LMFDB - Embedded newform 189.2.i.b.152.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(143,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("189.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.i (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	10.0.288778218147.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 7x^{8} - 4x^{7} + 34x^{6} - 19x^{5} + 64x^{4} - x^{3} + 64x^{2} - 21x + 9 $ x^10 - x^9 + 7x^8 - 4x^7 + 34x^6 - 19x^5 + 64x^4 - x^3 + 64x^2 - 21*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			152.3
Root			$-0.539982 - 0.935277i$ of defining polynomial
Character	$\chi$	$=$	189.152
Dual form			189.2.i.b.143.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.293869i q^{2} +1.91364 q^{4} +(-1.53014 - 2.65027i) q^{5} +(-1.41763 - 2.23391i) q^{7} -1.15010i q^{8} +O(q^{10})$	\(q-0.293869i q^{2} +1.91364 q^{4} +(-1.53014 - 2.65027i) q^{5} +(-1.41763 - 2.23391i) q^{7} -1.15010i q^{8} +(-0.778834 + 0.449660i) q^{10} +(3.37445 + 1.94824i) q^{11} +(-2.02935 - 1.17164i) q^{13} +(-0.656477 + 0.416597i) q^{14} +3.48930 q^{16} +(1.68263 + 2.91440i) q^{17} +(2.20696 + 1.27419i) q^{19} +(-2.92813 - 5.07167i) q^{20} +(0.572527 - 0.991647i) q^{22} +(-2.58141 + 1.49038i) q^{23} +(-2.18263 + 3.78042i) q^{25} +(-0.344311 + 0.596363i) q^{26} +(-2.71283 - 4.27489i) q^{28} +(3.67241 - 2.12027i) q^{29} +0.472735i q^{31} -3.32560i q^{32} +(0.856452 - 0.494473i) q^{34} +(-3.75130 + 7.17527i) q^{35} +(-3.89395 + 6.74451i) q^{37} +(0.374446 - 0.648559i) q^{38} +(-3.04808 + 1.75981i) q^{40} +(-3.12737 + 5.41676i) q^{41} +(2.06191 + 3.57133i) q^{43} +(6.45748 + 3.72823i) q^{44} +(0.437976 + 0.758597i) q^{46} +4.05388 q^{47} +(-2.98068 + 6.33369i) q^{49} +(1.11095 + 0.641408i) q^{50} +(-3.88344 - 2.24211i) q^{52} +(-4.99439 + 2.88351i) q^{53} -11.9243i q^{55} +(-2.56921 + 1.63041i) q^{56} +(-0.623082 - 1.07921i) q^{58} +4.68705 q^{59} -1.60018i q^{61} +0.138922 q^{62} +6.00131 q^{64} +7.17110i q^{65} +1.57566 q^{67} +(3.21994 + 5.57711i) q^{68} +(2.10859 + 1.10239i) q^{70} -13.6132i q^{71} +(-0.856452 + 0.494473i) q^{73} +(1.98201 + 1.14431i) q^{74} +(4.22333 + 2.43834i) q^{76} +(-0.431520 - 10.3001i) q^{77} -9.27815 q^{79} +(-5.33910 - 9.24760i) q^{80} +(1.59182 + 0.919038i) q^{82} +(-5.49361 - 9.51520i) q^{83} +(5.14930 - 8.91884i) q^{85} +(1.04950 - 0.605932i) q^{86} +(2.24067 - 3.88095i) q^{88} +(2.15849 - 3.73861i) q^{89} +(0.259511 + 6.19433i) q^{91} +(-4.93989 + 2.85205i) q^{92} -1.19131i q^{94} -7.79874i q^{95} +(4.98797 - 2.87980i) q^{97} +(1.86128 + 0.875930i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 8 q^{4} - 6 q^{7}+O(q^{10}) $ 10 * q - 8 * q^4 - 6 * q^7	$ 10 q - 8 q^{4} - 6 q^{7} - 15 q^{10} + 12 q^{11} - 6 q^{13} - 12 q^{14} + 12 q^{16} - 12 q^{17} + 3 q^{19} - 3 q^{20} + 5 q^{22} + 15 q^{23} + 7 q^{25} + 3 q^{26} + 2 q^{28} + 15 q^{29} - 3 q^{34} - 15 q^{35} + 6 q^{37} - 18 q^{38} + 15 q^{40} - 9 q^{41} + 3 q^{43} + 24 q^{44} - 13 q^{46} - 30 q^{47} + 4 q^{49} - 3 q^{50} - 12 q^{52} - 9 q^{53} + 30 q^{56} + 8 q^{58} + 36 q^{59} + 12 q^{62} + 6 q^{64} + 20 q^{67} + 27 q^{68} + 6 q^{70} + 3 q^{73} + 30 q^{74} - 9 q^{76} - 39 q^{77} - 40 q^{79} - 30 q^{80} + 9 q^{82} - 15 q^{83} + 18 q^{85} - 54 q^{86} - 8 q^{88} + 24 q^{89} - 24 q^{91} - 39 q^{92} - 6 q^{97} + 45 q^{98}+O(q^{100}) $ 10 * q - 8 * q^4 - 6 * q^7 - 15 * q^10 + 12 * q^11 - 6 * q^13 - 12 * q^14 + 12 * q^16 - 12 * q^17 + 3 * q^19 - 3 * q^20 + 5 * q^22 + 15 * q^23 + 7 * q^25 + 3 * q^26 + 2 * q^28 + 15 * q^29 - 3 * q^34 - 15 * q^35 + 6 * q^37 - 18 * q^38 + 15 * q^40 - 9 * q^41 + 3 * q^43 + 24 * q^44 - 13 * q^46 - 30 * q^47 + 4 * q^49 - 3 * q^50 - 12 * q^52 - 9 * q^53 + 30 * q^56 + 8 * q^58 + 36 * q^59 + 12 * q^62 + 6 * q^64 + 20 * q^67 + 27 * q^68 + 6 * q^70 + 3 * q^73 + 30 * q^74 - 9 * q^76 - 39 * q^77 - 40 * q^79 - 30 * q^80 + 9 * q^82 - 15 * q^83 + 18 * q^85 - 54 * q^86 - 8 * q^88 + 24 * q^89 - 24 * q^91 - 39 * q^92 - 6 * q^97 + 45 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		−	0.293869i		−	0.207797i	−0.994588	−	0.103899i	$-0.966868\pi$
$2$		−	0.293869i		−	0.207797i	0.994588	−	0.103899i	$-0.0331317\pi$
$3$		0			0
$3$		0			0
$4$	1.91364			0.956820
$5$	−1.53014	−	2.65027i	−0.684297	−	1.18524i	−0.973657	−	0.228017i	$-0.926776\pi$
$5$	−1.53014	−	2.65027i	−0.684297	−	1.18524i	0.289360	−	0.957220i	$-0.406558\pi$
$6$		0			0
$7$	−1.41763	−	2.23391i	−0.535812	−	0.844337i
$7$	−1.41763	−	2.23391i	−0.535812	−	0.844337i
$8$		−	1.15010i		−	0.406622i
$9$		0			0
$10$	−0.778834	+	0.449660i	−0.246289	+	0.142195i
$11$	3.37445	+	1.94824i	1.01743	+	0.587416i	0.913360	−	0.407154i	$-0.133479\pi$
$11$	3.37445	+	1.94824i	1.01743	+	0.587416i	0.104074	+	0.994570i	$0.466812\pi$
$12$		0			0
$13$	−2.02935	−	1.17164i	−0.562840	−	0.324956i	0.191445	−	0.981503i	$-0.438683\pi$
$13$	−2.02935	−	1.17164i	−0.562840	−	0.324956i	−0.754285	+	0.656548i	$0.772016\pi$
$14$	−0.656477	+	0.416597i	−0.175451	+	0.111340i
$15$		0			0
$16$	3.48930			0.872326
$17$	1.68263	+	2.91440i	0.408097	+	0.706845i	0.994677	−	0.103047i	$-0.0328591\pi$
$17$	1.68263	+	2.91440i	0.408097	+	0.706845i	−0.586579	+	0.809892i	$0.699526\pi$
$18$		0			0
$19$	2.20696	+	1.27419i	0.506312	+	0.292319i	0.731316	−	0.682038i	$-0.238906\pi$
$19$	2.20696	+	1.27419i	0.506312	+	0.292319i	−0.225004	+	0.974358i	$0.572240\pi$
$20$	−2.92813	−	5.07167i	−0.654750	−	1.13406i
$21$		0			0
$22$	0.572527	−	0.991647i	0.122063	−	0.211420i
$23$	−2.58141	+	1.49038i	−0.538261	+	0.310765i	−0.744374	−	0.667763i	$-0.767252\pi$
$23$	−2.58141	+	1.49038i	−0.538261	+	0.310765i	0.206113	+	0.978528i	$0.433919\pi$
$24$		0			0
$25$	−2.18263	+	3.78042i	−0.436525	+	0.756084i
$26$	−0.344311	+	0.596363i	−0.0675249	+	0.116956i
$27$		0			0
$28$	−2.71283	−	4.27489i	−0.512676	−	0.807879i
$29$	3.67241	−	2.12027i	0.681949	−	0.393724i	−0.118640	−	0.992937i	$-0.537853\pi$
$29$	3.67241	−	2.12027i	0.681949	−	0.393724i	0.800589	+	0.599214i	$0.204520\pi$
$30$		0			0
$31$			0.472735i			0.0849057i	0.999098	+	0.0424528i	$0.0135172\pi$
$31$			0.472735i			0.0849057i	−0.999098	+	0.0424528i	$0.986483\pi$
$32$		−	3.32560i		−	0.587888i
$33$		0			0
$34$	0.856452	−	0.494473i	0.146880	−	0.0848014i
$35$	−3.75130	+	7.17527i	−0.634086	+	1.21284i
$36$		0			0
$37$	−3.89395	+	6.74451i	−0.640161	+	1.10879i	0.345236	+	0.938516i	$0.387799\pi$
$37$	−3.89395	+	6.74451i	−0.640161	+	1.10879i	−0.985397	+	0.170275i	$0.945534\pi$
$38$	0.374446	−	0.648559i	0.0607431	−	0.105210i
$39$		0			0
$40$	−3.04808	+	1.75981i	−0.481943	+	0.278250i
$41$	−3.12737	+	5.41676i	−0.488413	+	0.845956i	−0.999911	−	0.0133282i	$-0.995757\pi$
$41$	−3.12737	+	5.41676i	−0.488413	+	0.845956i	0.511498	+	0.859284i	$0.329091\pi$
$42$		0			0
$43$	2.06191	+	3.57133i	0.314438	+	0.544623i	0.979318	−	0.202328i	$-0.0648506\pi$
$43$	2.06191	+	3.57133i	0.314438	+	0.544623i	−0.664880	+	0.746950i	$0.731517\pi$
$44$	6.45748	+	3.72823i	0.973501	+	0.562051i
$45$		0			0
$46$	0.437976	+	0.758597i	0.0645761	+	0.111849i
$47$	4.05388			0.591319			0.295659	−	0.955293i	$-0.404461\pi$
$47$	4.05388			0.591319			0.295659	+	0.955293i	$0.404461\pi$
$48$		0			0
$49$	−2.98068	+	6.33369i	−0.425811	+	0.904812i
$50$	1.11095	+	0.641408i	0.157112	+	0.0907087i
$51$		0			0
$52$	−3.88344	−	2.24211i	−0.538537	−	0.310924i
$53$	−4.99439	+	2.88351i	−0.686033	+	0.396081i	−0.802124	−	0.597157i	$-0.796297\pi$
$53$	−4.99439	+	2.88351i	−0.686033	+	0.396081i	0.116091	+	0.993239i	$0.462963\pi$
$54$		0			0
$55$		−	11.9243i		−	1.60787i
$56$	−2.56921	+	1.63041i	−0.343326	+	0.217873i
$57$		0			0
$58$	−0.623082	−	1.07921i	−0.0818146	−	0.141707i
$59$	4.68705			0.610201			0.305101	−	0.952320i	$-0.401310\pi$
$59$	4.68705			0.610201			0.305101	+	0.952320i	$0.401310\pi$
$60$		0			0
