LMFDB - Embedded newform 1170.2.bj.a.829.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1170,2,Mod(199,1170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1170, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("1170.199");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.bj (of order $6$, degree $2$, 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:	$9.34249703649$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.50027374224.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 20x^{6} + 132x^{4} + 332x^{2} + 256 $ x^8 + 20x^6 + 132x^4 + 332*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			829.2
Root			$-1.17644i$ of defining polynomial
Character	$\chi$	$=$	1170.829
Dual form			1170.2.bj.a.199.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.235468 - 2.22364i) q^{5} +(1.04346 - 1.80732i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.235468 - 2.22364i) q^{5} +(1.04346 - 1.80732i) q^{7} +1.00000 q^{8} +(-2.04346 + 0.907896i) q^{10} +(-2.59135 + 1.49612i) q^{11} +(-1.51883 - 3.27004i) q^{13} -2.08692 q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.09135 + 0.630092i) q^{17} +(-3.37028 - 1.94583i) q^{19} +(1.80799 + 1.31574i) q^{20} +(2.59135 + 1.49612i) q^{22} +(0.778928 - 0.449714i) q^{23} +(-4.88911 - 1.04719i) q^{25} +(-2.07252 + 2.95036i) q^{26} +(1.04346 + 1.80732i) q^{28} +(0.235468 + 0.407843i) q^{29} -0.277015i q^{31} +(-0.500000 + 0.866025i) q^{32} -1.26018i q^{34} +(-3.77313 - 2.74584i) q^{35} +(-3.51883 - 6.09479i) q^{37} +3.89166i q^{38} +(0.235468 - 2.22364i) q^{40} +(-9.66804 + 5.58184i) q^{41} +(6.74056 + 3.89166i) q^{43} -2.99224i q^{44} +(-0.778928 - 0.449714i) q^{46} +11.3189 q^{47} +(1.32239 + 2.29044i) q^{49} +(1.53766 + 4.75769i) q^{50} +(3.59135 + 0.319674i) q^{52} -12.0148i q^{53} +(2.71664 + 6.11451i) q^{55} +(1.04346 - 1.80732i) q^{56} +(0.235468 - 0.407843i) q^{58} +(-10.7029 - 6.17932i) q^{59} +(-3.82102 + 6.61820i) q^{61} +(-0.239902 + 0.138508i) q^{62} +1.00000 q^{64} +(-7.62901 + 2.60733i) q^{65} +(2.00000 + 3.46410i) q^{67} +(-1.09135 + 0.630092i) q^{68} +(-0.491403 + 4.64054i) q^{70} +(-4.07532 - 2.35289i) q^{71} -15.2984 q^{73} +(-3.51883 + 6.09479i) q^{74} +(3.37028 - 1.94583i) q^{76} +6.24455i q^{77} -1.63645 q^{79} +(-2.04346 + 0.907896i) q^{80} +(9.66804 + 5.58184i) q^{82} -11.1943 q^{83} +(1.65807 - 2.27840i) q^{85} -7.78333i q^{86} +(-2.59135 + 1.49612i) q^{88} +(5.98533 - 3.45563i) q^{89} +(-7.49486 - 0.667134i) q^{91} +0.899428i q^{92} +(-5.65944 - 9.80244i) q^{94} +(-5.12041 + 7.03609i) q^{95} +(1.28916 - 2.23289i) q^{97} +(1.32239 - 2.29044i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 4 q^{4} + 3 q^{5} - 5 q^{7} + 8 q^{8}+O(q^{10}) $ 8 * q - 4 * q^2 - 4 * q^4 + 3 * q^5 - 5 * q^7 + 8 * q^8	$ 8 q - 4 q^{2} - 4 q^{4} + 3 q^{5} - 5 q^{7} + 8 q^{8} - 3 q^{10} + 3 q^{11} - 4 q^{13} + 10 q^{14} - 4 q^{16} - 15 q^{17} + 9 q^{19} - 3 q^{22} - 6 q^{23} + 5 q^{25} - q^{26} - 5 q^{28} + 3 q^{29} - 4 q^{32} - 15 q^{35} - 20 q^{37} + 3 q^{40} - 21 q^{41} - 18 q^{43} + 6 q^{46} + 6 q^{47} - 15 q^{49} - 4 q^{50} + 5 q^{52} + 31 q^{55} - 5 q^{56} + 3 q^{58} - 30 q^{59} - 5 q^{61} - 6 q^{62} + 8 q^{64} - 21 q^{65} + 16 q^{67} + 15 q^{68} - 18 q^{70} - 26 q^{73} - 20 q^{74} - 9 q^{76} + 4 q^{79} - 3 q^{80} + 21 q^{82} - 48 q^{83} - 29 q^{85} + 3 q^{88} + 39 q^{89} + 19 q^{91} - 3 q^{94} - 15 q^{95} + 4 q^{97} - 15 q^{98}+O(q^{100}) $ 8 * q - 4 * q^2 - 4 * q^4 + 3 * q^5 - 5 * q^7 + 8 * q^8 - 3 * q^10 + 3 * q^11 - 4 * q^13 + 10 * q^14 - 4 * q^16 - 15 * q^17 + 9 * q^19 - 3 * q^22 - 6 * q^23 + 5 * q^25 - q^26 - 5 * q^28 + 3 * q^29 - 4 * q^32 - 15 * q^35 - 20 * q^37 + 3 * q^40 - 21 * q^41 - 18 * q^43 + 6 * q^46 + 6 * q^47 - 15 * q^49 - 4 * q^50 + 5 * q^52 + 31 * q^55 - 5 * q^56 + 3 * q^58 - 30 * q^59 - 5 * q^61 - 6 * q^62 + 8 * q^64 - 21 * q^65 + 16 * q^67 + 15 * q^68 - 18 * q^70 - 26 * q^73 - 20 * q^74 - 9 * q^76 + 4 * q^79 - 3 * q^80 + 21 * q^82 - 48 * q^83 - 29 * q^85 + 3 * q^88 + 39 * q^89 + 19 * q^91 - 3 * q^94 - 15 * q^95 + 4 * q^97 - 15 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.235468	−	2.22364i	0.105305	−	0.994440i
$5$	0.235468	−	2.22364i	0.105305	−	0.994440i
$6$		0			0
$7$	1.04346	−	1.80732i	0.394390	−	0.683104i	−0.598633	−	0.801024i	$-0.704289\pi$
$7$	1.04346	−	1.80732i	0.394390	−	0.683104i	0.993023	+	0.117919i	$0.0376224\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	−2.04346	+	0.907896i	−0.646198	+	0.287102i
$11$	−2.59135	+	1.49612i	−0.781322	+	0.451096i	−0.836899	−	0.547358i	$-0.815634\pi$
$11$	−2.59135	+	1.49612i	−0.781322	+	0.451096i	0.0555766	+	0.998454i	$0.482300\pi$
$12$		0			0
$13$	−1.51883	−	3.27004i	−0.421248	−	0.906946i
$13$	−1.51883	−	3.27004i	−0.421248	−	0.906946i
$14$	−2.08692			−0.557752
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.09135	+	0.630092i	0.264692	+	0.152820i	0.626473	−	0.779443i	$-0.284498\pi$
$17$	1.09135	+	0.630092i	0.264692	+	0.152820i	−0.361781	+	0.932263i	$0.617831\pi$
$18$		0			0
$19$	−3.37028	−	1.94583i	−0.773195	−	0.446404i	0.0608181	−	0.998149i	$-0.480629\pi$
$19$	−3.37028	−	1.94583i	−0.773195	−	0.446404i	−0.834013	+	0.551744i	$0.813962\pi$
$20$	1.80799	+	1.31574i	0.404279	+	0.294208i
$21$		0			0
$22$	2.59135	+	1.49612i	0.552478	+	0.318973i
$23$	0.778928	−	0.449714i	0.162418	−	0.0937719i	−0.416588	−	0.909095i	$-0.636774\pi$
$23$	0.778928	−	0.449714i	0.162418	−	0.0937719i	0.579006	+	0.815324i	$0.303441\pi$
$24$		0			0
$25$	−4.88911	−	1.04719i	−0.977822	−	0.209438i
$26$	−2.07252	+	2.95036i	−0.406455	+	0.578614i
$27$		0			0
$28$	1.04346	+	1.80732i	0.197195	+	0.341552i
$29$	0.235468	+	0.407843i	0.0437254	+	0.0757346i	0.887060	−	0.461654i	$-0.152744\pi$
$29$	0.235468	+	0.407843i	0.0437254	+	0.0757346i	−0.843334	+	0.537389i	$0.819411\pi$
$30$		0			0
$31$		−	0.277015i		−	0.0497534i	−0.999691	−	0.0248767i	$-0.992081\pi$
$31$		−	0.277015i		−	0.0497534i	0.999691	−	0.0248767i	$-0.00791932\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$		−	1.26018i		−	0.216120i
$35$	−3.77313	−	2.74584i	−0.637775	−	0.464132i
$36$		0			0
$37$	−3.51883	−	6.09479i	−0.578492	−	1.00198i	−0.995653	−	0.0931448i	$-0.970308\pi$
$37$	−3.51883	−	6.09479i	−0.578492	−	1.00198i	0.417161	−	0.908833i	$-0.363025\pi$
$38$			3.89166i			0.631311i
$39$		0			0
$40$	0.235468	−	2.22364i	0.0372308	−	0.351588i
$41$	−9.66804	+	5.58184i	−1.50989	+	0.871738i	−0.509960	+	0.860198i	$0.670340\pi$
$41$	−9.66804	+	5.58184i	−1.50989	+	0.871738i	−0.999933	+	0.0115395i	$0.996327\pi$
$42$		0			0
$43$	6.74056	+	3.89166i	1.02793	+	0.593473i	0.916390	−	0.400287i	$-0.131090\pi$
$43$	6.74056	+	3.89166i	1.02793	+	0.593473i	0.111536	+	0.993760i	$0.464423\pi$
$44$		−	2.99224i		−	0.451096i
$45$		0			0
$46$	−0.778928	−	0.449714i	−0.114847	−	0.0663067i
$47$	11.3189			1.65103			0.825514	−	0.564381i	$-0.190885\pi$
$47$	11.3189			1.65103			0.825514	+	0.564381i	$0.190885\pi$
$48$		0			0
$49$	1.32239	+	2.29044i	0.188912	+	0.327206i
$50$	1.53766	+	4.75769i	0.217458	+	0.672839i
$51$		0			0
$52$	3.59135	+	0.319674i	0.498031	+	0.0443309i
$53$		−	12.0148i		−	1.65036i	−0.564868	−	0.825181i	$-0.691073\pi$
$53$		−	12.0148i		−	1.65036i	0.564868	−	0.825181i	$-0.308927\pi$
$54$		0			0
$55$	2.71664	+	6.11451i	0.366311	+	0.824480i
$56$	1.04346	−	1.80732i	0.139438	−	0.241514i
$57$		0			0
$58$	0.235468	−	0.407843i	0.0309185	−	0.0535525i
$59$	−10.7029	−	6.17932i	−1.39340	−	0.804479i	−0.399709	−	0.916642i	$-0.630889\pi$
$59$	−10.7029	−	6.17932i	−1.39340	−	0.804479i	−0.993690	+	0.112163i	$0.964222\pi$
$60$		0			0
$61$	−3.82102	+	6.61820i	−0.489232	+	0.847374i	−0.999923	−	0.0123900i	$-0.996056\pi$
$61$	−3.82102	+	6.61820i	−0.489232	+	0.847374i	0.510692	+	0.859764i	$0.329389\pi$
