LMFDB - Embedded newform 429.2.bi.a.5.17

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			5.17
Character	$\chi$	$=$	429.5
Dual form			429.2.bi.a.86.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.507638 + 0.996296i) q^{2} +(1.52061 - 0.829312i) q^{3} +(0.440661 + 0.606518i) q^{4} +(2.02501 - 1.03179i) q^{5} +(0.0543225 + 1.93596i) q^{6} +(2.69211 + 0.426388i) q^{7} +(-3.03677 + 0.480978i) q^{8} +(1.62448 - 2.52211i) q^{9} +O(q^{10})$	\(q+(-0.507638 + 0.996296i) q^{2} +(1.52061 - 0.829312i) q^{3} +(0.440661 + 0.606518i) q^{4} +(2.02501 - 1.03179i) q^{5} +(0.0543225 + 1.93596i) q^{6} +(2.69211 + 0.426388i) q^{7} +(-3.03677 + 0.480978i) q^{8} +(1.62448 - 2.52211i) q^{9} +2.54129i q^{10} +(1.68348 - 2.85760i) q^{11} +(1.17306 + 0.556829i) q^{12} +(-3.47335 + 0.967375i) q^{13} +(-1.79143 + 2.46569i) q^{14} +(2.22356 - 3.24831i) q^{15} +(0.599048 - 1.84368i) q^{16} +(0.282206 - 0.868541i) q^{17} +(1.68812 + 2.89879i) q^{18} +(-3.75182 + 0.594229i) q^{19} +(1.51814 + 0.773532i) q^{20} +(4.44724 - 1.58423i) q^{21} +(1.99242 + 3.12787i) q^{22} -6.60586 q^{23} +(-4.21885 + 3.24981i) q^{24} +(0.0971341 - 0.133694i) q^{25} +(0.799415 - 3.95157i) q^{26} +(0.378582 - 5.18234i) q^{27} +(0.927694 + 1.82070i) q^{28} +(-1.49894 - 2.06311i) q^{29} +(2.10752 + 3.86429i) q^{30} +(6.90189 + 3.51669i) q^{31} +(-2.81543 - 2.81543i) q^{32} +(0.190066 - 5.74142i) q^{33} +(0.722066 + 0.722066i) q^{34} +(5.89148 - 1.91426i) q^{35} +(2.24555 - 0.126118i) q^{36} +(0.560147 + 0.0887185i) q^{37} +(1.31254 - 4.03957i) q^{38} +(-4.47935 + 4.35149i) q^{39} +(-5.65322 + 4.10731i) q^{40} +(1.86973 + 11.8050i) q^{41} +(-0.679230 + 5.23499i) q^{42} +7.55005i q^{43} +(2.47503 - 0.238173i) q^{44} +(0.687295 - 6.78343i) q^{45} +(3.35339 - 6.58139i) q^{46} +(-2.01588 + 0.319284i) q^{47} +(-0.618070 - 3.30031i) q^{48} +(0.408237 + 0.132644i) q^{49} +(0.0838894 + 0.164642i) q^{50} +(-0.291167 - 1.55475i) q^{51} +(-2.11730 - 1.68037i) q^{52} +(-1.54130 + 0.500797i) q^{53} +(4.97097 + 3.00794i) q^{54} +(0.460606 - 7.52367i) q^{55} -8.38040 q^{56} +(-5.21223 + 4.01501i) q^{57} +(2.81639 - 0.446073i) q^{58} +(-1.50315 + 9.49051i) q^{59} +(2.95000 - 0.0827758i) q^{60} +(-1.00993 + 3.10825i) q^{61} +(-7.00732 + 5.09112i) q^{62} +(5.44868 - 6.09714i) q^{63} +(7.92158 - 2.57388i) q^{64} +(-6.03544 + 5.54273i) q^{65} +(5.62367 + 3.10393i) q^{66} +(9.13590 - 9.13590i) q^{67} +(0.651142 - 0.211569i) q^{68} +(-10.0449 + 5.47831i) q^{69} +(-1.08357 + 6.84141i) q^{70} +(-1.47927 + 0.753727i) q^{71} +(-3.72011 + 8.44043i) q^{72} +(-2.61849 - 0.414729i) q^{73} +(-0.372742 + 0.513035i) q^{74} +(0.0368290 - 0.283850i) q^{75} +(-2.01369 - 2.01369i) q^{76} +(5.75056 - 6.97516i) q^{77} +(-2.06149 - 6.67174i) q^{78} +(-0.647963 - 1.99422i) q^{79} +(-0.689220 - 4.35156i) q^{80} +(-3.72210 - 8.19426i) q^{81} +(-12.7104 - 4.12986i) q^{82} +(-2.37172 + 1.20845i) q^{83} +(2.92059 + 1.99922i) q^{84} +(-0.324685 - 2.04998i) q^{85} +(-7.52209 - 3.83270i) q^{86} +(-3.99026 - 1.89410i) q^{87} +(-3.73790 + 9.48761i) q^{88} +(0.554147 - 0.554147i) q^{89} +(6.40941 + 4.12828i) q^{90} +(-9.76312 + 1.12328i) q^{91} +(-2.91094 - 4.00657i) q^{92} +(13.4115 - 0.376321i) q^{93} +(0.705235 - 2.17049i) q^{94} +(-6.98434 + 5.07442i) q^{95} +(-6.61602 - 1.94629i) q^{96} +(11.6070 + 5.91406i) q^{97} +(-0.339389 + 0.339389i) q^{98} +(-4.47241 - 8.88806i) 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 $

$2$	−0.507638	+	0.996296i	−0.358955	+	0.704488i	−0.997901	−	0.0647636i	$-0.979371\pi$
$2$	−0.507638	+	0.996296i	−0.358955	+	0.704488i	0.638946	+	0.769251i	$0.279371\pi$
$3$	1.52061	−	0.829312i	0.877922	−	0.478803i
$3$	1.52061	−	0.829312i	0.877922	−	0.478803i
$4$	0.440661	+	0.606518i	0.220330	+	0.303259i
$5$	2.02501	−	1.03179i	0.905611	−	0.461432i	0.0618100	−	0.998088i	$-0.480313\pi$
$5$	2.02501	−	1.03179i	0.905611	−	0.461432i	0.843801	+	0.536656i	$0.180313\pi$
$6$	0.0543225	+	1.93596i	0.0221771	+	0.790354i
$7$	2.69211	+	0.426388i	1.01752	+	0.161159i	0.642845	−	0.765996i	$-0.277754\pi$
$7$	2.69211	+	0.426388i	1.01752	+	0.161159i	0.374676	+	0.927156i	$0.377754\pi$
$8$	−3.03677	+	0.480978i	−1.07366	+	0.170051i
$9$	1.62448	−	2.52211i	0.541495	−	0.840704i
$10$			2.54129i			0.803625i
$11$	1.68348	−	2.85760i	0.507588	−	0.861600i
$11$	1.68348	−	2.85760i	0.507588	−	0.861600i
$12$	1.17306	+	0.556829i	0.338634	+	0.160743i
$13$	−3.47335	+	0.967375i	−0.963335	+	0.268302i
$13$	−3.47335	+	0.967375i	−0.963335	+	0.268302i
$14$	−1.79143	+	2.46569i	−0.478779	+	0.658982i
$15$	2.22356	−	3.24831i	0.574121	−	0.838711i
$16$	0.599048	−	1.84368i	0.149762	−	0.460920i
$17$	0.282206	−	0.868541i	0.0684450	−	0.210652i	−0.910984	−	0.412442i	$-0.864676\pi$
$17$	0.282206	−	0.868541i	0.0684450	−	0.210652i	0.979429	+	0.201790i	$0.0646759\pi$
$18$	1.68812	+	2.89879i	0.397894	+	0.683251i
$19$	−3.75182	+	0.594229i	−0.860726	+	0.136326i	−0.571166	−	0.820834i	$-0.693509\pi$
$19$	−3.75182	+	0.594229i	−0.860726	+	0.136326i	−0.289560	+	0.957160i	$0.593509\pi$
$20$	1.51814	+	0.773532i	0.339467	+	0.172967i
$21$	4.44724	−	1.58423i	0.970468	−	0.345707i
$22$	1.99242	+	3.12787i	0.424785	+	0.666865i
$23$	−6.60586			−1.37742			−0.688708	−	0.725039i	$-0.741822\pi$
$23$	−6.60586			−1.37742			−0.688708	+	0.725039i	$0.741822\pi$
$24$	−4.21885	+	3.24981i	−0.861170	+	0.663365i
$25$	0.0971341	−	0.133694i	0.0194268	−	0.0267387i
$26$	0.799415	−	3.95157i	0.156778	−	0.774966i
$27$	0.378582	−	5.18234i	0.0728582	−	0.997342i
$28$	0.927694	+	1.82070i	0.175318	+	0.344080i
$29$	−1.49894	−	2.06311i	−0.278346	−	0.383111i	0.646839	−	0.762627i	$-0.276091\pi$
$29$	−1.49894	−	2.06311i	−0.278346	−	0.383111i	−0.925185	+	0.379516i	$0.876091\pi$
$30$	2.10752	+	3.86429i	0.384778	+	0.705520i
$31$	6.90189	+	3.51669i	1.23962	+	0.631616i	0.945956	−	0.324295i	$-0.105127\pi$
$31$	6.90189	+	3.51669i	1.23962	+	0.631616i	0.293659	+	0.955910i	$0.405127\pi$
$32$	−2.81543	−	2.81543i	−0.497702	−	0.497702i
$33$	0.190066	−	5.74142i	0.0330862	−	0.999453i
$34$	0.722066	+	0.722066i	0.123833	+	0.123833i
$35$	5.89148	−	1.91426i	0.995842	−	0.323569i
$36$	2.24555	−	0.126118i	0.374259	−	0.0210197i
$37$	0.560147	+	0.0887185i	0.0920875	+	0.0145852i	0.202308	−	0.979322i	$-0.435156\pi$
$37$	0.560147	+	0.0887185i	0.0920875	+	0.0145852i	−0.110221	+	0.993907i	$0.535156\pi$
$38$	1.31254	−	4.03957i	0.212922	−	0.655306i
$39$	−4.47935	+	4.35149i	−0.717269	+	0.696796i
$40$	−5.65322	+	4.10731i	−0.893853	+	0.649422i
$41$	1.86973	+	11.8050i	0.292002	+	1.84363i	0.500665	+	0.865641i	$0.333089\pi$
$41$	1.86973	+	11.8050i	0.292002	+	1.84363i	−0.208663	+	0.977988i	$0.566911\pi$
$42$	−0.679230	+	5.23499i	−0.104807	+	0.807776i
$43$			7.55005i			1.15137i	0.817671	+	0.575686i	$0.195265\pi$
$43$			7.55005i			1.15137i	−0.817671	+	0.575686i	$0.804735\pi$
$44$	2.47503	−	0.238173i	0.373125	−	0.0359060i
$45$	0.687295	−	6.78343i	0.102456	−	1.01121i
$46$	3.35339	−	6.58139i	0.494430	−	0.970373i
$47$	−2.01588	+	0.319284i	−0.294046	+	0.0465723i	−0.301715	−	0.953398i	$-0.597559\pi$
$47$	−2.01588	+	0.319284i	−0.294046	+	0.0465723i	0.00766867	+	0.999971i	$0.497559\pi$
$48$	−0.618070	−	3.30031i	−0.0892107	−	0.476359i
$49$	0.408237	+	0.132644i	0.0583195	+	0.0189492i
$50$	0.0838894	+	0.164642i	0.0118638	+	0.0232839i
$51$	−0.291167	−	1.55475i	−0.0407715	−	0.217708i
$52$	−2.11730	−	1.68037i	−0.293617	−	0.233025i
$53$	−1.54130	+	0.500797i	−0.211713	+	0.0687898i	−0.412954	−	0.910752i	$-0.635503\pi$
$53$	−1.54130	+	0.500797i	−0.211713	+	0.0687898i	0.201240	+	0.979542i	$0.435503\pi$
$54$	4.97097	+	3.00794i	0.676463	+	0.409328i
$55$	0.460606	−	7.52367i	0.0621080	−	1.01449i
$56$	−8.38040			−1.11988
$57$	−5.21223	+	4.01501i	−0.690377	+	0.531802i
$58$	2.81639	−	0.446073i	0.369811	−	0.0585722i
$59$	−1.50315	+	9.49051i	−0.195693	+	1.23556i	0.672787	+	0.739836i	$0.265097\pi$
$59$	−1.50315	+	9.49051i	−0.195693	+	1.23556i	−0.868481	+	0.495723i	$0.834903\pi$
$60$	2.95000	−	0.0827758i	0.380843	−	0.0106863i
$61$	−1.00993	+	3.10825i	−0.129308	+	0.397970i	−0.994661	−	0.103193i	$-0.967094\pi$
$61$	−1.00993	+	3.10825i	−0.129308	+	0.397970i	0.865353	+	0.501163i	$0.167094\pi$
$62$	−7.00732	+	5.09112i	−0.889931	+	0.646573i
$63$	5.44868	−	6.09714i	0.686469	−	0.768167i
$64$	7.92158	−	2.57388i	0.990198	−	0.321735i
$65$	−6.03544	+	5.54273i	−0.748604	+	0.687490i
$66$	5.62367	+	3.10393i	0.692226	+	0.382067i
$67$	9.13590	−	9.13590i	1.11613	−	1.11613i	0.123823	−	0.992304i	$-0.460485\pi$
$67$	9.13590	−	9.13590i	1.11613	−	1.11613i	0.992304	−	0.123823i	$-0.0395155\pi$
$68$	0.651142	−	0.211569i	0.0789626	−	0.0256565i
$69$	−10.0449	+	5.47831i	−1.20926	+	0.659512i
$70$	−1.08357	+	6.84141i	−0.129512	+	0.817705i
$71$	−1.47927	+	0.753727i	−0.175557	+	0.0894509i	−0.539561	−	0.841947i	$-0.681410\pi$
$71$	−1.47927	+	0.753727i	−0.175557	+	0.0894509i	0.364003	+	0.931398i	$0.381410\pi$
$72$	−3.72011	+	8.44043i	−0.438419	+	0.994714i
$73$	−2.61849	−	0.414729i	−0.306472	−	0.0485403i	0.00130450	−	0.999999i	$-0.499585\pi$
$73$	−2.61849	−	0.414729i	−0.306472	−	0.0485403i	−0.307776	+	0.951459i	$0.599585\pi$
$74$	−0.372742	+	0.513035i	−0.0433304	+	0.0596391i
$75$	0.0368290	−	0.283850i	0.00425264	−	0.0327761i
$76$	−2.01369	−	2.01369i	−0.230986	−	0.230986i
$77$	5.75056	−	6.97516i	0.655337	−	0.794893i
$78$	−2.06149	−	6.67174i	−0.233417	−	0.755426i
