	0.187455	+	0.108227i
$803$	22.3404	+	3.93922i	0.788377	+	0.139012i
$804$	−3.33909	+	12.1669i	−0.117761	+	0.429095i
$805$	32.8822	+	13.0676i	1.15895	+	0.460571i
$806$	0.957968	+	5.43290i	0.0337430	+	0.191366i
$807$	−20.9935	+	9.63533i	−0.739005	+	0.339180i
$808$	4.87450	−	5.80920i	0.171484	−	0.204367i
$809$	50.0898			1.76106			0.880532	−	0.473986i	$-0.157185\pi$
$809$	50.0898			1.76106			0.880532	+	0.473986i	$0.157185\pi$
$810$	−3.67794	−	4.89122i	−0.129230	−	0.171860i
$811$	−22.3607			−0.785192			−0.392596	−	0.919711i	$-0.628423\pi$
$811$	−22.3607			−0.785192			−0.392596	+	0.919711i	$0.628423\pi$
$812$	1.68742	−	2.01099i	0.0592168	−	0.0705718i
$813$	−31.0603	+	14.2557i	−1.08933	+	0.499968i
$814$	−0.630190	−	3.57398i	−0.0220881	−	0.125268i
$815$	0.111013	−	0.279344i	0.00388861	−	0.00978499i
$816$	−3.35446	+	12.2229i	−0.117430	+	0.427888i
$817$	−0.458782	−	0.0808957i	−0.0160508	−	0.00283018i
$818$	3.55405	+	2.05193i	0.124264	+	0.0717441i
$819$	−55.3235	−	10.4463i	−1.93316	−	0.365023i
$820$	9.87732	+	18.3236i	0.344931	+	0.639887i
$821$	−12.3587	+	4.49819i	−0.431321	+	0.156988i	−0.548552	−	0.836117i	$-0.684821\pi$
$821$	−12.3587	+	4.49819i	−0.431321	+	0.156988i	0.117230	+	0.993105i	$0.462598\pi$
$822$	−3.65204	−	5.28335i	−0.127380	−	0.184278i
$823$	14.5049	+	17.2863i	0.505611	+	0.602563i	0.957116	−	0.289705i	$-0.0935573\pi$
$823$	14.5049	+	17.2863i	0.505611	+	0.602563i	−0.451505	+	0.892268i	$0.649113\pi$
$824$	11.1101	−	9.32250i	0.387040	−	0.324765i
$825$	25.4162	−	0.580025i	0.884880	−	0.0201939i
$826$	5.35565	−	1.94930i	0.186347	−	0.0678247i
$827$	−3.32717	+	1.92094i	−0.115697	+	0.0667978i	−0.556732	−	0.830692i	$-0.687945\pi$
$827$	−3.32717	+	1.92094i	−0.115697	+	0.0667978i	0.441035	+	0.897490i	$0.354612\pi$
$828$	24.8157	+	9.37350i	0.862404	+	0.325752i
$829$	22.2051	−	38.4603i	0.771214	−	1.33578i	−0.165685	−	0.986179i	$-0.552983\pi$
$829$	22.2051	−	38.4603i	0.771214	−	1.33578i	0.936898	−	0.349602i	$-0.113683\pi$
$830$	−0.937445	+	4.53746i	−0.0325392	+	0.157498i
$831$	−44.4304	+	11.6176i	−1.54127	+	0.403011i
$832$	11.0287	−	30.3010i	0.382350	−	1.05050i
$833$	−9.70943	+	1.71203i	−0.336412	+	0.0593185i
$834$	−0.126912	−	0.0118769i	−0.00439460	−	0.000411265i
$835$	22.7231	−	25.5279i	0.786365	−	0.883430i
$836$	24.6985			0.854214
$837$	17.0516	+	1.80399i	0.589389	+	0.0623551i
$838$			0.620768i			0.0214441i
$839$	−5.58926	−	4.68995i	−0.192963	−	0.161915i	0.541188	−	0.840902i	$-0.317975\pi$
$839$	−5.58926	−	4.68995i	−0.192963	−	0.161915i	−0.734150	+	0.678987i	$0.762419\pi$
$840$	12.5433	+	9.45877i	0.432785	+	0.326359i
$841$	−5.00757	−	28.3994i	−0.172675	−	0.979289i