$61$		−	1.60018i		−	0.204883i	−0.994739	−	0.102441i	$-0.967335\pi$
$61$		−	1.60018i		−	0.204883i	0.994739	−	0.102441i	$-0.0326654\pi$
$62$	0.138922			0.0176432
$63$		0			0
$64$	6.00131			0.750164
$65$			7.17110i			0.889465i
$66$		0			0
$67$	1.57566			0.192498			0.0962489	−	0.995357i	$-0.469316\pi$
$67$	1.57566			0.192498			0.0962489	+	0.995357i	$0.469316\pi$
$68$	3.21994	+	5.57711i	0.390476	+	0.676324i
$69$		0			0
$70$	2.10859	+	1.10239i	0.252025	+	0.131761i
$71$		−	13.6132i		−	1.61559i	−0.589462	−	0.807796i	$-0.700660\pi$
$71$		−	13.6132i		−	1.61559i	0.589462	−	0.807796i	$-0.299340\pi$
$72$		0			0
$73$	−0.856452	+	0.494473i	−0.100240	+	0.0578737i	−0.549282	−	0.835637i	$-0.685099\pi$
$73$	−0.856452	+	0.494473i	−0.100240	+	0.0578737i	0.449042	+	0.893511i	$0.351765\pi$
$74$	1.98201	+	1.14431i	0.230404	+	0.133024i
$75$		0			0
$76$	4.22333	+	2.43834i	0.484450	+	0.279697i
$77$	−0.431520	−	10.3001i	−0.0491763	−	1.17380i
$78$		0			0
$79$	−9.27815			−1.04387			−0.521937	−	0.852984i	$-0.674790\pi$
$79$	−9.27815			−1.04387			−0.521937	+	0.852984i	$0.674790\pi$
$80$	−5.33910	−	9.24760i	−0.596930	−	1.03391i
$81$		0			0
$82$	1.59182	+	0.919038i	0.175787	+	0.101491i
$83$	−5.49361	−	9.51520i	−0.603002	−	1.04443i	−0.992364	−	0.123345i	$-0.960638\pi$
$83$	−5.49361	−	9.51520i	−0.603002	−	1.04443i	0.389362	−	0.921085i	$-0.372695\pi$
$84$		0			0
$85$	5.14930	−	8.91884i	0.558519	−	0.967384i
$86$	1.04950	−	0.605932i	0.113171	−	0.0653393i
$87$		0			0
$88$	2.24067	−	3.88095i	0.238856	−	0.413710i
$89$	2.15849	−	3.73861i	0.228799	−	0.396292i	−0.728653	−	0.684883i	$-0.759853\pi$
$89$	2.15849	−	3.73861i	0.228799	−	0.396292i	0.957452	+	0.288591i	$0.0931868\pi$
$90$		0			0
$91$	0.259511	+	6.19433i	0.0272041	+	0.649342i
$92$	−4.93989	+	2.85205i	−0.515019	+	0.297346i
$93$		0			0
$94$		−	1.19131i		−	0.122874i
$95$		−	7.79874i		−	0.800133i
$96$		0			0
$97$	4.98797	−	2.87980i	0.506451	−	0.292400i	−0.224923	−	0.974377i	$-0.572213\pi$
$97$	4.98797	−	2.87980i	0.506451	−	0.292400i	0.731374	+	0.681977i	$0.238880\pi$
$98$	1.86128	+	0.875930i	0.188017	+	0.0884823i
$99$		0			0
$100$	−4.17676	+	7.23437i	−0.417676	+	0.723437i
$101$	−8.57900	+	14.8593i	−0.853642	+	1.47855i	0.0242566	+	0.999706i	$0.492278\pi$
$101$	−8.57900	+	14.8593i	−0.853642	+	1.47855i	−0.877899	+	0.478846i	$0.841055\pi$
$102$		0			0
$103$	8.50422	−	4.90992i	0.837946	−	0.483788i	−0.0186195	−	0.999827i	$-0.505927\pi$
$103$	8.50422	−	4.90992i	0.837946	−	0.483788i	0.856566	+	0.516038i	$0.172594\pi$
$104$	−1.34751	+	2.33395i	−0.132134	+	0.228863i
$105$		0			0
$106$	0.847377	+	1.46770i	0.0823045	+	0.142556i
$107$	3.00501	+	1.73494i	0.290505	+	0.167723i	0.638170	−	0.769896i	$-0.279692\pi$
$107$	3.00501	+	1.73494i	0.290505	+	0.167723i	−0.347664	+	0.937619i	$0.613025\pi$
$108$		0			0
$109$	0.611066	+	1.05840i	0.0585295	+	0.101376i	0.893806	−	0.448455i	$-0.148025\pi$
$109$	0.611066	+	1.05840i	0.0585295	+	0.101376i	−0.835276	+	0.549831i	$0.814692\pi$
$110$	−3.50418			−0.334110
$111$		0			0
$112$	−4.94652	−	7.79478i	−0.467403	−	0.736537i
$113$	1.87681	+	1.08358i	0.176555	+	0.101934i	0.585673	−	0.810547i	$-0.300830\pi$
$113$	1.87681	+	1.08358i	0.176555	+	0.101934i	−0.409118	+	0.912482i	$0.634164\pi$
$114$		0			0
$115$	7.89981	+	4.56096i	0.736661	+	0.425311i
$116$	7.02767	−	4.05743i	0.652503	−	0.376723i
$117$		0			0
$118$		−	1.37738i		−	0.126798i
$119$	4.12515	−	7.89035i	0.378152	−	0.723308i
$120$		0			0
$121$	2.09126	+	3.62216i	0.190114	+	0.329287i
$122$	−0.470245			−0.0425740
$123$		0			0
$124$			0.904645i			0.0812395i
$125$	−1.94249			−0.173742
$126$		0			0
$127$	2.74889			0.243925			0.121962	−	0.992535i	$-0.461081\pi$
$127$	2.74889			0.243925			0.121962	+	0.992535i	$0.461081\pi$
$128$		−	8.41480i		−	0.743770i
$129$		0			0
$130$	2.10737			0.184828
$131$	3.73911	+	6.47632i	0.326687	+	0.565839i	0.981852	−	0.189647i	$-0.0607343\pi$
$131$	3.73911	+	6.47632i	0.326687	+	0.565839i	−0.655165	+	0.755486i	$0.727401\pi$
$132$		0			0
$133$	−0.282224	−	6.73647i	−0.0244719	−	0.584126i
$134$		−	0.463039i		−	0.0400005i
$135$		0			0
$136$	3.35185	−	1.93519i	0.287418	−	0.165941i
$137$	10.5731	+	6.10439i	0.903321	+	0.521533i	0.878276	−	0.478153i	$-0.158694\pi$
$137$	10.5731	+	6.10439i	0.903321	+	0.521533i	0.0250451	+	0.999686i	$0.492027\pi$
$138$		0			0
$139$	−11.5501	−	6.66842i	−0.979663	−	0.565608i	−0.0774943	−	0.996993i	$-0.524692\pi$
$139$	−11.5501	−	6.66842i	−0.979663	−	0.565608i	−0.902168	+	0.431384i	$0.858025\pi$
$140$	−7.17864	+	13.7309i	−0.606706	+	1.16047i
$141$		0			0
$142$	−4.00051			−0.335715
$143$	−4.56528	−	7.90730i	−0.381768	−	0.661242i
$144$		0			0
$145$	−11.2386	−	6.48859i	−0.933312	−	0.538848i
$146$	0.145310	+	0.251685i	0.0120260	+	0.0208296i
$147$		0			0
$148$	−7.45161	+	12.9066i	−0.612519	+	1.06091i
$149$	7.33827	−	4.23675i	0.601174	−	0.347088i	−0.168329	−	0.985731i	$-0.553837\pi$
$149$	7.33827	−	4.23675i	0.601174	−	0.347088i	0.769503	+	0.638643i	$0.220504\pi$
$150$		0			0
$151$	1.67827	−	2.90685i	0.136576	−	0.236556i	−0.789623	−	0.613593i	$-0.789724\pi$
$151$	1.67827	−	2.90685i	0.136576	−	0.236556i	0.926198	+	0.377037i	$0.123057\pi$
$152$	1.46545	−	2.53823i	0.118863	−	0.205877i
$153$		0			0
$154$	−3.02688	+	0.126811i	−0.243913	+	0.0102187i
$155$	1.25288	−	0.723348i	0.100633	−	0.0581007i
$156$		0			0
$157$			16.7085i			1.33349i	0.745288	+	0.666743i	$0.232312\pi$
$157$			16.7085i			1.33349i	−0.745288	+	0.666743i	$0.767688\pi$
$158$			2.72657i			0.216914i
$159$		0			0
$160$	−8.81374	+	5.08862i	−0.696787	+	0.402290i
$161$	6.98883	+	3.65383i	0.550797	+	0.287962i
$162$		0			0
$163$	12.6662	−	21.9385i	0.992094	−	1.71836i	0.387363	−	0.921927i	$-0.373386\pi$
$163$	12.6662	−	21.9385i	0.992094	−	1.71836i	0.604731	−	0.796430i	$-0.293281\pi$
$164$	−5.98466	+	10.3657i	−0.467324	+	0.809428i
$165$		0			0
$166$	−2.79623	+	1.61440i	−0.217029	+	0.125302i
$167$	−0.875828	+	1.51698i	−0.0677736	+	0.117387i	−0.897921	−	0.440157i	$-0.854923\pi$
$167$	−0.875828	+	1.51698i	−0.0677736	+	0.117387i	0.830147	+	0.557544i	$0.188256\pi$
$168$		0			0
$169$	−3.75450	−	6.50298i	−0.288808	−	0.500229i
$170$	−2.62097	−	1.51322i	−0.201020	−	0.116059i
$171$		0			0
$172$	3.94575	+	6.83424i	0.300861	+	0.521106i
$173$	−23.9266			−1.81910			−0.909551	−	0.415592i	$-0.863574\pi$
$173$	−23.9266			−1.81910			−0.909551	+	0.415592i	$0.863574\pi$
$174$		0			0
$175$	11.5393	−	0.483436i	0.872286	−	0.0365443i
$176$	11.7745	+	6.79799i	0.887533	+	0.512418i
$177$		0			0
$178$	−1.09866	−	0.634313i	−0.0823482	−	0.0475438i
$179$	−21.9857	+	12.6935i	−1.64329	+	0.948755i	−0.663639	+	0.748053i	$0.730989\pi$
$179$	−21.9857	+	12.6935i	−1.64329	+	0.948755i	−0.979652	+	0.200702i	$0.935678\pi$
$180$		0			0
$181$			22.4032i			1.66522i	0.553859	+	0.832610i	$0.313155\pi$
$181$			22.4032i			1.66522i	−0.553859	+	0.832610i	$0.686845\pi$
$182$	1.82032	−	0.0762622i	0.134931	−	0.00565293i
$183$		0			0
$184$	1.71408	+	2.96888i	0.126364	+	0.218869i
$185$	23.8331			1.75224
$186$		0			0
$187$			13.1126i			0.958890i
$188$	7.75766			0.565786
$189$		0			0
$190$	−2.29181			−0.166265
$191$		−	4.28895i		−	0.310337i	−0.987888	−	0.155169i	$-0.950408\pi$
$191$		−	4.28895i		−	0.310337i	0.987888	−	0.155169i	$-0.0495921\pi$
$192$		0			0
$193$	−23.3449			−1.68041			−0.840203	−	0.542272i	$-0.817564\pi$
$193$	−23.3449			−1.68041			−0.840203	+	0.542272i	$0.817564\pi$
$194$	−0.846286	−	1.46581i	−0.0607598	−	0.105239i
$195$		0			0
$196$	−5.70394	+	12.1204i	−0.407425	+	0.865743i
$197$			18.7811i			1.33809i	0.743220	+	0.669047i	$0.233298\pi$
$197$			18.7811i			1.33809i	−0.743220	+	0.669047i	$0.766702\pi$
$198$		0			0
$199$	−3.92927	+	2.26856i	−0.278539	+	0.160814i	−0.632762	−	0.774347i	$-0.718079\pi$
$199$	−3.92927	+	2.26856i	−0.278539	+	0.160814i	0.354223	+	0.935161i	$0.384745\pi$