$79$	−0.647963	−	1.99422i	−0.0729015	−	0.224368i	0.907966	−	0.419044i	$-0.137635\pi$
$79$	−0.647963	−	1.99422i	−0.0729015	−	0.224368i	−0.980868	+	0.194676i	$0.937635\pi$
$80$	−0.689220	−	4.35156i	−0.0770571	−	0.486519i
$81$	−3.72210	−	8.19426i	−0.413567	−	0.910474i
$82$	−12.7104	−	4.12986i	−1.40363	−	0.456067i
$83$	−2.37172	+	1.20845i	−0.260330	+	0.132645i	−0.579285	−	0.815125i	$-0.696668\pi$
$83$	−2.37172	+	1.20845i	−0.260330	+	0.132645i	0.318955	+	0.947770i	$0.396668\pi$
$84$	2.92059	+	1.99922i	0.318662	+	0.218133i
$85$	−0.324685	−	2.04998i	−0.0352170	−	0.222352i
$86$	−7.52209	−	3.83270i	−0.811128	−	0.413290i
$87$	−3.99026	−	1.89410i	−0.427801	−	0.203068i
$88$	−3.73790	+	9.48761i	−0.398462	+	1.01138i
$89$	0.554147	−	0.554147i	0.0587395	−	0.0587395i	−0.677127	−	0.735866i	$-0.736775\pi$
$89$	0.554147	−	0.554147i	0.0587395	−	0.0587395i	0.735866	+	0.677127i	$0.236775\pi$
$90$	6.40941	+	4.12828i	0.675611	+	0.435159i
$91$	−9.76312	+	1.12328i	−1.02345	+	0.117752i
$92$	−2.91094	−	4.00657i	−0.303487	−	0.417714i
$93$	13.4115	−	0.376321i	1.39071	−	0.0390227i
$94$	0.705235	−	2.17049i	0.0727395	−	0.223869i
$95$	−6.98434	+	5.07442i	−0.716578	+	0.520624i
$96$	−6.61602	−	1.94629i	−0.675245	−	0.198642i
$97$	11.6070	+	5.91406i	1.17851	+	0.600482i	0.929789	−	0.368092i	$-0.119989\pi$
$97$	11.6070	+	5.91406i	1.17851	+	0.600482i	0.248724	+	0.968575i	$0.419989\pi$
$98$	−0.339389	+	0.339389i	−0.0342835	+	0.0342835i
$99$	−4.47241	−	8.88806i	−0.449494	−	0.893283i
$100$	0.123891			0.0123891
$101$	−5.25329	−	16.1680i	−0.522721	−	1.60877i	−0.768778	−	0.639516i	$-0.779135\pi$
$101$	−5.25329	−	16.1680i	−0.522721	−	1.60877i	0.246057	−	0.969255i	$-0.420865\pi$
$102$	1.69679	+	0.499160i	0.168008	+	0.0494242i
$103$	−9.76504	−	13.4404i	−0.962178	−	1.32432i	−0.945900	−	0.324457i	$-0.894818\pi$
$103$	−9.76504	−	13.4404i	−0.962178	−	1.32432i	−0.0162780	−	0.999868i	$-0.505182\pi$
$104$	10.0825	−	4.60831i	0.988671	−	0.451882i
$105$	7.37110	−	7.79671i	0.719346	−	0.760881i
$106$	0.283478	−	1.78981i	0.0275338	−	0.173842i
$107$	−4.28767	+	5.90146i	−0.414504	+	0.570516i	−0.964310	−	0.264777i	$-0.914702\pi$
$107$	−4.28767	+	5.90146i	−0.414504	+	0.570516i	0.549806	+	0.835293i	$0.314702\pi$
$108$	3.31001	−	2.05404i	0.318506	−	0.197650i
$109$	14.3743	−	14.3743i	1.37681	−	1.37681i	0.526851	−	0.849958i	$-0.323373\pi$
$109$	14.3743	−	14.3743i	1.37681	−	1.37681i	0.849958	−	0.526851i	$-0.176627\pi$
$110$	7.26199	+	4.27820i	0.692403	+	0.407911i
$111$	0.925338	−	0.329630i	0.0878292	−	0.0312871i
$112$	2.39882	−	4.70796i	0.226668	−	0.444860i
$113$	−4.15454	+	5.71823i	−0.390826	+	0.537926i	−0.958412	−	0.285388i	$-0.907877\pi$
$113$	−4.15454	+	5.71823i	−0.390826	+	0.537926i	0.567586	+	0.823314i	$0.307877\pi$
$114$	−1.35421	−	7.23110i	−0.126834	−	0.677255i
$115$	−13.3769	+	6.81588i	−1.24740	+	0.635584i
$116$	0.590791	−	1.81827i	0.0548536	−	0.168822i
$117$	−3.20258	+	10.3317i	−0.296078	+	0.955164i
$118$	−8.69231	−	6.31533i	−0.800192	−	0.581373i
$119$	1.13006	−	2.21788i	0.103593	−	0.203312i
$120$	−5.19008	+	10.9339i	−0.473788	+	0.998122i
$121$	−5.33179	−	9.62144i	−0.484708	−	0.874676i
$122$	−2.58405	−	2.58405i	−0.233949	−	0.233949i
$123$	12.6331	+	16.4001i	1.13909	+	1.47875i
$124$	0.908459	+	5.73578i	0.0815820	+	0.515088i
$125$	−1.71891	+	10.8527i	−0.153744	+	0.970699i
$126$	3.30859	+	8.52364i	0.294753	+	0.759346i
$127$	−2.85859	−	0.928811i	−0.253659	−	0.0824187i	0.179428	−	0.983771i	$-0.442575\pi$
$127$	−2.85859	−	0.928811i	−0.253659	−	0.0824187i	−0.433086	+	0.901353i	$0.642575\pi$
$128$	−0.211230	+	1.33365i	−0.0186702	+	0.117879i
$129$	6.26135	+	11.4807i	0.551281	+	1.01082i
$130$	−2.45838	−	8.82678i	−0.215614	−	0.774160i
$131$		−	18.9708i		−	1.65749i	−0.559626	−	0.828745i	$-0.689055\pi$
$131$		−	18.9708i		−	1.65749i	0.559626	−	0.828745i	$-0.310945\pi$
$132$	3.56602	−	2.41474i	0.310383	−	0.210176i
$133$	−10.3537			−0.897776
$134$	4.46433	+	13.7398i	0.385659	+	1.18694i
$135$	−4.58047	−	10.8849i	−0.394224	−	0.936823i
$136$	−0.439247	+	2.77330i	−0.0376651	+	0.237808i
$137$	−7.00826	−	13.7545i	−0.598756	−	1.17513i	−0.969201	−	0.246271i	$-0.920795\pi$
$137$	−7.00826	−	13.7545i	−0.598756	−	1.17513i	0.370445	−	0.928855i	$-0.379205\pi$
$138$	−0.358846	−	12.7887i	−0.0305470	−	1.08865i
$139$	−2.93489	+	2.13232i	−0.248934	+	0.180861i	−0.705254	−	0.708954i	$-0.749167\pi$
$139$	−2.93489	+	2.13232i	−0.248934	+	0.180861i	0.456320	+	0.889816i	$0.349167\pi$
$140$	3.75718	+	2.72975i	0.317539	+	0.230706i
$141$	−2.80057	+	2.15730i	−0.235850	+	0.181677i
$142$		−	1.85641i		−	0.155787i
$143$	−3.08295	+	11.5540i	−0.257809	+	0.966196i
$144$	−3.67683	−	4.50590i	−0.306402	−	0.375491i
$145$	−5.16407	−	2.63123i	−0.428853	−	0.218512i
$146$	1.74244	−	2.39826i	0.144205	−	0.198482i
$147$	0.730770	−	0.136856i	0.0602729	−	0.0112877i
$148$	0.193025	+	0.378834i	0.0158666	+	0.0311399i
$149$	8.33301	−	4.24588i	0.682667	−	0.347836i	−0.0780229	−	0.996952i	$-0.524861\pi$
$149$	8.33301	−	4.24588i	0.682667	−	0.347836i	0.760690	+	0.649115i	$0.224861\pi$
$150$	0.264103	+	0.180786i	0.0215639	+	0.0147611i
$151$	−0.363955	−	2.29792i	−0.0296182	−	0.187002i	0.968444	−	0.249233i	$-0.0801785\pi$
$151$	−0.363955	−	2.29792i	−0.0296182	−	0.187002i	−0.998062	+	0.0622309i	$0.980178\pi$
$152$	11.1076	−	3.60908i	0.900946	−	0.292735i
$153$	−1.73212	−	2.12269i	−0.140034	−	0.171609i
$154$	4.03012	+	9.27011i	0.324756	+	0.747007i
$155$	17.6049			1.41406
$156$	−4.61313	−	0.799271i	−0.369346	−	0.0639929i
$157$	−7.52015	−	5.46371i	−0.600173	−	0.436051i	0.245767	−	0.969329i	$-0.420960\pi$
$157$	−7.52015	−	5.46371i	−0.600173	−	0.436051i	−0.845940	+	0.533277i	$0.820960\pi$
$158$	2.31577	+	0.366782i	0.184233	+	0.0291796i
$159$	−1.92839	+	2.03973i	−0.152931	+	0.161761i
$160$	−8.60620	−	2.79632i	−0.680380	−	0.221069i
$161$	−17.7837	−	2.81666i	−1.40155	−	0.221984i
$162$	10.0534	+	0.451404i	0.789869	+	0.0354656i
$163$	−7.02703	+	13.7913i	−0.550400	+	1.08022i	0.433442	+	0.901181i	$0.357299\pi$
$163$	−7.02703	+	13.7913i	−0.550400	+	1.08022i	−0.983842	+	0.179039i	$0.942701\pi$
$164$	−6.33602	+	6.33602i	−0.494760	+	0.494760i
$165$	−5.53907	−	11.8225i	−0.431216	−	0.920382i
$166$		−	2.97639i		−	0.231013i
$167$	12.0647	+	6.14727i	0.933594	+	0.475690i	0.853497	−	0.521097i	$-0.174477\pi$
$167$	12.0647	+	6.14727i	0.933594	+	0.475690i	0.0800964	+	0.996787i	$0.474477\pi$
$168$	−12.7433	+	6.94997i	−0.983166	+	0.536201i
$169$	11.1284	−	6.72007i	0.856028	−	0.516929i
$170$	2.20721	+	0.717166i	0.169285	+	0.0550041i
$171$	−4.59605	+	10.4278i	−0.351469	+	0.797435i
$172$	−4.57924	+	3.32701i	−0.349164	+	0.253682i
$173$	7.44342	+	5.40796i	0.565913	+	0.411160i	0.833618	−	0.552341i	$-0.186265\pi$
$173$	7.44342	+	5.40796i	0.565913	+	0.411160i	−0.267705	+	0.963501i	$0.586265\pi$
$174$	3.91269	−	3.01397i	0.296620	−	0.228488i
$175$	0.318501	−	0.318501i	0.0240764	−	0.0240764i
$176$	−4.26002	−	4.81564i	−0.321111	−	0.362993i
$177$	5.58490	+	15.6779i	0.419786	+	1.17842i
$178$	0.270789	+	0.833401i	0.0202965	+	0.0624661i
$179$	1.79090	+	1.30117i	0.133858	+	0.0972539i	0.652700	−	0.757617i	$-0.273636\pi$
$179$	1.79090	+	1.30117i	0.133858	+	0.0972539i	−0.518841	+	0.854871i	$0.673636\pi$
$180$	4.41713	−	2.57233i	0.329234	−	0.191731i
$181$	8.68914	+	2.82327i	0.645859	+	0.209852i	0.613587	−	0.789627i	$-0.289726\pi$
$181$	8.68914	+	2.82327i	0.645859	+	0.209852i	0.0322715	+	0.999479i	$0.489726\pi$
$182$	3.83701	−	10.2972i	0.284418	−	0.763278i
$183$	1.04200	+	5.56396i	0.0770268	+	0.411300i
$184$	20.0605	−	3.17727i	1.47888	−	0.234231i
$185$	1.22584	−	0.398300i	0.0901256	−	0.0292836i
$186$	−6.43325	+	13.5528i	−0.471709	+	0.993743i
$187$	−2.00686	−	2.26860i	−0.146756	−	0.165897i
$188$	−1.08197	−	1.08197i	−0.0789107	−	0.0789107i
$189$	3.22887	−	13.7900i	0.234866	−	1.00307i
$190$	−1.51011	−	9.53444i	−0.109555	−	0.691701i
$191$	−1.31297	−	1.80715i	−0.0950032	−	0.130761i	0.758869	−	0.651243i	$-0.225752\pi$
$191$	−1.31297	−	1.80715i	−0.0950032	−	0.130761i	−0.853872	+	0.520482i	$0.825752\pi$
$192$	9.91105	−	10.4833i	0.715269	−	0.756568i
$193$	5.10691	−	2.60210i	0.367603	−	0.187303i	−0.260424	−	0.965494i	$-0.583862\pi$
$193$	5.10691	−	2.60210i	0.367603	−	0.187303i	0.628028	+	0.778191i	$0.283862\pi$
$194$	−11.7843	+	8.56181i	−0.846065	+	0.614702i
$195$	−4.58087	+	13.4336i	−0.328043	+	0.961997i
$196$	0.0994429	+	0.306054i	0.00710306	+	0.0218610i
$197$	−0.824498	−	0.824498i	−0.0587430	−	0.0587430i	0.677125	−	0.735868i	$-0.263226\pi$
$197$	−0.824498	−	0.824498i	−0.0587430	−	0.0587430i	−0.735868	+	0.677125i	$0.763226\pi$
$198$	11.1255	+	0.0560726i	0.790655	+	0.00398491i
$199$			18.8213i			1.33421i	0.744965	+	0.667103i	$0.232466\pi$
$199$			18.8213i			1.33421i	−0.744965	+	0.667103i	$0.767534\pi$
$200$	−0.230671	+	0.452716i	−0.0163109	+	0.0320119i
$201$	6.31559	−	21.4686i	0.445467	−	1.51428i
$202$	18.7748	+	2.97364i	1.32099	+	0.209225i
$203$	−3.15562	−	6.19325i	−0.221481	−	0.434681i
$204$	0.814674	−	0.861713i	0.0570386	−	0.0603320i
$205$	15.9665	+	21.9760i	1.11515	+	1.53487i
$206$	18.3478	−	2.90600i	1.27835	−	0.202471i
$207$	−10.7311	+	16.6607i	−0.745864	+	1.15800i
$208$	−0.297175	+	6.98326i	−0.0206053	+	0.484202i
$209$	−4.61804	+	11.7216i	−0.319436	+	0.810798i
$210$	4.02598	+	11.3017i	0.277819	+	0.779892i
$211$	5.21392	+	16.0468i	0.358941	+	1.10471i	0.953689	+	0.300795i	$0.0972521\pi$
