LMFDB - Embedded newform 429.2.bi.a.5.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(5,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 8, 15]))

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

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

chi := DirichletCharacter("429.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bi (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$416$
Relative dimension:	$52$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			5.15
Character	$\chi$	$=$	429.5
Dual form			429.2.bi.a.86.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.667273 + 1.30960i) q^{2} +(0.852386 + 1.50779i) q^{3} +(-0.0942200 - 0.129683i) q^{4} +(3.33356 - 1.69853i) q^{5} +(-2.54337 + 0.110172i) q^{6} +(0.619167 + 0.0980665i) q^{7} +(-2.67070 + 0.422997i) q^{8} +(-1.54688 + 2.57044i) q^{9} +O(q^{10})$	\(q+(-0.667273 + 1.30960i) q^{2} +(0.852386 + 1.50779i) q^{3} +(-0.0942200 - 0.129683i) q^{4} +(3.33356 - 1.69853i) q^{5} +(-2.54337 + 0.110172i) q^{6} +(0.619167 + 0.0980665i) q^{7} +(-2.67070 + 0.422997i) q^{8} +(-1.54688 + 2.57044i) q^{9} +5.49900i q^{10} +(-1.36709 - 3.02177i) q^{11} +(0.115223 - 0.252604i) q^{12} +(2.83576 + 2.22676i) q^{13} +(-0.541581 + 0.745422i) q^{14} +(5.40251 + 3.57851i) q^{15} +(1.32720 - 4.08469i) q^{16} +(-2.16943 + 6.67683i) q^{17} +(-2.33405 - 3.74097i) q^{18} +(-2.10072 + 0.332722i) q^{19} +(-0.534358 - 0.272269i) q^{20} +(0.379905 + 1.01717i) q^{21} +(4.86952 + 0.226011i) q^{22} +6.92972 q^{23} +(-2.91425 - 3.66630i) q^{24} +(5.28866 - 7.27922i) q^{25} +(-4.80838 + 2.22785i) q^{26} +(-5.19423 - 0.141363i) q^{27} +(-0.0456204 - 0.0895351i) q^{28} +(2.46387 + 3.39123i) q^{29} +(-8.29135 + 4.68727i) q^{30} +(-0.368539 - 0.187780i) q^{31} +(0.639682 + 0.639682i) q^{32} +(3.39091 - 4.63699i) q^{33} +(-7.29635 - 7.29635i) q^{34} +(2.23060 - 0.724765i) q^{35} +(0.479089 - 0.0415838i) q^{36} +(-5.12330 - 0.811450i) q^{37} +(0.966023 - 2.97311i) q^{38} +(-0.940324 + 6.17380i) q^{39} +(-8.18444 + 5.94634i) q^{40} +(-1.50210 - 9.48391i) q^{41} +(-1.58558 - 0.181205i) q^{42} -5.83274i q^{43} +(-0.263064 + 0.461998i) q^{44} +(-0.790626 + 11.1961i) q^{45} +(-4.62402 + 9.07514i) q^{46} +(-1.75352 + 0.277730i) q^{47} +(7.29015 - 1.48059i) q^{48} +(-6.28364 - 2.04168i) q^{49} +(6.00386 + 11.7832i) q^{50} +(-11.9165 + 2.42018i) q^{51} +(0.0215863 - 0.577555i) q^{52} +(0.0586559 - 0.0190585i) q^{53} +(3.65110 - 6.70802i) q^{54} +(-9.68983 - 7.75119i) q^{55} -1.69509 q^{56} +(-2.29230 - 2.88385i) q^{57} +(-6.08521 + 0.963803i) q^{58} +(0.0323136 - 0.204020i) q^{59} +(-0.0449539 - 1.03778i) q^{60} +(-0.797652 + 2.45492i) q^{61} +(0.491833 - 0.357337i) q^{62} +(-1.20985 + 1.43984i) q^{63} +(6.90481 - 2.24351i) q^{64} +(13.2354 + 2.60639i) q^{65} +(3.80993 + 7.53487i) q^{66} +(10.8778 - 10.8778i) q^{67} +(1.07027 - 0.347753i) q^{68} +(5.90680 + 10.4486i) q^{69} +(-0.539267 + 3.40480i) q^{70} +(5.77365 - 2.94182i) q^{71} +(3.04395 - 7.51919i) q^{72} +(3.15708 + 0.500032i) q^{73} +(4.48131 - 6.16799i) q^{74} +(15.4835 + 1.76950i) q^{75} +(0.241078 + 0.241078i) q^{76} +(-0.550121 - 2.00504i) q^{77} +(-7.45773 - 5.35105i) q^{78} +(-4.44795 - 13.6894i) q^{79} +(-2.51369 - 15.8708i) q^{80} +(-4.21434 - 7.95232i) q^{81} +(13.4224 + 4.36121i) q^{82} +(5.03389 - 2.56490i) q^{83} +(0.0961142 - 0.145105i) q^{84} +(4.10888 + 25.9424i) q^{85} +(7.63853 + 3.89203i) q^{86} +(-3.01310 + 6.60564i) q^{87} +(4.92927 + 7.49195i) q^{88} +(-3.41572 + 3.41572i) q^{89} +(-14.1349 - 8.50628i) q^{90} +(1.53744 + 1.65683i) q^{91} +(-0.652919 - 0.898665i) q^{92} +(-0.0310041 - 0.715742i) q^{93} +(0.806360 - 2.48172i) q^{94} +(-6.43773 + 4.67729i) q^{95} +(-0.419252 + 1.50976i) q^{96} +(-8.60532 - 4.38463i) q^{97} +(6.86668 - 6.86668i) q^{98} +(9.88199 + 1.16029i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 416 q - 12 q^{3} - 14 q^{6} - 12 q^{7} - 12 q^{9}+O(q^{10}) $ 416 * q - 12 * q^3 - 14 * q^6 - 12 * q^7 - 12 * q^9	$ 416 q - 12 q^{3} - 14 q^{6} - 12 q^{7} - 12 q^{9} - 20 q^{13} - 30 q^{15} + 32 q^{16} + 2 q^{18} - 4 q^{19} - 12 q^{21} - 24 q^{22} - 78 q^{24} - 36 q^{27} - 84 q^{28} - 28 q^{31} - 44 q^{33} - 24 q^{34} - 12 q^{37} + 54 q^{39} + 88 q^{40} - 56 q^{42} + 8 q^{45} - 92 q^{46} + 40 q^{48} - 44 q^{52} - 176 q^{54} - 72 q^{55} - 6 q^{57} - 4 q^{58} + 12 q^{60} - 48 q^{61} - 46 q^{63} + 204 q^{66} - 64 q^{67} + 56 q^{70} - 66 q^{72} - 12 q^{73} - 104 q^{76} - 92 q^{78} + 104 q^{79} + 124 q^{81} + 16 q^{84} - 12 q^{85} - 24 q^{87} - 84 q^{91} - 124 q^{93} + 328 q^{94} - 152 q^{96} + 52 q^{97} - 142 q^{99}+O(q^{100}) $ 416 * q - 12 * q^3 - 14 * q^6 - 12 * q^7 - 12 * q^9 - 20 * q^13 - 30 * q^15 + 32 * q^16 + 2 * q^18 - 4 * q^19 - 12 * q^21 - 24 * q^22 - 78 * q^24 - 36 * q^27 - 84 * q^28 - 28 * q^31 - 44 * q^33 - 24 * q^34 - 12 * q^37 + 54 * q^39 + 88 * q^40 - 56 * q^42 + 8 * q^45 - 92 * q^46 + 40 * q^48 - 44 * q^52 - 176 * q^54 - 72 * q^55 - 6 * q^57 - 4 * q^58 + 12 * q^60 - 48 * q^61 - 46 * q^63 + 204 * q^66 - 64 * q^67 + 56 * q^70 - 66 * q^72 - 12 * q^73 - 104 * q^76 - 92 * q^78 + 104 * q^79 + 124 * q^81 + 16 * q^84 - 12 * q^85 - 24 * q^87 - 84 * q^91 - 124 * q^93 + 328 * q^94 - 152 * q^96 + 52 * q^97 - 142 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{2}{5}\right)$	$-1$

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 $

$2$	−0.667273	+	1.30960i	−0.471833	+	0.926025i	0.525340	+	0.850892i	$0.323938\pi$
$2$	−0.667273	+	1.30960i	−0.471833	+	0.926025i	−0.997174	+	0.0751326i	$0.976062\pi$
$3$	0.852386	+	1.50779i	0.492125	+	0.870524i
$3$	0.852386	+	1.50779i	0.492125	+	0.870524i
$4$	−0.0942200	−	0.129683i	−0.0471100	−	0.0648414i
$5$	3.33356	−	1.69853i	1.49081	−	0.759606i	0.496695	−	0.867925i	$-0.334547\pi$
$5$	3.33356	−	1.69853i	1.49081	−	0.759606i	0.994116	+	0.108319i	$0.0345466\pi$
$6$	−2.54337	+	0.110172i	−1.03833	+	0.0449777i
$7$	0.619167	+	0.0980665i	0.234023	+	0.0370656i	0.272344	−	0.962200i	$-0.412201\pi$
$7$	0.619167	+	0.0980665i	0.234023	+	0.0370656i	−0.0383212	+	0.999265i	$0.512201\pi$
$8$	−2.67070	+	0.422997i	−0.944234	+	0.149552i
$9$	−1.54688	+	2.57044i	−0.515626	+	0.856814i
$10$			5.49900i			1.73894i
$11$	−1.36709	−	3.02177i	−0.412192	−	0.911097i
$11$	−1.36709	−	3.02177i	−0.412192	−	0.911097i
$12$	0.115223	−	0.252604i	0.0332620	−	0.0729205i
$13$	2.83576	+	2.22676i	0.786499	+	0.617591i
$13$	2.83576	+	2.22676i	0.786499	+	0.617591i
$14$	−0.541581	+	0.745422i	−0.144744	+	0.199223i
$15$	5.40251	+	3.57851i	1.39492	+	0.923967i
$16$	1.32720	−	4.08469i	0.331799	−	1.02117i
$17$	−2.16943	+	6.67683i	−0.526165	+	1.61937i	0.235836	+	0.971793i	$0.424217\pi$
$17$	−2.16943	+	6.67683i	−0.526165	+	1.61937i	−0.762001	+	0.647576i	$0.775783\pi$
$18$	−2.33405	−	3.74097i	−0.550142	−	0.881755i
$19$	−2.10072	+	0.332722i	−0.481939	+	0.0763316i	−0.392677	−	0.919677i	$-0.628451\pi$
$19$	−2.10072	+	0.332722i	−0.481939	+	0.0763316i	−0.0892619	+	0.996008i	$0.528451\pi$
$20$	−0.534358	−	0.272269i	−0.119486	−	0.0608812i
$21$	0.379905	+	1.01717i	0.0829022	+	0.221964i
$22$	4.86952	+	0.226011i	1.03818	+	0.0481857i
$23$	6.92972			1.44495			0.722474	−	0.691398i	$-0.243005\pi$
$23$	6.92972			1.44495			0.722474	+	0.691398i	$0.243005\pi$
$24$	−2.91425	−	3.66630i	−0.594870	−	0.748380i
$25$	5.28866	−	7.27922i	1.05773	−	1.45584i
$26$	−4.80838	+	2.22785i	−0.943001	+	0.436918i
$27$	−5.19423	−	0.141363i	−0.999630	−	0.0272053i
$28$	−0.0456204	−	0.0895351i	−0.00862145	−	0.0169206i
$29$	2.46387	+	3.39123i	0.457529	+	0.629735i	0.973994	−	0.226573i	$-0.0727523\pi$
$29$	2.46387	+	3.39123i	0.457529	+	0.629735i	−0.516465	+	0.856308i	$0.672752\pi$
$30$	−8.29135	+	4.68727i	−1.51379	+	0.855774i
$31$	−0.368539	−	0.187780i	−0.0661916	−	0.0337263i	0.420581	−	0.907255i	$-0.361826\pi$
$31$	−0.368539	−	0.187780i	−0.0661916	−	0.0337263i	−0.486773	+	0.873528i	$0.661826\pi$
$32$	0.639682	+	0.639682i	0.113081	+	0.113081i
$33$	3.39091	−	4.63699i	0.590282	−	0.807197i
$34$	−7.29635	−	7.29635i	−1.25131	−	1.25131i
$35$	2.23060	−	0.724765i	0.377040	−	0.122508i
$36$	0.479089	−	0.0415838i	0.0798481	−	0.00693063i
$37$	−5.12330	−	0.811450i	−0.842265	−	0.133402i	−0.279631	−	0.960108i	$-0.590212\pi$
$37$	−5.12330	−	0.811450i	−0.842265	−	0.133402i	−0.562634	+	0.826706i	$0.690212\pi$
$38$	0.966023	−	2.97311i	0.156710	−	0.482303i
$39$	−0.940324	+	6.17380i	−0.150572	+	0.988599i
$40$	−8.18444	+	5.94634i	−1.29407	+	0.940200i
$41$	−1.50210	−	9.48391i	−0.234589	−	1.48114i	−0.770813	−	0.637062i	$-0.780150\pi$
$41$	−1.50210	−	9.48391i	−0.234589	−	1.48114i	0.536223	−	0.844076i	$-0.319850\pi$
$42$	−1.58558	−	0.181205i	−0.244660	−	0.0279605i
$43$		−	5.83274i		−	0.889484i	−0.895659	−	0.444742i	$-0.853295\pi$
$43$		−	5.83274i		−	0.889484i	0.895659	−	0.444742i	$-0.146705\pi$
$44$	−0.263064	+	0.461998i	−0.0396584	+	0.0696489i
$45$	−0.790626	+	11.1961i	−0.117860	+	1.66902i
$46$	−4.62402	+	9.07514i	−0.681774	+	1.33806i
$47$	−1.75352	+	0.277730i	−0.255777	+	0.0405111i	−0.283006	−	0.959118i	$-0.591332\pi$
$47$	−1.75352	+	0.277730i	−0.255777	+	0.0405111i	0.0272292	+	0.999629i	$0.491332\pi$
$48$	7.29015	−	1.48059i	1.05224	−	0.213705i
$49$	−6.28364	−	2.04168i	−0.897663	−	0.291669i
$50$	6.00386	+	11.7832i	0.849074	+	1.66640i
$51$	−11.9165	+	2.42018i	−1.66864	+	0.338893i
$52$	0.0215863	−	0.577555i	0.00299348	−	0.0800924i
$53$	0.0586559	−	0.0190585i	0.00805701	−	0.00261788i	−0.304986	−	0.952357i	$-0.598652\pi$
$53$	0.0586559	−	0.0190585i	0.00805701	−	0.00261788i	0.313043	+	0.949739i	$0.398652\pi$
$54$	3.65110	−	6.70802i	0.496851	−	0.912846i
$55$	−9.68983	−	7.75119i	−1.30658	−	1.04517i
$56$	−1.69509			−0.226516
$57$	−2.29230	−	2.88385i	−0.303623	−	0.381975i
$58$	−6.08521	+	0.963803i	−0.799028	+	0.126554i
$59$	0.0323136	−	0.204020i	0.00420688	−	0.0265612i	−0.985496	−	0.169701i	$-0.945720\pi$