$200$	4.34786	+	2.51024i	0.307440	+	0.177501i
$201$		0			0
$202$	4.36668	+	2.52111i	0.307239	+	0.177384i
$203$	−9.94258	−	5.19808i	−0.697832	−	0.364833i
$204$		0			0
$205$	19.1412			1.33688
$206$	−1.44287	−	2.49913i	−0.100530	−	0.174123i
$207$		0			0
$208$	−7.08101	−	4.08822i	−0.490980	−	0.283467i
$209$	4.96485	+	8.59937i	0.343426	+	0.594831i
$210$		0			0
$211$	−3.44148	+	5.96082i	−0.236921	+	0.410360i	−0.959829	−	0.280584i	$-0.909472\pi$
$211$	−3.44148	+	5.96082i	−0.236921	+	0.410360i	0.722908	+	0.690944i	$0.242805\pi$
$212$	−9.55747	+	5.51801i	−0.656410	+	0.378978i
$213$		0			0
$214$	0.509847	−	0.883081i	0.0348524	−	0.0603662i
$215$	6.31000	−	10.9292i	0.430338	−	0.745368i
$216$		0			0
$217$	1.05605	−	0.670161i	0.0716890	−	0.0454935i
$218$	0.311031	−	0.179574i	0.0210657	−	0.0121623i
$219$		0			0
$220$		−	22.8188i		−	1.53844i
$221$		−	7.88576i		−	0.530454i
$222$		0			0
$223$	5.57176	−	3.21686i	0.373113	−	0.215417i	−0.301705	−	0.953401i	$-0.597556\pi$
$223$	5.57176	−	3.21686i	0.373113	−	0.215417i	0.674818	+	0.737985i	$0.264222\pi$
$224$	−7.42908	+	4.71445i	−0.496376	+	0.314998i
$225$		0			0
$226$	0.318430	−	0.551537i	0.0211816	−	0.0366877i
$227$	9.86983	−	17.0951i	0.655084	−	1.13464i	−0.326789	−	0.945097i	$-0.605967\pi$
$227$	9.86983	−	17.0951i	0.655084	−	1.13464i	0.981873	−	0.189541i	$-0.0607000\pi$
$228$		0			0
$229$	9.44564	−	5.45344i	0.624185	−	0.360373i	−0.154311	−	0.988022i	$-0.549316\pi$
$229$	9.44564	−	5.45344i	0.624185	−	0.360373i	0.778497	+	0.627649i	$0.215983\pi$
$230$	1.34033	−	2.32151i	0.0883785	−	0.153076i
$231$		0			0
$232$	−2.43852	−	4.22364i	−0.160097	−	0.277295i
$233$	−17.9944	−	10.3891i	−1.17885	−	0.680611i	−0.223104	−	0.974795i	$-0.571619\pi$
$233$	−17.9944	−	10.3891i	−1.17885	−	0.680611i	−0.955749	+	0.294184i	$0.904952\pi$
$234$		0			0
$235$	−6.20298	−	10.7439i	−0.404638	−	0.700853i
$236$	8.96932			0.583853
$237$		0			0
$238$	−2.31873	−	1.21226i	−0.150301	−	0.0785789i
$239$	−23.6739	−	13.6681i	−1.53134	−	0.884119i	−0.999300	−	0.0373991i	$-0.988093\pi$
$239$	−23.6739	−	13.6681i	−1.53134	−	0.884119i	−0.532039	−	0.846720i	$-0.678574\pi$
$240$		0			0
$241$	−18.4688	−	10.6630i	−1.18968	−	0.686861i	−0.231445	−	0.972848i	$-0.574345\pi$
$241$	−18.4688	−	10.6630i	−1.18968	−	0.686861i	−0.958234	+	0.285987i	$0.907679\pi$
$242$	1.06444	−	0.614556i	0.0684250	−	0.0395052i
$243$		0			0
$244$		−	3.06218i		−	0.196036i
$245$	21.3468	−	1.79179i	1.36380	−	0.114473i
$246$		0			0
$247$	−2.98580	−	5.17155i	−0.189982	−	0.329058i
$248$	0.543692			0.0345245
$249$		0			0
$250$			0.570839i			0.0361030i
$251$	26.7381			1.68769			0.843847	−	0.536584i	$-0.180286\pi$
$251$	26.7381			1.68769			0.843847	+	0.536584i	$0.180286\pi$
$252$		0			0
$253$	−11.6144			−0.730193
$254$		−	0.807815i		−	0.0506868i
$255$		0			0
$256$	9.52977			0.595611
$257$	1.52640	+	2.64380i	0.0952140	+	0.164916i	0.909698	−	0.415271i	$-0.136313\pi$
$257$	1.52640	+	2.64380i	0.0952140	+	0.164916i	−0.814484	+	0.580186i	$0.802980\pi$
$258$		0			0
$259$	20.5868	−	0.862480i	1.27920	−	0.0535919i
$260$			13.7229i			0.851058i
$261$		0			0
$262$	1.90319	−	1.09881i	0.117580	−	0.0678847i
$263$	−14.0447	−	8.10868i	−0.866030	−	0.500003i	−3.24009e−6	−	1.00000i	$-0.500001\pi$
$263$	−14.0447	−	8.10868i	−0.866030	−	0.500003i	−0.866027	+	0.499997i	$0.833334\pi$
$264$		0			0
$265$	15.2842	+	8.82433i	0.938901	+	0.542074i
$266$	−1.97964	+	0.0829370i	−0.121380	+	0.00508519i
$267$		0			0
$268$	3.01525			0.184186
$269$	−0.303255	−	0.525254i	−0.0184898	−	0.0320253i	0.856632	−	0.515927i	$-0.172552\pi$
$269$	−0.303255	−	0.525254i	−0.0184898	−	0.0320253i	−0.875122	+	0.483902i	$0.839219\pi$
$270$		0			0
$271$	19.8948	+	11.4863i	1.20852	+	0.697742i	0.962437	−	0.271505i	$-0.0875215\pi$
$271$	19.8948	+	11.4863i	1.20852	+	0.697742i	0.246088	+	0.969248i	$0.420855\pi$
$272$	5.87120	+	10.1692i	0.355994	+	0.616599i
$273$		0			0
$274$	1.79389	−	3.10711i	0.108373	−	0.187708i
$275$	−14.7303	+	8.50455i	−0.888271	+	0.512844i
$276$		0			0
$277$	−6.64173	+	11.5038i	−0.399063	+	0.691197i	−0.993611	−	0.112863i	$-0.963998\pi$
$277$	−6.64173	+	11.5038i	−0.399063	+	0.691197i	0.594548	+	0.804060i	$0.297331\pi$
$278$	−1.95965	+	3.39421i	−0.117532	+	0.203571i
$279$		0			0
$280$	8.25228	+	4.31437i	0.493168	+	0.257833i
$281$	−5.68377	+	3.28153i	−0.339065	+	0.195759i	−0.659859	−	0.751390i	$-0.729384\pi$
$281$	−5.68377	+	3.28153i	−0.339065	+	0.195759i	0.320793	+	0.947149i	$0.396050\pi$
$282$		0			0
$283$		−	2.97234i		−	0.176687i	−0.996090	−	0.0883437i	$-0.971843\pi$
$283$		−	2.97234i		−	0.176687i	0.996090	−	0.0883437i	$-0.0281574\pi$
$284$		−	26.0508i		−	1.54583i
$285$		0			0
$286$	−2.32371	+	1.34160i	−0.137404	+	0.0793303i
$287$	16.5340	−	0.692689i	0.975970	−	0.0408882i
$288$		0			0
$289$	2.83753	−	4.91475i	0.166914	−	0.289103i
$290$	−1.90680	+	3.30267i	−0.111971	+	0.193940i
$291$		0			0
$292$	−1.63894	+	0.946243i	−0.0959118	+	0.0553747i
$293$	−3.03087	+	5.24962i	−0.177065	+	0.306686i	−0.940874	−	0.338756i	$-0.889994\pi$
$293$	−3.03087	+	5.24962i	−0.177065	+	0.306686i	0.763809	+	0.645443i	$0.223327\pi$
$294$		0			0
$295$	−7.17181	−	12.4219i	−0.417559	−	0.723234i
$296$	7.75686	+	4.47843i	0.450858	+	0.260303i
$297$		0			0
$298$	−1.24505	−	2.15649i	−0.0721239	−	0.124922i
$299$	6.98477			0.403940
$300$		0			0
$301$	5.05500	−	9.66892i	0.291366	−	0.557307i
$302$	−0.854235	−	0.493193i	−0.0491557	−	0.0283801i
$303$		0			0
$304$	7.70076	+	4.44604i	0.441669	+	0.254998i
$305$	−4.24092	+	2.44850i	−0.242834	+	0.140201i
$306$		0			0
$307$			21.6030i			1.23295i	0.787375	+	0.616474i	$0.211439\pi$
$307$			21.6030i			1.23295i	−0.787375	+	0.616474i	$0.788561\pi$
$308$	−0.825775	−	19.7106i	−0.0470529	−	1.12312i
$309$		0			0
$310$	−0.212570	−	0.368182i	−0.0120732	−	0.0209113i
$311$	−11.0234			−0.625081			−0.312540	−	0.949905i	$-0.601180\pi$
$311$	−11.0234			−0.625081			−0.312540	+	0.949905i	$0.601180\pi$
$312$		0			0
$313$		−	13.5542i		−	0.766129i	−0.923722	−	0.383064i	$-0.874869\pi$
$313$		−	13.5542i		−	0.766129i	0.923722	−	0.383064i	$-0.125131\pi$
$314$	4.91012			0.277094
$315$		0			0
$316$	−17.7551			−0.998800
$317$		−	11.1541i		−	0.626479i	−0.949674	−	0.313240i	$-0.898586\pi$
$317$		−	11.1541i		−	0.626479i	0.949674	−	0.313240i	$-0.101414\pi$
$318$		0			0
$319$	16.5231			0.925118
$320$	−9.18282	−	15.9051i	−0.513335	−	0.889123i
$321$		0			0
$322$	1.07375	−	2.05380i	0.0598377	−	0.114454i
$323$			8.57595i			0.477179i
$324$		0			0
$325$	8.85862	−	5.11453i	0.491388	−	0.283703i
$326$	−6.44706	−	3.72221i	−0.357070	−	0.206154i
$327$		0			0
$328$	6.22982	+	3.59679i	0.343984	+	0.198599i
$329$	−5.74688	−	9.05598i	−0.316836	−	0.499272i
$330$		0			0
$331$	−19.0202			−1.04544			−0.522722	−	0.852503i	$-0.675083\pi$
$331$	−19.0202			−1.04544			−0.522722	+	0.852503i	$0.675083\pi$
$332$	−10.5128	−	18.2087i	−0.576964	−	0.999331i
$333$		0			0
$334$	0.445794	+	0.257379i	0.0243927	+	0.0140832i
$335$	−2.41098	−	4.17593i	−0.131726	−	0.228156i
$336$		0			0
$337$	3.32635	−	5.76140i	0.181198	−	0.313843i	−0.761091	−	0.648645i	$-0.775336\pi$
$337$	3.32635	−	5.76140i	0.181198	−	0.313843i	0.942289	+	0.334802i	$0.108669\pi$
$338$	−1.91103	+	1.10333i	−0.103946	+	0.0600134i
$339$		0			0
$340$	9.85390	−	17.0675i	0.534403	−	0.925613i
$341$	−0.921000	+	1.59522i	−0.0498749	+	0.0863859i
$342$		0			0
$343$	18.3743	−	2.32024i	0.992121	−	0.125281i
$344$	4.10738	−	2.37140i	0.221455	−	0.127857i
$345$		0			0
$346$			7.03128i			0.378004i
$347$			26.6501i			1.43065i	0.698792	+	0.715325i	$0.253721\pi$
$347$			26.6501i			1.43065i	−0.698792	+	0.715325i	$0.746279\pi$
$348$		0			0
$349$	−20.5135	+	11.8435i	−1.09806	+	0.633966i	−0.935711	−	0.352768i	$-0.885241\pi$