$211$	5.21392	+	16.0468i	0.358941	+	1.10471i	−0.594747	+	0.803913i	$0.702748\pi$
$212$	−0.982931	−	0.714141i	−0.0675080	−	0.0490474i
$213$	−1.62432	+	2.37290i	−0.111296	+	0.162588i
$214$	−3.70302	−	7.26759i	−0.253134	−	0.496803i
$215$	7.79009	+	15.2889i	0.531280	+	1.04270i
$216$	1.34292	+	15.9197i	0.0913743	+	1.08320i
$217$	17.0811	+	12.4102i	1.15954	+	0.842458i
$218$	7.02412	+	21.6180i	0.475733	+	1.46416i
$219$	−4.32564	+	1.54091i	−0.292299	+	0.104125i
$220$	4.76621	−	3.03602i	0.321338	−	0.204689i
$221$	−0.139996	+	3.28975i	−0.00941716	+	0.221292i
$222$	−0.141327	+	1.08924i	−0.00948527	+	0.0731052i
$223$	−16.4884	+	2.61150i	−1.10414	+	0.174879i	−0.681787	−	0.731551i	$-0.738797\pi$
$223$	−16.4884	+	2.61150i	−1.10414	+	0.174879i	−0.422356	+	0.906430i	$0.638797\pi$
$224$	−6.37897	−	8.77989i	−0.426213	−	0.586631i
$225$	−0.179398	−	0.462166i	−0.0119598	−	0.0308111i
$226$	−3.58805	−	7.04194i	−0.238673	−	0.468423i
$227$	18.8934	+	2.99243i	1.25400	+	0.198614i	0.747872	−	0.663843i	$-0.231076\pi$
$227$	18.8934	+	2.99243i	1.25400	+	0.198614i	0.506129	+	0.862458i	$0.331076\pi$
$228$	−4.73200	−	1.39205i	−0.313385	−	0.0921908i
$229$	12.0404	−	23.6306i	0.795651	−	1.56155i	−0.0314541	−	0.999505i	$-0.510014\pi$
$229$	12.0404	−	23.6306i	0.795651	−	1.56155i	0.827105	−	0.562047i	$-0.189986\pi$
$230$		−	16.7874i		−	1.10693i
$231$	2.95975	−	15.3755i	0.194737	−	1.01163i
$232$	5.54425	+	5.54425i	0.363998	+	0.363998i
$233$	−0.732734	−	2.25512i	−0.0480030	−	0.147738i	0.924182	−	0.381952i	$-0.124748\pi$
$233$	−0.732734	−	2.25512i	−0.0480030	−	0.147738i	−0.972185	+	0.234214i	$0.924748\pi$
$234$	−8.66766	−	8.43547i	−0.566623	−	0.551444i
$235$	−3.75273	+	2.72652i	−0.244801	+	0.177859i
$236$	−6.41854	+	3.27041i	−0.417811	+	0.212886i
$237$	−2.63913	−	2.49507i	−0.171430	−	0.162072i
$238$	1.63600	+	2.25176i	0.106046	+	0.145960i
$239$	1.37373	+	8.67340i	0.0888593	+	0.561035i	0.991445	+	0.130525i	$0.0416664\pi$
$239$	1.37373	+	8.67340i	0.0888593	+	0.561035i	−0.902586	+	0.430510i	$0.858334\pi$
$240$	−4.65683	−	6.04543i	−0.300597	−	0.390231i
$241$	2.45851	+	2.45851i	0.158367	+	0.158367i	0.781843	−	0.623476i	$-0.214280\pi$
$241$	2.45851	+	2.45851i	0.158367	+	0.158367i	−0.623476	+	0.781843i	$0.714280\pi$
$242$	12.2924	−	0.427833i	0.790187	−	0.0275021i
$243$	−12.4555	−	9.37346i	−0.799018	−	0.601308i
$244$	−2.33024	+	0.757141i	−0.149178	+	0.0484710i
$245$	0.963544	−	0.152610i	0.0615586	−	0.00974992i
$246$	−22.7525	+	4.26100i	−1.45064	+	0.271671i
$247$	12.4565	−	5.69338i	0.792591	−	0.362261i
$248$	−22.6509	−	7.35973i	−1.43833	−	0.467343i
$249$	−2.60427	+	3.80447i	−0.165039	+	0.241099i
$250$	−9.93996	−	7.22181i	−0.628658	−	0.456747i
$251$	3.61521	+	11.1265i	0.228190	+	0.702297i	0.997952	+	0.0639659i	$0.0203749\pi$
$251$	3.61521	+	11.1265i	0.228190	+	0.702297i	−0.769762	+	0.638331i	$0.779625\pi$
$252$	6.09904	+	0.617953i	0.384203	+	0.0389274i
$253$	−11.1208	+	18.8769i	−0.699160	+	1.18678i
$254$	2.37650	−	2.37650i	0.149115	−	0.149115i
$255$	−2.19379	−	2.84795i	−0.137381	−	0.178345i
$256$	12.2555	+	8.90415i	0.765970	+	0.556509i
$257$	15.5885	−	11.3257i	0.972385	−	0.706479i	0.0163914	−	0.999866i	$-0.494782\pi$
$257$	15.5885	−	11.3257i	0.972385	−	0.706479i	0.955994	+	0.293386i	$0.0947822\pi$
$258$	−14.6166	+	0.410138i	−0.909992	+	0.0255341i
$259$	1.47015	+	0.477679i	0.0913504	+	0.0296816i
$260$	−6.02134	−	1.21814i	−0.373428	−	0.0755456i
$261$	−7.63841	+	0.429000i	−0.472806	+	0.0265544i
$262$	18.9006	+	9.63033i	1.16768	+	0.594964i
$263$		−	6.82154i		−	0.420634i	−0.977633	−	0.210317i	$-0.932550\pi$
$263$		−	6.82154i		−	0.420634i	0.977633	−	0.210317i	$-0.0674497\pi$
$264$	2.18431	+	17.5268i	0.134435	+	1.07870i
$265$	−2.60442	+	2.60442i	−0.159988	+	0.159988i
$266$	5.25592	−	10.3153i	0.322261	−	0.632473i
$267$	0.383079	−	1.30220i	0.0234440	−	0.0796934i
$268$	9.56691	+	1.51525i	0.584392	+	0.0925586i
$269$	6.69787	+	2.17627i	0.408376	+	0.132690i	0.505999	−	0.862534i	$-0.331124\pi$
$269$	6.69787	+	2.17627i	0.408376	+	0.132690i	−0.0976228	+	0.995223i	$0.531124\pi$
$270$	13.1698	+	0.962085i	0.801489	+	0.0585507i
$271$	9.26599	+	1.46759i	0.562869	+	0.0891497i	0.431384	−	0.902169i	$-0.358025\pi$
$271$	9.26599	+	1.46759i	0.562869	+	0.0891497i	0.131485	+	0.991318i	$0.458025\pi$
$272$	−1.43226	−	1.04060i	−0.0868434	−	0.0630954i
$273$	−13.9143	+	9.80474i	−0.842132	+	0.593410i
$274$	17.2612			1.04279
$275$	−0.218520	−	0.502641i	−0.0131772	−	0.0303104i
$276$	−7.74909	−	3.67833i	−0.466440	−	0.221410i
$277$	−23.6751	+	7.69252i	−1.42250	+	0.462199i	−0.916396	−	0.400273i	$-0.868915\pi$
$277$	−23.6751	+	7.69252i	−1.42250	+	0.462199i	−0.506105	+	0.862472i	$0.668915\pi$
$278$	−0.634563	−	4.00647i	−0.0380586	−	0.240292i
$279$	20.0815	−	11.6945i	1.20225	−	0.700133i
$280$	−16.9704	+	8.64684i	−1.01417	+	0.516748i
$281$	−1.40807	−	2.76350i	−0.0839987	−	0.164857i	0.845186	−	0.534472i	$-0.179489\pi$
$281$	−1.40807	−	2.76350i	−0.0839987	−	0.164857i	−0.929185	+	0.369615i	$0.879489\pi$
$282$	−0.727629	−	3.88532i	−0.0433297	−	0.231368i
$283$	8.38063	−	11.5349i	0.498177	−	0.685682i	−0.483693	−	0.875238i	$-0.660705\pi$
$283$	8.38063	−	11.5349i	0.498177	−	0.685682i	0.981870	+	0.189556i	$0.0607049\pi$
$284$	−1.10901	−	0.565067i	−0.0658074	−	0.0335305i
$285$	−6.41215	+	13.5084i	−0.379823	+	0.800167i
$286$	−9.94621	−	8.93679i	−0.588132	−	0.528444i
$287$			32.5775i			1.92299i
$288$	−11.6744	+	2.52721i	−0.687923	+	0.148917i
$289$	13.0786	+	9.50213i	0.769327	+	0.558949i
$290$	5.24296	−	3.80924i	0.307877	−	0.223686i
$291$	22.5543	−	0.632865i	1.32216	−	0.0370992i
$292$	−0.902327	−	1.77092i	−0.0528047	−	0.103635i
$293$	5.01192	−	31.6440i	0.292800	−	1.84866i	−0.201649	−	0.979458i	$-0.564630\pi$
$293$	5.01192	−	31.6440i	0.292800	−	1.84866i	0.494449	−	0.869207i	$-0.335370\pi$
$294$	−0.234618	+	0.797537i	−0.0136832	+	0.0465133i
$295$	6.74835	+	20.7693i	0.392904	+	1.20924i
$296$	−1.74371			−0.101351
$297$	−14.1717	−	9.80621i	−0.822328	−	0.569014i
$298$			10.4575i			0.605788i
$299$	22.9445	−	6.39034i	1.32691	−	0.369563i
$300$	0.188389	−	0.102744i	0.0108766	−	0.00593193i
$301$	−3.21925	+	20.3256i	−0.185555	+	1.17155i
$302$	2.47417	+	0.803905i	0.142372	+	0.0462596i
$303$	−21.3964	−	20.2285i	−1.22919	−	1.16210i
$304$	−1.15195	+	7.27312i	−0.0660688	+	0.417142i
$305$	1.16195	+	7.33626i	0.0665330	+	0.420073i
$306$	2.99411	−	0.648147i	0.171162	−	0.0370521i
$307$	−20.5608	−	20.5608i	−1.17347	−	1.17347i	−0.981377	−	0.192092i	$-0.938473\pi$
$307$	−20.5608	−	20.5608i	−1.17347	−	1.17347i	−0.192092	−	0.981377i	$-0.561527\pi$
$308$	6.76460	+	0.414134i	0.385449	+	0.0235975i
$309$	−25.9951	−	12.3393i	−1.47881	−	0.701960i
$310$	−8.93691	+	17.5397i	−0.507582	+	0.996186i
$311$	−11.7522	−	8.53845i	−0.666404	−	0.484171i	0.202415	−	0.979300i	$-0.435121\pi$
$311$	−11.7522	−	8.53845i	−0.666404	−	0.484171i	−0.868820	+	0.495129i	$0.835121\pi$
$312$	11.5098	−	15.3690i	0.651613	−	0.870096i
$313$	9.72883	−	29.9423i	0.549906	−	1.69244i	−0.159124	−	0.987259i	$-0.550867\pi$
$313$	9.72883	−	29.9423i	0.549906	−	1.69244i	0.709030	−	0.705178i	$-0.249133\pi$
$314$	9.26099	−	4.71871i	0.522628	−	0.266292i
$315$	4.74264	−	17.9687i	0.267218	−	1.01242i
$316$	0.924000	−	1.27178i	0.0519791	−	0.0715431i
$317$	−3.24993	+	6.37834i	−0.182534	+	0.358243i	−0.964083	−	0.265600i	$-0.914430\pi$
$317$	−3.24993	+	6.37834i	−0.182534	+	0.358243i	0.781549	+	0.623844i	$0.214430\pi$
$318$	−1.05325	−	2.95669i	−0.0590635	−	0.165803i
$319$	−8.41900	+	0.810165i	−0.471373	+	0.0453605i
$320$	13.3856	−	13.3856i	0.748275	−	0.748275i
$321$	−1.62569	+	12.5296i	−0.0907374	+	0.699335i
$322$	11.8339	−	16.2880i	0.659477	−	0.907693i
$323$	−0.542673	+	3.42630i	−0.0301951	+	0.190644i
$324$	3.32978	−	5.86841i	0.184988	−	0.326023i
$325$	−0.208049	+	0.558330i	−0.0115405	+	0.0309706i
$326$	−10.1731	−	14.0020i	−0.563434	−	0.775500i
$327$	9.93687	−	33.7784i	0.549510	−	1.86795i
$328$	−11.3559	−	34.9498i	−0.627023	−	1.92978i
$329$	−5.56309			−0.306703
$330$	14.5906	+	0.483012i	0.803185	+	0.0265889i
$331$	−0.226442	+	0.226442i	−0.0124464	+	0.0124464i	−0.713303	−	0.700856i	$-0.752801\pi$
$331$	−0.226442	+	0.226442i	−0.0124464	+	0.0124464i	0.700856	+	0.713303i	$0.252801\pi$
$332$	−1.77807	−	0.905972i	−0.0975843	−	0.0497217i
$333$	1.13371	−	1.26863i	0.0621268	−	0.0695206i
$334$	−12.2490	+	8.89942i	−0.670235	+	0.486954i
$335$	9.07391	−	27.9266i	0.495761	−	1.52579i
$336$	−0.256699	−	9.14832i	−0.0140041	−	0.499082i
$337$	−7.87989	−	10.8457i	−0.429245	−	0.590805i	0.538535	−	0.842603i	$-0.318978\pi$
$337$	−7.87989	−	10.8457i	−0.429245	−	0.590805i	−0.967780	+	0.251798i	$0.918978\pi$
$338$	1.04600	+	14.4985i	0.0568948	+	0.788616i
$339$	−1.57522	+	12.1406i	−0.0855541	+	0.659386i
$340$	1.10027	−	1.10027i	0.0596707	−	0.0596707i
$341$	21.6685	−	13.8026i	1.17341	−	0.747452i
$342$	−8.05607	−	9.87259i	−0.435622	−	0.533849i
$343$	−15.9576	−	8.13082i	−0.861631	−	0.439023i
$344$	−3.63141	−	22.9278i	−0.195792	−	1.23618i
$345$	−14.6885	+	21.4579i	−0.790803	+	1.15525i
$346$	−9.16650	+	4.67057i	−0.492794	+	0.251091i
$347$	17.9250	+	5.82420i	0.962267	+	0.312660i	0.747690	−	0.664048i	$-0.231163\pi$
$347$	17.9250	+	5.82420i	0.962267	+	0.312660i	0.214577	+	0.976707i	$0.431163\pi$
$348$	−0.609550	−	3.25482i	−0.0326753	−	0.174477i
$349$	−3.99593	−	25.2293i	−0.213897	−	1.35049i	−0.827761	−	0.561081i	$-0.810386\pi$