$59$	0.0323136	−	0.204020i	0.00420688	−	0.0265612i	0.989702	+	0.143140i	$0.0457198\pi$
$60$	−0.0449539	−	1.03778i	−0.00580352	−	0.133977i
$61$	−0.797652	+	2.45492i	−0.102129	+	0.314320i	−0.989046	−	0.147609i	$-0.952842\pi$
$61$	−0.797652	+	2.45492i	−0.102129	+	0.314320i	0.886917	+	0.461929i	$0.152842\pi$
$62$	0.491833	−	0.357337i	0.0624628	−	0.0453819i
$63$	−1.20985	+	1.43984i	−0.152427	+	0.181402i
$64$	6.90481	−	2.24351i	0.863102	−	0.280439i
$65$	13.2354	+	2.60639i	1.64165	+	0.323282i
$66$	3.80993	+	7.53487i	0.468970	+	0.927478i
$67$	10.8778	−	10.8778i	1.32893	−	1.32893i	0.422625	−	0.906305i	$-0.361109\pi$
$67$	10.8778	−	10.8778i	1.32893	−	1.32893i	0.906305	−	0.422625i	$-0.138891\pi$
$68$	1.07027	−	0.347753i	0.129790	−	0.0421712i
$69$	5.90680	+	10.4486i	0.711095	+	1.25786i
$70$	−0.539267	+	3.40480i	−0.0644548	+	0.406951i
$71$	5.77365	−	2.94182i	0.685206	−	0.349130i	−0.0764844	−	0.997071i	$-0.524370\pi$
$71$	5.77365	−	2.94182i	0.685206	−	0.349130i	0.761691	+	0.647941i	$0.224370\pi$
$72$	3.04395	−	7.51919i	0.358733	−	0.886145i
$73$	3.15708	+	0.500032i	0.369508	+	0.0585243i	0.338427	−	0.940993i	$-0.390105\pi$
$73$	3.15708	+	0.500032i	0.369508	+	0.0585243i	0.0310808	+	0.999517i	$0.490105\pi$
$74$	4.48131	−	6.16799i	0.520942	−	0.717015i
$75$	15.4835	+	1.76950i	1.78788	+	0.204325i
$76$	0.241078	+	0.241078i	0.0276536	+	0.0276536i
$77$	−0.550121	−	2.00504i	−0.0626921	−	0.228496i
$78$	−7.45773	−	5.35105i	−0.844422	−	0.605888i
$79$	−4.44795	−	13.6894i	−0.500433	−	1.54017i	−0.808315	−	0.588750i	$-0.799620\pi$
$79$	−4.44795	−	13.6894i	−0.500433	−	1.54017i	0.307882	−	0.951424i	$-0.400380\pi$
$80$	−2.51369	−	15.8708i	−0.281039	−	1.77441i
$81$	−4.21434	−	7.95232i	−0.468260	−	0.883591i
$82$	13.4224	+	4.36121i	1.48226	+	0.481615i
$83$	5.03389	−	2.56490i	0.552542	−	0.281534i	−0.155345	−	0.987860i	$-0.549649\pi$
$83$	5.03389	−	2.56490i	0.552542	−	0.281534i	0.707886	+	0.706326i	$0.249649\pi$
$84$	0.0961142	−	0.145105i	0.0104869	−	0.0158322i
$85$	4.10888	+	25.9424i	0.445670	+	2.81385i
$86$	7.63853	+	3.89203i	0.823684	+	0.419688i
$87$	−3.01310	+	6.60564i	−0.323038	+	0.708199i
$88$	4.92927	+	7.49195i	0.525462	+	0.798644i
$89$	−3.41572	+	3.41572i	−0.362065	+	0.362065i	−0.864573	−	0.502508i	$-0.832411\pi$
$89$	−3.41572	+	3.41572i	−0.362065	+	0.362065i	0.502508	+	0.864573i	$0.332411\pi$
$90$	−14.1349	−	8.50628i	−1.48994	−	0.896640i
$91$	1.53744	+	1.65683i	0.161168	+	0.173683i
$92$	−0.652919	−	0.898665i	−0.0680715	−	0.0936924i
$93$	−0.0310041	−	0.715742i	−0.00321498	−	0.0742190i
$94$	0.806360	−	2.48172i	0.0831697	−	0.255970i
$95$	−6.43773	+	4.67729i	−0.660498	+	0.479880i
$96$	−0.419252	+	1.50976i	−0.0427897	+	0.154090i
$97$	−8.60532	−	4.38463i	−0.873738	−	0.445192i	−0.0411941	−	0.999151i	$-0.513116\pi$
$97$	−8.60532	−	4.38463i	−0.873738	−	0.445192i	−0.832544	+	0.553960i	$0.813116\pi$
$98$	6.86668	−	6.86668i	0.693640	−	0.693640i
$99$	9.88199	+	1.16029i	0.993177	+	0.116613i
$100$	−1.44229			−0.144229
$101$	2.37310	+	7.30366i	0.236133	+	0.726741i	0.996969	+	0.0777979i	$0.0247889\pi$
$101$	2.37310	+	7.30366i	0.236133	+	0.726741i	−0.760837	+	0.648944i	$0.775211\pi$
$102$	4.78208	−	17.2207i	0.473496	−	1.70510i
$103$	−1.82947	−	2.51805i	−0.180263	−	0.248111i	0.709317	−	0.704889i	$-0.249003\pi$
$103$	−1.82947	−	2.51805i	−0.180263	−	0.248111i	−0.889581	+	0.456778i	$0.849003\pi$
$104$	−8.51537	−	4.74747i	−0.835001	−	0.465528i
$105$	2.99413	+	2.74550i	0.292197	+	0.267933i
$106$	−0.0141806	+	0.0895328i	−0.00137734	+	0.00869619i
$107$	1.92103	−	2.64406i	0.185713	−	0.255611i	−0.706002	−	0.708210i	$-0.749503\pi$
$107$	1.92103	−	2.64406i	0.185713	−	0.255611i	0.891714	+	0.452599i	$0.149503\pi$
$108$	0.471068	+	0.686921i	0.0453285	+	0.0660990i
$109$	1.43515	−	1.43515i	0.137463	−	0.137463i	−0.635027	−	0.772490i	$-0.719011\pi$
$109$	1.43515	−	1.43515i	0.137463	−	0.137463i	0.772490	+	0.635027i	$0.219011\pi$
$110$	16.6167	−	7.51761i	1.58434	−	0.716776i
$111$	−3.14353	−	8.41654i	−0.298370	−	0.798862i
$112$	1.22233	−	2.39895i	0.115499	−	0.226680i
$113$	−5.09480	+	7.01239i	−0.479278	+	0.659670i	−0.978366	−	0.206881i	$-0.933669\pi$
$113$	−5.09480	+	7.01239i	−0.479278	+	0.659670i	0.499088	+	0.866551i	$0.333669\pi$
$114$	5.30626	−	1.07768i	0.496977	−	0.100934i
$115$	23.1006	−	11.7704i	2.15414	−	1.09759i
$116$	0.207638	−	0.639043i	0.0192787	−	0.0593336i
$117$	−10.1103	+	3.84464i	−0.934700	+	0.355437i
$118$	0.245622	+	0.178455i	0.0226114	+	0.0164281i
$119$	−1.99801	+	3.92133i	−0.183158	+	0.359467i
$120$	−15.9422	−	7.27186i	−1.45531	−	0.663827i
$121$	−7.26215	+	8.26203i	−0.660195	+	0.751094i
$122$	−2.68270	−	2.68270i	−0.242881	−	0.242881i
$123$	13.0194	−	10.3488i	1.17392	−	0.933121i
$124$	0.0103719	+	0.0654859i	0.000931428	+	0.00588080i
$125$	2.33970	−	14.7723i	0.209269	−	1.32127i
$126$	−1.07831	−	2.54518i	−0.0960631	−	0.226743i
$127$	0.509966	+	0.165698i	0.0452521	+	0.0147033i	0.331556	−	0.943436i	$-0.392427\pi$
$127$	0.509966	+	0.165698i	0.0452521	+	0.0147033i	−0.286303	+	0.958139i	$0.592427\pi$
$128$	−1.95234	+	12.3266i	−0.172564	+	1.08953i
$129$	8.79456	−	4.97174i	0.774318	−	0.437737i
$130$	−12.2449	+	15.5939i	−1.07395	+	1.36767i
$131$		−	16.1219i		−	1.40858i	−0.709914	−	0.704288i	$-0.751266\pi$
$131$		−	16.1219i		−	1.40858i	0.709914	−	0.704288i	$-0.248734\pi$
$132$	−0.920830	−	0.00284519i	−0.0801480	−	0.000247642i
$133$	−1.33333			−0.115614
$134$	6.98704	+	21.5039i	0.603589	+	1.85765i
$135$	−17.5554	+	8.35132i	−1.51093	+	0.718767i
$136$	2.96962	−	18.7494i	0.254643	−	1.60775i
$137$	9.01883	+	17.7005i	0.770531	+	1.51225i	0.856610	+	0.515964i	$0.172566\pi$
$137$	9.01883	+	17.7005i	0.770531	+	1.51225i	−0.0860796	+	0.996288i	$0.527434\pi$
$138$	−17.6249	+	0.763464i	−1.50033	+	0.0649904i
$139$	−9.57003	+	6.95303i	−0.811719	+	0.589748i	−0.914328	−	0.404973i	$-0.867281\pi$
$139$	−9.57003	+	6.95303i	−0.811719	+	0.589748i	0.102610	+	0.994722i	$0.467281\pi$
$140$	−0.304157	−	0.220983i	−0.0257059	−	0.0186764i
$141$	−1.91343	−	2.40721i	−0.161140	−	0.202723i
$142$			9.52415i			0.799249i
$143$	2.85201	−	11.6132i	0.238497	−	0.971143i
$144$	8.44645	+	9.73000i	0.703871	+	0.810833i
$145$	13.9736	+	7.11988i	1.16044	+	0.591274i
$146$	−2.76147	+	3.80084i	−0.228541	+	0.314560i
$147$	−2.27766	−	11.2147i	−0.187858	−	0.924975i
$148$	0.377486	+	0.740858i	0.0310292	+	0.0608982i
$149$	0.193317	−	0.0985000i	0.0158372	−	0.00806943i	−0.446054	−	0.895006i	$-0.647171\pi$
$149$	0.193317	−	0.0985000i	0.0158372	−	0.00806943i	0.461891	+	0.886937i	$0.347171\pi$
$150$	−12.6491	+	19.0964i	−1.03279	+	1.55922i
$151$	0.480580	+	3.03427i	0.0391091	+	0.246925i	0.999496	−	0.0317450i	$-0.0101064\pi$
$151$	0.480580	+	3.03427i	0.0391091	+	0.246925i	−0.960387	+	0.278670i	$0.910106\pi$
$152$	5.46965	−	1.77720i	0.443647	−	0.144150i
$153$	−13.8065	−	15.9046i	−1.11619	−	1.28581i
$154$	2.99288	+	0.617475i	0.241173	+	0.0497575i
$155$	−1.54750			−0.124298
$156$	0.889232	−	0.459752i	0.0711956	−	0.0368096i
$157$	7.94600	+	5.77311i	0.634160	+	0.460744i	0.857839	−	0.513919i	$-0.171807\pi$
$157$	7.94600	+	5.77311i	0.634160	+	0.460744i	−0.223679	+	0.974663i	$0.571807\pi$
$158$	20.8955	+	3.30953i	1.66236	+	0.263292i
$159$	0.0787336	+	0.0721958i	0.00624398	+	0.00572550i
$160$	3.21893	+	1.04590i	0.254479	+	0.0826853i
$161$	4.29066	+	0.679574i	0.338151	+	0.0535579i
$162$	13.2264	−	0.212722i	1.03917	−	0.0167131i
$163$	−1.20304	+	2.36110i	−0.0942294	+	0.184936i	−0.933310	−	0.359071i	$-0.883093\pi$
$163$	−1.20304	+	2.36110i	−0.0942294	+	0.184936i	0.839081	+	0.544007i	$0.183093\pi$
$164$	−1.08837	+	1.08837i	−0.0849875	+	0.0849875i
$165$	3.42772	−	21.2173i	0.266847	−	1.65176i
$166$			8.30386i			0.644504i
$167$	0.570328	+	0.290597i	0.0441333	+	0.0224871i	0.475918	−	0.879490i	$-0.342116\pi$
$167$	0.570328	+	0.290597i	0.0441333	+	0.0224871i	−0.431785	+	0.901977i	$0.642116\pi$
$168$	−1.44487	−	2.55584i	−0.111474	−	0.197188i
$169$	3.08311	+	12.6291i	0.237162	+	0.971470i
$170$	−36.7159	−	11.9297i	−2.81598	−	0.914967i
$171$	2.39432	−	5.91446i	0.183098	−	0.452290i
$172$	−0.756405	+	0.549561i	−0.0576754	+	0.0419036i
$173$	−19.3467	−	14.0562i	−1.47091	−	1.06868i	−0.980350	−	0.197266i	$-0.936794\pi$
$173$	−19.3467	−	14.0562i	−1.47091	−	1.06868i	−0.490556	−	0.871410i	$-0.663206\pi$
$174$	−6.64016	−	8.35371i	−0.503390	−	0.633293i
$175$	3.98841	−	3.98841i	0.301496	−	0.301496i
$176$	−14.1574	+	1.57365i	−1.06715	+	0.118618i
$177$	0.335164	−	0.125182i	0.0251925	−	0.00940923i
$178$	−2.19400	−	6.75243i	−0.164447	−	0.506116i
$179$	−18.7753	−	13.6411i	−1.40333	−	1.01958i	−0.994250	−	0.107085i	$-0.965848\pi$
$179$	−18.7753	−	13.6411i	−1.40333	−	1.01958i	−0.409084	−	0.912497i	$-0.634152\pi$
$180$	1.52644	−	0.952369i	0.113774	−	0.0709854i
$181$	16.1890	+	5.26013i	1.20332	+	0.390983i	0.840982	−	0.541064i	$-0.181978\pi$
$181$	16.1890	+	5.26013i	1.20332	+	0.390983i	0.362339	+	0.932046i	$0.381978\pi$
$182$	−3.19567	+	0.907872i	−0.236879	+	0.0672959i
$183$	−4.38142	+	0.889845i	−0.323884	+	0.0657792i
$184$	−18.5072	+	2.93125i	−1.36437	+	0.216095i
$185$	−18.4571	+	5.99707i	−1.35699	+	0.440913i
$186$	0.958022	+	0.436993i	0.0702456	+	0.0320418i
$187$	23.1416	−	2.57228i	1.69228	−	0.188104i
$188$	0.201233	+	0.201233i	0.0146764	+	0.0146764i
$189$	−3.20223	−	0.596907i	−0.232928	−	0.0434186i
$190$	−1.82964	−	11.5519i	−0.132736	−	0.838060i
$191$	1.71889	+	2.36584i	0.124374	+	0.171186i	0.866664	−	0.498893i	$-0.166260\pi$
$191$	1.71889	+	2.36584i	0.124374	+	0.171186i	−0.742289	+	0.670080i	$0.766260\pi$
$192$	9.26831	+	8.49869i	0.668883	+	0.613340i
$193$	−4.48357	+	2.28449i	−0.322734	+	0.164441i	−0.607850	−	0.794052i	$-0.707968\pi$
$193$	−4.48357	+	2.28449i	−0.322734	+	0.164441i	0.285116	+	0.958493i	$0.407968\pi$
$194$	11.4842	−	8.34375i	0.824517	−	0.599047i
$195$	7.35177	+	22.1779i	0.526471	+	1.58819i