$62$	−0.239902	+	0.138508i	−0.0304676	+	0.0175905i
$63$		0			0
$64$	1.00000			0.125000
$65$	−7.62901	+	2.60733i	−0.946262	+	0.323400i
$66$		0			0
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	0.961946	−	0.273241i	$-0.0880957\pi$
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	−0.717607	+	0.696449i	$0.754762\pi$
$68$	−1.09135	+	0.630092i	−0.132346	+	0.0764099i
$69$		0			0
$70$	−0.491403	+	4.64054i	−0.0587339	+	0.554651i
$71$	−4.07532	−	2.35289i	−0.483651	−	0.279236i	0.238286	−	0.971195i	$-0.423415\pi$
$71$	−4.07532	−	2.35289i	−0.483651	−	0.279236i	−0.721937	+	0.691959i	$0.756748\pi$
$72$		0			0
$73$	−15.2984			−1.79054			−0.895272	−	0.445520i	$-0.853019\pi$
$73$	−15.2984			−1.79054			−0.895272	+	0.445520i	$0.853019\pi$
$74$	−3.51883	+	6.09479i	−0.409056	+	0.708505i
$75$		0			0
$76$	3.37028	−	1.94583i	0.386598	−	0.223202i
$77$			6.24455i			0.711633i
$78$		0			0
$79$	−1.63645			−0.184115			−0.0920574	−	0.995754i	$-0.529344\pi$
$79$	−1.63645			−0.184115			−0.0920574	+	0.995754i	$0.529344\pi$
$80$	−2.04346	+	0.907896i	−0.228466	+	0.101506i
$81$		0			0
$82$	9.66804	+	5.58184i	1.06766	+	0.616412i
$83$	−11.1943			−1.22873			−0.614367	−	0.789020i	$-0.710589\pi$
$83$	−11.1943			−1.22873			−0.614367	+	0.789020i	$0.710589\pi$
$84$		0			0
$85$	1.65807	−	2.27840i	0.179843	−	0.247127i
$86$		−	7.78333i		−	0.839298i
$87$		0			0
$88$	−2.59135	+	1.49612i	−0.276239	+	0.159487i
$89$	5.98533	−	3.45563i	0.634444	−	0.366296i	−0.148027	−	0.988983i	$-0.547292\pi$
$89$	5.98533	−	3.45563i	0.634444	−	0.366296i	0.782471	+	0.622687i	$0.213959\pi$
$90$		0			0
$91$	−7.49486	−	0.667134i	−0.785674	−	0.0699347i
$92$			0.899428i			0.0937719i
$93$		0			0
$94$	−5.65944	−	9.80244i	−0.583727	−	1.01104i
$95$	−5.12041	+	7.03609i	−0.525343	+	0.721888i
$96$		0			0
$97$	1.28916	−	2.23289i	0.130894	−	0.226716i	−0.793127	−	0.609056i	$-0.791548\pi$
$97$	1.28916	−	2.23289i	0.130894	−	0.226716i	0.924022	+	0.382340i	$0.124882\pi$
$98$	1.32239	−	2.29044i	0.133581	−	0.231369i
$99$		0			0
$100$	3.35145	−	3.71050i	0.335145	−	0.371050i
$101$	0.783361	+	1.35682i	0.0779474	+	0.135009i	0.902364	−	0.430974i	$-0.141830\pi$
$101$	0.783361	+	1.35682i	0.0779474	+	0.135009i	−0.824417	+	0.565983i	$0.808497\pi$
$102$		0			0
$103$		−	0.916364i		−	0.0902920i	−0.998980	−	0.0451460i	$-0.985625\pi$
$103$		−	0.916364i		−	0.0902920i	0.998980	−	0.0451460i	$-0.0143753\pi$
$104$	−1.51883	−	3.27004i	−0.148934	−	0.320654i
$105$		0			0
$106$	−10.4051	+	6.00741i	−1.01064	+	0.583491i
$107$	−10.1345	+	5.85118i	−0.979743	+	0.565655i	−0.902193	−	0.431334i	$-0.858043\pi$
$107$	−10.1345	+	5.85118i	−0.979743	+	0.565655i	−0.0775504	+	0.996988i	$0.524710\pi$
$108$		0			0
$109$		−	15.9902i		−	1.53159i	−0.643087	−	0.765793i	$-0.722347\pi$
$109$		−	15.9902i		−	1.53159i	0.643087	−	0.765793i	$-0.277653\pi$
$110$	3.93700	−	5.40993i	0.375378	−	0.515817i
$111$		0			0
$112$	−2.08692			−0.197195
$113$	−2.40930	−	1.39101i	−0.226648	−	0.130855i	0.382377	−	0.924007i	$-0.375106\pi$
$113$	−2.40930	−	1.39101i	−0.226648	−	0.130855i	−0.609025	+	0.793151i	$0.708439\pi$
$114$		0			0
$115$	−0.816587	−	1.83794i	−0.0761471	−	0.171389i
$116$	−0.470937			−0.0437254
$117$		0			0
$118$			12.3586i			1.13771i
$119$	2.27756	−	1.31495i	0.208784	−	0.120541i
$120$		0			0
$121$	−1.02326	+	1.77234i	−0.0930240	+	0.161122i
$122$	7.64204			0.691878
$123$		0			0
$124$	0.239902	+	0.138508i	0.0215439	+	0.0124384i
$125$	−3.47980	+	10.6250i	−0.311243	+	0.950330i
$126$		0			0
$127$	−7.53415	+	4.34985i	−0.668548	+	0.385986i	−0.795526	−	0.605919i	$-0.792805\pi$
$127$	−7.53415	+	4.34985i	−0.668548	+	0.385986i	0.126978	+	0.991906i	$0.459472\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	6.07252	+	5.30325i	0.532595	+	0.465126i
$131$	15.8740			1.38692			0.693459	−	0.720496i	$-0.256086\pi$
$131$	15.8740			1.38692			0.693459	+	0.720496i	$0.256086\pi$
$132$		0			0
$133$	−7.03350	+	4.06079i	−0.609882	+	0.352115i
$134$	2.00000	−	3.46410i	0.172774	−	0.299253i
$135$		0			0
$136$	1.09135	+	0.630092i	0.0935827	+	0.0540300i
$137$	3.61155	−	6.25538i	0.308555	−	0.534433i	−0.669491	−	0.742820i	$-0.733488\pi$
$137$	3.61155	−	6.25538i	0.308555	−	0.534433i	0.978047	+	0.208386i	$0.0668212\pi$
$138$		0			0
$139$	9.93700	−	17.2114i	0.842846	−	1.45985i	−0.0446337	−	0.999003i	$-0.514212\pi$
$139$	9.93700	−	17.2114i	0.842846	−	1.45985i	0.887479	−	0.460848i	$-0.152455\pi$
$140$	4.26453	−	1.89470i	0.360419	−	0.160132i
$141$		0			0
$142$			4.70577i			0.394900i
$143$	8.82819	+	6.20147i	0.738250	+	0.518593i
$144$		0			0
$145$	0.962340	−	0.427562i	0.0799180	−	0.0355071i
$146$	7.64921	+	13.2488i	0.633053	+	1.09648i
$147$		0			0
$148$	7.03766			0.578492
$149$	0.851450	+	0.491585i	0.0697535	+	0.0402722i	0.534471	−	0.845187i	$-0.320511\pi$
$149$	0.851450	+	0.491585i	0.0697535	+	0.0402722i	−0.464718	+	0.885459i	$0.653844\pi$
$150$		0			0
$151$			8.06034i			0.655941i	0.944688	+	0.327971i	$0.106365\pi$
$151$			8.06034i			0.655941i	−0.944688	+	0.327971i	$0.893635\pi$
$152$	−3.37028	−	1.94583i	−0.273366	−	0.157828i
$153$		0			0
$154$	5.40794	−	3.12228i	0.435784	−	0.251600i
$155$	−0.615981	−	0.0652284i	−0.0494768	−	0.00523927i
$156$		0			0
$157$		−	2.73373i		−	0.218176i	−0.994032	−	0.109088i	$-0.965207\pi$
$157$		−	2.73373i		−	0.218176i	0.994032	−	0.109088i	$-0.0347930\pi$
$158$	0.818224	+	1.41721i	0.0650944	+	0.112747i
$159$		0			0
$160$	1.80799	+	1.31574i	0.142934	+	0.104018i
$161$		−	1.87703i		−	0.147931i
$162$		0			0
$163$	12.2885	−	21.2842i	0.962506	−	1.66711i	0.246334	−	0.969185i	$-0.420774\pi$
$163$	12.2885	−	21.2842i	0.962506	−	1.66711i	0.716172	−	0.697924i	$-0.245893\pi$
$164$		−	11.1637i		−	0.871738i
$165$		0			0
$166$	5.59715	+	9.69455i	0.434423	+	0.752443i
$167$	6.91817	+	11.9826i	0.535344	+	0.927243i	0.999147	+	0.0413047i	$0.0131514\pi$
$167$	6.91817	+	11.9826i	0.535344	+	0.927243i	−0.463802	+	0.885939i	$0.653515\pi$
$168$		0			0
$169$	−8.38631	+	9.93327i	−0.645101	+	0.764097i
$170$	−2.80219	−	0.296734i	−0.214918	−	0.0227584i
$171$		0			0
$172$	−6.74056	+	3.89166i	−0.513963	+	0.296737i
$173$	11.4079	+	6.58638i	0.867330	+	0.500753i	0.866460	−	0.499247i	$-0.166390\pi$
$173$	11.4079	+	6.58638i	0.867330	+	0.500753i	0.000869643		1.00000i	$0.499723\pi$
$174$		0			0
$175$	−6.99420	+	7.74350i	−0.528712	+	0.585354i
$176$	2.59135	+	1.49612i	0.195330	+	0.112774i
$177$		0			0
$178$	−5.98533	−	3.45563i	−0.448620	−	0.259011i
$179$	1.55786	+	2.69828i	0.116440	+	0.201679i	0.918354	−	0.395759i	$-0.129519\pi$
$179$	1.55786	+	2.69828i	0.116440	+	0.201679i	−0.801915	+	0.597438i	$0.796185\pi$
$180$		0			0
$181$	7.91439			0.588272			0.294136	−	0.955764i	$-0.404968\pi$
$181$	7.91439			0.588272			0.294136	+	0.955764i	$0.404968\pi$
$182$	3.16967	+	6.82430i	0.234952	+	0.505851i
$183$		0			0
$184$	0.778928	−	0.449714i	0.0574233	−	0.0331534i
$185$	−14.3812	+	6.38946i	−1.05732	+	0.469763i
$186$		0			0
$187$	−3.77077			−0.275746
$188$	−5.65944	+	9.80244i	−0.412757	+	0.714916i
$189$		0			0
$190$	8.65364	+	0.916364i	0.627801	+	0.0664800i
$191$	6.98046	−	12.0905i	0.505088	−	0.874839i	−0.494894	−	0.868953i	$-0.664793\pi$
$191$	6.98046	−	12.0905i	0.505088	−	0.874839i	0.999983	−	0.00588562i	$-0.00187346\pi$
$192$		0			0
$193$	6.81379	+	11.8018i	0.490467	+	0.849514i	0.999940	−	0.0109726i	$-0.00349276\pi$
$193$	6.81379	+	11.8018i	0.490467	+	0.849514i	−0.509472	+	0.860487i	$0.670159\pi$
$194$	−2.57832			−0.185113
$195$		0			0
$196$	−2.64477			−0.188912
$197$	−8.86097	−	15.3477i	−0.631318	−	1.09348i	−0.987282	−	0.158976i	$-0.949181\pi$
$197$	−8.86097	−	15.3477i	−0.631318	−	1.09348i	0.355964	−	0.934500i	$-0.384152\pi$
$198$		0			0
$199$	7.18270	−	12.4408i	0.509168	−	0.881905i	−0.490775	−	0.871286i	$-0.663286\pi$
$199$	7.18270	−	12.4408i	0.509168	−	0.881905i	0.999944	−	0.0106193i	$-0.00338028\pi$