$349$	−20.5135	+	11.8435i	−1.09806	+	0.633966i	−0.162350	+	0.986733i	$0.551907\pi$
$350$	−0.142067	−	3.39104i	−0.00759380	−	0.181258i
$351$		0			0
$352$	6.47905	−	11.2221i	0.345335	−	0.598137i
$353$	−2.29422	+	3.97371i	−0.122109	+	0.211499i	−0.920599	−	0.390509i	$-0.872299\pi$
$353$	−2.29422	+	3.97371i	−0.122109	+	0.211499i	0.798490	+	0.602008i	$0.205632\pi$
$354$		0			0
$355$	−36.0788	+	20.8301i	−1.91486	+	1.10555i
$356$	4.13057	−	7.15435i	0.218920	−	0.379180i
$357$		0			0
$358$	3.73022	+	6.46094i	0.197148	+	0.341471i
$359$	5.30942	+	3.06540i	0.280221	+	0.161785i	0.633523	−	0.773724i	$-0.281608\pi$
$359$	5.30942	+	3.06540i	0.280221	+	0.161785i	−0.353303	+	0.935509i	$0.614941\pi$
$360$		0			0
$361$	−6.25288	−	10.8303i	−0.329099	−	0.570016i
$362$	6.58363			0.346028
$363$		0			0
$364$	0.496610	+	11.8537i	0.0260294	+	0.621303i
$365$	2.62097	+	1.51322i	0.137188	+	0.0792056i
$366$		0			0
$367$	22.8860	+	13.2132i	1.19464	+	0.689725i	0.959355	−	0.282202i	$-0.0910650\pi$
$367$	22.8860	+	13.2132i	1.19464	+	0.689725i	0.235283	+	0.971927i	$0.424398\pi$
$368$	−9.00732	+	5.20038i	−0.469539	+	0.271088i
$369$		0			0
$370$		−	7.00381i		−	0.364111i
$371$	13.5217	+	7.06926i	0.702011	+	0.367018i
$372$		0			0
$373$	−10.0581	−	17.4211i	−0.520789	−	0.902033i	−0.999708	−	0.0241735i	$-0.992305\pi$
$373$	−10.0581	−	17.4211i	−0.520789	−	0.902033i	0.478919	−	0.877859i	$-0.341029\pi$
$374$	3.85340			0.199255
$375$		0			0
$376$		−	4.66236i		−	0.240443i
$377$	−9.93679			−0.511771
$378$		0			0
$379$	−17.4561			−0.896660			−0.448330	−	0.893868i	$-0.647981\pi$
$379$	−17.4561			−0.896660			−0.448330	+	0.893868i	$0.647981\pi$
$380$		−	14.9240i		−	0.765584i
$381$		0			0
$382$	−1.26039			−0.0644872
$383$	14.0317	+	24.3036i	0.716985	+	1.24185i	0.962189	+	0.272383i	$0.0878117\pi$
$383$	14.0317	+	24.3036i	0.716985	+	1.24185i	−0.245204	+	0.969471i	$0.578855\pi$
$384$		0			0
$385$	−26.6377	+	16.9041i	−1.35758	+	0.861515i
$386$			6.86037i			0.349183i
$387$		0			0
$388$	9.54517	−	5.51091i	0.484583	−	0.279774i
$389$	29.6520	+	17.1196i	1.50342	+	0.867999i	0.999992	+	0.00396103i	$0.00126084\pi$
$389$	29.6520	+	17.1196i	1.50342	+	0.867999i	0.503426	+	0.864038i	$0.332072\pi$
$390$		0			0
$391$	−8.68710	−	5.01550i	−0.439325	−	0.253645i
$392$	7.28437	+	3.42807i	0.367916	+	0.173144i
$393$		0			0
$394$	5.51918			0.278052
$395$	14.1968	+	24.5896i	0.714320	+	1.23724i
$396$		0			0
$397$	−11.2926	−	6.51981i	−0.566762	−	0.327220i	0.189093	−	0.981959i	$-0.439445\pi$
$397$	−11.2926	−	6.51981i	−0.566762	−	0.327220i	−0.755855	+	0.654739i	$0.772778\pi$
$398$	0.666662	+	1.15469i	0.0334167	+	0.0578795i
$399$		0			0
$400$	−7.61585	+	13.1910i	−0.380792	+	0.659552i
$401$	15.8943	−	9.17659i	0.793725	−	0.458257i	−0.0475475	−	0.998869i	$-0.515141\pi$
$401$	15.8943	−	9.17659i	0.793725	−	0.458257i	0.841272	+	0.540612i	$0.181807\pi$
$402$		0			0
$403$	0.553877	−	0.959344i	0.0275906	−	0.0477883i
$404$	−16.4171	+	28.4353i	−0.816782	+	1.41471i
$405$		0			0
$406$	−1.52756	+	2.92182i	−0.0758113	+	0.145007i
$407$	−26.2798	+	15.1727i	−1.30264	+	0.752081i
$408$		0			0
$409$			6.46786i			0.319815i	0.987132	+	0.159907i	$0.0511196\pi$
$409$			6.46786i			0.319815i	−0.987132	+	0.159907i	$0.948880\pi$
$410$		−	5.62501i		−	0.277800i
$411$		0			0
$412$	16.2740	−	9.39581i	0.801764	−	0.462899i
$413$	−6.64448	−	10.4704i	−0.326953	−	0.515216i
$414$		0			0
$415$	−16.8119	+	29.1191i	−0.825265	+	1.42940i
$416$	−3.89642	+	6.74880i	−0.191038	+	0.330887i
$417$		0			0
$418$	2.52709	−	1.45902i	0.123604	−	0.0713629i
$419$	−7.11542	+	12.3243i	−0.347611	+	0.602080i	−0.985825	−	0.167779i	$-0.946340\pi$
$419$	−7.11542	+	12.3243i	−0.347611	+	0.602080i	0.638214	+	0.769859i	$0.279674\pi$
$420$		0			0
$421$	15.1718	+	26.2784i	0.739429	+	1.28073i	0.952753	+	0.303747i	$0.0982378\pi$
$421$	15.1718	+	26.2784i	0.739429	+	1.28073i	−0.213324	+	0.976982i	$0.568429\pi$
$422$	1.75170	+	1.01135i	0.0852716	+	0.0492316i
$423$		0			0
$424$	3.31633	+	5.74405i	0.161055	+	0.278956i
$425$	−14.6902			−0.712579
$426$		0			0
$427$	−3.57466	+	2.26846i	−0.172990	+	0.109779i
$428$	5.75051	+	3.32006i	0.277962	+	0.160481i
$429$		0			0
$430$	−3.21177	−	1.85432i	−0.154885	−	0.0894230i
$431$	2.12663	−	1.22781i	0.102436	−	0.0591415i	−0.447907	−	0.894080i	$-0.647830\pi$
$431$	2.12663	−	1.22781i	0.102436	−	0.0591415i	0.550343	+	0.834939i	$0.314497\pi$
$432$		0			0
$433$		−	12.4545i		−	0.598525i	−0.954171	−	0.299262i	$-0.903259\pi$
$433$		−	12.4545i		−	0.598525i	0.954171	−	0.299262i	$-0.0967406\pi$
$434$	−0.196940	−	0.310340i	−0.00945342	−	0.0148968i
$435$		0			0
$436$	1.16936	+	2.02539i	0.0560022	+	0.0969987i
$437$	−7.59610			−0.363371
$438$		0			0
$439$		−	17.5300i		−	0.836663i	−0.908294	−	0.418331i	$-0.862615\pi$
$439$		−	17.5300i		−	0.836663i	0.908294	−	0.418331i	$-0.137385\pi$
$440$	−13.7141			−0.653794
$441$		0			0
$442$	−2.31739			−0.110227
$443$			9.00464i			0.427824i	0.976853	+	0.213912i	$0.0686205\pi$
$443$			9.00464i			0.427824i	−0.976853	+	0.213912i	$0.931379\pi$
$444$		0			0
$445$	−13.2111			−0.626266
$446$	−0.945337	−	1.63737i	−0.0447630	−	0.0775318i
$447$		0			0
$448$	−8.50761	−	13.4064i	−0.401947	−	0.633392i
$449$		−	30.8120i		−	1.45411i	−0.686581	−	0.727054i	$-0.740889\pi$
$449$		−	30.8120i		−	1.45411i	0.686581	−	0.727054i	$-0.259111\pi$
$450$		0			0
$451$	−21.1063	+	12.1857i	−0.993856	+	0.573803i
$452$	3.59154	+	2.07357i	0.168932	+	0.0975327i
$453$		0			0
$454$	−5.02371	−	2.90044i	−0.235775	−	0.136125i
$455$	16.0196	−	10.1659i	0.751009	−	0.476586i
$456$		0			0
$457$	13.8286			0.646874			0.323437	−	0.946250i	$-0.395162\pi$
$457$	13.8286			0.646874			0.323437	+	0.946250i	$0.395162\pi$
$458$	−1.60260	−	2.77578i	−0.0748846	−	0.129704i
$459$		0			0
$460$	15.1174	+	8.72803i	0.704852	+	0.406947i
$461$	−6.16989	−	10.6866i	−0.287360	−	0.497723i	0.685818	−	0.727773i	$-0.259444\pi$
$461$	−6.16989	−	10.6866i	−0.287360	−	0.497723i	−0.973179	+	0.230050i	$0.926111\pi$
$462$		0			0
$463$	6.37802	−	11.0471i	0.296412	−	0.513401i	−0.678900	−	0.734230i	$-0.737543\pi$
$463$	6.37802	−	11.0471i	0.296412	−	0.513401i	0.975312	+	0.220830i	$0.0708765\pi$
$464$	12.8141	−	7.39825i	0.594882	−	0.343455i
$465$		0			0
$466$	−3.05303	+	5.28801i	−0.141429	+	0.244962i
$467$	5.48999	−	9.50894i	0.254046	−	0.440021i	−0.710590	−	0.703607i	$-0.751572\pi$
$467$	5.48999	−	9.50894i	0.254046	−	0.440021i	0.964636	+	0.263585i	$0.0849051\pi$
$468$		0			0
$469$	−2.23370	−	3.51988i	−0.103143	−	0.162533i
$470$	−3.15730	+	1.82287i	−0.145635	+	0.0840825i
$471$		0			0
$472$		−	5.39057i		−	0.248121i
$473$			16.0683i			0.738823i
$474$		0			0
$475$	−9.63396	+	5.56217i	−0.442036	+	0.255210i
$476$	7.89406	−	15.0993i	0.361824	−	0.692075i
$477$		0			0
$478$	−4.01665	+	6.95704i	−0.183717	+	0.318208i
$479$	5.59729	−	9.69478i	0.255747	−	0.442966i	−0.709351	−	0.704855i	$-0.751012\pi$
$479$	5.59729	−	9.69478i	0.255747	−	0.442966i	0.965098	+	0.261889i	$0.0843454\pi$
$480$		0			0
$481$	15.8043	−	9.12464i	0.720616	−	0.416048i
$482$	−3.13352	+	5.42741i	−0.142728	+	0.247212i
$483$		0			0
$484$	4.00191	+	6.93152i	0.181905	+	0.315069i
$485$	−15.2645	−	8.81298i	−0.693126	−	0.400177i
$486$		0			0
$487$	−1.48332	−	2.56919i	−0.0672158	−	0.116421i	0.830459	−	0.557080i	$-0.188078\pi$
$487$	−1.48332	−	2.56919i	−0.0672158	−	0.116421i	−0.897675	+	0.440659i	$0.854745\pi$
$488$	−1.84037			−0.0833097
$489$		0			0
$490$	−0.526553	−	6.27318i	−0.0237872	−	0.283393i
$491$	20.1795	+	11.6507i	0.910690	+	0.525787i	0.880653	−	0.473762i	$-0.157104\pi$
$491$	20.1795	+	11.6507i	0.910690	+	0.525787i	0.0300367	+	0.999549i	$0.490438\pi$
$492$		0			0
$493$	12.3586	+	7.13524i	0.556603	+	0.321355i
$494$	−1.51976	+	0.877435i	−0.0683773	+	0.0394776i
$495$		0			0
$496$			1.64952i			0.0740654i