$842$	0.286147	−	0.786181i	0.00986126	−	0.0270936i
$843$	8.04872	−	7.95198i	0.277213	−	0.273881i
$844$	−3.37948	+	19.1660i	−0.116327	+	0.659721i
$845$	20.2224	−	32.7772i	0.695672	−	1.12757i
$846$	0.127127	−	10.5130i	0.00437073	−	0.361446i
$847$	7.04308	−	4.06633i	0.242003	−	0.139721i
$848$	−13.6804	−	37.5866i	−0.469787	−	1.29073i
$849$	10.0563	+	4.76355i	0.345130	+	0.163485i
$850$	2.58456	−	1.92323i	0.0886497	−	0.0659661i
$851$	14.4361	−	12.1134i	0.494864	−	0.415240i
$852$	19.1138	−	40.3509i	0.654827	−	1.38240i
$853$	18.7864	+	51.6153i	0.643235	+	1.76727i	0.641317	+	0.767276i	$0.278388\pi$
$853$	18.7864	+	51.6153i	0.643235	+	1.76727i	0.00191802	+	0.999998i	$0.499389\pi$
$854$	−3.55667	−	6.16033i	−0.121707	−	0.210802i
$855$	1.22143	−	29.5625i	0.0417722	−	1.01102i
$856$	−1.00492	+	1.74058i	−0.0343476	+	0.0594917i
$857$	8.75197	+	1.54321i	0.298961	+	0.0527150i	0.321117	−	0.947040i	$-0.395942\pi$
$857$	8.75197	+	1.54321i	0.298961	+	0.0527150i	−0.0221554	+	0.999755i	$0.507053\pi$
$858$	−6.04686	+	5.97418i	−0.206436	+	0.203955i
$859$	4.71452	+	1.71594i	0.160857	+	0.0585473i	0.421194	−	0.906971i	$-0.361611\pi$
$859$	4.71452	+	1.71594i	0.160857	+	0.0585473i	−0.260336	+	0.965518i	$0.583833\pi$
$860$	0.445762	−	0.0652431i	0.0152003	−	0.00222477i
$861$	−16.6934	+	23.5365i	−0.568910	+	0.802123i
$862$	−3.92787	+	4.68106i	−0.133784	+	0.159437i
$863$		−	15.4472i		−	0.525828i	−0.964819	−	0.262914i	$-0.915316\pi$
$863$		−	15.4472i		−	0.525828i	0.964819	−	0.262914i	$-0.0846836\pi$
$864$	14.3981	+	10.4759i	0.489834	+	0.356398i
$865$	0.987421	−	33.8041i	0.0335733	−	1.14938i
$866$	2.76310	+	2.31851i	0.0938939	+	0.0787863i
$867$	2.01904	−	21.5746i	0.0685703	−	0.732713i
$868$	−21.1614	+	3.73132i	−0.718264	+	0.126649i
$869$	6.50312	+	2.36694i	0.220603	+	0.0802930i
$870$	−0.462672	+	0.106650i	−0.0156860	+	0.00361577i
$871$	3.64555	−	20.6749i	0.123525	−	0.700544i
$872$	−15.7992	−	9.12165i	−0.535027	−	0.308898i
$873$	−1.24822	−	0.471485i	−0.0422459	−	0.0159573i
$874$	−3.10869	−	5.38441i	−0.105153	−	0.182130i
$875$	9.86559	+	36.8689i	0.333518	+	1.24639i
$876$	2.07141	+	25.4474i	0.0699865	+	0.859789i
$877$	−7.74532	−	9.23051i	−0.261541	−	0.311692i	0.619254	−	0.785191i	$-0.287435\pi$
$877$	−7.74532	−	9.23051i	−0.261541	−	0.311692i	−0.880794	+	0.473499i	$0.842991\pi$
$878$	7.32037	+	8.72408i	0.247051	+	0.294423i
$879$	−19.9336	+	13.7788i	−0.672344	+	0.464748i
$880$	−21.5208	+	7.12853i	−0.725467	+	0.240303i
$881$	17.1975	+	29.7869i	0.579398	+	1.00355i	0.995548	+	0.0942507i	$0.0300455\pi$
$881$	17.1975	+	29.7869i	0.579398	+	1.00355i	−0.416151	+	0.909296i	$0.636621\pi$
$882$	−0.787623	+	4.17125i	−0.0265207	+	0.140453i