$200$	−4.88911	−	1.04719i	−0.345712	−	0.0740477i
$201$		0			0
$202$	0.783361	−	1.35682i	0.0551171	−	0.0954656i
$203$	0.982807			0.0689795
$204$		0			0
$205$	10.1355	+	22.8125i	0.707892	+	1.59330i
$206$	−0.793595	+	0.458182i	−0.0552924	+	0.0319231i
$207$		0			0
$208$	−2.07252	+	2.95036i	−0.143704	+	0.204571i
$209$	11.6448			0.805486
$210$		0			0
$211$	10.1115	+	17.5137i	0.696108	+	1.20569i	0.969806	+	0.243878i	$0.0784197\pi$
$211$	10.1115	+	17.5137i	0.696108	+	1.20569i	−0.273698	+	0.961816i	$0.588247\pi$
$212$	10.4051	+	6.00741i	0.714628	+	0.412591i
$213$		0			0
$214$	10.1345	+	5.85118i	0.692783	+	0.399978i
$215$	10.2408	−	14.0722i	0.698419	−	0.959715i
$216$		0			0
$217$	−0.500656	−	0.289054i	−0.0339868	−	0.0196223i
$218$	−13.8479	+	7.99511i	−0.937901	+	0.541497i
$219$		0			0
$220$	−6.65364	−	0.704577i	−0.448588	−	0.0475026i
$221$	0.402849	−	4.52577i	0.0270985	−	0.304436i
$222$		0			0
$223$	−5.57252	−	9.65189i	−0.373164	−	0.646338i	0.616887	−	0.787052i	$-0.288394\pi$
$223$	−5.57252	−	9.65189i	−0.373164	−	0.646338i	−0.990050	+	0.140714i	$0.955060\pi$
$224$	1.04346	+	1.80732i	0.0697190	+	0.120757i
$225$		0			0
$226$			2.78203i			0.185058i
$227$	8.65364	−	14.9885i	0.574362	−	0.994825i	−0.421748	−	0.906713i	$-0.638583\pi$
$227$	8.65364	−	14.9885i	0.574362	−	0.994825i	0.996111	−	0.0881117i	$-0.0280833\pi$
$228$		0			0
$229$		−	9.90350i		−	0.654442i	−0.944948	−	0.327221i	$-0.893888\pi$
$229$		−	9.90350i		−	0.654442i	0.944948	−	0.327221i	$-0.106112\pi$
$230$	−1.18341	+	1.62616i	−0.0780319	+	0.107226i
$231$		0			0
$232$	0.235468	+	0.407843i	0.0154593	+	0.0267762i
$233$		−	19.1742i		−	1.25614i	−0.778156	−	0.628070i	$-0.783845\pi$
$233$		−	19.1742i		−	1.25614i	0.778156	−	0.628070i	$-0.216155\pi$
$234$		0			0
$235$	2.66524	−	25.1691i	0.173861	−	1.64185i
$236$	10.7029	−	6.17932i	0.696699	−	0.402240i
$237$		0			0
$238$	−2.27756	−	1.31495i	−0.147632	−	0.0852356i
$239$			2.16448i			0.140009i	0.997547	+	0.0700043i	$0.0223013\pi$
$239$			2.16448i			0.140009i	−0.997547	+	0.0700043i	$0.977699\pi$
$240$		0			0
$241$	−13.9442	−	8.05067i	−0.898223	−	0.518589i	−0.0215996	−	0.999767i	$-0.506876\pi$
$241$	−13.9442	−	8.05067i	−0.898223	−	0.518589i	−0.876623	+	0.481178i	$0.840209\pi$
$242$	2.04653			0.131556
$243$		0			0
$244$	−3.82102	−	6.61820i	−0.244616	−	0.423687i
$245$	5.40449	−	2.40118i	0.345280	−	0.153406i
$246$		0			0
$247$	−1.24407	+	13.9763i	−0.0791580	+	0.889293i
$248$		−	0.277015i		−	0.0175905i
$249$		0			0
$250$	10.9414	−	2.29891i	0.691997	−	0.145396i
$251$	−9.04439	+	15.6653i	−0.570877	+	0.988787i	0.425600	+	0.904912i	$0.360063\pi$
$251$	−9.04439	+	15.6653i	−0.570877	+	0.988787i	−0.996476	+	0.0838757i	$0.973270\pi$
$252$		0			0
$253$	−1.34565	+	2.33073i	−0.0846003	+	0.146532i
$254$	7.53415	+	4.34985i	0.472735	+	0.272934i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−8.69939	+	5.02260i	−0.542653	+	0.313301i	−0.746154	−	0.665774i	$-0.768102\pi$
$257$	−8.69939	+	5.02260i	−0.542653	+	0.313301i	0.203500	+	0.979075i	$0.434768\pi$
$258$		0			0
$259$	−14.6870			−0.912607
$260$	1.55649	−	7.91058i	0.0965294	−	0.490594i
$261$		0			0
$262$	−7.93700	−	13.7473i	−0.490350	−	0.849310i
$263$	13.6855	−	7.90133i	0.843884	−	0.487217i	−0.0146985	−	0.999892i	$-0.504679\pi$
$263$	13.6855	−	7.90133i	0.843884	−	0.487217i	0.858583	+	0.512675i	$0.171346\pi$
$264$		0			0
$265$	−26.7166	−	2.82911i	−1.64119	−	0.173791i
$266$	7.03350	+	4.06079i	0.431251	+	0.248983i
$267$		0			0
$268$	−4.00000			−0.244339
$269$	3.69294	−	6.39635i	0.225162	−	0.389993i	−0.731206	−	0.682157i	$-0.761042\pi$
$269$	3.69294	−	6.39635i	0.225162	−	0.389993i	0.956368	+	0.292164i	$0.0943754\pi$
$270$		0			0
$271$	26.8493	−	15.5014i	1.63098	−	0.941645i	0.647184	−	0.762334i	$-0.275947\pi$
$271$	26.8493	−	15.5014i	1.63098	−	0.941645i	0.983793	−	0.179310i	$-0.0573866\pi$
$272$		−	1.26018i		−	0.0764099i
$273$		0			0
$274$	−7.22309			−0.436363
$275$	14.2361	−	4.60104i	0.858471	−	0.277453i
$276$		0			0
$277$	4.07668	+	2.35368i	0.244944	+	0.141419i	0.617447	−	0.786612i	$-0.288167\pi$
$277$	4.07668	+	2.35368i	0.244944	+	0.141419i	−0.372503	+	0.928031i	$0.621500\pi$
$278$	−19.8740			−1.19196
$279$		0			0
$280$	−3.77313	−	2.74584i	−0.225488	−	0.164095i
$281$			10.7771i			0.642910i	0.946925	+	0.321455i	$0.104172\pi$
$281$			10.7771i			0.642910i	−0.946925	+	0.321455i	$0.895828\pi$
$282$		0			0
$283$	25.2204	−	14.5610i	1.49919	−	0.865561i	0.499195	−	0.866489i	$-0.333629\pi$
$283$	25.2204	−	14.5610i	1.49919	−	0.865561i	1.00000		0.000928800i	$0.000295646\pi$
$284$	4.07532	−	2.35289i	0.241826	−	0.139618i
$285$		0			0
$286$	0.956541	−	10.7462i	0.0565615	−	0.635434i
$287$			23.2977i			1.37522i
$288$		0			0
$289$	−7.70597	−	13.3471i	−0.453292	−	0.785125i
$290$	−0.851450	−	0.619630i	−0.0499988	−	0.0363859i
$291$		0			0
$292$	7.64921	−	13.2488i	0.447636	−	0.775328i
$293$	12.7124	−	22.0186i	0.742668	−	1.28634i	−0.208609	−	0.977999i	$-0.566894\pi$
$293$	12.7124	−	22.0186i	0.742668	−	1.28634i	0.951277	−	0.308339i	$-0.0997731\pi$
$294$		0			0
$295$	−16.2608	+	22.3443i	−0.946738	+	1.30094i
$296$	−3.51883	−	6.09479i	−0.204528	−	0.354253i
$297$		0			0
$298$		−	0.983169i		−	0.0569535i
$299$	−2.65364	−	1.86408i	−0.153464	−	0.107803i
$300$		0			0
$301$	14.0670	−	8.12158i	0.810808	−	0.468120i
$302$	6.98046	−	4.03017i	0.401680	−	0.231910i
$303$		0			0
$304$			3.89166i			0.223202i
$305$	13.8167	+	10.0549i	0.791144	+	0.575744i
$306$		0			0
$307$	25.3305			1.44569			0.722843	−	0.691012i	$-0.242835\pi$
$307$	25.3305			1.44569			0.722843	+	0.691012i	$0.242835\pi$
$308$	−5.40794	−	3.12228i	−0.308146	−	0.177908i
$309$		0			0
$310$	0.251501	+	0.566069i	0.0142843	+	0.0321506i
$311$	24.3495			1.38074			0.690368	−	0.723459i	$-0.257449\pi$
$311$	24.3495			1.38074			0.690368	+	0.723459i	$0.257449\pi$
$312$		0			0
$313$			15.6891i			0.886802i	0.896323	+	0.443401i	$0.146228\pi$
$313$			15.6891i			0.886802i	−0.896323	+	0.443401i	$0.853772\pi$
$314$	−2.36748	+	1.36687i	−0.133605	+	0.0771367i
$315$		0			0
$316$	0.818224	−	1.41721i	0.0460287	−	0.0797240i
$317$	−19.4607			−1.09302			−0.546510	−	0.837453i	$-0.684044\pi$
$317$	−19.4607			−1.09302			−0.546510	+	0.837453i	$0.684044\pi$
$318$		0			0
$319$	−1.22036	−	0.704577i	−0.0683272	−	0.0394487i
$320$	0.235468	−	2.22364i	0.0131631	−	0.124305i
$321$		0			0
$322$	−1.62556	+	0.938516i	−0.0905888	+	0.0523015i
$323$	−2.45211	−	4.24717i	−0.136439	−	0.236319i
$324$		0			0
$325$	4.00137	+	17.5781i	0.221956	+	0.975057i
$326$	−24.5769			−1.36119
$327$		0			0
$328$	−9.66804	+	5.58184i	−0.533828	+	0.308206i
$329$	11.8108	−	20.4569i	0.651150	−	1.12782i
$330$		0			0
$331$	5.73925	+	3.31356i	0.315457	+	0.182129i	0.649366	−	0.760476i	$-0.275034\pi$
$331$	5.73925	+	3.31356i	0.315457	+	0.182129i	−0.333909	+	0.942605i	$0.608368\pi$
$332$	5.59715	−	9.69455i	0.307184	−	0.532058i
$333$		0			0
$334$	6.91817	−	11.9826i	0.378546	−	0.655660i
$335$	8.17384	−	3.63158i	0.446584	−	0.198415i
$336$		0			0
$337$		−	11.0614i		−	0.602555i	−0.953537	−	0.301277i	$-0.902587\pi$
$337$		−	11.0614i		−	0.602555i	0.953537	−	0.301277i	$-0.0974130\pi$
$338$	12.7956	+	2.29613i	0.695990	+	0.124893i
$339$		0			0
$340$	1.14412	+	2.57514i	0.0620484	+	0.139656i
$341$	0.414448	+	0.717844i	0.0224436	+	0.0388734i
$342$		0			0
$343$	20.1279			1.08680
$344$	6.74056	+	3.89166i	0.363427	+	0.209824i
$345$		0			0
$346$		−	13.1728i		−	0.708172i
$347$	−15.3466	−	8.86035i	−0.823847	−	0.475649i	0.0278940	−	0.999611i	$-0.491120\pi$
$347$	−15.3466	−	8.86035i	−0.823847	−	0.475649i	−0.851741	+	0.523962i	$0.824453\pi$
$348$		0			0
$349$	15.3172	−	8.84341i	0.819913	−	0.473377i	−0.0304733	−	0.999536i	$-0.509701\pi$
$349$	15.3172	−	8.84341i	0.819913	−	0.473377i	0.850387	+	0.526158i	$0.176368\pi$