$349$	−3.99593	−	25.2293i	−0.213897	−	1.35049i	0.613864	−	0.789412i	$-0.289614\pi$
$350$	0.155638	+	0.479004i	0.00831919	+	0.0256038i
$351$	3.69832	+	18.3663i	0.197402	+	0.980323i
$352$	−12.7851	+	3.30566i	−0.681447	+	0.176192i
$353$	0.913533	+	0.913533i	0.0486225	+	0.0486225i	0.731000	−	0.682378i	$-0.239054\pi$
$353$	0.913533	+	0.913533i	0.0486225	+	0.0486225i	−0.682378	+	0.731000i	$0.739054\pi$
$354$	−18.4549	−	2.39450i	−0.980869	−	0.127266i
$355$	−2.21785	+	3.05261i	−0.117711	+	0.162016i
$356$	0.580291	+	0.0919091i	0.0307554	+	0.00487117i
$357$	−0.120928	−	4.30969i	−0.00640021	−	0.228093i
$358$	−2.20548	+	1.12375i	−0.116563	+	0.0593920i
$359$	−3.22037	+	20.3326i	−0.169965	+	1.07311i	0.744255	+	0.667896i	$0.232805\pi$
$359$	−3.22037	+	20.3326i	−0.169965	+	1.07311i	−0.914220	+	0.405219i	$0.867195\pi$
$360$	1.17552	+	20.9303i	0.0619553	+	1.10312i
$361$	−4.34706	+	1.41244i	−0.228792	+	0.0743392i
$362$	−7.22376	+	7.22376i	−0.379672	+	0.379672i
$363$	−16.0867	−	10.2087i	−0.844334	−	0.535818i
$364$	−4.98351	−	5.42651i	−0.261207	−	0.284427i
$365$	−5.73039	+	1.86192i	−0.299942	+	0.0974571i
$366$	−6.07231	−	1.78634i	−0.317405	−	0.0933736i
$367$	−8.26642	+	6.00591i	−0.431504	+	0.313506i	−0.782250	−	0.622965i	$-0.785928\pi$
$367$	−8.26642	+	6.00591i	−0.431504	+	0.313506i	0.350746	+	0.936471i	$0.385928\pi$
$368$	−3.95723	+	12.1791i	−0.206285	+	0.634879i
$369$	32.8108	+	14.4614i	1.70806	+	0.752828i
$370$	−0.225459	+	1.42349i	−0.0117211	+	0.0740039i
$371$	−4.36287	+	0.691010i	−0.226509	+	0.0358755i
$372$	6.13816	+	7.96847i	0.318249	+	0.413146i
$373$	−15.6715			−0.811439			−0.405719	−	0.913998i	$-0.632979\pi$
$373$	−15.6715			−0.811439			−0.405719	+	0.913998i	$0.632979\pi$
$374$	3.27896	−	0.847794i	0.169551	−	0.0438384i
$375$	6.38653	+	17.9282i	0.329799	+	0.925811i
$376$	5.96819	−	1.93918i	0.307786	−	0.100006i
$377$	7.20216	+	5.71589i	0.370930	+	0.294383i
$378$	12.0998	+	10.2172i	0.622348	+	0.525518i
$379$	−7.17766	−	14.0869i	−0.368691	−	0.723598i	0.629899	−	0.776677i	$-0.283096\pi$
$379$	−7.17766	−	14.0869i	−0.368691	−	0.723598i	−0.998590	+	0.0530796i	$0.983096\pi$
$380$	−6.15545	−	2.00003i	−0.315768	−	0.102599i
$381$	−5.11706	+	0.958304i	−0.262155	+	0.0490954i
$382$	2.46697	−	0.390729i	0.126221	−	0.0199915i
$383$	−13.5433	+	26.5803i	−0.692031	+	1.35819i	0.230807	+	0.973000i	$0.425863\pi$
$383$	−13.5433	+	26.5803i	−0.692031	+	1.35819i	−0.922838	+	0.385188i	$0.874137\pi$
$384$	0.784815	+	2.20313i	0.0400499	+	0.112428i
$385$	4.44800	−	20.0581i	0.226691	−	1.02226i
$386$			6.40892i			0.326205i
$387$	19.0421	+	12.2649i	0.967964	+	0.623462i
$388$	1.52777	+	9.64595i	0.0775607	+	0.489699i
$389$	16.8967	−	12.2762i	0.856697	−	0.622427i	−0.0702874	−	0.997527i	$-0.522392\pi$
$389$	16.8967	−	12.2762i	0.856697	−	0.622427i	0.926984	+	0.375100i	$0.122392\pi$
$390$	−11.0584	−	11.3833i	−0.559963	−	0.576416i
$391$	−1.86421	+	5.73746i	−0.0942773	+	0.290156i
$392$	−1.30352	−	0.206457i	−0.0658378	−	0.0104277i
$393$	−15.7327	−	28.8472i	−0.793612	−	1.45515i
$394$	1.23999	−	0.402897i	0.0624698	−	0.0202977i
$395$	−3.36976	−	3.36976i	−0.169551	−	0.169551i
$396$	3.41995	−	6.62921i	0.171859	−	0.333130i
$397$	−1.21184	−	1.21184i	−0.0608206	−	0.0608206i	0.676042	−	0.736863i	$-0.263694\pi$
$397$	−1.21184	−	1.21184i	−0.0608206	−	0.0608206i	−0.736863	+	0.676042i	$0.763694\pi$
$398$	−18.7516	−	9.55441i	−0.939932	−	0.478919i
$399$	−15.7438	+	8.58641i	−0.788178	+	0.429858i
$400$	−0.188300	−	0.259173i	−0.00941502	−	0.0129587i
$401$	7.91663	+	15.5373i	0.395337	+	0.775894i	0.999785	−	0.0207517i	$-0.00660595\pi$
$401$	7.91663	+	15.5373i	0.395337	+	0.775894i	−0.604447	+	0.796645i	$0.706606\pi$
$402$	18.1831	+	17.1905i	0.906888	+	0.857383i
$403$	−27.3747	−	5.53798i	−1.36363	−	0.275866i
$404$	7.49123	−	10.3108i	0.372703	−	0.512981i
$405$	−15.9921	−	12.7530i	−0.794653	−	0.633702i
$406$	7.77223			0.385729
$407$	1.19652	−	1.45132i	0.0593092	−	0.0719393i
$408$	1.63201	+	4.58136i	0.0807963	+	0.226811i
$409$	18.1673	+	9.25671i	0.898316	+	0.457715i	0.841244	−	0.540655i	$-0.181824\pi$
$409$	18.1673	+	9.25671i	0.898316	+	0.457715i	0.0570714	+	0.998370i	$0.481824\pi$
$410$	−29.9998	+	4.75151i	−1.48159	+	0.234660i
$411$	−22.0636	−	15.1031i	−1.08832	−	0.744982i
$412$	3.84878	−	11.8453i	0.189616	−	0.583578i
$413$	−8.09328	+	24.9085i	−0.398244	+	1.22567i
$414$	−11.1515	−	19.1490i	−0.548066	−	0.941121i
$415$	−3.55588	+	4.89425i	−0.174551	+	0.240249i
$416$	12.5025	+	7.05540i	0.612988	+	0.345919i
$417$	−2.69445	+	5.67637i	−0.131948	+	0.277973i
$418$	−9.33387	−	10.5513i	−0.456534	−	0.516079i
$419$		−	5.04903i		−	0.246662i	−0.992366	−	0.123331i	$-0.960642\pi$
$419$		−	5.04903i		−	0.246662i	0.992366	−	0.123331i	$-0.0393576\pi$
$420$	7.97700	+	1.03500i	0.389238	+	0.0505029i
$421$	28.9046	−	4.57804i	1.40872	−	0.223120i	0.594699	−	0.803949i	$-0.297271\pi$
$421$	28.9046	−	4.57804i	1.40872	−	0.223120i	0.814026	+	0.580829i	$0.197271\pi$
$422$	−18.6342	−	2.95136i	−0.907097	−	0.143670i
$423$	−2.46949	+	5.60294i	−0.120071	+	0.272424i
$424$	4.43969	−	2.26214i	0.215611	−	0.109859i
$425$	−0.0887065	−	0.122094i	−0.00430290	−	0.00592243i
$426$	−1.53955	−	2.82288i	−0.0745913	−	0.136769i
$427$	−4.04416	+	7.93711i	−0.195711	+	0.384104i
$428$	−5.46875			−0.264342
$429$	4.89394	+	20.1258i	0.236282	+	0.971685i
$430$	−19.1868			−0.925272
$431$	−8.26360	+	16.2182i	−0.398044	+	0.781205i	−0.999848	−	0.0174387i	$-0.994449\pi$
$431$	−8.26360	+	16.2182i	−0.398044	+	0.781205i	0.601804	+	0.798644i	$0.294449\pi$
$432$	−9.32780	−	3.80246i	−0.448784	−	0.182946i
$433$	23.9782	+	33.0031i	1.15232	+	1.58603i	0.736273	+	0.676685i	$0.236584\pi$
$433$	23.9782	+	33.0031i	1.15232	+	1.58603i	0.416044	+	0.909344i	$0.363416\pi$
$434$	−21.0353	+	10.7180i	−1.00972	+	0.514480i
$435$	−10.0346	+	0.281568i	−0.481124	+	0.0135002i
$436$	15.0525	+	2.38408i	0.720882	+	0.114177i
$437$	24.7840	−	3.92539i	1.18558	−	0.187777i
$438$	0.660657	−	5.09184i	0.0315674	−	0.243298i
$439$		−	5.34643i		−	0.255171i	−0.991828	−	0.127586i	$-0.959277\pi$
$439$		−	5.34643i		−	0.255171i	0.991828	−	0.127586i	$-0.0407228\pi$
$440$	2.21996	+	23.0692i	0.105833	+	1.09978i
$441$	0.997717	−	0.814141i	0.0475104	−	0.0387686i
$442$	−3.20650	−	1.80948i	−0.152518	−	0.0860682i
$443$	−9.81836	+	13.5138i	−0.466484	+	0.642061i	−0.975838	−	0.218497i	$-0.929885\pi$
$443$	−9.81836	+	13.5138i	−0.466484	+	0.642061i	0.509353	+	0.860558i	$0.329885\pi$
$444$	0.607687	+	0.415978i	0.0288395	+	0.0197415i
$445$	0.550387	−	1.69392i	0.0260909	−	0.0802994i
$446$	5.76830	−	17.7530i	0.273137	−	0.840629i
$447$	9.15007	−	13.3670i	0.432783	−	0.632236i
$448$	22.4232	−	3.55149i	1.05940	−	0.167792i
$449$	6.94099	+	3.53661i	0.327566	+	0.166903i	0.610037	−	0.792373i	$-0.291154\pi$
$449$	6.94099	+	3.53661i	0.327566	+	0.166903i	−0.282472	+	0.959276i	$0.591154\pi$
$450$	0.551523	+	0.0558802i	0.0259991	+	0.00263422i
$451$	36.8816	+	14.5305i	1.73669	+	0.684216i
$452$	−5.29895			−0.249242
$453$	−2.45912	−	3.19240i	−0.115540	−	0.149992i
$454$	−12.5724	+	17.3044i	−0.590051	+	0.812135i
$455$	−18.6114	+	12.3482i	−0.872516	+	0.578891i
$456$	13.8972	−	14.6997i	0.650798	−	0.688374i
$457$	9.17166	+	18.0004i	0.429032	+	0.842023i	0.999782	+	0.0208990i	$0.00665284\pi$
$457$	9.17166	+	18.0004i	0.429032	+	0.842023i	−0.570749	+	0.821124i	$0.693347\pi$
$458$	17.4309	+	23.9916i	0.814493	+	1.12105i
$459$	−4.39424	−	1.79130i	−0.205105	−	0.0836108i
$460$	−10.0286	−	5.10984i	−0.467587	−	0.238248i
$461$	−20.3835	−	20.3835i	−0.949353	−	0.949353i	0.0494252	−	0.998778i	$-0.484261\pi$
$461$	−20.3835	−	20.3835i	−0.949353	−	0.949353i	−0.998778	+	0.0494252i	$0.984261\pi$
$462$	13.8160	+	10.7540i	0.642780	+	0.500320i
$463$	4.54323	+	4.54323i	0.211142	+	0.211142i	0.804752	−	0.593611i	$-0.202298\pi$
$463$	4.54323	+	4.54323i	0.211142	+	0.211142i	−0.593611	+	0.804752i	$0.702298\pi$
$464$	−4.70166	+	1.52766i	−0.218269	+	0.0709200i
$465$	26.7701	−	14.5999i	1.24143	−	0.677055i
$466$	2.61873	+	0.414767i	0.121311	+	0.0192137i
$467$	−0.171755	+	0.528609i	−0.00794790	+	0.0244611i	−0.954952	−	0.296761i	$-0.904094\pi$
$467$	−0.171755	+	0.528609i	−0.00794790	+	0.0244611i	0.947004	+	0.321222i	$0.104094\pi$
$468$	−7.67759	+	2.61034i	−0.354897	+	0.120663i
$469$	28.4902	−	20.6994i	1.31556	−	0.955808i
$470$	−0.811391	−	5.12292i	−0.0374267	−	0.236303i
$471$	−15.9663	−	2.07160i	−0.735688	−	0.0954542i
$472$		−	29.5435i		−	1.35985i
$473$	21.5751	+	12.7104i	0.992022	+	0.584423i
$474$	3.82555	−	1.36276i	0.175713	−	0.0625938i
$475$	−0.284985	+	0.559314i	−0.0130760	+	0.0256631i
$476$	1.84316	−	0.291927i	0.0844809	−	0.0133805i
$477$	−1.24074	+	4.70086i	−0.0568097	+	0.215238i
$478$	−9.33863	−	3.03431i	−0.427139	−	0.138786i
$479$	17.1740	+	33.7058i	0.784698	+	1.54006i	0.840622	+	0.541622i	$0.182190\pi$
$479$	17.1740	+	33.7058i	0.784698	+	1.54006i	−0.0559238	+	0.998435i	$0.517810\pi$
$480$	−15.4057	+	2.88512i	−0.703169	+	0.131687i
$481$	−2.03141	+	0.233721i	−0.0926244	+	0.0106568i
$482$	−3.69744	+	1.20137i	−0.168414	+	0.0547210i
$483$	−29.3778	+	10.4652i	−1.33674	+	0.476182i
$484$	3.48606	−	7.47361i	0.158457	−	0.339710i
$485$	29.6064			1.34436
$486$	15.6616	−	7.65099i	0.710425	−	0.347056i
$487$	−38.9747	+	6.17299i	−1.76611	+	0.279725i	−0.953129	−	0.302563i	$-0.902158\pi$
$487$	−38.9747	+	6.17299i	−1.76611	+	0.279725i	−0.812983	+	0.582288i	$0.802158\pi$
$488$	1.57193	−	9.92479i	0.0711580	−	0.449274i