$196$	0.327274	+	1.00725i	0.0233767	+	0.0719462i
$197$	13.8873	+	13.8873i	0.989430	+	0.989430i	0.999945	−	0.0105150i	$-0.00334709\pi$
$197$	13.8873	+	13.8873i	0.989430	+	0.989430i	−0.0105150	+	0.999945i	$0.503347\pi$
$198$	−8.11349	+	12.1672i	−0.576601	+	0.864685i
$199$			19.6796i			1.39505i	0.716561	+	0.697524i	$0.245715\pi$
$199$			19.6796i			1.39505i	−0.716561	+	0.697524i	$0.754285\pi$
$200$	−11.0453	+	21.6777i	−0.781022	+	1.53284i
$201$	25.6734	+	7.12936i	1.81087	+	0.502866i
$202$	−11.1484	−	1.76573i	−0.784396	−	0.124236i
$203$	1.19298	+	2.34136i	0.0837310	+	0.164331i
$204$	1.43662	+	1.31733i	0.100584	+	0.0922316i
$205$	−21.1161	−	29.0638i	−1.47481	−	2.02990i
$206$	4.51839	−	0.715643i	0.314811	−	0.0498612i
$207$	−10.7194	+	17.8125i	−0.745052	+	1.23805i
$208$	12.8592	−	8.62787i	0.891627	−	0.598235i
$209$	3.87728	+	5.89303i	0.268197	+	0.407629i
$210$	−5.59340	+	2.08910i	−0.385981	+	0.144162i
$211$	0.264503	+	0.814056i	0.0182091	+	0.0560419i	0.959748	−	0.280862i	$-0.0906203\pi$
$211$	0.264503	+	0.814056i	0.0182091	+	0.0560419i	−0.941539	+	0.336904i	$0.890620\pi$
$212$	−0.00799811	−	0.00581097i	−0.000549313	−	0.000399099i
$213$	9.35704	+	6.19790i	0.641134	+	0.424673i
$214$	2.18081	+	4.28008i	0.149077	+	0.292580i
$215$	−9.90709	−	19.4438i	−0.675658	−	1.32605i
$216$	13.9320	−	1.81960i	0.947953	−	0.123808i
$217$	−0.209773	−	0.152409i	−0.0142403	−	0.0103462i
$218$	0.921833	+	2.83711i	0.0624344	+	0.192153i
$219$	1.93710	+	5.18644i	0.130897	+	0.350467i
$220$	−0.0922198	+	1.98692i	−0.00621746	+	0.133958i
$221$	−21.0197	+	14.1031i	−1.41394	+	0.948677i
$222$	13.1199	+	1.49938i	0.880547	+	0.100632i
$223$	−1.53565	+	0.243223i	−0.102834	+	0.0162874i	−0.207640	−	0.978205i	$-0.566578\pi$
$223$	−1.53565	+	0.243223i	−0.102834	+	0.0162874i	0.104805	+	0.994493i	$0.466578\pi$
$224$	0.333339	+	0.458801i	0.0222721	+	0.0306550i
$225$	10.5299	+	24.8542i	0.701993	+	1.65695i
$226$	−5.78378	−	11.3513i	−0.384731	−	0.755078i
$227$	−16.5798	−	2.62598i	−1.10044	−	0.174292i	−0.420307	−	0.907382i	$-0.638078\pi$
$227$	−16.5798	−	2.62598i	−1.10044	−	0.174292i	−0.680132	+	0.733090i	$0.738078\pi$
$228$	−0.158004	+	0.568988i	−0.0104641	+	0.0376821i
$229$	−8.92245	+	17.5113i	−0.589612	+	1.15718i	0.382783	+	0.923838i	$0.374966\pi$
$229$	−8.92245	+	17.5113i	−0.589612	+	1.15718i	−0.972395	+	0.233340i	$0.925034\pi$
$230$			38.1065i			2.51267i
$231$	2.55428	−	2.53854i	0.168059	−	0.167024i
$232$	−8.01473	−	8.01473i	−0.526193	−	0.526193i
$233$	−2.71297	−	8.34966i	−0.177732	−	0.547004i	0.822015	−	0.569465i	$-0.192850\pi$
$233$	−2.71297	−	8.34966i	−0.177732	−	0.547004i	−0.999748	+	0.0224612i	$0.992850\pi$
$234$	1.71141	−	15.8059i	0.111879	−	1.03326i
$235$	−5.37371	+	3.90423i	−0.350543	+	0.254684i
$236$	−0.0295025	+	0.0150323i	−0.00192045	+	0.000978518i
$237$	16.8494	−	18.3752i	1.09448	−	1.19360i
$238$	−3.80213	−	5.23319i	−0.246456	−	0.339217i
$239$	1.75495	+	11.0803i	0.113518	+	0.716725i	0.977142	+	0.212588i	$0.0681893\pi$
$239$	1.75495	+	11.0803i	0.113518	+	0.716725i	−0.863624	+	0.504137i	$0.831811\pi$
$240$	21.7873	−	17.3182i	1.40636	−	1.11788i
$241$	−14.8591	−	14.8591i	−0.957156	−	0.957156i	0.0419630	−	0.999119i	$-0.486639\pi$
$241$	−14.8591	−	14.8591i	−0.957156	−	0.957156i	−0.999119	+	0.0419630i	$0.986639\pi$
$242$	−5.97410	−	15.0235i	−0.384030	−	0.965748i
$243$	8.39820	−	13.1328i	0.538745	−	0.842469i
$244$	0.393515	−	0.127861i	0.0251922	−	0.00818546i
$245$	−24.4147	+	3.86691i	−1.55980	+	0.247048i
$246$	4.86528	+	23.9556i	0.310199	+	1.52736i
$247$	−6.69804	−	3.73428i	−0.426186	−	0.237606i
$248$	1.06369	+	0.345613i	0.0675442	+	0.0219464i
$249$	8.15815	+	5.40379i	0.517002	+	0.342451i
$250$	17.7845	+	12.9212i	1.12479	+	0.817207i
$251$	8.84504	+	27.2222i	0.558294	+	1.71825i	0.687083	+	0.726579i	$0.258891\pi$
$251$	8.84504	+	27.2222i	0.558294	+	1.71825i	−0.128789	+	0.991672i	$0.541109\pi$
$252$	0.300714	+	0.0212352i	0.0189432	+	0.00133769i
$253$	−9.47353	−	20.9400i	−0.595596	−	1.31649i
$254$	−0.557284	+	0.557284i	−0.0349671	+	0.0349671i
$255$	−35.6135	+	28.3083i	−2.23020	+	1.77273i
$256$	−3.09293	−	2.24714i	−0.193308	−	0.140446i
$257$	1.67353	−	1.21589i	0.104392	−	0.0758450i	−0.534365	−	0.845254i	$-0.679449\pi$
$257$	1.67353	−	1.21589i	0.104392	−	0.0758450i	0.638757	+	0.769409i	$0.279449\pi$
$258$	0.642606	+	14.8348i	0.0400069	+	0.923576i
$259$	−3.09260	−	1.00485i	−0.192165	−	0.0624382i
$260$	−0.909036	−	1.96198i	−0.0563760	−	0.121677i
$261$	−12.5283	+	1.08742i	−0.775480	+	0.0673098i
$262$	21.1132	+	10.7577i	1.30438	+	0.664613i
$263$		−	2.95469i		−	0.182194i	−0.995842	−	0.0910970i	$-0.970963\pi$
$263$		−	2.95469i		−	0.182194i	0.995842	−	0.0910970i	$-0.0290373\pi$
$264$	−7.09466	+	13.8183i	−0.436646	+	0.850460i
$265$	0.163161	−	0.163161i	0.0100229	−	0.0100229i
$266$	0.889693	−	1.74612i	0.0545506	−	0.107062i
$267$	−8.06170	−	2.23868i	−0.493368	−	0.137005i
$268$	−2.43556	−	0.385755i	−0.148775	−	0.0235637i
$269$	10.3666	+	3.36832i	0.632065	+	0.205370i	0.607489	−	0.794328i	$-0.292177\pi$
$269$	10.3666	+	3.36832i	0.632065	+	0.205370i	0.0245752	+	0.999698i	$0.492177\pi$
$270$	0.777353	−	28.5631i	0.0473082	−	1.73829i
$271$	1.25698	+	0.199086i	0.0763561	+	0.0120936i	0.194496	−	0.980903i	$-0.437693\pi$
$271$	1.25698	+	0.199086i	0.0763561	+	0.0120936i	−0.118139	+	0.992997i	$0.537693\pi$
$272$	24.3935	+	17.7229i	1.47907	+	1.07461i
$273$	−1.18766	+	3.73040i	−0.0718805	+	0.225774i
$274$	−29.1985			−1.76394
$275$	−29.2261	−	6.02978i	−1.76240	−	0.363609i
$276$	0.798463	−	1.75048i	0.0480618	−	0.105366i
$277$	9.30221	−	3.02247i	0.558916	−	0.181603i	−0.0159175	−	0.999873i	$-0.505067\pi$
$277$	9.30221	−	3.02247i	0.558916	−	0.181603i	0.574833	+	0.818271i	$0.305067\pi$
$278$	−2.71985	−	17.1724i	−0.163126	−	1.02993i
$279$	1.05276	−	0.656836i	0.0630273	−	0.0393238i
$280$	−5.65068	+	2.87916i	−0.337692	+	0.172063i
$281$	−6.66088	−	13.0727i	−0.397355	−	0.779853i	0.602478	−	0.798135i	$-0.294180\pi$
$281$	−6.66088	−	13.0727i	−0.397355	−	0.779853i	−0.999833	+	0.0182827i	$0.994180\pi$
$282$	4.42925	−	0.899560i	0.263758	−	0.0535680i
$283$	−2.43099	+	3.34597i	−0.144508	+	0.198898i	−0.875135	−	0.483879i	$-0.839228\pi$
$283$	−2.43099	+	3.34597i	−0.144508	+	0.198898i	0.730628	+	0.682776i	$0.239228\pi$
$284$	−0.925497	−	0.471564i	−0.0549182	−	0.0279822i
$285$	−12.5398	−	5.71992i	−0.742794	−	0.338819i
$286$	13.3055	+	11.4841i	0.786772	+	0.679072i
$287$		−	6.01943i		−	0.355316i
$288$	−2.63377	+	0.654755i	−0.155197	+	0.0385818i
$289$	−26.1203	−	18.9775i	−1.53649	−	1.11632i
$290$	−18.6484	+	13.5488i	−1.09507	+	0.795614i
$291$	−0.723939	−	16.7124i	−0.0424381	−	0.979700i
$292$	−0.232614	−	0.456532i	−0.0136127	−	0.0267165i
$293$	2.79322	−	17.6357i	0.163181	−	1.03029i	−0.761117	−	0.648615i	$-0.775349\pi$
$293$	2.79322	−	17.6357i	0.163181	−	1.03029i	0.924298	−	0.381672i	$-0.124651\pi$
$294$	16.2066	+	4.50047i	0.945188	+	0.262473i
$295$	−0.238816	−	0.734999i	−0.0139044	−	0.0427933i
$296$	14.0260			0.815245
$297$	6.67380	+	15.8890i	0.387253	+	0.921974i
$298$			0.318894i			0.0184730i
$299$	19.6511	+	15.4308i	1.13645	+	0.892387i
$300$	−1.22938	−	2.17467i	−0.0709785	−	0.125555i
$301$	0.571996	−	3.61144i	0.0329693	−	0.208160i
$302$	−4.29434	−	1.39532i	−0.247112	−	0.0802914i
$303$	−8.98961	+	9.80368i	−0.516439	+	0.563207i
$304$	−1.42901	+	9.02239i	−0.0819591	+	0.517469i
$305$	1.51074	+	9.53845i	0.0865048	+	0.546170i
$306$	30.0414	−	7.46828i	1.71735	−	0.426933i
$307$	7.37863	+	7.37863i	0.421121	+	0.421121i	0.885589	−	0.464469i	$-0.153755\pi$
$307$	7.37863	+	7.37863i	0.421121	+	0.421121i	−0.464469	+	0.885589i	$0.653755\pi$
$308$	−0.208187	+	0.260257i	−0.0118626	+	0.0148295i
$309$	2.23729	−	4.90482i	0.127275	−	0.279025i
$310$	1.03260	−	2.02660i	0.0586479	−	0.115103i
$311$	−4.55280	−	3.30780i	−0.258165	−	0.187568i	0.451172	−	0.892437i	$-0.351006\pi$
$311$	−4.55280	−	3.30780i	−0.258165	−	0.187568i	−0.709338	+	0.704869i	$0.751006\pi$
$312$	−0.100176	−	16.8861i	−0.00567137	−	0.955987i
$313$	6.79115	−	20.9010i	0.383858	−	1.18139i	−0.553446	−	0.832885i	$-0.686688\pi$
$313$	6.79115	−	20.9010i	0.383858	−	1.18139i	0.937305	−	0.348510i	$-0.113312\pi$
$314$	−12.8626	+	6.55382i	−0.725878	+	0.369854i
$315$	−1.58749	+	6.85475i	−0.0894452	+	0.386221i
$316$	−1.35619	+	1.86663i	−0.0762916	+	0.105006i
$317$	6.36601	−	12.4940i	0.357551	−	0.701732i	−0.640240	−	0.768175i	$-0.721165\pi$
$317$	6.36601	−	12.4940i	0.357551	−	0.701732i	0.997790	+	0.0664428i	$0.0211650\pi$
$318$	−0.147084	+	0.0549350i	−0.00824807	+	0.00308060i
$319$	6.87917	−	12.0813i	0.385160	−	0.676425i
$320$	19.2069	−	19.2069i	1.07370	−	1.07370i
$321$	5.62415	+	0.642745i	0.313910	+	0.0358745i
$322$	−3.75301	+	5.16557i	−0.209147	+	0.287866i
$323$	2.33585	−	14.7480i	0.129970	−	0.820599i
$324$	−0.634203	+	1.29579i	−0.0352335	+	0.0719886i
$325$	31.2064	−	8.86557i	1.73102	−	0.491773i
$326$	−2.28933	−	3.15099i	−0.126794	−	0.174517i
$327$	3.38722	+	0.940609i	0.187313	+	0.0520158i
$328$	8.02333	+	24.6933i	0.443014	+	1.36346i
$329$	−1.11296			−0.0613593
$330$	25.4988	+	18.6466i	1.40366	+	1.02646i
$331$	−18.3926	+	18.3926i	−1.01095	+	1.01095i	−0.0110070	+	0.999939i	$0.503504\pi$
$331$	−18.3926	+	18.3926i	−1.01095	+	1.01095i	−0.999939	+	0.0110070i	$0.996496\pi$
$332$	−0.806916	−	0.411144i	−0.0442853	−	0.0225645i
$333$	10.0109	−	11.9139i	0.548594	−	0.652879i
$334$	−0.761129	+	0.552993i	−0.0416471	+	0.0302584i
$335$	17.7854	−	54.7378i	0.971720	−	2.99065i
$336$	4.65902	−	0.201817i	0.254170	−	0.0110100i
$337$	11.6420	+	16.0238i	0.634179	+	0.872873i	0.998288	−	0.0584832i	$-0.0186264\pi$
$337$	11.6420	+	16.0238i	0.634179	+	0.872873i	−0.364109	+	0.931356i	$0.618626\pi$
$338$	−18.5963	−	4.38944i	−1.01151	−	0.238754i
$339$	−14.9160	−	1.70464i	−0.810124	−	0.0925833i
$340$	2.97715	−	2.97715i	0.161458	−	0.161458i