$883$	23.5099	+	13.5734i	0.791171	+	0.456783i	0.840375	−	0.542006i	$-0.182335\pi$
$883$	23.5099	+	13.5734i	0.791171	+	0.456783i	−0.0492038	+	0.998789i	$0.515668\pi$
$884$	3.85844	−	21.8823i	0.129773	−	0.735982i
$885$	20.3327	+	6.22392i	0.683477	+	0.209215i
$886$	−4.24208	−	1.54399i	−0.142516	−	0.0518714i
$887$	−48.5493	+	8.56056i	−1.63013	+	0.287435i	−0.912526	−	0.409019i	$-0.865871\pi$
$887$	−48.5493	+	8.56056i	−1.63013	+	0.287435i	−0.717601	+	0.696454i	$0.754760\pi$
$888$	7.60432	−	3.49014i	0.255184	−	0.117121i
$889$	−33.8246	−	28.3822i	−1.13444	−	0.951908i
$890$	0.0345739	−	1.18363i	0.00115892	−	0.0396754i
$891$	12.6530	+	23.1933i	0.423890	+	0.777005i
$892$			43.7735i			1.46564i
$893$	32.6742	−	38.9396i	1.09340	−	1.30306i
$894$	2.79198	+	6.08317i	0.0933777	+	0.203452i
$895$	−0.514877	−	3.51781i	−0.0172105	−	0.117587i
$896$	−27.7062	−	10.0842i	−0.925598	−	0.336890i
$897$	−42.5660	−	11.6818i	−1.42124	−	0.390044i
$898$	5.31139	+	0.936541i	0.177243	+	0.0312528i
$899$	0.665171	−	1.15211i	0.0221847	−	0.0384250i
$900$	7.86803	+	27.5099i	0.262268	+	0.916996i
$901$	−12.2695	−	21.2514i	−0.408756	−	0.707987i
$902$	1.49004	+	4.09385i	0.0496129	+	0.136310i
$903$	0.355098	+	0.513716i	0.0118169	+	0.0170954i
$904$	−14.2674	+	11.9718i	−0.474526	+	0.398175i
$905$	38.1551	−	30.1621i	1.26832	−	1.00262i
$906$	−0.187856	−	2.30783i	−0.00624111	−	0.0766724i
$907$	4.60719	+	12.6581i	0.152979	+	0.420307i	0.992381	−	0.123204i	$-0.0393170\pi$
$907$	4.60719	+	12.6581i	0.152979	+	0.420307i	−0.839402	+	0.543511i	$0.817095\pi$
$908$	11.8034	−	6.81471i	0.391711	−	0.226154i
$909$	12.1285	+	14.8143i	0.402277	+	0.491360i
$910$	−10.8604	−	6.70049i	−0.360019	−	0.222119i
$911$	−4.06209	+	23.0373i	−0.134583	+	0.763259i	0.840566	+	0.541709i	$0.182223\pi$
$911$	−4.06209	+	23.0373i	−0.134583	+	0.763259i	−0.975149	+	0.221550i	$0.928888\pi$
$912$	6.67467	+	25.5265i	0.221020	+	0.845268i
$913$	6.84138	−	18.7965i	0.226417	−	0.622075i
$914$	−0.775793	−	4.39974i	−0.0256609	−	0.145530i
$915$	3.24332	−	26.3405i	0.107221	−	0.870790i
$916$	−27.3279	−	22.9309i	−0.902941	−	0.757657i
$917$		−	39.2858i		−	1.29733i
$918$	3.00815	+	1.46972i	0.0992838	+	0.0485081i
$919$	6.93563			0.228785			0.114393	−	0.993436i	$-0.463508\pi$
$919$	6.93563			0.228785			0.114393	+	0.993436i	$0.463508\pi$
$920$	9.19984	+	8.18903i	0.303310	+	0.269984i
$921$	15.8850	−	22.3967i	0.523428	−	0.737996i
$922$	−4.30436	+	0.758974i	−0.141756	+	0.0249955i
$923$	−25.4101	+	69.8136i	−0.836383	+	2.29794i
$924$	−23.2697	−	23.5527i	−0.765515	−	0.774828i
$925$	19.7779	+	4.69217i	0.650294	+	0.154278i
$926$	−1.23660	+	2.14186i	−0.0406372	+	0.0703857i