$489$	0.751964	+	26.7988i	0.0340050	+	1.21188i
$490$	−0.337087	+	1.03745i	−0.0152280	+	0.0468670i
$491$	−3.97160	+	2.88553i	−0.179236	+	0.130222i	−0.673786	−	0.738927i	$-0.735333\pi$
$491$	−3.97160	+	2.88553i	−0.179236	+	0.130222i	0.494550	+	0.869149i	$0.335333\pi$
$492$	−4.38005	+	14.8891i	−0.197468	+	0.671253i
$493$	−2.21491	+	0.719668i	−0.0997545	+	0.0324122i
$494$	−0.651121	+	15.3006i	−0.0292953	+	0.688406i
$495$	−18.2273	−	13.3838i	−0.819256	−	0.601556i
$496$	10.6182	−	10.6182i	0.476772	−	0.476772i
$497$	−4.30374	+	1.39837i	−0.193049	+	0.0627255i
$498$	−2.46836	−	4.52592i	−0.110610	−	0.202811i
$499$	−4.96594	+	31.3537i	−0.222306	+	1.40358i	0.583840	+	0.811869i	$0.301549\pi$
$499$	−4.96594	+	31.3537i	−0.222306	+	1.40358i	−0.806146	+	0.591716i	$0.798451\pi$
$500$	−7.33983	+	3.73983i	−0.328247	+	0.167250i
$501$	23.4436	−	0.657820i	1.04738	−	0.0293892i
$502$	−12.9205	−	2.04640i	−0.576670	−	0.0913355i
$503$	9.58890	−	13.1980i	0.427548	−	0.588470i	−0.539840	−	0.841768i	$-0.681515\pi$
$503$	9.58890	−	13.1980i	0.427548	−	0.588470i	0.967388	+	0.253298i	$0.0815153\pi$
$504$	−13.6138	+	21.1363i	−0.606408	+	0.941486i
$505$	−27.3199	−	27.3199i	−1.21572	−	1.21572i
$506$	−13.1616	−	20.6623i	−0.585106	−	0.918551i
$507$	11.3488	−	19.4475i	0.504019	−	0.863693i
$508$	−0.696327	−	2.14307i	−0.0308945	−	0.0950835i
$509$	−6.23197	−	39.3471i	−0.276227	−	1.74403i	−0.601922	−	0.798555i	$-0.705598\pi$
$509$	−6.23197	−	39.3471i	−0.276227	−	1.74403i	0.325695	−	0.945475i	$-0.394402\pi$
$510$	3.95105	−	0.739939i	0.174956	−	0.0327650i
$511$	−6.87243	−	2.23299i	−0.304018	−	0.0987816i
$512$	−17.4988	+	8.91606i	−0.773343	+	0.394038i
$513$	1.65913	+	19.6682i	0.0732523	+	0.868371i
$514$	3.37045	+	21.2802i	0.148664	+	0.938628i
$515$	−33.6420	−	17.1415i	−1.48245	−	0.755343i
$516$	−4.20409	+	8.85669i	−0.185075	+	0.389894i
$517$	−2.48130	+	6.29808i	−0.109128	+	0.276989i
$518$	−1.22221	+	1.22221i	−0.0537010	+	0.0537010i
$519$	15.8034	+	2.05046i	0.693692	+	0.0900053i
$520$	15.6623	−	19.7349i	0.686839	−	0.865433i
$521$	9.41422	+	12.9576i	0.412444	+	0.567681i	0.963813	−	0.266581i	$-0.0858940\pi$
$521$	9.41422	+	12.9576i	0.412444	+	0.567681i	−0.551368	+	0.834262i	$0.685894\pi$
$522$	3.45014	−	7.82790i	0.151009	−	0.342618i
$523$	−6.75760	+	20.7978i	−0.295489	+	0.909422i	0.687567	+	0.726121i	$0.258679\pi$
$523$	−6.75760	+	20.7978i	−0.295489	+	0.909422i	−0.983057	+	0.183302i	$0.941321\pi$
$524$	11.5061	−	8.35971i	0.502648	−	0.365195i
$525$	0.220178	−	0.748450i	0.00960934	−	0.0326650i
$526$	6.79628	+	3.46288i	0.296332	+	0.150989i
$527$	5.00214	−	5.00214i	0.217897	−	0.217897i
$528$	−10.4715	−	3.78981i	−0.455713	−	0.164930i
$529$	20.6373			0.897276
$530$	−1.27267	−	3.91687i	−0.0552812	−	0.170138i
$531$	21.4943	+	19.2083i	0.932773	+	0.833569i
$532$	−4.56245	−	6.27968i	−0.197807	−	0.272259i
$533$	−17.9141	−	39.1942i	−0.775945	−	1.69769i
$534$	1.10291	+	1.04271i	0.0477277	+	0.0451223i
$535$	−2.59347	+	16.3745i	−0.112125	+	0.707931i
$536$	−23.3495	+	32.1378i	−1.00854	+	1.38814i
$537$	3.80233	+	0.493346i	0.164083	+	0.0212894i
$538$	−5.56831	+	5.56831i	−0.240067	+	0.240067i
$539$	1.06630	−	0.943275i	0.0459289	−	0.0406297i
$540$	4.58345	−	7.57469i	0.197240	−	0.325963i
$541$	14.5110	−	28.4795i	0.623877	−	1.22443i	−0.335431	−	0.942065i	$-0.608882\pi$
$541$	14.5110	−	28.4795i	0.623877	−	1.22443i	0.959308	−	0.282362i	$-0.0911181\pi$
$542$	−6.16592	+	8.48667i	−0.264849	+	0.364534i
$543$	15.5541	−	2.91292i	0.667492	−	0.125005i
$544$	−3.23984	+	1.65078i	−0.138907	+	0.0707767i
$545$	14.2768	−	43.9394i	0.611550	−	1.88216i
$546$	−2.70499	−	18.8400i	−0.115763	−	0.806279i
$547$	12.4347	+	9.03437i	0.531671	+	0.386282i	0.820983	−	0.570953i	$-0.193426\pi$
$547$	12.4347	+	9.03437i	0.531671	+	0.386282i	−0.289311	+	0.957235i	$0.593426\pi$
$548$	5.25407	−	10.3117i	0.224443	−	0.440494i
$549$	6.19873	+	7.59645i	0.264555	+	0.324209i
$550$	0.611709	+	0.0374493i	0.0260833	+	0.00159684i
$551$	6.84971	+	6.84971i	0.291808	+	0.291808i
$552$	27.8691	−	21.4678i	1.18619	−	0.913729i
$553$	−0.894072	−	5.64495i	−0.0380198	−	0.240048i
$554$	4.35438	−	27.4925i	0.185000	−	1.16804i
$555$	1.53371	−	1.62226i	0.0651022	−	0.0688611i
$556$	−2.58658	−	0.840432i	−0.109696	−	0.0356423i
$557$	−3.17991	+	20.0771i	−0.134737	+	0.850696i	0.824039	+	0.566533i	$0.191716\pi$
$557$	−3.17991	+	20.0771i	−0.134737	+	0.850696i	−0.958776	+	0.284163i	$0.908284\pi$
$558$	1.45709	+	25.9437i	0.0616835	+	1.09828i
$559$	−7.30374	−	26.2240i	−0.308915	−	1.10916i
$560$		−	12.0087i		−	0.507462i
$561$	−4.93302	−	1.78534i	−0.208272	−	0.0753772i
$562$	3.46806			0.146291
$563$	−0.871742	−	2.68295i	−0.0367395	−	0.113073i	0.931005	−	0.365007i	$-0.118933\pi$
$563$	−0.871742	−	2.68295i	−0.0367395	−	0.113073i	−0.967744	+	0.251934i	$0.918933\pi$
$564$	−2.54254	−	0.747959i	−0.107060	−	0.0314947i
$565$	−2.51294	+	15.8661i	−0.105720	+	0.667491i
$566$	7.23790	+	14.2052i	0.304232	+	0.597088i
$567$	−6.52637	−	23.6469i	−0.274082	−	0.993076i
$568$	4.12969	−	3.00040i	0.173278	−	0.125894i
$569$	−13.5223	−	9.82455i	−0.566886	−	0.411866i	0.267087	−	0.963672i	$-0.413939\pi$
$569$	−13.5223	−	9.82455i	−0.566886	−	0.411866i	−0.833973	+	0.551806i	$0.813939\pi$
$570$	−10.2033	−	13.2458i	−0.427369	−	0.554804i
$571$		−	29.1551i		−	1.22010i	−0.792362	−	0.610051i	$-0.791149\pi$
$571$		−	29.1551i		−	1.22010i	0.792362	−	0.610051i	$-0.208851\pi$
$572$	−8.36625	+	3.22154i	−0.349811	+	0.134700i
$573$	−3.49520	−	1.65910i	−0.146014	−	0.0693098i
$574$	−32.4569	−	16.5376i	−1.35472	−	0.690266i
$575$	−0.641654	+	0.883161i	−0.0267588	+	0.0368303i
$576$	6.37687	−	24.1603i	0.265703	−	1.00668i
$577$	5.61772	+	11.0254i	0.233869	+	0.458993i	0.977878	−	0.209176i	$-0.0670782\pi$
$577$	5.61772	+	11.0254i	0.233869	+	0.458993i	−0.744009	+	0.668169i	$0.767078\pi$
$578$	−16.1061	+	8.20648i	−0.669926	+	0.341345i
$579$	5.60764	−	8.19199i	0.233046	−	0.340447i
$580$	−0.679719	−	4.29158i	−0.0282238	−	0.178198i
$581$	−6.90019	+	2.24201i	−0.286268	+	0.0930142i
$582$	−10.8189	+	22.7920i	−0.448458	+	0.944759i
$583$	−1.16366	+	5.24749i	−0.0481939	+	0.217329i
$584$	8.15125			0.337301
$585$	4.17491	+	24.2261i	0.172611	+	1.00163i
$586$	28.9826	+	21.0571i	1.19726	+	0.869860i
$587$	−33.6249	−	5.32566i	−1.38785	−	0.219814i	−0.582603	−	0.812757i	$-0.697966\pi$
$587$	−33.6249	−	5.32566i	−1.38785	−	0.219814i	−0.805244	+	0.592943i	$0.797966\pi$
$588$	0.405027	+	0.382918i	0.0167031	+	0.0157913i
$589$	−27.9843	−	9.09266i	−1.15307	−	0.374657i
$590$	−24.1181	−	3.81993i	−0.992927	−	0.157264i
$591$	−1.93750	−	0.569970i	−0.0796982	−	0.0234454i
$592$	0.499124	−	0.979585i	0.0205139	−	0.0402607i
$593$	11.3499	−	11.3499i	0.466085	−	0.466085i	−0.434559	−	0.900643i	$-0.643096\pi$
$593$	11.3499	−	11.3499i	0.466085	−	0.466085i	0.900643	+	0.434559i	$0.143096\pi$
$594$	16.9640	−	9.14125i	0.696042	−	0.375070i
$595$		−	5.65721i		−	0.231923i
$596$	6.24723	+	3.18313i	0.255897	+	0.130386i
$597$	15.6087	+	28.6198i	0.638823	+	1.17133i
$598$	−5.28082	+	26.1035i	−0.215949	+	1.06745i
$599$	−15.3666	−	4.99292i	−0.627864	−	0.204005i	−0.0222352	−	0.999753i	$-0.507078\pi$
$599$	−15.3666	−	4.99292i	−0.627864	−	0.204005i	−0.605629	+	0.795747i	$0.707078\pi$
$600$	0.0246841	+	0.879701i	0.00100772	+	0.0359136i
$601$	31.5800	−	22.9442i	1.28818	−	0.935914i	0.288409	−	0.957507i	$-0.406874\pi$
$601$	31.5800	−	22.9442i	1.28818	−	0.935914i	0.999767	+	0.0215930i	$0.00687380\pi$
$602$	−18.6161	−	13.5254i	−0.758734	−	0.551252i
$603$	−8.20064	−	37.8829i	−0.333956	−	1.54271i
$604$	1.23335	−	1.23335i	0.0501842	−	0.0501842i
$605$	−20.7242	−	13.9822i	−0.842560	−	0.568456i
$606$	31.0152	−	11.0485i	1.25991	−	0.448813i
$607$	−4.38566	−	13.4977i	−0.178009	−	0.547854i	0.821750	−	0.569849i	$-0.192998\pi$
$607$	−4.38566	−	13.4977i	−0.178009	−	0.547854i	−0.999758	+	0.0219949i	$0.992998\pi$
$608$	12.2360	+	8.88996i	0.496234	+	0.360535i
$609$	−9.93459	−	6.80051i	−0.402570	−	0.275570i
$610$	−7.89894	−	2.56652i	−0.319819	−	0.103915i
$611$	6.69299	−	3.05909i	0.270769	−	0.123758i
$612$	0.524170	−	1.98594i	0.0211883	−	0.0802771i
$613$	−0.879661	+	0.139325i	−0.0355292	+	0.00562727i	−0.174174	−	0.984715i	$-0.555725\pi$
$613$	−0.879661	+	0.139325i	−0.0355292	+	0.00562727i	0.138645	+	0.990342i	$0.455725\pi$
$614$	30.9222	−	10.0472i	1.24792	−	0.405473i
$615$	42.5037	+	20.1756i	1.71392	+	0.813561i
$616$	−14.1082	+	23.9479i	−0.568437	+	0.964887i
$617$	−18.7420	−	18.7420i	−0.754524	−	0.754524i	0.220796	−	0.975320i	$-0.429134\pi$
$617$	−18.7420	−	18.7420i	−0.754524	−	0.754524i	−0.975320	+	0.220796i	$0.929134\pi$
$618$	25.4897	−	19.6349i	1.02535	−	0.789831i
$619$	4.83742	+	30.5422i	0.194432	+	1.22760i	0.871025	+	0.491239i	$0.163456\pi$
$619$	4.83742	+	30.5422i	0.194432	+	1.22760i	−0.676593	+	0.736357i	$0.736544\pi$
$620$	7.75778	+	10.6777i	0.311560	+	0.428825i
$621$	−2.50086	+	34.2338i	−0.100356	+	1.37376i
$622$	14.4727	−	7.37420i	0.580301	−	0.295678i
$623$	1.72811	−	1.25554i	0.0692351	−	0.0503022i
$624$	5.33941	+	10.8652i	0.213748	+	0.434958i
$625$	7.97232	+	24.5363i	0.318893	+	0.981451i
$626$	24.8926	+	24.8926i	0.994910	+	0.994910i
$627$	2.69863	+	21.6537i	0.107773	+	0.864765i
$628$		−	6.96875i		−	0.278083i
$629$	0.235132	−	0.461473i	0.00937534	−	0.0184002i
$630$	15.4946	+	13.8467i	0.617318	+	0.551664i
$631$	−14.9116	−	2.36176i	−0.593620	−	0.0940202i	−0.147606	−	0.989046i	$-0.547157\pi$