$350$	10.2032	+	2.18540i	0.545382	+	0.116815i
$351$		0			0
$352$		−	2.99224i		−	0.159487i
$353$	16.8114	+	29.1183i	0.894783	+	1.54981i	0.834073	+	0.551654i	$0.186003\pi$
$353$	16.8114	+	29.1183i	0.894783	+	1.54981i	0.0607098	+	0.998155i	$0.480664\pi$
$354$		0			0
$355$	−6.19157	+	8.50799i	−0.328614	+	0.451557i
$356$			6.91127i			0.366296i
$357$		0			0
$358$	1.55786	−	2.69828i	0.0823352	−	0.142609i
$359$		−	17.4880i		−	0.922981i	−0.887145	−	0.461490i	$-0.847315\pi$
$359$		−	17.4880i		−	0.922981i	0.887145	−	0.461490i	$-0.152685\pi$
$360$		0			0
$361$	−1.92748	−	3.33849i	−0.101446	−	0.175710i
$362$	−3.95720	−	6.85407i	−0.207986	−	0.360242i
$363$		0			0
$364$	4.32518	−	6.15717i	0.226701	−	0.322723i
$365$	−3.60229	+	34.0181i	−0.188553	+	1.78059i
$366$		0			0
$367$	6.37373	−	3.67988i	0.332706	−	0.192088i	−0.324336	−	0.945942i	$-0.605141\pi$
$367$	6.37373	−	3.67988i	0.332706	−	0.192088i	0.657042	+	0.753854i	$0.271807\pi$
$368$	−0.778928	−	0.449714i	−0.0406044	−	0.0234430i
$369$		0			0
$370$	12.7240	+	9.25973i	0.661490	+	0.481390i
$371$	−21.7147	−	12.5370i	−1.12737	−	0.650887i
$372$		0			0
$373$	−25.2893	−	14.6008i	−1.30943	−	0.756000i	−0.327430	−	0.944875i	$-0.606183\pi$
$373$	−25.2893	−	14.6008i	−1.30943	−	0.756000i	−0.982001	+	0.188875i	$0.939516\pi$
$374$	1.88538	+	3.26558i	0.0974909	+	0.168859i
$375$		0			0
$376$	11.3189			0.583727
$377$	0.976027	−	1.38944i	0.0502680	−	0.0715596i
$378$		0			0
$379$	−13.2943	+	7.67544i	−0.682880	+	0.394261i	−0.800939	−	0.598746i	$-0.795666\pi$
$379$	−13.2943	+	7.67544i	−0.682880	+	0.394261i	0.118059	+	0.993007i	$0.462333\pi$
$380$	−3.53323	−	7.95245i	−0.181251	−	0.407952i
$381$		0			0
$382$	−13.9609			−0.714303
$383$	−1.59622	+	2.76474i	−0.0815632	+	0.141272i	−0.903922	−	0.427698i	$-0.859325\pi$
$383$	−1.59622	+	2.76474i	−0.0815632	+	0.141272i	0.822358	+	0.568970i	$0.192658\pi$
$384$		0			0
$385$	13.8856	+	1.47039i	0.707676	+	0.0749383i
$386$	6.81379	−	11.8018i	0.346813	−	0.600697i
$387$		0			0
$388$	1.28916	+	2.23289i	0.0654472	+	0.113358i
$389$	−28.9316			−1.46689			−0.733445	−	0.679749i	$-0.762089\pi$
$389$	−28.9316			−1.46689			−0.733445	+	0.679749i	$0.762089\pi$
$390$		0			0
$391$	1.13345			0.0573208
$392$	1.32239	+	2.29044i	0.0667906	+	0.115685i
$393$		0			0
$394$	−8.86097	+	15.3477i	−0.446409	+	0.773204i
$395$	−0.385332	+	3.63886i	−0.0193881	+	0.183091i
$396$		0			0
$397$	−2.49557	+	4.32245i	−0.125249	+	0.216937i	−0.921830	−	0.387594i	$-0.873306\pi$
$397$	−2.49557	+	4.32245i	−0.125249	+	0.216937i	0.796581	+	0.604531i	$0.206640\pi$
$398$	−14.3654			−0.720073
$399$		0			0
$400$	1.53766	+	4.75769i	0.0768830	+	0.237884i
$401$	−3.46032	+	1.99782i	−0.172800	+	0.0997662i	−0.583905	−	0.811822i	$-0.698476\pi$
$401$	−3.46032	+	1.99782i	−0.172800	+	0.0997662i	0.411105	+	0.911588i	$0.365143\pi$
$402$		0			0
$403$	−0.905851	+	0.420739i	−0.0451236	+	0.0209585i
$404$	−1.56672			−0.0779474
$405$		0			0
$406$	−0.491403	−	0.851136i	−0.0243879	−	0.0422412i
$407$	18.2371	+	10.5292i	0.903977	+	0.521911i
$408$		0			0
$409$	2.53695	+	1.46471i	0.125444	+	0.0724252i	0.561409	−	0.827538i	$-0.310259\pi$
$409$	2.53695	+	1.46471i	0.125444	+	0.0724252i	−0.435965	+	0.899964i	$0.643593\pi$
$410$	14.6885	−	20.1838i	0.725413	−	0.996809i
$411$		0			0
$412$	0.793595	+	0.458182i	0.0390976	+	0.0225730i
$413$	−22.3361	+	12.8957i	−1.09909	+	0.634558i
$414$		0			0
$415$	−2.63591	+	24.8920i	−0.129392	+	1.22190i
$416$	3.59135	+	0.319674i	0.176081	+	0.0156733i
$417$		0			0
$418$	−5.82239	−	10.0847i	−0.284782	−	0.493257i
$419$	4.85425	+	8.40780i	0.237145	+	0.410748i	0.959894	−	0.280363i	$-0.0904549\pi$
$419$	4.85425	+	8.40780i	0.237145	+	0.410748i	−0.722749	+	0.691111i	$0.757122\pi$
$420$		0			0
$421$			22.8217i			1.11226i	0.831094	+	0.556132i	$0.187715\pi$
$421$			22.8217i			1.11226i	−0.831094	+	0.556132i	$0.812285\pi$
$422$	10.1115	−	17.5137i	0.492222	−	0.852554i
$423$		0			0
$424$		−	12.0148i		−	0.583491i
$425$	−4.67591	−	4.22345i	−0.226815	−	0.204867i
$426$		0			0
$427$	7.97416	+	13.8116i	0.385897	+	0.668392i
$428$		−	11.7024i		−	0.565655i
$429$		0			0
$430$	−17.3073	−	1.83273i	−0.834631	−	0.0883820i
$431$	−10.0125	+	5.78073i	−0.482286	+	0.278448i	−0.721369	−	0.692551i	$-0.756487\pi$
$431$	−10.0125	+	5.78073i	−0.482286	+	0.278448i	0.239082	+	0.970999i	$0.423153\pi$
$432$		0			0
$433$	−10.8821	−	6.28278i	−0.522960	−	0.301931i	0.215185	−	0.976573i	$-0.430965\pi$
$433$	−10.8821	−	6.28278i	−0.522960	−	0.301931i	−0.738145	+	0.674642i	$0.764298\pi$
$434$			0.578108i			0.0277501i
$435$		0			0
$436$	13.8479	+	7.99511i	0.663196	+	0.382897i
$437$	−3.50027			−0.167441
$438$		0			0
$439$	−0.905142	−	1.56775i	−0.0432001	−	0.0748247i	0.843617	−	0.536946i	$-0.180422\pi$
$439$	−0.905142	−	1.56775i	−0.0432001	−	0.0748247i	−0.886817	+	0.462121i	$0.847089\pi$
$440$	2.71664	+	6.11451i	0.129511	+	0.291498i
$441$		0			0
$442$	−4.12085	+	1.91401i	−0.196009	+	0.0910400i
$443$		−	16.7633i		−	0.796450i	−0.917288	−	0.398225i	$-0.869626\pi$
$443$		−	16.7633i		−	0.796450i	0.917288	−	0.398225i	$-0.130374\pi$
$444$		0			0
$445$	−6.27471	−	14.1229i	−0.297450	−	0.669489i
$446$	−5.57252	+	9.65189i	−0.263867	+	0.457030i
$447$		0			0
$448$	1.04346	−	1.80732i	0.0492988	−	0.0853880i
$449$	−6.13311	−	3.54095i	−0.289439	−	0.167108i	0.348250	−	0.937402i	$-0.386776\pi$
$449$	−6.13311	−	3.54095i	−0.289439	−	0.167108i	−0.637689	+	0.770294i	$0.720109\pi$
$450$		0			0
$451$	16.7022	−	28.9290i	0.786475	−	1.36222i
$452$	2.40930	−	1.39101i	0.113324	−	0.0654277i
$453$		0			0
$454$	−17.3073			−0.812271
$455$	−3.24827	+	16.5087i	−0.152281	+	0.773942i
$456$		0			0
$457$	−0.545096	−	0.944133i	−0.0254985	−	0.0441647i	0.852995	−	0.521920i	$-0.174784\pi$
$457$	−0.545096	−	0.944133i	−0.0254985	−	0.0441647i	−0.878493	+	0.477755i	$0.841451\pi$
$458$	−8.57668	+	4.95175i	−0.400762	+	0.231380i
$459$		0			0
$460$	2.00000	+	0.211787i	0.0932505	+	0.00987462i
$461$	13.5007	+	7.79465i	0.628791	+	0.363033i	0.780284	−	0.625426i	$-0.215075\pi$
$461$	13.5007	+	7.79465i	0.628791	+	0.363033i	−0.151493	+	0.988458i	$0.548408\pi$
$462$		0			0
$463$	19.1896			0.891817			0.445908	−	0.895079i	$-0.352881\pi$
$463$	19.1896			0.891817			0.445908	+	0.895079i	$0.352881\pi$
$464$	0.235468	−	0.407843i	0.0109313	−	0.0189337i
$465$		0			0
$466$	−16.6053	+	9.58708i	−0.769226	+	0.444113i
$467$		−	23.1857i		−	1.07290i	−0.843931	−	0.536452i	$-0.819764\pi$
$467$		−	23.1857i		−	1.07290i	0.843931	−	0.536452i	$-0.180236\pi$
$468$		0			0
$469$	8.34767			0.385460
$470$	−23.1297	+	10.2764i	−1.06689	+	0.474013i
$471$		0			0
$472$	−10.7029	−	6.17932i	−0.492641	−	0.284426i
$473$	−23.2895			−1.07085
$474$		0			0
$475$	14.4400	+	13.0427i	0.662553	+	0.598441i
$476$			2.62990i			0.120541i
$477$		0			0
$478$	1.87449	−	1.08224i	0.0857374	−	0.0495005i
$479$	−3.01812	+	1.74251i	−0.137901	+	0.0796174i	−0.567363	−	0.823467i	$-0.692037\pi$
$479$	−3.01812	+	1.74251i	−0.137901	+	0.0796174i	0.429462	+	0.903085i	$0.358703\pi$
$480$		0			0
$481$	−14.5857	+	20.7637i	−0.665051	+	0.946742i
$482$			16.1013i			0.733396i
$483$		0			0
$484$	−1.02326	−	1.77234i	−0.0465120	−	0.0805611i
$485$	−4.66158	−	3.39240i	−0.211671	−	0.154041i
$486$		0			0
$487$	1.07023	−	1.85369i	0.0484967	−	0.0839988i	−0.840758	−	0.541411i	$-0.817890\pi$
$487$	1.07023	−	1.85369i	0.0484967	−	0.0839988i	0.889255	+	0.457412i	$0.151224\pi$
$488$	−3.82102	+	6.61820i	−0.172969	+	0.299592i
$489$		0			0
$490$	−4.78172	−	3.47983i	−0.216016	−	0.157203i
$491$	13.6201	+	23.5908i	0.614668	+	1.06464i	0.990443	+	0.137926i	$0.0440435\pi$
$491$	13.6201	+	23.5908i	0.614668	+	1.06464i	−0.375774	+	0.926711i	$0.622623\pi$
$492$		0			0
$493$			0.593468i			0.0267284i
$494$	12.7259	−	5.91077i	0.572565	−	0.265938i