$927$	17.9235	+	31.9300i	0.588686	+	1.04872i
$928$	1.19640	−	0.690742i	0.0392738	−	0.0226747i
$929$	−11.5336	+	4.19788i	−0.378404	+	0.137728i	−0.524218	−	0.851584i	$-0.675642\pi$
$929$	−11.5336	+	4.19788i	−0.378404	+	0.137728i	0.145814	+	0.989312i	$0.453420\pi$
$930$	3.46224	+	1.76559i	0.113531	+	0.0578959i
$931$	−15.7219	+	13.1922i	−0.515265	+	0.432358i
$932$	−30.2094	−	36.0022i	−0.989543	−	1.17929i
$933$	−11.6075	+	24.5046i	−0.380014	+	0.802243i
$934$	−6.16140	+	2.24257i	−0.201607	+	0.0733790i
$935$	−12.2429	+	6.59952i	−0.400385	+	0.215827i
$936$	−16.8523	−	10.0033i	−0.550836	−	0.326969i
$937$	−21.4835	−	12.4035i	−0.701836	−	0.405205i	0.106195	−	0.994345i	$-0.466133\pi$
$937$	−21.4835	−	12.4035i	−0.701836	−	0.405205i	−0.808031	+	0.589140i	$0.799467\pi$
$938$	−3.90389	−	0.688361i	−0.127466	−	0.0224758i
$939$	−1.23583	−	1.25086i	−0.0403297	−	0.0408203i
$940$	−18.1543	+	45.6822i	−0.592129	+	1.48999i
$941$	9.97338	+	56.5618i	0.325123	+	1.84386i	0.508811	+	0.860878i	$0.330085\pi$
$941$	9.97338	+	56.5618i	0.325123	+	1.84386i	−0.183688	+	0.982985i	$0.558804\pi$
$942$	−2.12293	−	1.50570i	−0.0691688	−	0.0490584i
$943$	−14.5415	+	17.3299i	−0.473537	+	0.564339i
$944$	−18.9621			−0.617162
$945$	−29.3419	+	26.6875i	−0.954493	+	0.868146i
$946$	0.0942865			0.00306552
$947$	2.64449	−	3.15158i	0.0859344	−	0.102413i	−0.721364	−	0.692556i	$-0.756484\pi$
$947$	2.64449	−	3.15158i	0.0859344	−	0.102413i	0.807298	+	0.590144i	$0.200929\pi$
$948$	−0.725742	+	7.75497i	−0.0235710	+	0.251870i
$949$	−7.37719	−	41.8381i	−0.239474	−	1.35812i
$950$	2.65761	−	6.15721i	0.0862243	−	0.199766i
$951$	19.3459	−	5.05855i	0.627333	−	0.164035i
$952$	−8.46404	−	1.49244i	−0.274321	−	0.0483702i
$953$	9.44189	+	5.45128i	0.305853	+	0.176584i	0.645069	−	0.764124i	$-0.276829\pi$
$953$	9.44189	+	5.45128i	0.305853	+	0.176584i	−0.339216	+	0.940708i	$0.610162\pi$
$954$	−10.4264	+	1.70873i	−0.337566	+	0.0553220i
$955$	8.36057	+	15.5098i	0.270542	+	0.501887i
$956$	31.2050	−	11.3577i	1.00924	−	0.367334i
$957$	2.04307	−	0.166305i	0.0660431	−	0.00537588i
$958$	−6.88676	−	8.20732i	−0.222501	−	0.265166i
$959$	−31.8880	+	26.7572i	−1.02972	+	0.864035i
$960$	−12.3658	−	19.0559i	−0.399105	−	0.615027i
$961$	18.8979	−	6.87826i	0.609609	−	0.221879i
$962$	−5.88589	+	3.39822i	−0.189769	+	0.109563i
$963$	−3.84741	−	3.30846i	−0.123981	−	0.106614i
$964$	6.95136	−	12.0401i	0.223888	−	0.387786i
$965$	39.0999	+	8.07808i	1.25867	+	0.260043i
$966$	−2.20578	+	8.03740i	−0.0709699	+	0.258599i
$967$	−12.2571	+	33.6762i	−0.394163	+	1.08295i	0.570920	+	0.821006i	$0.306587\pi$
$967$	−12.2571	+	33.6762i	−0.394163	+	1.08295i	−0.965082	+	0.261947i	$0.915635\pi$