$631$	−14.9116	−	2.36176i	−0.593620	−	0.0940202i	−0.446014	+	0.895026i	$0.647157\pi$
$632$	2.92689	+	5.74435i	0.116426	+	0.228498i
$633$	21.2361	+	20.0769i	0.844060	+	0.797985i
$634$	−4.70493	−	6.47578i	−0.186857	−	0.257186i
$635$	−6.74700	+	1.06862i	−0.267747	+	0.0424069i
$636$	−2.08690	−	0.270771i	−0.0827508	−	0.0107368i
$637$	−1.54627	−	0.0658018i	−0.0612653	−	0.00260716i
$638$	3.46664	−	8.79909i	0.137246	−	0.348359i
$639$	−0.502070	+	4.95531i	−0.0198616	+	0.196029i
$640$	0.948310	+	2.91860i	0.0374853	+	0.115368i
$641$	29.2121	+	21.2239i	1.15381	+	0.838292i	0.988983	−	0.148031i	$-0.0472934\pi$
$641$	29.2121	+	21.2239i	1.15381	+	0.838292i	0.164827	+	0.986322i	$0.447293\pi$
$642$	−11.6579	−	7.98018i	−0.460102	−	0.314953i
$643$	−9.61656	−	18.8736i	−0.379240	−	0.744300i	0.619946	−	0.784645i	$-0.287155\pi$
$643$	−9.61656	−	18.8736i	−0.379240	−	0.744300i	−0.999186	+	0.0403442i	$0.987155\pi$
$644$	−6.12821	−	12.0273i	−0.241485	−	0.473942i
$645$	24.5249	+	16.7880i	0.965669	+	0.661027i
$646$	−3.13813	−	2.27998i	−0.123468	−	0.0897048i
$647$	−3.75986	−	11.5717i	−0.147816	−	0.454929i	0.849547	−	0.527513i	$-0.176876\pi$
$647$	−3.75986	−	11.5717i	−0.147816	−	0.454929i	−0.997362	+	0.0725839i	$0.976876\pi$
$648$	15.2444	+	23.0939i	0.598858	+	0.907213i
$649$	24.5896	+	20.2725i	0.965226	+	0.795765i
$650$	−0.450649	−	0.490708i	−0.0176759	−	0.0192472i
$651$	36.2656	+	4.70539i	1.42136	+	0.184419i
$652$	−11.4612	+	1.81528i	−0.448856	+	0.0710918i
$653$	21.3479	+	29.3828i	0.835407	+	1.14984i	0.986892	+	0.161380i	$0.0515944\pi$
$653$	21.3479	+	29.3828i	0.835407	+	1.14984i	−0.151485	+	0.988460i	$0.548406\pi$
$654$	28.6090	+	27.0473i	1.11870	+	1.05763i
$655$	−19.5740	−	38.4161i	−0.764819	−	1.50104i
$656$	22.8847	+	3.62458i	0.893497	+	0.141516i
$657$	−5.29969	+	5.93042i	−0.206761	+	0.231368i
$658$	2.82404	−	5.54249i	0.110093	−	0.216069i
$659$			33.3092i			1.29754i	0.760983	+	0.648772i	$0.224717\pi$
$659$			33.3092i			1.29754i	−0.760983	+	0.648772i	$0.775283\pi$
$660$	4.72972	−	8.56927i	0.184104	−	0.333558i
$661$	1.79675	+	1.79675i	0.0698853	+	0.0698853i	0.741186	−	0.671300i	$-0.234264\pi$
$661$	1.79675	+	1.79675i	0.0698853	+	0.0698853i	−0.671300	+	0.741186i	$0.734264\pi$
$662$	−0.110653	−	0.340553i	−0.00430063	−	0.0132360i
$663$	2.51535	+	5.11851i	0.0976880	+	0.198787i
$664$	6.62114	−	4.81054i	0.256950	−	0.186685i
$665$	−20.9662	+	10.6828i	−0.813036	+	0.414263i
$666$	0.688419	+	1.77351i	0.0266757	+	0.0687223i
$667$	9.90179	+	13.6286i	0.383399	+	0.527703i
$668$	1.58801	+	10.0263i	0.0614420	+	0.387929i
$669$	−22.9066	+	17.6451i	−0.885619	+	0.682198i
$670$	23.2169	+	23.2169i	0.896948	+	0.896948i
$671$	7.18193	+	8.11865i	0.277255	+	0.313417i
$672$	−16.9812	−	8.06061i	−0.655063	−	0.310945i
$673$	−33.6345	+	10.9285i	−1.29651	+	0.421263i	−0.874368	−	0.485264i	$-0.838723\pi$
$673$	−33.6345	+	10.9285i	−1.29651	+	0.421263i	−0.422147	+	0.906527i	$0.638723\pi$
$674$	14.8057	−	2.34499i	0.570294	−	0.0903258i
$675$	−0.656073	−	0.553996i	−0.0252523	−	0.0213233i
$676$	8.97968	+	3.78828i	0.345372	+	0.145703i
$677$	3.01201	+	0.978662i	0.115761	+	0.0376130i	0.366325	−	0.930487i	$-0.380616\pi$
$677$	3.01201	+	0.978662i	0.115761	+	0.0376130i	−0.250564	+	0.968100i	$0.580616\pi$
$678$	−11.2960	−	7.73241i	−0.433819	−	0.296961i
$679$	28.7256	+	20.8704i	1.10239	+	0.800932i
$680$	1.97199	+	6.06916i	0.0756224	+	0.232742i
$681$	31.2111	−	11.1182i	1.19601	−	0.426052i
$682$	2.75171	+	28.5950i	0.105368	+	1.09496i
$683$	−20.7520	+	20.7520i	−0.794054	+	0.794054i	−0.982151	−	0.188097i	$-0.939768\pi$
$683$	−20.7520	+	20.7520i	−0.794054	+	0.794054i	0.188097	+	0.982151i	$0.439768\pi$
$684$	−8.34995	+	1.80754i	−0.319269	+	0.0691132i
$685$	−28.3836	−	20.6219i	−1.08448	−	0.787921i
$686$	16.2014	−	11.7710i	0.618573	−	0.449419i
$687$	−1.28844	−	45.9180i	−0.0491572	−	1.75188i
$688$	13.9199	+	4.52285i	0.530691	+	0.172432i
$689$	4.86901	−	3.23046i	0.185494	−	0.123071i
$690$	−13.9220	−	25.5270i	−0.530000	−	0.971795i
$691$	29.6106	+	15.0874i	1.12644	+	0.573950i	0.915005	−	0.403442i	$-0.132186\pi$
$691$	29.6106	+	15.0874i	1.12644	+	0.573950i	0.211436	+	0.977392i	$0.432186\pi$
$692$			6.89764i			0.262209i
$693$	−8.25045	−	25.8346i	−0.313409	−	0.981374i
$694$	−14.9021	+	14.9021i	−0.565675	+	0.565675i
$695$	−3.74306	+	7.34618i	−0.141982	+	0.278656i
$696$	13.0285	+	3.83271i	0.493846	+	0.145279i
$697$	10.7808	+	1.70750i	0.408350	+	0.0646764i
$698$	27.1643	+	8.82622i	1.02818	+	0.334077i
$699$	−2.98440	−	2.82149i	−0.112880	−	0.106718i
$700$	0.333527	+	0.0528255i	0.0126061	+	0.00199662i
$701$	4.58181	+	3.32888i	0.173053	+	0.125730i	0.670940	−	0.741512i	$-0.265891\pi$
$701$	4.58181	+	3.32888i	0.173053	+	0.125730i	−0.497887	+	0.867242i	$0.665891\pi$
$702$	−20.1757	−	5.63883i	−0.761484	−	0.212824i
$703$	−2.15429			−0.0812505
$704$	5.98070	−	26.9698i	0.225406	−	1.01646i
$705$	−3.44529	+	7.25815i	−0.129757	+	0.273358i
$706$	−1.37389	+	0.446405i	−0.0517072	+	0.0168007i
$707$	−7.24859	−	45.7658i	−0.272611	−	1.72120i
$708$	−7.04788	+	10.2960i	−0.264876	+	0.386946i
$709$	−34.0824	+	17.3659i	−1.27999	+	0.652188i	−0.955860	−	0.293824i	$-0.905072\pi$
$709$	−34.0824	+	17.3659i	−1.27999	+	0.652188i	−0.324132	+	0.946012i	$0.605072\pi$
$710$	−1.91544	−	3.75925i	−0.0718850	−	0.141082i
$711$	−6.08226	−	1.60535i	−0.228103	−	0.0602054i
$712$	−1.41629	+	1.94935i	−0.0530776	+	0.0730551i
$713$	−45.5929	−	23.2307i	−1.70747	−	0.869998i
$714$	4.35512	+	2.06728i	0.162986	+	0.0773661i
$715$	5.67837	+	26.5780i	0.212359	+	0.993959i
$716$			1.65959i			0.0620217i
$717$	9.28185	+	12.0496i	0.346637	+	0.449999i
$718$	−18.6225	−	13.5301i	−0.694987	−	0.504938i
$719$	−28.2852	+	20.5504i	−1.05486	+	0.766399i	−0.973130	−	0.230255i	$-0.926044\pi$
$719$	−28.2852	+	20.5504i	−1.05486	+	0.766399i	−0.0817281	+	0.996655i	$0.526044\pi$
$720$	−12.0948	−	5.33075i	−0.450745	−	0.198665i
$721$	−20.5577	−	40.3468i	−0.765609	−	1.50259i
$722$	0.799520	−	5.04797i	0.0297550	−	0.187866i
$723$	5.77730	+	1.69955i	0.214860	+	0.0632071i
$724$	2.11660	+	6.51422i	0.0786628	+	0.242099i
$725$	−0.421423			−0.0156513
$726$	18.3371	−	10.8448i	0.680554	−	0.402489i
$727$			19.8049i			0.734523i	0.930118	+	0.367262i	$0.119705\pi$
$727$			19.8049i			0.734523i	−0.930118	+	0.367262i	$0.880295\pi$
$728$	29.1081	−	8.10700i	1.07882	−	0.300465i
$729$	−26.7134	−	3.92388i	−0.989383	−	0.145329i
$730$	1.05394	−	6.65434i	0.0390082	−	0.246288i
$731$	6.55753	+	2.13067i	0.242539	+	0.0788057i
$732$	−2.91547	+	3.08381i	−0.107759	+	0.113981i
$733$	2.65309	−	16.7510i	0.0979943	−	0.618711i	−0.888994	−	0.457919i	$-0.848595\pi$
$733$	2.65309	−	16.7510i	0.0979943	−	0.618711i	0.986988	−	0.160793i	$-0.0514050\pi$
$734$	−1.78731	−	11.2846i	−0.0659708	−	0.416524i
$735$	1.33861	−	1.03114i	0.0493753	−	0.0380341i
$736$	18.5983	+	18.5983i	0.685543	+	0.685543i
$737$	−10.7267	−	41.4869i	−0.395122	−	1.52819i
$738$	−31.0638	+	25.3482i	−1.14348	+	0.933080i
$739$	8.23265	−	16.1575i	0.302843	−	0.594363i	−0.688564	−	0.725175i	$-0.741759\pi$
$739$	8.23265	−	16.1575i	0.302843	−	0.594363i	0.991407	+	0.130813i	$0.0417586\pi$
$740$	0.781756	+	0.567979i	0.0287379	+	0.0208793i
$741$	14.2199	−	18.9877i	0.522381	−	0.697532i
$742$	1.52631	−	4.69749i	0.0560325	−	0.172450i
$743$	−11.1980	+	5.70567i	−0.410815	+	0.209321i	−0.647169	−	0.762346i	$-0.724047\pi$
$743$	−11.1980	+	5.70567i	−0.410815	+	0.209321i	0.236354	+	0.971667i	$0.424047\pi$
$744$	−40.5466	+	7.59342i	−1.48651	+	0.278388i
$745$	12.4935	−	17.1959i	0.457728	−	0.630009i
$746$	7.95545	−	15.6134i	0.291270	−	0.571649i
$747$	−0.804970	+	7.94485i	−0.0294523	+	0.290687i
$748$	0.491605	−	2.21688i	0.0179749	−	0.0810571i
$749$	−14.0592	+	14.0592i	−0.513711	+	0.513711i
$750$	−21.1039	−	2.73819i	−0.770605	−	0.0999846i
$751$	14.3227	−	19.7135i	0.522643	−	0.719357i	−0.463344	−	0.886179i	$-0.653350\pi$
$751$	14.3227	−	19.7135i	0.522643	−	0.719357i	0.985987	+	0.166822i	$0.0533504\pi$
$752$	−0.618951	+	3.90790i	−0.0225708	+	0.142506i
$753$	14.7246	+	13.9208i	0.536595	+	0.507304i
$754$	−9.35081	+	4.27388i	−0.340536	+	0.155645i
$755$	−3.10799	−	4.27778i	−0.113111	−	0.155684i
$756$	9.78671	−	4.11834i	0.355939	−	0.149783i
$757$	4.08852	+	12.5832i	0.148600	+	0.457343i	0.997456	−	0.0712804i	$-0.0227085\pi$
$757$	4.08852	+	12.5832i	0.148600	+	0.457343i	−0.848857	+	0.528623i	$0.822709\pi$
$758$	17.6784			0.642109
$759$	−1.25555	+	37.9270i	−0.0455735	+	1.37666i
$760$	18.7692	−	18.7692i	0.680829	−	0.680829i
$761$	−21.5944	−	11.0029i	−0.782796	−	0.398854i	0.0164453	−	0.999865i	$-0.494765\pi$
$761$	−21.5944	−	11.0029i	−0.782796	−	0.398854i	−0.799241	+	0.601010i	$0.794765\pi$
$762$	1.64286	−	5.58458i	0.0595145	−	0.202308i
$763$	44.8262	−	32.5681i	1.62282	−	1.17905i
$764$	0.517493	−	1.59268i	0.0187222	−	0.0576211i
$765$	−5.69773	−	2.51127i	−0.206002	−	0.0907951i
$766$	−19.6067	−	26.9863i	−0.708419	−	0.975055i
$767$	−3.95992	−	34.4180i	−0.142984	−	1.24276i
$768$	26.0201	+	3.37606i	0.938920	+	0.121823i
$769$	−0.202122	+	0.202122i	−0.00728871	+	0.00728871i	−0.710742	−	0.703453i	$-0.751641\pi$
$769$	−0.202122	+	0.202122i	−0.00728871	+	0.00728871i	0.703453	+	0.710742i	$0.251641\pi$
$770$	17.7259	+	14.6138i	0.638796	+	0.526645i
$771$	14.3114	−	30.1497i	0.515414	−	1.08582i
$772$	3.82863	+	1.95079i	0.137795	+	0.0702103i