$341$	−0.0636027	+	1.37035i	−0.00344428	+	0.0742087i
$342$	6.14790	+	7.08215i	0.332440	+	0.382959i
$343$	−7.60032	−	3.87256i	−0.410379	−	0.209098i
$344$	2.46723	+	15.5775i	0.133024	+	0.839881i
$345$	37.4379	+	24.7981i	2.01559	+	1.33508i
$346$	31.3176	−	15.9571i	1.68364	−	0.857859i
$347$	−5.35221	−	1.73904i	−0.287322	−	0.0933565i	0.161810	−	0.986822i	$-0.448267\pi$
$347$	−5.35221	−	1.73904i	−0.287322	−	0.0933565i	−0.449132	+	0.893465i	$0.648267\pi$
$348$	1.14053	−	0.231637i	0.0611389	−	0.0124170i
$349$	1.87245	+	11.8222i	0.100230	+	0.632826i	0.985749	+	0.168223i	$0.0538028\pi$
$349$	1.87245	+	11.8222i	0.100230	+	0.632826i	−0.885519	+	0.464603i	$0.846197\pi$
$350$	2.56185	+	7.88457i	0.136937	+	0.421448i
$351$	−14.4148	−	11.9672i	−0.769406	−	0.638760i
$352$	1.05847	−	2.80747i	0.0564166	−	0.149639i
$353$	−9.55656	−	9.55656i	−0.508644	−	0.508644i	0.405466	−	0.914110i	$-0.367109\pi$
$353$	−9.55656	−	9.55656i	−0.508644	−	0.508644i	−0.914110	+	0.405466i	$0.867109\pi$
$354$	−0.0597083	+	0.522460i	−0.00317346	+	0.0277684i
$355$	14.2500	−	19.6135i	0.756312	−	1.04097i
$356$	0.764788	+	0.121131i	0.0405337	+	0.00641991i
$357$	−7.61562	+	0.329889i	−0.403062	+	0.0174596i
$358$	30.3926	−	15.4858i	1.60630	−	0.818450i
$359$	2.40541	−	15.1871i	0.126952	−	0.801546i	−0.839247	−	0.543750i	$-0.817004\pi$
$359$	2.40541	−	15.1871i	0.126952	−	0.801546i	0.966199	−	0.257796i	$-0.0829962\pi$
$360$	−2.62441	−	30.2359i	−0.138318	−	1.59357i
$361$	−13.7677	+	4.47341i	−0.724618	+	0.235443i
$362$	−17.6911	+	17.6911i	−0.929826	+	0.929826i
$363$	−18.6476	−	3.90738i	−0.978744	−	0.205084i
$364$	0.0700043	−	0.355486i	0.00366922	−	0.0186325i
$365$	11.3736	−	3.69551i	0.595322	−	0.193432i
$366$	1.75826	−	6.33166i	0.0919059	−	0.330961i
$367$	−15.8243	+	11.4970i	−0.826022	+	0.600140i	−0.918431	−	0.395581i	$-0.870543\pi$
$367$	−15.8243	+	11.4970i	−0.826022	+	0.600140i	0.0924091	+	0.995721i	$0.470543\pi$
$368$	9.19711	−	28.3058i	0.479432	−	1.47554i
$369$	26.7014	+	10.8094i	1.39002	+	0.562714i
$370$	4.46216	−	28.1730i	0.231977	−	1.46464i
$371$	0.0381868	−	0.00604820i	0.00198256	−	0.000314007i
$372$	−0.0898982	+	0.0714580i	−0.00466101	+	0.00370492i
$373$	30.7171			1.59047			0.795237	−	0.606299i	$-0.207347\pi$
$373$	30.7171			1.59047			0.795237	+	0.606299i	$0.207347\pi$
$374$	−12.0731	+	32.0226i	−0.624286	+	1.65585i
$375$	24.2678	−	9.06388i	1.25318	−	0.468057i
$376$	4.56563	−	1.48346i	0.235454	−	0.0765038i
$377$	−0.564485	+	15.1032i	−0.0290725	+	0.777852i
$378$	2.91847	−	3.79534i	0.150110	−	0.195211i
$379$	−0.295117	−	0.579199i	−0.0151591	−	0.0297515i	0.883303	−	0.468803i	$-0.155315\pi$
$379$	−0.295117	−	0.579199i	−0.0151591	−	0.0297515i	−0.898462	+	0.439051i	$0.855315\pi$
$380$	1.21313	+	0.394169i	0.0622321	+	0.0202204i
$381$	0.184849	+	0.910161i	0.00947012	+	0.0466290i
$382$	−4.24527	+	0.672384i	−0.217207	+	0.0344022i
$383$	14.9803	−	29.4006i	0.765459	−	1.50230i	−0.0965072	−	0.995332i	$-0.530767\pi$
$383$	14.9803	−	29.4006i	0.765459	−	1.50230i	0.861966	−	0.506966i	$-0.169233\pi$
$384$	−20.2501	+	7.56327i	−1.03338	+	0.385962i
$385$	−5.23949	−	5.74953i	−0.267029	−	0.293023i
$386$		−	7.39605i		−	0.376449i
$387$	14.9927	+	9.02253i	0.762122	+	0.458641i
$388$	0.242183	+	1.52908i	0.0122950	+	0.0776273i
$389$	−8.74400	+	6.35289i	−0.443339	+	0.322104i	−0.786960	−	0.617004i	$-0.788346\pi$
$389$	−8.74400	+	6.35289i	−0.443339	+	0.322104i	0.343621	+	0.939108i	$0.388346\pi$
$390$	−33.9497	−	5.17084i	−1.71911	−	0.261836i
$391$	−15.0336	+	46.2686i	−0.760280	+	2.33990i
$392$	17.6453	+	2.79475i	0.891224	+	0.141156i
$393$	24.3085	−	13.7421i	1.22620	−	0.693196i
$394$	−27.4534	+	8.92015i	−1.38308	+	0.449391i
$395$	−38.0793	−	38.0793i	−1.91598	−	1.91598i
$396$	−0.780612	−	1.39085i	−0.0392272	−	0.0698926i
$397$	−15.4497	−	15.4497i	−0.775396	−	0.775396i	0.203648	−	0.979044i	$-0.434720\pi$
$397$	−15.4497	−	15.4497i	−0.775396	−	0.775396i	−0.979044	+	0.203648i	$0.934720\pi$
$398$	−25.7723	−	13.1316i	−1.29185	−	0.658230i
$399$	−1.13651	−	2.01038i	−0.0568966	−	0.100645i
$400$	−22.7143	−	31.2635i	−1.13571	−	1.56317i
$401$	13.3379	+	26.1771i	0.666064	+	1.30722i	0.938576	+	0.345072i	$0.112145\pi$
$401$	13.3379	+	26.1771i	0.666064	+	1.30722i	−0.272512	+	0.962152i	$0.587855\pi$
$402$	−26.4678	+	28.8646i	−1.32009	+	1.43964i
$403$	−0.626950	−	1.35315i	−0.0312306	−	0.0674051i
$404$	0.723565	−	0.995902i	0.0359987	−	0.0495480i
$405$	−27.5560	−	19.3513i	−1.36927	−	0.961574i
$406$	−3.86228			−0.191682
$407$	4.55198	+	16.5907i	0.225633	+	0.822372i
$408$	30.8015	−	11.5042i	1.52490	−	0.569542i
$409$	−17.4091	−	8.87036i	−0.860823	−	0.438611i	−0.0329038	−	0.999459i	$-0.510475\pi$
$409$	−17.4091	−	8.87036i	−0.860823	−	0.438611i	−0.827919	+	0.560847i	$0.810475\pi$
$410$	52.1520	−	8.26007i	2.57560	−	0.407936i
$411$	−19.0011	+	28.6861i	−0.937255	+	1.41498i
$412$	−0.154175	+	0.474502i	−0.00759566	+	0.0233770i
$413$	0.0400151	−	0.123154i	0.00196901	−	0.00606000i
$414$	−16.1743	−	25.9239i	−0.794925	−	1.27409i
$415$	12.4242	−	17.1005i	0.609880	−	0.839428i
$416$	0.389570	+	3.23840i	0.0191002	+	0.158776i
$417$	−18.6411	−	8.50295i	−0.912858	−	0.416391i
$418$	−10.3047	+	1.14541i	−0.504019	+	0.0560237i
$419$			16.6032i			0.811120i	0.914068	+	0.405560i	$0.132923\pi$
$419$			16.6032i			0.811120i	−0.914068	+	0.405560i	$0.867077\pi$
$420$	0.0739374	−	0.646967i	0.00360777	−	0.0315688i
$421$	12.2053	−	1.93313i	0.594850	−	0.0942150i	0.148252	−	0.988950i	$-0.452635\pi$
$421$	12.2053	−	1.93313i	0.594850	−	0.0942150i	0.446598	+	0.894735i	$0.352635\pi$
$422$	−1.24258	−	0.196805i	−0.0604878	−	0.00958033i
$423$	1.99859	−	4.93693i	0.0971747	−	0.240042i
$424$	−0.148590	+	0.0757106i	−0.00721619	+	0.00367683i
$425$	37.1287	+	51.1032i	1.80101	+	2.47887i
$426$	−14.3605	+	8.11825i	−0.695766	+	0.393331i
$427$	−0.734625	+	1.44178i	−0.0355510	+	0.0697728i
$428$	−0.523889			−0.0253231
$429$	19.9413	−	5.59868i	0.962774	−	0.270307i
$430$	32.0742			1.54676
$431$	−6.42208	+	12.6040i	−0.309341	+	0.607115i	−0.992373	−	0.123273i	$-0.960661\pi$
$431$	−6.42208	+	12.6040i	−0.309341	+	0.607115i	0.683032	+	0.730388i	$0.260661\pi$
$432$	−7.47119	+	21.0292i	−0.359458	+	1.01177i
$433$	−0.703505	−	0.968292i	−0.0338083	−	0.0465331i	0.791778	−	0.610809i	$-0.209156\pi$
$433$	−0.703505	−	0.968292i	−0.0338083	−	0.0465331i	−0.825587	+	0.564276i	$0.809156\pi$
$434$	0.339570	−	0.173019i	0.0162999	−	0.00830520i
$435$	1.17555	+	27.1381i	0.0563634	+	1.30117i
$436$	−0.321335	−	0.0508944i	−0.0153891	−	0.00243740i
$437$	−14.5574	+	2.30567i	−0.696376	+	0.110295i
$438$	−8.08472	−	0.923946i	−0.386303	−	0.0441478i
$439$			41.7125i			1.99083i	0.0956474	+	0.995415i	$0.469508\pi$
$439$			41.7125i			1.99083i	−0.0956474	+	0.995415i	$0.530492\pi$
$440$	29.1573	+	16.6023i	1.39002	+	0.791484i
$441$	14.9680	−	12.9935i	0.712764	−	0.618739i
$442$	−4.44352	−	36.9379i	−0.211357	−	1.75696i
$443$	−11.4467	+	15.7550i	−0.543849	+	0.748543i	−0.989162	−	0.146832i	$-0.953092\pi$
$443$	−11.4467	+	15.7550i	−0.543849	+	0.748543i	0.445313	+	0.895375i	$0.353092\pi$
$444$	−0.795297	+	1.20067i	−0.0377431	+	0.0569812i
$445$	−5.58478	+	17.1882i	−0.264744	+	0.814798i
$446$	0.706172	−	2.17337i	0.0334382	−	0.102912i
$447$	0.313298	+	0.207522i	0.0148185	+	0.00981546i
$448$	4.49525	−	0.711978i	0.212381	−	0.0336378i
$449$	−10.3941	−	5.29606i	−0.490528	−	0.249936i	0.191188	−	0.981553i	$-0.438766\pi$
$449$	−10.3941	−	5.29606i	−0.490528	−	0.249936i	−0.681716	+	0.731617i	$0.738766\pi$
$450$	−39.5754	−	2.79465i	−1.86560	−	0.131741i
$451$	−26.6047	+	17.5043i	−1.25276	+	0.824247i
$452$	1.38942			0.0653527
$453$	−4.16540	+	3.31098i	−0.195708	+	0.155563i
$454$	14.5022	−	19.9606i	0.680623	−	0.936797i
$455$	7.93932	+	2.91174i	0.372201	+	0.136504i
$456$	7.34189	+	6.73224i	0.343816	+	0.315266i
$457$	12.7263	+	24.9769i	0.595313	+	1.16837i	0.970428	+	0.241390i	$0.0776033\pi$
$457$	12.7263	+	24.9769i	0.595313	+	1.16837i	−0.375115	+	0.926978i	$0.622397\pi$
$458$	−16.9790	−	23.3696i	−0.793378	−	1.09199i
$459$	12.2124	−	34.3743i	0.570025	−	1.60445i
$460$	−3.70295	−	1.88675i	−0.172651	−	0.0879701i
$461$	−5.89615	−	5.89615i	−0.274611	−	0.274611i	0.556342	−	0.830953i	$-0.312204\pi$
$461$	−5.89615	−	5.89615i	−0.274611	−	0.274611i	−0.830953	+	0.556342i	$0.812204\pi$
$462$	1.62007	+	5.03897i	0.0753722	+	0.234434i
$463$	−14.9566	−	14.9566i	−0.695093	−	0.695093i	0.268255	−	0.963348i	$-0.413553\pi$
$463$	−14.9566	−	14.9566i	−0.695093	−	0.695093i	−0.963348	+	0.268255i	$0.913553\pi$
$464$	17.1222	−	5.56333i	0.794876	−	0.258271i
$465$	−1.31906	−	2.33331i	−0.0611702	−	0.108204i
$466$	12.7450	+	2.01861i	0.590400	+	0.0935101i
$467$	3.70891	−	11.4148i	0.171628	−	0.528216i	−0.827836	−	0.560971i	$-0.810428\pi$
$467$	3.70891	−	11.4148i	0.171628	−	0.528216i	0.999463	+	0.0327547i	$0.0104280\pi$
$468$	1.45118	+	0.948892i	0.0670808	+	0.0438626i
$469$	7.80189	−	5.66841i	0.360258	−	0.261743i
$470$	−1.52724	−	9.64259i	−0.0704461	−	0.444779i
$471$	−1.93159	+	16.9018i	−0.0890031	+	0.778796i
$472$			0.558545i			0.0257091i
$473$	−17.6252	+	7.97386i	−0.810406	+	0.366638i
$474$	12.8210	+	34.3271i	0.588887	+	1.57670i
$475$	−8.68805	+	17.0513i	−0.398635	+	0.782365i
$476$	0.696781	−	0.110359i	0.0319369	−	0.00505831i
$477$	−0.0417448	+	0.180253i	−0.00191136	+	0.00825320i
$478$	−15.6818	−	5.09531i	−0.717267	−	0.233054i
$479$	6.55842	+	12.8716i	0.299662	+	0.588119i	0.990914	−	0.134494i	$-0.0429408\pi$
$479$	6.55842	+	12.8716i	0.299662	+	0.588119i	−0.691253	+	0.722613i	$0.742941\pi$
$480$	1.16678	+	5.74499i	0.0532560	+	0.262222i
$481$	−12.7216	−	13.7094i	−0.580053	−	0.625096i
$482$	29.3744	−	9.54433i	1.33797	−	0.434732i
$483$	2.63264	+	7.04868i	0.119789	+	0.320726i
$484$	1.75568	+	0.163326i	0.0798038	+	0.00742393i
$485$	−36.1337			−1.64075
$486$	11.5948	+	19.7614i	0.525950	+	0.896396i