$497$	−30.4107	+	19.2985i	−1.36411	+	0.865654i
$498$		0			0
$499$	2.29296	+	3.97152i	0.102647	+	0.177790i	0.912774	−	0.408464i	$-0.133935\pi$
$499$	2.29296	+	3.97152i	0.102647	+	0.177790i	−0.810127	+	0.586254i	$0.800602\pi$
$500$	−3.71723			−0.166240
$501$		0			0
$502$		−	7.85751i		−	0.350698i
$503$	23.1383			1.03169			0.515844	−	0.856683i	$-0.327479\pi$
$503$	23.1383			1.03169			0.515844	+	0.856683i	$0.327479\pi$
$504$		0			0
$505$	52.5081			2.33658
$506$			3.41313i			0.151732i
$507$		0			0
$508$	5.26039			0.233392
$509$	−4.82853	−	8.36326i	−0.214021	−	0.370695i	0.738948	−	0.673762i	$-0.235323\pi$
$509$	−4.82853	−	8.36326i	−0.214021	−	0.370695i	−0.952969	+	0.303067i	$0.901989\pi$
$510$		0			0
$511$	2.31873	+	1.21226i	0.102575	+	0.0536271i
$512$		−	19.6301i		−	0.867536i
$513$		0			0
$514$	0.776931	−	0.448561i	0.0342690	−	0.0197852i
$515$	−26.0252	−	15.0257i	−1.14681	−	0.662110i
$516$		0			0
$517$	13.6796	+	7.89791i	0.601627	+	0.347350i
$518$	−0.253457	−	6.04982i	−0.0111362	−	0.265814i
$519$		0			0
$520$	8.24748			0.361676
$521$	−5.00035	−	8.66086i	−0.219069	−	0.379439i	0.735454	−	0.677574i	$-0.236969\pi$
$521$	−5.00035	−	8.66086i	−0.219069	−	0.379439i	−0.954524	+	0.298135i	$0.903635\pi$
$522$		0			0
$523$	−10.7796	−	6.22361i	−0.471359	−	0.272139i	0.245449	−	0.969409i	$-0.421065\pi$
$523$	−10.7796	−	6.22361i	−0.471359	−	0.272139i	−0.716809	+	0.697270i	$0.754398\pi$
$524$	7.15531	+	12.3934i	0.312581	+	0.541406i
$525$		0			0
$526$	−2.38289	+	4.12729i	−0.103899	+	0.179959i
$527$	−1.37774	+	0.795437i	−0.0600152	+	0.0346498i
$528$		0			0
$529$	−7.05755	+	12.2240i	−0.306850	+	0.531480i
$530$	2.59320	−	4.49156i	0.112641	−	0.195101i
$531$		0			0
$532$	−0.540075	−	12.8912i	−0.0234152	−	0.558904i
$533$	12.6930	−	7.32833i	0.549797	−	0.317425i
$534$		0			0
$535$		−	10.6188i		−	0.459091i
$536$		−	1.81217i		−	0.0782737i
$537$		0			0
$538$	−0.154356	+	0.0891175i	−0.00665476	+	0.00384213i
$539$	−22.3977	+	15.5656i	−0.964735	+	0.670458i
$540$		0			0
$541$	6.96514	−	12.0640i	0.299455	−	0.518671i	−0.676557	−	0.736391i	$-0.736529\pi$
$541$	6.96514	−	12.0640i	0.299455	−	0.518671i	0.976011	+	0.217720i	$0.0698619\pi$
$542$	3.37547	−	5.84648i	0.144989	−	0.251128i
$543$		0			0
$544$	9.69211	−	5.59574i	0.415546	−	0.239916i
$545$	1.87003	−	3.23898i	0.0801032	−	0.138743i
$546$		0			0
$547$	−21.6768	−	37.5454i	−0.926834	−	1.60532i	−0.788584	−	0.614926i	$-0.789186\pi$
$547$	−21.6768	−	37.5454i	−0.926834	−	1.60532i	−0.138250	−	0.990397i	$-0.544148\pi$
$548$	20.2331	+	11.6816i	0.864316	+	0.499013i
$549$		0			0
$550$	2.49923	+	4.32879i	0.106567	+	0.184580i
$551$	10.8065			0.460372
$552$		0			0
$553$	13.1529	+	20.7265i	0.559320	+	0.881382i
$554$	3.38062	+	1.95180i	0.143629	+	0.0829241i
$555$		0			0
$556$	−22.1026	−	12.7610i	−0.937361	−	0.541186i
$557$	31.1339	−	17.9752i	1.31919	−	0.761632i	0.335588	−	0.942009i	$-0.391065\pi$
$557$	31.1339	−	17.9752i	1.31919	−	0.761632i	0.983598	+	0.180377i	$0.0577317\pi$
$558$		0			0
$559$		−	9.66329i		−	0.408714i
$560$	−13.0894	+	25.0367i	−0.553129	+	1.05799i
$561$		0			0
$562$	0.964340	+	1.67029i	0.0406782	+	0.0704568i
$563$	−6.11108			−0.257551			−0.128776	−	0.991674i	$-0.541105\pi$
$563$	−6.11108			−0.257551			−0.128776	+	0.991674i	$0.541105\pi$
$564$		0			0
$565$		−	6.63207i		−	0.279013i
$566$	−0.873481			−0.0367151
$567$		0			0
$568$	−15.6566			−0.656935
$569$			19.3045i			0.809285i	0.914475	+	0.404642i	$0.132604\pi$
$569$			19.3045i			0.809285i	−0.914475	+	0.404642i	$0.867396\pi$
$570$		0			0
$571$	12.7224			0.532415			0.266207	−	0.963916i	$-0.414229\pi$
$571$	12.7224			0.532415			0.266207	+	0.963916i	$0.414229\pi$
$572$	−8.73631	−	15.1317i	−0.365284	−	0.632690i
$573$		0			0
$574$	−0.203560	−	4.85883i	−0.00849644	−	0.202804i
$575$		−	13.0118i		−	0.542628i
$576$		0			0
$577$	7.05520	−	4.07332i	0.293712	−	0.169575i	−0.345903	−	0.938270i	$-0.612427\pi$
$577$	7.05520	−	4.07332i	0.293712	−	0.169575i	0.639615	+	0.768696i	$0.279094\pi$
$578$	−1.44429	−	0.833863i	−0.0600747	−	0.0346841i
$579$		0			0
$580$	−21.5066	−	12.4168i	−0.893012	−	0.515581i
$581$	−13.4682	+	25.7612i	−0.558755	+	1.06875i
$582$		0			0
$583$	−22.4711			−0.930657
$584$	0.568693	+	0.985005i	0.0235327	+	0.0407598i
$585$		0			0
$586$	1.54270	+	0.890680i	0.0637285	+	0.0367937i
$587$	−12.3041	−	21.3113i	−0.507843	−	0.879610i	−0.999959	−	0.00908019i	$-0.997110\pi$
$587$	−12.3041	−	21.3113i	−0.507843	−	0.879610i	0.492116	−	0.870530i	$-0.336224\pi$
$588$		0			0
$589$	−0.602354	+	1.04331i	−0.0248196	+	0.0429888i
$590$	−3.65043	+	2.10758i	−0.150286	+	0.0867676i
$591$		0			0
$592$	−13.5872	+	23.5336i	−0.558429	+	0.967227i
$593$	18.9321	−	32.7913i	0.777447	−	1.34658i	−0.155962	−	0.987763i	$-0.549848\pi$
$593$	18.9321	−	32.7913i	0.777447	−	1.34658i	0.933409	−	0.358814i	$-0.116819\pi$
$594$		0			0
$595$	−27.2236	+	1.14053i	−1.11606	+	0.0467572i
$596$	14.0428	−	8.10762i	0.575216	−	0.332101i
$597$		0			0
$598$		−	2.05261i		−	0.0839375i
$599$		−	10.6529i		−	0.435268i	−0.976030	−	0.217634i	$-0.930166\pi$
$599$		−	10.6529i		−	0.435268i	0.976030	−	0.217634i	$-0.0698339\pi$
$600$		0			0
$601$	39.8636	−	23.0153i	1.62607	−	0.938812i	0.640821	−	0.767691i	$-0.278594\pi$
$601$	39.8636	−	23.0153i	1.62607	−	0.938812i	0.985250	−	0.171122i	$-0.0547391\pi$
$602$	−2.84140	−	1.48551i	−0.115807	−	0.0605449i
$603$		0			0
$604$	3.21161	−	5.56267i	0.130679	−	0.226342i
$605$	6.39981	−	11.0848i	0.260189	−	0.450661i
$606$		0			0
$607$	3.74063	−	2.15965i	0.151827	−	0.0876576i	−0.422162	−	0.906521i	$-0.638729\pi$
$607$	3.74063	−	2.15965i	0.151827	−	0.0876576i	0.573989	+	0.818863i	$0.305395\pi$
$608$	4.23745	−	7.33947i	0.171851	−	0.297655i
$609$		0			0
$610$	0.719539	+	1.24628i	0.0291333	+	0.0504603i
$611$	−8.22672	−	4.74970i	−0.332818	−	0.192152i
$612$		0			0
$613$	14.3838	+	24.9135i	0.580956	+	1.00624i	0.995366	+	0.0961549i	$0.0306544\pi$
$613$	14.3838	+	24.9135i	0.580956	+	1.00624i	−0.414411	+	0.910090i	$0.636012\pi$
$614$	6.34846			0.256203
$615$		0			0
$616$	−11.8461	+	0.496291i	−0.477293	+	0.0199961i
$617$	−0.935498	−	0.540110i	−0.0376617	−	0.0217440i	0.481051	−	0.876693i	$-0.340255\pi$
$617$	−0.935498	−	0.540110i	−0.0376617	−	0.0217440i	−0.518713	+	0.854949i	$0.673589\pi$
$618$		0			0
$619$	−6.57128	−	3.79393i	−0.264122	−	0.152491i	0.362091	−	0.932143i	$-0.382063\pi$
$619$	−6.57128	−	3.79393i	−0.264122	−	0.152491i	−0.626214	+	0.779652i	$0.715396\pi$
$620$	2.39755	−	1.38423i	0.0962881	−	0.0555920i
$621$		0			0
$622$			3.23944i			0.129890i
$623$	−11.4116	+	0.478089i	−0.457197	+	0.0191542i
$624$		0			0
$625$	13.8854	+	24.0502i	0.555416	+	0.962010i
$626$	−3.98316			−0.159199
$627$		0			0
$628$			31.9741i			1.27591i
$629$	−26.2082			−1.04499
$630$		0			0
$631$	35.0387			1.39487			0.697435	−	0.716648i	$-0.254325\pi$
$631$	35.0387			1.39487			0.697435	+	0.716648i	$0.254325\pi$
$632$			10.6708i			0.424462i
$633$		0			0
$634$	−3.27786			−0.130181
$635$	−4.20618	−	7.28531i	−0.166917	−	0.289109i
$636$		0			0
$637$	13.4697	−	9.36096i	0.533687	−	0.370895i
$638$		−	4.85564i		−	0.192237i
$639$		0			0
$640$	−22.3015	+	12.8758i	−0.881544	+	0.508960i
$641$	−26.9229	−	15.5439i	−1.06339	−	0.613949i	−0.137023	−	0.990568i	$-0.543753\pi$
$641$	−26.9229	−	15.5439i	−1.06339	−	0.613949i	−0.926368	+	0.376619i	$0.877087\pi$
$642$		0			0
$643$	0.977928	+	0.564607i	0.0385657	+	0.0222659i	0.519159	−	0.854678i	$-0.326245\pi$
$643$	0.977928	+	0.564607i	0.0385657	+	0.0222659i	−0.480593	+	0.876944i	$0.659579\pi$
$644$	13.3741	+	6.99212i	0.527014	+	0.275528i
$645$		0			0
$646$	2.52021			0.0991564
$647$	13.5992	+	23.5545i	0.534640	+	0.926023i	0.999181	+	0.0404713i	$0.0128859\pi$
$647$	13.5992	+	23.5545i	0.534640	+	0.926023i	−0.464541	+	0.885552i	$0.653781\pi$
$648$		0			0