$773$	6.36074	+	40.1601i	0.228780	+	1.44446i	0.788120	+	0.615521i	$0.211054\pi$
$773$	6.36074	+	40.1601i	0.228780	+	1.44446i	−0.559341	+	0.828938i	$0.688946\pi$
$774$	−21.8860	+	12.7454i	−0.786676	+	0.458124i
$775$	1.14057	−	0.581148i	0.0409704	−	0.0208754i
$776$	−38.0924	−	12.3770i	−1.36744	−	0.444307i
$777$	2.63166	−	0.492847i	0.0944102	−	0.0176808i
$778$	3.65329	+	23.0660i	0.130977	+	0.826956i
$779$	−14.0297	−	43.1791i	−0.502667	−	1.54705i
$780$	−10.1663	+	3.14126i	−0.364012	+	0.112475i
$781$	−0.336473	+	5.49606i	−0.0120400	+	0.196664i
$782$	−4.76986	−	4.76986i	−0.170570	−	0.170570i
$783$	−11.2592	+	6.98696i	−0.402372	+	0.249694i
$784$	0.489107	−	0.673198i	0.0174681	−	0.0240428i
$785$	−20.8658	−	3.30482i	−0.744732	−	0.117954i
$786$	36.7269	−	1.03054i	1.31000	−	0.0367583i
$787$	16.2811	−	8.29564i	0.580359	−	0.295708i	−0.139060	−	0.990284i	$-0.544408\pi$
$787$	16.2811	−	8.29564i	0.580359	−	0.295708i	0.719419	+	0.694576i	$0.244408\pi$
$788$	0.136748	−	0.863396i	0.00487146	−	0.0307572i
$789$	−5.65718	−	10.3729i	−0.201401	−	0.369284i
$790$	5.06789	−	1.64666i	0.180308	−	0.0585855i
$791$	−13.6226	+	13.6226i	−0.484365	+	0.484365i
$792$	17.8567	+	24.8399i	0.634509	+	0.882647i
$793$	0.501004	−	11.7730i	0.0177912	−	0.418072i
$794$	1.82253	−	0.592177i	0.0646792	−	0.0210156i
$795$	−1.80042	+	6.12017i	−0.0638543	+	0.217060i
$796$	−11.4154	+	8.29381i	−0.404610	+	0.293966i
$797$	−5.97397	+	18.3860i	−0.211609	+	0.651266i	0.787768	+	0.615972i	$0.211237\pi$
$797$	−5.97397	+	18.3860i	−0.211609	+	0.651266i	−0.999377	+	0.0352935i	$0.988763\pi$
$798$	−0.562437	−	20.0443i	−0.0199100	−	0.709561i
$799$	−0.291582	+	1.84098i	−0.0103154	+	0.0651290i
$800$	−0.649878	+	0.102931i	−0.0229767	+	0.00363915i
$801$	−0.497418	−	2.29783i	−0.0175754	−	0.0811897i
$802$	−19.4985			−0.688516
$803$	−5.59331	+	6.78443i	−0.197384	+	0.239417i
$804$	15.8041	−	5.62985i	0.557368	−	0.198550i
$805$	−38.9183	+	12.6453i	−1.37169	+	0.445689i
$806$	19.4139	−	24.4620i	0.683825	−	0.861636i
$807$	11.9896	−	2.24537i	0.422055	−	0.0790409i
$808$	23.7295	+	46.5717i	0.834800	+	1.63839i
$809$	−4.96854	−	1.61438i	−0.174685	−	0.0567584i	0.220369	−	0.975417i	$-0.429274\pi$
$809$	−4.96854	−	1.61438i	−0.174685	−	0.0567584i	−0.395053	+	0.918658i	$0.629274\pi$
$810$	20.8240	−	9.45893i	0.731680	−	0.332353i
$811$	17.9267	−	2.83931i	0.629492	−	0.0997017i	0.166467	−	0.986047i	$-0.446764\pi$
$811$	17.9267	−	2.83931i	0.629492	−	0.0997017i	0.463025	+	0.886345i	$0.346764\pi$
$812$	2.36576	−	4.64306i	0.0830219	−	0.162940i
$813$	15.3070	−	5.45277i	0.536840	−	0.191237i
$814$	0.838547	+	1.92883i	0.0293911	+	0.0676056i
$815$			35.1780i			1.23223i
$816$	−3.04088	−	0.394548i	−0.106452	−	0.0138120i
$817$	−4.48646	−	28.3264i	−0.156961	−	0.991016i
$818$	−18.4448	+	13.4010i	−0.644909	+	0.468554i
$819$	−13.0270	+	26.4484i	−0.455200	+	0.924183i
$820$	−6.29303	+	19.3679i	−0.219762	+	0.676358i
$821$	−2.86123	−	0.453174i	−0.0998576	−	0.0158159i	0.106306	−	0.994333i	$-0.466098\pi$
$821$	−2.86123	−	0.453174i	−0.0998576	−	0.0158159i	−0.206163	+	0.978518i	$0.566098\pi$
$822$	26.2475	−	14.3149i	0.915487	−	0.499290i
$823$	7.69010	−	2.49867i	0.268060	−	0.0870980i	−0.171903	−	0.985114i	$-0.554992\pi$
$823$	7.69010	−	2.49867i	0.268060	−	0.0870980i	0.439963	+	0.898016i	$0.354992\pi$
$824$	36.1188	+	36.1188i	1.25826	+	1.25826i
$825$	−0.749129	−	0.583098i	−0.0260813	−	0.0203009i
$826$	−20.7078	−	20.7078i	−0.720518	−	0.720518i
$827$	17.7031	+	9.02016i	0.615596	+	0.313662i	0.733840	−	0.679323i	$-0.237726\pi$
$827$	17.7031	+	9.02016i	0.615596	+	0.313662i	−0.118244	+	0.992985i	$0.537726\pi$
$828$	−14.8338	+	0.833118i	−0.515510	+	0.0289528i
$829$	0.631041	+	0.868553i	0.0219170	+	0.0301661i	0.819835	−	0.572600i	$-0.194065\pi$
$829$	0.631041	+	0.868553i	0.0219170	+	0.0301661i	−0.797918	+	0.602766i	$0.794065\pi$
$830$	−3.07102	−	6.02722i	−0.106597	−	0.209208i
$831$	−29.6211	+	31.3314i	−1.02754	+	1.08687i
$832$	−25.0245	+	16.6031i	−0.867570	+	0.575610i
$833$	0.230414	−	0.317137i	0.00798336	−	0.0109882i
$834$	−4.28753	−	5.56601i	−0.148465	−	0.192735i
$835$	30.7738			1.06497
$836$	−9.14433	+	2.36432i	−0.316263	+	0.0817717i
$837$	20.8376	−	34.4366i	0.720253	−	1.19030i
$838$	5.03034	+	2.56308i	0.173770	+	0.0885403i
$839$	53.6846	−	8.50281i	1.85340	−	0.293550i	0.872581	−	0.488470i	$-0.162445\pi$
$839$	53.6846	−	8.50281i	1.85340	−	0.293550i	0.980819	+	0.194920i	$0.0624448\pi$
$840$	−18.6343	+	27.2222i	−0.642946	+	0.939254i
$841$	6.95187	−	21.3957i	0.239720	−	0.737782i
$842$	−10.1120	+	31.1216i	−0.348483	+	1.07252i
$843$	−4.43293	−	3.03446i	−0.152678	−	0.104512i
$844$	−7.43510	+	10.2335i	−0.255927	+	0.352253i
$845$	15.6013	−	25.0904i	0.536701	−	0.863135i
$846$	−4.32858	−	5.30461i	−0.148820	−	0.182376i
$847$	−10.2513	−	28.1753i	−0.352238	−	0.968116i
$848$			3.14166i			0.107885i
$849$	3.17757	−	24.4903i	0.109054	−	0.840504i
$850$	0.166673	−	0.0263984i	0.00571683	−	0.000905456i
$851$	−3.70025	−	0.586062i	−0.126843	−	0.0200899i
$852$	−2.15498	+	0.0604679i	−0.0738283	+	0.00207160i
$853$	−24.4836	+	12.4750i	−0.838302	+	0.427136i	−0.819771	−	0.572692i	$-0.805899\pi$
$853$	−24.4836	+	12.4750i	−0.838302	+	0.427136i	−0.0185315	+	0.999828i	$0.505899\pi$
$854$	−5.85474	−	8.05836i	−0.200345	−	0.275751i
$855$	1.45231	+	25.8586i	0.0496679	+	0.884345i
$856$	10.1822	−	19.9837i	0.348020	−	0.683028i
$857$	−3.38110			−0.115496			−0.0577481	−	0.998331i	$-0.518392\pi$
$857$	−3.38110			−0.115496			−0.0577481	+	0.998331i	$0.518392\pi$
$858$	−22.5357	−	5.34083i	−0.769354	−	0.182333i
$859$	−41.4844			−1.41543			−0.707715	−	0.706498i	$-0.750274\pi$
$859$	−41.4844			−1.41543			−0.707715	+	0.706498i	$0.750274\pi$
$860$	−5.84021	+	11.4621i	−0.199149	+	0.390853i
$861$	27.0169	+	49.5376i	0.920734	+	1.68824i
$862$	−11.9632	−	16.4660i	−0.407470	−	0.560834i
$863$	−32.9578	+	16.7929i	−1.12190	+	0.571635i	−0.913675	−	0.406446i	$-0.866768\pi$
$863$	−32.9578	+	16.7929i	−1.12190	+	0.571635i	−0.208223	+	0.978081i	$0.566768\pi$
$864$	−15.6564	+	13.5246i	−0.532641	+	0.460117i
$865$	20.6529	+	3.27110i	0.702219	+	0.111221i
$866$	−45.0531	+	7.13571i	−1.53097	+	0.242481i
$867$	27.7676	+	3.60279i	0.943036	+	0.122357i
$868$			15.8287i			0.537261i
$869$	−6.78953	−	1.50562i	−0.230319	−	0.0510746i
$870$	4.81344	−	10.1404i	0.163191	−	0.343792i
$871$	−22.8944	+	40.5700i	−0.775746	+	1.37466i
$872$	−36.7378	+	50.5652i	−1.24410	+	1.71235i
$873$	33.7713	−	19.6669i	1.14299	−	0.665623i
$874$	−8.67043	+	26.6848i	−0.293282	+	0.902628i
$875$	−9.25495	+	28.4838i	−0.312875	+	0.962929i
$876$	−2.84073	−	1.94456i	−0.0959793	−	0.0657005i
$877$	−42.3718	+	6.71104i	−1.43080	+	0.226616i	−0.823254	−	0.567673i	$-0.807844\pi$
$877$	−42.3718	+	6.71104i	−1.43080	+	0.226616i	−0.607541	+	0.794288i	$0.707844\pi$
$878$	5.32663	+	2.71405i	0.179765	+	0.0915949i
$879$	−18.6216	−	52.2746i	−0.628091	−	1.76318i
$880$	−13.5953	−	5.35625i	−0.458298	−	0.180559i
$881$	10.9501			0.368918			0.184459	−	0.982840i	$-0.440947\pi$
$881$	10.9501			0.368918			0.184459	+	0.982840i	$0.440947\pi$
$882$	0.304646	+	1.40731i	0.0102580	+	0.0473866i
$883$	28.8105	−	39.6543i	0.969551	−	1.33447i	0.0272780	−	0.999628i	$-0.491316\pi$
$883$	28.8105	−	39.6543i	0.969551	−	1.33447i	0.942273	−	0.334845i	$-0.108684\pi$
$884$	−2.05698	+	1.36475i	−0.0691838	+	0.0459016i
$885$	27.4858	+	25.9854i	0.923925	+	0.873491i
$886$	−8.47959	−	16.6421i	−0.284877	−	0.559103i
$887$	1.33872	+	1.84259i	0.0449498	+	0.0618681i	0.830900	−	0.556421i	$-0.187826\pi$
$887$	1.33872	+	1.84259i	0.0449498	+	0.0618681i	−0.785950	+	0.618289i	$0.787826\pi$
$888$	−2.65150	+	1.44608i	−0.0889784	+	0.0485272i
$889$	−7.29959	−	3.71932i	−0.244820	−	0.124742i
$890$	1.40825	+	1.40825i	0.0472045	+	0.0472045i
$891$	−29.6820	−	3.15858i	−0.994386	−	0.105817i
$892$	−8.84970	−	8.84970i	−0.296310	−	0.296310i
$893$	7.37347	−	2.39579i	0.246744	−	0.0801719i
$894$	8.67255	+	15.9018i	0.290053	+	0.531835i
$895$	4.96913	+	0.787033i	0.166100	+	0.0263076i
$896$	−1.13730	+	3.50026i	−0.0379947	+	0.116936i
$897$	29.5899	−	28.7453i	0.987978	−	0.959778i
$898$	−7.04703	+	5.11996i	−0.235162	+	0.170855i
$899$	−3.09019	−	19.5107i	−0.103064	−	0.650718i
$900$	0.201258	−	0.312466i	0.00670861	−	0.0104155i
$901$			1.48001i			0.0493062i
$902$	−33.1992	+	29.3688i	−1.10541	+	0.977873i
$903$	11.9610	+	33.5769i	0.398037	+	1.11737i
$904$	9.86605	−	19.3632i	0.328140	−	0.644011i
$905$	20.5086	−	3.24825i	0.681729	−	0.107975i
$906$	4.42892	−	0.829432i	0.147141	−	0.0275560i
$907$	31.5185	+	10.2410i	1.04655	+	0.340046i	0.781315	−	0.624137i	$-0.214549\pi$
$907$	31.5185	+	10.2410i	1.04655	+	0.340046i	0.265239	+	0.964183i	$0.414549\pi$
$908$	6.51063	+	12.7778i	0.216063	+	0.424048i
$909$	−49.3113	−	13.0152i	−1.63555	−	0.431687i
$910$	−2.85458	−	24.8109i	−0.0946285	−	0.822472i
$911$	−25.2879	+	8.21653i	−0.837825	+	0.272226i	−0.696338	−	0.717714i	$-0.745188\pi$
$911$	−25.2879	+	8.21653i	−0.837825	+	0.272226i	−0.141487	+	0.989940i	$0.545188\pi$
$912$	4.28003	+	12.0149i	0.141726	+	0.397852i
$913$	−0.539468	+	8.81184i	−0.0178538	+	0.291629i
$914$	−22.5896			−0.747198
$915$	7.85091	+	10.1919i	0.259543	+	0.336935i
$916$	19.6381	−	3.11037i	0.648861	−	0.102769i
$917$	8.08894	−	51.0715i	0.267120	−	1.68653i
$918$	4.01535	−	3.46863i	0.132526	−	0.114482i
$919$	3.65551	−	11.2505i	0.120584	−	0.371119i	−0.872487	−	0.488638i	$-0.837494\pi$