$487$	−16.1999	+	2.56581i	−0.734086	+	0.116268i	−0.512274	−	0.858822i	$-0.671197\pi$
$487$	−16.1999	+	2.56581i	−0.734086	+	0.116268i	−0.221811	+	0.975090i	$0.571197\pi$
$488$	1.09186	−	6.89375i	0.0494263	−	0.312065i
$489$	−4.58550	+	0.198632i	−0.207364	+	0.00898245i
$490$	11.2272	−	34.5537i	0.507193	−	1.56098i
$491$	−7.12743	+	5.17838i	−0.321656	+	0.233697i	−0.736882	−	0.676022i	$-0.763703\pi$
$491$	−7.12743	+	5.17838i	−0.321656	+	0.233697i	0.415226	+	0.909718i	$0.363703\pi$
$492$	−2.56875	−	0.713326i	−0.115808	−	0.0321592i
$493$	−27.9878	+	9.09380i	−1.26051	+	0.409564i
$494$	9.35982	−	6.27995i	0.421118	−	0.282548i
$495$	34.9130	−	12.9170i	1.56922	−	0.580576i
$496$	−1.25615	+	1.25615i	−0.0564027	+	0.0564027i
$497$	3.86335	−	1.25528i	0.173295	−	0.0563070i
$498$	−12.5205	+	7.07809i	−0.561057	+	0.317177i
$499$	1.88813	−	11.9212i	0.0845245	−	0.533666i	−0.908700	−	0.417451i	$-0.862924\pi$
$499$	1.88813	−	11.9212i	0.0845245	−	0.533666i	0.993224	−	0.116216i	$-0.0370764\pi$
$500$	−2.13615	+	1.08842i	−0.0955316	+	0.0486758i
$501$	0.0479800	+	1.10764i	0.00214359	+	0.0494856i
$502$	−41.5522	−	6.58122i	−1.85456	−	0.293734i
$503$	15.0918	−	20.7721i	0.672911	−	0.926183i	−0.326911	−	0.945055i	$-0.606008\pi$
$503$	15.0918	−	20.7721i	0.672911	−	0.926183i	0.999822	+	0.0188725i	$0.00600767\pi$
$504$	2.62210	−	4.35713i	0.116797	−	0.194082i
$505$	20.3164	+	20.3164i	0.904067	+	0.904067i
$506$	33.7444	+	1.56619i	1.50012	+	0.0696258i
$507$	−16.4141	+	15.4136i	−0.728975	+	0.684540i
$508$	−0.0265608	−	0.0817458i	−0.00117845	−	0.00362688i
$509$	3.84215	+	24.2584i	0.170300	+	1.07523i	0.913701	+	0.406387i	$0.133211\pi$
$509$	3.84215	+	24.2584i	0.170300	+	1.07523i	−0.743401	+	0.668846i	$0.766789\pi$
$510$	−13.3086	−	65.5286i	−0.589313	−	2.90166i
$511$	1.90572	+	0.619207i	0.0843042	+	0.0273921i
$512$	−17.2332	+	8.78078i	−0.761609	+	0.388059i
$513$	10.9587	−	1.43127i	0.483837	−	0.0631921i
$514$	0.475624	+	3.00297i	0.0209789	+	0.132456i
$515$	−10.3756	−	5.28665i	−0.457205	−	0.232958i
$516$	−1.47337	−	0.672065i	−0.0648616	−	0.0295860i
$517$	3.23644	+	4.91904i	0.142339	+	0.216339i
$518$	3.37955	−	3.37955i	0.148489	−	0.148489i
$519$	4.70300	−	41.1522i	0.206439	−	1.80638i
$520$	−36.4502	−	1.36234i	−1.59845	−	0.0597425i
$521$	−13.4415	−	18.5007i	−0.588883	−	0.810529i	0.405751	−	0.913984i	$-0.367010\pi$
$521$	−13.4415	−	18.5007i	−0.588883	−	0.810529i	−0.994634	+	0.103455i	$0.967010\pi$
$522$	6.93568	−	17.1326i	0.303566	−	0.749872i
$523$	−4.12878	+	12.7071i	−0.180539	+	0.555641i	−0.999843	−	0.0177177i	$-0.994360\pi$
$523$	−4.12878	+	12.7071i	−0.180539	+	0.555641i	0.819304	+	0.573359i	$0.194360\pi$
$524$	−2.09073	+	1.51901i	−0.0913340	+	0.0663581i
$525$	9.41337	+	2.61403i	0.410833	+	0.114086i
$526$	3.86945	+	1.97158i	0.168716	+	0.0859652i
$527$	2.05330	−	2.05330i	0.0894431	−	0.0894431i
$528$	−14.4403	−	20.0050i	−0.628432	−	0.870607i
$529$	25.0211			1.08787
$530$	0.104802	+	0.322549i	0.00455233	+	0.0140106i
$531$	0.474437	+	0.398655i	0.0205888	+	0.0173001i
$532$	0.125626	+	0.172909i	0.00544658	+	0.00749658i
$533$	16.8588	−	30.2389i	0.730234	−	1.30979i
$534$	8.31113	−	9.06376i	0.359658	−	0.392227i
$535$	1.91282	−	12.0771i	0.0826983	−	0.522137i
$536$	−24.4499	+	33.6524i	−1.05608	+	1.45356i
$537$	4.56409	−	39.9368i	0.196955	−	1.72340i
$538$	−11.3285	+	11.3285i	−0.488407	+	0.488407i
$539$	2.42081	+	21.7789i	0.104271	+	0.938082i
$540$	2.73709	+	1.48977i	0.117786	+	0.0641093i
$541$	11.1919	−	21.9654i	0.481178	−	0.944365i	−0.515014	−	0.857182i	$-0.672213\pi$
$541$	11.1919	−	21.9654i	0.481178	−	0.944365i	0.996192	−	0.0871833i	$-0.0277866\pi$
$542$	−1.09947	+	1.51329i	−0.0472263	+	0.0650015i
$543$	5.86810	+	28.8933i	0.251824	+	1.23993i
$544$	−5.65879	+	2.88330i	−0.242619	+	0.123620i
$545$	2.34651	−	7.22181i	0.100513	−	0.309348i
$546$	−4.09283	−	4.04455i	−0.175157	−	0.173091i
$547$	25.0460	+	18.1970i	1.07089	+	0.778048i	0.976072	−	0.217446i	$-0.0697727\pi$
$547$	25.0460	+	18.1970i	1.07089	+	0.778048i	0.0948191	+	0.995495i	$0.469773\pi$
$548$	1.44569	−	2.83732i	0.0617568	−	0.121204i
$549$	−5.07636	−	5.84778i	−0.216654	−	0.249577i
$550$	27.3984	−	34.2510i	1.16827	−	1.46047i
$551$	−6.30424	−	6.30424i	−0.268570	−	0.268570i
$552$	−20.1950	−	25.4064i	−0.859555	−	1.08137i
$553$	−1.41155	−	8.91221i	−0.0600254	−	0.378986i
$554$	−2.24889	+	14.1990i	−0.0955464	+	0.603256i
$555$	−24.7749	−	22.7176i	−1.05163	−	0.964309i
$556$	1.80338	+	0.585952i	0.0764802	+	0.0248499i
$557$	−0.690567	+	4.36007i	−0.0292603	+	0.184742i	−0.997990	−	0.0633778i	$-0.979813\pi$
$557$	−0.690567	+	4.36007i	−0.0292603	+	0.184742i	0.968729	+	0.248120i	$0.0798127\pi$
$558$	0.157710	+	1.81698i	0.00667640	+	0.0769191i
$559$	12.9881	−	16.5403i	0.549338	−	0.699578i
$560$		−	10.0732i		−	0.425671i
$561$	23.6040	+	32.7002i	0.996564	+	1.38060i
$562$	21.5646			0.909648
$563$	0.0252009	+	0.0775603i	0.00106209	+	0.00326878i	0.951586	−	0.307382i	$-0.0994530\pi$
$563$	0.0252009	+	0.0775603i	0.00106209	+	0.00326878i	−0.950524	+	0.310651i	$0.899453\pi$
$564$	−0.131890	+	0.474946i	−0.00555356	+	0.0199988i
$565$	−5.07303	+	32.0299i	−0.213424	+	1.34751i
$566$	−2.75974	−	5.41630i	−0.116001	−	0.227664i
$567$	−1.82953	−	5.33710i	−0.0768329	−	0.224137i
$568$	−14.1753	+	10.2989i	−0.594782	+	0.432134i
$569$	8.11701	+	5.89735i	0.340283	+	0.247230i	0.744781	−	0.667309i	$-0.232554\pi$
$569$	8.11701	+	5.89735i	0.340283	+	0.247230i	−0.404498	+	0.914539i	$0.632554\pi$
$570$	15.8583	−	12.6054i	0.664229	−	0.527980i
$571$		−	7.84208i		−	0.328181i	−0.986445	−	0.164090i	$-0.947531\pi$
$571$		−	7.84208i		−	0.328181i	0.986445	−	0.164090i	$-0.0524689\pi$
$572$	−1.77475	+	0.724338i	−0.0742058	+	0.0302861i
$573$	−2.10205	+	4.60834i	−0.0878143	+	0.192516i
$574$	7.88303	+	4.01661i	0.329031	+	0.167650i
$575$	36.6490	−	50.4430i	1.52837	−	2.10362i
$576$	−4.91409	+	21.2189i	−0.204754	+	0.884119i
$577$	1.09276	+	2.14466i	0.0454922	+	0.0892834i	0.912634	−	0.408779i	$-0.134045\pi$
$577$	1.09276	+	2.14466i	0.0454922	+	0.0892834i	−0.867141	+	0.498062i	$0.834045\pi$
$578$	42.2822	−	21.5439i	1.75871	−	0.896107i
$579$	−7.26627	−	4.81302i	−0.301976	−	0.200022i
$580$	−0.393263	−	2.48296i	−0.0163294	−	0.103099i
$581$	3.36835	−	1.09444i	0.139743	−	0.0454052i
$582$	22.3696	+	10.2037i	0.927250	+	0.422956i
$583$	−0.137778	−	0.151190i	−0.00570618	−	0.00626164i
$584$	−8.64311			−0.357654
$585$	−27.1731	+	29.9890i	−1.12347	+	1.23989i
$586$	21.2318	+	15.4258i	0.877077	+	0.637233i
$587$	0.861223	+	0.136404i	0.0355465	+	0.00563001i	0.174182	−	0.984713i	$-0.444272\pi$
$587$	0.861223	+	0.136404i	0.0355465	+	0.00563001i	−0.138636	+	0.990343i	$0.544272\pi$
$588$	−1.23976	+	1.35203i	−0.0511267	+	0.0557566i
$589$	0.836677	+	0.271853i	0.0344747	+	0.0112015i
$590$	1.12191	+	0.177693i	0.0461882	+	0.00731549i
$591$	−9.10184	+	32.7765i	−0.374400	+	1.34825i
$592$	−10.1141	+	19.8501i	−0.415689	+	0.815835i
$593$	−22.7335	+	22.7335i	−0.933554	+	0.933554i	−0.997926	−	0.0643720i	$-0.979496\pi$
$593$	−22.7335	+	22.7335i	−0.933554	+	0.933554i	0.0643720	+	0.997926i	$0.479496\pi$
$594$	−25.2614	−	1.86232i	−1.03649	−	0.0764119i
$595$			16.4656i			0.675026i
$596$	−0.0309881	−	0.0157892i	−0.00126932	−	0.000646752i
$597$	−29.6727	+	16.7746i	−1.21442	+	0.686538i
$598$	−33.3208	+	15.4384i	−1.36259	+	0.631323i
$599$	−39.1290	−	12.7138i	−1.59877	−	0.519471i	−0.631964	−	0.774998i	$-0.717751\pi$
$599$	−39.1290	−	12.7138i	−1.59877	−	0.519471i	−0.966802	+	0.255527i	$0.917751\pi$
$600$	−42.1003	+	1.82367i	−1.71874	+	0.0744512i
$601$	27.2970	−	19.8324i	1.11347	−	0.808982i	0.130262	−	0.991480i	$-0.458418\pi$
$601$	27.2970	−	19.8324i	1.11347	−	0.808982i	0.983206	+	0.182497i	$0.0584181\pi$
$602$	4.34785	+	3.15890i	0.177205	+	0.128747i
$603$	11.1341	+	44.7872i	0.453415	+	1.82388i
$604$	0.348212	−	0.348212i	0.0141685	−	0.0141685i
$605$	−10.1755	+	39.8769i	−0.413691	+	1.62123i
$606$	−6.84035	−	18.3145i	−0.277870	−	0.743975i
$607$	4.01332	+	12.3517i	0.162896	+	0.501341i	0.998875	−	0.0474196i	$-0.0150998\pi$
$607$	4.01332	+	12.3517i	0.162896	+	0.501341i	−0.835979	+	0.548761i	$0.815100\pi$
$608$	−1.55663	−	1.13096i	−0.0631296	−	0.0458664i
$609$	−2.51340	+	3.79451i	−0.101848	+	0.153761i
$610$	−13.4996	−	4.38629i	−0.546583	−	0.177596i
$611$	−5.59100	−	3.11708i	−0.226187	−	0.126104i
$612$	−0.761703	+	3.28901i	−0.0307900	+	0.132950i
$613$	−32.9762	+	5.22292i	−1.33190	+	0.210952i	−0.781476	−	0.623936i	$-0.785533\pi$
$613$	−32.9762	+	5.22292i	−1.33190	+	0.210952i	−0.550421	+	0.834887i	$0.685533\pi$
$614$	−14.5866	+	4.73947i	−0.588667	+	0.191269i
$615$	25.8231	−	56.6122i	1.04129	−	2.28282i
$616$	2.31733	+	5.12217i	0.0933681	+	0.206378i
$617$	16.8675	+	16.8675i	0.679060	+	0.679060i	0.959788	−	0.280727i	$-0.0905757\pi$
$617$	16.8675	+	16.8675i	0.679060	+	0.679060i	−0.280727	+	0.959788i	$0.590576\pi$
$618$	4.93045	+	6.20279i	0.198332	+	0.249513i
$619$	6.80687	+	42.9769i	0.273591	+	1.72739i	0.615921	+	0.787808i	$0.288784\pi$
$619$	6.80687	+	42.9769i	0.273591	+	1.72739i	−0.342330	+	0.939580i	$0.611216\pi$
$620$	0.145805	+	0.200684i	0.00585568	+	0.00805965i
$621$	−35.9946	−	0.979604i	−1.44441	−	0.0393102i
$622$	7.36984	−	3.75512i	0.295504	−	0.150567i
$623$	−2.44987	+	1.77993i	−0.0981519	+	0.0713115i
$624$	23.9701	+	12.0348i	0.959571	+	0.481777i
$625$	−3.38957	−	10.4320i	−0.135583	−	0.417281i
$626$	22.8403	+	22.8403i	0.912884	+	0.912884i
$627$	−5.58054	+	10.8693i	−0.222865	+	0.434077i
$628$		−	1.57440i		−	0.0628255i
$629$	16.5326	−	32.4470i	0.659196	−	1.29375i
$630$	−7.91766	−	6.65296i	−0.315447	−	0.265060i
$631$	−9.22659	−	1.46135i	−0.367305	−	0.0581754i	−0.0299461	−	0.999552i	$-0.509534\pi$
$631$	−9.22659	−	1.46135i	−0.367305	−	0.0581754i	−0.337359	+	0.941376i	$0.609534\pi$
$632$	17.6697	+	34.6787i	0.702862	+	1.37944i
$633$	−1.00197	+	1.09270i	−0.0398247	+	0.0434311i