$649$	15.8162	+	9.13148i	0.620839	+	0.358442i
$650$	−1.50300	−	2.60328i	−0.0589526	−	0.102109i
$651$		0			0
$652$	24.2386	−	41.9824i	0.949256	−	1.64416i
$653$	19.3030	−	11.1446i	0.755384	−	0.436121i	−0.0722517	−	0.997386i	$-0.523019\pi$
$653$	19.3030	−	11.1446i	0.755384	−	0.436121i	0.827636	+	0.561265i	$0.189685\pi$
$654$		0			0
$655$	11.4427	−	19.8193i	0.447102	−	0.774404i
$656$	−10.9123	+	18.9007i	−0.426055	+	0.737949i
$657$		0			0
$658$	−2.66128	+	1.68883i	−0.103747	+	0.0658375i
$659$	7.69208	−	4.44103i	0.299641	−	0.172998i	−0.342641	−	0.939467i	$-0.611321\pi$
$659$	7.69208	−	4.44103i	0.299641	−	0.172998i	0.642282	+	0.766469i	$0.277988\pi$
$660$		0			0
$661$		−	19.3670i		−	0.753291i	−0.926358	−	0.376645i	$-0.877078\pi$
$661$		−	19.3670i		−	0.753291i	0.926358	−	0.376645i	$-0.122922\pi$
$662$			5.58945i			0.217240i
$663$		0			0
$664$	−10.9434	+	6.31819i	−0.424687	+	0.245193i
$665$	−17.4216	+	11.0557i	−0.675583	+	0.428721i
$666$		0			0
$667$	−6.31999	+	10.9465i	−0.244711	+	0.423852i
$668$	−1.67602	+	2.90295i	−0.0648472	+	0.112319i
$669$		0			0
$670$	−1.22718	+	0.708512i	−0.0474101	+	0.0273722i
$671$	3.11754	−	5.39973i	0.120351	−	0.208454i
$672$		0			0
$673$	11.5828	+	20.0620i	0.446484	+	0.773333i	0.998154	−	0.0607292i	$-0.0193426\pi$
$673$	11.5828	+	20.0620i	0.446484	+	0.773333i	−0.551670	+	0.834062i	$0.686009\pi$
$674$	−1.69310	−	0.977511i	−0.0652157	−	0.0376523i
$675$		0			0
$676$	−7.18476	−	12.4444i	−0.276337	−	0.478630i
$677$	−3.12693			−0.120177			−0.0600887	−	0.998193i	$-0.519138\pi$
$677$	−3.12693			−0.120177			−0.0600887	+	0.998193i	$0.519138\pi$
$678$		0			0
$679$	−13.5043	−	7.06017i	−0.518247	−	0.270944i
$680$	−10.2576	−	5.92220i	−0.393359	−	0.227106i
$681$		0			0
$682$	0.468786	+	0.270654i	0.0179507	+	0.0103639i
$683$	27.1966	−	15.7020i	1.04065	−	0.600819i	0.120632	−	0.992697i	$-0.461508\pi$
$683$	27.1966	−	15.7020i	1.04065	−	0.600819i	0.920017	+	0.391878i	$0.128175\pi$
$684$		0			0
$685$		−	37.3621i		−	1.42753i
$686$	−0.681848	−	5.39966i	−0.0260331	−	0.206160i
$687$		0			0
$688$	7.19462	+	12.4614i	0.274292	+	0.475088i
$689$	13.5138			0.514835
$690$		0			0
$691$			44.1739i			1.68045i	0.542235	+	0.840227i	$0.317578\pi$
$691$			44.1739i			1.68045i	−0.542235	+	0.840227i	$0.682422\pi$
$692$	−45.7868			−1.74055
$693$		0			0
$694$	7.83164			0.297285
$695$			40.8144i			1.54818i
$696$		0			0
$697$	−21.0488			−0.797280
$698$	3.48043	+	6.02828i	0.131736	+	0.228174i
$699$		0			0
$700$	22.0820	−	0.925123i	0.834621	−	0.0349664i
$701$			9.69906i			0.366328i	0.983082	+	0.183164i	$0.0586340\pi$
$701$			9.69906i			0.366328i	−0.983082	+	0.183164i	$0.941366\pi$
$702$		0			0
$703$	−17.1876	+	9.92326i	−0.648242	+	0.374263i
$704$	20.2511	+	11.6920i	0.763242	+	0.440658i
$705$		0			0
$706$	1.16775	+	0.674202i	0.0439490	+	0.0253739i
$707$	45.3560	−	1.90019i	1.70579	−	0.0714638i
$708$		0			0
$709$	−1.09786			−0.0412311			−0.0206156	−	0.999787i	$-0.506563\pi$
$709$	−1.09786			−0.0412311			−0.0206156	+	0.999787i	$0.506563\pi$
$710$	6.12132	+	10.6024i	0.229729	+	0.397903i
$711$		0			0
$712$	−4.29977	−	2.48247i	−0.161141	−	0.0930346i
$713$	−0.704553	−	1.22032i	−0.0263857	−	0.0457014i
$714$		0			0
$715$	−13.9710	+	24.1985i	−0.522486	+	0.904972i
$716$	−42.0728	+	24.2908i	−1.57233	+	0.907788i
$717$		0			0
$718$	0.900826	−	1.56028i	0.0336185	−	0.0582290i
$719$	−11.3648	+	19.6844i	−0.423835	+	0.734103i	−0.996311	−	0.0858183i	$-0.972650\pi$
$719$	−11.3648	+	19.6844i	−0.423835	+	0.734103i	0.572476	+	0.819921i	$0.305983\pi$
$720$		0			0
$721$	−23.0241	−	12.0372i	−0.857462	−	0.448289i
$722$	−3.18269	+	1.83753i	−0.118448	+	0.0683858i
$723$		0			0
$724$			42.8718i			1.59332i
$725$			18.5110i			0.687482i
$726$		0			0
$727$	−3.47919	+	2.00871i	−0.129036	+	0.0744990i	−0.563129	−	0.826369i	$-0.690402\pi$
$727$	−3.47919	+	2.00871i	−0.129036	+	0.0744990i	0.434093	+	0.900868i	$0.357069\pi$
$728$	7.12409	−	0.298463i	0.264036	−	0.0110618i
$729$		0			0
$730$	0.444689	−	0.770224i	0.0164587	−	0.0285073i
$731$	−6.93885	+	12.0184i	−0.256643	+	0.444518i
$732$		0			0
$733$	−7.20188	+	4.15801i	−0.266008	+	0.153580i	−0.627072	−	0.778961i	$-0.715747\pi$
$733$	−7.20188	+	4.15801i	−0.266008	+	0.153580i	0.361064	+	0.932541i	$0.382413\pi$
$734$	3.88296	−	6.72549i	0.143323	−	0.248242i
$735$		0			0
$736$	4.95640	+	8.58473i	0.182695	+	0.316437i
$737$	5.31698	+	3.06976i	0.195854	+	0.113076i
$738$		0			0
$739$	−2.28507	−	3.95785i	−0.0840576	−	0.145592i	0.820932	−	0.571026i	$-0.193455\pi$
$739$	−2.28507	−	3.95785i	−0.0840576	−	0.145592i	−0.904989	+	0.425434i	$0.860121\pi$
$740$	45.6079			1.67658
$741$		0			0
$742$	2.07744	−	3.97361i	0.0762653	−	0.145876i
$743$	−1.51258	−	0.873286i	−0.0554910	−	0.0320378i	0.471998	−	0.881600i	$-0.343533\pi$
$743$	−1.51258	−	0.873286i	−0.0554910	−	0.0320378i	−0.527489	+	0.849562i	$0.676866\pi$
$744$		0			0
$745$	−22.4571	−	12.9656i	−0.822764	−	0.475023i
$746$	−5.11954	+	2.95577i	−0.187440	+	0.108218i
$747$		0			0
$748$			25.0929i			0.917486i
$749$	−0.384277	−	9.17242i	−0.0140412	−	0.335153i
$750$		0			0
$751$	−2.91647	−	5.05147i	−0.106423	−	0.184331i	0.807895	−	0.589326i	$-0.200607\pi$
$751$	−2.91647	−	5.05147i	−0.106423	−	0.184331i	−0.914319	+	0.404995i	$0.867273\pi$
$752$	14.1452			0.515822
$753$		0			0
$754$			2.92012i			0.106345i
$755$	−10.2719			−0.373834
$756$		0			0
$757$	−42.0967			−1.53003			−0.765015	−	0.644013i	$-0.777268\pi$
$757$	−42.0967			−1.53003			−0.765015	+	0.644013i	$0.777268\pi$
$758$			5.12982i			0.186323i
$759$		0			0
$760$	−8.96932			−0.325352
$761$	−0.293431	−	0.508238i	−0.0106369	−	0.0184236i	0.860658	−	0.509184i	$-0.170053\pi$
$761$	−0.293431	−	0.508238i	−0.0106369	−	0.0184236i	−0.871295	+	0.490760i	$0.836719\pi$
$762$		0			0
$763$	1.49810	−	2.86547i	0.0542348	−	0.103737i
$764$		−	8.20750i		−	0.296937i
$765$		0			0
$766$	7.14208	−	4.12348i	0.258054	−	0.148987i
$767$	−9.51165	−	5.49155i	−0.343446	−	0.198288i
$768$		0			0
$769$	−45.1905	−	26.0907i	−1.62961	−	0.940856i	−0.984208	−	0.177014i	$-0.943356\pi$
$769$	−45.1905	−	26.0907i	−1.62961	−	0.940856i	−0.645403	−	0.763843i	$-0.723310\pi$
$770$	4.96761	+	7.82800i	0.179020	+	0.282102i
$771$		0			0
$772$	−44.6738			−1.60785
$773$	16.3906	+	28.3894i	0.589530	+	1.02110i	0.994294	+	0.106674i	$0.0340202\pi$
$773$	16.3906	+	28.3894i	0.589530	+	1.02110i	−0.404764	+	0.914421i	$0.632646\pi$
$774$		0			0
$775$	−1.78714	−	1.03180i	−0.0641959	−	0.0370635i
$776$	−3.31206	−	5.73666i	−0.118896	−	0.205934i
$777$		0			0
$778$	5.03093	−	8.71383i	0.180368	−	0.312406i
$779$	−13.8040	+	7.96973i	−0.494579	+	0.285545i
$780$		0			0
$781$	26.5218	−	45.9371i	0.949024	−	1.64376i
$782$	−1.47390	+	2.55287i	−0.0527066	+	0.0912906i
$783$		0			0
$784$	−10.4005	+	22.1001i	−0.371446	+	0.789291i
$785$	44.2821	−	25.5663i	1.58050	−	0.912500i
$786$		0			0
$787$			40.9934i			1.46126i	0.682775	+	0.730628i	$0.260773\pi$
$787$			40.9934i			1.46126i	−0.682775	+	0.730628i	$0.739227\pi$
$788$			35.9402i			1.28032i
$789$		0			0
$790$	7.22614	−	4.17201i	0.257095	−	0.148434i
$791$	−0.240004	−	5.72872i	−0.00853356	−	0.203690i
$792$		0			0
$793$	−1.87485	+	3.24733i	−0.0665778	+	0.115316i
$794$	−1.91597	+	3.31856i	−0.0679954	+	0.117771i
$795$		0			0
$796$	−7.51921	+	4.34122i	−0.266511	+	0.153870i
$797$	17.0441	−	29.5213i	0.603734	−	1.04570i	−0.388516	−	0.921442i	$-0.627012\pi$
$797$	17.0441	−	29.5213i	0.603734	−	1.04570i	0.992250	−	0.124256i	$-0.0396544\pi$
$798$		0			0
$799$	6.82116	+	11.8146i	0.241315	+	0.417971i
$800$	12.5722	+	7.25854i	0.444493	+	0.256628i
$801$		0			0
$802$	−2.69672	−	4.67086i	−0.0952245	−	0.164934i
$803$	−3.85340			−0.135984
$804$		0			0
$805$	−1.01022	−	24.1132i	−0.0356055	−	0.849877i
$806$	−0.281922	−	0.162768i	−0.00993027	−	0.00573324i