$968$	2.78786	−	0.491574i	0.0896051	−	0.0157998i
$969$	6.75204	+	14.7114i	0.216907	+	0.472597i
$970$	−0.225899	−	0.201079i	−0.00725319	−	0.00645626i
$971$	28.9416			0.928779			0.464390	−	0.885631i	$-0.346274\pi$
$971$	28.9416			0.928779			0.464390	+	0.885631i	$0.346274\pi$
$972$	−21.6520	+	20.3810i	−0.694489	+	0.653721i
$973$			0.826134i			0.0264847i
$974$	5.11291	+	4.29024i	0.163828	+	0.137468i
$975$	−17.3003	−	44.3563i	−0.554054	−	1.42054i
$976$	4.10963	+	23.3069i	0.131546	+	0.746035i
$977$	−8.34110	+	22.9170i	−0.266855	+	0.733179i	0.731809	+	0.681510i	$0.238676\pi$
$977$	−8.34110	+	22.9170i	−0.266855	+	0.733179i	−0.998664	+	0.0516691i	$0.983546\pi$
$978$	0.0682801	+	0.0187388i	0.00218336	+	0.000599200i
$979$	−0.887716	+	5.03448i	−0.0283715	+	0.160903i
$980$	10.4213	−	16.8912i	0.332896	−	0.539570i
$981$	30.0308	−	34.9228i	0.958808	−	1.11500i
$982$	5.40679	−	3.12161i	0.172538	−	0.0996147i
$983$	0.899750	+	2.47204i	0.0286976	+	0.0788460i	0.953214	−	0.302296i	$-0.0977531\pi$
$983$	0.899750	+	2.47204i	0.0286976	+	0.0788460i	−0.924517	+	0.381142i	$0.875531\pi$
$984$	−8.26240	+	5.71126i	−0.263396	+	0.182068i
$985$	−13.1938	−	16.6902i	−0.420390	−	0.531793i
$986$	0.198985	−	0.166968i	0.00633696	−	0.00531734i
$987$	−67.9173	+	5.52844i	−2.16183	+	0.175972i
$988$	−15.8199	−	43.4647i	−0.503297	−	1.38280i
$989$	0.244802	+	0.424010i	0.00778426	+	0.0134827i
$990$	0.795524	+	5.93526i	0.0252834	+	0.188635i
$991$	9.51245	−	16.4761i	0.302173	−	0.523379i	−0.674455	−	0.738316i	$-0.735621\pi$
$991$	9.51245	−	16.4761i	0.302173	−	0.523379i	0.976628	+	0.214937i	$0.0689546\pi$
$992$	−11.1361	−	1.96360i	−0.353572	−	0.0623444i
$993$	−1.51752	−	5.80358i	−0.0481569	−	0.184171i
$994$	13.1824	+	4.79799i	0.418119	+	0.152183i
$995$	3.54217	+	24.2013i	0.112294	+	0.767232i
$996$	22.4149	+	2.09768i	0.710243	+	0.0664674i
$997$	10.8627	−	12.9456i	0.344025	−	0.409993i	−0.566094	−	0.824341i	$-0.691546\pi$
$997$	10.8627	−	12.9456i	0.344025	−	0.409993i	0.910118	+	0.414348i	$0.135990\pi$
$998$		−	7.77169i		−	0.246009i
$999$	5.09641	+	20.5003i	0.161243	+	0.648602i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.p.a.124.7	yes	96
3.2	odd	2		405.2.p.a.289.10		96
5.2	odd	4		675.2.l.h.151.7		96
5.3	odd	4		675.2.l.h.151.10		96
5.4	even	2	inner	135.2.p.a.124.10	yes	96
15.14	odd	2		405.2.p.a.289.7		96
27.5	odd	18		405.2.p.a.199.7		96
27.22	even	9	inner	135.2.p.a.49.10	yes	96
135.22	odd	36		675.2.l.h.76.7		96
135.49	even	18	inner	135.2.p.a.49.7	✓	96
135.59	odd	18		405.2.p.a.199.10		96
135.103	odd	36		675.2.l.h.76.10		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.p.a.49.7	✓	96	135.49	even	18	inner
135.2.p.a.49.10	yes	96	27.22	even	9	inner