$634$	12.1142	+	16.6738i	0.481117	+	0.662201i
$635$	1.98144	−	0.313830i	0.0786312	−	0.0124540i
$636$	0.00194426	−	0.0170127i	7.70949e−5	−	0.000674597i
$637$	−13.2726	−	19.7819i	−0.525880	−	0.783786i
$638$	11.2314	+	17.0705i	0.444655	+	0.675827i
$639$	−1.36935	+	19.3915i	−0.0541706	+	0.767115i
$640$	14.4288	+	44.4074i	0.570350	+	1.75536i
$641$	31.0269	+	22.5423i	1.22549	+	0.890369i	0.996544	−	0.0830705i	$-0.0264727\pi$
$641$	31.0269	+	22.5423i	1.22549	+	0.890369i	0.228944	+	0.973440i	$0.426473\pi$
$642$	−4.59458	+	6.93649i	−0.181334	+	0.273761i
$643$	14.6687	+	28.7889i	0.578476	+	1.13532i	0.976008	+	0.217735i	$0.0698668\pi$
$643$	14.6687	+	28.7889i	0.578476	+	1.13532i	−0.397532	+	0.917588i	$0.630133\pi$
$644$	−0.316137	−	0.620454i	−0.0124575	−	0.0244493i
$645$	20.8725	−	31.5114i	0.821854	−	1.24076i
$646$	17.7552	+	12.8999i	0.698571	+	0.507541i
$647$	−2.90310	−	8.93482i	−0.114133	−	0.351264i	0.877633	−	0.479334i	$-0.159122\pi$
$647$	−2.90310	−	8.93482i	−0.114133	−	0.351264i	−0.991765	+	0.128070i	$0.959122\pi$
$648$	14.6190	+	19.4556i	0.574290	+	0.764287i
$649$	−0.660677	+	0.181269i	−0.0259339	+	0.00711544i
$650$	−9.21288	+	46.7836i	−0.361359	+	1.83500i
$651$	0.0509936	−	0.446205i	0.00199860	−	0.0174881i
$652$	0.419544	−	0.0664493i	0.0164306	−	0.00260235i
$653$	25.2984	+	34.8202i	0.990001	+	1.36262i	0.931263	+	0.364346i	$0.118708\pi$
$653$	25.2984	+	34.8202i	0.990001	+	1.36262i	0.0587378	+	0.998273i	$0.481292\pi$
$654$	−3.49202	+	3.80824i	−0.136549	+	0.148914i
$655$	−27.3835	−	53.7432i	−1.06996	−	2.09992i
$656$	−40.7324	−	6.45138i	−1.59033	−	0.251884i
$657$	−6.16892	+	7.34160i	−0.240672	+	0.286423i
$658$	0.742646	−	1.45752i	0.0289513	−	0.0568202i
$659$		−	38.6996i		−	1.50752i	−0.657149	−	0.753761i	$-0.728238\pi$
$659$		−	38.6996i		−	1.50752i	0.657149	−	0.753761i	$-0.271762\pi$
$660$	−3.07447	+	1.55457i	−0.119674	+	0.0605117i
$661$	−19.8515	−	19.8515i	−0.772134	−	0.772134i	0.206346	−	0.978479i	$-0.433843\pi$
$661$	−19.8515	−	19.8515i	−0.772134	−	0.772134i	−0.978479	+	0.206346i	$0.933843\pi$
$662$	−11.8140	−	36.3597i	−0.459163	−	1.41316i
$663$	−39.1814	−	19.6720i	−1.52168	−	0.763998i
$664$	−12.3591	+	8.97938i	−0.479624	+	0.348468i
$665$	−4.44472	+	2.26470i	−0.172359	+	0.0878212i
$666$	8.92243	+	21.0601i	0.345737	+	0.816061i
$667$	17.0739	+	23.5003i	0.661106	+	0.909934i
$668$	−0.0160510	−	0.101342i	−0.000621030	−	0.00392103i
$669$	−1.67569	−	2.10812i	−0.0647860	−	0.0815045i
$670$	59.8168	+	59.8168i	2.31092	+	2.31092i
$671$	8.50865	−	0.945770i	0.328473	−	0.0365111i
$672$	−0.407644	+	0.893681i	−0.0157252	+	0.0344745i
$673$	−8.20431	+	2.66574i	−0.316253	+	0.102757i	−0.462842	−	0.886441i	$-0.653170\pi$
$673$	−8.20431	+	2.66574i	−0.316253	+	0.102757i	0.146589	+	0.989197i	$0.453170\pi$
$674$	−28.7531	+	4.55405i	−1.10753	+	0.175415i
$675$	−28.4995	+	37.0623i	−1.09695	+	1.42653i
$676$	1.34729	−	1.58974i	0.0518187	−	0.0611439i
$677$	−28.8296	−	9.36732i	−1.10801	−	0.360015i	−0.302832	−	0.953044i	$-0.597932\pi$
$677$	−28.8296	−	9.36732i	−1.10801	−	0.360015i	−0.805181	+	0.593029i	$0.797932\pi$
$678$	12.1854	−	18.3964i	0.467978	−	0.706511i
$679$	−4.89815	−	3.55871i	−0.187974	−	0.136571i
$680$	−21.9471	−	67.5463i	−0.841634	−	2.59028i
$681$	−10.1729	−	27.2372i	−0.389828	−	1.04373i
$682$	−1.75217	−	0.997693i	−0.0670940	−	0.0382036i
$683$	11.9861	−	11.9861i	0.458635	−	0.458635i	−0.439572	−	0.898207i	$-0.644870\pi$
$683$	11.9861	−	11.9861i	0.458635	−	0.458635i	0.898207	+	0.439572i	$0.144870\pi$
$684$	−0.992596	+	0.246759i	−0.0379529	+	0.00943507i
$685$	60.1296	+	43.6867i	2.29743	+	1.66918i
$686$	10.1430	−	7.36930i	0.387261	−	0.281361i
$687$	−34.0088	+	1.47317i	−1.29752	+	0.0562050i
$688$	−23.8249	−	7.74119i	−0.908317	−	0.295130i
$689$	0.208773	+	0.0765672i	0.00795361	+	0.00291698i
$690$	−57.4568	+	32.4815i	−2.18734	+	1.23655i
$691$	−44.5106	−	22.6793i	−1.69326	−	0.862760i	−0.988118	−	0.153695i	$-0.950883\pi$
$691$	−44.5106	−	22.6793i	−1.69326	−	0.862760i	−0.705143	−	0.709065i	$-0.749117\pi$
$692$			3.83332i			0.145721i
$693$	6.00482	+	1.68750i	0.228104	+	0.0641030i
$694$	5.84882	−	5.84882i	0.222018	−	0.222018i
$695$	−20.0923	+	39.4333i	−0.762143	+	1.49579i
$696$	5.25291	−	18.9162i	0.199111	−	0.717016i
$697$	66.5812	+	10.5454i	2.52194	+	0.399436i
$698$	−16.7317	−	5.43646i	−0.633304	−	0.205773i
$699$	10.2771	−	11.2077i	0.388714	−	0.423915i
$700$	−0.893017	−	0.141440i	−0.0337529	−	0.00534593i
$701$	32.3299	+	23.4890i	1.22108	+	0.887169i	0.996190	−	0.0872146i	$-0.0277966\pi$
$701$	32.3299	+	23.4890i	1.22108	+	0.887169i	0.224894	+	0.974383i	$0.427797\pi$
$702$	25.2908	−	10.8922i	0.954539	−	0.411101i
$703$	11.0326			0.416103
$704$	−16.2188	−	17.7977i	−0.611271	−	0.670775i
$705$	−10.4673	−	4.77454i	−0.394219	−	0.179819i
$706$	18.8921	−	6.13841i	0.711013	−	0.231022i
$707$	0.753104	+	4.75491i	0.0283234	+	0.178827i
$708$	−0.0478131	−	0.0316704i	−0.00179693	−	0.00119025i
$709$	12.4367	−	6.33680i	0.467069	−	0.237983i	−0.204585	−	0.978849i	$-0.565584\pi$
$709$	12.4367	−	6.33680i	0.467069	−	0.237983i	0.671654	+	0.740865i	$0.265584\pi$
$710$	16.1771	+	31.7493i	0.607115	+	1.19153i
$711$	42.0682	+	9.74259i	1.57768	+	0.365376i
$712$	7.67750	−	10.5672i	0.287727	−	0.396022i
$713$	−2.55388	−	1.30127i	−0.0956434	−	0.0487328i
$714$	4.64968	−	10.1935i	0.174010	−	0.381483i
$715$	−10.2180	−	43.5574i	−0.382133	−	1.62896i
$716$			3.72010i			0.139027i
$717$	−15.2109	+	12.0908i	−0.568062	+	0.451539i
$718$	18.2840	+	13.2841i	0.682351	+	0.495757i
$719$	1.99320	−	1.44814i	0.0743336	−	0.0540065i	−0.549998	−	0.835166i	$-0.685371\pi$
$719$	1.99320	−	1.44814i	0.0743336	−	0.0540065i	0.624331	+	0.781160i	$0.285371\pi$
$720$	44.6834	+	18.0889i	1.66525	+	0.674135i
$721$	−0.885813	−	1.73851i	−0.0329894	−	0.0647454i
$722$	3.32848	−	21.0152i	0.123873	−	0.782104i
$723$	9.73873	−	35.0700i	0.362187	−	1.30427i
$724$	−0.843182	−	2.59505i	−0.0313366	−	0.0964441i
$725$	37.7160			1.40074
$726$	17.5601	−	21.8135i	0.651717	−	0.809576i
$727$		−	3.82132i		−	0.141725i	−0.997486	−	0.0708624i	$-0.977425\pi$
$727$		−	3.82132i		−	0.141725i	0.997486	−	0.0708624i	$-0.0225751\pi$
$728$	−4.80687	−	3.77455i	−0.178155	−	0.139894i
$729$	26.9600	+	1.46854i	0.998520	+	0.0543904i
$730$	−2.74968	+	17.3608i	−0.101770	+	0.642551i
$731$	38.9442	+	12.6537i	1.44040	+	0.468015i
$732$	0.528215	+	0.484353i	0.0195234	+	0.0179022i
$733$	−6.52651	+	41.2068i	−0.241062	+	1.52201i	0.509074	+	0.860723i	$0.329988\pi$
$733$	−6.52651	+	41.2068i	−0.241062	+	1.52201i	−0.750136	+	0.661284i	$0.770012\pi$
$734$	−4.49734	−	28.3951i	−0.166000	−	1.04808i
$735$	−26.6413	−	33.5163i	−0.982678	−	1.23627i
$736$	4.43282	+	4.43282i	0.163396	+	0.163396i
$737$	−47.7409	−	17.9992i	−1.75856	−	0.663009i
$738$	−31.9731	+	27.7553i	−1.17694	+	1.02169i
$739$	18.8899	−	37.0735i	0.694875	−	1.36377i	−0.226083	−	0.974108i	$-0.572592\pi$
$739$	18.8899	−	37.0735i	0.694875	−	1.36377i	0.920958	−	0.389662i	$-0.127408\pi$
$740$	2.51674	+	1.82852i	0.0925173	+	0.0672177i
$741$	−0.0787970	−	13.2823i	−0.00289468	−	0.487937i
$742$	−0.0175603	+	0.0540451i	−0.000644660	+	0.00198406i
$743$	9.18141	−	4.67816i	0.336833	−	0.171625i	−0.277390	−	0.960757i	$-0.589469\pi$
$743$	9.18141	−	4.67816i	0.336833	−	0.171625i	0.614223	+	0.789132i	$0.289469\pi$
$744$	0.385559	+	1.89842i	0.0141353	+	0.0695993i
$745$	0.477128	−	0.656710i	0.0174806	−	0.0240600i
$746$	−20.4967	+	40.2271i	−0.750438	+	1.47282i
$747$	−1.19390	+	16.9069i	−0.0436824	+	0.618592i
$748$	−2.51398	−	2.75871i	−0.0919204	−	0.100868i
$749$	1.44873	−	1.44873i	0.0529354	−	0.0529354i
$750$	−4.32323	+	37.8291i	−0.157862	+	1.38132i
$751$	18.2180	−	25.0749i	0.664784	−	0.914997i	−0.334844	−	0.942274i	$-0.608684\pi$
$751$	18.2180	−	25.0749i	0.664784	−	0.914997i	0.999628	+	0.0272768i	$0.00868355\pi$
$752$	−1.19282	+	7.53118i	−0.0434977	+	0.274634i
$753$	−33.5061	+	36.5403i	−1.22103	+	1.33160i
$754$	−19.4024	−	10.8172i	−0.706593	−	0.393938i
$755$	6.75584	+	9.29861i	0.245870	+	0.338411i
$756$	0.224306	+	0.471515i	0.00815793	+	0.0171488i
$757$	2.59958	+	8.00069i	0.0944834	+	0.290790i	0.987119	−	0.159990i	$-0.0511461\pi$
$757$	2.59958	+	8.00069i	0.0944834	+	0.290790i	−0.892635	+	0.450780i	$0.851146\pi$
$758$	0.955441			0.0347032
$759$	23.4981	−	32.1331i	0.852927	−	1.16636i
$760$	15.2148	−	15.2148i	0.551897	−	0.551897i
$761$	0.426542	+	0.217334i	0.0154621	+	0.00787835i	0.461704	−	0.887034i	$-0.347238\pi$
$761$	0.426542	+	0.217334i	0.0154621	+	0.00787835i	−0.446242	+	0.894912i	$0.647238\pi$
$762$	−1.31529	−	0.365248i	−0.0476479	−	0.0132315i
$763$	1.02934	−	0.747859i	0.0372646	−	0.0270743i
$764$	0.144856	−	0.445820i	0.00524069	−	0.0161292i
$765$	−73.0394	−	29.5681i	−2.64075	−	1.06904i
$766$	28.5069	+	39.2364i	1.03000	+	1.41767i
$767$	0.545938	−	0.506599i	0.0197127	−	0.0182922i
$768$	0.751859	−	6.57892i	0.0271304	−	0.237396i
$769$	9.31474	−	9.31474i	0.335898	−	0.335898i	−0.518923	−	0.854821i	$-0.673667\pi$
$769$	9.31474	−	9.31474i	0.335898	−	0.335898i	0.854821	+	0.518923i	$0.173667\pi$
$770$	11.0257	−	3.02512i	0.397340	−	0.109018i
$771$	3.25980	+	1.48693i	0.117399	+	0.0535503i
$772$	0.718701	+	0.366197i	0.0258666	+	0.0131797i
$773$	−0.332576	−	2.09980i	−0.0119619	−	0.0755246i	0.980985	−	0.194082i	$-0.0621729\pi$
$773$	−0.332576	−	2.09980i	−0.0119619	−	0.0755246i	−0.992947	+	0.118558i	$0.962173\pi$
$774$	−21.8201	+	13.6139i	−0.784307	+	0.489342i
$775$	−3.31597	+	1.68957i	−0.119113	+	0.0606912i
$776$	24.8369	+	8.06999i	0.891592	+	0.289696i
$777$	−1.12099	−	5.51952i	−0.0402152	−	0.198012i
$778$	−2.48509	−	15.6902i	−0.0890947	−	0.562522i
$779$	6.31100	+	19.4233i	0.226115	+	0.695911i
$780$	2.18340	−	3.04300i	0.0781784	−	0.108957i
$781$	−16.7826	−	13.4249i	−0.600528	−	0.480381i
$782$	−50.5617	−	50.5617i	−1.80808	−	1.80808i