$919$	3.65551	−	11.2505i	0.120584	−	0.371119i	0.993071	+	0.117518i	$0.0374939\pi$
$920$	37.3444	−	27.1323i	1.23121	−	0.894524i
$921$	−48.3163	−	14.2136i	−1.59208	−	0.468354i
$922$	30.6554	−	9.96054i	1.00958	−	0.328033i
$923$	4.40890	−	4.04897i	0.145121	−	0.133274i
$924$	10.6297	−	4.98023i	0.349693	−	0.163837i
$925$	0.0662704	−	0.0662704i	0.00217896	−	0.00217896i
$926$	−6.83272	+	2.22009i	−0.224537	+	0.0729566i
$927$	−49.7614	+	2.79478i	−1.63438	+	0.0917925i
$928$	−1.58839	+	10.0287i	−0.0521415	+	0.329208i
$929$	−25.3186	+	12.9005i	−0.830675	+	0.423250i	−0.816987	−	0.576656i	$-0.804357\pi$
$929$	−25.3186	+	12.9005i	−0.830675	+	0.423250i	−0.0136884	+	0.999906i	$0.504357\pi$
$930$	0.956340	+	34.0824i	0.0313596	+	1.11761i
$931$	−1.61045	−	0.255070i	−0.0527804	−	0.00835959i
$932$	1.04488	−	1.43816i	0.0342263	−	0.0471085i
$933$	−24.9514	−	3.23740i	−0.816874	−	0.105988i
$934$	−0.439462	−	0.439462i	−0.0143796	−	0.0143796i
$935$	−6.40463	−	2.52328i	−0.209454	−	0.0825201i
$936$	4.75620	−	32.9153i	0.155461	−	1.07587i
$937$	4.70920	+	14.4934i	0.153843	+	0.473480i	0.998042	−	0.0625501i	$-0.0199233\pi$
$937$	4.70920	+	14.4934i	0.153843	+	0.473480i	−0.844199	+	0.536030i	$0.819923\pi$
$938$	6.15997	+	38.8925i	0.201130	+	1.26989i
$939$	−10.0378	−	53.5986i	−0.327570	−	1.74912i
$940$	−3.30736	−	1.07463i	−0.107874	−	0.0350505i
$941$	11.2337	−	5.72386i	0.366208	−	0.186592i	−0.261197	−	0.965286i	$-0.584117\pi$
$941$	11.2337	−	5.72386i	0.366208	−	0.186592i	0.627405	+	0.778693i	$0.284117\pi$
$942$	10.1690	−	14.8555i	0.331325	−	0.484020i
$943$	−12.3511	−	77.9820i	−0.402209	−	2.53944i
$944$	16.5970	+	8.45660i	0.540187	+	0.275239i
$945$	−7.68993	−	31.2564i	−0.250154	−	1.01677i
$946$	−23.6156	+	15.0429i	−0.767810	+	0.489086i
$947$	8.03418	−	8.03418i	0.261076	−	0.261076i	−0.564415	−	0.825491i	$-0.690898\pi$
$947$	8.03418	−	8.03418i	0.261076	−	0.261076i	0.825491	+	0.564415i	$0.190898\pi$
$948$	0.350340	−	2.70016i	0.0113785	−	0.0876970i
$949$	9.49615	−	1.09257i	0.308258	−	0.0354662i
$950$	−0.412573	−	0.567858i	−0.0133856	−	0.0184238i
$951$	0.347775	+	12.3941i	0.0112774	+	0.401908i
$952$	−2.36500	+	7.27872i	−0.0766501	+	0.235905i
$953$	5.52132	−	4.01148i	0.178853	−	0.129944i	−0.494757	−	0.869032i	$-0.664743\pi$
$953$	5.52132	−	4.01148i	0.178853	−	0.129944i	0.673610	+	0.739087i	$0.264743\pi$
$954$	−4.05360	−	3.62248i	−0.131240	−	0.117282i
$955$	−4.52338	−	2.30478i	−0.146373	−	0.0745808i
$956$	−4.65522	+	4.65522i	−0.150561	+	0.150561i
$957$	−12.1301	+	8.21392i	−0.392110	+	0.265518i
$958$	−42.2991			−1.36662
$959$	−13.0022	−	40.0168i	−0.419864	−	1.29221i
$960$	9.25335	−	31.4549i	0.298651	−	1.01520i
$961$	17.0476	+	23.4640i	0.549923	+	0.756904i
$962$	0.798367	−	2.14253i	0.0257404	−	0.0690781i
$963$	7.91891	+	20.4008i	0.255183	+	0.657407i
$964$	−0.407761	+	2.57450i	−0.0131331	+	0.0829191i
$965$	7.65670	−	10.5385i	0.246478	−	0.339248i
$966$	4.48689	−	34.5816i	0.144363	−	1.11264i
$967$	8.08476	−	8.08476i	0.259988	−	0.259988i	−0.565061	−	0.825049i	$-0.691147\pi$
$967$	8.08476	−	8.08476i	0.259988	−	0.259988i	0.825049	+	0.565061i	$0.191147\pi$
$968$	20.8191	+	26.6536i	0.669152	+	0.856681i
$969$	2.01628	+	5.66010i	0.0647723	+	0.181829i
$970$	−15.0293	+	29.4967i	−0.482563	+	0.947083i
$971$	−14.7185	+	20.2583i	−0.472340	+	0.650120i	−0.977010	−	0.213192i	$-0.931614\pi$
$971$	−14.7185	+	20.2583i	−0.472340	+	0.650120i	0.504670	+	0.863312i	$0.331614\pi$
$972$	0.196539	−	11.6850i	0.00630398	−	0.374795i
$973$	−8.81024	+	4.48904i	−0.282443	+	0.143912i
$974$	13.6349	−	41.9640i	0.436891	−	1.34461i
$975$	0.146669	+	1.02154i	0.00469717	+	0.0327154i
$976$	5.12562	+	3.72398i	0.164067	+	0.119202i
$977$	−13.4285	+	26.3549i	−0.429615	+	0.843167i	0.570151	+	0.821540i	$0.306885\pi$
$977$	−13.4285	+	26.3549i	−0.429615	+	0.843167i	−0.999766	+	0.0216271i	$0.993115\pi$
$978$	−27.0812	−	12.8549i	−0.865963	−	0.411055i
$979$	−0.650637	−	2.51643i	−0.0207944	−	0.0804254i
$980$	0.517157	+	0.517157i	0.0165200	+	0.0165200i
$981$	−12.9028	−	59.6044i	−0.411954	−	1.90302i
$982$	−0.858712	−	5.42170i	−0.0274026	−	0.173013i
$983$	−2.41541	+	15.2503i	−0.0770395	+	0.486408i	0.918758	+	0.394822i	$0.129194\pi$
$983$	−2.41541	+	15.2503i	−0.0770395	+	0.486408i	−0.995797	+	0.0915864i	$0.970806\pi$
$984$	−46.2521	−	43.7273i	−1.47446	−	1.39397i
$985$	−2.52033	−	0.818903i	−0.0803042	−	0.0260924i
$986$	0.407371	−	2.57204i	0.0129733	−	0.0819104i
$987$	−8.45927	+	4.61354i	−0.269262	+	0.146851i
$988$	8.94225	+	5.04626i	0.284491	+	0.160543i
$989$		−	49.8746i		−	1.58592i
$990$	22.5871	−	11.3657i	0.717865	−	0.361225i
$991$	−21.4956			−0.682830			−0.341415	−	0.939913i	$-0.610906\pi$
$991$	−21.4956			−0.682830			−0.341415	+	0.939913i	$0.610906\pi$
$992$	−9.53078	−	29.3327i	−0.302603	−	0.931315i
$993$	−0.156538	+	0.532119i	−0.00496758	+	0.0168863i
$994$	0.791553	−	4.99767i	0.0251065	−	0.158516i
$995$	19.4197	+	38.1133i	0.615645	+	1.20827i
$996$	−3.45508	+	0.0969483i	−0.109478	+	0.00307192i
$997$	−24.8236	+	18.0354i	−0.786171	+	0.571187i	−0.906825	−	0.421508i	$-0.861501\pi$
$997$	−24.8236	+	18.0354i	−0.786171	+	0.571187i	0.120654	+	0.992695i	$0.461501\pi$
$998$	−28.7167	−	20.8639i	−0.909011	−	0.660435i
$999$	0.671831	−	2.86928i	0.0212558	−	0.0907802i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bi.a.5.17	✓	416
3.2	odd	2	inner	429.2.bi.a.5.36	yes	416
11.9	even	5	inner	429.2.bi.a.317.36	yes	416
13.8	odd	4	inner	429.2.bi.a.203.17	yes	416
33.20	odd	10	inner	429.2.bi.a.317.17	yes	416
39.8	even	4	inner	429.2.bi.a.203.36	yes	416
143.86	odd	20	inner	429.2.bi.a.86.36	yes	416
429.86	even	20	inner	429.2.bi.a.86.17	yes	416

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bi.a.5.17	✓	416	1.1	even	1	trivial
429.2.bi.a.5.36	yes	416	3.2	odd	2	inner
429.2.bi.a.86.17	yes	416	429.86	even	20	inner
429.2.bi.a.86.36	yes	416	143.86	odd	20	inner
429.2.bi.a.203.17	yes	416	13.8	odd	4	inner
429.2.bi.a.203.36	yes	416	39.8	even	4	inner
429.2.bi.a.317.17	yes	416	33.20	odd	10	inner
429.2.bi.a.317.36	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)

\(f(q)\)	\(=\)	\(q+(-0.507638 + 0.996296i) q^{2} +(1.52061 - 0.829312i) q^{3} +(0.440661 + 0.606518i) q^{4} +(2.02501 - 1.03179i) q^{5} +(0.0543225 + 1.93596i) q^{6} +(2.69211 + 0.426388i) q^{7} +(-3.03677 + 0.480978i) q^{8} +(1.62448 - 2.52211i) q^{9} +O(q^{10})\)	\(q+(-0.507638 + 0.996296i) q^{2} +(1.52061 - 0.829312i) q^{3} +(0.440661 + 0.606518i) q^{4} +(2.02501 - 1.03179i) q^{5} +(0.0543225 + 1.93596i) q^{6} +(2.69211 + 0.426388i) q^{7} +(-3.03677 + 0.480978i) q^{8} +(1.62448 - 2.52211i) q^{9} +2.54129i q^{10} +(1.68348 - 2.85760i) q^{11} +(1.17306 + 0.556829i) q^{12} +(-3.47335 + 0.967375i) q^{13} +(-1.79143 + 2.46569i) q^{14} +(2.22356 - 3.24831i) q^{15} +(0.599048 - 1.84368i) q^{16} +(0.282206 - 0.868541i) q^{17} +(1.68812 + 2.89879i) q^{18} +(-3.75182 + 0.594229i) q^{19} +(1.51814 + 0.773532i) q^{20} +(4.44724 - 1.58423i) q^{21} +(1.99242 + 3.12787i) q^{22} -6.60586 q^{23} +(-4.21885 + 3.24981i) q^{24} +(0.0971341 - 0.133694i) q^{25} +(0.799415 - 3.95157i) q^{26} +(0.378582 - 5.18234i) q^{27} +(0.927694 + 1.82070i) q^{28} +(-1.49894 - 2.06311i) q^{29} +(2.10752 + 3.86429i) q^{30} +(6.90189 + 3.51669i) q^{31} +(-2.81543 - 2.81543i) q^{32} +(0.190066 - 5.74142i) q^{33} +(0.722066 + 0.722066i) q^{34} +(5.89148 - 1.91426i) q^{35} +(2.24555 - 0.126118i) q^{36} +(0.560147 + 0.0887185i) q^{37} +(1.31254 - 4.03957i) q^{38} +(-4.47935 + 4.35149i) q^{39} +(-5.65322 + 4.10731i) q^{40} +(1.86973 + 11.8050i) q^{41} +(-0.679230 + 5.23499i) q^{42} +7.55005i q^{43} +(2.47503 - 0.238173i) q^{44} +(0.687295 - 6.78343i) q^{45} +(3.35339 - 6.58139i) q^{46} +(-2.01588 + 0.319284i) q^{47} +(-0.618070 - 3.30031i) q^{48} +(0.408237 + 0.132644i) q^{49} +(0.0838894 + 0.164642i) q^{50} +(-0.291167 - 1.55475i) q^{51} +(-2.11730 - 1.68037i) q^{52} +(-1.54130 + 0.500797i) q^{53} +(4.97097 + 3.00794i) q^{54} +(0.460606 - 7.52367i) q^{55} -8.38040 q^{56} +(-5.21223 + 4.01501i) q^{57} +(2.81639 - 0.446073i) q^{58} +(-1.50315 + 9.49051i) q^{59} +(2.95000 - 0.0827758i) q^{60} +(-1.00993 + 3.10825i) q^{61} +(-7.00732 + 5.09112i) q^{62} +(5.44868 - 6.09714i) q^{63} +(7.92158 - 2.57388i) q^{64} +(-6.03544 + 5.54273i) q^{65} +(5.62367 + 3.10393i) q^{66} +(9.13590 - 9.13590i) q^{67} +(0.651142 - 0.211569i) q^{68} +(-10.0449 + 5.47831i) q^{69} +(-1.08357 + 6.84141i) q^{70} +(-1.47927 + 0.753727i) q^{71} +(-3.72011 + 8.44043i) q^{72} +(-2.61849 - 0.414729i) q^{73} +(-0.372742 + 0.513035i) q^{74} +(0.0368290 - 0.283850i) q^{75} +(-2.01369 - 2.01369i) q^{76} +(5.75056 - 6.97516i) q^{77} +(-2.06149 - 6.67174i) q^{78} +(-0.647963 - 1.99422i) q^{79} +(-0.689220 - 4.35156i) q^{80} +(-3.72210 - 8.19426i) q^{81} +(-12.7104 - 4.12986i) q^{82} +(-2.37172 + 1.20845i) q^{83} +(2.92059 + 1.99922i) q^{84} +(-0.324685 - 2.04998i) q^{85} +(-7.52209 - 3.83270i) q^{86} +(-3.99026 - 1.89410i) q^{87} +(-3.73790 + 9.48761i) q^{88} +(0.554147 - 0.554147i) q^{89} +(6.40941 + 4.12828i) q^{90} +(-9.76312 + 1.12328i) q^{91} +(-2.91094 - 4.00657i) q^{92} +(13.4115 - 0.376321i) q^{93} +(0.705235 - 2.17049i) q^{94} +(-6.98434 + 5.07442i) q^{95} +(-6.61602 - 1.94629i) q^{96} +(11.6070 + 5.91406i) q^{97} +(-0.339389 + 0.339389i) q^{98} +(-4.47241 - 8.88806i) 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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