135.2.p.a.124.7	yes	96	1.1	even	1	trivial
135.2.p.a.124.10	yes	96	5.4	even	2	inner
405.2.p.a.199.7		96	27.5	odd	18
405.2.p.a.199.10		96	135.59	odd	18
405.2.p.a.289.7		96	15.14	odd	2
405.2.p.a.289.10		96	3.2	odd	2
675.2.l.h.76.7		96	135.22	odd	36
675.2.l.h.76.10		96	135.103	odd	36
675.2.l.h.151.7		96	5.2	odd	4
675.2.l.h.151.10		96	5.3	odd	4

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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	135.p (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.195467 + 0.232949i) q^{2} +(-1.57417 + 0.722492i) q^{3} +(0.331239 + 1.87855i) q^{4} +(-2.07799 - 0.825805i) q^{5} +(0.139394 - 0.507924i) q^{6} +(-3.36181 - 0.592777i) q^{7} +(-1.02906 - 0.594126i) q^{8} +(1.95601 - 2.27465i) q^{9} +O(q^{10})\)	\(q+(-0.195467 + 0.232949i) q^{2} +(-1.57417 + 0.722492i) q^{3} +(0.331239 + 1.87855i) q^{4} +(-2.07799 - 0.825805i) q^{5} +(0.139394 - 0.507924i) q^{6} +(-3.36181 - 0.592777i) q^{7} +(-1.02906 - 0.594126i) q^{8} +(1.95601 - 2.27465i) q^{9} +(0.598549 - 0.322648i) q^{10} +(-2.75854 + 1.00403i) q^{11} +(-1.87866 - 2.71783i) q^{12} +(3.53380 + 4.21142i) q^{13} +(0.795210 - 0.667260i) q^{14} +(3.86774 - 0.201377i) q^{15} +(-3.24543 + 1.18124i) q^{16} +(-1.83496 + 1.05942i) q^{17} +(0.147541 + 0.900269i) q^{18} +(-2.20534 + 3.81976i) q^{19} +(0.863003 - 4.17714i) q^{20} +(5.72033 - 1.49575i) q^{21} +(0.305317 - 0.838853i) q^{22} +(4.56507 - 0.804944i) q^{23} +(2.04916 + 0.191769i) q^{24} +(3.63609 + 3.43203i) q^{25} -1.67179 q^{26} +(-1.43567 + 4.99388i) q^{27} -6.51167i q^{28} +(0.308828 + 0.259138i) q^{29} +(-0.709106 + 0.940348i) q^{30} +(-0.573021 - 3.24976i) q^{31} +(1.17202 - 3.22009i) q^{32} +(3.61701 - 3.57353i) q^{33} +(0.111885 - 0.634533i) q^{34} +(6.49629 + 4.00798i) q^{35} +(4.92094 + 2.92101i) q^{36} +(3.52072 - 2.03269i) q^{37} +(-0.458737 - 1.26037i) q^{38} +(-8.60551 - 4.07634i) q^{39} +(1.64774 + 2.08439i) q^{40} +(-3.73852 + 3.13699i) q^{41} +(-0.769703 + 1.62491i) q^{42} +(0.0361245 + 0.0992511i) q^{43} +(-2.79985 - 4.84948i) q^{44} +(-5.94299 + 3.11142i) q^{45} +(-0.704810 + 1.22077i) q^{46} +(-11.3497 - 2.00126i) q^{47} +(4.25542 - 4.20427i) q^{48} +(4.37252 + 1.59147i) q^{49} +(-1.51022 + 0.176174i) q^{50} +(2.12312 - 2.99344i) q^{51} +(-6.74082 + 8.03340i) q^{52} +11.5814i q^{53} +(-0.882691 - 1.31058i) q^{54} +(6.56135 + 0.191657i) q^{55} +(3.10730 + 2.60734i) q^{56} +(0.711828 - 7.60629i) q^{57} +(-0.120732 + 0.0212882i) q^{58} +(5.15923 + 1.87781i) q^{59} +(1.65944 + 7.19904i) q^{60} +(1.18992 - 6.74834i) q^{61} +(0.869034 + 0.501737i) q^{62} +(-7.92409 + 6.48745i) q^{63} +(-2.93269 - 