$783$	−12.3185	−	17.9631i	−0.440228	−	0.641949i
$784$	−16.6793	+	22.9570i	−0.595688	+	0.819894i
$785$	36.2943	+	5.74845i	1.29540	+	0.205171i
$786$	1.77619	+	41.0040i	0.0633545	+	1.46256i
$787$	−10.8817	+	5.54453i	−0.387892	+	0.197641i	−0.637051	−	0.770822i	$-0.719846\pi$
$787$	−10.8817	+	5.54453i	−0.387892	+	0.197641i	0.249159	+	0.968463i	$0.419846\pi$
$788$	0.492482	−	3.10941i	0.0175439	−	0.110768i
$789$	4.45506	−	2.51854i	0.158604	−	0.0896622i
$790$	75.2778	−	24.4592i	2.67826	−	0.870221i
$791$	−3.84221	+	3.84221i	−0.136613	+	0.136613i
$792$	−26.8826	+	1.08128i	−0.955231	+	0.0384215i
$793$	−7.72846	+	5.18539i	−0.274446	+	0.184139i
$794$	30.5420	−	9.92368i	1.08389	−	0.352178i
$795$	0.385090	+	0.106937i	0.0136577	+	0.00379267i
$796$	2.55210	−	1.85421i	0.0904568	−	0.0657207i
$797$	−11.8347	+	36.4234i	−0.419206	+	1.29018i	0.489228	+	0.872156i	$0.337279\pi$
$797$	−11.8347	+	36.4234i	−0.419206	+	1.29018i	−0.908434	+	0.418028i	$0.862721\pi$
$798$	3.39115	−	0.146896i	0.120045	−	0.00520005i
$799$	1.94978	−	12.3104i	0.0689784	−	0.435512i
$800$	8.03944	−	1.27332i	0.284237	−	0.0450187i
$801$	−3.49621	−	14.0636i	−0.123532	−	0.496913i
$802$	−43.1815			−1.52479
$803$	−2.80502	−	10.2235i	−0.0989870	−	0.360781i
$804$	−1.49440	−	4.00113i	−0.0527033	−	0.141109i
$805$	15.4574	−	5.02242i	0.544803	−	0.177017i
$806$	2.19043	+	0.0818678i	0.0771544	+	0.00288367i
$807$	3.75764	+	18.5018i	0.132275	+	0.651296i
$808$	−9.42726	−	18.5020i	−0.331650	−	0.650900i
$809$	23.6064	+	7.67017i	0.829956	+	0.269669i	0.693027	−	0.720912i	$-0.256277\pi$
$809$	23.6064	+	7.67017i	0.829956	+	0.269669i	0.136929	+	0.990581i	$0.456277\pi$
$810$	43.7298	−	23.1747i	1.53651	−	0.814274i
$811$	0.850150	−	0.134651i	0.0298528	−	0.00472822i	−0.141490	−	0.989940i	$-0.545189\pi$
$811$	0.850150	−	0.134651i	0.0298528	−	0.00472822i	0.171343	+	0.985211i	$0.445189\pi$
$812$	0.191231	−	0.375312i	0.00671090	−	0.0131709i
$813$	0.771251	+	2.06496i	0.0270490	+	0.0724215i
$814$	−24.7646	−	5.10929i	−0.867998	−	0.179081i
$815$			9.91426i			0.347281i
$816$	−5.92981	+	51.8871i	−0.207585	+	1.81641i
$817$	1.94068	+	12.2530i	0.0678957	+	0.428677i
$818$	23.2332	−	16.8799i	0.812330	−	0.590192i
$819$	−6.63702	+	1.38899i	−0.231916	+	0.0485354i
$820$	−1.77951	+	5.47678i	−0.0621433	+	0.191257i
$821$	15.6214	+	2.47419i	0.545192	+	0.0863499i	0.422954	−	0.906151i	$-0.360993\pi$
$821$	15.6214	+	2.47419i	0.545192	+	0.0863499i	0.122237	+	0.992501i	$0.460993\pi$
$822$	−24.8884	−	44.0253i	−0.868081	−	1.53556i
$823$	−23.0385	+	7.48566i	−0.803072	+	0.260934i	−0.681661	−	0.731669i	$-0.738742\pi$
$823$	−23.0385	+	7.48566i	−0.803072	+	0.260934i	−0.121411	+	0.992602i	$0.538742\pi$
$824$	5.95109	+	5.95109i	0.207316	+	0.207316i
$825$	−15.8203	−	49.2067i	−0.550792	−	1.71316i
$826$	0.134581	+	0.134581i	0.00468267	+	0.00468267i
$827$	−14.2541	−	7.26283i	−0.495664	−	0.252553i	0.188243	−	0.982122i	$-0.439721\pi$
$827$	−14.2541	−	7.26283i	−0.495664	−	0.252553i	−0.683907	+	0.729569i	$0.739721\pi$
$828$	3.31995	−	0.288164i	0.115376	−	0.0100144i
$829$	−28.4499	−	39.1579i	−0.988105	−	1.36001i	−0.932347	−	0.361566i	$-0.882242\pi$
$829$	−28.4499	−	39.1579i	−0.988105	−	1.36001i	−0.0557583	−	0.998444i	$-0.517758\pi$
$830$	14.1044	+	27.6814i	0.489570	+	0.960834i
$831$	12.4863	+	11.4495i	0.433146	+	0.397179i
$832$	24.5762	+	9.01328i	0.852025	+	0.312479i
$833$	27.2639	−	37.5255i	0.944638	−	1.30018i
$834$	23.5741	−	18.7385i	0.816305	−	0.648862i
$835$	2.39481			0.0828758
$836$	0.398907	−	1.05806i	0.0137965	−	0.0365937i
$837$	1.88773	+	1.02747i	0.0652496	+	0.0355146i
$838$	−21.7435	−	11.0789i	−0.751117	−	0.382713i
$839$	−19.2255	+	3.04502i	−0.663738	+	0.105126i	−0.479209	−	0.877701i	$-0.659076\pi$
$839$	−19.2255	+	3.04502i	−0.663738	+	0.105126i	−0.184530	+	0.982827i	$0.559076\pi$
$840$	−9.15774	−	6.06589i	−0.315972	−	0.209293i
$841$	3.53173	−	10.8696i	0.121784	−	0.374812i
$842$	−5.61265	+	17.2739i	−0.193425	+	0.595300i
$843$	14.0333	−	21.1862i	0.483333	−	0.729692i
$844$	0.0806475	−	0.111002i	0.00277600	−	0.00382084i
$845$	31.7287	+	36.8631i	1.09150	+	1.26813i
$846$	5.13178	+	5.91162i	0.176434	+	0.203246i
$847$	−5.30671	+	4.40341i	−0.182341	+	0.151303i
$848$		−	0.264886i		−	0.00909621i
$849$	−7.11718	−	0.813372i	−0.244261	−	0.0279149i
$850$	−91.6996	+	14.5238i	−3.14527	+	0.498162i
$851$	−35.5030	−	5.62313i	−1.21703	−	0.192758i
$852$	−0.0778593	−	1.79741i	−0.00266741	−	0.0615783i
$853$	−16.1934	+	8.25097i	−0.554453	+	0.282508i	−0.708683	−	0.705527i	$-0.750710\pi$
$853$	−16.1934	+	8.25097i	−0.554453	+	0.282508i	0.154230	+	0.988035i	$0.450710\pi$
$854$	−1.39796	−	1.92413i	−0.0478372	−	0.0658422i
$855$	−2.06431	−	23.7830i	−0.0705979	−	0.813362i
$856$	−4.01204	+	7.87408i	−0.137129	+	0.269130i
$857$	−0.638633			−0.0218153			−0.0109077	−	0.999941i	$-0.503472\pi$
$857$	−0.638633			−0.0218153			−0.0109077	+	0.999941i	$0.503472\pi$
$858$	−5.97427	+	29.8509i	−0.203958	+	1.01909i
$859$	−23.2718			−0.794022			−0.397011	−	0.917814i	$-0.629953\pi$
$859$	−23.2718			−0.794022			−0.397011	+	0.917814i	$0.629953\pi$
$860$	−1.58807	+	3.11677i	−0.0541529	+	0.106281i
$861$	9.07606	−	5.13088i	0.309311	−	0.174860i
$862$	−12.2209	−	16.8207i	−0.416246	−	0.572914i
$863$	15.6403	−	7.96911i	0.532401	−	0.271272i	−0.167055	−	0.985948i	$-0.553426\pi$
$863$	15.6403	−	7.96911i	0.532401	−	0.271272i	0.699456	+	0.714676i	$0.253426\pi$
$864$	−3.23223	−	3.41308i	−0.109963	−	0.116115i
$865$	−88.3684	−	13.9962i	−3.00462	−	0.475885i
$866$	1.73750	−	0.275193i	0.0590427	−	0.00935145i
$867$	6.34958	−	55.5601i	0.215643	−	1.88692i
$868$			0.0415639i			0.00141077i
$869$	−35.2854	+	32.1552i	−1.19697	+	1.09079i
$870$	−36.3244	−	16.5690i	−1.23151	−	0.561743i
$871$	55.0689	−	6.62462i	1.86594	−	0.224467i
$872$	−3.22579	+	4.43992i	−0.109239	+	0.150355i
$873$	24.5818	−	15.3370i	0.831968	−	0.519078i
$874$	6.69427	−	20.6029i	0.226437	−	0.696902i
$875$	2.89733	−	8.91705i	0.0979475	−	0.301451i
$876$	0.490078	−	0.739875i	0.0165582	−	0.0249981i
$877$	26.4375	−	4.18728i	0.892730	−	0.141395i	0.306817	−	0.951769i	$-0.400736\pi$
$877$	26.4375	−	4.18728i	0.892730	−	0.141395i	0.585913	+	0.810374i	$0.300736\pi$
$878$	−54.6266	−	27.8336i	−1.84356	−	0.939340i
$879$	28.9718	−	10.8208i	0.977196	−	0.364977i
$880$	−44.5215	+	29.2926i	−1.50082	+	0.987453i
$881$	−3.55714			−0.119843			−0.0599215	−	0.998203i	$-0.519085\pi$
$881$	−3.55714			−0.119843			−0.0599215	+	0.998203i	$0.519085\pi$
$882$	7.02849	+	28.2723i	0.236662	+	0.951979i
$883$	−9.16944	+	12.6207i	−0.308576	+	0.424719i	−0.934937	−	0.354815i	$-0.884544\pi$
$883$	−9.16944	+	12.6207i	−0.308576	+	0.424719i	0.626360	+	0.779534i	$0.284544\pi$
$884$	3.80940	+	1.39709i	0.128124	+	0.0469894i
$885$	0.904663	−	0.986587i	0.0304099	−	0.0331638i
$886$	−12.9947	−	25.5034i	−0.436564	−	0.856805i
$887$	15.1220	+	20.8137i	0.507748	+	0.698855i	0.983538	−	0.180704i	$-0.0578376\pi$
$887$	15.1220	+	20.8137i	0.507748	+	0.698855i	−0.475789	+	0.879559i	$0.657838\pi$
$888$	11.9556	+	21.1483i	0.401203	+	0.709691i
$889$	0.299505	+	0.152605i	0.0100451	+	0.00511822i
$890$	−18.7830	−	18.7830i	−0.629608	−	0.629608i
$891$	−18.2687	+	23.6063i	−0.612024	+	0.790839i
$892$	0.176230	+	0.176230i	0.00590063	+	0.00590063i
$893$	3.59124	−	1.16687i	0.120176	−	0.0390477i
$894$	−0.480826	+	0.271820i	−0.0160812	+	0.00909104i
$895$	−85.7584	−	13.5828i	−2.86659	−	0.454023i
$896$	−2.41765	+	7.44075i	−0.0807679	+	0.248578i
$897$	−6.51619	+	42.7827i	−0.217569	+	1.42847i
$898$	13.8714	−	10.0782i	0.462895	−	0.336313i
$899$	−0.271228	−	1.71247i	−0.00904597	−	0.0571140i
$900$	2.23104	−	3.70731i	0.0743680	−	0.123577i
$901$			0.432981i			0.0144247i
$902$	−5.17105	−	46.5215i	−0.172177	−	1.54900i
$903$	5.93286	−	2.21589i	0.197433	−	0.0737402i
$904$	10.6404	−	20.8830i	0.353896	−	0.694560i
$905$	62.9015	−	9.96262i	2.09092	−	0.331169i
$906$	−1.55659	−	7.66433i	−0.0517142	−	0.254630i
$907$	−9.20147	−	2.98974i	−0.305530	−	0.0992727i	0.152240	−	0.988344i	$-0.451351\pi$
$907$	−9.20147	−	2.98974i	−0.305530	−	0.0992727i	−0.457769	+	0.889071i	$0.651351\pi$
$908$	1.22160	+	2.39753i	0.0405403	+	0.0795649i
$909$	−22.4445	−	5.19794i	−0.744438	−	0.172405i
$910$	−9.11090	+	8.45439i	−0.302023	+	0.280260i
$911$	19.1154	−	6.21097i	0.633321	−	0.205778i	0.0252753	−	0.999681i	$-0.491954\pi$
$911$	19.1154	−	6.21097i	0.633321	−	0.205778i	0.608046	+	0.793902i	$0.291954\pi$
$912$	−14.8219	+	5.53591i	−0.490804	+	0.183312i
$913$	−14.6323	−	11.7048i	−0.484258	−	0.387373i
$914$	−41.2016			−1.36283
$915$	−13.0943	+	10.4083i	−0.432883	+	0.344089i
$916$	3.11159	−	0.492827i	0.102810	−	0.0162835i
$917$	1.58102	−	9.98215i	0.0522098	−	0.329640i
$918$	36.8675	+	38.9303i	1.21681	+	1.28489i
$919$	−12.9610	+	39.8898i	−0.427543	+	1.31584i	0.472994	+	0.881066i	$0.343173\pi$
$919$	−12.9610	+	39.8898i	−0.427543	+	1.31584i	−0.900538	+	0.434778i	$0.856827\pi$
$920$	−56.7159	+	41.2065i	−1.86987	+	1.35854i
$921$	−4.83600	+	17.4149i	−0.159352	+	0.573840i
$922$	11.6559	−	3.78724i	0.383867	−	0.124726i
$923$	22.9234	+	4.51421i	0.754534	+	0.148587i
$924$	−0.569869	−	0.0920642i	−0.0187473	−	0.00302869i
$925$	−33.0021	+	33.0021i	−1.08510	+	1.08510i
$926$	29.5673	−	9.60700i	0.971642	−	0.315706i
$927$	9.30248	−	0.807434i	0.305534	−	0.0265196i
$928$	−0.593213	+	3.74540i	−0.0194732	+	0.122949i
$929$	−33.6553	+	17.1482i	−1.10419	+	0.562615i	−0.908431	−	0.418036i	$-0.862719\pi$
$929$	−33.6553	+	17.1482i	−1.10419	+	0.562615i	−0.195764	+	0.980651i	$0.562719\pi$
$930$	3.93587	−	0.170491i	0.129062	−	0.00559064i
$931$	13.8795	+	2.19830i	0.454882	+	0.0720463i
$932$	−0.827191	+	1.13853i	−0.0270955	+	0.0372938i
$933$	1.10674	−	9.68420i	0.0362330	−	0.317046i
$934$	12.4740	+	12.4740i	0.408161	+	0.408161i
$935$	72.7748	−	47.8816i	2.37999	−	1.56590i
$936$	25.3753	−	14.5445i	0.829419	−	0.475402i