$495$		0			0
$496$	−0.239902	+	0.138508i	−0.0107719	+	0.00621918i
$497$	−8.50486	+	4.91028i	−0.381495	+	0.220256i
$498$		0			0
$499$		−	22.7855i		−	1.02002i	−0.860169	−	0.510010i	$-0.829642\pi$
$499$		−	22.7855i		−	1.02002i	0.860169	−	0.510010i	$-0.170358\pi$
$500$	−7.46163	−	8.32611i	−0.333694	−	0.372355i
$501$		0			0
$502$	18.0888			0.807341
$503$	8.31665	+	4.80162i	0.370821	+	0.214094i	0.673817	−	0.738898i	$-0.264654\pi$
$503$	8.31665	+	4.80162i	0.370821	+	0.214094i	−0.302996	+	0.952992i	$0.597987\pi$
$504$		0			0
$505$	3.20153	−	1.42242i	0.142466	−	0.0632969i
$506$	2.69130			0.119643
$507$		0			0
$508$		−	8.69969i		−	0.385986i
$509$	13.5627	−	7.83041i	0.601155	−	0.347077i	−0.168341	−	0.985729i	$-0.553841\pi$
$509$	13.5627	−	7.83041i	0.601155	−	0.347077i	0.769496	+	0.638652i	$0.220508\pi$
$510$		0			0
$511$	−15.9633	+	27.6492i	−0.706173	+	1.22313i
$512$	1.00000			0.0441942
$513$		0			0
$514$	8.69939	+	5.02260i	0.383714	+	0.221537i
$515$	−2.03766	−	0.215775i	−0.0897900	−	0.00950818i
$516$		0			0
$517$	−29.3312	+	16.9344i	−1.28998	+	0.744773i
$518$	7.34351	+	12.7193i	0.322655	+	0.558855i
$519$		0			0
$520$	−7.62901	+	2.60733i	−0.334554	+	0.114339i
$521$	−3.26689			−0.143125			−0.0715625	−	0.997436i	$-0.522799\pi$
$521$	−3.26689			−0.143125			−0.0715625	+	0.997436i	$0.522799\pi$
$522$		0			0
$523$	−13.8479	+	7.99511i	−0.605528	+	0.349602i	−0.771213	−	0.636577i	$-0.780350\pi$
$523$	−13.8479	+	7.99511i	−0.605528	+	0.349602i	0.165685	+	0.986179i	$0.447016\pi$
$524$	−7.93700	+	13.7473i	−0.346730	+	0.600553i
$525$		0			0
$526$	−13.6855	−	7.90133i	−0.596716	−	0.344514i
$527$	0.174545	−	0.302321i	0.00760331	−	0.0131693i
$528$		0			0
$529$	−11.0955	+	19.2180i	−0.482414	+	0.835565i
$530$	10.9082	+	24.5518i	0.473822	+	1.06646i
$531$		0			0
$532$		−	8.12158i		−	0.352115i
$533$	32.9369	+	23.1370i	1.42666	+	1.00217i
$534$		0			0
$535$	10.6245	+	23.9133i	0.459338	+	1.03386i
$536$	2.00000	+	3.46410i	0.0863868	+	0.149626i
$537$		0			0
$538$	−7.38587			−0.318428
$539$	−6.85354	−	3.95689i	−0.295203	−	0.170435i
$540$		0			0
$541$		−	7.38554i		−	0.317529i	−0.987316	−	0.158765i	$-0.949249\pi$
$541$		−	7.38554i		−	0.317529i	0.987316	−	0.158765i	$-0.0507511\pi$
$542$	−26.8493	−	15.5014i	−1.15327	−	0.665843i
$543$		0			0
$544$	−1.09135	+	0.630092i	−0.0467913	+	0.0270150i
$545$	−35.5564	−	3.76519i	−1.52307	−	0.161283i
$546$		0			0
$547$			11.4488i			0.489515i	0.969584	+	0.244757i	$0.0787083\pi$
$547$			11.4488i			0.489515i	−0.969584	+	0.244757i	$0.921292\pi$
$548$	3.61155	+	6.25538i	0.154278	+	0.267217i
$549$		0			0
$550$	−11.1027	−	10.0283i	−0.473420	−	0.427609i
$551$		−	1.83273i		−	0.0780768i
$552$		0			0
$553$	−1.70757	+	2.95759i	−0.0726131	+	0.125770i
$554$		−	4.70735i		−	0.199996i
$555$		0			0
$556$	9.93700	+	17.2114i	0.421423	+	0.729926i
$557$	9.70356	+	16.8071i	0.411153	+	0.712138i	0.995016	−	0.0997144i	$-0.0317929\pi$
$557$	9.70356	+	16.8071i	0.411153	+	0.712138i	−0.583863	+	0.811852i	$0.698460\pi$
$558$		0			0
$559$	2.48813	−	27.9527i	0.105237	−	1.18227i
$560$	−0.491403	+	4.64054i	−0.0207656	+	0.196099i
$561$		0			0
$562$	9.33328	−	5.38857i	0.393700	−	0.227303i
$563$	7.70563	+	4.44885i	0.324754	+	0.187497i	0.653509	−	0.756918i	$-0.273296\pi$
$563$	7.70563	+	4.44885i	0.324754	+	0.187497i	−0.328756	+	0.944415i	$0.606629\pi$
$564$		0			0
$565$	−3.66042	+	5.02988i	−0.153995	+	0.211608i
$566$	−25.2204	−	14.5610i	−1.06009	−	0.612044i
$567$		0			0
$568$	−4.07532	−	2.35289i	−0.170997	−	0.0987249i
$569$	−3.44997	−	5.97552i	−0.144630	−	0.250507i	0.784605	−	0.619996i	$-0.212866\pi$
$569$	−3.44997	−	5.97552i	−0.144630	−	0.250507i	−0.929235	+	0.369490i	$0.879533\pi$
$570$		0			0
$571$	−32.4491			−1.35795			−0.678975	−	0.734161i	$-0.737576\pi$
$571$	−32.4491			−1.35795			−0.678975	+	0.734161i	$0.737576\pi$
$572$	−9.78473	+	4.54470i	−0.409120	+	0.190023i
$573$		0			0
$574$	20.1764	−	11.6489i	0.842147	−	0.486214i
$575$	−4.27920	+	1.38301i	−0.178455	+	0.0576757i
$576$		0			0
$577$	−25.3915			−1.05706			−0.528530	−	0.848914i	$-0.677257\pi$
$577$	−25.3915			−1.05706			−0.528530	+	0.848914i	$0.677257\pi$
$578$	−7.70597	+	13.3471i	−0.320526	+	0.555167i
$579$		0			0
$580$	−0.110891	+	1.04719i	−0.00460449	+	0.0434823i
$581$	−11.6808	+	20.2317i	−0.484601	+	0.839354i
$582$		0			0
$583$	17.9756	+	31.1346i	0.744473	+	1.28946i
$584$	−15.2984			−0.633053
$585$		0			0
$586$	−25.4248			−1.05029
$587$	1.23196	+	2.13382i	0.0508485	+	0.0880722i	0.890329	−	0.455317i	$-0.150474\pi$
$587$	1.23196	+	2.13382i	0.0508485	+	0.0880722i	−0.839481	+	0.543389i	$0.817141\pi$
$588$		0			0
$589$	−0.539025	+	0.933619i	−0.0222101	+	0.0384691i
$590$	27.4811	+	2.91007i	1.13138	+	0.119806i
$591$		0			0
$592$	−3.51883	+	6.09479i	−0.144623	+	0.250494i
$593$	40.6651			1.66992			0.834958	−	0.550313i	$-0.185492\pi$
$593$	40.6651			1.66992			0.834958	+	0.550313i	$0.185492\pi$
$594$		0			0
$595$	−2.38768	−	5.37410i	−0.0978852	−	0.220316i
$596$	−0.851450	+	0.491585i	−0.0348767	+	0.0201361i
$597$		0			0
$598$	−0.287524	+	3.23016i	−0.0117577	+	0.132091i
$599$	−26.1916			−1.07016			−0.535079	−	0.844802i	$-0.679718\pi$
$599$	−26.1916			−1.07016			−0.535079	+	0.844802i	$0.679718\pi$
$600$		0			0
$601$	6.74916	+	11.6899i	0.275304	+	0.476840i	0.970212	−	0.242259i	$-0.0778882\pi$
$601$	6.74916	+	11.6899i	0.275304	+	0.476840i	−0.694908	+	0.719099i	$0.744555\pi$
$602$	−14.0670	−	8.12158i	−0.573328	−	0.331011i
$603$		0			0
$604$	−6.98046	−	4.03017i	−0.284031	−	0.163985i
$605$	3.70010	+	2.69270i	0.150431	+	0.109474i
$606$		0			0
$607$	8.51183	+	4.91431i	0.345485	+	0.199466i	0.662695	−	0.748890i	$-0.269413\pi$
$607$	8.51183	+	4.91431i	0.345485	+	0.199466i	−0.317210	+	0.948355i	$0.602746\pi$
$608$	3.37028	−	1.94583i	0.136683	−	0.0789139i
$609$		0			0
$610$	1.79946	−	16.9931i	0.0728580	−	0.688031i
$611$	−17.1915	−	37.0132i	−0.695492	−	1.49739i
$612$		0			0
$613$	10.3086	+	17.8551i	0.416362	+	0.721161i	0.995570	−	0.0940190i	$-0.0299715\pi$
$613$	10.3086	+	17.8551i	0.416362	+	0.721161i	−0.579208	+	0.815180i	$0.696638\pi$
$614$	−12.6652	−	21.9368i	−0.511127	−	0.885299i
$615$		0			0
$616$			6.24455i			0.251600i
$617$	8.90958	−	15.4318i	0.358686	−	0.621262i	−0.629056	−	0.777360i	$-0.716558\pi$
$617$	8.90958	−	15.4318i	0.358686	−	0.621262i	0.987742	+	0.156098i	$0.0498915\pi$
$618$		0			0
$619$			29.3377i			1.17918i	0.807701	+	0.589592i	$0.200711\pi$
$619$			29.3377i			1.17918i	−0.807701	+	0.589592i	$0.799289\pi$
$620$	0.364480	−	0.500841i	0.0146379	−	0.0201143i
$621$		0			0
$622$	−12.1748	−	21.0873i	−0.488164	−	0.845524i
$623$		−	14.4232i		−	0.577855i
$624$		0			0
$625$	22.8068	+	10.2397i	0.912271	+	0.409587i
$626$	13.5872	−	7.84457i	0.543053	−	0.313532i
$627$		0			0
$628$	2.36748	+	1.36687i	0.0944728	+	0.0545439i
$629$		−	8.86875i		−	0.353620i
$630$		0			0
$631$	−15.5662	−	8.98714i	−0.619680	−	0.357772i	0.157064	−	0.987588i	$-0.449797\pi$
$631$	−15.5662	−	8.98714i	−0.619680	−	0.357772i	−0.776744	+	0.629816i	$0.783130\pi$
$632$	−1.63645			−0.0650944
$633$		0			0
$634$	9.73033	+	16.8534i	0.386441	+	0.669335i
$635$	7.89841	+	17.7775i	0.313439	+	0.705477i
$636$		0			0
$637$	5.48135	−	7.80305i	0.217179	−	0.309168i
$638$			1.40915i			0.0557890i
$639$		0			0
$640$	−2.04346	+	0.907896i	−0.0807748	+	0.0358877i
$641$	12.7805	−	22.1365i	0.504800	−	0.874339i	−0.495185	−	0.868788i	$-0.664900\pi$
$641$	12.7805	−	22.1365i	0.504800	−	0.874339i	0.999985	−	0.00555129i	$-0.00176704\pi$
$642$		0			0
$643$	10.9914	−	19.0376i	0.433457	−	0.750769i	−0.563712	−	0.825972i	$-0.690627\pi$
$643$	10.9914	−	19.0376i	0.433457	−	0.750769i	0.997168	+	0.0752028i	$0.0239604\pi$
$644$	1.62556	+	0.938516i	0.0640560	+	0.0369827i
$645$		0			0
$646$	−2.45211	+	4.24717i	−0.0964769	+	0.167103i