5.07957i) q^{64} +(-3.86539 - 11.6695i) q^{65} +(0.125444 + 1.54108i) q^{66} +(-2.45463 - 2.92531i) q^{67} +(-2.59797 - 3.09614i) q^{68} +(-6.60462 + 4.56534i) q^{69} +(-2.20346 + 0.729873i) q^{70} +(6.75694 + 11.7034i) q^{71} +(-3.36427 + 1.17862i) q^{72} +(-6.69232 - 3.86382i) q^{73} +(-0.214673 + 1.21747i) q^{74} +(-8.20344 - 2.77554i) q^{75} +(-7.90610 - 2.87758i) q^{76} +(9.86885 - 1.74014i) q^{77} +(2.63167 - 1.20785i) q^{78} +(-1.80591 - 1.51534i) q^{79} +(7.71945 + 0.225486i) q^{80} +(-1.34805 - 8.89847i) q^{81} -1.48406i q^{82} +(-4.37992 + 5.21978i) q^{83} +(4.70463 + 10.2505i) q^{84} +(4.68790 - 0.686136i) q^{85} +(-0.0301816 - 0.0109852i) q^{86} +(-0.673373 - 0.184800i) q^{87} +(3.43521 + 0.605720i) q^{88} +(0.870723 - 1.50814i) q^{89} +(0.436858 - 1.99259i) q^{90} +(-9.38352 - 16.2527i) q^{91} +(3.02425 + 8.30907i) q^{92} +(3.24996 + 4.70167i) q^{93} +(2.68468 - 2.25271i) q^{94} +(7.73705 - 6.11625i) q^{95} +(0.481539 + 5.91574i) q^{96} +(-0.152119 - 0.417944i) q^{97} +(-1.22541 + 0.707493i) q^{98} +(-3.11193 + 8.23860i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 12 q^{4} - 9 q^{5} - 6 q^{6} - 18 q^{9}+O(q^{10}) \) 96 * q - 12 * q^4 - 9 * q^5 - 6 * q^6 - 18 * q^9	\( 96 q - 12 q^{4} - 9 q^{5} - 6 q^{6} - 18 q^{9} - 3 q^{10} - 6 q^{11} - 18 q^{14} - 21 q^{15} - 24 q^{16} - 6 q^{19} - 57 q^{20} + 24 q^{21} - 30 q^{24} + 3 q^{25} + 48 q^{26} - 30 q^{29} - 51 q^{30} - 30 q^{31} - 24 q^{34} - 12 q^{35} + 54 q^{36} - 6 q^{39} - 9 q^{40} - 12 q^{41} + 78 q^{44} + 45 q^{45} - 6 q^{46} - 30 q^{49} + 84 q^{50} - 90 q^{51} + 108 q^{54} - 12 q^{55} - 96 q^{56} + 66 q^{59} + 84 q^{60} + 6 q^{61} + 45 q^{65} - 150 q^{66} + 24 q^{69} - 33 q^{70} - 90 q^{71} + 66 q^{74} + 39 q^{75} + 12 q^{76} + 24 q^{79} + 30 q^{80} - 54 q^{81} + 198 q^{84} - 21 q^{85} + 18 q^{86} + 96 q^{89} + 90 q^{90} - 6 q^{91} + 24 q^{94} + 87 q^{95} + 42 q^{96} + 36 q^{99}+O(q^{100}) \) 96 * q - 12 * q^4 - 9 * q^5 - 6 * q^6 - 18 * q^9 - 3 * q^10 - 6 * q^11 - 18 * q^14 - 21 * q^15 - 24 * q^16 - 6 * q^19 - 57 * q^20 + 24 * q^21 - 30 * q^24 + 3 * q^25 + 48 * q^26 - 30 * q^29 - 51 * q^30 - 30 * q^31 - 24 * q^34 - 12 * q^35 + 54 * q^36 - 6 * q^39 - 9 * q^40 - 12 * q^41 + 78 * q^44 + 45 * q^45 - 6 * q^46 - 30 * q^49 + 84 * q^50 - 90 * q^51 + 108 * q^54 - 12 * q^55 - 96 * q^56 + 66 * q^59 + 84 * q^60 + 6 * q^61 + 45 * q^65 - 150 * q^66 + 24 * q^69 - 33 * q^70 - 90 * q^71 + 66 * q^74 + 39 * q^75 + 12 * q^76 + 24 * q^79 + 30 * q^80 - 54 * q^81 + 198 * q^84 - 21 * q^85 + 18 * q^86 + 96 * q^89 + 90 * q^90 - 6 * q^91 + 24 * q^94 + 87 * q^95 + 42 * q^96 + 36 * q^99

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