$807$		0			0
$808$	17.0896	+	9.86670i	0.601211	+	0.347109i
$809$	6.01547	−	3.47304i	0.211493	−	0.122105i	−0.390512	−	0.920598i	$-0.627702\pi$
$809$	6.01547	−	3.47304i	0.211493	−	0.122105i	0.602005	+	0.798492i	$0.294369\pi$
$810$		0			0
$811$		−	39.8573i		−	1.39958i	−0.714350	−	0.699789i	$-0.753277\pi$
$811$		−	39.8573i		−	1.39958i	0.714350	−	0.699789i	$-0.246723\pi$
$812$	−19.0265	−	9.94725i	−0.667700	−	0.349080i
$813$		0			0
$814$	4.45878	+	7.72284i	0.156280	+	0.270685i
$815$	−77.5240			−2.71555
$816$		0			0
$817$			10.5091i			0.367665i
$818$	1.90071			0.0664566
$819$		0			0
$820$	36.6294			1.27915
$821$		−	42.1017i		−	1.46936i	−0.678414	−	0.734680i	$-0.737332\pi$
$821$		−	42.1017i		−	1.46936i	0.678414	−	0.734680i	$-0.262668\pi$
$822$		0			0
$823$	32.6821			1.13923			0.569614	−	0.821913i	$-0.307093\pi$
$823$	32.6821			1.13923			0.569614	+	0.821913i	$0.307093\pi$
$824$	−5.64689	−	9.78070i	−0.196719	−	0.340727i
$825$		0			0
$826$	−3.07694	+	1.95261i	−0.107060	+	0.0679399i
$827$			31.4399i			1.09327i	0.837370	+	0.546637i	$0.184092\pi$
$827$			31.4399i			1.09327i	−0.837370	+	0.546637i	$0.815908\pi$
$828$		0			0
$829$	35.7122	−	20.6185i	1.24034	−	0.716109i	0.271174	−	0.962530i	$-0.412588\pi$
$829$	35.7122	−	20.6185i	1.24034	−	0.716109i	0.969163	+	0.246421i	$0.0792547\pi$
$830$	8.55721	+	4.94051i	0.297025	+	0.171488i
$831$		0			0
$832$	−12.1788	−	7.03141i	−0.422222	−	0.243770i
$833$	−23.4742	+	1.97036i	−0.813334	+	0.0682689i
$834$		0			0
$835$	5.36054			0.185509
$836$	9.50094	+	16.4561i	0.328597	+	0.569147i
$837$		0			0
$838$	3.62173	+	2.09100i	0.125110	+	0.0722326i
$839$	4.04385	+	7.00416i	0.139609	+	0.241810i	0.927349	−	0.374198i	$-0.122082\pi$
$839$	4.04385	+	7.00416i	0.139609	+	0.241810i	−0.787740	+	0.616009i	$0.788749\pi$
$840$		0			0
$841$	−5.50894	+	9.54177i	−0.189963	+	0.329026i
$842$	7.72241	−	4.45853i	0.266132	−	0.153651i
$843$		0			0
$844$	−6.58576	+	11.4069i	−0.226691	+	0.392641i
$845$	−11.4898	+	19.9009i	−0.395260	+	0.684611i
$846$		0			0
$847$	5.12695	−	9.80654i	0.176164	−	0.336957i
$848$	−17.4269	+	10.0615i	−0.598444	+	0.345512i
$849$		0			0
$850$			4.31700i			0.148072i
$851$		−	23.2138i		−	0.795759i
$852$		0			0
$853$	−24.5887	+	14.1963i	−0.841900	+	0.486071i	−0.857910	−	0.513801i	$-0.828237\pi$
$853$	−24.5887	+	14.1963i	−0.841900	+	0.486071i	0.0160098	+	0.999872i	$0.494904\pi$
$854$	0.666631	+	1.05048i	0.0228117	+	0.0359468i
$855$		0			0
$856$	1.99536	−	3.45606i	0.0682000	−	0.118126i
$857$	25.6587	−	44.4422i	0.876485	−	1.51812i	0.0213132	−	0.999773i	$-0.493215\pi$
$857$	25.6587	−	44.4422i	0.876485	−	1.51812i	0.855172	−	0.518344i	$-0.173451\pi$
$858$		0			0
$859$	14.5234	−	8.38509i	0.495532	−	0.286096i	−0.231334	−	0.972874i	$-0.574309\pi$
$859$	14.5234	−	8.38509i	0.495532	−	0.286096i	0.726867	+	0.686779i	$0.240976\pi$
$860$	12.0751	−	20.9146i	0.411756	−	0.713183i
$861$		0			0
$862$	−0.360816	−	0.624951i	−0.0122894	−	0.0212859i
$863$	14.2380	+	8.22033i	0.484668	+	0.279823i	0.722360	−	0.691517i	$-0.243057\pi$
$863$	14.2380	+	8.22033i	0.484668	+	0.279823i	−0.237692	+	0.971341i	$0.576391\pi$
$864$		0			0
$865$	36.6109	+	63.4119i	1.24481	+	2.15607i
$866$	−3.66000			−0.124372
$867$		0			0
$868$	2.02089	−	1.28245i	0.0685935	−	0.0435291i
$869$	−31.3086	−	18.0760i	−1.06207	−	0.613188i
$870$		0			0
$871$	−3.19757	−	1.84612i	−0.108345	−	0.0625532i
$872$	1.21726	−	0.702787i	0.0412217	−	0.0237994i
$873$		0			0
$874$			2.23226i			0.0755074i
$875$	2.75373	+	4.33934i	0.0930929	+	0.146697i
$876$		0			0
$877$	−3.06175	−	5.30311i	−0.103388	−	0.179073i	0.809690	−	0.586857i	$-0.199635\pi$
$877$	−3.06175	−	5.30311i	−0.103388	−	0.179073i	−0.913078	+	0.407784i	$0.866302\pi$
$878$	−5.15154			−0.173856
$879$		0			0
$880$		−	41.6074i		−	1.40258i
$881$	−41.3283			−1.39238			−0.696192	−	0.717855i	$-0.745124\pi$
$881$	−41.3283			−1.39238			−0.696192	+	0.717855i	$0.745124\pi$
$882$		0			0
$883$	24.2918			0.817483			0.408741	−	0.912650i	$-0.365968\pi$
$883$	24.2918			0.817483			0.408741	+	0.912650i	$0.365968\pi$
$884$		−	15.0905i		−	0.507549i
$885$		0			0
$886$	2.64619			0.0889005
$887$	−3.35036	−	5.80299i	−0.112494	−	0.194845i	0.804281	−	0.594249i	$-0.202551\pi$
$887$	−3.35036	−	5.80299i	−0.112494	−	0.194845i	−0.916775	+	0.399404i	$0.869217\pi$
$888$		0			0
$889$	−3.89690	−	6.14077i	−0.130698	−	0.205955i
$890$			3.88234i			0.130136i
$891$		0			0
$892$	10.6624	−	6.15591i	0.357002	−	0.206115i
$893$	8.94675	+	5.16541i	0.299392	+	0.172854i
$894$		0			0
$895$	67.2823	+	38.8455i	2.24900	+	1.29846i
$896$	−18.7979	+	11.9290i	−0.627993	+	0.398521i
$897$		0			0
$898$	−9.05470			−0.302159
$899$	1.00232	+	1.73608i	0.0334294	+	0.0579014i
$900$		0			0
$901$	−16.8074	−	9.70376i	−0.559936	−	0.323279i
$902$	3.58101	+	6.20249i	0.119235	+	0.206520i
$903$		0			0
$904$	1.24622	−	2.15852i	0.0414487	−	0.0717912i
$905$	59.3747	−	34.2800i	1.97368	−	1.13951i
$906$		0			0
$907$	−10.1494	+	17.5793i	−0.337005	+	0.583710i	−0.983868	−	0.178897i	$-0.942747\pi$
$907$	−10.1494	+	17.5793i	−0.337005	+	0.583710i	0.646863	+	0.762606i	$0.276081\pi$
$908$	18.8873	−	32.7138i	0.626798	−	1.08565i
$909$		0			0
$910$	−2.98746	−	4.70766i	−0.0990332	−	0.156057i
$911$	30.3982	−	17.5504i	1.00714	−	0.581472i	0.0967861	−	0.995305i	$-0.469144\pi$
$911$	30.3982	−	17.5504i	1.00714	−	0.581472i	0.910353	+	0.413833i	$0.135810\pi$
$912$		0			0
$913$		−	42.8114i		−	1.41685i
$914$		−	4.06380i		−	0.134419i
$915$		0			0
$916$	18.0756	−	10.4359i	0.597233	−	0.344813i
$917$	9.16685	−	17.5338i	0.302716	−	0.579018i
$918$		0			0
$919$	−16.9132	+	29.2946i	−0.557916	+	0.966339i	0.439754	+	0.898118i	$0.355066\pi$
$919$	−16.9132	+	29.2946i	−0.557916	+	0.966339i	−0.997670	+	0.0682206i	$0.978268\pi$
$920$	5.24555	−	9.08557i	0.172941	−	0.299542i
$921$		0			0
$922$	−3.14046	+	1.81314i	−0.103425	+	0.0597127i
$923$	−15.9499	+	27.6260i	−0.524996	+	0.909320i
$924$		0			0
$925$	−16.9981	−	29.4415i	−0.558893	−	0.968031i
$926$	−3.24639	−	1.87431i	−0.106683	−	0.0615935i
$927$		0			0
$928$	−7.05115	−	12.2130i	−0.231465	−	0.400910i
$929$	−32.1171			−1.05373			−0.526864	−	0.849950i	$-0.676632\pi$
$929$	−32.1171			−1.05373			−0.526864	+	0.849950i	$0.676632\pi$
$930$		0			0
$931$	−14.6486	+	10.1803i	−0.480087	+	0.333644i
$932$	−34.4348	−	19.8810i	−1.12795	−	0.651222i
$933$		0			0
$934$	−2.79439	−	1.61334i	−0.0914351	−	0.0527901i
$935$	34.7520	−	20.0641i	1.13651	−	0.656166i
$936$		0			0
$937$			13.9224i			0.454824i	0.973799	+	0.227412i	$0.0730263\pi$
$937$			13.9224i			0.454824i	−0.973799	+	0.227412i	$0.926974\pi$
$938$	−1.03439	+	0.656416i	−0.0337739	+	0.0214327i
$939$		0			0
$940$	−11.8703	−	20.5599i	−0.387166	−	0.670590i
$941$	−57.2094			−1.86497			−0.932487	−	0.361203i	$-0.882366\pi$
$941$	−57.2094			−1.86497			−0.932487	+	0.361203i	$0.882366\pi$
$942$		0			0
$943$		−	18.6438i		−	0.607127i
$944$	16.3545			0.532294
$945$		0			0
$946$	4.72200			0.153525
$947$			34.4861i			1.12065i	0.828274	+	0.560324i	$0.189323\pi$
$947$			34.4861i			1.12065i	−0.828274	+	0.560324i	$0.810677\pi$
$948$		0			0
$949$	2.31739			0.0752255
$950$	1.63455	+	2.83113i	0.0530318	+	0.0918538i
$951$		0			0
$952$	−9.07469	−	4.74434i	−0.294112	−	0.153765i
$953$		−	2.58761i		−	0.0838209i	−0.999121	−	0.0419104i	$-0.986656\pi$
$953$		−	2.58761i		−	0.0838209i	0.999121	−	0.0419104i	$-0.0133444\pi$
$954$		0			0
$955$	−11.3669	+	6.56267i	−0.367824	+	0.212363i
$956$	−45.3034	−	26.1559i	−1.46522	−	0.845943i
$957$		0			0
$958$	−2.84900	−	1.64487i	−0.0920470	−	0.0531434i
$959$	−1.35208	−	32.2731i	−0.0436608	−	1.04215i
$960$		0			0
$961$	30.7765			0.992791
$962$	−2.68145	−	4.64441i	−0.0864535	−	0.149742i
$963$		0			0
$964$	−35.3426	−	20.4051i	−1.13831	−	0.657203i
$965$	35.7209	+	61.8704i	1.14990	+	1.99168i