$647$	−26.9769	+	15.5751i	−1.06057	+	0.612321i	−0.925590	−	0.378527i	$-0.876431\pi$
$647$	−26.9769	+	15.5751i	−1.06057	+	0.612321i	−0.134981	+	0.990848i	$0.543097\pi$
$648$		0			0
$649$	36.9800			1.45159
$650$	13.2224	−	12.2543i	0.518625	−	0.480654i
$651$		0			0
$652$	12.2885	+	21.2842i	0.481253	+	0.833554i
$653$	−15.4449	+	8.91711i	−0.604405	+	0.348954i	−0.770773	−	0.637110i	$-0.780130\pi$
$653$	−15.4449	+	8.91711i	−0.604405	+	0.348954i	0.166367	+	0.986064i	$0.446796\pi$
$654$		0			0
$655$	3.73783	−	35.2980i	0.146049	−	1.37921i
$656$	9.66804	+	5.58184i	0.377473	+	0.217934i
$657$		0			0
$658$	−23.6216			−0.920865
$659$	−9.89464	+	17.1380i	−0.385440	+	0.667602i	−0.991830	−	0.127565i	$-0.959284\pi$
$659$	−9.89464	+	17.1380i	−0.385440	+	0.667602i	0.606390	+	0.795168i	$0.292617\pi$
$660$		0			0
$661$	−15.7895	+	9.11607i	−0.614140	+	0.354574i	−0.774584	−	0.632471i	$-0.782041\pi$
$661$	−15.7895	+	9.11607i	−0.614140	+	0.354574i	0.160444	+	0.987045i	$0.448707\pi$
$662$		−	6.62711i		−	0.257570i
$663$		0			0
$664$	−11.1943			−0.434423
$665$	7.37355	+	16.5961i	0.285934	+	0.643570i
$666$		0			0
$667$	0.366826	+	0.211787i	0.0142035	+	0.00820042i
$668$	−13.8363			−0.535344
$669$		0			0
$670$	−7.23196	−	5.26296i	−0.279395	−	0.203326i
$671$		−	22.8668i		−	0.882763i
$672$		0			0
$673$	17.1875	−	9.92322i	0.662530	−	0.382512i	−0.130710	−	0.991421i	$-0.541726\pi$
$673$	17.1875	−	9.92322i	0.662530	−	0.382512i	0.793240	+	0.608909i	$0.208392\pi$
$674$	−9.57948	+	5.53072i	−0.368988	+	0.213035i
$675$		0			0
$676$	−4.40930	−	12.2294i	−0.169589	−	0.470361i
$677$			4.02129i			0.154551i	0.997010	+	0.0772753i	$0.0246220\pi$
$677$			4.02129i			0.154551i	−0.997010	+	0.0772753i	$0.975378\pi$
$678$		0			0
$679$	−2.69037	−	4.65986i	−0.103247	−	0.178829i
$680$	1.65807	−	2.27840i	0.0635843	−	0.0873727i
$681$		0			0
$682$	0.414448	−	0.717844i	0.0158700	−	0.0274877i
$683$	5.19430	−	8.99680i	0.198754	−	0.344253i	−0.749370	−	0.662151i	$-0.769644\pi$
$683$	5.19430	−	8.99680i	0.198754	−	0.344253i	0.948125	+	0.317898i	$0.102977\pi$
$684$		0			0
$685$	−13.0593	−	9.50371i	−0.498970	−	0.363118i
$686$	−10.0639	−	17.4312i	−0.384242	−	0.665527i
$687$		0			0
$688$		−	7.78333i		−	0.296737i
$689$	−39.2889	+	18.2485i	−1.49679	+	0.695211i
$690$		0			0
$691$	−24.5864	+	14.1949i	−0.935309	+	0.540001i	−0.888487	−	0.458902i	$-0.848243\pi$
$691$	−24.5864	+	14.1949i	−0.935309	+	0.540001i	−0.0468225	+	0.998903i	$0.514910\pi$
$692$	−11.4079	+	6.58638i	−0.433665	+	0.250376i
$693$		0			0
$694$			17.7207i			0.672669i
$695$	−35.9320	−	26.1490i	−1.36298	−	0.991888i
$696$		0			0
$697$	−14.0683			−0.532875
$698$	−15.3172	−	8.84341i	−0.579766	−	0.334728i
$699$		0			0
$700$	−3.20897	−	9.92891i	−0.121288	−	0.375277i
$701$	−16.7917			−0.634213			−0.317106	−	0.948390i	$-0.602711\pi$
$701$	−16.7917			−0.634213			−0.317106	+	0.948390i	$0.602711\pi$
$702$		0			0
$703$			27.3882i			1.03297i
$704$	−2.59135	+	1.49612i	−0.0976652	+	0.0563871i
$705$		0			0
$706$	16.8114	−	29.1183i	0.632707	−	1.09588i
$707$	3.26962			0.122967
$708$		0			0
$709$	−41.9846	−	24.2398i	−1.57676	−	0.910345i	−0.995307	−	0.0967675i	$-0.969150\pi$
$709$	−41.9846	−	24.2398i	−1.57676	−	0.910345i	−0.581457	−	0.813577i	$-0.697517\pi$
$710$	10.4639	+	1.10806i	0.392704	+	0.0415848i
$711$		0			0
$712$	5.98533	−	3.45563i	0.224310	−	0.129505i
$713$	−0.124578	−	0.215775i	−0.00466547	−	0.00808083i
$714$		0			0
$715$	15.8686	−	18.1704i	0.593451	−	0.679535i
$716$	−3.11571			−0.116440
$717$		0			0
$718$	−15.1450	+	8.74400i	−0.565208	+	0.326323i
$719$	−6.14778	+	10.6483i	−0.229273	+	0.397113i	−0.957593	−	0.288125i	$-0.906968\pi$
$719$	−6.14778	+	10.6483i	−0.229273	+	0.397113i	0.728320	+	0.685238i	$0.240302\pi$
$720$		0			0
$721$	−1.65617	−	0.956188i	−0.0616789	−	0.0356103i
$722$	−1.92748	+	3.33849i	−0.0717333	+	0.124246i
$723$		0			0
$724$	−3.95720	+	6.85407i	−0.147068	+	0.254729i
$725$	−0.724141	−	2.24057i	−0.0268939	−	0.0832127i
$726$		0			0
$727$		−	36.1491i		−	1.34070i	−0.742046	−	0.670349i	$-0.766145\pi$
$727$		−	36.1491i		−	1.34070i	0.742046	−	0.670349i	$-0.233855\pi$
$728$	−7.49486	−	0.667134i	−0.277778	−	0.0247256i
$729$		0			0
$730$	31.2617	−	13.8894i	1.15705	−	0.514069i
$731$	4.90421	+	8.49435i	0.181389	+	0.314175i
$732$		0			0
$733$	22.4789			0.830278			0.415139	−	0.909758i	$-0.363733\pi$
$733$	22.4789			0.830278			0.415139	+	0.909758i	$0.363733\pi$
$734$	−6.37373	−	3.67988i	−0.235259	−	0.135827i
$735$		0			0
$736$			0.899428i			0.0331534i
$737$	−10.3654	−	5.98447i	−0.381815	−	0.220441i
$738$		0			0
$739$	10.6967	−	6.17575i	0.393485	−	0.227179i	−0.290184	−	0.956971i	$-0.593717\pi$
$739$	10.6967	−	6.17575i	0.393485	−	0.227179i	0.683669	+	0.729792i	$0.260383\pi$
$740$	1.65715	−	15.6492i	0.0609179	−	0.575276i
$741$		0			0
$742$			25.0740i			0.920494i
$743$	−11.4818	−	19.8871i	−0.421227	−	0.729587i	0.574832	−	0.818271i	$-0.305067\pi$
$743$	−11.4818	−	19.8871i	−0.421227	−	0.729587i	−0.996060	+	0.0886839i	$0.971734\pi$
$744$		0			0
$745$	1.29359	−	1.77756i	0.0473936	−	0.0651248i
$746$			29.2016i			1.06915i
$747$		0			0
$748$	1.88538	−	3.26558i	0.0689365	−	0.119401i
$749$			24.4219i			0.892355i
$750$		0			0
$751$	−16.4263	−	28.4511i	−0.599403	−	1.03820i	−0.992909	−	0.118874i	$-0.962071\pi$
$751$	−16.4263	−	28.4511i	−0.599403	−	1.03820i	0.393506	−	0.919322i	$-0.371262\pi$
$752$	−5.65944	−	9.80244i	−0.206379	−	0.357458i
$753$		0			0
$754$	−1.69130	−	0.150546i	−0.0615935	−	0.00548258i
$755$	17.9233	+	1.89796i	0.652294	+	0.0690737i
$756$		0			0
$757$	−28.6323	+	16.5309i	−1.04066	+	0.600826i	−0.920020	−	0.391871i	$-0.871828\pi$
$757$	−28.6323	+	16.5309i	−1.04066	+	0.600826i	−0.120640	+	0.992696i	$0.538495\pi$
$758$	13.2943	+	7.67544i	0.482869	+	0.278785i
$759$		0			0
$760$	−5.12041	+	7.03609i	−0.185737	+	0.255226i
$761$	27.3347	+	15.7817i	0.990882	+	0.572086i	0.905538	−	0.424266i	$-0.139468\pi$
$761$	27.3347	+	15.7817i	0.990882	+	0.572086i	0.0853441	+	0.996352i	$0.472801\pi$
$762$		0			0
$763$	−28.8995	−	16.6851i	−1.04623	−	0.604043i
$764$	6.98046	+	12.0905i	0.252544	+	0.437419i
$765$		0			0
$766$	3.19245			0.115348
$767$	−3.95074	+	44.3842i	−0.142653	+	1.60262i
$768$		0			0
$769$	−36.8445	+	21.2722i	−1.32865	+	0.767095i	−0.985090	−	0.172037i	$-0.944965\pi$
$769$	−36.8445	+	21.2722i	−1.32865	+	0.767095i	−0.343556	+	0.939132i	$0.611632\pi$
$770$	−5.66940	−	12.7605i	−0.204311	−	0.459856i
$771$		0			0
$772$	−13.6276			−0.490467
$773$	0.533226	−	0.923574i	0.0191788	−	0.0332187i	−0.856277	−	0.516517i	$-0.827228\pi$
$773$	0.533226	−	0.923574i	0.0191788	−	0.0332187i	0.875456	+	0.483299i	$0.160561\pi$
$774$		0			0
$775$	−0.290088	+	1.35436i	−0.0104203	+	0.0486500i
$776$	1.28916	−	2.23289i	0.0462782	−	0.0801561i
$777$		0			0
$778$	14.4658	+	25.0555i	0.518624	+	0.898283i
$779$	43.4453			1.55659
$780$		0			0
$781$	14.0808			0.503850
$782$	−0.566723	−	0.981592i	−0.0202660	−	0.0351017i
$783$		0			0
$784$	1.32239	−	2.29044i	0.0472281	−	0.0818015i
$785$	−6.07883	−	0.643708i	−0.216963	−	0.0229749i
$786$		0			0
$787$	0.0215610	−	0.0373447i	0.000768565	−	0.00133119i	−0.865641	−	0.500665i	$-0.833089\pi$
$787$	0.0215610	−	0.0373447i	0.000768565	−	0.00133119i	0.866409	+	0.499334i	$0.166422\pi$
$788$	17.7219			0.631318
$789$		0			0
$790$	3.34401	−	1.48572i	0.118975	−	0.0528597i
$791$	−5.02802	+	2.90293i	−0.178776	+	0.103216i
$792$		0			0
$793$	27.4453	+	2.44296i	0.974610	+	0.0867522i
$794$	4.99113			0.177129
$795$		0			0
$796$	7.18270	+	12.4408i	0.254584	+	0.440953i
$797$	−29.9559	−	17.2951i	−1.06109	−	0.612623i	−0.135359	−	0.990797i	$-0.543219\pi$
$797$	−29.9559	−	17.2951i	−1.06109	−	0.612623i	−0.925735	+	0.378174i	$0.876552\pi$
$798$		0			0
$799$	12.3529	+	7.13194i	0.437014	+	0.252310i