$937$	3.96169	+	12.1928i	0.129423	+	0.398322i	0.994681	−	0.103004i	$-0.0328455\pi$
$937$	3.96169	+	12.1928i	0.129423	+	0.398322i	−0.865258	+	0.501327i	$0.832846\pi$
$938$	2.21734	+	13.9997i	0.0723986	+	0.457107i
$939$	37.3031	−	7.57608i	1.21734	−	0.247236i
$940$	1.01262	+	0.329021i	0.0330281	+	0.0107315i
$941$	−3.32732	+	1.69535i	−0.108467	+	0.0552669i	−0.507382	−	0.861721i	$-0.669387\pi$
$941$	−3.32732	+	1.69535i	−0.108467	+	0.0552669i	0.398915	+	0.916988i	$0.369387\pi$
$942$	−20.8457	−	13.8077i	−0.679190	−	0.449881i
$943$	−10.4092	−	65.7209i	−0.338969	−	2.14017i
$944$	−0.790473	−	0.402766i	−0.0257277	−	0.0131089i
$945$	−11.6887	+	3.44927i	−0.380233	+	0.112205i
$946$	1.31826	−	28.4026i	0.0428604	−	0.923448i
$947$	22.6766	−	22.6766i	0.736892	−	0.736892i	−0.235083	−	0.971975i	$-0.575536\pi$
$947$	22.6766	−	22.6766i	0.736892	−	0.736892i	0.971975	+	0.235083i	$0.0755363\pi$
$948$	−3.97049	−	0.453760i	−0.128956	−	0.0147374i
$949$	7.83928	+	8.44802i	0.254474	+	0.274234i
$950$	−16.5330	−	22.7557i	−0.536400	−	0.738292i
$951$	24.2646	−	1.05108i	0.786835	−	0.0340836i
$952$	3.67738	−	11.3178i	0.119185	−	0.366813i
$953$	35.7459	−	25.9709i	1.15792	−	0.841281i	0.168410	−	0.985717i	$-0.446137\pi$
$953$	35.7459	−	25.9709i	1.15792	−	0.841281i	0.989514	+	0.144436i	$0.0461369\pi$
$954$	−0.208203	−	0.174947i	−0.00674082	−	0.00566410i
$955$	9.74847	+	4.96709i	0.315453	+	0.160731i
$956$	1.27157	−	1.27157i	0.0411256	−	0.0411256i
$957$	24.0799	+	0.0744022i	0.778392	+	0.00240508i
$958$	−21.2329			−0.686004
$959$	3.84835	+	11.8440i	0.124270	+	0.382462i
$960$	45.3317	+	12.5883i	1.46308	+	0.406287i
$961$	−18.1208	−	24.9411i	−0.584541	−	0.804552i
$962$	26.4426	−	7.51218i	0.852542	−	0.242202i
$963$	3.82482	+	9.02793i	0.123253	+	0.290921i
$964$	−0.526943	+	3.32698i	−0.0169717	+	0.107155i
$965$	−11.0659	+	15.2310i	−0.356225	+	0.490302i
$966$	−10.9876	−	1.25570i	−0.353521	−	0.0404014i
$967$	33.8866	−	33.8866i	1.08972	−	1.08972i	0.0941619	−	0.995557i	$-0.469983\pi$
$967$	33.8866	−	33.8866i	1.08972	−	1.08972i	0.995557	−	0.0941619i	$-0.0300171\pi$
$968$	15.9002	−	25.1372i	0.511051	−	0.807942i
$969$	24.2279	−	9.04898i	0.778313	−	0.290695i
$970$	24.1111	−	47.3206i	0.774160	−	1.51937i
$971$	−4.03213	+	5.54974i	−0.129397	+	0.178100i	−0.868800	−	0.495164i	$-0.835108\pi$
$971$	−4.03213	+	5.54974i	−0.129397	+	0.178100i	0.739403	+	0.673264i	$0.235108\pi$
$972$	−2.49437	+	0.148270i	−0.0800071	+	0.00475578i
$973$	−6.60731	+	3.36659i	−0.211821	+	0.107928i
$974$	7.44956	−	22.9274i	0.238699	−	0.734641i
$975$	39.9674	+	39.4959i	1.27998	+	1.26488i
$976$	8.96895	+	6.51632i	0.287089	+	0.208582i
$977$	2.37925	−	4.66955i	0.0761191	−	0.149392i	−0.849810	−	0.527088i	$-0.823284\pi$
$977$	2.37925	−	4.66955i	0.0761191	−	0.149392i	0.925930	+	0.377696i	$0.123284\pi$
$978$	2.79965	−	6.13770i	0.0895230	−	0.196262i
$979$	14.9911	+	5.65192i	0.479117	+	0.180636i
$980$	2.80183	+	2.80183i	0.0895012	+	0.0895012i
$981$	1.46897	+	5.90898i	0.0469006	+	0.188659i
$982$	−2.02565	−	12.7894i	−0.0646411	−	0.408128i
$983$	1.04836	−	6.61906i	0.0334374	−	0.211115i	−0.965313	−	0.261096i	$-0.915916\pi$
$983$	1.04836	−	6.61906i	0.0334374	−	0.211115i	0.998750	+	0.0499809i	$0.0159160\pi$
$984$	−30.3933	+	33.1457i	−0.968904	+	1.05665i
$985$	69.8822	+	22.7061i	2.22663	+	0.723476i
$986$	6.76631	−	42.7208i	0.215483	−	1.36051i
$987$	−0.948668	−	1.67811i	−0.0301964	−	0.0534148i
$988$	0.146818	+	1.22046i	0.00467091	+	0.0388281i
$989$		−	40.4193i		−	1.28526i
$990$	−6.38041	+	54.3410i	−0.202783	+	1.72707i
$991$	30.8621			0.980368			0.490184	−	0.871619i	$-0.336930\pi$
$991$	30.8621			0.980368			0.490184	+	0.871619i	$0.336930\pi$
$992$	−0.115628	−	0.355868i	−0.00367120	−	0.0112988i
$993$	−43.4097	−	12.0546i	−1.37757	−	0.382542i
$994$	−0.934000	+	5.89705i	−0.0296247	+	0.187043i
$995$	33.4264	+	65.6030i	1.05969	+	2.07975i
$996$	−0.0678834	−	1.56712i	−0.00215097	−	0.0496560i
$997$	33.1769	−	24.1044i	1.05072	−	0.763396i	0.0783739	−	0.996924i	$-0.475027\pi$
$997$	33.1769	−	24.1044i	1.05072	−	0.763396i	0.972350	+	0.233528i	$0.0750272\pi$
$998$	14.3521	+	10.4274i	0.454307	+	0.330073i
$999$	26.4969	+	4.93910i	0.838324	+	0.156266i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bi.a.5.15	✓	416
3.2	odd	2	inner	429.2.bi.a.5.38	yes	416
11.9	even	5	inner	429.2.bi.a.317.38	yes	416
13.8	odd	4	inner	429.2.bi.a.203.15	yes	416
33.20	odd	10	inner	429.2.bi.a.317.15	yes	416
39.8	even	4	inner	429.2.bi.a.203.38	yes	416
143.86	odd	20	inner	429.2.bi.a.86.38	yes	416
429.86	even	20	inner	429.2.bi.a.86.15	yes	416

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bi.a.5.15	✓	416	1.1	even	1	trivial
429.2.bi.a.5.38	yes	416	3.2	odd	2	inner
429.2.bi.a.86.15	yes	416	429.86	even	20	inner
429.2.bi.a.86.38	yes	416	143.86	odd	20	inner
429.2.bi.a.203.15	yes	416	13.8	odd	4	inner
429.2.bi.a.203.38	yes	416	39.8	even	4	inner
429.2.bi.a.317.15	yes	416	33.20	odd	10	inner
429.2.bi.a.317.38	yes	416	11.9	even	5	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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bi (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.667273 + 1.30960i) q^{2} +(0.852386 + 1.50779i) q^{3} +(-0.0942200 - 0.129683i) q^{4} +(3.33356 - 1.69853i) q^{5} +(-2.54337 + 0.110172i) q^{6} +(0.619167 + 0.0980665i) q^{7} +(-2.67070 + 0.422997i) q^{8} +(-1.54688 + 2.57044i) q^{9} +O(q^{10})\)	\(q+(-0.667273 + 1.30960i) q^{2} +(0.852386 + 1.50779i) q^{3} +(-0.0942200 - 0.129683i) q^{4} +(3.33356 - 1.69853i) q^{5} +(-2.54337 + 0.110172i) q^{6} +(0.619167 + 0.0980665i) q^{7} +(-2.67070 + 0.422997i) q^{8} +(-1.54688 + 2.57044i) q^{9} +5.49900i q^{10} +(-1.36709 - 3.02177i) q^{11} +(0.115223 - 0.252604i) q^{12} +(2.83576 + 2.22676i) q^{13} +(-0.541581 + 0.745422i) q^{14} +(5.40251 + 3.57851i) q^{15} +(1.32720 - 4.08469i) q^{16} +(-2.16943 + 6.67683i) q^{17} +(-2.33405 - 3.74097i) q^{18} +(-2.10072 + 0.332722i) q^{19} +(-0.534358 - 0.272269i) q^{20} +(0.379905 + 1.01717i) q^{21} +(4.86952 + 0.226011i) q^{22} +6.92972 q^{23} +(-2.91425 - 3.66630i) q^{24} +(5.28866 - 7.27922i) q^{25} +(-4.80838 + 2.22785i) q^{26} +(-5.19423 - 0.141363i) q^{27} +(-0.0456204 - 0.0895351i) q^{28} +(2.46387 + 3.39123i) q^{29} +(-8.29135 + 4.68727i) q^{30} +(-0.368539 - 0.187780i) q^{31} +(0.639682 + 0.639682i) q^{32} +(3.39091 - 4.63699i) q^{33} +(-7.29635 - 7.29635i) q^{34} +(2.23060 - 0.724765i) q^{35} +(0.479089 - 0.0415838i) q^{36} +(-5.12330 - 0.811450i) q^{37} +(0.966023 - 2.97311i) q^{38} +(-0.940324 + 6.17380i) q^{39} +(-8.18444 + 5.94634i) q^{40} +(-1.50210 - 9.48391i) q^{41} +(-1.58558 - 0.181205i) q^{42} -5.83274i q^{43} +(-0.263064 + 0.461998i) q^{44} +(-0.790626 + 11.1961i) q^{45} +(-4.62402 + 9.07514i) q^{46} +(-1.75352 + 0.277730i) q^{47} +(7.29015 - 1.48059i) q^{48} +(-6.28364 - 2.04168i) q^{49} +(6.00386 + 11.7832i) q^{50} +(-11.9165 + 2.42018i) q^{51} +(0.0215863 - 0.577555i) q^{52} +(0.0586559 - 0.0190585i) q^{53} +(3.65110 - 6.70802i) q^{54} +(-9.68983 - 7.75119i) q^{55} -1.69509 q^{56} +(-2.29230 - 2.88385i) q^{57} +(-6.08521 + 0.963803i) q^{58} +(0.0323136 - 0.204020i) q^{59} +(-0.0449539 - 1.03778i) q^{60} +(-0.797652 + 2.45492i) q^{61} +(0.491833 - 0.357337i) q^{62} +(-1.20985 + 1.43984i) q^{63} +(6.90481 - 2.24351i) q^{64} +(13.2354 + 2.60639i) q^{65} +(3.80993 + 7.53487i) q^{66} +(10.8778 - 10.8778i) q^{67} +(1.07027 - 0.347753i) q^{68} +(5.90680 + 10.4486i) q^{69} +(-0.539267 + 3.40480i) q^{70} +(5.77365 - 2.94182i) q^{71} +(3.04395 - 7.51919i) q^{72} +(3.15708 + 0.500032i) q^{73} +(4.48131 - 6.16799i) q^{74} +(15.4835 + 1.76950i) q^{75} +(0.241078 + 0.241078i) q^{76} +(-0.550121 - 2.00504i) q^{77} +(-7.45773 - 5.35105i) q^{78} +(-4.44795 - 13.6894i) q^{79} +(-2.51369 - 15.8708i) q^{80} +(-4.21434 - 7.95232i) q^{81} +(13.4224 + 4.36121i) q^{82} +(5.03389 - 2.56490i) q^{83} +(0.0961142 - 0.145105i) q^{84} +(4.10888 + 25.9424i) q^{85} +(7.63853 + 3.89203i) q^{86} +(-3.01310 + 6.60564i) q^{87} +(4.92927 + 7.49195i) q^{88} +(-3.41572 + 3.41572i) q^{89} +(-14.1349 - 8.50628i) q^{90} +(1.53744 + 1.65683i) q^{91} +(-0.652919 - 0.898665i) q^{92} +(-0.0310041 - 0.715742i) q^{93} +(0.806360 - 2.48172i) q^{94} +(-6.43773 + 4.67729i) q^{95} +(-0.419252 + 1.50976i) q^{96} +(-8.60532 - 4.38463i) q^{97} +(6.86668 - 6.86668i) q^{98} +(9.88199 + 1.16029i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 416 q - 12 q^{3} - 14 q^{6} - 12 q^{7} - 12 q^{9}+O(q^{10}) \) 416 * q - 12 * q^3 - 14 * q^6 - 12 * q^7 - 12 * q^9	\( 416 q - 12 q^{3} - 14 q^{6} - 12 q^{7} - 12 q^{9} - 20 q^{13} - 30 q^{15} + 32 q^{16} + 2 q^{18} - 4 q^{19} - 12 q^{21} - 24 q^{22} - 78 q^{24} - 36 q^{27} - 84 q^{28} - 28 q^{31} - 44 q^{33} - 24 q^{34} - 12 q^{37} + 54 q^{39} + 88 q^{40} - 56 q^{42} + 8 q^{45} - 92 q^{46} + 40 q^{48} - 44 q^{52} - 176 q^{54} - 72 q^{55} - 6 q^{57} - 4 q^{58} + 12 q^{60} - 48 q^{61} - 46 q^{63} + 204 q^{66} - 64 q^{67} + 56 q^{70} - 66 q^{72} - 12 q^{73} - 104 q^{76} - 92 q^{78} + 104 q^{79} + 124 q^{81} + 16 q^{84} - 12 q^{85} - 24 q^{87} - 84 q^{91} - 124 q^{93} + 328 q^{94} - 152 q^{96} + 52 q^{97} - 142 q^{99}+O(q^{100}) \) 416 * q - 12 * q^3 - 14 * q^6 - 12 * q^7 - 12 * q^9 - 20 * q^13 - 30 * q^15 + 32 * q^16 + 2 * q^18 - 4 * q^19 - 12 * q^21 - 24 * q^22 - 78 * q^24 - 36 * q^27 - 84 * q^28 - 28 * q^31 - 44 * q^33 - 24 * q^34 - 12 * q^37 + 54 * q^39 + 88 * q^40 - 56 * q^42 + 8 * q^45 - 92 * q^46 + 40 * q^48 - 44 * q^52 - 176 * q^54 - 72 * q^55 - 6 * q^57 - 4 * q^58 + 12 * q^60 - 48 * q^61 - 46 * q^63 + 204 * q^66 - 64 * q^67 + 56 * q^70 - 66 * q^72 - 12 * q^73 - 104 * q^76 - 92 * q^78 + 104 * q^79 + 124 * q^81 + 16 * q^84 - 12 * q^85 - 24 * q^87 - 84 * q^91 - 124 * q^93 + 328 * q^94 - 152 * q^96 + 52 * q^97 - 142 * q^99

Introduction

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