$966$		0			0
$967$	2.79472	−	4.84059i	0.0898721	−	0.155663i	−0.817585	−	0.575808i	$-0.804688\pi$
$967$	2.79472	−	4.84059i	0.0898721	−	0.155663i	0.907457	+	0.420145i	$0.138021\pi$
$968$	4.16585	−	2.40515i	0.133895	−	0.0773045i
$969$		0			0
$970$	−2.58986	+	4.48578i	−0.0831555	+	0.144030i
$971$	−8.01661	+	13.8852i	−0.257265	+	0.445597i	−0.965508	−	0.260372i	$-0.916155\pi$
$971$	−8.01661	+	13.8852i	−0.257265	+	0.445597i	0.708243	+	0.705969i	$0.249488\pi$
$972$		0			0
$973$	1.47701	+	35.2551i	0.0473507	+	1.13023i
$974$	−0.755007	+	0.435904i	−0.0241920	+	0.0139673i
$975$		0			0
$976$		−	5.58353i		−	0.178724i
$977$			43.9026i			1.40457i	0.711896	+	0.702285i	$0.247837\pi$
$977$			43.9026i			1.40457i	−0.711896	+	0.702285i	$0.752163\pi$
$978$		0			0
$979$	14.5674	−	8.41048i	0.465576	−	0.268800i
$980$	40.8502	−	3.42884i	1.30491	−	0.109530i
$981$		0			0
$982$	3.42377	−	5.93015i	0.109257	−	0.189239i
$983$	9.08808	−	15.7410i	0.289865	−	0.502061i	−0.683912	−	0.729564i	$-0.739723\pi$
$983$	9.08808	−	15.7410i	0.289865	−	0.502061i	0.973777	+	0.227503i	$0.0730563\pi$
$984$		0			0
$985$	49.7749	−	28.7376i	1.58596	−	0.915655i
$986$	2.09683	−	3.63181i	0.0667766	−	0.115660i
$987$		0			0
$988$	−5.71374	−	9.89649i	−0.181778	−	0.314849i
$989$	−10.6453	−	6.14604i	−0.338499	−	0.195433i
$990$		0			0
$991$	−23.8146	−	41.2481i	−0.756496	−	1.31029i	−0.944627	−	0.328145i	$-0.893576\pi$
$991$	−23.8146	−	41.2481i	−0.756496	−	1.31029i	0.188131	−	0.982144i	$-0.439757\pi$
$992$	1.57213			0.0499151
$993$		0			0
$994$	5.67123	+	8.93677i	0.179880	+	0.283457i
$995$	12.0246	+	6.94242i	0.381206	+	0.220090i
$996$		0			0
$997$	28.4838	+	16.4451i	0.902090	+	0.520822i	0.877878	−	0.478885i	$-0.158959\pi$
$997$	28.4838	+	16.4451i	0.902090	+	0.520822i	0.0242120	+	0.999707i	$0.492292\pi$
$998$	1.16711	−	0.673830i	0.0369442	−	0.0213297i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.i.b.152.3		10
3.2	odd	2		63.2.i.b.5.3	✓	10
4.3	odd	2		3024.2.ca.b.2609.1		10
7.2	even	3		1323.2.o.c.881.3		10
7.3	odd	6		189.2.s.b.17.3		10
7.4	even	3		1323.2.s.b.962.3		10
7.5	odd	6		1323.2.o.d.881.3		10
7.6	odd	2		1323.2.i.b.1097.3		10
9.2	odd	6		189.2.s.b.89.3		10
9.4	even	3		567.2.p.c.404.3		10
9.5	odd	6		567.2.p.d.404.3		10
9.7	even	3		63.2.s.b.47.3	yes	10
12.11	even	2		1008.2.ca.b.257.4		10
21.2	odd	6		441.2.o.d.293.3		10
21.5	even	6		441.2.o.c.293.3		10
21.11	odd	6		441.2.s.b.374.3		10
21.17	even	6		63.2.s.b.59.3	yes	10
21.20	even	2		441.2.i.b.68.3		10
28.3	even	6		3024.2.df.b.17.1		10
36.7	odd	6		1008.2.df.b.929.5		10
36.11	even	6		3024.2.df.b.1601.1		10
63.2	odd	6		1323.2.o.d.440.3		10
63.11	odd	6		1323.2.i.b.521.3		10
63.16	even	3		441.2.o.c.146.3		10
63.20	even	6		1323.2.s.b.656.3		10
63.25	even	3		441.2.i.b.227.3		10
63.31	odd	6		567.2.p.d.80.3		10
63.34	odd	6		441.2.s.b.362.3		10
63.38	even	6	inner	189.2.i.b.143.3		10
63.47	even	6		1323.2.o.c.440.3		10
63.52	odd	6		63.2.i.b.38.3	yes	10
63.59	even	6		567.2.p.c.80.3		10
63.61	odd	6		441.2.o.d.146.3		10
84.59	odd	6		1008.2.df.b.689.5		10
252.115	even	6		1008.2.ca.b.353.4		10
252.227	odd	6		3024.2.ca.b.2033.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.i.b.5.3	✓	10	3.2	odd	2
63.2.i.b.38.3	yes	10	63.52	odd	6
63.2.s.b.47.3	yes	10	9.7	even	3
63.2.s.b.59.3	yes	10	21.17	even	6
189.2.i.b.143.3		10	63.38	even	6	inner
189.2.i.b.152.3		10	1.1	even	1	trivial
189.2.s.b.17.3		10	7.3	odd	6
189.2.s.b.89.3		10	9.2	odd	6
441.2.i.b.68.3		10	21.20	even	2
441.2.i.b.227.3		10	63.25	even	3
441.2.o.c.146.3		10	63.16	even	3
441.2.o.c.293.3		10	21.5	even	6
441.2.o.d.146.3		10	63.61	odd	6
441.2.o.d.293.3		10	21.2	odd	6
441.2.s.b.362.3		10	63.34	odd	6
441.2.s.b.374.3		10	21.11	odd	6
567.2.p.c.80.3		10	63.59	even	6
567.2.p.c.404.3		10	9.4	even	3
567.2.p.d.80.3		10	63.31	odd	6
567.2.p.d.404.3		10	9.5	odd	6
1008.2.ca.b.257.4		10	12.11	even	2
1008.2.ca.b.353.4		10	252.115	even	6
1008.2.df.b.689.5		10	84.59	odd	6
1008.2.df.b.929.5		10	36.7	odd	6
1323.2.i.b.521.3		10	63.11	odd	6
1323.2.i.b.1097.3		10	7.6	odd	2
1323.2.o.c.440.3		10	63.47	even	6
1323.2.o.c.881.3		10	7.2	even	3
1323.2.o.d.440.3		10	63.2	odd	6
1323.2.o.d.881.3		10	7.5	odd	6
1323.2.s.b.656.3		10	63.20	even	6
1323.2.s.b.962.3		10	7.4	even	3
3024.2.ca.b.2033.1		10	252.227	odd	6
3024.2.ca.b.2609.1		10	4.3	odd	2
3024.2.df.b.17.1		10	28.3	even	6
3024.2.df.b.1601.1		10	36.11	even	6

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-0.293869i q^{2} +1.91364 q^{4} +(-1.53014 - 2.65027i) q^{5} +(-1.41763 - 2.23391i) q^{7} -1.15010i q^{8} +O(q^{10})\)	\(q-0.293869i q^{2} +1.91364 q^{4} +(-1.53014 - 2.65027i) q^{5} +(-1.41763 - 2.23391i) q^{7} -1.15010i q^{8} +(-0.778834 + 0.449660i) q^{10} +(3.37445 + 1.94824i) q^{11} +(-2.02935 - 1.17164i) q^{13} +(-0.656477 + 0.416597i) q^{14} +3.48930 q^{16} +(1.68263 + 2.91440i) q^{17} +(2.20696 + 1.27419i) q^{19} +(-2.92813 - 5.07167i) q^{20} +(0.572527 - 0.991647i) q^{22} +(-2.58141 + 1.49038i) q^{23} +(-2.18263 + 3.78042i) q^{25} +(-0.344311 + 0.596363i) q^{26} +(-2.71283 - 4.27489i) q^{28} +(3.67241 - 2.12027i) q^{29} +0.472735i q^{31} -3.32560i q^{32} +(0.856452 - 0.494473i) q^{34} +(-3.75130 + 7.17527i) q^{35} +(-3.89395 + 6.74451i) q^{37} +(0.374446 - 0.648559i) q^{38} +(-3.04808 + 1.75981i) q^{40} +(-3.12737 + 5.41676i) q^{41} +(2.06191 + 3.57133i) q^{43} +(6.45748 + 3.72823i) q^{44} +(0.437976 + 0.758597i) q^{46} +4.05388 q^{47} +(-2.98068 + 6.33369i) q^{49} +(1.11095 + 0.641408i) q^{50} +(-3.88344 - 2.24211i) q^{52} +(-4.99439 + 2.88351i) q^{53} -11.9243i q^{55} +(-2.56921 + 1.63041i) q^{56} +(-0.623082 - 1.07921i) q^{58} +4.68705 q^{59} -1.60018i q^{61} +0.138922 q^{62} +6.00131 q^{64} +7.17110i q^{65} +1.57566 q^{67} +(3.21994 + 5.57711i) q^{68} +(2.10859 + 1.10239i) q^{70} -13.6132i q^{71} +(-0.856452 + 0.494473i) q^{73} +(1.98201 + 1.14431i) q^{74} +(4.22333 + 2.43834i) q^{76} +(-0.431520 - 10.3001i) q^{77} -9.27815 q^{79} +(-5.33910 - 9.24760i) q^{80} +(1.59182 + 0.919038i) q^{82} +(-5.49361 - 9.51520i) q^{83} +(5.14930 - 8.91884i) q^{85} +(1.04950 - 0.605932i) q^{86} +(2.24067 - 3.88095i) q^{88} +(2.15849 - 3.73861i) q^{89} +(0.259511 + 6.19433i) q^{91} +(-4.93989 + 2.85205i) q^{92} -1.19131i q^{94} -7.79874i q^{95} +(4.98797 - 2.87980i) q^{97} +(1.86128 + 0.875930i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 8 q^{4} - 6 q^{7}+O(q^{10}) \) 10 * q - 8 * q^4 - 6 * q^7	\( 10 q - 8 q^{4} - 6 q^{7} - 15 q^{10} + 12 q^{11} - 6 q^{13} - 12 q^{14} + 12 q^{16} - 12 q^{17} + 3 q^{19} - 3 q^{20} + 5 q^{22} + 15 q^{23} + 7 q^{25} + 3 q^{26} + 2 q^{28} + 15 q^{29} - 3 q^{34} - 15 q^{35} + 6 q^{37} - 18 q^{38} + 15 q^{40} - 9 q^{41} + 3 q^{43} + 24 q^{44} - 13 q^{46} - 30 q^{47} + 4 q^{49} - 3 q^{50} - 12 q^{52} - 9 q^{53} + 30 q^{56} + 8 q^{58} + 36 q^{59} + 12 q^{62} + 6 q^{64} + 20 q^{67} + 27 q^{68} + 6 q^{70} + 3 q^{73} + 30 q^{74} - 9 q^{76} - 39 q^{77} - 40 q^{79} - 30 q^{80} + 9 q^{82} - 15 q^{83} + 18 q^{85} - 54 q^{86} - 8 q^{88} + 24 q^{89} - 24 q^{91} - 39 q^{92} - 6 q^{97} + 45 q^{98}+O(q^{100}) \) 10 * q - 8 * q^4 - 6 * q^7 - 15 * q^10 + 12 * q^11 - 6 * q^13 - 12 * q^14 + 12 * q^16 - 12 * q^17 + 3 * q^19 - 3 * q^20 + 5 * q^22 + 15 * q^23 + 7 * q^25 + 3 * q^26 + 2 * q^28 + 15 * q^29 - 3 * q^34 - 15 * q^35 + 6 * q^37 - 18 * q^38 + 15 * q^40 - 9 * q^41 + 3 * q^43 + 24 * q^44 - 13 * q^46 - 30 * q^47 + 4 * q^49 - 3 * q^50 - 12 * q^52 - 9 * q^53 + 30 * q^56 + 8 * q^58 + 36 * q^59 + 12 * q^62 + 6 * q^64 + 20 * q^67 + 27 * q^68 + 6 * q^70 + 3 * q^73 + 30 * q^74 - 9 * q^76 - 39 * q^77 - 40 * q^79 - 30 * q^80 + 9 * q^82 - 15 * q^83 + 18 * q^85 - 54 * q^86 - 8 * q^88 + 24 * q^89 - 24 * q^91 - 39 * q^92 - 6 * q^97 + 45 * q^98

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