$800$	3.35145	−	3.71050i	0.118492	−	0.131186i
$801$		0			0
$802$	3.46032	+	1.99782i	0.122188	+	0.0705453i
$803$	39.6436	−	22.8882i	1.39899	−	0.807708i
$804$		0			0
$805$	−4.17384	−	0.441982i	−0.147108	−	0.0155778i
$806$	0.817296	+	0.574120i	0.0287880	+	0.0202225i
$807$		0			0
$808$	0.783361	+	1.35682i	0.0275586	+	0.0477328i
$809$	3.04046	+	5.26623i	0.106897	+	0.185151i	0.914512	−	0.404560i	$-0.132575\pi$
$809$	3.04046	+	5.26623i	0.106897	+	0.185151i	−0.807615	+	0.589710i	$0.799242\pi$
$810$		0			0
$811$			5.47145i			0.192129i	0.995375	+	0.0960644i	$0.0306255\pi$
$811$			5.47145i			0.192129i	−0.995375	+	0.0960644i	$0.969375\pi$
$812$	−0.491403	+	0.851136i	−0.0172449	+	0.0298690i
$813$		0			0
$814$		−	21.0583i		−	0.738094i
$815$	−44.4348	−	32.3368i	−1.55648	−	1.13271i
$816$		0			0
$817$	−15.1450	−	26.2320i	−0.529858	−	0.917741i
$818$		−	2.92942i		−	0.102425i
$819$		0			0
$820$	−24.8240	−	2.62870i	−0.866891	−	0.0917981i
$821$	−38.1625	+	22.0331i	−1.33188	+	0.768961i	−0.985588	−	0.169166i	$-0.945892\pi$
$821$	−38.1625	+	22.0331i	−1.33188	+	0.768961i	−0.346291	+	0.938127i	$0.612559\pi$
$822$		0			0
$823$	10.8396	+	6.25823i	0.377844	+	0.218148i	0.676880	−	0.736094i	$-0.263332\pi$
$823$	10.8396	+	6.25823i	0.377844	+	0.218148i	−0.299036	+	0.954242i	$0.596665\pi$
$824$		−	0.916364i		−	0.0319231i
$825$		0			0
$826$	22.3361	+	12.8957i	0.777171	+	0.448700i
$827$	51.7679			1.80015			0.900074	−	0.435738i	$-0.143512\pi$
$827$	51.7679			1.80015			0.900074	+	0.435738i	$0.143512\pi$
$828$		0			0
$829$	6.95883	+	12.0531i	0.241690	+	0.418620i	0.961196	−	0.275867i	$-0.0889649\pi$
$829$	6.95883	+	12.0531i	0.241690	+	0.418620i	−0.719506	+	0.694487i	$0.755632\pi$
$830$	22.8751	−	10.1633i	0.794006	−	0.352772i
$831$		0			0
$832$	−1.51883	−	3.27004i	−0.0526559	−	0.113368i
$833$			3.33290i			0.115478i
$834$		0			0
$835$	28.2740	−	12.5620i	0.978462	−	0.434725i
$836$	−5.82239	+	10.0847i	−0.201371	+	0.348786i
$837$		0			0
$838$	4.85425	−	8.40780i	0.167687	−	0.290443i
$839$	43.3416	+	25.0233i	1.49632	+	0.863899i	0.999991	−	0.00423634i	$-0.00134847\pi$
$839$	43.3416	+	25.0233i	1.49632	+	0.863899i	0.496327	+	0.868136i	$0.334682\pi$
$840$		0			0
$841$	14.3891	−	24.9227i	0.496176	−	0.859402i
$842$	19.7642	−	11.4109i	0.681120	−	0.393245i
$843$		0			0
$844$	−20.2231			−0.696108
$845$	20.1132	+	20.9871i	0.691917	+	0.721977i
$846$		0			0
$847$	2.13547	+	3.69874i	0.0733755	+	0.127090i
$848$	−10.4051	+	6.00741i	−0.357314	+	0.206295i
$849$		0			0
$850$	−1.31966	+	6.16118i	−0.0452638	+	0.211327i
$851$	−5.48183	−	3.16493i	−0.187915	−	0.108493i
$852$		0			0
$853$	−12.7392			−0.436183			−0.218092	−	0.975928i	$-0.569983\pi$
$853$	−12.7392			−0.436183			−0.218092	+	0.975928i	$0.569983\pi$
$854$	7.97416	−	13.8116i	0.272870	−	0.472625i
$855$		0			0
$856$	−10.1345	+	5.85118i	−0.346391	+	0.199989i
$857$		−	30.3306i		−	1.03607i	−0.855359	−	0.518036i	$-0.826663\pi$
$857$		−	30.3306i		−	1.03607i	0.855359	−	0.518036i	$-0.173337\pi$
$858$		0			0
$859$	48.7446			1.66314			0.831572	−	0.555417i	$-0.187441\pi$
$859$	48.7446			1.66314			0.831572	+	0.555417i	$0.187441\pi$
$860$	7.06645	+	15.9049i	0.240964	+	0.542353i
$861$		0			0
$862$	10.0125	+	5.78073i	0.341028	+	0.196893i
$863$	17.6100			0.599451			0.299725	−	0.954026i	$-0.403105\pi$
$863$	17.6100			0.599451			0.299725	+	0.954026i	$0.403105\pi$
$864$		0			0
$865$	17.3319	−	23.8162i	0.589303	−	0.809776i
$866$			12.5656i			0.426995i
$867$		0			0
$868$	0.500656	−	0.289054i	0.0169934	−	0.00981114i
$869$	4.24061	−	2.44832i	0.143853	−	0.0830535i
$870$		0			0
$871$	8.29009	−	11.8015i	0.280899	−	0.399877i
$872$		−	15.9902i		−	0.541497i
$873$		0			0
$874$	1.75014	+	3.03132i	0.0591992	+	0.102536i
$875$	15.5718	+	17.3759i	0.526423	+	0.587413i
$876$		0			0
$877$	20.9644	−	36.3115i	0.707918	−	1.22615i	−0.257709	−	0.966222i	$-0.582968\pi$
$877$	20.9644	−	36.3115i	0.707918	−	1.22615i	0.965628	−	0.259928i	$-0.0836989\pi$
$878$	−0.905142	+	1.56775i	−0.0305471	+	0.0529091i
$879$		0			0
$880$	3.93700	−	5.40993i	0.132716	−	0.182369i
$881$	−14.9695	−	25.9280i	−0.504336	−	0.873535i	−0.999987	−	0.00501392i	$-0.998404\pi$
$881$	−14.9695	−	25.9280i	−0.504336	−	0.873535i	0.495652	−	0.868521i	$-0.334929\pi$
$882$		0			0
$883$		−	35.3391i		−	1.18926i	−0.804001	−	0.594629i	$-0.797299\pi$
$883$		−	35.3391i		−	1.18926i	0.804001	−	0.594629i	$-0.202701\pi$
$884$	3.71800	+	2.61176i	0.125050	+	0.0878430i
$885$		0			0
$886$	−14.5175	+	8.38166i	−0.487724	+	0.281587i
$887$	−36.8682	+	21.2859i	−1.23791	+	0.714709i	−0.968667	−	0.248362i	$-0.920108\pi$
$887$	−36.8682	+	21.2859i	−1.23791	+	0.714709i	−0.269246	+	0.963071i	$0.586774\pi$
$888$		0			0
$889$			18.1555i			0.608917i
$890$	−9.09343	+	12.4955i	−0.304812	+	0.418850i
$891$		0			0
$892$	11.1450			0.373164
$893$	−38.1478	−	22.0246i	−1.27657	−	0.737026i
$894$		0			0
$895$	6.36683	−	2.82874i	0.212820	−	0.0945544i
$896$	−2.08692			−0.0697190
$897$		0			0
$898$			7.08190i			0.236326i
$899$	0.112979	−	0.0652284i	0.00376806	−	0.00217549i
$900$		0			0
$901$	7.57045	−	13.1124i	0.252208	−	0.436837i
$902$	−33.4044			−1.11224
$903$		0			0
$904$	−2.40930	−	1.39101i	−0.0801323	−	0.0462644i
$905$	1.86359	−	17.5987i	0.0619478	−	0.585002i
$906$		0			0
$907$	−12.5097	+	7.22247i	−0.415377	+	0.239818i	−0.693098	−	0.720844i	$-0.743755\pi$
$907$	−12.5097	+	7.22247i	−0.415377	+	0.239818i	0.277720	+	0.960662i	$0.410421\pi$
$908$	8.65364	+	14.9885i	0.287181	+	0.497412i
$909$		0			0
$910$	15.9211	−	5.44129i	0.527780	−	0.180377i
$911$	42.9419			1.42273			0.711364	−	0.702824i	$-0.248078\pi$
$911$	42.9419			1.42273			0.711364	+	0.702824i	$0.248078\pi$
$912$		0			0
$913$	29.0084	−	16.7480i	0.960037	−	0.554278i
$914$	−0.545096	+	0.944133i	−0.0180302	+	0.0312292i
$915$		0			0
$916$	8.57668	+	4.95175i	0.283382	+	0.163610i
$917$	16.5639	−	28.6895i	0.546987	−	0.947410i
$918$		0			0
$919$	−20.3770	+	35.2940i	−0.672175	+	1.16424i	0.305111	+	0.952317i	$0.401307\pi$
$919$	−20.3770	+	35.2940i	−0.672175	+	1.16424i	−0.977286	+	0.211925i	$0.932027\pi$
$920$	−0.816587	−	1.83794i	−0.0269221	−	0.0605952i
$921$		0			0
$922$		−	15.5893i		−	0.513406i
$923$	−1.50432	+	16.9001i	−0.0495151	+	0.556273i
$924$		0			0
$925$	10.8215	+	33.4830i	0.355810	+	1.10091i
$926$	−9.59481	−	16.6187i	−0.315305	−	0.546124i
$927$		0			0
$928$	−0.470937			−0.0154593
$929$	11.3326	+	6.54286i	0.371809	+	0.214664i	0.674249	−	0.738504i	$-0.264468\pi$
$929$	11.3326	+	6.54286i	0.371809	+	0.214664i	−0.302439	+	0.953169i	$0.597801\pi$
$930$		0			0
$931$		−	10.2926i		−	0.337325i
$932$	16.6053	+	9.58708i	0.543925	+	0.314035i
$933$		0			0
$934$	−20.0794	+	11.5928i	−0.657017	+	0.379329i
$935$	−0.887897	+	8.38482i	−0.0290373	+	0.274213i
$936$		0			0
$937$			41.0546i			1.34120i	0.741821	+	0.670598i	$0.233962\pi$
$937$			41.0546i			1.34120i	−0.741821	+	0.670598i	$0.766038\pi$
$938$	−4.17384	−	7.22930i	−0.136281	−	0.236045i
$939$		0			0
$940$	20.4644	+	14.8927i	0.667476	+	0.485746i
$941$		−	24.4162i		−	0.795945i	−0.917397	−	0.397973i	$-0.869714\pi$
$941$		−	24.4162i		−	0.795945i	0.917397	−	0.397973i	$-0.130286\pi$
$942$		0			0
$943$	−5.02047	+	8.69570i	−0.163489	+	0.283171i
$944$			12.3586i			0.402240i
$945$		0			0
$946$	11.6448	+	20.1693i	0.378604	+	0.655762i
$947$	−2.30433	−	3.99122i	−0.0748807	−	0.129697i	0.826154	−	0.563445i	$-0.190524\pi$
$947$	−2.30433	−	3.99122i	−0.0748807	−	0.129697i	−0.901034	+	0.433748i	$0.857191\pi$
$948$		0			0
$949$	23.2357	+	50.0264i	0.754262	+	1.62393i
$950$	4.07532	−	19.0268i	0.132221	−	0.617310i
$951$		0			0
$952$	2.27756	−	1.31495i	0.0738162	−	0.0426178i
$953$	−4.09617	−	2.36493i	−0.132688	−	0.0766075i	0.432187	−	0.901784i	$-0.357742\pi$
$953$	−4.09617	−	2.36493i	−0.132688	−	0.0766075i	−0.564875	+	0.825177i	$0.691075\pi$
$954$		0			0
$955$	−25.2412	−	18.3689i	−0.816787	−	0.594405i
$956$	−1.87449	−	1.08224i	−0.0606255	−	0.0350021i
$957$		0			0
$958$	3.01812	+	1.74251i	0.0975111	+	0.0562980i
$959$	−7.53700	−	13.0545i	−0.243383	−	0.421551i
$960$		0			0
$961$	30.9233			0.997525
$962$	25.2747	+	2.24976i	0.814889	+	0.0725352i
$963$		0			0
$964$	13.9442	−	8.05067i	0.449111	−	0.259295i
$965$	27.8474	−	12.3724i	0.896440	−	0.398282i
$966$		0			0
$967$	−23.8186			−0.765955			−0.382977	−	0.923758i	$-0.625101\pi$
$967$	−23.8186			−0.765955			−0.382977	+	0.923758i	$0.625101\pi$
$968$	−1.02326	+	1.77234i	−0.0328889	+	0.0569653i
$969$		0			0
$970$	−0.607113	+	5.73325i	−0.0194932	+	0.184083i
$971$	−15.8349	+	27.4269i	−0.508167	+	0.880170i	0.491789	+	0.870715i	$0.336343\pi$
$971$	−15.8349	+	27.4269i	−0.508167	+	0.880170i	−0.999955	+	0.00945572i	$0.996990\pi$
$972$		0			0
$973$	−20.7377	−	35.9188i	−0.664820	−	1.15150i
$974$	−2.14046			−0.0685847
$975$		0			0
$976$	7.64204			0.244616
$977$	−13.4354	−	23.2707i	−0.429835	−	0.744497i	0.567023	−	0.823702i	$-0.308095\pi$
$977$	−13.4354	−	23.2707i	−0.429835	−	0.744497i	−0.996858	+	0.0792052i	$0.974762\pi$
$978$		0			0
$979$	−10.3401	+	17.9095i	−0.330470	+	0.572391i
$980$	−0.622761	+	5.88101i	−0.0198934	+	0.187862i
$981$		0			0
$982$	13.6201	−	23.5908i	0.434636	−	0.752812i
$983$	8.22637			0.262380			0.131190	−	0.991357i	$-0.458120\pi$
$983$	8.22637			0.262380			0.131190	+	0.991357i	$0.458120\pi$
$984$		0			0
$985$	−36.2141	+	16.0897i	−1.15388	+	0.512660i
$986$	0.513958	−	0.296734i	0.0163678	−	0.00944993i
$987$		0			0
$988$	−11.4818	−	8.06556i	−0.365286	−	0.256600i
$989$	7.00054			0.222604
$990$		0			0
$991$	11.1157	+	19.2530i	0.353102	+	0.611591i	0.986791	−	0.161997i	$-0.0517935\pi$
$991$	11.1157	+	19.2530i	0.353102	+	0.611591i	−0.633689	+	0.773588i	$0.718460\pi$
$992$	0.239902	+	0.138508i	0.00761691	+	0.00439762i
$993$		0			0
$994$	8.50486	+	4.91028i	0.269758	+	0.155745i
$995$	−25.9725	−	18.9011i	−0.823384	−	0.599206i
$996$		0			0
$997$	20.4122	+	11.7850i	0.646459	+	0.373234i	0.787098	−	0.616827i	$-0.211582\pi$
$997$	20.4122	+	11.7850i	0.646459	+	0.373234i	−0.140639	+	0.990061i	$0.544916\pi$
$998$	−19.7328	+	11.3928i	−0.624632	+	0.360631i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.bj.a.829.2		8
3.2	odd	2		130.2.m.b.49.3	yes	8
5.4	even	2		1170.2.bj.b.829.3		8
12.11	even	2		1040.2.df.a.49.2		8
13.4	even	6		1170.2.bj.b.199.3		8
15.2	even	4		650.2.m.e.101.2		16
15.8	even	4		650.2.m.e.101.7		16
15.14	odd	2		130.2.m.a.49.2	✓	8
39.2	even	12		1690.2.b.e.339.13		16
39.11	even	12		1690.2.b.e.339.5		16
39.17	odd	6		130.2.m.a.69.2	yes	8
39.23	odd	6		1690.2.c.f.1689.5		8
39.29	odd	6		1690.2.c.e.1689.5		8
60.59	even	2		1040.2.df.c.49.3		8
65.4	even	6	inner	1170.2.bj.a.199.2		8
156.95	even	6		1040.2.df.c.849.3		8
195.2	odd	12		8450.2.a.cr.1.5		8
195.17	even	12		650.2.m.e.251.2		16
195.29	odd	6		1690.2.c.f.1689.4		8
195.89	even	12		1690.2.b.e.339.12		16
195.119	even	12		1690.2.b.e.339.4		16
195.128	odd	12		8450.2.a.cr.1.4		8
195.134	odd	6		130.2.m.b.69.3	yes	8
195.158	odd	12		8450.2.a.cs.1.4		8
195.167	odd	12		8450.2.a.cs.1.5		8
195.173	even	12		650.2.m.e.251.7		16
195.179	odd	6		1690.2.c.e.1689.4		8
780.719	even	6		1040.2.df.a.849.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.m.a.49.2	✓	8	15.14	odd	2
130.2.m.a.69.2	yes	8	39.17	odd	6
130.2.m.b.49.3	yes	8	3.2	odd	2
130.2.m.b.69.3	yes	8	195.134	odd	6
650.2.m.e.101.2		16	15.2	even	4
650.2.m.e.101.7		16	15.8	even	4
650.2.m.e.251.2		16	195.17	even	12
650.2.m.e.251.7		16	195.173	even	12
1040.2.df.a.49.2		8	12.11	even	2
1040.2.df.a.849.2		8	780.719	even	6
1040.2.df.c.49.3		8	60.59	even	2
1040.2.df.c.849.3		8	156.95	even	6
1170.2.bj.a.199.2		8	65.4	even	6	inner
1170.2.bj.a.829.2		8	1.1	even	1	trivial
1170.2.bj.b.199.3		8	13.4	even	6
1170.2.bj.b.829.3		8	5.4	even	2
1690.2.b.e.339.4		16	195.119	even	12
1690.2.b.e.339.5		16	39.11	even	12
1690.2.b.e.339.12		16	195.89	even	12
1690.2.b.e.339.13		16	39.2	even	12
1690.2.c.e.1689.4		8	195.179	odd	6
1690.2.c.e.1689.5		8	39.29	odd	6
1690.2.c.f.1689.4		8	195.29	odd	6
1690.2.c.f.1689.5		8	39.23	odd	6
8450.2.a.cr.1.4		8	195.128	odd	12
8450.2.a.cr.1.5		8	195.2	odd	12
8450.2.a.cs.1.4		8	195.158	odd	12
8450.2.a.cs.1.5		8	195.167	odd	12

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:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.235468 - 2.22364i) q^{5} +(1.04346 - 1.80732i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.235468 - 2.22364i) q^{5} +(1.04346 - 1.80732i) q^{7} +1.00000 q^{8} +(-2.04346 + 0.907896i) q^{10} +(-2.59135 + 1.49612i) q^{11} +(-1.51883 - 3.27004i) q^{13} -2.08692 q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.09135 + 0.630092i) q^{17} +(-3.37028 - 1.94583i) q^{19} +(1.80799 + 1.31574i) q^{20} +(2.59135 + 1.49612i) q^{22} +(0.778928 - 0.449714i) q^{23} +(-4.88911 - 1.04719i) q^{25} +(-2.07252 + 2.95036i) q^{26} +(1.04346 + 1.80732i) q^{28} +(0.235468 + 0.407843i) q^{29} -0.277015i q^{31} +(-0.500000 + 0.866025i) q^{32} -1.26018i q^{34} +(-3.77313 - 2.74584i) q^{35} +(-3.51883 - 6.09479i) q^{37} +3.89166i q^{38} +(0.235468 - 2.22364i) q^{40} +(-9.66804 + 5.58184i) q^{41} +(6.74056 + 3.89166i) q^{43} -2.99224i q^{44} +(-0.778928 - 0.449714i) q^{46} +11.3189 q^{47} +(1.32239 + 2.29044i) q^{49} +(1.53766 + 4.75769i) q^{50} +(3.59135 + 0.319674i) q^{52} -12.0148i q^{53} +(2.71664 + 6.11451i) q^{55} +(1.04346 - 1.80732i) q^{56} +(0.235468 - 0.407843i) q^{58} +(-10.7029 - 6.17932i) q^{59} +(-3.82102 + 6.61820i) q^{61} +(-0.239902 + 0.138508i) q^{62} +1.00000 q^{64} +(-7.62901 + 2.60733i) q^{65} +(2.00000 + 3.46410i) q^{67} +(-1.09135 + 0.630092i) q^{68} +(-0.491403 + 4.64054i) q^{70} +(-4.07532 - 2.35289i) q^{71} -15.2984 q^{73} +(-3.51883 + 6.09479i) q^{74} +(3.37028 - 1.94583i) q^{76} +6.24455i q^{77} -1.63645 q^{79} +(-2.04346 + 0.907896i) q^{80} +(9.66804 + 5.58184i) q^{82} -11.1943 q^{83} +(1.65807 - 2.27840i) q^{85} -7.78333i q^{86} +(-2.59135 + 1.49612i) q^{88} +(5.98533 - 3.45563i) q^{89} +(-7.49486 - 0.667134i) q^{91} +0.899428i q^{92} +(-5.65944 - 9.80244i) q^{94} +(-5.12041 + 7.03609i) q^{95} +(1.28916 - 2.23289i) q^{97} +(1.32239 - 2.29044i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 4 q^{4} + 3 q^{5} - 5 q^{7} + 8 q^{8}+O(q^{10}) \) 8 * q - 4 * q^2 - 4 * q^4 + 3 * q^5 - 5 * q^7 + 8 * q^8	\( 8 q - 4 q^{2} - 4 q^{4} + 3 q^{5} - 5 q^{7} + 8 q^{8} - 3 q^{10} + 3 q^{11} - 4 q^{13} + 10 q^{14} - 4 q^{16} - 15 q^{17} + 9 q^{19} - 3 q^{22} - 6 q^{23} + 5 q^{25} - q^{26} - 5 q^{28} + 3 q^{29} - 4 q^{32} - 15 q^{35} - 20 q^{37} + 3 q^{40} - 21 q^{41} - 18 q^{43} + 6 q^{46} + 6 q^{47} - 15 q^{49} - 4 q^{50} + 5 q^{52} + 31 q^{55} - 5 q^{56} + 3 q^{58} - 30 q^{59} - 5 q^{61} - 6 q^{62} + 8 q^{64} - 21 q^{65} + 16 q^{67} + 15 q^{68} - 18 q^{70} - 26 q^{73} - 20 q^{74} - 9 q^{76} + 4 q^{79} - 3 q^{80} + 21 q^{82} - 48 q^{83} - 29 q^{85} + 3 q^{88} + 39 q^{89} + 19 q^{91} - 3 q^{94} - 15 q^{95} + 4 q^{97} - 15 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 - 4 * q^4 + 3 * q^5 - 5 * q^7 + 8 * q^8 - 3 * q^10 + 3 * q^11 - 4 * q^13 + 10 * q^14 - 4 * q^16 - 15 * q^17 + 9 * q^19 - 3 * q^22 - 6 * q^23 + 5 * q^25 - q^26 - 5 * q^28 + 3 * q^29 - 4 * q^32 - 15 * q^35 - 20 * q^37 + 3 * q^40 - 21 * q^41 - 18 * q^43 + 6 * q^46 + 6 * q^47 - 15 * q^49 - 4 * q^50 + 5 * q^52 + 31 * q^55 - 5 * q^56 + 3 * q^58 - 30 * q^59 - 5 * q^61 - 6 * q^62 + 8 * q^64 - 21 * q^65 + 16 * q^67 + 15 * q^68 - 18 * q^70 - 26 * q^73 - 20 * q^74 - 9 * q^76 + 4 * q^79 - 3 * q^80 + 21 * q^82 - 48 * q^83 - 29 * q^85 + 3 * q^88 + 39 * q^89 + 19 * q^91 - 3 * q^94 - 15 * q^95 + 4 * q^97 - 15 * q^98

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